[tex]\text{Given that,}~\\\\f(x) =a^x\\\\\text{L.H.S}\\\\=f(m+n+p)\\\\=a^{m+n+p}\\\\\text{R.H.S}\\\\=f(m) \cdot f(n) \cdot f(p)\\\\=a^m \cdot a^n \cdot a^p\\\\=a^{m+n+p}\\\\ \text{L.H.S} = \text{R.H.S}\\\\\text{Proved.}[/tex]
A principal of $3900 is invested at 7.5% interest compounded annually how much will the investment be worth after 9 years
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3900\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &9 \end{cases} \\\\\\ A=3900\left(1+\frac{0.075}{1}\right)^{1\cdot 9}\implies A=3900(1.075)^9\implies A\approx 7477.23[/tex]
Question 4
1 pts
in 2013, the number of rabbits in a local park is 120, but this number is decreasing
each year by a constant percent. the number of rabbits in the park t years after 2013
can be found using the given formula. about how many rabbits will be left in the park
after 10 years?
r=120(0.99)
1,188
247
1
108
After 10 years, there will be 108 rabbits left in the park.
What is Exponential Equation?An exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
Here, the given equation;
R = 120 (0.99)ⁿ
where, n is the number of years
n = 10 years (given)
R = 120 (0.99)¹⁰
R = 120 X 0.904
R = 108.52
Thus, After 10 years, there will be 108 rabbits left in the park.
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I would really appreciate it if someone helped answer these 4 questions. I will rate 5 stars. Thank you (:
Answer:
7. 13.6
8. 19.5
9. 6.5
10. 12.6
Step-by-step explanation:
Recall the three main trig functions
Sine = opposite / hypotenuse
Cosine = adjacent / hypotenuse
Tangent = opposite / adjacent
( remember hypotenuse = longest side length , opposite = side length opposite of angle , and adjacent = side length thats not the opposite or hypotenuse )
We will use these to solve each problem
7.
We are given :
An angle with a measure of 39 degreesThe angles opposite side length The adjacent side as the unknownWhen dealing with opposite and adjacent we use tangent
We have tan = opp / adj
==> plug in opp = 11 and adj = x as well as given angle 39
tan(39) = 11/x
==> multiply both sides by x
xtan(39) = 11
divide both sides by tan(39)
x = 11/tan(39)
plugging this into a calculator , we get x = 13.6 ( rounded )
8.
We are given :
an angle with a measure of 46 degreesthe hypotenuse which has a length of 28and the adjacent as the unknownWhen dealing with adjacent and hypotenuse we use cos
We have cos = adj / hyp
==> plug in given angle 46 , adj = x and hyp = 28
cos(46) = x/28
==> multiply both sides by 28
x = 28cos(46)
plugging this into a calculator we get x = 19.5 ( rounded )
9.
We are given :
an angle with a measure of 51 degreesits opposite side length with a length of 8 the adjacent side length as the unknownWhen dealing with the opposite and adjacent we use tangent
We have tan = opp / adj
==> plug in 51 degrees for angle , opp = 8 and adj = x
tan(51) = 8/x
==> multiply both sides by x
xtan(51) = 8
==> divide both sides by tan(51)
x=8/tan51
plugging this into a calculator we get that x = 6.5 ( rounded )
10.
We are given:
an angle with a measure of 24 degreesthe hypotenuse which has a length of 31the side length opposite of given angle as the unknownWhen dealing with the opposite and hypotenuse we use sine
We have sin = opp / hyp
==> plug in angle as 24 , opp = x and hyp = 31
sin(24) = x / 31
==> multiply both sides by 31
31sin(24) = x
plugging this into a calculator we get that x = 12.6 ( rounded )
And we are done!
Let me know if you have any doubts in the comments ! : )
In Walter's class, 14 of the 25 students ride the bus. In Sasha's class, 11 of the 20 students ride the bus. Which class has a greater percent of students who ride the bus?
The class which has a greater percent of students who ride the bus is Walter's class
How to find percentage?Walter's class:
14 of the 25 students ride the busPercentage of students who ride bus = 14 / 15 × 100
= 0.933 × 100
= 93.3%
Sasha's class:
11 of the 20 students ride the busPercentage of students who ride bus = 11 / 20 × 100
= 0.55 × 20
= 55%
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please help!
[3 x 2⁵ - 13 x (-2)] + 2³
(-2² +3²) - 3
Give your answer in simplest form.
Answer:
122x + 37
Step-by-step explanation:
hope this helps u
Answer:
[3×2⁵+13×2]+2³(-2²+3²)-3=
[3×32+26]+2³(-4+9)-3=
[96+26]+2³(5)-3=
122+40-3
162-3=
159...
note:-a×(-b)=+ab
Help!! Due tomorrow. x(x − 8) = 0
Answer: x = 0, 8
Step-by-step explanation:
x = 0
x - 8 = 0 ⇒ x = 8 (move 8 to the right)
x = 0, 8
Enter the number that belongs in the green box.
Answer:
the green box is 0
Step-by-step explanation:
we are asked to find the x-intercept, which means y = 0
(x, y)
Another way to test this is plug it in 1 for x! (1, y) where x = 1
[tex]y = \frac{2x^{2} -3x+1}{2x^{2} +8x+6} \\\\[/tex]
[tex]y = \frac{2(1)^{2} -3(1)+1}{2(1)^{2} +8(1)+6}[/tex]
[tex]y = \frac{2(1) -3(1)+1}{2(1) +8+6}[/tex]
[tex]y = \frac{2 - 3 + 1}{2 + 8 + 6}[/tex]
[tex]y = \frac{-1+1}{10 + 6}[/tex]
[tex]y = \frac{0}{16}[/tex]
y = 0
7. A triangle has an area of 20 in². If the height of the
triangle is 5 inches, find the base of the triangle.
Step-by-step explanation:
the area of a triangle is
baseline × height / 2
in our case
baseline × 5 / 2 = 20 in²
baseline × 5 = 40
baseline = 8 in
What is the area, in square units, of the polygon shown here?
A figure in the shape of a block letter L with a vertical height of 8 units and a length of 5 units is shown. The length of the top of the L is 2 units and the height of the right side of the L is 1 unit.
14 units2
16 units2
17 units2
19 units2
The area of a 2D form is the amount of space within its perimeter. The correct option is D.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The area of the L block will be the sum of the area of A and B. Therefore, the area can be written as,
Area of L block = Area of A + Area of B
= (7×2) units² + (1 × 5) units²
= 14units² + 5units²
= 19units²
Hence, the correct option is D.
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f(x) =2x^2+4x-6. g(x)=4x^3-6x^2+3 find (f+g)(x)
Answer:
=4x³-4x²+4x-3
Step-by-step explanation:
(f+g)(x)=4x³+2x²-6x²+4x-6+3
=4x³-4x²+4x-3
What is the area of the following triangle in square meters? Do not round your answer.
A
=
m
2
The area of the triangle will be 3240 square centimeters.
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 diagram is given below.
The height of the triangle is 120 cm and the base of the triangle is 54 cm.
Then the area of the triangle will be
Area = 1 / 2 x 120 x 54
Area = 3240 square cm
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Answer:
0.324
Step-by-step explanation:
How do I solve this using Sin or Cosine law?
Those two have both two formulas but when dealing with a not-right triangle which is a particular case you use this formula for sines.
[tex]\frac{SinC}{c} =\frac{SinR}{r}[/tex]
Substitute
Note: the capital letters are for the angles and the small letter are for the sides.
But since we used side R and there is no angle to substitute. you will basically have to find it by adding the two angles given and subtracting it by 180, which is a 100.
[tex]\frac{Sin(7)}{1.9} =\frac{Sin100}{x}[/tex]
now you do the butterfly method or cross multiplication method.
[tex]xsin(7)=1.9sin(100)[/tex]
You have to isolate the x
[tex]\frac{xsin(7)}{sin(7)} =\frac{1.9sin(100)}{sin(7)}[/tex]
now cancel and plug the right side of the equation into your calculator and u get the answer for the missing side.
[tex]x= 15.35[/tex] or if u want to round it [tex]15.4[/tex]
<R = 100 and side CK= 15.35 or 15.4
Hope I helped! ^w^
TheOneAndOnlyLara~
Serena bought a video game on sale for $23.88. The original price was $44.69. How much
money did Serena save buying the game on sale?
Answer:
i just need points
Step-by-step explanation:
sorrry ehburbvuygvuywhefe2b yvfb we
A survey found that 3 out of 100 randomly selected people have red hair. How many people in a group of 12,000 randomly selected people are likely to have red hair?
Answer:
360 people out of 1200 are likely to have red hair.
Step-by-step explanation:
So I just saw that 100 x 120 equals 1200. So I just need to multiply 3 x 120 and I got 360. I think this is how to solve?
1940 people attended a basketball game. 679 of the people attending supported the home team, while 1261 supported the visiting team. What percentage of people attending supported the home team?
Answer:
35%
Step-by-step explanation:
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
The percentage of people who supported the home team is 35%.
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
20% = 20/100 = 1/5
25% = 25/100 = 1/4
We have,
Number of people who attended the basketball game = 1940
Number of people who supported the home team = 679
Number of people who supported the visiting team = 1261
The percentage of people who supported the home team.
= [ Number of people who supported the home team / Total number of people who attended the basketball game ] x 100
= [679 / 1940] x 100
= 67900 / 1940
= 35%
Thus,
The percentage of people who supported the home team is 35%.
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please help me grades are do today
Answer:
28
Step-by-step explanation:
[tex]sin=\frac{opp}{hyp}[/tex]
[tex]cos = \frac{adj}{hyp}[/tex]
[tex]cos^{-1}\left(\frac{45}{51}\right)[/tex]
which is 28.07 degree
[tex]sin\left(28.07\right)=\frac{x}{51}[/tex]
x= 23.99
23.99+4=h=28
Please help me, greatly appreciate it!
Answer: See the screenshots below
I'm answering in this format because the questions aren't numbered, so its hard to reference them consistently (so we're both on the same page).
All decimal values are approximate. I decided to round to 4 decimal places, but feel free to use another level of precision.
solve. -16 < 3x + 5 < 14
Answer: -7 < x < 3
Step-by-step explanation:
-21 < 3x < 9
-7 < x < 3
If the perimeter of this triangle is 15 centimeters, what is the value of n?
The value of n from the triangle = 2.5
Calculation of perimeter of trianglePerimeter of a triangle= a +b+c
Where,
a= n
b= 5n - 6
C= 2n + 1
P= 15
Therefore n
15 = n + 2n + 1 + 5n - 6
15 = 8n-5
8n= 15+5
8n = 20
n= 20/8
n= 2.5
Therefore, the value of n = 2.5
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If x^2+y^2=13 and xy=6 then find the value of x^4+y^4
Recall that (a + b)² = a² + 2ab + b².
Let a = x² and b = y². Then
(x² + y²)² = (x²)² + 2x²y² + (y²)²
⇒ x⁴ + y⁴ = (x² + y²)² - 2 (xy)²
Given that x² + y² = 13 and xy = 6, we have
x⁴ + y⁴ = 13² - 2×6² = 97
Vanessa uses the expressions (3x² + 5x + 10) and (x² – 3x - 1) to represent the length and width of her patio.
Which expression represents the area (w) of Vanessa's patio?
a) 3x4-4x³-8x²-35x-10
b) 3x4+14x³+22x²+25x-10
c) 3x4-4x³+22x²+35x+10
d) 3x1+14x³+28x²+35x+10
I’m not really the best at math, my apologies. Thank you.
Answer:
a) 3x⁴-4x³-8x²-35x-10
Step-by-step explanation:
3x2(x²-3x-1)+5x(x²-3x-1)+10(x²-3x-1)
3x⁴-9x³-3x²+5x³-15x²-5x+10x²-30x-10
3x⁴-9x³+5x³-3x²-15x²+10x²-5x-30x-10
3x⁴-4x³-8x²-35x-10
The expression 3x⁴ + 11x³ - 15x² - 40x - 10 represents the area (w) of Vanessa's patio
What is Expression?An expression is combination of variables, numbers and operators.
The area (w) of Vanessa's patio can be found by multiplying the length and width expressions:
w = (3x² + 5x + 10)(x² – 3x - 1)
Expanding this expression using the distributive property, we get:
w = 3x⁴ - 4x³ - 8x² + 15x³ - 25x² - 10x + 10x² - 30x - 10
Simplifying this expression, we get:
w = 3x⁴ + 11x³ - 15x² - 40x - 10
Hence, the expression 3x⁴ + 11x³ - 15x² - 40x - 10 represents the area (w) of Vanessa's patio
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Help quick!
An unknown number is not equal to 4.98 but rounds to 4.98 when rounded to the nearest hundredth. Which of the following could be the unknown number?
4.999
4.992
4.986
4.984
Answer:
the answer is 4.979
Step-by-step explanation:
Answer:
The answer is 4.979
Step-by-step explanation:
Peter built a chest that measures 2 feet by 11
2
feet by 1 foot. He wants to fill the chest with plastic coins.
A prism has a length of 2 feet, height of 1 foot, and width of 1 and one-half feet.
What is the maximum amount of space that the chest can hold?
The maximum amount of space is
cubic feet.
Answer:
3
Step-by-step explanation:
got it on edge
What is the area of a polygon with vertices of (-2,-4), (4,-4), (4, 4), and (-5, 4)?
216 square units
30 square units
120 square units
60 square units
Answer: 60 square units
Step-by-step explanation: i hope that helps buddy :)
When surveyed, the ratio of students who preferred Science class to English class was 5:4. If 90 students were surveyed, how many students chose Science?
50 students preferred science...
Explanation:
we can consider the numbers 5 and 4 in the ratio as units
now we need to know how much each unit represent
units = 5 + 4 = 9
my sample = 90 students
each unit = 90/9 = 10 students
so each unit represents 10 students
back to the ratio
who preferred science = 5
who preferred English = 4
Number of students choose Science = 5 * 10 = 50
Solving for interior angle measures, what is the m
Using the triangle sum theorem, the value of angle ACB in the triangle is: B. 50°.
What is the Triangle Sum Theorem?According to the triangle sum theorem, the sum of all the angles in a triangle equals 180 degrees.
90 + 7x - 20 + 4x = 180
70 + 11x = 180
11x = 180 - 70
11x = 110
11x/11 = 110/11
x = 10
m∠ACB = 7x - 20
Plug in the value of x
m∠ACB = 7(10) - 20
m∠ACB = 50° (option B).
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At what rate per cent per annum will rs 6000 amount to rs 6615 in two years when interest is compounded annually?
Answer: 5%
Step-by-step explanation:
[tex]6615=6000(1+r)^{2} \\ \\ 1.1025=(1+r)^{2} \\ \\ 1.05=1+r \\ \\ r=0.05=\boxed{5\%}[/tex]
What is the inverse of f(x)=x^4+7 for x>0 where function g is the inverse of function f?
-
Answer:
[tex]g(x) = \sqrt[4]{x-7},~ x\geq 7[/tex]
Step by step explanation:
[tex]y= f(x) = x^4+7\\\\\text{Replace x with y and solve for y:}\\\\~~~~~~~x = y^4 +7\\\\\implies y^4 = x-7\\\\\implies y = \pm\sqrt[4]{x-7}\\\\ \implies f^{-1}(x) = \pm\sqrt[4]{x-7}[/tex]
2x(x-5) -x (3 + 2x) = 26
help me pls
Answer:
x = -2
Step-by-step explanation:
[tex]2x(x-5)-x(3+2x) = 26\\2x^{2} -10x-3x-2x^{2} = 26\\-13x=26\\x=\frac{26}{-13} \\=-2[/tex]
Its basically the order of operations, from left to right , evaluate brackets (if possible), then multiplication or division, lastly followed by addition or subtraction.
2x2-10x-3x-2x2=26
Eliminam opusele
reducem termenii
-13x=26
imparte ambele parti
x=-2
Step-by-step explanation:
Calvin deposits $400 in a savings account that accrues 5% interest compounded monthly. after c years, calvin has $658.80. makayla deposits $300 in a different savings account that accrues 6% interest compounded quarterly. after m years, makayla has $613.04. what is the approximate difference in the number of years that calvin and makayla have their money invested?
The approximate difference in years for Calvin and Makayla is that B. Makayla invests her money 2 years longer.
Calculations and Parameters:Given:
Interest rate= 5%Deposit of Calvin= $400Final amount after c years= $658.80We use the compound interest formula,
[tex]A= P(1 + r/t)^t[/tex]
[tex]658.8/400= (1205/1200)^1^2^c[/tex]
c= 10 years approx.
For Makayla,
Amount deposited= $300Interest rate= 6%Final amount= $613.4m= ?We use the same formula:
[tex]A= P(1 + r/t)^t\\[/tex]
[tex]613.4/300= (1206/1200)^1^2^m[/tex]
m= 12 years approx.
Hence, the difference in the years would be:
12-10
= 2 years.
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Answer:
Makayla invests her money 2 years longer
Step-by-step explanation:
b on edge