What does replacement value in math? Say if you have to find a replacement value for the variable X, what does that mean?

Answers

Answer 1

A replacement value is a value that can be substituted for a variable in an equation or expression in order to solve for that variable or simplify the expression.

What is an expression?

An expression is a combination of numbers, variables, and/or operators that represents a mathematical relationship or calculation. An expression can be as simple as a single number or variable, or it can be more complex and involve multiple operations and variables.

What is a variable?

A variable is a symbol or letter that represents a quantity or value that can change or vary in different contexts.

In the given question,

A replacement value is a value that can be substituted for a variable in an equation or expression in order to solve for that variable or simplify the expression.

For example, suppose you have the equation 2x + 3 = 7, and you want to solve for x.

To do so, you can use a replacement value.

You can subtract 3 from both sides of the equation to isolate the term with x, which gives you:

2x = 4

Now, you can divide both sides of the equation by 2 to solve for x:

x = 2

In this case, the replacement value was the number 2, which was substituted for the variable x in the equation in order to solve for x.

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Related Questions

f(s) = 3s + 2
p(s) = s^3+ 4s
Find (f • p)(-5)

Answers

The value of (f • p)(-5) is 1885 when functions are given as f(s) = 3s + 2 and p(s) = s³+ 4s.

What is function?

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. It is often represented by an equation or formula, and can be visualized as a graph. Functions are widely used in various areas of mathematics, science, engineering, and other fields to model real-world phenomena and solve problems.

Here,

f(s) = 3s + 2

p(s) = s³+ 4s

To find (f • p)(-5), we need to first find f(-5) and p(-5), and then multiply them together. To find f(-5), we substitute -5 into the function f(s) and simplify:

f(-5) = 3(-5) + 2

= -13

To find p(-5), we substitute -5 into the function p(s) and simplify:

p(-5) = (-5)³ + 4(-5)

= -125 - 20

= -145

Now we can multiply f(-5) and p(-5) together to find (f • p)(-5):

(f • p)(-5) = f(-5) * p(-5)

= (-13) * (-145)

= 1885

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1. In the figure below, solve for the missing side (seems harder then it should be)
A.7
B.8
C.9
D.10

Answers

Answer:

1. a square plus b square is c square where c is the hypotenuse.

so 1. 7^2 + 6^2 = c^2

49+36=c^2

85=c^2

the square root of 85 is c

9.22 is c

all the other questions are blurry :OO

Step-by-step explanation:

The area of a trapezium is 156cm2, the parallel sides are 17cm and 35cm respectively. What is the height of the trapezium​

Answers

Answer:

  6 cm

Step-by-step explanation:

You want the height of a trapezium with bases 17 cm, 35 cm and area 156 cm².

Area formula

The formula for the are of a trapezium is ...

  A = 1/2(b1 +b2)h

Filling in the given values, we have ...

  156 = 1/2(17 +35)h = 26h

  6 = h . . . . . . . . . . divide by 26

The height of the trapezium is 6 cm.

Answer:

6cm

Step-by-step explanation:

To find:-

The height of the trapezium.

Answer:-

We are here given that the area of the trapezium is 156cm² and two of the parallel sides are 17cm and 35cm .We are interested in finding out the height of the trapezium.

The area of the trapezium is given by the formula,

[tex]:\implies \sf Area =\dfrac{1}{2}\times (s_1+s_1)\times h \\[/tex]

where s1 and s2 are the || sides of the trapezium and h is the height of the trapezium.

Now on substituting the respective values in the given formula, we have;

[tex]:\implies \sf 156cm^2 =\dfrac{1}{2} (17cm+35cm)\times h \\[/tex]

[tex]:\implies \sf 156cm^2(2) = 52cm (h) \\[/tex]

[tex]:\implies \sf h =\dfrac{156(2)}{52} cm\\[/tex]

[tex]:\implies \sf \pink{ height = 6 cm }\\[/tex]

Hence the height of the trapezium is 6cm .

PLEASE HELP MEE with all four questionsss

Answers

Therefore, the distance between the 90 degree angle and the hypotenuse is approximately 0.829 units.

What is triangle?

A triangle is a two-dimensional geometric shape that is formed by three straight line segments that connect to form three angles. It is one of the most basic shapes in geometry and has a wide range of applications in mathematics, science, engineering, and everyday life. Triangles can be classified by the length of their sides (equilateral, isosceles, or scalene) and by the size of their angles (acute, right, or obtuse). The study of triangles is an important part of geometry, and their properties and relationships are used in many areas of mathematics and science.

Here,

1. To find HF, we can use the angle bisector theorem, which states that if a line bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the adjacent sides. Let's denote the length of HF as x. Then, by the angle bisector theorem, we have:

JF/FH = JG/HG

Substituting the given values, we get:

15/x = 18/21

Simplifying and solving for x, we get:

x = 15 * 21 / 18

x = 17.5

Therefore, HF is 17.5 cm.

2. Let's denote the length of the hypotenuse as h and the length of the leg opposite the 18-unit perpendicular as a. We can then use the Pythagorean theorem to write:

h² = a²  + 18²

We are told that the hypotenuse is divided into segments of length x and 6 units, so we can write:

h = x + 6

Substituting this expression into the first equation, we get:

(x + 6)² = a² + 18²

We are also told that the leg adjacent to the angle opposite the 4-unit segment is divided into segments of length 4 and (a - 4), so we can write:

a = 4 + (a - 4)

Simplifying this equation, we get:

a = a

Now we can substitute this expression for a into the previous equation and solve for x:

(x + 6)² = (4 + (a - 4))² + 18²

Expanding and simplifying, we get:

x² + 12x - 36 = 0

Using the quadratic formula, we get:

x = (-12 ± √(12² - 4(1)(-36))) / (2(1))

x = (-12 ± √(288)) / 2

x = -6 ± 6√(2)

Since the length of a segment cannot be negative, we take the positive root:

x = -6 + 6sqrt(2)

x ≈ 1.46

Therefore, the value of x is approximately 1.46 units.

3. Let's denote the length of the hypotenuse as h and the length of the leg adjacent to the angle opposite the 9-unit perpendicular as b. We can then use the Pythagorean theorem to write:

h² = b² + 9²

We are told that the hypotenuse is divided into segments of length x and 6 units, so we can write:

h = x + 6

Substituting this expression into the first equation, we get:

(x + 6)² = b² + 9²

Expanding and simplifying, we get:

x² + 12x - b² = 27

We also know that the length of the leg opposite the 9-unit perpendicular is:

a = √(h² - 9²)

= √((x + 6)² - 9²)

= √(x² + 12x + 27)

Now we can use the fact that the tangent of the angle opposite the 9-unit perpendicular is equal to the ratio of the lengths of the opposite and adjacent sides:

tan(θ) = a / b

Substituting the expressions for a and b, we get:

tan(θ) = √(x² + 12x + 27) / (x + 6)

We also know that the tangent of the angle theta is equal to the ratio of the length of the opposite side to the length of the adjacent side:

tan(θ) = 9 / b

Substituting the expression for b, we get:

tan(θ) = 9 / √(h² - 9²)

Substituting the expression for h, we get:

tan(θ) = 9 / √((x + 6)² - 9²)

Since the tangent function is the same for equal angles, we can set these two expressions for the tangent equal to each other:

√(x² + 12x + 27) / (x + 6) = 9 / √((x + 6)² - 9²)

Squaring both sides, we get:

(x² + 12x + 27) / (x + 6)² = 81 / ((x + 6)² - 81)

Cross-multiplying and simplifying, we get:

x⁴ + 36x³ + 297x² - 1458x - 2916 = 0

Using a numerical method such as the Newton-Raphson method or the bisection method, we can find the approximate solution to this equation:

x ≈ 9.449

Therefore, the value of x is approximately 9.449 units.

4. Let's denote the length of the hypotenuse as h and the length of the leg adjacent to the angle opposite the distance we want to find as b. We can use the Pythagorean theorem to write:

h² = b² + d²

We are told that the hypotenuse is divided into segments of length 9 and 4 units, so we can write:

h = 9 + 4 = 13

Substituting this expression into the first equation, we get:

13² = b² + d²

Simplifying and solving for d, we get:

d = √(13² - b²)

Now, we need to find the value of b. We know that the hypotenuse is divided into segments of length 9 and 4 units, so we can use similar triangles to write:

b / 4 = 9 / 13

Simplifying and solving for b, we get:

b = 36 / 13

Substituting this expression for b into the equation we found earlier for d, we get:

d = √(13² - (36/13)²)

Simplifying and finding a common denominator, we get:

d =√ (169*13 - 36²) / 13²

Simplifying further, we get:

d = √(169169 - 3636) / 169

Calculating this expression, we get:

d ≈ 0.829

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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).

Answers

The true statements are:

The graph of the function is a parabola.

The graph contains the point (0, 0).

The graph does not contain the point (20, -8).

How to deal with quadratic equation?

The quadratic function is f(x) = x^2 - 5x + 12. Here are the statements that are true:

The value of f(-10) = 82:

To find f(-10), we substitute -10 for x in the function:

[tex]$$f(-10) = (-10)^2 - 5(-10) + 12 = 100 + 50 + 12 = 162$$[/tex]

Therefore, the statement "The value of f(-10) = 82" is false.

The graph of the function is a parabola:

Since the highest power of x in the function is 2, the graph of the function will be a parabola. Therefore, the statement "The graph of the function is a parabola" is true.

The graph of the function opens down:

The coefficient of [tex]$x^2$[/tex] in the function is positive (+1), which means the parabola opens upwards. Therefore, the statement "The graph of the function opens down" is false.

The graph contains the point (20, –8):

To see whether the point (20, -8) is on the graph of the function, we substitute x=20 into the function:

[tex]$$f(20) = (20)^2 - 5(20) + 12 = 400 - 100 + 12 = 312$$[/tex]

Since the y-coordinate of the point (20, -8) is not equal to 312, the statement "The graph contains the point (20, –8)" is false.

The graph contains the point (0, 0):

To see whether the point (0, 0) is on the graph of the function, we substitute x=0 into the function:

[tex]$$f(0) = (0)^2 - 5(0) + 12 = 12$$[/tex]

Since the y-coordinate of the point (0, 0) is equal to 12, the statement "The graph contains the point (0, 0)" is true.

Therefore, the true statements are:

The graph of the function is a parabola.

The graph contains the point (0, 0).

The graph does not contain the point (20, -8).

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When I first look at an equation, HOW DO I KNOW which method to use to solve it?
for example:

-4(7j+2) = 10

What do I look for (by looking at it) to know if I should start to solve it by distributing, or just use division?

Please help! I am really confused. Thank you

Answers

Answer:

j = - 9/14

Step-by-step explanation:

-4(7j+2) = 10

Distributing First

-28j - 8 = 10

Try to get the variable on one side.

-28j = 18

Divide both sides by -28

j = -18/28 = - 9/14

10% of the cars in my neighborhood are red, and the rest of the cars in the neighborhood are silver. We'll call "seeing a red car" a success, and "seeing a silver car" a failure for the purposes of this problem.

Suppose that I watch 3 cars pass my house and that I become interested in the probability that exactly one of the three cars is red.

Apply the binomial formula to find the probability that exactly one of the three cars is red. Be sure to clearly state the values of n, x, and p in this case.

Answers

Answer:

In this scenario, we have:

n = 3 (since we are watching 3 cars)

x = 1 (since we are interested in the probability of exactly one car being red)

p = 0.1 (since the probability of a car being red is 10%, or 0.1)

The binomial formula for calculating the probability of exactly x successes in n independent trials with a probability of success p is:

P(x) = (nCx) * p^x * (1-p)^(n-x)

where nCx is the binomial coefficient, which can be calculated as:

nCx = n! / (x! * (n-x)!)

Using these values and the binomial formula, we can calculate the probability of exactly one of the three cars being red as:

P(1) = (3C1) * 0.1^1 * (1-0.1)^(3-1)

= (3) * 0.1 * 0.81

= 0.243

Therefore, the probability of exactly one of the three cars being red is 0.243.

In this problem, we want to find the probability that exactly one of the three cars is red, given that 10% of the cars in the neighborhood are red and we watch 3 cars pass by.

Let's define the following variables:

n = 3 (the number of trials or cars we observe)
x = 1 (the number of successes we want, i.e. seeing one red car)
p = 0.1 (the probability of success, i.e. seeing a red car)

Using the binomial formula, the probability of getting exactly one red car in three cars passing by is:

P(x = 1) = (n choose x) * p^x * (1 - p)^(n - x)

where (n choose x) is the binomial coefficient, which represents the number of ways to choose x objects from a set of n objects, and is calculated as:

(n choose x) = n! / (x! * (n - x)!)

Plugging in the values for n, x, and p, we get:

P(x = 1) = (3 choose 1) * 0.1^1 * (1 - 0.1)^(3 - 1)
= 3 * 0.1 * 0.81
= 0.243

Therefore, the probability that exactly one of the three cars is red is 0.243 or approximately 24.3%.

A company rents storage sheds shaped like rectangular prisms. Each shed is 11 feet long, 7 feet wide, and 12 feet tall. The rental cost is $3 per cubic foot. How much does it cost to rent one shed?

Answers

The cost to rent one shed of the rectangular prism shaped shed is $2772.

What is area?

The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

What is a prism?

A rectangular prism is a polyhedron in geometry that has two parallel and congruent sides. It also goes by the name cuboid. Six faces, each with a rectangle form and twelve edges, make up a rectangular prism. It is referred to as a prism because of the extent of its cross-section.

Volume of prism= BH

where B= area of base and H= height

B= 11*7 = 77 feet²

H= 12 feet

Volume= 77*12=924 cubic feet

Cost =$3 per cubic foot

Total cost= 3*924= $2772

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Assuming boys and girls are equally likely, find the probability of a couple's last child being a baby boy. They have a total of 3 children not including the last child in question and all were boys before the last child was born.
Express your answer as a percentage rounded to the nearest hundredth without the % sign.

Answers

Answer:

Step-by-step explanation:

The probability of a baby being a boy or a girl is 1/2 or 50% each. Since the couple has already had three boys, the probability of the fourth child being a boy or a girl is still 1/2 or 50%, as the gender of each child is independent of the others. Therefore, the probability of the couple's last child being a baby boy is 50%.

The required probability of a couple having a baby boy when their third child is​ born is 1/2 / 50%.

What is probability?

probability is the ratio of the number of favorable outcomes and the total number of possible outcomes. The chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%.

Given:

Assuming boys and girls are equally​ likely.

The first two children were both boys

According to given question we have

The probability of having a baby girl is an independent probability.

The first two children were both boys

So, it is not related to the previous child.

So required probability = 1/2 / 50%

Therefore, the required probability of a couple having a baby boy when their third child is​ born is 1/2 / 50%.

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In a group of rectangles, the length of each rectangle is twice the width. Is this an additive or multiplicative relationship? Explain your reasoning.​

Answers

Answer:

Multiplicative

Step-by-step explanation:

If the area of the first rectangle is l*w, the area of the second would be 2w*w. The area is multiplied by 2 and the relationship is therefore multiplicative.

5/9=

1/14=

12/13=

2/13=

9/11=

9/17=
To round each fraction

Answers

Answer:

Step-by-step explanation:

1. Rounded to 0.56

2. Rounded

. If h> 3 and h - 2g= 0, which of
the following must be true?
A. g> 2.5
B. g> 1.5
C. g <0.5
D. g <1.5
E. g>2

Answers

By linear equality , g >1.5 is must be true.

What are equality and inequality along a line?

Equal (=) is the symbol used in linear equations. Example. Using the inequality symbols (>,, is greater than or equal to, and is less than or equal to), linear inequalities are expressed.

                          x - 5 > 3x - 10 is an illustration of a linear inequality. As the larger than symbol is employed in this inequality, the LHS is strictly greater than the RHS. After being solved, the inequality appears as 2x 5 x (5/2).

If h> 3 and h - 2g= 0

H=2g

2g>3

g >1.5

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a
21 units squared
b
27.6 units squared
c
32.2 units squared
d
42 units squared

Answers

The area of the right triangle given in this problem is given as follows:

21 units squared -> Option A.

How to obtain the area of a triangle?

To calculate the area of a triangle, you can use the formula presented as follows:

Area = (1/2) x base x height

In which the parameters are given as follows:

"base" is the length of the side of the triangle that is perpendicular to the height."height" is the length of the perpendicular line segment from the base to the opposite vertex.

For a right triangle, we can consider one side to be the base and the other side to be the height, hence the parameters are given as follows:

Base of 7 units.Height of 6 units.

Hence the area of the triangle is given as follows:

A = 0.5 x 7 x 6 = 21 units squared.

Missing Information

The complete problem is defined as follows:

"Calculate the area of the given triangle".

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Question 20
There were 750 shirts in a box. 20% of them were pink and 18% were green. The
remaining shirts were either yellow or black. If there were 85 more black shirts than
yellow shirts, what was the total number of black and green shirts in the box?

Answers

Answer:

410 Black and Green shirts

Step-by-step explanation:

150 shirts were pink

135 shirts were green

so knowing this we can set up the equation 2x+85=465

there were 275 black shirts in the box

and 190 yellow shirts

therefore there were 410 Black and Green shirts in the box

Solve the following problems.
Given: AABC, DE AC,
BD DC, mZ1=m22,
mZBDC= 100°
Find: m< A, m< b , m

Answers

The value of the angles in the triangle are:

∠A = 60°, ∠B = 80° and ∠C = 40°

How to find the value of m∠A, m∠B, m∠C in the triangle?

We  are given that BD = DC

Thus, ∠DBC = ∠BCD ---- 1  (angle in isosceles triangle)

We also have ∠BDC = 100°

In ΔBDC

∠BDC + ∠DBC + ∠BCD = 180°  (sum of angles of triangle is 180°)

Using 1:

∠BDC + 2∠DBC = 180°  

100° + 2∠DBC = 180°  

2∠DBC = 180 - 100

2∠DBC = 80

∠DBC = 80/2

∠DBC = 40°

∠DBC = ∠BCD = ∠2 = 40°

Thus, ∠C = 40°

We are given that  m∠1 = m∠2

Thus, ∠1 = ∠2 = 40°

Now,  ∠BDC +  ∠BDA = 180° (Linear pair)

100° + ∠BDA = 180°

∠BDA = 180 - 100

∠BDA = 80°

In ΔABD

∠ABD + ∠BDA +  ∠BAD = 180° (sum of angles of triangle is 180°)

∠1 + ∠BDA +  ∠BAD = 180°

40° +  80° +  ∠BAD = 180°

120° +  ∠BAD = 180°

∠BAD = 60°

So,  ∠A = 60°

∠B =  ∠1  + ∠2 = 40° + 40° = 80°

Therefore,  ∠A = 60°, ∠B = 80° and ∠C = 40°

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Complete Question

m∠1=m∠2

D∈

AC

, BD = DC

m∠BDC = 100°

Find: m∠A, m∠B, m∠C

Find the Z-score for each of the following IQ scores
90 160(Einstein's IQ)

Answers

Answer:

z=3.75

Step-by-step explanation:

Help pleaseeeeeeeeee!

Answers

Answer:

y = 0.8x

Step-by-step explanation:

machine fills 24 jars in 30 seconds , then

fills 1 jar in [tex]\frac{24}{30}[/tex] = 0.8 seconds

thus number of jars filled in x seconds is

y = 0.8x

Question 4 X Suppose that starting today, you make deposits at the beginning of each quarterly period for the next 40 years. The first deposit is for 400, but you decrease the size of each deposit by 1% from the previous deposit. Using an nominal annual interest rate of 8% compounded quarterly, find the future value (i.e. the value at the end of 40 years) of these deposits. Give your answer as a decimal rounded to two places (i.e. X.XX).

Answers

if we make quarterly deposits and invest them at an nominal annual interest rate of 8% compounded quarterly for 40 years, we will have $143,004.54 at the end of the 40 years.

The first step in solving this problem is to calculate the amount of each quarterly deposit. We know that the first deposit is $400, and each subsequent deposit decreases by 1% from the previous deposit. This means that each deposit is 99% of the previous deposit. To calculate the size of each deposit, we can use the following formula:

deposit_ n = deposit_(n-1) * 0.99

Using this formula, we can calculate the size of each quarterly deposit as follows:

deposit_1 = $400

deposit_2 = deposit_1 * 0.99 = $396.00

deposit_3 = deposit_2 * 0.99 = $392.04

deposit_4 = deposit_3 * 0.99 = $388.12

...

We can continue this pattern for 40 years (160 quarters) to find the size of each quarterly deposit.

Next, we need to calculate the future value of these deposits using an nominal annual interest rate of 8% compounded quarterly. We can use the formula for compound interest to calculate the future value:

[tex]FV = PV * (1 + r/n)^(n*t)[/tex]

where FV is the future value, PV is the present value (which is zero since we are starting with deposits), r is the nominal annual interest rate (8%), n is the number of times the interest is compounded per year (4 since we are compounding quarterly), and t is the number of years (40).

We can substitute the values into the formula and solve for FV:

[tex]FV = $400 * (1 + 0.08/4)^(440) + $396.00 * (1 + 0.08/4)^(439) + $392.04 * (1 + 0.08/4)^(4*38) + ... + $1.64 * (1 + 0.08/4)^4[/tex]

After solving this equation, we get a future value of $143,004.54, rounded to two decimal places. This means that if we make quarterly deposits and invest them at an nominal annual interest rate of 8% compounded quarterly for 40 years, we will have $143,004.54 at the end of the 40 years.

This calculation highlights the power of compound interest over long periods of time. By making regular contributions and earning interest on those contributions, our investment grows exponentially over time. It also shows the importance of starting early and consistently contributing to an investment over time in order to achieve long-term financial goals.

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Question 2 (2 points) ✓ Saved
In the news, you hear "tuition is expected to increase by 12% next year." If tuition
this year was $5,500 per year, what will it be next year?
660
6160
4840
Cannot be solved.

Answers

Answer: 6,160

Step-by-step explanation:

Immediately, without even doing any math, the only logical answer would be 6160. This is because the current tuition is 5,500 and it is increasing so the answer cannot be lower.

However, mathematically you can prove this by turning 12% into a decimal and multiplying it by 5,500. 12% could be converted to .12 and because it is increasing you must add 1, or 100%, since that is what it started with. 5,500 x 1.12 = 6,160.

LetY1,Y2,Yn denote a random sample of size n from a population whose density is given by f(y)={αyα−1θα,0≤y≤θ0,elsewhere,where α>0 is a known, fixed value, but θ is unknown. Consider the estimator ˆθ=max(Y1,Y2,...Yn).(a) Show that ˆθ is a biased estimator for θ.(b) Find a multiple of ˆθ that is an unbiased estimator of θ.(c) Derive MSE(ˆθ).

Answers

(a) θ is a biased estimator for θ.

(b) (α+1)Y/α is an unbiased estimator of θ.

(c) MSE(θ) = αθ^2/[(α+1)^2(α+2)]

(a) To show that θ is a biased estimator for θ, we need to show that E(θ) ≠ θ.

Using the definition of the maximum function, we have

P(θ ≤ y) = P(Y1 ≤ y, Y2 ≤ y, ..., Yn ≤ y) = (F(y))^n

where F(y) is the cumulative distribution function of Y.

Differentiating both sides with respect to y, we get:

f(θ) = n(F(θ))^(n-1)f(θ)

Simplifying, we get

F(θ) = (1/n)^(1/(n-1))

Using this result, we can find the expected value of θ

E(θ) = ∫₀^∞ θf(θ)dθ = ∫₀^θ θαθ^α-1dθ = αθ/(α+1)

Thus, E(θ) ≠ θ, which means that θ is a biased estimator for θ.

(b) To find a multiple of θ that is an unbiased estimator of θ, we can use the method of moments.

We know that the population mean of Y is

μ = ∫₀^θ yf(y)dy = αθ/(α+1)

The sample mean is

Y = (Y1+Y2+...+Yn)/n

Equating these two expressions and solving for θ, we get

θ = (α+1)Y/α

Thus, (α+1)Y/α is an unbiased estimator of θ.

(c) The mean squared error (MSE) of θ can be written as

MSE(θ) = E[(θ - θ)^2]

Expanding the square and using the linearity of expectation, we have

MSE(θ) = E[θ^2] - 2θE[θ] + E[θ]^2

We already know that E[θ] = αθ/(α+1).

To find E[θ^2], we can use the fact that θ = max(Y1,Y2,...Yn)

P(θ ≤ y) = P(Y1 ≤ y, Y2 ≤ y, ..., Yn ≤ y) = (F(y))^n

Differentiating both sides with respect to y, we get

f(θ) = n(F(θ))^(n-1)f(θ)

Using this result, we can find E[θ^2]

E[θ^2] = ∫₀^∞ θ^2f(θ)dθ = ∫₀^θ θ^2αθ^α-1dθ = αθ^2/(α+2)

Substituting these expressions into the MSE formula, we get

MSE(θ) = αθ^2/(α+2) - 2θ(αθ/(α+1)) + (αθ/(α+1))^2

Simplifying, we get

MSE(θ) = αθ^2/[(α+1)^2(α+2)]

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11/12 x 8/25 x 15/16 x 9/44

Answers

Exact form:

9/160

Decimal form:

0.05625

Can the binomial distribution be approximated by a normal distribution? n = 31, p = 0.9 Explain why or why not.​

Answers

Therefore, we can use the normal distribution with mean 27.9 and standard deviation 1.67 to approximate the binomial distribution with n = 31 and p = 0.9.

What is binomial distribution?

The binomial distribution is characterized by two parameters: the number of trials, denoted by n, and the probability of success on each trial, denoted by p. The probability of obtaining exactly k successes in n trials is given by the binomial probability mass function:

P(k) = (n choose k) * [tex]p^{k}[/tex] * [tex](1-p)^{(n-k)}[/tex],

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items.

Given by the question.

Yes, the binomial distribution with n = 31 and p = 0.9 can be approximated by a normal distribution.

The conditions for a binomial distribution to be approximated by a normal distribution are as follows:

n*p >= 10

n*(1-p) >= 10

In this case, n = 31 and p = 0.9, so:

np = 310.9 = 27.9 >= 10

n*(1-p) = 31*0.1 = 3.1 >= 10

Condition 1 is satisfied, but condition 2 is not. Therefore, it is recommended to use a correction factor to improve the approximation.

The correction factor is given by:

[tex]\sqrt[2]{np(1-p)}[/tex]

Substituting the values, we get:

[tex]\sqrt[2]{310.90.1}[/tex]= 1.67

The corrected values for mean and standard deviation are:

mean = np = 310.9 = 27.9

standard deviation = [tex]\sqrt[2]{np(1-p)}[/tex] = 1.67

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PLEASE ASAP!!Graph the line 4x+5y=20

Answers

Step-by-step explanation:

Might be a little easier to visualize if yo re-arrange it into y = mx + b form:

4x+ 5y = 20

5y = -4x + 20

y = - 4/5 x + 4         y-axis intercept at y = 4

                                x axis intercept is found by:

                                     0 = -4/5 x + 4

                                             - 4 = -4/5 x

                                                 x = 5

So===> plot the two intercept points ( 0,4)  and  ( 5,0)  and connect the dots

2.35 [5] <$2.9> For the following code: Ibu $t0,($t1) sw $t0,($t2) Assume that the register $t1 contains the address 0x10000000 and the data at address is 0x11223344. 2.35.1 [5] <$2.3, 2.9> What value is stored in 0x10000004 on a big-endian machine? 2.35.2 [5] <$2.3, 2.9> What value is stored in 0x10000004 on a little-endian machine?

Answers

The value stored in 0x10000004 on a big-endian machine is given by 0x00000011.

The word "endianness" refers to the arrangement of bytes as they are stored in computer memory. Endianness is classified as big or little depending on which value is stored first.

The "big end" (the most important item in the sequence) is put first and at the lowest storage address in a big-endian order. The "small end" (the least important item in the sequence) is put first in a little-endian order.

(1)In Big-endian Machine, first byte of multi-byte data will be stored first(at lower memory address)

Address                 Data

0x10000000            0x11

0x10000001            0x22

0x10000002            0x33

0x10000003            0x44

---------------------------------------------------------------------

lbu $t0, 0($t1)

Load unsigned byte in Register $t0 at address 0x10000000

Here byte at address 0x10000000 is 0x11

$t0 = 0x00000011

----------------------------------------------------

sw $t0, 0($t2)

Store a word(4 bytes) from Register $t0 to memory address 0x10000004

value stored in 0x10000004 is 0x00000011

--------------------------------------------------------------------------------

(2)In Little-endian Machine, last byte of multi-byte data will be stored first(at lower memory address)

Address                 Data

0x10000000            0x44

0x10000001            0x33

0x10000002            0x22

0x10000003            0x11

---------------------------------------------------------------------

lbu $t0, 0($t1)

Load unsigned byte in Register $t0 at address 0x10000000

Here byte at address 0x10000000 is 0x44

$t0 = 0x00000044

----------------------------------------------------

sw $t0, 0($t2)

Store a word(4 bytes) from Register $t0 to memory address 0x10000004

value stored in 0x10000004 is 0x00000044.

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5 Mrs. Newsome bought a piece of fabric 142 centimeters long to make a quilt for her son's bedroom. She bought a piece of fabric 2 meters long for curtains. How could Mrs. Newsome find the total length, in centimeters, of both pieces of fabric? Multiply 2 by 2,000, then add 142. Add 2 and 142, then multiply by 100. Divide 142 by 100, then add 2,000. O Multiply 2 by 100, then add 142. B C​

Answers

Answer:

Step-by-step explanation:

To find the total length of both pieces of fabric in centimeters, we need to add the length of the first piece of fabric (142 cm) and the length of the second piece of fabric (2 meters).

However, we need to make sure that the units are consistent before we add the lengths. We can convert the length of the second piece of fabric from meters to centimeters by multiplying by 100. Therefore, the total length in centimeters is:

142 cm + 2 meters * 100 cm/meter = 142 cm + 200 cm = 342 cm

The option that correctly gives the answer is "Multiply 2 by 100, then add 142" (Option C).

6TH GRADE MATH PLS HELP TYSM

Answers

Answer:

m = 1

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (-1,0) (0,1)

We see the y increase by 1 and the x increase by 1, so the slope is

m = 1

3 Tell whether each statement is True or False.
A 20° angle and a 70° angle can be
composed into a 90° angle.
b. Three 50° angles compose an angle
that measures 350⁰.
c. A 15° angle and a 60° angle compose
an angle that measures 75°.
d. Four 50° angles can be composed
into a 200° angle.
True False
True
True
True
4 Look at the drawing of a hand fan at the right. The
False
False
Fal

Answers

d. True. The sum of four 50° angles is 200°, so they can compose a 200° angle.

what is a geometric sequence?

A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed constant called the common ratio. The common ratio is denoted by the letter r.

The general formula for a geometric sequence is:a₁, a₁r, a₁r², a₁r³, ...

a. False. The sum of a 20° angle and a 70° angle is 90°, so they can compose a 90° angle.

b. False. The sum of three 50° angles is 150°, so they cannot compose an angle that measures 350⁰.

c. False. The sum of a 15° angle and a 60° angle is 75°, so they can compose an angle that measures 75°.

Therefore, d. True. The sum of four 50° angles is 200°, so they can compose a 200° angle.

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HELP ASAP PLEASE! A yard plan includes a rectangular garden that is surrounded by bricks. In the drawing, the garden is 7 inches by 4 inches. The length and width of the actual garden will be 35 times larger than the length and width in the drawing.

What is the perimeter of the drawing? Show your work.

What is the perimeter of the actual garden? Show your work.

What is the effect on the perimeter of the garden with the dimensions are multiplied by 35? Show your work.

Answers

The perimeter of the garden in the drawing is 22 inches and the perimeter of the actual garden is 770 inches

The perimeter of the drawing

The perimeter of the garden in the drawing is calculated as

Perimeter of garden in drawing = 2(length + width)

So, we have

Perimeter of garden in drawing = 2(7 inches + 4 inches)

Evaluate

Perimeter of garden in drawing = 22 inches

So the perimeter of the garden in the drawing is 22 inches.

The perimeter of the actual garden

For the perimeter of the actual garden, we have

Perimeter of actual garden = 22 inches * 35

Perimeter of actual garden = 770 inches

The effect on the perimeter

We can see that the perimeter of the actual garden is 35 times larger than the perimeter of the garden in the drawing.

This makes sense since the length and width of the actual garden are 35 times larger than the length and width in the drawing, so the perimeter (which is the sum of the lengths of all four sides) would also be 35 times larger.

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Total of 18 students 5 students prefer country. what is the probability?

Answers

Answer:

27.78%

Step-by-step explanation:

We know

Total of 18 students 5 students prefer country.

What is the probability?

5/18 = 27.78%

So, the answer is 27.78%

Determine whether each of these functions from
Z
to
Z
is one-to-one (i.e., injective). (3 pts in total) (a)
f(n)=n−3
(b)
f(n)=n 2
−1
(c)
f(n)=n 5

Answers

The function f(n) = n - 3 maps distinct integers to distinct integers, and thus is injective.

(a) The function f(n) = n - 3 is one-to-one (injective). To prove this, suppose that f(a) = f(b) for some integers a and b. Then, we have a - 3 = b - 3, which implies a = b. Therefore, the function f(n) = n - 3 maps distinct integers to distinct integers, and thus is injective.

(b) The function f(n) = n^2 - 1 is not one-to-one (not injective). To see this, note that f(1) = f(-1) = 0, so different inputs map to the same output. In general, for any positive integer k, we have f(k) = f(-k), since (k^2 - 1) = ((-k)^2 - 1). Therefore, the function f(n) = n^2 - 1 is not injective.

(c) The function f(n) = n^5 is one-to-one (injective). To prove this, suppose that f(a) = f(b) for some integers a and b. Then, we have a^5 = b^5, which implies a = b (since the fifth root of a non-zero real number is unique). Therefore, the function f(n) = n^5 maps distinct integers to distinct integers, and thus is injective.

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