if charlene brewster has times of 8.4, 8.6, 8.3, 8.5, 8.7, and 8.5 and a performance rating of 110%, what is the normal time for this operation? is she faster or slower than normal? [px]

Answer:

a. 0.8 = 0.5 + 0.3

b. 30.9 = 2.7 + 28.2

c. 15.4 = 3.1 + 2.4 + 9.9

d. 17.4 = 15.2 + 1.4 + 0.8

e. 42.5 = 39.2 + 2.5 + 0.8

f. 8 = 4 + 4

g. 35 = 23 + 8 + 4

h. 84 = 53 + 3 + 28

i. 121 = 11 + 17 + 93

j. 35 = 24 + 8 + 3

Among the given lines line a y = 5x - 3, line b x + 5y = 2, and line c -10y - 2x =0, lines a and line b are intersecting, lines a and c are intersecting whereas lines b and c are parallel to each other.

Write the given lines in standard form

Line a -5x + y = -3

Line b x + 5y = 2

Line c -2x - 10y = 0

a1 = -5, b1 = 1, c1 = -3

a2 = 1, b2 = 5, c2 = 2

a3 = -2, b3 = -10, c3 = 0

a1/a2 = -5/1

b1/b2 = 1/5

c1/c2 = -3/2

As we see that

a1/a2 ≠ b1/b2

Hence, lines a and b are intersecting.

a1/a3 = -5/-2

b1/b3 = 1/-10

As we see that

a1/a3 ≠ b1/b3

Hence, lines a and c are intersecting.

a2/a3 = 1/-2

b2/b3 = 5/-10 = 1/-2

c2/c3 = 2/0

As we see that

a2/a3 = b2/b3 ≠ c2/c3

Hence, lines b and c are parallel.

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Answer:

49.5ft³

Step-by-step explanation:

If it is 2 ft more than 3 times as long as it is wide then:

l = 3w + 2

which means:

w = (l-2)/3

and:

d = 1/2((l-2)/3)

Now just substitute in 11 for l

w = (11 - 2)/3

w = 9/3

w = 3

d = 1/2((11-2)/3)

d = 1/2(9/3)

d = 1/2(3)

d = 1.5

So the total volume is:

11 * 3 * 1.5

49.5

2x+32+x = 17

Combine 2x and X to get 3x.

3x+32 = 17

Subtract 32 on both sides.

3x = 17−32

Remains 32 of 17 to obtain −15.

3x = −15

Divide both sides by 3.

x = -15/3

Divide −15 by 3 to get −5.

x = −5

The value of x after solving the given equation 2x + 32 + x = 17, is x = -5, which is the last option.

Given an equation:

2x + 32 + x = 17

It is required to find the value of x after solving or simplifying the equation.

In order to get the value of x, the equation has to be solved in such a way that the terms with the variable have to be placed on one side and the constant terms on the other side.

Consider:

2x + 32 + x = 17

Add x and 2x since they are like terms in variables.

3x + 32 = 17

Subtract 32 from both sides of the equation.

3x = 17 - 32

3x = -15

Divide both sides of the equation by 3.

x = -5

Hence, the value of x is -5.

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Answer:

The average yearly growth o

Explanation:

Given that the tree grew from 18 ft 35 1/2 feet in 3 1/2 years.

The growth within these years is:

35 1/2 - 18

= 35.5 - 18

= 17.5

Now, this averages:

17.5/3.5 (3.5 is the number of years)

= 5

The average is 5 ft per year

Area = 300 ft^2

Formula

Area = length of a side x length of a side

Substitution

300 = length of a side ^2

The length of a side is between 17 and 18

Answer:

The length of the side of the square is approximately [tex]17.32[/tex] feet, which lies between the whole numbers [tex]17[/tex] and [tex]18[/tex].

Step-by-step explanation:

Step 1: Assume your variable

Since all the sides of a square are the same, let's consider the side to be the variable: [tex]x[/tex].

Step 2: Create an equation

The formula for the area of a square is:

[tex]\text{Area}=\text{Side}^{2}[/tex]

We have assumed the side to be [tex]x[/tex], and the area is said to be [tex]300[/tex], so substitute these values into the formula:

[tex]\text{Area}=\text{Side}^{2}\\300=x^{2}[/tex]

Step 3: Solve the equation

Using the formula for the area of a square, we came to find an equation:

[tex]x^{2}=300[/tex]

Now, let's find the value of [tex]x[/tex]:

[tex]x^{2}=300\\\\\text{Square root both sides of the equation:}\\\sqrt{x^{2}}=\sqrt{300}\\\\\text{Simplify:}\\x=\sqrt{300}\\\\\text{Calculate:}\\x\approx 17.32[/tex]

The length of the side of the square is approximately [tex]17.32[/tex] feet.

As we know, this number lies between [tex]17[/tex] and [tex]18[/tex].

The car will need 6 gallons of gasoline to travel 102 miles

Given that the car travels 442 miles on 26 gallons of gasoline.

Because the more the distance, the more the volume of gasoline used, this is a direct proportion.

So, we have:

It will need 6 gallons.

Given:

Type 41 words per min.

Find-:

How many min. take you to type 615 words

Explanation-:

1 min words type = 41

For 615 words,

41 words typed in 1 min.

For 1 words type it take min is:

For 615 words:

For type 615 words take time is 15 min.

Answer:

15 minutes.

Step-by-step explanation:

615 / 41

= 15

Answer:

x = 2.64

Step-by-step explanation:

Do the distributive property first.

0.9(x + 1.4)

0.9(x) + 0.9(1.4)

0.9x + 1.26 - 2.3 + 0.1x = 1.6

Simplify the left side by adding like terms. I'm going rewrite the equation and group the like terms together.

0.9x + 0.1x + 1.26 - 2.3 = 1.6

1x - 1.04 = 1.6

1x is the same as x, so I am going to remove the 1. Solve for x.

x - 1.04 + 1.04 = 1.6 +1.04

x = 2.64

Answer: [tex]x=90[/tex]

Step-by-step explanation:

Using the alternate exterior angles theorem,

[tex]180-x=x\\\\180=2x\\\\x=90[/tex]

Expression represents the probability that a student chooses an art elective and a history elective is equal to (³C₁⁴C₁) / ¹²C₂.

As given in the question,

Number of art electives students = 3

Number of history electives students = 4

Number of computer electives students = 5

Choosing an art electives students = ³C₁

Choosing an history electives students = ⁴C₁

Expression represents the probability that a student chooses an art elective and a history elective

= (³C₁⁴C₁) / ¹²C₂

Therefore, expression represents the probability that a student chooses an art elective and a history elective is equal to (³C₁⁴C₁) / ¹²C₂.

The complete question is:

At a high school, students can choose between three art electives, four history electives, and five computer electives. Each student can choose two electives.

Which expression represents the probability that a student chooses an art elective and a history elective?

a. ⁷C₂ / ¹²C₂

b. ⁷P₂ / ¹²P₂

c. (³C₁⁴C₁) / ¹²C₂

d. (³P₁⁴P₁) / ¹²P₂

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Part B

The most appropriate choice for linear equation will be given by -

Third option is correct

c = 7.36p  is the required equation for total cost of p pounds of meat

The cost is $58.88

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here,

Price of one pound of meat = $7.36

Cost of p pounds of meat = $7.36p

By the problem,

c = 7.36p

This is the required equation for total cost of p pounds of meat

Putting p = 8

c = [tex]7.36 \times 8\\[/tex]

c = $58.88

Third option is correct

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The triangles are similar. The smaller is isosceles, so the 3 of them are as well.

Let's Start by finding the hypotenuse of the smaller one:

a² = 2

Given:

The length of the rectangular room is 6 more than the width.

The area of the room, A = 27 square units.

Required:

We need to find the dimensions of the given rectangular room.

Explanation:

Let w be the width of the rectangle.

6 more than means add 6.

The length of the rectangle, l= w+6.

Consider the area of the rectangle formula.

Substitute A = 27, and l=w+6 in the formula.

Subtract 27 from both sides of the equation.

Take out the common multiple.

The measure is always positive.

Substitute w =3 in the equation l =w+6.

We get l =9 units and w =3 units.

Final answer:

The dimensions of the room are 3 and 9.

Answer:

The answer is 75 degrees

Step-by-step explanation:

Remember that the sum of the three angles of any triangle is 180 degrees.

So, 180=58+47+x

180=105+x

75=x

Step-by-step explanation:

mode = the number appearing the most often in the list of data.

median = the middle number. half of the other numbers are smaller, and the other half is larger.

so, we know one number already : 12 in the middle.

that gives us

_ _ 12 _ _

a good mode is when it has a real majority (e.g. every other number appears only once, but the mode number appears twice).

so, 8 should appear twice.

as 8 is smaller than 12, it can only be on the left side of 12.

that gives us

8 8 12 _ _

note we need 2 numbers larger than 12, but each appearing only once.

so, e.g.

8 8 12 13 14

ANSWER

The boundary line is a solid horizontal line that passes through (0, -3). The half-plane that does not contan the origin is shaded.

(the answer is the second option)

EXPLANATION

The graph is

Answer:

B, D, E

Step-by-step explanation:

2x - 5 = 15

2x = 20

x = 10

B) 2x = 20

x = 10

D) 2x - 20 = 0

2x = 20

x = 10

E)4x - 10 = 30

4x = 40

x = 10

The dimension of the length of the classroom in the drawing is calculated to be 7 ft

The scale of a map represents by how much a map is reduced or increased. Most of the times the map is smaller than what is being represented hence the scale is usually a reduction.

Give that

1 in in drawing represent 7 ft in actual length

If the actual length of your classroom is 49 feet then we solve as follows to get the dimension in the drawing:

1 in = 7 ft

? in = 49 ft

cross multiplying gives

7 * ? = 49 * 1

? = 49 / 7

? = 7 in

Hence, the conclusion is that the unknown dimension in the drawing represented as ? is equal to 7 in.

This implies that 7 in in the drawing represents actual distance of 49 ft and this is a reduction

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Answer:

√105 meters, or about 10.25 meters

Step-by-step explanation:

[tex] {x}^{2} + {4}^{2} = {11}^{2} [/tex]

[tex] {x}^{2} + 16 = 121[/tex]

[tex] {x}^{2} = 105[/tex]

[tex]x = \sqrt{105} = 10.25[/tex]

Answer:

10.246 or sqrt(105)

Step-by-step explanation:

Given,

length of the ladder = 11 m

distance of the foot of the ladder from the base of the wall = 4 m

According to Pythagoras' theorem,

(hypotenuse)^2 = (side1)^2 + (side2)^2

As per the problem,

hypotenuse = 11m

side1 = distance from wall = 4 m

side2 = height reached by the ladder on the wall

that is, (11)^2 = (4)^2 + (side2)^2

              121 = 16 + (side2)^2

               121 - 16 = (side2)^2

                (side2)^2 = 105

                  (side2) = sqrt(105) = 10.246 m

Hence, the ladder can reach up to 10.246 m height on the wall.

The total area of the figure is 298.17 ft².

For the given question;

Let divide the given the figure in three parts;

The dimensions of the rectangle is;

Length = 26 - 9 = 15 ft

Breadth = 9 ft

Area = length x breadth

Area = 15 x 9

Area = 135 ft²

The dimension of the triangle is-

Base = 9 ft

Height = 15 - 7 = 8 cm

Area = (1/2) base x height

Area = (1/2) x 9 x 8

Area = 36 ft²

The dimension of semi circle is -

Radius = 9 ft

Area = πr²/2

Area = 3.14 x 9² / 2

Area = 127.17 ft²

Total area = rectangle +triangle + semicircle

Total area = 135 + 36 + 127.17

Total area = 298.17 ft²

Thus, the total area of the figure is 298.17 ft².

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Answer:

76 square feet of wood.

Explanation:

Bethany is building a storage trunk with the following dimensions:

• Length = 5 ft.

• Height = 4 ft.

• Width = 2 ft.

We are to determine how much wood is needed to make the trunk.

The amount of wood that will be needed to make the truck is the surface area of the trunk. The storage trunk is in the shape of a rectangular prism.

The surface area of a rectangular prism is found using the formula below:

Substitute the given dimensions:

Bethany needs 76 square feet of wood to make the trunk.

Answer:

3 1/3  I am assuming that you cannot by 1/3 of an aubergines, so you would need to buy 4.  if you can buy a partial one then it would be 3 1/3

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] = [tex]\frac{a}{10}[/tex]    Set up a proportion and then cross multiply and solve for a

3a = 10  Divide both sides by 3

a = [tex]\frac{10}{3}[/tex] = 3 1/3

The volume of gasoline in the tank as a function of time can be determined as,

The time taken to fill the tank can be determined as,

Thus, the requried domain is,

The range of the function can be determined as,

Thus, the above expressions gives the required domain and range of the function.

Answer:

[tex]\textsf{Point-slope form}: \quad y-1=\dfrac{1}{5}(x-3)[/tex]

Step-by-step explanation:

Define the given points:

Substitute the defined points into the slope formula to find the slope of the line:

[tex]\implies \textsf{Slope $(m)$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-1}{-7-3}-\dfrac{-2}{-10}=\dfrac{1}{5}[/tex]

Substitute the found slope and one of the points into the point-slope formula:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-1=\dfrac{1}{5}(x-3)[/tex]

Simplify to slope-intercept form, if necessary:

[tex]\implies y-1=\dfrac{1}{5}x-\dfrac{3}{5}[/tex]

[tex]\implies y=\dfrac{1}{5}x+\dfrac{2}{5}[/tex]

The number of DVDs that he can put side-by-side on the shelf is 19.

From the information, Mr Washington is putting his DVDs on a shelf that is 10 2⁄3 inches long and each DVD is 11⁄20 inches wide.

The number of DVDs that can be put will be the division of the numbers that are given. This will be:

= Length of shelf / Width of each DVD

= 10 2/3 ÷ 11/20

= 32/3 ÷ 11/20

= 32/3 × 20/11

= 640 / 33

= 19 13/33

= 19 approximately

He can put 19 DVD.

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Answer:

-9

Step-by-step explanation:

−6 − 3

= −6 + −3

= -9

Answer:

-9!

Step-by-step explanation:

When you add negatives, it becomes more negative. Think of -6 getting 3 smaller.

If Bob only fixes 50 computers, his total loss is $3,750.

The total loss results from the negative difference between the total revenue and the total costs.

The total costs consist of variable and fixed costs.

The result is a loss when the total costs exceed the total revenue.  This result becomes a profit or income when the total revenue exceeds the total costs.

Equipment = $5,000

Premises = $6,000

Advertising = $4,000

Total fixed costs = $15,000

Variable cost per unit = $25

Selling price per unit = $250

Total number of computers fixed = 50

The total variable cost for 50 units = $1,250 (50 x $25)

The total costs (fixed and variable) = $16,250

The sales revenue for 50 units = $12,500 (50 x $250)

Loss = $3,750 ($12,500 - $16,250)

Thus, Bob will incur a total loss of $3,750 if he fixes only 50 computers based on his fixed and variable costs.

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The mean lifetime of a bulb is 520 hours, while the variance of the lifetime is 225. The probability that a light bulb will survive at most 533 hours is 0.86.

Given that,

The lifespan of light bulbs is generally distributed. The mean lifetime of a bulb is 520 hours, while the variance of the lifetime is 225.

We have to calculate the probability that a light bulb will survive at most 533 hours.

We would use the normal distribution formula, which is stated as, because the lifespan of light bulbs is distributed regularly,

z = (x - µ)/σ

Where

x = life of light bulbs.

µ = mean lifetime

σ = standard deviation

From the information given,

µ = 520 hours

Variance = 225

σ = √variance = √225

σ = 15

The probability that a light bulb will last for no more than 560 hours is given by

P(x ≤ 533)

For x = 533

z = (533 - 520)/15 = 0.86

According to the normal distribution table, 0.86 represents the probability for the z score.

Therefore, the probability that a light bulb will survive at most 533 hours is 0.86.

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