The value of R² is 3/2
What are solids ?
A three-dimensional object that is closed (which may, according to some terminology conventions, be self-intersecting). A solid is any constrained area of space that is bounded by surfaces, according to Kern and Bland (1948, p. 18). The sphere, cube, cone, and cylinder, as well as the polyhedra more broadly, are some of the most basic solids.
We can see that EJCI is a rhombus and
Area of rhombus is given by
Area of rhombus = Lenth of one diagonal * length of another dialonal / 2
Thus,
EC = (a^2 + a^2 + a^2)^0.5
=> EC = a * (3)^0.5
JI = (a^2 + a^2 )^0.5
=> JI = a * (2)^0.5
So, the area of EJCI = EC * JI / 2
=> Area = (1/2) * (a^2) * (6)^0.5
Area of face = a^2
R = [ (1/2) * (a^2) * (6)^0.5] / a^2
=> R = 1/2 * 6^0.5
So, the required R² is
R^2 = (1/4) * 6
=> R^2 = 3/2
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Eva loves to go fishing. Each time she catches a fish, there is a 70% chance that it is a northern pike and a
30% chance it is a walleye. Let W be the random variable that represents the number of walleye Eva gets
if she catches 2 fish.
0
1
2
W = # of walleye
P(W)
0. 49
0. 42
0. 09
Calculate the mean of W.
walleye
The mean of the walleye 'W' for the given number of walleye and its probability to represent that 30% chances are of walleye is equal to 1.4.
As given in the question,
Let 'W' is the random variable represents the number of walleye.
'P(W)' represents its probability
The values are given as follow:
W : 0 1 2
P(W) : 0.09 0.42 0.49
Mean of the walleye 'W' is given by :
= W₁P(W₁) + W₂P(W₂) + W₃P(W₃)
= ( 0 × 0.09 ) + ( 1 × 0.42 ) + ( 2 × 0.49 )
= 0 + 0.42 + 0.98
= 1.4
Therefore, the mean of the walleye 'W' for the given number of walleye and its probability is given by 1.4.
The above question is incomplete , the complete question is :
Eva loves to go fishing. Each time she catches a fish, there is a 70% chance that it is a northern pike and a 30% chance it is a walleye. Let W be the random variable that represents the number of walleye Eva gets
if she catches 2 fish.
W : 0 1 2
P(W) : 0.09 0.42 0.49
Calculate the mean of W.
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Robert is building a deck in his backyard. Each piece of wood measures 42.5 inches. If he has 8 boards, how long are they altogether?
The length of the wood altogether is 340 inches
How to calculate the length of the wood?Robert is building a deck
Each piece of the wood measures 42.5 inches
Robert has 8 boards
The length of the wood altogether is
= 42.5 × 8
= 340
Hence the length of the wood is 340 inches
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write the equation of the line passing through the point (4, -6) with a slope of 1/2?
Answer:
Step-by-step explanation:
We know that , the equation of line when the slope and the coordinates are given is:
y - y1 = m(x - x1)
where x1 = 4 , y1 = -6 and m = 1/2
therefore, y -(-6) = 1/2(x - 4)
y + 6 = x/2 - 2
6+2 = x/2 - y
8 = x - 2y/2
16 = x - 2y
required equation : x-2y-16=0
becky is doing research in which she needs 28 g of a substance that is 30% protein how many grams of each two ingredients one that is 50% protein in the other 25% protein should she mix together
Therefore, Becky must combine 25.6 grams of the second ingredient (25 percentage protein) with 2.4 grams of the first ingredient (50 percent protein) to create 28 grams of
Define percentage.A percentage (%) is a number that can alternatively be written as a decimal or fraction and represents a quantity as a proportion of 100. You can change a percentage to a fraction by putting 100 in the numerator and also the percentage number in the numerator.
Here,
Becky will need to blend several substances to obtain the necessary level of protein in order to generate 28 grams of a material that is 30% protein.
Let's name the first ingredient's percentage of protein (50%) "x" and the second ingredient's percentage of protein (25%) "y".
That which we are aware of is
28 grams of the combination are present in total.
It has 30% protein.
50% of the first component is protein.
25% protein makes up the second component.
To express the issue, we can build up the following equations:
x + y = 28 (the total amount of the mixture is 28 grams) (the total amount of the mixture is 28 grams)
(0.50)x + (0.25)y = 0.30(28) (the mixture is 30% protein)
Now we can use the first equation to solve for one variable in terms of the other. If we solve for y, we get:
y = 28 - x
We can substitute this into the second equation:
(0.50)x + (0.25)y = 0.30(28) (28) (30% of the mixture is protein)
We may now solve for one variable in terms of the other using the first equation. If we figure out y, we obtain:
y = 28 - x
This can be used as a substitution in the second equation:
(0.50)x + (0.25)(28-x) = 0.30(28) (28)
which results in:
0.50x + 7 - 0.25x = 8.4
And simplifying even more
0.25x = 0.6
x = 2.4
We now know that 2.4 grams of the combination are made up of the first component, which is 50% protein. Using this knowledge, we can calculate the quantity of the second ingredient:
y=28 - x=28 - 2.4=25.6 grams
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Pls help me with math
The correct expression to represent the similarity of these two triangles is,
21/35 = x/30.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know two triangles are similar if the ratio of their corresponding sides is equal.
Therefore, The correct way to represent the similarity is,
21/35 = x/30.
We can solve for x here,
35x = 21×30.
5x = 3×30.
x = 3×6.
x = 18.
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What is the area of equilateral ∆ having side 12 cm?
Therefore , the solution of the given problem of triangle comes out to be the equilateral triangle are is 62.28 cm².
Describe the triangle.In geometry, triangular polygons are ones that have three vertices and a right side. This object in two dimensions has three straight sides. Triangles are examples of three-sided polygons. The sum of a triangle's three angles is 180 degrees. The triangle lies on one plane.
Here,
Given : side = 12cm
Area of an equilateral triangle
=> √3/4 * side²
Side of triangle =12 cm
Area of an equilateral triangle
= > √3/4 * 12²
=>√3/4 * 12*12
=> 62.28 cm²
Therefore , the solution of the given problem of triangle comes out to be the equilateral triangle are is 62.28 cm².
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Sal brought 2 dozen apples to a science club meeting. He divided the apples equally among the 8 people there. How many apples did he give each person?
Division is the antithesis of multiplication. When you divide twelve into three equal groups, you get four in each group when you multiply three groups of four to create twelve.
How do you explain division?The opposite of multiplication is division. When you multiply three groups of four to produce twelve, you get four in each group when you split twelve into three equal groups. The basic objective of splitting is to determine how many equal groups are created or how many people are in each group after a fair distribution.
The phrase to use is "divide in half," not "divide by half," when discussing splitting something into two equal portions. In mathematics, multiplying by two is equivalent to dividing by half. Additionally, see "multiply by two."
The French term "douzaine," which denotes a group of 12, is where the word "dozen" originates.
2 dozen apples equals 24, and 24 divided by 8 is 3.
Therefore, the answer is 3.
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Find m (angle) 1 . Then classify the triangle by its angles.
M (angle) 1 =
Answer:
right triangle m=5
Step-by-step explanation:
because it has a 90 degree angle
What is BPT Theoram please solve
In a triangle, a line is drawn parallel to one side of the triangle. Then it ratio of the two similar triangles will be con
What is the Basic Proportionality theorem?The Basic Proportionality Theorem, often known as the Thales Theorem, was developed by the eminent Greek mathematician Thales. He asserted that the ratio of any two matching sides is constant for any two equiangular triangles. He developed the basic proportionality theorem based on this idea (BPT). Similar triangles have presented this idea. When two triangles resemble one another.
Think about the triangle ΔABC in the given illustration. A line PQ connecting the sides AB and AC of P and Q in this triangle is drawn parallel to the side BC of the triangle.
AP/PB = AQ/QC
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Find the range, mean, median and mode for the scores. Round to the nearest tenth when necessary.a.40; 75.5; 75; 75c.40; 74.5; 75; 100b.35; 75.5; 75; 75d.40; 74.5; 75; 75
How do you tell if a system of equations has no solution or infinitely many?
If you solve the equation and get the same number as yourself, there are infinite solutions, and if you get the wrong equation, there is no solution.
Without graphing, how can you determine if a system of equations has one solution or an infinite number of solutions?You can see that both slopes are the same (-3). This shows that the lines are parallel without creating a graph. Therefore, the system of equations cannot be solved.
What distinguishes infinitely many solutions from zero? If the equation is wrong, the system has no solution. If the equation statement is true, there are infinitely many solutions.
A linear algebra problem is a linear system of n equations with n unknown variables. A system may have one solution, no solution, or an infinite number of solutions.
solution - all linear equations intersect or intersect at some point in space
No Solution - System is inconsistent and not all linear equations intersect or intersect.
Infinitely many solutions - some linear equations are the same line in space, some variables are unbounded.
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What is the equation of a line with a slope of 3 and y-intercept equal to 5?
The equation of a line is given by y = mx + b, where m is the slope and b is the y-intercept. Given that the slope is 3 and the y-intercept is 5, the equation of the line is y = 3x + 5.
The equation of a line is a mathematical expression of the form y = mx + b, where m is the slope and b is the y-intercept. This equation can be used to describe the relationship between the x-coordinate and y-coordinate of points on a line. In this specific equation, the slope is 3 and the y-intercept is 5, which means that the line passes through the point (0, 5) and has a slope of 3. Substituting 3 for m and 5 for b in the equation, we get y = 3x + 5, which is the equation of the line with a slope of 3 and a y-intercept of 5. We can use this equation to determine the y-coordinate of any given point on the line, provided we know the x-coordinate of the point. It is important to note that this equation is only applicable to straight lines, and not curves.
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In regression analysis, which of the following is not a required assumption about the error term e?
Answer
O The expected value of the error term is zero.
O The variance of the error term is the same for all values of x.
O The values of the error term are independent.
O All are required assumptions about the error term.
All are required assumptions about the error term.
In regression analysis, there are several assumptions that need to be met regarding the error term :
The expected value of the error term is zero: It is the assumption that the mean of the error term is zero, which means that on average, the predicted values of the dependent variable will be equal to the true values of the dependent variable.The variance of the error term is the same for all values of x: It is the assumption that the spread of the error term is constant across all levels of the independent variable.The values of the error term are independent: It is the assumption that there is no relationship between the error term at different levels of the independent variable.All three assumptions are required for valid regression analysis, and any violation of these assumptions can lead to biased or inefficient estimates of the model parameters.To know more about error terms click below:
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b. The original amount on the gift card was $200. Does Arleen have
enough left on the card to buy a
wheelbarrow for $50? Explain.
Answer:
Yes
Step-by-step explanation:
If there was 200 hundred dollars just subtract 50 dollars if there is still money then yes.
Answer: yes
Step-by-step explanation:
200-50=159
A basket of the fruit contains 4 bananas, 3 apples, and 5 oranges. You intend to draw a piece of fruit from the basket, keep it, draw the 2nd piece of fruit from the basket, keep that, and then draw a third piece of fruit from the same basket. What is the probability of selecting one banana, then one apple, then one orange, in that order, from the basket if you are blindfolded?
A. 5/144
B. 5/108
C. 1/28
D. 1/22
The probability of selecting one banana, then one apple, then one orange, in that order, from the basket if you are blindfolded is 1/22.
What is the probability:The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out.
The outcome of an event may be known to us or unknown to us. When this happens, we indicate that there is a probability that the event will happen or not.
It is also defined as the ratio of the number of favorable outcomes to the total number of outcomes.
The formula for the probability of an event is given by
P(E) = No of favorable outcomes/ Total No of outcomes ]
Here we have
A basket of fruit contains 4 bananas, 3 apples, and 5 oranges.
Total number of fruits = 4 + 3 + 5 = 12
By the given formula,
Probability of selecting 1 banana = 4/12 = 1/3
Probability of selecting 1 apple = 3/12 = 1/4
Probability of selecting 1 orange = 5/12
The order of the fruits that is given is 1 banana, then 1 apple, then 1 orange
Let's assume that,
We taken 1 banana
=> The probability of selecting one banana = 1/3
After taking one banana, remaining fruits = 12 - 1 = 11
Now we have drawn 1 apple
=> The probability of selecting one apple in 11 fruits = 3/11
After taking one apple remaining fruits = 11 - 1 = 10
=> The probability of selecting one orange from 10 fruits = 5/10 = 1/2
From the above calculations,
The probability of selecting in given order = (1/3)(3/11)(1/2) = 3/66 = 1/22
Therefore,
The probability of selecting one banana, then one apple, then one orange, in that order, from the basket if you are blindfolded is 1/22.
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What is an inverse variation graph called?
The graph of the inverse variation equation is called a rectangular hyperbola.
A form of proportionality called inverse variation occurs when one number falls as the other rises or the other way around. This suggests that if one number rises while the other decreases, the magnitude or absolute value of the first quantity will decrease, resulting in a constant product. The constant of proportionality is another name for this item.
An inverse variation is a relationship between two variables in which the product is constant; as a result, while one of the variables changes, the other changes correspondingly to maintain the same value of the product. This connection has the form of a hyperbola.
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Cheese pizza was preferred by 40 students pepperoni pizza was preferred by 28 based on the results how many of the 340 students can be expected to prefer cheese pizza?
The number of students expected to prefer cheese pizza from the 340 students is 200 stduents.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
Cheese pizza = 40 students
Pepperoni pizza = 28
The ratio of cheese and Pepperoni pizzas.
= 40:28
= 10:7
Now,
Cheese pizza = 10x
Pepperoni pizza = 7x
The number of expected students who prefer cheese pizza.
= (10x)/(17x) x 340
= 10/17 x 340
= 10 x 20
= 200
Thus,
The number of expected students preferring cheese pizza is 200.
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Which expression is equivalent to -9 - \left(-4\dfrac13\right)
Answer:
B) -9 + 4 2/3
Explanation:
The answer is B because -9 - (-4 1/3) is -4 2/3 which is equal to -14/3, so that means B also has the same sum.
I hope this helps you! :)
Given function g, which is defined by g(x)=x to the power of 3 -x , what is the value of g(3)?
Really sorry, misunderstood the equation. This is the answer though.
Answer:
24
Step-by-step explanation:
We have our function g(x) = [tex]x^{3}[/tex] - x
Now, we will substitute 3 in for x, giving us:
[tex]3^{3} - 3[/tex]
Now, we will simplify our exponent, giving us:
27 - 3 = 24
So your answer is 24.
Hope this helped!
a) Find f(t).
ℒ−1
e−????s
s2 + 1
f(t)=? + (?) (t - ?)
The value of function, f(t) for L⁻¹ ( e−s /(s²+ 1)) is equals to sin( t - π ) u(t-π) .
The Laplace transform is the essential term of the given derivative function. Moreover, it comes with a real variable (t) for converting into complex function with variable (s). For ‘t’ ≥ 0, let ‘f(t)’ be given, the Laplace transform of ‘f(t)’, denoted by 'L{f(t)}' or ‘F(s)’ is definable with the equation:
[tex] L(f(t)) = F(s) = ₀∫^{ \infty } e⁻ˢᵗ f(t)dt[/tex]
we have L⁻¹ ( e−s /(s²+ 1))
Now, L⁻¹ (1 /(s²+ 1)) = sin(t)
so, L⁻¹ ( e−s /(s²+ 1)) = sin( t - π ) u(t-π)
where u(t-π) is unit of step function.
so, required function f(t) is sin( t - π ) u(t-π).
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Complete question:
Find f(t) ℒ−1 (e−s /(s²+ 1))
f(t)=? + (?) (t - ?)
In the arrangement below, each number is the non-negative difference of the two numbers above it. What is the sum of the four greatest distinct possible values for $z$
The numbers in the arrangement can be represented by x, y, z, a, b, c and d, where x is at the top and d is at the bottom. The relationship between the numbers is as follows:
x = y - z
y = a - b
z = c - d
We can use this information to find the values of z, c, and d in terms of x, y, and a:
z = y - x
c = z + d
d = z - c
Since we are looking for the four greatest distinct possible values for z, we can assume that x, y, and a are as small as possible (i.e. 0) and c and d are as large as possible.
Thus, the four greatest distinct possible values for z are:
z = y - x = 0 - 0 = 0
z = a - y = 0 - 0 = 0
z = c - d = c
z = c - d = d
The sum of these four values is 0 + 0 + c + d = c+d.
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The following dotplot shows the centuries during which the 111111 castles whose ruins remain in Somerset, England were constructed. Each dot represents a different castle. According to the 1.5.IQR rule for outliers, how many high outliers are there in the data set?
The conclusion which we get after analyzing the data given is that there aren't outliers in the displayed data set.
We will calculate the interquartile range and us the rule 1.5 .
The formula to calculate interquartile range is to subtract the value of first quartile by the value of second quartile.
IQR = Q3 - Q1
Therefore, interquartile range becomes,
IQR = 17 - 13
IQR = 4
Now , we will apply rule 1.5 and for that we will multiply 4 by 1.5 first
4 * 1.5 = 6
and then,
17 + 6 = 23
on applying the rue we will get ,
13 - 6 = 7 .
This value means that there is no outlier in the displayed data set.
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Becky says that line c and d are parallel
what must true for Becky to be correct
Answer:
c) m <2 =m <3
Step-by-step explanation:
since the angles 2 and 3 are equal then they should be alternate angles
then c and d are parallel lines
What does -= mean in Python?
In Python an operator -= is subtracts the value on its right to the variable and assigns the result to the variable on its left.
As we know an operator is nothing but a symbol that represents a mathematical or logical process.
We know that in Python the operator -= provides a way to subtract a value to an existing variable and assign the new value back to the same variable.
If m -= n
This means, the variable m the left side is getting added to the value on the right side (n), and the result is then reassigned to the variable on the left.
i.e., m = m - n
-= is an assignment operator.
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Phyllis invested $10,500, a portion earning a simple interest rate of
3 1/2% per year and the rest earning a rate of 3% per year. After one year the total interest earned on these investments was $352. 50. How much money did she invest at each rate?
Please answer ASAP
The money invested by Phyllis with simple interest rate 3 1/2% and 3% per year is given by $7500 , and $3,000 respectively.
As given in the question,
Total amount with Phyllis is equal to $10,500
Let 'x' be the portion of Phyllis earning invested with 3 1/2% per year simple interest rate
Then $( 10,500 - x ) invested by Phyllis with simple interest rate 3% per year
Total interest earned by the investment = $352.50
0.035x + 0.03( 10,500 - x ) = $352.50
⇒0.035x + 315 - 0.03x = 352.50
⇒0.005x = 352.50 - 315
⇒0.005x = 37.5
⇒x = $7500
and $( 10,500 - x ) = $( 10,500 - 7500 )
= $ 3,000
Therefore, the amount of invested with simple interest rate 3 1/2% per year and 3% is equal to $7500 and $3,000 respectively.
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Help please
Work out
A) 4/5 of 30
B) 2/9 x 45
C) 24 x 1/6
Answer:
A) 24
B) 10
C) 4
Step-by-step explanation:
i multiplied for each question
Four students are in the final rounds of a chess tournament. Based on their chess rankings, Gloria is twice as likely as Devon to win. Devon is twice as likely as Janet to win. Janet is just as likely as Harry to win. Create a table of fractional probabilities of winning for the four-person sample space.
need pointz
Step-by-step explanation:
What is the 3 variable?
A three-variable system is a system of equations or inequalities involving three variables.
The three variables could refer to any three related quantities, such as a person's age, height, and weight. In a three-variable system, the number of equations is equal to the number of variables, so three equations are needed to solve the system. Each equation in the system will involve all three variables and will be solved through a combination of algebraic manipulation, substitution, and elimination techniques. Once all three equations have been solved, the values of the variables can be found.
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3 tenths and 24 hundredths, after regrouping, there are
3 tenths and 24 hundredths, after regrouping gives 0.54
What does Regroup Mean?In math, regrouping can be defined as the process of making groups of tens when carrying out operations like addition and subtraction with two-digit numbers or larger. To regroup means to rearrange groups in place value to carry out an operation. We use regrouping in subtraction, when digits in the minuend are smaller than the digits in the same place in the subtrahend.
Given here, 3 tenths and 24 hundredths after regrouping we get
(3 tenths + 24 hundreths) = 0.54
Hence, 3 tenths and 24 hundredths after regrouping gives 0.54
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Find three consecutive numbers such that the sum of twice the first, three times the second and four times the third togetherbmakes 191.
Answer:
find 3 consecutive numbers such that twice the first , 3 times the second and 4 times the third together make 191 ?
Let n-1,n and n+1 be three consecutive numbers.
Given
2(n-1)+3n+4(n+1)=191
2n-2+3n+4n+4=191
9n+2=191
9n = 189
n = 21
So, n-1=20 and n+1=22
So the answer is 20,21,22
[tex] \huge \bold{\color{red}{ANSWER}}[/tex]
[tex]\pmb { \orange{Given }:} \sf{ Three \: Consecutive \: numbers}[/tex]
[tex]\pmb{\orange{To find}: } \sf{Least \: of \: the \: numbers}[/tex]
[tex]\pmb{\orange{Solution}: }[/tex]
[tex]\sf{Let \: the \: three \: consecutive \: numbers \: be }[/tex]
[tex] \sf\red x, \red {x+1}, \red{x+2}[/tex]
[tex]\sf{Twice \: the \: number = 2\red x}[/tex]
[tex]\sf{3 \: times \: the \: Second \: number = 3(\red{ x+1})}[/tex]
[tex]\sf{4 \: times \: the \: third \: number= 4(\red {x+2})}[/tex]
☆ according to question
[tex] \pmb{2\red x + 3(\red{x+1})+4(\red{x+2})= 191}[/tex]
[tex] \pmb{2\red{x} + 3\red{x}+3+4\red{x}+8= 191}[/tex]
[tex] \pmb{9\red{x}=191-11 = 180}[/tex]
[tex] \pmb{\red{x}=20}[/tex]
[tex] \sf{∴the \: three \: Consecutive \: numbers \: are} [/tex]
[tex] \pmb{\pink{20}, \pink{21}, \pink{22}}[/tex]
_________________......
[tex] \purple{ \pmb{LearningLifeII}}[/tex]