If [tex]u=x^5+2[/tex], then [tex]du=5x^4\,dx[/tex], so the integral transforms to
[tex]\displaystyle \int_{x=-2}^{x=4} x^4 \cos(x^5+2) \, dx = \frac15 \int_{u=-30}^{u=1026} \cos(u) \, du[/tex]
since
[tex]x = -2 \implies u = (-2)^5 + 2 = -32 + 2 = -30[/tex]
[tex]x=4 \implies u = 4^5 + 2 = 1024 + 2 = 1026[/tex]
Scores of an IQ test have a bell-shaped distribution with a mean of
100 and a standard deviation of
19. Use the empirical rule to determine the following.
(a) What percentage of people has an IQ score between
81 and
119?
(b) What percentage of people has an IQ score less than
43 or greater than
157?
(c) What percentage of people has an IQ score greater than
119?
Question content area bottom
Part 1
(a)
enter your response here
% (Type an integer or a decimal.)
Part 2
(b)
enter your response here
% (Type an integer or a decimal.)
Part 3
(c)
enter your response here
% (Type an integer or a decimal.)
Scores of an IQ test have a bell-shaped distribution with a mean of
100 and a standard deviation of
19. Use the empirical rule to determine the following.
(a) What percentage of people has an IQ score between
81 and
119?
(b) What percentage of people has an IQ score less than
43 or greater than
157?
(c) What percentage of people has an IQ score greater than
119?
Question content area bottom
Part 1
(a)
enter your response here
% (Type an integer or a decimal.)
Part 2
(b)
enter your response here
% (Type an integer or a decimal.)
Part 3
(c)
enter your response here
% (Type an integer or a decimal.)
Using the Empirical Rule, it is found that:
a) 68% of the people have an IQ score between 81 and 119.
b) 0.3% of people has an IQ score less than 43 or greater than 157.
c) 16% of people has an IQ score greater than 119.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In item a, 81 and 119 are the bounds within 1 standard deviation of the mean, hence 68% of the people have an IQ score between 81 and 119.
In item b, 43 and 157 are the bounds within 3 standard deviations of the mean, hence 0.3% of the distribution is outside this range, that is, 0.3% of people has an IQ score less than 43 or greater than 157.
In item c, considering the symmetry of the normal distribution, the upper 16% has IQ score greater than 119, hence 16% of people has an IQ score greater than 119.
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As Sara rode her bike at 9 mph, how many feet did she travel in 28 seconds? (1 mi =
5280 ft)
the answer was 369.6 I’m trying to know how that’s the answer
Answer:
Step-by-step explanation: This vould be the answer because it could have been turned into an epression
Explain. You stand at the edge of a 5m high diving platform. A beach ball is exactly 9 m from the base of the platfo
To the nearest tenth of a meter, what is the distance d from the top of the platform to the beach ball?
the distance, d from the top of the platform to the beach ball is equal to 10.29 m.
We are given that:
Height of the platform = 5 m
distance between bas of the platform and the beach = 9 m
We need to find the distance from the top of the platform to the beach ball.
We know that this distance d will be the hypotenuse of the triangle formed.
So, we have:
Perpendicular = 5 m
Base = 9 m
Hypotenuse = d
So, by using the Pythagoras theorem, we get that:
d² = 5² + 9²
d² = 25 + 81
d² = 106
d = √ 106
d = 10.29 m.
Therefore, we get that, the distance, d from the top of the platform to the beach ball is equal to 10.29 m.
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Simplify the expression 1-cotx/tanx-1
The expression 1-cotx/tanx-1 is cot x.
Given,
1-cotx/tanx-1
cot x = 1/tan x
1-cotx/tanx-1 = 1- (1/tan x) / tan x-1
= [(tan x -1 )/tan x ]/ [tan x -1]
= (tan x -1 )/ [tan x (tan x -1)]
= 1/tan x
= cot x
Expressions in mathematics are mathematical assertions that comprise at least two phrases that contain numbers, variables, or both, and are connected by an operator in between. Addition, subtraction, multiplication, and division are examples of mathematical operators. For example, x + y is an expression in which x and y are terms separated by an addition operator. There are two sorts of expressions in mathematics: numerical expressions, which contain simply numbers, and algebraic expressions, which contain both numbers and variables.
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Solve for X using the image below
Answer:
x = 3.
Step-by-step explanation:
ADE and ABC are similar right isoceles triangles.
Step-by-step explanation:
AD / AB = ED /CB12 / 3 = 12 / X
X = 3 .........order the following expressions from least to greatest.
2 √3 √pie
The order of expressions from the least to greatest is [tex]\sqrt{3}[/tex], [tex]\sqrt{pie}[/tex] and 2
In order to find the value of these given expressions, we will have to convert them into a standard form, therefore we will find the value of these expressions by removing the root and finding its actual value
Value of 2 will remain the same as it is already in standard form
Value of [tex]\sqrt{3}[/tex] in standard form = 1.732
Value of [tex]\sqrt{pie}[/tex] in standard form = [tex]\sqrt{3.1459}[/tex] = 1.77
No ordering these expressions we find that 2 is the greatest, followed by 1.77 and 1.732
Hence, the expressions from least to greatest is [tex]\sqrt{3}[/tex], [tex]\sqrt{pie}[/tex] and 2
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Use the frequency distribution shown below to construct and expand frequency distributions
The expanded frequency distribution is attached
How to get the expand frequency distributionThis will have additional columns which include
midpointrelative frequencycumulative frequencyThe midpoint
The mid point is gotten by adding the lower class limit and the lower class limit and dividing by two
for instance: 10 + 20 / 2 = 10
The relative frequency
In this column they are in percent and the alue is gotten by first summing up all the frequency then finding the percent of each.
for instance: the total sum of the frequency is 365 so
( 17 / 365 ) * ( 100 / 1 ) = 4.66%
The cumulative frequency
The cumulative frequency is solved by sequential addition of the frequency
for instance:
17 next is
17 + 44 = 61
61 + 68 = 129
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the cost of 5 popcorns and 2 drinks is $11.50. The cost of 3 popcorns and 4 drinks is $12.50. find the cost of one popcorn. find the cost of one drink
Answer:
I tried to solve I got the value of a drink but a popcorn's value comes in negative... Can you recheck it please.......
How many hours did he take to drive one mile?
A) In one hour Graham drove 33 3/4 miles
B) To drive one mile Grahman will take 4/127 hours
a) change into improper fractions
42 1/3 = 127/3
1 1/3 = 4/3
he takes 4/3 hours to drive 127/3 miles
in one hour he will drive 127/3 × 3/4 = 127/4 = 33 3/4 miles
So in 1 hour he will drive 33 3/4 miles
b) he covers 127/3 miles in 4/3 hours
to cover 1 mile he will take = 4/3 × 3/127 = 4/127 hours
Graham will take 4/127 hours to cover 1 mile.
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quadratic equation
4x2-4x-1=0
The solutions to the given quadratic equation 4x² - 4x - 1 = 0 are x = ( 1 - √2 )/2, ( 1 +√2 )/2.
What is the solution(s) to the given quadratic equation?A quadratic equation in its standard form is;
ax² + bx + c = 0
Where x is the unknown
To solve for x, we use the quadratic formula
x = (-b±√(b² - 4ac)) / (2a)
Given the equation in the question;
4x² - 4x - 1 = 0
Compared to the standard form ax² + bx + c = 0
a = 4b = -4c = -1Plug these values into the quadratic formula above.
x = (-b±√(b² - 4ac)) / (2a)
x = (-(-4) ± √((-4)² - ( 4 × 4 × -1 ))) / (2 × 8)
x = ( 4 ± √( 16 - ( -16) ) / (8)
x = ( 4 ± √( 16 + 16) ) / (8)
x = ( 4 ± √( 32) ) / (8)
32 can be written as 4²×2
x = ( 4 ± √( 4²×2 ) ) / (8)
x = ( 4 ± 4√2 ) / (8)
x = ( 1 ± √2 ) / 2
x = ( 1 - √2 )/2, ( 1 +√2 )/2
Therefore, the solutions to the given quadratic equation 4x² - 4x - 1 = 0 are x = ( 1 - √2 )/2, ( 1 +√2 )/2.
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The heaviest load that an elevator can safely carry is 1,500 pounds. Gregg who weighs 155 pounds, is going to take boxes of supplies weighing 17 pounds each with him in the elevator. How many boxes of supplies can Gregg safely take with him on the elevator at one time?
Answer:
79 boxes
Step-by-step explanation:
1500-155= 1345
1345/17=79.11
Rewrite (132 + 228) using factoring.
4(32 + 57)
6(22 + 222)
4(33 + 57)
16(116 + 14)
The expression using factoring is 4 * (33 + 57)
How to rewrite the expression using factoring?The expression is given as
(132 + 228)
Factor out 2 from the expression
So, we have
(132 + 228) = 2 * (66 + !14)
Factor out 2 from the expression
So, we have
(132 + 228) = 2 * 2 * (33 + 57)
This gives
(132 + 228) = 4 * (33 + 57)
Hence, the expression using factoring is 4 * (33 + 57)
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If n×n×n=60 , then which of the following best approximates n ?
[tex] \eta \times \eta \times \eta = 60 \\ \eta {}^{3} = 60 \\ \eta = \sqrt[3]{60} \approx3.91487[/tex]
[tex]\frac{-332}{-4}[/tex]
Answer:
83
Step-by-step explanation:
[tex] \frac{ - 332}{ - 4} = 83[/tex]
In ΔTUV, = 24 inches, = 29 inches and ∠T=130°. Find the area of ΔTUV, Round to the nearest square inch
The area of ΔTUV, to the nearest square inch is given as 267 square inch
Given data
ΔTUV, = 24 inches, = 29 inches and ∠T=130°
How to solve for are of triangle with two sides and one angle givenlet the Area of the triangle = A
let the two sides be a and b
let the given angle be β
A = a * b * sin β / 2
A = 24 * 29 * sin 130 / 2
A = 696 * 0.7660 / 2
A = 696 * 0.3830 = 266.583
A = 266.583 square inch
A = 267 square inch ( to the nearest square inch )
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Solve 17.04x6.2= how many gallons?
Answer:
17.04 x 6.2= 105.648
Hope this helps :)
Geometry: What is the value of X
I know the answer is x=7
I just need to know, how do you get 7 as x.
So someone pls help with the strategies+details of every step!!
Answer:
x = 7
Step-by-step explanation:
The dashes on each side of the rectangle indicate congruency.
This means that PS = QR, or 2x - 3 = 11.
Now we would solve for this like normal.
2x - 3 = 11 add 3 to each side
+ 3 + 3
--------------
2x = 14 now divide by 2 to find x
÷ 2 ÷2
--------------
x = 7
What is the radius of a circle that has a diameter of 73.2 ft?
Answer:
36.6
Step-by-step explanation:
For the function f(x) = 2 - 3x, find f(-4).
-10
-5
12
14
Answer: 12
Step-by-step explanation: f(-4)= 2-3(-4) which =2+12=14
convert 3.338 m cubed to cubic yards
4.3659392
hope this helps
If an air conditioner is rated at 16000 BTU per hour, how many watts does it require? Round to the nearest 100 watts
The number of watts will be 4700 watts to the nearest 100 watt.
How to calculate the value?It should be noted that 1 watt equals to 3.41 Btu per hour.
In this case, the air conditioner is rated at 16000 BTU per hour.
Therefore, the number of watt will be:
= 16000/3.41.
= 4692
= 4700 watts to the nearest 100 watt.
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A plane is flying at a height of 35,000 ft. (feet) above sea level. At a particular point, it is directly above a submarine floating 3,500 ft. below sea level and a military drone flying at a height of 3,500 ft. By how much must the military drone ascend so that it is vertically in the middle of the plane and the submarine?
The military drone must ascend 12250 from its position of 3500ft above sea level feet so that it is vertically in the middle of the plane and the submarine.
To solve this problem we need to understand the concept of sea-level. The sea-level is defined as the average height of all water bodies of the earth. Below sea level is effectively taken as negative length and above sea -level is taken as positive length.
Let us consider the drone will have to ascend x feet to be vertically in between the plane and the submarine.
The submarine is 3500 feet below the sea level.
The plane is 35000 feet above the sea level.
Now we know that the drone is at a height of 3500 feet above the sea level.
Total distance between the drone and the ship=35000-(-3500)=38500ft
Middle point of the two=38500/2 = 19250 feet from the plane
Height above sea level for the drone should be=35000-19250=15750 ft
height of the drone=3500ft
The drone should ascend=15750-3500=12250 feet
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Change 1,314,000 minutes to years
Answer:
1,314,000 minutes is equal to 2.5 years.
Brainliest, please :)
1. A jar contains 50 jelly beans in total. 20 of them are red, 15 are green and the other 15 are blue. If a jelly bean
is selected at random from the jar, what is the probability that it is red or blue?
70%
Given: 50 total, 20 red, 15 blue
20 + 15 = 35
35 ÷ 50 = .7
.7 • 100 = 70
70% are blue or red.
anne and nanny use a metal alloy that is 16% copper to make jewelry how many ounces of an alloy that is 10% copper must be mixed with an alloy that is 20% copper to form 55 ounces of the desired alloy
By solving a system of equations we conclude that they need to use 22 ounces of the 10% alloy and 33 ounces of the 20% alloy.
How many ounces of each alloy should they use?
First, let's define the variables we will use to solve this problem:
x = ounces of the 10% alloy copper they need to use.y = ounces of the 20% alloy copper they need to use.We know that they want to get 55 ounces, then:
x + y = 55
And the concentration of these 55 ounces must be 16%, then we can write other equation:
0.1*x + 0.2*y = 0.16*55
Then we have a system of equations:
x + y = 55
0.1*x + 0.2*y = 0.16*55
Isolating x on the first equation we get:
x = 55 - y
Now we can replace that in the other equation so we get:
0.1*(55 - y) + 0.2*y = 0.16*55 = 8.8
Now we can solve this for y.
5.5 - 0.1*y + 0.2*y = 8.8
5.5 + 0.1*y = 8.8
y = (8.8 - 5.5)/0.1 = 33
Then the value of x is:
x = 55 - y = 55 - 33 = 22
We conclude that they need to use 22 ounces of the 10% alloy and 33 ounces of the 20% alloy.
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I need help plsss
What is the equivalent decimal?
Drag the answer into the box to match the fraction.
10/66
A. 0.15
__
B. 0.15
__
C. 0.54
__
D. 0.46
The decimal form of the fraction 10 / 66 is 0.15.
How to convert from fraction to decimals?Fractions represent the parts of a whole or collection of objects.
In other words fractions are represented as a numerical value, which defines a part of a whole.
Fractions has a numerator and a denominator.
The numerator is at the top while the denominator is below.
A decimal is a number that consists of a whole and a fractional part.
Therefore, let's convert the fractions 10 / 66 to decimal.
Hence,
10 / 66 ÷ 2 / 2 = 5 / 33
Therefore,
5 / 33 = 0.15151515151 = 0.15
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Nico Joven presently earns $348.40 per week. He claims himself and his mother as allowances. He is single. He is to get a new job classification, which will result in a 15% increase in pay. He also plans to marry. After his marriage, he will claim his wife, himself, and his mother as allowances. How much less will be withheld weekly for federal income tax?
Answer: The amount less will be with held weekly for federal income tax is $40.65.
Step-by-step explanation:
Given data,
Nico Joven presently earns $348.40 per week.
The amount of money deducted from federal income tax is:
= $348.40/2
= $174.20
He claims himself and his mother as allowances.
He is single. He is to get a new job classification, which will result in a 15% increase in pay.
The increase in pay will be:
= 15% × $348.40
= $52.26
After his marriage, he will claim his wife, himself, and his mother as allowances.
The new salary will be the addition which is $400.66.
The new money with held will be:
= $400.66/3
= $133.55
The amount less withheld will be:
= $174.20 - $133.55
= $40.65
Therefore,
The amount less will be with held weekly for federal income tax is $40.65.
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Geometry homework… the questions after the photo are “9. Find the value of angle RIG” and “10. Find the value of angle ZIM” If you can seriously help me it would mean a lot. Thanks
Answer: The value of RIG is 59 degrees and the value of ZIM is 31 degrees.
Given: Lines AM,ZG, RI are parallel
angle RIM = 90 degree and lines AM,ZG and RI intersect at point I.
Concept: All angles on the same line make an angle of 180 degree.
Since all angles on a line make an angle sum of 180 degree
So using the above property of straight lines,
Angle RIA + angle RIG + angle GIM = 180 degree
90 + 4z+7 +x+2 = 180
4z+x = 81 ----- (1)
Angle AIZ + angle AIR + angle RIG = 180 degree
3x-56 + 90 + 4z+7=180
3x +4z =139 ----- (2)
3(81-4z) +4z =139
243 -8z =139
z=13
x= 81- 52 = 29
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Answer:
timmy neorons, descaration
Step-by-step explanation:
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Help me with geometry
Answer:
X = 36.5
Z = 19
Angle RIG is 69
angle ZIM is 126.5
Step-by-step explanation:
angle AIZ and ZIP
x + 3x - 56 = 90
4x - 56 = 90
4x = 90 + 56
4x/4 = 146/4
x = 36.5
Plugin the value of x in (3x -56)
3x - 56
(3(36.5) - 56)
(109.5 - 56) = 53.5
Angle AIZ = 53.5
Angle RIG is 4z + 7. Convert the letter x in (x + 2) to Z and solve for z
4z + 7 + z + 2 = 90
5z + 9 = 90
5z = 90 - 9
5z/5 = 81/5
z = 16.2
Z + 2
16.2 + 2 = 18.2
Angle GIM is 18.2 degrees
Plugin the the value of z into 4z + 7 for angle RIG
4z + 7
(4(16.2) + 7) = 71.8
Angle RIG = 71.8 degrees
You know the perimeter of a square to be 34 meters. Find the length of one side.
Step 2 of 3: Without substitution, solve the formula for the unknown variable in terms of the known variables.
The side of one side of the square is determined as: 8.5 meters.
What is a Square?A square is a quadrilateral shape that has four sides that have the same length and four interior angles that are right angles (90 degrees).
What is the Perimeter of a Square?The perimeter of a square is the sum of all the sides of a square which can be calculated using the following formula given as,:
Perimeter = 4(s), where s represents the length of one side of the square.
We are given that:
Perimeter of the square = 34 meters
Therefore:
34 = 4(s)
Divide both sides by 4
34/4 = 4(s)/4
8.5 = s
s = 8.5 m
Thus, the side of one side of the square is determined as: 8.5 meters.
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