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3 years ago

A discount voucher offering 15% off is sued to pay a bill

Mathematics

1 answer:

mel-nik [20]3 years ago

6 0

Answer:244.8

Step-by-step explanation:

15% of y=36.72

15/100 x y=36.72

15y/100=36.72

Cross multiply

15y=36.72 x100

15y=3672

Divide both sides by 15

15y/15=3672/15

y=244.8

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Pls help me I rlly don’t get it :(

zhenek [66]

Step-by-step explanation:

Use SOH-CAH-TOA.

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

Let's start with #12. The hypotenuse is 18. The side adjacent to ∠B is 6. Since we have the adjacent side and hypotenuse, we should use cosine.

cos B = 6/18

Solving for B:

B = cos⁻¹(6/18)

Using a calculator:

B ≈ 70.5°

Now let's do #14. The side adjacent to ∠B is 19, and the side opposite of ∠B is 22. Since we have the adjacent side and opposite side, we should use tangent.

tan B = 22/19

Solving for B:

B = tan⁻¹(22/19)

Using a calculator:

B ≈ 49.2°

8 0

2 years ago

A study was conducted and two types of engines, A and B, were compared. Fifty experiments were performed using engine A and 75 u

USPshnik [31]

Answer:

a) -6 mpg.

b) 2.77 mpg

c) The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

Step-by-step explanation:

To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Gas mileage A: Mean 36, standard deviation 6, sample of 50:

$\mu_A = 36, s_A = \frac{6}{\sqrt{50}} = 0.8485$

Gas mileage B: Mean 42, standard deviation 8, sample of 50:

$\mu_B = 42, s_B = \frac{8}{\sqrt{50}} = 1.1314$

Distribution of the difference:

Mean:

$\mu = \mu_A - \mu_B = 36 - 42 = -6$

Standard error:

$s = \sqrt{s_A^2+s_B^2} = \sqrt{0.8485^2+1.1314^2} = 1.4142$

A. Find the point estimate.

This is the difference of means, that is, -6 mpg.

B. Find the margin of error

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = zs = 1.96*1.4142 = 2.77$

The margin of error is of 2.77 mpg

C. Construct the 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results(5 pts)

The lower end of the interval is the sample mean subtracted by M. So it is -6 - 2.77 = -8.77 mpg

The upper end of the interval is the sample mean added to M. So it is -6 + 2.77 = -3.23 mpg

The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

8 0

2 years ago

Maya has read two less than four times

SashulF [63]

Answer:

2(2n - 1)

Step-by-step explanation:

Let x = the number of books Theo has read

Then 4x = four times the number of books Theo has read.

And 4n - 2 = 2 less than four times the number of books Theo has read

But 4n -2 = the number of books Maya has read

Factor the expression

4n - 2 = 2(2n - 1)

The factored expression is 2(2n - 1).

3 0

3 years ago

Which property is illustrated by (7.3 + 5.1) + x = 7.3 + (5.1 + x)?

Troyanec [42]

C. assosiative property
as it follows the rule....

(a+b)+c = a+(b+c)

so c is the correct answer.....

HOPE IT HELPS YOU '_'

6 0

2 years ago

Read 2 more answers

A dish tv satellite dish is the shape of a paraboloid. the dish is 36 inches wide, and 8 inches deep. how many inches should the

MrRa [10]

Refer to the diagram shown below. It shows a vertical cross-section of the paraboloid through its axis of symmetry.

Let the vertex of the parabola be at the origin. Then its equation is of the form
y = bx²

Because the parabola passes through (18,8), therefore
8 = b(18²)
b = 0.02469
The parabola is y = 0.02469x².

The receiver should be placed at the focal point of the paraboloid for optimal reception.
The y-coordinate of the focus is
a = 1/(4b) = 1/0.098765 = 10.125 in

Answer: The receiver is located at 10.125 inches from the vertex.

4 0

3 years ago