10. Supose you bought a digital album from your favorite artist and set iTunes to play
the album in random order without repeats. The album has 10 songs and it turns
out you really like 5 of them. Find the following probabilities for the first 2 songs
played at random.


a) You like both of them 2
b) B) you like neither of the songs ,
c) C) you like at least one of the songs

Answer:

Step-by-step explanation:

To solve this equation, use the distributive property. Isolate the difference between the numbers from one side of the equation.

Distributive property:

A(B+C)=AB+AC

-1.9 = 0.5(p +1.7)

First, switch sides.

0.5(p+1.7)=-1.9

Divide by 0.5 from both sides.

[tex]\sf{\dfrac{0.5\left(p+1.7\right)}{0.5}=\dfrac{-1.9}{0.5}}[/tex]

Solve.

-1.9/0.5=-3.8

p+1.7=-3.8

Then, you subtract by 1.7 from both sides.

p+1.7-1.7=-3.8-1.7

Solve.

Add or subtract the numbers from left to right.

-3.8-1.7=-5.5

[tex]\rightarrow \boxed{\sf{p=-5.5}}[/tex]

Therefore, the correct answer is p=-5.5.

I hope this helps, let me know if you have any questions.

The value of p on the equation - 1.9 = 0.5(p +1.7) is - 5.5.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given, we have to solve for p in the equation - 1.9 = 0.5(p +1.7).

0.5(p + 1.7) = - 1.9

First, we'll distribute the terms.

0.5p + 0.85 = - 1.9.

0.5p = - 1.9 - 0.85.

0.5p = - 2.75.

p = - 2.75/0.5.

p = - 5.5

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a. A function rule is a representation of dependent variable, here n, in terms of the independent variable, here P, and is expressed as ƒ(P) = 1.5n.

b. This type of reason is useful because functions in an equation can take input from many variables, but always give the same result, which is unique to that function.

The connection between the input or domain and the output or range is called a function rule. When there is exactly one value in the range for each domain value, a relation is a function.

f(x), where x is the input value, is how functions are expressed.

All functions have the general form y = f(x)

On any part of the function, a vertical line is drawn. It is a function if and only if it crosses the function at that single point. It is not a function if the line crosses itself more than once.

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For this question, we recall the point-slope form of the equation of a line:

and the slope-intercept form:

Therefore for the given data, the point-slope form is:

and the slope-intercept form is:

Answer:

150°

Step-by-step explanation:

Both the measure of <1 and <2 are 150°

If angle theta is given as;

And angle theta is in the third quadrant, then we can find the value of y by using the pythagoras' theorem as follows;

Note also that;

However, the angle theta is in the third quadrant where y is also negative. Therefore, sin theta would be;

Note also that cosec theta is given as;

Note also that, tan theta is given as;

Therefore, we would have;

ANSWER:

The sequence has its 15th term to be 268435456

From the question, the given parameters are

1, -4, 16

The above sequence is a geometric sequence, with the following parameters

Evaluate the quotient

So, we have

r = -4

The nth term of a geometric sequence is

Tn = a * r^(n-1)

Where

a = 1 and r = -4

Also, we have n = 15

Substitute a = 1 and r = -4 in the equation Tn = a * r^(n-1)

So, we have

Tn = 1 * (-4)^(n-1)

Substitute 15 for n

Tn = 1 * (-4)^(15-1)

Evaluate

Tn = 268435456

Hence, the 15th term of this sequence is 268435456

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Answer:

===========================

The triangles PTS and POR are similar, so we can take the ratios of the side to order

We can then solve for x by collecting like terms

180x - 150x = 390 + 60

30x = 450

Divide both sides by 30

x = 450/ 30

x = 15

Given:

The triangle FTP and triangle JTA is given.

In the given triangles,

As only three angles of both triangles are similar we can not say that the given traingles are congruent.

So, Option A is correct.

To change the number from scientific notation to normal number multiply 9.9 by 10^7

The number is 99,000,000

The sketch of the given parametric equations is as appended.

Given parametric equations,

x(t) = 1+2t

y(t) = [tex]t^{2}[/tex]

y = [tex]\frac{(x-1)^{2}}{4}[/tex]

For bounding range of -2 ≤ t ≤ 2, corresponding values of x are as follows,

x = 2t + 1

For t = -2, x = 2(-2) + 1 = -3

For t = 2, x = 2(2) + 1 = 5

Hence the graph has been drawn with bounding limits of -3 ≤ x ≤ 5

The outcome is a parabola with vertex at (1,0) and open upwards. The curve moves towards infinity in upwards direction if there are no bounds / range.

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Regarding perfect squares, it is found that:

Perfect square expressions are formed with the notable products of the square of the sum or the square of the subtraction, as follows:

The constant term of perfect squares, in both cases, is given by:

b².

Since the number is squared, it will always be a positive value, meaning that a negative constant term guarantees that the polynomial is not a perfect square.

The polynomial with a negative constant in this problem has a constant of -121, hence it is not a perfect square.

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All we simply need to do is to apply the law of indices that states;

Hence;

The correct option is

Answer

Largest Area that can be enclosed = 361250 m²

Explanation

Let the length of the fencing along the river be L

Let the width of the fencing be W

A sketch of the problem will make it clearer

Perimeter = L + 2W

Perimeter is giving as the total length of the fencing to be 1700 m

L + 2W = 1700

L = 1700 - 2W

The area of the structure is given as

Area = LW

The area is what we want to maximize

Recall, L = 1700 - 2W

Area = LW = (1700 - 2W) × W = 1700W - 2W²

A = 1700W - 2W²

At maximum point, the derivative of any function is zero

Hence,

(dA/dW) = 1700 - 4W

At maximum point,

(dA/dW) = 0

1700 - 4W = 0

4W = 1700

Divide both sides by 4

(4W/4) = (1700/4)

W = 425 m

Recall, L = 1700 - 2W

L == 1700 - 2(425)

L = 1700 - 850

L = 850 m

Maximum Area

= (Length at maximum area) × (Width at maximum area)

= 850 × 425

= 361250 m²

Hope this Helps!!!

The simplified equation is sin(2x) = 2

The trigonometry ratio is given as

2sinxcosx/sin^2x+cos^2x-1= 1

Rewrite the equation of the trigonometry formula properly

So, we have the following equation

2sin(x)cos(x)/sin^2(x)+cos^2(x) -1 = 1

Add 1 to both sides of the equation

So, we have the following equation

2sin(x)cos(x)/sin^2(x)+cos^2(x) = 2

Express 2sin(x)cos(x) as sin(2x)

So, we have the following equation

sin(2x)/sin^2(x)+cos^2(x) = 2

Express sin^2(x)+cos^2(x) as 1

So, we have the following equation

sin(2x)/1 = 2

Multiply both sides by 2

So, we have the following equation

sin(2x) = 2

Hence, the simplified equation of the trigonometry formula is sin(2x) = 2

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Answer:

She should pour 11.68 more grams

Step-by-step explanation:

If Melissa wanted to pour 30.78 grams of salt into a container and already has poured 19.1 grams she should pour 11.68 grams more

Answer:

Explanation:

Given the expression:

We want to write the given expression in the form:

That is, to factorize the expression.

When an expression is to be factorized, follow the steps below:

Step 1: Multiply the coefficient of x² and the constant.

Step 2: Find two terms that multiply to give the product -6y², and add to give the middle term, 5y. To do this, list the factors of -6: 1, 2,3, and 6

Step 3: Rewrite the middle term, 5y with those numbers.

Step 4: Factor the first two and last two terms separately. Ensure that the expression in the brackets is the same.

Solving a linear equation we will see that there are 47 worms in the container

We know that the mass of the container is 225 grams, and the mass of each worm is 11.2 grams.

Then if there are x worms on the containers, the total mass is:

M(x) = 225g + x*11.2g

In this case, we know that the total mass is 751.4 grams, then we can write:

751.4 g = 225g + x*11.2g

Solving this linear equation we get:

751.4g - 225g = x*11.2g

526.4g = x*11.2g

526.4g/11.2g = x = 47

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The Zeros of the polynomial function partially graphed below have even multiplicity are x = -3 and x = 3.

The zeros of a Polynomial graph are simply the points where the graph curve crosses the x-axis.

In simply terms, the Zeros of a function are the values of the independent variable that make the function equal to 0. Multiplicity just refers to how many copies of a given zero exist.

From the given graph, the zeros of the Polynomial function are x = 2 and x = 3 and x = -3

An odd multiplicity means the graph of the function crosses the x-axis at that point. An even multiplicity means the curve contacts the x-axis at that point and backs instead of crossing.

Thus, the odd multiplicity is at x = 3

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The fraction which is a constant is equal to 1/6

Given data

A ball is dropped from a height of 180 inches

After the second bounce it is still 5 inches

the height the ball bounces is always the same fraction of the height reached on the previous bounce

Let the first height be x, this the initial drop height = 180

Let the second height be, the first bounce y

Let the third height be w, the second bounce = 5

the fraction is said to be:

height of y / height of x = height of w / height of y

y / x = w / y

y / 180 = 5 / y

y^2 = 180 * 5

y^2 = 900

y = √900

y = 30

the fraction is then 30 / 180 = 1 / 6

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Ive attached it on this photo. ur welcome :)

Answer:

Step-by-step explanation:

In the given expression :

we need to find the value of n at which, an = -24

Thus, at n=3, the an = -24

Given graph shown a function plotted.

The aim is to determine where the function is strictly decreasing.

The interval where the function is strictly decreasing is given by the union of intervals where the graph is descending from a point.

From the graph, it is clear that the function decreases from

and again from

Therefore, the intervals where the function is strictly decreasing is:

Insurance -  A financial service that protects a consumer

Liability - A responsibility to pay for or to fix a problem

Compensate - To pay the value of something that has been lost or stolen

Premium - The amount of money a consumer must pay an insurance company

Deductible - The money of a consumer must pay for a claim before the policy takes over

Insurance is a legal agreement, evidenced by a policy, under which a policyholder receives financial security or compensation from an insurance provider against losses.

Liability is a general phrase that refers to many types of coverages to assist in defending you or your company in the event that a claim or lawsuit is made against you or your organization.

The amount that the insurance provider has agreed to pay for insured losses that are mentioned in your policy is referred to as "compensation."

You pay a premium when you purchase an insurance policy. Your recurring payments for many popular insurance products, such as life, car, business, homeowners, and renters, are known as premiums.

The sum of money you must contribute to an insured loss is known as a deductible.

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By definition, a sample space is a collection or a set of possible outcomes of a random experiment. In our problem, we have four different outcomes. A, B, C and D. This is our sample space

Answer:

1. 0.30

2.4 over 20

3. x is greater than 1.5

4. 19.2

5. 468.11

Step-by-step explanation:

1) 1.4m = 0.42.

Divide both sides by 1.4

1.4m/1.4 = 0.42/1.4

m = 0.30

2) 13/20=j+9/20

Flip equation

j + 9/20 = 13/20

Substract 9/20 from both sides

j + 9/20 - 9/20 = 13/20 - 9/20

j = 13 - 9/20

j = 4/20

3) x − 1.3 = 1.5?

Add 1.3 to both sides

x - 1.3 + 1.3 = 1.5 + 1.3

x = 2.8

So, x is greater than 1.5

4) x/6 + 0.4 =3 + 0.6

Substract 0.4 from both sides

x/6 + 0.4 - 0.4 = 3 + 0.6 -0.4

x/6 = 3 + 0.2

x/6 = 3.2

Multiply both sides by 6

x/6 • 6 = 3.2 • 6

x = 19.2

5) k − 173.54 = 294.57.

Add 173.54 to both sides

k - 173.54 + 173.54 = 294.57 + 173.54

k = 468.11

The value of m from the given equation is 0.3.

The given equation is 1.4m = 0.42.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

1) 1.4m = 0.42

⇒ m = 0.42/1.4

⇒ m = 0.3

2) 13/20 = j+9/20

⇒ j = 13/20 - 9/20

⇒ j = 4/20

⇒ j = 1/5

3) x - 1.3 = 1.5

⇒ x = 1.5 + 1.3

⇒ x = 2.8

4) x/6 + 4/10 = 3 + 6/10

⇒ x/6+0.4=3.6

⇒ x/6 = 3.2

⇒ x = 19.2

5) k − 173.54 = 294.57

⇒ k = 294.57+173.54

⇒ k = 468.11

Therefore, the value of m from the given equation is 0.3.

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The probability distribution table corresponds with the given frequency distribution table is option (D)

Probability is defined as the ratio of number of favorable outcome to the total number of outcomes. The value of the probability varies from 0 to 1.

Probability =  Number of favorable outcomes / Total number of outcomes

The total frequency = 3+7+2+3+5

= 20

The probability of each outcomes

Substitute the values in the equation

p(1) = 3/20 = 0.15

p(2) = 7/20 = 0.35

p(3) = 2/20 = 0.1

p(4) = 3/20 = 0.15

p(5) = 5/20  = 0.25

Hence, the probability distribution table corresponds with the given frequency distribution table is option (D)

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Recall that to evaluate an expression at some given values, we substitute each variable with the corresponding given value.

Evaluating 2c²d-3cd at c=-1 and d=-2 we get:

Simplifying the above result we get:

Answer: Option a.

Answer:

-10

Step-by-step explanation:

Substitute variable values for variables.

[tex]2(-1)^2(-2) - 3(-1)(-2)[/tex]

Simplify

2(1)(-2) - 6

-4 - 6

-10