The radius of the sphere with a volume of 4,500π cubic inches is 15 inches, not 2,000 inches as the student had incorrectly calculated.
What is volume?
Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
The volume of the sphere is given as 4,500π cubic inches.
The formula for volume of the sphere is -
V= 4/3πr³
Substituting the values in the equation -
4,500π = 4/3πr³
4,500 = 4/3r³
The mistake in the student's calculation is in the step where they simplified 4/3πr³ to 4,500.
To correct this, we need to isolate r³ by dividing both sides by 4/3 -
4,500 = (4/3)r³
4,500 ÷ (4/3) = r³
4,500 × 3/4 = r³
3,375 = r³
Then, we can take the cube root of both sides to find r -
r = ∛3,375 = 15
Therefore, the radius of the sphere is 15 inches.
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3x (x-4) (3x + 5) = 0
Therefore, x = 0, x = 4, and x = -5/3 are the answers to the equation 3x(x-4)(3x+5) = 0.
what is equation ?An equation in mathematics is a claim that two expressions are equivalent. An equals sign (=) separates the left and right sides of an equation, which usually has two sides. Variables, constants, and mathematical operations like addition, subtraction, multiplication, division, exponents, and roots may be used in the formulas on either side of the equals sign. Finding the number of the variable or variables that make an equation true is the goal of an equation.
given
The zero product property, which asserts that at least one of the factors must be zero if the product of two or more factors equals zero, can be used to solve the equation 3x(x-4)(3x+5) = 0.
We then solve for x by setting each component equal to zero:
3x = 0, 3x + 4, or 3x + 5 = 0.
When we factor x into each solution, we obtain:
3x = 0 --> x = 0
x-4 = 0 —> x = 4
Therefore, x = 0, x = 4, and x = -5/3 are the answers to the equation 3x(x-4)(3x+5) = 0.
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a computer table is given a discount of 20% the original price of the computer id php 850. What is the discounted price
the travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes. the probability that she will finish her trip in 60 minutes or less is
The probability that the student will finish her trip in 60 minutes or less is 0.4
To find the probability that the student will finish her trip in 60 minutes or less, we need to find the proportion of the total area under the uniform distribution curve that lies to the left of 60 minutes.
Since the travel time is uniformly distributed between 40 and 90 minutes, the probability density function is
f(x) = 1/(90-40) = 1/50, for 40 ≤ x ≤ 90
The probability of finishing the trip in 60 minutes or less is therefore
P(X ≤ 60) = ∫[40, 60] f(x) dx
= (60-40)/50
Do the arithmetic operations
= 0.4
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What percent of 15 is 5?
Answer: 33.33%
Step-by-step explanation:
5/15 divided
PACKAGING A video game system is packaged in a box that is in the shape of a cube. The length of the packaging box is 4x^2 y^5 . What is the volume of the packaging box in terms of x and y?
Answer: 64x^6y^15
Step-by-step explanation:
If the packaging box is in the shape of a cube, then all its sides are equal in length. Let's call the length of each side "s".
We know that the length of the packaging box is 4x^2 y^5, so:
s = 4x^2 y^5
To find the volume of the packaging box, we need to calculate s^3 (since the box is a cube).
s^3 = (4x^2 y^5)^3
s^3 = 4^3 (x^2)^3 (y^5)^3
s^3 = 64x^6 y^15
Therefore, the volume of the packaging box in terms of x and y is 64x^6 y^15.
Consider the following hypothesis test. H0: μ ≤ 50 Ha: μ > 50 A sample of 60 is used and the population standard deviation is 8. Use the critical value approach to state your conclusion for each of the following sample results. Use α = 0. 5. (Round your answers to two decimal places. ) (a) x = 52. 7 Find the value of the test statistic. State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail. ) test statistic ≤ test statistic ≥ (b) x = 51 what is the test statistics? c) x = 51. 8 what is the test statistics?
the test statistic (1.58) is greater than the critical value for a right-tailed test with α = 0.05.
To test the hypothesis H0: μ ≤ 50 vs Ha: μ > 50 at a significance level of α = 0.05, we can use a one-tailed z-test.
a) For the sample result x = 52.7, the test statistic is given by:
z = (x - μ) / (σ / [tex]\sqrt{n}[/tex]) = (52.7 - 50) / (8 / [tex]\sqrt{60}[/tex] ) = 2.38
To find the critical values for the rejection rule, we need to determine the z-value that corresponds to a right-tail probability of 0.05. Since we are using a one-tailed test, we can look up the z-value in the standard normal distribution table. The critical value for a right-tailed test with α = 0.05 is:
zα = 1.645
Since the test statistic (2.38) is greater than the critical value (1.645), we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis at a significance level of α = 0.05.
b) For the sample result x = 51, the test statistic is given by:
z = (x - μ) / (σ /[tex]\sqrt{n}[/tex] ) = (51 - 50) / (8 / [tex]\sqrt{60}[/tex] ) = 0.53
Since the test statistic (0.53) is less than the critical value for a right-tailed test with α = 0.05, we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the alternative hypothesis at a significance level of α = 0.05.
c) For the sample result x = 51.8, the test statistic is given by:
z = (x - μ) / (σ / [tex]\sqrt{n}[/tex] ) = (51.8 - 50) / (8 / [tex]\sqrt{60}[/tex]) = 1.58
Since the test statistic (1.58) is greater than the critical value for a right-tailed test with α = 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis at a significance level of α = 0.05.
In summary, the test statistic represents the number of standard deviations between the sample mean and the hypothesized population mean, and the critical values represent the cutoff points for rejecting the null hypothesis. The decision to reject or fail to reject the null hypothesis depends on whether the test statistic falls within or outside the critical values for the given level of significance.
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a 17 ft ladder is leaning against a wall. if the bottom of the ladder is pulled along the ground away from the wall at a constant rate of 2ft/s, how fast will the top of the ladder be coming down the wall when the top is 8 ft above the ground
The top of the ladder is coming down the wall at a rate of 15.39 ft/s
Let's assume that the ladder makes a right angle with the wall and the ground. Let's call the distance between the bottom of the ladder and the wall "x" and the height of the ladder at a given time t "y". We want to find the rate of change of "y" with respect to time "t", or dy/dt, when y = 8 ft.
We can use the Pythagorean theorem to relate "x" and "y":
x^2 + y^2 = 17^2
Taking the derivative of both sides with respect to time "t", we get
2x(dx/dt) + 2y(dy/dt) = 0
We want to find dy/dt when y = 8 ft and dx/dt = 2 ft/s. We can solve for dy/dt
2x(dx/dt) + 2y(dy/dt) = 0
2y(dy/dt) = -2x(dx/dt)
dy/dt = -x/y(dx/dt)
Substituting x = sqrt(17^2 - y^2) and dx/dt = 2 ft/s, we get:
dy/dt = -(17^2 - y^2)/y
When y = 8 ft, we get
dy/dt = -(17^2 - 8^2)/8 = -15.39 ft/s
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Compare the variations.
The mean absolute deviation of the number of wins is 1 of 2.
greater/leaser
for the Bears than for the Saints. This means the data values for the, 2 of 2.
saints/bears
are closer to the mean.
Therefore , the solution of the given problem of mean comes out to be one team's data values are closer to the median mean than that of the other.
Define mean.The result from a set, also known as the arithmetic mean, is the sum of all values split by all of the values. It is frequently referred to as "mean" and is thought to be among the most commonly employed primary trend average. To obtain this answer, multiply the total number of numbers in the collection by the total number of values present.
Here,
The closer the data values are to the mean, the less variable they are, and the smaller the MAD.
A higher MAD shows that the data values are more variable and dispersed from the mean.
In this instance, the Bears' MAD of the amount of victories is 1, while the Saints' MAD is unspecified.
We cannot compare the distinctions of the two teams based solely on MAD since the Saints' MAD is not stated.
Since we cannot tell which team has a larger or smaller MAD, we cannot draw the conclusion that one team's data values are closer to the median mean than that of the other.
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A population of a town increases by 7% every year. If its population today is 40,000, what is its population in 3 years?
A = 40,000(1 + 0.07)^3
A = 40,000(1.07)^3
A = 47,676.08
Therefore, the population of the town in 3 years will be approximately 47,676.
a particular employee arrives at work sometime between 8:00 a.m. and 8:50 a.m. based on past experience the company has determined that the employee is equally likely to arrive at any time between 8:00 a.m. and 8:50 a.m. find the probability that the employee will arrive between 8:30 a.m. and 8:35 a.m. round your answer to four decimal places, if necessary.
Theprobability of the employee arriving between 8:30 a.m. and 8:35 a.m. is 0.5 or 1/2.
The probability that the employee will arrive between 8:30 a.m. and 8:35 a.m. has to be determined. The given data is that the particular employee arrives at work sometime between 8:00 a.m. and 8:50 a.m.
Based on past experience the company has determined that the employee is equally likely to arrive at any time between 8:00 a.m. and 8:50 a.m.To find the probability that the employee will arrive between 8:30 a.m. and 8:35 a.m.
Using the above data, the probability that the employee will arrive between 8:00 a.m. and 8:50 a.m. is one. Therefore, the probability that the employee will arrive between 8:00 a.m. and 8:30 a.m. is 0.5, and the probability that the employee will arrive between 8:35 a.m. and 8:50 a.m. is 0.5.
The probability that the employee will arrive between 8:30 a.m. and 8:35 a.m. is also equally likely, so its probability is 0.5.
Therefore, the probability that the employee will arrive between 8:30 a.m. and 8:35 a.m. is 0.5 or 0.5 or 1/2.
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Please help 30 points I've been struggling
Identify the Slope and y - intercept from the graph
Slope (m) =
b =
Write the equation of the line in Slope-Intercept form
Solve for the missing angle measures
(4x-7)°
(3x-15)°
plss help
The measure of the missing angles of the right triangle are 57 degree and 33 degrees.
What are the measures of the missing angles?The sum of the interior angles of a triangle equals 180 degrees.
From the diagram:
Angle A = (4x - 7) degrees
Angle B = (3x - 15) degrees
Angle C = 90 degrees
In a right triangle, the sum of the two acute angles is 90 degrees.
So, we have:
angle A + angle B + 90 = 180 (sum of angles in a triangle)
(4x - 7) + (3x - 15) + 90 = 180
Solve for x
4x - 7 + 3x - 15 + 90 = 180
4x + 3x - 15 - 7 + 90 = 180
7x - 15 - 7 + 90 = 180
7x + 68 = 180
7x = 180 - 68
7x = 112
x = 112/7
x = 16
Therefore, the missing angles will be:
angle A = (4x - 7) = 4(16) - 7 = 57 degrees
angle B = (3x - 15) = 3(16) - 15 = 33 degrees.
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Answer:
The measure of the missing angles of the right triangle are 57 degree and 33 degrees.
Step-by-step explanation:
suppose we do the below hypothesis test for the mean and obtained a p value 0.025 if 95% confidence interval for the true mean of the target population is calculated using the same data, will 10 be inside or outside the confidence interval? explain.
We select H1: μ ≠ 10, we will estimate the true mean of the target population 10 outside of the confidence interval.
p-value = 0.025
Confidence interval = 95% = 0.95
Level of significance (α) = 1 - Confidence interval
Level of significance (α) = 1- 0.95
Level of significance (α) = 0.05
However we are aware that the null hypothesis is rejected if the p-value is less than 0.05.
Due to the fact that our p-value (0.025) is below the α, we may thus reject our null hypothesis with α level of significance.
We choose H1: μ ≠ 10, the true mean of the target population 10 will be estimated outside of the confidence interval using the same data.
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The complete question is:
Suppose we do the below hypothesis test for the mean and obtained a p value 0.025.
H(0): μ = 10 Vs. H1: μ ≠ 10
If 95% confidence interval for the true mean of the target population is calculated using the same data, will 10 be inside or outside the confidence interval? Explain.
Please help! Im a struggling depressed student that needs to desperately catch up.
Answer:
25%
Step-by-step explanation:
30/120 = 1/4
1/4 = 25%
Which picture should be next in the sequence?
The next picture in the sequence of pictures is a picture that has 16 cells
Identifying the next picture in the sequenceA pattern is a recurring design, shape, or arrangement that has a regular or logical repetition.
From the figure, we can see that teh pattern is
Picture = 2^n
Where n is the position
For the next picture, we have
n = 4
This means that
Picture = 2^4
So, we have
Picture = 16
Hence, the next picture would have 16 cells
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The pilot, Sully Sullenberger, made the decision to land on the Hudson river when he was 1650 feet above the ground descending at 2° degrees, which was 30 seconds after the bird strike.
6a) Would he have been able to make it back to LaGuardia Airport? Remember he landed within 8 miles from making the decision to land in the Hudson River. Support your answer by finding the horizontal distance back to LaGuardia Airport.
The Airbus A320 Sullenberger was piloting typically cruises at about 550 miles, or 807 ft per minute. His greatest horizontal range would have been between 4.4 and 6.0 nautical miles.
How are miles used?In certain circumstances, you may trade your miles for items like cash back and gift cards in addition to using them to pay for flights. Most of the time, redeeming airline points is straightforward. By entering into your account while making your reservation with most flights, you may use your points to get a free ticket.
Where do miles come from?You may also determine distance in miles unless you already know your speed and how long it takes to go a particular distance. Just double the time by the speed.
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what is 6pints equal to in cups ?
Answer: 12 cups
Step-by-step explanation:
Answer:
12 cups
Step-by-step explanation:
1 pint = 2 cups
6 pints = 6 × 2 cups = 12 cups
what is the probability that a senior nutrition major and then a sophomore non-nutrition major are chosen at random? express your answer as a fraction or a decimal number rounded to four decimal places.
Answer: 60%
Step-by-step explanation:
As mentioned earlier, we need to know the number of senior nutrition majors and sophomore non-nutrition majors to calculate the exact probability. Without this information, we cannot provide a specific answer to the question.
However, we can provide a general formula for computing the probability, assuming that the selections are made without replacement and the population of students is large enough to assume independence:
Probability of selecting a senior nutrition major and then a sophomore non-nutrition major = (Number of senior nutrition majors / Total number of students) × (Number of sophomore non-nutrition majors / (Total number of students - 1))
Once we have the values for the number of senior nutrition majors and sophomore non-nutrition majors, we can substitute them into this formula to obtain the probability, which will be a decimal number rounded to four decimal places.
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What is the mode of this data set?
The line graph is titled Amount of Rainfall. The Y axis is labeled inches. The X axis is labeled weeks. Week 1 has a dot at 2 inches. Week 2 has a dot at 3 inches. Week 3 has a dot at 1 inch. Week 4 has a dot at 3 inches. Week 5 has a dot at 5 inches. Week 6 has a dot at 4 inches. The dots are connected one to the next by a line to show a change in the amount of rainfall.
2
3
4
There is no mode.
The mode of this data set is 3 inches.
In the given data set, the values of rainfall in inches for each week are as follows:
Week 1: 2 inches
Week 2: 3 inches
Week 3: 1 inch
Week 4: 3 inches
Week 5: 5 inches
Week 6: 4 inches
The mode is the value that appears most frequently, which in this case is 3 inches. Therefore, the mode of this data set is 3 inches.
Note that a data set can have more than one mode if there are two or more values that appear with the same frequency and are more frequent than any other value in the data set.
However, in this data set, there is only one mode, which is 3 inches.
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What is the area of this figure?
Enter your answer in the box.
Answer:
Step-by-step explanation:
wios,wal
pl z help ill give brianliest
Answer:
The correct answer is 21 km.
Step-by-step explanation:
Because
A = (1/2) · (p + q) · h
Where p is 9 and q is 5 (the bases)
and h is the height (3)
Then:
A = (1/2) · (p + q) · h
A = (1/2) · (9 + 5) · 3
A = (1/2) · (14) · 3
A = (1/2) · 42
A= 21
Brainliest Please!
answer: 21
7 times 3 = 21
Kevin bought snacks for his team's practice. He bought a bag of popcorn for $1.60 and a 8-pack of juice bottles. The total cost before tax was $16.80. How much was each bottle of juice?
Answer:
$1.90
Step-by-step explanation:
16.80 - 1.60 = 15.20, since we are finding the price of each bottle of juice.
1) Set up and equation equated to 15.20.
8x = 15.20
x = 15.20/8
x = 1.90
Therefore, each bottle of juice costs $1.90.
pleaseeee help!!!!!!!!!
The phrase that reflects the amount of recordings, in thousands, owned by the collector 4 years later if it continues to expand at this rate is: [tex]O 12 • (1.02)^48[/tex] Thus, option C is correct.
What number of records will increase by a factor?o calculate the number of records that will increase by a factor, you first need to know the initial number of records. Let's call this number "N".
To increase the number of records by a factor of "F", you can simply multiply the initial number of records by the factor:
New number of records = N x F
For example, if you have 100 records and you want to increase the number of records by a factor of 3, the new number of records would be:
New number of records [tex]= 100 x 3 = 300[/tex]
So, the new number of records would be 300.
The growth rate is 2% per month, which means that the number of records will increase by a factor of 1.02 each month. After 4 years (48 months), the number of records owned by the collector can be calculated using the formula:
[tex]12,000 x (1.02)^48[/tex]
Simplifying this expression, we get:
[tex]12,00x0 1.02^48[/tex]
Therefore, the expression that represents the number of records, in thousands, owned by the collector 4 years later if it continues to grow at this rate is: O 12 • (1.02)^48
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Determine how many meters Penelope jogs in three laps
Penelope jogs a distance of 2898 meters in three laps around the rectangular playground.
To solve this problem, we need to first find the perimeter of the rectangle. For a rectangle with a length of L and a width of W, the perimeter P can be found using the following formula:
P = 2L + 2W
In this case, the length of the playground is 320 m and the width is 163 m. So, the perimeter of the playground is:
P = 2(320 m) + 2(163 m)
P = 966 m
This means that if Penelope jogs around the entire playground once, she will run a distance of 966 meters.
Since Penelope jogs three laps around the playground, we need to multiply the perimeter by 3 to find out how far she runs in total. So, the distance that Penelope jogs in three laps is:
Distance = 3 x P
Distance = 3 x 966 m
Distance = 2898 m
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Complete Question:
Every day, Penelope jogs three laps around the playground to keep in shape. The playground is rectangular with a width of 163 m and a length of 320 m.
Determine how many meters Penelope jogs in three laps.
if the odds on a bet are 41:1 against, what is the probability of winning? express your answer as a fraction.
The probability of winning is 1/42 expressed as a fraction.
Given that the odds on a bet are 41:1 against, we are to find the probability of winning.
We know that odds against = (Number of unfavorable outcomes) : (Number of favorable outcomes).
Thus, odds against = 41:1. This implies that the number of unfavorable outcomes is 41 and the number of favorable outcomes is 1.Probability of winning is given by the formula P(winning) = Number of favorable outcomes / Total number of possible outcomes. In this case, the total number of possible outcomes is the sum of the number of favorable and unfavorable outcomes.
Number of favorable outcomes = 1 and Number of unfavorable outcomes = 41
Therefore, the total number of possible outcomes = 1 + 41 = 42
Thus, P(winning) = Number of favorable outcomes / Total number of possible outcomes
P(winning) = 1 / 42
Therefore, the probability of winning is 1/42 expressed as a fraction.
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There are 14 muffins in a basket Tina put some on a plane now there are six in the basket. How many muffins does Tina put on the plate?
Answer:
Step-by-step explanation:
All you have to do is subtract 6 from 14. The answer is 8. If the question is something like this one, always take the remainder and subtract it from how many you had in the beginning to get the answer.
Good luck
Peyton
how many ways can rudy choose 5 pizza toppings from a menu of 20 toppings if each topping can only be chosen once?
Compared to smaller firms, larger companies tend to:Multiple Choicedelay exporting until after their domestic market is fully saturated.systematically scan foreign markets to see where export opportunities lie.be intimidated by the complexities and mechanics of exporting to foreign countries.hesitate to seek export opportunities because they do not know how big the opportunities actually are.be reactive about seeking opportunities for profitable exporting.The main reason most international transactions require full payment before the buyer receives the merchandise is:Multiple Choicestrict government regulations.an underlying lack of trust.an excess of factor endowments.to trigger lower tariffs.the inability to charge interest on the cost of goods.b
Compared to smaller firms, larger companies tend to option (B) systematically scan foreign markets to see where export opportunities lie.
Larger companies tend to systematically scan foreign markets to identify potential export opportunities due to their greater resources, including financial and human capital. This allows them to invest in researching and analyzing foreign markets, and to create effective exporting strategies. Furthermore, larger companies often have established distribution networks and greater brand recognition, which can make exporting a more viable option.
In contrast, smaller firms may lack the necessary resources and expertise to effectively navigate the complexities of exporting to foreign countries, and may therefore be more hesitant to seek out export opportunities.
Therefore, the correct option is (B) systematically scan foreign markets to see where export opportunities lie.
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The given question is incomplete, the complete question is:
Compared to smaller firms, larger companies tend to
Multiple Choice
A) delay exporting until after their domestic market is fully saturated.
B) systematically scan foreign markets to see where export opportunities lie.
C) be intimidated by the complexities and mechanics of exporting to foreign countries.
D) hesitate to seek export opportunities because they do not know how big the opportunities actually are
E) be reactive about seeking opportunities for profitable exporting.
how to do this.............
Answer:
The one selected is correct
Step-by-step explanation:
Make a graph of kinetic energy versus mass for the bikers. Label each biker on your
graph. (4 points)
See Below
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