Refer to figure 6-5 A government imposed price of $12 in this market is an example of a

The two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

To solve the system of equations, let's assign variables to the two integers. Let the first integer be represented by 'x' and the second integer by 'y'.

According to the given information:

a. Fourteen more than twice the first integer gives the second integer:

This can be expressed as: 2x + 14 = y

b. The second integer increased by one is the square of the first integer:

This can be expressed as: y + 1 = x^2

Now, we have a system of equations:

1) 2x + 14 = y

2) y + 1 = x^2

To solve this system, we can substitute the value of 'y' from equation 1) into equation 2):

2x + 14 + 1 = x^2

2x + 15 = x^2

Rearranging the equation, we have:

\(x^2 - 2x - 15 = 0\)

Factoring the quadratic equation, we get:

(x - 5)(x + 3) = 0

Setting each factor equal to zero:

x - 5 = 0   -->   x = 5

x + 3 = 0   -->   x = -3

Substituting the values of 'x' back into equation 1), we can find the corresponding values of 'y':

For x = 5:

2(5) + 14 = y

10 + 14 = y

y = 24

For x = -3:

2(-3) + 14 = y

-6 + 14 = y

y = 8

Therefore, the two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

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Answer:

Since the calculated value of z= 1.869 does not fall in the critical region we accept the null hypothesis H0: p1≠ p2  the data provides evidence that the proportion of high school students in metropolitan areas who have internet access during school hours is different than the proportion of rural high school students who have internet access during school hours.

Step-by-step explanation:

Let p1= proportion of the high school students having internet access

p2= proportion of the rural school students having internet access

1) The null and alternate hypothesis are

H0: p1≠ p2  against the claim   Ha: p1= p2

2) We choose significance level ∝ =0.05

3) The test statistic under H0 is

z= p1^- p2^/√ p^q^( 1/n1 + 1/n2)

Now

p1^= 768/850= 0.9035

p2^= 308/355= 0.8670

p^= 768+ 308/850+ 355= 1076/1205

p^= 0.8929

q^= 1-p^= 0.1070

Putting the values

z= p1^- p2^/ √p^q^( 1/n1 + 1/n2)

Z= 0.9035-0.8670/sqrt [0.8929*0.1070( 1/850 + 1/355)]

z= 0.0365/ sqrt [ 0.0955403 (0.001176 + 0.002816)]

z= 0.0365/ 0.019531

z= 1.8688

The critical region is  z∝/2 = ± 1.96

The value of z is 1.8666. The value of p is 0.06148 which is greater than 0.05

Conclusion:

Since the calculated value of z= 1.869 does not fall in the critical region we accept the null hypothesis H0: p1≠ p2  the data provides evidence that the proportion of high school students in metropolitan areas who have internet access during school hours is different than the proportion of rural high school students who have internet access during school hours.

The ways to prove triangles are similar are SSS rule, SAS rule, ASA rule and AAS rule

The rules of congruence of triangle are
SSS rule : If three sides of the triangle is equal to the three sides of another triangle, both triangles are congruent

SAS rule : If two sides and one included angle of one triangle is equal to the two sides and one included angle of another triangle, then both triangles are congruent

ASA rule : If two angles and one includes side of one triangle is equal to the two angles and one included side of another triangle, then both triangles are congruent

AAS rule : If two angles and one non-included sides of one triangle is equal to the two angles and one non-included side of another triangle, then both triangles are congruent

Therefore, theses are the rules of congruence of the triangle

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The image of the point after the reflection over x axis is P' ( -1 , 4 )

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the point be represented as P

Now , the coordinates of the point P is P ( -1 , -4 )

The point P is reflected over the line x axis ,

So , when you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse.

Substituting the values in the equation , we get

The image of the reflected point is P' ( -1 , - ( -4 ) )

The image of the reflected point is P' ( -1 , 4 )

Hence , the reflected point is P' ( -1 , 4 )

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The distance from Maria's desk to Monique's desk is  \(2\sqrt{13}\)

Given,

In the question:

Maria's desk is located at (2, −1), and Monique's desk is located at (−2, 5).

To find the  distance from Maria's desk to Monique's desk.

Now, According to the question:

We know that :

The formula of Distance:

\(\sqrt{(x_{2} -x_{1} )^2+(y_{2}-y_{1} )^2}\)

Substitute (2, -1) and (-2, 5) into distance formula:

\(\sqrt{(-2-2)^2+(5+1)^2}\)

Calculate:

\(\sqrt{(-4)^2+(6)^2}\)

\(\sqrt{16+36}\\ \\\sqrt{52}\)

= \(2\sqrt{13}\)

Hence, The distance from Maria's desk to Monique's desk is  \(2\sqrt{13}\)

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Answer: square root of 52

Step-by-step explanation:

did the practice test

The Solution:

Given:

Required:

Determine the correct option.

The complete data set is:

Thus, the correct answer is:

Answer:

[option A]

Answer:

The sample consisting of 64 data values would give a greater precision.

Step-by-step explanation:

The width of a (1 - α)% confidence interval for population mean μ is:

\(\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{n}}\)

So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (n).

That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.

Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.

The two sample sizes are:

n₁ = 25

n₂ = 64

The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.

        \(\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{25}}=\frac{1}{5}\ [2\cdot z_{\alpha/2}\cdot \sigma]\)

        \(\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{64}}=\frac{1}{8}\ [2\cdot z_{\alpha/2}\cdot \sigma]\)

Thus, the sample consisting of 64 data values would give a greater precision.

The number of data values would you expect to give a greater precision (a smaller width) for estimating the population mean is 64 and this can be determined by using the formula of width.

Given :

The following steps can be used in order to determine the number of data values would you expect to give a greater precision for estimating the population mean:

Step 1 - The below formula of width is used in order to determine the number of data values.

Step 2 - The formula of width is given below:

\(w = 2\times z_{\alpha /2}\times \dfrac{\sigma}{\sqrt{n} }\)

where \(z_{\alpha /2}\) is the z-score, \(\sigma\) is the standard deviation, and 'n' is the sample size.

Step 3 - Now, at n = 25 the formula of 'w' becomes:

\(w = 2\times z_{\alpha /2}\times \dfrac{\sigma}{\sqrt{25} }\)

\(w = \dfrac{1}{5}\left(2\times z_{\alpha /2}\times\sigma }\right)\)

Step 4 - Now, at n = 64 the formula of 'w' becomes:

\(w = 2\times z_{\alpha /2}\times \dfrac{\sigma}{\sqrt{64} }\)

\(w = \dfrac{1}{8}\left(2\times z_{\alpha /2}\times\sigma }\right)\)

The number of data values would you expect to give a greater precision (a smaller width) for estimating the population mean is 64.

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Answer:

x=4,y=2

Step-by-step explanation:

3x-2y=8 ..........1

2x+y=10...........2

multiply equation 2 by 2 and adding equation 1 and 2 ,we get

3x-2y=8

4x+2y=20

+_________

7x=28

x=28/7=4

:.x=4

again substituting value of x in equation 1 we get

3×4-2y=8

12-8=2y

y=4/2=2

:.y=2

The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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The calculated measure of m∠PNM is 87 degrees

from the question, we have the following parameters that can be used in our computation:

The circle

Where, we have

PM = 360 - 64 - 122

Evaluate

PM = 174

Next, we have

m∠PNM = 1/2 * 174

So, we have

m∠PNM = 87

Hence, the measure of m∠PNM is 87 degrees

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Answer:

Y=1

Step-by-step explanation:

If you take -3 and add 4 you must add the three first to get to zero, then go back for the remaining one. This leaves you with one.

Answer:

  see below

Step-by-step explanation:

The first answer choice is the only one that has the first sale correctly represented. Each term is the product of the number of pens of the type and the cost of pens of that type.

  12 dozen roller-ball pens will have a cost of 12x

  5 dozen ballpoint pens will have a cost of 5y

The total cost of these will be 116 (dollars).

The equation is written ...

  12x +5y = 116 . . . . . . . this equation is only found in choice A

Answer:

  23,500,710

Step-by-step explanation:

Answer:

uh explain please and i'll edit my answer but the number form of this is 23,500,710

Step-by-step explanation:

The actual consumer spending at a price of $27 per unit is $268.26.

Substitute the given price into the supply equation to get the corresponding quantity supplied:

p = q + 10

27 = q + 10

q = 17

Substitute q = 17 into the demand equation to get the corresponding price:

4q² + p² = 1405

4(17)² + p² = 1405

p² = 1405 - 1156

p² = 249

p = 15.78

The actual consumer spending can be calculated by multiplying the quantity demanded by the price:

Actual consumer spending = quantity demanded x price per unit

= 17 x 15.78

= $268.26

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The demand and supply equations for a certain product are given by space 4 q squared plus p squared equals 1405 and p equals q plus 10 where p is in dollars per unit and q is in units. For a price of $27 per unit, determine the actual consumer spending.

Answer:

Exact form: 21/4

Decimal Form: 5.25

Mixed Number Form: y= 5 1/4

Step-by-step explanation:

Answer:

Based on the information given, we know that angles 3 and 4 are supplementary (they add up to 180 degrees) and angles 2 and 4 are vertical angles (they are congruent). Therefore, we can write:

m∠4 + m∠3 = 180 (since angles 3 and 4 are supplementary)

m∠4 = m∠2 (since angles 2 and 4 are vertical angles)

Substituting m∠4 = m∠2 into the first equation, we get:

m∠2 + m∠3 = 180

Now we can solve for m∠2 and m∠3:

m∠3 = 43 (given)

m∠2 = 180 - m∠3 = 180 - 43 = 137

Since angles 1 and 2 are also supplementary, we can find m∠1 by subtracting m∠2 from 180:

m∠1 = 180 - m∠2 = 180 - 137 = 43

Therefore, m∠1 = 43 degrees and m∠2 = 137 degrees.

Answer:

it would be 7 dollars per football

Step-by-step explanation:

\(42 \div 6\)

Answer:

30inches

kkkkkkkkkkkkkkkk

Answer:

y=3/4x+2

Step-by-step explanation:

I found this by using desmos graphing calculator

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{20}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{20}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{2}}}\implies 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{6}(x-\stackrel{x_1}{2})\)

Answer:  y-2 = -6 (x-2)

Step-by-step explanation: Point slope form is this equation:

y-y1 = m (x-x1)

y1 is 2 because (2,2) ; The left 2 is x1 and the right 2 is y1.

(-1,20); The -1 is x2 and the 20 is y2.

If you use the equation above it helps a lot. I hope this helps you! :)

The value of the formula for the sequence is,

⇒ a (n) = 5ⁿ - 2

We have to given that;

The sequence is,

⇒ 3, 23, 123, 623, 3123, ...

Now, We can formulate;

⇒ 3 = 5 - 2

⇒ 23 = 5² - 2

⇒ 123 = 5³ - 2

⇒ 623 = 5⁴ - 2

Thus, The value of the formula for the sequence is,

⇒ a (n) = 5ⁿ - 2

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Based on the data, the estimated number of lemon candies in the bag of 100 assorted candies is about 19.

In mathematics, proportion refers to the relationship between two quantities that are equivalent or have a constant ratio. It is usually expressed as a fraction or a ratio. For example, if a recipe calls for 2 cups of flour and 1 cup of water, the proportion of flour to water is 2:1 or 2/1. Proportions are used in a variety of mathematical and real-world situations, such as solving problems involving ratios, rates, and percentages.

In the given question,

We can use a simple proportion to estimate the number of lemon candies in the bag. We know that Ridgette handed out a total of 6 lemon candies out of a total of candies. Therefore, the proportion of lemon candies in the bag is:

6/total candies = number of lemon candies/100

We can cross-multiply to solve for the number of lemon candies:

number of lemon candies = 6 x 100 / total candies

We can also use the information about the other flavors to estimate the total number of candies in the bag. The total number of candies is:

total candies = lemon + orange + grape + cherry

Using the information from the table, we can estimate the total number of candies:

total candies = 6 + 5 + 8 + 13 = 32

Therefore, the estimated number of lemon candies in the bag is:

number of lemon candies = 6 x 100 / 32 = 18.75

We can round this to the nearest whole number to estimate that there were about 19 lemon candies in the bag of 100 assorted candies.

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Answer:

1. C(n) = 2.25n + 120

2. R(n) = 3.51n

3. P(n) = 1.26n - 120

1. 96 frozen bananas must be sold in order to make a positive profit.

2. In order to make a profit, I have to sell a minimum of 96 frozen bananas.

Step-by-step explanation:

1. Write a function, C(n), to represent your total costs for the week if you sell n frozen bananas.

Total cost is the addition of total variable cost and total fixed cost. Therefore, the function is as follows:

C(n) = 2.25n + 120

Where 2.25n is the total variable cost while 120 is the total fixed cost.

2. Write a function, R(n), to represent the revenue from the sale of n frozen bananas during the week.

Revenue is equal to selling price per unit multiplied by the number of units sold. Therefore, the function is as follows:

R(n) = 3.51 * n

R(n) = 3.51n

Where 3.51 is the selling price per unit while n the number of units sold.

3. Write a function, P(n), that represents the profits for selling n frozen bananas in a given week.

Profit is equal to total revenue minus total cost. Therefore, the function can be derived as follows:

P(n) = R(n) - C(n)

P(n) = 3.51n - 2.25n + 120

P(n) = 1.26n - 120

1. How many frozen bananas must you sell in order to make a positive profit? Write your answer as a whole number.

This can be obtained by equating the profit function to zero and solve for n as follows:

P(n) = 0 => 1.26n - 120 = 0

Therefore, we have:

1.26n = 120

n = 120 / 1.26

n = 95.2380952380952 frozen bananas

Writing it as a whole number, we have:

n = 95 frozen bananas

However, using this whole number will result in a negative profit by substituting it into the profit function as follows:

P(n) = (1.26 * 95) - 120 = -$0.30

Therefore, n has to be increased by one to 96 which is also a whole number to have a positive profit as follows:

P(n) = (1.26 * 96) - 120 = $0.96

Therefore, 96 frozen bananas must be sold in order to make a positive profit.

2. Complete the following sentence to explain the meaning of #1:

In order to make a profit, I have to sell a minimum of 96 frozen bananas.

Answer:

28

Step-by-step explanation:

the formula for finding the area of a triangle is 1/2×base×height. the height is the spot where you can create a right angle with the base, which here is 14 meaning the equation is 1/2(4)(14)

Here we have a dilation of scale factor 2.

We can see that bot figures we have the same slope, so we just have a dilation of scale factor K to go from figure A to figure B.

To find the value of K, notice that for some side length L in figure A, the correspondent length L' in figure B must be:

L' = K*L

Here if we use the left sides, we will get:

for figure A; L= 2

for figure B: L = 4

4 = K*2

4/2 = K

2 = K

So this is a dilation of scale factor k = 2.

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Given:-

\( \: \)

\( \: \)

put the given value of x = 4 in given eqⁿ

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

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hope it helps∼

Answer:

answer 4

Step-by-step explanation:

Answer:

(- ∞, 7]  GIVE BRAINLIEST PLZ

Step-by-step explanation:

The equation from that word -5b > -35

Solve that and you get (- ∞, 7]