Abigail's car uses 3 2/3 gallons of gas every hour on a long distance trip. How many gallons does the car use in 8 1/2 hours?

Answer:

The width of the roof is 12

Step-by-step explanation:

Divide the figure as shown in the attachment.

Recall that slope is rise over run.

Then the slope of the roof in terms of x is

[tex] \frac{8}{x} [/tex]

But we were given in the question that the slope is 2/3.

This implies that:

[tex] \frac{8}{x} = \frac{2}{3} [/tex]

Cross multiply to get:

[tex]2x = 3 \times 8[/tex]

[tex]2x = 24[/tex]

[tex]x = 12[/tex]

The appropriate measure of central tendency for the data in the stem and leaf plot, which is skewed to the right is the median

What is the median of a dataset?; The median of a dataset is the value located at the center of the dataset when the data are arranged in increasing order of magnitude.

The data in the stem and leaf plot can be presented as follows;

5, 6, 10, 12, 13, 13, 14, 21, 29, 42, 51

The number of data points are 11, therefore, the median is the 6th term, which is the number 13

The mode of the data is 13

The mean of the data is; (5+6+10+12+13+13+14+21+29+42+51)/11 ≈ 19.64

The mean is larger than the median, which indicates that the data values are skewed to the right

The appropriate measure of the center of the data whereby some of the values are much larger than the median and a few values, hence the data is skewed is the median

For the stem-and-leaf plot of pounds of food collected, the most appropriate measure of center is the median, providing a robust representation of the central tendency of the data.

In the given stem-and-leaf plot depicting the pounds of food collected, the most appropriate measure to describe the center of the data is the median.

The median is the middle value in a dataset when it is ordered from least to greatest. In this case, the stem-and-leaf plot already presents the data in ascending order within each stem. To find the median, we look for the middle value. Since the data is arranged systematically, we can identify the median as the value that separates the lower half from the upper half of the dataset.

Looking at the stems and their corresponding leaves, the median is the value in the middle of the dataset, which is the 3 in the second stem. The median is less sensitive to extreme values or outliers than the mean, making it a robust measure of central tendency.

In contrast, the mean (average) might be influenced by extreme values, the interquartile range focuses on the spread of the middle 50% of the data, and the range considers the difference between the maximum and minimum values.

The question probable may be:

Which measure is most appropriate to describe the center of the data in the stem-and-leaf plot below?

A stem and leaf plot showing the pounds of food collected is shown.

Stem    Leaf

0           5    6

1            0    2   3   3   4

2            1    9

3

4            2

5            1

interquartile range

median

mean

range

Answer:7

Step-by-step explanation:

7+7+7+7 is 49

Answer:

perimeter is 36

Step-by-step explanation:

49 square root is 9

since it is a square 4 side lengths x 9 = 36

Answer:

F=70.7

Step-by-step explanation:

This is a simple substitution problem.

The resulting temperature in Fahrenheit is 70.7°F.

To convert a temperature from Celsius (°C) to Fahrenheit (°F), you can use the formula:

F = (9/5)C + 32

Given that the temperature is 21.5°C, we can substitute this value into the formula:

Multiply the Celsius temperature by 9: 9 * 21.5 = 193.5

Divide the result by 5: 193.5 / 5 = 38.7

Add 32 to the quotient: 38.7 + 32 = 70.7

Therefore, the temperature in Fahrenheit is 70.7°F.

Answer:

[tex]\left(\left(-x^2\right)-\left(12x^3\right)-8\right)^2:\quad 144x^6+24x^5+x^4+192x^3+16x^2+64[/tex]

Step-by-step explanation:

Considering the expression

[tex]\left(\left(-x^2\right)-\left(12x^3\right)-8\right)^2[/tex]

Solving the expression

[tex]\left(\left(-x^2\right)-\left(12x^3\right)-8\right)^2[/tex]

[tex]\mathrm{Remove\:parentheses}:\quad \left(a\right)=a[/tex]

[tex]\left(-x^2-12x^3-8\right)^2[/tex]

As

[tex]\left(-x^2-12x^3-8\right)^2=\left(-x^2-12x^3-8\right)\left(-x^2-12x^3-8\right)[/tex]

So

[tex]\left(-12x^3-x^2-8\right)\left(-12x^3-x^2-8\right)[/tex]

[tex]\mathrm{Expand}\:\left(-x^2-12x^3-8\right)\left(-x^2-12x^3-8\right):\quad 24x^5+144x^6+192x^3+x^4+16x^2+64[/tex]

i.e.

[tex]\left(-x^2\right)\left(-x^2\right)+\left(-x^2\right)\left(-12x^3\right)+\left(-x^2\right)\left(-8\right)+\left(-12x^3\right)\left(-x^2\right)+\left(-12x^3\right)\left(-12x^3\right)+\left(-12x^3\right)\left(-8\right)+\left(-8\right)\left(-x^2\right)+\left(-8\right)\left(-12x^3\right)+\left(-8\right)\left(-8\right)[/tex]

[tex]\mathrm{Apply\:minus-plus\:rules}[/tex]

[tex]\left(-a\right)\left(-b\right)=ab[/tex]

[tex]x^2x^2+12x^3x^2+8x^2+12x^3x^2+12\cdot \:12x^3x^3+12\cdot \:8x^3+8x^2+8\cdot \:12x^3+8\cdot \:8[/tex]

[tex]\mathrm{Group\:like\:terms}[/tex]

[tex]12x^3x^2+12x^3x^2+12\cdot \:12x^3x^3+12\cdot \:8x^3+8\cdot \:12x^3+x^2x^2+8x^2+8x^2+8\cdot \:8[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:8x^2+8x^2=16x^2[/tex]

[tex]12x^3x^2+12x^3x^2+12\cdot \:12x^3x^3+12\cdot \:8x^3+8\cdot \:12x^3+x^2x^2+16x^2+8\cdot \:8[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:12x^3x^2+12x^3x^2=24x^3x^2[/tex]

[tex]24x^3x^2+12\cdot \:12x^3x^3+12\cdot \:8x^3+8\cdot \:12x^3+x^2x^2+16x^2+8\cdot \:8[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:12\cdot \:8x^3+8\cdot \:12x^3=2\cdot \:8\cdot \:12x^3[/tex]

[tex]24x^3x^2+12\cdot \:12x^3x^3+2\cdot \:8\cdot \:12x^3+x^2x^2+16x^2+8\cdot \:8[/tex]

As

[tex]24x^3x^2=24x^5[/tex]

[tex]12\cdot \:12x^3x^3=144x^6[/tex]

[tex]2\cdot \:8\cdot \:12x^3=192x^3[/tex]

[tex]x^2x^2=x^4[/tex]

[tex]8\cdot \:8=64[/tex]

So

[tex]24x^5+144x^6+192x^3+x^4+16x^2+64[/tex]

[tex]\mathrm{Rewrite\:in\:standard\:form}[/tex]

[tex]144x^6+24x^5+x^4+192x^3+16x^2+64[/tex]

Therefore,

[tex]\left(\left(-x^2\right)-\left(12x^3\right)-8\right)^2:\quad 144x^6+24x^5+x^4+192x^3+16x^2+64[/tex]

Keywords: expression

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Option A: [tex]C(x)=1,200+120 x R(x)=200 x[/tex] is the equation.

Explanation:

Let x represents the number of hours per month the store is open.

It is given that the the monthly rent(expense) = $1200

Also, the employee salary for each hour(expense) = $120x

Thus, the total expense C(x) is [tex]1200+120x[/tex]

It is also given that the income per hour(revenue) is $200x

Thus, the revenue function R(x) is [tex]200x[/tex]

The break - even point is given by

Total expense = Revenue

Thus, [tex]C(x)=1,200+120 x R(x)=200 x[/tex] is the equation.

Hence, Option A is the correct answer.

Answer:

A

Step-by-step explanation:

Answer:

10.07$

Step-by-step explanation:

6 meters of fabric = 10.35

divide 3.45 by 2

1.72

add 1.72+10.35

10.07$

Answer:

Set up a proportion 2m/$3.45 = 7m/x

then cross multiply

7(3.45)=2x

then divide both sides by 2

x=12.075 which is roughly $12.08

Step-by-step explanation:

Answer:

Length = 45

Width = 38

Step-by-step explanation:

2a + 2(a + 7) = 166

4a + 14 = 166

4a = 152

a = 38

a = Width

38 = Width

a + 7 = Length

(38 + 7) = Length

45 = Length

Answer:

Andy

Step-by-step explanation:

Since hes 0 away from it meaning he’s there

Answer: 1) Andy 2) Caedin 3) 9:08am 4) Berta

Step-by-step explanation: first is Andy because it says “the locations starting at 9am “and the starting point is 0 and Andy is the only one there. Second is Caedin because he decreases at first but increases later on. Third because they started at 9am and the x-axis (minutes) says 8 so it could only mean they cross paths at 9:08am, the last one is Berta because she closest

Answer:

0.2  (compression)

Step-by-step explanation:

Given

Length of paper = 11 inches,

Width of paper = 8 1/2 = 17/2 inches

Length of logo = 2 1/5 = 11/5 inches

Width of logo = 1 7/10 = 17/10 inches

Scale factor based on Length

=Length of Logo ÷ Length of paper

= 11/5 ÷ 11

= 0.2  (since it is less than 1, this is a compression)

(Sanity Check: Check width scale factor = length scale factor)

Scale factor based on width

=Width of Logo ÷ Width of paper

= 16/10 ÷ 17/2

= 0.2  (this is the same as the length scale factor so this checks out ok!)

Answer:

     [tex]\large\boxed{\large\boxed{1/36}}[/tex]

Explanation:

1. By definition

2. Possible outcomes

The possible outcomes is the sample space. The first toss has 6 possible outcomes and the second toss has other 6 possible outcomes; thus, the sample space has 6 × 6 = 36 different outcomes.

3. Favorable outcomes

Tossing exactly two 5's is just one of the 36 possible outcomes. Thus. the number of favorable otucomes is 1.

4.  Computation

Answer:

4(2x+3y)

Step-by-step explanation:

Answer:

Choice D.

82.8

Step-by-step explanation:

We can use law of cosines since we are given three sides.

[tex]z^2=y^2+x^2-2yx \cos(Z)[/tex]

Since [tex]z[/tex] is opposite side of angle [tex]Z[/tex], then [tex]z=12[/tex]:

[tex]12^2=10^2+8^2-2(10)(8) \cos(Z)[/tex]

[tex]144=100+64-160 \cos(Z)[/tex]

[tex]144=164-160 \cos(Z)[/tex]

[tex]-20=-160 \cos(Z)[/tex]

[tex]\frac{-20}{-160}=\cos(Z)[/tex]

[tex]\frac{20}{160}=\cos(Z)[/tex]

[tex]\frac{1}{8}=\cos(Z)[/tex]

[tex]\cos^{-1}(\frac{1}{8})=Z[/tex]

[tex]82.819^\circ=Z[/tex]

Option D is correct.

Answer:

11 boys 8 girls

Step-by-step explanation:

There are 19 total students.

There are 3 more boys than girls

girls + 3 = boys ( because there are three more boys)

boys + girls = 19

You can substitute g +3 for b so:

2 girls +3 = 19

19 - 3 = 16

16/2 = girls

8 = girls

Once you find g just subtract the amount of girls from 19 to get the amount of boys.

19 kids - 8 girls = 11 boys

The next three numbers in sequence are 22, 32 and 44

Solution:

Given sequence is:

2, 4, 8, 14, ...

We have to find the next 3 numbers in sequence

Let us understand the logic used in this sequence

[tex]First\ term = 1^2 -1+2 = 1 + 1 = 2\\\\Second\ term = 2^2 -2 + 2 = 4\\\\Third\ term = 3^2 - 3 + 2 = 9 - 1 = 8\\\\Fourth\ term = 4^2 -4 + 2 = 16-2 = 14[/tex]

Thus the formula used is:

[tex]a_n = n^2 - n +2[/tex]

Where, "n" is the location of term in sequence

To find the next three terms:

[tex]Fifth\ term = 5^2 - 5 + 2 = 25 - 3 = 22\\\\Sixth\ term = 6^2 - 6 + 2 = 36 - 4 = 32\\\\Seventh\ term = 7^2 -7 + 2 = 49 - 5 = 44[/tex]

Thus the next three numbers in sequence are 22, 32 and 44

Answer:

Therefore d = 100 is a solution of the given equation.

A question that solving this problem could answer is "what is the range of d"

d < 171.43

Step-by-step explanation:

i) the given equation is 10 - 0.035d > 4

ii) if d = 100 then 10 - (0.035[tex]\times[/tex] 100) = 10 - 3.5 = 6.5 > 4

Therefore d = 100 is a solution of the given equation.

A question that solving this problem could answer is "what is the range of d"

10 - 0.035d > 4

therefore -0.035d > 4 - 10

therefore -0.035d > -6

therefore 0.0035d < 6

therefore d < 6 / 0.035 [tex]\Rightarrow[/tex] d < 171.43

Final answer:

100 is a solution to the inequality 10 - 0.035d > 4 because, after substituting d with 100, the inequality 6.5 > 4 holds true.

Explanation:

To determine whether 100 is a solution of the inequality 10 - 0.035d > 4, we substitute d with 100 and check if the inequality holds true:

10 - 0.035(100) > 4

10 - 3.5 > 4

6.5 > 4

Since 6.5 is indeed greater than 4, we can confirm that 100 is a solution to the inequality.

A corresponding question this problem could answer might be: "If a part-time employee loses $0.035 from their savings for each day they work, after how many days will their savings be reduced to less than $4 if they initially had $10?" Solving the inequality would help find the maximum number of days the employee can work before their savings fall below $4.

Answer:

Is a reflection across the x-axis

Step-by-step explanation:

The complete question is

Point D (9,-8) is  reflected to D' (9,8). Is it on the x axis or y axis?

we know that

The rule of the reflection of a point across the x-axis is

(x,y)-----> (x,-y)

the x-coordinate remains the same, but the y-coordinate is transformed into its opposite

In this problem we have

D (9, -8) ------> D' (9, 8)

The y-coordinate is transformed into its opposite

therefore

Is a reflection across the x-axis

a) The expression for perimeter of rectangle is 4x+34.

b) The expression for area of rectangle is 24x+60.

Step-by-step explanation:

Given figure is a rectangle;

Length of rectangle = 12

Width of rectangle = (x+5)+x = 2x+5

a) Perimeter of model

Perimeter of rectangle = 2(Length + Width)

Perimeter of rectangle = [tex]2(12+2x+5)[/tex]

Perimeter of rectangle = [tex]2(2x+17)[/tex]

Perimeter of rectangle = 4x+34

The expression for perimeter of rectangle is 4x+34.

b) Total area of rectangle

Area of rectangle = Length * Width

Area of rectangle = [tex]12*(2x+5)[/tex]

Area of rectangle = 24x+60

The expression for area of rectangle is 24x+60.

Keywords: area, rectangle

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Answer:

Y= -5/6 - 9

Step-by-step explanation:

Answer:

(a) 3 inches

(b) Her scale model drawing WILL fit on the piece of paper 8.5 by 7 inches

Step-by-step explanation:

Scaling

We use scales to represent realities in reduced spaces. In the case of lengths or surfaces, the scale allows us to draw the shapes in normal sheets of paper.  

(a)

Kelly's rock garden has a length of 6 feet. She uses a 1 inch:2 feet scale. this means that the model length is

6 feet*1 inch/2 feet = 3 inches

(b)

The width of the model is 5 inches, keeping the same scale it means the real length is

5 inches * 2 feet / 1 inch = 10 feet

The model will have 3 inches by 5 inches, it perfectly fits on any regular piece of paper

Answer:

About 51.43 degrees.

Step-by-step explanation:

In order to find the angle measures, you divide 360 by the number of sides your shape has. In this case you divide 360 by 7.

Answer:

The graph is shown attached.

Step-by-step explanation:

i) The graph is shown attached

ii) The values shown are for the points with black dots.

Answer:

False, False, True, False

Step-by-step explanation:

The correct statements are:

(2x+y) is a factor of the expression 3(2x+y).

(2x+y) is a sum of two terms.

a) 2x is a factor of the expression (2x+y): False.

2x is not a factor of (2x+y) because it doesn't divide evenly into it.

b) (2x+y) is a factor of the expression 3(2x+y): True.

(2x+y) is a factor of 3(2x+y) because it divides evenly into it.

c) (2x+y) is a sum of two terms: True.

(2x+y) is a sum of the two terms 2x and y.

d) 3(2x+y) is a product of two terms: False.

3(2x+y) is a product of three terms: 3, 2x, and y.

Hence the b and c are the correct statements.

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the answer to this equation is 120

Answer:

120

Step-by-step explanation:

Answer:

the answer is savings (d).

Step-by-step explanation:

I had a test and this helped a LOT so now I can help you,

hope it helped.

If you are not prepared for an emergency, the most likely missing element from your financial plan is savings.

Setting and accomplishing financial objectives through the process of developing a plan to control income, spending, and investments is known as financial planning. Financial planning is to assist people and families in achieving independence, stability, and security in their financial lives.

In conclusion, financial planning is a thorough process that includes establishing financial objectives, assessing your present financial condition, creating a budget and savings plan, controlling debt and risk, and routinely reviewing and modifying your plan. Individuals and families may attain financial security and stability by following these steps as they work towards their long-term financial objectives.

Given data ,

Savings are most likely the component of your financial plan that is lacking if you are not ready for an emergency.

Each financial plan must include savings since they provide as a safety net in the event of crises like unanticipated medical costs, auto repairs, or job loss. Lack of funds may compel you to rely on high-interest loans or credit cards, which might result in long-term financial issues.

While having funds to cover unexpected costs should be a key concern, a financial plan should also include a budget, investments, and financing.

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An expression that is equivalent to [tex](12x^4-4x^3+7x+6)+(3x^2-4x+14)[/tex] include the following: D. [tex]12x^4-4x^3+3x^2+3x+20[/tex]

In Mathematics and Euclidean Geometry, the degree of a polynomial function is the highest power among each of its term.

The leading coefficient represents the coefficient of the leading term while the leading term is the term with the highest degree. Also, a constant polynomial is a polynomial that has only a constant term and no variable.

In this exercise and scenario, your are required to add the polynomial functions together.

First of all, we would rearrange the polynomial functions by collecting like terms and then add them together as follows;

[tex]12x^4-4x^3+3x^2-4x+7x+6+14\\\\12x^4-4x^3+3x^2+3x+20[/tex]

Complete Question:

Which of the following expressions is equivalent to [tex](12x^4-4x^3+7x+6)+(3x^2-4x+14)[/tex]?

A [tex]12x^4-x^3+3x+20[/tex]

B [tex]15x^6-8x^4+21x+6[/tex]

C  [tex]15x^6-4x^3+3x+20[/tex]

D [tex]12x^4-4x^3+3x^2+3x+20[/tex]

Final answer:

To find the equivalent expression, add like terms from both expressions, resulting in 12x⁴ - 4x³ + 3x² + 3x + 20.

Explanation:

To find the expression equivalent to (12x⁴-4x³+7x+6)+(3x²-4x+14), we simply add the like terms from both expressions.

Firstly, observe that there are no other terms with the same degree as 12x⁴ and -4x³, so they will remain as they are.

Next, add the coefficients of the x terms and the constants: 7x + (-4x) = 3x and 6 + 14 = 20.

However, there's a 3x² term in the second expression which doesn't have a matching term in the first expression, so it also remains unchanged.

Combining all these, the equivalent expression is 12x⁴ - 4x³ + 3x² + 3x + 20.

Answer:

x ( 3x − 7 ) ( x ^3 + 2 )

Step-by-step explanation:

Answer:

  2.30

Step-by-step explanation:

The side of interest is opposite the given angle, and the hypotenuse is given. The sine relation tells you ...

  sin(A) = a/c

  a = c·sin(A) = 3·sin(50°)

  a = BC ≈ 2.2981 ≈ 2.30

Answer:

4

Step-by-step explanation:

5y-3=17

5y=17+3

5y=20

y=20/5

y=4