Use the polynomial remainder theorem. It says that a polynomial \(f(x)\) has remainder \(f(c)\) upon division by \(x-c\).
Here we have
\(f(x)=x^4+3x^3-8x^2+5x-9\)
and \(c=-5\), so the remainder is
\(f(-5)=(-5)^4+3(-5)^3-8(-5)^2+5(-5)-9=\boxed{16}\)
PLEASE HELP!! Rational functions, find the sum
Answer:
Answer is option D
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Problem 1.) A researcher claims that 96% of college graduates say their college degree has
been a good investment. In a random sample of 2000 graduates, 1500 say their college degree has
been a good investment. At a = 0.05 is there enough evidence to reject the researcher's claim?
Answer:
|Z| = |-52.5| = 52.5 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
We rejected the researcher's claim
A researcher do not claims that 96% of college graduates say their college degree has been a good investment.
Step-by-step explanation:
Explanation:-
Given data A researcher claims that 96% of college graduates say their college degree has been a good investment.
Population proportion 'P' = 0.96
Q = 1-P = 1- 0.96 = 0.04
In a random sample of 2000 graduates, 1500 say their college degree has
been a good investment.
Sample proportion
\(p^{-} = \frac{x}{n} = \frac{1500}{2000} = 0.75\)
Level of significance ∝ = 0.05
\(Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96\)
Test statistic
\(Z = \frac{p^{-} - P }{\sqrt{\frac{PQ}{n} } }\)
\(Z = \frac{0.75 - 0.96 }{\sqrt{\frac{0.96 X 0.04}{2000} } }\)
\(Z = \frac{-0.21}{0.00435} = -52.5\)
|Z| = |-52.5| = 52.5 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
We rejected the researcher's claim
Conclusion:-
A researcher do not claims that 96% of college graduates say their college degree has been a good investment.
witch expression represents a number 5 times the difference of 6 and 2
Answer:
i think it is 20
Step-by-step explanation:
6-2=4
4×5=20
A number between 10 and 100 is four times the sum of its digits. If the product of two digits is 8, find the sum of digits of the number.
Answer:
24 is the number. The sum of its digits is 6.
Step-by-step explanation:
There are four two-digit numbers the product of whose digits is 8: 18, 24, 42, and 81. Of these numbers, 24 is four times the sum of its digits:
24 = 4 × 6 = 4 × (2 + 4)
A father is four times as old as his son. In two years the will have been five times as old as his son was two years ago. How old is the father?
Answer:
Q13)A man is four times as old as his son. After 20 years, he will be twice as old as his son at that time. Find their present ages. Present age of the father is = 4 x = 4 × 10 = 40 4x=4\times10=40 4x=4×10=40 years.
Been stuck on this problem for the past 40 mins! Please help me
Answer:
EFDBAC
Step-by-step explanation:
The math clues tell you ...
F ≈ 6.23×1.7 -8.73 = 10.591 -8.73 = 1.861 ≈ 2
A = (3 1/3)/(2/3) = (10/3)/(2/3) = 10/2 = 5
So, the seat occupants are ...
__ F __ __ A __
Since Freddy is one of two who sit between Bella and Ella, we know that Bella and Ella must be in seats 1 and 4. Charlie is in an end seat, so must be in seat 6. That leaves Danielle in seat 3. Danielle does not sit next to Ella, so Bella must be in seat 4.
The seat order is ...
EFDBAC
Josh bought 8 chocolate bars for $7.00. What is the unit rate? ( round to the nearest cent)
Answer:
87
Step-by-step explanation:
If g(x) = x2 + 3, find g(4).
11
19
16
8
Two thousand nine hundred seveteen
Answer:
in written form, it would be 2,917
hope this helps! <3
Why are all of the questions that I ask I get the wrong answers I paid to be able to use this site and all of the answers I get on this site are wrong
Answer:
I have no idea
Step-by-step explanation:
double check with other people before trusting people from the internet some people would rather see you fail than succeed hope you figure out whatever problems you were having good luck
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Answer:
they all go straight across
Step-by-step explanation:
Answer:
Go across from each
Step-by-step explanation:
What is the volume in milliliters of 7.06 g of acetone?
Express your answer to three significant figures and include the appropriate units.
Answer:
V = 9 mL
Step-by-step explanation:
Given that,
The mass of acetone, m = 7.06 g
The density of acetone, d = 0.784 g/cm³
We need to find the volume of 7.06 g of acetone.
We know that,
Density = mass/volume
\(V=\dfrac{m}{d}\\\\V=\dfrac{7.06\ g}{0.784\ g/cm^3}\\\\V=9\ cm^3\)
or
V = 9 mL
So, the required volume is 9 mL.
Find the value of X below
what is .006 is 1/10 of __
.06 or 6/100
1) To find out the factor that multiplied by 1/10 yields .0006 let's do the following:
2) Rewrite .006 as a fraction:
\(0.006=\frac{6}{1000}\)2.2) Then we can write out the following equation:
\(\begin{gathered} \frac{6}{1000}=\frac{1}{10}\cdot\frac{6}{100} \\ \frac{6}{10000}=\frac{6}{10000}\text{True!} \\ \\ 0.006=\frac{1}{10}\cdot0.06 \\ 0.006=0.006\text{ True} \end{gathered}\)Note that 0.006 or 6/1000 is 1/10th of 0.06
3) Hence, then the answer is 0.006 is 1/10 of 0.06
Evaluate the expression (2b+3a)×(c to the power of 2) when a=4 , b=3 , and c=1/3 .
Answer:
2
Step-by-step explanation:
(2b+3a) x (c power 2)2*3+3*4 x 1/3 power 2
6+12 x 1/9
18 x 1/9
2 x 1 (because 9 and 18 are cutted by each other)
2
2
Step-by-step explanation:To evaluate the expression (2b+3a)×(c^2) when a=4, b=3, and c=1/3, we substitute the given values into the expression and perform the indicated arithmetic operations:
(2b + 3a) × (c^2)
= (2(3) + 3(4)) × ((1/3)^2) (substitute a=4, b=3, c=1/3)
= (6 + 12) × (1/9) (evaluate 2(3) + 3(4) and (1/3)^2)
= 18/9
= 2
Therefore, when a=4, b=3, and c=1/3, the expression (2b+3a)×(c^2) equals 2.
I NEED HELP PLS HURRY
1. Write each expression with a single exponent:
a. (10^7)²
b. (10^9)³
c. (10^6)³
d. (10^2)³
e. (10³)²
f. (10^5)^7
Answer:
We use the rule,
\((a^b)^c = a^{bc}\)
a. (10^7)²
\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)
10^14
b. (10^9)³
\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)
10^27
c. (10^6)³
\(10^{(6)(3)}= 10^{18}\)
10^18
d. (10^2)³
\(10^{(2)(3)} = 10^{6}\)
10^6
e. (10³)²
\(10^{(3)(2)}=10^{6}\)
10^6
f. (10^5)^7
\(10^{(5)(7)} = 10^{35}\)
10^35
Step-by-step explanation:
A recipe requires 3 cups of flour to make 15 servings and 7 cups of flour to make 35 servings how many cups of flour are needed to make 20 servings?
Answer:
a = 8
b = 2
c = 48
Step-by-step explanation:
3 cups of flour is needed to make 24 servings.
3:24
Simplify. First, divide 3 from both sides of the ratio.
(3)/3 : (24)/3
1:8
Next, solve for b. You multiply 2 to 8 to get 16. Next, multiply 2 to 1
1 x 2 = b = 2
Finally, multiply 8 to 6 to get c.
8 x 6 = c = 48
~
There are 3 feet in 1 yard. Find the number of feet in 15 yards
Answer:
45 feet
Step-by-step explanation:
15 times 3 =45
Answer: 45 ‘
Step-by-step explanation:
4x-3(x+4)=7 i need to know this i need help with this.
Answer:
x=19
Step-by-step explanation:
4x-3x-12=7
x-12=7
x=7+12
x=19
Answer:
x=19
Step-by-step explanation:
first you would distribute the -3 to the x and the 4 which would give you
4x-3x-12=7
next you would combine like terms (there's always an invisible 1 one front of a variable)
x-12=7
then to get the variable by itself you would add 12 on each side
x=19
hope this helped :)
free think fast 20X10
Answer:
200 yessir
Step-by-step explanation:
A lot of points. PLEASE HELP! I will mark brainliest. Whoever gets it right first.
1/2 sin x sin (2x) + Cos 3 x
Answer:
1.047734151
Step-by-step explanation:
Type into calculator
1/2sin(2x)+cos(3x)
what value of X makes the model true?
The value of x is -1 which makes the model true
The equation from the given model will be 5x+6=1
We have to find the value of x
5x+6=1
Subtract 6 from both sides
5x=-5
Divide both sides by 5
x=-1
Hence, the value of x is -1 which makes the model true
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5x≥25 help th bewbsanks
Identify the y-intercept of the graph of the equation:
y = ½ x – 8
Question 1 options:
-8
1/2
-1/2
8
Answer:
-8
Step-by-step explanation:
This function is in slope intercept form, y=mx+b.
m being the slope, b being the y-intercept.
Notice -8 stands for b in this problem.
Thus, the y-intercept of this function is -8.
What is the distance of AB
Answer:
It's around 9.22
Step-by-step explanation:
Answer:
\(\sqrt{85}\)
Step-by-step explanation:
Distance formula.
(-7, -2) (2, -4)
-7 minus 2, you get -9. Squared is 81.
-2 minus -4 gets you 2. Squared is 4.
Add 81 & 4. You get 85.
Square root 85, there's your answer.
b. Passes through the point (2, -4) and is parallel to 3x + y = 5
c. Passes through the point (2, -4) and is perpendicular to 3x + y = 5
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
\(3x+y=5\implies y=\stackrel{\stackrel{m}{\downarrow }}{-3}x+5\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)
so we're really looking for the equation of a line that has a slope oif -3 and it passes through (2 , -4)
\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 3}(x-\stackrel{x_1}{2}) \implies y +4 = - 3 ( x -2) \\\\\\ y+4=-3x+6\implies {\Large \begin{array}{llll} y=-3x+2 \end{array}}\)
now, keeping in mind that perpendicular lines have negative reciprocal slopes
\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ -3 \implies \cfrac{-3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-3} \implies \cfrac{1}{ 3 }}}\)
so for this one, we're looking for the equation of a line whose slope is 1/3 and it passes through (2 , -4)
\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{2}) \implies y +4 = \cfrac{1}{3} ( x -2) \\\\\\ y+4=\cfrac{1}{3}x-\cfrac{2}{3}\implies y=\cfrac{1}{3}x-\cfrac{2}{3}-4\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x-\cfrac{14}{3} \end{array}}\)
Convert to decimal form/ 3.1 x 10^6
Answer:
0.000036 i think it the answer
Hey guys i need your help please
The matrix after the row operation is:
\(\left[\begin{array}{ccc}1&4/9&-1\\-43&-19&44\end{array}\right]\)
We have,
We use the operation R1 → R1/9.
This will give us,
Row 1 values will change to 9/9, 4/9, -9/9
So,
1, 4/9, -1
Now,
\(\left[\begin{array}{ccc}1&4/9&-1\\-43&-19&44\end{array}\right]\)
Thus,
The matrix after the row operation is:
\(\left[\begin{array}{ccc}1&4/9&-1\\-43&-19&44\end{array}\right]\)
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Which of the following is a right triangle?
A.
a triangle with sides measuring 13, 15, and 19
B.
a triangle with sides measuring 17, 25, and 36
C.
a triangle with sides measuring 20, 21, and 29
D.
a triangle with sides measuring 18, 23, and 41
Answer:
Step-by-step explanation:
the right choice is C
you use c^2=a^2+b^2
where the largest side is the hypotenuse
Answer:
C.
a triangle with sides measuring 20, 21, and 29
Step-by-step explanation:
As, √(20)²+(21)² = √400+441 = √841 = 29
The longest side is taken as the hypotenuse. So 29 is the hypotenuse. Which by using Pythagoras' theorem gives us 29 ( h=√b²+p² )