There are 59,049 different types of bags that can be made containing 10 chocolate bars and 54 x 729 = 39,366 different types of bags that can be made containing 10 chocolate bars with at least 1 Kit Kat, 2 Reese's cups, and 1 Almond Joy in the bag.
(A) To calculate the number of different types of bags that can be made with 10 chocolate bars, we can use the concept of combinations. Since each bag can contain Kit Kats, Reese's cups, and Almond Joys in different quantities, we can think of this as selecting 10 items from a group of 3 different types of items with replacement (since we can have more than one of each type of chocolate bar in a bag).
The formula for the number of combinations with replacement is: n^r, where n is the number of items to choose from and r is the number of items to choose
In this case, n = 3 (since there are 3 different types of chocolate bars) and r = 10 (since we are choosing 10 chocolate bars for each bag). Therefore, the number of different types of bags that can be made is: 3^10 = 59,049
So there are 59,049 different types of bags that can be made containing 10 chocolate bars.
(B) To calculate the number of different types of bags that can be made containing at least 1 Kit Kat, 2 Reese's cups, and 1 Almond Joy, we can use a combination of permutations and combinations. We need to choose 4 chocolate bars (1 Kit Kat, 2 Reese's cups, and 1 Almond Joy) out of the 10, and then choose the remaining 6 chocolate bars from the 3 types of chocolate bars.
First, we choose the 4 chocolate bars with the required distribution:
We can choose 1 Kit Kat in 3 ways (since there are 3 Kit Kats to choose from).
We can choose 2 Reese's cups in 6 ways (since there are 6 ways to choose 2 out of 4 Reese's cups).
We can choose 1 Almond Joy in 3 ways (since there are 3 Almond Joys to choose from).
Therefore, the number of ways to choose the 4 required chocolate bars is: 3 x 6 x 3 = 54
Next, we choose the remaining 6 chocolate bars from the 3 types of chocolate bars. This can be done using the formula for combinations with replacement, as in part (A): n^r, where n is the number of items to choose from and r is the number of items to choose
In this case, n = 3 (since there are 3 types of chocolate bars) and r = 6 (since we are choosing 6 chocolate bars for each bag). Therefore, the number of different types of bags that can be made with the required distribution of chocolate bars is: 3^6 = 729
So there are 54 x 729 = 39,366 different types of bags that can be made containing 10 chocolate bars with at least 1 Kit Kat, 2 Reese's cups, and 1 Almond Joy in the bag.
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A company wants to research the satisfaction levels from customers. Explain how the company could use a systematic sampling method.
Answer:
Step-by-step explanation:
There are four methods of sampling namely Random sampling,Stratified sampling, Cluster sampling and Multistage sampling. Let’s look at them one by one.
Random sampling - When each subject of the population is equally likely to be included in the sample, the sampling method is called random sampling.
Stratified sampling- Under this, the data are first divided into stratas. Each stratum consists of homogeneous subjects and strata are heterogeneous among themselves. Samples are randomly taken from each strata. Example- In an investigation of mortality rate of the insured, we can first subdivide the data into males and females and then take sample from each group. Here, male and female groups represent stratas.
Cluster sampling- Under this we first divide the data into clusters that are homogeneous among themselves and then select few of them and sample all observations from the randomly selected clusters. For example- suppose we want to take a sample of people's weight in a specific city. We observed that the areas in that city are similar to each other , so instead of travelling to each area and collecting data we can select few areas and then take observations from all people of those areas.
Multistage sampling - This adds one more stage to cluster sampling. Unlike cluster sampling where we sample all observations from the selected clusters, In multistage sampling we randomly sample observations from each selected cluster.
I hope this helped.
Jay has an album that holds 800 hockey cards. Each page of the album holds 8 hockey cards. If 22% of the album is empty, how many pages are filled with hockey cards?
Using the given percentage we can see that there are 78 filled pages.
How many pages are filled with hockey cards?We know that there are 800 cards and each page holds 8 cards, then the number of pages is:
N = 800/8 = 100
And we know that 22% of the album is empty, then 78% (the complement) of the album is filled, this means that the number of filled pages is given by the formula below.
F = 100*(78%/100%) = 100*0.78 = 78
We divide the percentage by 100% to make it a decimal number, so we can use it in the operation.
There are 78 filled pages in the album.
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[tex]In(\frac{6}{e^8})[/tex]Use the properties of logarithms to rewrite and simplify the logarithmic expression
The manager of a coffee shop recorded the number of customers who put vanilla creamer or chocolate creamer in their coffee during one hour and classified them by age. The results are shown in the table. Coffee Creamer. Vanilla. Chocolate. Age 18 to 30. 2, 6. Age 31 plus. 4, 8 What percentage of these customers put chocolate creamer in their coffee during this hour?
The percentage of customers who put chocolate creamer in their coffee during the hour is 70%.
Finding the percentage of customers:To find the required percentage, find the number of customers that chose chocolate creamer and total the number of customers who came to choose the creamer in the hour.
Divide the number of customers that chose chocolate creamer by the total number of customers and multiply by 100.
Here we have
The manager of a coffee shop recorded the number of customers who put vanilla creamer or chocolate creamer in their coffee during one hour
The bale given is
Vanilla Chocolate
Age 18 - 30 2 6
Age 30 + 4 8
Here, number of customers = 2 + 4 + 6 + 8 = 20
No of customers that choose chocolate creamer = 6 + 8 = 14
The percentage of customers that put chocolate creamer
= [ 14/20 ] × 100 = 70%
Therefore,
The percentage of customers who put chocolate creamer in their coffee during the hour is 70%.
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Answer: 70%
Step-by-step explanation:
Gary earns $9.12 per hour at his job. He worked 24 hours last week. Calculate Gary's pay before taxes.
Gary's pay before taxes is $218.88.
Gary's pay before taxes can be calculated by multiplying his hourly rate by the number of hours he worked.
Taxes are compulsory payments made by a government organisation, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools.
Step 1: Identify the hourly rate and number of hours worked.
Hourly rate: $9.12
Hours worked: 24
Step 2: Multiply the hourly rate by the number of hours worked.
$9.12 * 24 = $218.88
Step 3: The result is Gary's pay before taxes.
Gary's pay before taxes is $218.88.
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A car tire has a diameter of 28 inches. How many revolutions does the tire make while traveling 500 feet? Round your answer to the nearest whole number.
Rounding to the nearest whole number, the tire makes 214 revolutions while traveling 500 feet.
What is Circumference?
Circumference is a term used in geometry to refer to the distance around the edge of a circle or any circular object. It is the total length of the boundary or perimeter of the circle. The circumference is determined by the diameter or radius of the circle, and it is calculated using the formula:
Circumference = π × diameter
The circumference of the tire is equal to the distance it travels in one revolution. Since the diameter of the tire is 28 inches, its radius is 14 inches. Therefore, the circumference of the tire is:
C = 2πr = 2π(14 inches) = 28π inches
To convert the distance of 500 feet to inches, we multiply by the conversion factor 12 inches/foot:
500 feet × 12 inches/foot = 6000 inches
Now we can find the number of revolutions of the tire:
number of revolutions = distance traveled / circumference of tire
number of revolutions = 6000 inches / 28π inches ≈ 214 revolutions
Therefore, rounding to the nearest whole number, the tire makes 214 revolutions while traveling 500 feet.
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Ella purchased a new car in 2000 for $27,600. The value of the car has been depreciating exponentially at a constant rate. If the value of the car was$8,300 in the year 2004, then what would be the predicted value of the car in the year 2009,? answer to the nearest dollar
The predicted value of the car in the year 2009 is $6,232.
How to predict the value of the car in the year 2009 ?First we need to use the formula for exponential decay:
V(t) = V0 × e^(-rt)
Where
V(t) is the value of the car at time tV0 is the initial value of the carr is the rate of decayt is the time elapsed since the initial purchaseWe know that the car was purchased in 2000 for $27,600, and that its value in 2004 was $8,300. Therefore, we can use these values to solve for the rate of decay:
$8,300 = $27,600 × e^(-r x 4)
e^(-4r) = 0.3
Taking the natural logarithm of both sides:
-4r = ln(0.3)
r = -0.3567
Now that we have the rate of decay, we can use the same formula to predict the value of the car in 2009, which is 9 years after the initial purchase:
V(9) = $27,600 × e^(-0.3567 x 9) = $6,232
Therefore, the predicted value of the car in the year 2009 is $6,232.
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I am needing some help with this
As you have two side lengths but no angle measures, the Pythagorean Theorem should be used to obtain the value of x.
Then the value of x is given as follows:
x = 36.3.
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
The parameters for this problem are given as follows:
Sides x and 19.Hypotenuse 41.Hence the value of x is obtained as follows:
x² + 19² = 41²
x = sqrt(41² - 19²)
x = 36.3.
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If g(z)=28z^(4)-9z^(3)-26z^(2)+10z+34, use synthetic division to find g(1). Submit
Using synthetic division, the value of g(1) is 37.
To find g(1) using synthetic division, we need to divide the polynomial g(z) by the binomial (z - 1). The process of synthetic division is as follows:
1. Write down the coefficients of the polynomial g(z): 28, -9, -26, 10, 34
2. Write down the value of z that we are plugging in, which is 1, in the leftmost column.
3. Bring down the first coefficient, which is 28, to the bottom row.
4. Multiply the value in the bottom row by the value of z, which is 1, and write the result in the next column.
5. Add the value in the top row to the value in the bottom row and write the result in the bottom row.
6. Repeat steps 4 and 5 until all the columns are filled.
7. The last value in the bottom row is the remainder, and the values in the bottom row before the remainder are the coefficients of the quotient polynomial.
The synthetic division table looks like this:
1 | 28 -9 -26 10 34
| 28 19 -7 3
| 28 19 -7 3 37
The remainder is 37, so g(1) = 37.
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Carys calculates the total amount E, in dollars, theat she earns for working h hours using the equation E=10h. . At that rate, how many hours does it take Carts to earn one dollar
It takes Carys 1/10 οf an hοur, οr 6 minutes, tο earn οne dοllar.
What is the linear functiοns?In mathematics, the term linear functiοn refers tο twο distinct but related nοtiοns: In calculus and related areas, a linear functiοn is a functiοn whοse graph is a straight line, that is, a pοlynοmial functiοn οf degree zerο οr οne.
Tο find the number οf hοurs it takes Carys tο earn οne dοllar, we can set E (the amοunt earned) equal tο $1 and sοlve fοr h (the number οf hοurs):
E = 10h
$1 = 10h
h = $1/10
Hence, it takes Carys 1/10 οf an hοur, οr 6 minutes, tο earn οne dοllar.
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Carys earns one dollar in one-tenth of an hour, or six minutes.
What exactly are linear functions?The word linear function in mathematics refers to two distinct but related concepts: A linear function in calculus and related fields is a function whose graph is a straight line, Namely, a polynomial function of degree zero or one.
Set E (the amount earned) to $1 and solve for h (the number of hours):
According to the given data:E = 10h
$1 = 10h
h = $1/10
As a result, it takes Carys one-tenth of an hour, or six minutes, to earn one dollar.
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a) Consider the linear system :⎩⎨⎧x+2y−3z=43x−y+5z=24x+y+(a2−14)z=a+2, For which values ofadoes the linear system has (i) A unique solution. (ii) Infinitely many solutions. (iii) No solution.adgbehcfi=3, then find3fci+2c3ebh+2b3dag+2a
The linear system has a unique solution for all values of a except √(97/13), and infinitely many solutions or no solution for a = √(97/13).
To find the values of a for which the linear system has a unique solution, infinitely many solutions, or no solution, we can use the determinant of the coefficient matrix. The determinant of a 3x3 matrix is given by:
|A| = adg - beh + cfi - 3fci - 2c - 3ebh - 2b - 3dag - 2a
For a unique solution, the determinant of the coefficient matrix must be nonzero. For infinitely many solutions or no solution, the determinant must be zero.
For the given system, the coefficient matrix is:
⎡⎣⎢1 2 −32 −1 54 1 a2−14⎤⎦⎥
The determinant of this matrix is:
|A| = (1)(-1)(a2-14) - (2)(5)(4) - (-3)(-1)(1) - (3)(4)(a2-14) - (2)(1)(-3) - (3)(2)(4) - (2)(-1)(-3)
Simplifying this expression gives:
|A| = -a2 + 14 - 40 - 3 - 12a2 + 168 - 6 - 24 - 6
|A| = -13a2 + 97
For a unique solution, |A| ≠ 0:
-13a2 + 97 ≠ 0
13a2 ≠ 97
a2 ≠ 97/13
a ≠ √(97/13)
For infinitely many solutions or no solution, |A| = 0:
-13a2 + 97 = 0
13a2 = 97
a2 = 97/13
a = √(97/13)
Therefore, the linear system has a unique solution for all values of a except √(97/13), and infinitely many solutions or no solution for a = √(97/13).
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Find the missing length indicated. Leave your answer in simplest radical form.
The value of x is 9.75
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
Therefore, the other side of the small triangle = √12²+9² = √ 144+81 = √225 = 15
15/9+x = 12/15
225 = 12(9+x)
225/12 = 9+x
18.75 = 9+x
x = 18.75 -9
x = 9.75
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O linear equations Additive property of equality with a nee Solve for u. 82-u=266
The solution to the equation [tex]82-u=266[/tex] is [tex]u=-184[/tex].
To solve for u in the equation [tex]82-u=266[/tex], we can use the additive property of equality. The additive property of equality states that if you add the same value to both sides of an equation, the equation will still be true.
Step 1: We can start by isolating the variable u on one side of the equation. To do this, we can add u to both sides of the equation:
[tex]82-u+u=266+u[/tex]
Step 2: Simplify the equation by canceling out the u terms on the left side of the equation:
[tex]82=266+u[/tex]
Step 3: Next, we can use the additive property of equality again to isolate the variable u on one side of the equation. To do this, we can subtract 266 from both sides of the equation:
[tex]82-266=266+u-266[/tex]
Step 4: Simplify the equation by canceling out the 266 terms on the right side of the equation:
[tex]-184=u[/tex]
Step 5: The final step is to write the solution in the form of u=____. We can do this by simply switching the sides of the equation:
[tex]u=-184[/tex]
Therefore, the solution to the equation [tex]82-u=266[/tex] is [tex]u=-184[/tex].
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which shows the multiplicative identity property of 1?
A) 4/5 x 1/5 = 1/5 x 4/5
B) 3/8x(1/2x2/3) = (3/8x1/2) x 2/3
C) 1/4x 4= 1
D) 9/10x1=9/10
Option C multiplies one and demonstrates that the result is one, proving that one has the attribute of multiplicative identity.
How is multiplicative identity property of 1 determined?Any number multiplied by one is equal to itself, according to the multiplicative identity condition of 1. Hence, the following equation illustrates the multiplicative identity feature of 1.
C) 1/4 x 4 = 1
Adding 1/4 to 4 results in: 1/4 x 4 = (1 x 4) / 4 = 4/4 = 1
This demonstrates that when we multiple any number by 1, the result is always the same. Because they involve multiplying many numbers, not just 1, Options A, B, and D do not demonstrate the multiplicative identity characteristic of 1. Option C, on the other hand, multiplies one and demonstrates that the result is one, proving that one has the attribute of multiplicative identity.
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What is the area of the shaded part of the following composite figure? Round your answer to the nearest whole.
By adding the rectangle, the shaded area is [tex]53 in^2[/tex], rοunded tο the nearest whole figure.
what is surface area?The entire area οf a three-dimensional οbject's surface is known as surface area. It is a measurement of an οbject's expοsed surface. Indicating an οbject's surface area typically involves using square measurements like square inches οr square meters. The surface area οf a cube, fοr instance, is equal to the tοtal οf the areas οf each οf its six faces. The calculatiοn fοr a cube's surface area is: Surface Area Equals 6*[tex]side^2[/tex] where "side" denοtes the cube's extent οn οne side.
given:
The bigger semicircle has a radius οf 5 inches and a diameter οf 10 inches. Consequently, the bigger semicircle's area is:
(5 in) * (1/2) * π = 39.27 in (rοunded tο twο decimal places)
The smaller semicircle has a radius of οf 2 inches and a width of οf 4 inches. Consequently, the smaller semicircle's size is:
(2 in) * (1/2) * π * 6.28 in (rοunded tο twο decimal places)
The rectangle's area is: because it is 10 inches long and 2 inches wide.
10 in + 2 in equals [tex]20 in ^2.[/tex]
We can add the area οf the rectangle tο the area οf the larger semicircle after subtracting the areas οf the smaller and larger semicircles tο determine the area οf the shaded regiοn:
[tex]39.27 in^2 - 6.28 in^2+ 20 in^2 = 52.99 in^2.[/tex]
By adding the rectangle, the shaded area is 53 in2, rοunded tο the nearest whole figure.
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Cool Down
1.5 Signed Numbers
Here is a set of signed numbers: 7, -3,2 -0.8, 0.8,-10-2
1. Order the numbers from least to greatest.
2. If these numbers represent temperatures in degrees C
What equation models the objective function for the cost, C ?
A. C=1x+.80y B. C=1x-.80y c. C=.80x+1y D. C=.80x-1y
The equation that models the objective function for the cost, C=1x+.80y. (A)
This equation is the correct model because it represents the cost, C, as a function of the number of x and y items. The cost of each x item is $1, and the cost of each y item is $0.80.
Therefore, the total cost will be the sum of the cost of x items and the cost of y items, which is represented by the equation C=1x+.80y.
In contrast, options B, C, and D do not accurately represent the cost as a function of the number of x and y items. Option B includes a subtraction of the cost of y items, which would not accurately represent the total cost.
Options C and D include incorrect coefficients for the cost of x and y items, which would also not accurately represent the total cost.
Therefore, the correct equation to model the objective function for the cost, C, is option A. C=1x+.80y.
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find the measure of ycg
Answer:
59
Step-by-step explanation:
Opposite angles are equal
C or KCG isn121
Straight line angle is 180
YCG + GCK = 180
YCG = 180- 121
Another method
All the four angles at a point is 360
YCH + HCK + KCG +YCG is 360
C is 121
121 + X + 121 + X = 360
2X + 242 =360
Subract 242 from both sides
2X = 118
Divide both sides by 2 = 59
Given that x = - 9 is a root of |(x,3,7)(2,x,2)(7,6,x)| = 0
x-3-7
2-x-2 = 0
7-6-x
find-the-other-roots
The other two roots are x = (9 + √137) / 2 and x = (9 - √137) / 2.
Given that x = -9 is a root of |(x,3,7)(2,x,2)(7,6,x)| = 0, we can use the determinant of the matrix to find the other roots. The determinant of the matrix is given by:
| (x,3,7)(2,x,2)(7,6,x) | = x(x*x - 2*6) - 3(2*x - 7*2) + 7(2*6 - 7*x)
= x^3 - 12x - 3(2x - 14) + 7(12 - 7x)
= x^3 - 12x - 6x + 42 + 84 - 49x
= x^3 - 67x + 126 = 0
Since x = -9 is a root, we can divide the polynomial by (x + 9) to get:
(x^3 - 67x + 126) / (x + 9) = x^2 - 9x - 14
Now we can use the quadratic formula to find the other two roots:
x = (-(-9) ± √((-9)^2 - 4(1)(-14))) / (2(1))
x = (9 ± √(81 + 56)) / 2
x = (9 ± √137) / 2
Therefore, the other two roots are x = (9 + √137) / 2 and x = (9 - √137) / 2.
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Suppose the annual interest rate is 7.5% and the interest is compounded annually. How much will an investment of $1,000 be worth after 3 years?
An investment of $1,000 at an annual interest rate of 7.5%, compounded annually, will be worth $1,232.28 after 3 years.
What is value?Value is a term used to describe the worth of something, either in terms of money, or in terms of importance or usefulness. Value can be determined in terms of the amount of money something is worth, or the level of importance or usefulness it has to someone. When something has a high value, it means that it is worth a lot of money or has a high level of importance or usefulness.
The value of an investment of $1,000 after 3 years at an annual interest rate of 7.5%, compounded annually, can be calculated using the following formula:
Future Value (FV) = Present Value (PV) × (1 + r)ⁿ
Where PV is the present value of the investment ($1,000 in this case), r is the annual interest rate (7.5%) and n is the number of years (3).
Using this formula, we can calculate the future value of the investment after 3 years as follows:
FV = $1,000 × (1 + 0.075)³
FV = $1,000 × 1.23228
FV = $1,232.28
Therefore, an investment of $1,000 at an annual interest rate of 7.5%, compounded annually, will be worth $1,232.28 after 3 years.
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10 pages in 1 day = 20 pages in
days
Answer:2
Step-by-step explanation:
20 divided by 10 equals 2
(Answer quick) Someone mind helping?
Answer:
x=25°
Step-by-step explanation:
please mark as brainliest
Answer:
See below.
Step-by-step explanation:
We are asked to find the value of x, and what these 2 angles are.
We know that these angles are Vertical Angles.
What are Vertical Angles?Vertical Angles are angles that are opposite of each other and are equal. They're equal due to the two straight lines crossing over each other at the same angle.
These angles aren't Adjacent Angles because they aren't next to each other. These angles don't share a common side. (Ray)
Since Vertical Angles are equal:
[tex]75 = 4x - 25[/tex]
Simplify for x:
[tex]100=4x\\25 = x[/tex]
x will equal 25°.
how many quarts are in 1 1/2 gallon
Answer:
6
Step-by-step explanation:
[tex]1\frac{1}{2}[/tex] ÷ [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{2}[/tex] ÷ [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{2}[/tex] × [tex]\frac{4}{1}[/tex] = [tex]\frac{12}{2}[/tex] = 6
Condense to a single logarithm with a leading coefficient of
1.
ln(3) + ln(x) + ln(y)
The condensed form of the given logarithmic expression ln(3) + ln(x) + ln(y) is: ln(3*x*y)
To condense the given logarithmic expression to a single logarithm with a leading coefficient of 1, we can use the product property of logarithms.
The product property states that the sum of two logarithms with the same base is equivalent to the logarithm of the product of the two numbers.
Using this property, we can combine the three logarithmic terms in the given expression: ln(3) + ln(x) + ln(y) = ln(3*x*y)
Therefore, the condensed form of the given logarithmic expression is:
ln(3*x*y). This is a single logarithm with a leading coefficient of 1, as required.
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The interior angles of the pentagon
he has drawn are all less than 180°.
Ben attempts to express the
interior angles of his pentagon
using algebra.
His expressions are
xᵒ, (x +40)°, (2x − 30)°,
3(x - 40) and 3xº
Show that Ben is incorrect.
Input note: include the angle sum
of a pentagon, the value of x and
the size of any angles that don't
meet the criteria set out in the
question.
Ben is incorrect because…
Ben is incorrect because, all of Ben's expressions are erroneous since none of them equal the number 108 degrees. The correct equation is (n-2) x 180 / n.
What is the equation of interior angle in a regular polygon?A polygon is a geometric shape with a limited number of sides and two dimensions. The sides or edges of a polygon are formed by joining end-to-end segments of a straight line to form a closed shape. The intersection of two line segments, which results in an angle, is referred to as a vertex or corners.
The formula for calculating an interior angle in a regular polygon with n sides is (n-2) x 180 / n.
An internal angle in a pentagon has a measure of (5-2) x 180 / 5 = 108 degrees.
Substituting the angle in Ben's expression:
xᵒ + (x + 40)° + (2x - 30)° + 3(x - 40)° + 3x°
9x - 27° = 108
We observe that none of the value of x results in 108 degrees.
Hence, all of Ben's expressions are erroneous since none of them equal the number 108 degrees.
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what table models the quadratic function with a range [5, ∞]?
Answer:
It is D
Step-by-step explanation:
Its D it has to be 5 and bigger than 5
A= [ 1 1 1]
[ 1 2 3]
[ 4 5 6]
v = [ 2 ]
[ 3 ] [ -1]. (a) Find the image ofvunderTA. (b) Can you find vectorswthat are different fromvbut that get mapped to the same image? (c) Find all vectorszthat get mapped to zero. (Hint: No new row reduction is needed.) (d) Write down a nontrivial linear dependence relation between the columns ofA.
One possible solution is c1 = 1, c2 = -2, and c3 = 1, which gives us the linear dependence relation A1 - 2A2 + A3 = 0.
A= [ 1 1 1] [ 1 2 3] [ 4 5 6] and v = [ 2 ] [ 3 ] [ -1]. To find the image of v under TA, we simply multiply A and v to get:
TA = [ 1 1 1] [ 2 ] = [ 4 ]
[ 1 2 3] [ 3 ] [ 7 ]
[ 4 5 6] [ -1] [ 17 ]
So the image of v under TA is [ 4 7 17 ].
To find vectors w that are different from v but that get mapped to the same image, we can use the equation TA*w = TA*v. Since TA*v = [ 4 7 17 ], we can set up the following system of equations:
1w1 + 1w2 + 1w3 = 4
1w1 + 2w2 + 3w3 = 7
4w1 + 5w2 + 6w3 = 17
Solving this system of equations will give us all the possible vectors w that get mapped to the same image as v. One possible solution is w = [ 1 2 0 ], which is different from v but gets mapped to the same image.
To find all vectors z that get mapped to zero, we can use the equation TA*z = 0. This gives us the following system of equations:
1z1 + 1z2 + 1z3 = 0
1z1 + 2z2 + 3z3 = 0
4z1 + 5z2 + 6z3 = 0
Solving this system of equations will give us all the possible vectors z that get mapped to zero. One possible solution is z = [ -3 2 1 ], which gets mapped to zero under TA.
Finally, to write down a nontrivial linear dependence relation between the columns of A, we can use the equation c1*A1 + c2*A2 + c3*A3 = 0, where A1, A2, and A3 are the columns of A and c1, c2, and c3 are constants. One possible solution is c1 = 1, c2 = -2, and c3 = 1, which gives us the linear dependence relation A1 - 2A2 + A3 = 0.
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Write three rational expressions that simplify to (x)/(x+1), none of which may have a monomial in either the numerator or denominator. Show that your expressions simplify.
Three rational expressions that simplify to (x)/(x+1) are:
1) (x+2-2)/(x+1)
2) (2x-3x+3)/(2x+2-3x+1)
3) (3x+5-5-2x)/(x+2+1-2)
To simplify these expressions, we can combine like terms in the numerator and denominator:
1) (x+2-2)/(x+1) = (x)/(x+1)
2) (2x-3x+3)/(2x+2-3x+1) = (-x+3)/(-x+3) = (x)/(x+1)
3) (3x+5-5-2x)/(x+2+1-2) = (x)/(x+1)
As shown, all three expressions simplify to (x)/(x+1), fulfilling the requirements of the question.
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1.Classify the number 11+8i. O complex number O imaginary number O real number 2, Express √−81 as a complex number
√−81…..?
The correct classification for 11+8i is a complex number.√−81 can be expressed as the complex number 9i.
The number 11+8i is a complex number. This is because it has both a real part (11) and an imaginary part (8i). A complex number is any number that can be expressed in the form a+bi, where a and b are real numbers and i is the imaginary unit. Therefore, the correct classification for 11+8i is a complex number.
To express √−81 as a complex number, we can use the fact that √−1 = i. So, √−81 = √(81)*√(−1) = 9*i = 9i. Therefore, √−81 can be expressed as the complex number 9i.
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