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2 years ago

The sum of two numbers is 90. The larger number is 14 more than 3 times the smaller number. Find the numbers

Mathematics

1 answer:

e-lub [12.9K]2 years ago

7 0

Answer:

The numbers are 19 and 71.

Step-by-step explanation:

Let x and y represent the two numbers. Then x + y = 90.

Also, if we assume that the larger number is y, then y = 3x + 14.

We must solve this system of linear equations. Since we already have the result of solution for y (y = 3x + 14), let's use the substitution method to find the solution:

x + y = 90 becomes x + 3x + 14 = 90, or:

4x = 76. Thus, x = 76/4, or 19. If x = 19, then y = 3(19) + 14, or y = 71.

The numbers are 19 and 71.

Note that these add up to 90, as they must, and that 71 is 14 more than 3 times 19.

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Cory made 4{,}500 \text{ g}4,500 g4, comma, 500, start text, space, g, end text of candy. He saved 1\text{ kg}1 kg1, start text,

Len [333]

Your question is not well formatted and it's incomplete

Question goes thus:

Cory made 4500 g of candy. He saved 1 kg to eat later. He divided the rest of the candy over 7 bowls to serve at his party.

How many grams of candy did Cory serve in each bowl?

Answer:

There are 500 g of candy in each bowl served at the party

Step-by-step explanation:

Given

Size of candy = 4,500 g

Saved candy = 1 kg

Number of bowls = 7

Required

Size of candy served per bowl.

From the question, 1 kg of candy was saved to eat at a later time.

This means that the candy shared at the party is 1kg less than the total candy made.

Mathematically, we have

Shared candy = Total candy - saved candy

Shared candy = 4,500g - 1kg

----------------------------

Convert 1kg to grams

1 kg = 1,000 g.

----------------------------

So,

Shared candy = 4,500g - 1,000g

Shared candy = 3,500g

To get the size of candy in each bowl, we divide the shared candy by number of bowls.

Size of candy = 3,500 ÷ 7

Size of candy = 500.

Hence, there are 500 g of candy in each bowl served at the party

4 0

2 years ago

The following differential equation is separable as it is of the form dP/dt = g(P)h(t).

dedylja [7]

Answer:

$P(1-P) = Ae^t$

Step-by-step explanation:

given differential equation is

$\frac{dP}{dt} =P-P^2\\\frac{dP}{dt} = g(P) h(t)\\g(P) = P-P^2\\h(t) = 1$

So this is separable

We separate as

$\frac{dP}{P-P^2} =1dt\\\frac{dP}{P(1-P)} =1dt$

Resolve into partial fractions to solve this

$dP(\frac{1}{P}+ \frac{1}{1-P} ) = 1dt\\ln P(1-P) = t+C\\P(1-P) = Ae^t$

So solution is $P(1-P) = Ae^t$

7 0

2 years ago

On a coordinate plane, a line is drawn from point K to point J. Point K is at (160, 120) and point J is at (negative 40, 80).

Nadusha1986 [10]

Answer:

the answer is (40,96)

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

A quality control manager at an auto plant measures the paint thickness on newly painted cars. A certain part that they paint ha

Scorpion4ik [409]

Answer:

78.88% probability that the mean thickness in the sample of 100 points is within 0.1 mm of the target value

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 2, \sigma = 0.8, n = 100, s = \frac{0.8}{\sqrt{100}} = 0.08$

What is the probability that the mean thickness in the sample of 100 points is within 0.1 mm of the target value?

This is the pvalue of Z when X = 2 + 0.1 = 2.1 subtracted by the pvalue of Z when X = 2 - 0.1 = 1.9. So

X = 2.1

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{2.1 - 2}{0.08}$

$Z = 1.25$

$Z = 1.25$ has a pvalue of 0.8944

X = 1.9

$Z = \frac{X - \mu}{s}$

$Z = \frac{1.9 - 2}{0.08}$

$Z = -1.25$

$Z = -1.25$ has a pvalue of 0.1056

0.8944 - 0.1056 = 0.7888

78.88% probability that the mean thickness in the sample of 100 points is within 0.1 mm of the target value

8 0

2 years ago

Cameron buys 2.45 pounds of apples and 1.65 pounds of pears. Apples and pears each cost c dollars per pound. If the total cost a

Leto [7]

Answer:

2.45c + 1.65c = 4.12 + 0.75

Step-by-step explanation:

To write an equation to find the value for c, we need to declare what c is first.

c = price of fruit

2.45c + 1.65c = 4.12 + 0.75

Now we multiplied c to 2.45 and 1.65 and added them together, because whatever the value of c is will give us the equivalence of the sum of 4.12 + 0.75.

Now to check if the equation is right, let's solve for c.

2.45c + 1.65c = 4.12 + 0.75

4.1c = 4.87

Now to get the value of c, we divide both sides of the equation by 4.1.

$\dfrac{4.1c}{4.1}=\dfrac{4.87}{4.1}$

c = 1.19

Now let's substitute the value of c in the equation to see if we got it right.

2.45(1.19) + 1.65(1.19) = 4.12 + 0.75

2.92 + 1.96 = 4.87

4.87 = 4.87

Therefore concluding that the value of c is 1.19.

7 0

2 years ago