The volume of the pyramid is one-third of the product of its height and the area of its base. That is volume of the pyramid is linearly proportional to its height and the area of its base.
A pyramid is a solid with a base and rectangle face on the edge of base meeting at a vertex. Generally we consider a right pyramid.
Consider a pyramid of base area A and height h, the volume of the pyramid is one-third of the product of its height and the area of its base, that is the volume formula of pyramid is
V = A × h/ 3
That is
V ∝ A and
V ∝ h
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there are six balls in a box if we select three balls what is the probability of having one white ball
The probability of having one white ball is 1/20 or approximately 0.05.
To find the probability of selecting one white ball out of three balls, you need to know the number of white balls in the box and the total number of balls in the box. You also need to know whether the balls are being selected randomly or not.
Assuming that there is only one white ball in the box and the rest are some other color, and that the balls are being selected randomly.
The probability of selecting one white ball out of three would be:
Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)
Since there is only one white ball, there is only one way to select one white ball out of three. The total number of ways to select three balls out of six is 6 choose 3, which is equal to 20.
Therefore, the probability of selecting one white ball out of three would be
Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)
Probability = 1/20
Probability = approximately 0.05.
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If f(x) is a third degree polynomial function and g(x) = f(−2x), which of the following is NOT true?
F f(x) and g(x) have the same x-intercepts.
G f(x) and g(x) have the same y-intercept.
H f(2) = g(−1)
J f(x) and g(x) have the same
number of zeros.
Answer:
F
Step-by-step explanation:
F. False. The graph of [tex]g[/tex] involved performing a horizontal compression on the graph of [tex]f[/tex].
G. True. Setting [tex]x=0[/tex] yields [tex]g(0)=f(0)[/tex].
H. True. Set [tex]x=-1[/tex].
J. True. The horizontal compression does not change the number of their roots, just the location.
the school of business has 3 fax machines. the toner in each machine needs to be changed after about 5 hours of use. there is one unit secretary who is responsible for the fax machine maintenance. it takes him 15 minutes to replace the toner cartridge. what is the average time spent in the system? a. 0.2749 hrs b. 0.0142 hrs c. 0.1563 hrs d. 0.0249 hrs e. none of the above
The average time spent in the system which consists three fax machines is 0.026470 hour. So, option (e) none of the above is right here.
What is Queuing System?The M/M/1 queuing system is a single-server, infinite-capacity system in which the arrival interval is exponentially distributed with the parameter lambda and the service time is also exponentially distributed with the parameter. If the number of servers is maximum and all are equal, this model is considered an M/M/C queue.
We have, total number of fax machine in a business school is equals to three.
The toner of each machine needs to be changed in 5 hours of use . Time taken by secretary to replace toner cartridge = 15 minutes
We have to calculate average time spent in the system. fax machines , k = 3
Service person , R = 1
Arrival rate, λ = 3/5per hour = 0.6/hour
Service rate, μ =( 60/15) per hour
= 4/hour
Now, using the equation of finite population model M/M/1, the average time spent to maintain the fax machines in system is ,
L = λ² /μ (μ - λ )
plugging the value of μ and λ in above formula we get, L = (0.6)²/4(4-0.6)
= 0.36/13.6 = 0.026470
So, required answer is 0.026470 hour .
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The speed of a runner increased steadily during the first three seconds of a race. her speed at half-second intervals is given in the table. find lower and upper estimates for the distance that she traveled during these three seconds.
t(s) 0 0.5 1.0 1.5 2.0 2.5 3.0
V (ft/s) 0 6.2 10.8 14.9 18.1 19.4 20.2
She can only move a certain distance in three seconds, with a lower distance of 33.45 feet and a upper distance of 43.45 feet.
The first three seconds of a race saw a runner's speed rapidly grow.
The time is therefore 3 seconds.
The table provides her speed at half-second intervals.
We are aware,
Speed = Distance / Time
Similarly
Distance = Speed × Time
t equals 0.5 seconds
Then, the lower distance traveled overall is equal to 0.5(0 + 6.7 + 9.2 + 14.1 + 17.5 + 19.4).
Terms are multiplied and added.
= 0.5 × 66.9
= 33.45 feet
The upper distance traveled is equal to 0.5 (6.7 + 9.2 + 14.1 + 17.5 + 19.4 + 20)
= 0.5 × 86.9
= 43.45 feet
As a result, Her lower distance in three seconds is therefore 33.45 feet, and her upper distance in three seconds is 43.45 feet.
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prove the identity
sin2theta = 2 tan theta over 1 + tan squared theta
help!
Step-by-step explanation:
kya tablet side apply the side of the wall has 22 M and 20 m
p varies directly with T and p = 400. When T = 500. Find the value of p when T = 600
Answer:
Step-by-step explanation:
When the temperature T is 500, the pressure p is 400. If we let "k" represent the constant of proportionality that relates p and T, then we can write the relationship between p and T as:
p = k * T
Substituting the known values of p and T into this equation, we get:
400 = k * 500
Solving for the constant of proportionality k, we find that:
k = 400/500 = 0.8
Now that we know the value of the constant of proportionality k, we can use it to find the value of p when T = 600. Substituting this value of T into the equation above and solving for p, we get:
p = 0.8 * 600 = 480
Therefore, when T = 600, the pressure p is 480.
The ratio of reeta and neha income is 8:6. If reeta income is 2800. Find the income of neha
Answer: I don't believe the explanation above provides the correct answer. You would need to use the concept of proportions to solve this problem. The Answer I got is 2100.
Step-by-step explanation:
It is very simple all you have to do is setup a proportion with Reena's on top and Neha's on the bottom.
8/6 = 2800/x
Now cross multiply,
2800 * 6 = 8x
x=16800/8
x=2100
Now we can double-check by dividing the original ratio with the ratio we found.
8/6 = 1.3333333...
2800/2100 = 1.333333...
Thus, the answer is correct.
Please help me with this question
many thanks
The surface area of the cuboid is 148 cm².
What is surface area of a cuboid?The surface area of a cuboid is the total space occupied by it. A cuboid is a six-faced three-dimensional shape in which each face is in the shape of a rectangle.
Given that, a cuboid has volume of 120 cm³ and the area of the base of the cuboid is 30 cm².
We know that, the volume of cuboid is l×b×h.
Here, l×b=30
Now, 30×h=120
h=4 cm
We know that, surface area of the cuboid is 2(lb+bh+hl)
= 2(30+h(b+l))
= 2(30+4(b+l))
We have, l×b=30
Pair of factors of 30 are
2×15=30
3×10=30
5×6=30
So, the possible surface area is
2(30+4(2+17))
= 2×106
= 212 cm²
2(30+4(3+10))
= 2×82
= 164 cm²
2(30+4(5+6))
= 2×74
= 148 cm²
Therefore, the surface area of the cuboid is 148 cm².
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A student randomly guesses on 10 true or false questions. Use the binomial model to find the probability that the student gets 7 out of the 10 questions right.
As per the binomial distribution, the probability that the student gets 7 out of the 10 questions right is 0.1171875
The term binomial distribution refers a probability distribution used in statistics that summarizes the likelihood that a value will take one of two independent values under a given set of parameters or assumptions.
Here we have given that the student randomly guesses on 10 true or false questions
And we have to use the binomial model to find the probability that the student gets 7 out of the 10 questions right.
While we looking into the given question, the thing we have identified are listed as follows:
Number of questions = 10
Number of right answer = 7
The probability of getting right answer = 1/2
The probability of getting wrong answer = 1/2
Now, as per the binomial distribution formula it can be written as,
=> P(r) = [10!/7!(10-7)!] x [1/2]⁷ x [1/2]¹⁰⁻⁷
When we simplify this one, then we get,
=> P(r) = 0.1171875
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if ABC = PQR, then AC =
Answer:
PR
Step-by-step explanation:
Because both triangles are equal to each other, so their sides will equal each other too!
A mountain in jackson county is eroding and losing elevation at a rate of 5% every millennium. If the current elevation is 1,300 meters, how tall will the mountain be in 8 millennia?.
So the mountain will be approximately 798.02 meters tall after 8 millennia.
The mountain loses 5% of its elevation every millennium, which is the same as losing 0.05 * its current elevation. Therefore, after 1 millennium, the mountain's elevation will be 1 - 0.05 = 0.95 times its current elevation. After 2 millennia, it will be 0.95 * 0.95 = 0.9025 times its current elevation, and so on.
After 8 millennia, the mountain's elevation will be 0.95^8 times its current elevation. We can calculate this as follows:
Elevation after 8 millennia = 1,300 meters * 0.95^8
= 1,300 meters * 0.6134
= approximately 798.02 meters
So the mountain will be approximately 798.02 meters tall after 8 millennia.
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After 8 millennia, the mountain's elevation will be 0.95^8 times its current elevation. We can calculate this as follows:
Elevation after 8 millennia = 1,300 meters * 0.95^8
= 1,300 meters * 0.6134
= approximately 798.02 meters
So the mountain will be approximately 798.02 meters tall after 8 millennia.
a statistics instructor wants to conduct a hypothesis test to determine if the mean number of credit hours taken by all ucf students is more than 11 hours. the instructor takes a sample of 27 ucf students and finds that they have a mean of 11.3 hours and a standard deviation of 3.0 hours. assume the population distribution of credit hours taken is approximately normal. what are the hypotheses for the test?
Hypotheses for the test are Null hypothesis and Alternative hypothesis
What is Hypothesis?
A hypothesis is an educated guess while using reasonable thinking, about the answer to a scientific question. Although it is not proof in an experiment, it is the predicted outcome of the experimentation. It can either be supported or not supported at all, but it depends on the data gathered.
The hypotheses for the test in this case are:
Null hypothesis (H0): The mean number of credit hours taken by all UCF students is not significantly different from 11 hours.
Alternative hypothesis (H1): The mean number of credit hours taken by all UCF students is significantly greater than 11 hours.
The null hypothesis represents the assumption that there is no difference between the mean number of credit hours taken by all UCF students and the value being tested (in this case, 11 hours). The alternative hypothesis is the opposite of the null hypothesis, and represents the claim that the mean number of credit hours taken by all UCF students is significantly different from 11 hours.
In this case, the instructor is specifically interested in testing whether the mean number of credit hours taken by all UCF students is significantly greater than 11 hours. Therefore, the alternative hypothesis is that the mean number of credit hours taken by all UCF students is significantly greater than 11 hours.
Hypotheses for the test are Null hypothesis and Alternative hypothesis
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What is special about rigid motion transformations?
A rigid body motion, also known as a rigid transformation, happens when a point or object travels while maintaining its size and shape.
What are the characteristics of a rigid motion transformations?While the image's size and shape are unaffected by rigid body motion, its location and orientation are. The three fundamental movements of a rigid body are translation, reflection, and rotation. Prior to movement, archetypes depict points or forms.
A rigid body motion, also known as a rigid transformation, happens when a point or object travels while maintaining its size and shape. Stretching and other non-rigid motions, which alter an object's size, are not comparable to this.
Area of triangle = 1/2 X b X h
b= 10
h=5
A = 1/2 X 10X 5
A = 25 unit sq.
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the proportion of people in each sample who experience side effects is recorded. are the sample sizes large enough to assume that the sampling distribution of the difference in sample proportions is approximately normal?
As the sample size is large enough to assume so the sample proportion mentioned in the above question is approximately normally distributed.
What is approximately normal distribution?It is a statistical expression used to determine an approximate value of some random variables.
How to calculate if a sample proportion is approximately normal?we measure the approximately normal proportion by the outcome of the product of the size of population, n and the proportion of population, p
p =X/n, where X is the sample size and n denote the size of population
If n×p ≥ 10 then the sampling distribution is approximately normal.
hence, as we have large proportion of sample, so it is approximately normal.
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What do you call 2 4 6 8 10?
The general rule that describe 2 4 6 8 10 the sequence.
What exactly are sequence and example?
An ordered list of numbers is a sequence. To go forward in the defined pattern, three dots are shown. A phrase is used to describe each number in the series.
One is the first word, three is the second, five is the third, and so on, in the series 1, 3, 5, 7, 9,...
Which four forms of sequence are there?
Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four primary categories of distinct sequences you need to be familiar with.
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How do I solve for x?
Step-by-step explanation:
I just answered this question. how often did you post it ?
in short again :
360 = 8x + 20 + 104 + arc angle KJP
arc angle KJP = 2× opposite angle of K and P =
= 2×(5x + 1)
so, together
360 = 8x + 124 + 2×(5x + 1) = 8x + 124 + 10x + 2 =
= 18x + 126
234 = 18x
x = 13
How many numbers are on a fair dice?
Answer:
When you roll a fair die you have an equal chance of getting each of the six numbers 1 to 6. The expected value of your die roll, however, is 3.5.
Step-by-step explanation:
hope this helps
mark me brainliest
If the truth values of both and are , then which of the following is a valid statement?
The truth value of p → q is F.
The truth value of p → q is T.
The truth value of p → q cannot be determined without knowing what p and q represent.
The truth value of p → q could be either T or F.
The valid statement regarding the truth value is B. The truth value of p → q is T.
What is a truth value?A truth value, also known as a logical value, is a measure of how true a proposition is in logic and mathematics. In classical logic, there are only two possible truth values.
A proposition's attribute indicating whether it is true or false is the definition of a truth value. A statement or proposition's truth or falsehood determines its truth value. Every statement has one of the two truth values, true or false, according to our theory.
Since the truth values of p and q are both false, the truth value of p → q is T according to the truth table.The correct option is B.
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Complete question
If the truth values of both p and q are false, then which of the following is a valid statement?
The truth value of p → q is F.
The truth value of p → q is T.
The truth value of p → q cannot be determined without knowing what p and q represent.
The truth value of p → q could be either T or F.
3,286-(1,221+217)…….
Answer:
1848
Step-by-step explanation:
Aiden misses 20% of the free throws he attempts in a season. How many total free throws did he attempt if he missed 54?
Answer: 270
Step-by-step explanation:
20 percent = 2/5
Times 54 or 54/1 with 2/5
You should get 270. So Aiden missed 270 free throws.
Hope This Helps:)!You are about to take a major assessment, and each question is one two types. Multiple-choice questions are worth 2 points each, and short-response questions are worth 4 points each. The assessment is worth 100 total points. Let x represent the number of multiple-choice questions, and let y represent the number of short-response questions.
2X + 4Y = 100 is the equation.
What is the equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Let's assume that X is the quantity of multiple-choice questions and Y is the quantity of short-answer questions.
Given that the short-answer questions are worth four points and the multiple-choice questions are for two, the equation is 2X + 4Y = 100.
Thus the equation for 2 points each, and short-response questions are worth 4 points each. The assessment is worth 100 total points where x represent the number of multiple-choice questions, and let y represent the number of short-response questions.
2X + 4Y = 100.
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algebra 1 please help i will give brainliest :)
The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2,200 people enter the fair and $5,050 is collected. Determine how many children and adults attended?
What is the multiplicative of 5?
Answer:
1/5 apparently
teachers' salaries california and new york lead the list of average teachers' salaries. the california yearly average is while teachers in new york make an annual salary of . random samples of teachers from each state yielded the following. california new york sample mean population standard deviation use for the average teachers' salaries in california. at , is there a difference in means of the salaries?
Therefore, we lack adequate data to draw the conclusion that population means differ.
What does the test statistic actually mean?A result of a statistical test of a hypothesis is a number known as the test statistic. It displays how closely the distribution predicted by your observed data fit the null hypothesis of that statistical test.
Here,
First hypothesis : [tex]H_{0}[/tex] : u1 - u2 = 0
Alternate hypothesis : [tex]H_{A}[/tex]: u1 - u2 ≠ 0
for 0.1 level with two tail test , critical z = 1.645
Rule of Decision: [tex]H_{0}[/tex] Reject if the test statistic's absolute value is |z|>1.645
California , New York
x1 = 64510.00 x2 = 62900.00
n1 = 45 n2 = 45
σ1 = 8200.00 σ2 = 7800.00
std error σx1-x2=√(σ21/n1+σ22/n2)=[tex]\sqrt{(8200^2/45+7800^2/45) }[/tex]= 1687.0750
test stat z =(x1-x2-Δo)/σx1-x2 =(64510-62900)/1687.0750 = 0.95
We cannot reject the null hypothesis because the test statistic does not fall into the rejection zone.
Therefore, we lack adequate data to draw the conclusion that population means differ.
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Why is it called a real number?
A set of all rational and irrational numbers is called the real numbers. All real numbers can be plotted on the number line. It is not imaginary number which cannot be quantified. It is denoted by capital Latin letter R.
Rational numbers are number that can be expressed as p/q where p and q are integers and value of q not equal to 0.
For example, -3/4, 5/3, 6/1.
Irrational numbers are not rational numbers but they can be plotted on the number line. It cannot be expressed as a simple ratio.
For example π, √2, -√7.
But √(-7) is an imaginary number.
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Which of the following represents a linear inequality in open-sentence form? (Select all that apply.)
2x + 8 = 10y
2x - 7y > 10
8 + x > 5
3 < 5
Answer:
2x - 7y > 10
8 + x > 5
3 < 5
Step-by-step explanation:
The equations are
Ax + By + C < 0 or Ax + By + C > 0
There is no equal in a linear inequality
The first option 2x + 8 = 10y is an equation, so it is wrong. The other 3 are correct!
if two distinct numbers are chosen at random from the set {1, 5, 10, 100} what is the probability that their sum will be greater than 100?
can someone save my grades and ego and explain this
please!
The probability of having the sums that would exceed 100 has been calculated to be 0.5
How to solve for the probabilityWe have the set or the sample space as:{1 , 5 , 10 , 100) It is said that two numbers would be able to be gotten from the set that we have. Given that the total numbers are 4, we would have ⁴C₂ = 6
The two numbers would be gotten from the set of 4 numbers in 6 different ways.
We are to find the numbers which when we add them up would be able to give us a sum that is greater than 100 these values are (100, 1), (100, 5), (100, 10)
Hence three pairs out of the given six that we already have would be able to give us values that are more than 10. We would have to divide through such that 3 / 6 = 1 / 2 = 0.5
Hence the probability that their values when summed would have to be greater than 100 is 0.5
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What is the solution to the system of equations 3x 2y Z 7 5x 5y 4z 3 3x 2y 3z 1?
The answer is x = 4
y = -1
z = -3
3x+2y+z=7
5x+5y+4z=3
3x+2y+3z=1
________
Let's take the first and the third equation, multiply the first one by (-1) and sum them up:
3x+2y+z=7
3x+2y+3z=1
____
-3x-2y-z=-7
3x+2y+3z=1
____
2z = -6
z = -6/2
z = -3
Substitute z in all equations:
3x+2y+z=7
5x+5y+4z=3
3x+2y+3z=1
______
3x + 2y - 3 = 7
5x + 5y - 12 = 3
3x + 2y - 9 = 1
______
3x + 2y = 10
5x + 5y = 15
3x + 2y = 10
The first and the third equations are the same, so one can be excluded:
3x + 2y = 10
5x + 5y = 15
Multiply the first equation by -5 and the second equation by 2 and sum them up:
-15x - 10y = -50
10x + 10y = 30
_________
-5x = -20
x = -20/-5
x = 4
Substitute x:
3x + 2y = 10
12 + 2y = 10
2y = 10 - 12
2y = -2
y = -2/2
y = -1
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5
6
A curve has equation y = x³ + ax + b.
The stationary points of the curve have coordinates (2, k) and (-2, 10-k).
Work out the value of a, the value of b and the value of k.
The value of 'a' is equal to -12, the value of 'b' is equal to 5 and the value of 'k' is equal to -11.
The stationary points of a curve are those points at which the first derivative of the function f(x) becomes zero. At the stationary points, the nature of the function is neither increasing nor decreasing.
→ The stationary points of a curve can either be a local minima or a local maxima of the function.
→ If we plot the graph of the curve, then stationary points can be said to be those points at which the tangent to the curve becomes horizontal which means the tangent becomes parallel to the x-axis.
→ Therefore for a point (a,b) to be the stationary point of a function f(x): f'(a) must be equal to zero.
→ For the given question:
f(x) = y = x³ + ax + b
f'(x) = 3x² + a
(2, k) is a stationary point:
f'(2) = 0
f'(2) = 3(2)² + a = 0
a = -12
The value of 'a' comes out to be equal to -12.
→ Hence the equation of the curve is: y = x³ - 12x + b
→ The stationary points (2, k) and (-2, 10-k) must be lying on the curve, hence they must satisfy the equation of the curve:
→ Putting (2, k) in the equation of the curve:
k = (2)³ - 12(2) + b
(k - b) = -16 - Equation (i)
→ Putting (-2, 10 - k) in the equation of the curve:
(10 - k) = (-2)³ -12(-2) + b
(10 - k) = -8 + 24 + b
b = -6 - k - Equation (ii)
→ Putting the value of 'b' from the equation (ii) in equation (i):
k - (-6 - k) = -16
k + 6 + k = -16
2k = -22
k = -11
∴ The value of 'k' comes out to be equal to -11.
→ Putting the value of 'k' in equation (i):
k - b = -16
-11 - b = -16
b = 5
∴ The value of 'b' comes out to be equal to 5.
Therefore, the value of 'a' is equal to -12, the value of 'b' is equal to 5 and the value of 'k' is equal to -11.
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Find the measure of each angle indicated. Round to the nearest tenth.
The measurement of angles are given as 20.92°, 40.83°, 57.76°, 71.17°, 26.21° and 44.7°respectively.
What are trigonometric ratios?The trigonometric ratios are defined for a right angled triangle.
The example of these ratios are sin, cos, tan, cosec, sec and cot.
The trigonometric ratios are useful in determining the heights and distances of the large objects.
The given problem can be solved by applying the trigonometric ratios to all of the triangle as follows,
(11) In the given triangle,
Sinθ = 5/14
=> θ = Sin⁻¹(5/14) = 20.92°
(12) In the given triangle,
Tanθ = 7/8.1
=> θ = Tan⁻¹(7/8.1) = 40.83°
(13) In the given triangle,
Cosθ = 8/15
=> θ = Cos⁻¹(8/15) = 57.76°
(14) In the given triangle,
Tanθ = 8.8/3
=> θ = Tan⁻¹(8.8/3) = 71.17°
(15) In the given triangle,
Tanθ = 6.4/13
=> θ = Tan⁻¹( 6.4/13) = 26.21°
(16) In the given triangle,
Tanθ =9.4/9.5
=> θ = Tan⁻¹( 9.4/9.5) = 44.7°
Hence, the measures of the angles indicated in the triangles are obtained as 20.92°, 40.83°, 57.76°, 71.17°, 26.21° and 44.7°respectively.
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