There will be 4 plants left over after putting them in 7 equal rows.
Calculating the number of left over plantsTo find out how many plants will be left over after putting them in 7 equal rows, we need to divide the total number of plants (438) by the number of rows (7) and then find the remainder.
We can use integer division to find out how many plants will be in each row:
438 ÷ 7 = 62
So each row will have 62 plants.
To find out how many plants will be left over, we can subtract the total number of plants from the product of the number of rows and the number of plants in each row:
438 - (7 x 62) = 438 - 434 = 4
Therefore, the number of plants remaining is 4 plants
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The three circles are arranged so that they touch each other, as shown in the
figure. Use the given radii for the circles with centers A, B, and C, respectively,
to solve triangle.
5.4, 4.4, 3.4
***
A=
□°
(Do not round until the final answer. Then round to the nearest degree as needed.).
B = 0°
(Do not round until the final answer. Then round to the nearest degree as needed.)
c=
(Do not round until the final answer. Then round to the nearest degree as needed.)
B
Therefore , the solution of the given problem of triangle comes out to be the triangle has a side c of 2.15 and angles A = 42.5°, B = 0°, and C = 40.3°.
What precisely is a triangle?If a polygon has at least one additional segment, it is a hexagon. Its structure is a simple rectangle. Something like this can only be distinguished from a regular triangular form by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.
Here,
The centers of the three circles must make an equilateral triangle because they are positioned so that they touch one another. Angles A and C are both 60 degrees, so we know this.
With lengths that are 5.4 and 4.4 in length, we can use the Law of Cosines to determine angle A:
=> cos(A) = (4.4² + 5.4² - 3.4²) / (2 * 4.4 * 5.4)
=> cos(A) = 0.731
=> A = cos⁻¹(0.731)
=>A ≈ 42.5°
We can apply the Law of Cosines once more to determine side b:
=> b² = 4.4² + 5.4^2 - 2 * 4.4 * 5.4 * cos(60)
=> b ≈ 2.15
Finally, we can apply the Law of Sines to determine angle C:
=> Sin(60) / 2.15 = sin(C) / 5.4 =
=> sin(C) ≈ 0.635
=> C ≈ sin⁻¹(0.635)
=> C ≈ 40.3°
As a result, the triangle has a side c of 2.15 and angles A = 42.5°, B = 0°, and C = 40.3°.
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find the interest rate if £9000 has a final value of £13102 in 5 years. give your answer to 1.d.p
The rate of interest is 7.7 % if £9000 has a final value of £13102 in 5 years
When interest is compounding, it indicates that the balance as a whole, rather than just the principal, is taken into account when the following interest period begins.
For instance, after a year, a $100 loan with 5% annual compound interest will have a debt of $105 due. The interest will be applied to the entire $105, creating a new amount of $110.25 the next year, rather than being taken as 5% of $100.
The interest will be added to that $110.25 the following year, and so on throughout the loan.
This is distinct from simple interest, which is a periodic payment to the loan holder of a fixed sum of money derived from a percentage of the principal
We have given that the final amount is 13102 and the principal amount is 9000 and time n is 5 years we have to find the rate
We have the formula
[tex]A=p(1-\frac{r}{100})^n[/tex]
A= 13102
P=9000
n=5
r = ?
[tex]13102=9000(1-\frac{r}{100})^5\\\\1.455=(1-\frac{r}{100})^5\\\\1.077=1-\frac{r}{100}\\\\r=7.7[/tex]
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Examine the pattern and determine how many shaded squares then unshaded squares will be in the 100x100 square in the sequence shown in the diagram on the right.
There are 2500 Shaded squares and 7500 unshaded squares in the 100x100 square, based on the given sequence in the diagram.
1. First, analyze the given diagram and observe the pattern. Notice that there are alternating shaded and unshaded squares, with the shaded squares being on the main diagonal.
2. Next, identify the sequence in the pattern. It appears that there is a continuous increase of shaded squares, starting from 1 and increasing by 2 each time. This forms an arithmetic sequence: 1, 3, 5, 7, and so on.
3. To find the number of shaded squares in the 100x100 square, calculate the sum of the first 50 terms of the sequence (since there are 100 rows/columns and each shaded area covers 2 rows/columns). The formula for the sum of an arithmetic sequence is: Sn = n * (a1 + an) / 2, where Sn is the sum of the sequence, n is the number of terms, a1 is the first term, and an is the last term.
4. In our case, n = 50, a1 = 1, and an = 99 (the 50th term in the sequence). Plugging these values into the formula, we get: S50 = 50 * (1 + 99) / 2 = 50 * 100 / 2 = 2500.
5. Thus, there are 2500 shaded squares in the 100x100 square.
6. To find the number of unshaded squares, subtract the number of shaded squares from the total number of squares in the 100x100 square. The total number of squares is 100 * 100 = 10,000.
7. Now, calculate the number of unshaded squares: 10,000 - 2500 = 7500.
In conclusion, there are 2500 shaded squares and 7500 unshaded squares in the 100x100 square, based on the given sequence in the diagram.
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HELP PLEASEEEE QUICK!! THANK YOU SM♥️
Select numbers to complete the
three expressions so that each is
equivalent to 24x + 36y.
1. 12 (— x+—y) 2. —(4x+—y) 3.—(—x+12y)
0. 0. 0
1. 1. 1
2. 2. 2
3. 3. 3
4. 4. 4
5. 5. 5
6. 6. 6
7. 7. 7
8. 8. 8
9. 9. 9.
After answering the presented question, we can conclude that As a equation result, for any x and y values, these expressions will be identical to 24x + 36y.
What is expression?Expressions can be used to represent numerical or algebraic quantities, and can be used to perform calculations. For example, the expression "2 + 3" represents the sum of the numbers 2 and 3, which is 5. Similarly, the expression "x + 5" represents the sum of the variable x and the number 5, and can be evaluated to a specific value depending on the value of x.
[tex]12(2x-y)[/tex]
[tex]-6(4x-3y)[/tex]
[tex]3(x+12y)[/tex][tex]12(2x-y)=24x-12y[/tex]
So,[tex]24x-12y+24=24x+36y-6(4x-3y)=-24x+18y[/tex]
So,[tex]-24x+18y+42x+18y=24x+36y[/tex]
[tex]3(x+12y)=3x+36y[/tex]
So,[tex]3x+36y+21x-24y=24x+36y[/tex]
As a result, for any x and y values, these expressions will be identical to 24x + 36y.
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Mar 30, 11:25:22 PM
Omar owns a small business selling bagels. He knows that in the last week 91
customers paid cash, 8 customers used a debit card, and 27 customers used a
credit card.
If next week, he is expecting 1900 customers, about how many would you
expect to pay with a credit card? Round your answer to the nearest whole
number.
Rounding this to the nearest whole number, we can estimate that about 407 customers would pay with a credit card next week.
How to estimate number of customers?
To estimate the number of customers who would pay with a credit card next week, we can use the proportion of customers who paid with a credit card in the last week as a guide.
First, we need to find the total number of customers who visited Omar's business in the last week:
Total customers = Cash customers + Debit card customers + Credit card customers
Total customers = 91 + 8 + 27
Total customers = 126
Next, we can find the proportion of customers who paid with a credit card:
Proportion of credit card customers = Credit card customers / Total customers
Proportion of credit card customers = 27 / 126
Proportion of credit card customers = 0.2143
Now, we can estimate the number of customers who would pay with a credit card next week by multiplying the total number of expected customers by the proportion of credit card customers from the last week:
Expected credit card customers = Total expected customers x Proportion of credit card customers
Expected credit card customers = 1900 x 0.2143
Expected credit card customers = 407.17
Rounding this to the nearest whole number, we can estimate that about 407 customers would pay with a credit card next week.
However, it is important to note that this estimate is based on the assumption that the proportion of customers paying with a credit card remains the same next week. Factors such as changes in consumer behavior or market conditions may affect this proportion, and hence, the accuracy of the estimate.
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Help with math problems
The graph that shows the solution of the inequality 7 ≥ n + 5 is the graph of option D.
What is the solution to the inequality 7 ≥ n + 5?
The solution to the inequality 7 ≥ n + 5 is as follows:
7 ≥ n + 5
7 - 5 ≥ n
2 ≥ n
n ≤ 2
2, Let p be the number of pages Eduardo wrote before today. Then, the inequality that represents the situation is:
p + 16 > 50
To solve for p, first subtract 16 from both sides of the inequality:
p + 16 - 16 > 50 - 16
p > 34
Therefore, Eduardo wrote at least 34 pages before today.
Let r be the number of rows of seeds the farmer needs to plant. Then, the equation that represents the situation is:
6.5r ≥ 52
divide both sides of the equation by 6.5:
r ≥ 8
Therefore, the farmer needs to plant at least 8 rows of seeds to harvest at least 52 bushels of tomatoes.
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present age of father is four times the age of his son when the son will be as old as his father is now the sum of there is will be 99. find their present age
My art teacher is painting a picture in the shape of a square that has an area of 225 square inches. What is the perimeter?
If GH is a diameter of circle F, find the measurement of the minor arc JI.
A. 51 degrees
B. 102 degrees
C. 112 degrees
D. 258 degrees
Answer:
B) 102
Step-by-step explanation:
To find x, we need to simplify and solve the equation (5x+6)=(7x-12):
5x + 6 = 7x - 12 // distribute the 5 and 7
6 + 12 = 7x - 5x // group the x terms and constants
18 = 2x
Now, we can solve for x by dividing both sides by 2:
18/2 = x
9 = x
Therefore, x is 9.
To find the solution if x = 9, we can simply substitute 9 for x in the given expressions:
(5x+6) = (5(9) + 6) = 51
(7x-12) = (7(9) - 12) = 51
Therefore, both expressions are equal to 51 when x = 9.
Use rounding to estimate the product of 5555 and 4444. Round both numbers to the nearest thousand to find your answer.
Answer: 6666 and 3333
Step-by-step explanation: 5 or above give it a shove, 4 or below let it go.
3. When Ahmad goes to work, he has to pass through two sets of traffic lights, P and Q. The
7
probability that he has to stop at P is
The probability that he has to stop at Q, given that he has
20
to stop at Pis
stop at P is
2
5
7
The probability that he does not have to stop at Q, given that he does not have to
10
(a) Construct a tree diagram to represent the above information..
(b) Find the probability that he has to stop at both P and Q.
(c) Find the probability that he has to stop at least once.
(d) If he has to stop at Q, what is the probability that he would have stopped at P.
[3 marks]
[2 marks]
[2 marks]
[3 marks]
P(stop at P|stop at Q) = P(stop at P and stop at Q) / P(stop at Q) is 28/47
How to solve questions?
(a) Tree diagram:
| P stop 7/20
|
-------|-------
| |
Q stop| P stop 2/5 | P not stop 3/5
| |
------|------- |
| |
Q not stop| P stop 1/10 | P not stop 9/10
| |
-------|-------
|
| P not stop 13/20
(b) The probability that he has to stop at both P and Q is:
P(stop at P) * P(stop at Q|stop at P) = (7/20) * (2/5) = 7/50
(c) The probability that he has to stop at least once is:
P(stop at P and/or stop at Q) = 1 - P(not stop at P) * P(not stop at Q|not stop at P)
= 1 - (13/20) * (9/10) = 11/20
(d) If he has to stop at Q, the probability that he would have stopped at P is:
P(stop at P|stop at Q) = P(stop at P and stop at Q) / P(stop at Q)
= (7/50) / (13/20 * 2/5 + 7/50)
=28/47
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Marcus drew a scale drawing of the rectangular park in his neighborhood. on his drawing, the length of the park is 8 inches and the width of the park is 6 inches. the key on his drawing shows 1 inch=20 feet. what is the actual area of the park?
the actual area of the park is 19,200 square feet.
Marcus drew a scale drawing of the rectangular park in his neighborhood. He drew the length of the park as 8 inches and the width of the park as 6 inches. The key on his drawing shows 1 inch=20 feet. To find the actual area of the park, we need to convert the measurements in Marcus's drawing to the actual measurements in feet.
Since 1 inch on Marcus's drawing represents 20 feet in actuality, we can use a scale factor of 1 inch : 20 feet to convert the measurements. We can then multiply the actual length and width of the park in feet to find the actual area of the park in square feet.
To convert the length of 8 inches to feet, we multiply it by the scale factor:
8 inches × (20 feet/1 inch) = 160 feet
Similarly, we can convert the width of 6 inches to feet:
6 inches × (20 feet/1 inch) = 120 feet
So the actual length of the park is 160 feet and the actual width of the park is 120 feet.
To find the actual area of the park, we multiply the actual length by the actual width:
160 feet × 120 feet = 19,200 square feet
Therefore, the actual area of the park is 19,200 square feet.
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Apply the formula d=r⋅t to answer the following questions.
Part A
Tom drove a total of 150 miles in 3 hours. Assuming he drove at a constant speed, what speed was Tom driving?
______ miles per hour
Question 2
Part B
Zac drove for 2.5 hours at a constant speed of 40 miles per hour. How many miles did he drive?
______ miles
Question 3
Part C
Dan drove 130 miles at a constant speed of 65 miles per hour. How many hours did he drive?
_____ hours
Using the formula d = rt we have: Part A: Tom was driving at a speed of 50 miles per hour. Part B: Zac drove 100 miles. Part C: Dan drove for 2 hours.
What is distance formula?The link between distance, rate, and time is demonstrated by the equation d = r*t. The product of the rate (r) and the time (t) yields the distance (d) (t). In other words, the velocity of motion and the amount of time spent travelling affect the distance covered. Assuming that the time spent travelling is constant, increasing the rate of movement will result in an increase in the amount of distance travelled in a given amount of time. According to this, as journey duration increases, so does the distance travelled.
The given formula is d = r(t).
Part A:
Tom drove a total of 150 miles in 3 hours, so:
150 miles = r * 3 hours
r = 50 miles per hour
Part B:
constant speed of 40 miles per hour for 2.5 hours, so:
d = 40 miles per hour * 2.5 hours
d = 100 miles
Part C:
constant speed of 40 miles per hour for 2.5 hours, so:
130 miles = 65 miles per hour * t
t = 130 miles / 65 miles per hour
t = 2 hours
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Writing & Solving Equations
1. Sofia paid a total of $365 for her accommodation in Bali, Indonesia. Sofia will be
spending 5 nights at the hotel. The cost per night is $59 US Dollars.
a) Write an equation to help Sofia figure out how much money was charged in fees.
b) Determine the amount of money charged for fees. Show all your work to justify
your answer.
1
After answering the presented question, we can conclude that variable
a) equation to help Sofia figure out how much money was charged in fees is 365 = 59 × 5 + f
b) the amount of money charged for fees is $70.
What is a Variable?A variable is something that can be altered in the context of a mathematical notion or experiment. Variables are frequently denoted by a single symbol. The characters x, y, and z are frequently used as generic variables symbols. Variables are qualities with a wide range of values that can be investigated. Size, age, money, where you were born, academic position, and type of housing are just a few examples. Variables can be classified into two major groups using both numerical and categorical methods.
a) Total cost = Cost per night × Number of nights + Fees
365 = 59 × 5 + f
b) Solving for f, we get:
f = 365 - 295
f = 70
Therefore, the amount of money charged for fees is $70.
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Which interval contains the median response time? 40–50 seconds 50–60 seconds 60–70 seconds 70–80 seconds
Answer: b
Step-by-step explanation:
A triangle has sides with lengths of 63 inches, 73 inches, and 98 inches. Is it a right triangle?
Thus, the given side of triangle with lengths of 63 inches, 73 inches, and 98 inches does not form a right triangle.
Explain about the features of right triangle:A triangle is considered to be correct when one of its angles is 90 degrees. Moreover, a right angle is one that measures 90 degrees or more.
The non-right angle measurements of right triangles must add up to 90 degrees, which is a crucial condition. This results from the fact that a triangle's total number of angles equals 180 degrees.
In right triangle, the longest side is called hypotenuse.
Then,
hypotenuse H = 98 inches
Let Side S1 = 63 inches,
Let Side S2 = 73 inches,
Then, Pythagorean theorem must satisfy for right triangle
H² = (S1)² + (S2)²
98² = (63)² + (73)²
9604 = 3969 + 5329
9604 = 9298
But, 9604 ≠ 9298
Thus, the given side of triangle with lengths of 63 inches, 73 inches, and 98 inches does not form a right triangle.
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A company has two manufacturing plants with
daily production levels of 5x + 11 items and
2x - 3 items, respectively, where x represents a
minimum quantity. The first plant produces how
many more items daily than the second plant?
Hence, compared to the second plant, the first plant produces [tex]3x + 14[/tex]more things per day.
What is production?Production is the process of creating goods or services that can be used or consumed by individuals or other entities. It involves converting raw materials, labor, and capital into finished products or services that are suitable for sale or distribution in the market.
given
We must take the daily production of the second plant away from the daily production of the first plant in order to calculate how many more things are produced daily by the first plant than the second plant.
The first plant's daily output is equal to [tex]5x + 11.[/tex]
Daily output of the second plant is equal to [tex]2x - 3.[/tex]
As a result, the two facilities' daily production differences are as follows:
[tex](5x + 11) - (2x - 3) = 5x + 11 - 2x + 3[/tex]
[tex]= 3x + 14[/tex]
Hence, compared to the second plant, the first plant produces 3x + 14 more things per day.
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Question 10
Clarke is buying clothes for school.
• He buys 2 pairs of pants for $25.50 each and 2 shirts for $16 each.
The shirts are on sale for 25% off.
• He also has a coupon for 20% off the entire purchase.
How much will Clarke pay for the clothes before adding taxes?
Answer:
$60
Step-by-step explanation:
2*25.50=51
25% of 16=4
16-4=12
12*2=24
51+24=75
20% of 75=15
75-15 =
60
Mary has $20 .she wants to buy a book that is marked do 30% from it's original price of $28. It the sales tax is 2.5%,does Mary have enough money to buy the book
Answer:
she does not have enough!
Step-by-step explanation:
thirty percent of $28 is $8.4, so you would subtract the two leaving you with $19.6
2.5 sales tax of $19.6 is $0.49
Adding those two the total comes to $20.09 which is just over the budget!
Answer: She does not have enough money.
She needs 9 cents (aka $0.09)
========================================================
Explanation:
A discount of 30% means Mary would pay the remaining 70% (because 100-30 = 70)
The decimal form of 70% is 0.70
Let A = 0.70 since we'll use it later.
An increase of 2.5% means we will also have the multiplier 1.025; which you can think of it like saying 100% + 2.5% = 1 + 0.025 = 1.025
Let B = 1.025 since we'll use it later
Multiply the values of A and B to get: 0.70*1.025 = 0.7175
This is the net multiplier when combining the 30% discount and 2.5% tax.
The original price $28 then becomes 0.7175*28 = 20.09 which is 9 cents (aka $0.09) over the goal of $20
Therefore, Mary does not have enough money to buy the book. She'll need that remaining 9 cents.
I NEED HELP WITH Assessment: Plot Twists
Note that the line plot or number line for the data above is given as attached.
What is the explanation for the above response?1) To create an inequality for a line plot using the given data set, we can use the minimum and maximum distances as the endpoints of the inequality.
The minimum distance is 1 3/8, which is equivalent to 1.375 miles. The maximum distance is 3 1/4, which is equivalent to 3.25 miles.
Therefore, the inequality can be written as:
1.375 ≤ x ≤ 3.25
where x represents the distance of a ski trail in miles.
This inequality states that any value of x (distance of a ski trail) that is between 1.375 and 3.25, inclusive, is a valid value for the data set.
2. The total number of ski trails is 12.
3. The difference in length between the longest ski trail (3 1/4) and the shortest ski trail (1 3/8) is: 3 1/4 - 1 3/8 = 1 7/8
4. The total length of the ski trails that are 2 7/8 is:
2 7/8 + 2 7/8 + 2 7/8 = 8 1/4
5. The sum of the lengths of the shortest (1 3/8) and the longest (3 1/4) ski trails is:
1 3/8 + 3 1/4 = 4 5/8
6. Sam is correct. The longest ski trail is 3 1/4 miles and the shortest ski trail is 1 3/8 miles, so:
3 1/4 > 3 * 1 3/8
10 1/4 > 4 1/8
2.5 > 1
Therefore, the longest ski trail is indeed more than three times the length of the shortest ski trail.
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Math write your answer step by step
Find the area of the shaded region of circle W below. Round your answer to the nearest tenth if necessary.
The area of the shaded region is = area of the sector - the area of the right angle triangle. so the area is [tex]9\pi /4 -9/2[/tex]
What do you know about area of circle?Area of circle formula = [tex]\pi r^{2}[/tex]. The area of a circle is [tex]\pi[/tex] multiplied by the square of the radius. The area of a circle when the radius 'r' is given is [tex]\pi r^{2}[/tex]
The area of a circle when the diameter 'd' is known is [tex]\pi d\frac{2}{4}[/tex]. π is approx. [tex]3.14 or \frac{22}7}[/tex]. Area(A) could also be found using the formulas A = [tex](\frac{\pi}{4} )*d^{2}[/tex], where 'd' is the radius and A= [tex]\frac{c^{2} }{4\pi }[/tex], where 'C' is the given circumference.
According to the given information
The area of the shaded region is = area of the sector - the area of the right angle triangle.
A = [tex]9\pi /4 -9/2[/tex]
Therefore the area of the shaded region is = area of the sector - the area of the right angle triangle. so the area is [tex]9\pi /4 -9/2[/tex]
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find the area of triangle if the angles are 3 cm 4 cm and 5 cm
Answer:3x4x5 = 60
but how r angles Cm did u mean sides or lxhxw
Step-by-step explanation:
Answer:
It's not possible to determine the area of a triangle based on the given information about the angles.
To find the area of a triangle, we need to know at least one side length in addition to the angles. The formula for the area of a triangle is:
Area = (1/2) * base * height
where the base is any side of the triangle, and the height is the perpendicular distance from that side to the opposite vertex.
Without knowing any side lengths, we cannot calculate the height and therefore cannot find the area of the triangle.
90 percent% of seven7 years
The value of the given percent that satisfied the relation through which it justified it is 6.3 years.
What about percent?
Percent: A percent is a way of expressing a number as a fraction of 100. The symbol for percent is "%". For example, if you say that 50% of a group are females, it means that 50 out of every 100 people in the group are female. Percentages are often used to describe the proportion of something or to compare different quantities.
According to the given information:
90 % of 7 years
⇒ [tex]\frac{90}{100}[/tex] x 7 years
⇒ [tex]\frac{630}{100}[/tex]
⇒ 6.3 years
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What is the solution to the system of equations below? x + 3 y = 15 and 4 x + 2 y = 30 (4, 10) (3, 6) (6, 3) (10, 4)
Answer:
x=15-3yin second equation,
4x+2y=30
2(2x+y)=30
2x+y=15
Now,putting the value of x from above
2×(15-3y)+y=15
30-6y+y=15
30-15=5y
y=3
Then,
x=15-3×3
x=6
#(6,3) is ans
Answer:
(6,3)
Step-by-step explanation:
Suppose you model a game of chance with a discrete probability distribution. Let X be the net amount of money won or lost by the player. Let P ( X ) be the probability of the corresponding outcome. The three events are as follows: There is a 23% chance the player wins 5 dollars. There is a 29% chance the player breaks even. There is a 48% chance the player loses 3 dollars. Complete the table below to model the scenario
Mathematicians have used probability to determine how likely certain events are to occur. The possible values of X will be 10, 0, -5 with following probabilities:
P(X = 10 ) = 0.23
P(X = 0 ) = 0.48
P(X = -5) = 0.29
What in mathematics is probability?Probability is the ability to happen. . From 0 to 1 is used to express the value. Whenever we are unsure of how an event will turn out, we can talk about the probabilities of various outcomes, or how likely they are. The study of probability-based events is often known as statistics. The amount of favorable outcomes and the overall number of outcomes thus affect how likely an event is to occur. The probability is typically expressed as a ratio between the number of positive outcomes and all of the outcomes in the sample space.
Given:
The probability distribution of X can be represented as:
X P(X=x)
-5 0.29
0 0.48
10 0.23
The outcomes is attached as table below.
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The complete question is:
The table below to model the scenario is attached below:
A poster storage tube in the shape of a cylinder has a diameter of 3.5 inches and a volume of 122.5 pie cubic inches.
What is the height of the poster storage tube in inches?
The height of the poster storage tube is approximately 40 inches.
What is Volume?
Vοlume is the amοunt οf space that a three-dimensiοnal οbject οccupies. It is measured in cubic units such as cubic meters, cubic feet, οr cubic inches. The fοrmula fοr calculating the vοlume οf a sοlid οbject depends οn its shape. Fοr example, the vοlume οf a cube can be calculated using the fοrmula V = s³, where s is the length οf a side, while the vοlume οf a cylinder can be calculated using the fοrmula V = πr²h, where r is the radius οf the base and h is the height.
The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height of the cylinder.
Since the diameter of the cylinder is given as 3.5 inches, the radius is half of that or 1.75 inches. Also, the volume is given as 122.5π cubic inches.
Therefore, we can use the formula to solve for the height:
V = π[tex]r^{2}[/tex]h
122.5π = π(1.75)(1.75)h
122.5 = 3.0625h
h = 122.5/3.0625
h ≈ 40
Therefore, the height of the poster storage tube is approximately 40 inches.
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The figure below is a square pyramid.
What is the surface area of the figure?
51 square meters
96 square meters
120 square meters
180 square meters
5 m
A
6 m
The surface area of the square pyramid with a side length of 6 and a slant height of 5 is 96 square units.
How to find surface area?To calculate the surface area of a square pyramid, we need to find the area of the square base and the area of each triangular face.
The formula for the surface area of a square pyramid is:
[tex]S = (a^2) + 2as[/tex]
where a is the length of one side of the square base and s is the slant height.
Plugging in the given values, we get:
[tex]S = (6^2) + 2(6)(5)[/tex]
[tex]S = 36 + 60[/tex]
[tex]S = 96[/tex]
Therefore, the surface area of the square pyramid with a side length of 6 and a slant height of 5 is 96 square units.
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The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 71° is changed to 93°, which of the following measures changes the most and what is the new value?
Mean 82.3°
Median 86.5°
Range 48°
IQR 34°
From the above calculations, we can see that the IQR changes the most with a difference of 3°. The new value of the IQR is 34°.
To determine which measure changes the most when a value of 71° is changed to 93°, we need to calculate each measure before and after the change. Mean:
The mean is calculated by adding all the temperatures and dividing by the total number of temperatures.
Before the change:
Mean = (58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12
= 82.3°
After the change:
Mean = (58 + 61 + 93 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12
= 84.8°
The difference between the means is: 84.8° - 82.3° = 2.5°
Median:
The median is the middle value when the temperatures are arranged in order.
Before the change:
Median = 82°
After the change:
Median = 84°
The difference between the medians is: 84° - 82° = 2°
Range:
The range is the difference between the highest and lowest temperatures.
Before the change:
Range = 105° - 57°
= 48°
After the change:
Range = 105° - 58°
= 47°
The difference between the ranges is: 47° - 48° = -1°
IQR:
The IQR is the difference between the third quartile and the first quartile.
Before the change:
Quartiles:
Q1 = 66°
Q3 = 97°
IQR = Q3 - Q1
= 97° - 66°
= 31°
After the change:
Quartiles:
Q1 = 66°
Q3 = 100°
IQR = Q3 - Q1
= 100° - 66°
= 34°
The difference between the IQRs is: 34° - 31° = 3°
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A skeleton was found at an archaeological dig. A technique used for estimating age indicated that the skeleton was 60 centuries old,
plus or minus 0.8 centuries. According to this estimate, what is the greatest possible age of the skeleton?
The greatest possible age of the skeleton is centuries.
To find the greatest possible age of the skeleton, we need to add the error to the estimate:
60 centuries + 0.8 centuries = 60.8 centuries
Therefore, the greatest possible age of the skeleton is 60.8 centuries.