what is the degree of f(x) = (x + 3)(x - 1)(2x + 2)?
A. 1 B.2 C.3 D.4
Answer:
I believe the answer is c) 3
Step-by-step explanation:
f(x) = (x + 3)(x - 1)(2x + 2)
x(x) + x(-1) + 3(x) + 3(-1)
f(x) = (x^2 - x + 3x - 3)(2x + 2)
f(x) = (x^2 + 2x - 3)(2x + 2)
2x(x^2) + 2x(2x) + 2x(-3) + 2(x^2) + 2(2x) + 2(-3)
f(x) = (2x^3 + 4x^2 - 6x + 2x^2 - 6)
f(x) = (2x^3 + 6x^2 - 6x - 6)
A researcher initially plans to take an SRS of size 160 from a certain population and calculate the sample mean. Later, the researcher decides to increase the sample size so that the standard deviation of the sampling distribution of will be half as big as when using a sample size of 160.
What sample size should the researcher use?
Answer:
640
Step-by-step explanation:
Using the Central Limit Theorem, it is found that the researcher should use a sample size of 640.
Central Limit Theorem The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]. From this, we can take that the standard deviation is inversely proportional to the square root of the sample size.Hence, for the standard deviation to be cut be half, the sample size has to be multiplied by 4, which means that it should be of 4 x 160 = 640.
To learn more about the Central Limit Theorem, you can take a look at https://brainly.com/question/25581475
solve x please i will give brainleset thingy
Answer:
x = 84
Step-by-step explanation:
1. Solve for m<R
The sum of angles in a triangle is 180 degrees, regardless of each individual angle measure in the triangle. One can apply that to triangle QRS by stating that;
m<SQR + m<R + m<QSR = 180
Substitute
68 + 3x + m<R = 180
Inverse operations,
m<R = 112 - 3x
2. Solve or m<PSR
Verticle angles theorem states that when two lines intersect, four angles are formed. The angles that are opposite each other are congruent. Using this, one can concluce that;
m<TSU = m<PSR = 4x
3. Solving for x
Now all one has to do is apply the sum of angles in a triangle theorem for triangle PSR
m<P + m<R + m<PSR = 180
Substitute,
x + 112 - 3x + 4x = 180
Simplify
2x + 112 = 180
Inverse operations
2x + 112 = 180
-112 -112
2x = 168
/5 /5
x = 84
Given u( – 5) = -5, u'( – 5) = 2, U( – 5) = 6, v'( – 5) = 4, find w'( – 5).
Give exact answers.
a. w(2) = 5u(2) + 8v(2)
w'(-5) =
b. w(x) = u(z)v(3)
w'(-5) =
u(30)
c. W(2) =
v(x)
w'(-5) =
u(2)
d. W(x) =
u(2) + v()
w'(-5) =
(a) w(x) = 5u(x) + 8v(x)
Differentiating with the sum rule gives
w'(x) = 5u'(x) + 8v'(x)
so that
w' (-5) = 5u' (-5) + 8v' (-5)
… = 5×2 + 8×4 = 42
(b) w(x) = u(x) v(x)
Differentiate using the product rule:
w'(x) = u'(x) v(x) + u(x) v'(x)
Then
w' (-5) = u' (-5) v (-5) + u (-5) v' (-5)
… = 2×6 + (-5)×4 = -8
(c) w(x) = u(x) / v(x)
Quotient rule:
w'(x) = (u'(x) v(x) - u(x) v'(x) ) / v(x) ²
Then
w' (-5) = (u' (-5) v (-5) - u (-5) v' (-5) ) / v (-5)²
… = (2×6 - (-5)×4) / 6² = 32/36 = 8/9
(d) w(x) = u(x) / (u(x) + v(x) )
Chain and quotient rule:
w'(x) = (u'(x) (u(x) + v(x)) - u(x) (u(x) + v(x))' ) / (u(x) + v(x) )²
… = (u'(x) (u(x) + v(x)) - u(x) (u'(x) + v'(x))) / (u(x) + v(x) )²
Then
w' (-5) = (u' (-5) (u (-5) + v (-5)) - u (-5) (u' (-5) + v' (-5))) / (u (-5) + v (-5) )²
… = (2×((-5) + 6) - (-5)×(2 + 4)) / ((-5) + 6)²
… = (2×1 + 5×6) / 1² = 32
Elijah invested $79,000 in an account paying an interest rate of 2% compounded
daily. Landon invested $79,000 in an account paying an interest rate of 3 %
compounded continuously. After 7 years, how much more money would Landon have
in his account than Elijah, to the nearest dollar?
Answer: He would have 16590 but if we want to know in total
it would be, 11060 (just from the percent) if you want to know in total add 16590 and 79,000 which would be (95,590 for Landon) and (Elijah would be 90060) in total
Step-by-step explanation:So in total Landon would have:
Landon-(95,590)
Elijah-(90,060)
So Landon would have 5,530 more dollars in 7 years than Elijah.
Calculate the product:
2/9 x 63
A.
7
B.
14
C.
18
D.
45
Answer:
14
Explanation: 2/9x 63= 2x 63/9= 2x7
Answer:
14
Step-by-step explanation:
i believe so....
The value of y varies directly with x and y= 7.2 when x= 1.6, find y when x=2.4
Answer:
When x = 2.4, we have y = 10.8
Step-by-step explanation:
A direct variation of two variables, x, and y, can be written as:
y = k*x
Where k is a constant, called the constant of variation.
We know that y = 7.2, when x = 1.6
Then we can replace these two in the above equation to get:
7.2 = k*1.6
Now we can solve this for k:
7.2/1.6 = k = 4.5
Then our relation is:
y = 4.5*x
Now we want to find the value of y, when x = 2.4
Then we just need to replace x by 2.4 in the above equation:
y = 4.5*(2.4) = 10.8
y = 10.8
help! is it e? I’ll give u Brainly
Answer:
B
Step-by-step explanation:
If you look at 3 on the X-axis and go down 4 then you will get point B as your answer.
Answer:
E is the correct answer because A is (-4,-3), B is (-4,3), C is (5,1), D is (4,-3), E is (3,-4), and F is (-2,-4)
Suppose there are 4 defective batteries in a drawer with 10 batteries in it. A sample of 3 is taken at random without replacement. Let X denote the number of defective batteries in the sample. Find the probability that the sample contains a) Exactly one defective battery b) at most one defective battery. c) at least one defective battery.
Answer:
a.) 0.5
b.) 0.66
c.) 0.83
Step-by-step explanation:
As given,
Total Number of Batteries in the drawer = 10
Total Number of defective Batteries in the drawer = 4
⇒Total Number of non - defective Batteries in the drawer = 10 - 4 = 6
Now,
As, a sample of 3 is taken at random without replacement.
a.)
Getting exactly one defective battery means -
1 - from defective battery
2 - from non-defective battery
So,
Getting exactly 1 defective battery = ⁴C₁ × ⁶C₂ = [tex]\frac{4!}{1! (4 - 1 )!}[/tex] × [tex]\frac{6!}{2! (6 - 2 )!}[/tex]
= [tex]\frac{4!}{(3)!}[/tex] × [tex]\frac{6!}{2! (4)!}[/tex]
= [tex]\frac{4.3!}{(3)!}[/tex] × [tex]\frac{6.5.4!}{2! (4)!}[/tex]
= [tex]4[/tex] × [tex]\frac{6.5}{2.1! }[/tex]
= [tex]4[/tex] × [tex]15[/tex] = 60
Total Number of possibility = ¹⁰C₃ = [tex]\frac{10!}{3! (10-3)!}[/tex]
= [tex]\frac{10!}{3! (7)!}[/tex]
= [tex]\frac{10.9.8.7!}{3! (7)!}[/tex]
= [tex]\frac{10.9.8}{3.2.1!}[/tex]
= 120
So, probability = [tex]\frac{60}{120} = \frac{1}{2} = 0.5[/tex]
b.)
at most one defective battery :
⇒either the defective battery is 1 or 0
If the defective battery is 1 , then 2 non defective
Possibility = ⁴C₁ × ⁶C₂ = 60
If the defective battery is 0 , then 3 non defective
Possibility = ⁴C₀ × ⁶C₃
= [tex]\frac{4!}{0! (4 - 0)!}[/tex] × [tex]\frac{6!}{3! (6 - 3)!}[/tex]
= [tex]\frac{4!}{(4)!}[/tex] × [tex]\frac{6!}{3! (3)!}[/tex]
= 1 × [tex]\frac{6.5.4.3!}{3.2.1! (3)!}[/tex]
= 1× [tex]\frac{6.5.4}{3.2.1! }[/tex]
= 1 × 20 = 20
getting at most 1 defective battery = 60 + 20 = 80
Probability = [tex]\frac{80}{120} = \frac{8}{12} = 0.66[/tex]
c.)
at least one defective battery :
⇒either the defective battery is 1 or 2 or 3
If the defective battery is 1 , then 2 non defective
Possibility = ⁴C₁ × ⁶C₂ = 60
If the defective battery is 2 , then 1 non defective
Possibility = ⁴C₂ × ⁶C₁
= [tex]\frac{4!}{2! (4 - 2)!}[/tex] × [tex]\frac{6!}{1! (6 - 1)!}[/tex]
= [tex]\frac{4!}{2! (2)!}[/tex] × [tex]\frac{6!}{1! (5)!}[/tex]
= [tex]\frac{4.3.2!}{2! (2)!}[/tex] × [tex]\frac{6.5!}{1! (5)!}[/tex]
= [tex]\frac{4.3}{2.1!}[/tex] × [tex]\frac{6}{1}[/tex]
= 6 × 6 = 36
If the defective battery is 3 , then 0 non defective
Possibility = ⁴C₃ × ⁶C₀
= [tex]\frac{4!}{3! (4 - 3)!}[/tex] × [tex]\frac{6!}{0! (6 - 0)!}[/tex]
= [tex]\frac{4!}{3! (1)!}[/tex] × [tex]\frac{6!}{(6)!}[/tex]
= [tex]\frac{4.3!}{3!}[/tex] × 1
= 4×1 = 4
getting at most 1 defective battery = 60 + 36 + 4 = 100
Probability = [tex]\frac{100}{120} = \frac{10}{12} = 0.83[/tex]
The price of a shirt has been discounted by $20. The sale price is $24.95. What percent of the original list price is the discount?
(a) Use the verbal description to write a verbal model.
o change in price = (original price)/(percent)
o change in price = (percent)(original price)
O change in price = (percent) - (original price)
o change in price = (original price) + (percent)
O change in price = (percent)/(original price)
(b) Assign labels to the quantities in the verbal model.
--Select-
= 20
---Select-
---Select-
= 44.95
(C) Use the labels to write a mathematical model.
(d) Solve the problem. (Round your answer to the nearest whole number.)
%
Answer:
this is an example
Step-by-step explanation:
There are a few different ways to approach this problem, including the following two methods.
1) Find 20% of the original price, then subtract that amount from the original price.
To find a percentage of a number, you multiply the number by the percentage. (You are finding a part of a whole.)
20% = 20/100 = 1/5 or 20% = 0.20
Original Price: $24 Find 20% of $24. (Note: "of" is taking part of a whole, so you multiply.)
0.20 x 24 = 4.80 This is the mark down, or the amount you subtract from original price.
Sale Price = Original Price - Mark Down
= 24.00 - 4.80
= 19.20
2) If you save 20%, you are still paying 80%. (100-20 = 80) Therefore the sale price is 80% of the original price.
80% = 80/100 = 4/5 or 80% = 0.80
Sale Price = 80% of Original Price
= 0.80 x 24
= 19.20
5/8 * z = 1/2 what is the value of z
Answer:
z = 4/5
Step-by-step explanation:
Of 50 laptop computers available in a supply room, 20 have a wireless card, 12 have aCD/DVD burner, and 24 have neither. In an experiment, a laptop is randomly selected from thesupply room and whether or not it has a wireless card or a CD/DVD burner recorded. Using W to denote the event that the selected laptop has a wireless card and C to denote the event that the selected laptop has a CD/DVD burner, symbolically denote the following events and find the number of laptop computers represented by each.
Required:
a. The selected laptop has both a wireless card and a CD/DVD burner.
b. The selected laptop has either a wireless card or a CD/DVD burner.
c. The selected laptop has a CD/DVD burner only.
d. The selected laptop has either a wireless card or a CD/DVD burner but not both.
Answer:
ANSWER IS D
Step-by-step explanation:
forgive me if is wrong
how do you solve for x? 3 + 2x = 4y
Answer:
x= 2y - 3/2
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
x=2y - 3/2
Step-by-step explanation:
Tyrone is building a fence around his square garden. The area of the garden is 484 square ft How many feet of fencing does Tyrone need for each side of the fence?
Answer:
121 feet
Step-by-step explanation:
Equation:
484 / 4 = 121
Word Explanation:
If there are 4 sides in a square and the total of all 4 sides is 484, We have to divide 484 by 4 and get 121 feet.
The perimeter of the square fence is P = 88 feet and Tyrone needs 22 feet of fence on each side
What is the perimeter of a square?The perimeter of a square is given by four times the length of its each side
The equation for the perimeter of the square with the side 'a' is given by
Perimeter of Square = 4a
Given data ,
Let the perimeter of the square be represented as P
Now , the equation will be
Let the side length of the square be a²
The area of the square is A = 484 feet²
Taking square roots on both sides of the equation , we get
A = a²
a² = 484
a = 22 feet
Now , perimeter of the square P = 4a
Substituting the values in the equation , we get
Perimeter of the square P = 4 x 22
Perimeter of the square P = 88 feet
Hence , the perimeter of the square is 88 feet
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Which is not a correct name for the line showing?
Answer:
The third one
Step-by-step explanation:
mP is not correct
PLEASE HELP ME!!!!
For the given functions f and g, find the indicated composition.
f(x) = -6x +5, g(x) = 2x + 8; (g of)(x)
A. - 12x - 2
В.- 12x + 53
C. 12x + 18
D.- 12x + 18
Answer:
D. -12x + 18
Step-by-step explanation:
f(x) = -6x +5; g(x) = 2x + 8
[g o f](x) = g(f(x))
this means that in g(x), everywhere there's an x, f(x) replaces it. [g o f](x) is represented at the following: (f(x) is in bold)
g(f(x)) = 2(-6x +5) + 8 distribute the 2 to (-6x + 5)
g(f(x)) = -12x + 10 + 8 combine like terms
g(f(x)) = -12x + 18
What is the answer for this?
Frank and Carl do some fundraising for their scout group. Together they raised 237 dollars. If Frank raised m dollars, and Carl raised
137 dollars:
Write an equation that represents the relationship between the amounts each contributed. (Note that we are not looking to solve for m yet.)
Answer:
237 = m + 137
this is the equation showing the relationship
Xavier's teacher gave an extra / of a grade point for each correct bonus question on a test. Xavier answered 9 bonus questions correc
How many extra points did he earn?
Hi there! Your answer to this question would be 90%..
Step By Step Explanation:
So we know that 100% is the average grade for an correct for an entire test.
But how can we find 90%?
Let think like this. 10=100%.
Well if 10 is 100% then 9 would be 90% since every 1 of 10 is 10%.
Final Result: 90%
y = x ÷ 2 when y is -10
Answer:
The answer is 20.
X = -20
Answer: -20
Step by step explanation:
-10=x÷2
•2 •2
-20=x
Can you help me understand question number 2?
Given:
[tex]\{(x,y)|5x-7y<0, x\in I, y\in I\}[/tex]
To find:
The test point is in the solution set for the linear inequality.
Solution:
The inequality is
[tex]5x-7y<0[/tex]
Here, [tex]x\in I, y\in I[/tex]. It means, both x and y both are integers. So, the option D is incorrect because 1.5 and 3.5 are not integers.
For option A, the point is (-2,-1).
Putting x=-2 and y=-1 in the given inequality, we get
[tex]5(-2)-7(-1)<0[/tex]
[tex]-10+7<0[/tex]
[tex]-3<0[/tex]
This statement is true. So, the point (-2,-1) is in the solution set.
For option B, the point is (-4,-3).
Putting x=-4 and y=-3 in the given inequality, we get
[tex]5(-4)-7(-3)<0[/tex]
[tex]-20+21<0[/tex]
[tex]1<0[/tex]
This statement is false. So, the point (-4,-3) is not in the solution set.
For option C, the point is (-2,-4).
Putting x=-2 and y=-4 in the given inequality, we get
[tex]5(-2)-7(-4)<0[/tex]
[tex]-10+28<0[/tex]
[tex]18<0[/tex]
This statement is false. So, the point (-2,-4) is not in the solution set.
Therefore, the correct option is A.
What is 6(8) + 4(23)? Ty !
Answer: 140
Step-by-step explanation:
6(8) = 48
4(23) = 92
48 + 92 = 140
Because of this, 6(8) + 4(23) = 140.
Answer: 41 i think
Step-by-step explanation:
Help i can’t find this answer anywhere.
Answer:
B, I think that's the answer
With compound interest, what happens when you start compounding more and more frequently?
a. there is no correlation between compound c. the computed value gets larger
interest and the computed value
b. the computed value stays the same d. the computed value gets smaller
Please select the best answer from the choices provided
A
B
ОООС
Answer:
The further compounding cycles in a given year, the greater the effect on the valuation of potential investment. Therefore, the more interest-posting dates, irrespective of the interest rate, the more compounding raises the account balance.
Step-by-step explanation:
Answer:
C
the computed value gets larger
Step-by-step explanation:
Need help on only 27 please need ASAP thanks
Answer:
8 is not in the solution set
Step-by-step explanation:
Given, -y + 7 < -4
To find out if 8 is in the solution set, substitute y = 8 in the inequality and solve to see if the statement would be true.
Thus:
-8 + 7 < -4
-1 < -4
This -1 is less than -4. This is actually not TRUE. -1 is rather greater than -4.
Therefore, 8 is not in the solution set.
graph: y-3= 1/2(x+2)
Answer: (-8,0) (0,4)
Step-by-step explanation: graphing it would be for coordinate one (-8,0) and for the second coordinate it would be (0,4.) and for the x y chart it goes for x's it goes -8 and then next is 0 and for the y's, it's 0 then next is 4. give me brainliest thankssss
F
is inversely proportional to
d
2
.
When
F
=
18
,
d
=
2
Work out
F
when
d
=
6
Answer:
12
Step-by-step explanation:
[tex]F \alpha \frac{1}{d^{2} }[/tex]
[tex]F = \frac{K}{d^{2} }[/tex]
When F = 18; d = 2
[tex]18 = \frac{K}{2^{2} }[/tex]
[tex]18 = \frac{K}{4}[/tex]
Cross multiply;
18 x 4 = K
72 = K
There the equation connecting F and [tex]d^{2}[/tex] is
[tex]F = \frac{72}{d}[/tex]
Now, Find F when d = 6
All you do is to substitute d = 6 in to [tex]F = \frac{72}{d}[/tex]
[tex]F = \frac{72}{6}[/tex]
Therefore;
F = 12
Please mark me brainiest if correct.
Can someone solve this please
What is the probability of randomly choosing an odd single digit number or the number 8
Q6.
Nimes was driving to a hotel.
He looked at his Sat Nav at 13 30
Time
1330
Distance to destination
65 miles
Nimec arrived at the hotel at 14 48
Work out the average speed of the car from 13 30 to 14 48
You must show all your working.
Answer:
The average speed at which Nimes drove his car was 50 miles per hour.
Step-by-step explanation:
Given that Nimes was driving to the hotel at 1:30 p.m., being 65 miles away from it, and finally arriving at its destination at 2:48 p.m., to determine the average speed at which the circle should be made. following calculation:
14:48 - 13:30 = 1:18
60 = 100
18 = X
(18 x 100) / 60 = X
1,800 / 60 = X
30 = X
65 / 1.30 = X
50 = X
Therefore, the average speed at which Nimes drove his car was 50 miles per hour.