Answer:
$15,000 was invested in CDs.
$40,000 was invested in bonds.
$75,000 was invested in stocks.
Step-by-step explanation:
Let C be the amount invested for CDs, B be the amount invested for bonds, and S be the amount invested for stocks.
We know that the total amount invested must be $130,000 because that was the amount given to the Scholarship Fund. So:
[tex]C+B+S=130000[/tex]
We know that CDs pay 2% or 0.02 interest; Bonds pay 2.9% or 0.029 interest; and Stocks pay 9.9% or 0.099 interest. In total, the investment earned $8,885. So:
[tex]0.02C+0.029B+0.099S=8885[/tex]
Let's remove the decimals by multiplying everything by 1000. This yields:
[tex]20C+29B+99S=8885000[/tex]
Now, we know that $25000 more was invested in bonds than CDs. So:
[tex]B=25000+C[/tex]
We have a triple system of equations. We can solve this using substitution. Let's substitute our third equation into the second equation. This yields:
[tex]20C+29(25000+C)+99S=8885000[/tex]
We want to isolate the C variable. Here, we removed the B but we still have an S.
So, to remove the S, we can go back to our first equation. We have:
[tex]C+B+S=13000[/tex]
Subtract C and B from both sides:
[tex]S=130000-C-B[/tex]
We can now substitute this for S:
[tex]20C+29(25000+C)+99(130000-C-B)=8885000[/tex]
We got a B again. But, we already know what B is. Substitute:
[tex]20C+29(25000+C)+99(130000-C-((25000)+C))=8885000[/tex]
So, our equation is now in terms of C. Solve for C. Distribute on the far right:
[tex]20C+29(25000+C)+99(130000-C-25000-C)=8885000[/tex]
Combine like terms:
[tex]20C+29(25000+C)+99(105000-2C)=8885000[/tex]
Distributive Property:
[tex]20C+725000+29C+10395000-198C=8885000[/tex]
Combine like terms:
[tex](20C+29C-198C)+(725000+10395000)=8885000[/tex]
Add:
[tex]-149C+11120000=8885000[/tex]
Subtract 1112000 from both sides:
[tex]-149C=-2235000[/tex]
Divide both sides by -149:
[tex]C=15000[/tex]
So, a total of $15,000 was invested in CDs.
Since $25,000 more was invested in bonds than in CDs, this means that a total of $25000+$15000 or $40,000 was invested in bonds.
To find out how much was invested in stocks, we can use our first equation again:
[tex]C+B+S=130000[/tex]
Substitute 15000 for C and 40000 for B:
[tex]15000+40000+S=130000[/tex]
Add:
[tex]55000+S=130000[/tex]
Subtract 55000 from both sides:
[tex]S=\$75000[/tex]
So, $15,000 was invested in CDs, $40,000 was invested in bonds, and $75,000 was invested in stocks.
And we're done!
Answer:
$15,000 was invested in CDs.
$40,000 was invested in bonds.
$75,000 was invested in stocks.
Step-by-step explanation:
Solve this equation, and show work. worth 40 points.
Recall the following property of exponents:
[tex]a^b\cdot a^c=a^{b+c}[/tex]
[tex]\implies 216^{-3k}\cdot 216^{-2k}=216^{-3k-2k}=216^{-5k}[/tex]
Now, notice that 6² = 36 and 6³ = 216, which means that
[tex]216^{-5k}=36^{2k-1} \iff (6^3)^{-5k}=(6^2)^{2k-1}[/tex]
Recall another property of (real) exponents:
[tex](a^b)^c=a^{bc}[/tex]
[tex]\implies(6^3)^{-5k}=6^{3(-5k)}=6^{-15k}\text{ and }(6^2)^{2k-1}=6^{2(2k-1)}=6^{4k-2}[/tex]
So we have
[tex]216^{-5k}=36^{2k-1} \iff 6^{-15k}=6^{4k-2}[/tex]
Since both sides are equal powers of 6, that must mean that the exponents must be equal, so
[tex]-15k=4k-2[/tex]
Solve for k :
[tex]-15k-4k=(4k-4k)-2[/tex]
[tex]-19k=-2[/tex]
[tex]k=\dfrac{-2}{-19}=\boxed{\dfrac2{19}}[/tex]
Logarithms:
A law was established, in which it considers that a driver who has more than 0.8 grams of alcohol per liter of blood, is in a state of drunkenness. It is estimated that the risk that a person has of suffering an accident when driving a vehicle under the influence of alcohol is given by the expression [tex]R(x) = 6 * e^{kx}[/tex] , where R(x) is the risk expressed as probability, X is the concentration of alcohol in the blood and K a constant:
A) Calculate the value of the constant K knowing that the concentration of 0.04 g / L of alcohol in the blood (x = 0.04) corresponds to an accident risk of 10% (R = 10)
B) A person who, according to the Law, drives while intoxicated, that is to say 0.8 g / L in blood, what are the risks of suffering an accident?
C) If a driver is under the influence of alcohol, that is 0.3 g / L, what is the risk of having an accident?
(Develop each one step by step)
Answer:
A) k = 18.75B) R(0.8) = 161419C) R(0.3) = 275Step-by-step explanation:
Given expression
R(x) = 6*e^(kx)A) Given
x = 0.04R = 10Solving for k
10 = 6*e^(0.04k)e^(0.04k) = 10/6ln (e^0.04k) = ln (1.6666)0.04k = 0.51k = 0.51/0.04k = 12.75B) Given
x = 0.8R= ?The value of R(0.8) is:
R(0.8) = 6*e^(0.8*12.75) =6*e^(10.2) = 161419 roundedC) Given
x = 0.3R = ?The value of R(0.3) is:
R(0.3) =6*e^(0.3*12.75) = 6*e^(3.825) =275 roundedDimensions of a rectangular section of forest land are 5.5×10 to the 5th m in 4.2 times complete the following sentences
Answer:
Step-by-step explanation:
2.31x10⁴
There are 567 calories in one hot dog. If the Carsey family ate 6,237
calories worth of hot dogs, how many hot dogs did they eat?
Answer:
11 hot dogs
Step-by-step explanation:
divide 6237 by 567
Answer:
11 hot dogs
Step-by-step explanation:
567/6237=11
Suppose that you are interested in estimating the average impact a job training program has on wages. After controlling for observed factors that influence wages, participation in the training program, you find that the coefficient for the training is 0.55 and the standard error is 1.06. Thus, we can infer that the training program has a positive and statistically significant impact on wages at a 95% confidence level.
a) true
b) false
Answer:
False
Step-by-step explanation:
From the question we are told that
The coefficient for the training is [tex]r = 0.55[/tex]
The standard error is [tex]SE = 1.06[/tex]
The confidence level is 95%
Generally the level of significant is mathematically represented as
[tex]\alpha =( 100 -95)\%[/tex]
=> [tex]\alpha = 0.05 [/tex]
Generally the critical value of [tex]\alpha = 0.05 [/tex] obtained from the normal distribution table is [tex]Z_{0.05} = 1.645[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{r }{SE}[/tex]
=> [tex]t = \frac{0.55}{1.06}[/tex]
=> [tex]t = 0.5189 [/tex]
Generally given that the [tex]t < Z_{\alpha }[/tex]
Hence there is no sufficient evidence to conclude that the program has a positive and statistically significant impact on wages at a 95% confidence level.
So the answer is False
whats the slope for this question?
Answer:
Slope: 1
Step-by-step explanation:
A variable is always worth 1 if there is no number in front of it. In this case there is no number, so just draw in a one.
Answer:
A: Slope = Positive
Step-by-step explanation:
Step 1:
y = mx + b Slope Intercept Form
Step 2:
y = x - 1 Equation/Given
Step 3:
Slope = 1
Answer:
A: Slope = Positive
Since there are no symbols or numbers in front of the x it means that the slope is x and the slope is positive.
Hope This Helps :)
This table gives a few (x, y) pairs of a line in the coordinate plane. What is the x-intercept of the line?
Answer:
(-14,0)
Step-by-step explanation:
-94 24
-74 18
-54 12
-34 6
-14 0
Answer:
-14,0
Step-by-step explanation:
khan academy
Solve for the value of Q
Answer:
q=9
Step-by-step explanation:
5q+1+44=90
5q+45=90
5q=45
q=9
f(x)=5(2-x) if f(-6)?
Answer:
f(-6) = 40
Step-by-step explanation:
Step 1: Define
f(x) = 5(2 - x)
f(-6) is x = -6
Step 2: Substitute and Evaluate
f(-6) = 5(2 - (-6))
f(-6) = 5(2 + 6)
f(-6) = 5(8)
f(-6) = 40
can you help me find the answer please
Answer:
give more details
Step-by-step explanation:
multiply [3] [-4] [2]
Answer: -24
Explanation: you multiply 3 times 4 times two, but then count the negative signs and if its and odd number add it if its even then its positive.
7/4+1/2+5/3+1/3+1/4+1/2
In AFGH, h = 9.6 inches, f = 2.5 inches and 2G=78°. Find the length of g, to the
nearest 10th of an inch.
Answer:9.4
Step-by-step explanation:
comment section
Your firm needs $630 for one quarter to finance a deficit. Interest charges are 2% per quarter. Your bank
requires a 10% compensating balance. How much must your firm borrow in order to obtain the needed funds?
$700.00
$705.00
O $693.00
$715.91
1
f(x) =1/10x-4 g(x)=1/x+2
Answer:
what do you want to find??
Clay thinks the next term in the sequence 2, 4,... is 6. Given the same pattern, Ott thinks the next term is 8, and Stacie thinks the next term is 7. What conjecture is each person making? Is there enough information to decide who is correct?
Clay and ott are correct but stacie is wrong.
What is an Arithmetic progression?An Arithmetic progression (AP) is a special type of progression in which the difference between two consecutive terms is always a constant. The terms of an arithmetic progression series is a a+d, a + 2d, a + 3d, a + 4d, a + 5d,…
Given here, the sequence as 2,4,6..... thus this is an arithmetic sequence with common difference 2 and therefore the subsequent terms are as follows : 2,4,6,8,18......
∴ Clay and Ott predicted correctly.
Hence, Clay and ott are correct but stacie is wrong.
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What is the greatest common factor of 9 and 12?
Answer:
9=3⋅3 and 12=2⋅2⋅3 ,
Step-by-step explanation: in this case the only common factor is 3 and therefore the greatest.
Answer:
3 is the answer
Step-by-step explanation:
what is the rate in 20 chairs 2 rows
Answer:
10 chairs one row 20 divided by 2
Answer:20/2 Unit rate 10
Step-by-step explanation:
A die is thrown. What is the probability of getting 6?
(a) 0
b 1/6
c 1/2
d 1
Answer:
1/6
Step-by-step explanation:
There are 6 sides on a die, labeled 1,2,3,4,5,6
P(6) = number of 6's / total numbers
= 1/6
Completează tabelul de mai jos:
Predecesor
Predecesor Predecesor
par
impar
Număr
Răsturnat
Ok Succesor
Succesor
par
23 148
300 000
111 111
101 101
729 143
A child walks 3/10 of a mile in 1/5 hour. At this rate, how far will the child walk in 1 hours ?
Answer:
1.5 miles
Step-by-step explanation:
.3 miles/12 minutes x 5/5 = 1.5 miles/ 1 hour
As men age, their testosterone levels gradually decrease. This may cause a reduction in lean body mass, an increase in fat, and other undesirable changes. Do testosterone supplements reverse some of these effects? A study in the Netherlands assigned 237 men aged 60 to 80 with low or low-normal testosterone levels to either a testosterone supplement or a placebo. The report in the Journal of the American Medical Association described the study as a "double-blind, randomized, placebo-controlled trial." Explain each of these terms to someone who knows no statistics.1) Explain the term "double-blind" study?2) True or False: :"Randomized means that the subjects were selected randomly from the population of men aged 60 to 80 with low or low-normal testosterone levels."3) Explain the meaning of the term "placebo-controlled" trial?
Answer:
Answered below.
Step-by-step explanation:
1) A double - blind study is simply an experiment in which neither the participants nor the people who carry out the experiment know who is receiving any particular treatment. This method is usually used in order to prevent a biased view in research results.
2) True because randomized simply means that subjects were assigned to the group randomly.
3) Placebo - controlled trial simply means that there was a control group that received only a placebo treatment which is mainly designed not to have real effect.
State weather the following can be expressed as a ratio 12g and 45kg
Answer:
The anwser is always Jesus
Step-by-step explanation:
Also there is no following
The ratio of 12gm and 45 kg in simplest form is 3750 : 1.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, Are two weights in different measurement forms, To write them as a ratio we have to make their scale of measurement equal.
We know 1kg is equal to 1000 grams.
Therefore, 45 kg is equal to 45000 grams.
So, The ratio of 12gm and 45 kg is 45000 : 12.
22500 : 6.
11250 : 3.
3750 : 1.
learn more about proportion here :
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Michael has 20 table tennis balls and 16 table tennis paddles. He wants to sell packages of balls and paddles bundled together. What is the greatest number of packages she can sell with no leftover balls or paddles?
PLEASE HELP
Which of the following is the inverse of f(x)=3-x/5
Answer:
f^-1(x) = 3 - 5x, second option
Step-by-step explanation:
To determine the inverse simply interchange the variables and solve for y;
f(x) = 3 - x / 5 -> Interchange the variables
x = 3 - y/5 -> Multiply either side by 5
5x = 3 - y -> Subtract three from either side
- y = 5x - 3 -> Divide either side by - 1
y = - 5x + 3
Your solution is f^-1(x) = 3 - 5x
Please help asap I'm tired and this is due soon
Answer:
56
Step-by-step explanation:
Answer:
56
Step-by-step explanation:
An electrician completes 1/6 of a job in 2/3 hour. How long does it take the electrician to complete the job?
Answer:1/4
Step-by-step explanation:
A company requires a password to access a data storage vault. The password must be 4 characters long and may
contain digits and lowercase letters only.
How many passwords are possible if characters can be repeated? Enter your answer as a number, like this: 425
Answer:
There are 36 possibilities per character (26 lower case letters + 10 numbers), so the total number of permutations are 36^4 = 1,679,616
Step-by-step explanation:
31. Find the value of each variable.
Answer:
z = 50
x = 26
Step-by-step explanation:
set 3z + 10 = 4z - 40 and solve: z = 50
create equation for 5x:
5x + 50 = 180, solve: x = 26
Convert 14.8 inches(1 inch= 2.54 cm)
Answer:
37.592 cm
Step-by-step explanation:
Answer:
you just did
Step-by-step explanation: