At a hockey game, a vender sold a combined total of 192 sodas and hot dogs. The number of sodas sold was two times the number of hot dogs sold. Find the
number of sodas and the number of hot dogs sold.

Answer:

The point estimate that should be used in constructing the confidence interval is 3.5.

The 95% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students, in inches, is (2.25, 4.75).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

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.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

American students:

Sample of 12, mean height of 68.4 inches with a standard deviation of 1.64 inches. This means that:

[tex]\mu_A = 68.4[/tex]

[tex]s_A = \frac{1.64}{\sqrt{12}} = 0.4743[/tex]

Non-American students:

Sample of 17, mean height of 64.9 inches with a standard deviation of 1.75 inches. This means that:

[tex]\mu_N = 64.9[/tex]

[tex]s_N = \frac{1.75}{\sqrt{17}} = 0.4244[/tex]

Distribution of the difference:

[tex]\mu = \mu_A - \mu_N = 68.4 - 64.9 = 3.5[/tex]

[tex]s = \sqrt{s_A^2+s_N^2} = \sqrt{0.4743^2 + 0.4244^2} = 0.6365[/tex]

The point estimate that should be used in constructing the confidence interval is 3.5.

Confidence interval:

[tex]\mu \pm zs[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].  

The lower bound of the interval is:

[tex]\mu - zs = 3.5 - 1.96*0.6365 = 2.25[/tex]

The upper bound of the interval is:

[tex]\mu + zs = 3.5 + 1.96*0.6365 = 4.75[/tex]

The 95% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students, in inches, is (2.25, 4.75).

9514 1404 393

Answer:

  1/3

Step-by-step explanation:

The scale factor is the ratio of image lengths to original lengths.

  B'C' = 1 unit

  BC = 3 units

The scale factor is B'C'/BC = 1/3.

_____

Additional comment

The center of dilation in this figure is 3 units below D' on the same vertical line. (It is 1 unit off the bottom of the grid shown.)

The missing side length is 10 unit.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

We have,

Perpendicular = 6

Base = 8

Using Pythagoras theorem

c² = P² + B²

c² = 6² + 8²

c²= 36 + 64

c² = 100

c= 10 unit.

Thus, the missing length is 10 unit.

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Let missing side be x

Using basic proportionality theorem

[tex]\\ \sf\longmapsto \dfrac{45}{35}=\dfrac{x}{56}[/tex]

[tex]\\ \sf\longmapsto \dfrac{9}{7}=\dfrac{x}{56}[/tex]

[tex]\\ \sf\longmapsto 7x=9(56)[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{9(56)}{7}[/tex]

[tex]\\ \sf\longmapsto x=72[/tex]

Answer:

a.. 1/

Step-by-step explanation:

Answer:

For some reason I cannot open the photo you have provided.

Step-by-step explanation:

Please try to re-upload?

Answer:

upper left...

there are zeros at (x)(x+3) (x-2)

Step-by-step explanation:

Answer:

167.6 cm³

Step-by-step explanation:

the volume of a cone :

ground area × height / 3 = pi×r² × height / 3

r = 4 cm

height = 10 cm

pi×4² × 10 / 3 = pi×16×10/3 = pi×160/3 = 167.6 cm³

Answer:

give fufcy UC fugu stuff c

Step-by-step explanation:

zp staff book

9514 1404 393

Answer:

  c. y = (x +2)² -5

Step-by-step explanation:

If you replace the squared term with zero, you are choosing the minimum of the remaining values. (A squared term cannot have a negative value.)

  a) 3

  b) 4

  c) -5 . . . . the graph with the least possible y-value

  d) 0

Answer:

2520

Step-by-step explanation:

210×12=2520

2520three

Answer:

32/166=9/29 if two ratio are equivalent to other

9514 1404 393

Answer:

Step-by-step explanation:

Let x represent the quantity of 15% alcohol required. Then (5-x) is the amount of 10% alcohol needed. The amount of alcohol in the mix is ...

  0.15x +0.10(5-x) = 0.13(5)

  0.05x +0.5 = 0.65 . . . . . . . simplify

  0.05x = 0.15 . . . . . . . . . subtract 0.5

  x = 3 . . . . . . . . . . . . . divide by 0.05

3 gallons of 15% alcohol and 2 gallons of 10% alcohol should be mixed.

Answer:

P moves = 70.73 m

Step-by-step explanation:

Given data

Radius = 38

initial position of P = ( 38,0 )

initial position of center S = ( 14,0)

position of P ( after s moved counterclockwise )

:  x = 14cost + 24cos(7/12t)

  y = 14sint - 24sin(7/12t)

Determine how far P moves before returning to its initial position

attached below  is the solution

P moves = 70.74 m

Answer:

D: y = 2x - 2

Step-by-step explanation:

1. [tex]\frac{16-8}{9-5}[/tex] = 2

2. y = 2x + b

3. Insert the points into the equation: 8 = 10 + b

4. b = -2

5. y = 2x - 2

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

Explanation:

Apply the slope formula

m = (y2-y1)/(x2-x1)

m = (16-8)/(9-5)

m = 8/4

m = 2

Then use this slope, along with another point such as (x,y) = (5,8) to find b

y = mx+b

8 = 2*5+b

8 = 10+b

8-10 = b

-2 = b

b = -2

Or you could use the other point (x,y) = (9,16)

y = mx+b

16 = 2*9+b

16 = 18+b

16-18 = b

-2 = b

b = -2

Either way, we get the same y intercept.

So because m = 2 is the slope and b = -2 is the y intercept, we go from y = mx+b to y = 2x-2

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

To help verify the answer, note how plugging x = 5 leads us to...

y = 2x-2

y = 2*5 - 2

y = 10-2

y = 8

So x = 5 and y = 8 pair up together. This verifies (5,8) is on the line.

Through similar steps, you should find that the input x = 9 leads to the output y = 16. So that would confirm (9,16) is also on the line, and fully confirm the answer.

This is ur answer plz mark brainliest

3/(x ² - 1) = 3/((x - 1) (x + 1)) = a/(x - 1) + b/(x + 1)

==>   3 = a (x + 1) + b (x - 1)

==>   3 = (a + b) x + a - b

==>   a + b = 3 and a - b = 0

==>   a = b

==>   a + b = 2a = 3   ==>   a = 2/3 and b = 2/3

So you have

3/(x ² - 1) = 2/(3(x - 1)) + 2/(3(x + 1))

Answer:

Step-by-step explanation:

x=120°

Answer:

[tex]MSE = 10[/tex]

Step-by-step explanation:

Given

[tex]SSTR = 200[/tex]

[tex]SST = 800[/tex]

Required

Determine MSE

This is calculated as:

[tex]MSE = \frac{1}{ddf} * SSE[/tex]

Where:

[tex]SSE = SST - SSTR[/tex]

[tex]ddf \to[/tex] denominator df

So, we have:

[tex]SSE = 800 - 200[/tex]

[tex]SSE = 600[/tex]

To calculate the df, we have:

[tex]r = 13[/tex] --- observations

[tex]n = 5[/tex] treatments

So:

[tex]ddf = Total\ df - Numerator\ df[/tex]

[tex]Total = n*r-1 = 5*13 -1 = 64[/tex]

[tex]Numerator =n - 1 = 5 - 1 =4[/tex]

[tex]ddf =64-4=60[/tex]

So, we have:

[tex]MSE = \frac{1}{ddf} * SSE[/tex]

[tex]MSE = \frac{1}{60} * 600[/tex]

[tex]MSE = 10[/tex]

Answer:

2.7

Step-by-step explanation:

ratios help

2.5 : 5.8 :: x : 6.2

2.5/5.8 = x/6.2

solve for x :

x = approx.   2.7

Answer:

You can cut the plank down from the size you buy to the

exact size, but you want to waste as little wood as possible.

Answer:

scientists

Step-by-step explanation:

Answer:

The score of a person who did better than 85% of all the test-takers was of 624.44.

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.

One year, the average score on the Math SAT was 500 and the standard deviation was 120.

This means that [tex]\mu = 500, \sigma = 120[/tex]

What was the score of a person who did better than 85% of all the test-takers?

The 85th percentile, which is X when Z has a p-value of 0.85, so X when Z = 1.037.

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

[tex]1.037 = \frac{X - 500}{120}[/tex]

[tex]X - 500 = 1.037*120[/tex]

[tex]X = 624.44[/tex]

The score of a person who did better than 85% of all the test-takers was of 624.44.

Answer:

80 minutes

Step-by-step explanation:

* means multiply

make 1 hour into 60 minutes

3 miles/60 minutes = 4 miles/x minutes

3x = 240

x = 80

Answer:

125

Step-by-step explanation:

To find the common ratio, take the second term and divide by the first term

1000/2000 = 1/2

We multiply each term by 1/2

2000, 1000, 500

To find the next term 500*1/2 = 500/2 = 250

To find the 5th term

250*1/2 = 125

Answer:

(4,0)

Step-by-step explanation:

the dot is on 4 and the line is 0 so answer is 4,0

Answer:

140

Step-by-step explanation:

Suppose,

x drinks were sold for 2$

y drinks were sold for 5$

therefore, x+y = 250....( 1 )

and 2x+5y = 830......( 2 )

multiply equation ( 1 ) with 2,

2x+2y = 500......( 3 )

Subtract equation ( 3) from (2)

3y = 330

or, y = 110

so, x = 140

so, 140 drinks were sold for 2$

140 drinks were sold for $2.

A variable is any letter or symbol that represents a number with an unknown value.

We can define them simply by any alphabet like x or y.

A linear equation is generally of the form Ax + By = C, where the two variables are x and y, while A, B and C are constants.

A constant is a value or number that never changes and it's constantly the same.

We have to choose our variables and put them in the equation such that it holds properly and satisfies all the conditions for the given question.

There are several methods of solving linear equations. we may have the linear equation with two or three or many variables. The methods are:

In the given question first, let's make our variables.

Let, the number of drinks was sold for 2$ is x, and the number of drinks was sold for 5$ is y.

And now we will try to make the linear equation with two variables because we have two variables satisfying the conditions in the question given.

One thing to remember carefully is that we have to have two equations if we have two variables.

The restaurant sold a total of 250 drinks so we can write,

x + y = 250  

The total sales of drinks for the night was $830 so again we can write,

2x + 5y = 830

Now, we have made the two equations, so we will solve them with help of the substitution method.

Let's, take the equation and just find the value of x,

x + y = 250

x = 250 - y

Now, we will substitute the value of x in the other equation,

2×(250 - y) +5y = 830

Multiplying 2 with the term (250 - y),

500 - 2y + 5y = 830

Now, solve for y,

500 +3y = 830

subtracting 500 both sides we get,

500 - 500 + 3y = 830 - 500

3y = 330

Dividing both sides by 3 we get,

(3y) / 3 = 330 / 3

y = 110

Now, again putting the value of y in the equation x + y = 250 we get,

x + 110 = 250

Subtracting 110 both sides we get,

x + 110 - 110 = 250- 110

x = 140

Now, we can conclude that the number of drinks sold for 2$ is 140 and the number of drinks sold for 5$ is 110.

Therefore, 140 drinks were sold for $2.

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Answer: 40

Step-by-step explanation:

You multiple 15X4=60

And now multiple 10x4=40

Answer:

40$

Step-by-step explanation:

There are 60 minutes in an hour so if we break it down:

$10 = 15 minutes

$10 = 15 minutes

$10 = 15 minutes

$10 = 15 minutes

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

Add them together and we get:

$40 = 60 minutes or 1 hour  

Meaning they would make 40$ in 1 hour.

Answer:

C. As x approaches positive infinity, g(x) approaches positive infinity.

Step-by-step explanation:

We are given the following function:

[tex]g(x) = \frac{|x-3|}{2} - 7[/tex]

End behavior:

Limit of g(x) as x goes to negative and positive infinity.

Negative infinity:

[tex]\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} \frac{|x-3|}{2} - 7 = \frac{|-\infty-3|}{2} - 7 = |-\infty| = \infty[/tex]

Positive infinity:

[tex]\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} \frac{|x-3|}{2} - 7 = \frac{|\infty-3|}{2} - 7 = |\infty| = \infty[/tex]

So in both cases, it approaches positive infinity, and so the correct option is c.