(4√7 + √3) (√7 - 2√3)
Solve by multiplying and simplifying radical expression

The scale factor of the dilation is 2.5.

A scale factor is a number that is used to change the size of shapes in geometry. It is the ratio of the length of a new shape to the length of the original shape.

Given that, a triangle with vertices, A(0, 0), B(0, 4), and C(6, 0) is dilated to yield a triangle with vertices at A(0, 0), B(0, 10), and C(15, 0).

We need to find the scale factor,

Taking the coordinates of B,

B(0, 4) → B(0, 10)

Scale factor = 10/4 = 2.5

Hence, the scale factor of the dilation is 2.5.

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Answer:

z=10

Step-by-step explanation:

We know that the ratio 7:21 is equal to the ratio of 10:3z.

Let's model that in proportions:

7               10

-       =        -

21             3z

Now that the equation is in proportional form, we can cross-multiply to find the value of z.

7 * 3z = 21 * 10 - Multiply both sides

21z = 210 - Divide both sides by 21

z=10

The answer is z=10.

Answer:

i believe the answer is 13,250

Step-by-step explanation:

all i did was divide the 5400/0.40 because i thiink its correct, maybe not

The employer contribute to her retirement plan is $2120.

Many American firms provide 401(k) plans, which are retirement savings plans with favourable tax treatment for the saver. It bears a section number from the United States Internal Revenue Code (IRC).

When a worker enrols in a 401(k), they consent to have a portion of each paycheck put directly into an investing account. A portion or the entire contribution may be matched by the employer. The employee has a variety of investing alternatives, most often mutual funds.

Given:

Jayne contributes $5,300

Now, the contribution of $0.40 for each dollar

So, employer contribute to her retirement plan

= 5300 x 0.40

= $2120

Hence, The employer contribute to her retirement plan is $2120.

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The equations which define y as a function of x are; −12x−85y=0 and 3x−4y=−2.

Any number that one can think of, except complex numbers, is a real number. Real numbers therefore include rational numbers like positive and negative integers, fractions, and irrational numbers.

On this note, the equations as displayed in the answers provided above define y as a function of x.

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The diet which is developed by the nutritionist is effective at the 0.05 level of significance. Claim is agreed.

The two-sample t-test is used to determine if two population means are equal.

A nutritionist has developed a diet that she claims will help people lose weight. In this,

Here are the original weights, in pounds, with the weight after 6 months in parentheses.

The mean of the weights before 6 moths is,

[tex]\overline X_1=\dfrac{192+ 212 +171 +215 +180 +207 +165 +168 +190 +184 +200 +196 }{12}\\\overline X_1=190[/tex]

The mean of the weights after 6 months is,

[tex]\overline X_2=\dfrac{ 183 +196 +174 +211 +160 +191 +162 +175 +190 +179 +189 +195 }{12}\\\overline X_1=183.75[/tex]

Standard deviation of both the data is 16.9 and 14.7.

1. Null and Alternative Hypotheses.

The following null and alternative hypotheses need to be tested:

[tex]\begin{array}{ccl} H_0: \mu_1 & = & \mu_2 \\\\ \\\\ H_a: \mu_1 & > & \mu_2 \end{array}[/tex]

This corresponds to a right-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.

Based on the information provided, the significance level is α=0.05 and the degrees of freedom are df = 22. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal:

[tex]df_{Total} = df_1 + df_2 = 11 + 11 = 22[/tex]

Hence, it is found that the critical value for this right-tailed test is

[tex]t_c=1.717[/tex], for α=0.05 and df=22

The rejection region for this right-tailed test is,

[tex]R = \{t: t > 1.717\}[/tex]

(3) Test Statistics

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

[tex]t = \displaystyle \frac{\bar X_1 - \bar X_2}{\sqrt{ \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2}(\frac{1}{n_1}+\frac{1}{n_2}) } }[/tex]

[tex]\displaystyle \frac{ 190 - 183.75}{\sqrt{ \frac{(12-1)16.9^2 + (12-1)14.7^2}{ 12+12-2}(\frac{1}{ 12}+\frac{1}{ 12}) } } = 0.967[/tex]

Since it is observed that t=0.967≤tc=1.717 it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.1721 and since p=0.1721≥0.05p = 0.1721  it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis H₀ is not rejected. Therefore, there is not enough evidence to claim that the population mean μ1​ is greater than μ2​, at the α=0.05 significance level.

Confidence Interval

The 95% confidence interval is −7.16<μ<19.66

Thus, the diet which is developed by the nutritionist is effective at the 0.05 level of significance. Claim is agreed.

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Answer:

Step-by-step explanation:

The end solution has same volume as initial volumes of mixture.

The concentration of solution is calculated as below

Answer:

35 grams

Step-by-step explanation:

25+10=30 grams of the mixture

Answer:

16

Step-by-step explanation:

6.48 + 9.34= 15.82 so when u round the number it 16 so the estimate is 16.

Answer: A.) 0.9

Step-by-step explanation: hope this helps xlXCherryColaXlx. have a great day :3...(pls mark me brainliest)

Answer:

it is the domain

Step-by-step explanation:

because if you put 5x on the other side it will be a -5

Step-by-step explanation:

it needs 4×2 = 8 cubes asking the length, 5×2 = 10 cubes along the width, and 3 1/2 × 2 = 7 cubes along the height.

so, altogether

8×10×7 = 560 cubes

Answer:

The formula for area of a trapezoid is (b_{1} + b_{2})*\frac{1}{2} h=A(b

1

+b

2

)∗

2

1

h=A

b=base

h=height AKA altitude.

A=area.

Base 1 is 483.

Base 2 is 405.

483+405=888

888×320 (h) = 284160

284160 × \frac{1}{2}

2

1

= 142080

The approximate area of Nevada is 142080 square miles.

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Answer:

choice B

Step-by-step explanation:

using the formula:

[tex]theta \div 360\pi \times r ^{2} [/tex]

Answer:

B

Step-by-step explanation:

Formula

[tex]\textsf{Area of a sector of a circle}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]

Solution

Given:

[tex]\begin{aligned}\implies \textsf{Area} & =\left(\dfrac{60^{\circ}}{360^{\circ}}\right) \pi \cdot 9^2\\\\ & = \dfrac16 \cdot \pi \cdot81\\\\ & = \dfrac{81}{6} \pi\\\\ & = \dfrac{27}{2} \pi \: \sf cm^2\end{aligned}[/tex]

Answer:g(x) = f(x) + 1.5g(

Step-by-step explanation:g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5

Answer:

Since , we're given three distinct measures , we can make out that the dimensions are most probably of a cuboid.

[tex]Volume \: of \: cuboid = l \times b \times h \\ \\ \implies \: 8 \times 9 \times 3 \\ \\ \bold\red{\implies216 \: units^{3}}[/tex]

hope helpful ~

Answer:

Most of the time you can go on a website that can cauculate it.

Step-by-step explanation:

How to cauculate the MAD:

Take each number in the data set, subtract the mean, and take the absolute value. Then take the sum of the absolute values. Now compute the mean absolute deviation by dividing the sum above by the total number of values in the data set. Finally, round to the nearest tenth.

Answer:

No Solutions

Step-by-step explanation:

First to complete the square, it will need to look something like

a^2+2ab+b^2

so in order to get that we can see that 4n^2+8n seems to be missing a piece.

a is the square root of 4n^2 which is 2n.

8n/2n=4

4/2=2

b=2

so now add 2 to both sides of the equation so now it's

4n^2+8n+4=-13

rewrite as (2n+2)^2=-13

Now you see a negative number as the result of a exponent.

A number squared will never be negative.

Therefore the answer is

No Solutions

Answer:

Step-by-step explanation:

4

Answer:

14cm²

Step-by-step explanation:

Add up all the squares and the other bits to get the answer.

Hi!

Your answer is the 1st one, 36 inches of ribbon.

The question states this is a square picture frame. That means that all the side lengths are the same.

We are given a side length of 6 inches.

In order to find the area of a square, we multiply the length and the width together.

In this problem, the sides of the picture frame measure 6 inches. Therefore:

[tex]6*6=36[/tex]

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Side of the Square picture frame= 6 inches

How much inches of ribbon she requires to cover the square frame.

There is a square picture frame. And we know Area of square= (side)²

[tex] \text{Area of Square picture frame = (side)²}[/tex]

[tex] = (6) {}^{2} \\ = 36 \: \: \text{inches of ribbon}[/tex]

[tex] \therefore \text{Option A= 36 inches of ribbon}[/tex]

Answer:

Step-by-step explanation:

5 Digit Lock - Level One

*

242

-4x+11y=-50

[tex]x = \frac{25}{2} + \frac{11y}{4} [/tex]

The paragraph to show the comparision between two classes semester grades on the basis of the terms

is given below:

A box and whisker plot is defined as a graphical method of displaying variation in a set of data.

From the first figure, write all the values where dark point is drawn

53, 62, 80, 86, 89  

        The upper extreme is the highest value, which is 89.

        The upper quartile is 86 and the lower quartile is 62.

       = Highest - Lowest

       =89-53

       =36

From the second figure, write all the values where dark point is drawn

56, 62, 74, 89, 96

        The upper extreme is the highest value, which is 96.

       The upper quartile is 89 and the lower quartile is 62.

       = Highest - Lowest

       =96-62

       =34

From the above discussion,  

The comparision of the two classes on the basis of extremes, quartile, median, range is concluded above.

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he should have covered 0.95-mile

Answer:

y = -1.25x + 3

OR
y = -1 1/4x + 3

OR

y = -5/4x + 3

Answer:

[tex]\sf \dfrac{2}{3} = \dfrac{32}{48} = \dfrac{30}{45}[/tex]

[tex]\sf \rightarrow \dfrac{2}{x} = \dfrac{32}{48}[/tex]

[tex]\sf \rightarrow 2(48)= {32x}[/tex]

[tex]\sf \rightarrow 32x= 96[/tex]

[tex]\sf \rightarrow x = 3[/tex]

[tex]\rightarrow \sf \dfrac{32}{48} = \dfrac{30}{y}[/tex]

[tex]\rightarrow \sf {32y} = 30(48)[/tex]

[tex]\rightarrow \sf {32y} = 1440[/tex]

[tex]\rightarrow \sf y = 45[/tex]

Answer:

6x4=24 as a fraction it could be 24/1 48/2 72/3 etc.

Step-by-step explanation:

Answer:

Line D

Step-by-step explanation:

Let's see how much points fall under each line's region

Majority of points lie under line D

Hence line D should be correct