The relationship between the volume of a prism and pyramid with congruent bases and heights is that the volume of pyramid is one-third of the volume of prism.
As the prism and pyramid have congruent bases and heights, let us consider the area of the triangular base is A and the height is h.
For a prism of base area A and height h, volume is determined by the formula
Vpm = A×h
For a pyramid of base area A and height h, volume is determined by the formula
Vpd = A×h/3
From both relations for volume
Vpd = Vpm/3
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Determine if the given sequence is an arithmetic sequence. If it is, find the common difference, d.
-3, 0, 3, 6, ...
Is this an arithmetic sequence?
O No
O Yes
We need to solve this question using Arithmetic Progression concept. Yes the given sequence is Arithmetic and value of d is 3.
What do you mean by Arithmetic Progression?A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms. One arithmetic progression with a common difference of 2 is the sequence 5, 7, 9, 11, 13, 15,...
The n-th term of the sequence (a n) is provided by: If the first term of an arithmetic progression is a and the common difference between each succeeding component is
{a {n}=a+(n-1)d},
If the AP contains m terms, then a m denotes the final term, which is provided by:
{a {m}=a+(m-1)d}.
The term "finite arithmetic progression" or "arithmetic progression" refers to a finite segment of an arithmetic progression. An arithmetic series is the total of a finite arithmetic progression.
CalculationThe given sequence is -3,0,3,6,....
We know that an=a + (n-1)d where d is the common difference
⇒ 0= -3 + d
∴ d=3
So hence proved that the given sequence is arithmetic.
We need to solve this question using Arithmetic Progression concept. Yes the given sequence is Arithmetic and value of d is 3.
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What is AAS similarity theorem?
The triangles are congruent if two angles and the excluded side of one triangle match equivalent areas in another triangle, it is known as the AAS similarity theorem.
What is the AAS similarity theorem?
Angle-Angle-Side is abbreviated as AAS.
The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.
AAS congruence can be demonstrated with a few simple methods.
If and only if the corresponding sides and angles are in proportion, two triangles are said to be comparable.
Similar to how there are particular ways to demonstrate triangle congruence (SSS, ASA, SAS, AAS, and HL), there are particular ways to demonstrate triangle similarity.
Therefore, the triangles are congruent if two angles and the excluded side of one triangle match equivalent areas in another triangle, it is known as the AAS similarity theorem.
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Suppose a merry-go-round is spinning once every 3 seconds. If a point on the outside edge has a speed of 12.56 feet per second, what is the radius of the merry-go-round? (Use 3.14 for
Answer:
r = 6 feet
Step-by-step explanation:
Ler r represents the radius
Hence perimeter = edge speed times 3second
2 times 3.14 times r = 12.56 times 3
r = 6 feet
need help
- Given the line 3x-4y+24=0, determine the value of a, and b if the points (8.3,a) and (b, -10.2) are on the line.
Answer:
To find a, you'll put the value 8.3 as x in the equation to get the value of y which is equal to a. For the second point you'll put -10.2 as the value of y in the equation to get x which is equivalent to b.
Step-by-step explanation:
every point represents an ordered pair of (x, y) values.
if the point is on the given line (or any other form of curve/ function), then these x and y values make the functional equation true. if the equation turns out to be false with these values, then the point is not on that functional curve.
so, we need to find a and b to make the equations true.
(8.3, a)
3×8.3 - 4a + 24 = 0
24.9 + 24 = 4a
48.9 = 4a
a = 48.9/4 = 12.225
(b, -10.2)
3b - 4×-10.2 + 24 = 0
3b + 40.8 + 24 = 0
3b + 64.8 = 0
3b = -64.8
b = -64.8/3 = -21.6
HELP 100 POINTS PLEASE WILL MARK BRAINLIEST
The adjusted trial balance for revenue in the accounting worksheet is 20,000.
What is Trial Balance?Trial balance in the accounting worksheet is a financial report where the credit entries and debit entries are listed which is used to audit the accounting system of business or organization internally. It is used to confirm that the sum of all credits and debits must be equal.
Here we have the credit of 15,000 for revenues.
Then the trial balance is adjusted with a credit of 5000.
If we have two debits or credits, we will add them.
So the adjusted trial balance = 15,000 + 5,000 = 20,000
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What can good debt do to your credit score?
Responses
nothing
increase it
negatively affect it
decrease it
The effect of good debt to ones credit score is that is would increase it. That is option B.
What is a credit score?A credit score is defined as the expression that can be used to show a customer's worth regarding the payment of their debts.
A customer's credit score can be rated as follows:
BadFairGood orExcellent credit score.A good debt is the ability of a customer to quickly pay off their debt which has been noted as one of the qualities that raise their credit score.
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How do you tell if a triangle is similar or congruent?
When the sides and angles of two triangles match that triangle is congruent and When the angles of two triangles match that triangle is similar.
When the sides and angles of two triangles match, the triangles are said to be congruent. When the angles of two triangles match, the triangles are said to be similar. Thus, two triangles can be superimposed side to side and angle to angle.
Hence, when the sides and angles of two triangles match that triangle is congruent and When the angles of two triangles match that triangle is similar.
If two triangles have an equal number of comparable angles and sides, they are said to be similar. Similar figures are items that have two or more figures with the same shape but varying sizes.
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Is 4 a linear expression?
No, 4 is not a linear expression.
A linear expression is an algebraic expression involving two or more variables, where the highest power of each variable is one. Linear expressions can be written in the form of an equation, such as y = 2x + 5. In this equation, y and x are variables, and 2 and 5 are constants. The highest power of each variable is one, so this is a linear expression. In contrast, 4 is a constant and does not involve any variables, so it is not a linear expression.
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does anyone know this?!?
The answers for the given proof of a parallelogram are explained below:
What is a parallelogram?A parallelogram is a straightforward (non-self-intersecting) quadrilateral in Euclidean geometry that has two sets of parallel sides. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size. The Euclidean parallel postulate, or one of its equivalent formulations, is a necessary precondition for both the congruence of opposite sides and opposite angles, and neither condition can be demonstrated without using it. In contrast, a quadrilateral with just one set of parallel sides is referred to as a trapezoid or trapezium in British or American English. A parallelepiped is the parallelogram's three-dimensional counterpart.
1) CPCTC(corresponding parts of congruent triangles are congruent)
2) Reflexive property
3) Corresponding angles theorem converse(If corresponding angles are equal then the lines are parallel)
4) Alternative angles theorem converse(If alternative angles are congruent then the lines are parallel)
5) SSS
6) Given.
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What is the 1 value?
The value 1 is the multiplicative identity of any number.
In the field of mathematics, the 1 value can be described as the multiplicative identity of any number which has any mathematical value. 1 value describes that when any number is multiplied by the digit 1, the result that arises is the number itself. Hence, value 1 represents the multiplicative identity.
Based on the 1 value, we know that any mathematical expression, digit, or value when multiplied by the digit 1 has an answer that is the same value. As this property is common to all the numbers when multiplied by 1, hence it is referred to as 1 value.
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Is 7x 2x² a quadratic equation?
It is a quadratic equation, indeed. 7x =2x²
A quadratic equation is what?A quadratic equation is any equation of the form where x is a variable, b, and c are any real values, and a 0.
As is common knowledge, the formula for the quadratic equation's roots is the discriminant formula
Is the equation 7x 2x 2 quadratic?By replacing, we can create the following equation given the information in the question:7x =2x²
2x^2-7x=0
This is a quadratic equation because, as we can see, x has a power of two.
An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
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How do you find discontinuity?
There are a few ways to find discontinuities in a function. One way is to look for places where the function is not defined or where it produces an undefined result, such as division by zero. Another way is to look for places where the function exhibits a sudden change in behavior, such as a jump or a sharp turn.
To find discontinuities more formally, you can use mathematical techniques such as limits or derivatives. If you are familiar with these concepts, you can use them to identify discontinuities in a function.
For example, if you are trying to find the discontinuities of a function f(x), you can consider the limit of the function as x approaches a certain value, say x=c. If the limit of the function as x approaches c from both the left and the right is different, then there is a discontinuity at x=c. Similarly, if the derivative of the function is not defined at a certain value of x, then there is a discontinuity at that point.
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if you are trying to find the discontinuities of a function f(x), you can consider the limit of the function as x approaches a certain value, say x=c. If the limit of the function as x approaches c from both the left and the right is different, then there is a discontinuity at x=c. Similarly, if the derivative of the function is not defined at a certain value of x, then there is a discontinuity at that point.
What is the value of discriminant X² 4x +4 0?
The value of the discriminant of the given expression x² + 4x +40 = 0 is equal to -144.
As given in the question,
Given expression is equal to :
x² + 4x +40 = 0
Standard formula of the discriminant for the general quadratic equation
ax² + bx + c = 0 is given by :
Discriminant is represented by 'D'
D = b² - 4ac
Here b = 4 , a = 1 and c = 40
Substitute the value in the formula we get,
D = 4² - 4(1)(40)
⇒D = 16 - 160
⇒ D = -144
Therefore , the value of the discriminant of the given expression x² + 4x +40 = 0 is equal to -144.
The above question is incomplete ,the complete question is :
What is the value of discriminant x² + 4x +40 = 0?
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Can somebody help me???????????
The complete table is given and rate of change is 1 per 28 pair of jeans.
What is rate of change?How quickly something evolves over time is referred to as its rate of change (ROC).
Given, of the 84 pair of jeans only 3 are defected.
And rate of change is constant.
And 1 defected pair of jeans is 84 /3 = 28.
That means,
total number of jeans = n x 28
Where n is the number of defected pair of jeans.
So, for n = 3,6,8,12,15
Then, number of jeans =84, 168, 224, 336, 420.
The table is given in the image.
The basic formula for the rate of change is:
Rate of change = (Change in quantity 1) / (Change in quantity 2)
In every 28 pair of jeans there is one defected jeans.
Therefore, the complete table is given and rate of change is 1 per 28 pair of jeans.
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Paul pay the newpaper company 70% of what he collect how much would he keep for himelf in a month when he collected 450. 0
Answer:
£135
Step-by-step explanation:
70% of £450
=£315
£450-£315=135
The odds in favor of an event are 3 to 4. What is the probability of the event?
37
The probability from the odds is 3/7
How to determine the probability?The value of the odds is given as
Odds = 3 to 4
Represent the odds as a fraction
So, we have the following representation
Odds = 3/4
To convert the odds to probability, we make use of the following equation
Probability = Odds/(1 + Odds)
Substitute the known values in the above equation, so, we have the following representation
Probability = (3/4)/(3/4 + 1)
Evaluate the sum
Probability = (3/4)/(7/4)
Evaluate the quotient
Probability = 3/7
Hence, the probability is 3/7
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how can we find out if a clustering method in unsupervised learning is a good one? group of answer choices the svm accuracy on data has the accuracy close to 100% the predicted labels are equal to actual labels the distances between different clusters are minimum the sum of distances between objects in the same cluster are minimum
What is Clustering method in unsupervised learning?
An method known as unsupervised learning discovers patterns in untagged data. The idea is to compel the computer to create a clear representation of its surroundings and then produce innovative material from it through imitation, which is a crucial learning method for people.
There are several ways to evaluate the performance of a clustering method in unsupervised learning. Some common evaluation metrics include:
The sum of distances between objects in the same cluster (also known as the intra-cluster distance): This measure indicates how closely the objects in each cluster are related to each other. A good clustering method will have a low intra-cluster distance, indicating that the objects within each cluster are similar to each other.The distances between different clusters (also known as the inter-cluster distance): This measure indicates how distinct the different clusters are from each other. A good clustering method will have a high inter-cluster distance, indicating that the clusters are well separated from each other.The predicted labels are equal to the actual labels: This measure is only applicable if you have labeled data and you are using the clustering method to classify the data into different categories. If the predicted labels are equal to the actual labels, it means that the clustering method is correctly identifying the different categories.The SVM accuracy on the data: This measure is only applicable if you are using a support vector machine (SVM) as a classifier after the clustering step. The SVM accuracy indicates how well the SVM is able to classify the data based on the clusters produced by the clustering method. A good clustering method will result in high SVM accuracy.To know more about Clustering method in unsupervised learning visit,
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Somebody pls help
The maximum capacity of a theater is 471 people. So far, 254 people are seated in the theater. If p represents the number of people that can still enter the theater, write an inequality that represents the situation.
Answer: [tex]p + 254 \leq 471[/tex]
Step-by-step explanation:
The number of people in the theater plus 254 )the number of people already in the theater) must be less than or equal to the maximum amount allowed to be seated, 471.
So, [tex]p + 254[/tex] represents the number of people in the theater.
471 is the maximum amount of people.
So, p + 254 must be less than or equal to [tex]p + 254[/tex].
Therefore, we can say that:
[tex]p + 254 \leq 471[/tex]
Use the drop-down menus to identify the domain and range of each function below.
drop down menu is the same for all
ANSWER ASAP I NEED HELP!!!
The domain and range of g(x) = |x - 3| are all real numbers and all positive real numbers while the domain and range of the function h(x) = x - 3 are all positive real numbers.
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
As per the given function,
g(x) = |x - 3|
Since it is a mode function thus the value of the function will always positive.
Thus, the range will be [0, ∞) or all positive real numbers.
In the function h(x) = x - 3 here we have negative real numbers as well as positive thus the range of it will be all real numbers.
Hence "While the domain and range of the function h(x) = x - 3 are all positive real numbers, those of g(x) = |x - 3| are all real numbers and all negative real numbers.".
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what is the cost of 1.2kg cheese if 200g is $9.75
Answer:
$58.50
Step-by-step explanation:
1.2 kg = 1200g
To get from 200 to 1200, we time 6, so we take $9.75 times 6 to get the price.
$9.75 times 6 = $58.50
So, the cost of 1.2kg cheese is $58.50
The answer is $58.50
I have attached the explanation! :)
Danielle received the following scores on her essay tests:
84, 85, 83, 86, 80, 85, 86, 88, 89, 86, 83
What is the mean of her scores?
85.5
84.5
86
85
Answer:
85
Step-by-step explanation:
Think of mean as the average of a set of values. In this case, we have to find the average of Danielle's scores. To do this, add all of the values together and divide it by the number of values we have:
We have 11 scores so we will divide all of them by 11:
[tex]\frac{84+85+83+86+80+85+86+88+89+86+83}{11} = \frac{935}{11} = 85[/tex]
brainteaser there are 5 people sitting arund a table with different birthdays, what is the probability they sit in the right order both clockwise and counter clockwise
The probability that 5 people sit in the correct order in either direction clock or anti-clock is equal to the probability of any one of the orders occurring, which is 1/2, or 50%.
To calculate the probability that they sit in the correct order in both directions, you would multiply the probability of each event occurring. Since the probability of either event occurring is 1/2, the probability of both events occurring is (1/2) * (1/2) = 1/4, or 25%. This means that there is a 25% chance that the 5 people will sit in the correct order in both directions around the table.
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Write an equation of the line with the given slope and y-intercept.
m = 0; (0, 2)
Group of answer choices
A. x = 2
B. y = 0
C. y = 2x
D. y = 2
Answer:
D. y = 2
Step-by-step explanation:
It can't be A because this is the equation for the slope is undefined.
It can't be B because this equation has no y-intercept!
It can't be C because the equation is y=mx + b. And we see that this equation has a slope of 2, so it is wrong.
So, the answer is D
Question 7 (Essay Worth 6 points)
(04.04 MC)
The relative frequency table describes the relationship between students who completed an exam review and their performance on the exam.
Passed exam Did not pass exam Row Totals
10%
65%
Completed exam review
55%
Did not complete exam review 20%
Column Totals
75%
15%
25%
35%
100%
Part A: What is the percentage of students who passed the exam, given that they completed the exam review? Round to the nearest percentage. (2 points)
Part B: What is the percentage of students who passed the exam, given that they did not complete the exam review? Round to the nearest percentage. (2 points)
Part C: Is there an association between passing the exam and completing the exam review? Justify your answer. (2 points)
83% of pupils passed the test as a group.
Explain about the proportion?An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls)
It is claimed that two ratios are in proportion if they are the same. A/B Equals C/D if the four elements are a, b, c, and d in that order. The terms a and d are referred to as extremes, whereas b and c are referred to as medium terms. The ratio equates the product of extremes to the product of means.
Results in total: 65% of the review was finished.
The desired results were 55% exam pass.
The percentage is as follows:
p = 55/65 x 100%
= 82.3%.
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A 100 meter dah i run on a track in the direction of the vector v = 2i6j. The wind velocity w i 5ij km/h. The rule ay that a legal wind peed meaured in the direction of the dah mut not exceed 5 km/hr. Will the race reult be diqualified due to an illegal wind? Jutify your anwer
The race result will not be disqualified due to an illegal wind.
In order to determine whether the wind velocity during the race was legal, we need to compare the wind velocity w to the legal wind speed limit of 5 km/hr. In this case, the wind velocity is given as 5ij km/h, which is purely vertical wind. The direction of the wind is not relevant in this case, since the race is run in the direction of the vector v, which is a purely horizontal direction. Since the wind velocity w is purely vertical and the race is run in a purely horizontal direction, the wind velocity w has no effect on the race result. Therefore, the race result will not be disqualified due to an illegal wind.
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Angel sum theorem PLEASE HELP
Answer:
y=90 degrees
Step-by-step explanation:
x+y+70=180 degrees ==> these three angles make up a triangle, and the
the total sum of angles in a triangle is 180 degrees
Notice that y is on a straight line?
Straight lines are 180-degree angles called straight angles.
Hence:
(180-y)+x+70=180 ==> these three angles also make up a triangle, and the
the total sum of angles in a triangle is 180 degrees
180-y+x+70=x+y+70 ==> since both expressions equal 180, they both are
equal to each other
180-y+x+70 + y = x+y+70 + y ==> add y on both sides to isolate y to one side
180 - y + y + x + 70 = x + y + y + 70 ==> simplify
180 + x + 70 = x + 2y + 70
180+x+70 - x = x+2y+70 - x ==> subtract x on both sides to eliminate x
180 + x - x + 70 = x - x + 2y + 70 ==> simplify
180 + 70 = 2y + 70
180 + 70 - 70 = 2y + 70 - 70 ==> subtract both sides by 70 to simplify the equation
180 = 2y
y = 180/2
y = 90 degrees
Did 8 is a prime number?
A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number, 8 is divisible by 2 and 4 other than itself and 1, so 8 is not a prime number.
What is a prime number?A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.
what is whole number?Complete numbers the range of numbers that includes zero and natural numbers. not a decimal or fraction.
factor of 8 = 2x2x2,
since 8 is divided by 2, so it is not a prime number.
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HELP HELP HELP ITS DUE TODAY Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold 43 cards, which was 5% of the cards sold for Mother's Day. How many cards were sold for Mother's Day?
Answer:
860 cards
Step-by-step explanation:
[tex]\frac{5}{100} =\frac{43}{x}[/tex]
43 cards only represents 5% of the total cards sold on Mother's Day. So create proportions and solve for the number of cards that represents 100%.
5x = 43*100
5x = 4300
x = 860
What type of sequence is 8 17 26 35?
This is a geometric sequence since common difference is same between previous and next term.
What is arithmetic series?The sum of arithmetic sequence is know as arithmetic series.
What is the general formula to find arithmetic series?The general formula to find arithmetic series is:
[tex]S_{n} =\frac{n}{2} [2a_{1} +(n-1)d][/tex]
Since 8 17 26 and 35 have a common difference that is d=9 always between previous and next term so given sequence is arithmetic sequence.
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Is 7 3x is a factor of 3x² 7x?
The term (7 + 3x) is a factor of the quadratic equation 3x² + 7x .
A number is called a factor of the quadratic equation if that number satisfies the equation .
the term is given as : 7 + 3x ,
solving it we get ; 3x = - 7
So , x = -7/3 .
to check whether it is a factor , we substitute the value of x in the equation ,
we get , 3x² + 7x
= 3(-7/3)² + 7(-7/3)
= 49/3 - 49/3
= 0
Therefore , Yes , (7 + 3x) is the factor of 3x² + 7x .
The given question is incomplete , the complete question is
Is (7 + 3x) is a factor of the quadratic equation 3x² + 7x ?
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