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4 years ago

If the length of the rectangle is 15 units long and the width is 11 units long, how long is the diagonal

Mathematics

1 answer:

OleMash [197]4 years ago

4 0

Answer:

18.6 units

Step-by-step explanation:

A rectangle is a four sided shape with 4 perpendicular angles. It has two pairs of parallel sides which are equal in distance: width and length. A diagonal can be drawn between opposite corners that splits the triangle into two equal right triangles. The distance of this diagonal is found using the Pythagorean Theorem a² + b² = c². In the rectangle a = 11 and b = 15. Substitute these values and simplify using a square root operation.

11² + 15² = c²

121 + 225 = c²

346 = c²

√346 = c

18.6= c

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Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.42 and a standard deviation of 1.52.

Roman55 [17]

Answer:

The percentage of the women have size shoes that are greater than

9.94 is 16%

Step-by-step explanation:

* Lets revise the empirical rule

- The Empirical Rule states that almost all data lies within 3 standard

deviations of the mean for a normal distribution.

- 68% of the data falls within one standard deviation.

- 95% of the data lies within two standard deviations.

- 99.7% of the data lies Within three standard deviations

* The empirical rule shows that

# 68% falls within the first standard deviation (µ ± σ)

# 95% within the first two standard deviations (µ ± 2σ)

# 99.7% within the first three standard deviations (µ ± 3σ).

* Lets solve the problem

- The shoe sizes of American women have a bell-shaped distribution

with a mean of 8.42 and a standard deviation of 1.52

∴ μ = 8.42

- The standard deviation is 1.52

∴ σ = 1.52

- One standard deviation (µ ± σ):

∵ (8.42 - 1.52) = 6.9

∵ (8.42 + 1.52) = 9.94

- Two standard deviations (µ ± 2σ):

∵ (8.42 - 2×1.52) = (8.42 - 3.04) = 5.38

∵ (8.42 + 2×1.52) = (8.42 + 3.04) = 11.46

- Three standard deviations (µ ± 3σ):

∵ (8.42 - 3×1.52) = (8.42 - 4.56) = 3.86

∵ (8.42 + 3×1.52) = (8.42 + 4.56) = 12.98

- We need to find the percent of American women have shoe sizes

that are greater than 9.94

∵ The empirical rule shows that 68% of the distribution lies

within one standard deviation in this case, from 6.9 to 9.94

∵ We need the percentage of greater than 9.94

- That means we need the area under the cure which represents more

than one standard deviation (more than 68%)

∵ The total area of the curve is 100% and the area within one standard

deviation is 68%

∴ The area greater than one standard deviation = (100 - 68)/2 = 16

∴ The percentage of the women have size shoes that are greater

than 9.94 is 16%

8 0

3 years ago

What Is the answer for 11/12+6/10?

kirill115 [55]

Answer:

91/60

1.516

1 31/60

Step-by-step explanation:

comment how it helps

3 0

3 years ago

Students from Williams Middle School are also recycling aluminum cans. The data for the numbers of cans brought in

Rina8888 [55]

Median is 19
IQR is 12
Range is 22

See photo below for explanation

4 0

3 years ago

Write an equation in slope-intercept form for the line with slope −32 and y-intercept 7.

gladu [14]

Equation in slope-intercept form:
y=mx+b
m=slope
b=y-intercept

Data:
m=-32
b=7
Therefore:
y=-32x+7

Answer: y=-32x+7

6 0

3 years ago

6 Last year, all purchases of a certain product were made either online or in a store. If 55 percent of the purchases were made

anastassius [24]

We solve as follows:

*First: We determine the percentage of store purchases:

$100-55=45$

*Second: The ratio is obtained as follows:

$55\colon45=11\colon9$

So, the ratio is 11 to 9 purchases.

6 0

1 year ago