The probability of selecting a mystery book, then without replacing it, selecting a nonfiction book is approximately 0.1462.
How to determine the probability of selecting a mystery book, then without replacing it, selecting a non-fiction bookOn the bookcase, there are 24 + 12 + 4 = 40 volumes.
The odds of picking a mystery book on the first draw are 24/40.
There are 39 books remaining after the first is drawn, including 12 nonfiction works. Because the initial book was never replaced, there are currently only 11 nonfiction volumes left.
Given that a mystery book was chosen without replacement in the first draw, the probability of selecting a nonfiction book in the second draw is 12/39.
When we multiply these probability together, we get:
P(nonfiction after mystery, not replacing) * P(mystery, not replacing) = (24/40) * (12/39) = 0.14615...
P(nonfiction after mystery, not replacing) * P(mystery, not replacing) = 0.1462
So, the probability of selecting a mystery book, followed by a nonfiction book without replacing it is roughly 0.1462.
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A wildlife group is trying to determine how many wild hogs are in a certain area. They trapped, tagged, and released 20 wild hogs. Later, they counted 8 wild hogs out of the 40 they saw.
What can the wildlife group estimate is the total population of wild hogs in that area
A. 80
B. 90
C. 100
D. 16
Answer:
The correct answer is 16
Step-by-step explanation:
Answer:
C. 100
Step-by-step explanation:
Assuming that the proportion of tagged hogs in the population is the same as the proportion of tagged hogs in the sample that was later observed, we can set up a proportion to estimate the total population of wild hogs:
tagged hogs in population / total population = tagged hogs in sample / size of sample
We know that 20 wild hogs were tagged and released, and that 8 out of 40 hogs observed were tagged. So we can plug these numbers into the proportion and solve for the total population:
20 / total population = 8 / 40
Simplifying this equation, we get:
total population = (20 * 40) / 8 = 100
Therefore, the wildlife group can estimate that the total population of wild hogs in the area is 100. Answer choice C is correct.
Hope this helps!
You work independently as a copier salesperson. Last month, you sold 26 printers at a cost of $1,750 each. The cost of goods sold for each printer is $975. Additional operating expenses include your salary ($3,000/month), advertising ($50/month), and office lease ($550/month). Use this information to calculate (a) your gross profit and (b) your net income.
(A) The gross profit is $20,150.
(B) The net income is $16,550
To solve this problem(A) To calculate the gross profit, we need to subtract the cost of goods sold from the total revenue generated by selling the printers.
Total revenue = 26 x $1,750 = $45,500
Cost of goods sold = 26 x $975 = $25,350
Gross profit = Total revenue - Cost of goods sold
Gross profit = $45,500 - $25,350
Gross profit = $20,150
Therefore, the gross profit is $20,150.
(B) To calculate the net income, we need to subtract all the operating expenses from the gross profit.
Gross profit = $20,150
Salary = $3,000
Advertising = $50
Office lease = $550
Total operating expenses = $3,600
Net income = Gross profit - Total operating expenses
Net income = $20,150 - $3,600
Net income = $16,550
Therefore, the net income is $16,550.
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Please help mee
I'm struggling really hard on this I failed 2 times already
(the picture has the question)
Algebra II (2019) Sem 2 L 1.8.4 Quiz: More Than One Vertical Asymptote Question 2 of 10 Which of the following rational functions is graphed below? O A. F(x) = B. F(x) = x(x+3)(x-3) (x-3)(x+3) ○ C. F(x) = x(x-3) ○ D. F(x) = (x+3)
As per the given graph, the rational function that is graphed in the given image is option B: F(x) = x(x+3)(x-3) / (x-3)(x+3) as per the factors.
Based on the graph, we can see that the function has vertical asymptotes at x = -3 and x = 3.
Option A has only one factor of (x+3) and one factor of (x-3), so it would have only one vertical asymptote at x = 3 or x = -3, but not both.
Option B has two factors of (x-3) and two factors of (x+3), so it has two vertical asymptotes at x = 3 and x = -3, which matches the graph.
Option C has only one factor of (x-3) and no factor of (x+3), so it would have only one vertical asymptote at x = 3 or x = -3, but not both.
Option D has only one factor of (x+3) and no factor of (x-3), so it would have only one vertical asymptote at x = -3 or x = 3, but not both.
Therefore, the rational function that is graphed in the given image is option B: F(x) = x(x+3)(x-3) / (x-3)(x+3).
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Andre wants to buy a new car. Gas is so expensive; Andre wants to purchase a
car that has the best gas millage rate.
•
Car 1 has gas mileage that can be described as y = 25x, where x is the
number of gallon of gas used and y is the total miles driven.
Car 2 has he gas mileage rate displayed in the table below.
Number of
Gallons of
Gas
2
5
7
8
11
60
150
210
240
330
Which car should Andre buy? How many more miles per gallon can he
drive in this car than the other car?
Answer: Andre should buy Car 2. Brainliest?
Step-by-step explanation:
To compare the gas mileage of the two cars, we need to find out how many miles each car can travel per gallon of gas.
For Car 1: y = 25x
This means that for every gallon of gas used (x), the car can travel 25 times that amount in miles (y). So, the gas mileage for Car 1 is 25 miles per gallon (mpg).
For Car 2: we can calculate the miles per gallon by dividing the total miles traveled by the number of gallons of gas used:
For 2 gallons of gas, the car can travel 60 miles. So, the gas mileage is 30 mpg (60 miles ÷ 2 gallons).
For 5 gallons of gas, the car can travel 150 miles. So, the gas mileage is 30 mpg (150 miles ÷ 5 gallons).
For 7 gallons of gas, the car can travel 210 miles. So, the gas mileage is 30 mpg (210 miles ÷ 7 gallons).
For 8 gallons of gas, the car can travel 240 miles. So, the gas mileage is 30 mpg (240 miles ÷ 8 gallons).
For 11 gallons of gas, the car can travel 330 miles. So, the gas mileage is 30 mpg (330 miles ÷ 11 gallons).
Therefore, Car 2 has a consistent gas mileage of 30 mpg.
From the above calculations, we can see that Car 2 has a better gas mileage compared to Car 1. Car 2 can travel 30 miles on a gallon of gas, while Car 1 can only travel 25 miles on a gallon of gas.
Therefore, Andre should buy Car 2 if he wants to get the best gas mileage. Car 2 can travel 5 more miles per gallon than Car 1.
Tickets to concerts, sporting events, and other forms of entertainment should be taxed.
a. completely agree
b. mostly agree
c. mostly disagree
d. completely disagree
Super Markets Incorporated, is considering expanding into the Scottsdale, Arizona, area. You, as director of planning, must present an analysis of the proposed expansion to the operating committee of the board of directors. As a part of your proposal, you need to include information on the amount people in the region spend per month for grocery items. You would also like to include information on the relationship between the amount spent for grocery items and income. Your assistant gathered the following sample information.
Household Amount Spent Monthly Income
1 $ 555 $ 4,340
2 489 4,510
. . .
. . .
. . .
39 1,206 9,814
40 1,145 9,835
picture Click here for the Excel Data File
a-1. Draw a scatter diagram.
1. On the graph below, use the point tool to plot the point corresponding to the Monthly Income and the Amount Spent (Amount 1).
2. Repeat the process for the remainder of the sample (Amount 2, Amount 3, … ).
3. To enter exact coordinates, double-click on the point and enter the exact coordinates of x and y.
a-2. Based on these data, does it appear that there is a relationship between monthly income and amount spent?
b-1. Determine the correlation coefficient. (Round your answer to 4 decimal places.)
b-2. Can we conclude that there is a positive correlation between monthly income and amount spent? Use the 0.05 significance level.
c. Determine the coefficient of determination. (Round your answer to 4 decimal places.)
d. Determine the standard error of estimate. (Round your answer to 4 decimal places.)
e. Would you recommend using the regression equation to predict amount spent with monthly income?
multiple choice
Yes
No
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The above is an analysis of data related to income and expenditure. See the working below as well as the attached information.
What is the analysis of the given data?R Calculation
Note that:
X: X Values
Y: Y Values
Mx: Mean of X Values
My: Mean of Y Values
X - Mx & Y - My: Deviation scores
(X - Mx)2 & (Y - My)2: Deviation Squared
(X - Mx)(Y - My): Product of Deviation Scores
X Values
∑ = 273195
Mean = 6829.875
∑(X - Mx)2 = SSx = 119242794.375
Y Values
∑ = 33625
Mean = 840.625
∑(Y - My)2 = SSy = 2396869.375
X and Y Combined
N = 40
∑(X - Mx)(Y - My) = 15978328.125
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = 15978328.125 / √((119242794.375)(2396869.375)) = 0.9451
Thus, the value of R is 0.9451.
4. This is a strong positive correlation, which means that high X variable scores go with high Y variable scores (and vice versa).
5) The value of R², the coefficient of determination, is 0.8932.
To drive this, just square the coefficient of determination. That is
R² = 0.9451² = 0.8932
5. To compute the standard errors of the estimate:
SE = √(SSE / (n-2))
where SSE is the sum of squared errors and n is the sample size.
From the regression output, we have SSE = 0.9326 and n = 40.
SE = √ (0.9326 / (40-2)) = 0.1570
Therefore, the standard error of estimate is 0.1570.
6) Yes, because the coefficient of determination is high (0.8932), indicating that 89.32 % of the variability i n the amount spent can be explained by the linear relationship with monthly income.
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Full Question:
Although part of your question is missing, you might be referring to this full question: See attached.
I don't understand how you substituted the equation of this question noted the length,d m,of a rectangular field is 40m greater than the width. The perimeter of the field is 400m . Kindly simplify
The width of the rectangular field is 80 meters and the length is 120 meters for the given perimeter 400m.
What is the perimeter?Perimeter is a mathematical term that refers to the total distance around the outside of a closed two-dimensional shape. It is the sum of the lengths of all the sides of the shape.
According to the given information:
Let's break down the information given in the question:
Length of the rectangular field is 40m greater than the width.
The perimeter of the field is 400m.
Let's denote the width of the rectangular field as 'w' meters. According to the first information, the length of the field would be 'w + 40' meters, as it is 40m greater than the width.
Now, let's use the formula for the perimeter of a rectangle, which is given by:
Perimeter = 2 * (Length + Width)
Substituting the values we have:
Perimeter = 2 * (w + 40 + w)
Perimeter = 2 * (2w + 40)
Since the given perimeter is 400m, we can set up the equation:
400 = 2 * (2w + 40)
Now we can solve for 'w' by dividing both sides of the equation by 2:
400/2 = 2w + 40
200 = 2w + 40
Next, we subtract 40 from both sides of the equation to isolate the term with 'w':
200 - 40 = 2w
160 = 2w
Finally, we divide both sides of the equation by 2 to solve for 'w':
160/2 = w
80 = w
So, the width of the rectangular field is 80 meters. And since the length is 40 meters greater than the width, the length would be:
Length = Width + 40 = 80 + 40 = 120 meters.
So, the width of the rectangular field is 80 meters and the length is 120 meters.
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Darlena has started taking photos at amateur dog racing events, later offering the photos for sale to the dog owners by email. The prices she has charged per photo at each of her first three events, and the corresponding number of photos sold and total revenue raised appear in the table below. Price per Photo $56 $52 $24 Number of Photos Sold 4 5 12 Revenue $224 $260 $288 Treating revenue as a function of the number of photos sold, a graph of the three data points is also shown. If she uses quadratic regression to fit a curve to the data, what number of photos are sold, and what price per photo will maximize her revenue?
Find the final amount of money in an account if $7, 300 is deposited at 2% interest compounded semi annually and the money is left for 7 years
The final amount of money in the account after 7 years would be $8,790.56.
To calculate the final amount of money in an account, we can use the formula for compound interest:
A = [tex]P(1 + r/n)^{(nt)[/tex]
where A is the final amount of money, P is the initial amount of money, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, we have P = $7,300, r = 0.02 (since the interest rate is 2%), n = 2 (since the interest is compounded semi-annually), and t = 7 (since the money is left for 7 years). Plugging these values into the formula, we get:
A = $7,300(1 + 0.02/2)¹⁴
A = $7,300(1.01)¹⁴
A = $8,790.56
This means that the initial investment of $7,300 earned $1,490.56 in interest over the 7-year period due to the compounding effect of the semi-annual interest payments.
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18. Un comerciante vende una vaca por S/700.
Si le había costados S/500, ¿qué parte
representa la ganancia sobre el costo?
a) 2/5
b) 3/5
c) 4/5
d) 1/5 e) 6/5
Dejon saves eight dollars in a week author saves four times the amount Dejon saves in the same week
The amount that Author saves in the same week is $32.
What is a simple equation?An equation which has a variable of unknown value is referred to as a simple equation. Thus, the value of the variable is to be determined.
From the given question, it can be deduced that;
Dejon saves $8 per week, while Author saves four times that of Dejon.
Thus, this implies that;
the amount that Author saves same week = 4 * $8
= $32
Therefore, the amount that Author save in the same week is $32.
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a. A bag contains 4 red marbles, 5 yellows marbles, and 7 whites marbles. If a marble is drawn from the bag, replaced, and another marble is drawn,
what is the probability of drawing first a marble and then a marble?
Answer: 5/64
Step-by-step explanation:
The probability of drawing a red marble on the first draw is 4/16 = 1/4 (since there are 4 red marbles out of 16 total marbles).
After replacing the first marble, the probability of drawing a yellow marble on the second draw is 5/16 (since there are 5 yellow marbles remaining out of 16 total marbles).
Therefore, the probability of drawing a red marble and then a yellow marble is (1/4) x (5/16) = 5/64
Find the critical value zc necessary to form a confidence interval at the level of confidence shown below.
c =0.81
Hence, the critical value for the 81% confidence interval is 1.311 occurs while comparing equations (1) and (2).
Explain about the Critical Values:The cut-off scores used during confidence intervals, hypothesis testing, and other statistical techniques are known as the crucial values. They are used to establish the boundaries of confidence intervals in the case of confidence intervals.
Level of confidence c = 0.81
The degree of assurance c = 81%.
Now, the overall confidence level is shown as (1−α) , where α is the significance level.
= 1.0 - 0.81
= 0.19
Thus, the 81% confidence level suggests a significance level of 0.19.
Critical value Z(α/2) is:
P(Z > Z(α/2)) = (α/2)
= 0.19/2
P(Z > Z(α/2)) = 0.095 ...eq 1
Using the z-table online, check the p-value for the z 0.095.
P(Z > 1.311) = 0.095 ...eq 2
Hence, the critical value for the 81% confidence interval is 1.311 occurs while comparing equations (1) and (2).
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Mamadou has 64 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 247 square meters. Solve for the dimensions (length and width) of the field.
Answer: The length and width are 13 and 19
Step-by-step explanation:
This is because the factors of 247 are 1, 13, 19, and 247. 13 times 19 is 247, but if 13 and 19 are the sides, the perimeter would be 64 as well.
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and I only need #2
Answer:
Whenever the base of an exponential function is less than 1 (5/7 < 1), the graph exhibits exponential decay and when the base is greater than 1, the graph exhibits exponential decay (7 > 1).
Final answer: a base of 7 will cause the graph to increase as you go from left to right in both the x coordinates and the y coordinates.
I provided a picture of a graph that shows both bases just in case you want to alter my answer slightly, but aren't sure how the graph would look
An integer A written in an n-based number system is 647, while written in an (n+2)-based number system is 513. Write the number A in the 10 number system! (n is of course a positive integer)
Answer:
79
Step-by-step explanation:
Let's start by writing out what we know:
A = 647 in base-n
A = 513 in base-(n+2)
To find A in base-10, we need to use the place value system and the definition of each base. Let's first convert A to base-10 using the given information.
In base-n, A is equal to:
A = 6n^2 + 4n + 7
In base-(n+2), A is equal to:
A = 5(n+2)^2 + 1(n+2) + 3
A = 5(n^2 + 4n + 4) + (n + 2) + 3
A = 5n^2 + 21n + 20
Now we have two expressions for A, so we can set them equal to each other and solve for n:
6n^2 + 4n + 7 = 5n^2 + 21n + 20
Simplifying and rearranging, we get:
n^2 + 8n + 13 = 0
Using the quadratic formula, we can solve for n:
n = (-8 ± sqrt(8^2 - 4(1)(13))) / (2(1))
n = (-8 ± 2) / 2
n = -3 or n = -5
Since n is a positive integer, we can disregard the negative solution and conclude that n = 3.
Now that we know n, we can substitute it back into the expression for A in base-n and solve for A in base-10:
A = 6n^2 + 4n + 7
A = 6(3^2) + 4(3) + 7
A = 79
Therefore, the number A written in base-10 is 79.
Hope this helps!
adam bought a skateboard that is on sale for 35% off the original cost is 150 what is the sale price
Answer:
$97.50
Step-by-step explanation:
To calculate the sale price of the skateboard, we need to apply a discount of 35% to the original cost of $150:
Discount amount = 35% x $150 = $52.50
The sale price is the original cost minus the discount amount:
Sale price = $150 - $52.50 = $97.50
Therefore, the sale price of the skateboard after a 35% discount is $97.5
The sale price of the skateboard is $97.50.
To calculate the sale price, we need to first determine the amount of the discount, and then subtract that discount from the original price.
The discount is 35% of the original price:
Discount = 0.35 x 150 = 52.50
So the sale price is the original price minus the discount:
Sale price = 150 - 52.50 = 97.50
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Identify the domain and range of the function. y=√x−4
A. Domain: x≥−4, Range: y≥0
B. Domain: x≥4, Range: y≥0
C. Domain: x≤4, Range: y≤0
D. Domain: x≥0, Range: y≥4
Using the function y = √ (x-4) has the following:
Domain: x≥−4, Range: y≥0.
Correct answer is A.
Define a function?A function is a relationship between each element of a non-empty set A and at least one element of another non-empty set B. A relation f between a set A (the function's domain) and a set B is how a function is defined in mathematics (its co-domain). Anytime an A and b B exist, f = (a,b)|
The domain of the function y=√ (x-4) is restricted by the square root of a non-negative number, which means that x-4 must be greater than or equal to zero. Thus, we have:
x-4 ≥ 0
x ≥ 4
Therefore, the domain of the function is x≥4.
The range of the function is determined by the output values of the function. Since the square root of any non-negative number is always non-negative, the output values of the function y=√x-4 will always be non-negative. Thus, the range of the function is y≥0.
Therefore, the correct answer is A. Domain: x≥−4, Range: y≥0.
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How many website graphics can be created?
I do not understand what do you mean
A composite figure is created using a rectangle and a semi circle. What is the area of the figure? Use 3.14 for Pi by the way.
Rectangle = 216 (12x18) ( already solved just need semi circle)
The value of the calculated area of the figure is 343.17 sq units
What is the area of the figure?From the question, we have the following parameters that can be used in our computation:
Composite figure
The shapes in the composite figure are
SemicircleRectangleThis means that
Area = Semicircle + Rectangle
Using the area formulas on the dimensions of the individual figures, we have
Area = 12 * 18 + 1/2 * 3.14 * (18/2)^2
Evaluate the sum of products
Area = 343.17
Hence, the area of the figure is 343.17 sq units
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12(x-20)=-48 for 7th grade math equation algebra
Answer: 16
Step-by-step explanation:
1. Distribute the 12 to the x variable and the constant.
You will get 12x - 240 = -48
2. -48 + 240 = 192. You now have 12x = 192
3. solve for x. x = 192/12 -> x = 16
In In a study of the effects of college student employment on academic performance, two random samples (one from students who worked and the other from students who did not work) were selected from college students at a large university. The following summary statistics for GPA were reported. Employed students sample size 114
Mean GPA 3.15
Std deviation 0.485
Non-employed students
Sample size 114
Mean GPA 3.23
std deviation 0.524
Compute a 90% confidence interval for the mean GPAs of non-employed students. Assume that the normal condition is met.
a. Identify the variables needed to solve the problem.
b. Find the standard deviation.
c. Calculate the point estimate and margin of error.
d. Calculate the confidence interval
The standard deviation for non-employed students is given as 0.524,
the margin of error is 0.083 and the 90% confidence interval for the mean GPAs of non-employed students is (3.147, 3.313).
Variables needed to solve the problem Sample size (n)
Sample mean, Sample standard deviation (s), Confidence level (CL)
Margin of error (E)
b. The standard deviation for non-employed students is given as 0.524.
c. Point estimate:
The point estimate for the mean GPA of non-employed students is the sample mean, which is given as 3.23.
Margin of error:
We can use the formula for the margin of error:
E = z(s/√n)
For a 90% confidence level, the critical value is 1.645.
E = 1.645(0.524/√114) = 0.083
Therefore, the margin of error is approximately 0.083.
d. Confidence interval:
The confidence interval is given by the formula:
(3.23 - 0.083, 3.23 + 0.083)
= (3.147, 3.313)
Therefore, the 90% confidence interval for the mean GPAs of non-employed students is (3.147, 3.313).
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Determine the length of a chord whose central angle is 80° in a circle with a radius of 4 centimeters. Question 9 options: 3.94 cm 2.57 cm 5.14 cm 7.88 cm
The length of the chord whose central angle is 80° in a circle with a radius of 4 centimeters is 5.14 cm using the law of cosines.
Given that,
Central angle of a chord = 80°
Radius of the circle = 4 centimeters
There will be a triangle formed by the chord and the two radius.
Let a be the length of the chord.
Using the law of cosines,
a² = 4² + 4² - (2 × 4 × 4) cos (80°)
a² = 16 + 16 - 32 cos (80°)
a² = 32 - 32 cos (80°)
a² = 26.4433
a = 5.14
Hence the length of the chord is 5.14 cm.
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Margarita borrows $14,000 from her uncle and agrees to repay it in monthly installments of $400. Her uncle charges 0.9% interest per month on the balance.
(a) If her balance An in the nth month is given recursively by A0 = 14,000 and An = k · An − 1 − 400, what is k?
(b) Find her balance after two months. (Round your answer to the nearest cent.)
Answer:
Step-by-step explanation:
(a) We know that the balance An in the nth month is given by:
An = k · An-1 - 400
where A0 = 14,000. Substituting n = 1, we get:
A1 = k · A0 - 400
A1 = k · 14,000 - 400
We also know that her uncle charges 0.9% interest per month on the balance. This means that the balance after one month should be:
A1' = A0 + 0.009 · A0 - 400
A1' = 14,000 + 0.009 · 14,000 - 400
A1' = 14,126
Setting A1 = A1', we can solve for k:
k · 14,000 - 400 = 14,126
k = 1.009
Therefore, k is approximately 1.009.
(b) To find her balance after two months, we can use the recursive formula with n = 2:
A2 = k · A1 - 400
A2 = 1.009 · 14,126 - 400
Using a calculator, we get:
A2 ≈ 14,272.34
Therefore, her balance after two months is approximately $14,272.34.
answer with explanation
Answer:
Area = 20 [tex]units^{2}[/tex]
Perimeter = 18 units
Step-by-step explanation:
Helping in the name of Jesus.
An object launched directly in the air at a speed of 24 feet per second from a platform located 16 feet above the ground. The position of the object can be modeled using the function f(t)=-16t^2+24t+16
The maximum height that the object will reach is 40 feet.
How to find the maximum height that the object will reach?For any quadratic equation of the form, f(t) = at² + bt + c,
where a, b and c are constants
The maximum value of f(t) is give by the formula:
f(t) = c - (b²/4a)
Since the position of the object can be modeled using the function:
f(t) = -16t² + 24t + 16
where a = -16, b = 24 and c = 16
Thus, the maximum height will be:
maximum height = 16 - (24² / 4(-6))
maximum height = 16 - 576/(-24)
maximum height = 16 + 24
maximum height = 40 feet
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Complete Question
An object launched directly in the air at a speed of 24 feet per second from a platform located 16 feet above the ground. The position of the object can be modeled using the function f(t)=-16t^2+24t+16, where t is the time in seconds and f(t) is the height, in feet, of the object. What is the maximum height, in feet, that the object will reach? Do not include units in your answer.
Question 5
Which of the following functions best describes this graph?
4
Ay=x²-2x+4
OB. y +9x+18
OC. ys (x+5)(x-4)
Answer:
D. y = (x - 3)(x - 6)
Step-by-step explanation:
The graph shows a parabola and the parabola intersects the x-axis at (-6, 0) and at (-3, 0). When a function intersects the x-axis, the y value must automatically equal 0, since there is only horizontal movement on the x-axis.
(x-3)(x-6) is a binomial expression that will make a quadratic equation when expanded. We refer to the coordinate where a parabola intersects the x-axis as roots, which are numbers that make the quadratic equation equal 0.
We know from the zero-product property, that when the product of two numbers is 0, at least on the numbers must be 0 (e.g., 4 * 0 = 0 or even 0 * 0 = 0). Thus, we can solve any quadratic equation in the the x-intercept form (i.e., the form tha (x-3)(x-6) is currently in) by setting both expressions equal to 0 and solving for x. This wil give an x-coordinate both times, but since you set the equations equal to 0, you know that your y-coordinate each time is 0:
Solution for x - 3 = 0:
x - 3 = 0
x = 3
Solving for x - 6 = 0
x - 6 = 0
x = 6
You can check by plugging in 3 for x and 6 for x and see if you get 0:
3 for x:
(3 - 3)(3 - 6) = 0
0 * -3 = 0
0 = 0
6 for x:
(6 - 3)(6 - 6) = 0
3 * 0 = 0
0 = 0
A planter box has dimensions 30 in × 15 in × 18 in (Length × Width × Height).
a. Find the volume of the box in cubic feet and in cubic yards.
b. Potting soil is sold in 1.5 cubic-foot bags, and each bag weighs 11.2 pounds. How many
pounds of soil does the box hold?
c. You’d like to paint the sides (but not the bottom) of the planter box. You plan on
applying one coat of paint. How many square feet of paint will you need?
88
Okay, let's solve this step-by-step:
a)
Length = 30 in = 2.5 ft
Width = 15 in = 1.25 ft
Height = 18 in = 1.5 ft
Volume (cubic ft) = Length x Width x Height
= 2.5 x 1.25 x 1.5 = 3.75 cubic ft
Volume (cubic yards) = 3.75 / 27 = 0.14 cubic yards
b)
Since the box volume is 3.75 cubic ft and potting soil bags are 1.5 cubic ft,
you will need 3.75 / 1.5 = 2.5 bags of soil.
Each bag weighs 11.2 lbs, so 2.5 bags will weigh 2.5 * 11.2 = 28 lbs of soil.
c)
To paint the sides of the box, you need:
Length (2 sides) = 30 in x 2 = 60 in
Width (2 sides) = 15 in x 2 = 30 in
Height (4 sides) = 18 in x 4 = 72 in
Total inches of sides = 60 + 30 + 72 = 162 in
Conversion: 162 in / 12 in = 13.5 square ft
So you will need about 14 square feet of paint.
Let me know if you have any other questions!
Q2: The population of a herd of deer is represented by the function P(t) = 205(1.13)t where t is given in years. To the nearest whole number, what will the herd population be after 6 years?
Answer:
584
Step-by-step explanation:
To find the herd population after 6 years, we need to evaluate P(6) using the given function:
P(6) = 205(1.13)^6
Using a calculator, we get:
P(6) ≈ 584
Rounding this to the nearest whole number, we get:
The herd population after 6 years ≈ 584.
-1+2-3+4-5+6...-99+100
Can someone pls help
-1 +
2 -
3 +
4 -
5 +
6 -
...
-99 +
100
= -1 + 2 - 3 + 4 - 5 + 6 - ... - 99 + 100
= 1