Choose the solution to this inequality. < 3 34 O A. y. -12 B. ys o o c. y< 1 / 3 O D. y> 4​

The probability of randomly selecting a red, then a free marble from a bag of 5 red, 8 green, and 3 marbles

a)  0.1563

b) 0.1667

Since we are  given with bag of  5 red, 8 green, and 3 marbles. so, r=5, g=8 and b=  3. For the first  case, we replace the first  marble before drawing the second,  the total number of marble =  5 + 8 + 3 = 16. So, the probability of drawing a red marble at the 1st attempt is: 5/16. Then, the first marble is replaced back into the bag before making the second draw. Probability of drawing green marbles at the second draw is: 8/16= 1/2, Therefore the probability of selecting a red, then a green marble is: 5/16 * 1/2 = 5/32 =0.1563

For the second case , we do not replace the first marble, the probability of drawing a red marble at the 1st draw is:5/16 . Since we don't replace the balls  so the number of marbles remaining in the bag is: 16-1 =15 ,the probability of drawing green marbles at the second draw is: 8/15, therefore the combined probability of selecting a red, then a green marble is: 5/16 * 8/15  =0.1667

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Answer:

(3,6.3), (7, 14.7)

Step-by-step explanation:

For this question, you want to find the values where 2.1×x is the same as y. It's mostly just trial and error.

x is always first in the bracket, so by multiplying it by 2.1, you would get y (the second value) if it applies.

3*2.1=6.3, so the first one is true.

6.3*2.1=13.23, so the second one is false.

2.1*2.1=4.41, so the third one is false.

7*2.1=14.7, so the fourth one is true.

10.5*2.1=22.05, so the fifth one is false.

14.7*2.1=30.87, so the sixth one is false.

This leaves the first one (3,6.3) and the fourth one (7, 14.7) as true.

** This is mostly algebra, so you may want to look at that. If this question was supposed to be done without a calculator, look at multiplying decimals too. I'm always happy to help!

Answer:

They are (3, 6.3) and (7, 14.7)

Answer:

40

Step-by-step explanation:

I hope you know the basics of algebra.

Divide becomes multiply. Add becomes subtract...

Comparing experiment data to public opinion polls helps evaluate media accuracy, detect biases, and understand the influence on public opinion, while describing data trends and comparing theoretical and empirical probabilities aids in making informed decisions.

In conclusion, comparing the data collected from experiments to public opinion polls allows for the assessment of media accuracy and biases, while analyzing data trends and comparing theoretical and empirical probabilities provides valuable insights for decision-making.

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Answer:

sin(150) or 1/2

Step-by-step explanation:

Using the double angle identity of sin2x = 2sinxcosx, you can determine the value of x and rewrite the function; 2sin(75)cos(75) = sin(2(75)) = sin(150) = 1/2

Answer:

3 \(\frac{17}{27}\)

Step-by-step explanation:

\(\frac{14}{27}\) ÷ 7

= \(\frac{14}{27}\) * 7

= (14 * 7 ) ÷ 27

= 98 ÷ 27

= 3 \(\frac{17}{27}\)

Explanation:

Pick any two negative numbers to represent the x and y intercepts. Let's say we go for -2 and -3 as the x and y intercepts.

That leads to the locations (-2,0) and (0,-3)

Find the slope through these two points.

m = (y2-y1)/(x2-x1)

m = (-3-0)/(0-(-2))

m = (-3-0)/(0+2)

m = -3/2

m = -1.5

We get a negative slope. The line moves downhill as we move to the right.

The distance it will reach to  x, = 46.6 feet

acc to our question-

hence,The distance it will reach to  x, = 46.6 feet

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Answer:x=11.8

Step-by-step explanation:

In an instruction like "z = x y," the symbols x, y, and z are examples of variables.

Variables are placeholders that represent unknown or changing values in mathematical expressions or equations. They allow us to generalize mathematical relationships and solve problems using algebraic methods.

In mathematics, variables are symbols that represent unknown or varying quantities. They are used to express mathematical relationships, equations, and formulas.

In the given instruction "z = x y," the symbols x, y, and z are variables.

In this case, x and y represent the input values, and z represents the output or result of the mathematical operation defined by the equation.

Variables are used extensively in algebra to solve equations, manipulate expressions, and analyze mathematical relationships. They enable us to express and solve problems symbolically, without knowing the specific values of the variables.

By assigning specific values to variables, we can evaluate expressions, solve equations, and find solutions to mathematical problems.

Variables can represent a wide range of quantities, including numbers, measurements, constants, or even abstract concepts. They provide flexibility and generality in mathematical modeling and problem-solving.

By using variables, we can establish connections between different mathematical quantities and derive meaningful conclusions based on their relationships.

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The highest point on a bell-shaped curve represents the peak or maximum value of the distribution. This point is known as the mode of the distribution.

In a bell-shaped curve, also known as a normal distribution or Gaussian distribution, the data is symmetrically distributed around the mean. The curve is characterized by a central peak, and the highest point on this peak corresponds to the mode.

The mode represents the most frequently occurring value or the value that has the highest frequency in the dataset. It is the point of highest density in the distribution.

The bell-shaped curve is often used to model naturally occurring phenomena and is widely applied in statistics and probability theory. The mode provides information about the most common or typical value in the dataset and is useful for understanding the central tendency of the distribution.

While the mean and median also have significance in a normal distribution, the highest point on the bell-shaped curve specifically represents the mode, indicating the value with the highest occurrence in the dataset.

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Answer:

Gross pay per week = $234

Federal income tax = $421.2

Social security = $174.96

Medicare =$40.71

net pay per week = $181

Total gross pay = $2,808

Total net pay = $2172

Step-by-step explanation:

Hi, to answer this question, first, we have to calculate Angela gross income per week:

18 hours per week x $13 per hour = $234 per week (gross)

234 x 12 =2,808

Amount taken ; multiply weekly gross pay by each percentage discount in decimal form (divided by 100)

Federal income tax = 234 x (15/100) = $35.1  (in 12 weeks = 35.1 x 12 = $421.2)

Social security = 234 x (6.2/100)= $14.508 (in 12 weeks = 14.5 x 12 = $174.96)

Medicare = 234 x (1.45/100)=$3.393  (in 12 weeks = 3.39x 12 = $40.71)

Total amount taken (per week)= 35.1+14.508+3.393=$53.001

Net pay per week = 234-53 = $181

For the total gross pay we have to multiply the weekly gross pay by the number of weeks (12)

Total gross pay = 234 x 12 =$2,808

Total net pay = 181 x 12 = 181 per week x 12 = $2172

Answer:

16 minutes

Step-by-step explanation:

Given

Represent minutes with M and Phone calls with P.

When M = 8; P = 2

Required

Determine M when P = 4

First, we need to determine the constant of proportion using:

\(M = k * P\)

Where k represents the constant:

\(8 = k * 2\)

Divide through by 2

\(4 = k\)

\(k = 4\)

Solving for M, when P = 4

Substitute 4 for P and 4 for k in \(M = k * P\)

\(M = 4 * 4\)

\(M = 16\)

Hence:

She spent 16 minutes in total

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 table of values that represents exponential decay is (c)

From the question, we have the following parameters that can be used in our computation:

The table of values

An exponential function is represented as

y = abˣ

Where

Rate = b

When the rate is less than 1, then the table represents a decay

i.e when y reduces as x increases

The table that has the above features is the table (c)

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Answer:

It is irrational.

Hope you could get an idea from here.

Doubt clarification - use comment section.

The cost of renting a tank is: 235.5 * 3 = $706.5

What is the volume of a cylinder?

The amount of space inside a cylinder is its volume. You can find it by dividing the base area by the height. V = πr²h is the formula for the volume of a cylinder with base radius "r" and height "h."

Here, we have

Given: A company rents water tanks shaped like cylinders. Each tank has a diameter of 10 feet and a height of 3 feet The cost is 3$.

We have to find the volume of one tank and multiply it by the cost of renting the tank per cubic foot.

The volume of a cylinder is:

V = πr²h

where r = radius

h = height

Each tank has a diameter of 10 feet (radius = 5 feet) and a height of 3 feet.

The volume of the tank is therefore:

V =  π(5)²(3)

V = 235.5ft

The cost of renting is $3 per cubic foot.

Hence, the cost of renting a tank is:

235.5 * 3 = $706.5

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0.3514 * 380 ≈ 133.7 To find out how many students had scores between 35 and 61, we need to first calculate the interquartile range (IQR) which is the difference between the third quartile (Q3) and the first quartile (Q1).
Q1 is the median of the lower half of the data, which in this case is (11+35)/2 = 23.
Q3 is the median of the upper half of the data, which in this case is (70+79)/2 = 74.5.
So, IQR = Q3 - Q1 = 74.5 - 23 = 51.5.

Scores between 35 and 61 fall within one IQR from Q1. So, we need to find out what proportion of the scores fall within this range.
To do this, we need to calculate the z-scores for 35 and 61, using the formula z = (x - μ)/σ, where x is the score, μ is the mean, and σ is the standard deviation.
We don't have the mean and standard deviation, but we can estimate them using the five-number summary. The median (Q2) is (61+35)/2 = 48, and the mean is likely to be close to this value since the data is roughly symmetric. The range (max-min) is 79-11 = 68, so the standard deviation is roughly σ = range/4 = 17.
Using these estimates, we can calculate the z-scores as follows:
z1 = (35 - 48)/17 = -0.76
z2 = (61 - 48)/17 = 0.76

We can look up the proportion of scores between these two z-scores in a standard normal distribution table, or use a calculator or software to calculate it. It turns out to be about 0.3514, or 35.14%.
To find out how many students had scores between 35 and 61, we can multiply this proportion by the total number of students:
0.3514 * 380 ≈ 133.7
So, the answer is not one of the choices given.

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The answer is not one of the choices given.0.3514 * 380 ≈ 133.7 To find out how many students had scores between 35 and 61, we need to first calculate the interquartile range (IQR) which is the difference between the third quartile (Q3) and the first quartile (Q1).

Q1 is the median of the lower half of the data, which in this case is (11+35)/2 = 23.

Q3 is the median of the upper half of the data, which in this case is (70+79)/2 = 74.5.

So, IQR = Q3 - Q1 = 74.5 - 23 = 51.5.

Scores between 35 and 61 fall within one IQR from Q1. So, we need to find out what proportion of the scores fall within this range.

To do this, we need to calculate the z-scores for 35 and 61, using the formula z = (x - μ)/σ, where x is the score, μ is the mean, and σ is the standard deviation.

We don't have the mean and standard deviation, but we can estimate them using the five-number summary. The median (Q2) is (61+35)/2 = 48, and the mean is likely to be close to this value since the data is roughly symmetric. The range (max-min) is 79-11 = 68, so the standard deviation is roughly σ = range/4 = 17.

Using these estimates, we can calculate the z-scores as follows:

z1 = (35 - 48)/17 = -0.76

z2 = (61 - 48)/17 = 0.76

We can look up the proportion of scores between these two z-scores in a standard normal distribution table, or use a calculator or software to calculate it. It turns out to be about 0.3514, or 35.14%.

To find out how many students had scores between 35 and 61, we can multiply this proportion by the total number of students:

0.3514 * 380 ≈ 133.7

So, the answer is not one of the choices given.

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We know that the answer is: Yes, the series converges.

Consider the series 1- 1/2 - 1/3 + 1/4 + 1/5 - 1/6 - 1/7 + . . . which comes in pairs. The first two terms of each pair are of opposite signs, while the remaining terms of each pair are positive. If we group these terms together, we get:

(1 - 1/2) + (-1/3 + 1/4) + (1/5 - 1/6) + (-1/7 + 1/8) + . . .

Notice that the terms in each pair cancel each other out, leaving us with a series of positive terms only. Therefore, if this series converges, the original series also converges.

To determine whether this series converges, we can use the alternating series test. This test tells us that if a series has alternating signs and its terms decrease in absolute value, then the series converges.

In this case, the terms alternate in sign and their absolute values decrease as we move further along the series. Therefore, by the alternating series test, this series converges.

Thus, the answer is: Yes, the series converges.

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The distribution over the random variable X, representing the number of kids between Izzy and Lizzy in line, is given by P(X=x) = 1/2, 1/4, 1/6, and 1/12 for x=1, 2, 3, and 4, respectively.

Let us assume that the other two kids are named A and B. We can represent the order of the four kids as a string of letters: ALIB or ALBI or ABLI or ABIL or AIBL or AILB. There are 4! = 24 possible ways to order the four kids, and in half of them, Izzy comes before Lizzy, and in half of them, Lizzy comes before Izzy. So there are 12 possible orders in which Izzy comes before Lizzy.

In 6 of these orders, there is one kid between Izzy and Lizzy (e.g., AILB). In 3 of these orders, there are two kids between Izzy and Lizzy (e.g., ABLI). In 2 of these orders, there are three kids between Izzy and Lizzy (e.g., ALBI). And in 1 of these orders, there are four kids between Izzy and Lizzy (e.g., ABIL).

Therefore, the distribution over x is

P(X=1) = 6/12 = 1/2

P(X=2) = 3/12 = 1/4

P(X=3) = 2/12 = 1/6

P(X=4) = 1/12

So the probability mass function of X is

P(X=x) =

1/2 if x=1

1/4 if x=2

1/6 if x=3

1/12 if x=4

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Answer:

\(-\frac{1}{64}\)

Step-by-step explanation:

Evaluate the following limit.

\(\lim_{x \to 0} \frac{\frac{1}{x+8} -\frac{1}{8} }{x}\)

(1) - Simplify the limit

\(\lim_{x \to 0} \frac{\frac{1}{x+8} -\frac{1}{8} }{x}\\\\\Longrightarrow \lim_{x \to 0} \frac{\frac{1(8)}{(x+8)(8)} -\frac{1(x+8)}{8(x+8)} }{x}\\\\\Longrightarrow \lim_{x \to 0} \frac{\frac{8-x-8}{8(x+8)} }{x} \\\\\Longrightarrow \lim_{x \to 0} \frac{\frac{ -x}{8(x+8)} }{x} \\\\\Longrightarrow \lim_{x \to 0} \frac{-x}{8x(x+8)} \\\\\Longrightarrow \boxed{\lim_{x \to 0} \frac{-1}{8(x+8)} }\)

(2) - Plug in the limit

\(\lim_{x \to 0} \frac{-1}{8(x+8)}\\\\\Longrightarrow \lim_{x \to 0} \frac{-1}{8((0)+8)}\\\\\Longrightarrow \lim_{x \to 0} \frac{-1}{8(8)} \\\\\therefore \boxed{\boxed{\lim_{x \to 0} \frac{\frac{1}{x+8} -\frac{1}{8} }{x}=-\frac{1}{64} }}\)

The slope of all the given options  are equal and it is equal to slope of given equation .

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula. We shall comprehend the slope-finding method and its applications in this essay.

Given

Equation of a given line is x+2 y=6

Lets find out slope m by writing the equation in \($y= \mathbf{m}+\mathbf{b}$\) form

\($$\begin{aligned}& x+2 y=6 \\& 2 y=-x+6 \\& y=\frac{-1}{2} x+6\end{aligned}$$\)

The slope of the line is \($\frac{-1}{2}$\)

Now we find slope of each option using formula \($m=\frac{y_2-y_1}{x_2-x_1}$\)

Lets pick two points from the graph to find out slope

Pick (0,3) and (6,0)

\($$\begin{aligned}& m=\frac{y_2-y_1}{x_2-x_1} \\& m=\frac{0-3}{6-0}=\frac{-1}{2}\end{aligned}$$\)

Now pick two points from option \($\mathbf{B}$\) to find slope

(-10,-3) and (0,-8)

\(m=\frac{-8+3}{0+10}=\frac{-1}{2}$$\)

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Answer:

Step-by-step explanation:

Answer:1 1/12

Step-by-step explanation: 3/4+1/3=13/12=1 1/12

Answer:

look at the picture i have sent

XR0. Conversely, if an integer x is not of this form, then x + 0 is odd, and hence x is not related to 0 under R.

a) To prove that R is an equivalence relation, we need to show that it satisfies three properties:

Reflexivity: ∀x ∈ Z, xRx.

Symmetry: ∀x,y ∈ Z, if xRy then yRx.

Transitivity: ∀x,y,z ∈ Z, if xRy and yRz then xRz.

Reflexivity: Let x be any integer. Then x + x = 2x, which is even. Therefore, xRx, and R is reflexive.

Symmetry: Let x and y be any integers such that xRy, i.e., x + y is even. Then (x + y) - x = y is also even. Therefore, yRx, and R is symmetric.

Transitivity: Let x, y, and z be any integers such that xRy and yRz, i.e., x + y and y + z are both even. Then (x + y) + (y + z) = x + 2y + z is even. Therefore, xRz, and R is transitive.

Since R satisfies all three properties of an equivalence relation, R is an equivalence relation.

b) To find the equivalence classes of R, we need to determine the set of all integers that are related to a given integer under the relation R. Let's consider the integer 0 as an example:

The equivalence class of 0 is the set of all integers that can be written in the form 2k, where k is an integer. This is because for any integer x in this set, x + 0 = x, which is even, and therefore xR0. Conversely, if an integer x is not of this form, then x + 0 is odd, and hence x is not related to 0 under R.

We can apply the same argument to any integer n, and conclude that its equivalence class is the set of all integers that can be written in the form n + 2k, where k is an integer.

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Answer:

150

Step-by-step explanation:

150

Percentage Calculator: 135 is what percent of 90? = 150.