In any production process in which one or more workers are engaged in a variety of tasks, the total time spent in production varies as a function of the size of the workpool and the level of output of the various activities. In a large metropolitan department store, it is believed that the number of man-hours worked (y) per day by the clerical staff depends on the number of pieces of mail processed per day (x1) and the number of checks cashed per day (x2). Data collected for n = 20 working days were used to fit the model:
E(y) = Bo + B1x1+ B2x2
A partial printout for the analysis follows: Predicted
OBS x1 x2 Actual value predicted value Residual lower 95%CL Upper 95% CL
1 7781 644 74.707 83.175 -8.468 47.224 119.126
Interpret the 95% prediction interval for y shown on the printout.
A)We are 95% confident that the number of man-hours worked per day falls between 47.224 and 119.12.
B)We are 95% confident that the mean number of man-hours worked per day falls between 47.224 and 119.126 for all days in which 7,781 pieces of mail are processed and 644 checks are cashed
C)We expect to predict number of man-hours worked per day to within an amount between 47.224 and 119.126 of the true value.
D)We are 95% confident that between 47.224 and 119.126 man-hours will be worked during a single day in which 7,781 pieces of mail are processed and 644 checks are cashed.

The remaining amount of the sample after 't' days would be 51. 74g

We have the formula for amount to be;

A = Ao × (1/2)^ t/t^1/2

Where

t1/2 = half -life = 138 days

t = 1

Ao  = 52g

A = Amount after decay

Substitute into formula

A = 52 × (1/2) ^ 1/138

A = 52 ×

[tex] { \frac{1}{2} }^{0.00724} [/tex]

A = 52 × 0. 9950

A= 51. 74 g

Thus, the remaining amount of the sample after 't' days would be 51. 74g

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Answer:

A

Step-by-step explanation:

From left to right of the graph, we can observe that the generally the points are going down. This means that the trend line drawn will have a negative slope.

In the slope-intercept form, which is the form the given equations are in, we have y= mx +c, where m is the slope and c is the y-intercept.

We are only interested in the slope in this case, since no actual values are given. Thus, let's focus on the coefficients of x to determine whether the slope is positive or negative.

Option A: Slope= -⅔ (negative)

Option B: Slope= 3 (positive)

Since we have a negative slope, option A would be the best answer.

The attached image shows 2 graphs. The graph in blue shows the shape of a graph with negative slope, while the graph in red has a positive slope.

The average rate of change of credit card is $ 401.79 /year.

Solution

The difference of credit card debt between the year 2006 and 1992 = 8900 - 3275 = $5625

The difference of years between the year 2006 and 1992 = 2006 - 1992 = 14

average rate of change of credit card debt with respect to time = [tex]\frac{difference of credit card debt}{difference of years}[/tex]

average rate = [tex]\frac{5625}{14}[/tex] = $ 401.79 / year

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Step-by-step explanation:

gallons to quarts have the ratio 1:4.

there are 4 quarts in a gallon (hence the name of quarts by the way).

so, the question is really, which order pair have also a 1:4 ratio between x and y ?

(1, 4)

(2, 8)

(3, 12)

the (4, 1) would represent a 4:1 ratio.

and as you know, 4/1 is different to 1/4.

a ratio is nothing else than a fraction. just the "whole" is different.

the pure fraction 1/4 means that the whole is 4/4, has 4 times 1/4.

a ratio 1:4 (you can also write as 1/4) means that the whole has 5 (1+4) parts.

other than that they are compared and calculated with the same way as normal fractions.

Answer:

Answer

Step-by-step explanation:

(a) B ⊄ A (b) C ⊂ A (c) B ⊄ C (d) ∅ ⊂ B (empty set is an element of any set)

(e) C ⊂ C (reflexitivity).

Answer:

e) B. 45°

f) A. 30°

Step-by-step explanation:

e) sec theta = 1/ cos theta

the value of cos theta is 1/√2 at 45°

so , sec 45° = √2 and theta = 45°

f) cot theta = 1/ tan theta

the value of tan theta is 1/ √3 at 30°

so, cot 30° = √3 , theta = 30°

The answers are :

e) B

f) A

For part (e), convert into terms of cosθ.

For part (f), convert into terms of tanθ.

Answer:

1/3 and -1/2

Step-by-step explanation:

You can use the factoring method to identify the solutions of x

6x^2+x-1

2 numbers have to multiply to 6 and subtract to 1 because x is the same as 1x

So, you get 3x and 2x

since you know that -1x1 is -1 you will get

(3x-1)(2x+1)=0

Now, since (3x-1) and (2x+1) multiply to get 0, if either (3x-1) or (2x+1) is 0 the statement will be valid

3(1/3)-1=0

2(-1/2)+1=0

So, your answers are 1/3 and -1/2

The height is changing by 0.5 each minute

The question implies that we calculate the slope of the table

From the table of values, we have the following points

(0, 150) and (1, 150.5)

The slope is then calculated as:

m = (y2 - y1)/(x2 -x1)

This gives

m = (150.5 - 150)/(1 - 0)

Evaluate

m = 0.5

Hence, the height is changing by 0.5 each minute

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Snow reaches at a 15 inches after 16 hours. and 8 inches melt in next 6 hours.

According to the statement

we have a given that there was 1 inch snow on the ground before the snowstorm starts.

then snow fell at constant rate of 3 inches every 2 hours until the snow level reaches at 12 inch had fallen

It means after that there was 13 inch snow on the ground.

and in 1 hour only 1.5 inches snow increases

and if snow takes 2 hours to increase at 3 inches then

it takes 10 hours to reach at 12 inches.

So, snow falls for 10 hours to increase at 12 inches.

And then the snow falls at constant rate of 1 inch per hour for 2 hours.

It means now snow reaches at a 15 inches after 16 hours.

Then sun melt the snow at a 4 inches per 3 hours and sun came for 6 hours then

it means now the level of snow reduced and came at the 7 inches.

because sun reduced 8 inches snow in 6 hours.

So, this is the data collected by a person.

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Answer + Step-by-step explanation:

2x – y + 1 = 0

We know that the graph of a linear equation is a line.

So ,in order to draw it we need to find two points A and B of the line

Afterward, we join A and B to get the graph.

2x – y + 1 = 0

If x = 0 → y = 1 ⇒ A(0 , 1) lie on the line AB (the graph)

If x = 1 → y = 3 ⇒ B(1 , 3) lie on the line AB

Now ,all we have to do is plotting A and B

on the coordinates plane ,then connecting then with a line.

According to the graph (check the attached image) :

If (h,4) ∈ line AB ⇒ h = 3/2

If (1/2 , k) ∈ line AB ⇒ k = 2

Answer:

the answer is 22

Step-by-step explanation:

12,15,22,37,49

since 22 is in the middle its the median (make sure you put the #'s from least to greatest)

Answer:

22

Step-by-step explanation:

22, 37, 49, 15, 12

First put the data set from least to greatest.

12, 15, 22, 37, 49

The median is the middle number of the data. In this case, the median is 22.

Hope this helps!

Answer:

7

Step-by-step explanation:

this is probably a 45-45-90 triangle if its both legs

Answer:

The first chose is correct

Step-by-step explanation:

You can see in the first picture that graphed both of the triangles and then I followed the directions.  It is very, very helpful if you have tracing paper.  You can trace the original and then translate it three up.  For the 90 rotation, put a small + on the origin of your tracing paper, then move the tracing paper one one turn on the plus sign.  That would be 90 degrees.

Answer:

Step-by-step explanation:

First prime factorize 135,

135 = 5×3×3×3

Now prime factorize 128,

128=2×2×2×2×2×2×2 = 2^7

the highest prime factor of 135 is 5,

Let 5 be x

the highest power of the lowest prime factor of 128 which is the power 2 is 7

Let 7 be y

According to the question x^y = 5^7

Answer:

1 1/2

Step-by-step explanation:

When you are subtracting a negative number is is the same as adding a positive.  So the problem is really 5/8 + 7/8, since the denominators are the same, just add the numerators to get 12/8  divide the top and bottom by 4 to get 3/2 or 1 1/2, if I divide 3 by 2.

Since the height (feet) of the spray of water is given by this equation h(x) = -x² + 10x + 9.5, we can logically deduce that the irrigation system is positioned 9.5 feet above the ground to start.

For any quadratic equation with a parabolic curve, the axis of symmetry is given by:

Xmax = -b/2a

Xmax = -10/2(-1)

Xmax = 5.

Thus, the maximum height on the vertical axis is given by:

h(x) = -x² + 10x + 9.5

h(5) = -(5)² + 10(5) + 9.5

h(5) = -25 + 50 + 9.5

h(5) = 34.5 feet.

Therefore, the spray reaches a maximum height of 84.5 feet at a horizontal distance of 5 feet away from the sprinkler head.

Also, the spray reaches all the way to the ground at about:

Maximum distance = √34.5 + 5

Maximum distance = 10.87 feet.

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Complete Question:

An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(x) = -x² + 10x + 9.5, where x is the number of feet away from the sprinkler head (along the ground) the spray is.

1. The irrigation system is positioned____ feet above the ground to start.

2. The spray reaches a maximum height of ____feet at a horizontal distance of feet away from the sprinkler head.

3. The spray reaches all the way to the ground at about_____ feet away​

Answer:30 degress

3 angles in a triangle equal 180-120=60 60÷2=30

Step-by-step explanation:

Answer:

x = -8, 1.

Step-by-step explanation:

x^2 + 7x - 8 = 0

(x + 8)(x - 1) = 0

x = -8, 1.

Answer:

-8 and 1

Step-by-step explanation:

Quadratic expression.

A quadratic expression is an expression with 2 as the highest power of the unknown.

Solving the question:

[tex]x {}^{2} + 7x - 8 \\ x {}^{2} + 8x - x - 8 \\ x(x + 8) - 1(x + 8) \\ (x - 1)(x + 8) \\ x = 1 \: or \: x = - 8[/tex]

Check each number's prime factorization, then add any factors necessary to make each one a cube.

(a) 3

[tex]3087 = 3^2 \times 7^3 \implies \boxed{3}\times3087 = (3\times7)^3 \implies 9261=21^3[/tex]

(b) 25

[tex]2560 = 2^9\times5^1 \implies \boxed{5^2}\times2560 = \left(2^3\times5\right)^3 \implies 64000 = 40^3[/tex]

Answer:

B. 52= 3.25n

Step-by-step explanation:

Unit price multiplied by quantity equals total. So, each notebook cost $3.25 and she buys 'n' notebooks.

She totally spends $52.

In conclusion, 3.25 (unit price × n [quantity]) = 52.

And that is.. 52 = 3.25n.

<3

Answer:

B

Step-by-step explanation:

Let's think about what does the given info mean.

Because of n notebooks, she spent $52

One notebook is $3.25.

So 3.25n = 52

Take it this way if you don't understand

Let's say I spent 4$ on two (2) pens

What's the value of one pen?

We want to find the value of one pen and then multiply it by 2, to get 4$

So we normally would do 4/2

However, to set up an equation, we would create

v (value of one pen) x 2 (pens) = 4$ (cost)

v = 4$/2 = 2$

1. The average rate of change in a riders height between 1 and 3 seconds -30 ft/s

2. The average rate of change in a riders height between 0 and 5 seconds -24 ft/s

3. Another word for rate of change in this situation is speed

Speed is defined as the rate of change of the distance travelled with time. Mathematically, it can be expressed as:

Speed = distance / time

With the above idea, we can obtain the answers to the question given above.

Rate = Change in height / change in time

Rate = -60 / 2

Rate = -30 ft/s

Rate = Change in height / change in time

Rate = -120 / 5

Rate = -24 ft/s

From the definition of speed given above, we can say that: another word for rate of change is speed

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A, C, D are correct. In this question the options that are correct are

We have first with legs height to be =529 m and 229 m;

second with legs height =529 m and 347 m.

Then tan x = 529/229

tan y = 529/347

We can see that tanx > tany

Hence x> y

We have alternate angles in the question. This makes x=v, y=w

For D

x > y while x = v

This tells us that v>y

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Answer:

acd

Step-by-step explanation:

The number of pounds of 60% protein and 20% protein supplement used is 700 and 700 pounds respectively.

let

x + y = 1400

0.60x + 0.20y = 1400×0.40

0.60x + 0.20y = 560

From (1)

x + y = 1400

x = 1400 - y

Substitute into (2)

0.60x + 0.20y = 560

0.60(1400 - y) + 0.20y = 560

840 - 0.60y + 0.20y = 560

- 0.60y + 0.20y = 560 - 840

-0.40y = -280

y = -280/-0.40

y = 700 pounds

Recall,

x + y = 1400

x + 700 = 1400

x = 1400 - 700

x = 700 pounds

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Using addition or multiplication, Teresa has twice a number of wood as Samuel.  

According to the question,

Teresa needs twice as many feet of wood as Samuel  in order to find the number of pieces of wood Teresa need only if we add the number Teresa has by itself or multiply it by 2.

Hence, we need to do only multiply it by 2

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Solution,

Let P =  ( x, -x + 6) = (x, 6 - x)

We want to solve this

( Distance from P to (0,0) )^2  = (Distance from P to (10, -10) )^2

x^2 + (6 - x)^2  =  [ ( x - 10)^2 + ( 6 - x + 10)^2

x^2 + x^2 - 12x + 36  =   x^2 - 20x + 100  + x^2 - 32x + 256     simplify

-12x + 36  =  -52x + 356

40x =  320

x = 8

And y = -(8) + 6  =  -2

So...P  =  ( 8, -2)

In mathematics, an equation is an equation that expresses two equations by joining them with an equal sign =. Equations in other languages ​​and the word their relatives can have slightly different meanings; for example, in French, an equation is defined as containing one or more variables, but in English, it is an equal sign.

A well-formed expression consisting of two combined equations is an equation, and a variable makes the equation true. The variable for which the equation must be solved is also called the unknown, and the value of the unknown that satisfies the equation is called the solution of the equation. There are two types of equations: identities and constraint equations. The ID applies to all values ​​of the variable. Constraint equations apply only to specific values ​​of variables

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Answer b. The probability that at least 41 of them like to swim is 33%.

Solution:

The probability of an event is always 1 or 100%

The probability of at most 40 of them like to swim is 67% = 0.67

The probability of at most 40 not swimming = 1 - 0.67 = 0.33

Hence the probability of at least 41 people swimming is 33%.

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Answer:53.32

Step-by-step explanation:

$54 retail price

sales tax 8%

$54x8%= 4.32

sales tax is $4.32

$54+$4.32= $58.32

total with tax is $58.32

$58.32-$5= 53.32