Answers
Answer:
a) growth
b) $500
c) 6% = 0.06
d) [tex]f(x)=500(1.06)^x[/tex]
e) $595.51
Step-by-step explanation:
Part (a)
Exponential GROWTH, since interest is applied to the account each year.
Part (b)
Initial amount = $500
Part (c)
Growth factor = 6% = 0.06 (in decimal form)
Part (d)
General form of exponential growth function:
[tex]f(x)=a(1+r)^x[/tex]
where:
a = initial amountr = rate of growth (in decimal form)x = time (in years)Given:
a = 500r = 0.06[tex]\implies f(x)=500(1+0.06)^x[/tex]
[tex]\implies f(x)=500(1.06)^x[/tex]
Part (e)
when x = 3
[tex]\begin{aligned}\implies f(3) & =500(1.06)^3\\ & = 595.51\: \sf(nearest\:hundredth)\end{aligned}[/tex]
Related Questions
Marcia has an abundant supply of 3 cent stamps and 8 cent stamps. She needs to mail a package which requires exactly $2.00 postage. How can she come p with exactly $2.00 using any combination of the 3 cent and 8 cent stamps?
There are 9 different solutions to this problem. Try to find them all and list them.
Answers
The possible hours of daylight in a given day is a function of the day of the year . In Poughkeepsie , New York , the minimum hours of daylight ( occurring on the Winter solstice ) is equal to 9 hours and the maximum hours of daylight ( occurring on the Summer solstice ) is equal to 15 hours If the hours of daylight can be modeled using a sinusoidal equation what is the equation's ampltitude ?
Answers
Considering a sinusoidal equation, and the concept of amplitude, if it found that the equation's amplitude is of 3 hours.
What is the amplitude of a sinusoidal equation?It is given by half the difference between the greatest and the smallest value.
In this problem:
The greatest value is of 15 hours.The smallest value is of 9 hours.0.5 x (15 - 9) = 3.
Hence, the equation's amplitude is of 3 hours.
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solve for x
x over 7 = 6
Answers
Answer:
X = 42
Step-by-step explanation:
What divided by 7 equals 6..... 42! to prove we are right let us plug it into our equation.
42 / 7 = 6
DING DING DING Correct !
Answer:
X = 42
Step-by-step explanation:
Think of this problem as a division problem.
? ÷ 7 = 6
So solve this multiply 7 by 6.
This would leave you with 42.
Therefore 42/7 = 6
Easy Peasy :) Hope this helped! <3
Find the value of the trigonometric ratio. Express your answer as a fraction in lowest terms.
Find the value of the trigonometric ratio. Express your answer as a fraction in lowest terms.
\frac{20}{29}
29
20
\frac{21}{29}
29
21
\frac{21}{20}
20
21
\frac{29}{21}
21
29
Answers
Answer:
21/29
Step-by-step explanation:
Sin = hypotenuse side / opposite side to the angle
then: Sin (C) = 21 / 29
What is the greatest common factor of 13x and 14x^3?
Answers
Answer:
x
Step-by-step explanation:
13 and 14 share no factors except for 1Both have x in them, so the answer is xhard question help me
Answers
help me due today it is math
Answers
Answer:
Exact form = 1/49
Step-by-step explanation:
Decimal form = 0.02
Hope this helps! :)
Answer:
[tex]\frac{1}{7}^{2} = \frac{1}{49}[/tex]
Step-by-step explanation:
The power of the 2 means to multiply it two times itself.
Example: 7^2 = 7 * 7 = 49
Apply that to a faction.
[tex]\frac{1}{7}^{2} =\frac{1}{7} *\frac{1}{7} = \frac{1}{49}[/tex]
Are the two cones congruent? explain and include details to support your claim.
Answers
The two cones are not congruent because one of the cones is oblique in nature.
What are congruent shapes?Congruent shapes are identical in size and shape. To put it another way, if you hold an object or element in a mirror, the picture you get is congruent to the object.
However, two figures may seem to be identical, but one side or angle in one figure may deviate significantly from the other. The easiest technique to assess sides and angles to check if they are equivalent or congruent is to use markings on figures.
When we apply that technique to the two figures, we realized that the two cones are not congruent because one of the cones is oblique in nature, this resulted in a difference in the slant height of the cones.
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7( x + 3 ) ≤ 4x − 5
Give your answer as an improper fraction in its simplest form.
Answers
Answer:
-26/3
Step-by-step explanation:
We open the bracket to get 7x +21 ≤ 4x -5
hich is the joint relative frequency for the people who can only see the sunset?
StartFraction 5 Over 38 EndFraction
StartFraction 7 Over 38 EndFraction
StartFraction 12 Over 38 EndFraction
StartFraction 14 Over 38 EndFraction
Answers
Answer:
12/38
Step-by-step explanation:
Answer:
12/38
Step-by-step explanation:
Given the line y=3/5x+2 find the perpendicular line passing through the point (12,-7)
Answers
Answer:
y=-5/3x+13.
Step-by-step explanation:
As a line that is perpendicular to anoher line has a slope that is the negative reciprocal of the line's original slope, we know that the slope of our new line is -5/3. As it passes point (12, -7), we can use the point slope formula which is y-y1=m(x-x1). So plug in, y+7=-5/3(x-12) and that gives us y+7=-5/3x+20 which gives our final answer of y=-5/3x+13.
The population of New York City is about 8.4 × 10^6. What is 1/4of the population?
A. 2.1 x 105
B. 2.1 x 106
C. 4.2 x 105
D. 4.2 x 106
Answers
Answer:
2.1 x 10^6
Step-by-step explanation:
8.4 x 10^6 / 4 = 2.1 x 10^6
solve for x 1 + 2r = 35
Answers
Answer:
r = 17
Step-by-step explanation:
calculate: 2r=35-1
divide both sides: 2r=34
Karen is using a number line to represent the doors in the school hallway. She labels 0. 25, 0. 5, and 0. 75 on the number line as a scale reference. Where should Karen place a mark to represent a door that is 0. 7 from the start of the hallway? Explain. A. 0. 7 is less than 0. 75, so it is a little to the left of 0. 75. B. 0. 7 is less than 0. 75, so it is a little to the right of 0. 75. C. 0. 7 is greater than 0. 75, so it is a little to the right of 0. 75. D. 0. 7 is greater than 0. 75, so it is a little to the left of 0. 75
Answers
Answer:
A
Step-by-step explanation:
What is the area of the figure below?
Answers
Answer:
B. 33cm^2
Step-by-step explanation:
To calculate the area of a figure, you'll need to multiply the base times the height.
So, you calculate the area of the two figures and you add them up.
(4x2) + (5x5) = 33cm^2
Answer:
The answer is B. 33 cm^2
Step-by-step explanation:
Area Formula of Square/Rectangle: Area = Length * Width
Left Box:
Area = Length * Width
Area = 4 cm * 2 cm = 8 cm^2
Right Box:
Area = Length * Width
Area = 5 cm * 5 cm = 25 cm^2
Total Area = 8 cm^2 + 25 cm^2 = 33 cm^2
What is the first quartile in this box plot? Enter your answer in the box.
Answers
Answer:
30
Step-by-step explanation:
the beginning of the box is the first quartile the middle is the median the end it the third quartile
20) What fraction of the square is shaded if the line inside divides the square into two equal parts?
please help me fast please
Answers
Answer:
3/8 of the area is shaded
Step-by-step explanation:
this can be determined by deviding the total shape into parts and determining those parts
so we see the top right 1/4 of the shape has a square that is shaded, with the triangle only covering 1/2 of this shape becuase the hypotenuse ((diagnal edge of a right triangle)) devides the square in half
beings that 1/2 of the 1/4 square is shaded, we know that in reation to the whole shape that the small shaded area is equal to 1/8 ((1/2 ÷ 1/4 = 1/8))
same can be said for the bottum shape, with the bottum half of the whole shape half covered we can determine its total shaded area in relation to the shape ((1/2 ÷ 1/2 = 1/4))
the left top shape is completely unshaded so we wont need to calculate any shadded area into the equation
with the total shape covered by 1/4 + 1/8 we can find the least common denominator between the two fractions to get a simplifide answer for the total shaded area
1/4 = 2/8
2/8 + 1/8 = 3/8
this leaves 5/8 of the shape unshaded
3/8 fraction of the square is to be shaded.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
In the top right 1/4 of the shape has a square that is shaded, with the triangle only covering 1/2 of this shape because the hypotenuse divides the square in half.
1/2 of the 1/4 square is shaded, we know that in relation to the whole shape that the small shaded area is equal to 1/8.
same can be said for the bottom shape, with the bottom half of the whole shape half covered we can determine its total shaded area in relation to the shape.
1/4 = 2/8
2/8 + 1/8 = 3/8
Hence, 3/8 fraction of the square is to be shaded.
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How many times greater is 8.4 x 109 than 1.5 × 10²?
Answers
Answer:
900.6 times greater!
Step-by-step explanation:
8.4 x 109 = 915.6
10 by the power of 2 is 100 so;
1.5 x 100 = 15
915.6 > 15
915.6 - 15 = 900.6
The distance between city A and city B is 22 miles. The distance between city B and city C is 54 miles. The distance between city A and city C is 51 miles.
What type of triangle is created by the three cities?
an acute triangle, because 222 + 542 >512
an acute triangle, because 222 + 512 >542
an obtuse triangle, because 222 + 542 >512
an obtuse triangle, because 222 + 512 >542
Answers
Answer:
54 is the hypotenuse due to being the longer side(s).
54 ^2=2916 / 51^2=2601 / 22^2=484 = 2916=2601+484 // 22^2+51^2>54^2
Option B.
Find the original price of a salt lamp that is $45 after a 70% discount.
Answers
So 0.1= $6.43
Therefore 1 (100%) = $64.29
Answer:
$150.00
Step-by-step explanation:
original price = sale price/1-discount
OP=45/1-0.7
OP=45/0.3
OP=150
The graph of r = -10 cos θ has which of the following characteristics?
Answer choices are listed below.
Answers
Step-by-step explanation:
If we convert
[tex]r = - 10 \cos(x) [/tex]
to a Cartesian equation,
[tex] {r}^{2} = - 10 r \: \cos(x) [/tex]
[tex] {x}^{2} + {y}^{2} = - 10x[/tex]
[tex] {x}^{2} + 10x + {y}^{2} = 0[/tex]
[tex] {x}^{2} + 10x + 25 + {y}^{2} = 25[/tex]
[tex](x + 5) {}^{2} + {y}^{2} = 25[/tex]
So we have a circle with center (-5,0), with a diameter of 10.
prove that y=2x^2-6x+7 and y=x^2-2x+3 touch each other and find the point of contact
Answers
Answer:
See below ~
Step-by-step explanation:
We need to prove they are equal.
Equate the values to each other.
2x² - 6x + 7 = x² - 2x + 3x² - 4x + 4 = 0(x - 2)² = 0x = 2Now input the x-value in the 1st equation.
y = 2(2)² - 6(2) + 7y = 8 - 12 + 7y = -4 + 7y = 3Now input the same in the 2nd equation.
y = (2)² - 2(2) + 3y = 4 - 4 + 3y = 3Since the same x-value, on inputting in both equations, give the same y-value, it is proved they touch each other.
Point of Contact
(x, y)(2, 3)5 positive integers are arranged in ascending order, as follows: 7 , 8 , 8 , 10 , x The median and the range are equal. Find x .
Answers
Answer:
6.6, 7, 8, 8, 10
Step-by-step explanation:
7+8+8+10+X = 33/5
= 6.6
X= 6.6
Carl has 9 1/2 cups of juice for a party. If each party goer gets exactly 3/5 cup of juice each, how many party goers will get their 3/5 cup of juice
Answers
Answer: 158
Step-by-step explanation:
Okay so the total is 9 5/10.
Each party goer needs 6/10
So 95/10 / 6/0=. 95/10x10/6
=950/6 = 158.
Write a description of the rule.
(x, y) - (x-1, y +9)
translation 1 unit
to the right and 9 units down
translation 1 unit to the left and 9 units down
translation 1 unit to the
right and 9 units up
translation 1 unit to the left and 9 units up
Answers
The value a = -1 < 0 represents the translation -1 units to the left and
b = 9 > 0 represents the translation 9 units up is correct.
The rule of transformation is defined as,
( x , y ) → ( x + a , y + b ) (equation - 1)
Where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units right and if a<0, then the graph shifts a units left.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
Based on the given conditions, formulate,
(x, y) → (x-1, y+9) (equation - 2)
From (1) and (2) equations,
We get,
a = -1 , b = 9
The value a = -1 < 0 represents the translation -1 units to the left and
b = 9 > 0 represents the translation 9 units up.
Therefore,
Description of the rule is,
The value a = -1 < 0 represents the translation -1 units to the left and
b = 9 > 0 represents the translation 9 units up is correct.
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How would you find the two triangles are similar?
Answers
Answer:
The answer should be A.
Step-by-step explanation:
Well, to determine how two triangles are similar you first look at the image of what they give you.
As you can see the images shows only degree angles.
Looking at your option to see degree angles.
In some options, there is a side length of a triangle, but we aren't given a side length on both triangles so that answer does that apply.
Our last option is between A and D.
D is false as we determine the triangles are similar to each other.
RCW and VCB are vertically opposite meaning their 25° are the same to each other.
We know that every triangle adds up to 180.
HELPP?!!!
A supermarket is holding a raffle for a new wrist watch. Out of the 500 tickets sold, David buys tickets numbered 5, 6, 7, and 8. What are the odds in favor of David's winning the raffle?
Answers
Answer:
1/125
Step-by-step explanation:
He buys 4 tickets out of 500:
4/500 = 2/250 = 1/125
Need now pleasee! :(
Find the units digit for the sum
13^35 + 57^30 + 34^33
Give explanation/steps.
Answers
Answer:
The answer is 47796816366096114154433241462805777065938231744772710
Step-by-step explanation:
hope this helps you
5x^(-2)-17x^(-1)+6
for the love of god help please
Answers
Answer:
Pfffttttt- Amateurs, it is quite simple really. Take a nice long look. In the picture is he answer. And I was just joking around, even I had to use a calculator for the answer.
Step-by-step explanation:
Put the x's together, the negatives and the positives.
Answer number 8 and 9 please
Answers
Answer:
15%
Step-by-step explanation:
number 8 is 15% because you divide 42 by 280 the number of people to get the pecent you ha e which is 15%