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3 years ago

A rectangle is 7 feet long by 2 feet wi

Mathematics

1 answer:

arsen [322]3 years ago

4 0

Answer:

Step-by-step explanation:

L = W+2A = 63 = W × (W+2)W^2 + 2W = 63W^2 + 2W — 63 =0(W+9)(W-7) = 0W = 7….. L = W+2 = 9Dimenions are 9′ × 7′

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There are 7 students in a class. If there are 3 seats in the front row, how many ways can the students sit in the front row, ass

oksian1 [2.3K]

Answer:

<h2>35 different ways</h2>

Step-by-step explanation:

Since there are 7 students in a classroom to fill a front row containing 3 seats, we will apply the combination rule since we are to select 3 students from the total number of 7 students in the class.

In combination, if r objects are to be selected from a pool of n objects, this can be done in nCr number of ways.

nCr = n!/(n-r!)r!

Selecting 3 students from 7 students to fill the seats can therefore be done in 7C3 number of ways.

7C3 = 7!/(7-3)!3!

7C3 = 7!/(4)!3!

7C3 = 7*6*5*4!/4!*3*2

7C3 = 7*6*5/6

7C3 = 7*5

7C3 = 35

Hence there are 35 different ways that the student can sit in the front assuming there are no empty seats.

3 0

3 years ago

Which of these lengths is the shortest?Immersive Reader (1 Point) 2.17 m 2007 cm 2 m 107 cm 2.07 m

o-na [289]

Answer:

107 cm

Step-by-step explanation:

2.17 m in cm is 217 cm

2 m is 200 cm

2.07 m is 207 cm

so 107 is the smallest number when all are calculated in cm

4 0

3 years ago

What is the simplified form of the quantity of x plus 6, all over the quantity of x plus 4 + the quantity of x minus 3, all over

11Alexandr11 [23.1K]

Answer:

(x² + 4x + 6)/ 3x + 12

This is the most simplified form

Step-by-step explanation:

Let's simplify the expression:

(x + 6)/(x + 4) + (x - 3)/3

Least Common Denominator : 3 * (x + 4)

[3 * (x + 6) + (x - 3) (x + 4)]/ 3 * (x + 4)

Solving parentheses:

[3x + 18 + x² - 3x + 4x - 12]/ 3 * (x + 4)

Like terms:

(x² + 4x + 6)/ 3x + 12

This is the most simplified form

6 0

4 years ago

A grower believes that one in five of his citrus trees are infected with the citrus red mite. How large a sample should be taken

mihalych1998 [28]

Answer:

n=6147

Step-by-step explanation:

1) Notation and definitions

$X=1$ number of citrus trees that are infected with the citrus red mite.

$n=5$ random sample taken

$\hat p=\frac{1}{5}=0.2$ estimated proportion of citrus trees that are infected with the citrus red mite.

$p$ true population proportion of citrus trees that are infected with the citrus red mite.

Me=0.01 represent the margin of error desired

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

In order to find the critical values we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical values would be given by: