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Related Questions
What is (44x600)+56-67+99+3x6=?
Answers
Answer:
Than thats great
Evaluate the algebraic expression when f = 6, g = 8, h = 12 and j = 2.
A. 10
B. 12
C. 20
D. 22
please hurry
Answers
Answer:
Step-by-step explanation:
There is no algebraic expression in the question????
Bus #7 left River Street School partially filled with students and then stopped to pick up 15 more students at the Park School. it continued its route as follows:
At the next 4 stops it dropped off two students at each stop.
Three students got off at the following stop.
The next six stops let off one student at each stop.
Ten students then got off at the Centerville after-school-program, where five kindergarten students boarded the bus.
The bus then dropped off seven kids at its last stop, leaving only the driver aboard.
How many students were on the bus when it left the River Street School? Show your work and explain your reasoning.
Answers
14 students were on the bus when it left River Street School.
To find out how many students were on the bus when it left River Street School, we need to work backwards from the end of the route and account for all the students that were picked up and dropped off along the way.
At the last stop, seven students were dropped off, leaving only the driver aboard. This means that there were 7 students on the bus before the last stop.
Before that, five kindergarten students boarded the bus at the Centerville after-school-program, which means that there were 7 - 5 = 2 students on the bus before the kindergarten students boarded.
Before that, ten students got off at the Centerville after-school-program, which means that there were 2 + 10 = 12 students on the bus before they got off.
Before that, the bus made six stops and let off one student at each stop, which means that there were 12 + 6 = 18 students on the bus before those stops.
Before that, three students got off at one stop, which means that there were 18 + 3 = 21 students on the bus before that stop.
Before that, the bus made four stops and dropped off two students at each stop, which means that there were 21 + (4 x 2) = 29 students on the bus before those stops.
Finally, before that, the bus picked up 15 students at the Park School, which means that there were 29 - 15 = 14 students on the bus when it left River Street School.
14 students were on the bus when it left River Street School.
Starting from the end of the route and working backwards, we accounted for all the students that were picked up and dropped off along the way. By subtracting the number of students that were picked up from the number of students that were on the bus at each stop, we were able to find out how many students were on the bus when it left River Street School.
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4. Let X be uniformly distributed on [10, 100). Calculate Tx (a) by using Risk Adjusted Premium Principle with risk index p = 2 (b) by using Risk Adjusted Premium Principle with risk index p = 10
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Let X be uniformly distributed on [10, 100). By using Risk Adjusted Premium Principle
(a) Tx = 106.9615242
(b) Tx = 314.8076211
We can calculate Tx using the formula:
Tx = E[X] + p * σ[X]Where E[X] is the expected value of X, p is the risk index, and σ[X] is the standard deviation of X.For a uniformly distributed random variable X on the interval [a, b), the expected value is:
E[X] = (a + b) / 2And the standard deviation is:
σ[X] = √((b - a)² / 12)For X uniformly distributed on [10, 100), we have:
a = 10b = 100
So:
E[X] = (10 + 100) / 2 = 55σ[X] = √((100 - 10)² / 12) = 25.98076211
Now we can calculate Tx for each risk index:
(a) For p = 2:Tx = 55 + 2 * 25.98076211 = 106.9615242
(b) For p = 10:Tx = 55 + 10 * 25.98076211 = 314.8076211
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Select each equation that has no real solution
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The equation that has no real solution is 12x + 12 = 3(4x + 5), the correct option is (d).
To determine whether an equation has real solutions, we need to solve it and check whether the solutions are real numbers or not.
-5x - 25 - 5x + 25 = 0 simplifies to -10x = 0, which has the solution x = 0. This is a real number solution.
7x + 21 = 21 simplifies to 7x = 0, which has the solution x = 0. This is a real number solution.
12x + 15 = 12x - 15 simplifies to 15 = -15, which is false. This equation has no solution, but it doesn't have any variables left to solve for, so it's not an option for our answer.
12x + 12 = 3(4x + 5) simplifies to 12x + 12 = 12x + 15, which simplifies further to 12 = 15. This is false, which means the equation has no solutions. Therefore, this is the equation that has no real solution, the correct option is (d).
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The complete question is:
Select each equation that has no real solution
a. -5x- 25 - 5x + 25
b. 7x + 21 = 21
c. 12x + 15 = 12x - 15
d. 12x + 12 = 3(4x + 5)
Santa's elves are creating treat bags containing a selection of Kit Kats, Reese's cups and Almond Joys. (A) How many different types of bags can they make containing 10 chocolate bars. (B) How many different types of bags can they make containing 10 chocolate bars if Santa wants to have at least 1 Kit Kat(s), 2 Reese's cup(s) and 1 Almond Joy(s) in the bag
Answers
There are 59,049 different types of bags that can be made containing 10 chocolate bars and 54 x 729 = 39,366 different types of bags that can be made containing 10 chocolate bars with at least 1 Kit Kat, 2 Reese's cups, and 1 Almond Joy in the bag.
(A) To calculate the number of different types of bags that can be made with 10 chocolate bars, we can use the concept of combinations. Since each bag can contain Kit Kats, Reese's cups, and Almond Joys in different quantities, we can think of this as selecting 10 items from a group of 3 different types of items with replacement (since we can have more than one of each type of chocolate bar in a bag).
The formula for the number of combinations with replacement is: n^r, where n is the number of items to choose from and r is the number of items to choose
In this case, n = 3 (since there are 3 different types of chocolate bars) and r = 10 (since we are choosing 10 chocolate bars for each bag). Therefore, the number of different types of bags that can be made is: 3^10 = 59,049
So there are 59,049 different types of bags that can be made containing 10 chocolate bars.
(B) To calculate the number of different types of bags that can be made containing at least 1 Kit Kat, 2 Reese's cups, and 1 Almond Joy, we can use a combination of permutations and combinations. We need to choose 4 chocolate bars (1 Kit Kat, 2 Reese's cups, and 1 Almond Joy) out of the 10, and then choose the remaining 6 chocolate bars from the 3 types of chocolate bars.
First, we choose the 4 chocolate bars with the required distribution:
We can choose 1 Kit Kat in 3 ways (since there are 3 Kit Kats to choose from).
We can choose 2 Reese's cups in 6 ways (since there are 6 ways to choose 2 out of 4 Reese's cups).
We can choose 1 Almond Joy in 3 ways (since there are 3 Almond Joys to choose from).
Therefore, the number of ways to choose the 4 required chocolate bars is: 3 x 6 x 3 = 54
Next, we choose the remaining 6 chocolate bars from the 3 types of chocolate bars. This can be done using the formula for combinations with replacement, as in part (A): n^r, where n is the number of items to choose from and r is the number of items to choose
In this case, n = 3 (since there are 3 types of chocolate bars) and r = 6 (since we are choosing 6 chocolate bars for each bag). Therefore, the number of different types of bags that can be made with the required distribution of chocolate bars is: 3^6 = 729
So there are 54 x 729 = 39,366 different types of bags that can be made containing 10 chocolate bars with at least 1 Kit Kat, 2 Reese's cups, and 1 Almond Joy in the bag.
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If \( f(x)=5 x, g(x)=-2 x+1 \), and \( h(x)=x^{2}+6 x+8 \), find f(h \( (-3)] \).
Answers
The f(h \((-3)]\) = -5.
To find f(h \((-3)]\), we need to first find the value of h \((-3)]\) and then plug that value into the function f(x).
Step 1: Find h \((-3)]\)
h(x) = x^2 + 6x + 8
h(-3) = (-3)^2 + 6(-3) + 8
h(-3) = 9 - 18 + 8
h(-3) = -1
Step 2: Plug the value of h(-3) into the function f(x)
f(x) = 5x
f(h(-3)) = 5(-1)
f(h(-3)) = -5
Therefore, f(h \((-3)]\) = -5.
I hope this helps! Let me know if you have any further questions.
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read the ss
PLS HELP
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Answer:
x intercept
Step-by-step explanation:
please give brainliest
Question 4 \( 1 \mathrm{pts} \) The norm of vector \( v=\left[\begin{array}{c}4 \\ \sqrt{3} \\ \sqrt{6}\end{array}\right] \) is \( \|v\|=? ? ? \) ? \[ \begin{array}{l} 50 \\ \sqrt{13} \\ 4+\sqrt{3}+\s
Answers
\(\|v\|=\sqrt{50}\)
The norm of vector \(v\) is \( \|v\|=\sqrt{4^2 + \sqrt{3}^2 + \sqrt{6}^2}=\sqrt{50} \). Therefore, the answer is \(\|v\|=\sqrt{50}\).
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Please Answer these questions asap
Question 1: Find the radius of the small
circle.
A = 125 pie
R = 15
r = ?
Question 2: Find the shaded area.
Answers
1) The radius of the small circle r is 5√5 and 2) The shaded area will be 13.5π cm².
Area of circle A = 125 π, Radius of circle R = 15, We need to find the radius of the small circle r. By comparing both circles,Area of circle A = πR² 125π = π × 15² 125π = π × 225, 125π = 225 πr², r² = (125π) / πr² = 125r = √125r = 5√5. Hence, the radius of the small circle r is 5√5.
A circle of radius 9 cm with a sector of angle 60° cut out. We know that the area of the circle is given by ,Area of circle = πr² Where, r = 9 cm Area of circle = π × 9²= π × 81= 81 π. Since we have cut a sector of 60°,The remaining angle = 360° - 60° = 300° Fraction of the circle left = (300/360) = 5/6
Therefore,The area of the circle left = (5/6) × 81 π= 67.5 π. The area of the shaded portion = (Area of circle) – (Area of the circle left) Area of the shaded portion = 81 π – 67.5 π= 13.5 π cm², Hence, the shaded area is 13.5π cm².
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Joe wants $75,000 in 18 years to give his grandkids for college. How much must he deposit now at 3.75% interest, compounded monthly?
Answers
Answer:
$35,734.12
Step-by-step explanation:
To determine the amount Joe must deposit now to have $75,000 in 18 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A is the future value we want to have ($75,000 in this case)
P is the present value we need to deposit now
r is the annual interest rate (3.75%)
n is the number of times interest is compounded per year (12 for monthly compounding)
t is the number of years (18)
Substituting the given values, we get:
$75,000 = P(1 + 0.0375/12)^(12*18)
Simplifying the exponent:
$75,000 = P(1.003125)^216
Dividing both sides by (1.003125)^216:
P = $75,000 / (1.003125)^216
P ≈ $35,734.12
Therefore, Joe must deposit approximately $35,734.12 now to have $75,000 in 18 years at an interest rate of 3.75% compounded monthly.
please solve this homework please
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Answer:
Step-by-step explanation:
first you find the numbers that go with the numbers like base times height
times length then you add it all up read this two times to understand
if tan 45 is equal to 1 what is the value of sin 45 + cos 45
Answers
Answer: [tex]\sqrt2[/tex] or 1.41
And we know that tan=sin/cos
We need to change sin(45) +cos(45) to be sin(45)/cos(45) = 1
Or you could find the value if sin(45) which is = 0,7071067812 and cos(45)=0,7071067812 and when you divide the values of sin and cos your answer is 1
Artemio borrows $90,000 to buy a business. The bank gives him a loan, with a simple interest rate of 4% each year. It takes Artemio 10 years to pay the bank back – how much does he pay back in total?
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The amount he would pay back in total is $126,000.
How much would he payback in total?The amount he would pay back is the sum of the amount borrowed and the interest rate on the loan.
Amount that would be paid back = amount borrowed + interest
Simple interest is a linear function of the amount borrowed, interest rate and the duration of the loan. The simple interest is the cost of borrowing.
Interest = amount borrowed x interest rate x time
$90,000 x 0.04 x 10 = $36,000
Amount that would be paid back = interest + amount that is borrowed
= $36,000 + $90,000 = $126,000
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5-6 MathXL for School: Practice and Application Cop Solve the equation by factoring. v^(2)-2v+1=0
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The equation v^(2)-2v+1=0 can be solved by factoring. Factoring is a process of breaking down a number or expression into its component parts. In this case, we can factor the equation into (v-1)(v-1), which is equal to zero. Therefore, the solution to the equation is v = 1.
Factoring is a useful tool for solving equations. By factoring, we can break a complex equation into simpler parts, which makes it easier to solve. It can also be used to identify solutions that are not obvious by looking at the equation. It is a valuable skill to have in mathematics, as it can be used to solve many equations quickly and efficiently. It is also an important skill to have when working with polynomials, as it allows us to identify the zeros of a polynomial.
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You can fill a 15 gallon tank of gas for $26. 99 or buy gas for $2. 10 gallon
Answers
Answer: finish the question if you need help
Step-by-step explanation:
Answer: 15 gallon for 26.99
Step-by-step explanation:
15 (gallons) x 2.10 ($ per gallon) = 31.5
therefore cheaper to buy 15 gallons
Brendan is 5 years older than Valerie. In 6 years the sum of their ages will be 81 . How old is Brendan now? years old
Answers
Brendan is currently 37 years old.
To solve this problem, we can use algebra. Let's let V represent Valerie's age and B represent Brendan's age. We can set up the following equations based on the information given in the question:
B = V + 5 (Brendan is 5 years older than Valerie)
B + 6 + V + 6 = 81 (In 6 years, the sum of their ages will be 81)
Simplifying the second equation, we get:
B + V + 12 = 81
B + V = 69
Substituting the first equation into the second equation, we get:
V + 5 + V = 69
2V = 64
V = 32
Now that we know Valerie's age, we can use the first equation to find Brendan's age:
B = 32 + 5
B = 37
So Brendan's current age is calculated to be 37 years
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Given a circle centered at point O and any three points A, B, and C on the circle, show that the angle BAC is half the corresponding central angle BOC. What does this say about the angle BAC if we keep points B and C fixed, but allow the point A to move around the circle? What if B and C are endpoints of the diameter of the circle?
Answers
The angle BAC will always be a right angle (90 degrees).
Given a circle centered at point O and any three points A, B, and C on the circle, the angle BAC will always be half of the corresponding central angle BOC.
If we keep points B and C fixed and allow point A to move around the circle,
then the angle BAC will stay the same.
If points B and C are endpoints of the diameter of the circle, then the angle BAC will always be a right angle (90 degrees).
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you finish, write the letters from the remaining boxes Harry can paint a room in 3 hours, and Kerry can paint it in 4 hours. How long will it take if they work together?
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The amount of time it will take them when working together is 12/7 hours, or approximately 1.71 hours.
If Harry can paint a room in 3 hours, and Kerry can paint it in 4 hours, then we can use the formula for combined work (work rate) to find how long it will take if they work together. The formula is:
1/t = 1/t₁ + 1/t₂, where t is the time it takes for them to complete the work together, t₁ is the time it takes for Harry to complete the work alone, and t₂ is the time it takes for Kerry to complete the work alone.
Plugging in the values we have, we get:
1/t = 1/3 + 1/4.
Multiplying both sides of the equation by 12t, we get:
12 = 4t + 3t.
Simplifying, we get:
12 = 7t.
Dividing both sides of the equation by 7, we get:
t = 12/7.
Therefore, it will take Harry and Kerry 12/7 hours, or approximately 1.71 hours, to paint the room together.
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A laundry detergent company's 32-ounce bottles pass inspection 98/100 of the time. If the bottle does not pass inspection, the company loses the unit cost for each bottle of laundry detergent that does not pass inspection, which is $3. 45. If 800 bottles of laundry detergent are produced, about how much money can the company expect to lose?
Answers
The business can anticipate losing roughly $55.20 as a result of subpar inspections.
Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
If the bottles pass inspection with probability 98/100, then they fail inspection with probability 1 - 98/100 = 2/100 = 0.02.
Out of 800 bottles of laundry detergent, we can expect about 0.02*800 = 16 bottles to fail inspection.
The cost to the company for each failed bottle is $3.45, so the total cost to the company is approximately 16*$3.45 = $55.20.
Therefore, the company can expect to lose about $55.20 due to failed inspections.
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If Tina is x years old then what is her age two years befor
Answers
Answer:
x-2
Step-by-step explanation:
If you start of with X, you don't know what the value of X is, so you take away two from what we label as X
The total interest he paid on this loan is \( \$ \) (Round to the nearest cent as needed.)
Vifredo bought a new boat for \( \$ 14,200 \). He paid \( \$ 2,500 \) for the down payment and financed the
Answers
The total interest he paid on this loan is $1,507.69
Vifredo bought a new boat for $14,200. He paid $2,500 for the down payment and financed the remaining amount for 48 months at an APR of 5.6%.
The total interest he paid on this loan is $1,507.69 (Round to the nearest cent as needed.)
To calculate the total amount that Vifredo will pay for his boat after 48 months, we need to add the amount he paid for the down payment to the total amount he will pay in 48 months at an APR of 5.6%.Vifredo's loan amount = $14,200 - $2,500 = $11,700
Calculating total amount for 48 months:Total amount = Monthly payment × Number of months Monthly payment can be calculated using the formula:PMT = (P × r) / (1 - (1 + r)^-n)where,PMT = Monthly paymentP = Principal amountr = Rate of interest per month (APR / 12) = 5.6% / 12n = Number of months= 48In our case,P = $11,700r = 5.6% / 12n = 48PMT = (11700 × (5.6 / 12)) / (1 - (1 + (5.6 / 12))^-48) = $267.34Total amount for 48 months = 267.34 × 48 = $12,840.16The total interest he paid on this loan is $1,507.69 (Round to the nearest cent as needed.)Therefore, the total amount Vifredo will pay for his boat is $2,500 (down payment) + $12,840.16 (total amount for 48 months) = $15,340.16.
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Rationalise the denominator of (6 + √3)(6-√3) √33
Answers
The value of the fraction expression after rationalise the denominator will be √33.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ [(6 + √3)(6 - √3)] / √33
Simplify the expression, then we have
⇒ [(6 + √3)(6 - √3)] / √33
⇒ [6² - (√3)²] / √33
⇒ [36 - 3] / √33
⇒ 33 / √33
⇒ √33
The value of the fraction expression after rationalise the denominator will be √33.
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What is the value of the first quartile?
3
6
8
11
Answers
The requried value of the first quartile is 4.5.
What is the Interquartile range?Interquartile range (IQR): The IQR is the range of the middle 50% of values in a data set. To calculate the IQR, we first need to find the quartiles of the data set.
To find the first quartile (Q1), we need to arrange the given values in ascending order and then find the median of the lower half of the values.
The given values arranged in ascending order are:
3, 6, 8, 11
The lower half of the values are:
3, 6
The median of the lower half is:
(Q1) = (3 + 6)/2 = 4.5
Therefore, the value of the first quartile is 4.5.
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14. A candle has the shape of a right prism whose bases are regular polygons with 12 sides. On each base, the distance from one vertex to the opposite vertex, measured through the centre of the base, is approximately 2 in. The candle is 5 in. high.
a) What is the area of the base, to the nearest square inch?
b) What is the volume of wax in the candle, to the nearest cubic inch?
Answers
a) Area of the base is approximately 182 square inches.
b) Volume of wax in the candle is approximately 912 cubic inches.
What is circumradius of a regular polygon?
The distance between any vertex and the center of a regular polygon is its radius. Every vertex will have the same situation. The polygon's radius is also equal to the diameter of the circle that encircles each vertex.
a) Since the base of the candle is a regular polygon with 12 sides, it can be considered a dodecagon. Each angle of a regular dodecagon measures:
(12 - 2) x 180° / 12 = 150°
The distance from one vertex to the opposite vertex, measured through the center of the base, is the same as the diameter of the circumcircle of the dodecagon. We can use the formula for the circumradius of a regular polygon to find this distance:
r = s / (2 sin(180°/n))
where r is the circumradius, s is the side length, and n is the number of sides. Since the dodecagon is regular, all the side lengths are equal, so we can just use one of them.
s = 2 in (approximately, given in the problem)
r = 2 / (2 sin(180°/12)) = 2 / (2 sin(15°)) ≈ 7.88 in
The area of the dodecagon base is:
[tex]A = (12/2) r^2 sin(360/12) \\\\ A = 6 * 7.88^2 x sin(30) \\\\A = 182.42 in^2[/tex]
So the area of the base is approximately 182 square inches.
b) The volume of the candle is equal to the area of the base multiplied by the height:
V = A x h
where A is the area of the base and h is the height of the prism.
The height of the candle is given as 5 in, and we just calculated the area of the base as approximately 182.42 in^2. Therefore, the volume of the candle is:
[tex]V = 182.42\ in^2 * 5 \ in\\\\ V= 912.1 in^3[/tex]
So the volume of wax in the candle is approximately 912 cubic inches.
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Graph the system of equations below on the coordinate grid provided.
y= 4x - 2
y= 1/2x + 5
SHOW ALL OF YOUR WORK and write the answer as an ordered pair.
Answers
A solution to the given system of linear equations is (2, 6).
How to graph the solution to this system of equations?In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
y = 4x - 2 ......equation 1.
y = 1/2(x) + 5 ......equation 2.
Next, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.
Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is given by the ordered pair (2, 6).
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Someone help me solve this!
I’ll mark brainiest!
Answers
Answer: 10,210$
Step-by-step explanation:
Its simple really. The formula is 800 x 2.65 x 1. 10,210.
Use this next time, good luck :)
Answer: $879.50
Step-by-step explanation:
The simple interest formula is I = prt
Plug values in:
(Percent move decimal over 2 and time has to be in years, so 3 years and 9 months is 3.75 years)
I = (800)(0.0265)(3.75)
I = (21.2)(3.75)
I = 79.5
Add the interest to the principle:
800 + 79.5 = $879.50
Hope this helps!
3) The height of a ball above the ground t seconds after it is thrown is h(t) = 20 + 32t - 16t
a) How long will it take for the ball to hit the ground?
b) How long does it take to reach its maximum height?
c) What is the ball's maximum height?
d) If the ball was thrown from a height of 30 feet what would the equation be?
Answers
a) The time it takes for the ball to hit the ground is given as follows: 2.5 seconds.
b) The time it takes for the maximum height is of: 1 second.
c) The maximum height is of: 36 feet.
d) The equation would be of: h(t) = 30 + 32t - 16t².
How to obtain the features?The quadratic function for the ball's height is given as follows:
h(t) = 20 + 32t - 16t².
In which:
20 feet is the initial height.32 feet per second is the initial velocity.-16 ft/s² is the gravity.The coefficients are given as follows:
a = -16, b = 32, c = 20.
Then the discriminant is of:
D = b² - 4ac
D = 32² - 4 x (-16) x 20
D = 2304.
The positive root gives the time it takes for the ball to hit the ground, as follows:
t = (32 + sqrt(2304))/32
t = 2.5 seconds.
The time to reach the maximum height is the t-coordinate of the vertex, hence:
t = -b/2a
t = -32/-32
t = 1 second.
The maximum height is of:
h(1) = 20 + 32 - 16
h(1) = 36 feet.
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Find all the zeros. Write the answer in exact form. p(x)=4x^(4)-15x^(3)+9x^(2)+16x-12
Answers
The zeros of the polynomial p(x)=4x^(4)-15x^(3)+9x^(2)+16x-12 are approximately -0.764, 0.621, 2.572, and 3.071.
To find the zeros of the given polynomial p(x)=4x^(4)-15x^(3)+9x^(2)+16x-12, we need to solve the equation p(x)=0.
First, let's try to factor the polynomial. We can use the Rational Root Theorem to find the possible rational zeros of the polynomial. The possible rational zeros are ±1, ±2, ±3, ±4, ±6, and ±12.
Let's try each of these possible zeros until we find one that makes the polynomial equal to zero.
When we plug in x=1, we get p(1)=4(1)^(4)-15(1)^(3)+9(1)^(2)+16(1)-12=2, which is not equal to zero.
When we plug in x=2, we get p(2)=4(2)^(4)-15(2)^(3)+9(2)^(2)+16(2)-12=20, which is not equal to zero.
When we plug in x=3, we get p(3)=4(3)^(4)-15(3)^(3)+9(3)^(2)+16(3)-12=90, which is not equal to zero.
When we plug in x=-1, we get p(-1)=4(-1)^(4)-15(-1)^(3)+9(-1)^(2)+16(-1)-12=-30, which is not equal to zero.
When we plug in x=-2, we get p(-2)=4(-2)^(4)-15(-2)^(3)+9(-2)^(2)+16(-2)-12=4, which is not equal to zero.
When we plug in x=-3, we get p(-3)=4(-3)^(4)-15(-3)^(3)+9(-3)^(2)+16(-3)-12=-162, which is not equal to zero.
So, none of the possible rational zeros are actually zeros of the polynomial.
Therefore, the polynomial does not have any rational zeros. The zeros of the polynomial are irrational or complex numbers.
To find these zeros, we need to use a different method, such as the Quadratic Formula or synthetic division.
Unfortunately, these methods are beyond the scope of this answer. However, you can use a graphing calculator or an online polynomial solver to find the approximate values of the zeros.
The approximate zeros of the polynomial are -0.764, 0.621, 2.572, and 3.071.
So, the zeros of the polynomial p(x)=4x^(4)-15x^(3)+9x^(2)+16x-12 are approximately -0.764, 0.621, 2.572, and 3.071.
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Find the value of each trigonometric value.
Answers
The values of the trigonometric functions for angle C in the given right-angled triangle are
[tex]sin(C) = 0.6 \\ cos(C) = 0.8 \\ tan(C) = 0.75 \\ csc(C) = 1.7\\ sec(C) = 1.25 \\ cot(C) = 1.3[/tex]
What is Pythagoras theorem?
According to Pythagorean theorem to find the length of the other leg of the triangle,
[tex]a^2 + b^2 = c^2[/tex] where a and b are the legs of the triangle and c is the hypotenuse.
So, in this case,
[tex]a^2 + 30^2 = 50^2 \\ a^2 + 900 = 2500 \\ a^2 = 1600 \\ a = 40
[/tex]
Here given all three sides of the triangle.
We need to find the values of the trigonometric functions:
[tex]sin(C) = \frac{opposite \: leg}{hypotenuse }= \frac{30}{50} = 0.6 \\ cos(C) = \frac{adjacent}{hypotenuse} = \frac{40}{50} = 0.8 \\ tan(C) = \frac{opposite}{adjacent} =\frac{ 30}{40} = 0.75 \\ csc(C) =\frac{ hypotenuse}{opposite} = \frac{50}{30} = 1.666... \\ sec(C) = \frac{hypotenuse}{adjacent} = \frac{50}{40} = 1.25 \\ cot(C) = \frac{adjacent}{opposite} = \frac{40}{30} = 1.333...
[/tex]
Therefore, the values of the trigonometric functions for angle C in the given right-angled triangle are
[tex]sin(C) = 0.6 \\ cos(C) = 0.8 \\ tan(C) = 0.75 \\ csc(C) = 1.666... = 1.7\\ sec(C) = 1.25 \\ cot(C) = 1.333... = 1.3[/tex]
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