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2 years ago

What are the solutions of the compound inequality 2d + 3 ≤ –11 or 3d – 9 > 15?

Mathematics

1 answer:

pentagon [3]2 years ago

3 0

Step-by-step explanation:

$2d + 3 \leqslant - 11 \\ 2d \leqslant - 11 - 3 \\ 2d \leqslant - 14 \\ \frac{2d}{2} \leqslant \frac{ - 14}{2} \\ d \leqslant - 7$

$3d - 9 > 15 \\ 3d > 15 + 9 \\ 3d > 24 \\ \frac{3d}{3} > \frac{24}{3} \\ d = 8$

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If a certain number is increased by 5 one half of the result is three-fifths of the excess of 61 over the number find the number

PSYCHO15rus [73]

Answer:

= 391/11

Let say number = N

a certain number is increased by 5

= N + 5

,one-half of the result

= (N + 5)/2

Three -fifths of the excess of 61 over the number.

= (3/5)(61 - N)

Equating both

(N + 5)/2 = (3/5)(61 - N)

multiplying by 10 both sides

=> 5(N + 5) = 6(61 - N)

=> 5N + 25 = 366 - 6N

=> 11N = 391

=> N = 391/11

Step-by-step explanation:

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2 years ago

Sophia was selling tickets at the high school dance. At the end of the evening, she picked up the cash box and noticed a $5 bill

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The first thing we will do in this case is to define variables:
x = number of individual tickets.
y = number of tickets per couple.
We have then that the system of equations that represents the problem is:
10x + 15y = 590
x + 2y = 68
Solving the system we have:
x = 32
y = 18
Substituting we have:
10 (32) + 15 (18) = 590
320 + 270 = 590
590 = 590
Equality is met, therefore the $ 5 bill belongs to the box.
Answer:
the $ 5 bill belong inside the cash box

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An electric guitar costs $830, with a $225 full-replacement warranty. If the manufacturer sells 532,475 warranties and has to ho

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2 years ago

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What are the possible values of x if (4x – 5)2 = 49? check all that apply. -4/5 -1/2 3 5 7

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4 x - 5 = - 7
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x = - $\frac{1}{2}$
or
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Answer B) and C)

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2 years ago

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The heights of students in a class are normally distributed with mean 55 inches and standard deviation 5 inches. Use the Empiric

maks197457 [2]

Answer: c)[50,60]

Step-by-step explanation:

The Empirical rule says that , About 68% of the population lies with the one standard deviation from the mean (For normally distribution).

We are given that , The heights of students in a class are normally distributed with mean 55 inches and standard deviation 5 inches.

Then by Empirical rule, about 68% of the heights of students lies between one standard deviation from mean.

i.e. about 68% of the heights of students lies between $\text{Mean}\pm\text{Standard deviation}$

i.e. about 68% of the heights of students lies between $55\pm5$

Here, $55\pm5=(55-5, 55+5)=(50,60)$

i.e. The required interval that contains the middle 68% of the heights. = [50,60]

Hence, the correct answer is c) (50,60)

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2 years ago