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stiks02 [169]
2 years ago
15

Suppose that a company claims that its chocolate bars weigh 1.6 ounces on average. It took many large samples, and each time the

mean weight of the sample was within the 95% confidence interval. Which of the following would be a reasonable conclusion?
A. The company's chocolate bars weigh fewer than 1.6 ounces on average.
B. The company's chocolate bars weigh 1.6 ounces on average.
C. The company's chocolate bars do not weigh 1.6 ounces on average.
D. The company's chocolate bars weigh more than 1.6 ounces on average.
Mathematics
2 answers:
Nuetrik [128]2 years ago
4 0

Answer:

The company's chocolate bars weigh 1.6 ounces on average.

Step-by-step explanation:

We are given that  a company claims that its chocolate bars weigh 1.6 ounces on average.

It took many large samples, and each time the mean weight of the sample was within the 95% confidence interval.

95% confidence level means a range of values that you can be 95% certain contains the true mean of the population.

Thus by definition we can say that The company's chocolate bars weigh 1.6 ounces on average.

Hence Option B is correct.

adell [148]2 years ago
4 0

Answer:

The company's chocolate bars weigh 1.6 ounces on average

Step-by-step explanation:

apex

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It is recommended that adults consume at least 1,000 mg of calcium every day. One ounce of whole milk contains about 25 mg of ca
gregori [183]

Given:

It is recommended that adults consume at least 1,000 mg of calcium every day.

25x+200y\geq 1000

Step-by-step explanation:

Let, x be the quantity of milk in ounces and y be the quantity of cheddar cheese in ounces.

A person meets the recommendation, if

25x+200y\geq 1000

For option A,

Substitute x=50 and y=2 in the given inequality.

25(50)+200(2)\geq 1000

1250+400\geq 1000

1650\geq 1000

This statement is true. So, option A is correct.

Similarly,

For option B,

Substitute x=0 and y=4.5 in the given inequality.

25(0)+200(4.5)\geq 1000

900\geq 1000

This statement is false. So, option B is incorrect.

For option C,

Substitute x=10 and y=3 in the given inequality.

25(10)+200(3)\geq 1000

850\geq 1000

This statement is false. So, option C is incorrect.

For option D,

Substitute x=39 and y=0 in the given inequality.

25(39)+200(0)\geq 1000

975\geq 1000

This statement is false. So, option D is incorrect.

Therefore, the correct option is only A.

3 0
2 years ago
$16.46 is what percent of $634.40?
tia_tia [17]

Answer:

104.42224

Step-by-step explanation:

16.46% of 634.40 = 0.1646 × 634.40 = 104.42224

3 0
2 years ago
Read 2 more answers
() and () are inverses of one another and drawn on the same graph with the same scale on both the horizontal and vertical axis.
Gelneren [198K]

Answer: Option A.

Step-by-step explanation:

We have the functions f(x) and g(x), that are inverses between them.

This means that if:

f(x) = y

then:

g(y) = x.

now, remember that:

When we have a point (x, y), and we reflect it over the line y = x, our new point will be (y, x).

So before we whe had:

f(x) = y.

and now in that same place, we have:

g(y) = x.

So the old graph of f(x) now coincides with the graph of g(x). (And the old graph of g(x) now coincides with the graph of f(x) )

So A is true.

B) This depends on the function:

if we have f(x) = x  + 1.5

then f(0) = 1.5

now we want that:

g(1.5) = 0, then we can write:

g(x) = x - 1.5

Now f(x) and g(x) are inverses, and we would have that:

f(x) = g(x) + 3.

So f(x) is g(x) translated up by 3 units, but this is a particular case, not a general one, so B is not always true.

C and D) When we do rotations of 90° or 180°, we are effectively changing the quadrant of our point. so rotations will cause not only changes as the reflection over the x = y line, those will also cause changes in the sign of our variables, so, while for some functions f(x) and g(x) we can have that the rotations will map one into the other, this is not the general case.

6 0
2 years ago
A person invests 9500 dollars in a bank. The bank pays 5.75% interest compounded quarterly. To the nearest tenth of a year, how
sweet [91]

Answer:

4.9 years

Step-by-step explanation:

Future value is the sum of amount invested and its compounded interest for a specific period of time and on a specific interest rate.

Investment = Present value = $9,500

Future value = $12,600

To find the numbers of years we will use following formula

Future value = Present value x ( 1 + r )^n

r = interest rate = 5.75%

n = number of periods = ?

Placing values in the formula

$12,600 = $9,500 x ( 1 + 5.75%/4 )^n

$12,600 / $9,500 = 1.014375^n

1.3263 = 1.014375^n

Log 1.3263 = n log 1.014375

n = Log 1.3263 / log 1.014375

n = 19.7856 Quarters

n = 4.9 years

6 0
2 years ago
A supermarket has two customers waiting to pay for their purchases at counter I and one customer waiting to pay at counter II. L
Pachacha [2.7K]

Answer:

b. 0.864

Step-by-step explanation:

Let's start defining the random variables.

Y1 : ''Number of customers who spend more than $50 on groceries at counter 1''

Y2 : ''Number of customers who spend more than $50 on groceries at counter 2''

If X is a binomial random variable, the probability function for X is :

P(X=x)=(nCx)p^{x}(1-p)^{n-x}

Where P(X=x) is the probability of the random variable X to assume the value x

nCx is the combinatorial number define as :

nCx=\frac{n!}{x!(n-x)!}

n is the number of independent Bernoulli experiments taking place

And p is the success probability.

In counter I :

Y1 ~ Bi (n,p)

Y1 ~ Bi(2,0.2)

P(Y1=y1)=(2Cy1)(0.2)^{y1}(0.8)^{2-y1}

With y1 ∈ {0,1,2}

And P( Y1 = y1 ) = 0 with y1 ∉ {0,1,2}

In counter II :

Y2 ~ Bi (n,p)

Y2 ~ Bi (1,0.3)

P(Y2=y2)=(1Cy2)(0.3)^{y2}(0.7)^{1-y2}

With y2 ∈ {0,1}

And P( Y2 = y2 ) = 0 with y2 ∉ {0,1}

(1Cy2) with y2 = 0 and y2 = 1 is equal to 1 so the probability function for Y2 is :

P(Y2=y2)=(0.3)^{y2}(0.7)^{1-y2}

Y1 and Y2 are independent so the joint probability distribution is the product of the Y1 probability function and the Y2 probability function.

P(Y1=y1,Y2=y2)=P(Y1=y1).P(Y2=y2)

P(Y1=y1,Y2=y2)=(2Cy1)(0.2)^{y1}(0.8)^{2-y1}(0.3)^{y2}(0.7)^{1-y2}

With y1 ∈ {0,1,2} and y2 ∈ {0,1}

P( Y1 = y1 , Y2 = y2) = 0 when y1 ∉ {0,1,2} or y2 ∉ {0,1}

b. Not more than one of three customers will spend more than $50 can mathematically be expressed as :

Y1 + Y2 \leq 1

Y1 + Y2\leq 1 when Y1 = 0 and Y2 = 0 , when Y1 = 1 and Y2 = 0 and finally when Y1 = 0 and Y2 = 1

To calculate P(Y1+Y2\leq 1) we must sume all the probabilities that satisfy the equation :

P(Y1+Y2\leq 1)=P(Y1=0,Y2=0)+P(Y1=1,Y2=0)+P(Y1=0,Y2=1)

P(Y1=0,Y2=0)=(2C0)(0.2)^{0}(0.8)^{2-0}(0.3)^{0}(0.7)^{1-0}=(0.8)^{2}(0.7)=0.448

P(Y1=1,Y2=0)=(2C1)(0.2)^{1}(0.8)^{2-1}(0.3)^{0}(0.7)^{1-0}=2(0.2)(0.8)(0.7)=0.224

P(Y1=0,Y2=1)=(2C0)(0.2)^{0}(0.8)^{2-0}(0.3)^{1}(0.7)^{1-1}=(0.8)^{2}(0.3)=0.192

P(Y1+Y2\leq 1)=0.448+0.224+0.192=0.864\\P(Y1+Y2\leq 1)=0.864

7 0
2 years ago
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