E(Y|X) is the conditional expectation of Y given X. We can use the law of iterated expectations to show that E(u) = 0.
This law states that E(E(X|Y)) = E(X). Therefore, E(u) = E(Y - E(Y|X)) = E(Y) - E(E(Y|X)) = E(Y) - E(Y) = 0.
b. We can use the law of iterated expectations again to show that E(uX) = 0. This law states that E(E(XY|Z)) = E(X)E(Y|Z). Therefore, E(uX) = E(YX - E(YX|X)) = E(YX) - E(E(YX|X)) = E(YX) - E(Y)E(X) = 0.
c. Let Ỹ = g(x) denote a different prediction of Y using X and let v = Y - Ỹ denote its error. We can use the equation h(X) = g(x) - E(Y|X), so that v = [Y - E(Y|X)] - h(X). Using this equation, we can derive E(v2) = E[(Y - E(Y|X))2] - 2E[(Y - E(Y|X))h(X)] + E[h(X)2]. Since E(Y - E(Y|X)) = 0, this reduces to E(v2) = E[h(X)2] < E[(Y - Ỹ)2], which shows that E[(Y - Ỹ)?] > E[(Y - Ỹ)2].
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Select the correct answer.
Solve the equation for x in terms of c.
(cx + 1) == //
O A.
OB.
O C.
O D.
x =
X=
x =
x =
4c
27
8c
29
18c
29
8c
The equation for x in terms of c is x = 29/8c (D).
From the case we have the equation of:
[tex]\frac{2}{3}(cx + \frac{1}{2})-\frac{1}{4}=\frac{5}{2}[/tex]
We will use distribution to isolate x on the left side and all terms of c from others on the right side.
2cx + 2 - 1 = 5
3 6 4 2
We will use the lowest common multiple to eliminate the numerator:
2cx + 2 - 1 = 5
3 6 4 2
--------------------------- x 12 --> lowest common multiple
8cx + 4 - 3 = 30
8cx + 1 = 30
8cx = 29
x = 29/8c
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g) h) i) 2x. x w/f X + < 5 3 2 a+20 3a + 2 3 3x+2 12 2 3 4x-1 1/4-x)
The answer to the equation X + 5 3 2 a + 20 3 a + 2 3 3x + 2 12 2 3 4x-1 1/4-x is [tex]33 x-\frac{1}{4}$$[/tex] .
What is the basic rule for solving any equation?Simplify [tex]$34 x-1 \cdot \frac{1}{4}-x: \quad 33 x-\frac{1}{4}$[/tex]
[tex]$$34 x-1 \cdot \frac{1}{4}-x$$[/tex]
like phrases together
[tex]$$=34 x-x-1 \cdot \frac{1}{4}$$[/tex]
Add comparable elements: [tex]34 x-x=33 x$[/tex]
[tex]$$=33 x-1 \cdot \frac{1}{4}$$[/tex]
Multiply: [tex]$1 \cdot \frac{1}{4}=\frac{1}{4}$[/tex]
[tex]=33 x-\frac{1}{4}$$[/tex]
Both the addition rule and the multiplication/division rule are introduced to us in algebra 1 as the two rules for solving equations. According to the equation addition rule, an equation's solution set can be changed by adding the same amount to either side of an equation without doing so.
Identification, prioritisation, and selection of potential solutions are all steps in the process of problem solving, which also involves characterising the issue at hand, figuring out its root cause, and putting a plan of action into action. Algebraic Golden Rule: "Do unto one side of the equal sign as you will unto the other."
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4y squared - 3y squared
Answer:
y²
Step-by-step explanation:
4y² - 3y² = (4 - 3) × y² = 1y² = y²
jim holzman at ace ticket has a few premium seats in the front row. he would like to find out how much extra he can charge for those tickets, relative to identical seats right behind in the second row. to do so, he decided to run a survey.
The price difference, which can then be used to determine the extra he can charge for the front row tickets.
To calculate the price difference between the front row and second row tickets, Jim should first identify the mean price of the second row tickets, P2. He can then compare the mean price of the second row tickets to the mean price of the front row tickets, P1. He can then calculate the price difference between the two rows by subtracting the mean price of the second row tickets from the mean price of the first row tickets, (P1-P2). This will give him the price difference, which can then be used to determine the extra he can charge for the front row tickets.
For example, if the mean price of the second row tickets, P2, is $15 and the mean price of the first row tickets, P1, is $20, then the price difference would be $5, meaning he can charge an extra $5 for the front row tickets.
Formula: Price Difference = P1 - P2
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Salim has a flock of 300 chickens, 15% of which are infected with a virus. He plans on taking an SRS of 7 chickens to test for the virus. Which of the following would find the probability that exactly 4 of the 7 chickens sampled have the virus? Choose 1 answer: (0) (0.15)*(0.85) © ()(0.15)*(0.85) (390) (0.1 (0.15)*(0.85) (0.15) (0.85) (0.15)*(0.85)
The probability of exactly 4 of the 7 hens contracting the disease is ⁷C₄(0.15)⁴(0.85)³.. The ideal response is (A).
How can the binomial distribution be used to calculate probability?
The binomial theorem, which can be expressed as (a + b)n = nC0anb0 + nC1an1b1 + nC2an2b2 +....+ nCna0bn, is the foundation of the binomial distribution.Events must be independent of one another and have probabilities that add up to 1 in order for the probability to be used.
Due to that,There is a 15% chance that the chicken will be affected it is spelled as as,
15% P(infected)
= 15/100
= 0.15
Consequently, the likelihood of avoiding diseased chicken is,
P(not contaminated) = 1 - 0.15= 0.85
Seven chickens in all will be used for the test.
Now, the binomial distribution may be used to determine the likelihood of having exactly 4 sick chickens.
nCxpxqnx is a general expression for the binomial distribution.
n = 7 and x = 4 for the case where p = P(infected) and q = P(not infected) are given
Consequently, the likelihood is given as,
P = 7C4(0.15)4(0.85)3 (Exact 4 are infected).
Therefore, the likelihood that the virus infects precisely 4 out of the 7 chickens sampled is ⁷C₄(0.15)⁴(0.85)³.
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Then Venn diagram shows sets shade (A n B) ‘U C’
The diagram of the required shaded region of the Venn representing the set of elements (A ∩ B)' ∪ C, created with MS Word, is attached.
What is a Venn diagram?A Venn diagram consists of circles or curved enclosures, representing sets, located in a universal set which is a rectangle.
The sdets shown in the Venn diagram = Set A, Set B, and Set C
The required region to be shaded in the Venn diagram = (A ∩ B)' ∪ C'
A ∩ B (A intersection B) is the set of elements common to both Set A and Set B
(A ∩ B)' (A intersection B) complement is the set of all elements which are not in the set of elements common to both Set A and Set B
(A ∩ B)' ∪ C (A intersection B) comliment union C; The set of elements not in the intersection of Set A and Set B, but contains the elements in Set C
(A ∩ B)' ∪ C' (A intersection B) comliment union C complement; The set of elements not in the intersection of Set A and Set B, but includes elements in the universal set, excluding all elements in the Set C.
The required shaded region is; A ∩ (B ∪ C)', B ∩ (A ∪ C)' and (A ∪ B ∪ C)'
Please find attached the diagram of the Venn diagram, created with MS Word, with the shaded region representing (A ∩ B)' ∪ C'
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In each of the following scenarios, state what type of distribution should be used to model the response Y: Binomal, Multinomial, Poisson, or Normal. a. The response is if an employed person commutes more than 10 minutes to work. b. The response is how many days a week an employed person commutes more than 10 minutes to work c. The response is how many minutes a week a student studies. d. The response is what blood type a subject is (A,B,AB, or O)
A. Binomial distribution. B. Poisson distribution. C. Normal distribution. D. Multinomial distribution. is the types of distribution as given in the conditon below.
A binomial distribution should be utilized since the answer—whether or not an employed person commutes more than 10 minutes to work—is a yes or no question.
B. The answer is the percentage of days a week on which a working person travels more than 10 minutes to go to work. The Poisson distribution should be utilized since the number of days is a count variable and the mean number of days does not always equal the variance.
C. The answer is the number of minutes a student studies each week. Since the number of study minutes is a continuous variable with an equal mean and variance, the normal distribution should be applied.
D. The answer is the subject's blood type (A,B,AB, or O). Given that there are four alternative outcomes for blood type, multinomial distribution should be employed.
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A 1.25” diameter shaft is being stretched by a load of 39,000 lb. Calculate the stress on the part.
I got 31784.84108 psi
is this correct?
It has a diameter of 1.25 inches and yield stress of 63,000 psi. Find the variable component stress.
Calculate the stress at the component?alternative the fee of weight for pressure in the formula for stress, σ = F/A, wherein F is the force and A is the vicinity of go-phase.
In easy phrases we can define pressure because the pressure of resistance per unit area, provided by means of a frame against deformation. strain is the ratio of force over area (S =R/A, in which S is the strain, R is the inner resisting force and A is the move-sectional location).
while the forces acting on the frame are trying to squash it's far compression. The method underneath is used to calculate the pressure: strain =force/ cross-sectional location. σ= F/A.
If we are about to layout a beam or a member. We need strain fee to evaluate with extraordinary pass-sectional shapes and distinct material homes to reach at a feasible section.”
Therefore, It has a diameter of 1.25 inches and yield stress of 63,000 psi.
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find the smallest positive real number $c,$ such that for all nonnegative real numbers $x$ and $y,$ \[\sqrt{xy} c |x - y| \ge \frac{x y}{2}.\]
The smallest positive real number c that satisfies the above inequality is [tex]$c = \frac{2}{\sqrt{xy}}[/tex]
We can rewrite the inequality as [tex]$\sqrt{xy} c \ge \frac{2}{|x - y|}$[/tex]. To make the inequality hold for all nonnegative real numbers x and y, we need c to be minimized. We can do this by taking the reciprocal of the right side of the inequality, giving us [tex]$\sqrt{xy} c \ge \frac{2}{|x - y|}$[/tex]. The smallest positive value that c can take is[tex]$\frac{2}{\sqrt{xy}}$[/tex].
We can rewrite the inequality as [tex]$\sqrt{xy} c \ge \frac{2}{|x - y|}$[/tex]. To make the inequality hold for all nonnegative real numbers x and y, we need c to be minimized.
We can do this by taking the reciprocal of the right side of the inequality, giving us [tex]$c \ge \frac{2}{\sqrt{xy}|x - y|}$[/tex]. The smallest positive value that c can take is [tex]$\frac{2}{\sqrt{xy}}$[/tex].
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consider the following function f(x) 6x2 x3 find f' (x) f' (x) ~3x2 + 12x find the equation of the tangent line to the given curve at the point (1, 5). y =
The equation of the tangent line to the given curve at the point (1, 5) is y = 15x – 10.
The given function is f(x) = 6x2 - x3.
We need to find the equation of the tangent line to the given curve at the point (1, 5).
To find the equation of the tangent line, we need to find the slope of the tangent line. The slope of the tangent line is given by the derivative of the curve at the given point.
The derivative of the given curve is f' (x) = 3x2 + 12x.
Substituting the value of x as 1, we get the slope of the tangent line at (1, 5) as f' (1) = 3(1)2 + 12(1) = 15.
Therefore, the equation of the tangent line at (1, 5) is given by y – 5 = 15(x – 1).
This can be simplified to y = 15x – 10.
Hence, the equation of the tangent line to the given curve at the point (1, 5) is y = 15x – 10.
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pairs in the form (h,g), where h is the
number of hours driven and g is the gallons of
gas left.
Katie after 1 hour of driving, he had 6.75 gallons of gas. Also, after 6 hours of driving, she had 1.5 gallons left.
What is linear equation?An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Ax+By=C represents a two-variable linear equation in its standard form. As an illustration, the conventional form of the linear equation 2x+3y=5 It is rather simple to locate both intercepts when an equation is stated in this way (x and y).
We can write these values as coordinate points, on the form:
As a result, the sentence: "After an hour of driving, Katie had $6.75 worth of gas." can be seen as the following:
(1,6.75)
And: "After 6 hours of driving, there was only 1.5 gallons left" will have the point:
(6,1.5)$
Part B
With this in mind, we can find the slope of a linear function that passes through those two points. Then,
[tex]$m=\frac{y_2-y_1}{x_2-x_1}=\frac{1.5-6.75}{6-1}=\frac{-5.25}{5}=-1.05$[/tex]
Thus, the slope is -1.05.
Part C
Now, we will write a linear equation that relates[tex]$\mathrm{g}$[/tex] and[tex]$\mathrm{h}$[/tex]. As we already have the slope, we can use it to find the y-intercept as:
[tex]$$y=m x+b$$[/tex]
[tex]$g=m h+b$[/tex]Writing it with the variable[tex]s $\mathrm{g}$[/tex]and [tex]$\mathrm{h}$[/tex].
[tex]$$1.5=(-1.05)(6)+b$$[/tex]
[tex]1.5+6.3=b \\[/tex]
7.8=b
This means that an equation for g in terms of h is given by:
[tex]$$g=-1.05 h+7.8$$[/tex]
Part D
For this portion, we will apply the linear equation we discovered for calculating how much gas she will still have after a three-hour drive. Thus, h will have a value of 3, and we replace on the function to get the following result:
[tex]g=-1.05(3)+7.8 \\[/tex]
=-3.15+7.8
=4.65
This means that Katie will have 4.65 gallons left after driving for 3 hours.
The complete question is,
Katie noticed that after 1 hour of driving, she had 6.75 gallons of gas. After 6 hours of driving, there was only 1.5 gallons left. (Hint: Leave your answers as decimals). A.) Represent the information as two coordinate pairs in the form of (h, g), where h is the number of hours driven and g is the gallon of gas left. B.) Calculate the slope between the two coordinates. C.) Assuming the relationship between h and g is linear, create an equation for g in terms of h. D.) How much gas would she have left after dving for 3 hours?
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Ms. Morales bought the kiddie pool shown below for her children. A diagram of a kiddie pool is shown. The height of the pool is labeled twelve inches. A line drawn under the pool from one side of the pool to the other is labeled fifty-four inches.
If she filled the pool 3/4 of the way with water, how much water did Ms. Morales put in the pool in terms of π?
A) 5,832π in.^3
B) 6,561π in.^3
C) 7,776π in.^3
D) 8,748π in.3
The water volume in the kiddie pool is 6561π [tex]in^{3}[/tex], the correct answer is B. 6561π [tex]in^{3}[/tex].
The volume can be found by using cylinder volume formula V = π[tex].r^{2}.h[/tex]
Find the height of the waterSo, the kiddie pool has 6561π [tex]in^{3}[/tex] of water.
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A cash bix of$1 and $5 bills is worth $45. The number of $1 bills is three more than the number of $5 bills. Hiw many each bill does it contain?
Answer:
10 $1 bills
7 $5 bills
Step-by-step explanation:
Let s = number of $1 bills.
Let f = number of $5 bills.
1s + 5f = 45
s = f + 3
f + 3 + 5f = 45
6f = 42
f = 7
s = f + 3 = 7 + 3 = 10
10 $1 bills
7 $5 bills
Directions: solve for x round to the nearest tenth
To solve for x in this problem, we need to use the Law of Cosines.
Solve for x round to the nearest tenth?This law states that in any triangle, the sum of the squares of the lengths of the two sides is equal to the square of the length of the third side.In this case, we have two sides, AB and BC, and we need to find the measure of angle A.We can set up the equation as follows:
a² = b² + c² - 2bc cos(x)
We can substitute the values for a, b, and c, which are 22, 10, and 10 respectively. This gives us the equation:
22² = 10² + 10² - 2(10)(10) cos(x)
Simplifying the equation gives us:
484 = 200 - 200cos(x)
Therefore,
200cos(x) = 284
We can divide both sides by 200 to get cos(x) = 1.42.
We can take the inverse cosine of both sides to get x = 54.15°.
Rounding to the nearest tenth, x = 54.
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What solid will this lesson focus on?A- rectangular solidB- coneC- regular square pyramidD- triangular prism
Solid will this lesson focus on the regular square pyramid
Regular square pyramid.
The justification is stated below:
Four triangular faces, five vertices, and eight edges make up the typical square pyramid's square base. The main formulae for a square pyramid are volume and surface area.
By definition, a regular square pyramid is one that has a base that is square, meaning that each of its sides is the same length.
Because it has an apex, a height, lateral faces that are congruent isosceles triangles, and slant height, you can tell that it is a pyramid (the altitude of the lateral faces).
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Write an equation in the form y = a(x-r)(x-s) to represent the parabola shown.
The equation in the form y = a(x-r)(x-s) to represent the parabola is d. y = -4(x-2)(x-2).
What is the parabola?
The parabola is a smooth curve without any sharp points. It has a minimum value of a turning point called the vertex. As we can see the minimum value of this parabola is at zero, zero. That is this parabola exists only above the origin. The parabola is symmetrical about a central line called the axis of symmetry.
To represent the parabola shown in the form y = a(x-r)(x-s), we need to first identify the vertex and the axis of symmetry of the parabola.
The vertex of the parabola is (4,-4) and the axis of symmetry is x = 4.
Given that the vertex form of the parabola is y = a(x-h)² + k where (h,k) is the vertex.
Therefore, substituting the values we get:
y = a(x-4)² -4
Now, we need to find the value of a which will give us the same parabola.
If we look at the parabola, we can see that the y-coordinate of the vertex is -4 and the x-coordinate is 4.
So we substitute these values into the equation to get:
-4 = a(4-4)² -4
Solving this equation gives us a = -1
So the equation that represents the parabola is:
y = -1(x-4)² -4
which is the same as y = -1(x-4)(x-4)
thus the correct answer is d. y=-4(x-2)(x-2)
Hence, The equation in the form y = a(x-r)(x-s) to represent the parabola is d. y = -4(x-2)(x-2).
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evaluate f(-x)=x/x2+1
To evaluate f(-x) when f(x) = x/(x^2 + 1), we need to substitute -x for x in the function.
So f(-x) = (-x)/((-x)^2 + 1)
Simplifying the denominator we get:
f(-x) = (-x)/(x^2 + 1)
The function f(-x) is equivalent to the function f(x) with the x-value negated. The value of the function f(-x) is the same as the value of the function f(x) but with the x-value negated.
It's important to note that we can also express this as f(-x) = -f(x)
So the value of f(-x) is x/(x^2 + 1) with the x-value negated.
A podcast host is curious how her listeners like the show. She decides to poll the next 100 listeners who send her fan emails. 80 out of 90 listeners polled said they liked it. The result may lead to
-volunteer vias
-response bias
-selection bias -non response bias
The probability result may lead to selection bias, as the podcast host is only polling her next 100 fans who send emails, and not all of her listeners.
The podcast host is polling the next 100 listeners who send her fan emails in order to find out how they like the show. The results of the poll show that 80 out of 90 listeners polled said they liked it. This result may lead to selection bias, as the podcast host is only polling her next 100 fans who send emails, and not all of her listeners. This means that the results of the poll may not be reflective of the opinion of all of the podcast host's listeners. Furthermore, the results may be influenced by the volunteer bias, as the respondents may have volunteered to take part in the poll because they already liked the show and wanted to show their support. Additionally, the results may be affected by non-response bias, as those who chose not to take part in the poll may have different opinions than those who did.
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Boris is making iced tea. He has a container that has a volume of 7.6 dm3 to hold the iced tea. Find how many kiloliters of iced tea will completely fill the container. Use the table of conversion facts, as needed.
The capacity of the container is equal to 7.6 × 10⁻³ kiloliters.
How many kiloliters are required to fill a container?
This is a unit conversion question, in which we need to determine how many kiloliters are equivalent to the capacity of a container.
According to capacity tables, a cubic decimeter or 1000 cubic centimeters equals a liter. Then, we can determine the number of kiloliters by using the following cross multiplication:
x = 7.6 dm³ × (1 L / 1 dm³) × (1 kL / 1000 L)
x = 7.6 × 10⁻³ kL
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A 10 foot vertical post cast a 2 foot shadow at the same time a nearby cellphone tower cast a 116 foot shadow. How tall is the cell phone
Answer:23.2
Step-by-step explanation:
10/2=5
10/5=2
116/5=23.2
Answer:
580 ft.
Step-by-step explanation:
The height of the cellphone tower can be found using the following proportion:
(shadow of cellphone tower) / (shadow of 10 foot post) = (height of cellphone tower) / (10 feet)
Solving for the height of the cellphone tower:
(116 feet) / (2 feet) = (height of cellphone tower) / (10 feet)
Which brings us to:
116 ÷ 2 = x ÷ 10
58 = x ÷ 10
580 = x
The cell phone tower is 580 ft.
Consider the sampling distribution of a sample ed toward the o th m an obtained by random sampling from an infinite population. This e me that is highly skewed toward the larger values. a. How is the mean of the sampling distribution related to the mean of the population? b. How is the standa rd deviation of the sampling distribution related to the standard deviation of the population? c. How is the shape of the sampling distribution affected by the sample size?
The mean of the sampling distribution is related to the mean of the population, the standard deviation of the sampling distribution is related to the standard deviation of the population and the shape of the sampling distribution is affected by the sample size.
a. The mean of the sampling distribution is related to the mean of the population. The mean of the sampling distribution is an estimate of the population mean and is usually denoted by x⁻. The mean of the sampling distribution is expected to be close to the population mean, as the sample size increases. However, if the sample size is small, there will be more variation in the sample means and the sample mean will not be an accurate estimate of the population mean.
b. The standard deviation of the sampling distribution is related to the standard deviation of the population. The standard deviation of the sampling distribution is an estimate of the population standard deviation and is usually denoted by s. The standard deviation of the sampling distribution is expected to be smaller than the population standard deviation, as the sample size increases. The standard deviation of the sampling distribution is also affected by the sample size, it decreases as sample size increases.
c. The shape of the sampling distribution is affected by the sample size. As the sample size increases, the shape of the sampling distribution becomes more normal and less skewed, regardless of the shape of the population. The larger the sample size, the less spread in the sample means and more likely that the sample mean will be close to the population mean.
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If it took Rachel and David 10 minutes to play a game of checkers, and they started playing at 2:25 P.M., at what time did they finish playing the game?
Answer:
2:35
Step-by-step explanation:
you are gust adding so 25 +10 = 35
About how fast was the car traveling at t = 10 seconds? At t = 20? At t = 30?
Answer:
Step-by-step explanation:
I'm sorry, I am missing more information to calculate the speed of the car at t = 10 seconds, t = 20 and t = 30. The speed of the car depends on the mathematical function that describes the position of the car in time. Without the knowledge of that function, I'm not able to determine the car's speed at different points in time.
convert 549999549999 to a decimal. responses a .549.5 49 b .549.549 c 5.4955. 495 d .549
In decimal form, 549/999 is expressed as.549, which repeats.
Why do we use decimals?
One of the number types in algebra that has a whole integer and a fractional portion separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5.
Divide 549 by 999 to get the decimal equivalent of 549/999.
The solution is.549549.
Over the repeated numerals is a bar.
In decimal form, 549/999 is expressed as.549, which repeats.
In decimal form, 549/999 is expressed as.549, which repeats.
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Multiple Choice. 4. A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. Which of the following would result in the smallest margin of error in estimating the mean salt content, u? A. 90% confidence, n = 25 B. 90% confidence, n = 50 C. 95% confidence, n = 25 D. 95% confidence, n = 50 E. n = 100 at any confidence level 1 =
The right response is E. n = 100 at whatever degree of confidence.
We are aware that the sample size's square root and the margin of error are inversely proportional. The margin of error therefore decreases as n increases, but we also know that margin of error is proportional to the critical value, which increases as confidence level increases. However, for t and z, and for a relevant confidence level, the critical value lies between 1-3, so the sample size has the greatest impact.Because of this, choice E is the right one.
Therefore, The right response is E. n = 100 at whatever degree of confidence.
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determine an appropriate interval width for a random sample of 110 observations that fall between and include each of the following: (a) 20 to 85 (b) 30 to 190 (c) 140 to 500
The appropriate interval width for a random sample of 110 observations.
a) w=1
b) w=2
c) w=2
and d) w=4
The interval width is a value that is used to divide the usage distribution into usage rate intervals.
we shall determine an appropriate interval width for a random sample of 110 observations that fall between and include each of the following.
let's start.
we are aware the formula to calculate class width.
[tex]w=\frac{L.O-S.O}{N.C}[/tex],
where,
w for width, L.O is stand for largest observation and S.O for smallest observation and N.C is number of classes.
We solve it by options.
so first come on option (a)
given interval is 20 to 85.
[tex]w=\frac{85-20}{110} \\w=\frac{65}{110} \\w=0.59[/tex]
since we need to round upward the class width, w=1
for option (b)
[tex]w=\frac{190-30}{110} \\\\w=\frac{160}{110} =1.45[/tex]
since we need to round upward the class width, w=2
for option (c)
[tex]w=\frac{230-40}{110} \\\\w=\frac{190}{110}=1.73[/tex]
since we need to round upward the class width, w=2
for option (d)
[tex]w=\frac{360}{110} =3.27[/tex]
since we need to round upward the class width, w=4,
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given the triangle below, find the length of side x. triangle is not drawn to scale. round your final answer to 4 decimal places.
The length of the x is 12 units .
What is Pythagorean theorem?The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be written as c² = a²+ b², where c is the hypotenuse and a,b are the other two sides.
Since the given triangle is a right anlgled triangle so we will use Pythagorean theorem:
using Pythagorean theorem :
H² = P² + B²
where H is hypotenuse , P is perpendicular and B is base of the triangle
H = 13
P = 12
B = x
=> 13² = 12² + x²
=> 169 = 144 + x²
=> x² = 169- 144
=> x² =25
=> x = 5
so the value of x = 5 units
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Complete question:
given the triangle below, find the length of side x.
Point A is 4 miles due west of home. Point B is 6 miles due north of
home. Point C is 7 miles due east of home. Kayla goes on a bike trip
along the triangular path from home to point A, to point B, to Point
C and back to home. How far, in miles, does Kayla travel?
The distance covered on the triangular path to home along point A to B to C is 23.42 miles.
What is Pythagorean theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.
Given that the trip to home goes from point A to point B and then to point C.
The path traced thus, represents the hypotenuse of the two triangles. Triangle BHA and triangle BCH.
The Pythagorean theorem is given as follows:
a^2 + b^2 = c^2
For triangle BHA substitute the value of a = 4 and b =6.
4^2 + 6^2 = c^2
16 + 36 = c^2
c = 7.21
For triangle BHC, substitute the value of a = 7 and b =6.
7^2 + 6^2 = c^2
49 + 36 = c^2
c = 9.21
Now, from point B to point H the additional distance is 7 miles, hence the total distance traveled is:
D = 7.21 + 9.21 + 7
D = 23.42
Hence, the distance covered on the triangular path to home along point A to B to C is 23.42 miles.
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Graph the system on a separate piece of paper and determine the number of solutions it has. If it has one solution determine its coordinates.
y = x - 3
y = -5x + 3
A) no solution
B) 1 solution (-2 , 1)
C) 1 solution (1 , -2)
D) infinitely many solutions
If there is only one answer, it is the coordinates. y = 1/2x - 1, y = 4x + 6 equals (0,6) (-3/2, 0), and so forth.
What is meant by equations? The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.An equation is a mathematical expression with two equal sides and an equal sign in between. An equation is something like 4 + 6 = 10.Given,
y = 1/2x - 1
y= 4x + 6
You may also rapidly graph them on paper as follows.
To get two points for each line, find the x and y intercepts for each line.
y = 1/2x - 1
(0, -1) (2, 0)
For the next line
y= 4x + 6
(0, 6) (-3/2, 0)
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A club has 18 girls and 12 boys as members. The president wants to break the club into groups, with each group containing the same combination of girls and boys. The president also wants to make sure that no one is left out. What is the greatest number of groups the president can make?
By finding the greatest common factor between the given numbers, we conclude that the maximum number of groups will be 6.
How to find the greatest number of groups that the president can make?To find it, we just need to find the greatest common factor between the numbers of boys and girls, to find it, we will decompose these numbers as a product of prime factors.
We will get:
18 = 2*3*3
12 = 2*2*3
The greatest common factor is 2*3 = 6
That is the maximum number of groups alowed, such tthat each group will have:
18/6 = 3 girls.
12/6 = 2 boys.
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