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:
3
1
1 point
Solve the equation below. Round your answer to the nearest hundredth (2 decimal places) if needed.
4
X/15 +15=19
Type your answer.
5
Answer: X= 570
Step-by-step explanation:
X
_____ = 19
15 + 15
Multiply both sides by 30
30X
_____ = 19 x 30
15 + 15
Simplify
x=570
PLEASE HURRY!
Evaluate the following expression.
Your answer must be exact.
Answer:
1Step-by-step explanation:
= [tex](-\frac{\sqrt{3}}{2} - \frac{1}{2}i)^1^2[/tex]
= [tex](-\frac{\sqrt{3}}{2} - \frac{i}{2})^1^2[/tex]
= [tex](\frac{\sqrt{3} -i}{2})^1^2[/tex]
apply the exponential rule:
([tex]-\sqrt{3}-i[/tex])¹²
= --------------
2¹²
note: ([tex]-\sqrt{3}-i[/tex])¹² = 4096
= 4096
4096
= 1
9.215
627
How to work the problem
Answer:
multiply
Step-by-step explanation:
Which ones no long answer just which one
A,C,D
(going top left to bottom right)
(a) b
(c) (d)
e f
It is generally claimed that the average body temperature for healthy human adults is 98.6°F. To test this claim a simple random sample of 9 adults are chosen. The average temperature of the 9 adults is only 98.1°F with a SD of 0.9°F. The question is whether the data on these 9 people is sufficient evidence to conclude that average body temperature among all healthy adults is really lower than 98.6°F. Assume the average body temperatures follow the normal curve.
1. Which significance test should be used?
a. z-test because the 50 of the population is known.
b. t-test because the SD of the population is known.
c. neither since it is untkely that temperatures would follow the nermal curve.
d. a t-test because the 50 of the sample is unknown.
e. a t-test because the SD of the pepulation is unknown.
Since the sample size is small and temperatures are lkely to be normaly distributed ether test may be used.
2. What is the null hypothesis?
A. That the average temperature in the population is 98.1 F.
B. That the average temperature in the pepulation is 98.6.
C. That the average temperature in the population is less than 98.6 F.
D. That the average temperature in the sample is 98.1.
3. What is the abernative hypothesis?
A. That the average temperature in the pepulation is 98.1 F.
B. That the average temperature in the population is 98.6F.
C. That the average temperature in the population is less than 98.6.
D. That the average temperabure in the sample is 98.17.
4. Compute SD.
5. Compute the best statistic.
6. How many degrees of freedom are there?
Answer:
Explained below.
Step-by-step explanation:
The information provided is as follows:
[tex]\mu=98.6^{o}F\\\bar x=98.1^{o}F\\s=0.9^{o}F\\n=9[/tex]
(1)
A single mean test is to be performed in this case.
As the population standard deviation is not provided, a one-sample t-test will be used.
The correct option is b.
(2)
The null hypothesis is:
H₀: The average temperature in the population is 98.6°F, i.e. μ = 98.6°F.
The correct option is b.
(3)
The alternative hypothesis is:
Hₐ: The average temperature in the population is less than 98.6°F, i.e. μ < 98.6°F.
The correct option is c.
(4)
The standard deviation of the sample mean is as follows:
[tex]SD_{\bar x}=\frac{s}{\sqrt{n}}=\frac{0.9}{\sqrt{9}}=0.3^{o}F[/tex]
Thus, the value of SD is 0.3°F.
(5)
Compute the value of test statistic as follows:
[tex]t=\frac{\bar x-\mu}{SD_{\bar x}}[/tex]
[tex]=\frac{98.1-98.6}{0.3}\\\\=-1.666666667\\\\\approx -1.67[/tex]
Thus, the value of test statistic is -1.67.
(6)
The degrees of freedom of the test are:
df = n - 1
= 9 - 1
= 8
Thus, the degrees of freedom of the test is 8.
Testing the hypothesis, it is found that:
1. e. a t-test because the SD of the population is unknown.
2. B. That the average temperature in the population is 98.6.
3. C. That the average temperature in the population is less than 98.6.
4. The standard error is of 0.3.
5. The test statistic is t = -1.67
6. There are 8 df.
We have the standard deviation for the sample, hence, a t-test should be used.
At the null hypothesis, it is tested that the average body temperature among all healthy adults is of 98.6ºF, hence the answer to question 2 is b.
At the alternative hypothesis, it is tested if the average is lower, hence, the answer to question 3 is C.
In this problem:
The standard deviation of the sample is [tex]s = 0.9[/tex]The sample has 9 adults, hence [tex]n = 9[/tex]The sample mean is of [tex]\overline{x} = 98.1[/tex]The standard error is of:
[tex]s_e = \frac{0.9}{\sqrt{9}} = 0.3[/tex]
The test statistic is:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 98.6[/tex] is the value tested at the null hypothesis, hence:
[tex]t = \frac{98.1 - 98.6}{0.3}[/tex]
[tex]t = -1.67[/tex]
The amount of degrees of freedom is one less than the sample size, hence there are 8 df.
A similar problem is given at https://brainly.com/question/13873630
or numbers 8a–8c, choose Yes or No to indicate whether the statement is correct.
15 points
Yes No
8a. 1,289 ÷ 22 is 58 r13.
8b. 189 ÷ 17 is 11 r2.
8c. 1,427 ÷ 13 is 190 r1.
8a. 1,289 ÷ 22 is 58 r13.
8b. 189 ÷ 17 is 11 r2.
8c. 1,427 ÷ 13 is 190 r1.
Answer:
1,289 divided by 22 is 58 r13
Step-by-step explanation:
Simplify the expression: (4x2 - 3x + 1) - (3x2 - 5x + 4)
Answer:
x² + 2x - 3
Step-by-step explanation:
Step 1: Write expression
(4x² - 3x + 1) - (3x² - 5x + 4)
Step 2: Distribute negative
4x² - 3x + 1 - 3x² + 5x - 4
Step 3: Combine like terms (x²)
x² - 3x + 1 + 5x - 4
Step 4: Combine like terms (x)
x² + 2x + 1 - 4
Step 5: Combine like terms (constants)
x² + 2x - 3
solve this equation, and show work. worth 40 points.
Answer:
[tex]r=-3/5=-0.6[/tex]
Step-by-step explanation:
We have the equation:
[tex]6^{-3r}=6^{2r+3}[/tex]
Since their bases are the same, the exponents must be equivalent. So:
[tex]-3r=2r+3[/tex]
Solve for r, subtract 2r from both sides:
[tex]-5r=3[/tex]
Divide both sides by -5:
[tex]r=-3/5=-0.6[/tex]
So, the value of r is -3/5.
And we're done!
Which function describes the graph?
2
y= 5x+1
c.
2
y = 5x-1
b.
2
d.
2
y=5x+1
y=54-1
Answer: A
Step-by-step explanation:
The y intercept is positive 1, so it’s not C or D
The slope is positive because it’s going up from left to right so it’s not B
What do you have to know about any segments and angles in a figure to decide whether the figure has line symmetry?
Answer:
Explained below.
Step-by-step explanation:
When drawing line of symmetry on a figure and reflecting, we have to know that pairs of segments in that figure must have the same length while pairs of angles must have the same measurement. This is to ensure that half of that figure must concise with the other half part of it when that figure is folded across a line of symmetry.
Peter has a part time job in factory and he can work 6 1/2 hours a day while his friend Joseph can work 1 2/3 hours more than Peter.how many hours can Joseph work more than Peter?
Given parameters:
Number of hours worked by Peter = 6.5hrs
His friend Joseph works [tex]1\frac{2}{3}[/tex] hours more than Peter;
Unknown:
Number of hours Joseph can work more than Peter = ?
This problem is pretty straight forward.
We see from the given parameters, it was explicitly stated that Joseph, the friend of Peter works [tex]1\frac{2}{3}[/tex] more hours .
Therefore, Peter's friend worked [tex]1\frac{2}{3}[/tex] more hours.
Joe has $800 to spend on a new dining room table and chairs. If the sales tax is 8%, how much can he afford to spend on the table and chairs?
Answer:
no
Step-by-step explanation:
800x8%=64
64+800=864
Answer:
$736
Step-by-step explanation:
800 x (100% - 8%)
800 x 92%
=736
State all integer values of xx in the interval \left[-1, 5\right][−1,5]
Answe67
Step-by-step explanation:
The range of the following relation R(3,-2), (1, 2), (-1, -4),(-1, 2)} is {-1, 1, 3) {-1, -1, 1.3} (-4, -2, 2. 2) (-4, -2.2 without it saying brainly plus
Answer:
{-4, -2, 2}Step-by-step explanation:
Given relation
R {(3,-2), (1, 2), (-1, -4),(-1, 2)}Its range is the set of second values in the pairs
{-2, 2, -4}In the ascending order
{-4, -2, 2}Answer:
{-4, -2, 2}
Step-by-step explanation:
The relation is {(3, -2), (1, 2), (-1, -4),(-1, 2)}
The range is all possible y values apart from any duplicates.
y = -2, 2, -4, 2
Removing all duplicates we get.
y = -2, 2, -4
Put them in order.
y = -4, -2, 2
Best of Luck!
Which is bigger 1.30 or 1.3
Answer:
They are both exactly the same
Step-by-step explanation:
1.30000000000000000000000
is the same as
1.3
the 0s dont matter unless they are not at the end
I need help on this one please
Answer:
B
Step-by-step explanation:
Answer:
k' = (-3,0)
j' = (0,5)
l' = (-3,3)
Step-by-step explanation:
if you reflected over the x- axis
then the y points would would change to the opposite
k = (-3,0)
j = (0,-5)
l = (-3,-3)
What is the equation in point-slope form of a line perpendicular to y= ⅕ x+8, through the point (-2, 3) *
Answer:
it was right but ok
Step-by-step explanation:
First find the total number
6+4+5+3 = 18
6th graders : total
4 : 18
Divide each side by 2
4/2: 18/2
2 : 9
A rectangle has an area of 171 square meters. Its width is ten meters less than the length. Find the measures of the length and width of the rectangle.
Step-by-step explanation:
The area of a rectangle is 171 m²
Let l is the length and b is the width of the rectangle
It width is 10 m less than the length. So,
b = l-10 ...(1)
Area of a rectangle is given by :
[tex]A=l\times b\\\\171=l(l-10)\\\\l^2-10l=171\\\\l^2-10l-171=0\\\\l^2-19l+9l-171=0\\\\\text{taking common together}\\\\l(l-19)+9(l-19)=0\\\\(l-9)(l-19)=0[/tex]
or
l = 9 m or l = 19 m
If l = 9 m,
b = 9-10 = -1 m (can't be possible)
If l = 19 m
b = 19-10 = 9 m
So, the length an the breadth of the rectangle is 19 m and 9 m respectively.
Pls help me 8th grade math pls solve all the problems correctly
Answer:
A.$12
B.$4.5
C.4.5$ per game + 12$
Step-by-step explanation:
It shows the first payment being 12$ so A is 12$
then it goes up to 16.5$ so
16.5-12= 4.5$
So 4.5$ per game.
C. 4.5$ per game + 12$
There are four $20 bills, six $10 bills, eight $5 bills, and two $1 bills in your wallet. You select one bill at random. What is the expected value for this experiment? Must be answered in terms of statistics and probability please. Thank you
Answer:
total no. of possibilities =20
Step-by-step explanation:
probability of $20 bill=4/20=1/5
probability of $10 bill=6/20=3/10
probability of $5 bill=8/20=2/5
m - 6 > -9
Solve the inequality
Answer:
m> -3
Step-by-step explanation:
m-6 > - 9
you use inverse opperations and you add six to the other side.
m-6 > - 9
+6 +6
m > -3
A scientific calculator costs $3.50 today. I remember when they cost about $75. What is the percent decrease in the price of a scientific calculator?
In other words: The decrease in price is what percent of the original price?
% Decrease= (Decrease in price(New price-Old Price))/(Original Price(old price))×100
Answer:
A scientific calculator costs $3.50 today. I remember when they cost about $75. What is the percent decrease in the price of a scientific calculator?
In other words: The decrease in price is what percent of the original price?
% Decrease= (Decrease in price(New price-Old Price))/(Original Price(old price))×100
(g + 12) ÷ h
Answer please
Answer:
g+12/4
Step-by-step explanation:
Unit 1 Cumulative Assessment
Multiple Choice
Let f(x) = x2 and g(x) = x - 6. What is f-g?
a
A. X²-6
B. x2 - 36
O
C. x2 - 12x - 36
D. x2 - 12x + 36
Luke had $9. He had to spend 3/4 of it for a birthday gift. How much cash money did
he spend?
Answer:
He spent $2.25.
Step-by-step explanation:
Multiply $9 by 3/4 and we get $6.75.
Now subtract $6.75 from $9.
We get $2.25
The length of the window is 2m longer than its width and the are is 32m²
Find the slope of a pipe that slopes down 1/3 inch per foot
Answer:
-1/36
Step-by-step explanation:
The slope is of [tex]\mathbf{-\frac{1}{3}}[/tex]
----------------------
We use a linear function to understand this question, which has equation given by:
[tex]y = mx + b[/tex]
The slope is m, which is the rate of change, that is, how much y changes when x changes by 1.In this problem, for each foot, the pipe slopes down [tex]\frac{1}{3}[/tex] of an inch. Thus, the slope is [tex]m = -\frac{1}{3}[/tex]A similar problem is given at https://brainly.com/question/18594541
1 ft. = 12 in
Convert 4 feet to inches.
Convert 48 inches to feet.
Answer:
48 inches, 4 feet
Step-by-step explanation:
since each foot is 12 inches and we have 4 feet, we can multiply both numbers to convert 4 feet to inches. 12*4= 48 inches
to convert 48 inches to feet, we can divide by 12 since 12 inches is a foot. 48/12=4 feet
Which of these equations, when solved, gives a different value of x than the other three?
9.1 = -0.2x + 10
10 = 9.1 + 0.2x
10 – 0.2x = 9.1
9.1 – 10 = 0.2x
Answer:
D. 9.1 – 10 = 0.2x
Step-by-step explanation:
I got it right
The odd equation with a different value is equation d
Data;
9.1 = -0.2x + 1010 = 9.1 + 0.2x10 - 0.2x = 9.19.1 - 10 = 0.2xLinear EquationTo solve this problem, we have to solve each of the linear equations and get the value of x.
a)
[tex]9.1 = -0.2x + 10\\10 - 9.1 = 0.2x\\0.9 = 0.2x\\\frac{0.2x}{0.2} = \frac{0.9}{0.2} \\x = 4.5[/tex]
b)
[tex]10 = 9.1 + 0.2x\\0.2x = 10 - 9.1\\0.2x = 0.9\\\frac{0.2x}{0.2} = \frac{0.9}{0.2} \\x = 4.5\\[/tex]
c)
[tex]10 - 0.2x = 9.1\\-0.2x = 9.1 - 10\\-0.2x = -0.9\\x = 4.5[/tex]
d)
[tex]9.1 - 10 = 0.2x\\0.2x = -0.9\\x = -4.5[/tex]
The odd equation with a different value is equation d
Learn more on linear equation here;
https://brainly.com/question/1884491
Solve the following system of equations.
6x -5y=13 & 9y-15+2x=0
x = 3
y = 1
Step-by-step explanation:Hi !
6x - 5y = 13
9y - 15 + 2x = 0
6x - 5y = 13
2x + 9y = 15 | ×(-3)
6x - 5y = 13
- 6x - 27y = - 45
add
6x - 6x - 5y - 27y = 13 - 45
- 32y = - 32 | ×(-)
32y = 32
y = 1
replace y = 1
6x - 5(1) = 13
6x - 5 = 13
6x = 13 + 5
6x = 18
x = 3
Good luck !
