Answer:
21 minutes or 8:21 a.m
Step-by-step explanation:
6+15=21
A function, fix), models the depth of water in a wading pool that is filling at a rate of 11 gallons per minute. Which of these
describes why f(x) can be considered a linear function?
I. For every 1 minute interval, the depth of water in the wading pool increases by the same amount.
II. The function grows by equal factors every minute.
III. The slope of the function is constant.
a. I only
b. I and III only
c. II and III only
d. I, II, and III
Answer: the answer is C trust me bye
Step-by-step explanation:
3x = y and x - 2y = 10
Answer: Rewrite equations:
3x=y;x−2y=10
Step: Solve3x=yfor y:
3x=y
3x+−y=y+−y(Add -y to both sides)
3x−y=0
3x−y+−3x=0+−3x(Add -3x to both sides)
−y=−3x
−y
−1
=
−3x
−1
(Divide both sides by -1)
y=3x
Step: Substitute3xforyinx−2y=10:
x−2y=10
x−23x=10
−5x=10(Simplify both sides of the equation)
−5x
−5
=
10
−5
(Divide both sides by -5)
x=−2
Step: Substitute−2forxiny=3x:
y=3x
y=(3)(−2)
y=−6(Simplify both sides of the equation)
Step-by-step explanation:
Which table does not represent a function
Answer:
B.
Step-by-step explanation:
B. table B has 2 y values for one x, and that makes it not a function but a relation / equation.
The indefinite integral of ((6e^4x)(e^arctan(3e^4x)))/(1+9e^8x)
Answer:
[tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{e^\big{arctan(3e^{4x})}}{2} + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Integration
Integrals[Indefinite Integrals] Integration Constant CIntegration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
U-Substitution
U-SolveStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx[/tex]
Step 2: Integrate Pt. 1
[Integrand] Rewrite: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \int {\frac{6e^\big{arctan(3e^{4x}) + 4x}}{1 + 9e^\big{8x}}} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = 6\int {\frac{e^\big{arctan(3e^{4x}) + 4x}}{1 + 9e^\big{8x}}} \, dx[/tex]Step 3: integrate Pt. 2
Set variables for u-substitution.
Set u: [tex]\displaystyle u = 4x[/tex][u] Differentiate [Basic Power Rule, Multiplied Constant]: [tex]\displaystyle du = 4 \ dx[/tex]Step 4: Integrate Pt. 3
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{4e^\big{arctan(3e^{4x}) + 4x}}{1 + 9e^\big{8x}}} \, dx[/tex][Integral] U-Substitution: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{e^\big{arctan(3e^u) + u}}{1 + 9e^\big{2u}}} \, du[/tex]Step 5: Integrate Pt. 4
Set variables for u-substitution #2.
Set v: [tex]\displaystyle v = 9e^{2u} + 1[/tex] [v] Differentiate [Exponential Differentiation, Chain Rule]: [tex]\displaystyle dv = 18e^{2u} \ du[/tex][v] U-Solve: [tex]\displaystyle u = ln \Big( \frac{\sqrt{v - 1}}{3} \Big)[/tex][dv] U-Solve: [tex]\displaystyle du = \frac{e^{-2u}}{18} \ dv[/tex][U-Solve] Rewrite u: [tex]\displaystyle e^u = \frac{\sqrt{v - 1}}{3}[/tex]Step 6: Integrate Pt. 5
[Integral] U-Solve: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{e^\big{arctan(3(\frac{\sqrt{v - 1}}{3})) + ln(\frac{\sqrt{v - 1}}{3})}}{1 + 9(\frac{\sqrt{v - 1}}{3})^2} \frac{1}{18e^{2u}}\, dv[/tex][Integral] Simplify: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{\sqrt{v - 1}e^\big{arctan(\sqrt{v - 1})}}{3[1 + v - 1]} \frac{1}{18(\frac{\sqrt{v - 1}}{3})^2}\, dv[/tex][Integral] Simplify: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{\sqrt{v - 1}e^\big{arctan(\sqrt{v - 1})}}{3v} \frac{1}{2(v - 1)}\, dv[/tex][Integral] Simplify: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{e^\big{arctan(\sqrt{v - 1})}}{6v\sqrt{v - 1}} \, dv[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{1}{4}\int {\frac{e^\big{arctan(\sqrt{v - 1})}}{v\sqrt{v - 1}} \, dv[/tex]Step 7: Integrate Pt. 6
Set variables for u-substitution #3.
Set z: [tex]\displaystyle z = arctan(\sqrt{v - 1})[/tex][z] Differentiate [Arctrig Differentiation, Chain Rule]: [tex]\displaystyle dz = \frac{1}{2v\sqrt{v - 1}} \ dv[/tex]See attachment for rest of work (would not fit entire answer in answering box).
ayee someone help pleasee
Answer:
Both are solutions of x.
Step-by-step explanation:
[tex]x^{2} =49[/tex]
For [tex]x^{2} =f(a)[/tex] the solutions are [tex]x=\sqrt{f(a)} ,-\sqrt{f(a)}[/tex]
[tex]x=\sqrt{49} ,x=-\sqrt{49}[/tex]
[tex]\sqrt{49}[/tex]
Factor the number: [tex]49=7^{2}[/tex]
Apply radical rule: [tex]\sqrt[n]{x^n} =a[/tex]
[tex]\sqrt{7^2} =7[/tex]
=7
[tex]-\sqrt{49}[/tex]
Factor the number: [tex]49=-7^2[/tex]
Apply radical rule: [tex]\sqrt[n]{x^n} =a[/tex]
[tex]-\sqrt{7^2}=7[/tex]
[tex]=-7[/tex]
8
Find the slope of the line that passes through the points (10,8) and (6, 14).
Write your answer as a simplified fraction.
Help meeee pleaseeeeee
Answer:
432
Step-by-step explanation:
8x9=72
72x6=432
What is the answer to Y=30x+25
Answer:
x=1/30y + -5/6
Step-by-step explanation:
Diego tried to solve the equation 13(x+15)=3
Answer:
x=0.107
Step-by-step explanation:
First we distribute 13 to x and 15. That gives us 13x+15x=3. Now we add 13x and 15x, that gives us 28x=3. Now we divide by 28 on both sides. That gives us x=0.107
What is the wavelength measurement?
A. 2 m
B. 2 s
C. 0.4 m
D. 0.8 m
The wavelength measurement of the figure is,
⇒ 2 meter
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
We have to given that;
The figure is shown in image.
Since, We know that;
Wavelength is the distance between identical points in the adjacent cycles of a waveform signal propagated in space or along a wire.
Hence, We get;
The wavelength measurement of the figure is,
⇒ 3.5 - 0.5 meter
⇒ 2 meter
Thus, The wavelength measurement of the figure is,
⇒ 2 meter
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find an equation for the line that passes through the points (2,-6) and (-4,-4)
Answer:
-1/3 I think
Step-by-step explanation:
use the slope formula
Isabella is making a bracelet for her friend. She has to decide which type of band to use, either leather or Siver. She also plans on picking two charms for the
bracelet. One of the charms will be of an animal, either a cat or a dog. The other charm will be of a sport, either basketbal, baseball, or soccer. How many
different bracelet combinations does Isabella have to choose from?
O 3
07
O 8
O 12
Answer:
There are 12 combinations.
Step-by-step explanation:
Options:
1. Silver or Leather
2. Cat or Dog
3. Basketball, baseball, or soccer
Now we need to multiply the options together, so 2 × 2 × 3 = 12.
A board 30 metres long is to be divided into 2pieces so that the larger piece is 3 metres longer than twice the shorter piece. How long will the pieces be?
Answer: 9 and 21
Step-by-step explanation:
board=30m
divide by 2 pieces
one piece, we call it a
b, the other piece is b= 2a+3
a+b=30
a+2a+3=30
3a=30-3
3a=27
a=9
b=21
There is an installation fee to join the Pine River country club as well as monthly dues the total cost of her seven month membership will be $3200 and after one and a half years $3970 find both the intuition feet and the monthly dues
Answer:
Monthly charges = $70
Intuition charges = $2710
Step-by-step explanation:
There is intuition fee and per month fee for joining the Pine River country club.
Total cost for 7 months is $3200
Total cost for one and a half years is $3970
one and a half years means 18 months.
To find:
Intuition fee and monthly dues?
Solution:
Let the intuition fee = [tex]i[/tex]
Let the monthly dues = [tex]m[/tex]
Total cost for 7 months can be represented as
[tex]i+7m = 3200[/tex] ..... (1)
Total cost for 18 months can be represented as
[tex]i+18m = 3970 .... (2)[/tex]
Here, we have 2 equations and 2 variables whose values are to be found.
Let us use elimination method to solve the equations.
Subtracting equation (1) from (2):
[tex]11m = 770\\\Rightarrow m = 70[/tex]
Therefore, the monthly dues are $70.
Using equation (1), we can find the value of [tex]i[/tex].
[tex]i + 70\times 7 = 3200\\\Rightarrow i = 3200 - 490\\\Rightarrow i = \$2710[/tex]
Therefore, intuition charges are $2710.
Donald has 5 amount of 20 dollar bills and 1 ten dollar bill. Write an expression to show how to find how much money Donald has.
Answer:
He has 110
Step-by-step explanation:
5x20 = 100
100 + 10 = 110
Please help!! I can't get it!
Answer:
B is the answer
hope it helps
Luke made 25% of his free throws over the season if he shot 200 free throws how many did he make?
Based on the number of throws Luke had and the percentage he made, the number he made was 50 throws.
Number of Free Throws MadeThere were 200 free throws in the season and Luke was able to make about 25% of them.
The formula to find this is therefore:
= Number of free throws x Percentage made
Solving gives:
= 200 x 25%
= 50 throws
In conclusion, Luke made 50 throws.
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Teacher made a table to show which months her students birthdays took place. There are four birthdays in August and in total they are 33 students. What is the ratio of students with August birthdays to the total number of students
Answer:
4:33 or 4/33
Step-by-step explanation:
Six more than seven times a number equals 10 times the number -12
Answer:
The equation becomes
[tex]7x+6 = 10x-12[/tex]
Thus, the number = x = 6
Step-by-step explanation:
Let 'x' the number
seven times a number = 7x
Six more than seven times a number = 7x+6
10 times the number -12 = 10x-12
Given that Six more than seven times a number equals 10 times the number -12.
Thus, the equation becomes
[tex]7x+6 = 10x-12[/tex]
We can further solve for x
[tex]7x+6 = 10x-12[/tex]
[tex]6+12 = 10x-7x[/tex]
[tex]18 = 3x[/tex]
[tex]x = 6[/tex]
Thus, the number = x = 6
PLEASE HELP :) 20 POINTS FOR IT IF U JUST ANSWER LIKE IDK OR SUM IMMA REPORT
Answer:
BC = [tex] 1.8 [/tex]
Step-by-step explanation:
∆ABC is an equilateral ∆ because all three angles are equal. Therefore, all its sides would be equal also. This means AB = BC = AC
Thus, let's find the value of x.
[tex] \frac{7}{4}x - 1 = \frac{9}{3}x - 3 [/tex]
Collect like terms
[tex] \frac{7}{4}x - \frac{9}{3}x = 1 - 3 [/tex]
[tex] \frac{7x}{4} - 3x = -2 [/tex]
[tex] \frac{7x - 12x}{4} = -2 [/tex]
[tex] \frac{-5x}{4} = -2 [/tex]
Multiply both sides by 4
[tex] \frac{-5x}{4}*4 = -2*4 [/tex]
[tex] -5x = -8 [/tex]
Divide both sides by -5
[tex] x = \frac{8}{5} [/tex]
AB = BC = AC
Therefore,
BC = [tex] \frac{7}{4}x - 1 [/tex]
Plug in the value of x
BC = [tex] \frac{7}{4}*\frac{8}{5} - 1 [/tex]
BC = [tex] \frac{56}{20} - 1 [/tex]
BC = [tex] 2.8 - 1 [/tex]
BC = [tex] 1.8 [/tex]
Divide the fractions:
5/8 divided by 1/24 =
Answer:
The answer to this question is 15.
Step-by-step explanation:
We know that dividing a fraction by another fraction is the same as multiplying a fraction by the other fractions reciprocal, where the numerator and denominator are switched.
5/8 ÷ 1/24 =
5/8 x 24/1 =
120/8
120 ÷ 8 = 15.
Hence, the answer to this question is 15.
Hope this helps! :D
Final Answer:
15
Step-by-step explanation:
5/8 ÷ 1/24
5/8 ÷ 24/1
5/8 × 24/1 = 120/8
120/8 ⇒ 15/1 ⇒ 15
Please answer this as quick as you can
Answer:
B is correct because there cannot be negative people in a cafeteria.
Step-by-step explanation:
The $40 million lottery payment that you have just won actually pays $2
Answer:
wait what is the question?
Step-by-step explanation:
??
1. What value of x makes the equation 3x - 6 = 9 true?
Answer:
5
Step-by-step explanation:
this is basic algebra so it's important to understand this concept now. you need to combine like terms so 3x-6=9 becomes 3x=15 (you add the 6 to add like terms). You then divide the 3 from 3x on both sides to get x=5
The value of x makes the equation 3x - 6 = 9 true is: x = 5.
Here, we have,
given that,
the equation is: 3x - 6 = 9
so have,
3x-6=9
We need to combine like terms
=> 3x = 9 + 6
(we add the 6 to add like terms).
becomes, => 3x=15
we then divide the 3 from on both sides
=> 3x/3 = 15/3
we get
=> x=5
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Christian earns $12 per hour working at the coffee shop. if he works for 8 hours on Saturday, how much money will he earn
Answer:
$96
Step-by-step explanation:
$12 per hour / 8 hours
$12 x 8 $96
Find the total amount due on a loan of $5,000 for 8 years at 10% simple interest.
$4,000
$5,500
$9,000
$9,500
$5,400
A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let ^ p denote the proportion in the sample who say they support the increase. Suppose that 13% of all adults in Ohio support the increase. The standard deviation of the sampling distribution is
Answer:
The standard deviation of the sampling distribution is [tex]\sigma =0.0087[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 1500
The population proportion is [tex]p = 0.013[/tex]
Generally the standard deviation of this sampling distribution is mathematically represented as
[tex]\sigma = \sqrt{ \frac{p (1- p)}{ n} }[/tex]
=> [tex]\sigma = \sqrt{\frac{0.13(1-0.13)}{1500} }[/tex]
=> [tex]\sigma =0.0087[/tex]
The standard deviation of the considered sampling distribution of the proportion supporting the increase is 0.0027 approx.
How to find the sample standard deviation for distribution of a sample proportion?Suppose the sample proportion be denoted by [tex]\hat{p}[/tex], then, its distribution is normally distributed with mean [tex]p[/tex] and the standard deviation of distribution of [tex]\hat{p}[/tex] is given by
[tex]\sigma = \sqrt{\dfrac{p(1-p)}{n}}[/tex]
where n is the sample size. It is true until [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex]
For the given case, we're given that:
Sample size= n = 10Proportion average value = p = 13% = 0.13 Standard deviation = [tex]\sigma = \sqrt{\dfrac{0.13(1-0.13)}{1500}} = \sqrt{\dfrac{0.13 \times 0.87}{1500}} \approx 0.0027[/tex]Thus, standard deviation of the sampling distribution is approximately 0.0027
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Don’t worry about number 4 just tell me the answer to number two
Answer:
B
Step-by-step explanation:
First, you must combine like terms.
5a - a - a would be 3a.
-6 + 4 would be -2.
3a-2
Answer:
The answer would be B. -a+4+5a-a-6.
You would need to put like terms together. 4 and -6 is -2. -a, 5a, and -a is 3a.
Perform the indicated operation and simplify the result. Leave your answer in factored form.
[tex]\frac{5x+20}{8x^{5} }[/tex]·[tex]\frac{x}{x^{2} -16}[/tex]
Answer:
First, you have to factorize the expressions :
[tex] \frac{5x + 20}{8 {x}^{5} } \times \frac{x}{ {x}^{2} - 16} [/tex]
[tex] = \frac{5(x + 4)}{8 {x}^{5} } \times \frac{x}{(x + 4)(x - 4)} [/tex]
Second, you have to cross out the similar expressions :
[tex] = \frac{5}{8 {x}^{5} } \times \frac{x}{(x - 4)} [/tex]
Third, you have to multiply both fractions :
[tex] = \frac{5x}{8 {x}^{5}(x - 4) } [/tex]
Lastly, you have to simplify :
[tex] = \frac{5}{8 {x}^{4}(x - 4) } [/tex]
When should the direct pattern be used to communicate negative nows?