A school administrator believes that 80% of the students at his large school arrive by bus, 10% drive themselves, and 10% are dropped off by an adult. To investigate this belief, the administrator stands at the school entrance and asks the first 80 students who come through the door how they came to school. He would like to know if the data provide convincing evidence that the distribution of transportation method differs from what he believes it to be. Are the conditions for inference met?

No, the random condition is not met.
No, the 10% condition is not met.
No, the Large Counts condition is not met.
Yes, all of the conditions for inference are met.
Mark this and return

- x + 4x = -20-7

3x = -21

x = -7

good day

Answer:

\(\fbox{3\sqrt{2}}\)\(3\sqrt2\)

Step-by-step explanation:

Step 1:

Let us figure out the measurements of all the angles first. We are given one angle of 45º, and another of 90º. The angles of a triangle must add up to 180º, hence we can use basic addition and subtraction to find the last angle.

\(\angle=180-90-45\\\angle=45\)

Great our angle is 45º! Notice something...?

Step 2:

We now have two 45º angles in our triangle. This means we have an isosceles triangle.

According to BATh (base angle theorem), in an isosceles triangle, the angles opposite the congruent sides are congruent. Thus, y is congruent to the given side of \(3\sqrt2\).

y=\(\fbox{3\sqrt{2}}\)\(3\sqrt2\)

I hope this helps! Let me know if you have any questions :)

The average speed of the second car was 60 miles per hour.

1. Let's calculate the time difference between when the first car started and when the second car caught up. The second car started two hours after the first car, therefore it travelled for five hours (9:00 PM - 4:00 PM).

2. We know that the first car traveled for a longer period than the second car, as it started at 2:00 PM and was overtaken at 9:00 PM. Therefore, we need to find the total distance traveled by the first car during this time.

  Time traveled by the first car = (9:00 PM - 2:00 PM) = 7 hours.

The first car's speed is 40 miles per hour.

Distance travelled by the first automobile = Speed Time = 40 mph per hour 7 hours = 280 miles.

3. Since the second car caught up with the first car, we can conclude that the distance traveled by the second car is equal to the distance traveled by the first car, which is 280 miles.

4. We know that the second automobile drove for 5 hours. 280 miles is the distance travelled by the second automobile. The second automobile travelled for 5 hours.

5. To get the average speed of the second vehicle, divide the distance travelled by the time required: The second car's average speed = Distance Time = 280 miles 5 hours = 56 miles per hour.

As a result, the second car's average speed was 56 miles per hour.

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Answer: 60 cents

Step-by-step explanation: 1 Dime= 10 cents; 10x6= 60.

Answer: 60 cents.

Step-by-step explanation:

One dime is worth 10 cents. Therefore, if you have six of them it's simple repeated addition

10+10+10+10+10+10

or simple multiplication.

10(6)

Which are both the same exact thing.

So six dimes are 60 cents. Hope that helps!!

With the point (150,190), we get a grand total cost of 150 x 2.75 + 190 x 1.95 = $783, which is over our budget of $750.

-> D

Answer:

5f + 4s

Step-by-step explanation:

Third option

You have the following system of equations:

y = 9x - 9

y = 9

In order to solve the previous system of equations, replace y = 9 into the first equation and solve for x:

9 = 9x - 9 add 9 both sides and simplify

9 + 9 = 9x

18 = 9x divide by 9 both sides

18/9 = x

2 = x

x = 2

Hence, the solution to the system is x = 2 and y = 9.

Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6

Answer:

the y intercept is same for both

Step-by-step explanation:

that is the only answer

Answer:

Last 2 choices

Step-by-step explanation:

Points on the graph:

(-2, 4) and (0, -4)

To find b, using the first point

So the equation for the graph is:

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

1. The slope is positive. no, it is -4 for both

2. Lines are same, so answer is no

3. yes

4. yes

Using mathematical operations, we know that Sofia will spend $56 and order 7 additional rolls of sushi (84 pieces).

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).

So, they require at least 100 sushi pieces.

24 pieces of sushi had previously been ordered and paid for by Sofia.

Roll sushi is available.

Each roll = 12 pieces at $8

R = additional rolls that Sofia orders

Additional sushi = Needed sushi - ordered sushi

=100-24

=76 pieces of sushi

A roll contains 12 pieces.

76/12 = 6.33

Rolls must be ordered by Sofia.

She will therefore place 7 additional sushi rolls, each with 12 pieces.

12*7=84 pieces

Remember that they need at least 100 pieces, so there may be more than 100 in total.

84 pieces plus the 24 pieces Sofia has previously ordered.

The total number of pieces will be 108.

Therefore, using mathematical operations, we know that Sofia will spend $56 and order 7 additional rolls of sushi (84 pieces).

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Complete question:
Sofia ordered sushi for a company meeting. They change plans and increase how many of people

will be at the meeting, so they need at least 100 pieces of sushi in total.

Sofia had already ordered and paid for 24 pieces of sushi, so she needs to order additional sushi.

The sushi comes in rolls, and each roll contains 12 pieces and costs $8. How many more sushi Sofia will order and of what amount?

Yes, you can remove a message you've already sent, but there are other options as well. The unsend feature is only compatible with iMessage (iPhone to iPhone).

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The two statements that are true about the company's Market share going from 50 to 65 percent of the total market . The initial market share and multiply by 100, which gives 30 percent. Option B is correct answer.

The two statements that are true about the company's market share going from 50 to 65 percent of the total market are:

The company's market share increased by 30 percent: The difference between the initial market share of 50 percent and the final market share of 65 percent is 15 percentage points. To calculate the percentage increase, we can divide the difference by the initial market share and multiply by 100, which gives (15/50) x 100 = 30 percent.

The company's relative market position improved: With a market share of 65 percent, the company now holds a greater proportion of the total market than before. This means that its relative market position has improved compared to its competitors, who have a smaller share of the market. This could translate into increased bargaining power, profitability, and other benefits for the company.

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a company’s market share went from 50 to 65 percent of the total market. of the following choices, which two statements about the company's market shares are true?
A) 40

B) 30

C) 35

D) 45

A plot that will present the information that will highlight how many trees are in a range of heights, such as 60–64, 65–69, etc. : histogram

In this question, we have been given the tree heights recorded on a school campus.

A science teacher wants to choose a data display that will highlight how many trees are in a range of heights, such as 60–64, 65–69, etc.

We need to find a correct plot that will present the information in this way.

We know that in bar charts, each bar represents one value(category). And  in a histogram, each bar will represent a continuous data

Therefore, a plot that will present the information that will highlight how many trees are in a range of heights, such as 60–64, 65–69, etc. : histogram

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Answer:

Step-by-step explanation:

A plot that will display information highlighting the number of trees in a range of heights, such as 60-64, 65-69, and so on: histogram

We were provided the tree heights reported on a school grounds in this question. A science instructor needs to select a data presentation that will show how many trees are in a given height range, such as 60-64, 65-69, and so on. We must find a suitable plot to portray the data in this manner. We know that each bar on a bar chart represents one value (category). And each bar in a histogram represents continuous data.

a) H₀ = 87, H₁ ≠ 87

b) We reject the null hypothesis and have evidence to suggest that the average grade on the statistics final examination is different from 87.

c) We fail to reject the null hypothesis and do not have sufficient evidence to suggest that the average grade on the statistics final examination is different from 87.

a. The null hypothesis (H₀): The average grade on the statistics final examination is 87.

The alternative hypothesis (H₁): The average grade on the statistics final examination is not 87.

b. To test the hypotheses using the critical value approach, we need to calculate the test statistic and compare it to the critical value. The test statistic (t-score) is calculated as:

t = (sample mean - population mean) / (sample standard deviation / √(sample size))

= (83.96 - 87) / (12 / √(36))

= -3.04

Next, we need to determine the critical value for a two-tailed test with a significance level of 5%. Since the sample size is 36, we have degrees of freedom (df) equal to n - 1 = 35. Consulting the t-distribution table or using statistical software, we find the critical value for a two-tailed test with df = 35 and alpha = 0.05 is approximately ±2.032.

Since the absolute value of the test statistic (-3.04) is greater than the critical value (2.032), we reject the null hypothesis. The test result is statistically significant at the 5% level of significance.

Hypothesis Test Conclusion: We reject the null hypothesis and have evidence to suggest that the average grade on the statistics final examination is different from 87.

c. To test the hypotheses using the confidence interval approach, we need to calculate the confidence interval and check if the hypothesized value (87) falls within the interval. The confidence interval is calculated as:

CI = sample mean ± (critical value × (sample standard deviation / √(sample size)))

= 83.96 ± (2.032 × (12 / √(36)))

= 83.96 ± 4.86

The confidence interval is (79.10, 88.82).

Since the hypothesized value of 87 falls within the confidence interval, we fail to reject the null hypothesis. The test result is not statistically significant at the 5% level of significance.

Hypothesis Test Conclusion: We fail to reject the null hypothesis and do not have sufficient evidence to suggest that the average grade on the statistics final examination is different from 87.

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Answer: No

Step-by-step explanation:

Let \(f(x)=x^3 +8x^2 +11x-20\).

Then, \(f(5)=5^3 +8(5)^2 +11(5)-20=360\).

Since \(f(5) \neq 0\), \((x-5)\) is not a factor of \(f(x)\) by the factor theorem.

Answer:

y = x + 2

Step-by-step explanation:

As the equation of a line is in the form y = mx + c:

Step 1 - Calculate the y intercept

This can be done by looking at the y coordinate where x = 0:

y = mx + c

In the picture, the y intercept is 2 so:

y = mx + 2

Step 2 - Calculate the slope

This can be calculated by:

\(\frac{\text{change in y}}{\text{change in x}}\)

Get two sets of coordinates:

(0, 2) and (2, 4)

Calculate the changes by subtracting from one another:

\(\frac{4 - 2}{2 - 0} \\\frac{2}{2}\\=1\)

So the gradient is 1, meaning the equation of the line is:

\(y = 1x + 2 \\\text{or}\\y = x + 2\)

Hope this helps!

The option which is least likely to be a warning sign that one's debt is at a critical point is having several credit cards.

The most likely warning sign for credit cards is not paying or clearing the debt of the credit card in full each month.

The options given in the problem are,

In these options, least likely to be a warning sign is having several credit cards as having multiple cards and well management of them required the carefulness and awareness.

Thus, the option which is least likely to be a warning sign that one's debt is at a critical point is having several credit cards.

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(a) (i) If the yearly interest rate is 5%, the amount in the account in the year 2012 would be approximately $1,012,469.71.

(a) (ii) If the yearly interest rate is 7%, the amount in the account in the year 2012 would be approximately $23,127,812.13.

To calculate the amount in the account in the year 2012, we can use the continuous compounding formula: A = \(pe^{rt}\), where A is the final amount, P is the initial principal (the sale price of $24), e is Euler's number approximately equal to 2.71828, r is the interest rate, and t is the time in years.

(a) (i) For a 5% yearly interest rate: r = 0.05 and t = 2012 - 1626 = 386 years. Plugging these values into the formula, we have A = 24\(e^{ 0.05 * 386}\)

(a) (ii) For a 7% yearly interest rate: r = 0.07 and t = 386. Plugging these values into the formula, we have A = \(24e^{0.07 * 386 }\)

Calculating these expressions will give us the amount in the account in the year 2012 for the respective interest rates of 5% and 7%.

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After 5 years, Larry's car would have depreciated by approximately 31.36% of its original value. Therefore, the approximate value of Larry's car after 5 years would be $16,496.

Depreciation rate is the percentage at which an asset's value decreases over time. In this case, Larry's car depreciates at a rate of 5.6% per year. To calculate the approximate value after 5 years, we need to find the value that is 31.36% less than the original value. We can calculate this by using the following formula:

Approximate value = Original value - (Original value x Depreciation rate x Number of years)

Plugging in the given values, we get:

Approximate value = $24,000 - ($24,000 x 0.056 x 5) = $16,496

In conclusion, Larry's car would be worth approximately $16,496 after 5 years, given that its original value was $24,000 and it depreciates at a rate of 5.6% per year. It's important to keep track of depreciation when purchasing or selling assets, as it can greatly affect their value over time.

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Yes, this holds even if 2n is replaced with 2n + 1. To show this, we can use the fact that the transition probability is symmetric.

This means that the probability of going from x to y in n steps is the same as the probability of going from y to x in n steps. Therefore, the probability of being at x after 2n steps is the same as the probability of being at x after 2n + 1 steps, since we can simply reverse the last step to get back to x. Hence, for all x є S and all integers n, P^n(x,x) = P^{2n}(x,x) = P^{2n+1}(x,x).
An aperiodic, discrete-time Markov chain Xn on a state space S, excluding {1}, has symmetric transition probabilities if P(Xn+1 = y | Xn = x) = P(Xn+1 = x | Xn = y) for all x, y ∈ S. This property implies that for all x ∈ S and even integers 2n, P(X2n = x | X0 = x) will also hold, as the chain can traverse an even number of symmetric transitions and return to the starting state. However, for odd integers (2n + 1), this property may not necessarily hold. An odd number of transitions can cause an imbalance in the probability of returning to the initial state. Thus, while the Markov chain's symmetry holds for even transitions, it may not be valid for odd transitions (2n + 1).

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Answer:

VS and PR

Step-by-step explanation:

Step-by-step explanation:

it just means to convert these equations into function definitions.

and a function looks like

y = ... something with x, factors, other functions, constants

1)

x + y = z

y = -x + z or z - x

2)

x - y = z

x - z = y or y = x - z

3)

x × y = z

y = z/x

4)

x/y = z

x = z × y

x/z = y or y = x/z

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

According to me , independent is the word which is associated with multiplication when computing probabilities . Because when the events are independent then we multiply the probabilities .

According to the multiplication rule of probability, the probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.

The probability of the union of two events is equal to the sum of individual probabilities. The union of two set contains all the elements of previous sets. The union is denoted by ∪. The equation for the students earnings will be expressed as P(A∪B). The occurrence of event A changes the probability of B then the events are dependent. If the probability of two events happening together is zero then the events are mutually exclusive.

Therefore,

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

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Answer:

f(x)=2x is your answer

when x=-9

f(-9)=-9×2=-18

other similar to this.

Answer:

m = 6

Step-by-step explanation:

We know that m and n vary directly and that m = 3 when n = 2. How would we find m when n = 4? For starters, we can see that the value of n doubled (we know this because 2 doubled is 4), and since m and n vary directly, when n doubles, so does m so the answer is m = 3 * 2 = 6.

the volume of the silo is approximately 11,657.88 cubic meters.

To find the volume of the silo, we need to calculate the volumes of the cylinder and the cone separately, and then add them together.

The radius of the base of the silo is half the diameter, so it's 10 meters / 2 = 5 meters.

The height of the cylinder is given as 27 meters. Since the height of the cone is half the height of the cylinder, the height of the cone is 27 meters / 2 = 13.5 meters.

The volume of a cylinder is calculated using the formula:

Volume of Cylinder = π * radius^2 * height

Plugging in the values, we get:

Volume of Cylinder = π * 5^2 * 27 = 3375π cubic meters (approximately 10,598.07 cubic meters)

The volume of a cone is calculated using the formula:

Volume of Cone = (1/3) * π * radius^2 * height

Plugging in the values, we get:

Volume of Cone = (1/3) * π * 5^2 * 13.5 = 337.5π cubic meters (approximately 1059.81 cubic meters)

Adding the volumes of the cylinder and the cone, we get:

Volume of Silo = 3375π + 337.5π = 3712.5π cubic meters (approximately 11,657.88 cubic meters)

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Answer:

y - 8 = (-1/27)(x + 3)

Step-by-step explanation:

the slope of a line perpendicular to the given y = 27x + 117 is the negative reciprocal of 27, that is, -1/27.  Using the point-slope form  y - k =m(x - h)  to write the new equation, we get:

y - 8 = (-1/27)(x + 3)

Answer:

The radius will be half of your diameter so,

since 26 is your diameter half of that is = 13 is your new radius.

Now finding the area:

13^2 = 169

169 x 3.14 = 530.66 cm2 is your area.

Formula of an area of a circle:

πr^2

pi(3.14 or 22/7 depending on whatever they tell you to use for pi) x radius being squared

The value of x in the chord is 4.8 units

From the question, we have the following parameters that can be used in our computation:

The circle

Next, we calculate the radius using each chord using the Pythagoras theorem

Using the above as a guide, we have the following:

r² = x² + (37/2)²

r² = 13² + (28/2)²

By substitution, we have

x² + (37/2)² = 13² + (28/2)²

So, we have

x² = -(37/2)² + 13² + (28/2)²

Evaluate

x² = 22.75

Take the square root

x = 4.8

Hence, the value of x is 4.8 units

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