Answer:
0
Step-by-step explanation:
Hello, please consider the following.
For any a and b real numbers we can write.
[tex](a-b)(a+b)=a^2-b^2[/tex]
We apply this formula two times here, as below.
[tex](x+1)(x^{2}+1)(x-1)=(x+1)(x-1)(x^{2}+1)\\\\=(x^2-1^2)(x^2+1)=(x^2-1)(x^2+1)\\\\=(x^2)^2-1^2=x^4-1[/tex]
We have the coefficient of 1 for [tex]x^4[/tex] and the constant term is -1, so the sum of the coefficients is 0.
Thank you.
Answer:
1
Step-by-step explanation:
(x + 1)(x² + 1)(x - 1)
= (x³ + x + x² + 1)(x - 1)
= x^4 - x³ + x² - x - x³ - x² + x - 1
= x^4 - 1
Coefficient of x^4 = 1
Find all values of x on the graph of f(x) = 2x3 + 6x2 + 7 at which there is a horizontal tangent line.
Answer:
the equation is not correct, u have to write like
ax'3+bx'2+cx+d
Answer:
x=-2 and x=0
Step-by-step explanation:
So I know it isn't x=-3 and x=0. So my guess is that it is x=0 and x=-2 and heres why.
First, I find the derivative of f(x)=2x^3+6x^2+7 which is 6x^2+12x
Then, I plugged in all the values of x's I had and I found out that you get 0 for -2 and 0 when you plug them in
So, in conclusion I believe the answer to be x=-2 and x=0
help help help help help help
Answer:
75 yards long and 90 yards wide.
Step-by-step explanation:
Let's first find the perimeter of the main rectangle:
100x2 + 65x2 =
330
_________________________________________
Next we need to find two numbers that match:
75 and 90
75x2 + 90x2 =
330
_________________________________________
75x90 is 6750 (More Area)
100x60 is 6500 (Less Area)
What is the value of b.
C=25
s=9
B=4c-s2
Answer:
82
Step-by-step explanation:
Plug in the variables into the equation and solve for B but remember your order of operations when solving multiplication/division before addition/subtraction.
B = 4*25-9*2
B = 100-18
B = 82
Which graph best represents the equation –x + 2y = 4?
Answer:
C
Step-by-step explanation:
Convert the equation into slope intercept form : y=mx+b
2y=x+4
y=1/2x + 2
The m is the slope and the b is the y intercept
In this equation, the slope is 1/2 and the y intercept is 2
The only graph with y intercept 2 is C
Ever since Renata moved to her new home, she's been keeping track of the height of the tree outside her window. H represents the height of the tree (in centimeters), t years since Renata moved in. H = 210 + 33t How fast does the tree grow? ANSWER centimeters per year.
Answer:
The tree grows 33cm per year
Step-by-step explanation:
Here in this question, we are interested in knowing how fast the growth of the tree is.
This is easily obtainable from the equation for the height of the tree.
Mathematically, the equation is given as;
H = 210 + 33t
Interpreting this, we can have 210 as the original height of the tree when Renata moved in, while the term 33 represents the growth per year.
So we can say the tree adds a height of 33 cm each year and this translates to the yearly growth of the tree
In 2018, the population of a district was 25,000. With a continuous annual growth rate of approximately 4%, what will the
population be in 2033 according to the exponential growth function?
Round the answer to the nearest whole number.
Answer:
40,000 populationsStep-by-step explanation:
Initial population in 2018 = 25,000
Annual growth rate (in %) = 4%
Yearly Increment in population = 4% of 25000
= 4/100 * 25000
= 250*4
= 1000
This means that the population increases by 1000 on yearly basis.
To determine what the population will be in 2033, we need to first know the amount of years we have between 2018 and 2033.
Amount of years we have between 2018 and 2033 = 2033-2018
= 15 years
After 15 years, the population will have increased by 15*1000 i.e 15,000 more than the initial population.
Hence the population in 2033 will be Initial population + Increment after 15years = 25,000+15000 = 40,000 population.
Find the measure of a.
A. 60
B. 57
C. 40
D. 80
Answer:
Option (C)
Step-by-step explanation:
Since angle 'a' is the inscribed angle of the given triangle
Therefore, angle measure of the intercepted arc will be equal to the double of the inscribed angle.
x = 2a ⇒ a = [tex]\frac{x}{2}[/tex]
By the tangent-chord theorem,
"Angle between a chord and tangent measure the half of the angle measure of intercepted minor arc"
[tex]\frac{x}{2}[/tex] = 40°
Therefore, a = [tex]\frac{x}{2}[/tex] = 40°
Option (C) will be the answer.
Solve x/10 = -7 A. x = 3 B. x = -0.7 C. x = -17 D. x = -70
Answer:
x = -70
Step-by-step explanation:
x/10 = -7
Multiply each side by 10
x/10*10 = -7*10
x = -70
Solve the equation. - 2(2x-4)= 4x
Answer:
-2(2x-4) = -4x+8 or 2(2x-4) ≠ 4x ; -4x+8 ≠ 4x
Step-by-step explanation:
Did you accidentally write =4x after your expression? If so, then let me explain why my answer is correct. I used distributive property of multiplication, so I multiplied -2 with 2x to get -4x, and -2 multiplied with -4 to get 8. So my final answer was -4x+8. If you did not accidentally put -4x, then my answer would be, 2(2x-4) ≠ 4x or -4x+8 ≠ 4x. Hope this helped.
If f(x)=ax+b and f(2)=1 and f(-3)=11, what is the value of A?
Answer:
a = -2
Step-by-step explanation:
f(x)=ax+b
f(2)=1
f(-3)=11
f(2) = 1 means 2a+b =1
f(-3)=11 means -3a + b = 11
Subtracting the two equations
-(-3a +b =11) becomes 3a -b = -11 so we can add
2a+b =1
3a - b = -11
----------------------
5a = -10
Divide by 5
5a/5 = -10/5
a=-2
A chemical company makes two brands
of antifreeze. The first brand is 30% pure
antifreeze, and the second brand i$ 80% pure
antifreeze. In order to obtain 80 gallons of a
mixture that contains 70o£ pure antifreeze, hov
mabry gallons of each band ot antifneze must
bo used?
Answer:
16 bags for the first(30% pure) and 64 bags of the second(80% pure)
Step-by-step explanation:
If they are mixed in a ratio of x bags to y bags
(0.3x+0.8y)/(x+y) = 0.7
0.3x + 0.8y = 0.7(x+y)
Multiply both sides with 10
3x + 8y = 7(x+y)
4x = y ——(1)
x + y = 80 ——(2)
Solve simultaneously
x + 4x = 80
5x = 80
x = 16 bags
y = 4x = 64 bags
On a coordinate plane, line P Q goes through (negative 6, 4) and (4, negative 4). Point R On a coordinate plane, a line goes through (negative 4, 0) and (4, negative 4). A point is at (2, 3). What is the equation of the line that is parallel to the given line and passes through the point (2, 3)? x + 2y = 4 x + 2y = 8 2x + y = 4 2x + y = 8
Answer:
x + 2y = 8.
Step-by-step explanation:
Line goes through (-4, 0) and (4, -4).
The slope is (-4 - 0) / (4 - -4) = -4 / (4 + 4) = -4 / 8 = -1/2.
Since we are looking for the equation of the line parallel to that line, the slope will be the same.
We have an equation of y = -1/2x + b. We have a point at (2, 3). We can then say that y = 3 when x = 2.
3 = (-1/2) * 2 + b
b - 1 = 3
b = 4.
So, we have y = -1/2x + 4.
1/2x + y = 4
x + 2y = 8.
Hope this helps!
ANSWEAr
x + 2y = 8
because it is
Please answer this correctly without making mistakes
Answer:
Put 1/10 in the box.
Step-by-step explanation:
Since, Bluepoint and Milford are at same distance from Weston, the distance further than this to Oakdale is 1/10 miles.
Best Regards!
Answer:
To Oakdale to Milford:
2/5 mi
Step-by-step explanation:
1/10 + 3/20 + 3/20
1/10 = 2/20
then;
2/20 + 3/20 + 3/20 = (2+3+3)/20 = 8/20
8/20 = 2/5
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 19 4 12 35
Female 3 13 5 21
Total 22 17 17 56
Let pp represent the percentage of all male students who would receive a grade of A on this test. Use a 99.5% confidence interval to estimate p to three decimal places.
Enter your answer as a tri-linear inequality using decimals (not percents).
< p
Answer:
Using Anova for a tri linear probability at ∝= 0.005
Step-by-step explanation:
Here simple probability cannot be used because we want to enter your answer as a tri-linear inequality using decimals (not percents).
So we can use ANOVA
Null hypothesis
H0: µA = µB=µC
all the means are equal
Alternative hypothesis
H1: Not all means are equal.
The significance level is set at α-0.005
The test statistic to use is
F = sb²/ sw²
Which if H0 is true has an F distribution with v₁=k-1 and v₂= n-k degrees of freedom .
The computations are as follows
XA (XA)² XB (XB)² XC (XC)² Total ∑X²
Male 19(361) 4(16) 12(144) 35 521
Female 3(9) 13 (169) 5 (25) 21 203
TotalTj 22 17 17 56 724
T²j (22)(22)
484 289 289 1062
∑X² 370 285 169
Correction Factor = CF = Tj²/n = (56)²/6= 522.67
Total SS ∑∑X²- C. F = 724- 522.67= 201.33
Between SS ∑T²j/r - C.F = 1062/ 2 - 522.877 =8.33
Within SS = Total SS - Between SS
=201.33- 8.33= 193
The Analysis of Variance Table is
Source Of Sum of Mean Computed
Variation d.f Squares Squares F
Between
Samples 1 8.33 8.33 8.33/ 48.25= 0.1726
Within
Samples 4 193 48.25
The critical region is F >F ₀.₀₀₅ (1,4) = 31.3328
Calculated value of F = 0.1726
Since it is smaller than 5 % reject H0.
However the decimal probability will be
Male 19 4 12 35
Female 3 13 5 21
Total 22 17 17 56
There are total 22 people who get an A but only 19 males who get an A
So the probability that a male gets an A is = 19/22= 0.8636
What is the slope of the line joining (5.9) and (-2, 9)?
0-1
0-
00
O No slope
Answer:
0
Step-by-step explanation:
The slope of the line is m=(9-9)/(-2-5)=0/-7=0
Find the value of m.
L
R
A
3m +21 U
6m
O A. 14
ОВ. 7
Answer:
B
Step-by-step explanation:
Since LR=LA, RU=RA. 3m+21=6m, 3m=21, m=7
Solve for
x. Round to the nearest tenth of a degree, if necessary.
Answer:
[tex]\displaystyle x \approx 30.8[/tex]
Step-by-step explanation:
Note that the figure is a right triangle, and that we are given the length of the side adjacent to x and the hypotenuse of the triangle.
Therefore, we can use the cosine ratio. Recall that:
[tex]\displaystyle \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
The adjacent side is 8.5 and the hypotenuse is 9.9. Therefore:
[tex]\displaystyle \cos x = \frac{8.5}{9.9}[/tex]
We can take the inverse cosine of both sides:
[tex]\displaystyle x = \cos^{-1} \frac{8.5}{9.9}[/tex]
Use a calculator. Hence:
[tex]\displaystyle x \approx 30.8[/tex]
Sammy the Sailor swears entirely too much. The following probability distribution shows the number of times Sammy swears per day and the corresponding probabilities:
# of swear words: 2 5 9 14 20
Probability: 0.01 0.09 0.30 0.40 0.20
In an effort to reduce his amount of swearing, Sammy places $1.00 in a jar every time he swears. Further, if at the end of the day he swears more than 10 times, he places an extra $2.00 in the jar per swear word over 10. If Sammy swears less than 5 times, he takes out $0.50 for each of his swear words.
A B C D E F G
1 # of swear word Probability
2 Cost per swear word $1.00 2 0.01
3 Extra cost per swear
word over 10 $2.00 5 0.09
4 Refund per swear word
less than 5 $0.50 9 0.3
5 14 0.4
6 20 0.2
7
8
9 # Regular Extra cost Refund Total
swear swear if over 10 if under money
words word swear 5 swear in the jar
cost words words for the
day
10
Based off the partial simulation spreadsheet above, answer the following questions:
A) What formula should go into cell C10 to calculate the Regular Swear word cost?
B3*B4 SUMPRODUCT(B2:B4, B10) B4*B10 SUM(B2:B4) B2*B10 B3*B2 B3*B10
B) What formula should go into cell D10 to calculate the Extra Swear word cost?
=IF(B10>10,(B10-10)*B3,0) =IF(B10>10,(10-B10)*B3,0) =(B10-10)*B3 =IF(B10>10,0,(B10-10)*B3) SUMPRODUCT(B10,B3) B10*B3
C) What formula should go into cell E10 to calculate the Refund amount?
B10*B4 =IF(B10>5,(B10-5)*B4,0) =IF(B10<5,0,B10*B4) =IF(B10<5,B10*B4,0) SUMPRODUCT(B10:B4) =IF(B10<5,(B10-5)*B4,0)
D) What formula should go into cell F10 to calculate the total money in the jar?
Full question attached:
Answer and explanation:
A) B2*B10: cell B2 and B10 have the values regular swear costs and number of swears respectively and we need to multiply these two values to get our answer
B) =IF(B10>10,(B10-10)*B3,0): Sam is supposed to pay an extra $2 for swear words over 10 and so we check if his swear words are above 10 and if they are we find out how many they are by subtracting 10 from them and then we multiply the value gotten by the cost for extra swear words($2)
C) =IF(B10<5,B10*B4,0): here we check if swear words are less than 5 and if they are we multiply number of swears words less than by 5 by the cost ($0.50)
D) F10=C10+D10+E10: to calculate total money in jar(F10), we simply add up regular cost(C10), extra cost(D10) and refund(E10)
A population culture begins with 20 strands of bacteria and then doubles every 4 hours. This can be modeled by , where t is time in hours. How many strands of bacteria are present at 20 hours?
Question 13 options:
A)
425 strands of bacteria
B)
567 strands of bacteria
C)
640 strands of bacteria
D)
375 strands of bacteria
Answer:
C) 640 strands of bacteria
Step-by-step explanation:
We are told in the question that the population doubles every 4 hours
Hence, formula to solve this question =
P(t) = Po × 2^t/k
From the question, we have the following information:
Beginning amount (Po) = 20 strands of bacteria
Rate(k) = 4 hours
Time(t) = 20 hours
Ending time (P(t)) = unknown
Ending amount = 20 × 2^20/4
= 20 × 2^5
= 20 × 320
= 640 strands of bacteria.
Therefore, the number of strands left after 20 hours is 640 strands of bacteria.
For a certain instant lottery game, the odds in favor of a win are given as 81 to 19. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Answer: 0.81
Step-by-step explanation:
[tex]81:19\ \text{can be written as the fraction}\ \dfrac{81}{81+19}=\dfrac{81}{100}=\large\boxed{0.81}[/tex]
What is the slope of the line showed?
Answer:
2
Step-by-step explanation:
The formula for the slope of a line is rise over run. We know that the slope of the line will be positive because the line is going up from left to right.
Rise is the change on the y-axis, going up and down. Run is the change on the x-axis, going from left to right.
Let's start from the origin (0,0). To reach the next point on the line, we have to go up two points (rise) and over one point (run).
Slope = rise/run
Slope = 2/1
Slope = 2
Hope that helps.
Answer:
slope=2
Step-by-step explanation:
take two points from graph (0,0) and (1,2)
m=y2-y1/x2-x1
m=2-0/1-0
m=2
What is the volume of the sphere shown below with a radius of 6?
A. 483 Cu, units
B. 2887 cu units
C. 1627 cu units
D. 14431 Cu, units
Answer:
B
Step-by-step explanation:
Volume of the sphere = (4/3)*pi*6^3=288*pi
Answer:
288 pi units^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
V = 4/3 pi (6)^3
V = 4/3 pi (216)
V = 288 pi units^3
To prove a statement by mathematical induction, all we have to do is show that it is true for n+1. (True or False)
Answer:
False
Step-by-step explanation:
We also need to show that it is true for n=1
and for n=k+1
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 407 gram setting. It is believed that the machine is underfilling the bags. A 20 bag sample had a mean of 397 grams with a standard deviation of 13. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. State the null and alternative hypotheses.
Answer:
Null hypothesis: μ = 407
Alternative hypothesis: μ < 407.
Step-by-step explanation:
In this case, the machine is SUPPOSED to fill the bag so that the bag weighs 407 grams. So, the null hypothesis will be that the machine is doing what it is supposed to be doing. And so, μ = 407 grams would be the null.
The worker thinks the machine is filling the bags to LESS THAN what it is supposed to. So, the alternative hypothesis is that the machine is NOT doing what it is supposed to and μ < 407 grams.
Hope this helps!
If a dog has 2,000,000 toys and he gives 900,000 away. Then gets 2,000 more, also looses 2,000,000. He's sad but then also got 5,000,000,000 more and gives 1,672,293 out. How much does he have now? And how much he gave away. And how much he got.
Answer:
See below.
Step-by-step explanation:
He does not have enough to loose 2,000,000 at that point, so this whole problem is nonsense.
Find x. A. 3√3 B. 3 C. 2√3/3 D. √63
Answer:
[tex]\huge\boxed{\sf x = 3\sqrt{3}}[/tex]
Step-by-step explanation:
Cos 30 = Adjacent / Hypotenuse
Where Adjacent = x , Hypotenuse = 6
[tex]\frac{\sqrt{3} }{2}[/tex] = x / 6
x = [tex]\frac{\sqrt{3} }{2}[/tex] * 6
[tex]\sf x = 3\sqrt{3}[/tex]
While walking in the country, you count 39 heads and 116 feet in a field of cows and chickens. How many of each animal are there?
Answer: 58
Step-by-step explanation:
its 58 because chickens have two feet each so divide 2 % 166 and its 58
because each chicken has 2 legs count the 2 legs up to 116 then u get ur answer
Let x1 represent a quantitative independent variable and x2 represent a dummy variable for a 2-level qualitative independent variable. Which of the following models is the equation that produces two parallel curves, one for each level of your QL variable?
A. E(y) = ?0 + ?1x1 + ?2x12 + ?3x2
B. E(y) = ?0 + ?1x1 + ?3x2
C. E(y) = ?0 + ?x11 + ?3x2 + ?4x1x2
D. E(y) = ?0 + ?1x1 + ?2x12 + ?3x2 + ?4x1x2 + ?5x12x2
Answer:
D. E(y) = ?0 + ?1x1 + ?2x12 + ?3x2 + ?4x1x2 + ?5x12x2
Step-by-step explanation:
Quantitative variables are measured in terms of numbers, and figures. Independent variables are those which are reason for change in other variables. Dummy variables are numerical that represents categorical data. The range of these variables is small and they can take on only two quantitative values.
look the image below
Answer:
Does the answer help you?
Does the answer help you?Please choose my answer as a brainliest answer and please rate.
Does the answer help you?Please choose my answer as a brainliest answer and please rate.It take a few mins to solve your question.
Answer:
V≈696.91
Step-by-step explanation:
V=4
3πr3=4
3·π·5.53≈696.90997
PLEASE ANSWER ASAP THANK YOU!!! How much money will be in a bank account after 3 years if $9 is deposited at an interest rate of 5% compounded annually? Round to the nearest dollar.....
Answer:
10 bucks
Step-by-step explanation:
Money=9*(1+0.05)^3
Money=9*(1.05)^3=10.41≈10