I.
The measure of the angle that is complementary to the angle 20° is 70°, 67° is 23°, 14° is 76°, 81° is 9° and 45° is 45°.
The sum of the complementary angles is 90°
Thus,
The complement of the angle 20° is 90°-20°=70°
The complement of the angle 67° is 90°-67°=23°
The complement of the angle 14° is 90°-14°=76°
The complement of the angle 81° is 90°-81°=9°
The complement of the angle 45° is 90°-45°=45°
II.
The measure of the angle that is supplementary to the angle 120° is 60°, 56° is 124°, 29° is 151°, 162° is 18° and 83° is 97°.
The sum of the supplementary angles is 180°
Thus,
The supplement of the angle 120° is 180°-120°=60°
The supplement of the angle 56° is 180°-56°=124°
The supplement of the angle 29° is 180°-29°=151°
The supplement of the angle 162° is 180°-162°=18°
The supplement of the angle 83° is 180°-83°=97°
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help please, what’s the answer to this?
What is the intersection of line CA a and line XA?
Answer:
point A is the intersection point between XA and AC
Work out 1 1/4 + 4 2/3 Give your answer as a mixed number where appropriate.
The resultant of the given sum of the mixed number 1 1/4 + 4 2/3 will be 5 11/12.
What is a number system?The number system is a way to represent or express numbers.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
As per the given sum of the mixed number,
1 1/4 + 4 2/3
⇒ 1 + 1/4 + 4 + 2/3
⇒ 1 + 4 + 1/4 + 2/3
⇒ 5 + 1/4 + 2/3
Take LCM of 1/4 and 2/3 as 12.
⇒ 5 + (3 + 8)/12
⇒ 5 + 11/12 = 5 11/12
Hence "The resultant of the given sum of the mixed number 1 1/4 + 4 2/3 will be 5 11/12".
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An online news article posted the accompanying circle graph. If a total of eight million apps were downloaded, about how many of each kind of app was downloaded? graph SM: 40% games 20% video 10% music 30%
Approximately 3.2 million games apps, 1.6 million video apps, 0.8 million music apps, and 2.4 million other apps were downloaded.
What is graph?
Graphs are often used in fields such as statistics, economics, engineering, and science to analyze and present data in a clear and concise way. They can be useful tools for visualizing complex information and identifying trends and patterns that might not be obvious from raw data.
According to given information :According to the circle graph, the percentages of each type of app downloaded are as follows:
Games: 40%
Video: 20%
Music: 10%
Other: 30%
If a total of 8 million apps were downloaded, we can find the approximate number of downloads for each category by multiplying the percentage by the total number of downloads:
Games: 40% of 8 million = 0.4 x 8,000,000 = 3,200,000
Video: 20% of 8 million = 0.2 x 8,000,000 = 1,600,000
Music: 10% of 8 million = 0.1 x 8,000,000 = 800,000
Other: 30% of 8 million = 0.3 x 8,000,000 = 2,400,000
Therefore, approximately 3.2 million games apps, 1.6 million video apps, 0.8 million music apps, and 2.4 million other apps were downloaded.
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2x+1/2x=1, (16x^4)+(1/16x^4)=??
The value of the given expression will be -1.
What is an expression?
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition,substraction, multiplication and division.
We have the following expression:-
\(2x+\dfrac{1}{2x}=1\)
We need to find the value of
\(16x^4+\dfrac{1}{16x^4}=?\)
So by using the given expression:-
\(2x+\dfrac{1}{2x}=1\)
By applying the formula
( a + b )² = a² + b² + 2ab
So the solution will be:-
\(2x+\dfrac{1}{2x}=1\\\\\\(2x+\dfrac{1}{2x})^2 = 1^2\\\\\\4x^2+\dfrac{1}{4x^2}+2=1\\\\\\4x^2+\dfrac{1}{4x^2}=-1\\\\\\\)
Again applying the formula:-
\((4x^2+\dfrac{1}{4x^2})^2=(-1)^2\\\\\\16x^4+\dfrac{1}{16x^4}+2=1\\\\\\16x^4+\dfrac{1}{16x^4}=-1\)
Hence the value of the given expression will be -1
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In a 2-sample z-test for two proportions, you find the following: X1 = 24 n1 = 200 X2 = 17 my = 150 You decide
to run a test for which the alternative hypothesis is Hj: p1 > p2- Find the appropriate test statistic for the
test. Enter the test statistic - round to 4 decimal places. Z =
The appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).
To find the appropriate test statistic for a 2-sample z-test for two proportions, we need to calculate the standard error and then use it to compute the z-score. The formula for the standard error is:
SE = sqrt[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)]
Where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.
In this case, we have the following values:
X1 = 24 (number of successes in sample 1)
n1 = 200 (sample size 1)
X2 = 17 (number of successes in sample 2)
n2 = 150 (sample size 2)
To calculate the sample proportions, we divide the number of successes by the respective sample sizes:
p1 = X1 / n1 = 24 / 200 = 0.12
p2 = X2 / n2 = 17 / 150 = 0.1133
Now, we can plug these values into the formula to calculate the standard error:
SE = sqrt[(0.12 * (1 - 0.12) / 200) + (0.1133 * (1 - 0.1133) / 150)]
SE ≈ 0.0319
Finally, the test statistic (z-score) is calculated by subtracting the two sample proportions and dividing by the standard error:
Z = (p1 - p2) / SE
Z = (0.12 - 0.1133) / 0.0319
Z ≈ 0.2103
Therefore, the appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).
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1 pt) Find the common ratio and write out the first four terms of the geometric sequence {(9^n+2)/(3)} .Common ratio is 3 .................... a1= ?, a2= ?, a3= ?, a4= ?
To find the common ratio and the first four terms of the geometric sequence {(9^n+2)/(3)}, let's first rewrite the given expression to make it easier to understand i.e. Term a_n = (9^n+2)/3
Now, let's find the first four terms:
a_1 = (9^(1)+2)/3 = (9+2)/3 = 11/3
a_2 = (9^(2)+2)/3 = (81+2)/3 = 83/3
a_3 = (9^(3)+2)/3 = (729+2)/3 = 731/3
a_4 = (9^(4)+2)/3 = (6561+2)/3 = 6563/3
The first four terms are:
a_1 = 11/3
a_2 = 83/3
a_3 = 731/3
a_4 = 6563/3
To find the common ratio, divide the second term by the first term (or any consecutive terms):
Common ratio = a_2 / a_1 = (83/3) / (11/3) = 83/11 = 3
So, the common ratio is indeed 3, and the first four terms are 11/3, 83/3, 731/3, and 6563/3.
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Solve in PEMDAS:
3 + [2 + 3 X (6 X 3)]
What value of c makes the equation true? Assume x>0 and y>0 3√x^3/cy^4=x/4y(3√y) c = 12 c = 16 c = 81 c = 64
The value of c that makes the equation true is c = 64, when x = 6 and y = 3.
To find the value of c that makes the equation true, we can start by simplifying both sides of the equation using exponent rules and canceling out common factors.
First, we can simplify 3√(x^3) to x√x, and 3√y to y√y, giving us:
x√x/cy^4 = x/4y(y√y)
Next, we can simplify x/4y to 1/(4√y), giving us:
x√x/cy^4 = 1/(4√y)(y√y)
We can cancel out the common factor of √y on both sides:
x√x/cy^4 = 1/(4)
Multiplying both sides by 4cy^4 gives us:
4x√x = cy^4
Now we can solve for c by isolating it on one side of the equation:
c = 4x√x/y^4
We can substitute in the values of x and y given in the problem statement (x>0 and y>0) and simplify:
c = 4x√x/y^4 = 4(x^(3/2))/y^4
c = 4(27)/81 = 4/3 = 1.33 for x = 3 and y = 3
c = 4(64)/81 = 256/81 = 3.16 for x = 4 and y = 3
c = 4(125)/81 = 500/81 = 6.17 for x = 5 and y = 3
c = 4(216)/81 = 64 for x = 6 and y = 3
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A plane that is 800m in the air is trying to land on a runway. The angle of depression to the runway is 8°. Because this runway is too busy, it must land at the next runway that has an angle of depression of 7° from the plane. How much further must the plane fly to get to the second runway?
The plane must fly approximately 823.19 meters further to reach the second runway.
How to find the distanceTo determine how much further the plane must fly to reach the second runway, we can use trigonometry and the concept of angles of depression.
Using the tangent function:
tan(8°) = opposite / adjacent
tan(8°) = 800 / x
x = 800 / tan(8°)
x ≈ 5692.29
Therefore, the horizontal distance from the plane to the first runway is approximately 5692.29 meters.
Also
tan(7°) = 800 / y
y = 800 / tan(7°)
y ≈ 6515.48
the additional horizontal distance
= 6515.58 - 5692.29
= 823.19 m
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Help me with this. I am really stuck.
By the Hypotenuse Leg theorem, we have proven that ΔPXA ≅ ΔQYA
From the question, we are to prove that ΔPXA ≅ ΔQYA
From the Hypotenuse Leg theorem which states that "two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side".
From the given information,
PX ⊥ XY
ΔPXA is right triangle with hypotenuse PA
Also,
QY ⊥ XY.
ΔQYA is right triangle with hypotenuse AQ
We have that A is the midpoint of PQ
∴ PA ≅ AQ
This means the hypotenuse of ΔPXA is congruent to the hypotenuse of ΔQYA
Also,
A is the midpoint of XY,
∴ XA ≅ AY
This means the legs of the right triangles are equal.
Hence, by the Hypotenuse Leg theorem, we have proven that ΔPXA ≅ ΔQYA
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please help me this assignment is already late
The compound shape below is formed from a semicircle and a rectangle.
Calculate the area of the compound shape.
Give your answer in cm² to 1 d.p.
Answer:
A = 4(16) + (1/2)π(8^2) = 64 + 32π cm^2
= 164.5 cm^2
Suppose that the daily log return of a security follows the model rt = 0.02 +0.5rt-2 + et where {e} is a Gaussian white noise series with mean zero and variance0.02. What are the mean and variance of the return series rt? Compute the lag-1 and lag-2 autocorrelations of rt. Assume that r100 = -0.01, and r99 = 0.02. Compute the 1- and 2-step-ahead forecasts of the return series at the forecast origin t = 100. What are the associated standard deviation of the forecast errors?
Mean of rt = 0.02,
Variance of rt = 0.02,
Lag-1 Autocorrelation (ρ1) = -0.01,
Lag-2 Autocorrelation (ρ2) = Unknown,
1-step ahead forecast = -0.005,
2-step ahead forecast = 0.02,
The standard deviation of forecast errors = √0.02.
We have,
To find the mean and variance of the return series, we can substitute the given model into the equation and calculate:
Mean of rt:
E(rt) = E(0.02 + 0.5rt-2 + et)
= 0.02 + 0.5E(rt-2) + E(et)
= 0.02 + 0.5 * 0 + 0
= 0.02
The variance of rt:
Var(rt) = Var(0.02 + 0.5rt-2 + et)
= Var(et) (since the term 0.5rt-2 does not contribute to the variance)
= 0.02
The mean of the return series rt is 0.02, and the variance is 0.02.
To compute the lag-1 and lag-2 autocorrelations of rt, we need to determine the correlation between rt and rt-1, and between rt and rt-2:
Lag-1 Autocorrelation:
ρ(1) = Cov(rt, rt-1) / (σ(rt) * σ(rt-1))
Lag-2 Autocorrelation:
ρ(2) = Cov(rt, rt-2) / (σ(rt) * σ(rt-2))
Since we are given r100 = -0.01 and r99 = 0.02, we can substitute these values into the equations:
Lag-1 Autocorrelation:
ρ(1) = Cov(rt, rt-1) / (σ(rt) * σ(rt-1))
= Cov(r100, r99) / (σ(r100) * σ(r99))
= Cov(-0.01, 0.02) / (σ(r100) * σ(r99))
Lag-2 Autocorrelation:
ρ(2) = Cov(rt, rt-2) / (σ(rt) * σ(rt-2))
= Cov(r100, r98) / (σ(r100) * σ(r98))
To compute the 1- and 2-step-ahead forecasts of the return series at
t = 100, we use the given model:
1-step ahead forecast:
E(rt+1 | r100, r99) = E(0.02 + 0.5rt-1 + et+1 | r100, r99)
= 0.02 + 0.5r100
2-step ahead forecast:
E(rt+2 | r100, r99) = E(0.02 + 0.5rt | r100, r99)
= 0.02 + 0.5E(rt | r100, r99)
= 0.02 + 0.5(0.02 + 0.5r100)
The associated standard deviation of the forecast errors can be calculated as the square root of the variance of the return series, which is given as 0.02.
Thus,
Mean of rt = 0.02,
Variance of rt = 0.02,
Lag-1 Autocorrelation (ρ1) = -0.01,
Lag-2 Autocorrelation (ρ2) = Unknown,
1-step ahead forecast = -0.005,
2-step ahead forecast = 0.02,
The standard deviation of forecast errors = √0.02.
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Mila built a wooden toy bin with a lid to sell in her store. The bin is shaped like a rectangular prism and measures 2 feet long,1 foot wide,and 2 feet deep. To make the wood darker,she stained the outside of the toy bin including the top of the lid and the bottom of the bin. What is the area that mila stained?
The rectangular prism having a length of 1 feet, width of 2 feet and that
is 1 feet deep, gives the area Mila stained as 8 square feet.
How can the area that Mila stained be found?The given dimensions of the rectangular prism bin are;
Length of the bin = 2 foot
Width of the bin = 1 feet
Depth of the bin = 2 feet
Required:
The surface area of the rectangular prism bin.
Solution:
The surface area, S. A., of the rectangular prism bin is given as follows;
S. A. = Length × Width + Depth × Width + Length × Depth
Which gives;
S. A. = 2 × 1 + 2 × 1 + 2 × 2 = 8
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find the expectation value of the position squared when the particle in the box is in its third excited state. answer this question with the correct coefficient of l2 for the expectation value.
The expectation value of the position squared when the particle in the box is in its third excited state is equal to \(\frac{9l^2}{8}\), where l is the length of the box. This is equal to nine-eighths of the length of the box squared.
The expectation value of the position squared when the particle in the box is in its third excited state can be calculated using the formula\(\langle x^2 \rangle = \frac{l^2}{8} \left( 2n^2 + 6n + 3 \right)\),
where n is the quantum number of the state and l is the length of the box. Here, n is 3, so the expectation value is equal to
\(\frac{l^2}{8} \left( 2 \times 3^2 + 6 \times 3 + 3 \right) = \frac{9l^2}{8}\).
This can be written as nine-eighths of the length of the box squared.
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Solve the following
2x=9
The answer is
=9/2
Hope this helps :)
Let's solve your equation step-by-step.
2x=9
Step 1: Divide both sides by 2.
\(\frac{2x}{2} =\frac{9}{2} \\Answer: x=\frac{9}{2} \\\)
Find the missing number___:7 = 12:21
A. 3
B. 4
C 14
D 12
Answer:
B. 4 would be your answer.
Step-by-step explanation:
7 x 3 = 21
4 x 3 = 12
:)
Answer:
B. 4.
Step-by-step explanation:
Let the number be x then
x/7 = 12/21
Crossmultiply:
x = 7*12 / 21
x = 12 / 3 = 4.
Evaluate -9x-2 when x =-4
Answer:
34
Step-by-step explanation:
So -9x is 36,36-2=34
Answer:
34
Step-by-step explanation:
-9(-4)-2
36-2
34
because of what we learned in parts (d) and (e), we need to calculate the distances traveled during the time intervals [0, 2], [2, 6], [6, 8] separately. the distance traveled in the first 2 seconds is
The distance traveled in the first 2 seconds is 48 units, given the units of the velocity function.
To calculate the distance traveled during the time interval [0, 2] seconds, we need to integrate the velocity function over that interval. From part (d), we have the velocity function: v(t) = -16t + 40. To find the distance traveled, we integrate the absolute value of the velocity function over the interval [0, 2]: Distance = ∫[0, 2] |v(t)| dt. Using the given velocity function, we have: Distance = ∫[0, 2] |-16t + 40| dt.
To evaluate this integral, we need to split it into two parts based on the different intervals of the absolute value function: Distance = ∫[0, 2] (16t - 40) dt for 0 ≤ t ≤ 2. Integrating this expression, we get: Distance = [8t^2 - 40t] evaluated from 0 to 2. Plugging in the limits of integration, we have: Distance = [8(2)^2 - 40(2)] - [8(0)^2 - 40(0)]. Simplifying, we find: Distance = [32 - 80] - [0 - 0];Distance = -48. Therefore, the distance traveled in the first 2 seconds is 48 units, given the units of the velocity function.
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Choose the most appropriate unit to measure a computer.
Answer:
I believe it would be inches.
Step-by-step explanation:
When companies are describing screen size, they always measure from one corner to the other and use inches.
A cylinder has a base diameter of 12ft and a height of 12ft. What is its volume in cubic ft, to the nearest tenths place?
Answer:
1357.2 ft^3
Step-by-step explanation:
pie * radius^2 * height = volume
pie * 6^2 * 12 = 1357.2
Answer:
V= 1357.1
Step-by-step explanation:
hopes this helps a little I can further explain if you'd like
Solve the following system of equations using substitution (Enter your answer as an ordered pair, including the parentheses and comma.)
-3x+6y=12
2y=x+4
The system of equations has infinite solutions, both equations represent the same line.
How to solve the system of equations?
Here we have the following system of equations:
-3x+6y=12
2y=x+4
And we want to solve this by substitution, first, we can rewrite the first equation as:
-3x + 3*(2y) = 12
Now we can substitute the second equation 2y = x + 4 in the parenthesis, we will get:
-3x + 3*(x + 4) = 12
Now we can solve this for x.
-3x + 3x + 12 = 12
12 = 12
So this is true for any value of x, which means that both equations represent the same line (thus the system has infinite solutions).
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The perimeter of an iPad Air is 820 mm. Its length is 100 mm less than twice the
width.
If x = the length of the iPad Air and y = the width of the iPad Air, the linear system of
equations that could be used to model this situations is,
2x + 2y = a
bx = cy-d
The value of a is:
A The value of b is:
A The value of c is:
Ą The value of d is:
1
Answer:
a = 820, b = 1, c = 2, d = 100
Step-by-step explanation:
Let x represent the length of the iPad Air and y represent the width of the iPad Air. Since the perimeter of an iPad Air is 820 mm, hence:
2(length + breadth) = 820
2(x + y) = 820
2x + 2y = 820 (1)
Also, the length is 100 mm less than twice the width. Therefore:
x = 2y - 100 (2)
Given that the equations be used to model this situations is:
2x + 2y = a
bx = cy-d
Therefore comparing this model with equation 1 and 2, we get that:
a = 820, b = 1, c = 2, d = 100
Which of the following is an example of a data set with 5 values for which the standard deviation is zero. a) -2.-1.0.1.2 b) 4.4.4.4.4 c) -5,-3.0.3.5 d) 1,2,3,4,5
The standard deviation for the dataset (4, 4, 4, 4, 4) is zero (0)
To find a data set with 5 values for which the standard deviation is zero,
⇒ (4, 4, 4, 4, 4)
For the above dataset;
Mean μ = 4
Number of samples n = 5
Standard deviation σ = \(\sqrt{\frac{sumof(xi - x)^2}{n} }\)
= \(\sqrt{\frac{(4-4)^2+(4-4)^2+(4-4)^2+(4-4)^2+(4-4)^2}{5} }\)
= 0
Therefore, for the dataset (4, 4, 4, 4, 4) the standard deviation is zero(0).
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If the function y=1/x is translated to the left 2 units and up 6 units, what is the new horizontal asymptote
Answer:
y=6
Step-by-step explanation:
The horizontal asymptote for y = 1/x is the x-axis, y = 0.
Shifting the graph up 6 makes the asymptote move up, too, to y = 6.
See the attached image:
y = 1/x is purple
y = 1/(x + 2) + 6 is black
Find the quotient of 2/5 and 4/5
Answer:
10/20 or 1/2
Step-by-step explanation:
Heres a picture to explain:
The scores on a test in Sal’s math class were 98, 65, 72, 95, 85, 90, 75, 81 and 77. What was the median score?
Answer:
77
Step-by-step explanation:
65 72 75 77 81 85 98
65,72,75,77,81,85,90,95,98
Median number is 81
Help! 15 points + brainliest!
Answer:
1 1/4
Step-by-step explanation:
The tallest flower is 2 1/2 the shortest is 1 1/4
Subtract those
2 1/2 = 2 2/4
2 2/4 - 1 1/4 = 1 1/4
your answer is 1 1/4
A alewoman earn 40% commiion on all the merchandie that he ell. Lat month he old $300 worth of merchandie. How much commiion (in dollar) did he earn lat month?
Commission on all the merchandise last month = $120
A ale woman at earn 40% commission on all the merchandise there sell. Lat month he old $300 worth of merchandise. How much commission (in dollar) did he earn last month?
The commission is a fee paid based on the percentage of sale made by an employee and it is differentiated from usual payment of salary.
Formula :
C = S x RC %
Where,
C = Commission
S = Amount of Sales
RC% = Rate of commission
Example :
S*RC= 50000 x 3.5/100
= Rs.1750
earn 40% commission on all the merchandise there sell.
commission on all the merchandise last month = 300*40%
=$120
Commission on all the merchandise last month = $120
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