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The library had 102 shelves of books. Each shelf had 14 books.Librarians checked out 807 books to students. how many books does the library have remaining?

The weighted-average unit contribution margin is $46.20.

The weighted-average unit contribution margin can be calculated by multiplying the unit contribution margin of each model by its respective sales mix percentage, and then summing up the results.

To find the weighted-average unit contribution margin, we first calculate the unit contribution margin for each model by subtracting the unit variable costs from the selling price:

For Model A12:

Unit contribution margin = Selling price - Unit variable cost

                     = $60 - $42

                     = $18

For Model B22:

Unit contribution margin = Selling price - Unit variable cost

                     = $120 - $84

                     = $36

For Model C124:

Unit contribution margin = Selling price - Unit variable cost

                     = $480 - $360

                     = $120

Next, we multiply each unit contribution margin by its respective sales mix percentage:

Weighted contribution margin for Model A12 = 60% * $18 = $10.80

Weighted contribution margin for Model B22 = 15% * $36 = $5.40

Weighted contribution margin for Model C124 = 25% * $120 = $30.00

Finally, we sum up the weighted contribution margins:

Weighted-average unit contribution margin = $10.80 + $5.40 + $30.00 = $46.20. Therefore, the weighted-average unit contribution margin is $46.20.

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The area of the rectangle with side lengths of (ax + b) and ( x + c) is given by the quadratic expression ax² + (ac + b)x + bc.

The area of a rectangle is expressed as;

Area = length × breadth

To find the area of a rectangle with side lengths of (ax+b) and (x+c), we need to multiply the two sides together:

Area = length × breadth

Area = (ax + b) × (x + c)

We can simplify this expression by using the distributive property of multiplication, which states that:

a(b + c) = ( a × b ) + ( a × c )

Using this property, we can expand the expression for the area of the rectangle as follows:

Area = (ax + b) × (x + c)

Area = ( ax ×  x ) + ( ax × c ) + ( b × x ) + ( b × c )

Now we can simplify this expression by combining like terms:

Area = ax² + (ac + b)x + bc.

Therefore, the area of the rectangle is ax² + (ac + b)x + bc.

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Answer:

7921 is the correct answer

Answer:

7,291

Step-by-step explanation:

Just multiply. 89 x 89

Answer:0.24 = 24 hundredths, not 24

Step-by-step explanation:

The sequence that shows a pattern where each term is 1.5 times the previous term is option D

Series of numbers can be in a sequence either in arithmetic or in geometric. In the above question, it is geometric because the sequence shows a pattern where each term is 1.5 times the previous term.

Let us test each option one by one.

Option A

1.5 x -4 = -6

But the next number in the series is 6

Option B

1.5 x 10 = 15

1.5 x 15 = 22.5

But the next number in the series is 25

Option C

1.5 x 98 = 147

But the next number in the series is 99.5

Option D

1.5 x -200 = -300

1.5 x -300 = -450

1.5 x -450 = -675

Therefore, the sequence that shows a pattern where each term is 1.5 times the previous term is option D

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Answer: D (-200,-300,-450,-675,...)

Step-by-step explanation:

Recognizing the pattern in a sequence is used to write the function that represents it.

Answer:

x ≈ 5.6 cm

Step-by-step explanation:

Using the sine ratio in the right triangle

sin44° = \(\frac{opposite}{hypotenuse}\) = \(\frac{x}{y}\) = \(\frac{x}{8}\) ( multiply both sides by 8 )

8 × sin44° = x , then

x ≈ 5.6 cm ( to 1 dec. place )

Answer:

\(d(t) = -23t +556\)

Step-by-step explanation:

Assuming the hurricane continues on the same path at the same speed means the relationship between speed and time will be linear. This means our function can be written in slope-intercept form, \(y=mx+b\). For our function, it will be written as \(d(t)=mt+b\), where t is time, d is distance, m is the slope of the line, and b is the y-intercept. We can solve for slope by using the formula \(\frac{y_{2}-y_1 }{x_2-x_1}\), where x2 and x1 are the times 8 and 3, respectively, and y2 and y1 are the distances 372 and 487, respectively. This gives us a slope of -23.

We can solve for b by inputting the values we've been given and using algebra.

\(d(t)=mt+b\\487 =-23(3)+b\\487=-69+b\\b=556\)

This gives us the equation \(d(t) = -23t +556\)

Something to note, since we let 3:00 pm and 8:00 pm be the values x=3 and x=8, 12:00 pm would be x=0, and values in the morning would be negative, like 9:00 am would be x=-3.

The number of square units enclosed by the polygon is 18.

First, count the number of dots that are enclosed by the polygon (including those on the boundary). There are 14 such dots.Next, count the number of dots on the boundary of the polygon. There are 8 dots on the boundary.Each of the dots on the boundary corresponds to a line segment of the polygon.

So, the perimeter of the polygon is 8 units (the length of each of these line segments).Now, we can use Pick's theorem to find the area of the polygon. Pick's theorem states that A = i + b/2 - 1, where A is the area of the polygon, i is the number of dots inside the polygon, and b is the number of dots on the boundary of the polygon.

So, plugging in the values we have: A = 14 + (8/2) - 1 = 14 + 4 - 1 = 17

Therefore, the area of the polygon is 17 square units.However, we have to remember that the dots are spaced one unit apart, horizontally and vertically.

Therefore, each square that is enclosed by the polygon has an area of 1 square unit. We counted 17 such squares, so the total area enclosed by the polygon is 17 square units.

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Counting numbers from 101 to 200, those with 6 as a digit are 19

Let's start by listing all the number between 101 and 200

101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200

Now, let's count the numbers with 6 as a digit

= 19 numbers has 6 as a digit

Thus, counting numbers from 101 to 200, those with 6 as a digit are 19

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In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.

a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.

b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.

c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.

d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).

e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.

f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

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The number is -2 when three times the sum of a number and 4, subtracted from 10, is the same as two times the same number, increased by 8.

According to the question,

We have the following information:

Three times the sum of a number and 4, subtracted from 10, is the same as two times the same number, increased by 8.

Now, let's take the number to be x.

So, we have the following expression:

10-3(x+4) = 2x+8

10-3x-12 = 2x+8

-2 = 2x+3x+8

5x+8 = -2

5x = -2-8

5x = -10

x = -10/5

x = -2

Hence, the number is -2 when some of the conditions are given.

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5 ori 5 fac 25 și cu 25 egal 14 și cu 14 egal 100 și cu 100 egal 12

Step-by-step explanation:

sper ca team ajutat

Answer:

∠ 6 = 45°

Step-by-step explanation:

∠ 6 and 45° are vertically opposite angles and are congruent , so

∠ 6 = 45°

Answer: 5 under each splat

Step-by-step explanation:

Count how many circles there are. Which is 7 subtract from 22 and u get 15. 15 divided by 3 is 5

Answer: $88

Step-by-step explanation:

$99/9= $11 per hour

If Brian works 8 hours:

8x11= 88

Review algebra, geometry, statistics, and number systems. Practice solving equations, simplifying expressions, working with shapes, analyzing data, and understanding number patterns. Understand key terms and notation.

To prepare for your grade 9 mathematics test, focus on key areas like algebra, geometry, statistics, and number systems. Review solving equations, simplifying expressions, and working with geometric shapes. Practice analyzing data, understanding measures of central tendency and dispersion, and interpreting graphs. Refresh your knowledge of integers, fractions, decimals, and percentages, and practice performing operations on them.

Understand the laws of exponents, ratios, proportions, and percentages. Practice problem-solving by working on sample questions covering various topics, applying the appropriate formulas and theorems. Familiarize yourself with mathematical terms, definitions, and notation to enhance understanding and communication. Dedicate study time, create a plan, and seek clarification if needed.

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Answer: Unable to answer

Step-by-step explanation: If you do not show what the constant rate is, I am unable to solve it for you.

Answer:

x = 2 and x = -1

Step-by-step explanation:

The zeroes of the function are found by setting g(x) equal to 0:

g(x) = (x - 2)(3x + 3) = 0

By the Zero Product Property, in order for this equation to be equal to 0, each of (x - 2) or (3x + 3) or both has to equal 0. So, set each equal:

x - 2 = 0

x = 2

3x + 3 = 0

3x = -3

x = -3/3 = -1

The zeroes are thus x = 2 and x = -1.

~ an aesthetics lover

Answer:

x=2 x=(-1)

Step-by-step:

Solve: (x-2)(3x+3)=0

= x-2=0                   3x+3=0

=x-2(+2)=0(+2)       =3x-3(-3)=0(-3)

=x=2                      =3x=(-3)

                              =3x/3=(-3)/3

                              =x=(-1)

We have proven that the expression (36⁵ - 6⁹)(38⁹ - 38⁸) is divisible by both 30 and 37.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

To prove that the expression (36⁵- 6⁹)(38⁹ - 38⁸) is divisible by 30 and 37, we need to show that it can be written as the product of 30 and 37 with some integer coefficient.

First, let's look at the factorization of 30: 30 = 2 x 3 x 5.

We can see that 6 is a factor of 36, so we can rewrite 36^5 as (6²)⁵. Similarly, we can write 6⁹ as (6²)⁵ x 6³.

Now, let's factor out (6²)⁵ from the first factor in the expression:

(36⁵ - 6⁹) = (6²)⁵ (6⁵ - 6³)

We can factor out 38⁸ from the second factor in the expression:

(38⁹ - 38⁸) = 38⁸ (38 - 1)

So the original expression can be written as:

(36⁵ - 6⁹)(38⁹ - 38⁸) = (6²)⁵ (6⁵ - 6³) 38⁸ (38 - 1)

Now, let's look at the factorization of 37. We can see that 38 - 1 = 37, so we can rewrite the expression as:

(6²)⁵(6⁵ - 6³) 38⁸ (38 - 1) = (2⁵ x 3⁵) (6³) 38⁸ (37)

We can see that the expression contains a factor of 2⁵, a factor of 3⁵, and a factor of 37, so it is divisible by both 30 and 37.

Therefore, we have proven that the expression (36⁵ - 6⁹)(38⁹ - 38⁸) is divisible by both 30 and 37.

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Answer:

69

Step-by-step explanation:

6+64-1

=69

............

The first step is converting both the velocity and the wind in vector form, as follows:

Then the true speed of the plane is given by the addition of these two vectors, as follows:

\(\vec{v_1} + \vec{v_2} = \sqrt{|v_1|^2 + |v_2|^2 + 2 \cdot |v_1| \cdot |v_2| \cdot \cos(\theta)}\)

The magnitudes of each vector are given as follows:

The angle between these two vectors is given as follows:

\(\theta = 100^\circ - 42^\circ = 58^\circ\)

Thus the resulting speed is obtained as follows:

\(\vec{v_1} + \vec{v_2} = \sqrt{180^2 + 30^2 + 2 \cdot 180 \cdot 30 \cdot \cos(58^\circ)} = 197.54\)

The resulting angle of the plane is then obtained as follows:

\(\angle = \arctan\left(\frac{|v_1| \cdot \sin(\theta) + |v_2| \cdot \sin(\theta_2)}{|v_1| \cdot \cos(\theta) + |v_2| \cdot \cos(\theta_2)}\right)\)

Hence:

\(\angle = \arctan\left(\frac{180 \cdot \sin(58^\circ) + 30 \cdot \sin(42^\circ)}{180 \cdot \cos(58^\circ) + 30 \cdot \cos(42^\circ)}\right)\)

\(\angle = 59.87^\circ\)

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Answer:

  197.5 km/h

Step-by-step explanation:

You want the resultant speed with an airplane at a speed of 180 km/h at 100° is acted upon by a wind at a speed of 30 km/h at 42°. Angles are bearings CW from north.

A vector calculator makes short work of this. The resultant speed is ...

  197.5 km/h at 92.6°

The law of cosines can be used to find the side opposite the known angle in the triangle with sides 30 km/h and 180 km/h. The known angle is ...

  180° -(100° -42°) = 122°

So, the resultant speed is ...

  c = √(a²+b²-2ab·cos(C))

  = √(30² +180² -2(30)(180)·cos(122°)) ≈ √39023.13

  c ≈ 197.543

The true speed of the plane is about 197.5 km/h.

__

Additional comment

You will notice that we used bearing angles directly in the calculator computation. As long as angles are consistently measured, it doesn't matter how they're measured.

When plotting the vectors on the Cartesian plane, we need to subtract the bearing angles from 90° to make them correspond to the vectors plotted on a map with north at the top.

The high temperature for today using a 3-day moving average is 92 degrees.

To calculate the high temperature for today using a 3-day moving average, we take the average of the temperatures from the past three days, including today.

Given the daily high temperatures in St. Louis for the last week:

92, 92, 93, 95, 95, 86, 95 (yesterday)

To find the 3-day moving average for today's high temperature, we consider the temperatures from yesterday, the day before yesterday, and three days ago.

(95 + 86 + 95) / 3 = 92

Therefore, the high temperature for today, calculated using a 3-day moving average, is approximately 92 degrees Fahrenheit, rounded to one decimal place.

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Answer  k=16

A recipe says to use 3 cups of flour to make 48 cookies.

the number of cookies made, y, to the number of cups of flour used,x .

Than

y = kx

Where k is the constant of proportionality.

48 = 3k

k = 16

Therefore the constant of proportionality is 16.

Answer: 35.

Step-by-step explanation: The parenthesis with no operation in between is multiplication. double negative makes a positive so its 7 times 5 which is 35.

Option A) 15% is the most suitable representation of the probability of an unlikely event since it falls within the valid range of 0 to 1.

To determine the probability of an event, we typically express it as a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In this case, we are looking for the probability of an unlikely event, which means the probability value should be relatively low.

Let's analyze each option:

A) 15%:

This option represents a probability value of 15%, which can also be expressed as 0.15. Since 0.15 is greater than 0 and less than 1, it falls within the valid range for a probability value. Therefore, option A) 15% is a reasonable representation of the probability of an unlikely event.

B) 9/2:

This option represents a fraction, 9/2, which is equal to 4.5. Since 4.5 is greater than 1, it does not fall within the valid range for a probability value. Therefore, option B) 9/2 is not a suitable representation of the probability of an unlikely event.

C) 0.99:

This option represents a probability value of 0.99. Although 0.99 is close to 1, it is still greater than 0. Therefore, option C) 0.99 is not a suitable representation of the probability of an unlikely event.

D) -3:

This option represents a negative value, -3. In probability theory, probabilities cannot be negative since they represent the likelihood of an event occurring. Therefore, option D) -3 is not a valid representation of the probability of an event.

In summary, option A) 15% is the most suitable representation of the probability of an unlikely event since it falls within the valid range of 0 to 1.

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The rate of formation of b is also 0.135 m/s. This means that for every 0.135 meters of a that decomposes, 0.135 meters of b is formed.

The rate of formation of b can be calculated using the equation for the decomposition of a. The equation is:

rate of decomposition of a = rate of formation of b

Given that the rate of decomposition of a is 0.135 m/s, we can plug this value into the equation to find the rate of formation of b:

0.135 m/s = rate of formation of b

Therefore, the rate of formation of b is also 0.135 m/s. This means that for every 0.135 meters of a that decomposes, 0.135 meters of b is formed.

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We can use Coulomb's law to calculate the magnitude of the electric field at a distance r away from a point charge Q:

E = k * Q / r^2

where k is Coulomb's constant, Q is the charge of the point charge, and r is the distance from the point charge.

In this problem, we have a point charge Q of -10 nC located at (1.2 cm, 0 cm), and we want to find the x-component of the electric field at a distance r = 5.3 cm away at position (-4.1 cm, 0 cm).

To find the x-component of the electric field, we need to use the cosine of the angle between the electric field vector and the x-axis, which is cos(180°) = -1.

So, the x-component of the electric field at position (-4.1 cm, 0 cm) is:

E_x = - E * cos(180°) = - (k * Q / r^2) * (-1)

where k = 9 x 10^9 N*m^2/C^2 is Coulomb's constant.

Substituting the given values, we get:

E_x = - (9 x 10^9 N*m^2/C^2) * (-10 x 10^-9 C) / (0.053 m)^2

E_x ≈ -30,566.04 N/C

Rounding this to two significant figures and including the appropriate units, we get:

The x-component of the electric field is about -3.1 x 10^4 N/C (to the left).

Answer:

To solve the given system of equations using the substitution method, we need to solve one equation for one variable and then substitute that expression into the other equation for that same variable. Let's solve the second equation for y.

-x + y = 4

y = x + 4

Now we can substitute this expression for y into the first equation and solve for x.

-2x + 2(x + 4) = 7

-2x + 2x + 8 = 7

8 = 7

The equation 8 = 7 is not true, which means the system of equations has no solution. We can see this visually by graphing the two lines. They are parallel and will never intersect, which means there is no point that satisfies both equations.

Therefore, the solution to the system of equations is "No solution."

Note: Please be sure to double-check your work to avoid mistakes.

Step-by-step explanation:

Hope this helps you!! Have a wonderful day/night!!

Clyde needs an additional 1 cup of flour to make twice the recipe.

If the recipe requires 1} cups of flour, then double the recipe would require 2(1.5) = 3 cups of flour. Since Clyde already has 2 cups of flour, he still needs to get an additional amount of flour, which we can represent as "c".

The equation that represents the problem is:

2 + c = 3

where "2" represents the cups of flour that Clyde already has, "c" represents the additional amount of flour that he needs, and "3" represents the total amount of flour required for the doubled recipe.

Simplifying the equation, we get:

c = 3 - 2

c = 1

Therefore, Clyde needs an additional 1 cup of flour to make twice the recipe.

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