2. Classify each pair of events: Dice are rolled, then a coin is flipped.
O a. independent
O b. outcome
O c. complementary
O d. dependent

Answer:

A=73

B=17

Step-by-step explanation:

From above, you can see that A+B=90

So I can add my two angles together and have it equal to 90

( 5 x + 8 ) + ( x + 4 ) = 90

5 x + 8 + x + 4=90

6 x + 12 = 90

6 x = 90 − 12

6 x = 78  

x = 13  

So  A = 5 x + 8=5 ( 13 ) + 8 = 65 + 8 = 73  

and  B = x + 4 = 13 + 4 = 17

Just to make sure you are correct, add your A and B together and they should equal to 90  

A + B = 73 + 17 = 90

Hope This Helps You :)

Answer:

(2x-1)(2x+3)

Step-by-step explanation:

4x^2 + 4x - 3

4x^2 + 6x - 2x - 3

2x(2x + 3) - 1(2x + 3)

(2x - 1) (2x + 3)

Answer:

5.0587

Step-by-step explanation:

First, you have to count to the fourth number after the decimal;

That number is 7, the number after it is the one that will help you round.

Since that number is 0 you round down to 7.

Answer:

5.0587

Step-by-step explanation:

So we look at 5.05870

we count to four after the decimal place and land on the seven, next we look at the digit behind to seven to determine if we can round (remember 5 or more round the score, four or less let it rest).

The solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

As per data the system of linear equations,

\(\[ \left\{\begin{array}{c} x+2 y+3 z=9 \\ 2 x-y+z=8 \\ 3 x-z=3 \end{array}\right. \] 1)\)

Write the system in the matrix form \(\( A . X=B \)\)

We know that the matrix form of the system of linear equations is as follows.

\(\[A. X = B\]\)

Where

\(\[A=\begin{pmatrix} 1 & 2 & 3 \\ 2 & -1 & 1 \\ 3 & 0 & -1 \end{pmatrix}\[X=\begin{pmatrix} x \\ y \\ z \end{pmatrix}\]\)

and

\(\[B=\begin{pmatrix} 9 \\ 8 \\ 3 \end{pmatrix}\]2)\)

To solve the system, we can use row reduction method.

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 2 & -1 & 1 & 8 \\ 3 & 0 & -1 & 3 \end{pmatrix}\]\)

Applying the elementary row operations

\(\[R_{2}\to R_{2}-2R_{1}\]\)

and

\(\[R_{3}\to R_{3}-3R_{1}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & -6 & -10 & -24 \end{pmatrix}\]\)

Now applying the elementary row operations

\(\[R_{3}\to R_{3}-(6/5)R_{2}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & 0 & -1 & -2 \end{pmatrix}\]\)

Now, we need to apply back substitution method. Using the third row, we can get the value of z as z = 2.

Now, using the second row,

\(\[-5y - 5z = -10\]\\\-5y - 5(2) = -10\]\)

Solving this equation, we get y = 0.

Finally, using the first row, we can get the value of x as

\(\[x + 2y + 3z = 9\]\\x = 3\]\)

Hence, the solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

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The perimeter of  isosceles triangle PRQ is 24.65 units.

The lengths of its three sides and add them up. We can use the distance formula to find the length of each side.

Distance formula: The distance d between two points (x1, y1) and (x2, y2) is given by:

d = \(sqrt((x2 - x1)^2 + (y2 - y1)^2)\)

Using this formula, we can find the lengths of the sides PR, RQ, and PQ.

PR = \(sqrt((-1 - (-7))^2 + (4 - (-1))^2) = sqrt(36 + 25) = sqrt(61)\)

RQ =\(sqrt((3 - (-1))^2 + (-1 - 4)^2) = sqrt(16 + 25) = sqrt(41)\)

PQ = \(sqrt((3 - (-7))^2 + (-1 - (-1))^2) = sqrt(100) = 10\)

Therefore, the perimeter of triangle PRQ is:

PR + RQ + PQ = \(sqrt(61) + sqrt(41) + 10 ≈ 24.65\) (rounded to two decimal places)

So, the perimeter of triangle PRQ is approximately 24.65 units.

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Logos is the use of logic to try to persuade somebody by showing factual information and making reasonable arguments for or against something.

This refers to the use of persuasion to try and convince a person to take action on something.

There are three main persuasive techniques and they are:

Please note that your question is incomplete so I gave you a general overview to help you get a better understanding of the concept.

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Using area of the rectangle, we can find that the new flower garden will be 13m in length (greater dimension).

The formula for calculating a rectangle's area can be used to determine how much space the rectangle takes up within its perimeter. Multiplying the length by the width yields the area of a rectangle (breadth).

As a result, the following formula can be used to determine the area of a rectangle whose length and breadth are "l" and "w," respectively. The rectangle's area is L × W. A rectangle's area is therefore equal to length * width.

Now here the dimensions of the rectangle are, l = 13m and b, = 9m.

Area of the rectangle is 13 × 9 = 117m².

Now the area of the rectangle is increased to 221m².

So, when we increase the length from 13 m to 17m and the breadth from 9m to 13m, we get area = 17 × 13 = 221m².

Therefore, length of the new garden will be 17m long.

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1200/240=5

so 240 goes into 1200 5 times, just like 20% goes into 100% 5 times.

The answer would be 20%.

Hope this helps!

Answer:

yeah so it is 74882828 it is pretty easy

Answer:

1 ; 5 : 4

Step-by-step explanation:

The ratio of blue : red : yellow is \(\frac{1}{10}\) : \(\frac{1}{2}\) : \(\frac{2}{5}\)

Multiply each part by 10 to clear the fractions , thus

blue : red : yellow = 1 : 5 : 4

The shape of JKL is an Isosceles triangle

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, add up to 180 degrees.

The three vertices of shape JKL  \which are J(3, 0), K(6, 8) and L(-5, 3), points that the shape is a triangle since triangles have 3 vertices.

The shape is plotted and attached and the graph which is a pictorial representations represents the shape to be a triangle

The plot shows that LJ = JK = 8.5

Also, distance between points J(3, 0) and K(6, 8)  is calculated as follows

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

d =√{(3 - 6)² + (0 - 8)²}

d =√{9 + 64}

d = √73

d = 8.54 units

distance between point J(3, 0) and L(-5, 3)

d =√{(3 - (-5))² + (0 - 3)²}

d =√{64 + 9}

d = √73

d = 8.54 units

distance between point K(6, 8) and L(-5, 3)

d =√{(6 - (-5))² + (8 - 3)²}

d =√{121 + 25}

d = √146

d = 12.08 units

since LJ = JK, the triangle is isosceles

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Answer:2/4 3/6 4/8

Step-by-step explanation:

Answer:

Yes, because they both have two sets of parallel lines.

Hope that helps!

Step-by-step explanation:

Answer:

540

Step-by-step explanation:

546-56=490

490+17+30=537

537+3=540

A≈907.92in²

Because:

A=πr2=π·172≈907.92028in²

Answer:

289π or 907.46 in

Step-by-step explanation:

The formula for area of a circle is π r².

The radius is 17, so the first step is 17².

17²= 289

Next, you multiply 289 by pi (3.14).

3.14 x 289 = 907.46.

Therefore, the area in terms of pi is 289π or 907.46 in.

Answer:

All real numbers are solutions

Step-by-step explanation:

2x + 8 = 2(x + 4)

~Simplify right side

2x + 8 = 2x + 8

~Subtract 8 to both sides

2x = 2x

~Divide 2 to both sides

0 = 0

Best of Luck!

Answer: the answer is infinite

Step-by-step explanation: so first you need to distribute the 2 into the () and you would get 2x+8 and since it is the same on both sides it cancles eachother out therefore there is infinite answers

Answer:

79°

Step-by-step explanation:

PQO is straight angle with measure of 180°

the given angles' sum makes 101° and we need 79 to complete it to 180° therefore the angle STQ = 79°

Answer:

12

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

.  .  .             Remainder:   .  .            

.  .  .

.  .  .

.  .  .

.  .  .

.  .  .                      

thats the best i could do with an array

Answer:

x = -2

Step-by-Step Explanation:

Look at the attachment. You can either deduce that both exponents are equal because their base is 3, or you can take the log base 3 of each side.

Answer: C

Step-by-step explanation: Trust me on this ok?

The required probability = 0.13

first since there are 4 red marbles, 4 blue marbles, and 12 yellow marbles

Total marbles =  20 marbles now.

Since there are 4 marbles,

the probability of pulling red marbles = 4/20.

So now that she took 1 red marble away, we have 19 marbles left.

So now that has been finished,

she pulled 1 more yellow marble away so now we have

probability of pulling yellow marble = 12/19.

Now that it's completed you multiply the two, and now you should have

= 4 /20 × 12 / 19

= 12 / 95

Probability = 0.126315789

=  0.13

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Answer:

Step-by-step explanation:

We can graph the function and determine the points where the y value line is greater than 64 feet.  We could also solve the equation for h = 64.

Graphing:

A graph is attached.  The intersections of the line at height = 64 feet are at (1,64) and (4,64).  The first is going up and the second coming down.  The period of time the rocket is above 64 feet is from 1 to 4 seconds.

Solving:

h= -16t^2+ 80t

64 = -16t^2+ 80t

-16t^2+ 80t - 64 = 0

Solve using the quadratic formula:

We get two answers:  1 and 4 (seconds)

Thus, the p-value is greater than 0.10 (the significance level α), indicating that there is not enough evidence to support the alternative hypothesis.

To find the p-value, we need to calculate the test statistic and compare it to the critical value.

Given:

Sample 1: sample size (n1) = 22, variance (\(s_{1}^2\))

= 8, mean (x1(bar))

= 51

Sample 2: sample size (n2) = 20, variance (\(s_{2}^2)\)

= 11, mean (x2(bar))

= 50.5

To calculate the test statistic, we can use the formula for the difference in means:

t = (x1(bar) - x2(bar)) / √((\(s_{1}^2\)/n1) + (\(s_{2}^2\)/n2))

Substituting the given values:

t = (51 - 50.5) / √((8/22) + (11/20))

  = 0.5 / √(0.3636 + 0.55)

  = 0.5 / √0.9136

  ≈ 0.53

Now we need to find the degrees of freedom. For independent samples with equal variance, the degrees of freedom (df) can be calculated using the formula:

df = n1 + n2 - 2

Substituting the given values:

df = 22 + 20 - 2

  = 40

With α = 0.10, the critical value for a one-tailed test (upper tail) with 40 degrees of freedom is 1.684.

Now, we can determine the p-value. Since the alternative hypothesis is μ1 - μ2 > 0, we are conducting an upper-tailed test.

The p-value is the probability of obtaining a test statistic as extreme as the one observed (t = 0.53) under the null hypothesis.

By comparing the test statistic to the critical value, we can determine the conclusion:

Since the test statistic (0.53) is less than the critical value (1.684), we fail to reject the null hypothesis.

Therefore, the conclusion is: "We don't have enough evidence to conclude that the difference in means is > 0; therefore, H0 is not rejected."

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Answer:

Step-by-step explanation:

I am using trig identities and the formula for the difference of the cos of 2 angles to solve this. I'll do the steps one at a time. It's super tricky. First I'm just going to work on simplifying the sec² part and then I'll introduce the sin²(x) - sin⁴(x) when I need it. Beginning with the identity for the difference of the cos of 2 angles, knowing that sec²(x) = \(\frac{1}{cos^2(x)}\):

\(sec^2(\frac{\pi}{2}-x)=\frac{1}{cos^2(\frac{\pi}{2}-x )}\) and expand that using the formula for the difference:

\(\frac{1}{cos(\frac{\pi}{2}-x)cos(\frac{\pi}{2}-x) }=\) \(\frac{1}{(cos\frac{\pi}{2}cos(x)+sin\frac{\pi}{2}sin(x))(cos\frac{\pi}{2}cos(x)+sin\frac{\pi}{2}sin(x)) }\) and all of that simplifies down to

\(\frac{1}{(0cos(x)+1sin(x))(0cos(x)+1sin(x))}\) which simplifies further to

\(\frac{1}{(sin(x))(sin(x))}=\frac{1}{sin^2(x)}\) Now we'll bring in the other term. This is what we have now:

\(\frac{1}{sin^2(x)}(\frac{sin^2(x)-sin^4(x)}{1})\) and distribute in to get:

\(\frac{sin^2(x)}{sin^2(x)}-\frac{sin^4(x)}{sin^2(x)}\) which simplifies to

\(1-sin^2(x)\) and that, finally, simplifies down to a simple

\(cos^2(x)\)

For the given triangle, hypotenuse side is x and length of legs of right triangle is,

Determine the value of x by using pythagoras theorem in right angle triangle.

Answer: Option C (2√5 yd)

The confidence interval of 99% for μ₂ - μ₁ for the given mean and standard deviation is equal to (23.7377, 49.7713).

Confidence interval = 99%  

Confidence interval for μ₂ - μ₁, we need to follow these steps,

Calculate the sample mean difference and the standard error of the mean difference.

Sample mean difference

= ¯x₂ - ¯x₁

= 162.75 - 126

= 36.75

Standard error of the mean difference

= √[(s₁^2/n₁) + (s₂^2/n₂)]

= √[(8.062^2/5) + (3.5^2/4)]

= 4.0065 (rounded to four decimal places)

The t-value for a 99% confidence level with degrees of freedom

= n₁ + n₂ - 2

= 5 + 4 - 2

= 7.

Using a t-distribution table attached ,

The t-value for a 99% confidence level with 7 degrees of freedom is 3.250.

Margin of error

= t-value x standard error of the mean difference

= 3.250 x 4.0065

= 13.0213 (rounded to four decimal places)

Confidence interval

= Sample mean difference ± Margin of error

= 36.75 ± 13.0213

= (23.7377, 49.7713)

Therefore, the 99% confidence interval for μ₂ - μ₁ is (23.7377, 49.7713).

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The sequence cos(0),cos(π),cos(2π),cos(3π),cos(4π),… can be represented as a function k: N -> R, where N is the set of natural numbers and R is the set of real numbers. The domain of the function is the set of natural numbers, and the codomain is the set of real numbers. The function l: N -> {-1,1}, where l(n) = (-1)^(n).

The sequence 1,14,19,116,… can be represented as a function f: N -> N, where N is the set of natural numbers. The rule for determining the outputs of the function is as follows: f(1) = 1, f(2) = 14, f(3) = 19, f(4) = 116, and so on.
The sequence 13,19,127,181,… can be represented as a function g: N -> N, where N is the set of natural numbers. The rule for determining the outputs of the function is as follows: g(1) = 13, g(2) = 19, g(3) = 127, g(4) = 181, and so on. The domain of the function is the set of natural numbers, and the codomain is also the set of natural numbers. We can see that this sequence is not equal to any of the other sequences given.

The sequence 1,−1,1,−1,1,−1,… can be represented as a function h: N -> {-1,1}, where N is the set of natural numbers. The rule for determining the outputs of the function is as follows: h(1) = 1, h(2) = -1, h(3) = 1, h(4) = -1, and so on. The domain of the function is the set of natural numbers, and the codomain is the set {-1,1}. We can see that this sequence is equal to the function f: N -> {-1,1}, where f(n) = (-1)^(n+1).

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