A dolphin was swimming 3 feet below sea level. The number line shows the location of the dolphin. It then dove down 6 feet. Describe how to use the number line to find the new location of the dolphin.

Answer:

1/6 or 16 2/3 %

Step-by-step explanation:

There are 6 possibilities, 10, 10, 10, 11, 11, 12 out of 36 total possible outcomes.

6/36

1/6

Answer:

Step-by-step explanation:

Range is largest value - smallest value. 12-3=9! EZ

Given:

Let

So square of both side is:

Here :

So the given statement is is false.

Answer:

28098576000

Step-by-step explanation:

The equation for time is URM:

\(time = \frac{distance}{speed \: (rate)} \)

\(t(s) = \frac{4s {}^{3} - 6s {}^{2} + 4s + 14}{s + 1} = \frac{2(s + 1)(2s {}^{2} - 5s + 7) }{s + 1} \\ t(s) = 2(2s {}^{2} - 5s + 7) \\ t(s) = 4s {}^{2} - 10s + 14\)

Answer:

Volume V = 18.735 m3

Step-by-step explanation:

hope this helps

After considering all the given data we conclude that the area of the given figure is 80, under the condition that the given figure is a rhombus.

Let us name the rhombus as ABCD, now looking at the figure we can detect that there are two diagonals crossing each other making a point  E, this allows the  two  diagonals to split in four smaller lines that are congruent in value
Then
Line AE = 5ft and Line ED = 5ft (because of congruency)
Line CE = 8ft and Line EB = 8ft(because of congruency)
Therefore,
Now we know that the diagonals
AD = 10ft
CB = 18 ft
The area of a rhombus can be evaluated applying the formula
Area = (d1 × d2) / 2,
Here,
d1 and d2 = lengths of the diagonals.
For this case, the diagonals are 10 ft and 16 ft.
Then, the area of the rhombus is
(10 × 16) / 2
= 80
Then, the area of the given figure is 80.
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A) The percentage of nurses completing the task in less than 5 minutes is approximately 4.75%. b) The percentage of nurses requiring more than 10 minutes to complete the task is approximately 50%

To solve this problem, we will use the properties of the normal distribution and z-scores. Given that the average completion time for the task is 10 minutes and the standard deviation is 3 minutes, we can proceed with the following calculations:

a) To find the percentage of nurses completing the task in less than 5 minutes, we need to calculate the z-score corresponding to a time of 5 minutes and then determine the area under the normal distribution curve to the left of that z-score.

The z-score formula is given by: z = (x - μ) / σ

where x is the time in question (5 minutes), μ is the mean (10 minutes), and σ is the standard deviation (3 minutes).

z = (5 - 10) / 3 = -5/3 ≈ -1.67

Using a standard normal distribution table or a calculator, we can find that the area to the left of -1.67 is approximately 0.0475 or 4.75%. Therefore, approximately 4.75% of nurses complete the task in less than 5 minutes.

b) To find the percentage of nurses requiring more than 10 minutes to complete the task, we calculate the z-score for a time of 10 minutes and find the area to the right of that z-score.

z = (10 - 10) / 3 = 0

The area to the right of z = 0 is 0.5 or 50%. Therefore, approximately 50% of nurses require more than 10 minutes to complete the task.

c) To find the probability that a nurse will take between 8 and 12 minutes to complete the task, we need to find the area under the curve between the z-scores for 8 and 12 minutes.

z1 = (8 - 10) / 3 = -2/3 ≈ -0.67

z2 = (12 - 10) / 3 = 2/3 ≈ 0.67

Using a standard normal distribution table or a calculator, we find the area to the left of z = -0.67 as approximately 0.2514, and the area to the left of z = 0.67 as approximately 0.7514. Therefore, the probability that a nurse will take between 8 and 12 minutes to complete the task is approximately 0.7514 - 0.2514 = 0.5 or 50%.

d) To find the task times that qualify staff nurses for additional training, we need to determine the z-score corresponding to the slowest 20% of completion times and then convert it back to the original time scale.

The z-score corresponding to the slowest 20% is found by locating the z-score that has an area of 0.2 to its left. Using a standard normal distribution table or a calculator, we find this z-score to be approximately -0.84.

Now, we can convert the z-score back to the original time scale:

z = (x - μ) / σ

-0.84 = (x - 10) / 3

Solving for x, we have:

-0.84 * 3 = x - 10

-2.52 = x - 10

x = 10 - 2.52

x ≈ 7.48

Therefore, the task times that qualify staff nurses for additional training are approximately greater than 7.48 minutes.

In summary:

a) The percentage of nurses completing the task in less than 5 minutes is approximately 4.75%.

b) The percentage of nurses requiring more than 10 minutes to complete the task is approximately 50%

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Question 6

\(\left(\frac{-7-2}{2}, \frac{-10-3}{2} \right)=(-4.5, -6.5)\)

Question 7

\(\left(\frac{-4+8}{2}, \frac{-3+2}{2} \right)=(2, -0.5)\)

Answer: It will  take you about 61 years for you to reach your goal.

Step-by-step explanation:

We will represent this situation by an exponential function. So if you earn 5% yearly then we could represent it by 1.05.So in exponential function we need to find the initial value and the common difference and in this case the common difference is 1.05 and the initial value or amount is 50,000 dollars.

We could represent the whole situation by the equation.

y= \(50,000(1.05)^{x}\)  where x is the number of years. so if you aspire to have 1,000,000 in some years then we will put in 1 million dollars for y and solve for x.

1,000,000 = 50,000(1.05)^x   divide both sides by 50,000

20 = (1.05)^x

x= 61.40

Answer:

1C
2A
3D
4E
5B

Step-by-step explanation:

1) Scale factor -5    EXPANSION (since is higher than 1) TO THE OPPOSITE SIDE (Since is negative)

2) Scale factor 1/2    CONTRACTION  (since is lower than 1) TO THE SAME SIDE (Since is positive)

3) Scale factor -0.4    CONTRACTION  (since is lower than 1) TO THE OPPOSITE SIDE (Since is negative)

4) Scale factor 3/2 EXPANSION (since is higher than 1) TO THE SAME SIDE (Since is positive)

5) scale factor 1  NOT a dilatation since factor is positive 1.

Answer:

1 - D

2 - A

3 - C

4 - E

5 - B

Step-by-step explanation:

Using the definition of scale factor as the ratio of corresponding lengths of two similar figures, we can determine the expansion or contraction of a figure based on whether the scale factor is greater than 1 or less than 1, respectively.

Based on this definition, we can identify the scale factor in Column A as follows:

1. Scale factor = -5

This is a contraction (opposite side) because the scale factor is negative, indicating that the image is reflected across the line of reflection.

2. Scale factor = 1/2

This is a contraction (same side) because the scale factor is less than 1.

3. Scale factor = -0.4

This is an expansion (opposite side) because the scale factor is negative and less than -1, indicating that the image is reflected across the line of reflection and expanded.

4. Scale factor = 3/2

This is an expansion (same side) because the scale factor is greater than 1.

5. Scale factor = 1

This is not a dilation because the scale factor is equal to 1, which means that the two figures are the same size and shape.

The true statement for the function p(x) is p(-2) and p(0) cannot be compared as p(0) is undefined. Option D is correct.

The given function is a logarithmic function and it is undefined at x = 0.

First, let us understand the logarithmic function:

A logarithmic function is a function of the form which is read as “ y equals the log of x, base b” or “ y equals the log, base b, of x.” In both forms, x > 0 and b > 0, b ≠ 1.

We are given:

p(x) = log 5x

substitute x = 0 in the above equation, we will get;

p(0) = log 5 × 0

p(0) = log 0

p(0) = undefined

Thus, the true statement for the function p(x) is p(-2) and p(0) cannot be compared because p(0) is undefined. Option D is correct.

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Using the equation of the function p(x) below, determine which of the statements below is true. Show your work.

Captionless Image

p(-2) > p(0)

p(-2) < p(0)

p(-2) and p(0) cannot be compared because p(-2) is undefined.

p(-2) and p(0) cannot be compared because p(0) is undefined.

The reasons for the steps are given below.

The value of x is -4.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

-2(4x + 3) = 26

[ The distributive property of multiplication over addition ]

-2(4x) + -2(3) = 26

-8x - 6 = 26

[ Adding 6 on both sides ]

-8x - 6 + 6 = 26 + 6

-8x = 32

[ Divide -8 into both sides ]

-8x/-8 = 32/-8

x = -4

Thus,

The reasons for the steps are given above.

x = -4

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Each friend had originally 13 action figures before buying 11 more.

Given that there are 5 friends and each of them has x action figures in his or her collection. When they buy 11 more action figures, the total number of action figures they will have is 120.

a) We need to find an equation that models the problem. Let x be the original number of action figures that each friend had.

Therefore, the total number of action figures that each friend will have after purchasing 11 more is x + 11.

The total number of action figures will be 5(x + 11) = 5x + 55.

Now, according to the problem,5x + 55 = 120

This is our equation that models the problem.

b) We have to solve the equation 5x + 55 = 120 to find the original number of action figures, x, that each friend had before buying 11 more action figures.

5x + 55 = 120

5x = 120 - 55 (subtract 55 from both sides)

5x = 65x = 13

Therefore, each friend had originally 13 action figures before buying 11 more.

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Answer:

1. 57/16 or 3.5625 ounces of water

8 : 4.75

1 : 19/32  -----> divide both by 8

19/32x6=57/16 = 3.56 ounces

2. 2.4375 ounces of other ingredients

6-3.5625=2.4375

The contractor has a maximum of 29 hours (rounded down) to complete the job while keeping the total cost under $2000.

To find the number of hours the contractor has for the job while keeping the total cost under $2000, we can use the given cost model equation: C = 43H + 750.

Since the owner wants the total cost to be under $2000, we can set up the inequality:

43H + 750 < 2000

Now, let's solve this inequality for H, the number of hours:

43H < 2000 - 750

43H < 1250

Dividing both sides of the inequality by 43:

H < 1250/43

To determine the maximum number of hours the contractor has for the job, we need to round down the result to the nearest whole number since the contractor cannot work a fraction of an hour.

Using a calculator, we find that 1250 divided by 43 is approximately 29.07. Rounding down to the nearest whole number, we get:

H < 29

Using the cost model equation C = 43H + 750, where C represents the total cost and H represents the number of hours, we set up the inequality 43H + 750 < 2000 to satisfy the owner's requirement of a total cost under $2000.

By solving the inequality and rounding down to the nearest whole number, we find that the contractor has a maximum of 29 hours to complete the job within the specified cost limit.

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Answer:

a. The initial amount was 10 mg.

b. The percentage of the drug leaving the body each hour is 0.18, this is 18% per hour.

c. The amount of drug that remains in the body 6 hours after dosing is 3.04 mg.

d.  The time until only 1 mg of the drug remains in the body is 11.6 hours.

Step-by-step explanation:

You know that at time t hours after taking the cough suppressant hydrocodone bitartrate, the amount, A, in mg, remaining in the body is given by :

\(A=10*(0.82)^{t}\)

a. The initial quantity occurs when time t is the initial t, that is, t is equal to 0. Then:

\(A=10*(0.82)^{t}=10*(0.82)^{0}=10*1\\\)

A=10

The initial amount was 10 mg.

b. Considering that an exponential growth is determined by:

\(A=A0*(1-r)^{t}\), where A is the amount after a certain number of a certain time, Ao is the initial amount, r is the rate and t is the time, so the percentage of the drug that leaves the body each hour is :

1-r=0.82

Solving:

1-r -1= 0.82 -1

-r= -0.18

r= 0.18

The percentage of the drug leaving the body each hour is 0.18, this is 18% per hour.

c. The amount of drug that remains in the body 6 hours after dosing is when t = 6:

\(A=10*(0.82)^{6}\)

Solving:

A= 3.04 mg

The amount of drug that remains in the body 6 hours after dosing is 3.04 mg.

d. The time that passes until only 1 mg of the drug remains in the body is calculated taking into account that A = 1 mg:

\(1=10*(0.82)^{t}\)

Solving:

\(0.1=(0.82)^{t}\)

㏒ 0.1= t*㏒ 0.82

㏒ 0.1  ÷ ㏒ 0.82= t

11.6 hours= t

The time until only 1 mg of the drug remains in the body is 11.6 hours.

Answer:*

Step-by-step explanation:

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

For the points (0, 0) and (5, 3), the numerical expression 3 − 0 gives the rise and the numerical expression 5 − 0 gives the run.

Step-by-step explanation:

Answer:

Starting with the point on the left, sketch a right triangle, going from the first point to the second point.

Step-by-step explanation:

Answer:

y = 1/6x

Step-by-step explanation:

linear equations don't have exponents

Answer:

Hello, the answer is 6, C.

Step-by-step explanation:

50 percent of 12 is 6.

Answer:

660 LOL bro and also next time put like multiplied by a fraction of a second to make it harder.

Step-by-step explanation:

110 + 110 = 220

220 x 3 is 660

The expression (-3)0 has a value of 0 when evaluated because a number multiplied by 0 gives 0

From the question, we have the following parameters that can be used in our computation:

(-3)0

The above statement is a product expression that multiplies the values of -3 and 0

Also, there is no need to check if there are like terms in the expression or not

This is  because we are multiplying the factors

So, we have

(-3)0 = 0

This means that the value of the expression is 0 i.e a number multiplied by 0 gives 0

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First, we need to find the equations of the two dotted lines.

One of the lines is parallel to the x-axis and passes through the point (0, 2), then its equation is:

y = 2

The other line has a slope of 1 and intercepts the y-axis at the point (0,0). Using the slope-intercept form with m = 1 and b = 0, its equation is:

y = mx + b

y = 1*x + 0

y = x

Given that the shaded region is below both lines and the lines are not included in the solution, then we need to use a "<" sign in the inequalities. Finally, the system of inequalities is:

y < x

y < 2

Answer:

Answer is attached below

Step-by-step explanation:

A length of fabric sampled = 10 yards

number of flaws in a piece of fabric having  length = l yards

Poisson distribution mean = 0.02l

If the flaws are > k  = process out of control hence would be stopped and fixed

Calculate The value of  K  such that the probability of stopping the process when it is really in control is at most 5%

using Poisson distribution

attached below is the detailed solution