Answer:
-1.13 m/s
Step-by-step explanation:
Parameters given:
Mass of first footballer, M = 92 kg
Initial velocity of first footballer, U = 6.5 m/s (taking North to be the +ve y axis)
Mass of second footballer, m = 85 kg
Initial velocity of second footballer, u = -6.0 m/s (taking South to be the -ve y axis)
Final velocity of first footballer, V = 2.0 m/s
We need to find the final velocity of the second football (v)
Applying the principle of conservation of momentum, we have that, in a system:
Total Initial Momentum = Total Final Momentum
(M * U) + (m * u) = (M * V) + (m * v)
(92 * 6.5) + (85 * -6) = (92 * 2) + (85 * v)
598 - 510 = 184 + 85v
88 = 184 + 85v
88 - 184 = 85v
-96 = 85v
=> v = -96 / 85
v = -1.13 m/s
The final velocity of the 85 kg player is -1.13 m/s i.e 1.13 m/s South
Final answer:
To find the unknown velocity of the 85.0 kg football player after the collision, we use the conservation of momentum, setting up an equation based on the initial and final momenta of both players and solving for the unknown velocity.
Explanation:
The question concerns the topic of conservation of momentum during a collision between two football players, which falls under the category of Physics. To solve for the velocity of the 85.0 kg football player after the collision, we can use the principle that the total momentum before the collision is equal to the total momentum after the collision in an isolated system.
The total momentum before the collision can be calculated as follows:
Momentum of the 92.0 kg player = mass × velocity = 92.0 kg × 6.50 m/s (North).
Momentum of the 85.0 kg player = mass × velocity = 85.0 kg × 6.00 m/s (South).
Since they are moving in opposite directions, we assign a positive direction (e.g., north) as positive momentum and the opposite direction (south) as negative momentum.
The total momentum after the collision consists of:
Momentum of the 92.0 kg player = 92.0 kg × 2.00 m/s (North).
Momentum of the 85.0 kg player = 85.0 kg × v (where v is the unknown velocity).
By applying the conservation of momentum, we can write the equation:
(92.0 kg × 6.50 m/s) + (85.0 kg × -6.00 m/s) = (92.0 kg × 2.00 m/s) + (85.0 kg × v).
Solving for v gives:
v = [(92.0 kg × 6.50 m/s) - (92.0 kg × 2.00 m/s) - (85.0 kg × -6.00 m/s)] / 85.0 kg.
Calculate the value to find the final velocity of the 85.0 kg player.
v = 10.87 m/s
What is the yellow structure and what role does it play in a cell?
what is the probability of tossing at least 1 tail of you toss 3 coins at once
Explanation: Probability of NOT getting a tail in 3 coin toss is (12)3=18 . Probability of getting at least 1 tail in 3 coin toss is 1−18=78
The radius of a circle is (7x+3)cm. Write an expression to represent the area of the circle in simplified form
Answer:
A = π(7x + 3)² cm²
Step-by-step explanation:
A = πr² is the appropriate equation. If r = 7x + 3 cm, then the area of this particular circle is:
A = π(7x + 3)² cm²
Final answer:
The area of a circle with radius (7x+3)cm is represented by the simplified expression 49x²π + 42xπ + 9π square centimeters.
Explanation:
To find the area of a circle with radius (7x+3)cm, we use the formula for the area of a circle, which is A = πr². So, substituting the given radius into this formula, we get:
A = π(7x+3)²
To simplify the expression, we square the binomial:
A = π(49[tex]x^2[/tex] + 42x + 9)
Therefore, the area of the circle in simplified form is 49[tex]x^2[/tex]π + 42xπ + 9π square centimeters.
A car was purchased for $25,000. Research shows that the car has an average yearly depreciation rate of 18.5%. Create a function that will determine the value V(t), of the car t years after purchase. Determine to the nearest cent, how much the car will depreciate from year 3 to year 4
Answer:
V(t) = 25000 * (0.815)^t
The depreciation from year 3 to year 4 was $2503.71
Step-by-step explanation:
We can model V(t) as an exponencial function:
V(t) = Vo * (1+r)^t
Where Vo is the inicial value of the car, r is the depreciation rate and t is the amount of years.
We have that Vo = 25000, r = -18.5% = -0.185, so:
V(t) = 25000 * (1-0.185)^t
V(t) = 25000 * (0.815)^t
In year 3, we have:
V(3) = 25000 * (0.815)^3 = 13533.58
In year 4, we have:
V(4) = 25000 * (0.815)^4 = 11029.87
The depreciation from year 3 to year 4 was:
V(3) - V(4) = 13533.58 - 11029.87 = $2503.71
The depreciation from year 3 to year 4 was $2503.71
Exponential functionThe standard exponential function is expressed as:
[tex]y=a(1\pm r)^t[/tex]
r is the rate
t is the time
Given the following parameters
a = 25000,
r = -18.5% = -0.185,
Substitute into the formula
y = 25000 * (1-0.185)^t
y = 25000 * (0.815)^t
In year 3, we have:
y(3) = 25000 * (0.815)^3 = 13533.58
In year 4, we have:
y(4) = 25000 * (0.815)^4 = 11029.87
The depreciation from year 3 to year 4 was:
y(3) - y(4) = 13533.58 - 11029.87 = $2503.71
The depreciation from year 3 to year 4 was $2503.71
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NGC is a hot air balloon in the sky from her spot on the ground. The angle of elevation from Angie to the balloon is 40°. If she steps back 200 feet, the new angle of elevation is 10°. If Angie is 5.5 feet tall, how far off the ground is a hot air balloon?
Answer:
The distance from hot air balloon to the ground [tex]AC=50.1457 ft[/tex].
Step-by-step explanation:
Labelled diagram of given scenario is shown below.
Given that,
An angle of elevation of Hot air balloon by Angie is [tex]40[/tex]°.
When she stepped back [tex]200 ft[/tex] then angle of elevation was [tex]10[/tex]°.
Height of Angie is [tex]5.5 ft[/tex].
To find: How far off the ground is a hot air balloon.
So, from figure
Height of Angie [tex](BC) = 5.5ft[/tex]
In triangle Δ[tex]ABD[/tex],
⇒ [tex]tan {40\si {\degree}} = \frac{AB}{BD}[/tex]
⇒ [tex]AB = tan (40) \times BD[/tex] ....................(1)
Now, In triangle Δ[tex]ABE[/tex]
⇒ [tex]tan (10)= \frac{AB}{200+BD}[/tex]
⇒ [tex]AB = tan(10)\times (200+BD)[/tex]
Here, substituting the value [tex]AB[/tex] from Equation (1) we get,
[tex]tan(10)\times (200+BD)= tan(40)\times BD[/tex]
[tex]tan(10)\times 200+tan(10)\times BD= tan(40)\times BD[/tex]
⇒ [tex]BD\times (tan(40)-tan(10))=tan(10)\times 20[/tex]
⇒ [tex]BD\times 0.6628 = 35.2654[/tex]
⇒ [tex]BD = \frac{35.2654}{0.6628} =53.2067 ft[/tex]
Now, finding the value of [tex]AB[/tex] from equation (1)
[tex]AB= tan(40)\times 53.2067=0.8391\times 53.2067[/tex]
[tex]AB=44.6457 ft[/tex]
Therefore Length of [tex]AC= AB+BC[/tex] = [tex](44.6457 + 5.5) ft[/tex]
[tex]AC=50.1457 ft[/tex].
Hence,
The distance from hot air balloon to the ground [tex]AC=50.1457 ft[/tex].
Micah recorded the amount of time his mom and dad spend reading bedtime stories. He plotted the data in the box plot below.
A box plot titled Minutes mom spends reading. The number line goes from 10 to 25. The whiskers range from 13 to 25, and the box ranges from 15 to 19. A line divides the box at 16.
Minutes Mom Spends Reading
A box plot titled Minutes dad spends reading. The number line goes from 10 to 25. The whiskers range from 11 to 19, and the box ranges from 12 to 15. A line divides the box at 13.
Minutes Dad Spends Reading
Which is an accurate comparison of the two data sets?
The lengths of time that his mom reads are typically longer and have less variability than the lengths of time that his dad reads.
The lengths of time that his mom reads are typically longer and have more variability than the lengths of time that his dad reads.
The lengths of time that his mom reads are typically shorter and have less variability than the lengths of time that his dad reads.
The lengths of time that his mom reads are typically shorter and have more variability than the lengths of time that his dad reads.
Answer:
The lengths of time that his mom reads are typically longer and have more variability than the lengths of time that his dad reads.
Step-by-step explanation:
The Mom's plot is longer in ranges, therefore, she would have more variability than the dad.
Answer:
B
Step-by-step explanation:
Ethan and Chloe shared £50 in the ratio 1:4
Ethan's share is £10, and Chloe's share is £40, resulting in a total of £50.
To determine the amounts Ethan and Chloe received when sharing £50 in the ratio 1:4, follow these steps:
1. Calculate the Total Parts in the Ratio:
Add the parts of the ratio: 1 + 4 = 5.
2. Determine the Share for Each Part:
Divide the total amount by the total parts: £50/5 = £10.
3. Multiply the Share per Part by Respective Parts:
- Ethan's share: £10 * 1 = £10
- Chloe's share: £10 * 4 = £40
Therefore, Ethan received £10, and Chloe received £40.
In summary, when the ratio is 1:4, the total ratio parts are 5, and each part represents £10. Ethan's share is £10, and Chloe's share is £40, resulting in a total of £50.
Complete question:
Ethan and Chloe shared £50 in the ratio 1:4. What is the amount received by each of them.
Ethan received £10 and Chloe received £40.
Ethan and Chloe shared £50 in the ratio 1:4. To determine the amount received by each of them, we can follow these steps:
1. Calculate the total parts in the ratio:
o The ratio is 1:4, which means there are a total of 1 + 4 = 5 parts.
2. Divide the total amount (£50) into these parts:
o Each part is worth £50 ÷ 5 = £10.
3. Allocate the shares based on the ratio:
o Ethan receives 1 part, which is £10.
o Chloe receives 4 parts, which is 4 × £10 = £40.
Therefore, Ethan received £10 and Chloe received £40.
Complete question:
Ethan and Chloe shared £50 in the ratio 1:4. What is the amount received by each of them?
What are the coordinates of point C of the directed segment from A(-8,4) to B(10,-2) that partitions the segment such that AC:CB is 2:1?
Final answer:
To find the coordinates of point C that partitions the segment from A(-8,4) to B(10,-2) in the ratio 2:1, we use the formula for internal division of a line segment, resulting in the coordinates (4, 0).
Explanation:
The coordinates of point C that partitions the segment from A(-8,4) to B(10,-2) in the ratio 2:1 can be found using the formula for internal division of a line segment. Since AC:CB is 2:1, we consider the section ratio to be 2/3 and multiply it by the difference in the corresponding x and y coordinates of A and B, then add to the coordinates of point A.
The x-coordinate of point C is calculated as follows:
Cx = Ax + (Bx - Ax) * m/(m+n)
Where Ax is the x-coordinate of point A, Bx is the x-coordinate of point B, and m/n is the ratio (2/1 in this case), so m=2 and n=1.
Cx = (-8) + (10 - (-8)) * 2/(2+1) = -8 + 18 * 2/3 = -8 + 12 = 4
The y-coordinate of point C is calculated similarly:
Cy = Ay + (By - Ay) * m/(m+n)
Cy = 4 + ((-2) - 4) * 2/(2+1) = 4 + (-6) * 2/3 = 4 - 4 = 0
Thus, the coordinates of point C are (4, 0).
Ahmed was studying the shapes of quartz crystals, one of which he outlined below.
A figure can be broken into a parallelogram and triangle. The parallelogram has a base of 3 feet and height of 5 feet. The triangle has a base of 3 feet and height of 2 feet.
What is the area of the quartz crystal he was studying, in square feet?
Feet squared
Answer:
The answer is 18 feet squared
Step-by-step explanation:
Answer:
The answer is 18 ft squared
Step-by-step explanation:
i just got 100% i know all the right answers
What is the area of a rectangle 15 feet by 2 feet's rectangle. The shape of a flag is a rectangle. The length is 15 ft. And the width is 2 feet. What is the total area of the rectangle?
Answer:
30 ft^2
Step-by-step explanation:
Area of rectangle is length x width
= 15ft x 2ft = 30 ft^2
Which scatterplot is labeled correctly if it is meant to show the relationship between the number of minutes that gym members spend running on a treadmill and the number of calories that they burn?
A graph titled Members versus Calories Burned has Members on the x-axis and calories burned on the y-axis. Points plotted are (10, 200), (20, 300), (30, 400), (35, 425), (40, 650), (50, 700).
A graph titled Minutes versus Calories Burned has Minutes on the x-axis and calories burned on the y-axis. Points plotted are (10, 200), (20, 300), (30, 400), (35, 425), (40, 650), (50, 700).
A graph titled Calories Burned versus Minutes has Calories burned on the x-axis and minutes on the y-axis. Points plotted are (160, 11), (200, 15), (300, 20), (376, 25), (390, 30), (400, 35).
A graph titled Calories Burned versus Members has Calories burned on the x-axis and members on the y-axis. Points plotted are (160, 11), (200, 15), (300, 20), (376, 25), (390, 30), (400, 35).
Answer:The answer is the 2nd graph cuh
Step-by-step explanation:
Answer:the second graph
Step-by-step explanation:
Each month. Diana donates the same amount of money to a charity. If she donates 1,500 in one year, how much does she donate each month?
Answer: $125
Step-by-step explanation:
1500/12=125
Cross sections are formed by slicing through figure parallel to its base. in which figure will the cross section and the base NOT be the same size?
Answer:
B
Step-by-step explanation:
The second one gets smaller as it gets taller.
Answer:
the answer is BStep-by-step explanation:
Add 3 to x, double what you have, then subtract 1 from the result
Answer:
-6
Step-by-step explanation:
3x * 2 = 6x - 1 = -6
The required result of the given expression is 2x - 5.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now the given expression is,
Add 3 to x, double what you have, then subtract 1
So, we can write,
Add 3 to x = 3 + x
Double = 2(3 + x)
Subtract from = 1 - 2(3 + x)
Simplifying we get,
1 - 6 + 2x
solving we get,
1 - 6 + 2x = 2x - 5
this is the required result.
Thus, the required result of the given expression is 2x - 5.
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A theme park ride has a ride that is located in a sphere. The ride goes around the widest circle of the sphere which has a circumference of 521.24 yd. What is the surface area of the sphere? Use 3.14
Answer:
The surface area of the sphere is 86525.84 square yards
Step-by-step explanation:
The widest circle of the sphere has the same radius of the sphere
Use the circumference of the circle to find its radius, then use it to find the surface area of the sphere
The formula of the circumference of the circle is C = 2π r
The formula of the surface area of the sphere is SA = 4π r²
∵ The circumference of the widest circle is 521.24 yards
∴ C = 521.24
- Equate the formula of the circumference by it
∴ 2π r = 521.24
∵ π ≈ 3.14
∴ 2(3.14) r = 521.24
∴ 6.28 r = 521.24
- Divide both sides by 6.28
∴ r = 83 yards
Now use the formula of the surface area of the sphere to find it
∵ The radius of the sphere = the radius of the widest circle
∴ The radius of the sphere is 83 yards
∵ SA = 4π r²
- Substitute r by 83 and π by 3.14
∴ SA = 4(3.14)(83)²
∴ SA = 86525.84
The surface area of the sphere is 86525.84 square yards
A racecar can go round the track 48 times in 8 minutes how many times can it go around the track per minute
Answer:
6 times
Step-by-step explanation:
48/8=6
Answer: 10 seconds for one time around the track.
Step-by-step explanation:
48 times=8 minutes
1 time= 8/48
8/48=4/24
4/24=2/12
1/6. 1/6 of a minute equals 10 seconds.
The answer is 10 seconds
A group of hikers climbed to the top of a mountain. They climbed 2000 feet each day for five days to get to the top. Approximately how many miles tall was the mountain?
Answer:
The mountain is 1.89 miles tall
Step-by-step explanation:
Firstly, we need to compute the value in feet of the total distance traveled by the group.
We were told they traveled 2000 feet per day for 5 days, the total distance they have hiked would be 2000 * 5 = 10,000 feet
Now, we need to convert this to miles
Mathematically ;
1 foot = 0.000189 mile
Hence, 10,000 feet = 10,000 * 0.000189 = 1.89 miles
This means the mountain is 1.89 miles tall
What is the image point of (6,-
1) after a translation left 4 units and down 5 units?
Answer:
(2, -6)
Step-by-step explanation:
Answer:
The Right Answer Is (2,-6)
Step-by-step explanation:
I hope this help you!
The top of the chimney needed to be replaced. The new top for the chimney will cost $800 plus $40 per hour for labor. If it took the chimney guy 75 minutes to complete the work, how much will Mrs. Bredice pay?
Answer:
Step-by-step explanation:
What is 10 plus 10 divided by 10
Answer:
11
Step-by-step explanation
u need to do the problem using order of operation
first u do division it is 10 divided by 10 which is 1
10 plus the answer of 10 divided by 10 which is 11
Answer:
11
Step-by-step explanation:
using PEMDAS:
first divide 10/10 and then you get 1+1 which equals 11
Maria is making a candle in the shape of a cylinder. She wants the candle to have a height of 3 cm and a radius of 2 cm. How much wax does Maria need?
12 cm3
12 cm2
18 cm3
20 cm2
Answer:
V(cylinder) = πr²h
h=3 cm
r=2 cm
V(cylinder) = πr²h = π*2²*3 =12π cm³
Answer : 12π cm³.
Answer:
A
Step-by-step explanation:
12π cm³
The formula m=logl/s determines the magnitude of an earthquake, where I is the intensity of the earthquake and S is the intensity of a “standard earthquake.” How many times stronger is an earthquake with a magnitude of 8 than an earthquake with a magnitude of 6? Show your work.
Final answer:
An earthquake with a magnitude of 8 is 100 times stronger than an earthquake with a magnitude of 6, as each whole number increase on the Richter scale represents a 10-fold increase in energy released.
Explanation:
The formula m=log(I/S) determines the magnitude of an earthquake, where I is the intensity of the earthquake and S is the intensity of a standard earthquake. To calculate how many times stronger an earthquake with a magnitude of 8 is than an earthquake with a magnitude of 6, we use the fact that each whole number increase on the Richter scale represents a 10-fold increase in the amount of energy released.
So, for an increase of one unit in magnitude:
10^1 = 10 times stronger
For an increase of two units in magnitude (from magnitude 6 to magnitude 8):
10^2 = 100 times stronger
Therefore, an earthquake with a magnitude of 8 is 100 times stronger than an earthquake with a magnitude of 6 when considering the energy released.
An earthquake with a magnitude of 8 is 1.33 times stronger than an earthquake with a magnitude of 6.
1. Understand the formula:
The formula m = log(I/S) relates the magnitude (m) of an earthquake to its intensity (I) and the intensity of a standard earthquake (S). The logarithm used is typically base-10.
2. Substitute the values:
We are given that the magnitude of the two earthquakes are 8 and 6. Let's substitute these values into the formula:
Earthquake 1: m1 = log(I1/S) (magnitude 8)
Earthquake 2: m2 = log(I2/S) (magnitude 6)
3. Simplify the equation:
We want to find the ratio of the intensities (I1/I2). To do this, we can manipulate the equations and solve for I1/I2:
Divide both equations by m2 (magnitude of earthquake 2):
m1 / m2 = log(I1/S) / log(I2/S)
Since both sides of the equation have the same base (10), we can equate the exponents:
m1 / m2 = I1/I2
4. Calculate the ratio:
Now, plug in the magnitudes (m1 = 8, m2 = 6):
8 / 6 = I1/I2
5. Solve for the ratio:
Simplify the fraction:
I1/I2 = 4/3
Therefore, an earthquake with a magnitude of 8 is 1.33 times stronger than an earthquake with a magnitude of 6.
A rectangular page is to contain 24 sq. in. of print. The margins at the top and bottom of the page are each 1.5 inches. The margins on each side are 1 inch. What should the dimensions of the page be so that the least amount of paper is used
Answer:
Dimensions of page should be width of 6 inches and height of 9 inches
Step-by-step explanation:
Let x be the width of the printed part in inches
Let y be height of the printed part in inches.
Thus, Area of printed part; A = xy
And area of printed part is given as 24.
Thus, xy = 24
Making y the subject, we have;
y = 24/x
Now, the question says the top and bottom margins are 1.5 inches.
Thus, width of page = x + 1 + 1 = x + 2
And also the margins on each side are both 1m in length, thus the height of page will be:
y + 1.5 + 1.5 = y + 3
So area of page will now be;
A = (x + 2)•(y+3)
From earlier, we got y = 24/x
Thus,plugging this into area of page, we have;
A = (x + 2)•((24/x)+3)
A = 24 + 3x + 48/x + 6
A = 30 + 3x + 48/x
For us to find the minimum dimensions, we have to find the derivative of A and equate to zero
Thus,
dA/dx = 3 - 48/x²
Thus, dA/dx = 0 will be
3 - 48/x² = 0
Multiply through by x²:
3x² - 48 = 0
Thus,
3x² = 48
x² = 48/3
x = √16
x = 4 inches
Plugging this into y = 24/x,we have;
y = 24/4 = 6 inches
We want dimensions of page at x = 4 and y = 6.
From earlier, width of page = x + 2.
Thus,width = 4 + 2 = 6 inches
Height = y + 3 = 6 + 3 = 9 inches
So dimensions of page should be width of 6 inches and height of 9 inches
To minimize paper usage, we need to find the dimensions of the rectangular page. By setting up an equation and solving it, we can find the width and length of the page that result in the least amount of paper used.
Explanation:To minimize the amount of paper used, we need to find the dimensions of the page that will result in the smallest possible area. Let's assume the length of the page is 'L' inches and the width is 'W' inches. We can set up the equation:
Next, we can use the quadratic formula to solve for L:
To find the minimum value of L, we can consider the factors contributing to the uncertainty:
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Do you think there are any ordered pairs that are solutions to BOTH y = x + 5 and y = –2x – 1? Explain.
Answer:
The ordered pair is [tex](-2,3)[/tex]
Step-by-step explanation:
[tex] y=x+5\\
y=-2x-1\\
\implies x+5=-2x-1\\
\implies 3x=-6\\
\boxed{x=-2}\\
\implies y=-2+5=\boxed {3}\\[/tex]
Answer:
(-2,3)
Step-by-step explanation:
Set the two equations equal to each other since they both equal y
x + 5 = -2x - 1
+2x +2x Add 2x to both sides
3x + 5 = -1
- 5 - 5 Subtract 5 from both sides
3x = -6 Divide both sides by 3
x = -2
Plug this into one of the original equations
y = x + 5
y = -2 + 5 Add
y = 3
Y=6x-14
y=-8x what is the equation
Step-by-step explanation:
Putting value of y
-8x = 6x - 14
-8x - 6x = - 14
-14x = - 14
x = - 14/-14
x = 1
Are the following two matrices inverses of one
another? (Urgent please help)
A=[ 4 2] B= [ -4 -2]
[-11 -6] [ 11 7]
a)Yes, because they are opposites.
b)Yes, because their product is equal to the
identity matrix
c)No, because they are not opposites.
d)No because their product is not equal to the matrix
Answer: D
Step-by-step explanation:
The correct answer is d) No because their product is not equal to the identity matrix.
The matrices are given in the question as follows:
[tex]A= \left[\begin{array}{ccc}4&2\\-11&-6\end{array}\right] \\B= \left[\begin{array}{ccc}-4&-2\\11&6\end{array}\right][/tex]
To determine if two matrices are inverses of each other, we need to check if their product is equal to the identity matrix.
Let's calculate the product of matrices A and B:
[tex]A{\times}B = \left[\begin{array}{ccc}4\times-42+2\times11&4\times-2+2\times6\\-11\times-4+(-6\times11)&-11\times-2-6\times6\end{array}\right][/tex]
Simplifying the calculations to get:
[tex]A{\times}B = \left[\begin{array}{ccc}6&4\\-22&-14\end{array}\right][/tex]
The resulting matrix is not equal to the identity matrix:
[tex]A{\times}B = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]
Therefore, matrices A and B are not inverses of each other.
The correct answer is d) No because their product is not equal to the identity matrix.
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The Roosevelt’s and the jaspers live in the same city and pay the same sales tax rate, and both families made 16,000 in taxable purchase last year if the Roosevelt’s made 91,000 and the jaspers made 37,000 last year is the sales tax in their city an example of a regressive tax
Answer:
Yes, the sales tax in their city is an example of regressive tax
Step-by-step explanation:
Firstly, we need to understand what is meant by the term regressive tax.
What is meant by a regressive tax system is a system of taxation in which there is a decrease in tax rate as there is an increase in amount subjected to tax.
Now, the key to knowing if what we have in the question is a regressive taxation is by calculating the percentage of the tax that was paid.
For the Roosevelt’s , the percentage of tax paid would be 16,000/91,000 * 100% = 17.6%
For the Jasper’s, the percentage of tax paid would be 16,000/37,000 * 100% = 43.24%
We can see that at a lower amount subjected to tax, the Jasper’s paid more and thus we can conclude irrevocably that sales tax in their city is an example of a regressive tax
an elevator at a construction site has a maximum capacity of 2500 pounds. if the elevator operator weights 160 pounds and each cement bag weighs 60 pounds, how many bags of cement can be safely lifted on the elevator in one trip?
Answer:
39 bags (at max)
Step-by-step explanation:
160 + 60x《2500
60x《2340
x《39
Answer: the answer would be 39 bags of cement
Step-by-step explanation: 2500- 160= 2340
2340/60 (each bag of cement) it equals 39
HEEEEEELP PLLLEEEEEEEZZZZZZ!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Lara has a triangle that has side lengths of 26, 34, and 58. She wants to reduce the triangle by one half, so she divides each side and each angle measurement by 2.
What error did Lara make?
Lara should have multiplied each measurement by 1/2.
Lara should have only divided the angles by 2 in order to reduce the triangle.
Lara should have only divided the side lengths by 2 in order to reduce the triangle.
Lara did not make an error.
C is correct,
A is wrong as it halves both the angles and lengths by two which is the same as what she did in the first place so it cannot be correct.
B is also wrong for a similar reason, a triangle cannot have less than 180 degrees, which is impossible as the angles just change naturally which is why all triangles must have 180 degrees, which is the reason she is wrong in the first place.
And D is just incorrect, if she wanted to have shorter sides she should have only decreased all the lengths as it the the ratio of angles that determine the shape of a triangle while the sum of all angles is 180 degrees.
Answer: C
Step-by-step explanation:
f the angle of elevation from the point on the ground to the top of the tree is 34° and the point is 25 feet from the base of the tree, what is the height of the tree (to the nearest tenth of a foot)?
A) 14.0 feet
B) 16.9 feet
C) 19.3 feet
D) 20.7 feet
Given:
The angle of elevation from the point on the ground to the top of the tree is 34° and the point is 25 feet from the base of the tree.
We need to determine the height of the tree.
Height of the tree:
Let the height of the tree be h.
The height of the tree can be determined using the trigonometric ratio.
Thus, we have;
[tex]tan \ \theta=\frac{opp}{adj}[/tex]
Substituting the values, we get;
[tex]tan \ 34^{\circ}=\frac{h}{25}[/tex]
Multiplying both sides by 25, we have;
[tex]tan \ 34^{\circ} \times 25=h[/tex]
[tex]0.6745 \times 25=h[/tex]
[tex]16.8625=h[/tex]
Rounding off to the nearest tenth of a foot, we get;
[tex]16.9=h[/tex]
Thus, the height of the tree is 16.9 feet.
Hence, Option B is the correct answer.
Correct option is B. The height of the tree can be found using the tangent of the angle of elevation, which is the ratio of the tree's height to the distance from the base. Applying the formula, the height is approximately 16.9 feet, matching option B.
To calculate the height of the tree given the angle of elevation and the distance from the point on the ground to the base of the tree, we can use trigonometric functions, specifically the tangent function in a right triangle. The tangent of an angle in a right triangle is the ratio of the opposite side (height of the tree) to the adjacent side (distance from the point on the ground to the tree).
Using the formula:
tangent(angle) = opposite / adjacent
Substitute the given values:
tangent(34°) = height of the tree / 25 ft
Now solve for the height:
height = 25 ft * tangent(34°)
Use a calculator to find:
height = 25 ft * 0.6745
height = 16.9 ft
Therefore, the height of the tree is approximately 16.9 feet (to the nearest tenth of a foot), making option B the correct answer.