Find the most general antiderivative of the function. (Use C for the constant of the antiderivative).
f(x) = 6x5 − 7x4 − 9x2
F(x) = ?
Answer:
[tex]x^6 - \frac{7x^5}{5} - 3x^3 + C[/tex]
{4.OA.A.3} There are 1,492 chairs in the auditorium. Ms. Jones wants to put them into 10 rows. If she splits the chairs evenly into 10 rows, how many chairs will Ms. Jones have left over?
Answer:
2 chairs will be left over.
Step-by-step explanation:
Given that
There are a total of 1492 chairs.
which are to divided in 10 rows evenly.
To find:
Number of chairs left ?
Solution:
Let the number of chairs in each row = [tex]x[/tex]
There are 10 rows so number of chairs in rows = 10[tex]x[/tex]
Let the number of chairs left = [tex]y[/tex]
Total number of chairs =10[tex]x[/tex] + [tex]y[/tex] = 1492
The above equation is like:
Divisor [tex]\times[/tex] Quotient + Remainder = Dividend
So, we have to find the remainder in this question where we are given Divisor and Dividend.
10 [tex]\times[/tex] 149 + 2 = 1492
So, dividing 1492 with 10, we get remainder as 2.
Hence, 2 chairs will be left.
Find the first five terms of the sequence of partial sums. (Round your answers to four decimal places.) [infinity] (−5)n + 1 n!
Answer:
25.0000 + -37.5000 + 66.6667 + -63.5416 + 66.6667
Step-by-step explanation:
The actual formatting of the question has been attached to this response.
From the question,
Let the sequence of terms be [tex]b_{n}[/tex] i.e
[tex]b_{n}[/tex] = [tex]\frac{(-5)^{n+1} }{n!}[/tex]
Let the sequence of partial sums be [tex]S_{n}[/tex] i.e
[tex]S_{n}[/tex] = s₁ + s₂ + s₃ + . . . + sₙ
Therefore the first five terms of the sequence of partial sums will be S₅ i.e
S₅ = s₁ + s₂ + s₃ + s₄ + s₅
Where;
s₁ = b₁
s₂ = b₁ + b₂ = s₁ + b₂
s₃ = b₁ + b₂ + b₃ = s₂ + b₃
s₄ = b₁ + b₂ + b₃ + b₄ = s₃ + b₄
s₅ = b₁ + b₂ + b₃ + b₄ + b₅ = s₄ + b₅
Where;
b₁ can be found by substituting n = 1 into equation (i) as follows;
[tex]b_{1}[/tex] = [tex]\frac{(-5)^{1+1} }{1!}[/tex]
[tex]b_{1}[/tex] = 25
[tex]b_{1}[/tex] = 25.0000
Recall that
s₁ = b₁
∴ s₁ = 25.0000 to 4 decimal places
--------------------------------------------------------------------------
b₂ can be found by substituting n = 2 into equation (i) as follows;
[tex]b_{2}[/tex] = [tex]\frac{(-5)^{2+1} }{2!}[/tex]
[tex]b_{2}[/tex] = -62.5
[tex]b_{2}[/tex] = -62.5000
Recall that
s₂ = s₁ + b₂
∴ s₂ = 25.000 + -62.5000 = -37.5000
-----------------------------------------------------------------------------------------
b₃ can be found by substituting n = 3 into equation (i) as follows;
[tex]b_{3}[/tex] = [tex]\frac{(-5)^{3+1} }{3!}[/tex]
[tex]b_{3}[/tex] = 104.1667
Recall that
s₃ = s₂ + b₃
∴ s₃ = -37.5000 + 104.1667 = 66.6667
--------------------------------------------------------------------------------
b₄ can be found by substituting n = 4 into equation (i) as follows;
[tex]b_{4}[/tex] = [tex]\frac{(-5)^{4+1} }{4!}[/tex]
[tex]b_{4}[/tex] = -130.2083
Recall that
s₄ = s₃ + b₄
∴ s₄ = 66.6667 + -130.2083 = -63.5416
-------------------------------------------------------------------------
b₅ can be found by substituting n = 5 into equation (i) as follows;
[tex]b_{5}[/tex] = [tex]\frac{(-5)^{5+1} }{5!}[/tex]
[tex]b_{5}[/tex] = 130.2083
Recall that
s₅ = s₄ + b₅
∴ s₅ = -63.5416 + 130.2083 = 66.6667
------------------------------------------------------------------------------
Therefore, the first five terms of the partial sum is:
25.0000 + -37.5000 + 66.6667 + -63.5416 + 66.6667
a milha eh uma unidade usada para medir distancias. ela equivale a cerca de 1,6 quilometros. se cada carro percorrer 240 quilometros, quantas milhas tera percorrido? urgente
Classica aplicação de regra de 3:
é dito que: 1 milha = 1,6km
Logo, eis a regra de 3:
milha km
1 -------- 1,6
X -------- 240
1,6X = 240.1
X = 240/1,6
X = 150milhasLogo 240km equivalem a 150milhas
A researcher reports a 98% confidence interval for the proportion of Drosophila in a population with mutation Adh-F to be [0.34, 0.38]. Therefore, there is a probability of 0.98 that the proportion of Drosophola with this mutation is between 0.34 and 0.38. True or False
Answer:
False
Step-by-step explanation:
The 98% is confidence interval its not a probability estimate. The probability will be different from the confidence interval. Confidence interval is about the population mean and is not calculated based on sample mean. Every confidence interval contains the sample mean. There is 98% confidence that the proportion of Drosophola with his mutation is between 0.34 and 0.38.
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
if G is the midpoint of FH, FG = 14x + 25 and GH = 73 - 2x, find FH.
Answer:
FH = 134
Step-by-step explanation:
From the question given:
G is the midpoint of FH
FG = 14x + 25
GH = 73 - 2x
FH =?
Next, we shall determine the value of x. The value of x can be obtained as follow:
Since G is the midpoint of FH, this implies that FG and GH are equal i.e
FG = GH
With the above formula, we can obtain the value of x as follow:
FG = 14x + 25
GH = 73 - 2x
x =?
FG = GH
14x + 25 = 73 - 2x
Collect like terms
14x + 2x = 73 - 25
16x = 48
Divide both side by 16
x = 48/16
x = 3
Next, we shall determine the value of FG and GH. These can be obtained as shown below:
FG = 14x + 25
x = 3
FG = 14x + 25
FG = 14(3) + 25
FG = 42 + 25
FG = 67
GH = 73 - 2x
x = 3
GH = 73 - 2x
GH = 73 - 2(3)
GH = 73 - 6
GH = 67
Finally, we shall determine FH as follow:
FH = FG + GH
FG = 67
GH = 67
FH = FG + GH
FH = 67 + 67
FH = 134
Therefore, FH is 134
A political candidate has asked his/her assistant to conduct a poll to determine the percentage of people in the community that supports him/her. If the candidate wants a 10% margin of error at a 95% confidence level, what size of sample is needed
Answer:
The desired sample size is 97.
Step-by-step explanation:
Assume that 50% people in the community that supports the political candidate.
It is provided that the candidate wants a 10% margin of error (MOE) at a 95% confidence level.
The confidence interval for the population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
Then the margin of error is:
[tex]MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
Compute the critical value of z as follows:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]
*Use a z-table.
Compute the sample size as follows:
[tex]MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]n=[\frac{z_{\alpha/2}\times \sqrt{\hat p(1-\hat p)} }{MOE}]^{2}[/tex]
[tex]=[\frac{1.96\times \sqrt{0.50(1-0.50)} }{0.10}^{2}\\\\=[9.8]^{2}\\\\=96.04\\\\\approx 97[/tex]
Thus, the desired sample size is 97.
 evaluate the expression for c=-10, d=9 and f=-1
Answer:
99
Step-by-step explanation:
(-10)(9)(-1) + 9 =
90 + 9 = 99
Let A represent going to the movies on Friday and let B represent going bowling on Friday night. The P(A) = 0.58 and the P(B) = 0.36. The P(A and B) = 94%. Lauren says that both events are independent because P(A) + P(B) = P(A and B) Shawn says that both events are not independent because P(A)P(B) ≠ P(A and B) Which statement is an accurate statement? Lauren is incorrect because the sum of the two events is not equal to the probability of both events occurring. Shawn is incorrect because the product of the two events is equal to the probability of both events occurring. Lauren is correct because two events are independent if the probability of both occurring is equal to the sum of the probabilities of the two events. Shawn is correct because two events are independent if the probability of both occurring is not equal to the product of the probabilities of the two events.
Answer:
Shawn is correct because two events are independent if the probability of both occurring is equal to the product of the probabilities of the two events.
Step-by-step explanation:
We are given that A represent going to the movies on Friday and let B represent going bowling on Friday night. The P(A) = 0.58 and the P(B) = 0.36. The P(A and B) = 94%.
Now, it is stated that the two events are independent only if the product of the probability of the happening of each event is equal to the probability of occurring of both events.
This means that the two events A and B are independent if;
P(A) [tex]\times[/tex] P(B) = P(A and B)
Here, P(A) = 0.58, P(B) = 0.36, and P(A and B) = 0.94
So, P(A) [tex]\times[/tex] P(B) [tex]\neq[/tex] P(A and B)
0.58 [tex]\times[/tex] 0.36 [tex]\neq[/tex] 0.94
This shows that event a and event B are not independent.
So, the Shawn statement that both events are not independent because P(A)P(B) ≠ P(A and B) is correct.
Answer:
Shawn is correct
Step-by-step explanation:
Solve for x (x+4)/3 = 2.
a. x = -2
b. x=2
c. x = 2/3
d. x= -10/3
Answer:
The answer is option BStep-by-step explanation:
[tex] \frac{x + 4}{3} = 2[/tex]
To solve it first of all cross multiply
That's
x + 4 = 6
Move 4 to the right side of the equation
The sign changes to negative
That's
x = 6 - 4
We have the final answer as
x = 2Hope this helps you
a golfer hits the golf ball. the quadratic y = -14x^2+84x gives the time x seconds when the golf ball is at height 0 feet. In total, how long is the golf ball in the air?
Answer: 6 seconds
Step-by-step explanation:
x refers to time. Since we want to know how long it is in the air, we need to find the time (x) when the ball lands on the ground (y = 0)
0 = -14x² + 84x
0 = -14x(x - 6)
0 = -14x 0 = x - 6
0 = x 6 = x
x = 0 seconds is when the ball was hit
x = 6 seconds is when the ball landed on the ground
NEED HELP ASAP
Which point represents the center of the circle shown below?
Answer:
Point O represents the center of the circle
Step-by-step explanation:
HOPE IT HELPS. PLEASE MARK IT AS BRAINLIEST
A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below. Construct a 95% confidence interval for the mean difference between the before and after scores. Is there evidence to suggest the logic course improves abstract reasoning? You may assume that the differences for the dependent samples are normally distributed . Before 74, 83, 75, 88, 84, 63, 93, 84, 91, 77 After 73, 77, 70, 77, 74, 67, 95, 83, 84, 75
Note : define d = before - after, then đ = 3.7 and s = 4.95
Please sketch the rejection region and show computation for the test statistic
Answer:
1. confidence interval = (0.163, 7.237)
1. confidence interval = (0.163, 7.237)2. t = 2.366
1. confidence interval = (0.163, 7.237)2. t = 2.3663. critical value of one tailed test = 1.833
Step-by-step explanation:
before after dt(before - after) d²
74 73 1 1
83 77 6 36
75 70 5 25
88 77 11 121
84 74 10 100
63 67 -4 16
93 95 -2 4
84 83 1 1
91 84 7 49
77 75 2 4
∑dt = 37
d* = 37/10
since sample space = 10
d* = 3.7
s.d from the question = 4.95
df = 10 - 1 = 9
critical value at 0.05 significance
t(0.025 at df of 9) = ±2.262
marginal error computation:
= (2.262) × (4.945/√10)
= 2.262 × 1.5637
= 3.5370
confidence interval CI = d* + marginal error
= 3.7 ±3.5730
= (0.163, 7.237)
The logic course give an improvement on abstract reasoning. The confidence interval shows that the result is significant.
H₀: Цd = 0
H₁: Цd > 0
∝ = 0.05
t = (3.7 - 0)/(4.945/√10)
t = 3.7/1.564
t = 2.366
for a right tailed test at 0.05 significance, and df of 9, the critical value is 1.833
please refer to the attachment to see the rejection region.
Helppppp thank you!!!
Answer:
G.) 72°
Step-by-step explanation:
A regular pentagon has all it's sides equal.
And all it's internal angles = 108°
The sum of all it's internal angles= 540°
AEB = TRIANGLE
And sum of internal angles In a triangle= 180°
EBDC is quadrilateral and a quadrilateral has it's internal angles summed up to 360°
But DEB = CBE
Let DEB = X
x + x +108+108= 360
2x= 360-216
2x= 144
X= 144/2
X=72
DEB = 72°
savanah solved the equation 3+4 multiplied by the absolute value of x/2+3=11 for one solution. her work is shown below. what is the other solution to the given absolute value equation: savanah's solution was x= -2
Answer:
-10Step-by-step explanation:
Given the equation solved by savanah expressed as [tex]3+4|\frac{x}{2} + 3| = 11[/tex], IF she solved for one of the solution and got x = -2, we are to solve for the other value of x.
Note that the expression in modulus can be expressed as a positive expression and negative expression.
For the positive value of the expression [tex]|\frac{x}{2} + 3|[/tex] i.e [tex]\frac{x}{2} + 3[/tex], the expression becomes;
[tex]3+4(\frac{x}{2} + 3) = 11[/tex]
On simplification;
[tex]3+4(\frac{x}{2} + 3) = 11\\\\3 + 4(\frac{x}{2} )+4(3) = 11\\\\3 + \frac{4x}{2}+ 12 = 11\\\\3 + 2x+12 = 11\\\\2x+15 = 11\\\\Subtract \ 15 \ from \ both \ sides\\\\2x+15-15 = 11-15\\\\2x = -4\\\\x = -2[/tex]
For the negative value of the expression [tex]|\frac{x}{2} + 3|[/tex] i.e [tex]-(\frac{x}{2} + 3)[/tex], the expression becomes;
[tex]3+4[-(\frac{x}{2} + 3)] = 11[/tex]
On simplifying;
[tex]3+4[-(\frac{x}{2} + 3)] = 11\\\\3+4(-\frac{x}{2} - 3)= 11\\\\3-4(\frac{x}{2}) -12 = 11\\\\3 - \frac{4x}{2} - 12 = 11\\\\3 - 2x-12 = 11\\\\-2x-9 = 11\\\\add \ 9 \ to \ both \ sides\\\\-2x-9+9 = 11+9\\-2x = 20\\\\x = -20/2\\\\x = -10[/tex]
Hence her other solution of x is -10
Suppose that a polynomial function of degree 4 with rational coefficients has 6, 4, 6i as zeros. Find the other zero
Answer:
-6i
Step-by-step explanation:
Complex roots have to come in conjugate pairs
So if we have 6i as a root, we must have -6i as a root
Answer:
-6i
Step-by-step explanation:
Hello, because this polynomial function has real coefficients and 6i is a zero, the conjugate of 6i is a zero as well. It means -6i is a zero.
The degree is 4 the number of zeroes is less or equal to 4 and we have already, 6, 4, 6i and -6i. So we have all the zeroes.
Thank you
Assume a random sample of size n is from a normal population. Assume a single sample t test is used to for hypothesis testing. The null hypothesis is that the population mean is zero versus the alternative hypothesis that it is not zero. If the sample size is decreased, and the Type I error rate is unchanged, then the Type II error rate will increase.a. Trueb. False
Answer:
true
Step-by-step explanation:
type 1 and type 2 are not independent of each other - as one increases, the other decreases
(-1, 4) and (-2, 2).
Answer:
Slope : 2
slope-intercept: y = 2x + 6
Point-slope (as asked): y - 4 = 2 (times) (x + 1)
standered: 2x - y = -6
Step-by-step explanation:
Layla is going to drive from her house to City A without stopping. Layla plans to drive
at a speed of 30 miles per hour and her house is 240 miles from City A. Write an
equation for D, in terms of t, representing Layla's distance from City A t hours after
leaving her house.
Answer:
D = 240 - 30t
Step-by-step explanation:
If the equation represents her distance from City A, we need to include 240 in the equation to represent the distance to the city.
Then, we need to subtract 30t from 240 in the equation because 30t represents how far she will have traveled in t hours.
So, D = 240 - 30t is the equation that will represent Layla's distance from the city.
is [tex]\sqrt[4]{5x^{5} }[/tex] equal [tex](\sqrt[4]{5x} )^{5}[/tex] ?
3 With 72 million bicycles, correct to the
nearest million, Japan is at the top of the list
of countries with most bicycles per person.
On average, Japanese people travel about
2 km by bicycle, correct to the nearest km,
each day. Calculate the upper bound for the
total distance travelled by all the bicycles in
Japan.
Answer:
181 million km
Step-by-step explanation:
"Correct to the nearest unit" means the actual value might be 1/2 unit larger (or smaller) than the reported value.
The upper bound would be the product of the maximum number of bicycles and the maximum distance each travels:
(72.5 · 10^6 bicycles)(2.5 km/bicycle) = 181.25 · 10^6 km
__
Since the given numbers are good to 2 significant figures (or so), we might reasonably put the upper bound as 180·10^6 km.
Help please!! Thank you
Answer:
D
Step-by-step explanation:
-3, 3, 6, 9, 15, 18, 21,
Find the value of angle X. x = 40 x = 55 x = 109 x = 130 I will mark as Brainliest
Answer:
130 degree
Step-by-step explanation:
Interior angles of the triangle:
81, 49, (180-x)
and by sum of all angles of triangle is 180 degree,
therefore,
81 + 49 + 180 - x = 180
x = 130 degree
The volume of a rectangular prism is the products it’s dimensions. If the dimensions of a rectangle prism are approximately 1.08 feet,5.25 feet, and 3.3 feet ,what is the approximate volume of the cube?Express your answer using an approximate level of accuracy.
Answer:
18.711
Step-by-step explanation:
Volume = L * W * H
V = 1.08 * 5.25 * 3.3
1.08 * 5.25 = 5.67
5.67 * 3.3 =
V = 18.711
is perpendicular to . How many 90° angles are formed by the intersection?
Answer:
if a is perpendicular to b then four 90 degree angles are formed
Step-by-step explanation:
if a line is perpendicular to another that means that it forms a 90 degree angle on all of the angles
Answer:
Four
That is the right answer for Edmentum and Plato users
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multiple choice plz answer be the correct answer and show working out if can it has to be correct plz "multiple coordinate transfermation"
Answer:
Solution : Option B
Step-by-step explanation:
1. This point first underwent a translation of 1 unit up and 4 units left. After a translation of 1 unit up, the coordinate would be ( - 2, 8 ), and after moving 4 units left the coordinate would be ( - 6, 8 ). This is our new point after the translation.
2. Next, point ( - 6, 8 ) was reflected about the x - axis. This would make the coordinate ( - 6, - 8 ) - as it now enters the third quadrant, where all possible x and y coordinates are taken to be negative.
3. Now point ( - 6, - 8 ) is rotated 90 degrees anticlockwise about the origin. Remember that this point is in the third quadrant. If it moves anticlockwise 90 degrees, it will end up in the fourth quadrant, seemingly at point ( 8, - 6 ).
the box plots shows the price for two different brands of shoes
Answer:
A. The interquartile range (IQR) for brand A, $10, is less than the IQR for brand B, $25.
Step-by-step explanation:
The most appropriate measure that can be used to compare the SPREAD of the data of the 2 brands plotted on a box plot, is the Interquartile range (IQR).
Interquartile range is the difference between Q3 and Q1.
Q3 is the value which lies at the end of the rectangular box, while the Q1 lies at the beginning of the box.
From the box plot given,
IQR for brand A = 80 - 70 = $10
IQR for brand B = 50 - 25 = $25
Therefore, the correct option is "A. The interquartile range (IQR) for brand A, $10, is less than the IQR for brand B, $25."
The force of gravity on an object varies directly with its mass. The constant of variation due to gravity is 32.2 feet per second squared. Which equation represents F, the force on an object due to gravity according to m, the object’s mass? F = 16.1m F = F equals StartFraction 16.1 Over m squared EndFraction. F = 32.2m F = F equals StartFraction 32.2 Over m squared EndFraction.
Answer:
F = 32.2mStep-by-step explanation:
According to newton second law, the force of gravity on an object varies directly with its mass and it is expressed mathematically as Fαm i.e
F = mg where;
F is the force of gravity
m is the mass of the body
g is the proportionality constant known as the acceleration due to gravity.
If the constant of variation due to gravity is 32.2ft/s², the equation that represents F, the force on an object due to gravity according to m, the object’s mass can be gotten by substituting g = 32.2 into the formula above according to the law as shown;
F = m*32.2
F =32.2m
Hence the required equation is F = 32.2m
What is the sign of -1.69+(-1.69)
Answer: Negative sign
Adding two negative values results in another negative value.
-1.69 + (-1.69) = -3.38
It's like starting $1.69 in debt and then adding 1.69 dollars of more debt. You'll slide further into debt being $3.38 in debt total.
The sign is negative as the value of -1.69 + (-1.69) is -3.38.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
-1.69 + (-1.69)
= -1.69 - 1.69
= -3.38
This means,
The sign is negative.
Thus,
The value of -1.69 + (-1.69) is -3.38.
Learn more about expressions here:
https://brainly.com/question/3118662
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