In the picture, you see 1 paper cup and 5 paper cups that are stacked together. The table shows the heights of stacks with different numbers of cups.

Which function rule gives the height of a stack of cups in terms of the number of cups in a stack?

There are 8 small rooms and 6 large rooms.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Let s be the number of small rooms reserved.

Let l be the number of large rooms reserved.

Each small room can accommodate 3 guests, hence s small rooms can hold 3s guests.

Each large room can accommodate 4 guests, so all large rooms can hold 5l guests.

Thus, the total number of guests

48 =3s+4l

3s+4l=48

3s+4l=48

as,  Khadija reserved 2 more small rooms than large rooms,

So, s=l+2

s=l+2

Now, solving the equations

3s+5l= 54

s=l+2

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Answer:

There are 54 Republicans, and 58 Democrats

Step-by-step explanation:

See the attached image

Answer: 15 minutes

Step-by-step explanation:

Let's make a proportion

16  miles    -    20 minutes

12  miles    -      х  minutes

Hence,

[tex]\displaystyle\\x=\frac{12(20)}{16} \\\\x=\frac{3(4)(4)(5)}{4(4)} \\\\x=3(5)\\\\x=15\ minutes[/tex]

Yes, the graphs of a power function and its inverse are symmetric about the line y=x.

What is an inverse function?

A function that "undoes" another function is called an inverse. In other words, if f(x) yields y, then y entered into the inverse of f yields the output x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f⁻¹.

What is a power function?

Any function where y = xⁿ, where n is any real constant integer, is referred to be a power function. In reality, many of our parent functions, including linear and quadratic functions, are power functions.

Here,

The graphs of self-inverse functions are symmetrical about the line y=x. The domain of a one-to-one function f is the same as the range of its inverse f⁻¹ and the range of f is the same as the domain of f⁻¹.

Hence, the graphs of a power function and its inverse are symmetric about the line y=x.

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Answer: I don't know  

Step-by-step explanation:

95km/h is the average speed for the whole journey

Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement

Given,

Simon drives 75 km at an average speed of 120 km/h

9 km at 70 km/h without stopping.

We need to find the average speed.

Average speed = Total distance/Total time

The total distance is 75km+9km

84 km

The average speed is sum of speeds by two

120+70=190/2=95km/h

Hence, 95km/h is the average speed for the whole journey

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The sequence is geometric and the common ratio is 1/7

An arithmetic sequence is a sequence of numbers in which each differs from the preceding one by a constant value e.g 2, 4, 6, etc. That is: 6-4 = 4-2 = 2

A geometric sequence is a sequence of numbers with a constant ratio between each number and the one before e.g.  9, 27, 81, etc. That is: 81/27 = 27/9 = 3

Given: 147, 21, 3

This sequence does not have a common difference. Thus, it is not arithmetic

This sequence has a common ratio. Thus, it is geometric

common ratio = 21/147 = 1/7 or 3/21 = 1/7

Therefore, the sequence is geometric and has a common  ratio of 1/7

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Answer:

Step-by-step explanation:480/3000

The numerical expression to model the situation when Kristen read her book is 2 + 1.

A numerical expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, Kristen read her book for 2 hours after school, then she read for another hour before she went to sleep. The expression will be:

= 2 + 1

= 3

She read for 3 hours.

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Answer:

Step-by-step explanation:

Given is a kite because:

Since MQ and QP are congruent, set equation and solve for y:

Answer:

y = 3

Step-by-step explanation:

Forming the equation,

→ 12y + 7 = 43

Now the value of y will be,

→ 12y + 7 = 43

→ 12y = 43 - 7

→ 12y = 36

→ y = 36/12

→ [ y = 3 ]

Hence, the value of y is 3.

Answer:

[tex]5x-4y=-3[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Answer:

Step-by-step explanation:

Area of circle equation:

Circumference of circle equation:

Use circumference equation to find the radius:

Find the area:

The smallest possible perimeter of the triangle is, 72.4 inches.

What is perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.

As given the longest side of an acute triangle measure 30 inches.

The two remaining sides' combined length must be longer than the opposite side.

The sum of the two remaining sides should be greater than 30 inches if the side is 30.

Assume the other two sides add up to 31 inches.

So, The perimeter of a triangle is equal to the sum of its three sides, which comes to 30 + 31 = 64 inches.

Consequently, the circumference must be greater than 64 inches.

Hence, based on the possibilities, the triangle's smallest conceivable perimeter is 72.4 inches.

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Answer:

27 miles, 40.5 miles, and 47.25 miles

Step-by-step explanation:

9 miles in 2/3 hours. To get to a whole number, we can multiply by the reciprocal of 2/3, which is 3/2. 2/3*3/2=1. Now lets multiply 9 by 3/2. 9*3/2=13.5

We now have a unit rate which is 13.5 miles each hour.

Now lets solve for 2 hours.

13.5*2= 27 miles

Now lets solve for 3 hours.

13.5*3=40.5 miles

Now lets solve for 3.5

13.5*3.5= 47.25 miles

Answer:

The two numbers are 17 and 44.

Step-by-step explanation:

x --> smaller number

y --> larger number

x + y = 61

y = 3x - 7

x + 3x - 7 = 61

4x - 7 = 61

4x = 68

x = 17

y = 3(17) - 7

y = 51 - 7

y = 44

Answer: y= (7a+9b)/8

Step-by-step explanation:

I can only provide the answer now, If you want more explanations reply this

Step-by-step explanation:

(2y - a)/3 = (a + 3b)/4

first we get rid of the fractions by multiplying everything first by 3 and then also by 4 ;

(2y - a) = 3(a + 3b)/4

4(2y - a) = 3(a + 3b)/4

8y - 4a = 3a + 9b

8y = 7a + 9b

y = (7a + 9b)/8

Answer:

Step-by-step explanation:

Answer: I Can't Read it

Step-by-step explanation: Its to far

Using the Work time problem solving technic, Betty and Bullwinkle to mow the entire lawn in 30 minutes if they are working together.

As we know that if A is complete the work of z in x days and B is complete the same work (z) in y days then both of can do complete work together then Equation of both A and B are completing work (z) together in

( 1/x + 1/y = 1/z ) days

Since Betty can mow a lawn is 120 minutes, then

Betty's mowing rate is 1/120th of a lanw per minute.

Since Bullwinkle can mow a lawn is 40 minutes, then Bullwinkle mowing rate is 1/40th of a lawn per minute.

Suppose working together they can a lawn in x minutes.

both together they can mow a lawn is x minutes, then their combined mowing rate is 1/x th of a lawn per minute.

To get the equation,

the sum of their mowing rates must equal their combined mowing rate,

1/40 + 1/120 = 1/x

Solve that by multiplying through by LCD of 40 and 120 is 120 then 4x = 120 => x = 30

Hence, when both are working together they complete the work together in 30 minutes .

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Answer:

- 3/4

PLEASE GIVE BRAINLIEST THANK YOU!!!

The set of scores has a mean of 5 and a standard deviation of 2. The score which corresponds to a z score of -2.0 is 1.

Given in the question,

Mean (m) = 5

Standard deviation σ =2

Z-score = -2

The score x,

= Z = x - m / σ

= -2 = x - 5 / 2

= -4 = x - 5

= x = 1

Standard deviation in statistics means the amount of dispersion or variations in the set of values. A lower standard deviation means the value is closer to the mean while a higher standard deviation means the value is farther away from the mean.

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Answer:

The rate of change, or slope, is 1/2.

To find the slope of a line, first, pick two points on the line and determine their coordinates. Then, determine the difference in y-coordinates of these two points (rise). After that, determine the difference in x-coordinates for these two points (run). Then you have your slope!

[tex]y = \cfrac{2}{5}x + 0\implies y=\cfrac{2}{5}x\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer: 6 units^3

Step-by-step explanation:
using the volume of a rectangular prism formula:

L*W*H

We are already given the AREA which is the part L*W of the previous formula.

Now we multiply:

1 1/3 units * 4 1/2 units^2

Convert the fractions into 4/3 * 9/2 for an easier multiplication.

Resulting in 36/6 which is equivalent to 36 divided by 6.

Which gives us our answer of 6.

The shopper bought a watermelon costing $4.45.

Let x represent the cost of watermelon

y = cost of napkin + cost of paper plates

The tax rate on non-food items is 5%, hence:

5% of y = 0.19

0.05y = 0.19

y = $3.8

The total for the three items he bought was $8.25 before tax,

x + y = 8.25

x + 3.80 = 8.25

x = 4.45

The shopper bought a watermelon costing $4.45.

A tax is a compulsory monetary charge or a few other sorts of levy imposed on a taxpayer (a man or woman or criminal entity) by using a governmental agency if you want to fund authorities' spending and numerous public expenses (regional, neighborhood, or countrywide), and tax compliance refers to coverage movements and character behavior geared toward making sure that taxpayers are paying the right amount of tax on the proper time and securing the right tax allowances and tax reliefs. the first known taxation passed off in historical Egypt around 3000–2800 BC. A failure to pay in a well-timed way (non-compliance), together with evasion of or resistance to taxation, is punishable by means of regulation. Taxes consist of direct or oblique taxes and may be paid in cash or as its labor equivalent.

Maximum nations have a tax system in the region, so as to pay for public, common societal, or agreed-on country-wide needs and for the capabilities of the presidency. a few levies a flat percentage rate of taxation on private annual profits, however, maximum scale taxes are modern and based on brackets of annual earnings amounts. most nations charge a tax on a character's profits as well as on corporate earnings. nations or subunits regularly additionally impose wealth taxes, inheritance taxes, estate taxes, gift taxes, property taxes, sales taxes, use taxes, payroll taxes, duties, and/or tariffs.

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Z in terms of m and n is z = [tex]3^{m} -2^{n}[/tex]

Exponentiation is the process of expressing large numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself. For example, 6 is multiplied by itself four times, yielding 6 6 6 6. This is written as [tex]6^{4}[/tex]. The exponent is 4 and the base is 6.

Given that 1000 to the power of m divided by 100 to the power of n

When powers of the equal base are divided, the same base is placed and the exponents are subtracted, which is an important mathematical property of powers.

Then, as powers of the same base, we can write 1000m and 100n:

1000m = [tex](10^{3})^{m}[/tex] = [tex]10^{3m}[/tex]

100n= [tex](10^{2)^{n} }[/tex] = [tex]10^{2n}[/tex]

Now we perform the division of powers of the same base (10)

103m/102n

= 103m-2n

Finally

103m-2n = 10z

z = 3m-2n

Therefore Z in terms of m and n is z = [tex]3^{m} -2^{n}[/tex]

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The given statement is FALSE.

If one or more data items are much greater than the other items, the median, rather than the mean, is more representative of the data.

When one or more data items are much greater than the other items, these extreme values can greatly influence the mean.

When you have a skewed distribution, the median is a better measure of central tendency than the mean

The median and mean can only have one value for a given data set. The mode can have more than one value

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Answer:

$193.60

Step-by-step explanation:

160x1.21=$193.60

160+21%=$193.60

Answer:

Step-by-step explanation:

Let the number of weeks be x after which both boys have same weight.

Mike's weight after x weeks:

Tom's weight after x weeks:

Equate both expressions and solve for x:

Answer:

After 8 weeks, both boys weigh same.

Step-by-step explanation:

Forming the equation,

→ 200 - 2x = 160 + 3x

Now the value of x will be,

→ 200 - 2x = 160 + 3x

→ -2x - 3x = 160 - 200

→ -5x = -40

→ x = -40/-5

→ x = 40/5

→ [ x = 8 weeks ]

Hence, the value of x is 8.