Which expression represents the prime factorization of 192?
A. 2 x 2 x 2 x 2 x 12
B. 2 x 2 x 2 x 2 x 2 x 3
C. 3 x 2 x 2 x 2 x 2 x 2 x 2
D. 2 x 2 x 2 x 2 x 2 x 3 x 3

Answer:

4.15 or

Step-by-step explanation:

100/20=5 times 3 is 15

so its 4.15 which equals 4 3/20

The slope-intercept form of the equation of the line through (5, 0) and perpendicular to y = -5/3x is y = 3/5x - 3.

What is the slope-intercept form of a linear equation, and how can we determine the equation of a line perpendicular to another line?

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. This form is useful for graphing lines and solving problems involving linear relationships.

To determine the equation of a line perpendicular to another line, we use the fact that the slopes of perpendicular lines are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

Calculate the slope-intercept form:

We are given that the line we are looking for passes through the point (5, 0) and is perpendicular to the line y = -5/3x. To find the equation of the line, we need to determine its slope and y-intercept.

The slope of the given line is -5/3, so the slope of the line perpendicular to it is:

-1/(-5/3) = 3/5

Therefore, the slope of the line we are looking for is 3/5.

Next, we can use the point-slope form of the equation of a line to find the equation of the line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line. We can substitute m = 3/5 and (x1, y1) = (5, 0) to get:

y - 0 = 3/5(x - 5)

Simplifying this equation, we get:

y = 3/5x - 3

which is the slope-intercept form of the equation of the line we were looking for.

Therefore, the slope-intercept form of the equation of the line through (5, 0) and perpendicular to y = -5/3x is y = 3/5x - 3.

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The coordinates of each point after the quadrilateral RSTU is rotated 90 degrees about the origin are R' (2, 1), S' (4, 2), T' = (5, 4), and U' = (3, 3).

In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices of triangle RSTU, the coordinates of the vertices of the image are as follows:

(x, y)                               →            (-y, x)

Ordered pair R  = (1, -2) → Ordered pair R' = (-(-2), 1) = (2, 1).

Ordered pair S  = (2, -4) → Ordered pair S' = (-(-4), 2) = (4, 2).

Ordered pair T  = (4, -5) → Ordered pair T' = (-(-5), 4) = (5, 4).

Ordered pair U  = (3, -3) → Ordered pair U' = (-(-3), 3) = (3, 3).

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[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=17 \end{cases}\implies C=2\pi (17)\implies C=34\pi[/tex]

Answer:

The formula to calculate the minimum sample size required to estimate the population mean is given as:

n = (z^2 * σ^2) / E^2

Where,

z = the z-value for the given confidence level, which is 1.96 for c = 0.95

σ = the population standard deviation

E = the maximum error of estimate, also known as the margin of error

Plugging in the values, we get:

n = (1.96^2 * 9.1^2) / 1^2

n = 301.63

Rounding up to the nearest whole number, the minimum sample size required is 302.

Therefore, a sample size of at least 302 is needed to estimate the population mean with a 95% confidence level, assuming a population standard deviation of 9.1 and a maximum error of estimate of 1.

Step-by-step explanation:

The area of the trapezoidal flower garden from the dimensions is 123.5 square meters

The trapezoidal flower garden represents the given parameter, where we have the following readings

Parallel sides = 9 m and 10 m

Height = 13 m

Using the above dimensions, we have the area to be

Area = 1/2 * Sum of parallel sides * Height

When the dimensions are substituted, we have

Area = 1/2 * (9 + 10) * 13

Evaluate the products

Area = 123.5

HEnce, the area is 123.5 square meters

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To show how c and b are related, we can draw a line through these points. A positive sloped straight line should appear on the graph.

Identifying the slope and y-intercept is necessary before putting the equation in y-intercept (y=mx+b) form and figuring out the equation of a graphed line. The slope is the y-to-x change ratio.

Plotting points on the coordinate plane with values for b and calculating the appropriate values for c is necessary to graph the equation c = 2b + 6.

Let's pick some b values and determine the matching c values:

c = 2(0) + 6 = 6 when b = 0.

If b = 1, then c = 2(1) + 6 = 8.

c = 2(2) + 6 = 10 when b = 2

These points can be used to plot the graph:

Set the scene (0, 6)

Set the scene (1, 8)

Set the scene (2, 10)

Now we may illustrate the relationship between c and b by drawing a line across these locations. A positive sloped straight line should appear on the graph.

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The number of terms in the expression is 2

From the question, we have the following:

20 - (4 to the second power divided by 2)

Express properly

so, we have the following representation

20 - (4^2/2)

A term is a mathematical expression that can be added or subtracted to form a larger expression.

For example, in the expression 3x + 2y - 5, each of the three parts (3x, 2y, and -5) is a term.

Using the above definition, we have the terms to be

20 and (4^2/2) i.e. 2 terms

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The two measures of these data that best describe the typical number of minutes Addison spent reading each day are mean and median.

Mean is the average value of a set of numbers, found by adding up all the numbers and dividing by the total count of numbers. Median is the middle value in a set of numbers when they are listed in order.

To find the mean of the data set, we add up all the values and divide by the total count:

(90 + 60 + 89 + 94 + 60 + 93) / 6 = 85.33

To find the median of the data set, we first put the values in order:

60, 60, 89, 90, 93, 94

Since there are an even number of values, we take the average of the two middle values:

(89 + 90) / 2 = 89.5

Therefore, the mean is 85.33 minutes and the median is 89.5 minutes, which are the two measures that best describe the typical number of minutes Addison spent reading each day.

Answer:

5a + 3b = 13

7a + 6b = 20

And solve for the values of "a" and "b" using algebraic methods like substitution or elimination.

Step-by-step explanation:

Solving for a and b in the system of equations:

5a + 3b = 13

7a + 6b = 20

We can multiply the first equation by 2 to get:

10a + 6b = 26

Then, we can subtract the second equation from this to eliminate b:

(10a + 6b) - (7a + 6b) = 26 - 20

3a = 6

Solving for a, we get:

a = 2

Substituting this value into the first equation, we can solve for b:

5a + 3b = 13

5(2) + 3b = 13

10 + 3b = 13

3b = 3

b = 1

Therefore, the solution to the system of equations is:

a = 2

b = 1.

Answer:

y = -3 sin(4x)

or

y = -3 cos(4(x - π/8))

Step-by-step explanation:

We can see that this is a graph of sine or cosine with the following characteristics:

amplitude: 3

period: π/2

vertical shift: 0

We can use these characteristics to form the following equations:

y = -3 sin(4x)

y = -3 cos(4(x - π/8))

Note that we solved for b using the period derivation:

period = 2π / b

[tex]\dfrac{\pi}{2} = \dfrac{2\pi}{b}[/tex]

[tex]b \cdot \dfrac{\pi}{2} = 2\pi}[/tex]

[tex]b = 2\pi \cdot \dfrac{2}{\pi}[/tex]

[tex]b = \dfrac{4\pi}{\pi}[/tex]

[tex]b = 4[/tex]

— sidenote —

These graphs can be infinitely shifted by any integer number of periods left or right, and we can show that using an auxiliary variable multiplied by the period. However, that is clearly not the intent of the problem, so I have not included that in my answer.

The model of the exponential function is y = 3.40(1.86)^x

From the question, we have the following parameters that can be used in our computation:

(6, 140) and (7, 260)

The exponential function for the model can be expressed as:

y = ab^x

Where

b = 260/140

b = 1.86

So, we have

y = a(1.86)^x

Substitute the known values in the above equation, so, we have the following representation

140 = a(1.86)^6

This gives

a = 140/(1.86)^6

Evaluate

a = 3.40

This means that

y = 3.40(1.86)^x

Hence, the function is y = 3.40(1.86)^x

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y = 5(10)ˣ is the equation for the  exponential function

The general form of the exponential function is y = abˣ

From the table, when x = 0, y = 5. Substitute the values into the function:

y = abˣ

5 = ab⁰             (Note: b⁰ = 1)

5 = a(1)

5= a

a = 5

Also, from the table, when x = 1, y = 50. Substitute the values into the function:

y = abˣ

50 = 5 × b¹

50 = 5b

5b = 50

b = 50/5 = 10

We can now write the equation for the exponential function:

y = abˣ

y = 5(10)ˣ

Therefore, the equation for the exponential function is y = 5(10)ˣ

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hi

im pretty sure the answer is

a. numerators

hope this helps

good luck;)

Answer:

A

Step-by-step explanation:

You have to add the numerator and keep the denominators the same! :)

The mathematical expression for 21 fewer stars than three times a number h is : 3h - 21

A mathematical expression is the collection of mathematical symbols that results from the proper combination of numbers and variables using operations like addition, subtract, multiplication, division, exponents, and other as-yet-unlearned operations and functions.

The given statement is-

21 fewer stars than three times a number h

so,

mathematical expression is:

3h - 21

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The ball with the greater maximum height is the second ball

From the question, we have the following parameters that can be used in our computation:

f(t) - 4t^2 + 16t

g(t) = -16t^2 + 64t + 192

Differentiate and set them to 0

-8t + 16 = 0

-32t + 64 = 0

Solve for t

t = 2 in both cases

So, we have

f(2) = -4(2)^2 + 16(2) = 16

g(2) = -16(2)^2 + 64(2) + 192 = 256

Hence, the ball with the greater maximum height is the second ball

To do this, we set the function to 0 and calculate t

So, we have

f(t) = -4t^2 + 16t = 0

g(t) = -16t^2 + 64t + 192 = 0

Using a graphing tool, we have

t = 4

t = 6

This means that the first ball landed first

To change the term, we set the constant term in g(t) = -16t^2 + 64t + 192 to a negative number > -192

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The diagonal length of his current TV is 65 inches.

Pythagoras theorem states that for a right-angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude. It can be used to find the diagonal of a rectangle if we know the length and the width.

As per the given data:

Length of the TV (l) = 56 inches

Width of the TV (b) = 33 inches

To find the diagonal length (d) of the TV:

From Pythagoras theorem:

[tex]d = \sqrt{l^2 +b^2}\\d = \sqrt{(56)^2 +(33)^2}\\d = \sqrt{3136 +1089}\\d = \sqrt{4225}\\d = 65 inches[/tex]

Hence, the diagonal length of his current TV is 65 inches.

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Answer: because we need it for life

Step-by-step explanation: we do math because when we go to pay something we need money and they say this much money or when you cook it said 3/4 and you don’t know what is 3/4 is also on tests.

Answer:

See below.

Step-by-step explanation:

We are asked to simplify the expression provided.

An easy way to simplify this expression is by Combining Like Terms.

Combining Like Terms means adding terms that are similar, whether that's natural numbers, or variables.

For example, 8x + 9x are like terms since they both have the same variables. There's no exponents or any other variables that make these terms different from each other.

Using what we've learned, let's combine like terms for our problem now.

Combine Like Terms:

[tex]7h+6.3d-15+4d-3.4h[/tex]

[tex]7h - 3.4h = 3.6h[/tex]

[tex]6.3d + 4d = 10.3d[/tex]

-15 has no like terms.

We should have;

[tex]10.3d-15+3.6h[/tex]

This will be our final answer. There's no more like terms to combine and we can't simplify this expression further.

Answer:

8.407

Step-by-step explanation:

8.767−0.36

= 8.767−0.36

=8.767+(−0.36)

= 8.407

Therefore, at least 49 street lights can be installed along one side of the street with equal distance between the lights.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

The distance between point A and B is AB, and the distance between point B and C is BC. Let's assume that the distance between each street light is "d".

Since there must be a street light at points A, B, and C, there will be a total of two gaps between these three street lights, which are AB and BC. Thus, the number of street lights required is equal to the sum of the lengths of AB and BC, divided by the distance "d" between the street lights, plus 1 for the street light at point B.

So, the total number of street lights required is

Number of street lights = (AB + BC) / d + 1

We know that AB = 1170 m and BC = 1625 m, and the distance between each street light should be equal. Therefore, we need to find the greatest common factor (GCF) of 1170 and 1625 to determine the distance between each street light.

1170 = 2 x 3 x 3 x 5 x 13

1625 = 5 x 5 x 13

The GCF of 1170 and 1625 is 65, which means the distance between each street light should be 65 meters.

Now we can calculate the total number of street lights required:

Number of street lights = (1170 + 1625) / 65 + 1

= 49

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Answer:

Step-by-step explanation:

The answer to this question is as follows The formula for the letter C is: equation  $1.25C = $72.50

A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two sentences that are written on opposite sides of a letter. Frequently, the logo and the particular software are identical. like in 2x - 4 = 2, for example.

Let C represent the volume of vehicles that passed through the booth.

As $1.25 is the amount collected per vehicle, the following equation represents the total amount collected:

Total = $1.25 plus C

Also, we are aware that $72.50 was collected in one hour, allowing us to create another equation:

$72.50 = $1.25 × C

We may divide both sides by $1.25 to find C:

C = $72.50 ÷ $1.25

C = 58

58 vehicles passed through the booth as a result.

The formula for the letter C is:

$1.25C = $72.50

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Answer:

alot

Step-by-step explanation:

Answer:

One solution, x = -10

Step-by-step explanation:

16 (3x − 6) = 18 (4x + 8)

48x - 96 = 72x + 144

-24x = 240

x = - 10

The better deal is 12 donuts for $10 because the unit rate is $0.83.

Generally speaking, a unit price can be defined as the price that is being charged by a seller for the sale of a single unit of product.

In order to determine the unit price, we would determine the unit price for number of donuts by using the following mathematical expression;

Unit price = Cost of donuts/Number of donuts

Substituting the given parameters into the unit price formula, we have the following;

Unit price = $10/12

Unit price = $0.83.

For the second deal, we have:

Unit price = $6/6.99

Unit price = $0.86.

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Answer:

Step-by-step explanation:

We need to find the least common multiple (LCM) of 3 and 4, which will give us the number of days after which both Julio and Larry will wear a blue shirt on the same day again.

The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...

The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, ...

We can see that the least common multiple of 3 and 4 is 12, because it is the smallest number that appears in both lists.

This means that Julio and Larry will wear a blue shirt on the same day every 12 days.

Since they both wore blue shirts on April 12, the next date that they will both wear a blue shirt is 12 days later, on April 24.

Answer:

To find the next date that they will both wear a blue shirt, we need to find the least common multiple (LCM) of 3 and 4, which is 12.

So, Julio will wear a blue shirt on April 12, 15, 18, 21, and so on.

Larry will wear a blue shirt on April 12, 16, 20, 24, and so on.

The next date they will both wear a blue shirt is when their dates coincide, which is April 24.

Therefore, Julio and Larry will both wear a blue shirt again on April 24.

Step-by-step explanation:

The area of the figure is equal to:

A = 28[tex]unit[/tex]² + 7[tex]unit[/tex]² + 7[tex]unit[/tex]² =42[tex]unit[/tex]²

You could also draw the shape on a grid and count the squares there: The rectangle has a 15 surface area. For instance, if the space is 15 m2 and each square is one meter in size (15 square meters).

Answer:

42[tex]units[/tex]²

Step-by-step explanation:

we know that

The area of the figure is equal to the area of a rectangle plus the area of two triangles

Find the area of rectangle

Observing the graph

The area of rectangle is equal to

A= bh = (2+5)(2+2)= 28[tex]unit[/tex]²

Find the area of the top triangle

A = 1/2bh = 1/2(2+5)(2+2) = 7[tex]unit[/tex]²

Find the area of the bottom triangle

A = 1/2bh = 1/2(2+5)(2+2) = 7[tex]unit[/tex]²

the area of the figure is equal to

A = 28[tex]unit[/tex]² + 7[tex]unit[/tex]² + 7[tex]unit[/tex]² =42[tex]unit[/tex]²

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Tge coordinates of point c is - 3 and 1

Answer: The fourth vertex is D(8, 0)

The inverse of the given functions are f⁻¹(x) = 3/4(x + 7) and f⁻¹(x) = x^2 + 10x + 25

The inverse of a function is a new function that undoes the effects of the original function.

In other words, if we have a function f(x) that maps x to y, then the inverse of f(x), denoted by f^-1(y), maps y back to x.

Given that:

f(x) = 4/3x - 7

Write as an equation

y = 4/3x - 7

Interchange the variables

x = 4/3y - 7

Solve for y

y = 3/4(x + 7)

Replace y with f⁻¹(x) to show the final answer.

f⁻¹(x) = 3/4(x + 7)

Also, the inverse of the function f(x) = √x -5 is computed as follows:

Interchange the variables and solve for y;

x = √y -5

y = x^2 + 10x +25

Replace y with f⁻¹(x) to show the final answer.

f⁻¹(x) = x^2 + 10x + 25

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