We know, standard normal distribution is given by Z~N(0, 1) => σ=1Now, P(-0.62 P(Z P(u P(Z P(u) = 0.7392
Given, Random variable Z follows standard normal distribution. To find the value of u such that P(−0.62-0.62)Now, we will find the Z value for -0.62 using standard normal table as follows:-We get the value of P(Z<-0.62) as 0.2676Now, P(Z>-0.62)=1-P(Z<-0.62)=1-0.2676=0.7324Now, P(-Z<0.62)=P(Z<0.62)=0.7324We know, 0.62 lies between u=0 and u', we can find u' using standard normal table as follows:-From the standard normal table, we get that P(Z<0.62)=0.7315P(Z<0)=0.5Now, Z follows standard normal distribution, Z~N(0, 1) => 0.62=(u'-0)/1 => u'=0.62To find the value of u, let's use the formula Z = (X - μ) / σ where X is the observation, μ is the mean and σ is the standard deviation. We know, standard normal distribution is given by Z~N(0, 1) => σ=1Now, P(-0.62 P(Z P(u P(Z P(u) = 0.7392Now, using standard normal table, we get the value of Z when P(Z
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What is the most specific category this shape can be sorted into?
A Venn diagram titled Triangles. Inside the diagram are circles, there is one labeled Scalene and one labeled Isosceles. Inside the Isosceles circle is another circle labeled Equilateral. Below the diagram is a triangle with a single tick mark on each side.
Equilateral
Isosceles
Scalene
Triangle
Therefore, the most specific category this shape can be sorted into is "Triangle."
What would you say about a triangle?3 sides, 3 angles, and 3 vertices make up a closed triangle. It has only two dimensions. Triangles are a part of polygons as well.
The most specific category this shape can be sorted into is "Triangle."
In the given Venn diagram, the category "Triangle" represents the overall group of all types of triangles, which includes "Equilateral," "Isosceles," and "Scalene" triangles.
The triangle with a single tick mark on each side may represent any type of triangle that is not necessarily equilateral, isosceles, or scalene, but it is still a triangle.
Therefore, the most specific category this shape can be sorted into is "Triangle."
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A person invested $ 790 in an account growing at a rate allowing the money to double
every 13 years. How much money would be in the account after 30 years, to the
nearest dollar?
Answer:
Submit Answer
attempt i out of
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A doubling equation in exponential growth can be used to solve the question. The amount after 30 years will be $3911.22
The growth rate is governed by exponential equation. Doubling equation means to the time needed to make the initial amount double. If the number of years and doubling time given, then the doubling equation is,
P = P₀[tex](2)^{t/d}[/tex]
P is the final amount
P₀ is the initial amount
t is the time in years
d is the doubling time
P₀ = 790 t= 30 d= 13
P = 790 [tex](2)^{30/13}[/tex]
= 3911.21506157
So the amount after 30 years will be $3911.22
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The computer lab at school has a new computer system. The system had a total cost of $1895. There is a special printer that can be added to the system. The printer can be purchased separately for $649. Writ an equation and solve to determine the cost of the system with the printer.
There’s a spinner with 12 equal areas numbered one through 12 if the spinner is one one time what is the probability that the result is a multiple of five and a multiple of two
The probability that the result is a multiple of five and a multiple of two is 1/3, since there are only three multiples of five and two that can be produced on the spinner: 10, 6, and 2.
The spinner has 12 equal areas, numbered one through 12. The probability of getting a multiple of five and a multiple of two on one spin is 1/3, since there are only three multiples of five and two that can be produced: 10, 6, and 2. To calculate this probability, we need to look at the total number of possible outcomes and divide it by the number of outcomes that are multiples of five and a multiple of two. In this case, the total number of outcomes would be 12, and the number of outcomes that are multiples of five and a multiple of two is three (10, 6, and 2). Dividing 12 by 3 gives us the probability of 1/3.
Total number of outcomes = 12
Number of outcomes that are multiples of five and two = 3 (10, 6, and 2)
Probability = 3/12 = 1/3
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
12 units
Step-by-step explanation:
It’s the average distance to the ____ also measures how far is the data spread apart in the population.
*
It’s the average distance to the Mean also measures how far is the data spread apart in the population.
What is Population?
In statistics, a population refers to the entire group or set of individuals, objects, or events that share a common characteristic or feature. The population can be any size, from a small group of people to an entire country or even the whole world.
In order to make statistical inferences about a population, it is often not practical or feasible to study the entire population. Instead, researchers typically take a sample from the population, which is a smaller subset of the population, and use the sample data to make predictions or draw conclusions about the population as a whole.
The average distance to the mean (or average) also measures how far the data is spread apart in the population.
This is commonly known as the standard deviation, which is a measure of the amount of variation or dispersion in a set of data values. A larger standard deviation indicates a greater amount of variability or spread in the data, while a smaller standard deviation indicates that the data points are closer to the mean.
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In a sequence of numbers, a4=12, a5=14, a6=16, a7=18, and a8=20.
Which equation can be used to find the nth term of the sequence, an?
an=2n+12
an=3n+12
an=3n
an=2n+4
The correct equation to find the nth term of the given sequence is an=2n+12, which can be demonstrated by calculating the 4th to 8th terms and verifying that they match the given values.
The formula an=2n+12 can be used to find the nth term of the sequence. This formula states that the nth term is equal to twice the value of n (2n) plus 12 (2n + 12). To demonstrate, for the 4th term of the sequence (a4), we can use the formula and calculate a4 = 2(4) + 12 = 20, which is equal to the given value of a4 = 12. Similarly, we can calculate the other values of the sequence using the same formula: a5 = 2(5) + 12 = 22 (which is equal to the given value of a5 = 14), a6 = 2(6) + 12 = 24 (which is equal to the given value of a6 = 16), a7 = 2(7) + 12 = 26 (which is equal to the given value of a7 = 18), and a8 = 2(8) + 12 = 28 (which is equal to the given value of a8 = 20). Therefore, we can conclude that an=2n+12 is the correct equation to find the nth term of the sequence.
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Find the slope of the line that contains the points (10, 0) and (-20, -18)
The slope of the line that contains the points (10, 0) and (-20, -18) is: slope = (change in y)/(change in x) = 3/5.
The slope of a line is the measure of its steepness, and it's found by dividing the change in the y-coordinates by the change in the x-coordinates between two points on the line. In this case, the slope of the line that passes through the points (10, 0) and (-20, -18) can be calculated as follows:
slope = (change in y-coordinates) / (change in x-coordinates)
slope = (-18 - 0) / (-20 - 10)
slope = -18 / -30
slope = 3/5
Therefore, the slope of the line is 3/5.
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What are the domain and range for the function f(x)=2x?
The domain and range for the function f(x) = 2x include the following:
Domain = (-∞, ∞).
Range = (-∞, ∞).
What is a domain?In Mathematics, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-∞, ∞} or {x|x ∈ R}.
Range = {-∞, ∞} or {y|y ∈ R}.
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Solve for x to make A||B.
B
3x
A
X =
?
7x
Enter
Answer:
x = 18
Step-by-step explanation:
the angle vertically opposite 7x is 7x
making 3x and 7x same- side interior angles summing to 180° , that is
3x + 7x = 180
10x = 180 ( divide both sides by 10 )
x = 18
for A and B to be parallel then x = 18
solve 6x^2+1≥5x graphically
Answer:
[tex]x \leq \frac{1}{3}[/tex] or [tex]x \geq \frac{1}{2}[/tex]
Answer:
Below
Step-by-step explanation:
From the graph below you can see that
x < = .33 3 and x >= .5
combined
.333 ≥ x ≥ .5
Find the next term in the series.
240, 332, 118, 168, 57, 86, ? ,45
Answer:
32 or 24 or 13 or 21
Step-by-step explanation:
332-240=92
168-118 = 50
86-57 = 29
45-13= 32
or
45-21= 24
The answer to the question please
Answer:
2/9
Step-by-step explanation:
Answer:2/9
Step-by-step explanation:
PLEASE SHOW WORK!!!!!!!!!
1) The equal expressions are I and III
2) The value of the expression is 3 41/80
What is an absolute value expression?An absolute value expression is a mathematical expression that represents the distance of a number from zero, regardless of the sign of the number. The absolute value of a number is always positive, so an absolute value expression represents a positive number or zero.
The absolute value of a number x is denoted by |x| and is defined as follows:
|x| = x, if x is positive or zero
|x| = -x, if x is negative
Since -/x/ = -x then this are the equal expressions.
[tex]a^2/a + 1 + a + 1/a^2[/tex]
Then;
[tex]4^2/4 + 1 + 4 +1/4^2[/tex]
16/5 + 5/16
= 3 41/80
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i have to use the information given to create an equation then create a table to find points to graph the expressions.
Answer:
A) Missing Table Values. See the attached worksheet
B) The car will be worth less than $8,000 in 9.8 years
Step-by-step explanation:
Part B: Years until car is less than $8,000
The new $25,000 car depreciates by 11% each year. Expressed another way, it retains 89% of its value each year. The value, y, after x years can be calculated from:
y = ($25,000)*(0.89)^x
This function is graphed on the attached worksheet. The line intersets the $800 on the y axis at 9.8 years. The car will be worth less than $8,000 after 9.8 years.
One can also calculate the value of x:
$,8000 = ($25,000)*(0.89)^x
x = 9.77, mathematically
Part A: Table of values
See the attached worksheet. The values are not exactly a straight line, but come close to f(x) = 8x+50, from which the missing values may be calculated. Legally, however, this is a slightly more complex line, for which I'm unclear about the best approach for its derivation.
You and a friend play a game where you each toss a balanced coin. If the upper faces on the coins are both tails, you win $1; if the faces are both heads, you win $2; if one shows a head and the other a tail, you lose $1.a) Give the probability distribution for X=your winnings on a single play of this game.b) What are your expected winnings?c) Suppose you change the rules so that if both coins are heads you win $100; if both coins are tails you win $5; if the coins do not match, you lose $52. What are your expected winnings?d) Find Var(X) for both games.e) Which game would you rather play? (Use the variance to help make this decision).
According to the probability distribution, you should rather play the second game than the first one.
a) The probability distribution for your winnings on a single play of this game is given by:
P(X=1) = 1/4
P(X=2) = 1/4
P(X=-1) = 1/2
b) Your expected winnings in this game is 0, since the expected value of X = 1*(1/4) + 2*(1/4) - 1*(1/2) = 0.
c) The probability distribution for your winnings in this game is given by:
P(X=100) = 1/4
P(X=5) = 1/4
P(X=-52) = 1/2
d) Your expected winnings in this game is 22, since the expected value of X = 100*(1/4) + 5*(1/4) - 52*(1/2) = 22.
e) The variance of X for the first game is
Var(X) = (1-0)2*(1/4) + (2-0)2*(1/4) + (-1-0)2*(1/2) = 0.75.
The variance of X for the second game is Var(X) = (100-22)2*(1/4) + (5-22)2*(1/4) + (-52-22)2*(1/2) = 1344.5.
You would rather play the second game, since its variance is much larger, which means there is a greater potential for large gains.
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point) Use the quadratic formula to solve thequadratic equation2x²−3x−5=0Solutions (separate by commas): x=
The solution to the quadratic equation 2x²−3x−5=0 are x=5/2 or x=-1/2
The quadratic formula can be used to solve the quadratic equation 2x²−3x−5=0. Here’s how to do it:
First, identify the coefficients of the equation. In this case, a=2, b=-3, and c=-5.
Next, plug these values into the quadratic formula: x = (-b ± √(b²-4ac)) / 2a,Substitute the values in the equation: x = (-(-3) ± √((-3)²-4(2)(-5))) / 2(2)
Simplify the equation to get:x = (3 ± √(9+40)) / 4,
x = (3 ± √49) / 4
x = (3 + 7) / 4 or x = (3 - 7) / 4
x = 5/2 or x = -1/2
In summary, the quadratic formula can be used to solve quadratic equations with ease. It is important to know the values of the coefficients of the equation and substitute them into the quadratic formula. The formula will simplify the equation and give the solutions.
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Please I need help with quiz corrections should be easy if you are good at geometry!!
A right triangle, also known as a right-angled triangle, is a triangle that has one angle measuring 90 degrees.
What is a right angle triangle?Right triangles have some unique properties that make them useful in various applications, such as in geometry and trigonometry. For example, the Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
We know that;
Tan 45 = 14/x
x = 14
Sin 45 = 14/y
y = 20
Again;
Tan 60 = 16√3/x
x = 16√3 * 1/√3
x = 16
Sin 60 = 16√3/y
y = 16√3 ^ 2/√3
y = 32
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cory and quentin went bowling on friday night corey has his own bowling shoes but quentin had to rent his at the alley shoes rent for a flat fee of $4 plus $2 per hour the equation y=2x+4 describes the cost of renting the shoes if quentin only had $11 how many hours can he rent the bowling shoes.
Therefore , the solution of the given problem of equation comes out to be he can hire the shoes for three hours with his meagre $11 budget.
Equation : What is it?Complex algorithms frequently employ a variable term to guarantee congruence with the two opposing assertions. Equations, which are academic expressions, are used to demonstrate the equality of different academic figures. In this instance, the normalise method provides b + 6 rather than merely expression separating 12 into two pieces for using the data from y + 6.
Here,
To begin, we can construct an expression to symbolise the circumstance:
=> y = 2x + 4
where x represents the number of hours that Quentin rents the shoes for and y represents the overall cost of the rental.
We can put y equal to 11 because we know that Quentin only has $11 to spend:
=> 11 = 2x + 4
We can now determine x:
=> 2x = 11 - 4
=> 2x = 7
=> x = 7/2
Quentin can therefore spend $11 to hire the shoes for 3.5 hours (7/2 hours).
He would have to pay either $10 or $12 to hire the shoes for either three or four hours. He can hire the shoes for three hours with his meagre $11 budget.
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Yall PLease help with this one.
Answer:
i think 4<6
Step-by-step explanation:
Answer:
=
Step-by-step explanation:
5j543nn al
the population of a community is known to increase at a rate proportional to the number of people present at time t. if an initial population p0 has doubled in 4 years, how long will it take to triple? (round your answer to one decimal place.) 4.8 incorrect: your answer is incorrect. yr how long will it take to quadruple? (round your answer to one decimal place.)
The population will take around 6.9 years to triple and 9.2 years to quadruple.
Let P(t) be the population at time t. According to the problem, the rate of increase of the population is proportional to the population itself, which means: dP/dt = kP
where k is the proportionality constant. This is a separable differential equation that can be solved by separating the variables and integrating both sides:
∫ dP/P = ∫ k dt
ln|P| = kt + C
where C is the constant of integration. Applying the initial condition that the population doubles in 4 years, we get:
ln|2p0| = k(4) + C
ln|p0| + ln|2| = 4k + C
ln|p0| + ln|2| - 4k = C
Substituting C into the previous equation and using it for the new population level, we get:
ln|3p0| = kt + ln|p0| + ln|2| - 4k
ln|3p0|/|p0| = kt - 4k + ln|2|
ln|3/2| = (k/ln2)t - 4k/ln2
ln|3/2|/(k/ln2) = t - 4/ln2
t = ln|3/2|/(k/ln2) + 4/ln2
Therefore, it will take approximately 6.9 years for the population to triple and 9.2 years to quadruple.
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Write the following as a radical expression.
7^{\frac{7}{8}}
Answer: $\sqrt[8]{7^7}$
Step-by-step explanation:
trust me and use tutorly.ai
Express sin A as a fraction in simplest terms.
Answer:
7/25
Step-by-step explanation:
Sin = [tex]\frac{opposite}{Hypotenuse}[/tex]
Hypotenuse = 50
Adjacent = 48
Pythagorean Theorem: a² + b² = c²
48² + b² = 50²
2304 + b² = 2500
b² = 196
b = 14
Opposite = 14
Sin A = 14/50 = 7/25
Is enough information given to prove that GHF =KHJ using the SAS Congruence Theorem? yes no If yes, complete the two-column proof. If no, complete only the last line with an explanation of why no
No, because the SAS Congruence Theorem requires two pairs of congruent sides and one congruent angle.
No, because the SAS Congruence Theorem requires two pairs of congruent sides and one congruent angle. To use the SAS Congruence Theorem to prove that GHF =KHJ, it would be necessary to have information about the lengths of the corresponding sides and the measure of the included angle in each triangle. Without this information, it is not possible to prove that GHF =KHJ using the SAS Congruence Theorem. To prove that GHF =KHJ using this theorem, it would be necessary to show that the two sides GK and KH are congruent, the two sides HF and HJ are congruent, and the included angle GHF is congruent to the included angle KHJ.
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Write an equation of the line that passes through the points. 13. (2,5), (0,5) 14. (-3,0), (0,0) 15. (0,-2), (4,-2)
The line that goes through the points (0, -2) and (4, -2) can be represented by the equation y = (-1/2)x - 2.
Since both points have the same y-coordinate of 5, the line must be a horizontal line passing through y = 5. Therefore, the equation of the line is y = 5.
Since both points have the same y-coordinate of 0, the line must also be a horizontal line passing through y = 0. Therefore, the equation of the line is y = 0.
The slope of the line passing through the two points can be found using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Substituting the given values, we get:
m = (-2 - 0) / (4 - 0) = -1/2
Using the point-slope form of the equation of a line, we can write the equation of the line as:
y - y₁ = m(x - x₁)
Substituting one of the given points, such as (0, -2), we get:
y - (-2) = (-1/2)(x - 0)
Simplifying, we get:
y + 2 = (-1/2)x
Therefore, the equation of the line passing through the points (0, -2) and (4, -2) is y = (-1/2)x - 2.
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The equations of four lines are given. Identify which lines are parallel.
Line 1:
y = 8x - 3
Line 2: y-6=(x-4)
Line 3:
Line 4:
y = 3x + 4
1
x - 3y = -4
O All four lines are parallel.
O Lines 3 and 4 are parallel.
O Lines 1 and 3 are parallel.
O Lines 2 and 3 are parallel.
►
For the given equations, using slope formula option B: Lines 3 and 4 are parallel, is the correct option.
What is slope?
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
The four different equations are given.
To identify parallel lines, we need to compare their slopes.
If two lines have the same slope, they are parallel.
Line 1 is in slope-intercept form (y = mx + b) where the slope is m = 8.
Line 2 is in point-slope form (y - y1 = m(x - x1)) where the slope is m = 1/8.
Line 3 is in slope-intercept form where the slope is m = 3.
Line 4 is in slope-intercept form where the slope is m = 1/3.
Comparing the slopes, we see that -
Lines 1 and 2 have different slopes, so they are not parallel.
Lines 1 and 3 have different slopes, so they are not parallel.
Lines 1 and 4 have different slopes, so they are not parallel.
Lines 2 and 3 have different slopes, so they are not parallel.
Lines 2 and 4 have different slopes, so they are not parallel.
Lines 3 and 4 have the same slope (m = 3), so they are parallel.
Therefore, lines 3 and 4 are parallel.
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work out the value of 7a - 7b
when a-b=5
Answer:
35
Step-by-step explanation:
Simplification :
7(a-b) as 7 is common
as we know a-b is 5 ,
7 * 5 = 35 in the answer.
Please mark me as the brainliest TQ!
Answer: 35
Step-by-step explanation:
7a - 7b
= 7(a-b)
= 7(5)
= 35
Look at this table:
Write a linear (y=mx+b), quadratic (y=ax2), or exponential (y=a(b)x) function that models the data.
x y
–
1 1
0 3
1 9
2 27
3 81
We may state with confidence that the exponential function y = [tex]3(3^{x} )[/tex]models the provided data because both of these values agree with the data.
How is exponential function determined?
Since the output values (y) increase by a factor of three every time the input value (x) increases by one, the data demonstrate exponential growth. As a result, we can use an exponential function of the form y = a(b)x to represent this data.
We can utilise the first two data points to determine the values of a and b.
With y = 3 and x = 0, we get:
3 = [tex]a(b^{0} )[/tex]
3 = a
With x=1 and y=9, we get:
9 = [tex]a(b^{x} )[/tex]
b = 3
Hence, y = [tex]3(3^{x} )[/tex] is the exponential function that represents the data.
We may substitute the other input values and compare them to the appropriate output values to validate this model:
If x = 2, then y = [tex]3(3^{2} )[/tex] = 27.
If x = 3, then y = [tex]3(3^{3} )[/tex] = 81.
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Help me plsssssssssssssssssssss
Answer:
157°
Step-by-step explanation:
We can see that the angle here is an alternate angle, this means it is an opposite angle that has the same value as each other.
Knowing this, we can see that if the angles are alternated the missing angle should be 157 as well.
Hope this helps have a lovely day! :)
A _______ is an educated guess based on patterns in data figures
A. deductive
B. inductive
C. postulate
D. conjecture
E. counter example
F. converse
Answer:
B. inductive
Step-by-step explanation:
An inductive reasoning process involves making a generalization based on specific observations. In the case of the given question, the statement is: "A _______ is an educated guess based on patterns in data figures."
To use inductive reasoning to find the answer, we can follow these steps:
Look for patterns in the data figures. Identify the commonalities between different examples of educated guesses.
Based on these patterns, make an initial generalization about what the blank might be. For example, if we notice that all educated guesses involve making a prediction based on previous observations, we might guess that the missing word is "conjecture."
Test the generalization by looking at additional examples. Do these examples fit the pattern we identified earlier? If so, our initial guess might be correct. If not, we might need to revise our generalization or consider other options.
Continue testing and refining the generalization until we feel confident that it accurately describes the relationship between the given words.
In this case, using inductive reasoning, we can make an educated guess that the missing word is "conjecture," as it fits the pattern of being an educated guess based on patterns in data figures.