the diamtery of a standard basketball is 9.5 inches. if there basketballs are covered in rubber, what is the minimum amount of rubber needed to manufacture a set of four basketballs?
Therefore, the minimum amount of rubber needed to manufacture a set of four basketballs is 1130.96 square inches.
To determine the minimum amount of rubber needed to manufacture a set of four basketballs, we need to calculate the total surface area of one basketball. The formula to calculate the surface area of a sphere is 4πr², where r is the radius of the sphere. The diameter of a standard basketball is 9.5 inches, so the radius is half of that, which is 4.75 inches.
Using the formula, we can calculate the surface area of one basketball as 4π(4.75)² = 282.74 square inches. To manufacture a set of four basketballs, we need to multiply the surface area of one basketball by four, which gives us 1130.96 square inches.
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if the saving rate is 1 (i.e., s = 1), we know that
If the saving rate is 1, it means that an individual or an economy saves their entire income and spends nothing. This implies that the consumption rate is 0, and all income is being saved.
In this scenario, the investment rate is equal to the saving rate, as there is no consumption spending. Therefore, the economy is investing all of its income in capital goods and not in consumption goods. This approach may result in high economic growth in the future due to the increased production capacity of the economy. However, in the short term, it may lead to a decrease in consumer demand and a decrease in output and employment in sectors producing consumer goods.
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Find the surface area of each cylinder. Round to the tenth place.
SA=
9m
15 m
sq. m.
The surface area of each cylinder would be = 777.15m²
How to calculate the surface area of the given cylinder?To calculate the surface area of the given cylinder, the formula that should be use will be written below. That is;
Surface area of cylinder = 2πr²+2πrh
Where;
radius = diameter/2 = 15/2 = 7.5m
height = 9m
Surface area= 2×3.14×7.5×7.5+2×3.14×7.5×9
= 353.25+ 423.9
= 777.15m²
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A trapezoid has bases of lengths 14 and 21. Find the trapezoid's height if it's area is 245
Answer: 8575/2
Step-by-step explanation:
Literally don’t know the answer to this question can y’all help?
Answer: 12.3 cm
Step-by-step explanation:
We are given the perimeter and all but one of the missing side lengths. The perimeter is equal to all of the side lengths added together. Using this information, we can create an equation to solve for the missing length, ?.
? = 65.9 cm - (9.2 cm + 4.7 cm + 4.7 cm + 2.2 cm + 9.2 cm + 2.2 cm + 12 cm + 4.7 cm + 4.7 cm)
? = 65.9 cm - 53.6 cm
? = 12.3 cm
there are seven nickels and six dimes in your pocket. you randomly pick a coin out of your pocket and then return it to your pocket. then you randomly pick another coin. find the probability that both coins are nickels.
Step-by-step explanation:
a probability is airways the ratio
number of desired cases / number of totally possible cases
so, we have 7 nickels and 6 dimes. together that means we have 7+6 = 13 coins in total in the pocket.
since we return the coin from the first pull, we have the exact same probabilities for the second pull.
the 2 pulls are to be considered one combined event, so we need to combine the individual probabilities for the overall event probability.
the probabilty to pull a nickel in a pull is
7/13
7 desired possible outcomes over 13 total possible outcomes.
the combination of the probabilities of both pulls is simply their product.
so, the probability to pull 2 nickels is
7/13 × 7/13 = 49/169 = 0.289940828...
the solution set for 3 => x-4/2 + x/3 => 2, x belongs to an integer
Answer:
To solve the inequality 3 ≤ (x - 4)/2 + x/3 < 2, we can start by simplifying the expression on the right-hand side:
(x - 4)/2 + x/3 = (3(x - 4) + 2x)/6 = (5x - 12)/6
Substituting this back into the inequality, we have:
3 ≤ (5x - 12)/6 < 2
Multiplying both sides by 6, we get:
18 ≤ 5x - 12 < 12
Adding 12 to all sides, we get:
30 ≤ 5x < 24
Dividing all sides by 5, we get:
6 ≤ x < 4.8
Since x is an integer, the only integer that satisfies this inequality is x = 6. Therefore, the solution set for the inequality 3 ≤ (x - 4)/2 + x/3 < 2, where x belongs to an integer, is {6}.
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Find the measure of < A C B :
< A C B = °
The measure of the angle m∠ACB subtended by the arc AB at the center is equal to 140°
What is angle subtended by an arc at the centerThe angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.
The arc AB completes the circumference of the circle, with the other arc ADB
So since;
arc AB = 360° - 220°
arc AB = 140°
so;
m∠ACB = 140°
Therefore, the measure of the angle m∠ACB subtended by the arc AB at the center is equal to 140°
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x^4+13x^2+36=4x^3+36
Answer:
Step-by-step explanation:
x^4+13^x^2+36=4x^3+36
4x+26x+36=4x^3+36
30x+36=12x+36
30x=12x
so,x=1
a program is divided into 3 blocks that are being compiled on 1 computer. each block takes an exponential amount of time, 5 minutes on the average, independently of other blocks. the program is completed when all three blocks are compiled. let t represent the time the program is completed. what distribution does t follow?
The distribution that t follows is the maximum of three independent exponential distributions with a mean of 5 minutes each.
Each block takes an exponential amount of time with a mean of 5 minutes, which means that the time it takes to compile each block follows an exponential distribution with a rate parameter of 1/5. Since the blocks are being compiled independently of each other, the time it takes to compile all three blocks is the maximum of the three independent exponential distributions.
This distribution is known as the maximum of exponential distributions or the generalized extreme value distribution with a shape parameter of 0 and scale parameter of 5 minutes. Therefore, t follows a generalized extreme value distribution with a shape parameter of 0 and scale parameter of 5 minutes.
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A historian wants to estimate the average age at which men married in the United States in 1956. He locates marriage records for 1956 in his state's archives and records his findings. What step of the data analysis process is he using?
The historian is engaged in the process of data collection, which is the first step in the data analysis process. In this case, the historian is collecting marriage records from the archives to estimate the average age at which men married in the United States in 1956.
Once the historian has collected the data, he will move on to the next steps in the data analysis process, which include data preparation, data analysis, and interpretation of results. In data preparation, the historian will clean, transform, and organize the data so that it is ready for analysis. In data analysis, he will use statistical methods to analyze the data and answer his research question. Finally, in interpretation of results, he will draw conclusions from the analysis and communicate his findings.
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The historian is engaged in the process of data collection, which is the first step in the data analysis process. In this case, the historian is collecting marriage records from the archives to estimate the average age at which men married in the United States in 1956.
Once the historian has collected the data, he will move on to the next steps in the data analysis process, which include data preparation, data analysis, and interpretation of results. In data preparation, the historian will clean, transform, and organize the data so that it is ready for analysis. In data analysis, he will use statistical methods to analyze the data and answer his research question. Finally, in interpretation of results, he will draw conclusions from the analysis and communicate his findings.
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In 1-3 find the diagonal distance between the two points to the nearest tenth
1. point A is 2Y 1X point B is 9Y 9X
2. point A is 4Y -1X point B is -15Y 3X
3. point A is 7Y 1X point B is 5Y 9X
The Diagonal distance between point A and point B is approximately 8.2 units.
1. To find the diagonal distance between point A (2Y, 1X) and point B (9Y, 9X), we can use the distance formula:
distance = √((y2 - y1)^2 + (x2 - x1)^2)
distance = √((9 - 2)^2 + (9 - 1)^2)
distance = √(49 + 64)
distance = √113
distance ≈ 10.6
Therefore, the diagonal distance between point A and point B is approximately 10.6 units.
2. To find the diagonal distance between point A (4Y, -1X) and point B (-15Y, 3X), we can use the distance formula:
distance = √((y2 - y1)^2 + (x2 - x1)^2)
distance = √((-15 - 4)^2 + (3 - (-1))^2)
distance = √(361 + 16)
distance = √377
distance ≈ 19.4
Therefore, the diagonal distance between point A and point B is approximately 19.4 units.
3. To find the diagonal distance between point A (7Y, 1X) and point B (5Y, 9X), we can use the distance formula:
distance = √((y2 - y1)^2 + (x2 - x1)^2)
distance = √((5 - 7)^2 + (9 - 1)^2)
distance = √4 + 64
distance = √68
distance ≈ 8.2
Therefore, the diagonal distance between point A and point B is approximately 8.2 units.
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Which table contains only points that lie on the equation below?
y = 1/2 x
The equation y= 1/2 x means that you want the y-values to be half of the x-value.
If x = 4, then y = 2. If x = 10, then y = 5.
The only table table that shows this relationship is B.
a furniture store is having a weekend sale and is offering a 20% discount on patio chairs and tables. the sales tax on furniture is 6.25%. using function composition how can you represent the total amount, A, that you would need to pay for furniture that costs X dollars?
well, we know the store is having a 20% off sale, so if you go and buy a few items and the total cost is X, well, since the items are on sale, you won't be paying 100% of X, you'll be paying only 100% - 20% = 80% of X, hmmm how much is 80% of X anyway?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{80\% of X}}{\left( \cfrac{80}{100} \right)X}\implies 0.80X \\\\[-0.35em] ~\dotfill\\\\ ~\hspace{12em}\stackrel{ \textit{total amount} }{A}~~ = ~~0.80X[/tex]
ruby company has an annual profit, in billions, that has a normal distribution with variance that is equal to the cube of its mean. the probability of an annual loss is 5%. calculate the company's expected annual profit.
Therefore, the expected annual profit of Ruby Company is 2.703 billion dollars using probability.
Let X be the annual profit of the company. We know that X follows a normal distribution with variance equal to the cube of its mean, i.e., Var(X) = (E[X])^3.
To find the expected annual profit, we need to find the mean of X, denoted as E[X].
We are given that the probability of an annual loss is 5%. This means that the probability of making a profit is 1 - 0.05 = 0.95.
Let Z be a standard normal random variable, then we have:
P(X < 0) = P((X - E[X]) / sqrt(Var(X)) < (0 - E[X]) / sqrt(Var(X)))
= P(Z < -E[X] / (E[X])^(3/2))
Since P(X < 0) = 0.05, we have:
0.05 = P(Z < -E[X] / (E[X])^(3/2))
Using a standard normal table or calculator, we can find that P(Z < -1.645) = 0.05, where -1.645 is the 5th percentile of the standard normal distribution.
Thus, we have:
-E[X] / (E[X])^(3/2) = -1.645
this equation, we get:
E[X]^(1/2) = 1.645
Taking the square of both sides, we get:
E[X] = 2.703
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Choose the INCORRECT statement below.
Answer: #4
Step-by-step explanation:
I haven't done anything like this in years but I think it is the 4th answer :)
Sorry if I'm wrong. I am a year ahead in math and in an honors class so i would think I'm pretty smart
What is the missing ratios of the values below
The missing values from the ratio table are underlined:
Peppermints: 14, 2, 2/7.
Chocolates: 21, 21, 189.
How to find the missing value of the ratio table?To fill in the missing values in the ratio table, we need to find the common ratio between the given values.
For the Peppermints row:
Common ratio = (2nd value) / (1st value) = 2 / 14 = 1/7
So, the missing value can be found by multiplying the 2nd value (2) by the common ratio:
Missing value = (2nd value) * (common ratio) = 2 * (1/7) = 2/7
Therefore, the missing value in the Peppermints row is 2/7.
For the Chocolates row:
Common ratio = (3rd value) / (2nd value) = 189 / 21 = 9
The missing value in the Chocolates row can be found by dividing the 3rd value (189) by the common ratio:
Missing value = (3rd value) / (common ratio) = 189 / 9 = 21
Therefore, the missing value in the Chocolates row is 21.
The completed ratio table is as follows:
Peppermints - 14, 2, 2/7
Chocolates - 21, 21, 189
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Estimate the value of 64.127 x 3.413
Answer:
192
Step-by-step explanation:
To estimate the value of 64.127 × 3.413, we can simply round each decimal downwards:
Why do we round downwards?We round downwards because to in order to estimate the product of 2 numbers, we need to make the equation as simple as possible. One way we can do this is round each number either upwards, or downwards.
To find out if we round upwards or downwards, we use the rule 5 or more rounds up.
64.127. 1 is less than 5, so we round downward. It now becomes 64.3.413. Once again, 4 is less than 5 so we round down. It now becomes 3.Now we can solve.
64 × 3 = 192Therefore, the estimated value of 64.127 × 3.413 is 192.
volume of cones and spheres questions
The volume of the cone is 57.44 cubic cm
The volume of the cone and sphere is 229.88 cubic cm
The height of the square pyramid will be 115.03 cm
How to find the volume of the coneThe volume of a cone can be calculated using the formula:
V = (1/3)πr²h
where
V = volume of the cone
π = pi, approximately 3.14
r = radius of the base of the cone
h = height of the cone
2 x V = 2 * (1/3) * 3.14 * 2.8² * 3.5
The volume of the cone is 57.44 cubic cm
2.
Volume = volume of cone + volume of sphere
= (4/3)πr³ + (1/3)πr²h
= (4/3) * 3.14 * 3.4³ + (1/3) * 3.14 * 3.4² * 5.4
= 229.88 cubic cm
3. Volume of square pyramid
= base area * h/3
when base is 230
= 230² * 147/3 = 2592100
when base is 260
260² * h/3 = 2592100
h/3 = 2592100 / 260²
h = 115.03 cm
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the computations for the p-value of a hypothesis test about a population mean rely on the mathematical properties of
The computations for the p-value of a hypothesis test about a population mean rely on the mathematical properties of the t-distribution and the sample statistics.
What is a p-value?The p-value in statistics is the probability that the null hypothesis will be rejected if it is true. In hypothesis testing, p-values are utilized to determine whether or not the null hypothesis should be rejected. The p-value is calculated utilizing a test statistic that is based on the sample statistics and the assumptions of the null hypothesis.
The significance level, alpha, is usually set at 0.05 or 0.01 in hypothesis testing.A p-value of less than or equal to the significance level (alpha) indicates that the null hypothesis should be rejected
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Andrea is keeping track of how many calories she eats. On Friday, she ate 4 cookies at snack time and 1700 calories with her meals. On Saturday, she ate 5 cookies at snack time and 1650 calories with her meals. If Andrea ate the same amount of calories both days, how many calories are in each cookie?
If Andrea ate the same amount of calories both days, Each cookie has 100 calories.
To find out how many calories are in each cookie, we need to determine the total number of calories consumed and divide it by the total number of cookies.
On Friday, Andrea ate 4 cookies and 1700 calories with her meals, resulting in a total of 1700 + (4 * C) calories, where C represents the calories per cookie.
On Saturday, Andrea ate 5 cookies and 1650 calories with her meals, resulting in a total of 1650 + (5 * C) calories.
Since Andrea ate the same amount of calories both days, we can set up an equation:
1700 + (4 * C) = 1650 + (5 * C)
Simplifying the equation, we get:
50 = C
Therefore, each cookie has 50 calories.
It's worth noting that the solution assumes that the calorie content of the meals on both days is the same and only the calorie content from the cookies varies.
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2. A coach formed teams of 8 from all the players in a soccer league. There are 14 teams. How many players are in the league? y = 14 +8 Y 8 1 = 14 y = 14 y = 14.8 y =
Answer:112 players
Step-by-step explanation:
To solve the problem, we can use the formula:
Total number of players = Number of teams × Number of players per team
Since there are 14 teams with 8 players each, we have:
Total number of players = 14 × 8 = 112
Therefore, there are 112 players in the soccer league.
A circle is centered on point B. Points A, C and D lie on its
circumference.
If
Answer:
122°-------------------
∠ADC and ∠ABC subtend the same arc AC, hence ∠ABC is double the measure of ∠ADC:
m∠ABC = 2*m∠ADCm∠ABC = 2*61°m∠ABC = 122°The intersection of a right cylinder and a plane makes an oval cross section. Which option is true about the plane of intersection?
1.The right cylinder is cut with a plane that is neither parallel nor perpendicular to the base.
2.The right cylinder is cut with a plane perpendicular to the base and passing through the center.
3.The right cylinder is cut with a plane parallel to the base.
4.The right cylinder is cut with a plane perpendicular to the base but not passing through the center.
An answer option that is true about the plane of intersection include the following: 1. The right cylinder is cut with a plane that is neither parallel nor perpendicular to the base.
What is a plane?In Mathematics and Geometry, a plane is sometimes referred to as a two-dimensional surface and it can be defined as a flat, two-dimensional surface with zero curvature and zero thickness, that extends indefinitely (infinitely). Additionally, two (2) planes generally intersect at a line.
In order to have an intersection of a right cylinder and a plane that would make an oval cross section, the right cylinder must be cut with a plane that is neither parallel nor perpendicular to its base.
However, if the right cylinder is cut with a plane that is parallel to its base, then, the shape of cross section that would be formed is a circle.
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a recent personalized information sheet from your wireless phone carrier claims that the mean duration of all your phone calls was μ = 2.4 minutes with a standard deviation of o = 1.8 minutes. complete parts a through c below.
a. is the population distribution of the duration of your phone calls likely to be bell shaped, right, or left skewed?
b. You are on a shared wireless plan with your parents, who are statisticians. They look at some of your recent monthly statements that list each call and its duration and randomly sample 45 calls from the thousands listed there. They construct a histogram of the duration to look at the data distribution. Is this distribution likely to be bell shaped, right-, or left-skewed?
c. From the sample of n = 45 calls, your parents compute the mean duration. Is the sampling distribution of the sample mean likely to be bell shaped, right-, or left-skewed, or is it impossible to tell?
Answer:
a. The population distribution of the duration of your phone calls is likely to be bell shaped. This is because the mean, median, and mode are all equal to 2.4 minutes. This means that the data is evenly distributed around the mean.
b. The distribution of the 45 calls is likely to be bell shaped as well. This is because the sample size is large enough to be representative of the population. Additionally, the sample was randomly selected, so it is unlikely to be biased.
c. The sampling distribution of the sample mean is also likely to be bell shaped. This is because the central limit theorem states that the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is large enough. In this case, the sample size is 45, which is large enough to satisfy the requirements of the central limit theorem.
It is important to note that the sampling distribution of the sample mean will only be exactly normal if the population distribution is normal. However, in most cases, the sampling distribution will be approximately normal, even if the population distribution is not.
Step-by-step explanation:
Find all positive interger x, y, z so that 2x^5 + y^5 = 3z^5 and 2x + y + 2z is a prime number.
The solution to the system of equations is
x = 3
y = 2
z = 2
Here, we have,
To solve for x, y, and z, we can use the elimination method or substitution method. Here, we will use the elimination method.
First, we will eliminate y from the equations by multiplying the first equation by 3 and the second equation by 1, and then adding them:
(3) (2x – y + 3z = 10)
6x – 3y + 9z = 30
(1) (x + 3y – 2z = 5)
x + 3y – 2z = 5
Adding the two equations gives:
7x + 7z = 35
Simplifying, we get
x + z = 5 (Equation 1)
Next, we will eliminate y again by multiplying the second equation by 2 and the third equation by 3, and then adding them:
(2) (x + 3y – 2z = 5)
2x + 6y – 4z = 10
(3) (3x – 2y + 4z = 12)
9x – 6y + 12z = 36
Adding the two equations gives:
11x + 8z = 46
Substituting x + z = 5 from Equation 1 into the above equation, we get:
11(x + z) + 8z = 46
11x + 19z = 46
Solving for z, we get:
z = 2
Substituting z = 2 into x + z = 5 from Equation 1, we get:
x + 2 = 5
x = 3
Finally, substituting x = 3 and z = 2 into any of the original equations, we can solve for y:
2x – y + 3z = 10
2(3) – y + 3(2) = 10
6 – y + 6 = 10
y = 2
Therefore, the solution to the system of equations is:
x = 3
y = 2
z = 2
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complete question:
Solve for x, y and z
2x – y + 3z = 10
x + 3y – 2z = 5
3x – 2y + 4z = 12
What is (-i)^5?
O A. -i
OB. -1
O C. 1
O D. i
Answer:
A,-i
Step-by-step explanation:
-i⁵=-i*-i*-i*-i*-i
=i*-i*-i*-i
=-i*-i*-i
=i*-i
=-i
There are 20 students in a class. Everyone in the class scored 6 out of 10
in a test. What is the range of their scores?
Answer: 0
Step-by-step explanation:
Range = Highest number - lowest number
range = 6 - 6
range = 0
Question in the picture below
The best estimate of the random sample in the survey that support the proposal is the option; 4.1
What is a random sample?A random sample is a collection of data selected from a population such that each member of the population have the same chance of being selected.
The best estimate can be obtained from the mean value of the result from the poll, which can be obtained as follows;
The mean response = The sum of the response ÷ The count or the number of responses
The responses are; 7, 2, 6, 7, 3, 5, 5, 3, 2, 1
The sum of the response = 7 + 2 + 6 + 7 + 3 + 5 + 5 + 3 + 2 + 1 = 41
The number of response = 10
The mean of the response = (7 + 2 + 6 + 7 + 3 + 5 + 5 + 3 + 2 + 1)/10 = 4.1
The best estimate of the state citizens that support the proposal, therefore is; 4.1, which indicates that the citizens in the sample are slightly in support of the proposal.
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Let P(x,y) be a point on the graph of y=√x
Express the distance d from P to the point (0,0)(0,0) as a function of x
(a) d=√x2+x
(b) d=x2+x
(c) d=√x2+3x+1
(d) d=x2+3x+1
(e) None of the above.
The distance d from P to the point (0,0) is √x²+x.
What is the distance formula?
The d-distance between two places is calculated using the distance formula. The distance formula determines how far apart two areas are from one another. The dimensions of these points are unlimited.
Here, we have
Given: Let P(x,y) be a point on the graph of y=√x.
We have to find the distance d from P to the point (0,0)(0,0) as a function of x.
Since P = (x,y) is on the graph of y =√x,
P can be expressed as (x,√x).
Now, we apply the distance formula and we get
d = √[(x - 0)² + (√x - 0)²]
d = √x²+x
Hence, the distance d from P to the point (0,0) is √x²+x.
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