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1) A museum borrows $2,000,000 at simple annual interest to purchase new exhibits. Let x represent the amount borrowed at 7%, y represent the amount borrowed at 8.5%, and z represent the amount borrowed at 9.5%. Set up a system of linear equations to determine how much is borrowed at each rate given that the total annual interest is $169,750 and the amount borrowed at 8.5% is four times the amount borrowed at 9.5%. Then write the system in matrix form. You do not have to solve the system.
Based on the information the amount borrowed at each rate is:
Z=9.5%=$350,000Y= 8.5%=$1,400,000X=7% =$250,000Let x=9.5%
Let 4x= 8.5%
Let 7% =$2,000,000 - 5x
Formulate
0.095x + 0.085(4x) + 0.07(2,000,000-5x) = 169,750
Collect like terms
0.095x + 0.34x + 140,000 - 0.35x = 169,750
Divide both side by 0.085x
0.085x = 29,750
x=29,750/0.085
x =$350,000
Amount borrowed at each rate:
Z=9.5% =$350,000
Y= 8.5% =$350,000×4
Y= 8.5% =$1,400,000
X=7% =$2,000,000 - 5($350,000)
X=7%=$2,000,000-$1,750,000
X=7% =$250,000
Matrix form
Z $350,000
Y $1,400,000
X $250,000
Inconclusion the amount borrowed at each rate is: $350,000; $1,400,000; $250,000.
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The graph of the function f is shown below
Find f(0)
Answer:
2
Step-by-step explanation:
Write that down before Katie deletes it. There is no work to show, only read the graph.
NO LINKS
A jaguar can run 40 miles per hour while a giraffe can run 32 per mile if they both run for 4 hours how much farther will the jaguar run? Show TWO ways to write the expression or equation and solve
Answer:
(40*4)-(32*4)=32
160-128=32
Step-by-step explanation:
3x2 - 4x – 7
factor
Answer:
3x2 = 6
6-4x-7
(6-4x) - 7
2x - 7 = messi ok no xd
3.5-
Step-by-step explanation:
Answer:
[tex](3x-7)(x+1)[/tex]
Step-by-step explanation:
Use the slide-and-divide method:
[tex]3x^2-4x-7[/tex]
[tex]x^2-4x-21[/tex] <-- Multiply last term by the leading coefficient 3
[tex](x-7)(x+3)[/tex] <-- Factor
[tex](3x-7)(x+1)[/tex]
Please help me with this
Answer:
The measure of <Y = 85 degrees
Step-by-step explanation:
you can solve this problem algebraically if you know that the sum of the interior angles of a triangle is 180 degrees.
if you add all of these angles and set them equal to 180, you can find what "a" is.
a+2a+a+10=180 so 4a+10=180 so a is 42.5 (which is equal to angle x)
then looking at all of the options, it can be seen that the first two options are incorrect because angle x is equal to 42.5 degrees.
you know that angle y is equal to 2a, so multiplying "a" by two, you can find that angle y is 85 degrees.
Danielle earns a 7.75% commission on everything she sells at the electronics store where she works. She also earns a base salary of $800 per week. How much did she earn last week if she sold $4,700 in electronics merchandise? Round your intermediate calculations and answer to the nearest cent.
Answer:
1164.25
Step-by-step explanation:
sin(83)cos(7) + cos(83)sin(7)
Answer:
1
Step-by-step explanation:
correct on edge
sin(83 radians) * cos(7 radians)) + (cos(83 radians) * sin(7 radians)) =
0.893996664
Answer:
hope it helps
Which of the following are steps in practical problem solving?
Answer:
Assign an identifying variable to the quantity to be found. Write a sentence stating conditions placed on the quantity. Solve the sentence for the variable.
Step-by-step explanation:
can you mark me as brainlist
Select the correct answer.
What is the factored form of this expression?
433 – 8x2 – 9x + 18
--
-
A. (2x − 3)(2x - 3)(x - 2)
B. (2x + 3) (2x − 3)(x + 2)
C. (2x + 3)(2x + 3)(x - 2)
D. (2x + 3)(2x − 3)(x - 2)
Answer:
Option D
Step-by-step explanation:
Use Factoring Methods
[tex]4x^3-8x^2-9x+18\\[/tex]
put bracket around each 2 terms as such [tex](4x^3-8x^2)+(-9x+18)[/tex]
And then factor each respective bracket. We'll start with the first one
[tex](4x^3-8x^2) = 4x^2(x-2)[/tex]
Then do the other, and try to get similar brackets as the first
[tex](-9x+18)=-9(x-2)[/tex]
Since they are both simiar, the equation is now: [tex](4x^2-9)(x-2)[/tex]
Now factor the first bracket again for final result
[tex]4x^2-9=(2x-3)(2x+3)[/tex]
Ans when you put it all together, you get: [tex](2x-3)(2x+3)(x-2)[/tex]
Correct answer is option D
At the end of the year, company A paid a dividend of 3,000 VND/share. Speed
constant annual dividend growth of 5%.
The current selling price of stock A is VND 60,000/share.
Definition of cost of common equity
Answer:
all u do is take 3000×5%=150
A newborn child receives a $6000 gift toward a college education from her grandparents. How much will the $6000 be worth in 18 years if it is invested at 7.6% compounded quarterly?
Answer:
333.333333333
Step-by-step explanation:
you have to divide
An ice cream stand uses the expression to determine the cost (in dollars) of an ice cream cone that has scoops of ice cream.2 + 0.5x2+0. 5x2, plus, 0, dot, 5, xxxx
How much does an ice cream cone with scoops cost?55
Answer:
answer: 0
Step-by-step explanation:
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
(x+4)•(x-1)
——————————— • 2 = 0 • 2
2
Now, on the left hand side, the 2 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
(x+4) • (x-1) = 0
7.2 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
simple form
x = 1
x = -4
90 is 95% of what number?
Answer:
94.74
Step-by-step explanation:
Hope this helps!
Answer:
94.74
Step-by-step explanation:
Josh and Adelina are staff members for a political candidate. They are considering hiring callers who will call voters and ask for donations. (picture below)
a) only adelina's
b) only josh's
c) both statements are correct
d) neither statements are correct
Answer:
Adelina
Step-by-step explanation:
Roy used 1/4 of his money on 3 pens and 6 notebooks. The cost of each pen is 3 times the cost of each notebook. He bought some more pens with 2/3 of his remaining money. How many pens did Roy buy altogether?
=========================================================
Explanation:
Roy spends 1/4 of his money on 3 pens and 6 notebooks. That means 3/4 of it is leftover.
2/3 of 3/4 = (2/3)*(3/4) = 1/2 of his money is spent on buying some unknown number of additional pens. We'll come back to this later.
---------------
In terms of cost,
1 pen = 3 notebooks
which is another way of saying 1 pen is the same price as 3 notebooks.
Multiply both sides by 2 to get
2 pens = 6 notebooks
Therefore, saying "3 pens + 6 notebooks" is the same as "3 pens + 2 pens = 5 pens" when just thinking about costs.
---------------
In short, Roy buying 3 pens and 6 notebooks is the same as him buying 5 pens. He spends 1/4 = 25% of his money on getting these 5 pens.
Multiply those two values by 2 to find that 50% = 1/2 of his money would allow him to get 10 pens.
--------------
Recall that at the end of the first section, we concluded that Roy spent 1/2 of his money on buying those unknown additional number of pens. Then the previous section mentioned that 1/2 of his money gets him 10 pens. Therefore, he must have bought 10 additional pens on top of the original 3 mentioned in the instructions.
Overall, he purchased 3+10 = 13 pens
Answer:
13 pens
Step-by-step explanation:
If a pen costs 3 times the cost of a notebook, then the cost of 3 notebooks will equal the cost of a pen. The 6 notebooks that Roy bought are equivalent in cost to 2 pens, so 1/4 of Roy's money is the cost of 3+2 = 5 pens.
After the first purchase, Roy has (1 -1/4) = 3/4 of his money remaining. If he spends 2/3 of that on more pens, he will have spent ...
(2/3)(3/4) = 2/4
of his money on more pens. We've already seen that 1/4 of his money buys 5 pens, so 2/4 will buy 10 more pens.
Roy bought 3 +10 = 13 pens altogether.
The answer is A but I couldn’t tell you why. If someone know, please let me know.
Answer:
a.0.311
Step-by-step explanation:
BRAINLIEST ANSWERHow do I solve this and what is the answer to this?! Number 14.
Answer:
You'll have to give more information about the question or about what you need solved.
Step-by-step explanation:
Dave and Kyle are 40 miles apart on a path when they start moving toward each other. Dave runs at a constant speed of 8 miles per hour, while Kyle walks at a constant speed of 5 miles per hour. How long does it take until they meet?
Answer:
About 3 hours
Step-by-step explanation:
together, they go 13 miles in one hour. 40/13 = 3 with remainder 1
What Is the answer
Plz it's urgent
for the answer I think it is 2 cm
the answer : 10 cm :>
a man buys an article for $600 and sells it for $710/ what is the profit or loss
Answer:
110$ (profit)Step-by-step explanation:
a man buys an article for $600 and sells it for $710/ what is the profit or loss?
a financial gain, especially the difference between the amount earned and the amount spent in buying, operating, or producing something.
so
710 - 600 = 110$ (profit)
Answer:
Profit of 110
Step-by-step explanation:
As he sells it at a higher price, he makes a profit.
Help help please …thanksss
what is the output of the function when the input is −3
It depends on the function. Please add a picture or type your function.
1. A stack of boards is 21 inches high. Each board is 1¾ inches thick. How many boards are there
Answer:
12
Step-by-step explanation:
We can solve this by setting up an equation with the variable x representing the number of boards. Since x number of 1.75 inches thick boards sum up to the height of 21 inches, the equation is 1.75x = 21, so x = 12. There are 12 boards.
Find the quotient: 7,308 divided by 18. A) 46 B) 406 C) 406 10/18. D) 408
Answer:
7308 / 18
= 406
B is the answer.
Help me with this plzzzzzzzzz
Answer:
B : x € (-∞, 1)
Step-by-step explanation:
we have 4x +9 -2 +3x < 14
7x +7 < 14
7(x+1) < 14
x + 1 < 2
x < 1
=> x € (-∞, 1)
the IQR of the box plot is...
Answer:
IQR = 3
Step-by-step explanation:
Subtract your Q1 and Q3.
Q1 = 3
Q3 = 6
Help anyone?? Not that hardd
no links ! :(
Answer:
1.2
Step-by-step explanation:
First, you cancel out [tex]\frac{6}{20}[/tex] to become [tex]\frac{3}{10}[/tex]
Then that becomes [tex]-\frac{3}{10}+1.5[/tex]
Now, you convert the element to a decimal form to be [tex]-0.3+1.5[/tex]
Finally, you subtract them (because a negative plus a positive is subtraction) to get the final answer of 1.2
Hope this helps!
What is the approximate surface area of the sphere? Round to the nearest hundredth and use 3.14 for Pi. Recall the formula S A = 4 pi r squared. A sphere with a radius of 9. 113.04 square units 226.08 square units 1,017.36 square units 4,069.44 square units
Answer:
Step-by-step explanation:
A = 4πr² = 4π9² = 324π units²
324(3.14) = 1,017.36 units²
10x-9y=24
y= x-2
find x and y
Answer:
x=6,y=4
Step-by-step explanation:
10x-9(x-2)=24
10x-9x+18=24
x=24-18
x=6
sub x
y=6-2
y=4
Answer:
x=6 y=4
Step-by-step explanation:
Substitute x-2 in for y: 10x-9(x-2)=24
Distribute: 10x-9x+18=24
Subtract 10x-9x=1x
Subtract 18 from both sides
x=6
Substitute 6 for x
y=6-2
y=4
x=6 y=4
Amina recently moved and got a new job. The quickest way to get to work is to take a
freeway that charges a toll. There are two options for paying the tolls.
Option A: No monthly fee, each trip on the tollway is $2.80.
Option B: $30 monthly fee, each trip on the tollway is half-priced at $1.40.
a. Write a linear model for Option A showing the total cost, C, in dollars, for x trips on
the tollway.
b. Write a linear model for Option B showing the total cost, C, in dollars, for x trips on
the tollway.
c. How many trips on the tollway are needed for Option B to be cheaper? Show your
work or explain how you found this number.
d. If Amina plans to travel to and from work 5 times a week which option, should she
purchase? (assume a month has 4 weeks) Show your work and explain in words why
you choose the option that you choose.
22 trips on the tollway are needed for Option B to be cheaper. Thus, if Amina plans to travel to and from work 5 times a week (20 round trips per month, that is, 40 trips), she must choose Option B.
Since Amina recently moved and got a new job, and the quickest way to get to work is to take a freeway that charges a toll, and there are two options for paying the tolls:
Option A: No monthly fee, each trip on the tollway is $ 2.80.
Option B: $ 30 monthly fee, each trip on the tollway is half-priced at $ 1.40.
To determine how many trips on the tollway are needed for Option B to be cheaper; y, if Amina plans to travel to and from work 5 times a week, which option should she purchase; the following calculation must be performed:
Option A = 2.80X Option B = 30 + 1.40X 2.80 x 20 = 56 30 + 1.40 x 20 = 58 2.80 x 25 = 70 30 + 1.40 x 25 = 65 2.80 x 24 = 67.2 30 + 1.40 x 24 = 63.6 2.80 x 22 = 61.6 30 + 1.40 x 22 = 60.8
Therefore, 22 trips on the tollway are needed for Option B to be cheaper. Thus, if Amina plans to travel to and from work 5 times a week (20 round trips per month, that is, 40 trips), she must choose Option B.
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