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2 years ago

A rectangle has vertices at (1, 5), (4, 9), (1, 9), and (4, 5). What is the length of the longer side of the rectangle?

2 answers:

6 0

The y coordinates are four units apart while the x coordinates are only 3 units apart.

So the rectangles longer side is the height of 4 units.

scoray [572]2 years ago

5 0

The longer side is 4 units long

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Identify two numbers less than 20 with the most factors

Anastaziya [24]

<u>Answer</u>

18 and 12

<u>Explanation</u>

Factor is a number or algebraic expression that divides another number or expression evenly that is with no remainder.

Odd number have few factors so the can't be the answer.

WE are going to try the even numbers.

18 ⇒ 18, 9, 6, 3, 2, 1

16 ⇒ 16, 8, 4, 2, 1

12 ⇒ 12, 6, 4, 3, 2, 1

10 ⇒ 10, 5, 2, 1

Other number less than 10 has factors less than 5.

It can be seen from above that 18 and 12 have the most factors.

3 0

2 years ago

Read 2 more answers

The table below shows the population of a town over x years. A 2-column table with 5 rows. The first column is labeled years wit

mel-nik [20]

Answer:

10,346.0(1.1)^x

112,096 people

Step-by-step explanation:

edg

8 0

2 years ago

Read 2 more answers

A consensus forecast is the average of a large number of individual analysts' forecasts. Suppose the individual forecasts for a

stealth61 [152]

Answer:

a) 0.954

b) 0.937

c) 0.891

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 6 percent

Standard Deviation, σ = 1.3 percent

We are given that the distribution of particular interest rate is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(At least 3.8 percent.)

$P(x \geq 3.8)$

$P( x \geq 3.8) = P( z \geq \displaystyle\frac{3.8 - 6}{1.3}) = P(z > -1.69)$

$= 1 - P(z < -1.69)$

Calculation the value from standard normal z table, we have,

$P(x \geq 3.8) = 1 - 0.046 = 0.954 = 95.4\%$

b) P(At most 8 percent)

$P(x \leq 8) = P(z \leq \displaystyle\frac{8-6}{1.3}) = P(z \leq 1.53)$

Calculating the value from the standard normal table we have,

$P( x \leq 8) =0.937= 93.7\%$

c) P(Between 3.8 percent and 8 percent. )

$P(3.8 \leq x \leq 8) = P(-1.69 \leq z \leq 1.53)\\\\= P(z \leq 1.53) - P(z < -1.69)\\= 0.937 - 0.046 = 0.891 = 89.1\%$

$P(3.8 \leq x \leq 8) = 89.1\%$

3 0

2 years ago

An acute angle θ is in a right triangle with sin θ = six sevenths. What is the value of cot θ?

inysia [295]

$\sin \theta =\dfrac{6}{7}\\
\cot \theta=\dfrac{x}{6}\\
x^2+6^2=7^2\\
x^2=49-36\\
x^2=13\\
x=\sqrt{13}\\
\boxed{\cot \theta =\dfrac{\sqrt{13}}{6}}$

4 0

2 years ago

Read 2 more answers

. According to Management Accounting, salary figures for certified management accountants (CMAs) who are in the field less than

Mice21 [21]

Answer:

The Mean is not equal to $31,129.

Step-by-step explanation:

Consider the provided information.

The mean is $31129

Thus, the null hypothesis $H_0: \mu = 31129$

Alternative hypothesis $H_a: \mu \neq 31129$

A random sample of 15 firstyear CMAs in Denver produces a mean salary of $32,279, with a standard deviation of $1,797.

Thus the value mean of sample is 32279, standard deviation is 1797 and number of samples are 15.

Now use the 2 sided t-test.

$t=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

Now substitute the respective values in the above formula.

$t=\frac{32279-31129}{\frac{1797}{\sqrt{15}}}$

$t=\frac{1150}{464}$

Test Value = 2.4785 approximately

Now, find the corresponding p-value in your t-table with DF(degree of freedom) 14.

p = 0.0265

as the value of p < 0.05, so you reject null hypothesis.

Thus, the Mean is not equal to $31,129.

7 0

2 years ago