The ball will hit the ground after 4 seconds (x2 = 4).
How to solveGiven the formula h(x) = -16x^2 + v0x + h0, we can plug in the values for the initial velocity (v0) and the initial height (h0) to find the equation that describes the ball's height as a function of time.
v0 = 64 ft/s (initial velocity)
h0 = 12 ft (initial height)
Now, we can write the function for the ball's height:
h(x) = -16x^2 + 64x + 12
To find when the ball hits the ground, we need to solve for x when h(x) = 0:
0 = -16x^2 + 64x + 12
This is a quadratic equation, and we can solve it using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = -16, b = 64, and c = 12.
x = (-64 ± √(64^2 - 4*(-16)12)) / 2(-16)
First, we find the discriminant (b^2 - 4ac):
64^2 - 4*(-16)*12 = 4096 + 768 = 4864
Now we can plug the discriminant back into the quadratic formula:
x = (-64 ± √4864) / (-32)
We have two possible solutions:
x1 = (-64 + √4864) / (-32)
x1 = (-64 + 64) / (-32)
x1 = 0
x2 = (-64 - √4864) / (-32)
x2 = (-64 - 64) / (-32)
x2 = 128 / 32
x2 = 4
Since x1 = 0 represents the initial time when the ball is kicked, we discard this solution.
Therefore, the ball will hit the ground after 4 seconds (x2 = 4).
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The height, in feet, after x seconds of an object launched straight up can be found by the function h(x)=−16x2+v0x+h0, where v0 is the initial velocity of the object and h0 is the initial height.
A ball is kicked straight up into the air from a height of 12 ft with an initial velocity of 64 ft/s. After how many seconds does the ball hit the ground?
Cual es el resultado de de esta ecuacion con valor obsoluto
| x + 1 | = | x - 5 |
Answer:
Well the absolute vaule will allways be postive. Therefore the answer being 2. I Think.
Step-by-step explanation:
Felipe calculated that he uses about 545 gallons of fuel each year. His car's owner's manual says that it is approved to use regular fuel. How much money can he save each year by switching from premium fuel, at $4.59 per gallon, to regular fuel at $4.18 per gallon?
$0.41
$2,501.55
$223.45
$2,278.10
$4,779.65
Answer:
$223.45
Step-by-step explanation:
premium fuel: 4.59 x 545
= 2501.55
regular fuel: 4.18 x 545
=2278.1
2501.55-2278.1 = 223.45
Laura has 4 buckets. She pours a total of 40 liters of water into these buckets. If every bucket gets the same amount, what is the volume of water in each bucket?
Answer:
40,000Step-by-step explanation:
4L × 1000milliliters = 40,000PLEASE HELP! i don’t understand this :(((
Answer:
b : ( 3, 0, -1 )
Step-by-step explanation:
you need to sub the range into the equation to find their domains
Plot the set {-2.5, - 1.5, - 1.0, 1.0) on the number line.
To plot the set {-2.5, -1.5, -1.0, 1.0} on the number line, you would start at zero and mark each of the numbers given on the line. So, starting at zero, you would first mark -2.5 to the left, then -1.5 to the left of that, then -1.0 to the left of that, and finally 1.0 to the right of zero. Your number line should now have 5 marks on it: 1.0, 0, -1.0, -1.5, and -2.5. I
To plot the set {-2.5, -1.5, -1.0, 1.0} on the number line, follow these steps:
1. Draw a horizontal line to represent the number line.
2. Mark the integers on the number line with equal spaces between them (e.g., -3, -2, -1, 0, 1, 2, 3).
3. Locate and mark the positions of each number in the set on the number line:
- For -2.5, mark a point halfway between -2 and -3.
- For -1.5, mark a point halfway between -1 and -2.
- For -1.0, mark a point directly on -1.
- For 1.0, mark a point directly on 1.
4. Label each point with its corresponding value from the set.
Now you have successfully plotted the set {-2.5, -1.5, -1.0, 1.0} on the number line!
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An investment will pay $150 at the end of each of the next 3 years, $250 at the end of Year 4,$400 at the end of Year 5 , and $500 at the end of Year 6 . If other investments of equal risk earn 8% annually, what is its present value? Its future value? Do not round intermediate calculations, Round your answers to the nearest cent:
Present value: $ _______
Future value: $ ______
Given data are: Payment of $150 at the end of each of the next 3 years,Payment of $250 at the end of Year 4,Payment of $400 at the end of Year 5,Payment of $500 at the end of Year 6,Rate of interest = 8% annually
Hence, the Present Value of the investment is $382.20
Present value and future value of investment Formula used: PV = Pmt/(1+r)^n,
FV = Pmt((1+r)^n-1)/r
Let's find the Present Value of the Investment: Given, n = 3 years
Pmt = $150
Rate = 8% annually
PV = 150/(1+8%)³
PV = $382.20
Let's find the Future Value of the Investment: Given, n1 = 3 years
Pmt1 = $150
Rate = 8% annually
n2 = 1 year
Pmt2 = $250
n3 = 1 year
Pmt3 = $400
n4 = 1 year
Pmt4 = $500
FV = (150((1+8%)³-1)/8%)+((250+400+500)(1+8%)³)
FV = $1579.51
Hence, the Future Value of the investment is $1579.51.
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The Zearn Fair charges $1.75 for entrance and $1.05 for each ride. Mr. Sawicki brings $20 with him to the fair. What is the greatest number of rides Mr. Sawicki can go on if he uses $2.50 for food? How much money can Mr. Sawicki spend in total
Step-by-step explanation:
So
Total money = 20
Entrance fee = 1.75
Food = 2.50
Ride = 1.05
Amount spend = 1.75 + 2.05 = 3.8
Left for rides = 20 - 3.8 = 16.2
So rides = 16.2 ÷ 1.05 = 15
I think atleast 15 rides
In a certain class of 40 students, there are 11 boys from Wilmette, 3 girls from Kenilworth, 9 girls from Wilmette, 5 boys from Glencoe, 5 boys from Kenilworth and 7 girls from Glencoe. If the teacher calls upon a student to answer a question, what is the probability that the student will be from Kenilworth
The probability that the student who will be called upon to answer the question will be from Kenilworth is 0.2 or 1/5.
The probability that the student who will be called upon to answer the question will be from Kenilworth can be calculated as follows:
There are a total of 40 students in the class.
Out of these students, there are 3 girls from Kenilworth and 5 boys from Kenilworth.
Hence, the total number of students from Kenilworth is: 3 + 5 = 8
So, the probability that a student from Kenilworth will be called upon to answer the question is:
8/40 = 1/5
= 0.2
Therefore, the probability that the student who will be called upon to answer the question will be from Kenilworth is 0.2 or 1/5.
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pls help me with this
Answer:
P = 22 cm
Step-by-step explanation:
the perimeter (P) is the sum of the 6 sides of the figure
starting with the base and counting clockwise
P = 7 + 4 + 3 + 2 + 4 + 2 = 22 cm
answer two questions about the following rational division.
1. The quotient in lowest terms of the given rational division is (x+2)/(3x-9).
2. The values of r is A. x=-2 and B. x=0.
What is factor?Factor is a quantity which when multiplied by another quantity, produces a given product. Factors are used to simplify and solve equations, as well as in other areas of mathematics. Factors can be numbers, variables, and expressions.
To find the lowest terms, we must divide the numerator and denominator by the same number. The largest common factor of the numerator and denominator is 3. Dividing both the numerator and denominator by 3, we get (x+2)/(3x-9) = (x+2)/(x-3).
The values of r that must be excluded from the domains of the expressions are x=0 and x=3. x=0 must be excluded because it will create a zero in the denominator which is not allowed. x=3 must also be excluded because it will create a zero in the numerator, and thus make the entire expression equal to 0. Thus, the correct answer is A. x=-2 and B. x=0.
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A small plane and a large plane are 6.8km from each other, at the same altitude (height). From an observation tower, the two airplanes are separated by an angle of 58°. The large plane is 5.2km from the observation tower. a. Draw a diagram to represent this situation. b. How far is the small plane from the observation tower, to the nearest tenth of a kilometer?
Answer:
7.9km
Step-by-step explanation:
(a)See attached for the diagram representing this situation.
(b)
In Triangle ABC
\(\text{Using Law of Sines}\\\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \\\dfrac{\sin A}{5.2}=\dfrac{\sin 58^\circ}{6.8} \\\sin A=5.2 \times \dfrac{\sin 58^\circ}{6.8}\\A=\arcsin (5.2 \times \dfrac{\sin 58^\circ}{6.8})\\A=40.43^\circ\)
Next, we determine the value of Angle B.
\(\angle A+\angle B+\angle C=180^\circ\\40.43+58+\angle B=180^\circ\\\angle B=180^\circ-(40.43+58)\\\angle B=81.57^\circ\)
Finally, we find b.
\(\text{Using Law of SInes}\\\dfrac{b}{\sin B}=\dfrac{c}{\sin C} \\\dfrac{b}{\sin 81.57^\circ}=\dfrac{6.8}{\sin 58^\circ} \\b=\dfrac{6.8}{\sin 58^\circ} \times \sin 81.57^\circ\\b=7.9km $ (to the nearest tenth of a kilometer)\)
The distance between the small plane and the observation tower is 7.9km.
suppose we want there to be exactly three 8s in the phone number (starting the number with 0 is ok). how many different phone numbers can be created under these conditions?
To find the number of different phone numbers that can be created with exactly three 8s, we need to consider the possible positions of the 8s within the number.
Let's break it down step by step:
1. Determine the total number of positions in the phone number:
- Phone numbers typically have 10 digits (0-9).
- Since we can start the number with 0, we have 11 possible positions (including the first digit).
2. Choose the positions for the three 8s:
- We need to select 3 positions out of the 11 available positions.
- This can be calculated using combinations. The number of combinations of selecting 3 positions out of 11 is denoted as "11 choose 3" or C(11,3).
- The formula for combinations is: C(n, r) = n! / (r! * (n-r)!), where n is the total number of positions and r is the number of positions we need to choose.
- Substituting the values, C(11,3) = 11! / (3! * (11-3)!)
3. Calculate the number of phone numbers:
- Once we have the number of combinations, we need to calculate the number of phone numbers that can be created.
- For each of the selected positions for the 8s, we have 10 choices (0-9) for the remaining digits.
- So, the total number of phone numbers that can be created is the product of the number of combinations and the number of choices for each position: C(11,3) * 10^8
Let's calculate the number of different phone numbers:
C(11,3) = 11! / (3! * 8!) = (11 * 10 * 9) / (3 * 2 * 1) = 165
Number of phone numbers = C(11,3) * 10^8 = 165 * 10^8 = 1,650,000,000
Therefore, under the given conditions, there are 1,650,000,000 different phone numbers that can be created with exactly three 8s.
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Harry took a loan from the bank.
D represents Harry's remaining debt (in dollars) after t months.
D=200t + 9000
What was the size of Harry's loan?
[100 PTS] (I NEED A ANSWER QUICK!)
Given the equation 3x + 15 = 84:
Part A: Write a short word problem about a purchase made to illustrate the equation. (6 points)
Part B: Solve the equation showing all work. (4 points)
Part C: Explain what the value of the variable represents. (2 points)
Answer:
Alex has 3x dollars and an extra 15 dollars in his coat pocket. He buys a new Nike shoe for 84 dollars. How much money did Alex spend that was not in his pocket.
Step-by-step explanation:
Answer:
Part A: Word problem
Maria went to the store and purchased some books for her book club. Each book cost $3, and she also bought some bookmarks at $15 each. Maria's total purchase, including tax, amounted to $84. If Maria bought x books, write an equation to represent the situation.
Part B: Solution
To solve the equation 3x + 15 = 84, we need to isolate the variable x on one side of the equation.
Step 1: Subtract 15 from both sides of the equation to eliminate the constant term on the left side:
3x + 15 - 15 = 84 - 15
3x = 69
Step 2: Divide both sides of the equation by 3 to isolate x:
3x/3 = 69/3
x = 23
So, the solution to the equation is x = 23.
Part C: Explanation
In the given equation 3x + 15 = 84, the variable x represents the number of books Maria purchased. The equation states that the cost of x books at $3 each, represented by 3x, plus the cost of $15 for bookmarks, totals to $84. Thus, the value of x represents the number of books Maria bought in this scenario. In the solution, x = 23, it means Maria purchased 23 books for her book club.
Step-by-step explanation:
Suppose y varies inversely with x, and y = 49 when x = 17
. What is the value of x when y = 7 ?
Answer:
119 is the value of x when y = 7
Step-by-step explanation:
Since y varies inversely with x, we can use the following equation to model this:
y = k/x, where
k is the constant of proportionality.Step 1: Find k by plugging in values:
Before we can find the value of x when y = k, we'll first need to find k, the constant of proportionality. We can find k by plugging in 49 for y and 17 for x:
Plugging in the values in the inverse variation equation gives us:
49 = k/17
Solve for k by multiplying both sides by 17:
(49 = k / 17) * 17
833 = k
Thus, the constant of proportionality (k) is 833.
Step 2: Find x when y = k by plugging in 7 for y and 833 for k in the inverse variation equation:
Plugging in the values in the inverse variation gives us:
7 = 833/x
Multiplying both sides by x gives us:
(7 = 833/x) * x
7x = 833
Dividing both sides by 7 gives us:
(7x = 833) / 7
x = 119
Thus, 119 is the value of x when y = 7.
P{multiples of 3}and
P{factors of 12}are subsets of U={x:1≤ x≤ 12}
a. Draw a Venn diagram to illustrate the information
b.List PNQ
C.PUQ
d.PUQ
e. PNQ
b. P(N ∪ Q) = P(multiples of 3 οr factors οf 12) = {1, 2, 3, 4, 6, 8, 9, 10, 12}
c. P(U) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
d. P(U) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
e. P(N) = P(multiples of 3) = {3, 6, 9, 12}
What is sets?Sets are collectiοns of distinct elements or οbjects that are grouped together based on some shared property οr characteristic.
b. P(N ∩ Q) = P(multiples of 3 and factοrs of 12) = {3, 6, 12}
P(U) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
P(N ∪ Q) = P(multiples οf 3 or factοrs of 12) = {1, 2, 3, 4, 6, 8, 9, 10, 12}
c. P(U) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
d. P(U) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
e. P(N) = P(multiples of 3) = {3, 6, 9, 12}
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HELPPPPP
4x10^0/6.5x10^2
Answer:
\(\frac{2}{325}\)
Step-by-step explanation:
Assuming you mean simplify \(\frac{4*10^{0} }{6.5*10^{2} }\), first you need to simplify the numerator.
Simplifying the numerator:
\(4*10^{0}=4*1=4\)
This simplifies to 4 because any expression raised to the 0 power is 1.
Simplifying the denominator:
\(6.5*10^{2} =6.5*100=650\)
Dividing the numerator by the denominator:
\(\frac{4}{650} =\frac{2}{325}\)
The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet. 2 0, 1, 3 3 1, 1, 5 4 1, 3, 4 5 0, 8 6 2 Key: 4|1 means 4.1 What is the mean, and what does it tell you in terms of the problem? 4.59 feet; The value means that a typical throw of the ball results in 4.59 feet. 4.1 feet; The value means the furthest the ball went. 3.825 feet; The value means that a typical throw of the ball results in 3.825 feet. 3.1 feet; The value means this measurement had the most occurrences.
Using the data in the stem- and -leaf plot, mean value of given data is 4.59 feet means that a typical throw of the ball results in 4.59 feet.
What is mean?Mean or arithmetic mean is the ratio of sum of all the observation to the number of observations in a data set. It is given by the formula,
\(Mean = \frac{sum of observations}{number of observations}\)
The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet.
The data are given below:
2.0, 2.1, 3.3, 3.1, 3.1, 5.4, 5.1, 5.3, 4.5, 4.0, 8.6, 8.2.
Number of data = 12.
\(Mean = \frac{sum of observations}{number of observations}\)
= \(\frac{2.0+2.1+3.3+3.1+3.1+5.4+5.1+5.3+4.5+4.0+8.6+8.2}{12}\)
=\(\frac{54.7}{12}\)
= 4.59 feet.
Hence, using the data in the stem- and -leaf plot, mean value of given data is 4.59 feet means that a typical throw of the ball results in 4.59 feet.
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Answer:4.59 feet; The value means that a typical throw of the ball results in 4.59 feet.
Step-by-step explanation:
i did in class want it to help yall ik how hard school can be
HELP ASAP I WILL MARK YOU BRAINLEAST
Mack checked 12 dozens of bananas. 4 of the dozens have at least 1 rotten banana. What is the experimental probability that a dozen of bananas has at least 1 rotten banana?
Answer:
1/3
Step-by-step explanation:
4/12 = 4x1/4x3 = 1/3 (simplify)
So the experimental probability is 1/3.
4. Create a story problem that you can create an equation to solve.
Camden drove 34 miles in 4/5 hours. On average, how fast did he drive, in miles per hour?
The rate at which body cover distance is given by speed.
The formual for the speed is,
\(s=\frac{d}{t}\)For the given question, distance is d=34 miles and time is t=4/5 hours.
Substitute the value in the formula to obtain the speed of Camden.
\(\begin{gathered} s=\frac{34\text{ miles}}{\frac{4}{5}\text{ hr}} \\ =\frac{34\cdot5}{4}\text{ miles/hr} \\ =\frac{85}{2}\text{ miles/hr} \end{gathered}\)So the speed at which camden cover distance is 85/2 miles per hour.
At a garage sale, Curtis paid $20 for a box of 40 baseball cards. He plans to re-sell the cards for $4 each. If x is the number of cards that he can re-sell, then the equation y = -20 +4x can be used to determine Curtis's profit (y, in dollars).
Answer:
180
Step-by-step explanation:
Well, I'm not sure but maybe??
What is a requirement of the data in order for us to be allowed to control for individual variability?.
Statistics help present data precisely and draw meaningful conclusions. While presenting data, one should be aware of using adequate statistical measures.
Readers are generally interested in knowing the variability within the sample, descriptive data should be precisely summarized with SD. The use of SEM should be limited to computing CI which measures the precision of population estimate. Journals can avoid such errors by requiring authors to adhere to their guidelines.
Studying the entire population is time and resource-intensive and not always feasible; therefore studies are often done on the sample, and data are summarized using descriptive statistics. These findings are further generalized to the larger, unobserved population using inferential statistics.
For example, to understand the cholesterol levels of the population, the cholesterol levels of the study sample, drawn from the same population are measured.
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How many times does the line y=-1 touch the graph? (Ensure to draw your line on the graph)
Answer:
The answer is 2 times
Step-by-step explanation:
Well, the line y equals to negative 1 is a horizontal line that crosses through the y axis.
So, if we were to draw that line in how many times is that line intersecting or coming into contact with our graph well it's happening in these two places right here (shown in attached photo) so that would intersect two times.
Thus, The answer is 2 times
-TheUnknownScientist 72
5.66. what is the probability that an irs auditor will catch only 2 income tax returns with illegitimate deduc-tions if she randomly selects 5 returns from among 15 returns, of which 9 contain illegitimate deductions?
The probability that an irs auditor will catch only 2 income tax returns with illegitimate deduc-tions = 0.24
Let us assume that X be the number of returns containing illegitimate deductions in the sample.
Here, X has a hypergeometric distribution.
We need to find the probability that an IRS auditor will catch only 2 income tax returns with illegitimate deduc-tions.
Here, N = 15, r = 9, n = 5
So, P (X = 2) = (⁹C₂ × ⁶C₃) / (¹⁵C₅)
We know that the combination formula:
⁹C₂ = 9! / (2! × 7!)
= 36
⁶C₃ = 6! / (3! × 3!)
= 20
¹⁵C₅ = 15! / (5! 10!)
= 3003
P (X = 2) = (⁹C₂ × ⁶C₃) / (¹⁵C₅)
= (36 × 20) / (3003)
= 0.24
Therefore, the required probability is: 0.24
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A dirt bike has been marked down 12% and now costs $4286.70. What was the original cost?
Answer:
$4871.25
Step-by-step explanation:
You know that the dirt bike has been "marked down," so to find the percentage of the original cost, subtract 0.12 from 1 to get 0.88. Then, define x as the original cost, and set up an equation:
0.88x = 4286.70
You know that 4286.70 is 88% of the original cost, so 0.88 times the original cost will equal the marked down cost. Now, divide both sides by 0.88 to get the answer:
x = 4871.25
y = 4x – 3 DON'T KNOW THE ANSWER
Answer:
x=3/4, x=0.75
Step-by-step explanation:
Find the area (will give brainliest)
Answer:
∆ area: 24 in²semicircle area: 14.13 in²Figure area: 38.13 in²Step-by-step explanation:
You want the area of the figure composed of a triangle and a semicircle.
TriangleThe area of the triangle is ...
A = 1/2bh
A = 1/2(8 in)(6 in) = 24 in²
SemicircleThe area of the semicircle is ...
A = 1/2πr²
The radius is half the diameter, so this is ...
A = 1/2(3.14)(3 in)² = 14.13 in²
FigureThe area of the figure is the sum of the areas of the triangle and semicircle:
Figure = triangle + semicircle
Figure = 24 in² +14.13 in² = 38.13 in²
The area of the figure is about 38.13 square inches.
__
Additional comment
Using the "pi button" for π, we get about 38.1372 square inches for the total area.
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Paula's room is 11 feet wide and 13 feet long. What is the area of her room?
Answer:
143
Step-by-step explanation:
11x13=143
Answer: 143
Step-by-step explanation: L * W =A so, 11 multiplied by 13 gives you 143
What is an explicit formula for the geometric sequence 64,16,4,1,... where the first term
should be f(1)
[Choose two answers]
A. f(n)=64(1/4)n-1
B. f(n)=16(1/4)n-1
C. f(n)=64(1/4)n
D. f(n)=16(1/4)n-2
Answer:
A
Step-by-step explanation:
The explicit formula for a geometric sequence is
f(n) = f(1) \((r)^{n-1}\)
where f(1) is the first term and r the common ratio
Here f(1) = 64 and r = \(\frac{f(2)}{f(1)}\) = \(\frac{16}{64}\) = \(\frac{1}{4}\) , then
f(n) = 64 \((\frac{1}{4}) ^{n-1}\) → A