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Answer:

0.12995

0.47508

0.0841

0.738

Step-by-step explanation:

Given that:

Percentage of STEM (p) = 27% = 0.27

Sample size (n) = 47

Using Normal approximation :

Mean (m) = n*p = 47 * 0.27 = 12.69

Standard deviation (s) = √(n*p*q)

q = 1 - p = 1 - 0.27 = 0.73

Standard deviation (s) = √(47*0.27*0.73) = 3.04

a. Exactly 13 of them major in STEM.

P(12.5 < x < 13.5)

USing the z formula :

(x - m) / s

(12.5 - 12.69) / 3.04 < x (13.5 - 12.69) / 3.04

-0.0625 < z < 0.2664

Using the z probability calculator:

P(Z < - 0.0625) = 0.47508

P(Z < 0.2664) = 0.60503

0.60503 - 0.47508

= 0.12995

b. At most 12 of them major in STEM.

P(X ≤ 12.5)

Zscore = (x - m) / s

Zscore = (12.5 - 12.69) / 3.04

Zscore = −0.0625

P(Z ≤ - 0.0625) = 0.47508

c. At least 9 of them major in STEM.

P(X ≥ 8.5)

Zscore = (x - m) / s

Zscore = (8.5 - 12.69) / 3.04

Zscore = −1.378

P(Z ≤ - 1.378) = 0.0841

d. Between 8 and 15 (including 8 and 15) of them major in STEM.

(8.5 - 12.69) / 3.04 < x (15.5 - 12.69) / 3.04

-1.378 ≤ z ≤ 0.924

Using the z probability calculator:

P(Z ≤ 0.924) = 0.82226

P(Z ≤ - 1.378) = 0.084102

0.82226 - 0.084102

= 0.738

Answer:

1

Step-by-step explanation:

Answer:

B. 1

Step-by-step explanation:

The quotient will have 1 decimal place because one of the numbers in the calculation has one decimal place, and the answer is only allowed to be as exact as the numbers used in the equation.

To make sure the answer is correct, we can do the math:

170.8/14 = 12.2

12.2 only has one decimal place, so answer choice B is correct.

Hope this helps :)

Answer:

1 y=3x 2 y=38x 3 y=202x 4 y=2x 5 y=16x

Step-by-step explanation:

Answer:do yo use I’ll need help

Step-by-step explanation:

Answer:

6 cups of lemon juice

Step-by-step explanation:

Answer:

$3.16

Step-by-step explanation:

6% x $52.60 = $3.16 (2dp)

Topic: Percentage

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Answer:

The calculated value   t = 0.452< 2.2621 at 0.05 level of significance

null hypothesis is accepted

Based on the sample, can it be concluded that μ is not different from 45 centimeters

Step-by-step explanation:

Step( i ):-

Heights were measured for a random sample of 10 plants

Size of the sample 'n' = 10

Mean of the sample (x⁻ ) = 46 centimeters

Standard deviation of the sample (s) = 7 centimeters

Mean of the Population ( μ ) = 45

Step(ii):-

Null Hypothesis :H₀:( μ ) = 45

Alternative Hypothesis : H₁:  μ ) ≠ 45

Test statistic

             [tex]t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }[/tex]

            [tex]t = \frac{46-45}{\frac{7}{\sqrt{10} } }[/tex]

           t = 0.452

  Degrees of freedom

                 γ = n-1 = 10 -1 = 9

t₀.₀₅ =  2.2621

The calculated value   t = 0.452< 2.2621 at 0.05 level of significance

null hypothesis is accepted

Based on the sample, can it be concluded that μ is not different from 45 centimeters

Answer:

84.24 - 6.24 = p

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

there is a maximum of 24 hours in a day and the highest we can have is 23:59.. it's impossible for it to be the 25th hour in a day

Step-by-step explanation:

Identify the slope, m. This can be done by calculating the slope between two known points of the line using the slope formula. (or just count and plug it into rise over run format)

Find the y-intercept. This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.

Answer:

BC>XY

Step-by-step explanation:

BCs angle is less than XYs angle

Answer:

2

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

If its right let me know I think this is right

Answer:

44,55,77

Ratio is 11/1

Step-by-step explanation:

176=4x+5x+7x

176=16x

11=x

44,55,77

Step-by-step explanation:

Answer:

£1.44

Step-by-step explanation:

11.52/8=1.44

:)

Answer:

I think the answer is $1.44 each necklaces

Step-by-step explanation:

We know the total amount is $11.52 and there were 8 candy necklaces, so you divide 11.52 by 8 and that gives you 1.44

Answer:

1/5

Step-by-step explanation:

Answer:

The value of cos Ф is ± [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

There are important rules for sin Ф and cos Ф

∵ sin Ф = [tex]\frac{\sqrt{3}}{2}[/tex]

∴ sin²Ф = [tex](\frac{\sqrt{3}}{2})^{2}[/tex]

∴ sin²Ф = [tex]\frac{3}{4}[/tex]

→ By using the third rule above

∵ cos²Ф = 1 - sin²Ф

∴ cos²Ф = 1 - [tex]\frac{3}{4}[/tex]

∴ cos²Ф = [tex]\frac{1}{4}[/tex]

→ Take square root for both sides

∴ cos Ф = ± [tex]\frac{1}{2}[/tex]

∴ The value of cos Ф is ± [tex]\frac{1}{2}[/tex]

Answer:

Answer:

100 inches

Step-by-step explanation:

Given

20 inch ≈ 0.5 m

Required

Determine the equivalent of 2.5m in inches

The question illustrated conversion between units of same measurements.

And we have that:.

20 in ≈ 0.5 m

Which can be rewritten as:

0.5 m ≈ 20 in

To solve further, we multiply both sides by 5

0.5 m * 5 = 20 in * 5

2.5 m ≈ 100 in

Hence, we can conclude that the 2.5m rope is approximately 100 inches long

The 2.5m rope is approximately 100 inches long

We have to given that,

20 inch ≈ 0.5 m

And, To Determine the equivalent of 2.5m in inches.

Since, It is illustrated conversion between units of same measurements.

And we have that;

20 in ≈ 0.5 m

Which can be rewritten as:

0.5 m ≈ 20 in

we multiply both sides by 5

0.5 m x 5 = 20 in x 5

2.5 m ≈ 100 in

Hence, we can conclude that the 2.5m rope is approximately 100 inches long.

Learn more about the multiplication visit:

https://brainly.com/question/10873737

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Answer:

40

Step-by-step explanation:

Answer:

Your answer would be 92 Hours

Step-by-step explanation:

4 x 115 = 460

460 x 12 = 5,520

5,520 ÷ 60 = 92

Therefore your answer would be 92

Based on Lauren's spending patterns and the balance in her account, her new balance must be an overdraft of $180.

Her balance after the vacation can be found as:

= Balance before vacation - ( Amount spent)

= 60 - ( 80 x 3)

= 60 - 240

= -$180

In conclusion, she will have a bank overdraft of $180.

Find out more about bank overdrafts at https://brainly.com/question/8283687.

Answer:

Step-by-step explanation:

Given the expression;

secθ − tan θ = cosθ

We are to find the solution in the interval [0, 2π).This is as shown;

From trigonometry identity;

secθ = 1/cosθ

tanθ = sinθ/cosθ

Substitute into the formula;

secθ − tan θ = cosθ

1/cosθ-sinθ/cosθ = cosθ

Multiply through by cosθ

1 - sinθ = cos²θ

1-sinθ = (1-sin²θ)

1-sin²θ-1+sinθ =0

-sin²θ+sinθ = 0

sin²θ = sinθ

sinθ = 1

θ = arcsin 1

θ = 90

θ = π/2

Hence the solution is π/2

The equation is an illustration of trigonometry ratios and identities

The solution in the interval  [0, 2π) is [tex]\mathbf{\theta = \frac{\pi}{2}}[/tex]

The equation is given as:

[tex]\mathbf{sec\theta - tan \theta = cos\theta}[/tex]

In trigonometry identity, we have:

[tex]\mathbf{sec\theta = \frac{1}{cos\theta}}[/tex]

and

[tex]\mathbf{tan\theta = \frac{sin\theta}{cosθ}}[/tex]

So the equation becomes

[tex]\mathbf{\frac{1}{cos\theta} -\frac{sin\theta}{cos\theta} = cos\theta}[/tex]

Multiply through by cosθ

[tex]\mathbf{1 - sin\theta = cos\²\theta}[/tex]

In trigonometry,

[tex]\mathbf{cos\²\theta = 1 - sin^2\theta }[/tex]

So, we have:

[tex]\mathbf{1-sin\theta = 1-sin\²\theta}[/tex]

Subtract 1 from both sides

[tex]\mathbf{sin\theta = sin\²\theta}[/tex]

Divide both sides by [tex]\mathbf{sin\theta}[/tex]

[tex]\mathbf{1 = sin\theta}[/tex]

Rewrite as:

[tex]\mathbf{sin\theta = 1}[/tex]

Take arc sin of both sides

[tex]\mathbf{\theta = sin^{-1}(1)}[/tex]

This gives

[tex]\mathbf{\theta = \frac{\pi}{2}}[/tex]

Read more about trigonometry ratios at:

https://brainly.com/question/24888715

Answer

3y^2\left(2y\:+\:1\right)\left(4y^2\:-\:2y\:+\:1\right)

Step-by-step-explanation

Answer:

I think the answer is b the person who answered may have worded it weird but from trying to read it it looks like b so

Answer:

The answer is "50".

Step-by-step explanation:

Let,

[tex]\to p(200) = 400[/tex]

If we assume the $20 reduction would raise the number of items sold to $40 so the increment is (x - 200) if x is the number of units sold.

[tex]\to (\frac{1}{40}) \times 20 = 0.5[/tex]

[tex]\to D(x) = 400 - 0.5 \times ( x - 200 ) \\\\ \ and \\ \to R(x) = x \times (D(x) \\\\[/tex]

            [tex]= x \times [ 400 - 0.5\times ( x - 200 )]\\\\ = x\times[400 - 0.5x - 100]\\\\= x\times [300 - 0.5 x]\\\\= 300x - 0.5 x^2[/tex]

[tex]R(x)= 300x- \frac{1}{2} x^2\\\\R'(x)=300-x\\[/tex]

if R'(x)=0

x=300

if  0 < x  < 300  and R(x) > 0 then R(x) for maximum x is = 300

[tex]D(300) = 400 - 0.5\times ( x - 200 )\\\\[/tex]

            [tex]= 400 - 0.5\times ( 300- 200 )\\\\ = 400 - 150+ 100\\\\ = 500 - 150 \\\\=350[/tex]

The rebate must be  : 400 - 350  = 50

Answer:

First 3 terms of the sequence are:

8,9,10

Step-by-step explanation:

The nth term of a sequence is n+7 .

We have to find the first three terms of the sequence

First term(n=1)   = 1+7 =8

Second term(n=2)   = 2+7 =9

Third term(n=3)      = 3+7 =10

Hence, first 3 terms of the sequence are:

8,9,10

Answer:

The shape of a distribution is described by its number of peaks and by its possession of symmetry, its tendency to skew, or its uniformity. (Distributions that are skewed have more points plotted on one side of the graph than on the other.) PEAKS: Graphs often display peaks, or local maximums.

Answer: It is Skewed

Step-by-step explanation: More positive space than negative. So it is positively skewed.