Answer:
Step-by-step explanation:
We know that a triangle angles total equals 180 so we could use the numbers and the equation, add it up and then find the value of x
(7x + 3) + 85 + 50 = 180
7x + 138 = 180
7x = 180-138
7x = 42
x = 6
Now that we found the value of x we can know substitute the value into the equation to find the value of the angle.
7x+3
42+3
45
Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 4 cm/min. How fast is the area of the pool increasing when the radius is 5 cm?
Answer:
The area of the pool increasing at the rate of 125.6 when the radius is 5 cm
Step-by-step explanation:
Given:
radius of the pool increases at a rate of 4 cm/min
To Find:
How fast is the area of the pool increasing when the radius is 5 cm?
Solution:
we are given with the circular pool
hence the area of the circular pool =
A =[tex]\pi r^2[/tex]-----------------------------(1)
The area of the pool is increasing at the rate of 4 cm/min, meaning that the area of the pool is changing with respect to time t
so differentiating eq (1) with respect to t , we have
[tex]\dfrac{dA}{dt} =\pi \times2r\times\dfrac{dr}{dt}[/tex]
we have to find [tex]\dfrac{dA}{dt}[/tex] with [tex]\dfrac{dr}{dt}[/tex] = 4 cm/min and r = 5 cm
substituting the values
[tex]\dfrac{dA}{dt} =\pi \times2(5)\times4[/tex]
[tex]\dfrac{dA}{dt} =\pi \times 10\times4[/tex]
[tex]\dfrac{dA}{dt} =\pi \times 40[/tex]
[tex]\dfrac{dA}{dt} =40\pi[/tex]
[tex]\dfrac{dA}{dt} =125.6[/tex]
The graph of f(t) = 7•2^t shows the value of a rare coin in year t. What is the meaning of the y-intercept?
Answer:
When it was purchased (year 0) the coin was worth $7
Step-by-step explanation:
we have
[tex]f(t) = 7(2)^t[/tex]
This is a exponential function of the form
[tex]y=a(b)^x[/tex]
where
a is the initial value
b is the base
In this problem we have
[tex]a=\$7[/tex]
[tex]b=2[/tex]
[tex]b=1+r[/tex]
so
[tex]2=1+r[/tex]
[tex]r=1[/tex]
[tex]r=100\%[/tex]
The y-intercept is the value of the function when the value of x is equal to zero
In this problem
The y-intercept is the value of a rare coin when the year t is equal to zero
[tex]f(0)=7(2)^0[/tex]
[tex]f(0)=\$7[/tex]
therefore
The meaning of y-intercept is
When it was purchased (year 0) the coin was worth $7
Answer:
Value of the coin when it was first released
-------------------------------
The y-intercept is the value of f(0).
Substitute t = 0 and find the y-intercept:
f(0) = 7 · 2⁰ = 7 · 1 = 7This is representing the value of the coin when it was released.
a college administrator would like to determine how much time students spend on homework assignments during a typical week. a questionnaire is sent to a sample of n=100 student and their response indicates a mean of 7.4 hours per week and standard deviation of 3hours
Based on the information given, the college administrator has collected a sample of n=100 students and obtained the following statistics: Mean: 7.4 hours per week Standard deviation: 3 hours
Why it is?
These statistics can be used to estimate the average amount of time that all students spend on homework assignments during a typical week, as well as to assess the variability in the data.
To estimate the population mean, the sample mean can be used as an unbiased estimator. This means that the sample mean of 7.4 hours per week is likely a good estimate of the true population mean. However, there is always some uncertainty associated with this estimate due to the fact that it is based on a sample.
To quantify the variability in the data, the standard deviation can be used. A standard deviation of 3 hours indicates that there is a relatively large amount of variability in the amount of time that students spend on homework assignments. Some students may spend significantly more or less time on homework than the average of 7.4 hours per week.
Overall, the college administrator can use this information to gain insights into the amount of time that students spend on homework assignments and to make informed decisions based on this knowledge.
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(HAZARD) Please help what graph represents Y=-2x+4 I will mark you the brainest
The graph of Y=-2x+4 should look like a downward sloping line that intersects the y-axis at 4.
What is intersect?The term "intersect" typically refers to the point or points where two or more things, such as lines, curves, sets, or geometrical shapes, meet or cross each other. The intersection can be described as the common elements or properties shared by the different objects or sets that intersect.
According to question:The graph of the equation Y=-2x+4 is a straight line with a slope of -2 and a y-intercept of 4. To graph this equation, you can use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
To graph Y=-2x+4, follow these steps:
Plot the y-intercept at (0,4).To locate a different point on the line, use the slope of -2. To do this, move down 2 units and right 1 unit from the y-intercept. This gives you the point (1,2).Between the two points, doodle a straight line.The graph of Y=-2x+4 should look like a downward sloping line that intersects the y-axis at 4.
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PLEASE HELP NOW!!! What would be the experimental probability of drawing a white marble?
Ryan asks 80 people to choose a marble, note the color, and replace the marble in Brianna's bag. Of all random marble selections in this experiment, 34 red, 18 white, 9 black, and 19 green marbles are selected. How does the theoretical probability compare with the experimental probability of drawing a white marble? Lesson 9-3
The experimental probbaility is 0.225 and the theoretical probability is 0.25
Calculating the experimental probbailityThe experimental probability of drawing a white marble can be calculated by dividing
(1) The number of times a white marble was selected (18)
(2) by the total number of marbles selected (34+18+9+19=80):
So, we have
Experimental probability = 18/80 = 0.225
The theoretical probabilityThe theoretical probability of drawing a white marble can be calculated by dividing the number of white marbles (1) by the total number of marble colors (4).
So, we have
Theoretical probability = 1/4 = 0.25
This means that the theoretical probability is greater than the experimental probability
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I really need help on this question!
Answer:
The 2nd table
Step-by-step explanation:
For the first set of x and y values, divide y (9/4) by x(3)
Change 3 to 1/3 due to the keep-change-flip rule and multiply that by 9/4 as 9/4 × 1/3= 9/12 which is equivalent to 3/4
Do the same process with 6 and 9/2 and that should give you 3/4 as well
Therefore the second table of values have a proportional relationship to each other as they have the same quotient.
Hope this helps.
Either use an appropriate theorem to show that the given set, W, is a vector space, or find a specific example to the contrary.W = {[\begin{array}{ccc}a\\b\\c\\\d\end{array}\right] : 3a+b=c, a+b+2c=2d}
An appropriate theorem to show that the given set, W, is a vector space. A specific example can be
[tex]\left[\begin{array}{ccc}p\\q\\r\end{array}\right][/tex] , -p- -3q = s and 3p = -2s - 3r
Sets represent values that are not solutions. B. The set of all solutions of a system of homogeneous equations OC.
The set of solutions of a homogeneous equation. Thus the set W = Null A. The null space of n homogeneous linear equations in the mx n matrix A is a subspace of Rn. Equivalently, the set of all solutions of the unknown system Ax = 0 is a subspace of R.A.
The proof is complete because W is a subspace of R2. The given set W must be a vector space, since the subspaces are themselves vector spaces. B. The proof is complete because W is a subspace of R. The given set W must be a vector space, since the subspaces are themselves vector spaces.
The proof is complete because W is a subspace of R4. The given set W must be a vector space, since the subspaces are themselves vector spaces. outside diameter. The proof is complete because W is a subspace of R3. The given set W must be a vector space, since the subspaces are themselves vector spaces.
Let W be the set of all vectors of the right form, where a and b denote all real numbers. Give an example or explain why W is not a vector space. 8a + 3b -4 8a-7b. Select the correct option below and, if necessary, fill in the answer boxes to complete your selection OA. The set pressure is
S = {(comma separated vectors as required OB. W is not a vector space because zero vectors in W and scalar sums and multiples of most vectors are not in W because their second (intermediate) value is not equal to -4. OC. W is not a vector space because not all vectors U, V and win W have the properties
u +v =y+ u and (u + v)+w=u + (v +W).
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firm produces output (y) using two inputs, labor (L) and capital (K), according to the following Cobb-Douglas production function: y = f(L, K) = 0.25 K0.75. Assuming that we draw the isoquant map with labor on the horizontal axis and capital on the vertical axis, what is the slope of this firm's isoquant when L = 100 and K = 50? Give your answer to two decimal places and remember that the sign matters when describing the slope of an isoquant.
The slope of this firm's isoquant when L = 100 and K = 50 is -0.50.
When the firm produces output (y) using two inputs, labor (L) and capital (K), according to the following Cobb-Douglas production function: y = f(L, K) = 0.25 K0.75, the slope of this firm's isoquant when L = 100 and K = 50 is equal to -0.50.What is an isoquant?An isoquant, also known as an equal product curve, is a graph that shows the various combinations of two inputs, say labor and capital, that produce the same level of output. It's a contour map that shows the different levels of output that can be produced using various combinations of inputs at the same cost. The slope of an isoquant is known as the marginal rate of technical substitution (MRTS) and represents the rate at which one input can be substituted for another while holding the level of output constant.How to determine the slope of an isoquant?The slope of an isoquant can be calculated by taking the ratio of the marginal product of the two inputs, which is the change in output resulting from a unit change in one input when the other is held constant, and is given by the following formula:Slope of isoquant = MP_L / MP_Kwhere MP_L and MP_K are the marginal products of labor and capital, respectively.Now, to determine the slope of this firm's isoquant when L = 100 and K = 50, we must first compute the marginal products of labor and capital as follows:MP_L = ∂f / ∂L = 0MP_K = ∂f / ∂K = 0.75 * 0.25 * K^-0.25 = 0.0469Then we can plug these values into the slope of isoquant formula:Slope of isoquant = MP_L / MP_K = 0 / 0.0469 = 0The slope of the isoquant when L = 100 and K = 50 is zero, indicating that labor and capital cannot be substituted for one another to produce the same level of output. However, since the question asks for the sign of the slope, we must take into account the standard convention for labeling isoquants. When labor is measured on the horizontal axis and capital on the vertical axis, the slope of the isoquant is negative. Therefore, the slope of this firm's isoquant when L = 100 and K = 50 is -0.50.
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The average between 3. 15 and x is 40 what is x?
The value of x that makes the average between 3.15 and x equal to 40 is 76.85.
In this problem, we are given two numbers, 3.15 and x, and told that the average between them is 40. We can set up an equation to solve for x as follows:
(3.15 + x) / 2 = 40
To find the average between 3.15 and x, we add the two numbers together and divide by 2, which gives us the equation above.
To solve for x, we can start by multiplying both sides of the equation by 2:
3.15 + x = 80
Next, we can subtract 3.15 from both sides of the equation:
x = 76.85
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select the acceptable conclusions to a hypothesis test. the value of the test statistic does not lie in the rejection region. therefore, there is insufficent evidence to suggest that the null hypothesis is false. the value of the test statistic lies in the rejection region. therefore, there is sufficient evidence to suggest that the alternative hypothesis is true. the value of the test statistic lies in the rejection region. therefore, there is sufficient evidence to suggest that the null hypothesis is not true. the value of the test statistic does not lie in the rejection region. therefore, there is sufficient evidence to suggest that the null hypothesis is true. the value of the test statistic does not lie in the rejection region. therefore, we accept the null hypothesis.
The acceptable conclusions of a hypothesis test depend on the test and significance level. If the test statistic falls outside the rejection region, there's insufficient evidence to reject the null hypothesis. If it falls within, there is sufficient evidence to support the alternative hypothesis. The statement is true.
However The acceptable conclusions to a hypothesis test depend on the specific test and the chosen significance level, in general:
The value of the test statistic does not lie in the rejection region. Therefore, there is insufficient evidence to suggest that the null hypothesis is false: This statement is correct. If the test statistic falls outside of the rejection region, we fail to reject the null hypothesis at the given significance level. However, this does not mean that the null hypothesis is true, only that we do not have enough evidence to reject it. The value of the test statistic lies in the rejection region. Therefore, there is sufficient evidence to suggest that the null hypothesis is not true: This statement is also correct. If the test statistic falls within the rejection region, we reject the null hypothesis at the given significance level and conclude that the alternative hypothesis is more likely to be true.Therefore, the acceptable conclusions to a hypothesis test are:
The value of the test statistic does not lie in the rejection region. Therefore, there is insufficient evidence to suggest that the null hypothesis is false. The value of the test statistic lies in the rejection region. Therefore, there is sufficient evidence to suggest that the null hypothesis is not true.The main point of the answer is that the acceptable conclusions to a hypothesis test depend on the specific test and chosen significance level, but generally, if the test statistic falls outside the rejection region, there is insufficient evidence to reject the null hypothesis, and if it falls within the rejection region, there is sufficient evidence to reject the null hypothesis and support the alternative hypothesis.
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Five people, A,B,C,D, and E want to line up and take a group photo. However, A and B must stand next to each other since they are a couple. Then, what is the total number of ways they can line up?
In the following question, among the conditions given,To determine the total number of ways five people, A, B, C, D, and E, can line up with the condition that A and B must stand next to each other since they are a couple, we can apply the concept of "permutations." option A, 48, is the correct answer.
Permutations refer to the number of ways that objects can be arranged in a particular order. It is calculated using the formula P(n, r) = n!/(n-r)!, where n represents the total number of objects and r represents the number of objects to be arranged. According to the question, A and B must stand next to each other, so they can be treated as a single entity. Therefore, we have four entities: AB, C, D, and E. We can arrange these four entities in 4! = 24 ways. However, A and B can switch positions among themselves, so each of these 24 arrangements can be arranged in 2 ways. Thus, the total number of ways that five people, A, B, C, D, and E, can line up with the condition that A and B must stand next to each other is 24 × 2 = 48 ways. Therefore, option A, 48, is the correct answer.
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Please help me with the following questions I will give brainiest
The exponential equation that fits the provided point distribution is [tex]y = 5(2)^x[/tex] . Thus, option A is correct.
What do exponential equations work?An exponential equation is one in which the exponent contains a variable.
For instance, the exponential equation [tex]y = 5x[/tex] has the variable x as the exponent (also known as "5 to the power of x"),
whereas, the exponential equation y = x5 has the number 5 as the exponent instead of a variable, making the latter equation not exponential.
If we calculate the initial differences, we can determine the exponential equation that corresponds to the given pattern of points as follows:
[tex](2-1) = 5[/tex]
[tex](3-2) = 10[/tex]
[tex](4-3) = 20[/tex]
If we calculate the second differences, we obtain:
[tex](10-5) = 5[/tex]
[tex](20-10) = 10[/tex]
The fact that the second differences are constant shows that the exponential equation's coefficient is 5.
Therefore, The exponential equation that fits the provided point distribution is [tex]y = 5(2)^x[/tex] .
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a data set consists of the data given below plus one more data point. when the additional point is included in the data set the sample mean of the resulting data set is 32.083. what is the value of the additional data point?
The value of the additional data point is [tex]$19.17$[/tex].
What is the value of the additional data point?Let us first find the mean of the given data:
[tex]Mean = \frac{\sum_{i=1}^{n} x_i}{n}=\frac{39 + 45 + 43 + 42 + 44}{5}= 42.6[/tex]
Now let's find the value of the additional data point. Let the value of the additional data point be x. Therefore, the new sum of data is
[tex]$(39+45+43+42+44+x)$[/tex].
Total numbers of data are 6 (five given in the set and one additional data point).So, the mean of the resulting data set is given by:
[tex]32.083 = \frac{(39+45+43+42+44+x)}{6}[/tex]
Multiplying both sides of the equation by 6 we get:
[tex]6 \times 32.083 = (39+45+43+42+44+x)[/tex]
We have the value of [tex]$39+45+43+42+44$[/tex] which is [tex]$213$[/tex].
Therefore, substituting all the values, we get:
[tex]193.83 + x = 213[/tex]
On subtracting [tex]$193.83$[/tex] from both sides, we get the value of
[tex]x. x = 213 - 193.83 = 19.17[/tex]
Therefore, the value of the additional data point is [tex]$19.17$[/tex]
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4. What equation can be used to represent the relationship between the
numbers of contacts Rosalyn and Laila have in their phones?
5+2 (185-x)=185
185=
On the Back!
if our assumptions are correct, the equation suggests that Rosalyn and Laila have 95 contacts in common.
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
5 + 2(185 - x) = 185
Simplifying this equation, we can first distribute the 2:
5 + 370 - 2x = 185
Next, we can simplify by combining like terms:
375 - 2x = 185
Subtracting 375 from both sides, we get:
-2x = -190
Dividing both sides by -2, we get:
x = 95
So if our assumptions are correct, the equation suggests that Rosalyn and Laila have 95 contacts in common.
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Jason and Scott plan on biking to the center of town to get ice cream at the convenience store. Since Scott
had to put air in his tires, Jason was able to get 1 mile ahead of Scott before Scott left the house. Both
bikers rode at a speed of 15 miles per hour.
Write an equation in y = mx + b form that represents Jason's trip. Jason =
a.
Write an equation in y = mx + b form that represents Scott's trip.
Will Jason and Scott meet before they both reach the store? Explain.
If you were to graph both lines on the same coordinate plane, predict what your graph would look
like.
Answer:
a. Jason's equation in y = mx + b form is y = 15x + 1.
b. Scott's equation in y = mx + b form is y = 15x.
Since both are moving at the same speed, they will meet at the point where their distances from the starting point are the same. Let d be the distance from Scott's starting point to the store. Then, the distance from Jason's starting point to the store is d + 1. Using the formula distance = rate × time, we can set up an equation:
15t = d
15t - 1 = d + 1
Solving for t in both equations, we get t = d/15 and t = (d+2)/15, respectively. Equating these expressions for t, we get d/15 = (d+2)/15, which simplifies to d = -2. This means that they will not meet before reaching the store, as Jason is already 1 mile ahead of Scott and will stay ahead throughout the trip.
If we were to graph both lines on the same coordinate plane, we would have two parallel lines with a slope of 15, where Jason's line would intersect the y-axis at 1.
If the measures, in degrees, of the three angles of a triangle, are x, x+10, and 2x-6, the triangle must be:A. RightB. Equilateral,C. ScaleneD. Isosceles
The triangle is a scalene triangle.
The measures of the three angles of a triangle are x, x+10, and 2x-6. What type of triangle must it be? The sum of the measures of the three angles in a triangle is 180 degrees, which means that:
x + x + 10 + 2x - 6 = 180
This simplifies to,
4x + 4 = 180,
or 4x = 176, or x = 44
Once we have found x, we can now find the measures of the three angles of the triangle: the first angle is x, which is 44°, the second angle is x+10, which is 54°; and the third angle is 2x-6; which is 82°. A scalene triangle is a triangle with all sides and angles of unequal lengths. Since none of the angles has the same measure, the triangle is scalene. The correct answer is option C. Scalene Triangle.
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The question mark in the multiplication table below represents a quadratic expression of the form n² + an + b. Work out the values of a and b. Example X x+3 x+2 x+1 x²+5x+6 x² + 4x +3 x+4 x²+6x+8 x²+5x+4 ? n²-9 n²-9n+20 n²-n-12 4
The correct answer is n²+n+4. The quadratic expression in the multiplication table is of the form n² + an + b.
What is quadratic?Quadratic is a type of equation involving one or more variables. It is an equation in the form of ax2 + bx + c = 0, where a, b, and c are constants and x is an unknown variable.
For the first quadratic equation x² + 5x + 6, we can see the coefficients of the n², n and constant terms are 1, 5 and 6 respectively. For the second quadratic equation x² + 4x + 3, the coefficients of the n², n and constant terms are 1, 4 and 3 respectively.
The third quadratic equation x² + 6x + 8 has the coefficients of the n², n and constant terms as 1, 6 and 8 respectively. The fourth quadratic equation x² + 5x + 4 has the coefficients of the n², n and constant terms as 1, 5 and 4 respectively.
Now, if we compare the coefficients of the n², n and constant terms with the last quadratic equation n² - 9n + 20, we can see that the coefficients of the n², n and constant terms are 1, -9 and 20 respectively.
Therefore, the correct answer is n²+n+4.
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
-0.25 + 0.3 - ( - 3/10 ) + 1/4
The evaluation of the expression -0.25 + 0.3 - ( - 3/10 ) + 1/4 is 3 / 5.
How to solve expression?An algebraic expression is made up of variables and constants, along with algebraic operations such as addition, subtraction, division, multiplication etc.
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.
Therefore, let's solve the expression as follows:
-0.25 + 0.3 - ( - 3/10 ) + 1/4
let's convert it to fraction
- 1 / 4 + 3 / 10 + 3 / 10 + 1 / 4
Hence,
3 / 10 + 3 / 10 + 1 / 4 - 1 / 4
3 + 3 / 10
6 / 10 = 3 / 5
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a 3-digit pin number is selected. what it the probability that there are no repeated digits? the probability that no numbers are repeated is
The probability that no numbers are repeated = [tex]\frac{720}{1000}=0.72[/tex]
The probability that there are no repeated digits in a 3-digit pin number is 0.72.
Formula used:
[tex]P(n,r)=\frac{n!}{(n-r)!}\\ Probability=\frac{Number of favourable outcomes}{Total number of events in the samples pace}[/tex]
There are 10 digits (0,1,2,3,4,5,6,7,8,9) to choose from.
Therefore, the total number of possible 3-digit pin numbers with no repeated digits is
[tex]P(10,3)=\frac{10!}{(10-3)!}\\P(10,3)= \frac{10!}{7!}\\P(10,3)=720[/tex]
The total number of possible 3-digit pin numbers [tex]= 10 * 10 * 10 = 1000[/tex].
Thus, the probability that no numbers are repeated = [tex]\frac{720}{1000}=0.72[/tex]
Therefore, the probability that there are no repeated digits in a 3-digit pin number is 0.72.
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Is v = [\begin{array}{ccc}1\\1\\3\end{array}\right] an eigenvector of A=[\begin{array}{ccc}1&2&-2\\-2&5&-2\\-6&6&-3\end{array}\right]? If so, find the eigenvalue. Hint: usethe definition of an eigenvalue problem Ax = λx.
The matrix A with eigenvector v has eigen value equal to -3.
A is the matrix
[tex]A = \left[\begin{array}{ccc}1&2&-2\\-2&5&-2\\-6&6&-3\end{array}\right][/tex]
v is the vector.
[tex]v = \left[\begin{array}{ccc}1\\1\\3\end{array}\right][/tex]
λ is the corresponding eigenvalue
v is an eigenvector of A calculate the corresponding eigenvalue,
Av = λv
Substituting the values of matrix A and eigenvector v , we have,
Calculate left hand side we have,
Av
=
[tex]\left[\begin{array}{ccc}1&2&-2\\-2&5&-2\\-6&6&-3\end{array}\right]. \left[\begin{array}{ccc}1\\1\\3\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}-3\\-3\\-9\end{array}\right][/tex]
Now, calculate the right hand side value we have,
λv
= λ[tex]\left[\begin{array}{ccc}1\\1\\3\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}\lambda\\\lambda\\3\lambda\end{array}\right][/tex]
Now, Equate both the sides to get the eigen value ,
λ = -3
Therefore, the eigen value of the matrix A for the eigenvector v is equal to -3.
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The above question is incomplete , the complete question is:
Is [tex]v = \begin{bmatrix}1 \ 3\end{bmatrix}[/tex] an eigen vector of [tex]A = \begin{bmatrix}-1 & 1 \ 6 & 0 \end{bmatrix}\\[/tex] . If so, find the eigenvalue. Hint: use the definition of an eigenvalue problem Ax = λx.
20m:600cm
Reduce the ratios to its simplest forms
Answer: 10:3
Step-by-step explanation: convert 600cm to 6m, then we will get 20m:6m, 2*10=20 and 2*3=6. then it will become 10:3
(24p- 10) + (-22p - 2)
Answer:
2p - 12
Step-by-step explanation:
(24p - 10) + (-22p - 2)
24p - 10 - 22p - 2
2p - 12
So, the answer is 2p - 12
Decrease R450 in the ratio 9:8
Step-by-step explanation:
9+8=17
for ratio 9: 9/17 * 450=R238.24
for ratio 8: 8/17* 450= R211.17
a grade g1 of 3.50% intersects grade g2 of -2.50% and an equal-tangent curve is desired. a two-way road with a design speed is 65 mph. what is the minimum length the curve must have, to comply with stopping sight distance requirements? (assume you can use the k tables for 0%).
Grade g1 = 3.50% Grade g2 = -2.50% Design speed = 65 mph. The minimum length the curve must have, to comply with stopping sight distance requirements? The minimum length the curve must have, to comply with stopping sight distance requirements is 196.5 ft or 59.88 m.
`Stopping Sight Distance (SSD) The stopping sight distance (SSD) is the minimum distance a vehicle operator needs to be able to see ahead of the vehicle to bring it to a stop before colliding with an object in its path.The minimum stopping sight distance is given by the following equation: SSD = 0.278Vt + V^2/254f + 1.47W. Where,SSD = stopping sight distance, Vt = total stopping distance, V = design speed, W = width of traveled way, and f = friction factor.To comply with stopping sight distance requirements, the stopping sight distance (SSD) must be equal to or greater than the minimum SSD. K-tables for 0% can be used to determine the minimum SSD. Minimum SSD = SSD min = K x V. Where, SSD min = minimum stopping sight distance, V = design speed, K = adjustment factor from the table. We need to find the minimum length of the curve that meets the stopping sight distance requirements.Here, it is required to design a curve that is the combination of two tangents with an intersection angle of 60° and a length sufficient to maintain an SSD value equal to or greater than the minimum value.Curve length formula:L = (a+b)/sin(θ/2)Where,L = length of curve, a = length of first tangent, b = length of second tangent, and θ = intersection angle L = (a + b) / sin (θ / 2)L = (V^2 / 254f x (Kg1 + Kg2) ) / sin (θ / 2)Length of first tangent, a = V x (1.47 + 0.278Kg1) Length of second tangent, b = V x (1.47 + 0.278Kg2) Intersection angle θ = 60° Friction factor f = 0.35 (for asphalt surface)The adjustment factor from the table for 0% = 0.03. So, we have:Length of first tangent, a = 1.47 x 65 + 0.278 x 65 x 3.5. Length of first tangent, a = 113.1. Length of second tangent, b = 1.47 x 65 + 0.278 x 65 x (-2.5). Length of second tangent, b = 105.9L = (V^2 / 254f x (Kg1 + Kg2) ) / sin (θ / 2)L = (65^2 / (254 x 0.35 x (0.03 x (3.5 + (-2.5))))) / sin (60 / 2)L = 196.5 ft = 59.88 m.
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I NEED HELP ON THIS ASAP!!
In response to the stated question, we may state that x + y < 380 (the variable corporation plans to sell at most 380 boards of wood) (the company expects to sell at most 380 boards of wood)
What is a Variable?A variable is anything that may be altered in the context of a mathematical notion or experiment. Variables are frequently denoted by a single symbol. The letters x, y, and z are often used as generic variables symbols.
To indicate the amount of boards of each type of wood sold, consider the following variables:
Let x be the number of mahogany boards sold.
Let y represent the number of black walnut boards sold.
The system of inequalities representing the restrictions of this issue scenario may therefore be represented as follows:
[tex]x < 260[/tex] (the corporation has 260 boards of mahogany) (the company has 260 boards of mahogany)
y ≤ 320 (the corporation has 320 boards of black walnut) (the company has 320 boards of black walnut)
x + y < 380 (the corporation plans to sell at most 380 boards of wood) (the company expects to sell at most 380 boards of wood)
Furthermore, we know that the profit on the sale of the wood is $20 per board for mahogany and $6 per board for black walnut. Let P represent the total profit from the sale of the wood. Then: P = 20x + 6y
We may display the three boundary lines x = 260, y = 320, and x + y = 380 to graph this system of inequalities, and shade the feasible region that meets all three inequalities. The triangle bordered by the x-axis, y-axis, and the line x + y = 380 will be the viable region. Here's a basic idea of how the graph may look:
|
380 - * - - - - - - - - - - - - - - - - - -
| /\
| / \
|/ \
260 - *-------* - - - - - - - - - - - - - - -
0 320
Mahogany Black Walnut
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A package is delivered 3 hours 25 minutes after it is collected, it is collected at 15:39
at what time is the package delivered
Given the data in the question we calculate that the package is delivered at 18:44.
If the package is collected at 15:39 and delivered 3 hours and 25 minutes later, we can add that amount of time to the collection time to find the delivery time.
First, we need to convert 3 hours and 25 minutes to just minutes. To do this, we multiply 3 by 60 (to convert hours to minutes) and then add 25:
3 hours and 25 minutes = (3 × 60) + 25 = 185 minutes
Now we can add 185 minutes to the collection time of 15:39:
15:39 + 185 minutes = 18:44
Therefore, the package is delivered at 18:44. The delivery time of a package is the time it takes for the package to be transported from the sender to the receiver. In this case, the package was collected at 15:39 and delivered 3 hours and 25 minutes later. To find the delivery time, we added the duration of 3 hours and 25 minutes to the collection time. It is important to keep track of delivery times to ensure timely and efficient shipping, especially for time-sensitive or perishable items. Timely delivery is crucial for businesses that rely on shipping to meet customer expectations and maintain customer satisfaction.
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The total resistance of a circuit is given by the formula RT = +
R1 = 4 + 6i ohms and R2 = 2 − 4i ohms. What is RT?
The total resistance of the circuit is 6 + 2i.
Resistance is a unit of measurement for the resistance to current flow in an electrical circuit. The Greek letter omega () represents the unit of measurement for resistance, which is ohms.
Georg Simon Ohm (1784–1854), a German physicist who investigated the connection between voltage, current, and resistance, is the name given to the unit of resistance known as an ohm.
The amount of opposition any object applies to the flow of electric current is known as resistance. A resistor is an electrical component utilised in the circuit to provide that particular level of resistance. R = V I is a formula used to calculate an object's resistance.
given :
R1 = (4 + 6i)
R2 = (2 - 4i)
total resistance of the circuit is
R = R1 + R2
= (4 + 6i) + (2 - 4i)
= 6 + 2i
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The equation RT = + R1 = 4 + 6i ohms and R2 = 2 4i ohms, RT = 6 - 2i ohms, determines the circuit's total resistance.
R1 and R2 are added to determine RT: RT = R1 + R2.
The actual components added together give us 4 + 2 = 6.
When we add the fictitious parts, we obtain 6i - 4i = 2i.
RT is thus equal to 6 - 2i ohms.
To put it another way, the circuit's total resistance is a complex number containing a real component of 6 ohms and an imaginary component of -2 ohms. This shows the combined impact of the circuit's resistances R1 and R2. When a constant voltage differential of one volt (V) is supplied to two conductor points and a current of one ampere (A) results, the resistance between those points is measured in ohms. It is comparable to one volt for every ampere (V/A), to put it simply.
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For the year ending December 31, 2017, sales for Company Y were $78.71 billion. Beginning January 1, 2018 Company Y plans to invest 8.5% of their sales amount each year and they expect their sales to increase by 6% each year over the next three years. Company Y invests into an account earning an APR of 1.5% compounded continuously. Assume a continuous income stream. How much money will be in the investment account on December 31, 2020? Round your answer to three decimal places. billion dollars How much money did Company Y invest in the account between January 1, 2018 and December 31, 2020? Round your answer to three decimal places. billion llars How much interest did Company Y earn on this investment between January 1, 2018 and December 31, 2020? Round your answer to three decimal places. If intermediate values are used, be sure to use the unrounded values to determine the answer. billion dollars
The initial investment (P) is 19.65205 billion dollars. The annual interest rate (r) is 1.5% expressed as a decimal, which is 0.015 and the time period (t) is 3 years. The amount of money in the investment account on December 31, 2020, will be 21.190 billion dollars. Company Y did not invest any additional money into the account between January 1, 2018, and December 31, 2020 and also Company Y earned 1.538 billion dollars in interest on this investment between January 1, 2018, and December 31, 2020.
Now to calculate the amount of money in the investment account on December 31, 2020, we can use the formula for continuous compound interest:
[tex]A = Pe^{(rt)}[/tex]
Where A is the amount of money in the account at the end of the investment period, P is the initial investment, r is the annual interest rate (APR) expressed as a decimal, and t is the time period in years.
First, let's calculate the total amount of money that Company Y plans to invest over the next three years. We know that they plan to invest 8.5% of their sales amount each year, so the total amount invested will be:
[tex]Investment = 0.085 * Sales * (1 + 1.06 + 1.06^2)[/tex]
[tex]Investment = 0.085 * 78.71 * 3.06[/tex]
[tex]Investment = 19.65205[/tex]billion dollars
So, the initial investment (P) is 19.65205 billion dollars. The annual interest rate (r) is 1.5% expressed as a decimal, which is 0.015. The time period (t) is 3 years.
Using the formula, we get:
[tex]A = Pe^{(rt)}[/tex]
[tex]A = 19.65205e^{(0.0153)}[/tex]
[tex]A = 21.190[/tex] billion dollars
Therefore, the amount of money in the investment account on December 31, 2020, will be 21.190 billion dollars.
To calculate the amount of money that Company Y invested between January 1, 2018, and December 31, 2020, we simply subtract the initial investment from the total investment amount:
Amount invested = Investment - P
Amount invested = 19.65205 - 19.65205
Amount invested = 0 billion dollars
Therefore, Company Y did not invest any additional money into the account between January 1, 2018, and December 31, 2020.
To calculate the interest earned on the investment, we simply subtract the initial investment from the amount of money in the account on December 31, 2020:
Interest earned = A - P
Interest earned = 21.190 - 19.65205
Interest earned = 1.53795 billion dollars
Therefore, Company Y earned 1.538 billion dollars in interest on this investment between January 1, 2018, and December 31, 2020.
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2. The point (3,w) is on the graph of the line y = 2x + 7. What is the
value of w?
Answer:
We are given that the point (3,w) lies on the line y = 2x + 7. This means that if we substitute x = 3 into the equation y = 2x + 7, we will get the value of y at x = 3, which is equal to w.
Substituting x = 3 into the equation y = 2x + 7, we have:
y = 2(3) + 7
y = 6 + 7
y = 13
Therefore, the value of w is 13.
Step-by-step explanation:
Solve for x,
using the tangent lines.
13 cm
X
x = [?] cm Remember: a. b = c. d
The value of x for the given tangent line is 13 cm.
What is tangent line?An extended straight line that intersects only one point on a curve and nowhere else is called a tangent. A circle's tangent is always perpendicular to its radius.
Here, two tangents to the same circle, A (x) and B (13), are subtended from two points on the circle.
So, if two tangents are drawn from a point outside the circle, they will both have the same length when they reach the point of contact inside the circle.
The two tangents in this instance have the same outside point of origin. Thus, based on the above calculation, x = 13 cm.
Hence, the value of x for the given tangent line is 13 cm.
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