Question 3 (2 points)
For the following, find the arc length:
(Use π=3.14 and round your final answer to the hundredths.)

probabilities for choosing 2 marbles from a bag of 10 marbles is Dependent events

Given the following probabilities for choosing 2 marbles from a bag of 10 marbles are:-

P(blue) = 3/10, P(green) = 1/5, P(blue and green) = 3/100

We know the fact that two event are independents if we have following:-

P(X and Y) = P(X) times P(Y)

For this problem, we must have P(blue and green) = P(blue) times P(green).

P(blue and green) = (3/10) * (1/5) = 3/50

But given P(blue and green) = 3/100

Since we have 3/100 ≠ 3/50

Hence, the events are not independent events.

So, they are dependent events.

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Answer:

60 inches squared

Step-by-step explanation:

Answer:

11,100

Step-by-step explanation:

1% of 30,000 is 300 so if we times 300 by 37 we get 11,100

there is 11,100 sheep in 37%.

hope this helps :)

The transformation was a reflection over the x-axis. This is because \(g(x)=-f(x)\).

Answer:

x=3

Step-by-step explanation:

Simplifying

9x + -4 = 3x + 14

Reorder the terms:

-4 + 9x = 3x + 14

Reorder the terms:

-4 + 9x = 14 + 3x

Solving

-4 + 9x = 14 + 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.

-4 + 9x + -3x = 14 + 3x + -3x

Combine like terms: 9x + -3x = 6x

-4 + 6x = 14 + 3x + -3x

Combine like terms: 3x + -3x = 0

-4 + 6x = 14 + 0

-4 + 6x = 14

Add '4' to each side of the equation.

-4 + 4 + 6x = 14 + 4

Combine like terms: -4 + 4 = 0

0 + 6x = 14 + 4

6x = 14 + 4

Combine like terms: 14 + 4 = 18

6x = 18

Divide each side by '6'.

x = 3

Simplifying

x = 3

Answer:

Explanation:

Write your equation

Subtract 9x from both sides

3x + 14 − 9x = 9x − 4 − 9x

−6x + 14 = −4

Subtract 14 from both sides

−6x + 14 − 14 = −4 − 14

−6x = −18

Divide both sides by -6

−6x / -6 = −18 / -6

[ zyxx ]

Answer:

33cm

Step-by-step explanation:

385 / 35 = 11

11 times 3 = 33

The conditional probability for this problem is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For this problem, we have that 5 students play soccer, and of those, 2 play basketball, hence the conditional probability is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

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Answer:

30

Step-by-step explanation:

Given

f(x) = x² - x

Then

f(-5) = (-5)² - (-5)

= 25 + 5

= 30

Answer: x=18

im assuming that this is a right angle

so if it is then that means the total of the angle should be 90 degrees. so 2x+3x should be equal to 90. Just combine like terms to get that 5x=90 and then isolate the variable (divide by 5 on both sides) so x ends up equaling 18.

so x=18

Answer:

Two possible answers depending on full context: 13 ft or 13 1/3 ft

Step-by-step explanation:

Background: You can get area by multiplying length by width

1. The area is already given in this equation, 160. The length is also given, meaning that we just need to find the width (w).

We can even form an equation: 160 = 12 * w

2. Divide 160 by 12 to find the maximum width

3. When you divide 160 by 12 you get 13 1/3 ft as the width. If you are looking for whole numbers you can round back to 13 ft.

Answer:

C

Step-by-step explanation:

All sides make a cube

Answer:

D

Step-by-step explanation:

Answer: (x+5)

Step-by-step explanation:

The only other possible factor is (x+5). We can test it out to see if it multiplies out to x²-25.

(x+5)(x-5)          [FOIL]

x²-5x+5x-25     [combine like terms]

x²+0x-25

x²-25

Therefore, we know that (x+5) is the correct other factor.

In order to dilate the figure around the origin by a scale of 4, we need to multiply the coordinates of each point by 4. This is done below:

The coordinates are: F'(-4, 8), G'(8,-8) and E'(-8,0).

Answer:so the answer is 1,9,7,3,5,2

Step-by-step explanation:

The set of all possible outcomes is S = {A, C, G, T}. The set of all possible outcomes is also called the sample space. Events of interest might be E1 = an A

Answer:

The domain of the function is all real numbers. That is (-infinity , infinity)

Answer:

A) (-9/7,0), (3/8,0)

Step-by-step explanation:

Zeros of a quadratic function:

x for which y = 0.

In this question:

\(y = 6(7x + 9)(8x - 3)\)

It's 0 if one of the factors is 0. 6 is never 0, now about the other to:

\(7x + 9 = 0\)

\(7x = -9\)

\(x = -\frac{9}{7}\)

So (-9/7, 0) is a zero of the quadratic function.

The other is:

\(8x - 3 = 0\)

\(8x = 3\)

\(x = \frac{3}{8}\)

(3/8,0) is the other zero.

Thus, the correct answer is given by option A.

Answer:

they are

Step-by-step explanation:

divide 12*4=3

9*3=3

same ratio

Answer:

D) 4, H) 14

Step-by-step explanation:

D) both angles form a linear pair so 101-5x + 2x+70 = 180

Simplify

171-3x = 180

-3x = 9

x = -3

H) 11x-23 = 41 + 90 because they are opposite angles

Simplify

11x = 154

x = 14

Answer:

1-{0.2(m-3)+¼}=0

1{0.2m-0.6+¼}=0

1-{(0.8m-2.4+1)/4}=0

1-(0.8m-1.4)/4=0

lcm

(4-0.8m-1.4)/4=0

(2.6-0.8m)/4=0

cross multiply

2.6-0.8m=0

m=2.6/0.8

m=3.25

The solution of the expression are,

⇒ m = 3.25

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Expression is,

⇒ 1 - | 0.2 (m - 3) + 1/4 | = 0

Now, We can simplify as;

⇒ 1 - | 0.2m - 0.6 + 1/4| = 0

⇒ 1 - |0.2m - 0.6 + 0.25| = 0

⇒ 1 - |0.2m - 0.35| = 0

⇒ 1 = 0.2m + 0.35

⇒ 1 - 0.35 = 0.2m

⇒ 0.2m = 0.65

⇒ m = 3.25

Thus, The solution of the expression are,

⇒ m = 3.25

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The next three numbers of the repeating decimal produced by the fraction 5/6 is 0.833333333...

After a decimal point, recurring decimal numbers are ones that consistently repeat the same value. They are also known as Repeating Decimals. Non-recurring numbers in mathematics are those whose values don't repeat themselves after a decimal point. Non-terminating decimals and non-Repeating Decimal Numbers are other names for them.

When 5 is divided by 6 we get a recurring number.

Hence, the next three numbers of the repeating decimal produced by the fraction 5/6 is 0.833333333...

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Answer:

Converse: If I passed, then I studied.

Inverse: If I don't study, then I will not pass

Contrapositive: If I didn't pass, then I didn't study.

Step-by-step explanation:

Answer: 9/1

Step-by-step explanation: Apologies for the mistake. Let's calculate the probability again.

To find the probability of rolling a sum of 9 on two number cubes, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.

For a sum of 9, the following combinations are favorable:

(3, 6), (4, 5), (5, 4), (6, 3)

So, there are 4 favorable outcomes.

The total number of possible outcomes is still 6 × 6 = 36.

The probability of rolling a sum of 9 is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 4 / 36

Simplifying the fraction, we get:

Probability = 1 / 9

Therefore, the probability of rolling a sum of 9 is 1/9, not 11/18 as previously stated.

Answer:

33.33%

Step-by-step explanation:

% increase : new value - old value/old value * 100%

                   1200 - 900/900 * 100% (to make it easier, cut the zeros the best                  

                   you can)

                   300/ 9

                   = 33.33 or 33 1/3%

In the given graph, the x-intercepts are (2,0) and (6,0).

The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.

The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).

The sign of the leading coefficient is positive, since it is 1/2.

To find the equation of the quadratic function, we start by using the vertex form:

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

where (h, k) is the vertex. Plugging in the given vertex (4,-2), we get:

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

Next, we use the other two points to find two additional equations:

\(6 = a(8 - 4)^2 - 2 (plugging in (8,6))\\0 = a(2 - 4)^2 - 2 (plugging in (2,0))\)

Simplifying these equations, we get:

\(6 = 16a - 2\\8a = 4 -- > a = 1/2 \\0 = 4a - 2 \\4a = 2 -- > a = 1/2 \\\)

So the equation of the quadratic function is:

\(y = (1/2)(x - 4)^2 - 2\)

Now, we can answer the questions:

The y-intercept is the point where the graph intersects the y-axis. To find it, we set x = 0 in the equation:

\(y = (1/2)(0 - 4)^2 - 2 = 6\)

So the y-intercept is (0,6).

To find the x-intercepts, we set y = 0 in the equation:

\(0 = (1/2)(x - 4)^2 - 2\)

Simplifying, we get:

\((x - 4)^2 = 4\\ - 4 = \pm 2 \\= 2, 6\)

So the x-intercepts are (2,0) and (6,0).

The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.

The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).

The sign of the leading coefficient is positive, since it is 1/2.

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The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.

The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.

The confidence interval formula is \(\bar x\pm t\frac{s}{\sqrt{n}}\).

Where, \(\bar x\) is the sample mean, t is the critical value, n is the sample size and s is the standard deviation for the sample.

Here,

\(\bar x\) =1.267, s=1.23, n=30

The standard error is Se= 1.23/√30

= 0.2246

Item a:

The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.

Item b:

Using a t-distribution calculator, considering a confidence level of 0.99 with 30 - 1 = 29 df, the critical value is t = 2.7564.

\(\bar x\pm tS_c\)

\(\bar x+ tS_c\) =1.267-2.7564(0.2246) =0.6479

\(\bar x- tS_c\) =1.267+2.7564(0.2246) =1.8861

Therefore, the 99% confidence interval to estimate the true mean score on this question is (0.6479, 1.8861). It means that we are 99% that the true mean score of all students in this question is between 0.6479 and 1.8861.

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Answer:

B.

Step-by-step explanation:

m=y2-y1/x2-x1

6.5-2=4.5

7-4=3

4.5/3=1.5

the slope is 1.5

hope this helps :3

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Answer: 12 people

Step-by-step explanation:

0.30 x 40 = 12

Answer:

eight squared or 64

Answer:

8 to the 2nd power.

Step-by-step explanation:

First add all the power. This will get you 8*11/8*9. Next, divide this by subtracting which will get you 8*2! Have a nice day!!!

Answer:

a)P ( A∩S) =  0.116

b) P (x= 5) =0.272

c)  P (at most 5) = 0.950647

Step-by-step explanation:

Let A be an event that the  maize (modern-day corn) ears carry single spikelets and B be an event that the  maize carry paired spikelets.

Then P (B) = 60% = 0.6

P (A) = 1-P (b) = 0.4

Let S be the event that seed with single spikelets will produce an ear with single spikelets and Q be the event that seed with  paired spikelets will produce an ear with single spikelets .

Then

P (S) = 29% = 0.29

P (Q ) = 26% = 0.26

n= 10

We want to find out that exactly 5 single spikelets  seeds produce single spikelets .

P ( A∩S) = P(A) *P(S) = 0.4 * 0.29= 0.116

Now we have to find that exactly five of the ears produced by these seeds have single spikelets.

b) P (x= 5) =  P(A) *P(S)+  P(B) *P(R)

= 0.4 * 0.29 + 0.6 * 0.26

= 0.116+ 0.156= 0.272

At most five ears have single spikelets.This follows a binomial distribution where n is fixed and also p and q are same.

P ( x= at most 5) = 10C5 ( 0.116)^ 5(0.884)^5 +10C4 ( 0.116)^ 4(0.884)^6+10C3 ( 0.116)^ 3(0.884)^7+10C2 ( 0.116)^ 2(0.884)^8 +10C9 ( 0.116)^ 1(0.884)^9+10C10 ( 0.116)^ 0(0.884)^10    

=0.002857+0.018145+ 0.0000234+0.2558+ 0.3824+ 0.29144

= 0.950647