8a^3-36a^2+54a-27-64p^3

Solve the following system of equations using the elimination method.

Margaret [11]

So for eliminating, you only solve for one variable first.

I solved for y, so I multiplied by -4 to eliminate the x.

Then I got y= -1

I then substituted that to one of the equations to get x.

3 0

2 years ago

one group of friends has 5 cookies to share between 3 people.a second group of friends has 8 cookies to share between 6 people.w

Paul [167]

Group 1:-
5 cookies
3 people
5/3

Group 2:
8 cookies
6 people
8/6

Group 1 each person gets 5/3 and in group 2 each person gets 8/6.

Which is more?

5/3

5 ÷ 3 ≈ 1.6

8/6

8 ÷ 6 ≈ 1.3

Is 1.3 more or 1.6?

1.6 is more.

5/3 (group 1) receive more.

8 0

2 years ago

So, Christian has a collection of 18 shark teeth. He identified them as 6 tiger shark teeth, 8 sand shark teeth, and the rest as

svetoff [14.1K]

Answer:

So, the question means that if we add the number of tiger shark teeth and the sand shark teeth and subtract it from the total number of teeth, we will get the number of bull shark teeth. And, the number of bull shark teeth is 4.

Step-by-step explanation:

So, the question means that if we add the number of tiger shark teeth and the sand shark teeth and subtract it from the total number of teeth, we will get the number of bull shark teeth.

Since Christian has 18 shark teeth, and 6 are tiger shark teeth, 8 are sand shark teeth and the rest are bull shark teeth.

Let x represent the number of bull shark teeth.

So, total number of shark teeth = number of tiger shark teeth + number of sand shark teeth + number of bull shark teeth.

18 = 6 + 8 + x

18 = 14 + x

subtracting 14 from both sides, we have

18 - 14 = 14 - 14 + x

4 = 0 + x

4 = x

x = 4

So, the number of bull shark teeth is 4.

4 0

2 years ago

Suppose the standard deviation of a normal population is known to be 3, and H0 asserts that the mean is equal to 12. A random sa

blagie [28]

Answer:

$z=\frac{12.95-12}{\frac{3}{\sqrt{36}}}=1.9$

$p_v =P(z>1.9)=0.0287$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 5% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=12.95$ represent the sample mean

$\sigma=3$ represent the population standard deviation for the sample

$n=36$ sample size

$\mu_o =12$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

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

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 12, the system of hypothesis would be:

Null hypothesis: $\mu \leq 12$

Alternative hypothesis: $\mu > 12$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{12.95-12}{\frac{3}{\sqrt{36}}}=1.9$

P-value

Since is a right tailed test the p value would be:

$p_v =P(z>1.9)=0.0287$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 5% of signficance.

4 0

3 years ago

Read 2 more answers

The equation below represents the function p.

svet-max [94.6K]

Answers:

1)Tthe first answer is that as x increases the value of p(x) approaches a number that is greater than q (x).

2) the y-intercept of the function p is greater than the y-intercept of the function q.

Explanation:

1) Value of the functions as x increases.

Function p:

$p(x)= ( \frac{2}{5} )^{x} -3$

As x increases, the value of the function is the limit when x → ∞.

Since [2/5] is less than 1, the limit of [2/5]ˣ when x → ∞ is 0, and the limit of p(x) is 0 - 3 = -3.

While in the graph you see that the function q has a horizontal asymptote that shows that the limit of q (x) when x → ∞ is - 4.

Then, the first answer is that as x increases the value of p(x) approaches a number that is greater than q (x).

2) y - intercepts.

i) To determine the y-intercept of the function p(x), just replace x = 0 in the equation:
p(x) = [ 2 / 5]⁰ - 3 = 1 - 3 = - 2

ii) The y-intercept of q(x) is read in the graph. It is - 3.

Then the answer is that the y-intercept of the function p is greater than the y-intercept of the function q.

4 0

2 years ago

8a^3-36a^2+54a-27-64p^3​

8a^3-36a^2+54a-27-64p^3