You work at Happy Joe's family restaurant and want to see if customer meal satisfaction and gender are related to one another. You take a sample of customers and ask them if they were satisfied with their meal and note their gender. To determine if Satisfaction and Gender are dependent, what are the appropriate hypotheses

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Answer:

  133 1/3 km/hour

Step-by-step explanation:

Average speed is computed as ...

  average speed = (total distance)/(total time)

  = (80 km +120 km +200 km)/(2/3 + 1 + 1 1/3 hour) = 400 km/(3 hour)

  = 133 1/3 km/hour

Answer:

[tex]\begin{array}{cc}{Class}& {Frequency} & 138 - 202 & 14 & 203 - 267 & 5 & 268 - 332 & 3 & 333 - 397 & 1 & 398 - 462 & 3 \ \end{array}[/tex]

The class with the greatest is 138- 202 and the class with the least relative frequency is 333 - 397

Step-by-step explanation:

Solving (a): The frequency distribution

Given that:

[tex]Lowest = 138[/tex] --- i.e. the lowest class value

[tex]Class = 5[/tex] --- Number of classes

From the given dataset is:

[tex]Highest = 459[/tex]

So, the range is:

[tex]Range = Highest - Lowest[/tex]

[tex]Range = 459 - 138[/tex]

[tex]Range = 321[/tex]

Divide by the number of class (5) to get the class width

[tex]Width = 321 \div 5[/tex]

[tex]Width = 64.2[/tex]

Approximate

[tex]Width = 64[/tex]

So, we have a class width of 64 in each class;

The frequency table is as follows:

[tex]\begin{array}{cc}{Class}& {Frequency} & 138 - 202 & 14 & 203 - 267 & 5 & 268 - 332 & 3 & 333 - 397 & 1 & 398 - 462 & 3 \ \end{array}[/tex]

Solving (b) The relative frequency histogram

First, we calculate the relative frequency by dividing the frequency of each class by the total frequency

So, we have:

[tex]\begin{array}{ccc}{Class}& {Frequency} & {Relative\ Frequency} & 138 - 202 & 14 & 0.53 & 203 - 267 & 5 & 0.19 & 268 - 332 & 3 & 0.12 & 333 - 397 & 1 & 0.04 & 398 - 462 & 3 & 0.12 \ \end{array}[/tex]

See attachment for histogram

The class with the greatest is 138- 202 and the class with the least relative frequency is 333 - 397

Answer:

30 gallons of each brand

Step-by-step explanation:

1 gallon of 60% + 1 gallon of 80% = 2 gallons 70% (60/2 = 30)

Answer:

Step-by-step explanation:

correct me if I am wrong

Answer:

Step-by-step explanation:

Given;

first leg of the right triangle, a = 15.21 cm

second leg of the right triangle, b = 17.34 cm

Angle C = 90 ⁰

The missing parameters;

Use Pythagoras theorem to calculate the missing side "c", which is the hypotenuse

c² = a² + b²

c² = (15.21)²  +  (17.34)²

c² = 532.02

c = √532.02

c = 23.1 cm

The missing angle A is calculated as;

[tex]tan(A) = \frac{a}{b} \\\\tan(A) = \frac{15.21}{17.34} \\\\tan(A) = 0.8772 \\\\A = tan^{-1} (0.8772)\\\\A = 41.26^0[/tex]

The missing angle is calculated as;

B = 90⁰ - A

B = 90⁰ - 41.26⁰

B = 48.74⁰

9514 1404 393

Answer:

Step-by-step explanation:

One way to write the relationship between time, speed, and distance is ...

  time = distance/speed

For the first part of the trip, the time is ...

  t1 = 240/r

For the second part of the trip, the time is ...

  t2 = 72/(r+10)

The total time is 6 hours, so we have ...

  t1 +t2 = 6

  240/r +72/(r+10) = 6

We can simplify this a bit by multiplying by (r)(r+10)/6 to get ...

   40(r+10) +12(r) = r(r+10)

  r² -42r -400 = 0 . . . . . . . . subtract the left side and collect terms

  (r -50)(r +8) = 0 . . . . . . . . factor

  r = 50 . . . . . the positive solution of interest.

The two average speeds were 50 mph and 60 mph.

Answer:

200 kids and 500 adults

Step-by-step explanation:

x+y=700

7x+10y=6,400

(200,500)

kids=200

adults=500

Answer:

The total distance Allie traveled was 0.81 miles.

Step-by-step explanation:

Since Allie rode her bike up a hill at an average speed of 12 feet / second, and she then rode back down the hill at an average speed of 60 feet / second, and the entire trip took her 2 minutes, to determine what is the total distance she traveled, the following calculation must be performed:

12 + 60 = 72

72 x 60 = 4320

1000 feet = 0.189394 miles

4320 feet = 0.8181818 miles

Therefore, the total distance Allie traveled was 0.81 miles.

Answer: D. 38x + 1,450 > 4,000

Step-by-step explanation:

It has to be greater than 4,000 so A makes no sense

The parentheses are in the wrong place completely changing the meaning for B

C disregards the info we have about how she's already typed 1,450 words

The answer has to be D

Answer:

B = 25

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

4(9y - 5) = 10(3y + 17) - 40

Step 2: Solve for y

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{4(9y - 5) = 10(3y + 17) - 40}\\\\\large\textsf{4(9y) + 4(-5) = 10(3y) + 10(17) - 10(40)}\\\\\large\textsf{36y - 20 = 30y + 170 - 40}\\\\\large\textsf{COMBINE the LIKE TERMS}\\\\\large\textsf{36y - 20 = (30 y)+ (170 - 40)}\\\\\large\textsf{36y - 20 = 30y + 130}\\\\\large\textsf{SUBTRACT 30y to BOTH SIDES}\\\\\large\textsf{36y - 20 - 30y = 30y + 130 - 30}}\\\\\large\textsf{Cancel out: 30y - 30y because that gives you 0}\\\\\large\textsf{Keep: 20 - 30y because helps solve for the y-value}[/tex]

[tex]\large\textsf{NEW EQUATION: 6y - 20 = 130}\\\\\large\textsf{ADD 20 to BOTH SIDES}\\\\\large\textsf{6y - 20 + 20 = 130 + 20}\\\\\large\textsf{Cancel out: -20 + 20 because that gives you 0}\\\\\large\textsf{Keep: 130 + 20 because that helps solve for the y-value}\\\\\large\textsf{130 + 20 = \bf 150}\\\\\large\textsf{NEW EQUATION: 6y = 150}\\\\\large\textsf{DIVIDE 6 to BOTH SIDES}\\\\\mathsf{\dfrac{6y}{6}= \dfrac{150}{6}}\\\\\large\textsf{Cancel: }\mathsf{\dfrac{6}{6}\large\textsf{ because that gives you 1}}[/tex]

[tex]\large\textsf{Keep: }\mathsf{\dfrac{150}{6}}\large\textsf{ because it helps solve for the y-value}\\\\\large\textsf{\bf y = }\mathsf{\dfrac{150}{6}}\\\\\large\textsf{OR }\\\\\mathsf{\dfrac{150}{6} }\large\textsf{ = \bf y}\\\\\\\large\textsf{SIMPLIFY ABOVE AND TOU YOU HAVE YOUR Y-VALUE}\uparrow\\\\\\\\\boxed{\boxed{\large\textsf{\huge\textsf{Answer: \bf y = 25} (Option B.)}}}\huge\checkmark\\\\\\\\\large\text{Good luck on your assignment and enjoy your day!}\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]

Answer: 49 cherry tomatoes.

Step-by-step explanation:

7 x

— = — cross multiply and done.

15 105

Answer:

C) 20

Step-by-step explanation:

The absolute value of a number represents the positive distance between the number and zero. Absolute value is therefore always positive.

The distance between -20 and 0 is 20 and therefore the answer is C) 20.

Answer:

20

Step-by-step explanation:

Absolute value = | -20 |

= 20

Option C is correct .

Answer:

0.0668 = 6.68% probability that an individual man’s step length is less than 1.9 feet.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with a mean of 2.5 feet and a standard deviation of 0.4 feet.

This means that [tex]\mu = 2.5, \sigma = 0.4[/tex]

Find the probability that an individual man’s step length is less than 1.9 feet.

This is the p-value of Z when X = 1.9. So

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

[tex]Z = \frac{1.9 - 2.5}{0.4}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a p-value of 0.0668

0.0668 = 6.68% probability that an individual man’s step length is less than 1.9 feet.

Answer:

First term=1

Second term=-x

Third term=[tex]2x^2[/tex]

Fourth term =[tex]-\frac{28}{3!}x^3[/tex]

Step-by-step explanation:

We are given that function

[tex]f(x)=(1+3x)^{-1/3}[/tex]

We have to find the  first four non zero terms of the Maclaurin series for the binomial.

Maclaurin series of function f(x) is given by

[tex]f(x)=f(0)+f'(0)x+\frac{1}{2!}f''(0)x^2+\frac{1}{3!}f'''(0)x^3+....[/tex]

[tex]f(0)=(1+3x)^{\frac{-1}{3}}=1[/tex]

[tex]f'(x)=-\frac{1}{3}(1+3x)^{-\frac{4}{3}}(3)=-(1+3x)^{-\frac{4}{3}}[/tex]

[tex]f'(0)=-1[/tex]

[tex]f''(x)=\frac{4}{3}\times 3 (1+3x)^{-\frac{7}{3}}[/tex]

[tex]f''(0)=4[/tex]

[tex]f'''(x)=-4\times \frac{7}{3}\times 3(1+3x)^{-\frac{10}{3}}[/tex]

[tex]f'''(0)=-28[/tex]

Substitute the values we get

[tex](1+3x)^{-\frac{1}{3}}=1-x+\frac{4}{2!}x^2+\frac{-28}{3!}x^3+...[/tex]

[tex](1+3x)^{-\frac{1}{3}}=1-x+2x^2+\frac{-28}{3!}x^3+...[/tex]

First term=1

Second term=-x

Third term=[tex]2x^2[/tex]

Fourth term =[tex]-\frac{28}{3!}x^3[/tex]

Step-by-step explanation:

true

Answer:

19.634954085

Step-by-step explanation:

Pipe Diameter = Height of the trench

Pipe Height = Width of the trench

V = Pi*r^2*L/ Pi*r^2*h

= 22/7 x (2.5/2)^2 x 4

= 19.634954085

Answer:

125 boxes

Step-by-step explanation:

5*5*5

Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as the vertices of the triangle are not given.

A general explanation is as follows;

To calculate distance between two points, we use:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

Take for instance;

[tex]A = (1,4)[/tex]

[tex]B = (3,-2)[/tex]

Distance AB is:

[tex]AB = \sqrt{(1 - 3)^2 + (4 - -2)^2}[/tex]

[tex]AB = \sqrt{(- 2)^2 + (4 +2)^2}[/tex]

[tex]AB = \sqrt{(- 2)^2 + (6)^2}[/tex]

Evaluate the exponents

[tex]AB = \sqrt{4 + 36}[/tex]

[tex]AB = \sqrt{40}[/tex]

[tex]AB = 6.32[/tex]

Answer:

for edmentum

Step-by-step explanation:

Answer:

NO

Step-by-step explanation:

NO

Given:

The triangle ABC is reflected over the x-axis.

The distance between point A and A’ is 14.

To find:

The distance between the x-axis and A’.

Solution:

If a figure is reflected across the x-axis then the corresponding parts are mirror image of each other about the x-axis.

It means the distance between A and x-axis is same as the distance between x-axis and A'.

The distance between point A and A’ is 14.

Let d be the distance between the x-axis and A’. Then,

[tex]d+d=14[/tex]

[tex]2d=14[/tex]

[tex]d=\dfrac{14}{2}[/tex]

[tex]d=7[/tex]

Therefore, the correct option is 1.

Answer:

G(x)=1/x+15

Step-by-step explanation:

.

==========================================================

Explanation:

The phrasing "no less than" means the same as "at least".

Saying "at least 37" means 37 is the lowest we can go.

If x is the number of disconnected calls, then [tex]x \ge 37[/tex] and we want to find the probability of this happening (the max being 295).

We could use the binomial distribution to find the answer, but that would require adding 295-37+1 = 259 different values which could get tedious. So we could use the normal approximation to make things relatively straight forward.

Assuming this binomial meets the requirements of the normal approximation, then we'd look under the normal curve for the area to the right of 36.5; which is why the answer is choice A.

Why 36.5 and not 37? This has to do with the continuity correction factor when translating from a discrete distribution (binomial) to a continuous one (normal).

If we used 37, then we'd be missing out on the edge case. So we go a bit beyond 37 to capture 36.5 instead. It's like a fail safe to ensure we do account for that endpoint of 37. It's like adding a buffer or padding.

------------

Side notes:

Answer:

0.7994 = 79.94% probability that the proportion of persons with myopia will differ from the population proportion by less than 3%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose 42% of the population has myopia.

This means that [tex]p = 0.42[/tex]

Random sample of size 442 is selected

This means that [tex]n = 442[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.42[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.42*0.58}{442}} = 0.0235[/tex]

What is the probability that the proportion of persons with myopia will differ from the population proportion by less than 3%?

Proportion between 0.42 + 0.03 = 0.45 and 0.42 - 0.03 = 0.39, which is the p-value of Z when X = 0.45 subtracted by the p-value of Z when X = 0.39.

X = 0.45

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.45 - 0.42}{0.0235}[/tex]

[tex]Z = 1.28[/tex]

[tex]Z = 1.28[/tex] has a p-value of 0.8997

X = 0.39

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

[tex]Z = \frac{0.39 - 0.42}{0.0235}[/tex]

[tex]Z = -1.28[/tex]

[tex]Z = -1.28[/tex] has a p-value of 0.1003

0.8997 - 0.1003 = 0.7994

0.7994 = 79.94% probability that the proportion of persons with myopia will differ from the population proportion by less than 3%.

Simon will pay £18 in VAT for using 3000 units of electricity in one year.

The VAT rate for gas and electric is 5%.

Therefore, Simon will pay VAT on his electricity usage.

Let's calculate Simon's annual electricity cost without VAT:

Cost per unit of electricity = 12p

= £0.12

Number of units used in one year = 3000

Electricity cost without VAT = Cost per unit × Number of units

= £0.12 × 3000

= £360

Now, let's calculate the VAT amount:

VAT rate = 5% = 0.05

VAT amount = Electricity cost without VAT × VAT rate

= £360 × 0.05

= £18

Therefore, Simon will pay £18 in VAT for using 3000 units of electricity in one year.

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Answer:

please provide an image.

Answer:

The first mechanic charged $ 85 an hour, and the second mechanic charged $ 55 an hour.

Step-by-step explanation:

Given that two mechanics worked on a car, and the first mechanic worked for 10 hours, and the second mechanic worked for 5 hours, and together they charged a total of $ 1125, to determine what was the rate charged per hour by each mechanic if the sum of the two rates was $ 140 per hour, the following calculation must be performed:

1125/15 = X

75 = X

80 x 10 + 60 x 5 = 800 + 300 = 1100

85 x 10 + 55 x 5 = 850 + 275 = 1125

Therefore, the first mechanic charged $ 85 an hour, and the second mechanic charged $ 55 an hour.

Answer:

So 912$ is 58% of 1584 $

Step-by-step explanation:

Answer:

68

Step-by-step explanation:

I did it on my test

The missing value in the table is 68. The correct answer would be option (B).

A linear relationship is a connection that takes the shape of a straight line on a graph between two distinct variables - x and y. When displaying a linear connection using an equation, the value of y is derived from the value of x, indicating their relationship.

The table shows the relationship between the number of faculty members and the number of students at a local school.

Faculty     Students

1                     17

2                   34

3                   51

4                    ?

The relationship between the number of faculty members and the number of students at the local school is that for every faculty member, there are 17 students.

Therefore, if there are 4 faculty members, we can find the number of students by multiplying 4 by 17, which gives us 68.

Thus, the missing value in the table is B. 68.

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Answer:

Take the picture you uploaded.

Click the rotate 'button' once.

Change the x to y and y to x on the graph. (axis labels)

Done

J (0, -1)

K(-4,-3)

I ( -4,-1)

Answer:

3/8

Step-by-step explanation:

the total number of possible results is 4×4=16.

out of these 16 only the results

1 2

1 3

1 4

2 2

2 3

3 2

are desired results. these are 6.

so the probability of a desired result is 6/16 = 3/8