Answers
The values of x and y are 100 and 40, respectively
How to determine the values of x and yFrom the question, we have the following parameters that can be used in our computation:
The circle
On the circle, we have the following congruent angles
ADC and ABC
Using the above as a guide, we have the following:
x = 100
The sum of angles in a triangle is 180
So, we have
y + y + x = 180
This gives
2y + 100 = 180
So, we have
y = 40
Hence, the value of y is 40
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Related Questions
Find the value to the variable.
Answers
The required side length of the variable "x" is 12.8 units for the given figure.
What is Thales's theorem?When a line parallel to one side of a triangle intersects the other two sides in distinct spots, the other two sides are separated in the same ratio.
As we can see that both are similar quadrilaterals,
According to Thales's Theorem,
5:8 = 8:x
So, 5/8 = 8/x
Apply the cross-multiplication, and we get
5x = 8 × 8
x = 64/5
Apply the division operation, and we get
x = 12.8
Thus, the required side length of the variable "x" is 12.8 units.
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A store scanner has a red laser wavelength of 650 nm. While a
green laser pointer has a wavelength of 502 μm. Find the ratio of
green to red wavelengths for these lasers. Round to the nearest
tenth.
Answers
A store scanner has a red laser wavelength of 650 nm. While a green laser pointer has a wavelength of 502 μm. The ratio of green to red wavelengths is 0.77.
To find this ratio, we need to divide the wavelength of the green laser by the wavelength of the red laser:
502 μm / 650 nm = 0.77
Note that we need to convert the units of the green laser wavelength from micrometers (μm) to nanometers (nm) in order to divide it by the red laser wavelength, which is already in nanometers. To do this, we multiply the green laser wavelength by 1000:
502 μm * 1000 = 502000 nm
So the ratio of green to red wavelengths is 502000 nm / 650 nm = 0.77.
This ratio indicates that the green laser has a shorter wavelength than the red laser. Generally, shorter wavelengths correspond to higher energy and higher frequency light. In the case of lasers, this means that the green laser is capable of producing a more intense and focused beam of light than the red laser.
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A cuboidal box with dimension 3×3×2 cu. Units is melted into another cuboid whose width is 15 units . Find the length and height of the cuboidformed if l=h
Answers
Answer:
Let's first find the volume of the original cuboidal box:
Volume = Length x Width x Height = 3 x 3 x 2 = 18 cubic units
We can then set up an equation to relate the volume of the original box to the volume of the new cuboid:
Volume of new cuboid = Volume of original box
Let's call the length and height of the new cuboid "x" (since we know that the length and height are the same). We know that the width of the new cuboid is 15 units. Therefore, we can write:
Volume of new cuboid = Length x Width x Height = x x 15 x x = 15x^2
Now we can set up the equation:
15x^2 = 18
Dividing both sides of the equation by 15 gives:
x^2 = 18/15
Simplifying the right side of the equation gives:
x^2 = 1.2
Taking the square root of both sides of the equation gives:
x ≈ 1.095
Therefore, the length and height of the new cuboid are approximately 1.095 units.
2x°
(3x + 25)°
Please helppppppp
Answers
The answer of the given question based on the sum of the two angles is ,the answer is 5x + 25° degrees.
What is Distributive property?The distributive property is fundamental property of arithmetic and algebra that allows us to multiply single term or sum by factor. The property states that:
a×(b+c)=a×b+a×c
In words, this means that the when number or variable (a) is multiplied by sum of two other numbers or variables (b + c), it is same as multiplying a by each term of sum (b and c) and then adding two products. The distributive property can be used in reverse to factor out common factor from sum of terms.
The sum of these two angles is:
2x° + (3x + 25)°
= 2x° + 3x° + 25° (using the distributive property of multiplication)
= 5x° + 25°
Therefore, the sum of the two angles is 5x + 25° degrees.
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Helppppppppp pleaseeeeeeeeeeeee
Answers
Answer:
Step-by-step explanation:
As before, I'll put slope-intercept first:
5. y = 1/4x + 1 ; y-2 = 1/4(x-4)
6. y = -1/2x + 2 ; y-1 = -1/2(x-2)
7. y = 1/3x + 1 ; y-2 = 1/3(x-3)
8. y = -x ; y-1 = 1(-x+1)
9. y = 2/3x -1 ; y-1 = 2/3(x-3)
Hope this helps!
2 1/2 minutes converted to hours?
Answers
Answer:
1/24 hour
Step-by-step explanation:
2 1/2 minutes = 2.5 minutes
2.5/60 = 1/24 hour
How many numbers cansisting of 3 digits can be made from 1,2,3,4,5, and 6 if letter A repitition is allowed, letfer B repitition is not allowed.
Answers
Answer:
If repetition of letter A is allowed and letter B cannot be repeated, then there are two cases to consider when constructing a 3-digit number:
Case 1: The first digit is letter A. In this case, there are 6 options for the first digit (since any of the 6 digits can be used), and there are 5 options for each of the remaining digits (since letter B cannot be repeated). Therefore, the total number of 3-digit numbers that can be formed in this case is:
6 x 5 x 5 = 150
Case 2: The first digit is not letter A. In this case, there are 5 options for the first digit (since letter A cannot be repeated), and there are 5 options for each of the remaining digits (since letter B cannot be repeated). Therefore, the total number of 3-digit numbers that can be formed in this case is:
5 x 5 x 4 = 100
To get the total number of 3-digit numbers that can be made from 1, 2, 3, 4, 5, and 6 with letter A repetition allowed and letter B repetition not allowed, we add the number of possibilities from Case 1 and Case 2:
Total = 150 + 100 = 250
Therefore, there are 250 different 3-digit numbers that can be made from 1, 2, 3, 4, 5, and 6 with letter A repetition allowed and letter B repetition not allowed.
There are 720 numbers consisting of 3 digits that can be made from 1, 2, 3, 4, 5, and 6 if letter A repetition is allowed and letter B repetition is not allowed.
This can be calculated by taking the number of possible combinations for each digit (6 for A, 5 for B, 4 for C) and multiplying them together: 6 x 5 x 4 = 120. Since there are 6 possible numbers for each digit, there are 120 combinations for a 3-digit number. Then, multiplying 120 by 6 (since repetition is allowed) yields 720 possible 3-digit numbers.
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43.5 and a number, n, is no greater than 50. possible values of n? Show your work.
Answers
Answer:
n ≤ 6.5
Step-by-step explanation:
43.5 + n ≤ 50
43.5 + n - 43.5 ≤ 50 - 43.5
n ≤ 6.5
Show that Col A is the subspace spanned by the columns of A. Hint: use Definition 2.4 to show that Ax b implies that b is a linear combination of the columns of A. Definition 3.11 Given is a k x n matrix A. We define the following set: {b e Rk | there exists x e RN such that Ax = b } and will be denoted This set is called the column-space of the matrix by Col A. Definition 3.4 The null-space of a k x n-matrix A is defined as the fol- lowing subspace of RN: Null A = {XER"" | Ax = 0 }
Answers
To show that Col A is the subspace spanned by the columns of A, we need to show that:
Col A is a subspace of RN.
Col A is spanned by the columns of A.
To show that Col A is a subspace of RN, we need to show that it satisfies the three subspace properties:
a. Col A contains the zero vector. This is true since the equation Ax = 0 always has a solution x = 0, which means that the zero vector is in Col A.
b. Col A is closed under addition. Suppose b1 and b2 are in Col A, so there exist x1 and x2 such that Ax1 = b1 and Ax2 = b2. Then, for any scalars c1 and c2, we have:
A(c1x1 + c2x2) = c1Ax1 + c2Ax2 = c1b1 + c2b2
which shows that c1b1 + c2b2 is also in Col A.
c. Col A is closed under scalar multiplication. Suppose b is in Col A, so there exists x such that Ax = b. Then, for any scalar c, we have:
A(cx) = c(Ax) = cb
which shows that cb is also in Col A.
Therefore, Col A is a subspace of RN.
To show that Col A is spanned by the columns of A, we need to show that any vector b in Col A can be expressed as a linear combination of the columns of A. By definition, there exists an x such that Ax = b.
This means that b is a linear combination of the columns of A, with the coefficients given by the entries of x. Specifically, if A has columns a1, a2, ..., an, then:
b = Ax = x1a1 + x2a2 + ... + xn an
Therefore, Col A is spanned by the columns of A.
Overall, we have shown that Col A is the subspace spanned by the columns of A.
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Score on last try:
4.74
of 5 pts. See Details for more. You can retry this quest Round all ainsurers to 3 decintal places. The vertex of kis
Answers
The vertex of this function would be (-1, -8).
The question seems to be incomplete and there are some typos in it. However, I will try to provide a general answer based on the given information.
When finding the vertex of a function, you can use the formula -b/2a to find the x-coordinate of the vertex. Once you have the x-coordinate, you can plug it back into the original function to find the y-coordinate of the vertex.
For example, if the function is y = 2x^2 + 4x - 6, the formula for the x-coordinate of the vertex would be -4/(2*2) = -1. The y-coordinate of the vertex would be 2(-1)^2 + 4(-1) - 6 = -8.
So the vertex of this function would be (-1, -8).
Remember to Round all answers to 3 decimal places, as instructed in the question.
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biologist is studying diseases in chimpanzees. He takes three random samples of the same size from a troop of 150 chimpanzees. One sample indicates that 3% of the chimpanzees are hairless, another sample indicates that 5% are hairless, and a third sample indicates that 4% are hairless. How many hairless chimpanzees should the biologist expect to find in the troop?
Answers
6 hairless chimpanzees should the biologist expect to find in the troop.
What is the percentage?
A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a part per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
The sample number is 150.
Given that 3% of the chimpanzees are hairless, another sample indicates that 5% are hairless, and a third sample indicates that 4% are hairless.
The average percentage of chimpanzees of hairless is
(3% + 5% + 4%)/3
= 12%/3
= 4%
Now calculate 4% of 150:
4% of 150
= (4/100) × 150
= 6
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In the coordinate plane, the point A (0, 0) is translated to the point A '(1, 3). Under the same translation, the points B (-3, -2) and C (3, 3) are translated to B' and C', respectively. What are the coordinates of B' and C'?
Answers
Therefore , the solution of the given problem of coordinates comes out to be B' = (-2, 1) and C' = (4, 6) .
What is coordinates ?A coordinate system is a method that employs one or more values or coordinates to accurately locate points or even other mathematical objects on a space, such as Euclidean space. Coordinates, that are pairs of numbers, are used to locate a point or object on a double plane. The y and x vectors are two integers that specify where a point is situated on a two - dimensional plane. a group of numerals designating particular places. Usually, the number has two numbers.
Here,
By adding 1 to the x-coordinate and 3 to the y-coordinate, we can determine that position A is translated to point A'. As a result, we can determine the values of B' and C' using the same translation vector.
We increase the x-coordinate for position B by one
=> (-3 + 1 = -2) and
the y-coordinate by three
=> (-2 + 3 = 1). Consequently, B"s values are (-2, 1).
We increase the x-coordinate for position C by one
=> (3 + 1 = 4) and
the y-coordinate by three
=>(3 + 3 = 6). Consequently, C"s dimensions are (4, 6).
Consequently, the translated locations' coordinates are as follows:
=> B' = (-2, 1)
=> C' = (4, 6)
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A box of cookies cost 9 dollars what is the cost for 1 cookie
Answers
Answer:
Either x/9 or 0.75 per cookie
Step-by-step explanation:
Let the number of cookies in a box be x.
The cost of x=9$
Then, the cost of one cookie= x/9
alternatively:
Considering one box contains 12 cookies,
The cost of a box of cookies= 9$
Then, the cost of one cookie= 9/12=0.75
The wind farms in southern California contain wind generators whose power production varies directly with the cube of the wind's speed. one such generator produces 1000W of power in a 25mph wind, find the power it generate in a 35mph wind.
Answers
The wind generator will produce 2744W of power in a 35mph wind.
Determine the generate powerTo find the power generated by the wind generator in a 35mph wind, we can use the formula P = kV³, where P is the power generated, k is a constant, and V is the wind's speed.
First, we need to find the value of k. We can do this by plugging in the given values of P and V into the formula and solving for k:
1000W = k(25mph)³ 1000W = k(15625mph³)
k = 1000W/15625mph³
k = 0.064W/mph³
Now that we have the value of k, we can plug it back into the formula along with the new wind speed of 35mph to find the power generated:
P = (0.064W/mph³)(35mph)³
P = (0.064W/mph³)(42875mph³)
P = 2744W
Therefore, the wind generator will produce 2744W of power in a 35mph wind.
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Suppose the annual interest rate is 7.5% and the interest is compounded annually. How much will an investment of $1,000 be worth after 3 years?
Answers
The value of an investment with $1000 as principal amount compounding annually for 3 years with interest rate 7.5% is $1242.29
What is interest rate?The interest rate is the amount that the lender charges the borrower and is the principal - a percentage of the loan amount. Loan interest rates are usually quoted on an annual basis known as the annual rate (APR).
Solution according to the given information in the question:
Given, Principal = $1000
Time = 3 years
Interest rate = 7.5%
∴ Amount = P×(1 + r/100)³
= 1000×(1 + 7.5/100)³
= 1000×(1 + 0.075)³
= 1000×(1.075)³
= 1000 × 1.24
Amount = $1242.29
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The table lists the ring size S for a finger with circumference x in centimeters. x (cm) 4.87 5.66 5.92 6.71 S (size) 4 7 8 11 a. Find a linear function S that models the data. b. Find the circumference of a finger with a ring size of 6.
Answers
The linear function that models the data is S = 3.8x - 14.506 and the circumference of a finger with a ring size of 6 is 5.4 cm.
a. To find a linear function S that models the data, we need to find the slope and y-intercept of the line that best fits the data. The slope can be found by using the formula:
m = (y2 - y1) / (x2 - x1)
Using the first two data points, we can find the slope:
m = (7 - 4) / (5.66 - 4.87)
m = 3 / 0.79
m = 3.8
To find the y-intercept, we can use the formula:
y = mx + b
Substituting one of the data points and the slope into the formula and solving for b:
4 = (3.8)(4.87) + b
b = 4 - (3.8)(4.87)
b = -14.506
So the linear function that models the data is:
S = 3.8x - 14.506
b. To find the circumference of a finger with a ring size of 6, we can substitute S = 6 into the linear function and solve for x:
6 = 3.8x - 14.506
3.8x = 20.506
x = 5.4 cm
So the circumference of a finger with a ring size of 6 is 5.4 cm.
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For items 1-4, tell whether each statement is true or false. If false, indicate what makes the statement false.
1. The probability that it will rain tomorrow is .4 and the probability that it will not rain tomorrow is .52
2. The probabilities that a printer will make 0, 1, 2, 3, or 4 or more mistakes in printing a document are, respectively, .19, .34, -.25, .43, and .29
3. The probabilities that an automobile salesperson will sell 0, 1, 2, or 3 cars on any given day in February are, respectively, .19, .38, .29, and .15.
4. On a single draw from a deck playing cards, the probability of selecting a heart is ¼, the probability of selecting a black card is ½, and the probability of selecting both a heart and a black card is 1/8.
5. In tossing a fair coin, what is the probability of getting a head? Of either a head or tail? Of neither head nor tail?
Answers
1. False. The probabilities of two mutually exclusive events should add up to 1. In this case, the probability of it raining and not raining should add up to 1, but .4 + .52 = .92, which is not equal to 1.
2. False. The probabilities of all possible outcomes should add up to 1. In this case, the probabilities of the printer making 0, 1, 2, 3, or 4 or more mistakes should add up to 1, but .19 + .34 + -.25 + .43 + .29 = .97, which is not equal to 1. Additionally, the probability of an event cannot be negative, so -.25 is not a valid probability.
3. True. The probabilities of all possible outcomes add up to 1 (.19 + .38 + .29 + .15 = 1) and none of the probabilities are negative.
4. True. The probabilities of the three events add up to 1 (1/4 + 1/2 + 1/8 = 7/8) and none of the probabilities are negative.
5. The probability of getting a head on a fair coin toss is 1/2. The probability of getting either a head or a tail is 1, since those are the only two possible outcomes. The probability of getting neither a head nor a tail is 0, since there are no other possible outcomes.
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Find a model for the Body Mass Index (BMI) of a person, given
that BMI varies directly as a person’s weight in pounds and
inversely as the square of the person’s height in inches. If a
6ft6ft t
Answers
The model for the BMI of a person is:
BMI = (152100/weight in pounds)/(height in inches)^2
The Body Mass Index (BMI) of a person can be calculated using the formula:
BMI = (weight in pounds)/(height in inches)^2
In this case, the BMI varies directly as a person's weight in pounds and inversely as the square of the person's height in inches. This means that as the weight increases, the BMI increases and as the height increases, the BMI decreases.
To find a model for the BMI of a person, we can use the formula:
BMI = k(weight in pounds)/(height in inches)^2
Where k is a constant of proportionality. To find the value of k, we can use the given information that a 6ft 6in tall person has a BMI of 25.
First, we need to convert the height from feet and inches to inches. 6ft 6in is equivalent to 78 inches. Then, we can plug in the values into the formula and solve for k:
25 = k(weight in pounds)/(78 inches)^2
25(78 inches)^2 = k(weight in pounds)
152100 = k(weight in pounds)
Therefore, the model for the BMI of a person is:
BMI = (152100/weight in pounds)/(height in inches)^2
This model can be used to calculate the BMI of a person given their weight in pounds and height in inches.
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Write an equation in slope-intercept form of the line that passes through
-9, 5 and -3, 3
Answers
Answer: y = 1/3x + 2
Step-by-step explanation:
y = mx+b
to find m: m = 3 - 5 / -3 - (- 9) = -2 / 6 = - 1 / 3
to find b:
3 = -1 / 3 (-3) + b
3 = 1 + b
b = 2
An amount of $1100 is deposited for 8 years in an account that earns 8% interest. ( Round your answer to two decimal places.) (a) Calculate the simple interest earned. $ _____
(b) Calculate the interest earned if interest is compounded daily. $ _____
(c) How much more interest is earned on the account when the interest is compounded daily?
$ _____
Answers
a) The simple interest earned is $704,
b) The interest earned when compounded daily is $975.19,
c) The difference between the two is $271.19.
To solve this problem, we will use the formulas for simple interest and compound interest.
Simple Interest = Principal x Interest Rate x Time
Compound Interest = Principal x (1 + Interest Rate / Number of Compounding Periods) ^ (Number of Compounding Periods x Time) - Principal
(a) Calculate the simple interest earned.
Simple Interest = $1100 x 0.08 x 8
Simple Interest = $704
(b) Calculate the interest earned if interest is compounded daily.
Compound Interest = $1100 x (1 + 0.08 / 365) ^ (365 x 8) - $1100
Compound Interest = $1100 x (1.000219178) ^ 2920 - $1100
Compound Interest = $1100 x 1.886533 - $1100
Compound Interest = $2075.19 - $1100
Compound Interest = $975.19
(c) How much more interest is earned on the account when the interest is compounded daily?
Difference = Compound Interest - Simple Interest
Difference = $975.19 - $704
Difference = $271.19
Therefore, the simple interest earned is $704, the interest earned when compounded daily is $975.19, and the difference between the two is $271.19.
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Miguel volunteers at his local food pantry and takes note of how much money is donated each day during a 10-day fundraising phone-a-thon. Below is the graph that represents the data that he collected. The slope of the line that represents the data that Miguel collected is 25, and the y-intercept is 50. What do the slope and y-intercept represent in Miguel’s situation?
Answers
Answer: Your welcome!
Step-by-step explanation:
The slope of the line represents the amount of money that is donated each day, which is 25. The y-intercept represents the amount of money donated on the first day, which is 50.
HELPPPPPP!!!!!!!!!!!!!!!!
Answers
Answer:
The answer is -3 because it passes through (0,0) and (2,-6).
HELP PLSSSS
algebra grade 11
Answers
The time taken for Ben's ball to land after Andrew's ball is 2.5 seconds.
What is the time taken for Ben's ball to land?To calculate the time taken for the Ben's ball to land after Andrews ball is calculated as follows;
Since the value of parameter a is -5 for both balls, the height of each ball follows the equation:
h(t) = -5t² + vt + h0
where;
h(t) is the height of the ball at time t, v is the initial velocity of the ball (in meters per second), and h0 is the initial height of the ball (in meters).Let's assume that Andrew's ball is hit with an initial velocity of v1, and Ben's ball is hit with an initial velocity of v₂. We also know that Ben's ball reaches a maximum height 50% greater than Andrew's, which means that:
h_max2 = 1.5h_max1
At the maximum height, the velocity of the ball is zero, so we can find the time it takes for each ball to reach the maximum height by setting v = 0 in the equation for h(t):
t_max1 = v₁ / (2 x 5)
t_max2 = v₂ / (2 x 5)
Since Ben's ball reaches a maximum height that is 50% greater than Andrew's, we can write:
h_max2 = 1.5h_max1
-5(t_max2)² + v₂t_max2 + h0 = 1.5(-5(t_max1)² + v1 * t_max1 + h0)
Simplifying this equation, we get:
-5(t_max2)² + v₂t_max2 = -7.5(t_max1)² + 1.5v₁t_max1
We also know that Andrew's ball lands after 4 seconds, which means that h(4) = 0:
h(4) = -5(4)² + v1 * 4 = 0
-80 + 4v1 = 0
v1 = 80/4
v1 = 20 m/s
Solving these equations for t_max2 and v2, we get:
t_max1 = v1 / (2 x 5)
t_max1 = 20 / (2 x 5) = 2 s
t_max2 = 1.5t_max1 = 3 s
v2 = 1.5v1 = 30 m/s
To find the time it takes for Ben's ball to land, we need to find the time t2 when h(t2) = 0.
We can use the equation for h(t) with v = v2, h0 = 0, and solve for t:
-5t² + v₂t = 0
-5t² + 30 = 0
5t² = 30
t² = 30/5
t² = 6
t = √6
t = 2.5 s
Therefore, Ben's ball lands approximately 2.5 seconds after Andrew's ball.
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When are two events X and Y marginally dependent?
Roulette example:
• 1-36 numbers, each number is Red or Black
• X = color of my attempt, Y = number
Assume that all odd numbers are RED. Find the following probabilities.
P[X = red | Y = 15] =
P(Y=15 | X = red) =
P(X = Red, Y = 15) =
P(Y=15) =
P(X = Red) =
Answers
|The events X and Y are marginally dependent in the roulette example.
Two events X and Y are marginally dependent when the probability of one event occurring affects the probability of the other event occurring. In the roulette example, the events X and Y are marginally dependent because the probability of X = red depends on the probability of Y = 15, and vice versa.
The probabilities can be calculated as follows:
P[X = red | Y = 15] = 1, since all odd numbers are red and 15 is an odd number.
P[Y = 15 | X = red] = 1/18, since there are 18 red numbers and only one of them is 15.
P[X = Red, Y = 15] = P[X = red | Y = 15] * P[Y = 15] = 1 * 1/36 = 1/36, since there are 36 numbers in total and only one of them is both red and 15.
P[Y = 15] = 1/36, since there are 36 numbers in total and only one of them is 15.
P[X = Red] = 18/36 = 1/2, since there are 18 red numbers and 36 numbers in total.
Therefore, the events X and Y are marginally dependent in the roulette example.
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Perform the addition or subtraction and simplify.
x
x − 4
−
3
x + 8
Answers
The simplified expression after doing this calculation is -1/3. To perform the addition or subtraction and simplify the given expression, we need to find a common denominator for the two fractions. The common denominator for x and 3 is 3x.
Multiply each fraction by the necessary factor to get the common denominator. For the first fraction, we multiply by 3/3, and for the second fraction, we multiply by x/x.
3/3 * (x/x) - x/x * (4/3) = (3x - 4x)/3x = (-x)/3x. Now, we can simplify the expression by canceling out the common factor of x in the numerator and denominator. (-x)/3x = -1/3
The simplified expression is -1/3.
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What is the volume of the rectangular prism? I NEED IT NOW PLSSSS!!!!!!
Answers
Answer: 256
Step-by-step explanation: This is a rectangular prism and shows the length, width, and height, so we need to use the formula length times width times height. So 8 * 8 * 4 equals 256.
Find the average rate of change of the given function on the
interval [5,10].
h(x)=3x2+6x−7
Answers
The average rate of change of the function h(x)=3x2+6x−7 on the interval [5,10] is 94.6.
The average rate of change of the function h(x)=3x2+6x−7 on the interval [5,10] is calculated by taking the change in the y-value (h(10) - h(5)) and dividing it by the change in the x-value (10-5):
Average rate of change = (h(10)-h(5))/(10-5)
= (3(10)2+6(10)-7 - (3(5)2+6(5)-7))/(10-5)
= (745-272)/5
= 473/5
= 94.6
Therefore, the average rate of change of the function h(x)=3x2+6x−7 on the interval [5,10] is 94.6.
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For the points ( 9.6,-19.7) and (6.6,-23.7) (a) Find the exact distance between the points. (b) Find the midpoint of the line segment whose endpoints are the given points. Part 1 of 2 (a)
Answers
The midpoint of the line segment whose endpoints are the given points is (8.1 , -21.7).
To find the exact distance between the points (9.6,-19.7) and (6.6,-23.7), we can use the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the given values:
distance = sqrt((6.6 - 9.6)^2 + (-23.7 - (-19.7))^2)
Simplifying:
distance = sqrt((-3)^2 + (-4)^2)
distance = sqrt(9 + 16)
distance = sqrt(25)
distance = 5
Therefore, the exact distance between the points is 5.
To find the midpoint of the line segment whose endpoints are the given points, we can use the midpoint formula:
midpoint = ((x1 + x2)/2 , (y1 + y2)/2)
Substituting the given values:
midpoint = ((9.6 + 6.6)/2 , (-19.7 + (-23.7))/2)
Simplifying:
midpoint = (16.2/2 , -43.4/2)
midpoint = (8.1 , -21.7)
Therefore, the midpoint of the line segment whose endpoints are the given points is (8.1 , -21.7).
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Question 4: Abstract Vector Spaces LetWbe the set of all vectorsu=(x,y)inR2such that the product of its componentsxandysatisfy the equationx⋅y=0. Check whether this set (a) is closed under operation of standard scalar multiplication in the plane. (b) is closed under operation of standard vector addition in the plane. Is the information you found is sufficient to conclude whether this set forms a vector space or not? Explain why yes or why not. What does this set represent geometrically?
Answers
The set W represents the x-axis and y-axis in the plane. Any vector with one of its components equal to 0 will satisfy the equation x⋅y = 0, and these vectors lie on either the x-axis or y-axis.
(a) The set W is closed under standard scalar multiplication in the plane. This is because for any scalar c and any vector u = (x,y) in W, the product of the components of cu = (cx,cy) is (cx)(cy) = c2(xy) = c2(0) = 0, so cu is also in W.
(b) The set W is not closed under standard vector addition in the plane. For example, the vectors u = (1,0) and v = (0,1) are both in W, but their sum u + v = (1,1) is not in W because the product of its components is 1(1) = 1, which does not satisfy the equation x⋅y = 0.
Since the set W is not closed under standard vector addition, it does not form a vector space. A set must be closed under both scalar multiplication and vector addition in order to be a vector space.
Geometrically, the set W represents the x-axis and y-axis in the plane. Any vector with one of its components equal to 0 will satisfy the equation x⋅y = 0, and these vectors lie on either the x-axis or y-axis.
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1. Interpret the effect size (hp2) for your ANOVA results.
a. Remember, for ANOVAs, SPSS reports a partial-eta squared which has a slightly different interpretation than Cohen’s d or correlations.
possible medication to treat high blood pressure. They decide it would be best to have 3 groups of randomly selected male participants: • One group (n=5) will be given a high dose of HyBlox: • One group (n=5) will be given a low dose of HyBlox: • One group (n=5) will be given a placebo sugar pill. They measure participants' blood pressures on a continuous scale. Participants are blind to condition and don't know which pill they've been given. The experimenters hypothesize that the participants given the highest level of HyBlox will have the lowest mean blood pressure level, the low dose HyBlox will have the second-lowest mean blood pressure level, and that the placebo group will have the highest mean blood pressure level. QUESTIONS: 1. Is this study within-subjects, between-subjects, or mixed? 2. What are the independent and dependent variables?
Answers
ANOVA results
1. This study is a between-subjects design.
2. The independent variable is the type of medication given and the dependent variable is the participants' blood pressure levels.
The effect size (hp2) for the ANOVA results is a measure of the strength of the relationship between the independent variable (type of medication) and the dependent variable (blood pressure levels).
A larger effect size indicates a stronger relationship between the two variables. It is important to remember that SPSS reports a partial-eta squared, which has a slightly different interpretation than Cohen's d or correlations.
Partial-eta squared is the proportion of the total variance in the dependent variable that is explained by the independent variable, after controlling for other factors. A partial-eta squared of .01 is considered a small effect, .06 is considered a medium effect, and .14 is considered a large effect.
Hence,
1. This study is a between-subjects design because each participant is only assigned to one group and is only exposed to one level of the independent variable.
2. The independent variable is the type of medication given (high dose HyBlox, low dose HyBlox, or placebo) and the dependent variable is the participants' blood pressure levels.
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