100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
Refer to the step-by-step.
Step-by-step explanation:
Verify the given identity.
[tex]E_0\cos^4(\theta)=E_0(\frac{1}{2} +\frac{\cos(2\theta)}{2} )^2[/tex]
Pick the more complex side to manipulate, in this case it is the R.H.S.
(1) - Apply the following double-angle identity
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Double-Angle Identity:}}\\\\\cos(2A)=1-2\sin^2(A)\end{array}\right}[/tex]
[tex]E_0(\frac{1}{2} +\frac{\cos(2\theta)}{2} )^2\\\\\Longrightarrow \boxed{ E_0\Big(\frac{1}{2} +\frac{1-2\sin^2(\theta)}{2}\Big )^2}[/tex]
(2) - Split of the right fraction
[tex]E_0(\frac{1}{2} +\frac{1-2\sin^2(\theta)}{2} )^2\\\\\Longrightarrow E_0(\frac{1}{2} +\frac{1}{2} -\frac{2\sin^2(\theta)}{2})^2\\\\\Longrightarrow \boxed{E_0(1 -sin^2(\theta))^2}[/tex]
Apply the following Pythagorean identity
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Pythagorean Identity:}}\\\\1-\sin^2(A)=\cos^2(A)\end{array}\right}[/tex]
[tex]E_0(1 -sin^2(\theta))^2\\ \\\Longrightarrow E_0(\cos^2(\theta))^2\\\\\therefore \boxed{E_0\cos^4(\theta)=E_0\cos^4(\theta)}[/tex]
Thus, the identity is verified.
It has been proven and verified that [tex]E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{cos2 \theta}{2} )^2[/tex] below.
How to verify the equality of the cosine function?In Mathematics and Geometry, the standard equation of a cosine function is represented or modeled by the following mathematical equation (formula):
y = Acos(Bx - C) + D
Where:
A represents the amplitude.B = 2π/P.P represents the period.C represents the phase shift.D represents the center line (midline).In this exercise, you are required to prove that the right-hand side of the cosine function is equal to left-hand side of the cosine function;
[tex]E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{cos2 \theta}{2} )^2[/tex]
From the double-angle formulas, we have:
2sin²θ = 1 - cos2θ
cos2θ = 1 - 2sin²θ
Next, we would evaluate the right-hand side of the cosine function by substituting "1 - 2sin²θ" for cos2θ as follows;
[tex]E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{1-2sin^2 \theta}{2} )^2\\\\E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{1}{2} -\frac{2sin^2 \theta}{2})^2\\\\E_0cos^4 \theta = E_0(1 -\frac{2sin^2 \theta}{2})^2\\\\E_0cos^4 \theta = E_0(1 -sin^2 \theta)^2\\\\[/tex]
E₀cos⁴θ = E₀(1² - (sin²θ)²)
E₀cos⁴θ = E₀(1 - sin⁴θ) ⇒ (Verified).
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Related Questions
Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted:
rectangle with a length of x plus 25 and width of x plus 15 with a rectangle in the bottom right corner labeled bench that has a length of 10 and width of 3
Write an equation to determine the area, A, of the patio that will be painted.
A. A = (x + 18)(x + 35)
B. A = (x + 15)(x + 25) + 30
C. A = (x + 5)(x + 22)
D. A = (x + 25)(x + 15) − 30
Answers
The correct equation to determine the area, A, of the patio that will be painted is,
D. A = (x + 25)(x + 15) - 30
We have to given that;
Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted.
Here, rectangle with a length of x plus 25 and width of x plus 15 with a rectangle.
And, in the bottom right corner labeled bench that has a length of 10 and width of 3.
Hence, Area of rectangle is,
A = (x + 25) (x + 15)
And, Area of bottom right corner is,
A = 10 x 3
A = 30
Thus, The equation to determine the area, A, of the patio that will be painted is,
⇒ A = (x + 25)(x + 15) - 30
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A cone has a volume of 48 cubic feet and a height of 9 feet. Find the radius.
The radius is ___ ft
Answers
Cone - A cone is a three-dimensional geometric object used in mathematics that smoothly taper from a flat, typically circular base to a point known as the apex or vertex.
The following is the formula for a cone's volume:
[tex]V = (1/3)πr^2h[/tex]
where the volume is [tex]V[/tex], the radius is [tex]r[/tex], and the height is [tex]h[/tex].
In putting the values provided yields:
[tex]48 = (1/3)πr^2(9)[/tex]
By dividing both sides by [tex]3[/tex], we arrive at:
[tex]144/π = r^2(9)[/tex]
When we multiply both sides by [tex]9[/tex], we get:
[tex]16/π = r^2[/tex]
When we square the two sides, we obtain:
[tex]r = √(16/π)[/tex]
(Rounded to two decimal places) [tex]r = 2.52 feet[/tex]
As a result, the radius is roughly [tex]2.52 feet.[/tex]
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A football is catapulted into the air so that its height h, in meters, after t seconds is h = -4.9t² +27t +
2.4 a) How high is the football after 1 second? b) For how long is the football more than 30 m high? c)
What is the maximum height of the football?
Answers
After 1 second the football is 24.5 meters.
Given that, a football is catapulted into the air so that its height h, in meters, after t seconds is h = -4.9t² +27t +2.4
a) Here, t=1
Now, h =-4.9(1)²+27(1)+2.4
= -4.9+27+2.4
= 24.5 meters
b) Given that, h=30 meter
30=-4.9t² +27t +2.4
30+4.9t²-27t-2.4=0
4.9t²-27t+27.6=0
Factor and set each factor equal to zero.
Exact Form:
t=(135+√4701)/49, (135−√4701)/49
Decimal Form:
t=4.15436405…, and 1.35584002...
c) To find maximum height, set h=0
-4.9t² +27t +2.4=0
Factor and set each factor equal to zero.
Exact Form:
t=(135+√19401)/49, (135−√19401)/49
Decimal Form:
t=5.59770352…,−0.08749943…
Therefore, after 1 second the football is 24.5 meters.
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PLEASE HELP
Lily is a botanist who works for a garden that many tourists visit. The function f(s) = 2s + 30 represents the number of flowers that bloomed, where s is the number of seeds she planted. The function s(w) = 40w represents the number of seeds she plants per week, where w represents the number of weeks.
Part A: Write a composite function that represents how many flowers Lily can expect to bloom over a certain number of weeks. (4 points)
Part B: What are the units of measurement for the composite function in Part A? (2 points)
Part C: Evaluate the composite function in Part A for 35 weeks. (4 points)
Answers
Step-by-step explanation:
Part A:
To find the composite function, we need to plug in the expression for s(w) into f(s):
f(s(w)) = 2s(w) + 30
= 2(40w) + 30
= 80w + 30
Therefore, the composite function that represents how many flowers Lily can expect to bloom over a certain number of weeks is f(s(w)) = 80w + 30.
Part B:
The units of measurement for the function f(s(w)) are the same as the units of measurement for f(s) and s(w). From the given information, we know that s(w) represents the number of seeds planted per week and f(s) represents the number of flowers bloomed based on the number of seeds planted. Thus, the units of measurement for f(s(w)) are "flowers" per week.
Part C:
To evaluate the composite function f(s(w)) for 35 weeks, we need to substitute w = 35 into the expression we found in Part A:
f(s(35)) = 80(35) + 30
= 2,830
Therefore, Lily can expect 2,830 flowers to bloom after planting 40 seeds per week for 35 weeks.
Answer: c
Step-by-step explanation:
i took the test
The producer of a weight-loss pill advertises that people who use the pill lose, after one week, an average (mean) of 1.8 pounds with a standard deviation of 1.02 pounds. In a recent study, a group of 45 people who used this pill were interviewed. The study revealed that these people lost a mean of 1.73 pounds after one week.
If the producer's claim is correct, what is the probability that the mean weight loss after one week on this pill for a random sample of 45 individuals will be 1.73 pounds or less?
Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
Answers
The probability that the mean weight loss after one week on the pill for a random sample of 45 individuals will be 1.73 pounds or less is approximately 0.3231, or 32.31%.
How to find the probability that the mean weight loss after one week on this pill for a random sample of 45 individuals will be 1.73 pounds or lessCalculating the standard error of the mean (SE) using the formula:
SE = σ / sqrt(n)
where σ is the standard deviation and n is the sample size.
SE = 1.02 / sqrt(45) ≈ 0.1522
We can calculate the z-score using the formula:
z = (x - μ) / SE
where x is the observed mean and μ is the claimed mean.
z = (1.73 - 1.8) / 0.1522 ≈ -0.4582
Using a standard normal distribution table or a calculator, we find that the probability is approximately 0.3231.
Therefore, the probability that the mean weight loss after one week on the pill for a random sample of 45 individuals will be 1.73 pounds or less is approximately 0.3231, or 32.31%.
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manager states that all 80 crates can be packed in a 2m x 2m area e store room. (Assume that the height of the store room is adequate stacked crates) y if this statement is correct. Show all your calculations.
Answers
Note that based on the volume calculations, the manager's statement is NOT correct. The given area of 2m × 2m is insufficient to store all 80 crates.
How is this so ?To verify if the manager's statement is correct, we need to derive the volume of each crate and the total volume required to store all 80 crates.
Volume = Length × Width × Height
Recall that
Length (L) = 690 mm
Width (W) = 445 mm
Height (H) = 180 mm
Thus, the Volume of one crate is
Volume = 690 mm × 445 mm × 180 mm
Converting mm to meters we have,
Volume = (690 / 1000) × (445 / 1000) × (180 / 1000)
= 0.690 × 0.445 × 0.180
= 0.055269 m³
Next , we calculate the total volume required for 80 crates as
Total Volume = Volume of one crate × Number of crates
= 0.055269 m³ × 80
= 4.42152 m³
Recall that the manager stated that all 80 crates can be packed in a 2m × 2m area in the store room.
Since area of store room is
Area = 2 m × 2 m
Area = 4 m²
Comparing the total volume required (4.380208 m³) with the available area (4 m²), we see that the volume exceeds the area. Tus, the manager's statement is incorrect.
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Full question:
Manager states that all 80 crates can be packed in a 2m x 2m area e store room. (Assume that the height of the store room is adequate stacked crates) y if this statement is correct. Show all your calculations.
See attached Image.
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Desert Landing is symmetric
Mean, because Sunny Town is skewed
Mean, because Desert Landing is symmetric
Median, because Sunny Town is skewed
Answers
The answer is C. Mean, because Desert Landing is symmetric.
What is distributions?A distribution refers to the pattern of how data is spread out or distributed across different values or intervals. It is a way to describe and analyze the shape, center, and spread of a set of data.
According to question:To determine the location with the most consistent temperature, we need to measure the variability of the temperature data in both locations. The measure of variability that is appropriate for this purpose is the Mean, which measures the spread of the middle of the data.
The answer is C. Mean, because Desert Landing is symmetric. depending on the shape of the distributions. If the temperature data in Desert Landing is symmetric, then the Mean would be appropriate to measure the spread of the data. If the temperature data in Sunny Town is skewed, then the Mean would also be appropriate to measure the spread of the data. However, if the temperature data in either location is not skewed, then the range would not be an appropriate measure of variability.
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Mean, Fractiles, median, and mode are called the measures of central tendency
Answers
The mean monthly income is $3300, the median monthly income is $3000, there is no mode, and the range of the monthly income is $3000.
To find the mean, median, mode, and range of the monthly incomes, we'll perform the following calculations:
Mean:
The mean is calculated by summing all the values and dividing by the total number of values.
Mean = (2000 + 2500 + 3000 + 4000 + 5000) / 5
Mean = 16500 / 5
Mean = 3300
The mean monthly income is $3300.
Median:
The median is the middle value when the data is arranged in ascending order. In this case, since we have an odd number of values, the median is the middle value.
Arranging the incomes in ascending order: $2000, $2500, $3000, $4000, $5000
The median monthly income is $3000.
Mode:
The mode is the value(s) that appear most frequently in the data. In this case, there is no value that appears more than once, so there is no mode.
The data has no mode.
Range:
The range is calculated by subtracting the minimum value from the maximum value.
Range = Maximum Value - Minimum Value
Range = $5000 - $2000
Range = $3000
The range of the monthly income is $3000.
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The complete question is as follows:
Mean, Fractiles, median, and mode are called the measures of central tendency. A group of friends recorded their monthly incomes in dollars. The incomes are as follows: $2000, $2500, $3000, $4000, $5000. Determine the mean, median, mode, and range of their monthly incomes.
The distance between Marisa's house and the post office is 720 m. If she walks from her house to the post office at an average speed of 80 m/min, how long will she take?
Answers
Okay, let's break this down step-by-step:
* The distance between Marisa's house and the post office is 720 m
* Marisa walks at an average speed of 80 m/min
* To calculate the time:
** Distance / Speed = Time
** 720 m / 80 m/min = 9 minutes
Therefore, if the distance is 720 m and Marisa's average walking speed is 80 m/min, it will take her 9 minutes to walk from her house to the post office.
What is the measure of angle HEK in this figure?
a protractor, with segment DEF along the bottom, EH point to the 55 degree on the left, EJ to 90 degrees, EK to the 30 degrees on the right
85°
150°
95°
55°
Answers
Answer:
Measure of angle HEK is: 85°.
Step-by-step explanation:
Given that point E is the center of the protractor, we have:
angle HEJ = 55° (EH points to 55 degrees)
angle JEK = 30° (EK points to 30 degrees)
Since angle HEJ and angle JEK meets at a point E, then we can find angle HEK by summing up the two angles:
angle HEK = angle HEJ + angle JEK
angle HEK = 55° + 30°
angle HEK = 85°
Can anyone help me with this <3
Answers
Answer:
[tex]3.23*10^{16}[/tex]
Step-by-step explanation:
Just multiply. You have to do:
[tex](1.12*10^7)*(2.88*10^9)\\=3.23*10^{16}[/tex]
Write the equation of the conic section shown below.
Answers
The vertex form of the equation of a parabola is equal to y + 1 = - (1 / 12) · (x - 2)².
How to determine the equation of a parabola in vertex form
In this problem we need to determine the equation of a parabola, this can be done by knowing the distance between vertex and focus and the coordinates of the focus. The vertex form of the equation of the parabola is:
y - k = [1 / (4 · p)] · (x - h)²
Where:
h, k - Coordinates of the vertex.p - Distance of the focus with respect to vertex.If we know that (h, k) = (2, - 1) and p = - 3, then the equation of the parabola in vertex form is:
y + 1 = - (1 / 12) · (x - 2)²
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Answer:
[tex](x-2)^2=-12(y+1)[/tex]
Step-by-step explanation:
From observation of the given diagram, we can see that the graphed conic section is a vertical parabola that opens downwards, with a vertex at (2, -1) and a focus at (2, -4).
The equation of a vertical parabola in standard form is:
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Standard form of a vertical parabola}\\\\$(x-h)^2=4p(y-k)$\\\\where:\\ \phantom{ww}$\bullet$ $p\neq 0$\\ \phantom{ww}$\bullet$ Vertex: \;$(h,k)$\\ \phantom{ww}$\bullet$ Focus:\; $(h,k + p)$\\\end{minipage}}[/tex]
Given the vertex is (2, -1):
[tex]h = 2[/tex][tex]k = -1[/tex]Given the formula for the focus is (h, k+p), then:
[tex]\begin{aligned}(h, k+p)&=(2, -4)\\(2,-1+p)&=(2,-4)\\\\\implies -1+p&=-4\\p&=-4+1\\p&=-3\end{aligned}[/tex]
To write the equation of the graphed conic section, substitute the found values of h, k and p into the standard formula:
[tex](x-2)^2=4(-3)(y-(-1))[/tex]
[tex](x-2)^2=-12(y+1)[/tex]
Therefore, the equation of the graphed conic section is:
[tex]\boxed{(x-2)^2=-12(y+1)}[/tex]
You take out a 45-day loan for $2600. At the end of the loan, you owe $70.52 in interest. What is the annual percentage rate? Round your answer to the nearest tenth of a percent.
Answers
the annual percentage rate for the loan is 571.2%, rounded to the nearest tenth of a percent.
Find the quotient and remainder using synthetic division for
x^5
-
x^4
+
9
x^3
-
9
x^2
+
9
x
-
10
/x
-
1
The quotient is x2+9x2+9
The remainder is −1
Answers
The division of x⁵ - x⁴ + 9x³ - 9x² + 9x - 10 by x - 1 will have a quotient of x⁴ + 9x² + 9 and a remainder of -1 using synthetic division.
Dividing with synthetic divisionThe procedure for synthetic division involves the following steps:
Divide.
Multiply.
Subtract.
Bring down the next term, and
Repeat the process to get zero or arrive at a remainder.
We shall divide x⁵ - x⁴ + 9x³ - 9x² + 9x - 10 by x - 1 as follows;
x⁵ divided by x equals x⁴
x - 1 multiplied by x⁴ equals x⁵ - x⁴
subtract x⁵ - x⁴ from x⁵ - x⁴ + 9x³ - 9x² + 9x - 10 will give 9x³ - 9x² + 9x - 10
9x³ divided by x equals 9x²
x - 1 multiplied by 9x² equals 9x³ - 9x²
subtract 9x³ - 9x² from 9x³ - 9x² + 9x - 10 will give 9x - 10
9x divided by x equals 9
x - 1 multiplied by 9 equals 9x - 9
subtract 9x - 9 from 9x - 10 will give us a remainder of -1
Therefore by synthetic division, x⁵ - x⁴ + 9x³ - 9x² + 9x - 10 divided by x - 1 will result to a quotient of x⁴ + 9x² + 9 and a remainder of -1.
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Drew designs and produces vintage looking clothing, but using modern materials. Drew would like to sell the clothing, but does not want to set up a store front either physically or online. What might Drew choose as an option for selling the clothing?
a)mail order
b)door to door sales
c)consignment
d)e-commerce direct
Answers
Consignment cab be used as an option for selling the clothing
What is consignment?Consignment involves providing your goods to an established business, like a boutique or vintage store, which then sells the items on your behalf and takes a cut of the profits. This approach lets Drew benefit from the store's customer base and avoids the need to manage a storefront.
Mail order (option a) could also work if Drew is willing to manage shipping and handling, and has a method for advertising the products effectively without a physical or online storefront.
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how many liters each of a 50% acid solution and a 85% acid solution must be used to produce 70 liters of a 75% acid solution
Answers
We can set up a system of two equations to represent the problem:
x + y = 70 (the total volume of the mixture is 70 liters)
0.5x + 0.85y = 0.75(70) (the total amount of acid in the mixture is 75% of 70 liters)
Simplifying the second equation, we get:
0.5x + 0.85y = 52.5
Now we can solve for x and y using the system of equations. One way to do this is to multiply the first equation by 0.5 and subtract it from the second equation:
0.5x + 0.85y = 52.5
-0.5x - 0.5y = -35
--------------------
0.35y = 17.5
y = 50
So we need 50 liters of the 85% acid solution. Substituting this value into the first equation, we get:
x + 50 = 70
x = 20
Therefore, we need 20 liters of the 50% acid solution and 50 liters of the 85% acid solution to produce 70 liters of a 75% acid solution.
What is the least common denominator of -2x/x-1 + x+3/x^2-1 =
Answers
The least common denominator will be (x-1)(x²-1).
When two or more fractions have the same denominators, they are termed as the common denominators.
The least common denominator (LCD) refers to the smallest number that is a common denominator for a given set of fractions.
For addition and subtraction of fractions and for comparing two or more fractions, the given fractions need to have common denominators.
The least common denominator is defined as the smallest common multiple of all the common multiples of the denominators when 2 or more fractions are given.
Given is an expression, -2x/x-1 + x+3/x²-1, we need to find the least common denominator,
So,
-2x/x-1 + x+3/x²-1
Taking the LCM,
-2x(x²-1) + (x+3)(x-1) / (x-1)(x²-1).
Hence the least common denominator will be (x-1)(x²-1).
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1 in 20 children play chess and 1 in 5 children play a musical instrument. Research shows that the probability
of a child playing a musical instrument given that that child plays chess is 0.2.
What is the probability of a randomly chosen child playing chess and playing a musical instrument?
O 0.04
O 0.25
O 0.2
O 0.01
Answers
The probability that we will get a lead role, given that we are chosen to be in the play is 0.7.
We have,
Probability is the ratio that shows the likelihood of an event occurring from a given set of possible events.
We can find the required probability below:
The probability that we will be chosen for the play is 0.5.
The probability that we will get the lead role is 0.2.
In this situation, the probability can be found by adding the probability of being chosen and the probability that we will get the lead role.
The probability that we get a lead role, = The probability that we will be chosen for the play + The probability that we will get the lead role
= 0.5 + 0.2
= 0.7
The probability of us getting a lead role given that we have already been chosen for the play is found to be 0.7. The correct answer is option C.
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complete question:
You are trying out for the school play. The probability that you are chosen to
be in the play is 0.5. The probability that you get a lead role is 0.2. What is the
probability that you get a lead role, given that you are chosen to be in the
play?
O A. 0.5
Oo oo
O B. 0.4
O c. o7
O D.0.3
2( x - 4) + 3(2 - x) + 2x + 7
Answers
Answer:
The Answer to This question Is x + 5 So Basically 5
Triangle BCD with vertices B(-2, 3), C(8, 7), and D(-1,-5): y = x
B' (-3, 2); C'(7,8); D'(-5,-1)
B' (-3,-2); C'(7,8); D'(-5,-1)
B' (3,-2); C'(7,8); D'(-5,-1)
B' (3,-2); C'(7,-8); D'(-5,-1)
Answers
Answer:
(c) B'(3, -2); C'(7, 8); D'(-5, -1)
Step-by-step explanation:
Apparently, you want to know the coordinates of B', C', and D' after reflection of B(-2, 3), C(8, 7), and D(-1,-5) in the line y = x.
ReflectionThe reflection in the line y = x has the effect of swapping the x- and y-coordinates:
(x, y) ⇒ (y, x)
No sign changes are involved.
The reflected coordinates are ...
B'(3, -2); C'(7, 8); D'(-5, -1)
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Calculator
A point is selected at random inside the given figure.
What is the probability the point will be in the region labeled A?
Enter your answer, as a fraction in simplest form, in the box.
P(A) =
Basic
5 in.
B
3 in.
A
C
4 in.
3 in.
D
4 in.
Answers
The probability of the point being in region A is 0.5294.
The area of the entire figure can be found by adding the areas of the four triangles:
Area of entire figure
= Area of triangle ABC + Area of triangle ACD + Area of triangle ABD + Area of triangle BCD
= (1/2)(5)(3) + (1/2)(3)(4) + (1/2)(4)(3) + (1/2)(3)(4)
= 7.5 + 6 + 6 + 6
= 25.5 square inches
Similarly, the area of region A can be found by adding the areas of triangles ABC and ABD:
Area of region A
= Area of triangle ABC + Area of triangle ABD
= (1/2)(5)(3) + (1/2)(4)(3)
= 7.5 + 6
= 13.5 square inches
Therefore, the probability of the point being in region A is:
P(A) = Area of region A / Area of entire figure
P(A) = 13.5 / 25.5
P(A) = 0.5294
So the probability of the point being in region A is 0.5294.
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At the end of the week, a paper company in Scranton, PA, determines whether they broke even, made a profit, or made a loss. The likelihood of making a profit is 0.75, whereas the probability of breaking even is 0.21. What is the likelihood that for two consecutive weeks, the company makes a profit and then makes a loss? A. 0.32 B. 0.06 C. 0.03 D. 0.16
Answers
The likelihood of profit and loss in the following week is 18.75%. The Option D is correct.
What is the probability?A probability means the branch of math which deals with finding out the likelihood of the occurrence of an event. Its measures the chance of an event happening.
To get probability of the company making a profit and then making a loss in two consecutive weeks, we need to multiply the probabilities of each event occurring.
The probability of making a profit in one week is 0.75
The probability of making a loss in the following week will be:
= 1 - 0.75
= 0.25.
So, probability of the company making a profit in one week and then making a loss in the following week is:
= 0.75 * 0.25
= 0.1875
= 18.75%.
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1. How does the author support her argument that
some modern voting laws might be intended to
prevent minorities from exercising their civil rights?
Cite evidence from the text in your response.
PAMENT
Answers
The author references a couple of situations that occured in the country and are occuring presently, justified by laws, which reduces the ability of social minorities to vote.
How does the author pose her argument?The author of this article cites several laws passed in states that make it harder for minorities, especially blacks, to vote regularly. He said that even after an amendment was passed allowing blacks to vote, he passed other laws preventing blacks from voting, such as requiring voter education.
These laws were enacted with increasing force until the passage of the Civil Rights Act in the 1960s.
Every year since civil rights, different laws have been passed making it harder for blacks, women, the working class, and homosexuals to vote among other members of social minorities. Many of these laws are still in effect.
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helpppp me please this is really hard for me to do right now
Answers
Part A: At her current rate, the distance Amy can ride her bike within 12 minutes is A. 1.6 miles.
Part B: Sebastian can ride his bike for C: 7.5 miles in 1 hour.
Part C: The time it will take for one to wait is B: Amy will have to wait 1.5 minutes for Sebastian.
How to determine the distance a rider can ride his bike?Part A:
To find the distance Amy can ride her bike in 12 minutes, we set up a proportion based on her current rate.
Amy's rate: 4 miles / 30 minutes = x miles / 12 minutes
Cross-multiplying:
30x = 4 * 12
30x = 48
Dividing both sides by 30:
x = 48 / 30
x ≈ 1.6
So, Amy can ride her bike at 1.6 miles in 12 minutes.
Part B:
To find the distance Sebastian can ride his bike in 1 hour, convert the time to minutes first.
1 hour = 60 minutes
Sebastian's rate: 3 miles / 24 minutes = x miles / 60 minutes
Cross-multiplying:
24x = 3 * 60
24x = 180
Dividing both sides by 24:
x = 180 / 24
x ≈ 7.5
Therefore, Sebastian can ride his bike at 7.5 miles in 1 hour.
Part C:
Amy's home to Park = 3 miles,
Park to Sebastian's home = 3 miles.
Amy's rate = 4 miles in 30 minutes, equivalent to 1 mile in 7.5 minutes.
Sebastian's rate = 3 miles in 24 minutes, equivalent to 1 mile in 8 minutes.
Then, we estimate the time it takes for each to cover a distance of 3 miles.
Amy:
Time = Distance / Rate = 3 miles / (2/15 miles/minute)
= 3 * (15/2) minutes
= 22.5 minutes
Sebastian:
Time = Distance / Rate = 3 miles / (1/8 miles/minute)
= 3 * 8 minutes
= 24 minutes
Since Amy= 22.5 mins and Sebastian takes 24 mins,
24 - 22.5 = 1.5
Hence, Amy will have to wait 1.5 minutes for Sebastian.
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The approximate mass of a hydrogen atom is grams. The mass
of a single lead atom is approximately grams. How many times
heavier is a lead atom than a hydrogen atom?
Answers
A lead atom is 200 times heavier than a hydrogen atom.
To determine how many times heavier a lead atom is compared to a hydrogen atom, we can calculate the ratio of their masses.
Mass of hydrogen = 1.7 × 10⁻²⁴ grams
Mass of lead atom = 3.4 × 10⁻²² grams
To find the ratio of their masses, we divide the mass of the lead atom by the mass of the hydrogen atom:
Ratio = 3.4 × 10⁻²² / 1.7 × 10⁻²⁴
= (3.4 / 1.7)× 10⁻²² / 10⁻²⁴
= 2×10²
= 200
Therefore, a lead atom is 200 times heavier than a hydrogen atom.
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The approximate mass of a hydrogen atom is 1.7*10^-24 grams. The mass of a single lead atom is approximately 3.4*10^-22 grams. How many times heavier is a lead atom than a hydrogen atom.
A. 5 times heavier
B. 20 times heavier
C. 50 times heavier
D. 200 times heavier
True or false,if f(s)=f(t) then s=t
Answers
For example if f = x^2 then
If s = 1 then f(s) = 1 and if t = -1 then f(t) = 1 also
So here we have f(s) = f(t) but s is not = t.
So your answer is
False.
PLEASE HELP!!!!!
Two cards are drawn without replacement from a standard deck of 52
playing cards. What is the probability of choosing a red card for the second card drawn, if the first card, drawn without replacement, was a heart? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answers
Answer:
25/51
Step-by-step explanation:
If the first card was a heart, we've drawn one red card already.
The ratio of black to red cards in the deck is now 26:25.
On the second draw, there will be only 51 cards to choose from, rather than 52 because you have already taken out a card. Therefore, you only have a 25/51 chance of drawing a red card compared to the 26/52 or 1/2 chance on the first draw.
Answer is 25/51.
what are the coefficients in the polynomial
Answers
Answer: 7 and -4
Step-by-step explanation:
Coefficients are numbers in front of variables
6 doesn't have a variable so it's a constant
7 and -4 are the coefficients
A friend has a 80% average before the final exam for a course. The score includes everything but the final, which counts for 15% of the course grade. What is the best course grade your friend can earn? What is the minimum score would your friend need on the final to earn a 75% for the course?
Answers
Your friend would need to score at least 46.67% on the final exam to earn a 75% for the course.
Since the final exam counts for 15% of the course grade, the weighted average can be calculated as follows:
Weighted average = (0.85 × 80%) + (0.15 × final exam score)
If we assume that your friend wants to get the highest possible grade, then they would need to get a perfect score on the final exam, which would be 100%.
Plugging this into the equation above, we get:
Weighted average = (0.85 × 80%) + (0.15 × 100%) = 83%
Therefore, the best course grade your friend can earn is 83%.
We can set up an equation where x is the minimum score needed on the final exam:
Weighted average = (0.85 × 80%) + (0.15 × x) = 75%
Simplifying this equation, we get:
0.85 × 80% + 0.15x = 75%
68% + 0.15x = 75%
0.15x = 7%
x = 46.67%
Therefore, your friend would need to score at least 46.67% on the final exam to earn a 75% for the course.
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ABDE is a parallelogram.
AB=AC
B
Show that x = 38°
A
C
82°
D
68%
E
Not drawn
accurately
[3 marks]
Answers
The proof that the value of x is 38° is shown below
How to show that the value of x is 38°From the question, we have the following parameters that can be used in our computation:
ABDE is a parallelogram.
The measure of the angle opposite the vertex x is
Angle = 180 - 68
Evaluate the like terms
So, we have
Angle = 112
Also, we have
B = 68
AB = AC
So, we have
y = 180 - 68 - 68
y = 44
Using the above as a guide, we have the following:
x + 44 = 82
So, we have
x = 82 - 44
Evaluate
x = 38
Hence, we have shown that the value of x is 38°
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