Find the area of the shaded region.f(x)=4x+3x2−x3,g(x)=0
The area is _____.
Answer:
The answer is " [tex]\bold{\frac{7}{2}}[/tex]"
Step-by-step explanation:
Given value:
[tex]\to f(x)=4x+3x^2-x^3\\\\\to g(x)=0[/tex]
Find:
area=?
calculation:
[tex]\ Area = \int_{-1}^{0} -(4x+3x^2-x^3) dx + \int_{0}^{1} (4x+3x^2-x^3) dx \\\\[/tex]
[tex]= -(2x^2+x^3- \frac{x^4}{4})_{-1}^{0} + (2x^2+x^3- \frac{x^4}{4})_{0}^{1}\\\\\\= -( 2x^2+x^3- \frac{x^4}{4})_{-1}^{0} + (2x^2+x^3- \frac{x^4}{4})_{0}^{1}\\\\\\= ( 2- 1 -\frac{1}{4}) + (2+1- \frac{1}{4})\\\\\\= ( \frac{8-4-1}{4}) + (\frac{8+4-1}{4})\\\\= ( \frac{3}{4}) + (\frac{11}{4})\\\\= \frac{3}{4} + \frac{11}{4}\\\\= \frac{11+3}{4}\\\\= \frac{14}{4}\\\\= \frac{7}{2}\\\\[/tex]
The sum of the ages of Caleb and Linda is 55 years. 8 years ago, Caleb's age was 2 times Linda's age. How old is Caleb now?
Answer:
34
Step-by-step explanation:
1. if to guess the Caleb's age is 'x' years and Linda's age is 'y' years now, then
2. according to the 'sum of the ages of Caleb and Linda is 55 years' it may be written: x+y=55 - the first equation of the system;
3. according to the condition '8 years ago, Caleb's age was 2 times Linda's age' it may be written: (x-8)(y-8)=2 - the second equation of the system;
4. if to make up the system of two equation and calculate the values of 'x' and 'y':
5. if x=34, then Caleb is 34 old now.
Which display makes it easier to find that the interquartile range is 4 songs?
Choose 1 answer:
A
The dot plot
B
The box plot
Answer:
The box plot
Step-by-step explanation:
a number times 10 is equal to 28
Answer:
2.8
Step-by-step explanation:
2.8*10=28
Also, when you multiply 2.8 by 10, you can just move the decimal to the right once, giving you 28.
Is 2^5 the same as 5^2? Yes or No?
Explain why please help me thank you!!
Answer:
No, they are not equivalent.
Step-by-step explanation:
2^5 means 2 to the 5th power, so we multiply it by itself 5 times.
2x2x2x2x2=32
Same as 5^2
5x5=25
32>25
There is your answer, no.
6^-2 = PLEASE HELP .....................................................................
Answer:
6^-2 =0.02777777777
Step-by-step explanation:
BRAINLIST! I put the picture down bellow its on equations A. Incorrect division or multiplication B. Incorrect addition or subtraction C. Failure to combine like terms D.Added terms instead of multiplying
Answer:
i think it is b .
Step-by-step explanation:
Identify the constraints modeled by this graph.
A different car seats. One car seat designed for a child up to and including 34lb. Another car seat designed for a child between 16 lb and 40lb. A third car seat is designed a child between 34lb and 90 lb, inclusive. Model those ranges with compound inequalities . Which car seats are appropriate for a 33lb child? The inequality for a child up to and including 34 lb is what?
Answer:
the first and second car seats are appropriate for a 33 lb. child. The first seat suits children up to 34 lb. The second seat suits children that weight between 16 to 40 lb.
The only seat that is not appropriate would be the third one that is too large, since children between 34 to 90 lb. should use it.
seat 1 ≤ 34 lb ⇒ simple inequality
16 lb < seat 2 and seat 2 < 40 lb ⇒ compound inequality
34 lb < seat 3 and seat 3 ≤ 90 lb ⇒ compound inequality
what is x6y6z2 please asap
Dear student,
I request you to make you question more clear.
thank you,
________ ___________________________________
Find the area of a square with sides of length 6.5 inches
Answer:
A=42.25
Step-by-step explanation:
6.5^2
Find the volume of oxygen in a room with the dimensions of 144.78 cm x 198.12 cm x 144.78
Answer:
4,152,842.53301 cm³ ≈ 4.1528 m³
Step-by-step explanation:
The volume of a rectilinear room of those dimensions will be the product of those dimensions:
(144.78 cm)(198.12 cm)(144.78 cm) = 4,152,842.53301 cm³
A more appropriate unit for such a volume is cubic meters. There are a million cubic centimeters in a cubic meter, so the volume (to 5 significant digits) is ...
4.1528 m³
_____
We assume that any oxygen is uniformly distributed in the space, so the volume of oxygen will be the same as the volume of the room.
_____
Additional comment
These dimensions correspond to those of a room that is 57 inches square and 78 inches high.
A basketball player makes 80% of his free throws. We set him on the free throw line and told him to shoot free throws until he misses. Let the random variable X be the number of free throws taken by the player until he misses. Assuming that his shots are independent, what is the probability of this player missing a free throw for the first time on the fifth attempt
Answer: 0.08192
Step-by-step explanation:
Given: Probability of free throws = 0.80
Then, probability of missing the free throw = 1-0.80=0.20
Now, According to the negative binomial probability distribution, the probability that the rth success is achieved in xth trial is given by ;-
[tex]P(X=x)= pC_{r-1}^{x-1}p^{r-1}(1-p)^{(x-r}[/tex]
Put p = 0.20 , x=5 and r =1, we get
The probability of this player missing a free throw for the first time on the fifth attempt as [tex](0.20)\ ^{5-1}C_{1-1}(0.20)^{1-1}(1-0.20)^{5-1}[/tex]
[tex]= (0.20)\ ^{4}C_{0}(0.20)^{0}(0.80)^{4}\\\\=(0.20)(1)(0.80)^4\\\\=(0.20)(0.4096)\\\\=0.08192[/tex]
hence the required probability =0.08192
Answer:0.08912
Step-by-step explanation:
You work at a coffee shop and they pay you $12.80 an hour. If you work 34
works this week, what is your straight-time pay?
A. $435.20
B. $438.80
C. $442.20
D. $444.60
E. $446.40
F. $448.20
Answer:
answer is A $435.20
Step-by-step explanation:
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a brownie recipe requires 2/3 cup of sugar for 1/3 batch of brownies. how much sugar is need for 1 batch of brownies?
Answer: 2 Cups
Step-by-step explanation:
1/3 * 3 = 1
2/3 * 2 = 2
Answer:
you will need 2 cups of sugar for 1 batch of brownies
Step-by-step explanation:
2/3 cup ×3 = 6/3 cups or 2 cups
There are many ways to produce crooked dice. To load a die so that 6 comes up too often and 1 , which is opposite 6 , comes up too seldom, add a bit of lead to the filling of the spot on the 1 face. If a die is loaded so that 6 comes up with probability 0.2 and the probabilities of the 2,3,4 , and 5 faces are not affected, which of the choices is the correct assignment of probabilities to the six faces
Answer:
1 2 3 4 5 6
2 ÷ 15 1 ÷ 6 1 ÷ 6 1 ÷ 6 1 ÷ 6 1 ÷ 5
Step-by-step explanation:
As it is mentioned in the question that the probability of faces like 2,3,4,5 are not affected so in this case
P(2) = P(3) = P(4) = P(5) = 1 ÷ 6
And, P(6) = 0.2
As we know that
P(1) + P(2) +P(3) +P(4) +P(5) +P(6) = 1
This results P(1) = 2 ÷ 15
So,
1 2 3 4 5 6
2 ÷ 15 1 ÷ 6 1 ÷ 6 1 ÷ 6 1 ÷ 6 1 ÷ 5
Hence, the correct option is 2nd
In the first 1/6 hour of a rain storm, 1/10 inch of rain fell. If the rain continues to fall at the same rate, how much rain fell in 2 1/2 hours?
Answer:
3/2 inches
Step-by-step explanation:
Write the point-slope form of the line satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation.
Slope,=6 passing through (-2,8)
Type the point-slope form of the equation of the line.
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
Answer:
Step-by-step explanation:
y - 8 = 6(x + 2)
y - 8 = 6x + 12
y = 6x + 20
Of 150 goldfish in the fish pound, 27 are red. What percentage of goldfish are red?
To get the percent, divide 27 by 150 then multiply the quotient by 100.
(27 / 150) * 100 = 18%
Suppose a student just found out that she scored a 75 on her first statistics exam, with a z-score of 0.5. Her friend, who is in a different section with the same professor, also scored a 75 but had a z-score of −0.5. What can you conclude about the mean exam scores in the two classes?
Answer:
The mean exam scores in the second section is greater than the mean exam scores in the first section
Step-by-step explanation:
Here, we are interested in making a conclusion.
Mathematically;
z-score = (score - mean)/SD
so basically, what determines the sign of the z-score is dependent entirely on the mean.
If the mean is larger than the score, we will have a negative z-score. If the mean is smaller than the score, then will have a positive z-score
So basically what drives the sign is the mean value since the scores are the same for both students in this case, irrespective of the standard deviation in both classes.
So, for the first girl with a positive z-score, we can conclude that her score is larger than the mean; while for the second girl with a negative z-score, her score is smaller to the mean.
Thus, what we conclude here is that the mean score of the second section with the professor is greater than the mean score of the first section with the professor.
If 9 (x) = – 5x2 – 4x + 19 find f (–3)
Answer:
- 14
Step-by-step explanation:
[tex]f(x) = - 5 {x}^{2} - 4x + 19 \\ plug \: x = - 3 \\ f( - 3) = - 5 {( - 3)}^{2} - 4( - 3) + 19 \\ f( - 3) = - 5 \times 9 + 12 + 19 \\ f( - 3) = - 45 + 31 \\ f( - 3) = -14[/tex]
Bentley signed up for a streaming music service that costs $13 per month. The service allows Bentley to listen to unlimited music, but if he wants to download songs for offline listening, the service charges $0.75 per song. How much total money would Bentley have to pay in a month in which he downloaded 10 songs? How much would he have to pay if he downloaded s songs
Answer:
multiply 0.75 × 10 = 7..50
Please I really need help
Answer:
Answer 1: 1
Answer 2: 11
Answer 3: 5
by adding answers from 1 ,2 and 3
we get,
Answer 4: 17
A cylindrical container has a height of 24 inches. Currently, the container is filled with water to a height of 18 inches. A leaky faucet drips into the container, causing the height of the water in the container to increase by 2 inches per hour. The equation below can be used to find t, the number of hours it would take to fill the container.
18 + ?t = 24
What number should be the coefficient of t?
2
3
18
24
Answer:
a) 2
Step-by-step explanation:
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What is the value of the expression below after it has been simplified completely? (2)(3)-(6)(4) A. –24 B. –18 C. 18 D. 24
Answer:
B
Step-by-step explanation:
2x3=6 and 6x4=24 so 6-24= -18
Answer:
B
Step-by-step explanation:
-18
0.0769 to the nearest hundred
Answer:
0.0800
Step-by-step explanation:
Answer:
[tex]0.0769[/tex] rounded to the nearest hundred is: [tex]0.08[/tex]
Step-by-step explanation:
Rounded to the nearest 0.01 or
the Hundredths Place.
Hope this helps you!
1/2x=14
Help please I’ve been stuck on this how do I check it?
what is the Answer for 2(-4)
Answer2(-4)= -8 :
Step-by-step explanation:
Answer:
-8
Step-by-step explanation:
2×(-4)= -8
The answer will be negative because if you multiply a negative by a positive it will always be a negative.
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−10= -0.8x+1.8(-4x+1)-7
Answer X= 0.6
Step-by-step explanation:
If 25% of a number is 30, then what is 40% of the same number?
Divide 30 by 25% to find the full amount:
30/0.25 = 120
Now multiply the full amount by 40%:
120 x 0.40 = 30