You leave a 20% tip on your $70 dinner bill.How much was the tip?

Answer:

(what is the question).

There are 5 possible combinations for Jacob's lock combination with increasing digits from left to right, and the product of the digits being 84.

Multiplication is a mathematical operation that involves combining two or more quantities to find their total or product. It is often represented by the "x" symbol or the multiplication sign "⋅". Multiplication is a fundamental operation in arithmetic and is used to calculate the total or result of repeated addition or groups of equal quantities.

The product of the digits being 84 implies that the possible combinations of digits are limited to those whose product is 84. The prime factorization of 84 is 2^2 * 3 * 7. Since the digits must be increasing from left to right and cannot repeat, the possible combinations of digits are:

1, 2, 42

1, 3, 28

1, 4, 21

2, 3, 14

2, 6, 7

So, there are 5 possible combinations for Jacob's lock combination.

Therefore, There are 5 possible combinations for Jacob's lock combination with increasing digits from left to right, and the product of the digits being 84.

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Hello!
In this question, we are solving "Composite Functions".

We were given the functions:

We will use these to solve each part of the question.

Solve:

Whenever we see "(f ∘ g)", it means f of g. Another way to write (f ∘ g) is f(g(x)) where g(x) is plugged into the "x" variable of our f(x) function.

(a)

(f ∘ g)(x) = f(g(x))

Plug the g(x) function into the "x" variable of the f(x) function.

(f ∘ g)(x) = 4x + 5 − 2

Simplify.

(f ∘ g)(x) = 4x + 3

(b)

For question "b", it is the same concept but reversed. Plug the f(x) function into the "x" variable of the g(x) function.

(g ∘ f)(x) = g(f(x)) = 4(x − 2) + 5

Simplify.

(g ∘ f)(x) = g(f(x)) = 4(x − 2) + 5

Use the distributive property to distribute the 4.

(g ∘ f)(x) = g(f(x)) = 4x − 8 + 5

(g ∘ f)(x) = g(f(x)) = 4x − 3

(c)

For problem "c", we will plug our number into the "x" variable after compositing the functions. Use the same concept described above.

(f ∘ g)(5) = f(g(x))

(f ∘ g)(5) = 4x + 5 − 2

Simplify.

(f ∘ g)(5) = 4x + 3

Plug in "5" to "x" and simplify.

(f ∘ g)(5) = 4(5) + 3

(f ∘ g)(5) = 23

(d)

Problem "d" is just like problem "c", but the functions are reversed

(g ∘ f)(5) = g(f(x)) = 4(x − 2) + 5

Use the distributive property to distribute the 4.

(g ∘ f)(5) = g(f(x)) = 4x − 8 + 5

(g ∘ f)(5) = g(f(x)) = 4x − 3

Plug in "5" to "x" and simplify.

(g ∘ f)(5)  = 4(5) − 3

(g ∘ f)(5) = 17

Answer:

(a) 4x + 3

(b) 4x − 3

(c) 23

(d) 17

The slope of a line is a measure of its steepness and is defined as the ratio of the change in y (vertical distance) to the change in x (horizontal distance) between any two points on the line.

We can use the point-slope form of the equation of a line to find the equation of the line that passes through the point (2, 5) and has a slope of -3. The point-slope form of the equation of a line is:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

Substituting the values we have, we get:

y - 5 = -3(x - 2)

Simplifying this equation, we get:

y - 5 = -3x + 6

Adding 5 to both sides, we get:

y = -3x + 11

Therefore, the equation of the line that passes through the point (2, 5) and has a slope of -3 is y = -3x + 11.

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We can say that the domain of f(x) is (-∞, ∞), which means that any real number can be plugged into the function and it will produce a valid output.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

The function f(x) = -x³ + 6x² -10x + 4 is a polynomial function, which means that it is defined for all real values of x. Unlike some functions (such as square roots or logarithms) which have restrictions on their input values, a polynomial function can take any real number as an input.

To express the domain of the function in interval notation, we use the notation (-∞, ∞), which represents all real numbers. The symbol ∞ stands for infinity, and the open interval notation with the parentheses indicates that there are no specific endpoints for the domain; it extends indefinitely in both directions along the real number line.

Therefore, we can say that the domain of f(x) is (-∞, ∞), which means that any real number can be plugged into the function and it will produce a valid output.

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Answer:

center:(0,0)

Radius:7

Step-by-step explanation:

the equation of circle:

(x-h)^2+(y-k)^2=r^2

the point h and k are the center of the circle
(h,k)  ———-> (0,0)

since r^2 =49

So, the radius will be the square root of that number
[tex]r^{2} =49[/tex]

[tex]\sqrt{r^{2} } =\sqrt{49}[/tex]

[tex]r=7[/tex]

to have $110,000 available for the child's education in 12 years at 6% interest, we need to set aside $54,661.55 now. This assumes that the interest rate remains constant over the 12-year period, which may not be the case in reality.

To calculate how much money must be set aside at 6% interest, we can use the future value formula:

[tex]FV = PV*(1 + r)^n[/tex]

where:
FV = future value (the amount of money we want to have in the future)
PV = present value (the amount of money we need to set aside now)
r = interest rate per period (in this case, per year)
n = number of periods (in this case, the number of years until the child starts college)

In this case, we want to have $110,000 in the future, the child is 6 years old now, and we assume that the child will start college at age 18, which is 12 years from now. The interest rate is given as 6% per year.

So, we can plug in the values into the formula:

[tex]110,000 = PV*(1 + 0.06)^12[/tex]

Simplifying the right-hand side of the equation:

110,000 = PV x 2.012594

Dividing both sides by 2.012594:

PV = 110,000 / 2.012594

PV = $54,661.55 (rounded to the nearest cent)

Therefore, to have $110,000 available for the child's education in 12 years at 6% interest, we need to set aside $54,661.55 now. This assumes that the interest rate remains constant over the 12-year period, which may not be the case in reality.
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Answer:

[tex]\frac{-2(24t-25)}{45}[/tex]

Step-by-step explanation:

In order to find the expression, you have to read the problem from left to right and make sure to follow PEMDAS.

[tex](-\frac{7}{5} * t+\frac{2}{9})-(-\frac{1}{3}*t+\frac{4}{3})\\\\\\(-\frac{7t}{5} +\frac{2}{9} )-(-\frac{t}{3} +\frac{4}{3} )\\\\(-\frac{7t}{5} *\frac{9}{9} +\frac{2}{9} *\frac{5}{5} )-(\frac{-t+4}{3} )\\\\(-\frac{63t}{45} +\frac{10}{45} )+\frac{t-4}{3} \\\\\frac{-63t+10}{45} +\frac{t-4}{3} \\\\\frac{-63t+10}{45}*\frac{3}{3}+\frac{t-4}{3}*\frac{45}{45}\\\\\frac{3(-63t+10)}{135}+\frac{45(t-4)}{135}\\\\\frac{-189t+30}{135}+\frac{45t-180}{135}\\\\\frac{-189t+30+45t-180}{135}[/tex]

Once you have it combined into only one expression, simplify the expression.

[tex]\frac{-189t+30+45t-180}{135}\\\\\frac{-144t-150}{135}\\\\\frac{-6(24t-25)}{135}\\\\\frac{-2(24t-25)}{45}\\\\[/tex]

The article's development of key ideas by showcasing the importance of precise criteria and the ever-evolving nature of scientific knowledge. The IAU's decision on Pluto serves as a prime example of these concepts in action.

Lines 25 and 26 contribute to the development of key ideas in the article "Ideas That Work... And Those That Don't" from "When is a Planet Not a Planet? The Story of Pluto" by providing a comparison between two concepts in the field of astronomy. These lines state, "The IAU's decision to demote Pluto was based on a more nuanced understanding of what constitutes a planet."

Firstly, this statement demonstrates that the International Astronomical Union (IAU) relies on a "nuanced understanding" to define what a planet is, emphasizing the importance of precise criteria in categorizing celestial bodies. The IAU's decision-making process shows that some ideas work, such as establishing clear guidelines for planetary classification, while others don't, like the previous, less accurate definition of a planet.

Secondly, by mentioning the demotion of Pluto, the article highlights the impact of changing scientific perspectives on our understanding of the solar system. This reinforces the idea that knowledge is constantly evolving, and sometimes previously accepted ideas must be reconsidered or discarded to make way for more accurate information.

In summary, lines 25 and 26 contribute to the article's development of key ideas by showcasing the importance of precise criteria and the ever-evolving nature of scientific knowledge. The IAU's decision on Pluto serves as a prime example of these concepts in action.

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1. The each ingredient amount will be multiplied by 2.5.

2. [tex]\frac{5}{8}[/tex] ounces of yeast will make 30 rolls.

3.  [tex]\frac{5}{6}[/tex] cup of powdered milk will make 30 rolls.

4. 15 tablespoons of butter will make 30 rolls.

5.  [tex]\frac{15}{2}[/tex] more cups of bread flour than whole wheat flour will be needed to make 30 rolls.

6. The original recipe has been multiplied by 1.5 and this will serve 18 people.

The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

All real numbers are thought to be sufficiently described by the four basic operations, also referred to as "arithmetic operations." Quotient, product, sum, and difference are the mathematical operations that come after division, multiplication, addition, and subtraction.

1. We are given that the given recipe makes 12 rolls.

In order to make 30 rolls, the amount will be multiplied by 2.5 because when 12 is multiplied by 2.5, we get 30.

2. For 12 rolls, [tex]\frac{1}{4}[/tex] ounce package is required.

So, using the multiplication operation, we get

⇒ [tex]\frac{1}{4}[/tex] * 2.5 = [tex]\frac{5}{8}[/tex]

So,  [tex]\frac{5}{8}[/tex] ounces of yeast will make 30 rolls.

3. For 12 rolls, [tex]\frac{1}{3}[/tex] cup of powdered milk is required.

So, using the multiplication operation, we get

⇒ [tex]\frac{1}{3}[/tex] * 2.5 = [tex]\frac{5}{6}[/tex]

So,  [tex]\frac{5}{6}[/tex] cup of powdered milk will make 30 rolls.

4. For 12 rolls, 6 tablespoons of butter is required.

So, using the multiplication operation, we get

⇒ 6 * 2.5 = 15

So,  15 tablespoons of butter will make 30 rolls.

5. 4. For 12 rolls, 3 [tex]\frac{1}{2}[/tex] cups of bread flour is required.

So, using the multiplication operation, we get

⇒ 3 [tex]\frac{1}{2}[/tex]  * 2.5 = [tex]\frac{35}{4}[/tex]

Similarly, for 12 rolls,  [tex]\frac{1}{2}[/tex] cup of wheat flour is required.

So, using the multiplication operation, we get

⇒ [tex]\frac{1}{2}[/tex]  * 2.5 = [tex]\frac{5}{4}[/tex]

Now, using the subtraction operation, we get

⇒ [tex]\frac{35}{4}[/tex] -  [tex]\frac{5}{4}[/tex] =  [tex]\frac{30}{4}[/tex]

⇒ [tex]\frac{35}{4}[/tex] -  [tex]\frac{5}{4}[/tex] = [tex]\frac{15}{2}[/tex]

So, [tex]\frac{15}{2}[/tex] more cups of bread flour than whole wheat flour will be needed to make 30 rolls.

6. Let the number be x.

So,

⇒ [tex]\frac{1}{4}[/tex]x = [tex]\frac{3}{8}[/tex]

⇒ x = 1.5

So, the original recipe has been multiplied by 1.5.

Now,

⇒ Number of people served = 12 * 1.5

⇒ Number of people served = 18

So, this will serve 18 people.

Hence, the required solutions have been obtained.

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The complete question has been attached below.

Question:

Recipe:

Cinnamon Rolls

makes 12 rolls

1/4 -ounce package active dry yeast

1 cup warm water

3 tablespoons molasses

1/3 cup powdered milk

1 egg yolk,beaten

1 egg white, beaten

3 1/2 cups bread flour, divided

6 tablespoons butter, melted and divided

1 teaspoon salt

1/2 cup whole wheat flour

1/3 cup raisins

1 large egg, beaten

​​​​​​​1/4 cup water

You will use the recipe above to answer the following questions:

Respond to the questions about the second recipe:

1. This recipe makes 12 rolls, but you need to make 30 rolls. What number will you need to multiply the amount of each ingredient by to adjust the recipe? How did you determine this number?

2. How many ounces of yeast will you need to make 30 rolls?

3. How many cups of powdered milk will you need to make 30 rolls?

4. How many tablespoons of butter will you need to make 30 rolls?

5. How many more cups of bread flour than whole wheat flour will you need to make 30 rolls?

6. notice that the original recipe calls for 1/4 cup of water. If you put in 3/8 cup of water, by how much have you multiplied the original recipe? How many people will your new recipe serve?

If the quadratic function f(x) has roots of 3 and 7, and it passes through the point (1, 12), the correct vertex form of the equation is f(x) = (x-5)² - 4. So, correct option is D.

Since the quadratic function has roots of 3 and 7, we can write it in factored form as f(x) = a(x-3)(x-7), where "a" is a constant.

To find the value of "a", we can use the point (1,12) that the function passes through.

Substituting x=1 and y=12 in the equation f(x) = a(x-3)(x-7), we get:

12 = a(1-3)(1-7)

12 = a(-2)(-6)

12 = 12a

a = 1

Therefore, the equation of the function in factored form is f(x) = (x-3)(x-7), and we can expand it to vertex form by completing the square:

f(x) = (x-5)² - 4

The vertex of the parabola is at (5, -4) and the coefficient of the squared term is positive, which means the parabola opens upwards.

So, correct option is D.

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The right number that fits the sequence 54 , 48 , 18 , 24 , 6 , 12 , is 2

To find the next number in the sequence, we need to look for a pattern in the given numbers.

So, we have

54 .. 18 .. 6 ... division by 3

48 .. 24 .. 12 .. division by 2

So, it seems that we are dividing each pair of consecutive numbers by a certain factor.

So, the factor by which we are dividing each pair of consecutive numbers seems to be decreasing by a factor of 3 each time, for the first sequence.

Therefore, the next number in the sequence should be:

6/3 = 2

So, the complete sequence is:

54, 48, 18, 24, 6, 12, 2

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Answer:

Let's start with the distance each person covers in 3 minutes.

Beth's distance = 70 meters/minute x 3 minutes = 210 meters

Liz's distance = 60 meters/minute x 3 minutes = 180 meters

Now we can find their distance apart after 3 minutes.

Distance apart = Initial distance - distance covered

Distance apart = 520 meters - (210 meters + 180 meters)

Distance apart = 520 meters - 390 meters

Distance apart = 130 meters

Therefore, Beth and Liz are 130 meters away from each other after walking towards each other for 3 minutes.

Answer:

B

Step-by-step explanation:

Given:

1 furlong has 660 feet

1 yard has 0,5 fathom

Find:

How many fathoms are there in one furlong?

.

We know that 1 yd has 3 ft, that means:

There's 660 ft in one furlong and 3 ft in 0,5 of a fathom (6 ft in one fathom)

Now, in order to find how many fathoms are there in one furlong, we have to divide the number of feet in a furlong by the number of feet in a fathom:

[tex] \frac{660}{6} = 110 \: fathoms[/tex]

Answer:

3.17

Step-by-step explanation:

First change 63.4 to 634/10

Then simplify

You get 317 over 5 then divide by 20 and get

3.17000

Then round

It would take approximately 1.3 hours for 12 rice to reach the velocity of Earth's orbit at a velocity of 23 km/hr.

The velocity of Earth's orbit around the sun is approximately 30 km/s.

To determine how many hours it takes for 12 rice to reach this velocity, you must use the formula for calculating average speed:

Average Speed = Total Distance/Total Time

Since the total distance is the speed of Earth's orbit (30 km/s) and the total time is the amount of time it takes to reach this speed, then you can solve for the total time by rearranging the equation:

Total Time = Total Distance/Average Speed

Therefore, the total time it takes to reach the velocity of Earth's orbit is:

Total Time = 30 km/s/23 km/hr

= 1.3 hours

It would take approximately 1.3 hours for 12 rice to reach the velocity of Earth's orbit at a velocity of 23 km/hr.

This is because the average speed of the rice is equal to the total distance (30 km/s) divided by the total time (1.3 hours).

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Answer:

the answer is the 3rd one and I am 100% sure

The lines are tangent,     The value of x is -7.

To determine the value of x, we need to apply the Tangent-Chord Angle Theorem, which states that the measure of an angle formed by a chord and a tangent line is equal to half the difference of the intercepted arc measures.

In this case, let's call the angle WZY as angle A and angle WYX as angle B. According to the given information, angle A = 2x + 9, and angle B = 3x + 6.

Since , we can apply the Tangent-Chord Angle Theorem:

Angle A = (1/2) * (arc WY - arc ZX)

Substitute the given angle measures:

2x + 9 = (1/2) * ((3x + 6) - (2x + 9))

Multiply both sides by 2 to get rid of the fraction:

4x + 18 = (3x + 6) - (2x + 9)

Simplify the equation:

4x + 18 = x - 3

Subtract x from both sides:

3x + 18 = -3

Subtract 18 from both sides:

3x = -21

Divide both sides by 3:

x = -7

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Answer:

247277 cubic in

Step-by-step explanation:

The percentage change in attendance after rounding off the answer to the nearest hundredth of a percent will be approximately 48.78%.

To find the percentage change in attendance, we need to calculate the difference between the new and old attendance, divide by the old attendance, and then multiply by 100 to express the result as a percentage:

percentage change = (new attendance - old attendance) ÷ old attendance × 100%

Plugging in the given values, we get:

percentage change = (61 - 41) ÷ 41 × 100%

percentage change = 20 ÷ 41 × 100%

percentage change = 0.4878 × 100%

percentage change ≈ 48.78%

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Answer:

x = 10.20240940

Step-by-step explanation:

[tex]x(2x + 9) = 2x^2 + 9x[/tex]

[tex]2x^2 + 9x = 300[/tex]

- 300 on both sides

[tex]2x^2 + 9x - 300 = 0[/tex]

solve using the quadratic formula

[tex]x = -b +/- \ \text{all root} (b)^2 - 4(a)(c) \ \text{All over} \ 2(a)[/tex]

When all the values are plugged in:

When using "+" in the equation you should get:

x = 10.20240940

When using "-" in the equation you should get:

x = −14.70240940

Now.. you CANNOT have a negative length, so you cross of the negative value leaving you one value for x which is 10.20240940.

Your answer is: x   =  10.20240940

After answering the presented question, we can conclude that As a result, the player may expect to lose a total of $5,580, with an average loss of $5.58 per game.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many fields, including statistics, economics, science, and engineering.

(38/39) x $315 - (1/39) x $9 = $306.54

The player will lose the remaining 620 games, totaling $9 x 620 = $5,580.

As a result, the player may expect to lose a total of $5,580, with an average loss of $5.58 per game.

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The correct option is "IQR, because Desert Landing is skewed."

Skewness is a term used in statistics to describe the degree of asymmetry of a probability distribution or a dataset. If a dataset is skewed, it means that the distribution of the data is not symmetrical.

To determine the location with the most consistent temperature between the two sets of data, we should use the IQR (Interquartile Range) measure of variability. This is because the IQR is a measure of the spread of the middle 50% of the data, which is a good measure of variability for skewed data such as the data from Desert Landing.

In the case of Flower Town, the range measure of variability could also be used, but it is generally less robust than the IQR and can be affected by extreme values. The symmetry of the histograms does not necessarily determine which measure of variability should be used.

Therefore, the correct option is "IQR, because Desert Landing is skewed." This is because the IQR is a robust measure of variability that is less affected by extreme values and is suitable for skewed data. The data from Desert Landing is skewed, while the data from Flower Town is not specified as being skewed or symmetric, so the IQR is the best choice for both sets of data.

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Answer:

B. S(15) - S(10) = -40 means that there were 40 less students in 2010 than there were in 2015. This statement is true because S(15) represents the number of students in the year 2015, and S(10) represents the number of students in the year 2010. Subtracting S(10) from S(15) gives the change in the number of students over that 5-year period.

C. S(0) = 2,000 means that there were no students in the year 2000. This statement is also true because S(t) represents the number of students in terms of the number of years after 2000. Therefore, S(0) represents the number of students in the year 2000, which is the starting point for the function.

Step-by-step explanation:

From the line plot, we can see that the statement "Team C has the most people" is true, since the count of 7 appears three times, which is more than any other count.

A line plot is a type of graph used to display data along a number line. It is also known as a dot plot or a strip plot. In a line plot, each data point is represented by a dot or a symbol above the number line, indicating the frequency or count of the data point. The dots or symbols are aligned horizontally along the number line, making it easy to see the distribution of the data.

Here,

To create a line plot from the data, we need to count the number of people on each team and mark a dot on the number line for each count. The number line should start at the smallest count (which is 3 in this case) and end at the largest count (which is 8).

Looking at the data, we can see that there are two counts of 3, three counts of 5, three counts of 7, one count of 6, and one count of 8.

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Complete question:

The cost is minimized when all the remaining requirements are met by Food B, we can purchase 36 units of Food A and 30 units of Food B to meet all the requirements and minimize the cost.

What is probability?

Probability is a measure of the likelihood of an event occurring.

Let x be the number of units of Food A and y be the number of units of Food B.

The objective is to minimize the cost, which is given by the expression 2x + y.

The constraints are:

50x + 20y >= 2400 (minimum vitamin requirement)

30x + 20y >= 1800 (minimum mineral requirement)

10x + 40y >= 1200 (minimum calorie requirement)

x >= 0, y >= 0 (non-negative quantities)

We can use linear programming to solve this problem. The standard form is:

Minimize: 2x + y

Subject to:

50x + 20y >= 2400

30x + 20y >= 1800

10x + 40y >= 1200

x >= 0, y >= 0

Therefore, the minimum cost is $30, and it is achieved by purchasing 30 units of Food B.

To find the number of units of Food A, we can use one of the constraints, for example:

50x + 20y >= 2400

50x + 20(30) >= 2400

50x >= 1800

x >= 36

So, we need at least 36 units of Food A to meet the vitamin requirement.

Since the cost is minimized when all the remaining requirements are met by Food B, we can purchase 36 units of Food A and 30 units of Food B to meet all the requirements and minimize the cost.

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Answer: 2.4

(Hopefully this helps! If you can, please mark me brainliest tomorrow)

Explanation:

We divide the feet by 5280 to find that amount in miles.

12,672/5280 = 2.4

Therefore, the answer is 2.4 miles.

Answer:

13

Hope this helps!

Step-by-step explanation: