he table below models the cost, y, of using a high-efficiency washing machine and a standard washing machine over x number of years. Which equation represents the cost of the high-efficiency washing machine over a given number of years? Which equation represents the cost of the standard washing machine over a given number of years? After how many years of use would the washing machines cost the same amount? Which washing machine would be the more practical purchase if kept

Answer:

No because x-coordinate 17 appears twice.

Step-by-step explanation:

In a function, no two ordered pairs can have the same x-coordinate.

Here, points (17, 2) and (17, 8) have 17 as the x-coordinate. Since the same x-coordinate, 17, is used more than once, this relation is not a function.

Answer:

9

Step-by-step explanation:

a.) cube root of 729

³√729

= 9

b.) look for a number that you will multiply thrice to get 729

which is 9 or u will use your calculator

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On average the 50 students need to raise $25 each.

What is average?

In plain English, an average is a single number chosen to represent a group of numbers; it is typically the sum of the numbers divided by the number of numbers in the group. The average of the numbers 2, 3, 4, 7, and 9 is, for instance, 5.

Given: Fifty students in the seventh grade are trying to raise at least $2,000 for sports supplies. They have already raised $750.

To find the number of students should each student raise, on average, in order to meet the goal.

Let, $2000 - $750 = $1250

So,

$1250/50 = 25

Hence, on average the 50 students need to raise $25 each.

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The area of the floor in the scale drawing will be equal to 150 in².

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the given information in the question,

Length of the classroom, l = 30 feet and,

The width of the classroom, w = 20 feet.

As per the scale drawing, the length of the classroom, l' = 15 feet

Let the scale width, w' = x feet

As we can see that the original length is twice the scale drawing.

Then, the original width also is twice the scale drawing.

So, w' = 20/2 = 10 feet.

Now, the area of the floor in the scale drawing will be,

A = wl

A = (15)(10)

A = 150 in².  

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The median or the middle value of 42 48 52 54 59 61 61 64 65 67 68 70 72 75 80 is 64.

It is the middle value of the given set of numbers after arranging the given set of numbers in order.

We have,

42 48 52 54 59 61 61 64 65 67 68 70 72 75 80

The given set of numbers is in ascending order.

There are 15 numbers.

The middle number will be the 8th number.

8th number = 64

Thus,

The median is 64.

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The data item in this distribution corresponding to a z-score of -7 will be 290.

The standard score in statistics is the number of standard deviations that a raw score's value is above or below the mean value of what is being observed or measured. Raw scores that are higher than the mean have positive standard scores, whereas those that are lower than the mean have negative standard scores. The Z-score measures how much a particular value deviates from the standard deviation. The Z-score, also known as the standard score, is the number of standard deviations above or below the mean for a given data point. The standard deviation reflects the level of variability within a particular data collection.

Here,

z=(X-μ)/σ

-7=(X-500)/30

-210=X-500

X=290

The data item in this distribution that corresponds to we given z-score

z equals to -7 will be 290.

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Answer: (x+1)(x+4)

Step-by-step explanation:

Step 1: Use the sum-product pattern

x^2 + 5x + 4

x^2 + 4x + x + 4

Step 2: Common factor from the two pairs

x(x+4) + x+4

Step 3: Rewrite in factored form

(x+1)(x+4)

a) The mode is 2.

b) 32 Students were there altogether.

c) 15 dinners were served during the week.

d)The mean number of dinners is 2.5.

This refers to the value that appears most often in a set of data values.

What is mean?

This refers to the average of the given set of numbers. It is calculated by dividing the sum of given numbers by the total number of numbers.

Given in the question:

a)The number of school dinners 2 has a frequency of 12.

Hence, the mode is 2.

b) To calculate the number of students altogether, we add then frequencies

Total number of students = 0 + 8+ 12 + 6+ 4 + 2

Total number of students = 32

c) To get the number of dinners served during the week, we add the number of dinners together.

Number of  dinners served during the week= 0 + 1 + 2 + 3 + 4 + 5

Number of  dinners served during the week = 15

D) The mean number of dinners =

1+1+1+1+1+1+1+1+2+2+2+2+2+2+2+2+2+2+2+2+3+3+3+3+3+3+4+4+4+4+5+5

                                                32

The mean number of dinners = 80

                                                    32

The mean number of dinners = 2.5

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Answer:

27.6•\• is the answer from me

The equation of the line is  f(X)=(-1/6)x—(19/6)

What is equation?

In arithmetic, an equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main body:

first linear functions have their general form as y= mx + c, where y belongs to the range and X belongs to the domain, m is the slope, and c is the y-intercept.

So using f(x) =y

Given that f(—5)=-4 , X=—5 and y=-4, hence by substituting into the general eqn y= mx+c, You get

-4= -5m+c ------(1)

Also given that f(1)=—3, X=1 and y=—3, hence by substituting into the general eqn y= mx+c, You get

-3= m+c --—-(2)

Solve equation (1) and (2), simultaneously to find the value of m and c. After which you will substitute into y=mx+c or f(X)=mx+c to get your f(X).

Note: you will get m=—1/6 and c=-19/6, from the simultaneous equations.

Hence f(X)=(-1/6)x—(19/6) and correct option is D.

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Answer:

y ≤ -3x - 3

Step-by-step explanation:

The graph crosses the y axis at -3.  The slope is -3.  (0, -3) .  From that point do down vertical 3 spaces and horizontally 1 space.  You will be at the point (1,-6)  Draw a line to join those 2 points.  The inequality is ≤ that means the solutions are the points on the line and below the line.  This is shown in the pink shading.

y ≤ -3x - 3

Step-by-step explanation:

The graph crosses the y-axis at -3.  The slope is -3.  (0, -3) .  From that point do down vertical 3 spaces and horizontally 1 space.  You will be at the point (1,-6) Draw a line to join those 2 points.  

The inequality is ≤ which means the solutions are the points on the line and below the line.  This is shown in the pink shading.

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Answer:

  (a)  For every day that passes, a person drives 54 miles

Step-by-step explanation:

You want to know the situation in which one quantity changes relative to another at a constant rate.

The rate of change is described as 54 miles for each day. This is a constant rate of change. Miles relative to days are described by a linear function.

We assume the description means that the balance in the savings account increases by 1.5% with each passing month. While this interest rate is a constant, the amount by which the balance changes each month is not constant. The balance relative to time is described by an exponential function.

If the vine doubles in length twice a week, its length increases by 300% each week. As with savings, this growth rate is constant, but the amount of growth each week is not. The length of the vine is described by an exponential function.

As with savings, this growth rate is constant, but the amount of increase each year is not. The population is described by an exponential function.

The situation with a constant rate of change is ...

  For every day that passes, a person drives 54 miles.

__

Additional comment

When the quantity is graphed, the "rate of change" refers to the slope of the curve on the graph. The graph of an exponential growth function does not have a constant slope, but has a slope that increases exponentially.

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Answer:

Linear function:  y = x + 7.75

Step-by-step explanation:

A store sells packages of comic books with a poster. We are told that:

Let p be the cost of one poster.

Let c be the cost of one comic book.

Write a system of equations using the given information and the defined variables:

[tex]\begin{cases}p + 4c = 11.75\\p + 11c = 18.75\end{cases}[/tex]

Subtract the first equation from the second equation to eliminate p:

[tex]\begin{array}{crcrcl}&p&+&11c&=&18.75\\-&(p&+&4c&=&11.75)\\\cline{2-6}&&&7c&=&\;\;7.00\\\cline{2-6}\end{array}[/tex]

Solve for c:

[tex]7c=7.00[/tex]

 [tex]c=1.00[/tex]

Therefore, the cost of one comic book is $1.00.

Substitute the found value of c into one of the equations and solve for p:

[tex]\begin{aligned}p+4(1.00)&=11.75\\p+4.00&=11.75\\p&=7.75\end{aligned}[/tex]

Therefore, the cost of one poster is $7.75.

Now we know the cost of one poster and one comic, we can write a linear function that models the cost y of a package containing x number of comic books:

[tex]y = 1.00x + 7.75[/tex]

[tex]y =x + 7.75[/tex]

We are told that another store sells a similar package modeled by a linear function rule with initial value $6.99.  The initial value is the y-intercept of each function, i.e. the cost of the package when zero comics are sold. So the linear function for this package is:

[tex]y = x + 6.99[/tex]

To determine which store has the better deal, we need to compare the y-intercepts (the initial values). The store with the lower initial value provides a better deal because it charges less for the basic package (when the number of comic books is zero).

Since 6.99 is less than 7.75, the other store offers a better deal, as it has a lower initial cost for the basic package.

Answer:

[tex]\Huge \boxed{ \texttt{\bf{y = x + 7.75} }}[/tex]

Step-by-step explanation:

To find the linear function rule that models the cost [tex]\texttt{y}[/tex] of a package containing any number [tex]\texttt{x}[/tex] of comic books, we can use the given information:

Let's denote the cost of a poster as [tex]\texttt{P}[/tex] and the cost of a comic book as [tex]\texttt{C}[/tex]. Then, we can write two equations:

To solve these equations, we can use the method of elimination. Let's use this method to eliminate [tex]$$P$$[/tex]:

Now, substituting the value of [tex]\texttt{C}[/tex] back into equation 1:

Now that we have the cost of a poster (P) and a comic book (C), we can write the linear function rule as:

[tex]\Large \boxed{\texttt{y = x + 7.75}}[/tex]

Now, suppose another store sells a similar package modelled by a linear function rule with an initial value of $6.99. This means that the cost of a poster at the other store is $6.99. Since the cost of a comic book is the same at both stores ($1), the linear function rule for the other store is:

[tex]\Large \boxed{ \texttt{y = x + 6.99}}[/tex]

Comparing the two linear function rules, we can see that the second store has a better deal because the initial cost of a poster is lower ($6.99) compared to the first store ($7.75).

________________________________________________________

The probability that the sample mean is greater than 18 as calculated  is 0.8413.

Given data,

n = 36, sample size

μ = 17, population mean

σ = 6, population standard deviation

when x = 18

z = (18 - 17)/1 = 1

P(x <18) = 0.8413

Therefore , the probability = 0.8413

A population's standard deviation serves as a gauge for how widely distributed its individual data points are. It's a way to express how dispersed from the mean the data is.

While a large standard deviation indicates that the data is more spread, a small standard deviation indicates that the data points are often close to the mean.

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There were two candidate A and B contesting for the municipal corporation election in a town. The total number of voter in the town were 80,000. If 90% of the voter had voted and 60% of vote polled were cat in favour of A, 28,800 the number of vote received by B.

A state-incorporated city, town, village, or county that has the power to manage local governmental matters, such as creating a police force. A municipal corporation is established by a state's legislature, which also determines its lifespan, privileges, and powers. likewise known as a municipality.

A local governing body, such as cities, counties, towns, townships, charter townships, villages, and boroughs, is referred to legally as a "municipal corporation." Municipally-owned companies can also be referred to as this

Regulation of building construction and land usage. Town planning is included in urban planning. preparing for social and economic progress. water supply for residential, commercial, and industrial uses.

Given that,

Total number voters = 80,000

Total number of votes polled = 90%

Thus,

= (90/100) × 80,000

= 72,000

So, total percent of votes received by B if A gets 60% of polled votes.

= 100% - 60%

= 40%

Hence, total number of votes received by B

= (40/100) × 72,000

= 28,800

Therefore, the number of votes received by B, out of total votes polled is 28,800 votes.

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The acceleration of the dolly-sandbag system is 1.23 m/s²

Given parameters:

The mass of the dolly and actor combined is: M = 94 kg

the mass of the sandbag is: m = 35 kg.

The coefficient of kinetic friction between the dolly and the stage floor is 0.20.

Let the acceleration is a.

Hence, From Newton's 2nd law of motion, we can write that:

ΣF = (m+M) a

mg - μMg = (m+M) a

a = g (m- μM)/ (m+M)

= 9.8 (35 - 0.20 × 94)/(35 + 94)

= 9.8 (16.2)/(129)

= 1.23 m/s².

Hence, the acceleration of the dolly-sandbag system is 1.23 m/s².

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Answer:

No

Step-by-step explanation:

When the 2 equations are graphed the point (13, 17) is not

a solution to the system of linear equations.

So the answer is no.

If you want to look for the solution**- the solution to the equation is (12, 18)

The integers are -47, -11, -6, 12, 20 in order of least to greatest.

A whole number that can be positive, negative, or zero is called an integer. It is not a fraction. -5, 1, 5, 8, 97, and 3, 043 are some examples of integers. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers.

Positive numbers, negative numbers, and zero make up integers. Thus, integers include 0 through 3, as well as -1, -2, and -3. No further parts, such as fractions or decimals, are allowed in integers. Therefore, fractional and decimal numbers like 3 1/2 and -7.5 are NOT integers.

Integer is derived from the Latin integer, which means whole or untouched, from the prefix in (for "not") with tangere ("to touch"). The words "entire" and "integer" are both derived from the same root, which is the French word entire.

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Answer:

Step-by-step explanation:

You want to find the effect of compounding 2% annual interest on $1000 at different intervals for a year. The intervals are ...

The attached calculator display shows the result:

Answer: 9.8

Step-by-step explanation:

Answer:

This is an irrational number.

Step-by-step explanation:

If you see the decimal, it has the values of 1 and 0, but are not constant.

If it were to be 0.010101010... it would be rational.

But this decimal does not look like that, so its irrational.

Hope this helps.

The relative frequencies for the following number set is 10 30 40 50 60 70 10 30 40 60 60 80 20 30 50 60 70 90 20 30 50 60 70 90

How do you find the relative frequency in a frequency distribution?

Divide the frequency by the total number of data values to obtain the relative frequency. Add all of the earlier relative frequencies to the relative frequency for the current row to obtain the cumulative relative frequency. Divide the total number of occurrences of the result you're interested in by the total number of occurrences if your data are observational. This may be expressed mathematically as relative frequency = frequency of the desired result / all occurrences.

There are 24 items.

Relative Frequency:

10 - (2) - 8.33%

20 - (1) - 4.17%

30 - (4) - 16.67%

40 - (2) - 8.33%

50 - (3) - 12.5%

60 - (5) - 20.83%

70 - (3) - 12.5%

80 - (1) - 4.17%

90 - (2) - 8.33%

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The absolute error and the percent error of the police officer’s estimate will be 4.29%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

A cop is assessing the separation from one side of a road to the next. The genuine distance is 13.4 m. The cop's gauge is 14 m.

The absolute error and the percent error of the police officer’s estimate are calculated as,

%error = [(14 - 13.4) / 14] x 100

%error = (0.60 / 14) x 100

%error = 4.29%

The outright mistake and the percent blunder of the cop's gauge will be 4.29%.

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The graph of y = k/x has k = 4.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

y = k/x

The coordinates from the graph:

(1, 4) and (2, 2).

This can be considered as,

(1, 4) = (x, y) = (2, 2)

Now,

y = k/x

4 = k/1

k = 4

y = k/x

2 = k/2

k = 4

Thus,

The value of k is 4.

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The expected value for the given problem is E(x) = 1.4.

What is expected value?

The expected value is a generalization of the weighted average in probability theory. Informally, the expected value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.

A projected average value for an investment at some point in the future is known as the expected value (EV).

Investors use expected value to gauge an investment's merit, frequently in relation to how risky the investment is.

The formula for to find the expected value is given as,

E ( X ) = μ = ∑ x P ( x ) .

E(x) =  0*0.30 + 1*0.25 + 2*0.25 + 3*0.15 + 4*0.05

E(x) = 1.4

Hence, the expected value for the given problem is E(x) = 1.4.

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The equation that is equivalent to quadratic equation x^ 2-8x+19=0 is

(x-4)^ 2+k = 0 using quadratic equation properties .

What is quadratic equation ?

A quadratic equation is a second order equation written as ax2 + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.

Properties of graph of quadratic equation :

1. The shape of curve y = f(x) is a parabola.

2. If a>0, the parabola opens upwards.

3. If a<0, the parabola opens downwards.

4.The coordinates of vertex of parabola in all these cases is

(-b/2a , -D/4a).

The given equation is x^ 2-8x+19=0

a  = 1,

b = -8,

c = 19.

As a>0, 2nd property is correct i.e. no maximum value , only minimum value can be find that will be at vertex.

So, the vertex = (4,3)

The minimum value = 3 at 4.

So, the value of k = 3,

Given equation can be written as x^ 2-8x+16+3 = 0.

                                                      = (x-4)^ 2 +3 = 0.

The option A is correct.

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The x−intercept is 6 and the y-intercept is 5.

What is an equation of a line?

In high school algebra, "the equation of a line" is a crucial concept. This refers to an equation in the (x,y) plane with a line as its solution set. The "slope-intercept" form is the most widely used form in algebra. y = mx + b. In essence, x is used as a parameter in this formula, and y is written as a function of x: y = f(x) = mx+b.

Here, we have

The given equation of a line is:

−10x − 12y = −60

10x + 12y = 60

x/6 = y/5 = 1

Hence, the x−intercept is 6 and the y-intercept is 5.

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The value of the function g(f(x))=4x²+4x-15 if f(x) = x²+x-6

g(x) = 4x +9.

An exact one of each element of Y is assigned to each element of X via a mathematical function from a set X to a set Y. The sets X and Y are denoted by the terms "domain" and "codomain," respectively.

The fundamental concept of functions was the connection between fluctuating quantities and other variables. One illustration of this is the impact of time on a planet's position. Beginning at the end of the 17th century and continuing until the 19th century, the concept was developed using the infinitesimal calculus.

Given,

f(x) = x²+x-6

g(x) = 4x +9

f(g(x))=f(4x+9)

g(f(x))=4(x²+x-6)+9

g(f(x))=4x²+4x-24+9

g(f(x))=4x²+4x-15

Therefore, the value of the function g(f(x))=4x²+4x-15 if f(x) = x²+x-6

g(x) = 4x +9.

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