A rectangle has a width (3x-2) and a length of (5x). The rectangle has the same perimeter as a square with a perimeter of 44 units.
Find the value of x.

The rate of acceleration of a bicycle. if it went from a complete stop to 15 meters per second in 5 seconds is

acceleration is solved using the formula

a = (v - u) / t

definition of variables

final velocity = v

initial velocity = u

time taken  = t

form the question we have that

v = 15 meters per seconds

u = 0 (bicycle went from complete stop)

t = 5 seconds

a = (15 - 0) / 5

a = 15 /5

a = 3 meters per seconds squared

The bicycle is travelling at an acceleration of 3 meters per seconds squared

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The sentence which represents the algebraic equation is; "Twice the sum of 3 and and five times a number n is equal to the product of the number and another number, a".

It follows from the task content that the sentence which represents the equation given be determined.

First, the expression 3 + 5n can be interpreted as; the sum of 3 and 5 times a number, n.

Also, the expression "an" can be interpreted as the product of n and another number a.

Therefore, the whole equation; 2(3+5n)=an can be interpreted as;

"Twice the sum of 3 and and five times a number n is equal to the product of the number and another number, a".

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If the nex day, the biologist retums to the lake and takes a sample of 7 fish. Of those fish, 2 of them have tags. The estimated number of fish in the lake is 35 fish.

Let x represent the estimated number of fish in the lake

Hence,

x /10 = 7/2

Cross multiply

2x = 10 × 7

2x = 70

Divide both side by 2x

x =70/2

x = 35 fish

Therefore 35 is the number of fish.

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Answer:

Assessment Practice 5. A science teacher has $225 to spend on lab equipment. He buys 4 posters with a guide to classifying rocks, for $19 each. Student rock collections cost $9 each. How many rock collections can he buy? Explain how you solve

Let

x -----> number of rock collections that he can buy

so

the algebraic expression that represents this situation is

Solve the inequality for x

subtract 76 both sides

Divide both sides by 9

therefore

The maximum number of rock collections that he can buy is 16

Step-by-step explanation:

The equation is 9x+76=225 and the number of rock collections he can buy is 17.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, a science teacher has $225 to spend on lab equipment.

Let the number of rocks collected be x.

He buys 4 posters with a guide to classifying rocks, for $19 each.

That is 19×4=76

Student rock collections cost $9 each.

Now, 9×x=9x

So, the equation is 9x+76=225

Subtract 76 on both the sides of equation, we get

9x=149

Divide 9 on both the sides of equation, we get

x=16.5

x≈17

Therefore, the number of rock collections he can buy is 17.

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The statement which is true about the y-values of the graph of the function as required is; Choice B; The y-values are all greater than or equal to 2.

It follows from the task content that the statement which is true regarding the y-values of the graph defined by; f(x) = lx-5l +2 is to be determined.

Therefore, we must recall that expressions enclosed in the absolute value sign upon evaluation are always greater than or equal to zero.

Hence, it can be concluded that we the y-values of the resulting graph to be greater than or equal to 2 (on the occasion that; lx-5l = 0).

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Answer:

Step-by-step explanation:

x=5

The percent of the people surveyed were satisfied with the​ car will

be 45%.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

Total number of people in a survey of car = 1,500

And, 675 people said they would buy that type of car again.

Now,

Total number of people in a survey of car = 1,500

And, The people surveyed were satisfied with the​ car = 675

Hence, The percent of the people surveyed were satisfied with the​ car is;

= 675 / 1500  x 100

= 0.45 x 100

= 45%

Thus, The percent of the people surveyed were satisfied with the​ car will

be 45%.

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Answer:

$9.25

Step-by-step explanation:

$397.75÷43=$9.25

Weekly salary divided by hours of work = hourly pay

Answer:

2 pairs of parallel sides

The value of x in the second ordered pair is - 0.5 or - 1/2 and that of y in the first ordered pair is 8.

The given ordered pair is (-3,y) and (x,2)

the equation y=-2x+2

In the first step we put the value of x as -3 as given in (-3,y) in the equation y=-2x+2, we get

y=-2(-3)+2

⇒y=6+2

⇒y=8

So the value of y is 8 then the ordered pair will be (-3,8).

Again, in the second step, we put the value of y as 2 as given in (x,2) in the equation y=-2x+2, and we get

2=-2x+2

⇒2x=2-2

⇒2x=0

⇒x=0

So the value of x is 0, and the ordered pair will be (0,2).

The table:

I have provided a photo of the table:

The range of function f(x) = 4x + 5 for given input values is {-3, 1, 5, 9, 13}

The correct answer is an option (C)

In this question, we have been given a function f(x) = 4x + 5

We need to find the range of given function for input {-2, -1, 0, 1 , 2}

We know that the range of  a function is the set of all output values for given input.

for x = -2,

f(-2) = 4(-2) + 5

f(-2) = -3

for x = -1,

f(-1) = 4(-1) + 5

f(-1) = 1

for x = 0,

f(0) = 4(0) + 5

f(0) = 5

for x = 1,

f(1) = 4(1) + 5

f(1) = 9

for x = 2,

f(2) = 4(2) + 5

f(2) = 13

Therefore, the range of function f(x) = 4x + 5 for given input values is {-3, 1, 5, 9, 13}

The correct answer is an option (C)

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Using the z-distribution to test the hypothesis, it is found that:

a) The conclusion is that there is not enough evidence to conclude that the percentage has changed from 2016.

b) A Type II error would mean finding that there is not enough evidence that the percentage is significantly below 58.1% when in fact it is.

At the null hypothesis, it is tested if the proportion is the same as in 2016, that is:

[tex]H_0: p = 0.581[/tex]

At the alternative hypothesis, it is tested if the proportion is different, hence:

[tex]H_1: p \neq 0.581[/tex]

A Type II error is the non-rejection of a false null hypothesis, that is, finding that there is not enough evidence that the percentage is significantly below 58.1% when in fact it is.

The equation calculating the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which the variables are listed as follows:

For this problem, the value for these variables is given as follows:

[tex]\overline{p} = \frac{586}{1048} = 0.559, n = 1048, p = 0.581[/tex]

Hence the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.559 - 0.581}{\sqrt{\frac{0.581(0.419)}{1048}}}[/tex]

z = -1.44.

The critical value for a two-tailed test is with a significance level of 0.05 is:

|z| = 1.96.

The absolute value of the test statistic is of |z| = 1.44 < 1.96, meaning that there is not enough evidence to conclude that the percentage has changed from 2016.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$50000\\ P=\textit{original amount deposited}\\ r=rate\to 5.9\%\to \frac{5.9}{100}\dotfill &0.059\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &7 \end{cases}[/tex]

[tex]50000=P\left(1+\frac{0.059}{4}\right)^{4\cdot 7} \implies 50000=P(1.01475)^{28} \\\\\\ \cfrac{50000}{(1.01475)^{28}}=P\implies 33183.05\approx P[/tex]

Answer:

6x^2-17x+12

Step-by-step explanation:

Distribute

2x^2-3x+1+x^2-2x+2(-2x+3)^2

Square (2x+3)

(-2x+3)(-2x+3)

FOIL

4x^2-6x-6x+9

Combine like terms

4x^2-12x+9

re-write equation

2x^2-3x+1+x^2-2x+2+4x^2-12x+9

Combine like terms

6x^2-17x+12

The completed table of the two column method to prove DE = FD is presented as follows;

Statement [tex]{}[/tex]                             Reason

1. CE = CD + DE[tex]{}[/tex]                    Segment addition postulate

2. FG = FD + DG              [tex]{}[/tex]     Segment addition postulate

3. CE = FG              [tex]{}[/tex]               Given

4. CD + DE = FD + DG      [tex]{}[/tex]    Substitution property of equality

5. CD = DG              [tex]{}[/tex]              Given

6. DG + DE = FD + DG    [tex]{}[/tex]      Substitution property of equality

7. DE = FD               [tex]{}[/tex]              Subtraction property of equality

A two column method consists a number of statements alongside the reasons that are known to make the statements true.

The segment addition postulate state that a point B is located on a segment AC if and only if AB + BC = AC, therefore;

The substitution property of equality states that if a = b, and a + c = d, then b + c = d

Which gives;

Similarly; CD = DG, then DG + DE = FD + DG

The subtraction (and addition) property of equality states that a quantity of known value can be subtracted (or added) to both sides of an equation and both sides of the equation remains equal.

Mathematically, if x = y, then x - z = y - z, therefore;

Then;

∴ DE = FD

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The y-intercept of the line passes through the point (-4,5) with slope 2 is y = 13.

Given:

(-4,5) and slope m = 2

substitute in y=mx+c

5 = 2*(-4) + c

5 = -8 + c

c = 5 + 8

c = 13.

c value in y = 2x + c

y = 2x + 13

To find y-intercept put x = 0.

y = 2(0) + 13

y = 0+13

y = 13

Therefore the y-intercept of the line passes through the point (-4,5) with slope 2 is y = 13.

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The exponential growth of 16.63% will take approximately 10.80 years to reach a population of 1134

An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on.

Data;

f(x) = P(1 + r)ˣ

x = time

Substituting the values

1134 = 215(1 + 0.1663)^ˣ

x = 10.80

It will take approximately 10.8 years to reach a growth of 1134

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Answer: The correct answer is "10.0 years"

Step-by-step explanation:

I took the test

2 printers takes 7 minutes to print the same number of leaflets.

From the question, we have

1 printers takes 14 minutes to print the leaflets.

2 printers takes = 14/2 = 7 minutes to print the leaflets.

Divide:

Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.

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Answer: 7

Step-by-step explanation: because 1 printer takes 14 mins but if u have 2 u half the 14 it gives you 7 so it will take 2 printers 7 mins to print the same amount of leaflets. hope this helps.

The percentage of people over speeding on this road on purpose is 9%

Percent of people speeding on this road noticed the sign = Percentage of people who notice the speed limit at the beginning of the road - Percentage of people who notice the sign and follow the speed limit

= 84% - 75%

= 9%

In conclusion, the percentage of people who intentionally speed on purpose is 9%

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Answer: mode  50  Mean x¯¯¯ 158.33333333333

Median x˜ 167.5

Step-by-step explanation: hope this helps

Range 250

Minimum 50

Maximum 300

Count n 12

Sum 1900

a. The number of permutations of three letter words that can be formed with repetition is 1000 words

b. The number of permutations of three letter words that can be formed without repetiton is 720 words

Permutations are the number of ways in which x objects can be arranged out of n objects.

The number of permutations is given by ⁿPₓ = n(n - 1)(n -2)...(n - x + 1)

Since we require the number of three-letter "words" can be made from 10 letters "FGHIJKLMNO" with repetition, we note that there are 10 letters.

Since repetition is allowed, for the first slot, we have 10 letters, for the second position, we have 10 letters and for the third position, we have 10 letters.

So, the total number of permutations is n = 10 × 10 × 10

= 1000 words

So, the number of three letter words that can be formed is 1000 words

Since we require the number of three-letter "words" can be made from 10 letters "FGHIJKLMNO" without repetition, we note that there are 10 letters.

Since repetition is not allowed, for the first slot, we have 10 letters, for the second position, we have 9 letters and for the third position, we have 8 letters.

So, the total number of permutations is ¹⁰P₃ = 10 × 9 × 8

= 720 words

So, the number of three letter words that can be formed is 720 words

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Answer: 2.333333...

Step-by-step explanation:

If we apply rise over run, we see that it rises 3.5 spaces, and runs 1.5, which means that   [tex]m = \frac{rise}{run} = \frac{3.5}{1.5} = 2.33333...[/tex]

Answer:

what are the given ratio?

Step-by-step explanation:

The pH of the liquid which is 3.886 indicates that it is more acidic than coffee.

The pH of a solution gives a measure of the concentration of hydronium ions in the solution, and therefore, indicates the level of acidity or basicity of the solution.

pH values ranges from 0 to 14, with solutions that are more acidic having a pH of less than 7, while basic solutions have a pH of more than 7.

The given pH of coffee = -4.886

The concentration of the liquid = 10 × The concentration of the ions in coffee

Which gives;

-㏒₁₀C = 4.886

Concentration of the hydronium ions in coffee, C = [tex]10^{(-4.886)}[/tex]

Concentration of ions in the unknown liquid = 10 ×  [tex]10^{(-4.886)}[/tex] = [tex]10^{(-3.886)}[/tex]

pH of the unknown liquid = [tex]-log_{10} \left(10^{(-3.886)}\right) = 3.886[/tex]

The pH of the unknown liquid indicates that it is more acidic than coffee

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The speed of the current is equal to 8 miles per hour.

Mathematically, speed of any physical object can be calculated by using this formula;

Speed = distance/time

Let the variable c represent the speed of the current in miles per hour. Therefore, the downstream and upstream speed relative to the water would be given by this mathematical expression:

Speed downstream = 14 + c.

Speed upstream = 14 - c.

Additionally, the total time would be given by:

Total time = total distance/speed

Time upstream + time downstream = 6.5 hours

33/(14 - c) + 33/(14 + c) = 7.0

Multiplying both sides of the equation by (14 - c)(14 + c), we have:

33(14 + c) + 33(14 - c) = 7.0(14 - c)(14 + c)

462 + 33c + 462 - 33c = 7.0(196 - c²)

924 = 7.0(196 - c²)

Dividing both sides of the equation by 7.0, we have:

132 = 196 - c²

Speed of the current, c² = 196 - 132

Speed of the current, c² = 64

Speed of the current, c = √64

Speed of the current, c = 8 miles per hour.

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A total of 12 5/8 pages is not meant for advertisement

From the question, we have the following parameters

First section = 16 pages

Pages for advertisement = 3 and 3/8 pages

Rewrite the above parameters as

First section = 16 pages

Pages for advertisement = 3 3/8 pages

The number of pages that are not for adverts is then calculated as

Pages not for adverts = First section - Pages for advertisement

Substitute the known values in the above equation

So, we have the following equation

Pages not for adverts = 16 - 3 3/8

Evaluate the difference

Pages not for adverts = 12 5/8

Hence, the number of pages that are not for adverts is 12 5/8 pages

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By using percentage, it can be calculated that

1) Percentage increase in area = 25 %

2) Percentage increase in area = 60 %

3) Percentage decrease in area = 25 %

4) Percentage decrease in area = 40 %

What is percentage?

Sometimes there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

For example 2% means [tex]\frac{2}{100}[/tex]. Here 2 is expressed as a fraction of 100

1) Original area = 12 sq. yard

   New area = 15 sq. yard

   Increase in area = 15 - 12 = 3 sq. yard

   Percentage increase = [tex]\frac{3}{12}\times 100 \\[/tex]

                                       = 25 %

1) Original area = 15 sq. yard

   New area = 24 sq. yard

   Increase in area = 24 - 15 = 9 sq. yard

   Percentage increase = [tex]\frac{9}{15}\times 100 \\[/tex]

                                       = 60 %

1) Original area = 12 sq. yard

   New area = 9 sq. yard

   Increase in area = 12 - 9 = 3 sq. yard

  Percentage decrease = [tex]\frac{3}{12}\times 100 \\[/tex]

                                       = 25 %

1) Original area = 10 sq. yard

   New area = 6 sq. yard

   Increase in area = 10 - 6 = 4 sq. yard

   Percentage increase = [tex]\frac{4}{10}\times 100 \\[/tex]

                                       = 40 %

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