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2 years ago

The sum of two numbers is 80. The larger number is four more than three times the smaller number. Find both numbers.

Mathematics

1 answer:

nexus9112 [7]2 years ago

3 0

Let the smaller number = X

Then the larger number is 3x+4 ( four more than 3 times the smaller number)

The sum of both numbers = 80

so you have X + 3X+4 = 80

Simplify the left side:

4x+4 = 80

Subtract 4 from each side:

4x = 76

Divide both sides by 4:

X = 76/4

X = 19

The smallest number is 19

The largest number is 80 - 19 = 61 ( check: 3*19 = 57+4 = 61)

The two numbers are 19 and 61

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A juice drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of drink on an average. Any overfill

ozzi

Answer:

d. The average is equal to 12 ounces.

Step-by-step explanation:

In this problem, the drink filling machine must be perfectly calibrated at 12 ounces since it needs to be shut down in cases of overfilling (mean > 12 ounces) and underfilling (mean < 12 ounces). Therefore, the correct approach would be to test if the mean is 12 ounces and the correct set of hypothesis would be:

$H_0:\mu=12\\H_a:\mu\neq 12$

The correct alternative is d. The average is equal to 12 ounces.

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2 years ago

Samir is an expert marksman. When he takes aim at a particular target on the shooting range, there is a 0.950.950, point, 95 pro

bearhunter [10]

The question is incomplete. Here is the complete question:

Samir is an expert marksman. When he takes aim at a particular target on the shooting range, there is a 0.95 probability that he will hit it. One day, Samir decides to attempt to hit 10 such targets in a row.

Assuming that Samir is equally likely to hit each of the 10 targets, what is the probability that he will miss at least one of them?

Answer:

40.13%

Step-by-step explanation:

Let 'A' be the event of not missing a target in 10 attempts.

Therefore, the complement of event 'A' is $\overline A=\textrm{Missing a target at least once}$

Now, Samir is equally likely to hit each of the 10 targets. Therefore, probability of hitting each target each time is same and equal to 0.95.

Now, $P(A)=0.95^{10}=0.5987$

We know that the sum of probability of an event and its complement is 1.

So, $P(A)+P(\overline A)=1\\\\P(\overline A)=1-P(A)\\\\P(\overline A)=1-0.5987\\\\P(\overline A)=0.4013=40.13\%$

Therefore, the probability of missing a target at least once in 10 attempts is 40.13%.

6 0

2 years ago

Read 2 more answers

Determine the number of atoms in 98.3 g mercury, Hg

Arisa [49]

The answer is 2.95 × 10²³ atoms

Atomic mass is 200.59 g.
So, 1 mole has 200.59 g. Let's calculate how many moles have 98.3 g:
1M : 200.59g = x : 98.3g
x = 98.3 g * 1 M : 200.59 g = 0.49 M

To calculate this, we will use Avogadro's number which is the number of units (atoms, molecules) in 1 mole of substance:

6.023 × 10²³ atoms per 1 mole
How many atoms are in 0.49 mole:
6.023 × 10²³ atoms : 1M = x : 0.49M
x = 6.023 × 10²³ atoms : 1M * 0.49M = 2.95 × 10²³ atoms

8 0

2 years ago

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A business breaks even when the production costs are equal to the revenue. The expression 120+4x represents the cost of producin

nika2105 [10]

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

The expression 120+4x represents the cost of producing x items. The selling price is $5 for each item.

The net income formula:

y= (5 - 4)x - 120

(5-4)= contribution margin per unit sold (x)

120= fixed costs

To calculate the break-even point in units, we need to use the following formula:

Break-even point in units= fixed costs/ contribution margin per unit

Break-even point in units= 120 / 1

Break-even point in units= 120 units

Prove:

y= 1*120 - 120

y= 0

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2 years ago

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2 years ago