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3 years ago

Geometry

Mathematics

1 answer:

g100num [7]3 years ago

7 0

$A=27 \ cm^2 \\ \\ d_{1}=3x , \ \ d_{2} = 2x \\ \\ S=\frac{1}{2}\cdot d_{1}\cdot d_{2}\\ \\27 = \frac{1}{2}\cdot 3x \cdot 2x \\ \\ 3x^2 = 27 \ \ /:3$

$x^2 = 9 \\ \\3x=x=\sqrt{9}\\ \\x=3 \ cm \\ \\ d_{1}=3x = 3*3 =9 \ cm \\ \\d_{2}=2x=2*3 = 6 \ cm \\ \\ Answer : \\ The \ length \ of \ the \ diagonal \ is: \ d_{1}= 9 \ cm \ and \ d_{2}= 6 \ cm$

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alina1380 [7]

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Step-by-step explanation:

the formula for the area of a triangle is 1/2•b•h

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3 years ago

How many quarters are in $375.75?

DanielleElmas [232]

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3 years ago

Read 2 more answers

Sir Ving Spoon earned $5,436 on his $7,550 certificate of deposit. If he had the CD for 12 years, what simple interest rate did

Lilit [14]

6% or 0.06 is the simple interest rate the bank pays him.

<u>Step-by-step explanation:</u>

Sir Ving Spoon earned $5,436 on his $7,550 certificate of deposit.

From this given information,

It can be determined that the Principal amount is $7550 and the interest amount is $5436.

The CD is for 12 years. Therefore, the number of years is 12.

<u>To find the interest rate (r) :</u>

Using the simple interest formula,

Interest = P×r×t

where,

P is the principal amount = $7550
r is the rate of interest.
t is the number of years = 12

⇒ 5436 = 7550 × r × 12

⇒ 5436 = 90600 × r

⇒ r = 5436 / 90600

⇒ r = 0.06

Multiply by 100 to represent in rate %

⇒ r = 0.06 × 100

⇒ r = 6%

∴ 6% or 0.06 is the simple interest rate the bank pays him.

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3 years ago

A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. The number of subjects needed to estima

Ludmilka [50]

Answer:

$n=(\frac{1.64(14.7)}{3})^2 =64.57 \approx 65$

So the answer for this case would be n=65 rounded up to the nearest integer

And the sample size would decrease by 160-65=95 subjects

Step-by-step explanation:

1) Previous concepts

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

ME represent the margin of error

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

2) Solution to the problem

Since the new Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$