Answer:
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Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = 8x3 − 12x2 − 48x
Answer:
(2, -1)Step-by-step explanation:
Given the function f(x) = 8x³ − 12x² − 48x, the critical point of the function occurs at its turning point i,e at f'(x) = 0
First we have to differentiate the function as shown;
[tex]f'(x)= 3(8)x^{3-1}- 2(12)x^{2-1} - 48x^{1-1}\\ \\f'(x) = 24x^2 - 24x-48x^0\\\\f'(x) = 24x^2 - 24x-48\\\\At \ the\turning\ point\ f'(x)= 0\\24x^2 - 24x-48 = 0\\\\\\[/tex]
[tex]Dividing \ through \ by \ 24\\\\x^2-x-2 = 0\\\\On \ factorizing\\\\x^2-2x+x-2 = 0\\\\x(x-2)+1(x-2) = 0\\\\(x-2)(x+1) = 0\\\\x-2 = 0 \ and \ x+1 = 0\\\\x = 2 \ and \ -1[/tex]
Hence the critical numbers of the function are (2, -1)
Which is a correct expansion of (4x + 1)(2x2 – 2)?
Answer:
option A is correct
4x.2x²+4x.(-2)+1.2x²+1.(-2)
hope this will help :)
Answer:
A. 4x * 2x² + 4x( -2) + 1 * 2x² + 1 * (-2)
Step-by-step explanation:
(4x + 1)(2x² – 2)
apply the FOIL method
= 4x * 2x² + 4x( -2) + 1 * 2x² + 1 * (-2)
Help me please thank you
Answer:
x = 7
Step-by-step explanation:
The angles are alternate interior angles, so for the lines to be parallel, the angle measures must be equal.
7x - 7 = 4x + 14
3x = 21
x = 7
what is the slope for the line y= -2?
Answer:
[tex]\boxed{Slope = 0}[/tex]
Step-by-step explanation:
Hey there!
We’ll y = -2 creates a horizontal line,
and horizontal lines have a slope of zero.
Slope = 0
Hope this helps :)
Answer:
The slope of a linear equation is always the coefficient of the x value when the equation is solved for y. Since we don't have an x value on this expresion, the coefficient of x is 0. Hence, the slope of the line is 0.
How does one solve for the n+1st term with the nth term of a sequence
Answer:
The answer is option BStep-by-step explanation:
The nth term of the sequence is
A(n) = 5n + 7
To find the (n+1)st term substitute n+1 into the general equation
That's
For (n + 1)st term
A(n+1) = 5(n+ 1) + 7
A(n+1) = 5n + 5 + 7
A(n+1) = 5n + 12Hope this helps you
[tex] n^{\text{th}} \text{ term is } 5n+7 [/tex]
forget n for a while.
let's call it t .
The [tex] t^{\text{th}} \text{ term is } 5t+7 [/tex]
agreed? I don't think there should be a problem.
you're asked what's the [tex](t+1)^{\text{th}}[/tex] term.
let's call it u . so just like we did before,
[tex] u^{\text{th}} \text{ term is } 5u+7 [/tex]
but we know, [tex]u=t+1[/tex]
So, [tex]5u+7=5(t+1)+7=5t+12[/tex]
does that answer your question?
Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
a^2-2a-224=0
Answer:
{-14, 16}
Step-by-step explanation:
The coefficients of this quadratic are a = 1, b = -2 and c = -224.
Thus, the discriminant is b^2 - 4ac, or (-2)^2 - 4(1)(-224), or 900, whose square root is 30.
Thus, the roots (solutions) are
-(-2) ± 30
x = ----------------- = {-14, 16}
2
In the year 2010, 148 million Americans will be enrolled in an HMOt is the sum of the geometric series ? Is this descriptive or inflectional statistics
Answer:
His own problem to his explanation
If (a, b, c) is a solution to the system of equations above, what is the value of c?
•-26
•-6
•6
•It cannot be determined from the information given
Answer:
Option (3)
Step-by-step explanation:
The given system of the equations is,
-2x + 4y - 3z = 10 ------(1)
x - 2y + z = 8 -------(2)
If the system of equations has the solution as (a, b, c),
Which shows,
x = a, y = b and z = c
Multiply equation (2) by 2 and add it to equation (1),
2(x - 2y + z) + -2x + 4y - 3z = 10 - 16
2x - 2x - 4y + 4y + 2z - 3z = 10 - 16
-z = -6
z = 6
Therefore, z = c = 6 will be the answer.
Option (3) will be the correct option.
a) which function has the graph with the greatest y intercept?
b) which functions have graphs with slopes less than -3
c) which functions graph is the least steep?
Answer:
a =4,b=2, c=3
Step-by-step explanation:
On May 1st, Jay’s mom gives him 1 cent. Each day, she pays him double the amount she paid the day before. How much money did Mike earn in total by May 15?
Answer: $1.83
Step-by-step explanation:
1. Solve this problem: 1+2+4+6+8+10+12+14+16+18+20+22+24+26. There are 15 numbers for 15 days. You want to solve this because each day is doubled. For example: first day is 1 cent, second day is 2 cents, third day is 4 cents, and so on.
2. Answer is 183 cents.
3. Convert 183 cents to dollars.
4. Your answer is $1.83.
Hope it helps!
Answer:
$1.83.
You start with one cent, and add two more cents after that day.
Compute the flux of the vector field LaTeX: \vec{F}=F → =< y + z , x + z , x + y > though the unit cubed centered at origin.
Assuming the cube is closed, you can use the divergence theorem:
[tex]\displaystyle\iint_S\vec F\cdot\mathrm dS=\iiint_T\mathrm{div}\vec F\,\mathrm dV[/tex]
where [tex]S[/tex] is the surface of the cube and [tex]T[/tex] is the region bounded by [tex]S[/tex].
We have
[tex]\mathrm{div}\vec F=\dfrac{\partial(y+z)}{\partial x}+\dfrac{\partial(x+z)}{\partial y}+\dfrac{\partial(x+y)}{\partial z}=0[/tex]
so the flux is 0.
find the slope of the line y = 4
Answer:
Brainleist!
Step-by-step explanation:
0
there is no y=mX+b
there is no x no XXXX
that means the slope must be 0 (bc theres a y)
Sorry if my explanation is bad... let me know in comments if u need more help
is this a function {(-2, 6), (-3, 7), (-4, 8), (-3, 10)}
No, that is not a function.
To be a function, each different input (x) needs a different output (y)
In the given function there are two -3’s as inputs and they have different y values, so it can’t be a function.
Answer: no
Step-by-step explanation: To determine if a relation is a function, take a look at the x–coordinate of each ordered pair. If the x–coordinate is different in each ordered pair, then the relation is a function.
Note that the only exception to this would be that if the x-coordinate pairs up with the same y-coordinate in a relation more than once, it's still classified ad a function.
Ask yourself, do any of the ordered pairs
in this relation have the same x-coordinate?
Well by looking at this relation, we can see that two
of the ordered pairs have the same x-coordinate.
In this case, the x-coordinate of 3 appears twice.
So no, this relation is not a function.
Write the perimeter of the triangle as a
simplified expression.
3y + 5
бу
Y-4
Answer:
10y+1
Step-by-step explanation:
The perimeter is the three sides added together
3y+5+6y+y-4=
10y+1
Answer:
[tex]\huge\boxed{P_\triangle=10y+1}[/tex]
Step-by-step explanation:
The formula of a perimeter of a triangle:
[tex]P_\triangle=a+b+c[/tex]
We have:
[tex]a=3y+5,\ b=6y,\ c=y-4[/tex]
Substitute:
[tex]P_\triangle=(3y+5)+(6y)+(y-4)=3y+5+6y+y-4[/tex]
Combine like terms:
[tex]P_\triangle=(3y+6y+y)+(5-4)=10y+1[/tex]
square root of 49/64 answered as a fraction
Answer:
Hey there!
That would be 7/8
Let me know if this helps :)
Find the measure of F. A. 44 B. 88 C. 90 D. 46
Answer:
A. 44º
Step-by-step explanation:
The sum of internal angles in a triangle is equal to 180 degrees, whereas the sum for a square is equal to 360 degrees. Given that three triangles depicted on figure constructs a square, it is to conclude that each is an isosceles triangle. The following relations are presented:
1) [tex]e + 92^{\circ} = 180^{\circ}[/tex] Given
2) [tex]a = b[/tex], [tex]c = d[/tex] Given
3) [tex]a + b + 92^{\circ} = 180^{\circ}[/tex] Given.
4) [tex]c + d + e = 180^{\circ}[/tex] Given.
5) [tex]b + c = 90^{\circ}[/tex] Given.
6) [tex]2\cdot a + 92^{\circ} = 180^{\circ}[/tex] 2) in 3)
7) [tex]a = 44^{\circ}[/tex] Algebra
8) [tex]b = 44^{\circ}[/tex] By 2)
9) [tex]b= f[/tex] Alternate internior angles.
10) [tex]f = 44^{\circ}[/tex] By 8). Result
Hence, the answer is A.
Determine if the matrix is symmetric.
(-1 -5 -9 8)
The transpose of the given matrix is nothing. Because this is_____to the given matrix, the given matrix_____symmetric.
Answer:
because this is equal to the given matrix, the given matrix is symmetric.
Step-by-step explanation:
A symmetric matrix is a square matrix which has same number of rows and columns. Square matrix is equal to transpose. Equal matrices have equal dimensions. The given matrix is symmetric because the rows and columns are equally distributed.
The mouse weights (in grams) of a random sample of 100 mice involved in a nutrition experiment are: Interval 41.5----43.5 43.5-----45.5 45.5------47.5 47.5--------49.5 49.5--------51.5 51.5----53.5 53.5----55.5 55.5---- 57.5 57.5--------59.5 Frequency Interval 3 7 13 24 15 16 13 7 2Required:a. Find the mean of the weight of the mice. (Round to two decimal places.)b. Find the standard deviation of the weight of the mice. (Round to two decimal places.)
Answer:
(a) The mean of the weight of the mice is 50.26 grams.
(b) The standard deviation of the weight of the mice is 14.08 grams.
Step-by-step explanation:
(a)
The mean is given as follows:
[tex]\bar X=\frac{\sum f_{i}x_{i}}{\sum f_{i}}[/tex]
[tex]=\frac{5026}{100}\\\\=50.26[/tex]
Thus, the mean of the weight of the mice is 50.26 grams.
(b)
Compute the standard deviation as follows:
[tex]s=\frac{1}{\sum f_{i}-1}[\sum f_{i}x_{i}^{2}-\frac{1}{\sum f_{i}}(\sum f_{i}x_{i})^{2}][/tex]
[tex]=\frac{1}{100-1}[254001-\frac{1}{100}(5026)^{2}]\\\\=\frac{1}{99}\times 1394.24\\\\=14.08323\\\\\approx 14.08[/tex]
Thus, the standard deviation of the weight of the mice is 14.08 grams.
According to a Pew Research Center study, in May 2011, 40% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students. She selects 341 community college students at random and finds that 147 of them have a smart phone. Then in testing the hypotheses:
H0: p = 0.4 versus
Ha: p > 0.4,
what is the test statistic?
z =________________. (Please round your answer to two decimal places.)
B.)
According to a Pew Research Center study, in May 2011, 33% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students. She selects 349 community college students at random and finds that 138 of them have a smart phone. In testing the hypotheses:
H0: p = 0.33 versus
Ha: p > 0.33,
she calculates the test statistic as z = 2.5990.
Then the p‑value =________________ .
(Please round your answer to four decimal places.)
Answer:
z = 1.17
P - value = 0.0047
Step-by-step explanation:
A.
From the given information;
H0: p = 0.4 versus
Ha: p > 0.4,
Let's calculate the population proportion for the point estimate;
the population proportion [tex]\hat p[/tex] = 147/341
the population proportion [tex]\hat p[/tex] = 0.431085
However; the test statistics can therefore be determined by using the formula:
[tex]z = \dfrac{\hat p - p_o}{\sqrt{\dfrac{p_o(1-p_o)}{n}}}[/tex]
[tex]z = \dfrac{0.431085 - 0.40}{\sqrt{\dfrac{0.40(1-0.40)}{341}}}[/tex]
[tex]z = \dfrac{0.031085}{\sqrt{\dfrac{0.40(0.60)}{341}}}[/tex]
[tex]z = \dfrac{0.031085}{\sqrt{\dfrac{0.24}{341}}}[/tex]
[tex]z = \dfrac{0.031085}{\sqrt{7.03812317 \times 10^{-4}}}[/tex]
[tex]z = \dfrac{0.031085}{0.0265294613}[/tex]
z = 1.1717
z = 1.17 to two decimal places
B.)
The null and the alternative hypothesis is given as:
H0: p = 0.33 versus
Ha: p > 0.33,
The z = 2.5990.
The objective here is to determine the p-value from the z test statistics.
P - value = P(Z > 2.5990)
P- value = 1 - P(Z < 2.5990)
P - value = 1 - 0.9953
P - value = 0.0047
Rewrite to make true: There are five terms in the series (attached)
Answer:
There are six terms in the series
Step-by-step explanation:
We can see that n starts from 0, and ends at 5. There are therefore 6 terms in this series - as 0 is included. Therefore there will be 6 terms in this series, not 5.
There are six terms in the given series.
The Masmim family’s monthly budget is shown in the circle graph provided in the image. The family has a current monthly income of $5,000. How much money do they spend on food each month? A. $250 B. $500 C. $750 D. $1,100 Please include ALL work! <3
The correct answer is $750
Explanation:
The total of food the Masmin family spend according to the graph is 15%. Now, to know the amount of money this represents, it is necessary to find the 15% of $5000, which is the total budget. The steps to do this are shown below.
1. To calculate the percentage of a given number, first, write all values
5000 = 100%
x = 15%
2. Use cross multiplication, this means you multiply 5000 by 15 and x by 15
x 100 = 75000
3. Solve the equation to find x or the 15% of 5000
x = 75000 ÷ 100
x = 750
You work for a pharmacy and monthly sales of asthma inhalers in your pharmacy follows a normal distribution with a mean of 191 inhalers per month and a standard deviation of 21 due to a storm the next shipment of inhalers did not arrive. The pharmacy only has 163 inhalers currently in stock and available to sell for the current month. What is the z score corresponding to selling 163 inhalers?
Answer: -1.33 .
Step-by-step explanation:
Formula to find the Z-score :
[tex]Z=\dfrac{\text{Expected value - Mean}}{\text{Standard deviation}}[/tex]
Given: Mean = 191 and Standard deviation = 21
Then , the z-score corresponding to the expected value of 163 will be :
[tex]Z=\dfrac{163-191}{21}\\\\=\dfrac{-28}{21}\approx-1.33[/tex]
Hence, the z score corresponding to selling 163 inhalers is -1.33 .
let d equal the distance in meters and t equal the time in seconds. Which is a direct variation equation for this relationship
Answer:
d = s x t
Step-by-step explanation:
The formula for distance.
George buys a pizza he eats 3-8 of pizza for lunch and 1-4 of pizza for dinner what fraction of pizza has George eaten
Answer:
George has eaten 5/8 of the pizza
Step-by-step explanation:
Step 1: Multiple 1/4 by 2 so it shares a common denominator with 3/8
1.4 x 2 = 2/8
Step 2: Because they share a denominator you can add the numerator together
2/8 + 3/8 = 5/8
Therefore George has eaten 5/8(Five Eigths) of the pizza
George has eaten 5 by 8 of the pizza
The calculation is as follows:
Here we have to Multiple 1 by 4 with 2 so it shares a common denominator with 3 by 8
[tex]1.4 \times 2 = 2\div 8[/tex]
Now
since they share a denominator you can add the numerator together
So, [tex]\frac{2}{8} + \frac{3}{8} = \frac{5}{8}[/tex]
Learn more: https://brainly.com/question/17429689?referrer=searchResults
xThe closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $18 and $28 per share. What is the probability that the stock price will be: More than $20? (Round your answer to 4 decimal places.)
Answer:
The probability is [tex]P(X > 20 ) = 0.8[/tex]
Step-by-step explanation:
From the question we are told that
The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $18 and $28 per share.
Given that the stock is uniformly distributed then the probability that the stock price will be more than $20 is mathematically evaluated as
[tex]P(X > 20 ) = 1 - P(X < 20 )[/tex]
Since it is uniformly distribute between $18 and $28 per share then we can solve is as follows
=> [tex]P(X > 20 ) = 1 - [\frac{ 20 - 18 }{28 -18} ][/tex]
=> [tex]P(X > 20 ) = 0.8[/tex]
The volume of a spherical sculpture is 256 ft³. Rhianna wants to estimate the surface area of the sculpture. To do the estimate, she approximates π using 3 in both the surface area and volume formulas for a sphere.
Using this method, what value does she get for the approximate surface area of the sculpture?
Answer:
192 [tex]ft^2[/tex]
Step-by-step explanation:
Given that
Volume of spherical sculpture = 256 ft³
[tex]\pi[/tex] is used as 3.
To find:
Surface area of sculpture = ?
Solution:
First of all, let us learn about the formula for Volume and Surface Area of Sphere:
1. [tex]Volume =\frac{4}{3}\pi r^3[/tex]
2. [tex]Surface\ Area = 4\pi r^2[/tex]
Given volume is 256 ft³.
[tex]256 = \dfrac{4}{3}\pi r^3\\\Rightarrow 256 = \dfrac{4}{3}\times 3 r^3\\\Rightarrow 256 = 4 r^3\\\Rightarrow r^3=64\\\Rightarrow \bold{r = 4\ ft}[/tex]
Now, let us put r = 4 in the formula of Surface Area to find the value of Surface Area:
[tex]Surface\ Area = 4\pi 4^2 = 4 \times 3 \times 16 = \bold{192\ ft^2}[/tex]
So, approximate surface area of sculpture is 192 [tex]ft^2[/tex].
Answer:
192
Step-by-step explanation:
Which equation has no solution?
Answer:
number 3
Step-by-step explanation:
PLEASE HELP WITH THIS 3 QUESTIONS.... a) Sarah had a balance of $155 in her bank account at the start of the week. She withdrew $65.50 on Monday, $23.25 on Wednesday, and $26.45 on Thursday. On Friday she deposited $165.30. Write an expression that represents Sarah's spending. * b) Simplify your expression (using PEMDAS). How much money is in Sarah’s account at the end of the week? * c) Find the difference between Sarah’s bank account balance at the start of the week and her current balance. *
Answer:
155 + 165.3 - 65.5 - 23.25 - 26.45
At the end of the week, she had a total of $205.10.
The difference between her starting balance and the current balance is -$50.1.
or
The difference between her current balance and starting balance is $50.1.
Step-by-step explanation:
She had $155 dollars in the starting = +155
She withdrew $65.5 = -65.5
She withdrew another $23.25 = -23.25
She withdrew another $26.45 = -26.45
She deposited $165.3 = +165.3
The expression looks like:
155 + 165.3 - 65.5 - 23.25 - 26.45
We could simplify the expression:
155 + 165.3 - 65.5 - 23.25 - 26.45
=> 320.3 - 88.75 - 26.45
=> 320.3 -115.2
=> 205.1
At the end of the week, she had a total of $205.10.
Starting balance - Current balance:
=> 155 - 205.1
=> -$50.1
The difference between her starting balance and the current balance is -$50.1.
If it is Current Balance - Starting Balance:
=> 205.1 - 155
=> $50.1
The difference between her current balance and starting balance is $50.1.
y varies directly as z, y=180, z=10 , find ywhen z=14
Step-by-step explanation:
To find the value of y when z = 14 we must first find the relationship between them
The statement
y varies directly as z is written as
y = kz
where k is the constant of proportionality
when y = 180
z = 10
180 = 10k
Divide both sides by 10
k = 18
The formula for the variation is
y = 18z
When z = 14
y = 18(14)
y = 252Hope this helps you
I NEED HELP! I will name the person who answers this corectly the Brainliest
Answer:
[tex]\large \boxed{\sf \bf \ \ 12 \ \ }[/tex]
Step-by-step explanation:
Hello, we can see that this shape is ...
...at the left, a right triangle of side = 2
area = (2*2)/2 =2
... at the middle, a square of side = 2
area = 2*2 = 4
... at the right, a right triangle of sides 2 and 6
area= (2*6)/2 = 6
So the total is 2 + 4 + 6 = 12
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
