The factors 2t - 3 represent the time it takes for the mountain lion to reach its highest point and return back to the ground.
Used the concept of a quadratic equation that states,
An algebraic equation with the second degree of the variable is called a Quadratic equation.
Given that,
The equation h = -16t² + 24t represents the height (h) of the mountain lion above the ground at any given time (t) in seconds.
Now, By factoring the equation as,
h = -16t² + 24t
h = -8t × (2t - 3)
Here, Factor 2t - 3 indicates the time it takes for the height (h) to reach zero, which corresponds to the mountain lion being on the ground.
So, when 2t - 3 equals zero, the height is zero, indicating that the mountain lion has returned to the ground.
Therefore, factors 2t - 3 help us determine the point in time when the mountain lion reaches its peak height and when it returns back to the ground.
To learn more about the quadratic equation visit:
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What is the volume of this composite solid?
Answer:
A: 64 cubic meters
Step-by-step explanation:
Multiply 7m, 2m, and 4m. You get 56
Then for the smaller cube multiply 2, 2, and 2
A tree that is 8 feet tall is growing at a rate of 2 feet each year. A tree that is 16 feet tall is growing at a rate of 1 1/2 feet each year. Enter the number of years it will take the two trees to reach the same height
Answer: 8.
This is because for every 2 years the 10 foot tree will grow one foot and for every year the 8 foot tree will grow one foot.
It takes 8 years fort the 10 ft tree to be:16
This is because you do:
2+2+2+2+2+2+2+2=16
It takes 8 years for the 8 food tree to be: 16
You do:
2+2+2+2+2+2+2+2=16 and we added it 8 times and in 8 years it will be 16
- - Hope this helps! - -
Heart or brain me!
There were f frogs in a pond. 36 of the frogs hopped away. Write the expression that shows how many frogs are in the pond now.
Answer: f - 36
Step-by-step explanation:
Number of frogs in the pond originally was f.
Then 36 of them hopped away which means that these 36 have to be subtracted from the original f to find out the number of frogs still in the bond.
Expression is therefore:
= Number of frogs originally in the pond - Number of frogs that left
= f - 36
The high school students who attend Springfield Women's Academy are eligible to tryout for various teams within the athletic department. Students are 74% likely to tryout for softball; 27% likely to tryout for volleyball; 42% likely to tryout for tennis; and 88% likely to tryout for swimming. Many students choose to tryout for multiple teams. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors.If Event A = freshman or sophomore, what is Event A'?
Event A' = freshman or senior
Event A' = freshman or junior
Event A' = sophomore or senior
Event A' = junior or senior
Answer:
Event A' = Freshman or Junior
Step-by-step explanation:
Hamal has a new part time job bagging groceries after school. The equation y=10x+50 show the relationship between his hours of work (x) and the money in his bank account (y)
How much is Hamal earning per hour??
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Answer:
uhhhhhhh
Step-by-step explanation:
Answer:
about 314 units
Step-by-step explanation:
i was confused but i hope this helps
Remove parentheses using the distributive property 9 ( x + 8)
Answer:
9x + 72
Step-by-step explanation:
Answer:
9x + 8
Step-by-step explanation:
Hope this helps have a nice day :)
*You don't have to read this part*
Parentheses can be removed by multiplying the outside factor to each term inside the parentheses using distributive property.
Which is the simplified form of p⁰?
O p
O 1/p
O 0
O 1
Answer:
It is p = 1
Step-by-step explanation:
p⁰=1 because it is basically saying and when simplifying fractional exponents we can flip the bottom exponent up to the top if we change the sign, leaving us with : (p⁵-p⁵)=p⁰
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# 84 square inches
4
4. Luke has a cylinder with a radius of 5 inches and a height of 6 inches. What is the total.
surface area of his cylinder in cubic inches? 8.7B-R
F
G
345.6 in?
251.3 in?
188.5 in
471.2 in?
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Use Pi symbol on ca This assignment has been submitted and is no longer editable.
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Complete Question
Luke has a cylinder with a radius of 5 inches and a height of 6 inches. What is the volume of his cylinder in cubic inches?
Answer:
471.24 cubic inches
Step-by-step explanation:
The formula for the volume of a cylinder =
πr²h
r = Radius = 5 in
h = Height = 6 in
Hence,
Volume = π × (5 in)² × 6 in
= 471.24 cubic inches
Therefore, the volume of his cylinder in cubic inches = 471.24 cubic inches
A recent article in Business Week listed the "Best Small Companies." We are interested in the current results of the companies' sales and earnings. A random sample of 8 companies was selected and the sales and earnings, in millions of dollars, are reported below. Sales ($million) 89.2 18.6 18.2 71.7 58.6 46.8 17.5 11.9 Earnings ($million) 4.9 4.4 1.3 8 6.6 4.1 2.6 1.7 Let sales be the independent variable and earnings be the dependent variable. (i) Determine the estimated regression equation and comment on the coefficient of X. (ii) For a small company with $50.0 million in sales, estimate the earnings. (iii) Calculate the standard error of estimate and comment on it. (iv) Find the coefficient of determination and interpret the result.
Answer:
(i) The estimated regression equation is;
[tex]\hat y[/tex] ≈ 1.6896 + 0.0604·X
The coefficient of 'X' indicates that [tex]\hat y[/tex] increase by a multiple of 0.0604 for each million dollar increase in sales, X
(ii) The estimated earnings for the company is approximately $4.7096 million
(iii) The standard error of estimate is approximately 29.34
The high standard error of estimate indicates that individual mean do not accurately represent the population mean
(iv) The coefficient of determination is approximately 0.57925
The coefficient of determination indicates that the probability of the coordinate of a new point of data to be located on the line is 0.57925
Step-by-step explanation:
The given data is presented as follows;
[tex]\begin{array}{ccc}Sales \ (\$million)&&Earning \ (\$million) \\89.2&&4.9\\18.6&&4.4\\18.2&&1.3\\71.7&&8\\58.6&&6.6\\46.8&&4.1\\17.5&&2.6\\11.9&&1.7\end{array}[/tex]
(i) From the data, we have;
The regression equation can be presented as follows;
[tex]\hat y[/tex] = b₀ + b₁·x
Where;
b₁ = The slope given as follows;
[tex]b_1 = \dfrac{\Sigma(x_i - \overline x) \cdot (y_i - \overline y)}{\Sigma(x_i - \overline x)^2}[/tex]
b₀ = [tex]\overline y[/tex] - b₁·[tex]\overline x[/tex]
From the data, we have;
[tex]{\Sigma(x_i - \overline x) \cdot (y_i - \overline y)}[/tex] = 364.05
[tex]\Sigma(x_i - \overline x)^2}[/tex] = 6,027.259
[tex]\overline y[/tex] = 4.2
[tex]\overline x[/tex] = 41.5625
∴ b₁ = 364.05/6,027.259 ≈ 0.06040059005
b₀ = 4.2 - 0.06040059005 × 41.5625 ≈ 1.68960047605 ≈ 1.69
Therefore, we have the regression equation as follows;
[tex]\hat y[/tex] ≈ 1.6896 + 0.0604·X
The coefficient of 'X' indicates that the earnings increase by a multiple of 0.0604 for each million dollar increase in sales
(ii) For the small company, we have;
X = $50.0 million, therefore, we get;
[tex]\hat y[/tex] = 1.6896 + 0.0604 × 50 = 4.7096
The estimated earnings for the company, [tex]\hat y[/tex] = 4.7096 million
(iii) The standard error of estimate, σ, is given by the following formula;
[tex]\sigma =\sqrt{\dfrac{\sum \left (x_i-\mu \right )^{2} }{n - 1}}[/tex]
Where;
n = The sample size
Therefore, we have;
[tex]\sigma =\sqrt{\dfrac{6,027.259 }{8 - 1}} \approx 29.34[/tex]
The standard error of estimate, σ ≈ 29.34
The high standard error of estimate indicates that it is very unlikely that a given mean value within the data is a representation of the true population mean
(iv) The coefficient of determination (R Square) is given as follows;
[tex]R^2 = \dfrac{SSR}{SST}[/tex]
Where;
SSR = The Sum of Squared Regression ≈ 21.9884
SST = The total variation in the sample ≈ 37.96
Therefore, R² ≈ 21.9884/37.96 ≈ 0.57925
The coefficient of determination, R² ≈ 0.57925.
Therefore, by the coefficient of determination, the likelihood of a new introduced data point to located on the line is 0.57925
use distributive property to rewrite the expression 3x(x+4)
Answer:
3x^2 + 12x
Step-by-step explanation:
3x(x +4)
3x^2 + 12x
- Multiply 3x * x = 3x^2
- Multiply 3x * 4 = 12x
Which Gives You 3x^2 + 12x
State if the three numbers can be the measures of the sides of a triangle,
6,8,9
No
Yes
answer plz i really need it
answer
root 15
Step-by-step explanation:
root 15 =3.87 and it is closer to root 4
solve for x
5 - 2x^2 = -15
2x^2-5x+1=4 factor step by step please
Answer in screen shot below
The volume of a cylinder is 8T cubic centimeters. The
radius and the height are equal. What is radius of the
cylinder? Explain how you know.
The box plots summarize the attendance for the spring musical and the fall musical. Each musical was performed for six evenings.
Please help me to do this question with steps
Answer:
x = 71°
Step-by-step explanation:
Segments of tangents from the same external point are congruent, that is
AT = BT
Then Δ ABT is isosceles with base angles congruent , so
x = [tex]\frac{180-38}{2}[/tex] = [tex]\frac{142}{2}[/tex] = 71°
An overnight Train left at 21 55 on a journey that took 9 h 18 min. Given that the train departed on a monday find the day and the time at which it arrived at its destination
Answer:
wait do i have to multiply??
Step-by-step explanation:
A farmer sells 7.7 kilograms of apples and pears at the farmer's market.
1
4
of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market? answer
ttbhbidek umm in 10th grade and idek but u can ask others
The salary of the president and vice president were a total of $576,300 a year. If the president makes $203,700 more a year than the vice president, how much does the vice president make?
A. $166,300
B. $186,300
C. $390,000
D.$286,000
Answer:
The answer is C
Calculate the product below and give your answer in scientific notation.
(1.3 x 10-^2) x (0.05) = ?
Answer:
0.02549509756
nearest hundredth: 0.03
nearest thousandth: 0.025
nearest ten-thousandth: 0.0255
Step-by-step explanation:
1.3x10^-2 = 0.013
0.013x0.05= .00065
Square root of .00065 is 0.02549509756
Which table represents a quadratic function?
Answer:
the first table
Step-by-step explanation:
step by step explanation:in a quadratic function, the second different are the same
50 points plzz help Combine the radicals .
Answer:
D) [tex]-2\sqrt{3}[/tex]
Step-by-step explanation:
[tex]5\sqrt{27} =15\sqrt{3} \\\\15\sqrt{3}-17\sqrt{3} =-2\sqrt{3}[/tex]
Jacob sells homemade skateboard decks for a profit of $27 per deck. He is considering switching to a new type of material that will increase his profit, as expressed by the function y = 32x, where x is the number sold and y is the amount of profit.
How many more dollars will Jacob earn on each skateboard deck if he switches to the new material? Explain how you found your answer. (5 points)
solve with solution
1. A cow is tied to a tree using a rope. The rope measures 5m. How many
meters can the cow walk around the tree?
Answer:
It sounds like you want the circumference of a circle with a 5m radius.
C = 2πr = 2(3.14)(5) = 31.4 m
Trisha helped clean up her neighborhood by picking up plastic she collected 3/4 pound of plastic the first day and 1/6 pound of plastic the second day how much more trash did she collect the first day than the second day?
Find the derivative of
y = 1/ (3x^3) with steps
Answer:
[tex] - 9 {x}^{ - 4} [/tex]
Step-by-step explanation:
[tex]y = \frac{1}{ {3x}^{3} } = {3x}^{ - 3} [/tex]
[tex]y = < - 3 \times 3 > {x}^{ - 3 - 1} \\ = - 9 {x}^{ - 4} [/tex]
Which statement is true about the equation (x – 4)(x + 2) = 16? O The equation x - 4 = 16 can be used to solve for a solution of the given equation. O The standard form of the equation is x2 - 2x - 8 = 0. O The factored form of the equation is (x + 4)(x - 6) = 0. O One solution of the equation is x = -6. vity
Answer:
The factored form of the equation is (x + 4)(x - 6) = 0
Step-by-step explanation:
(x - 4)(x + 2) = 16
[tex]x^{2} -2x - 8 = 16[/tex]
[tex]x^{2} -2x - 24[/tex] = 0
(x - 6)(x + 4) = 0
x = 6 or x = -4
(7y - 23)
(23x - 16)
(8x – 21)
In need of help ASAP