F(x) = - 2x² – 12x - 17

Does the function have a minimum or maximum value?

O Minimum

O Maximum

Answer:

Step-by-step explanation:

\(f(x) = {x}^{3} + 5\)

To find the inverse of f (x) , equate f(x) to y

That's

y = f(x)

\(y = {x}^{3} + 5\)

Next interchange the terms

That's x becomes y and y becomes x

\(x = {y}^{3} + 5\)

Next solve for y

Send 5 to the other side of the equation

\( {y}^{3} = x - 5\)

Find the cube root of both sides to make y stand alone

That's

\( \sqrt[3]{ {y}^{3} } = \sqrt[3]{x - 5} \)

\(y = \sqrt[3]{x - 5} \)

We have the final answer as

\( {f}^{ - 1} (x) = \sqrt[3]{x - 5} \)

Hope this helps you

Answer:

Well first you must do what's in the parenthesis.

10^2 = 100

100^3 = 1000000

Answer:

14+4x+6=8x. x=5

Step-by-step explanation:

subtract 4x from both sides. 14+6=4x. and then solve x. 20=4x. divide by 4 on both sides 5=x.

Answer:

Soccer:3 dollars

Basketball:4dollars

Step-by-step explanation:

Answer:

Step-by-step explanation:

The world record for memorizing and reciting the most digits of pi is held by Rajveer Meena from India. He recited 50,000 decimal places of pi in 2020, which is the current recognized world record.

Pi (π) is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is an irrational number, which means it cannot be expressed as a finite decimal or a fraction. The decimal representation of pi is non-repeating and goes on indefinitely without a pattern. The value of pi is approximately 3.14159, but it is commonly approximated as 3.14 for simplicity in mathematical calculations. However, the exact value of pi has been calculated to trillions of digits using various computational methods. The quest to calculate more digits of pi continues to this day, and the computation of pi serves as a benchmark for testing the performance of supercomputers and computational algorithms. The current record for calculating the most digits of pi is trillions of digits, achieved through the use of powerful computers and advanced algorithms.

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The value of the double integral is 140/3.

To calculate the double integral of the function f(x, y) = 7x * x^2 * y^2 over the region R = [1, 3] × [0, 1], we integrate with respect to y first, and then with respect to x.

The integral is given by:

∫∫R 7x * x^2 * y^2 da

First, we integrate with respect to y:

∫[0, 1] 7x * x^2 * y^2 dy

Integrating this with respect to y, we get:

[7x * x^2 * (y^3)/3] evaluated from y = 0 to y = 1

= 7x * x^2 * (1^3)/3 - 7x * x^2 * (0^3)/3

= 7x * x^2/3

Now, we integrate this result with respect to x:

∫[1, 3] 7x * x^2/3 dx

Integrating this with respect to x, we get:

[7/12 * x^4] evaluated from x = 1 to x = 3

= 7/12 * (3^4) - 7/12 * (1^4)

= 7/12 * 81 - 7/12

= 567/12 - 7/12

= 560/12

= 140/3

Therefore, the value of the double integral is 140/3.

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Answer:

Part A:

A pair of linear equations can only have one solution or infinitely many solutions. In this case, there would only be one solution as they intersection at only one point.

Part B:

The solution would be (3, 4) because it is the point of intersection between the two linear lines.

Answer:

18.2

Step-by-step explanation:

To round 18.194 to the nearest tenth consider the hundredths’ value of 18.194, which is 9 and equal or more than 5. Therefore, the tenths value of 18.194 increases by 1 to 2.

18.194 rounded to the nearest tenth = 18.2

Answer:

Probability of getting number 10  = 0

Step-by-step explanation:

Given;

Total sides of cube die = 6

Find:

Probability of getting number 10

Computation:

Total number of cube = 1, 2, 3, 4, 5, 6

Favorable outcome for 10 = 0

Probability of an event = Favorable outcome / Number of outcomes

Probability of getting number 10 = 0 / 6

Probability of getting number 10  = 0

$79333

\(salary:x\)

\(12\%x=8500\)

\(x=8500\div 12\%\)

\(x=70833\)

\(70833+8500=\$79333\)

I hope this helps you

:)

Answer:

The unit rate is 2700 ÷ 3 = 900 2700 \div 3 = 900 2700÷3=900 kilometers per hour.

Step-by-step explanation:

Answer: Can you Please Provide The Table?

Then I am Sure I can Get You 100% On this question.

Answer:

48 different breakfast platters

Step-by-step explanation:

Hope this helps!

Answer:

x=-2

Step-by-step explanation:

R=3x+2y

y=7, R=8

x=?

Substitute R and y with the values given

8=3x+2(7)

8=3x+14

Combine like terms

8-14=3x

-6=3x

x=-2

Answer:

80%

Step-by-step explanation:

you're occupying 800 out of 1000

the way to write this mathematically is to write: 800/1000,

which equals 0.8

then to make this a percentage you x100

and your answer is 80%

Answer:

No, the reasoning is not correct.

Step-by-step explanation:

39.99 x .14 = 5.5986  Does it make sense that the sales price plus the tax would be $5.60?  Doesn't that seem really low?

39.99 x .3  = 11.997 is the amount that we are taking off of the original price.

39.99 - 12 (Rounded to the nearest cent) is 27.99.

Now we pay the tax on the discounted amount of the item.  

27.99 x .16 = 4.4784 or 4.48 rounded to the nearest cent.

The out the door cost of the item

is 27.99 + 4.48 = 32.48

Age will be 40 years old.

R, in beats per minute, can be approximated by the formulas, where a represents the person's age.

where R= 143 - 0.65a for women.... (1)

and R= 165 - 0.75a for men,..... (2)

So by implementing these two equation we get a = 40

If the sum of ages is X and Y, and the ratio of their ages is p:q, then the age of Y can be calculated using the formula shown below: Y's age = Y's ratio/Sum of ratios x sum of ages The age dependency ratio is the ratio of dependents (people under the age of 15 or over the age of 64) to the working-age population (people between the ages of 15 and 64). The proportion of dependents per 100 working-age population is shown in the data.

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Answer:

The school is 1.5 miles away from Jonathan's home

Step-by-step explanation:

Let D be the distance remaining after 1  mile

We are given that He biked at the speed of 15 mph. His mother saw the homework when he was already 1 mile from home, and started chasing him. She drove at a speed of 25 mph and caught him at the school entrance.

So, Time taken to cover D distance by Son is equal to the time taken by mother from home to school entrance(D+1) since she caught him at school entrance

Speed of Jonathan bike = 15 mph

Speed of Mother's bike = 25 mph

So, \(\frac{D}{15}=\frac{D+1}{25}\)

25D=15D+15

10D=15

D=1.5

So, the school is 1.5 miles away from Jonathan's home

The 90% CI for the change in blood pressure is (-5.843, 7.977)., the 99.9% CI for the change in blood pressure is (-14.077, 16.211).

a) To calculate a 90% confidence interval (CI) for the change in blood pressure, we use the formula:

CI = x ± t(α/2, df) * (s/√n)

where x is the sample mean of the change in blood pressure, t(α/2, df) is the t-value for the desired confidence level and degrees of freedom, s is the sample standard deviation of the change in blood pressure, and n is the sample size.

Using the given data, we have:

x = 1.067
s = 26.691
n = 15
df = n - 1 = 14

From the t-distribution table, the t-value for a 90% confidence level and 14 degrees of freedom is 1.761.

Plugging in the values, we get:

CI = 1.067 ± 1.761 * (26.691/√15) = (-5.843, 7.977)

Therefore, the 90% CI for the change in blood pressure is (-5.843, 7.977).

b) To calculate a 99.9% CI for the change in blood pressure, we use the same formula but with a different t-value:

t(α/2, df) = 3.922 for a 99.9% confidence level and 14 degrees of freedom.

Plugging in the values, we get:

CI = 1.067 ± 3.922 * (26.691/√15) = (-14.077, 16.211)

Therefore, the 99.9% CI for the change in blood pressure is (-14.077, 16.211).

c) The interval calculated in part (a) does include 0, while the interval calculated in part (b) does not include 0. This is important because if the interval includes 0, it means we cannot conclude that there is a significant difference in blood pressure before and after the medication. On the other hand, if the interval does not include 0, it means we can be confident that there is a significant difference.

d) To conduct a one sample t-test with p = 0 and a = 10, we first calculate the t-statistic using the formula:

t = (x - p) / (s/√n)

where x is the sample mean of the change in blood pressure, s is the sample standard deviation of the change in blood pressure, and n is the sample size.

Plugging in the values, we get:

t = (1.067 - 0) / (26.691/√15) = 0.444

From the t-distribution table, the t-value for a one-tailed test with 14 degrees of freedom and a significance level of 10% is 1.345.

Since our calculated t-value (0.444) is less than the critical t-value (1.345), we fail to reject the null hypothesis that there is no significant difference in blood pressure before and after the medication. Therefore, the results are not consistent with the 90% CI calculated in part (a).

e) To conduct a one sample t-test with y = 0 and a = 0.001, we use the same formula as in part (d):

t = (x - y) / (s/√n)

Plugging in the values, we get:

t = (1.067 - 0) / (26.691/√15) = 0.444

From the t-distribution table, the t-value for a one-tailed test with 14 degrees of freedom and a significance level of 0.001 is 3.746.

Since our calculated t-value (0.444) is less than the critical t-value (3.746), we fail to reject the null hypothesis that there is no significant difference in blood pressure before and after the medication. Therefore, the results are not consistent with the 99.9% CI calculated in part (b).

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Answer: F. n = s/180 + 2

Step-by-step explanation:

         To find the equation that solves for n, we will isolate the n variable.

Given:

     S = (n - 2) x 180

Divide both sides of the equation by 180:

     \(\frac{S}{180}\) = n - 2

Add 2 to both sides of the equation:

     \(\frac{S}{180}\) + 2 = n

Reflexive property:

    n = \(\frac{S}{180}\) + 2

                   F. n = s/180 + 2

Answer:

the common difference is 6.

Step-by-step explanation:

Given;

first term of an AP, a = -7

let the common difference = d

The third term is written as;

T₃ = a + 2d

The eight term is written as;

T₈ = a + 7d

The ratio of the eight term to third term = 7:1

\(\frac{T_8}{T_3} = \frac{7}{1} = \frac{a+ 7d}{a + 2d} \\\\7 = \frac{a+ 7d}{a + 2d}\\\\Recall, a = -7\\\\7 = \frac{-7+ 7d}{-7 + 2d}\\\\7(-7 + 2d) = -7+ 7d\\\\-49 + 14d = -7 + 7d\\\\14d -7d = -7 + 49\\\\7d = 42\\\\d = \frac{42}{7} \\\\d = 6\)

Therefore, the common difference is 6.

Answer: 15

Step-by-step explanation: Line them up from smallest to largest. 5, 6, 7, 8, 10, 15, 17, 20. Then do the largest number minus the smallest number. In this case, its 20 - 5. That equals 15, so thats your answer

The options B and C represent the line segment between the points (1,5) and (3,13).

To find the equation of the line segment between the points (1,5) and (3,13), we first find the slope:

slope = (change in y) / (change in x) = (13 - 5) / (3 - 1) = 4

Then, using the point-slope form of a line, we get:

y - 5 = 4(x - 1)

Simplifying, we get:

y = 4x + 1

To check if the given options represent the same line segment, we can substitute the x and y values of the two points into each equation and see if they satisfy the equation. Doing this for the options, we get:

B. x = 1 + 2t, y = 5 + 4t, for t in [0,1]

At t=0, x=1, y=5

At t=1, x=3, y=13

So this represents the line segment between the points.

C. x = 1 + t, y = 5 + 4t, for t in [0,2]

At t=0, x=1, y=5

At t=2, x=3, y=13

So this represents the line segment between the points.

Therefore, the options B and C represent the line segment between the points (1,5) and (3,13).

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A 40 gram sample of a substance that’s used for drug research has a k-value of 0.1472. The substance's half-life, in days, is approximately 4.7 days.

The half-life of a substance is the time it takes for half of the substance to decay or undergo a transformation. The half-life can be determined using the formula:

t = (0.693 / k)

where t is the half-life and k is the decay constant.

In this case, we are given that the sample has a k-value of 0.1472. We can use this value to calculate the half-life.

t = (0.693 / 0.1472) ≈ 4.7 days

Therefore, the substance's half-life, rounded to the nearest tenth, is approximately 4.7 days.

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Answer:

the output is 3

Step-by-step explanation:

look for the point on the graph whose coordinate is -1

the point on the graph whose x coordinate is -1 is (-1,3)

so its 3

Answer:

∠DCB = 102°

Explanation:

∠CDB = ∠CBD

∠DCB = 180° - ∠CBD - ∠CDB

∠DCB = 180° - 39° - 39°

∠DCB = 102°

Answer:

2

Step-by-step explanation:

12:1,2,3,4,6,12

18:1,2,3,6,9,18

32:1,2,4,8,16,32

h.c.f = 2

In this situation, interval measurement is being employed as the measurement level.

As the height of each student can be measured on a continuous scale with equal intervals between the values. It's important to note that the teacher may have rounded the measurements to the nearest unit, which would make it a discrete measurement.

Interval measurement is a level of measurement in which the values are measured on a continuous scale and have equal intervals between them, but there is no true zero point. This means that the difference between any two values on the scale is meaningful and consistent, but it is not possible to say that one value is "zero" or has no quantity of the measured attribute.

For example, measuring temperature in degrees Celsius or Fahrenheit is an example of interval measurement. In this case, the difference between 10 and 20 degrees is the same as the difference between 20 and 30 degrees, but there is no true zero temperature - a temperature of 0 degrees does not mean the absence of heat.

Another example of interval measurement is measuring time in minutes or hours. The difference between 10 minutes and 20 minutes is the same as the difference between 20 minutes and 30 minutes, but there is no "zero" point in time - even if nothing is happening, time continues to pass.

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Answer:

\(Volume = 54\,\pi\)

Step-by-step explanation:

Recall the formula for the volume of a cylinder:

\(Volume=\pi \,R^2\,H\)

where R is the radius of the cylinder's base, and H is the cylinder's height.

Therefore, in our case the volume becomes:

\(Volume=\pi \,R^2\,H\\Volume=\pi \,3^2\,*\,6\\Volume = 54\,\pi\)