The missing terms in the blanks and number of terms are determined below.
How many terms will it take to get to zero starting?
The missing terms in the blanks for the pattern and number of terms can be determined as follows:
1. 32, 30, 28, 26, 32__________________________, 0
The difference is 2. Thus, subtract 2 till you reach 0. That is:
32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0
Number of terms: 16
2. 75, 70, 65, 60, 55, 50, ____________________, 0
The difference is 5. Thus, subtract 5 till you reach 0. That is:
75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5, 0
Number of terms: 15
3. 30, 27, 24, 21, ___________________________, 0
The difference is 3. Thus, subtract 3 till you reach 0. That is:
30, 27, 24, 21, 18, 15, 12, 9, 6, 3, 0
Number of terms: 10
4. 81, 72, 63, ______________________________, 0
The difference is 9. Thus, subtract 9 till you reach 0. That is:
81, 72, 63, 54, 45, 36, 27, 18, 9, 0
Number of terms: 9
5. 48, 44, 40, 36, __________________________, 0
The difference is 4. Thus, subtract 4 till you reach 0. That is:
48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0
Number of terms: 12
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Alexander stacked unit cubes to build the rectangular prism below. Use the rectangular prism to answer
Alexander stacked 16 unit cubes required to build the rectangular prism.
What is a prism?A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.
Here we need to find the number of cubes required to build the rectangular prism.
Here first we need to find how many cubes stack in the base layer
Number of unit cubes in the base layer = Number of cubes along the length * Number of cubes along the width
The number of unit cubes in the base layer = 2 * 4 = 8 cubes.
Total number of unit cubes in prism =Number of unit cubes in the base layer *Number of layers = 8 * 2 = 16 unit cubes
So, there are 16 unit cubes are required to build the rectangular prism.
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Complete question :
Alexander stacked unit cubes to build the rectangular prism below. Use the rectangular prism to answer the question.
How many cubes are required to build the rectangular prism?
Suppose we have n+ positive training examples and n− negative training examples. Let C+ be the center of the positive examples and C− be the center of the negative examples, i.e., C+ = 1 n+ P i: yi=+1 xi and C− = 1 n− P i: yi=−1 xi . Consider a simple classifier called CLOSE that classifies a test example x by assigning it to the class whose center is closest. • Show that the decision boundary of the CLOSE classifier is a linear hyperplane of the form sign(w · x + b). Compute the values of w and b in terms of C+ and C−. • Recall that the weight vector can be written as a linear combination of all the training examples: w = Pn++n− i=1 αi · yi · xi . Compute the dual weights (α’s). How many of the training examples are support vectors?
To show that the decision boundary of the CLOSE classifier is a linear hyperplane, we need to show that it can be represented as sign(w · x + b), where w is the weight vector, b is the bias term, and sign is the sign function that outputs +1 or -1 depending on whether its argument is positive or negative.
Let x be a test example, and let d+ = ||x - C+|| be the distance from x to the center of the positive examples, and d- = ||x - C-|| be the distance from x to the center of the negative examples. The CLOSE classifier assigns x to the positive class if d+ < d-, and to the negative class otherwise. Equivalently, it assigns x to the positive class if
||x - C+[tex]||^2[/tex] - ||x - C-[tex]||^2[/tex] < 0.
Expanding the squares and simplifying, we get
(x · x - 2C+ · x + C+ · C+) - (x · x - 2C- · x + C- · C-) < 0,
which is equivalent to
2(w · x) + (C+ · C+ - C- · C-) - 2(w · (C+ - C-)) < 0,
where w = C+ - C- is the vector pointing from the center of the negative examples to the center of the positive examples. Rearranging, we get
w · x + b < 0,
where b = (C- · C-) - (C+ · C+) is a constant.
Thus, the decision boundary of the CLOSE classifier is a hyperplane defined by the equation w · x + b = 0, and the classifier assigns a test example x to the positive class if w · x + b > 0, and to the negative class otherwise.
To compute the values of w and b in terms of C+ and C-, we can use the definition of w and b above. We have
w = C+ - C-,
b = (C- · C-) - (C+ · C+).
To compute the dual weights α's, we need to solve the dual optimization problem for the support vector machine (SVM) with a linear kernel:
minimize 1/2 ||w||^2 subject to yi(w · xi + b) >= 1 for all i,
where yi is the class label of the i-th training example, and xi is its feature vector. The dual problem is
maximize Σi αi - 1/2 Σi Σj αi αj yi yj xi · xj subject to Σi αi yi = 0 and αi >= 0 for all i,
where αi is the dual weight corresponding to the i-th training example. The number of support vectors is the number of training examples with nonzero dual weights.
In our case, the training examples are the positive and negative centers C+ and C-, so we have n+ + n- = 2 training examples. The feature vectors are simply the centers themselves, so xi = C+ for i = 1 and xi = C- for i = 2. The class labels are yi = +1 for i = 1 (positive example) and yi = -1 for i = 2 (negative example). Plugging these into the dual problem, we get
maximize α1 - α2 - 1/2 α[tex]1^2[/tex] d(C+, C+) - 2α1α2 d(C+, C-) - 1/2 α[tex]2^2[/tex] d(C-, C-) subject to α1 - α2 = 0 and α1,
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You are on a plane leaving from Miami, Florida Heading directly towards Africa on a bearing of E 20 S.
The planes average air speed is 600 mph and you fly for 4 hours before the pilot indicates that you will
with the same average air speed. The pilot is unable to outrun the storm and the turbulence is too much,
have to re-route around a storm. The pilot adjusts his bearing to S 5'E for 2 hours then E 5°S for an hour
the plane goes down, and your group are the only survivors stranded on an unknown island. You have
enough battery on a satellite phone one of you grabbed from the plane to make one phone call to the
they need to travel on from Miami to rescue
you. What do you tell them?
rescue authorities in Miami and tell them the exact distance you are from Miami and the exact bearing
To determine the exact distance and bearing of the island from Miami, we can use basic trigonometry and vector addition.
First, we need to break down the flight path into its components. The initial bearing of E 20 S can be broken down into an eastward component of 600 mph [tex]cos(20°) = 562.57[/tex] mph and a southward component of 600 mph [tex]sin(20°) = 208.38[/tex] mph.
After flying for 4 hours, the plane has traveled a distance of 600 mph × 4 = 2400 miles, with a displacement of 562.57 mph × 4 = 2250.28 miles eastward and 208.38 mph × 4 = 833.52 miles southward.
When the pilot adjusts the bearing to S 5'E, the plane travels 600 mph × 2 = 1200 miles with a displacement of 600 mph cos(5°) × 2 =996.18 miles eastward and 600 mph sin(5°) × 2 = 104.57 miles southward.
Finally, when the pilot adjusts the bearing to E 5°S, the plane travels 600 mph × 1 = 600 miles with a displacement of 600 mph cos(5°) = 598.31 miles eastward and 600 mph sin(5°) = 52.42 miles southward.
To find the total displacement from Miami to the island, we can add up the eastward and southward components:
Total eastward displacement = 2250.28 + 996.18 + 598.31 = 3844.77 miles
Total southward displacement = 833.52 + 104.57 + 52.42 = 990.51 miles
Using the Pythagorean theorem, we can find the total distance from Miami to the island:
[tex]Distance = sqrt((3844.77)^2 + (990.51)^2) =3985.21 miles[/tex]
To find the bearing from Miami to the island, we can use inverse trigonometry:
[tex]Bearing = tan^{-1} (\frac{990.51}{3844.77}) = 14.76°[/tex]
Therefore, you should tell the rescue authorities in Miami that you are approximately 3985.21 miles away from Miami and the bearing to the island is approximately N 75°E.
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A die is rolled three times and a curious pattern emerges. On the first roll, the number is greater than 3. On the second roll, the under is greater than 4, and on the third roll, the number is greater than 5. If all three rolls are independent, what is the probability that this occurs?
Therefore, the probability of the curious pattern occurring is 1/36.
What is probability?Probability theory is an important branch of mathematics that is used to model and analyze random phenomena, such as the outcomes of games of chance, the behavior of particles in physics, or the performance of complex systems in engineering. It has many practical applications in fields such as statistics, finance, economics, and computer science.
Here,
The probability of rolling a number greater than 3 on a fair die is 3/6 = 1/2, since there are three numbers (4, 5, 6) that satisfy this condition out of the six possible outcomes.
Similarly, the probability of rolling a number greater than 4 on a fair die is 2/6 = 1/3, and the probability of rolling a number greater than 5 is 1/6.
Since each roll is independent, we can multiply these probabilities together to get the probability that all three conditions are satisfied:
P = (1/2) × (1/3) × (1/6)
= 1/36
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You are working as a financial planner. a couple has asked you to put together an investment plan for the education of their daughter. she is a bright seven-year-old (her birthday is today), and everyone hopes she will go to university after high school in 10 years, on her 17th birthday. you estimate that today the cost of a year of university is $17,500, including the cost of tuition, books, accommodation, food, and clothing. you forecast that the annual inflation rate will be 5. 6%. you may assume that these costs are incurred at the start of each university year. a typical university program lasts 4 years. the effective annual interest rate is 6. 75% and is nominal. a. suppose the couple invests money on her birthday, starting today and ending one year before she starts university. how much must they invest each year to have money to send their daughter to university? (do not round intermediate calculations. round your answer to 2 decimal places. )
investment per year $
b. if the couple waits 1 year, until their daughter’s 8th birthday, how much more do they need to invest annually? (do not round intermediate calculations. round your answer to 2 decimal places. )
additional yearly payments $
The couple needs to invest $9,060.52 per year to have enough money to send their daughter to university. The couple needs to invest an additional $1,322.18 per year if they wait one year to start saving for their daughter's university education.
a. The amount of money the couple needs to invest each year can be calculated using the present value of annuity formula. The future value of the university cost after 10 years can be calculated by compounding the current cost for 10 years at an annual inflation rate of 5.6%.
Then, the present value of this future cost can be found by discounting it back to the present using the effective annual interest rate of 6.75%. Finally, this present value can be divided by the present value of an annuity factor for 9 years (one year before the university starts) at an effective annual interest rate of 6.75%.
Using these calculations, the couple needs to invest $9,060.52 per year to have enough money to send their daughter to university.
b. If the couple waits for one year, they will have nine years to save for their daughter's university education. This means they will have one less year to invest, so they will need to invest more each year to have enough money for their daughter's university education.
The additional amount they need to invest can be found by subtracting the present value of an annuity of $9,060.52 for 9 years from the present value of an annuity of $9,060.52 for 8 years.
Using these calculations, the couple needs to invest an additional $1,322.18 per year if they wait one year to start saving for their daughter's university education.
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(2) Use the Comparison Test or the Limit Comparison Test to determine the convergence or divergence of the following series. Justify your answer. 23-1 5k - 1 k=1 (3) Use the Integral Test to determine the convergence or divergence of the following series. Justify your answer. Ink k k=1
2)By using Comparison Test,the series 23-1 5k-1 k=1,is divergent.
3)By using Integral Test the series Ink k k=1 is divergent.
2) To determine the convergence or divergence of the series 23-1 5k - 1 k=1:
For the first series, 23-1 5k-1 k=1, we can use the Limit Comparison Test.
Let's compare it to the series 5k-1 k=1.
We take the limit as k approaches infinity of the ratio of the two series:
lim(k->∞) [(23-1 5k-1) / (5k-1)] = lim(k->∞) [23 / 5] = 23/5
Since this limit is finite and positive, and the series 5k-1 diverges (as it is a p-series with p=1),
we can conclude that the given series also diverges.
3)To determine the convergence or divergence of the series Ink k k=1:
For the second series, Ink k=1, we can use the Integral Test.
We need to check if the following improper integral converges or diverges:
∫(1 to ∞) ln(x) dx
Integrating by parts, we get:
∫(1 to ∞) ln(x) dx = [xln(x) - x]1∞ + ∫(1 to ∞) dx/x
The first term evaluates to -∞, and the second term is the divergent harmonic series.
Therefore, the improper integral and the series both diverge.
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Consider the following.g(x) = 2e−x + ln x; h(x) = 9x2.5Find the derivative for f(x) = g(x) · h(x).f '(x) =
This is the derivative of f(x) with respect to x:
f'(x) = (-2e^(-x) + 1/x)·(9x^2.5) + (2e^(-x) + ln(x))·(22.5x^1.5)
To find the derivative of f(x) = g(x) · h(x), we'll use the product rule, which states that (u·v)' = u'·v + u·v'. Let u = g(x) and v = h(x).
u = g(x) = 2e^(-x) + ln(x)
v = h(x) = 9x^2.5
Now, find the derivatives of u and v:
u' = g'(x) = -2e^(-x) + 1/x
v' = h'(x) = 22.5x^1.5
Now apply the product rule:
f'(x) = u'·v + u·v'
f'(x) = (-2e^(-x) + 1/x)·(9x^2.5) + (2e^(-x) + ln(x))·(22.5x^1.5)
This is the derivative of f(x) with respect to x.
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Find the length of PQ.
Assume that lines which appear tangent are tangent.
Applying the secant-tangent theorem, the length of PQ is calculated as: 6 units.
How to Find the Length Using the Secant-Tangent Theorem?In the image given, line segment QS is a secant while QP is a tangent. This, according to the secant-tangent theorem, we have:
(x - 3)(x - 3 + 5) = (x - 1)²
(x - 3)(x + 2) = (x - 1)(x - 1)
Expand:
x² - x - 6 = x² - 2x + 1
Combine like terms:
x² - x² - x + 2x = 6 + 1
x = 7
length of PQ = x - 1
Plug in the value of x:
length of PQ = 7 - 1 = 6 units.
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Solve for x trigonometry
Answer:
x ≈ 36.87°
Step-by-step explanation:
using the sine ratio in the right triangle
sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{5}[/tex] , then
x = [tex]sin^{-1}[/tex] ( [tex]\frac{3}{5}[/tex] ) ≈ 36.87° ( to the nearest hundredth )
sum of 3 consecutive even numbers is 18
Answer:
Step-by-step explanation:
5 6 7
A box contains 10 red buttons, 30 green buttons, 40 blue buttons, and 20 yellow buttons. ten buttons were removed, tallied, and then returned to the box. three additional samples were taken in the same way. which sample is the best representation of the buttons in the box?
The best representation of the buttons in the box is the third sample.
To determine which sample is the best representation of the button in the box, we need to examine the samples and compare them to the known ratios of the colors of buttons in the box.
First sample: 6 red, 2 green, 1 blue, 1 yellow (out of 10)
Second sample: 3 red, 3 green, 3 blue, 1 yellow (out of 10)
Third sample: 2 red, 2 green, 5 blue, 1 yellow (out of 10)
To compare the samples to the known ratios, we can calculate the percentage of each color in each sample and compare it to the percentage of each color in the box.
The percentages of each color in the box are:
Red: 10/100 = 10%
Green: 30/100 = 30%
Blue: 40/100 = 40%
Yellow: 20/100 = 20%
First sample:
Red: 6/10 = 60%
Green: 2/10 = 20%
Blue: 1/10 = 10%
Yellow: 1/10 = 10%
Second sample:
Red: 3/10 = 30%
Green: 3/10 = 30%
Blue: 3/10 = 30%
Yellow: 1/10 = 10%
Third sample:
Red: 2/10 = 20%
Green: 2/10 = 20%
Blue: 5/10 = 50%
Yellow: 1/10 = 10%
Based on these percentages, we can see that the third sample is the best representation of the buttons in the box, as it is closest to the known ratios of colors in the box.
The first sample is skewed towards red buttons and away from blue and green buttons, while the second sample has equal percentages of red, green, and blue buttons, which is not reflective of the known ratios in the box.
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I need to find the equation?
To determine the person who made the best kick, you could use an equation that relates distance, speed, and height: distance = speed × time.
How to determine the person with the best kickTo determine the person with the best kick, it is vital that a correlation be drawn between the distance and height. In the absence of information about time, the person with the farthest distance and longest height can be determined as the person with the best kick.
So, to get the result without having the complete data, you can compare the height to determine the individual with the farthest distance and highest kick.
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A company randomly assigns employees four-digit security codes using the numbers
1 through 4 to activate their e-mail accounts.
Any of the digits can be repeated. Is it likely that more than 3 of the 1,280 employees will be assigned the code 4113? PLEASE I WILL GIVE U BRAINLIEST!!
Answer:
1email is given by its boss and another email is given by its assistent
What are the measures of ∠1 and ∠2?
The screen of a 32-inch high definition television has a diagonal length of 31. 5 inches. If the TV screen is 27. 5 inches wide, find the height of screen to the nearest tenth of an inch.
The height of the TV screen is?
Using the Pythagorean theorem we get , the height of the TV screen is approximately 15.4 inches to the nearest tenth of an inch.
The screen of a 32-inch high definition television has a diagonal length of 31.5 inches. If the TV screen is 27.5 inches wide, you need to find the height of the screen to the nearest tenth of an inch. To do this, you can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (diagonal) of a right triangle is equal to the sum of the squares of the other two sides (width and height).
1. Let the height of the TV screen be h inches.
2. According to the Pythagorean theorem, (width)^2 + (height)^2 = (diagonal)^2.
3. Substitute the given values: (27.5)^2 + (h)^2 = (31.5)^2.
4. Calculate the squares: 756.25 + h^2 = 992.25.
5. Subtract 756.25 from both sides: h^2 = 236.
6. Find the square root of 236: h ≈ 15.4 inches.
The height of the TV screen is approximately 15.4 inches to the nearest tenth of an inch.
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HELP
Fran has been assigned the task of determining the
probability of drawing 3 spades from a standard deck of
52 cards. Recall there are 4 suits (diamonds, hearts, spades,
and clubs) of 13 cards each, in a deck. Each card is drawn
one at a time and held until the remaining cards of the hand
are drawn.
How many ways are there to draw the first card?
o 13
O 52
04
01
52
How many ways to draw?There are 52 ways to draw the first card from a standard deck of 52 cards. Each card in the deck is distinct, so there are 52 different possibilities for the first card.
The deck consists of 4 suits (diamonds, hearts, spades, and clubs) with 13 cards in each suit. Therefore, there are 13 cards of the spades suit. Since each card is equally likely to be drawn, the probability of drawing a spade as the first card is 13/52 or 1/4.
This is because out of the 52 possible cards, 13 of them are spades. So, regardless of the specific spade that is drawn, there are 13 ways to draw a spade as the first card.
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Find the surface area of the regular pyramid shown to the nearest whole number. The figure is not drawn to scale.
*
Captionless Image
1209 m^2
790 m^2
1125 m^2
898 m^2
The surface area of the regular pyramid is 1209 m².
How to find the surface area of the regular pyramid?A pyramid is a three-dimensional shape. It has a flat polygon base. All the other faces are triangles and are called lateral faces.
A pyramid is called by the shape of its base.
The surface area of the regular hexagonal pyramid is given by the formula:
SA = 3b(a + s)
Where a is the apothem, b is the base and s is the slant height of the pyramid.
In this case:
a = 8.5√3 m
b = 17 m
s = 9 m
SA = 3 * 17 * (8.5√3 + 9)
SA = 1209 m²
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Maddy is an event coordinator who helps
raise money for a children's hospital. At
last year's event, she sold 1200 tickets at
$8 each.
Part A: This year Maddy will reduce ticket
prices by 25%. What will be the price of a
new ticket? Explain your reasoning.
D
Part B: Based on the new price, how many
more tickets will Maddy need to sell to
raise the same amount of money as last
year? Explain your reasoning.
The price of a new ticket after reducing the ticket price by 25% is $6. Maddy will need to sell 400 more tickets this year to raise the same amount of money as last year.
Number of tickets sold = 1200
Cost of each ticket = $8
Part A:
If Maddy lowers ticket costs by 25%, The price of a new ticket will be:
Ticket price = $8 - (25% of $8)
Ticket price = $6
The New ticket price will be calculated by multiplying 0.75 for reducing the 25% tickets
New ticket price = $8 x 0.75 = $6
Part B:
To find how many tickets Maddy requires to sell to equal the same amount of money collected in the previous year:
Total revenue = total number of tickets x Ticket price
1200 tickets x $8 per ticket = $9,600
= $9,600 / $6
= 1,600
Total tickets need to sell = 1600-1200 = 400
Therefore we can conclude that Maddy will need to sell 400 more tickets this year.
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Last year at a certain high school, there were 124 boys on the honor roll and 125 girls on the honor roll. This year, the number of boys on the honor roll decreased by 25% and the number of girls on the honor roll decreased by 20%. By what percentage did the total number of students on the honor roll decrease? Round your answer to the nearest tenth (if necessary).
Answer:
22.5%
Step-by-step explanation:
Last year, there were 124 boys and 125 girls, meaning 249 total.
This year, if boys decreased by 25%:
[tex]0.25 * 124 = 31.[/tex]
A decrease of 31 boys.
If girls decreased by 20%:
[tex]0.2 * 125 = 25.[/tex]
A decrease of 25 girls.
If there was a total decrease of 56 students from last year to this year, the total decrease is:
[tex]56/249*100=22.5.[/tex]
A decrease of 22.5%.
Salazar made an investment in 140 shares of stock in a no-load fund for $2,993.20. after one year the stock had a net asset value of $24.53 per share. if salazar redeems all 140 shares, which of the following is a correct statement? a. salazar will have a loss of $441. b. salazar will have a profit of $441. c. salazar will have a profit of $3,434.20. d. there is not enough information to calculate profit or loss.
Salazar will have a profit of $441 if they redeem all 140 shares(B).
Salazar's initial investment of $2,993.20 for 140 shares means that the purchase price per share was $2,993.20/140 = $21.38. After one year, the net asset value per share has increased to $24.53, so the value of Salazar's 140 shares is 140 x $24.53 = $3,435.40.
To calculate the profit or loss, we need to subtract the initial investment from the current value, which gives a profit of $3,435.40 - $2,993.20 = $442.20.
However, we need to take into account any fees or expenses associated with redeeming the shares. Since the question states that it is a no-load fund, we can assume that there are no fees, and thus Salazar's profit is $441(B).
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CAN SOMEONE SHOW ME STEP BY STEP ON HOW TO DO THIS SOMEONE GAVE ME THE WRONG STEPS
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
A polygon with a horizontal top side labeled 45 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 10 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 12 yards.
What is the area of the playground?
900 square yards
855 square yards
1,710 square yards
1,305 square yards
Unlocked badge showing an astronaut’s boot touching down on the moon
The area of the playground include the following: 900 square yards.
How to calculate the area of a regular polygon?In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:
Area = (n × s × a)/2
Where:
n is the number of sides.s is the side length.a is the apothem.In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:
Area of a parallelogram, A = base area × height
Area of playground, A = 45 × 20
Area of a playground, A = 900 square yards.
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The volume of this cone is 3.0144 cubic centimeters. What is the height of this cone? Use ≈ 3.14 and round your answer to the nearest hundredth.
Therefore, the height of the cone is approximately 4.23 centimeters.
What is volume?Volume is a measure of the amount of space occupied by a three-dimensional object or region. It is the total amount of space enclosed by the boundaries of the object or region. Volume is usually measured in cubic units, such as cubic centimeters (cm³) or cubic meters (m³). Knowing the volume of an object can be useful for many purposes, such as determining how much material is needed to fill a container or how much space is needed to store a certain quantity of objects.
Here,
The formula for the volume of a cone is given by:
V = (1/3)πr²h
where V is the volume, r is the radius, and h is the height.
We are given that the volume of the cone is 3.0144 cubic centimeters, so we can plug this into the formula:
3.0144 = (1/3)πr²h
Next, we need to find the radius of the cone. Since we are not given the radius directly, we may need to use other information that is not given in the problem. If we assume that the cone is a right circular cone, then we can use the fact that the radius and height are proportional to find the radius:
r/h = 1/3
r = (1/3)h
We can substitute this expression for r into the volume formula:
3.0144 = (1/3)π((1/3)h)²h
Simplifying this equation:
3.0144 = (1/27)πh³
Multiplying both sides by 27/π:
h³ = 84.96
Taking the cube root of both sides:
h = 4.23 (rounded to the nearest hundredth)
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Miss kito’s grandfather passed away and she attended the reading of the will. the estate was valued at $4,567,890. it was decided that 3/5 of the estate value would be given to various charities. of the remaining amount, 1/4 would be used to create a scholarship for mathematics majors at fishtopia university and the rest would be divided evenly among his three grandchildren, of which miss kito was one.
Miss Kito will receive $456,789 from her grandfather's estate.
Let's break down the information given in the problem step by step.
The estate was valued at $4,567,890.
3/5 of the estate value would be given to various charities.
To find out how much money is left after 3/5 is given to charities, we can subtract 3/5 from 1:
1 - 3/5 = 2/5
So, 2/5 of the estate value is left. We can find out how much that is by multiplying:
2/5 x $4,567,890 = $1,827,156
Therefore, $1,827,156 is left after 3/5 of the estate value is given to charities.
1/4 of the remaining amount would be used to create a scholarship for mathematics majors at Fishtopia University.
To find out how much money will be used to create the scholarship, we can multiply:
1/4 x $1,827,156 = $456,789
Therefore, $456,789 will be used to create the scholarship.
The rest would be divided evenly among his three grandchildren, of which Miss Kito was one.
To find out how much money Miss Kito will receive, we can subtract $456,789 from $1,827,156:
$1,827,156 - $456,789 = $1,370,367
Finally, we can divide $1,370,367 by 3 to find out how much money each grandchild will receive:
$1,370,367 ÷ 3 = $456,789
Therefore, Miss Kito will receive $456,789 from her grandfather's estate.
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Calculating the relative frequencies from the data given in the table. Choose all that correctly describe an association between favorite subject and grade
From the given data, the statement "A higher percentage of 8th graders than 7th graders prefer Math/Science" is correct. So, correct option is C.
To calculate the relative frequencies, we need to divide the frequency of each category by the total number of responses.
For 7th grade:
Relative frequency of English: 38/116 = 0.3276
Relative frequency of History: 36/116 = 0.3103
Relative frequency of Math/Science: 28/116 = 0.2414
Relative frequency of Other: 14/116 = 0.1207
For 8th grade:
Relative frequency of English: 47/182 = 0.2582
Relative frequency of History: 45/182 = 0.2473
Relative frequency of Math/Science: 72/182 = 0.3956
Relative frequency of Other: 18/182 = 0.0989
From the data, we can see that a higher percentage of 8th graders prefer Math/Science than 7th graders. Therefore, the statement "A higher percentage of 8th graders than 7th graders prefer Math/Science" correctly describes the association between favorite subject and grade.
The statements "A higher percentage of 8th graders than 7th graders prefer History" and "A higher percentage of 7th graders than 8th graders prefer English" are incorrect as the relative frequencies for these subjects are similar in both grades.
Overall, we can conclude that the choice of favorite subject is not strongly associated with the grade level of the students.
So, correct option is C.
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Complete question is:
Calculating the relative frequencies from the data given in the table. Choose all that correctly describe an association between favorite subject and grade.
A) A higher percentage of 8th graders than 7th graders prefer History.
B) A higher percentage of 7th graders than 8th graders prefer English.
C) A higher percentage of 8th graders than 7th graders prefer Math/Science.
A vehicle has a mass of 1295 kg and uses petrol. Another vehicle has a mass of 1290 kg and uses diesel fuel, 1L of petrol has a mass of 737g and 1L of diesel has a mass of 820g. How many litres of fuel will result in the two vehicles having the same mass? Round to the nearest tenth of a litre.
Answer:
Another vehicle has a mass of 1290 kg and uses diesel fuel. 1 L of petrol has a mass of 737 g. 1L of diesel has a mass of 820g.
Choose an adult age 18 or over in the united states at random and ask, "how many cups of coffee do you drink on average per daycall the response x for short. based on a large sample survey, a probability model for the answer you will get is given in the table. number 2 3 4 or more probability 0.360.190.08 0,11. what is p(x < 4) ? give your answer to two decimal places.
To find the probability P(X < 4) for the given probability model, where X represents the number of cups of coffee an adult aged 18 or over drinks on average per day in the United States. The probabilities for each number of cups are given in the table:
- 2 cups: 0.36
- 3 cups: 0.19
- 4 or more cups: 0.11
To find P(X < 4), we need to sum the probabilities of X being 2 or 3 cups, as those are the only values less than 4:
P(X < 4) = P(X = 2) + P(X = 3)
P(X < 4) = 0.36 + 0.19
Now, we just need to add these probabilities together:
P(X < 4) = 0.55
So, the probability that a randomly chosen adult drinks fewer than 4 cups of coffee per day is 0.55 or 55% when expressed as a percentage.
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Qiang wants to style a 3ft x 3ft entryway. estimate to determine which style of tile will be the least expensive for this project. EXPLAIN.
The style that will be least expensive for the project, based on the product of the fractions representing the dimensions is the Style D that will yield a total cost of $25.92
What are fractions?A fraction is a representation of a part of a whole. It is a quantity which forms part of a whole number.
The area Qiang wants to tile = 3 ft × 3 ft
The price list and area of each tile, based on the product of the fractions of the tile dimensions are;
A; (5/6) × (1 1/12) = 65/72 cost 3.25
B; (5/6) × (2 1/12) = 125/72 cost 6.20
C; (5/6) × (5/6) = 5/16 cost 2.75
D; (5/12) × (3/4) = 5/16 cost 0.90
E; (5/12) × (5/12) = 25/144 cost 0.65
The areas of the tiles are;
The number of tiles required, are;
Cost of tiles style A = 9/(65/72) × 3.25 = 32.4
Cost of tiles style B = 9/(125/72) × 6.20 = 32.14
Cost of tiles style C = 9/(5/16) × 2.75 = 79.2
Cost of tiles style D = 9/(5/16) × 0.90 = 25.92
Cost of tiles style E = 9/(25/144) × 0.65 = 33.696
The least expensive style for the project is style D
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the Senators 118 more games than they lost they played 78 games. how many games did they win?
The Number of games lost cannot be negative .
The number of games the Senators won as "W." According to the given information, the Senators won 118 more games than they lost. This can be expressed as:
W = L + 118,
where "L" represents the number of games the Senators lost.
the Senators played a total of 78 games, which means the number of games they won and lost combined should equal 78:
W + L = 78.
Substituting the first equation into the second equation, we have:
(L + 118) + L = 78,
2L + 118 = 78,
2L = 78 - 118,
2L = -40,
L = -40/2,
L = -20.
Since the number of games lost cannot be negative.
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Nine out of eleven people at a math convention are bored to tears by cable news. If 2462 people at the convention are not bored by cable news, then how many people at the convention are bored by cable news?
The number of people at the convention are bored by cable news are 11079
How many people at the convention are bored by cable news?From the question, we have the following parameters that can be used in our computation:
Proportion = Nine out of eleven people at a math convention are bored to tears by cable news.
This means that
Proportion = 9/11
If 2462 people at the convention are not bored by cable news, then we have
(1 - 9/11) * x = 2462
This gives
x = 2462/(1 - 9/11)
Evaluate
x = 13541
Next, we have
Bored = 13541 - 2462
Bored = 11079
Hence, the number of people is 11079
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The function f (x) = 15(0.85)^x
models the height, in feet, of a bouncing ball after x seconds.
What is the initial height of the bouncing ball?
What is the percent rate of change?
What is the height of the bouncing ball after 5 seconds? Express your answers as a decimal rounded to the nearest hundredth.
a. The initial height of the bouncing ball is 15 feet.
b. The percent rate of change is 85%.
c. The height of the bouncing ball after 5 seconds is approximately 6.79 feet (rounded to the nearest hundredth).
What is Function ?In mathematics, a function is a rule that assigns each element in a set (the domain) to a unique element in another set (the range). The domain and range can be any sets, but they are typically sets of real numbers.
The function f(x) = 15 (0.85)ˣ models the height, in feet, of a bouncing ball after x seconds.
a. The initial height of the bouncing ball is given by f(0). Plugging in x = 0, we get:
f(0) = 15*1
f(0) = 15(1)
f(0) = 15
Therefore, the initial height of the bouncing ball is 15 feet.
b. The percent rate of change is given by the coefficient of the base, which is 0.85 in this case. To convert this decimal to a percentage, we can multiply by 100:
0.85 × 100 = 85
Therefore, the percent rate of change is 85%.
c. The height of the bouncing ball after 5 seconds is given by f(5). Plugging in x = 5, we get:
f(5) = 15
f(5) ≈ 6.79
Therefore, the height of the bouncing ball after 5 seconds is approximately 6.79 feet (rounded to the nearest hundredth).
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