A car is 160 inches long. A truck is 75% longer than the car.
How long is the truck?

Answer:

Just two corrections!  See attached image.

Step-by-step explanation:

The product of 8 and b taken from 10 means begin with 10 and subtract 8b from it.

8 times the difference of 10 and b means find 10 - b first, then multiply by 8.

Answer:

The coordinates of point B are (4,1)

Step-by-step explanation:

The easiest way of solving and explaining this question would to go by steps from each point. From point A to the midpoint, we go 1 left on the x axis from 6->5 and 3 up on the y axis from -5->-2. You then repeat these steps again to go from the midpoint to B. (5-1,-2+3) = (4,1)

Answer:

a. x = 4.8989794855663561963945681494118 or 4.9 rounded

b. x = 8.6023252670426267717294735350497 or 8.6 rounded

Step-by-step explanation:

7² - 5² = x²

49 - 25 = x

49 - 25 = 24

√24 = 4.8989794855663561963945681494118

7² + 5² = x²

49 + 25 = x

49 + 25 = 74

√74 = 8.6023252670426267717294735350497

Answer:hi

Step-by-step explanation:

Hi

The rate of the passenger train must be 45 miles per hour, and the rate of the freight train must be 30 miles per hour.

Let's denote the rate of the passenger train as "P" and the rate of the freight train as "F". We are given that the passenger train's rate exceeds the freight train's rate by 15 miles per hour. Therefore, we can write the following equation:

P = F + 15

We are also given that the two trains start from points that are 300 miles apart and meet after 4 hours. We can use the formula distance = rate × time to set up two equations:

Distance covered by the passenger train: P × 4

Distance covered by the freight train: F × 4

Since they meet each other, the sum of their distances should add up to 300 miles:

P × 4 + F × 4 = 300

Substituting P = F + 15 into the equation, we can solve for F:

(F + 15) × 4 + F × 4 = 300

4F + 60 + 4F = 300

8F = 240

F = 30

Now that we have the rate of the freight train, we can substitute it back into the equation P = F + 15 to find the rate of the passenger train:

P = 30 + 15

P = 45

Therefore, the rate of the passenger train must be 45 miles per hour, and the rate of the freight train must be 30 miles per hour.

For such more questions Train Rates

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Answer:

false

Step-by-step explanation:

(8,8) or (4,4)

Answer:

the answer is A.

Answer:

Step-by-step explanation:

 Slope = 3.200/2.000 = 1.600

 x-intercept = 5/8 = 0.62500

 y-intercept = 5/-5 = 1/-1 = -1.00000

Answer:

26.01

Step-by-step explanation:

Answer:

1,317,840

17×17=289×16=4,624×19=87,856×15=1,317,840

Answer:

the sqare root of 19.9 is 4.46094160464

Answer:

2,000,000 - 2 million

20,00,000 - 20 lakhs

Answer:

10 lakh = 1,000,000

So 20 lakh is = 2 million

Hope it helps!

Answer:

The answer is A

Step-by-step explanation:

We can tell by finding out what each points coordinates are.

Its quite hard to describe how to do this on a phond yet you use the rule of

X coordinate first, then Y coordinate.

so (-5,5). -5 is the x coordinate

and 5 is the y coordinate.

Graphs can be quite difficult but for now, just remember x is across and y is up.

Good luck with future questions!

Answer:

12 feet

Step-by-step explanation:

48 divided by 4 is 12 and 48 is the total area

Answer:

12 sq. ft.

Step-by-step explanation:

To find the area of a square (or rectangle) you multiply the length by the width.

To find the length of one side, when you have the area and one side, you divide the area by the side you have.

48 divided by 4 equals 12.

Hope this helps :)

Answer:

[tex]x = 7[/tex] --- toppings

[tex]y = 27[/tex] ---- amount

Step-by-step explanation:

Given

[tex]y \to\ amount[/tex]

[tex]x \to\ topping[/tex]

The first deal is:

[tex]y = 6 + 3x[/tex]

The second is:

[tex]y = 20 + x[/tex]

Required

The value of  x and y [for which both deals are equal]

We have:

[tex]y = 6 + 3x[/tex]

[tex]y = 20 + x[/tex]

Equate both

[tex]y=y[/tex]

So, we have:

[tex]6 + 3x = 20 + x[/tex]

Collect like terms

[tex]3x - x = 20 - 6[/tex]

[tex]2x =14[/tex]

Divide by 2

[tex]x = 7[/tex]

Substitute [tex]x = 7[/tex] in [tex]y = 20 + x[/tex]

[tex]y = 20 + 7[/tex]

[tex]y = 27[/tex]

Answer:

See below for answers and explanations

Step-by-step explanation:

Part A:

Given:

Pooled sample size: [tex]n=15[/tex]

Sample size (with academic scholarships): [tex]n_1=6[/tex]

Sample size (no academic scholarships): [tex]n_2=9[/tex]

Population standard deviations: Unknown

Sample mean (with academic scholarships): [tex]\bar{x}=\frac{25+24+23+21+22+20}{6}=22.5[/tex]

Sample mean (no academic scholarship):[tex]\bar{x}=\frac{23+25+30+32+29+26+27+29+27}{9}=27.\bar{5}[/tex]

Sample standard deviation (with academic scholarships): [tex]s_1=1.7078[/tex]

Sample standard deviation (no academic scholarships): [tex]s_2=2.5868[/tex]

Degrees of freedom: [tex]df=n-2=15-2=13[/tex]

Significance level: [tex]\alpha =0.02[/tex]

Decide which test is most appropriate to conduct:

Therefore, we will conduct a 2-sample t-test assuming our conditions are satisfied.

List null and alternate hypotheses:

[tex]H_o:\mu_1=\mu_2[/tex] -> There's no difference in ACT scores between students with and without an academic scholarship

[tex]H_a:\mu}_1\neq\mu_2[/tex] -> There's a difference in ACT scores between students with and without an academic scholarship (it's two-sided)

Determine the value of the test statistic:

We will use the formula [tex]t=\frac{\bar{x}_1-\bar{x}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} } }[/tex] to compute the test statistic [tex]t[/tex]. Therefore, the test statistic is [tex]t=\frac{\bar{x}_1-\bar{x}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} } }=\frac{27.\bar{5}-22.5}{\sqrt{\frac{1.7078^2}{6}+\frac{2.5868^2}{9} } }=4.5592[/tex]

Calculate the p-value:

Because the test is two-sided, [tex]p=2tcdf(4.5592,1e99,13)=2(0.0003)=0.0006[/tex]

Interpret p-value and conclude test:

Given our significance level is [tex]\alpha =0.02[/tex], since [tex]p<\alpha[/tex], we reject the null hypothesis and conclude that there is significant evidence that suggests that there is a difference in ACT scores between students with and without an academic scholarship (it's more likely that the alternate hypothesis is true)

Part B:

The formula for a confidence interval for the difference in 2 population means is [tex]CI=(\bar{x}_1-\bar{x}_2)\pm t^*\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}[/tex] where [tex]\bar{x}_1-\bar{x}_2[/tex] is the difference of the 2 sample means and [tex]t^*[/tex] is the critical score for the desired confidence level.

The critical score for our 98% confidence interval would be [tex]t^*=invT(0.99,13)=2.6503[/tex]

Therefore, our 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is [tex]CI=(27.\bar{5}-22)\pm 2.6503\sqrt{\frac{1.7078^2}{6}+\frac{2.5868^2}{9}}}=[2.6167,8.4944][/tex]

This means that we are 98% confident that the true difference in the ACT scores between students with and without an academic scholarship is contained within the interval [tex][2.6167,8.4944][/tex]

The evaluation of sub-parts results in:

Part A: Yes, the data provides convincing evidence of a difference in A at CT scores between students with and without an academic scholarship at α = 0.02

Part B: The 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is evaluated to be [tex]CI \approx [-7.00, -2.14][/tex]

If the sample sizes < 30, and we want to test the difference between the sample means, then we perform t-test.

Let we have:

Then, the value of t-test statistic is obtained as:

[tex]t = \dfrac{\overline{x}_1 - \overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}}[/tex]

If the level of significance is [tex]\alpha[/tex], then as we have:

the degree of freedom (d.f) = [tex]n_1 + n_2 - 2[/tex], the critical value of t is found to be [tex]t_{\alpha/2}[/tex], then if we get:

[tex]|t| < t_{\alpha/2}[/tex]null hypothesis

and if we get [tex]|t| > t_{\alpha/2}[/tex] null hypothesis, and thus, accept the alternate hypothesis.

For this case, we want to test if there is

Thus, we form the hypotheses as:

Null hypothesis: There's no difference in ACT scores between students with and without an academic scholarship

or: [tex]H_0: \mu_1 = \mu_2[/tex]

Alternative hypothesis:  There's a difference in ACT scores between students with and without an academic scholarship (it's two-sided)

or [tex]H_1: \mu_1 \neq \mu_2[/tex]

where we have:

For this case, we evaluate the mean and standard deviation as:

Sample size = [tex]n_1 = 6[/tex]

Mean = sum of all observation/ number of observations = 135/6 =22.5

Thus, standard deviation = [tex]s_1 = \sqrt{\dfrac{1}{n}\sum{(x_i - \overline{x_1})^2}} = \sqrt{\dfrac{17.5}{6}} \approx1.71[/tex]

Sample size = [tex]n_2 = 9[/tex]

Mean = sum of all observation/ number of observations = 248/9 ≈27.56

Thus, standard deviation = [tex]s_2 = \sqrt{\dfrac{1}{n}\sum{(x_i - \overline{x_2})^2}} \approx \sqrt{\dfrac{60.22}{9}} \approx 2.59[/tex]

The t-test statistic is evaluated as:

[tex]t = \dfrac{\overline{x}_1 - \overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_1}}} = \dfrac{22.5 -27.56}{\sqrt{\dfrac{2.92}{6} + \dfrac{6.69}{9}}} \approx -4.56[/tex]

Degree of freedom = [tex]n_1 + n_2 - 2 = 6 + 9 - 2 = 13[/tex]

Level of significance = 0.02 = 2%

The critical value of t is found to be [tex]t_{0.02/2} =2.65[/tex]

Thus, we get: [tex]|t| \approx 4.56 > 2.65 =t_{\alpha/2}[/tex]

Thus, we may reject the null hypothesis.

That means, there is enough evidence of a difference in ACT scores between students with and without an academic scholarship at 0.02 level of significance.

Now, the 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is calculated as:

[tex]CI = (\overline{x}_1 - \overline{x}_2) \pm t_{\alpha/2}\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_1}}\\\\CI = -5.06 \pm 2.65(\sqrt{\dfrac{2.92}{6} + \dfrac{6.69}{9}})\\\\CI \approx -5.06 \pm 2.65 \times 1.11\\CI \approx -5.06 \pm 2.94\\CI \approx [-5.06 - 2.94, -5.06 + 2.94] = [-7.00, -2.14][/tex]

Thus, the evaluation of sub-parts results in:

Part A: Yes, the data provides convincing evidence of a difference in A at CT scores between students with and without an academic scholarship at α = 0.02

Part B: The 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is evaluated to be [tex]CI \approx [-7.00, -2.14][/tex]

Learn more about two sample t-test here:

https://brainly.com/question/16285453

Answer:

5+6f>8f-7

5+7>8f-6f

12>2f

6>f

f<6

Step-by-step explanation:

Given:

Consider the given expression is:

[tex]\dfrac{x^4y^{-4}z^{-2}}{x^2y^{-2}z^4}[/tex]

To find:

The simplified form of the given expression.

Solution:

We have,

[tex]\dfrac{x^4y^{-4}z^{-2}}{x^2y^{-2}z^4}[/tex]

By using the quotient property of exponents, we get

[tex]=x^{4-2}y^{-4-(-2)}z^{-2-4}[/tex]              [tex]\left[\because \dfrac{a^m}{a^n}=a^{m-n}\right][/tex]

[tex]=x^{2}y^{-4+2}z^{-6}[/tex]

[tex]=x^{2}y^{-2}z^{-6}[/tex]

By using negative exponent property, we get

[tex]=\dfrac{x^{2}}{y^{2}z^{6}}[/tex]           [tex]\left[\because a^{-n}=\dfrac{1}{a^n}\right][/tex]

The simplified form of the given expression is [tex]\dfrac{x^{2}}{y^{2}z^{6}}[/tex].

Therefore, the correct option is B.

Answer: I'm going to say 3

Step-by-step explanation:

Answer:

I think the height is 22.

Answer:

(3, - 1)

Step-by-step explanation:

We want to solve the system of equations:

2*x - y = 7

x - 2*y = 5

graphically.

To do it, we need to graph both lines, it will be easier if we rewrite both lines in a more general way, like in the slope-intercept form:

y = -7 + 2*x

y = -(5/2) + x/2

Now, a solution of the system is a point (x, y) such that the point is a solution to both equations, then, when we graph the lines, as that point belongs to both equations, we should see that both lines pass through that point.

Then to find the solution of the system, we just need to graph the lines and find the point where the lines intersect.

Below, you can see a graph of the lines, and is easy to see that the lines do intersect at the point (3, - 1)

Answer:

x = 10

Step-by-step explanation:

2x = 20°

x = 20/2

x =10

Answer:ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]a^{2} +b^{2} =c^{2} \\6^{2} +7^{2} =x^{2} \\\sqrt{85} = x[/tex]

Answer:

sqrt(85) =x

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem to find the hypotenuse

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

6^2 + 7^2 = x^2

36+49 = x^2

85 = x^2

Take the square root of each side

sqrt(85) = sqrt(x^2)

sqrt(85) =x

Answer:

x = 3

Step-by-step explanation:

92 - 8x = 68

-8x = -24

x = 3

The two angles mentioned in the problem, if AD || EH, are congruent because they are corresponding angles.

Answer:

Step-by-step explanation:

Answer:

D. 150 cm²

[tex]area = 5 \times 5 \\ = 25 \: {cm}^{2} [/tex]

= 25 × 6 sides

= 150 cm²

Answer:

405 cycles

Step-by-step explanation:

We have the equation:

y = 6*sin(324*π*t)

For the properties of the sin function, we know that the period is 2π.

So between:

Sin(x) and Sin(x + 2*pi)

we have a cycle.

between:

Sin(x) and Sin(x + 6*pi)

we have 3 cycles.

and so on.

Now we want to find how many cycles will occur between t = 3 s, and t = 5.5 seconds

Between these times, the difference in the argument of the sin function is:

324*π*5.5 - 324*π*3 = 324*π*(5.5 - 3) = 324*π*2.5

Now, the number of cycles that we will have between these times is equal to the number of times that "2*π" is in 324*π*2.5

That number is just the quotient between 324*π*2.5 and 2*π

N = (324*π*2.5)/(2*π) = (324*2.5)/(2) = 405

There are 405 cycles between 3 seconds and 5.5 seconds.

Answer:

all real numbers

Step-by-step explanation:

3 + 8x = 8x + 3

Subtract 8x from both sides.

3 = 3

Since 3 = 3 is a true statement, the solution is

x = all real numbers

Every number is a solution of this equation.