The personnel department of a large manufacturing firm selected a random sample of 23 workers. The workers were interviewed and given several tests. On the basis of the test results, the following variables were investigated: X2 = manual dexterity score, X3 = mental aptitude score, and X4 = personnel assessment score. Subsequently, the workers were observed in order to determine the average number of units of work completed (Y) in a given time period for each worker. Regression analysis yielded these results: Y = -212 + 1.90X2 + 2.00X3 + 0.25X4, R2 = .75. (.050) (.060) (.20) What is the correct estimate for the number of units of work completed by a worker with a manual dexterity score of 100, a mental aptitude score of 80 and a personnel assessment score of 10?

Answer:

An expression is a syntactic construct. It must be well-formed: the allowed operators must have the correct number of inputs in the correct places, the characters that make up these inputs must be valid, have a clear order of operations, etc.

Answer:

The Correct answer is variable (s)

Answer:

Step-by-step explanation:

We need to find the number of teenagers in the group, given that the product of their ages is 18,727,200.

To solve this problem, we need to factorize the given number into its prime factors and then determine how many distinct factors there are.

18,727,200 can be factorized as:

18,727,200 = 2^6 × 3^2 × 5^2 × 13^2

To find the number of distinct factors, we add 1 to each exponent and then multiply them together:

(6+1) × (2+1) × (2+1) × (2+1) = 7 × 3 × 3 × 3 = 189

Therefore, there are 189 factors of 18,727,200, which means that there are 189 ways to multiply whole numbers together to get this number.

Since we want to find the number of teenagers in the group, we need to look for combinations of factors that result in whole numbers for the ages. We can start by dividing the total number of factors by 2 (since we are looking for pairs of factors) and then slowly increase the divisor until we find the smallest number that results in a whole number.

189 ÷ 2 = 94.5 (not a whole number)

189 ÷ 3 = 63 (not a whole number)

189 ÷ 4 = 47.25 (not a whole number)

189 ÷ 5 = 37.8 (not a whole number)

189 ÷ 6 = 31.5 (not a whole number)

189 ÷ 7 = 27 (a whole number)

Therefore, there are 27 pairs of factors that result in whole numbers for the ages. Each pair corresponds to a group of teenagers, and since each group has the same number of teenagers, there are 27 teenagers in the group.

The solution to the equation 125x³ - 27 = 0 is (5x−3)(25x ^2 +15x+9)

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculationsolving the equation 125x³ - 27 = 0 by grouping

Rewriting 125x^ 3 −27 as (5x) ^3 −3³

The difference of cubes can be factored using the rule:: a ^3 −b^ 3 =(a−b)(a^ 2 +ab+b^ 2 )

Polynomial 25x^ 2 +15x+9 is not factored since it does not have any rational roots.

Hence, (5x−3)(25x ^2 +15x+9)

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The value of the ratio based on the angle illustrated is 1:12.

From the information given, it should be noted that the angle in a circle is 360°. Therefore, the value of theta will be:

= 360° - 330°

= 30°

The equivalent expression based on the angle will be:

= 30/360

= 1/12

= 1:12

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Answer:

31 ft.

Step-by-step explanation:

so 52.5% leaves 47.5% left. and so you can take 21 * 1.475 (147.5%) and get 30.975. you round to the nearest tenth which goes up to 31 ft.

Answer:

40

Step-by-step explanation:

I got this by working through all the answer choices, this one is most logical :) I also submitted my assignment and got this correct !

stay happy :)

The domain is all real numbers, and the range is (y ≤ -4.855). (option b)

To sketch the graph of a quadratic equation, you can use a graphing calculator, which is a handy tool that can produce a visual representation of the equation. For instance, let's take the quadratic equation y = -0.5x² + 0.7x - 5.1 and sketch its graph using a graphing calculator.

When we enter this equation into the graphing calculator, we can see a U-shaped curve that is symmetric about the vertical line passing through the vertex. The vertex is the point where the parabola changes direction and is given by the formula x = -b/2a, y = f(x), where f(x) is the value of y at the vertex.

Now let's examine the given options and determine their domain and range based on the graph of the quadratic equation.

all real numbers, R: (y ≤ -4.855)

For this option, we can observe that the parabola opens upward, and the vertex is at (0.7, -5.35).

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Answer:

d = 4

Step-by-step explanation:

C = 2*pi r or C = pi * d

Area = pi *r^2= pi (d/2)^2 = pi * d^2  /4

So if they are numerically equal, you get

pi * d = pi * d^2 / 4           Divide both sides by pi

d = d^2 / 4                        Multiply both sides by 4

4*d = d^2                          Divide both sides by d

4 = d

Answer:

The answer is 390 × pi.

Step-by-step explanation:

Big cone:

V = 1/3 x pi x r^2 x h

= 1/3 x 3.14 x 9^2 x 15

= 1272.3 cubic inches

Small cone:

V = 1/3 x pi x r^2 x h

= 1/3 x 3.14 x 3^2 x 5

= 47.1 cubic inches  

1272.3 - 47.1 = 1225.2 cubic inches

1272/3.14 ≈ 390

The answer is 390 × pi.

Answer:

Huh? what do you mean?

Step-by-step explanation:

Answer:

-15

Step-by-step explanation:

5 * -3 = -15

x = -3

5x = 5(-3)

5(-3) = -15

Answer:

8(3+4p)

Step-by-step explanation:

8 goes into 24 and 32, so it can be factored out:

\(24+32p=8(3+4p)\)

Answer:

8(3 + 4p)

Step-by-step explanation:

Factor 24 + 32p

First, factor out the GCF. In this case, the GCF is 8, and we have

8(3 + 4p)

We can't factor anymore so the answer is 8(3 + 4p)

Answer:

1750

Step-by-step explanation:

2000-10-240

Answer: Approximately 0.78388 seconds

==========================================

Explanation:

Plug in t = 0 to find that

h = -16t^2 - 64t + 60

h = -16(0)^2 - 64(0) + 60

h = 60

The starting height is 60 feet.

-----

Now plug in h = 0 and solve for t.

h = -16t^2 - 64t + 60

0 = -16t^2 - 64t + 60

-16t^2 - 64t + 60 = 0

From here use the quadratic formula

\(t = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\t = \frac{-(-64)\pm\sqrt{(-64)^2-4(-16)(60)}}{2(-16)}\\\\t = \frac{64\pm\sqrt{7936}}{-32}\\\\t = \frac{64+\sqrt{7936}}{-32} \ \text{ or } \ t = \frac{64-\sqrt{7936}}{-32}\\\\t \approx -4.78388 \ \text{ or } \ t \approx 0.78388 \\\\\)

We ignore the negative t value as a negative time doesn't make sense.

The only practical answer is roughly t = 0.78388 seconds.

The volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis is 51π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

V = 2π ∫ [a, b] x * h(x) dx

Where:

- V is the volume of the solid

- π represents the mathematical constant pi

- [a, b] is the interval over which we are integrating

- x is the variable representing the x-axis

- h(x) is the height of the cylindrical shell at a given x-value

In this case, we need to solve for x in terms of y to express the equation in terms of y.

Rearranging the given equation:

x = 5 ± √(1 - y)

Since we are only interested in the region in the first quadrant, we take the positive square root:

x = 5 + √(1 - y)

Now we can rewrite the volume formula with respect to y:

V = 2π ∫ [c, d] x * h(y) dy

Where:

- [c, d] is the interval of y-values that correspond to the region in the first quadrant

To determine the interval [c, d], we set the equation equal to zero and solve for y:

1 - (x - 5)² = 0

Expanding and rearranging the equation:

(x - 5)² = 1

x - 5 = ±√1

x = 5 ± 1

Since we are only interested in the region in the first quadrant, we take the value x = 6:

x = 6

Now we can evaluate the integral to find the volume:

V = 2π ∫ [0, 1] x * h(y) dy

Where h(y) represents the height of the cylindrical shell at a given y-value.

Integrating the expression:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * h(y) dy

To find h(y), we need to determine the distance between the y-axis and the curve at a given y-value. Since the curve is symmetric, h(y) is simply the x-coordinate at that point:

h(y) = 5 + √(1 - y)

Substituting this expression back into the integral:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

Now, we can evaluate this integral to find the volume

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

To simplify the integral, let's expand the expression:

V = 2π ∫ [0, 1] (25 + 10√(1 - y) + 1 - y) dy

V = 2π ∫ [0, 1] (26 + 10√(1 - y) - y) dy

Now, let's integrate term by term:

\(V = 2\pi [26y + 10/3 * (1 - y)^\frac{3}{2} - 1/2 * y^2]\)] evaluated from 0 to 1

V = \(2\pi [(26 + 10/3 * (1 - 1)^\frac{3}{2} - 1/2 * 1^2) - (26 * 0 + 10/3 * (1 - 0)^\frac{3}{2} - 1/2 * 0^2)]\)

V = 2π [(26 + 0 - 1/2) - (0 + 10/3 - 0)]

V = 2π (25.5)

V = 51π cubic units

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Answer:

Following are the solution to the given question:

Step-by-step explanation:

Given:

\(\to x^2+y^2=49\)

When

 \(x=0\\\\0^2+y^2=49\\\\y^2=49\\\\y= \pm 7\)

So, order pass \((0,\pm 7)\)

Similarly When  

\(y=0\\\\x^2+0^2=49\\\\x^2=49\\\\x= \pm 7\)

So, order pass \((\pm 7,0)\)  

\(x \ \ \ \ \ \ \ 7 \ \ \ \ \ \ \ -7\ \ \ \ \ \ \ 0 \ \ \ \ \ \ \ 0 \\\\y \ \ \ \ \ \ \ 0 \ \ \ \ \ \ \ 0 \ \ \ \ \ \ \ 7 \ \ \ \ \ \ \ -7 \\\\\)

Answer:

Area of annulus is 40.85cm² to 2d.p

Step-by-step explanation:

Area of shaded part=Area of bigger circle -Area of smaler circle

Area of annulus= πR²- πr²= π(R²-r²)

A=3.142(7²-6²)

A=3.142(49-36)

A=3.142×13

A=40.846cm²

A=40.85cm² to 2d.p

Value of m is -4

Value of x is 5

To solve linear equations, follow the following steps:

Equation 1.

2-6m = -4m+10

6m-4m = 2-10

2m = -8

m = -8/2

m = -4

Value of x is -4

Equation 2.

2.5+1.75 = -3.25+1.5x

1.5x = 4.25+3.25

1.5x = 7.5

x = 7.5/1.5

x = 5

Value of x is 5

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Circumference of a circle is

where r is the radius, and P the value of circunference or perimeter, then replace P and pi to solve r

radius is 3.25 inches

Area

Apply formula of the area of a circle

repalce pi and r to find the area

The rounded value of the area is 33.2 square inches

Answer:

$58.80

Step-by-step explanation:

The subtotal is $56.

56*1.05=$58.80.

The equation that should be used to determine the time at which the height of the projectile reaches 20 ​ft is

t = {60 ± √(3600 - 1280)}/32

Given is that a projectile is launched vertically upward from the ground with an initial velocity of 60 ft per​ sec, then neglecting air​ resistance, its height s​ (in feet) above the ground t seconds after projection is given by S = - 16t² + 60t.

For the height of {S} = 20 ft, we can write the equation as -

S = - 16t² + 60t

- 16t² + 60t = 20

16t² - 60t + 20 = 0

t = {60 ± √(3600 - 1280)}/32

Therefore, the equation that should be used to determine the time at which the height of the projectile reaches 20 ​ft is

t = {60 ± √(3600 - 1280)}/32

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Answer:

7a

Step-by-step explanation:

Answer:

option B

polynomial cannot have negative power

hope it helps

Answer:

3√3v/3x V

Step-by-step explanation:

d/dt[32/3π, sin (tim), 3√3v/3x, V]

The transformation from f(x) to g(x) is (b) a rotation and a translation

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

f(x) = x

g(x) = 1/9x - 2

First f(x) = x is transformed to f'(x) = 1/9x

This transformation is a rotation

Next, f'(x) = 1/9x is transformed to g(x) = 1/9x - 2

This transformation is a translation

This means that the transformation from f(x) to g(x) is a rotation and a translation

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Answer:

128

Step-by-step explanation:

You get this by doing PEMDAS. We start with parenthises and then exponet so we do 4x4 which is 16 now we have 18-16+2 so we go in order and the anwser for the first line is 4 but we have an exponet so 16

now the second line we divide 1 and 4 we get 4 and now we multiply by 1/2 and we get 2. now we have 16/2 that is our anwser and we can put that to a whole number of 128

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The total number of people want in all is 531.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of buses = 9

Number of buses that has 63 people = 5

Number of buses that has 54 people = 4

The total number of people in all the buses.

= 5 x 63 + 4 x 54

= 315 + 216

= 531

Thus,

The total number of people want in all is 531.

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Using a geometric sequence, it is found that the rule for the number of matches played in the nth round is given by:

\(a_n = 64\left(\frac{1}{2}\right)^n\)

The rule makes sense for values of n of at most 6, as in the last round, which is the 6th and final round, 1 game is played.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term.

In this problem, we have that:

Thus, the rule is:

\(a_n = 64\left(\frac{1}{2}\right)^n\)

The last round is the final, in which 1 game is played, hence:

\(1 = 64\left(\frac{1}{2}\right)^n\)

\(\left(\frac{1}{2}\right)^n = \frac{1}{64}\)

\(\left(\frac{1}{2}\right)^n = \left(\frac{1}{2}\right)^6\)

\(n = 6\)

Hence, the rule makes sense for values of n of at most 6, as in the last round, which is the 6th and final round, 1 game is played.

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Answer:

the ordered list is x, x+2, x+4, x+6, x+8, x+10

formula is Tn = 2n - 2