Create a linear system to model this situation:

Cheri operates a grass-cutting business. She

charges $20 for a small lawn and $30 for a large

lawn. One weekend, Cheri made $290 by cutting

12 lawns.

A. S + L = 290

20s + 30L = 12

B. S + L = 290

30s + 20L = 12

C. S + L = 12

20s + 30L = 290

D. S + L = 12

30s + 20L = 290

The product of \((-3+5i)(3+i)\) is \(-14 + 12i\) in standard form, where the real part is \(-14\) and the imaginary part is \(12\).

Finding the product of \((-3+5i)(3+i)\) and writing the result in standard form.

To begin, we use the distributive property to expand the expression:

\((-3+5i)(3+i) = -3 \cdot 3 + (-3) \cdot i + 5i \cdot 3 + 5i \cdot i\)

Simplifying the multiplication:

\((-3+5i)(3+i) = -9 - 3i + 15i - 5\)

Next, we combine like terms:

\((-3+5i)(3+i) = -14 + 12i\)

Therefore, the product of \((-3+5i)(3+i)\) is \(-14 + 12i\) in standard form. The standard form of a complex number is written as \(a + bi\), where \(a\) and \(b\) are real numbers. In this case, the real part is \(-14\) and the imaginary part is \(12\).

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The probability that an incoming call is for firefighting equipment (or any other reason besides medical assistance) is 0.33 or 33%.

The statement "the probability that an incoming call is for medical assistance is 0.67" can be expressed as:

P(Medical Assistance) = 0.67

This means that out of all incoming calls to the fire station, the probability that the call is for medical assistance is 0.67 or 67%. The complement of this event, which is the probability that an incoming call is NOT for medical assistance, is:

P(Not Medical Assistance) = 1 - P(Medical Assistance) = 1 - 0.67 = 0.33

In science, the probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability

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The values of a and b that make f(x) continuous everywhere are a = 2x and b = 2a - 3/2 = 2(2x) - 3/2 = 4x - 3/2.

The limit is a concept in mathematics that describes the behavior of a function near a particular value, called the limit point. The limit of a function gives the value that the function approaches as the input (variable) approaches the limit point.

For f(x) to be continuous everywhere, the function must have the same value and the same limit as x approaches 2 from the left and the right. In other words, f(2-) = f(2+) and the limit of f(x) as x approaches 2 from the left and the right must be equal.

Let's start by finding f(2-), which is the value of f(x) as x approaches 2 from the left. In this case, f(x) = (x2 - 4)/(x - 2) for x < 2, so as x approaches 2 from the left, f(x) approaches (2^2 - 4)/(2 - 2) = 0.

Next, let's find f(2+), which is the value of f(x) as x approaches 2 from the right. In this case, f(x) = ax^2 - bx + 3 for 2 <= x < 3, so as x approaches 2 from the right, f(x) approaches a(2^2) - b(2) + 3 = 4a - 2b + 3.

Since f(x) must be continuous at x = 2, we need to have f(2-) = f(2+), so we can set f(2-) = f(2+) and solve for a and b:

0 = 4a - 2b + 3

2b = 4a - 3

b = 2a - 3/2

Now that we have an expression for b in terms of a, we can substitute b = 2a - 3/2 into the expression for f(x) for x >= 3 to find the value of a that makes f(x) continuous everywhere:

f(x) = 2x - a + b for x >= 3

f(x) = 2x - a + (2a - 3/2) for x >= 3

f(x) = 2x + 3/2 - a for x >= 3

Since f(x) must be continuous at x = 2, we need to have f(2+) = f(2+), so we can set f(2+) = f(2+) and solve for a:

4a - 2b + 3 = 2x + 3/2 - a for x >= 3

4a - 2(2a - 3/2) + 3 = 2x + 3/2 - a

4a - 4a + 3 + 3/2 = 2x + 3/2 - a

3/2 = 2x + 3/2 - a

a = 2x

So, the values of a and b that make f(x) continuous everywhere are a = 2x and b = 2a - 3/2 = 2(2x) - 3/2 = 4x - 3/2.

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Answer:

Number of terms = 3

Degree = 6

Step-by-step explanation:

A polynomial is a mathematical expression that gives the detailed combination of variables with their coefficients, their positive exponential, and other variables using the operations of subtraction, addition, and multiplication

The number of terms in a polynomial is the number of different powers of added or subtracted in the expression

Therefore, the number of terms in the expression -3·s⁶ + 2·s⁴ + 3·s³ is 3 terms

Number of terms = 3

The degree of a polynomial is given by the highest power of the variables in the polynomial. Therefore, the degree of the given polynomial is 6

Degree = 6

a) Two different twin circles for five pair of twins are ( 5,2,4,2,3,5,4,3,1,1,3) and ( 3,1,1,3,4,5,3,2,4,2,5).

b) No twin circles in 3 pair of twins because any of arrangement of them cannot fulfil the condition of twin circle.

c) The partial twin circle ( third circle) present in above figure can't be completed because 4 positions are fixed there and after that number of persons more than seats.

We have a pair twins are numbered 1, 1, 2, 2, 3, 3, and so on. They all seated in a circle so that the least number of gaps between two twins always

equals their assigned number. This is called a twin circle. That is Number of persons between 1 and 1 twins = 0

Number of persons between 2 and 2 twins = 1,

so on.. Reflections (flips) and rotations (turns) of a twin circle are regarded as the same.

a) We have to make two twin circles for five pair twins. The arrangement of pair twins in two different ways with the satisfaction of conditions. So, first arrangement is ( 5,2,4,2,3,5,4,3,1,1,3) and

other arrangement is ( 3,1,1,3,4,5,3,2,4,2,5).

b) There is no twin circle between the arrangement of 3 twin pairs. Because in case of 3 twin pair total members = 3×2 = 6 and number of members can be seat between pairs are 3( 1+2+0). As we know, it is fixed that no person between (1,1). So, we cannot be arrange the 2 pairs with desirable 3 gaps that is 1 person between (2,2) and 2 persons between (3,3).

c) There is total 12 positions to seat in circles. The position of 6 and 1 is fixed. According to above scenario, position next to 1 is for 1 (clockwise) and 5th position from given 1 position in (clockwise) is other member of twin 6. Now, four positions are fixed. Eight positions are left and 4 twin pairs (2,2) , (3,3), (4,4),(5,5). Number of persons seat between 4 pairs are 10 in counts ( greater than position ) so, no such arrangement is possible. Hence, this partial circle can't be completed.

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Complete question:

The above figure complete question.

Pairs of twins are numbered 1, 1, 2, 2, 3, 3, and so on. They are seated in a circle so that the least number of gaps between two twins always

equals their assigned number. This is called a twin circle. Note that this means there is no person between the twins numbered 1 and 1, there is just one person between the twins numbered 2 and 2, and so on. Reflections (flips) and rotations (turns) of a twin circle are regarded as the same. For example, the following are the same twin circles for 4 pairs of twin.

a) Find two twin circles for five pairs of twin

b) Explain why no twin circles in 3 pairs of twin

c) explain why this partial twin circle can't be completed ? ( third circle)

i) The multiplication of (3.1x\(10^0\)) and (1.5x10) results in 4.65x\(10^1\).

j) The division of (3.1x10) by (1.5x\(10^{-1\)) equals 2.07x\(10^1\).

i) To multiply numbers in scientific notation, we multiply the coefficients (3.1 and 1.5) and add the exponents (0 and 1) together. In this case, 3.1 multiplied by 1.5 gives us 4.65. Adding the exponents, \(10^0\) multiplied by \(10^1\) results in \(10^1\). Therefore, the final result is 4.65x\(10^1\).

j) When dividing numbers in scientific notation, we divide the coefficients (3.1 and 1.5) and subtract the exponents (1 and -1) from each other. Dividing 3.1 by 1.5 gives us approximately 2.07. Subtracting the exponents, \(10^1\)divided by \(10^{-1\) is equivalent to \(10^{(1-(-1))}\) which simplifies to 10^2. Hence, the result is 2.07x\(10^1\).

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All the reasonable measurement for each object can be define as given table below.

Measurements refer to the process of determining the magnitude, quantity, or degree of something using standardized units or instruments. It involves observing and recording data about an object, event, or phenomenon, and then comparing it to a reference standard to obtain a numerical value. They allow us to quantify and compare physical properties accurately and provide a universal language for expressing quantities.

                Objects                                           Measurements

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answer is in the image below:

Answer:

Discretionary expenses are Optional and Can be reduced to help save money. For example, a Magazine Subscription is a discretionary expense.

Step-by-step explanation:

Fits the definition of a discretionary expense and the example matches too because it is Optional.

To determine whether the series converges or diverges, we can use the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms of a series is less than 1, then the series converges. If the limit is greater than 1 or approaches infinity, then the series diverges.

Using the ratio test, we have:
|6^(n+1)/(5^(n+1)-1)| / |6^n/(5^n-1)| = |6/(5-1/5^n)|
As n approaches infinity, the denominator 1/5^n approaches 0, and the absolute value of the ratio approaches infinity. Therefore, the series diverges.
we can further explain that the terms in the series 6^n/(5^n-1) grow faster than those in a geometric series with a common ratio of 5/6, which is convergent since the ratio is less than 1. As n increases, the denominator of each term in the given series becomes very close to 5^n, while the numerator remains constant. This makes the fraction approach infinity, and so the series diverges.

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Answer:

Letter A.

Step-by-step explanation:

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

The solutions to the quadratic equation are:

x = (-9 + 3√(5)) / 2 or x = (-9 - 3√(5)) / 2

Option A is the correct answer.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

Quadratic equation x² + 9x + 9 = 0.

a = 1, b = 9 and c = 9

We can use the quadratic formula.

x = (-b ± √(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

Now,

Plugging in the given values.

x = (-9 ± √(9^2 - 4(1)(9))) / 2(1)

Simplifying.

x = (-9 ± √(81 - 36)) / 2

x = (-9 ± √(45)) / 2

x = (-9 ± 3√(5)) / 2

Therefore,

The solutions to the quadratic equation x^2 + 9x + 9 = 0 are:

x = (-9 + 3√(5)) / 2 or x = (-9 - 3√(5)) / 2

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Answer: A. addition property of equality.

Step-by-step explanation:

Molly added 3d to both sides of the equation.

Answer:

325.58

Step-by-step explanation:

so im not good at explaining but JUST their DINNER costed $262.57. so you also have to ADD TAX because everything has tax so to find the 4% sale tax you need to set up the equation 262.57 x .04 (which is 4%). you will get 10.50 if you round. now you need to ADD TIP which is 20%. so to find that you need to do 262.57 x .20 (which is 20%). you will get 52.51. so now take BOTH 52.51 and 10.50 and ADD them. when you get this you also add it to the 262.57 and it gets you to 325.58

There were 425 guests at a hotel. 170 guests ordered food. 40 percentage of the guests ordered food.

A percentage is a fraction of a whole in mathematics, which is denoted by the symbol per 100. A single unit out of a hundred, or one hundredth of something, is represented as a single percent, such as 1%. The Latin phrase per centum, which means by the hundred, is where the word percent originates. Percentage does really refer to a hundredth or 1/100 of something.

Given,

Total number of guests = 425

Guest who ordered food = 170

For percentage,

Value/ Total × 100%

170/425 × 100%

0.4 × 100%

40%

There were 425 guests at a hotel. 170 guests ordered food. 40 percentage of the guests ordered food.

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The y-intercept for function f(x) has the same value as the x-intercept of f-inverse.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

As

we can see from figure that y-intercept for f(x)=3

and x-intercept for f inverse = 3

Hence,

         The y-intercept for function f(x) has the same value as the x-intercept of f-inverse

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Answer:

x-intercept

domain of f

Step-by-step explanation:

i just did it

The probability the next customer pays using a debit card based on the last three weeks is 30% or 0.3.

This is the chance or likelood for an event to occur. For example, if in a city it has snowed every year on December 25th, there is a high probability it will snow this year and in the next years.

Total of a specific outcome/ total of outcomes

Based on this, let's calculate the probability the next customer pays using the debit card:

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We have that because the central angle is 90°, the sector represents 1/4 of a circle with a radius of 10 yd.

So, length of the safety rail is given by:

Where:

r = 10 yd

pi = 3.14

Substitute, we have:

The Answer is 15.7 yd

Next, area of the deck is given by:

Substitute the values:

The answer is 78.5 yd^2

Victor will pay $13,500 in interest over the 36-month term of his line of credit.

To calculate the interest that Victor will pay on his 36-month line of credit for $15,000 at an interest rate of 2.5%, we can use the formula for simple interest:

I = P × r × t

Where I is the interest, P is the principal (the amount borrowed), r is the interest rate per period, and t is the number of periods.

Here, P = $15,000, r = 0.025 (since the interest rate is 2.5%), and t = 36 months.

I = P × r × t

Substituting values into the formula, we get:

I = 15,000 × 0.025 × 36

I = $13,500

Therefore, he will pay $13,500 in interest over the 36-month term of his line of credit.

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Answer:

26-x

Step-by-step explanation:

we don't know how many has moved out so we use x to represent that. Obviously for example if he had 5 leave his class we would do 26-5.

Answer:

Probability ≈ 0.0714

Step-by-step explanation:

Consider permutation and combination;

\(Total Combinations - 8C4,\\8C4 = 8! / 4! * ( 8 - 4 )!,\\8 * 7 * 6 * 5 / 4!,\\\\Total Combinations = 70,\\\\Combinations of Dance Classes - 5C4,\\5C4 = 5! / 4! * ( 5 - 4 )!,\\5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1,\\\\Dance Classes = 5,\\\\Probability - 5 / 70 = 0.0714,\\Conclusion; Probability = ( About ) 0.0714\)

Answer:

Sen^2 x

Step-by-step explanation:

1-sen^2x.tan^2x

cos^2x.sen^2x/cos^2x

cos cancells cos

sen^2x

Answer:

46cm

Step-by-step explanation:

11 x 4 =44 +(.5 x 4)=46cm

The solution to the system of inequality expression is 1 < x < 10

Inequality expressions are expressions not separated by an equal sign

Given the inequality expressions

- 4x – 2 < -6 and - 4x – 2 > -42

For the inequality - 4x – 2 < -6

- 4x – 2 + 2 < -6 + 2

-4x < -4

x > 1

For the inequality  - 4x – 2 > -42

- 4x – 2 + 2> -42 +2

-4x > -40

x < 10

Combining both inequality solutions:

1 < x < 10

Hence the solution to the system of inequality expression is 1 < x < 10

Representing on the number line we have:

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The general solution of the pair of equations:

- 4x – 2 < -6 and - 4x – 2 > -42 is; 1 < x > 10

By solving the first inequality;

By dividing both sides by -4, we have;

x > 1

Subsequently, by solving the second inequality;

By dividing both sides by -4, we have;

x < 10

Therefore, the inequality that satisfies both equations is;

1 < x > 10

The image attached contains the solution on the number line.

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Answer:

a

Step-by-step explanation:

Answer:

Hard

Step-by-step explanation:

I don't know sorry

Answer:

8x20+22

160+22

182.

48x4= 192 (closest to 182) since you can’t have a remainder of kids.

(I’m in 6th grade so I hope I helped and didn’t get it wrong)

So the answer is 4 or 5 busses.

The percent that the new frame is bigger than the original frame if the width of the frame remains the same is 9.1%.

From the information, the painting, square in shape, is placed in a wooden frame with width of 10% of the length of the side of the paining. The painting was enlarged by 10%.

Let the length be Illustrated as 10cm.

Width = 10% × 10cm

= 1cm

New Length = 10cm + (10% × 10cm)

= 11cm

The old perimeter will be:

= 2(1 + 10)

= 22cm

New perimeter will be:

= 2(1 + 11)

= 24cm

The percentage increase will be:

= (24 - 22) / 22 × 100

= 2/22 × 100

= 9.1%

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There are 9438 different committees possible without Tarzan and Jane together.

a) To find the total number of possible committees, we need to choose 7 people out of 16 people, regardless of their gender. We can do this using the combination formula:

\(${{16}\choose{7}} = \frac{16!}{7!(16-7)!} = 11440$\)

Therefore, there are 11440 different 7-person committees possible.

b) If the committee must be made up of women only, we need to choose 7 women out of the 10 women available. We can do this using the combination formula again:

\(${{10}\choose{7}} = \frac{10!}{7!(10-7)!} = 120$\)

Therefore, there are 120 different 7-woman committees possible.

c) If the committee must be made up of 5 men and 2 women, we need to choose 5 men out of 6 men available, and 2 women out of 10 women available. We can do this using the combination formula:

\(${{6}\choose{5}} \times {{10}\choose{2}} = \frac{6!}{5!(6-5)!} \times \frac{10!}{2!(10-2)!} = 6 \times 45 \times 9 = 2430$\)

Therefore, there are 2430 different committees possible with 5 men and 2 women.

d)

i) If Tarzan and Jane must be together on the committee, we can treat them as a single entity and then choose 6 more people out of the remaining 14 people. We can do this using the combination formula:

\(${{14}\choose{6}} = \frac{14!}{6!(14-6)!} = 3003$\)

Therefore, there are 3003 different committees possible with Tarzan and Jane together.

ii) If Tarzan and Jane refuse to serve on the committee, we need to choose 7 people out of the remaining 14 people. We can do this using the combination formula:

\(${{14}\choose{7}} = \frac{14!}{7!(14-7)!} = 3432$\)

Therefore, there are 3432 different committees possible without Tarzan and Jane.

iii) If Tarzan and Jane are not on the committee together, we can count the number of committees that include both of them and subtract it from the total number of committees. The number of committees that include both Tarzan and Jane can be found by treating them as a single entity and choosing 5 more people out of the remaining 14 people. We can do this using the combination formula:

\(${{14}\choose{5}} = \frac{14!}{5!(14-5)!} = 2002$\)

Therefore, the number of committees that do not include both Tarzan and Jane is:

\($11440 - 2002 = 9438$\)

Therefore, there are 9438 different committees possible without Tarzan and Jane together.

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If A(3,-4) and B(13,11), the coordinates of the point 3/5 from A to B is, (9, 5).

The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

Section formula for a point which divides line joining points into m:n ratio,

(X,Y) = { (mx₂+nx₁)/m+n , (my₂+ny₁)/m+n }

Given that, two points,

A(3, -4) and B(13, 11),

the coordinates of the point 3/5 from A to B

Difference, in x coordinates

13 - 3 = 10

It is 3/5 from A to B

So,    x coordinate is,3 + 10 × 3/5 = 9

Difference, in y coordinates

11 -(-4) = 15

It is 3/5 from A to B

So,    y coordinate is, -4 + 15 × 3/5 = 5

Hence, the point is (9, 5)

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Answer:

A, 6:00 P.M. EST

Step-by-step explanation:

The time difference between EST and PST is -3 hours

11 am - 9am = 2 hours

2 - (-3) = 2+3 = 5 hours

The flight time is 5 hours

Then:

The time difference between PST and EST is +3 hours

5 + 3 = 8

If the fly leaves Los Angeles at 10:00 AM PST

10 + 8 = 18

The plane will arrive at 6:00PM EST

Answer:

If a = b and b = c, then a = c

Step-by-step explanation:

The transitive property of equality tells us that if we have two things that are equal to each other and the second thing is equal to a third thing, then the first thing is also equal to the third thing.

Answer:

If a = b and b = c, then a = c

Step-by-step explanation:

i got it right on a test