Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.


Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper.

so the sample space will be simply all the cookies in the jar, namely 5 + 6 + 9 = 20.

the probability that Mark will NOT pick a Peanut Butter one hmm, that means that Mark will pick either a Chocolate Chip or an Oatmeal one, now this is an OR case so that means sum. so what are the chances Mark will pick either one?  P(Chocolate) + P(Oatmeal)

[tex]\stackrel{P(Chocolate)}{\cfrac{5 }{20}}~~ + ~~\stackrel{P(Oatmeal)}{\cfrac{9}{20}}\implies \cfrac{5+9}{20}\implies \cfrac{14}{20}\implies \cfrac{7}{10}\implies 0.7~\hfill \text{\LARGE 70\%}[/tex]

Answer:

Step-by-step explanation: 80

Answer: THE ANSWER IS 28%

worked it out on the calculator in the end

Step-by-step explanation:

No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing by one and two (separately). No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing the number into two separate parts and then dividing each part by 1 and 2 respectively.

No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing the number into two separate parts and then dividing each part by 1 and 2 respectively. For example, if we have the number 10, dividing by 1/2 would give us 5 (10/2), while dividing by 1 and 2 would give us 5 and 5 (10/1 = 10 and 10/2 = 5).

No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing by one and two (separately).

No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing the number into two separate parts and then dividing each part by 1 and 2 respectively.

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On solving the provided question, we can say that by unitary method 14 more hours must she work to earn an additional 154 dollars

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

jessie worked = 22 hours last week at the auto shop

shop and earned = 242 dollars

1 hour = 242/22

154 dollars = 22/242*154 = 0.0909090909 * 154 = 13.9999999986 = 14 hours

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Answer:

simple 5×-5 the answer divide by -5

The price of an adult ticket is $20

The price of a child's ticket is $19

Let x represent the price of a child ticket

Let y represent the price of an adult ticket

Three adults and four children must pay 136

3y + 4x= 136.........equation 1

Two adults and three children must pay $97

2y + 3x= 97.........equation 2

From equation13 1

3y+4x= 136

3y= 136-4x

y= 136-4x/3

Substitute 136-4x/3 for y in equation 2

2(136-4x) + 3x= 97

272-8x/3 + 3x/1= 97

272-8x+9x/3= 97

cross multiply

272-8x+9x=291

collect the like terms

-8x+9x= 291-272

x= 19

Substitute 19 for x in equation 1

3y+4x= 136

3y + 4(19)= 136

3y+ 76= 136

3y= 136-76

3y=60

y= 60/3

y= 20

Hence children tickets cost $19 and adult tickets cost $20

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The distance travelled is 1035 meters, The period T is 1.67m/s and The wavelength is 0.575 meters.

Because sound is a wave, we can use the proper definitions of the terms to derive the relationship between the wavelength, frequency, and speed of a wave. The wavelength is the distance travelled by the wave in one time period of its cycle, whereas the frequency is the number of cycles per second.

Formula used:

Speed = Distance/time

Frequency of wave = 1/Time period of the wave

Wavelength = Distance travelled by the wave in one time period

Given,

a)The distance travelled is 2d,

where d is the distance to the wall

Thus d = 345 × 6/2= 1035 m

b)The frequency is 600 Hz thus the period T = 1/f= 1.67ms

c)The wavelength λ = Velocity/Frequency

= 345/600

= 0.575 meters

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Option D)  The slope of the line that contains the points (2, -8) and (-4, 4) is -2

A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.

Slope is give by 2 points on a line is [tex]\frac{y\x_{2}- y\x_{1} }{x_{2}-x_{1}}[/tex]

so the slope is

[tex]\frac{4 - (-8)}{-4 - 2} = \frac{12}{-6} = -2[/tex]

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Answer:

Step-by-step explanation:

12. i) By walking the 20 kilometers in the charity walk, Vreni raised $250 at a unit rate of $12.50 per kilometer.

12. ii) The total money raised by all participants in the charity walk was $3,100, using proportions.

12. iii) The percentage increase on the previous year's total is 26.53%.

Part B:

11. i) Based on a ratio of 3:2 of road and footpath distance, the road distance covered 12 kilometers.

11. ii) Using the distance, time, and speed formula, Vreni took 7 hours and 12 minutes to walk the 20 kilometers.

11. iii) Vreni's average speed is 2.78 km/h.

11. iv) Vreni finished the charity walk at 16:07.

Part C: The scale of the map to the total distance covered by Vreni was 1: 4 or a scale factor of 25%.

The ratio is the quotient of a value compared to another.

Ratios are proportionate values, which are equated to each other.

The average speed and scale factor show the ratios of one value and the whole.

12) Charity Walk and Vreni:

The total distance walked = 20 kilometers

The unit rate of raising money per kilometer = $12.50

i) The total amount raised = $250 ($12.50 x 20)

Money raised in 12. 1 = 5/52 of the total money raised

ii) The total money raised in the charity walk = $3,100 ($250 ÷ 5/52)

iii) The total amount raised in the previous year = $2,450

The total amount raised in the current year = $3,100

Difference between current and previous year = $650 ($3,100 - $2,450)

Percentage increase on the previous year's total = 26.53% ($650/$2,450 x 100)

11b) Ratio of road and footpath walk = 3:2

The sum of ratios = 5

Road distance = 3/5 x 20 = 12 kilometers

Footpath distance = 2/5 x 20 = 8 kilometers

Vreni's walking speed along the road = 3 km/h

Road distance = 12 kilometers

Time to walk the road = 4 hours (12/3)

Vreni's walking speed along the footpath = 2.5 km/h

Footpath distance = 8 kilometers

Time to walk the footpath = 3.2 hours or 3 hours and 12 minutes (8/2.5) or 192 minutes (8/2.5 x 60)

Total time spent by Vreni = 7 hours and 12 minutes (4 hr + 3 hr + 12 min)

Vreni's average speed = Distance/Time

= 20 km/7.2 hrs

= 2.78 km/h

Starting time = 08:55

Total hours = 7 hours and 12 minutes

Finishing time = 16:07 (08:55 + 7 hrs + 12 min)

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Answer: A rectangle has two dimensions: length and width. The area of a rectangle is given by the formula A = L * W, where L is the length and W is the width.

Given the area can be represented by the expression 16x^4 + 48x^3 + 82, we can see that it's a polynomial of 4 degree.

So, one of the dimensions (L or W) must be represented by a polynomial of degree 4 and the other dimension by a polynomial of degree 3.

So the expressions that could represent one of the dimensions of the rectangle are:

L = 16x^4

W = 48x^3 + 82

It's important to note that this is just one of the possible representations of the dimensions of the rectangle, depending on the values of x.

Step-by-step explanation:

Answer:

If two triangles are similar, the ratio of their corresponding side lengths is the same as the ratio of their areas.

We know that the area of the first triangle is 18 cm^2, and the area of the second triangle is 8 cm^2. So, the ratio of their areas is 18/8 = 9/4

We also know that one of the sides of the first triangle is 4.5 cm.

So the ratio of the corresponding side of the second triangle to the first triangle is:

(length of corresponding side of second triangle) / 4.5 = 9/4

We can cross-multiply and solve for the length of the corresponding side of the second triangle:

4.5 * (9/4) = 9 * (9/4) / 4 = 9 * 2.25 / 4 = 20.25 / 4 = 5.0625 cm

So, the length of the corresponding side of the second triangle is 5.0625 cm.

Answer:

Step 1: The nth term of an arithmetic sequence is given by an = a + (n – 1)d. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula. Step 2: Now, to find the fifth term, substitute n = 5 into the equation for the nth term.

The differential equation for the time evolution of the toxic chemical in the pond is dy/dt = -200y + (100/2000)x

where y represents the amount (in kg) of the contaminant in the pond and x represents the amount of contaminant added to the pond per minute (5 kg/minute in this case). The negative sign in the equation indicates that the amount of contaminant is decreasing in the pond, while the positive term (100/2000)x indicates that the contaminant is being added to the pond at the rate of 5 kg/minute.

To solve for y, we can integrate the equation with respect to time. We start by multiplying both sides by dt, giving us the integral form of the equation: dy = -200y dt + (100/2000)x dt. Integrating both sides gives us the solution y = -200y(t) + (100/2000)x(t) + C, where C is an integration constant. Since we know the initial amount of contaminant in the pond is 5 kg, we can set y(0) = 5 and solve for C, giving us C = 5. Therefore, the solution to the differential equation is y(t) = -200y(t) + (100/2000)x(t) + 5.

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Therefore, the function f is decreasing on the interval (- [infinity], -1].

A. (- [infinity], -1] only

We can use the first derivative test to determine where a function is increasing or decreasing. The first derivative test states that if the derivative of a function is positive, then the function is increasing, and if the derivative is negative, then the function is decreasing.

For this problem, the derivative of the function f is f'(x) = x^2 - 2/x.

We can see that for x < 0, the derivative is negative, so the function is decreasing on that interval. For x > 0, the derivative is positive, so the function is increasing on that interval.

Therefore, the function f is decreasing on the interval (- [infinity], -1].

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Answer:

Step-by-step explanation:

1. What stock did you buy?

Apple Inc.

2. Why did you think buying this stock would be a good idea?

Apple products are becoming more and more popular every day. The company is always introducing new and exciting devices. I knew it would be a safe choice to invest in.

3. How much would you have made or lost on an investment of $1,000?

I would have made $105.

Hint: First find out how many shares you could've bought one year ago by dividing $1,000 by the price of the stock one year ago today. You may have to estimate the stock price from the graph. Round the number of shares to the nearest whole number. Then, find out the current value of your shares by multiplying the number of shares you bought by the price of the stock today. Compare that to your initial investment of $1,000.

4. Could you have made more money by selling sooner?

Yes, on October 3, 2018 it was at its peak for the year.

your investment would be doing great today. you would make $115 from the given investment.

A stock usually referred to as equity, is a type of investment that denotes ownership in a portion of the issuing company. Shares, also known as units of stock, entitle their owners to a share of the company's assets and income in proportion to the number of shares they possess.

Given, you're going to imagine that you invested $1,000 in a company one year ago

Therefore, Today, your investment would be flourishing. Your return on the stated investment would be $1,115.

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As, the moon has an elliptical orbit around a planet, the maximum distance between the planet and its moon is 88.54 Mm.

What is an elliptical orbit?

When an object moves around another object in an oval shaped path (ellipse), it is known to be revolving in an elliptical orbit.

The standard form of the equation of an ellipse with center at the origin (0,0) and x - axis major axis is given by

x²/a² + y²/b² = 1

Now,

Given that a moon's elliptical orbit around a planet is modeled by the equation 225x² + 576y² = 176,400, where distance is measured in megameters (Mm). and the planet is the center of the orbit's path.

Since the equation of the path is the equation of an ellipse, we write it in standard form

As standard form of the equation of an ellipse with center at the origin (0,0) and x - axis major axis is

x²/a² + y²/b² = 1  (1) where

a = vertex of major axis and

b = vertex of minor axis

So, converting 225x² + 576y² = 176,400 into standard form, we have

225x² + 576y² = 176,400

225x²/1764,000 + 576y²/1764,000 = 176,400/1764,000

x²/7840 + y²/3062.5 = 1  (2)

Comparing equation (2) with (1), we have that

a² = 7840 and b² = 3062.5

⇒ a = √7840 = 88.54 and

⇒ b = √3062.5 = 55.34

Since a = 88.54 is greater than b = 55.34, so, a is the major axis, and the maximum distance between the planet and its moon is 88.54 Mm

So, the maximum distance between the planet and its moon is 88.54 Mm

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Since the moon's has an elliptical orbit around a planet, the maximum distance between the planet and its moon is 88.54 Mm

How to find the maximum distance between the planet and its moon?

x²/a² + y²/b² = 1  (1) where

a = vertex of major axis and

b = vertex of minor axis

o, converting 225x² + 576y² = 176,400 into standard form, we have

225x² + 576y² = 176,400

225x²/1764,000 + 576y²/1764,000 = 176,400/1764,000

x²/7840 + y²/3062.5 = 1  (2)

Comparing equation (2) with (1), we have that

a² = 7840 and b² = 3062.5

⇒ a = √7840 = 88.54 and

⇒ b = √3062.5 = 55.34

Since a = 88.54 is greater than b = 55.34, so, a is the major axis, and the maximum distance between the planet and its moon is 88.54 Mm

So, the maximum distance between the planet and its moon is 88.54 Mm

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The absolute value of a number is always positive or zero because it represents the distance of a number from zero on a number line, and the distance between two points can never be negative.

The absolute value of a number is defined as the distance of that number from zero, regardless of its sign. For example, the absolute value of -5 is 5 and the absolute value of 5 is also 5. When we apply the absolute value function to a number, the result is always positive or zero.

Additionally, the definition of absolute value is |x| = { x if x >=0, -x if x<0 }

if x is greater or equal to 0, the absolute value of x is x, otherwise is -x, which is positive.

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Answer: 3

Step-by-step explanation:

[tex]f(0)=3(0)-3=-3\\\\\implies g(f(0))=g(-3)=-(-3)=3[/tex]

Answer:

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

The scale factor is 2, since each side is twice the initial length.

There are 4 congruent copies, as we can see on the picture.

The dilated area is 12*4 = 48 square units, since the area is the product of two dimensions, each dimension is twice the initial value therefore the area is 2*2 = 4 times greater.

According to the given information the detection angle is 72.

An angle is formed anytime two straight lines and rays meet at a single terminal. The intersection of two points at such an angle is known as the vertex. The word "angle" comes from the Latin word "angulus," which meaning "corner."

Degrees are a measure representing circularity or rotation and are used to express angles. You would turn 360° in order to face back in the exact direction after completing a full revolution. As a result, a quarter-circle, or straight angle, is 90°, and a half-circle is 180°. The sum of any two or maybe more angles on the a straight line is 180°.

[tex]\begin{aligned}5\theta & =360^{\circ} \\\theta & =\frac{360^{\circ}}{6} \\& =72^{\circ}\end{aligned}[/tex]

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For feet we will divide the given no. of inches by 12 and for inches we will multiply the given number of feet by 12.

Since 1 foot is equal to 12 inches, the given value (in feet) is converted to inches by multiplying by 12. To compare lengths given in different units or to perform arithmetic operations on them, it is crucial to learn how to convert feet to inches (ft to in).

We know that 1 feet = 12 inches.

And to find how many feet are in a given number of inches

We will divide the given no. of inches by 12.

And

To find how many inches are given in a number of feet

We will multiply the given number of feet by 12.

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It can include things like answers to equations, solutions to problems, and visualizations of data.

1. Input: The data and instructions a system receives.

2. Process: The manipulation of data and instructions to produce an output.

3. Output: The result of the system's processing of the data and instructions.

4. Feedback: Information from the output that is used to improve the system's performance.

1. Input: The first part of a system in mathematics is the input. This is the data and instructions that the system receives. It can include things like numbers, equations, formulas, and instructions for how to process the data.

2. Process: The second part of a system in mathematics is the process. This is where the data and instructions are manipulated to produce an output. This can include things like calculations, algorithms, and other mathematical operations.

3. Output: The third part of a system in mathematics is the output. This is the result of the system's processing of the data and instructions. It can include things like answers to equations, solutions to problems, and visualizations of data.

4. Feedback: The fourth part of a system in mathematics is the feedback. This is information from the output that is used to improve the system's performance. This can include things like error messages, suggested changes, and suggestions for optimization.

The four parts of a system in mathematics are input, process, output, and feedback. Input is the data and instructions a system receives. Process is the manipulation of data and instructions to produce an output. Output is the result of the system's processing of the data and instructions. Feedback is information from the output that is used to improve the system's performance.

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The rate of the plane in still air is 1,000 kph and the speed of the wind is 250 kph. The result is obtained by using elimination and substituting method.

To eliminate equations, we can either add or subtract the equations. Substitution is substituting the value of one variable in the other equation.

A plane can travel:

Find the rate of the plane in still air and the speed of the wind!

Let's say

The speed of the plane with the wind is

v + w = 3750 km/3 h

v + w = 1250 kph ... (equation 1)

The speed of the plane against the wind is

v - w = 3750 km/5 h

v - w = 750 kph ... (equation 2)

Eliminate the equation 1 and 2!

v + w = 1250

v - w = 750 +

2v = 2000

v = 1000 m/s

Substitute the value of v in equation 1!

v + w = 1250

1000 + w = 1250

w = 1250 - 1000

w = 250 m/s

Hence, the speed of the plane when there is no wind and the speed of the wind respectively are 1000 m/s and 250 m/s.

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Answer:

distance from beginning is 225 and the change is -65 per hour

Step-by-step explanation:

The probability that at least 3 copiers will break down on a given day is 0.0909.

1. Calculate the probability that 0 copiers will break down:

P(0) = (1-0.66)^5

= 0.0729

2. Calculate the probability that 1 copier will break down:

P(1) = 5 * 0.66 * (1-0.66)^4

= 0.2221

3. Calculate the probability that 2 copiers will break down:

P(2) = 5C2 * 0.66^2 * (1-0.66)^3

= 0.3088

4. Calculate the probability that 3 copiers will break down:

P(3) = 5C3 * 0.66^3 * (1-0.66)^2

= 0.2197

5. Calculate the probability that at least 3 copiers will break down:

P(at least 3) = 1 - (P(0) + P(1) + P(2))

= 0.0909

The probability that at least 3 copiers will break down on a given day is 0.0909. This was calculated by first calculating the probability of 0 copiers breaking down (P(0)) which is (1-0.66)^5, then the probability of 1 copier breaking down (P(1)) which is 5 * 0.66 * (1-0.66)^4, and then the probability of 2 copiers breaking down (P(2)) which is 5C2 * 0.66^2 * (1-0.66)^3. Finally, the probability that at least 3 copiers will break down (P(at least 3)) was calculated by subtracting the sum of P(0), P(1), and P(2) from 1. This gives us the final result of 0.0909.

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Answer:

whats ..... representating

is it a continuous series?

Answer:

B

Step-by-step explanation:

You solve all until you get the exact expression being found.

(x-7)(x+2) Step.1 ) Distribute Multipliciation

=X^2 +2x -7x -14. Step 2.) Add like terms

=X^2 -5x -14. Step 3.) Solve

Final Answer: B

a) The random variable in this problem is the number of left-handed people in a grouping of 15 people.

x = number of left-handed people in a group of 15 people

b) This is a binomial experiment because it meets the following criteria:

The experiment consists of a fixed number of trials (15 people in this case)

Each trial has two possible outcomes (left-handed or not left-handed)

The probability of success (left-handed) is constant for each trial (10% or 0.1)

c) To find the probability that none are left-handed, we use the binomial probability formula:

P(x = 0) = (15 choose 0)(0.1)^0(0.9)^15 = 0.3429

d) To find the probability that seven are left-handed, we use the binomial probability formula:

P(x = 7) = (15 choose 7)(0.1)^7(0.9)^8 = 0.1540

e) To find the probability that at least two are left-handed, we need to find the probability of getting 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15 left-handed people, and add them up. We can use the binomial probability formula to find the probability of getting each of these values of x, and add them up to find the total probability:

P(x ≥ 2) = P(x = 2) + P(x = 3) + P(x = 4) + ... + P(x = 15)

f) To find the probability that at most three are left-handed, we need to find the probability of getting 0, 1, 2, and 3 left-handed people, and add them up. We can use the binomial probability formula to find the probability of getting each of these values of x, and add them up to find the total probability:

P(x ≤ 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)

g) To find the probability that at least seven are left-handed, we need to find the probability of getting 7, 8, 9, 10, 11, 12, 13, 14, and 15 left-handed people, and add them up. We can use the binomial probability formula to find the probability of getting each of these values of x, and add them up to find the total probability:

P(x ≥ 7) = P(x = 7) + P(x = 8) + P(x = 9) + ... + P(x = 15)

h) The mean of x is given by:

E(x) = 15(0.1) = 1.5

i) The variance of x is given by:

Var(x) = 15(0.1)(0.9) = 1.35

j) The standard deviation of x is given by:

SD(x) = √1.35 = 1.16

So, the mean of x is 1.5 and the standard deviation is 1.16. The probability of getting at least 2 left-handed people is 0.717, the probability of getting at most 3 left-handed people is 0.547 and the probability of getting at least 7 left-handed people is 0.0256.

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