Rewrite using the
distributive property :
45 + 9

When multiple of the same number are multiplied together, this can be represented as an exponent. An exponent is a way to write repeated multiplication of a number by itself. In your case, 7 multiplied by itself 3 times (7*7*7) can be written using exponents as 7^3.

In mathematics, when you multiply the same number multiple times, you can express that multiplication as an exponent. An exponent tells you how many times to multiply the number, or the base, by itself. For example, in your question, the number 7 is multiplied by itself 3 times (7*7*7), so this multiplication can also be written with exponents. The correct way to express this multiplication using exponents is 73.

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Answer:

yes the ratio of the area of a new rectangle is equivalent to the ratio of side lengths of a new ratio

Step-by-step explanation:

Answer:7,836,664

Step-by-step explanation:I used a calculator

Answer:

Step-by-step explanation: 36,211,762

The answer is D, 26. [tex]3\pi^2[/tex] is about 26.6!

Final answer:

The number that is between 21 and 3π/2 is 5.

Explanation:

To find the number that is between 21 and 3π/2, we need to determine the value of 3π/2 first. Since π is approximately 3.14, 3π/2 is approximately (3)(3.14)/2 = 4.71.

Now we can compare this value to 21. Since 4.71 is less than 21, we need to find a number that is greater than 4.71 but less than 21. The only option in the given choices that fits this criteria is Option C, 5.

Answer:

3.11 is infinite so we would plot that 1 tick past 3 as the graph is going in increments of .50 and the square root of 7 is 2.64 which we would round to 2.7 (i could be wrong about rounding) soo in your case i would go with 2.6  which is 1 tick past 2.5

Step-by-step explanation:

its been a long time since ive done this and im currently in pre calc 11th grade math so if i got some of the wrong im very sorry :-(

Answer:

m=8

Step-by-step explanation:

m-7=1

+7     +7

m=8

Answer:

5

Step-by-step explanation:

Each term is 1/3 of the preceding term

135 / 3 = 45

45 / 3 = 15

15 / 3 = 5

Answer:

Keep dividing the number by 3.

The next number is 5.

Step-by-step explanation:

Answer:

B and D

Step-by-step explanation:

Expression B = 1/[tex]x^{-1}[/tex] = 1/ (1/x) = x

Expression D = [tex]x^{1/3}[/tex] [tex]x^{1/3}[/tex] [tex]x^{1/3}[/tex]

= [tex]x^{1/3 + 1/3 + 1/3}[/tex]

= [tex]x^{1}[/tex]

= x

as shown above the both the value of B and D are equal to x and hence the expressions are equivalent

Answer:

The midpoint is 5

Step-by-step explanation:

we know that

The formula to calculate the midpoint between two numbers is

[tex]M=(\frac{x1+x2}{2})[/tex]

we have

[tex]x1=-2, x2=12[/tex]

substitute

[tex]M=(\frac{-2+12}{2})[/tex]

[tex]M=(\frac{10}{2})[/tex]

[tex]M=5[/tex]

therefore

The midpoint is 5

Final answer:

Manuel spent 90% of his total grocery expenses on fruit. To calculate this, the amount spent on fruit ($36) is divided by the total spent ($40), and then multiplied by 100%.

Explanation:

Manuel spent a total of $40 at the grocery store and out of that, $36 was spent on fruit. To find out the percentage that he spent on fruit, you can use the formula:

Percentage = (Amount spent on fruit / Total amount spent) x 100%

Plugging in the values gives us:

Percentage = ($36 / $40) x 100% = 0.9 x 100% = 90%.

Thus, Manuel spent 90% of his total grocery expenses on fruit.

Answer:

(-4,0)(-7,0)

Step-by-step explanation:

The x axis is crossed when y = 0.

That happens in two places.

x +4=0 is one place

x = - 4 when it does.

x + 7 =0 is the other.

x = - 7

I am sorry but I do not see the underlined digit, but I will put it this way. 7 in the thousands place is worth 7000, 2 in the hundreds place is worth 200, 7 in the tens place is worth 70, and 0 in the ones place is worth 0.

Hope this helped!

Nate

There are 3 dots in each row of Fritz's array. This conclusion is reached by dividing the total number of dots (15) by the number of rows (5). This is an exercise in simple division and understanding arrays in mathematics.

The subject of this question from Fritz is Mathematics, specifically, it's about arrays and simple division.

To find out how many dots are in each row of Fritz's array, we need to use division. In this case, the total number of dots (15) would be divided by the number of rows (5).

So, we calculate: 15 ÷ 5 = 3.

So, there are 3 dots in each row of Fritz's array. We know this is correct because the definition of an array in mathematics is a collection of objects or numbers arranged in rows, and each row has the same number of items.

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Answer:

Part a) and Part b) see the explanation

Step-by-step explanation:

Part a)  Illustrate both girls’ solutions

Carly

Carly gives each child 2 whole cereal bars and then divides the remaining cereal bar among the 3 children

so

1) Each child receive first 2 whole cereal bars

the remaining is

[tex]7-(2+2+2)=7-6=1\ cereal\ bar[/tex]

2) Divides the remaining cereal bar among the 3 children

Each child receive 1/3 cereal bar

3) Each child receive in total

[tex]2+\frac{1}{3}=2\frac{1}{3}\ cereal\ bar[/tex]

Gina

Gina divides all the cereal bars into thirds and shares the thirds equally among the 3 children.

so

1) Divide the total bars by 3

Each child receive

[tex]\frac{7}{3}\ cereal\ bar[/tex]

Part b) Explain why they are both right

Compare the results

Carly ----> [tex]2\frac{1}{3}\ cereal\ bar[/tex]

Gina ----> [tex]\frac{7}{3}\ cereal\ bar[/tex]

Convert mixed number to decimal number

[tex]2\frac{1}{3}\ cereal\ bar=2+\frac{1}{3}=\frac{2*3+1}{3}=\frac{7}{3}\ cereal\ bar[/tex]

so

[tex]2\frac{1}{3}\ cereal\ bar=\frac{7}{3}\ cereal\ bar[/tex]

therefore

Carly and Gina are right

Answer:

It is A

Explanation:

Two points will always be collinear, but the same can't be said for three, since in some occasions one point is outside the line.

Answer:

a=2B/d-l

Step-by-step explanation:

da-la=2B

1) Factor out an a from (da-la):

a(d-l)=2B

2) Divide both sides by (d-l):

a=2B/d-l

Answer:

2.058 x 10 to the -1st

Step-by-step explanation:

Answer:

A. x radians

Step-by-step explanation:

The circumference of the unit circle is

[tex]2\pi r=2\pi \cdot 1=2\pi[/tex]

The full rotation angle has the measure [tex]2\pi[/tex] radians.

So,

[tex]\begin{array}{cc}\text{Angle}&\text{Arc length}\\ \\2\pi &2\pi \\\theta &x\end{array}[/tex]

Write a proportion:

[tex]\dfrac{2\pi }{\theta}=\dfrac{2\pi }{x}[/tex]

Cross multiply:

[tex]2\pi x=2\pi \theta\\ \\\theta=x[/tex]

Answer:

Option C (The expression 2.35c + 1.75m represents the money earned from selling c bags of cookies and m bags of muffins).

Step-by-step explanation:

It is given that a bag of cookies is priced at $2.35 and a bag of muffin is priced at $1.75. It is also given that the student sells c bags of cookies and m bags of muffins. The total revenue earned by the student by selling c bag of cookies = $2.35 * c bags = $2.35c and the total revenue earned by the student by selling m bag of muffins = $1.75 * m bags = $1.75m. Therefore, the total revenue earned by the student by selling both cookies and muffins = 2.35c + 1.75m. This expression (2.35c + 1.75m) represents the money earned from selling c bags of cookies and m bags of muffins. Therefore, C is the correct choice!!!

Answer:

4428

Step-by-step explanation:

Answer:

Mixture 1 and Mixture 2 will create the same color

Step-by-step explanation:

we know that

If two mixtures create the same color, then the proportion of the painting in the mixtures must be the same

Let

x ----> the ounces of a red paint in the mixture

y ----> the ounces of a blue paint in the mixture

Verify the proportion of the paints in each mixture

Mixture 1) x=2, y=1

[tex]\frac{2}{1}=2[/tex]

Mixture 2) x=7, y=3.5

[tex]\frac{7}{3.5}=2[/tex]

Mixture 3) x=4.5, y=2

[tex]\frac{4.5}{2}=2.25[/tex]

Mixture 4) x=5.5, y=2.5

[tex]\frac{5.5}{2.5}=2.2[/tex]

therefore

Mixture 1 and Mixture 2 will create the same color, because have the same ratio

Answer:

Mixture 1 and Mixture 2

Step-by-step explanation:

It is given that Raj is mixing different colors (blue and red) of paint to make a new color.

If two mixtures have same ratio of red and blue color, then that will create the same color.

The ratio of red and blue color in each mixture is shown below:

Mixture 1: [tex]\frac{Red}{Blue}=\frac{2}{1}=2:1[/tex]

Mixture 2: [tex]\frac{Red}{Blue}=\frac{7}{3.5}=\frac{2}{1}=2:1[/tex]

Mixture 3: [tex]\frac{Red}{Blue}=\frac{4.5}{2}=\frac{9}{4}=9:4[/tex]

Mixture 4: [tex]\frac{Red}{Blue}=\frac{5.5}{2.5}=\frac{11}{5}=11:5[/tex]

From the above calculation it is clear that the ratio of red and blue color in mixture 1 and mixture 2 is same.

Therefore, Mixture 1 and Mixture 2 will create the same color.

Answer:

[tex]\boxed{39}[/tex]

Step-by-step explanation:

[tex]\begin{array}{rcc}& \textbf{Archery Sign Up} & \textbf{Total Campers}\\\textbf{Week 1} & 36 & 120\\\textbf{Week 2} & 45 & 150\\\textbf{Week 3} & ? & 130\\\end{array}[/tex]

Let x = Total campers

and y = Archery sign up

In a direct proportionality,

y = kx

1. Calculate the value of k

Substitute a pair of values for x and y

150 = k × 45

Divide each side by 45

k = 150/45 = 10/3

2. Calculate the value of x in Week 3

[tex]\begin{array}{rcl}130& = & \dfrac{10}{3}x\\\\390 & = & 10x\\x & = & \mathbf{39}\\\end{array}[/tex]

[tex]\boxed{\textbf{39 campers}} \text{ will sign up for archery in Week 3}[/tex]

The diagram is a graph of your proportionality. It shows that y = 130 when x = 39.

Answer:

t = [tex]\frac{6}{7}[/tex]

Step-by-step explanation:

Given that t varies inversely as the square root of u then the equation relating them is

t = [tex]\frac{k}{\sqrt{u} }[/tex] ← k is the constant of variation

To find k use the condition t = 3 when u = 4, thus

k = t[tex]\sqrt{u}[/tex] = 3 × [tex]\sqrt{4}[/tex] = 3 × 2 = 6

t = [tex]\frac{6}{\sqrt{u} }[/tex] ← equation of variation

When u = 49, then

t = [tex]\frac{6}{\sqrt{49} }[/tex] = [tex]\frac{6}{7}[/tex]

The value of 't' when 'u = 49' in the equation [tex]'t = k/\sqrt(u)[/tex]' is approximately '0.86'. This was calculated using the concept of inverse variation in mathematics.

The question is dealing with the concept of inverse variations in math. The given expression states that 't' varies inversely with the square root of 'u'. This can be represented mathematically as  [tex]'t = k/\sqrt(u)',[/tex] where 'k' is the constant of variation.

From the problem we know that 't = 3' when 'u = 4'. Substituting these terms in into the equation above, we can solve for 'k'. Doing this yields  [tex]'k = 3\times \sqrt(4) = 6.'[/tex]

Now that we have found 'k', we can find the value of 't' when 'u = 49'. We can do this by plugging in the known values into the equation. So [tex]'t = 6/\sqrt(49)'.[/tex] It simplifies to 't = 6/7' or about '0.86'.

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3/4 is greater than 7/10.

Find the least common denominator or LCM of the two denominators:

LCM of 4 and 10 is 20

For the 1st fraction, since 4 × 5 = 20,

3 /4=  

3 × 5

4 × 5  =  

15 /20

Likewise, for the 2nd fraction, since 10 × 2 = 20,

7 /10  =  

7 × 2

10 × 2  =  

14 /20

Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction

15 /20  >  14 /20  or  3 /4  >  7 /10

Answer:

3/4 is larger

Step-by-step explanation:

The common denominator is 40

multiply

30/40 and 28/40

30/40 is larger, simplify 3/4 is bigger than 7/10

Answer:

The estimate of the product is about 35 answer C

Step-by-step explanation:

- We use rounding to estimate the product of two fractions

- The mixed number has whole number and fraction

- To round the mixed number we look to the fraction

- If the numerator is half or greater than half the denominator, then we

  add the whole number by 1 and cancel the fraction

- If the numerator is less than half the denominator, then we keep the

  whole number as it and cancel the fraction

- Ex: If the mixed number is [tex]2\frac{3}{4}[/tex], 3 is more than

 half 4 then we will add 2 by 1 and cancel the fraction part, the

 mixed number [tex]2\frac{3}{4}[/tex] after rounding is 3

- Ex: If the mixed number is [tex]5\frac{1}{4}[/tex], 1 is less than

 half 4 then we will keep 5 as it and cancel the fraction part, the

 mixed number [tex]5\frac{1}{4}[/tex] after rounding is 5

* Lets solve the problem

∵ In the part [tex]4\frac{3}{4}[/tex] 3 is more than half 4

∴ The rounding value of [tex]4\frac{3}{4}[/tex] is 5

∵ In the part [tex]7\frac{2}{17}[/tex] 2 is less than half 17

∴ The rounding value of [tex]7\frac{2}{17}[/tex] is 7

∴ [tex]4\frac{3}{4}*7\frac{2}{17}=5*7=35[/tex]

* The estimate of the product is about 35

Answer:

5/3

Step-by-step explanation:

If you do 5/ 3/5 what youre really doing is just doing two division problems which by the way equals 5/0.6 or 8.3333333

But one thing i realized when i was doing division by fractions is that if you flip the fraction then you can multiply and you get the same exact answer. SO lets try: 5/3 = 1.6666

1.6666*5=8.3333333

So you can use that trick when dividing a whole number by fractions. It makes it a lot easier.

The official answer is instead of dividing 5 by 3/5 you can instead multiply 5 by 5/3 and get the same answer!