Answers
Answer:
\(t = \frac{3k+6}{k-2}\)
Step-by-step explanation:
Step 1: Multiply both sides by t - 3.
\(kt - 3k = 2t + 6\)Step 2: Add -2t to both sides.
\(kt - 3k -2t = 2t + 6 -2t\) \(kt-3k -2t = 6\)Step 3: Add 3k to both sides.
\(kt-3k-2t+3k=6+3k\) \(kt - 2t = 3k + 6\)Step 4: Factor our the variable.
\(t(k-2)=3k+6\)Step 5: Divide both sides by (k - 2).
\(\frac{t(k-2)}{(k-2)} = \frac{3k+6}{k-2}\) \(t = \frac{3k+6}{k-2}\)Related Questions
What expression -5+(-5r)+10
Answers
0
a) What is a fraction between 25% and
50%? How do you know?
Answers
Answer:
30/100
Step-by-step explanation:
25%= 25/100
50%= 50/100
3/100 is in the middle of the two fractions. So one of the possible answer can be 30/100 or 30%
Answer:
\(\sf \dfrac{2}{5}\)
Step-by-step explanation:
"per cent" means "per hundred". Therefore, to change a percent to a fraction, remove the % sign and place the number as the numerator of a fraction with 100 as the denominator.
\(\sf 25\%=\dfrac{25}{100}\)
\(\sf 50\%=\dfrac{50}{100}\)
Any percent between 25% and 50% can be written as a fraction in the same way.
Choose a number between 25 and 50, place it as the numerator of a fraction with 100 as the denominator:
\(\sf \dfrac{40}{100}\)
Now reduce the fraction to its simplest term by dividing the numerator and denominator by the greatest common factor (GCF):
\(\sf \dfrac{40 \div 20}{100\div 20}=\dfrac{2}{5}\)
Therefore, the fraction ²/₅ is between 25% and 50% as it is equivalent to 40%.
Out of 500 milliliters of hydrochloric acid, 237 milliliters were left after an experiment that used the acid. How much acid was used in the experiment? A. 156 ml B. 189 ml C. 263 ml D. 307 ml
Answers
Answer:
c. 263 ml
Step-by-step explanation:
have a nice day
cya
Please answer please I’ll give you brainless. It’s important. Please
Answers
I believe it is BCA
Step-by-step explanation
what is this −n+(−4)−(−4n)+6
Answers
Answer:
3n + 2
Step-by-step explanation:
\(−n+(−4)−(−4n)+6\)
Open the parentheses
\( - n - 4 + 4n + 6 \\ \)
Add similar elements
\( - n + 4n - 4 + 6 \\ 3n + 2 \\ \)
Answer:
\( - n + 6\)
Step-by-step explanation:
\( - n + ( - 4) - ( - 4n) + 6 = - n - 4n + 4n + 6 = - 5n + 4n + 6 = - n + 6\)
40 points please help
Answers
The athlete that has the shortest training ride is athlete A.
The athlete that has the shorter range is Athlete B.
The athlete that has the greater median is Athlete B.
The athlete that has the greater IQR is athlete A.
What are the summary statistics?A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers. The first whisker represents the minimum number and the second whisker represents the maximum number. The difference between the whiskers is known as range.
Range of Athlete A = 36 - 13 = 13
Range of Athlete B = 30 - 19 = 11
Training ride of Athlete A = 16
Training ride of Athlete B = 21
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
Median of Athlete A = 20
Median of Athlete B = 25
IQR of Athlete A = 30 - 16 = 14
IQR of Athlete B = 28 - 21 = 7
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when a sample statistic is measured with nominal data, the only appropriate proportion measure is .
Answers
when a sample statistic is measured with nominal data, the only appropriate proportion measure is sample percentage.
What is the percentage?
It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol %.
when a sample statistic is measured with nominal data, the only appropriate proportion measure is sample percentage.
A small portion of the population is surveyed to produce sample percentages. A sample percentage is what you get when you calculate a percentage from a small portion of the population.
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14. assuming p-value is 0.03, what is the conclusion of testing at the 0.10 level of significance whether the fruit drink distributor should sell this drink? a. based on the sample data, there isn't sufficient evidence to conclude that the average rating is more than 4.75. b. based on the sample data, there isn't sufficient evidence to conclude that the average rating is no more than 4.75. c. based on the sample data, there is sufficient evidence to conclude that the average rating is no more than 4.75. d. based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75. e. none of the above.
Answers
Based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75, thus the correct option is (d). The question is related to hypothesis testing in statistics.
If the p-value is 0.03 and the level of significance is 0.10, we reject the null hypothesis if the p-value is less than 0.10.
Since the null hypothesis is not specified in the question, we assume that it is that the average rating of the fruit drink is no more than 4.75.
Therefore, if the p-value is less than 0.10, we would reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the average rating of the fruit drink is more than 4.75.
Since the p-value, in this case, is 0.03, which is less than the level of significance of 0.10, we would reject the null hypothesis and conclude that based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75.
Therefore, the correct answer is (d) based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75.
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Research Case 4-5 (Static) FASB codification: locate and extract relevant information and cite authoritative support for a financial reporting issue; restructuring costs; exit or disposal cost obligations [LO4-2, 4-3) Access the FASB Accounting Standards Codification at the Fasa website www.asb.org). Determine each of the following: Research Case 4-5 (Static) FASB codification; locate and extract relevant information and cite authoritative support for a financial reporting issue; restructuring costs; exit or disposal cost obligations (Part 1) Pint Hences Required: The tople number (Topic XXX) that addresses exit or disposal cost obligations: Yopilo 2. The specific eight-digit codification citation (XXX-XXXXX) that addresses the initial measurement of these obligations Tople Paragraph Salced 3. The amount for which these obligations and related costs are measured Abity for a cod with an out or disposal dictivity issued att Book Print erences 4. The specific eight-digit codification citation (XXX-XX-XX-X) that describes the disclosure requirements in the notes to the financial statements for exit or disposal obligations Tople Subtopic Section Paragraph
Answers
According to ASC 420 Exit or Disposal Cost Obligations, exit or disposal cost obligations are liabilities that arise from one-time termination benefits provided to employees, costs associated with closing a facility, and other expenses incurred as a result of an exit or disposal activity.
These obligations are recognized and measured based on the principles of other applicable GAAP.
The relevant topic number for exit or disposal cost obligations is Topic 420. The specific eight-digit codification citation (XXX-XXXXX) that addresses the initial measurement of these obligations is 420-10-25-1. This paragraph notes that the fair value of the liability at the initial recognition date is the amount for which these obligations and related costs are measured.
The amount for which these obligations and related costs are measured is determined based on the fair value of the liability at the initial recognition date. This amount includes the estimated costs associated with employee severance arrangements, lease termination fees, and other direct costs associated with the exit or disposal activity.
The specific eight-digit codification citation (XXX-XX-XX-X) that describes the disclosure requirements in the notes to the financial statements for exit or disposal obligations is 420-10-50-2. This paragraph requires entities to disclose information about the nature and scope of the exit or disposal activity, including its timing, the expected completion date, the associated costs, and any significant uncertainties or risks that could affect the outcome or timing of the activity.
In summary, under ASC 420, exit or disposal cost obligations are recognized and measured based on their fair value at the initial recognition date. Entities are required to disclose information about the nature and scope of the exit or disposal activity, as well as any significant uncertainties or risks that could affect the outcome or timing of the activity.
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Solve the recurrence relations below. Fill in the blanks for the closed form expression and rate of growth. T(n)=
⎩
⎨
⎧
1,
1,
T(n−2)+2,
n<2
n=2
n>2
Provide final answers only in simplified form. Closed form expression of T(n) : Rate of Growth: O()
Answers
Given the recurrence relation as follows:T(n)= {1, n < 2;1, n = 2;T(n-2) + 2, n > 2}The closed form expression of T(n) is as follows:If n is odd, then let n= 2k+1 for some k ∈ ℕ0,T(n) = T(2k+1) = T(2k-1 + 2) = T(2k-1) + 2 = T(2(k-1)+1) + 2 = T(2(k-1)-1 + 2) + 2 = T(2(k-1)-1) + 4 = T(2(k-2)+1) + 4 = … = 2k-1 + 2(k-1) = 3k -1.
If n is even, then let n = 2k for some k ∈ ℕ0,T(n) = T(2k) = T(2k-2 + 2) = T(2k-2) + 2 = T(2(k-1)) + 2 = T(2(k-1)-2 + 2) + 2 = T(2(k-1)-2) + 4 = T(2(k-2)) + 4 = … = 2k + (k-1)2 = 3k - 2.The rate of growth of T(n) is O(n).Therefore, the final answers are as follows:Closed form expression of T(n): T(n)= {3k-1, if n is odd;3k-2, if n is even.}Rate of growth: O(n).
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Charles has four songs on a playlist. Each song is by a different artist. The artists are Cardi B, Post Malone, Taylor Swift, and BTS. He programs his player to play the songs in a random order, without repetition. What is the probability that the first song is by Cardi B and the second song is by Taylor Swift
Answers
The probability that the first song is by Cardi B and the second song is by Taylor Swift is 1/24.
To calculate the probability of the first song being by Cardi B and the second song being by Taylor Swift, we need to consider the total number of possible outcomes and the number of favorable outcomes.
There are four songs in total, and we want to determine the probability that the first song is by Cardi B and the second song is by Taylor Swift. Since the order matters (the first song and then the second song), we can use the concept of permutations.
The total number of possible outcomes is the number of ways to arrange four songs, which is 4!.
The number of favorable outcomes is the number of ways to arrange the songs such that the first song is by Cardi B and the second song is by Taylor Swift. Since each song can only be played once, there are 1 way to choose Cardi B as the first song and 1 way to choose Taylor Swift as the second song.
The probability can be calculated as:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 1 / 4!
Simplifying:
4! = 4 x 3 x 2 x 1 = 24
Probability = 1 / 24
The probability that the first song is by Cardi B and the second song is by Taylor Swift is 1/24.
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Find the area of this shape.
4 cm
2 cm
4 cm
4 cm
-
1
5.75 cm
1
1
The area of the shape is __
square centimeters.
Answers
Answer:
shape AREA= 35cm^2
Step-by-step explanation:
you should know that this shape is a combination of triangle and trapezoid. therefore you have to find the area of each shape and add them.
A=h/2(b1 + b2) for trapezoid
A=2/2((4+4)+4)
A=1*12
A=12cm^2
A=bh/2. for TRIANGLE
A=1/2((4+4)*5.75)
A=1/2(46)
A=23cm^2
shape AREA= triangle AREA + trapezoid AREA
shape AREA=12cm^2 + 23cm^2
shape AREA= 35cm^2
The volume of a cylinder is 60 cubic centimeters. What is the number of cubic centimeters in the volume of the sphere it circumscribes
Answers
Call the radius of the cylinder and sphere, r And the height of the cylinder = 2r
How to Calculate Volume in Cubic Centimeters?Calculating volume is just another way of saying that you're measuring the amount of space inside a three-dimensional object. You can use standardized formulas for calculating the volume of shapes like cubes, cylinders and spheres, as long as you know their basic measurements.So60 = pi * r^2 * 2r30 = pi * r^330/pi = r^3[30/pi]^1/3 = rSo...the volume of the sphere is(4/3)pi [ (30/pi)^1/3 ]^3 =(4/3) pi * 30/pi =40 cm^3A cubic centimetre (or cubic centimeter in US English) (SI unit symbol: cm3; non-SI abbreviations: cc and ccm) is a commonly used unit of volume that corresponds to the volume of a cube that measures 1 cm × 1 cm × 1 cm. One cubic centimetre corresponds to a volume of one millilitre.How to Work out Volume with Cubic Centimetres. If a container was filled with water and it had a length of 20 cm, a height of 5 cm and a depth of 4 cm to work out the volume of water you would need to multiply all 3 numbers together. 20 cm x 5 cm x 4 cm = 400 cm³To learn more about Volume in Cubic Centimeters refers to:
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a cube measuring 1 cm on each side, what is the volume, if the cube was dropped into 28ml of water. what would the
Answers
Answer:
29 ml
Step-by-step explanation:
Vcube = 1cm×1cm×1cm = 1 cm³
1 cm³ = 1 ml
If this cube is dropped into a 28ml of water the new reading will be 29 ml.
hope this helped :)
I am multiple of 70 I am between 300 and 500 I am more than a multiple of 100 who am I
Answers
Answer:
The answer is 420.
Step-by-step explanation:
The multiple of 70 lies between 300-500 has three possibilities such as 350,420,490
Answer:
420 hope this helps
Step-by-step explanation:
Worth 100 points :)
Add 3/4+(−2 1/2) using the number line.
Select the location on the number line to plot the sum.
Answers
Answer:
-1 1/4. Because a negative and a positive make a negative
Step-by-step explanation:
Find the solution to this equation.
x + 4 = 2x + 8
2
A
All real numbers
B.
No solution
Answers
Answer:
A. All real numbers.
Step-by-step explanation:
\(x + 4 = \frac{2x + 8}{2} \: \: multipling \: both \: sides \: by \: 2 \\ 2(x + 4) = 2x + 8 \\ 2x + 8 = 2x + 8\)
When you end up with a true statement like this, it means that the solution to the equation is “all real numbers”. Any value for x that you can think of will make this equation true.
Do the integral from (-2,2) of the function by Trapezoidal Rule
in Matlab.
1/((25+x^2))^3/2
Answers
Here's how you can use the Trapezoidal Rule to approximate the integral of the function \(f(x) = \frac{1}{{(25+x^2)}^{\frac{3}{2}}}\) from -2 to 2 in MATLAB:
```matlab
a = -2; % Lower limit
b = 2; % Upper limit
n = 1000; % Number of subintervals (increase for higher accuracy)
h = (b - a) / n; % Step size
x = a:h:b; % Generate evenly spaced x values
y = 1 ./ (25 + x.^2).^1.5; % Evaluate the function at x
approximation = h * (sum(y) - (y(1) + y(end)) / 2); % Trapezoidal Rule approximation
fprintf('Approximation: %.6f\n', approximation);
```
1. We define the lower limit `a` as -2, the upper limit `b` as 2, and the number of subintervals `n` as 1000 (you can adjust `n` for higher accuracy).
2. We calculate the step size `h` by dividing the range (`b - a`) by the number of subintervals (`n`).
3. We generate an array `x` of evenly spaced values from `a` to `b` using the step size `h`.
4. We evaluate the function `f(x)` at each point in `x` and store the results in the array `y`.
5. Finally, we use the Trapezoidal Rule formula to approximate the integral by summing the values in `y` and adjusting for the endpoints, multiplying by the step size `h`.
The Trapezoidal Rule approximation for the integral of the function \(f(x) = \frac{1}{{(25+x^2)}^{\frac{3}{2}}}\) from -2 to 2 is the value calculated using the MATLAB code above.
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Find the ellipse centered at the origin that runs through the points (1, 2), (2, 2), and (3, 1). write your equation in the form ax2 bxy cy2 = 1.
Answers
The ellipses centered at the origin that runs through the points (1, 2), (2, 2), and (3, 1) is mathematically given as
-0.3523x^2 0.5284xy 15.9268y^2 = 1.
Find the ellipse centered at the origin that runs through the points (1, 2), (2, 2), and (3, 1).?Generally, the equation for three points is mathematically given as
a+2b+4c=1.....1 for the variable (1, 2)
4a+4b+4c=1.....2 for the variable (2, 2)
9a+3b+c=1.....3 for the variable (3, 1)
Step 1
Here we solve equations 1 and 2 simultaneously to find the value of b
Therefore
equ 2-equ1
3a+2b=0
b=-1.5a....4
Step 2
We solve equations 1 and 3 simultaneously to find the value of c
Where
9*equ1-equ3 gives
-15b-35c=-8
c=8-15b
subbing equ 4 we have
c=8+22.5a ....5
Step 3
Put values of b and c in equation 2, and we have
4a-6a+32+90a=1
a=-31/88
a=-0.3523
The value of b will be
b=-1.5*a
b=0.5284
The value of b will be
c=8-22.5*a
c=15.9268
Step 4
In conclusion, the equation is given as
By substituting the values of a b and c into the general formula we have
-0.3523x^2 0.5284xy 15.9268y^2 = 1.
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What is the interpretation for the slope of the linear regression prediction equation?
Answers
The interpretation for the slope of the linear regression prediction equation is change in y with a unit change in x.
The linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables.
A slope of a line is the change in y coordinate with respect to the change in x coordinate.
Consider the slope of the line as m
m= Change in y coordinate / Change in x coordinate
When change in x coordinate is 1 unit
Then,
m= Change in y coordinate
If the change in x is 1 unit, then slope of the line will change depends on change in y coordinate
Hence, The interpretation for the slope of the linear regression prediction equation is change in y with a unit change in x.
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hello pleASE I need helppppppp
Answers
I can help you with that problem i just did that on my own.
Angie packed same-size cubes into a rectangular prism. Image shows a base of cubes 3 units long, 2 units wide, and with a column of cubes 1 cube wide and 7 cubes tall. Which expression could be used to find the number of cubes that would fill the prism? A. ( 3 + 2 ) + 7 B. ( 3 × 2 ) × 6 C. ( 3 × 2 ) + 7 D. ( 3 × 2 ) × 7
Answers
Answer:
I believe it's C. (3 x 2) + 7!
The expression that could be used to find the number of cubes that would fill the prism will be (3 x 2) x 7. The correct option is D.
What is a rectangular prism?A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. It also goes by the name cuboid. Six faces, each with a rectangle shape and twelve edges, make up a rectangular prism. It is referred to as a prism because of the length of its cross-section.
The rectangular prism has a base of cubes that is 3 units long and 2 units wide, which means it has an area of 3 x 2 = 6 square units.
The prism is also 7 cubes tall. To find the total number of cubes in the rectangular prism, we need to multiply the area of the base by the height of the prism. Therefore, the expression that could be used to find the number of cubes that would fill the prism is:
(3 x 2) x 7 = 6 x 7 = 42
So the answer is D. (3 x 2) x 7.
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The formula for the area of a regular polygon is uppercase A = one-half a p. What is the equation solved for a?
Answers
Answer:
D (A=24/d)
Step-by-step explanation:
Answer:
\(a=\frac{2A}{p}\)
Step-by-step explanation:
\(A=\frac{1}{2}ap\)
To get rid of the fraction on the right, multiply both sides by 2.
\(2A=ap\)
To separate a from p, notice they are "connected" by multiplication. Divide both sides of the equation by p.
\(\frac{2A}{p}=\frac{ap}{p}\\\frac{2A}{p}=a\)
You want to know the approximate height of a tall oak tree. You place a mirror on the ground and stand where you can see the top of the tree in the mirror. How tall is the tree? The mirror is 24 feet from the base of the tree. You are 36 inches from the mirror and your eyes are 5 feet above the ground. Round your answer to the nearest tenth
Answers
The approximate height of the tall oak tree is 60.0 feet.
To find the height of the tree, follow these steps:
1. Convert the distance between you and the mirror from inches to feet: 36 inches = 3 feet.
2. Create a proportion using similar triangles, where the height of the tree (h) divided by the distance from the tree to the mirror (24 feet) equals your eye height (5 feet) divided by the distance from your eyes to the mirror (3 feet).
3. Set up the proportion: h / 24 = 5 / 3.
4. Solve for h: h = (5 / 3) * 24.
5. Calculate h: h = 40 feet (height of tree above your eye level).
6. Add your eye height (5 feet) to the height of the tree above your eye level: 40 + 5 = 60 feet.
7. Round the answer to the nearest tenth: 60.0 feet.
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Unit:transformations homework 5 identifying transformations
Answers
The transformation given as A(-8,7) → A'(-8,-7) represents a reflection over x-axis .
In the reflection of the point (x,y) over x-axis transformation ,the x-coordinate of each point remains the same, but the y-coordinate is negated (changes sign).
Let's consider the coordinates of point A that is (-8, 7).
The transformation takes this point to A' (-8, -7).
We can see that the x-coordinate of the point remains the same which is -8. but , the y-coordinate changes from 7 to -7.
We know that in a reflection over the x-axis, the x-coordinate remains the same while the y-coordinate changes sign.
Therefore , the transformation that takes A to A' is a reflection over the x-axis.
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The given question is incomplete , the complete question is
Identify the Transformation given as A(-8,7) → A'(-8,-7)?
An angle in a rectangular coordinate system is in standard position if its vertex is at the_______.
Answers
An angle in a rectangular coordinate system is in standard position if its vertex is at the origin of the plane, the initial side of the angle is on the positive x-axis, and the terminal side of the angle is in one of the four quadrants. The angle is measured in a counterclockwise direction from the positive x-axis and is considered positive if it lies in the counterclockwise direction and negative if it lies in the clockwise direction.
The position of an angle is measured from the reference line called the initial side, which is the positive x-axis, and it ends at the terminal side, which is the side where the angle is located. An angle in a rectangular coordinate system is in a standard position if its vertex is at the origin of the plane. An angle is said to be in a standard position if its vertex is located at the origin of the coordinate system.
To summarize, an angle in a rectangular coordinate system is in standard position if its vertex is at the origin of the plane, the initial side of the angle is on the positive x-axis, and the terminal side of the angle is in one of the four quadrants. The position of an angle is measured from the reference line called the initial side, which is the positive x-axis, and it ends at the terminal side, which is the side where the angle is located.
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The NWBC found that 16.5% of women-owned businesses did not provide any employee benefits. What sample size could be 99% confident that the estimated (sample) proportion is within 6 percentage points of the true population proportion?
Answers
A sample size of 329 would be required to be 99% confident that the estimated proportion of women-owned businesses not providing employee benefits is within 6 percentage points of the true population proportion.
To calculate the required sample size, we can use the formula:
n = (\(z^2\) * p * q) /\(e^2\)
where n is the sample size, z is the z-score corresponding to the desired level of confidence (in this case, 2.576 for 99% confidence), p is the estimated population proportion (0.165, based on the NWBC's finding), q is 1-p, and e is the maximum error we want to tolerate (in this case, 0.06 or 6 percentage points).
Substituting the values, we get:
n = (2.576^2 * 0.165 * 0.835) / \(0.06^2\)
Solving for n, we get:
n ≈ 329
Therefore, a sample size of 329 would be required to be 99% confident that the estimated proportion of women-owned businesses not providing employee benefits is within 6 percentage points of the true population proportion. Note that this assumes a simple random sample and that the population size is much larger than the sample size, so the finite population correction is not needed.
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The free throw fine in basketball is 4.57 m(15 ft) from the basket, which is 3.05 m (10 ft ) above the floor. A player standing on the free throw line throws the ball with an hitial speed of 7.50 m/5, releasing it at a height of 2.44 m above the floor. At what angle above the horizontal must the ball be thrown to exactly hit the basket? Nete that most players will use a large initial angle rather than a flat shot because it aliows for a larger margin of error. X above the horisontal
Answers
The equation involves trigonometric functions, it will require numerical methods or software to obtain the exact value of θ.
To determine the angle above the horizontal at which the ball must be thrown to hit the basket, we can analyze the projectile motion of the ball.
Given:
Initial speed (v₀) = 7.50 m/s
Initial height (h) = 2.44 m
Horizontal distance to the basket (x) = 4.57 m
Vertical distance to the basket (y) = 3.05 m
We can break down the motion into horizontal and vertical components. The time it takes for the ball to reach the basket is the same for both components.
1. Horizontal Component:
The horizontal component of motion is unaffected by gravity. We can use the formula:
x = v₀ * t * cosθ
where θ is the angle above the horizontal.
2. Vertical Component:
The vertical component of motion is affected by gravity. We can use the formula:
y = h + v₀ * t * sinθ - (1/2) * g * t²
where g is the acceleration due to gravity (approximately 9.8 m/s²).
We can solve these equations simultaneously to find the angle θ. Rearranging the equations:
x = v₀ * t * cosθ
t = x / (v₀ * cosθ)
y = h + v₀ * t * sinθ - (1/2) * g * t²
Substituting the expression for t:
y = h + (v₀ * x * sinθ) / (v₀ * cosθ) - (1/2) * g * (x² / (v₀² * cos²θ))
Simplifying:
y = h + (x * tanθ) - (1/2) * g * (x² / (v₀² * cos²θ))
Rearranging and substituting the given values:
0 = 3.05 - 4.57 * tanθ - (1/2) * 9.8 * (4.57² / (7.50² * cos²θ))
Solving this equation for θ will give us the angle above the horizontal at which the ball should be thrown to hit the basket. Since the equation involves trigonometric functions, it will require numerical methods or software to obtain the exact value of θ.
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14. Suppose a math class contains 35 students, 17 females (five of whom speak French) and 18 males (three of whom speak French). Compute the probability that a randomly selected student speaks French, given that the student is male.
Answers
The formula to calculate the conditional probability of A given B is given to be:
\(P(A|B)=\frac{P(A\cap B)}{P(B)}\)If French is represented by F, and males by M, the formula to calculate the probability of a student speaking French given they are male is given to be:
\(P(F|M)=\frac{P(F\cap M)}{P(M)}\)The probability formula is given to be:
\(P(A)=\frac{n(A)}{n(T)}\)Therefore, we have:
\(\begin{gathered} P(F\cap M)=\frac{n(F\cap M)}{n(Students)} \\ n(F\cap M)=students\text{ that speak french and are male}=3 \\ n(Students)=35 \\ \therefore \\ P(F\cap M)=\frac{3}{35} \end{gathered}\)and
\(P(M)=\frac{18}{35}\)Therefore, the conditional probability is:
\(\begin{gathered} P(F|M)=\frac{\frac{3}{35}}{\frac{18}{35}}=\frac{3}{35}\times\frac{35}{18} \\ P(F|M)=\frac{3}{18}=\frac{1}{6}=0.167 \end{gathered}\)The probability is 0.167 or 1/6
Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. (2 points)log2 (x^9 y^5/8)
Answers
We have the following:
as a sum
\(\log _2\frac{x^9y^5}{8}=\log _2x^9+\log _2y^5-\log _28=9\log _2x^{}+5\log _2y^{}-\log _28\)The answer is the option b