Rick and Tom rented party halls. The Celebrations party hall charged Rick a rental fee of $65, including music, and $25 per guest. The Feast party hall charged Tom a rental fee of $40, $25 for music, and $25 per guest.If each of them spent the same amount of money, how many guests attended Rick and Tom's party?

A.
Five more guests attended Rick's party than Tom's party.
B.
Fifteen more guests attended Tom's party than Rick's party.
C.
The same number of guests attended Rick and Tom's party.
D.
Twenty-five more guests attended Rick's party than Tom's party.

Answers

Answer 1

Answer:

Answer:

C. The same number of guests attended Rick and Tom's party.

Step-by-step explanation:

Let R and T represent the number of guests at Rick's and Tom's parties, respectively. The charges Rick and Tom paid are equal, so we have ...

65 +25R = 40+25+25T

25R = 25T . . . . . . . . . . . . subtract 65

R = T . . . . . . . . . . . . . . . . . divide by 25

The number of guests at each party is the same.

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A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. When he started his diet, he weighed 79.5 kilograms. He gained weight at a rate of 5.5 kilograms per month. Let y represent the sumo wrestler's weight (in kilograms) after x months. Which of the following could be the graph of the relationship? graph of an increasing linear function in quadrant 1 with a positive y-intercept (Choice B) B graph of an increasing linear function in quadrants 1 and 4 with a positive x-intercept and negative y-intercept (Choice C) C graph of a decreasing linear function in quadrants 1 and 4 with a positive x-intercept and positive y-intercept (Choice D) D graph of a decreasing linear function in quadrant 4 with a negative y-intercept

Answers

Answer:

(Choice A) A graph of an increasing linear function in quadrant 1 with a positive y-intercept.

Step-by-step explanation:

The weight of the sumo wrestler starts at a positive value of 79.5 kilograms, and we are given that the sumo wrestler gains a linear amount of weight per month at 5.5 kilograms per month.

If we were to graph this relationship, the sumo wrestler's weight would be represented on the y-axis, and the amount of time on the x-axis.

So the initial weight would occur at (0, 79.5) which is the positive y-intercept.

And since his weight is increasing at 5.5 kilograms per month, the slope of the linear function is positive.

Hence, the graph of the linear increasing function in quadrant 1 with a positive y-intercept.

Cheers.

Nolan wrote 1.63 as a fraction in simplestform. Which number did Nolan write in
the numerator of the fraction?

Answers

Answer:

163/100 or 1 $(63)/(100)$

Step-by-step explanation:

Formula of simple intrest

Answers

Formula : A = P (1 + r*t)

a - final amount

p- initial balance

r- interest rate

t- time

Approximately 1 in 28 people of Ashkenazi Jewish descent are Tay-Sachs carriers. In randomly sampling one man and one woman from this population, what is the probability neither is a Tay-Sachs carrier? What is the probability both are carriers?

Answers

Answer:

a) probability that neither is Tay-Sachs carrier is 0.9298

b) the probability that both are carriers is 0.001276

Step-by-step explanation:

Given that;

1 in 28 people of Ashkenazi jewish descent are Tay-Sachs carrier.

so P(Carrier) = 1/28 =

also P( Not a carrier) = 1 - 1/28 = 0.9643

Now After Sampling 1 man and 1 woman from the population;

the probability neither is Tay-Sachs carrier

P( Neither is a Carrier) = 27/28 × 27/28 = 0.9298

Therefore probability that neither is Tay-Sachs carrier is 0.9298

the probability both are carriers

P( Both are Carriers) = 1/28 × 1/28 = 0.001276

Therefore the probability that both are carriers is 0.001276

Final answer:

The probability of both a man and a woman of Ashkenazi Jewish descent not being Tay-Sachs carriers is calculated as (27/28) * (27/28). The probability of both being carriers is (1/28) * (1/28).

Explanation:

The probability of an event occurring is calculated as the number of favorable outcomes divided by the total number of outcomes. In this case, the problem is related to genotypes and their associated probabilities, aligning with the concept of probability in mathematics.

The probability of a person of Ashkenazi Jewish descent not being a Tay-Sachs carrier is 27/28 because 1 out of 28 are carriers, and thus 27 out of 28 are not. For two independent events, the probability of both occurring is obtained by multiplying their individual probabilities. Therefore, the probability of both the man and the woman not being carriers is (27/28) * (27/28).

Similarly, the probability that both are carriers would be calculated as (1/28) * (1/28).

Learn more about Probability here:

brainly.com/question/22962752

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A certain test preparation course is designed to help students improve their scores on the MCAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 6 students' scores on the exam after completing the course: 19, 15, 9, 17, 7, 16. Using these data, construct a 95% confidence interval for the average net change in a students's score after completing the course. Assume the population is approx. normal.Step 1. calculate the sample mean for the given sample data (round answer to 1 decimal place)Step 2. Calculate the sample standard deviation for the given sample data ( round answer to 1 decimal place)Step 3. Find the critical value that should be used in constructing the confidence interval. ( round answer to 3 decimal placed)Step 4. construct the 95% confidence interval (round answer to 1 decimal place)

Answers

Answer:

1) $\bar X =(\sum_(i=1)^n X_i)/(n)=13.8$

2) $s=\sqrt{(\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)}=4.8$

3) $t_(\alpha/2)=2.571$

4) The 95% confidence interval would be given by (8.8;18.8)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

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

Step 1. calculate the sample mean for the given sample data (round answer to 1 decimal place)

$\bar X =(\sum_(i=1)^n X_i)/(n)=13.8$

Step 2. Calculate the sample standard deviation for the given sample data ( round answer to 1 decimal place)

$s=\sqrt{(\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)}=4.8$

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n=6 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_(\alpha/2)(s)/(√(n))$ (1)

Step 3. Find the critical value that should be used in constructing the confidence interval. ( round answer to 3 decimal places)

In order to calculate the critical value $t_(\alpha/2)$ we need to find first the degrees of freedom, given by:

$df=n-1=6-1=5$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,5)".And we see that $t_(\alpha/2)=2.571$