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GrogVix [38]
3 years ago
15

Dr. Blumen invested $5,000 part of it was invested in bonds at a rate of 6% in the rest was invested in a money market at the ra

te of 7.5% if the annual interest of is 337.50 how much did she invest in bonds
Mathematics
2 answers:
abruzzese [7]3 years ago
6 0
So... let's say the amounts invested were "a" at 6% and "b" at 7.5%.

ok.. hmm what's 6% of a? well, (6/100) * a or 0.06a.
what's 7.5% of b? well, (7.5/100) * b or 0.075b.

now... we know, whatever "a" and "b" are, they total the investment of 5000 bucks, thus a + b = 5000

and the interest yielded was 337.50, thus 0.06a + 0.075b = 337.50

thus    \bf \begin{cases}
a+b=5000\implies \boxed{b}=5000-a\\
0.06a+0.075b=337.50\\
----------\\
0.06a+0.075\left( \boxed{5000-a} \right)=337.50
\end{cases}

solve for "a", to see how much was invested at 6%.

what about "b"?  well, b = 5000 - a.
defon3 years ago
3 0
X = amount invested in bonds  (5000-X) = amount invested in money mkt
X (.06) + (5000-X)(.075) = 337.50
.06X + 375 - .075 X = 337.50
375 - 337.50 = .075 X - .06X
37.50 = .015 X
X = $2500 invested in bonds

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It would be 3.25 cups

Since there is 2.5 cups for 10 servings then 0.25 per serving multiply that by 13 servings and you get 3.25.So it would be 3.25 cups for 13 servings
4 0
3 years ago
Rachael got a 550 on the analytical portion of the Graduate Record Exam (GRE). If GRE scores are normally distributed and have m
valina [46]

Answer:

Z=-2

This value means that the score of Rachel 550 it's 2 deviations below the mean of the population \mu=600

Step-by-step explanation:

1) Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

\mu=600 represent the population mean for the Graduate Record Exam (GRE)

\sigma=25 represent the population standard deviation for Graduate Record Exam (GRE)

2) Solution to the problem

Let X the random variable that represent the Graduate Record Exam (GRE) of a population, and for this case we know the distribution for X is given by:

X \sim N(600,25)  

Where \mu=600 and \sigma=25

We want to find the z score for a score of 550. And in order to do this we need to apply the formula for the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

z=\frac{550-600}{25}=-2

So the answer for our case would be Z=-2

This value means that the score of Rachel 550 it's 2 deviations below the mean of the population \mu=600

7 0
3 years ago
Which equation can be used to solve for the rate, r, for Sam to change all the light bulbs in the office building by himself?
Bad White [126]

Answer:

\frac{3}{r}+\frac{3}{8}=1

Step-by-step explanation:

Given question is incomplete; here is the complete question.

Working together, Sam and Charlie can change all light bulbs in the office building in 3 hours. It would have taken Charlie 8 hours to do the job alone. Which equation can be be used to solve for the rate 'r', for Sam to change all the light bulbs in the office building by himself.

Let Sam can change the bulbs in the office alone in 'r' hours  

Per hour work done by Sam alone = \frac{1}{r}

Let Sam takes he time to change the same bulbs in the office alone = 8 hours

Per hour work done by Sam = \frac{1}{8}

Since, Sam and Charlie complete the work together in time = 3 hours

Therefore, per hour work done by both = \frac{1}{3}

Equation for per work done by both will be,

Per hour work done by both = Per hour  work done by Sam alone + Per hour work done by Charlie

\frac{1}{r}+\frac{1}{8}=\frac{1}{3}

Therefore, equation for the rate 'r' will be,

\frac{1}{r}+\frac{1}{8}=\frac{1}{3}

\frac{3}{r}+\frac{3}{8}=1

8 0
2 years ago
Read 2 more answers
Please! Find the values of x,y and Z
bearhunter [10]

Answer:

x = 24

y = 10

z = 17

Explanation:

It's long to explain, so heres a picture of how solved each. hope this helps!! :)

3 0
2 years ago
An arithmetic sequence is defined by:a_1=-8a1​=−8a_n=a_{n-1}+4an​=an−1​+4What is the 7th term of the sequence?
oksian1 [2.3K]

Answer:

Step-by-step explanation:

5 0
2 years ago
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