in estimating a population mean with a confidence interval based on a random sample x1,...,xn from a normal distribution with an unknown mean and a known variance, compare the length of the 95% and 90% confidence intervals for the unknown mean based on x1,...,xn.

The answer choice which corrects justifies the step as described is; Choice B; addition property of equality.

It follows from the task content that the answer choice which corrects justifies the step as given is to be determined.

Since the starting step is;

2x + 3 = -5x - 1

By adding 5x to both sides of the equation;

2x + 5x + 3 = -5x - 1 + 5x

7x + 3 = -1

Recall that; the addition property of equality postulates that;

if x = y;

Then, x + a = y + a.

On this note, the property which justifies the step is; Choice B; Addition property of equality.

Read more on addition property of equality;

https://brainly.com/question/3474035

#SPJ1

For the stated question;

x = 300 - 2p + 8q

Partial Derivatives of 'x' with respect to p is

∂x/∂p = -2

For ; y= 500 + 8p- 3q

Partial Derivatives of 'y' with respect to p is

∂y/∂p = 8

Thus,

To know more about the Partial Derivatives, here

https://brainly.com/question/29655602

#SPJ1

The correct question is-

A supermarket sells two brands of granola: brand A at $p per pound and brand B at $q per pound. The daily demands x and y (in pounds) for brands A and B, respectively, are given by the following equations.

x= 300 - 2p + 8q and y= 500 + 8p- 3q

Find ∂y/∂p and ∂x/∂p and interpret the results.

Answer:

the slope is 1

Step-by-step explanation:

where: m is the slope and b is the y-intercept. Therefore, for the equation y=x+5 , the slope is 1 , and the y-intercept is 5

The features of the linear function in this problem are given as follows:

The slope of a linear function represents the rate of change of the output variable y relative to the input variable x.

Hence, if we are given two points in a linear function, the slope is calculated as the division of the change in y by the change in x.

The two points for the function in this problem are given as follows:

(0, -4) and (2,5).

Hence the slope of the function is calculated as follows:

m = (5 - (-4))/(2 - 0) = 9/2 = 4.5.

The intercept of a linear function is given by the value of y when the graph of the function crosses or touches the y-axis, that is, the value of y when x = 0. One point for this problem is (0,-4), hence the intercept is given by y = -4.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

The simplified form of the expression (81x⁴y⁹)¹/² is 9x²y⁴√y

From the question, we have the following parameters that can be used in our computation:

what is the simplified form of (81x^4y^9)^1/2

Rewrite the superscripts properly

(81x⁴y⁹)¹/²

The above expression is a radical expression

And the radicand is 81x⁴y⁹

The superscript outside the bracket represents square root

So, we have the following representation

(81x⁴y⁹)¹/² = 9x²y⁴√y

Hence, the solution is 9x²y⁴√y

Read more about expressions at

brainly.com/question/15775046

#SPJ1

Answer: f

Step-by-step explanation:

The domain of a composite function f(g(x)) is the set of those inputs x in the domain of g for which g(x) is in the domain of .

The kinetic energy will be maximum if the potential energy is minimum.

Given that,

On the graph, an object's mechanical energy is represented by the horizontal red line, and its potential energy as a function of x is shown by the blue line beneath it. at what x value is:

Value of x at which

1) potential energy at the largest

2kinetic energy at the largest

3)The force on the object in the negative direction.

4)The force on the object the largest magnitude.

More above the x-axis, greater the value of potential energy. Therefore, the point at which potential energy is large at x = 4

Mechanical energy is sum of potential energy and kinetic energy

So, kinetic energy will be maximum if the potential energy is minimum.

To learn more about Mechanical energy click here:

https://brainly.com/question/29509191

#SPJ4

The Thrift segment will demand 7,741 thousand units and the Core segment will demand 9,771 thousand units true from the following statements.

The options that are true from the following statements will be:

The Thrift segment will demand 7,741 thousand units

The Core segment will demand 9,771 thousand units

Based on the complete information options that are given, it can be inferred that the growth rate for the companies was given.

Growth rate simply means the percentage change of assets or investments for a particular period. From the table, it can be inferred that the thrift segment will demand 7,741 thousand units while the core segment will demand 9,771 thousand units.

To learn more about the thrift segment visit: https://brainly.com/question/23989155

#SPJ4

1) The equation that solves for Katherine age, x is 5(x - 4) = 400.

2) Katherine is 84 years old.

3) Mabel is 80 years old.

An algebraic equation represents the mathematical form of two expressions that are related by an equal in between them.

From the given information, we can write,

Katherine's age is represented by 'x'

Mabel is 4 years younger than Katherine ie., x - 4

Five times Mabel's age is equal to 400 i.e., 5(x - 4) = 400

Thus, the equation that solves Katherine's age is 5(x - 4) = 400.

On simplifying the obtained equation, we get

5(x - 4) = 400

⇒ 5x - 20 = 400

⇒ 5x = 400 + 20

⇒ 5x = 420

∴ x = 420/5 = 84

Thus, the age of Katherine is 84 years.

Then, Mabel's age = x - 4 = 84 - 4 = 80 years.

Learn more about an algebraic equation here:

https://brainly.com/question/4344214

#SPJ1

Step-by-step explanation:

you marked the important pieces of information correctly.

a parallel line must have the same slope. otherwise it is tilted differently, and it is therefore not parallel.

the slope in a y = ... equation is always the factor of x.

in our case therefore 1/5.

so, the parallel line starts with

y = (1/5)x + b

and to get b we use the x and y coordinates of the given point :

3 = (1/5)×5 + b = 5/5 + b = 1 + b

b = 2

and our equation is

y = (1/5)x + 2

Therefore, The mathematical equation can be used to calculate that there are 5 inches between the top of the picture frame and the ceiling.

equation: a statement that two expressions having variable- and/or number-filled expressions are equivalent. Since equations are essentially questions, the search for a way to respond to them has spurred the development of mathematics. Equations can be as simple as addition-and-multiplication algebraic equations or as complex as integral equations, differential equations, and exponential equations that include exponential expressions.

Given: A mirror measures 28 inches in width and 24 inches in height.

On an 8-foot-high wall, the mirror's center will be suspended 514 feet above the ground.

The procedures listed below can be used to calculate the distance between the ceiling and the top of the picture frame:

Step 1: Keep in mind that one foot is equal to 12 inches. Consequently, the value of 8 feet is converted to (8 12) 96 inches, and the value of 5 1/4 feet is changed to 63 inches.

Step 2:As a result, the following is the distance between the frame's center and bottom:

Step 3 - At this point, the distance between the mirror's center and the ground is:

= 14 + 63

77 inches.

Step 4: At this point, the distance between the picture frame's top and the ceiling is:

= 96 - 77 - 14

5 inches.

To know more about equation, visit

https://brainly.com/question/12788590

#SPJ1

Acceleration resulting from gravity will be = (-9.8 ms sq.)

First of all we have to know more about gravity which means it is the force by which a planet or other body draws objects toward its center. The force of gravity keeps all of the planets in orbit around the sun.

When you throw a ball up in the air, its speed decreases, until it momentarily stops at the very top of the ball's motion. Its acceleration is

(−9.8 ms sq )

at the very top since the body is moving upward against the gravity. In other words, the acceleration due to gravity will be

g = 9.8 ms -sq

To know more about the Gravity

https://brainly.com/question/4939529

#SPJ4

Option A) is correct

There is only one solution: x = 1. The solution x = 3 is an extraneous solution.  

Solution :

Given Equations:

[tex]\frac{1}{x} +\frac{1}{1-x} =\frac{x-2}{y-3}[/tex]

solving The given Equation have :

[tex]\frac{1}{x}+ \frac{1}{x-3} =\frac{x-2}{y-3}[/tex]

[tex]\frac{2x-3}{x(x-3)} =\frac{x-2}{y-3}[/tex]

[tex]2x-3=x^{2} -2x[/tex]

[tex]x^{2} -4x+3=0[/tex]

[tex]x^{2} -x-x3+3=0[/tex]

[tex]x(x-1)-3(x-3)=0\\x-3)(x-1)=0\\x=1,x=3[/tex]

Extraneous solutions:

Due to its exclusion from the original equation's domain, an auxiliary solution is not a root of the original equation.

We may get this conclusion, but we cannot accept it as a conclusion since it is insufficient.

However, x = 3 cannot be a solution to the preceding equation because it produces a denominator of zero when used in the provided equation.

As a result, the following equation's solution is x = 1, while its superfluous solution is x = 3.

To Learn More about Extraneous solutions: : https://brainly.com/question/15395568

#SPJ1

Answer:

Below

Step-by-step explanation:

(x-10)^2 = 90     sqrt both sides

x-10  =  ± sqrt (90)

x  =   10 ± sqrt (90)

The statement is AB=CD,BC=AD due to definition of parallelogram. The statement is AC=AC due to Reflexive property of equality.

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. A quadrilateral with the opposing sides parallel is called a parallelogram. A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.

Here,

1. Statement: AB=CD,BC=AD

Reason: By definition of parallelogram.

2. Statement: AC=AC

Reason: Reflexive property of equality.

The definition of a parallelogram causes the sentence to be AB=CD,BC=AD. Due to the reflexive feature of equality, the assertion is AC=AC.

To know more about parallelogram,

https://brainly.com/question/12520140

#SPJ4

If we assume that σ = 15 then the required sample size is 216 .

In the question ,

it is given that ,

the standard deviation is (σ) = 15

we want to be  95% confident . So , α [tex]=[/tex] 1 - 0.95 = 0.05

So , [tex]Z_{\frac{\alpha }{2} }[/tex] is = [tex]Z_{\frac{0.05 }{2} }[/tex] = Z₀.₀₂₅

from z table ,

Z₀.₀₂₅  = 1.96 .

e is given to be = 2 IQ points

the sample size (n) is calculated using the formula .

n = (σ × [tex]Z_{\frac{\alpha }{2} }[/tex]/e)²

Substituting the values ,

we get ,

n = (15 * 1.96/2)²

n = (29.4/2)²

n = (14.7)²

n = 216.09

n ≈ 216

Therefore , the sample size necessary to estimate the mean IQ score of statistics students is 216 .

The given question is incomplete , the complete question is

The standard IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of all adults. We wish to find the sample size necessary to estimate the mean IQ score of statistics students. Suppose we want to be 90% confident that our sample mean is within 2 IQ points of the true mean. Assume then that σ = 15 and determine the required sample size .

Learn more about Sample Size here

https://brainly.com/question/23210694

#SPJ4

Using the regression model you predict the sales to be $ 250.38 on day 60.

A regression model is an equation used to ascertain the relationship between two variables.

Given that an electronics retailer used regression to find a simple model to predict sales growth in the first quarter of the new year (January through March). The model is good for 90 days, where x is the day.

The model can be written as follows:

ŷ = 103.38 + 2.45x

where ŷ is in thousands of dollars.

Since we require the sales gtowth after 0 days, substituting x = 60 into the equation for the regression model, we have that

ŷ = 103.38 + 2.45x

ŷ = 103.38 + 2.45(60)

ŷ = 103.38 + 2.45(60)

ŷ = 103.38 + 147

ŷ = 250.38

So, you predict the sales to be $ 250.38 on day 60.

Learn more about regression model here:

https://brainly.com/question/25987747

#SPJ1

Step 1: Isolate w^2:

     w^2 = 54

Step 2: Apply the sq. rt. property:

     w = ± sqrt(54)

Step 3: Simplify the sqrt:

     w = ± sqrt(9 · 6)

     w = ± sqrt(9) · sqrt(6)

     w = ± 3 sqrt(6)

Step 4: Approximate:

     w ≈ ± 7.3

The value which is round off to the nearest thousand for 231469.335329 is 232000.

What is rounding off?

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done. The important figures are preserved when numbers are rounded off.

The given value in the question is 231469.335329

The rules for rounding off says,

If the last digit of the given number is above 5 or equal to 5 then 1 is added to pre digit of last number and last digit is replaced by 0.

So, the given value,

231469.335329 the digit after the point is less than 5 so we eliminate the value without adding 1.

It becomes, 231469.00

In above value, if 231469 we add one to the before the last digit, it becomes 231470

As a next step, add the number in the 2 digit by adding 1 to before the 2nd digit, it becomes 231500.

Now Finally, the process of adding one to the 4 digit depends on the values of 3rd digit takes place and it becomes 232000.  

Hence, the number is 232000.

To know more about rounding-off, go to link

https://brainly.com/question/18559777

#SPJ1

The formula for simple interest.

SI = P( x R x T) / 100

The outstanding balance of her loan after the first month is $608355

It is the interest calculated on the principal at a given rate for a time period.

The formula for simple interest.

SI = P( x R x T) / 100

We have,

The purchase price of the home = $210,000

The down payment.

= 30% of 210,000
= 3/10 x 210,000

= 3 x 21,000

= $63,000

Now,

The remaining amount.

= 210,000 - 63,000

= $147,000

Now,

Simple interest for 30 years.

= (147,000 x (21/2) x 30) / 100

= (147,000 x 21 x 30) / 200

= 1470 x 21 x 15

= $463,050

Thus,

The total amount to pay for 30 years.

= 147,000 + 463,050

= $610050

The monthly payment for 30 years.

= 610050 / (30 x 12)

= $1694.58

Now,

The outstanding balance of her loan after the first month.

= 610050 - 1694.58

= $608355

Thus,

The outstanding balance of her loan after the first month is $608355

Learn more about simple interests here:

https://brainly.com/question/25845758

#SPJ1

The simplest radical representation of square root of 200 is 10√2.

The radical symbol used to denote a number's root is "." The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number. For instance, the square of 3 is 9, the square root of 9 is 9, and 32 also equals 9.

e that divides into the initial number or pair should be located.

Add the square to the initial number or pair.

Drop the following pair down.

The square's leading digit should be multiplied by two.

Create the following factor equation.

If we are aware of a number's prime factors, we can write the square root of that number in radical form. Thus, 200 can be factored into its primes as 2 ,2 ,2 ,5 ,5. As a result, 10√2. should be the square root of 200 in the simplest radical form.

In order to learn more about square root visit:

https://brainly.com/question/3120622

#SPJ4

2.5% of values will lie above 29.

What is normal distribution?

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

The 68-95-99.7 rule is an illustration of how those many percentage of values lie in between  mean +/- 1, 2, and 3 standard deviations respectively.

For values to lie above 29, their z value comes out to be

(29-19) / 5 = 10/5 = 2

(Note: z value means how many standard deviations above the mean)

Thus for a z value = 2 (which 29 is in this problem) the percentage of values that lie between mean +/- 2*(standard deviation) is 95 (as stated by the 68-95-99.7 rule).

Thus only 5% values wont lie between mean +/-2 standard deviations.

So 5% values wont lie between 29 (z value=2) and 9 (z value=-2).

Since normal curve is symmetric, half of the values of the 5% will lie above 29 and the rest half will lie below 9.

So 50% of 5 % which is 2.5% of values will lie above 29.

Hence, 2.5% of values will lie above 29.

To know more about normal distribution, click on the link

https://brainly.com/question/4079902

#SPJ4

Answer:

Step-by-step explanation:

its all explained in picture

On solving the provide question, based on the congruent triangles properties, we got to know that x= 76° and 90°.

Congruent triangles are two triangles that are identical in terms of their size and form. The two congruent triangles remain congruent whether you rotate, flip, or flip one of them. If two triangles have the same number of sides, then their angles and congruence must match.

As a result, we can determine that two triangles are congruent if all three of their sides are equal. We also understand that if there is a side, an angle between the sides, and a third side that is congruent, the three sides are congruent. which means sides, corners, and sides.

For green -

=> x = 76° ( both side are same)

For orange -

=> x = 90°

To know more about congruent triangle visit:

https://brainly.com/question/22062407

#SPJ1

Answer:

The answer is option (C). Four Rivers Bank

Explanation:

a). The total amount Jane will receive after 5 years after investing $40,000 in the Mystic Bank can be expressed as follows;

A = P (1 + r/n) (nt)

where;

A = the future value of the initial investment

P = initial investment amount/principal amount

r = the annual interest rate

n = the number of times that interest is compounded per unit t

t = the time the money is invested for

In our case;

P=$40,000

r=12/100=0.12

n=interest is compounded quarterly which is four times a year=4

t=5 years

Replacing values in the formula;

A=40,000(1+0.12/4)^(4×5)

A=40,000(1+0.03)^20

A=40,000×1.806

A=72,244.45

The total amount Jane will receive after 5 years if she chooses to invest with the Mystic Bank is $72,244.45

b). The total amount Jane will receive after 5 years after investing $40,000 in the Four Rivers Bank can be expressed as follows;

A = P (1 + r/n) (nt)

where;

P=$40,000

r=14/100=0.14

n=interest is compounded semiannually which is two times a year=2

t=5 years

Replacing values in the formula;

A=40,000(1+0.14/2)^(2×5)

A=40,000(1+0.07)^10

A=40,000×1.967

A=78,686.05

The total amount Jane will receive after 5 years if she chooses to invest with the Four Rivers Bank is $78,686.05

c). The best deal would be to invest with Four Rivers Bank for 5 years since the total amount Jane will receive after 5 years will be $78,686.05 which is greater than $72,244.45, which is the total amount she will receive if she chooses to invest with Mystic Bank

Standard Deviation is a measure of the spread of a data set. The smaller the standard deviation, the closer the values are to the mean.

In the box and whisker plots, the box represents the middle portion of the dataset (the middle 50%), the whiskers represent the outer 25% of the data, and the line inside the box is the median.In this case, the box and whisker plot with the smallest standard deviation is the plot on the right, which shows a box that is wider than the other plot but with less variation in the whiskers. This indicates that the values in the plot on the right are closer to the median than in the plot on the left, which suggests that the standard deviation of the plot on the right is smaller than the standard deviation of the plot on the left.

Learn more about standard deviation here

https://brainly.com/question/13905583

#SPJ4

Answer:

48 reindeer

Step-by-step explanation:

the 5 part of the ratio relates to 60 moose , then

60 ÷ 5 = 12 ← value of 1 part of the ratio

then

4 × 12 = 48 ← number of reindeer

The floor area of a rhombus is equal to (1/2) × diag1 × diag2 is equal to 100 ft^2

diag1 = sqrt((10 ft)^2 + (10 ft)^2)

diag2 = sqrt((10 ft)^2 + (10 ft)^2)

Floor area = (1/2) × (sqrt((10 ft)^2 + (10 ft)^2)) × (sqrt((10 ft)^2 + (10 ft)^2))

= (1/2) × (14.14 ft) × (14.14 ft)

= 100 ft^2

1. Find the length of the diagonals of the rhombus.

diag1 = sqrt((10 ft)^2 + (10 ft)^2)

diag2 = sqrt((10 ft)^2 + (10 ft)^2)

2. Use the formula for the floor area of a rhombus.

Floor area = (1/2) × diag1 × diag2

3. Substitute the diagonals into the formula.

Floor area = (1/2) × (sqrt((10 ft)^2 + (10 ft)^2)) × (sqrt((10 ft)^2 + (10 ft)^2))

4. Simplify.

Floor area = (1/2) × (14.14 ft) × (14.14 ft)

= 100 ft^2

Find the length of the diagonals of the rhombus (sqrt((10 ft)^2 + (10 ft)^2)). Use the formula for the floor area of a rhombus (1/2 × diag1 × diag2). Substitute the diagonals into the formula and simplify to find the floor area (100 ft^2).

Learn more about area here

https://brainly.com/question/13194650

#SPJ4

Answer:

To solve this system of equations, we need to find the values of x and y that make both equations true at the same time.

One way to solve this system is to use the substitution method. We can start by setting the two expressions for y equal to each other:

3x = -x + 4

Then we can solve for x by adding x to both sides and simplifying:

4x = 4

x = 1

Now that we know the value of x, we can substitute it back into either of the original equations to solve for y:

Y = 3x

Y = 3(1)

Y = 3

Therefore, the solution to the system of equations is (x, y) = (1, 3).

Answer:

150-3x

Step-by-step explanation:

Use distrubitive property:

180-6x +3x-30

Factor:

150-3x

Answer:

-3x+150

Step-by-step explanation:

6(30-x)+3(x-10)

6(30)+6(-x)+3(x)+3(-10)

180-6x+3x-30

180-3x-30

-3x+150

hopes this helps please mark brainliest