Tania Ramirez purchases 25 hanging file folders for $6.99. What is the price
per folder?

Answer:

7(1+2)

Step-by-step explanation:

So find the Greatest common factor first which is7 in this case

now we divide each number by 7

1+2 now

now we put that around parthesis and multiply it by 7

7(1+2)

Thats how you factpr

Check:

using distributive property

7+14, same answer.

Answer:

7(1+2)

Step-by-step explanation:

Find the factors of each number

7 has factors of 1,7

14 has factors of 1,2,7,14

The greatest common factor is 7

7*1 + 2*7

Factor out the 7

7(1+2)

The current temperature is 48°F, in expected to drop 1.5°F each hour, then the hours per word 8 hours the temperature will be 36°F.

The current temperature is = 48°F.

It is expected to drop = 1.5°F each hour.

We can assume, temperature = 36°F

Let x hours the temperature will be 36°F.

Temperature is a measure of the average kinetic energy of the particles in an object. When the temperature increases, the motion of these particles also increases. Temperature is measured with a thermometer or a calorimeter.

Then,

48 - 1.5x = 36

It's expected to drop 1.5F per hour,

We can list the equation,

So,

We can write,

48 - 1.5x = 36

48 - 36 = 1.5x

We can sum or difference of the product,

1.5x = 12

x = 12/1.5

We can divide the products,

x = 8 hours

Therefore,

In expected to drop 1.5°F each hour, then the hours per word 8 hours the temperature will be 36°F.

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Answer:

The present temperature is 48°F; it is anticipated to decrease by 1.5°F every hour, reaching 36°F in 8 hours.

Step-by-step explanation:

48°F is the current temperature.

An hourly decrease of 1.5°F is anticipated.

We'll assume that it's 36°F.

The temperature will be 36°F in x hours.

The average kinetic energy of the particles in an object is measured by its temperature. The velocity of these particles likewise increases as the temperature rises. A thermometer or a calorimeter is used to determine the temperature.

Then,

48 - 1.5x = 36

It's expected to drop 1.5F per hour,

We can list the equation,

So,

We can write,

48 - 1.5x = 36

48 - 36 = 1.5x

We can sum or difference of the product,

1.5x = 12

x = 12/1.5

We can divide the products,

x = 8 hours

Therefore,

In expected to drop 1.5°F each hour, then the hours per word 8 hours the temperature will be 36°F.

Answer: his total bill is 7.24

Step-by-step explanation:

a = amount invested at 4%

how much is 4% of "a"? (4/100) * "a", namely 0.04a.

b = amount invested at 10%

how much is 10% of "b"? (10/100) * "b", namely 0.10b.

c = amount invested at 14%

how much is 14% of "c"? (14/100) * "c", namely 0.14c.

we know the total amount invested is 6000, so whatever "a" and "b" and "c" might be, we know that a + b +c = 6000.

we also know that the yielded amount in interest is $652, so if we simply add their interest, that'd be 0.04a + 0.10b + 0.14c.

the combined amount of "a" and "b" is simply a + b, and we also know that "c" is that much plus 200, namely "c = a + b + 200".

\(a+b+c=6000\hspace{5em}\underline{c=a+b+200} \\\\\\ a+b+\stackrel{c}{(a+b+200)}=6000\implies 2a+2b+200=6000\implies 2a+2b=5800 \\\\\\ 2b=5800-2a\implies b=\cfrac{5800-2a}{2}\implies \boxed{b=2900-a} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{c=a+b+200}\implies \stackrel{substituting}{c=a+(\underset{b}{2900-a})+200}\implies c=a+2900-a+200 \\\\\\ c=2900+200\implies {\Large \begin{array}{llll} c=3100 \end{array}} \\\\[-0.35em] ~\dotfill\)

\(0.04a+0.10b+0.14c=652\implies \stackrel{\textit{substituting}}{0.04a+0.10(\underset{b}{2900-a})+0.14(\underset{c}{3100})}=652 \\\\\\ 0.04a+290-0.10a+434=652\implies 0.04a-0.10a+724=652 \\\\\\ 0.04a-0.10a=-72\implies -0.06a=-72 \\\\\\ a=\cfrac{-72}{-0.06}\implies {\Large \begin{array}{llll} a=1200 \end{array}} \hspace{5em} \stackrel{6000-3100-1200}{{\Large \begin{array}{llll} b=1700 \end{array}}}\)

Step-by-step explanation:

Taking the provided equation ,

\(\implies \dfrac{3x+4}{5}-\dfrac{2}{x+3} =\dfrac{8}{5} \)

1) Here denominator of two fractions are 5 and x +3 . So their LCM will be 5(x+3)

\(\implies \dfrac{(x+3)(3x+4)-(2)(5)}{5(x+3)}=\dfrac{8}{5} \)

2) Transposing 5(x+3) to Right Hand Side . And 5 to Left Hand Side .

\(\implies 5(3x^2+4x+9x+12 -10) = 40(x+3)\)

3) Multiplying the expressions.

\( \implies 5(3x^2+13x+2) = 40x + 120 \)

4) Opening the brackets .

\(\implies 15x^2+ 65x + 10 = 40x + 120 \)

5) Transposing all terms to Left Hand Side .

\(\implies 15x^2 + 65x - 40x + 10 - 120 = 0 \\\\\implies 15x^2 +25x - 110 = 0\)

6) Solving the quadratic equation .

\(\implies 5(3x^2+5x -22) = 0 \\\\\implies 3x^2+13x-22 = 0 \\\\ \implies x = \dfrac{-b\pm \sqrt{b^2-4ac}}{4ac} \\\\\implies x = \dfrac{-5\pm \sqrt{5^2-4(-22)(3)}}{2(3)} \\\\\implies x = \dfrac{-5\pm \sqrt{289}}{6}\\\\\implies x =\dfrac{-5\pm 17}{6} \\\\\implies x = \dfrac{17-5}{6},\dfrac{-17-5}{6}\\\\\implies x = \dfrac{12}{6},\dfrac{-22}{6} \\\\\underline{\boxed{\red{\bf\implies x = 2 , \dfrac{-11}{3}}}}\)

Answer:

\(x=2\\x=-\frac{11}{3}\)

Step-by-step explanation:

Solve the rational equation:

\(\displaystyle \frac{3x+4}{5}-\frac{2}{x+3}=\frac{8}{5}\)

To eliminate denominators, multiply by 5(x+3) (x cannot have a value of 3):

\(\displaystyle 5(x+3)\frac{3x+4}{5}-5(x+3)\frac{2}{x+3}=5(x+3)\frac{8}{5}\)

Operate and simplify:

\(\displaystyle (x+3)(3x+4)-5(2)=(x+3)(8)\)

\(\displaystyle 3x^2+4x+9x+12-10=8x+24\)

Rearranging:

\(\displaystyle 3x^2+4x+9x+12-10-8x-24=0\)

Simplifying:

\(\displaystyle 3x^2+5x-22=0\)

Rewrite:

\(\displaystyle 3x^2-6x+11x-22=0\)

Factoring:

\(\displaystyle 3x(x-2)+11(x-2)=0\)

\(\displaystyle (x-2)(3x+11)=0\)

Solving:

\(x=2\\x=-\frac{11}{3}\)

1.07 PER BAR                  4.28 DIVIDED BY 4

Answer:

$1.07

Step-by-step explanation:

4.28/4= 1.07

Answer:

6 Inches

Step-by-step explanation:

First Photograph

Length:Width = 24:18

Second Photograph

Let the unknown width =x

Length:Width = 8:x

Since the proportions of the two photographs are the same

\(8:x=24:18\\\\\dfrac{8}{x}= \dfrac{24}{18}\\\\24x=8 \times 18\\\\x=(8 \times 18) \div 24\\\\x=6$ inches\)

The width of the photograph is 6 inches.

Answer:

the functions domain is;  x < -19 or x > -19

x= -19

Sorry otherwise im not sure what you need here :P

The correct function that expresses the town's population after n decades is: p(n) = 8000 × 2ⁿ. So the initial population of the town is 8,000, which is consistent with the problem statement.

A function is a mathematical concept that describes the relationship between a set of inputs, called the domain, and a set of outputs, called the range.

A function assigns a unique output to each input, meaning that for a given input, there is only one possible output.

Starting with a population of 8,000, the population doubles every decade, which means it multiplies by 2.

After n decades, the population will have doubled n times, so we can express the population as 8,000 multiplied by 2 raised to the power of n:

p(n) = 8000 × 2ⁿ

This function gives us the population of the town after n decades, where n is a non-negative integer. If we substitute n=0 into the function, we get:

p(0) = 8000 × 2⁰ = 8000

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Answer:

20

Step-by-step explanation:

20.

\(\frac{8}{\frac{2}{5} }\)

Check the attached image below.

\(\frac{8}{1}* \frac{5}{2}\)

\(\frac{8}{1}*\frac{5}{2}=\\\\ \frac{8*5}{1*2} =\\\\ \frac{40}{2}=\\ \\20\)

\(\frac{8}{\frac{2}{5} }=20\).

Answer:

Treatment for HIV/AIDS involves taking highly effective medicines called antiretroviral therapy (ART) that work to control the virus [1][2]. ART involves taking a combination of HIV medicines (called an HIV regimen) to suppress the virus and stop the progression of the disease [1]. The goal of treatment is to reduce the amount of HIV in the body and keep it at a low, undetectable level to help prevent further damage to the immune system and reduce the risk of transmitting HIV to others.

Answer:

four times a number less 10 is equall to 16 ia not

Answer:

27

Step-by-step explanation:

3/10 / 30% / .3

3        x

10        90            -use criss cross method so 3 and 90 and x times 10

270 =10x

27=x

you can also go on a calculator and type 90 times 0.3 and get the answer too

Answer:

Step-by-step explanation:

Is 2/10 greater than or lesser than 3/5?

fraction = division

2/10 = 0.2

3/5 = 0.6

2/10 is lesser than 3/5

The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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To divide 240g in the ratio 5:3:4, we need to find out the total number of parts of the ratio:

5 + 3 + 4 = 12

Now, we can find the value of one part of the ratio by dividing the total quantity by the total number of parts:

240g ÷ 12 = 20g

So, one part of the ratio is equal to 20g.

To find the quantities of each part of the ratio, we multiply the value of one part by the respective ratio number:

5 parts x 20g = 100g (for the first part)

3 parts x 20g = 60g (for the second part)

4 parts x 20g = 80g (for the third part)

Therefore, the quantities of 240g divided in the ratio 5:3:4 are 100g, 60g, and 80g respectively.

The graphs of y = x + 1 and y = 2^x intersect at approximately (-0.3517, 0.6483) and (1.561, 3.561).

To find the points of intersection between the graphs of y = x + 1 and y = 2^x, we need to set the two equations equal to each other and solve for x.

Setting y = x + 1 equal to y = 2^x, we have:

x + 1 = 2^x

To solve this equation, we can use numerical methods or make observations to find the points of intersection. By observing the behavior of the two functions, we can see that they intersect at two points: one when x is negative, and another when x is positive.

For x < 0, the exponential function y = 2^x approaches 0 as x approaches negative infinity, while the linear function y = x + 1 continues to decrease as x becomes more negative. Thus, there is one point of intersection in this region.

For x > 0, the exponential function grows faster than the linear function, so there is another point of intersection in this region.

However, finding the exact values for the points of intersection requires numerical methods such as using a graphing calculator or solving the equation numerically. Approximate values for the points of intersection can be found as x ≈ -0.3517 and x ≈ 1.561.

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Answer: C

Step-by-step explanation: Brainliest please

The average number of hours that adults spend working each day is 8 hours and Ryan is correct because he got the average of 8 right.

We know that,

The sample mean is a statistic that is computed by taking the arithmetic mean of the values of a variable in a sample. If the sample is taken from probability distributions with a shared expected value, the sample mean is an estimator of that value.

The mean is gotten from the formula;

x' = ∑x/n

Number of hours of work per day are; 6, 7, 8, 9 and 10

Thus; sum up all of it

∑x = 6 + 7 + 8 + 9 + 10

∑x = 40

Mean is; x' = 40/5

x' = 8

Since Ryan concluded that the average is 8 hours,

Therefore,

We can say that Ryan is correct.

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Answer:

Refer to the step-by-step explanation, please follow along very carefully. Answers are encased in two boxes.

Step-by-step explanation:

Given the following function, find it's derivative using the definition of derivatives. Evaluate the function when θ=1, 11, and 3/11

\(p(\theta)=\sqrt{11\theta}\)

\(\hrulefill\)

The definition of derivatives states that the derivative of a function at a specific point measures the rate of change of the function at that point. It is defined as the limit of the difference quotient as the change in the input variable approaches zero.

\(f'(x) = \lim_{{h \to 0}} \dfrac{{f(x+h) - f(x)}}{{h}}\)\(\hrulefill\)

To apply the definition of derivatives to this problem, follow these step-by-step instructions:

Step 1: Identify the function: Determine the function for which you want to find the derivative. In out case the function is denoted as p(θ).

\(p(\theta)=\sqrt{11\theta}\)

Step 2: Write the difference quotient: Using the definition of derivatives, write down the difference quotient. The general form of the difference quotient is (f(x+h) - f(x))/h, where "x" is the point at which you want to find the derivative, and "h" represents a small change in the input variable. In our case:

\(p'(\theta) = \lim_{{h \to 0}} \dfrac{{p(\theta+h) - p(\theta)}}{{h}}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h}\)

Step 3: Take the limit:

We need to rationalize the numerator. Rewriting using radical rules.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h} \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11\theta + 11h} - \sqrt{11\theta} }{h}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h}\)

Now multiply by the conjugate.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h} \cdot \dfrac{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} } \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{(\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} )(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )} \\\\\\\)

\(\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11h}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\)

Step 4: Simplify the expression: Evaluate the limit by substituting the value of h=0 into the difference quotient. Simplify the expression as much as possible.

\(p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta+(0)} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\)

\(\therefore \boxed{\boxed{p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta} }}}\)

Thus, we have found the derivative on the function using the definition.

It's important to note that in practice, finding derivatives using the definition can be a tedious process, especially for more complex functions. However, the definition lays the foundation for understanding the concept of derivatives and its applications. In practice, there are various rules and techniques, such as the power rule, product rule, and chain rule, that can be applied to find derivatives more efficiently.\(\hrulefill\)

Now evaluating the function at the given points.  

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}; \ p'(1)=??, \ p'(11)=??, \ p'(\frac{3}{11} )=??\)

When θ=1:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(1)= \dfrac{\sqrt{11} }{2\sqrt{1}}\\\\\\\therefore \boxed{\boxed{p'(1)= \dfrac{\sqrt{11} }{2}}}\)

When θ=11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(11)= \dfrac{\sqrt{11} }{2\sqrt{11}}\\\\\\\therefore \boxed{\boxed{p'(11)= \dfrac{1}{2}}}\)

When θ=3/11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(\frac{3}{11} )= \dfrac{\sqrt{11} }{2\sqrt{\frac{3}{11} }}\\\\\\\therefore \boxed{\boxed{p'(\frac{3}{11} )= \dfrac{11\sqrt{3} }{6}}}\)

Thus, all parts are solved.

Answer:

54

Step-by-step explanation:

27 is half of what number?

27 x 2 = 54

:)

Answer:

135

Step-by-step explanation:

27 x 0.5 = 135

Hope it helps!!!!!

Answer:

I would say

Step-by-step explanation:

303030 divided by 666 =455

666x455=303030

455-666=2110

so it would be 2110

Answer:

x < -6

Step-by-step explanation:

Answer:

-7 or x <-6

Step-by-step explanation:

To add to a number that’s in a subtracting equation you must use a negative number because a negative with a subtraction equals adding

Answer:

7: 63

8: 73

arithmetic sequence

y = 10x - 7

or f(n) = 10x -7

or

\(a_{n}\) = 3 + (n-1)10

Step-by-step explanation:

the output increases by 10 every time that the input increases by 1.  That gives us our common difference or slope.  The y intercept is -7. That is the value is you worked backwards until you get to n = 0.  The initial value  is 3.  That is when n is 1.

When n is 3, f(n) is 23

When n is 2, f(n) is 13

When n is 1, f(n) is 3

When n is 0, f(n) is -7

I am not sure if this is clear.  I am assuming that you have a lot of knowledge of linear equations and how to write arithmetic sequence.  If my explanation is confusing it is me and not you.

Answer:

a. 63,73

b. Arithmetic sequence

c.t(n)=10n-7

Explanation:

a. Here is the completed table:

n | t(n)

4 | 33

5 | 43

6 | 53

7 | 63

8 | 73

b.

The type of sequence is arithmetic.

An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant.

In this case, the difference between any two consecutive terms is 10.

c.

The equation for the arithmetic sequence is:

t(n)=a+(n-1)d

where:

For Question:

Now

equation becomes:

t(4) = a+(4-1)10

33=a+30

a=33-30

a=3

Now, the Equation becomes

t(n) = 3+(n-1)10

t(n) = 3+10n-10

t(n)=10n-7

The solution is

a=2s-b

Answer:

9

Step-by-step explanation:

81 / 9 = 9

81 crayons and each student gets 9.

9x9=81

The person that has the winning time is Alex.

From the information given, three runners run 100 yards race. Sara runs the race in 9.25 seconds and Alex runs the race in 8.625 seconds and Tonya runs the race in 9.8 seconds.

It should be noted that in a race, the person that has the lowest time wins.

In this situation, the person with 8.625 seconds is the lowest.

Therefore, Alex wins.

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