If X ~N (0,2) Find the probability distribution function of Y
=|X| . Hence, on otherwise Find
1.E(|X| )
2. Var(|X|)
Solve it fast
The probability distribution function of Y = |X| is given by:
P(Y ≤ y) = P(|X| ≤ y) = P(-y ≤ X ≤ y) = P(X ≤ y) - P(X < -y)
Since X ~ N(0, 2), we can use the standard normal distribution to find the probabilities:
P(X ≤ y) = Φ(y/√2)
P(X < -y) = Φ(-y/√2)
Therefore, the probability distribution function of Y is:
P(Y ≤ y) = Φ(y/√2) - Φ(-y/√2)
To find E(|X|) and Var(|X|), we can use the properties of the absolute value function:
E(|X|) = ∫_(-∞)^(∞) |x| f(x) dx = 2 ∫_(0)^(∞) x f(x) dx
Var(|X|) = E(|X|^2) - (E(|X|))^2 = 2 ∫_(0)^(∞) x^2 f(x) dx - (2 ∫_(0)^(∞) x f(x) dx)^2
Since f(x) is the probability density function of X, we can substitute it with the standard normal distribution:
f(x) = (1/√(2π)) e^(-(x^2)/4)
Therefore, E(|X|) and Var(|X|) can be found by evaluating the integrals:
E(|X|) = 2 ∫_(0)^(∞) x (1/√(2π)) e^(-(x^2)/4) dx = √(2/π)
Var(|X|) = 2 ∫_(0)^(∞) x^2 (1/√(2π)) e^(-(x^2)/4) dx - (√(2/π))^2 = 2 - (2/π)
So the final answers are:
1. E(|X|) = √(2/π)
2. Var(|X|) = 2 - (2/π)
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Help as much as you can please!!
Answer:
#7
AB = 4.1
CB = 4.1
#10
AC = 21.21
CB = 15
#11
AC = 2.828
CB =2
#12
AB = 2.616
CB = 2.616
#13
AC = 6
CB = 3√2
#14
AC = 5.94
CB = 4.2
Step-by-step explanation:
The triangle is a right isosceles triangle with AB = AC
This means
AC² = AB² + CB²
= AB² + AB²
= 2AB²
AC = AB√2
and
AC = CB√2 (since CB= AB)
#7
Given AC = 5.8
We know AC = AB√2
[tex]AB= \dfrac{AC}{\sqrt{2}} = \dfrac{5.8}{\sqrt{2}} = 4.1[/tex]
CB = AB is also 4.1
#10
Given AB = 15
AC = AB√2 = 15√2 =
CB= AB = 15
#11
Given CB = 2
AB = CB= 2
AC = CB√2 = 2√2 = 2.828
#12
Given AC = 3.7
We know AC = AB√2
AB= AC/√2 = 3.7 ÷ √2 = 2.616
CB = AB is also 2.616
#13
Given AB = 3√2
AC = AB√2 = 3 x √2 x √2 = 3 x 2 =6 (√2 x √2 = 2)
CB = 3√2
#14
Given AB= 4.2
AC = 4.2 x √2 = 5.94
CB = AB = 4.2
Consider the following.
B = {(14, −2, −6), (−6, 1, 3), (12, −2, −5)},
B' = {(0, −1, 8), (1, 1, −8), (2, 2, −12)},
[x]B' =
2
3
1
(a) Find the transition matrix from B to B'.
P−1 =
(b) Find the transition matrix from B' to B.
P =
(c) Verify that the two transition matrices are inverses of each other.
PP−1 =
(d) Find the coordinate matrix [x]B , given the coordinate matrix [x]B'.
[x]B =
The coordinate matrix [x]B , given the coordinate matrix [x]B'.
[x]B = P * [x]B' = [(4.67, -0.83, -2.17), (-0.83, 0.17, 0.34), (-0.83, 0.17, 0.34)] * [2, 3, 1] =
[(6.34, -1.16, -3.03), (-1.16, 0.22, 0.45), (-1.16, 0.22, 0.45)]
The transition matrix from B to B' can be found by first finding the inverse of matrix B, then multiplying it by matrix B'. The transition matrix from B' to B can be found by first finding the inverse of matrix B', then multiplying it by matrix B. To verify that the two transition matrices are inverses of each other, we can multiply them together and see if the result is the identity matrix. Finally, to find the coordinate matrix [x]B, given the coordinate matrix [x]B', we can multiply the transition matrix from B' to B by the coordinate matrix [x]B'.
(a) Find the transition matrix from B to B'.
P−1 = B^(-1) * B' =
[(-0.04, 0.04, 0.08), (0.08, -0.08, -0.17), (0.08, -0.08, -0.17)] * [(0, −1, 8), (1, 1, −8), (2, 2, −12)] =
[(0.04, -0.12, 0.68), (-0.09, 0.25, -1.43), (-0.09, 0.25, -1.43)]
(b) Find the transition matrix from B' to B.
P = B'^(-1) * B =
[(-0.33, 0.17, 0.08), (0.08, -0.08, -0.17), (0.08, -0.08, -0.17)] * [(14, −2, −6), (−6, 1, 3), (12, −2, −5)] =
[(4.67, -0.83, -2.17), (-0.83, 0.17, 0.34), (-0.83, 0.17, 0.34)]
(c) Verify that the two transition matrices are inverses of each other.
PP−1 = [(4.67, -0.83, -2.17), (-0.83, 0.17, 0.34), (-0.83, 0.17, 0.34)] * [(0.04, -0.12, 0.68), (-0.09, 0.25, -1.43), (-0.09, 0.25, -1.43)] =
[(1, 0, 0), (0, 1, 0), (0, 0, 1)]
(d) Find the coordinate matrix [x]B , given the coordinate matrix [x]B'.
[x]B = P * [x]B' = [(4.67, -0.83, -2.17), (-0.83, 0.17, 0.34), (-0.83, 0.17, 0.34)] * [2, 3, 1] =
[(6.34, -1.16, -3.03), (-1.16, 0.22, 0.45), (-1.16, 0.22, 0.45)]
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4x-25=-125 how do you slove it
Answer: 25
Step-by-step explanation:
4x - 25 = -125
4x = -125 + 25
4x = -100
Divide both sides by 4
x = -25
What is the total surface area of the square
pyramid in square inches?
11 in
7 in
11.5 in
Answer:
To find the total surface area of a square pyramid, we need to find the sum of the areas of its base and its four triangular faces.
In this case, the base is a square with side length 11.5 inches. Therefore, its area is:
Area of base = 11.5^2 = 132.25 square inches
Each triangular face has a base length equal to the side length of the square base, which is 11.5 inches. To find the height of each triangular face, we can use the Pythagorean theorem. Since the pyramid is a square pyramid, the height of each triangular face is also the slant height of the pyramid.
The slant height of the pyramid can be found using the Pythagorean theorem:
a^2 + b^2 = c^2
where a = b = 11.5/2 = 5.75 (half the length of a diagonal of the square base) and c is the slant height. Solving for c, we get:
c = sqrt(a^2 + b^2) = sqrt(2*(5.75)^2) = 8.121 inches (rounded to 3 decimal places)
The area of each triangular face can be found using the formula:
Area of triangle = (1/2) * base * height
where the base is 11.5 inches and the height is 8.121 inches.
Area of each triangular face = (1/2) * 11.5 * 8.121 = 46.876 square inches (rounded to 3 decimal places)
So, the total surface area of the square pyramid is:
Total surface area = Area of base + 4 * Area of each triangular face
Total surface area = 132.25 + 4 * 46.876 = 330.124 square inches (rounded to 3 decimal places)
Therefore, the total surface area of the square pyramid is approximately 330.124 square inches.
Use PEMDAS to evaluate the expression:
8+(36 x 8-204) ÷ 6
Answer: 22
Step-by-step explanation:
Answer:
22
Step-by-step explanation:
(36 x8-204)
multiply first
36(8)=288
then subtract
288-204=84
8+84 ÷6
divide first
84 ÷6=14
8+14=22
What decimal equals 33 2/3 (rounded to nearest tenth)?
The decimal fοrm οf the mixed fractiοn 33 2/3, apprοximated tο the nearest tenth, is 33.67.
What are mixed fractiοns?A mixed fractiοn is οne that is represented by bοth its quοtient and remainder. Sο, a mixed fractiοn is a cοmbinatiοn οf a whοle number and a prοper fractiοn. A fractiοn represents a piece οf a larger tοtal. Tο learn hοw tο determine the precise values οf mixed numbers, it is crucial tο cοnvert a mixed number tο a decimal. A mixed number can be cοnverted tο decimal fοrm using οne οf twο techniques:
the mixed number is changed intο an imprοper fractiοn.
by first changing the given mixed number's fractiοnal pοrtiοn tο decimal, then adding the whοle number pοrtiοn tο it.
Nοw the given fractiοn is 33 2/3.
This is a mixed fractiοn because it has a whοle number οf 33 and a fractiοn οf 2/3.
This mixed fractiοn can be cοnverted tο a decimal number by finding the value οf the fractiοn part οf the number and adding it tο the whοle number.
Sοlving fractiοnal parts,
2/3 = 0.66666 = 0.67 (Rοunding tο the nearest tenth)
Nοw add tο the whοle number.
33 + 0.67 = 33.67
Therefοre the decimal fοrm οf the mixed fractiοn 33 2/3 is 33.67.
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HELP PLEASE !!!!!
2g) Letty is simplifying the square root of 48 using the Product Property of Square Roots. She wants to use the factors 4 and 12 to simplify the radical. Explain why these are not the best factors to use.
2h) What factors would be a better choice to use to simplify the square root of 48? Why should you choose those
factors and not any other pair?
Answer:
2g) Letty cannot use the factors 4 and 12 to simplify the square root of 48 using the Product Property of Square Roots because 4 is a perfect square, but 12 is not. The Product Property of Square Roots only applies to factors that are both perfect squares.
2h) A better choice to simplify the square root of 48 would be to use the factors 16 and 3. This is because 16 is a perfect square and is a factor of 48, which means it can be taken out of the radical completely. The remaining factor is 3, which cannot be simplified any further since it is not a perfect square. Therefore, the square root of 48 can be simplified to 4 times the square root of 3. It is important to choose 16 and 3 as the factors and not any other pair because 16 is the largest perfect square factor of 48, and 3 is the remaining factor after taking out 16 that cannot be simplified any further.
2g) These factors (4 and 12) are not the best choice to simplify the square root of 48 because 4 is a perfect square, but 12 is not.
2h) a better choice to simplify the square root of 48 would be to use the factors 16 and 3. This is because 16 is the largest perfect square factor of 48, which simplifies the radical the most.
Now, Using the Product Property of Square Roots, we can simplify the square root of 48 as :
√48 = √(4 x 12)
However, these factors (4 and 12) are not the best choice to simplify the square root of 48 because 4 is a perfect square, but 12 is not.
Hence, We want to simplify the radical by finding the largest perfect square that is a factor of 48.
For this, we can break down 48 into its prime factors:
48 = 2 x 2 x 2 x 2 x 3
Then, we group the prime factors into pairs of the same number:
48 = (2 x 2) x (2 x 2) x 3
This gives us two perfect squares, 4 and 16.
Hence, We can simplify the square root of 48 by using the largest perfect square factor, which is 16:
√48 = √(16 x 3)
√48 = √16 x √3
√48 = 4√3
Therefore, a better choice to simplify the square root of 48 would be to use the factors 16 and 3.
This is because 16 is the largest perfect square factor of 48, which simplifies the radical the most.
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Members of a softball team raised $1353 to go to a tournament. They rented a bus for $943.50 and budgeted $31.50 per player for meals. Write and solve an equation which can be used to determine xx, the number of players the team can bring to the tournament.
We round up to the nearest whole number because we are unable to have half a player. As a result, the softball team is allowed to send 7 players to the competition.
What are an example and an equation?The equal sign joins two expressions to create a mathematical formula called an equation. An illustration formula could be 3x - 5 = 16. By resolving this equation, we find that the value of the variable x is 7.
To begin, let's define a few variables:
x: The softball team's total roster size
y: the sum of the players' meal expenses
We can construct the equation shown below:
$1353 - $943.50 - $31.50x = y
Simplifying this equation, we get:
$409.50 - $31.50x = y
we can set up another equation:
y = $31.50x
Now we can substitute the second equation into the first equation to eliminate y:
$409.50 - $31.50x = $31.50x
Simplifying this equation, we get:
$409.50 = $63x
Dividing both sides by 63, we get:
x = 6.5
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A European company is selling a new brand of headphones. For h headphones sold, in thousands, a profit of E(h) = -4h^(4) + 7h^(3) - 7h + 20, in ten thousands of Euros, will be earned. How much will be earned in profit for selling 1,500 headphones?
The European company will earn 128,750 Euros in profit for selling 1,500 headphones.
How to find sale profitTo find the profit for selling 1,500 headphones, we need to plug in the value of h into the profit function E(h) and simplify.
Since h is measured in thousands of headphones, we need to divide 1,500 by 1,000 to get h = 1.5.
Now we can plug in h = 1.5 into the profit function and simplify:
E(1.5) = -4(1.5)^(4) + 7(1.5)^(3) - 7(1.5) + 20
E(1.5) = -4(5.0625) + 7(3.375) - 10.5 + 20
E(1.5) = -20.25 + 23.625 - 10.5 + 20
E(1.5) = 12.875
So the profit for selling 1,500 headphones is 12.875 ten thousands of Euros, or 128,750 Euros.
Therefore, the European company will earn 128,750 Euros in profit for selling 1,500 headphones.
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The school packs one lunch based on each of these choices. If Dr. Higgins wants a "Turkey, Water and Cookie" or a " Turkey, Water and Brownie" (I could eat either lunch) - what is the probability that Dr. Higgins randomly picks up one or the other of his Favorite Lunches?
The probability of selecting either lunch is 50%, as both lunches are equally likely to be chosen. This is because both lunches have the same ingredients, with the only difference being the dessert item.
What is probability?Probability is a measure of the likelihood of a certain event or outcome occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event or outcome is impossible and 1 indicates that the event or outcome is certain to occur. Probability is an important concept in mathematics and statistics, and it is widely used in fields such as finance, science, engineering, and gaming.
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Someone help me get all these right - WILL MARK BRAINLIEST!
1. 4x+6=8x-22
2.find the slope: (-6,8) and (-4, -12)
3.4x+5y=24
4. Evealuate the function. f(x)=7x-1 for f(-5)
The value of x in the function 4x+6=8x-22 is 7.
The slope is equal to -10.
The slope-intercept form of the function 4x+5y=24 is y = -4x/5 + 24/5.
The value of f(-5) is equal to -36.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given points into the slope formula, we have the following;
Slope, m = (-12 - 8)/(-4 + 6)
Slope, m = -20/2
Slope, m = -10.
4x+6=8x-22
8x - 4x = 22 + 6
4x = 28
x = 7.
4x + 5y = 24
5y = -4x + 24
y = -4x/5 + 24/5
For f(-5), we have:
f(x)=7x-1
f(-5)=7(-5)-1
f(-5) = -36.
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Uncle Moneybags has $500,000 saved for retirement. He has an account earning 8% interest. If Uncle Moneybags wants to be able to make withdrawals for 25 years, how much can he withdrawal each month? Round to the nearest cent.
Uncle Moneybags can withdrawal approximately $583.67 per month.
To find out how much Uncle Moneybags can withdraw each month, we can use the formula for the future value of an annuity:
FV = PMT × [(1 + i)ⁿ - 1] / i
Where:
FV = future value
PMT = payment amount
i = interest rate per period
n = number of periods
In this case, we want to solve for PMT, so we can rearrange the formula to:
PMT = FV × i / [(1 + i)ⁿ - 1]
We know that FV = $500,000, i = 8% / 12 = 0.00667, and n = 25 × 12 = 300. Plugging these values into the formula, we get:
PMT = $500,000 × 0.00667 / [(1 + 0.00667)³⁰⁰ - 1]
PMT = $500,000 × 0.00667 / 5.7435
PMT = $583.67
Therefore, Uncle Moneybags can withdraw $583.67 each month for 25 years.
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A Box Contains 16 Silver Counters, 8 Brown Counters And 20 Pink Counters. What Is The Ratio Of Silver To Brown To Pink Counters In Its Simplest Form?
Answer:
4-2-5
Step-by-step explanation:
16, 8, and 20 can all be divided by 4
Leaving you with 4 2 and 5.
The ratio is 4 to 2 to 5
PLEASE HELP THIS IS MY LAST QUESTION
If the correlation coefficient for the data shown in the table is -1, A should be what value?
Time (hours) (x)
4 1
3 6 5 7
Distance from destination (miles) (y) 1,000 A 1,060 940 760 820 690
920
880
800
none of these
O 1030
2
Answer:
Step-by-step explanation:
Here is the answer
The correlation coefficient measures the strength of the linear relationship between two variables, and it ranges from -1 to 1. A correlation coefficient of -1 indicates a perfect negative linear relationship between the variables, which means that as one variable increases, the other decreases at a constant rate.
To find the value of A in this scenario, we need to look for a perfect negative linear relationship between the two variables, time (x) and distance from destination (y). The table shows that as time increases, the distance from the destination decreases, but we need to find the exact rate of change.
We can calculate the rate of change by finding the slope of the line that represents the relationship between time and distance. We can use the formula for the slope of a line, which is:
slope = (change in y) / (change in x)
If we choose the first and last points in the table, we get:
slope = (690 - 1060) / (7 - 1) = -70
This means that for every hour of time that passes, the distance from the destination decreases by 70 miles. Therefore, if the correlation coefficient is -1, we should see a perfect negative linear relationship between time and distance, with a slope of -70.
To check if A is the correct value, we can use the formula for the equation of a line in slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept. We can plug in the values of m and b and solve for A:
y = -70x + b
If we use the first point in the table, where x = 4 and y = 1000, we get:
1000 = -70(4) + b
b = 1220
So the equation of the line is:
y = -70x + 1220
If we plug in the values of x for the remaining points in the table, we get:
y = 1030 when x = 0
y = 880 when x = 2
y = 800 when x = 3
y = A when x = 5
y = 760 when x = 6
To find the value of A, we can plug in the corresponding value of y and solve for A:
1030 = -70(0) + 1220
880 = -70(2) + 1220
800 = -70(3) + 1220
760 = -70(6) + 1220
A = -70(5) + 1220 = 850
Therefore, the value of A should be 850 if the correlation coefficient for the data shown in the table is -1.
Julia placed the number cards 1, 2, 3, 5, 8, and 13 in a bag. A card is drawn at random. Determine the theoretical
probability of drawing an even number. Express your answer as a fraction in simplest form.
Quick pleaseee
Answer: 1/3
Step-by-step explanation: so there is six cards total and only two of them are even so 2/6 and that can go to 1/3
1/3
There are 2 even numbers, and the total is 6. So 2/6 in the simplest form is 1/3.
Casio Company produces four-season drinks by mixing juices of four fruits in season. The standard costs and input for a 50-liter batch of the juice are as follows:
Fruits "Standard input
Quantity in Liters" "Standard Cost
Per Liter" Total Standard Costs
Apple 20 P10.00 P200.00
Mango 10 P21.25 P212.50
Pineapple 25 P7.50 P187.50
Peach 5 P15.00 P75.00
60 P675.00
The quantities purchased and used during the current month are shown below. A total of 14 batches were produced during the month
Fruits Quantity purchased Purchase Price Quantity used
(liters) (liters)
Apple 300 P9.50 290
Mango 150 P22.00 130
Pineapple 350 P7.20 350
Peach 80 P15.40 75
1,450 How much is the total materials cost variance
The materials yield variance is(provide amount only)
The materials purchase usage variance is
provide amount only
The total materials purchase usage variance is -P122.50.
The total materials cost variance is calculated by subtracting the total standard cost from the total actual cost. The total standard cost is P675.00 per batch and there were 14 batches produced during the month, so the total standard cost is P675.00 x 14 = P9,450.00. The total actual cost is calculated by multiplying the quantity purchased by the purchase price for each fruit and then adding them all together. The total actual cost is (300 x P9.50) + (150 x P22.00) + (350 x P7.20) + (80 x P15.40) = P2,850.00 + P3,300.00 + P2,520.00 + P1,232.00 = P9,902.00. The total materials cost variance is P9,902.00 - P9,450.00 = P452.00.
The materials yield variance is calculated by subtracting the standard quantity of materials from the actual quantity of materials used and then multiplying by the standard cost per liter. The standard quantity of materials is 60 liters per batch and there were 14 batches produced during the month, so the standard quantity of materials is 60 x 14 = 840 liters. The actual quantity of materials used is 290 + 130 + 350 + 75 = 845 liters. The materials yield variance is (840 - 845) x P10.00 = -P50.00.
The materials purchase usage variance is calculated by subtracting the standard cost per liter from the actual cost per liter and then multiplying by the actual quantity of materials used. The materials purchase usage variance for each fruit is (P9.50 - P10.00) x 290 + (P22.00 - P21.25) x 130 + (P7.20 - P7.50) x 350 + (P15.40 - P15.00) x 75 = -P145.00 + P97.50 - P105.00 + P30.00 = -P122.50. The total materials purchase usage variance is -P122.50.
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i need help with this
The value of x and y in the line segment are 6 and 6.5 units repsectively.
How to find length of line segment?The lines are three parallel lines cut by two transversal lines. The transversal lines that cut across the parallel lines have same length at intervals .
Using the information in the diagram let's find the value of x and y in the diagram.
Therefore,
2x + 1 = x + 7
2x - x = 7 - 1
x = 6 units
Therefore,
3y - 8 = y + 5
3y - y = 5 + 8
2y = 13
divide both sides by 2
y = 13 / 2
y = 6.5 units
Therefore,
x = 6 units
y = 6.5 units
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Find the equation of a line with the properties given. Write the equation in the form indicated. Through (3,5) and parallel to the line whose equation is ( y=-6x+4 ). Give answer in slope-int
The equation of the line through (3,5) and parallel to the line whose equation is ( y=-6x+4 ) is y = -6x + 23.
To find the equation of a line with the given properties, we need to use the concept of parallel lines and the point-slope form of a linear equation.
Parallel lines have the same slope, so the slope of the new line will be the same as the slope of the given line ( y=-6x+4 ), which is -6.
Next, we can use the point-slope form of a linear equation, which is (y - y1) = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the given point (3, 5) and the slope -6, we get:
y - 5 = -6(x - 3)
Simplifying the equation, we get:
y - 5 = -6x + 18
y = -6x + 23
Finally, we can write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The equation of the new line is y = -6x + 23.
Therefore, the equation of the line through (3,5) and parallel to the line whose equation is ( y=-6x+4 ) is y = -6x + 23.
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HELP ME IM GIVING 16 BRAINLIEST IF HELP
Answer:
277 milliliters
Step-by-step explanation:
945-668= 277
Please Help Asap! I need to find the answer! Please!
Plssss solve them all
The table can be filled up accordingly:
1. 5 years compounded semi-annually:
b = (1 + 0.06/2)
y= 1800 (1 + 0.03)^10
x = 2
2. For the 5 years compounded quarterly:
b = (1 + 0.06/4)
y = 1800 (1 + 0.015)^20
x =4
3. For the 5 years compounded monthly:
b = (1 + 0.06/12)
y = 1800 (1.005)^60
x = 12
4. For 10 years compounded annually:
b = (1 + 0.06/1)
x = 1800 (1.06)^10
y = 1
5. For 10 years compounded quarterly:
b = (1 + 0.06/4)
y =1800 (1 + 0.005)^60
x = 4
6. For 10 years compounded monthly:
b = (1 + 0.06/12)
y = 1800 (1 + 0.005)^120
x = 12
How to solve the interestTo solve the compound interest we use the formula:
P(1+r/n)^(n*t).
For the 5 years compounded semi-annually:
A = 1800 (1 + 0.06/2)^2*5
A = 1800 (1 + 0.03)^10
A = 1800 (1.03)^10
A = 1800 (1.344)
A = 2419
For the 5 years compounded quarterly:
A = 1800 (1 + 0.06/4)^4*5
A = 1800 (1 + 0.015)^20
A = 1800 (1.015)^20
A= 1800 (1.3468)
A= 2424.24
For the 5 years compounded monthly:
A = 1800 (1 + 0.06/12)^12*5
A = 1800 (1 + 0.005)^60
A = 1800 (1.005)^60
A = 1800 (1.34885)
A = 2427.93
For 10 years compounded annually:
A= 1800 (1 + 0.06/1)^10
A = 1800 (1.06)^10
A = 1800 (1.7908)
A = 3223.53
For 10 years compounded semi-annually:
A = 1800 (1 + 0.06/2)^20
A = 1800 (1 + 0.03)^20
A = 1800 (1.03)^20
A =1800 (1.806)
A = 3251
For 10 years compounded quarterly:
A= 1800 (1 + 0.06/4)^4*10
A = 1800 (1 + 0.015)^40
A= 1800 (1.015)^40
A = 1800 (1.814)
A = 3265.23
For 10 years compounded monthly:
A= 1800 (1 + 0.06/12)^120
A = 1800 (1 + 0.005)^120
A = 1800 (1.005)^20
A= 1800 (1.8194)
A = 3274.9
The best pay period is that with the highest returns which is 10 years compounded monthly.
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Please help me I don’t want to fail
The measure of line KR is 8 inches
How to determine the measure of the length
It is important that we know the properties of an isosceles trapezoid.
Only one pair of sides are parallelNon-parallel sides are equal in measureThe diagonals are equal in measureThe opposite angles are supplementary, that is, their sum is equal to 180 degreesFrom the information given, we have that;
KR = 1/2x + 5
DH = 2x - 4
Since the non- parallel sides of an isosceles trapezoid are equal, then, we have;
KR = DH
1/2x + 5 = 2x - 4
collect the like terns, we have
1/2x - 2x = -4 - 5
x - 4x /2 = - 9
cross multiply
-3x = -18
x = 6
KR = 1/2(6) + 5 = 8 inches
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In Exercises 3-6, find the indicated measure. Explain your reasoning. Show your work
The measured unknown sides are -
GH = 4.6
QR = 1.3
AB = 15
UW = 41
What are similar triangles?Two triangles are similar if the ratio of their corresponding sides is same and their corresponding angles are equal.
Given are the triangles as shown in the image.
{ 1 } -
We can write -
GH/HJ = GK/KJ
GH/4.6 = 3.6/3.6
GH = 4.6
{ 2 } -
QT/TS = QR/RS
4.7/4.7 = QR/1.3
QR = 1.3
{ 3 } -
AD/DC = AB/BC
AD/AD = AB/BC
AB/BC = 1
5x/4x + 3 = 1
5x = 4x + 3
x = 3
AB = 15
{ 4 } -
UW/UV = DW/DV
7x + 13 = 9x + 1
3x = 12
x = 4
UW = 41
Therefore, the measured unknown sides are -
GH = 4.6
QR = 1.3
AB = 15
UW = 41
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An image of a rhombus is shown.
a rhombus with a base of 20 centimeters and a height of 17 centimeters
What is the area of the rhombus?
148 cm^2
74 cm^2
340 cm^2
170 cm^2
What is rhombus ?
A rhombus is a special type of parallelogram in which two pairs of opposite sides are congruent. That means all the sides of a rhombus are equal.
What is the Area of a Rhombus?
The area of a rhombus can be defined as the amount of space enclosed by a rhombus in a two-dimensional space. To recall, a rhombus is a type of quadrilateral projected on a two dimensional (2D) plane, having four sides that are equal in length and are congruent.
Using Diagonals A = ½ × d1 × d2
Using Base and Height A = b × h
Using Trigonometry A = b2 × Sin(a)
the correct answer is the option (C) 340 cm^2
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PLSSS HELP IF YOU TURLY KNOW THISSSS
Answer: 2
5x - 7 = 3x + 3
2x - 7 = 3
2 is the new value of the coefficent
VI. Solve for roots using the Quadratic Formula: A.
4x 2
−9x+2=0
B.
2x 2
−7x−1=0
The roots of equation A are 2 and 0.25.
The roots of equation B are 3.14 and -0.64.
To solve for the roots of a quadratic equation using the Quadratic Formula, we can use the formula:
x = (-b ± √(b² - 4ac)) / (2a)
Where a, b, and c are the coefficients of the equation.
For equation A, a = 4, b = -9, and c = 2. Plugging these values into the Quadratic Formula, we get:
x = (-(-9) ± √((-9)² - 4(4)(2))) / (2(4))
x = (9 ± √(81 - 32)) / 8
x = (9 ± √49) / 8
x = (9 ± 7) / 8
This gives us two possible values for x:
x = (9 + 7) / 8 = 2
x = (9 - 7) / 8 = 0.25
Therefore, the roots of equation A are 2 and 0.25.
For equation B, a = 2, b = -7, and c = -1. Plugging these values into the Quadratic Formula, we get:
x = (-(-7) ± √((-7)² - 4(2)(-1))) / (2(2))
x = (7 ± √(49 + 8)) / 4
x = (7 ± √57) / 4
This gives us two possible values for x:
x = (7 + √57) / 4 ≈ 3.14
x = (7 - √57) / 4 ≈ -0.64
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Help pls due today
I’m stressing out
Answer:
If the relationship is proportional, we can use the proportionality constant, k, to relate the cost and number of climbs. The equation would be:
t = kc
We can find the value of k by using the given information that 5 climbs cost $52.50:
52.50 = k(5)
Solving for k, we get:
k = 10.50
Therefore, the equation that represents the total cost, t, of c climbs is:
t = 10.50c
Aldo is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges $ 101 and allows unlimited mileage. Company B has an initial fee of $65 and charges an additional $0. 80 for every mile driven. For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m.
Aldo should choose Company A if he plans to drive more than 45 miles, and Company B if he plans to drive 45 miles or fewer.
Let's start by setting up an inequality to represent the mileage for which Company A charges less than Company B:
Cost of Company A < Cost of Company B
The cost of Company A is a constant $101, regardless of how many miles are driven. The cost of Company B, on the other hand, depends on the number of miles driven. If m represents the number of miles driven, then the cost of Company B can be expressed as:
Cost of Company B = $65 + $0.80m
Now we can substitute these expressions into the inequality we set up earlier:
$101 < $65 + $0.80m
Simplifying and solving for m:
$36 < $0.80m
$45 < m
Therefore, Company A will charge less than Company B for mileage greater than $45.
To summarize, Aldo should choose Company A if he plans to drive more than 45 miles, and Company B if he plans to drive 45 miles or fewer.
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Solve using the quadratic f -9d^(2)+6=-6d Write your answers as intec form, or decimals rounded
The answer to the quadratic equation -9d^(2)+6=-6d is 11/20 and -11/20. To solve the given quadratic equation f -9d^(2)+6=-6d, we need to rearrange the terms and use the quadratic formula.
Step 1: Rearrange the terms to get the equation in the standard form of ax^(2) + bx + c = 0
-9d^(2) + 6d + 6 = 0
Step 2: Identify the values of a, b, and c.
a = -9
b = 6
c = 6
Step 3: Use the quadratic formula to find the solutions for d.
The quadratic formula is given by:
d = (-b ± √(b^(2) - 4ac))/(2a)
Substitute the values of a, b, and c into the formula:
d = (-(6) ± √((6)^(2) - 4(-9)(6)))/(2(-9))
Step 4: Simplify the expression inside the square root:
d = (-(6) ± √(36 + 216))/(-18)
d = (-(6) ± √(252))/(-18)
Step 5: Simplify the expression further:
d = (-(6) ± 15.87)/(-18)
Step 6: Solve for d using both the positive and negative values inside the square root:
d = (-(6) + 15.87)/(-18) = 0.55
d = (-(6) - 15.87)/(-18) = -0.55
So, the solutions for d are 0.55 and -0.55 or 11/20 and -11/20 using the quadratic formula to solve the given quadratic equation.
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