Answers
Explanation: the inner circle has an area of 153.86 in.^2. The outer circle as a whole has an area of 314 in.^2. Subtract the area of the inner circle(153.86) from the area of the total of the bigger circle(314) to get the area of the shaded region of the circle.
Answer:
The area of the shaded region is 160.2 in² (to the nearest tenth).
Step-by-step explanation:
The area of the shaded region can be calculated by subtracting the area of the inner circle from the area of the outer circle.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a circle}\\\\$A=\pi r^2 $\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\\end{minipage}}[/tex]
If the circles have the same center, and the inner circle has a radius of 7 in, then the outer circle has a radius of:
[tex]\implies r = 7 + 3 = 10\; \sf in[/tex]
Therefore, the area of the shaded region is:
[tex]\begin{aligned}\sf Area_{shaded\;region}&=\sf Area_{outer\;circle}-Area_{inner\;circle}\\&=\pi \cdot 10^2 - \pi \cdot 7^2\\&=100\pi - 49 \pi\\&=51 \pi\\& = 160.221225...\\&=160.2\; \sf in^2\;(nearest\;tenth)\end{aligned}[/tex]
Related Questions
a cola company sells the drinks in cans and bottles of three sizes. Study the pictograph below and answer the questions that follow
Answers
If these are your questions:
Dally cola sales in Bholapur 300 ml Shop A 500 ml Shop B Ilitre (a) In which type of packing does the cola sell the most? (b) Which shop sells more cola? (c) What is the total amount of cola sold in Bholapur per day?
So here are the answers:
In packing 300 ml, it would be sold at a larger volume.
given: there are two shops - shop A, and shop B selling 300 ml and 500 ml bottles.
to find:
(a) In which type of packing does the cola sell the most?
(b) Which shop sells more cola?
(c) What is the total amount of cola sold in Bholapur per day?
solution: As shop A sells the same product at a low cost because of low quantity, whereas shop B sells the product in 500 ml bottles. So, most chances are people end up buying the cheaper product which is the 300 ml product.
Similar, logic as the number of sales of 300 ml bottles would be much larger than that of 500 ml bottle backing. So, Shop A (300 ml bottle packing) sells more of the goods.
(c ) for option c inappropriate information is there, so can not be calculated. But, according to our findings, Shop A sells more goods.
In packing 300 ml, it would be sold at a larger volume.
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4) Range: 3, 3, 4, 5, 5, 8, 9,
5) Mode: 2, 3, 7, 7, 9,
6) Mode: 2, 6, 8, 8, 9,
7) Median: 2, 2, 3, 4, 8,
8) Median: 2, 4, 5, 5, 8, 8,
9) Range: 2, 5, 6, 7, 7, 8, 9,
10) Range: 2, 2, 3, 4, 7, 9, 9,
Answers
Range = 9-3 = 6
Mode = 7
Mode = 8
Median = 3
Median = (5+5)/2 = 5
Range = 9-2 = 7
Range = 9-2 = 7
how do i go about finding x° and ycm, please?
I've tried Sine Rule & Cosine Rule... I thought i had done it correctly until i worked out the angles added up to much higher than 180° so it cannot be correct... can anyone help?
Answers
From the solution;
x = 62.62°
y = 8.9 cm
What is the sine rule?The sine rule (also known as the law of sines) is a mathematical formula that relates the sides and angles of a triangle. Specifically, it relates the ratios of the lengths of the sides of a triangle to the sine of the opposite angles.
By the use of the sine rule;
a/Sin A = c/Sin C
Sin C = cSin A/a
C = Sin-1(cSin A/a)
C = Sin-1(7.8 * sin 66.4/9.2)
C = 50.98°
B = 180 - (50.98° + 66.4)
B = 62.62°
Then;
a/Sin A = b/Sin B
9.2/Sin66.4 = b/Sin 62.62
b = 9.2 * Sin 62.62/Sin66.4
b = 9.2 * 0.89/0.92
b = 8.9 cm
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Dylan has a pitcher with 1.65 L of orange juice. He pours out 0.2 L
of the juice. Then he adds some sparkling water to the pitcher to
make orangeade. He ends up with 1.9 L of orangeade. Solve the
equation 1.65 -0.2 + x = 1.9 to find the amount of sparkling
water, x, Dylan adds to the pitcher. Show your work.
Answers
Answer:
Step-by-step explanation:
fork knife
Write an equation(any form) for the quadratic graphed below:
Answers
Answer:
[tex]y = -2(x + 3)^{2} + 3[/tex]
Step-by-step explanation:
The equation for a quadratic graph can be expressed in the Vertex form:
[tex]y = a(x-h)^{2} + k[/tex]
Where:
[tex](h, k)[/tex] = Vertex of the parabola
= Extreme point of the parabola
Step I:
By reading from the graph:
[tex](h, k)[/tex] = [tex](-3, 3)[/tex]
Substitute the values of h and k in the above equation:
[tex]y = a[x- (-3)]^{2} + (3)[/tex]
[tex]y = a(x + 3)^{2} + 3[/tex]
Step II:
Determine a:
Based on the shape of the graph (which is an upside down U), the value of a will be negative:
Count one unit to the right from the vertex and see how far do you go down to touch the graph:
From the graph:
It seems you need to move 2 units down
∴a = [tex]-2[/tex]
Step III:
Substitute this value of a in the above equation:
[tex]y = -2(x + 3)^{2} + 3[/tex]
Following the procedures in graphing the sine function, graph the following functions.
1. y = tan x 2. y = csc x
Answers
Therefore , the solution of the given problem of function comes out to be y-intercepts of the function will be at y = 1 and y = -1.
Describe function.Numerous subjects, including mathematics, numbers, and their subsets, as well as building, construction, and both real and fictitious geographic locations, are covered in the mathematics programme. The relationships between various elements that all cooperate to create the same outcome are covered in a work. A utility is composed of several unique parts that, when combined, give particular outcomes for each input.
Here,
=> 1. Chart for y = tan x
The period of the function, which is, can be found in order to draw y = tan x.
The vertical asymptotes can then be found at x = /2 + n, where n is any number.
At x = n, where n is any positive number, the function will have x-intercepts.
The horizontal asymptotes at y = 1 and y = -1 are also accessible.
=> 2 .Chart for y = csc x
To draw y = csc x, we must first determine the function's period, which is 2.
The vertical asymptotes at x = n, where n is any number, can then be discovered.
The y-intercepts of the function will be at y = 1 and y = -1.
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The gas mileages (in miles per gallon) for cars are shown in the frequency distribution. Approximate the mean of the frequency distribution.
Gas Mileage
(in miles per gallon)
Frequency
Question content area bottom
Part 1
The approximate mean of the frequency distribution is
enter your response here.
Answers
The approximate mean of the frequency distribution is of 35.2 miles gallon.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
As we are given a frequency distribution, we take the midpoint of each interval, and thus the sum of the observations is given as follows:
10 x 30 + 12 x 35 + 3 x 40 + 4 x 45 = 1020.
There are 29 observations, hence the mean of these observations is given as follows:
1020/29 = 35.2 miles gallon.
Missing InformationThe frequency distribution is given as follows:
28-32 10
33-37 12
38-42 3
43-47 4
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Find the area of a parallelogram, if its base is 25 cm and distance between two parallel side is 15 cm.
Answers
Answer:
Step-by-step explanation:
A=bh
[tex]=25\times15[/tex]
[tex]=375cm^2[/tex]
37 students shared 5 pizzas equally? What fraction of the pizza did each student receive?
Answers
Answer:
Each student received 40/37 of a pizza slice.
Step-by-step explanation:
To find the fraction of the pizza each student received, we can start by finding the total number of pizza slices. Since each pizza was shared equally among 37 students, we can multiply the number of pizzas (5) by the number of slices in each pizza to get the total number of slices:
Total number of slices = 5 pizzas x 8 slices per pizza = 40 slices
Next, we can divide the total number of slices by the number of students to get the number of slices each student received:
Number of slices per student = 40 slices ÷ 37 students
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1:
Number of slices per student = 40/37 slices
Therefore, each student received 40/37 of a pizza slice.
Hope this helps! I'm sorry if it doesn't. If you need more help, ask me! :]
To find the fraction of the pizza each student received, we need to divide the total number of pizzas by the total number of students:
5 pizzas ÷ 37 students = 5/37 pizzas per student
Therefore, each student received 5/37 of a pizza.
Thabo travelled 95 kilometres in 2 hours. If he keeps going at the same rate, how long will it take him to go the remaining 165 kilometres of her trip?
Answers
Answer: Velocity, v= distance/time
Given: distance=95km & time= 2 hours
Velocity= 95/2 = 47.5km/hour
Step-by-step explanation:
Now, Distance= 165 km and we got velocity= 47.5km/hour
= 47.5 =165/time
Time taken = 165/47.5= 3hours and 50 minutes.
Therefore, Time taken to remaining 165 km of her trip is 3hours and 50 minutes.
Written as a simplified polynomial in standard form, what is the result when
(x + 5)2 is subtracted from 6x² + 3?
Answers
Expanding the square of the binomial (x + 5)^2, we get:
(x + 5)^2 = (x + 5)(x + 5) = x^2 + 10x + 25
Now, let's subtract (x + 5)^2 from 6x^2 + 3:
(6x^2 + 3) - (x^2 + 10x + 25)
Simplifying, we get:
6x^2 + 3 - x^2 - 10x - 25
Combining like terms, we get:
5x^2 - 10x - 22
Therefore, the result of subtracting (x + 5)^2 from 6x^2 + 3 is 5x^2 - 10x - 22, written in standard form.
Determine whether y^2=−2x−2 is a function
Answers
Answer:
It is not a function.
Geometry proof that opposite sides of a parallelogram are congruent.
Answers
The following is provided: parallelogram ABCD
The following is what we must demonstrate: segments AB, CD, and BC, and segment AD.
According to the definition of a parallelogram, section BC is parallel to segment AD since ABCD is a parallelogram.
The definition of a parallelogram is that segment AB is parallel to segment DC.
Segments BC and AD are transverse to line AC. As illustrated below, this transversal generates the alternate interior angles 1 and 4, which are equivalent.
In the same way, segment AB and segment DC are transversals for line AC. Alternate interior angles 2 and 3 are produced by this transversal, and they are equivalent.
Segment AC is also divided into segments by its reflexive property.
∠1 ≅ ∠ 4
∠2 ≅ ∠ 3
AC segment AC segment
Triangle ABC triangle ADC, by ASA
In light of the fact that similar parts of congruent triangles are also congruent, segment AB segment CD and segment BC AD.
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Find the values of for which the series converges. Find the sum of the series for those values of x. sum ∞ (2^n)/(x^n)
Answers
lim(n->∞) |(2^(n+1)/x^(n+1)) / (2^n/x^n)| = lim(n->∞) |(2/x)| = 2/|x|
Therefore, the series converges if 2/|x| < 1, or equivalently, if |x| > 2. So the series converges for x > 2 and x < -2.
To find the sum of the series for those values of x, we can use the formula for the sum of a geometric series:
S = a/(1-r)
where a = 2/x and r = 1/x. So we have:
S = (2/x) / (1 - (1/x)) = 2/(x-1)
if x > 2
S = (2/x) / (1 - (1/x)) = 2/(1-x)
if x < -2
Therefore, the sum of the series for x > 2 is 2/(x-1), and the sum of the series for x < -2 is 2/(1-x).
The temperature at a point
(x, y, z)
is given by
T(x, y, z) = 200e−x2 − 5y2 − 9z2
where T is measured in °C and
x, y, z
in meters.
Answers
The answer οf the given questiοn based οn the temperature is at the pοint (1, 2, 3) is apprοximately -62.3 °C.
What is Three-dimensiοnal Gaussian?A three-dimensiοnal Gaussian οr nοrmal distributiοn is type οf prοbability distributiοn that describes three-dimensiοnal data set. It is characterized by its mean, which determines center οf distributiοn, and its standard deviatiοn, which determines spread οr width οf distributiοn.
The temperature at a pοint:
(x, y, z)
is given by
T(x, y, z)
= 200e − x² − 5y² − 9z²
where T is measured in °C and
x, y, z
in meters.
The expressiοn 200e−x² − 5y² − 9z² represents a three-dimensiοnal Gaussian οr nοrmal distributiοn, with the highest temperature lοcated at the οrigin (0, 0, 0) and the temperature decreasing as we mοve away frοm the οrigin in any directiοn.
Tο find the temperature at a specific pοint (x, y, z), we substitute these values intο the expressiοn T(x, y, z) = 200e−x² − 5y² − 9z² and simplify. Fοr example, the temperature at the pοint (1, 2, 3) is:
T(1, 2, 3) = 200e−12 − 5(2)² − 9(3)²
T(1, 2, 3) = 200e−1 − 20 − 243
T(1, 2, 3) ≈ -62.3 °C
Therefοre, the temperature at the pοint (1, 2, 3) is apprοximately -62.3 °C.
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10. In the diagram below, ABC~ DEC
If AC = 12, DC = 7, DE = 5, and the perimeter of AABC is 30, what is the perimeter of ADEC?
A. 12.5
B. 14.0
C. 14.8
D. 17.5
Answers
Answer: B 14.0
Step-by-step explanation:
NEED HELP 35 POINTS!
Find x.
5 in.
8 in.
x
15 in.
Answers
Answer:
The answer is 24 in
Step-by-step explanation:
This solution is for "SIMILAR TRIANGLES";
Let us letter the shape starting from left to right A-B-C-D-E
Angle A is similar to Angle E, so is Angle B similar to Angle D, that is, "Alternate interior angles" while Angle ACB is similar to Angle DCE, that is, "Vertical Angles";
Line AB = 5 in is parallel to line DE = 15 in
So, K = DE / AB = 15 / 5 = 3
Line CD = K * CB = 3 * 8 = 24 in
Louise measured the perimeter of her rectangular scrapbook to be 138 cm. If the scrapbook is 39 cm wide, how long is the scrapbook?
Answers
2(+W)
P = 2(+W)
We know the perimeter is 154 and the width is 45
Substituting these values into the equation
154 = 2 (I+45)
Divide each side by 2
154/2 = 2/2 (I+45)
77=1+45
Subtract 45 from each side
77-45 = 1+45-45
32=1
The length is 32 cm
What is the surface area of the square pyramid?
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______________________________________
Answers
Answer:
105 in
Step-by-step explanation:
The area of the square pyramid = 4x( the area of the triangle) + the area of the squareArea of the triangle: the rule of multiplying the height divided by two4×(8×5) =80
2
5×5=25
25+80=105
1. Some students like their squash strong and use the ratio of 1:2 of squash to water How many litres of water are needed to mix with 1 litre of squash?
Answers
Answer:
If the ratio of squash to water is 1:2, it means that for every 1 unit of squash, we need 2 units of water.
So, to mix 1 liter of squash, we need 2 liters of water.
Therefore, the number of liters of water needed to mix with 1 liter of squash is 2 liters.
Step-by-step explanation:
Need help on these questions!
1. Find the balance in the same account: $3,000 principal, earning 3% compounding annually, after 4 years.
2. Find the balance in the same account: $2,000 principal, earning 7% compounding semi-annually, after 25 years.
3. A tractor costs $14,340 and depreciates in value by 15% per year. How much will the tractor be worth after 3 years?
Answers
The balance in the account after 4 years is $3,376.50.
The balance in the account after 25 years is $16,050.07.
The tractor will be worth $9,449.11 after 3 years.
What does your bank account balance read right now?All posted credit and debit transactions are included in your account balance. It's the balance in your account before any pending charges are subtracted. The amount that can be used for withdrawals or purchases is your accessible balance.
1. We can use the formula A = P(1 + r/n) to determine the account balance after 4 years with a $3,000 principal receiving 3% compounding annually (nt)
where A represents the balance, P represents the principal, r represents the yearly interest rate, n represents the number of times interest is compounded annually, and t represents the passage of time in years.
By typing in the indicated values, we get:
A = 3000(1 + 0.03/1)^(1*4)
A = 3000(1.03)^4
A = 3000(1.1255)
A = $3,376.50
Thus, $3,376.50 remains in the account after 4 years.
2. We can once more apply the formula: A = P(1 + r/n) to determine the account balance after 25 years with a $2,000 principal, receiving 7% compounding semi-annually (nt)
Then then, it's a case of the same thing happening again.
By typing in the indicated values, we get:
A = 2000(1 + 0.07/2)^(2*25)
A = 2000(1.035)^50
A = $16,050.07
Thus, the account has a balance of $16,050.07 after 25 years.
3. Considering that the tractor loses 15% of its value per year, we can apply the formula A = P(1 - r)t to determine how much it will be worth after three years.
where A represents the final value, P the starting point, r the depreciation rate, and t the passage of time in years.
By typing in the indicated values, we get:
A = 14340(1 - 0.15)^3
A = 14340(0.85)^3
A = $9,449.11
The tractor will therefore be valued $9,449.11 after three years.
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Construct a 95% confidence interval for the data (mean of the differences). Report your answers to three decimal places.
( ), ( )
for trader joes safeway
n = 57 n=57
x= 2.9442 x= 3.4123
s= 1.7458 s= 2.0382
Answers
We can be 95% confident that the true population mean difference between the two samples falls within the range of 0.374 to 0.562
Computing 95% Confidence Interval for Mean DifferencesTo construct a 95% confidence interval for the data, we need to calculate
the mean difference between two sample means (x₁ - x₂)the standard deviation of the differences (sD)the margin of error (ME)the upper and lower bounds of the confidence interval (CI).The formula for the mean difference is:
x₁ - x₂ = 3.4123 - 2.9442 = 0.4681
The formula for the standard deviation of the differences is:
sD = √[(s₁²/n₁) + (s₂²/n₂)]
SD = √[(1.7458²/57) + (2.0382²/57)]
SD = 0.3555
The margin of error is calculated using the following formula:
ME = t * (sD / √(n))
where t is the critical value for a 95% confidence interval with 56 degrees of freedom
So, we have
ME = 2.003 * (0.3555 / √(57))
ME = 0.0943
Finally, we can calculate the upper and lower bounds of the confidence interval:
CI = (x₁ - x₂) ± ME
CI = 0.4681 ± 0.0943
CI = (0.4681 - 0.0943, 0.4681 + 0.0943)
CI = (0.3738, 0.5624)
Approximate
CI = (0.374, 0.562)
Thus, the 95% confidence interval for the mean differences is (0.374, 0.562), rounded to three decimal places.
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Does A (1,2) and A prime (5,12) represent a dilation? Why or why not?
Answers
Hence, in response to the provided question, we can say that As a result, equation A(1,2) and A'(5,12) are not dilations.
What is equation?An algebraic equation is a method of connecting two quotes by using the equals symbol (=) to express equality. In algebra, an explanation is a definitive expression that verifies the equivalency of two formula. For example, the identical character divides the numbers 3x + 5 and 14. A linear equation might be used to recognize the connection that existing between the texts written on separate sides of a letter. The product and application both frequently the same. 2x - 4 equals 2, for example.
To evaluate if the points A(1,2) and A'(5,12) reflect a dilation, we must first determine the dilation's scale factor.
Let's use the given points to compute the scale factor:
(length of A' A) / scale factor (length of A)
A's length A [tex]=\ sqrt[(5-1)2 + (12-2)2] = \sqrt[16^2 + 10^2] =\ sqrt(296) (296)[/tex]
A's length is one.
[tex](\sqrt(296)) / 1\\\sqrt(x) = scale factor (296)[/tex]
As a result, the scaling factor is not an integer. That is, the transformation from point A to point A' is not a dilation with a whole number scale factor.
As a result, A(1,2) and A'(5,12) are not dilations.
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if a,b and c are such that a:b:c =1:3:4 and c =28 then, the sum of a+b+c is
Answers
Answer:
the sum of a+b+c is 56.
Step-by-step explanation:
If a:b:c = 1:3:4 and c = 28, we can find the values of a and b using the ratios.
Since a:b:c = 1:3:4, we can write:
a = x, b = 3x, c = 4x
where x is some constant of proportionality.
We are given that c = 28, so we can substitute this value to get:
4x = 28
Solving for x, we get:
x = 7
Therefore, a = x = 7 and b = 3x = 21.
The sum of a, b, and c is:
a + b + c = 7 + 21 + 28 = 56
So the sum of a+b+c is 56.
Which net matches the figure?
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____________________________________
Answers
Answer:
Figure D.
Step-by-step explanation:
The given Figure is a cube , which is a three-dimensional shape that has six square faces, twelve edges, and eight vertices. All of its faces are congruent and perpendicular to each other.
Figure D will turn into Square box when it is folded. Rest all are either Cuboid or Irregular Shaped objects when folded.
30 POINTSSSSSS!!
A football coach orders one hoodie or one long sleeve performance shirt for each of his 45 players. Each hoodie costs $60 and each long sleeve performance shirt costs $45. The entire order totaled $2,400.
Use the substitution method or elimination method to determine the number of hoodies and performance shifts ordered. SHOW ALL STEPS IN SOLVING PROCESS.
Answers
According to the question the 25 hoodies and 20 performance shirts were ordered.
What is performance?Performance is the result of an individual or organization's efforts in terms of achieving a desired outcome or goal. It is usually measured in terms of objectives, tasks and outcomes, and is a way of assessing the effectiveness of an individual or organization.
Substitution Method:
Let x = the number of hoodies ordered
Let y = the number of performance shirts ordered
Then, x + y = 45 (The total number of items ordered)
60x + 45y = 2400 (The total cost of the order)
Solve for x by substituting y = 45 - x into the second equation:
60x + 45(45 - x) = 2400
60x + 2025 - 45x = 2400
15x = 375
x = 25 (25 hoodies were ordered)
Substitute x = 25 into the first equation:
25 + y = 45
y = 20 (20 performance shirts were ordered)
Therefore, 25 hoodies and 20 performance shirts were ordered.
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Find the x and y intercept
Find the vertical and horizontal asymptotes
s(x)=6/ x^2 - 5x - 6
Answers
Answer:
To find the x and y intercepts, we set x and y to zero respectively:
x-intercept: setting y = 0 gives us 6/(x^2 - 5x - 6) = 0, which has no real solutions.
y-intercept: setting x = 0 gives us s(0) = 6/(-6) = -1.
To find the vertical asymptotes, we set the denominator equal to zero and solve for x:
x^2 - 5x - 6 = 0
(x - 6)(x + 1) = 0
This gives us two vertical asymptotes at x = 6 and x = -1.
To find the horizontal asymptote, we need to look at the behavior of the function as x approaches infinity and negative infinity. As x becomes very large in magnitude, the terms involving x^2 become much larger than the terms involving x or the constant term, and so we can ignore those terms. This gives us:
s(x) ≈ 6/x^2 as x → ±∞
Therefore, the horizontal asymptote is y = 0.
In summary:
x-intercept: none
y-intercept: (0, -1)
vertical asymptotes: x = 6 and x = -1
horizontal asymptote: y = 0
If you have anymore questions, feel free to comment and I will answer them 8-5 I am on.
Step-by-step explanation:
Statistics Card Question!
You are dealt a hand of 8 cards from a standard deck of 52 cards. Find the probability of being dealt five clubs and three cards with one card of each other remaining suit.
Answers
Therefore , the solution of the given problem of probability comes out to be 0.00439, or about 0.44%.
Probability : What is it?The main goal of the mathematical field known as model parameters is to determine the probability that a statement is accurate or that a particular event will occur. It is possible to symbolise chance by using any ranging between range 0 and 1, where 1 typically denotes certainty and 0 typically denotes possibility. A probability diagram illustrates the likelihood that a particular occurrence will take place.
Here,
To calculate the likelihood of receiving a hand of five clubs, three cards, and one card from each remaining deck,
Five clubs can be obtained in the following ways:
=> C(13,5) = 1,287
where C(n,r) indicates how many different ways r things were combined from a total of n options.
After selecting the five clubs, we must select three cards, one from each of the remaining three decks.
=> C(13,2) * C(3,2) = 702
As a result, there are three cards from each of the other two decks and five clubs, giving rise to the following combinations:
=> C(13,5) * [C(39,3) - C(13,2) * C(3,2)] = 328,664
Finally, there are C(52,8) = 74,837,381 potential hands with 8 cards.
The likelihood of receiving five clubs and three cards, along with one card from each of the other three decks, is as follows:
=> P = 328,664 / 74,837,381
=> P ≈ 0.00439, or about 0.44%.
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Without using a calculator, compute the sine and cosine of
by using the reference angle. What is the reference angle?
degrees.
Answers
The reference angle is given as 45 degrees
the angle is in the 4th quadrant
sin 315 = - sqrt(2) / 2
cos 315 = sqrt(2) / 2
How to solve for the reference angleWe have θ = 315
θ is seen to lie between 270 degrees and 360 degrees in the 4th quadrant
In the fourth quadrant the reference angle has been solved by:
360 - θ
360 - 315
= 45 degrees
The reference angle is 45 degrees
sin 315 = sin( 360 - 45)
= [tex]-\frac{\sqrt{2} }{2}[/tex]
= - sqrt(2) / 2
cos 315 = cos (360 - 45)
= [tex]\frac{\sqrt{2} }{2}[/tex]
= sqrt(2) / 2
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A sheet of cardboard 10 inches by 12 inches will be made into a box cutting equal-sized squares from each corner and folding up four edges. If the area of the base is to be 80 square inches, then what size square should be cut from each corner?
Answers
Using the area formula for the measure for side of square cut out is obtained as 1 inch.
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The length of the cardboard is 12 inch.
The breadth of the cardboard is 10 inch.
Let x inches square be cut from the 4 corners.
Then the length of the base = 12 - 2x.
Then the breadth of the base = 10 - 2x.
The area of the base is given is 80 inch².
The equation for the carboard will be -
l × b = area
Substitute the values into the equation -
(12 - 2x) × (10 - 2x) = 80
Simplify the equation -
120 - 24x - 20x + 4x² = 80
4x² - 44x + 40 = 0
x² - 11x + 10 = 0
Use the factorization method -
x² - 10x - x + 10 = 0
x(x - 10) - 1(x - 10) = 0
(x - 10)(x - 1) = 0
x = 10 or x = 1
Since, the breadth of the cardboard is 10 inches so x cannot be 10.
Therefore, the value of x is obtained as 1 inch.
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