6. A library owner wants to purchase books for the library. He wants to purchase a maximum of 27 book
between short stories and novels. The cost of each short-story book is $6 and the cost of each novel is
$10.
If he cannot spend more than $90 on books, which system of inequalities below can be used to
determine the number of short-story books, s, and the number of novels, n, he can purchase?

The calculated values of the angle measures when converted to radians are 1.31π rad and 3.34π rad

To convert angles from degrees to radians, we multiply the number of degrees by π/180.

This means that

Angle = Degree measure * π/180

Using the above as a guide, we have the following:

Angle 236 = 236 * π/180

Evaluate the products

Angle 236 = 1.31π rad

Next, we repeat the same process for the second angle 601 degrees

Angle 601 = 601 * π/180

Evaluate the products

Angle 601 = 3.34π rad

Hence, the angles are 1.31π rad and 3.34π rad

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The discontinuity at x = -2 is a removable discontinuity or a hole in the graph of the function.

To identify the discontinuities in the function f(x), we first need to find the values of x that make the denominator zero, since division by zero is undefined.

The denominator of f(x) is x² + x - 2, which can be factored as (x - 1)(x + 2). Therefore, the function f(x) is undefined at x = 1 and x = -2, since they would make the denominator zero.

Now we need to determine the type of discontinuity at these points.

At x = 1, the function f(x) approaches infinity as x approaches 1 from both sides of the graph.

At x = -2, the function f(x) has a hole in the graph.

This means that the function is undefined at x = -2, but if we "plug in" x = -2, we can factor the numerator and cancel out the common factor with the denominator, resulting in a new function that is continuous at x = -2. The new function is:

f(x) = (x⁴ - 5x² + 4) / (x² + x - 2)

= [(x² - 1)(x² - 4)] / [(x - 1)(x + 2)]

= (x - 1)(x + 1)(x - 2), for x ≠ -2

Therefore, the discontinuity at x = -2 is a removable discontinuity or a hole in the graph.

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Answer:

70.4%

Step-by-step explanation:

Assuming the test is the only graded assignment, and the remaining 80% of her grade is still at 73%, we can calculate Kayla's new overall grade as follows:

New overall grade = (0.80 x 73) + (0.20 x 60)

New overall grade = 58.4 + 12

New overall grade = 70.4

Therefore, Kayla's new overall grade is 70.4%

Answer:

70.4% or a C-.

Step-by-step explanation:

To calculate Kayla's new grade after taking the test, you need to first find out what percentage of her overall grade the test is worth. If the test is worth 20% of her grade, then the remaining 80% of her grade is based on other factors, such as homework, quizzes, and other tests.

To calculate Kayla's new grade, you can use the following formula:

New grade = (Current grade x Weight of current assignments) + (Grade on test x Weight of test)

Plugging in the numbers given in the problem, we get:

New grade = (0.73 x 0.80) + (0.60 x 0.20)

New grade = 0.584 + 0.12

New grade = 0.704

Therefore, Kayla's new grade after taking the test would be approximately 70.4%, or a C-.

Jim must pay tax  $3.57.

The correct answer is (a) $3.57.

To calculate the sales tax that Jim must pay, we need to find 7% of the total cost of the shoes and laces.

The total cost of the shoes and laces is $50 (shoes) + $1 (laces) = $51.

To calculate the sales tax, we multiply the total cost by the tax rate:

Sales tax = 7% of $51

[tex]= 0.07 \times $51[/tex]

= $3.57.

Therefore, Jim must pay $3.57 in sales tax.

The correct answer is (a) $3.57.

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a. The slopes of the lines are:

Slope of line 1 = 1/4

Slope of line 2 = -4

Slope of line 3 = -1/3

b.

Line 1 and Line 2 : Perpendicular

Line 1 and Line 3 : Neither

Line 2 and Line 3 : Neither

From the question, we are to determine the slope of each of the given lines:

Using the formula,

m = (y₂ - y₁) / (x₂ - x₁)

Where m is the slope

m = (-3 - 0) / (-4 - 8)

m = (-3) / (-12)

m = 1/4

m = (2 - 6) / (0 - (-1))

m = (-4) / (1)

m = -4

m = (-7 - (-4)) / (6 - (-3))

m = (-3) / (9)

m = -1/3

b.

NOTE: Two lines are said to be parallel if they have equal slopes; and they are said to be perpendicular if the slope of one is the negative reciprocal of the other.

Thus,

Line 1 and Line 2 : Perpendicular

Line 1 and Line 3 : Neither

Line 2 and Line 3 : Neither

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Answer:

The expanded notation of -6⁷ means writing the number -6⁷ as a sum of its place values.

-6⁷ can be written as:

-6 × 6 × 6 × 6 × 6 × 6 × 6

or

-6 × (6 × 6 × 6 × 6 × 6 × 6)

or

-6 × 6⁶

In expanded notation form, it can be written as:

-6 × (6 × 6 × 6 × 6 × 6 × 6)

= -6 × (46656)

= -279936

Therefore, the expanded notation of -6⁷ is -279936.

Step-by-step explanation:

Answer:  C, yes

Step-by-step explanation:

Again you have do the same thing to both sides

They added 1 to both sides

Answer is C , yes they are same

The equation expressing d as a function of t can be found by using the formula for distance traveled with constant speed:

d = vt

where d is the distance, v is the constant speed, and t is the time elapsed.

In this case, the speed is 150 cm/s, so the equation is:

d = 150t

To find the total distance traveled in meters at t = 2 seconds, we need to first find the total distance traveled in centimeters at t = 2 seconds:

d = 150t

d = 150(2)

d = 300 cm

To convert to meters, we divide by 100:

d = 300/100

d = 3 meters

Therefore, at t = 2 seconds, the object has traveled a total distance of 3 meters.

An estimate for the mean time spent watching television is approximately 24.375 hours.

Midpoint of 0 < h ≤ 10 = (0 + 10) / 2 = 5

Midpoint of 10 < h ≤ 20 = (10 + 20) / 2 = 15

Midpoint of 20 < h ≤ 30 = (20 + 30) / 2 = 25

Midpoint of 30 < h ≤ 40 = (30 + 40) / 2 = 35

Sum of observations = (5 × 5) + (15 × 15) + (25 × 50) + (35 × 10) = 125 + 225 + 1250 + 350 = 1950

Total number of observations = 5 + 15 + 50 + 10 = 80

Mean = Sum of observations / Total number of observations = 1950 / 80 = 24.375

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a. The slopes of the lines are:

Slope of line 1 = -5/2

Slope of line 2 = 7/5

Slope of line 3 = -5/2

b.

Line 1 and Line 2 : Neither

Line 1 and Line 3 : Parallel

Line 2 and Line 3 : Neither

From the question, we are to determine the slope of each of the given lines:

Using the formula,

m = (y₂ - y₁) / (x₂ - x₁)

Where m is the slope

m = (2 - 7) / (-2 - (-4))

m = (-5) / (2)

m = -5/2

m = (-8 - (-1)) / (-5 - 0)

m = (-7) / (-5)

m = 7/5

m = (-2 - 8) / (2 - (-2))

m = (-10) / (4)

m = -5/2

b.

NOTE: Two lines are said to be parallel if they have equal slopes; and they are said to be perpendicular if the slope of one is the negative reciprocal of the other.

Thus,

Line 1 and Line 2 : Neither

Line 1 and Line 3 : Parallel

Line 2 and Line 3 : Neither

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The angle of rotation about the origin, (0, 0) that maps WXYZ TO W’ X’ Y’Z are

180 degrees

540 degrees

900 degrees

The transformation rule for an angle of 180 degrees is simply a reflection or a flip. This means that any object or figure that undergoes this transformation will be flipped over a line or axis.

The rule is (x, y) will become (-x, -y)

Where 540 degrees = 360 + 180

where 900 degrees = 360 + 360 + 180

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From the attached graph the solution set is (3, 3) for the inequalities

The first inequality is y < -(2/3)x + 5.

We can graph this by plotting the y-intercept of 5 and then using the slope of -2/3 to find additional points.

We then draw a dashed line through these points to indicate that the points on the line are not included in the solution set.

Since the inequality is y <, we shade the region below the line.

The second inequality is y ≥ (4/3)x - 1.

We can graph this by plotting the y-intercept of -1 and then using the slope of 4/3 to find additional points.

We then draw a solid line through these points to indicate that the points on the line are included in the solution set.

Since the inequality is y ≥, we shade the region above the line.

Hence, from the attached graph the solution set is (3, 3) for the inequalities

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The answers of the matrix of A after  adding  -5 times row 1 to row 3 of matrix is

1  -1  5  |  -1

1  -1 -4  |   5

0   9 -25 |   4

A matrix is described as  a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

Matrices are useful for describing systems of linear or differential equations, as well as representing a linear application.

We perform the row operation and have:
1  -1  5  |  -1

1  -1 -4  |   5

0   9 -25 |   4

The result after  adding  -5 times row 1 to row 3 of matrix is shown below:

1  -1  5  |  -1

1  -1 -4  |   5

0   9 -25 |   4

In conclusion,  in  a matrix function, the input and the output values are matrices.

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Answer:

C. (–3, –7)

Step-by-step explanation:

We can check each ordered pair by substituting the values of x and y into the equation y = x - 4 and see if the equation is true.

A. (-3, 7)

y = x - 4

7 = -3 - 4

7 = -7

This is not true, so (-3, 7) is not a solution.

B. (3, -7)

y = x - 4

-7 = 3 - 4

-7 = -1

This is not true, so (3, -7) is not a solution.

C. (-3, -7)

y = x - 4

-7 = -3 - 4

-7 = -7

This is true, so (-3, -7) is a solution.

D. (3, 7)

y = x - 4

7 = 3 - 4

7 = -1

This is not true, so (3, 7) is not a solution.

Therefore, the only ordered pair that is a solution of y = x - 4 is (–3, –7).

The height of the traffic barrel is 42.97 inches.

The surface area of a cylinder is derived with A = 2πr² + 2πrh. A = surface area, r = radius and h = height.

Since diameter is given as 18 inches, we can get radius by dividing the diameter by 2:

r = 18 / 2

r = 9 inches.

Substituting these values, we get:

2,939.04 = 2π(9²) + 2π(9)h

2,939.04 = 162π + 18πh

2,939.04 - 162π = 18πh

h = (2,939.04 - 162π) / (18π)

h = 42.9736382161

h = 42.97 inches

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According to the information, Hannah donated b/50 books in total.

First, we need to find the average number of books donated by each student. We can do this by dividing the total number of books donated by the number of students:

Hannah donated 3 times this amount, so we can multiply the average by 3 to find how many books she donated:

Simplifying this expression, we get:

Therefore, Hannah donated b/50 books in total.

Note: This question is in Spanish. Here is the question in English:

Hannah's school organized a book donation. There are 150 students in her school who donated a total of b books. Hannah donated 3 times the average number of books donated by each student. How many books did Hannah donate?

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The lateral and total surface area of the prism are 1000 square feet and 1120 square feet.

In this problem we need to determine the lateral and total surface area of a prism with a triangular base. The lateral surface area is the sum of the areas of the three rectangles and the total surface area is the sum of the lateral surface area and the areas of the two triangles.

The area formulas for the triangle and the rectangle are, respectively:

Triangle:

A = s · √[s · (s - a) · (s - b) · (s - c)]

s = 0.5 · (a + b + c)

Where:

Rectangle:

A = w · h

Where:

Now we proceed to determine each surface area:

Lateral surface area:

A = 2 · (20 ft) · (17 ft) + (20 ft) · (16 ft)

A = 1000 ft²

Total surface area:

s = 0.5 · (17 ft + 17 ft + 16 ft)

s = 25 ft

A = √[(25 ft) · (25 ft - 17 ft)² · (25 ft - 16 ft)] + 1000 ft²

A = 1120 ft²

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Answer:

1. True

2.True

3.True

4.False

5.False

6.True

7.True

8.True

Step-by-step explanation:

1. The area of a rectangle is found by the formula A=bh.

2. There are 4 rectangles making up the lateral area of the prism. 2+3=5. 5*6=30, and multiply by 2 since there are two of the 2x6 and two of the 3x6 rectangles to get 60. The bases of the prism have an area of 6 square inches each.

60+12+12=84

3. 3*5=15

4. The base is not a square, so you cannot multiply by 4 to get the area of all the triangles. You can multiply by two, and also multiply 1/2(3)(4) by 2 to get the area of the other two triangles.

5. The base is a triangle. 1/2(3)(4)=6.

6. 2[1/2(3)(4)]=12. 2(8*5)=80. 3*8=24. 80+24+12=116

7. A cube has 6 identical sides, so you can find the area of one side and multiply by 6 to get the surface area of the cube.

8. 9^2=81. 81*6=486.

Answer: First, let's convert the room's dimensions from feet to yards, since the carpet cost is given per square yard:

17 feet = 5.67 yards (rounded to two decimal places)

16 feet = 5.33 yards (rounded to two decimal places)

Next, we can calculate the area of the room in square yards by multiplying these values:

Area = 5.67 yards × 5.33 yards = 30.23 square yards (rounded to two decimal places)

Finally, we can multiply the area by the cost per square yard to get the total cost:

Total cost = 30.23 square yards × $101/square yard = $3,056.23 (rounded to two decimal places)

Therefore, it will cost $3,056.23 to carpet the room.

The expected value for playing roulette if a person bet $16 on red is -$0.84.

b. The statement that best describes what this value means is option b. Over the long run, the player can expect to lose about $1.05 for each game played.

To be able to calculate the expected value, you need to multiply the probability of winning by the amount won hence it will be:

Expected value = (18/38) x  $16 - (20/38) x  $16

= -$0.84

Based on the fact that the expected value has a negative sign, it implies that, on average, the player tend to lose money over the long run.

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See full question below

one option in a roulette game is to bet $16 on red. (there are 18 red compartments, 18 compartments, and two compartments that are neither red nor black) if the ball lands on red, you get to keep the $16 you paid to play the game and you are awarded $16. If the ball lands elsewhere, you are awarded nothing and the $16 that you bet is collected.

a. what is the expected value for playing roulette if you bet $16 on red?

$__________ (round to the nearest cent)

b. chosen the statment below that best describes what this value means???

Pick One!

a. over the long run, the player can expect to win about $1.05 for each game played

b. over the long run, the player can expect to lost about $1.05 for each game player

c. over the lung run, the player can expect to break even

The area, in square inches, of the label needed to cover the face of the box is 96 in².

Option A is correct.

We must first determine the length and breadth of the rectangle before multiplying them together to determine the area of the rectangular face.

The distance between the x-coordinates of two opposite points determines the length of the rectangle:

length equals 3 - (-5) = 8.

The distance between the y-coordinates of the same two opposite points determines the rectangle's width:

width = 8 + (-4) = 12

In conclusion, the rectangle's size is: 8 × 12 = 96 square inches is the area formula.

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To find the slope in this problem, we can use the formula for calculating slope, which is change in distance divided by change in time. In this case, the change in distance is 350 miles - 200 miles = 150 miles, and the change in time is 4:00 pm - 1:00 pm = 3 hours.

So, the slope (rate of driving) is 150 miles / 3 hours = 50 miles per hour.

Therefore, Sue will drive an additional 50 miles by 5:00 pm, making her total distance driven by 5:00 pm 200 miles + 150 miles + 50 miles = 400 miles. So, Sue will drive 400 miles by 5:00 pm if she continues at the same rate. Note that in this problem, we are assuming that Sue maintains a constant speed throughout her drive. If her speed changes, the solution may be different.

Answer:

2

Step-by-step explanation:

The value of cube root of 8, ∛8, is 2.

Answer:

2

Step-by-step explanation:

cube root 8 means:

a number x such that x * x * x = 8

the answer is 2, since 2 * 2 * 2 = 8

answer is : r=1.6 in since the volume of cylinder is :

[tex]\pi {r}^{2} h[/tex]

In the given diagram, the volume of the composite shape is 12,672 ft³

From the question, we are to calculate the volume of the given composite shape

The composite shape is made up of a pyramid and a cuboid

Thus,

Volume of the shape = Volume of pyramid + Volume of cuboid

Volume of pyramid = 1/3 × base area × height

Volume of cuboid = Length × Width × Height

Calculating the volume of the pyramid

Volume of pyramid = 1/3 × 24² ×15

Volume of pyramid = 1/3 × 576 ×15

Volume of pyramid = 576 × 5

Volume of pyramid = 2880 ft³

Calculating the volume of the cuboid

Volume of the cuboid = 24² × 17

Volume of the cuboid = 9792 ft³

Thus,

Volume of the shape = 2880 ft³ + 9792 ft³

Volume of the shape = 12,672 ft³

Hence, the volume of the shape is 12,672 ft³

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Answer:10.66 years. Punch again to double check

Step-by-step explanation:

A=Pe^(rt)

11700=5850e^(.065t)

isolate the variable expression

2=e^(.065t) divide by 5850

ln2=lne^(.065t) take the natural log of both sides

ln2=.065t. Bring down the power, lne equals

t is about 10.66 years. Divide ln2 by .065

The value of 3.1 divided by 6 leaving 7 digits after the decimal point without rounding is 0.5166666

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

3.1 divided by 6

When represented as an expression, we have

3.1 divided by 6 = 3.1/6

The above expression can be calculated using a calculator

Using a calculator, we have

3.1/6 = 0.51666666666

This means that

3.1 divided by 6 = 0.51666666666

Leaving 7 digits after the decimal point without rounding, we have

3.1 divided by 6 = 0.5166666

Hence, the value of 3.1 divided by 6 is 0.5166666

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Since Q is the midpoint of NP, we know that NQ = QP. Similarly, we know that RS is the midpoint of OP, so we have RS = SO.

Let's label the length of QS as x. Then, we know that QR = 2x and SR = 3x.

To find the perimeter of triangle NOP, we need to find the lengths of NO, OP, and NP.

Using the Pythagorean Theorem, we can find that:

NO^2 = NQ^2 + OQ^2

NO^2 = (QP)^2 + (SO)^2

NO^2 = (x)^2 + (2x)^2

NO^2 = 5x^2

NO = x√5

Similarly, we can find that:

OP^2 = OQ^2 + PQ^2

OP^2 = (SO)^2 + (QP)^2

OP^2 = (3x)^2 + (x)^2

OP^2 = 10x^2

OP = x√10

Finally, we know that NP = NO + OP, so:

NP = x√5 + x√10

NP = x(√5 + √10)

To find the perimeter of NOP, we add up the three sides:

Perimeter of NOP = NO + OP + NP

Perimeter of NOP = x√5 + x√10 + x(√5 + √10)

Perimeter of NOP = x(2√5 + 2√10)

Perimeter of NOP = 2x(√5 + √10)

We can substitute the value we found for QS, which is x, to get:

Perimeter of NOP = 2(5 + 2√10)

Perimeter of NOP = 10 + 4√10

Therefore, the perimeter of triangle NOP is 10 + 4√10 units.