MATHEMATICS HIGH SCHOOL

Grandma Gertrude's Chocolates, a family owned business, has an opportunity to supply its product for distribution through a large coffee house chain. However, the coffee house chain has certain specifications regarding cacao content as it wishes to advertise the health benefits (antioxidants) of the chocolate products it sells. In order to determine the mean percentage of cacao in its dark chocolate products, quality inspectors sample 36 pieces. They find a sample mean of 60% with a standard deviation of 8%. What is the correct value of t to construct a 90% confidence interval for the true mean percentage of cacao? (Round to the nearest thousandth.)Select Answer:
A. (0.577, 0.623)
B. (0.539, 0.561)
C. (0.527, 0.573)
D. (0.589, 0.611)

Answers

Answer 1

Answer:

Answer with explanation:

Given : Sample size : n = 36

Significance level for 90% confidence : $\alpha: 1-0.9=0.1$

Sample mean : $\overline{x}=0.60$

Standard deviation : $\sigma=0.08$

By using standard normal table for t-values,

Critical t-value : $t_((n-1, \alpha/2))=t_((35,\ 0.05))=1.690$

Thus, the correct value of t to construct a 90% confidence interval for the true mean percentage of cacao : $t_((35,\ 0.05))=1.690$

Confidence interval for population mean :

$\overline{x}\pm t_((n-1, \alpha/2))(\sigma)/(√(n))\n\n=0.60\pm(1.69)(0.08)/(√(36))\n\n=0.60\pm0.0225333333333\n\n\approx0.60\pm0.023\n\n=(0.60-0.023,\ 0.60+0.023)=(0.577,\ 0.623)$

Hence, A is the correct answer .

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The sum of three number is 126. The third number is 4 times the second. The second number is 6 less than the first. What are the numbers?

Answers

The numbers are 26, 20, and 80.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Threenumbers:

First = a

Second = b

Third = c

Now,

a + b + c = 126 ____(1)

c = 4b ____(2)

b = a - 6 _____(3)

From (1), (2), and (3) we get,

a + (a - 6) + 4b = 126

a + a - 6 + 4b = 126

2a + 4b = 126 + 6

2a + 4b = 132

2a + 4(a - 6) = 132

2a + 4a - 24 = 132

6a = 132 + 24

6a = 156

a = 26

Now,

a = 26

b = a - 6 = 20

c = 4b = 4 x 20 = 80

Thus,

The numbers are 26, 20, and 80.

Learn more about expressions here:

brainly.com/question/3118662

#SPJ2

Step-by-step explanation:

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ALGEBRA II

Ingrid H.

asked • 04/02/20

The sum of three numbers is 126 . The third number is 3 times the first. The second number is 6 more than the first. What are the numbers?

The sum of three numbers is 126

. The third number is 3

times the first. The second number is 6

more than the first. What are the numbers?

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1 Expert Answer

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Mackenzie K. answered • 04/02/20

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Lets define a=1st number, b=2nd number, and c=3rd number

We know that a+b+c=126

We also know that the second number is 6 more than the first, so we can represent this as b=a+6

We also know that the third number is 3 times the first which can be represented as c=3a

We can plug these new values into our original equation and get:

a+(a+6)+(3a)=126

2a+6+3a=126 COMBINE LIKE TERMS

5a+6=126

5a=120

a=24

Our first number is 24.

Our second number is 6 more than our first number, so the second number is 24+6=30

Our third number is 3 times the first number, so the third number is 3(24)=72

We can check by plugging these numbers in for a, b, and c in our original equation

a+b+c=126

24+30=72=126

126=126

Evaluate the summation of 20 times 0.5 to the n minus 1 power, from n equals 3 to 12.

Answers

Answer:

The sum of the series is 9.99

Step-by-step explanation:

We are given the series $\sum_(n=3)^(12)20(0.5)^(n-1)$ .

So, $a_(n)=20(0.5)^(n-1)$ , where n=3 to 12

Then, we have,

$1.\ a_(3)=20(0.5)^(3-1)\na_(3)=20(0.5)^(2)\na_(3)=5$

$2.\ a_(4)=20(0.5)^(4-1)\na_(4)=20(0.5)^(3)\na_(4)=2.5$

Thus, the common ratio is $r=(2.5)/(5)=0.5$

Since, the sum of first n terms of a series is $S=(a_(1)(1-r^(n)))/(1-r)$ .

As n = 3 to 12, then the number of terms = 10, first term=a₃= 5 and r= 0.5

So, the sum of 10 terms is $S=(5(1-(0.5)^(10)))/(1-0.5)$

i.e. $S=(5(1-0.00098))/(0.5)$

i.e. $S=(5* 0.99902)/(0.5)$

i.e. $S=(4.9951)/(0.5)$

i.e. S = 9.99

Hence, the sum of the series is 9.99

Answer: 9.99

Step-by-step explanation:

I just took the quiz!

A 25 kg rock , is raised to the top of a hill 10 m high. What is the Potential Energy of the rock ?

Answers

Answer:

2450 J

Step-by-step explanation:

mass(m)=25kg

height(h)=10m

gravity(g)=9.8

now,

PE=mgh

=25×10×9.8

=2450J

ANS

What are the zeros of the function F of X equals X squared -13 X -30

Answers

Hello,

x²-13x-30=0
==>x²-15x+2x-30=0
==>x(x-15)+2(x-15)=0
==>(x-15)(x+2)=0
==>x=15 or x=-2

What is -a^-2 if a=-5

Answers

Answer:

the answer is 25

Step-by-step explanation:

cause -5 times -5 is 25 cause negative times negative is positive, and 5 times 5 is 25.

Well, -2 times -2 is 4 and 4 times -2 is -8 times -2 is 16 and 16 times -2 is -32 and -32 times -2 is 64 and -64 times -2 is 128

So 128

Solve for p, w = Q+P
-------
Q-QP

Answers

alright, here it is
w=(q+p)/(q-pq)
factor out the q in the bottom part

w=(q+p)/[(q)(1-p)]
multiply both sides by q
wq=(q+p)/(1-p)
add 1 to both sides, but add (1-p)/(1-p) to the right side since that equals 1
wq+1=(q+1+p-p)/(1-p)=(q+1)/(1-p)
multiply both sdies by (1-p)
(wq+1)(1-p)=q+1
divide both sdies by (wq+1)
1-p=(q+1)/(wq+1)
subtract 1 from both sdies
-p=[(q+1)/(wq+1)]-1
multiply by -1
p=-[(q+1)/(wq+1)]+1 or
$p= -((q+1))/((wq+1))+1$

Remove the extra parentheses.
w=q+p/q−qp

Since p is on the right-hand side of the equation switch the sides so it is on the left-hand side of the equation.
q+p/q−qp=w

Factor q out of q−qp.
q+p/q⋅(1−1p)=w

Rewrite −1p as −p.
q+p/q⋅(1−p)=w

Multiply q by 1−p to get q(1−p).
q+p/q(1−p)=w

Multiply each term in the equation by (1−p).
q+p/q(1−p)⋅(1−p)=w⋅(1−p)

1+p/q=w−wp

Since −wp contains the variable to solve for, move it to the left-hand side of the equation by adding wp to both sides.
1+p/q+wp=w

Find the LCD of the terms in the equation.
It is q

Multiply each term in the equation by q in order to remove all the denominators from the equation.
p+wpq=−q+wq

Solve the equation.
p=q(w−1)/qw+1

Answer:
p=q(w−1)/qw+1

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