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3 years ago

Can someone solve this inequality for x (x–2)a ≤ x+1 if a>1

Mathematics

1 answer:

fiasKO [112]3 years ago

7 0

Answer:

x ≤ (1+2a) / (a-1) where a > 1

Step-by-step explanation:

(x–2)a ≤ x+1

x(a) -2(a) ≤ x + 1

ax -2a ≤ x + 1 (subtract x from both sides)

ax -2a - x ≤ 1 (add 2a to both sides)

ax - x ≤ 1 + 2a (factor out x from left side)

x (a - 1) ≤ 1 + 2a

x ≤ (1+2a) / (a-1) where a > 1

You might be interested in

What is equivalent to 5(x + 12) A x +12 B 2x - 60 C 5x + 60 D 2x - 60

Alex73 [517]

Answer:

$\boxed{\boxed{\pink{\sf Option \ C \ is \ correct .}}}$

Step-by-step explanation:

Given to us is , 5 ( x + 12 ) and we need to find which is its equivalent in the given options .

So,

$\bf = 5 ( x + 12 ) \\\\=\bf 5x + 5\times 12 \\\\=\boxed{\red{\bf 5x + 60 }}$

<h3>Hence option C is correct.</h3>

4 0

2 years ago

The General Social Survey asked a large number of people how much time they spent watching TV each day. The mean number of hours

DerKrebs [107]

Answer:

Yes, we can conclude that the population standard deviation of TV watching times for teenagers is less than 2.66

Step-by-step explanation:

H0 : σ² = 2.66²

H1 : σ² < 2.66²

X²c = (n - 1)*s² ÷ σ²

sample size, n = 40

Sample standard deviation, s = 1.9

X²c = ((40 - 1) * 1.9²) ÷ 2.66²

X²c = 140.79 ÷ 7.0756

X²c = 19.897

Using a confidence level of 95%

Degree of freedom, df = n - 1 ; df = 40 - 1 = 39

The critical value using the chi distribution table is 25.6954

Comparing the test statistic with the critical value :

19.897 < 25.6954

Test statistic < Critical value ; Reject the Null

Hence, we can conclude that the population standard deviation of TV watching times for teenagers is less than 2.66

8 0

3 years ago

A group of 54 college students from a certain liberal arts college were randomly sampled and asked about the number of alcoholic

Ket [755]

Answer:

$t=\frac{5.25-4.73}{\frac{3.98}{\sqrt{54}}}=0.9601$

P-value

First we find the degrees of freedom given by:

$df = n-1= 54-1=53$

Since is a two-sided test the p value would be:

$p_v =2*P(t_{53}>0.9601)=0.3414$

Step-by-step explanation:

Data given and notation

$\bar X=5.25$ represent the sample mean

$s=3.98$ represent the sample standard deviation

$n=54$ sample size

$\mu_o =4.73$ 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 differs from 4.73, the system of hypothesis would be:

Null hypothesis: $\mu =4.73$

Alternative hypothesis: $\mu \neq 4.73$

Since we know don't 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:

$t=\frac{5.25-4.73}{\frac{3.98}{\sqrt{54}}}=0.9601$

P-value

First we find the degrees of freedom given by:

$df = n-1= 54-1=53$

Since is a two-sided test the p value would be:

$p_v =2*P(t_{53}>0.9601)=0.3414$

7 0

3 years ago

The sum of eight times a number and negative exceeds twelve.

11111nata11111 [884]

Answer:8x + -4 > 12

8x > 16

x > 2

Step-by-step explanation:

6 0

2 years ago

Find the missing lengths in the triangle. round to the nearest tenth if necessary

lubasha [3.4K]

Answer:

$x=8,\\y\approx 6.9$

Step-by-step explanation:

The side lengths of all 30-60-90 triangles are in ratio $x:x\sqrt{3}:2x}$ , where $2x$ is the hypotenuse of the triangle and $x$ is the side opposite to the 30 degree angle.

In the given diagram, the side labelled 4 is opposite to the 30 degree angle. Since $x$ is labelled as the hypotenuse of the triangle, $x$ must be $4\cdot 2=\boxed{8}$ .

Variable $y$ must then represent $x\sqrt{3}$ for $x=4$ , yielding $y=4\sqrt{3}\approx \boxed{6.9}$

7 0

2 years ago