Answer:
f(x) = 8x⁴-8x²+1
Step-by-step explanation:
I will assume that f(cos θ) = cos(4θ). Otherwise, f would not be a polynomial. lets divide cos(4θ) in an expression depending on cos(θ). We use this properties
cos(2a) = cos²(a) - sin²(b)sin(2a) = 2sin(a)cos(a)sin²(a) = 1-cos²(a)cos(4θ) = cos(2 * (2θ) ) = cos²(2θ) - sin²(2θ) = [ cos²(θ)-sin²(θ) ]² - [2cos(θ)sin(θ)]² = [cos²(θ) - ( 1 - cos²(θ) ) ]² - 4cos²(θ)sin²(θ) = [2cos²(θ)-1]² - 4cos²(θ) (1 - cos²(θ) ) = 4 cos⁴(θ) - 4 cos²(θ) + 1 - 4 cos²(θ) + 4 cos⁴(θ) = 8cos⁴(θ) - 8 cos²(θ) + 1
Thus f(cos(θ)) = 8 cos⁴(θ) - 8 cos²(θ) + 1, and, as a result
f(x) = 8x⁴-8x²+1.
There are twelve shirts in your closet: five blue, four green, and three red. You randomly select one to wear. What is the probability it is blue or green?
A)
5
36
B)
11
12
C)
2
5
D)
3
4
Madhu is hanging a string of flowers on the perimeter of a rectangular pool deck. The deck is 30 feet long and 24 feet wide. How long does the string of flowers need to be?
Answer:
108 feet long
Step-by-step explanation:
You know that to find the perimeter you have to add up all the sides. A rectangle has 4 sides, so 30+30 is 60 and 24+24 is 48. Add 60 and 48 up and you get 108 as the perimeter. Since Madhu is hanging a string of flowers on the PERIMETER, the flower string will need to be 108 feet long.
Hope this Helped!
The height of water in a rectangular tank is given by h(w), where w is the volume of water (in liters) that has been removed from the tank. The height of the water decreases 10mm per liter removed.
a. From the time when 7 L have been removed to the time when 15 L have been removed, the accumulated change in the height of the water is
b. If the initial height of the water is 600mm, then the height of the water after w liters have been removed is
Answer:
a) ΔL = 80mm
b) h = 600 - 10w mm
Step-by-step explanation:
a. From the time when 7 L have been removed to the time when 15 L have been removed, the change in the volume has been 8L and how the height of the water decreases 10mm per liter removed, then the acumulate change in the height of water has been (8lt)(10mm/lt) = 80 mm
b) If w liters have been removed, then the change in the height of water is (10mm/lt)(wlt) = 10w mm and thus the water's height at this precise point in time is 600 - 10w mm
Megan’s art class painted two regular murals.The size of the first mural is shown below.
Answer:C) 4 feet and 12 feet
Step-by-step explanation:
The diagram of the first mural is shown. The formula for determining the perimeter of a rectangle is expressed as
Perimeter of rectangle = 2(L + W)
The length of the first mural is given as 8ft while the width of the first mural is given as 6 ft. The perimeter becomes
P = 2(8 + 6) = 2×14 = 28ft
The area of a rectangle is expressed as L×W
The area if the first mural would be
6 × 8 = 48ft^2
The second mural has the same area as the first mural but has a different perimeter. The side lengths of the second mural are
4 ft and 12ft
Area = 4×12 = 48 ft^2
Perimeter = 2(12+4) = 32ft
So area is the same and perimeter is different.
an automobile 16 feet long overtakes a truck that is 28 feet long and is traveling 30 mph. At what rate must the automobile travel to pass the truck in 4 seconds?
Step-by-step explanation:
Length of automobile = 16 feet = 4.88 m
Length of truck = 28 feet = 8.53 m
Speed of truck = 30 mph = 48 km/h = 13.33 m/s
Time in which automobile to pass truck = 4 s
Distance traveled by truck in 4 seconds = 4 x 13.33 = 53.33 m
Distance which need to cover by automobile in 4 seconds to pass truck is the sum of length of automobile, length of truck and distance traveled by truck in 4 seconds.
Distance which need to cover by automobile in 4 seconds = 4.88 + 8.53 + 53.33
Distance which need to cover by automobile in 4 seconds = 66.74 m
Distance = Speed x Time
66.74 = Speed x 4
Speed = 16.69 m/s = 60 km/h = 96 mph
Automobile must travel at 96 mph to pass the truck in 4 seconds.
Joe wants to build a doll house for his daughter. He wants the doll house to look just like his house. His house is 28 feet wide and 36 feet tall at the highest point of the roof. If the dollhouse will be 2.5 feet wide, how many feet will its highest point be?
The highest point for the dollhouse will be 3.12 feet
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
His house is 28 feet wide and 36 feet tall at the highest point of the roof.
And, The dollhouse will be 2.5 feet wide.
Now,
Let the highest point for the dollhouse = x
So, By definition of proportion, we get;
⇒ 28 / 36 = 2.5 / x
Solve for x as;
⇒ x = 2.5 × 36/28
⇒ x = 3.12 feet
Thus, The highest point for the dollhouse = 3.12 feet
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The shadow of the moon during a solar eclipse travels 2300 miles in one hour in the first 20 minutes the Shoadow traveled seven 66 2/3 miles how long does it take for the Shadow to reach 1150 miles
Final answer:
It takes 30 minutes for the moon's shadow to travel 1150 miles during a solar eclipse based on the speed of 2300 miles per hour.
Explanation:
The question asks us to calculate the amount of time it takes the moon's shadow to travel a certain distance during a solar eclipse, based on given speeds and distances. We know that the shadow travels 2300 miles in one hour, so the speed of the shadow is 2300 miles per hour. In the first 20 minutes, the shadow traveled 766 ⅓ miles. To find the time it takes the shadow to reach 1150 miles, we set up a proportion since the motion of the shadow is at a constant speed.
First, let's convert the 20-minute travel time to hours by dividing by 60, which is ⅓ of an hour (20 / 60 = ⅓). Then we can set up the proportion as follows:
766 ⅓ miles is to ⅓ hour, as 1150 miles is to T hours. Which gives us:
(766 ⅓ / 2300) = (⅓ / 1)
(1150 / 2300) = (T / 1)
Now, we solve for T:
⅓ = 1150 / 2300
T = ⅓
So, T is ⅓ of an hour, which means that it takes ⅓ of an hour for the shadow to reach 1150 miles. We can convert ⅓ of an hour to minutes by multiplying by 60, thus:
T = ⅓ × 60
T = 30 minutes
Therefore, it takes 30 minutes for the shadow to reach 1150 miles.
What is the vertex of the graph of y = -2|x-4|+ 11?
Please show work on how to get the answer. Thanks!
Answer:
The vertex is the point [tex](4,11)[/tex]
Step-by-step explanation:
we know that
The equation of the absolute value in vertex form is equal to
[tex]y=a\left|x-h\right|+k[/tex]
where
a is a coefficient
(h,k) is the vertex
In this problem we have
[tex]y=-2\left|x-4\right|+11[/tex]
so
[tex]a=-2[/tex] ---> the vertex represent a maximum
[tex]h=4[/tex]
[tex]k=11[/tex]
therefore
The vertex is the point [tex](4,11)[/tex]
Mark and his three friends are out of Applebee's. Their total is 52.35 If they left the server a 20% tip how much would each person pay splitting the bill evenly
Answer:
per person$15.71
Please I need help
Solve the system by substitution.
{
2
.
5
x
−
3
y
=
−
13
3
.
25
x
−
y
=
−
14
Answer:
(x, y) = (-3 5/8, 1 5/16)
Step-by-step explanation:
Add y+14 to the second equation to get ...
3.5x +14 = y
Substitute this for y in the first equation:
2.5x -3(3.5x +14) = -13
2.5x -10.5x -42 = -13
-8x = 29
x = -29/8 = -3 5/8
Using this in the formula for y, we get ...
3.5(-29/8) +14 = y
-203/16 +14 = y = 21/16 = 1 5/16
Answer : The value of x and y is, 4 and 27 respectively.
Step-by-step explanation :
The given equations are:
[tex]2.5x-3y=-13[/tex] ...........(1)
[tex]3.25x-y=-14[/tex] .........(2)
or,
[tex]y=3.25x+14[/tex] ..........(3)
Now put equation 3 in 1, we get the value of 'x'.
[tex]2.5x-3y=-13[/tex]
[tex]2.5x-3(3.25x+14)=-13[/tex]
[tex]2.5x-9.75x-42=-13[/tex]
[tex]-7.25x=-13+42[/tex]
[tex]-7.25x=29[/tex]
[tex]x=-\frac{29}{7.25}[/tex]
[tex]x=-4[/tex]
Now put the value of 'x' in equation 3, we get the value of 'y'.
[tex]y=3.25x+14[/tex]
[tex]y=3.25(4)+14[/tex]
[tex]y=13+14[/tex]
[tex]y=27[/tex]
Therefore, the value of x and y is, 4 and 27 respectively.
A pile of newspaper was 17 3/4 inches high. Each consecutive week for the next 5 weeks the height of pile increase by 8 7/12 inches. What is the height in inches, of the pile after 3 weeks?
Answer: the height in inches, of the pile after 3 weeks is 34 11/12 inches
Step-by-step explanation:
Each consecutive week for the next 5 weeks the height of pile increase by 8 7/12 inches. Converting 8 7/12 inches to improper fraction, it becomes 103/12 inches. The height is increasing in an arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence.
d represents the common difference.
n represents the number of terms in the sequence.
From the information given,
a = 17 3/4= 71/4 inches
d = 103/12 inches
n = 3 weeks
the height in inches, of the pile after 3 weeks, T3. Therefore,
T3 = 71/4 + (3 - 1)103/12
T3 = 71/4 + 2 × 103/12 = 71/4 + 103/6
T3 = 419/12 inches = 34 11/12 inches
Sara completes 2/5 of her math homework in class. What percent of homework is left for Sara to finish?
Answer:
.006%
Step-by-step explanation:
Given f(x) = 3x - 1 and g(x)= -x + 6, find f(-2) + g(5).
answer choices are:
-6
6
8
Answer:
-6Step-by-step explanation:
f(x)=3x-1 g(x)=-x+6f(-2)=3*(-2)-1 g(5)=-5+6f(-2)=-7 g(5)=1 f(-2)+g(5)=-7+1=-6A firm is hiring labor and capital in the cost-minimizing combination. Which of the following would cause the firm to increase hiring capital and decrease hiring of labor?
The productivity of labor increases by 5% would cause the firm to increase hiring capital and decrease hiring of labor
Step-by-step explanation:
A company can convert input data to output data. So, it gets divided the data into broad categories called production factors. Productivity variations, or more precisely the marginal products of labour, work in the same way as differences in real wages. Remember that marginal prices depend on both - real wages and the productivity.
If in case, productivity increases, perhaps because the company has increased its capital base, thereby marginal costs will decrease. Companies will produce more products and employ more employees. Conversely, if productivity drops, companies will produce less and destroy jobs.
When a firm faces union demands for higher wages, they may increase hiring of capital and decrease hiring of labor. This can result in increased labor productivity. In the United States in the 1970s, firms shifted towards more capital and less labor due to union demands for higher wages.
Explanation:When a firm is confronted with union demands for higher wages, they may choose to increase hiring of capital and decrease hiring of labor. This is because using more physical capital and less labor can result in increased labor productivity.
For example, if the cost of machines increases relative to labor, the firm may shift towards using less capital and more labor to minimize costs. In this situation, the firm would hire more capital and decrease hiring of labor.
In the United States in the 1970s, this situation occurred where firms faced union demands for higher wages, causing a shift towards more capital and less labor in production methods.
I don’t get this please help ASAP
Answer:
AE = 70
Step-by-step explanation:
Given that ACE is a triangle and B , D , F are mid-points of AC, CE, AE respectively.
⇒ BF, FD, BD are mid-segments.
Mid-segment is a line segment joining mid points of two sides of a triangle,
And it as two properties :
1) mid-segment is always parallel to the third side
2) mid-segment is half in length of the third side
⇒ Here, BD is the mid-segment and is parallel to third side AE
And also BD is half of AE
⇒ AE = 2×BD = 2×35
⇒ AE = 70.
Given: ∆AKM, R = 2, m∠A = 33°, O∈ AM . Find: perimeter of ∆AKM
Answer:
∆AKM is a right triangle for it is inscribed in semicircle O.
AM = diameter of semi-circle O = 2R = 2(2) = 4
%22AK%22%2F%22AM%22=cos%2833%5Eo%29
AK+=+AM%2Acos%2833%5Eo%29
AK+=+4cos%2833%5Eo%29
%22KM%22%2F%22AM%22=sin%2833%5Eo%29
KM+=+AM%2Asin%2833%5Eo%29
KM+=+4sin%2833%5Eo%29
The perimeter of a triangle is the sum of the three sides.
perimeter=AK%2BKM%2BAM
perimeter=4cos%2833%5Eo%29%2B4sin%2833%5Eo%29%2B4
Approximately 9.533238412
Step-by-step explanation:
Answer:
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Step-by-step explanation:
JUST ONE MORE I NEED HELP ON HW IM STRUGGLING 15pts
A pilot was scheduled to depart at 4:00 pm, but due to air traffic, her departure has been delayed by 16 minutes. Air traffic control approved a new flight plan that will allow her to arrive four times faster than she calculated in her original flight plan. Let x represent the time, in minutes, of her original flight. Create an equation that can be used to predict the number of minutes after 4:00 pm she will arrive at her destination.
y equals one fourth times x minus 16
y = 4x − 16
y equals one fourth times x plus 16
y = 4x + 16
Answer:
y equals one fourth times x minus 16
y = 4x − 16
Step-by-step explanation:
this is because you're taking the time it took to get there minus 16 because of the delay
Answer:
Answer is three because it is one fourth of the time don't listen to the other person's.
Step-by-step explanation:
Sheila predicts that 480 people will attendthe fall concert. There was an actual total of 350 people who attended the fall concert. What is the percent error?
Final answer:
To calculate the percent error, subtract the actual attendance from the predicted attendance, take the absolute value, divide by the actual attendance, and multiply by 100%. Sheila's prediction has a percent error of 37.14%.
Explanation:
The question is asking for the calculation of the percent error between Sheila's prediction for concert attendance and the actual attendance. To find the percent error, you subtract the actual value from the predicted value, take the absolute value of the difference, divide by the actual value, and then multiply by 100 to convert it to a percentage.
Steps to Calculate Percent Error
Subtract the actual number of attendees (350) from the predicted number (480) to get the difference: 480 - 350 = 130.Take the absolute value of the difference: |130| = 130.Divide the absolute difference by the actual number of attendees: 130 / 350 = 0.3714.Multiply by 100 to get the percent: 0.3714 * 100 = 37.14%.The percent error in Sheila's prediction is 37.14%.
Which expression is equivalent to (64 y Superscript 100 Baseline) Superscript one-half?
8y10
8y50
32y10
32y50
Answer:
[tex]8y^{50}[/tex]
Step-by-step explanation:
This expression is equal :
[tex]{(64y^{100})}^{\frac{1}{2}}[/tex]
Here we can use this rule :
[tex](a^mb^n)^y=a^{my}b^{ny}[/tex]
Now, 64 we can write like : [tex]8^2[/tex]
[tex](8^2y^{100})^{\frac{1}{2}}[/tex]
Now we can use our rule :
[tex]8^{2*\frac{1}{2}}y^{100*\frac{1}{2}[/tex]
When we simplify, we have :
8y^{50}
Answer:
b
Step-by-step explanation:
WILL GIVE BRAINLIEST!!!! PLEASE HELP!!!
A function is shown: f(x) = 16x2 − 1. Choose the equivalent function that best shows the x-intercepts on the graph.
A. f(x) = (4x + 1)(4x − 1)
B. f(x) = (8x + 1)(8x − 1)
C. f(x) = 4(x2 + 1)
D. f(x) = 8(x2 − 1)
Answer:
it is option a
Step-by-step explanation:
. f(x) = (4x + 1)(4x − 1) is the correct answer overall you have the check it and just make sure you fully to your capability of those steps
The equivalent function that best shows the x-intercepts on the graph is f(x)=(4x-1)(4x+1).
What is a Function?
A function assigns the value of each element of one set to the other specific element of another set.
As the function is given to us that f(x)=16x²-1, therefore, the equivalent function that best shows the x-intercepts on the graph can be written as,
[tex]f(x)= 16x^2-1\\\\f(x)=16x^2-1^2\\\\f(x)=(4x-1)(4x+1)[/tex]
If we solve the roots of the given function,
(4x-1)=0
x = 1/4 = 0.25
(4x+1)=0
x = -1/4 = -0.25
Thus, the x-intercept of the function is 0.25 or -0.25.
Thus, the equivalent function that best shows the x-intercepts on the graph is f(x)=(4x-1)(4x+1).
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help me on this question please
Answer:
Step-by-step explanation:
The diameter equals the side length of the outer square. The radius of the circle is √2. The diameter of the circle would be
2 × radius = 2 × √2 = 2√2
The area of a square is expressed as length^2. This means that the area of the outer square would be
( 2√2)^2 = 4×2 = 8
The area of the circle is expressed as πr^2. Therefore, the area of the circle would be
π×√2^2 = 2π = 2×3.14 = 6.28
Looking at the inner square, to find the length of the base, we would apply Pythagoras theorem.
√2^2 = base^2 + 1^2
2 = base^2 + 1
base^2 = 2 -1 = 1
base = √1
Area of the inner square would be
√1^2 = 1
Total shaded area would be
6.28 - 1 = 5.28
The probability that the dart will land on the shaded area is
5.28/8 = 0.66
Madison spent 3 times as long on her social project as she did on her other project. If she spent a total of 8 hours on he projects how long did she spend on her social project
Answer:
6 hours
Step-by-step explanation:
Suppose Madison spent x hours on her social project,
then the number of hours spent on other project will be 1/3 of x=x/3
Total hours spend on all projects will be the addition of hours spent on social project and hour spent on other project, i.e
x + x/3 = 4x/3
It si given that this is 8 hours, therefore
4x/3=8
Multiplying both sides by 3:
4x=24
Dividing across board by 4:
x= 6 hours
If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, what is the value of a?(1) a^n = 64(2) n=6
Answer:
a=2
Step-by-step explanation:
Well, first let us find product of the first 8 positive integers, which is 1*2*3*4*5*6*7*8=40320. It can also be written as 40320=[tex]2^{7}[/tex]*3²*5*7. From the formula above, it can be extracted that if a=2, n can be any number from 3 to 7 (considering that a and n are not equal and greater than 1).
In (1) a^n=64 and in (2) n=6 so it can be written as 2^6=64 so a=2 and n=6. So the value of a is 2. a=2
Two roads that cross at right angles are used as coordinate axes for a map. A library is located at point L . Use the drop-down menus to complete the statements about the location of the library.
The question is incomplete. Here is the complete question:
Two roads that cross at right angles are used as coordinate axes for a map. A library is located at point L.
Use the drop-down menus to complete the statements about the location of the library.
(a) The library is located at point (_,_).
(b) The library is __ miles from Road X and __ miles from Road Y.
Answer:
(a) The library is located at point (3.25, -1.5).
(b) The library is 1.5 miles from Road X and 3.25 miles from Road Y
Step-by-step explanation:
Given:
The roads are at right angles to each other. Point 'L' is the location of the library.
(a)
From the graph, we can conclude that,
The length of each square in the graph is 0.5 miles. So,
The coordinates of point L are (3.25, -1.5).
The 'x' value is 3.25 and the 'y' value is -1.5.
Since the point 'L' is the location of library, therefore, the library is located at point (3.25,-1.5).
(b)
The distance of point L from road X is obtained by moving vertically up from point L till we reach the road X. In other words, the perpendicular distance between point L and horizontal x axis is the required distance.
The perpendicular distance is the absolute value of the y-coordinate of point L. The absolute value of 'y' of point L is |-1.5| = 1.5 miles.
Hence, the library is 1.5 miles from road X.
Similarly, the distance of point L from road Y is the perpendicular distance of point L to the road Y.
The perpendicular distance is the absolute value of the x-coordinate of point L. The absolute value of 'x' of point L is |3.25| = 3.25 miles.
Therefore, the library is 3.25 miles from road Y.
So, the library is 1.5 miles from Road X and 3.25 miles from Road Y
Given a positive integer N, find all of the positive integers from 1 to N that can be written as a sum of 2 cubic numbers (also have to be positive) in two different ways.
Answer:
There are infinite such positive integers which can be written as a sum of cubes of two positive integers. Some of them are written below:
1³+12³=9³+10³=17292³+24³=18³+20³=1383210³+27³=19³+24³=2068315³+945³=744³+756³=843912000Hence it is not possible to write all such numbers which can be written in this format. Though some of them can be enlisted if the value of maximum integer "N" is given.
A 4-inch tall box with a square base is constructed in order to hold a set of 16 identical cupcakes, each with a diameter of 2 inches. What is the area of the base, in square inches, of the smallest box that can hold the cupcakes?
Answer:
64 square inches
Step-by-step explanation:
The base is square, and there are 16 cupcakes, so there are 4 cupcakes along the width and 4 cupcakes along the length.
Each cupcake is 2 inches, so the base is 8 inches by 8 inches. Therefore, the area is 64 square inches.
Twenty years ago, you began investing $3,000 a year. Because your investments earned an average of 8 percent a year, your investment portfolio has a current dollar value of $92,000. How much did you earn on your investments over the 20-year period of time? a.) $40,000
b.) $132,000
c.) $92,000
d.) $52,000
e.) $2,000
Answer:
$32,000
Step-by-step explanation:
Yearly investment = $3,000
Number of years = 20
Investments earned an average of 8 percent a year.
Total invested amount = $3,000 × 20 = $60,000
Current value of investment = $92,000.
We need to find the total earnings on the investment.
Earnings = Current value of investment - Total invested amount
Earnings = $92,000 - $60,000
Earnings = $32,000
Therefore, the total earnings is $32,000.
To find out how much was earned on the investments over a 20-year period, we subtract the total amount invested ($60,000) from the final value of the portfolio ($92,000), yielding $32,000 as the total earnings. However, this option is not offered in the question.
Explanation:This type of question is typically encountered in personal finance or mathematics related to investment portfolios. The total amount invested over twenty years is calculated by multiplying the yearly investment by the number of years, so $3,000 * 20 years = $60,000. This is the amount you've put in from your own pocket. The value of the investment portfolio now is given as $92,000, which is the sum of your investment and the earnings. So to calculate your earnings alone, you subtract the total amount you invested from the current value of your portfolio: $92,000 (total value) - $60,000 (your total investment) = $32,000. So the amount you earned on your investments over this 20-year period is not given in the question as none of the options match our calculation of $32,000.
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Write an equation for the line that is parallel to y = −2x and passes through the point (0,7).
A. y=2x–7
B. y=-2x + 7
C. y=-2x-7
D. y=2x+7
Answer:
B. [tex]\displaystyle y = -2x + 7[/tex]
Step-by-step explanation:
The y-intercept is given to us, which is [tex]\displaystyle [0, 7],[/tex]and Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], so −2 remains the way it is.
I am joyous to assist you anytime.
AB = x + 4 DC = 12 AD = x + 2 BC = ? Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Show that quadrilateral ABCD is a parallelogram by finding the lengths of the opposite side pairs. What is the length of BC?
Answer:
AB = DC = 12
AD = BC = 10
Step-by-step explanation:
For ABCD to be a parallelogram, opposite side pairs must be congruent. That will be the case when ...
AB = DC
x+4 = 12 . . . . substitute expressions for length
x = 8 . . . . . . . subtract 4
Then the lengths of AD and BC must be ...
BC = AD = x+2 = 8+2 = 10
___
The figure will be a parallelogram when x=8 and sides have lengths ...
AB = DC = 12
AD = BC = 10
_____
Comment on the problem
Of course, if x ≠ 8, or BC ≠ AD, the figure will not be a parallelogram. You are asked to show the figure IS a parallelogram, but all you can really show is that the figure CAN BE a parallelogram. In order to do anything useful with the given expressions for side lengths, you must assume the figure is a parallelogram.
WILL GIVE BRAINLIEST FOR THE CORRECT ANSWER AND POINTS!
Answer:
c
Step-by-step explanation: