The value of P(A/B) will be = 1/4
As per the question,
As a fair six-sided die is rolled twice
So, the total number of outcomes will be N=6^2=36
A: sum of the two rolls is 5
[tex]$$\begin{aligned}& A=\{(1,4),(2,3),(3,2),(4,1)\} \\& n(A)=4 \\& P(A)=\frac{n(A)}{N}=\frac{4}{36}\end{aligned}$$[/tex]
B: The first roll results in a 2
[tex]B=\{(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)\}$ \\$n(B)=6$ \\$P(B)=\frac{n(B)}{N}=\frac{6}{36}$ \\$B \cap A=\{(2,3)\}$ \\$\cap(B \cap A)=1$ \\$P(B \cap A)=\frac{n(B \cap A)}{N}=\frac{1}{36}$\\$P(B \mid A)=\frac{P(B \cap A)}{P(A)}=\frac{1 / 36}{4 / 36}=\frac{1}{36} \times \frac{36}{4}$$P(B \mid A)=\frac{1}{4}$[/tex]
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What is 1 2/3 - 5/6 ??
The Subtraction of the given fraction using the number line is 5/6.
The correct answer option is option A
How to subtract fraction?Fraction refers to a number which consists of a numerator and a denominator.
A numerator is the upper value of a fraction while a denominator is the lower value or bottom value of a fraction.
1 2/3 - 5/6
= 5/3 - 5/6
Find the lowest common multiple of the denominators and divide
= (10-5) / 6
= 5/6
In conclusion, 5/6 is the answer to the subtraction of fraction.
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Find axis of symmetry
Answer:
Step-by-step explanation:
x=-4
A soccer coach surveyed the players to determine the number who preferred selling coupon books, magazine subscriptions, or both for their fundraiser. The results are given in the Venn diagram. To the nearest whole percent, what is the value of a in the relative frequency table for the survey results? a = 27% a = 42% a = 81% a = 88%
The value of a in the relative frequency table for the survey results a = 27%
From the given Venn diagram, the total number of players = 11 + 3 + 7 + 5 = 26
The number of players preferred magazines books which are not coupon books = 7
The relative frequency for the players who preferred magazines books which are not coupon books (a)=
magazine books but not coupon books/ total player = 7 / 26 = 0.269
In percent,
7/26 x 100 = 26.9 = 27%
Hence, a = 27%
Therefore, the value of a in the relative frequency table for the survey results a = 27%
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For which values of x does each expression make sense?
Square root of x+5
Square root of |x|+1
Square root of (-2x)^2
Square root of (-5x)^3
The value of x that makes sense for the expression is the domain of the expression
The value of x makes sense for √-2x² is 0
The value of x must not exceed 0 for √(-2x)³ to make sense
What is Angle Sum Property?
The sum of all angles of a triangle is equal to the angle of a straight line i.e. 180°. If we have a triangle ABC, then the Sum of angles A , B, and angle C will be 180 ° and the value of the exterior angle is equal to the sum of two interior opposite angles.
√-2x²
For the above expression to have a defined value, the expression in the bracket must be positive.
However, x² will always be positive, and -2 will ensure that the expression is always negative, except when x = 0
Hence, the value of x makes sense for √-2x² is 0.
√(-2x)³
For the above expression to have a defined value, the expression in the square root must be positive.
However, the power of 3 will ensure that the expression is always positive only when x is less than or equal to 0
Hence, the value of x must not exceed 0 for √(-2x)³ to make sense.
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The original price of a scarf was $16, During a store closing sale, a shopper saved $12 on the scarf, What percentage discount did she receive? Explain or show your reasoning.
Answer:
The shopper received a 75% discount
Step-by-step explanation:
ok so first we turn it into an equation
let x=percentage discount
16(x)=12
x=.75
discount=75%
Jacob's body metabolizes caffeine at a rate of 13.5% per hour (so the amount of caffeine in Jacob's body decreases by 13.5% each hour) a. If Jacob consumes a cup of coffee with 96 mg of caffeine in it, how long will it take for Jacob's body to metabolize half of the 96 mg of caffeine? hours Preview b. If Jacob consumes an energy drink with 212 mg of caffeine in it, how long will it take for Jacob's body to metabolize half of the 212 mg of caffeine? hours Preview c. If Jacob consumes a cup of coffee with c mg of caffeine in it, how long will it take for Jacob's body to metabolize half of the cmg of caffeine? (Hint: your answer will be a numerical value.) hours Preview Submit
Jacob's body metabolizes caffeine at a rate of 13.5% per hour.
a)Jacob's body will takes 4.77 ~5 hours to metabolize half of the 96 mg of caffeine.
b) If Jacob consumes an energy drink with 212 mg of caffeine in it, Jacob's body will take 4.77948 ~ 5 hours to metabolize half of the 212 mg of caffeine.
c) Jacob consumes a cup of coffee with c mg of caffeine in it. Jacob's body will take 4.77948~ 5 hours to metabolize half of the c mg of caffeine.
What is decay rate?The volume will slowly decrease at regular intervals and at a regular rate. This growth reduction is calculated using the exponential decay formula. The general form is y = a(1- r)ᵗ
We have, decay rate r = 13.5 % = 0.135
Initial value , a = 96 mg
plugging the value in formula we get,
y = 96(1 - 0.135)ᵗ --(1)
Now, Half of 96 is 48
so, 48 = 96(0.865)ᵗ --(2)
dividing equation by 96 we get
=> 48/96 = (0.865)ᵗ
taking natrual logarithm both sides,
=> ln(1/2) = ln ((0.865))
=> ln(1/2) = t In (0.865)
=> t = ln(1/2)/In (0.865)
=> t = 4.77948
Since, decay rate is constant so, half never changes for any .
a) 4.779~5 hours, long will it take for Jacob's body to metabolize half of the 96 mg of caffeine.
b) Jacob's body to metabolize half of the 212 mg of caffeine is 4.779~ 5 hours.
c) for Jacob's body to metabolize half of the cmg of caffeine is 4.77948.. So, we have 4.77948 ~ 5 hours is decay constant rate.
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a line with a y-intercept of 4 passes through the point (14, -3). it also passes through point (x, -8). what is the x coordinate for that point?: * a) 8 b) 24 c) -24 d) 6 e) -6
The x-coordinate for the point (x, -8), if Y-intercept is 4, and the coordinates of the point is (14, -3), is 24, so option B is correct.
What is line?
An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.
Given:
Y-intercept = 4,
Coordinates of point = (14, -3), (x, -8)
Calculate the line equation as shown below,
y = m x + 4
Here, m is the slope,
Put point (14, -3) in the equation,
-3 = m × 14 + 4
m = -7 / 14
m = -1 / 2
Hence, the equation of a line is,
y = -1/2 x + 4
Put point (x, -8),
-8 = -1/2 x + 4,
-12 = -1/2x
x = 24
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Which ordered pair is a solution to the system of inequalities shown on the graph?
A)(3, 3)
B) (1,2)
C)(-3,-2)
D) (0, 1)
Answer:
C) (-3,-2)
Step-by-step explanation:
Solutions to the graphed system of inequalities are any points that are contained within the overlapping shaded region.
Plot the points on the given coordinate grid.
The only point that is contained with the overlapping shaded region is:
(-3, -2)A systems analyst is testing the feasibility of using a new computer system. He wants to see if the new system uses less processing time than the old system. (Assume the original populations are normally distributed.) A sample of 25 jobs was selected and the processing time for each in seconds was recorded on each of the two systems. The results are as follows:Old System: mean = 27.2 seconds, s = 3.2 seconds, n - 25New System: mean = 24.3 seconds, s = 2.1 seconds, n = 25Difference (Old -New): mean = 2.9 seconds, s = 1.4 seconds, n = 25What is the alternative hypothesis for this problem?a. HA: µD≠0b. HA: µD>0c. HA: µD=0d. HA: µD<0
The alternative hypothesis for this problem b. HA: µD>0
What is meant by hypothesis?
In math, A hypothesis is an assumption made based on some evidence.
Here we have given that systems analyst is testing the feasibility of using a new computer system. He wants to see if the new system uses less processing time than the old system.
And we need to find the alternative hypothesis for this problem
While we looking into the given question we have identified the following values,
Old System: mean = 27.2 seconds, s = 3.2 seconds, n - 25
New System: mean = 24.3 seconds, s = 2.1 seconds, n = 25
Difference (Old -New): mean = 2.9 seconds, s = 1.4 seconds, n = 25
Basically, while written the hypothesis, we have to follow the order of the following,
=> (Old-New, Larger-Smaller>)
Therefore, the correct option is (B).
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Find all solutions of the equation 2sinx +√3 = 0
The answer is A+Bkπ and C+Dkπ where k is any integer, 0
Answer:
Step-by-step explanation:
2sin x=-√3
[tex]sin~x=-\frac{\sqrt{3} }{2} =-sin~\frac{\pi }{3} =sin (\pi +\frac{\pi }{3} ),sin(2\pi -\frac{\pi }{3} )\\=sin(\frac{4\pi }{3} +2k\pi ),sin (\frac{5\pi }{3} +2k\pi )\\=sin(A+Bk\pi ),sin(C+Dk\pi )\\x=A+Bk\pi ,C+Dk\pi \\where~A=\frac{4\pi }{3} ,B=2\\C=\frac{5\pi }{3} ,D=2[/tex]
Allie had four and three-fourths tubes of purple paint. She used two and one-fourth tubes. Later, she found three and three-eighths more tubes. How many tubes of purple paint does she have now?
five and thirteen over twenty-four tubes
five and nine over twenty-four tubes
five and seven over eight tubes
five and one over eight tubes
By subtracting and adding mixed numbers, we can see that at the end she has (5 + 7/8) tubes of paint.
How many tubes of purple paint does she have now?We know that initially Allie had (4 + 3/4) tubes of purple paint, and she sed (2+ 1/4) tubes.
So at this point we need to take the difference between the two mixed numbers, we will get:
(4 + 3/4) - (2 + 1/4) = (4 - 2) + (3/4 - 1/4)
(4 - 2) + (3/4 - 1/4) = 2 + 2/4
2 + 2/4 = 2 + 1/2
Then she founds (3 + 3/8) more. Now we need to add that:
2 + 1/2 + (3 + 3/8) = (2 + 3) + (1/2 + 3/8)
(2 + 3) + (1/2 + 3/8) = 5 + (4/8 + 3/8)
5 + (4/8 + 3/8) = 5 + 7/8
She has 5 + 7/8 tubes of purple paint.
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Y=x^3-4x^2-20x+48 use the rational zero theorem
The roots of the given polynomial using the rational zero theorem are; 2, -4 and 6.
How to use the rational zero theorem?We are given the polynomial;
y = x³ - 4x² - 20x + 48
Since all coefficients are integers, we can apply the rational zeros theorem.
The trailing coefficient (the coefficient of the constant term) is 48
Find its factors (with the plus sign and the minus sign): ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.
These are the possible values for p.
The leading coefficient (the coefficient of the term with the highest degree) is 1.
These are the possible rational roots:
±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.
Checking the possible roots: if a is a root of the polynomial P(x), the remainder from the division of P(x) by x - a should equal 0 (according to the remainder theorem, this means that P(a)=0
Plugging in those values, the only ones that yield P(a) = 0 are; 2, -4 and 6.
Thus, these are the roots of the given polynomial.
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Work out the value of d in the equality below. 0.0043 = 4.3 × 10d
Answer:
d= -3
Step-by-step explanation:
Rearrange variables to the left side of the equation: -4.3x 10d= -0.0043
Divide both sides of the equation by the coefficient of variable
Reduce the fraction
Convert fraction into negative exponential form
Convert both sides of the equation into terms with the same with same base
Simplify using exponent power rule
Based on the given conditions, corresponding exponents are equal
Write the equation in slope-intercept form.
–2x + 4y = 12
Answer:
y = [tex]\frac{1}{2}[/tex] x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
- 2x + 4y = 12 ( add 2x to both sides )
4y = 2x + 12 ( divide through by 4 )
y = [tex]\frac{2}{4}[/tex] x + [tex]\frac{12}{4}[/tex] , that is
y = [tex]\frac{1}{2}[/tex] x + 3
A horse owner needs to replace four sections of a coral for the horses. The first section
needs 26 yards of fencing, the second needs 10 3/5, the third, 10 1/5 yards, and the fourth,
8 3/10 yards. How many yards are needed to repair four sections of the fencing?
10
Answer:
55 1/10 yd
Step-by-step explanation:
26 + 10 + 3/5 + 10 + 1/5 + 8 + 3/10 =
= 54 + 4/5 + 3/10 =
= 54 + (8 + 3)/10 =
= 54 + 11/10 =
= 54 + 10/10 + 1/10 =
= 54 + 1 + 1/10 =
= 55 1/10
Answer:
55[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
Convert all the mixed numbers to fractions with a common denominator (10) then add them up:
26 + 53/5 + 51/5 + 83/10 =
26 + 106/10 + 102/10 + 83/10 =
26 + 291/10 =
26 + 29[tex]\frac{1}{10}[/tex] = 55[tex]\frac{1}{10}[/tex]
True or False. If a cylinder and cone
have the same height and diameter, the
volume of the cylinder will always be
greater than that of the cones.
Answer:
This statement is false
Step-by-step explanation:
This statement is false. The volume of a cylinder with a given height and diameter will always be greater than that of a cone with the same height and diameter if the base of the cone is smaller than the base of the cylinder. However, if the base of the cone is the same size as the base of the cylinder, then the volume of the cone will be equal to that of the cylinder.
8.11 a total of 725 auto-mode social/recreational trips are made from an origin (residential area) during the peak hour. a logit model estimation is made, and three factors were found to influence the destination choice: (1) population at the destination, in thousands (coefficient
Based on this information, we can estimate that a 1,000-person increase in population at the destination, an increase of 441 auto-mode social/recreational trips from the origin during the peak hour time
a 10-mile increase in distance to the destination, and the presence of recreational facilities at the destination are associated with an increase of 725 x (0.43 + (-0.07) + 0.62) = 441 auto-mode social/recreational trips from the origin during the peak hour.
1. Calculate the total increase in auto-mode social/recreational trips from the origin during the peak hour associated with a 1,000-person increase in population at the destination, a 10-mile increase in distance to the destination, and the presence of recreational facilities at the destination by multiplying the coefficients of the logit model by 725 (the total number of trips):
725 x (0.43 + (-0.07) + 0.62) = 441
2. Therefore, we can estimate that a 1,000-person increase in population at the destination, a 10-mile increase in distance to the destination, and the presence of recreational facilities at the destination are associated with an increase of 441 auto-mode social/recreational trips from the origin during the peak hour time.
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Solve
16) -x<-x+7(x-2)
The solution of the given inequality -x < -x + 7 ( x - 2 ) is given by x > 2.
As given in the question,
Inequality is given by :
-x < -x + 7 ( x - 2 )
Open the parenthesis of the given inequality we have,
⇒ -x < -x + 7x - 14
Collect all the like terms on the same side we get,
⇒ - x < 6x - 14
Subtract 6x from both the side of the inequality we get,
⇒ - x - 6x < 6x - 6x - 14
⇒ -7x < -14
Divide both the side of the inequality by -7 we get,
⇒ -7x/ -7 > -14 / -7
⇒ x > 2
x has all the value greater than 2.
Therefore, for the given inequality the solution is given by x > 2.
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FIND THE COTANGENT! Help me pls.
Answer: 5/8
Step-by-step explanation:
(please explain and show work/drawing. thank you so much!) In a certain Algebra 2 class of 22 students, 5 of them
play basketball and 11 of them play baseball. There are 3
students who play both sports. What is the probability that
a student chosen randomly from the class plays basketball
or baseball?
Answer:
59%
Step-by-step explanation:
First, let's find the number of students who play basketball but not baseball: 5 students - 3 students = <<5-3=2>>2 students
Next, let's find the number of students who play baseball but not basketball: 11 students - 3 students = <<11-3=8>>8 students
Now, let's add up the number of students who play basketball but not baseball, the number of students who play baseball but not basketball, and the number of students who play both sports to find the total number of students who play basketball or baseball: 2 students + 8 students + 3 students = <<2+8+3=13>>13 students
Finally, we can divide the total number of students who play basketball or baseball by the total number of students in the class to find the probability that a student chosen at random plays basketball or baseball: 13 students / 22 students = 0.59
Therefore, the probability that a student chosen at random from the class plays basketball or baseball is 0.59.
Answer:
13/22
Step-by-step explanation:
The class has 22 students.
5 play basketball.
11 play baseball.
3 play both.
Break down the 5 who play basketball into:
2 play only basketball
3 play both basketball and baseball
Break down the 11 who play baseball into:
8 play only baseball
3 play both basketball and baseball (These 3 are the same 3 above)
Now we have:
2 play only basketball
8 play only baseball
3 play both
This is a total of 13.
The class has 22, so 9 don't play any sport.
That means out of 22 students, 13 play either sport, and 9 play nothing.
p(basketball or baseball) = 13/22
find the integral please
Done :) Refer to the photo taken. Let me know if this is what you where looking for. Sorry for the sideways image.
Y^5y^5-(y^-2)^4 complete the equation
Answer: x =2, -1
Step-by-step explanation:
Determine the coordinates of the point shown.
Answer ASAP
A coordinate grid shown. There are increments of 0.5 for each grid line on each of the two axes. A point is located at 3 grid lines to the right and 1 grid line down from the origin.
(4 points)
(1.5, −0.5)
(−0.5, 1.5)
(3, −1)
(1, −1)
Answer:
(1.5, −0.5)
Step-by-step explanation:
Shaquanna kicks a football. It’s height in feet is given by h= -16t^2 + 16t where t represents the time in seconds after kick. After how many seconds does the football hit the ground?
Answer:
Step-by-step explanation:
the question is asking, or implying, when is [tex]t^{2}[/tex] = t :?
if you are thinking at 1, you're correct. so the ball will hit the ground at 1 second
3 1/2 + 4 3/4 + 5 3/10
Answer: 13.55 or 13 11/20.
Step-by-step explanation: First, you have to find a common denominator, in this case, it would be 20. 2 can go into 20 10 times, 4 can go into 20 5 times, and 10 can go into 20 2 times. Then, you would NOW have 3 10/20 + 4 15/20 + 5 6/20, to have all the equal denominators. When you add, you would get 12 31/20, but now you have to simplify. Now, you SHOULD get 13 11/20 after simplifying. As a decimal, it would be 13.55 I hoped this helped!
consider two medical tests, a and b, for a virus. test a is 90% effective at recognizing the virus when it is present, but has a 5% false positive rate (indicating that the virus is present, when it is not). test b is 95% effective at recognizing the virus, but has a 10% false positive rate. the two tests use independent methods of identifying the virus. the virus is carried by 2% of all people.Say that a person is tested for the virus using only one of the tests, and that test comes back positive for carrying the virus.Which test returning positive is more indicative of someone really carrying the virus? Justify your answer mathematically (i.e. writing down your calculations).
We observe, that P(V|B)>P(V|A), so the person is more likely to have virus, however is still very small probability (only 15%), so in order to confirm illness, he should make one more test.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
P(V/A) is not 0.95. It is opposite:
P(A/V)=0.95
From the text we can also conclude, that
P(A/∼V)=0.1
P(B/V)=0.9
P(B/∼V)=0.05
P(V)=0.01
P(∼V)=0.99
P(V/A) is not 0.95. It is opposite:
P(A/V)=0.95
From the text we can also conclude, that
P(A/∼V)=0.1
P(B/V)=0.9
P(B/∼V)=0.05
P(V)=0.01
P(∼V)=0.99
What we need to calculate and compare is P(V/A) and P(V/B)
P(V∩A)=P(A)⋅P(V/A)⇒P(V/A)=P(V∩A)/P(A)
P(V∩A) means, that person has a virus and it is detected, so
P(V∩A)=P(V)⋅P(A/V)
=0.01⋅0.95
=0.0095
P(A) is sum of two options: "Person has virus and it is detected" and "Person has no virus, but it was mistakenly detected", therefore:
P(A)=P(V)⋅P(A/V)+P(∼V)⋅P(A/∼V)=0.01⋅0.95+0.99⋅0.1=0.1085
Dividing those two numbers we obtain
P(V/A)=0.0095/0.1085=0.08755760368663594
Analogically,
P(V/B)=P(V∩B)/P(B)=P(V)⋅P(B/V)/P(V)⋅P(B/V)+P(∼V)⋅P(B/∼V)
=0.01⋅0.9/0.01⋅0.9+0.99⋅0.1
=0.1538461538461539
We see that P(V|B)>P(V|A), meaning the individual is more likely to have a virus, but is still very unlikely (only 15%), therefore person should perform another test to confirm illness.
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find the value h(-6) where h(t) = 6t-2
Answer:
Step-by-step explanation:
Quite literally you plug in -6 into t. So therefore:
h(t)=6t-2
h(-6)=6(-6)-2
h(-6)=-36-2
h(-6)=-38
-38 is your answer
h can be replaced with f and t can be replaced with x to get your standard f(x) equation if that helps you understand it better. Remember f(x) really just means the y value of the function with an input of value x. So f(x) = x is really just y=x or a linear line.
James fenced in his backyard. The perimeter of his fence is 20 feet, and the width of his yard is 2 feet wide. Use the perimeter formula to find the length of his rectangular yard in inches: P = 2L + 2W. (1 foot = 12 inches)
The length of James's rectangular yard, given a fence perimeter of 20 feet and a width of 2 feet, is 8 feet, equivalent to 96 inches.
How to use the perimeter of a rectangle?Given: Perimeter (P) = 20 feet, Width (W) = 2 feet,
Conversion factor: 1 foot = 12 inches
Using the formula for perimeter: P = 2L + 2W
Substitute the given values: 20 = 2L + 2(2)
Simplify: 20 = 2L + 4
Subtract 4 from both sides: 16 = 2L
Divide by 2: L = 8 feet
Convert feet to inches: Length (in inches) = 8 feet * 12 inches/foot = 96 inches
So, the length of the rectangular yard is 96 inches.
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To find the length of James' rectangular yard in inches, we can use the perimeter formula P = 2L + 2W. Given that the perimeter is 20 feet and the width is 2 feet, we can substitute these values into the formula and solve for the length in inches. The length of James' rectangular yard is 108 inches.
Explanation:To find the length of James' rectangular yard in inches, we can use the perimeter formula P = 2L + 2W. Given that the perimeter is 20 feet and the width is 2 feet, we can substitute these values into the formula. However, since we need the length in inches, we will convert the feet to inches using the conversion factor of 1 foot = 12 inches.
Let's solve:
Convert the width from feet to inches: 2 feet * 12 inches/foot = 24 inchesSubstitute the values into the formula: 20 feet = 2L + 24 inchesSince the units don't match, we need to convert 20 feet to inches: 20 feet * 12 inches/foot = 240 inchesNow we have the equation: 240 inches = 2L + 24 inchesIsolate L by subtracting 24 inches from both sides: 240 inches - 24 inches = 2LSimplify: 216 inches = 2LDivide both sides by 2: 216 inches / 2 = LSolve: L = 108 inchesThe length of James' rectangular yard is 108 inches.
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a town's population was 7500 at the beginning of the year 2000 and has been decreasing by 3.2 % each year thereafter.
Answer:
In 2022, the town's population is 2220.
Step-by-step explanation:
It currently the year 2022. Hence, 22 years have passed since 2000.
2022 − 2000 = 22
To solve for the town's population today, first multiply the years passed since 2000 by the percent decrease each year.
[tex]22 \, \textrm{years} \times \dfrac{3.2 \, \%}{\textrm{year}} = 70.4 \, \%[/tex]
Then, subtract that percent of the population in 2000 from the population in 2000.
[tex]7500-(70.4 \,\% \cdot 7500)[/tex]
[tex]= 7500 - 5280[/tex]
[tex]=2220[/tex]
for cos(theta) = -3/5, and pi/2 < theta < pi, find the following trig values
sin theta
tan theta
csc theta
sec theta
cot theta
For the given range of theta, cos(theta) is negative, which means that theta is in the third or fourth quadrant. In these quadrants, the sine function is positive, the tangent function is negative, and the cotangent function is negative.
Since cos(theta) = -3/5, we can use the Pythagorean identity to find the value of sin(theta):
sin^2(theta) + cos^2(theta) = 1
sin^2(theta) = 1 - cos^2(theta)
sin^2(theta) = 1 - (-3/5)^2
sin^2(theta) = 1 - 9/25
sin^2(theta) = 16/25
sin(theta) = sqrt(16/25) = 4/5
Therefore, the value of sin(theta) is 4/5.
We can also use the identity cot(theta) = 1/tan(theta) to find the value of cot(theta):
cot(theta) = 1/tan(theta)
cot(theta) = 1/(sin(theta)/cos(theta))
cot(theta) = cos(theta)/sin(theta)
cot(theta) = (-3/5)/(4/5)
cot(theta) = -3/4
Therefore, the value of cot(theta) is -3/4.
The values of the other trigonometric functions can be found using the definitions of these functions:
tan(theta) = sin(theta)/cos(theta) = (4/5)/(-3/5) = -4/3
csc(theta) = 1/sin(theta) = 1/(4/5) = 5/4
sec(theta) = 1/cos(theta) = 1/(-3/5) = -5/3
Therefore, the values of the trigonometric functions for the given range of theta are:
sin(theta) = 4/5
tan(theta) = -4/3
csc(theta) = 5/4
sec(theta) = -5/3
cot(theta) = -3/4