I need help writing an expression

larisa86 [58]

Part A
To estimate this, we should first look at our fractions and see if they can be combined to form a whole number. In this case, $\frac{3}{5}$ and $\frac{2}{3}$ equal approximately 1. We can add this "1" to the other to full gallons to estimate that the painter needs about 3 gallons.

Part B
To find the exact amount, we should first change the mixed numbers to improper fractions. We do this by multiplying the denominator by the whole number, adding the numerator, and placing that value over the denominator.

$1 \frac{3}{5} \\ \\ (5*1)+3 =8 \\ \\ \frac{8}{5} \\ \\ \\ \\ 1 \frac{2}{3} \\ \\ (3*1)+2=5 \\ \\ \frac{5}{3} 
$

Now, we need to find the least common denominator. This is the lowest value that both denominators will divide evenly into. In this case, that number is 15.

Next, we should multiply both fractions so that the denominator is that number. Remember that we must also multiply the numerator for the fraction to remain equivalent to its original value.

$\frac{8}{5} *3 = \frac{24}{15} \\ \\ \frac{5}{3} *5 = \frac{25}{15}$

Now, we can simply add our numerators.

$25+24=49$

We know that he needs $\frac{49}{15}$ gallons of paint, but this is not in the most simplified format. To simplify, we need to turn our improper fraction back to a mixed number. To do this, we need to divide our numerator by the denominator to create our whole number, and the remainder becomes our new numerator.

$\frac{49}{15} \\ \\ 49 / 15 = 3(Remainder: 4) \\ \\ 3\frac{4}{15}$

Using that logic, we can see that the painter needs exactly $3 \frac{4}{15}$ gallons of paint.

4 0

2 years ago

The sum of 4 and the product of 5 and x is equal to 5 less than the product of 2 and x. What is the value of x?

Alexxandr [17]

Answer:

b. -3

Step-by-step explanation:

i hope this helps :)

7 0

2 years ago

Evaluate: xy+2x^2, if x=0.1 and y=9.8

shepuryov [24]

Answer: 1

Step-by-step explanation:

$(0.1)(9.8)+2(0.1)^2\\0.98+0.02=1$

6 0

2 years ago

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A math teacher tells her students that eating a healthy breakfast on a test day will help their brain function and perform well

kogti [31]

Answer:

Step-by-step explanation:

Hello!

To test the claim that eating a healthy breakfast improves the performance of students on their test a math teacher randomly asked 46 students what did they have for breakfast before they took the final exam and classified them as:

Group 1: Ate healthy breakfast

X₁: Number of students that ate a healthy breakfast before the exam and earned 80% or higher.

n₁= 26

Group 2: Did not eat healthy breakfast

X₂: Number of students that did not eat a healthy breakfast before the exam and earned 80% or higher.

n₂= 20

After the test she counted the number of students that got 80% or more in the test for each group obtaining the following sample proportions:

p'₁= 0.50

p'₂= 0.40

The parameters of study are the population proportions, if the claim is true then p₁ > p₂

And you can determine the hypotheses as

H₀: p₁ ≤ p₂

H₁: p₁ > p₂

α: 0.05

$Z= \frac{(p'_1-p'_2)-(p_1-p_2)}{\sqrt{p'(1-p')[\frac{1}{n_1} +\frac{1}{n_2}] } } }$ ≈N(0;1)

pooled sample proportion: $p'= \frac{x_1+x_2}{n_1+n_2} =\frac{13+8}{46} = 0.46$

$Z_{H_0}= \frac{(0.5-0.4)-0}{\sqrt{0.46(1-0.46)[\frac{1}{26} +\frac{1}{20}] } } }= 0.67$

p-value: 0.2514

The decision rule is:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

The p-value: 0.2514 is greater than the significance level 0.05, the test is not significant.

At a 5% significance level you can conclude that the population proportion of math students that obtained at least 80% in the test and had a healthy breakfast is equal or less than the population proportion of math students that obtained at least 80% in the test and didn't have a healthy breakfast.

So having a healthy breakfast doesn't seem to improve the grades of students.

I hope this helps!

5 0

2 years ago

HELPPPPPP AHHH PLAESEEEEEEE

weqwewe [10]

Answer:

The answer is D 3x+y=1 and 3x-2y=16

Step-by-step explanation:

4 0

2 years ago

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I need help writing an expression​

I need help writing an expression