Answer:
3:8 = 12:32
For easier understanding, we make 3:8 into 3/8 and 12:32 into 12/32
3/8 = 12/32
Cross multiply
3*32 = 8*12
96 = 96
Since the products are equal, the ratios are equivalent.
You can also simplify 12:32
12 / 4 = 3
32 / 4 = 8
Find the height of a triangle whose area is 24cm squared and has a base of 3cm
Answer:
4cm
Step-by-step explanation:
Area of a triangle=[tex]\frac{1}{2}[/tex]×b×h
[tex]\frac{1}{2}[/tex]×3cm×h=[tex]24cm^{2}[/tex]
L.C.M=2
6cmh=[tex]24cm^{2}[/tex]
h=[tex]24cm^{2}[/tex]÷6cm
h=4cm
Answer:
Step-by-step explanation:
area = [tex]\frac{1}{2} base[/tex]×height
24 = [tex]\frac{1}{2}[/tex](3)×height
24 = 1.5×height
[tex]\frac{24}{1.5}[/tex] = [tex]\frac{1,5}{1,5}[/tex]height
16 = height
Last night, the two dinner specials at Adam's favorite restaurant were salmon filet and steak. The restaurant served 35 specials in all, 35 of which were the salmon filet. What percentage of the specials were salmon filets?
Write your answer using a percent sign (%).
Answer:
100%
Step-by-step explanation:
If 35 specials were served and 35 of them were salmon, then salmon was 100% of the special served.
in general, the first step in conducting exploratory research is to group of answer choices assemble a focus group. perform an experience survey. conduct a literature search. perform an analysis of selected cases. narrow a group of hypotheses to one specific hypothesis for investigation.
The first step in conducting exploratory research is to conduct a literature search. (Option 3)
Exploratory research is a type of research design used when the researcher has little or no knowledge about the research problem. The purpose of exploratory research is to gain a better understanding of the problem, identify potential research questions, and develop a hypothesis or research design.
The first step in exploratory research is to conduct a literature search, which involves reviewing existing research and publications related to the research problem. This helps the researcher to identify key concepts and theories related to the problem, as well as to identify any gaps or limitations in the existing research.
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Complete Question:
in general, the first step in conducting exploratory research is to___.
group of answer choices
assemble a focus group. perform an experience survey. conduct a literature search. perform an analysis of selected cases. narrow a group of hypotheses to one specific hypothesis for investigation.What percentage of people would exed to score higher than a 2.5, but lower than 3.5? The mean: X=3.00 The SDis= + 0.500 18% 999 o 50% 03%
Therefore, approximately 68.26% of people are expected to score higher than 2.5 but lower than 3.5.
Based on the information provided, the mean (X) is 3.00 and the standard deviation (SD) is 0.50. To find the percentage of people expected to score higher than 2.5 but lower than 3.5, we will use the standard normal distribution (z-score) table.
First, we need to calculate the z-scores for both 2.5 and 3.5:
z1 =[tex] (2.5 - 3.00) / 0.50 = -1.0[/tex]
z2 = [tex](3.5 - 3.00) / 0.50 = 1.0[/tex]
Now, we can use the standard normal distribution table to find the probability of the z-scores. For z1 = -1.0, the probability is 0.1587 (15.87%). For z2 = 1.0, the probability is 0.8413 (84.13%).
To find the percentage of people expected to score between 2.5 and 3.5, subtract the probability of z1 from the probability of z2:
Percentage = [tex](0.8413 - 0.1587) x 100 = 68.26%[/tex]
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A bag contains 4
blue marbles, 4
green marbles, and 2
yellow marbles. Sydney selects a marble without looking and then puts it back. If she does this 5
times, what is the best prediction possible for the number of times Sydney will pick a yellow marble?
Which relationships describe angles 1 and 2?
Select each correct answer.
adjacent angles
complementary angles
vertical angles
supplementary angles
Answer:
1+2=90° .so complementary angle
the procedure of comparing different instrumental variables estimates of the same parameter is an example of testing . (a) overidentifying restrictions (b) endogeneity (c) heteroskedasticity (d) heteroskedasticity
The procedure of comparing different instrumental variables estimates of the same parameter is an example of testing over identifying restrictions
Testing the over identifying restrictions is the procedure of comparing different instrumental variables estimates of the same parameter. It is a method used to assess the validity of a set of instruments in a two-stage least squares (2SLS) regression model. In this method, the same parameter is estimated in two different ways using different sets of instruments. The difference between these two estimates is then tested to see if they are statistically different. If they are statistically different, then this indicates that the instruments are not valid and need to be revised.
The over identifying restrictions test is typically used in cases where there is a large number of instruments and the researcher wants to be sure that the instruments are appropriate for the regression model.
This test is also useful for assessing homogeneity, which is when the independent variable is correlated with the error term in the regression model. Heteroscedasticity is another potential issue in regression models, where the variance of the error term is not constant across all observations. The over identifying restrictions test can be used to detect this issue as well.
In summary, the procedure of comparing different instrumental variables estimates of the same parameter is an example of testing over identifying restrictions. It is a method used to assess the validity of a set of instruments in a 2SLS regression model, and can also be used to detect issues such as homogeneity and heteroscedasticity.
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Mrs Ndlovu invests 5 200 into a savings account which offers an interest rate of 5,5% per annum compounded annually.How much will Mrs Ndlovu have in her account at the end of 9 years
After a time period of 9 years Mr. Lucas' investment will be 17940 x 10^5
What does investment mean in everyday language?
A purchase made with the intention of earning money or gaining notoriety is referred to as an investment. The acquisition of things that are not used right away but will be utilized to create wealth down the road is known as an investment in an economic perspective. There are numerous investment options available.
Rate in percentage (R) = 5.5%
Principal Amount (P) = 5 200
Total time period (t) = 9 years
Number of times interest is compounded per t (n) = 1
r = R/100
r = 5.5/100
r = 0.055 rate per year,
Then solve the equation for A
A = P(1 + r/n)^(nt)
A = 5200(1 + 0.055/1)⁽¹⁾⁽⁹⁾
A = 5200(1 + 0.055)⁹
A = 5200(1.055)⁹
A = 5200 * 3.45 x 10^5
= 17940 x 10^5
Hence, after a time period of 9 years Mr. Lucas' investment will be 17940 x 10^5
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ming Math th grade > Assessment Language arts Analytics S.11 Solve two-step equations: word problems D2Y Science 18c+ 4 = 42 4c+18 42 Painted Pots lets customers choose and paint their own pottery. The store has teap multiple sizes. Rebecca chose to paint the largest teapot offered, which cost $18. She a painted 4 small teacups to go with her teapot. Rebecca spent a total of $42 on pottery. Which equation can you use to find c, the cost of each teacup? Learn with an example ✓ OF Watch a video > Social studies 4(c + 18) 42 = Recommendations 18(c + 4) = 42
The equation representing the cost of each teacup is given as follows:
4c + 18 = 42.
Hence the cost is of: $6.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the rate of change.b is the y-intercept of the function, which is the initial value.The meaning of the slope and of the intercept for this problem are given as follows:
Slope -> cost per teacup.Intercept: fixed cost.Hence the function is given as follows:
C = xc + 18.
(as the cost of the pot is of $18).
4 teacups push the price up to $42, hence the equation is given as follows:
4c + 18 = 42
4c = 24
c = 6.
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Here are a few pairs of positive numbers whose sum is 50.
a. Find the product of each pair of numbers.
b. Find a pair of numbers that have a sum of 50
and will produce the largest possible product.
First
Number
1
2
10
Second
Number
49
48
40
c. Explain how you determined which pair of numbers have the largest
product.
tor ic
Product
Answer:
a. The product of each pair of numbers is:
1 x 49 = 49
2 x 48 = 96
10 x 40 = 400
b. The pair of numbers that will produce the largest possible product is when the two numbers are equal to half of the sum, which is 25. So the pair of numbers is 25 and 25, and the product is 25 x 25 = 625.
c. We can determine the pair of numbers that have the largest product by using the following reasoning: For any two numbers whose sum is fixed, their product is maximized when the two numbers are as close together as possible. This is because the product of two numbers that are far apart is always smaller than the product of two numbers that are closer together and have the same sum. In this case, the sum is 50, so the two numbers that are closest together and add up to 50 are 25 and 25, which give the largest possible product.
kim rolls a dice and flips a coin calculate the probability that he gets a 2 and a head
The probability of Kim getting a 2 and a head is 1/12.
What is probability?A subfield of mathematics known as probability studies random occurrences and the possibility that they will occur. It is a technique of putting a number on the degree of ambiguity surrounding a situation or result. A number between 0 and 1, where 0 denotes an improbable event and 1 denotes a certain event, is used to express probability. The probability of an occurrence is determined by dividing the number of possible outcomes by the number of ways the event may occur. Several disciplines, including science, engineering, economics, and statistics, employ probability.
For a fair dice, the probability of getting a 2 on the dice is 1/6.
The probability of getting a head on the coin is 1/2.
Thus,
P(getting a 2 and a head) = P(getting a 2) × P(getting a head)
= (1/6) × (1/2)
= 1/12
Hence, the probability of Kim getting a 2 and a head is 1/12.
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If Julie drives from york to Corby via Dorby how many miles will she have driven?
The answer to this question is 289 miles. The sum of 89 + 73 + 127 is 289, so Julie will have driven a total of 289 miles.
What is sum?Sum is the total of two or more numbers added together. It is a mathematical operation used to find the aggregate of two or more numbers or amounts. Sum is calculated by adding the numbers together to get the total.
This is because Julie will be driving a total of 89 miles from York to Derby, then 73 miles from Derby to Corby, for a total of 162 miles. She will then have to drive 127 miles from Derby back to York, giving a total of 289 miles.
Once these distances are determined, the total number of miles is simply the sum of the three distances. The sum of 89 + 73 + 127 is 289, so Julie will have driven a total of 289 miles.
To further illustrate this answer, it can be thought of as a triangle, where each location is a vertex and the lines connecting them are the distances between the locations.
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Find the mean, median, mode, and range of the following list.
35, 16, 28, 4, 62, 15, 48, 22, 16, 28
Mean
Median
Mode
Range
To find the mean, we add up all the numbers in the list and divide by the total number of numbers:Mean = (35 + 16 + 28 + 4 + 62 + 15 + 48 + 22 + 16 + 28) / 10 = 27.4To find the median, we first need to put the numbers in order:4, 15, 16, 16, 22, 28, 28, 35, 48, 62The median is the middle number. In this case, there are 10 numbers, so the middle two are 22 and 28. The median is the average of these two numbers:Median = (22 + 28) / 2 = 25To find the mode, we look for the number that appears most often. In this case, both 16 and 28 appear twice, while all the other numbers appear only once. So the mode is 16 and 28.Mode = 16, 28To find the range, we subtract the smallest number from the largest number:Range = 62 - 4 = 58Therefore, the mean is 27.4, the median is 25, the mode is 16 and 28, and the range is 58.
Answer: the mean is 25.4, the median is 25, the mode is 16 and 28, and the range is 58.
Step-by-step explanation:
To find the mean, we add up all the values and divide by the total number of values:
Mean = (35 + 16 + 28 + 4 + 62 + 15 + 48 + 22 + 16 + 28) / 10
Mean = 254 / 10
Mean = 25.4
So the mean is 25.4.
To find the median, we need to first put the list in numerical order:
4, 15, 16, 16, 22, 28, 28, 35, 48, 62
The median is the middle number in the list, so in this case it is 25, which is between the 5th and 6th numbers in the list.
So the median is 25.
To find the mode, we need to find the number that appears most frequently in the list. In this case, the numbers 16 and 28 each appear twice, which is more than any other number, so both 16 and 28 are modes of the list.
So the mode is 16 and 28.
To find the range, we subtract the smallest value from the largest value:
Range = 62 - 4
Range = 58
So the range is 58.
Therefore, the mean is 25.4, the median is 25, the mode is 16 and 28, and the range is 58.
the measures of two acute angles of a right triangle differ by 22 degrees. find the measure of each angle.
Answer:
In a right triangle, one of the angles measures 90 degrees, and the other two angles are acute angles that add up to 90 degrees. Let's call the measures of the two acute angles x and y.
We know that x and y differ by 22 degrees. So we can set up an equation:
x - y = 22
We also know that x + y = 90, since the two acute angles add up to 90 degrees.
Now we can solve this system of equations for x and y. One way to do this is to add the two equations together, which eliminates y:
x - y + x + y = 22 + 90
2x = 112
x = 56
Now we can substitute x = 56 into one of the equations to find y:
x + y = 90
56 + y = 90
y = 34
Therefore, the measures of the two acute angles of the right triangle are 56 degrees and 34 degrees.
One - third a decreased by 2
Six times a number divided by 3.
Eight more than a number n squared.
Twice the difference of
8 and a number.
9 more than the quotient of
14 and a number n.
The sum of 15 and twice m.
Four more than twice a number y is 72.
One - half a number x is 6 less than the number.
4 times the sum of a number n and 7 is 16.
PLEASE SOMEONE HELP ME PUT THESE IN ALGEBRAIC EXPRESSIONS I WILL LOVE YOU FOREVER
The algebraic expressions for each statement is given below:
The Algebraic StatementsHere are the algebraic expressions for the given statements:
One-third a decreased by 2: (1/3)a - 2
Six times a number divided by 3: (6b)/3 = 2b
Eight more than a number n squared: n^2 + 8
Twice the difference of 8 and a number: 2(8 - c) = 16 - 2c
9 more than the quotient of 14 and a number n: (14/n) + 9
The sum of 15 and twice m: 15 + 2m
Four more than twice a number y is 72: 2y + 4 = 72
One-half a number x is 6 less than the number: (1/2)x = x - 6
4 times the sum of a number n and 7 is 16: 4(n + 7) = 16
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Solve the attached CLT question
Thanks!!
The weight of the cylinder when it is full, in grams, given the volume and radius, can be found to be d. 240, 000, 000πg.
How to find the weight of the cylinder?To find the weight of the cylinder when it's full, we need to first find the volume of the cylinder and then multiply it by the density of the fluid.
The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height.
V = π(400 cm)²(1000 cm)
V = π(160000 cm²)(1000 cm)
V = 160000000π cm³
Then, find the mass of the fluid inside the cylinder:
Mass = Density × Volume
Mass = 1.5 g/cm³ × 160000000π cm³
Mass = 240,000,000π g
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a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 404.0 404.0 gram setting. it is believed that the machine is underfilling the bags. a 41 41 bag sample had a mean of 396.0 396.0 grams. a level of significance of 0.05 0.05 will be used. determine the decision rule. assume the standard deviation is known to be 25.0 25.0 . enter the decision rule.
The decision rule is as follows: If Z < -1.96, reject the null hypothesis. If not, fail to reject the null hypothesis.
The decision rule in statistics is a statement that instructs on the null hypothesis’s rejection or acceptance. It is a predetermined criterion used to test a hypothesis. When the calculated test statistic falls outside the critical region, the null hypothesis is rejected. A chocolate chip producer wants to know if the 404.0 gramme setting on their bag-filling machine is correct.
It is suspected that the machine is underfilling the bags. The chocolate chip manufacturer uses a 41 bag sample with an average weight of 396.0 grams to determine whether the machine works correctly at 404.0 gram setting.
With a significance level of 0.05, the decision rule is as follows:
If Z < -1.96, reject the null hypothesis. If not, fail to reject the null hypothesis.
Z can be calculated as follows:
z = (x - μ) / (σ / √n)
where:
x = sample mean = 396.0
μ = population mean = 404.0
σ = standard deviation = 25.0
n = sample size = 41
Substitute the values in the equation:
z = (396.0 - 404.0) / (25.0 / √41)z = -2.67Z < -1.96
Thus, reject the null hypothesis that the machine is filling bags correctly at 404.0 gram setting.
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This graph shows a proportional relationship.
What is the constant of proportionality?
Enter your answer in the box.
need help ASAP before 12 am, giving 20 points!!
The constant of proportionality is equal to 12.
What is a proportional relationship?In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
y represent the earnings.x represent the time.k is the constant of proportionality.In order to have a proportional relationship and equivalent ratios, the variables representing the earnings and time must have the same constant of proportionality:
Constant of proportionality, k = y/x
Constant of proportionality, k = 36/3 = 60/5 = 72/6 = 84/7
Constant of proportionality, k = 12.
Therefore, the required equation is given by:
y = kx
y = 12x
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quinn is 7 years older than banu. in 3 years the sum of their ages will be 75. how old is quinn now?
Quinn is currently 38 years old.
Let's start by using variables to represent their ages.
Let Q be Quinn's current age and B be Banu's current age.
We know that Quinn is 7 years older than Banu, so we can write:
Q = B + 7
In 3 years, their ages will increase by 3, so we can write:
(Q + 3) + (B + 3) = 75
Now we can substitute Q = B + 7 into the second equation:
(B + 7 + 3) + (B + 3) = 75
Simplifying the left side:
2B + 13 = 75
Subtracting 13 from both sides:
2B = 62
Dividing both sides by 2:
B = 31
So Banu is currently 31 years old. Using Q = B + 7, we can find Quinn's age:
Q = 31 + 7 = 38
Therefore, Quinn is currently 38 years old.
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781 decreased by 30%
Answer:
546.7
Step-by-step explanation:
Sasha is playing a board game and rolls two dice. Let A = {the sum of the dice is odd}, and let B = {the second die shows an odd number}. Are events A and B independent?
Probability is a branch of mathematics that deals with the measurement of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.
What is the probability?The events A and B are not independent.
To see this, note that the probability of A is given by:
[tex]P(A) = 1/2[/tex] , since there are 6 ways to get an odd sum[tex](1+2, 2+1, 3+4[/tex] , [tex]4+3, 5+6, 6+5)[/tex] out of a total of 12 possible outcomes when rolling two dice.
The probability of B is also 1/2, since there are 3 odd numbers on a standard die and 6 possible outcomes for the second die.
Now, to calculate P(A ∩ B), we need to find the probability that both events A and B occur simultaneously.
This happens when we roll an odd sum (which has a 1/2 probability) and then get an odd number on the second die (which has a 1/2 probability). Multiplying these probabilities together, we get:
[tex]P(A ∩ B) = (1/2) * (1/2) = 1/4[/tex]
Finally, we can check whether the events A and B are independent by comparing P(A ∩ B) to P(A)P(B):
[tex]P(A)P(B) = (1/2) * (1/2) = 1/4[/tex]
Therefore, Since [tex]P(A ∩ B) ≠ P(A)P(B)[/tex] , we can conclude that the events A and B are not independent.
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Events A and B are not independent. Let A = {the sum of the dice is odd}, and let B = {the second die shows an odd number}.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
The probability of two events A and B being independent is determined by whether the occurrence of one event affects the occurrence of the other. In the given problem, event A is the sum of two dice being odd, and event B is the second die showing an odd number.
The probability of A and B occurring separately can be calculated, as can the probability of A and B occurring together. While P(A ∩ B) = P(A) * P(B), the events are not independent since knowing that one event has occurred affects the probability of the other event.
If A occurs, the probability of B changes, and if B occurs, the probability of A changes.
No, because P(A∩B) = P({1,3,5})∩P({1,3,5}) = P({1,3,5}) = 1/2, and P(A)P(B) = (1/2) * (1/2) = 1/4, which are not equal.
Therefore, events A and B are not independent.
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Does anyone have the answers to Edmentum's Unit 3 Post Test: Extending to Three Dimensions?
Extending to Three Dimensions depend on the specific questions asked and can be calculated using the formula for the volume of a three-dimensional object.
The answers to Edmentum's Unit 3 Post Test: Extending to Three Dimensions depend on the specific questions asked. Generally, the test covers topics such as the definition of three-dimensional objects, the properties of three-dimensional space, and the relationships between three-dimensional figures. For example, a question might ask how to calculate the volume of a rectangular prism. To answer this, one would need to calculate the area of each of the rectangles that make up the prism and then multiply them together to get the volume. For example, if the length of the prism is 4, the width is 3, and the height is 2, the volume of the prism would be 24 (4 * 3 * 2 = 24).
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what did one dog say to the other dog
Answer: I like "Hot Dogs"?
Step-by-step explanation:
An applicant must score at least 80 points on a particular psychology test to be eligible for the Peace Corps. From nearly 30 years of experience, it is known 0.6% of the applicants meet this requirement. Let the random variable x be the number of applicants who meet this requirement out of a (randomly selected) group of 300 applicants.
a. Find the mean of x.
b. Find the standard deviation of x.
c. What is the probability that 3 or more applicants meet the requirement?
d. Using the Empirical Rule, within what limits would you expect most (say, 95%) of the measurements to be?
In other words, we can expect that 95% of the time, the number of applicants who meet the 80-point requirement for the Peace Corps in a randomly selected group of 300 will fall within a range of 67 and 93.
Based on the information provided, it is likely that 0.6% of applicants will meet the 80-point requirement for the Peace Corps. Using the Empirical Rule, we can estimate that 95% of measurements will fall within two standard deviations of the mean. For the random variable x, which is the number of applicants out of 300 who meet the 80-point requirement, this would be approximately[tex]80 +/- 2(6.47),[/tex] or between 67.06 and 92.94.
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If ΔDEF is similar to ΔPRY, what is the measure of PY?
A 12 centimeters
B 21 centimeters
C 24 centimeters
D 48 centimeters
the volume of the right cone below is 392\piπ units^3 3 . Find the value of xx.
The value of x is approximately 8.15.
To find the value of x, we need to use the formula for the volume of a cone, which is V = (1/3)πr^2h, where r is the
radius of the base and h is the height of the cone. We know that the volume of the cone below is 392π, so we can set
up the equation:
[tex]392π = (1/3)πx^2h[/tex]
Simplifying, we can divide both sides by π and multiply by 3 to get:
[tex]1176 = x^2h[/tex]
Using the Pythagorean theorem, we can relate the height, radius, and slant height of the cone:
[tex]h^2 + r^2 = x^2[/tex]
Since the cone is a right cone, we know that the radius is half of the diameter, which is equal to x/2. Substituting this in,
we get:
[tex]h^2 + (x/2)^2 = x^2[/tex]
Simplifying:
[tex]h^2 = x^2 - (x/2)^2
h^2 = 3x^2/4[/tex]
Now we can substitute this expression for [tex]h^2[/tex] into our equation for the volume:
[tex]1176 = x^2(3x^2/4)[/tex]
Simplifying again:
[tex]1176 = 3x^4/4[/tex]
[tex]1568 = 3x^4[/tex]
[tex]x^4 = 1568/3[/tex]
Taking the fourth root of both sides:
[tex]x = (1568/3)^(1/4)[/tex]
x ≈ 8.15
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Answer: 14
Step-by-step explanation:
a rectangular prism has a length of 6 cm, a width of 3 cm, and a height of 412cm. the prism is filled with cubes that have edge lengths of 12 cm. how many cubes are needed to fill the rectangular prism?
The dimensions of a rectangular prism are 6 cm long, 3 cm wide, and 4 ½ cm tall. 648 cubes are required to completely fill the rectangular prism.
The formula for calculating the rectangular prism's volume is:
Volume = Length x Width x Height
Substituting the given values, we get:
Volume = 6 cm x 3 cm x 4 ½ cm
Volume = 81 cm³
Since the cubes have an edge length of ½ cm, their volume is:
Volume of one cube = (1/2 cm)³ = 1/8 cm³
To find the number of cubes needed to fill the rectangular prism, we can divide the volume of the prism by the volume of one cube:
Number of cubes = Volume of prism / Volume of one cube
Substituting the values, we get:
Number of cubes = 81 cm³ / (1/8 cm³)
Number of cubes = 81 cm³ x 8
Number of cubes = 648
Therefore, 648 cubes are needed to fill the rectangular prism.
The complete Question is:-
A rectangular prism has a length of 6 cm, a width of 3 cm, and a height of 4 1/2cm. the prism is filled with cubes that have edge lengths of ½ cm. how many cubes are needed to fill the rectangular prism?
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the product of two consecutive positive integers is 3 less than three times their sum find the integers
The two consecutive positive integers are 5 and 6.
Let the two consecutive positive integers be x and x + 1. We are given that the product of these integers is 3 less than three times their sum. This can be expressed as:
[tex]x(x + 1) = 3(x + x + 1) - 3[/tex]
Now we can solve for x:
[tex]x^2 + x = 6x + 3 - 3[/tex]
[tex]x^2 + x = 6x[/tex]
[tex]x^2 - 5x = 0[/tex]
Factoring the left side of the equation, we get:
[tex]x(x - 5) = 0[/tex]
From this equation, x can be 0 or 5.
However, since the question asks for positive integers, we can't use x = 0. Therefore, x = 5.
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3. a committee of 4 is to be selected from a group of 12 people. how many possible committees can be selected?
According to combinations formula there are 495 possible committees that can be selected from a group of 12 people.
To calculate this, you can use the formula for combinations
nCr = n!/(r!(n-r)!)
where n is the total number of people (12) and r is the number of people on the committee.
Therefore, the possible number of committees that can be selected is;
= {12!}/{4!8!}
= 12*11*10*9/4*3*2*1
= 11880/24
= 495
Therefore, 495 possible committees can be selected from a group of 12 people if a committee of 4 is to be selected.
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__are the most common location for a collision between a bike and a car.
A: driveways
B: left turns
C: right turns
D: parking lots