The distance of 2 laps around a park is 2.5 miles. Walking 5 laps around the same park is 6.25 miles.
Complete the table to show the relationship between the number of laps and the number of miles. Enter the answers in the boxes.

The graph of f(x) = (3/4)ˣ is attached. The values are f(-2) = 16/9, f(-1) = 4/3, f(0) = 1, f(1) = 3/4 and f(2) = 9/16

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the exponential function:

f(x) = (3/4)ˣ

Hence:

f(-2) = (3/4)⁻² = 16/9

f(-1) = (3/4)⁻¹ = 4/3

f(0) = (3/4)⁰ = 1

f(1) = (3/4)¹ = 3/4

f(2) = (3/4)² = 9/16

The graph of f(x) = (3/4)ˣ is attached.

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Answer:

Step-by-step explanation:

put the day and the amount of money you made

As per the given confidence interval, the value of P is lees than significant.

Confidence interval:

In statistics, a range around a measurement that conveys how precise the measurement is referred as confidence interval.

Given,

A precision instrument is guaranteed to read accurately to within 2 units. a sample of four instrument readings on the same object yielded the measurements 353, 351, 351, and 355. find a 90% confidence interval for the population variance.

Here we need to find the assumptions of the given situation,

From the given question we have identified the following,

Reading of instruments = 353, 351, 351, and 355.

Confidence interval = 90% = 0.09

Number of units = 2.

Based on these details, the standard deviation of this temple is 0.7.

So, the Z score is the same as the sample mean minus the population mean divided by the standard error, which is 2.857.

Therefore, P value was less than significant.

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The radical expression 2√2 + 3√5 cannot be simplified

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

2√2 + 3√5

The above expression is a radical expression

The radicals in the expression are √2 and √5

The numbers 2 and 5 do not have common factors

This means that 5 cannot be expressed in terms of 2, and vice versa

So, we cannot simplify the given expression 2√2 + 3√5

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The solutions to this system of linear equation 3x−2y=14 is ( [tex]\frac{2y + 14}{3}[/tex] ,   [tex]\frac{3x}{2}[/tex]-7).

Add 2y to both sides.

3x=14+2y

The equation is in standard form.

3x=2y+14

Divide both sides by 3.

[tex]\frac{3x}{3}[/tex] = [tex]\frac{2y + 14}{3}[/tex]

Dividing by 3 undoes the multiplication by 3.

x = [tex]\frac{2y + 14}{3}[/tex]

​Now,

3x−2y=14

Subtract 3x from both sides.

−2y=14−3x

Divide both sides by −2.

[tex]\frac{-2y}{-2}[/tex] = [tex]\frac{14 - 3x}{-2}[/tex]

Dividing by −2 undoes the multiplication by −2.

y =  [tex]\frac{14 - 3x}{-2}[/tex]

Divide 14−3x by −2.

y = [tex]\frac{3x}{2}[/tex] - 7

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Answer:

no

Step-by-step explanation:

\frac{1}{6}f^3a=

6

1

​

\frac{1}{6}f^3a=

6

1

​

f

3

a=

\,\,D

D

Answer:

  $951.74

Step-by-step explanation:

You want the future value of $750 earning 3% per year for 8 years, compounded semi-annually.

The value of an account earning interest at rate r on principal P compounded n times per year for t years is ...

  A = P(1 +r/n)^(nt)

For P=750, r=0.03, n=2, t=8, this is ...

  A = 750(1 +0.03/2)^(2·8) = 750(1.015^16) ≈ 951.74

The account will be worth about $951.74 in 8 years.

__

Additional comment

All spreadsheets and many graphing calculators have the necessary financial functions for computing this value. Apps are available for the purpose, as well.

Answer:

Step-by-step explanation:

k=x÷y

Multiply both sides of the equation by y.

ky=x

Swap sides so that all variable terms are on the left-hand side.

x=ky

Under a dilation, the point (2, 6) is moved to (6, 18). the scale factor of the dilation is 3

We know that if we transform point (x,y) by using dilation with scale factor k then the coordinate of the image will be (kx,ky).

Given: under a dilation, the point (2, 6) is moved to (6, 18)

Here (x,y)=(2,6) and (kx,ky)=(6,18)

x = 2

kx = 6

k = 6/x

k = 6/2

k = 3

Similarly taking y into account

y = 6

ky = 18

k = 18/y

k = 18/6

k = 3

Hence, Under a dilation, the point (2, 6) is moved to (6, 18). the scale factor of the dilation is 3

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The measure of the interior angle adjacent to the sixth exterior angle of the heaxagon is 118°.

Interior angles are those that lie inside a polygon.

To calculate an interior angle of a hexagon, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

Recall that, the sum of an interior and exterior angle is 180°

Where:

Substitute the value of a into equation 2

Hence, the value of the interior angle is 118°.

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Answer: The inverse of the function f(x)  = 4(x-3)² + 2 is

The given function is:

f(x)   =  4(x  - 3)²  +  2

To find the inverse of the function:

Make x as the subject of the formula

Replace x by  and replace f(x) by x

Therefore, the inverse of the function is:

Step-by-step explanation:

The value of x is (5t-a) when the formula is 6x+a=5(x+t).

According to the question,

We have the following information:

6x+a=5(x+t)

Now, from this formula, we have to mark the value of x or in other words, we have to find the value of x.

Now, multiplying 5 into the bracket on the right hand side:

6x+a = 5x+5t

Subtracting 5x from both sides of the equation:

6x-5x+a = 5t

x+a = 5t

Subtracting a from both sides of the equation, we will get the final value of x in terms of t and a:

x = 5t-a

Hence, the value of x is (5t-a) when the formula is 6x+a=5(x+t).

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When you cube root a number, the answer is always smaller. This is true.

The cube root, denoted by, is the inverse of the cube of a number. For example, 216, or the cube root of 216, equals 6 because multiplying 6 three times yields 216. In other words, because 6³ = 216.

A number's cube root is a value that, when multiplied by itself three times, yields the original value. For example, the cube root of 27 is 3, denoted as 3³ because multiplying 3 by itself three times yields 3 x 3 x 3 = 27.

In this case, we have showed that the answer will be smaller than the original number.

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Answer:

The value of k is 1.

Step-by-step explanation:

Answer:

The value of k=1

Step-by-step explanation:

The image of the coordinates after a dilation of (9, −7) by a scale factor of 4 centered at the origin include the following: (36, -28).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

Next, we would have to dilate the coordinates of the preimage (9, -7) by using a scale factor of 4 centered at the origin as follows:

Coordinate A (9, -7) → Coordinate A' (9 × 4, -7 × 4) = Coordinate A' (36, -28).

In conclusion, the coordinates of the image after a dilation are  (36, -28).

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The statement about the changing features of the family that is not true of todays Commonwealth Caribbean societies is C. parents are becoming more autocratic.

It should be noted that nowadays, men and women choose their own partners, husband and wives usually treat each other as equals and generally, families have fewer children

While role changes are often difficult, many positive things can occur as a result. Families may learn to work better together and support one another. Learning new tasks can help children gain confidence. Families may discover that, despite the changes, life can still be enjoyable.

In conclusion, the correct option is C.

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Triangle xyz was translated up 2 and right 3 units, creating triangle cab.

To find out the relationship between the parts of the two triangles must be true:

YZ ≅ AB

A translation is known as a rigid transformation.  This is because it preserves congruence.  Since CAB is created from XYZ, this tells us that:

X corresponds to C; Y corresponds to A; Z corresponds to B; XY corresponds to CA; YZ corresponds to AB; and XZ corresponds to CB.

Since the triangles are congruent, the corresponding pieces are congruent as well.

Out of these corresponding congruent pieces of triangles, the only one in our options is YZ ≅ AB.

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The quotient of the division is 2x² - x - 11 and 0 is the remainder.

Given,

The expression; 2x³ + x² - 10x -11 ÷ x + 1

We have to find the quotient and remainder

One of the arithmetic operations carried out on two given polynomials is to divide them. In this, the divisor is typically a polynomial of lower degree than the dividend.

Lets solve ;

2x³ + x² - 10x -11 / x + 1   (2x²)

= -x² - 10x - 11 / x + 1   (-x)

= -11x - 11  / x + 1  (-11)

= 0

Here,

The quotient = 2x² - x - 11

Remainder = 0

That is,

The quotient of the division is 2x² - x - 11 and 0 is the remainder.

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The perimeter of the parallelogram ABCD is, 58 units.

What is perimeter?

The length of a shape's boundary taken as a whole is referred to as its perimeter. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet.

Consider the given vertices, A(1, 1), B(17, 1), C(22, 13), D(6, 13).

The perimeter of parallelogram is the sum of all sides of parallelogram.

So, first to find the length of each side of parallelogram, using the distance formula,

[tex]d = \sqrt{(x_2 -x_1)^2+(y_2-y_1)^2}[/tex]

So,

[tex]AB = \sqrt{(17-1)^2+(1-1)^2}=\sqrt{16^2-0} = 16\\ BC = \sqrt{(22-17)^2+(13-1)^2} = \sqrt{5^2+12^2}= \sqrt{25+144}=13\\ CD = \sqrt{(6-22)^2+(13-13)^2} = \sqrt{16^2+0}=16\\ AD = \sqrt{(6-1)^2+(13-1)^2}=\sqrt{5^2+12^2} =\sqrt{25+144}=13[/tex]

Therefore, the perimeter of the parallelogram ABCD is,

P = AB + BC + CD + AD

P = 16 + 13 + 16 + 13

P = 58

Hence, the perimeter of  the parallelogram ABCD is, 58 units.

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Answer: 0.06 repeated, I'm sorry if it's wrong! I used a calculator.

Step-by-step explanation:

Calculating 2 divided by 5 / 6 should give you the answer 0.06666666666.

Answer:

1

Step-by-step explanation:

Change is y over the change in x

The y's are 4 and 7.

The x's are -1 and 2

[tex]\frac{4-7}{-1-2}[/tex] = [tex]\frac{-3}{-3}[/tex] = 1

0.9660  is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 15% rate of defects

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

  If the number of tablets in a shipment is sufficiently large, we can consider the testing procedure you describe (selecting a random sample of 29 ibuprofen tablets and counting the number of defective tablets in the sample) to be a binomial probability experiment.  

Let X = (Number of defective ibuprofen tablets in a random sample of 29 tablets.)  Then we may reasonably assume that X follows a binomial distribution.  For each "trial" (that is, each tablet selected), there are two possible outcomes, "success" (the tablet is defective), or "failure" (the tablet is not defective).  Note that the word success as used in the binomial distribution does not carry the connotation of being a "good" outcome.  A "success" is simply the outcome you are interested in counting, which in this case is the number of defectives in the sample.  The important parameters for a binomial distribution are n (the number of trials) and p (the probability of success on any one trial.)   For this situation, we have p = .01 (since we are told 1% of the tablets in the shipment are defective) and n = 29.  The general formula for the binomial distribution is

P(x) = nCx·px·(1 - p)n-x

where x is the number of successes in n trials (In this problem, x is the number of defectives in a random sample of 29 tablets.)  The symbol nCx is the "number of combinations of n things taken x at a time". This is the number ways of choosing x distinct objects from a set of n objects, without regard to order. It is given by

nCx = n!/[x!·(n-x)!]

where ! is the factorial symbol.

We want to find the probability that the shipment is accepted.  We are told that a shipment will be accepted if at most one tablet doesn't meet the required specifications.  That is, the number of defectives must be less than or equal to one.

P(Shipment accepted) = P(X ≤ 1).  (In this case, X ≤ 1 if and only if X=0 or X=1)= P(0) + P(1).

So we calculate P(0) (the probability of 0 defective tablets in the shipment), and P(1) (the probability of 1 defective.)  Using the formula for the binomial distribution, we have

P(0) = 29C0·(.01)0·(1 - .01)29 - 0.

But 29C0 = 1, so

P(0) = 1·(.01)0·(.99)29 ≅ .74717

Also,

P(1) = 29C1·(.01)1·(1 - .01)29 - 1.

Calculating 29C1, we have

    29C1 =  29!/[1!·(29-1)!] = 29, so

          P(1) = 29·(.01)1·(99)28

          P(1) ≅ .21887

Finally, then, we have

P(Shipment accepted) ≅ .74717 + .21887 ≅ .9660 (to 4 decimal places.)

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[tex]\frac{5}{3}[/tex]The point on the number line to plot the point which is opposite [tex]\frac{5}{3}[/tex] is [tex]\frac{-5}{3}[/tex]

A number line is a horizontal representation of a number of parts with equal intervals.

What exactly is a number line?

A number line is a horizontal line with evenly spaced numerical increments. It shows how to answer plotted the number on the line.

If two numbers are the same distance from 0 and on opposite sides of the number line, they are opposites.

For example, 4 is the inverse of -4, and -4 is the inverse of 4. They are both equal distances from zero.

Given: number is [tex]\frac{5}{3}[/tex]

The opposite of 5/3 is the additive inverse let x be the additive inverse

[tex]\frac{5}{3}[/tex] + x = 0

x = 0 - [tex]\frac{5}{3}[/tex]

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

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Answer:

Step-by-step explanation:

The proportional relationship is:

Let's find the value of k for each pair and compare:

As we see thee of the pairs have same value of k, 5/3 and one is different 7/4.

The answer is no.

Answer choices given in the comment:

For corporation p to file a consolidated tax return with corporation s, p must own 80% of s's voting stock

The consolidated tax return is defined as a single income tax return filed by an affiliated group of corporations that combines their tax liability.

The percentage is the ratio that can be represented as the fraction of hundred.

The voting stock is defined as the shares that give the stockholder, that is the right to vote on the policymaking of the corporation

Here, p must own 80% of s's voting stock

Hence, for corporation p to file a consolidated tax return with corporation s, p must own 80% of s's voting stock

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Answer:

Step-by-step explanation:

A matrix is a form of writing items in rows and columns.

The matrice B is

[tex]B=\left[\begin{array}{ccc}9&-6\\12&15\\-3&-18\end{array}\right][/tex]

The value of [tex]b_{11}[/tex] = 9

The value of [tex]b_{22}[/tex] = 15

The value of [tex]b_{31}[/tex] = -3

The value of [tex]b_{32}[/tex] = -18

A matrix is a form of writing items in rows and columns.

[tex]\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{array}\right][/tex]

We have,

[tex]A=\left[\begin{array}{ccc}3&-2\\4&5\\-1&-6\end{array}\right][/tex]

B = 3A

We will multiply 3 with all the items in matrices A.

[tex]B=\left[\begin{array}{ccc}9&-6\\12&15\\-3&-18\end{array}\right][/tex]

This is in the form of

[tex]B=\left[\begin{array}{ccc}b_{11}&b_{12}\\b_{21}&b_{22}\\b_{31}&b_{32}\end{array}\right][/tex]

Now,

The value of [tex]b_{11}[/tex] = 9

The value of [tex]b_{22}[/tex] = 15

The value of [tex]b_{31}[/tex] = -3

The value of [tex]b_{32}[/tex] = -18

Thus,

The matrice B is

[tex]B=\left[\begin{array}{ccc}9&-6\\12&15\\-3&-18\end{array}\right][/tex]

This is in the form of

[tex]B=\left[\begin{array}{ccc}b_{11}&b_{12}\\b_{21}&b_{22}\\b_{31}&b_{32}\end{array}\right][/tex]

The value of [tex]b_{11}[/tex] = 9

The value of [tex]b_{22}[/tex] = 15

The value of [tex]b_{31}[/tex] = -3

The value of [tex]b_{32}[/tex] = -18

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Answer:n1=-9,n2=10

Step-by-step explanation: