it would take 6 men 20 minutes to dig a hole that is 4 x 4 x 3 meters
To solve this problem, we can use the formula that relates the time taken to do a job to the number of workers available, assuming that all workers have the same productivity. This formula is given by the equation:Work Done = Productivity x Time Taken x Number of Workers available. If we let the work done be W, the productivity be P, and the time taken be T, then the equation becomes:W = P x T x N. We are given that 3 men can dig a hole that is 3 x 2 x 4 meters in 20 minutes. We can find the volume of this hole by multiplying its dimensions:V = 3 x 2 x 4 = 24 cubic metersThis means that 3 men can dig a volume of 24 cubic meters in 20 minutes.
To find their productivity, we can use the formula: Productivity = Work Done / (Time Taken x Number of Workers)P = W / (T x N) = 24 / (20 x 3) = 0.4 cubic meters per minute per worker. Now we can use this productivity to find the time taken for 6 men to dig a hole that is 4 x 4 x 3 meters. We can find the volume of this hole by multiplying its dimensions:V = 4 x 4 x 3 = 48 cubic meters.
To dig this hole, the amount of work done would be 48 cubic meters. The productivity per worker is still 0.4 cubic meters per minute, but the number of workers is now 6. Therefore, the time taken would be:T = W / (P x N) = 48 / (0.4 x 6) = 20 minutes.Therefore, it would take 6 men 20 minutes to dig a hole that is 4 x 4 x 3 meters, given that 3 men can dig a hole that is 3 x 2 x 4 meters in 20 minutes.
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A math class is set up to have assignments worth 45%, quizzes worth 40% and the final exam is worth the rest of the grade. If Serena has 78% on assignments and 65% on quizzes and 96% on the final, what is her overall grade to 2 decimal places?
Serena's overall grade in the course is 75.5%. It's important to note that in a weighted grading system like this, the final exam is often a major determinant of the final grade.
To calculate Serena's overall grade, we need to first determine the weight of the final exam. We know that the assignments are worth 45% and the quizzes are worth 40%, which leaves 100% - 45% - 40% = 15% for the final exam.
Next, we can calculate Serena's grade for each component of the course. Her grade for assignments is 78% and her grade for quizzes is 65%. We can calculate her grade for the final exam by multiplying her score of 96% by the weight of the final, which is 15%:
Final grade = (0.45 * 78%) + (0.4 * 65%) + (0.15 * 96%)
Final grade = 35.1% + 26% + 14.4%
Final grade = 75.5%
Therefore, Serena's overall grade in the course is 75.5%. It's important to note that in a weighted grading system like this, the final exam is often a major determinant of the final grade. In this case, Serena's strong performance on the final exam helped to boost her overall grade, even though her scores on the assignments and quizzes were not as high. It's also worth noting that this calculation assumes that all assignments, quizzes, and the final exam were weighted equally within their respective categories (i.e., each assignment was worth the same percentage of the assignment grade).
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a searchlight is shaped like a paraboloid of revolution. if the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across, how deep should the searchlight be?
A searchlight is shaped like a paraboloid of revolution. if the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across, 2.5 feet deep should the searchlight be.
As per the given information,
A searchlight is shaped like a paraboloid of revolution. If the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across.
Here we have to Find: How deep should the searchlight be.
First of all, we need to find the equation of the paraboloid of revolution.
Let's assume that the axis of the paraboloid is along the y-axis and the vertex is at the origin (0, 0, 0).
So, the equation of the paraboloid is given by:
y² = 4ax
Where, a = 2 feet (distance of light source from vertex)
So, the equation of the paraboloid is:
y² = 8x ..... (1)
The opening of the paraboloid is given to be 5 feet across.
We know that the diameter of a circle is equal to twice the radius. Hence, the radius of the opening is 2.5 feet.
The vertex is the point (0, 0, 0). We need to find the depth of the searchlight. The depth is nothing but the perpendicular distance from the vertex to the plane of the opening. The plane of the opening is given by the equation x = -2.5 (since the opening is along the yz-plane)
The equation of the plane is given by x = -2.5
Now, we need to find the coordinates of the point where the paraboloid intersects the plane of the opening.
We can substitute x = -2.5 in equation (1) to get:
y² = -20
Squaring both sides, we get:
y = ±√(-20)
Since y can only be positive (since we are considering the upper half of the paraboloid),
y = √(-20) = i√20 = 2√5 i
So, the point where the paraboloid intersects the plane of the opening is (-2.5, 2√5 i, 0)
The depth is nothing but the perpendicular distance from the vertex (0, 0, 0) to the point (-2.5, 2√5 i, 0). Hence, the depth is given by:√((-2.5 - 0)² + (2√5 i - 0)² + (0 - 0)²)= √(6.25 + 20 - 0) = √26.25 = 2.5 feet
Hence, the depth of the searchlight should be 2.5 feet.
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Can someone please help me? 100 points.
"Finally, Alicia wants to show the dog and a puppy. Write a transformation rule that shows dilating the dog to one - half it's size and moving it to the location of the smaller puppy on the graph."
The transformation rule to show dilating the dog to one-half its size and moving it to the location of the smaller puppy on the graph is:
1. Dilate the dog by a scale factor of 1/2 with respect to the center of dilation.
2. Translate the dilated dog by a vector that moves it to the location of the smaller puppy on the graph.
The mathematical expression of this rule is:
(x', y') = 1/2(x - h, y - k) + (a, b)
There's a roughly linear relationship between the number of times a species of cricket
will chirp in one minute and the temperature outside. For a certain type of cricket,
this relationship can be expressed using the formula T = 37+0.28c, where T
represents the temperature in degrees Fahrenheit and c represents the number of
times the cricket chirps in one minute. What could the number 37 represent in the
equation?
4
How long the cricket continues to chirp.
The expected temperature in degrees Fahrenheit if the cricket has chirped 37
times per minute.
The expected temperature in degrees Fahrenheit if the cricket has chirped o
times per minute.
The change in cricket chirps per minute for each additional degree Fahrenheit. no
The correct response is: The anticipated temperature in Fahrenheit if the cricket has not yet chirped once every minute.
what is linear equation ?Each term in the algebraic equation is either a constant or the result of a constant and one variable. Y = mx + b, where x is the independent variable, m is the slope, and b is the y-intercept, is the general form of a linear equation. Several real-world phenomena, like as the link between speed and time in a moving object and the relationship between price and quantity in economics, are modeled using linear equations.
given
The correct response is: The anticipated temperature in Fahrenheit if the cricket has not yet chirped once every minute.
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Perform the indicated operation and reduce to lowest term.−16/5 ⋅ (−15/56)
By reducing −16/5 ⋅ (−15/56) in lowest term, the answer is 6/7.
To perform the indicated operation and reduce the result to lowest terms, we need to multiply the two fractions:
(-16/5) x (-15/56) = (16 x 15) / (5 x 56)
(when we multiply two negative numbers, the result is positive)
= 240 / 280
Now we can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 40:
240 / 280 = (240 ÷ 40) / (280 ÷ 40) = 6/7
Therefore, -16/5 ⋅ (-15/56) = 6/7 in lowest terms.
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Find the measure of the missing angle.
Answer:
43 degrees.
Step-by-step explanation:
Since we have a box on the angle, we know that the sum of these angles is 90 degrees. These are complementary angles.
Here is a equation
x + 47 = 90
subtract 47
x = 43.
the task of framing a building has been estimated to take an average of 25 days with a standard deviation of five days. what is the probability that the duration will be done within 22 days?
The probability that the duration for complete the task of framing a building will be done within 22 days is equals to the 0.32.
The normal distribution shapes like mount, therefore, it is also known as the mounted-shaped distribution. There is only one peak of the mount, that lies at the center because the distribution belongs to the family of symmetric distributions. We have a task of framing a building has been estimated.
Average or mean, μ = 25 days
standard deviations, σ = 5 days
we have to determine the probability that the duration will be done within 22 days, P( X= 20). Assuming a normal distribution, first we determine the Z-statistic or Z-Score value. Formula for Z-score is written as, Z = ( X− μ)/σ
here, X = 20, so plug all known values
=> Z = ( 20 - 25)/5
=> Z = -5/5 = - 1
The P value is defined as the probability under the assuming that no effect or no difference (null hypothesis). Using the normal distribution table, for Z = -1 , the p value, P( Z = - 1) = P( X= 20) = 0.317311.
Hence, required probability is 0.32.
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A penny is 19 mm wide. What is the area of the front side of the penny? Use 3.14 for π. Round to the nearest hundredth if necessary.
HELP ME QUICK PLEASE!
Answer:
≈283,39 mm^2
Step-by-step explanation:
The diameter is 19 mm, so the radius is half diameter (9,5 mm)
[tex]a = \pi \times {r}^{2} = 3.14 \times {9.5}^{2} = 3.14 \times 90.25 ≈ 283.39[/tex]
you have an srs of 23 observations from a large population. the distribution of sample values is roughly symmetric with no outliers. what critical value would you use to obtain a 98% confidence interval for the mean of the population?
The Critical value to be used to gain the 98 confidence interval for the population mean is2.508 and can be determined using the t- distribution table.
critical value is the value of a test statistic that defines the upper and lower bounds of the confidence interval or determines the position of statistical significance in a statistical test.
Given
You have an SRS of 23 compliances from a large population.The distribution of the sample values is roughly symmetric, with no outliers.98% confidence interval.The following way can be carried out to determine the critical value
Step 1-First determine the degrees of freedom using the following formula
degrees of freedom = n- 1
where n is the sample size.
Step 2- Replace" n" in the below formula.
degrees of freedom = 23- 1
= 22
Step 3- Now you can use the t- distribution table to determine the critical value to get a 98 confidence interval.
critical value = 2.508
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.
You buy 4 small candles and 1 large candle for $18. Your friend buys 5 small candles
and 2 large candles for $27. What is the cost of each small candle? of each large candle?
Answer: The cost of each small candle is $3 and the cost of each large candle is $6.
Step-by-step explanation:
Let's use variables to represent the cost of each small candle and each large candle. Let's call the cost of each small candle "x" and the cost of each large candle "y".
We can set up two equations based on the information given:
4x + 1y = 18 (equation 1)
5x + 2y = 27 (equation 2)
We can solve for one variable in terms of the other by using one equation to eliminate one variable. Let's solve for "y" in terms of "x" by multiplying equation 1 by 2 and subtracting it from equation 2:
5x + 2y = 27
(8x + 2y = 36)
-3x = -9
Dividing both sides by -3, we get:
x = 3
Now that we know the cost of each small candle is $3, we can substitute that value into one of the equations to solve for the cost of each large candle. Let's use equation 1:
4x + 1y = 18
4(3) + 1y = 18
12 + y = 18
y = 6
Therefore, the cost of each small candle is $3 and the cost of each large candle is $6.
Mark earned a 64 on his lasT science quiz
If Mark's z-score was -2.8 and the standard deviation was 10, find the mean grade on the quiz.
Step-by-step explanation:
find the inverse of the following functions. the domain and range of the iverse a) f(x) = x
If shirts cost $16 each, and sales tax is 4.75%, what would be the total bill if you buy three shirts?
Answer:
$45.72
Step-by-step explanation:
16×3=48
48×0.0475(4.75%)=2.28. <----- tax
2.28+48=45.72
Brooke has scores of 84, 72, 90, 95, and 87 on her first five quizzes. After taking the sixth quiz, Brooke’s mean score increased.
Which could be Brooke’s sixth quiz score? Select three options.
85
90
83
86
92
Answer:
90, 86, and 92 are three options
Step-by-step explanation:
in the number 240.149, how does the value of the 4 in the hundredths place compare to the value of the 4 in the tens place?
The 4 in the hundredths place has a smaller value than the 4 in the tens place.
In the decimal number system, each digit to the left of the decimal point represents a power of 10, starting with 10^0 = 1 for the rightmost digit. Each digit to the right of the decimal point represents a negative power of 10, with the place value decreasing as you move farther to the right.
In the number 240.149, the 4 in the tens place represents 4 x 10 = 40. The 4 in the hundredth place represents 4/100 or 0.04, which is smaller than 40. Therefore, the 4 in the tens place has a greater value than the 4 in the hundredths place.
Hence, the value of a digit in a decimal number depends on its position relative to the decimal point. Digits to the left of the decimal point represent whole numbers, while digits to the right of the decimal point represent fractions or parts of a whole.
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a normal distribution has a mean of 61 and a standard deviation of 14. what is the median? (enter an exact number as an integer, fraction, or decimal.)
The median of a normal distribution with a mean of $\mu$ and standard deviation of $\sigma$ is simply equal to the mean $\mu$. Therefore, for a normal distribution with a mean of 61 and a standard deviation of 14, the median is also 61.
This is because the normal distribution is a symmetric distribution, with the mean, median, and mode all located at the same point on the horizontal axis. The mean represents the center of the distribution and is also the balance point for the distribution, so half of the observations will be less than the mean and half will be greater than the mean.
Therefore, for a normal distribution with a given mean and standard deviation, we can use the mean as an estimate of the median. In this case, the mean is exactly equal to the median, so the median is 61.
It is worth noting that this property of normal distributions only holds for normal distributions, and not necessarily for other types of distributions. For example, in a skewed distribution, the mean and median may be quite different from each other.
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Luis models a can of ground coffee as a right cylinder. He measures its height as 51/1
3
in and its radius as in. Find the volume of the can in cubic inches. Round your
4
answer to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
Answer: I can’t find it please help
Step-by-step explanation:
A human organism developing in the uterus from the ninth week until birth is called a (n) ____________.`
A human organism developing in the uterus from the ninth week until birth is called a(n) fetus.
A fetus is the term used to describe a human organism that is developing in the uterus from the ninth week of gestation until birth. During this time, the fetus undergoes significant growth and development, as all of the major organs and body systems are formed and begin to function.
The ninth week of gestation is considered a significant milestone in fetal development, as most of the critical stages of organogenesis have been completed by this time. From this point onward, the fetus primarily grows and matures in preparation for life outside of the womb.
During the remaining weeks of gestation, the fetus undergoes a number of important developmental processes, including continued brain development, growth of the nervous system, and development of the lungs and other vital organs. At the same time, the fetus also gains weight and size, and begins to develop a layer of fat that will help to regulate body temperature after birth.
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3. Some of the neighbors played a penny game. Players tossed a penny in a hole and earned that number of points. Each player tossed 3 pennies. The scores from each penny that went in a hole were added for a final score. Was it possible to get a score of 9? If so, how could it have happened?
It is not possible to get a score of 9 because 9 is an odd number.
What are numbers?
Numbers are mathematical symbols used to represent values or quantities. They are classified into different types based on their properties and can be used in different areas for counting, measuring, and solving problems.
What is meant by odd numbers?
Odd numbers are integers that are not evenly divisible by 2. They are characterized by having a remainder of 1 when divided by 2. They are expressed as 2n+1, where n is an integer. Examples are 1, 3, 5, 7, 9, etc.
Possibilities:
1.All three pennies score 1: total score is 3.
2.Two pennies score 1 and one penny scores 0: total score is 2.
3.Two pennies score 0 and one penny scores 1: total score is 1.
4.All three pennies score 0: total score is 0.
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Tom makes $273.60 in 6 days. How much does he make in 4 days?
Answer:
Step-by-step explanation:
$105.20
in the packet of mixed candies there are 2 fruit centers for every 3 caramel centers. there are 30 candies in the packet
Answer: there are 12 fruit centers and 15 caramel centers
Step-by-step explanation:
please answer!! A rectangle is 1/3 yards long and 2/3 yards wide.
What is the area of the rectangle?
Enter your answer as a fraction in simplest form by filling in the boxes
Answer:
2/9yd²
Step-by-step explanation:
We know that area is calculated by length × width, so we will do the same here. To get the area, we must multiply 1/3 by 2/3.
1/3 × 2/3 is 2/9. So, the area of the rectangle is 2/9yd². :D
.. Sasha Abbott earns $62,550.00 in taxable income each year. The tax rate is 3.6%, and she takes zero deductions. How much tax does her employer withhold each year? A $2,380.50 B $2,251.80 C $2,500.40 D $1,823.20
Answer: B $2,251.80
Step-by-step explanation:
:)
graph
y = -6
4x + y = 2
There are 8 red cards, 6 blue cards, 7 purple cards, and 4 green cards in a hat.
Part A. What is the theoretical probability of drawing a red card from the hat?
Part B. In a trial, a card is drawn from the hat and then replaced 1,150 times. A red card is drawn 437 times. How much greater is the experimental probability than the theoretical probability?
Oh, wait- I figured it out hehe
Part A: The theoretical probability of drawing a red card is 0.32 or 32%.
Part B: The experimental probability of drawing a red card is 0.38 or 38%, and it is 6% greater than the theoretical probability.
Part A: The theoretical probability of drawing a red card from the hat is the number of red cards divided by the total number of cards in the hat:
[tex]P_{red}[/tex] = 8 ÷ (8 + 6 + 7 + 4)
= 8 ÷ 25
= 0.32 or 32%.
Part B: The experimental probability of drawing a red card can be calculated by dividing the number of times a red card was drawn by the total number of trials:
[tex]P_{red}[/tex] = 437 ÷ 1150
= 0.38 or 38%.
The difference between the experimental probability and the theoretical probability can be calculated as follows:
0.38 - 0.32
= 0.06 or 6%
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if a study group draws 20 random samples of 15 from a population that has normal distribution, can the study group claim a normal distribution of the sample means?
Yes, the study group can claim a normal distribution of the sample means.
This is because when a group takes random samples from a population that has a normal distribution, the means of those samples will also follow a normal distribution. The reason for this is due to the Central Limit Theorem, which states that when a large enough number of samples are taken from a population, the distribution of the sample means will become more and more normal.
Since the study group is taking 20 random samples of 15 from a population with a normal distribution, it can be assumed that the means of the sample will have a normal distribution. Therefore, when the study group draws 20 random samples of 15 from a population that has a normal distribution, they can be certain that the sample means will also follow a normal distribution.
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A customer bought the following items from Herman’s Market.
1 1/3
pounds of American cheese at $6.99/pound
2 1/4
pounds of turkey at $5.99/pound
2/3
pound of cheddar cheese at $3.99/pound
How much did the customer pay for all the items?
A: $16.97
B: $22.96
C: $25.46
D: $26.96
Answer:
1 1/3 pounds of American cheese is equivalent to 4/3 pounds of American cheese.
2 1/4 pounds of turkey is equivalent to 9/4 pounds of turkey.
2/3 pound of cheddar cheese is equivalent to 0.67 pounds of cheddar cheese.
So the cost of each item is:
American cheese: (4/3) x $6.99 = $9.32 (rounded to the nearest cent)
Turkey: (9/4) x $5.99 = $13.48 (rounded to the nearest cent)
Cheddar cheese: 0.67 x $3.99 = $2.67 (rounded to the nearest cent)
To find the total cost, we add up these amounts:
$9.32 + $13.48 + $2.67 = $25.47
Therefore, the customer paid $25.47 for all the items.
The distance from Elena's chin to the top of her head is 150
mm in an image. For a U.S. passport photo, this
measurement needs to be between 25 mm and 35 mm.
The height of the image after being scaled down by 80% three times is 76.8mm, which is not within the required range for a U.S. passport photo.
What is scaling?Scaling is the process of increasing or decreasing the size of a picture by dividing or multiplying its dimensions. An picture is expanded when it is scaled up, and its size is decreased when it is scaled down. An picture is affected by scaling when its size and, consequently, appearance, are altered. An picture may become pixelated or fuzzy if it is scaled up or down excessively, and information may be lost if it is scaled down too much. The aspect ratio of an image—the proportion of its width to its height—can also be impacted by scaling. The picture could look stretched or squished if the aspect ratio is modified.
Given that the image is 150 mm in height.
Thus, 80% of the image is:
150mm x 0.8 = 120mm
The scaling is performed 3 times, thus:
120mm x 0.8 = 96mm
96mm x 0.8 = 76.8mm
Hence, the height of the image after being scaled down by 80% three times is 76.8mm, which is within the required range for a U.S. passport photo.
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The complete question is:
2,10,50,... find the sum of the first 6 terms. r=
a¹ (1,-rn)
(1-r)
A.8,215
B.14,610
C.7,812
D.6,694
there are 23 marbles, each a different color, in a bag. one of them is black. what is the probability of selecting a black marble?
Probability of selecting a black marble is 1/23.
There are a total of 23 marbles in a bag, each with a different color. Among these marbles, there is only one black marble. If one wants to find the probability of selecting a black marble from this bag, they would have to divide the number of black marbles by the total number of marbles.
The formula for probability is as follows:P (A) = number of favorable outcomes/number of possible outcomes. In this case, the probability of selecting a black marble is: 1/23.The denominator is 23 because there are 23 marbles in the bag, and the numerator is 1 because there is only one black marble among these marbles.
Thus, the probability of selecting a black marble from this bag is 1/23.
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the length of a highway is 900. If 0.5 inch on a map represents 50 miles, what is the length of the highway on map?
Answer:
Step-by-step explanation:
We simply have to divide 900 by 50 to get us 18. Now multiply 18 by 0.5 to get an answer of 9 inches. Hope this helped!