Which expression shows the sum 9 + 21 rewritten as a product of the GCF and a sum?

A- 9(1 + 21)
B- 3(3 + 7)
C- 3(3 + 21)
D- 9(1 + 3)

total ages = 60 
Generally, if the mode is 8 would mean there are more than one age of 8 
suppose there are two with age 8, 
leaving 44 for the other 4 
(11 for the average of the remaining 4) 

could have 9 and 13, and 8 and 14 

so we could have: 
8,8,8,9,13,14 

or we could have: 
8,8,9,10,12,13 

check:of the 1st answer 
mean = (8+8+8+9+13+14)/6 = 10 
the mode is 8 

you check the 2nd case

Answer:

Step-by-step explanation:

−5(4x 6)<−18x 6 4x given

−20x−30<−18x 6 4x  distributive property

−20x−30<−14x 6  combine like terms

−6x−30<6  addition property of order

−6x < 36  addition property of order

x>−6 division property of order

The ratio of perimeters is equal to the ratio of corresponding sides. The ratio of areas is the square of the ratio of corresponding sides.

The ratio of perimeters is equal to the ratio of corresponding sides. The ratio of areas is the square of the ratio of corresponding sides.

For a right triangle with legs of length 6 cm and 8 cm and a hypotenuse of length 10 cm, if each dimension is multiplied by 1/2 to form a similar triangle, the corresponding sides of the new triangle will be 3 cm, 4 cm, and 5 cm. The ratio of perimeters, 4 + 3 + 5 = 12, is equal to the ratio of corresponding sides, 6 + 4 + 5 = 15. So, the statement that the ratio of perimeters is equal to the ratio of corresponding sides is true.

The ratio of areas can be calculated by squaring the ratio of corresponding sides. So, the ratio of areas for the original right triangle will be (6 * 8) = 48 and for the similar triangle it will be (3 * 4) = 12. The ratio of areas, 48:12, simplifies to 4:1, which is indeed the square of the ratio of corresponding sides, 15:3.

2.37 + 0.35 = 2.72 total spent

5.00 - 2.72 = $2.28 change back

The equation that could be used to solve the number of hours Ben ran during each half of the race will be y = 5x + 3 and y = 5.5x + 2

During the first half of the race, he walked 3 miles and ran at a rate of 5 miles per hour for x hours. Therefore, the number of miles covered will be:

y = 5x + 3

During the second half of the race, he walked for 2 miles and ran at a rate of 5.5 miles per hour for x hours. Therefore, the number of miles covered will be:

y = 5.5x + 2

Then using both equations will be:

y = 5x + 3

y = 5.5x + 2

Subtract the equations

0.5x = 1

x = 1/0.5 = 2

Therefore, the value of y will be:

y = 5x + 3 = 5(2) + 3 = 13

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To solve Elizebeth's challenge, we can arrange 6 tiles in different ways to find a pattern where the number of toothpicks is more than double the number of tiles. The pattern is that the number of toothpicks is the same as the number of tiles when the tiles are arranged in a straight line.

To solve Elizebeth's challenge, we need to find a pattern where the number of toothpicks is more than double the number of tiles. Let's start with 6 tiles. We can arrange these tiles in various ways and count the number of toothpicks:

So, for 6 tiles, the number of toothpicks is either 1, 2, 3, 4, 5, or 6. The pattern we can observe is that the number of toothpicks is the same as the number of tiles when the tiles are arranged in a straight line.

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Answer:

The overall average of the classes is 89.125%

Step-by-step explanation:

For calculate the average of the class using weighted means, it is necessary to take into account the number of students of every period. So, the average can be calculated as:

[tex]Average =\frac{(x_1*a_1) +( x_2*a_2) + (x_3*a_3)}{x_1 + x_2 + x_3}[/tex]

Where is[tex]x_1, x_2[/tex] and [tex]x_3[/tex] are the number of students for period 1 , 2 and 3 respectively and [tex]a_1, a_2[/tex] and [tex]a_3[/tex] are the average of period 1, 2 and 3 respectively.

Replacing the values of x1 by 15 students, x2 by 21 students, x3 by 12 students, a1 by 86%, a2 by 88% and a3 by 95%, we get:

[tex]Average = \frac{(15*86)+(21*88)+(12*95)}{15+21+12}[/tex]

Average = 89.125%

So, using weighted means, the overall average of the classes is 89.125%

Answer:

Step 2 has an error

Step-by-step explanation:

Given equation,

2(10 - 13x) = -34x + 60

By distributive property,

20 - 26x = -34x + 60

Now, we need to isolate x on the left side of the equation,

For this we need to eliminate constant term from the left side,

20 will be eliminated by subtracting 20 from both sides ( subtraction property of equality )

I.e. Step 2 has an error,

We need to use subtraction property of equality instead of using addition property of Equality,

Note : The correct steps would be,

Step 2 : 20 - 26x = -34x + 60 ( Subtraction property of equality )

Step 3 : 8x = 40  ( addition property of Equality )

Step 4 :  x = 5  (  Division Property of Equality )

The 'Share' plan will be enough for Liza with 650 minutes.

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, Lizzie makes 20 minutes of phone calls each day

There are 30 days in June,

Minutes required in the given month = 20*30 = 600

She should choose the Share plan with 650 minutes so that she will have enough minutes plus 50 minutes left.

Hence, The 'Share' plan will be enough for Liza with 650 minutes.

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Answer with Step-by-step explanation:

A function is a map from a set A to another set B such that

the image of any point in a has a unique image in set B.

A = {(1, 2), (2, 3), (3, 4), (4, 5)}

It is a function since image of 1,2,3 and 4 is unique.

B = {(1, 2), (2, 1), (3, 0), (4, -1)}

It is  a function since image of 1,2,3 and 4 is unique.

C = {(-1, 3), (0, 3), (1, 3), (2, 3)}

It is  a function since image of -1,0,1 and 2 is unique.

D = {(1, 1), (1, 2), (1, 3), (1, 4)}

It is  not a function since image of 1 is not unique.

E = {(6, 2), (7, 3), (6, -1), (5, 4)}

It is  not a function since image of 6 is not unique.

Hence, sets that are not functions are:

D = {(1, 1), (1, 2), (1, 3), (1, 4)}

E = {(6, 2), (7, 3), (6, -1), (5, 4)}

Answer:

D) it shows the functional relationship , the cost of the apples is a function of weight.

Step-by-step explanation:

Given : Graph between cost of the apples and the weight of apples.

To find : Which is true about the functional relationship shown in the graph.

Solution : We can see from the graph is showing the relation between cost of an apple and weight of apple .

Therefore, D) it shows the functional relationship , the cost of the apples is a function of weight.

To calculate the area of the blanket, multiply the length (2.25 meters) by the width (1.8 meters) to get 4.05 square meters. Then convert this to square centimeters by multiplying by 10,000 (since 1m^2 is 10,000 cm^2), resulting in an area of 40500 square centimeters.

The area of the blanket can be calculated by multiplying its length by its width. We start with the measurements in meters and then convert the result into centimeters.

First, we find the area in square meters:
Area = length × width = 2.25 m × 1.8 m = 4.05 m²

Since there are 100 centimeters in a meter, we need to convert each dimension from meters to centimeters before we can find the area in square centimeters. This means we multiply each meter by 100 to get the dimension in centimeters:

So, the area of the blanket is 40500 cm².

The probability that a dart hits the circle when moved from Quadrant IV to Quadrant II stays the same if the size of the circle and the rectangular region remain unchanged, as it is dependent on the area ratio of the circle to the rectangle.

When the circle is moved from Quadrant IV to the shaded region in Quadrant II, the probability that a dart hitting the rectangular region lands in the circle depends on whether the size of the circle or its position relative to the overall dartboard (the rectangle) changes. The probability is determined by the ratio of the area of the circle to the area of the rectangle. If the circle remains the same size and merely shifts positions, the probability does not change. However, if moving the circle changes its size or if it overlaps differently with the rectangular region, then the probability will be affected. To calculate the probability, you would divide the area of the circle by the area of the rectangle. Provided there are no changes to the size of the circle or rectangular area, the probability remains constant despite the move.

 The sunlight takes about 8 minutes and 20 seconds to reach earth.

We have given that,

The speed of light is 3 x 10^8 meters/seconds.

D = r x t  distance is equal to the rate of speed multiplied by time. 

Thus t = d ÷ r  

This is the relationship we'll use to solve this problem.

 Now, let's organize our data

 r = 300,000,000 m/s  

Let's write this using scientific notation

r = 3 x 108 m/s 

d = 1.5 x 1011 m 

t = d ÷ r  ⇒  t = 1.5 x 1011 ÷ 3 x 108  or

 t = 0.5 x 103  

That is 500 seconds or about 8.3 minutes so basically the answer is the sunlight takes about 8 minutes and 20 seconds to reach earth.

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The cost price is 16500

Let's learn about the basic formula about Profit and Loss

[tex]\texttt{Profit = Selling Price - Cost Price}[/tex]

[tex]\texttt{Selling Price = Cost Price ( 100\% + Profit\% )}[/tex]

[tex]\texttt{Loss = Cost Price - Selling Price}[/tex]

[tex]\texttt{Selling Price = Cost Price ( 100\% - Loss\% )}[/tex]

Let us tackle the problem !

Given:

Gain Percentage = 5%

Loss Percentage = 5%

Difference of Sales Price = 1650

Unknown:

Cost Price = ?

Solution:

[tex]\texttt{Initial Sales Price} = \texttt{Cost Price} \times ( 100\% + \texttt{Gain Percentage} )[/tex]

[tex]\texttt{Initial Sales Price} = \texttt{Cost Price} \times ( 100\% + 5\% )[/tex]

[tex]\texttt{Initial Sales Price} = \texttt{Cost Price} \times ( 105\% )[/tex]

[tex]\texttt{ }[/tex]

[tex]\texttt{Final Sales Price} = \texttt{Cost Price} \times ( 100\% - \texttt{Loss Percentage} )[/tex]

[tex]\texttt{Final Sales Price} = \texttt{Cost Price} \times ( 100\% - 5\% )[/tex]

[tex]\texttt{Final Sales Price} = \texttt{Cost Price} \times ( 95\% )[/tex]

[tex]\texttt{ }[/tex]

[tex]\texttt{Difference of Sales Price} = \texttt{Initial Sales Price} - \texttt{Final Sales Price}[/tex]

[tex]1650 = \texttt{Cost Price} \times ( 105\% ) - \texttt{Cost Price} \times ( 95\% )[/tex]

[tex]1650 = \texttt{Cost Price} \times ( 105\% - 95\% )[/tex]

[tex]1650 = \texttt{Cost Price} \times ( 10\% )[/tex]

[tex]\texttt{Cost Price} = 1650 \div ( 10\% )[/tex]

[tex]\texttt{Cost Price} = 16500[/tex]

Grade: Middle School

Subject: Mathematics

Chapter: Percentage

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent , cookies , chocolate , chip , paper , fourth , pieces

Answer:25233

Step-by-step explanation:

Answer:11 boxes

Step-by-step explanation:

Answer:

It is 48

Step-by-step explanation:

The number ​​0.00000000058 in standard form is equal to [tex]58\times10^{-11}[/tex].

In Mathematics and Statistics, any numerical data (number) can be written in scientific notation as shown below:

a × [tex]b^{n}[/tex]

Where

Based on the information provided above, the numerical data (number) is given by 0.00000000058. When expressed in decimal notation, it can be computed as follows;

Numerical data = 0.00000000058

Numerical data = [tex]5.8\times10^{-10}=58\times10^{-11}[/tex]

Note: The number of zeros must be equal to ten (10).