Ns

A larger number is 2 more than 4 times a smaller number. The larger number is also 8 more than 2 times the smaller number.

pogonyaev

Answer:

see the explanation

Step-by-step explanation:

Let

x ----> the smaller number

y ----> the larger number

we know that

A larger number is 2 more than 4 times a smaller number

Identify the key words

is (=)---> equal

more (+) ---> addition

times (*) ---> multiplication

That means

The larger number y is equal to multiply the smaller number x by 4 and then adds 2

so

$y=4x+2$ ----> equation A

The larger number is also 8 more than 2 times the smaller number

Identify the key words

is (=)---> equal

more (+) ---> addition

times (*) ---> multiplication

That means

The larger number y is equal to multiply the smaller number x by 2 and then adds 8

so

$y=2x+8$ ----> equation B

Solve the system of equations by substitution

equate equation A and equation B

$4x+2=2x+8$

$4x-2x=8-2\\2x=6\\x=3$

Find the value of y

substitute the value of x in equation A or equation B

$y=4(3)+2=14$

therefore

The smaller number is 3 and the larger number is 14

5 0

3 years ago

Read 2 more answers

deandre downloaded 8 apps onto his tablet in 12 secs at this rate how many apps could he download in one minute

Misha Larkins [42]

Because 1 minute is 60 seconds, and it takes 12 seconds to download 8 apps, the first thing we need to do is find out how many "sets" of 12 seconds can go in 60 seconds:

60 / 12 = 5

Now, all we have to do is multiply the number of apps by 5, and we get our answer:

8 · 5 = 40

So, it would take Deandre 1 minute to download 40 apps.

7 0

3 years ago

A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. State the h

Soloha48 [4]

Answer:

Null hypothesis: $\mu \leq 60$

Alternative hypothesis: $\mu > 60$

Since we don't know the population deviation, 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:

$t=\frac{67-60}{\frac{12}{\sqrt{16}}}=2.33$

Step-by-step explanation:

Data given and notation

$\bar X=67$ represent the sample mean

$s=12$ represent the population standard deviation for the sample

$n=16$ sample size

$\mu_o =60$ represent the value that we want to test

$\alpha$ 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 higher than 60, the system of hypothesis would be:

Null hypothesis: $\mu \leq 60$

Alternative hypothesis: $\mu > 60$

Since we don't know the population deviation, 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:

$t=\frac{67-60}{\frac{12}{\sqrt{16}}}=2.33$

4 0

3 years ago

An airplane flies 2700 miles to Los Angeles to NYC. When the plane flies back to LA, is it flying in a negative direction? use a

dolphi86 [110]

Answer:

Distance = abs(-1700)

Distance = 1700 miles

Step-by-step explanation:

NYC is located East of Los Angels.

The Airplane flies from Los Angeles to the left direction from NYC.

Which is negative direction.

Therefore, distance = -1700

Here the distance cannot be negative even though if it flies in negative direction.

Therefore, we use the absolute value.

The absolute value of a number is always positive.

So, distace = abs( -1700)

Distance = 1700 miles.

Hope this will help you understand the concept.

Thank you.

5 0

4 years ago

What is the center of the circle given by the equation below?

Helen [10]

Answer:

C: (4, 8)

Step-by-step explanation:

Rewrite the given equation x² - 8x = -y² + 16y - 44 in std. form:

x² - 8x + 16 - 16 + y² - 16y + 64 = 64 - 44, or

(x - 4)² + (y - 8)² = 64 - 44 + 16

Comparing this to (x - h)² + (y - k)² = 6²

we see that h = 4 and k = 8. The radius is 6. The center is at (4, 8) (Answer C).

5 0

4 years ago