Chris's uncle has a model car. the model is 6 inches long and 3 inches wide. the actual car is 75 inches long. what is the car's actual width, if we assume the model's proportions are accurate? if necessary, round to the nearest tenth of an inch.

Answer:

39 degrees

Step-by-step explanation:

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Final answer:

To solve the equation 4x=7(x-3), distribute 7, simplify, isolate the variable, and divide by -3 to find that x=7.

Explanation:

To solve the equation 4x=7(x-3) step by step:

1. First, distribute 7 to (x-3), resulting in 4x=7x-21. (Reason: applying the distributive property)

2. Next, subtract 7x from both sides of the equation, giving us 4x-7x=-21. (Reason: isolating the variable term)

3. Combine like terms on the left side to get -3x=-21. (Reason: simplifying the equation)

4. Finally, divide both sides of the equation by -3 to solve for x, resulting in x=7. (Reason: isolating the variable)

After solving the given equation, that is, 4x=7(x-3), we get the answer x=7.

Answer: A. [tex]11x=55[/tex]

Step-by-step explanation:

The given system of equations:

[tex]y = 3x.....................(1)\\\2x + 3y = 55.................(2)[/tex]

When we substitute the value of y in equation (2), we get

[tex]2x+3(3x)=55\\\\\Rightarrow\ 2x+9x=55\\\\\Rightarrow\ 11x=55[/tex]

Hence, the result of using the first equation to substitute for y in the second equation, then combining like terms is [tex]11x=55[/tex]

The system of linear inequalities that represent the situation are

$0.24x + $0.80y ≤ $12 and x + y ≥ 20

Here is the complete question:

Write a system of linear inequalities to represent this situation.

Darcy is buying apples and oranges for a large fruit basket to give away as a door prize at a charity event. Apples cost $0.24 each and oranges cost $0.80 each. She has $12 to spend and would like to purchase at least 20 pieces of fruit total.

To write a system of linear inequalities to represent the situation, we will consider the statements one after the other.

Let x represent the number of apples and y represent the number of oranges.

From the second statement,

"Apples cost $0.24 each and oranges cost $0.80 each"; and

From the next statement,

"She has $12 to spend"

That means, she can either spend $12 or less than $12.

Therefore, we can write that

$0.24x + $0.80y ≤ $12

Also, from the following statement

"and would like to purchase at least 20 pieces of fruit total"

That means, she will either purchase 20 pieces of fruit or greater than 20 pieces of fruit.

Then we can write that

x + y ≥ 20

Hence, the system of linear inequalities that represent the situation are

$0.24x + $0.80y ≤ $12 and x + y ≥ 20

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Answer:

A) 956.5 in^2

Step-by-step explanation:

took the test

the answer will be 120,000

We know that:

1 south African rand = 0.075 usd

1 kuwaiti dinar = 3.31 usd

1 japanese yen = 0.0089 usd

Therefore the total money in usd is:

total usd = 150 rand * (0.075 usd / 1 rand) + 350 dinar * (3.31 usd / 1 dinar) + 200 yen * (0.0089 usd / 1 yen)

total usd = 1,171.53 us dollars 

The speed of the dog is 4.8m/s

Data;

This is calculated as the ratio between the distance covered to the time taken.

The formula is given as

[tex]speed = \frac{distance }{time taken}[/tex]

Let's plug in our values and solve

[tex]speed = \frac{24}{5}\\ speed = 4.8m/s[/tex]

The speed of the dog is 4.8m/s

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Final answer:

To find the speed of a dog that covers 24 meters in 52 seconds, divide the distance by the time to get an average speed of approximately 0.4615 meters per second (m/s).

Explanation:

To calculate the speed of a dog running through a yard that covers a distance of 24 meters in 52 seconds, you would use the formula for speed, which is:

Speed = Distance ÷ Time

In this case, the dog covers a distance (Distance) of 24 meters in a time (Time) of 52 seconds. Substituting these values into the formula we get:

Speed = 24 m ÷ 52 s

Now, we perform the division to find the speed:

Speed = 0.4615 meters per second (m/s)

Therefore, the dog is running at an average speed of approximately 0.4615 m/s.

Answer:

[tex]17[/tex]

Step-by-step explanation:

Let the number of students in pottery class be [tex]x[/tex]

Price each student pays for the class = [tex]\$15[/tex]

Price each student pays for the material = [tex]\$27[/tex]

Total earning of pottery class = [tex]\$714[/tex]

We can write this in expression as-

[tex]15x + 27x = 714[/tex]

Solving the expression we get[tex]15x + 27x = 714\\42x = 714\\x = \frac{714}{42} \\x = 17[/tex]

There are total [tex]17[/tex] students in the class this month

Answer:

to the right

to the left

below

(4.5,200)

144 degrees is the measure of the interior angles of the polygon.

In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and a finite number of sides. Additionally, some examples of a polygon include the following:

• Triangle

• Quadrilateral

• Pentagon

• Hexagon

• Heptagon

• Octagon

• Nonagon

Generally speaking, the measure of the angle at the center of a regular polygon is equal to 360 degrees. Therefore, the smallest angle of rotation that maps (carries) a regular polygon onto itself can be calculated by using this formula:

α = 360/n

The sum of the measures of the interior angles of an n-sided polygon is given by the formula:

S = (n - 2) × 180 degrees

So, for a 10-sided polygon, we have:

S = (10 - 2) × 180 = 8 × 180 = 1440 degrees

To find the measure of each interior angle, we divide the sum by the number of angles (which is the same as the number of sides for a polygon):

m = S/n = 1440/10 = 144 degrees

Therefore, each interior angle of a 10-sided polygon has a measure of 144 degrees.

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Answer:

MN ≅ M′N′

Step-by-step explanation:

When you rotate an image on a certain pivot point, you´ll end up with two equal images in shape and form, but with different angles from the center, since the image is the same shape, form and length, their sides and angles should be the same, so the sentece that is true is that MN ≅ M′N′.

we know that

In the right triangle LJK

m∠LJK°=m∠x°

[tex]cos\ x=\frac{adjacent\ side\ angle\ x}{hypotenuse}[/tex]

in this problem

[tex]adjacent\ side\ angle\ x=JL=10\ in\\ hypotenuse=KJ=15\ in[/tex]

substitute

[tex]cos\ x=\frac{10}{15}[/tex]

therefore

the answer is the option

[tex]cos\ x=\frac{10}{15}[/tex]

The equation that can be used to find the measure of angle LJK is cos(x) = 10/15.

The image in the diagram is a right triangle. A right angle is a triangle that has an angle that measures 90 degrees. In the triangle, angle L measures 90 degrees. The hypotenuse is 15 inches.

Sin = opposite / adjacent

sin x = √(15² - 10²) / 15

sin x = 11.1 / 15

Tan = opposite / adjacent

tan x = 11.1 / 15

Cos = adjacent / hypotenuse

cos x = 10 / 15

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Answer:

The mean of original sample is 29.

Step-by-step explanation:

After 5 points are subtracted from every score, the sample mean is found to be m = 24

So, the mean for the original sample was = [tex]24+5=29[/tex]

Here we are talking about mean so 5 points are subtracted from every score. when we are talking in terms of mean, 5 will be added to the mean, that will give 5 added to every score.

Answer:

C) Rolling an even number and an odd number.

Step-by-step explanation:

We are asked to choose the correct option that represents two mutually exclusive events.

Since we know that mutually exclusive events are those events, who can not happen at the same time. As we cannot have both heads and tails in one toss, either we will get heads or we will get tails.

Let us check our given choices one by one.

A) Rolling a multiple of 2 and a multiple of 4.

Multiples of 2: 2, 4, 6,..

Since 4 is a multiple of 2, so both events are not mutually exclusive and option A is not a correct choice.

B) Rolling a multiple of 3 and a multiple of 6.

Multiples of 3: 3, 6, 9,...

Since 6 is a multiple of 3, so both events are not mutually exclusive and option B is not a correct choice.

C) Rolling an even number and an odd number.

Odd numbers on a cube: 1, 3, 5.

Even numbers on a cube: 2, 4, 6.

Since on one roll of dice we can either have an odd or an even number, both events are not possible with a single roll, therefore, option C is the correct choice.

D) Rolling a prime number and an even number.

Prime number on a cube: 2, 3, 5.

Even numbers on a cube: 2, 4, 6.

We can clearly see that 2 is a prime number and it is even as well, therefore, option D is not a correct choice.

Answer:

51

Step-by-step explanation:

The number could be 51 if the square root of a number is between 7 and 8 option (c) 51 is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

It is given that:

The square root of a number is between 7 and 8.

Let the number is x:

The square root of the number will be √x

7 < √x < 8

Squaring both sides:

49 < x < 64

The number will lie between 49 and 64

From the option, the number 51 lies between 49 and 64.

Thus, the number could be 51 if the square root of a number is between 7 and 8 option (c) 51 is correct.

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Answer: B would be the correct answer on edg. (X+1)(x-1)(x^2+9)

Final answer:

Quartiles are more reliable than mean and standard deviation for judging outliers because they are less affected by extreme values, making them a robust measure, especially for skewed distributions.

Explanation:

Quartiles are generally more reliable for judging outliers than mean and standard deviation because they are less sensitive to extreme values. While mean and standard deviation can be significantly affected by a single outlier, quartiles, particularly the Interquartile Range (IQR), measure the spread of the middle 50 percent of the data, thus minimizing the impact of outliers. The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3), which defines the range where the central half of the data points lie.

Outliers are typically identified using criteria based on the IQR, such as data points that fall below Q1 - 1.5*IQR or above Q3 + 1.5*IQR. Compared to standard deviation, which is affected by the skewness of the data, quartiles present a more robust measure, especially in skewed distributions. Therefore, quartiles offer a more resistant and accurate way of identifying outliers and understanding the data's spread without being unfairly influenced by extreme values.

The part of the total that is not sold is 1/4.

If you sell 7/4 of the lot, the part of the total that is not sold is 1 - 7/4 = 1/4.

Another way to think about it is that if you have 4 slices of pie and you sell 7 of them, you have 1 slice left. Therefore, 1/4 of the pie is not sold.

Suppose you have a lot that is 100 square meters in size. If you sell 7/4 of the lot, you will sell 7/4 * 100 square meters = 175 square meters. This means that you will have 100 square meters - 175 square meters = 25 square meters left.

Therefore, the part of the total that is not sold is 25 square meters / 100 square meters = 1/4.

In general, if you sell a fraction of a total, the part of the total that is not sold is 1 - (fraction sold).

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