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2 years ago

Simplify 8(7x-1)+4(x+5)

Mathematics

1 answer:

Talja [164]2 years ago

8 0

First of all, distribute the product of the two parentheses:

$8(7x-1)+4(x+5) = 8\cdot7x - 8\cdot 1 + 4\cdot x + 4 \cdot 5 = 56x-8+4x+20$

Sum like terms:

$60x +12$

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The volume of a gas is 10.0 liters and its pressure is 1.5 atm. If the pressure is decreased to 0.75 atm,

JulsSmile [24]

Answer:

The new volume is 20litres

Step-by-step explanation:

This problem bothers on the expansion of gases

According to Boyle's law

The volume of a given mass of gas at constant temperature is inversely proportional to the pressure

P∝1/v

Pv= constant

Given data

P1= 1.5atm

v1 = 10 litter

P2=0.75atm

v2=?

Applying P1v1= P2v2

v2= P1v1/P2

v2= 1.5*10/0.75

v2= 15/0.75

v2= 20litres

3 0

3 years ago

Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The results from 100 sam

Vlad [161]

Answer

$P(A) = 0.30$

$P(B) = 0.77$

$P(A\ n\ B) = 0.22$

$P(A\ u\ B) = 0.85$

Explanation:

Given

See attachment for proper data presentation

$n = 100$ --- Sample

A = Supplier 1

B = Conforms to specification

Solving (a): P(A)

Here, we only consider data in sample 1 row.

Here:

$Yes = 22$ and $No = 8$

$n(A) = Yes + No$

$n(A) = 22 + 8$

$n(A) = 30$

P(A) is then calculated as:

$P(A) = \frac{n(A)}{Sample}$

$P(A) = \frac{30}{100}$

$P(A) = 0.30$

Solving (b): P(B)

We only consider data in the Yes column.

Here:

$(1) = 22$ $(2) = 25$ and $(3) = 30$

$n(B) = (1) + (2) + (3)$

$n(B) = 22 + 25 + 30$

$n(B) = 77$

P(B) is then calculated as:

$P(B) = \frac{n(B)}{Sample}$

$P(B) = \frac{77}{100}$

$P(B) = 0.77$

Solving (c): P(A n B)

Here, we only consider the similar cell in the yes column and sample 1 row.

i.e. [Supplier 1][Yes]

This is represented as: n(A n B)

$n(A\ n\ B) = 22$

The probability is then calculated as:

$P(A\ n\ B) = \frac{n(A\ n\ B)}{Sample}$

$P(A\ n\ B) = \frac{22}{100}$

$P(A\ n\ B) = 0.22$

Solving (d): P(A u B)

This is calculated as:

$P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)$

This gives:

$P(A\ u\ B) = \frac{30}{100} + \frac{77}{100} - \frac{22}{100}$

Take LCM

$P(A\ u\ B) = \frac{30+77-22}{100}$

$P(A\ u\ B) = \frac{85}{100}$

$P(A\ u\ B) = 0.85$

7 0

2 years ago

LeBron James shot 30 shots per game last season. His season high in shots was 2,000. He wants to earn a different shot per game

laila [671]

Answer:

1700

Step-by-step explanation:

8 0

2 years ago

A sphere has radius of 3 cm. What is the volume of the sphere?

Alex17521 [72]

Answer: 113.04 cm³

Step-by-step explanation: To find the volume of a sphere, start with the formula for the volume of a sphere which is shown below.

$V = \frac{4}{3} \pi r^{3}$

Here, we are given that our sphere has a radius of 3 centimeters.

So plugging into the formula, we have $(\frac{4}{3})(\pi)(3 cm)^{3}$ .

Start by simplifying the exponent.

(3 cm)³ is equal to 3 centimeters · 3 centimeters ·

3 centimeters or 27 cm³.

So we have $(\frac{4}{3})(27 cm^{3})(\pi)$ .

Notice that we can cross-cancel 3 and 27 to 1 and 9.

So we have (4)(9 cm³) which is equal to 36 cm³.

So we have 36π cm³.

So the volume of the sphere is 36π cm³.

Remember that π is approximately equal to 22/7 or 3.14 so we can estimate the value of the volume by plugging in 3.14 for π.

So we have (36)(3.14) which is equal to 113.04 which means

that the volume of approximately equal to 113.04 cm³.

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2 years ago

Is 100 inches greater than 3yd 1 ft?

marshall27 [118]

(3*36 inches) + 12 inches = 120 inches. So no, 100 inches is not greater than 3 yards and a foot.

5 0

2 years ago

Read 2 more answers