Math for Liberal Arts Lecture Class, Fall 2021 = Homework: Ch... Question 2, 1.1.3 Part 2 of 3 HW Score: Points: An election is held to choose the chair of a department at a university. The candidates are Professors Arg for short). The following table gives the preference schedule for the election. Use the table to complete pa Number of Voters 7 9 2 5 3 6 1st choice А A B D A 2nd choice B D D А E E 3rd choice D B E C B B 4th choice E C A B C D 5th choice C E C D A C (a) How many people voted in this election? ... 32 voters (Type a whole number.) (b) How many first-place votes are needed for a majority?

Composing f(x)=2x-8 and g(x)=1/2x+4 results in the identity function, f(g(x)) = x.

To compose the two functions, we substitute g(x) into f(x) in place of x:

f(g(x)) = 2(g(x)) - 8

= 2(1/2x + 4) - 8

= x + 8 - 8

= x

Therefore, composing the two functions results in the identity function, f(g(x)) = x.

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Answer:

0

Step-by-step explanation:

\( {x3 \: - 4 {x \: }^{2} + 3x \: = 0}^{} \)

solve for x

\(x 1 = 0 \\ x2 \: = 1 \\ x3 \: = 3\)

Answer:4) All are solutions

Given statement solution is :- The actual length of the part is 3751/64 inches.

To find the length of the actual part, you can use the scale factor and the length of the part on the drawing. The formula for finding the actual length is:

Actual Length = Length on Drawing × Scale Factor

In this case, the length on the drawing is given as 3 7/8 inches, and the scale factor is given as 15 ¹/8. Let's calculate the actual length:

Length on Drawing = 3 7/8 inches = (3 × 8 + 7) / 8 = 31/8 inches

Scale Factor = 15 ¹/8

Now we can substitute the values into the formula:

Actual Length = (31/8 inches) × (15 ¹/8)

To perform the multiplication, we can convert the mixed fraction into an improper fraction:

15 ¹/8 = (15 × 8 + 1) / 8 = 121/8

Now we can multiply the fractions:

Actual Length = (31/8) × (121/8)

To multiply fractions, we multiply the numerators together and the denominators together:

Actual Length = (31 × 121) / (8 × 8)

Actual Length = 3751 / 64

Therefore, the actual length of the part is 3751/64 inches.

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Answer:

54

Step-by-step explanation:

46+80=126 and every triangle adds up to 180 so subtract 180 from 126 (180-126=54)

Hope this helped!

Answer:

c)54 degrees

Step-by-step explanation:

A triangle has to be 180 degrees.

46+80=126

180-126=54

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Given:

A paddleboard is originally priced at $80

The online retailer gives a discount and the paddleboard is now $56

We need to find the percentage amount for the cost of the paddleboard

So, the percentage =

So, the online price is 70% of the original price.

The relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:

3/20.

A relative frequency is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of at bats in this problem is given as follows:

80.

In 12 of them, the pitcher threw exactly four pitches, hence the relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:

12/80 = 3/20.

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The production schedule for maximum profit is; X = 3 and Y = 6 with a maximum profit of $960

We are told that  two products X and Y, has a total production capacity of 9 tones per day, X and Y requiring the same production capacity

The firm has a permanent contract to supply at least 2 tones of X and at least 3 tones of Y per day to another company.

Let product A be x and product B be y. Therefore we have the following inequalities and constraints as;

x + y ≤ 9

x ≥ 2

y ≥ 3

Now, we are told that each tonne of A requires 20 machine hours of production time and each tonne of B requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. Thus, we have;

20x + 50y ≤ 360

Wea re told that all the firm's output can be sold and the profit made is $80 per tonne of A and $120 per tonne of B. Thus, we have the inequality as;

Z = 80x + 120y  maximize

The solution from the graph attached is;

x = 3, y = 6

Thus, the maximum profit is;

Z = 80(3) + 120(6)

Z = 960

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Answer:

a 0, 16, 64,144 graph A edge

Step-by-step explanation:

The graph that best represents the equation is option A.

What is an Equation?

An equation is a mathematical statement that is formed when two algebraic expressions are equated using an equal sign.

The equation is

s = 16t²

The table is

s              t

0             16*0 = 0

1              16 * 1 = 16            

2              16 * 4 = 64

3               16 * 8 = 108

The points represents a parabola opening upwards, vertex is at (0,0) and goes through the point (-1,16)

This has been confirmed by the graph plotted for the equation.

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A function of the form y= A sin (Bx-C)+D that has period 8, phase shift -2, and the range -12 ≤y≤-4 is y = 4 sin (π/4 x + π/2) - 8

To write a function of the form y = A sin (Bx - C) + D that has a period of 8 and phase shift of -2, we can use the general formula:

y = A sin [(2π/P)(x - C)] + D

where P is the period, C is the phase shift, and D is the vertical shift. In this case, P = 8 and C = -2, so we have:

y = A sin [(2π/8)(x + 2)] + D

Simplifying the equation, we get:

y = A sin (π/4 x + π/2) + D

To find the amplitude A and vertical shift D that satisfy the range -12 ≤ y ≤ -4, we can use the fact that the sine function oscillates between -1 and 1. If we set A = 4, then the maximum value of y is 4 + D, and the minimum value of y is -4 + D. To ensure that the range is -12 ≤ y ≤ -4, we need to choose D such that:

4 + D ≤ -4 and -4 + D ≥ -12

Solving these inequalities, we get:

-8 ≤ D ≤ 0

Therefore, a function that satisfies the given conditions is:

y = 4 sin (π/4 x + π/2) - 8

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Answer:

A. They are one-dimensional

B. They connect two endpoints

Both statements A and B are true about line segments. Line segments are one-dimensional figures that have two endpoints and connect them with a straight path.

Statement C is not true. Line segments do not have a unit of measure on their own, but their length can be measured using a unit of measure such as inches, centimeters, or meters.

Statement D is not true either. Line segments are flat, one-dimensional objects and cannot grow to become three-dimensional objects. However, multiple line segments can be connected to form a three-dimensional object, such as a cube or pyramid.

Answer:

3+jk+k^6

j=2 & k=6

substituting the values, we have

= 3+2(6)+6^3

= 3+12+216

= 231

Ans=231

Step-by-step explanation:

j=2 and k=6

Now

Answer:2,440,000,000

Step-by-step explanation:

Answer:

\(x=-\frac{4}{5}\)

Step-by-step explanation:

\(6=\frac{3}{4}(10x+16)\\\mathrm{or,\ }6\times 4=3(10x+16)\\\\\mathrm{or,\ }24=30x+48\\\\\mathrm{or,\ }-24=30x\\\\\mathrm{\therefore}\ x=-\frac{4}{5}\)

Answer:

\(281\)

Explanation:

\(-3n+296\)

\(-3(5)+296\)

\(-15+296\)

Answer:

281

Step-by-step explanation:

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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\( \sf \: x = - \frac{91}{30} \: or \: x = - 3 \frac{1}{30} \)

The required solution to the given equation is - 3 1/30 which is a mixed number.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question,

⇒ x − (-2 5/6) = −1/5

Convert the mixed number into the fraction as

⇒x − (-17/6) = −1/5

Distribute the negative sign in the above equation,

⇒x  + 17/6 = −1/5

Rearrange the terms of fractions,

⇒x = - 1/5 - 17/6

Take the LCM of the terms of fractions,

⇒x = -91 / 30

Convert the fraction into the mixed number,

⇒x = - 3 1/30

Therefore, the required solution to the given equation is - 3 1/30 which is a mixed number.

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A. The null hypothesis H₀ and the alternative hypothesis H₁ are:

H₀: μ = 35 minutes       H₁: μ > 35 minutes

B. If the consultant decides not to reject the null hypothesis, she might be making a Type II error.

C. A Type II error would be failing to reject the hypothesis that μ is = to 35 minutes when, in fact, μ is 43 minutes.

A Type II error occurs when the null hypothesis is false, but the test does not reject it.

In this case, the consultant would be concluding that the mean shopping time is 35 minutes, when in fact it is greater than 35 minutes.

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The measures of angle 4 (m<4) and angle 7 (m<7) are 42° and 96°, respectively.

To find the measures of angles 4 and 7, we need to apply some geometric principles. Since the top and bottom pieces of the crib are parallel to each other, we can use the property of alternate interior angles.

Angle 4 (m<4) is formed by a transversal (the line connecting the top and bottom pieces of the crib) intersecting two parallel lines. Given that angle m<2 is 42°, we know that angle 4 is congruent to angle 2. Therefore, m<4 = m<2 = 42°.

Angle 7 (m<7) is formed by a transversal intersecting two parallel lines as well. However, in this case, angle 7 is an exterior angle, which is equal to the sum of the two remote interior angles. The remote interior angles are angles 2 and 4. We know that m<2 = 42° (as given) and m<4 = m<2 = 42° (as explained above). Therefore, the sum of angles 2 and 4 is 42° + 42° = 84°. Since angle 7 is an exterior angle, it is equal to 180° minus the sum of the remote interior angles. Thus, m<7 = 180° - 84° = 96°.

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Answer:

70

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

It's a standard angle, you can find it on most charts

Answer:

KL = 3.2 units

Step-by-step explanation:

To rewrite the law of sines using L, K, and J (l, k and j for the sides) instead of A, B, and C (a, b, and c for the sides), we have:

sin (L) / l = sin (K) / k = sin (J) = j

Before we can kind KL, we'll need to know the measure of J.  

In order to find J, we'll first need to find K by plugging in 105 for L, 4.7 for l, and 2.7 for k to find the measure of K:

Step 1:  Simplify on the left-hand side and multiply both sides by 2.7:

sin (105) / 4.7 = sin (K) / 2.7

(0.2055161333 = sin (K) / 2.7)

0.5548935598 = sin

Step 2:  Use inverse sine to find K:

sin^-1 (0.5548935598) = K

33.70338376 = K

The sum of the measures of the angles of any triangle is 180°.

Thus, we can find the measure of angle J by subtracting the sum of the measures of angles L and J from 180:

J + L + K = 180

J + 105 + 33.70338376 = 180

(J + 138.7033838 = 180) -  138.7033838

J =41.29661624

Now we can find the length of KL (aka j in the law of sines) by plugging in  105 for L, 4.7 for l, and 41.29661624 for J:

Step 1:  Simplify on the left-hand side:

sin (105) / 4.7 = sin (41.29661624) / j

0.2055161333 = sin (41.29661624) / j

Step 2:  Multiply both sides by j:

(0.2055161333 = sin (41.29661624) / j) * j

0.2055161333j = sin (41.29661624)

Step 3:  Divide both sides by 0.2055161333 to find j (aka KL):

(0.2055161333j = sin (41.29661624) / 0.2055161333

j = 3.211218937

j = 3.2

Thus, KL is approximately 3.2 units.

The approximate length of KL is 3.17 units, which is determined by the law of sines. The correct answer is option (D).

In triangle JKL:

∠L = 105°

JK = 4.7 units

JL = 2.7 units

To find the length of KL using the law of sines, we can use the following formula:

sin(A) / a = sin(B) / b = sin(C) / c

Here, A, B, and C are the angles of the triangle, and a, b, and c are the respective sides opposite those angles.

Let's find the length of KL (let's call it x).

We know that:

sin(A) = sin(∠J) = JL / x

sin(B) = sin(∠K) = JK / x

Since the angles in a triangle add up to 180°, we can find ∠J using:

∠J = 180° - ∠K - ∠L

∠J = 180° - ∠K - 105°

∠J = 75°

Now, we can set up the equation using the law of sines:

sin(75°) / JL = sin(105°) / JK

Now, plug in the given values:

sin(75°) / 2.7 = sin(105°) / 4.7

Let's solve for x:

x = JL * sin(105°) / (sin(75°) / JK)

x = 2.7 * sin(105°) / (sin(75°) / 4.7)

x ≈ 3.17 units

Thus, the approximate length of KL is 3.17 units.

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What is the approximate length of KL? Use the law of sines to find the answer.

A. 1.8 units

B. 2.0 units

C. 3.2 units

D. 3.7 units

The given quadrilaterals, 1 and 2,  are parallelograms because the pair of opposite sides are parallel and the other pairs are congruent.

3. According to Theorem 7.9, quadrilateral ABCD is a parallelogram.

4. According to Theorem 7.12, quadrilateral PQRS is a parallelogram.

3. Quadrilateral ABCD with vertices A(0,0), B(7,1), C(5,6), D(-2,5), and Theorem 7.9:

Theorem 7.9 states that if the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Using the distance formula, we can calculate the lengths of the sides of quadrilateral ABCD:

AB = √((7 - 0)² + (1 - 0)²) = √50

BC = √((5 - 7)² + (6 - 1)²) = √29

CD = √((-2 - 5)² + (5 - 6)²) =√50

DA = √((0 - (-2))² + (0 - 5)²) = √29

We can see that AB = CD and BC = DA, indicating that the opposite sides are congruent.

Quadrilateral PQRS with vertices P(-2,0), Q(3,1), R(4,4), S(-1,3), and Theorem 7.12:

Theorem 7.12 states that if both pairs of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.

Using the slope formula, we can calculate the slopes of the sides of quadrilateral PQRS:

Slope of PQ = (1 - 0) / (3 - (-2)) = 1/5

Slope of RS = (4 - 3) / (4 - (-1)) = 1/5

Slope of QR = (4 - 1) / (4 - 3) = 3

Slope of SP = (3 - 0) / (-1 - (-2)) = 3

The lengths of opposite sides can be calculated using the distance formula:

PQ = √((3 - (-2))² + (1 - 0)²) = √(25 + 1) = √26

RS = √((4 - 4)² + (4 - 1)²) = √(9) = 3

QR = √((4 - 3)² + (4 - 1)²) = √(1 + 9) = √10

SP = √((-1 - (-2))² + (3 - 0)²) = √(1 + 9) = √10

We can see that PQ = RS and QR = SP, indicate that the opposite sides are parallel and congruent.

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Answer:1

Step-by-step explanation:

a) Either 3 or 4 questions did Mike answer correctly.

b) Either 7 or 8 questions did Sheila answer correctly.

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

a) Let mike did x correct

then, incorrect will be (10- x)

The equation is:

Now, 5x + (10 - x) (-3) = 0

=> 5x - 30 + 3x = 0

=> 8x = 30

=> x = 30/8

=> x > 3 and x < 4

b) Let Sheila did y correct

then, incorrect = (10 - y)

Now, 5y + (10 - y) (-3) = 32

=> 5y - 30 + 3y = 32

=> 8y = 62

=> y > 7 and y< 8

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The given question is incomplete, complete question is:

In a school test consisting of 10 questions, 5 points are awarded for a correct answer but 3 points are deducted for an incorrect answer.

A blank answer scores (). Mike scored a total of () and he did not leave all of the answers blank. (a) How many questions did Mike answer correctly? _ _ _ _ _ _ _ _ Sheila scored a total of 32. (b) How many questions did Sheila answer correctly?

Answer:

6 of x and 5 of y

Step-by-step explanation:

x = number of closets of the first type

y = number of closets of the second type

1200 = 100x + 120y

100 = 10x + 8y

10x = 100 - 8y

10x(100 - 8y) + 120y = 1200

1000 - 80y + 120y = 1200

40y = 200

y = 5

100 = 10x + 8×5 = 10x + 40

60 = 10x

x = 6

20x + 24y = max

20×6 + 24×5 = 120 + 120 = 240