PLEASE MATH HELP!!
The area of this circle is 96π m².
What is the area of a 30º sector of this circle?
4π m²
8π m²
9π m²
16π m²
Answers
30 degrees / 360 degrees = 0.0833
0.0833 * 96 = 8
answer is 8π m²
The area of a [tex]30^{\circ}[/tex] sector of this circle is [tex]8\pi \ m^2[/tex]. The correct option is B. [tex]8\pi \ m^2[/tex].
Given,The area of circle is [tex]96 \pi \ m^2[/tex].
We have to calculate the area of [tex]30^{\circ}[/tex] sector of this circle.
Area of circle:We know that, Area of circle is,
[tex]A=\pi r^{2}[/tex]
Here, [tex]96\pi =\pi r^{2}[/tex]
Or,
[tex]r^{2} =96[/tex]
[tex]r=\sqrt{96}[/tex]
[tex]r=4\sqrt{6}[/tex]
So, radius of the circle,
[tex]r=4\sqrt{6}[/tex] [tex]m[/tex].
Now we know that Area of a Sector of Circle
Say [tex]A_{1}[/tex],
[tex]A_{1} = \frac{\Theta}{360} \pi r^{2}[/tex]
where [tex]\Theta[/tex] is the angle subtended at the center, given in degrees, and '[tex]r[/tex]' is the radius of the circle.
So,
[tex]A_{1} =\frac{30}{360} \pi (4\sqrt{6} )^{2}[/tex]
[tex]A_{1} =\frac{1}{12} \pi \times96[/tex]
[tex]A_{1} =8\pi \ m^2[/tex].
Hence the area of a [tex]30^{\circ}[/tex] sector of this circle is [tex]8\pi \ m^2[/tex]. the correct option is B [tex]8\pi \ m^2[/tex].
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Related Questions
devise a plan for simplifying th fourth root of a number that is not a perfect fourth power.
Answers
Final answer:
To simplify the fourth root of a non-perfect power, use a calculator to raise the number to the power of 0.25, or calculate the square root twice. For non-integer powers, calculate roots with corresponding fractional exponents. Request assistance from your instructor if necessary.
Explanation:
Simplifying the Fourth Root of Non-Perfect Powers
When simplifying the fourth root of a number that is not a perfect fourth power, you can utilize the power function on a calculator. This involves raising numbers to the power of 0.25, which equates to calculating the fourth root. For example, using the y* button (or equivalent) you can calculate the fourth root of any number by raising it to the power of 0.25. This is analogous to how raising a number to the 0.5 power gives us the square root of that number. If your calculator doesn't have this function, another technique is to calculate the square root of the number twice, since the fourth root is essentially the square root of the square root.
To work through a non-integer power, like 31.7, you can find the tenth-root of 3 by raising it to the power of 0.1 and then raise the result to the 17th power. Similarly, for expressions with fractional exponents like x0.5, you can interpret this as the square root of x. Understanding that fractional powers represent roots can help in simplifying complex expressions without a calculator as well.
If you are dealing with equilibrium problems or other scenarios that require finding roots of numbers, it's crucial to be comfortable with these techniques. If you are unsure about how to perform these operations, don't hesitate to ask for assistance from your instructor. Developing a natural and forgiving relationship with numbers, and only representing precision as needed, is also an important aspect of working with mathematical problems.
The perimeter of a fence is 140 feet. The sum of three times the length and two times the width is 180 feet. What are the length and width of the fence?
Answers
Final answer:
The perimeter problem is solved using two simultaneous equations derived from the given information about the perimeter and sum of sides. The solution reveals that the width (w) of the fence is 30 feet and the length (l) is 40 feet.
Explanation:
We are given that the perimeter of a fence is 140 feet. The perimeter formula for a rectangle is P = 2l + 2w, where l is the length and w is the width of the rectangle.
According to the problem, we also know that 3 times the length plus 2 times the width equals 180 feet (3l + 2w = 180).
Let's assign variables: Let l represent the length and w represent the width of the fence. We can now set up two equations:
2l + 2w = 140 (Perimeter equation)3l + 2w = 180 (Given equation)We can solve these equations simultaneously to find the values for l and w.
First, simplify the perimeter equation by dividing everything by 2: l + w = 70. Now substitute l from the simplified equation into the given equation to find w:
3(70 - w) + 2w = 180210 - 3w + 2w = 180-w = -30w = 30Now that we have the width, we can find the length using the simplified perimeter equation:
l + 30 = 70l = 40Therefore, the width (w) is 30 feet, and the length (l) is 40 feet.
The length of the fence is 40 feet and the width is 30 feet.
Explanation:To solve this problem, we can set up a system of equations. Let's denote the length of the fence as 'l' and the width as 'w'. From the given information, we have the following equations:
2l + 2w = 140 (equation 1)
3l + 2w = 180 (equation 2)
We can solve this system of equations by eliminating a variable. Multiply equation 1 by 3 and equation 2 by 2 to eliminate 'w':
6l + 6w = 420 (equation 3)
6l + 4w = 360 (equation 4)
Subtract equation 4 from equation 3 to eliminate 'l':
6w - 4w = 420 - 360
2w = 60
w = 30
Substitute the value of 'w' into equation 1 to solve for 'l':
2l + 2(30) = 140
2l + 60 = 140
2l = 80
l = 40
Therefore, the length of the fence is 40 feet and the width is 30 feet.
Which is the focus of a parabola with equation y2=-12x
Answers
y²=-12x
the vertex is the point (0,0)------------- > see the attached figure
standard form: (y-k)^2=4p(x-h), with (h,k) being the (x,y) coordinates of the vertex.
vertex(0,0)
4p=-12---- > p=-12/4
p=-3
Focus:(-3,0)
the answer is (-3,0)
Melissa needs to memorize words on a vocabulary list for Russian class. She has memorized 30 of the words, which is five-sixths of the list. How many words are on the list?
Answers
[tex] \frac{5}{6} x=30[/tex]
Solve for x by isolating it. First we multiply both sides by 6 to cancel out the one-sixth.
[tex]5x = 180[/tex]
Next divide both sides by 5 to cancel out the 5 being multiplied to the x.
[tex]x = 36[/tex]
The answer is 36 words.
The list has 36 words
Explanation:
Assume that the number of words on the list is x.
We are given that:
5/6 of the number of words on the list is equal to 30 words.
This means that:
(5/6)*x = 30
Solve for x as follows:
(5/6)*x = 30
5x = 6*30
5x = 180
x = 180/5
x = 36
Hope this helps :)
find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule A(n)=-6+(n-1)(1/5)
Answers
A(4) = -6 +(4 -1)*(1/5) = -5 2/5
A(10) = -6 +(10 -1)*(1/5) = -4 1/5
The formula that represents the nth term of a arithmetic sequence is given by:
[tex]A(n)=-6+(n-1)(\dfrac{1}{5})[/tex]
Now, we are asked to find the first, fourth, and tenth terms of the arithmetic sequence.
i.e. we are asked to find the value of A(n) when n=1 ,4 and 10
when n=1 we have:[tex]A(1)=-6+(1-1)(\dfrac{1}{5})\\\\i.e.\\\\A(1)=-6+0\\\\i.e.\\\\A(1)=-6[/tex]
now when n=4 we have:[tex]A(4)=-6+(4-1)\times (\dfrac{1}{5})\\\\i.e.\\\\A(4)=-6+3\times \dfrac{1}{5}\\\\i.e.\\\\A(4)=-6+\dfrac{3}{5}\\\\i.e.\\\\A(4)=\dfrac{-6\times 5+3}{5}\\\\i.e.\\\\A(4)=\dfrac{-30+3}{5}\\\\i.e.\\\\A(4)=\dfrac{-27}{5}[/tex]
when n=10 we have:[tex]A(10)=-6+(10-1)\times (\dfrac{1}{5})\\\\i.e.\\\\A(10)=-6+9\times \dfrac{1}{5}\\\\i.e.\\\\A(10)=-6+\dfrac{9}{5}\\\\i.e.\\\\A(10)=\dfrac{-6\times 5+9}{5}\\\\i.e.\\\\A(10)=\dfrac{-30+9}{5}\\\\i.e.\\\\A(10)=\dfrac{-21}{5}[/tex]
What is the point of maximum growth rate for the logistic function f(x) ?
Answers
a speed of limit of 100 kilometers per hour is approximately equal to 62 miles per hour predict the following measures round your answers to the nearest whole number
a. a speed limit in mph for a speed limit of 75 kph
b. a speed limit in kph for a speed limit of 20 mph
Answers
The ratio is 1.6kph for every 1mph so for the first one you divide by 1.6 and the second you multiply
Answer:
a. 46.5 mph
b. 32.3 kph
Step-by-step explanation:
If the speed limit is 100 km/hour we and this equals 62 mile per hour we can determine how many kilometers is in miles and vice versa:
WE can do this as:
[tex]62/100=0.62[/tex]
Therefore the 0.62 miles per kilometer
a) For 75 kph we can use the conversion we determine to convert to miles per hour:
[tex]75*0.62=46.5[/tex]
It takes a speed limit of 46.5 mph for a 75 kph limit
b) For 20 mph we can use the conversion we determine to convert to kilometers per hour:
[tex]20/0.62=32.3[/tex]
It takes a speed limit of 32.3 kph for a 20 mph limit
Find the radius of a sphere with a surface area of 804 cm^2.
A. 9cm
B. 8cm
C. 64cm
D. 204cm
Answers
We have then:
A = 4 * π * R ^ 2
Substituting:
804 = 4 * π * R ^ 2
Clearing the value of R we have:
R = root (804 / (4 * π))
R = 7.99876785 cm
Nearest whole number:
R = 8 cm
Answer:
The radius of a sphere is:
B. 8cm
Final answer:
The radius of a sphere with a surface area of 804 cm² is found by using the formula A = 4πr², solving for r, and taking the square root. The correct answer is B. 8cm.
Explanation:
To find the radius of a sphere with a given surface area, we use the formula for the surface area of a sphere, which is A = 4πr². Given that the surface area (A) is 804 cm², we can solve for the radius (r).
Plugging the given surface area into the formula yields:
804 cm² = 4πr²
Next, we divide both sides of the equation by 4π to solve for r²:
r² = 804 cm² / (4π)
To find r, we take the square root of both sides:
r = [tex]\sqrt{(804[/tex]cm² / (4π))
Calculating the right side of the equation gives us the radius:
r ≈ [tex]\sqrt{(804[/tex] cm² / 12.5663706143592)
r ≈ [tex]\sqrt{(64[/tex]
r = 8 cm
Therefore, the correct answer is B. 8cm.
Each cone of the hourglass has a height of 18 millimeters . the total height of the sand within the top portion of the hour glass is 54 millimeters. The radius of both cylinder and cone is 8 millimeters. Sand drips from the top to the bottom at a rate of 10n cublic millimeters per second. How many seconds will it take until all the sand has dripped to the bottom of the hour glass?
Answers
Vco------------------- >Volume cone
Vcy------------------ >Volume cylinder
r= 8mm
hco----------- > height of cone=18 mm
hcy------------ > height of cylinder =54-18=36 mm
then
Vco=π*r² *hco/3--------- > π*8² *18/3=π*384 mm³
Vcy=π*r² *hcy--------- > π*8² *36=π*2304 mm³
the total cubic millimeters of sand=Vco+Vcy=π*384+π*2304=π*2688
if 10π cubic millimeters --------------------- > 1 seg
π*2688--------------------------------- X
X=π*2688/10π=268.8 seg
the answer is 268.8 seg
The volume of the sand in the top portion of the hourglass is calculated using the volume formula for cones. Given the dripping rate, it takes about 115 seconds for all the sand to drip to the bottom.
To determine how many seconds it will take for all the sand to drip to the bottom, we need to find the volume of sand in the top cone.
Each cone has a height of 18 millimeters and a radius of 8 millimeters.The volume of a cone is given by the formula: V = (1/3)πr²h.Substituting the given values, we get: V = (1/3)π(8)²(18) = 1,206.37 cubic millimeters of sand per cone.The total height of sand in the top portion is 54 millimeters, which means the equivalent of three cones of sand (since 54 mm / 18 mm/cone = 3).
Thus, the total volume of sand is 3 x 1206.37 = 3619.11 cubic millimeters.
Given the sand drips at a rate of 10π cubic millimeters per second, we find the total time by dividing the volume by the rate:
Time = Total Volume / Rate = 3619.11 / 10π ≈ 115.13 seconds.
Therefore, it will take approximately 115 seconds for all the sand to drip to the bottom of the hourglass.
For which interval is the average rate of change of f(x) negative?
Answers
For this case, the first thing you should do is observe the intervals for which the function decreases.
Remember that the definition of average rate of change is given by:
[tex]AVR = (f (x2) - f (x1)) / (x2-x1) [/tex]
For AVR to be negative, it must necessarily pass:
[tex]x2\ \textgreater \ x1 f (x1) \ \textgreater \ f (x2)[/tex]
The interval that meets both conditions is:
x = 0 to x = 2.5
Answer:
x = 0 to x = 2.5
option 3
Answer:
c on edge
Step-by-step explanation:
took the exam
A pendulum has 887 J of potential energy at the highest point of its swing. How much kinetic energy will it have at the bottom of its swing?
Answers
WILL GIVE BRAINLIEST!!! 12 POINTS!!!!
The table below shows the quiz grades for two students.
Drew 90 81 86 79 97 84 92
Nancy 96 68 91 94 69 99 92
Which statement is true about the data above?
* The students have the same mean, but Nancy's quiz grades have a higher interquartile range.
* The students have the same mean, but Drew's quiz grades have a higher interquartile range.
* The students' grades have the same interquartile range, but Drew has a higher mean.
* The students' grades have the same interquartile range, but Nancy has a higher mean.
Answers
data set for Drew : [90,81,86,79,97,84,92], sorted : [79,81,84,86,90,92,97]
mean, μ 1 =(79+81+84+86+90+92+97)/7=87
Interquartile range, IQR 1 = (92-81)=11
data set for Nancy: [96,68,91,94,69,99,92], sorted : [68,69,91,92,94,96,99]
mean, μ 2 = (68+69+91+92+94+96+99)/7=87 Therefore the means are the same
Interquartile range, IQR 2 = 96-69 = 27 Therefore Nancy has a higher IQR
Note: There are different ways to calculate quartiles. Above method excludes median, which is how it is taught in many schools.
At the city museum, child admission is $5.20 and adult admission is $8.90 . on friday, 159 tickets were sold for a total sales of $1100.60 . how many adult tickets were sold that day?
Answers
Total sales = $1100.60
Child admission = $5.20
Adult admission = $8.90
Assumed all 159 tickets are Child admission tickets
Total sales = 159 x 5.2 = $826.80
Difference in amount = $1100.60 - $826.80 = $273.80
The difference must be contributed by the Adult Admission Tickets, which has a difference of $8.90 - $5.20 = $3.70
$273.80 ÷ $3.70 = 74 adult tickets
159 - 74 = 85 child tickets
Suppose you invest $400 at an annual interest rate 7.6% compounded continuously. How much will you have in the account after 1.5 years? Round the solution to the nearest dollar
Answers
You can expect to have approximately $447 in your account after 1.5 years of continuously compounded interest on your $400 investment.
How much will you have in the account after 1.5 years?
To find out how much you'll have in your account after 1.5 years, we can follow these steps:
1. Formula: Use the formula for continuous compounding:
[tex]Final\ amount = Initial\ amount * (1 + annual\ interest\ rate)^{time}\[/tex]
2. Plug in the values: We know:
Initial amount = $400
Annual interest rate = 7.6% (remember to convert it to a decimal by dividing by 100, so 7.6% becomes 0.076)
Time = 1.5 years
3. Calculation: Substitute the values and calculate:
Final amount = $400 * (1 + 0.076)^{1.5}
[tex]Final\ amount = $400 * (1 + 0.076)^{1.5} = 446.5[/tex]
4. Round the answer: Round the final amount to the nearest dollar:
Final amount = 447
algebra 2 function operations (link)
Answers
g(x) = x - 1
f(x).g(x) - [f(x) + g(x)] = (2x^2 + x - 3) (x - 1) - [2x^2 + x - 3 + x - 1]
f(x).g(x) - [f(x) + g(x)] = (2x^3 - 2x^2 + x^2 - x - 3x + 9) - [2x^2 + 2x - 4]
f(x).g(x) - [f(x) + g(x)] = (2x^3 - x^2 - 4x + 9) - [2x^2 + 2x - 4]
f(x).g(x) - [f(x) + g(x)] = 2x^3 - x^2 - 4x + 9 - 2x^2 - 2x + 4
f(x).g(x) - [f(x) + g(x)] = 2x^3 - 3x^2 - 6x + 13
Which ordered pairs are solutions to the inequality 2x+3y>-1?
Select each correct answer.
(0,1)
(0,-1)
(-2,1)
(-6,0)
(2,-1)
Answers
2(0)+3(1) = 3 Yes 3 is greater than -1
2(0)+3(-1) = -3 No -3 is not greater than -1
2(-2)+3(1) = -1 No -1 is not greater than -1
2(-6)+3(0) = -12 no -12 is greater than -1
2(2)+3(-1) = 1 Yes 1 is greater than -1
2x+3y>-1?
Select each correct answer.
(0,1)
(0,-1)
(-2,1)
(-6,0)
(2,-1)
The ordered pairs are (0, 1), and (2, -1) which are solutions to the inequality 2x+3y>-1 option first and fifth are correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have an inequality:
2x+3y>-1
The above inequality is a straight line and represents a region.
After plotting the inequality on the graph.
The points are in the region of the inequality:
(0, 1)(2, -1)These points satisfy the inequality.
Thus, the ordered pairs are (0, 1), and (2, -1) which are solutions to the inequality 2x+3y>-1 option first and fifth are correct.
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Which dot plot has more than one mode?
Answers
Answer:
The dot plot representing the calico crayfish has more than one mode.
Step-by-step explanation:
We know that mode of the data is the value corresponding to the highest frequencies.
or we may say the mode of a data set is the number that occurs most frequently.
Clearly from the dot plot we could see that the data representing the calico crayfish have two quantities with four dots ( one is when number of calico crayfish are 5 and the other when number of calico crayfish are 8)
Also by making a frequency table we may check it as:
Number of calico crayfish frequency
1 1
2 0
3 1
4 3
5 4
6 1
7 2
8 4
9 0
10 2
The dot plot shows calico crayfish has more than one mode. In the data set each column of a table represents a specific variable and each row represents a specific record of the data sets.
What is a data set?A data set is a set of information corresponds to one or more database tables in the case of tabular data,
From the table of the calico crayfish, it is observed that the data no 5 on the x-axis the frequency is 4. As well as on data no 8 the frequency is 4.
The dot plot shows calico crayfish has more than one mode. because it shows the same frequency at two other variables;
Hence the dots plot shows calico crayfish has more than one mode.
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Solve (4 - x ≤ -1) ∩ (2 + 3x ≥ 17). Click on the graph until the solution set appears.
Answers
The solution set appears at x ≥ 5 for (4 - x ≤ -1) ∩ (2 + 3x ≥ 17).
What are sets and subsets?A set is a collection of well-defined objects.
A subset contains all the elements or a few elements of the given set.
The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.
The symbol ∩ represents an intersection or common between them.
Given, (4 - x ≤ -1) ∩ (2 + 3x ≥ 17).
( x ≥ 5) ∩ ( x ≥ 5).
So, x ≥ 5.
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A) Inverse Property of Multiplication
B) Commutative Property of Multiplication
C) Associative Property of Addition
D) Commutative Property of Addition
Answers
Hope this helps!
The answer is B, the commutative property of multiplication.
The commutative property of multiplication states that you get the same value in an expression, not depending on the order. See here, you have -3/9 and 2, and even though they're in different orders, when you multiply them, they're equal.
Notice how it doesn't work in other operations such as subtraction and division (it works in addition):
10/5 ≠ 5/10
4-10 ≠ 10-4
However,
5 + 10 = 10 + 5
Hope this helps!
Find the quotient
A. 7r5
B. 6r1
C. 5r5
D. 5r3
Answers
Answer is 5r5
Solve the following equation, answer as a reduced, mixed number. Then place the correct number in the box provided.
15(2 - x) = 13(3 - x)
x=(written as a fraction)
Answers
the answer i got was x = - 9/2
hope this helps
+15x +15x
30 = 39 + 2x
-39 -39
-9 = 2x
-9/2 = x
Simplified: x= -4 1/2
Which table represents a linear function that has a slope of 5 and a y-intercept of 20?
Answers
y=5x+20
We substitute the data of each of the tables and see that table 4 is appropriate
Answer: table 4
Table 4 represents the linear function that has slope of 5 and a y-intercept of 20.
Further explanation:
The linear equation with slope [tex]m[/tex] and intercept [tex]c[/tex] is given as follows.
[tex]\boxed{y = mx + c}[/tex]
Given:
The y-intercept is [tex]\left( { - 9, - 3} \right).[/tex]
The slope of the linear function is [tex]- 6.[/tex]
Explanation:
The linear function can be expressed as follows,
[tex]y = 5x + 20[/tex]
In table 1,
Substitute [tex]-60[/tex] for [tex]x[/tex] and 8 for [tex]y[/tex] in linear function to check whether the point satisfy the linear function.
[tex]\begin{aligned}8&= 5\left({ - 60} \right) + 20\\8&= - 300 + 20\\8&= - 280\\\end{aligned}[/tex]
Table 1 is not correct.
In table 2,
Substitute 20 for [tex]x[/tex] and [tex]0[/tex] for [tex]y[/tex] in linear function to check whether the point satisfy the linear function
[tex]\begin{aligned}0&= 5\left( {20} \right) + 20\\0&= 100 + 20\\&0\ne120\\\end{aligned}[/tex]
Table 2 is not correct.
In table 3,
Substitute [tex]-20[/tex] for [tex]x[/tex] and 0 for [tex]y[/tex] in linear function to check whether the point satisfy the linear function
[tex]\begin{aligned}- 20&= 5\left( 0 \right) + 20\\- 20 &\ne 20\\\end{aligned}[/tex]
Table 3 is not correct.
In table 4,
Substitute [tex]-4[/tex] for [tex]x[/tex] and 0 for [tex]y[/tex] in linear function to check whether the point satisfy the linear function
[tex]\begin{aligned}0&= 5\left( { - 4} \right) + 20\\0&= - 20 + 20\\0&= 0\\\end{aligned}[/tex]
Table 4 is correct.
Table 4 represents the linear function that has slope of 5 and a y-intercept of 20.
Learn more:
1. Learn more about the equation in the intercept form https://brainly.com/question/1473992.
2. Learn more about binomial and trinomials https://brainly.com/question/1394854.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: linear function, numbers, slope 5, y-intercept of 20, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation.
is 1 over 3 rational
Answers
George and Chin work as landscapers. George charges $90 for a 6-hour job. Chin charges $84 for the same job.The table shows their price structures. An equation representing George’s charges is written in the chart.
Landscaping Cost
George
Chin
George charges one hourly rate for the first three hours and then reduces his rate for additional hours. Chin charges the same initial rate as George for the first two hours and the same reduced rate for additional hours.
mc016-1.jpg
What is the equation for Chin’s charges needed to solve the system and find the cost of the initial and additional hours?
Answers
Answer:
C
Step-by-step explanation:
did the test
Answer:
c
Step-by-step explanation:
sorry wrong problem if ab =58 find the value of x
Answers
5x - 2 = 58
5x = 60
x = 12
answer
x = 12
Answer:
x=12
Step-by-step explanation:
if ab =58 find the value of x
The length of AB= 58
Given : AC= 3x-6
CB= 2x+4
[tex]AC + CB=AB[/tex]
Now replace the expressions
[tex]3x-6+2x+4=58[/tex]
now we solve for x, combine like terms
[tex]5x-2=58[/tex]
Add 2 on both sides
[tex]5x=60[/tex]
Divide both sides by 5
x=12
How many ways can you choose the 5 cards out of a 52 card deck?
Answers
There are 2,598,960 ways to choose 5 cards out of a 52-card deck.
Explanation:To determine the number of ways to choose 5 cards out of a deck of 52 cards, we can use the concept of combinations. In this case, order doesn't matter, so we use the formula for combinations. The formula is:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of items to choose from and r is the number of items to be chosen.
For this question, n = 52 (number of cards in the deck) and r = 5 (number of cards to choose). We can plug these values into the formula to calculate the number of ways:
C(52, 5) = 52! / (5!(52-5)!) = 2,598,960
So, there are 2,598,960 ways to choose 5 cards out of a 52-card deck.
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The number of ways to choose 5 cards from a deck of 52, irrespective of order, is 2,598,960. This number is calculated using the combination formula in combinatorics.
Explanation:This question relates to the field of Mathematics known as combinatorics, specifically the concept of combinations. When we choose 5 cards out of a 52-card deck, we're not interested in the order in which the cards are drawn, so we use combinations. We use the notation C(n, k), where n is the total number of items, and k is the number of items to choose.
The formula for finding combinations is C(n, k) = n! / [k!(n-k)!]. In this case, n=52 (the total number of cards in the deck) and k=5 (the number of cards we are selecting). Plug these values into the formula to get C(52, 5) = 52! / [5!(52-5)!] = 52! / (5!47!) = 2,598,960
So, there are 2,598,960 ways to choose 5 cards out of a 52 card deck. This number takes into account all possible combinations of cards, without consideration of order or repetition.
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A stadium brings in $16.25 million per year. it pays football-related expenses of $13.5 million and stadium expenses of $2.7 million per year. whatis the stadium's current profit margin
Answers
To find the stadium's profit margin, subtract its expenses from its revenue and divide by the revenue, then multiply by 100 to get the percentage.
Explanation:In order to find the stadium's current profit margin, we need to subtract its total expenses from its total revenue and then divide the result by the total revenue. The stadium brings in $16.25 million per year and has football-related expenses of $13.5 million and stadium expenses of $2.7 million per year.
To calculate the profit margin, we subtract the total expenses ($13.5 million + $2.7 million) from the total revenue ($16.25 million): $16.25 million - ($13.5 million + $2.7 million) = $16.25 million - $16.2 million = $0.05 million.
Finally, we divide the profit ($0.05 million) by the total revenue ($16.25 million) and multiply by 100 to get the profit margin as a percentage: ($0.05 million / $16.25 million) * 100 = 0.003076923076923 * 100 = 0.3076923076923%.
Avi's pet hamster Chubby loves to run in his hamster wheel. During one "race", Avi counts 100 rotations of the wheel. She wants to know how far Chubby ran, so she measures the diameter of the wheel and finds that it 8 inches.
how far did chubby run?
i need the answer in terms of pi
Answers
c=pi*d
c=8pi
Multiply by 100 and you get 800pi inches
which is the correct form of q(x) + r(x)/b(x) for expression 7x^4+x+14/x+2
Answers
(7x^4+x+14)----------------------|(x+2)
-14x³+x+14-------------------------7x³-14x²+28x-55------> q(x)
28x²+x+14
-55x+14
110+14=124------------------------> r(x)
r(x)=124
b(x)=x+2
q(x)=7x³-14x²+28x-55
then
q(x) + r(x)/b(x)---------> (7x³-14x²+28x-55)+(124)/(x+2)
the answer is (7x³-14x²+28x-55)+(124)/(x+2)
The expression [tex]\(\frac{7x^4 + x + 14}{x + 2}\)[/tex] is [tex]\(7x^3 - 14x^2 + 28x - 55 + \frac{124}{x + 2}\)[/tex].
To find the correct form of the expression [tex]\(\frac{7x^4 + x + 14}{x + 2}\)[/tex] in the form [tex]\(q(x) + \frac{r(x)}{b(x)}\)[/tex], where [tex]\(q(x)\)[/tex] is the quotient and [tex]\(r(x)\)[/tex] is the remainder, we need to perform polynomial long division. Here, [tex]\(b(x) = x + 2\)[/tex].
Step-by-Step Solution:
1. Setup the Division:
Divide [tex]\(7x^4 + 0x^3 + 0x^2 + x + 14\)[/tex] by [tex]\(x + 2\)[/tex].
2. First Term:
- Divide the leading term of the dividend by the leading term of the divisor: [tex]\(\frac{7x^4}{x} = 7x^3\)[/tex].
- Multiply [tex]\(7x^3\)[/tex] by [tex]\(x + 2\)[/tex]: [tex]\(7x^3 \cdot (x + 2) = 7x^4 + 14x^3\)[/tex].
- Subtract this from the original polynomial:
[tex]\[ (7x^4 + 0x^3 + 0x^2 + x + 14) - (7x^4 + 14x^3) = -14x^3 + 0x^2 + x + 14. \][/tex]
3. Second Term:
- Divide the leading term of the new polynomial by the leading term of the divisor: [tex]\(\frac{-14x^3}{x} = -14x^2\)[/tex].
- Multiply [tex]\(-14x^2\) by \(x + 2\)[/tex]: [tex]\(-14x^2 \cdot (x + 2) = -14x^3 - 28x^2\)[/tex].
- Subtract this from the current polynomial:
[tex]\[ (-14x^3 + 0x^2 + x + 14) - (-14x^3 - 28x^2) = 28x^2 + x + 14. \][/tex]
4. Third Term:
- Divide the leading term of the new polynomial by the leading term of the divisor: [tex]\(\frac{28x^2}{x} = 28x\)[/tex].
- Multiply [tex]\(28x\)[/tex] by [tex]\(x + 2\)[/tex]: [tex]\(28x \cdot (x + 2) = 28x^2 + 56x\)[/tex].
- Subtract this from the current polynomial:
[tex]\[ (28x^2 + x + 14) - (28x^2 + 56x) = -55x + 14. \][/tex]
5. Fourth Term:
- Divide the leading term of the new polynomial by the leading term of the divisor: [tex]\(\frac{-55x}{x} = -55\)[/tex].
- Multiply [tex]\(-55\)[/tex] by [tex]\(x + 2\)[/tex]: [tex]\(-55 \cdot (x + 2) = -55x - 110\)[/tex].
- Subtract this from the current polynomial:
[tex]\[ (-55x + 14) - (-55x - 110) = 124. \][/tex]
Final Result:
- Quotient [tex]\(q(x) = 7x^3 - 14x^2 + 28x - 55\)[/tex]
- Remainder [tex]\(r(x) = 124\)[/tex]
Thus, the expression [tex]\(\frac{7x^4 + x + 14}{x + 2}\)[/tex] can be written as:
[tex]\[7x^3 - 14x^2 + 28x - 55 + \frac{124}{x + 2}\][/tex]
This is the required form [tex]\(q(x) + \frac{r(x)}{b(x)}\)[/tex].
True or false: when comparing two populations, the larger the standard deviation, the more dispersion the distribution has, provided that the variable of interest from the two populations has the same unit of measure. choose the correct answer below.
a. false, because the larger the standard deviation is, the less dispersion the distribution has.
b. true, because the standard deviation is the difference between the largest and smallest observation. when the standard deviation is larger, there is more distance between the largest and smallest observation, and therefore, more dispersion in the distribution.
c. true, because the standard deviation describes how far, on average, each observation is from the typical value. a larger standard deviation means that observations are more distant from the typical value, and therefore, more dispersed.
d. false, because the standard deviation measures the spread of the distribution, not the dispersion of the distribution.
Answers
C) true, because the standard deviation describes how far, on average, each observation is from the typical value. a larger standard deviation means that observations are more distant from the typical value, and therefore, more dispersed.
The larger the standard deviation, the more dispersed the distribution is, because the standard deviation measures how far each observation is from the mean value of the distribution.
The correct option is C. The typical value being referred to in the option is the mean. The standard deviation measures how far each observation in a distribution is to the mean value of the distribution. Option D is wrong, because, the spread is also the degree of dispersion. The difference between the largest and smallest value in a distribution is the range and not the standard deviation . Hence, option B is wrong. The larger the standard deviation, the greater the dispersion. Hence, option A is wrong.Learn more : https://brainly.com/question/12402189?referrer=searchResults