Using compound interest, it is found that:
a) $1,270.70 will be in the account after 6 years.
b) It will take 17.53 years for the $1000 to double.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.In this problem, the parameters are given as follows:
[tex]A(0) = 1000, r = 0.04, n = 12[/tex]
Item a:
Over 6 years, that is t = 6, thus:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(t) = 1000\left(1 + \frac{0.04}{12}\right)^{12 \times 6}[/tex]
[tex]A(t) = 1270.7[/tex]
$1,270.70 will be in the account after 6 years.
Item b:
This is t for which A(t) = 2P = 2000, hence:
[tex]2000 = 1000\left(1 + \frac{0.04}{12}\right)^{12t}[/tex]
[tex](1.0033)^{12t} = 2[/tex]
[tex]\log{(1.0033)^{12t}} = \log{2}[/tex]
[tex]12\log{(1.0033)} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{12\log{1.0033}}[/tex]
[tex]t = 17.53[/tex]
It will take 17.53 years for the $1000 to double.
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Mrs. Jones decided to buy some pencils for her class. She bought 3 packages of pencils, and each package contained 44 pencils. There are 22 students in her class and she divided up the pencils so that each student had the same amount of pencils. If there were no pencils left over, how many pencils did each student get?
A. 6
B. 66
C. 2
D. 25
Answer:
A
Step-by-step explanation:
First, multiple 3 by 44 to find the number of pencils total. 3x44=132.
Then, divide 22 into 132. 132/22=6.
Therefore, each student received 6 pencils.
Solve the polygon for x
[tex]\\ \rm\Rrightarrow 5(10x+15)+2(14x)+6x-3=1080[/tex]
[tex]\\ \rm\Rrightarrow 50x+75+28x+6x-3=1080[/tex]
[tex]\\ \rm\Rrightarrow 84x+72=1080[/tex]
[tex]\\ \rm\Rrightarrow 84x=1008[/tex]
[tex]\\ \rm\Rrightarrow x=1008/84[/tex]
[tex]\\ \rm\Rrightarrow x= 12[/tex]
f(x) = 3x – 7
g(x) = 2x – 4
1. Find (f + g)(x).
A store sold 6 3/8 boxes
of Milky Way bars and 7 2/5
boxes of Snickers one
week. In total, how many
boxes of candy bars did
they sell?
Answer:
We add the two fractions:
6 3/8 + 7 2/5 = 13 31/40 boxes of candy bars.
Answer:
Add the two fractions 6 3/8 + 7 2/5 = 13 31/40
Step-by-step explanation:
First multiply the whole numbers by the denominator then add it to the numerator, then find the most common factor (in the denominators) which is 40 (8x5 and 5x8) and multiply the numerator by the same number as the denominator, you will get 255/40 and 296/40 add them then simplify then you will get 13 31/40, thank you.
Judy bought 20 apples at the store, and the total weight was 2 kilograms. If the apples all had about the same weight, how much did each apple weigh?
it would be 0.1 kilograms per apple
if secx+cosecy = 2, and sinx+cosy=k evaluate 3k/4.
Need help ASAP!
The equations secx+cosecy = 2, and sinx+cosy=k are trigonometry equations
The result of [tex]\frac {3k}4[/tex] is [tex]\frac{3\sin(y)\cos(x)\sin(x) + 3\sin(y)\cos(x)\cos(y)}{2[\cos(x) + \sin(y)]}[/tex]
How to evaluate 3k/4The equations are given as:
secx+cosecy = 2, and sinx+cosy=k
Divide both equations
[tex]\frac{\sin(x) + \cos(y)}{\sec(x) + \csc(y)} = \frac k2[/tex]
Divide through by 2
[tex]\frac{\sin(x) + \cos(y)}{2[\sec(x) + \csc(y)]} = \frac k4[/tex]
Express sec and cosec as inverse ratios
[tex]\frac{\sin(x) + \cos(y)}{2[1/\cos(x) + 1/\sin(y)]} = \frac k4[/tex]
Take the LCM
[tex]\frac{\sin(y)\cos(x)[\sin(x) + \cos(y)]}{2[\cos(x) + \sin(y)]} = \frac k4[/tex]
Expand
[tex]\frac{\sin(y)\cos(x)\sin(x) + \sin(y)\cos(x)\cos(y)}{2[\cos(x) + \sin(y)]} = \frac k4[/tex]
Multiply through by 3
[tex]\frac{3\sin(y)\cos(x)\sin(x) + 3\sin(y)\cos(x)\cos(y)}{2[\cos(x) + \sin(y)]} = \frac {3k}4[/tex]
Rewrite as:
[tex]\frac {3k}4 =\frac{3\sin(y)\cos(x)\sin(x) + 3\sin(y)\cos(x)\cos(y)}{2[\cos(x) + \sin(y)]}[/tex]
Hence, the result of [tex]\frac {3k}4[/tex] is [tex]\frac{3\sin(y)\cos(x)\sin(x) + 3\sin(y)\cos(x)\cos(y)}{2[\cos(x) + \sin(y)]}[/tex]
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A grain silo is composed of a cylinder and a hemisphere. the diameter is 4.4 meters. the height of its cylindrical portion is 6.2 meters. a half-sphere is stacked on top of a cylinder. they both share a circular base. the cylinder has a height of 6.2 meters and the sphere has a diameter of 4.4 meters. what is the approximate total volume of the silo? use 3.14 for π and round the answer to the nearest tenth of a cubic meter. 37.1 m3 71.9 m3 116.5 m3 130.8 m3
The total volume of the silo is 116.6 m³.
What is a grain silo in this problem?It is a solid where a hemisphere is kept on top of a cylinder sharing common circular bases.
Diameter of the cylinder of the silo= 4.4m
So, the radius r of the cylinder will be = 2.2m
The radius r of hemisphere = 2.2m (same as cylinder due to common circular bases)
Height h of the cylinder = 6.2m
The total volume of the silo will be the combined volume of the cylinder and hemisphere.
The volume of cylinder = [tex]\pi r^{2} h[/tex]
The volume of hemisphere = [tex]\frac{2}{3} \pi r^{3}[/tex]
Total volume = [tex]\pi r^{2} h+ \frac{2}{3} \pi r^{3}[/tex]
total volume = [tex]\pi r^{2} (h+\frac{2}{3} r)[/tex]
Total volume = [tex]\pi *2.2^{2} (6.2+\frac{2}{3} *2.2)[/tex]
Total volume = 116.6 m³.
Therefore, the total volume of the silo is 116.6 m³.
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Answer:
116.6
Step-by-step explanation:
e2020
Gracie's water bottle says is holds 650 milliliters of water. How many liters does
Gracie's bottle hold?
Answer:
0.65 liters
Step-by-step explanation:
Step-by-step explanation:
milliliters change to liters
650 milliliters ÷1000 = 0.65 litersSo,Gracie's bottle hold is 0.65 liters
An ammonia and water mixture fills a five-gallon container. Eighty percent of the mixture is ammonia but some of the mixture will be drained and replaced with pure water. If a five-gallon mixture of fifty percent ammonia is desired, how many quarts of the mixture need to be drained before the water is added
Answer:
The volume of the 80% ammonia that is to be drained before water is added is 7.5 quartz
Step-by-step explanation:
The volume of the ammonia and water mixture = 5 gallons
The percentage of ammonia in the mixture = 80%
The volume of ammonia desired = 5 gallons
The percentage concentration of ammonia desired = 50%
The diluting solution = Pure water
The measure of 4 quarts = 1 gallon
Therefore, we have, by equivalence solutions;
80% × x gallon = 50% × 5 gallons
x gallon = 50% × 5 gallons/(80%) = 3.125 gallons
x = 3.125 gallons
The volume of the 80% ammonia that is to be drained = 5 gallons - 3.125 gallons = 1.875 gallons
4 quarts = 1 gallon
1 gallon = 4 quarts
∴ 1.875 gallons = 4 × 1.875 quartz = 7.5 quartz
The volume of the 80% ammonia that is to be drained before water is added = 7.5 quartz
Which equation represents the function on the graph?
Answer:
The equation represents the function on the graph will be Sin 2x
Given : Graph in diagram.
According to the given trigonometry function shape either of sine or cosine.
Here, it is intersecting at the origin it is likely a sine graph. A normal sine graph starts at Origin, crests out at 1 , and it crosses back down at the x-axis at (3.14, 0).
We knows this graph starts at origin and crosses back again at half that value. This graph is horizontally compressed on multiplying of a number maximum than 1.
Therefore, this graph is Sin 2x.
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Step-by-step explanation:
welcome
question in the image please help!!
the average boa constrictor is about 7 1/2 feet long. How many inches is that?
im fialing so please help me progress reports are friday
Answer:
6
Step-by-step explanation:
B reflected across the x-axis would be (-3, 1), so C is (-3, 1)
the distance between B and C is 6
Let me know if this helped
Answer:
4 points
Step-by-step explanation: One: there are two points in between B and c Two: it is skip counting in by two's so you should do the same when calculating the distance.
Hope this helped!
help me please i appreciate everyone who is helping
Answer:
m=21
Step-by-step explanation:
Each side has the same length.
63/3=21
Sean and Glen share a 16 ounce box of cereal. By the end of the week, Sean has eaten 5/8 of the box,glen has eaten 1/4 of the box of cereal. How many ounces are left in the box?
Answer:
2 ounces are left
Step-by-step explanation:
Sean =
[tex] \frac{5}{8} \times 16[/tex]
= 10 ounces
Gien =
[tex] \frac{1}{4} \times 16[/tex]
= 4 ounces
Sean + gien = 10 + 4 = 14 ounces
so therefore the remaining portion
= 16 - 14 = 2 ounces of cereal is left
if this helped pls give brainliest
If you start with $160 and save $125 per month, how many months will it take for you to save a total of
$660?
This is a solving equation word problem
Answer:
4 weeks
Step-by-step explanation:
660-160=500
500/125= 4 weeks
will give brainliest to right answer
Step-by-step explanation:
again, in a geometric sequence all terms are created by multiplying the previous term by a constant factor.
7640 × f = 764
f = 764/7640 = 1/10
a1 = 7640
a2 = a1 × 1/10 = 7640 × 1/10 = 764
a3 = a2 × 1/10 = a1 × 1/10 × 1/10 = 7640 × 1/100 = 76.4
an = 7640 × (1/10)^(n-1)
a6 = 7640 × (1/10)⁵ = 7640 × 1/100000 = 0.0764
hey guys i need help
Answer:
9 yards
Step-by-step explanation:
from the maple-> end, it is 28 2/6 yards. that means we add the segments that are already there to find how much of 28 2/6 is there between the maple and oak.
11 3/6 + 7 5/6 = 19 1/3
28 2/6 - 19 1/3 = 9
Everyday Fitness charges a $28 dollar membership fee plus $2 per visit. Fitness King charges $16 membership fee plus $4 per visit. For how many visits will the total cost for both companies be the same? What will the amount be?
Answer:
The total cost of the companies will be the same after 6 visits. The cost will be $40 after 6 visits
Step-by-step explanation:
HOW DO I SOLVE THIS PLEASE HELP
Answer:
18 unitsStep-by-step explanation:
Use the property of 45°x45°x90° and 30°x60°x90° right triangles.
Ratio of sides:
45°x45°x90° triangle 1 : 1 : √230°x60°x90° triangle 1 : √3 : 2Find the longer leg of the second triangle:
6√6*√3 = 6√18 = 6*3√2 = 18√2Find the value of x, of the first triangle:
x = 18√2/√2 = 189 kg of washing powder cost $10.80. What is the cost of 1 kg of washing powder?
Answer:
cost of 1 kg of washing powder is $1.2
Step-by-step explanation:
9 kg = $10.80
cost for 1 kg =
10.80 ÷ 9$1.2Answer:
1.2
Step-by-step explanation:
How I would calculate it would be 10.80 divided by 9 or start timesing 1 with a decimal like 1.1 or 1.2.
but anyway 10.80 divided by 9=1.2 and if you just want to make sure then what is 1.2 x 9 it = 10.80
Here is my calculations for what is 1.20 x 9
1 . 20
9
_________
10 . 8 0
Since there is no didget beside the 2 you would add a zero
since 9 x 2=18 you add a 1 for 1 x 9 =9 + 1=10 and there's your answer.
Answer=1.2
Hope this helps have a great day:)
Help me, and fast please!
Answer:
D.
Step-by-step explanation:
To get the rectangle, multiply 10*3 = 30
Then to find both triangles, multiply 10*5=50
30+50=80
Let me know if this helped <3
Answer:
130 ft.
Step-by-step explanation:
the rectangle area is 30, cause l×h = area
triangle area is b×h and theres two so 5 x10 = 50 then multiply by 2 again so 100
then add both sums: 100+30 equalsssss 130.
Expression that is equivalent to (6)(6)(6)
Answer:
36×6
Step-by-step explanation:
(6)(6)(6)
6×6×6
36×6
216
The answer is: " 6³ " .
__________
Step-by-step explanation:
Note: " (6)(6)(6) " ; is the value of the
[number "6" ; multiplied by that same number, "6" —two additional times;
→ so the same number, "6" ; being multiplied: "3 (three) times'
= 6 * 6 * 6 = 6³ ; that is: the number "6", raised to the third power (as an exponent);
→ since: there are 3 (three) of the same numbers being multiplied;
⇒ hence the exponent, "3" .
__________
The answer is: " 6³ " .
__________
Hope this helps!
HELP FOR BRAINLEST!!! PLEASE
Answer:
3/14
Step-by-step explanation:
Put the number of students that want to be a therapist AND have a fear of height (this would be 3) over the TOTAL amount of students in the sample, in this case it's 14.
so it's 3/14 and it doesn't simplify
you're welcome
Answer:
21%
Step-by-step explanation:
First we need to find the total amount of people that did the personality test. We can do that by adding all the numbers in the table
[tex]4+5+2+3=14\\[/tex]
now, to find the percentage of students that want to be a therapist and a fear of heights, we simply divide the number of students who fit that demographic by the total number of students
[tex]3/14= 0.214[/tex]
therefore, there is a 21% chance of picking a student in that demographic at random
How is ordering factions on a number line similar and different from ordering whole numbers on a number line
Answer:
Fractions and whole numbers ordered on the number line are similar because it tells parts throughout the line, like skip counting using adding or subtraction for example.
What's different from them is because the fractions tell the parts more detailed between the whole numbers, such as 2 3/4 as a fraction on the number line. And 3 as a whole number on the number line.
Step-by-step explanation:
Find the value of f (x)
F(x) = 2 x f(4) = .........
A. 8
B. -6
C. 10
Answer:
F(4)=8
Step-by-step explanation:
F(x)=2(x)
F(4)
Replace x with 4
F(4)=2(4)
Multiply
F(4)=8
Dr. Matthews is a professor of physics at the local university. He keeps a record of the number of students attending his class every day. Which of the following is a statistical question that Dr. Matthews can be asked? A.
How many male students attended your class today?
B.
How many students attended your class today?
C.
How many students have enrolled for your class this semester?
D.
How many students attend your class each day?
Answer:
d.How many students attend your class each day?
Dr Matthews can be asked How many students attend your class each day?
What are statistics?The practise or science of organising and interpreting numerical data in big quantities, particularly for the objective of concluding proportions in a whole from those in an expected sample.
Dr Matthews can be asked How many students attend your class each day?
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plez help with this im confuzzled 10 points
Answer:
y = 7
x=3
z=3
Step-by-step explanation:
we have, 5y +5=40
5y = 40 - 5
5y=35
y= 35/5
x=7
and, x + 10 = 13
x=13-10
x=3
10z-3 = 27
10z = 27 +3
10z = 30
z= 30/10
z = 3
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hi pls help answer this!
Answer:
363-138=-5x
Step-by-step explanation:
Let c = cost
We know that the total cost is $363:
363-??????
We also know that he spent $138 on parts:
363-138?????
And we are solving for the cost of labor per hour:
363-138=5x
We can use this equation to find the total cost of labor per hour.
Hence, your equation will be 363-138=5x
What is the product? (9 t minus 4)(negative 9 t minus 4) negative 81 t squared minus 16 negative 81 t squared 16 negative 81 t squared minus 72 t 16 negative 81 t squared 72 t 16
The product of the provided binomial numbers (9 t minus 4)(negative 9 t minus 4) is equal to the option B which is,
[tex]-81t^2+16[/tex]
What is the product?Product is the resultant number which is obtained by multiplying a number with another. Let a number a is multiplied by number b. Then the Product of these two number will be,
[tex]p=a\times b[/tex]
Here, (a, b) are the real numbers.
The binomial given in the problem are,
[tex](9t-4)\\(-9t-4)[/tex]
Let the product of the above function is p. Thus,
[tex]p=(9t-4)\times(-9t-4)[/tex]
To find the product of these two binomials, multiply the first term of first binomial with both the terms of the second binomial.
Similarly, multiply the second term of first binomial with both the terms of second binomial. Thus,
[tex]p=9t(-9t-4)-4(-9t-4)\\p=-81t^2-36t+36t+16\\p=-81t^2+16[/tex]
Thus, the product of the provided binomial numbers (9 t minus 4)(negative 9 t minus 4) is equal to the option B which is,
[tex]-81t^2+16[/tex]
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Answer: B
Step-by-step explanation: