PT=x+2, TR=y, QT=2x, TS=y+3

Evaluate the expression 1/2x - 2/3y when x = 4 and y = -3

ollegr [7]

Answer:

-1

Step-by-step explanation:

Equation: 1/2x-2/3y

Swap out the x and y with the numbers.

1/2 x 4/1 -2/3 x -3

Solve.

2-3

-1

3 0

3 years ago

Read 2 more answers

Shelia's measured glucose level one hour after a sugary drink varies according to the normal distribution with μ = 117 mg/dl and

TiliK225 [7]

Answer:

The level L such that there is probability only 0.01 that the mean glucose level of 6 test results falls above L is L = 127.1 mg/dl.

Step-by-step explanation:

To solve this problem, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 117, \sigma = 10.6, n = 6, s = \frac{10.6}{\sqrt{6}} = 4.33$

What is the level L such that there is probability only 0.01 that the mean glucose level of 6 test results falls above L ?

This is the value of X when Z has a pvalue of 1-0.01 = 0.99. So X when Z = 2.33.

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$2.33 = \frac{X - 117}{4.33}$

$X - 117 = 2.33*4.33$

$X = 127.1$

The level L such that there is probability only 0.01 that the mean glucose level of 6 test results falls above L is L = 127.1 mg/dl.

6 0

3 years ago

the probability that we encounter a green light at the corner of college and main is 0.35, a yellow light 0.04, and a red light

Ostrovityanka [42]

Answer:

21% probability you will hit a green light on monday and a red light on tuesday

Step-by-step explanation:

When two events, A and B, are independent, we have that:

$P(A \cap B) = P(A) \times P(B)$

In this problem, we have that:

Event A: Green light on monday.

Event B: Red light on tuesday.

The probability that we encounter a green light at the corner of college and main is 0.35

This means that $P(A) = 0.35$

The probability that we encounter a red light is 0.61:

This means that $P(B) = 0.61$

These events are independent, that is, the light color on Tuesday is independent of the color on Monday. So

$P(A \cap B) = P(A) \times P(B) = 0.35 \times 0.6 = 0.21$

21% probability you will hit a green light on monday and a red light on tuesday

8 0

3 years ago

A hot tub that holds 300 gallons of water drains at a rate of 8 gallons write an equation that represents how many gallons of wa

Salsk061 [2.6K]

Answer:the number of gallons of water left in the tub after it has drained for x minutes is 300 - 8x

Step-by-step explanation:

A hot tub that holds 300 gallons of water drains at a rate of 8 gallons.

Let x represent the number of minutes for which the hot tub has drained water.

If the hot tub drains 8 gallons of water per minute, it means that in x minutes, the number of gallons of water that the hot tub would have drained is 8x

Therefore, the number of gallons of water left in the tub after it has drained for x minutes would be

300 - 8x

7 0

3 years ago

An animal park has lions,tiger an zebras.2/5 of the animals are lions and 3/10 of the animals are zebras. what percentage are ti

maksim [4K]

Answer:

3/10

Step-by-step explanation:

You have to make them the same fraction.

2/5 = 4/10

3/10 =3/10

3/10 + 4/10 = 7/10

10/10 - 10/10 =3/10

3/10 is the amount of tigers.

4 0

2 years ago