Choose the correct answer below.
A. The statement is true because the definition of the instantaneous rate of change for a function f at x is the same as the definition of the derivative of a function f at x
B. The statement is false because the derivative is the average rate of change of x with respect to y=f(x).
C. The statement is false because the derivative is the average rate of change of y=f(x)with respect to x
D. The statement is false because the derivative is the instantaneous rate of change of x with respect to y=f(x)

Answer:

........

Step-by-step explanation:

...

....

.....

......

.......

Answer: 5x³

Step-by-step explanation:

The answer will be 13 km that is displacement of the car.

What is displacement?

When a body shifts from one position to another, displacement is the smallest (straight line) distance between the starting position and the ending position of the body, which is symbolized by an arrow pointing from the starting position to the ending position. Displacement is a vector quantity that describes "how far out of place an object is"; it represents the overall change in the position of the object.

A car travels 12 km north and turns left to travel 5km.

So the final position of car from the initial position is :

So the placement of the car is √(12²+5²) = √169 =13km

Hence the Displacement of the car is 13 km

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The equivalent function of the exponential function is (a) f(x) = (7/4)ˣ

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

f(x) = (4/7)^-x

This function can be properly expressed as

f(x) = (4/7)⁻ˣ

Solving further, we need to apply the exponent law of indices

This is represented as

a⁻ˣ = 1/aˣ

When the above rule is applied, we have

f(x) = 1/(4/7)ˣ

Evaluate the quotient

f(x) = (7/4)ˣ

Hence, the equivalent is (a) f(x) = (7/4)ˣ

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By using the formula for compound interest, it can be calculated that

He must pay back $81095 after 9 years

What is Compound interest?

If the interest on a certain principal at a certain rate over a certain period of time increases exponentially, rather than linearly, then the interest earned is called compound interest

If p is the principal, r is the rate and t is the time, then the amount is calculated by the formula

[tex]A = p(1 + \frac{r}{100})^n[/tex]

The difference between the amount and the principal gives the compound interest.

Principal = $48000

Rate = 6%

Time = 9 years

Amount = [tex]48000(1+ \frac{6}{100})^9\\[/tex]

             = $81095

He must pay back $81095 after 9 years

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Answer: would be -120 + 78, or -42 feet.

Step-by-step explanation:

The range of the data divided by four gives the standard deviation, which is approximately.

The range of the data divided by four gives the standard deviation, which is approximately. Simply put, that's it. To determine the range, find the highest value—the maximum—and deduct the lowest—the minimum. The range should then be divided by 4.

The range rule states that a sample's standard deviation is roughly equal to one-fourth of the data range.

In order to calculate the standard deviation, we must first determine the mean, take this mean away from each data point, square the differences, add them, divide by one less than the number of data points, and (at the very end) take the square root. The range rule, however, only needs one division and one subtraction.

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Answer:

8(x^2)+172x+920

Step-by-step explanation:

2(2x+20)+6

=4x+46

(4x+46)×(2x+20)

=4x(2x+20)+46(2x+20)

=8(x^2)+80x+92x+920

=8(x^2)+172x+920

Answer:

$5,227.41

Step-by-step explanation:

The compound interest formula is

[tex]A=P(1+\frac{r}{n}) ^{nt}[/tex]

A is the final amount

P is the initial amount

r is the interest rate as a decimal

n is the # of times the interest is applied per time period

t is the # of time periods.

We are given

Note: semi annually is twice per year.

[tex]P=4550[/tex]

[tex]r=0.035[/tex]

[tex]n=2[/tex]

[tex]t=4[/tex]

Lets solve for A.

[tex]A=4550(1+\frac{0.035}{2} )^{2*4}[/tex]

[tex]A=4550(1.0175)^{8}[/tex]

[tex]A=4550(1.14888178)[/tex]

[tex]A=5227.41211244[/tex]

Round to two decimals.

$5,227.41

By using the concept of mathematical expression, it is obtained that

(62−42)×3 is represented by  3 times the difference between 62 and 42

First option is correct

What is mathematical expression?

A mathematical expression consist of numbers connected with addition, subtraction, multiplication and division.

Here the given  mathematical expression is (62−42)×3

Here, the signs shown are subtraction and multiplication. So the concept of difference and times will be used here

(62−42)×3  means whole of (62 - 42) is multiplied with 3

So, this is 3 times the difference between 62 and 42

First option is correct

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Correct Question

Which phrase represents this expression?

(62−42)×3

a) 3 times the difference of 62 and 42

b) 3 times the difference of 42 and 62

c) The difference of 62 and the product of 3 times 42

d) The difference of the product of 3 times 42 and 62

The value of the house when it was purchased is 260,000 units

The house has increased in value by 15 percent since it was purchased. The current value is 299,000.

The value of the house when it was purchased can be calculated as follows:

let the amount purchased = x

Hence,

15% of x + x  = 299000

0.15x + x  = 299000

1.15x = 299000

divide both sides by 1.15

Hence,

x = 299000 / 1.15

x = 260000

Therefore, the value of the purchase is 260,000 units

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The conversion of .51 kg to milligrams using unit fractions is given by 510,000 mg

Units can be converted from one form to another.

Convert kilogram to milligram:

1000g = 1 kg

1 kg = 1,000,000 mg

That is,

A kilogram is equivalent to one million milligrams.

.51 kg to milligrams

= .51 × 1,000,000

= 510,000 mg

Hence, the conversion of .51 kg to milligrams is 510,000 mg.

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The differentiated form of the function with respect to x will be e³ˣ³.9x².

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range. The exponential function is that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x where a is a constant and a>1.

It is given that the function is,

y=e³ˣ³

Differentiate the function with respect to x.

[tex]=\frac{dy}{dx} \\\\ =\frac{d}{dx}\left(\left(e^3\right)^{x^3}\right) \\\\ =e^{3x^3}\frac{d}{dx}\left(3x^3\right) \\\\ =e^{3x^3}\cdot \:9x^2[/tex]

Thus, the differentiated form of the function with respect to x will be e³ˣ³.9x².

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The settle price at which you will get a demand for additional funds to be posted is $1.4840 per €.

What is contract?

An agreement between parties that results in legal duties for both parties is known as a contract. Mutual consent, demonstrated by a valid offer and acceptance, sufficient consideration, capability, and legality are the fundamental components needed for the agreement to be a legally enforceable contract.

Provided data from the question;

Futures contract to buy in euros = €62,500

Future contract to buy in dollar = $93,750 ( €62,500 × $1.50)

Initial performance of bond = $1,500

Maintenance level = $500

To determine the settle price at which you get a demand for additional funds to be posted =

Future contract to buy in dollar - (initial bond performance - maintenance level) ÷ future contract to in euros

$93,750 - ($1,500 - $500)

= $93,750 - $1,000

$92,750 ÷ €62,500

= $1.484

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Answer:

7x-5=86

Step-by-step explanation:

Answer:

[tex]\frac{1}{27}((13)^{\frac{3}{2}}-(6)^ {\frac{3}{2}})[/tex]

Step-by-step explanation:

Step-by-step explanation:

Statements                                                Reasons

1. AK - angle bisector                                 1. Given

2. FP perpendicular AK                             2. Given

3. <FAK congr <PAK                                  3. Definition angle bisector

4. Seg AK congr seg AK                           4. Congr of seg's is reflexive

5. <AKF & <AKP are rt. angles                  5. Def perpendicular lines

6. <AKF is congr <AKP                              6. Thrm: Right angles are congr.

7. Triangle KAF congr triangle KAP         7. ASA

8. A_F = A_P                                                    8. Corresp parts of congr tr are

                                                                           congr

The time taken for the rocket to reach its maximum height as required in the task content is; 2.25 seconds.

The maximum height reached by the toy rocket is; 88 feet.

It follows from the task content that the maximum height reached by the rocket is to be determined.

The given function is; h (t) = -16 t² + 72t + 7.

Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.

Therefore; at maximum height;

h'(t) = 0

h'(t) = -32t + 72 = 0

-32t = -72

t = -72/-32

t = 2.25 seconds.

Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.

Also, the maximum height reached by the rocket is at; h (2.25);

h(2.25) = -16(2.25)² + 72 (2.25) + 7

= -81 + 162 + 7

= 88.

The maximum height reached is; 88 feet.

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The solutions to a system of linear inequalities are located in the region where all the shaded regions of the inequalities overlap. the region of overlap called the intersection.        

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.

Thus, the solutions to a system of linear inequalities are located in the region where all the shaded regions of the inequalities overlap. the region of overlap called the intersection.        

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The distance of the line segment from ( -5,5 ) to ( 3,-1 ) is 10 units

What is the distance of a line between 2 points?

The distance of a line between 2 points is always positive and given by the formula

[tex]D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]

Given data ,

Let the two points be A and B

A ( x₁ , y₁ ) = A ( -5 , 5 )

B ( x₂ , y₂ ) = B ( 3 , -1 )

So , the distance between 2 points is given by the formula

[tex]D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]

Substituting the values of x₁ , y₁ , x₂ , y₂ in the formula , we get

[tex]D = \sqrt{(-5-3)^{2} + (5-(-1))^{2} }[/tex]

[tex]D = \sqrt{(8)^{2} + (6)^{2} }[/tex]

[tex]D=\sqrt{(64+36)}[/tex]

[tex]D = \sqrt{100}[/tex]

[tex]D= 10 units[/tex]

Hence , the distance of the line is 10 units

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The solution to inequalities are as follows.

What is inequality equation?

Inequalities are the mathematical expressions during which either side don't seem to be equal. In difference, in contrast to in equations, we tend to compare 2 values. The equal sign up between is replaced by but (or but or equal to), larger than (or larger than or equal to), or not capable sign.

Main body:

A) m-1 <-3

   to solve this we need to take link terms to one side

  = m< -3+1

  = m < -2

B) -4y <-20

  cancelling -ve sign on both sides,

= 4y <20

= y <5

C) 5+b>1

take link terms to one side

b > -4

Hence the graph is as given

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Answer:

36 minutes

Step-by-step explanation:

The total distance covered by the two vehicles per hour: 70 + 50 = 120 miles.

Time is distance over velocity.

[tex]t=\frac{72}{120}[/tex]  hours

Which simplifies to

[tex]\frac{3}{5}[/tex]  hours.

Convert hours to minutes.

There is 60 minutes in 1 hour.

[tex]\frac{1}{60}=\frac{\frac{3}{5} }{x}[/tex]

[tex]x=36[/tex]

Step-by-step explanation:

Solving -8 + x > -9 for x is: x > -1.

-8 + x > -9

add 8 to both sides:

-8 + x + 8 > -9 + 8

x > -1

True

Answer:

The F value is used in analysis of variance (ANOVA). It is calculated by dividing two mean squares. This calculation determines the ratio of explained variance to unexplained variance. The F distribution is a theoretical distribution.

Step-by-step explanation:

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The F ratio in ANOVA is the difference between two mean square values. If

Analysis of variance is a collection of statistical models and the estimation procedures that go with them that are used to analyze the differences between means. Ronald Fisher, a statistician, invented ANOVA. The ANOVA test compares more than two groups at the same time to see if there is a relationship between them.

If the null hypothesis is correct, you should expect F to be close to 1.0 most of the time. A high F ratio indicates that the variation among group means is greater than would be expected by chance.

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The procedure to calculate the p-value from z-score depends on one of two choices: one-tailed (which may be Left-tailed or Right-tailed) or two-tailed tests.

A z-table, otherwise termed the standard normal table, provides the area under the curve to the left of a z-score.

The technique for using z-tables to find p-values depends on the test being carried out; which may be; one- or two-tailed test.

For one-tailed tests, the directionality is also a factor.

It therefore follows that;

For a Left-tailed z-test: the p-value = Φ(Zscore)

For a Right-tailed z-test: the p-value = 1 - Φ(z-score).

For a Two-tailed z-test: the p-value = 2 * Φ(−|z-score|).

The procedure described above represents how to calculate p-value from z-score.

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The following formulas can be used to determine the p-value from its corresponding z-score

From the question, the parameters are given as

Also, from the question, we understand that:

The p value depends on the z-score for its own value

There are three types of test for z-score; these test are:

The p-value would assume different value for a z-score when the type of test is different

This means that the p value for z = 0.2 at right tail test is different at a left tailed test.

This means that there are three formulas for calculating the p-value from the z-score, and these formulas are

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We can rewrite the equation of the circle as:

(x + 4)^2 + (y + 4)^2 = 12^2

So the center is (-4, -4) and the radius is 12 units.

For a circle of radius R and center (a, b) the equation is:

(x - a)^2 + (y - b)^2 = R^2

Here we have the equation:

x^2 + 8x + y^2 + 8y - 112 = 0

We can complete squares to get:

(x^2 + 8x) + (y^2 + 8y) - 112 = 0

(x^2 + 2*4*x + 4^2) +  (y^2 + 8y + 4^2) - 4^2 - 4^2 - 112 = 0

(x + 4)^2 + (y + 4)^2 = 112 + 16 +  16 = 144

(x + 4)^2 + (y + 4)^2 = 12^2

So we have a circle of radius of 12 units, with a center at (-4 , -4)

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Answer: 11z+2

Step-by-step explanation:

The person needs to sell a minimum amount of $550000 to earn $22000.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, the income of the person is 4% of the total selling value.

Let the person sells $x to earn $22000, therefore,

4% of x is $22000

Or, 4x/100 = 22000

     4x = 2200000

       x = 550000

Hence, the person needs to sell a minimum amount of $550000 to earn $22000.

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The solution to the algebraic problem is [tex]x^{2}[/tex]

What is an Algebraic Equation?

An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.

Solution:

([tex]x^{3}[/tex] – 1) = (x+2)

On dividing ([tex]x^{3} - 1[/tex]) by (x+2)

The first term of the quotient will be x^2 by following the Long Division Method of Algebraic Division.

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