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The spinner below shows 10 equally sized slices. Charmaine spun the dial 40 times and got the following results.
Outcome Grey White Black
Number of Spins 25 9 6
Fill in the table below. Round your answers to the nearest thousandth.
(a) From Charmaine's results, compute the experimental probability of landing on white.

(b) Assuming that the spinner is fair, compute the theoretical probability of landing on white.
(c) Assuming that the spinner is fair, choose the statement below that is true:

1. The experimental and theoretical probabilities must always be equal.

2. As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.

3. As the number of spins increases, we expect the experimental and theoretical probabilities to become farther apart.

The total volume of the two circular cylinders intersecting perpendicularly is\(V=πr2+πr3=πr2(1+r)\).

The volume of the two circular cylinders intersecting perpendicularly can be calculated using the triple integral formula in rectangular coordinates. The triple integral formula is V=∫∫∫dzdydx.

We can separate the integral into three components. The x-component is ∫dx from \(-√r2-y2 to √r2-y2\). The y-component is ∫dy from -r to r. The z-component is ∫dz from 0 to r.

Substituting the components into the equation for the triple integral, we get \(V=∫-rrdr∫-√r2-y2√r2-y2dx∫0rdz\).

We can solve the integral by splitting the y-component into two pieces:

\(V=∫-rrdr∫-r0dx∫0rdz+∫-rrdr∫0√r2-y2dx∫0rdz\)

The first integral can be solved easily and yields V=πr2. The second integral can be solved using the substitution u=r2-y2 and yields V=πr3.

Hence, the total volume of the two circular cylinders intersecting perpendicularly is V=πr2+πr3=πr2(1+r).

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Answer:

8.) 9.15 x 10^18

Step-by-step explanation:

to get scientific notation, you move the decimal place until all numbers except one are past the decimal. If you move it to the left, the exponent is postitive. If you move it to the right, it's negative. So, 9,150,000,000,000,000,000 expressed in scientific notation is 9.15 x 10^18 because you moved the decimal 18 spaces to the left.

The number 9,150,000,000,000,000,000 expressed in scientific notation will be 9.15 × 10¹⁸ or 9.15E18. Then the correct options are A and B.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The number is given below.

⇒ 9,150,000,000,000,000,000

The number represented in the scientific notation will be given as,

⇒ 9,150,000,000,000,000,000

⇒ 9.15 × 10¹⁸

⇒ 9.15E18

The number 9,150,000,000,000,000,000 expressed in scientific notation will be 9.15 × 10¹⁸ or 9.15E18. Then the correct options are A and B.

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Answer:

45

Step-by-step explanation:

9x

Replace x with 5

9*5

45

Answer:

45

Step-by-step explanation:

9x5 equals 45

Answer:

10:51

Step-by-step explanation:

Given that :

Distance from A to B = 130km

Departure time = 8 : 15

Average speed = 50 km/hr

Recall :

Speed = distance / time

Time = distance / speed

Time = (130 km) ÷ (50km/hr)

Time = 130 / 50

Time = 2.6 hours = 2 hours + (0.6 * 60) = 2 hours 36 minutes

Arrival time = (8:15) + (2 hours 36 minutes) = 10:51

Answer:

A

Step-by-step explanation:

B isn't applicable, because it's below
C and D aren't because it's not negative

Answer:

50,000

Step-by-step explanation:

10*5,000=50,000

Answer: 50,000

Step-by-step explanation:

10× 5,000= 50,000

Or

Just add one zero to 5,000 :)

Hope this helps :)

The Laplace transform of the solution is Y(s) = (2 + e^(-4s))/(s+1).

Solution y(t) = L^-1{(2/(s+1)) + (e^(-4s)/(s+1))}.

Solution as a piecewise-defined function

a) To find the Laplace transform of the solution, we apply the Laplace transform to both sides of the differential equation and use the fact that the Laplace transform of a delta function is 1:

sY(s) - y(0) + Y(s) = 2 + e^(-4s)

sY(s) + Y(s) = 2 + e^(-4s)

Y(s) = (2 + e^(-4s))/(s+1)

b) To obtain the solution y(t), we take the inverse Laplace transform of Y(s):

y(t) = L^-1{(2 + e^(-4s))/(s+1)}

y(t) = L^-1{(2/(s+1)) + (e^(-4s)/(s+1))}

Using the Laplace transform table, we know that the inverse Laplace transform of 2/(s+1) is 2e^(-t). We can also use the table to find that the inverse Laplace transform of e^(-4s)/(s+1) is e^(-t)u(t-4), where u(t) is the Heaviside step function. Substituting these into the equation above, we get:

y(t) = 2e^(-t) + e^(-(t-4))u(t-4)

c) The solution y(t) can be expressed as a piecewise-defined function as follows:

y(t) = { 2e^(-t) for t < 4

{ 2e^(-t) + e^(-(t-4)) for t >= 4

At t = 4, there is a discontinuity in the derivative of the solution due to the presence of the delta function in the initial value problem. The solution jumps from 2e^(-4) just before t = 4 to 2e^(-4) + 1 just after t = 4. This discontinuity is known as a "shock" and is a characteristic feature of systems with sudden changes or impulses in the input. The graph of the solution will have a vertical tangent at t = 4, indicating the discontinuity in the derivative.

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Answer:

Step-by-step explanation:

300

The forecast value for time period 2 is 210, and the forecast error is -110 when the actual value is 100. Option B

To calculate the forecast value for time period 2, we substitute W = 2 into the regression equation:

y = 200 + W + 2W^2

= 200 + 2 + 2(2^2)

= 200 + 2 + 2(4)

= 200 + 2 + 8

= 210

Therefore, the forecast value for time period 2 is 210.

To calculate the forecast error, we compare the forecasted value with the actual value for time period 2. Given that the actual value is 100, the forecast error can be calculated as the difference between the actual value and the forecast value:

Forecast error = Actual value - Forecast value

= 100 - 210

= -110

Hence, the forecast error is -110.

Therefore, the correct answer is:

Forecast value = 210; forecast error is -110. So Option B is correct.

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Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

The set B(N,N') of all continuous linear transformations from a normed linear space N to another normed linear space N' forms a normed linear space itself. This is true for any normed linear spaces N and N', and the norm on B(N,N') is defined as the supremum of the norms of the transformed vectors.

To show that B(N,N') is a normed linear space, we need to verify that it satisfies the properties of a normed space. Firstly, we define the norm ∥T∥ of a linear transformation T in B(N,N') as the supremum of the norms of the transformed vectors, i.e., ∥T∥ = sup{∥T(x)∥ : ∥x∥ ≤ 1}. This definition ensures that the norm is non-negative, satisfies the triangle inequality, and is homogeneous.

The set B(N,N') forms a vector space under the pointwise linear operations, where addition and scalar multiplication are defined component-wise. This means that for any two linear transformations T1 and T2 in B(N,N') and any scalar α, the operations T1 + T2 and αT1 are well-defined and also belong to B(N,N').

Continuity of the linear transformations in B(N,N') ensures that the set is closed under these operations, as the sum or scalar multiple of continuous functions is also continuous. Therefore, B(N,N') is a vector space.

Now, if N' is a Banach space (a complete normed linear space), we need to show that B(N,N') is also complete. This can be proven by establishing that every Cauchy sequence of linear transformations in B(N,N') converges to a limit that is also a linear transformation in B(N,N').

The completeness of N' guarantees the convergence of the sequence, and continuity ensures that the limit is also a continuous linear transformation.Therefore, B(N,N') is a normed linear space, and if N' is a Banach space, then B(N,N') is also a Banach space.

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If the stock of Company A lost $5. 31 throughout the day and ended at a value of $112. 69. The stock of Company A declined by 4.5% throughout the day.

The percentage decline in stock price is calculated by dividing the loss in value by the original value of the stock. To find out the percentage loss of stock A, we can use the formula:

(Loss in value / Original value) x 100%

Let us substitute the values we know:

Loss in value = $5.31

Original value = $118.00

Percent change = (5.31 / 118.00) x 100%

Percent change = 0.045 or 4.5%

Therefore, the stock of Company A declined by 4.5% throughout the day.

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Answer:

steps below

Step-by-step explanation:

f(x)=(x+6)²+3  ... Gray graph

horizontal shrink by a factor of 1/2: f(2x) = (2x+6)²+3 ... green

translation 1 unit down: f(2x)-1 = (2x+6)²+2   ... purple

reflection in the x-axis: g(x) = - ((2x+6)²+2) = - (2x+6)²-2 = -4(x+3) - 2  .. Red

parabola equation: y = a(x-h)² + k    (h,k): vertex

vertex (-3 , -2)

The rule of function g(x) is \(g(x) = -4(x + 3)^2 -2\), and the vertex of the function is (-3,-2)

The equation of the function is given as:

\(f(x) = (x + 6)^2 + 3\)

The rule of shrinking the function by a factor of 1/2 is:

\((x,y) \to (2x,y)\)

So, we have:

\(f'(x) = (2x + 6)^2 + 3\)

When the function is translated down by 1 unit, the rule of the transformation is:

\((x,y) \to (x,y-1)\)

So, we have:

\(f"(x) = (2x + 6)^2 + 3-1\)

\(f'"x) = (2x + 6)^2 + 2\)

Lastly, the function is reflected across the x-axis,

The rule of this transformation is:

\((x,y) \to (x-y)\)

So, we have:

\(g(x) = -(2x + 6)^2 -2\)

Factor out 2

\(g(x) = -(2(x + 3))^2 -2\)

Expand

\(g(x) = -4(x + 3)^2 -2\)

The above represents the rule of function g(x), and the vertex of the function is (-3,-2)

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If lisa is on her way home in her car, she has driven 24 miles so far, which is three-fourths of the way home, Lisa's total drive is 32 miles.

Let's represent the total length of Lisa's drive as x. We know that she has driven 24 miles so far, which is three-fourths of the total length. We can write this information as:

24 = (3/4) x

To find x, we need to isolate it on one side of the equation. We can start by multiplying both sides by 4/3 to get rid of the fraction:

24 * (4/3) = x

Simplifying, we get:

32 = x

We can say that Lisa has already driven 24 miles, which is three-fourths of the total distance. To find the total distance, we use the equation 24 = (3/4) x, where x represents the total distance.

To solve for x, we multiply both sides of the equation by 4/3 to cancel out the fraction, giving us 32 = x. Therefore, Lisa's total drive is 32 miles.

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Answer:

c

Step-by-step explanation:

I attached a desmos graph so you could get a better understanding but it's right 1, down 2

Domain: (-∞, ∞)

Range: (-∞,1]

Answer:

Domain = All Real Numbers

Range = y≤1

Step-by-step explanation:

Since parabolas are continuous, the domain is all real numbers. The range, or y value, is all real numbers less than or equal to 1 (y≤1), since 1 is the vertex.

Hope this helps :)

The length of arc XPY in terms of π include the following: B.12π m

In Mathematics and Geometry, the arc length formed by a circle can be calculated by using the following equation (formula):

Arc length = 2πr × θ/360

Where:

By substituting the given parameters into the arc length formula, we have the following;

Arc length XPY = 2 × π × 8 × 3/4

Arc length XPY = 12π meters.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

c. the number of persons allegric to penicillin

Answer:  first problem 3rd choice  The graph shifts vertically up 5 units

11.) the y intercept is  -5

19.)  f(-8) = -18

last item  third choice  All real numbers such that  are ≥ 0 and ≤ 40

Step-by-step explanation:

19.)  f(x)=2(-8 -3) + 4

              2 (-11)  + 4

                -22 + 4

        f(-8) = -18

Answer:

answer is D

Step-by-step explanation:

A) if sum of four and some number = x + 4

B) if product of some number and 4 = 4x

C) the different between 4 and some number = x - 4

D) if quotient of some number and 4 = x/4

∵therefore D is the answer

Answer:

4

Step-by-step explanation:

Greatest Common Factor or Divisor is 4, because it is the greatest number that divides evenly into all of them.

Hope this helps! :)

It is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

In the given scenario, it is not completely true that based only on the r and p values listed above, you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

Let's first understand what is meant by the term "moderator.

"Moderator: A moderator variable is a variable that changes the strength of a connection between two variables. If there is a statistically significant bivariate relationship between the amount of texting during driving and the number of accidents, scientists investigate whether this bivariate relationship is moderated by age.

Therefore, based on the values of r and p, it is difficult to determine if age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

As we have to analyze other factors also to determine whether the age is a moderator or not, such as the sample size, the effect size, and other aspects to draw a meaningful conclusion.

So, it is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

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Answer:

30

Step-by-step explanation:

WE use permutation for this question:

since the letters in SQUARE are all distinct, so：

\(^{6}P_{2} = 6*5=30\)

The number of ways of arranging 2 letters from the word S Q U A R E is given by A = 15 ways

The number of ways of selecting r objects from n unlike objects is given by combinations

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

Let the number of ways of arranging 2 letters from the word S Q U A R E be represented as A

Now , to select 2 letters from the 6 letters in the word SQUARE, without regard to order.

This is a combination problem, since the order in which we select the letters does not matter. Therefore, we can use the formula:

6 C 2 = 6! / 2!(6 - 2)!

= 6 x 5 / (2 x 1) x (4 x 3 / (2 x 1))

= 15

Hence , there are 15 ways to arrange 2 letters from the word SQUARE

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Answer:

y=35

x=27.8

Step-by-step explanation:

Answer:

Sabemos que el piso es un rectángulo de 435 cm de largo y 375 cm de ancho.

Recordar que para un rectángulo de largo L, y ancho W, el área es:

A = L*W

Entonces el área del piso, será:

A = 435cm*375cm = 163,125 cm^2

Primero, sabemos que se utilizaran baldosas (las cuales son cuadradas) y queremos saber la longitud de lado que tendrían las baldosas.

No tenemos ningún criterio para encontrar este lado, solo que (si queremos usar un número entero de baldosas) el largo L del lado de la baldosa deberá ser un divisor de tanto el ancho como el largo del suelo.

Dicho de otra forma

el largo, 435cm, tiene que ser múltiplo de L

el ancho, 375cm, tiene que ser múltiplo de L.

Por ejemplo, ambos números son múltiplos de 5, entonces podríamos tomar L = 5cm

En este caso, el área de cada baldosa es:

a = L^2 = 5cm*5cm = 25cm^2

Y el número total de baldosas que necesitaría usar esta dado por el cociente entre el área del suelo y el area de cada baldosa.

N = ( 163,125 cm^2)/(25cm^2) = 6,525 baldosas.

También sabemos que ambos números (435cm y 375cm) son múltiplos de 15cm

Entonces las baldosas podrían tener 15cm de lado.

En este caso, el área de cada baldosa es:

A = (15cm)^2 = 225cm

En este caso el número total de baldosas necesarias será:

N =  ( 163,125 cm^2)/(225cm^2) = 725 baldosas.

we have

15!12!(4−1)!

15!12!(3!)=3,758,268,687,305,932,800,000

therefore

the answer is

Answer:

1

Step-by-step explanation:

Because the shape divided has to create another shape and for 1 it's an oval at the beginning and then after the lines of symmetry go through its seen as 8 triangles.

Answer:

the set of odd numbers that are divisible by 2

The area bounded by the two functions f(x) = −x2 4x 2 and g(x) = −2x is =64 unit

To find the area bounded by the two functions f(x) = −x2 + 4x + 2 and g(x) = −2x + 10, we must first determine where the two functions intersect.

To do this, we set the two functions equal to each other and solve for x:

−x2 + 4x + 2 = −2x + 10
−x2 − 2x + 8 = 0
(x − 4)(x − 2) = 0
x = 4, x = 2

Now, we can calculate the area of the bounded region between f(x) and g(x):

Area = ∫24(g(x) − f(x)) dx

Area = ∫24(−2x + 10 − (−x2 + 4x + 2)) dx

Area = ∫24(x2 − 2x + 8) dx

Area = [x3/3 − x2/2 + 8x]24

Area = (64/3) − (32/2) + (64) = 64

Therefore, the area bounded by the two functions is 64.

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