Translate the sentence into an inequality.The sum of a number times 8 and 21 is at least 20 .Use the variable y for the unknown number.

Answer:

If a line is parallel to another line, both of the lines have the same slope. So far the equation is y=-1/5+b. To find the value of b, substitute the given point into the equation. 0=-1/5(5)+b, 0=-1+b, b=1. So the equation of the line is y=-1/5x+1.

:)

Answer:

5. Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

\(\\ \rm\rightarrowtail \dfrac{-6}{7}\div (\dfrac{-3}{8})\)

\(\\ \rm\rightarrowtail \dfrac{-6}{7}\times \dfrac{8}{-3}\)

\(\\ \rm\rightarrowtail \dfrac{-2}{7}(8)\)

\(\\ \rm\rightarrowtail -16/7\)

\(\\ \rm\rightarrowtail -2\dfrac{2}{7}\)

Answer:

Step-by-step explanation:

The conversion is a. 12 mm ≈ 0.47 inches

b. 75 km ≈ 46.60 miles

c. 150 m ≈ 492.13 feet

d. 63 square meters ≈ 678.13 square feet

e. 45 meters per second ≈ 147.64 feet per second

f. 1.9 L ≈ 2.01 U.S. quarts

To convert the metric units into the given English units, we'll use the following conversion factors:

1 inch = 25.4 mm

1 mile = 1.60934 km

1 meter = 3.28084 feet

1 square meter = 10.7639 square feet

1 meter per second = 3.28084 feet per second

1 liter = 1.05669 U.S. quarts

a. 12 mm to inches:

12 mm * (1 inch / 25.4 mm) ≈ 0.47 inches

b. 75 km to miles:

75 km * (1 mile / 1.60934 km) ≈ 46.60 miles

c. 150 m to feet:

150 m * (3.28084 feet / 1 meter) ≈ 492.13 feet

d. 63 square meters to square feet:

63 square meters * (10.7639 square feet / 1 square meter) ≈ 678.13 square feet

e. 45 meters per second to feet per second:

45 meters per second * (3.28084 feet per second / 1 meter per second) ≈ 147.64 feet per second

f. 1.9 L (liters) to U.S. quarts:

1.9 L * (1.05669 U.S. quarts / 1 liter) ≈ 2.01 U.S. quarts

So, after rounding to two decimal places:

a. 12 mm ≈ 0.47 inches

b. 75 km ≈ 46.60 miles

c. 150 m ≈ 492.13 feet

d. 63 square meters ≈ 678.13 square feet

e. 45 meters per second ≈ 147.64 feet per second

f. 1.9 L ≈ 2.01 U.S. quarts

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Answer:

each shirt cost $12

Step-by-step explanation:

4:27

Step-by-step explanation:

just subtract 45 and 18. common sense

She uses 12 gallons of petrol to drive 420 miles, averaging 35 miles per gallon.

A number is split in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of items being distributed among a set of individuals. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each. The outcome of dividing one integer by another is a quotient. When dividing a number into units of a measurable quantity, this is known as quotative division. For instance, we could wish to know how many groups there will be if we divide 8 into groups of 2.

Here,

Weight of gas=12 gallon

Distance travelled=420 miles

miles did her car travel per gallon of gas,

=420/12

=35 miles/gallon

She travels 35 miles/gallon when she used 12 gallons of gas to travel 420 miles.

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The average grade for this test is given as follows:

1.85.

The average grade is obtained as the mean of the data-set containing all the grades, which is given by the sum of all grades divided by the number of grades.

Considering the numerical equivalents of each letter, the grades in this problem are given as follows:

The total number of grades is given as follows:

11 + 18 + 52 + 13 + 6 = 100.

The sum of these grades is given as follows:

11 x 0 + 18 x 1 + 52 x 2 + 13 x 3 + 6 x 4 = 185.

Hence the average grade is of:

185/100 = 1.85.

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Answer:

11 out of 39

Step-by-step explanation:

Answer:

\frac{11}{39}

39

11

Step-by-step explanation:

There are 39 fruits in all.

11 + 6 + 9 + 13= 3911+6+9+13=39

Therefore, there would be 39 total events.

There are 11 preferred events, as there are eleven oranges out of the 39 fruits.

\frac{preferred}{total} =\frac{11}{39}

total

preferred

=

39

11

So, there should be a 11/39 chance that a person would pick an orange.

\frac{11}{39}

39

11

is already in it's lowest terms

From the graph, she walked at a rate of \(\frac{25-10}{5-2}=5 \text{ ft/s}\).

Therefore, she walked faster on her next three walks compared to her first two walks.

Answer:

D

Step-by-step explanation:

The increase in certain individuals leads to:

An increase in certain individuals within a bacterial population can lead to:

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The activity rate for Cost Pool A is $7.97 per unit of Product A, and the activity rate for Cost Pool B is $6.06 per unit of Product B.

The activity rate is a cost accounting term that refers to the cost that a company incurs for each unit of a particular activity or process. It is calculated by dividing the total cost of an activity or process by the total number of units produced or processed.

The purpose of calculating activity rates is to allocate the cost of a particular activity or process to the products or services that use that activity or process. This helps to determine the true cost of producing a product or service and to make informed decisions about pricing, profitability, and resource allocation.

In order to calculate the activity rate for each cost pool, we need to know the total cost for each cost pool.

Let's assume that there are two cost pools: Cost Pool A and Cost Pool B.

If we know the total cost for each cost pool, we can calculate the activity rate for each cost pool by dividing the total cost by the total number of units produced.

For example, if the total cost for Cost Pool A is $100,000 and 12,539 units of Product A were produced, then the activity rate for Cost Pool A would be:

Activity Rate for Cost Pool A = Total Cost for Cost Pool A / Total Units of Product A

Activity Rate for Cost Pool A = $100,000 / 12,539 units

Activity Rate for Cost Pool A = $7.97 per unit of Product A

Similarly, if the total cost for Cost Pool B is $50,000 and 8,254 units of Product B were produced, then the activity rate for Cost Pool B would be:

Activity Rate for Cost Pool B = Total Cost for Cost Pool B / Total Units of Product B

Activity Rate for Cost Pool B = $50,000 / 8,254 units

Activity Rate for Cost Pool B = $6.06 per unit of Product B

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The correct answer is A, Canada. This is because the select() function allows you to specify the exact variables to be included in the data frame, and Company.Location is one of the variables that was specified in this case.

The first row of the table created using the select() function contains the data for the three selected variables from the original flavors_df data frame. The select() function was used to create a new data frame with only three variables: Rating, and Cocoa.Percent, and Company.Location. This function was used to filter out all the other variables from the original flavors_df data frame, leaving only the three variables of interest.

When looking at the first row of the table, the value in the Company.Location column is Canada, which is the country in the company producing the chocolate is located in.

Complete question:

After previewing and cleaning your data, you determine what variables are most relevant to your analysis. Your main focus is on Rating, Cocoa.Percent, and Company.Location. You decide to use the select() function to create a new data frame with only these three variables.

Assume the first part of your code is:

trimmed_flavors_df <- flavors_df %>%

Add the code chunk that lets you select the three variables.

select(Rating, Cocoa.Percent, Company.Location)

What company location appears in row 1 of your table?

Single Choice Question. Please Choose The Correct Option &#x2714;

A. Canada

B. Scotland

C. France

D. Columbia

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Answer:

  y = x³ -2x² -13x -10

Step-by-step explanation:

You want a polynomial with x-intercepts -2, -1, and 5, and a y-intercept of -10.

A polynomial with zero x = p will have a factor of (x -p). The three given zeros mean factors of the desired polynomial will be ...

  p(x) = (x -(-2))(x -(-1))(x -5) = (x +2)(x +1)(x -5)

Expanding this gives ...

  p(x) = (x +2)(x² -4x -5) = x³ -2x² -13x -10

This polynomial has a constant of -10, which will be its y-intercept. No additional scaling is needed.

The polynomial function is ...

  y = x³ -2x² -13x -10

Answer:

16, 24, 32

Step-by-step explanation:

The ratio is 8:3 so you would multiply both by the same number and that would give you 16:6, 24:9, 32:12

The statement about the function is: "The function is decreasing for all real values of x where x < -4." D.

The given information tells us that the graph represents a downward-opening parabola.

The vertex of the parabola is located at (-4, 4) indicates that this point is the highest point on the graph.

As we move to the left of the vertex, the function values decrease, indicating a decreasing trend.

Moreover, the graph passes through the point (-6, 0), which lies to the left of the vertex.

This confirms that the function is decreasing for all real values of x less than -4, including x < -6.

On the other hand, the graph also passes through the point (-2, 0), which lies to the right of the vertex.

This does not impact the conclusion that the function is decreasing for x < -4, as the graph's behavior to the right of the vertex is not relevant to this particular statement.

Based on the given information and the properties of the downward-opening parabola, we can conclude that the function is decreasing for all real values of x where x < -4.

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The man is 27 years old and the son is 9 years old.

We can write the son's age as 'x', and therefore write the man's age as 4x. In 3 years, both their ages will increase by 3, so the son's age is now x + 3, and the man's age is 4x + 3.

We are told that the man is now 3 times older than his son, which means his current age, 4x + 3, is the same as 3 times the son's current age, which is x + 3.

Therefore we can write an equation:

4x + 3 = 3(x + 3)

4x + 3 = 3x + 9

- 3x

x + 3 = 9

- 3

x = 6

We can now substitute this in to find their current ages:

Son's age = x + 3 = 6 + 3 = 9

Man's age = 4x + 3 = 24 + 3 = 27

I hope this helps! Let me know if you have any questions :)

Answer:

x= 4

Step-by-step explanation:

Answer:

the first one is (23)

number 7 is ( 34.069)

Step-by-step explanation:

a) He needs 500 g of sugar to make apple crumble for 16 people.

b) She needs 45 g of flour to make apple crumble for 2 people.

c) 500g of apples is enough to make apple crumble for 6 people.

The amounts for this problem are obtained according to the proportions given in the problem.

For 8 people, the amount of sugar needed is of 250 g. For 16 people, the  number of people doubles, hence the amount of sugar needed will also double, as follows:

2 x 250 = 500 g.

For 2 people, the amount of each item is divided by 4, hence the amount of flour needed is given as follows:

180/4 = 45 g.

The amount of apple needed per people is of:

700/8 = 87.5 grams.

For 6 people, the amount is given as follows:

6 x 87.5 = 525 grams.

Hence 500g of apples is enough to make apple crumble for 6 people.

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The football is approximately 96.4 feet from the base of the goal post.

The tangent function in trigonometry is used to determine the proportion between the lengths of the adjacent and opposite sides in a right triangle. Where theta is the angle of interest, the tangent function is defined as:

tan(theta) = opposing / adjacent.

When the lengths of one side and one acute angle are known, the tangent function is used to solve for the unknown lengths or angles in right triangles. In order to utilise the tangent function, we must first determine the angle of interest, name the triangle's adjacent and opposite sides in relation to that angle, and then calculate the ratio of those sides using the tangent function.

Given, the angle of elevation is 16 degrees 42'.

That is,

Angle of elevation = 16 degrees 42' = 16 + 42/60 = 16.7 degrees

Using tangent function we have:

tan(16.7) = 30/x

x = 30 / tan(16.7)

x = 96.4 feet

Hence, the football is approximately 96.4 feet from the base of the goal post.

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The solution in interval notation is; (-∞,  49/2).

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

To solve the equation 5/16x - 7/4 < 3/4x + 21/2, we can simplify both sides:

5/16x - 7/4 < 3/4x + 21/2

Combining like terms:

5/16x  -3/4x  < 21/2 + 7/4

8/16x < 49/4

1/2x < 49/4

Simplifying the fraction;

x < 49/2

Therefore, the solution in interval notation is (-∞,  49/2).

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Answer:

595.

Step-by-step explanation:

Take $2000 and subtract $810 from it. You now have the total of the two pieces of equipment without the extra pricing. You should get $1,190. Then divide that number by 2. You will get $595.

1st Piece of Equipment = $595

2nd Piece of Equipment = $1,405

2nd Piece is $810 more expensive and the two pieces combined is $2,000.

Answer:

C. 40,25,-16,-2 Celsius

Answer:

Let us prove that p=-5

33 + 6 x -5 = 2(-5 - 1) - 3 x -5

3 = 3

Check the picture below.

so hmm we have a 6x6 square atop and a triangle with base of 6 and a height of "h", let's get "h".

\(\sin( 42^o )=\cfrac{\stackrel{opposite}{h}}{\underset{hypotenuse}{2}} \implies 2\sin(42^o)=h \implies 1.34\approx h \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Areas} }{\stackrel{triangle}{\cfrac{1}{2}(\underset{b}{6})(\underset{h}{1.34})}~~ + ~~\stackrel{ square }{(6)(6)}} ~~ \approx ~~ 4.02+36~~ \approx ~~ \text{\LARGE 40.0}\)

\(f^(-1)(2) = 6\), which is consistent with our earlier result.

A function that "undoes" another function is known as an inverse function. If f(x) is a function, then f(x inverse, )'s indicated by f-1(x), is a function that accepts f(x output )'s as an input and outputs f(x initial )'s input.

Given the function f(x) = √(2x - 8), if f^(-1)(x) is the inverse function of f(x), what is \(f^(-1)(2)\)?

Solution:

To find f^(-1)(2), we need to find the value of x such that  \(f(x) = 2\) . We can set up an equation:

\(f(x) = \sqrt(2x - 8) = 2\)

Squaring both sides, we get:

\(2x - 8 = 4\)

\(2x = 12\)

\(x = 6\)

Therefore, \(f^(-1)(2) = 6.\)

We can also verify this result by using the definition of an inverse function. If f^(-1)(x) is the inverse function of f(x), then by definition:

\(f(f^(-1)(x)) = x\)

We can substitute x = 2 and solve for f^(-1)(2):

\(f(f^(-1)(2)) = 2\)

\(f^(-1)(2) = (f(6))^(-1)\)

f(6) = √(2(6) - 8) = √4 = 2

Therefore,\(f^(-1)(2) = 6\), which is consistent with our earlier result.

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