MATHEMATICS COLLEGE

Drag each description to the correct location on the chart. In a large single-elimination basketball tournament, the first round of play begins with 64 teams. In each successive round, the number of teams remaining in the tournament is reduced by half. This relationship can be described by the following exponential function. When this relationship is graphed, determine the quantity and axis that will represent each of the variables. x-axis y-axis Teams Remaining Tournament Round

Answers

Answer 1

Answer:

After the first round only 32 teams will left.

After the second round 16 teams will left.

After the third round 8 teams will left.

After the fourth round only 4 teams will left.

After the fifth round only 3 teams will left.

After the sixth round only 1 team will left.

What is independent and dependent variable?

If x and y are two variables in an algebraic equation and every value of x is linked with any other value of y, then 'y' value is said to be a function of x value known as an independent variable, and 'y' value is known as a dependent variable.

What is an exponential function?

An exponential function is a mathematical function in the form f(x) = $a^(x)$ where x is a variable, and a is a constant called the base of the function.

According to the given question

We have an exponential function

$f(x) = 64((1)/(2) )^(x)$

And y-axis represents the teams remaining and x axis represents the tournaments round

Since, here the values of x are independent variables and values of y are dependent variables.

Now for the

Tournament round 1 ,

y = f(1) = $64((1)/(2) )=32$

⇒ 32 teams are remaining

Tournament round 2

$y = f(2) = 64((1)/(2)) ^(2)$

⇒ y = 16, only 16 teams are remaining

For round 3

$y = f(3) = 64((1)/(2)) ^(3) =8$

For round 4

$y = f(4) = 64((1)/(2) )^(4)= 4$

⇒ Only 4 teams are remaining

For round 5

$y = f(5) = 64((1)/(2) )^(5) = 2$

⇒ only 2 teams are remaining

For round 6

$y = f(6) = 64((1)/(2)) ^(6)=1$

⇒ only one team is remaining

By using these parameters we will plot a graph for tournament rounds .

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Answer 2

Answer:

Answer: Left column x- axis

Right column : Tournament round

Left column: y-axis.

Right column: number of teams remaining

Step-by-step explanation:

You expect the y -value, teams remaining to decrease as you go from the first round to the last round in the x-values.

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At a concession stand, seven hot dogs and two hamburgers cost $16.25; two hot dogs and seven hamburgers cost $17.50. Find the cost of one hot dog and the cost of one hamburger.
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A university administrator obtains a sample of the academic records of past and present scholarship athletes at the university. The administrator reports that no significant difference was found in the mean GPA (grade point average) for male and female scholarship athletes ( P = 0.287 ) . This means that: a. the maximum difference in GPAs between male and female scholarship athletes is 0.287.
b. the chance of obtaining a difference in GPAs between male and female scholarship athletes as large as that observed in the sample if there is no difference in mean GPAs is 0.287.
c. the GPAs for male and female scholarship athletes are identical, except for 28.7% of the athletes.
d. the chance that a pair of randomly chosen male and female scholarship athletes would have a significant difference in GPAs is 0.287.

Answers

Answer:

Step-by-step explanation:

The probability of obtaining results as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct is known as p-value.

The p-value is used as an option to reject points to provide the smallest level of significance at which the null hypothesis would be rejected. A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis.

Only the statement expressed by option C is in correlation with the meaning of p-value.

Question 3 (1 point)What is the value of x in the equation 8+4 = 2(x - 1)?
a
11/2
b
13/2
c
5
d
7

Answers

Answer:

D. 7

Step-by-step explanation:

(8+4) = 2(x-1) multiply (x-1) by 2

(8+4) = 2x-2 add 8 and 4

12 = 2x-2 add 2 on both sides

14 = 2x divide both sides by 2

7 = x

Answer is D

12 = 2x - 2

14 = 2x

14/2 = x

7 = x

The speed of light is 300,000,000 meters per second. The sun is approximately meters 1.5 x 10¹¹ from Earth. How many seconds does it take for the sunlight to reach Earth?

Answers

Final answer:

By using the formula for time (distance divided by speed), it is found that sunlight takes approximately 500 seconds, or about 8.3 minutes, to reach the Earth from the Sun.

Explanation:

The speed of light is 300,000,000 meters per second (m/s) and the distance from the Earth to the Sun is approximately 1.5 x 10¹¹ meters. We can calculate the time it takes for sunlight to reach Earth by using the formula for time, which is distance divided by speed. Plugging these values into the formula, we have:

Time = distance/speed = (1.5 x 10¹¹ meters) / (3.0 x 10⁸ m/s) = 500 seconds.

This means that it takes approximately 500 seconds, or about 8.3 minutes, for sunlight to travel from the Sun to the Earth.

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Answer:

about 500 seconds

Step-by-step explanation:

The distances between stars across the universe are very great, so astronomers use light years as a larger unit than miles or kilometers. To calculate the actual distance of a light year, you simply need to multiply the speed of light by the number of seconds in a year. This means 300,000,000 multiplied by 500 and you would get 1.5 x 10¹¹ which is equal too 150,000,000,000

A person's blood pressure is monitored by taking 8 readings daily. The probability distribution of his reading had a mean of 129 and a standard deviation of 7. a. Each observation behaves as a random sample. Find the mean and the standard deviation of the sampling distribution of the sample mean for the eight observations each day. b. Suppose that the probability distribution of his blood pressure reading is normal. What is the shape of the sampling distribution? c. Refer to (b). Find the probability that the sample mean exceeds 140.

Answers

Answer:

a) $\mu_(\bar X)= 129$

$\sigma_(\bar X)= (7)/(√(8))=2.475$

b) If the distribution is normal then the sampling distribution would be bell shaped and normal

c) $P(\bar X >140)$

And we can use the z score formula given by:

$z =(\bar X -\mu)/(\sigma_(\bar X))$

And replacing we got:

$z =(140-129)/(2.475)= 4.44$

And then we can find the probability using the complement rule and the normal standard distribution or excel and we got:

$P(\bar X>140) = P(Z>4.44) =1-P(z<4.44) \approx 0$

Step-by-step explanation:

For this case we have the following info:

$n=8$ represent the sample size

$\bar X=129$ the sample mean

$s=7$ the standard deviation

Part a

If we assume that the distirbution is bell shaped then we can find the parameters like this:

$\mu_(\bar X)= 129$

$\sigma_(\bar X)= (7)/(√(8))=2.475$

Part b

If the distribution is normal then the sampling distribution would be bell shaped and normal

Part c

We want this probability:

$P(\bar X >140)$

And we can use the z score formula given by:

$z =(\bar X -\mu)/(\sigma_(\bar X))$

And replacing we got:

$z =(140-129)/(2.475)= 4.44$

And then we can find the probability using the complement rule and the normal standard distribution or excel and we got:

$P(\bar X>140) = P(Z>4.44) =1-P(z<4.44) \approx 0$

Which equation could have been used to create this function table? A.
y = 4x

B.
y = 5x

C.
y = x + 7

D.
y = x + 2

Answers

A : for x = 4 y = 16 not 6 FALSE
B : for x = 4 y = 20 not 6 FALSE
C : for x = 4 y = 11 not 6 FALSE
D : for x = 4 y = x + 2 = 6 is
6 The Last one verifying the first row of the table

pls mark as brainliest

Which ordered pair would form a proportional relationship with the point graphed below?(10.-20)
(-30, 20)
(-10,5)
(35, -20

Answers

The third option but can also be the first option, The would proportionate properly.

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