a) The height of the scale model is 105 m. b) The actual dimensions of the bed, couch, and desk are twice as large as their corresponding dimensions in the scale model.
a) To determine the height of the scale model, we multiply the height of the actual building by the scale factor of 0.5:
Height of scale model = 0.5 x 210 m = 105 m.
b) Since the scale factor is 0.5, the actual dimensions of the bed, couch, and desk are twice as large as their corresponding dimensions in the scale model.
For example, if the length of the couch in the scale model is 10 cm, then the actual length of the couch is 2 x 10 cm = 20 cm. Similarly, if the width of the desk in the scale model is 8 cm, then the actual width of the desk is 2 x 8 cm = 16 cm.
Therefore, to find the actual dimensions of the bed, couch, and desk, we simply multiply the corresponding dimensions in the scale model by 2.
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Find the equation for the plane through the points Po(-3,- 2,4), Qo(-5, - 1,2), and Ro(1,1,5). C. Using a coefficient of 7 for x, the equation of the plane is (Type an equation.)
The equation for the plane through the points Po(-3,-2,4), Qo(-5,-1,2), and Ro(1,1,5) is:
3x - 3y + 2z - 11 = 0
Using a coefficient of 7 for x, the equation of the plane is:
21x - 3y + 2z - 11 = 0
To find the equation of the plane, we can use the cross product of the vectors formed by the points Qo-Po and Ro-Po.
Let's call the vector formed by Qo-Po "u" and the vector formed by Ro-Po "v". Then, we can find the normal vector to the plane by taking the cross product of "u" and "v":
u = Qo - Po = (-5+3, -1+2, 2-4) = (-2,1,-2)
v = Ro - Po = (1+3, 1+2, 5-4) = (4,3,1)
n = u x v = (1(2) - (-2)(3), (-2)(4) - 1(1), (-2)(3) - 1(4)) = (8,-7,-10)
Now that we have the normal vector to the plane, we can find the equation of the plane by using the point-normal form of the equation of a plane:
n · (P - Po) = 0
where "·" denotes the dot product, P is any point on the plane, and Po is one of the given points on the plane.
Let's use the point Po(-3,-2,4) to find the equation of the plane:
n · (P - Po) = 0
(8,-7,-10) · (x+3, y+2, z-4) = 0
8(x+3) - 7(y+2) - 10(z-4) = 0
8x - 7y - 10z + 11 = 0
So the equation of the plane through the points Po, Qo, and Ro is:
3x - 3y + 2z - 11 = 0
To use a coefficient of 7 for x, we can simply multiply both sides of the equation by 7:
21x - 21y + 14z - 77 = 0
Simplifying, we get:
21x - 3y + 2z - 11 = 0
Therefore, the equation of the plane with a coefficient of 7 for x is 21x - 3y + 2z - 11 = 0.
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The city is 30 miles long and two-thirds as wide, and 555,000 citizens currently live there. The mayor calculates that the minimum number of people who would have to move outside the city for adequate services to be maintained is 75,000. Enter the maximum population density , in citizens per square mile , that is assumed in the mayor's calculation
The maximum population density evaluated is 1200 citizens per square mile, under the condition that the city is 30 miles long and two-thirds as wide, and 555,000 citizens currently live there.
Now to evaluate the maximum population density that is considered in the mayor's calculation is
Let us first calculate the area of the city which is (2/3) × (30 miles)
= 20 miles.
So, now we can calculate the current population density which is
555,000 / (20 × 20)
= 1387.5 citizens per square mile.
Hence the mayor evaluates that at least 75,000 people must transfer out of the city for adequate services to be exercised, we can find the new population as
555,000 - 75,000
= 480,000 citizens.
Therefore, the new population density would be 480,000 / (20 × 20)
= 1200 citizens per square mile
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Is there a relationship between the raises administrators at State University receive and their performance on the job? A faculty group wants to determine whether job rating (x) is a useful linear predictor of raise (y). Consequently, the group considered the straight-line regression model, (y) hat = (b) with subscript (1)x+ (b) with subscript (0). Using the method of least-squares regression, the faculty group obtained the following prediction equation, (y) hat=2,000x+ 14,000.
Interpret the estimated y-intercept of the line.
A)There is no practical interpretation, since rating of 0 is not likely and outside the range of the sample data.
B)For an administrator who receives a rating of zero, we estimate his or her raise to be $14,000.
C) The base administrator raise at State University is $14,000.
D) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase $14,000
Yes, there is a relationship like a straight line between the raises administrators at State University receive and their performance on the job
The estimated y-intercept of the line in the given straight-line regression model is $14,000.The interpretation of this value is that for an administrator who receives a rating of zero, we estimate his or her raise to be $14,000. This value represents the base raise amount for the administrators at State University, regardless of their job performance rating.To obtain this interpretation, we consider the equation of the regression line, which relates the predicted raise amount (y hat) to the job performance rating (x). The y-intercept term in this equation is the value of y hat when x equals zero. Therefore, the estimated y-intercept of $14,000 represents the predicted raise amount for an administrator whose job performance rating is zero, which corresponds to the base raise amount at State University.
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Emmanuel weighs 150 pounds and he has normal liver function. It will take him approximately ________ hours to metabolize one standard drink
Emmanuel weighs 150 pounds and he has normal liver function. It will take him approximately 1 hour to metabolize one standard drink. Metabolism of alcohol is primarily done in the liver where it is broken down into acetaldehyde, which is then further broken down into water and carbon dioxide.
The liver can only metabolize a certain amount of alcohol per hour, which is why it takes time for the body to process and eliminate alcohol. However, other factors such as age, gender, body composition, and food consumption can also affect how quickly alcohol is metabolized.
It is important to drink responsibly and be aware of how alcohol can affect your body.
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Beatrice used a slingshot to launch an egg into the air. She recorded the egg’s path using a motion detector. The following data represents the height (in feet) of the egg at certain time points (in seconds): { ( 0.0 , 16 ) , ( 1.7 , 20.46 ) , ( 2.5 , 23.16 ) , ( 3.7 , 23.51 ) , ( 5.1 , 20.07 ) , ( 6.6 , 12.4 ) , ( 7.3 , 5.62 ) , ( 8.0 , 0.15 ) }
Step 4: Determine the height from which the egg was launched.
8 feet
3 feet
16 feet
0 feet
Answer:
mmm, well, not much we can do per se, you'd need to use a calculator.
I'd like to point out you'd need a calculator that has regression features, namely something like a TI83 or TI83+ or higher.
That said, you can find online calculators with "quadratic regression" features, which is what this, all you do is enter the value pairs in it, to get the equation.
Step-by-step explanation:
for wich scatterplot would a line best fit be described by the equation y=1/2x+2
The scatterplot that would describe is Option A.
What is a scatterplot?A scatter plot is described as a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data.
The slope - intercept form of the equation of a line is:
y = mx + c
where m = the slope
c = the y-intercept
Only in the first scatterplot can the line of best fit intersect the y-axis at 2 if a line of best fit is drawn on each of the scatterplots. Only when a line of best fit is established on the first scatterplot is a slope of 1/2 conceivable.
That is, c = 2
m = 1/2
In conclusion, only the first scatterplot would have the line of best fit represented by the equation y = 1/2 x + 2.
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Morgan bought a sofa for $216. 0. the finance charge was $25 and she paid for it over 15 months.
use the formula approrimate apr =
(finance charge: #months)(12)
amount financed
to calculate her approximate apr
round the answer to the nearest tenth.
The approximate APR for Morgan's sofa purchase is 1.7%.
To calculate the approximate APR (Annual Percentage Rate) for Morgan's sofa purchase, we can use the formula:
APR ≈ (finance charge / # of months) x 12 / amount financed
Here, the finance charge is $25, the number of months is 15, and the amount financed is the total cost of the sofa minus the finance charge, which is:
financed= $216.00 - $25.00 = $191.00
on substitution:
APR ≈ (25 / 15) x 12 / 191
APR ≈ 0.2778 x 0.06283
APR ≈ 0.01743
Rounding the answer to the nearest tenth, we get:
APR ≈ 1.7%
Therefore, the approximate APR for Morgan's sofa purchase is 1.7%.
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why zero is neither positive or negative probe with scientific ?
Answer: As the Integers being positive or negative depends on the 0 As it is reference present on the centre of the number line
Numbers on the left side are negative while that on right side being positive
Step-by-step explanation:
If x -1/x=3 find x cube -1/xcube
Answer:
Sure. Here are the steps on how to solve for x^3 - 1/x^3:
1. **Cube both sides of the equation x - 1/x = 3.** This will give us the equation x^3 - 3x + 1/x^3 = 27.
2. **Subtract 1 from both sides of the equation.** This will give us the equation x^3 - 1/x^3 = 26.
3. **The answer is 26.**
Here is the solution in detail:
1. **Cube both sides of the equation x - 1/x = 3.**
```
(x - 1/x)^3 = 3^3
```
```
x^3 - 3x + 1/x^3 = 27
```
2. **Subtract 1 from both sides of the equation.**
```
x^3 - 1/x^3 - 1 = 27 - 1
```
```
x^3 - 1/x^3 = 26
```
3. The answer is 26.
The marginal cost function, in dollars per item, for producing the x th item of a certain brand of bar stool is given by MC(x)=20−0. 5 x , 0≤ x≤ 100. The fixed cost is $200. Estimating the total cost of producing 100 bars tools using the left-rectangle approximation with five rectangles, we conclude that the total cost is approximately $
Total cost = VC(80) + Fixed cost = 1325.34 + 200 = $1525.34
How to solveTo find the total cost of producing 80 barstools, we need to calculate the variable cost and add it to the fixed cost.
First, integrate the marginal cost function to find the variable cost function:
VC(x) = ∫[tex](20 - 0.5\sqrt{x dx} )[/tex]
VC(x) = [tex]20x - (1/3)x^(^3^/^2^) + C[/tex]
The constant C is irrelevant in this case, as we are interested in the difference between VC(80) and VC(0).
Now, evaluate the variable cost function at x = 80:
VC(80) = 20(80) - [tex](1/3)(80^(^3^/^2^))[/tex]
VC(80) = 1600 - [tex](1/3)(80\sqrt{80} )[/tex]
VC(80) ≈ 1325.34
Finally, add the fixed cost:
Total cost = VC(80) + Fixed cost = 1325.34 + 200 = $1525.34
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A sheep rancher plans to fence a rectangular pasture next to an irrigation canal. No fence will be needed along the canal, but the other three sides must be fenced. The pasture must have an area of 180,000 m² to provide enough grass for the sheep. Find the dimensions of the pasture which require the least amount of fence.
The dimensions of the pasture that require the least amount of fence are approximately 600 meters by 300 meters.
To minimize the amount of fence needed, we want to maximize the length of the side next to the canal. Let's call this side x and the other two sides y.
We know that the area of the rectangle must be 180,000 m², so we have x*y = 180,000. We want to minimize the amount of fence, which is the perimeter of the rectangle: P = x + 2y
To solve for the dimensions that require the least amount of fence, we need to eliminate one variable. We can do this by using the area equation to solve for one variable in terms of the other:
y = 180,000/x
Substituting this into the perimeter equation, we have:
[tex]P = x + 2(180,000/x)[/tex]
To find the minimum value of P, we take the derivative with respect to x and set it equal to zero:
[tex]P' = 1 - 360,000/x^2 = 0x = sqrt(360,000) ≈ 600[/tex]
Substituting this back into the area equation, we find:
[tex]y = 180,000/x ≈ 180,000/600 ≈ 300[/tex]
So, the dimensions of the pasture which require the least amount of fence are approximately 600 meters by 300 meters.
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(1 point) Evaluate the integral by reversing the order of integration. 7 STE dedy
the integral by reversing the order of integration. the result will be F(β) - F(α), which is the integral evaluated after reversing the order of integration.
First, let's rewrite your integral more clearly:
∫∫ R 7x dy dx, where R is the region of integration.
To reverse the order of integration, we first need to determine the limits of integration for R in terms of x and y. Let's assume the current limits are a to b for x and c(y) to d(y) for y.
Now, we need to express these limits in terms of y and x. Let's denote the new limits as α to β for y and γ(x) to δ(x) for x.
After finding the new limits, we can rewrite the integral as:
∫∫ R 7x dx dy
Now, evaluate the integral by integrating first with respect to x and then with respect to y:
1. Integrate 7x with respect to x: (7/2)x^2 + C₁(x)
2. Apply the limits of integration for x: [(7/2)δ(x)^2 + C₁(δ(x))] - [(7/2)γ(x)^2 + C₁(γ(x))]
3. Integrate the result with respect to y: ∫[α, β] [(7/2)(δ(y)^2 - γ(y)^2)] dy
4. Apply the limits of integration for y: F(β) - F(α)
The final result will be F(β) - F(α), which is the integral evaluated after reversing the order of integration.
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Can someone please answer numbers 12, 13, 14, and 15?
Let x, y, and z represent three rational numbers, such that y is 512 times x and z is 50. 25 more than x. If y=15. 5, what is the value of z?
If x, y, and z represent three rational numbers, such that y is 512 times x and z is 50. 25 more than x and y = 15.5 , then value of z = 50.280.
Let x, y, and z represent three rational numbers, such that y is 512 times x and z is 50.25 more than x. If y = 15.5, the value of z can be found as follows:
Find the value of x.
Since y is 512 times x, we have the equation:
y = 512x
Substitute y with 15.5:
15.5 = 512x
Now, divide both sides by 512 to find x:
x = 15.5 / 512
x ≈ 0.0302734375
Find the value of z.
Since z is 50.25 more than x, we have the equation:
z = x + 50.25
Substitute x with the value we found (x = 0.0302734375):
z ≈ 0.0302734375 + 50.25
z ≈ 50.2802734375
So, the value of z is approximately 50.2802734375.
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In the diagram shown, segments AE and CF are both perpendicular to DB. DE=FB, AE=CF. Prove that ABCD is a parallelogram.
Given:- ABCD is a parallelogram, and AE and CF bisect ∠A and ∠C respectively. To prove:- AE∥CF Proof:- Since in a parallelogram, opposite angles are equal.
What is a Parallelogram?A parallelogram is a geometric shape that has four sides and four angles. It is a type of quadrilateral, which means it has four sides, and its opposite sides are parallel to each other.
The opposite sides of a parallelogram are also equal in length. The opposite angles of a parallelogram are also equal in measure.
The shape of a parallelogram looks similar to a rectangle, but it differs from a rectangle in that its angles are not necessarily right angles. A square is a special case of a parallelogram in which all four sides are equal in length and all four angles are right angles
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Convert the number 35/4 into decimal form rounded to the nearest hundred.
Answer: 8.75
Step-by-step explanation:
We know that 4 goes into 35 eight times.
35 - (4 * 8) = 3
Next, we know that 3/4 is equal to 0.75 by dividing.
This leaves us with 8.75. Eight wholes and a part of 0.75.
The point k lies on the segment JL. Find the coordinates of k so that the ratios of JK to KL is 3 to 4
After considering all the given data we conclude that the coordinates of k so that the ratios of JK to KL is 3 to 4 is (-16x₁x₂-16y₁y₂)
The two values of X and Y are the coordinates of K. Let us assume that the coordinates of points J and L are (x₁, y₁) and (x₂, y₂) respectively.
Then, the coordinates of point K can be placed as (x, y), here x and y are unknowns that we need to find.
Now, we know that the ratio of JK to KL is 3:4. This means that:
JK/KL = 3/4
We can use the distance formula to find the distances JK and KL in terms of their coordinates:
JK = √((x-x₁)²+(y-y₁²) KL = √((x-x₂)²+(y- y₂)²)
Staging these distances into the above equation, we get:
√(x-x₁)²+(y-y₁))/√((x-x₂)²+(y-y₂)²) = 3/4
Squaring both sides and simplifying, we get:
16(x-x1)²+16(y-y₁)²= 9(x-x₂)²+9(y-y₂)²
Expanding and simplifying, we get:
7x²-14xx₁-9x₂²+ 7y2-14yy₁-9y₂²= -16x₁x₂-16y₁y₂
This is a quadratic equation in x and y. We can solve this equation to find the values of x and y that satisfy the given conditions. The solution to this quadratic equation gives two values of x and y, which are the coordinates of point K.
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In ΔSTU, t = 3. 4 cm, u = 6. 9 cm and ∠S=21°. Find the area of ΔSTU, to the nearest 10th of a square centimeter.
4.20 cm² is the area of the triangle STU to the nearest 10th of a square centimeter.
Given, t = 3.4 cm, u = 6.9 cm and ∠S = 21°
We know that the formula for the area of the triangle = 1/2 * t*u *sin(S)
Substituting the values
Area = 1/2 × 3.4 × 6.9 × sin(21°)
Area = 11.73 × sin(21°)
Area = 11.73 × 0.3583
Area = 4.2016
Rounding to the nearest 10th of a square centimeter .
Area = 4.20 cm²
Hence, 4.20 cm² is the area of the triangle STU to the nearest 10th of a square centimeter.
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A large diamond with a mass of 481. 3 grams was recently discovered in a mine. If the density of the diamond is g over 3. 51 cm, what is the volume? Round your answer to the nearest hundredth.
The volume of the large diamond is approximately 3.51 cm³.
To find the volume of the large diamond with a mass of 481.3 grams and a density of (g/3.51 cm), you can use the formula:
Volume = Mass / Density
The volume of the large diamond, we can use the formula Volume = Mass / Density. Given that the mass is 481.3 grams and the density is (g/3.51 cm), we can substitute these values into the formula.
Simplifying the equation, we find that the volume is equal to 3.51 cm³. This means that the large diamond occupies a space of approximately 3.51 cubic centimeters.
1. First, rewrite the density as a fraction: g/3.51 cm = 481.3 g / 3.51 cm³
2. Next, solve for the volume by dividing the mass by the density: Volume = 481.3 g / (481.3 g / 3.51 cm³)
3. Simplify the equation: Volume = 481.3 g * (3.51 cm³ / 481.3 g)
4. Cancel out the grams (g): Volume = 3.51 cm³
So, the volume of the large diamond is approximately 3.51 cm³, rounded to the nearest hundredth.
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Answer:
Step-by-step explanation:
Density = mass
volume
We have density (3.51 cm) and we have mass (481.3)
We need to solve for V (volume)
3.51 = 481.3
V
Multiply both sides by V to clear the fraction:
3.51 V = 481.3
Divide both side by 3.51
3.51 V = 481.3
3.51 3.51
V = 137.122cm³
rounded to 137.12 cm³
HELPPPPPPPPPp WILL GIVE BRAINLEISTTT!!!
Answer:
100
Step-by-step explanation:
i think this is right
The spies of Syracuse report that enemies are marching towards the city. Archimedes needs to build death rays and claws to defend the city with. He'll need at least 10 machines but the city only gave him 3000 lbs of gold to build the machines with. A claw costs 200 lbs of gold to build while a death ray is worth 350 lbs of gold. Write a system of inequalities to find a possible number of claws and death rays that Archimedes can build. â
Possible number of death rays (D) and claws (C) that Archimedes can build are given by the following system of inequalities: 350D + 200C ≤ 3000. D, C ≥ 0
The first inequality represents the fact that the total amount of gold used to build the machines cannot exceed the 3000 lbs of gold given by the city. The second inequality ensures that the number of death rays and claws cannot be negative.
To explain this system, let us assume that Archimedes builds x death rays and y claws. The amount of gold required to build x death rays and y claws is given by 350x + 200y. The first inequality ensures that this value cannot exceed 3000 lbs of gold. The second inequality ensures that the number of death rays and claws cannot be negative.
Therefore, the solution to this system of inequalities gives us all the possible combinations of death rays and claws that Archimedes can build with the given amount of gold.
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Kali has a choice of 20 flavors for her triple scoop cone. If she
chooses the flavors at random, what is the probability that the 3 flavors she
chooses will be vanilla, chocolate, and strawberry?
The probability that a certain science teacher trips over the cords in her classroom during any independent period of the day is 0. 35. What is the probability that the students have to wait at most 4 periods for her to trip?
0. 0150
0. 0279
0. 0961
0. 1785
0. 8215
The probability that the students have to wait at most 4 periods for the teacher to trip is approximately 0.8215
How tro solve for the probabilityThe probability of the teacher not tripping during a single period is 1 - 0.35 = 0.65.
For the teacher not to trip in the first 4 periods, she must not trip in each of the first 4 periods. Since the periods are independent, we can multiply the probabilities together:
P(not tripping in first 4 periods) = 0.65 * 0.65 * 0.65 * 0.65 = 0.65^4 ≈ 0.1785
Now, we subtract this probability from 1 to find the probability that the students have to wait at most 4 periods for the teacher to trip:
P(at most 4 periods) = 1 - P(not tripping in first 4 periods) = 1 - 0.1785 ≈ 0.8215
So, the probability that the students have to wait at most 4 periods for the teacher to trip is approximately 0.8215, or 82.15%.
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. Select two choices that are true about the function f(x)
A There is an asymptote at x = 0.
☐ B There is a zero at 23.
OC
There is a zero at 0.
D
There is an asymptote at y = 23.
23x+14
x
Answer:
A. There is an asymptote at x = 0.
D. There is an asymptote at y = 23.
The diagram below shows a quadratic curve. Determine the equation of the curve, giving your answer in the form ax²+bx+c y = = 03 where a, b and care integers. y i 32 (2.0) (8.0)
Answer:
Step-by-step explanation:
Without a diagram, I cannot determine the equation of the curve. However, I can provide you with the general steps to find the equation of a quadratic curve given three points on the curve.
Let the three points be (x1, y1), (x2, y2), and (x3, y3). Then the equation of the quadratic curve in the form ax²+bx+c can be found using the following system of equations:
y1 = a(x1)² + b(x1) + c
y2 = a(x2)² + b(x2) + c
y3 = a(x3)² + b(x3) + c
Solving this system of equations simultaneously will give us the values of a, b, and c, which we can use to write the equation of the quadratic curve.
However, since you have only provided three y-values (32, 2.0, and 8.0), without their corresponding x-values or the diagram, it is not possible to determine the equation of the curve.
x= 3y-5 make y the subject
Answer:
y = (x + 5)/3
Step-by-step explanation:
To make y the subject, you need to isolate y on one side of the equation.
x = 3y - 5
Add 5 to both sides:
x + 5 = 3y
Divide both sides by 3:
y = (x + 5)/3
Therefore, y is the subject of the formula when it is expressed as:
y = (x + 5)/3
The table shows the number of runs earned by two baseball players.
Player A Player B
2, 1, 3, 8, 2, 3, 4, 3, 2 2, 3, 1, 4, 2, 2, 1, 4, 6
Find the best measure of variability for the data and determine which player was more consistent.
Player A is the most consistent, with an IQR of 1.5.
Player B is the most consistent, with an IQR of 2.5.
Player A is the most consistent, with a range of 7.
Player B is the most consistent, with a range of 5.
Answer:
To determine the best measure of variability for the data, we need to consider the type of data we are dealing with. In this case, the data is numerical and discrete, so the best measure of variability would be the range or the interquartile range (IQR).
The range is the difference between the maximum and minimum values in a dataset, while the IQR is the range of the middle 50% of the data. The IQR is less sensitive to outliers than the range, so it is often a better measure of variability.
To calculate the range and IQR for each player, we first need to order the data:
Player A: 1, 2, 2, 2, 3, 3, 3, 4, 8
Player B: 1, 1, 2, 2, 2, 3, 4, 4, 6
Player A has a range of 8 - 1 = 7, and an IQR of Q3 - Q1 = 4 - 2.5 = 1.5.
Player B has a range of 6 - 1 = 5, and an IQR of Q3 - Q1 = 4 - 1.5 = 2.5.
Therefore, Player B has a higher range and a higher IQR, indicating more variability in their performance. Player A has a lower range and a lower IQR, indicating greater consistency in their performance. Therefore, the answer is: Player A is the most consistent.
If f(x) and f^1(x)
are inverse functions of each other and f(x) - 2x+5, what is f^-1(8)?
-1
3/2
41/8
23
Answer:
3/2
Step-by-step explanation:
f(x) = 2x+5
f-¹(x) = ?
to find f-¹(x)
let f(x) be y
y = 2x+5
then we'll make x the subject of formula
y-5 = 2x
x = y-5/2
change y to x and x to y
f-¹(x) = x-5/2
f-¹(8) = 8-5/2 = 3/2
for each rectangle find the radio of the longer side to shorter side
[tex]\cfrac{\stackrel{\textit{longer side}}{12}}{\underset{\textit{shorter side}}{3\sqrt{3}}}\implies \cfrac{4}{\sqrt{3}}\implies \cfrac{4}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}}\implies \cfrac{4\sqrt{3}}{3}[/tex]
Tara tosses two coins. What is the conditional probability that she tosses two heads, given she has tossed one head already?
The conditional probability that she tosses two heads, given she has tossed one head already is: 1/3
How to solve conditional probability?Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.
We are given that she has two coins.
She has tossed one head already
Let A be the event that two heads result and B the event that there is at least one head.
If S denote the sample space, then S={(H,H),(H,T)(T,H)(T,T)}
A={(H,H)}
B={(H,H),(H,T)(T,H)}
So, A∩B = {H,H}
P(B)= 3/4
P(A∩B)= 1/4
Hence P(A∣B) = P(A∩B)/P(B)
P(A∣B) = (1/4)/(3/4)
= 1/3
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