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3 years ago

5(4 – x)= -5x + 20 How many solutions do this equation has?

Mathematics

1 answer:

Artyom0805 [142]3 years ago

4 0

It has 2 solutions i believe

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Find all integers $n$ for which $\frac{n^2+n+1}{n-1}$ is an integer.

Grace [21]

$\dfrac{n^2+n+1}{n-1}=\dfrac{(n-1)^2+3(n-1)+3}{n-1}=n-2+\dfrac3{n-1}$

The remainder term $\dfrac3{n-1}$ will never vanish, and will always be rational as long as the denominator is not 1, 3, or -3.

$n-1=1\implies n=2$
$n-1=3\implies n=4$
$n-1=-3\implies n=-2$

7 0

3 years ago

Guided Practice

s2008m [1.1K]

Answer:

1.125%; 0.375%

Step-by-step explanation:

Quarterly interest rate is 4.5 / 4 = 1.125%.

Monthly rate is 4.5 / 12 = 0.375%.

6 0

3 years ago

Solve the system by the elimination method. Check your work. 2a + 3b = 6 5a + 2b - 4 = 0

Lyrx [107]

Solve the system by the elimination method.
2a + 3b = 6
5a + 2b - 4 = 0

multiply thru the top equation by 2
Multiply thru the bottom equation by 3

4a + 6b = 12
15a+ 6b = 12

Subtract and solve for "a":
11a = 0
a = 0

Solve for "b" using 2a + 3b = 6
2*0 + 3b = 6
b = 2

4 0

3 years ago

Is a prime number is a number times itself yes it is

Sladkaya [172]

Answer:

yup

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

In Pennsylvania the average IQ score is 101.5 The variable is normally distributed and the population standard deviation is know

elena-14-01-66 [18.8K]

Answer:

P-value = 0.0368

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 101.5

Sample mean, $\bar{x}$ = 106.4

Sample size, n = 30

Alpha, α = 0.05

Population standard deviation, σ = 15

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 101.5\\H_A: \mu> 101.5$

We use One-tailed(right) z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{106.4 - 101.5}{\frac{15}{\sqrt{30}} } = 1.789$

Now, $z_{critical} \text{ at 0.05 level of significance } = 1.64$

Since,

$z_{stat} > z_{critical}$

We reject the null hypothesis and accept the alternate hypothesis. Thus, students in Pennsylvania have an IQ that is significantly greater than the state average.

P-value can be calculated with the standard normal table.

P-value = 0.0368

P-value is lower than the significance level.

4 0

3 years ago