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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Consider f and c below. f(x, y) = x2 i + y2 j c is the arc of the parabola y = 2x^2 from (−1, 2) to (0, 0)
(a) find a function f such that f = ∇f.
f(x, y) =
(b) use part (a) to evaluate c ∇f · dr along the given curve C.
(a) If there is a scalar function f(x, y) such that ∇ f(x, y) = x² i + y² j, then
∂f/∂x = x²
∂f/∂y = y²
Integrating both of these equations with respect to x and y (respectively) gives
f(x, y) = 1/3 x³ + g(y)
f(x, y) = 1/3 y³ + h(x)
Differentiating with respect to the other variable gives
∂f/∂y = g'(y) = y²
∂f/∂x = h'(x) = x²
so it follows that
f(x, y) = 1/3 x³ + 1/3 y³ + C
for some constant C.
(b) By the gradient theorem,
[tex]\displaystyle \int_C \nabla f \cdot d\vec r = f(0,0) - f(-1,2) = \boxed{-\dfrac73}[/tex]
20% percent tip on 8 dollar
Answer:
9.60 dollars tip is $1.60
Step-by-step explanation:
4. Mother pays Php 199.50 for 2.85 kg of rice. How much does a kilogram of rice cost?
a.35
b.70
c.75
d.105
please answer it correctly.
Answer:
B. 70
Step-by-step explanation:
If 199.50 PHP gets you 2.85KG of rice.
A kilogram of rice would cost = Total Amount / Total Weight.
199.50/2.85
= 70PHP
Express the following surds in the simplest form
a)
[tex] \sqrt{128} [/tex]
b)
[tex] \sqrt{48} [/tex]
c)
[tex] \sqrt{300} [/tex]
[tex] \sqrt{128} \\ = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2} \\ = \sqrt{ {2}^{2} \times {2}^{2} \times {2}^{2} } \\ = 2 \times 2 \times 2 \\ = 8[/tex]
[tex] \sqrt{48} \\ = \sqrt{2 \times 2 \times 2 \times 2 \times 3} \\ = \sqrt{ {2}^{2} \times {2}^{2} \times 3 } \\ = 2 \times 2 \sqrt{3} \\ = 4 \sqrt{3} [/tex]
[tex] \sqrt{300} \\ = \sqrt{2 \times 2 \times3 \times 5 \times 5} \\ = \sqrt{ {2}^{2} \times 3 \times {5}^{2} } \\ = 2 \times 5 \sqrt{3} \\ = 10 \sqrt{3} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
Area =12
X+2
X+4
X =
Answer:
To find area of the square you'll need to square one side
(3X)^2 = 81
9(X)^2 = 81
(x)^2 = 81/9
x^2 = 9
X = (9)^1/2
X = 3
TRUE OR FALSE
There are whole numbers that are not integers.
There are rational numbers that are not whole
numbers.
All rational numbers are integers.
All whole numbers are rational numbers.
ANSWERS:
[tex]1. False \\ 2. True \\ 3. False \\ 4. True \\ [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
Determine whether or not the given value is a solution. 1. -5x + 4 = -1; x = -1 2.4x3 = -7; x = -1 3. 3y -4 = 5; y = // 4.-2y + 7 = 12; y = -1/2 5.3a-6 = 18 - a; a = -3 6. 5(2t - 1) = 2 = t; t = 2 7. ax = b = 0; x = b/a 8. ax + b = 2b; x = b/a
#1
[tex]\\ \sf\hookrightarrow -5x+4=-1[/tex]
[tex]\\ \sf\hookrightarrow -5x=-5[/tex]
[tex]\\ \sf\hookrightarrow x=1[/tex]
Incorrect
#2
[tex]\\ \sf\hookrightarrow 4x-3=-7[/tex]
[tex]\\ \sf\hookrightarrow 4x=-4[/tex]
[tex]\\ \sf\hookrightarrow x=-1[/tex]
Correct
#3
[tex]\\ \sf\hookrightarrow 3y-4=5[/tex]
[tex]\\ \sf\hookrightarrow 3y=9[/tex]
[tex]\\ \sf\hookrightarrow y=3[/tex]
Ans not given
#4
[tex]\\ \sf\hookrightarrow -2y+7=12[/tex]
[tex]\\ \sf\hookrightarrow -2y=5[/tex]
[tex]\\ \sf\hookrightarrow y=-5/2[/tex]
Incorrect
#5
[tex]\\ \sf\hookrightarrow 3a-6=18-a[/tex]
[tex]\\ \sf\hookrightarrow 4a=24[/tex]
[tex]\\ \sf\hookrightarrow a=6[/tex]
Incorrect
#6
[tex]\\ \sf\hookrightarrow 5(2t-1)=2[/tex]
[tex]\\ \sf\hookrightarrow 10t=7[/tex]
[tex]\\ \sf\hookrightarrow t=7/10[/tex]
Incorrect
#7
[tex]\\ \sf\hookrightarrow ax-b=0[/tex]
[tex]\\ \sf\hookrightarrow x=\dfrac{b}{a}[/tex]
Correct
Done
What is with simplifying
-3p + 6p
Answer:
-3p+6p=3p
Step-by-step explanation:
It's just like saying -3+6,
but just with the p.
-3+6=3
therefore the answer is 3p
solve the sinusoidal equation:
5sin(3x)-1=3
Answer:
[tex]x=0.3090984+\frac{2\pi n}{3},0.73809914+\frac{2\pi n}{3}[/tex]
Step-by-step explanation:
[tex]5sin(3x)-1=3[/tex]
[tex]5sin(3x)=4[/tex]
[tex]sin(3x)=\frac{4}{5}[/tex]
[tex]3x=0.92729521+2\pi n,2.21429743+2\pi n[/tex]
[tex]x=0.3090984+\frac{2\pi n}{3},0.73809914+\frac{2\pi n}{3}[/tex]
How much pizza will each person get if 4 people share
of a pizza equally?
A)1/3
B)1/4
C)1/6
D)3/16
Answer: B)1/4
Step-by-step explanation: If you divide a pizza into 4 pieces, each person will get a fourth of the pizza.
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 please and thanks
Answer:
Rate of change of length of shadow is [tex]\frac{15}{7} ft/s[/tex]
Step-by-step explanation:
Consider the figure
We have
[tex]\begin{aligned}&\frac{d x}{d t}=\text { rate of person walking } \\&\frac{d y}{d t}=\text { rate of change of shadow length } \\&\frac{d x}{d t}+\frac{d y}{d t}=\text { rate of change of tip of shadow }\end{aligned}[/tex]
[tex]\begin{aligned}&\frac{6}{20}=\frac{y}{x+y} \\&6(x+y)=20 y \\&6 x+6 y=20 y \\&6 x=14 y\end{aligned}[/tex]
[tex]6\left(\frac{d x}{d t}\right)=14\left(\frac{d y}{d t}\right)\\\\6(5)=14\left(\frac{d y}{d t}\right)\\\\\frac{30}{14}=\frac{d y}{d t}\\\\\frac{15}{7}=\frac{d y}{d t}\\\\[/tex]
Rate of change of length of shadow is [tex]\frac{15}{7} ft/s[/tex]
Which expression is undefined?
Answer:
D: [tex]\frac{3}{(6-6)}[/tex]
Step-by-step explanation:
Option A equates to [tex]-\frac{0}{2}=0[/tex]
Option B equates to [tex]\frac{(-4+0)}{8}=\frac{-4}{8}=-\frac{1}{2}[/tex]
Option C equates to [tex]0\div11 =0[/tex]
Option D equates to [tex]\frac{3}{(6-6)}=\frac{3}{0}[/tex] which cannot be defined as division by 0 is impossible
A gardener measures the dimensions of a rectangular garden that is 9 meters wide by 12 meters long. If the gardener draws a blueprint of the garden, where each meter is equivalent to
inch, which statements are true?
Select ALL that apply.
The area of the blueprint is square inches
The area of the blueprint is 108 square inches
The length of the blueprint is 6 meters
The perimeter of the blueprint is 28 inches.
The width of the blueprint is 8 meters
Calculator
Answer:
Catalog Name:*Shimmering Chic Earrings*
Base Metal: Alloy
Plating: Gold Plated
Stone Type: Cubic Zirconia/American Diamond
Type: Jhumkhas
Multipack: 1
Easy Returns Available In Case Of Any Issue
*Proof of Safe Delivery! Click to know on Safety Standards of Delivery Partners- https://ltl.sh/y_nZrAV3
The statements are true:
The area of the blueprint is square inches
The area of the blueprint is 108 square inches
What is Area of rectangle?The Area of Rectangle is product of its length to its width.
So, Area of Rectangle = length x width
Given:
length= 12 inch
and width= 9 inch
Area of Blue print = l x w
= 12 x 9
= 108 square inches.
Perimeter of Blue print = 2 ( l+ w)
= 2( 12+ 9)
= 42 inches
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Part A: James bought a cake that weighs pounds. How many ounces does the cake weigh? Show your work. (5 points)
[16 ounces = 1 pound]
Part B: A running tap dispenses 0.15 gallons of water every second. How many pints of water is dispensed after 20 seconds? Show your work. (5 points)
[1 gallon = 4 quarts, 1 quart = 2 pints]
Question 4 options:
Answer:
For part a multiply the pound amount by 16. Your work would look something like this... (not actual answer) 10 pounds x 16= 160 ounces. So 10 pounds= 160 ounces!
For part B
0.15 gallons=1.2 pints
Example: .15 x 4= .6
.6 x 2= 1.2 pints
1.2 x 20 seconds= 24 pints!
Hope this helps
Step-by-step explanation:
:)
Answer:
Part A: 52 oz
Part B: 24 pints
Step-by-step explanation:
Part A:
Since 1 pound = 16 ounces, the number of ounces is 16 times the number of pounds. To convert pounds to ounces, multiply the pounds by 16.
3 1/4 lb × 16 oz/lb =
= 13/4 × 16 oz
= 13 × 4 oz
= 52 oz
Answer: 52 oz
Part B:
We need to convert from gallons to pints.
1 gallon = 4 quarts
1 quart = 2 pints
That means that 1 gallon = 8 pints.
0.15 gallon/second × 8 pints/gallon =
= 1.2 pints/second
The tap dispenses 1.2 pints/second.
Now we calculate the number of pints dispensed in 20 seconds.
1.2 pints/second × 20 seconds = 24 pints
Answer: 24 pints
help help help meeee
Answer:
122
Step-by-step explanation:
since line m and line n are parallel the sum of the angles is equal to 180 degrees
58 + x = 180 subtract 58 from both sides
x = 122
Jenny bought 5 pounds of carrots for $2.50. What is the unit rate for
Jenny's purchase? Identify the true statement that corresponds to this
situation.
A. 2 pounds of carrots per $1
B. $5 per pound
Answer:
A. 2 pounds of carrots per $1
Step-by-step explanation:
[tex]\frac{5 pounds }{2.5 dollars}=\frac{2pounds }{1 dollars}[/tex]
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
identify a possible explicit rule for the nth term of the sequence 9, 17, 25, 33, 41
Answer:
The explicit formula for the nth term of the sequence is [tex]a_n=9+8(n-1)[/tex]
Step-by-step explanation:
Recall:
The explicit formula for a sequence is [tex]a_n=a_1+(n-1)d[/tex] where [tex]a_n[/tex] is the [tex]n[/tex]th term, [tex]a_1[/tex] is the first term, and [tex]d[/tex] is the common difference
Given:
First term --> [tex]a_1=9[/tex]
Common Difference --> [tex]d=8[/tex]
Substitute:
[tex]a_n=9+(n-1)(8)[/tex]
[tex]a_n=9+8(n-1)[/tex]
How do you pass 10th grade geometry
Answer:
Study hard and stay determined
Find simple steps to help you remember and "wrap you head" around it better.
If you ask for help and try your best you should be able to get enough passing grades to pass 10th grade geometry. If I did, that means you can too.
How do you pass any course?
Study and study some more.
There is no easy road to success.
Math is not easy. If math were easy, everybody would get an A. What specific geometry topic are you stuck on? I am not that smart. I passed geometry at FDR HIGH SCHOOL back in the 1980s. We had no internet back then. At least you have YOU TUBE. If I passed, so can you.
Hello can anyone help me with these problems please and thank you
Answer:
94)=154°
95)=40°
96)=11
97)=11
98)=9
1985 x 99 I already know the answer: 196515
Answer:
196515
Step-by-step explanation:
Answer:
196515
Step-by-step explanation:
I want a way to solve such a problem
Answer: please calculate the answer.
Step-by-step explanation:\\ Bro use this formula (sum of all numbers of the question) \ no. of seen numbers.
Arithmetic mean = ( 24+124+243+...) \ 12
Juan has 6 times as many baseball cards as Nick. If Juan has 192 cards, how many does Nick have?
32
Step-by-step explanation:Divide 192 by 6, to find the amount of baseball cards Nick has.
192 ÷ 6 = 32
Check:32 · 6 = 192
192 ÷ 6 = 32
Nick has 32 baseball cards, which is 6 times less than Juan's amount.
Don Swifter earns $9.75 per hour as a clerk. He starts work Monday through Friday morning at 8:00 AM. He takes a one-half hour lunch break every day. If he finishes work at 3:30 PM Monday through Thursday, how late must he work on Friday to have total pay of $360.75 for the week?
Answer:
He works until 5:30.
Step-by-step explanation:
ok so first, every day don would take a total of 7 hours and 30 minutes on mon-Thurs. If we subtract his lunch from that total it would be 7 hours so next we do 7 hours times 9.75 which is 68.25$. Now that we know how much he makes per day, we times that by 4 since mon-thurs is 4 days. This would be 273$. Now we need to get to 360.75 so we subtract that. This would be 87.75$. Now if a normal day is 68.25$ and friday is 87.75, we find the diffrence which is 19.50. which is also 9.75(an hour) x 2 resulting in 2 hours extra. Therefore, he works 9 hours and 30 minutes on fridays (until 5:30). Thanks for putting in the work to understand and have a nice day!
Don must work approximately 9 additional hours on Friday to have a total pay of $360.75 for the week.
How to determine how late he must workDon works from 8:00 AM to 3:30 PM Monday through Thursday. Let's calculate his total work hours for these four days:
Total work hours from Monday to Thursday:
(3:30 PM - 8:00 AM) - 0.5 hours (lunch break)
= 7.5 hours - 0.5 hours
= 7 hours (per day)
Total work hours for the week (Monday to Thursday):
4 days x 7 hours/day = 28 hours
Total pay for the week = Hourly rate x Total work hours + Additional hours on Friday
$360.75 = $9.75 x 28 hours + Additional hours on Friday
Additional hours on Friday = ($360.75 - $9.75 x 28) / $9.75
Additional hours on Friday = ($360.75 - $273) / $9.75
Additional hours on Friday = $87.75 / $9.75
Additional hours on Friday ≈ 9 hours (rounded to the nearest hour)
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pls help im gonna fail geometry:(
(4 points) Given two lengths of a triangle 2.2 ft. and 3.2 ft. which inequality will give all the
possible lengths of the third side, s?
A 2.2 ft < s <3.2 ft tabclft < s < 5.4 ft
B 2.2 ft < s < 5.2 ft
1326
Answer:
its ether a or d
Step-by-step explanation:
ps (id like to tell you the exact answer but that would be considered plagerism and i dont want anyone to receive the consenquesnces of that. I hope you understand and that this helps you)
what is the product of -2/7 and -3/7?
Answer:
6/49
Step-by-step explanation:
2/7 * 3/7
2 * 3/ 7 * 7
3 * 3/7¹⁺¹
2 * 3/7²
6/49
Answer:
D
Step-by-step explanation:
f(x) = 11 – 5x for f(9)
A.-46
B.-44
C.44
D.45
Answer:45
Step-by-step explanation: math solver
Answer:
the answer is not there. the answer is -34
Step-by-step explanation:
11-5(9) . 11-45
Is the product of -5 and v121 rational or irrational
Answer:
Rational.
Step-by-step explanation:
-5 times √121
= -5 * 11
=-55
Rational.
SOMEBODY HELP NO LINKS PLZ AND THANK YOU
given the table below which function shos an exponential function
table
x f(x) g(x) h(x)
1 64 65 5
2 32 54 7
3 16 43 10
4 8 32 14
A f(x)
B g(x)
C h (x)
D none of the above
2 squared all divided by 4
please
Answer:
think answer is 0.5 each