Answer:
$5000 at 10%, $10000 at 12% and 10000 at 16%Step-by-step explanation:
One part of $ 25,000 is invested at 10% interest, another part at 12%, and the rest at 16%. The total annual income from the three investments is $ 3,200. Also, the income from the investment at 16% is equal to the income from the other two investments combined. How much was invested at each interest rate?==================
Let the parts be x, y and z
As per given we get below system of equations:
x + y + z = 250000.1x + 0.12y + 0.16z = 32000.1x + 0.2y = 0.16zSubstitute 0.1x + 0.2y in the second equation:
0.16z + 0.16z = 32000.32z = 3200z = 3200/0.32z = 10000Now we have:
x + y + 10000 = 25000 ⇒ x + y = 15000and
0.1x + 0.12y + 0.16*10000 = 3200 ⇒ 0.1x + 0.12y = 1600Multiply the second equation and then subtract the first one:
10(0.1x + 0.12y) = 10(1600) ⇒ x + 1.2y = 16000x + 1.2y - (x + y) = 16000 - 150000.2y = 1000y = 10000Then
x = 15000 - 10000 = 5000So the parts are:
$5000 at 10%, $10000 at 12% and 10000 at 16%
Matt and Chris leave their uncle's house in Phoenix at the same time, Matt drives west on 1-60 at a speed of 79 miles per hour. Chris drives east on 1-60 at a speed of 83 miles per hour.
How many hours will it take them to be 64 miles apart
Two boats leave the same dock in Cairo at the same time. One heads north on the Mississippi River while the other heads south. The northbound boat travels five miles per hour. The
southbound boat goes seven miles per hour How many hours will it take them to be 66 miles apart?
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Addit
Answer:
It will take them (Matt and Chris) 0.395 hours to be 64 miles apart
It will take 5.5 hours for the boats to be 66 miles apart
Step-by-step explanation:
We are to determine the time when Matt and Chris will be 64 miles apart, that is, when the total distance traveled by both of them will be 64 miles.
Let the time be t and
Let the distance covered by Matt be S₁ and the distance covered by Chris be S₂.
For Matt,
From the question, Matt drives at a speed of 79 miles per hour
From the formula
Distance = Speed × Time
S = v × t
∴ S₁ = 79×t
S₁ = 79t
For Chris,
From the question, Chris drives at a speed of 83 miles per hour
Using the same formula,
∴ S₂ = 83 × t
S₂ = 83t
To determine when they will be 64 miles apart, that is when S₁ + S₂ = 64 miles.
Hence,
S₁ + S₂ = 79t + 83t
∴64 = 79t + 83t
64 = 162t
t = 64/162
t = 0.395 hours
Hence, it will take them 0.395 hours to be 64 miles apart.
For the boats,
To determine how many hours it will take them to be 66 miles apart, that is when the total distance traveled by the two boats will be 66 miles.
Let the time be t and
Let the distance traveled by the northbound boat be S₁ and the distance traveled by the southbound both be S₂.
From the question,
The northbound boat travels five miles per hour
From the formula
Velocity = Distance / Time
Then, Distance = Velocity × Time
That is, S = v × t
Hence, for the northbound boat,
S = S₁
v = 5 miles per hour
∴ S₁ = 5t
Also from the question,
The southbound boat goes seven miles per hour
Hence, for the southbound boat
S = S₂
v = 7 miles per hour
∴ S₂ = 7t
To determine when the boats will be 66 miles apart, that is when S₁ + S₂ = 66 miles
Then,
S₁ + S₂ = 5t + 7t
Hence,
66 = 5t + 7t
66 = 12t
t = 66/12
t = 5.5 hours
Hence, it will take 5.5 hours for the boats to be 66 miles apart.
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Answer: the answer is b
Step-by-step explanation:
Answer: B.63
Step-by-step explanation: OK so if angle VKQ is 153, then angle DKJ also has to be 153 because of vertical angles. Then we know that angle MKJ is 90, so angle DKM is angle DKJ. Minus 90. 153-90=63.
In a particular country railroad miles have been on the decline and the miles of roads in the highway system have been increasing. The function y=-1250.2x + 142,602 represents the railrond miles, while the function y=501.5x + 158,449 models the number of
highway miles. For each function, x is the number of years after 1995
b. Find the year in which it is estimated that the number of the country's railroad miles and the number of the country's highway miles were the same.
It is estimated that the number of railroad miles and the number of highway miles were the same during the year ___.(Round down to the nearest your)
Answer:
1986
Step-by-step explanation:
Function that represents railroad miles
[tex]y=-1250.2x + 142602[/tex]
Function that represents number of highway miles
[tex]y=501.5x + 158449[/tex]
We have to find in which year (1995+x) the miles of railroad and highway is the same so
[tex]-1250.2x + 142602=501.5x + 158449\\\Rightarrow -1250.2x-501.5x=158449-142606\\\Rightarrow -1751.7x=15843\\\Rightarrow x=-\dfrac{15843}{1751.7}\\\Rightarrow x=-9.044\ \text{years}\approx -9\ \text{years}[/tex]
So, the year is [tex]1995+x=1995+(-9)=1986[/tex]
In the year 1986 the railroad and highway miles were equal.
It is estimated that the number of railroad miles and the number of highway miles were the same during the year 1986.
Given
The function y =-1250.2x + 142,602 represents the railrond miles.
While the function y =501.5x + 158,449 models the number of highway miles.
For each function, x is the number of years after 1995.
The year in which it is estimated that the number of the country's railroad miles and the number of the country's highway miles were the same.
Therefore,
[tex]\rm -1250.2x + 142,602=501.5x + 158,449\\\\-1250.2x -501.5x = 158,449-142,602\\\\-1751.7x=15847\\\\x = \dfrac{15847}{-1751.7}\\\\x=-9[/tex]
Then,
1995 - 9 = 1986
It is estimated that the number of railroad miles and the number of highway miles were the same during the year 1986.
To know more about Equation click the link given below.
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Solve: (3x-9) and (x + 5)
Answer:
2
Step-by-step explanation:
Got it right on my test
A notebook costs $4.50 plus sales tax . After sales tax , the notebook is $4.86. What is the sales tax rate?
Answer:
8%
Step-by-step explanation:
0.36/4.50=0.08=8%
can someone help me pls
cos 60 degrees=1/2 and sin 60 degrees = square root 3/2 true or false
Answer:
cos 60 degrees=1/2 and sin 60 degrees = square root 3/2
The answer it's true.
Samantha has 146 ft of yarn. She wants to cut the yarn into equal pieces to give her 18 students. How much yarn will she give each student?
Answer:
8 ft of yarn
Step-by-step explanation:
146/18= 8.111
Round that number down to 8 to make all students get equal amounts of yarn
Answer:
8.11 ft
Step-by-step explanation:
146 ft divided into 18 prices
146 ÷ 18 = 8.11 ft for each student.
Find answer to picture problem
Answer:
Can you add the picture please???
Step-by-step explanation:
find the radii of a circle 6.16ha
Answer:
88m
Step-by-step explanation:
area = 6.16msq
πrsq=6.16
22/7*rsq=6.16/100
22/7*rsq=616
rsq=616*7/22
rsq=4321/22
rsq=196
r=√196
r=14m
diameter=14*2=28m
radius=14m
circumfrence=2πr
=2*22/7*14
=44*2
=88m
Is the cost of the apples proportinal to the weight of the apples?
Answer:
What is the cost/ weight of the apples?
Step-by-step explanation:
What is a combination of operations on letters and numbers?
A: Expression
B: Term
C: Factor
D: Variable
Answer:
A. Expression
Step-by-step explanation:
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
If a freight train travels at a speed of 20 miles per hour for 6 hours, how far will it travel? A 120 miles B 80 miles C 26 miles D 12 miles
Answer: The answer is A
Step-by-step explanation: Because 6*20= 120
I need the answer
I don't need you to make it a whole paragraph
Answer:
3
Step-by-step explanation:
Answer:
3 cups
Step-by-step explanation:
Combine like terms: 3 + 2 + 7t - 4t *
An angle turns through 75/360 of a circle. what is the measure of the angle?
Answer:
It is an acute angle....
The required measure of the angle through 75/360 of the circle is 75°.
What are the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
What is a circle?The circle is the locus of a point whose distance from a fixed point is constant.
Since 75/360 of the circle represents the rotational factor as it describes is 75 part of 360 and 75 in the expressions is the angle measure.
Thus, the required measure of the angle through 75/360 of the circle is 75°.
Learn more about Angles here:
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I need serious help please!
Equation of a line: given that m equals 5 and P(2,3), find the y-intercept (b), and write the equation of the line in slope intercept form
Equation of a line: given that m equals -2 and P(-4,5), find the y-intercept (b), and right equation of the line and slope intercept form
Giving P(3, -5) and Q(6,3). Find the slope of the line passing through the two points
Answer:
1. y-intercept = -7
equation: y = 5x - 7
2. y-intercept = -3
equation: y = -2x - 3
3. slope = [tex]\frac{8}{3}[/tex]
Step-by-step explanation:
slope-intercept form: y = mx + b
slope formula: [tex]\frac{y2 - y1}{x2 - x1}[/tex]
To write an equation in slope-intercept form, you need to know the slope(m) and the y-intercept(b).
1. Given: m = 5, P(2, 3). To find the y-intercept, input the given values of m and the point into the equation format and solve for b:
y = mx + b
3 = 5(2) + b
3 = 10 + b
-7 = b
The y-intercept is -7.
Now that we know the slope and the y-intercept, we can write the equation:
y = 5x - 7
2. Given: m = -2, P(-4, 5). To find the y-intercept, input the given values of m and the point into the equation and solve for b:
y = mx + b
5 = -2(-4) + b
5 = 8 + b
-3 = b
The y-intercept is -3.
Now that we know the slope and the y-intercept, we can write the equation:
y = -2x - 3
3. Given: P(3, -5), Q(6, 3). To find the slope, input the given points into the slope formula:
(3, -5) = (x1, y1)
(6, 3) = (x2, y2)
[tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{3-(-5)}{6-3}[/tex]
Simplify:
3 - (-5) = 3 + 5 = 8
6 - 3 = 3
[tex]\frac{8}{3}[/tex]
The slope of the line passing through points P and Q is [tex]\frac{8}{3}[/tex].
I hope this helps. :)
Use the tape diagram to write an equivalent ratio in simplest form. Write your ratio using a colon and no spaces.
Answer:
4:3
Step-by-step explanation:
There are 8 yellow spots and 6 blue spots
8:6
We can divide each side by 2 since they are both even
8/2: 6/2
4:3
Answer:
4:3
Step-by-step explanation:
Which shows the best estimate of the quotient of 4,346 +82?
between 50 and 60
between 60 and 70
between 500 and 600
between 600 and 700
Answer:
between 500 to 600 because I like
What function represents the amount of change given from a $10 bill, f(x), based on x, the number of bagels purchased? f(x) = 4x + O f(x) = -x + 10 Of(x) = x + 10 O f(x) = -x + 10
Answer:
the answer is c
Step-by-step explanation:hope this helps
Answer:
C or the third option, 3/4 x + 10
Step-by-step explanation:
100% correct please mark brainlist. HAVE A GREAT DAY
can someone help me pls
Answer:
27/36
Step-by-step explanation:
Count the white region (which is 36), and then count the shaded region (which is 27). And write the shaded region on the upper part (numerator), and the white part on the lower portion (denominator).
Solve the following equation for I. A = 2 πr + πrl. Explain each step.
BRAINLY IF CORRECT
Answer:
Step-by-step explanation:
A = 2π +πrl
A - 2π = πrI subtract by 2π
(A- 2π)/(πr) = I divide by πr to isolate I
Show work
Bonita and Vince are jogging to school 2.5 miles west of
Vinces' house. It takes
them 15 minutes to arrive. As soon as they got there Boneta needed to run east
5 miles to the discount store for personal supplies. This took her 5 minutes. She
then slowly walks back to school, which takes her another 10 minutes
What is the average velocity in miles/min for Bonita for the entire trip?
Show how you convert this to mis? Show your setup and answer.
What is her average speed in miles/min?
- Show how you convert the average speed to mis. Show your set up and answer.
Answer:
V_avg = 0.5556 miles/min
V_avg = 0.00926 miles/sec
Step-by-step explanation:
Bonita jogs 2.5 miles west of Vinces' house to school. It took her 15 minutes to arrive.
Speed 1; distance/time = V1 = 2.5/15 = 1/6 miles/min
Furthermore she ran 5 miles to the discount store for personal supplies. This took her 5 minutes.
Thus;
Speed 2; V2 = 5/5 = 1 mile/min
She then slowly walks back to school, which takes her another 10 minutes. Distance from the discount stor to school is 5 miles as stated in speed 2.
Thus;
Speed 3: V3 = 5/10 = ½ mile/min
Her average speed is;
V_avg = (V1 + V2 + V3)/3
V_avg = (1/6 + 1 + ½)/3
V_avg = 10/18 = 0.5556 miles/min
Converting to miles/seconds
60 seconds make 1 minutes, therefore 1 mile/min = 1/60 miles/seconds
Thus;
V_avg = 0.5556 miles/min = 0.5556 × 1/60 miles/sec = 0.00926 miles/sec
Maxwell buys a bag of dog food that contains 18 cups of food, Maxwell feeds his dog 1 cups each day. Maxwell says he will be able to feed his dog for 27 days.
correct?
Answer:
No. He will not have enough dog food for 27 days.
Step-by-step explanation:
If he only has 18 cups and he feeds one cup to his dog everyday. He will not have enough for 27 days. he will only have enough for 18.
What are the different ways to write multiplication in math
Answer:
Different ways to write multiplication include:
3 times 5
3x5
(3)(5)
3(5)
(3)5
etc
Step-by-step explanation:
I hope this helps!
Answer: 3 x 5, 3 · 5, 3 * 5 , (3) (5), 3 (5), and (3) 5. Hope this helps.
Step-by-step explanation:
please solve this i will give you brainliest
Answer:
1
Step-by-step explanation:
gvgbkhbgvbhjbjhbjhbhjnnj
Ise9urgyobrhrstbydfdsfwefwefsdfewfds
27/15 = 72/a ASAP plz help
Answer:
[tex] \frac{27}{15} = \frac{72}{a} \\ \\ 27 \times a = 15 \times 72 \\ \\ a = \frac{1080}{27 } \\ \\ a = 40[/tex]
Plz help I am timed
What is the rule for this pattern?
7, 10, 5, 8, 3, 6, 1
A.start with 7 and add 3 repeatedly
B.start with 7 and subtract 5 repeatedly
C.start with 7 and alternate adding 3 and then
subtracting 5
D.start with 7 and alternate adding 5 and then
subtracting 3
Answer:
C
Step-by-step explanation:
Answer:
plus 3 minus 3
Step-by-step explanation: