a. The cost of renting the gym and paying for supplies, which is $300. b. $10, c. y = 10x - 300 d. $200 e. 30 tickets f. the slope of the line is 1/6.
Describe Linear Equation?The slope of a line is the ratio of the change in the y-coordinate to the change in the x-coordinate. It represents the rate of change of the line. A positive slope indicates that the line is increasing, while a negative slope indicates that the line is decreasing. A slope of zero indicates that the line is horizontal.
The y-intercept is the point where the line crosses the y-axis. It represents the value of y when x is equal to zero.
Linear equations can be solved algebraically or graphically. In algebra, the goal is to isolate the variable and find its value. In graphing, the equation is plotted on a coordinate plane and the solution is the point where the line intersects with the x- or y-axis.
a. The constant in this situation is the cost of renting the gym and paying for supplies, which is $300.
b. The rate in this situation is the cost per ticket, which is $10.
c. Let x be the number of tickets sold and y be the total profit. The linear equation that represents this situation is:
y = 10x - 300
d. If Amanda sells 50 tickets, then the profit is:
y = 10(50) - 300 = $200
e. To break even, the profit must be 0. So we can set y = 0 and solve for x:
0 = 10x - 300
10x = 300
x = 30
Therefore, Amanda needs to sell 30 tickets to break even.
f. The graph of the linear equation is:
graph{y=10x-300 [-10, 50, -500, 500]}
To calculate the slope of a line that goes through points (10, 6) and (-2, 4), we can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
Substituting the given values, we get:
slope = (4 - 6) / (-2 - 10) = -2 / -12 = 1/6
Therefore, the slope of the line is 1/6.
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Sketch the qraphs. 2x+3y=1
Answer:
y = -2/3x + 1/3
Step-by-step explanation:
2x + 3y = 1
3y = -2x + 1
y = -2/3x + 1/3
To sketch:
Pretend x is 3. y would be -1 2/3.
Now that you have this point, draw through the point (0, 1/3).
There ya go
Please help me I need this
of six dvd players, two are defective and four are not. if cecil randomly chooses two of these dvd players, without replacement, the probability that the two he chooses are not defective is , what is the value of ??
The probability of selecting two non-defective DVD players from a group of six is 2/5. This is based on the assumption that the selection is done without replacement.
We can use the formula for calculating probabilities of combinations:
P(not defective) = number of ways to choose 2 non-defective DVD players / total number of ways to choose 2 DVD players
Total number of ways to choose 2 DVD players out of 6 is:
C(6,2) = 6! / ([2!] [4!]) = 15
Number of ways to choose 2 non-defective DVD players out of 4 is:
C(4,2) = 4! / ([2!] [2!]) = 6
Therefore, the probability that Cecil chooses 2 non-defective DVD players is:
P(not defective) = 6/15 = 2/5
So the value of P(not defective) is 2/5.
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How do I work this out
Therefore, the equation of the line is y = 6x + 1, in slope-intercept form.
What is equation?In mathematics, an equation is a statement that shows the equality of two expressions. An equation usually contains one or more variables, which represent unknown values that we are trying to solve for. Equations can also be more complex, involving multiple variables and operations such as exponents, logarithms, and trigonometric functions. Solving equations is an important part of mathematics, and has many practical applications in science, engineering, and everyday life.
Here,
The equation of a straight line in slope-intercept form is y = mx + b, where m is the gradient (or slope) of the line, and b is the y-intercept (where the line crosses the y-axis). We are given that the gradient of the line is 6, and that it passes through the point (3, 19). We can use this information to find the equation of the line. First, 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 (3, 19) with a gradient of 6. The point-slope form is:
y - y1 = m(x - x1)
where (x1, y1) is the point the line passes through, and m is the slope of the line.
Substituting the values we know, we get:
y - 19 = 6(x - 3)
Expanding the brackets, we get:
y - 19 = 6x - 18
Adding 19 to both sides, we get:
y = 6x + 1
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In GeoGebra, display the measure of the circumscribed angle, ∠ECD. To explore the relationship between the central angle and the circumscribed angle, move point B to different locations on the coordinate plane anywhere between A and C. Find m∠ECD + m∠EAD for five different data sets, and fill in the table.
The sum of the circumscribed angle m∠ECD and central angle m∠EAD for five different data sets are 90°, 90°,120°,150°,180°.
What is central angle?A central angle is an angle in a circle that has its vertex at the center of the circle. Its arms, which are the two rays that make up the angle, both pass through points on the circumference of the circle.
m∠ECD m∠EAD m∠ECD + m∠EAD
45° 45° 90°
60° 30° 90°
100° 20° 120°
140° 10° 150°
180° 0° 180°
The measure of the circumscribed angle, ∠ECD, is the angle formed by the intersection of two lines, AB and CD.
The measure of the central angle, ∠EAD, is the angle formed by the intersection of the lines AB and ED.
The relationship between the circumscribed angle and the central angle can be explored by moving point B to various different locations on the coordinate plane between A and C.
By doing so, both the circumscribed angle and the central angle can be measured.
From the table above, it can be seen that the sum of the measures of the circumscribed angle and the central angle is always equal to 90°.
This is because the circumscribed angle and the central angle are supplementary angles, meaning that the sum of their measures always equal to 180°.
In this case, since the sum of the measures of the circumscribed angle and the central angle is always equal to 90°, the measures of the circumscribed angle and the central angle themselves must always add up to 90°.
Since the sum of the measures of the circumscribed angle and the central angle is always equal to 90°, the measures of the circumscribed angle and the central angle themselves must always add up to 90°.
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A stock investment was worth $1569 in the year 2000, and the stock grew steadily by 4.6% every year. Write a function to model the value of the stock t years since 2000.
V = __
Therefore , the solution of the given problem of function comes out to be growth factor resulting from the 4.6% yearly growth rate is represented by the constant factor e(0.046t).
What does the term function actually mean?On the midterm exam, there will be inquiries on design, arithmetic numbers, every class, and both actual and hypothetical places. a description of the connections between various components that come together to produce the same outcome. A service is built from a variety of unique parts that work together to deliver unique outcomes for each input. Each post also has a location, which might be the enclave, a municipality, or even something else altogether.
Here,
The value of the stock t years since 2000 can be represented by the function by assuming that the stock's value increases constantly at a rate of 4.6% per year:
=> V(t) = 1569 * e^(0.046t)
where t is the number of years since the year 2000 and e is the algebraic constant
=>e = 2.71828.
With this function, exponential growth is represented by multiplying the stock's starting value in the year 2000 (1569) by the constant factor e(0.046t) to get the value of the stock t years later.
The growth factor resulting from the 4.6% yearly growth rate is represented by the constant factor e(0.046t).
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Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle B?
simple smoothing time period actual series forecast series forecast error 1 100 100 0 2 110 3 115 if a smoothing constant of .3 is used, what is the exponentially smoothed forecast for period 4? multiple choice 106.6. 103.0. 115.0. 104.4. 112.6.
The exponentially smoothed forecast for period 4 is 106.6.
As per given information,
Time period Actual series Forecast series Forecast error 1 100 100 0 2 110 3 115
Smoothing constant α=0.3
For calculating exponentially smoothed forecast for period 4,
First, we need to calculate exponentially smoothed forecast for period 2.
Smoothed forecast for period 2 = α (Actual demand for period 1) + (1-α) (Smoothed forecast for period 1)
= 0.3 (100) + (0.7) (100)= 30 + 70= 100
Next, we can calculate exponentially smoothed forecast for period 3.
Smoothed forecast for period 3 = α (Actual demand for period 2) + (1-α) (Smoothed forecast for period 2)
= 0.3 (110) + (0.7) (100)
= 33 + 70
= 103
Now, we can calculate exponentially smoothed forecast for period 4.
Smoothed forecast for period 4 = α (Actual demand for period 3) + (1-α) (Smoothed forecast for period 3)
= 0.3 (115) + (0.7) (103)= 34.5 + 72.1
= 106.6
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What is the volume of a sphere with a radius of 60.5ft
Answer: V ≈ 927,587
Step-by-step explanation:
Formula for volume of a sphere:
V = [tex]\frac{4}{3}[/tex]πr³
Substitute the known value for radius:
V = [tex]\frac{4}{3}[/tex]π(60.5ft)³
Simplify:
V ≈ 927,587
in a batch of 100 cell phones, there are, on average, 6 defective ones. if a random sample of 25 is selected, find the probability of 4 defective ones
The probability of 4 defective cell phones in a sample of 25 can be found using the binomial probability formula and is equal to 0.0263.
What is probability?Probability is a branch of mathematics that deals with calculating the likelihood of a given event occurring. In probability, we calculate the number of ways an event can happen and divide it by the total number of possible outcomes.
Probability ranges from 0 to 1, with 0 indicating no chance of occurrence and 1 indicating that the event will definitely occur.
What is the binomial probability formula?If there are only two possible outcomes in a given event, the binomial probability formula is used to calculate the probability of the event happening.
The binomial probability formula is given by: P(X = x) = (nCx)px(1 - p)n - x
Where, P(X = x) is the probability of x successes in n trials
nCx is the number of ways x successes can occur in n trials
px is the probability of a single success in a given trial(1 - p)n - x is the probability of the remaining trials being failures.
How to solve the problem?The probability of 4 defective cell phones in a sample of 25 can be calculated using the binomial probability formula.
P(X = 4) = (25C4)(0.06)4(0.94)21 = 0.0263.
Therefore, the probability of 4 defective cell phones in a sample of 25 is 0.0263.
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Help me with these please!!
The properties of a parallelogram indicates that the variables in the segments and angles are;
b = 1, a = 3x = 15, y = 50x = 18, y = 9x = 2, y = 4.5What is a parallelogram?A parallelogram is a four sided figure with two pairs of sides that are parallel.
Whereby the figures are parallelogram, we get;
The length of the opposite sides are the same, therefore;
1. b + 1 = 2·b
1 = 2·b - b = b
1 = b
b = 1 (symmetric property)
3·a - 4 = a + 2
3·a - a = 4 + 2
2·a = 6
a = 6/2 = 3
a = 3
2. The opposite angles of a parallelogram are congruent, therefore;
(y + 10)° = (2·y - 40)°
10 + 40 = 2·y - y = y
50 = y
y = 50
The adjacent interior angles of a parallelogram are supplementary, therefore;
(4·x)° + (2·y - 40)° = 180°
(4·x)° + (2 × 50 - 40)° = 180°
(4·x)° = 180° - (2 × 50 - 40)° = 60°
x = 60°/4 = 15°
x = 15
3. The diagonals of a parallelogram bisect each other, therefore;
y + 3 = 12
y = 12 - 3 = 9
y = 9
x - 3 = 15
x = 15 + 3 = 18
x = 18
4. The diagonals of a parallelogram bisect each other therefore;
x + 6 = 4·x
4·x = x + 6
4·x - x = 6
3·x = 6
x = 6/3 = 2
x = 2
5·y - 8 = 3·y + 1
5·y - 3·y = 1 + 8 = 9
2·y = 9
y = 9/2 = 4.5
y = 4.5
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PLSSSS HELP IF YOU TURLY KNOW THISSS
Given:-
[tex] \tt \: 3x = 12[/tex][tex] \: [/tex]
Solution:-
[tex] \tt \: 3x = 12[/tex][tex] \: [/tex]
[tex] \tt \: \: x = \cancel{ \frac{12}{3} }[/tex][tex] \: [/tex]
[tex] \boxed{ \tt{ \green{ \: x = 4 \: }}}[/tex][tex] \: [/tex]
__________________
hope it helps ⸙
Question 5(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
0 5
1 0, 3, 7
2 4, 6, 8
3 2
4
5 8
Key: 5|8 means 58
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.
Question 6(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The line plot displays the cost of used books in dollars.
A horizontal line starting at 1 with tick marks every one unit up to 9. The line is labeled Cost in Dollars, and the graph is titled Cost of Used Books. There are two dots above 1, 2, 3, 5, and 6. There are four dots above 7.
Which measure of center is most appropriate to represent the data in the graph, and why?
The median is the best measure of center because there are no outliers present.
The median is the best measure of center because there are outliers present.
The mean is the best measure of center because there are no outliers present.
The mean is the best measure of center because there are outliers present.
Therefore, the correct answer is: The range is the best measure of variability, and it equals 78.
What is range?Range is a measure of variability that represents the difference between the maximum and minimum values in a dataset. It gives an indication of how spread out the data is. To find the range of a dataset, you simply subtract the minimum value from the maximum value. Range is often used as a quick and simple measure of variability, but it can be sensitive to outliers and extreme values.
Here,
1. For question 5, the appropriate measure of variability for the given data set is the range, which is the difference between the maximum value and the minimum value in the data set.
To find the maximum and minimum values from the given stem-and-leaf plot, we can look at the highest and lowest digits in each row. The highest value is 83 and the lowest value is 5, so the range is:
Range = 83 - 5 = 78
2. For question 6, the appropriate measure of center to represent the data in the given line plot is the median, because the data is skewed to the right and there are outliers present. The median is less sensitive to outliers than the mean.
Therefore, the correct answer is: The median is the best measure of center because there are outliers present.
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WILL GIVE BRIANLIST TO BEST ASNWWR
Richard buys a new car for $28,000. The car depreciates in value by 9% each year. Which of the following uses the variable y to represent the value of the car after t years in an exponential model to represent the situation?
y=28,000(1.09)
y=28,000(91)
y-28,000(-9)
y=28,000(0.09)
The variable y is used to represent the worth of the car after t years like an exponential model to reflect the scenario, and the third option, y=28,000(0.91)t, is the correct response.
The formula for the exponential model is what?A = A0(b)t/c is the formula for an exponential model, where A0 denotes the starting quantity of the thing being modeled. t stands for passing time. The quantity at time t is equal to A.
The exponentially decaying formula for an asset's value over time with such a consistent rate of depreciation is: y = a(1-r)t
Where:
Y is equal to the car's value after t years.
In this scenario, the car's original value is $28,000, and its rate of depreciation is 9%, or 0.09 in decimal notation.
t equals the amount of years
The exponential model can be expressed using the following formula: y = 28,000(1-0.09)t
By condensing the formula, we obtain the following result: y = 28,000(0.91)t
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what is the cop of a carnot refrigerator, when t(cold) is 275 k and t(hot) is 158 c?(write as a fraction, not a percent)
In the following question, among the conditions given, the cop of a Carnot refrigerator, when t(cold) is 275 k and t(hot) is 158 c. Then the COP of the Carnot refrigerator is 1.76 (written as a fraction "88/50").
The COP of a Carnot refrigerator is calculated as: COP = T(Cold) / (T(Hot) - T(Cold))The COP of a Carnot refrigerator is given by the formula:
COP = T(Cold) / (T(Hot) - T(Cold))Where T(Cold) is the temperature of the cold reservoir and T(Hot) is the temperature of the hot reservoir.
T(Cold) = 275 K and T(Hot) = 158 °C = 431 K By substituting these values into the formula: COP = 275 / (431 - 275)COP = 275 / 156COP = 1.76 The COP of the Carnot refrigerator is 1.76 (written as a fraction 88/50).
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how do u sovle Find x .
Two non-congruent parallelograms. The width and length of one parallelogram are marked 4 centimeters and 6 centimeters respectively. The width and length of the other parallelogram are marked 6 centimeters and x respectively.
The length of the second parallelogram is 2 cm.
What are parallelograms ?
A parallelogram is a quadrilateral with opposite sides parallel and equal in length. It has two pairs of parallel sides and opposite angles are equal. Some common properties of parallelograms include:
According to the question:
To solve for x, we need to use the fact that opposite sides of a parallelogram are equal in length.
For the first parallelogram, we know that the width is 4 cm and the length is 6 cm. Therefore, the opposite side lengths are also 4 cm and 6 cm.
For the second parallelogram, we know that the width is 6 cm. Since the opposite sides are equal in length, the length of the parallelogram must be x cm.
So, we have:
Width of first parallelogram = Width of second parallelogram
4 cm = 6 cm
Length of first parallelogram = Length of second parallelogram
6 cm = x cm
Simplifying the first equation, we get:
2 cm = x
Therefore, the length of the second parallelogram is 2 cm.
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Kevin is hiking on a trail that is 4. 9 miles long. So far, he has hiked 90% of the total distance. How many more miles does Kevin have to hike in order to complete the trail? Complete the explanation on how you found your answer. Part 1 out of 2 Kevin has to hike more miles in order to complete the trail
Kevin has 0.49 miles, or approximately 0.5 miles, left to hike in order to complete the trail.
Kevin has hiked 90% of the trail, which means he still has to hike 10% of the trail to complete it. To find out how many miles he has left to hike, we can use the proportion:
10/100 = x/4.9
where x represents the number of miles Kevin has left to hike.
To solve for x, we can cross-multiply and simplify:
10 * 4.9 = 100x
49 = 100x
x = 49/100
x = 0.49
Therefore, Kevin has 0.49 miles, or approximately 0.5 miles, left to hike in order to complete the trail.
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Complete Question:
Kevin is hiking on a trail that is 4. 9 miles long. So far, he has hiked 90% of the total distance. How many more miles does Kevin have to hike in order to complete the trail?
ten chairs are arranged in a circle. find the number of subsets of this set of chairs that contain at least three adjacent chairs.
Ten chairs are arranged in a circle. The number of subsets of this set of chairs that contain at least three adjacent chairs is 310.
The given that 10 chairs arranged in a circle.
Now we have to find the number of subsets of this set of chairs that contain at least three adjacent chairs.
To solve this, we can use the concept of permutations and combinations. The first step is to consider the number of ways in which three chairs can be selected and arranged in a subset that is adjacent to each other.
This can be done in 10 different ways, as there are 10 chairs in total and we can select any one of them as the starting point.
The next step is to consider the number of ways in which we can add additional chairs to this subset. For example, we can add a fourth chair to the subset in two different ways: either to the left of the first chair or to the right of the third chair.
Similarly, we can add a fifth chair to the subset in four different ways, a sixth chair in six different ways, and so on. Using this logic, we can create the following table:
Length of subset number of ways to select the subset number of ways to add chairs
Total number of subsets31 (adjacent)
= 10 ---43 (adjacent) 10*2
=20---55 (adjacent)10*4
=40---67 (adjacent)10*6
=60---79 (adjacent)10*8
=80---810 (adjacent)10*10
=100---
As we can see from the table, the total number of subsets that contain at least three adjacent chairs is given by:
Total number of subsets = 10 + 20 + 40 + 60 + 80 + 100
= 310
Therefore, the number of subsets of this set of chairs that contain at least three adjacent chairs is 310.
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the procedure used to obtain your sample (i.e., random or nonrandom sampling) is not the same as the procedure for assigning participants to conditions; distinguish between random sampling and random assignment.
Random sampling is used to ensure that the sample is representative of the population, while random assignment is used to control for extraneous variables and increase the internal validity of the study.
Random sampling and random assignment are two distinct procedures that are often used in research studies, and it's important to understand the difference between them.
Random sampling refers to the process of selecting individuals or units from a larger population in such a way that every member of the population has an equal chance of being included in the sample. Random sampling is used to ensure that the sample is representative of the population and that the results can be generalized to the larger population.
Random assignment, on the other hand, refers to the process of assigning participants to different experimental conditions in a way that is completely random. This means that every participant has an equal chance of being assigned to any condition. Random assignment is used to control for extraneous variables that could influence the results of the study. By randomly assigning participants to conditions, researchers can be more confident that any differences observed between the groups are due to the manipulation of the independent variable, rather than pre-existing differences between the participants.
In summary, random sampling is used to ensure that the sample is representative of the population, while random assignment is used to control for extraneous variables and increase the internal validity of the study.
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Determine the intercept of the line
4x-3y=17
Answer:
x = 17/4, or 4.25
The x-intercept is (4.25, 0)
Step-by-step explanation:
We can get the intercepts by isolating x and y.
4x - 3y = 17
Subtract 4x from both sides.
-3y = -4x + 17
Divide both sides by -3.
y = 4/3x - 17/3
Input 0 for x.
y = -17/3
The y-intercept is (0, -17/3)
4x - 3y = 17
Add 3y to both sides.
4x = 3y + 17
Divide both sides by 4.
x = 3/4y + 17/4
Input 0 for y.
Jessie is painting a cardboard box for a school project and needs to know much paint she needs to cover the box.
A prism has a length of 10 inches, height of 6 inches, and width of 4 inches.
Which statement is correct about the amount of paint Jessie needs to cover the whole box?
A. Jessie should use surface area to find out she needs to cover 240 in.2 of the cardboard box with paint.
B. Jessie should use surface area to find out she needs to cover 248 in.2 of the cardboard box with paint.
C. Jessie should use volume to find out she needs to cover 240 in.3 of the cardboard box with paint.
D. Jessie should use volume to find out she needs to cover 248 in.3 of the cardboard box with paint.
help 100pts + brlnst
Option (C) is correct which is "Jessie should use volume to determine that the cardboard box requires 240 in3 of paint."
What is volume?The measurement of three-dimensional space is volume.
It is typically quantified using a variety of imperial or US-standard units as well as SI-derived units.
The concept of length and volume are related.
Volume is the three-dimensional space inhabited by matter or encompassed by a surface, and it is measured in cubic units.
The SI unit of volume is the cubic meter (m³), which is a derived unit.
So, the volume would be:
length x breadth x height
Step 1 : substitute the values given
Step 2 : 10 x 4 x 6
Then, we got: 240 inches
Therefore, option (C) is correct which is "Jessie should use volume to determine that the cardboard box requires 240 in3 of paint."
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Answer:
c
Step-by-step explanation: I was correct
calculate the amount of heat produced, in kj, when 52.40 g of methane, ch4, burns in an excess of air, according to the following equation.
Therefore, the amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air is -39568.2 kJ
The amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air can be calculated using the following equation:
[tex]Q = mcΔT[/tex]
Where Q is the amount of heat produced (in kJ), m is the mass of the methane (in g), and ΔT is the change in temperature (in K).
Using the equation, the amount of heat produced can be calculated as follows:
Q = [tex](52.40 g)(-753.15 K) = -39568.2 kJ[/tex]
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Help please hurry
Maria spins a penny 100 times and it lands head side up 62 times. Explain why Maria's experimental probability may be different from the theoretical probability of spinning a coin. (10 points)
Answer:
To solve the question we shall proceed as follows:
Theoretical probabilities generally deals with the nature of the experiment and events, this differs from the experimental probabilities relies on the fact of actual occurrence of the experiment and the events. In other words, experimental probability is an estimate simply based on the probabilities that cannot at all be determined by simple logic. It is the ratio of the number of times an event is occurring to the total number of times or trials that an activity has been repeated for.
From the question, the experimental probability will be:
62/100
=0.62
this differs with theoretical probability which states that at any occasion the probability of the coin coming up heads when tossed is 1/2
Step-by-step explanation: I really hope this helps!! :))). Mark me brainliest!! :))
Xavier receives a paycheck of $2250. First, he spends 20% of his paycheck to buy a new mattress. Then, he spends 29 of the remaining amount to fix a leak in his kitchen. After Xavier pays these two expenses, how much will be left over from his paycheck?
Answer:
Step-by-step explanation:
he's rich
Xavier will have $1278 left over from his paycheck after spending 20% on a new mattress and 29% on fixing a leak.
Explanation:To find out how much will be left over from Xavier's paycheck after he spends 20% on a new mattress and 29% on fixing a leak, we can follow these steps:
Calculate 20% of $2250, which is $450.Subtract $450 from $2250 to find the remaining amount after buying the mattress, which is $1800.Calculate 29% of $1800, which is $522.Subtract $522 from $1800 to find the amount left over after fixing the leak, which is $1278.Therefore, Xavier will have $1278 left over from his paycheck.
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4x = 28 I need help with this.
Answer:
x=7
Step-by-step explanation:
28/4 = 7
Answer:x=7
Step-by-step explanation:
Use the rational zeros theorem to find all the real zeros of the polynomial function. use the zeros to factor f over the real numbers. f(x)=x^3-5x^2-61x-55???
The polynomial function f(x) = x³ - 5x² - 61x - 55 has the following
Real zeros: x = -5, x = -1, and x = 11.
To find the rational zeros of a polynomial, we use the rational zeros theorem. We look at the factors of the leading coefficient and the factors of the constant coefficient.
The states that if a polynomial function is defined as P(x) = anxn + an-1xn-1 + ... + a1x + a0 with integers, then each rational zero of the polynomial can be expressed in the form p/q where p is a factor of a0 and q is a factor of an.
For example, if P(x) = 2x³ - 5x² + 3x + 6 then p can be any factor of 6 and q can be any factor of 2.
The factors of the leading coefficient, 1, and the factors of the constant coefficient, -55, are: ±1, ±5, ±11, ±55. So the possible rational zeros are: ±1, ±5, ±11, ±55, ±1/1, ±5/1, ±11/1, ±55/1, ±1/1, ±5/1, ±11/1, ±55/1.
Simplifying the results, we have that the potential rational zeros are: ±1, ±5, ±11, ±55, ±1, ±5, ±11, and ±55.
By testing each possible rational zero, we find that x = -5, x = -1, and x = 11 are the real zeros of f(x).
Hence, using synthetic division, we get:
(x + 5)(x + 1)(x - 11) = x³ - 5x² - 61x - 55
Thus, the function can be factored over the real numbers as
f(x) = (x + 5)(x + 1)(x - 11).
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Franklin is an ecologist monitoring the catfish population in Athena Lake each year. When he first started monitoring the population one year ago, he estimated that there were 800 catfish in the lake. Today, Franklin estimates the population has decreased to 760 and it will continue decreasing each year.
I am a triangle
My base is 32
My second base is two times for the first base
My hight is 21.6
What is my area?
Answer: The area of a triangle is 1036.8 square units.
To find the area of a triangle, we can use the formula
Area = (1/2) * base * height
In this case, we are given that the first base is 32 and the second base is twice the first base, or 2*32 = 64. The height is given as 21.6. Therefore, we can plug these values into the formula and solve for the area:
Area = (1/2) * (32 + 64) * 21.6
Area = (1/2) * 96 * 21.6
Area = 1036.8
Therefore, the area of the triangle is 1036.8 square units.
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Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h.
A. h(-3) = -1
B. h(13) = 18
C. h(2) = 16
D. h(8) = 21
The statement that could be true for h for given function is Option C h(2) = 16 is correct.
What is Domain?The set of all potential values for the independent variable (typically designated as x) for which the function is specified is known as the domain of a function. In other terms, it refers to the entire set of input values for which a function returns a result.
We can state that for any value of x between -3 and 11, the corresponding value of h(x) will be between 1 and 25 because the function h has a domain of -3 x 11 and a range of 1 h(x) 25.
Indicates that the function h is not fixed and that its values change depending on the value of x.
Now, evaluate your options:
Option A h(-3) = -1 - This statement is false because the range of h(x) is stated to be between 1 and 25, so h(-3) cannot be less than 1.
OptionB h(13) = 18 - This statement cannot be true because h(x) is specified to have a range between -3 and 11, so h(13) is not defined.
OptionC h(2) = 16 - The statement may be accurate given that the value of h(x) for any x between -3 and 11 could range from 1 to 25, and there is no evidence to the contrary.
OptionD h(8) = 21 - Since we know that h(8) = 19, this assertion is false.
Therefore, the statement that could be true for h is: h(2) = 16
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you are placing 11 different pictures on separate pages of a photo album. how many different ways can you order the 11 pictures in the album?
The number of different ways to order 11 different pictures in a photo album is 39,916,800.
To calculate this number, we can use the formula for permutations, which is:
n! / (n - r)!
where n is the total number of items to choose from (in this case, 11 pictures) and r is the number of items to be selected (also 11, since we want to order all the pictures).
Plugging in the values, we get:
11! / (11 - 11)! = 11! / 0! = 11!
We can simplify 11! as:
11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Using a calculator or by hand, we can find that 11! equals 39,916,800.
Therefore, there are 39,916,800 different ways to order 11 different pictures in a photo album.
Hence, the number of ways to order 11 pictures in a photo album can be calculated using the permutation formula, which gives a total of 39,916,800 possible arrangements.
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