Look at the following numbers:
-7, 0, 7, 14
Which pair of numbers has a sum of 0?
O 0,7
O-7,7
07, 14
O-7, 14

The derivative of function f(w) = \(2/(w^2 - 4)^5 ~is ~f'(w) = -40~w~(w^2 - 4)^{-6}.\)

We have,

To find the derivative of the function \(f(w) = 2/(w^2 - 4)^5\), we can use the chain rule and the power rule for differentiation.

Let's go through the steps:

First, rewrite the function as \(f(w) = 2(w^2 - 4)^{-5}.\)

Now, let's differentiate f(w) with respect to w:

\(f'(w) = d/dw~ [2(w^2 - 4)^{-5}]\)

To apply the chain rule, we need to differentiate the outer function and multiply it by the derivative of the inner function.

Using the power rule, the derivative of (w² - 4) with respect to w is 2w.

Applying the chain rule:

\(f'(w) = -10 \times 2(w^2 - 4)^{-6} \times 2w\)

Simplifying further:

\(f'(w) = -40w(w^2 - 4)^{-6}\)

Therefore,

The derivative of function f(w) = \(2/(w^2 - 4)^5 ~is ~f'(w) = -40~w~(w^2 - 4)^{-6}.\)

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There are no solutions to the system of inequalities Option (d)

Inequalities are a fundamental concept in mathematics and are commonly used in solving problems that involve ranges of values.

A system of two inequalities is a set of two inequalities that are considered together. In this case, the system of inequalities is

y > 3x + 1

y < 3x - 3

The inequality y > 3x + 1 represents a line on the coordinate plane with a slope of 3 and a y-intercept of 1. The inequality y < 3x - 3 represents another line on the coordinate plane with a slope of 3 and a y-intercept of -3. We can draw these lines on the coordinate plane and shade the regions that satisfy each inequality.

The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.

We can start by analyzing the inequality y > 3x + 1. This inequality represents the region above the line with a slope of 3 and a y-intercept of 1. Therefore, any point that is above this line satisfies this inequality.

Next, we analyze the inequality y < 3x - 3. This inequality represents the region below the line with a slope of 3 and a y-intercept of -3. Therefore, any point that is below this line satisfies this inequality.

To determine which values satisfy both inequalities, we need to find the region that satisfies both inequalities. This region is the intersection of the regions that satisfy each inequality.

When we analyze the regions that satisfy each inequality, we see that there is no region that satisfies both inequalities. Therefore, there are no values that satisfy the system of inequalities shown.

There are no solutions to the system of inequalities y > 3x + 1 and y < 3x - 3 by analyzing the regions that satisfy each inequality on a coordinate plane. The lack of a solution is determined by the fact that there is no region that satisfies both inequalities.

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Complete Question :

Which is true about the solution to the system of inequalities shown?

y > 3x + 1

y < 3x – 3

On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.

Options:

a)Only values that satisfy y > 3x + 1 are solutions.

b)Only values that satisfy y < 3x – 3 are solutions.

c)Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.

d)There are no solutions.

Answer:

D

Step-by-step explanation:

Answer:

i think the fourth one is equvilent ratio

Step-by-step explanation:

Earth's diameter is 0.0092 times less than the sun's diameter.

The Diameter of Earth = 1.3 * 10⁴ km

The Diameter of Moon = 3.5 * 10³ km

Let the diameter of sun be x km

According to the question

The diameter of the sun is 400 times that of the moon.

x = 400 * 3.5 * 10³ km

= 14 * 10⁵ km

The Diameter of earth / diameter of sun

=  1.3 * 10⁴ / 14 * 10⁵

= 0.0092

Hence, The diameter of the Earth is 0.0092 times that of the Sun.

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Answer:

x = 14

y = 54

Step-by-step explanation:

m∠AON = m∠MON - m∠MOA

              = 90°- 72°

              = 18°

Since, ∠AOD ≅ ∠BOC [Vertically opposite angles]

2x° + 18° = 3x°

3x - 2x = 18

x = 18

Since, ∠BOC, ∠COM and ∠AOM are the linear angles,

m∠BOC + m∠COM + m∠MOA = 180°

3x + y + 72° = 180°

3x + y = 180 - 72

3x + y = 108

3(18) + y = 108

54 + y = 108

y = 108 - 54

y = 54

The area of the segment is 9( π-2) units²

The area of a figure is the number of unit squares that cover the surface of a closed figure.

A segment is the area occupied by a chord and an arc. A segment can be a major segment or minor segment.

Area of segment = area of sector - area of triangle

area of sector = 90/360 × πr²

= 1/4 × π × 36

= 9π

area of triangle = 1/2bh

= 1/2 × 6²

= 18

area of segment = 9π -18

= 9( π -2) units²

therefore the area of the segment is 9(π-2) units²

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Answer:

The circumference of the​ circle is \(C=56.55 \:m\).

Eugene confused the radius with the diameter to find the circumference of the circle.

Step-by-step explanation:

The circumference of a circle is the distance around the outside of the circle.

The circumference of a circle is found using this formula:

\(\begin{matrix} C=\pi \cdot d\\or\\ \, C=2\pi \cdot r \end{matrix}\)

From the information given the diameter of the circle is 18 m. Therefore, the circumference of the​ circle is

\(C=\pi \cdot d\\\\C=3.14 \cdot 18 \approx 56.55 \:m\)

Eugene used the wrong formula to find the circumference of a circle.

\(C=2\cdot(3.14)\cdot 18=113.04 \:m\)

He confused the radius with the diameter.

Answer:

Eugene used the wrong formula to find the circumference of a circle.

He confused the radius with the diameter.

Step-by-step explanation:

Step-by-step explanation:

If you want the "root" of the equation...

First get y by itself on one side. You should get y = - x - 8.

Notice that this is the equation of a straight line.

Then let y = 0, and solve for x. You should get x = -8.

So the solution or "root" of the equation is at the point (-8,0)

Answer:

X=0, y=0, x=3

Put the values into the equation. You should get -4,0

-2(-4) –2(0)=8

The monthly loan payment for a $60,000 loan with a $4,000 down payment, 13% interest rate, and a term of 60 months is approximately $1,289.49.

To calculate the monthly loan payment, we need to use the loan amount, down payment, interest rate, and term.

Loan amount: $60,000

Down payment: $4,000

Principal amount: Loan amount - Down payment = $60,000 - $4,000 = $56,000

Interest rate: 13% per annum (or 0.13 as a decimal)

Monthly interest rate: 13% / 12 = 0.0133 (approx.)

Term: 60 months (5 years)

Now, let's calculate the monthly loan payment using the formula for a fixed-rate loan:

Monthly payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

P = Principal amount

r = Monthly interest rate

n = Total number of payments

Substituting the values into the formula:

Monthly payment = $56,000 * (0.0133 * (1 + 0.0133)^60) / ((1 + 0.0133)^60 - 1)

Using a calculator, the approximate monthly loan payment comes out to be $1,289.49.

Therefore, the monthly loan payment for a $60,000 loan with a $4,000 down payment, 13% interest rate, and a term of 60 months is approximately $1,289.49.

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Answer:

5 + 3 = 8

10 + 6 = 16

15 + 9 = 24

No she will need a total of 48

Step-by-step explanation:

24 + 16 + 8 = 48

Answer:

25 liters blue for a total of 40.

The rest of the table is:

Blue:       White:      Total:

15            9               24

20           12             32

25           15            40

Step-by-step explanation:

I multiplied 8 times 5 to get 40 (the total amount of liters)

Then I also had to multiply 5 by 5 to balance out the equation, and got 25.

Answer:

Two angles are said to be supplementary when they add up to 180°.

Answer:

Angles are supplementary if the add up to 180 degrees

Step-by-step explanation:

So many different angles can be supplementary.

Examples:

Ajacent Angles

Corresponding Angles

Alternate Interior Angles

Alternate Exterior Angles

And a few other angles

Hope This Helps :)

Answer:

  c.) hourly rate

Step-by-step explanation:

The value the coefficient represents can often be learned from its units. The term 8t gives a value in currency units, since the expression 8t+20 is an amount that is to be paid. (We can only add like terms, so both 8t and 20 must have currency units.)

The value of t has units of hours, so the coefficient 8 must have units that are ...

  8 currency units/hour

That is, multiplying by hours gives currency units.

In this context, a number with units of currency units per hour is most likely the hourly rate of the rental.

Answer:

0 :/

Step-by-step explanation:

S(48) = (48/2)(2a+47d),

S(36) = (36/2)(2a+35d).

Now S(48) = 4S(36)

24(2a+47d) = 4*18(2a+35d) = 72(2a+35d).

Then 2a+47d = 3(2a+35d) and

6a +105d -2a -47d = 0,

4a +58d = 0,

2a+29d = 0.

Now S(30) = (30/2)(2a+29d) = (15)(2a+29d)=0

Answer:

12 cm³

Step-by-step explanation:

the volume of the sphere = 4/3 πr³

the volume of the cylinder (h=2r)= πr².2r

= 2πr³

the volume ratio of S : C =

4/3 πr³ : 2 πr³

= 4/3 : 2

= 4 : 6

= 2 : 3

so, the volume of the Sphere =

2/3 × 18 = 12 cm³

Answer:

Solution given:

radius [r]=height[h]

volume of cylinder=πr²h

18cm³=πr³

again

volume of sphere

=4/3 πr³

=4/3*18=24cm³

the volume of the sphere:24cm³

The percentage error in the density of metal will be 3.4%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the density of the metal in the handbook is 4.018 g/mL and the measured value of the density is 4.16 g/mL.

The percentage error will be calculated as:-

Percentage = [ ( 4.16 - 4.018 ) / 4.16 ] x 100

Percentage = 0.034x 100

Percentage = 3.4%

Hence, the percentage error will be 3.4% for the densities.

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Answer:

The geometric mean of 16 and 36 is 24

Answer:

x=-4

When x is -4, the y value (which is what the function spits out) is 8.

Therefore, according to the given information, The formulas to find the area of a circle are\(\pi r^2 and (d/2)^2\pi or r^2\pi\).

The area of a circle is given by the formula A = πr², where r is the radius of the circle.

The area of a circle can be found using either of the following formulas:

\(\pi r^2\), where π (pi) is a mathematical constant approximately equal to 3.14159 and r is the radius of the circle.

\(A = (d/2)^2π,\) where d is the diameter of the circle. This formula can also be written as \($A = r^2\pi$\), where r is the radius of the circle and A is the area.

Both formulas are equivalent and can be used interchangeably, depending on the given information about the circle.

Therefore, according to the given information, The formulas to find the area of a circle are\(\pi r^2 and (d/2)^2\pi or r^2\pi\).

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Answer:

The p-value for this test is 0.1375.

Step-by-step explanation:

A student believes that the average grade on the statistics final examination was 87. The student wants to test whether the average is different from 87 at 90% level of confidence.

At the null hypothesis, we test if the average is 87, that is:

\(H_0: \mu = 87\)

At the alternate hypothesis, we test if the average is different from 87, that is:

\(H_a: \mu \neq 87\)

The test statistic is:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(s\) is the standard deviation of the sample and n is the size of the sample.

87 is tested at the null hypothesis:

This means that \(\mu = 87\)

The average grade in the sample was 83.96 with a standard deviation of 12. Sample of 36

This means that \(X = 83.96, s = 12, n = 36\)

Value of the test-statistic:

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{83.96 - 87}{\frac{12}{\sqrt{36}}}\)

\(t = -1.52\)

Pvalue:

Probability of the sample mean differing of 87, which means that we have a two-tailed test, with t = -1.52 and 36 - 1 = 35 degrees of freedom.

With the help of a calculator, the pvalue is of 0.1375.

The p-value for this test is 0.1375.

Answer:

50 lbs

Step-by-step explanation:

Plz mark brainliest

At Priscilla's school, the final grade for her Calculus course is weighted as follows: Tests: 50% Quizzes: 30% Homework: 20% Priscilla has an average of 87% on her tests, 100% on her quizzes, and 20% on her homework. What is Priscilla's weighted average?

Weighted Average gives weights to each percent of the average as follows:

Weighted Average = Average * weighting percent

Weighted Average = Test Average * Test Weighting + Quiz Average. * Quiz Weighting + Homework Average * Homework Weighting

Weighted Average = 87% * 50% + 100% * 30% + 20% * 20%

Weighted Average = 43.5% + 30% + 4%

Weighted Average = 77.5%

77.5%

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Converting fractions into decimals

Thank You!

Answered by: ms115

Answer:

v(0) = 19,900, v(11) = 3,787.36

Step-by-step explanation:

v(0) = 19,900 (0.86)^0 = 19,900 * 1 = 19,000

v(11) = 19,900 (0.86)^11 = 19,900 * 0.190319 = 3,787.36

Answer:

1.) M=9,100(1 + 0.05)^6

Step-by-step explanation:

\(A=P(1+\frac{r}{n})^{nt}\)

In this formula the "P" represents the principle amount, or the original amount. The "r" represents the interest rate in decimal form, while the "n" represents the number of compounds in the time unit (usually years), and the "t" represents the amount of time that has passed (usually years)

In this case it says annual interest rate of 5% and nothing of compound monthly, etc... so n=1, and r=0.05. We're also given the principle amount of 9,100 and the time passed is just 6 years, so t=6. Plugging all this information into the equation we get:

\(A=9,100(1+0.05)^6\)

which makes the first option correct.

Answer:

  1, -0.5, -6.25

Step-by-step explanation:

The number in the left box is the leading coefficient. The coefficient of x^2 is 1, so that goes in the first box.

__

The number in the second box is half the coefficient of x, divided by the leading coefficient:

  (1/2)(-1)/1 = -1/2

__

The number in the third box (k) is the number required to make the rewritten g(x) match the original g(x). So far, we have ...

  g(x) = 1(x -1/2)^2 + k = x^2 -x -6

  x^2 -x +1/4 +k = x^2 -x -6 . . . . . expand the square

  1/4 +k = -6 . . . . . . . . . . . . . . . . . subtract the x-terms from both sides

  k = -6 1/4 . . . . . . . . . . . . . . . . . . subtract 1/4

So, you have ...

  \(g(x)=\boxed{1}(x+\boxed{-0.5})^2+\boxed{-6.25}\)

Answer: Number 4

Step-by-step explanation: None