Evaluate. Write your answer as a whole number or as a simplified fraction.
36.
When you divide powers with the same base (in this case, 6), you subtract the exponents.
See details:
[tex]\frac{6^{8} }{6^{6} } \\8-6=2\\6^{2}=36[/tex]
An investor puts $800 in an account that pays 2% interest compounded annually. Find the account balance after 5 years.
The account balance is $883.264 after 5 years.
The Principal amount is $800, the time given is 5 years and the rate of interest is 2%.
We have to find the account balance after 5 years.
Formula to find the amount
Amount = Principal × [tex](1 +\frac{rate}{100}) ^{time}[/tex]
Now putting the value we get,
Amount = 800 × [tex](1 + \frac{2}{100} )^{5}[/tex]
= 800 × [tex]\frac{102}{100 } ^{5}[/tex]
= 800 ×[tex]1.02^{5}[/tex]
= 800× 1.104
= 883.264
Therefore the amount is $883.264 that is the account balance after 5 years.
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Max is designing a hot tub for a local spa.
He wants the hot tub to have a diameter of 90 inches, what is the approximate area required for the installation of the hot tub? (Use 3.14 for.)
Max is designing a hot tub for a local spa, he wants the hot tub to have a diameter of 90 inches, the approximate area required for the installation of the hot tub is [tex]6358.5in^{2}[/tex]
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant. The radius of a circle is separation between any point on the circle and its center. The radius must typically be a positive integer. A degenerate case is a circle with r=0. Except when otherwise specified, this article discusses circles in Euclidean geometry, namely the Euclidean plane.
A circle, specifically, is a straightforward closed curve that separates the plane into its inner and exterior. In common parlance, the word "circle" can apply to either the figure's boundary or its entirety, including its inside; in rigorous technical parlance, the circle only refers to the boundary and the entire shape is referred to as a disc.
A circle can also be described as a particular type of ellipse where the semi-major and semi-minor axes are equal, the eccentricity is 0, and the two foci are coincident, or as the two-dimensional shape with the greatest area per unit perimeter squared when applying calculus of variations.
if, diameter= 90 inches
radius = 90/2= 45inches
area= [tex]\pi r^{2}[/tex]
= 3.14* 45* 45
= 6358.5[tex]in^{2}[/tex]
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prediction of the mean value of the dependent variable y for values of the independent variables x 1, x 2, . . . , x q that are outside the experimental range is called
Prediction of the mean value of the dependent variable y for values of the independent variables x 1, x 2, . . . , x q that are outside the experimental range is called extrapolation of data.
What is extrapolation of data?In statistics and mathematics, especially in the branch of data-science it is quite common to use a range of values from a parameter to predict the values of the dependent variable.
One of the most common applications of this is regression equations, when pairs of one of the independent variables with the dependent variable are used to predict the dependent variable.
In the case of this problem, we want to predict the dependent variable, but with values that are outside the experimental range, hence we extrapolate the data inside the experimental range for values that are outside the experimental range.
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is 5,521 a reasonable answer for 218x12
Answer:
No
Step-by-step explanation:
Without even answering 218*12 it is obvious this is the wrong answer
the last digit of each number determines the last digit in the answer
218 has 8 as the last number and 12 has 2
multiply them together
2*8 is 16
the last digit is 6 and not 1
Answer:
No- 218 * 12 = 2616.
Multiply with an algorithm and add the partial products up to check. You don't get 5,521 when you multiply 218 * 12.
A bag contains ten tlles labeled B, C, D, E, F, G, H, I, J, and K. One tile will be randomly picked.What is the probability of picking a letter that is not a vowel?Write your answer as a fraction in simplest form.
The number of vowels is:
[tex]2[/tex]The total number of tiles is:
[tex]10[/tex]Therefore, the total number of letters not vowels is given by:
[tex]10-2=8[/tex]Hence, the probability of picking a letter that is not a vowel:
[tex]\frac{8}{10}=\frac{4}{5}[/tex]Therefore the required probability is 4/5
At a store, shirts are regularly priced $9.95 each. The store is having a sale in which if a customer buys two shirts, he or she will get the third shirt at half-price. Sales tax is 7%. About how much will a customer spend on three shirts? *
.
.
A. $16
B. $25
C. $27
D. $32
Answer:
C. $27
Step-by-step explanation:
9.95÷2=4.975
9.95+9.95+4.975=24.875 or 24.88
24.88×7%+24.88=26.62
PLEASE HELP THIS MAKES NO SENSE AND WOULD BE VERY MUCH HELPFUL IF YOU CAN JUST ANSWER THEM GRADES ARE DUE TOMORROW, please help.
Distance between M(6,-7) and a line that contains the points C(-6,-2) and H(-1,10) is 7.846
First we will find the equation of the line containing the points C(-6,-2) and H(-1,10).
Take (x₁, y₁) = (-6,-2) and (x₂, y₂) = (-1,10).
Then the slope of the line, m = y₂-y₁/x₂-x₁
= 10- -2/-1- -6
= -12/7
So the equation of the line is
y-y₁ = m(x-x₁)
⇒ y- -2 = -12/7(x- -6)
⇒ y+2 = -12/7(x+6)
⇒7(y+2) = -12(x+6)
⇒ 7y +14 = -12x -72
⇒ 12x+7y +14+72 = 0
⇒ 12x+7y+86 = 0
This is in the form ax+ by+ c = 0
Also given the point (x, y) = (6, -7).
Distance between a point (x, y) and a line ax+ by+ c = 0 is,
[tex]\frac{|ax+by+c|}{\sqrt{a^2+b^2} }[/tex].
So Distance between M(6,-7) and the line 12x+7y+86 = 0 is
[tex]\frac{|12.6+7.-7+86|}{\sqrt{12^2+7^2} }[/tex] = |72-49+86|/√(144+49)
= 109/√193
= 7.846
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pete's pizza sells 12 inch pizzas. if pizza diameter has a mean of 12 inches and a standard deviation of .25 inches, what percent of pizzas are less than 12.04 inches? (z value of .16 is equal to a cumulative standardized normal distribution of .5636). 56.36% 43.64% 6.36% cannot be determined with the information given
The percent of pizzas that are less than 12.04 inches is 56.36%
Given the following:
Mean, μ=12
Standard deviation, σ=0.25
Percent of pizzas less than 12.04:
Let P(X<12.04) be percent of pizzas less than 12.04
P(X<12.04)=P(Z<(x-μ)/σ)
=P(Z<(12.04-12)/0.25)
=P(Z<0.16)
Z-value of 0.16 from cumulative standardized normal distribution is 0.5636
Given that P(X<12.04)=P(Z<0.16), and P(Z<0.16) from normal distribution table is 0.5636,
P(X<12.04)=P(Z<0.16)=0.5636
P(X<12.04)=0.5636
=56.36%
Hence, the correct choice is 56.36%
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If f(x) = kx^3+ x^2 − kx + 2, find a number k such that the graph of f contains the point (k, -10)
If we write [tex]k[/tex] where we see [tex]x[/tex] in the equation and set the result equal to [tex]-10[/tex], we get the result.
[tex]f(k)=k(k)^3+k^2-k(k)+2[/tex][tex]=k^4+k^2-k^2+2[/tex][tex]=k^4+2=-10[/tex][tex]k^4=-12[/tex][tex]k_{1}=\sqrt[4]{3}(-1-i)[/tex][tex]k_{2}=\sqrt[4]{3}(-1+i)[/tex][tex]k_{3}=\sqrt[4]{3}(1-i)[/tex][tex]k_{4}=\sqrt[4]{3}(1+i)[/tex]Rewrite the power as a product of powers (2ax)^3
The power can be re written as a product of (2ax)^3 as (2ax *2ax* 2ax ).
What is product and power?Product can be described as the multiplication operation of two or more terms so that another term can be gotten just like the one that is been given in the question that we were asked to rewrite.
Power serves as the degree that is been found on the terms , the degree that can be on the term is 3, then this can be expressed in three terms which will be done below.
Therefore, the given expression (2ax)^3 can be rewritten as (2ax *2ax* 2ax )
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urgent pls help!!!!
The number that makes the mixed fraction equation true is -1.
What number makes the equation true?The number that makes the equation true is calculated by applying the following formula as follows;
The given equation;
-7 ¹/₂ + ? = - 8 ¹/₂
The solution of the equation is calculated as follows;
Convert each mixed fraction into improper fraction;
-7 ¹/₂ = -15/2
-8 ¹/₂ = -17/2
-15/2 + ? = -17/2
Collect the similar terms together as follows;
? = -17/2 + 15/2
? = (-17 + 15) / 2
? = -2/2
? = - 1
Thus, the number that makes the equation true is -1.
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In the diagram below of triangle DEF, G is a midpoint of D E and H is a midpointof EF. If MZGHE = x + 52, and mZDFH = 96 – 102, what is the measureof ZDFH?
According to the given figure, angles GHE and DFH are corresponding angles, which are equal because GH and DF are parallels. So, we can express the following
[tex]m\angle GHE=m\angle DFH[/tex]Replacing the given expressions, we have
[tex]x+52=96-10x[/tex]Let's solve for x
[tex]\begin{gathered} x+10x=96-52 \\ 11x=44 \\ x=\frac{44}{11} \\ x=4 \end{gathered}[/tex]Then, we find the measure of the angle DFH
[tex]\begin{gathered} m\angle DFH=96-10x=96-10\cdot4=96-40 \\ m\angle DFH=56 \end{gathered}[/tex]Hence, the angle DFH measures 56°.its takes 8 lemons and 18 cups of water to make lemonade. You have one lemon. How many water do you need to make lemonade?
How many cups of water do you need to make lemonade? 9/4 cups
How is the number of cups calculated?
Given:
8 lemons need =18 cups of water
1 lemon needs= x cups of water
By cross- multiplication method,
[tex]\frac{8}{1} =\frac{18}{x}[/tex]
8x = 18
x = 18/8
= 9/4 cups of water is needed to make lemonade
What is the cross- multiplication method?
In the cross multiplication method, we multiply the numerator of one fraction by its denominator and the first term's denominator by its numerator. We employ the cross multiplication approach to locate the answers to two linear equations.Cross-multiplication can be used to compare unlike fractions.To learn more about cross- multiplication method, refer:
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Using the SSS congruence criterion, what additional information is needed to show that ARST AUTS?
Marsha used a graphing calculator to graph an expense and a revenue function for her family’s printing business. The graph looked like the one below.
Answer:
a
Step-by-step explanation:
is it right? but there isn't a square root for 3. And also I need an answer for the other one.. I need a great explanation quickly help!
Answer:
[tex]x=0, \quad x=3[/tex]
Step-by-step explanation:
Given equation:
[tex]9x^2-27x=0[/tex]
Factor out the common term 9x:
[tex]\implies 9x(x-3)=0[/tex]
Zero Product Property: If a⋅b = 0 then either a = 0 or b = 0 (or both).
Using the Zero Product Property, set each factor equal to zero and solve for x:
[tex]\begin{aligned}\underline{\sf Case\; 1} & & \underline{\sf Case \;2}\\9x&=0 & x-3&=0\\\dfrac{9x}{9} & =\dfrac{0}{9} & \quad \quad x-3+3 & =0+3\\x&=0 & x&=3\end{aligned}[/tex]
Therefore, the solutions to the given equation are:
[tex]x=0, \quad x=3[/tex]
simplyfy 5x-2x
How?!
Answer: 3x
Step-by-step explanation:
5x-2x=
5*x-2*x=
x(5-2)=
x*3=3x
Answer:3x
Step-by-step explanation:
combine like terms
5x-2x
2x is a negative
so 5-2=3
so in conclusion 3x
DONT IGNORE HELP PLEASE
Answer:
y = - [tex]\frac{3}{2}[/tex] x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (2, 0) ← 2 points on the line
m = [tex]\frac{0-3}{2-0}[/tex] = [tex]\frac{-3}{2}[/tex] = - [tex]\frac{3}{2}[/tex]
the line crosses the y- axis at (0, 3 ) ⇒ c = 3
y = - [tex]\frac{3}{2}[/tex] x + 3 ← equation of line
what is 12 times 12 i just need to know
Answer:
144
Step-by-step explanation:
12 * 12 = 144
Answer:
It's 144.
..............
PLEASE HELP ME I NEED HELP
The ordered pairs are (0,-7).
How Can an Ordered Pair Be Found?Any equation's ordered pair can be calculated by substituting any integer or the rational number for one of the variables, then solving for the remaining variable.
Consequently, we obtain values for both variables that meet the stated equation.
Solution:
5x - y = 7
Lets take, x = 0
Then,
5(0) - y = 7
y = -7
Then,
The ordered pair is (0,-7).
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Mary Beth collected 8 pounds of aluminum cans to recycle to start. She plans on collecting 3 more pounds each week.
How many total pounds of aluminum cans will she have collected after 3 weeks?
Answer:
She will have a total of 17 pounds.
Step-by-step explanation:
You could simply put the question is slop intercept form to figure it out from there.
y = m(x) + b
y = 3(x) + 8
y = 3(3) + 8
y = 9 + 8
y = 17
Pls mark Brainliest with the crown
please help
with answer
Answer:
-12 is the answer
Step-by-step explanation:
Substitute 1/4 for a and 6 for b in the equation
-8ab
-8(1/4)(6) Multiply
-8(1.5) Multiply
-12
51 points composite functions need help soon
Answer:
(f∘g)(12) = 24
Step-by-step explanation:
Pre-SolvingWe are given the functions f(x)=4x+8 and [tex]g(x)=\sqrt{x+4}[/tex]. We want to find (f∘g)(12).
(f∘g)(12) means that we first find the value of g(12), and then plug that value into f(x).
SolvingFirst, we find g(12). To do this, substitute x as 12.
[tex]g(12) = \sqrt{12 + 4}[/tex]
Add 12 and 4 together under the radical.
[tex]g(12) = \sqrt{16}[/tex]
Take the square root of 16.
g(12) = 4
Now, substitute 4 as x in f(x) = 4x + 8.
f(4) = 4(4) + 8
Multiply.
f(4) = 16 + 8
Add 16 and 8 together.
f(4) = 24
f(4) has the same value as (f∘g)(12), since 4 is the value of (g)(12), and then the value of g(12) was plugged in as x in f(x).
Therefore, (f∘g)(12) is 24.
NEED HELP ASAP - 100 POINTS (Algebra 2)
When solving quadratic equations, there are benefits to utilizing one method over the other. In your own words, explain what the advantages may be of using the method of completing the square to solve quadratic equations.
Answer:
Step-by-step explanation:
Comment
That's an awful lot of points to give away. Ten or 15 should be enough.
Completing the square.
1. First of all you can find the minimum or maximum immediately.
2. Second it cuts out the need to use the givens (a, b, c) in the quadratic formula which can at times be very cumbersome.
3. It gives you the opportunity to estimate the x and y roots without calculating them. Estimating on a test is a very valuable asset.
Estimation Solve the equation. First estimate using the perfect square closest to 85. Then use a calculator.
72 = 85
Estimate.
Z~ 9, -9"
(Use a comma to separate answers as needed.)
Use a calculator.
zan
(Round to the nearest tenth as needed. Use a comma to separate answers as needed.)
Answer: z aprox = 9.2
Step-by-step explanation:
1) Square root 85 to get the answer
sqrt(z^2)=sqrt(85)
z = sqrt(85)
z = 9.2195
z aprox = 9.2
The highest temperature recorded in the town of Westgate this summer was 95°F. Last winter, the lowest temperature recorded was −5°F. Find the difference between these extremes.
Pentagon A’B’C’D’E’ is the image of pentagon ABCDE under a dilation with a scale factor of 3/4.
What is the length of segment AE?
The length of segment A'E' under a dilation with a scale factor of 3/4 is; 3/2 units.
How to Interpret Scale of Dilation?
From the included graph the coordinates of the points A and E, in the pentagon ABCDE with reference to point A are;
A: (0, 0)
E: (0, 2)
The length of the segment AE = √((2 - 0)² + (0 - 0)²) = √(2²) = 2
When a pentagon ABCDE is dilated to pentagon A'B'C'D'E' with a scale factor of 3/4, we have;
Length of segment A'E' = 3/4 × Length of segment AE
Therefore;
Length of segment A'E' = 3/4 × 2 = 3/2 units.
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Jacob has 7 marbles. Darren has 17 marbles.
How many more marbles does Darren have
than Jacob?
A theater manager is planning an upcoming concert. Regular tickets will cost $12 and student tickets will cost $8. The theater can
seat at most 200 people The manager wants to collect at least $1000 from ticket sales.
Let x represent the number of regular tickets sold. Let y represent the number of student tickets sold.
Which inequalities are among the constraints lor this situation?
Select each correct answer.
0 z t y ≥ 1000
O 12z + 8y ≥ 1000
O 12 + 8y ≤ 1000
O zty 2 200
O z+ yS 200
D 12z + 8y ≤ 200
The inequalities that are the constraints for the situation are 12x + 8y ≥ 1000 and x + y ≤ 200 options (B) and (D) are correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
It is given that:
A theater manager is planning an upcoming concert. Regular tickets will cost $12 and student tickets will cost $8.
Let x represent the number of regular tickets sold. Let y represent the number of student tickets sold.
Total collection = 12x + 8y
12x + 8y ≥ 1000
x + y ≤ 200
Thus, the inequalities that are the constraints for the situation are 12x + 8y ≥ 1000, and x + y ≤ 200 options (B) and (D) are correct.
The missing options are:
12x+8y≤100012x+8y≥1000x+y≥1000x+y≤200x+y≥20012x+8y≤200Learn more about inequality here:
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