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vlabodo [156]
3 years ago
10

Ryan is cleaning out his room. His sister gives him 4 boxes of books to put with the 3 books he already had. When he finishes cl

eaning he discovers he now has 35 books on his shelves. How many books were in each box? Write an algebraic expression to represent this problem then solve.
Mathematics
1 answer:
ahrayia [7]3 years ago
3 0

Answer:

8 books were in each box

Step-by-step explanation:

According to the Question,

Assume X is the Number of Books In Each Box.

  • We have, 4 boxes With the Same Number of Books In each Box,Thus Total Book in all box is 4X.
  • And, 3 books Ryan Already Put In Shelves.
  • Now, Total Number Of Book After Cleaning is 35 Books.

Algebraic Expression,

4X + 3 = 35

4X = 35 - 3

4X = 32  ⇔  X=8 books in Each Box.

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Find the surface area of the cube shown.<br> (_________) square centimeters
Step2247 [10]

Answer:

The answer is: 181.5 square centimeters.

Step-by-step explanation:

The cube has six faces, and each face is a square with sides of length 5.5, so the area of one of this faces is 5.5^2=30.25, adding the six faces, we get the answer: A=6\times 30.25=181.5

5 0
3 years ago
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What is the vertex of the quadratic function?
Debora [2.8K]

Answer:

f(x) = x² - 4x - 12

Step-by-step explanation:

f(x) = (x - 6)(x + 2)

f(x) = x² + 2x - 6x - 12

f(x) = x² - 4x - 12

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3 years ago
2. A marketing firm is trying to estimate the proportion of potential car buyers that would consider
Maurinko [17]

Answer:

a. The number of people that should be in the pilot study are 600 people

b. The point estimate is 0.62\overline 6

c. At 95% confidence level the true population proportion of potential car buyers of hybrid vehicle is between the confidence interval (0.588, 0.6654)

d. Two ways to reduce the margin of error are;

1) Reduce the confidence interval

2) Use a larger sample size

Step-by-step explanation:

a. The given parameters for the estimation of sample size is given as follows;

The margin of error for the confidence interval, E = 4% = 0.04

The confidence level = 95%

The sample size formula for a proportion as obtained from an online source is given as follows;

n = \dfrac{Z^2 \times P \times (1 - P)}{E^2}

Where, P is the estimated proportions of the desired statistic, therefore, we have for a new study, P = 0.5;

Z = The level of confidence at 95% = 1.96

n + The sample size

Therefore, we have;

n = \dfrac{1.96^2 \times 0.5 \times (1 - 0.5)}{0.04^2} = 600.25

Therefore, the number of people that should be in the pilot study in order to meet this goal at 95% confidence level is n = 600 people

b. The point estimate for the population proportion is the sample proportion  given as follows;

\hat p = \dfrac{x}{n}

Where;

x = The number of the statistic in the sample

n = The sample size

From the question, we have;

The number of potential car buyers, n = 600

The number of respondent in the sample that indicated that they would consider purchasing a hybrid, x = 376

Therefore, the point estimate, for the proportion of potential car buyers that would consider buying a hybrid vehicle, \hat p = 376/600 = 0.62\overline 6

c. The confidence interval for a proportion is given as follows

CI=\hat{p}\pm z\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

Therefore, we get;

CI=0.62 \overline 6\pm 1.96\times \sqrt{\dfrac{\hat{0.62 \overline 6}\cdot (1-\hat{0.62 \overline 6})}{600}}

C.I. ≈ 0.6267 ± 0.0387

The 95% confidence interval for the true population proportion of potential buyers of hybrid vehicle, C.I. =  (0.588, 0.6654)

d. The margin of error is given by the following formula;

MOE_\gamma = z_\gamma  \times \sqrt{\dfrac{\sigma ^2}{n} }

Where;

MOE_\gamma = Margin of error at a given level of confidence

z_\gamma = z-score

σ = The standard deviation

n = The sample size

Therefore, the margin error can be reduced by the following two ways;

1) Reducing the confidence interval and therefore, the z-score

2) Increasing the sample size

6 0
2 years ago
The ratio of boys to girls in a school is 5:4. if there are 180 students, how many girls are there?
vladimir2022 [97]
Salutations!

<span>The ratio of boys to girls in a school is 5:4. if there are 180 students, how many girls are there?

Let the number of girls and boys be 'x'.

</span>5x + 4x = 180
<span>
Add 5 and 4

</span>9x = 180
<span>
</span>x = 20
<span>
Now, multiply the ratios by 20.

Boys = 20 </span>× 5 = 100

Girls = 20 × 4 = 80.

There were 80 girls.

Hope I helped (:

Have a great day!
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tia_tia [17]

Answer:

Step-by-step explanation:

Yes, a rhombus

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