Yes, an 11, 60, 61 triangle has a right angle. This is because the Pythagorean theorem applies to right triangles, stating that the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).
In this case, we can apply the theorem and see that 11^2 + 60^2 = 3721 + 3600 = 7321. Taking the square root of 7321 gives us approximately 85.4, which is the length of the hypotenuse.
Now, if we compare the square of the hypotenuse (85.4^2 = 7291.16) to the sum of the squares of the legs (11^2 + 60^2 = 3721 + 3600 = 7321), we can see that they are not equal. Therefore, the 11, 60, 61 triangle is not a right triangle.
However, if we compare the square of the hypotenuse (61^2 = 3721) to the sum of the squares of the legs (11^2 + 60^2 = 3721), we can see that they are equal. Therefore, the 11, 60, 61 triangle is a right triangle.
In conclusion, the 11, 60, 61 triangle has a right angle because it satisfies the Pythagorean theorem, which applies only to right triangles.
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what is the answer to the file attached.
Answer:
88
Step-by-step explanation:
The formula for a parallelogram to find the area is:
B x h
So, the numbers we are given is the:
base: 11
height: 8
slant height: 9
We do not need the slant height for finding the area, so we can just substitute the base and height values into the equation:
8 x 11
=88
So, the area of this parallelogram is 88 square units
Hope this helps :)
STT 1.3 Sarah starts at a positive position along the x-axis. She then undergoes a negative displacement. Her final position
A is postive
B Is negative
C Could be either positive or negative
Sarah's final position would be negative. Therefore, option B is the correct answer.
Given that, Sarah starts at a positive position along the x-axis. She then undergoes a negative displacement.
A negative displacement means that Sarah has moved backward along the x-axis, so her final position would be negative.
Therefore, option B is the correct answer.
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The length is 5.4 meters.
The width is 1.5 meters.
Howard will increase both the length and the width by 20% each.
Part A
What will be the perimeter, in meters, of the enlarged garden?
Enter your answer in the box.
Part B
By how many square meters will the area of the garden increase?
Answer:
Step-by-step explanation:
whats the meaning of life...
lim sin(pi/3+h) - sin(pi/3)/ h as h approaches 0 is
A. 0
B. 1/2
C. 1
D. Square root of 3/2
E. Nonexistent
lim sin(pi/3+h) - sin(pi/3)/ h as h approaches 0 is Non existent. The correct answer is option e.
To evaluate the limit, we can use the formula for the derivative of sin(x), which is:
lim f(x+h) - f(x) / h as h approaches 0 = f'(x)
where f(x) = sin(x).
So, in this case, we have:
lim sin(pi/3+h) - sin(pi/3) / h as h approaches 0
which can be rewritten as:
lim [sin(pi/3+h) - sin(pi/3)] / h as h approaches 0
Using the identity for the difference of two sines, we can simplify this expression to:
lim [2cos(2pi/6+h/2)sin(h/2)] / h as h approaches 0
Now, we can cancel out the factor of sin(h/2) in the numerator and denominator, and we are left with:
lim 2cos(2pi/6+h/2) / h as h approaches 0
We can evaluate the limit using direct substitution, and we get:
2cos(pi/3) / 0
Since the denominator is 0, the limit does not exist. Therefore, the answer is option E: Nonexistent.
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Assume the distribution of IQ scores for adults can be modeled with a normal distribution with a mean score of 100 points and a standard deviation of 10 points. 90% of adults will have an IQ score higher than what value?
The IQ score that is higher than 90% of the population is 112.8.
We know that the IQ scores follow a normal distribution with a mean of 100 and a standard deviation of 10.
Let X be the random variable representing the IQ scores. We want to find the value x such that 90% of the observations lie above x.
Using the standard normal distribution table or calculator, we can find the z-score corresponding to the 90th percentile as 1.28.
The z-score formula is z = (x - μ) / σ, where μ is the mean, σ is the standard deviation and x is the value we want to find.
Plugging in the values, we get 1.28 = (x - 100) / 10. Solving for x, we get x = 100 + 12.8 = 112.8.
Therefore, the IQ score that is higher than 90% of the population is 112.8.
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A rectangle frame has a length of 3/4 of 1/2 what is the
perimeter of the frame
Answer:
2 1/2 ft
Step-by-step explanation:
Is this what you meant?
Length = 1/2 ft
Width = 3/4 ft
If so, then:
Perimeter = length + length + width + width
P = 1/2 ft + 1/2 ft + 3/4 ft + 3/4 ft
P = 2/4 ft + 2/4 ft + 3/4 ft + 3/4 ft
P = 10/4 ft
P = 5/2 ft
P = 2 1/2 ft
Image shows line WS and line KV as parallel. Line RT intersects line WS and line KV forming right angles.
Line WS is parallel to line KV. Line RT is perpendicular to line KV. Explain the relationship of line RT to line WS. Provide at least one reason to support your answer.
Answer:
RT is perpendicular to WS because when parallel lines are cut by a transversal, the corresponding angles are equal.
Step-by-step explanation:
=
#7 i
Find the surface area of the sphere. Round your answer to the nearest
hundredth.
40 ft
The surface area is about
Previous
Support powered by
square feet.
In the given diagram, the surface area of the given sphere is approximately 5026.55 ft²
Calculating the surface area of a sphereFrom the question, we are to calculate the surface area of the sphere
The surface area of a sphere is given by the formula
Surface area = 4πr²
Where r is the radius of the sphere
From the given information,
Diameter of the sphere = 40 ft
Thus,
Radius of the sphere = 40 ft / 2
Radius of the sphere = 20 ft
Therefore,
Surface area of the sphere = 4 × π × 20²
Surface area of the sphere = 4 × π × 400
Surface area of the sphere = 1600π ft²
Surface area of the sphere = 5026.5482 ft²
Surface area of the sphere ≈ 5026.55 ft²
Hence, the surface area of the sphere is 5026.55 ft²
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Tyson traveled at an average speed of 60 miles per hour for 1.5 hours
and then traveled at an average speed of 70 miles per hour for 2.5
hours. What was the total distance in miles that Tyson traveled during
this time?
A 260.5 mi
B. 420 mi
C.
265 mi
D 257.5 mi
C.
Step-by-step explanation:
To calculate the total distance Tyson traveled, we need to use the formula: distance = speed x time. First, we calculate the distance traveled during the first segment at 60 mph for 1.5 hours: distance = 60 x 1.5 = 90 miles. Then, we calculate the distance traveled during the second segment at 70 mph for 2.5 hours: distance = 70 x 2.5 = 175 miles. Adding these two distances together, we get: 90 + 175 = 265 miles. Therefore, the answer is C, 265 miles.
The nextDouble( ) method of r, a variable of type Random, returns a double in a range of [0,1). Which of these expressions would you use to create a random number in the range of [-3,3)?
a. r.nextDouble( ) * 3.0 - 3.0
b. (r.nextDouble( ) - 0.5) * 6.0
c. r.nextDouble( ) * 6.0 + 3.0
d. r.nextDouble( ) * 6.0 + 0.5
e. (r.nextDouble( ) - 3.0) * 6.0
The correct expression to create a random number in the range of [-3,3) would be option A: r.nextDouble() * 6.0 - 3.0.
Explanation: The nextDouble() method of Random class returns a double in the range of [0,1), which means it can generate any random value between 0 (inclusive) and 1 (exclusive). To create a random number in the range of [-3,3), we need to scale and shift the output of the nextDouble() method.
Option A is the correct expression as it first scales the output by multiplying it by 3.0 (which will give a range of [0,3)) and then shifts it down by subtracting 3.0 (which will give a range of [-3,0)). Therefore, we need to modify the expression to r.nextDouble() * 6.0 - 3.0 to generate a random number in the range of [-3,3).
Option B multiplies the output of nextDouble() by 6.0, which gives a range of [0,6)) and then subtracts 0.5, which shifts the range to [-0.5,5.5). This is not the correct expression to generate a random number in the range of [-3,3).
Option C multiplies the output of nextDouble() by 6.0, which gives a range of [0,6)) and then adds 3.0, which shifts the range to [3,9). This is not the correct expression to generate a random number in the range of [-3,3).
Option D multiplies the output of nextDouble() by 6.0, which gives a range of [0,6)) and then adds 0.5, which shifts the range to [0.5,6.5). This is not the correct expression to generate a random number in the range of [-3,3).
Option E subtracts 3.0 from the output of nextDouble() and then multiplies it by 6.0, which gives a range of [-3,3). However, this expression is not the correct way to scale and shift the output of the nextDouble() method.
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Show that the numbers are all rational by writing each number as a ratio of integers.
320.5492492492...
The number 320.5492492492... is rational and can be expressed as the fraction 1829/333.
To show that the number 320.5492492492... is rational, we can follow the same approach as before and express it as a sum of rational numbers.
Let x = 320.5492492492...
We can separate the integer part of x and the repeating decimal part:
x = 320 + 0.5492492492...
To express the repeating decimal part as a fraction, we can subtract a portion of it from the original number, like this:
1000x - 320000 = 549.2492492...
100000x - 32000000 = 549249.2492492...
Now we can subtract the first equation from the second equation:
99900x = 549249.2492492... - 549.2492492...
This simplifies to:
99900x = 548700
x = 548700/99900
Simplifying the fraction by dividing both numerator and denominator by their greatest common factor, we get:
x = 1829/333
Therefore, the number 320.5492492492... is rational and can be expressed as the fraction 1829/333.
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Suppose that 60 percent of the voters in a particular region support a candidate. Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 4 percentage points of the actual proportion.
The probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 4 percentage points of the actual proportion is 98.6%.
We are given that the population proportion, p, is 0.6, and we want to find the probability that a sample of 1000 voters would yield a sample proportion within 0.04 of p. Let's first find the standard error of the sample proportion:
SE = √(p*(1-p) / n)
where p is the population proportion, 1-p is the proportion of voters who do not support the candidate, and n is the sample size.
Substituting the given values, we get:
SE = √(0.6 * 0.4 / 1000) = 0.01549193338
To find the probability that the sample proportion is within 0.04 of p, we can use the normal distribution and the z-score formula:
z = (sample proportion - p) / SE
where the sample proportion follows a normal distribution with mean p and standard deviation SE.
Substituting the values, we get:
z = (0.64 - 0.6) / 0.01549193338 = 2.590020246
z = (0.56 - 0.6) / 0.01549193338 = -2.590020246
Using a standard normal distribution table or calculator, we can find the area under the curve between z = -2.590020246 and z = 2.590020246 to be approximately 0.986.
Therefore, the probability that a sample of 1000 voters would yield a sample proportion within 0.04 of the actual proportion is approximately 0.986 or 98.6%.
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Audra is climbing a mountain at a constant rate her height at various times are given 11:13- 5211 1:33-5651 1:48-5981 which of the following represents the rate at which she is climbing?
A 40 feet per minute
B 30 feet per minute
C 25 feet per minute
D 22 feet per minute
With Audra climbing a mountain at a constant rate and her height at various times given as 11:13- 5211 1:33-5651 1:48-5981, she is climbing at the unit rate of D. 22 feet per minute.
What is the unit rate?The unit rate is the ratio that compares two values or quantities.
The unit rate is also described as the slope, which is calculated as the quotient between the Rise and the Run or the speed (the quotient between the total distance and the total time).
Time Height
11:13- 5211
1:33- 5651
1:48- 5981
Unit rate (Slope) = Rise/Run
5,981 - 5,651 = 330 feet
1:48 - 1:33 = 15 minutes
330 ÷ 15 = 22 feet per minute
Thus, we can conclude that Audra is climbing the mountain at a rate or speed of Option D. 22 feet per minute.
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In each game of a certain tournament, a contestant either loses 3 points or gains 2 points. If Pat had 100 points at the beginning of the tournament, how many games did Pat play in the tournament
Pat played a total of 11 + 7 = 18 games in the tournament.
Let's denote the number of games Pat lost as L and the number of games Pat won as W.
We are given the following information:
Pat started with 100 points.
In each game, Pat either loses 3 points (L games) or gains 2 points (W games).
We can set up the following equations based on this information:
Total points = Initial points + Gained points - Lost points
Total points = 100 + 2W - 3L
We need to find the total number of games Pat played, which is the sum of games won and lost (W + L).
To solve for W + L, we need to find a relationship between W and L.
We can rearrange the Total points equation to find such a relationship:
2W - 3L = Total points - 100
2W = 3L + (Total points - 100)
Now, we know that both W and L must be integers since Pat can't win or lose a fraction of a game.
As 2W and 3L are both integers, their sum (3L + (Total points - 100)) must be even.
Thus, the total points must be an even number.
We can try different even values for the total points and check if the corresponding W and L values are integers. After trying different values, we find that:
Total points = 122
W = 11
L = 7.
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The radius of Circle A is 4 in. The radius of Circle B is 5 in. greater than the radius of Circle A. The radius of Circle C is 5 in. greater than the radius of Circle B. The radius of Circle D is 1 in. less than the radius of Circle C. What is the area of each circle? How many times greater than the area of Circle A is the area of Circle D?
The area of circle D is 10.56 times greater than the area of the circle A.
Given that, the radius of circles A, B, C and D,
Radius of A = 4 in
Radius of B = 9 in
Radius of C = 14 in
Radius of D = 13 in
Area of the circles = A = πr²
A = 3.14×4²
A = 50.24 in²
B = 3.14×9²
B = 254.34 in²
C = 3.14×14²
C = 615.44 in²
D = 3.14×13
D = 530.66 in²
The area of circle D is 530.66/50.24 = 10.56 times greater than the area of the circle A.
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Create and interpret a 95% confidence interval for each example.
6. Xavier loves to exercise by riding his bike each day. The health data on his cell phone
contains the distances he has traveled for the last year. Xavier found the average of the
past 30 days to be 8.6 miles and a standard deviations 0.2 miles.
The 95% confidence interval for Xavier's average distance traveled is (8.527, 8.673) miles, which means that we are 95% confident that the true population mean of Xavier's daily distance traveled is between 8.527 and 8.673 miles.
To create a 95% confidence interval for Xavier's average distance traveled, we can use the following formula:
[tex]CI = \bar{X} \pm z\times (\sigma /\sqrt{n } )[/tex]
Where:
[tex]\bar{X}[/tex] is the sample mean (8.6 miles)
σ is the population standard deviation (0.2 miles)
n is the sample size (30)
z is the z-score corresponding to the desired confidence level (95% confidence level corresponds to a z-score of 1.96)
Plugging in the values, we get:
CI = 8.6 ± 1.96*(0.2/√30)
CI = 8.6 ± 0.073
Therefore, the 95% confidence interval for Xavier's average distance traveled is (8.527, 8.673) miles.
Interpretation: We are 95% confident that the true population mean of Xavier's daily distance traveled is between 8.527 and 8.673 miles.
This means that if we were to repeat this study many times, we would expect the true population mean to be within this range 95% of the time.
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4.27 Working backwards, one-sided. You are given the following hypotheses: H0 :μ=30
HA :μ>30
We know that the sample standard deviation is 10 and the sample size is 70. For what sample mean would the p-value be equal to 0.05? Assume that all conditions necessary for inference are satisfied.
The population mean is greater than 30.To determine the sample mean that would result in a p-value of 0.05, we need to work backwards from the given significance level.
First, we need to find the test statistic. Since the alternative hypothesis is one-sided (μ>30), we will use a one-sample z-test. The test statistic is calculated as:
z = (xbar - μ) / (s / sqrt(n))
where xbar is the sample mean, μ is the hypothesized population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size.
Since we want the p-value to be equal to 0.05, we need to find the z-score that corresponds to a one-tailed area of 0.05. Using a standard normal distribution table or calculator, we find that this z-score is 1.645.
Substituting this value into the formula for the test statistic, we get:
1.645 = (xbar - 30) / (10 / sqrt(70))
Solving for xbar, we get:
xbar = 30 + 1.645 * (10 / sqrt(70))
xbar = 31.77
Therefore, the sample mean that would result in a p-value of 0.05 is 31.77. This means that if we were to obtain a sample mean of 31.77 or higher, we would reject the null hypothesis at a significance level of 0.05 in favor of the alternative hypothesis that the population mean is greater than 30.
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What is the tenth term?
1) 1, 2, 8, 14, 20
2) 15, 23, 31,
Find the missing term:
3) 4, __, 22,
4) 25, __, 53,
The solution to each of the arithmetic sequence are:
1) a₁₀ = 56
2) a₁₀ = 87
3) missing term is 13
4) missing term is 14
What is the nth term of the arithmetic sequence?The formula for the nth term of an arithmetic sequence is:
aₙ = a + (n - 1)d
where:
a is first term
n is nth term
d is common difference
1) a = 2
d = 6
a₁₀ = 2 + (10 - 1)6
a₁₀ = 2 + 54
a₁₀ = 56
2) a = 15
d = 8
a₁₀ = 15 + (10 - 1)8
a₁₀ = 87
3) The missing term will be gotten by finding the common difference.
d = (22 - 4)/2
d = 18/2
d = 9
missing term = 4 + 9 = 13
4) The missing term will be gotten by finding the common difference.
d = (53 - 25)/2
d = 28/2
d = 14
missing term = 4 + 9 = 14
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\frac{\left(-6x^{2}y^{3}\right)^{4}}{8x^{9}y^{7}\cdot3xy^{5}}
Answer:
54/x²-----------------------
Simplify the expression in below steps:
[tex]\cfrac{\left(-6x^{2}y^{3}\right)^{4}}{8x^{9}y^{7}\cdot3xy^{5}}=[/tex] Power of power and product of exponents rules
[tex]\cfrac{\left6^4x^{2\cdot4}y^{3\cdot4}\right}{(8\cdot3)x^{9+1}y^{5+7}}=[/tex] Multiply or add up powers
[tex]\cfrac{\left2^43^4x^8y^{12}\right}{(2^3\cdot3)x^{10}y^{12}}=[/tex] Subtract powers or cancel same terms
[tex]\cfrac{\left2\cdot3^3\right}{x^2}}=[/tex] Simplify
[tex]54/x^2[/tex] Answer
Help my sister, please answer fast and whoever does first, GETS BRAINLIEST
Answer: The answer is D
Step-by-step explanation:
Brainliest Please! Good luck to your sis!
Answer: 9 inches is correct
Step-by-step explanation: 1 and half times 6 = 9 so your answer was correct.
Hope this helps!
The equation of circle D is (x + 2)2 + y² = 32.
Select all the points that lie on circle D.
□ (-6,-4)
□ (-2,16)
□ (-4,6)
□ (0,14)
□ (2,4)
The equation of circle D is (x + 2)2 + y² = 32 then the points (-6,-4) and (-4,6) lie on circle D
The equation of a circle with center (h,k) and radius r is (x - h)² + (y - k)² = r².
This is called the standard form of the equation of a circle.
In the given equation, (x + 2)² + y² = 32, we can see that the center of the circle is (-2, 0) and the radius is √32 = 4√2.
To determine which points lie on the circle, we substitute the x and y coordinates of each point into the equation and check if the equation is true.
If it is true, then the point lies on the circle.
Let us check if (-6, -4) lies on the circle, we substitute x = -6 and y = -4 into the equation:
(-6 + 2)² + (-4)² = 32
(-4)² + (-4)² = 32
16 + 16 = 32
32 = 32
Since the equation is true, (-6, -4) lies on the circle.
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A fruit stand owner is putting together orange baskets that contain eight oranges each. The owner begins with 185 oranges. How many complete baskets can be made?
The fruit stand owner can make 23 complete orange baskets.
Division is a mathematical operation which involves the sharing of an amount into equal-sized groups. For example, “12 divided by 4” means “12 shared into 4 equal groups”, which would be 3.
To determine the number of complete orange baskets that can be made, divide the total number of oranges by the number of oranges per basket.
Total oranges: 185
Oranges per basket: 8
Divide 185 by 8 to find the number of complete baskets:
185 ÷ 8 = 23
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Which equation represents the linear function in the table?
Answer: B. y = 3x - 5
Step-by-step explanation:
First ,we know Option C will not be an option because of the y-intercept (the point at which the line intersects the y-axis) is -5. This is shown by the point (0, -5). Option C shows it as 1.
We will substitute a point into the given equations and see if the simplified version remains true.
✗ A ➜ y = -3x - 5
➜ -2 = -3(1) - 5
➜ -2 ≠ -8
✓ B ➜ y = 3x - 5
➜ -2 = 3(1) - 5
➜ -2 = -2
✗ D ➜ y = -x - 5
➜ -2 = -1 - 5
➜ -2 ≠ -6
Using this method of substitution, we can see the answer is B.
Marilyn created this box and whiskers plot to represent the number of inches of snow that fell during the winter in several different cities. (a) What was the least amount of snowfall in any of the cities? Show your work
(b) What is the median amount of snowfall? Show your work
(c) In which quarter is the data most concentrated? Explain how you know.
a. the smallest value is approximately 5 inches. b. the median is approximately 12 inches. c. the data is more spread out in those ranges.
(a) To find the least amount of snowfall, we look at the smallest value on the box and whisker plot. From the plot, we can see that the smallest value is approximately 5 inches.
(b) To find the median amount of snowfall, we look for the line that divides the box in half. From the plot, we can see that the median is approximately 12 inches.
(c) The data is most concentrated in the second quarter. We can see this because the box is the largest in the second quarter, indicating that the data is most tightly clustered in that range. The first and fourth quarters have smaller boxes, indicating that the data is more spread out in those ranges.
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Callie uses leather cord to make necklace she has a piece of leather cord that gas a lengh of 4 yards each necklace will have a lengh of 28 inches how many necklace can callie make
Since Callie cannot make a fraction of a necklace, she can make a maximum of 5 necklaces from the given length of leather cord.
To determine the number of necklaces Callie can make from the given length of leather cord, we need to convert the measurements to a consistent unit.
Given:
Length of leather cord = 4 yards
Length of each necklace = 28 inches
First, let's convert the length of the leather cord from yards to inches:
1 yard = 36 inches (since there are 3 feet in a yard and 1 foot = 12 inches)
4 yards = 4 * 36 = 144 inches
Now we can calculate the number of necklaces:
Number of necklaces = Length of leather cord / Length of each necklace
Number of necklaces = 144 inches / 28 inches ≈ 5.143
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What's the calculation for an F ratio?
The requried to calculate an F ratio, we need to perform an analysis of variance (ANOVA) test.
To calculate an F ratio, we need to perform an analysis of variance (ANOVA) test. The F ratio is the ratio of two variances, and it is calculated by dividing the mean square of the between-group variability by the mean square of the within-group variability.
The formula for the F ratio is:
F = MSB / MSW
Where MSB is the mean square of the between-group variability and MSW is the mean square of the within-group variability.
The F ratio is used to test the null hypothesis that the means of the groups are equal. If the F ratio is greater than the critical value for a given level of significance (based on the degrees of freedom), we reject the null hypothesis and conclude that at least one group's mean is different from the others.
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Bob makes a scale drawing of a statue using the scale 1 cm: 5 ft.
His drawing measures 16 cm. Kia makes a scale drawing of the
same statue using the scale 1 cm: 8 ft. How many centimeters tall
is the statue in Kia's drawing?
1. 40 cm
2. 128 cm
3. 10 cm
4. 80 cm
Given circle E with diameter CD and radius EA. AB is tangent to E at A. If AD=10 and CD=26, solve for AC. Round your answer to the nearest tenth if necessary. If the answer cannot be determined, click "Cannot be determined."
The answer to AC of the circle geometry with tangent is 26.
Solving the Circle GeometrySince CD is the diameter of the circle, then triangle ADC is a right-angle triangle with right angle at D.
Using Pythagorean theorem to find AC:
AC² = AD² + DC²
AC² = 10² + 26²
AC² = 676
AC = √676
AC = 26
Therefore, AC = 26.
Pythagorean Theorem is a fundamental theorem in Euclidean geometry that relates to the three sides of a right triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In other words:
a² + b² = c²
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Anissa said that distance, d, could be an either an independent or dependent variable. Explain Anissa's statement.
Anissa's statement suggests that the variable "distance," denoted as "d," can be considered both an independent variable and a dependent variable, depending on the context or the specific relationship being examined.
Independent Variable: In certain situations or experiments, the distance can be treated as an independent variable. This means that the distance is manipulated or controlled by the researcher or experimenter, and it is used to determine or study the effect it has on other variables. In this case, the distance would be considered the cause or predictor variable, and its value is intentionally set or changed to observe how it influences the dependent variable(s).
Example: In a study on the impact of distance on running performance, researchers may vary the distance of a race (e.g., 5 km, 10 km, or 15 km) and measure the effect it has on the runners' performance times. Here, distance would be the independent variable, as it is being deliberately altered to observe its influence on the dependent variable (performance time).
Dependent Variable: Conversely, in other scenarios, the distance can be considered a dependent variable. This means that the distance is the outcome or result of other factors or variables that are being studied or manipulated. In this case, the distance is observed or measured as the response to changes in other variables.
Example: Suppose researchers are investigating the relationship between the time spent studying and the distance walked to school for a group of students. The researchers measure the students' study time and observe the corresponding distance they walk to school. In this context, the distance would be the dependent variable, as it is influenced by the independent variable (study time) and is used to assess the relationship between the two.
In summary, Anissa's statement indicates that the variable "distance" can be considered either an independent variable or a dependent variable, depending on the specific context and the relationship being examined in a given study or experiment.
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In a research study conducted to determine if arrests were related to the socioeconomic class of the offender, the chi square critical score was 9.488 and the chi square test statistic was 12.2. We can conclude that
We can conclude that the socioeconomic class of the offender is related to the likelihood of arrests.
Based on the information provided, we can conclude that there is a significant relationship between arrests and the socioeconomic class of the offender.
Identify the chi-square critical score: 9.488
Identify the chi-square test statistic: 12.2
Compare the test statistic to the critical score:
If the test statistic (12.2) is greater than the critical score (9.488), then there is a significant relationship between the variables.
In this case, 12.2 > 9.488, so there is a significant relationship between arrests and the socioeconomic class of the offender.
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