The area of a figure in the shape of a parallelogram is 74.4 m2 . If the height of the parallelogram is 6 m, the length of the parallelogram is 12.4 meters.
Describe Parallelogram?A parallelogram is a four-sided plane figure with opposite sides parallel and equal in length. It is a special type of quadrilateral, which is a polygon with four sides.
The opposite sides of a parallelogram are parallel, which means they have the same slope and never intersect. The opposite sides are also equal in length, which means they have the same distance between them.
The adjacent angles of a parallelogram are supplementary, which means they add up to 180 degrees. This property is known as the parallelogram law, which states that the sum of the squares of the diagonals of a parallelogram equals the sum of the squares of its sides.
The area of a parallelogram can be calculated by multiplying the base by the height. The base is one of the parallel sides, and the height is the perpendicular distance between the base and the opposite side.
The area (A) of a parallelogram is given by the formula:
A = base x height
where the base is the length of one of the sides of the parallelogram and the height is the perpendicular distance between the base and the opposite side.
In this problem, we are given the area of the parallelogram as 74.4 m² and the height as 6 m. Let the length of the parallelogram be denoted by b. Then, we can use the formula for the area of a parallelogram to write:
74.4 m² = b x 6 m
Solving for b, we get:
b = 74.4 m² / 6 m
b = 12.4 m
Therefore, the length of the parallelogram is 12.4 meters.
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5. Jay cuts identical squares from the corners of a
rectangular sheet of paper as shown in the adjoining
figure. Find the area of remaining portion.
The area of the remaining portion of the sheet is -4x² + 12x + 6.
How to find the area of a figure?Jay cuts identical squares from the corners of a rectangular sheet of paper as shown in the adjoining figure.
Therefore, the area of the remaining portion can be found as follows:
area of the rectangle = 3(4x + 2)
area of the rectangle = 12x + 6
Therefore,
area of each square cut out = x²
area of the 4 square cut out = 4x²
Therefore,
area of the remaining portion = 12x + 6 - 4x²
area of the remaining portion = -4x² + 12x + 6
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At a recent baseball game of 5,000 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Mustard Chili
63 27 60
Based on the data in this sample, how many of the people in attendance would prefer mustard on a hot dog?
900
2,000
2,100
4,000
Answer:
We can estimate that 900 people in attendance would prefer mustard on a hot dog.
Step-by-step explanation:
What is proportion?
Proportion is a mathematical concept that refers to the relationship between two quantities, expressed as a ratio or a fraction. It represents the size of one quantity relative to another quantity, typically within a larger population or sample.
To determine the number of people who would prefer mustard on a hot dog, we need to use the proportion of people in the sample who prefer mustard and apply it to the total number of people in attendance.
The proportion of people in the sample who prefer mustard is:
27/150 = 0.18
To estimate the number of people who prefer mustard in the entire population of 5,000 attendees, we can multiply this proportion by the total number of attendees:
0.18 x 5,000 = 900
Therefore, we can estimate that 900 people in attendance would prefer mustard on a hot dog.
Answer:
2000 people prefer mustard on their hot dog.
900 people prefer chili on their hot dog
2100 people prefer ketchup on their hot dog
Step-by-step explanation:
hope this helps
Bhavik bought 3 liters of milk and 5 loaves of bread for a total of $11. A month later, he bought 4 liters of milk and 4 44 loaves of bread at the same prices, for a total of $10. How much does a liter of milk cost, and how much does a loaf of bread cost?
The cost of a liter of milk is $2.50 and the cost of a loaf of bread is $2.50.
What is cost?Cost is the value of goods or services measured in money or other forms of exchange. It is the amount that must be given up in exchange for something else. Costs are typically incurred in the production of goods and services, and can include both tangible and intangible elements, such as labor, materials, overhead, and financing.
The total cost for 3 liters of milk and 5 loaves of bread was $11. Therefore, the cost for 1 liter of milk was ($11 / 3) = $3.67. The cost for 1 loaf of bread was ($11 / 5)
= $2.20.
The total cost for 4 liters of milk and 4 loaves of bread was $10. Therefore, the cost for 1 liter of milk was ($10 / 4) = $2.50. The cost for 1 loaf of bread was ($10 / 4)
= $2.50.
Therefore, the cost of a liter of milk is $2.50 and the cost of a loaf of bread is $2.50.
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One hundred adults were asked to name
their favorite sport, and the results are
shown in the circle graph. What percent of
adults preferred soccer or baseball?
Volleyball, 3
Other. 4
Golf, 7
Soccer, 11.
Baseball, 14
Football,39
Basketball, 22
The percentage of adults who preferred soccer or basketball is 25%.
What is circle graph?The size of each slice in a circle graph, also called a pie chart, indicates the proportion or percentage of each category, and the information is displayed as a circle divided into sections or slices. Circle graphs are frequently used to compare various categories in a dataset or to illustrate how various components contribute to the overall. They are particularly helpful when working with data that can be broken down into distinct categories, such survey results or demographic data.
From the circle graph we see that, percentage of adults who preferred soccer is 11%, and the percentage who preferred baseball is 14%.
Thus,
11% + 14% = 25%
Hence, the percentage of adults who preferred soccer or basketball is 25%.
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Find the surface area and volume of the composite solid.
According to the information, the surface area of the solid is 758m² and the volume is 594m³
How to find the surface area of the solid?To find the surface area of the solid we have to perform the following procedure:
12m * 11m = 132m²
132m² * 2 = 264m²
16m * 9m = 144m²
144m² - 18m² = 126m²
126m² * 2 = 252m²
16m * 11m = 176m²
176m² - 66m² = 110m²
3m * 11m = 33m²
33m² * 2 = 66m²
6m * 11m = 66m²
264m² + 66m² + 66m² + 110m² +252m² = 758m²
To find the volume we have to perform the following procedure:
8m * 11m * 9m = 792m³
792m³ - 198m³ = 594m³
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You take out a loan in the amount of your tuition and fees cost $70,000. The loan has a monthly interest rate of 0.25% and a monthly payment of $250. How long will it take you to pay off the loan? Use the formula N= (-log(1-i*A/P))/(log(1+i)) to determine the number of months it will take you to pay off the loan. Let N represent the number of monthly payments that will need to be made, i represent the interest rate in decimal form, A represent the amount owed (total amount of the loan), and P represent the amount of your monthly payment. Be sure to show your work for all calculations made.
With given compound interest, it will take approximately 31 years and 5 months to pay off the loan.
What is Compound interest?
Compound interest is computed on both the starting principal and the accrued interest from prior periods. In other words, it is the interest gained not just on the principle amount but also on any past interest earned.
Now,
Using the given formula:
N = (-log(1 - i * A / P)) / (log(1 + i))
where i = 0.0025 (0.25% monthly interest rate), A = $70,000, and P = $250
N = (-log(1 - 0.0025 * 70000 / 250)) / (log(1 + 0.0025))
N = (-log(1 - 175)) / (log(1.0025))
N = (-log(0.9883)) / (0.0025)
N = 376.48
Rounding up to the nearest whole number, it will take 377 months to pay off the loan.
Therefore, it will take approximately 31 years and 5 months to pay off the loan.
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A Bakery sold 382 cakes in one week. this was twice as the day so the previous week. write an equation that can be used to find the number of cakes and that were sold the previous week 
Answer:
164 Cakes
Step-by-step explanation:
382 Cakes are made in Week A. This was twice the amount of Week B. 328 divided by two equals 164.
Try It
For a project, the teacher asked a group of seven students to each count the number of pedestrians that cross the street where they live on a certain day. The data collected had a range of 33 Sox of the seven data values
are shown below Find the missing data value
29,
15
22,,
11,
31,
15
The missing data value in the project is 25.5.
What is range?Range is a statistical measure that represents the difference between the highest and lowest values in a dataset. It is calculated by subtracting the smallest value in the dataset from the largest value.
According to question:To find the missing data value, we need to use the given range and the known data values.
The range is the difference between the highest and lowest values in the data set. So, if we sort the given data values in increasing order, we have:
11, 15, 15, 22, 29, 31
The range is 33, which means that:
highest value - lowest value = 33
31 - 11 = 33
So, the missing data value must be between 22 and 29 (since those are the values that are next to each other in the sorted list). To find the exact value, we can take the average of 22 and 29:
(22 + 29) / 2 = 25.5
Therefore, the missing data value is 25.5.
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PLEASE HELP ASAP DUE TODAY
Question 4(Multiple Choice Worth 1 points)
(08.07 MC)
The quadratic function f(x) has roots of 3 and 7, and it passes through the point (1, 12). What is the vertex form of the equation of f(x)?
f(x) = −(x + 5)2 − 4
f(x) = −(x − 5)2 − 4
f(x) = (x + 5)2 − 4
f(x) = (x − 5)2 − 4
As a result, the vertex form of the f(x) equation is: [tex]f(x) = -(x - 5)^2 + 2[/tex]which is equivalent to choice (b).
what is quadratic equation ?A quadratic function is a sort of second-degree polynomial equation, meaning it has at least two squared element. A quadratic equation's generic form is: [tex]ax^2 + bx + c = 0[/tex] where the variable x and the constants a, b, and c. If the coefficient a were zero, the expression would be linear rather than quadratic. Several ways to solve a quadratic equation, including factoring, squaring the square, and utilising the quadratic formula. The negative numbers or roots of the quadratic equation are the values of x which it make the equation true and are the solutions to the quadratic equation.
given
The factored form of the quadratic function f(x), which has roots of 3 and 7, is as follows:
f(x) = a(x - 3)(x - 7) (x - 7) where "a" stands for a fixed coefficient.
We can utilise the point (1, 12) through which the function passes to determine the value of "a"
12 = a(1 - 3) (1 - 3)(1 - 7)
12 = -24a
a = -1/2
Inputting the value of "a" into the factored form yields the following results:
[tex]f(x) = -1/2(x - 3)(x - 7) (x - 7)[/tex]
By extending this phrase, we get:
[tex]f(x) = -1/2(x^2 - 10x + 21)[/tex]
We need to finish the square before we can transform this into vertex form. To achieve this, add and remove the square of the coefficient of x's half:
[tex]f(x) = -1/2(x^2 - 10x + 25 - 4)[/tex]
If we condense this phrase, we get:
[tex]f(x) = -1/2[(x - 5)^2 - 4][/tex]
As a result, the vertex form of the f(x) equation is: [tex]f(x) = -(x - 5)^2 + 2[/tex]which is equivalent to choice (b).
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. Where is the vertex of the graph that represents y=(x−2)2−8 ? Type the answers in the boxes below. ( , ) b. Where is the y -intercept? Type the answers in the boxes below.
The vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.
Given equation :
y=(x−2)2−8
y = 2x - 4 - 8
= 2x - 12
The final equation is y = 2x - 12.
Compare this equation with slope and y-intercept formula :
y = mx+c
So that c = -12
The value of y-intercept according to the solution is -12.
To find the vertex. Let's assume x=0; Substitute in the equation
y = 2(0) -12
y = -12
The first vertex will be (0, -12)
If x = 1; y = 2(1) -12
y = -10
Then the second vertex will be (1, -10).
Hence, the vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.
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Can someone help me plssss
The independent variable x represents the number of hours since the snow began to fall while the dependent variable is total amount of snow on Samir's lawn after x hours because the total amount of snow on Samir's lawn depends on the number of hours the snow fell.
The function M(6) refers to the amount of snow on Samir's Lawn after 6 hours
How to Identify Independent and Dependent Variables?An independent variable is defined as the variable that causes a change.
However, a dependent variable is defined as the variable that occurs as a result or effect of a change.
The independent variable x represents the number of hours since the snow began to fall while the dependent variable is total amount of snow on Samir's lawn after x hours because the total amount of snow on Samir's lawn depends on the number of hours the snow fell.
The function M(6) refers to the amount of snow on Samir's Lawn after 6 hours
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Leah said on her birthday: “Today I am exactly three times as old as I was four years ago.“ And that was true. In how many years can Leah truthfully say on her birthday: “Today I am exactly twice as old as I was four years ago“?
in 2 years, Leah will be exactly twice as old as she was four years ago. Therefore, the answer is 2 years.
How to determine In how many years can Leah truthfully say on her birthday: “Today I am exactly twice as old as I was four years ago“Let's start by setting up an equation based on the given information.
Let Leah's current age be represented by "x". Then, we know that:
x = 3(x-4)
Expanding the right side of the equation:
x = 3x - 12
Bringing the "x" term to the left side and simplifying:
2x = 12
x = 6
So Leah is currently 6 years old. Now we want to find out how many years it will take for her to be exactly twice as old as she was four years ago. Let's represent this number of years as "y". Then we can set up another equation:
6 + y = 2(6 - 4 + y)
Simplifying:
6 + y = 2(2 + y)
6 + y = 4 + 2y
2 = y
So in 2 years, Leah will be exactly twice as old as she was four years ago. Therefore, the answer is 2 years.
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find g(x+5): g(x)=3x^2+2 simplify as much as possible
The answer of the given question based on the expression is , the simplified expression for g(x+5) is 3x² + 30x + 73.
What is Expression?An expression is combination of numbers, variables, and operators (such as +, -, ×, ÷) that represents value or quantity. Expressions can be as simple as a single number or variable, or they can be complex with multiple terms and operations. Expressions can be evaluated or simplified by performing the indicated operations according to the rules of arithmetic and algebra.
To find g(x+5), we replace every occurrence of x in the expression for g(x) with x+5:
g(x+5) = 3(x+5)² + 2
Expanding the square and simplifying, we get:
g(x+5) = 3(x² + 10x + 25) + 2
g(x+5) = 3x² + 30x + 73
Therefore, the simplified expression for g(x+5) is 3x² + 30x + 73.
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How many different possible outcomes are there if you roll two fair six-sided dice in the shape of a cube?
Answer: 36
Step-by-step explanation:
help please!! state the key features for this graph
Axis of symmetry: x = 1[tex]\\[/tex]
Vertex: (0,1)
Y-intercept: (0,1)
Min / Max: 0 / infinity
Domain: -infinity ≥ x ≥ infinity
Range: 0 ≥ y ≥ infinity
Melissa collected the data in the table.
When x = 4, what is the residual?
–3
–1
1
3
From the data in the table, we can conclude that when x = 4, then the residual will equal -1.
How to determine the residualTo determine the residual, we can begin by obtaining the difference between the given and the predicted values of y.
So, Residual = Gven value - Predicted value.
When x = 4 in the table, Given value is 9 and predicted value is 10. So, 9 - 10 = -1. So, we can say that the residual value is -1.
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Answer:
The residual is the difference between the actual y-value and the predicted y-value on a regression line. Since no table or equation is provided, we cannot calculate the exact residual. However, I can explain the concept to you.
Step-by-step explanation:
In general, to calculate the residual, we would need a regression equation or a line of best fit. This equation allows us to predict the y-values for different x-values. Then, we can compare the predicted values to the actual values given in the table to find the residuals.
If you have the regression equation or the line of best fit, I can help you calculate the residual for a specific x-value.
Consider a triangle ABC.
.............................
Convert the equation f(t) = 227e b= -0.09€ to the form f(t) = ab* Give answers accurate to three decimal places
Can you please help me with this.
The probability that a committee of 10 members consisting of 6 males and 4 females will be selected is 0.3633.
The total number of ways to develop the complex would be 665, 280 ways.
How to find the probability ?To find the probability that a committee of 10 members consisting of 6 males and 4 females be selected for this committee, we need to calculate the number of possible ways to choose 6 males from the 28 males and 4 females from the 12 females.
Using combinations, we have:
Number of ways to choose 6 males = C(28, 6) = 28! / (6! x (28 - 6)!)
Number of ways to choose 4 females = C(12, 4) = 12! / (4! x (12 - 4)!)
Now, we find the probability:
Probability = (Number of ways to choose 6 males * Number of ways to choose 4 females) / Total ways to choose 10 members
Probability = (C(28, 6) x C(12, 4)) / C(40, 10)
Probability = 0.3633
How to find the number of ways ?To find the number of different ways the complex can be developed given the basic designs, we need to consider the following:
The number of ways to arrange the remaining 5 unique designs on the 5 stands is a permutation of 11 designs taken 5 at a time:
P(11, 5) = 11! / (11 - 5)!
Total ways to develop the complex = 12 x P(11, 5)
= 12 x 55440 = 665,280 ways
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Write the complex number in rectangular form. If necessary, round to the nearest tenth.
24( cos 275° + i sin 275°)
Answer:
Step-by-step explanation:
We first have to find cos 275 and sin 275 and then put them into the formula:
cos 275 = .0872
sin 275 = -.9962
Therefore,
24(.0872 - .9962i) distributes to
2.1 - 23.9i
in row 2, write the standard form equation of a circle whose diameter endpoints are shown here (-3,4) (2,1)
The standard form equation of a circle whose diameter endpoints are (-3,4) (2,1) is [tex](x - (-0.5))^2 + (y - 2.5)^2[/tex] = 6.5
What is the general form of equation of a circle?The general form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r represents the radius. This equation is derived using the Pythagorean theorem, which states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. By setting (x - h)² and (y - k)² equal to r² and then combining the two equations, we get the standard form equation of a circle.
The center of the circle lies in the middle of the diameter, so we find the midpoint of the end points:
[tex](\frac{-3+2}{2} , \frac{4+1}{2} )[/tex] = (-0.5, 2.5)
And radius of the circle is half of the diameter, which is:
[tex]\frac{\sqrt{( 2-(-3))^2 + (1-4)^2 )}}{2}[/tex] = [tex]\frac{\sqrt{26}}{2}[/tex]
Therefore, the circle equation is:
[tex](x - (-0.5))^2 + (y - 2.5)^2[/tex] = [tex](\frac{\sqrt{26} }{2} )^2[/tex] = 26/4 = 6.5
[tex](x - (-0.5))^2 + (y - 2.5)^2[/tex] = 6.5
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a red car travels 20km in one hour .
a blue car travels 130km in the sAME TIME
which car thas greater average speed???
Answer:
The answer is the Blue car
Step-by-step explanation:
let Red car be x
let blue car be y
x=120km---->1hr
y=130km----->1hr
Average speed =distance(km)/time(hr)=km/hr
let A be average speed
A(x)=120/1=120km/hr
A(y)=130/1=130km/hr
therefore,
the blue car has the greatest average speed
Write this in System of Equations from Context
A company produces fruity drinks that contain a percentage of real fruit juice. Drink A contains 20% real fruit juice and Drink B contains 10% real fruit juice. The company used 70 liters of real fruit juice to make 3 times as many liters of Drink A as liters of Drink B. Write a system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made. Define the variables that you use to write the system.
Therefore, the system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made is.
[tex]0.1x + 0.2y = 70[/tex]
[tex]y = 3x[/tex]
Where x represents the number of liters of Drink B made, and y represents the number of liters of Drink A made.
Let's define the variables as follows:
Let x be the number of liters of Drink B produced.
Since the company produced 3 times as many liters of Drink A as liters of Drink B, let y be the number of liters of Drink A produced, so y = 3x.
Now, let's write the system of equations:
The total amount of real fruit juice used is 70 liters, so we can write:
[tex]0.1x + 0.2y = 70[/tex]
Substituting y = 3x into the above equation, we get:
[tex]0.1x + 0.2(3x) = 70[/tex]
Simplifying the equation:
[tex]0.1x + 0.6x = 70[/tex]
[tex]0.7x = 70[/tex]
[tex]x = 100[/tex]
So, the company made 100 liters of Drink B and 3 times as many liters of Drink A, or 300 liters of Drink A.
Therefore, the system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made is:
[tex]0.1x + 0.2y = 70[/tex]
[tex]y = 3x[/tex]
Where x represents the number of liters of Drink B made, and y represents the number of liters of Drink A made.
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Find the Volume of this shape.
Therefore, the volume of the prism is 60 cubic feet.
What is volume?Volume is the amount of space occupied by a three-dimensional object or the capacity of an object. It is typically measured in cubic units such as cubic meters, cubic feet, or cubic centimeters. The formula for finding the volume of a solid object depends on its shape. In general, the volume of a shape can be found by dividing it into smaller, more easily measured shapes and adding up their volumes. This is known as the method of integration in calculus, and it is used to find the volumes of irregularly shaped objects or fluids. Understanding the concept of volume is important in many fields, such as architecture, engineering, physics, and chemistry. In these fields, volume is used to determine the capacity of containers, the displacement of fluids, and the amount of materials needed for a construction project.
Here,
The volume of a prism is given by the formula:
V = Bh
where B is the area of the base and h is the height of the prism.
Substituting the given values:
V = (20 ft)(3 ft)
V = 60 cubic feet
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differentiate with respect to x the implicit function sin(y)+x^2y^3-cos(x)=2y
Answer:
To differentiate the implicit function sin(y) + x^2y^3 - cos(x) = 2y with respect to x, we will use the chain rule and product rule.
First, we will take the derivative of both sides of the equation with respect to x:
d/dx [sin(y) + x^2y^3 - cos(x)] = d/dx [2y]
Next, we will differentiate each term on the left side of the equation:
cos(x) - 2xy^2 dx/dx + 3x^2y^2 + sin(y) dy/dx = 2 dy/dx
We can simplify this equation by moving all the terms involving dy/dx to the left side:
cos(x) - 2xy^2 - 2 dy/dx sin(y) = dy/dx [2 - sin(y)]
Now we can solve for dy/dx by isolating it on one side of the equation:
dy/dx [2 - sin(y)] = cos(x) - 2xy^2
dy/dx = (cos(x) - 2xy^2) / [2 - sin(y)]
Therefore, the derivative of the implicit function sin(y) + x^2y^3 - cos(x) = 2y with respect to x is:
dy/dx = (cos(x) - 2xy^2) / [2 - sin(y)]
Which is more, 19 ounces or 1 pound?
Consequently, 1 pound weighs more than 19 ounces.
What additional weight units are there?
The weight can also be expressed in terms of grams, kilograms, pounds, and tons.
What is a pound?Pound has two different definitions. When used as a noun, it refers to a 16 oz. weight unit. Or it can be used as a verb to strike or hit hard and frequently.
What does ounce mean?The weight unit known as an ounce is 1/16th of a pound.
What fraction of a ton is one pound?A ton weighs 2000 pounds.
16 ounces make up one pound. Consequently, 1 pound weighs more than 19 ounces.
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Oriana's Pizza Kitchen has an oven that is shaped like a
rectangular prism. Inside, the oven is 5 feet wide and 4
feet deep so it can bake
their super large pizzas. It is also 3 feet high. What is
the oven's volume?
12 ft³
15 ft3
60 ft³
20 ft³
Answer:
Step-by-step explanation:
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The true statements are:
1. The radius of the circle is 3 units
2. The standard form of the equation is (x-1)^2+y^2=3
3. The center of the circle lies on X-axis
4. The radius of this circle is the same as the radius of the circle whose equation is x^2+y^2=9
The given equation is: x^2+y^2-2x-8=0
The equation in the standard form of the circle can be written as (x-h)^2+(y-k)^2=r^2, where h= center of the circle and r= radius of the circle
The given equation in standard form can be written as
(x^2-2x+1)+y^2-9=0
(x-1)^2+y^2=3^2
Hence from the above equation, the center of the circle is at (1,0) and the radius is 3 units.
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A fair coin is tossed three times in succession. The set of equally likely outcomes is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. Find the probability of getting exactly one tail.
The probability of getting exactly one tail when a fair coin is tossed three times is 3/8.
What is probability?Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.
In the given question,
There are 8 possible outcomes, and we want to find the probability of getting exactly one tail. We can list the outcomes with exactly one tail as HHT, HTH, and THH.
So, the probability of getting exactly one tail is:
P(exactly one tail) = P(HHT) + P(HTH) + P(THH)
We know that each individual toss of a fair coin has a probability of 1/2 of resulting in either heads or tails. Using the multiplication rule of probability, we can find the probabilities of each of these outcomes:
P(HHT) = (1/2) * (1/2) * (1/2) = 1/8
P(HTH) = (1/2) * (1/2) * (1/2) = 1/8
P(THH) = (1/2) * (1/2) * (1/2) = 1/8
So, the probability of getting exactly one tail is:
P(exactly one tail) = P(HHT) + P(HTH) + P(THH) = 1/8 + 1/8 + 1/8 = 3/8
Therefore, the probability of getting exactly one tail when a fair coin is tossed three times is 3/8.
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A factory received a shipment of 24 lightbulbs, and the vendor who sold the items knows there are 4 lightbulbs in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the lightbulbs in the sample are defective, he will refuse the shipment. For each of the following, give your responses as reduced fractions. If a sample of 4 lightbulbs is selected, find the probability that all in the sample are defective. If a sample of 4 lightbulbs is selected, find the probability that none in the sample are defective.
The probability that none of the 4 lightbulbs in the sample are defective is 805/1763 as a reduced fraction.
What is probability?
Let's first calculate the total number of ways to choose 4 lightbulbs from 24:
24 choose 4 = (24!)/(4! * 20!) = 10,626
Probability that all 4 lightbulbs in the sample are defective:
There are 4 defective lightbulbs in the shipment, so the number of ways to choose all 4 from the 24 is:
4 choose 4 = 1
So, the probability that all 4 lightbulbs in the sample are defective is:
1/10,626 = 1/5313
Therefore, the probability that all 4 lightbulbs in the sample are defective is 1/5313 as a reduced fraction.
Probability that none of the 4 lightbulbs in the sample are defective:
There are 4 defective lightbulbs in the shipment, so the number of ways to choose 4 non-defective bulbs from the remaining 20 is:
20 choose 4 = (20!)/(4! * 16!) = 4,845
So, the probability that none of the 4 lightbulbs in the sample are defective is:
4,845/10,626 = 805/1763
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