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Karo-lina-s [1.5K]

2 years ago

12

To pay for new machinery in 5 years a company owner invests $10000 at 7.5% compounded quarterly. How much money will be availabl

e in 5 years

1 answer:

sukhopar [10]2 years ago

6 0

Answer:

37 500

Step-by-step explanation:

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In the right ΔABC, AN is the altitude to the hypotenuse. Find BN, AN, and AC, if AB=2√5 in and NC= 1 in.

kipiarov [429]

Answer:

$BN=4\ \text{in}$

$AN=2\ \text{in}$

$AC=\sqrt{5}\ \text{in}$

Step-by-step explanation:

Let $BN=x$

$BC=c$

$NC=y=1\ \text{in}$

$AB=a=2\sqrt{5}\ \text{in}$

$AC=b$

We have the relation

$\dfrac{BC}{AB}=\dfrac{AB}{BN}\\\Rightarrow \dfrac{c}{a}=\dfrac{a}{x}\\\Rightarrow c=\dfrac{a^2}{x}\\\Rightarrow x+1=\dfrac{a^2}{x}\\\Rightarrow x^2+x=20\\\Rightarrow x^2+x-20=0\\\Rightarrow x=\frac{-1\pm \sqrt{1^2-4\times 1\times \left(-20\right)}}{2\times 1}\\\Rightarrow x=4,-5$

$\boldsymbol{BN=4\ \text{in}}$

$h=\sqrt{a^2-x^2}\\\Rightarrow h=\sqrt{(2\sqrt{5})^2-4^2}\\\Rightarrow h=2\ \text{in}$

$\boldsymbol{AN=2\ \text{in}}$

$b=\sqrt{h^2+y^2}\\\Rightarrow b=\sqrt{2^2+1^2}\\\Rightarrow b=\sqrt{5}\ \text{in}$

$\boldsymbol{AC=\sqrt{5}\ \text{in}}$

8 0

2 years ago

Which graph correctly represents (5/2)x - y < 3?

Setler79 [48]

You can rewrite the inequality as

$y > \cfrac{5}{2}\ x - 3$

Note that

$y = f(x) = \cfrac{5}{2}\ x - 3$

is the equation of the line drawn in the pictures. This means that, for every point on the line, the y coordinate is exactly image of the x coordinate, i.e. $f(x)$

The inequality is satisfied by all points whose y coordinate exceeds the image of the x coordinate. Since the y axis is positively oriented upwards, a greater value for the y coordinate means that the point has to be higher than the line.

Also, since the equality inlves a $>$ and not a $\geq$ sign, the line itself is excluded.

So, the correct graph is the second one.

3 0

3 years ago

Read 2 more answers

Increase £40 by 5percent

natulia [17]

40(105/100)=42
.........................

5 0

3 years ago

What is the length of the line?

klemol [59]

Answer:

It might be 7

Step-by-step explanation:

count the squares the blue line is in and you have your answer

5 0

2 years ago

Scores on a college entrance exam are normally distributed with a mean of 550 and a standard deviation of 100. Find the value th

Alinara [238K]

Answer:

The value that represents the 90th percentile of scores is 678.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 550, \sigma = 100$

Find the value that represents the 90th percentile of scores.

This is the value of X when Z has a pvalue of 0.9. So X when Z = 1.28.

$Z = \frac{X - \mu}{\sigma}$

$1.28 = \frac{X - 550}{100}$

$X - 550 = 100*1.28$

$X = 678$

The value that represents the 90th percentile of scores is 678.

4 0

2 years ago