Newborn babies weigh an average of 7.5 pounds with a standard deviation of 1.25 pounds. Find the 2-score for a baby who weighs 6.70 pounds. Round your answer to 2 decimal places. I

X denote the amount of time a book on two-hour reserve is actually checked out, and for the given cdf the following are the answers for the questions asked

(a) P(X ≤ 1) ≈ 0.0625

(b) P(0.5 ≤ X ≤ 1) ≈ 0.0469

(c) P(X > 1.5) ≈ 0.8594

(d) Median checkout duration ≈ 2.828

(e) Density function f(x) is defined as:

f(x) = 0 for x < 0

f(x) = x/8 for 0 ≤ x ≤ 4

f(x) = 0 for x > 4

(f) Expected value E(X) ≈ 2.667

(g) Variance V(X) ≈ 0.889, Standard Deviation σ(X) ≈ 0.943

(h) Expected charge E[h(X)] = 8

In probability theory, a cumulative distribution function (CDF) provides information about the probabilities of certain events occurring in a random variable. In this scenario, let's consider a book that is on a two-hour reserve and denote the amount of time it is checked out as X. We are given the CDF of X and we will use it to calculate various probabilities and statistics related to the checkout duration of the book.

The given CDF is as follows:

F(x) = 0 for x < 0

F(x) = x²/16 for 0 ≤ x ≤ 4

F(x) = 1 for x > 4

(a) P(X ≤ 1):

To calculate this probability, we need to find F(1) since F(x) represents the cumulative probability up to x. From the given CDF, we see that F(x) = x²/16 for 0 ≤ x ≤ 4. Substituting x = 1 into the equation, we get:

F(1) = (1²)/16 = 1/16.

(b) P(0.5 ≤ X ≤ 1):

To calculate this probability, we need to find F(1) - F(0.5) since F(x) represents the cumulative probability up to x. From the given CDF, we have F(0.5) = (0.5²)/16 = 1/64 and F(1) = (1²)/16 = 1/16. Therefore,

P(0.5 ≤ X ≤ 1) = F(1) - F(0.5) = (1/16) - (1/64) = 3/64.

(c) P(X > 1.5):

To calculate this probability, we need to find 1 - F(1.5) since F(x) represents the cumulative probability up to x. From the given CDF, we have F(1.5) = (1.5²)/16 = 9/64. Therefore,

P(X > 1.5) = 1 - F(1.5) = 1 - (9/64) = 55/64.

(d) Median checkout duration:

The median is the value that divides the distribution into two equal parts, meaning that half of the checkouts are below this value and half are above it. We need to solve the equation F(median) = 0.5. From the given CDF, we have:

F(median) = 0.5

0.5 = (median²)/16

Solving for the median, we get median = √(8) ≈ 2.828.

(e) Density function f(x):

The density function f(x) represents the derivative of the cumulative distribution function F(x). To obtain f(x), we differentiate the given CDF:

f(x) = F'(x)

For x < 0, f(x) = 0 since F(x) is constant in that range.

For 0 ≤ x ≤ 4, we have F(x) = x²/16.

Differentiating with respect to x, we get:

f(x) = d/dx (x²/16) = (2x)/16 = x/8.

For x > 4, f(x) = 0 since F(x) is constant in that range.

Therefore, the density function f(x) is:

f(x) = 0 for x < 0

f(x) = x/8 for 0 ≤ x ≤ 4

f(x) = 0 for x > 4

(f) Expected value E(X):

The expected value of a random variable X is a measure of its average value. To calculate E(X), we integrate the product of x and the density function f(x) over the entire range of X:

E(X) = ∫[x * f(x)] dx

For x < 0 and x > 4, f(x) = 0, so we only need to consider the interval 0 ≤ x ≤ 4:

E(X) = ∫[x * (x/8)] dx

= (1/8) ∫[x²] dx (integrating x²)

= (1/8) * (x³/3) + C (integrating x²)

= (1/24) * (x³) + C

Evaluating this expression from x = 0 to x = 4, we get:

E(X) = (1/24) * (4³) - (1/24) * (0³)

= 64/24

= 8/3

≈ 2.667

(g) Variance V(X) and Standard Deviation σ(X):

Variance is a measure of the spread or dispersion of a random variable. To calculate V(X), we need to calculate the second moment E(X²) and subtract the square of the expected value [E(X)]². The standard deviation σ(X) is the square root of the variance.

E(X²):

E(X²) = ∫[x² * f(x)] dx

For x < 0 and x > 4, f(x) = 0, so we only need to consider the interval 0 ≤ x ≤ 4:

E(X²) = ∫[x² * (x/8)] dx

= (1/8) ∫[x³] dx (integrating x³)

= (1/8) * (x⁴/4) + C (integrating x³)

= (1/32) * (x^4) + C

Evaluating this expression from x = 0 to x = 4, we get:

E(X²) = (1/32) * (4⁴) - (1/32) * (0⁴)

= 256/32

= 8

V(X):

V(X) = E(X²) - [E(X)]²

= 8 - (8/3)²

= 8 - 64/9

= 8 - 7.111

≈ 0.889

Standard deviation:

σ(X) = √(V(X))

= √(0.889)

≈ 0.943

(h) Expected charge E[h(X)]:

Given the function h(X) = X², we want to calculate the expected value of h(X). This can be done by finding E[h(X)] = E(X²).

From the previous calculations, we know that E(X²) = 8. Therefore, the expected charge is E[h(X)] = 8.

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Answer:

3,454 cm³

Step-by-step explanation:

This is a cylinder so the volume formula is [tex]V=\pi r^{2} h[/tex]

The problem gives us the diameter (20 cm) and the height (11 cm). Since the formula uses the radius instead of the diameter, we have to divide the diameter by 2.

20 ÷ 2 = 10

The radius is 10 cm

Now, we plug our height and radius into the formula to find the volume.

[tex]V=\pi r^{2} h\\V=(\frac{22}{7})(10)^{2}(11)\\V=(\frac{22}{7})(100)(11)\\[/tex]

V≈3,454

Answer:

v = -3/2

Step-by-step explanation:

6v = -9

v = -9/6

v = -3/2

Answer:  358 + 360n   where n is an integer

Reason:

Coterminal angles point in the same direction.

We add on multiples of 360 to rotate a full circle, and we get back to the same direction that 358 degrees points in (almost directly to the east). The variable n is an integer {..., -3, -2, -1, 0, 1, 2, 3, ...}

If n is negative, then we subtract off multiples of 360.

Answer:

40.2 in²

Step-by-step explanation:

h*b/2

h= 6.7

b= 12

the value of A in the function f(x) = 2x³ + Ax² + 8x - 3 is -7.

To find the value of A in the function f(x) = 2x³ + Ax² + 8x - 3, we are given that f(2) = 1. Substituting x = 2 into the function, we have:

f(2) = 2(2)³ + A(2)² + 8(2) - 3

Simplifying further:

1 = 2(8) + 4A + 16 - 3

1 = 16 + 4A + 13

Combining like terms:

1 = 29 + 4A

To isolate A, we subtract 29 from both sides:

-28 = 4A

Finally, we divide both sides by 4 to solve for A:

A = -7

Therefore, the value of A in the function f(x) = 2x³ + Ax² + 8x - 3 is -7.

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Answer:

C NO TOO HOT OR TOO COLD

Step-by-step explanation:

Answer:

the answer is c

Step-by-step explanation:

Brainliest plz

In part (a) of the problem, the task is to find the determinant of the given matrix M by showing all the steps of the calculation. In part (b), we are given three matrices A, B, and C with det A = -2.

(a) To find the determinant of matrix M, we can use various methods such as cofactor expansion or row operations. Let's use cofactor expansion along the first row:

det M = 2 * (-1)^(1+1) * det [[2 8 0] [17 24 0] [10 -13 1]]

- 2 * (-1)^(1+2) * det [[4 8 0] [1 24 0] [10 -13 1]]

Simplifying and evaluating the determinants of the 2x2 matrices, we get:

det M = 2 * (2 * 24 - 17 * (-13))

- 2 * (4 * 24 - 1 * (-13))

After performing the calculations, we find the determinant of matrix M.

(b) The given information states that det A = -2. However, no specific task or question is mentioned regarding matrices A, B, and C. Further instructions or requirements are needed to provide a specific answer or analysis based on the given information.

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The integral becomes:

V = ∫₀¹ ∫₀²π (1 − r²) r dθ dr

To find the volume of the solid enclosed by the surface z = 1 − x² − y² and the xy-plane, we need to integrate the function f(x, y) = 1 − x² − y² over the region in the xy-plane where z is positive.

Since the surface z = 1 − x² − y² represents a downward-opening paraboloid, we can set up the integral as follows:

V = ∬R (1 − x² − y²) dA

Here, R represents the region in the xy-plane bounded by the curve x² + y² = 1. To evaluate this integral, we can switch to polar coordinates. In polar coordinates, the region R corresponds to the interval 0 ≤ θ ≤ 2π and 0 ≤ r ≤ 1. The differential area element dA in polar coordinates is r dr dθ.

Evaluating this double integral will give us the volume of the solid enclosed by the surface and the xy-plane.

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The harmonic conjugate of u(x, y) = 2x(1 - y) is v(x, y) = 2y - y² - x² + C, where C is an arbitrary constant.

Here we want to find the harmonic conjugate of:

u(x, y) = 2x*(1 - y)

To do so, we need to use the Cauchy-Riemann equations state that for a function f(z) = u(x, y) + iv(x, y) to be analytic (holomorphic), the partial derivatives of u and v must satisfy the following conditions:

∂u/∂x = ∂v/∂y

∂u/∂y = -∂v/∂x

Let's find the harmonic conjugate by solving these equations:

Given u(x, y) = 2x(1 - y)

∂u/∂x = 2(1 - y)

∂u/∂y = -2x

Setting these derivatives equal to the respective partial derivatives of v:

∂v/∂y = 2(1 - y)

∂v/∂x = -2x

Now, integrate the first equation with respect to y, treating x as a constant:

v(x, y) = 2y - y² + f(x)

Differentiate the obtained equation with respect to x:

∂v/∂x = f'(x)

Comparing this derivative with the second equation, we have:

f'(x) = -2x

Integrating f'(x) with respect to x:

f(x) = -x² + C

where C is a constant of integration.

Now, substitute f(x) into the equation for v(x, y):

v(x, y) = 2y - y² - x² + C

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Answer:

A

Step-by-step explanation:

Because I am smart and u best mark me brainlist

To calculate the probability of winning a certain lottery where you must select 5 numbers out of 29 in any order, we can use the concept of combinations. The probability of winning can be determined by dividing the number of successful outcomes (winning combinations) by the total number of possible outcomes.

In this lottery, you need to select 5 numbers out of 29, and the order of selection doesn't matter. The total number of possible outcomes is given by the combination formula, which is denoted as C(29, 5) and calculated as

29! / (5! * (29-5)!).

To win, you have only one successful outcome, which is the combination of the 5 winning numbers. Therefore, the probability of winning can be calculated as 1 / C(29, 5). Evaluating this expression will give you the probability of winning the lottery with a single-ticket purchase.  

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Answer:

Multiply the volume of the cone by 3

Step-by-step explanation:

Required

Volume of a cylinder from a cone of the same dimension

The volume of a cone is:

[tex]V_1 = \frac{1}{3}\pi r^2h[/tex]

The volume of a cylinder is:

[tex]V_2 = \pi r^2h[/tex]

Recall that:

[tex]V_1 = \frac{1}{3}\pi r^2h[/tex]

Split:

[tex]V_1 = \frac{1}{3}*[\pi r^2h][/tex]

Substitute: [tex]V_2 = \pi r^2h[/tex]

[tex]V_1 = \frac{1}{3}*V_2[/tex]

Make V2 the subject

[tex]V_2 =3V_1[/tex]

This implies that, we simply multiply the volume of the cone by 3

(a) To calculate the final frequencies in the contingency table, we need to sum up the frequencies for each combination of variables. The final frequencies are as follows:

Size of restaurant: Seats 100 or fewer

- Excellent: 182

- Fair: 200

- Poor: 161

Size of restaurant: Seats over 100

- Excellent: 186

- Fair: 316

- Poor: 155

(b) To find the expected frequency for each cell in the contingency table, we can use the formula:

Expected Frequency = (row total * column total) / grand total

The expected frequencies for each cell in the contingency table are as follows:

Size of restaurant: Seats 100 or fewer

- Excellent: (513 * 368) / 1200 ≈ 157.60

- Fair: (513 * 516) / 1200 ≈ 220.95

- Poor: (513 * 356) / 1200 ≈ 151.77

Size of restaurant: Seats over 100

- Excellent: (557 * 368) / 1200 ≈ 171.53

- Fair: (557 * 516) / 1200 ≈ 237.85

- Poor: (557 * 356) / 1200 ≈ 164.62

(a) The final frequencies in the contingency table are obtained by summing up the frequencies for each combination of the variables "Size of restaurant" and "Rating." This gives us the observed frequencies for each category.

(b) The expected frequency for each cell is calculated using the formula mentioned above. It considers the row total, column total, and grand total of the contingency table.

The expected frequencies represent the frequencies we would expect to see in each cell if the variables were independent of each other. These values are used to assess the association between the two variables.

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Answer:

20 yards

Step-by-step explanation:

By the given ratio, the side measurements are 1x, 3x, 4x, 6x, and 9x

We are given the perimeter of this shape is 115. Therefore, 1x+3x+4x+6x+9x=115.

We can solve that for x, so we can find each side measurements' numerical value.

(1+3+4+6+9)x=115

(23)x=115

x=115/23

x=5

So the side measurements are:

1x=1(5)=5

3x=3(5)=15

4x=4(5)=20

6x=6(5)=30

9x=9(5)=45

The third longest sife is 20 yards.

Answer: [tex]w\geq 20[/tex]

Step-by-step explanation:

Solve this like it's an equation

6w+30>150 (i know it is larger than or equal to)

6w>120

w>120/6

w>20

Answer:

The answer is 20

Step-by-step explanation:

6w+30≥150

6w≥150-30

6w≥120

divide both sides by 6

6w/6≥120/6

w≥20

we can say

w=20 since w is greater than or equal to

Answer:

628 ft

Step-by-step explanation:

The volume of cylinder is, V= 628 ft³.

The amount of space occupied by a three-dimensional figure as measured in cubic units.

Given:

radius,r= 5 ft, height, h = 8 ft

Volume= πr²h

V= 3.14 * 5 *5 * 8

V= 628 ft³

Hence, the volume of cylinder is 628 ft³.

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Answer:

12(2v - 3)

Step-by-step explanation:

GCF of 24 and 36 is 12

24v - 36

12(2v - 3)

Answer:

x = 5°

EF = 58°

GH = 55°

Step-by-step explanation:

From The diagram :

Recall ; Angle on a straight line = 180°

This means :

EF + FG + GH = 180

EF = (10x + 8)°

GH = (11x)°

FG = 67°

HENCE;

10x + 8 + 11x + 67 = 180

21x + 75° = 180°

21x = 180 - 75

21x = 105

x = 105 / 21

x = 5

EF = 10x + 8 = 50 + 8 = 58°

GH = 11x = 11 * 5 = 55°

Answer:

one hundred thirty-two

Step-by-step explanation:

should be it if it is can i get brainliest?

Answer:

173.8 units

Step-by-step explanation:

If it's asking for a

139 * 1/4= x

34.75= x

34.75 + 139= 173.75

round to get 173.8

The exact time at which the maximum concentration occurs is given by: [tex]t = (ln(7/8) + 8) / 7[/tex]

To find the exact time at which the maximum concentration occurs, we need to determine the value of t that maximizes the concentration function c(t).

Given the concentration function:

[tex]c(t) = (D / (1 - (7/8))) * ((e^{-7t}) - (e^{-8}))[/tex]

To find the maximum concentration, we can differentiate c(t) with respect to t and set the derivative equal to zero, then solve for t.

Differentiating c(t) with respect to t:

[tex]c'(t) = (D / (1 - (7/8))) * ((-7e^{-7t}) - (-8e^{-8}))\\ = (D / (1 - (7/8))) * (-7e^{-7t} + 8e^{-8})[/tex]

Setting c'(t) equal to zero:

[tex](D / (1 - (7/8))) * (-7e^{-7t} + 8e^{-8}) = 0[/tex]

Since D is a positive constant, we can ignore it in the equation. So we have:

[tex]-7e^{-7t} + 8e^{-8} = 0[/tex]

[tex]-7 + 8e^{-8+7t} = 0\\8e^{-8+7t} = 7\\e^{-8+7t} = 7/8\\-8 + 7t = ln(7/8)\\7t = ln(7/8) + 8\\t = (ln(7/8) + 8) / 7[/tex]

Therefore, the exact time at which the maximum concentration occurs is given by: t = (ln(7/8) + 8) / 7

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Answer:

The answer to this problem Is A I think

Step-by-step explanation:

Answer:

$400

Step-by-step explanation:

Let the initial total cost be represented = $X.

Hence, for 20 family members

= $ x/20 each .......1

Now that they are 25 members

= $x/25 each.......2

Each in the original group which is equation 1 owed $4 less.

That is,

x/20 - 4 ........ 3

Now equate 2 and 3

X/20 - 4/1 = X/25

Taking the LCM of both sides

X-80/20 = X/25

Cross multiply both sides

25( x-80 ) = 20x

25x-2000 = 20x

Collecting like terms

25x-20x = 2000

5x = 2000

Divide through by 5

X = 2000/5

X = 400

The total cost for the catered meal is $400.

To check if it was correct

Put 400 into equation 1 and 2 and then minus whatever you get from each other, you will get $4

From equation 1

400/20 = $20

From equation 2

400/25 =$16

$20-$16 = $4

Thanks

Answer:

-822

Step-by-step explanation:

i just typed it in the calculator

but if you're doing it by hand, 1st multiply 4*12*3*6 and then subtract 42 from it

Answer:

Step-by-step explanation:

       Location    Reflect over x              Reflect over y

B      -0.75 ,1         -0.75 ,-1                           +0.75 ,1

C     1.75 ,-1          1.75,1                                 -1.75,+1

D      -2,-2           -2,+2                                  +2 ,-2

Answer:

37 yards

Step-by-step explanation:

Given data

Distance from house to the library= 18 yards

Distance from  the library to the post office= 288 feet

Total distance in yards, first let us have all units to yards

288ft to yard= 96 yards

Hence the total distance in yards is

=18+19

=37 yards