The number of ways to choose 2 toppings from a menu of 18 toppings is a classic example of a combinatorial problem.
We have a set of 18 items (toppings), and we want to know how many ways there are to choose 2 of these items. The answer is given by the binomial coefficient C(18, 2), which is the number of ways to choose 2 items from a set of 18 items, where order does not matter and repetition is not allowed.
The formula for a binomial coefficient is:
C(n, k) = n! / (k! * (n - k)!)
where n! means n factorial, which is the product of all positive integers from 1 to n. So, for example, 5! = 5 * 4 * 3 * 2 * 1 = 120.
Using this formula, we can calculate the number of ways to choose 2 toppings from a menu of 18 toppings:
C(18, 2) = 18! / (2! * (18 - 2)!) = 18 * 17 / (2 * 1) = 153 ways
So there are 153 different ways to choose 2 toppings from a menu of 18 toppings.
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List the angles of triangle KLM in order from least to greatest if
KL = x - 4, LM = x + 4, KM = 2x - 1, and the perimeter if the triangle is 27.
Answer:
B, C, A.
Step-by-step explanation:
In order to find the angles of triangle KLM and their order from least to greatest, we need to use the Law of Cosines and the perimeter equation of the triangle. The Law of Cosines states that in any triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of the lengths of these sides and the cosine of the angle between them.
Let's assume that the length of sides KL, LM, and KM are x - 4, x + 4, and 2x - 1, respectively. We can use the Law of Cosines to find the cosine of the angle between KM and KL:
cos A = (x - 4)^2 + (2x - 1)^2 - (x + 4)^2 / 2 * (x - 4) * (2x - 1)
Next, we can use the perimeter equation of the triangle, which is
KL + LM + KM = 27, to find the value of x:
x - 4 + x + 4 + 2x - 1 = 27
4x = 36
x = 9
So, the lengths of the sides of the triangle are
KL = x - 4 = 5, LM = x + 4 = 13, and KM = 2x - 1 = 17.
Next, we can use the Law of Cosines to find the cosine of the angle between KM and KL:
cos A = (5)^2 + (17)^2 - (13)^2 / 2 * (5) * (17)
cos A = 74 / 60
A = cos^-1 (74/60) = approximately 49.7°
Finally, we can use the perimeter equation of the triangle and the Law of Sines to find the other two angles of the triangle:
B + C = 180° - 49.7° = 130.3°
B / sin B = LM / sin A
B = sin^-1 (sin B / sin A) * LM / sin A
C = 130.3° - B
The angles of triangle KLM in order from least to greatest are approximately:
B, C, A.
PLEASE HELP
Simplify quantity 4 x squared plus 12 x minus 16 all over quantity 2x plus 10 over quantity 6 x plus 24 over quantity x squared plus 9x plus 20 . (2 points)
Exponents, terms in parenthesis, multiplication, division, addition, and finally subtraction. You can use PEMDAS as a helpful acronym to help you remember this.
What is subtraction?One of the four operations used in mathematics, along with addition, multiplication, and division, is subtraction. Removal of items from a collection is represented by the operation of subtraction. For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches. The number that the other number is deducted from is known as a minuend. Subtrahend: The amount that needs to be deducted from the minuend is known as a subtrahend. Difference: A difference is the outcome obtained by deducting a subtractor from a minimum.[tex]$\frac{4 x^2+12 x-16}{\frac{2 x+10}{\frac{6 x+24}{x^2+9 x+20}}}$[/tex]
Here we have two fractions top and bottom
[tex]$\frac{4 x^2+12 x-16}{2 x+10}$ divide by $\frac{6 x+24}{x^2+9 x+20}$[/tex]
We have division in between . we reverse the second fraction and multiply it with first fraction.
[tex]$\frac{4 x^2+12 x-16}{2 x+10} * \frac{x^2+9 x+20}{6 x+24}$[/tex]
Now we factor both numerator and denominator
[tex]$\begin{aligned} & 4 x^{\wedge} 2+12 x-16=4(x+4)(x-1) \\ & 2 x+10=2(x+5) \\ & x^{\wedge} 2+9 x+20=(x+5)(x+4) \\ & 6 x+24=6(x+4)\end{aligned}$[/tex]
Replace the factors,
[tex]$\frac{4(x+4)(x-1)}{2(x+5)} * \frac{(x+5)(x+4)}{6(x+4)}$[/tex]
We cancel out same factors at the top and bottom
So it becomes ,[tex]$\frac{(x-1)(x+4)}{3}$[/tex]
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1.Which quadrant will the terminal ray falls for an angle of rotation equal to 1.2 radians.
A.) QIV
B.)QII
C.)QI
D.)QIII
Answer:
D.) QIII
Step-by-step explanation:
Because 1.2 radians is in between 7π/6 and 5π/4
By first completing the square, solve x² + 12x + 4 = 0.
Give your answers fully simplified in the form x = a +b√c, where a, b and c are integers.
Answer:
x=-2(3-2√2), -2(3+2√2)
look at the inequality below
-6>13+5x
which of these values of x makes the inequality true
a.-3.9
b.-1.2
c.-7/15
d.3/13
I know that a number in scientific notation is written as the _______ of two factors.
power of ten
Step-by-step explanation:
The table shows the number of condo sales per month for a new building. Select all
the equations that could represent the number of sales,
Month
1
2
3
4
Sold
12
9
6
3
A. y 12-3(x-1)
B. y+6=-3(x+3)
C. y 12 = 3(x - 1)
Answer:
Option 1 and 5 will be your answer :)
Step-by-step explanation:
Let the equation representing number of sold is,
y - y' = m(x - x')
Where m = number of condo sold per month
(x', y') is a point from the given table,
Slope of line passing through two points and =
Slope of the passing through (1, 8) and (0, 11) will be,
m = = -3
Therefore, equation of the line passing through (3, 2) and slope (-3),
y - 2 = (-3)(x - 3)
y - 2 = -3(x - 3)
Similarly, equation of the line passing through (0, 1) and slope (-3),
y - 11 = -3(x - 0)
Therefore, Option (1) and (5) will be the answer.
Factor each quadratic expression. If it cannot be factored, write PRIME. Use slide division if needed. 1. 8x^2+2x-3
2. 16x^2-1
3. 36x^2+6
The factored form of 8x^2+2x-3 is (8x-3)(x+1).
The factored form of 16x^2-1 is (4x+1)(4x-1). The expression 6x^2+1 cannot be factored further,
So the factored form of 36x^2+6 is 6(6x^2+1).
Factoring is a mathematical process that involves breaking down a complex expression into simpler terms that can be multiplied together to obtain the original word. In algebra, factoring is finding the factors or the prime numbers that multiply together to give the original polynomial.
For example, the expression x^2 + 5x + 6 can be factored as (x+2)(x+3). Factoring is a useful tool in solving equations and simplifying expressions, as it allows us to manipulate the original expression in a more manageable way. In addition, factoring is used in various fields such as cryptography, signal processing, and computer science. For instance, factoring large numbers is an important problem in cryptography and is used to secure data transmission.
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joint and/or inverse variation. show you solution.
The force is 80,000 Dynes.
What is joint variation?We know that when we talk about the joint variation then we have a lot of variables that are being altered at the same time and this is what we are going to work on in the questions that we have here.
We are told that;
C α mr/t^2
Then;
C = kmr/t^2
k = Ct^2/mr
k = 6000 * 2^2/6 * 10
k = 400
Then, to find C;
C = 400 * 18 * 100/3^2
C = 80,000 Dynes
\
Hence, we can see from the calculation that the centrifugal force that is required is 80,000 Dynes.
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m ∠ a = ____ degrees
Answer:
m<a = 44°
Step-by-step explanation:
Left triangle:
95 + 39 + x = 180
x = 46
Right triangle:
46 + 90 + a = 180
a = 44
E) Find the area of a rectangular field measuring 27.04 m by 20.21 m.
i) How much would it cost to spray insecticide on the field if the rate is $0.70 per square metre? Give your answer to the nearest dollar.
A tower with a wire that extends from the top of the tower to the ground is shown below. 55 ft. 68 ft. X 40 ft. Which of the following ratios could be used to find the measurement of angle æ, in degrees?
The ratio used to find the measurement of angle x is given as follows:
cos(x) = 40/68.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.For angle x, we have that:
The adjacent side is of 40 ft.The hypotenuse is of 68 ft.Hence the ratio is given as follows:
cos(x) = 40/68.
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In ΔOPQ, the measure of ∠Q=90°, OQ = 45, QP = 28, and PO = 53. What is the value of the cosine of ∠O to the nearest hundredth?
The value of the trigonometric relation cos ∠O = 0.849
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔPQR
Now , the measure of ∠PQR = 90° and it is a right triangle
The measure of the hypotenuse PO = 53
The measure of adjacent side OQ = 45
The measure of opposite side QP = 28
Now , from the trigonometric relations ,
cos θ = adjacent / hypotenuse
cos θ = OQ / PO
Substituting the values in the equation , we get
cos θ = 45 / 53
cos θ = 0.849
Therefore , the value of cos ∠O is 0.849
Hence , the trigonometric relation cos θ = 0.849
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Find the total surface area of the prism. 8.6. 7. 14.5.
The total surface area of the given prism would be = 504
How to calculate the surface area of a prism?The formula that can be used to calculate the total surface area of a square prism = 2a² + 4a L
where a = 7
L = 14.5
Area = 2(7²) + 4 ( 7× 14.5)
= 2×49 + 4( 101.5)
= 98 + 406
= 504
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In circle M with m/LMN = 84 and LM = 13 units find area of
sector LMN. Round to the nearest hundredth.
Answer:
123.88 square units
Step-by-step explanation:
r = radius of circle
= radius of sector
= Length of LM
= Length of MN
= 13 units
When the angle is measured in degrees:
Area of a sector: [tex]\frac{Angle OfSector}{360^{o}}[/tex]× [tex]\pi r^{2}[/tex]
= [tex]\frac{84}{360}[/tex]×[tex][\pi (13)^{2}][/tex]
= 123.883 [tex]units^{2}[/tex]
= 123.88 square units (Rounded to the nearest hundredth)
4. Suppose the account in 3 above paid interest quarterly instead of annually. Find the
account balance after 5 years
The account's balance after 5 years is given as follows:
[tex]A(5) = P\left(1 + \frac{r}{4}\right)^{20}[/tex]
In which:
P is the principal.r is the interest rate.What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.
Quarterly compounding means that the value of n is given as follows:
n = 4.
Then the balance of the account after 5 years, when t = 5, is given as follow:
[tex]A(5) = P\left(1 + \frac{r}{4}\right)^{20}[/tex]
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What was the CPI for 2020 if 2019 was the base year?
A. 120
B. 125
C. 130
D. 135
What was the CPI for 2021 if 2019 was the base year?
A. 145
B. 150
C. 155
D. 160
Answer: D and C
Step-by-step explanation:
To get the value of a market basket you would add up the cost of each year so
2019 market basket = 2.50 + 1.00 + 3.75 = 7.25
2020 market basket = 2.25 + 3.00 + 4.50 = 9.75
2021 market basket = 3.00 + 3.25 + 5.00 = 11.25
now CPI for 2020 would be 9.75 / 7.25 x 100 = 134.828 which is around 135
CPI 2021 would be 11.25 / 7.25 x 100 = 155.172 which is around 155
Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plan in still air.
The speed of the plane is 135 km/h and wind speed is 23 km/h. The solution has been obtained by forming linear equations.
What is a linear equation?
This is the linear equation with the largest degree of one. This demonstrates that there are no variables in linear equations with exponents greater than 1. A straight line appears on the graph as a result of such an equation.
Let the plane speed be 'P' and the wind speed be 'W'.
We are given that while flying to Kampala with a tailwind a plane averaged 158 km/h.
So, we get an equation as
P + W = 158 ...(1)
Also, on the return trip plane only averaged 112 km/h while flying back into the same wind.
So, we get another equation as
P - W = 112 ...(2)
Now, on adding the equations we get,
⇒P + W + P - W = 158 + 112
⇒2P = 270
⇒P = 135
Now substituting the value into either equation, we get
⇒P + W = 158
⇒135 + W = 158
⇒W = 23
Hence, the speed of the plane is 135 km/h and wind speed is 23 km/h.
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Some wooden chest in a store. A green chest has a length out 165cm a width of 70cm and a height of 10cm. If another box, a blue box is proportional in size, what is is length if it's width is 18cm
The blue box measures about 641.667 cm in length.
What do length and width mean?The width and length of a figure indicate its breadth and length, respectively. The term "breadth" is also used to describe width. Although breadth and width are synonymous (thus the idiom hair's breadth, denoting a very small width), there are two significant differences between the two.
We are aware that the blue box's width is 18 cm, which is smaller than the green box's width (70cm).
As a result, the value of "k" must be lower than 1. By creating a proportion, we can determine the value of "k":
width of green box / width of blue box = k
70 / 18 = k
k = 70/18
k ≈ 3.8889
So the factor "k" is approximately 3.8889. To find the length of the blue box, we can use this factor to scale the length of the green box:
length of blue box = k * length of green box
length of blue box = 3.8889 * 165cm
length of blue box ≈ 641.667cm
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Rahul drives 10 miles in 20 minutes. If he drove three hours in total at the same rate, how far did he go?
Before you try that problem, answer the question below.
How many minutes did Rahul drive in total?
180
180
How far would Rahul drive in 180 minutes?
The distance travelled by Rahul at a speed of 0.5 miles/min in 180 minutes is 90 miles.
What is meant by the speed of an object?
A scalar quantity, speed is defined as the magnitude of the change in an object's location over time. The rate at which an object travels a distance can be thought of as its speed. A fast-moving object travels at a high speed and completes a significant distance in a brief period of time. This is in contrast to an object travelling slowly, which travels a relatively short distance in the same length of time. Zero speed refers to an object that is not moving at all.
The formula of speed = Distance covered /Time taken
Given,
Distance travelled = 10 miles
Time taken to travel 10 miles = 20 minutes
Speed = Distance/ time = 10/20 = 0.5miles/min
Now given the speed remains constant throughout the journey.
So the distance travelled in 3 hours = 3 * 60 = 180 minutes
Distance = speed * time = 0.5 * 180 = 90 miles.
Therefore the distance travelled by Rahul at a speed of 0.5 miles/min in 180 minutes is 90 miles.
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Anshumann wants to paint the wall shown in the diagram below. In order to buy the paint, he will need to know the area of the wall. What is the area of the wall?
1 point
Answer: 240 ft²
Step-by-step explanation:
Break the diagram into a rectangle and triangle:
Area of Rectangle + Area of Triangle = Total area of Wall
(20x10) + 1/2(20 x 4) = Area of wall
200 + 40 = Area of wall
240 ft² = Area of wall
Hare Krishna :)
A family wants to rent a car to go on vacation. Company A charges $35.50 and 9¢ per mile. Company B charges $75.50 and 14¢ per mile. How much more does Company B charge for x miles than Company A?
(Write a simplifed expression. Use integers or decimals for any numbers in your expression.)
No need for explainations, please provide the answer. I have a C in Math and I want to increase my grade! Thank you!
How To Solve:
Write the expression to represent how much Company B charges to rent a car, then do the same for Company A. Next, subtract the expression which represents how much Company A charges to rent a car from the express which represents how much Company B charges to rent a car. Subtract the two expressions by subtracting each term of the second expression. They simplify by combining like terms.
Answer:
75.50 + 14x - (35.50 + 9x) = 40 + 5x
Step-by-step explanation:
MANUFACTURING The profit P of a company in thousands of dollars can be modeled by P = 8.5√³, where c is
the number of customers in hundreds. What is the profit of the company if the company has 1800 customers. Round
to the nearest dollar.
The profit of the company if the company has 1800 customers is 649124 dollars
What is profit ?
A monetary gain, specifically the sum remaining after expenses for purchasing, running, or producing an item have been deducted.
P = 8.5√c³ ------->(1)
c = 1800 customers = 18 hundreds
(1) => P = 8.5√(18)³
= 8.5 √5832 ( cube of 18=5832
= 8.5 * 76.3675
= 649.124 thousands of dollars
( convert into dollars by multiplying by 1000)
= 649124.025 dollars
≈ 649124 dollars
The profit of the company if the company has 1800 customers is 649124 dollars
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Answer: 48148
Step-by-step explanation:
a person eating at a cafeteria must choose 3 of 19 vegetable on offer. calculate the number of elements in the sample space for this experiment
The number of elements in the sample space for this experiment is 969.
If a person eating at a cafeteria must choose 3 of 19 vegetables on offer, we can calculate the number of elements in the sample space, or the total number of possible outcomes, using the formula for combinations:
nCr = n! / [r!(n - r)!]
where n is the total number of items in the set and r is the number of items being chosen.
In this case, we have 19 vegetables and we want to choose 3 of them, so we can plug in n = 19 and r = 3:
19C3 = 19! / [3!(19 - 3)!]
= 19! / (3!)(16!)
= 969
Therefore, there are 969 possible combinations of 3 vegetables that a person can choose from a selection of 19 vegetables.
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Determine, by inspection, which of the following products are multiples of 30. 22 x 3 x 5 2 x 3² x 5 22 × 53 23 x 3² x 5²
By inspection, the following products which are multiples of 30 are:
2² x 3 x 52 x 3² x 52³ x 3² x 5²What is a Multiple?This is referred to as a number that may be divided by another a certain number of times without a remainder.
The multiple of 30 in the options are those who have 2, 3 and 5 as the common values and is therefore the reason why options A, C and D were chosen as the correct choice.
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Riley is training to compete in a marathon, following a training plan recommended by her favorite running podcast. She plans to run 12 miles in her first week of training and will increase her mileage by about 10% each week after.
Write an exponential equation in the form y=a(b)x that can model Riley's target mileage per week, y, x weeks after she starts training.
Use whole numbers, decimals, or simplified fractions for the values of a and b
The exponential function that shows Riley's target mileage is y = 12(1.1)ˣ
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
The standard exponential equation is:
y = abˣ
where b is the rate of change and a is the initial value.
Let y represent Riley target mileage x weeks after she starts training.
She plans to run 12 miles in her first week of training and will increase her mileage by about 10% each week after. Hence:
a = 12; b = 100% + 10% = 110% = 1.1
The exponential function is y = 12(1.1)ˣ
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The test scores for two algebra classes are shown in the stem-and-leaf plot. how many students in period 5 scored greater than 80?
The complete question:
The stem-and-leaf plot shows the test scores for a chemistry class.
How many students had a score greater than 90 points?
A. 6
B. 7
C. 8
D. 9
Solution:
The number of students had a score greater than 90 points is 7. So option B is correct.
What is stem and leaf plot ?
A stem-and-leaf plot is a type of data visualization that shows the distribution of a set of data. It is particularly useful for small to medium-sized data sets. In a stem-and-leaf plot, each data point is split into two parts: the stem and the leaf. The stem is the leftmost digit or digits of the data point, and the leaf is the rightmost digit.
To the left of the vertical bar are the tens places.
As we want to find the scores greater than 90, we start at the row in the stem and leaf plot with a 9 to the left.
To the right are 6 values - 1, 2, 3, 4, 6, and 7.
So there are six scores here higher than 90:
91, 92, 93, 94, 96, and 97.
Now we move lower to 10 in the tens place.
There is one score there - 100. (That smart kid.)
Total up the six scores in the 9 row and the 1 in the 10 row to get 7 scores higher than 90 in this stem and leaf plot.
Hence, the number of students is 7
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everything should be in the picture
Answer:
1.666... or 1 2/3
Step-by-step explanation:
The table needs to change number of Bags to Clementines.
And we know that they are only sold in pairs of 3 so we divide 5 by 3 to find the unit price
Monica has 2. 2 litres of milk 1. 5kg of each other ingredient. Calculate the greatest number of people she can serve with pasta bake
It is not possible to determine the greatest number of people Monica can serve with pasta bake based solely on the information provided.
The amount of milk and other ingredients she has does not necessarily indicate how many portions she can make. Other factors such as the recipe she is using, the size of each serving, and the equipment she has available will also impact how many people she can serve. In order to determine the number of portions she can make, more information is needed about the recipe and the serving size she is aiming for.It is not possible to determine the greatest number of people Monica can serve with pasta bake based solely on the information provided.
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QUESTION FOR FOR LIH04
