Steve needs 250 note cards to pass out at a workshop. The cards come 100 to a pack. How many packs should he buy?

Therefore, the interest portion of the seventh payment is:7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7 - 7,000.

We have the following payments and their corresponding times of payment:At the end of year 1: $1,000At the end of year 2: $2,000At the end of year 3: $3,000At the end of year 4: $4,000At the end of year 5: $5,000At the end of year 6: $6,000At the end of year 7: $7,000

At the end of year 8: $8,000At the end of year 9: $9,000At the end of year 10: $10,000The present value of these payments is:PMT x [(1 - (1 + r)-n) / r]where PMT is the payment, r is the interest rate per year, and n is the number of years till payment.

For the first payment (end of year 1), the present value is:1,000 x [(1 - (1 + r)-1) / r]which equals

1,000 x (1 - 1 / (1 + r)) / r = 1,000 x ((1 + r - 1) / r) = 1,000

For the second payment (end of year 2), the present value is:2,000 x [(1 - (1 + r)-2) / r]which equals 2,000 x (1 - 1 / (1 + r)2) / r = 2,000 x ((1 + r - 1 / (1 + r)2) / r) = 2,000 x (1 + r) / r2

For the seventh payment (end of year 7), the present value is:

7,000 x [(1 - (1 + r)-7) / r]

which equals

7,000 x (1 - 1 / (1 + r)7) / r = 7,000 x ((1 + r - 1 / (1 + r)7) / r) = 7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7

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Given the information on the picture, we can use the trigonometric function cosine on angle Q to find the length of the missing side y:

then, solving for y, we get:

therefore, y = 65.6

Answer:(2,-3)

Step-by-step explanation:

The total cupcakes the bakery sell that day is 80

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

Number of sales = 76

Proportion = 95%

This implies that

Number of sales = Proportion * Total number of cupcakes

Substitute the known values in the above equation, so, we have the following representation

76 = 95% * Total number of cupcakes

Divide both sides by 95%

Total number of cupcakes = 80

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Answer:

Step-by-step explanation:

Solve the System of Equations

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(−1,7)

Equation Form:

x=−1,y=7

-5⁵/(-5)⁶ = -5⁵×(-5)-⁶ =-5^(5-6) = -5^-1 = -1/5

The book has a lower cost per minute than the movie.

To find the cost per minute of the book, we divide the cost by the number of minutes:

cost per minute of book = $15 / 200 minutes = $0.075 per minute

To find the cost per minute of the movie, we need to convert the time to minutes.

2 hours and 39 minutes is equal to:

2 hours x 60 minutes/hour = 120 minutes

39 minutes = 39 minutes

Total minutes = 120 + 39 = 159 minutes

cost per minute of movie = $14 / 159 minutes = $0.088 per minute

Therefore, the book has a lower cost per minute than the movie.

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Answer:

I belive the answer is 1380.

Answer/Step-by-step explanation:

1. Sin A = opp/hyp

Opp = 3

Hyp = 5

\( sin(A) = \frac{3}{5} \) (substitution)

\( sin(A) = 0.6 \)

2. Sin B = opp/hyp

Opp = 4

Hyp = 5

\( sin(B) = \frac{4}{5} \) (substitution)

\( sin(B) = 0.8 \)

3. Cos Q = adjacent/hypotenuse

Adjacent = 12

Hypotenuse = 13

\( cos(Q) = \frac{12}{13} \) (substitution)

\( cos(Q) = 0.9231 \) (4 decimal places)

4. Cos S = adjacent/hypotenuse

Adjacent = 5

Hypotenuse = 13

\( cos(S) = \frac{5}{13} \) (substitution)

\( cos(S) = 0.3846 \) (4 decimal places)

To prove this statement, we will use the following definitions and properties:

A finite dimensional vector space is a vector space that has a finite number of basis vectors.

A basis for a vector space is a set of vectors that span the space, meaning that any vector in the space can be written as a linear combination of the basis vectors.

A linear combination of a set of vectors is an expression of the form a_1v_1 + a_2v_2 + ... + a_nv_n, where v_1, v_2, ..., v_n are the basis vectors and a_1, a_2, ..., a_n are scalars from the field.

A non-zero element of a finite dimensional vector space is a vector that is not equal to the zero vector, the additive identity of the space.

Now, let's assume that V is a finite dimensional vector space over a field F, and let B be a basis for V. We will show that every non-zero element of V can be expressed as a unique linear combination of the basis vectors in B.

Let v be a non-zero element of V. Since B spans V, there exists a set of scalars a_1, a_2, ..., a_n from the field F such that v = a_1v_1 + a_2v_2 + ... + a_nv_n, where v_1, v_2, ..., v_n are the basis vectors in B. This is a valid linear combination representation of v with respect to B.

To show that this linear combination representation of v is unique, let's assume that there exists another set of scalars b_1, b_2, ..., b_n from the field F such that v = b_1v_1 + b_2v_2 + ... + b_nv_n. Then, subtracting the second equation from the first one, we get:

0 = (a_1 - b_1)v_1 + (a_2 - b_2)v_2 + ... + (a_n - b_n)v_n.

Since B is a basis for V, the only way for the left-hand side of the equation to be the zero vector is for all the scalars in the linear combination to be equal, i.e. a_1 = b_1, a_2 = b_2, ..., a_n = b_n. Thus, v can be expressed as a unique linear combination of the basis vectors in B, which completes the proof.

Answer:

x = .5, - 1.5

Step-by-step explanation:

4x^2 + 4x =3

To solve for x, we can complete the square.

4 ( x^2 + x) = 3

x^2 + x = 3/4

Take the coefficient of x, divide by 2, and square.

(1/2)^2

Then add to each side.

x^2 + x + 1/4= 3/4 +1/4

(x+1/2) ^2 = 1

Take the square root of each side.

x+1/2 = ±1

x = ±1 -1/2

x = 1-1/2  or -1-1/2

x = 1/2, -3/2

x = .5, - 1.5

Answer:

x = 1/2   or   -3/2

Step-by-step explanation:

Rewrite in Standard Form:

4x²+4x=3 ==>  4x²+4x-3=0

Identify:  a=4   b=4   c= -3

Quadratic Formula:

\(x=\frac{-b+\sqrt{b^2-4ac}}{2a} or \frac{-b-\sqrt{b^2-4ac}}{2a}\\ \\=\frac{-4+\sqrt{4^2-4(4)(-3)}}{2(4)} or \frac{-4-\sqrt{4^2-4(4)(-3)}}{2(4)}\\\\=\frac{-4+\sqrt{16+48}}{8} or \frac{-4-\sqrt{16+48}}{8}\\\\=\frac{-4+\sqrt{64}}{8} or \frac{-4-\sqrt{64}}{8}\\\\=\frac{-4+8}{8} or \frac{-4-8}{8}\\\\=\frac{4}{8} or \frac{-12}{8}\\\\=\frac{1}{2} or -\frac{3}{2}\)

Using the concept of correlation, it is found that a strong positive correlation is expected between these two variables.

In this problem, the older the car, the more it should have traveled, that is, the higher the read on the odometer, hence, there is a direct proportional relationship, which means that the variables have a strong positive correlation.

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Answer:

20 men

Step-by-step explanation:

1. 4:9 = 20:45

men to women

a. 45 divided by 9 = 5

b. 4 x 5 = 20

Answer:

.........................

Assume she sells 20 pairs of earrings in one day. Given this information, the total cost is $40.

Whole Revenue is the total sum that the producer makes from the sale of the good at market value. The result of price and quantity is total revenue.

Crafted earrings are being sold by Cathy. The earrings cost her $2 to make, but she can sell each pair for $15. Consider that she sells 20 sets of earrings in a single day.

Total Revenue = Price * quantity

= $15 * 20

= $300

Total cost = Per unit cost * quantity

= $2 * 20

= $40

Therefore, the total cost of earrings is $40.

Profit = Total Revenue - Total Cost

= 300 - 40

= $260

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A percent is a specific type of ratio that compares one value to the number 100.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

The percentage is the ratio that compares a number with the total value of 100.

Thus,

Percent compares one value to the number 100.

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Divide total feet by total inches

90 feet / 2 1/2 inches = 36 feet per inch

1 inch = 36 feet

Answer:

-10

Step-by-step explanation:

Let the number be x

x - 40 = 5x

⇒ -40 = 5x - x

⇒ 4x = -40

⇒ x = -40/4

⇒ x = -10

Answer:

-10

Step-by-step explanation:

Let the number be x

x - 40 = 5x

4x = -40

x = -10

Answer:

A polynomial function is a relationship that provides a value that is determined by a polynomial for each input value.

Explanation:

A polynomial is a mathematical expression constructed with constants and variables using the four operations:

Polynomial Example Degree

Constant 1 0

Linear 2x+1 1

Quadratic 3x2+2x+1 2

Cubic 4x3+3x2+2x+1 3

Quartic 5x4+4x3+3x2+2 x+1 4

In other words, we have been calculating with various polynomials all along. When two polynomials are divided it is called a rational expression.

In such cases you must be careful that the denominator does not equal zero. Division by zero is not defined and thus x may not have a value that allows the denominator to become zero. Otherwise, any other value may be substituted for x.

Example

x3−x6−x

x must not have the value of 6 since 6-6=0.

Answer:

length = 4ft

width= 2ft

Step-by-step explanation:

The length of a rectangular garden is twice the width, then

width = w

length = 2w

Area of Rectangle = length *width

8= w*2w

8= 2w^2

w^2= 4

w= 2ft.

length =2*2= 4 ft

Answer:

\(\boxed{{\bf 94}^{ \circ}}\)

Step-by-step explanation:

The Given two angles are supplementary angles.

Given angle :

\( \rightarrow86 {}^{ \circ}\)

Solution :

We know that,

Two angles are known as supplementary angles if their sum is 180.Each angle is a supplement of other.

Let the measure of supplement be y.

So,

\(\tt \implies{y} + 86{}^{ \circ} = 180\)

Now find the value of y of this equation, that would be the supplement.

\( \bf \: Step \: 1 : \rm \: Subtract \; 86{}^{ \circ}\; from \; both\; sides :-\)

\(\tt \implies{y} + 86{}^{ \circ} - 86{}^{ \circ} = 180{}^{ \circ} - 86{}^{ \circ}\)

\(\tt \implies{y} + 0{}^{ \circ} = 94{}^{ \circ}\)

\(\tt \implies{y} = 94{}^{ \circ}\)

Hence, 94° is the supplement of 86°.

\( \rule225pt{2pt}\)

I hope this helps!

Let me know if you have any questions.

The value of the second angle is equal to 94°

Data;

Supplementary angles are those angles  that have their sum angles equal to 180 degrees.

Let the unknown angle be represented by x

\(x+86 = 180\\x = 180 - 86\\x = 94\)

The value of the second angle is equal to 94°

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Part A:

This data appears to be modeling a geometric sequence because the time to complete each station is increasing by a constant factor. For example, the time to complete station 2 is 4 minutes, which is double the time it took to complete station 1. Similarly, the time to complete station 3 is 8 minutes, which is double the time it took to complete station 2, and so on.

Part B:

To find the time Aurora will take to complete station 5 using a recursive formula, we can use the formula:

a_n = a_1 * r^(n-1)

where a_n is the time it takes to complete station n, a_1 is the time it takes to complete station 1, and r is the common ratio (the factor by which the time increases from one station to the next).

We are given that a_1 = 2 and a_2 = 4, so we can solve for r:

r = a_2 / a_1

= 4 / 2

= 2

Then we can use this value of r to find the time it takes to complete station 5:

a_5 = a_1 * r^(5-1)

= 2 * 2^4

= 2 * 16

= 32

Therefore, Aurora will take 32 minutes to complete station 5.

Part C:

To find the time Aurora will take to complete station 9 using an explicit formula, we can use the formula:

a_n = a_1 * r^(n-1)

where a_n is the time it takes to complete station n, a_1 is the time it takes to complete station 1, and r is the common ratio (the factor by which the time increases from one station to the next).

We are given that a_1 = 2 and a_2 = 4, so we can solve for r:

r = a_2 / a_1

= 4 / 2

= 2

Then we can use this value of r to find the time it takes to complete station 9:

a_9 = a_1 * r^(9-1)

= 2 * 2^8

= 2 * 256

= 512

Therefore, Aurora will take 512 minutes to complete station 9.

say no more

Answer:

$522

Step-by-step explanation:

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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Answer:

3/8÷2/5=3/8×5/2=15/16

Step-by-step explanation:

When dividing by fractions, invert and multiply.

3/8÷2/5=3/8×5/2=15/16

Answer: 9

Step-by-step explanation: To divide we need to flip the second fraction we are dividing by. For example:

10/1 divided by 1/4 = 10/1 times 4/1. So in this case, the answer is 40.

Now lets try it with 1/9.

X divided by 1/9 = X times 9/1.

So dividing by 1/9 is equal to multiplying by 9.