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3 years ago

5 − (x + 5) > −2(x + 4)

2 answers:

8 0

$5-(x+5) > -2(x+4)\\\\5-x-5 > -2\cdot x-2\cdot4\\\\5-5-x > -2x-8\\\\-x > -2x-8\ \ \ |add\ 2x\ to\ both\ sides\\\\x > -8\to x\in(-8;\ \infty)$

Georgia [21]3 years ago

4 0

X>−8 answer <<

step by step work

Let's solve your inequality step-by-step.5−(x+5)>−2(x+4)
Step 1: Simplify both sides of the inequality.−x>−2x−8
Step 2: Add 2x to both sides.−x+2x>−2x−8+2x

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Match the following equation to the correct situation.

IRISSAK [1]

Answer:

option D is right

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3 0

3 years ago

1/6(x-5)=1/2(x+6) what is the solution to this equation

Alexandra [31]

Answer:

Exact Form:

x= -23/2

Decimal:

x= -11.5

Mixed Number:

x= -11/2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable

3 0

3 years ago

Read 2 more answers

A small business owner estimates his mean daily profit as $970 with a standard deviation of $129. His shop is open 102 days a ye

Katena32 [7]

Answer:

The probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we select appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e ∑X, will be approximately normally distributed.

Then, the mean of the distribution of the sum of values of X is given by,

$\mu_{x}=n\mu$

And the standard deviation of the distribution of the sum of values of X is given by,

$\sigma_{x}=\sqrt{n}\sigma$

The information provided is:

μ = $970

σ = $129

n = 102

Since the sample size is quite large, i.e. n = 102 > 30, the Central Limit Theorem can be used to approximate the distribution of the shopkeeper's annual profit.

Then,

$\sum X\sim N(\mu_{x}=98940,\ \sigma_{x}=1302.84)$

Compute the probability that the shopkeeper's annual profit will not exceed $100,000 as follows:

$P (\sum X \leq 100,000) =P(\frac{\sum X-\mu_{x}}{\sigma_{x}}$

$=P(Z$

*Use a z-table for the probability.

Thus, the probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.

6 0

3 years ago

Suppose you just purchased a digital music player and have put 12 tracks on it. After listening to them you decide that you like

Vilka [71]

Answer:

a) 9% , not unusual

b) 42.4%

c) 48.4%

d) 11.1% , 44.4% , 44.4%

Step-by-step explanation:

We have the following information from the statement:

n = 12

r = 4

P (likebothofthem) = P (likefirstsong) * P (likesecondsong)

P = 4/12 * 3/11

P = 0.09 = 9%

The probability is not unusual, unusual is considered less than 0.05 or 5%

P (likeneither) = P (notlikefirstsong) * P (notlikesecondsong)

P = 8/12 * 7/11

P = 0.424 = 42.4%

c) P (likeexactlyoneofthem) = P (firstsongliked) * P (secondsongnotliked) + P (firstsongnotliked) * P (secondsongliked)

P = (4/12 * 8/11) + (8/12 * 4/11)

P = 0.484 = 48.4%

P (likebothofthem) = P (likefirstsong) * P (likesecondsong)

P = 4/12 * 4/12

P = 0.111 = 11.1%

The probability is not unusual, unusual is considered less than 0.05 or 5%

P (likeneither) = P (notlikefirstsong) * P (notlikesecondsong)

P = 8/12 * 8/12

P = 0.444 = 44.4%

c) P (likeexactlyoneofthem) = P (firstsongliked) * P (secondsongnotliked) + P (firstsongnotliked) * P (secondsongliked)

P = (4/12 * 8/12) + (8/12 * 4/12)

P = 0.444 = 44.4%

8 0

3 years ago

Solve the equation. show all work 18^(r-10)=93

Elina [12.6K]

Recall the logarithm rules :

a^y = x is the same as log_a x = y

In this case,

a = 18
y = r - 10
x = 93

So,

18^ (r-10) = 93

is the same as

log_18 93 = r - 10

Solve for r to get :

10 + log_18 93 = r

3 0

3 years ago