In a recent report, Joe's, a Memphis-style barbecue chain, states that 11% of its customers order for delivery. A random sample of 6 Joe's customers is chosen. Find the probability that at most 1 of them order for delivery. " Do not round your intermediate computations, and round your answer to three decimal places.
P(X ≤ 1) = P(X = 0) + P(X = 1) ≈ 0.901
So the probability that at most 1 customer in the sample orders for delivery is approximately 0.901, rounded to three decimal places.
To solve this problem, we can use the binomial distribution since we have a fixed number of trials (6) and each trial can result in one of two outcomes (ordering for delivery or not).
Let X be the number of customers in the sample who order for delivery. Then X follows a binomial distribution with parameters n = 6 and p = 0.11 (the probability of ordering for delivery).
We want to find the probability that at most 1 customer orders for delivery. This can be written as:
P(X ≤ 1) = P(X = 0) + P(X = 1)
To calculate these probabilities, we can use the binomial probability formula:
P(X = k) = (n choose k) *[tex]p^k[/tex]*[tex](1 - p)^(n - k)[/tex]
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items.
Using this formula, we can calculate:
P(X = 0) = (6 choose 0) * 0.11^0 * [tex]0.89^6[/tex] ≈ 0.530
P(X = 1) = (6 choose 1) * 0.11^1 * 0.89^5 ≈ 0.371
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One angle of a triangle measures 10°. The other two angles are in a ratio of 4:13. What are the measures of those two angles?
Answer:
Step-by-step explanation:
Let's call the two angles in the ratio of 4:13 "x" and "y".
We know that the sum of all three angles in a triangle is always 180 degrees.
So, we can set up an equation:
10 + x + y = 180
We also know that x and y are in a ratio of 4:13, which means we can write:
x = 4k
y = 13k
where "k" is a constant that we need to find.
Substituting these expressions for x and y into the equation, we get:
10 + 4k + 13k = 180
17k = 170
k = 10
Now we can find the values of x and y:
x = 4k = 4(10) = 40
y = 13k = 13(10) = 130
Therefore, the measures of the two angles in the ratio of 4:13 are 40 degrees and 130 degrees, respectively.
PLEASE HELP ASAP!! The image is attached 30 points!!
Answer:
366 times
Step-by-step explanation:
Two circles, C1 and C2, intersect at point A and B. Passes through the center O of circle C2. The point P lies on circle C2 so that the line PAT is target to circle Ci and point A. Let ∠APB =.
The value of ∠APB = 180°. It is a straight line.
Given the information, we can deduce that the line passing through the center O of circle C2 and point A also passes through point B, as AB is the intersection of the two circles.
Now, consider the line segment AP. Since PAT is tangent to circle C1 at point A, we know that ∠APT = 90°. Additionally, since AB is a diameter of circle C1, we know that ∠ABP = 90°.
Using these angles, we can see that ∠APB is equal to the sum of ∠APT and ∠ABP. Therefore,
∠APB = ∠APT + ∠ABP = 90° + 90° = 180°.
So, we have shown that ∠APB is a straight line.
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simplify and rearrange the equation to the form c=
For given equation x = (-b ± √(b²-4ac))/2a the equation in the form c= is: c = -x²(a/b) - x.
What is equation?
An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division.
What is goal of equation?
The goal of solving an equation is to determine the value or values of the variable that make the equation true. Equations are used extensively in mathematics and science to describe relationships between quantities and to solve problems.
According to given information:Starting with the equation:
x = (-b ± √(b²-4ac))/2a
We can simplify and rearrange it to the form c= as follows:
Multiply both sides by 2a to get rid of the denominator:
2a x = -b ± √(b²-4ac)
Add b to both sides:
2a x + b = ± √(b²-4ac)
Square both sides:
(2a x + b)² = b² - 4ac
Expand the left side:
4a² x² + 4abx + b² = b² - 4ac
Simplify:
4a² x² + 4abx = -4ac
Divide both sides by 4a:
x² + bx/a = -c/a
Rearrange to the form c=:
c = -x²(a/b) - x
Therefore, the equation in the form c= is:
c = -x²(a/b) - x
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There is a rope running from the top of a flagpole to a hook in the ground. The flagpole is 24 feet high, and the hook is 32 feet from its base. How long is the rope?
Answer:
Step-by-step explanation:
Len works at a photo gallery. He charges $50 for a large photo and $30 for a large frame. Sales tax is 4%. How much total tax will a customer pay on both? Fill in the blanks to show how to write and simplify expressions that represent the problem. calculate the total tax is 0.04(50 + 30). The total tax is $ 4 of 4 QUESTIONS
Step-by-step explanation:
4% tax is .04 in decimal:
($ 50 + 30 ) * .04 = 3.20 tax
What’s the answer I need help pls?
Answer:
A, C, F
Step-by-Step:
The amplitude is whatever the coefficient is behind the trig function
Daniel read 77 pages in \frac{2}{5}
of an hour. if he continues reading at the same rate, how many pages will he read in an hour?
Daniel will read approximately 193 pages in one hour if he continues reading at the same rate.
How many pages will Daniel read in an hour?Since Daniel read 77 pages in $\frac{2}{5}$ of an hour, we can set up the proportion:
$\frac{77}{\frac{2}{5}} = x$
where $x$ is the number of pages he would read in 1 hour.
To solve for $x$, we can simplify the left side of the equation by multiplying both the numerator and denominator by 5, which gives:
$\frac{77 \times 5}{2} = x$
Simplifying this expression gives:
$192.5 = x$
Therefore, if Daniel continues reading at the same rate, he will read 192.5 pages in one hour. However, since the number of pages must be a whole number, we can round this answer to the nearest whole number to get:
$x \approx 193$
So, Daniel will read approximately 193 pages in one hour if he continues reading at the same rate.
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The y-values that a function approaches when the x-values are extremely large or extremely small. this is called the function's ____ behavior.
The y-values that a function approaches when the x-values are extremely large or extremely small is called the function's asymptotic behavior.
When we talk about the asymptotic behavior of a function, we are referring to what happens to the values of the function as the input (x-values) either tends to positive infinity or negative infinity.
In other words, we are interested in how the function behaves when the input values become extremely large or extremely small.
To understand asymptotic behavior, let's consider two types of asymptotes: horizontal and vertical asymptotes.
Horizontal Asymptotes:
A horizontal asymptote is a horizontal line that a function approaches as the x-values become extremely large or extremely small. We usually denote horizontal asymptotes as y = c, where c is a constant.
For example, let's consider the function f(x) = (2x^2 + 3) / (x^2 - 1). As x approaches positive or negative infinity, we can observe the following behavior:
As x becomes extremely large or extremely small, the function becomes closer and closer to the line y = 2. Therefore, we say that y = 2 is a horizontal asymptote for this function.
Vertical Asymptotes:
A vertical asymptote is a vertical line that the function approaches as the x-values approach a particular value. It typically occurs when there is a division by zero or when the function tends to infinity at a specific point.
For example, consider the function g(x) = 1 / (x - 2). As x approaches 2 from either side (but never equal to 2), we can observe the following behavior:
As x approaches 2 from the left (x < 2), the function g(x) becomes increasingly negative, tending towards negative infinity.
As x approaches 2 from the right (x > 2), the function g(x) becomes increasingly positive, tending towards positive infinity.
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The cost of manufacturing a certain type of headphone varies inversely as the number of headphones increases. If 8000 headphones can be manufactured for $8. 00 each, find the cost to manufacture 2000 headphones
The cost to manufacture 2000 headphones as the number of headphones varies inversely with the cost of manufacture is $32
Let x = number of headphones
y = cost of manufacturing headphones
The cost of manufacturing a certain type of headphones is inversely proportional to the number of headphones.
The equation for inversely proportional is
x₁ y₁ = x₂ y₂
x₁ = 8000 , y₁ = 8 , x₂ = 2000 y₂ = ?
Putting the value in the equation we get ,
8000 × 8 = 2000 × y₂
64000/2000 = y₂
y₂ = 32
Cost of manufacturing 2000 headphones is 32 .
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Write the decimal form of 129275775
Answer: 129275775.0
Step-by-step explanation:
129275775.0
whenever there is a whole number, the decimal is at the end of the number.
Nataly compra una falda, una blusa y un saco con los precios de la lista son s/78,s/65 y s/240 pero al pagar la falda se la dejan a s/69,la blusa a s/52 y el sacon a s/198.¿cuánto se ahorró nataly?
Nataly saved s/64.
Nataly compró una falda, una blusa y un saco por s/78, s/65 y s/240, respectivamente. Pero compró la falda por s/69, la blusa por s/52 y el saco por s/198. ¿Cuánto se ahorró Nataly?The original prices for the items are:
Skirt: s/78
Blouse: s/65
Jacket: s/240
The discounted prices Nataly paid are:
Skirt: s/69
Blouse: s/52
Jacket: s/198
To find out how much Nataly saved, we need to calculate the difference between the original prices and the discounted prices, and then add them up:
savings = (78 - 69) + (65 - 52) + (240 - 198)
savings = 9 + 13 + 42
savings = s/64
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A single number cube is rolled twice. The 36 equally-likely outcomes are shown to the right. What is the first step in finding the probability of getting two numbers whose sum is 12? Find the probability of getting two numbers whose sum is 12.
The probability of getting two numbers whose sum is 12 when rolling a single number cube twice is 1/36.
To find the probability of getting two numbers whose sum is 12 when a single number cube is rolled twice, we'll first need to identify the favorable outcomes.
A number cube has six faces, numbered from 1 to 6. When it is rolled twice, there are 6 x 6 = 36 equally-likely outcomes. To find the probability, we can use the formula:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
The first step is to identify the favorable outcomes, which are the pairs of numbers that add up to 12. Since we are dealing with a number cube that has faces numbered 1 to 6, there is only one possible pair that satisfies this condition: (6,6).
Now that we have determined the favorable outcome, we can find the probability:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Probability = 1 (for the pair 6,6) / 36
Thus, the probability of getting two numbers whose sum is 12 when rolling a single number cube twice is 1/36.
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0. 587. Write this value in
scientific notation.
. 0.587 in scientific notation is 5.87 x 10^-1.
Find out the scientific notation of the given value?Scientific notation is a way of writing numbers that are very large or very small in a compact and standardized way. In scientific notation, a number is expressed as a coefficient multiplied by 10 raised to some power.
For example, the number 0.587 can be written in scientific notation as 5.87 x 10^-1. The coefficient 5.87 is obtained by moving the decimal point one place to the right, while the negative exponent -1 indicates that the decimal point has been moved one place to the left, to the tenth place.
Scientific notation is commonly used in scientific and engineering fields where very large or very small numbers are often encountered, and it allows for easier calculation and comparison of these values.
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Use the nth-term test for divergence to show that the series is divergent, or state that the test is inconclusive.
∑ 1/n+13
Using the nth-term test for divergence on the series ∑ 1/n+13 is inconclusive. However, by comparing the series to the divergent harmonic series, we can conclude that ∑ 1/n+13 is also divergent.
We can use the nth-term test for divergence to determine the convergence or divergence of the series
lim n → ∞ (1/n+13) = 0
Since the limit of the nth term is 0, the nth-term test is inconclusive, and we cannot determine the convergence or divergence of the series using this test.
However, we can use the comparison test to show that the series diverges. We can compare the given series to the harmonic series, which we know diverges
1/1 + 1/2 + 1/3 + ...
Since each term of the given series is less than the corresponding term of the harmonic series, the given series must also diverge. Therefore, the series ∑ 1/n+13 is divergent.
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“The mode of a data set is one of the values in the data set.” This statement is ____________.
A hardware store carries 42 types of boxed nails and 36 types of boxed screws. the store manager wants to build a rack so that he can display the hardware in rows. he wants to put the same number of boxes in each row, but he wants no row to contain both nails and screws. what is the greatest number of boxes that he can display in one row? how many rows will there be if the manager puts the greatest number of boxes in each row?
There will be a total of 7 rows for nails and 6 rows for screws, making 13 rows in total.
To solve it, we need to find the greatest common divisor (GCD) of the number of boxed nails (42) and boxed screws (36). This will tell us the greatest number of boxes that can be displayed in one row without mixing nails and screws.
Step 1: List the factors of each number.
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Step 2: Find the greatest common divisor (GCD) by identifying the largest factor they have in common.
- The largest common factor is 6.
So, the greatest number of boxes that can be displayed in one row is 6.
Next, we'll find out how many rows will there be if the manager puts the greatest number of boxes in each row.
Step 3: Divide the total number of boxed nails and boxed screws by the GCD.
- Rows for nails: 42 ÷ 6 = 7
- Rows for screws: 36 ÷ 6 = 6
Therefore, there will be a total of 7 rows for nails and 6 rows for screws, making 13 rows in total.
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70% of a class is at lunch what percentage is still studying?
Answer:
30%
Step-by-step explanation:
If there are only 2 categories:
Students at lunch and students studying, then the whole is 100%
100% - 70% = 30%
Helping in the name of Jesus.
Write (0,15) + (1,5) as a linear function and also as an exponential function
Answer: Linear Function: y = -10x + 15 Exponential Function:
y = 15(1/3)(to the power of x)
Step-by-step explanation:
Linear Function:
First we need to find the slope by using the slope equation: (y2 - y1)/(x2 - x1)
In which, it should be (5 - 15)/(1 - 0)
So, we know that the slope is -10, and we already know that the y-intercept is 15, so, we are going to plug it in to the slope-intercept formula, which is
y = mx + b,
In which, it would become y = -10x + 15
Exponential Function =
The exponential function is y = ab(to the power of x)
Let's list out the points onto the equation, 15 = ab(0) and 5 = ab(1)
Know let's solve for each variable.
1. 15 = ab(0)
2. 15/b(0) = a
3. 15 = a
Know we know that a is 15, we can solve for b.
1. 5 = (15)b(1)
2. 5/15 = b(1)
3. 1/3 = b
Know we know that b is equal to 1/3, let's plug it into the equation.
y = 15(1/3)(to the power of x)
The mean number of days with 0. 01 inch or more precipitation per month for Lewiston, Idaho, is about 8. 7. Find the probability that in a given month
(a) There are exactly 9 days with 0. 01 inch or more precipitation.
(b) There are at most 9 days with 0. 01 inch or more of precipitation.
(c) There are more than 9 days with 0. 01 inch or more of precipitation
We will use the Poisson distribution, which is a probability distribution that models the number of events occurring in a fixed interval of time or space, given the average rate of occurrence and assuming that the events are independent and randomly distributed.
For this problem, we will assume that the number of days with 0.01 inch or more precipitation in Lewiston, Idaho, follows a Poisson distribution with parameter λ = 8.7.
(a) To find the probability that there are exactly 9 days with 0.01 inch or more precipitation, we can use the Poisson probability mass function:
P(X = k) = e^(-λ) * λ^k / k!
where X is the random variable representing the number of days with 0.01 inch or more precipitation, λ is the parameter of the Poisson distribution, and k is the number of events we are interested in.
Plugging in the values, we get:
P(X = 9) = e^(-8.7) * 8.7^9 / 9! ≈ 0.151
Therefore, the probability that there are exactly 9 days with 0.01 inch or more precipitation is approximately 0.151.
(b) To find the probability that there are at most 9 days with 0.01 inch or more precipitation, we can use the cumulative distribution function of the Poisson distribution:
P(X ≤ k) = ∑i=0^k e^(-λ) * λ^i / i!
Plugging in the values, we get:
P(X ≤ 9) = ∑i=0^9 e^(-8.7) * 8.7^i / i! ≈ 0.503
Therefore, the probability that there are at most 9 days with 0.01 inch or more precipitation is approximately 0.503.
(c) To find the probability that there are more than 9 days with 0.01 inch or more precipitation, we can subtract the probability of having 9 or fewer days from 1:
P(X > 9) = 1 - P(X ≤ 9) ≈ 0.497
Therefore, the probability that there are more than 9 days with 0.01 inch or more precipitation is approximately 0.497.
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(a) What is the mean of this stem and leaf plot? Show your work. What is the median of the data? Show your work
The mean of the given stem and leaf plot is 24.5 and the median of the data is 25.
The stem and leaf plot represents the given data as:
| 2 | 4, 5, 6, 9
| 3 | 1, 4, 5, 5, 7, 8
| 4 | 2, 5, 7, 8, 9
To find the mean, we need to add up all the values and divide by the total number of values.
Mean = (24 + 25 + 26 + 29 + 31 + 34 + 35 + 35 + 37 + 38 + 42 + 45 + 47 + 48 + 49) / 15
= 367 / 15
= 24.5
To find the median, we need to arrange the data in order and find the middle value. As there are 15 data points, the median will be the average of the 8th and 9th data points.
Data in order: 24, 25, 25, 26, 29, 31, 34, 35, 35, 37, 38, 42, 45, 47, 48
Median = (35 + 37) / 2
= 36.
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A new laptop is on sale for $550 dollars. To pay for it you place it on your credit card which charges 12% percent interest each month. Complete the table to determine the total cost of the laptop each month if you make no payments
To determine the total cost of the laptop each month if you make no payments, we need to calculate the balance on the credit card after each month, including the simple interest charged.
Starting balance = $550
Month Balance Interest Total Cost
0 $550 $0 $550
1 $616 $66 $616 + $66 = $682
2 $689.92 $73.92 $689.92 + $73.92 = $763.84
3 $770.15 $80.23 $770.15 + $80.23 = $850.38
4 $857.09 $86.94 $857.09 + $86.94 = $944.03
5 $951.19 $94.10 $951.19 + $94.10 = $1045.29
To calculate the balance for each month, we multiply the previous balance by 1.12, which represents the 12% interest charged. For example, for month 1, the balance is $550 * 1.12 = $616.
To calculate the interest charged each month, we subtract the previous balance from the new balance. For example, for month 1, the interest charged is $616 - $550 = $66.
To calculate the total cost each month, we add the new balance to the interest charged.
For example, for month 1, the total cost is $616 + $66 = $682.
Note that if you make no payments on the credit card, the balance will continue to grow each month due to the interest charged.
It is always advisable to make at least the minimum payment each month to avoid high interest charges and potential late fees.
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If using the method of completing the square to solve the quadratic equation x^2+4x+3=0x
2
+4x+3=0, which number would have to be added to "complete the square"?
If using the method of completing the square to solve the quadratic equation number 1 be added to both side of the equation to be added to "complete the square".
An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. The requirement that the coefficient of x² be a non-zero term (a 0) is necessary for an equation to qualify as a quadratic equation. The x² term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term.
Add 1 to both sides of the equation to get:
[tex]x^2+4x+4=1[/tex]
The left hand side is now a perfect square:
[tex]x^2+4x+4=(x+2)^2[/tex]
So we have:
[tex](x+2)^2=1[/tex]
Hence:
[tex]x+2=\pm\sqrt{1} =\pm1[/tex]
Subtract 2 from both ends to get:
x = -2 ± 1
That is:
x = -3 or x = -1.
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Simon bought a 10-pound bag of cat food. he give 0.3 pounds of food per day. write an equation in two variables to describe how the amount of cat food in the bag changes over time. explain variable in your equation represent
The equation in two variables that describes how the amount of cat food in the bag changes over time is: A = 10 - 0.3t
Where A represents the amount of cat food left in the bag after t days, and t represents the number of days that have passed since Simon bought the bag.
The variable A is the dependent variable because it depends on the value of t. As time passes and t increases, the amount of cat food left in the bag decreases. The variable t is the independent variable because it is the input that determines the value of A.
For example, after one day (t = 1), Simon will have used 0.3 pounds of cat food and there will be 9.7 pounds left in the bag (A = 10 - 0.3(1) = 9.7). After two days (t = 2), he will have used 0.6 pounds of cat food and there will be 9.4 pounds left in the bag (A = 10 - 0.3(2) = 9.4), and so on.
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A compound event may consist of two dependent events.
A. True
B. False
A. True. A compound event may consist of two dependent events. Dependent events are those in which the outcome of the first event affects the outcome of the second event. For example, drawing a card from a deck and not replacing it before drawing a second card would be an example of dependent events.
W X Y Z is a kite. Find the measure of angle W.
The measure of angle W in the kite WXYZ is 0 degrees.
To find the measure of angle W in the kite WXYZ, we can use the properties of kites. In a kite, the two opposite angles formed by the intersection of the diagonals are equal. Let's denote the measure of angle W as "x."
Step 1: Start with the given information that WXYZ is a kite.
Step 2: Recall that the diagonals of a kite intersect at right angles. Let's label the intersection point of the diagonals as point P.
Step 3: Draw the diagonals WX and YZ, which intersect at point P.
Step 4: Recognize that angles WXP and ZYP are congruent. Therefore, the measure of angle WXP is also x.
Step 5: Observe that the sum of the angles in a triangle is 180 degrees. Since triangle WXP is a triangle, we can write the equation: x + 90 + 90 = 180.
Step 6: Simplify the equation: x + 180 = 180.
Step 7: Subtract 180 from both sides: x = 0.
Step 8: Analyze the result. The measure of angle W, denoted by x, is equal to 0 degrees.
Therefore, the measure of angle W in the kite WXYZ is 0 degrees.
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For numbers 5-7, use the properties of exponents to determine what numbers should
replace each variable written as an exponent below that will make the equations true.
57.5b=53
5.
X =
8².8-811
=
6.
b=
7.
n=
x12.x = x12
12
Using the properties of exponents:
5. The value of x is 9
6. The value of b is -4
7. The value of n is 0
Calculating exponentsFrom the question, we are to calculate the value of the exponent in each question
5.
8² · 8ˣ = 8¹¹
Applying the multiplication law of indices, this can be written as
8² ⁺ ˣ = 8¹¹
Equate the powers
2 + x = 11
Solve for x by subtracting 2 from both sides
2 - 2 + x = 11 - 2
x = 9
6.
5⁷ · 5ᵇ = 5³
Applying the multiplication law of indices, this can be written as
5⁷ ⁺ ᵇ = 5³
Equate the powers
7 + b = 3
Solve for b by subtracting 7 from both sides
7 - 7 + b = 3 - 7
b = -4
7.
x¹² · xⁿ = x¹²
Applying the multiplication law of indices, this can be written as
x¹² ⁺ ⁿ = x¹²
Equate the powers
12 + n = 12
Solve for n by subtracting 12 from both sides
12 - 12 + n = 12 - 12
n = 0
Hence, the value of n is 0
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9 Real / Modelling Naomi rents a room to teach yoga to x people.
She uses this equation to work out her profit, y, in pounds:
y = 10x - 50
a Draw the graph of the line y = 10x - 50.
b i What is her profit when 0 people attend the class?
ii What does the y-intercept represent?
c How much does each person pay for the class?
Her profit when 0 people attend is -$50 and each person pays 10
Drawing the graph of the lineFrom the question, we have the following parameters that can be used in our computation:
y = 10x - 50.
The graph is added as an attachment
Her profit when 0 people attendThis means that
x = 0
So, we have
y = 10(0) - 50.
y = -50
She made a loss of 5-
What the y-intercept representsThis represents her profit when 0 people attend
How much each person pays per classThis represents the slope of the function
The slope of the function is 10
So, each person pays 10
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A bottle holds 24 ounces of water. It has x ounces of water in it.
What does 24 - x represent in this situation?
Write a question about this situation that has 24 − x for the answers.
Answer:
24 - x would mean the air, or empty space in the bottle not being used by the water in the bottle.
Question:
"Create an equation that shows how much space is not taken up by water in a 24 once water bottle if it currently has x ounces of water."
OR
"A standing garden bed has x cubic feet in the box. It can hold 24 cubic feet, counting from the bottom to very top. How much empty space is there from the top of the dirt in the box to the very top of the box?"