A copy machine makes 36 copies per minute. How many copies does it make in 5 minutes and 15 seconds? Clears your work. Undoes your last action.

Answer:

x = -11

Step-by-step explanation:

[tex]3x + 4(3 - \frac{1}{2} x) = 1[/tex]

[tex]3x + 12 - 2x = 1[/tex]

[tex]12 + x = 1[/tex]

[tex]x = - 11[/tex]

Answer:

Step-by-step explanation:

The quadratic function in vertex form is  f(x) = -(x + 5)^2 - 23

To find the quadratic function in standard form, we first need to determine the factors of the quadratic equation that corresponds to the given x-intercepts. Since the x-intercepts are at x = -12 and x = 2, we can write the quadratic equation in factored form as:

f(x) = a(x + 12)(x - 2)

where a is a constant that we need to determine.

To find the value of a, we can use the given minimum y-value of -49. Since the vertex of a quadratic function occurs at the axis of symmetry, which is the midpoint of the x-intercepts, we can find the x-coordinate of the vertex by taking the average of the x-intercepts:

x-coordinate of vertex = (-12 + 2)/2 = -5

Substituting this value of x into the factored form of the quadratic function, we get:

f(-5) = a(-5 + 12)(-5 - 2) = 49a

Since the minimum y-value is -49, we have:

f(-5) = 49a = -49

Solving for a, we get:

a = -1

Substituting this value of a into the factored form of the quadratic equation, we get:

f(x) = -(x + 12)(x - 2)

Expanding this equation, we get the quadratic function in standard form:

f(x) = -x^2 - 10x - 24

To find the quadratic function in vertex form, we can complete the square on the standard form of the equation:

f(x) = -x^2 - 10x - 24

f(x) = -(x^2 + 10x) - 24

f(x) = -(x^2 + 10x + 25) + 1 - 24

f(x) = -(x + 5)^2 - 23

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The measure of angle 4 is 45.6( nearest degree)

Two angles are complementary when the sum of the two angles is 90°. For example if x and y are complementary, then x+y = 90°.

Example of complementary angles are 50 and 40 , 30 and 60 , 25 and 65 e.t.c

Since angle 3 and angle 4 are complementary, therefore, 5x -15 + 3x+10 = 90

5x -15 + 3x+10 = 90

collect like terms

5x+3x -15 +10 = 90

8x -5 = 90

8x = 95

x = 95/8

x = 11.875

Therefore the measure of angle 4 is

3( 11.875) + 10

= 35.625 + 10

= 45.6 (nearest degree)

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The area of the original deck is 45 square feet and the area of the new deck is 28.8 square feet.

The area of the new deck is 64% of the area of the original deck.

What is a triangle?

A triangle is a three-sided polygon that is formed by connecting three non-collinear points in a plane. It is one of the basic shapes in geometry and is characterized by its three sides, three angles, and three vertices.

Part A:

The original deck has a base of 15 feet and a height of 6 feet. To create a 4:5 scaled version of the deck, we can multiply the base and height by the scale factor of 4/5:

New base = 15 * 4/5 = 12 feet

New height = 6 * 4/5 = 4.8 feet

Therefore, the dimensions of the new deck are 12 feet for the base and 4.8 feet for the height.

Part B:

The area of the original deck can be calculated using the formula for the area of a triangle:

Area of original deck = 1/2 * base * height = 1/2 * 15 * 6 = 45 square feet

The area of the new deck can be calculated in the same way, using the new dimensions:

Area of new deck = 1/2 * new base * new height = 1/2 * 12 * 4.8 = 28.8 square feet

Therefore, the area of the original deck is 45 square feet and the area of the new deck is 28.8 square feet.

Part C:

The ratio of the areas can be calculated by dividing the area of the new deck by the area of the original deck:

Area ratio = Area of new deck / Area of original deck = 28.8 / 45 = 0.64

The scale factor is 4/5, which is equal to 0.8. Therefore, we can compare the ratio of the areas to the scale factor to see if they are equivalent:

Area ratio / Scale factor = 0.64 / 0.8 = 0.8

Since the result is equal to the scale factor, we can conclude that the ratio of the areas and the scale factor are equivalent. This means that the area of the new deck is 64% of the area of the original deck.

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Answer: Problem 3:

The triangles are not similar. They have different angles.

Problem 4:

The triangles are similar by SSS~. A valid similarity statement is:

Triangle ABC ~ Triangle DEF.

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

23 - (-8)

23 + 8 = 31°

The temperature rose 31 degrees.

l-8 -23l = l-31l = 31  Absolute value is asking the distance from zero.

Helping in the name of Jesus.

Lauren assumed that the Roof Truss Diagram is an accurate representation of the actual roof design that will be used on the shed. She used the given measurements, such as the length of the bottom chord, and the angles in the diagram to calculate the pitch of the roof. If the diagram was not accurate, her calculations would not have been useful in determining the pitch of the actual roof. Therefore, Lauren had to make the assumption that the diagram was a reliable representation of the shed's roof design.

The logical assumption that Darin make about the Roof Truss Diagram is that the rise is 4.6 ft and the run is 9 feet.

A logical assumption is simply an idea that can be inferred, or identified, in a text without the writer stating it in an obvious way. One simple example may be the logical assumption that if you do not turn in your homework, your teacher will be disappointed in you.

Here, we have,

Based on the information provided, it appears that Darin assumed that the Roof Truss Diagram is symmetrical, meaning that both sides of the roof have the same dimensions and angles. This assumption is supported by his calculation that the pitch of both sides of the roof is close to 1/2.

Rise will be:

= 9 × tan 27°

= 9 × 0.5095

= 4.6 feet.

Run will be 9ft

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An equation for the line of best fit is y = 5x.

The y-intercept of the line of best fit is equal to (0, 0).

The size of a store which Feline Delights could expect to sell 20 bags per day is 4,000 square footage.

Feline Delights could expect to sell 20 bags per day in an 11,000 square foot store.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (45 - 30)/(9 - 6)

Slope (m) = 15/3

Slope (m) = 5

At data point (6, 30), a linear equation in slope-intercept form for this line can be calculated as follows:

y - y₁ = m(x - x₁)

y - 30 = 5(x - 6)

y = 5x - 30 + 30

y = 5x

When y = 20, the store size is given by;

20 = 5x

x = 20/5 = 4

In thousands, we have:

x = 4,000 square footage.

When x = 11,000 square footage, the number of bags is given by;

y = 5x

y = 5(11)

y = 55 bags.

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The domain of the given exponential function is also all real numbers. We can calculate it in the following manner.

The given exponential function is obtained by taking the negative of the original function f(x) = 2^(-x+1) and then subtracting 1 from it. Since the original function has a horizontal asymptote at y=0 and the given function has a horizontal asymptote at y=1, we need to flip the graph of the given function over the x-axis to obtain the graph of the original function.

The point (0, -6) on the given graph corresponds to the point (0, 5) on the graph of the original function, and the point (1, -3) on the given graph corresponds to the point (1, 2) on the graph of the original function.

The general form of an exponential function is f(x) = a^x, where "a" is a positive constant. In this case, we have f(x) = 2^(-x+1), so "a" is equal to 2^1 = 2.

Since "a" is positive, the domain of the function is all real numbers. Therefore, the domain of the given exponential function is also all real numbers.

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Answer:

A histogram would be the most appropriate graphical representation for the given data because it shows the distribution of the data and helps identify patterns or trends.

Answer:  I think the answer is bar chart, but it could also be Box plot

Step-by-step explanation:

All I know is that it is either one of those 2 options, it is NOT the others.

Value of angle C in the cyclic quadrilateral is 62°

A cyclic quadrilateral is a quadrilateral that can be circumscribed by a circle such that all four vertices of the quadrilateral lie on the circle.

Some properties of cyclic quadrilaterals include:

In the given diagram

∠B=3x°

∠D=x+20°

For cyclic quadrilateral opposite angle sum is 180°

∠B+∠D=180°

3x°+x°+20°=180°

4x+20=180°

x=160/4

x=40°

∠A+∠C=180°

C=180-2x+38

C=180-2*40-38

C=62°

Hence, Value of angle C in the cyclic quadrilateral is 62°

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The standard deviation of the normally distributed variable is given as follows:

s = 0.0434.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean this problem is given as follows:

[tex]\mu = p = 0.2[/tex]

Considering a sample size of 85, the standard deviation is given as follows:

s = sqrt(0.2 x 0.8/85)

s = 0.0434.

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The percent increase in the premium for Marcia's life insurance policy is approximately 17.06%.

To calculate the percent increase in the premium for Marcia's life insurance policy, we can use the following formula:

[tex]$Percent increase = \frac{ (New premium - Initial premium)}{ Initial premium} \times 100[/tex]

First, we need to find the initial premium, which can be calculated using the formula for the present value of a term life insurance policy:

[tex]Initial premium = \frac{Face amount of the policy}{Present value factor}= \frac{120,000}{4.3295} = $27,730.25[/tex]

Assuming the same face amount and an interest rate of 5%, the new premium can be calculated as follows:

[tex]New premium= \frac{\text{Face amount of the policy}}{\text{Present value factor}} \ &= \frac{120,000}{3.6962} \ &= $32,466.72 \end{aligned}[/tex]

Now we can use the formula above to calculate the percent increase in the premium:

[tex]Percent increase= \frac{(\text{New premium} - \text{Initial premium})}{\text{Initial premium}} * 100 \ &= \frac{(32,466.72 - 27,730.25)}{27,730.25} * 100 \ &= 17.06% \end{aligned}[/tex]

Therefore, the percent increase in the premium for Marcia's life insurance policy is approximately 17.06%.

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Warren Braxton paid $2,700.30 for his homeowner insurance policy.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

Formula for percentages: (Value/Total value) * 100

Given that, Warren Braxton purchased homeowner insurance for 70%.

Thus,

0.7 x $495,000 = $346,500.

Now, the premium is:

Premium = ($346,500 / 100) x $0.78 = $2,700.30

Hence, Warren Braxton paid $2,700.30 for his homeowner insurance policy.

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Corrected analysis of errors : Vertex: (-2, -8), x-intercepts: (-1,0) and (6,0), y-intercept: (0,-8), Axis of symmetry: x = -2

What are the errors?

There are multiple errors in the given analysis which are given below.

1. The x-coordinate of the vertex is incorrectly given as 1 instead of -2.

2. The y-coordinate of the vertex is incorrectly given as 8 instead of -8.

3. The x-coordinate of the axis of symmetry is incorrectly given as 1 instead of -2.

4. The given x-intercepts are incorrect. The correct x-intercepts are (-1,0) and (6,0).

5. The given y-intercept is incorrect. The correct y-intercept is (0,-8).

Corrected analysis:

Vertex: (-2, -8)

x-intercepts: (-1,0) and (6,0)

y-intercept: (0,-8)

Axis of symmetry: x = -2

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Answer: [tex]\frac{1}{3}[/tex] yds²

Step-by-step explanation:

    To find the area, we will multiply 2/3 by 2/4. When multiplying fractions, you multiply straight across.

[tex]\displaystyle \frac{2}{4} *\frac{2}{3} =\frac{2*2}{4*3} =\frac{4}{12} =\frac{1}{3}[/tex]

    We can also use the model, see attached.

Answer: 10

Step-by-step explanation: you look at x=1 and go over to x=3 and do rise over run

The standard deviation of all the average cholesterol levels we get will be close to 15 mg/dl.

The standard deviation of the average cholesterol levels will be given by the standard error of the mean, which is calculated as

standard error of the mean = standard deviation / sqrt(sample size)

In this case, the sample size is 4, so we have

standard error of the mean = 30 / sqrt(4) = 15

Therefore, if we take many samples of 4 fourteen-year-old boys and average their cholesterol levels, the standard deviation of all the average cholesterol levels we get will be close to 15 mg/dl.

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The Annual operating cost of the refrigerator = Energy consumed × Cost of electricity= 1324.74 kWh × $0.09 per kWh = $119.22 (approx.)Hence, the answer is $119.22 (approx.)

Given:Power consumed by the old refrigerator = 202 WAssuming the refrigerator operates for 18 hours every day.Cost of electricity is $0.09 per kWh.Solution:Power consumed by the old refrigerator in an hour = 202 WTime for which the refrigerator operates every day = 18 hours Energy consumed by the refrigerator in a day = Power consumed × Time = 202 W × 18 hours = 3636 Wh Energy consumed by the refrigerator in a year (365 days) = 3636 Wh × 365 days= 1324740 Wh = 1324.74 kWhCost of electricity is $0.09 per Therefore, Annual operating cost of the refrigerator = Energy consumed × Cost of electricity= 1324.74 kWh × $0.09 per kWh = $119.22 (approx.)Hence, the answer is $119.22 (approx.).

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The stem-and-leaf plot that correctly graphs the data set {15, 0, 26, 15, 20, 15, 34, 11, 20, 39, 31, 20, 23, 20, 39, 5} is given as follows:

0| 0 5

1| 1 5 5 5

2| 0 0 0 0 3 6

3| 1 4 9 9

Key 1|1 = 11

A stem and leaf plot is a type of data visualization that displays numerical data in a way that shows the distribution of the data while also preserving the individual data points. It is particularly useful for small to medium-sized data sets.

In a stem and leaf plot, the digits in each data point are split into two parts: the stem and the leaf. The stem is usually the leftmost digits of the number, while the leaf is the rightmost digit. The stems are listed in a column from top to bottom, and each leaf is listed next to its corresponding stem. The resulting plot looks like a table with two columns, where the first column shows the stems and the second column shows the leaves.

For example, as the team scored 20 points four times, we have the following observation:

2| 0 0 0 0

(one leaf of zero for each time, with the stem of 2).

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Answer: To show that △WZY ≅ △YXW, we need to show that they are congruent by proving that all corresponding sides and angles are equal.

Given:

WZ⊥ZY and WX⊥XY, which implies ∠WZY = ∠YXW = 90°

∠ZYW ≅ ∠XWY (given)

WX ≅ ZY and WZ ≅ XY (given)

To prove:

△WZY ≅ △YXW

Proof:

By the given information, ∠WZY = ∠YXW = 90°.

By the given information, ∠ZYW ≅ ∠XWY.

Therefore, ∠WZY + ∠ZYW ≅ ∠YXW + ∠XWY. Combining these angles gives us ∠WZY + ∠ZYW = ∠YXW + ∠XWY.

Since the sum of interior angles in a triangle is 180°, we have:

∠WZY + ∠ZYW + ∠YZW = 180° for △WZY

∠YXW + ∠XWY + ∠YWX = 180° for △YXW

Substituting in the angle congruence (∠ZYW ≅ ∠XWY), we have:

∠WZY + ∠XWY + ∠YZW = 180° for △WZY

∠YXW + ∠ZYW + ∠YWX = 180° for △YXW

By the given information, WX ≅ ZY and WZ ≅ XY.

Therefore, by the Side-Angle-Side (SAS) congruence postulate, △WZY ≅ △YXW.

Hence, we have proved that △WZY ≅ △YXW.

Step-by-step explanation:

Answer:

When the bases are the same, we can combine the exponents. Therefore, we can rewrite the equation as:

4^-2x * 4^x = 4^(-2x+x) = 4^(-x) = 64

To solve for x, we need to isolate x on one side of the equation. We can rewrite 64 as a power of 4:

4^3 = 4^(-x)

Now we can equate the exponents:

3 = -x

Therefore, x = -3.

To check the solution, we can substitute x = -3 back into the original equation:

4^-2(-3) * 4^(-3) = 4^6 * 4^(-3) = 4^3 = 64

So x = -3 is indeed a solution to the equation.

Answer:

g(x) = -5tan(x) - 3

Step-by-step explanation:

the parent tangent function would be g(x) = tan(x)

- reflection over the x-axis is going to make it negative

- horizontal stretch by a factor of 5 is going to multiply it by 5

- vertical shift down 3 units will subtract 3

so together, this would be the equation g(x) = -5tan(x) - 3.

The percent of chocolate chips in the mixture is a total of 30% as supreme cookie dough has 25% chocolate chips and Magic cookie dough has 35% chocolate chips.

Let one cup be equal to one gram,

therefore, one cup or gram of supreme cookie dough has 25% of chocolate cookie dough

25% of 4 cups = 25/100 x 400

= 100 gm of chocolate cookie dough

35% of chocolate cookie dough in one cup of Magic cookie dough

35% of 4 cups = 35/100 x 400

= 140 gm of chocolate cookie dough

therefore the dough Samantha has prepared has a total of 140 + 100 gm of chocolate cookie dough,

whereas total dough = 4 cups of magic cookie dough + 4 cups of supreme cookie dough = 8 cups

we assumed one cup will be 100 gm, therefore, 8 cups will be 800 gm

let the percentage of the chocolate cookie dough be x:

therefore, x/100 = 240/800

x = 240/800 x 100

x = 30

therefore, the percent of chocolate chips in the mixture is a total of 30%

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The second table is the one which represents a linear function.

In mathematics, the terms "linear function" refer to two distinct but connected concepts: In calculus and related subjects, a polynomial function of degree zero or one with a graph that is a straight line is referred to as a linear function.

⇒ The first table does not represent a linear function because for two different values of x, there is same value for y.

⇒ The second table represents the linear function as it forms a straight line on the graph.

⇒ The third table does not represent a linear function because it does not have a constant slope.

⇒ The last table does not represent a linear function because it does not have a constant slope.

Hence, the second table represents a linear function.

As x is constant as 1, then all the y inputs will be in a straight vertical line

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Question: Which of the following tables represents a linear function?

A. x | −4   −1    0    1    2

   y | −4    2   −4   0    2

B. x |   1      1     1    1   1

   y | −3   −2   −1   0   1

C. x |  −6       −1      0       2        3

    y |  −7     [tex]\frac{-16}{3}[/tex]    −5     [tex]\frac{-13}{3}[/tex]     −4

D. x | −2       −1      0    2    4

    y | −4      [tex]\frac{-2}{3}[/tex]     −1     [tex]\frac{2}{3}[/tex]     1

bearing in mind that the sum of all interior angles in a polygon is

180(n - 2)    n = number of sides in the polygon

a DECAgon, DECA=10, has 10 sides, and thus the sum of all its interior angles is 180(10 - 8) = 1440.

[tex]\bold{120+140+160+130+125+140+165+160+140+v=1440}[/tex]

[tex]\bold{1275+v=1440 \implies v=1440-1275 \implies v=165}[/tex]

By addressing the posed question, we can get the following conclusion: Volume equation of six tennis balls = 6 179.59 1077.54 cm

In mathematics, an equations is a promise that two expressions are equivalent. Two sides that are divided by the algebraic symbol (=) make up an equation. As an illustration, the claim "2x + 3 = 9" makes the statement "2x plus 3 equals the quantity "9." Finding the value or values of the variable(s) necessary for the equation to be true is indeed the goal of equation solving. Equations can include one or more parts and be simple or complex, regular or nonlinear. The formula "x2 + 2x - 3 = 0" raises the variable x to the second power. A line is utilized in many different areas of mathematics, such as algebra, calculus, and geometry. We can calculate the volume of the container and the volume of one tennis ball, and then check if the volume of six tennis balls is less than or equal to the volume of the container.

Volume of container = πr2h

Volume of container = π[tex](3.5)^2[/tex](40) ≈ 1540.48 cm

Volume of one tennis ball = 4/3 π[tex]r^3[/tex]

Volume of one tennis ball = 4/3 π[tex](3.5)^3[/tex] ≈ 179.59 cm

Volume of six tennis balls = 6 × volume of one tennis ball

Volume of six tennis balls = 6 × 179.59 ≈ 1077.54 cm

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As a result, the Frisbee's radius is 3 inches (rounded to the nearest hundredth) .

The distance from a circle's center to any point along its perimeter is known as the radius of a circle. It's typically indicated by "R" or "r" .

The distance around a circle's periphery is its circumference. It is the boundary across any two-dimensional circular surface measured linearly in one dimension.

C = 2πr, where C is the circumference and r is the radius, is the formula for calculating a circle's circumference.

This formula is rearranged to give us r = C /π 2 .

In this instance, we are aware that the Frisbee's circumference is 18.84 inches.

As a result, the radius can be determined using the formula r = C / 2π:

r = 18.84 / (2 * 3.14)

r = 18.84 / 6.28

r   = 3

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Answer: y=1/6x

Step-by-step explanation:

1. Identify the type of graph (linear)

2. the linear line equation is y=mx+b

3. find the slope, in this case, 1/6

a. to find the slope follow the equation (y1-y2)/(x1-x2)

b. plug in the x and y of two different points ex: (0,0) and (18,3)

4. plug into the equation the slope and a set of points - 3=18(1/6) +b

5. solve for b (0)

6. plug b and the slope into the original equation

7. y=1/6x

8. Done :)