x,y,z=(smaller z-value)=(-56/3, -32/3, 16/3)
x,y,z=(larger z-value)=(56/3, 32/3, -16/3)
These are the points on the cone that are closest to the point (14, 8, 0).
What is a point?In a two-dimensional space, a point is defined by two coordinates, typically denoted by (x, y), where x represents the horizontal position, and y represents the vertical position. In a three-dimensional space, a point is defined by three coordinates, typically denoted by (x, y, z), where x, y, and z represent the horizontal, vertical, and depth positions, respectively.
According to question:We want to minimize the distance between the point (14, 8, 0) and the surface of the cone defined by the equation z² = x² + y², subject to the constraint that we stay on the surface of the cone.
Let f(x,y,z) = (x-14)² + (y-8)² + z² be the function we want to minimize subject to the constraint g(x,y,z) = z² - x² - y² = 0.
The Lagrange multiplier method involves finding the critical points of the function L(x,y,z,λ) = f(x,y,z) - λg(x,y,z), where λ is the Lagrange multiplier.
So we have:
L(x,y,z,λ) = (x-14)² + (y-8)² + z² - λ(z² - x² - y²)
Taking the partial derivatives with respect to x, y, z, and λ, and setting them equal to zero, we get the following system of equations:
2(x-14) + 2λx = 0
2(y-8) + 2λy = 0
2z - 2λz = 0
z² - x² - y² = 0
The third equation simplifies to z(1-λ) = 0, which gives us two possibilities:
Case 1: z = 0
In this case, the fourth equation becomes -x² - y² = 0, which implies that x = y = 0. But this point does not lie on the surface of the cone, so it is not a valid critical point.
Case 2: λ = 1
In this case, the first two equations become x-14 = -xλ and y-8 = -yλ, which imply that x = -7λ and y = -4λ. Substituting into the fourth equation gives:
z² = x² + y² = 65λ²
To minimize the distance between the point (14, 8, 0) and the surface of the cone, we want to find the value of λ that minimizes the function f(x,y,z) subject to the constraint g(x,y,z) = 0. Substituting x = -7λ, y = -4λ, and z = √(65λ²) into f(x,y,z), we get:
f(λ) = (7λ-14)² + (4λ-8)² + 65λ²
To minimize this function, we take its derivative with respect to λ and set it equal to zero:
f'(λ) = 30λ - 80 = 0
Solving for λ, we get λ = 8/3. Substituting this back into x = -7λ, y = -4λ, and z = √(65λ²), we get:
x,y,z=(smaller z-value)=(-56/3, -32/3, 16/3)
x,y,z=(larger z-value)=(56/3, 32/3, -16/3)
These are the points on the cone that are closest to the point (14, 8, 0).
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Jessica kicks a football. Its height in feet is given by h(t) = -16t^2+80t where h is the height and t is the time, in seconds, after the football is kicked. Graph the equation from t=0 to t=5 seconds. Be sure to include the vertex in your graph and table.
State the coordinates of the vertex and explain its meaning in the context of the problem.
The point is where the vertex is situated [tex](2.5, 100)[/tex].
What in math is a vertex?A vertex, which is a unique point on a mathematical object, is often where 2 or more lines or edges come together. The shapes that include vertices most frequently are graphs, polygons, polyhedra, and angles. Vertices in a graph are sometimes called nodes.
Vertex and parabola definitions.A parabola's vertex is the location where its symmetry line and parabola intersect. The vertices of a parabola which equation is provided in standard form will be the lowest (lowest point) and highest (highest point) points on the graph, respectively.
To graph the equation [tex]h(t) = -16t^2 + 80t[/tex] from [tex]t=0[/tex] to [tex]t=5[/tex] seconds, we can create a table of values by plugging in values of t and calculating the corresponding values of [tex]h(t)[/tex]:
t h(t)
0 0
1 64
2 128
3 144
4 128
5 80
To find the vertex, we can use the formula [tex]t = -b/(2a)[/tex], where [tex]a = -16[/tex] and [tex]b = 80[/tex].
[tex]t = -b/(2a) = -80/(2(-16)) = 2.5[/tex]
So the vertex occurs at [tex]t = 2.5[/tex] seconds.
Now we can plot the points from the table and graph the equation,
Graph of [tex]h(t)=-16t^2+80t[/tex] from [tex]t=0[/tex] to [tex]t=5[/tex] seconds
The vertex is located at the point [tex](2.5, 100)[/tex].
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By selling a camera for Rs 60,000 there is a loss 20%. At what price should it be sold to get 12% profit? Find it.
Answer:
Rs 84000----------------------------------
Let the cost price of the camera be x.
When the selling price is 60000 there is a loss of 20%. Let's show this as equation and find the cost price:
x - 20% of x = 60000x - 0.2x = 600000.8x = 60000x = 60000/0.8x = 75000The cost price is Rs 75000, and we need a profit of 12%, it gives us the selling price of:
75000 + 12% = 75000 + 0.12*75000 = 75000 + 9000 = 84000Solve for a. Round to the nearest tenth of a degree, if necessary..
Answer: x=
२०
83
92
M
L
Submit Answer
attempt 1 out of 2
The value of angle x rounded to the nearest tenth of a degree is 53.6°.
How can trigonometric ratios be used to find the angle in a right triangle?
Trigonometric ratios are used to relate the sides of a right triangle to its angles. In a right triangle, one of the angles is always 90 degrees, which is the right angle. The three primary trigonometric ratios are sine, cosine, and tangent, which are defined as follows:
Sine (sin): The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.
Cosine (cos): The cosine of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
Tangent (tan): The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
To find the value of an angle in a right triangle, we can use the inverse trigonometric functions, also known as arc functions or anti trigonometric functions. These functions are denoted as [tex]sin^{-1}[/tex], [tex]cos^{-1}[/tex] , and [tex]tan^{-1}[/tex] , and they are used to find the angle whose trigonometric ratio is known.
Finding the value of x :
We can use the trigonometric ratio of sine to solve for x.
sin(x) = opposite/hypotenuse = MN/LN
[tex]sin(x) = 83/92[/tex]
Taking the inverse sine of both sides:
[tex]x = sin^{-1}(83/92)[/tex]
Using a calculator, we get:
[tex]x \approx 53.6^{o}[/tex]
Therefore, the value of x rounded to the nearest tenth of a degree is 53.6°.
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At cheap more super market,1 litre of fruit juice costs R25 and 1,5 litres cost R34 Which juice is cheaper. Show your calculation
The 1.5 liters of fruit juice is cheaper per liter compared to the 1 liter of fruit juice.
For the 1 liter of fruit juice, the cost per liter is R25/1 liter = R25/liter.
For the 1.5 liters of fruit juice, the cost per liter is R34/1.5 liters = R22.67/liter.
A supermarket is a large retail store that offers a wide range of food and household items to consumers. These stores are typically designed to be a one-stop shop for customers, allowing them to purchase everything they need in one convenient location. One of the primary advantages of shopping at a supermarket is the ability to choose from a wide variety of products at competitive prices.
Supermarkets usually have multiple departments, including a fresh produce section, a meat and seafood section, a bakery, and a deli. In addition to food items, supermarkets also offer a variety of household goods, such as cleaning supplies, personal care products, and pet food. Many supermarkets also offer loyalty programs, coupons, and other incentives to help customers save money.
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Hi. Please help me convert this non-linear to linear form y=mx+c. The answer is square root of y= 6/p x - 2/q .
Thank you so much.
Answer: To convert the given equation, √y = (6/p)x - (2/q), into the linear form y = mx + c, we can use the following steps:
Square both sides of the equation to eliminate the square root:
√y = (6/p)x - (2/q)
√y^2 = (6/p)x - (2/q)^2
Simplifying the right-hand side, we get:
y = (36/p^2)x - (4/q) + 4/q^2
Rearrange the equation to the form y = mx + c:
y = (36/p^2)x + (4/q^2 - 4/q)
So the linear form of the given non-linear equation is y = (36/p^2)x + (4/q^2 - 4/q).
Step-by-step explanation:
A young boy is growing at a rate of 3.5 centimeters per month. He is currently 90 cm tall. At that rate,
how many months will it take him to grow to a height of 132 cm?
Write an equation to represent this situation. Then, use algebra to solve. Show all steps.
Answer:
H = 3.5m + 90
m = 12 months
Step-by-step explanation:
We can use a linear equation (H = 3.5m + 90), where H is the height in centimeters and m is month.
We can let H = 132 to solve for m:
[tex]132=3.5m+90\\42=3.5m\\12=m[/tex]
Thus, it will take the boy 12 months to reach 132 cm.
Describe the shape of the dot plot. Are the dots evenly distributed or grouped on one
side?
The dot plot has a bell shape. The dots are more heavily clustered around the central point, with fewer dots on the ends.
What is heavily clustered?Heavily clustered refers to a situation when a large number of items, such as data points, are grouped together in a dense area. This can be seen in many forms of data visualisation, such as scatterplots, where items are represented in a graph and appear close together in a particular area. In some cases, the items can be so densely packed that they appear to form a single unit. Heavily clustered data can be used to identify areas of high concentration, or to identify trends or correlations.
This indicates that the data is normally distributed and that there is a higher probability of the data points falling around the central point. The dots are not evenly distributed, but rather grouped on one side.
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Determine whether the following subsets are subspaces of the given vector spaces or not.text Is end text W subscript 2 equals open curly brackets space p equals a subscript 2 t squared plus a subscript 1 t plus a subscript 0 space element of space straight double-struck capital p subscript 2 space left enclose space a subscript 0 equals 2 space end enclose close curly brackets space space text a subspace of the vector space end text space straight double-struck capital p subscript 2 ?(Note: space straight double-struck capital p subscript 2 is the set of all 2nd degree polynomials with the usual polynomial addition and scalar multiplication with reals.)Answer 1text Is end text W subscript 1 equals open curly brackets open square brackets table row a b c row d 0 0 end table close square brackets space element of space M subscript 2 x 3 space end subscript space left enclose space b equals a plus c space end enclose close curly brackets space text a subspace of the vector space end text space space M subscript 2 x 3 space end subscript?(Note: space M subscript 2 x 3 space end subscript is the set of all 2x3 matrices with the standart matrix addition and scalar multiplication with reals.)
Yes, W_2 = {p_2 = a_2t_2 + a_1t + a_0 ∈ ℙ_2 | a_0 = 2} is a subspace of the vector space ℙ_2.
Yes, W_1 = {[a b c; d 0 0] ∈ M_{2x3} | b = a + c} is a subspace of the vector space M_{2x3}.
Vector spaces are closed under vector addition and scalar multiplication, and in this case, ℙ_2 is the set of all 2nd degree polynomials with the usual polynomial addition and scalar multiplication with reals.
Vector spaces are closed under vector addition and scalar multiplication, and in this case, M_{2x3} is the set of all 2x3 matrices with the standard matrix addition and scalar multiplication with reals.
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in an examination, 90 % of the students passed out of 600 students. how many candidates passed the exam?
Answer:
Step-by-step explanation:
[tex]90 \% \text{ of }600=\frac{90}{100}\times600[/tex]
[tex]=90 \times 6[/tex]
[tex]=540[/tex]
So 540 students passed the exam.
When solving the equation 3(x-2)=-12, what is a possible first step?
A) Distributing the 3 into each term of the parenthesis.
B) She could either divide by 3 or distribute 3 into the parenthesis
C) Adding 2 to each side of the equation
D) Subtracting 2 on each side of the equation
E) Dividing each side of the equation by 3
F) none of the answer choices tell what the first step could be.
Rina is climbing a mountain. She has not
yet reached base camp. Write an inequality
to show the remaining distance, d, in feet
she must climb to reach the peak.
The distance she must climb to reach the peak is greater than 2,663 feet. An inequality to show the remaining distance, d, in feet she must climb to reach the peak is d > 2,663.
Inequlity represents a relationship between two values that is not equal. That is inequlity means no equal and the symbols which used for not equal is ≠ and for comparison are < , > , ≤ , ≥. For example, ax > b etc. We have, Rina is climbing a mountain and mountain height present in above figure. See the figure carefully, the main two points in figure are the following: height of mountain peak
= 12,358 feet
height of base camp = 9,695 feet
we have to write an inequality for the remaining distance, d, in feet. Also, it is specified that she has not reached base camp yet. So, his climbed distance is less than 9,695 feet. Let the remaining distance be 'd feet '. From the above figures, d + base camp height > 12,358
Substract 9695 from both sides
=> d > 12,358 - 9,695
=> d > 2,663
Hence, required inequalty is d > 2,663.
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Complete question:
Rina is climbing a mountain. She has not yet reached base camp. Write an inequality to show the remaining distance, d, in feet she must climb to reach the peak. See tha above figure.
a cyclist rides her bike at a speed of 21 kilometers per hour. what is this speed in kilometers per minute? how many kilometers will the cyclist travel in 2 minutes? (do not round the answer)
Answer:
see the answer and explanation in the attached figure below
Step-by-step explanation:
Determine the horizontal component of reaction at A Express your answer in pounds to three significant figures. Enter positive value if the force is exerted in the positive direction and negative value of the force is exerted in the negative direction.
We have that, finding the horizontal component of the reaction at A in pounds, it is 866.03 pounds, with zero horizontal component in the negative direction.
How to determine the horizontal component?To determine the horizontal component of the reaction at A, we first need to draw a free-body diagram of the given structure. So, we can use the equation of equilibrium for the horizontal direction to find the horizontal component of the reaction at A. The equation of equilibrium for the horizontal direction is as follows:
∑Fx=0∑Fx=0
Equilibrium equation for the horizontal direction, where ∑Fx is the sum of all forces acting horizontally in the positive direction and in the negative direction. Let's draw the free body diagram of the given structure: Here, RAY is the horizontal component of the reaction at A. We can see that there is no force acting horizontally in the negative direction.
Therefore,∑Fx=RAx∑Fx=RAx
Now, we need to find the force that acts horizontally in the positive direction. In the free body diagram, we can see that:
∑Fx=1000cos30°=866.03∑Fx=1000cos30°=866.03
Therefore
∑Fx=RAx=866.03RAx=866.03
So the horizontal component of the reaction at A is 866.03 pounds. Therefore, the answer is 866.03 (positive).
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Suppose the point (3, 6) is on the graph of y = f(x) What point does it transform to y = - f * (x) - 3 ?
The cat population in catonsville has been recorded since 2010. The population. p. can be represented by the equation p = 1600(2)t where is time in years since the begging of 2010. What was that cat population 2007
A. 4000
B. 200
C. 800
D. 100
The cat population in Catonsville in 2007 was 200. The answer is option B.
What is population?Population refers to the total number of people, animals, or objects in a particular group or area. It is the entire group or collection of individuals, things, or events that we are interested in studying or describing.
According to question:We can use the given equation to find the cat population at any given time in years since the beginning of 2010. However, to find the population in 2007, we need to make a conversion from years since the beginning of 2010 to years since the beginning of 2007.
From the beginning of 2007 to the beginning of 2010, there are 3 years, so if we subtract 3 from the number of years since the beginning of 2010, we will get the number of years since the beginning of 2007. Therefore, we need to substitute t = -3 into the given equation and solve for p:
[tex]p = 1600(2)^t\\p = 1600(2)^(-3)\\p = 1600(1/8)\\p = 200[/tex]
Therefore, the cat population in Catonsville in 2007 was 200. The answer is option B.
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A group of 500 middle school students were randomly selected and asked about their preferred television genre. A circle graph was created from the data collected.
a circle graph titled preferred television genre, with five sections labeled drama 14 percent, sports 22 percent, documentaries, reality 20 percent, and sci-fi 20 percent
How many middle school students prefer the Documentaries television genre?
24
76
120
86.4
80 middle school students prefer the documentaries television genre.
None of the given options match exactly, but the closest one is 76.
What is circle graph?A circle graph, also known as a pie chart, is a type of chart that displays data as a circular diagram, divided into slices to represent proportions of a whole. Each slice of the circle represents a percentage of the total data being represented, and the entire circle represents 100% of the data.
According to question:Based on the circle graph, the percentage of students who prefer documentaries is 16% (as the percentage for documentaries is missing from the given options, we need to calculate it).
To find out the actual number of students who prefer documentaries, we need to multiply this percentage by the total number of students in the sample:
16% of 500 = (16/100) x 500 = 80
Therefore, 80 middle school students prefer the documentaries television genre.
None of the given options match exactly, but the closest one is 76.
Circle graphs are commonly used to show proportions or percentages of different categories within a dataset. They are useful for displaying data in a way that is easy to understand, and they are often used in business and finance, as well as in education and research.
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Simplify.
Remove all perfect squares from inside the square root. Assume x is positive.
20x8 =
The simplified form of the given expression as required to be determined in the task content is; 2x⁴√5.
What is the simplified form of the given expression?It follows from the task content that the Simon form of the given expression √20x⁸ is required to be determined from the task content.
On this note, since the given expression is; √20x⁸.
We have that; = √ (4 × 5 × x⁸)
Therefore, since 4 and x⁸ are perfect squares; it follows that we have;
= 2x⁴ √5.
Ultimately, the simplified form of the given expression as required to be determined is; 2x⁴ √5.
Complete question; The correct expression is; √20x⁸.
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Marie had 10 ½ feet of ribbon to make bows. Each bow required ¾ foot of ribbon. She used the following steps to find the number of bows she could make with the ribbon.
Step 1: 10 ½ ÷ ¾
Step 2: 21/2 ÷ ¾
Step 3: ??????
Step 4: 84/6
Step 5: 14
Which expression best represents the expression Marie should have used in Step 3?
*
A 2/21 ÷ 4/3
B 2/21 ÷ ¾
C 21/2 × 4/3
D 21/2 × ¾
Therefore, the expression Marie should have used in Step 3 is option B: 2/21 ÷ ¾, which represents the division of the fraction 21/2 by 3/4.
What do you mean by fraction?A fraction is a way of expressing a quantity that represents a part of a whole or a ratio between two quantities. It is usually written as one number (the numerator) over another number (the denominator), separated by a horizontal line or slash. For example, the fraction 2/3 represents two parts out of three equal parts of a whole, or a ratio of two to three. Fractions can be expressed in various forms, such as proper fractions (where the numerator is smaller than the denominator), improper fractions (where the numerator is greater than or equal to the denominator), and mixed numbers (where a whole number and a proper fraction are combined). Fractions are an important concept in many areas of mathematics, including arithmetic, algebra, geometry and calculus.
by the question.
To solve this, Marie can use the following steps:
Step 1: 10 ½ ÷ ¾
Step 2: 21/2 ÷ ¾
Step 3: (21/2 ÷ 3/4) (finding the quotient of two fractions)
Step 4: (21/2) × (4/3) (dividing by a fraction is the same as multiplying by its reciprocal)
Step 5: 14
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Solve the inequalities 1/3x-1/4(x+2)>3x-4/3
Answer: x < -46/17
Step-by-step explanation:
To solve the inequality:
1/3x - 1/4(x + 2) > 3x - 4/3
First, we simplify the left-hand side by finding a common denominator:
4(1/3x) - 3/4(x + 2) > 3x - 4/3
4/3x - 3/4x - 9/2 > 3x - 4/3
Next, we simplify the equation:
7/12x - 9/2 > 3x - 4/3
To isolate the variable x on one side of the inequality, we will move all the x terms to the left-hand side and all the constants to the right-hand side:
7/12x - 3x > 9/2 - 4/3
-17/12x > 23/6
Finally, we can solve for x by dividing both sides by -17/12, remembering to reverse the inequality because we are dividing by a negative number:
x < (23/6) ÷ (-17/12)
x < -46/17
Therefore, the solution to the inequality is:
x < -46/17
A bus arrives every 10 minutes at a bus stop. It is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution.
a) What is the probability that the individual waits more than 7 minutes?
b) What is the probability that the individual waits between 2 and 7 minutes?A continuous random variable X distributed uniformly over the interval (a,b) has the following probability density function (PDF):fX(x)=1/0.The cumulative distribution function (CDF) of X is given by:FX(x)=P(X≤x)=00.
In the following question, among the various parts to solve- a) the probability that the individual waits more than 7 minutes is 0.3. b)the probability that the individual waits between 2 and 7 minutes is 0.5.
a) The probability that an individual will wait more than 7 minutes can be found as follows:
Given that the waiting time of an individual is a continuous uniform distribution and that a bus arrives at the bus stop every 10 minutes.Since the waiting time is a continuous uniform distribution, the probability density function (PDF) can be given as:fX(x) = 1/(b-a)where a = 0 and b = 10.
Hence the PDF of the waiting time can be given as:fX(x) = 1/10The probability that an individual waits more than 7 minutes can be obtained using the complementary probability. This is given by:P(X > 7) = 1 - P(X ≤ 7)The probability that X ≤ 7 can be obtained using the cumulative distribution function (CDF), which is given as:FX(x) = P(X ≤ x) = ∫fX(t) dtwhere x ∈ [a,b].In this case, the CDF of the waiting time is given as:FX(x) = ∫0x fX(t) dt= ∫07 1/10 dt + ∫710 1/10 dt= [t/10]7 + [t/10]10= 7/10Using this, the probability that an individual waits more than 7 minutes is:P(X > 7) = 1 - P(X ≤ 7)= 1 - 7/10= 3/10= 0.3So, the probability that the individual waits more than 7 minutes is 0.3.
b) The probability that the individual waits between 2 and 7 minutes can be calculated as follows:P(2 < X < 7) = P(X < 7) - P(X < 2)Since the waiting time is a continuous uniform distribution, the PDF can be given as:fX(x) = 1/10Using the CDF of X, we can obtain:P(X < 7) = FX(7) = (7 - 0)/10 = 0.7P(X < 2) = FX(2) = (2 - 0)/10 = 0.2Therefore, P(2 < X < 7) = 0.7 - 0.2 = 0.5So, the probability that the individual waits between 2 and 7 minutes is 0.5.
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Zach bought 200 shares of Goshen stock years ago for $21. 35 per share. He sold all 200 shares today for $43 per share. What was his gross capital gain?
B. $ 8,600
C. $ 4,000
A. $4,270
D. $4,330
The gross capital gain is option (D) $4330
Gross capital gain is the total amount of profit that an investor makes when they sell an asset, such as stocks, real estate, or other investments, for a higher price than the purchase price.
Zach's gross capital gain is the difference between the selling price and the purchase price of the shares.
Purchase price of 200 shares = 200 x $21.35 = $4,270
Selling price of 200 shares = 200 x $43 = $8,600
Therefore, the gross capital gain is
= $8,600 - $4,270
Subtract the numbers
= $4,330
Therefore, the correct option is (D) $4,330.
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The accurate scale diagram shows a telephone mast and a box.
Find an estimate for the real height, in metres, of the telephone mast.
telephone mast
5.5
+2.5 m
box
+
Total marks: 2
Using proportions, the real height of the telephone mast is estimated to be 9 meters.
What exactly is a proportion?A proportion is a fraction of a total amount, and equations are constructed using these fractions and estimates to find the desired measures in the problem using basic arithmetic operations like multiplication and division. Because the telephone box and the mast are similar figures in this problem, their side lengths are proportional.
The following proportional relationship is established as a result:
x / 1.5 cm = 10.8 cm / 1.8 cm.
The relationship's left side can be simplified as follows:
6 = x / 1.5 cm.
The estimate is then calculated using cross multiplication, as shown below:
6 x 1.5 cm = 9.5 cm².
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the primary purpose of statistical analysis is to: group of answer choices transform information into data.
The primary purpose of statistical analysis is to transform information into data. Therefore, the correct option is a)transform information into data.
What is statistical analysis?Statistical analysis is the method of using statistical techniques to collect and analyze data, evaluate its reliability and determine its statistical significance. The following are the primary purposes of statistical analysis:Provide summaries and descriptions of data: One of the most important applications of statistical analysis is to present data in a clear and concise manner. Summarizing the data can assist people in making sense of the data and drawing inferences from it.
For example, data can be summarized using graphs, charts, or tables. Identify patterns and relationships: The goal of statistical analysis is to identify any patterns or relationships that exist within the data. For example, statistical analysis can be used to determine if a product's sales are correlated with a specific time of year.
Test hypotheses and draw conclusions: Statistical analysis is used to test hypotheses and draw conclusions about a population or phenomenon. This is accomplished by using statistical techniques to determine whether or not the data supports a particular hypothesis. Statistical analysis can also be used to determine the probability of an event occurring in the future.
The primary purpose of statistical analysis is to transform information into data. Therefore, the correct option is a)transform information into data.
The complete question is as follows:
The primary purpose of statistical analysis is to:
a)transform information into data.
b)select samples and make inferences about populations
c)convert data into useful desicion-making information
d)perform statistical computations
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Solve the following system of equations using the method of substitution: 3x+2x=11 y=x+3
The solution to the system of equations 3x+2x=11 , y=x+3 is (x, y) = (1, 4) using the method of substitution.
To solve the system of equations using the method of substitution, we first need to solve for one variable in terms of the other in one of the equations. In this case, we can solve for y in terms of x in the second equation:
y = x + 3
We can then substitute this expression for y in the first equation:
3x + 2(x + 3) = 11
Simplifying the equation by distributing the 2:
3x + 2x + 6 = 11
Combining like terms:
5x + 6 = 11
Subtracting 6 from both sides:
5x = 5
Dividing both sides by 5:
x = 1
Now that we know the value of x, we can substitute it back into the second equation to find the value of y:
y = x + 3 = 1 + 3 = 4
In conclusion, the method of substitution involves solving one equation for one variable and substituting the resulting expression into the other equation.
By doing this, we can eliminate one variable and solve for the other. In this case, we solved for y in terms of x, substituted this expression for y in the first equation, and solved for x. Then, we substituted the value of x back into the second equation to solve for y.
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Find the distance between the two points rounding to the nearest tenth (if necessary).
(5,-8) and (-3, -1)
Answer:
5-8=-3
Step-by-step explanation:
-3-1=-4
please help solve: 8x=64
Answer:
X=8
Bcuz 8x=64
64÷8=8
So that the answer is 8
Answer:
[tex]\bf x=8[/tex]
Step-by-step explanation:
[tex]\bf 8x=64[/tex]
Divide both sides by 8:
[tex]\bf \cfrac{8x}{8}=\cfrac{64}{8}[/tex]
Simplify:-
[tex]\bf x=8[/tex]
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Hope this helps!
Using a minimum of three points, create two linear functions. Prove the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.
As we have proved that the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.
Let's start by defining what a linear function is. A linear function is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope represents the rate of change of the line, and the y-intercept represents the value of y when x is equal to zero. To create a linear function, we need two points on the line.
Now, let's create another linear function using points B and C:
slope (m) = (y₂ - y₁) / (x₂ - x₁) = (6 - 4) / (5 - 3) = 1
y-intercept (b) = y - mx = 4 - 1 * 3 = 1
Therefore, the linear function that passes through points B and C is also y = x + 1. We can check if point A lies on this line by substituting its x and y values into the equation:
2 = 1 + 1
This is true, so point A lies on the line created by points B and C. Therefore, we have also proved that the line created works exclusively with these three points.
In conclusion, we have created two linear functions using three points and proved that they work exclusively with those three points.
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The body of a cent in caterpillar is made up of five spherical parts, 3 of which are yellow and 2 are green. What is the greatest possible number of different types of this caterpillar that could exist?
The greatest possible number of different types of this caterpillar that could exist is 120.
What is the greatest possible number of the caterpillar?
If we assume that the order of the parts does not matter and that all caterpillars with the same color arrangement are considered identical, we can use combinations to find the number of different types of caterpillars that could exist.
First, we need to choose 2 out of the 5 parts to be green, which can be done in 5 choose 2 ways:
5 choose 2 = (5!)/(2!(5-2)!) = 10
For each green-yellow arrangement there are;
3! ways to permute the yellow parts and
2! ways to permute the green parts.
Therefore, the total number of different types of caterpillars is:
10 × 3! × 2! = 10 × 6 × 2 = 120
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I need help on 10 and 11
Answer:
x = +8
x = -8
That's the thing that I only know. Im a seventh grader(turned 13) so I wouldn't know this fully. Ask someone else to get it fully.
Step-by-step explanation:
5x + 6x - 10 + 12 = 90
11x = -88
x = -8
or
x = 8
the height of a diver above the water, is given by , where is time measured in seconds and is measured in meters. select all statements that are true about the situation. a. the diver begins 5 meters above the water. b. the diver begins 3 meters above the water. c. the function has 1 zero that makes sense in this situation. d. the function has 2 zeros that make sense in this situation. e. the graph that represents starts at the origin and curves upward. f. the diver begins at the same height as the water level.
Statement (b) and (c) are true about the situation.
Define the term measurement ?Using standardized instruments or units, measurements are the process of figuring out the size, quantity, or degree of anything.
Using the given function, h(t) = -5t^2 + 10t + 3, we can determine the true statements about the situation:
a. False: The diver begins at h(0) = 3 meters above the water, not 5 meters.
b. True: The diver begins at h(0) = 3 meters above the water.
c. True: The function has one zero that makes sense.
To find it, we set h(t) = 0 and solve for t: -5t² + 10t + 3 = 0
Using the quadratic formula, we find that: t ≈ 2.161
This means that the diver reaches a height of zero after 2.161 seconds.
d. False: As we found in part (c), the function has only one zero.
e. False: The graph of the function does not start at the origin.
f. False: The diver begins at 3 meters above the water, not at the same height as the water level.
Therefore, statement (b) and (c) are true about the situation.
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