Answer:
The antiderivative is [tex]F(X) = 6x + 6x^4 + 3x^6 - 15[/tex].
Step-by-step explanation:
Antiderivative F(x)
This is the integral of [tex]F^{\prime}(x)[/tex]
So
F′(x) = f(x) = 6 + 24x^3 + 18x^5
Then:
[tex]F(x) = \int (6 + 24x^3 + 18x^5) dx[/tex]
[tex]F(x) = 6x + \frac{24x^4}{4} + \frac{18x^6}{6} + K[/tex]
[tex]F(x) = 6x + 6x^4 + 3x^6 + K[/tex]
F(1)=0
[tex]F(X) = 0[/tex] when [tex]x = 1[/tex]. We use this to find K.
[tex]F(x) = 6x + 6x^4 + 3x^6 + K[/tex]
[tex]0 = 6 + 6 + 3 + K[/tex]
[tex]K = -15[/tex]
Thus
The antiderivative is [tex]F(X) = 6x + 6x^4 + 3x^6 - 15[/tex].
Six numbers have a mean of 4.5 and five of the numbers are 4,3,4,6,1.
The other number is x.
Work out the value ofx.
Answer:
X = 9
Step-by-step explanation:
4 + 3 + 4 + 6 + 1 + x / 6 = 4.5
18 + x / 6 = 4.5
cross multiply
18 + x = 4.5 × 6
18 + x = 27
collect like terms
x = 27 - 18
x = 9
Pencils cost x cents and erasers cost y cents each. Mary buys 7 pencils and 3 erasers. Write down the total cost in cents, in terms of x and y.
Answer:
7x + 3y.
Step-by-step explanation:
7 pencils cost 7x cents and 3 erasures cost 3y cents.
Which of the following pairs consists of equivalent fractions? .4/6 and 3/5 or 9/16 and 3/32 or 18/48 and 15/40 or 7/10 and 10/7
Answer:
18/48 and 15/40
Step-by-step explanation:
The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 42 ounces and a standard deviation of 10 ounces. Use the Empirical Rule.
a. 99.7% of the widget weights lie between _____ and _____.
b. What percentage of the widget weights lie between 26 and 66 ounces?
c. What percentage of the widget weights lie above 34?
Answer:
The answer is below
Step-by-step explanation:
The empirical rule states for a normal distribution, 68% of the data falls within one standard deviation, 95% falls within two standard deviations and 99.7% falls within three standard deviations.
z score is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Given that mean (μ) = 42 ounces, standard deviation (σ) = 10 ounces.
a) 99.7% falls within three standard deviations. Therefore:
99.7% falls within μ ± 3σ = 42 ± 3(10) = 42 ± 30 = (12, 72)
Therefore 99.7% falls within 12 ounce and 72 ounce.
b) For x > 26
[tex]z=\frac{26-42}{10}=-1.6\\[/tex]
For x < 66
[tex]z=\frac{66-42}{10}=2.4\\[/tex]
From the normal distribution table, P(26 < x < 66) = P(-1.6 < z < 2.4) = P(z < 2.4) - P(z < -1.6) = 0.9918 - 0.0548 = 0.937 = 93.7%
c) For x > 34
[tex]z=\frac{34-42}{10}=-0.8\\[/tex]
From the normal distribution table, P(x > 34) = P(z > -0.8) = 1 - P(z < -0.8) = 1 - 0.2119 = 0.7881 = 78.81%
Answer:
Step-by-step explanation:
Given that:
Mean [tex]\mu[/tex] = 42
standard deviation [tex]\sigma[/tex] = 10
Using Empirical Rule:
[tex]\mu[/tex] - [tex]\sigma[/tex] = 42 - 10 = 32 [tex]\mu[/tex] + [tex]\sigma[/tex] = 42 + 10 = 52
[tex]\mu[/tex] - 2[tex]\sigma[/tex] = 42 - 2(10) = 22 [tex]\mu[/tex] + 2[tex]\sigma[/tex] = 42 + 2(10) = 62
[tex]\mu[/tex] - 3[tex]\sigma[/tex] = 42 - 3(10) = 12 [tex]\mu[/tex] + 3[tex]\sigma[/tex] = 42 + 3(10) = 72
The curve is attached in the image below.
a). the widget of 99.7% lies between 12 and 72
b) 68 + 13.5 = 81.5%
c) 50 + 34 = 84%
The sum of two consecutive integers is -5. If 4
is subtracted from the smaller integer and 2 is
added to the larger integer, what is the quotient
when the larger of the two resulting numbers is
divided by the smaller number?
Please help me
Answer:
sim eu também preciso desta respota
You need to take a dosage of 10 ml of medicine every 8 hours for 9 days. How many fluid ounces of
medicine should you purchase? Round up to the next whole fluid ounce.
ounces
Answer:
270 ml
Step-by-step explanation:
30x9=270
2.What is 10:30 pm in the 24-hour clock?
3. How do you write 00:15 in the 12-hour clock?
4.How do you write 11:50 pm in the 24-hour clock?
11.How are the circumference and the diameter of any given circle related
12. The diameter of a circle is 22 cm long. What is its area?
13.What is the area of the largest circle that can be drawn on a square paper whose side is 20 cm? *
16. Two workers need to dig a rectangular pit that is 2 meters long, 1.5 meters wide, and 1 meter deep. How many cubic meters of soil must they remove? *
17.A cubical water tank has a 20 cm edge. How much water can it contain?
tulong
2. 22:30
just add 12 on the front
that is the formula
2 If 9:30pm is 21:30,then 10:30pm=22:30 pm
3 15 seconds
4. If 10:30 = 22:30 then 11:50pm = 23:50
16. 3*1.5*1=4.5m^3
I think this are the ones I can try ,I hope this helps.
Paige and her family went to the movies. They bought 4 tickets and paid $12 for popcorn. They spent $40. How much did each ticket cost?
I need equation and cost :)
Answer:
Cost of tickets: $7. Equation: 40 = 4x + 12.
Step-by-step explanation:
Answer:
4*t +12 = 40
Each ticket cost 7 dollars
Step-by-step explanation:
tickets + popcorn = total cost
4*t +12 = 40
Subtract 12 from each side
4t +12-12 = 40-12
4t = 28
Divide by 4
4t/4 = 28/4
t = 7
Each ticket cost 7 dollars
Find the domain of f/g f(x)= sqrt 4-x^2 g(x)= sqrt 3x+4
Answer:
(-4/3, 2]
Step-by-step explanation:
f(x)= sqrt (4-x^2)
g(x) = sqrt (3x+4)
domain of f(x)/ g(x)
The domain of the numerator is
4-x^2 ≥ 0
4 ≥x^2
Taking the square root of each side
-2 ≤x≤2
The domain of the denominator
3x+4 > 0 ( the denominator cannot be zero)
3x>-4
x > -4/3
Combine the restrictions to make it most restrictive
-4/3<x≤2
In interval notation
(-4/3, 2]
Solve the equation 2x2 + x - 41 =
- 15 to the nearest tenth.
I neeeddd
HEEEELPPPP
Answer: 22
Step-by-step explanation: 2x2 + x -41= -15
* 4 + x -41= -15
* x -37= -15
* x= 22
A square + B square
Soln: Formula for a²+b² can be given by two types.
(i). a²+b² = (a+b)² - 2ab
= a²+2ab+b²-2ab
= a²+b²
=> LHS = RHS
Therefore, hence proved!
(ii). a²+b² = (a-b)² + 2ab
= a²-2ab+b²+2ab
=> LHS = RHS
Therefore, hence proved!
Hence, a²+b² = (a+b)² - 2ab
'OR'
a²+b² = (a-b)² + 2ab
Thank you. ☺️
hope it helps
You have an employee who copes with stressful demands by working overtime and weekends. You are concerned this will eventually burn him out, and want him to cope in a way that better addresses the emotions he is feeling head on. Which of the following would be an emotion-focused coping strategy?
a. Ask a coworker to help lighten the load
b. Go for a run to clear his mind
c. Increase the hours he works, but decrease the number of days (e.g., Four 12-hour days)
d. Coming up with a strategy to fix the stressful demand
Answer:
b. Go for a run to clear his mind.
Step-by-step explanation:
Emotion focused coping strategy is one in which a person goes for self isolation to release his stress. The person focuses on emotional distance from people because he believes the stress can increase if other people stays around him. When an employee suffers from stressful demand at work the best for him is to go for a run or walk and release stress.
Simplify the expression given below. x+2/4x^2+5x+1 * 4x+1/x^2-4
Answer:
[tex]\frac{1}{(x+1)(x-2)}[/tex]
Step-by-step explanation:
[tex]\frac{x+2}{4x^2 + 5x + 1} \ \times \ \frac{4x+1}{x^2-4}\\\\=\frac{x+2}{4x^2 + 4x + x + 1} \ \times \ \frac{4x+1}{x^2-2^2}\\\\=\frac{x+2}{4x(x + 1) + 1( x + 1)} \ \times \ \frac{4x+1}{(x - 2)(x + 2)} \ \ \ \ \ \ \ \ [ \ (a^2 - b^2 = (a-b)(a+b) \ ]\\\\\\=\frac{x+2}{(4x + 1)(x+1)} \ \times \ \frac{4x+1}{(x-2)(x+2)}\\\\=\frac{1}{(x+1)} \ \times \ \frac{1}{(x-2)}\\\\= \frac{1}{(x+1)(x-2)}[/tex]
Answer:
D. 1/(x+1)(x-2)
Step-by-step explanation:
i looked it up on a simplifier :)
Will mark Brainlest helppp plllllssss
Answer:
2h
Step-by-step explanation:
f(3 + h) = 2(3 + h)^2 + 1
= 2(3^2 + h^2) + 1
= 2(9) + 2h^2 + 1
= 18 + 2h^2 + 1
= 2h^2 + 19
f(3) = 2(3)^2 + 1
= 2(9) + 1
= 18 + 1
= 19
2h^2 + 19 - 19 / h
2h^2 / h
2h
Translate this phrase into an algebraic jahauahahshshshshshshshshshshhs
Answer:
Step-by-step explanation:
Jdshdcjecjjwdjwddhwedhwedwedwehwdhw?
i think?
Use the nutrition label to determine how many calories would be consumed by a person drinking half of the one-liter bottle of this soda.
1 Liter Mountain Dew
Nutrition Facts
Serving Size 8 fl oz. (240 ml)
Servings Per Container 4
Amount Per Serving
Calories 110
Daily Value
Total Fat og
Ox
Sodium 50 mg
2%
Total Carb. 318
10%
Sugars 315
Protein og
OX
* Percent Daily Values are based on
a 2.000 calo de diet
110
220
I need help I’ll mark u as brainlest
Answer:
V = 64 in^3
Step-by-step explanation:
The volume of a cube is given by
V = s^3 where s is the side length
V = 4^3
V = 64 in^3
Answer:
64
Step-by-step explanation:
volume of a cube formula: V = a^3
a is just one of the edges
[tex]4^{3}[/tex] = 64 = V
:)
The following data represents the number of days absent and the final grade for a sample of college students in a general education course at a large state university.
No. of absences 0 1 2 3 4 5 6 7 8 9
Final Grade 89.2 86.4 83.5 81.1 78.2 73.9 64.3 71.8 65.5 66.2
a) Which variable is the explanatory variable?
b) Draw a scatter plot and describe your scatter plot (Direction, Strength, Form).
c) Compute the correlation coefficient
d) Does a linear relation exist between the number of absences and the final grade? Justify your answer.
e) Write out the least-squares regression line equation.
f) Compute and draw the residual (on your scatter plot) for a student who misses 5 class meetings.
g) Explain the slope in context.
h) Is the y-intercept meaningful in this situation? Explain.
i) Compute and interpret the coefficient of determination.
j) Construct a residual plot to verify the requirements of the least-squares regression model.
Factor the polynomial: -5x3 - 10x2 - 15x
A. -5x(x2 + 2x - 15)
O B. 5x(x2 + 2x - 3)
O C. -5x(-x2 - 2x - 3)
OD. -5x(x2 + 2x + 3)
Answer:
answer is d if its wrong i am sorry
22. You are traveling on a highway starting at point A. After you have
traveled 63 miles (point B), you see a sign that says it is 87 miles
(point B), you see a sign that says it is 87 miles to your destination
(point C). . Find the total distance you will travel to get to your
destination.
A А
63 mi
B.
87 mi
С
Answer:
150 miles
Step-by-step explanation:
63 + 87 = 150
Factor this expression completely, then place the factors in the proper location on the grid. a2b2 - d2
Answer:
[tex]{ \tt{ {a}^{2} {b}^{2} - {d}^{2} }} \\ \\ = { \tt{( {ab})^{2} - {d}^{2} }} \\ = { \tt{(ab - d)(ab + d)}}[/tex]
Which statement best describes the meaning of the term average waiting-
time?
Answer:
The average number of trials required to get the first success
A man, 1.5m tall, is on top of a building. He observes a car on the road at an angle of 75°. If the building is 30m, how far is the car from the building?
Patty's dog weighs 48 ounces. How many pounds does Patty's dog weigh?
Answer:
If Patty's dog weighs 48 ounces, and we convert ounces to pounds, our answer is 3. Patty's dog weighs 3 pounds
Step-by-step explanation:
simplify 3xy-2x-5xy+7x-1
Step-by-step explanation:
shshddbsjsnsbsbakskkamansnsbdgdhshzjzkznzn
-2xy+5x+1
Not entirely sure this is 100% correct, but this is what I got lol
Rewrite with only sin x and cos x.
sin 2x - cos x
Answer:
2sinxcosx - cosx OR cosx(2sinx - 1)
Step-by-step explanation:
Use the double angle identity for sin2x.
sin2x = 2sinxcosx
Substitute sin2x with 2sinxcosx.
2sinxcosx - cosx
Factor out cosx, if needed.
cosx * (2sinx - 1)
Answer:
[tex]{ \tt{ \sin2x - \cos x }} \\ = { \tt{(2 \sin x \cos x) - \cos x }} \\ = { \tt{ \cos x(2 \sin x - 1) }}[/tex]
ASAP please helppp
Answer:
1.3
Step-by-step explanation:
Raise/run = slope aka distance in this situation
8/6 = 1.3
Answer:
10 units
Step-by-step explanation:
use the distance formula as thought in school
The function h(x) is defined as shown.
What is the range of h(x)?
h(x) =
x + 2, x <3
- x +8. X23
0-00
Oh(x) s 5
Oh(x) 25
Oh(x) 23
PLEASE HELOOOOODOOOOODIEIE
9514 1404 393
Answer:
(b) h(x) ≤ 5
Step-by-step explanation:
The maximum vertical extent of the graph is h(x) = 5 at x = 3. The range is all values of h(x) less than or equal to that:
h(x) ≤ 5
Answer: Choice B
The range is [tex]h(x) \le 5[/tex]
==============================================================
Explanation:
If we graph y = x+2, but only draw the line for x values smaller than 3, then we'll end up with the red line shown in the diagram below.
The blue line is the graph of y = -x+8, but it's only drawn when [tex]x \ge 3[/tex]
The two lines form an upside down V shape. This is an absolute value graph.
The highest point is at the vertex (3,5). The y coordinate is y = 5. This tells us that the largest h(x) can get is h(x) = 5.
Therefore, the range is [tex]h(x) \le 5[/tex]
This is the same as saying [tex]y\le 5[/tex] since y and h(x) are both outputs of a function.
Find X:
X + 25% x X = -1,25
Answer:
- 100
Step-by-step explanation:
OK open
The Pdf and look at the working
What is it quadratic, radical, rational?
Answer:
quadratic formula is ur answer for letter B