in a certain isosceles right triangle, the altitude to the hypotenuse has length $6$. what is the area of the triangle?

About 50 percent of its former width.

Now, According to the question:

Let's assume that our parameter of interest is given by θ and in order to construct a confidence interval we can use the following formula:

θ = ± ME(θ vector)

Where θ vector is an estimator for the parameter of interest and the margin of error is defined usually if the distribution for the parameter is normal as:

ME = [tex]z_\alpha[/tex]SE

Where [tex]z_\alpha /2[/tex]  is a quantile from the normal standard distribution that accumulates [tex]\alpha /2[/tex] of the area on each tail of the distribution. And SE represent the standard error for the parameter.

If our parameter of interest is the population proportion the standard of error is given by:

SE =[tex]\frac{p(1-p)}{n}[/tex]

And if our parameter of interest is the sample mean the standard error is given by:

SE = [tex]\frac{1}{\sqrt{n} }[/tex]

As we can see the standard error for both cases assuming that the other things remain the same are function of n the sample size and we can write this as:

SE = f(n)

And since the margin of error is a multiple of the standard error we have that

ME = f(n)

Now if we find the width for a confidence interval we got this:

Width = θ + ME (θ) - [θ - ME (θ)]

Width = 2ME(θ)

And we can express this as:

Width = 2f(n)

And we can define the function f(n) = [tex]\frac{1}{\sqrt{n} }[/tex]  since as we can see the margin of error and the standard error are function of the inverse square root of n. So then we have this:

[tex]Width_i[/tex] = [tex]2\frac{1}{\sqrt{n} }[/tex]

The subscript i is in order to say that is with the sample size n

If we increase the sample size from n to 4n now our width is:

[tex]Width_f[/tex] = [tex]2\frac{1}{\sqrt{4n} }[/tex] = [tex]2\frac{1}{\sqrt{n}\sqrt{4} }[/tex] = [tex]\frac{1}{\sqrt{n} }[/tex] = 1/2 [tex]Width_i[/tex]

The subscript f is in order to say that is the width for the sample size 4n.

So then as we can see the width for the sample size of 4n is the half of the with for the width obtained with the sample size of n. So then the best option for this case is:

about 50 percent of its former width.

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This is incomplete question:

Complete question is this :

In constructing a 95 percent confidence interval, if you increase n to 4n, the width of your confidence interval will (assuming other things remain the same) be:

about 25 percent of its former width.

about two times wider.

about 50 percent of its former width.

about four times wider.

( π=3,14 , r= d/2= 7.6/2= 3,8m )

C= 2πr
C= 2·π·3.8
C≈23.87m

The probability that a randomly chosen subject completes at least three puzzles in the 5 minute period while listening to soothing music is 0.4.

Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen. The probability of a random variable can be given by,

                                ⇒    f ( x ) p ( x )    =   P ( X = x )

As per the question,

        P ( X = 1 )   =   0.2

        P ( X = 2 )   =   ?

        P ( X = 3 )   =   0.3

        P ( X = 4 )   =   0.1

⇒   P ( X ≥ 3 )   =   P ( X = 3 ) + P ( X = 4 )

                         =   0.3 + 0.1

      P ( X ≥ 3 )   =   0.4  

Therefore, 0.4 is the probability that a randomly chosen subject completes at least three puzzles in the 5-minute period while listening to soothing music.

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The complete question is

As per the concept of inverse function, For a function f: X → Y to have an inverse, it must have the property that for every y in Y, there is exactly one x in X such that f(x) = y.

Inverse function:

Inverse function refers a function that serves to “undo” another function.

Given,

Here we need to find the a function to have an inverse, it must be what type of function.

Based on the explanation of the inverse function, if the function is a inverse function, then it means that for all x values must have the relation in y similarly, for a the y values must have the x values.

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Answer:

the third opinion: [tex]y = \frac{1}{4}x - 1[/tex] (or as you put it, y equals one fourth times x minus 1)

This is because it's written in slope-intercept form: y = mx + b . m is the slope, which is 1/4, and b is the y-intercept, -1

Total force exerted is 50N.

What is force?

Force is any interaction that, when unopposed, will change the motion of an object.

Main body:

F=Mg-Ma

then implied:

a=(F-Mg)/M

which seems unsound, it should have said:

a = (Mg - F)/M

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

Now, let's begin and use the previous gentleman's notation:

Mass of bucket=M

mass of cylinder=m

Tension force=F

So, regarding the bucket:

F + Ma = Mg

F = Mg - Ma

a = (Mg - F)/M

Also, regarding the cylinder: T = Iα

∴ (By the dot product of torque, radial vector crossed with force, r cross F, which is Frsinθ for θ = 90 degrees)

T = Iα = Fr = (1/2)(mr2)(a/r)

where α = a/r

And T = Fr because that's what torque is, just the radial distance times the force.

So

a = 2F/m

and we also have:

a = (Mg-F)/M

So 2F/m = (Mg-F)/M

2F = mg - mF/M

2F+(mF)/M = mg

F(2+m/M) = mg

F = mg/(2+m/M)

F = (127.4 )/(2+0.56)

F = 49.765 N

That is to say, the tension that the rope induces on the bucket is 50.5 Newtons in the upward direction (positive).

Hence force exerted is approx 50 N.

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Answer:

24

Step-by-step explanation:

120 minus 80% = 120 times 20% (fractions division method)

120 times 20% = 120 times 0.2 (simplify)

120*0.2 = 24, so the answer is 24

The area of the region cut from the first quadrant by the cardioid is 3π/8 +1

A cardioid is a two-dimensional plane figure that has a heart-shaped curve. The equation of cardioid is r = a(1 ± sinθ) .

The area of the polar function can be calculated if the boundary condition that form the reason is given or can be found from the given information now we use the formula using the polar formula of the area as:

[tex]A = \int\limits^b_a {\frac{r^{2}}{2}} d\theta[/tex]

The Area of the region cut from the first quadrant by cardioid,

[tex]A = \int\limits^\frac{\pi}{2}_0 {\frac{r^{2}}{2}} d\theta[/tex]

Substituting r = 1 + sin ∅

[tex]A = \int\limits^\frac{\pi}{2}_0 {\frac{(1+ sin\theta)^{2}}{2}} d\theta[/tex]

Opening square ,

[tex]A = \frac{1}{2}\int\limits^\frac{\pi}{2}_0 {1 +2sin\theta + sin^{2}\theta d\theta[/tex]

=> [tex]A = [ \frac{1}{2} (\theta - 2cos\theta + \frac{1}{2} (\theta - \frac{1}{2}sin2\theta))]^\frac{1}{2}_{0}[/tex]

=> 3π / 8 - (-1)

=> 3π/8 +1

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If the customer makes a purchase and pays $5,500 on account and $6,600 cash, the total ammount he paid is $ 12100

The customer makes a purchase

He pays $5500 on account

He also pays 6600 in cash

We need to find the total amount he used to purchase

The total amount can be calculated by adding the price he paid in accound and in cash

The total amount is 5500 + 6600 = 12100

Therefore, if the customer makes a purchase and pays $5,500 on account and $6,600 cash, the total amount he paid is $ 12100

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The perimeter of the rectangle is: 2⅙ yd

The area of the rectangle is: 1/4 yd².

Given the following:

Length of rectangle = 3/4 yd

Width of rectangle = 1/3 yd

The perimeter of rectangle = 2(3/4 + 1/3) = 2(13/12)

Perimeter = 2⅙ yd

The area of the rectangle = (3/4)(1/3)

Area = 3/12

Area = 1/4 yd²

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On using the critical value (13.89 – 0.3485, 13.89 + 0.3485) when, the mean is13.89 the confidence level is 95%.

Given, a juice drink filling machine, when in perfect adjustment, fills the bottles with 14 ounces of drink on an average. a random sample of 41 bottles is selected, and the contents are measured.

as the standard deviation = 0.3485 ounces

mean = 13.89 ounces.

we have to find the confidence level,

The critical value we will use is (13.89 – 0.3485, 13.89 + 0.3485) when, the mean is 13.89.

The confidence interval for a population with a known standard deviation is based on the fact that the sample means follow an approximately normal distribution. Suppose

So, on using the critical value (13.89 – 0.3485, 13.89 + 0.3485) when, the mean is13.89 the confidence level is 95%.

Hence, on using the critical value (13.89 – 0.3485, 13.89 + 0.3485) when, the mean is13.89 the confidence level is 95%.

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The amount of bad debt expense will the company actually record is c)$139500.

So, correct option is c.

We have some details like total account receivable  as $1800000

allowance for doubtful accounts as $40,500

Now, we have also percentage of bad debt expense as 10% of accounts receivable.

So,10% of  of accounts receivable=(10/100)×1800000=$180000

Now, for getting information of bad debt expense we need to subtract allowance for doubtful accounts.

So, bad debt expense=10% of account receivable - allowance for doubtful debts

=>bad debt expense=$180000-$40500=$139,500

Hence, amount of bad debt expense is $139,500

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(Complete question) is:

Sheffield Corp. unadjusted trial balance includes the following balances (assume the normal balances): Accounts receivable as $1800000. Allowance for doubtful accounts as $40500. Bad debts are estimated to be 10% of the outstanding receivables. What amount of bad debt expense will the company actually record?

a)$137370

b)$182500

c)$139500

d)$177130

The correct answer is 7XS when RR' = 14, then RZ = 7 when the parallelogram PQRS is reflected across the line of reflection.

Given that,

If RR' = 14, then RZ = 7 when the parallelogram PQRS is reflected across the line of reflection.

SX = 5 if Y = 5.

In Euclidean geometry, a parallelogram is a straightforward (non-self-intersecting) quadrilateral with two sets of parallel sides.

A parallelogram has equal-length opposing angles and facing or opposing sides.

The Euclidean parallel postulate or one of its equivalent formulations must be used in order to demonstrate the congruence of opposite sides and angles because both requirements flow naturally from this postulate.

A quadrilateral with only one pair of parallel sides, on the other hand, is referred to in British or American English as a trapezoid or trapezium.

We get,

The parallelepiped is a three-dimensional representation of a parallelogram.

So, 7 XS is the right response to the question.

Therefore, The correct answer is 7XS when RR' = 14, then RZ = 7 when the parallelogram PQRS is reflected across the line of reflection.

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Answer:

1. 7

2. XS

Step-by-step explanation:

Answer:

Original = (8,-6) New = (0,1)

Step-by-step explanation:

Arrange the adjustments like this in the parenthesis of the original point

(8 - 8, -6 +7)

Then do the math and get (0,1)

The discriminant of the given quadratic equation is 17.

The discriminant is defined as the part of the quadratic formula underneath the square root symbol: b²-4ac. Thus, the discriminant usually tells us whether there are two solutions, one solution, or no solutions in a quadratic equation.

Now, the given quadratic equation is √2x² — 5x + √2 = 0.

This equation is of the general quadratic form of ax² + bx + c = 0.

Where,

a = √2

b = —5

c = √2

Now, discriminant is gotten as;

D = (b² - 4ac)

D= {(-5)² - (4 × √2 × √2)}

D = 25 - (4 × √4)

D = 25 - (4 × 2)

D = 25 - 8

D = 17

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It will cost $776.25 to paint the area of the rectangular wall

The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units (square centimeters, square inches, square feet, etc.) The area of a rectangle is the number of unit squares that can fit into a rectangle. Some examples of rectangular shapes are the flat surfaces of laptop monitors, blackboards, painting canvas, etc.

The formula of area of a rectangle is given as;

A = L * W

Imputing the values and calculate the area of the rectangular wall;

A = 12.5 * 18

A = 225ft²

But in the question, the cost of painting the wall is $3.45 per square feet.

1ft² = 3.45

225 = x

x = 3.45 * 225

x = 776.25

The cost of painting the wall is $776.25

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The equation of given line in slope-intercept form is 5x – 4y + 20 = 0 if the line makes intercepts –4 and 5 on the x- and y-axes respectively.

The diagram of the straight condition y = mx + c is a line with m as incline, m and c as the y-block. This type of the direct condition is known as the incline block structure, and the upsides of m and c are genuine numbers. The incline, m, addresses the steepness of a line. The incline of the line is additionally named as inclination, in some cases. The y-catch, b, of a line, addresses the y-direction of the place where the chart of the line converges the y-hub.

We have x-intercept as -4 and y-intercept as 5

Equation of the line in intercept form is:

(x/a) + (y/b) = 1

Substituting the values of a and b, we get the equation as:

=>(x/-4) + (y/5) = 1

=>(-5x + 4y)/20 = 1

-=>5x + 4y = 20

=>5x – 4y + 20 = 0

Hence, line equation is 5x – 4y + 20 = 0

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(Complete question) is:

What is the equation of the given line in slope-intercept form if x-intercept is -4 and y intercept is 5?

The length of SR will be 15 units, using Pythagoras' theorem

What is Pythagoras' theorem?

The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Remember that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.

Triangle SRT and triangle TRQ can be compared using the image. Since both triangles have equal sides and right angles (T), they are both triangles (RT)

Using Pythagoras theorem,  

RQ² = TQ² + TR²

20² = TR² + 16²

TR = 12

SR/RQ = TR/TQ

SR / 20 = 12 / 16

SR = 15 units

Hence the length of SR will be 15 units.

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Answer:

base is 4 units

Step-by-step explanation:

the formula for a triangle is (b x h)/2= a

So we can fill in what we know

(b x 12)/2=24

Our goal is to solve for b or the base

12b/2=24

X2.       x2

12b=48

/12.   /12

b=4

Hopes this helps please mark brainliest

According to the volume of the box, the height of the box is (2x + 3)

Volume:

Volume is defied as the space occupied within the boundaries of an object in three-dimensional space.

Given,

In order to package products for her business class, Jessica needs to determine the size of a box in which they would fit. To meet shipping specifications, the volume of the box should be 6x² - 15x-36. The box is in the shape of a rectangular prism. The width of the box must be 3, and the length of the box must be x - 4.

Now, we have to find the expression or the height of the box.

From the given details, we know that,

Volume of the box = 6x² - 15x-36

Width of the box = 3

length of the box = x - 4

Let us consider the height of the box is h.

By using the volume of the box formula, we have calculated the height of the box as,

=> 6x² - 15x-36 = (3) × (x-4) × h

Here we need the value of h,

The given expression is rewritten as,

=> (6x² + 15x-36) / 3(x - 4) = h

When we factorize the numerator, then we get,

=> 3(2x + 3)(x - 4)/3(x-4) = h

Therefore, the expression for h is 2x + 3.

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YES, the absolute value of an integral is always less than the integral of the absolute value for Lebesgue integrals.

An integral is like a sum, but fancier. So look at a sum 1+(-5)+2+(-3)=-5. Take the absolute value, |1+(-5)+2+(-3)|=5. But, if you take the absolute value of the individual terms and then add them, you get |1|+|-5|+|2|+|-3|=1+5+2+3=11. 11>5

The reason is that when you add them all up and then take the absolute value, the positive and negative terms of the sum get to cancel each other out and make the absolute value of the sum greater overall. When you take the absolute value of individual terms, you force them all to "point in the same direction" (positive) so they are working together and the sum gets higher.

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A tip of 18% was given to the restaurant after the meal and tax to the nearest percentage.

Cost of the food = $25.30

Tax on the food cost = 8%

Tax amount

= 8% of 25.30

= 0.08  × 25.30

= 2.204

Total cost of food before tip = 25.30 + 2.204 = $27.504

Tip given = 32.24 - 27.504 = 5.036

Tip percentage

= 5.036 / 27.504 × 100%

= 18.31%

≈ 18%

Hence a tip of 18% was given to the restaurant after the meal and tax to the nearest percentage.

Percentage increases and decreases are calculated by computing the difference between two numbers or by comparing that difference to the starting value.

One can calculate how significantly the initial value has changed mathematically by dividing the result by the starting value and using the absolute value of the difference between the two values.

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Hi, your answer is b. (1, 2)

Hope this helps.

The simplified expression is - (4z⁴ + 4z³ - 14z² - 47z - 70) / z + 2

Simplification of an algebraic expression can be defined as the process of writing an expression in the most efficient and compact form without affecting the value of the original expression.

The process entails collecting like terms, which implies adding or subtracting terms in an expression.

In the given expression;

7 - 2z - 4 [z³ - (z³ + 4z² + 11z + 14) / (z + 2) ]

This is simplified to ;

7 - 2z - 4 [z³ - (z³ + 4z² + 11z + 14) / (z + 2) ] = - (4z⁴ + 4z³ - 14z² - 47z - 70) / z + 2

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No, there is no price discrimination in the given question

Price discrimination is a marketing strategy where a firm levies its customers variously for a similar commodity based on the standards they have set. It is offering customers various products at various price points based on their purchasing power and demographics.

Since the retailer does not charge different prices for various products, there is no price discrimination in the given question. It cannot be argued that a local boutique owner is engaging in price discrimination if they offer a discount to a customer who is unaware of it without asking them first. Additionally, it is no priced discrimination if the shop owner does not give more than a 15% discount or any incentives for purchasing in bulk.

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From the four possible outcomes for signal detection theory exhibited in the given example is miss.

Signal detection theory refers to an approach of differentiating an individual ability to discriminate the presence and absence of a stimulus (or different stimulus intensities) from the individual’s criterion (physical/psychological state) to responses to those stimuli. It is a measure of the ability to differentiate between information-bearing patterns and random patterns that distract from the information. The four possible outcomes defined by the theory are hit (signal present and observer respond), miss (signal present and observer did not respond), false alarm (signal absent and observer respond), and correct rejection (signal absent and observer did not respond). As the brother is hiding under a pillow but the sister comes into the room and looks at the sofa, but seeing nothing, she leaves, it is a miss outcome.

Note: The question is incomplete. The complete question probably is: A brother and sister are playing hide and seek and the brother has hid under a pillow on the sofa. His sister comes into the room and looks at the sofa, but seeing nothing, she leaves. What signal detection theory potential outcome is shown in the example.

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The inverse of the functions are f⁻¹(x) = 2/[3(x + 4)], f⁻¹(x) = √[(x + 1)/2] and f⁻¹(x) = 1/x + 1

Function (a)

This function is given as

f(x)=2/(3x) - 4

The function needs to be represented as an equation

So, we have

y = 2/(3x) - 4

Swap the positions of x and y

x = 2/(3y) - 4

So, we have

2/(3y) = x + 4

Take the reciprocal of both sides

3y/2 = 1/(x + 4)

Multiply both sides by 2/3

y = 2/[3(x + 4)]

So, the inverse function is

f⁻¹(x) = 2/[3(x + 4)]

The inverse is a function with the domain x ≠ -4 and range of f(x) ≠ 0

See attachment 1 for the graphs

Function (b)

This function is given as

f(x) = 2x² - 1

The function needs to be represented as an equation

So, we have

y = 2x²- 1

Swap the positions of x and y

x = 2y² - 1

So, we have

2y²= x + 1

Divide both sides by 2

y²= 1/2(x + 1)

Take the square roots

y= √[(x + 1)/2]

So, the inverse function is

f⁻¹(x) = √[(x + 1)/2]

The inverse is a function with the domain x ≥ -1 and range of f(x) ≥ 0

See attachment 2 for the graphs

Function (c)

This function is given as

f(x) = 1/(x - 1)

The function needs to be represented as an equation

So, we have

y = 1/(x - 1)

Swap the positions of r and y

x = 1/(y - 1)

So, we have

y - 1 = 1/x

Add 1 to both sides

y = 1/x + 1

So, the inverse function is

f⁻¹(x) = 1/x + 1

The inverse is a function with the domain x ≠ 0 and range of f(x) ≠ 1

See attachment for the graphs

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Excess capacity (e.g., factories can make more than the optimal industry production quantity) within the industry is not a deterrent to entry into an industry

Barriers to entry is an economics and business term describing factors that can prevent or impede newcomers into a market or industry sector, and so limit competition. Barriers to entry may be caused naturally, by government intervention, or through pressure from existing firms

Common barriers to entry include special tax benefits to existing firms, patent protections, strong brand identity, customer loyalty, and high customer switching costs.

According to the question,

Prevalence of learning curves in the industry , Production that requires expensive machinery that can be resold and High economies of scale in the industry are all deterrent or barriers to entry

But Excess capacity (e.g., factories can make more than the optimal industry production quantity) within the industry is not a deterrent to entry into an industry because when there is excess capacity in the industry , existing firms can cut the prices making it harder for new entrant to make a profit.

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The net present value of the machine is rounded to the nearest dollar is $-76,447.56.

Net gift fee is the prevailing fee of after-tax coins flows from an funding much less the quantity invested.

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