4(3x-8)-4 = 24
12x-32-4= 24
12x-36 = 24
12x = 60
X=5
What methods did she use and in what order did she use them?

Answer:

7 - 2m can be translated to "7 minus two times m" or "the difference between 7 and twice m".

3(m + 2) = 15 can be translated to "three times the sum of m and 2 is equal to 15" or "the product of 3 and the sum of m and 2 is 15".

To solve the equation, we can start by distributing the 3 on the left side:

3(m + 2) = 15

3m + 6 = 15

Then, we can subtract 6 from both sides:

3m + 6 - 6 = 15 - 6

3m = 9

Finally, we can divide both sides by 3:

3m/3 = 9/3

m = 3

Therefore, the solution to the equation 3(m + 2) = 15 is m = 3.

5m - m(2 - m) can be translated to "5m minus the product of m and the difference between 2 and m" or "the difference between 5m and m times the quantity 2 minus m".

To simplify the expression, we can use the distributive property to expand the second term:

5m - m(2 - m) = 5m - 2m + m^2 = m^2 + 3m

Therefore, the simplified expression is m^2 + 3m.

The equation of a circle centered at the origin with a radius of 12, which is x² + y² = 144.

To find the equation of the circle, we use the standard form of the equation of a circle, which is:

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the center of the circle, and r is the radius.

In our problem, the center of the circle is at the origin, which means h = 0 and k = 0. The radius is given as 12, so we have r = 12. Substituting these values into the standard form equation, we get:

(x - 0)² + (y - 0)² = 12²

Simplifying, we get:

x² + y² = 144

Therefore, the equation of the circle centered at the origin with a radius of 12 is x² + y² = 144.

To know more about equation here

https://brainly.com/question/10413253

#SPJ4

Therefore, the teacher charging per hour is $\(44\).

What is the percentage?

A percentage is a number or ratio expressed as a fraction of \(100\). It is often denoted using the percent sign, "%".

Here given that,

Last year, Sara's piano teacher charged $\(40\) per hour for private lessons. This year, the teacher increased her rates by \(10\)%.

So,

\(\frac{40}{100}\)×\(10=4\)

And the teacher charged \(40\) $ per hour so it would be

\(40+4=44\) $

Hence, the teacher charging per hour is $\(44\).

To know more about the percentage

https://brainly.com/question/13244100

#SPJ2

Answer:

B

Step-by-step explanation:

If you Divide 60 by 2 you would get 30 but if you divide by four ill be 15 so for b ill be 2 and a will be 4

Answer:

20 dollars per month

Step-by-step explanation:

85 = 25 + x3

60 = x3

20 = x

Based on the IQR values, we conclude that Bus 18 is more consistent than Bus 47, as it has smaller IQR. This means the travel times of students on Bus 18 are more tightly clustered around the median, and are fewer outliers in data.

A line plot is a type of graph that displays data as points or dots along a number line. Each dot or point represents a single data value, and the number line shows the range of the data. Line plots are useful for displaying small to moderate-sized data sets and for identifying the central tendency and variability of the data.

To determine which bus is the most consistent, we need to look at the variability of data. The most appropriate measure of variability for this purpose is the interquartile range (IQR), which is the range of the middle 50% of the data.

From the given data, we can calculate the IQR for both buses as follows:

For Bus 18:

Lower quartile (Q1) = 8

Upper quartile (Q3) = 24

IQR = Q3 - Q1 = 24 - 8 = 16

For Bus 47:

Lower quartile (Q1) = 10

Upper quartile (Q3) = 34

IQR = Q3 - Q1 = 34 - 10 = 24

The range, which is the difference between the maximum and minimum values, is not as appropriate a measure of variability for this purpose, as it is heavily influenced by outliers. Therefore, we cannot use the range to determine the consistency of the data for either bus.

To know more about interquartile range visit:

https://brainly.com/question/29204101

#SPJ1

Answer:

What does the serving consist of?

Step-by-step explanation:

Answer:

it depends on what the servings are

Step-by-step explanation:

Answer:

check online for more information

The position function s(t) for a particle with acceleration a(t) = 4t - 1, initial velocity v(0) = -3 cm/s, and initial displacement s(0) = 4 cm is s(t) = t^2 - t + 4t + 4 cm.

To find the position function s(t), we need to integrate the acceleration function a(t) with respect to time twice. Given that a(t) = 4t - 1, we first integrate it once to obtain the velocity function v(t). The integral of 4t - 1 with respect to t is 2t^2 - t + C1, where C1 is a constant of integration. Since the initial velocity is v(0) = -3 cm/s, we can substitute t = 0 and v(0) = -3 into the velocity function to find C1. Solving for C1, we get C1 = -3.

Next, we integrate the velocity function v(t) = 2t^2 - t - 3 with respect to t to find the position function s(t). The integral of 2t^2 - t - 3 with respect to t is (2/3)t^3 - (1/2)t^2 - 3t + C2, where C2 is another constant of integration. Using the initial displacement s(0) = 4 cm, we substitute t = 0 and s(0) = 4 into the position function to find C2. Solving for C2, we get C2 = 4.

Therefore, the position function s(t) for the particle is given by s(t) = (2/3)t^3 - (1/2)t^2 - 3t + 4 cm. This function represents the particle's position at any given time t based on its initial velocity, acceleration, and displacement.

Learn more about displacement here:

https://brainly.com/question/11934397

#SPJ11

A box-and-whisker plot needs to be created. To have a mean distance of 6 miles on the 10th day, Chris needs to ride a specific distance. If Chris rides 20 miles on the 10th day, it will change the mean distance.

Part A: To create a box-and-whisker plot, we need to arrange the given data in ascending order: 1, 2, 3, 4, 5, 6, 8, 8, 9. The plot will consist of a box representing the interquartile range (from the first quartile to the third quartile), a line within the box representing the median, and whiskers extending to the minimum and maximum values (excluding outliers if any).

Part B: To determine how far Chris needs to ride on the 10th day to have a mean distance of 6 miles, we need to consider the current total sum of distances and the total number of days. By calculating the difference between the desired mean and the current mean, we can determine the additional distance Chris needs to ride on the 10th day.

Part C: If Chris rides 20 miles on the 10th day, it will change the mean distance. The extent of the change in the mean depends on the initial data. To calculate the new mean, we need to include the additional distance (20 miles) and recalculate the mean using the updated total sum of distances and the total number of days.

Note: Without knowing the total number of days and the current sum of distances, precise calculations for Parts B and C cannot be provided.

Learn more about distance here:

brainly.com/question/15256256

#SPJ11

Answer:

big bodie built

Step-by-step explanation:

i used to be dusty

Based on the calculations, the value of the given prefix expression is equal to 2205.

The preorder traversal of a tree (T) are typically used in discrete mathematics to determine the value of a prefix expression on a specific expression tree.

For the preorder traversal of this tree (T), we would start from the right most expression:

Prefix expression = * + 3 + 3 ↑ 3 + 3 3 3

Prefix expression = * + 3 + 3 ↑ 3 6 3

Prefix expression = * + 3 + 3  3⁶  3

Prefix expression = * + 3 3 729 3

Prefix expression = * + 3 732 3

Prefix expression = * 735 3   ⇒ 735 × 3

Value = 2205.

Read more on preorder traversal here: https://brainly.com/question/12947940

#SPJ11

Complete Question:

Given the following prefix expression:

* + 3 + 3 ↑ 3 + 3 3 3

What is the value of the prefix expression?

Answer:

Step-by-step explanation:

x^2+17x+72=12

x= -5 and -12

Keith is correct.

Answer:

I think Keith solved it correctly.

Step-by-step explanation:

x= -12 and that was one of keiths answers so he's right.

-12+12= 0

5 and 12

Fifty kilograms is equal to approximately 110.23 pounds. To convert from kilograms to pounds, multiply the number of kilograms by 2.2.

Kilograms and pounds are two weight measurement units. In the metric system, a kilogram is a unit of mass, whereas in the imperial system, a pound is a unit of mass. To convert kilograms to pounds, multiply the total number of kilograms by 2.2. For instance, 50 kilos equals 110.23 pounds. This is due to the fact that 50 kilograms multiplied by 2.2 equals 110.23 pounds. To convert pounds to kilograms, divide the total number of pounds by 2.2. It is crucial to note that the imperial pound and the international pound differ somewhat, and conversions should be made accordingly.

Learn more about kilogram here

https://brainly.com/question/28844288

#SPJ4

Answer:

the answer is d for this one

Answer:

D) 11x² + 7

Step-by-step explanation:

combine "like" terms

Surface area , Lateral area and volume of triangular prism area 262.25 square in, 231 square in and 156.25 cubic in respectively.

With two triangular bases and three rectangular sides, a triangular prism is a kind of polyhedron. Alternatively, because it has five faces overall, it may be thought of as a pentahedron in which the bases' edges and vertices are connected by three rectangular sides.

Given, base (b) =5 in ,

the height of the triangle (h) = 6.25 in

length of a prism (l) = 12 in

and the hypotenuse of the right triangle = 8 in

The surface area of a right triangular prism = b×h + (S1 + S2 + h)L

On substituting the values, we get

SA = (5 × 6.25) + [(5 + 6.25 + 8) × 12]

⇒ SA = 60 + (30 × 11)

⇒ SA =262.25 square in

Therefore, the total surface area of a right triangular prism is 262.25 square in.

Lateral  Area = ( S1 + S2 + S3 ) × l

On substituting the values, we get

LA=(5+6.25+8)×12

LA=(19.25)×12

LA=231 square in

Therefore, the lateral surface area of a right triangular prism is 231 square in.

the base area = (1/2) × (b×h) = (1/2) × (5 ×6.25) =15.625 square in

The length of the prism is, L = 12 in

Using the volume of the triangular prism formula,

The volume of the given triangular prism = base area × length of the prism = 15.625 ×10=156.25 cubic in

Hence, The volume of the given triangular prism is 156.25 cubic in.

To know more about Lateral area , visit:

https://brainly.com/question/14001755

#SPJ1

Answer:

is 30 hope I helped!!:D

Step-by-step explanation:

step 1 : cross multiply.

10/3= k/9

(10)*(9)=k*(3)

90=3k

step 2: flip the equation.

3k =90

step 3: Divide both sides by 3.

3k/3=90/3

k=30

The correct statements about the volume of the cone are:

- The volume of the cone is One-third the volume of the cylinder.

- The expression 84 pi over 3 finds the volume of the cone.

- The volume of the cone is less than the volume of the cylinder.

\(V=\pi\times r^2\times h\)

where 'r' is the radius of the base of the cylinder and 'h' is height of the cylinder

where 'r' is the radius of the base of the cone and 'h' is height of the cone

For given example,

The volume of the cylinder is 84 pi inches cubed.

Let \(V_1\) represents the volume of the cylinder.

\(V_1=84~~cu.in.\)

Using the formula of the volume of the cylinder,

\(V_1=\pi\times r^2\times h\)

where 'r' is the radius of the base of the cylinder and 'h' is height of the cylinder

Let \(V_2\) be the volume of the cone.

Assume that the base radius 'r' and height 'h' of the cone and the cylinder are equal.

Using the formula of the volume of the cone,

\(\Rightarrow V_2=\pi\times r^2\times \frac{h}{3}\\\\\Rightarrow V_2=\frac{1}{3}\times( \pi\times r^2\times h) \\\\\Rightarrow V_2=\frac{1}{3}\times V_1\)

This means, the volume of the cone is One-third the volume of the cylinder.

\(\Rightarrow V2=\frac{1}{3}\times 84\)

This means, the expression 84 pi over 3 finds the volume of the cone.

\(\Rightarrow V_2=28~~cu.in.\pi \\\\\Rightarrow V_2 < V_1\)

This means, the volume of the cone is less than the volume of the cylinder.

Therefore, the correct statements about the volume of the cone are:

- The volume of the cone is One-third the volume of the cylinder.

- The expression 84 pi over 3 finds the volume of the cone.

- The volume of the cone is less than the volume of the cylinder.

Learn more about the volume of the cylinder and the volume of the cone here:

https://brainly.com/question/16007458

#SPJ2

Answer

y(x-5)(x+2)

Step-by-step explanation:

The expected number of choices needed to select the first CS PhD student is 4.

To solve this problem, we can use the concept of geometric distribution. The geometric distribution represents the number of independent and identical trials that are needed to obtain the first success, where the probability of success is p.

In this case, the probability of selecting a CS PhD student on any given trial is 50/200 = 0.25. Therefore, the number of trials needed to obtain the first CS PhD student follows a geometric distribution with p = 0.25.

The expected value of a geometric distribution with parameter p is given by E(X) = 1/p. Therefore, the expected number of choices needed to select the first CS PhD student is

E(X) = 1/p = 1/0.25 = 4

Learn more about geometric distribution here

brainly.com/question/29210110

#SPJ4

The least volume to greatest volume will be sphere B, sphere C, sphere A and sphere D.

The volume of the sphere is calculated as:

= 4/3 πr³

where r = radius

The volume of sphere A will be:

= 4/3 πr³

= 4/3 × π × 4³

= 85.3π

The volume for sphere B will be:

= 4/3 πr³

= 4/3 × π × (6/2)³

= 4/3 × π × 3³

= 36π

The volume for C is given as 64π.

The volume for D has a radius double that of B. This will be Radius = 3 × 2 = 6

= 4/3 πr³

= 4/3 × π × 6³

= 288π

Learn more about volume on:

brainly.com/question/1972490

#SPJ1

Answer:

Step-by-step explanation:

The reference triangle always have a leg perpendicular to the x-axis, the hypotenuse is positive, and θ is the angle adjacent to the x-axis and hypotenuse.

What is reference triangle ?

The reference triangle is a right triangle and therefore, the properties of

the reference triangle are similar to right triangle properties.

The reference triangle always have a leg perpendicular to the x-axis, the hypotenuse is positive, and θ is the angle adjacent to the x-axis and hypotenuse.

The reference triangle is formed by the construction of a perpendicular

to the x-axis from the terminal side of an angle, oriented in the standard

position.

Therefore;

The reference triangle is a right triangle that always has a leg perpendicular to the x-axis.

The hypotenuse is taken as positive, given that the magnitude of the hypotenuse is the square root of the sum of the squares of the legs.

In the first quadrant, the reference angle, θ, is the same as the standard position angle and it is given by the angle formed between the x-axis and the hypotenuse side.

The correct options are therefore;

In Trigonometry it is important that the right triangle (reference triangles)

have a consistent orientation. The reference triangles always have a leg

perpendicular to the x-axis, the hypotenuse positive and the θ is

adjacent to the x-axis and hypotenuse.

To Learn more about reference angles from given link.

brainly.com/question/10657736

#SPJ1

Answer:

$2,928

Step-by-step explanation:

Using the equation below, note that for days in which she worked more than \(8\) hours, we will be multiplying the number hours worked over \(8\) hours by \(91.5.\)

\(61\) × \(1.5=91.5\)

Let \(x\) equal hours less than or equal to \(8.\)

Let \(y\) equal the number of hours worked over \(8\) hours.

Let \(t\) equal gross earnings.

Start with an equation:

\(61x+91.5y=t\)

Monday:

\(61(7)=427\)

Tuesday:

\(61(8)+91.5(1) = 579.5\)

Wednesday:

\(61(8)+91.5(1) = 579.5\)

Thursday:

\(61(8)+91.5(2) = 671\)

Friday:

\(61(7)=427\)

Saturday:

\(61(4)=244\)

Now, total the gross earnings of each day.

\(427+579.5+579.5+671+427+244\)

Solve.

\(2928\)

Not sure if I'm right but I think it's 3(x - 6) (x^2 + 5x)

Step-by-step explanation:

3x^3 - 3x^2 - 90x

Apply GCF: 3 (x^3 - x^2 - 30)

Split 30 into -6 and 5

(x^3 - 6x^2) (5x^2 - 30x)

GCF of both: x^2 (x - 6) and 5x (x - 6)

DON'T FORGET TO CARRY THE 3

And your answer is 3 (x - 6) (x^2 + 5x)

I hope this help

Step-by-step explanation:

Square Root of 38 to the nearest tenth, means to calculate the square root of 38 where the answer should only have one number after the decimal point.

Here are step-by-step instructions for how to get the square root of 38 to the nearest tenth:

Step 1: Calculate

We calculate the square root of 38 to be:

√38 = 6.16441400296898

Step 2: Reduce

Reduce the tail of the answer above to two numbers after the decimal point:

6.16

Step 3: Round

Round 6.16 so you only have one digit after the decimal point to get the answer:

6.2

To check that the answer is correct, use your calculator to confirm that 6.22 is about 38.

Answer:

.1

Step-by-step explanation:

6.164

thenths

=tenth=0.1

I guess

Scatter graphs are used to represent data by using dots or symbols to represent data on two variables. There are two axes, a horizontal (x-axis) and a vertical (y-axis), where the horizontal axis is used for one variable and the vertical axis is used for the other variable. the statement is true.

Scatter graphs can be used to answer different questions about data by analyzing the pattern of the data. The questions that we want to answer using the scatter graph given in the question are:

a) The same athlete had the longest javelin throw and the longest discus throw.

b) The shortest javelin throw was longer than the shortest discus throw.

c) The longest discus throw was shorter than the longest javelin throw.

Answer: a) The same athlete had the longest javelin throw and the longest discus throw. This statement can be observed from the scatter graph by identifying the dots that are the highest and on the right of the graph.

The athlete who had the longest javelin throw also had the longest discus throw. Therefore, the statement is true.

b) The shortest javelin throw was longer than the shortest discus throw.

This statement can be observed from the scatter graph by identifying the dots that are the lowest and on the left of the graph.

The shortest javelin throw is longer than the shortest discus throw. Therefore, the statement is true. c) The longest discus throw was shorter than the longest javelin throw.

This statement can be observed from the scatter graph by identifying the dots that are the highest and on the right of the graph. The longest discus throw is shorter than the longest javelin throw. Therefore, the statement is false.

To conclude, scatter graphs are used to represent data by using dots or symbols to represent data on two variables. They can be used to answer different questions about data by analyzing the pattern of the data.

The scatter graph in the question can be used to determine whether a statement is true or false by identifying the dots that represent the data.

For more such questions on vertical axis

https://brainly.com/question/2279678

#SPJ8

Answer: 60 degrees

Step-by-step explanation:

The quadratic function is A(x) = 2(405 + 36x – x²). Then the maximum potential area of this year's resized garden will be 1458.

The condition for the maximum will be

f(x)'' < 0

The condition for the minimum will be

f(x)'' > 0

Every summer, Richard plants a garden on a rectangular plot of land.

Last summer, Richard's garden measured 45 feet in length and 18 feet in width.

This summer, Richard decides to resize his garden by decreasing the length of the garden, and increasing the width of the garden by two times the length reduction.

The area of this year's garden, A(x), can be modeled by a quadratic function, where x is the number of feet that the length is reduced.

Length = (45 – x)

Width = (18 + 2x)

Then the maximum potential area of this year's resized garden will be

A(x) = (45 – x)(18 + 2x)

A(x) = 810 + 72x – 2x²

A(x) = 2(405 + 36x – x²)

For maximum potential, A'(x) = 0

    A'(x) = 0

36 - 2x = 0

       2x = 36

         x = 18

Then the maximum potential area will be

A(x) = 2(405 + 36 × 18 – 18²)

A(x) = 1458

More about the maximum and minimum value of the function link is given below.

https://brainly.com/question/13581879

#SPJ1

The expression for Total discount for 20 group tickets is 5 m, Amount of discount per ticket is 0.25 m, Number of tickets is 20 and Cost of buying 20 single ticket is 20 m.

We have:

a discount of 25% per ticket if a group buys 20 or more tickets.

The expression 20 m - 20 (0.25 m) describes the total cost of buying 20 tickets for a group.

Total discount for 20 group tickets will be:

Total discount = 20 × 0.25 m = 5 m

Amount of discount per ticket = 5 m / 20 = 0.25 m

Number of tickets = 20

Cost of buying 20 single ticket = 20 m

where m = cost of buying 1 ticket.

Therefore, the expression for Total discount for 20 group tickets is 5 m, Amount of discount per ticket is 0.25 m, Number of tickets is 20 and Cost of buying 20 single ticket is 20 m.

Learn more about cost here:

https://brainly.com/question/2021001

#SPJ9