Functions W and Z are both linear functions of x. Which statement comparing the functions is true? Select all that apply. A. The slope of Function W is less than the slope of Function Z. B. The slope of Function W is equal to the slope of Function Z. C. The slope of Function W is greater than the slope of Function Z. D. The y-intercept of Function W is less than the y-intercept of Function Z. E. The y-intercept of Function W is equal to the y-intercept of Function Z. F. The y-intercept of Function W is greater than the y-intercept of Function Z

Answer:

4x + 9

Step-by-step explanation:

the product of 4 and x is 4x

then 9 more is addition, so 4x + 9

The length of three sides will be 35 feet, 70 feet and 51 feet

Define Perimeter of triangle

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

Perimeter of Triangle = side1 + base + side2

Let, the shortest side of the triangle = x

The other side length is = 2x

and, the length of third side is = x + 16

given perimeter = 156 feet

We know, perimeter of triangle = a + b +c

where, 'a' and 'c' stands for sides of triangle

and, b stands for base

hence, the expression will be according to formula,

x + 2x + x + 16 = 156

solve for 'x'

4x + 16 = 156

4x = 156 - 16

x = 140/4

x = 35

2x = 2 * 35 = 70

x + 16 = 35 + 16 = 51

Therefore, the length of three sides will be 35 feet, 70 feet and 51 feet.

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Answer: The slope is 3.

Step-by-step explanation: Hope this helps :)

Number of possible area codes = 144

The telephone area codes consist 3 digits.

The possible digits are 1, 2, 3,4,5,6,7,8,9,0. That is, a total of 10 digits.

The first digit was not 0 or 1. So the remaining are 2,3,4,5,6,7,8,9. There are 8 possibilities in first place.

The second digit is either 0 or 1. So there are only two possibilities for second place.

The third digit was anything except 0. So the third digit has 9 possibilities.

The total possibilities of the three digit number is the product of possibilities of digits in each place.

Hence, Number of possible area codes = 8 x 2 x 9 = 144

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If the sample size were to increase, and all other numbers remaining stays the same, then the standard error would be less.

Standard error is defined as the measures of the preciseness of an estimate of a population mean. It can be calculated by dividing the sample standard deviation by the square root of the sample size.

SE = SD / √n

where SE = standard error

SD = sample standard deviation

n = sample size

Increasing the sample size, n, while the samples remain the same(hence, the standard deviation will be the same), will result to smaller standard error.

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a=1×10, b=2×2×5, c=5×5 and d=2×5. Option a, b and d are the prime factorization of 10 but option c is not a prime factorization of 10.

Given that,

a=1×10, b=2×2×5, c=5×5 and d=2×5

We have to find the prime factorization of 10.

A natural number other than 1 is said to have a prime factor if its only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11, and so on. So, let's take something like the number 20 as an example. That can be divided into two components. We can say, "Well, that's 4 times 5." Note that the number five is a prime.

Option a is 1×10

1×10=10

Option a is a prime factor of 10.

Option b is 2×2×5

2×2×5=10×2

Option b is a prime factor of 10.

Option c is 5×5

5×5=25

Option c is not a prime factor of 10.

Option d is 2×5

2×5=10

Option d is a prime factor of 10.

Therefore, Option a, b and d are the prime factorization of 10 but option c is not a prime factorization of 10.

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If a stick of length 60 inches is measured to be 63 inches long the the percent error will be 5% .

The Percent Error can be calculated by the formula

Percent Error = (measured value - actual value)/(actual value)  ×100

In the question ,

it is given that

the original length of the stick is 60 inches .

the measured length of the stick is 63 inches .

So, the measured value = 63 inches ,

actual value = 60 inches .

Substituting the measured values and actual value in the percent error formula , we get

Percent Error = (63-60)/60 × 100

= 3/60 × 100

= 1/20 × 100

= 100/20

= 5 %

Therefore , if a stick of length 60 inches is measured to be 63 inches long the the percent error will be 5% .

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Two or more expressions with an Equal sign is called as Equation.  Price of each basket is 24.ice of each basket is 24.

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

Given A youth organization raised $15, 336 by selling gift baskets.

Martin's team sold : 48 baskets

Amy's team sold : 138 baskets

Sharon's team sold :77 baskets

Juan's team sold : 250 baskets

Dee's team sold : 126 baskets

Let x be the price of each basket.

Let us form a equation by given data

48x+138x+77x+250x+126x=$15, 336

639x=$15, 336

Divide both sides by 639

x=24

Hence price of each basket is 24.

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An online place has the highest price for a board game because it costs $4.28 and a store costs $4.18 for each game respectively.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

From the data given:

At the toy store, you could get 2 board games for $8.36.

Each board game cost = 8.36/2 = $4.18

Online the price for 3 board games is $12.84.

Each board game costs = 12.84/3 = $4.28

4.28 > 4.18

Thus, an online place has the highest price for a board game because it costs $4.28 and a store costs $4.18 for each game respectively.

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1/4π is area of a circle when the radius is 6 cm.

What is the circumference of a circle?

 A = πr²

differentiate both sides with respect to 't'

dA/dt = πr² dr/dt

dA/dt = 2πr dr/dt

dA/dt = 3  ,     r = 6

3 = 2π * 6dr/dt

dr/dt = 1/4π

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The expression f(5)=10 tells us that if Polly is an artist and sells posters at a local cafe then it means that Polly makes 10 dollars when she sells 5 posters.

According to the question,

We have the following information:

Polly sells x posters then she makes f(x) dollars.

We have the following expression:

f(5) = 10

So, it simply means that in place of x in f(x) we have f(5) then we have 5 in place of x.

f(x) is the amount made in dollars. So, the total amount Polly made is 10 dollars.

Hence, the expression f(5) = 10 clearly states that Polly sold 5 posters as an artist and made 10 dollars out of it.

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The distance between the points is 2: x2 - x1 = -6 + 8. So, the midpoint would be located on a point that is half of this distance from both points.

2/2 = 1

-6 - 1 = -7
-8 + 1 = -7

-7 has a distance of 1 from both -8 and -6, so this is the midpoint.

In order to determine how many millimeters the spool has, you take into account the following identity:

1 meter = 1000 millimeters (1 m = 1000mm)

Then, you can proceed as follow:

100 m = 100(1m) = 100 (1000 mm) = 100,000 mm

where you have multiplied by 1000 the given quantity in meters, that is, you replace the unit meter (m) by its equivalence in millimeters (1000 mm)

That is, 100 meters are equivalent to 100,000 millimeters

Answer: 11.2

Step-by-step explanation: In order to find the length of n, you can use the given angle measure and base length as well as a trig ratio. Since 6.2 is adjacent to angle N, you can use tangent (opposite/ adjacent).

tan (61) = n/6.2

(multiply by 6.2 on both sides to isolate n)

• 6.2 • 6.2

tan (61) • 6.2 = n

11.185 = n

~11.2 = n.

Answer:

-4/27

Step-by-step explanation:

2x³ + XY is a binomial with a degree of 3

An algebraic expression containing only two terms is called a binomial. This is a binomial polynomial. It is also called the sum or difference of two or more monomials. This is the simplest form of a polynomial. A binomial is a polynomial with only terms. For example, x 2 is a binomial where x and 2 are two separate terms. Also, the coefficient of x is 1, the exponent of x is 1, and 2 is a constant here. Therefore, an A-binomial is a two-term algebraic expression that contains a variable, a coefficient, an exponent, and a constant.

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1. Reject the null.

2. Data is consistent with the null hypothesis.

3. Unable to tell using our staff confidence interval.

A confidence interval in frequentist statistics is a range of estimates for an unknown parameter. A confidence interval is calculated at a specified degree of confidence; the most popular level is 95%, but other levels, such 90% or 99%, are occasionally used. Confidence intervals are used by statisticians to assess a sample variable's level of uncertainty. For instance, a researcher might randomly select many samples from the same population, compute a confidence interval for each sample, and then examine how well each sample might reflect the true value of the population variable. The generated datasets are all unique, some of which contain the genuine population parameter and others which do not. An unknown population parameter is most likely to be found inside a range of values that is bounded above and below the statistic's mean.

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Answer:

24[tex]x^{5}[/tex][tex]y^{6}[/tex]

Step-by-step explanation:

(3x²y) × (2xy³) × (4x²y²)

= 3 × 2 × 4 × x² × x × x² × y × y³ × y²

= 24 × [tex]x^{(2+1+2)}[/tex] × [tex]y^{(1+3+2)}[/tex]

= 24[tex]x^{5}[/tex][tex]y^{6}[/tex]

The graph that shows the in the table is option (D)

From the table

The cost for hiring a plumber for zero hours = $50

The cost for hiring a plumber for 1 hours = $80

The cost for hiring a plumber for 2 hours = $110

The cost for hiring a plumber for 3 hours = $140

The domain is the set of all possible inputs.

The range is the set of all possible output

Here we have to plot the graph using the number of hours in the x axis and cost of hiring a plumber in y axis

The graph on option (D) matches the values in table. Because

At x= 0, y=50

At x= 1, y=80

At x= 2, y= 110

At x= 3, y= 140

Hence, the graph that shows the in the table is option (D)

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Considering Annie bought 5 pounds of apples, 4 pounds of oranges, and 3 pounds of bananas, and each pound of apple costed $1.75, orange $2.35 and bananas $1.50,

(i) Annie had to spend an exact amount of $22.65, to buy all the above mentioned fruits.

(ii) The amount of money that Annie spent on the fruits, can be represented by the expression [(1.75 * 5) + (2.35 * 4) + (1.50 * 3)]

(iii) Rounding the prices to the nearest whole dollar and estimating the total amount Annie spent, our estimation is an overestimation compared to the actual price Annie had spent.

As per the question statement, no information is provided about Annie's expenditure, and hence, we are considering that, Annie bought 5 pounds of apples, each pound costing $1.75, 4 pounds of oranges, each pound costing $2.35 and 3 pounds of bananas, each pound costing $1.50.

We are required to calculate:

(i) The exact amount Annie spent on the fruits.

(ii) A mathematical expression to represent the amount of money that Annie spent.

(iii) To determine whether it is an overestimation or underestimation if we round the prices to the nearest whole dollar and estimate the total amount Annie spent.

Starting with (i) and (ii),

Total amount Annie actually spent on her fruits

= [{(price of per pound apple) * (number of pounds of apple she bought)} + {(price of per pound orange) * (number of pounds of orange she bought)} + {(price of per pound banana) * (number of pounds of bananas she bought)}

= $[(1.75 * 5) + (2.35 * 4) + (1.50 * 3)]

= $(8.75 + 9.40 + 4.50)

= $22.65

And, the amount of money that Annie spent on the fruits, can be represented by the expression [(1.75 * 5) + (2.35 * 4) + (1.50 * 3)].

Now solving (iii), first, we need to round off the prices to the nearest whole dollar and then estimate the total amount Annie spent.

Now, $1.75 dollars rounded off the prices to the nearest whole dollar will become $2.

Similarly, $2.35 dollars rounded off the prices to the nearest whole dollar will become $2,

And, $1.50 dollars rounded off the prices to the nearest whole dollar will become $2.

That is, the rounded-off per pound cost of apples is $2, that of oranges is $2 and of bananas is also $2.

Therefore, on the same consideration that, Annie bought 5 pounds of apples, 4 pounds of oranges, and 3 pounds of bananas, the estimated total amount she spent on the fruits based on the above mentioned rounded-off per pound costs will be equal to

$[(2 * 5) + (2 * 4) + (2 * 3)] = ${10 + 8 +6) = $24

Since (24 > 22.60), thus, we can conclude that rounding-off the prices to the nearest whole dollar and estimating the total amount Annie spent, our estimation is an overestimation compared to the actual price Annie had spent.

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A . [tex]\sqrt{37}[/tex]  falls between integers 6 and 7

B. The decimal to the nearest tenth = 6.1

A. How are the two integers calculated?

[tex]\sqrt{37}[/tex]  =  6.082 , falls between integers 6 and 7

What are integers?

B: Estimate The Decimal To The Nearest Tenth

[tex]\sqrt{37}[/tex]  =  6.082

            [tex]\sqrt{37}[/tex]  =  6.082 = 6.1

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The triangle's edges measure (3x - 4) feet, (x² - 1) feet, and (2x² - 15) feet, respectively. The perimeter of the triangle is 42 feet.

Given that,

Kat is using reflective orange paint to outline a triangle stage prop. The triangle's edges measure (3x - 4) feet, (x² - 1) feet, and (2x² - 15) feet, respectively.

We have to find if x = 4, what is the triangle's perimeter.

The perimeter of the triangle is equal to sum of the three sides of the triangle.

=3x - 4 + x² - 1 + 2x² - 15

=3x²+3x-20

Take the x value as 4

We get,

=3(4)²+3(4)-20

=3×16+3×4-20

=48+14-20

=62-20

=42

Therefore, The perimeter of the triangle is 42 feet.

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T-Mobile charges a base fee of $15 per month plus $0.05 for each minute. 300 minutes long would you need to call for them to charge the same amount.

Given: While Verizon has a basic rate of only $10 per month but charges $0.10 for long-distance calls, T-Mobile has a base fee of $15 per month plus $0.05 for each minute you are on the phone.

We have to estimate how long would you need to call for them to charge the same amount.

Let the equation be 15 + 0.05 x = 0.10 x

⇒ 0.05 x - 0.10 x = -15

simplifying the above equation, we get

⇒ -0.05 x = -15

⇒ 0.05x = 15

⇒ x = 15 / 0.05

⇒ x = 300 minutes

Therefore, 300 minutes long would you need to call for them to charge the same amount.

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The equation of the line is y = -x + 3

Equation of a straight line is usually of the form y = mx + c

where:

m = slope

c = y intercept

slope = ( 5 - -2 ) / ( -2 - 5 )

= ( 5 + 2 ) / -7

= 7 / -7

= -1

The y intercept is found from the graph to be 3

the equation of lthe line is

y = -1 ( x ) + 3

y = -x + 3

Therefore the equation of the line as gotten from the graph is y = -x + 3

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The total number of dogs are 135.

The number of Retrievers dogs are 35.

The number of off leashed playing dogs are 47.

Determine the number of dogs that are not Retrievers.

Determine the number of dogs that are not retrievers and not lleashed.

So table can be filled as,

Not on a leash leashed Total

Retrievers 10 25 35

Not a Retrievers 37 63 100

Total 47 88 135

1.

The events are indpendent if occurence of event does not affect the other event. But it can be observed that not on a leash and retriever depend on each other. So event not on a leash and retriever are not indpendent.

4.

The number of dogs that are not retriever and is on a leash are 63. So probability is,

The Value of the horizontal asymptote is 0

What is horizontal asymptote?

The horizontal asymptote of a function y = f(x) is a line y = k and to calculate the horizontal asymptote please substitute [tex]x=[/tex]±∞. We can also find the vertical asymptote.

now we are given a function

[tex]f(x)=2(3)^{-x}[/tex]

Now substitute x=±∞ in the equation, as the x in denominator we get

f(x)= 0

This is the value of the horizontal asymptote

Hence the value of horizontal asymptote comes out to be 0

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The equation of a line in point-slope form that passes through the point (20,19) with slope 55 is y = 55x -1091.

As given in the question,

Line passes through the point ( x₁ , y₁ ) = ( 20, 19)

Slope of the line that passes through (20 , 19) is 55

Equation of a line in point-slope form that passes through the point (20,19) with slope 55

y - y₁ = m ( x- x₁)

⇒ y - 19 = 55 (x - 20)

⇒ y -19 = 55x - 1100

⇒ y= 55x - 1091

Therefore, the equation of a line in point-slope form that passes through the point (20,19) with slope 55 is y = 55x -1091.

The complete question is:

Use point-slope form to write the equation of a line that passes through the point (20,19) with slope 55.

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