DJ Titus is making a playlist for a radio show; he is trying to decide what 10 songs to play and in what order they should be played. Step 1 of 2 : If he has his choices narrowed down to 7 blues, 7 disco, 5 pop, and 7 reggae songs, and he wants to play no more than 4 reggae songs, how many different playlists are possible

To prove that triangles ABD and ΔABC are congruent by SSS, what needs to be true is: A. BC ≅ BD.

For two triangles to be congruent to each other by the SSS Congruence Theorem, the triangles must have three pairs of corresponding sides that are congruent to each other.

In the image given, we can deduce that the two triangles have the following properties:

AB ≅ AB (reflexive property)

AC ≅ AD (given)

This means that have two pairs of corresponding congruent sides. Therefore, in order to prove that ΔABD ≅ ΔABC by SSS, what needs to be true is: A. BC ≅ BD.

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Answer:

2400

Step-by-step explanation:

Answer:

88

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Answer:

5x+x=42

6x=42

x=7

Step-by-step explanation:

Answer:

y = 5x

x + y = 42

Step-by-step explanation:

If y is 5 times greater than x, this can be represented by y = 5x

The sum of x and y is 42, so this can be represented by x + y = 42

So, the system of equations will be:

y = 5x

x + y = 42

The future value of an investment is the worth of the investment in a given time.

Ed's monthly payment to meet up with Steve's is $4701.

We have:

Steve

\(n=46\) --- time

\(r = 8\%\) --- rate

\(PMT = 3200\) --- monthly payments

First, we calculate the Steve's future value

\(FV = \frac{PMT \times ((1 + r)^{n - 1}) \div r}{1 + r}\)

So, we have:

\(FV = \frac{3200 \times ((1 + 8\%)^{46 - 1}) \div 8\%}{1 + 8\%}\)

\(FV = \frac{3200 \times ((1 + 0.08)^{45}) \div 0.08}{1 + 0.08}\)

\(FV = \frac{3200 \times (1.08)^{45} \div 0.08}{1.08}\)

\(FV = 1182238.87\)

For Ed, we have, the following parameters

\(n=41\) --- time

\(r = 8\%\) --- rate

\(FV = 1182238.87\) ---- Ed's future value is the same as Steve's

So, we have:

\(FV = \frac{PMT \times ((1 + r)^{n - 1}) \div r}{1 + r}\)

\(1182238.87 = \frac{PMT \times ((1 + 0.08)^{41 - 1}) \div 0.08}{1 + 0.08}\)

\(1182238.87 = \frac{PMT \times ((1 + 0.08)^{41 - 1}) \div 0.08}{1.08}\)

Multiply by 1.08 x 0.08

\(0.08 \times 1.08 \times 1182238.87 = PMT \times ((1 + 0.08)^{41 - 1})\)

\(102145.44 = PMT \times ((1.08)^{40})\)

Make PMT the subject

\(PMT = \frac{102145.44}{(1.08)^{40}}\)

\(PMT = 4701\) --- approximated

Hence, Ed's monthly payment to meet up with Steve's is $4701.

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If \(f,g\) are inverses of one another, then

\(f\circ g(x) = g\circ f(x) = x\)

Given \(f(x)=x^2-1\) and \(g(x)=\sqrt{x-8}\), then

\(f\circ g (x) = f(g(x)) = f(\sqrt{x-8}) = \left(\sqrt{x-8}\right)^2 - 1 = \boxed{x - 9} \neq x\)

so right away we know \(f\) and \(g\) are not inverses.

In the other direction, we come to the same conclusion.

\(g\circ f(x) = g(f(x)) = g(x^2 - 1) = \sqrt{(x^2-1)-9} = \boxed{\sqrt{x^2 - 9}} \neq x\)

Answer:2,160ft

Step-by-step explanation: Volume=length * width * height

30x8x9=2160

Answer:

\({ \tt{ \delta x = \frac{x _{2} - x _{1} }{2} }} \\ \)

substitute for the values of x :

\({ \tt{ \delta x = \frac{0 - ( - 2)}{2} = \frac{2}{2} }} \\ \\ { \underline{ \tt{ \: \: \delta x = 1 \: \: }}}\)

The probability she pulls out a purple piece of candy would be 0.22.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is Sam's fathers collection.

We can write the equations for upstream and downstream as -

x - y = 7/2

x + y = 21/10

Solving the equations graphically -

{x} = 2.8

{y} = 0.7
In still water, the speed would be -

S = 3 - 0.7

S = 2.3 Km/h

Distance peddled upstream -

D = 2.8 x 3.5 = 9.8 Km

Therefore, the speed in still water would be 2.3 Km/h and the distance peddled upstream would be 9.8 Km.

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The value of the variable x = 21/32

Algebraic expressions are simply described as expressions that are composed of variables, coefficients, terms, constants and factors.

These expressions are also made up of certain arithmetic or mathematical operations.

These operations includes;

From the information given, we have that;

3/8=4/7x

cross multiply the values, we have;

7x(3) = 8(4)

multiply the values and expand the brackets, we get the values;

21x = 32

Divide both sides by the coefficient of the variable x, we get;

x = 32/21

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Step-by-step explanation:

The student incorrectly performed a rotation of 90° clockwise.

Answer:

C, the student incorrectly preformed a rotation of 90 degrees clockwise.

Step-by-step explanation:

The total principal and interest payment that Nelson will have to pay after 2 months is $4665.50.

To calculate the total principal and interest payment, we need to determine the interest amount and add it to the principal.

First, let's find the interest amount:

Interest = Principal x Interest Rate x Time

Given:

Principal = $4650

Interest Rate = 2% per year

Time = 2 months

Since the interest rate is given on an annual basis, we need to convert the time from months to years. There are 12 months in a year, so 2 months is equivalent to 2/12 = 1/6 years.

Interest = $4650 x 0.02 x (1/6) = $15.50

Now, we can calculate the total principal and interest payment:

Total Payment = Principal + Interest

Total Payment = $4650 + $15.50 = $4665.50

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Answer:

60 feet?

Step-by-step explanation:

Answer:

To find the number of miles Jodi's car traveled per gallon of gas, we need to divide the distance traveled by the amount of gas used:

miles per gallon = distance traveled / amount of gas used

distance traveled = 456 miles

amount of gas used = 12 gallons

miles per gallon = 456 miles / 12 gallons

miles per gallon = 38 miles/gallon

Therefore, Jodi's car traveled 38 miles per gallon of gas.

Answer:

38 miles

Step-by-step explanation:

Set up your division: 456 / 12

456 divided by 12 is 38

So, Jodi's car travels at 38 miles per gallon of gas.

Answer:

100KM PER HOUR

Step-by-step explanation:

Have a nice day

Answer:

He traveled at a speed of 1.6 miles per minute

Step-by-step explanation:

75/45=1.6

Answer:

Hey there!

The product of these two fractions would equal 15.

Hope this helps :)

Answer:

Hi! The answer to your question is 7 11/14 or rounded will be 15

Step-by-step explanation:

So first let’s take the whole numbers which is 4 and 3 if we add them up we will get 7.

Now we do LCD (least common denominator)

4/14+7/14=11/14

So the answer is 7 11/14 or 15

(In mixed number the answer is 7 11/14 and in whole the answer is 15)

Hope this helps! :)

The coordinates of the final point after the reflections across the x-axis twice is (6, -4)

Reflecting a point across the x-axis means that we keep the x-coordinate the same, but change the sign of the y-coordinate.

So reflecting (6,-4) across the x-axis gives us the point (6,4).

Reflecting this result again across the x-axis means that we keep the x-coordinate the same, but change the sign of the y-coordinate again.

So reflecting (6,4) across the x-axis gives us the point (6,-4).

Therefore, the final point after both reflections is (6, -4).

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Answer:

9.60 dollars tip is $1.60

Step-by-step explanation:

Answer:

y=9/2x-5

Step-by-step explanation:

I used desmos and messed around, but I guarantee that this is correct

There is a 2.28% chance that more than 250 books were borrowed in a week.

Probability can also be calculated using other methods, such as counting techniques and probability distributions. Probability distributions provide a way to model the behavior of random events and describe the likelihood of different outcomes occurring.

Probability has many applications in fields such as statistics, finance, engineering, and science. It is used to make predictions, analyze data, and make decisions based on uncertain information. Understanding probability is an important skill for many professions, as it allows individuals to make informed decisions and assess risk.

To solve this problem, we need to use the standard normal distribution and calculate the z-score.

First, we find the z-score:

z = (x - μ) / σ

z = (250 - 190) / 30

z = 2

We can then use a standard normal distribution table or calculator to find the probability of getting a z-score of 2 or higher.

Using a standard normal distribution table, we find that the probability of getting a z-score of 2 or higher is approximately 0.0228.

To convert this to a percentage, we multiply by 100:

0.0228 x 100 = 2.28%

Therefore, there is a 2.28% chance that more than 250 books were borrowed in a week.

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The complete question is:

The number of books borrowed from a library each week follows a normal distribution. When a sample is taken for several weeks, the mean is found to be 190 and the standard deviation is 30. There is a % chance that more than 250 books were borrowed in a week.

The price of a used compact disk is $9.99.

Well, this is a system of 2 equations and 2 unknowns.

Let n = the price of new compact disks and let

u = the price of used compact disks.

Then the first equation would be 6n + 2u = 127.92.

The second equation would be

3n+8u = 133.89.

So our system is,

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

6n + 2u = 127.92

3n+8u = 133.89

Since I don't like working with decimals I would multiply both equations by 100 that way it would get rid of the decimal.

Doing so results in the following system

600n+200u = 12792

300n+800u = 13389

Now we want to know how much one used disk sells for.

To do that we multiply the bottom equation by -2 and add it to the top equation.

-2(300n+800u = 13389)

=> -300n-1600u = -26778

Now we add that to the top equation

600n+200u = 12792

+(-300n-1600u = -26778)

----------------------------

-1400u = -13987

Now we solve for u by dividing both sides by -1400 and we see that

u = 9.99.

So the price of a used compact disk is $9.99.

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Answer:from top to bottom it’s

-4,-x^2,x^2,4

Step-by-step explanation:

Hope this helps :)

Julia needs to buy 42 packets of patties to make 500 hamburgers for the school function

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

Hamburger patties are sold in packets of 12. Let x represent the number of packet of patties to be bought to make 500 hamburgers. Hence:

12x = 500

x = 500/12

x = 41.67

x≅ 42

Julia needs to buy 42 packets

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Jerrica would have to win 40 additional games in a row to have an 80% winning record. This would bring her total wins to 20 + 40 = 60, and her total games played to 35 + 40 = 75.

To determine how many games Jerrica would have to win in a row in order to have an 80% winning record, we need to calculate the number of games she needs to win out of a certain total.

Let's denote the number of games she needs to win in a row as x. If she wins x additional games, her total wins would be 20 + x, and her total games played would be 35 + x.

To have an 80% winning record, she would need to win 80% of the total games played. Mathematically, this can be expressed as:

(20 + x) / (35 + x) = 80 / 100

Cross-multiplying, we get:

100(20 + x) = 80(35 + x)

Expanding and simplifying:

2000 + 100x = 2800 + 80x

Subtracting 80x from both sides:

20x = 800

Dividing by 20:

x = 40

Jerrica would have to win 40 additional games in a row to have an 80% winning record. This would bring her total wins to 20 + 40 = 60, and her total games played to 35 + 40 = 75.

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The rectangular garden has an area of 33 ft².

The length of the garden (l) is 4ft less than 7 times the width. If "w" represents the width, then the length of the garden can be expressed as follows:

The area of the garden is equal to the product between the length and the width:

Substitute A=33 and l=7w-4 in the formula:

Distribute the multiplication on the parentheses term:

Zero the equation by subtracting 33 to both sides of the equal sign:

Now that we have determined a quadratic expression for the area of the rectangular garden, we can determine the possible values of the width using the quadratic equation.

In this case, the independent variable is "w" which corresponds to the variable "x" in the quadratic formula:

Where

a is the coefficient of the quadratic term, in this case, a= 7.

b is the coefficient of the "x-term", in this case, b= -4.

c is the constant of the quadratic expression, in this case, c= -33.

Replace the values in the formula and solve:

-Addition

-Subtraction

Both values are correct, but lengths cannot be negative, then the width cannot be equal to -3/7ft.

The width of the rectangular garden is w=1 ft

Calculate the length:

The length of the rectangular garden is l=3ft

Projectile B begins its descent 1 seconds before Projectile A does.

In Mathematics and Geometry, the y-intercept of any graph or table such as a quadratic equation or function, generally occurs at the point where the value of "x" is equal to zero (x = 0).

By critically observing the table shown in the image attached above, we can reasonably infer and logically deduce the following y-intercept of Projectile A:

y-intercept = (0, 44).

Maximum height = (4, 300).

When t = 0, the y-intercept of Projectile B can be calculated as follows;

h(t) = -16t² + 96t

h(0) = -16(0)² + 96(0)

h(0) = 0.

For the maximum height, we have:

h(t) = -16t² + 96t

h'(t) = -32t + 96

32t = 96

t = 96/32

t = 3

Difference in time = 4 - 3

Difference in time = 1 seconds.

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Step-by-step explanation:

The answer is the second choice.  The outcome from rolling a fair die does not affect the outcome of drawing from a well-shuffled deck.  The probability of rolling a 5 will always be 1/6, and the probability of drawing an Ace will always be 4/52.

On the other hand, the weather of a city can depend on the weather from the previous day.