The Westbrook Pharmaceutical Company manufactures atorvastatin pills, designed to lower cholesterol levels. Listed below are the amounts (in mg) of atorvastatin in a random sample of the pills. Use a 0.05 significance level to test the claim that the pills come from a population in which the amount of atorvastatin is equal to 25mg.

24.1, 24.4, 24.3, 24.9, 24.1, 26.2, 25.1, 24.7, 24.4, 25.0, 24.7, 25.1, 25.3, 25.5, 25.5

Based on the triangle inequality theorem, the inequality that gives the range of possible values for x is: 4 < x < 20.

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side.

Therefore, the range of values that is possible for x would be:

12 - 8 < x < 12 + 8

4 < x < 20

The inequality is: 4 < x < 20

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Answer:

(8,-43)

(4,-22)

Step-by-step explanation:

In order for the ordered pair to be a solution of the inequality, you must be able to plug in the y-value of the ordered pair and it must be less than or equal to 0.

For example:

(4,-22)

x=4 ; y=-22

Plug y into the inequality

y≤0

-22≤0

Since the statement is true, I know that (4,-22) must be a solution to the inequality.

Another way to solve this problem is by graphing. If an ordered pair is in the shaded region, it is a solution to the inequality. Attached is a graph of both the inequality and ordered pairs plotted.

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Answer:

Step-by-step explanation:

To determine whether each ordered pair is a solution to the inequality y ≤ 0, we need to check if the y-coordinate of each pair is less than or equal to zero.

Let's check each ordered pair:

(8, -43):

The y-coordinate is -43. Since -43 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(4, -22):

The y-coordinate is -22. Since -22 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(-3, 25):

The y-coordinate is 25. Since 25 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

(-7, 45):

The y-coordinate is 45. Since 45 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

So, the solutions to the inequality y ≤ 0 are:

(8, -43) and (4, -22).

Answer:

12.48

Step-by-step explanation:

1) Use this rule: \(a\times\frac{b}{c} =\frac{ab}{c}\).

\(-\frac{4.8\times-13}{5}\)

2) Simplify 4.8 × -13 to -62.4.

\(-\frac{-62.4}{5}\)

3) Simplify \(\frac{-62.4}{4}\) to -12.48.

\(-(-12.48)\)

4) Remove parentheses.

12.48

Thank you,

Eddie

Answer:

100 cents

I think

Answer: 1.05

Step-by-step explanation:

Let x be the envelope

    y is stamp (1)

==> x+y= 1.10 ($)

the stamps costs $1 more than the envelope, so

x-y=1 --> x=y+1, instead of wards (1), we get

y+1+y= 1.10 -> 2y+1=1.10

                    ->y= 0.05 -> x= 1.05

Answer:

10 tons is 20000 pounds

Step-by-step explanation:

22000 pounds is heavier.

Answer:

They are not equal because 10 tons converted into pounds is 20,000, then you compare 20,000 and 22,000, 22,000 is bigger, and 20,000 is smaller.

Step-by-step explanation:

So, there are 5 widowed people (3+2) and there are 3 females in the widowed category. So:-

3/5*100 = 60%

Steps of reasoning:

Step-by-step explanation:

70 ÷ 3 = 23  1/3

The base length of the parallelogram found using the area formula is 4 units.

What is a parallelogram?

A basic quadrilateral with two sets of parallel sides is known as a parallelogram. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. A parallelogram has adjacent angles that add up to 180 degrees. 360 degrees is the sum of all interior angles.

A parallelogram's area is the area that it takes up in a two-dimensional plane. The parallelogram's area is calculated by multiplying the base length by the height.

Each shape's perimeter can be defined as either the entire length or total distance encircling the object. The entire distance between a parallelogram's boundaries is also known as the parallelogram's perimeter.

Given,

The area of the parallelogram A =36 sq. units

The height of the parallelogram  h = 9 units

We are asked to find the base length b.

Now the formula for the area of the parallelogram is:

A = b * h

36 = b * 9

b = 36/9 = 4 units.

Therefore the base length of the parallelogram, found using the area formula is 4 units.

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The probability of the event for the given odds in favor (4 to 7) is found as 4/11.

To continue solving, we must represent the ratio as a fraction.

Thus, we have the depiction shown below.

Odds ratio equals 4/7

We use the following equation to translate the aforementioned odd's expression into a probability expression.

This is displayed as

P = (Odds + 1)/(Odds).

Replace the unknown values in the equation above.

The following equation is what we have.

P = (4/7)/(4/7 + 1)

Analyze the amount

This results

P = (4/7)/(11/7)

Put the quotient in product form.

P = (4/7) * (7/11)

Evaluate

P = 4/11

Thus, the probability of event for the given odds in favor (4 to 7) is found as 4/11.

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Answer:

At the time the ball was thrown, it was 8 feet above the ground.

h'(x) = -32x + 64 = 0, so x = 2

The ball reaches its maximum height after 2 seconds.

answer: 85+85+85+25



Answer: 0.90

Step-by-step explanation:

If A and B are mutually exclusive events, P(A or B) is the sum of probability of A and probability of B.

P(A or B) = P(A) + P(B)

Given that, P(A) = 0.20 and P(B) = 0.70

Then,

P(A or B) = 0.20 + 0.70

P(A or B) = 0.90

The solution is, : 0.90 is P(A or B).

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

we know that,

If A and B are mutually exclusive events, P(A or B) is the sum of probability of A and probability of B.

P(A or B) = P(A) + P(B)

Given that, P(A) = 0.20 and P(B) = 0.70

Then,

P(A or B) = 0.20 + 0.70

P(A or B) = 0.90

Hence, The solution is, : 0.90 is P(A or B).

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so here we get two outcomes one is 2 and other is 4.

so there is total 2 outcomes.

total no. of possibility is 5

so the probability of waiting between 2 and 4 minutes to use the ATM is 2/5.

The solution to the system of inequalities in interval notation is [-2, 1].

Based on the information provided in the image below, we have the following system of inequalities;

-12 < 3x - 6

-3 ≥ 3x - 6

By adding 6 to both sides of the equation (inequality), we have;

-12 < 3x - 6

-12 + 6 < 3x - 6 + 6

-6 < 3x

-2 < x

x > -2 (flip)

-3 ≥ 3x - 6

-3 + 6 ≥ 3x - 6 + 6

3 ≥ 3x

1 ≥ x

x ≤ 1

Therefore, the solution to the system of inequalities is given by:

-2 < x ≤ 1

In interval notation, we have [-2, 1].

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

9.75

Step-by-step explanation:

-25 = -4p + 19

-25 - 19 = -4p

-39 ÷ -4 = p

9.75 = p

Answer:

As a simplified fraction, the probability that the first randomly taken candy will be red and second will be red again is \(\frac{2}{9}\)

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the candies are selected is not important. So we use the combinations formula to solve this question.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

Desired outcomes:

2 candies from a set of 5. So

\(D = C_{5,2} = \frac{5!}{2!(5-2)!} = 10\)

Total outcomes:

2 candies from a set of 10. So

\(T = C_{10,2} = \frac{10!}{2!(10-2)!} = 45\)

Probability:

\(p = \frac{D}{T} = \frac{10}{45} = \frac{2}{9}\)

As a simplified fraction, the probability that the first randomly taken candy will be red and second will be red again is \(\frac{2}{9}\)

Answer:

D) $8.20

Step-by-step explanation:

82 x 0.1 = 8.2

Answer: $8.20

Step-by-step explanation:

Take 82 and multiply it by 0.10

You can use this equation

82(n)

n will equal 0.10

82(0.10)

$8.20

Therefore, the interest portion of the seventh payment is:7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7 - 7,000.

We have the following payments and their corresponding times of payment:At the end of year 1: $1,000At the end of year 2: $2,000At the end of year 3: $3,000At the end of year 4: $4,000At the end of year 5: $5,000At the end of year 6: $6,000At the end of year 7: $7,000

At the end of year 8: $8,000At the end of year 9: $9,000At the end of year 10: $10,000The present value of these payments is:PMT x [(1 - (1 + r)-n) / r]where PMT is the payment, r is the interest rate per year, and n is the number of years till payment.

For the first payment (end of year 1), the present value is:1,000 x [(1 - (1 + r)-1) / r]which equals

1,000 x (1 - 1 / (1 + r)) / r = 1,000 x ((1 + r - 1) / r) = 1,000

For the second payment (end of year 2), the present value is:2,000 x [(1 - (1 + r)-2) / r]which equals 2,000 x (1 - 1 / (1 + r)2) / r = 2,000 x ((1 + r - 1 / (1 + r)2) / r) = 2,000 x (1 + r) / r2

For the seventh payment (end of year 7), the present value is:

7,000 x [(1 - (1 + r)-7) / r]

which equals

7,000 x (1 - 1 / (1 + r)7) / r = 7,000 x ((1 + r - 1 / (1 + r)7) / r) = 7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7

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Answer:

\((-\infty,2)\)

Step-by-step explanation:

Since \(-3x+6\nless 0\), then \(x\ngtr 2\), therefore, the domain of the function is \((-\infty,2)\).

Answer:

-4z

Step-by-step explanation:

-3z - 1z  Combine like terms

-4z

Answer: the box and whisker plot looks like this, the pink line starts between 8 and 10, the box starts between 10 and 12, the middle is between 14 and 16, the right side of the box is between 18 and 20, and lastly the pink line on the right ends at 22.

Step-by-step explanation: I did the test

Answer:

the first blank is corresponding and the second blank is 105.

Step-by-step explanation:

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The statement about the unit prices which is true is Kitty Kibbles has a lower unit price of $1.30/pound.

The correct answer choice is option D.

Cost of 16-pound bag of Kitty Kibbles = $20.80

Unit price of kitty kibbles = Price / number of pounds

= $20.80 / 16

= $1.30 per pound.

Cost of 8-pound bag of Feline flavor = $11.20

Unit price of feline flavor = Price / number of pounds

= $11.20 / 8

= $1.40 per pound

Ultimately, the unit price of kitty kibbles and feline flavor is $1.30 and $1.40 respectively.

Complete question:

A 16-pound bag of Kitty Kibbles is $20.80. An 8-pound bag of Feline Flavor is $11.20. Which statement about the unit prices is true?

A. Feline Flavor has a lower unit price of $1.40/pound.

B. Feline Flavor has a lower unit price of $1.30/pound.

C. Kitty Kibbles has a lower unit price of $1.40/pound.

D. Kitty Kibbles has a lower unit price of $1.30/pound.

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Answer:

A)  Sequence: -5, -10, -15, -20, -25, -30, -35, -40    cd = -5

B)  Sequence: -1, 2, 5, 8, 11, 14, 17, 20   cd = 3

C)  Sequence:  17, 19, 21, 23, 25, 27, 29, 31   cd = 2

D)  Sequence:  11, 16, 21, 26, 31 , 36, 41, 46   cd = 5

E)  Sequence:  -9, -6, -3, 0, 3, 6, 9, 12  cd = 3

Step-by-step explanation:

A)   Sequence: -5, -10, -15, -20, -25

The common difference (cd) - which is the number that we need to add to each term in order to get the next - is -5

and the next three terms are: -30, -35, -40.

B)  Sequence: -1, 2, 5, 8, 11,

The common difference is 3,   cd = 3

so the next three terms in the sequence are; 14, 17, 20  

C)  Sequence:  17, 19, 21, 23, 25,

the common difference is 2,  cd = 2

so the next three terms in the sequence are:  27, 29, 31  

D)  Sequence:  11, 16, 21, 26, 31

the common difference is 5,  cd = 5

so the next three terms of the sequence are: 36, 41, 46  

E)  Sequence:  -9, -6, -3, 0, 3,

the common difference is 3,   cd = 3

so the next three terms in the sequence are:  6, 9, 12

Answer:

144

Step-by-step explanation:

20²-16²

pythagorean theorem

a²=b²-c²

By looking at the graph, if we move from left to right along the x axis, we go down 3 units on y (-3) for every 4 units x.

Slope: m = y variation/ x variation

m = -3/4

Two paraller lines have the same slope.

So, the slope of the parallel line is also : -3/4