What fraction of the catapults flung a marshmallow 30 inches or less?
Answer:
1/4
Step-by-step explanation:
Each whisker represents 1/4 of data
What is the resulting integral?
Answer:
[tex]\displaystyle \int {\frac{2}{(1 + \sqrt{x})^5}} \, dx = \frac{-(4\sqrt{x} + 1)}{3(\sqrt{x} + 1)^4} + C[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Calculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Antiderivatives - Integrals
Integration Constant C
U-Substitution
U-SolveIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int {\frac{2}{(1 + \sqrt{x})^5}} \, dx[/tex]
Step 2: Identify Variables
Find the variables u-solve using u-substitution.
U-Substitution
[tex]\displaystyle u = 1 + \sqrt{x}[/tex]
[tex]\displaystyle du = \frac{1}{2\sqrt{x}}dx[/tex]
U-Solve
[tex]\displaystyle x = (u - 1)^2[/tex]
[tex]\displaystyle dx = 2\sqrt{x}du[/tex]
Step 3: Integration
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle 2\int {\frac{1}{(1 + \sqrt{x})^5}} \, dx[/tex][Integral] U-Solve: [tex]\displaystyle 2\int {\frac{1}{(1 + \sqrt{(u - 1)^2})^5}} \, 2\sqrt{x}du[/tex][Integral] Simplify: [tex]\displaystyle 2\int {\frac{2\sqrt{x}}{u^5}} \, du[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle 4\int {\frac{\sqrt{x}}{u^5}} \, du[/tex][Integral] U-Solve: [tex]\displaystyle 4\int {\frac{\sqrt{(u - 1)^2}}{u^5}} \, du[/tex][Integral] Simplify: [tex]\displaystyle 4\int {\frac{u - 1}{u^5}} \, du[/tex][Integral] Rewrite [Integration Property - Subtraction]: [tex]\displaystyle 4[\int {\frac{u}{u^5}} \, du - \int {\frac{1}{u^5}} \, du][/tex][Integrals] Simplify: [tex]\displaystyle 4[\int {\frac{1}{u^4}} \, du - \int {\frac{1}{u^5}} \, du][/tex][Integrals] Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle 4[\int {u^{-4}} \, du - \int {u^{-5}} \, du][/tex][Integrals] Reverse Power Rule: [tex]\displaystyle 4[\frac{u^{-3}}{-3} - \frac{u^{-4}}{-4}] + C[/tex]Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle 4[\frac{-1}{3u^3} + \frac{1}{4u^4}] + C[/tex][Brackets] Multiply: [tex]\displaystyle \frac{-4}{3u^3} + \frac{4}{4u^4} + C[/tex]Back-Substitute: [tex]\displaystyle \frac{-4}{3(1 + \sqrt{x})^3} + \frac{4}{4(1 + \sqrt{x})^4} + C[/tex]Combine: [tex]\displaystyle \frac{-(4\sqrt{x} + 1)}{3(\sqrt{x} + 1)^4} + C[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration
Book: College Calculus 10e
72 is what percent of 180
Answer:
.40 or 40 percent
Step-by-step explanation:
Dean Webber purchased 4 smoothies for $19.60. At this price, what is the cost per smoothie?
Answer:
$ 4.90 per smoothie
Step-by-step explanation:
The total cost of all of the 4 smoothies is $19.60. So, to find the answer you need to divide 19.60 with 4 and you'll get 4.9 or as dollars $4.90.
A manufacturing company with 350 employees is changing the employee health insurance plan to either plan A or plan B. The company wants to know if employees have a preference between the two plans and whether or not preference differs between those employees who have family members covered under the current plan (group 1) and those who do not (group 2). The human resources office takes a simple random sample from each of the two groups, sends information about both plans to the employees in each sample, and asks them whether they prefer plan A or plan B. The table summarizes the responses received, with expected cell counts in parentheses.
Plan A Plan B Total
Yes (group 1) 40 (32.5) 20 (27.5) 60
No (group 2) 6 (13.5) 19 (11.5) 25
Total 46 39 85
Which statement is true about whether the conditions for the chi-square test for homogeneity have been met?
a. A simple random sample should have been taken from all the employees, and then each employee in the sample should have been asked their plan preference and whether or not they have family members covered under the current health insurance plan.
b. The expected cell counts are not large enough to apply the chi-square test for homogeneity.
c. The total sample size is not large enough to apply the chi-square test for homogeneity.
d. The total sample size is too large to apply the chi-square test for homogeneity.
e. All conditions necessary to apply the chi-square test for homogeneity are satisfied here.
Answer: D. The total sample size is too large to apply the chi-square test for homogeneity.
Step-by-step explanation: When sampling without replacement, the sample size should not exceed 10 percent of the population size. Here, the sample size of 85 is just over 24 percent of the population of 350 company employees.
The total sample size is too large to apply the chi-square test for homogeneity.
We have given that,
A manufacturing company with 350 employees is changing the employee health insurance plan to either plan A or plan B.
Plan A Plan B Total
yes(group 1) 40(32.5) 20(27.5) 60
No (group 2) 6 (13.5) (11.5) 25 25
Total 46 39 85
We have to find which statement is true,
What is sampling without replacement?Each sample unit of the population has only one chance to be selected in the sample. we can select one sample only way and after selection we cannot pot this sample in the sample space again.
The sample size should not exceed 10 percent of the population size.when we use sampling without replacement,
Here, the sample size of 85 is just over 25 percent of the population of 350 company employees.
Therefore,the total sample size is too large to apply the chi-square test for homogeneity.
To learn more about the sample space replacement and without replacement visit:
https://brainly.com/question/17042101
Kenneth is painting his kitchen and bathroom. He bought 5 gallons of paint to paint the two rooms. He uses 1/4 of that amount to paint the bathroom and the rest to paint the kitchen.
Answer:
He used 1.25 gallons for the bathroom, and he used 3.75 gallons for the kitchen.
Step-by-step explanation:
1/4=25%=.25
Multiply 5 by .25
5*.25=1.25
Subtract 1.25 from 5
5-1.25=3.75
1.25 gallons for bathroom
3.75 gallons for kitchen
Hopefully this was helpful.
A snack recipe calls for 1 cup of sunflower seeds. The recipe makes 6 cups of the snack.
Joshua wants to make 24 cups of the snack to bring on a camping trip.
How many cups of sunflower seeds will Joshua need?
Answer:
4
Step-by-step explanation:
Bc if you want 24 servings but it serves 6 you have to multiply it by 4 do it's 1*4 =4 because 6*4 =24
Answer:
4/14 as a fraction
Step-by-step explanation:
i did the test
Help me with this, please!
Answer:
....
Step-by-step explanation:
The answer is a, yes yes
.....
Step-by-step explanation:
The answer is A yes. yes
427 diveided by 3 do you have any aneswerers
Answer:
142.333....
Step-by-step explanation: just use a calculator
Answer:
142.34
Step-by-step explanation:
427 ÷ 3 = 142.34
good luck, i hope this helps :)
A coin will be tossed three times, and each toss will be recorded as heads (H) or tails (T). Give the sample space describing all possible outcomes. Then give all of the outcomes for the event that the third toss is heads. Use the format to mean that the first toss is heads, the second is tails, and the third is heads. If there is more than one element in the set, separate them with commas.
Answer:
Sample space:
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Third toss is heads:
{HHT, HTT, THT, TTT}
First toss is heads, second tails and third heads:
{HTH}
Explanation:
In order to find the sample space we need to write all the possible outcomes from tossing the coin three times.You can start by writting all the possible outcomes for the first toss being a head and finish with all the possible outcomes for the first toss being Tails. The number of elements in the sample space can be found by multiplying the possible outcomes of each toss together, so 2*2*2=8
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
For the third toss being heads we will have one restriction this time. Which is that the third toss is Tails. You can take the elements from the sample space where the third element is a tails. In this case, the number of elements can be calculated by multiplying the possible outcomes for only the first two tosses 2*2=4
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
For first toss is heads, second tails and third heads there is only one possible way for you to get this outcome so there is only one element to this set.
{HTH}
I had to raise the number to49 pls help
Evaluate √−6x^2 + 4x when x = −6
Answer:
− 24 + 6 i √ 6
Step-by-step explanation:
What is the area of the figure?
O 11 square units
O 18 square units
24 square units
32 square units
Answer:
18
Step-by-step explanation:
Answer:
yes 18 is correct
Step-by-step explanation:
what is x .................
Answer:
x=95
Step-by-step explanation:
Answer pleaseeeeeeee
A scale drawing of a rectangle painting is 12 inches long and 8 inches tall. The actual painting is 12 feet tall. What is the scale of the drawing? What is the perimeter of the actual painting? What is the area of the actual painting?
Answer:
x = 18
Step-by-step explanation:
[tex]\frac{8}{12} = \frac{12}{x}[/tex]
then cross-multiply8x = 12 * 12
8x = 144
[tex]\frac{8x}{8} = \frac{144}{8}[/tex]
x = 18
Pls Answer correctly and I’ll give you the brainliest
Answer: x=7
Step-by-step explanation:
plug y into equation...
x-(-4x+23)=12
solve...
x+-1(-4x+23)=12
x+-1(-4x)+-1(23)=12
x+4x-23=12
5x-23=12
5x=35
x=7
Solve for x
70°
*
20
triangles
Answer:
x = 90°
Step-by-step explanation:
a triangles angles are equal to 180°
so if we have one that is 70° and one that is 20° what s x?
70° + 20° = 90°
180° - 90° = 90°
x = 90°
Which of the following statements are true? Select all that apply.
63=3*3*3*3*3*3
025=2x5
45=4*4x4x4x4x4
03=3*3*3*3
023=4*4*4
52=5*5
Answer:
a
Step-by-step explanation:
Which net can be folded to form a triangular pyramid?
The net that can be folded to form a triangular pyramid is net b
How to determine the net that can be foldedFrom the question, we have the following parameters that can be used in our computation:
The nets in the list of options
As a general rule, a triangular pyramid has 4 triangles such that
Three triangles are adjacent and one triangle is at the top or at the bottom
using the above as a guide, we have the following:
The net that can be folded to form a triangular pyramid is net b
Read more about triangular pyramid at
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Use the expression 7.6s+(45÷9)−15 to answer 9–10.
9.
Which part of the expression represents a quotient? Describe its parts.
10.
Which part of the expression represents a product of two factors? Describe its parts.
9. The part of the expression that represents a quotient is
10. The part of the expression that represents a product of two factors is
Answer:
45 ÷ 9, 7.6s
Step-by-step explanation:
9) A quotient is a result of dividing a quantity by another quantity. We see that 45 ÷ 9 is a form of division. We could say that 45 is divided into 9 parts. 45 ÷ 9 can also be written in fractional form: [tex]\frac{45}{9}[/tex]. Lastly, we see that the quotient would be 5.
10) A product is a result of multiplying a quantity by another quantity. We see that 7.6s is a simplified form of multiplication that actually represents 7.6 × s.
7.6 is a known numerical value. It is the coefficient of the variable x, which we do not know the value for.
What is the amplitude of the function?
Answer:
Step-by-step explanation:
The amplitude is half of the range.
a=(maximum-minimum)/2, in this case
a=(2-(-4))/2
a=6/2
a=3
Which probability indicates that an event will definitely occur?
1/4
1/2
3/4
1
Answer:
1
Step-by-step explanation:
because it is WHOLE where as other shows unsureness.
Lines that are not in the same plane are called lines O A. transversal O B. parallel O c. skew O D. perpendicular
Answer:
your answer is C.
Lines that are not coplanar and do not intersect are called skew lines.
and incase you need this answer too, Parallel Planes. Two planes that do not intersect are called parallel planes.
The spending limit on John's credit card is given by the function f(t) = 15,000 + 1.57, where x is his monthly income. 1-13) $60,000, his monthly income is The variable x represents in the inverse function. If John's spending limit is
2(T+1)=10 what does t equals ?
HELP NEEDED QUICK WILL GIVE BRAINLY
Question 3 (02.03)
Figure EFGH is reflected about the y-axis to obtain figure E’F’G’H’:
Which statement best describes the relationship between the two figures?
1.Figure EFGH is congruent to figure E’F’G’H’.
2.Figure EFGH is bigger than figure E’F’G’H’.
3.The measure of angle H is equal to the measure of angle E’.
4.The measure of angle H is equal to the measure of angle G’.
Answer:
1
Step-by-step explanation:
Figure EFGH is congruent to figure E'F'G'H'
Choose all values of a that make the following equation true: 3/4 = a/36.
A.23
B.27
C.22
D.108/4
9514 1404 393
Answer:
B, D
Step-by-step explanation:
The equation can be solved by multiplying by 36.
3/4 = a/36
a = 36(3/4) = 108/4 = 27
The listed values that make the equation true are 27 and 108/4.
Can someone help me please??
Answer:
the perimeter is just the distance around the shape so 7+10+15+8+8+2=50
What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2, 4)?
O y=-5/2x-1
O y= -5/2x+ 5
O y=2/5x-1
O y=2/5x+5
Answer:
[tex]y = -\frac{5}{2}x-1[/tex]
Step-by-step explanation:
5x + 2y = 12
2y = -5x + 12
[tex]y = -\frac{5}{2}x +6[/tex]
Parallel lines have the same slope so the -5/2 remains. Just remove the b value (6) and plug in (-2,4) to the x and y spots.
[tex](4) = -\frac{5}{2}(-2) + b[/tex]
4 = 5 + b
b = -1
The new equation is [tex]y = -\frac{5}{2}x-1[/tex]