Household Income and College Plans Exercise 3.93 introduces a survey of a representative sample of 920 US teens (ages 13 to 17). One of the questions asked ...

Answer:

i don't understand the question sorry

the coordinates of point c is (9/2, -3/2)

The original coordinate = C(6, -2)

scale factor r =3/4

New coordinate (c) = scale factor × the original coordinate

c = 3/4(6, -2)

c = (3/4×6, -2×3/4)

c = (18/4, -6/4)

c = (9/2, -3/2)

Hence, the coordinates of point c is (9/2, -3/2)

Answer:

1/5 = 20%

Step-by-step explanation:

We know

You have a spinner with 5 equal sections

What is the probability of landing on 2?

The number on each section will be: 1,2,3,4,5

There is only 1 way to land on 2, so the probability will be 1/5 = 20%

Answer: no solution

Step-by-step explanation:

\(8x^{2} +32=0\)

Factor out 8

\(8(x^{2} +4)=0\)

no solution

Why?

Think about the graph, \(x^{2}\) shifted up 4 has no zeros, even with a vertical stretch of 8.

The augmented matrix for the system of equations calculator that represents the given system of linear equations.

To write the augmented matrix for a system of linear equations, you need to identify the coefficients of the variables and the constants of each equation involved in the system. Augmented matrices are mathematical representations of systems of equations with variables. Each column of the matrix corresponds to a variable, while each row corresponds to an equation. The last column of the matrix is made up of the constant terms of the equations. The result is a matrix that contains all the information needed to solve the system of equations. The augmented matrix for a system of equations calculator is shown below.

The augmented matrix for the system of equations calculator is given as follows:

The augmented matrix for the system of equations calculator can be obtained by writing down the coefficients of the variables and the constants of each equation involved in the system as follows:

3x + 2y + 5z

= 4 4x - 3y + 2z

= 7 2x + 7y - 6z

= 8

Writing down the coefficients of the variables and the constants of each equation involved in the system in a matrix form, we get Augmented matrix = 3 2 5 | 4 4 -3 2 | 7 2 7 -6 | 8

The above is the augmented matrix for the system of equations calculator that represents the given system of linear equations.

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After the correction, the mean of the weights will now be 3.4 grams.

To find the new mean weight of the caterpillars after the correction, we need to first calculate the total weight of all 10 caterpillars before and after the correction.

Before the correction:
Mean weight = 3.3 grams
Total weight of all 10 caterpillars = 10 x 3.3 = 33 grams

After the correction:
Total weight of all 10 caterpillars = (33 - 2.5 + 3.5) = 34 grams

Therefore, the new mean weight of the caterpillars after the correction is:
New mean weight = Total weight of all 10 caterpillars / 10 = 34 / 10 = 3.4 grams

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Answer:

-17+4a=0

-17= -4a(-,-=+)

a=17/4

Answer:

i think it is 4a - 17 but i might be wrong or it is 3a - 17 try either one of those and if i am wrong i am sorry

Step-by-step explanation:

Answer:

The side lengths are 8 inches and 10 inches.

Step-by-step explanation:

Let l be the length and w be the width. w = l - 2.

We then have:

\(l(l - 2) = 80\)

\( {l}^{2} - 2l = 80\)

\( {l}^{2} - 2l - 80 = 0\)

\((l - 10)(l + 8) = 0\)

\(l = 10\)

\(w = l - 2 = 10 - 2 = 8\)

Answer:

3rd option

Step-by-step explanation:

the denominator cannot be zero as this would make the expression undefined.

equating the denominator to zero and solving gives the values that x cannot be.

x² - 7x - 18 = 0 ← in standard form

(x - 9)(x + 2) = 0 ← in factored form

equate each factor to zero and solve for x

x - 9 = 0 ⇒ x = 9

x + 2 = 0 ⇒ x = - 2

then

x = - 2, x = 9 ← are the excluded values

The investor should invest $5000 in AAA bonds, $2500 in B bonds, and the remaining $22500 in A bonds to have an interest income of $2000.

percentage, a relative value indicating hundredth parts of any quantity.

Let x be the amount invested in AAA bonds.

Since the investor wants to have twice as much in AAA bonds as in B bonds, the amount invested in B bonds is x/2.

The remaining amount invested in A bonds is 30000 - x - x/2 = 30000 - 3x/2.

The interest income from AAA bonds is 0.05x.

The interest income from A bonds is 0.06(30000 - 3x/2) = 1800 - 0.09x.

The interest income from B bonds is 0.1(x/2) = 0.05x.

The total interest income is the sum of the interest income from each type of bond, which is given to be $2000.

0.05x + 1800 - 0.09x + 0.05x = 2000

Simplifying and solving for x, we get:

-0.04x + 1800 = 2000

-0.04x = 200

x = 5000

Hence, the investor should invest $5000 in AAA bonds, $2500 in B bonds, and the remaining $22500 in A bonds to have an interest income of $2000.

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Answer:

5x-22<9<x

Step-by-step explanation:

5 times x = 5x

subtract 22 = 5x-22

less then = 5x-22<

9 more then x = 5x-22<9<x

a) The formula for the price elasticity of demand E is E = -5q/p.

b) The corresponding price elasticity of demand is -5

c) The resulting annual revenue would be approximately $2,050 billion.

(a) To obtain a formula for the price elasticity of demand E, we need to differentiate the equation for the demand q with respect to the selling price p and then multiply it by p/q:

E = (dp/dq) * (q/p)

Given that q = -5p + 3,070 million, we can differentiate it with respect to p:

dq/dp = -5

Plugging this value into the formula for E, we get:

E = (-5) * (q/p)

E = -5q/p

Therefore, the formula for the price elasticity of demand E is E = -5q/p.

(b) If the selling price was $335 per phone, we can substitute this value into the formula for E:

E = -5q/p

E = -5(335)/(335)

E = -5

The corresponding price elasticity of demand is -5.

Interpretation: The price elasticity of demand of -5 suggests that for every 1% increase in price, the demand decreases by about 5%. In other words, at the selling price of $335 per phone, a 1% increase in price would result in a 5% decrease in demand.

(c) To determine the selling price that would result in the largest annual revenue, we need to find the price where the price elasticity of demand is equal to -1. This is because at that point, a 1% increase in price would lead to a 1% decrease in demand, maximizing the revenue.

-5q/p = -1

Simplifying the equation, we get:

q/p = 1/5

Substituting the value of q from the demand equation:

(-5p + 3,070 million)/p = 1/5

Solving for p, we find:

p = 1,024 million

The selling price that would result in the largest annual revenue is $1,024 million.

To calculate the resulting annual revenue, we substitute this price back into the demand equation:

q = -5(1,024) + 3,070 million

q ≈ 2,050 million

Therefore, the resulting annual revenue would be approximately $2,050 billion.

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Answer:

Rs 1350 is the cost of 100 pens just multiply 100 and 13.5

Step-by-step explanation:

Answer:

Rs 1350

Step-by-step explanation:

Solution :

here ,

Cost of 1 pen = Rs 13.50

Cost of 100 pens = ?

Now ,

Cost of 100 pens = 13.50 × 100

= Rs 1350

Therefore , The cost of 100 pens is Rs 1350

Answer:

m = 1/8

Step-by-step explanation:

m = y-y/x-x

m = 5-7/-9-7

m = 1/8

Answer:

\( \huge{ \boxed{ \sf{ \frac{1}{4} }}}\)

Step-by-step explanation:

\( \star{ \sf{ \: Let \: the \: points \: be \: A \: and \: B}}\)

\( \star{ \sf{ \: A( - 9 \:, 5 \: ) \: \longrightarrow \: { \: (x1 \:, y1)}}}\)

\( \star{ \sf{ \: B( - 1 \:, 7 \: ) \: \longrightarrow{ ( \: x2 \:, y2)}}}\)

\( \text{ \underline{ Finding \: the \: slope}} : \)

\( \boxed{ \sf{Slope = \frac{y2 - y1}{x2 - x1} }}\)

\( \mapsto{ \sf{Slope = \frac{7 - 5}{ - 1 - ( - 9)}}} \)

\( \underline{ \text{Remember!}} : \sf{( - ) \times ( - ) = ( + )}\)

\( \mapsto{ \sf{Slope = \frac{7 - 5}{ -1 + 9}}} \)

\( \underline{ \text{Remember!}} : \)

\(\mapsto{ \sf{Slope = \frac{2}{8} }}\)

\( \mapsto{ \sf{Slope = \frac{1}{4} }}\)

Hope I helped!

Best regards! :D

~\( \text{TheAnimeGirl}\)

Answer:

P is the independent variable, where as S is dependent on P

Answer:

Volume = Area by height. V = A X h.

Step-by-step explanation:

i hope it helps

Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.

It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.

He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.

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Step-by-step explanation:

I guess option 4 is the correct answer.

{y,x} = {10,-5}

Step-by-step explanation:

sorry if this dont make sense

solve equation [2] for the variable y

y = 4x +30

plug this in for variable y in equation [1 ]

(4x+30) +3x= -5

solve [1] for the variable x

7x= - 35

x= - 5

by now we know this much

y= 4x+30

x= - 5

use the x value to solve for y

y=4 (-5) + 30 = 10

solution

{y,x} = {10,-5}

= 3×4+3×3-5×2/12

=12+9-10/12

=21-10/12

=11/12

Answer:

287

Step-by-step explanation:

Sum of A Finite Arithmetic Sequnece is

\( \frac{a _{1} + a _{n} }{2} n\)

Where a1 is first term

an is final term

N is the number of terms.

We know a1 is 1

An is 40 but we don't know n.

To find n, we use the definition of a Arithmetic Sequence

\(a _{n} = a + (n - 1)d\)

where d is the common difference. Let use the final term, 40 as a example.

Here the common difference is 3 so we have

\(40= 1 + (n - 1)3\)

\(39 = 3(n - 1)\)

\(13 = n - 1\)

\(14 = n\)

So we have 14 terms in this finite series.

Now we compute

\( \frac{1 + 40 }{2}(14) = \frac{41}{2} (14) = 41 \times 7 = 287\)

So the answer is 287

The slope intercept form of the line that includes the point (8, 1)

and has a slope of \(\frac{1}{8}\) is \(y = \frac{1}{8}x\)

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  \(\theta\) is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m =  \(tan\theta\)

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Slope = \(\frac{1}{8}\)

The line passes through (8, 1)

Required equation of line

\(y - 1 = \frac{1}{8}(x - 8)\\y - 1 = \frac{1}{8}x -1\\y = \frac{1}{8}x\)

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To calculate the 90% confidence interval for the given random sample of 5 observations, we need to find the sample mean and sample standard deviation.

The sample mean (X bar) can be calculated by summing up all the observations and dividing by the sample size (n):

X (bar) = (15 + 10 + 16 + 19 + 14) / 5 = 14.8

Next, we need to calculate the sample standard deviation (s). The formula for the sample standard deviation is as follows:

s = sqrt(Σ(xi - x(bar))² / (n - 1))

Using the formula, we calculate the sample standard deviation:

s = sqrt(((15 - 14.8)² + (10 - 14.8)² + (16 - 14.8)² + (19 - 14.8)² + (14 - 14.8)²) / (5 - 1))

 = sqrt((0.16 + 18.24 + 0.16 + 17.64 + 0.16) / 4)

 = sqrt(36.4 / 4)

 = sqrt(9.1)

 ≈ 3.02

Now, we can calculate the margin of error (E) using the formula:

E = t * (s / sqrt(n))

Since the sample size is small (n = 5) and the confidence level is 90%, we need to use the t-distribution. The degrees of freedom (df) for a sample size of 5 and 90% confidence level is 4. From the t-distribution table, the corresponding t-value is approximately 2.776. Plugging in the values:

E = 2.776 * (3.02 / sqrt(5))

 ≈ 3.26

Finally, we can construct the confidence interval by subtracting and adding the margin of error to the sample mean:

Confidence interval = (x(bar) - E, x(bar) + E)

                  = (14.8 - 3.26, 14.8 + 3.26)

                  ≈ (11.54, 18.06)

Therefore, the 90% confidence interval for the given random sample is approximately (11.54, 18.06).

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Central tendency, is the term that relates to the way data tend to cluster around some middle or central value.

Measures of central tendency are summary statistics that represent the center point or typical value of a dataset. Examples of these measures include the mean, median, and mode. These statistics indicate where most values in a distribution. Mode in statistics is the number of times a number is repeated. The number which is repeated maximum times in a series of data is known as the modular number. The mode is used to compare data that has extreme figures. Central tendency simply means most scores in a normally distributed set of data tend to cluster near the center of a distribution.

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Answer:

Step-by-step explanation:

Rewrite this function as g(x) = 3(x + 1)(x - 2)

Set each factor equal to zero in turn, solving for x each time:

x + 1 => x = -1  (the lesser zero)

x - 2  =>  x = 2  (the greater zero)

Answer:

lesser x =-1

greater x =2

Step-by-step explanation:

khan verified

Answer:

B

Step-by-step explanation:

\(-2<x+3<2 \implies -5<x<-1\)

Answer:

55 because it will make a equal 100 percent

Step-by-step explanation:

There were 352 students who took the bus.

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.

Given that, There were a total of 640 students at a school on Friday every student either walked or took the bus and 45% of the total number of students walked to school

Since, 45% of them walked to the school,

Therefore, percentage of the students took the bus =

100%-45% = 55%

Now, finding the number of students took the bus,

55% of 640 = 640×55/100 = 352

Hence, There were 352 students who took the bus.

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Answer:

Step-by-step explanation:

Given is 30 x 60 x 90 right triangle

The side ratios of this triangle is

Find the value of x and y using this ratio

Let's find

And

Answer:

length= 8 width = 4

Step-by-step explanation:

24-8=16

16/2=8

8+8+4+4=16+8=24

Answer:BC AND AD is parellogram since it has sides.

Step-by-step explanation: