a. Because [tex]f[/tex] is even,
[tex]\displaystyle \int_{-7}^7 f(x) \, dx = 2 \int_0^7 f(x) \, dx = 18 \\\\ ~~~~ \implies \int_0^7 f(x) \, dx = \frac{18}2 = \boxed{9}[/tex]
b. The product of an even function [tex](f)[/tex] by an odd function [tex](x)[/tex] is an odd function, whose integral over a symmetric interval is zero.
[tex]\displaystyle \int_{-7}^7 xf(x) \, dx = \boxed{0}[/tex]
What is an equation of the line that passes through the point (-2,-4) and is parallel to the line 5x-2y=6
5x-2y = -2 is the equation of line that passes through the point (-2,-4) and is parallel to the line 5x-2y=6.
Given that, (x₁, y₁) = (-2, -4) and parallel to 5x - 2y = 6
Let's calculate the slope of 5x - 2y = 6
Rewrite the equation in y = mx + c form
5x - 2y = 6
⇒ -2y = 6 - 5x
⇒ -y = 3 - 5/2x
⇒ y = -3 + 5/2x
⇒ y = 5/2x - 3
Thus, the slope (m) = 5/2
As the line is parallel to 5x - 2y = 6 it will have a slope of 5/2.
The point-slope formula states (y - y₁) = m(x - x₁)
Now, substituting the value of m = 5/2 and (x₁, y₁) = (-2, -4), we get
(y - y₁) = m(x - x₁)
⇒ (y - (-4)) = 5/2(x - (-2))
⇒ (y+4) = 5/2(x+2)
⇒ 2(y+4) = 5(x+2)
⇒ 2y+8 = 5x+10
⇒ 5x-2y+10-8 = 0
⇒ 5x-2y+2 = 0
⇒ 5x-2y = -2
Hence, the line that passes through the point (-2,-4) and is parallel to the line 5x-2y=6 is 5x-2y = -2.
Therefore, 5x-2y = -2 is the required answer.
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Which expression shows another way to write -2/5 divided by 3/2?
The expression that shows another way to write -2/5 divided by 3/2 will be -2/5 ÷ 3/2.
How to calculate the value?It should be noted that an expression simply shows the relationship between the variables.
Therefore, the expression that shows another way to write -2/5 divided by 3/2 will be:
= -2/5 ÷ 3/2
= -2/5 × 2/3
= -4/15.
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Three friends are making homecoming mums before the big game. When all three friends are working, they produce 6 mums per hour. When only Friend B and Friend C are working, they make 5 mums per hour. When only Friend A and Friend B are working, they make 4 mums per hour. How many mums can be created by each friend every hour?
The number of mums created every hour by each friend are:
Friend A working every hour creates 1 mum, Friend B working every hour creates 3 mums, and Friend C working every hour creates 2 mumsHow to find the number of mum created per hour by each friendGiven data
Friend A, Friend B, and Friend C working = 6 mums per hour
Friend B and Friend C working = 5 mums per hour
Friend A and Friend B are working = 4 mums per hour
A + B + C = 6 equation 1
B + C = 5 equation 2
A + B = 4 equation 3
from equation 2, make C the subject of the formula
B + C = 5
C = 5 - B
from equation 3, make A the subject of the formula
A + B = 4
A = 4 - B
substitute A and C into equation 1 to get
A + B + C = 6
4 - B + B + 5 - B = 6
4 + 5 - B = 6
9 - B = 6
-B = 6 - 9
-B = -3
B = 3
substituting B for A we have
A = 4 - 3
A = 1
substituting B for C we have
C = 5 - 3
C = 2
Therefore , Friend A working every hour creates 1 mum, Friend B working every hour creates 3 mums, and Friend C working every hour creates 2 mums,
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8,615-4,229= I need help
8,615-4,229=4386 Answer took the quiz!
Answer:
4386
Step-by-step explanation:
8615-4229
= (8000 + 600 + 10 + 5) - (4000 + 200 + 20 + 9)
= (8000-4000) + (600-200) + (10-20) + (5-9)
= 4000 + 400 + (-10) + (-4)
= 4000 + 300 + (100-10) + (-4)
= 4300 + 80 + (10-4) = 4386
HELP MEE!!
i need help with this!!
Answer:
2745
jow to get this is you do this then dis
Match the correct function to the graph.
Suppose the tangent line to the curve
y = f(x)
at the point
(1, 1)
has the equation
y = 7 − 6x.
If Newton's method is used to locate a solution of the equation
f(x) = 0
and the initial approximation is x1 = 1, find the second approximation x2.
Answer:
x2 = 7/6
Step-by-step explanation:
You want the second approximation using Newton's method, given that the first approximation is x1=1 and the function tangent at x=1 is y=7-6x.
Newton's methodNewton's method approximates the function by its tangent line at the point (x, f(x)). That is, the second approximation is the x-intercept of the tangent line y = 7 -6x. That value of x is ...
0 = 7 -6x
6x = 7 . . . . . add 6x
x = 7/6 . . . . divide by 6
The second approximation is x2 = 7/6.
A blogger found that the number of visits to her Web site increases 5.6% annually. The Web site had 80,000
visits this year. Write an exponential model to represent this situation. By what percent does the number of
visits increase daily? Explain how you found the daily rate.
f(t) = 80,00[tex](1+ 0.056)^{t}[/tex] is the exponential function that represents the model. The number of visits increase by 0.015% daily.
Here, we are given that a blogger found that the number of visits to her Web site increases 5.6% annually.
The exponential function is given as-
Final value = initial value [tex](1 + r)^{t}[/tex]
where r = rate of change
and t = time
here, r = 5.6%
r = 0.056
Further, the Web site had 80,000 visits this year ⇒ initial value = 80,000
Thus, we can get the following function-
f(t) = 80,00[tex](1+ 0.056)^{t}[/tex]
where f(t) represents the views after t years.
Now, since we are given that the views increase by 5.6% in 1 year
and 1 year = 365 days
⇒ daily rate = 5.6/365
= 0.015
Thus, the number of visits increase by 0.015% daily.
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name the relationship, corresponding laternate interior alternate exterior same side interior vertical linear
Answer:
see explanation
Step-by-step explanation:
the relationship between angles a and b
they are alternate interior angles
these angle pairs are on opposite ( alternate) sides of the transversal and are in between ( in the interior of )the parallel lines.
"Simplify. Your answer should contain only positive exponents with no fractional exponents in the denominator."
Can someone please explain the answer to me
Step-by-step explanation:
[tex] \frac{1}{ {x}^{ \frac{ - 1}{3} } } \times \frac{1}{3x} \\ \frac{1}{ {3x}^{ \frac{2}{3} } } \\ \frac{1}{ 3\sqrt[3]{x {}^{2} } } [/tex]
Consider 2 cylinders. The volume of these two cylinders are. If another cross section is taken at a different height, the areas of the cross sections will be
The volume of the two cylinders is 2424. The area of the cross-section will be equal if another cross-section is obtained at a different height.
The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it.
The formula for the volume of a cylinder is given as:
V=π r² h
Now from the figure,
We have, for the first cylinder the height is 16 units and the radius is 7 units.
Hence,
V = 22/7 × 7² × 16
V = 22/7 × 7 × 7 × 16
V = 2424
Therefore the volume of the two cylinders is 2424. The area of the cross-section will be equal if another cross-section is obtained at a different height.
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Evaluate 4|-2| - |-3|
5
-5
11
Answer:
5
Step-by-step explanation:
4(|−2|)−|−3|
=(4)(2)−|−3|
=8−|−3|
=8−3
=5
Which expression is equivalent to (10−2 • 45)−2?
1. ten raised to the fourth power divided by four raised to the tenth power)
2. negative ten raised to the fourth power divided by four raised to the tenth power)
3. four raised to the third power divided by ten raised to the fourth power)
4. negative four raised to the third power divided by ten raised to the fourth power)
The expression that is equivalent to the given expression (10^−2 • 4^5)^−2 is 10^(4) • 4^(−10)
How to determine the expression that is equivalent to the given expression?The expression is given as
(10−2 • 45)−2
Rewrite the above expression properly as follows:
(10^−2 • 4^5)^−2
Apply the power rule of indices
So, we have
(10^−2 • 4^5)^−2 = 10^(−2 * −2) • 4^(−2 * 5)
Evaluate the product of powers
So, we have
(10^−2 • 4^5)^−2 = 10^(4) • 4^(−10)
Hence, the expression that is equivalent to the given expression (10^−2 • 4^5)^−2 is 10^(4) • 4^(−10)
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Show that the roots of the quadratic equation given by(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0
are real and they can not be equal unless a=b=c
Expanding out the equation, we get
[tex]x^2 - ax - bx+ab+x^2 -bx-cx+bc+x^2 -ax-cx+ac=0 \\ \\ 3x^2 -x(2a+2b+2c)+(ab+bc+ac)=0[/tex]
Considering the discriminant,
[tex](2a+2b+2c)^2 - 4(3)(ab+bc+ac) \\ \\ =4a^2 + 4b^2 + 4c^2 + 8(ab+bc+ac)-12(ab+bc+ac) \\ \\ =4(a^2 + b^2 + c^2 - ab - bc - ac) \\ \\ =2((a-b)^2 + (b-c)^2 + (c-a)^2)[/tex]
This is always non-negative, meaning the roots are real.
The roots are equal if and only if the discriminant is 0, which is when a=b=c.
Solve the following proportion for 8/11 = v/6 .
Round your answer to the nearest tenth.
Answer:
v = 4.4
Step-by-step explanation:
Let's solve your equation step-by-step.
8/11 = v/6
Step 1: Cross-multiply.
8/11 = v/6
(8)*(6)=v*(11)
48=11v
Step 2: Flip the equation.
11v=48
Step 3: Divide both sides by 11.
11v/11 = 48/11
v= 48/11
v = 4.4
In a survey of employees at a fast food restaurant, it was determined that 13 cooked food, 16 washed dishes, 20 operated the cash register,
7 cooked food and washed dishes, 6 cooked food and operated the cash register, 8 washed dishes and operated the cash register, 3 did all
three jobs, and 5 did none of these jobs. Complete parts a) through f) below.
how many employees took the survey?
Answer:1
Step-by-step explanation:
HELLP
Find the coordinates of the point 3/10 of the way from A to B
The coordinates of the point
3/10 of the way from A to B are
Step-by-step explanation:
this is similar to the complete approach to find the midpoint. just instead of 1/2 we are looking for 3/10 of the distance.
the general approach is
A + (B - A)×factor
factor can be 1/2 or 3/10 or 7/10 or 24/29 or ...
so, we have
(-3, -6) + ((9 - -3)×3/10, (5 - -6)×3/10) =
= (-3, -6) + (12×3/10, 11×3/10) =
= (-3, -6) + (3.6, 3.3) = (0.6, -2.7)
the point 3/10 of the way from A to B is
(0.6, -2.7)
Which statement about AABC and ADEF is true?
Answer: D.
hope this helps
Question 1
What is the slope of the line that passes through the points
(-9, 8) and (-3,-1)?
Greetings from Brasil...
It is possible to answer this question through Determinant
| X Y 1 |
| X₁ Y₁ 1 | = 0
| X₂ Y₂ 1 |
We have:
(X₁; Y₁) = (-9; 8)
(X₂; Y₂) = (-3; -1)
then
| X Y 1 |
| -9 8 1 | = 0
| -3 -1 1 |
9X + 6Y + 33 = 09888-1111+4444
...........
Answer:
the answer is 13,221 ...........
Answer:
13221...........
Step-by-step explanation:
9888-1111=8777
8777+4444=13221
Transitive Property of Equality
If a +5=b+3 and a +5 = 12, then b + 3 =?
b+3=12
because a+5=b+3 and a+5=12 which means b+3 must be 12 as well
The population of a town increased from 3,250 in 2008 to 4,300 in 2010. Find the
absolute and relative (percent) increase.
The absolute change in the town's population from 2008 to 2010 is 1,050 and the percentage change is 32.3%.
Here, we are given that the population of a town increased from 3,250 in 2008 to 4,300 in 2010.
The absolute change can be calculate as-
Final population count - initial population count
= 4,300 - 3,250
= 1,050
Thus, absolute increase = 1,050
Now, the percentage increase can be calculated as follows-
percentage change = absolute change in population/ initial population count × 100
= 1,050/ 3,250 × 100
= 10500/ 325
= 32.3%
Thus, the absolute change in the town's population from 2008 to 2010 is 1,050 and the percentage change is 32.3%.
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Find the value of x. Round to the nearest tenth if necessary.
Answer:
1. 11.7
2. 15
3. 20.5
4. 15.3
Step-by-step explanation:
Use the Pythagorean theorem for each of the problems.
Answer:
Step-by-step explanation:
A can of soda takes an average (mean) of 26 minutes to move through an assembly line. If the standard deviation is 2 minutes and the distribution is normal, what is the probability that the can will take over 29 minutes?
The probability that a can will take more than 29 minutes is approximately 0.66807
How can the probability of an event be determined in a normal distribution?The mean time taken by the soda to move through the assembly line = 26 minutes
The standard deviation of the time it takes = 2 minutes
Required: The probability that the can takes more than 29 minutes
Solution: The Z-Score formula is presented as follows;
[tex]Z = \frac{x - \mu}{ \sigma} [/tex]
The Z-Score of a can that takes 29 minutes is given as follows;
[tex]Z = \frac{29 - 6}{ 2} = 1.5[/tex]
Which gives;
Z = 1.5
The probability P(x < Z) obtained online or from the Z-Score table gives;
P(x < 1.5) ≈ 0.93319Which gives;
The probability that the can will take more than 29 minutes P(x > Z) ≈ 1 - 0.93319 = 0.66807
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The length of a rectangle is nine more than triple the width. If the perimeter is 154 inches, find the dimensions.
Answer:
Length = 60 inches
Width = 17 inches
Step-by-step explanation:
Let width = w
Length = 3w + 9
Perimeter = 154
Perimeter = 2(length + width)
2(3w + 9 + w) = 154
8w + 18 = 154
8w = 154 - 18
8w = 136
w = 136/8
w = 17 inches
Length = 3w + 9 = 3(17) + 9 = 60 inches
What is the slope of the line that passes through the points (-7, -10) and
(-19, -10)? Write your answer in simplest form.
the length of a rectangle is three more than double the width. if the perimeter is 126 inches, find the dimensions.
The dimensions of the rectangle are 43inches and 20inches if the perimeter of the rectangle is 126 inches.
Leth the width of the revtangle be x.
According to the given question.
The perimeter of the rectangle is 126 inches.
The length of the rectangle is three more than double the width.
⇒ Length of the rectangle = 3 + 2x
Now, according to the given conditions we can say that
Perimeter of the rectangle = 2( length + width)
⇒ 126 = 2(3 + 2x + x)
⇒ 126 = 2(3 + 3x)
⇒ 63 = 3 + 3x
⇒ 63 - 3 = 3x
⇒ 60 = 3x
⇒ x = 20 inches
Therefore, the length of the rectangle = 3 + 2(20) = 3 + 40 = 43
Hence, the dimensions of the rectangle are 43inches and 20inches if the perimeter of the rectangle is 126 inches.
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The blueprint specifications for a machined part call for its thickness to be 3.145 in.
with a tolerance of +-0.010 in. Find the limit dimensions of the part?
The limit dimensions of the part are 3.135 inches and 3.155 inches
How to find the limit dimensions of the part?The given parameters are
Thickness = 3.145 inches
Tolerance = 0.010 inches
The limit dimensions of the part are calculated as
Limit = Thickness +/- Tolerance
So, we have
Limit = 3.145 inches +/- 0.010 inches
Expand the above expression
So, we have
Limit = (3.145 inches - 0.010 inches, 3.145 inches + 0.010 inches)
Evaluate the sum
Limit = (3.135 inches, 3.155 inches)
Hence, the limit dimensions of the part are 3.135 inches and 3.155 inches
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How many 4/13 pound boxes of cereal can be made from 11,804 pound of cereal?
will give brainliest if correct
The value of f(5) is 4375.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given:
f(1)= 7,
f(n) = 5f(n-1)
f(2) = 5f(1)
=5*7
f(2)= 35
f(3) = 5f(3-1)
f(3) = 5f(2)
f(3) = 5*35
f(3) = 175
f(4) = 5f(4-1)
f(4) = 5f(3)
f(4) = 5*175
f(4) = 875
f(5) = 5f(5-1)
f(5) = 5f(4)
f(5) = 5*875
f(5) = 4375
Hence, the value of f(5) is 4375.
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