8. What is the prime factorization of 120?​

Answer:

3.5

Step-by-step explanation:

Changed them to decimals ( top number divided by the bottom will get you the decimal) and I got the answer. message me if you need more help

There are approximately 2/7  7/10s in 1/5.

The calculation step by step to find out how many 7/10s are there in 1/5.

1. We have two fractions:

[tex]- \( \frac{7}{10} \)[/tex]

[tex]- \( \frac{1}{5} \)[/tex]

2. To compare these fractions, we need to make their denominators the same. The least common multiple (LCM) of 10 and 5 is 10.

3. Convert both fractions to have a denominator of 10:

[tex]- \( \frac{7}{10} \)[/tex] remains the same.

[tex]- \( \frac{1}{5} \) becomes \( \frac{2}{10} \) (since \( \frac{1}{5} = \frac{2}{10} \)).[/tex]

4. Now, let's divide [tex]\( \frac{2}{10} \) by \( \frac{7}{10} \)[/tex]:

[tex]- \( \frac{2}{10} \div \frac{7}{10} \)[/tex]

- Multiply by the reciprocal of the second fraction:

[tex]\( \frac{2}{10} \cdot \frac{10}{7} \)[/tex]

 - Multiply the numerators:[tex]\( 2 \cdot 10 = 20 \)[/tex]

- Multiply the denominators: [tex]\( 10 \cdot 7 = 70 \)[/tex]

[tex]- The result is \( \frac{20}{70} \), which simplifies to \( \frac{2}{7} \).[/tex]

5. Therefore, there are approximately 2/7 7/10s in 1/5.

The original equation was transformed using a series of mathematical properties. The associative and commutative properties of addition were used to rearrange the terms, and the distributive property was used to simplify the equation. This exercise helps to understand how different mathematical properties can be used to simplify algebraic expressions.

The student has made changes in the equation by applying different mathematical properties like associative, commutative, and distributive properties. In the first transformation of equation, student applied the associative property of addition and commutative property of addition to rearrange terms inside brackets, then applied distributive property to multiply each term inside the bracket with 3. Similarly, in the second transformation, the associative property of multiplication was used to group certain terms together, then the distributive property was used to multiply these terms. Finally, the equation was simplified using the commutative property of addition.

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Answer:

L = 15

Step-by-step explanation:

P = 2L + 2W

you know that P = 50, W=10

So you have to replace those values on the equation

50 = 2L + 2*(10)  --> Replace P and W

50 = 2L + 20  --> Multiply and now you are going to separate the unknown and the constants.

Remember that if you send a constant to the other side of the equal the sign will change to its opposite

50 - 20 = 2L  --> Solve the constants

30 = 2L    --> Now for the L, you have to leave it alone, so the 2 that is multiplying you have to send it to the other side of the equal but with the opposite operation,  the opposite operation of multiplying is dividing, so you have:

30/2 = L

L= 15

Answer:

Valid

Step-by-step explanation:

3(x-4)=x+4              Given

3x-12=x+4                Distribute

2x=16                      Subtract x from both sides and add 12 to both sides

x=8                           Divide each side by 2.

Hey there!

3(x - 4) = x + 4

3(x) + 3(-4) = x + 4

3x - 12 = x + 4

3(8) - 12 = 8 + 4

24 - 12 = 8 + 4

12 = 12

Therefore, this makes this statement TRUE

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

4

Step-by-step explanation:

First off, integers are Whole Numbers (1,2,3,4, etc), so we are rounding the answer to the nearest whole number.

The square root of lets just say 25 means you are finding a number that multiplied by itself will equal 25 (the answer is 5).

Now for 13, there is no perfect square, however the closest whole number that multiplied by itself to 13 is 4.

4*4= 16

3*3=9

5*5=25

As you can see above 4 is the closest number to 13.

Now, the ACTUAL value of the square root of 13 is 3.60555128, but we are rounding up to the nearest whole number which is 4 :)

The square root of 13 is approximately 3.6055, but to the nearest integer (whole number), it's 4.

The question asks for the square root of 13. First, it's important to understand what a square root is. In simple terms, the square root of a number is a value that, when multiplied by itself, gives the original number. So, if you take the square root of 16, for example, it's 4 because 4 multiplied by 4 equals to 16. Now, 13 is not a perfect square, so its square root is not a whole number. If you calculate the square root of 13, you'll get an answer somewhere around 3.6055. However, the question asks for the nearest integer. An integer is a whole number, so we're looking for the whole number closest to 3.6055. In this case, it's 4. So, the square root of 13, to the nearest integer, is 4.

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Carl travelled 840 km by bus and 1060 km by airplane.

To solve this problem, we can use the formula:

Distance = Speed x Time

Let x be the distance travelled by bus. Since the distance travelled by airplane is 1900 km - x, we can set up the equation:

x/60 + (1900 - x)/100 = 7

Solving for x, we get x = 840 km. Therefore, Carl travelled 840 km by bus and 1060 km by airplane.

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Carl traveled 420 km by bus and 1480 km by airplane.

To solve this problem, we need to use the formula:

Distance = Speed x Time

We know that the total traveling time was 7 hours, and the distances traveled by bus and airplane add up to 1900 kilometers. Let's use the formula to find the distance traveled by bus:

Distance by bus = Speed by bus x Time by bus

Since we know the average speed by bus is 60 km/h, we can substitute into the equation:

Distance by bus = 60 km/h x Time by bus

By rearranging the equation, we can solve for Time by bus:

Time by bus = Distance by bus / Speed by bus

And since the total traveling time was 7 hours, we can substitute this value into the equation:

7 hours = Distance by bus / 60 km/h

Multiplying both sides of the equation by 60 km/h, we get:

7 hours x 60 km/h = Distance by bus

Distance by bus = 420 km

Now that we know the distance traveled by bus, we can find the distance traveled by airplane:

Distance traveled by airplane = Total distance - Distance by bus

Substituting the given values, we get:

Distance traveled by airplane = 1900 km - 420 km

Distance traveled by airplane = 1480 km

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The speed of the boat was 35 kilometers per hour.

Distance is defined as the product of speed and time.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions. The operator that performs the arithmetic operations are called arithmetic operators.

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

Let us consider the speed of the boat is x km/h.

D = xt

Given that the current in that part of the river is 5 km per hr

Distance upstream  = (x-5) km

Distance downstream = (x+5) km/h

The distance is the same up and downstream

So (x-5)(1/3) =(x+5)(1/4)

Multiplying thru by 12

⇒ 4(x-5) =3(x+5)

⇒ 4x - 20 =3x + 15

Rearrange the likewise terms and apply the arithmetic operations,

⇒ 4x - 20 =3x + 15

⇒ 4x - 3x = 20 + 15

⇒ x = 35 kmph

Hence, the speed of the boat was 35 kilometers per hour.

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Final answer:

A terminating decimal has a finite number of decimal places, whereas a repeating decimal has one or more digits that repeat infinitely. Trailing zeros in a decimal number are significant when they come after a decimal point, affecting precision in arithmetic operations.

Explanation:

The difference between a terminating decimal and a repeating decimal lies in their decimal expansions. A terminating decimal has a finite number of decimal places; once you write out all the decimal places, the number ends. For example, 0.5 or 0.75 are terminating decimals because they stop after one or two decimal places, respectively. On the other hand, a repeating decimal has one or more digits that repeat infinitely. For instance, 0.333... (where the 3s go on forever) is a repeating decimal. The bar above the digit(s) indicates that it repeats indefinitely.

In the context of significant figures and rounding, trailing zeros in a decimal number are significant when a decimal point is present. This precision is important in arithmetic operations. When rounding off in addition or subtraction, the number of decimal places in the result should match the number in the expression with the fewest decimal places. The same concept of precision applies to multiplication and division, where the number of significant figures must align with the term having the least amount of them.

Hey!

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

Part A:

h - 40

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

Part B:

40 - 40 = 0 overtime hours.

44 - 40 = 4 overtime hours.

48 - 40 = 8 overtime hours.

52 - 40 = 12 overtime hours.

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

Hope This Helped! Good Luck!

Answer:

The required expression is [tex] O=h - 40[/tex].

For 40 hrs overtime is 0 hrs.

For 44 hrs overtime is 4 hrs.

For 48 hrs overtime is 8 hrs.

For 52 hrs overtime is 12 hrs.

Step-by-step explanation:

Consider the provided information.

Part (A)

It is given that Jim is paid for overtime when he works more than 40 hours per week.

Let Jim works for h hrs and O represents the overtime, Then overtime can be represented as:

O = h - 40

The expression for the number of hours he works overtime when he works h hours is:

[tex] O=h - 40[/tex]

Part (B) Find the number of hours Jim works overtime when he works 40, 44, 48, and 52 hours.

Substitute h=40 in the obtained expression.

[tex] O=40 - 40[/tex]

[tex] O=0[/tex]

Hence, for 40 hrs overtime is 0 hrs.

Substitute h=44 in obtained expression.

[tex] O=44 - 40[/tex]

[tex] O=4[/tex]

Hence, for 44 hrs overtime is 4 hrs.

Substitute h=48 in obtained expression.

[tex] O=48 - 40[/tex]

[tex] O=8[/tex]

Hence, for 48 hrs overtime is 8 hrs.

Substitute h=52 in obtained expression.

[tex] O=52 - 40[/tex]

[tex] O=12[/tex]

Hence, for 52 hrs overtime is 12 hrs.

Answeuse a caculator then write it our

Step-by-step explanation:

The standard form of 7 x 1 + 3 x ( 1/10 ) + 4 x ( 1 / 1000 ) is 0.7304 x [tex]10^{1}[/tex].

Given,

7 x 1 + 3 x ( 1/10 ) + 4 x ( 1 / 1000 )

We need to write this large number in standard form.

A standard form is a way of expressing a large number as a decimal number between 0 and 1 (including 1) and multiplied by a power of 10.

We have,

7 x 1 + 3 x ( 1 / 10 ) + 4 x ( 1 / 1000 )

7 + 0.3 + 0.004

7.304

Since we need a decimal point between 0 and 1.

We will multiply 7.304 by 10 / 10.

so we have,

7.304 x 10 / 10

(7.304 / 10 ) x 10

0.7304 x 10

Remember that a number to the power 1 is the number itself.

[tex]10^{1} = 10[/tex]

We see that in 0.7304 x [tex]10^{1}[/tex],

0.7304 is a decimal point between o and 1 and we have a power of 10.

It satisfies the standard form of a number.

Thus the standard form of 7 x 1 + 3 x ( 1/10 ) + 4 x ( 1 / 1000 ) is

0.7304 x [tex]10^{1}[/tex].

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The domain of the function F(x) = √(x+4) is all real numbers greater than or equal to -4, which corresponds to option C. x≥-4.

The student has asked about the domain of the function F(x) = √(x+4). To determine the domain of this function, we need to consider the values of x for which the expression under the square root, x+4, is non-negative, since the square root of a negative number is not defined in the set of real numbers.

The expression x+4 is non-negative when x ≥ -4. Therefore, any number greater than or equal to -4 is part of the domain of the function.

This means the correct answer to the question is C. x≥-4.

Answer:

-1 + 63x - 49a

Step-by-step explanation:

Following order of operations rules:

1*5 = 5

Next, 5 - 6 = -1, and so we now have -1 + 7(9x - 7a).

Apply the distribution rule for multiplication next, obtaining -1 + 63x - 49a

Answer:

13

Step-by-step explanation:

110two

[tex]2 \times ( {1}^{2} ) + 2( {1}^{1} ) + 2 \times ( {0}^{0} ) \times ( {1}^{2} ) + 2 \times ( {1}^{1} ) \times ( {1}^{0} )[/tex]

=2+2+2=6

and

111two=

[tex]2 \times ( {1}^{2} ) + 2( {1}^{1} ) + 2 \times ( {1}^{0} )[/tex]

but

[tex] {1}^{0} = 1[/tex]

now adding the results for that one also

2+2+2 +1=7

adding the total for all

6+7= 13

Final answer:

The sum of the binary numbers 110two and 111two is 1101two, which is equivalent to 13 in decimal form.

Explanation:

The question asks for the sum of two binary numbers: 110two and 111two. To add these two binary numbers, we align them by their least significant bits and perform binary addition:

110

+ 111

-----

1101

This is equivalent to the decimal addition of 6 (110two) + 7 (111two) which equals 13. In binary, 13 is represented as 1101two.

Answer:

see explanation

Step-by-step explanation:

Given

F = [tex]\frac{9}{5}[/tex](K - 273.15) + 32

Multiply through by 5 to clear the fraction

5F = 9(K - 273.15) + 160 ( subtract 160 from both sides )

5F - 160 = 9(K - 273.15) ← distribute

5F - 160 = 9K - 2458.35 ( add 2458.35 to both sides )

5F + 2298.35 = 9K ( divide both sides by 9 )

K = [tex]\frac{5F+2298.35}{9}[/tex]

(b)

When F = 180, then

K = [tex]\frac{5(180)+2298.35}{9}[/tex]

   = [tex]\frac{900+2298.35}{9}[/tex]

   = [tex]\frac{3198.35}{9}[/tex]

   ≈ 355.37 ( to the nearest hundredth )

Final answer:

The fraction equivalency of the decimal number 2.46 is 123/50.

Explanation:

To determine the fraction equivalency of the decimal number 2.46, we need to express it as a fraction with an integer numerator and a power of 10 in the denominator. To start, we can express 2.46 as 246/100 since moving the decimal point two places to the right converts the decimal into an integer and the equivalent power of 10 in the denominator. However, to find the simplest form of the fraction, we should divide both the numerator and the denominator by the greatest common divisor (GCD), which in this case is 2, to get 123/50. Therefore, the equivalent fraction for the decimal number 2.46 is 123/50.

Answer:

$8006

Step-by-step explanation:

312*17.5=5460

134*19=2546

5460+2546= 8006

Answer:

x = 9/2

Step-by-step explanation:

Solve for x:

4 (5 - 8 x) = -24 x - 16

Expand out terms of the left hand side:

20 - 32 x = -24 x - 16

Add 24 x to both sides:

24 x - 32 x + 20 = (24 x - 24 x) - 16

24 x - 24 x = 0:

24 x - 32 x + 20 = -16

24 x - 32 x = -8 x:

-8 x + 20 = -16

Subtract 20 from both sides:

(20 - 20) - 8 x = -20 - 16

20 - 20 = 0:

-8 x = -20 - 16

-20 - 16 = -36:

-8 x = -36

Divide both sides of -8 x = -36 by -8:

(-8 x)/(-8) = (-36)/(-8)

(-8)/(-8) = 1:

x = (-36)/(-8)

The gcd of -36 and -8 is -4, so (-36)/(-8) = (-4×9)/(-4×2) = (-4)/(-4)×9/2 = 9/2:

Answer:  x = 9/2

Answer:

x = 9/2

Step-by-step explanation:

-32x+20=-24x-16

-32x+24x+20=-16

-8x=-16-20

-8x=-36

x=9/2

Answer:

4(b-6)=b^2

Step-by-step explanation:

The difference would mean that it is subtraction and you multiply that difference by 4 and set it equal to b squared

According to the statement, the given equation is  4(b - 6) = b², and the value of b is 2 + 4.472i and 2 - 4.472i.

To solve the equation given: 4(b - 6) = b², we need to first expand and simplify.

4b - 24 = b²

b² - 4b + 24 = 0

b = 2 + 4.472i and 2 - 4.472i.

Answer:

4.5 or 4 and a half

Step-by-step explanation:

9/10 divided by 2/10

put 2/10 into it's reciprocal and multiply it by 9/10

10/2 * 9/10

10      9

_     *  _

2        10

^ (visualization)

multiple into 90/20, divide numerator and denominator by 10 to get 9/2

9/2 is 4.5

Answer: 4.5 or 9/2

Step-by-step explanation:

9/10 ÷ 2/10

9/10 x 10/2

9 x 10 = 90

10 x 2 = 20

Simplified: 9/2 or 4.5

Answer:

All you have to do is show that both are the same distance from the lines

Step-by-step explanation:

Answer:

Diego is 14 years old.

Sister is 19

Step-by-step explanation:

x = Diego's age

x + 24

2x-9 = 2

First to get rid of the fraction we multiply each side by 2

2(2x-9) = 2((x+24)/2)

4x-18 = x+24

The we isolate x

4x-18 = x+24

-x+18 -x+18

3x = 42 Now we divide each side 3

3 3

x = 14

So Diego is 14

Now we can solve for his sister. We can use one of the two equations from earlier to do this.

Plug 14 in for x and then solve for his sister

2(14)-9

28-9

19

His sister is 19

Answer:

Diego's age is 14 years.

His sister's age is 19 years.

Step-by-step explanation:

Let d represent Diego's age.

We have been given that Diego's sister is twice his age minus 9 years.

The age of Diego's sister would be [tex]2x-9[/tex].  

We are also told that she is also as old as half the sum of the ages of Diego and both of his 12-year-old twin brothers. We can represent this information in an equation as:          

[tex]2x-9=\frac{x+12+12}{2}[/tex]

Let us solve for x:

[tex]2x-9+9=\frac{x+24}{2}+9[/tex]

[tex]2x=\frac{x+24}{2}+\frac{2*9}{2}[/tex]

[tex]2x=\frac{x+24}{2}+\frac{18}{2}[/tex]

[tex]2x=\frac{x+24+18}{2}[/tex]

[tex]2x=\frac{x+42}{2}[/tex]

[tex]2*2x=\frac{x+42}{2}*2[/tex]

[tex]4x=x+42[/tex]

[tex]4x-x=x-x+42[/tex]

[tex]3x=42[/tex]

[tex]\frac{3x}{3}=\frac{42}{3}[/tex]

[tex]x=14[/tex]

Therefore, Diego's age is 14 years.

[tex]\text{His sister's age}=2x-9[/tex]

[tex]\text{His sister's age}=2(14)-9[/tex]

[tex]\text{His sister's age}=28-9[/tex]

[tex]\text{His sister's age}=19[/tex]

Therefore, his sister's age is 19 years.

Answer:

Step-by-step explanation:

[tex]\frac{5}{8} = \frac{12}{g}[/tex]

Multiplying both sides by [tex]g[/tex] gives us the following:

[tex]\frac{5g}{8} = 12[/tex]

Multiplying both sides by 8 gives us the following:

[tex]5g = 108[/tex]

Dividing both sides by 5 gives us the answer:

[tex]g = 21.6[/tex]

Hello.

To do this problem, cross multiply.

(8)(12)= 5g

96 = 5g

g = 96/5

g= 19.2

Hope that helped!

************************

Disclaimer:

Always double check your answer with a reliable source, as mistakes can be made.

Answer:

1444

Step-by-step explanation:

524 + 920 = 1444

Answer:

1,444/1

Step-by-step explanation:

The answer to the problem is 1,444. To put the answer in fraction form, you can say 1,444/1. If they are asking for the numbers to be put in fraction form, you can say 524/1 + 920/1. If they are asking both, 524/1 + 920/1 = 1,444/1.

Answer:

Sally's km/h during the first half hour is 7 .

The lowest average speed is between the 3rd and 4th stops.

Step-by-step explanation:

On the table during the first half hour, Sally traveled 7 km.

From the first stop to the second stop, she traveled 8 km; from the second stop to the third stop, she traveled 6 km; from the third stop to the fourth stop, she traveled 3 km; from the fourth stop to the fifth stop, she traveled 4 km; and from the fifth stop to the sixth stop she traveled 8 km. Therefore The lowest average speed is between the 3rd and 4th stops.

Plz rate Brainliest because this took a long time.

Answer:

(300 + 50x)/(2 + x)

Step-by-step explanation:

Let the cost of teachers' edition books be t

Let the cost of students' edition books be s

So t = 150; s = 50

Then the total cost of 2 teachers' editions and x students' editions is 2t + sx = 2 × 150 + 50x = 300 + 50x.

The total number of books is 2 + x.

So the average cost per book is (300 + 50x)/(2 + x)

Answer:

the answer is D.

Step-by-step explanation:

Answer:

SORRY DONT KNOW

Step-by-step explanation:

the measure of angle ∠21 must be 55 degrees for line b to be parallel to line a.

In order for line b to be parallel to line a, the measure of angle ∠21  must be 125 degrees. Corresponding angles are angles that are in the same position relative to two intersecting lines. Since lines a and b are parallel, we know that corresponding angles ∠1 and ∠21 are congruent.  Therefore, we can set up the following equation to find the measure of ∠21:

∠1 + ∠21 = 180° (because they are supplementary angles)

Substituting 125° for the measure of ∠1, we get:

125° + ∠21 = 180°

Solving for ∠21, we get:

∠21 = 180° - 125°

∠21 = 55°

Answer:

2

Step-by-step explanation:

it is 2 times as large because a is 3:3 and b is 6:6

3x2=6

so therefore your answer is 2

Answer:

- 4 < x ≤ 7

Step-by-step explanation:

Given

- 10 ≤ - 5x + 25 < 45 ( subtract 25 from all 3 intervals )

- 35 ≤ - 5x < 20

Divide all 3 intervals by - 5, reversing the inequality signs as a consequence.

7 ≥ x > - 4

Hence - 4 < x ≤ 7