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

The required  exponential function will be F(x)= [tex]4(0.5)^{x}[/tex]

Hence, Option A is the correct.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

From the assumption graph as shown in attached figure, we can determine that when x = 0  then y = 4.

Also, we can closely observe that the graph represents decay  

exponential function.

The reason is that when the value of x   increases, the graph of the particular function decreases.

But, the rate of decay must be less than 1 for decay exponential function because if it is greater than 1, then it would represent  the exponential growth function.  

Hence, the option B and D should be completely ruled out as these values represent the exponential growth.  

And from graph, it is clear that when  x = 0 then y = 4

The exponential function will be F(x)= [tex]4(0.5)^{x}[/tex]

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Answer:

14 units

Step-by-step explanation:

The perimeter of a figure is the sum of the lengths of all the sides.

Here, we know that ABCD is a rectangle, so by definition, AB = CD and AD = BC. We also are given that AB = 3y + 3 and BC = 2y, which means that:

AB = CD = 3y + 3

AD = BC = 2y

Adding up all the side lengths and setting that equal to the perimeter, which is 76 units, we get the expression:

AB + CD + AD + BC = 76

(3y + 3) + (3y + 3) + 2y + 2y = 76

10y + 6 = 76

10y = 70

y = 7

We want to know the length of AD, which is written as 2y. Substitute 7 in for y:

AD = 2y = 2 * 7 = 14

The answer is thus 14 units.

~ an aesthetics lover

Answer:

14

Step-by-step explanation:

The perimeter of a rectangle is found by

P = 2 (l+w)

P = 2( 3y+3+2y)

Combine like terms

P = 2(5y+3)

We know the perimeter is 76

76 = 2(5y+3)

Divide each side by 2

76/2 = 2/2(5y+3)

38 = 5y+3

Subtract 3 from each side

38-3 = 5y+3-3

35 = 5y

Divide each side by 5

35/5 = 5y/5

7 =y

We want the length of AD = BC = 2y

AD = 2y=2*y = 14

Answer:

D

Step-by-step explanation:

It would be a cone with a radius of 4 units rotating around y-axis.

Answer:

see below

Step-by-step explanation:

i is the imaginary number and it represents the square root of -1

Step-by-step explanation:

9 + 1/6 + 2 1/12

9 + 2.25

11.25

Answer:

When x is 2, y is 16

Step-by-step explanation:

If y is 48 and x is 6, then y is 8 when x is 1.

Because of this, when x is 2, y will be 16.

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Explanation:

We will discuss the probability of any given Compound event under two broad heading. Exclusivity and Dependence.

Two or more events are mutually exclusive if they cannot occur at the same time.

In mutually excusive events,

[tex]P(A \cap B)=0[/tex]

The probability of two mutually exclusive events is given as:

P(A or B)=P(A)+P(B)

If however the two events can occur at the same time, they are mutually inclusive and: [tex]P(A \cap B)\neq 0[/tex].

For mutually inclusive events A and B,

[tex]P(A or B)=P(A)+P(B)-P(A \cap B [/tex].

Two events are independent if the outcome of one does not affect the outcome of the other.

For two independent events, the probability of A and B,

[tex]P(A \cap B)=P(A) \times P(B)[/tex].

Two events are not independent if the outcome of one affect the outcome of the other.

For two dependent events, if A is dependent of B, we say that the probability of A given B,

[tex]P(A|B)=\dfrac{P(A) \cap P(B)}{P(B)}[/tex].

Answer:

A:

Step-by-step explanation:

Using tangent-secant theorem

AE²=(EC)(ED)

12²=(8)(8+x+10)

144=8(x+18)

144=8x+144

8x = 144-144

8x = 0

So

x = 0

Now

ED = 8+x+10

ED = 8+0+10

ED = 18

Answer:

3 apples / 4 people

3/4

to check divide fractions

Multiply reciprocal

3/1 x 4/1

3/1 / 1/4 = 3/4

3/4 x 4 = 12/4 = 3 apples

3/4 is the answer

Hope this helps

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

h(t) =|t +2| + 3

Let t=6

h(6) =|6 +2| + 3

       = |8| +3

        =8+3

         = 11

Answer:

40%

Step-by-step explanation:

To find the answer to this, you first can find out what percentage of students did wear spirit shirts. To do this you can divide 135 by 225 to give you 0.6. To convert the decimal into a percentage you can simply multiply by 100, giving you 60%. Then to find the percentage of students that did not wear spirit shirts, you can subtract 60 from 100, giving you 40%.

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:

3:12

Step-by-step explanation:

Answer:

1:3

Step-by-step explanation:

Think 4:12 as a fraction for a moment, it would be 4/12. Now completely simplify 4/12, you get 1/3. Now put 1/3 as a ratio, it would be 1:3.

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Answer:

[tex]51[/tex]

Step-by-step explanation:

[tex]\frac{25.5}{0.5}[/tex]

[tex]\frac{255}{5}[/tex]

[tex]=51[/tex]

Answer:

C

Step-by-step explanation:

It closely resembles to a sphere.

Answer:

[tex]13t^2[/tex] feet higher the stone will travel on the other plant than on Earth.

Step-by-step explanation:

Initial velocity of the stone thrown vertically = 79 ft/s

It is given that:

Height attained on a different planet with time [tex]t[/tex]:

[tex]s_p = 79t -3t^2[/tex]

Height attained on Earth with time [tex]t[/tex]:

[tex]s_e = 79t -16t^2[/tex]

If we have a look at the values of [tex]s_p\text{ and }s_e[/tex], it can be clearly seen that the part [tex]79t[/tex] is common in both of them and some values are subtracted from it.

The values subtracted are [tex]3t^2\text{ and } 16t^2[/tex] respectively.

[tex]t^2[/tex] can never be negative because it is time value.

So, coefficient of [tex]t^2[/tex] will decide which is larger value that is subtracted from the common part i.e. [tex]79t[/tex].

Clearly, [tex]3t^2\text{ and } 16t^2[/tex] have [tex]16t^2[/tex] are the larger value, hence [tex]s_e < s_p[/tex].

So, difference between the height obtained:

[tex]s_p - s_e = 79t - 3t^2 - (79t - 16t^2)\\\Rightarrow 79t -3t^2 - 79t + 16t^2\\\Rightarrow 13t^2[/tex]

So, [tex]13t^2[/tex] feet higher the stone will travel on the other plant than on Earth.

[tex]1. \: (x - y) {2} \\ = {x}^{2} - 2xy + {y}^{2} \\ 2. \: (a + b) ^{2} \\ = {a}^{2} + 2ab + {b}^{2} \\ 3. \: (2x + 3y) ^{2} \\ = {(2x)}^{2} + 2.2x.3y + (3y) ^{2} \\ = {4x}^{2} + 12xy + {9y}^{2} \\ 4.(3x - 2y) ^{2} \\ = (3x) ^{2} - 2.3x.2y + (2y) ^{2} \\ = {9x}^{2} - 12xy + {4y}^{2} \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]

Answer:

a) x^2−2xy+y^2

b) a^2 -ab+b^2

c)4x^2+12xy+9y^2

d)9x^2 -12xy+4y^2

Step-by-step explanation:

a) x^2−2xy+y^2

b) a^2 -ab+b^2

c)4x^2+12xy+9y^2

d)9x^2 -12xy+4y^2

We rewrite (x-y)^2 as (x-y) (x-y) to show and always see + sign at start for question a ) and question b)

a) x*x+x(−y)−yx−y(−y) = x^2−2xy+y^2

b) a^2 becomes a^2 -ab as a^2 -ab+b^2

c) As shown in notes attached and this will help you most.

d) the reasons we keep +4y is because -2y becomes -2y-2y and creates a plus.

Answer:

[tex] \bar x = 40, s =10[/tex]

And from these values we can estimate the sample variance like this:

[tex] s^2 = 10^2 =100[/tex]

And we can also estimate the coeffcient of variation given by:

[tex] \hat{CV} =\frac{s}{\bar x}[/tex]

And replacing we got:

[tex] \hat{CV} = \frac{10}{40}= 0.25[/tex]

And this coefficient is useful in order to see the variability in terms of the mean for this case since is lower than 1 we can conclude that this variation around the mean is low.

Step-by-step explanation:

For this case we have the following info given:

[tex] \bar x = 40, s =10[/tex]

And from these values we can estimate the sample variance like this:

[tex] s^2 = 10^2 =100[/tex]

And we can also estimate the coeffcient of variation given by:

[tex] \hat{CV} =\frac{s}{\bar x}[/tex]

And replacing we got:

[tex] \hat{CV} = \frac{10}{40}= 0.25[/tex]

And this coefficient is useful in order to see the variability in terms of the mean for this case since is lower than 1 we can conclude that this variation around the mean is low.

Answer:

21 and 10.5 respectively

Step-by-step explanation:

Remember circumference of a circle is given as;

C= 2×π×r; r is raduis

r = C / 2×π

=65.98/(2×3.142)= 10.50

D= 2× r = 2× 10.50= 21.0( D represent diameter)

Note π = 3.142 a known constant

Answer:

Step-by-step explanation:

A linear transformation must satisfy the following properties.

- T(0) = 0.

- For vector a,b then T(a+b) = T(a) + T(b).

- For a vector a and a scalar r, it must happen that T(ra) = rT(a)

In this case we have that T(a,b,c) = (a,0,c).

Note that T(0) = T(0,0,0) = (0,0,0) = 0. So, the first property holds.

Let [tex] a=(a_1,a_2,a_3), b=(b_1,b_2,b_3) [/tex]. Then

[tex]T(a+b) = T((a_1+b_1,a_2+b_2,a_3+b_3)) = (a_1+b_1,0,a_3+b_3) = (a_1,0,a_3)+(b_1,0,b_3) = T(a) + T(b)[/tex]

So the second property holds.

Finally, let r be a scalar and let [tex] a=(a_1,a_2,a_3)[/tex]. Then

[tex] T(ra) = T((ra_1,ra_2,ra_3)) = (ra_1,0,ra_3) = r(a_1,0,a_3)= rT(a)[/tex]

So, the three properties hold, and therefore, T is a linear transformation.

It is true that T represents a linear transformation

A linear transformation is such that have the following properties

For the first property, we have:

T(x1,x2,x3) = (x1,0,x3)

The above property becomes

T(0) = T(0,0,0)

T(0) = (0,0,0)

T(0)= 0.

So, we can conclude that the first property of the linear transformation is satisfied

For the second property, we make use of the following:

u = (u1, u2, u3) and b = (v1,v2,v3)

The above property becomes

T(u + v) = T(u1 + v1, u2 + v2, u3 + v3)

Expand

T(u + v) = T(u1 + v1, 0, u3 + v3)

Expand

T(u + v) = (u1,0,u3) + (v1, 0, v3)

Simplify

T(u + v) = T(u) + T(v)

The above means that the second property is also satisfied

Recall that:

u = (u1, u2, u3)

So, we have:

T(ru) = (ru1, ru2, ru3)

Where r is a scalar

Expand

T(ru) = (ru1, 0, ru3)

Further, expand

T(ru) = r(u1, 0, u3)

So, we have:

T(ru) = rT(u)

The above means that, the third property is also satisfied

Hence, T represents a linear transformation

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Answer: At the end, you have $750 remaining in the bank.

Step-by-step explanation:

I guess you want to know how much is left in the bank.

initially

Hand : $1000

Bank: $1000

you withdraw $250 from the bank:

Hand: $1000 + $250 = $1250

Bank: $1000 - $250 = $750

Answer:

lily has a larger ratio

Step-by-step explanation:

Answer:

x<_ 21

Step-by-step explanation:

5(x+27)>_ =6(x+26)

5x +135 >_ 6x +156

5x >_6x +21

-x>_21

x<_21

Here is the full question.

The average finishing time among all high school boys in a particular track event in a certain state is 5 minutes 17 seconds. Times are normally distributed with standard deviation 12 seconds.

A.  The qualifying time in this event for participation in the state meet is to be set so that only the fastest 5% of all runners qualify. Find the qualifying time in seconds (round it to the closest second). (Hint: Convert minutes to seconds.)  

B. In the western region of the state the times of all boys running in this event are normally distributed with standard deviation 12 seconds, but with mean 5 minutes 22 seconds. Find the proportion of boys from this region who qualify to run in this event in the state meet. (Hint: normalcdf)

Answer:

a. x ≅ 337 seconds.

b. P(x > 337 )  = 0.1056

Step-by-step explanation:

A.

Given that ;

Mean [tex]\mu =[/tex] 5 minutes 17 seconds =( (60× 5)+17  ) seconds  = 317 seconds   ( since 60 seconds make 1 minute.

Standard deviation: [tex]\sigma[/tex] = 12 seconds.

Only the fastest 5% of all runners qualify

The objective is to determine the qualifying time in seconds

Let's look for the Z-score of 0.95;

The Z-score is 1.645 from the tables

[tex]x= ( \sigma * z ) + \mu[/tex]

[tex]x = ( 12 * 1.645 ) + 317 \\ \\x = 336.74[/tex]

x ≅ 337 seconds.

B. Given that the standard deviation = 12 seconds

Mean = 5 minutes 22 seconds = (5 × 60 + 22 )seconds = 322 seconds

he objective is  to find P(x > 337 )   i.e the proportion of boys from this region who qualify to run in this event in the state meet.

we are using command normalcdf   (SEE THE ATTACHED FILE BELOW FOR THE COMPUTATION)

we have  P(x > 337 )  = 0.1056

Answer:

6.18% of the class has an exam score of A- or higher.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 80, \sigma = 6.5[/tex]

What percentage of the class has an exam score of A- or higher (defined as at least 90)?

This is 1 subtracted by the pvalue of Z when X = 90. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{90 - 80}{6.5}[/tex]

[tex]Z = 1.54[/tex]

[tex]Z = 1.54[/tex] has a pvalue of 0.9382

1 - 0.9382 = 0.0618

6.18% of the class has an exam score of A- or higher.

Answer:

to cm it's still 200 if you mean to metre 2m

Step-by-step explanation:

Answer:

It would still be 200

Step-by-step explanation:

Answer:

3 sqrt(5) =c

Step-by-step explanation:

We can use the pythagorean theorem

a^2 + b^2 = c^2

3^2 + 6^2 = c^2

9+36 = c^2

45 = c^2

Take the square root of each side

sqrt(45) = sqrt(c^2)

sqrt(9)sqrt(5) = c

3 sqrt(5) =c