Answer:
John invested $2,000 in money-market fund, $3,000 in municipal bonds, and $7,000 in mutual funds.
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
John invested his inheritance of $12,000 in three different funds: part in a money-market fund paying 3% interest annually; part in municipal bonds paying 4% annually; and the rest in mutual funds paying 7% annually. John invested $4,000 more in mutual funds than he invested in municipal bonds. The total interest earned in one year was $670. How much did he invest in each type of fund?
The explanation of the answer is now given as follows:
Let a, b and c represent the amount invested in money-market fund, municipal bonds and mutual funds respectively. Therefore, the sum of the three principal amounts can be represented as follows:
a + b + c = 12,000 ……………………….. (1)
Since John invested $4,000 more in mutual funds than he invested in municipal bonds, we have:
c = b + 4,000 ……………………………. (2)
The total amount of interest earned from each fund can be represented as follows:
0.03a + 0.04b + 0.07c = 670 ………………. (3)
Substituting equation (2) into equation (1), we have:
a + b + b + 4,000 = 12,000
a + 2b = 12,000 – 4,000
a + 2b = 8,000
a = 8,000 – 2b ……………………….. (4)
Also, substituting equation (2) into equation (3), we have:
0.03a + 0.04b + 0.07(b + 4,000) = 670
0.03a + 0.04b + 0.07b + 280 = 670
0.03a + 0.04b + 0.07b 0 = 670 – 280
0.03a + 0.11b = 390 ,,,,,,,,,,,,,,,,,,,,,, (5)
Substituting equation (4) into equation (5) and solve for b, we have:
0.03(8,000 – 2b) + 0.11b = 390
240 – 0.06b + 0.11b = 390
240 + 0.05b = 390
0.05b = 390 – 240
0.05b = 150
b = 150 / 0.05
b = 3,000
Substituting b = 3,000 into equation (2), we have:
c = 3,000 + 4,000
c = 7,000
Also, substituting b = 3,000 into equation (4), we have:
a = 8,000 – (2 * 3,000)
a = 8,000 – 6,000
a = 2,000
Therefore, John invested $2,000 in money-market fund, $3,000 in municipal bonds, and $7,000 in mutual funds.
A gardener measured the heights of two plants at the end of every week. The function y=3x+8.5 gives the hight of plant a in centimeters at the end of x weeks. The function y= 2.5x+14.5 gives the hight of plant b in centimeters at the end of x weeks
Answer:
12 weeks
Step-by-step explanation:
Step one:
given data
let the heights of the plants be y
and the number of weeks be x
Plant A
y=3x+8.5--------------1
Plant B
y=2.5x+14.5----------2
Required
The number of weeks taken for both plants to have the same height
,equate the two expressions above
3x+8.5=2.5x+14.5
3x-2.5x=14.5-8.5
0.5x= 6
divide both sides by 0.5
x= 6/0.5
x= 12 weeks
I NEED HELLLLPPPP:(((((
Answer: C. -1
Step-by-step explanation: -1 is your "a" value and is your leading coefficient.
A mobile phone carrier charges an extra fee if a customer uses more than 500 minutes each month. Tom has already used 230 minutes this month. Which inequality can be used to determine how many more minutes Tom can use this month without going over the 500-minute limit?
A. 230 + m > 500
B. 230 + m greater-than-or-equal-to 500
C. 230 + m < 500
D. 230 + m less-than-or-equal-to 500
Answer:
230 + m < 500
Step-by-step explanation:
The inequality shows that the combined total of 230 and m (stands for minutes Tom can use) is less than 500.
sorry but i have another question :| tysm all yall for helping meee ^w^
9514 1404 393
Answer:
4: {8, 12, 16, 24}7: {7, 42, 49}neither: {6, 11, 17}Step-by-step explanation:
Looking at the numbers individually, we have ...
16 = 4×4
42 = 2×3×7
6 = 2×3
17 = 1×17 (prime)
12 = 3×4
49 = 7×7
24 = 2×3×4
7 = 1×7 (prime, a multiple of 7)
11 = 1×11 (prime)
8 = 2×4
__
Multiples of 4:
16, 12, 24, 8
Multiples of 7:
42, 49, 7
Multiples of neither:
6, 17, 11
??
The multiplicative verse of
(3x+5) 1/3
Answer:
tanother way of writing this is the cube root of3x+5
Write -8 5/6 as the decimal round to the nearest hundredth
Answer:
-8.83
Step-by-step explanation:
I took 5/6 and converted into a decimal and it is 0.83333333333 and it is 0.83 rounded to the nearest hundredth and then I added -8 to get -8.83.
2a) Solve using substitution.
y = 2
2x + 2y = 10
Explain how you got the answer please step by step
Answer:
3
Step-by-step explanation:
2x+2 x 2= 10
2x + 4 = 10
-4 -4
2x= 6
divide them by 2 to get x by itself
x=3
Please help! To determine the height of the CN Tower in Toronto, Ontario, Canada a person stands away from the base of the tower and measures the angle of elevation to the top of the tower to be 60°. After moving 118 meters closer to the tower, the angle of elevation to the top of the tower is 70°. A. How tall is the CN tower? B. How far was the person standing from the base of the tower when each angle measurement was taken?
Answer:
A right triangle is formed by the tower, a point 1000m from the tower
Use the tangent. let h = the height of the tower
tan(28.81) = h%2F1000
h = 1000 * tan(28.81)
h = 550 meters
Step-by-step explanation:
If your friend is driving at a speed of 25 miles per hour, how many miles per second is your
friend traveling?
Answer:
0.0069444444
Step-by-step explanation:
Question Help
You invested $23,000 in two accounts paying 8% and 9% annual interest, respectively. If the total interest earned for the year was
$2040, how much was invested at each rate?
The amount invested at 8% is $
The amount invested at 9% is
Enter your answer in each of the answer hoxes
Can you guys please answer this it is due in 15 mins I really need help with all of them!
Answer:
3) is D
4)is A
5)
6)B
Step-by-step explanation:
hdhhdhdjd
True or False:
cot = 1/tan
Answer:
I think its true??? right... its true
Step-by-step explanation:
Answer:
it is true
Step-by-step explanation:
A class of 36 students has 18 boys. What is the ratio of girls to boys? What is the ratio of boys to girls?
Answer:
18:18
Step-by-step explanation:
You first do 36-18 and then add your answer with the 18 to check it and correct it.
Miles per Hour, Inches per Second, Feet per Min are all examples of ?
Grocery Mart has cookies on sale for $3.84 for 12 cookies. Food Shoppe has cookies on sale for $5.70 for 19 cookies. Which store has a better deal on cookies?
Grocery mart:
12÷$3.84=3.125
Food Shoppe:19÷$5.70=3.333
so grocery mart is cheaper by
0.2075333333
Answer:
grocery mart has cookies on sale for $3.84 is a better deal
Step-by-step explanation:
Please help, thank you
I found 30
all I did was 125÷5 which is 25
and 1.2x25 which is 30
Which value of x from the set (5, 6, 7, 8) makes this equation true?
3x24
O A 5
OB. 6
O c. 7
OD
8
Answer:
D. X = 8
Step-by-step explanation:
Reason: 8 x 3 Would get you 24
Can y’all help me with this math problem please! I don’t understand
KL = 23
so you just have to add both of the segment lengths together.
each individual equation is already given in the image, so I'll substitute it out below:
JK + KL = JL
4x+2 +4x+3 = 45
8x + 5 = 45
8x = 40
x = 5
BUT WE'RE NOT DONE. plug in 40 for the variable X:
KL = 4(5) + 3
KL = 20 + 3
KL = 23
now i'll check my answer really quickly:
23 + 4(5) + 2 = JL
23 + 20 + 2 = JL
23 + 22 =
45
therefore, KL is 23
41. Write a proof of the theorem that states if an angle of a quadrilateral is supplementary to both of its consecutive angles, the quadrilateral is a parallelogram.
Given: m∠F + m∠G = 180, m∠F + m∠J = 180
Prove: FGHJ is a parallelogram
What statement proves the theorem?
A. By the Angle Addition Postulate m∠F = m∠J and m∠G = m∠H. So, by the definition of a parallelogram, FGHJ is a parallelogram.
B. By the Converse of the Same-Side Interior Angles Postulate, FJ|| GHand FG||JH. So, by the definition of a parallelogram, FGHJ is a parallelogram.
C. By the Polygon Interior Angle-Sum Theorem, m∠F + m∠G + m∠F + m∠J = 360. So, by the definition of a parallelogram, FGHJ is a parallelogram.
D. By the Converse of the Same-Side Interior Angles Postulate, FJ = JH andFG=JH. So, by the definition of a parallelogram, FGHJ is a parallelogram.
Answer:
B.
there's proof that opposite sides are parallel so it must be a parallelogram
Step-by-step explanation:
According to the Center for disease control, 15% of US adults are estimated to have a chronic kidney disease. A random sample of 150 US adults are selected. What is the probability that exactly 35 have chronic kidney disease
Answer:
[tex]P(X=35) =0.2\%[/tex]
Step-by-step explanation:
From the question we are told that
Sample space n = 150
Sample percentage p = 0.15
Generally people without the disease in the set is give as X
[tex]X= 1-p[/tex]
[tex]X= 0.85[/tex]
35 have kidney disease,
[tex]P(X=35) = C(150,35)*(0.15)^35*(0.85)^115[/tex]
[tex]P(X=35) = 0.0021[/tex]
[tex]P(X=35) =0.2\%[/tex]
Please help me with 47 and 48
Answer:
42. -1
48. 2
Step-by-step explanation:
Answer:
-1
2
Step-by-step explanation:
Hey guys I need help on question 38 and 39 please! :)
HELP, WILL GIVE BRAINLIEST!!!!!!
What type of association is shown by the scatterplot?
linear, strong
linear, weak
nonlinear, strong
nonlinear, weak
Answer:
Non-linear, I believe its weak
Step-by-step explanation:
You can see clearly that the lines are not tightly packed, and they arent making a line.
Let me know if you need more help! :)
Hope this helps!
Help! Plz!!!!!!!!!!!!!!!!!!!!!!
Answer:
girl literally I have the same thing omg
Answer:
What grade is this? Do you have to simplify or something?
Lauren wants to build a model
airplane using a scale where 2 inches
represents 15 feet. If the airplane is
75 feet long, how long should the
model be?
Answer:
Step-by-step explanation:
you got this i believe in you!
needing help with this problem
Answer:
The answer is x+6
Step-by-step explanation:
The Y intercept from the translated unit and the one before are 6 units apart
Elsa received a $70 gift card for a coffee store. She used it in buying some coffee that cost $8.69 per pound. After buying the coffee, she had $43.93 left on her
card. How many pounds of coffee did she buy?
Answer:
3
Step-by-step explanation:
70 - 8,69 - 8,69 - 8,69
You substracted it 3 times which means your answer is 3 pounds
Ms. Taylor's checking account changes by-$1146 every year on her
electricity each year. How much does her account balance change per
month?
Answer:
-95.5
Step-by-step explanation:
if you do -1146 divided by 12 you get -95.5
Joe wants to buy the new Air Jordans for $170. He has saved up $180 by plowing driveways. He knows that he will have to pay 7.5% tax. Will Joe have enough money to buy the sneakers?
Answer:
No
Step-by-step explanation:
This is because 7.5% of $170 is $12.75. If you add this to the original price of $170, then it will equal $182.75.
Can anyone help me please
Answer:
11 im pretty sure y = 11 in your question