Use the table at the right.
a. What is the approximate volume of the small truck?

Answer:

112

Step-by-step explanation:

Given: Joe gave 1/4 of his total candies to his classmate.

            Then, he gave 4/6 of when he had left to his brother.

             He gave 25% of the remaining candies to his sister.

             Finally, he only had 21 candies left.

Lets assume the total number of candies at the beginning be "x".

First, finding the number candies left after giving candies to classmate.

∴ Remaining candies=  [tex]x- x\times \frac{1}{4}[/tex]

Solving it to find remaining candies after giving candies to clasmate.

⇒ Remaining candies= [tex]x-\frac{x}{4}[/tex]

Taking LCD as 4

⇒ Remaining candies= [tex]\frac{4x-x}{4} = \frac{3x}{4}[/tex]

∴ Remaining candies after giving candies to clasmate= [tex]\frac{3x}{4}[/tex]

now, finding the candies left after giving candies to his brother.

∴ Remaining candies= [tex]\frac{3x}{4} - \frac{3x}{4} \times \frac{4}{6}[/tex]

Solving it to find the remaining candies after giving candies to his brother.

⇒ Remaining candies= [tex]\frac{3x}{4} - \frac{x}{2}[/tex]

Taking LCD 4

⇒ Remaining candies= [tex]\frac{3x-2x}{4} = \frac{x}{4}[/tex]

∴ Remaining candies after giving candies to his brother= [tex]\frac{x}{4}[/tex]

We know, Joe was left with only 21 candies after giving candies to his sister.

Therefore, putting an equation for remaining candies to find the number of candies at the beginning.

⇒[tex]\frac{x}{4} - 25\% \times \frac{x}{4} = 21[/tex]

⇒[tex]\frac{x}{4} - \frac{0.25x}{4} = 21[/tex]

Taking LCD 4

⇒ [tex]\frac{x-0.25x}{4} = 21[/tex]

⇒ [tex]\frac{0.75x}{4} = 21[/tex]

Multiplying both side by 4

⇒[tex]0.75x= 21\times 4[/tex]

dividing both side by 0.75

⇒[tex]x= \frac{21\times 4}{0.75}[/tex]

∴[tex]x= 112[/tex]

Hence, Joe had 112 candies at the beginning.

x = 14 and y = 10

Two shapes are similar if they have the same form but not necessarily the same size. In other words, when shapes are similar they are in proportion. Since you haven't provided any diagram, I'll choose two irregular polygon that are similar as indicated in the figure below. So we can calculate both x and y with proportions as follows:

[tex]For \ x: \\ \\ \frac{x}{7}=\frac{16}{8} \\ \\ x=\frac{7\times 16}{8} \\ \\ x=14 \\ \\ \\ For \ y: \\ \\ \frac{y}{20}=\frac{8}{16} \\ \\ y=\frac{8\times 20}{16} \\ \\ y=10[/tex]

Translation: https://brainly.com/question/11131466

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Answer:

1) x = -4

2) x = 21

Step-by-step explanation:

6x = -24

6/6x=-24/6

x=-4

and

x/7 = 3

x/7*7=3*7

x=21

Answer:

12%

Step-by-step explanation:

There are a total of 175 units in an apartment complex.

Out of which, 154 units are occupied.

Now, we have to find the percentage of the apartment which are unoccupied.

So, the number of units that are not occupied is (175 - 154) = 21.

Hence, the percentage of the number of unoccupied units of the apartment complex will be [tex]\frac{21}{175}\times 100 \% = 12 \%[/tex] (Answer)

Answer:

18

Step-by-step explanation:

45-27=18

Answer:

18

Step-by-step explanation:

subtract 45 and 27 it gives u 18

A compound is a unique substance that forms when two or more elements combine chemically. It always has the same elements in the same proportions.

Answer:

[tex]c=5.1\ units[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the measure of angle B

we know that

In the right triangle ABC

[tex]m\angle A+m\angle B=90^o[/tex] ---> by complementary angles in a right triangle

we have

[tex]m\angle A=35^o[/tex]

substitute

[tex]35^o+m\angle B=90^o[/tex]

[tex]m\angle B=90^o-35^o=55^o[/tex]

step 2

Find the length side c

Applying the law of sines

[tex]\frac{c}{sin(C)}=\frac{b}{sin(B)}[/tex]

substitute the given values

[tex]\frac{c}{sin(90^o)}=\frac{4.2}{sin(55^o)}[/tex]

[tex]c=\frac{4.2}{sin(55^o)}=5.1\ units[/tex]

Hey there! I'm happy to help!

We have a room that is 22 by 17 feet. We know that for every foot, we draw a 1/2 inch. This means that we need multiply our dimensions by 1/2 to find the dimensions of the drawing.

22×1/2=11

17×1/2=8.5

Therefore, the dimensions of the room are 11 feet by 8.5 inches. These are the dimensions of a normal white paper!

Have a wonderful day! :D

To convert the actual room dimensions of 22 feet by 17 feet to a scale drawing with a scale of 1/2 inch equals 1 foot, the length becomes 11 inches, and the width becomes 8.5 inches in the drawing.

When creating a scale drawing, the dimensions of the actual room need to be converted into scale dimensions. According to the scale given, which is 1/2 inch equals 1 foot, the actual room dimensions of 22 feet by 17 feet should be converted using this scale ratio.

To do this conversion, each actual dimension must be divided by the scale factor. The scale factor is determined by the number of feet that are represented by 1/2 inch. Since 1/2 inch is equivalent to 1 foot, the scale factor is 1 foot per 1/2 inch. Therefore, we calculate the dimensions as follows:

Length: 22 feet / 1 foot per 1/2 inch = 22 x 1/2 inches = 11 inches

Width: 17 feet / 1 foot per 1/2 inch = 17 x 1/2 inches = 8.5 inches

Thus, the dimensions on the scale drawing for a room that is 22 feet by 17 feet would be 11 inches by 8.5 inches.

Step-by-step explanation:

[tex] \triangle \: ABC \cong \triangle \: FED[/tex]

Here, all the sides or angles of triangle ABC are congruent to the corresponding sides or angles of triangle FED. As both triangles are reflections of each other.

I think it might be D

The size of the sample space is the total number of possible outcomes. For example, when you roll 1 die, the sample space is 1, 2, 3, 4, 5, or 6. So the size of the sample space is 6. Then you need to determine the size of the event space.

Answer:

I think it's the last one

Step-by-step explanation:

Answer:

k = 6.

Step-by-step explanation:

k = 6

2k = 12

12 - 6 - 3 = 3

k = 1

2k = 2

2 - 6 - 3 = -7

So, the answer is k = 6 because it makes more sense.

Amil's unit rate is calculated by dividing the distance traveled (15 miles) by the time in hours (0.917 hours), resulting in approximately 16.36 mph. Abe's unit rate is faster but cannot be precisely determined without more information about his distance or time.

Amil rode 15 miles in 55 minutes. To find Amil's unit rate, we divide the total distance by the total time. The unit rate is a measure of speed, indicating how many miles are traveled in one minute. To find this unit rate, we perform the following calculation:

Convert the time from minutes to hours to find the unit rate in miles per hour (mph), since speed is often expressed this way: ​55 minutes × (1 hour/60 minutes) = 0.917 hours

Divide the distance by the time: 15 miles ÷ 0.917 hours = 16.36 mph (rounded to two decimal places).

Amil's unit rate is approximately 16.36 mph. This information can be used to estimate Abe's unit rate, knowing that Abe rode at a faster rate. If we knew how far Abe rode or his unit rate in miles per minute, we could compare the two directly. Without additional information about Abe's distance or time, we can only say that Abe's unit rate exceeds 16.36 mph.

Answer: No

Step-by-step explanation:

5 + 1/2 = 5 1/2

Answer: Noelle's age is 20 years

Noelle's father is 54 years

Step-by-step explanation: First of all, let Noelle's age be represented by x. Given that her father's age is 6 less than three times her age, her father's age would be expressed as

3n - 6

Note also that their ages sum up to 74.

Therefore,

n + (3n - 6) = 74

n + 3n - 6 = 74

4n - 6 = 74

Add 6 to both sides of the equation

4n = 80

Divide both sides of the equation by 4

n = 20

Hence, Noelle's father's age is 54 (that is 3n - 6)

While Noelle's age is 20

Noelle’s age is 20

her dads age is 54

To solve the equation 4r + 8 + 5 = -15 - 3r, combine like terms and isolate the variable r leading to the solution r = -4.

The student is asking how to solve the algebraic equation 4r + 8 + 5 = -15 - 3r. To solve for r, we must first simplify and combine like terms. This means we need to get all the terms with r on one side of the equation and the constant numbers on the other side.

Therefore, the solution to the equation is r = -4.

Final answer:

The solution to the equation 4r + 8 + 5 = -15 - 3r is r = -4.

Explanation:

The algebraic equation provided by the student is 4r + 8 + 5 = -15 - 3r.

To solve for r, we must first simplify and rearrange the equation by combining like terms and moving the variables to one side and the constants to the other.

By subtracting 3r from both sides and also subtracting 8 + 5 from both sides, we end up with 4r + 3r = -15 - 8 - 5. Simplifying further, we get 7r = -28.

Finally, dividing both sides by 7 yields r = -4.

Answer:

The number of nickel coins is 10 and the number of quarter coins is 5

Step-by-step explanation:

The correct question is

Mary has 15 coins with the total value of $1.75 if the coins are nickels and quarters how many of each kind are there

Let

x ----> the number of nickel coins

y ----> the number of quarter coins

Remember that

[tex]1\ nickel=\$0.05[/tex]

[tex]1\ quarter=\$0.25[/tex]

we know that

Mary has 15 coins

so

[tex]x+y=15[/tex] -----> equation A

The total value of the coins is $1.75

so

[tex]0.05x+0.25y=1.75[/tex] ----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (10,5)

therefore

The number of nickel coins is 10 and the number of quarter coins is 5

Answer:

The solution to the system of equations given is (3, 2)

Step-by-step explanation:

Let's solve the system of equations given:

2y = 4  

-x = -3

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

2y = 4

y = 4/2

y = 2

____________________

-x = - 3

x = 3

The solution to the system of equations given is (3, 2)

The solution to the system of equations is x = 3 and y = 2.

To solve this system of equations, we can use the method of substitution or elimination. Let's solve it using the substitution method.

From the first equation, we can solve for y:

2y = 4

y = 4/2

y = 2

Now, substitute this value of y into the second equation:

-x = -3

x = 3

So the solution to this system of equations is x = 3 and y = 2.

Answer:

(2,  5 )

Step-by-step explanation:

Given a quadratic in standard form : y = ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

y = 3x² - 12x + 17 ← is in standard form

with a = 3 and b = - 12, thus

[tex]x_{vertex}[/tex] = - [tex]\frac{-12}{6}[/tex] = 2

Substitute x = 2 into the function for corresponding value of y

y = 3(2)² - 12(2) + 17 = 12 - 24 + 17 = 5

vertex = (2, 5 )

Answer:

See explanation

Step-by-step explanation:

Let a,b, and c be real numbers.

The distributive property says that:

[tex]a(b + c) = ab + ac[/tex]

Assuming we want to simplify:

[tex]10(5*10^{-1}+150*10^{-3})[/tex]

We apply the distributive property to get:

[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{-1} \times 10+150*10^{-3} \times 10[/tex]

We can now use rules of exponents to simplify further:

[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{-1} \times 10^{1} +150*10^{-3} \times 10^{1} [/tex]

[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{-1 + 1} +150*10^{-3 + 1}[/tex]

[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{0} +150*10^{-2}[/tex]

[tex]10(5*10^{-1}+150*10^{-3}) = 5*1+1.50*10^{-2}x {10}^{2} [/tex]

[tex]10(5*10^{-1}+150*10^{-3}) = 5*1+1.50*10^{-2 + 2}[/tex]

[tex]10(5*10^{-1}+150*10^{-3}) = 5+1.50*10^{0} = 6.5 \times {10}^{0} [/tex]

Answer:

10  20 40

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

U will add 5 plus 3 and then divide 8 by 2

Answer:4

Step-by-step explanation:

Step-by-step explanation:

Given, Total number of students is 80.

and 30% of the total students take a car to school

30% of 80

[tex]=\frac{30}{100}\times 80[/tex]

=24

Therefore 24 students take a car to school.

Answer:

24 students take a car to school

Answer:loss 20

Step-by-step explanation:

She lost 20

Step-by-step explanation:

60 take away 40 is 20

Answer- You can get 10 Small rafts

12 x 100+ 1200

1600-1200=400

400/40 =10 Rafts

A linear equation representing the given situation and the number of small rafts is required.

The required equation is [tex]100x+40y=1600[/tex]

The number of small rafts will be [tex]10[/tex]

Cost of one large raft = $100

Cost of one small raft = $40

Total amount to spend = $1600

Let the number of large rafts be [tex]x[/tex]

and small rafts be [tex]y[/tex]

The equation will be

[tex]100x+40y=1600[/tex]

The number of large rafts [tex]x=12[/tex]

[tex]100\times 12+40y=1600\\\Rightarrow y=\dfrac{1600-100\times 12}{40}\\\Rightarrow y=10[/tex]

Learn more:

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Answer:

The mid point of the line segment is [tex]$ \bigg(- \frac{3}{2}, -\frac{3}{2} \bigg ) $[/tex].

Step-by-step explanation:

From the graph we can find the end points of the line segment. The end points are: [tex]$ (- 1, - 4) $[/tex] and [tex]$ (4, 1) $[/tex].

When the end points of a line segment are known, the mid point of the line segment is given by:

                                   [tex]$ \bigg ( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \bigg ) $[/tex]

where [tex]$ (x_1, y_1) $[/tex] and [tex]$ (x_2, y_2) $[/tex] are the end points.

Here: [tex]$ (x_1, y_1) = (- 1, - 4) $[/tex] and [tex]$ (x_2, y_2) = (4, 1) $[/tex]

Therefore, the mid point of the line segment would be:

[tex]$ \bigg ( \frac{- 1 + 4}{2}, \frac{- 4 + 1}{2} \bigg) $[/tex]

[tex]$ \bigg(- \frac{3}{2}, -\frac{3}{2} \bigg ) $[/tex] is the required answer.

Answer:9.4 miles

Hope this helps

Answer:

0.097

move your decimal to the left twice