Dominique throws a softball from the outfield. After 1 second, the ball is 10 feet high. After 4 seconds, the ball reaches its maximum height of 46 feet. After 7 seconds, it returns to a height of 10 feet.
What is the equation of the quadratic function that models the height of the ball h(t) at time t?
Answers
The quadratic equation that models the height of the ball h(t) at time t is given as follows:
h(t) = -4(t - 4)² + 46.
How to model the quadratic function?The vertex-form definition of a quadratic function is given as follows:
y = a(x - h)² + k.
We have that the parameters are given as follows:
The coordinates of the vertex are (h,k).a is the leading coefficient of the function.After 4 seconds, the ball reaches its maximum height of 46 feet, hence the coordinates of the vertex are given as follows:
(4,46).
Thus:
h(t) = a(t - 4)² + 46.
After 1 second, the ball is 10 feet high, hence when t = 1, h(t) = 10, meaning that the leading coefficient of the quadratic function is obtained as follows:
10 = a(1 - 4)² + 46
9a = -36
a = -36/9
a = -4.
Then the quadratic function for the height is defined as follows:
h(t) = -4(t - 4)² + 46.
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Related Questions
yup yup help me please so i can hurry and finish this test
Answers
Answer:
y= -2x-4
Step-by-step explanation:
CAN SOMEONE PLEASE HELP ME PLEASE
Answers
Answer:
Should be <ABC = 25
degrees
Step-by-step explanation:
100 + 55 = 155
180 (Interior Angles of a Triangle Rule) - 155 = 25
(a) Explicitly check that 17) +[21] 98] [-5] in Z13. (b) Suppose that [5] .[7) [8] . [9] makes sense. Find the value of n if we are working in the ring Zn 157
Answers
(a) \([17] + [21] \cdot [98] - [5] = [12]\) in \(\mathbb{Z}_{13}\).
(b) If we are working in the ring \(\mathbb{Z}_{157}\), the value of \(n\) is 157.
(a) To explicitly check the expression \([17] + [21] \cdot [98] - [5]\) in \(\mathbb{Z}_{13}\), we need to perform the operations using modular arithmetic.
First, let's compute \([21] \cdot [98]\):
\[ [21] \cdot [98] = [21 \cdot 98] \mod 13 = [2058] \mod 13 = [0] \mod 13 = [0]\]
Next, we can substitute the results into the original expression:
\[ [17] + [0] - [5] = [17] - [5] = [12]\]
(b) We are given the expression \([5] \cdot [7] \cdot [8] \cdot [9]\) in \(\mathbb{Z}_n\) and we need to find the value of \(n\) if the expression makes sense.
To find the value of \(n\), we can evaluate the expression:
\[ [5] \cdot [7] \cdot [8] \cdot [9] = [5 \cdot 7 \cdot 8 \cdot 9] \mod n\]
We are given that the result is equal to 157:
\[ [5 \cdot 7 \cdot 8 \cdot 9] \mod n = [157] \mod n\]
To find \(n\), we can solve the congruence equation:
\[ [5 \cdot 7 \cdot 8 \cdot 9] \mod n = [157] \mod n\]
Since 157 is a prime number, there are no factors other than 1 and itself. Therefore, we can conclude that the value of \(n\) is 157.
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Guys what's (√8 + √2)²
Answers
Answer:
10
Step-by-step explanation:
Since the whole thing is squared, we can cancel out the square roots.
8 + 2 = 10
Find the volume of the right prism or right cylinder. Round your final answer to the nearest whole number if necessary.
Answers
The volume of the hexagonal prism is 2630.5 \(cm^{3}\)
What is Hexagonal Prism?Hexagonal Prism is a three-dimensional prism with a hexagonal base and top. The hexagonal prism contains 2 hexagons (one is the base and the other on the top) and 6 rectangles connecting the hexagonal faces.
How to determine this
Volume of Hexagonal prism = (3√3/2) * \(s^{2} h\)
Where s is the sides of the hexagonal base
h is the height of the hexagonal base
Volume of hexagonal base = 3√3/2 * (\((7.5^{2} )\) * 18
Volume = 3√3/2 * 56.25 * 18
Volume = 3√3/2 *1012.5
Volume = 2.598 * 1012.5
Volume = 2630.475
Volume = 2630.5 \(cm^{2}\)
Therefore, the volume of hexagonal prism is 2630.5 \(cm^{2}\)
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Find the output, y, when the input, c, is -1.
y
у
8
6
41
2+
+
+
2
-6
- 2
4
6
- 2
-6
Answers
Answer:
41
Step-by-step explanation:
Look
The robotics club is selling shirts for a fundraiser. They have purchased a box of shirts for $400 at $5 per shirt. To promote their fundraiser, they have also spent $60 on advertising.
Which equation can the club use to calculate the selling price per shirt if they want to make a profit of $300? Select all that apply.
400x=5x+360
80x-460=300
80x+300=460
400x-60=300
80x=760
5x=300
2000x=360
400/5x=300
Answers
Answer:
1, 8, 3
Step-by-step explanation:
Explanation:
Find two consecutive even integers whose sum is 86. Which of the following equations could be used to solve the problem?
4x = 86
2x + 1 = 86
2x + 2 = 86
x2 + 2= 86
Answers
Answer:
ucg
Step-by-step explanation:
Answer:
2x+1=86
Step-by-step explanation:
I think thats the answer, Im not sure though
Wildlife scientists studying a certain species of frogs know that past records indicate the adults should weigh an average of 118 grams with a standard deviation of 14 grams. The researchers collect a random sample of 50 adult frogs and weigh them. In their sample the mean weight was only 110 grams. One of the scientists is alarmed, fearing that environmental changes may be adversely affecting the frogs. Do you think this sample result is unusually low? Explain.
Answers
Therefore, based on the analysis, the sample result of 110 grams is considered unusually low compared to the expected population mean of 118 grams.
To determine if the sample result of 110 grams is unusually low, we can use statistical analysis by comparing the sample mean to the population mean and considering the standard deviation.
Population mean (μ) = 118 grams
Standard deviation (σ) = 14 grams
Sample size (n) = 50
Sample mean (x) = 110 grams
First, we can calculate the standard error of the sample mean using the formula:
Standard Error (SE) = σ / √(n)
SE = 14 / √(50)
≈ 1.98 grams
Next, we can calculate the z-score, which measures the number of standard deviations the sample mean is away from the population mean. The formula for the z-score is:
z = (x - μ) / SE
z = (110 - 118) / 1.98
≈ -4.04
The z-score tells us how many standard deviations the sample mean is below the population mean. In this case, the z-score is approximately -4.04. To determine if the sample result is unusually low, we need to compare the z-score to a critical value. Typically, a z-score beyond a certain threshold (usually 2 or -2) is considered unusual. Using a threshold of 2 standard deviations, if the z-score falls beyond -2, it would indicate that the sample mean is unusually low. In this case, the z-score of -4.04 is significantly below -2, which suggests that the sample mean of 110 grams is indeed unusually low.
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Percentage:
The ratio of the volume of water in a glass jar to the volume of water in a ceramic jar is 2:3. If the volume of water in the glass jar is increased by 200%, by what percentage should the volume of water in the ceramic jar be increased such that both jars each end up with the same volume of water?
Answers
Answer:
100%
glass.......x
ceramic....y
x:y = 2:3
x/y = 2/3
after the increase in both jars:
3x:ny = 1:1
3x/ny = 1
3/n × x/y = 1
3/n × 2/3 = 1
3/n = 3/2
n = 2
volume of vater in the ceramic (y) is two times larger than before
2y = y + y = y + 100%y
you increased one more time the original volume of water or 100% of the original volume
What language do Pattie and Jairo speak to each other upon meeting?
Answers
The language that Pattie and Jairo speak to each other upon meeting was Spanish.
What happens in "Counting by Sevens"?Holly Goldberg Sloan's novel "Counting by Sevens" centers around Willow Chance, a math and science prodigy who finds difficulty in connecting with others emotionally.
Following an unforeseen incident that drastically alters her life, Willow meets various individuals whose guidance enables her to understand love, friendship, and family. When Pattie and Jairo first encounter each other, they communicate solely in Spanish. Overall, the book is an inspiring and reflective read, skillfully examining topics such as resilience, loss, grief, and community.
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A random variable follows a binomial distribution with a probability
of success equal to 0.66. For a sample size of n = 6, find the
values below.
a. the probability of exactly 4 successes
b. the probability of 5 or more successes
c. the probability of exactly 6 successes
d. the expected value of the random variable
Answers
a. The probability of exactly 4 successes is approximately 0.2967.
b. The probability of 5 or more successes is approximately 0.5332.
c. The probability of exactly 6 successes is approximately 0.1399.
d. The expected value of the random variable is 3.96
To solve these problems, we'll use the binomial probability formula:
P(X = k) = C(n, k)× \(p^{k}\)× \((1-p)^{(n-k)}\)
where:
P(X = k) is the probability of getting exactly k successes,
n is the sample size,
p is the probability of success,
C(n, k) is the number of combinations of n items taken k at a time.
Now let's solve each part of the problem:
a. The probability of exactly 4 successes:
P(X = 4) = C(6, 4) × (0.66)⁴ × (1 - 0.66)⁽⁶⁻⁴⁾
C(6, 4) = 6! / (4! × (6 - 4)!) = 6! / (4! × 2!) = (6 × 5) / (2 × 1) = 15
P(X = 4) = 15 × (0.66)⁴ × (0.34)² ≈ 0.2967 (rounded to four decimal places)
b. The probability of 5 or more successes:
P(X ≥ 5) = P(X = 5) + P(X = 6)
P(X = 5) = C(6, 5) × (0.66)⁵ × (1 - 0.66)⁽⁶⁻⁵⁾ = 6 × (0.66)⁵ × (0.34)¹ ≈ 0.3933
P(X = 6) = C(6, 6) × (0.66)⁶ × (1 - 0.66)⁽⁶⁻⁶⁾ = 1 × (0.66)⁶× (0.34)⁰ = 0.1399
P(X ≥ 5) = P(X = 5) + P(X = 6) = 0.3933 + 0.1399 ≈ 0.5332 (rounded to four decimal places)
c. The probability of exactly 6 successes:
P(X = 6) = C(6, 6) × (0.66)⁶ × (1 - 0.66)⁽⁶⁻⁶⁾ = 1 × (0.66)⁶ × (0.34)⁰= 0.1399
d. The expected value of the random variable:
The expected value (mean) of a binomial distribution is given by:
E(X) = n × p
E(X) = 6 × 0.66 = 3.96
Therefore:
a. The probability of exactly 4 successes is approximately 0.2967.
b. The probability of 5 or more successes is approximately 0.5332.
c. The probability of exactly 6 successes is approximately 0.1399.
d. The expected value of the random variable is 3.96
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which of these expressions are equivalent to 225^3/2? select all that apply.
Answers
Answer:
Step-by-step explanation:
(A) and (B)
Not much explanation can be given as these are basically just following definitions
sinx =căn 2/3
sinx=5/4
sinx =1
sin3x=can3/2
sin(x-60)=-1/2
sin3x=1/2
Answers
Answer:
Correct option is
B
0
D
−1
sinx+sin2x+sin3x
=sin(2x−x)+sin2x+sin(2x+x)
=2sin2xcosx+sin2x [ by using sin(A+B)=sinAcosB+sinBcosA and sin(A−B)=sinAcosB−sinBcosA ]
=sin2x(2cosx+1)........(i)
cosx+cos2x+cos3x
=cos(2x−x)+cos2x+cos(2x+x)
=2cos2xcosx+cos2x [By using cos(a−b)=cosa⋅cosb+sina⋅sinb and cos(a+b)=cosa⋅cosb−sina⋅sinb]
=cos2x(2cosx+1).....(ii)
∴(sinx+sin2x+sin3x)
2
+(cosx+cos2x+cos3x)
2
=1
sin
2
2x(2cosx+1)
2
+cos
2
2x(2cosx+1)
2
=1.......[From(i)(ii)]
⇒(2cosx+1)
2
=1
⇒2cosx+1=±1
∴cosx=0or−1
Plsase help me with this question
Answers
2,750 milliliters into gallons.
Answers
According to the question 2,750 milliliters is equivalent to approximately 0.725 gallons which can be measured by conversion factor.
Define conversion?Unit conversion is crucial because, save from three countries, the majority of the world utilises the metric system. Because science employs the metric system, unit conversion is crucial. Measurements in the metric system include cm, m, l, and mL.
To convert 2,750 milliliters to gallons, we can use the following conversion factor:
1 gallon = 3,785.41 milliliters
So, we can calculate the number of gallons as follows:
2,750 milliliters ÷ 3,785.41 milliliters/gallon = 0.725 gallons
Therefore, 2,750 milliliters is equivalent to approximately 0.725 gallons.
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The radius is of a circle is 7 kilometers what is the area of a sector bounded by a 180 arc
Answers
Answer:
77 square units
Step-by-step explanation:
Taking π as 22/7
=>(180/360)×(22/7)×(7)^2
=>1/2×22×7
=>11×7
=>77
Suppose the following list of events describes all of the economic activity resulting from an increase in government spending Suppose that at each step after the initial one, the marginal propensity to consume is 0.58 and the tax rate is 12% Step 0. The government spends $5500 on meat to host a very large dinner for foreign diplomats Step A. The butcher takes the income earned by selling the meat saves some and spends the rest on a wedding cake for his daughter. Step B. The baker who produced the wedding cake saves some of her earnings and uses the rest to purchase beautiful candlesticks as gifts for all of her friends. Step C. The local candlestick maker saves some of his revenue for retirement and spends the rest on building materials to improve his house. Instructions: Modify the settings in the interactive tool to represent this event. Then click 'Spending Rounds and use the table to answer the following questions. Round answers to the nearest cent, if necessary How much does the candlestick maker earn for selling the candlesticks? SDS How much does the candlestick maker spend on building materials?
Answers
To find out how much the candlestick maker earns for selling the candlesticks and how much he spends on building materials, we need to follow the marginal propensity to consume (MPC) and tax rate through each step.
Step 0: Government spends $5,500 on meat for foreign diplomats.
Step A: Butcher's income is $5,500. He pays 12% in taxes, so his after-tax income is $5,500 * (1 - 0.12) = $4,840. He spends 0.58 * $4,840 = $2,806.80 on a wedding cake.
Step B: Baker's income is $2,806.80. She pays 12% in taxes, so her after-tax income is $2,806.80 * (1 - 0.12) = $2,470.99. She spends 0.58 * $2,470.99 = $1,433.17 on candlesticks.
Step C: Candlestick maker's income is $1,433.17. He pays 12% in taxes, so his after-tax income is $1,433.17 * (1 - 0.12) = $1,261.19.
So, the candlestick maker earns $1,433.17 for selling the candlesticks.
Now, we calculate how much the candlestick maker spends on building materials:
Candlestick maker spends 0.58 * $1,261.19 = $731.09 on building materials.
Your answer: The candlestick maker earns $1,433.17 for selling the candlesticks and spends $731.09 on building materials.
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find two unit vectors that make an angle of 60° with v = 8, 6
Answers
The two unit vectors are (2/5 +√5/10, 3/10 + 2√5/15) and (2/5 -√5/10, 3/10 - 2√5/15).
Given that, Angle = 60°, v = 8, 6
Consider unit vector a = (x, y)
x² + y² = 1 …. (1)
Now apply the dot product of unit vector with v
a.v = |a||v|cos Ø
a.v = √ (x² + y²) √ (8² + 6²) cos 60º
8x + 6y = 1 × 10 × ½
So we get,
8x + 6y = 5 …. (2)
y = (5 - 8x) / 6
Substituting the value of y in equation (1)
x² + y² = 1
x² + [(5 - 8x)/6]² = 1
x² + 25/36 + 16x²/9 - 20x/9 = 1
25x²/9 - 20x/9 = 11/36
So we get,
4 × (25x² - 20x) = 11
100x² - 80x = 11
100x² - 80x - 11 = 0
Now solve the quadratic equation,
x = { 2/5 ± √5/10}
Substituting the value of x in equation (2)
y = 3/10 ± 2√5/15
Therefore, the two unit vectors are (2/5 +√5/10, 3/10 + 2√5/15) and (2/5 -√5/10, 3/10 - 2√5/15).
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The length of a rectangle is four times its width.
If the perimeter of the rectangle is 60 cm, find its length and width.
Answers
Answer: Length=24ft Width=6ft
Step-by-step explanation:
Perimeter= 2L+2W= 10 W= 60 and W=6ft and L=24ft
Area= Length x Width
A bakery sells apple pies for $9.15. If the pie has a diameter of 6 inches, what is the approximate cost per square inch of the apple pie? Round to the nearest hundredth.
a $1.30
b $0.64
c $0.32
d $0.08
Answers
Based on the diameter of the pie, and the cost of the apple pie, the approximate cost per square inch of the apple pie is $0.32
How to find the approximate cost?First, find the area of the apple pie sold by the bakery because this will be needed to find the approximate cost per square inch.
Area of the pie will be the area of a circle:
= π x radius x radius
Radius is:
= 6 / 2
= 3 inches
The area of the apple pie is:
= π x 3 x 3
= 28.29 inch²
The approximate cost per square inch is:
= 9.15 / 28.29
= $0.32
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Answer: the answer is C $0.32
Step-by-step explanation:
This answer is proving the other person's answer correct
I got the questions on this test correct so I know the answer
Here is photo proof that it is correct
You can trust me because I always try my best to provide the correct answers on these tests. Have a good day FLVS students :)
Simplify: (5) - (+8)
Answers
Answer:
-3
Step-by-step explanation:
hope it help
Answer:
Hello there!^^
Step-by-step explanation:
✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰
Remove the parentheses And than subtract the numbers~~~~~~~~~~~~~~~~~~~~~~~~
→ 1. =5-8
→ 2. = -3
(You can also you a number line to solve this problem)
Answer: -3Hence, your answer would be -3
By your fellow brainly user: xCherryxUwU
#Thanks!
✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰
Solve the equation d divided by 1.2 is equal to 6 PLS HELPP
Answers
Answer:
The answer is 7.2.
Step-by-step explanation:
Have a great day.
Answer:
d = 7.2
Step-by-step explanation:
all you have to do is multiply 1.2 by 6 to get your answer
\(1.2 \times 6 = 7.2\)
Item 4
Find the surface area of the prism.
The surface area is
a
square feet.
Answers
Answer:
xnxnxnzznchamschdntjekdfurnthsjdnfjdjdjdkdkr
Step-by-step explanation:
xmxmxnxmxmxnxmxnxndmsndfhakxufmrjdkxddjrf7sjrifxisufkf8dhrkfdkshgshdbfjdddnfjfkdnfmcmcmdmdkfkfkkfdkfkfkfkfkfkfkfkkfkfkfkfkfkdkdkdmdkdkdkdkdmdmrmddmrm1520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126152019512615201951261520195126
What is the domain of the step function f(x) = [2x]- 1?
O {x|x2-1}
O {x|x ≥ 1}
O x x is an integer}
O {x|x is a real number}
Answers
Domain: {x | x is a real number}
Option D, "{x | x is a real number}" accurately represents the domain of the function.
The domain of the step function f(x) = [2x] - 1, where [2x] represents the greatest integer less than or equal to 2x, can be determined by considering the restrictions on the input values.
In this case, the step function is defined for all real numbers. However, the greatest integer function imposes a restriction. Since the greatest integer function only outputs integers, the input values (2x) must be such that they produce integer outputs.
For any real number x, the greatest integer less than or equal to 2x will always be an integer. Therefore, the domain of the function f(x) = [2x] - 1 is:
Domain: {x | x is a real number}
Option D, "{x | x is a real number}" accurately represents the domain of the function.
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Write a real world problem you could answer by solving the equation 8x + 60 = 300
Answers
You need to make $300 for a new computer. You have $60 already and you can earn $8 for every lawn that you mow. How many lawns do you need to mow to earn at least $300?
y is greater than negative 4 over 3x plus 2
Answers
In Standard Form , \(y = -\frac{4x}{3} + 2\) can be written as 4x+3y =6 .
What is Standard Form of a Equation ?
Ax+By=C
The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y).
The standard form of a linear equation is helpful for determining the x and y-intercepts of a graphed equation. It also helps you understand the concept of least common denominators, which is finding the lowest number to multiply and thus convert two fractions into whole numbers.
Given Equation :\(y = -\frac{4x}{3} + 2\\\)
To convert it into Standard form , Multiply both sides with 3
\(3y = 3(\frac{-4x}{3} +2)\)
\(3y = -4x + 6\\4x + 3y = 6\)
Hence , In Standard Form , \(y = -\frac{4x}{3} + 2\) can be written as 4x+3y =6 .
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EVALUATING EXPI
Evaluate the expression below
when g = 10
6g²
Answers
Answer:
600Step-by-step explanation:
Expression given:
6g²Find its value when g = 10:
6g² = 6(10²) = 6(100) = 600Simplify.
3(x + 4) plzzz answer
Answers
Answer:
3x+12
Step-by-step explanation:
When we multipy 3 with (x+4) it becomes 3x+12
Answer:
3x+12
Step-by-step explanation:
3(x+4)
3*x=3.....keep the x with 3 because x just represents 1
3*4=12
so your answer should be
3x+12
hope this helps :)
Determine the equation of the line that passes through (-8,9) and (2,-6)
Express you answer as a fraction in lowest terms.
Answers
The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.
We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.
Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.
Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.
The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.
Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.
Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.
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