*
01/10
Probability=
Permutation Formula
n!
(n-r)!
nPr =
Number of Favorable Outcomes
Total Number of Outcomes
Combination Formula
n!
(n-r)!r!
nCr
=
1 po
A bucket contains the names of 10 people including you and your friend.
If 2 names are randomly selected find the probability the first name
selected is yours and the second name selected is your friend's name.
Answers
The probability of the first name selected is yours and the second name selected is your friend's name is 1/100 or in ratio 1:100.
What is probability?Probability is the branch of mathematics that studies how random events turn out. In mathematics, the term "probability" is used to describe chance or potential outcomes. It makes it clear how likely it is that a certain outcome will occur. The phrases "It will likely rain today," "He'll mostly pass the test,"
"There's not much chance of getting a storm tonight," & "The price of onions will probably go up again" are common phrases. Instead of words like possibility, uncertainty, perhaps, likely, etc., the word probability is used in each of these sentences.
Probability, in its simplest form, can be defined as the capacity to forecast an outcome based on the variety and quantity of possible outcomes or by examining historical data.
The probability of first name selected is yours is = 1/10
The probability of 2nd name selected is yours is = 1/10
The probability of selecting your name and your friend name consecutively
= 1/10 * 1/10
= 1/100
Thus, the probability of the first name selected is yours and the second name selected is your friend's name is 1/100.
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Related Questions
Solve for q
1/p + 1/q= -1/f
where p + q = 3 and f=5
Answers
1/p + 1/q = -1/f
1/(3-q) + 1/q = -1/5
Next, we can cross-multiply and combine like terms:
5 + 5q = -3 + 3q
8q = -8
q = -1
13. A 66 lb. child is to receive 1 mEq/kg of a drug. The drug is available in 2 meq/4 ml. How many ml will be given?
Answers
A child can receive 0.5 kg /ml of drug.
What is density?
It is the quantity of a substance per unit volume. A quantity of mass is divided by volume, and we get a density of a particular substance.
How many ml drug will be given?
A 66 lb. child can receive 1 meq/ kg of drug.
but the drug is available in 2 meq/ 4ml.
we need to divide kg by ml to estimate how much quantity is suitable.
From the standard unit, if we divide the quantity in kg by the quantity in ml we achieve a density of drug.
(1 meq / kg) / (2 meq/ 4ml) = 2 ml / kg
the above value is inversed, and we get a density.
the density of drug = 0.5 kg / ml
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What is the distance between the y intercepts of the functions below?
Answers
333 integers, there are 333 integers between 1 and 1,000 which are divisible by 3, by divisibility test.
what is divisibility test?The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.
here
add all the numbers,
1 + 2+ 3 + 4+ 5 = 15
and 15/3 = 5
so it is divisible by 3
not by 9
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On solving the provided question, we can say that from the graph, we have y-intercept of f(x); f(x) = 2(3)°; f(x) = 2 = (0, 2), y-intercept of g(x) = g(x) = (0, 3) so Distance = (3,-2)
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
from the graphs, we have
y-intercept of f(x)
f(x) = 2(3)°
f(x) = 2
(0, 2)
y-intercept of g(x)
g(x) = (0, 3)
Distance
(3,-2)
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An ice rink charges hockey teams for ice time to practice. The ice rink charges $10 for the first hour
and $12 for each additional hour. Write a function that represents the charges for up to 5 hours.
Answers
The function that represents the charges is [tex]t_{n}=[/tex] 10 + (n- 1 )12
What is the function representing the charges ?Here, let us apply Arithmetic sequence Let the charges for the first hour = a = $10 Let the common difference = d = $12The formula for the nth term is given by
[tex]t_{n}=[/tex] a +(n-1)d
The function that represents the charges is given by,[tex]t_{n}=[/tex] a +(n-1)d
[tex]t_{n}=[/tex] 10 + (n- 1 ) 12
a ) First hour
n = 1
[tex]t_{1 }=[/tex] 10 + (1- 1 ) 12
= 10
b ) Second hour
n = 2
[tex]t_{2 }=[/tex] 10 + (2- 1 ) 12
= 10 + 12
= 22
c ) Third hour
n = 3
[tex]t_{3}=[/tex] 10 + (3- 1 ) 12
= 10 + 24
= 34
d ) Fourth hour
n = 4
[tex]t_{4 }=[/tex] 10 + (4- 1 ) 12
= 10 + 36
= 46
e ) Fifth hour
n = 5
[tex]t_{4 }=[/tex] 10 + (5- 1 ) 12
= 10 + 48
= 58
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Jaxson earns $62 for 4 hours of work. If he makes a constant hourly wage, which
table represents the relationship between the number of hours he works and his total
earnings?
A
C
Time
(hours)
1
2
3
Time
(hours)
4
5
6
Pay
$15.50
$16.50
$17.50
Pay
$62
$77.50
$93
B
D
Time
(hours)
4
8
12
Time
(hours)
1
11
21
Pay
$62
$66
$70
Pay
$15.50
$25.50
$35.50
Answers
If Jaxson makes a constant hourly wage (unit rate) and earns $62 for 4 hours of work, the table representing the relationship between the number of hours he works, and his total earnings is C. as follows:
Time Pay
(Hours)
4 $62.00
5 $77.50
6 $93.00.
What is the unit rate?The unit rate is the ratio of two values.
The unit rate is the average of the total value divided by the total units.
We can also describe the unit rate as the constant rate of change, the variable cost per unit, or the slope in a linear equation.
Time Pay Unit
(Hours) Rate
4 $62.00 $15.50 ($62/4)
5 $77.50 $15.50 ($77.50/5)
6 $93.00 $15.50 ($93/6)
Thus, the unit rate of $15.50 is constant across all time hours that Jaxson works, making Option C to be correct.
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Answer:
Step-by-step explanation:
i dont know either
A factory sells backpacks for
$
40.00
$40.00 each. The cost to make
1
1 backpack is
$
10.00
$10.00. In addition to the costs of making backpacks, the factory has operating expenses of
$
12
,
000
$12,000 per week. The factory's goal is to make a profit of at least
$
980
$980 each week. Which inequality represents the number of backpacks,
x
x, that need to be sold each week for the factory to meet this goal? How many backpacks must the factory sell to meet its weekly goal?
Select the inequality that represents this situation and select the correct statement.
Answers
The inequality which represents the number of backpacks need to be sold is 40x - (10x + 12,000) ≥ 980. Factory should sell at least 433 backpacks in a week.
What are Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Selling price of 1 backpack = $40
Cost to make 1 backpack = $10
Operating expense per week = $12,000
Let x be the number of backpacks which are sold in a week.
Total revenue per week = 40x
Total expense per week = 10x + 12,000
Profit = Revenue - Expense
= 40x - (10x + 12,000)
Factory's goal is to make a profit of at least $980 each week.
40x - (10x + 12,000) ≥ 980
This is the inequality that represents the number of backpacks need to be sold.
Solving the inequality,
40x - (10x + 12,000) ≥ 980
40x - 10x - 12,000 ≥ 980
30x ≥ 980 + 12,000
30x ≥ 12,980
x ≥ 432.67 ≈ 433
Hence factory must at least a total of 433 backpacks to meet it's weekly goal of $980.
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Explain why multiplying by 8/3 gives the same result as first multiplying by 8 and then multiplying by 1/3
Answers
The outcome of multiplying by 8/3 is the same as multiplying with 8 and then by 1/3.
Explain multiplication of fraction?The two fractions that want to multiply come first when multiplying fractions.
You multiply both denominators (the lower numbers) by the sum of the numerators (this same top numbers). Finding the sum of two or maybe more fractions is known as multiplying fractions. When multiplying fractions, a different approach is taken than when adding and subtracting fractions.For the stated number.
The number given is 8/3.
Other set of numbers are-
Multiplying 1/3 with 8.
= 1/3*8
= (1*8)/3
= 8/3, which is equal to the stated number.
Thus, the outcome of multiplying by 8/3 is the same as multiplying with 8 and then by 1/3.
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Please answer this question and explain how you got it
Answers
1000 ml of sodium silicate is used to make 10 liters soap
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
The standard form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
Let y represent the amount of sodium silicate in x ml of liquid soap.
From the graph, using the points (1000, 100) and (3000, 300):
y - 100 = [(300 - 100)/(3000 - 1000)](x - 1000)
y - 100 = 0.1(x - 1000)
y = 0.1x
For 10 L (10000 ml)of soap:
y = 0.1(1000) = 1000 ml
1000 ml of sodium silicate is used to make the soap
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Monty works for a company that distributes multiple alcoholic beverages in the United States. Due to multiple events going on around the world, Monty has started wondering about the perceived home location of certain spirits. He takes a random sample of 135 people and find that 82 of them say that “Smirnoff” is produced in Russia. Monty takes a second random sample of 127 people and find that 74 of them say that “Stoli” is produced in Russia. At the .05 level of significance, is there a difference in the proportion of people who think Smirnoff is produced in Russia and the proportion of people who think Stoli is produced in Russia?
Answers
There is no evidence to reject the claim that there a difference in the proportion of people who think Red label is produced in Russia.
How to explain the critical value?It should be noted that we want to test the claim at 5% level of significance. The z critical value at 5% level of significance for two tailed test is 1.96.
The test statistic is 0.5. Since the z critical value is greater than the test statistic we do not reject the null hypothesis at 5% level of significance.
Therefore, we do not have enough evidence to reject the claim that there a difference in the proportion of people who think Red label is produced in Russia and the proportion of people who think Hennessy is produced in Russia.
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y= "-2x+4" y=2x How many solutions does the system of equations have? • One solution * Infinitely many solutions * No solution
Answers
Answer: one solution
Step-by-step explanation:
y=-2x+4 y=2x
2x=-2x+4
4x=4
x=1
Answer:
Step-by-step explanation:
one
ANYONE GOOD AT MATH! PLEASE HELP WILL GIVE BRAINLIEST!
Answers
Answer:
(f+6) (x)= x^3+3x^2+1 / x2
Step-by-step explanation:
NEED HELPS ASAP PLS AND THX PIS IS ATTACHED
Answers
The reasons are When two lines intersect, the angles formed opposite to each other are termed as vertical angles
what is right angle congruence theorem?Two right-angled triangles are said to be congruent to each other if the hypotenuse and one side of the right triangle are equal to the hypotenuse and the corresponding side of the other right-angled triangle.In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.Regarding right triangles, there are four theorems that prove congruence. They are the leg-leg theorem, the hypotenuse-leg theorem, the hypotenuse-angle theorem, and the leg-angle theorem Two right triangles can have all the same angles and not be congruent, merely scaled larger or smaller. If all the side lengths are multiplied by the same number, the angles will remain unchanged, but the triangles will not be congruent.To learn more about right angle congruence theorem refers to:
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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
Answers
Answer: yo wyd ?
Step-by-step explanation: pull up
Rewrite the ratio 15:42 as an equivalent ratio of the form 1:n.
Answers
Equalizing ratios refer to two ratios with the same value.Multiply or divide both values by the same number to arrive at an equivalent ratio. The ratio 1: 3.5 will be the equivalent of the ratio 8: 28.
What does ratio mean?A ratio shows how many of one number there are of another.Two numbers are expressed as x: y, which is equivalent to x/y, to represent their ratio.
where each of the two variables, x and y, is a separate quantity.Additionally, the combined total is given as x + y.
Knowing that;
is the ratio;
8 : 28
And the ratio has the following equivalent form: 1: n.
Now,
The ratios 8: 28 and 1: n are identical, thus.
in order to formulate;
8 : 28 = 1 : n
Calculate n as;
8 / 28 = 1 / n
n = 28 / 8
n = 3.5
As a result, 1: 3.5 will be the ratio that the ratio 8: 28 corresponds to.
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using the factor theorem which of the following is a factor of the polynomial below x^3 + 7x^2 + 4x -12
A.
x-6
B.
x-3
C.
`X+4
D.
X-2
Answers
Using the Factor Theorem, it is found that none of these options represent a linear factor of f(x) = x³ + 7x² + 4x - 12.
How to verify if a term is a factor of the polynomial?The Factor Theorem states that if x - a is a factor of the polynomial y = f(x), then f(a) = 0.
The polynomial for this problem is defined as follows:
f(x) = x³ + 7x² + 4x - 12.
The numeric values for each of the options are given as follows:
f(6) = 6³ + 7(6)² + 4(6) - 12 = 480.f(3) = 3³ + 7(3)² + 4(3) - 12 = 90.f(-4) = (-4)³ + 7(-4)² + 4(-4) - 12 = 20.f(2) = 2³ + 7(2)² + 4(2) - 12 = 32.As none of the values of a have f(a) = 0, none of these terms are linear factors of the polynomial x³ + 7x² + 4x - 12.
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Taub goes out to lunch. The bill, before tax and tip, was $11.85. A sales tax of 3% was added on. Taub tipped 24% on the amount after the sales tax was added. How much was the sales tax? Round to the nearest cent.
Answers
The value of the sales tax applied to the bill is $0.36
How much was the sales tax?If we have an initial value A, and we increase it by a percentage X, then the new value (after the increase) is given by:
A' = A*(1 + X/100%).
Here we know that the bill before the tax and the tip (it will be the initial value) is:
A = $11.85
And a sales tax of 3% is applied to that bill, then the new amount is:
A' = $11.85*(1 + 3%/100%)
A' = $11.85*(1 + 0.03) = $12.21
The sales tax is equal to the difference between the amount above and the initial value of the bill.
tax = $12.21 - $11.85 = $0.36
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A garage charges $55 per tire and $30 per hour of labor. If you need two tires and it takes half an hour to install, how much do you pay?
Answers
Answer: $125
Step-by-step explanation:
$55 per tire (2)
$30 per hour of labor (0.5)
$55(2)+30(0.5)=$125
Answer:
$125
Step-by-step explanation:
2 tires =$110 ($55 each tire)
half an hour of labor=$15
A rectangle has a length of 2X +4 and a width of X -7 what is the value of X if the perimeter of the rectangle measures 48
Answers
Answer:
Step-by-step explanation:
2(2x + 4) + 2(x-7) = 48
4x+8 +2x-14=48
6x-6 = 48
6x = 48+6
6x = 54
x = 54/6
x = 9
What do I put in an excel sheet for this info?
A. Owner invested $15, 000 cash in the company
B. The company purchased supplies for $500 cash
C. The company purchased $10,000 of equipment on credit. The credit was given based on a written note stating the terms of payment
D. The company purchased $200 of additional supplies on credit
E. The company purchased land for $9,000 cash
F. The company received $7000 cash for plowing service provided to JMD company
G. The company paid $600 for rent; $250 for utilities
H. The company provided $9500 plowing service to MMJ on credit
I. MMJ paid $9500 for the service received
J. The company paid $5000 on the notes payable for the equipment purchased on credit
Answers
This information can be entered into an Excel sheet by creating columns for each item (A-J) and entering the corresponding values in the corresponding cells.
What are the purpose of excel sheet? Excel is a powerful spreadsheet application used to create, edit, format, and calculate data. It is used by businesses, financial institutions, and individuals for a wide range of tasks. Excel is commonly used to organize, store, and analyze data. It can be used to create charts and graphs, build financial models, and perform complex calculations. Excel can also be used to track and manage large amounts of data.Excel sheets are used to organize, store, and analyze data. They can be used to create tables, perform calculations on data, and generate graphs and charts. Excel can also be used to create automated workflows that allow users to quickly access data, perform calculations, and generate reports. Excel can be used to easily summarize and compare data from multiple sources. It can also be used to create complex formulas that perform calculations and generate results. Excel is often used to analyze trends over time and determine correlations between different data sets. Excel is also used to create complex formulas that can be used to automate tasks, such as forecasting and budgeting.
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The closing stock price of MNM Corporation for the last 7 trading days is shown below.
Day Stock Price
O 84
O 87
O 84
O 88
O 85
O 90
O 91
The mode is
Answers
The mode is 2.
The mode is the value that appears often in a set of data values.
The mode is a way of expressing, in a single number, important details about a random variable. The numerical value of the model is the alike as that of the mean and median in a normal distribution, and it may be very different in highly skewed distributions.
Given Data :
84, 87,84,88,85,90,91
First, arranging the data in ascending order :
84, 84, 85, 87, 88, 90,91
Now, we have to find how many times this number occurs :
⇒ 84 occurs 2 times
⇒ 85 occurs 1 time
⇒ 87 occurs 1 time
⇒ 88 occurs 1 time
⇒ 90 occurs 1 time
⇒ 91 occurs 1 time
So, the mode is 2.
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Jasmine went for a run. She started running at 06:55 and finished at 08:15. How long was she running for?
Answers
Answer:
Step-by-step explanation:
6:55 to 7 o'clock is 5 minutes.
from 7 to 8 is 60 minutes
from 8 to 8: is 15 minutes.
So, 5+60+15=80 minutes, also calls one hour and 20 minutes.
she ran for 3hours
06:55
08:15
14:60 therefore 14 is 2hours and 60 is 1hour
The function fis defined for f(x)= cos x+sinx for 0≤x≤ 2. What is the x-coordinate of the point of inflection where
the graph of fchanges from concave down to concave up?
Answers
The maximum and minimum x-coordinates at the point of inflection are, respectively,[tex]$\left(\frac{\pi}{4}+2 \pi n, \sqrt{2}\right)$[/tex] and [tex]$\left(\frac{5 \pi}{4}+2 \pi n,-\sqrt{2}\right)$[/tex], and the function f is defined as f(x)=cos x+sin x for 0≤x≤ 2.
What is meant by x-coordinate of the point of inflection ?[tex]$\frac{d}{d x}(\cos (x)+\sin (x))$[/tex]
Continuity of [tex]$\cos (x)+\sin (x): \quad 2 \pi$[/tex]
Domain of [tex]$\cos (x)+\sin (x):\left[\begin{array}{cc}\text { Solution: } & -\infty < x < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$[/tex]
Range of [tex]$\cos (x)+\sin (x):\left[\begin{array}{cc}\text { Solution: } & -\sqrt{2} \leq f(x) \leq \sqrt{2} \\ \text { Interval Notation: } & {[-\sqrt{2}, \sqrt{2}]}\end{array}\right]$[/tex]
Axis points of interception [tex]$\cos (x)+\sin (x)$[/tex] [tex]: X Intercepts: $\left(\frac{3 \pi}{4}+2 \pi n, 0\right),\left(\frac{7 \pi}{4}+2 \pi n, 0\right)$,[/tex]
The Y intercept: (0,1)
the asymmetrical [tex]$\cos (x)+\sin (x)$[/tex] : None
Excessive Points of [tex]$\cos (x)+\sin (x): \quad$[/tex] Maximum [tex]$\left(\frac{\pi}{4}+2 \pi n, \sqrt{2}\right)$[/tex] , Minimum [tex]$\left(\frac{5 \pi}{4}+2 \pi n,-\sqrt{2}\right)$[/tex]
We put the second derivative of the function equal to zero to get the x-coordinate of the point of inflection. Re-inserting the x-coordinate into the initial function yields the point's y-coordinate.
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Find the common difference of the arithmetic
Answers
Answer:
4
Step-by-step explanation:
9 , 13, 17, 21
9 + 4 = 13
13 + 4 = 17
17 + 4 = 21
what rule about overtime does the fair labor standards act establish?
Answers
Answer: The Fair Labor Standards Act (FLSA) establishes a rule about overtime that requires covered employers to pay their employees a premium rate for any hours worked over 40 in a workweek. The premium rate is one and a half times the regular rate of pay for the employee. This overtime rule applies to all non-exempt employees, meaning those who are eligible for overtime pay.
Ray Rice, Adrian Peterson, Tom Brady,
and Ezekiel Elliot were suspended by the NFL.
Did the NFL succeed in upholding these suspen-
sions in arbitration and in court? Were the
decisions fair? Did the decisions to suspend
these players enhance or hurt the leagues
image. Does the commissioner of the NFL have
too much power in these cases, or is this type
of authority necessary to police the actions of
athletes and employees in the league?
Answers
Solving by function The NFL punished Ray Rice, Adrian Peterson, Tom Brady, and Ezekiel Elliott for a variety of reasons, but each of those reasons had to do with their personal lives.
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found.
By function
f(x) = 23x 243.2y + 23.2xy
we have Ray Rice struck his future wife. Adrian Peterson took part in kidnapping. In accordance with the NFL's Personal Conduct Policy, all of these players were suspended.
Also, both in arbitration and court, the NFL was successful in upholding these punishments.
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Function G is a _____ of function f. G(x)=____x2
Answers
Therefore , the solution of transformation of function is Translation shifting the graph of a function up or down, or left or right.
What is the transformation of function?A transformation of a function is a new function that is derived from the original function by applying some mathematical operation. The process of creating a new function from an existing one by applying a mathematical operation is called a transformation.
Here,
There are different types of transformations that can be applied to a function, such as:
Translation: shifting the graph of a function up or down, or left or right.
Reflection: flipping the graph of a function over the x-axis, y-axis, or a line of symmetry.
Stretching or compressing: changing the scale of the graph along the x-axis or y-axis.
Rotation: rotating the graph of a function about the origin.
Function G is a transformation of function f. G(x) = x^2
A transformation of a function is a new function that is derived from the original function by applying some mathematical operation. In this case, function G is derived from function f by squaring the input value. The result is a new function that maps the input value to its square. The notation G(x)= x^2 is a common notation to represent a function and it means that G is a function that takes x as input and returns the square of x as output.
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For a lower-tail test, the p-value in the output from an Excel tool:
Question 5 options:
1)
is correct if the test-statistic is negative.
2)
is the difference from 1.0 if the test-statistic is negative.
3)
is correct if the test-statistic is zero.
4)
is correct if the test-statistic is positive.
Answers
For a lower-tail test, a t-statistic that is negative and far from zero would then lead us to favor the alternative hypothesis
An alternative way to conduct a hypothesis test is to again assume initially that the null hypothesis is true, but then to calculate the probability of observing a t-statistic as extreme as the one observed or even more extreme
For a lower-tail test, the p-value is the area under the curve of the t-distribution (with n−1 degrees of freedom) to the left of the observed t-statistic.
Lower-tail tests work in a similar way to upper-tail tests, but all the calculations are performed in the negative (left-hand) tail of the t-distribution density curve
A lower-tail test would result in an inconclusive result for the home prices example (since the large, positive t-statistic means that the data favor neither the null hypothesis, NH: E(Y) = 255, nor the alternative hypothesis, AH: E(Y) < 255).
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The real numbers greater than or equal to 5 or less than or equal to -5
Answers
Answer:
x <= -5 or x >= 5.
Step-by-step explanation:
The boundary values (-5) and (5) contain closed circles to show that these values are included in the solution sets for the given inequalities.
Had our given compound inequality been:
x < -5 or x > 5
Then the boundary values (-5) and (5) would have contained open circles to show that these values are not included in the solution sets for these inequalities.
Please actually answer this for me please will mark brainiest
Answers
Answer:
[tex]\dfrac{155}{18} \pi \textrm{ cm}[/tex]
Step-by-step explanation:
This problem asks us to find the length of an arc ACB on the circumference of a circle with center O and a radius of 5 cm.
We first must solve for the total circumference (perimeter) of the circle. This is represented by the formula C = 2πr. Hence, the circumference of this circle is:
C = 2π(5) cm
C = 10π cm
Next, we have to find what fraction of 360º the major arc ACB is in order to deduce how much of the circle's total circumference the arc takes up.
[tex]\dfrac{(360 - 50)\textdegree}{360\textdegree} = \dfrac{31}{36}[/tex]
Finally, we can multiply the amount of circumference that arc ACB takes up by the length of the whole circumference to get the length of arc ACB.
[tex]\textrm{Length of arc } ABC = \dfrac{31}{36} \cdot 10\pi[/tex]
[tex]= \dfrac{310}{36} \pi[/tex]
[tex]= \dfrac{155}{18} \pi \textrm{ cm}[/tex]
Answer:
[tex]\textsf{Length of major arc $\overset{\frown}{ACB}$}: \;\; \boxed{\dfrac{155}{18}\pi\; \sf m}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Arc length}\\\\Arc length $= \pi r\left(\dfrac{\theta}{180^{\circ}}\right)$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}[/tex]
Angles around a point sum to 360°. Therefore:
[tex]\begin{aligned}\implies m \angle BOA&=360^{\circ}-m \angle AOB\\&=360^{\circ}-50^{\circ}\\&=310^{\circ}\end{aligned}[/tex]
Therefore, the given values are:
r = 5 mθ = m∠BOA = 310°To find the length of the major arc ACB, substitute the given values into the arc length formula:
[tex]\begin{aligned}\implies \overset{\frown}{ACB}&=\pi \cdot 5 \cdot \left(\dfrac{310^{\circ}}{180^{\circ}}\right)\\\\&=5\pi \cdot \dfrac{31}{18}\\\\&=\dfrac{155}{18}\pi\; \sf m\end{aligned}[/tex]
Given
w (x) = x² + 4x − 3
and
z (x) = x + 5
what is the value of
w (z (7))
Answers
Answer:
[tex]w(z(7))=189[/tex]
Step-by-step explanation:
[tex]z(7)=7+5=12 \\ \\ w(z(7))=w(12)=12^2+4(12)-3=189[/tex]