Rosie ran directly toward her home at a constant velocity for 78 seconds. In one-third of that time, she ran 52 meters. What was Rosie's velocity?

The venues would have the same cost when there are 14 attendees. At this point, both options would amount to a total cost of $1,220.

1. Let's denote the number of attendees as "x" for both the hotel and the restaurant. For the hotel venue, the total cost can be calculated as the sum of the reservation cost ($396) and the cost per person ($76) multiplied by the number of attendees: Total Cost for Hotel = $396 + $76x.

2. For the restaurant venue, the total cost can be calculated as the sum of the reservation cost ($890) and the cost per person ($74) multiplied by the number of attendees: Total Cost for Restaurant = $890 + $74x

3. To find the number of attendees at which the costs are the same, we set the two equations equal to each other: $396 + $76x = $890 + $74x

4. Rearranging the equation, we get: $2x = $890 - $396, Simplifying further: $2x = $494

x = $494 / $2

x = 247

5. Therefore, it would take 247 attendees for both the hotel and the restaurant venues to have the same cost. To calculate the total cost at this point, we substitute the value of x into either equation. Using the hotel equation: Total Cost = $396 + $76 * 247 = $1,220

6. Thus, with 247 attendees, the total cost for both venues would be $1,220.

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Answer:

P=22.6, T=67.4

Step-by-step explanation:

\(sin(P)=\frac{5}{13}\\ P= 22.6\\\\tan(T)=\frac{12}{5}\\ T=67.4\\\\cos(T)=\frac{5}{13} \\T=67.4\)

Answer:

  B.  $450

Step-by-step explanation:

The amount of commission is the commission rate (3%) times the amount of sales to which it is applied ($5000). Garrett's commission last week would be ...

  0.03 × $5000 = $150

He is also paid $300 each week in addition to his commission, so his total pay last week was ...

  pay = salary + commission

  pay = $300 +150 = $450

Julie is tracking the growth of a plant for a science project, then the plant grow at a rate of 2.5 inches per day.

Given that,

The height of the plant on the 2nd day she measured was 8 inches and on the 7th day it was 20. 5 inches.

A linear equation is an algebraic equation of the form y = mx + b involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

y = mx + b

where x, y are variables,

m is the rate of change and

b is the y intercept.

Let y represent the height of the plant after x days.

The height of the plant on the 2nd day she measured was 8 inches. It is given by: \((2,8)\)

The height of the plant on the 7th day she measured was 20.5 inches. It is given by: \((7,20.5)\)

\(x_{1} =2\\y_{1} = 8\\x_{2} = 7\\y_{2} = 20.5\)

The rate of change (m) is:

m = \(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)

m = \(\frac{20.5 - 8}{7-2}\)

m = \(\frac{12.5}{5}\)

m = 2.5 inches per day.

Therefore,

Julie is tracking the growth of a plant for a science project, then the plant grow at a rate of 2.5 inches per day.

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Domain

\(-\infty \: < x < \infty\)

Range

\(f\left(x\right)\ge \:-7\:\)

We first check if all the given values are non-negative. We can see that all the values given are greater than or equal to zero, so this condition is satisfied.

In part a, we are given a set of values and asked to determine if they form a valid probability distribution.

A probability distribution is a function that assigns probabilities to each possible value of a random variable. In order for a set of values to form a valid probability distribution, the following conditions must be met:

All values must be non-negative: This means that the probability of any event cannot be negative. In other words, the probability of any event occurring must be greater than or equal to zero.

The sum of all values must be equal to 1: Since the probability of an event occurring is always between 0 and 1, the sum of all probabilities must add up to 1. This ensures that all possible outcomes of an experiment are accounted for.

In part a, we first check if all the given values are non-negative. We can see that all the values given are greater than or equal to zero, so this condition is satisfied.

Next, we check if the sum of all values is equal to 1. We add up all the given values and get 1.3. Since this value is greater than 1, the sum of probabilities is not equal to 1 and hence, this is not a valid probability distribution.

In parts b, c, d and e, since the given distribution is not valid, we cannot calculate probabilities using it.

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The 90% confidence interval for the population mean number of days it takes to find a job using the website's service is approximately 77.09 to 82.91 days.

To calculate a 90% confidence interval for the population mean number of days it takes to find a job using the website's service, follow these steps:

1. Identify the sample mean (X), sample size (n), and population standard deviation (σ). In this case, X = 80 days, n = 32, and σ = 10 days.

2. Determine the desired confidence level. Here, it's 90%.

3. Find the critical value (z) associated with the 90% confidence level. You can look this up in a standard normal distribution table or use a calculator that provides this functionality. For a 90% confidence interval, the critical value is approximately 1.645.

4. Calculate the standard error (SE) by dividing the population standard deviation (σ) by the square root of the sample size (n). In this case, SE = σ/√n = 10/√32 ≈ 1.77.

5. Multiply the critical value (z) by the standard error (SE) to obtain the margin of error (MOE): MOE = z * SE = 1.645 * 1.77 ≈ 2.91.

6. Calculate the lower and upper bounds of the confidence interval by subtracting and adding the margin of error (MOE) from the sample mean (X). In this case, the lower bound = 80 - 2.91 ≈ 77.09, and the upper bound = 80 + 2.91 ≈ 82.91.

Thus, the 90% confidence interval for the population mean number of days it takes to find a job using the website's service is approximately 77.09 to 82.91 days.

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a) The probability that the sample proportion p will be between 0.20 and 0.40 is 0.6833.

b) The probability that the sample proportion p will be between 0.25 and 0.35 is 0.8994.

(a) The sample proportion is defined as the number of favorable outcomes divided by the number of total outcomes. Therefore, the sample proportion p will be between 0.20 and 0.40 when the favorable outcomes lie between 20% and 40%. The probability that the sample proportion p will be between 0.20 and 0.40 can be calculated using the following formula:

Probability = P (0.20 ≤ p ≤ 0.40) = P (z ≤ (0.40 – p) / √(pq/n)) – P (z ≤ (0.20 – p) / √(pq/n)) where p = sample proportion, q = 1 – p, and n = sample size Assuming that the sample size is greater than 30, we can use the normal distribution to approximate the sampling distribution of the sample proportion.

Therefore, z-statistic can be used to determine the probability of the sample proportion being between 0.20 and 0.40. Hence, P (0.20 ≤ p ≤ 0.40) = P (z ≤ (0.40 – p) / √(pq/n)) – P (z ≤ (0.20 – p) / √(pq/n))= P (z ≤ (0.40 – 0.30) / √(0.30 × 0.70/500)) – P (z ≤ (0.20 – 0.30) / √(0.30 × 0.70/500))= P (z ≤ 3.02) – P (z ≤ -0.48)= 0.9982 – 0.3149= 0.6833 Therefore, the probability that the sample proportion p will be between 0.20 and 0.40 is 0.6833.

(b) The sample proportion p will be between 0.25 and 0.35 when the favorable outcomes lie between 25% and 35%. Therefore, the probability that the sample proportion p will be between 0.25 and 0.35 can be calculated as follows:

Probability = P (0.25 ≤ p ≤ 0.35) = P (z ≤ (0.35 – p) / √(pq/n)) – P (z ≤ (0.25 – p) / √(pq/n)) where p = sample proportion, q = 1 – p, and n = sample size Again, assuming that the sample size is greater than 30, we can use the normal distribution to approximate the sampling distribution of the sample proportion.

Therefore, z-statistic can be used to determine the probability of the sample proportion being between 0.25 and 0.35. Hence, P (0.25 ≤ p ≤ 0.35) = P (z ≤ (0.35 – p) / √(pq/n)) – P (z ≤ (0.25 – p) / √(pq/n))= P (z ≤ (0.35 – 0.30) / √(0.30 × 0.70/500)) – P (z ≤ (0.25 – 0.30) / √(0.30 × 0.70/500))= P (z ≤ 1.51) – P (z ≤ -1.81)= 0.9345 – 0.0351= 0.8994Therefore, the probability that the sample proportion p will be between 0.25 and 0.35 is 0.8994.

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Answer: (5.5 , -1.5)

19 + (-8) / 2 = 5.5

15 + (-18) / 2 = -1.5

Answer:

8 inches

Step-by-step explanation:

The radius is 1/2 of the diameter.

r = 1/2 d

r = 1/2 ( 16 inches)

r = 8 inches

Answer:

the radius is 8"

Step-by-step explanation:

The radius of a circle is half the diameter of the circle.

In this case the diameter is 16" and therefore the radius is 8"

Thomas' annual rate of return after fees was 7.87%. Thomas' annual rate of return after fees can be calculated using the below-given formula.

Annual Rate of Return = (1 + Average Annual Rate of Return) x (1 - Expense Ratio) - 1
Plugging in the values given in the question, we get:
Annual Rate of Return = (1 + 0.084) x (1 - 0.005) - 1
Annual Rate of Return = 0.0787 or 7.87%

Therefore, Thomas' annual rate of return after fees was 7.87%. It is important to consider expenses like the expense ratio when calculating investment returns as they can significantly affect the overall performance of the investment. In this case, the 0.5% expense ratio reduced Thomas' annual rate of return from the fund's average of 8.4% to 7.87%. It is important to keep in mind the impact of fees and expenses when choosing an investment as they can eat into returns over time and affect the overall success of the investment.

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Answer:

108/100×1485=$1603.8

I'm not very sure about the simplification so please simplify again

Step-by-step explanation:

Answer: $118.80

Step-by-step explanation:

8% turns into 0.08

0.08 times 1485 = 118.80

Answer:

5 hours, y= how much money it will cost, and x represents how many hours

Step-by-step explanation:

y= 15x+45

120= 15x+45

-45 -45

75= 15x

75/15×= 5 hours

Answer:

$1296

Step-by-step explanation:

the markup is 700 so add that to the 500, then sales tax adds 96

Answer:

Step-by-step explanation:

https://www.numerade.com/questions/write-the-equation-for-the-graph-that-is-shown-check-your-book-to-see-graph-3/

The prove of given limit lim θ → 0 ( sin θ / θ ) = 1 is shown in below.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

⇒ lim θ → 0 ( sin θ / θ ) = 1

Here, The form of given limit is 0/0, so we can apply the L - Hospital Rule.

⇒ lim θ → 0 ( sin θ / θ ) = 1

Take LHS;

⇒ lim θ → 0 ( d/dθ (sin θ)/ dθ/dθ )

⇒ lim θ → 0 ( cos θ / 1 )

⇒ ( cos 0 )

⇒ 1

⇒ RHS

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The probability of drawing two orange balls, given that at least one ball is orange, is 1/5.

There are a total of 6 possible outcomes when selecting 2 balls from the urn without replacement: (O,O), (O,B), (B,O), (B,B), (O,B), (B,O).

The event that at least one of the balls selected is orange corresponds to the outcomes (O,O), (O,B), and (B,O). The probability of this event is the sum of the probabilities of the individual outcomes:

P(at least one orange) = P(O,O) + P(O,B) + P(B,O)

To calculate the individual probabilities, we can use the formula for the number of combinations of n items taken k at a time:

C(n,k) = n! / (k! (n-k)!).

The probability of each outcome is the number of ways it can occur divided by the total number of possible outcomes:

P(O,O) = C(2,2) / C(4,2)

= 2! / (2! (2!)) / (4! / (2! (2!)))

= 1/6

P(O,B) = C(2,1) * C(2,1) / C(4,2)

= 2 * 2! / (1! (2!)) / (4! / (2! (2!)))

= 2/6

P(B,O) = P(O,B) = 2/6

So,

P(at least one orange) = 1/6 + 2/6 + 2/6

=> 5/6

And the probability that both balls are orange is:

P(both orange) = P(O,O) = 1/6.

So, the probability of drawing two orange balls, given that at least one ball is orange, is 1/5.

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Answer:

10

Step-by-step explanation:

68 screwdrivers will be leftover at the end of day.

A division is a process of splitting a specific amount into equal parts.

Given that At the Medal Factory, the assembly line produces 98 screwdrivers in a batch.

The screwdrivers are packaged in boxes with 12 each.

If 5 batches are made in one day

We need to find  how many screwdrivers will be leftover at the end of it.

12 screwdrivers in each batch.

So for 5 batches there are 5×12=60 screwdrivers.

The left screwdrivers are 98-60=38

Hence, 68 screwdrivers will be leftover at the end of day.

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According to the given data set:

values10,11,12,13,14,17,17,18,18,19,19,19,21,23,23,25,26,27,27,27,31,32,33,33,36,37,37,38,38more than 20 and less than or equal to 29 values21,23,23,25,26,27,27,27more than 20 and less than or equal to 29 values.

A data set is a group of figures or values related to a specific topic. A data set might include, for instance, each student's test results in a certain class. A data set is the number of fish that each dolphin consumes in an aquarium.

There are eight values that are both bigger than 20 and less than 29.The data collection has 12 values that are both higher than or equal to 30 and lower than or equal to 39.Values greater than nor equal to 30 and less than or equal to 3931,32,33,33,35,36,37,37,37,38,38The data collection has 12 values that are both higher than or equal to 30 and lower than or equal to 39.

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Answer:

-3, 3, 9

Step-by-step explanation:

Answer on Edge

Answer:

(0,-4) and (12,0)

Step-by-step explanation:

Answer:

a) 540 b) 108

Step-by-step explanation:

to find the interiour angle of any shape subttract the number of side by 2 and then times by 180    180 (n-2)

and then 2 find one angle divide total by number of sides  180 (n-2) /n

if tht makes sense

The mean forecast error (MFE) can indicate if a forecast is consistently high. MFE measures the average difference between the forecasted values and the actual values over a given period.

If the MFE consistently shows a positive value, it suggests that the forecast tends to be higher than the actual values on average. The mean forecast error (MFE) is a common error measure used by forecasters to assess the accuracy of their forecasts. It is calculated by taking the average of the differences between the forecasted values and the corresponding actual values.

If the MFE consistently yields a positive value, it indicates that the forecast tends to be consistently higher than the actual values. This suggests a systematic bias in the forecasting process, where the forecaster consistently overestimates the future outcomes. The magnitude of the MFE also provides insights into the degree of overestimation, with larger positive values indicating a more significant discrepancy between the forecasted and actual values. By identifying such consistently high forecasts, forecasters can make adjustments to improve the accuracy and reliability of their predictions.

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Step-by-step explanation:

did you change the reference number ?

I think the original question was "90 is how many % of 80 ?"

now it is 81.

in % calculations the most important things to identify :

what are 100% (or any other reference % level).

then what is 1%.

and then multiply this 1% by the desired number of % or divide the target number by this 1% to find out how many % the target number is.

in our case here

100% = 81

1% = 100%/100 = 81/100 = 0.81

how many % are 90 ?

well, as many as how often 1% fits into these 90 :

90/0.81 = 111.111111111... %

when the reference was 80, then we had

90/0.8 = 112.5%

Answer:

iufiyutuiti7ti6ri6fu5eu5ru5s

The function C(F) to calculate the temperature in degrees Celsius for a given temperature in degrees Fahrenheit will be equal to \([(\frac{5}{9}F) -\frac{160}{9}]\)

As per the question statement,  the formula [F(C) = 9/5C + 32] is to calculate the temperature in degrees Fahrenheit for a given a temperature in degrees Celsius.

We are required to determine the function to calculate the temperature in degrees Celsius for a given temperature in degrees Fahrenheit.

Since, [F(C) = 9/5C + 32],

\(or, [F = \frac{9}{5} C + 32]\\or, (F-32)= \frac{9}{5} C\\or, \frac{9}{5} C=(F-32)\\or,C=\frac{5}{9} (F-32)\\or,C=\frac{5}{9}F-\frac{160}{9}\)

That is, the function to calculate the temperature in degrees Celsius for a given temperature in degrees Fahrenheit is \(C(F)=[(\frac{5}{9}F) -\frac{160}{9}]\).

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Answer:

inverse

C(F)=5/9F-106/9

check all

Step-by-step explanation:

23