In a park, the ratio of adults to children is 11 to 9. If there are 320 people in the park, how many children are there?

The length of one side of the pentagon after translation is 9 units

Step-by-step explanation:

To be clear, "A translation is an isometry that translates all points of a figure the same distance in the same direction." The dimensions of any geometric figure will never change as a result of translation. The figure's measurements won't change; it will simply be moved from one location to another.

This means that even after being translated 2 units to the left, a regular pentagon with sides of 9 units will still have a side length of 9 units.

The length of one side of the pentagon after translation is 9 units(option B)

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a) The table with the output values is completed on the first image at the end of the answer.

b) The graph of the proportional relationship is given by the second image at the end of the answer.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

He covers a 150-square-foot floor in 3 hours, hence the constant of proportionality is obtained as follows:

k = 150/3 = 50 sq feet per hour.

Then the equation is given as follows:

y = 50x.

Then the numeric values for the table are given as follows:

The problem is given by the image shown at the end of the answer.

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(b) is the correct response. the students spend on textbooks in a semester between $250 and $2,000

The Gaussian distribution is another name for the normal distribution. It is a typical continuous probability distribution with a standard deviation of one and a mean of zero.

The tails of the curve are asymptotic, extending to infinity without touching the horizontal axis, and the curve is unimodal and symmetric about the mean. Since the majority of observations are centered on the mean, mean=mode=median.

99.7% of the area under the curve is approximately -3, or 3 standard deviations from the mean, according to the 68-95-99.7 rule. The z score is determined utilizing the accompanying recipe:

For z=3, solve for both x by equating the z score formula with -3 and 3.

3 = x 235 5 x = (3 5) + 235 x = 250 for z=-3:

3 = x 235 5 x = (3 5) + 235 x = 220 A student spends between $220 and $250 on textbooks each semester.

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Full Question = The distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a mean of $235 and a standard deviation of $5. According to the standard deviation rule, how much did almost all (99.7%) of the students spend on textbooks in a semester?

a. Between 230 and 240 dollars.

b. Between 220 and 250 dollars.

c. Between 175 and 295 dollars.

d. Less than 220 dollars or more than 250 dollars.

e. Less than 230 dollars or more than 240 dollars.

Answer: C its C

Step-by-step explanation:

GOT DANG JUST READ THE ANSWER ITS CCCCCCCCCCCCCCCCCCCCCCCCCCCCC

183  tickets must be sold to break even. The price at which a good or service must be provided in order to recoup its expenses of production.

The band costs $650,

decorations cost $45

refreshments cost $2.20 per person

let x be the  no of ticket

Total cost = 650+ 45+ 2.20x

break even

tickets cost = $6

6x =   650+ 45+ 2.20x

6 x - 2.20x = 695

3.8 x  = 695

x = 182.89

183  tickets must be sold to break even.

tickets must be sold to clear $700

700/6 =116.6

700/ 7.5 = 93.33

117 tickets must be sold to clear $700

94 tickets must be sold to clear $700,  If admission tickets are $7.50 each.

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Answer:

There were 56 signers.

Step-by-step explanation:

First, set up the two equations for the two situations we are given.

7 is 10% of y . . . . .(1):

[tex]7 = \frac{10}{100}(y)[/tex]

n is 80% of y . . . . .(2):

[tex]n = \frac{80}{100}(y)[/tex]

Now, solve for y in the 1st equation, and substitute y in the second equation to solve for n.

[tex]7 = \frac{10y}{100}[/tex]

[tex]700 = 10y\\[/tex]

[tex]70 = y[/tex]

[tex]n = \frac{80*70}{100}[/tex]

[tex]n = \frac{5600}{100}[/tex]

[tex]n = 56[/tex]

Answer:

--------------------------------

7 is 10% of y, find y:

n is 80% of y, find n:

Answer:

umm i would say 40$

Step-by-step explanation:

sorry if i have misunderstood the question

Answer:

  (b)  _Congruent

Step-by-step explanation:

You want to know the relationship between corresponding angles where a transversal crosses parallel lines.

The Corresponding Angles theorem tells you that corresponding angles at a transversal are congruent if and only if the lines are parallel.

Corresponding angles are congruent.

__

Additional comment

This fact is the basis for the simplest method of constructing a line parallel to a given line through an external point. (A transversal is drawn, and the angle is copied, making congruent corresponding angles.)

All of the other angle relationships at a transversal can be derived from this one using the usual relationships of linear pairs and vertical angles.

A right Riemann sum has the formula  A=∑ni=1Δxf(xi) A = ∑ i = 1 n Δ x f ( x i ) where x is the width of each of the n rectangles and f(xi) is the height.

A specific method of approximating an integral with a finite sum in mathematics is known as a Riemann sum. Riemann is the name of a German mathematician who lived in the 19th century. Approximating the area of functions or lines in graphs, as well as the length of curves and other approximations, is a highly typical application. The picked points in each subinterval of the partition are all in the upper Riemann sum, given an interval partition. The interval is often separated into subintervals of equal size.

Riemann  sum formula is A=∑f(xi)Δx A = ∑ f ( x i ) Δ x ,

where A is the curve's area under the evaluable interval,

f(xi) f ( x i ) is each rectangle's height (or the average of the two heights in the case of a trapezoid)

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The upper control limit(UCL) is 160

sample mean X =35

sample size n   =25

sample size n=25, average sample standard deviation is 5

Upper control limit is shown by the top dashed line (UCL). The data that is plotted on the control chart is used to calculate the upper control limit. It is positioned 3 sigma off the average line (of the data being plotted).

A control chart is made up of various components. It has an average line and two control limits. The lower control limit is represented by the dashed bottom line (LCL). The statistic's average is represented by the solid center line. The higher control limit appears as the top dashed line (UCL).

a)

Upper control limit(UCL) =X+A2R =160

Control line (CL) = X=35

Lower control limit (LCL)=X-A2R =90

Hence, The upper control limit (UCL) is 160

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Answer:

Step-by-step explanation:

Look at the original value of the gallons of water =12568 this is in July

Look at the value of the gallons of water in August =11,562

Find the difference between the two values=12568-11562=1006

Place the larger value of gallons of water first, as you are going from a large number to a small number you are decreasing by 1006

We put this value of the difference over the original gallons of water and then multiply by 100%

1006/12568 x100%=

This can be done on your calculator

1006÷12568 x100=8.004455761

Rounding to the nearest whole percent gives 8% decrease

The value of x in the parallelogram is zero.

A parallelogram is a two-dimensional geometrical shape(quadrilateral) whose sides are parallel to each other.

Therefore, the properties of a parallelogram are as follows:

Therefore, let's find the value of x using the properties of a parallelogram.

Hence,

ST = RU

2x + 15 = x + 15

2x - x = 15 - 15

Therefore,

x = 0

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Answer:

Step-by-step explanation:

You have ages in the ratio 3:5:7, with the average age being 25, and you want to know the age of the youngest. You have 45 L of a solution in the ratio sugar : salt = 1 : 2, and you want to know how much sugar solution to add to make the ratio 2 : 1.

The age ratios are an arithmetic progression with an odd number of terms, so the middle one is the average. That is, the average age of 25 years corresponds to 5 ratio units. Then the youngest boy is ...

  3/5 × 25 = 15 . . . . years old

The ratio 1 : 2 of sugar solution to salt solution tells you that the fraction that is sugar is 1/(1+2) = 1/3 of the whole amount, or ...

  sugar solution = 1/3 · 45 L = 15 L

Then the salt solution is ...

  salt solution = 45 L -15 L = 30 L . . . . . . . or (2/3·45 L)

To make the solution have twice as much sugar solution as salt solution, we need a total of 2·(30 L) = 60 L of sugar solution. We already have 15 L, so we need to add ...

  added sugar solution = 60 L -15 L = 45 L

45 L of sugar solution must be added to make the sugar : salt ratio be 2 : 1.

__

Additional comment

The "solution" problem can also be worked by considering "ratio units." The original sugar:salt ratio is 1:2. To make it be 2:1 while keeping the salt constant, we need to increase the ratio from 1:2 to 4:2. That is, we need to add 4-1 = 3 units of sugar solution. The 45 L amount is the amount of 1+2=3 units of solution, so we need to add 45 L of sugar solution.

Answer:

128

Step-by-step explanation:

DO the "E"

  125 + 28/7   -1    do the  division next

  125  +   4     - 1     now do the + or -  or both

     128

When 6 times a number is equal to the number increased by 10. The number is 5.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the number be represented as x.

Six times a number is equal to the number increased by 10. This will be:

(6 × x) = x + 10

6x + x = 10

Collect the like terms

6x - x = 10

5x = 10

Divide.

x = 10 / 2

x = 5.

The number is 5

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Answer:

A) -3

Step-by-step explanation:

To evaluate this mathematical expression, we must follow the following steps:

Perform the operation between parentheses: (0-1) = -1

Multiply the previous result by 2: -1 * 2 = -2

Add 1.5 to the previous result: -2 + 1.5 = -0.5

Therefore, the correct answer to the mathematical expression is A) -3.

From 2018 to 2019:

From 2019 to 2020:

Compare the percent increase we obtained:

Period 2018 to 2019 had a higher percent increase.

Answer:

C. Translation [tex](x,y) \longrightarrow (x-7, y+0)[/tex], Reflection in the [tex]y[/tex]-axis

The irrational solution of an exponential function, 3⁽¹⁻⁴ˣ⁾ = 4ˣ in exact form, is equals to the 0.190 in a decimal rounded to three decimal places.

The exponential function is a mathematical function of the form f(x) = aˣ , where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0. The most commonly used exponential base is the transcendental number e, which is approximately equal to 2.71828.

We have given an exponential equation is

3⁽¹⁻⁴ˣ⁾ = 4ˣ

Require to solve this Exponential equation.

Now, 3⁽¹⁻⁴ˣ⁾= 4ˣ

taking logarithm both sides we get,

ln ( 3⁽¹⁻⁴ˣ⁾ ) = ln(4ˣ)

=> (1-4x) ln(3) = xln(4) [using ln( aˣ)= x ln(a) ]

=> ln (3) - 4x ln (3) = x ln (4)

=> ln (3) = x ln(4) + 4x ln(3)

=> ln (3) = x[ ln (4) + 4 ln (3) ]

=> x = ln (3) / [ ln (4) + 4 ln (3) ]

=> x ~ 0.190

Therefore, solution set is ln (3) / [ ln (4) + 4 ln (3) ].

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Gonzalez Family Sprinklers used 15 liters and Walkers Family Sprinklers used 40 liters.

From the information, the Gonzalez family's sprinkler was used for 35 hours. The Walker family's sprinkler was used for 40 hours. There was a combined total output of 2125L of water.

Let Gonzalez = g

Let Walker = w

The equation will be:

g + w = 55 .... i

35g + 40w = 2125 ....

From equation i g = 55 - w

Put the above into equation ii

35g + 40w = 2125

35(55 - w) + 40w = 2125

1925 - 35w + 40w = 2125

Collect like terms

5w = 2125 - 1925

5w = 200

Divide

w = 200 / 5

w = 40

Walkers Family Sprinklers used 40 liters.

Since g + w = 55

g + 40 = 55

g = 55 - 40

g = 15

Gonzalez Family Sprinklers used 15 liters.

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Answer: x=-3

Step-by-step explanation:

-4=3x+5

isolate x by moving all other variables  to the right

-4-5=3x+5-5

-9=3x

x=-3

Answer:

-7

Step-by-step explanation:

To find the solution you'd have to plug in the -4 for every x you see but in this solution there is only one x so then you'd plug it in for that x. So then you'd have f(-4= 3(-4) + 5 and then you'd solve it. To solve it you would first multiply the 3 with the -4 because when something is in a parenthesis and there is a number beside with no sign that means you multiply. When you multiply you should get -12. After you get -12 you add 5 and your answer is -7.

When they give you an equation with an f(x) they sometimes give you inputs which you plug in to get your output. -4 was an input and -7 (your answer) is an output.
(hopefully you understood how i solved..)

The missing parts of the table for the compound interest problem are;

2)  $487.91

3) 435(1.039)^(t) and  $487.91

4) 435(e)^(0.039t) and $499

1) In this account, we are given the formula for the compound interest as;

P(1 + rt)

The balance after t years is expressed as;

435(1 + 0.039t)

Balance after 3 years is;

435(1 + 0.039(3)) = $485.90

2) In this account, we are given the formula for the compound interest as;

P(1 + (r/n))^(nt)

The balance after t years is expressed as;

435(1.039)^(t)

Balance after 3 years is;

435(1.039)^(3) = $487.91

3) Same as 2 above

4) In this account, we are given the formula for the compound interest as;

P₀e^(rt)

The balance after t years is expressed as;

435(e)^(0.039t)

Balance after 3 years is;

435(e)^(0.039 * 3) = $499

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Answer:

  (c)  see below

Step-by-step explanation:

You want the graph of the compound inequality x > -6 or x > -2.

The graph of the inequality x > -2 is shown as the top selection.

The graph of the inequality x > -6 is shown as the bottom selection.

You will notice that the bottom graph overlaps and includes the top graph. Hence the "OR" of the inequalities will look like the bottom graph, attached.

The set {(1, 2), (1, 4), (1, 6)} represents a function because each value of x corresponds to only one value of y.

In contrast, the sets {(3, 5), (-1, 7), (3, 9)} and {(1, 2), (3, 2), (5, 7)} do not represent functions because they contain multiple values of x that correspond to the same value of y. Specifically, the set {(3, 5), (-1, 7), (3, 9)} contains two values of x (3 and -1) that correspond to the same value of y (7), while the set {(1, 2), (3, 2), (5, 7)} contains two values of x (3 and 1) that correspond to the same value of y (2).

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Statements must be true concerning event A and event B are that event A and B are independent and not mutually exclusive.

Events that do not take place at the same time are said to be mutually exclusive. For instance, if a coin is tossed, the outcome will either be head or tail; we cannot obtain both outcomes. Since they do not occur at the same time, such occurrences are also known as disjunct events. Two events are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time. The results of a single coin flip, which can result in either heads or tails but not both, serve as an obvious illustration.

Given

The owner of the company believes that: the probability of being awarded the first job (event A) is 0.17.

The probability of being awarded the second job (event B) is 0.5; the probability of being awarded both jobs (A and B) is 0.375.

Statements must be true concerning event A and event B:

Event A and B are independent and not mutually exclusive.

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0.4166667 is the difference between 2/ 3 and 1 /4.

A fraction is a symbol used in mathematics to represent a part or element of the whole. It represents the proportional components of the whole. A fraction is made up of the denominator and the numerator. The top number is the numerator, and the lower number is the denominator.

More manageable pieces of a whole are represented by fractions. The components could be combined to make one thing or several things. In any instance, they come together to create the concept of a whole. As parts of wholes or sets, as the result of dividing two numbers, as the ratio of two quantities, as operators, and as measures are only a few examples of how to use fractions, they are all examples of fractions.

= 2/3 - 1/4

= 512

= 0.4166667

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This is a case of Compound Interest.

It takes around 3.22 years for investment to grow to 1500$ from 1000$.

The interest charged on a loan or deposit is known as compound interest. It is the idea that we employ the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The major distinction between compound and simple interest is this.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

Annual amount, A=P(1+[tex]\frac{r}{n}[/tex])∧nt

Given,

P=1000$

A=1500$

r=13%=0.13

A=P(1+[tex]\frac{r}{n}[/tex])∧nt

n=2(Compounded semi-annually)

⇒1500=1000(1+[tex]\frac{0.13}{2}[/tex])^2t

⇒[tex]\frac{1500}{1000}[/tex]=(1.065)^2t

⇒1.5=(1.065)^2t

Taking log on both sides

㏒(1.5)=2t㏒(0.625)

⇒t=[tex]\frac{log(1.5)}{2log(0.625)}[/tex]

⇒t=3.219years≈3.22years

This is a case of Compound Interest.

It takes around 3.22 years for investment to grow to 1500$ from 1000$.

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Applying the net operating income ratio, the rent per unit needs to be $8,354.22 to generate an NOI of $100,000.

The net operating income (NOI) is the result of the subtraction of the operating expenses from the gross operating income.

The net operating income ratio can be computed by subtracting the given operating expenses ratio from the operating gross income, which represents 100%.

                                                                                            Total

Rent per unit (per month) = $696.19 ($8,354.22/12)   $150,376

Vacancy Rate (5% of Potential Gross Income)                   7,519

Effective Gross Income                                                $142,857

Operating Expenses (30% of Effective Gross Income) 42,857

Net Operating Income (NOI)                                      $100,000

Number of Units 18

Gross operating income = net operating income + operating expenses

Operating expenses = 30% of effective gross income

Net operating income = 70% of effective gross income (100 - 30%)

= $100,000

Effective Gross Income (100%) = $142,857 ($100,000 ÷ 70%)

Vacancy rate = 5% of potential gross income

Effective Gross Income = 95% (100 - 5)

Potential gross income = $150,376 ($142,857 ÷ 95%)

Number of units = 18

Rent per unit = $8,354.22 ($150,376/18)

Rent per month = $696.19 ($8,354.22 ÷ 12)

Thus, a rent of $8,354.22 per unit can generate a Net operating income of $100,000.

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Answer:

Step-by-step explanation:

we are told that JK and KL sides are the same (b/c of the marks) so set them equal and solve for x

8x =  13x-15

8x - 8x  + 15   =  13x - 8x  -15 + 15

15 = 5x

divide by 5

3 = x

Use the fact that it's 180°  around the interior angles of the triangle to solve for y

180  = 5y -3  + 52 + 76

52 = 5y - 3

55 = 5y

11 = y

Penny currently budgeted for her trip, in US dollars is $993.95.

What is  Penny currently?

Pennies are constructed of copper-coated zinc. Only nickels—that identical alloy of 75% copper and 25% nickel—are one solid substance.

Given: Exchange rate of the US dollar to Egyptian pound is 1:5.3841

Item Cost Currency Plane ticket =

[tex]3,241.77 £=\frac{3,241.77}{5.3841}=\$ 602.100629632 \approx \$ 602.10[/tex]

Passport =  $65.00

Tour guide [tex]$=494.25 £=\$ 91.7980721012 \approx \$ 91.80$[/tex]

International phone card [tex]$=\$ 41.38$[/tex]

Hotel reservation [tex]$=398.26 £=\frac{398.26}{5.3841}=\$ 73.9696513809 \approx \$ 73.97$[/tex]

Car rental [tex]$=644.48 £=\frac{644.48}{5.3841}=\$ 119.700599915=\$ 119.70$[/tex]

Therefore, the total budgeted for her trip, in US dollars= [tex]602.10+91.80+41.38+73.97+119.70+65$ $=\$ 993.95$[/tex]

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