An engineer believes that there is a linear relationship between the thickness of an air filter and the amount of particulate matter that gets through the filter; that is, less pollution should get through thicker filters. The engineer tests many filters of different thickness and fits a linear model. If a linear model is appropriate, what should be apparent in the residual plot

Answer:

22b+24

Step-by-step explanation:

If a box lunch costs b and a bag of chips is $2 extra then we would have:

box lunch = b dollars

box lunch with bag of chips = b + 2 dollars

Now, we need to find the expression for the cost of 12 lunches with chips and 10 lunches without chips, this would be:

12 lunches with chips = 12 (b + 2)

10 lunches without chips = 10b

Let's sum up and simplify these two expressions:

[tex]12(b+2)+10b\\12b+24+10b\\22b+24[/tex]

Thus, the cost of 12 lunches with chips and 10 lunches without chips is 22b+24

Answer:

4x - 8

Step-by-step explanation:

k - H(x)

(9x -2) - (5x + 6)

4x -8

Answer:

The length of the side opposite the 60 degree angle 'c' = 4

Step-by-step explanation:

Step(i):-

Given data ∠A = 90° , ∠B = 60° and ∠C = 30°

Given data the length of the side opposite the 30 degree angle is 8

let  'a' = 8

step(ii):-

By using sine rule formula in properties of triangle

[tex]\frac{a}{Sin A} = \frac{b}{Sin B} = \frac{c}{Sin C} = 2 R[/tex]

[tex]\frac{a}{Sin A} = \frac{c}{Sin C}[/tex]

[tex]\frac{8}{Sin 90} = \frac{c}{Sin 30}[/tex]

cross multiplication , we get

[tex]\frac{8 X sin 30}{Sin 90} = c[/tex]

we know that trigonometry formulas

sin 30° = [tex]\frac{1}{2}[/tex]   and sin 90°= 1

C =  8 X 1/2 = 4

conclusion:-

The length of the side opposite the 60 degree angle 'c' = 4

Answer:

a)3145 x 0.01 = 31.45  3145- 31.45 = 3113.55

Compute the sample correlation 3113.55 -? we find the least square pressing at least 15x on the calculator then minus this from 3113.55 to find a better fit and minimum regression.

We add the differences of units then divide by distribution as seen below.

b) unsure.

c) = (see below) just test each number shown unit sold per day / price then x can show the differences in each number from day 1 to day 2.

d) = 16 sold.

Step-by-step explanation:

a) We count the units up and deduct from it from the equation p is recognized as units sold. R1 is cost R2 is total days.

b) The line of best fit is described by the equation ŷ = bX + a, where b is the slope of the line and a is the intercept (i.e., the value of Y when X = 0).

c) r 2= decimal ; the regression equation has accounted for percentage of the total sum of squares. You cna do this one.

d) = 16 sold at $28 each. - Why ? We using 7 day data and prove a how many units can be sold p/d if the price of flash drive is set to $28 each per unit.

Day 1 = 34  /  28  =  1      =    1.21428571429 = 1 no difference day prior.

Day 2 = 336   / 28   = 12  = 12 = difference day prior is 11

Day 3 = 432  / 28  = 15    =  15.4285714286   = 15 difference day prior is 3

Day 4 = 635  / 28 =  23   =  22.6785714286  = 23 difference day prior is 8

Day 5  = 530  /  28 = 19    =  18.9285714286  = 19 difference day prior is minus - 4

Day 6 = 938  / 28  =  34   = 33.5 = 34 difference day prior is 15

Day 7 = 240  / 28  =   9    =   8.57142857143 = 9 difference day prior is minus -25

Total days 7 = Total revenue / price = average units sold

Average units sold total = 1+ 12+15 +23 +19+34+9 = 113 rounded.

Average units sold total = 1.21428571429 + 12 + 15.4285714286

+ 22.6785714286

+18.9285714286

+ 33.5

+ 8.57142857143 =  112.321428572 units sold weekly when priced at $28

To answer D we divide this by 7  to show;

112.321428572/ 7 = 16.0459183674

Daily units sold = 16

Answer:

[tex]\frac{dV}{dt}[/tex]  = 1017.87 in³/min

[tex]\frac{dV}{dt}[/tex] = 17203.35 in³/min

Step-by-step explanation:

given data

radius r of a sphere is increasing at a rate = 3 inches per minute

[tex]\frac{dr}{dt}[/tex]  = 3

solution

we know volume of sphere is V = [tex]\frac{4}{3} \pi r^3[/tex]

so [tex]\frac{dV}{dt} = \frac{4}{3} \pi r^2 \frac{dr}{dt}[/tex]  

and when r = 9

so rate of change of the volume will be

rate of change of the volume [tex]\frac{dV}{dt} = \frac{4}{3} \pi (9)^2 (3)[/tex]

[tex]\frac{dV}{dt}[/tex]  = 1017.87 in³/min

and

when r = 37 inches

so rate of change of the volume will be

rate of change of the volume [tex]\frac{dV}{dt} = \frac{4}{3} \pi (37)^2 (3)[/tex]

[tex]\frac{dV}{dt}[/tex] = 17203.35 in³/min  

Answer:

  cos(20°)

Step-by-step explanation:

The "cofunction" is the function having the same value for the complement of the angle that this function has for the angle.

The cofunction of sine is cosine. The complement of 70° is 90° -70° = 20°.

  sin(70°) = cos(20°)

Answer:

4 pizza recipes

Step-by-step explanation:

It shows 4 Xs after the [tex]\frac{3}{4}[/tex] mark. So there are 4 recipes that use MORE than [tex]\frac{3}{4}[/tex] cups of cheese.

Answer:

4 cups of cheese

Step-by-step explanation:

More than 3/4 are (3+1) = 4 cups of cheese

Mark Wishing the Brainliest because he deserves it :)

Answer:

C.

Step-by-step explanation:

Base area = 9 × 13

= 117 square feet

Now

Volume of pyramid = (1/3)(A)(H)

= (1/3)(117)(30)

= 117 × 10

= 1170 cubic feet

Answer:

A.

Step-by-step explanation:

Density = Mass / Volume

D = 3/0.2

D = 15 kg/m³

Answer:

density=mass/volume

d=3kg/0.2m3

=15kgm-3

Answer:

Step-by-step explanation:

Hello!

The objective is to test if the proportion of "X: gloves fitness, categorized: Fit poorly and Fit well" is the same for two populations of interest, "male firefighters" and "female firefighters"

To do this you have to conduct a Chi-Square test of Homogeneity.

In the null hypothesis you have to state that the proportion of the  categories of the variable are the same for all the populations of interest.

Be

M: the firefighter is male

F: the firefighter is female

Y: represents the category that the gloves "fit poorly"

W: represents the category that the gloves "fit well"

The null hypothesis will be:

H₀: P(Y|M)=P(Y|F)=P(Y)

P(W|M)=P(W|F)=P(W)

H₁: At least one of the statements in the null hypothesis is false.

α: 0.01

To calculate the statistic under the null hypothesis you have to calculate the expected frequencies first:

[tex]E_{ij}= O_{.j}*\frac{O_{i.}}{n}[/tex]

O.j= total of the j-column

Oi.= total of the i-row

n= total of observations

[tex]E_{11}= 547*\frac{152}{586} = 141.88[/tex]

[tex]E_{12}=39*\frac{152}{586}= 10.12[/tex]

[tex]E_{21}= 547*\frac{434}{586} = 405.12[/tex]

[tex]E_{22}= 39*\frac{434}{586} = 28.88[/tex]

[tex]X^2= sum \frac{(O_{ij}-E_{ij})^2}{E_{ij}} ~~~X^2_{(r-1)(c-1)}[/tex]

r= number of rows (in this case 2)

c=number of columns (in this case 2)

[tex]X^2_{H_0}= \frac{(132-141.88)^2}{141.88} +\frac{(20-10.12)^2}{10.12} +\frac{(415-405.12)^2}{405.12} +\frac{(19-28.88)^2}{28.88} = 13.95[/tex]

Using the critical value approach, you have to remember that this test is always one-tailed to the right, meaning that you'll have only one critical value from which the rejection region is defined:

[tex]X^2_{(r-1)(c-1);1-\alpha }= X^2_{1;0.99}= 6.635[/tex]

The decision rule is then:

If [tex]X^2_{H_0}[/tex] ≥ 6.635, reject the null hypothesis.

If [tex]X^2_{H_0}[/tex] < 6.635, do not reject the null hypothesis.

The calculated value is greater than the critical value, the decision is to reject the null hypothesis.

So at a 1% level you can conclude that this test is significant. This means that the proportions of gloves fitness, categorized in "Fit poorly" and "Fit well" are different for the male and female firefighters populations.

I hope this helps!

Answer:

The Chi - Square Test Statistics is  13.98

p-value = 0.0002

CONCLUSION: Since the p-value is less than the level of significance ; (i.e p-value < ∝) we reject the null hypothesis and accept the alternative hypothesis.

Thus; there is a difference in the population proportion of glove fitness for the two genders.

Step-by-step explanation:

From the information given ; the structure of the table can be well represented as follows;

Observed data                  Males                    Females             Total

Gloves fit poorly                132                         20                       152

Gloves fit well                    415                         19                        434

Total                                   547                        39                       586

Expected data                  Males                   Females              Total

Gloves fit poorly

Gloves fit well

Total

The objective of this question is to  use the chi-square test to determine if there is a difference in the population proportion of glove fitness for the two genders.

We call represent the hypothesis as follows:

The null hypothesis: [tex]H_o:[/tex] states that there is no difference  in the population proportion of glove fitness for the two genders.

The alternative hypothesis: [tex]H_a[/tex] states that there is difference  in the population proportion of glove fitness for the two genders.

The expected frequency of a particular cell can be calculated by multiplying the sum of the rows and columns together, then dividing it by the Total sum

For row 1 column 1 (gloves fit poorly (male) ; we have:

[tex]= \dfrac{547*152}{586} =141.884\\[/tex]

For row 2 column 1 (gloves fit well(male) ; we have:

[tex]= \dfrac{547*434}{586} =405.116[/tex]

For row 1 column 2 (gloves fit poorly (female)) ; we have:

[tex]= \dfrac{39*152}{586} =10.116[/tex]

For row 2 column 2 ( gloves fit well ( female ) ; we have:

[tex]= \dfrac{39*434}{586} =28.884[/tex]

Thus; we can have the complete table to now be:

Observed data                  Males                    Females             Total

Gloves fit poorly                132                         20                       152

Gloves fit well                    415                         19                        434

Total                                   547                        39                       586

Expected data                  Males                   Females              Total

Gloves fit poorly                141.884                 10.116                  152

Gloves fit well                    405.116                28.884                 434

Total                                    547                        39                     586

The Chi - Square Test Statistics can be calculated via the formula:

[tex]X^2 = \dfrac{\sum (f_o-f_e)^2}{f_e}[/tex]

where;

[tex]f_o[/tex] = observed data frequency

[tex]f_e[/tex] = expected data frequency

∴

The Chi - Square Test Statistics is as follows:

[tex]=\dfrac{(131-141.884)^2}{141.884} + \dfrac{(20-10.116)^2}{10.116}+ \dfrac{(415-405.116)^2}{405.116}+ \dfrac{(39-28.884)^2}{28.884}[/tex]

= 0.68+9.6+0.2+3.5

= 13.98

We are given the level of significance ∝  to be = 0.01

numbers of rows = 2; number of column = 2

Thus; the degree of freedom = (2-1)(2-1) = 1×1 = 1

Using the Excel Function : [ = CHISQ.DIST.RT²(X²,df)]

p-value = 0.0002

CONCLUSION: Since the p-value is less than the level of significance ; (i.e p-value < ∝) we reject the null hypothesis and accept the alternative hypothesis.

Thus; there is a difference in the population proportion of glove fitness for the two genders.

Answer:

Step-by-step explanation:

At 300 miles per week, Chris drives 300×52 = 15,600 miles per year. His gas cost can be figured as ...

  (5 years)×(miles per year)÷(miles/gallon)×($ per gallon) = $273,000/(miles per gallon)

__

a) old car cost = repair cost + gas cost + insurance cost

  = 5($1200) + $273,000/22 + 5($500) ≈ $20,909 . . . over 5 years

__

b) new car cost = purchase cost + gas cost + insurance cost

  = $20,000 + $273,000/50 +5($900) = $29,960 . . . over 5 years

Answer:

a) [tex]\mathbf{4 + \dfrac{x}{1!}- \dfrac{2x^2}{2!} ...}[/tex]

b)  See Below for proper explanation

Step-by-step explanation:

a) The objective here  is to Use the power series expansions for ex, sin x, cos x, and geometric series to find the first three nonzero terms in the power series expansion of the given function.

The function is [tex]e^x + 3 \ cos \ x[/tex]

The expansion is of  [tex]e^x[/tex] is [tex]e^x = 1 + \dfrac{x}{1!}+ \dfrac{x^2}{2!}+ \dfrac{x^3}{3!} + ...[/tex]

The expansion of cos x is [tex]cos \ x = 1 - \dfrac{x^2}{2!}+ \dfrac{x^4}{4!}- \dfrac{x^6}{6!}+ ...[/tex]

Therefore; [tex]e^x + 3 \ cos \ x = 1 + \dfrac{x}{1!}+ \dfrac{x^2}{2!}+ \dfrac{x^3}{3!} + ... 3[1 - \dfrac{x^2}{2!}+ \dfrac{x^4}{4!}- \dfrac{x^6}{6!}+ ...][/tex]

[tex]e^x + 3 \ cos \ x = 4 + \dfrac{x}{1!}- \dfrac{2x^2}{2!} + \dfrac{x^3}{3!}+ ...[/tex]

Thus, the first three terms of the above series are:

[tex]\mathbf{4 + \dfrac{x}{1!}- \dfrac{2x^2}{2!} ...}[/tex]

b)

The series for [tex]e^x + 3 \ cos \ x[/tex] is [tex]\sum \limits^{\infty}_{x=0} \dfrac{x^x}{n!} + 3 \sum \limits^{\infty}_{x=0} ( -1 )^x \dfrac{x^{2x}}{(2n)!}[/tex]

let consider the series; [tex]\sum \limits^{\infty}_{x=0} \dfrac{x^x}{n!}[/tex]

[tex]|\frac{a_x+1}{a_x}| = | \frac{x^{n+1}}{(n+1)!} * \frac{n!}{x^x}| = |\frac{x}{(n+1)}| \to 0 \ as \ n \to \infty[/tex]

Thus it converges for all value of x

Let also consider the series [tex]\sum \limits^{\infty}_{x=0}(-1)^x\dfrac{x^{2n}}{(2n)!}[/tex]

It also converges for all values of x

Answer:

x - 3y= -14

Step-by-step explanation:

Slope is rise over run

m = (6-5)/(4-1) = 1/3

we write in slope-intercept form:

y = 1/3x + b

solve for b by plugging in either point

i'm going to plug in H

5 = 1/3 + b

b = 14/3

we get our equation

y = 1/3x + 14/3

now re-write it in standard form

-1/3x + y = 14/3

make it pretty

x - 3y = -14

Answer:

36

Step-by-step explanation:

since there are six outcomes for the spinner and six outcomes for the cube,

6 x 6 = 36

Answer: B

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

Well the diagonals bisect each other.

4x = 8

x = 2

Answer:

x = 2

Step-by-step explanation:

5x = 3x+4

2x = 4

x = 2

Answer:

Vector is equal to vector b. For two vectors to be equal, they must have both the magnitude and the directions equal.

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Tuesday : -1/2

Wednesday + 3/4

Thursday : -3/8

Add them together

-1/2 + 3/4- 3/8

Get a common denominator

-4/8 + 6/8 - 3/8

-1/8

The closest integer value to -1/8 is 0

Answer:

350 miles long.

Step-by-step explanation:

First, we analyze the breakdown of the journey

Let the total distance of the journey =x

Therefore:

10% of the total distance of the journey =35 miles

10% of x=35

0.1x=35

Divide both sides by 0.1

x-350 miles

Therefore, the journey was 350 miles long.

Answer:

The journey was 350 miles long

Step-by-step explanation:

The parameters given are;

Distance traveled by Abena alone = 40% and the last half

∴  Distance traveled by Abena alone = 40% + 50% = 90%

Distance Abena traveled with Saralyn = 35 miles = 100% - 90% = 10%

Hence 10% of Abena's journey = 35 miles

The total distance of Abena's journey therefore, is given as follows

10% = 35 miles

Total distance of Abena's journey = 100% of Abena's journey = 10 × 10%

10 × 10% = 10 × 35 miles = 350 miles

The total distance of Abena's journey = 350 miles.

Answer:

81/64

Step-by-step explanation:

(9/8)²=9²/8²=81/64

Answer:one would get 12 one would get 20

Step-by-step explanation:just plug it in to the equation

Answer:

(x, y) → (4/5 x, 4/5 y)

Question:

The answer choices to determine the rule that represent the dilation were not given. Let's consider the following question:

A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated using the origin as the center of dilation. Which rule could represent this dilation?

A) (x, y) → (0.5 − x, 0.5 − y)

B) (x, y) → (x − 7, y − 7)

C) (x, y) → ( 5/4 x, 5/4 y)

D) (x, y) → (4/5 x, 4/5 y)

Step-by-step explanation:

To determine the rule that could represent the dilation, we would multiply each coordinate by a dilation factor (a constant) to create a dilation. Since the dilation would be used to create a smaller polygon, the constant multiplied with the coordinates of x and y would be less than 1.

Let's check the options out.

In option (A), the coordinates is subtracted from the constant (0.5).

In option (B), the constant (7) is subtracted from the coordinates.

In option (C), the coordinates are multiplied by constant (5/4).

But 5/4 = 1.25. This is greater than 1.

In option (D), the coordinates are multiplied by constant (4/5).

4/5 = 0.8

The constant multiplied with the coordinates of x and y is less than 1 in option (D) = (x, y) → (4/5 x, 4/5 y)

4/5 = 0.8

0.8 is less than 1

Answer:

-26

Step-by-step explanation:

2(x-4)=3(x+6)

2x-8=3x+18

2x-2x -8 = 3x-2x +18

-8 =X+18

-8-18=x+18-18

-26 = x

The value of the unknown number is -26.

Given that, twice the difference of a number and 4 is equal to three times the sum of the number and 6.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the unknown number x.

Twice the difference of a number and 4 = 2(x-4)

Three times the sum of the number and 6 = 3(x+6)

So, equation is 2(x-4)=3(x+6)

⇒ 2x-8=3x+18

⇒ 3x-2x=-8-18

⇒ x=-26

Therefore, the value of the unknown number is -26.

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Answer:

2cm

Step-by-step explanation:

h=v/(l)w

h=24/(6)2

h=24/12

h=2cm or 2cm²

Answer:

f(g(x))=12x+1

Step-by-step explanation:

f(g(x)) = -2(-6x+3)+7

f(g(x))= 12x-6+7

f(g(x))=12x+1

Domain: All real numbers

Answer:

0.35 cups/hour

Step-by-step explanation:

To be able to determine the rate at which the water is leaking from the pipe with the information given, you have to divide the number of cups by the number of hours in which they were collected:

12 cups/34 hours= 0.35 cups/hour

According to this, the answer is that the rate at which the water is leaking from the pipe is 0.35 cups/hour.

Answer:

The geometric mean growth rate of sales is 1.4422.

Step-by-step explanation:

We have two sales values, one from 6 years ago and the other from now.

We have to calculate the geometric growth rate of sales.

We have:

[tex]y(-6)=1,000,000\\\\y(0)=9,000,000[/tex]

We can write the relation between these two values as:

[tex]y(0)=y(-6)k^{0-(-6)}\\\\9,000,000=1,000,000k^6\\\\k^6=9\\\\k=9^{1/6}= 1.4422[/tex]

The geometric mean growth rate of sales is 1.4422.

Answer:

The probability that if Sunday is sunny, then Tuesday is also sunny is 0.86.

Step-by-step explanation:

Let us denote the events as follows:

Event 1: a sunny day

Event 2: a rainy day

From the provided data we know that the transition probability matrix is:

                 [tex]\left\begin{array}{ccc}1&\ \ \ \ 2\end{array}\right[/tex]

[tex]\text{P}=\left\begin{array}{c}1&2\end{array}\right[/tex]  [tex]\left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right][/tex]

In this case we need to compute that if Sunday is sunny, what is the probability that Tuesday is also sunny.

This implies that we need to compute the value of P₁₁².

Compute the value of P² as follows:

[tex]P^{2}=P\cdot P[/tex]

     [tex]=\left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right]\cdot \left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right]\\\\=\left[\begin{array}{cc}0.86&0.14\\0.70&0.30\end{array}\right][/tex]

The value of P₁₁² is 0.86.

Thus, the probability that if Sunday is sunny, then Tuesday is also sunny is 0.86.

Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Given that;

Triangle ABC is similar to A"B"C".

Now, If a point A(x, y) is rotated clockwise by 180 degrees, the new point is at A'(y, -x)

Hence, Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.

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