In artwork consists of the triangle shown with the shaded triangle is cut out of the larger triangle. What is the area of the remaining unshaded portion?

Answer:

6.02

Step-by-step explanation:

sin 37=x/10

x/10=sin 37

x=10(sin 37)

x=6.02

According to the information, the number of people who likes folk song is 90, and the number of people who likes modern song 80. So, the total number of people in the survey is 250.

Let the number of people who like modern songs be 8x, and the number of people who like folk songs be 9x.

From the given information, we know that:

50 people like both modern and folk songs

40 people like only folk songs

The total number of people who like at least one type of song is (8 + 9)x - 50 = 17x - 50

80 people like none of the songs

Therefore, we can write the following equation:

(8x + 9x) - 50 - 40 + 80 = 17x

Simplifying this equation, we get:

17x - 10 = 17x

Thus, x = 10.

So, the number of people who like folk songs is 9x = 9(10) = 90.

Similarly, the number of people who like modern songs is 8x = 8(10) = 80.

The total number of people in the survey is the sum of the number of people who like modern songs, the number of people who like folk songs, and the number of people who like none of the songs.

So, the total number of people in the survey is:

80 + 90 + 80 = 250.

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The current outdoor temperature is 37.89°C, which is less than the highest temperature limit, i.e., 47.8°.

Both Celsius and Fahrenheit have different zero points and the temperature increments also vary quite differently. 100 degrees separate freezing and boiling on the Celsius scale, but for Fahrenheit the difference is 180 degrees. This means Celsius is 1.8 times larger than Fahrenheit.

To determine whether the medication has been exposed to temperatures higher than 47.8°C, we need to convert the outdoor temperature from Fahrenheit to Celsius. The conversion formula is:

°C = (°F - 32) x 5/9

Using this formula, we can get the temperature in Celsius form,

°C = (100.2 - 32) x 5/9

   = 37.89°C

Since the outdoor temperature is lower than the maximum temperature the medication can be exposed to, it is safe to assume that the medication has not been exposed to temperatures higher than 47.8°C.

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(a) The linear density (mass/length) rho has SI units of kg/m. Since rho = a + bx, the SI units of a must be kg/m and the SI units of b must be kg/m^2.
(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod:
m = ∫₀ᴸ ρ(x) dx
Substituting in ρ(x) = a + bx:
m = ∫₀ᴸ (a + bx) dx
m = [ax + (1/2)bx²] from 0 to L
m = aL + (1/2)bL²
Therefore, the mass of the rod in terms of a, b, and L is m = aL + (1/2)bL².

(a) In this problem, rho (ρ) represents linear density, which has units of mass per length. In SI units, mass is measured in kilograms (kg) and length in meters (m). Therefore, the units of linear density are kg/m. Since ρ = a + bx, the units of a and b must be consistent with this equation. The units of a are the same as those of ρ, so a has units of kg/m. For b, since it is multiplied by x (which has units of meters), b must have units of kg/m² to maintain consistency in the equation.

(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod (from x=0 to x=L). Let's set up the integral:

Mass (M) = ∫(a + bx) dx, with limits from 0 to L

Now, we can integrate:

M = [a * x + (b/2) * x²] evaluated from 0 to L

Substitute the limits:

M = a * L + (b/2) * L²

So, the mass of the rod in terms of a, b, and L is:

M = aL + (bL²)/2

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Answer:

I dont know the answer to be honest..

JUST KIDDING.. ill answer this step by step lol

To solve the inequality 9/x + 81 > 45, we can follow these steps:

Step 1: Subtract 81 from both sides of the inequality to isolate the fraction on the left-hand side:

9/x + 81 - 81 > 45 - 81

9/x > -36

Step 2: Take the reciprocal of both sides of the inequality to eliminate the fraction:

1 / (9/x) < 1 / (-36)

x/9 < -1/36

Step 3: Multiply both sides of the inequality by 9 to get rid of the fraction in the numerator:

9 * (x/9) < 9 * (-1/36)

x < -1/4

So, the solution to the inequality 9/x + 81 > 45 is x < -1/4. This means that x must be less than -1/4 for the inequality to be true.

(b) The volume of the medium box is 5832 cubic inches.

In mathematics, a ratio is a comparison of two quantities or numbers. It is expressed as the quotient of one number divided by another, and is often written as "a:b" or "a/b". Ratios are used to compare the sizes of two or more quantities, and they can be used to solve problems involving proportions and percentages.

For example, if a recipe calls for a ratio of 2 cups of flour to 1 cup of sugar, this means that for every 2 cups of flour used, 1 cup of sugar should be used as well. Similarly, if a company has a debt-to-equity ratio of 2:1, this means that for every $2 of debt, the company has $1 of equity.

(a) Let x be the length of the sides of the original box. Then the volume of the box is x^3 = 216, so x = 6.

When the length, width, and height are all tripled, the new side length of the medium box is 3x = 18.

The ratio of the sides of the medium box to the original box is 18:6, or simplified, 3:1.

The area of the base of the original box is. [tex]x^2 = 6^2 = 36[/tex]square inches.

The area of the base of the medium box is. [tex](3x)^2 = 18^2 = 324[/tex] square inches.

The ratio of the 5832 of the bases of the medium box to the original box is 324:36, or simplified, 9:1.

The volume of the medium box is. [tex](3x)^3 = 18^3 = 5832[/tex]cubic inches.

The ratio of the volumes of the medium box to the original box is 5832:216, or simplified, 27:1.

(b) The volume of the medium box is 5832 cubic inches.

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Answer: The function that is an exponential function that is decreasing is described as:

an exponential function that is decreasing.

A quadratic function that is increasing then decreasing would have a U-shaped graph, and a quadratic function that is decreasing then increasing would have an inverted U-shaped graph. However, neither of these options describes an exponential function that is decreasing.

Therefore, the correct choice is: an exponential function that is decreasing.

Step-by-step explanation:

In table 9.1, the marginal cost of producing the seventh unit of output is equal to $8.
Marginal cost refers to the additional cost incurred when producing one more unit of output. To find the marginal cost of producing the seventh unit of output, follow these steps:

1. Locate the total cost column in table 9.1.
2. Identify the total cost of producing 6 units of output.
3. Identify the total cost of producing 7 units of output.
4. Subtract the total cost of producing 6 units from the total cost of producing 7 units.

The difference you get from step 4 is the marginal cost of producing the seventh unit of output.

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Therefore , the solution of the given problem of coordinates comes out to be  (1, -4) are the coordinates of the vertex of the function  F(x) = x² - 2x - 3.

When used in connection with particular other algebraic components on this place, such as Euclidean space, a parameter can reliably detect placement using a number of qualities or coordinates. Coordinates, which appear as collections of numbers when traversing in reflected space, can be utilised to identify particular places or things. Using the two y & x measurements, one can find something over both sides.

Here,

The formula x = -b/2a can be used to determine the vertex of a quadratic function with the form

F(x) = ax² + bx + c. A and B are equal in the given function

=>  F(x) = x² - 2x - 3.

With these values entered into the formula, we obtain:

=> x = -b/2a x = -(-2)/(2*1)

=> x = 2/2 x = 1

Consequently, the vertex's x-coordinate is 1.

Now, we can enter the value of x into the following function, F(x), to determine the vertex's y-coordinate:

=> F(1) = 1² - 2(1) - 3

=> F(1) = 1 - 2 - 3

=> F(1) = -4

Therefore, the vertex's y-coordinate is -4.

As a result, (1, -4) are the coordinates of the vertex of the function

=> F(x) = x² - 2x - 3.

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Probability about at least one customer arrives at the shop while a one-minute interval is almost 0.632 or 63.2%.

The probability that at least one customer arrives at the shop during a one-minute interval can be calculated using the Poisson distribution, which is commonly used to model the arrival of events over a given time period.

Let's assume that the average number of customers arriving at the shop per minute is [tex]l[/tex]. Poisson probability mass function is;

[tex]P(X = k) = (e^{-l} * l^k) / k![/tex]

where X is the random variable representing the number of customers arriving in a one-minute interval, and k is the number of customers that arrive.

To find the probability of at least one customer arriving, we need to calculate the probability of X being greater than or equal to 1. That is,

[tex]P(X > = 1) = 1 - P(X = 0)[/tex]

When [tex]l[/tex] is relatively small, we can use approximation:

[tex]P(X = 0) = e^{-l[/tex]

Therefore,

[tex]P(X > = 1) = 1 - P(X = 0)[/tex]

[tex]≈ 1 - e^{-l[/tex]

We don't have the value of [tex]l[/tex], but assuming an average arrival rate of 1 customer per minute (i.e., [tex]l[/tex] = 1), we get:

[tex]P(X > = 1) = 1 - e^{-1[/tex]

≈ 0.632

Therefore, the probability about  at least one customer arrives at the shop while a one-minute interval is almost 0.632 or 63.2%.

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Therefore, the range is 172 points and the interquartile range is 42 points. Therefore, the range without the outlier is 140 points and the interquartile range without the outlier is 40 points.

In statistics, the range is the difference between the largest and smallest values in a dataset. It is a measure of dispersion that indicates the spread of the data. The range provides a quick and simple way to get an idea of the variability of the data, but it can be affected by outliers and is therefore not always a reliable measure of dispersion. To calculate the range, you simply subtract the smallest value from the largest value in the dataset.

Here,

a. To find the range, we subtract the smallest value from the largest value:

Range = 193 - 21 = 172

To find the interquartile range, we first need to find the first and third quartiles.

Arrange the data in order from smallest to largest:

21, 53, 74, 82, 84, 103, 108, 116, 122, 193

Find the median (middle value) of the lower half of the data (Q1):

Q1 = median(21, 53, 74, 82, 84) = 74

Find the median (middle value) of the upper half of the data (Q3):

Q3 = median(103, 108, 116, 122, 193) = 116

Subtract Q1 from Q3 to get the interquartile range:

IQR = Q3 - Q1 = 116 - 74 = 42

b. To identify the outlier(s), we can use the rule that any value less than Q1 - 1.5 x IQR or greater than Q3 + 1.5 x IQR is considered an outlier.

Q1 - 1.5 x IQR = 74 - 1.5 x 42 = 11

Q3 + 1.5 x IQR = 116 + 1.5 x 42 = 181

The value 21 is less than the lower bound of 11, so it is an outlier.

To find the range and interquartile range without the outlier, we need to remove it from the data set:

74 82 84 122 193 53 103 108 116

The range without the outlier is:

193 - 53 = 140

To find the interquartile range without the outlier, we need to find the first and third quartiles of the new data set:

Q1 = median(53, 74, 82, 84, 108) = 82

Q3 = median(116, 122, 193) = 122

IQR = Q3 - Q1 = 122 - 82 = 40

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Answer:

it A or B

Step-by-step explanation:

the other two C and D dont make sense to what the question is asking

We get a probability of 3/8 or 0.375.

To find the probability of two successes (i.e., drawing two red balls) out of three draws from an urn containing 14 balls (7 of which are red), we can use the binomial probability formula:

[tex]P(X = 2) = (n\ choose\ x) * p^x * (1-p)^{(n-x)[/tex]

where

n is the total number of draws (3 in this case),

x is the number of successes (2 in this case),

p is the probability of a success on any given draw (7/14 or 1/2 in this case),

and (n choose x) is the number of ways to choose x items out of n items.

Plugging in the values, we get:

[tex]P(X = 2) = (3\ choose\ 2) * (1/2)^2 * (1/2)^{(3-2)} = 3/8[/tex]

Therefore, the probability of getting two red balls out of three draws is 3/8 or 0.375.

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For quadrilateral ABCD x=85 and angle B= 23°.

A quadrilateral is a polygon with four sides and four angles. It is a closed figure and can have different shapes and sizes, depending on the length of its sides and the angles between them.

(a) Supplementary equation used to solve for x:

∠A + ∠C = 180°

(b) All math used to calculate for x:

∠A + ∠C = 180°

(x - 5) + (x + 15) = 180 (substitute the given values for ∠A, ∠C)

2x - 10 = 180

2x = 170

x = 85

(c) Correct value for x:

x = 85

(d) Plugging x into expressions for angles A, C, D:

∠A = x - 5 = 2(85) - 5 = 165

∠C = x + 15 = 85 + 15 = 100

∠D = x - 13 = 85 - 13 = 72

(e) All math used to calculate the measures of angles A, C, D:

∠A + ∠B + ∠C + ∠D = 360° (sum of angles in a quadrilateral)

165 + ∠B + 100 + 72 = 360

∠B = 23

Therefore, the measures of the angles are:

∠A = 165°

∠B = 23°

∠C = 100°

∠D = 72°

(f) All math used to calculate the measure of angle B:

∠B = 360 - ∠A - ∠C - ∠D

∠B = 360 - 165 - 100 - 72

∠B = 23°

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The minimum value,  or lowest value, of the data set is the same value as the leftmost point of the box and whisker plot.

We know that a box-and-whisker plot is nothing but a graph summarising a set of data. This plot shows how the data is distributed. It also shows any outliers.

In box-and-whisker plot, the median is in the middle of the box. The minimum value in the dataset is displayed at the far left end of the plot. The first quartile (Q1 or the 25th percentile) is in between the minimum value and median. The third quartile (Q3 i..e, the 75th percentile) at the right side, between the median and the maximum value. Latsly the maximum value in the dataset is displayed at the far right end of the plot.

Therefore, the minimum value is the same value as the leftmost point of the plot.

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The complete question is:

Holly and Brian’s social studies teacher gives them quizzes worth up to 20 points. Holly received the following scores: 5, 11, 17, 18, and 20. Brian’s scores were 16, 16, 17, 19, and 19

The box-and-whisker plot is shown below. The minimum, or lowest value, of the data set is 2. Move the leftmost blue dot back and forth. How does this relate to the position of the leftmost point of the box-and-whisker plot?

d) there must be at least 30 trials.

The correct answer is: Fast Chicken, because it has a smaller median.

What is median?

Median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude. To find the median, you need to arrange the values in order from smallest to largest and then find the middle value.

Based on the information provided, the drive-thru restaurant with less wait time is Fast Chicken, as it has a smaller median wait time of 12.5 minutes compared to the median wait time of 12 minutes for Super Fast Food. The mean wait time is not given, and even if it were, the median is a better measure of central tendency to compare in this scenario, as the box plots suggest some potential outliers.

Therefore, the correct answer is: Fast Chicken, because it has a smaller median.

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The perimeter of ΔNOP is equal to 25.6 units.

In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

By applying the basic proportionality theorem to the given triangles, we have the following:

ΔNOP ≅ ΔKLM

OP/ML = x/KL

x = (OP × KL)/ML

x = (8 × 7)/5

x = ON = 11.2 units.

For the perimeter of ΔNOP, we have;

Perimeter of ΔNOP = OP + NP + ON

Perimeter of ΔNOP = 8 + 6.4 + 11.2

Perimeter of ΔNOP = 25.6 units.

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The company must produce and sell at least 857 bottles of juice in a day to break-even, given the given expenses and selling price per bottle.

Let's denote the number of bottles of juice sold in a day as "x".

The total cost of production and business expenses :

Total cost = Business expenses + (Cost per bottle of juice) x (Number of bottles produced and sold)

Total cost = $1200 + $1.10x

The revenue generated from selling "x" bottles :

Revenue = (Selling price per bottle of juice) x (Number of bottles produced and sold)

Revenue = $2.50x

The company will break-even when revenue equals total cost, so we can set two expressions equal to each:

[tex]\\$2.50x = $1200 + $1.10x\\$2.50x - $1.10x = $1200\\$1.40x = $1200\\x = $1200 / $1.40\\[/tex]

x ≈ 857

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Correct expression would be, 5*(6-3)+14=19

What is expression?

An expression consists of one or more numbers or variables along with one more operation.

Given Expression:

         5×6-3+4 = 19

To make expression true we will add parentheses between 6 and 3

The correct expression would be, 5*(6-3)+14=19

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The distance travelled  in 4 seconds while driving at a constant speed of 50 mph is equal to 0.0556 miles (approximately).

Driving speed is equal to 50mph

And driving at a constant speed of 50 miles per hour ,

Then your speed in miles per second is ,

Since there are 60 minutes in an hour

⇒50 mph = 50/60 miles per minute

⇒50/60 miles per minute = 5/6 miles per minute

Since there are 60 seconds in a minute

⇒ 5/6 miles per minute = 5/360 miles per second

⇒ 5/360 miles per second = 0.0138888... miles per second

⇒ 5/360 miles per second  ≈0.0139 miles per second

When look down for 4 seconds while driving at 50 mph,

Travel a distance of,

distance = speed x time

Substitute the value we get,

⇒ distance = 0.0139 miles per second x 4 seconds

⇒ distance ≈ 0.0556 miles

Therefore,  travel a distance of  0.0556 miles approximately in 4 seconds while driving at a constant speed of 50 mph.

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The flour will fit into two of the container is 144 inches.

What is the volume of cuboids?

A cuboid is a six-sided solid known as a hexahedron. Quadrilaterals make up its faces. Cuboid is short for "like a cube". A cuboid is similar to a cube in that a cuboid can become a cube by varying the lengths of the edges or the angles between the faces.

Here, we have

Given: Mrs. Hanson is filling containers in her bakery with flour.

we have to find how much flour will fit into two of the containers.

Volume of cuboid = length × breadth × height

Length = 6 inches

Breadth = 3 inches

Height = 8 inches

The flour will fit into two of the containers = length × breadth × height

= 6 ×3 × 8

= 144 inches

Hence, The flour will fit into two of the container 144 inches.

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The endpoints of the rainbow are 2√60 cm apart.

The given equation for the rainbow is in vertex form, which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

In this case, the vertex is (1, 6), which means that the parabola is shifted horizontally by 1 unit to the right and vertically by 6 units upwards from the standard parabola y = ax^2.

Since the height of the rainbow is 6 cm, this means that the highest point of the parabola is at y = 6, which occurs at the vertex (1, 6).

To find the distance between the endpoints of the rainbow, we need to find the x-intercepts of the parabola. These occur where y = 0. Therefore, we need to solve for x in the equation:

0 = -0.1(x - 1)^2 + 6

-6 = -0.1(x - 1)^2

-6/-0.1 = (x - 1)^2

60 = (x - 1)^2

±√60 = x - 1

x = 1 ± √60

Since we are looking for the distance between the endpoints, we need to subtract the smaller x-value from the larger one:

Distance between endpoints = (1 + √60) - (1 - √60)

Distance between endpoints = 2√60

Therefore, the endpoints of the rainbow are 2√60 cm apart.

The given equation in the question is wrong, the correct equation is:

y = -0.1(x - 1)^2 + 6.

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An analysis of future events performed by the probability of those events and the potential outcomes is called probabilistic analysis.

Probabilistic analysis involves using mathematical models and statistical techniques to estimate the likelihood of different outcomes, given a set of assumptions and inputs. It is commonly used in risk management, financial analysis, and project management to evaluate the potential impact of different scenarios and make informed decisions. By quantifying the probabilities of different outcomes, probabilistic analysis helps decision-makers identify the best course of action and manage uncertainty and risk.

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Thus, the probability that two custard-filled donuts are selected in a row) 11/46.

sampling without replacement is the process of selecting a subset of observations at random; once an observation is chosen, it cannot be chosen again. sampling with replacement, whereby one observation may be chosen more than once and a subset of observations is chosen at random.

Given data:

two-dozen (24) donuts

probability = favourable outcome / total outcome

probability (1st custard-filled donut) = total custard-filled donut / total donuts

probability (1st custard-filled donut) = 12/24

probability (1st custard-filled donut) = 1/2

Now,1 is already taken, now total donuts left are 23 with 11 custard-filled donut.

probability (2nd custard-filled donut) = total custard-filled donut / total donuts

probability (2nd custard-filled donut) = 11/23

Now,

probability (two custard-filled donuts in a row) = 1/2 * 11/23

probability (two custard-filled donuts in a row) = 11 / 46

Thus, the probability that two custard-filled donuts are selected in a row) 11/46.

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The sum of the expression is 3.5x+6.8.

Given that are two expressions, we need to find the sum of the expressions,

The expression is a mathematical statement which is constructed by putting arithmetical operations, variables and numbers together.

So, finding the sum.

(-4.25x + 9) and (8x - 2.2)

Putting the sign of addition,

= (-4.25x + 9) + (8x - 2.2)

Opening the brackets,

= -4.5x + 9 + 8x - 2.2

Combining the like terms.

= 8x-4.5x + 9-2.2

Operating the like terms,

= 3.5x+6.8

Hence, the sum of the expression is 3.5x+6.8.

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The proof for the given proportion or two equivalent ratios given as (y+x):(y-x) = k:1 is shown below

What is a proportion?

On ratio and fractions, proportion is based. Two ratios are equal when they are represented as a fraction (a/b), a ratio (a:b), and then a proportion. A and B are two integers. Two sets of supplied numbers are said to be directly proportional if they increase or decrease in the same ratio for both sets. The symbols "::" or "=" are used to indicate proportions. If the ratio between the first and second is equal to the ratio between the second and third, then any three quantities are in continuing proportion.

Given that (y+x) : (y-x) = k : 1

We know that product of extremes = product of means

Extremes=(y+x) and 1

Means=(y-x) and k

(y+x) . 1   = (y-x) . k

y + x = ky - kx

y - ky = -kx - x

y - ky = - x(k + 1)

-(y - ky) = x(k + 1)

ky - y = x(k + 1)

y(k - 1) = x(k + 1)

y=[tex]\frac{x(k+1)}{(k-1)}[/tex]

Hence proved.

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To determine the effect of the interaction of the number of pages and cover type on cost, a statistical analysis would need to be performed using data on the number of pages, cover type, and cost. The analysis would likely involve running a regression model that includes both the number of pages and cover type as predictor variables, as well as an interaction term between the two.

 To answer your question, the effect of the interaction between the number of pages and cover type on the cost can be determined through a step-by-step process:

1. Identify the base cost of each cover type (e.g., hardcover, paperback, etc.).
2. Determine the cost per additional page for each cover type.
3. Calculate the cost for a specific number of pages and cover type by adding the base cost and the cost of additional pages.

For example:
- Base cost for hardcover: $5.00
- Base cost for paperback: $3.00
- Cost per additional page for hardcover: $0.10
- Cost per additional page for paperback: $0.05

Now, let's say you want to find the cost of a 100-page hardcover book:

1. Start with the base cost of a hardcover: $5.00
2. Multiply the number of pages (100) by the cost per additional page for hardcover ($0.10): 100 * $0.10 = $10.00
3. Add the base cost and the cost of additional pages: $5.00 + $10.00 = $15.00

So, the cost of a 100-page hardcover book is $15.00.

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The equivalent sum to the given equation is -9c - 20.

An algebraic expression is consists of variables, numbers with various mathematical operations.

Equivalent sums refers to addition or subtraction from the other number to maintain the same total value.

= 9c-12-15c-8-3c

To find the equivalent sum, first we can simplify this expression by first combining like terms:

= 9c - 15c - 3c - 12 - 8

= (9c - 15c - 3c) - (12 + 8)   (grouping the like terms)

Solving the expression for terms c and  for constant terms,

= -9c - 20

Therefore, the equivalent sum is -9c - 20.

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