Answer:
The annual interest rate was 4.5% in Angela's college fund.
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Investment when Angela was 10= US$ 5,000
Duration of the investment = 8 years
Balance of the account when Angela turned 18 = US$ 6,800
2. Let's find the annual interest rate of this investment after 8 years or 20 quarters, using the following formula:
FV = PV * (1 + r) ⁿ
PV = Investment when Angela turned 10 = US$ 5,000
FV = Balance of the account when Angela turned 18 = US$ 6,800
number of periods (n) = 8
Replacing with the real values, we have:
6,800 = 5,000 * (1 + r) ⁸
6,800/5,000 = (1 + r) ⁸ (Dividing by 5,000 at both sides)
34/25 = 1⁸ + r⁸
34/25 - 1 = r⁸ (1⁸ = 1)
34/25 - 25/25 =r⁸ (1 = 25/25)
9/25 = r⁸
0.36 = r⁸ (9/25 = 0.36)
⁸√0.36 = ⁸√r⁸
0.045 = r
r = 4.5%
The annual interest rate was 4.5% in Angela's college fund.
Answer:
The answer is 4.5
Step-by-step explanation:.
To determine the interest rate, substitute the numbers for the values in the I equals Prt formula. I equals one thousand eight hundred, P equals five thousand and t equals eight because the money was in the bank for eight years.
Multiply five thousand by eight.
Divide both sides by forty thousand and evaluate.
Finally, convert the decimal zero point zero four five to four point five percent.
sin x= 1.5
value of x
Answer:
x = π - sin^(-1)(3/2) + 2 π n_1 for n_1 element Z
or x = 2 π n_2 + sin^(-1)(3/2) for n_2 element Z
Step-by-step explanation:
Solve for x:
sin(x) = 1.5
1.5 = 3/2:
sin(x) = 3/2
Take the inverse sine of both sides:
Answer: x = π - sin^(-1)(3/2) + 2 π n_1 for n_1 element Z
or x = 2 π n_2 + sin^(-1)(3/2) for n_2 element Z
EAM
on of the system of equations,
2x + 2y = 16
10x - 2y = 24
Answer:
x=10/3, y=14/3. (10/3, 14/3).
Step-by-step explanation:
2x+2y=16
10x-2y=24
---------------
x+y=8
10x-2y=24
-----------------
x=8-y
10(8-y)-2y=24
80-10y-2y=24
80-12y=24
12y=80-24
12y=56
y=56/12=14/3
x=8-14/3=24/3-14/3=10/3
x=10/3, y=14/3.
-3(y+3)=2y+3
help plzs!!!!!!......
Answer:
For the given expression -3( y + 3 ) = 2 y + 3 the value of y = -2.4.
Step-by-step explanation:
Here, the given expression to be simplified : -3( y + 3 ) = 2 y + 3
Now, by DISTRIBUTIVE PROPERTY:
A (B +C) = AB + AC
Simplifying the given expression:
-3( y + 3 ) = 2 y + 3 ⇒ -3 ( y) - 3 ( 3) = 2 y + 3
or, -3y - 9 = 2y + 3
⇒ 3 y + 2 y = -3 - 9
or, 5 y = -12 ⇒ y = -12/5 = -2.4
⇒ y = - 2.4
Hence,for the given expression -3( y + 3 ) = 2 y + 3 the simplified value of y = -2.4
A line passes through the point (6,1) and has a slope of -3.
Write an equation in point-slope form for this line
[tex]\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{1})~\hspace{10em} \stackrel{slope}{m}\implies -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{-3}(x-\stackrel{x_1}{6})[/tex]
A sequence has a common ratio of Three-halves and f(5) = 81. Which explicit formula represents the sequence? f(x) = 24(Three-halves) Superscript x minus 1 f(x) = 16(Three-halves) Superscript x minus 1 f(x) = 24(Three-halves) Superscript x f(x) = 16(Three-halves) Superscript x
Answer:
[tex]f(x)=16\, (\frac{3}{2} )^{x-1}[/tex]
Step-by-step explanation:
Since we are given the common ratio (3/2), all we need to find to define the geometric sequence, is its multiplicative factor ([tex]a[/tex]) that corresponds to the first term of the sequence - remember that all consecutive terms will be generated by multiplying this first value repeatedly by the common ratio (3/2) as shown below:
[tex]f(1)=a\\f(2)=a\,*\,(\frac{3}{2} )\\f(3)=a\,*\,(\frac{3}{2} )^2\\f(4)=a\,*\,(\frac{3}{2} )^3\\f(5)=a\,*\,(\frac{3}{2} )^4[/tex]
Since we are given the information that [tex]f(5)=81[/tex] we can use this to find the value of the first term:
[tex]f(5)=\,a\,*\,(\frac{3}{2} )^4\\81=\,a\,*(\frac{81}{16} )\\a\,*\,81=\,81\.*\,16\\a\,=\,16[/tex]
Notice as well that the first term doesn't contain the common ratio, the second term contains the common ration (3/2) to the power one, the third one contains the common ratio to the power two, the fourth one contains it to the power three, and so forth. So the exponent at which the common ratio appears is always one unit less than the order (x) of the term in question. This concept helps us finalize the expression for the sequence's formula:
[tex]f(x)=16\,*\,(\frac{3}{2} )^{x-1}[/tex]
Answer:
B
The other answer was too long.
can you please help me i don't understand this
Answer:
10) Supplementary; 11) Supplementary; 12) Complementary
Step-by-step explanation:
Sum of supplementary angles equals 180° while sum of complementary angles equals 90°.
For question 10
x + 70° = 180° (sum of straight lines)
x = 180° - 70° = 110°
Hence, 70° and 110° are supplementary angles.
For question 11,
x + 85° = 180° (sum of straight lines)
x = 180° - 85° = 95°
Hence, 85° and 95° are supplementary angles.
For question 12,
x + 32° = 90° (sum of right angles)
x = 90° - 32° = 58°
Hence, 32° and 58° are complementary angles.
what is the percent decrease from 5000 to 4000?
Answer:
20%
Step-by-step explanation:
5000 - 4000 = 1000
[tex]\frac{1000}{5000}[/tex] × 100
[tex]\frac{1}{5}[/tex] × 100
0.2 × 100 = 20%
Check:
5000 - 20% of 5000
5000 - 2/10 × 5000
5000 - 1000
= 4000
Answer:
20% decrement
Steps:
➥5000-x% of 5000=400
➥5000-x% × 5000=4000
➥5000-4000=x% × 5000
➥1000=x% × 5000
➥x%=1000/5000
➥x%=0.2
➥x%=20/100
➥x%=20%
IM GIVING THE REST OF MY POINTS FOR THIS 45 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!
ANSWER QUICK THANK YOU
THERE ARE 5 QUESTIONS!!!!!!!!!!!
Answer:
1b 2d 3c 4d 5a
Step-by-step explanation:
If a person walks 2.4 miles in 1.5 hours, how far can he walk in 3 hours?
2.4 miles
6.2 miles
4.8 miles
Answer:
The answer is 4.8
Step-by-step explanation:
The answer is 4.8 because 1.5h is half of 3 hours so if he walks 3.0m (which is double the first amount he walked) the answer will double.
so 2.4+2.4 = 4.8
or 2.4x2 = 4.8
And there u go!
Rebecca started with 30 pieces of candy and gave away x
pieces. Ana started with 45 pieces of candy and gave away
twice as many pieces as Rebecca did. How many pieces of
candy did Rebecca give away if they had the same number of
pieces of candy left?
Answer:
The correct answer would be 15.
Step-by-step explanation:
30-15=15
45-2(15)=15
What additional information is required for the 2 triangles to be congruent by SAS?
Which statement shows the associative property of addition?
(d + 4) + 17 = 17 + (d + 4)
13 + 5a = 5a + 13
7⋅(4⋅x)=(7⋅4)⋅x
(18 + 6) + y = 18 + (6 + y)
Answer:
(18 + 6) + y = 18 + (6 + y)
Step-by-step explanation:
Answer:
the answer is (18 + 6) + y = 18 + (6 + y )
Step-by-step explanation:
i did the quiz and got it right!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
hope this helps!!!!!!!!!!!!!!!!!!!11
What is a quarter of 200
Answer:
50
Step-by-step explanation:
200/2=100
100/2=50
A quarter of something is just another word for a fourth of something (1/4th).
We can solve this using two different ways.
Solution #1:
1/4 = 0.25
200 * 0.25 = 50 (quarter of 200)
Solution #2:
200 / 4 = 50 (quarter of 200)
______
Best Regards,
Wolfyy :)
A book sold 34,100 copies in the first month the release suppose this represents 7.9% of the number of copies sold to date how many copies have you sold to date? Round to the nearest whole number
Answer:
431,646
Step-by-step explanation:
[tex]\frac{7.9}{100} = \frac{34,100}{x} \\[/tex]
Simply multiply 100x34,100 (3,410,000) and divide by 7.9 to get your answer= 431,645.57. Round to the nearest whole number and you get your finl outcome which is 431,646.
Answer:
Step-by-step explanation: Let the no. of copies sold to date be y
A.T.Q
7.9/100 * y = 34100
y = 34100*100/7.9
= 3410000/7.9
= 431645.56
Rounding it off to nearest no. it will be
Total 431646 copies have been sold to date.
Hope this helps u :)
Which describes the cross section of the square prism that passes through the vertices A, B, C, and D shown below?
a rectangle
a square
a kite
a trapezoid
Answer:
Trapezoid
Step-by-step explanation:
Is -2/-5 equivalent to 2/5?
Answer:
yes
Step-by-step explanation:
Note that a [tex]\frac{-}{-}[/tex] results in a +, thus
[tex]\frac{-2}{-5}[/tex] = [tex]\frac{2}{5}[/tex]
Ắner:-2:-1=2
-5:-1=5
-2/-5=2/5
Step-by-step explanation:
(3.6 x 10^-5) + (3.5 x 10^-5)
Write your answer in scientific notation.
Answer:
(3.6 × 10^-5) + (3.5 × 10^-5) = 7.1 × 10^-5
A gardener at a nursery is filling pots with soil to prepare to
transplant seedlings into these larger pots. Each new pot needs about 27 cubic inches
of soil. The amount of soil s (in cubic inches) it takes to fill p pots is given by the
function s = 27p
a.
The gardener is filling the pots from a bag of soil that contains 3456 cubic
inches of soil. How many pots can be filled from the bag?
b.
Suppose the gardener needs to fill at most 109 pots. How much soil (in cubic
inches) will the gardener need?
Answer:
a. 127 pots
b. 2,943 cubic inches
Step-by-step explanation:
To find the amount of pots of soil can be filled, you can use the equation given. s = 3456 in part a
a.
s = 27p
3456 = 27p
divide 3456 by 27 to isolate p
p = 127 pots
Instead of substituting for s like in part a, you can now substitute for p, since you know that you need to fill 109 pots.
b.
s = 27 * 109
s = 2943 cubic inches
The gardener can fill 128 pots with the 3456 cubic inches of soil available. If the gardener needs to fill at most 109 pots, they will require 2943 cubic inches of soil.
To solve both parts of the question, we will use the function s = 27p, where s represents the amount of soil (in cubic inches) and p represents the number of pots.
Part a: Calculating the Number of Pots
The gardener has a bag containing 3456 cubic inches of soil. To find out how many pots can be filled from the bag, we need to divide the total amount of soil by the amount needed per pot:
p = 3456 cubic inches / 27 cubic inches per pot = 128 pots
Part b: Soil Needed for a Maximum Number of Pots
If the gardener needs to fill at most 109 pots, the total amount of soil required can be calculated using the provided function:
s = 27 cubic inches per pot * 109 pots = 2943 cubic inches of soil
57 first-year teachers and 19 experienced teachers attended a school staff meeting meeting. What percentage of the teachers in the meeting were first-year teachers?
Write your answer using a percent sign (%).
Answer:
75%
Step-by-step explanation:
57 / (57+19) = 0.75
Final answer:
About 75% of the teachers in the meeting were first-year teachers, as calculated by dividing the number of first-year teachers by the total number of teachers and then multiplying by 100.
Explanation:
To determine what percentage of the teachers in the meeting were first-year teachers, we use the formula 'part over total, times one hundred, equals percent'. In this scenario, the 'part' is the number of first-year teachers which is 57, and the 'total' is the sum of first-year and experienced teachers, which is 57 + 19 = 76. The calculation then becomes 57/76 times 100, to find that percentage.
Carrying out the calculation:
(57 / 76) times 100 = 0.75 times 100 = 75%
Therefore, approximately 75% of the teachers at the meeting were first-year teachers.
TO TRANSMIT INFORMATION ON THE INTERNET, LARGE FILES ARE BROKEN INTO PACKETS OF SMALLER SIZES. EACH PACKET HAS 1,500 BYTES OF INFORMATION. AN EQUATION RELATING PACKETS TO BYES OF INFORMATION IS GIVEN BY B=1,500P REPRESENTS THE NUMBER OF PACKETS AND B REPRESENT THE NUMBER OF BYTES OF INFORMATION.
A. HOW MANY PACKETS WOULD BE NEEDED TO TRANSMIT 30,000BYTES OF INFORMATION
B. HOW MUCH INFORMATION COULD BE TRANSMITTED IN 30,000 PACKETS
Answer:
A. It would be needed 20 packets to transmit 30,000 bytes of information and B. 45'000,000 (45 million) of bytes could be transmitted in 30,000 packets.
Step-by-step explanation:
1. Let's review the information provided to us for solving the question:
Size of each packet of information = 1,500 bytes
Number of packets = P
Number of bytes of information = B
2. Let's answer the questions:
A. How many packets would be needed to transmit 30,000 bytes of information?
P = 30,000 ÷ 1,500
P = 20
It would be needed 20 packets to transmit 30,000 bytes of information
B. How much information could be transmitted in 30,000 packets?
B = 30,000 * 1,500
B = 45'000,000
45'000,000 (45 million) of bytes could be transmitted in 30,000 packets.
Note: Same answer provided to question 14037480, answered by me.
Which only lists multiples of 16?
O
1, 2, 4, 8, 16
16, 24, 32, 40
16, 32, 48, 64
1, 2, 4, 8, 12, 16
16, 32, 48, 64
16 = 16x1
32 = 16x2
48 = 16x3
64 = 16x4
Answer:
C
Step-by-step explanation:
A hockey puck slides across an ice pond at a constant speed of 18 meters per second. Complete the table to determine the distance the hockey puck slides at different times.
Answer:
1 18
2 36
3 54
4 72
Step-by-step explanation:
18 m/s every second means you multiply the time by rate (to get the distance traveled in 2 seconds, multiply 18m/s by 2 to get 36)
8 * 4 = (A * 7) – (A * 3)
Answer:
A=32
Step-by-step explanation:
Your company takes orders over the phone. The company’s average time is 4.6 minutes.The graph below shows 4 calls and the difference between the call time and the company’s average call time.
Answer:
0.4
Step-by-step explanation:
The mean difference between the call will be 0.4. Then the correct option is C.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.
Your company takes orders over the phone. The company’s average time is 4.6 minutes. The graph below shows 4 calls and the difference between the call time and the company’s average call time.
Then the mean difference between the call will be
Mean = (Sum of the observation) / (Number of the observation)
Mean = (-2.32 - 1.55 + 4.79 + 0.68) / 4
Mean = 1.6 / 4
Mean = 0.4
The mean difference between the call will be 0.4. Then the correct option is C.
Your question was incomplete, but the complete question is attached below.
More about the mean link is given below.
https://brainly.com/question/521501
#SPJ6
Solve.
5. During the summer, Jayden
volunteers at the library for 20 hours
each week for 7 weeks. How many
hours does Jayden volunteer in all?
How many hours did Jayden volunteer
Answer:
he volunteered 140 hours
Step-by-step explanation:
20*7=140
Molly has walked 80% of the way to school.She has walked 16 blocks.How many blocks is her whole trip to school?
Answer:
20 blocks
Step-by-step explanation:
80% = 0.8
16 / 0.8 = 20
PLEASE HELPPPP ! 16^x=64^x+4
Answer:
x = -12
Step-by-step explanation:
Set logs up on both sides-
log 16^x = log 64^x+4
The variable goes behind because of the exponent log property (exponents are permitted to go behind the log to multiply)-
x * log 16 = x + 4 * log 64
Divide both logs out-
log 64/log 16 = 1.5
Simplify-
x = x+4(1.5)
1.5x + 6 = x
Remove 1.5-
1 - 1.5 = -.5x
Simplify-
-.5x = 6
Divide both sides-
6/-.5x = -12
Hence, the answer would be -12
Paton knows she will make a selection from 36 total possible outcomes. Which statement might describe what Paton is doing? Check all that apply.
Answer: All but statement 1
Step-by-step explanation:
In order to get 36 as an outcome, the numbers need to multiply together in order to get 36. In other words, a*b*c*d*....= desired outcome number. In statement 1, 3*9=27, and therefore not 36 outcomes. The rest do multiply to 36.
Answer:
2,3,4,5
Step-by-step explanation:
Stay safe! Hope this helps!
A piece of cloth costs 200$.if the piece was 5m longer, and the cost of each metre of clth was 2$ less, the cost of the piece would have remained unchanged. How long is the piece and what is its original number of persons.
Answer:
20 m long,
each piece of cloth for $10
Step-by-step explanation:
Let x m be the length of the piece of cloth.
Original cloth:
Length = x m
Cost = $200
Cost per meter [tex]\dfrac{\$200}{x}[/tex]
Changed cloth:
Length = x + 5 m (5 m longer)
Cost = $200
Cost per meter [tex]\dfrac{\$200}{x}-\$2[/tex] (each metre of cloth was $2 less)
Hence,
[tex]\left(\dfrac{200}{x}-2\right)\cdot (x+5)=200[/tex]
Multiply the equation by x:
[tex](200-2x)(x+5)=200x\\ \\200x+1,000-2x^2-10x=200x\\ \\-2x^2-10x+1,000=0\\ \\x^2+5x-500=0\\ \\D=5^2-4\cdot(-500)=25+2,000=2,025\\ \\x_{1,2}=\dfrac{-5\pm\sqrt{2,025}}{2}=\dfrac{-5\pm 45}{2}=-25,\ 20[/tex]
The length cannot be negative, so x = 20 m, each metre for $10.
Answer:
The piece is 20 m long and costs $10 per meter
Step-by-step explanation:
The total cost of the cloth in $ can be expressed as
C = xu
Where x is the length of the cloth in m, and u is the unit cost in $/m
The problem states that if the length was 5 meters more and the unit cost was $2 less, the cost would not change, that is
C = (x+5)(u-2)
Operating:
C = xu-2x+5u-10
Since C = xu, then
-2x+5u=10 [1]
We also know that
xu=200 [2]
Isolating u in [1] we get
[tex]u=\frac{10+2x}{5}[/tex]
Replacing into [2]
[tex]x\frac{10+2x}{5}=200[/tex]
Simplifying
[tex]10x+2x^2=1000 \\=> x^2+5x-500=0[/tex]
Factoring
(x-20)(x+25)=0
Which gives x=20, x=-25. We can only use the positive value of x, so
x=20 m and therefore
u=200/20=10$
So the piece is 20 m long and costs $10 per meter
What is 0.3 divided 0.24 doing long division
Answer:
1.25
Step-by-step explanation:
Change 0.3 and 0.24 into whole numbers. So this would be 30 and 24. You do 30/24 and simplify it to 5/4 (because you divide 6; both numerator and denominator) which gives you 1.25.
Final answer:
Detailed explanation on dividing 0.3 by 0.24 using long division.
Explanation:
Dividing 0.3 by 0.24 using long division:
First, insert a decimal point after 0.3 to make it 0.30.
Then, perform long division: 0.30 ÷ 0.24 = 1 remainder 0.06.
Bring down another zero to continue dividing: 0.06 ÷ 0.24 = 0.25.