Arionna claims that since there are 3 feet in a yard, there are 9 cubic feet in a cubic yard. Which statement about her claim is true?
a.)Arionna is correct because there are 3 feet across the length of a cubic yard and 3 feet across the depth of a cubic yard. 3 times 3 = 9
b.)Arionna is correct because there are 3 feet in a yard and there are 3 dimensions in a cubic yard: length, depth, and height. 3 times 3 = 9
c.)Arionna is incorrect. There are only 3 cubic feet in a cubic yard because there are 3 feet in a yard, and the proportion will remain constant.
d.) Arionna is incorrect. There are 27 cubic feet in a cubic yard because a cubic yard is a prism with dimensions 3 ft Times 3 ft Times 3 ft. A prism with those dimensions will take 27 cubes to fill it if each cube is a unit cube of 1 ft.

The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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Answer:

Dataset 2

Step-by-step explanation:

The Coefficient of variation is the ratio of the standard deviation and the population mean.

Data Set 1: 2 = 12 and s = = 7

Data Set 2: 2

0.12 and s

= 0.3.

Coefficient of variation = (standard deviation / mean) * 100%

Dataset 1:

Standard deviation = 7 ; mean = 12

Coefficient of variation = (7 / 12 ) * 100% = 0.5833 = 58%

Dataset 2:

Standard deviation = 0.3 ; mean = 0.12

Coefficient of variation = (0.3 / 0.12) * 100% = 2.5 * 100% = 250

Hence dataset 2 varies the most with a greater value of variation Coefficient.

Answer:

0.9938

Step-by-step explanation:

Let mean blood pressure be = x

Pr ( x < 119 ) can be found using ' z value ' = ( x - u ) ÷ ( s / √n ) ; where                x = 119 , u = mean = 117 , n = no. of sample items = 144 , s = standard deviation = 9.6

z = (119 - 117) ÷ (9.6 / 144) = -2 ÷ (9.6 / 12)  = -2 / 0.8 → z = 2.5

Pr (x < 119) = P (z <  2.5)

P = 0.9938

Answer:

its ethier the photo or the beach ball but i dont know which is

Step-by-step explanation:

Answer:A beach ball.

Step-by-step explanation:

The 99% confidence interval for the population proportion p is (0.776, 0.824).

To find the 99% confidence interval for a proportion, we can use the formula:

CI = p^ ± z*(SE)

where p^ is the sample proportion, SE is the standard error, and z is the critical value from the standard normal distribution corresponding to the level of confidence.

For a 99% confidence interval, the critical value z is 2.576.

Substituting the given values into the formula, we have:

CI = 0.80 ± 2.576*(0.03/√200)

Simplifying this expression, we have:

CI = 0.80 ± 0.024

This means that we are 99% confident that the true population proportion falls between 0.776 and 0.824. We can interpret this interval as a range of plausible values for the population proportion, based on the sample data.

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Answer:

\(t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32\)    

The degrees of freedom are given by:

\(df=n-1=10-1=9\)  

The p value for this case is given by:

\(p_v =2*P(t_{(9)}>2.32)=0.0455\)    

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.

Step-by-step explanation:

Information given

data: 202.2 203.4 200.5 202.5 206.3 198.0 203.7 200.8 201.3 199.0

We can calculate the sample mean and deviation with the following formulas:

\(\bar X= \frac{\sum_{i=1}^n X_i}{n}\)

\(\sigma=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}\)

\(\bar X=201.77\) represent the sample mean    

\(s=2.41\) represent the sample standard deviation    

\(n=10\) sample size    

\(\mu_o =200\) represent the value that we want to test    

\(\alpha=0.05\) represent the significance level for the hypothesis test.    

t would represent the statistic

\(p_v\) represent the p value for the test

Hypothesis to test

We want to determine if the true mean is equal to 200, the system of hypothesis are :    

Null hypothesis:\(\mu = 200\)    

Alternative hypothesis:\(\mu = 200\)    

The statistic for this case is given by:

\(t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}\) (1)    

The statistic is given by:

\(t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32\)    

The degrees of freedom are given by:

\(df=n-1=10-1=9\)  

The p value for this case is given by:

\(p_v =2*P(t_{(9)}>2.32)=0.0455\)    

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.

The equations that are parallel to the line 3x - 4y = 7 and pass through the point (-4, -2) can be represented by: \(y + 2 = \frac{3}{4} (x + 4)\)  and  \(3x - 4y = -4\)

We know that the equation can represent the slope-intercept form of a line: y = mx + c, where b is y-intercept and m is the slope

We can represent the line 3x - 4y =7 in the equation of slope-intercept form:   => 3x - 4y = 7  =>  4y = 3x - 7

          => \(y = \frac{3}{4} x - \frac{7}{4}\)

by comparing this, we get slope for equation 3x - 4y = 7 => m = 3/4

Also, Parallel lines have the same slopes so the slope of the parallel line will be m = 3/4

We are given that the line passes through (-4, -2) and with m = 3/4 we can get the point-slope form of the line: y - y₁ = m(x - x₁)

where (-4, -2) = (x₁, y₁)  and m = 3=4

        =>  \(y - (-2) = \frac{3}{4}(x - (-4)\)         =>  \(y + 2 = \frac{3}{4} (x + 4)\)

So,   \(y + 2 = \frac{3}{4} (x + 4)\) is the parallel line

By simplifying this equation, we get :

\(y = \frac{3}{4} (x + 4) -2\)   =>  \(y = \frac{3x +12 -8}{4}\)

\(4y = 3x + 4\)     =>   \(3x - 4y = -4\)

Hence, The equations representing the lines parallel to 3x - 4y = 7 are: \(y + 2 = \frac{3}{4} (x + 4)\) and \(3x - 4y = -4\)

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The probability of ordering meat is 0.7 and the probability of ordering fish is 0.3.

P(+ | M) = 0.8 and P(- | M) = 0.2,

P(+ | F) = 0.95 and   P(- | F)  = 0.05.

P(M and +) = 0.56 and P(M and -) = 0.14,

P(F and +) = 0.285 and P(F and -) = 0.015.

C: the probability that the customer ordered fish is 0.3.

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.

Given The Humber, Room advertises two types of entrée, meat and fish,

70% of all customers order meat, and 30% order fish,

M represents the event of ordering meat, F is the event of ordering fish,

probability of M and F,

p(M) = 70% = 0.7

p(F) = 30% = 0.3

and 80% of those who ordered meat and 95% of those who ordered fish were satisfied,

+ is the event of being satisfied, and − is the event of not being satisfied,

probability of satisfied customers with meat,

p(+) = 80% = 0.8

not satisfied with meat,

p(-) = 1 - 0.8 = 0.2

probability of satisfied customers with fish,

p(+) = 95% = 0.95

not satisfied with fish,

p(-) = 1 - 0.95 = 0.05

B: calculating the joint probabilities,

P (M and +) = P(M ∩ +) = p(M)*p(+)

P (M and +) = 0.7*0.8

P (M and +) = 0.56

P (M and -) = P(M ∩ -) = p(M)*p(-)

P (M and -) = 0.7*0.2 = 0.14

P (F and +) = P(F ∩ +) = p(F)*p(+)

P (F and +) = 0.3*0.95

P (F and +) = 0.285

P (F and -) = P(F ∩ -) = p(F)*p(-)

P (F and -) = 0.3*0.05

P (F and -) = 0.015

C:  Determine the conditional probabilities,

P (+ | M) = P(M ∩ +)/p(M)

substitute the values

P (+ | M) = 0.56/0.7

P (+ | M) = 0.8

P (- | M) = P(M ∩ -) /p(M)

P (- | M) = 0.14/0.7

P (- | M) = 0.2

P (+ | F) = P(F ∩ +)/p(F)

substitute the values

P (+ | F) = 0.285/0.3

P (+ | F) = 0.95

P(- | F) = P(F ∩ -)/p(F)

P(- | F) = 0.015/0.3

P(- | F)  = 0.05

D: If a randomly selected customer was satisfied with his/her meal, what is the probability that the customer ordered fish,

to find P (F | +) = P(F ∩ +)/p(+)

substitute the values

P(F | +) = 0.285/0.95

P (F | +) = 0.3

Hence the probabilities are as followed.

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Answer:

Sum means addition so you add them together. I don't know why there are a bunch of percentage signs but the answer is 49.

Answer:

Step-by-step explanation:

You want the coordinates of the vertices of QRST after it has been translated right 2 units, then reflected across the y-axis. The original coordinates are Q(1, 5), R(3, -1), S(0, 0), T(-2, 3).

The problem statement is written as a composition of the transformations Ry and T(2,0). A composition of functions is generally executed right to left, meaning the translation will be done first, then the reflection.

The numbers in the translation vector are added to the coordinates:

  (x, y) ⇒ (x+2, y+0)

Reflection over the y-axis changes the sign of the x-coordinate:

  (x, y) ⇒ (-x, y)

Then the composition of transformations is ...

  (x, y) ⇒ (-(x+2), y)

  Q(1, 5) ⇒ Q'(-3, 5)

  R(3, -1) ⇒ R'(-5, -1)

  S(0, 0) ⇒ S'(-2, 0)

  T(-2, 3) ⇒ T'(0, 3)

Answer:

they are the same.

Step-by-step explanation:

Answer:

they are equal

Step-by-step explanation:

3/4 is the same thing as 0.75

Answer:

Range:

UCL = 4.73

LCL = 18.08

MEAN :

UCL = 27.115

LCL = 31.219

Step-by-step explanation:

Given the data:

The mean and range of each sample :

Sample __ Thread wear __ xbar __ R

1 ___31 __ 42 ___ 28 ____ 33.67 _14

2___ 26 _ 18 ____35____ 26.33 _17

3___25 __30 ___ 34____29.67 _ 9

4 __ 17 __ 25 ___ 21 _____ 21 ___ 8

5 __ 38 _ 29 ___ 35 _____ 34 __ 9

6 __ 41 __42 ___36 _____39.67_ 6

7 __ 21 __ 17 ___29 _____22.33 _12

8 __ 32 __26___28 ____ 28.67 _ 6

9 __ 41 __ 34 __ 33 ______ 36 __8

10__29___17___30 _____25.33_ 13

11 __26 __ 31 __ 40 _____32.33_ 14

12__23 __ 19 __ 45 _____12.33 __6

13 __17 __ 24 __ 32_____24.33__15

14 __43__ 35___17_____ 31.67 _ 26

15__18 ___25__ 29_____ 24 ___ 11

16__30___42___31 ____34.33__ 12

17__28___36 __ 32____ 32 ____8

18__40 __ 29 __ 31 ____33.33 __ 11

19__18 ___29__ 28____ 25 ____11

20_ 22 __ 34 __ 26 ___ 27.33 __12

Size per sample, sample size, n = 3

Number of samples, k = 20

We calculate the sample mean and range average :

Sample mean, x-- = Σxbar/n = 29.167

Range average, Rbar = ΣR/n = 11.4

The mean control limit :

x-- ± A2Rbar

From the x chart ;

A2 for n = 20 is A2 = 0.180

29.167 ± 0.180(11.40)

LCL = 29.167 - 0.180(11.40) = 27.115

UCL = 29.167 + 0.180(11.40) = 31.219

The Range control limit :

Rbar(1 ± 3(d3/d2))

From the R-chart :

d2 at n = 20 ; d2 = 3.735

d3 at n = 20 ; d3 = 0.729

LCL = 11.40(1 - 3(0.729/3.735)) = 4.725

UCL = 11.40(1 + 3(0.729/3.735)) = 18.075

35 is a reasonable prediction of the number of times he will select 2 yellow socks?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain to occur. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

In probability theory, an event is a set of outcomes or a subset of a sample space. In simpler terms, an event is anything that can happen, or any possible outcome of an experiment or observation. An event can be a single outcome, or it can consist of multiple outcomes.

In the given question,

The theoretical probability of drawing two yellow socks with replacement from a bag containing equal numbers of red, yellow, green, blue, and purple socks is:

P(drawing two yellow socks) = P(yellow) * P(yellow) = (1/5) * (1/5) = 1/25

So, the probability of drawing two yellow socks from the bag in any given trial is 1/25.

To predict the number of times the child will select two yellow socks in 175 trials, we can use the formula for the expected value of a discrete random variable:

E(X) = n * p

where E(X) is the expected number of times the event occurs, n is the number of trials, and p is the probability of the event occurring in a single trial.

In this case, n = 175 and p = 1/25. So,

E(X) = 175 * (1/25) = 7

Therefore, a reasonable prediction of the number of times the child will select two yellow socks in 175 trials is 7. Since this prediction is not one of the answer choices, the closest option is 35, which is more than five times the expected value. However, this is within the range of possible outcomes due to the random nature of the experiment.

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The total number of corn dogs sold is 28 corn dogs and number of hotdogs is 53

Total cost is the overall expense incurred for a particular product, service, or project. It includes both fixed and variable costs, such as materials, labor, and overhead. It is often used in business and economic analysis as a measure of the efficiency and profitability of a particular venture. The total cost of a product or service can also be used to set prices and make pricing decisions.

According to question:-

step1

h = number of hotdogs

c = number of corndogs.

cost of hotdog = $3

corn dog = $1.50

The equation:

3h + 1.50c = 201 (1)

h = 2c - 3 (2)

step2

substitute (2) into (1)

3(2c - 3) + 1.50c = 201

6c - 9 + 1.50c = 201

7.50c - 9 = 201

7.50c = 201 + 9

7.50c = 210

c = 210/7.50

c = 28

Therefore,

h = 2c - 3

= 2(28) - 3

= 56 - 3

= 53

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Answer:

think of the numbers as the grid. zero being the middle and each square being 1 2 3 4 5 6 etc to the right of 0 are your positive, -1 -2 -3 etc move to the left of that line, your other access from zero goes up to positive one positive 2 positive 3 etc, from zero down you would be negative one negative 2 negative 3 etc

Answer:

1) (-7, 8) and (-7, 0) - Undefined Slope.

2) (3, 5) and (-1, 2) - Positive Slope.

3) (2, 4) and (5, 1) - Negative Slope.

4) (6, -3) and (4, -3) - Zero Slope.

1) In the coordinates (-7, 8) and (-7, 0), we can see that the first number in both coordinates (the x point) is -7. If the x values are the same, that means that the line does not change at all horizontally/on the x-axis. The only solution to a line that passes through these points would be a vertical line. Vertical lines always have an undefined slope. To test, use the slope formula with the coordinates. y2 is the y in the second coordinate, y1 is the y from the first coordinate, x1 is the x from the first coordinate, and x2 is the x from the second coordinate.

\(\frac{y2 - y1}{x2 - x1} = slope\)        

\(\frac{0 - 8}{-7 - (-7)} = slope\)   0 - 8 = -8 and -7 - (-7) = -7 + 7 or 0. Any number divided by 0 is undefined.

2) In the coordinates (3, 5) and (-1, 2) there isn't any obvious abnormality in the coordinates that may cause undefined or 0. We can use the slope formula to find if it has a positive or negative slope.

\(\frac{y2 - y1}{x2 - x1} = slope\)        

\(\frac{2 - 5}{-1 - 3} = slope\)   2 - 5 = -3 and -1 - 3 = -4.  \(\frac{-3}{-4}\)  simplifies to 3/4, so the slope is positive.

3) (2, 4) and (5, 1) also don't have any repeating numbers in the coordinates so we can find the slope using the formula.

\(\frac{y2 - y1}{x2 - x1} = slope\)        

\(\frac{1 - 4 }{5-2} = slope\)   1 - 4 = -3 and 5 - 2 = 3   \(\frac{-3}{3}\) = -1, so the slope is negative.

4) (6, -3) and (4, -3) have the same y values in them, -3. If the y value stays constant then that means the line does not move along the y-axis. This means that it must be a straight line through 1 point on the y-axis. It is a horizontal line. The slope of a horizontal line is always 0 because is straight. You can check using the slope formula.

\(\frac{y2 - y1}{x2 - x1} = slope\)        

\(\frac{-3 - (-3) }{4 - 6} = slope\)   -3 - (-3) = -3 + 3 = 0 and 4 - 6 = -2. \(\frac{0}{2}\) = 0. The slope is 0.

Let me know if you have any questions!

Answer:

three boys to 1 girl

Step-by-step explanation:

a

A resemblance While retaining shape, metamorphosis can alter both location and size.

When the sides of two figures are proportionate and the accompanying angles are congruent, the figures are said to be comparable.

Get the two triangles to face in the same direction, or in the same orientation, to check if they resemble one another. You accomplish this by turning one shape so that it is in alignment with the other. A rotation is the name given to such a change.

Similarity refers to two figures that share the same shape but differ in size. A rigid motion and a rescaling make up a similarity transformation. To put it another way, a similarity transformation may change both location and size while maintaining shape.

Let the given points be G(-2, 3), H(4, 3), I(4, 0) and J(1, 0), K(6.-2), L(1, -2).

A resemblance While retaining shape, metamorphosis can alter both location and size.

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Answer:

  not similar

Step-by-step explanation:

You want to know if ∆GHI ~ ∆JKL when they are defined by coordinates G(-2, 3), H(4, 3), I(4, 0) and J(1, 0), K(6.-2), L(1, -2).

Corresponding angles of similar triangles are congruent, and corresponding sides are proportional.

Here, angle G is an acute angle less than 45°, while corresponding angle J is an acute angle greater than 45°. These corresponding angles in the similarity statement are not congruent, so the similarity statement is false.

__

Additional comment

Side ratios in ∆GHI are 3 : 6 : 3√5 = 1 : 2 : √5.

Side ratios in ∆JKL are 2 : 5 : √29.

For comparison purposes, we like to list them shortest to longest.

These ratios are different, so even if the order of the vertices were straightened out, the triangles still would not be similar. If the triangles had the same side length ratios, the vertex order for a proper similarity statement would be ∆GHI ~ ∆KLJ.

The correct answers to the given questions are given below:

CPU time, as opposed to elapsed time, which might include things like waiting for input/output operations or switching to low-power mode.

It is the length of time that a central processing unit was employed to process instructions from a computer program or operating system. The CPU time is expressed in seconds or clock ticks.

Thus, from the given question, the CPU time is measured and the expected value and variance of weekly CPU time are calculated (see image)

c. No, observing the above part, the weekly cost does not exceed $600 because the weekly cost for CPU time E(Y) =480

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Answer:

16

Step-by-step explanation:

5x / -6 = -40 / 3

Cross multiply

5x * 3 = -6 * -40

15x = 240

x = 16

Answer:

The value of x is 16.

Step-by-step explanation:

\(\star{\tt{\underline{\underline{\purple{CONCEPT : -}}}}}\)

Here, we will use the below following steps to find a solution using the transposition method:

\(\star{\tt{\underline{\underline{\pink{SOLUTION : -}}}}}\)

Solve for X.

\(\implies{\sf{\dfrac{5x}{ - 6} = \dfrac{ - 40}{3}}}\)

Enter your answer is the box.

\(\begin{gathered}\qquad{\dashrightarrow{\sf{\dfrac{5x}{ - 6} = \dfrac{ - 40}{3}}}}\\\\\qquad{\dashrightarrow{\sf{5x \times 3 = - 40 \times - 6}}}\\\\\qquad{\dashrightarrow{\sf{15x = 240}}}\\\\\qquad{\dashrightarrow{\sf{x = \dfrac{240}{15}}}}\\\\\qquad{\dashrightarrow{\sf{x = \cancel{\dfrac{240}{15}}}}}\\\\\qquad{\dashrightarrow{\sf{x = 16}}}\\\\\qquad\star{\underline{\boxed{\sf{\red{x = 16}}}}}\end{gathered}\)

Hence, the value of x is 16.

\(\rule{300}{2.5}\)

Answer:

  160 in²

Step-by-step explanation:

The formula for the area of a triangle is ...

  A = 1/2bh . . . . base length b, height h

Here, the triangle has a base length of 32 in, and a height of 10 in. Its area is ...

  A = 1/2(32 in)(10 in) = 160 in²

The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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Answer: \(g(-2)=2a\)

Step-by-step explanation:

\((f \cdot g)(-2)=f(-2)g(-2)\\\\\therefore a \cdot g(-2)=2a^2 \implies g(-2)=2a\)

The function g(-2) from the given functions is 2a.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are f(-2)=a and (f·g)(-2)=2a².

Here, (f·g)(-2)=2a²

f(-2)·g(-2)=2a²

a·g(-2)=2a²

g(-2)=2a²/a

g(-2)=2a

Therefore, the function g(-2) is 2a.

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Answer:

30

Step-by-step explanation:

To calculate the mean, add up all the numbers in the data and divide the sum by the number of numbers in the data.

(18+36+24+36+30+36)/6 = 30.

Answer:

30

Step-by-step explanation:

To find mean, add up all the numbers, then divide by how many numbers there are:

18 + 36 + 24 + 36 + 30 + 36/6

180/6 = 30

Hope this helps :)

The appropriate hypotheses for this test are: H0: There is no difference in the distribution of responses. Ha: There is a difference in the distribution of responses.

The chosen hypotheses are based on the objective of the investigation, which is to determine if there is convincing evidence that the distribution of responses about eating the potato salad differs between employees who are sick and those who are not sick.

The null hypothesis (H0) assumes that there is no difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This means that the proportion of employees who ate the potato salad would be the same in both groups, and any observed difference in the distribution of responses is due to random chance or factors unrelated to being sick or not sick.

On the other hand, the alternative hypothesis (Ha) proposes that there is a difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This suggests that the proportion of employees who ate the potato salad would be significantly different in the two groups, indicating a possible association between consuming the potato salad and getting sick.

By formulating these hypotheses, the investigation aims to evaluate whether the data provides convincing evidence to reject the null hypothesis in favor of the alternative hypothesis, indicating a meaningful relationship between eating the potato salad and falling sick.

Therefore, the correct answer is:

H0: There is no difference in the distribution of responses about eating the potato salad among those who are and are not sick.

Ha: There is a difference in the distribution of responses about eating the potato salad among those who are and are not sick.

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The ratio of losing to the total number of possible outcomes is 99.992:100, or 12499:12500.

In the game of Lucky Lauto, the probability of winning is 0.008%, which means that the probability of losing is 100% - 0.008% = 99.992%. This is the complement of the probability of winning, as the two probabilities must add up to 100%.

The ratio of the number of ways to succeed to the total number of ways that an experiment can happen is given by the probability of success. In this case, the probability of winning is 0.008%, so the ratio of winning to the total number of possible outcomes is 0.008:100, or 1:12500.

Similarly, the ratio of losing to the total number of possible outcomes is 99.992:100, or 12499:12500.

In conclusion, the probability of losing in Lucky Lauto is 99.992%, and the ratio of losing to the total number of possible outcomes is 12499:12500.

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Answer:

The answer is translation :)

Answer:

The value is  \(E(X) = 4 \ days\)

Step-by-step explanation:

From the question we are told that

   The mean is  \(\mu = 36^oC\)

    The standard deviation \(\sigma = 3^oC\)

Generally the probability that in June , the midday  temperature is between  

39°C and 42°C is mathematically represented as

      \(P(39 < X < 42) = P(\frac{39 - 36}{3} < \frac{X - \mu }{\sigma} < (\frac{42 - 36}{3} )\)

\(\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )\)

      \(P(39 < X < 42) = P(1 < Z <2 )\)

=>   \(P(39 < X < 42) = P(Z < 2) - P( Z <1 )\)

From the z table  the area under the normal curve to the left corresponding to  1 and  2  is

     P(Z   < 2)  = 0.97725

and

    P(Z   < 1)  = 0.84134

    \(P(39 < X < 42) = 0.97725 - 0.84134\)

=>  \(P(39 < X < 42) = 0.13591\)

Generally number of days in June would you expect the midday temperature to be between 39°C and 42°C

      \(E(X) = n * P(39 < X 42 )\)

Here n is the number of days in June which is  n = 30

       \(E(X) = 30 * 0.13591\)

=>    \(E(X) = 4 \ days\)

A) The algebraic expression will be 12d + 7 = 91

B) He drives 7 miles per day to work.

For 11 days straight, Ms. Chung drove the same distance every day going to and coming from work.

The distance she drove on Saturday was; 0.9 miles.

The number of miles she drives per day:

84 miles/12

= 7 miles per day

Let the number of miles she travels be day = d

12d + 7 = 91 miles

12d + 7 = 91

12d = 91 - 7

12d = 84

d = 84/12

d = 7 miles per day

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Answer:

The inverse of the function is \(f^{-1}(x) = \sqrt[3]{\frac{x-16}{8}}\)

Step-by-step explanation:

Inverse of a function:

Suppose we have a function y = g(x). To find the inverse, we exchange the values of x and y, and then isolate y.

In this question:

\(y = \frac{x^3}{8} + 16\)

Exchanging x and y:

\(x = \frac{y^3}{8} + 16\)

\(\frac{y^3}{8} = x - 16\)

\(y^3 = \frac{x-16}{8}\)

\(y = \sqrt[3]{\frac{x-16}{8}}\)

The inverse of the function is \(f^{-1}(x) = \sqrt[3]{\frac{x-16}{8}}\)