Select the linear function that describes the relationship between the domain and
range in the table below.
x fx)
-15
03
1 1

Answer:

2,808

Step-by-step explanation:

since 117 = d then we would just plug that into the equation of s = 24d and get s = 24(117), after that you would just solve.

Answer:

53

Step-by-step explanation:

Answer:

P=80

Step-by-step explanation:

R= 10  

P = R*2 *4

P of a square = 10*2 *4 = 80

Just divide by any fraction of the squares ratio.

ie) if square = 2/3 of the length of the circle then 80 x 2/3 = 53.333...

ie) if square = 3/4 of the length of the diameter of the circle then 80 x 3/4 = 60

As 3/4 pf 10 = 7.5

7.5 * 2  = 15

15* 4 = 60

Howver the square is outside of the circle as described circle inscribed exactly how much if it fits exactly then the length will be same as circles diameter = 10*2 = D;20.

20 *4 = 80. P;80

Etc.

Answer:

q < 11

Step-by-step explanation:

Distribute the -3

23 - q > 12

Add q and subtract 12

q < 11

Step-by-step explanation:

the answer is

q<11

23-q>12

Answer:

B: It takes too much time

Step-by-step explanation:

Once the points have been calculated and then graphed, the solutions to y = 0 can be found. Look for y = 0 and the solutions are -5 and -1. But that takes a lot of time. There must be an easier way, and fortunately, there is.

Answer:

5

Step-by-step explanation:

Since the diagonals of a parallelogram bisect each other, the two halves must be equal. Therefore:

[tex]15-x=2x \\\\15=3x \\\\x=5[/tex]

Hope this helps!

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

CE = EB since E is the midpoint of CB (proven by AD intersecting it).

If CE=EB, then:

[tex]2x=15-x\\[/tex]

Add [tex]x[/tex] to both sides

[tex]3x=15\\[/tex]

Divide both sides by 3

[tex]x=5[/tex]

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:

x = -7.33        OR         x = [tex]\frac{-22}{3}[/tex]

y = 13

Step-by-step explanation:

→You can use the substitution method. First, make y by itself in (-2 + 2y = 24):

-2 + 2y = 24

2y = 26

y = 13

→Then, plug in 13 for y into the other equation:

3x + 2y = 4

3x + 2(13) = 4

3x + 26 = 4

3x = -22

x = -7.33        OR         x = [tex]\frac{-22}{3}[/tex]

Answer:

You can do this two ways

1. Divide 170 into 4 parts and multiply by 3.

170/4=42.5

42.5 x 3 = 127.5 so 127.5 is the answer

2. 3/4=0.75

170 x 0.75 = 127.5

or 170/1 x 3/4 = 510/4 = 127 1/2

127 1/2 = 127.5 because 1 divided by 2 is 0.5__127 + 0.5 = 127.5

Hope this helps

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Answer:

The correct answer is D. The wording of the question is biased to strengthen opposition against a particular candidate. The question wording should be changed to be more neutral.

Step-by-step explanation:

The phrasing and setup of the poll will produce responses that are biased against the candidate. The setup of the poll should be changed to avoid influencing the opinions of the respondents.

Answer:

[tex]7x+1+6x+101=180\\13x=78\\x=6[/tex]

Answer:C

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

Source: Dude trust me

Answer:

p-value (0.0208) is less than alpha = 0.05 reject H0.

Step-by-step explanation:

we have the following data:

sample size = n = 75

x, the number to evaluate is 45

the sample proportion would be: x / n = 45/75

p * = 0.6

Now, the null and alternative hypotheses are:

H0: P = 0.72

Ha: P no 72

two tailed test

statistic tes = z = (p * - p) / [(p * (1-p) / n)] ^ (1/2)

replacing we have:

z = (0.6 - 0.72) / [(0.72 * (1-0.72) / 75)] ^ (1/2)

z = -2.31

p-vaule = 2 * p (z <-2.31)

using z table, we get:

p-vaule = 2 * (0.0104)

p-vaule = 0.0208

Therefore, p-value (0.0208) is less than alpha = 0.05 reject H0.

Answer:

After 121 passes, there will be 11 cups facing up

Step-by-step explanation:

Given that:

Peter initially  lines up 121 cups facing down in a straight line from left to right and consecutively labels them from 1 to 121.

We can have an inequality ; i.e 1 ≤ n ≤  121; if n represents the divisor including n itself for which n  = odd number. Thus at the end of this claim, the cup will be facing up.

On the ith pass, he flips over cups i, 2i, 3i, 4i,.... (By "flip," we mean changing the cup from face down to face up or vice versa.)

For each divisor on the ith pass of n;

[tex]i \ th \ pass \ = \ n \ \to \ p |n[/tex]  since we are dealing with possibility of having an odds number:

Thus; [tex]p =i[/tex] and [tex]i^2 = n[/tex]  where ; n = perfect square.

Thus ; we will realize that between 1 to 121 ; there exist 11 perfect squares. Therefore; as a result of that ; 11 cups will definitely be facing up after 121 passes

Answer:

The correct answer will be "0.400 gm".

Step-by-step explanation:

The give values are:

Needs of hospital, N = 0.100 gm

Time, t = 10 days

Minimum amount of Xenon, N₀ = ?

As we know,

⇒  [tex]N(t)=N_{0} \ e^{-\lambda t}[/tex]

∴  Decay constant, λ = [tex]\frac{ln2}{t_{1/2}}[/tex]

                                λ = [tex]\frac{ln2}{5}[/tex]

On putting values, we get

⇒  [tex]0.100=N_{0} \ e^{-\frac{ln2}{5}}\times 10[/tex]

⇒  [tex]0.1=N_{0} \ e^{-2ln2} = N_{0} \ e^{-ln4}[/tex]

⇒  [tex]0.1=N_{0} \ e^{ln\frac{1}{4}}[/tex]

⇒  [tex]0.1=\frac{N_{0}}{4}[/tex]

⇒  [tex]N_{0}=0.1\times 4[/tex]

⇒  [tex]MX_{e}=0.400 \ gm[/tex]

Answer:

126 in²

Dude just trust me

Answer:

3.75 feet

Step-by-step explanation:

The length of the frame is 3 times the width.

Let the width be x.

The length will be 3x.

Kyle uses 10 feet of wood to make the frame. This means that the perimeter is 10 feet.

The perimeter of a rectangle is:

P = 2(L + W)

=> 10 = 2(3x + x)

=> 10/2 = 4x

5 = 4x

=> x = 5/4 = 1.25 feet

The width is 1.25 feet. The length is therefore:

1.25 * 3 = 3.75 feet

Answer:

Step-by-step explanation:

Let x be the random variable representing the dollar value of unusual activity for a customer in a month. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 250

σ = √variance = √2400 = 48.99

a) the probability of $250 to $294 in unusual activity in a month is expressed as

P(250 ≤ x ≤ 294)

For x = 250,

z = (250 - 250)/48.99 = 0

Looking at the normal distribution table, the probability corresponding to the z score is 0.5

For x = 294

z = (294 - 250)/48.99 = 0.9

Looking at the normal distribution table, the probability corresponding to the z score is 0.8159

Therefore,

P(250 ≤ x ≤ 294) = 0.8159 - 0.5 = 0.3159

b) the probability of more than $294 in unusual activity in a month is expressed as

P(x > 294) = 1 - P(x < 294)

P(x > 294) = 1 - 0.8159 = 0.1841

c) since n = 10, the formula becomes

z = (x - µ)/(σ/n)

z = (294 - 250)/(48.99/√10) = 2.84

Looking at the normal distribution table, the probability is 0.9977

Therefore, the probability that at least one of these customers exceeds $294 in unusual activity in a month is

1 - 0.9977 = 0.0023

Answer:

  (0, 3/2)

Step-by-step explanation:

The equation can be put in the form ...

  x^2 = 4py

where p = 3/2.

In this form, the focus is distance "p" from the vertex in the direction the parabola opens.

The vertex is at (0, 0); the parabola opens upward. So, the focus is 3/2 units above the vertex, at ...

  focus = (0, 3/2) . . . . . matches choice A

Complete question is:

Seventy million pounds of trout are grown in the U.S. every year. Farm-raised trout contain an average of 32 grams of fat per pound, with a standard deviation of 7 grams of fat per pound. A random sample of 34 farm-raised trout is selected. The mean fat content for the sample is 29.7 grams per pound. Find the probability of observing a sample mean of 29.7 grams of fat per pound or less in a random sample of 34 farm-raised trout. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

Answer:

Probability = 0.0277

Step-by-step explanation:

We are given;

Mean: μ = 32

Standard deviation;σ = 7

Random sample number; n = 34

To solve this question, we would use the equation z = (x - μ)/(σ/√n) to find the z value that corresponds to 29.7 grams of fat.

Thus;

z = (29.7 - 32)/(7/√34)

Thus, z = -2.3/1.200490096

z = -1.9159

From the standard z table and confirming with z-calculator, the probability is 0.0277

Thus, the probability to select 34 fish whose average grams of fat per pound is less than 29.7 = 0.0277

Answer:

x = 15, AOB = 15, BOC = 165

Step-by-step explanation:

Assume that this is a straight line

2x - 15 + 11x = 180

Combine like terms

13x - 15 = 180

Add 15 on both sides

13x = 195

Divide 13 on both sides

x = 15

Substitute x for 15 in both equations

2(15) - 15 = 15

11(15) = 165

(For checking purposes, 165 + 15 = 180)

Answer:

432

Step-by-step explanation:

l x w

4x3

4x19

8x24

8x19

432

Answer:

Step-by-step explanation:

a) The probability of a Type I error in a lie detection test would be the probability that the lie detection machine incorrectly detected lie for the truth tellers. This is already given in the problem as 0.07.

Therefore,

[tex]P(Type-I) = 0.07[/tex]

Therefore 0.07 is the required probability here.

b) The probability of a Type II error in a lie detection test would be the probability that the lie detection machine incorrectly detected truth for the the people who are actually liars. This is thus 1 - reliability.

[tex]P(Type-II) = 1 - Reliability = 1- 0.86 = 0.14[/tex]

Therefore 0.14 is the required probability here.

Answer:

a) 0.070

b) 0.14

Step-by-step explanation:

Given that the tests are 86% reliable, i.e a probability of 0.86 a lie would be detected.

Probability of error = 0.070

a) For type I error, we have:

The probability of a type I error in this lie detector is the probability that the test erroneously detects a lie even when the individual is actually telling the truth, i.e

P(type I error) = P(rejecting true null)

= 0.070

b) The probability of a Type II error this lie detectot is the probability that the test erroneously detected truth insteax of lie.

i.e = 1 - reliability

P (Type II error) = P(Failing to reject false Null)

= P(Not detecting a lie)

= 1-0.86

= 0.14

Answer:

[tex]\frac{a^3 b^2}{\frac{1}{a} \frac{1}{b^3}}[/tex]

And simplifying we got:

[tex] a^3 b^2 a b^3[/tex]

[tex] a^3 a b^2 b^3 = a^{3+1} b^{2+3} = a^4 b^5[/tex]

Step-by-step explanation:

We want to simplify the following expression:

[tex] \frac{a^3 b^2}{a^{-1} b^{-3}}[/tex]

And we can rewrite this expression using this property for any number a:

[tex] a^{-1}= \frac{1}{a}[/tex]

And using this property we have:

[tex]\frac{a^3 b^2}{\frac{1}{a} \frac{1}{b^3}}[/tex]

And simplifying we got:

[tex] a^3 b^2 a b^3[/tex]

[tex] a^3 a b^2 b^3 = a^{3+1} b^{2+3} = a^4 b^5[/tex]

Answer:

  (0, ∞)

Step-by-step explanation:

A good place to start is by visualizing what the graph looks like on a number line.

For x > 0, it is an open circle at x=0, and shading to the right extending to infinity.

__

So, the left end of the interval is 0, but 0 is not included in the interval.

The right end of the interval is infinity, but there is no such number, so "infinity" is not included in the interval.

"Not included" means you use round brackets ( ) for the corresponding end of the interval. ("Included" would mean you use square brackets [ ].)

So, the interval 0 < x < ∞ is written in interval notation as ...

  (0, ∞)

Answer:

3¹²

Step-by-step explanation:

Move 3⁻² to the numerator using the negative exponent rule

1/b-n = bⁿ

(3⁵)² ⋅ 3²

Multiply the exponents

3¹⁰ · 3²

Multiply by adding the exponents

3¹⁰⋅ 3²

3¹²

Answer:

A. (Table Attached)

B. (See Step 3)

C. 0.06 (See Step 4)

D. NOT independent (See Step 5)

Step-by-step explanation:

Name the probabilities:

p₁ = 0.02,   p₂ = 0.07,   p₃ = 0.91

q₁ = 1-p₁ = 0.98 ,   q₂ = 1-p₂ = 0.93 ,   q₃ = 0.09

Let X and Y be the number of bits with high and moderate distortion out of three.

A.

The function will follow multinomial distribution:

[tex]f_{XY}(x,y) = P(X=x, Y=y) = \frac{3!}{x!y!(3-x-y)!} (p_1^x)(p_2^y)(p_3^{3-x-y})[/tex]

Substitute the values and make a table.

TABLE IN ATTACHMENT

B.

We calculate marginal distribution by:

[tex]P (X=x)=[/tex] ∑ [tex]P(X=x,Y=y)[/tex]

[tex]fx(x)[/tex] can be found by adding all the probabilities in each row for different value of X

For X=0 , ∑P = 0.94157441

For X=1 , ∑P = 0.057624

For X=2 , ∑P = 0.001176

For X=3 , ∑P =0.000008

The mathematic expectation E is the sum of product of each possibility with its probabiity.

[tex]E(X)=[/tex]∑ [tex]xP(X=x)[/tex]

Find E(X):

[tex]E(X)= (0*0.9415744)+(1*0.057624)+(2*0.001176)+(3*0.000008)[/tex]

[tex]E(X)=0.06[/tex]

Condition probability states:

[tex]P(A|B)=\frac{P(A,B)}{P(B)}[/tex]

It can also be written as:

[tex]f_{Y|X=1}(y)=\frac{f_{XY}(1,y)}{f_x(1)}[/tex]

Where [tex]f_x(1)\\[/tex] = 0.057624

Calculate the quotient:

[tex]Y|_{x=1}[/tex] = 0 ,  [tex]f_{Y|_X=1[/tex] = 0.862245

[tex]Y|_{x=1}[/tex] = 1 ,  [tex]f_{Y|_X=1[/tex] = 0.132653

[tex]Y|_{x=1}[/tex] = 2 ,  [tex]f_{Y|_X=1[/tex] = 0.000510

[tex]Y|_{x=1}[/tex] = 3 ,  [tex]f_{Y|_X=1[/tex] = 0

Find the dependency:

[tex]f_{XY}(y)=f_X(x)f_Y(y)[/tex]

We found that

[tex]f_{Y|_X=1[/tex] = 0.862245

Calculate [tex]f_Y(1)[/tex] from summing the column from the table

[tex]f_Y(1)=0.17428341+0.007644+0.000084\\f_Y(1)=0.18201141[/tex]

Which are not equal.

Conclusion:

X and Y are NOT Independent

Answer:

The diameter of the smallest circular opening through which the box will fit  is 5.7 cm to the nearest tenth

Step-by-step explanation:

The dimensions of the rectangle are :

height: 4 cm

length: 10 cm

breadth: 4 cm

The diameter of the smallest circular opening through which the box will fit will be equals to the diagonal of a face of the rectangular box.

The face we will try to fit in first will determine the diagonal that we will calculate.

Let us try to fit in the right side of the rectangular box. The face we will have at that side is a square of 4 cm by 4 cm which is formed by the height and the width of the box.

We can calculate the diagonal using Pythagoras Theorem:

diagonal = [tex]\sqrt{height^{2}+ breadth^{2}}= \sqrt{4^{2}+4^{2}}=5.657 \approx 5.7cm[/tex] to the nearest tenth