MATHEMATICS COLLEGE

What does the letter U stand for 25 > u-7

Answers

Answer 1

Answer:

Answer:

Solve for u by simplifying both sides of the inequality, then isolating the variable.

Inequality Form:

u<32

Interval Notation:

(−∞,32)

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Yoshi needs to find the inverse of f(x) = 5x – 2. What is the first step?

Answers

Yoshi needs to find the inverse of f(x) = 5x – 2. The first step is to Switch x and y. The correct answer is option C.

In mathematics, an inverse function is a function that "undoes" the actions of another function. If a function f(x) maps an input x to an output y, the inverse function, denoted as f^(-1)(x) or sometimes written as f(x)^(-1), maps the output y back to the original input x. The correct answer is option C.

To find the inverse of a function, the first step is to switch the x and y variables. In this case, the function is f(x) = 5x - 2.

To find the inverse, we need to switch x and y, so the new function becomes x = 5y - 2.

It's important to note that not all functions have an inverse. A function must be one-to-one (each input maps to a unique output) for an inverse to exist. Additionally, the domain and range of a function and its inverse are swapped.

Learn more about Inverse here:

brainly.com/question/11735394

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Answer:

D. Replace f(x) with y

Step-by-step explanation:

apex

In a city known for many tech start-ups, 311 of 800 randomly selected college graduates with outstanding student loans currently owe more than $50,000. In another city known for biotech firms, 334 of 800 randomly selected college graduates with outstanding student loans currently owe more than $50,000. Perform a two-proportion hypothesis test to determine whether there is a difference in the proportions of college graduates with outstanding student loans who currently owe more than $50,000 in these two cities. Use α=0.05. Assume that the samples are random and independent. Let the first city correspond to sample 1 and the second city correspond to sample 2. For this test: H0:p1=p2; Ha:p1≠p2, which is a two-tailed test. The test results are: z≈−1.17 , p-value is approximately 0.242

Answers

Answer:

Null hypothesis: $p_(1) - p_(2)=0$

Alternative hypothesis: $p_(1) - p_(2) \neq 0$

$z=\frac{0.389-0.418}{\sqrt{0.403(1-0.403)((1)/(800)+(1)/(800))}}=-1.182$

$p_v =2*P(Z<-1.182)=0.2372$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that we don't have significant difference between the two proportions.

Step-by-step explanation:

1) Data given and notation

$X_(1)=311$ represent the number college graduates with outstanding student loans currently owe more than $50,000 (tech start-ups)

$X_(2)=334$ represent the number college graduates with outstanding student loans currently owe more than $50,000 ( biotech firms)

$n_(1)=800$ sample 1

$n_(2)=800$ sample 2

$p_(1)=(311)/(800)=0.389$ represent the proportion of college graduates with outstanding student loans currently owe more than $50,000 (tech start-ups)

$p_(2)=(334)/(800)=0.418$ represent the proportion of college graduates with outstanding student loans currently owe more than $50,000 ( biotech firms)

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.05$ significance level given

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference in the two proportions, the system of hypothesis would be:

Null hypothesis: $p_(1) - p_(2)=0$

Alternative hypothesis: $p_(1) - p_(2) \neq 0$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_(1)-p_(2)}{\sqrt{\hat p (1-\hat p)((1)/(n_(1))+(1)/(n_(2)))}}$ (1)

Where $\hat p=(X_(1)+X_(2))/(n_(1)+n_(2))=(311+334)/(800+800)=0.403$

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.389-0.418}{\sqrt{0.403(1-0.403)((1)/(800)+(1)/(800))}}=-1.182$

4) Statistical decision

Since is a two sided test the p value would be:

$p_v =2*P(Z<-1.182)=0.2372$

Find the cost of lodging: A resort offers a double room for $87.00. Meals in the restaurant are $9.00 per person for breakfast, $14.00 per person for lunch, and $16.00 per person for dinner. How much would it cost two people to stay in the resort each day?

Answers

Answer:

Step-by-step explanation:

Hotel room = 87.00 a double room means for two people

breakfast = 9.00 X 2 = 18.00

Lunch 14.00 X 2 = 28.00

Dinner 16.00 X 2 = 32.00

add the amounts all together 87 + 18 + 28+ 32 =$165.00 for 2 people

Find the distance between (-8, -2)
and 6, -1)

Answers

The distance between the given coordinate points is $√(197)$ units.

The given coordinate points are (-8, -2) and (6, -1).

The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On $2D$ plane the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is Distance $= √((x_2-x_1)^2+(y_2-y_1)^2)$ .