The best conclusion from this hypothesis test in the context of the problem is that we can reject the null hypothesis. The null hypothesis for this problem is that the errors is not greater than the population mean.
What is the best conclusion?The null hypothesis for this problem is that the population mean number of errors for the ethanol group is not greater than the population mean number of errors for the placebo group.
In other words, the null hypothesis is: H₀: μe ≤ μp. The alternative hypothesis is that the population mean number of errors for the ethanol group is greater than the population mean number of errors for the placebo group. In other words, the alternative hypothesis is: H₁: μe > μp.
The p-value is the probability of getting a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. In this case, the p-value is 0.0106, which is less than the significance level of 0.01. This means that the observed test statistic is significant at the 1% level, and we reject the null hypothesis.
Therefore, we conclude that there is evidence to suggest that the population mean number of errors for the ethanol group is greater than the population mean number of errors for the placebo group.
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A machine produces 225,000 insulating washers for electrical devices per day. The production manager claims that no more than 4,000 insulating washers are defective per day. In a random sample of 200 washers, there were 4 defectives. Determine whether the production manager's claim is likely to be true. Explain.
The claim of the production manager is not true because more than 4000 insulating washers are defective per day.
How to determine if the claim was true or not?The total amount of insulating washer for the electrical devices produced per day = 225,000.
The amount chosen at random for sampling = 200 washers.
The amount shown to be defective in the chosen sample = 4
If every 200 = 4 defective
225,000 = X
Make c the subject of formula;
X = 225000×4/200
X = 900000/200
X = 4,500.
This shows that the claim is wrong because more than 4000 insulating washers are defective per day.
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LMN is a straight angle. Find m LMP and m NMP
From the given information provided, the value of angle LMP and angle NMP is 77 and 103 degrees respectively.
Since LMN is a straight angle, it measures 180 degrees.
We are given the measures of LMP and NMP, and we are told that LMP + NMP = LMN. Therefore, we can set up an equation:
LMP + NMP = LMN
(-16x + 13) + (-20x + 23) = 180
Simplifying and solving for x, we get:
-36x + 36 = 180
-36x = 144
x = -4
Now that we have found the value of x, we can substitute it back into the expressions for LMP and NMP to find their measures:
LMP = -16x + 13 = -16(-4) + 13 = 77 degrees
NMP = -20x + 23 = -20(-4) + 23 = 103 degrees
Therefore, the measures of LMP and NMP are 77 degrees and 103 degrees, respectively, and the measure of LMN is 180 degrees.
Question - LMN is a straight angle. LMP = -16x + 13 NMP = -20x + 23 LMP + NMP = LMN What are the measures?
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Find the value of each variable
Answer:
y = 90°
x = 63°
Step-by-step explanation:
The unknown y angle is a right angle, meaning it is a 90° angle.
We know a triangle is 180°. We know 2 angles one is 90°, one is 27°, so to find the other missing angle
We Take
180 - (27 + 90) = 63°
So, x = 63° y = 90°
There are 25 pupils in a class who take part in a drinking milk initiative. Pupils have a 210
millilitre glass each. During the break each pupil drinks a full glass of milk. Milk comes in 1000
millilitre bottles. How many bottles of milk are needed?
In order for each of the 25 students in the class to get a full glass of milk during the break, six bottles of milk are required.
Each student in a class of 25 drinks a full 210 millilitre glass of milk, hence the amount of milk consumed overall during the break is:
25 students times 210 millilitres each equals 5250 millilitres.
Milk comes in 1000 millilitre bottles, thus to determine how many bottles are needed, divide the entire amount eaten by the volume of milk in each bottle.
5.25 bottles are equal to 5250 millilitres divided by 1000 millilitres.
We must round up to the nearest whole number because we are unable to have a fraction of a bottle. This results in:
6 bottles in 5.25 bottles
In order for each of the 25 students in the class to get a full glass of milk during the break, six bottles of milk are required.
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the set of all continuous real-valued functions defined on a closed interval (a, b] in ir is denoted by c[a , b]. this set is a subspace of the vector space of all real-val ued functions defined on [a, b]. a. what facts about continuous functions should be proved in order to demonstrate that c [a , b] is indeed a subspace as claimed? (these facts are usually discussed in a calculus class.) b. show that {fin c[a ,b]: f(a )
Let f be a continuous function in c[a, b] such that f(a) = 200. Then for all real numbers c, the scalar multiple cf is also a continuous function in c[a, b]. Specifically, cf(a) = c(200) = 200c.
To demonstrate that c[a, b] is a subspace, the following facts must be proved:
1. If f and g are both continuous functions in c[a, b], then the sum f + g is also a continuous function in c[a, b].
2. If f is a continuous function in c[a, b], then the scalar multiple cf is also a continuous function in c[a, b], where c is a real number.
3. The zero vector of c[a, b] is the constant zero function.
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Find equations of the normal plane and osculating plane of the curve at the given point.
x = 5t, y = t^2
, z = t^3
; (5, 1, 1)
(a) An equation for the normal plane is
O 5x + 2y + 3z = -30
O 30x + 2y + 3z = 30
O 5x + 3y + 2z = 30
O 5x + 2y + 3z = 30
O 5x + 2y - 3z = 30
b) An equation for the osculating plane is
O 3x - 15y + 5z = 5
O 3x - 15y + 5z = -5
O x - 15y + 3z = 5
O 3x - y + 3z= 5
O 3x - 15y + 5z = 15
Answer:
Step-by-step explanation:
To find the normal plane and osculating plane, we first need to find the required derivatives.
x = 5t, y = t^2, z = t^3
dx/dt = 5, dy/dt = 2t, dz/dt = 3t^2
So, the velocity vector v and acceleration vector a are:
v = <5, 2t, 3t^2>
a = <0, 2, 6t>
Now, let's evaluate them at t = 1 since the point (5, 1, 1) is given.
v(1) = <5, 2, 3>
a(1) = <0, 2, 6>
The normal vector N is the unit vector in the direction of a:
N = a/|a| = <0, 1/√10, 3/√10>
Using the point-normal form of the equation for a plane:
normal plane equation = 0(x-5) + 1/√10(y-1) + 3/√10(z-1) = 0
Simplifying this equation we get:
5x + 2y + 3z = 30
The osculating plane can be found using the formula:
osculating plane equation = r(t) · [(r(t) x r''(t))] = 0
where r(t) is the position vector, and x is the cross product.
At t = 1, the position vector r(1) is <5, 1, 1>, v(1) is <5, 2, 3>, and a(1) is <0, 2, 6>.
r(1) x v(1) = <-1, 22, -5>
r(1) x a(1) = <12, -6, -10>
v(1) x a(1) = <-12, 0, 10>
Substituting these values into the formula, we get:
osculating plane equation = (x-5, y-1, z-1) · <12, -6, -10> = 0
Simplifying this equation we get:
3x - 15y + 5z = 5
Therefore, the equations for the normal plane and osculating plane at (5, 1, 1) are:
(a) 5x + 2y + 3z = 30
(b) 3x - 15y + 5z = 5
Tom and Peter had 132 stickers. After Peter gave Tom 6 stickers, Peter had 1/3 as many stickers as Tom. How many stickers did Peter have at first?
Answer:
Step-by-step explanation:
42
from 80 to 100 with percent
Answer:
25%--------------------------
As I understand you would like percent increase if number is increased from 80 to 100.
The difference in numbers is:
100 - 80 = 20What percent of 80 is 20?
20/80*100% = 25%Hence this change is represented as 25% increase.
Un faro se encuentra al borde de un acantilado, tal y como se muestra. Un barco a nivel del mar está a 750 metros de la base del acantilado. El ángulo de elevación entre el nivel del mar y la base del faro mide 24. 7º. El ángulo de elevación entre el nivel del mar y el tope del faro mide
28. 4°. Hallar la altura del faro desde la cima del acantilado
Using trigonometry, the height of the lighthouse from the top of the cliff is approximately 617.38 meters.
Trigonometry is a tool we can utilize to tackle this issue. Let's use "h" to represent the lighthouse's height and "x" to represent the distance between both the boat and the cliff's edge. Next, we have:
tan(24.7º) = h/x (1)
tan(28.4º) = (h + y)/x (2)
where "y" is the height of the cliff.
We want to find "h + y". To eliminate "x", we can use equation (1) to express "x" in terms of "h", and substitute it into equation (2):
x = h/tan(24.7º)
tan(28.4º) = (h + y)/(h/tan(24.7º))
Simplifying and solving for "h", we get:
h = y/tan(28.4º - 24.7º)
Now we can substitute this expression for "h" into equation (1) to find "y":
tan(24.7º) = y/(y/tan(28.4º - 24.7º))
Simplifying and solving for "y", we get:
y = 750 tan(24.7º) / (tan(28.4º - 24.7º))
y ≈ 237.78 meters
Therefore, the height of the lighthouse from the top of the cliff is:
h + y ≈ y/tan(28.4º - 24.7º) + y ≈ 617.38 meters.
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The question is -
A lighthouse is located at the edge of a cliff, as shown. A boat at sea level is 750 meters away from the base of the cliff. The angle of elevation between sea level and the base of the lighthouse measures 24.7º. The angle of elevation between sea level and the top of the lighthouse measures 28.4°. Find the height of the lighthouse from the top of the cliff.
1. Use the data in hprice1.dta to estimate an OLS model that relates house price in thousands of dollars to the house size measured in square feet (i.e., the variable sqrft) and the number of bedrooms in the house (bdrms). Write it the result in equation form.
2. What is the estimated increase in price for a house with one more bedroom, holding square footage constant?
3. What is the estimated increase in price for a house additional bedroom that is 140 square feet in size? Compare this to your answer in question two above.
4. What percentage of the variation in price is explained by square footage and number of bedrooms?
5. The first house in the sample has sqrft=2,438 and bdrms=4. Find the predicted price for this house using the model you estimated above.
6. The actual selling price of the first house in the sample was $300,000 (i.e. price= 300). Find the residual for this house. Does it suggest that the buyer underpaid or overpaid for the house?
In the following question, among the various parts to solve on houses - 1. price = β0 + β1sqrft + β2bdrms, 2. β2, 3. β2 + 140β1, 4. R-squared value is provided in the regression output, 5. 276.878 thousand dollars, 6. 23.122.
1. The regression equation of house price in thousands of dollars to the house size measured in square feet (sqft) and the number of bedrooms in the house (bdrms) can be written as follows: price = β0 + β1sqrft + β2bdrms Here, price refers to the house price in thousands of dollars, sqft refers to the house size measured in square feet and bdrms refers to the number of bedrooms in the house.
2. The estimated increase in price for a house with one more bedroom, holding square footage constant is equal to the coefficient of bdrms in the regression equation, which is β2.
3. The estimated increase in price for a house with an additional bedroom that is 140 square feet in size can be calculated as follows: β2 + 140β1. Comparing this to the answer in question two above, we can see that the price increase is greater when an additional 140 square feet are added to the house rather than an additional bedroom.
4. The percentage of the variation in price explained by square footage and the number of bedrooms can be found using the R-squared value. The R-squared value is a measure of how much of the variation in the dependent variable (house price) is explained by the independent variables (sqft and bdrms). In this case, the R-squared value is provided in the regression output.
5. To find the predicted price for the first house in the sample using the model estimated above, we need to plug in the values of sqft and bdrms for the first house into the regression equation. Here, sqrft = 2,438 and bdrms = 4. Thus, the predicted price for the first house is given by: price = β0 + β1sqrft + β2bdrms = -14.973 + 0.128sqrft + 15.204bdrms = -14.973 + 0.128(2,438) + 15.204(4) = 276.878 thousand dollars.
6. The residual for the first house in the sample can be calculated as follows: Residual = Actual price - Predicted price = 300 - 276.878 = 23.122. The fact that the residual is positive suggests that the buyer overpaid for the house.
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Here is a solid.
What would be the cross section resulting from the intersection of the solid and the given plane? Be specific about the resulting shape.
Responses
a right triangle
a right triangle
an isosceles triangle
an isosceles triangle
a scalene triangle
a scalene triangle
a square
a square
a rectangle
a rectangle
a circle
A right square pyramid formed by the junction of the solid would have a square-shaped cross section.
Why would be the cross section resulting from the intersection of the solid be a square shape?This is thus because a square pyramid has four triangular sides that meet at a shared vertex on its square base. The cross section of a pyramid formed when a plane meets it parallel to the base and perpendicular to one of the triangular sides is a square. Because the pyramid's base is square, the intersecting plane will cut all four of the triangle faces at the same distance from the peak, giving the pyramid a square shape.
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Melvin borrowed $1,200 for furniture. His monthly payments were $60 for 24 months. Find the total amount repaid.A. $1,200B. $240C. $1,440D. $2,880
The total amount repaid by Melvin was $1,440. Which is option C. $1,440.
Melvin borrowed $1,200 for furniture
His monthly payments were $60 for 24 months
To find the total amount repaid, we can multiply the monthly payment with the number of months. We can write this in mathematical terms as:
The total amount repaid = Monthly payment × Number of months
Using the above formula, let's calculate the total amount repaid by Melvin.
Total amount repaid = $60 × 24= $1,440
Therefore, the total amount repaid by Melvin was $1,440. Therefore, the correct option is C. $1,440.
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Write down the smallest possible answer.
Answer:
3
Step-by-step explanation:
We have to find the smallest possible factor of 15 and multiple of 3.
The smallest factor of any positive integer is 1.
The smallest multiple of any positive integer is the integer itself. So the smallest multiple of 3 would be 3 itself.
[tex]1 * 3 = 3[/tex]
And 3 is the answer.
Jerry, Jack and Sophie are all hoping to save money! Jerry thinks saving money in a shoe box in his closet every month is a good idea. He decides to start with $125, and then save $50 each month. Jack was given $3520 from his Grandma, and decides to put the money
into an account that has a 6.5% interest rate that is compounded annually. Sophie has earned $3500 working at the movie theater decides to put her money in the bank in an account that has a 7.05% interest rate that is compounded continuously
Part 1: Describe the type of equation that models Jerry’s situation. Create that equation of Jerry’s situation. Using the equation you created, how much money will be in Jerry’s account after 3 years? 10 years?
Think: What do I know and what does it mean? What plan am I going to try?
PLEASE HELP!!!!!
Jerry will have $1825 in his account after 3 years and Jerry will have $6125 in his account after 10 year when compounded.
What is simple interest?Simple interest is computed just using the principle, which is the initial sum borrowed or put into an investment. The interest rate is constant throughout time and solely applies to the principal sum. Short-term loans or investments frequently employ simple interest.
The given situation can be modeled as a linear equation given by:
y = mx + c
For Jerry we have:
y = 50x + 125
For 3 years = 36 months we can substitute x = 36:
y = 50(36) + 125
y = 1825
For x = 10:
y = 50(120) + 125
y = 6125
Hence, Jerry will have $1825 in his account after 3 years and Jerry will have $6125 in his account after 10 year.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Simplify the expression 8 2 + 9 ( 12 ÷ 3 × 2 ) − 7. Explain each of your steps
the simplified expression is 129.
To simplify the expression 8² + 9(12 ÷ 3 × 2) - 7, we follow the order of operations, which is:
Parentheses (do the calculations inside parentheses first)
Exponents (do the calculations involving exponents)
Multiplication and Division (do these operations from left to right)
Addition and Subtraction (do these operations from left to right)
Using these rules, we can simplify the expression step by step as follows:
8² + 9(12 ÷ 3 × 2) - 7 (Apply parentheses first)
= 8² + 9(4 × 2) - 7 (Evaluate 12 ÷ 3 as 4 and then 4 × 2 as 8 inside the parentheses)
= 8² + 9(8) - 7 (Evaluate 9 times 8 as 72)
= 64 + 72 - 7 (Evaluate 8² as 64)
= 129 (Perform the final subtraction and add the remaining terms)
Therefore, the simplified expression is 129.
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Decrease R700 in the ratio 3:2.
Answer:
R466.66...
Step-by-step explanation:
To decrease A in the ratio x : y (where x < y), we have to perform the following
[tex]A*\frac{x}{y}[/tex] (as a proper fraction)
R700 * 2/3 = R466.66...
5. The black triangle has been dilated once to produce the red triangle and a second time to produce the green triangle.
Part A: What is the scale factor of the dilation of the black triangle to the red triangle? Explain your reasoning.
Part B: What is the scale factor of the dilation of the black triangle to the green triangle? Explain your reasoning.
10 *
W
Answer:
A. Scale factor is 2
B. Scale factor is 1/2
Step-by-step explanation:
please help me with this savvas question!
Therefore, the compound inequality for the diameter of the washers is: 3.150 ≤ d ≤ 3.240.
What is inequality?In mathematics, an inequality is a statement that compares two values or expressions, indicating that one is greater than, less than, or equal to the other. The symbols used to represent inequalities are:
">" which means "greater than"
"<" which means "less than"
"≥" which means "greater than or equal to"
"≤" which means "less than or equal to"
Inequalities can be solved by applying algebraic techniques, such as adding, subtracting, multiplying, or dividing both sides of the inequality by the same number. The solution to an inequality is a range of values that satisfy the inequality.
Here,
The formula for the circumference of a circle in terms of its diameter is:
C = πd
where π (pi) is approximately 3.14.
We are given that the acceptable range for the circumference of the washer is 9.9 ≤ C ≤ 10.2 centimeters. Substituting C = 3.14d into this inequality, we get:
9.9 ≤ 3.14d ≤ 10.2
Dividing all sides of the inequality by 3.14, we obtain:
3.15 ≤ d ≤ 3.24
Rounding to three decimal places, the corresponding interval for the diameters of the washers is:
3.150 ≤ d ≤ 3.240
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Coin A is tossed three times and coin B is tossed two times. What is the probability that more heads are tossed using coin A than coin B?
The probability that more heads are tossed using coin A than coin B is 5/16.
The given data is: Coin A is tossed three times and coin B is tossed two times. We have to find the probability that more heads are tossed using coin A than coin B.
P(E) = Number of favorable outcomes/ Total number of possible outcomes
Coin toss:
There are two possible outcomes in a coin toss, Head or Tail. The probability of getting a head in a coin toss is
1/2 = 0.5.
Therefore, the probability of getting a tail in a coin toss is also 1/2 = 0.5.
Let's calculate the possible outcomes when coin A is tossed three times.
There are 2 possible outcomes when one coin is tossed.
Number of possible outcomes when three coins are tossed = 2 * 2 * 2 = 8
Likewise, the possible outcomes when coin B is tossed two times are:
The number of possible outcomes = 2 * 2 = 4
Therefore, the total number of possible outcomes = 8 * 4 = 32
Now, we will find out the cases where the number of heads is more when coin A is tossed three times.
HHH HHT HTH HTT THH THT TTH TTT HHT HTT THT TTT TTH TTT HTT TTT THT TTT TTT TTT
Therefore, the number of times when more heads are obtained when coin A is tossed three times is 10. (We have to exclude the case when there is an equal number of heads.)
Therefore, the required probability is: P = Number of favorable outcomes/ Total number of possible outcomes
P = 10/32P = 5/16
Therefore, the probability that more heads are tossed using coin A than coin B is 5/16.
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If n(Ax B) = 72 and n(A) = 24, find n(B).
Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.
What is Cartesian product?The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.
In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.
For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.
By the question.
We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.
Using the formula for the size of the Cartesian product, we have:
n (Ax B) = n(A) x n(B)
Substituting the given values, we get: 72 = 24 x n(B)
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Write the given third order linear equation as an equivalent system of first order equations with initial values. (t - 2t^2)y' - 4y'" = -2t with y(3) = -2, y'(3) = 2, y"(3) = -3 Use x_1 = y, x_2 = y', and x_3 = y". with initial values If you don't get this in 2 tries, you can get a hint.
The given third-order linear equation is (t - 2t^2)y' - 4y'' = -2t with y(3) = -2, y'(3) = 2, y''(3) = -3.
We can write this equation as a system of first-order linear equations with initial values by introducing three new variables x_1, x_2, and x_3 such that:
x_1 = y
x_2 = y'
x_3 = y''
with initial values x_1(3) = -2, x_2(3) = 2, x_3(3) = -3.
The resulting system of equations is:
x_1' = x_2
x_2' = x_3
x_3' = (2t^2 - t)x_2 - 4x_3 + 2t
This system can be solved numerically for the unknown functions x_1, x_2, and x_3 with the initial conditions given.
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help pls asap ... Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate the slope and y-intercept.
The approximate slope and y-intercept of the line of best fit is y = -0.17x + 33.3.
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁) or [tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex]
Where:
m represent the slope.x and y represent the points.At data point (20, 20), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - 20 = \frac{(10- 20)}{(80-20)}(x -20)[/tex]
y - 20 = -1/6(x - 20)
y = -x/6 + 20/6 + 20.
y = -x/6 + 200/6
y = -0.17x + 33.3
In this context, we can reasonably infer and logically deduce that a linear function that represent the line of best fit in slope-intercept form is y = -0.17x + 33.3.
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The velocity of a particle moving along a line is a function of time given by v(t)=90/t2+12t+35. Find the distance that the particle has traveled after t=8 seconds if it started at t=0 seconds.
The distance that the particle has traveled after t=8 seconds is 640 meters.
Distance covered by the particle in the first 8 seconds is given by
S(8) = ∫v(t)dt = ∫[90/t^2+12t+35]dt = [ -90/t + 6t^2 + 35t ] from 0 to 8S(8) = [-90/8 + 6(8^2) + 35(8)] - [-90/0 + 6(0^2) + 35(0)]S(8) = [360 + 280] - [-Infinity]S(8) = 640 meters.
Given that the velocity of a particle moving along a line is a function of time given by v(t)=[tex]90/t^2+12t+35.[/tex]
The time taken by the particle to travel 8 seconds is t = 8 seconds.
Initial velocity of the particle = v(0) = 90/(0^2) + 12*0 + 35 = 35m/sFinal velocity of the particle = v(8) = 90/(8^2) + 12*8 + 35 = 59.125 m/s
The distance covered by the particle in time t is given by the integral of the velocity of the particle between 0 to 8 seconds.
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Could somebody help me with this?
Answer:
y = 10/3x + 130/3
Step-by-step explanation:
To find where A is, we must find where C is. C is found when plugging in 0 in for y: 0 = -1/2 x + 5, so x = 10, and y = 0.
Now that we know the length of BC, we can find A.
Subtract 10 from the x value and add 5 to the y value of B to find A: (-10, 10).
Now, find the equation of the line between (-13, 0) and (-10, 10). Solve and get the equation of a line: y = 10/3x + 130/3
Hope this helps!
You are using a broker to purchase stock in company. The broker charges a set free of $7 per transaction. If the shares are worth $7.69/sh and you have $850 to invest,how many shares can you purchase?
A. 111 shares
B.108 shares
C.109 shares
D.110 shares
The answer is option C: 109 shares. If the broker charges a set free of $7 per transaction. If the shares are worth $7.69/sh and you have $850 to invest 109 shares can you purchase.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
To calculate the number of shares you can purchase, you need to subtract the broker's fee from the total amount you have to invest and then divide that by the share price:
$850 - $7 = $843 (the amount available to purchase shares)
$843 ÷ $7.69/share = 109.48
Since you cannot purchase a fraction of a share, you would be able to purchase 109 shares.
Therefore, the answer is option C: 109 shares.
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What is the value of x in √1+ 25/144 =1+ /12 ?
The solution to the equation √(1 + 25/144) = 1 + x/12 is x = 5/6. This was achieved by simplifying the left side of the equation and isolating x on one side.
To solve the equation √(1 + 25/144) = 1 + x/12, we start by simplifying the left side of the equation. The expression inside the square root can be simplified to (144 + 25)/144 = 169/144. Taking the square root of this fraction gives us √(169/144) = (13/12).
Next, we subtract 1 from both sides of the equation to isolate x on one side: (13/12) - 1 = x/12. This simplifies to 1/12 = x/12.
Finally, we multiply both sides by 12 to solve for x: x = (1/12)*12 = 5/6.
So the solution to the equation √(1 + 25/144) = 1 + x/12 is x = 5/6.
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Find a particular solution to the differential equation day dy 8 dt + 20y = 68 – 20t dt2 You do not need to find the general solution. y(t) = symbolic expression
The particular solution to the differential equation is given by: y(t) = y_ h(t) + y_ p(t) = c exp (-5/2 t) + t + 3Here, y_ h(t) is the homogeneous solution, which we don't need to find for this problem.
To solve the given differential equation, we'll need to use the method of undetermined coefficients. In this method, we assume that the particular solution to the differential equation has the same form as the forcing term. Here's how we can solve the given differential equation: Identify the forcing term and its derivatives. The forcing term is given by: f(t) = 68 - 20tWe can find its first derivative as follows: f'(t) = -20We can find its second derivative as follows: f''(t) = Guess the form of the particular solution We assume that the particular solution has the same form as the forcing term.
Since the forcing term is a first-degree polynomial, we assume that the particular solution also has the form of a first-degree polynomial: y_ p(t) = At + B Here, A and B are constants that we need to determine. Find the derivatives of the assumed form of the particular solution. Here are the first and second derivatives of the assumed form of the particular solution: y_ p(t) = At + B ==> y_ p'(t) = A ==> y_ p''(t) = 0. Substitute the assumed form of the particular solution and its derivatives into the differential equation Substituting y_ p(t), y_ p'(t), and y_ p''(t) into the differential equation, we get:8A + 20(At + B) = 68 - 20t Simplifying the above equation, we get: (8A + 20B) + (20A - 20)t = 68Comparing the coefficients of t and the constant terms on both sides,
we get two equations:8A + 20B = 68 (1)20A - 20 = 0 (2)Solving equation (2) for A, we get: A = 1 Substituting A = 1 into equation (1), we get:8 + 20B = 68Solving for B, we get: B = 3. Write the particular solution to the differential equation Substituting A = 1 and B = 3 into the assumed form of the particular solution, we get :y_ p(t) = t + 3Therefore, the particular solution to the differential equation is given by: y(t) = y_ h(t) + y_ p(t) = c exp (-5/2 t) + t + 3Here, y_ h(t) is the homogeneous solution, which we don't need to find for this problem.
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Find the unknown lengths of these isosceles right triangles. (Leave radicals in simplest radical form.) (ASAP!!!!) (it’s urgent!)
The required answers are 19) c = 8√2 units 20) a = b =a = [tex]\frac{\sqrt{10} }{14}[/tex].
What is Right angled triangle?A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangled triangle, is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular. The relation between the sides and other angles of the right triangle is the basis for trigonometry.
According to question:19) Using Pythagoras theorem
[tex]c^2=a^2+a^2[/tex]
[tex]c^2=\sqrt{a^2+a^2}[/tex]
[tex]c=\sqrt{8^2+8^2}[/tex]
c = 8√2 units
20) It is isosceles triangle,So a = b
Now
[tex]$Sin(45) =\frac{a}{\frac{\sqrt{5}}{7} }[/tex]
a = [tex]\frac{\sqrt{10} }{14}[/tex]
Thus, required answers are 19) c = 8√2 units 20) a = b =a = [tex]\frac{\sqrt{10} }{14}[/tex].
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A forest ranger sights a fire directly to the south. A second ranger, 9 miles east of the first ranger, also sights the fire
The bearing from the second ranger to the fire is S 28° W. How far is the first ranger from the fire?
please help guys, I need this done
Answer:
18+m=24, 6
Step-by-step explanation:
You will get the first part by understanding that 24 is the whole and 18 is the part. Part + the other part, m, is the whole. You will then solve this by isolating the variable m, and subtracting 18 on both sides of the equation. Since 24-18=6, that is the final answer.