at the audtions, 40 studens tried out for the school show choir, but only 12 will be chosen. How many different ways can the show choir be formed

Answer:

99% confidence interval for the proportion of all customers in Tacoma, Washington, who prefer boot-cut jeans is [0.225 , 0.405].

Step-by-step explanation:

We are given that a marketing researcher examined sales receipts for a random sample of 178 customers who purchased jeans from the firm’s Tacoma store. 56 of the customers in the sample purchased boot-cut jeans.

Firstly, the Pivotal quantity for 99% confidence interval for the population proportion is given by;

                           P.Q. =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of customers who purchased boot-cut jeans = [tex]\frac{56}{178}[/tex] = 0.315

           n = sample of customers = 178

           p = population proportion of customers who prefer boot-cut jeans

Here for constructing 99% confidence interval we have used One-sample z test for proportions.

So, 99% confidence interval for the population proportion, p is ;

P(-2.58 < N(0,1) < 2.58) = 0.99  {As the critical value of z at 0.5% level

                                                 of significance are -2.58 & 2.58}  

P(-2.58 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 2.58) = 0.99

P( [tex]-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99

P( [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99

99% confidence interval for p = [ [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex], [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]]

    = [ [tex]0.315-2.58 \times {\sqrt{\frac{0.315(1-0.315)}{178} } }[/tex] , [tex]0.315+2.58 \times {\sqrt{\frac{0.315(1-0.315)}{178} } }[/tex] ]

    = [0.225 , 0.405]

Therefore, 99% confidence interval for the proportion of all customers in Tacoma, Washington, who prefer boot-cut jeans is [0.225 , 0.405].

The interpretation of the above confidence interval is that we are 99% confident that the proportion of all customers in Tacoma, Washington, who prefer boot-cut jeans will lie between 0.225 and 0.405.

Answer:

A.

Step-by-step explanation:

The equation of circle is :

(x−a)² + (y−b)² = r²

So the equation is

(x-3)² + (y-(-2))² = (6)²

Where center = (a,b) = (3,-2) and

Radius = r = 6

Answer it would be 212 :)

Step-by-step explanation:

The measure of arc CED in the circle given is: D. 212°.

Measurement of an arc of a circle = measure of its central angle.

Thus:

Measure of arc CED = angle CBE + angle EBD

Substitute

Measure of arc CED = 52 + 160

Measure of arc CED = 212°

Therefore, the measure of arc CED in the circle given is: D. 212°.

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Answer:

True

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer:

  12 1/2

Step-by-step explanation:

Multiply the equation by the inverse of the coefficient of a.

  5 = (2/5)a

  5(5/2) = (2/5)(5/2)a

  25/2 = a

  12 1/2 = a . . . . written as a mixed number

The solution is 12 1/2.

Answer:

12 1/2

Step-by-step explanation:

Answer:

84

Step-by-step explanation:

We simply plug in 1.75 for x into y = 48x, and when we do so we get y = 48 * 1.75 = 84 cups of coffee. Hope this helps!

Answer:

B) 84

Step-by-step explanation:

48 times x is the cups of coffee sold in x hours.

if x = 1.75, then you times 48 by 1.75

48 x 1.75 = 84

Answer:

48∛9 ft²

Step-by-step explanation:

The length (L) and width (W) are given by:

[tex]L = 4\sqrt[3]{24}\\ W= 6\sqrt[3]{3}[/tex]

Since this is a rectangular region, the area is given by:

[tex]A=L*W=L \\A=4\sqrt[3]{24}* 6\sqrt[3]{3}\\A=24\sqrt[3]{72}\ ft^2[/tex]

The answer can be further simplified by factoring as follows:

[tex]A=24\sqrt[3]{72} = \\A=24\sqrt[3]{2*2*2*3*3}= 24\sqrt[3]{2^3*9}\\A=48\sqrt[3]{9}\ ft^2[/tex]

The exact area is its simplest form is 48∛9 ft²

Answer:

she will cover a distance of 0.85 km.

Step-by-step explanation:

We have,

Grace swam 0.6 kilometres during her first week of training and 0.25 kilometres during her second week of training.

It is required to find total distance covered by her in all.

It can be calculated simply adding the distance covered in first and second week of training. So,

Total distance, D = 0.6 km +0.25 km = 0.85 km

Hence, she will cover a distance of 0.85 km.

Answer:

SOS

Step-by-step explanation:

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Answer:

it is a

Step-by-step explanation:

its the only possible answer. :)

let me know if i am wrong!

Answer: D(x) = 2kg/h*x

where x is the number of hours.

Step-by-step explanation:

The information that we have is:

in 5 hours, we can prepare 10kg of dough.

With this, we can find the rate per hour, to do this we find the quotient:

R = 10kg/5h = 2kh/h

This meeans that in one hour, we can make 2kg of dough.

Then, in x hours, we can make x times 2kg of dough, then the equation will be:

D(x) = 2kg/h*x

where x is the number of hours.

Step-by-step explanation:

Refer The attachment.

Answer:

The probability of the next two customers both select key lime pie is 1/15

Step-by-step explanation:

No. of slices of cakes = 3

No. of key lime pies = 3

No. of ice cream sundaes = 4

Total deserts = 3+3+4=10

We are supposed to find The probability of the next two customers both select key lime pie

Probability of selecting key lime pie by first customer =[tex]\frac{3}{10}[/tex]

So,Total deserts =10-1=9

No. of key lime pies = 3-1=2

So,Probability of selecting key lime pie by second customer = [tex]\frac{2}{9}[/tex]

So,the probability of the next two customers both select key lime pie=[tex]\frac{3}{10} \times \frac{2}{9} =\frac{1}{15}[/tex]

Hence the probability of the next two customers both select key lime pie is 1/15

Answer:

On a coordinate plane, a line (y = mx + b) goes through point A(0, 4), then it has point A as y-intercept (the point with x component is 0).  And it goes through B(-2, 0).

Denote that line: y = mx + b

=> m*0 + b = 4 (it goes through A(0, 4))

=> b = 4

=> m*2 + 4 = 0 (it goes through B(-2, 0))

=> m = -2

=> Slope m = 2 and y-intercept (0, 4)

Hope this helps!

:)

Answer:

Slope: 2

y-intercept: 4

Step-by-step explanation:

m = (0-4)/(-2-0) = -4/-2 = 2

y -4 = 2(x - 0)

y = 2x + 4

Answer:

A tangent to a circle is a straight line which touches the circle at only one point.

Step-by-step explanation:

This point is called the point of tangency. The tangent to a circle is perpendicular to the radius at the point of tangency.

Step-by-step explanation:

Square root 8 = 2 square root 2

Answer:

  50√3 ≈ 86.6 m

Step-by-step explanation:

The geometry can be modeled by a right triangle with the height of the kite being the leg opposite the 60° angle. The hypotenuse has the given length of 100 m.

The mnemonic SOH CAH TOA reminds you that the relation between angles and the sides of interest here is ...

  Sin = Opposite/Hypotenuse

  sin(60°) = (kite height)/(100 m)

  kite height = (100 m)·sin(60°) = (100 m)(√3)/2

  kite height = 50√3 m ≈ 86.6 m

Answer:

multiply 12*7

Step-by-step explanation:

Answer:

84 m²

Step-by-step explanation:

12 times 7 (for a rectangle)

Answer:

[tex] \boxed{Circumference \: of \: circle = 572 \: mm} [/tex]

Step-by-step explanation:

Radius (r) = 91 mm

[tex]Circumference \: of \: circle = 2\pi r \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times \frac{22}{7} \times 91 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 22 \times 13 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 44 \times 13\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 572 \: mm[/tex]

Answer:

Step-by-step explanation:

Answer:

84 meters

Step-by-step explanation:

5 x 6 = 30 hypotenuse side not shown

3 x 4 ÷ 2 x 2 = 12 red (both ends)

3 x 6 = 18 green side

6 x 4 = 24 blue side

Answer:

(A)[tex]4X10^{12}[/tex]

Step-by-step explanation:

Given the quotient:

[tex]\dfrac{6*10^8}{1.5*10^{-4}}[/tex]

To evaluate, we first separate the given expression as follows.

[tex]=\dfrac{6}{1.5}X\dfrac{10^8}{10^{-4}}[/tex]

Next, we apply the division law of indices to the powers of 10.

Division Law of Indices: [tex]\frac{a^x}{a^y}=a^{x-y}[/tex]

[tex]=4X10^{8-(-4)}\\=4X10^{8+4}\\=4X10^{12}[/tex]

Therefore, our quotient is [tex]4X10^{12}[/tex].

The correct answer is A.

Answer:

Length of arc: 6π

Step-by-step explanation:

~ Let us answer this question in terms of π, remaining so ~

1. Assume that this is a complete circle, for the moment being. The chord with length of 12 units would act as the diameter, and using that information we could determine the circumference of this complete circle...which will help us in the future. Apply the formula π * d as such: π * 12 ⇒ 12π to get the circumference as 12π.

2. Knowing that the length of the complete circle's circumference is 12π, this arc is part of a semicircle, meaning that it's value would be half of that of the complete circle's circumference, or in other words: 12π/2 ⇒ Answer ~ Length of arc: 6π

Answer:Length of arc: 6π

Step-by-step explanation:

Step-by-step explanation:

Use double and triple angle identities:

sin(2x) + cos(3x)

2 sin x cos x + 4 cos³x − 3 cos x

Answer:

$638.14

Step-by-step explanation:

Our equation is [tex]p*(1+x)^{t}[/tex], with p being the starting amount, x being the interest rate, and t being the time. Plugging our variables in, we get

[tex]500*(1+0.05)^{5}[/tex] = around 638.14

Josh will receive $638 at the end of the term.  

Josh invests $500 in a 5-year fixed interest savings bond that pays 5% per annum,

Cost price is that price for buyer which he pays to seller for an object or product.

Principle amount = $500
Rate = 5 %
Tenure = 5 years

Amount = principle (1+R)^tenure

= 500 (1+5/100)^5
= $638

Thus, Josh will receive $638 at the end of the term.  

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Hello there!

$500 invested at 4% compounded annually for 10 years

time: 10 years

compound: annually

interest: 4%

y = 500(1.04)^10

1.04^10 = 1.48

500 x 1.48 = 740

Value after 10 years: $740

Answer:

  $740.12

Step-by-step explanation:

The amount is multiplied by 1.04 each year, so after 10 years, the balance will be ...

  $500(1.04^10) = $740.12

48%

Step-by-step explanation:

add the ratio together which is 25

pick the ratio of boy

divide 12 by 25 and multiply 100

12/25×100= 48%

Answer:

48%

Step-by-step explanation:

b/g=12/13

so b/12=g/13=k

b=12k

g=13k

so b+g=25k so k=b+g/25

b=12*(b+g)/25=12*4*(b+g)/25*4=48(b+g)/100

so 48%  are boys

Step-by-step explanation:

To randomly pick the 10 people needed in the sample, it can be done this way

1. Define the population: in this case, the total population is 280 and expressed as N and since we are interested in everyone in the neighborhood with no exclusion, our sampling frame is thus 280 people.

2. Choose your sample size: As given in the question, our sample size is to randomly pick 10 people expressed as n.

3. List your population and then assign numbers to each unit in the population: Getting the list of all 280 people in the population and then assigning numbers from 1 to N - in this case 1 - 280.

4. Then find random numbers using the random number table to help select your 10 people sample making them a representative of the population in residence.

Answer:

C: Lines r and s and lines t and u must be parallel.

Step-by-step explanation:

The true statement is (c) Only lines r and s must be parallel.

From the figure, we can see that:

Lines r and s point in the same direction, while lines t and u point in the same direction

If angle 8 = angle 10 and angle 1 = angle 7, then it means that:

Lines r and s must be parallel.

Line t and u may or may not be parallel.

Hence, the true statement is (c) Only lines r and s must be parallel.

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