A retiree has $200,000 to invest and needs to make $13,000 with her investments. If she can invest in government bonds at 6% or investment grade bonds at 8%, how much should she invest in each?
Answer:
She should invest 150,000 in government bonds and 50,000 in investment grade bonds
Step-by-step explanation:
Let the amount invested in government bonds be $y while the amount invested in investment bond be $x
Since total is $200,000
Then:
x + y = 200,000 ••••••(i)
Since 13,000 is what is expected to be earned, then this is like the interest.
thus;
6% of x + 8% of y = 13,000
6x/100 + 8y/100 = 13,000
Multiply through by 100
6x + 8y = 1300000 •••••••(ii)
From i, x = 200,000 - y
insert this into ii
6(200,000-y) + 8y = 1300000
1200000-6y + 8y = 1300000
2y = 1300000-1200000
2y = 100,000
y = 100,000/2
y = 50,000
but x + y = 200,000
thus, x = 200,000 - 50,000
x = 150,000
Evaluate the following algebraic expression for the given value of the variable
Answer:
[tex]\boxed{8}[/tex]
Step-by-step explanation:
-Solve the following expression when [tex]x = 4[/tex]:
[tex]\frac{5x + 12}{4}[/tex]
-Apply the value of [tex]x[/tex] onto the equation:
[tex]\frac{5x + 12}{4}[/tex]
[tex]\frac{5(4)+ 12}{4}[/tex]
-Multiply both the [tex]5[/tex] and [tex]4[/tex]:
[tex]\frac{5(4)+ 12}{4}[/tex]
[tex]\frac{20+ 12}{4}[/tex]
-Add both [tex]20[/tex] and [tex]12[/tex]:
[tex]\frac{20+ 12}{4}[/tex]
[tex]\frac{32}{4}[/tex]
-Divide [tex]32[/tex] by [tex]4[/tex]:
[tex]\frac{32}{4}[/tex]
[tex]\boxed{8}[/tex]
So, therefore, the final answer is [tex]8[/tex].
Answer:
Step-by-step explanation:
My answer is 8!!!
If x is equal to 4 then 5x4=20 because if there is no sign then that means that you have to multiply, then you add 20 and 12 which is equal to 32, And then you simplify 4 which equals 8, or you can think of dividing 32 and 4 which is also 8.
Write all prime numbers between 15 and 20
Answer:
17 and 19
Step-by-step explanation:
Answer:
17, 19
Step-by-step explanation:
15 is composite (5, 3) (15, 1)
16 is composite (8, 2) (4, 4) (16, 1)
17 is prime (17, 1)
18 is composite (9, 2) (6, 3) (18, 1)
19 is prime (19, 1)
20 is composite (2, 10) (4, 5) (20, 1)
Perform the indicated operation.
(-7) · (-5)
-12
-35
12
35
Please answer correctly !!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!
Answer:
1) B
2) A
Step-by-step explanation:
B because we use pemdes and for 2 they answers are both equivalent
Answer:
1) B. Add/subtract the same quantity to/from both sides
2) Yes
Step-by-step explanation:
To answer Part B, we have to answer to equation.
Step 1- Add x to both sides of the equation.
4x+2= 6-x
+x +x
5x+2= 6
Step 2- Subtract 2 to both sides of the equation.
5x+2= 6
-2 -2
5x= 4
Step 3- Divide 5 to both sides of the equation.
5x= 4
5 5
This gives us 4/5 or 0.80.
So, the answer is yes to Part B.
Hope this helps!
PLEASE HELP QUICKLY: (FIRST ANSWER GETS BRAINLIEST)
You are buying batteries, a stereo, and some CDs from the I.B. Electronics store. You can buy from this store online or in a physical store. You have a coupon for 10% off that can only be used in the physical store and a $5.00 off coupon that can only be used online. The sales tax of 5% only applies to the physical store. Shipping for the online store is a flat rate of $6.99. You are trying to decide whether to shop at the physical store or the online store. Using the pricing information below, how much would you pay at the physical store after all discounts, taxes, and shipping fees have been applied?
Item Quantity Physical Store Online Store
Batteries 2 packs $5.99/pack $4.99/pack
Stereo 1 system $100.00/system $90.00/system
CDs 3 CDs $7.95/CD $8.95/CD
$138.04
$118.42
$128.36
The Anwser is $128.32.
Which equation has solution x = -3?
A) 2x - 7 = -1
B) 3x + 8 = 1
C) 1/2x+8=10
D) 1/2(2x-6)=-6
Answer:
D) 1/2(2x-6)=-6 = x = -3
Step-by-step explanation:
A. x = 3
B. x = 7/3
C. x = 4
D. x = -3
Solve for x:
(2 x - 6)/2 = -6
Hint: | Multiply both sides by a constant to simplify the equation.
Multiply both sides of (2 x - 6)/2 = -6 by 2:
(2 (2 x - 6))/2 = -6×2
Hint: | Cancel common terms in the numerator and denominator of (2 (2 x - 6))/2.
(2 (2 x - 6))/2 = 2/2×(2 x - 6) = 2 x - 6:
2 x - 6 = -6×2
Hint: | Multiply 2 and -6 together.
2 (-6) = -12:
2 x - 6 = -12
Hint: | Isolate terms with x to the left hand side.
Add 6 to both sides:
2 x + (6 - 6) = 6 - 12
Hint: | Look for the difference of two identical terms.
6 - 6 = 0:
2 x = 6 - 12
Hint: | Evaluate 6 - 12.
6 - 12 = -6:
2 x = -6
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of 2 x = -6 by 2:
(2 x)/2 = (-6)/2
Hint: | Any nonzero number divided by itself is one.
2/2 = 1:
x = (-6)/2
Hint: | Reduce (-6)/2 to lowest terms. Start by finding the GCD of -6 and 2.
The gcd of -6 and 2 is 2, so (-6)/2 = (2 (-3))/(2×1) = 2/2×-3 = -3:
Answer: x = -3
Which of them is correct? I'm like, slow right now.
Answer:
c
Step-by-step explanation:
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................
Answer:
its the one you have clicked in the pic E
Step-by-step explanation:
Is the relation a function? And why
A)No
B)Yes
What is an equation of the line that passes through the point (-2, -3) and is
parallel to the line 4x - y = 12
Answer: y = 4x + 5
Step-by-step explanation:
Find the slope of the second line.
4x - y = 12
-y = -4x + 12
y = 4x - 12
slope = 4
Therefore, the slope of the second line must also be 4.
Use point-slope form to write the equation.
y + 3 = 4(x + 2)
y = 4x + 5
write an equation for a line perpendicular to y=5x+2 and passing through the point (-10,3)
Step-by-step explanation:
The perpendicular line *always* has a slope of the negative reciprocal. Your given line has a slope of -5, so the perpendicular slope is -1/(-5) = 1/5.
Use the point-slope form of a general line to find the equation.
(y - y_1) = m * (x - x_1)
y - 7 = (1/5) * (x - 15)
Noah and Diego left the amusement park’s ticket booth at the same time. Each moved at a constant speed toward his favorite ride. After 8 seconds, Noah was 17 meters from the ticket booth, and Diego was 43 meters away from the ticket booth. 1.Which line represents the distance traveled by Noah, and which line represents the distance traveled by Diego? Label each line with one name.
Answer:
the blue line
Step-by-step explanation:
Answer:
Step-by-step explanation:himxbe
A negative number is raised to an even exponent. The result is
zero
one
O positive
negative
Answer:
positive I guess that's the answer
Answer:
positive
Step-by-step explanation:
Identify a pair of alternate exterior angles.
a. 6 and 8
b. 2 and 7
c. 3 and 6
d. 3 and 2
15+3x=45 I'm sorry but there will be a lot of questions I need to ask. But can someone help me with this one too?
Answer:
x=10
Step-by-step explanation:
15+3x=45
-15 -15 *first subtract 15 from both sides
3x=30 * then divide by 3 on both sides to get x by itself
/3 /3
x=10
theres ur answer :D
Please help! Will give brainliest!
Answer:
D.5
Step-by-step explanation:
4*5=20
8*5=40
12*5=60
..etc
brainliest?
a lab uses negative numbers to describe a car moving backward on a road if the car was at -75.5 feet ,went forward 23 feet and then forward again 14.5 feet where is the car now
This graph shows a proportional relationship between the number of tulips and the number of daffodils in gardens planned by the Lindy Landscaping Company.
Lindy Landscaping Gardens
A line graph titled Lindy Landscaping Gardens has tulips on the x-axis, and Daffodils on the y-axis. There is 1 tulip for every 2 daffodils.
What is the constant of proportionality?
0.2
0.5
2
5
Answer: 2
Step-by-step explanation: I saw the answer somewhere else. Just wanted to tell you. I got it right on the test I think I was doing.
Answer:
2
Step-by-step explanation:
As you walk to your car, you notice that your tire is nearly flat! The initial psi level yesterday was 40 but it is now only 38 today. If this trend continues and the tire keeps losing the same percentage of air, how much should be left at the end of the week rounded to 1 decimal? (7 days later)
Answer:
Step-by-step explanation:
Given that:
Initial psi yesterday = 40 psi
psi today = 38 psi
If trend continues and tire loses the same percentage of air. How much air will be left in tire at the end of the week
1 week ( 7days)
Total loss after 7 days = (amount lost per day * number of days)
Total psi lost per day= [(40 - 38) = 2
% psi lost = (2/40) * 100
= 5%
Applying the exponential loss functin:
A = I ( 1 - r)^t
t = 7days ; r = 5% = 0.05 ; A = amount left ; I = Initial amount
A = 40(1 - 0.05)^7
A = 40(0.95)^7
A = 40 * 0.69833729609375
A = 27.933
A = 27.9 psi
A gold mine has two elevators, one for equipment and another for the miners. The equipment elevator descends 4 feet per second. The elevator for the miners descends 13 feet per second. One day, the equipment elevator begins to descend. After 33 seconds, the elevator for the miners begins to descend. What is the position of each elevator relative to the surface after another 12 seconds? At that time, which elevator is deeper?
Answer:
The position of the equipment elevator is 180 feet deep
The position of the miner's elevator is 156 feet deep
The equipment elevator is deeper.
Step-by-step explanation:
From the question,
For the equipment elevator
Velocity (v) = 4 feet/second
and for the miner's elevator,
Velocity (v) = 13 feet/second
To determine the position of each elevator, the position can be related to the distance covered.
From
Velocity = Distance / Time
Distance = Velocity × Time
Now, from the question,
The equipment elevator first descends for 33 seconds, after which the miner's elevator then start to descend both elevators descend for another 12 seconds. That is, the equipment elevator descends for a total of (33+12) seconds while the miner's elevator descends for 12 seconds.
Now, for the equipment elevator
Velocity = 4 feet/second
Time = (33 + 12 seconds) = 45 seconds
From
Distance = Velocity × Time
Distance = 4 × 45
Distance = 180 feet
The position of the equipment elevator is 180 feet deep
For the miner's elevator,
Velocity = 13 feet/second
Time = 12 seconds
Also, from
Distance = Velocity × Time
Distance = 13 × 12
Distance = 156 feet
The position of the miner's elevator is 156 feet deep
Hence, the equipment elevator is deeper.
If NK = 23, what is the value of x?
x + (2x + 40) + (3x – 50) = 15,002
Answer:
2497.22...
Step-by-step explanation:
Answer:
x + (2x + 40) + (3x - 50) = 15002
Remove the parentheses
x + 2x + 40 + 3x - 50 = 15002
Combine like terms
x + 2x + 3x + 40 - 50 = 15002
6x - 10 = 15002
6x = 15002 + 10
6x = 15012
x = 15012/6
x = 2502
Step-by-step explanation:
Hope it helps :)
Brainliest pls?
A store purchases an item wholesale for $60 and marks it up by 70 percent. If there is a 7 percent tax on the item, how much will the item cost?
Answer:
$106.20
Step-by-step explanation:
60x70%=42
60x7%=4.2
60+46.2
Answer:
b
Step-by-step explanation:
Use the distributive property to write an equivalent expression.
8(4t + 9)
Answer:
32t+72
Step-by-step explanation:
HELP HELP HELP PLS Does it matter which way you subtract the values when you are finding the distance between two numbers on a number line .Give example to support your answer please answer in complete sentence please it's about to be due.
Answer:
Yes, it matters which way you subtract values because if you subtract a larger number from a smaller number you will get a negative nummber, but when you subtract the smaller number from the bigger number you get a positive number
ex: 5-6= -1 but 6-5=1
Step-by-step explanation:
The temperature in Miami, Florida is 22 degrees warmer than three times the temperature in Bangor, Maine. The temperature in Miami is 82 degrees. Write an equation to determine the temperature in Bangor. NEEED HELP PLZ :(
A 3x + 82 = 22
B 3x + 22 = 82
C 3x − 22 = 82
D 3x − 82 = 22
Answer:
I think option 2 is correct
3x+22=82
Hope u like it
A factory can make 300 dozen doughnuts an hour. What is the unit rate in doughnuts per minute?
O 60 doughnuts a minute
O 58 doughnuts a minute
O 56 doughnuts a minute
50 doughnuts a minute
Answer:
60 doughnut per mintute
Step-by-step explanation:
Which of the following is an example of a rational number that is not an integer?
Evaluate a2-b for a = 8 and b = 17.
The value of the expression is
Answer:
-1
Step-by-step explanation:
Assumuning your asking what a2-b is.
8(2) - 17
-1
Answer:
-1
Step-by-step explanation:
If A= 8 and B= 17...
8(2)-17
16-17
-1
2. What is the solution to this equation?
2 x + 3 = x - 4
Answer: x=-7
Step-by-step explanation:
2x-x=-4-3
Collect terms
X=-4-3
Answer is x=-7