Let X and Y be IID Unif(0, 1). Find the expected value and the standard deviation of X-Y. i.e., the distance between X and Y.

The minimum distance between the point (2, -1) and the line y = 7 is 6 units.

The given line is y = 7, which means the y-coordinate of any point on the line is always 7. We need to find the minimum distance between the point (2, -1) and this line.

To calculate the minimum distance, we need to find the perpendicular distance from the point (2, -1) to the line y = 7.

Since the line is horizontal, any point on the line will have the same y-coordinate, which is 7. Therefore, the shortest distance from the point (2, -1) to the line y = 7 will be the vertical distance between these two points.

The formula to calculate the vertical distance between a point (x₁, y₁) and a horizontal line y = k is given by:

Distance = |y₁ - k|

In this case, k = 7 and the point is (2, -1). Substituting these values into the formula, we get:

Distance = |-1 - 7| = |-1 + 7| = |6| = 6

Therefore, the minimum distance between the point (2, -1) and the line y = 7 is 6 units.

For such more questions on minimum distance

https://brainly.com/question/30566585

#SPJ11

The error that Janice made is that she did not convert the improper fraction StartFraction 130 over 30 EndFraction to a mixed number correctly in her final answer.

The error that Janice made can be identified by analyzing her calculations. Let's examine each step she took:

Step 1: 10 and StartFraction 5 over 6 EndFraction divided by 1 and two-thirds

In this step, Janice correctly converted the mixed number to an improper fraction, which becomes 10 and StartFraction 5 over 6 EndFraction = StartFraction 65 over 6 EndFraction.

Step 2: StartFraction 65 over 6 EndFraction divided by five halves

In this step, Janice attempted to divide the fractions. However, she made an error by adding the numerators and denominators instead of multiplying. This is incorrect. The correct operation for dividing fractions is to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of five halves is two fifths.

Step 3: StartFraction 65 over 6 EndFraction times StartFraction 2 over 5 EndFraction

Here, Janice multiplied the fractions correctly. The product of these fractions is StartFraction 130 over 30 EndFraction.

Step 4: StartFraction 130 over 30 EndFraction = 4 and one-third

In this step, Janice attempted to convert the improper fraction to a mixed number. However, she made another error in her calculation. The fraction StartFraction 130 over 30 EndFraction is not equal to 4 and one-third. The correct conversion would yield 4 and two-sixths or 4 and one-third.

Therefore, the error that Janice made is that she did not convert the improper fraction StartFraction 130 over 30 EndFraction to a mixed number correctly in her final answer.

for more such question on improper fraction visit

https://brainly.com/question/19318336

#SPJ8

According to the information, the missing number from the box is number 40.

To find the missing number of the table we must take into account different elements. In particular we must look at the totals and the columns and rows in which the empty space is. Once we identify the totals we can subtract the other values from the total and find the missing number in the table.

According to the above we can infer that the missing number is 40.

Learn more about numbers in: https://brainly.com/question/24908711
#SPJ1

1. Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per m².

a = 51 m, b = 37 m, c = 20 m

semiperimeter:  p = (51+37+20):2 = 54 m

Area of triangle:

\(A=\sqrt{p(p-a)(p-b)(p-c)}\\\\A=\sqrt{54(54-51)(54-37)(54-20)}\\\\A=\sqrt{54\cdot3\cdot17\cdot34}\\\\A=\sqrt{9\cdot2\cdot3\cdot3\cdot17\cdot17\cdot2}\\\\A=3\cdot2\cdot3\cdot17\\\\A=306\,m^2\)

Rate:  ₹ 3 per m².

Cost:  ₹ 3•306 = ₹ 918

2. Find the area of the isosceles triangle whose perimeter is 11 cm and the base is 5 cm.

a = 5 cm

a+2b = 11 cm  ⇒  2b = 6 cm   ⇒  b = 3 cm

p = 11:2 = 5.5

\(A=\sqrt{5.5(5.5-3)^2(5.5-5)}\\\\ A=\sqrt{5.5\cdot(2.5)^2\cdot0.5}\\\\ A=\sqrt{11\cdot0.5\cdot(2.5)^2\cdot0.5}\\\\A=0.5\cdot2.5\cdot\sqrt{11}\\\\A=1.25\sqrt{11}\,cm^2\approx4.146\,cm^2\)

3. Find the area of the equilateral triangle whose each side is 8 cm.

a = b = c = 8 cm

p = (8•3):2 = 12 cm

\(A=\sqrt{12(12-8)^3}\\\\ A=\sqrt{12\cdot4^3}\\\\ A=\sqrt{3\cdot4\cdot4\cdot4^2}\\\\A=4\cdot4\cdot\sqrt{3}\\\\A=16\sqrt3\ cm^2\approx27.713\ cm^2\)

4. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.

a = 2x

b = 3x

2x + 2•3x = 32 cm  ⇒ 8x = 32 cm   ⇒  x = 4 cm  ⇒ a = 8 cm, b = 12 cm

p = 32:2 = 16 cm

\(A=\sqrt{16(16-8)(16-12)^2}\\\\ A=\sqrt{16\cdot8\cdot4^2}\\\\ A=\sqrt{2\cdot8\cdot8\cdot4^2}\\\\ A=8\cdot4\cdot\sqrt2\\\\ A=32\sqrt2\ cm^2\approx45.2548\ cm^2\)

After calculating we found that: a) 95% of widget weights lie between 42 and 54 ounces.b) 97.35% of widget weights lie between 39 and 54 ounces and c) 0.3% of widget weights lie above 45 ounces.

a) Since the distribution is bell-shaped and the mean is 48 ounces with a standard deviation of 3 ounces, we can use the 68-95-99.7 Rule to determine that 68% of the widget weights lie within one standard deviation of the mean, 95% lie within two standard deviations of the mean, and 99.7% lie within three standard deviations of the mean. Thus, we know that 95% of the widget weights lie between:

48 - 2(3) = 42 ounces and 48 + 2(3) = 54 ounces.

b) To find the percentage of widget weights that lie between 39 and 54 ounces, we need to determine how many standard deviations away from the mean these values are.

39 ounces is 9 ounces below the mean, so it is (9/3) = 3 standard deviations below the mean.

54 ounces is 6 ounces above the mean, so it is (6/3) = 2 standard deviations above the mean.

Using the 68-95-99.7 Rule, we know that 99.7% of the widget weights lie within three standard deviations of the mean. Since 39 ounces is three standard deviations below the mean, we can conclude that 0.15% (or 0.003 x 100) of the widget weights lie below 39 ounces.

Likewise, since 54 ounces is two standard deviations above the mean, we know that 2.5% of the widget weights lie above 54 ounces. Thus, the percentage of widget weights that lie between 39 and 54 ounces is:

100% - 0.15% - 2.5% = 97.35%

c) We need to find the percentage of widget weights that lie above 45 ounces. Since 45 ounces is three standard deviations below the mean, we know that 99.7% of the widget weights lie above 45 ounces. Therefore, the percentage of widget weights that lie above 45 ounces is:

100% - 99.7% = 0.3%.

To know more about standard deviation, visit: https://brainly.com/question/23907081

#SPJ1

The number of cookies and trays are illustrations of greatest common factors.

The given parameters are:

\(\mathbf{Chocolate\ chip=48}\)

\(\mathbf{Rainbow=64}\)

\(\mathbf{Oatmeal=120}\)

(a) The number of trays

To do this, we simply calculate the greatest common factor of 48, 64 and 120

Factorize the numbers, as follows:

\(\mathbf{48 = 2 \times 2 \times 2 \times 2 \times 3}\)

\(\mathbf{64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2}\)

\(\mathbf{120 = 2 \times 2 \times 2 \times 3 \times 5}\)

So, the GCF is:

\(\mathbf{GCF= 2 \times 2 \times 2}\)

\(\mathbf{GCF= 8}\)

Hence, the number of tray is 8

(b) The number of each type of cookie

We have

\(\mathbf{Chocolate\ chip=48}\)

\(\mathbf{Rainbow=64}\)

\(\mathbf{Oatmeal=120}\)

Divide each cookie by the number of trays

So, we have:

\(\mathbf{Chocolate\ chip = \frac{48}{8} = 6}\)

\(\mathbf{Rainbow = \frac{64}{8} = 8}\)

\(\mathbf{Oatmeal = \frac{150}{8} = 15}\)

Hence, 6 chocolate chips, 8 rainbows and 15 oatmeal cookies would fit each tray

Read more about greatest common factors at:

https://brainly.com/question/11221202

Answer:

Step-by-step explanation:

Given the angles 21° and 92° where three lines are coincident, you want the measures of angles d, e, and f.

Angles on opposite sides of the point where lines cross are vertical angles. They share a vertex, and are formed from opposite rays. They are not adjacent. Vertical angles are congruent.

Here, the angle marked d is a vertical angle with the one marked 92°. The angle marked e is a vertical angle with the one marked 21°

A linear angle is a straight line. Its angular measure is 180°. Here, the angles d, e, and f add up to form a linear angle:

  d + e + f = 180°

  92° +21° +f = 180°

  f = 180° -113°

  f = 67°

The area of the shaded region, with a frame of 3 units wide, is 264 square units. The inner rectangle is 6x4 units, and the outer rectangle is 18x16 units.

To solve the given problem, we have to find the area of the shaded region if the frame is 3 units wide. If the frame is 3 units wide, then the dimensions of the inner rectangle (the shaded region) will be (12 - 6) × (10 - 6) which simplifies to 6 × 4.

Therefore, we can say that the inner rectangle has a length of 6 units and a width of 4 units.The dimensions of the outer rectangle are (12 + 3 + 3) × (10 + 3 + 3) which simplifies to 18 × 16. Therefore, we can say that the outer rectangle has a length of 18 units and a width of 16 units.

The area of the shaded region can be obtained by subtracting the area of the inner rectangle from the area of the outer rectangle. Therefore, the Area of the outer rectangle = length × width= 18 × 16 = 288 square units

Area of the inner rectangle = length × width= 6 × 4 = 24 square units

Area of the shaded region = Area of the outer rectangle - Area of the inner rectangle = 288 - 24= 264 square units

Therefore, the area of the shaded region is 264 square units.

For more questions on the area of the shaded region

https://brainly.com/question/23973962

#SPJ8

True. A data model is an abstract representation of the data structures used in a database.

It is typically used to represent the structure of the data and the relationships between different elements of the data. Data models are used to define the structure of the data in a database, as well as the relationships between different elements of the data. A data model is a combination of entities, attributes, relationships, and constraints. It is used to describe the data that is stored in a database and how the data can be accessed and manipulated. The data model also defines the relationships between the different elements of the data, such as which element of the data is related to which other element. The data model also defines the constraints that must be met in order to ensure the integrity of the data. A data model is also used to define the data types that are used in the database and the operations that can be performed on the data. For example, a data model may define data types such as integers, strings, and dates, as well as operations such as arithmetic, comparison, and sorting. A data model also defines rules for the structure and organization of the data, such as which fields must be present in a record, the order in which records must be stored, and the types of relationships that can exist between records.

Learn more about combination here:

https://brainly.com/question/20211959

#SPJ4

The value of each variable is:

x = 11 units

y = 11√2 units

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

We can find the value of each variable using trigonometric ratios:

tan 45° = x/11 (tan = opposite/adjacent)

1 = x/11

x = 11 units

sin 45° =  9/y (sine = opposite/hypotenuse)

(√2)/2 = 11/y

y = 11/ (√2)/2

y = 11√2 units

Learn more about Trigonometry on:

brainly.com/question/11967894

#SPJ1

Answer:

If I calculated correctly, the tangent line is horizontal where x ≈ -5.3 + 9.3i, and -5.3 - 9.3i

I'm somewhat concerned at having gotten complex numbers, and strongly recommend going through the steps to see if I missed anything.  I checked it myself and don't see any errors.

Step-by-step explanation:

You can do this by taking the derivative of the function and solving for zero:

f(x) = 2x³ + 32x² + 220x + 11

f'(x) = 6x² + 64x + 220

f'(x) = 2(3x² + 32x + 110)

We can't factor that further, so let's do it the long way, starting by letting f'(x) equal zero:

0 = 2(3x² + 32x + 110)

0 = 3x² + 32x + 110

0 = 9x² + 96x + 990

0 = 9x² + 96x + 256 + 734

0 = (3x + 16)² + 734

(3x + 16)² = -734

3x + 16 = ± i√734

3x = -16 ± i√734

x = (-16 ± i√734) / 3

x ≈ (-16 + 27.9i) / 3, and  (16 - 27.9i) / 3

x ≈ -5.3 + 9.3i, and -5.3 - 9.3i

I'm always wary when I end up with complex numbers.  I'd suggest double checking everything here, but I'm fairly certain I did everything correctly.

Answer:

2 1/2 beacuse he needs 1 1/4 for one feeder

Step-by-step explanation:

answer:

1

Step-by-step explanation:

#'s between zero and two = one

the only number between 0 and two is 1

x = 1  y = 1  z = 1

the average value of the sum of the squares of x, y and z = 1

1, 1, 1

the average is 1

Triangles are shown to be congruent by the statement that "Angles are congruent by vertical angles."

Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.

Given two triangles, Where the base of these triangles are same

And also given that the two angles are the same.

Since,

Two intersecting lines form a pair of vertical angles. The vertical angles are opposite angles with a common vertex (which is the point of intersection).

Thus, the third angle is also equal

From AAS:

AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent

Therefore. "Angles are congruent by vertical angles" is used to show the triangles are congruent by AAS,

Learn more about congruent triangles here:

https://brainly.com/question/22062407

#SPJ1

Answer:

(-4 , 2)

Step-by-step explanation:

      3y - 2x ≥ 8

The ordered point (-4 ,2) satisfies the inequality. So, (-4,2) is the solution for the equation.

3*2 - 2*(-4) ≥ 8

     6 + 8  ≥ 8

         14  ≥ 8

The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

Learn more about LCM here :

https://brainly.com/question/6756370

#SPJ1

The writer paid $8575 in federal income tax last year.

To get federal income tax paid by the grant writer, we have to get amount of income taxed at each tax rate and then sum up the respective amounts.

Income taxed at 10%:

= $8350 - $0

= $8350

Tax paid at 10% rate: 10% of $8350 = $835

Income taxed at 15%:

= $33,950 - $8350

= $25,600

Tax paid at 15% rate: 15% of $25,600 = $3840

Income taxed at 25%:

= $49,550 - $33,950

= $15,600

Tax paid at 25% rate: 25% of $15,600 = $3900

The total federal income tax paid is:

= $835 + $3840 + $3900

= $8575.

Read more about income tax

brainly.com/question/30157668

#SPJ1

Answer:

75.36 feet

Step-by-step explanation:

It’s in the attachment below!

Answer:

okay, so we have a wall that is 60 ft. The area of the wall because the wall is a square is just side squared. So the area of the wall is \(60^{2}\), which is 30 600 square feet. The mirror is 20 ft by 60 ft. So the area of the mirror, because its a rectangle is length times width, so that's 20 a 60 so 20 x 60 is gonna give me 1200 square feet. So if we take the area of the mirror and put that over the area, the wall we get 1200 over 30 600, which reduces to one over three. So the mirror is one third the area of the wall.

Step-by-step explanation:

Answer: i think 15/8 but, im not sure

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

First in order to solve this problem we need to simplify the answer choices.

A. 6×8 + 6×6 = 48+ 36

B. 12×4 + 12×1=48+12

C. 4×44 + 4×3=176+12

D. 8×6 + 8×4 = 48+32

As you can see there is one expression that is equivalent to 48+12. Answer choice B is correct.

The expression that is equivalent to 48 + 12 is 12(4 + 1), Option B is correct.

An expression is combination of variables, numbers and operators.

To find the expression that is equivalent to 48 + 12, we need to simplify each of the given expressions and find the one that is equal to 60.

Because the value of 48+12 is 60

A. 6(8 + 6) = 6(14) = 84

B. 12(4 + 1) = 12(5) = 60

C. 4(44 + 3) = 4(47) = 188

D. 8(6 + 4) = 8(10) = 80

Out of the given expressions, only expression B simplifies to 60, which is equivalent to 48 + 12.

Therefore, the expression that is equivalent to 48 + 12 is 12(4 + 1), Option B is correct.

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ3

The formula of the function, where x is entered in radians is   y = -3sin(πx/5) -6

The key components: amplitude, period, phase shift, and vertical shift.

Amplitude is the distance between the midline and max/min points. Midline at (0, -6), so distance to min point (2.5, -9) is 3. Amplitude: 3.

Vertical shift: Displacement along y-axis. Midline at y = -6, vertical shift is -6. Period: distance between max/min points. Graph intersects midline at (0, -6) and minimum point at (2.5, -9).  Period is 5 (2 * 2.5). Freq: Reciprocal of period, 1/5.

Phase shift: Horizontal shift of graph. Graph intersects midline at x=0, no phase shift.

Hence:

The general form of the sinusoidal function is y = A sin (B(x-C)) + D

So, Substituting the known values into the general formula:

y = 3 x  sin((1/5)x - 0) - 6

Hence: Simplifying it will be:

y = 3 x sin(πx/5) - 6

Then, the formula of the function, where x is entered in radians, is: y = -3sin(πx/5) - 6

Based on the image attached, the first given point is one that informs one that the function is a sine (not a cosine) function, and that it is one that has its offset as -6.

Also, the second given point is one that informs you of the first peak is at x=2.5, hence the argument of the sine function is π/2 if x=2.5: (πx/5).

Based on the fact that the peak is 3 units smaller than the midline, the amplitude is said to be -3.

Therefore the  formula for the function is  seen as:  y = -3·sin(πx/5) -6

Learn more about sinusoidal function from

https://brainly.com/question/16300816

#SPJ1

Answer:

I think it's about 3840 in.^2

Step-by-step explanation:

The shape is a half circle and a parallelogram

Area of a half circle is 1/2 x pi x r ^2

R is half the diameter(8in), r = 4

Area of half circle = 1/2 x 3.14 x 4^2

Area of half circle = 25.12 square in.

Area of parallelogram = length x height

Area of parallelogram = 10 x 6 = 60 square in.

Total area = 25.12 + 60 = 85.12 square inches

Answer: 85.12 square inches

Correct question is;

Type the correct answer in the box bellow: If cos x = sin(20 + x)° and 0° < x < 90°, the value of x is ...........

Answer:

x = 35°

Step-by-step explanation:

We are told that;

cos x = sin(20 + x)°

and 0° < x < 90°

From trigonometric identities, we know that;

cos x = sin (90 - x)

Applying to our question gives;

sin (90 - x) = sin (20 + x)°

Comparing both sides, we have;

90 - x = 20 + x

Rearranging;

90 - 20 = x + x

70 = 2x

x = 70/2

x = 35°

The price of the bed after mark up is $475.00

Discount results in the reduction of the selling price of the product, which makes it more attractive for the customer.

The first discount given is 25% , therefore the price of the bed before mark up is

25/100 × 800

= 25×8

= 200

the price before mark up = 800-200 = $600

Another 25% is given after the first sale, there the price of the bed after mark up is

25/100 × 600

=$ 125

price after markup = 600-125

= $475.00

therefore the price of the bed after markup is $475.00

learn more about discount from

https://brainly.com/question/1548141

#SPJ1

Answer:

23/4

Step-by-step explanation:

Answer:

A mixed number is an addition of its whole and fractional parts.

\(5 \frac{3}{4} \)

Add:

\(5 \: and \: \frac{3}{4} \)

To write 5 as a fraction with a common denominator, multiply by

\( \frac{4}{4} \)

Combine:

\(5 \: and \: \frac{4}{4} \)

Combine the numerators over the common denominator.

\( \frac{5.4 + 3}{4} \)

Simplify the numerator.

Multiply 5 by 4.

Add 20 and 3.

\( \frac{23}{4} \)

Step-by-step explanation:

Thanks!!!!!!

Answer:

.

Step-by-step explanation:

ANSWER:

For this reason Eva is not right

STEP-BY-STEP EXPLANATION:

For two fractions to be equivalent in both the numerator and denominator, they must be multiplied by the same number, just like this:

Therefore, the correct drawing would be: