The time it takes for a ball thrown downwards at a velocity of 21 ft/s from a height of 255 ft to reach the ground is approximately 4.05 seconds.
Explanation:The physics problem presented is a classic example of a vertically descending projectile. Here, we can use the formula of motion to find the solution. The formula is h = vt + 0.5gt², where v is the initial velocity, g is the acceleration due to gravity, and h is the height.
Since the ball is thrown downwards, the initial velocity will be negative, -21 ft/s. We're also working in feet, so the gravitational acceleration should be in feet/s², which is approximately -32.2 ft/s² (remember it's negative as it's acting downwards).
So, substituting the values into the equation, we have 255 = (-21*t) + 0.5*(-32.2)*t². Simplifying this gives us a quadratic equation: 16.1t² - 21t - 255 = 0.
The roots of this equation represent the times at which the ball will be 255 ft below its starting point. We solve the equation and get t ≈ -3.9s or t ≈ 4.05s. Clearly, time cannot be negative, so the ball hits the ground after approximately 4.05 seconds from being thrown.
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The ball thrown from a height with initial downward velocity hits the ground after 3.79 seconds. This was found by solving the quadratic equation that stems from principles of physical motion (height vs time).
Explanation:The problem can be solved using the principles of kinematics in physics. The height of the ball after t seconds is given by the equation of motion, which is a quadratic equation. If we let h be 0 (height when the ball hits the ground), we can solve the equation for t.
Given: initial height = 255 feet, initial velocity = 21 feet/s, acceleration due to gravity = 32.2 ft/s² (downward); The equation of motion is: h = 255 + 21t - 16t²; We have to find the time when the ball hits the ground i.e when h=0. So, the equation becomes: 0 = 255+21t-16t².
On solving this quadratic equation, we get two roots. Assuming upward direction is positive, the negative time value reflects the time before the ball was launched and the positive value is the time it takes for the ball to hit the ground. The positive root gives us the answer, t = 3.79 s.
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A manufacturing machine has a 10% defect rate. if 4 items are chosen at random, what is the probability that at least one will have a defect?
The probability that at least one of the four randomly chosen items will be defective is 34.39%. This is calculated by subtracting the probability that all items are not defective from 1.
Explanation:The subject of the question relates to the field of Probability. This problem pertains to the concept known as 'probability of at least one' event. In this case, we are considering the probability that at least one item will have a defect.
To calculate this, it's easier to find the probability that none of the items have a defect and then subtract that from 1. Since the machine has a 10% defect rate, it means there's a 90% chance that any item chosen will NOT be defective. If we choose 4 items, the probability that all are good is 0.9 * 0.9 * 0.9 * 0.9 = 0.6561.
So, the probability that at least one defective item will be chosen is 1 - 0.6561 = 0.3439 or 34.39%.
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P(1+r)t Using the expression above, choose the correct answers for the new balance and the amount of interest earned in the following compound interest problem. $950 at 7% for 8 years, compounded annually. Total Amount = $ Interest Amount = $
Final answer:
The new balance after 8 years with an initial $950 at a 7% annual interest rate compounded annually is $1632.77, and the amount of interest earned is $682.77.
Explanation:
The compounded interest formula is P(1+r)^t, where P is the principal amount, r is the annual interest rate (in decimal form), and t is the time in years. To find the new balance and amount of interest earned for $950 at 7% for 8 years, compounded annually, we use the formula with P = $950, r = 0.07 (7% as a decimal), and t = 8.
First, we calculate the new balance:
Total Amount = $950(1 + 0.07)^8
Total Amount = $950(1.07)^8
Total Amount = $950 * 1.718186
Total Amount = $1632.77 (rounded to two decimal places)
Subsequently, to find the amount of interest earned, we subtract the original principal from the total amount:
Interest Amount = Total Amount - Original Principal
Interest Amount = $1632.77 - $950
Interest Amount = $682.77
Therefore, the new balance after 8 years is $1632.77, and the interest earned is $682.77.
A maintenance man has 12 keys on his key ring. if he tries the keys at random on a storage room door, discarding those that do not work, what is the probability that he will get the door open on his 4th try?
Final answer:
The probability that the maintenance man will open the storage door on his fourth try with 12 keys is 1/12.
Explanation:
The question asks for the probability that the maintenance man will open a storage room door on his fourth try with 12 unique keys at his disposal. This is a classic probability problem that involves permutations.
To solve this, we consider the scenario as a sequence of independent events. He has 1 out of 12 chances to pick the correct key on the first try, 1 out of 11 on the second try (after discarding the first incorrect key), 1 out of 10 on the third try, and so on. However, we want the first three attempts to be unsuccessful and the fourth to be successful.
Thus, the probability that the first three keys are incorrect is (11/12) * (10/11) * (9/10), and the probability the fourth key is correct is 1/9. The overall probability of the desired outcome is the product of these probabilities, which simplifies to:
(11/12) * (10/11) * (9/10) * (1/9) = 1/12.
arman needs 4 1/2 inches of cable to make A,3 3/4 inches to make B, and 5 1/8 inches to make C. He used a 12 inch piece of cable to make A and B.
Answer:
8 1/4
Step-by-step explanation:
there is a cafe at the park it is 13 meters long and 8 meters wide. what is the area of the cafe
An employee earned $3,300 working for an employer in the current year. the current rate for fica social security is 6.2% payable on earnings up to $117,000 maximum per year and the rate for fica medicare 1.45%. the employer's total fica payroll tax for this employee is:
lim θ→π/4 1 - tan θ / sin θ - cos θ
Each day a small business owner sells 200 pizza slices for $1.50 per slice and 85 sandwiches at $3.50 each. Business exspenses come to $130 per day. What is the owner's profit for a ten-day period.
Final answer:
The small business owner's profit for a ten-day period is $4,675, calculated by determining the total daily revenue from pizza slices and sandwiches, subtracting daily expenses, and then multiplying the result by ten.
Explanation:
The question pertains to calculating the profit for a small business over a ten-day period. To do this, we first calculate the daily revenue from selling pizza slices and sandwiches and then subtract the daily expenses. After that, we multiply the daily profit by ten.
Daily pizza slice revenue: 200 slices × $1.50/slice = $300Daily sandwich revenue: 85 sandwiches × $3.50/sandwich = $297.50Total daily revenue: $300 + $297.50 = $597.50Total daily expenses: $130Daily profit: $597.50 - $130 = $467.50Total 10-day profit: $467.50/day × 10 days = $4,675The owner's profit for the ten-day period would then be $4,675.
The spoke of a wheel reaches from the center of the wheel to its rim. If the circumference of the rim of the wheel is 42 inches, how long is each spoke? Round your answer to the nearest hundredth.
EASY 5 POINTS!!!! A new park in the shape of a hexagon will have 66 sides of equal length. On a scale drawing, the coordinates of the vertices of the park are: (6.5,5)6.5,5, (18.5,0)18.5,0, (6.5,-5)6.5,-5,
(-6.5,-5)-6.5,-5, (-18.5,0)-18.5,0, and (-6.5,5)-6.5,5. How long is each side of the park?
To solve this problem, first we have to plot the vertices in a Cartesian plane to know the plot. This would also give us an idea of which points are adjacent or interconnected forming a hexagon.
The plot is shown below. Now we can see which points are adjacent to each other. Let us take points (-6.5, 5) and (6.5, 5) for our calculation.
The distance formula given two points is:
d^2 = (x2 – x1)^2 + (y^2 – y^1)^2
Now we calculate the distance between 2 points:
d^2 = (6.5 – (-6.5))^2 + (5 – 5)^2
d^2 = 169
d = 13
Therefore the length of each side of the park is 13 units.
Answer:
13 units
To find the length of each side of the hexagon, you can use the distance formula. The distance formula is derived from the Pythagorean theorem for finding the length of the hypotenuse of a right triangle. By following the steps outlined, you can determine the length of each side of the hexagon.
Explanation:To find the length of each side of the hexagon, you can use the distance formula. The distance formula is derived from the Pythagorean theorem for finding the length of the hypotenuse of a right triangle. In this case, the coordinates of the vertices of the hexagon form a regular hexagon, meaning all sides are equal in length. Here's how you can find the length of one side:
Take the coordinates of two adjacent vertices of the hexagon.Use the distance formula, which is sqrt((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.Plug in the coordinates and calculate the distance.Repeat the process for different pairs of adjacent vertices to make sure all sides have the same length.By following these steps, you should be able to determine the length of each side of the hexagon.
Which of the following shows 2.1851 rounded to the nearest tenth?
A. 2.1
B.2.185
C.2.19
D.2.2
Harland just got his second major credit card, so his credit score rose from 671 to 711. According to the following table for a $150,000 mortgage, how much less per year would Harland have to pay on a $150,000 mortgage with the new credit score?
Answer:
2004
Step-by-step explanation:
Use the distributive property to write an equivalent expression for 4(x-2)
Verify that the divergence theorem is true for the vector field f on the region
e. give the flux. f(x, y, z) = 3xi + xyj + 4xzk, e is the cube bounded by the planes x = 0, x = 3, y = 0, y = 3, z = 0, and z = 3.
To verify the divergence theorem, we need to calculate the flux of the vector field through the surface of the cube and compare it with the divergence of the vector field integrated over the volume of the cube.
Explanation:To verify the divergence theorem for the given vector field f(x, y, z) = 3xi + xyj + 4xzk on the region e, which is a cube bounded by the planes x = 0, x = 3, y = 0, y = 3, z = 0, and z = 3, we need to calculate the flux of the vector field through the surface of the cube and compare it with the divergence of the vector field integrated over the volume of the cube.
The flux, Ƭ, can be calculated using the surface integral of the vector field over each face of the cube. According to the divergence theorem, this should be equal to the volume integral of the divergence of the vector field over the entire volume of the cube.
By calculating both sides of the equation, we can verify that the divergence theorem holds true for the given vector field on the specified region.
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The value of the given digits in the numbers 7s in 775 823 159
Rewrite the expression x^2-12x as a(x-h)^2+k
If one calendar year had two consecutive months with Friday the thirteenth, which months would they be?
how to prove a polygon is a rectangle?
Use the position equation
s = −16t^2 + v0t + s0
as the model for the problem.
A cargo plane flying at 6000 feet over level terrain drops a 700-pound supply package.
(a) How long will it take the package to strike the ground? (Round your answer to two decimal places.)
(b) The plane is flying at 600 miles per hour. How far will the package travel horizontally during its descent? (Round your answer to two decimal places.)
A. To solve for the time it takes for the package to strike the ground, all we have to do is to plug in the given values in to the position equation:
s = −16 t^2 + v0 t + s0
Where,
s = distance of the plane from the ground = - 6000 ft (negative since the package moves from top to bottom)
t = time for it to strike the ground = unknown
v0 = 0 since the package starts from rest
s0 = 0 since we take the plane as the reference point
Substituting the given values:
- 6000 = -16 t^2 + 0 * t + 0
16 t^2 = 6000
t^2 = 375
t = 19.36 s
B. s = v * t
where v = 600 miles / hr = 0.17 miles / s
s = (0.17 miles / s) * 19.36 s
s = 3.23 miles = 17,054 ft
the circle is centered at the origin and the length of its radius is 4. what is
the circles equation
Answer: [tex]x^2+y^2=16[/tex]
Step-by-step explanation:
The general equation of a circle having center at (h,k) and radius r is given by :-
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Given: Radius of the circle : r= 4 units
The center of the circle : (h,k)=(0,0)
Now, the equation of a circle having center at (0,0) and radius 4 units is given by :-
[tex](x-0)^2+(y-0)^2=4^2\\\\\Rightarrow\ x^2+y^2=16[/tex]
Answer:
X²+Y²=16
Step-by-step explanation:
A p e x
BE is the midsegment of triangle ACD. The value of x is:
5.
20.
35.
40.
Given m || n, find X....PLEASE HELP ASAP....SOS...SUCK AT MATH PLEASE HELP ME!!
Which number produces an irrational number when multiplied by 0.4?
The ticket sales for Fist Bump are as follows:
On Monday 1 /7 of the tickets are sold
On Tuesday 1/3 of the tickets are sold
On Wednesday 2/7 of the tickets are sold
What fraction of tickets was sold by Thursday?
To calculate the total fraction of tickets sold for the movie Fist Bump by Thursday, we find the least common denominator for the fractions (21), convert each fraction, and then sum them up to get 16/21 of the tickets sold.
Explanation:The question is asking how much of the tickets were sold by Thursday for the movie Fist Bump. To find the total fraction of tickets sold from Monday to Wednesday, we need to add up the fractions:
Monday: 1/7 of the ticketsTuesday: 1/3 of the ticketsWednesday: 2/7 of the ticketsFirst, let's find a common denominator for the fractions. The least common multiple of 7 and 3 is 21, so we'll convert all fractions to have a denominator of 21:
1/7 = 3/211/3 = 7/212/7 = 6/21Now we can add the fractions:
3/21 + 7/21 + 6/21 = 16/21
Therefore, by Thursday, a total of 16/21 of the tickets have been sold.
Evaluate x 1 - x -1 + x 0 for x = 2
a) 0
b)1/2
c)1 1/2
d)2 1/2
The solution of expression is, 7/2.
What is an expression?A mathematical expression is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.
We have to give that,
An expression is,
⇒ x¹ + x⁻¹ + x⁰
Now, Substitute x = 2 in the above expression and find the value,
⇒ x¹ + x⁻¹ + x⁰
⇒ 2¹ + 2⁻¹ + 2⁰
⇒ 2 + 1/2 + 1
⇒ 3 + 1/2
⇒ (6 + 1)/2
⇒ 7/2
Therefore, The solution is, 7/2
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Ahmed is working at the burger joint. His boss pays him $6.50 per hour and promises a raise of $0.25 per hour every 6 months. Which sequence describes Ahmed's expected hourly wages in dollars, starting with his current wage?
Answer:
Sequence will be $6.50, $6.75, $7.0, $7.25.......
Step-by-step explanation:
Ahmed is working at the burger joint and he was paid by his boss $6.50 per hour.
His boss promised him to raise $0.25 per hour every six months.
So we have to find the sequence which describes Ahmed's expected hourly wages starting with his current wage.
As at every 6 months increase in wages is $0.25 so the sequence formed will be an arithmetic sequence with common difference of 0.25 and first term 6.50
Sequence will be $6.50, $6.75, $7.0, $7.25,.........
Indicate in standard form the equation of the line through the given points.
P(0, -4), Q(5, 1)
A person in a casino decides to play blackjack until he loses a game, but he will not play more than 3 games. let l denote a loss and w denote a win. what is the sample space for this random experiment
The sample space for the random experiment of playing blackjack until a loss or a maximum of three games are played is represented by the set {l, wl, ww}.
Explanation:The sample space for this scenario comprises of all possible outcomes of playing "blackjack" until the person loses or has played three games. We represent win and loss by w and l respectively. By these definitions, we get the following possibilities: l (losing on the first game), wl (winning the first game then losing the second), and ww (winning the first two games and decide not to play a third game or it wasn't possible to play a third game). This assumes that the player stops after either losing a game or after playing the third game, even if he won that.
Note that the scenario where the player wins all three games (www) is not included in the sample space because the problem states that the player will stop playing as soon as they lose a game.
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Complete parts (a) and (b) using the probability distribution below.
The number of overtime hours worked in one week per employee
Overtime hours
0 1 2 3 4 5 6
Probability
0.026 0.072 0.154 0.303 0.215 0.164 0.066
(a) Find the mean, variance, and standard deviation of the probability distribution.
Find the mean of the probability distribution.
μ = 3.4
σ2 = 2.0
σ = 1.4
Choose the correct answer below.
A.
An employee works an average of 2.0 overtime hours per week with a standard deviation of approximately 1.4 hours.
B.
An employee works an average 3.4 of overtime hours per week with a standard deviation of approximately 4 hours.
C.
An employee works an average of 1.4 overtime hours per week with a standard deviation of approximately 3.4 hours.
D.
An employee works an average of 3.4 overtime hours per week with a standard deviation of approximately 1.4 hours.
The mean number of overtime hours worked is 3.4 with a standard deviation of approximately 1.4 hours, which corresponds to option D.
Explanation:The correct answer for the given probability distribution of overtime hours worked per employee in one week is D. An employee works an average of 3.4 overtime hours per week with a standard deviation of approximately 1.4 hours.
To find the mean (μ) of the probability distribution, we multiply each possible value by its corresponding probability and then sum all these products. The mean of this distribution is given as 3.4, which is found by summing up the product of each value of overtime hours and its corresponding probability:
μ = (0 * 0.026) + (1 * 0.072) + (2 * 0.154) + (3 * 0.303) + (4 * 0.215) + (5 * 0.164) + (6 * 0.066) = 3.4
The variance (σ2) is calculated by taking each value's deviation from the mean, squaring it, multiplying by the probability, and summing all these values. The variance for this distribution is given as 2.0:
σ2 = Σ [(x - μ)2 * P(x)] = 2.0
And the standard deviation (σ) is simply the square root of the variance:
σ = √σ2 = 1.4
Graph y=3x^2 -5 and it's inverse
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y=3x^{2}-5[/tex] -----> quadratic equation of a vertical parabola open upward
Find the inverse function
Exchange variables x for y and y for x
[tex]x=3y^{2}-5[/tex]
Isolate the variable y
[tex]3y^{2}=x+5[/tex] -----> inverse function (horizontal parabola open to the right)
or
[tex]y=(+/-)\sqrt{\frac{x+5}{3}}[/tex]
using a graphing tool
see the attached figure
The graph of function and it's inverse of the graph is shown in image.
We have to given that,
To graph the function y = 3x² - 5 and it's inverse.
Here, The equation is,
y = 3x² - 5
So, We can find it's inverse as,
y = 3x² - 5
y + 5 = 3x²
(y + 5) / 3 = x²
x² = (y + 5)/3
x = √(y + 5)/3
Hence, the inverse of function is,
f ⁻¹ (x) = √ (x + 5)/3
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