A bag contains 4 blue marbles, 2 yellow marbles, and 6 orange marbles. What is the probability of picking an orange marble and then another orange marble without replacing the marble? Round the answer to two decimal places. Write the answer just as a decimal.

To draw the graph of the function f(x) = 2 - x^2 using a graphing calculator, follow these steps: Turn on your graphing calculator and enter the function f(x) = 2 - x^2 into the calculator's equation editor.

Set the viewing window of the calculator to a suitable range, such as -5 ≤ x ≤ 5 and -5 ≤ y ≤ 5, to capture the shape of the graph. Press the "Graph" button to plot the graph of f(x). The graph of f(x) = 2 - x^2 should appear on the screen as a downward-opening parabola centered at the point (0, 2). You can use the arrow keys on the calculator to move around and explore different parts of the graph.

The graph of f(x) = 2 - x^2 will show a symmetric curve that opens downwards. The highest point on the graph will be at (0, 2), and the curve will extend infinitely in both the positive and negative x-directions.

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(a) To sketch a graph of the speed over a 3-second time span, we need to know the equation that describes the relationship between speed and time. Without this information, we cannot create an accurate graph.

(b) To find the volume of blood that passes along the artery in one second, we need to use the formula Q = A * v, where Q is the flow rate, A is the cross-sectional area of the artery, and v is the speed of blood flow. The cross-sectional area of the artery is given by A = pi * r^2, where r is the radius of the artery.

Thus, substituting the given values, we get:

A = pi * (5mm)^2 = 78.54 mm^2

v = 0.2 + 0.1 sin(2pit/0.8) (using the given information)

Q = A * v = 78.54 * (0.2 + 0.1 sin(2pit/0.8))

To find the volume of blood that passes along the artery in one second, we need to evaluate Q at t = 1 second, so we get:

Q = 78.54 * (0.2 + 0.1 sin(2pi1/0.8)) = 31.39 mm^3/s

Therefore, the volume of blood that passes along the artery in one second is approximately 31.39 cubic millimeters.

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Therefore, the infinite geometric series representing the decimal 0.44444... converges to the fraction 4/9.

To represent the decimal 0.44444... as an infinite geometric series, we can start by noticing that this decimal can be written as 4/10 + 4/100 + 4/1000 + ...

The pattern here is that each term is 4 divided by a power of 10, with the exponent increasing by 1 for each subsequent term.

So, we can express this as an infinite geometric series with the first term (a) equal to 4/10 and the common ratio (r) equal to 1/10.

The infinite geometric series can be written as:

0.44444... = (4/10) + (4/10)(1/10) + (4/10)(1/10)^2 + ...

To find the fraction to which this series converges, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

Plugging in the values, we have:

S = (4/10) / (1 - 1/10)

= (4/10) / (9/10)

= (4/10) * (10/9)

= 4/9

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Answer:

shorter leg = 6 cm

Step-by-step explanation:

let n be the shorter leg then n + 2 is the longer leg.

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

n² + (n + 2)² = 10² , that is

n² + n² + 4n + 4 = 100

2n² + 4n + 4 = 100 ( subtract 100 from both sides )

2n² + 4n - 96 = 0 ( divide through by 2 )

n² + 2n - 48 = 0 ← in standard form

(n + 8)(n - 6) = 0 ← in factored form

equate each factor to zero and solve for n

n + 8 = 0 ⇒ n = - 8

n - 6 = 0 ⇒ n = 6

However , n > 0 then n = 6

the shorter leg is 6 cm long

To form a five-letter code with no repeated letters, we need to select 5 different letters from the available options.

The number of different security codes possible can be calculated by multiplying the number of options for each component.

Assuming 26 letters in the alphabet, the number of ways to form such a code is given by the combination formula, which is C(26, 5) = 26! / (5! * (26-5)!) = 26! / (5! * 21!) = (26 * 25 * 24 * 23 * 22) / (5 * 4 * 3 * 2 * 1) = 65,780 ways.

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The missing frequency in the given table is 24.

What is frequency?

To find the missing frequency, we need to use the information given in the histogram and the frequency table.

We can see from the histogram that the missing class interval is 26-28.

The total frequency for all class intervals is the sum of the frequencies in the table:

110 + 36 + 180 + f = 326 + f

We also know that the total frequency is the number of phones recorded by the manufacturer, so we can assume that the total frequency is a whole number.

Since the sum of the frequencies in the table is 326, the missing frequency must be:

f = total frequency - sum of the other frequencies

f = 350 - 326

f = 24

Therefore, the missing frequency is 24.

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The solution of the function, h(-3) is - 1 / 2.

Function relates input and output. In other words, a function is an expression that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Therefore, let's solve the function as follows:

h(x) = 3x + 3 / x² + x + 6

Let's find h(-3) as follows:

We will input the value of x as -3 in the function.

Hence,

h(-3) = 3(-3) + 3 / (-3)² + (-3) + 6

h(-3) = -9 + 3 / 9 - 3 + 6

h(-3) = -6 / 12

h(-3) = - 1 / 2

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Answer:

smallest   angle measure 39 degrees

Step-by-step explanation:

the sum of the three interior angles in a triangle is always 180°

x= smallest

x +x+24 + 2x = 180

4x +24 = 180

4x = 156

x = 39

Answer:

B. 39°

Step-by-step explanation:

x + 24 + 2x + x = 180 is the equation I'll use.

x + 24 + 2x + x = 180 {Step 1: Combine 2x, x, x to get 4x.}

4x + 24 = 180 {Step 2: Subtract 24 from both sides (180 - 24 = 156)}

4x = 180 - 24

4x = 156 {Step 3: Divide both sides by 4 (156 / 4 = 39)}

x = 156/4

x = 39

The smallest angle is 39°. (The other two angles are 63° and 78°, respectively.)

Answer:

C and E

Step-by-step explanation:

Answer:

3 and 5

Step-by-step explanation:

The solution of this problem is in this picture.

The system of equations that can be used to determine whether the road intersects the boundary of the tower’s signal is

 \(y = 2x^2 - 16x + 34\\11y = -5x + 62\)

If a quadratic equation is written in the form

\(y=a(x-h)^2 + k\)

then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)

For the given situation, the quadratic equation has vertex (h,k) = (4,2) and it passes through (5,4).

If we consider the equation to be of the form \(y=a(x-h)^2 + k\),

then, as h = 4, k = 2, it becomes \(y = a(x-4)^2 + 2\)

Now since it passes through (5,4), thus at x = 5, and y = 4, the equation must be true, or:

\(y = a(x-4)^2 + 2|_{(x,y) = (5,4)}\\\\4 = a(5-4)^2 + 2\\4 = a + 2\\a = 2\)

Thus, the quadratic equation in consideration is: \(y = 2(x-4)^2 + 2 = 2x^2 + 32 -16x + 2\\y = 2x^2 - 16x + 34\)

The straight line in consideration connects points (–3, 7) and (8, 2).

Equation of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\)  is

\((y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)\)

Since we've got \((x_1, y_1) = (-3,7) \: \rm and \: \: (x_2, y_2) = (8,2)\)

We get the equation of the straight line in consideration as:

\((y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)\\\\(y-7) = \dfrac{2-7}{8 - (-3) } (x-(-3))\\\\y - 7 = -\dfrac{5}{11}(x+3)\\\\11y = -5x + 62\)

Therefore, the system of equations that can be used to determine whether the road intersects the boundary of the tower’s signal is

\(y = 2x^2 - 16x + 34\\11y = -5x + 62\)

These equations' graphs' intersection is the solution to this system

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Answer:

y-2(x-4)^2=2

5x+11y=62

Step-by-step explanation:

a on edge 22

Answer:

like an echo in the forest

yeahhhhh life goes on

Answer:

Step-by-step explanation:

4 - 12x

So option C is the correct answer

By showing that A can be expressed as the direct product of cyclic groups of prime order, we have proven that A≅Z/pqrZ without relying on the classification of finite abelian groups.

To prove that A is isomorphic to Z/pqrZ, we can show that A is isomorphic to Z/pZ × Z/qZ × Z/rZ.

Since A is a finite abelian group of order pqr, by the Fundamental Theorem of Finite Abelian Groups, A can be written as the direct product of cyclic groups of prime power order.

Let's consider A as a direct product of cyclic groups of orders p, q, and r.

Each of these cyclic groups is isomorphic to Z/pZ, Z/qZ, and Z/rZ respectively, because they are of prime order.

Therefore, we can conclude that A is isomorphic to Z/pZ × Z/qZ × Z/rZ.

This isomorphism holds because the direct product of cyclic groups of prime power order is isomorphic to the direct product of their corresponding prime cyclic groups.

Hence, A≅Z/pZ×Z/qZ×Z/rZ, and we have proven that A is isomorphic to Z/pqrZ.

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The population mean is 25 seconds, the sample mean is also 25 seconds, and the standard deviation of the sample mean is 0.55 seconds.

The mean length of advertisements produced by Majesty Video Production Incorporated, we can use a sample of 13 ads.

Since the population standard deviation is known to be 2 seconds, we can use the formula for the sampling distribution of the sample mean.
The formula is:

standard deviation of the sample mean = population standard deviation / square root of sample size.

In this case, the population standard deviation is 2 seconds and the sample size is 13.

So, the standard deviation of the sample mean is

2 / √13 ≈ 0.55 seconds.

Next, we want to determine the probability that the mean length of the sample ads is less than or equal to 25 seconds. We can use the Z-score formula to find the Z-score associated with 25 seconds.

The formula is:

Z-score = (sample mean - population mean) / standard deviation of the sample mean
In this case, the population mean is 25 seconds, the sample mean is also 25 seconds, and the standard deviation of the sample mean is 0.55 seconds.

Finally, we can use a Z-table or calculator to find the probability associated with the Z-score we calculated.

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a) When the vehicle's speed was dropped to 30 mph, it moved 73 feet.

b) When the vehicle's speed was dropped to 15 mph, it moved 117 feet.

Kinematic equations are a collection of equations that describe how an item moves when its acceleration is constant. The deceleration rate is then determined using this using method, \(a=\frac{v^2-v_0^2}{2\Delta\cdot s}\) where v is the final speed, v₀ is the initial speed, and Δs is the traveled distance.

Given v₀= 66 ft/s (45 mph), Δs=132 feet, and v=0 ft/s. Then,

\(\begin{aligned}a&=\mathrm{\frac{(0-66^2)ft^2/s^2}{2\times132\;ft}}\\&=\mathrm{-16.5\;ft/s^2}\end{aligned}\)

a) The distance covered by the vehicle at a 30 mph (44 ft/s) reduction in speed is,

\(\begin{aligned}\Delta s&=\frac{v^2-v_0^2}{2\cdot a}\\&=\mathrm{\frac{(44^2-66^2)\;ft^2/s^2}{2\times-16.5\;ft/s^2}}\\&=\mathrm{73.333\;ft}\\&\approx\mathrm{73\;ft}\end{aligned}\)

b) The distance covered by the vehicle at a 15 mph reduction in speed is,

\(\begin{aligned}\Delta s&=\mathrm{\frac{(22^2-66^2)ft^2/s^2}{2\times-16.5\;ft/s^2}}\\&=\mathrm{117.33\;ft}\\&\approx\mathrm{117\;ft}\end{aligned}\)

The required answers are 73 feet and 117 feet.

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The solution to the simultaneous equations 2x + y = 10 and 2y = x + 4 is determined as: (3.2, 3.6).

To solve the simultaneous equations 2x + y = 10 and 2y = x + 4 using the given graph, we need to identify the lines on the graph that represents both equations and find the point of intersection, which represents the solution.

First, let's rearrange the equations in slope-intercept form (y = mx + b):

Equation 1: 2x + y = 10

y = -2x + 10 (slope is -2 and y-intercept is 10)

Equation 2: 2y = x + 4

y = (1/2)x + 2 (slope is 1/2 and y-intercept is 2)

Now, from the graphs, the lines that represents both equations intersect at (3.2, 3.6), as shown in the image attached below. Therefore, the solution is: (3.2, 3.6).

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a. The parameters of the standard beta distribution can be found using the given mean (E(Y) = 10) and variance (V(Y) = 100/7).  b. By using the cumulative distribution function (CDF) of the standard beta distribution, we can calculate P(8 ≤ Y ≤ 12) as CDF(0.6) - CDF(0.4) c. probability is 0.1

The relevant standard beta distribution for the steel bar's snapping distance Y/20 has parameters that can be determined using the mean and variance provided. To compute probabilities, we can use the cumulative distribution function (CDF) and survival function (1 - CDF) of the standard beta distribution.

a. By solving the equations involving the mean and variance, we can determine the values of the parameters.

b. To compute the probability P(8 ≤ Y ≤ 12), we convert the range [8, 12] to the corresponding range in terms of Y/20, which is [0.4, 0.6].

c. To compute the probability that the bar snaps more than 2 in. from the expected position, we convert the distance of 2 in. to the corresponding value in terms of Y/20,  we can calculate the probability P(Y > 2) as 1 - CDF(0.1).

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The equation of the line that satisfies the given condition is:

y = mx + b

In the equation y = mx + b, 'y' represents the dependent variable (usually the output or the value we want to find), 'x' represents the independent variable (usually the input or the value we can control), 'm' represents the slope of the line (indicating the rate of change of y with respect to x), and 'b' represents the y-intercept (the value of y when x is equal to zero).

To find the equation of a line that satisfies a given condition, we need to determine the values of 'm' and 'b' based on the information provided. The condition could be in the form of coordinates of a point on the line, the slope of the line, or any other relevant information.

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9514 1404 393

Answer:

  False

Step-by-step explanation:

Corresponding angles in similar triangles are congruent. The similarity statement tells you angle B corresponds to angle Y, so those angles are congruent. The sines of congruent angles are identical.

  sin(B) > sin(Y) . . . . FALSE

  sin(B) = sin(Y) . . . . true

Answer:

The answer is true.

Step-by-step explanation:

The real-world problem involving a related set of two equations is given below:

Problem: Cost of attending a concert  is made up of base price and variable price per ticket. You are planning to attend a concert with your friends and want to know the number of tickets to purchase for lowest overall cost.

The related set of two equations are:

Equation 1: The total cost (C) of attending the concert is given by:

The equation C = B + P x N,

where:

B  = the base price

P  = the price per ticket,

N = the number of tickets purchased.

Equation 2: The maximum budget (M) a person have for attending the concert is:

The  equation M = B + P*X

where:

X = the maximum number of tickets a person can afford.

So by using the values of B, P, and M, you can be able to find the optimal value of N that minimizes the cost C while staying within your own budget M. so, you can now determine ticket amount to minimize costs and stay within budget.

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Answer:

Volume = 2640 in.^3

Step-by-step explanation:

The formula for the volume of a triangular prism is given by:

V = 1/2bhl, where

Since the base of the triangular prism is 30 in., the height is 8 in., and the length is 22 in., we can plug in 30 for b, 8 for h, and 22 for l in the triangular prism volume formula to find V, the volume of the triangular prism in in.^3.

V = 1/2(30)(8)(22)

V = 15 * 176

V =2640

Thus, the volume of the triangular prism is 2640 in.^3.

Answer:greengrocer should Dell 17 kg before profit. 500$ profit

Step-by-step explanation:

The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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Answer: AB/y = BC/z = AC/x

Step-by-step explanation:

Side AB corresponds to side y, side BC corresponds to side z, and side AC corresponds to side x.

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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The true statement about b is b = p + q, and about c is c = p*q.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.

Given a quadratic function, x² + bx + c

and factors of equation is (x + p)(x + q)

for any quadratic equation, the product of factors is equal to the product of a and c,

here a = 1 and c = c

c = p*q,

and the sum of factors is equal to b,

b = p + q.

Hence options A and C are correct.

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