Write an equation for the proportional relationship shown in the table.

Answer: x=500,000

Step-by-step explanation:

60,000=.12x

60,000/.12=x/.12

500,000=x

To find the circumference of a circle with a radius of 7 cm, Erin should use 2×7×π. This is because the circumference of a circle is calculated by the formula 2×π×r.

The circumference is the measure of the perimeter of a circle. Since we know that from every point on the circle to its center has an equal length and is said to be its radius, the perimeter of the circle we can write as

Circumference = 2 × π × r units.

Here r is the radius of the circle.

It is given that Erin wants to find the circumference of a circle with a radius of 7 cm.

So, first, she has to know the formula for finding the circumference.

Here the radius is given as 7 cm i.e., r = 7 cm

Then, the circumference of the given circle is

= 2 × π × r

On substituting the radius value into the above formula, we get

Circumference = 2 × π × 7 cm

⇒ 14π cm

So, she needs to use option A. 2 × 7 × π  for finding the required circumference. This is the first step for finding the circumference of a circle.

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Answer:

Answer Option A: AA Postulate

Answer:It will cost Mrs. Wu $44.5 to fill the gas tank.

Step-by-step explanation: 3.56x12.5= 44.5

The possible outcomes for one turn is a table with 4 columns and 3 rows. First Spinner is the label for the columns, and Second Spinner is the label for the rows. Entries 2 A, 2 B, and 2 C are in Column 1. 4A, 4B, and 4C are the entries in Column 2. 6A, 6B, and 6C are entries in column 3. 8A, 8B, and 8C are the entries in column 4. a 2-row, 4-column table.

To the complete question is

franz and his friends are using the spinners below to play a game. if one turn consists of spinning each spinner once, which table shows all the possible outcomes for one turn?

1. A 4-column table with 2 rows. The columns are labeled First Spinner and the rows are labeled Second spinner. Column 1 has entries 2 A, 2 B. Column 2 has entries 4 A, 4 B. Column 3 has entries 6 A, 6 B. Column 4 has entries 8 A, 8 B.

2. A 4-column table with 3 rows. The columns are labeled First Spinner and the rows are labeled Second spinner. Column 1 has entries 2 A, 2 B, 2 C. Column 2 has entries 4 A, 4 B, 4 C. Column 3 has entries 6 A, 6 B, 6 C. Column 4 has entries 8 A, 8 B, 8 C. A 4-column table with 2 rows.

3.The columns are labeled First Spinner and the rows are labeled Second spinner. Column 1 has entries 2, A. Column 2 has entries 4, B. Column 3 has entries 6, C. Column 4 has entries 8, D. A 4-column table with 3 rows.

4.The columns are labeled First Spinner and the rows are labeled Second spinner. Column 1 has entries 2 A, 2 A, 2 A. Column 2 has entries 4 B, 4 B, 4 B. Column 3 has entries 6 C, 6 C, 6 C. Column 4 has entries 8 A, 8 B, 8 C.

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Applying the exterior angles theorem, the measure of angle GHI is: 29°.

The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

In other words, if a triangle, for example triangle GHI, has angles G, H, and I, and angle HIJ is the exterior angle formed by extending side GI through point I to point J, then the measure of angle HIJ is equal to the sum of the measures of angles IGH and GHI.

Given the following:

m<IGH = (x+16)°,

m<HIJ = (4x – 12)°,

m<GHI= (x +10)°

Therefore:

m<HIJ = m<IGH + m<GHI

Substitute:

4x - 12 = x + 16 + x + 10

4x - 12 = 2x + 26

4x - 2x = 12 + 26

2x = 38

2x/2 = 38/2

x = 19

m<GHI= (x +10)° = 19 + 10 = 29°

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There will be "sample size."=102 Below is an additional explanation.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

hence, There will be "sample size."=102 Below is an additional explanation.

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The solution is Option D.

The equation of line that passes through the point P ( 4 , -3 ) and the point Q ( 0 , -2 ) is y = ( -1/4 )x - 2

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first point be P = P ( 4 , -3 )

Let the second point be Q = Q ( 0 , -2 )

Now , the slope of the line passing through the points is calculated from the formula slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( -2 - ( -3 ) ) / ( 0 - 4 )

Slope m = ( -2 + 3 ) / -4

Slope m = -1/4

Now , the equation of line is given by

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - ( -3 ) = ( -1/4 ) ( x - 4 )

On simplifying the equation , we get

y + 3 = ( -1/4 )x + 1

Subtracting 3 on both sides of the equation , we get

y = ( -1/4 )x - 2

Therefore , the value of A is y = ( -1/4 )x - 2

Hence , the equation of line is y = ( -1/4 )x - 2

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Addition is used to find the sum of the number of miles lauren ran

Two or more expressions with an Equal sign is called as Equation.

Given,

Lanren ran 2.76. Miles in a track event.

Then she ran 0.4 Mile home after the event

We need to find the sum of the number of miles lauren ran.

By addition we find the sum of the number of miles lauren ran.

Two point seven six plus zero point four

2.76+0.4

Three point one six

3.16

Hence, addition is used to find the sum of the number of miles lauren ran

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According to the hypothesis test we find out that the t-statistic is 0.634 and thus, conclude that the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.

It is given to us that -

Company manufactures small automobiles that have averaged 45 miles per gallon of gasoline in highway driving

Company now advertises that its new small cars average more than 45 miles per gallon in highway driving

52 automobiles were tested

Sample average is 46.1 miles per gallon

Sample standard deviation is 5.3 miles per gallon

Significance level is 0.01

We have to conduct an appropriate hypothesis test and find the t-statistic and determine the correct conclusion.

Let us assume that -

p = population of average gasoline of new small cars in highway driving

According to the given information,

Null hypothesis represents that the advertising campaign of the manufacturer is incorrect. This implies that -

[tex]H_{0}[/tex] : [tex]p\leq 45[/tex] miles per gallon

Alternative hypothesis represents that the advertising campaign of the manufacturer is correct. This implies that -

[tex]H_{A}[/tex] : [tex]p > 45[/tex] miles per gallon

For carrying out the hypothesis test for the given situation we have to apply one sample z test statistic since the sample standard deviation information is available to us.

According to one sample z test, the value of test statistic is given as -

[tex]T = \frac{(X_{avg} -p)}{\frac{S}{\sqrt{n} } }[/tex] ------ (1)

where,

[tex]X_{avg}[/tex] = Sample mean

p = hypothesized population mean

S = Sample standard deviation

n = Sample size

According to the given information, we have

[tex]X_{avg}[/tex] = 46.1 miles per gallon

p = 45 miles per gallon

S = 5.3 miles per gallon

n = 52

Substituting the above values in equation (1), we have

[tex]T = \frac{(X_{avg} -p)}{\frac{S}{\sqrt{n} } }\\= > T = \frac{(46.1 -45)}{\frac{5.3}{\sqrt{52} } }\\= > T = \frac{1.1}{0.735}\\ = > T = 0.634[/tex]

It is given to us that the significance level is 0.01. According to the z-table, the critical value of the test statistic at 0.01 significance level is 2.58.

But, we see that the test statistic that we obtained above is less than the critical value at significance level of 0.01. i.e.,

0.634 < 2.58

This implies that there is not sufficient evidence for us to reject the null hypothesis for this particular situation.

Therefore, we can conclude from the hypothesis test that the t-statistic is 0.634 and thus, the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.

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According to the hypothesis test we find out that the t-statistic is 0.634 and thus, conclude that the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.

It is given to us that -

Company manufactures small automobiles that have averaged 45 miles per gallon of gasoline in highway driving

Company now advertises that its new small cars average more than 45 miles per gallon in highway driving

52 automobiles were tested

Sample average is 46.1 miles per gallon

Sample standard deviation is 5.3 miles per gallon

Significance level is 0.01

We have to conduct an appropriate hypothesis test and find the t-statistic and determine the correct conclusion.

Let us assume that -

p = population of average gasoline of new small cars in highway driving

According to the given information,

Null hypothesis represents that the advertising campaign of the manufacturer is incorrect. This implies that -

H0 = p<= 45 :  miles per gallon

Alternative hypothesis represents that the advertising campaign of the manufacturer is correct. This implies that -

HA : p > 45 :  miles per gallon

For carrying out the hypothesis test for the given situation we have to apply one sample z test statistic since the sample standard deviation information is available to us.

According to one sample z test, the value of test statistic is given as -

T = (X - p)/(SD/√n)

where,

X = Sample mean

p = hypothesized population mean

S = Sample standard deviation

n = Sample size

According to the given information, we have

X = 46.1 miles per gallon

p = 45 miles per gallon

S = 5.3 miles per gallon

n = 52

Substituting the above values in equation (1), we have

T = 46.1-45/(5.2/√52)

T = 1.1/0.735

T = 0.634

It is given to us that the significance level is 0.01. According to the z-table, the critical value of the test statistic at 0.01 significance level is 2.58.

But, we see that the test statistic that we obtained above is less than the critical value at significance level of 0.01. i.e.,

0.634 < 2.58

This implies that there is not sufficient evidence for us to reject the null hypothesis for this particular situation.

Therefore, we can conclude from the hypothesis test that the t-statistic is 0.634 and thus, the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.

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Answer:

r = .5 units  

Step-by-step explanation:

8.7 R is an improper  FRACTION of the 2 pi R of the entire circle ....set up a ratio:

8.7 / (2 pi)  =  3.9 / x       where x is the entire circumference measurement

x = 3.9 / (8.7 / (2 pi) )   = 2.82 units    

To find the radius    circumf = 2 pi r

                                     2.82 = 2 pi r      shows r = .5 units

The linear equation that passes through the points (0,-8) and (5,-5) is:

y = (3/5)*x - 8

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

a = (y2 - y1)/(x2 - x1)

Here we have the two points: (0,-8) and (5,-5)

Then the slope is:

a = (-5 + 8)/(5 - 0) = 3/5

And because of the point (0, -8) we know that the y-intercept is -8, then the linear equation is:

y = (3/5)*x - 8

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An inequality representing c, the total number of 40-kilogram crates that can be loaded into the shipping container is; 7700 + (40c) ≤ 27500

The maximum number of 40 kg crate is 380.

We are given;

Weight of the crate = 40 kg

Greatest weight that the container can load = 27500 kg

Weight of the other shipments on the container = 7700 kg

The greatest number of 40 kg crates is represented by the letter "c".

Thus;

The weight of the other shipment + weight of crate x number of crates ≤ greatest weight of the container

Plugging in the relevant values gives;

7700 + (40c) ≤ 27500

7700 + 40c ≤ 23000

40c ≤ 27500 - 7700

40c ≤ 19800

c ≤ 19800/40

c ≤ 495

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The function depicted in the table has the following slope-intercept form:

y = -3x + 4

For such equation of every straight line, the slope-intercept form is provided by:

y = mx +c

where:

Choose 2 points from the provided table, such as (2,-2) and (3,-5) and to use the evidence that the slope is, to determine the line's slope.

m = (y2 - y1)/(x2 - x1)

m = -5 + 2 / 3 - 2

m = -3

You can use the point (2,-2) or other point listed in the table along with this relation, to determine the y-intercept b.

b = y1 - mx1

b = (-2) -(-3 + 2)

b = 4

Consequently, is the function represented by the table's slope-intercept form: y -3x + 4.

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For Sarah to know the company that costs the least amount per minute, the quotients she should find are:

The quotient is the result of a division operation.

A division operation is one of the four basic mathematical operations, including addition, subtraction, and multiplication.

A division operation has four parts:

                   Company A        Company B

Total charge      $18                     $21

Total minutes    120                      150

Per-minute rate  $0.15 ($18/120)  $0.14 ($21/150)

Thus, the quotients Sarah should find are Options B and D.

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Answer:

post cards cost .06 each and envelopes cost .08 each.

Step-by-step explanation:

Let p = the cost of the post cards

Let e = the cost of the envelopes

15p + 10e = 1.70

e = p + .02  Substitute  p + .02 for e in the first equation

15p + 10(p + .02) = 1.70   Distribute the 10

15p + 10p + .2 = 1.70     Combine like terms

25p + .2 = 1.70  Subtract .2 from both sides

25p = 1.50  Divide both sides by 25

p = .06

Post cards cost .06 each.

Envelopes cost .08 each

The minimum sample size required to estimate a population mean with a confidence of 95%, a margin error of 2 units and a standard deviation of 10 units is 96.

A minimum sample size is the number of participants one needs to maintain their target confidence interval (margin of error) and confidence level while obtaining results that accurately represent the population they are studying.

The formula to calculate the minimum sample size for the population mean is [tex]\bold{n=\left(\frac{z\times \sigma}{E}\right)^2}[/tex]. Here, n is the sample size, z is the confidence level, σ is the standard deviation, and E is the margin error.

Given, the z-value for 95% confidence is 1.96, E is 2 and σ is 10.

Then, the minimum sample size is,

[tex]\begin{aligned}n&=\left(\frac{1.96\times10}{2}\right)^2\\&=(9.8)^2\\&=96.04\\&\approx96\end{aligned}[/tex]

The answer is 96.

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The relative maxima and minima of the function g(x) are at the point (-4, 22) at the local maxima and at point (4,-124) at the local minima.

Given:

Function g(x) = x^3 - 48x + 4

Take the derivative and set it equal to zero

3x^2 - 48 = 0

x^2 = 48/3 = 16

x = sqr16 = ±4

At x=+4, y = (4)^3 -48(4) + 4 = 64 -192+4 = -124

Point (4,-124) is a local or relative minimum

At x-4 y=(-4)^3 -48(-4)+4 = -64 + 192 + 4 = 122

The point (-4, 22) is a local or relative maximum

Refer to this complete question:

Find the relative maxima and minima, if any, of the function. (If an answer does not exist, enter DNE.) f(x) = x3 − 48x + 4 relative maximum (x, y) = relative minimum (x, y) =?

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2 - 2i can be written in polar form as [tex]2\sqrt{2} \ cis\frac {-3\pi}{4}[/tex]

To convert a complex number in Cartesian form (such as 2 - 2i) to polar form, you can use the following steps:

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The circumference around the flower bed in yards is D) 8×π.

The circumference of a circle is defined as the linear distance around it.

The formula for the circumference of a circle is [tex]2\pi r[/tex]. Where r is the radius of the circle.

It is given that the radius of the flower bed is 4 yards.

The flower bed is in the shape of a circle.

The circumference of the flower bed is 2×π×r.

Substitute the value of r in the equation.

Therefore the circumference around the flower bed is 8×π.

The correct option is D) 8×π.

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The correct answer is : c) As the number of experiments increases, the mean of the observations will approach the mean of the random variable.

Mean of random Variable x :

The expected value of a discrete random variable X, symbolized as E(X), is often called the long-term average or mean (symbolized as μ). This means that if you run the experiment many times over time, you would expect this average. For example, let X = the number of heads you get when you toss 3 fair coins. If we repeat this experiment (tossing 3 fair coins) many times, the expected value of X will be the expected average number of heads per 3 tosses.

Standard Deviation of Random Variable:

A measure of the variance of a random variable distribution that determines how for a value is from its expected value.

The standard deviation of a random variable X is often written as σ or σₓ.

For discrete random variables, the standard deviation is computed by taking the square of the difference between the value of the random variable and the expected value multiplied by the associated probability of the value of the random variable. Calculate the value of a random variable and finally take the square root.

In symbols σ = √ (x - μ)² P(X =x)

The equivalent formula is σ = [tex]\sqrt{E(x^{2}) - [{E(x^2)]}[/tex]

The square of the standard deviation equals the variance Var(X) = σ².

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Answer: $96.25

Step-by-step explanation:

Take 89.75 divided by 100% = 0.8975

Then times 7.25% = $6.5

Total is 89.75 + 6.5 = $96.25

Therefore, there are 4 x 1128 = 4512 possible 5 card poker hands with at least 3 aces that can be dealt from a standard deck of 52 cards.

1. There are 4 aces in a standard deck of 52 cards, so the maximum number of aces in a 5-card poker hand is 3.

2. There are C(4,3) = 4 ways to choose 3 aces out of the 4 aces in the deck.

3. For the remaining 2 cards, there are C(48,2) = 1128 ways to choose them from the 48 non-ace cards.

4. Therefore, there are 4 x 1128 = 4512 possible 5 card poker hands with at least 3 aces that can be dealt from a standard deck of 52 cards.

There are 4 aces in a standard deck of 52 cards, so the maximum number of aces in a 5-card poker hand is 3. There are C(4,3) = 4 ways to choose 3 aces out of the 4 aces in the deck. For the remaining 2 cards, there are C(48,2) = 1128 ways to choose them from the 48 non-ace cards.

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Answer: T=25

Step-by-step explanation:

T=4m^2 -11

We know that m= -3

-3^2 = 9

So the equation is T=4 (9) -11

T = 36 -11

T= 25

[tex]6x^2=6[/tex]

Divide both sides by 6:

[tex]\dfrac{6x^2}{6} =\dfrac{6}{6}[/tex]

[tex]x^2=1[/tex]

Take square root:

[tex]x=\pm\sqrt{1}[/tex]

[tex]\fbox{x = 1 or x = -1}[/tex]

By using multiplication, it can be calculated that

There are 391 houses in 23 blocks

What is multiplication?

Repeated addition is called multiplication. Multiplication is used to find the product of two or more numbers.

This is a word problem on multiplication

Number of houses in one block = 17

Assuming there are equal number of houses in each block,

Number of houses in 23 blocks = 23 [tex]\times[/tex] 17 = 391

There are 391 houses in 23 blocks

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The value of p is -5

Simply use cross multiplication :

The process of multiplying numbers in the shape of a fraction is called cross multiplication. Cross multiplying, also known as cross multiplication, is the process of multiplying the numerator of one fraction by the denominator of the other fraction on the other side of an equal symbol. Cross multiplication is a method for comparing fractions.

Both fractions with like and unlike parts are multiplied across. When employing the cross-multiplication procedure, we multiply the denominators as well as the numerators when a fraction is dissimilar, or when the denominators of two fractions are not alike.

[tex]14p-8=22+20p\\or, 14p-20p=22+8\\or, -6p=30\\or, p=-\frac{30}{6} \\or, p= -5[/tex]

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Answer:

Use a model to find the sum of two fractions with the same denominator

Add fractions with a common denominator without a model

Add fractions with a common denominator that contain a variable

Step-by-step explanation:

j

The average rate of change to the function is (d) 3/2

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

g(x) = 3/2x + 1

Also, we have the interval to be

-2 < x < 8

This interval can be expressed as

a = -2 and b = 8

So, we start by calculating g(-2) and g(8)

Substitute the known values in the above equation, so, we have the following representation

g(-2) = 3/2 * (-2) + 1

g(-2) = -2

Also, we have

g(8) = 3/2 * (8) + 1

g(8) = 13

The average rate of change to the function is then calculated as

Rate = [g(8) - g(-2)]/[8 + 2]

So, we have

Rate = (13 + 2)/(8 + 2)

Evaluate

Rate = 3/2

Hence, the average rate is 3/2

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Answer:

9/100

Step-by-step explanation:

numerator = whole number

denominator = 100

9/100