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1 year ago

Choose the missing step in the given solution to the inequality −x − 10 > 14 + 2x.

Mathematics

2 answers:

Sphinxa [80]1 year ago

8 0

Answer:

a. $-3x>24$

Step-by-step explanation:

We have been given an inequality $-x-10>14+2x$ . We are asked to find the missing step to solve the given inequality.

Let us solve the given inequality.

$-x-2x-10>14+2x-2x$

$-3x-10>14$

$-3x-10+10>14+10$

$-3x>24$

$\frac{-3x}{-3}$

$x$

Therefore, our missing step is $-3x>24$ .

uranmaximum [27]1 year ago

6 0

Missing step : -3x > 24 <== to get that, 10 was added to both sides

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Answer: The probability that a randomly selected catfish will weigh between 3 and 5.4 pounds is 0.596

Step-by-step explanation:

Since the weights of catfish are assumed to be normally distributed,

we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = weights of catfish.

µ = mean weight

σ = standard deviation

From the information given,

µ = 3.2 pounds

σ = 0.8 pound

The probability that a randomly selected catfish will weigh between 3 and 5.4 pounds is is expressed as

P(x ≤ 3 ≤ 5.4)

For x = 3

z = (3 - 3.2)/0.8 = - 0.25

Looking at the normal distribution table, the probability corresponding to the z score is 0.401

For x = 5.4

z = (5.4 - 3.2)/0.8 = 2.75

Looking at the normal distribution table, the probability corresponding to the z score is 0.997

Therefore,.

P(x ≤ 3 ≤ 5.4) = 0.997 - 0.401 = 0.596

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1 year ago

The graph of the function f(x) = (x + 2)(x + 6) is shown below.

iren [92.7K]

Answer:

Step-by-step explanation:

f(x) = (x + 2)(x +6)

1) The function is positive for all real values of x where x > –4 :

COUNTER-EXAMPLE : x = - 3 you have -3>-4 but (-3+2)(-3+6) = -1 ×3 =-3 no positive .

2) The function is positive for all real values of x where

x < –6 or x > –3.

COUNTER-EXAMPLE : x = - 2.5 you have -2.5>-3 but (-2.5+2)(-2.5+6) = -0.5 ×3.5 =-1.75 no positive .

same method for the statement : "The function is negative for all real values of x where

x < –2."

conclusion : statement about the function is true: "The function is negative for all real values of x where

–6 < x < –2."

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2 years ago

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Nina's monthly budget is $2,250. Every month she makes the following payments: $175 for insurance, $129 for utilities, $283 for

choli [55]

The total costs that Nina would have to pay is the sum of the cost of insurance, utilities, and taxes.
C = $175 + $129 + $283 = $587
The highest house payment she could afford is then the difference between her budget and the costs,
P = $2,250 - $587 = $1663
Thus, the answer would be letter B. House B because all the rest of the monthly payment are way over her budget.

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2 years ago

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Times for an ambulance to respond to a medical emergency in a certain town are normally distributed with a mean of 400 seconds a

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Answer:

Step-by-step explanation:

In the normal distribution curve, the mean is in the middle and each line to the left and to the right of that mean represent 1- and 1+ the standard deviation. If our mean is 400, then 400 + 50 = 450; 450 + 50 = 500; 500 + 50 = 550. Going from the mean to the left, we subtract the standard deviation and 400 - 50 = 350; 350 - 50 = 300; 300 - 50 = 250. We are interested in the range that falls between 350 and 450 as a percentage. That range represents the two middle sections, each containing 34% of the data. So the total percentage of response times is 68%. We are looking then for 68% of the 144 emergency response times in town. .68(144) = 97.92 or 98 emergencies that have response times of between 350 and 450 seconds.

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2 years ago

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The telephone company is planning to introduce two new types of executive communications systems that it hopes to sell to its la

cluponka [151]

Answer:

x = 31 hundred dolars and

y = 91/2 = 45.5 hundred dolars

Step-by-step explanation:

Given

R(x) = (40−8x+5y)*x + (50+9x−7y)*y

C(x) = (40−8x+5y)*10 + (50+9x−7y)*29

We can use the equation

P(x) = R(x) - C(x)

where

P(x) is the profit

R(x) is the revenue

and C(x) is the costs

In order to maximize the telephone company's profit, we apply

P'(x) = R(x)' - C(x)' = 0

⇒ R(x)' = ((40−8x+5y)*x + (50+9x−7y)*y)' = (40x-8x²+14xy+50y-7y²)'

⇒ C(x)' = ((40−8x+5y)*10 + (50+9x−7y)*29)' = (1850+181x-153y)'

⇒ P'(x) = -8x²-7y²-141x+203y+14xy-1850

The first-order partial derivatives of these functions are

Px(x,y) = -16x-141+14y

Py(x,y) = -14y+203+14x

Setting these equal to zero and solving we obtain:

-16x+14y-141 = 0

14x-14y+203=0

we get the solution

x = 31 and y = 91/2 = 45.5

Finally, the company should produce 3100 units of the first system, and 4550 units of the second system.

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