# 8.The gas tank on Kayla's car holds 16 gallons of gas. The fuel gauge of her car shows that the gas tank is full. How many gallons of gas are in the gas tank? Your answer This is a required question

Answer: the answer you are looking for is 12! have a great day!:)

A. 11.1
B. 6.7
C. 13
D. 4.1

## C.13

2. A faucet for a 30-gallon bathtub fills at a rate of 3 gallons per minute.If the drain lets water out at 1.5 gallons per minute, how long would it
take for the tub to overflow if both the faucet and drain were open at the
same time?

20

Step-by-step explanation:

Knowing that it is a 30-gallon bathtub.

And it fills at a rate of 3 gallons per minute.

But also drains 1.5 gallons per minute.

So this is for the first minute.

3 - 1.5 = 1.5

So there will be 1.5 gallons of water in the tub after the first minute.

Now do,

30 ÷ 1.5 = 20

It will take 20 full minutes for the bathtub to fill up.

T/F: The shapes are similar.

Shape DCBA ~ Shape SRQP

Shape: SRQP
Hope this helps

consider a sequence of independent tosses of a biased coin at times k=0,1,2,…,n. On each toss, the probability of Heads is p, and the probability of Tails is 1−p.A reward of one unit is given at time k, for k∈{1,2,…,n}, if the toss at time k resulted in Tails and the toss at time k−1 resulted in Heads. Otherwise, no reward is given at time k.Let R be the sum of the rewards collected at times 1,2,…,n.We will find E[R] and var(R) by carrying out a sequence of steps. Express your answers below in terms of p and/or n using standard notation. Remember to write '*' for all multiplications and to include parentheses where necessary.We first work towards finding E[R].1. Let Ik denote the reward (possibly 0) given at time k, for k∈{1,2,…,n}. Find E[Ik].E[Ik]=2. Using the answer to part 1, find E[R].E[R]=The variance calculation is more involved because the random variables I1,I2,…,In are not independent. We begin by computing the following values.3. If k∈{1,2,…,n}, thenE[I2k]=4. If k∈{1,2,…,n−1}, thenE[IkIk+1]=5. If k≥1, ℓ≥2, and k+ℓ≤n, thenE[IkIk+ℓ]=6. Using the results above, calculate the numerical value of var(R) assuming that p=3/4, n=10.var(R)=

1. p*(1-p)

2. n*p*(1-p)

3. p*(1-p)

4. 0

5. p^2*(1-p)^2

6. 57/64

Step-by-step explanation:

1. Let Ik denote the reward (possibly 0) given at time k, for k∈{1,2,…,n}. Find E[Ik].

E[Ik]=  p*(1-p)

2. Using the answer to part 1, find E[R].

E[R]=  n*p*(1-p)

The variance calculation is more involved because the random variables I1,I2,…,In are not independent. We begin by computing the following values.

3. If k∈{1,2,…,n}, then

E[I2k]= p*(1-p)

4. If k∈{1,2,…,n−1}, then

E[IkIk+1]=  0

5. If k≥1, ℓ≥2, and k+ℓ≤n, then

E[IkIk+ℓ]=  p^2*(1-p)^2

6. Using the results above, calculate the numerical value of var(R) assuming that p=3/4, n=10.

var(R)= 57/64

8.1 Recognising and describing 2D shapes and solids Two pairs of opposite angles equal the name of each 2D shape that is described. rent lengths' One pair of opposite angles equal All angles 90° 8. TH It Two pairs of parallel sides ✓ One pair of parallel sides Two pairs of equal sides ✓ Four equal sides Quadrilateral Square Rectangle Parallelogram Rhombus Kite Trapezium Exercise 8.1 1 Copy and complete the table to show a description of the 2D quadrilaterals. The parallelogram has been done for you.​

Hopefully this graph helps you!

Here is the completed table showing the description of 2D quadrilaterals:

Quadrilateral Two pairs of opposite angles equal One pair of opposite angles equal Two pairs of parallel sides One pair of parallel sides Two pairs of equal sides All angles 90°
Square ✓ ✓ ✓
Rectangle ✓ ✓ ✓
Parallelogram ✓ ✓
Rhombus ✓
Kite
Trapezium ✓ ✓
Note: "Trapezium" is the British English term for what is called a "trapezoid" in American English.

Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. Identify the ​P-value.

hello your question has some missing parts below is the missing part

Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean.

Identify the p-value.

Source DF SS MS F p

Factor 3 13.500 4.500 5.17 0.011

Error 16 13.925 0.870

Total 19 27.425

A) 0.011 B) 4.500 C) 5.17 D) 0.870

answer :  p-value = 0.011 ( A )

Step-by-step explanation:

using this information

Source DF SS MS F P

Factor 3 13.500 4.500 5.17 0.011

Error 16 13.925 0.870

Total 19 27.425

significance level = 0.05

given that the significance level = 0.05

and

F statistics are given as :  F = 5.17 , F critical = 3.25

hence the p-value = 0.011

from the analysis the p-value is less than the significance level is lower than the significance level

The p-value in a Minitab analysis of variance (ANOVA) test helps determine whether to reject or accept the null hypothesis that the samples all come from populations with the same mean. You would reject the null hypothesis if your p-value is less than the significance level (α = 0.05). Please refer back to your Minitab results to find this p-value.

### Explanation:

In the context of your Minitab analysis of variance (ANOVA) results, the p-value that you should be looking at to determine the null hypothesis is not explicitly mentioned in your question. However, based on your description, you want to test the hypothesis that the different samples come from populations with the same mean (null hypothesis).

The p-value represents the probability that you would obtain your observed data (or data more extreme) if the null hypothesis were true. Therefore, if the p-value is less than the significance level (α = 0.05), you would reject the null hypothesis, suggesting that the samples do not all come from populations with the same mean. Conversely, if the p-value is larger than 0.05, you would fail to reject the null hypothesis, suggesting that the samples could come from populations with the same mean.

Please refer back to your Minitab results to find this p-value. Usually, it's labeled in the ANOVA table output as 'P' or 'Prob > F'.