(256⁴-1)
= (256-1)⁴
Using identity (a-b)⁴ = a⁴−4a³b+6a²b²−4ab³+b⁴
Let a be 256 and b be 1
Then
256⁴−4(256)³(1)+6(256)²(1)²−4(256)(1)³+(1)⁴
After solving
(256²-1)²
(a-b)² = a²-2ab+b²
256²-2×256×1+1²
= (256²-1)(256²+1)
Must click thanks and mark brainliest
Answer:
Use identity:
a² - b² = (a + b)(a - b)Consider that:
256 = 2⁸Now factorize:
256⁴ - 1 = (2⁸)⁴ - 1 = 2³² - 1 = (2¹⁶ - 1)(2¹⁶ + 1) = (2⁸ - 1)(2⁸ + 1)(2¹⁶ + 1) = (2⁴ - 1)(2⁴ + 1)(2⁸ + 1)(2¹⁶ + 1) = (2² - 1)(2² + 1)(2⁴ + 1)(2⁸ + 1)(2¹⁶ + 1) = (2 - 1)(2 + 1)(2² + 1)(2⁴ + 1)(2⁸ + 1)(2¹⁶ + 1)If an object of mass m is dropped from rest, one model for its speed v after t seconds, taking air resistance into account is: c= mg/c (1- e^ -ct/m), where g is the acceleration due to gravity and c is a positive constant describing air resistance.
Required:
a. Calculate lim v
t→[infinity]
b. What is the meaning of this limit? (choose from the following options)
1. It is the time it takes the object to reach its maximum speed.
2. It is the speed the object reaches before it starts to slow down.
3. It is the time it takes the object to stop.
4. It is the speed the object approaches as time goes on.
Answer:
a. mg/c b. 4. It is the speed the object approaches as time goes on.
Step-by-step explanation:
a. Calculate lim v as t→[infinity]
Since v = mg/c(1 - e^ -ct/m)
[tex]\lim_{t \to \infty} v = \lim_{t \to \infty} (\frac{mg}{c}[1 - e^{-\frac{ct}{m} } ] )[/tex]
[tex]\lim_{t \to \infty} v =[/tex] mg/c(1 - e^(-c(∞)/m))
[tex]\lim_{t \to \infty} v =[/tex] mg/c(1 - e^(-∞/m))
[tex]\lim_{t \to \infty} v =[/tex] mg/c(1 - e^(-∞))
[tex]\lim_{t \to \infty} v =[/tex] mg/c(1 - 0)
[tex]\lim_{t \to \infty} v =[/tex] mg/c(1)
[tex]\lim_{t \to \infty} v =[/tex] mg/c
b. What is the meaning of this limit?
4. It is the speed the object approaches as time goes on.
This is because, since t → ∞ implies a long time after t = 0, the limit of v as t → ∞ implies the speed of the object after a long time. So, the limit of v as t → ∞ is the speed the object approaches as time goes on.
Write the equation in slope-intercept form.
y+3 - 2(x-1)
Answer:
y = 2x - 5
Step-by-step explanation:
[tex]y+3=2(x-1)\\y+3=2x-2\\y+3-3=2x-2-3\\y=2x-5[/tex]
PLEASEEEE HELPPPP ASAPPPPPP
The football coach randomly selected 10 players and timed how long each player took to perform a certain drill. The result has a sample mean of 9.48 minutes and sample standard deviation of 2.14 minutes. Round answers to two decimals. The 95% confidence interval for the mean time for all players is : __________
Answer:
The 95% confidence interval for the mean time for all players, in minutes, is: (7.95, 11.01).
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 10 - 1 = 9
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.2622.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.2622\frac{2.14}{\sqrt{10}} = 1.53[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 9.48 - 1.53 = 7.95 minutes.
The upper end of the interval is the sample mean added to M. So it is 9.48 + 1.53 = 11.01 minutes.
The 95% confidence interval for the mean time for all players, in minutes, is: (7.95, 11.01).
F(x)=x+8;g(x)=x+2. Find f=g
Answer:
f(x) can not be equal to g(x)
Step-by-step explanation:
If the result is possible:
f(x) = g(x)
x + 8 = x + 2
x + 8 - (x + 2) = x + 2 - (x + 2)
6 = 0
Because 6 can't be equal to 0, so do f(x) can't be equal to g(x)
The scores of students on a standardized test are normally distributed with a mean of 300 and a standarddeviation of 40.
(a) What proportion of scores lie between 220 and 380 points?
(b) What is the probability that a randomly chosen student scores is below 260?
(c) What percent of scores are above 326.8 points?
Answer:
a) 0.9544 = 95.44% of scores lie between 220 and 380 points.
b) 0.1587 = 15.87% probability that a randomly chosen student scores is below 260.
c) 25.14% of scores are above 326.8 points.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 300 and a standard deviation of 40.
This means that [tex]\mu = 300, \sigma = 40[/tex]
(a) What proportion of scores lie between 220 and 380 points?
This is the p-value of Z when X = 380 subtracted by the p-value of Z when X = 220.
X = 380
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{380 - 300}{40}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772.
X = 220
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{220 - 300}{40}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.0228.
0.9772 - 0.0228 = 0.9544
0.9544 = 95.44% of scores lie between 220 and 380 points.
(b) What is the probability that a randomly chosen student scores is below 260?
This is the p-value of Z when X = 260. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{260 - 300}{40}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587.
0.1587 = 15.87% probability that a randomly chosen student scores is below 260.
(c) What percent of scores are above 326.8 points?
The proportion is 1 subtracted by the p-value of Z when X = 326.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{326.8 - 300}{40}[/tex]
[tex]Z = 0.67[/tex]
[tex]Z = 0.67[/tex] has a p-value of 0.7486.
1 - 0.7486 = 0.2514
0.2514*100% = 25.14%
25.14% of scores are above 326.8 points.
tìm cực trị của hàm số z(x,y)=x^{3}+y^{3}+3xy-30
Answer:
Hence, MEAN OF FIRST FIVE COMPOSITE NOS IS 7.5
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s = 17.6 milligrams.
Required:
Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.
Answer:
CI ≈ (173.8 < μ < 196.2)
Step-by-step explanation:
We are told that laboratory tested twelve chicken eggs. Thus;
n = 12
Mean; x¯ = 185 mg
S.D; s = 17.6 mg
DF = n - 1 = 12 - 1 = 11
We have a 95% confidence level. Thus; α = 0.05
Since n < 30, we will use t-sample test.
Thus, from t-table attached at 95% Confidence level and DF = 11, we have;
t = 2.201
Thus,formula for Confidence interval is;
CI = (x¯ - t(s/√n)) < μ < (x¯ + t(s/√n))
CI = (185 - 2.201(17.6/√12)) < μ < (185 + 2.201(17.6/√12))
CI = (185 - 11.1825) < μ < (185 + 11.1825)
CI = (173.8175 < μ < 196.1825)
CI ≈ (173.8 < μ < 196.2)
In one year the population of
Zebras in the park was 3400. In
the following year the population
reduced by 25%. What was the
size of the population after
reduction?
PLZ ANSWER QUESTION IN PICTURE
Answer: [tex]y=\frac{1}{3}x+\frac{13}{3}[/tex]
Step-by-step explanation:
(slope = m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-6}{-1-5}=\frac{-2}{-6}=\frac{1}{3}[/tex]
[tex]y=mx+b, (5,6), (-1,4), m=\frac{1}{3}[/tex]
[tex]y=mx+b\\6=\frac{1}{3}(5)+b\\b=6-\frac{5}{3} \\b=\frac{13}{3}\\y=\frac{1}{3}x+\frac{13}{3}[/tex]
Select all the terms that can be combined with 5.
4b
14a
100
3a’2
Both before and after a recent earthquake, surveys were conducted asking voters which of the three candidates they planned on voting for in the upcoming city council election. Has there been a change since the earthquake? Use a level of significance of 0.05. Table shows the results of the survey. Has there been a change in the distribution of voter preferences since the earthquake?
Peter Alan Sui
Before 1838 418 1475
After 1420 329 1140
What is the chi-square test-statistic for this data?
χ2=_____.
Answer:
0.05547
Step-by-step explanation:
Given :
_____Peter __ Alan __ Sui__total
Before 1838 __ 418 ___1475 _3731
After _ 1420 __ 329 ___1140_2889
Total _3258 __ 747 __ 2615 _6620
The expected frequency = (Row total * column total) / N
N = grand total = 6620
Using calculator :
Expected values are :
1836.19 __ 421.006 __ 1473.8
1421.81 ___325.994__ 1141.2
χ² = Σ(Observed - Expected)² / Expected
χ² = (0.00177817 + 0.0214571 + 0.000974852 + 0.00229642 + 0.0277108 + 0.00125897)
χ² = 0.05547
Solve for y. 14y-6(y-3)=22
Answer:
y=0.5
Step-by-step explanation:
14y-6(y-3)=22
14y-6y+18=22
8y+18=22
8y=4
y=0.5
Then we check our work...
14(0.5)-6((0.5)-3)=22
7-6(-2.5)=22
7+15=22
7+15 does equal 22, so this solution is correct.
use induction method to prove that 1.2^2+2.3^2+3.4^2+...+r(r+1)^2= n(n+1)(3n^2+11n+10)/12
Base case (n = 1):
• left side = 1×2² = 4
• right side = 1×(1 + 1)×(3×1² + 11×1 + 10)/12 = 4
Induction hypothesis: Assume equality holds for n = k, so that
1×2² + 2×3² + 3×4² + … + k × (k + 1)² = k × (k + 1) × (3k ² + 11k + 10)/12
Induction step (n = k + 1):
1×2² + 2×3² + 3×4² + … + k × (k + 1)² + (k + 1) × (k + 2)²
= k × (k + 1) × (3k ² + 11k + 10)/12 + (k + 1) × (k + 2)²
= (k + 1)/12 × (k × (3k ² + 11k + 10) + 12 × (k + 2)²)
= (k + 1)/12 × ((3k ³ + 11k ² + 10k) + 12 × (k ² + 4k + 4))
= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)
= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)
On the right side, we want to end up with
(k + 1) × (k + 2) × (3 (k + 1) ² + 11 (k + 1) + 10)/12
which suggests that k + 2 should be factor of the cubic. Indeed, we have
3k ³ + 23k ² + 58k + 48 = (k + 2) (3k ² + 17k + 24)
and we can rewrite the remaining quadratic as
3k ² + 17k + 24 = 3 (k + 1)² + 11 (k + 1) + 10
so we would arrive at the desired conclusion.
To see how the above rewriting is possible, we want to find coefficients a, b, and c such that
3k ² + 17k + 24 = a (k + 1)² + b (k + 1) + c
Expand the right side and collect like powers of k :
3k ² + 17k + 24 = ak ² + (2a + b) k + a + b + c
==> a = 3 and 2a + b = 17 and a + b + c = 24
==> a = 3, b = 11, c = 10
You decide to go on a 4 day backpacking trip. The first day you walk 8 miles at northeast, on the second day, you walk 4 miles at eastsouth, and on the third day you walk 3 miles at southwest. On the fourth day you need to head straight back to your car. How far do you have to walk, and in what direction
Answer:5
Step-by-step explanation:
Where the above parameters are given, you need to walk a distance of approximately √41 miles back to your car.
How to compute the aboveTo calculate the total distance you need to walk, you can use the Pythagorean theorem since you have a right triangle formed by the north and east displacements.
Distance = √((Distance north)² + (Distance east)²)
= √((5 miles)² + (4 miles)²)
= √(25 miles + 16 miles)
= √41 miles
Hence, you need to walk a distance of approximately √41 miles back to your car.
As for the direction, based on the net displacements, you are 5 miles north and 4 miles east of your car, so the direction would be a combination of north and east, often referred to as northeast.
Learn more about distance at:
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Write the polynomial in standard form. Then name the polynomial based on its degree and number of
terms.
y-7y3 + 15y9
Answer:
[tex]15y^9 - 7y^3 + y[/tex]
Nonic polynomial
Step-by-step explanation:
Given
[tex]y - 7y^3 + 15y^9[/tex]
Required
Write in standard form
The standard form of a polynomial is:
[tex]ay^n + by^{n-1} + ......... + k[/tex]
So, we have:
[tex]y - 7y^3 + 15y^9[/tex]
The standard form is:
[tex]15y^9 - 7y^3 + y[/tex]
And the name is: Nonic polynomial (because it has a degree of 9)
18 is 65% of what number
Answer:
65% of 27.69 is 18.
Step-by-step explanation:
Formula = Number x 100
Percent = 18 x 100
65 = 27.69
Following shows the steps on how to derive this formula
Step 1: If 65% of a number is 18, then what is 100% of that number? Setup the equation.
18
65% = Y
100%
Step 2: Solve for Y
Using cross multiplication of two fractions, we get
65Y = 18 x 100
65Y = 1800
Y = 1800
100 = 27.69
On a recent trip to the convenience Store you picked up 4 gallons of milk 4 bottles of water and 5 snack size bags of chips your total was $28.35 if a bottle of water cost twice as much as a bag of chips and a gallon of milk cost $2.10 more than a bottle of water how much does each item cost
Answer:
The milk cost $2.10 each the snacks cost $1.535 each the water cost $3.07 each
Step-by-step explanation:
I think Im right
In 10 words or fewer, what is the square root of -9?
Type answer here...
What is the square root of -9
Answer:
no solution
Step-by-step explanation:
a negative number cannot be square rooted
Answer:
"not possible". no such thing as a negative squared number
help me please i’ll give brainliest the
Answer:
y=-1/2x+-1
Step-by-step explanation:
try desmos with this equation.
y=mx+b
m=the slope which is -1/2. It goes down 1 it is negative because it is going down, and to the right 2.
b=y-intercept meaning the point which the line crosses the line y .-1
The sum of one and three times a number is -89. What is the number?
A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use
x
as your variable.
The equation is
B) Solve your equation in part [A] for
Answer:
A. 1 + 3x = -89
B. x = -30
Step-by-step explanation:
Let the unknown variable be x.
A. Translating the word problem into an algebraic expression, we have;
1 + 3x = -89
B. To solve for the unknown variable;
1 + 3x = -89
3x = -89 -1
3x = -90
x = -90/3
x = -30
Check:
1 + 3x = -89
Substituting the value of x;
1 + 3(-30) = -89
1 + (-90) = -89
1 - 90 = -89
-89 = -89
scientist has two solutions, which she has labeled solution a and solution b. solution a is 60% salt and solution b is 85% salt. she wants to obtain 140 ounces of mixture that is 80% salt. How many ounces of each solution should she use?
Answer:
We have 60% salt and 85% salt solutions and we need 140 ounces of a solution that is 80% salt.
We set up 2 equations:
A) x + y = 140
B) .60x + .85y = .80 * 140
Multiply equation A) by -.60
A) -.60x -.60y = -84 then we add this to B)
B) .60x + .85y = 112
.25y = 28
y = 112 ounces of 85% salt
x = 28 ounces of 60% salt.
Double Check
112 * .85 = 95.2 AND 28 * .60 = 16.80
95.2 + 16.80 = 112
and 112/140 = 80 per cent!!
Source: http://www.1728.org/mixture.htm
Step-by-step explanation:
50 money prize for solve
Answer:
-7.5
Alternatively,
-0.5(units^-1) + (-4(units^0)) + (-3(units))
Step-by-step explanation:
On graph, only clearly defined points:
1. x = -3 , y = 0
2. x = -3 , y = -8
3. x = 5 , y = -4
So for:
1. -3 = c ( + a×(0^2) + b×0)
And
2. -3 = a×((-8)^2) + b×(-8) + c = 64×a + (-8)×b + c
Since c = -3 ==> 64×a - 8×b = 0
Simplified ==> 8×a - b = 0 ==> b = 8×a
3. 5 = a×((-4)^2) + b×(-4) + c = 16×a + (-4)×b + c
Since c = -3 ==> 16×a - 4×b = 5 - (-3) = 8
Simplified ==> 4×a - b = 2
Since b = 8×a ==> 4×a - (8×a) = 2
Simplified ==> 2×a - 4×a = 1
==> -2×a = 1
==> a = -0.5
Since b = 8×a ==> b = 8×(-0.5) = -4
So...
c = -3
b = -4
a = -0.5
Then...
a + b + c = -0.5 - 4 - 3 = -7.5
I need to know the answer please
Focusing on the center point of f(x) (0,0), we can see that it has moved to the left 4 units and up 3 units.
g(x) = [tex](\sqrt[3]{x + 4}) + 3[/tex]
Option C
Hope this helps!
Will mark brainliest
Plz solve on a paper or draw on the picture thx in advance
9514 1404 393
Answer:
the red angle has no specific value
Step-by-step explanation:
There is sufficient information here to specify all of the angles except the two unknown angles in the 70° (dark blue) triangle. Those two angles must total 110°, but that measure cannot be allocated between them based on the information in the diagram.
The attachments show that all of the given angle constraints can be met while the red angle may vary considerably. It can range through the interval (0°, 110°), but cannot be either of those end values.
Which ordered pair would form a proportional
relationship with the points in the graph?
O (44)
O (69)
O (9,6)
O (8,5)
2. Approximately what is the ratio of customers
from Zone 1 to customers from Zone 3?
UA. 3:5
B. 3:2
OÇ. 2:1
D. 1:2
The ratio of customers from Zone 1 to from Zone 3 is 1 : 2
This question appears to be incomplete.
Please find attached the graph required to answer this question
Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
The graph is in the image is a bar graph
A bar graph is a pictorial representation of data. The rectangles measure the length of the data
Looking at the graph, the interval is 100
Looking at the rectangle that represents zone 1, it appears to be halfway between 400 and 500. It is concluded that the number of customers in zone 1 is 450
Looking at the rectangle that represents zone 3, it appears to lie on 900.
It can be concluded that there are 900 customers in zone 3
the ratio of zone 1 to 3
450 : 900
to convert to its simplest form, divide both side of the ratio by 450
1 : 2
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Solve for x the find the measure of A
Answer:
84°
Step-by-step explanation:
the total angle in a straight line sum up to 180°
A postal worker can sort a day's worth of mail in 8 hours. With her
supervisor helping, it takes 3 hours. How long would it take the
supervisor working alone?
Answer:
6 hours.
Step-by-step explanation:
x = supervisor's hours alone
Since there are two people working together, you need to incorporate some kind of 2 in this problem.
If the postal worker was cloned, it would take 4 hours.
3 x 2 = 6.
can earn 5 coins In my town, gas prices are always listed to the thousandths place. Since the smallest coin we have is the penny, we have to round them to the hundredths place. If the price of gas is $3.545, what will the price be when we round it to the hundredths place?
Answer:
$3.55
Step-by-step explanation:
1st number after 0 is tenths, 2nd is hundredths.
since the number after is 5, we round up
