Triangle properties help

Which equation represents a linear function

Katarina [22]

Answer: B

Step-by-step explanation:

4 0

3 years ago

PLZ HELP ILL GIVE 15 POINTS!!

Anna35 [415]

Answer:

There would be 14 cats and 9 dogs

Step-by-step explanation:

In order to find the amount of cats and dogs, we need to set up the system of equations. To do so, start by setting cats as x and dogs as y. Now we can write the first equation to show the total number of animals.

cats + dogs = 23

x + y = 23

Now we can write a second one that shows the difference in the number of cats and dogs.

cats - dogs = 5

x - y = 5

Now we can add the two equations together to solve for x.

x + y = 23

x - y = 5

2x = 28

x = 14

Now that we have the number of cats, we can find the number of dogs by using either equation.

x + y = 23

14 + y = 23

y = 9

7 0

4 years ago

Prove that given any three consecutive integers, one of them is divisible by 3. Hint: What are the possible remainders when we d

juin [17]

Answer:

it is proved that from the any three consecutive integers one of them is divisible by 3.

Step-by-step explanation:

Let the first integer = x

The second consecutive integer = x + 1

The third consecutive integer = x + 2

Case 1. take x = 1

The value of first integer = 1

The value of second integer = 1 +1 = 2

The value of third integer = 1 + 2 = 3

Here the third integer is divisible by 3.

Case 2. take x = 2

The value of first integer = 2

The value of second integer = 2 +1 = 3

The value of third integer = 2 + 2 = 4

Here the second integer is divisible by 3.

Case 3. take x = 3

The value of first integer = 3

The value of second integer = 3 +1 = 4

The value of third integer = 3 + 2 = 5

Here the first integer is divisible by 3.

Thus it is proved that from the any three consecutive integers one of them is divisible by 3.

8 0

3 years ago

9 + x + 1 + 2x<br><br> Can someone help me out with this :)

Crank

Answer:

3x + 10

Step-by-step explanation:

9 + x + 1 + 2x

Combine like terms

2x + x = 3x

Combine like terms

9 + 1 = 10

We’re left with 3x + 10

5 0

3 years ago

Read 2 more answers

A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a populat

eimsori [14]

Answer:

$t=\frac{25-24}{\frac{2}{\sqrt{16}}}=2$

$p_v =P(t_{15}>2)=0.0320$

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we reject the null hypothesis, and the true mean is significant higher than 24 years.

Step-by-step explanation:

1) Data given and notation

$\bar X=25$ represent the sample mean

$s=2$ represent the standard deviation for the sample

$n=16$ sample size

$\mu_o =24$ represent the value that we want to test

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

t would represent the statistic (variable of interest)

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

Confidence =0.95 or 95%

$\alpha=0.05$

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the mean is higher than 24, the system of hypothesis would be:

Null hypothesis: $\mu \leq 24$

Alternative hypothesis: $\mu > 24$

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-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:

$t=\frac{25-24}{\frac{2}{\sqrt{16}}}=2$

Calculate the P-value

First we need to calculate the degrees of freedom given by:

$df=n-1=16-1=15$

Since is a one-side upper test the p value would be:

$p_v =P(t_{15}>2)=0.0320$

Conclusion

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we reject the null hypothesis, and the true mean is significant higher than 24 years.

3 0

3 years ago