9. Convert to fractions and write in simplest form.
A) 0.02
B) 12%
C) 0.5%
D) 1.12

Answer: To solve this equation, we need to get x on one side of the equation and all the other terms on the other side.

We can start by combining like terms:

three fourths times the quantity x plus 6 end quantity minus one fourth times x equals two fourths times the quantity x plus 9 end quantity

3/4 * x + 3/4 * 6 - 1/4 * x = 2/4 * x + 2/4 * 9

3/4 * x - 1/4 * x + 3/2 = 2/4 * x + 9/2

1/2 * x + 3/2 = x + 9/4

then we can move x to the left side of the equation:

x = x + 9/4 - 3/2

x = 9/4

So the value of x is 9/4.

The answer is A: x = 1.

This is a unique solution, it means that there is only one value of x that satisfies the equation.

Step-by-step explanation:

The optimal production of wind and solar that will maximize overall power output is 3 units/day of solar power and 2 units/day of wind power.

To solve this question, we use the following representations

So, the objective function is to maximize z = x + y, which represents the overall power output.

From the question, we have the following constraints:

Using the Lagrangian function, we have:

L(x,y,λ1,λ2,λ3) = x + y + λ1(6-x) + λ2(y-1) + λ3(2x-y-1)

To find the optimal solution, we need to find the values of x, y, λ1, λ2, and λ3 that will make the partial derivatives of L equal to zero:

∂L/∂x = 1 + λ3 = 0

∂L/∂y = 1 - λ1 + λ2 + λ3 = 0

Using the variables x and y, we have

∂L/∂λ1 = -x + 6 = 0

∂L/∂λ2 = y - 1 = 0

∂L/∂λ3 = 2x - y - 1 = 0

Using a graphing calculator, the points that maximize the objective function are:

x = 3 and y = 2

i.e.

Power output is 3 units/day of solar power and 2 units/day of wind power.

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When the pyramid is cut out of the prism, it has a volume of 36 cubic meters and the same base and height.

It is also known as the object's capacity. The fundamental equation for volume is length, width, and height, as opposed to the fundamental equation for the area of a rectangular shape, which is length, breadth, and height. The math is the same regardless of how you refer to the different dimensions. For example, you can substitute "depth" for "height." Volume is used to describe an object's capacity.  Volume can also be used to describe how much space a three-dimensional object occupies.

given

The ratio of their volumes is always one to three

Since the volume of a prism is 108 cubic meters,

a pyramid's volume is 1/3 * 108, or 36 cubic meters.

When the pyramid is cut out of the prism, it has a volume of 36 cubic meters and the same base and height.

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It is TRUE that the given image represents the function.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.

The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Initially, functions represented the idealized relationship between two changing quantities.

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

So, the given image represents a function and it is a kind of many-to-one function.

Therefore, it is TRUE that the given image represents the function.

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Answer: We want to know how many ways we can pay $1.10 with nickels and dimes. Since nickels are worth $0.05 and dimes are worth $0.10, we can use different combinations of these coins to make $1.10.

One way to approach this problem is to use the method of generating functions.

Let x be the number of nickels and y be the number of dimes. Then the generating function for this problem is (x+y) = (x+y)(x^0y^0 + x^1y^0 + x^0y^1 + x^2y^0 + x^1y^1 + x^0y^2...)

We know that the sum of x and y should be 11 because 0.05x + 0.1y = 1.10

The coefficient of x^5y^6 in the expansion of (x+y)^11 gives the number of ways to pay $1.10 with 5 nickels and 6 dimes.

The coefficient of x^5y^6 = 252

So there are 252 ways to pay $1.10 with nickel and dime.

Step-by-step explanation:

Answer:

1/4.

Step-by-step explanation:

1/4 is the answer because 25 x 4 = 100. Lets say you had 50/100. That would be equivalent to 2/4 , because 50 x 2 = 100.

25 is often reffered to as a quarter, but if someone says it is lets say a quarter past 5:00, they are trying to say is is 5:15, because 15 x 4 = 60, and 60 minutes is an hour.

The graph of the new trapezoid is attached

Transformation is the movement of a point in the coordinate plane. Types of transformation are rotation, dilation, reflection and translation.

Dilation is the increase or decrease in size of a figure by a scale factor. The rule for dilation is:

(x, y) ⇒ (kx, ky)

The vertices of the trapezoid is P(1, -2), Q(2, -2), R(2, 1) and S(-2, 1)

If the trapezoid is dilated by a scale factor of 4 about the origin, the new points are:

P'(4, -8), Q'(8, -8), R'(8, 4) and S'(-8, 4)

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The length of the longest side of ∆XYZ will be 40 cm. Then the correct option is A.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The sides of triangle ∆ABC have lengths of 3 cm, 8 cm, and 10 cm. If the smallest side of a similar triangle ∆XYZ has a length of 12 cm.

Let 'x' be the length of the longest side. Then the equation is given as,

x / 10 = 12 / 3

Simplify the equation, then we have

x / 10 = 12 / 3

x / 10 = 4

x = 40 cm

The length of the longest side of ∆XYZ will be 40 cm. Then the correct option is A.

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Answer:

8) AD = 23

9) m<B = 63

10) G(1,-5)

-------------------------------

8)

AD = BC

Thus, x + 21 = 12x - 1

11x = 22

x = 2

So, AD = 23

9)

consecutive angles are supplementary, sum to 180

y/2 + y - 9 = 180

3/2 y  = 189

y = 126

so, m<B = 63

10)

Diagonals bisect each other. The midpoint of DF = (-1.5, 0.5)

-1.5 = 2+x/2

x = 1

0.5 = 6+y/2
y = -5

G(1,-5)

From the table given a linear function that relates y to x  is y = -7.

What is point - slope form of line?

The equation of a straight line that passes through a given point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.

The point - slope form of line is y - y1 = m(x - x1).

From the given table of values we have to find the linear function that relates y to x.

First to find the slope.

Slope = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{-7-(-7)}{0-(-2)} = \frac{0}{2} = 0[/tex]

Now consider the point - slope form of line,

 y - y1 = m(x - x1).

y - (-7) = 0(x - 0)

 y + 7 = 0

       y = -7

Hence, from the table given a linear function that relates y to x  is y = -7.

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The likelihood that the first question will be true is Equally likely and unlikely. That is option C

Probability is defined as the possibility of an outcome of an event which may likely or unlikely occur.

The true and false quiz given by the teacher;

P(true) = 0.5 for each question.

Therefore, False = 0.5 for each question making the probability of the first question being true to be equally likely and unlikely.

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Our velocity is said to be 10% of the speed of light. Therefore, we need to multiply by 10% the speed of light. As a result, our speed is three times 10 to 7 m/s. Our diameter is 500 metres.

Thus, our radius is 250 metres. It goes through a volume of space equal to pi r squared times V times T in one second. We then multiply 5.8, 8 times 10 to the 12 m3 by pi times 2, 50 squared times three times 10, and seven times one second. Our density is 10 to 6 atoms per cubic metre, or one atom per cubic centimetre.

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Answer:

[tex]x^2+7x-9+\dfrac{12}{x-7}[/tex]

Step-by-step explanation:

The detailed explanation is in the attached image. It is a real pain to type this in the brainly equation editor so I just used LateX and printed out the result in case you are interested.

I may have made typos in the detailed explanation, if so, let me know

Answer:

Step-by-step explanation:

Lets simplify this step by step

5(2x+2)+3x+6

Distribute:

=(5)(2x)+(5)(2)+3x+6

=10x+10+3x+6

Combine Like Terms:

=10x+10+3x+6

=(10x+3x)+(10+6)

=13x+16

13x+16

If the height of a right triangular prism is 1 5/6 inches and each side of the triangular base measures 10 inches. The surface area of the solid formed is: 598.33 in².

First step is to convert fraction into simple fraction

Right triangular prism=1 5/6 inches= 11/6 inches

Height of the base=8 2/3 inches = 26/3 inches

Second step is to find the surface area

Surface area = 5(10× 10) + (0.5÷ 10 × 26/3) + 3(10× 11/6)

Surface area = 5(100) +43.33+ 3(18.33)

Surface area = 500+43.33 + 55

Surface area = 598.33 in²

Therefore the surface area of the solid formed is about 598.33 in²

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There is a 46.7% increase in the number of bracelets made.

A percentage is a number or ratio that can be expressed as a fraction of 100 (100 as denominator). To calculate percent of a number, divide the number by the whole and multiply by 100.

Hence, it means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Maysol made;

This month = 75 bracelets

Last month = 40 bracelets

Change = 75 - 40

Change = 35

This means there was an increase

% increase = (35/75) x 100

% increase = 46.7%

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The interpretation of the likelihood of randomly selecting a terrier from the dog shelter where terriers are 85% is A. Likely.

Probability refers to the chance or likelihood of an expected event occurring when there are many possible chances.

Probability is depicted as a fractional value lying between zero and one when it is not 100% uncertain or certain.

Thus, since the percentage of terriers in the dog shelter is 85%, it is 85% likely that one selects a terrier.

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Answer: A: Likely.

Step-by-step explanation:

Answer:

employee worked 8 hours over 35 hours, for a total of 35 + 8 = 43 hours.

Step-by-step explanation:

(35 hours x $15/hour) + (x hours x $22.50/hour) = $705 (where x is the number of hours worked over 35 hours)

You can then solve for x:

35x15 + x*22.50 = 705

525 + 22.5x = 705

22.5x = 180

x = 8

So the employee worked 8 hours over 35 hours, for a total of 35 + 8 = 43 hours.

The surface area of the triangular prism is 608 cm².

Given,

base of triangle = 12 cm

height of triangle = 8 cm

length of triangle = 10 + 10 + 12 = 32 cm

Width of the triangle = 16 cm

Area of the rectangle = l x b = 32 x 16 = 512 cm²

Area of triangle = 1/2 x 12 x 8 = 48 cm²

There are 2 triangle, so 48 + 48 = 96 cm²

Add all these values, 512 + 96 = 608 cm²

∴The surface area of triangular prism = 608 cm²

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The sum of the surfaces of the five faces of a triangular prism is its surface area.

Having two triangular bases and three rectangular sides, a triangular prism is a type of polyhedron. It is a three-dimensional object with two base faces and three side faces that are joined by edges.

There are 6 vertices, 5 edges, and 5 faces on it. The other 3 faces have a rectangle-like shape, while the 2 bases are structured like a triangle. Camping tents, chocolate candies, roofs, etc. are a few instances of triangular prisms in the real world.

A solid object called a prism has plane faces enclosing each of its four sides. Faces in a prism come in two different varieties. Bases are used to describe the top and bottom faces, which are identical.

12 cm is the triangle's base.

triangle's height is 8 cm.

Triangle's length is 32 cm (10 + 10 + 10 cm).

Triangle width is 16 cm.

The rectangle's area is 512 cm2 (l x b = 32 x 16).

Triangle area equals 1/2 x 12 x 8 = 48 cm2.

Two triangles are present, therefore 48 + 48 = 96 cm2.

512 + 96 = 608 cm2 after adding all these values.

The triangular prism's surface area is 608 cm2.

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The surface area of the cylinder is 791.28 sqft.

A three-dimensional object's surface area is the sum of all of its faces. Real-world applications of the concept of surface areas include wrapping, painting, and eventually building things to achieve the best possible design.

The formula for the volume of a hollow cylinder is V = (R2 -r2)h cubic units if "R" denotes the outer radius, "r" denotes the inner radius, and "h" denotes the height.

Given,

radius=9ft

height=5ft

[tex]SA=2\pi rh+2\pi r^2\\SA=2*3.14*8*5+2*3.14*5^2\\SA=791.26 sqft[/tex]

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To write [tex]\dfrac{11}{15}[/tex] as a decimal, you need to divide the numerator by the denominator.

The numerator of the fraction is 11.

The denominator of the fraction is 15.

[tex]11\div15[/tex]

[tex]=\fbox{0.73}[/tex]

The required number line attached below shows the absolute value of the fraction 5/13 is from 0.

Absolute value is defined as the magnitude or size of a number, no negatives are allowed. The distance a number is from 0 on the number line is known as the absolute value of the number.  

The fraction is given in the question, as follows:

-5/13

We have to determine the absolute value of the fraction.

As per the question, we can write the absolute value of the fraction as:

⇒ 5/13

Thus, the number line attached below displays the distance of the fraction from 0.

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The constant of variation for the given graph is 1/4.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Slope can also be defined as the tangent of the angle that the line is making with the positive X axis.

Given that the equation of the line in the graph is a direct variation equation.

Direct variation equations are of the form,

y = k x, where k is a constant number called constant of variation.

We have to find the value of k.

y = k x is an equation in slope intercept form where k is the slope and the value of y intercept is 0, since the line passes through origin (0, 0).

It is enough to find the slope of the given line.

Take two points from the graph, let it be (4, 1) and (-4, -1).

Slope = (-1 - 1) / (-4 - 4) = -2 / -8 = 1/4

The value of k is 1/4.

Hence the value of constant of variation is 1/4.

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Answer: 70

Step-by-step explanation: First, let's find how many are worth each in numbers. Use this formula:

Part Percent * Whole number / 100

Plug in the numbers:

Red = 12 * 250 / 100

3000/100

= 30 red marbles

Blue = 16* 250 / 100

4000 / 100

= 40 blue marbles

40 + 30 = 70

White = 250 - 70

= 180 white marbles

We can check our answer by adding 12 + 16. That's 28. So by multiplying 250 by 28, we get 7000. 7000 divided by 100 = 70

70 = 70

Therefore, both statements are true

I hope this helped!

In order to estimate the hourly rate of any given babysitter, Ms. Wong can make use of the mean of the sample, because it most closely describes the values of the data in the dataset

The sample mean is the average of the values in the data sample.

Possible part of the question, obtained from a similar question online includes the following table of values;

Babysitter  [tex]{}[/tex]   Rate in dollars per hour

1                         [tex]{}[/tex] 9.6

2                        [tex]{}[/tex] 9.80

3                        [tex]{}[/tex] 15.50

4                        [tex]{}[/tex] 10.6

5                       [tex]{}[/tex]  9.7

6                        [tex]{}[/tex] 10.20

7                        [tex]{}[/tex]  8.80

8                        [tex]{}[/tex]  11.20

9                        [tex]{}[/tex]  8.80

10                        [tex]{}[/tex] 10.10

The estimate of the hourly rate of any given babysitter can be found using the descriptive statistic, such as the mean, median, or mode, which are measures that indicate the possible mid value of a data set.

The mean is the average value of the dataset, which is obtained by adding the individual data points together and dividing the sum by the number of data points as follows;

9.6 + 9.8 + 15.5 + 10.6 + 9.7 + 10.2 + 8.8 + 11.2 + 8.8 + 10.1 = 104.3

The number of datapoints in the data = 10

The mean = 104.3/10 = 10.43

The median is the middle value which is found by arranging the values  in increasing order, then selecting the middle value as follows;

The median values in the dataset that has 10 data points is the average of the 5th and 6th values, which are; 9.8 and 10.1

The median of the dataset is therefore; (9.8 + 10.1)/2 = 9.95

The mode of the dataset is the most common value within the dataset. The mode is therefore 8.8

Based on the above three values, the best estimate that most closely describe the data in the dataset is the mean

Therefore, to estimate the hourly rate of any babysitter, Ms. Wong can make use of the mean, because it most closely describes the values in the dataset.

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-2.25,-2.5,2.75 I think

The order pair solution of the given system of equations is (-5, -6).

Here we will use the substitution method to solve the given equation. In this obtain value of one variable from one equation and substitute the value in another equation to get the value of variables.  

Here we have

3x - 5y = 15 ---- (1)

2x - y = - 4 ---- (2)  

=> y = 2x + 4 --- (3)

From (1) and (3)

=> 3x - 5(2x + 4) = 15

=> 3x - 10x - 20 = 15

=> -7x = 35

=> x = -5

Substitute x = - 5 in 2x - y = - 4  

=> 2(-5) - y = -4

=> -10 - y = -4

=> y = - 6

Therefore,

The order pair solution of the given system of equations is (-5, -6).    

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Answer:

the answer I got was 18 over 1657

Step-by-step explanation:

its a fraction so the numerator is 18 and the denominator is 1657

Answer:

you forgot the question

Step-by-step explanation: