To calculate this sort of problem:
⇒ involves calculating the total profits over each year
⇒ with a constant increase periodically
⇒ need to use the Compound Interest Equation
[tex]A = P(1+\frac{r}{n})^{nt}[/tex]
A: total amount after t yearsP: initial amount in accountr: rate per periodn: number of times the profit increases per yeart: number of yearsLet's fill in some variables:
P: $247500r: 16% increase (in equation form, we plugin 0.16)n: 1 time per yeart: 10 yearsWhat do we want to know:
A: total amount after 10 yearsLet's solve:
[tex]A= 247500*(1+\frac{0.16}{1} )^{1*10}=\\A=247500*(1+0.16)^{10}\\A=247500*(1.16)^{10} \\A= 1,091,830.18[/tex]
To the nearest whole number
Answer: $1,091,830Hope that helps!
Which explicit function defines this arithmetic sequence?
-351, -343, -335, -327, -319
A.
f(n) = 8n − 351
B.
f(n) = -8n − 351
C.
f(n) = 8n − 359
D.
f(n) = -8n + 359
Answer:
C. f(n) = 8n − 359
Step-by-step explanation:
The given arithmetic sequence has first term -351, and common difference (-343 -(-351)) = 8. The common difference will be the multiplier of n in the explicit function.
__
You can identify the appropriate explicit function by finding the one that correctly describes the sequence. Evaluating each for n=1 is sufficient. (You will note that choices B and D have the wrong sign on the multiplier of n.)
A f(1) = 8 -351 = -343
B f(1) = -8 -351 = -359
C f(1) = 8 -359 = -351 . . . . correctly gives the first term
D f(1) = -8 +359 = 351
The sequence is defined by the explicit function ...
f(n) = 8n -359
Answer:A:f(n)=8n-359
Step-by-step explanation:
Two spinners are used in a game. Each spinner has four equal sections: red, green, white, and blue.
Create an organized list showing all the possible outcomes after both spinners are spun. Use R to represent red, G to represent green, W to represent white, and B to represent blue. Explain how to find the total number of outcomes from the list.
The total number of outcomes is 16 if the two spinners are used in a game. Each spinner has four equal sections: red, green, white, and blue.
What are permutation and combination?A permutation can be defined as the number of ways a set can be arranged, order matters, but in combination, the order does not matter.
Total number of outcomes on the first spinners = 4 (red, green, white, blue)
Total number of outcomes on the second spinners = 4 (red, green, white, blue)
Total number of outcomes = 4×4 = 16
Total outcomes:
RR RG RW RB
GR GG GW GB
WR WG WW WB
BR BG BW BB
Thus, the total number of outcomes is 16 if the two spinners are used in a game. Each spinner has four equal sections: red, green, white, and blue.
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A prism is completely filled with 270 cubes that have edge length of 1/3in.
what is the volume of the prism?
If the volume of the cube is 1/27 cubic inches. Then the volume of the prism will be 10 cubic inches.
What is a rectangular prism?A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.
A prism is completely filled with 270 cubes that have an edge length of 1/3in.
Then the volume of the prism will be given as
Volume of prism = 270 (volume of the cube)
Then the volume of the cube will be
Volume of cube = (edge)³
Volume of cube = (1/3)³
Volume of cube = 1/27 cubic inches
Then the volume of the prism will be
Volume of prism = 270 × (1/27)
Volume of prism = 10 cubic inches
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find the height of a right circular cone if the slant height is 4 units and the radius is 2 units
The slant height of the right circular cone will be [tex]l=2\sqrt5}[/tex]
What is slant height of cone?The formula for the slant height of the cone is given as:
[tex]l^2=r^2+h^2[/tex]
Here we have
r=2 units
h=4 units
By putting the values we will get
[tex]l=\sqrt{4^2+2^2[/tex]
[tex]l=\sqrt{16+4[/tex]
[tex]l=\sqrt{20}[/tex]
[tex]l=2\sqrt{5}[/tex]
Hence the slant height of the right circular cone will be [tex]l=2\sqrt5}[/tex]
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what is the volume of a cone with a diameter of 30 feet and height of 60 feet? use 3.14 for pi. enter your answer in the box
Answer:
volume = 14,137
Step-by-step explanation:
radius is the diameter divided by 2
30÷2=15
radius = 15 then square
15^2 = 225
formula of volume of a cone is 1/3*pi*raduis^2*the height
1/3(3.14)(225)(60)= 14,137
The volume of a cone with a diameter of 30 feet and a height of 60 feet is 14130.
What is the volume of a cone?The volume of the cone is given by;
[tex]\rm Volume \ of \ cone=\dfrac{1}{3}\pi r^2h\\\\Where;\ r = radius \ and \ h = height[/tex]
The volume of a cone with a diameter of 30 feet and a height of 60 feet.
The radius of the cone is;
[tex]\rm Radius =\dfrac{Diameter}{2}\\\\Radius=\dfrac{30}{2}\\\\Radius=15[/tex]
Substitute all the values in the formula
[tex]\rm Volume \ of \ cone=\dfrac{1}{3}\pi r^2h\\\\ Volume \ of \ cone=\dfrac{1}{3}\times 3.14 \times 15^2 \times 60\\\\Volume \ of \ cone=14130[/tex]
Hence, the volume of a cone with a diameter of 30 feet and height of 60 feet is 14130.
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The table below represents a breakdown of food costs for Eddie, a traveling
salesman. How much did he spend in total for food on Tuesday?
Mon.
Tue.
Wed.
Thurs.
Fri.
Breakfast $7.88
$12.02
$9.64
$6.98
$13.30
Lunch
$13.41
$11.79
$14.55
$16.09
$10.76
Dinner
$18.80
$22.13
$20.79
$24.82
$16.74
OA. $40.09
OB. $42.56
OC. $41.23
OD. $45.94
SURMIT
The total amount of money that was spent on lunch on Tuesday is $45.94.
What is the total amount spent on food?
The total amount that was spent on food on Tuesday can be determined by adding the amount spent on breakfast, lunch and dinner. Addition is the mathematical operation that is used to determine the sum of two or more numbers.
Total amount spent = 22.13 + 12.02 + 11.79 = $45.94
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Find the missing value (x)
Answer:
y=14; x=72
Step-by-step explanation:
y=(21×2)/3; x=(48×21)/14
solve the system using substitution. show all work
a magnifying glass makes objects appear 2.54 times largers than their actual size. How large does a 6-millimeter seed appear in the magnifying glass
Answer:
15.24 millimeters
Step-by-step explanation:
6 * 2.54 = 15.24 mm.
Answer: should be 15.24
Step-by-step explanation: quick maths
see attached question please please help!!
Based on the size of the pool that Mr. DelGrande wants to build, the ratio of the Olympic pool to the smaller pool is 2.5:1 and the area of an Olympic pool is 1,250 m².
What is the ratio of the length of an Olympic pool to Mr. DelGrande's pool?The ratio of the pools is:
Olympic pool length : Mr. DelGrande pool
50 : 20
Simplest terms give:
50 / 20 : 20 / 20
2.5 : 1
What is the area of a regulation Olympic Pool?Given the area of Mr. DelGrande's pool, the area of an Olympic pool is:
= Ratio ² x Area of Mr. DelGrande pool
= 2.5² x 200
= 1,250 m²
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Round 7.09 to the nearest tenth
Answer:
7.1
Step-by-step explanation:
To round 7.09 to the nearest tenth, you must use the hundredths' place value of 7.09, which is 9 and equal or more than 5. Therefore, the tenths value of 7.09 increases by 1 to 7.1.
plssssssssss help meeeeeeeeeeeeeeeee
Answer:
The A graph applies to the first and fourth statement
The B graph applies to the second and third statement
The number of ducks in a pond increasing is a 100% bar with an extra 40% added to it (looks like graph A from the previous question)
The number of mosquitos decreasing by 80% is a bar within the already existing 100% (looks like graph B from the previous question)
Step-by-step explanation:
none further needed
ok im super confused bc like it ask me put i dont know what to put.............pls help me
Answer:
u drag the green dot thing over to the coordinate (6,8)
Step-by-step explanation:
i put a black dot where i think ur supposed to drag the green dot to
Help please
5x-2y=-10
Answer:
[tex]5x - 2y = - 10 \\ 5x = - 10 + 2y \\ x = \frac{ - 10 + 2y}{5} \\ \\ [/tex]
when y=0,-5,5,-10,10
then x=-2,-4,0,-6,2
This is a substitution problem
Julianna has thirty two pieces of candy in a candy jar. Julianna only has two kinds of candy,
jolly rangers and twix. For every four twix bars, she has two pieces of jolly rangers. How many
pieces of each candy are in the candy jar?
a. The number of twix bars is 21
b. The number of jolly rangers is 11.
Julianna has thirty two pieces of candy and has four twix bars for every two jolly rangers, we need to find the ratio of candy bars.
What is the ratio of candy bars?Let
x = number of twix bars and y = number of jolly rangers.Since for every four twix bars, she has two pieces of jolly rangers, the ratio of candy bars is
x:y = 4:2 = 2:1
a. Number of twix barsThe number of twix bars is 21
The number of twix bars x = ratio of twix bars/total ratio × total number of candy bars
So, x = 2/(1 + 2) × 32
= 2/3 × 32
= 64/3
= 21.33
≅ 21
So, the number of twix bars is 21
b. Number of jolly rangersThe number of jolly rangers is 11.
The number of jolly rangers y = ratio of jolly rangers/total ratio × total number of candy bars
So, y = 1/(1 + 2) × 32
= 1/3 × 32
= 32/3
= 10.66
≅ 11
So, the number of jolly rangers is 11.
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Line segment AB has vertices A(-3, 4) and B(1, -2). A dilation centered at the orgin is applied to AB. The image has vertices A(-1, 4/3) and B(1/3, -2/3). What is tjr scale factor of the dilation?
1. 1/6
2. 1/3
3. 3
4. 6
Answer:
option 2
Step-by-step explanation:
consider the coordinates A (- 3, 4 ) and A' (- 1, [tex]\frac{4}{3}[/tex] )
since the dilatation is centred at the origin, then corresponding coordinates are multiples/ divisors of each other, then image to original gives scale factor.
scale factor = [tex]\frac{A'}{A}[/tex] = [tex]\frac{-1}{-3}[/tex] = [tex]\frac{1}{3}[/tex] and [tex]\frac{\frac{4}{3} }{4}[/tex] = [tex]\frac{1}{3}[/tex]
similarly B (1, - 2 ) and B' ([tex]\frac{1}{3}[/tex], - [tex]\frac{2}{3}[/tex] )
[tex]\frac{\frac{1}{3} }{1}[/tex] = [tex]\frac{1}{3}[/tex] and [tex]\frac{-\frac{2}{3} }{-2}[/tex] = [tex]\frac{1}{3}[/tex]
pls help, full explanation pls
Step-by-step explanation:
Apply exponent rule: (a. b)^n= a^n b^n
=3²(x¹⁰)²(y⁴)²
3²=9
=9(x¹⁰)²(y⁴)²
break =9(x¹⁰)²(y⁴)² into two
simplify (X¹⁰)² = (x²⁰)
simplify (y⁴)²=(y⁸)
=9(x²⁰)(y⁸)
What is the value of y?
2
5
7
8
I need help finding the slope and what m=
Find (a) the range and (b) the standard deviation of the data set 141,116,117,135,126,121. round to the nearest hundredth if necessary.
a) The range of the given data set is 25.
b) The standard deviation of the given data set is 10.1.
The given data set is 141, 116, 117, 135, 126, 121.
a) The range is the difference between the highest and lowest values within a set of numbers.
Range = Highest value - Lowest value
= 141-116
= 25
So, the range is 25.
b) Set up the formula for sample standard deviation. The standard deviation of a set of values is a measure of the spread of its values.
[tex]s=\sqrt{\frac{(x_i-\bar x)^2}{n-1} }[/tex]
Here, mean ([tex]\bar x[/tex]) = [tex]\frac{141+116+117+135+126+121}{6}[/tex]
= 126
[tex]s=\sqrt{\frac{(141-126)^2+(116-126)^2+(117-126)^2+(135-126)^2+(126-126)^2+(121-126)^2}{6-1}}[/tex]
[tex]s=\sqrt{\frac{(15^2+(-10)^2+(-9)^2+(9)^2+(0)^2+(-5)^2}{5}}[/tex]
[tex]s=\sqrt{\frac{(225+100+81+81+25)}{5}}[/tex]
[tex]s=\sqrt{\frac{512}{5}}[/tex]
s=10.1
So, the standard deviation is 10.1.
Therefore,
a) The range of the given data set is 25.
b) The standard deviation of the given data set is 10.1.
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Marcus states that the polynomial expression 3x3 – 4x2y y3 2 is in standard form. ariel states that it should be y3 – 4x2y 3x3 2. explain which student is correct and why.
The correct student is Marcus because the power of the polynomial decreases till 0
How to determine the correct student?The polynomial expressions are given as:
Marcus: 3x³ - 4x²y + y³ + 2
Ariel: y³ - 4x²y + 3x³ + 2
The standard form of a polynomial with the variable x is:
P(x) = ax³ + bx² + cx + d
This means that the power of the polynomial decreases till it gets to 0
Using the above form as a guide, the correct student is Marcus.
Marcus is correct because the power of the polynomial decreases till it gets to 0
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You travel 10 miles north and then 3 miles west.
How many miles are you from your starting location?
Round your answer to the nearest tenth.
Apply the means-extremes property to the ratios of the corresponding sides to determine if the polygons are similar. has sides of length 2 cm, 3 cm, and 3.5 cm. has sides of length 4 cm, 6 cm, and 7 cm.
The ratio of the sides of the triangles ΔABC and ΔDEF are constant that is 1/2. Then the triangles ΔABC and ΔDEF are similar triangles.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The triangles are given below.
The ratio of the sides of the triangles ΔABC and ΔDEF will be
AB / DE = BC / EF = CA / FD
2 / 4 = 3 / 6 = 3.5 / 7
1 / 2 = 1 / 2 = 1 / 2
The ratio of the sides of the triangles ΔABC and ΔDEF are constant that is 1/2. Then the triangles ΔABC and ΔDEF are similar triangles.
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Group the terms with variables on one side of the equal sign, and simplify.
8t −15 = 32t
Answer:
[tex] \implies \boxed{\rm t = \frac{ - 5}{8} }[/tex]
Step-by-step explanation:
8t-15=32t
Group the terms then subtract:
=>8t-32t=15
=>-24t=15
Divide both sides by -24:
[tex] \implies \rm \cfrac{ - 24t}{ - 24} = \cfrac{15}{ - 24} [/tex]
[tex] \rm \implies \: t = \cfrac{ - 5}{8} [/tex]
what is 40% of 526,367.50
Answer:
[tex]210547[/tex]
Hope this helps. :)
Answer:
210547
Step-by-step explanation:
Multiply 526, 367.50 by 40 percent than the answer you get from that subtract from 526,367.50 then you get 210547.
Hope this Helps!
:D
Wyatt has a loyalty card good for a discount at his local hardware store. To find the
total he has to pay, before tax, he multiplies the prices by 0.8. What percent discount
does the card give?
Answer:
80%
Step-by-step explanation:
You multiple .8 by 100 to find percentage, giving you 80%.
Answer:
i don’t know
Step-by-step explanation:
I don’t know
Hugo lives in the northwest corner of Greene County, Lena lives 29 miles away in the southeast corner, and the office where they work is directly between them. On Monday, Hugo took the bus into work, taking a direct route at 32 miles per hour. Lena left at the same time, taking her car along a direct route at a speed of 36 miles per hour. The two coworkers arrive at the office at the same time. How long did the commute take? If necessary, round your answer to the nearest minute.
Using the relation between velocity, distance and time, it is found that the commute took 48 minutes.
What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
[tex]v = \frac{d}{t}[/tex]
For Lena, we have that d = 29, v = 36, hence the time in hours is given by:
[tex]t = \frac{d}{v} = \frac{29}{36} = 0.8056[/tex]
In minutes, the time is given by:
tM = 0.8056 x 60 = 48.
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What is the range of f(x) = 3x + 9?
{y | y < 9}
{y | y > 9}
{y | y > 3}
{y | y < 3}
The egg delivery truck arrives to savers supermarket with 250 dozen eggs. how many total eggs are in that truck.
Answer:
3000
Step-by-step explanation:
12x250=3000
THIS IS EASY BUT PLEASE HELP ME IM BIT SLOW
Answer:
A: Isosceles (two sides the same)
B: Equilateral (all sides the same)
C: Scalene (all sides different)
Step-by-step explanation: