Answer:
Step-by-step explanation:
a) The tree diagram for the results of tossing a fair two-sided coin four times would look like this:
(1)
/ \
(H) (T)
/ \ / \
(2-H) (2-T) (2-H) (2-T)
/ \ / \ /
(3-HH) (3-HT) (3-TH) (3-TT)
b) There are four stages in the tree diagram.
c) The possible outcomes (the sample space) would be all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times. The possible outcomes are:
HHHHH
HHHTT
HHTHT
HHTTH
HTTHH
HTHHT
HTHTH
THHHH
THHTT
THTHT
TTHHT
TTHTH
TTTTT
d) There are 2^4 = 16 outcomes in the sample space.
ALSO:
a) Draw the Tree Diagram
Start with a root node labeled with the first toss (toss 1)
From the root node, draw two branches, one labeled with "Heads" (H) and the other with "Tails" (T) to represent the possible outcomes of the first toss.
Repeat this process for each of the next tosses (toss 2, 3, and 4)
Continue until all the possible outcomes of the four tosses have been represented.
Here is an example of the tree diagram:
(1)
/
(H) (T)
/ \ /
(2-H) (2-T) (2-H) (2-T)
/ \ / \ /
(3-HH) (3-HT) (3-TH) (3-TT)
/ \ / \ /
(4-HHH) (4-HHT) (4-THH) (4-TTT)
b) Number of Stages in the Tree Diagram
There are four stages in the tree diagram, one for each toss of the coin.
c) Possible Outcomes (Sample Space)
The possible outcomes (sample space) are all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times.
There are 16 possible outcomes in the sample space, as shown below:
HHHHH
HHHTT
HHTHT
HHTTH
HTTHH
HTHHT
HTHTH
THHHH
THHTT
THTHT
TTHHT
TTHTH
TTTHH
TTTTH
TTTTT
d) Number of Outcomes in the Sample Space
There are 2^4 = 16 outcomes in the sample space.
This is because for each toss, there are two possible outcomes (Heads or Tails), and since there are four tosses, there are 2 * 2 * 2 * 2 = 16 possible combinations.
ALSO:
a) Draw the Tree Diagram
Start with a root node labeled with the first toss (toss 1).
From the root node, draw two branches, one labeled with "Heads" (H) and the other with "Tails" (T) to represent the possible outcomes of the first toss.
Repeat this process for each of the next tosses (toss 2, 3, and 4).
Continue until all the possible outcomes of the four tosses have been represented.
Here is an example of the tree diagram:
(1)
/
(H) (T)
/ \ /
(2-H) (2-T) (2-H) (2-T)
/ \ / \ /
(3-HH) (3-HT) (3-TH) (3-TT)
/ \ / \ /
(4-HHH) (4-HHT) (4-THH) (4-TTT)
b) Number of Stages in the Tree Diagram
There are four stages in the tree diagram, one for each toss of the coin.
c) Possible Outcomes (Sample Space)
The possible outcomes (sample space) are all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times.
There are 16 possible outcomes in the sample space, as shown below:
HHHHH
HHHTT
HHTHT
HHTTH
HTTHH
HTHHT
HTHTH
THHHH
THHTT
THTHT
TTHHT
TTHTH
TTTHH
TTTTH
TTTTT
d) Number of Outcomes in the Sample Space
There are 2^4 = 16 outcomes in the sample space.
This is because for each toss, there are two possible outcomes (Heads or Tails), and since there are four tosses, there are 2 * 2 * 2 * 2 = 16 possible combinations.
I hope this step-by-step explanation with the diagram helps! Let me know if you need further clarification.
Write a equation with the slope of 3 and goes through the point (2,5)
The equation of the line with slope 3 that goes through the point (2, 5) is y = 3x - 1.
What is the slope-point form of the line?
The point-slope form of the equation of a line is given by:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is a point on the line.
Using the given slope of 3 and the point (2, 5), we can substitute into the point-slope form to get:
y - 5 = 3(x - 2)
Expanding the right-hand side:
y - 5 = 3x - 6
Adding 5 to both sides:
y = 3x - 1
Hence, the equation of the line with slope 3 that goes through the point (2, 5) is y = 3x - 1.
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A company made 500 flashlights and found that 5 were defective. If the company makes 12,500 flashligh
O 120
O125
0 250
O 1,250
The company can expect to find 125 defective flashlights in a production run of 12,500. The correct option is B, 125.
What is flashlights?Flashlight can be defined as a portable, battery-operated device used for illumination. It typical unit consists of one or more dry cell batteries arranged in a line inside a battery compartment that forms the handle of the light.
Assuming the proportion of defective flashlights remains the same, the number of defective flashlights in a production run of 12,500 would be:
(5/500) x 12,500 = 125
Therefore, the company can expect to find 125 defective flashlights in a production run of 12,500. The answer is option B, 125.
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11. Mike plans to make contributions to his retirement account for 15 years. After the last contribution, he will start withdrawing $10,000 a quarter for 10 years. Assuming Mike's account earns 8% compounded quarterly, how large must his quarterly contributions be during the first 15 years, in order to accomplish his goal?
Answer:
To solve this problem, we need to use the formula for compound interest:
A = P * (1 + r/n)^(nt)
where:
A = future value of the account
P = present value (the contributions)
r = interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
First, we need to find the future value of the account (A) after 10 years of withdrawals at $10,000 per quarter. This means there will be 40 quarters in total ($10,000 * 40 = $400,000).
Next, we need to find the present value of the account (P) after 15 years of contributions.
Let's call the quarterly contributions "x".
We can set up the equation as follows:
$400,000 = x * (1 + 0.08/4)^(4 * 15) - $10,000 * (1 + 0.08/4)^(4 * 10)
We can now solve for x using a financial calculator or by using a programming language to perform the calculation. The result of this calculation is that Mike's quarterly contributions should be $2,597.29 in order to accomplish his goal.
Please help fast!! What is the domain of the relation?
A: (-5,0,3,4)
B: (-4,-1,0,1,3)
C: (-5,-2,0,1,4)
D: (-5,-4,-2,-1,0,1,3,4)
Look at the picture below
The correct option is A {-5, 0, 3, 4}.
What do you mean by Domain?In mathematics, the domain of a function is the set of all possible input values (independent variable) for which the function is defined. In other words, the domain is the set of values that we can substitute for the independent variable in a function to produce a meaningful output.
For example, consider the function f(x) = 2x. Here, we can substitute any real number for x and get a meaningful output. Therefore, the domain of this function is all real numbers, or (-∞, ∞). However, if we consider the function g(x) = 1/x, we can see that we cannot substitute 0 for x because division by 0 is undefined. Therefore, the domain of this function is all real numbers except 0, or (-∞, 0) U (0, ∞).
The domain of a relation is the set of all possible values for the independent variable (x) for which there exists a corresponding value of the dependent variable (y). In this case, the given coordinates are (1,3), (4,1), and (-5,-4).
The domain of the relation would be the set of x-values that correspond to the given coordinates. So, the domain of this relation is {-5, 1, 4}.
Therefore, the correct answer is A: {-5, 0, 3, 4}.
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Dividends Per Share Sandpiper Company has 15,000 shares of cumulative preferred 2% stock, $50 par and 50,000 shares of $10 par common stock. The following amounts were distributed as dividends: 20Y1 20Y2 20Y3 Determine the dividends per share for preferred and common stock for each year. Round all answer to two decimal places. If an answer is zero, enter '0'. 20Y1 2012 $30,000 6,000 45,000 20Y3 Preferred Stock (dividends per share) Common Stock (dividends per share) LA
Answer: To calculate the dividends per share for preferred and common stock for each year, we need to divide the total dividends by the number of shares for each type of stock.
20Y1:
Preferred Stock: $30,000 / 15,000 shares = $2.00 per share
Common Stock: $6,000 / 50,000 shares = $0.12 per share
20Y2:
Preferred Stock: $30,000 / 15,000 shares = $2.00 per share (cumulative preferred stock means that if the company misses a dividend, they still have to pay it in the future, so the dividends per share remain the same)
Common Stock: $45,000 / 50,000 shares = $0.90 per share
20Y3:
Preferred Stock: $30,000 / 15,000 shares = $2.00 per share
Common Stock: $0 (there is no information about dividends for the common stock in 20Y3)
So, the dividends per share for each year would be:
20Y1:
Preferred Stock: $2.00 per share
Common Stock: $0.12 per share
20Y2:
Preferred Stock: $2.00 per share
Common Stock: $0.90 per share
20Y3:
Preferred Stock: $2.00 per share
Common Stock: $0.00 per share
Step-by-step explanation:
Statesvilles population in 2010 was about 24800 and was growing about 1.2% each year. If this continues, what will statesvilles population be in 2015?
yearly multiplication growth factor is (1+0.011) = 1.011. the year 2017, seven years after 2010, the population will be [tex]24800*2A1.011^7 = 26,774[/tex]
what is multiply ?
Along with addition, subtraction, and division, multiplication is one of the four arithmetic operations. Multiplication in math refers to regularly adding groups of the same size. The formula for multiplication is multiplicand multiplier Equals product. Specifically, multiplicand: First number (factor). divider: Second number (factor). After multiplying the multiplicand and the multiplier, the result is known as the product. Multiple additions are made while adding numerals. as in 5 times 4 Equals 5 + 5 + 5 + 5 = 20. I multiplied 5 by 4 times. Multiplication is frequently referred to as "doubling" because of this.
yearly multiplication growth factor is (1+0.011) = 1.011.
the year 2017, seven years after 2010, the population will be [tex]24800*2A1.011^7 = 26,774[/tex]
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A school administrator wants to know what proportion of teachers in their state have a Master's degree. The administrator takes an SRS of
100
100100 teachers from a statewide database containing every teacher, and they find
55
5555 teachers in the sample have a Master's degree. The administrator wants to use this data to construct a one-sample
z
zz interval for a proportion.
Which conditions for constructing this confidence interval did their sample meet?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
The data is a random sample from the population of interest.
(Choice B)
B
n
p
^
≥
10
n
p
^
≥10n, p, with, hat, on top, is greater than or equal to, 10 and
n
(
1
−
p
^
)
≥
10
n(1−
p
^
)≥10n, left parenthesis, 1, minus, p, with, hat, on top, right parenthesis, is greater than or equal to, 10
(Choice C)
C
Individual observations can be considered independent.
A) The data is a random sample from the population of interest. - Yes, it is mentioned that the administrator takes an SRS (Simple Random Sample) of 100 teachers from the statewide database containing every teacher.
What do you mean by SRS (Simple Random Sample)?Simple Random Sample (SRS) is a statistical technique for selecting a sample from a population, where each individual or item in the population has an equal chance of being selected for the sample. In other words, a simple random sample is a representative subset of a population where every individual or item in the population has an equal chance of being selected for the sample.
To take a simple random sample, each individual in the population is assigned a unique number, and then random numbers are generated to select the required number of individuals for the sample. This method ensures that the sample is not biased towards any particular subset of the population, and that the sample is representative of the whole population.
A) The data is a random sample from the population of interest. - Yes, it is mentioned that the administrator takes an SRS (Simple Random Sample) of 100 teachers from the statewide database containing every teacher.
B) np^≥10n p^ ≥10n, p, with, hat, on top, is greater than or equal to, 10 and n(1−p^)≥10n(1− p^ )≥10n, left parenthesis, 1, minus, p, with, hat, on top, right parenthesis, is greater than or equal to, 10 - Since the problem does not provide the value of p, we cannot determine if the condition np^≥10n and n(1−p^)≥10n are satisfied.
C) Individual observations can be considered independent. - The problem does not provide information about whether the individual observations can be considered independent. However, we can assume that since it is a random sample, the observations are independent.
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G(x)=-4x^2+36/x+3
What key features does f(x), shown in the graph, share
with g(x), shown in the equation? Select three options.
at least one x-intercept
at least one y-intercept
Dan oblique asymptote
O a vertical asymptote
the domain of x
The function g ( x ) in the graph has one x-intercept , y intercept and an oblique asymptote , a vertical asymptote
What are Asymptotes?An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote. When graphing functions, asymptotes are typically not required
There are 3 types of asymptotes
Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k. Horizontal Asymptote is when the function f(x) is tending to zero
Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k. Vertical asymptotes are defined when the denominator of a rational function tends to zero
Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b
Given data ,
Let the function be represented as g ( x )
Now , the value of g ( x ) is
g ( x ) = ( -4x² + 36 ) / ( x + 3 )
On simplifying , we get
g ( x ) = -4 ( x² - 9 ) / ( x + 3 )
On further simplification , we get
g ( x ) = -4 ( x + 3 ) ( x - 3 ) / ( x + 3 )
g ( x ) = -4 ( x - 3 )
g ( x ) = -4x + 12
Now , the function has a vertical asymptote at ( 0 , 12 )
The function has a horizontal asymptote at ( 3 , 0 )
Hence , the function is solved
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Answer:
at least one x-intercept
at least one y-intercept
domain of x
Step-by-step explanation:
took ed2023
Angela fully charged her laptop, then unplugged it and tracked the battery level at certain times under constant use. The table below shows her findings. The equation for the line of best
fit is below. Use the equation to estimate the battery level after two hours of constant use unplugged. Round to the nearest percent. (2:00 is an x-value of 0)
The battery level after two hours of constant use unplugged is found replacing the instance of x on the line of best fit by 2.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The variables for this problem are given as follows:
Variable x: time in hours.Variable y: battery percentage.Hence after a time of two hours the battery level is found as the numeric value at x = 2.
Missing InformationThe problem is incomplete, hence the general procedure to solve the problem is presented.
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You want to put a 6-inch thick layer of topsoil for a new 28 feet by 17 feet garden. The dirt store only sells topsoil by the cubic yard. How many cubic yards of topsoil will you need to order to fill this garden?
To fill a 6-inch thick layer of topsoil for a new 28 feet by 17 feet garden, you will need 79.33 cubic yards.
How is the volume determined?The volume is the product of the multiplication of the thickness, length, and width.
The thickness of the topsoil = 6 inches
12 Inches = 1 Feet
6 inches = 0.5 Feet (6/12)
The length of the garden = 28 feet
The width of the garden = 17 feet
The thickness of the soil = 0.5 feet
Volume of the topsoil = 28 x 17 x 0.5
= 238 ft³
3 Feet to 1 Yard
238 ft³ = 238/3 yards
= 79.33 cubic yards
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Find the indicated outputs for f(x) = 4x - 5x. f(2)=
Answer:
[tex] \sf \: f(2) = - 2[/tex]
Step-by-step explanation:
Given function,
→ f(x) = 4x - 5x
Now we have to,
→ Find the required value of f(2).
Then the value of f(2) will be,
→ f(x) = 4x - 5x
→ f(2) = 4(2) - 5(2)
→ f(2) = 8 - 10
→ [ f(2) = -2 ]
Hence, the value of f(2) is -2.
Your friend begins to divide the numerator and denominator
12
by 4 and then gets stuck. Explain why your friend gets stuck.
Answer:
maybe your friend gets stuck because youre not supposed to divide the denominator, only make a common one by multiplying one or both untill they are the same. Least common multiples
Rob loaded 9 trucks in 1 hour find his loading speed per hour
Answer:
9 trucks/hour
Step-by-step explanation:
If he loaded 9 trucks in one hour, his loading speed is 9 trucks per hour.
Suppose you bought ares company 4 years ago at a price of $63.00 per share sold it at $71.50 per share. How much money die you make? $37750 $382.50 $387.50 $392.50
The amount you made per share is $8.50.
How to determine the amount you madeFrom the question, we have the following parameters that can be used in our computation:
Initial amount = $63.00
Final amount = $71.50
To calculate the profit made, we need to find the difference between the selling price and the buying price per share, and then multiply by the number of shares.
The difference in price per share is:
Difference = $71.50 - $63.00
Evaluate the difference
Difference = $8.50
Hence, the profit per share is $8.50.
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Final question no more lives
who ever gives me correct answer will get brainliest
The time take to fill the pool will be 494 hours.
How to calculate the TimeInlet pipe fills in 38 hours = 1 pool
Inlet pipe fills in 1 hours = 1/38
Drain pipe empty in 39 hours = 1 pool
Drain pipe empty in 1 hour = 1/39
If both pipes are opened together then in pool fills in 1 hour = 1/38 - 1/39
= 1/1482
Therefore, 1/1482 fills in 1 hour.
. Therefore, 1/3 will be:
= 1/3 × 1482
= 494 hours.
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A bakery can make 42 cheesecakes for every 6 blocks of cream cheese. Which table represents the relationship between the number of cheesecakes the bakery makes and the number of blocks of cream cheese the bakery uses?
Answer:
Step-by-step explanation:
A boy contain 10 balls of which 6 are Red and the rest are White If a ball is pick at random find the probability of Either Red or White Not Red
Calculate the marked price on a bag of Cement selling 570 ksh after a discount of 5% is offered.
Answer:
541.5 ksh
Step-by-step explanation:
Question content area top
Part 1
Find the measure of side a.
Side a will be 58cm.In mathematics, a side is a feature of a geometric shape.
A side: What is it?The "A-side" of a record, which is the main song, is issued as a single. The "A-side" of an album is the side that this track is on. The word "side" is most frequently employed as a noun, however it can also be used as an adverb or a verb. The shapes we observe are made of points and lines (line segments) (vertices).
Finding the side, we obtain:
Given ∠A= 30°, b =100 cm .
In ΔABC,
tan A = [tex]\frac{a}{100}[/tex],
tan 30°= [tex]\frac{a}{100}[/tex]
0.577×100=a
a=57.7≅58 cm.
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solve the equations to find where they intersect
y = 6x - 8
y=-3x+10
Answer:
(2,4)
Step-by-step explanation:
-3x⁴+5x³+0x²+2x-1÷2x²-x
The quotient is -3x²/2 + 7x/4 + 7/8 and the remainder is 23x/8 - 1. The solution has been obtained by using polynomial long division method.
What is polynomial long division?
A formula for multiplying one polynomial by another of the same degree or lower is known as a long division polynomial. Like with long division of numbers, the components of long division of polynomials include the divisor, quotient, dividend, and remainder.
We are given dividend as -3x⁴+5x³+0x²+2x-1 and divisor as 2x²-x.
Using Polynomial Long Division,
Dividing : -3x⁴+5x³+0x²+2x-1 ("Dividend")
By : 2x²-x ("Divisor")
Dividend -3x⁴ + 5x³ + 0x² + 2x - 1
- divisor * -3x²/2 -3x⁴ + 3x³/2
Remainder + 7x³/2 + 0x² + 2x - 1
- divisor * 7x/4 + 7x³/2 - 7x²/4
Remainder 7x²/4 + 2x - 1
- divisor * 7/8 7x²/4 - 7x/8
Remainder 23x/8 - 1
Quotient : -3x²/2 + 7x/4 + 7/8
Remainder: 23x/8 - 1
Hence, the solution has been obtained.
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which is a true statement about two numerical sets of data that have negative association
Answer:
Option D.
Step-by-step explanation:
Negative correlation also called an " inverse correlation " is a relation between 2 variables where-by they behave in opposite manner. When one variable moves ---> in an increasing /\ direction, the other variable moves in a decreasing \/ direction.
Thus, Option D.
The function f (x) = 125,000 (1.028)x models the change in population of Pool City, where x represents the number of years since 2010. Which statement is NOT true?
A.) The domain of the function includes all real values of x .
B.) The point (1, 128500) represents the population of Pool City in 2011.
C.) The population of Pool City in 2010 is 125,000.
D.) The function has an asymptote at y = 125,000 .
Which of the following equations represents a parabola with a vertical axis of symmetry, vertex at (10, –4), and p = –3?
(y + 10)2 = 12(x – 4)
(y – 10)2 = –12(x + 4)
(x + 10)2 = 12(y – 4)
(x – 10)2 = –12(y + 4)
(x - 10)² = -12 (y + 4) represents a parabola with a vertical axis of symmetry, vertex at (10, –4), and p = –3 .
What's a vertical parabola?
A vertical parabola has its axis of symmetry at x = h, and the vertex is (h, v). With this information, you can find the focus and directrix. The focus is the distance from the vertex to the focus is 1/(4a), where a can be found in the equation of the parabola (it is the scalar in front of the parentheses).
we know that
If the axis of symmetry is parallel to the y-axis, then we have a vertical parabola
The equation of a vertical parabola is equal to
4p(y - k) = (x - h)²
where
(h,k) is the vertex
In this problem we have
(h,k) = (10, –4)
p= -3
substitute
4*(-3)(y - (-4)) = (x - 10)²
-12 (y + 4) = (x - 10)²
or
(x - 10)² = -12 (y + 4)
Hence , option D is correct.
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Please help!! Thank you!
Using angle relationships, the missing measures are:
m<3 = 138 degrees.
m<5 = 42 degrees.
m<8 = 138 degrees.
How to Find the Missing Angles?Using angle relationships, each of the measure of the angles can be calculated as follows:
Given that, m<1 = 138 degrees.
m<3 = m<1 [vertical angles are congruent]
Substitute:
m<3 = 138 degrees.
m<5 + m<3 = 180
Substitute:
m<5 + 138 = 180
m<5 = 180 - 138
m<5 = 42 degrees.
m<8 = m<3 [alternate interior angles are congruent]
m<8 = 138 degrees.
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You are given the yearly interest earned from a total of $18,000 invested in two funds paying the given rates of simple interest. Write and solve a system of equations to find the amount invested at each rate. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.
Yearly Interest: $579
Rate 1: 2.75%
Rate 2: 4.75%
(dollars invested at 2.75%, dollars invested at 4.75%) =
The amount of investment at a rate of 2.75% and 4.75% will be $13,800 and $4,200m, respectively.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
The formula for interest is written as,
I = (PRT)/100
Where P is the principal, R is the rate of interest, and T is the time.
Let 'x' be the amount of investment at a rate of 4.75%. Then the amount of investment at a rate of 2.75% is ($18,000 - x). Then the equation is given as,
(18,000 - x) × 0.0275 + 0.0475x = 579
495 - 0.0275x + 0.0475x = 579
0.02x = 84
x = $4,200
Then the value of ($18,000 - x) is given as,
$18,000 - x = $18,000 - $4,200
$18,000 - x = $13,800
The amount of investment at a rate of 2.75% and 4.75% will be $13,800 and $4,200m, respectively.
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Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 16. Complete parts (a) through (c) below.
a)The standard deviation is given by σ = sqrt(np(1-p)) = sqrt(24 × 0.75 × 0.25) = 2.12 . b)Significantly low: μ - 2σ = 18 - 2 × 2.12 ≈ 13.76 ,Significantly high: μ + 2σ = 18 + 2 × 2.12 ≈ 22.24 ,c)z = (x - μ) / σ = (3 - 18) / 2.12 ≈ -7.08.
How to calculate standard deviation?A group of 24 peas with green pods has a binomial distribution with n = 24 and p = 0.75. The mean is calculated as = np = 24 0.75 = 18, and the standard deviation is calculated as = sqrt(np(1-p)) = sqrt(24 0.75 0.25) = 2.12 (rounded to two decimal places).
b) The range rule of thumb states that results that deviate from the mean by more than two standard deviations are considered significantly low or significantly high. In this case, the values separating significantly low and significantly high results are:
Significantly reduced: - 2 = 18 - 2 2.12 13.76
Significantly greater: + 2 = 18 + 2 2.12 22.24
c) To see if a result of three peas with green pods is significantly low, we must calculate its z-score, which is given by:
z = (x - μ) / σ = (3 - 18) / 2.12 ≈ -7.08
Because the z-score is much lower than -2, the cutoff for significantly low results, we can conclude that a result of 3 peas with green pods is significantly low.
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Find the value of x that will make L||m
Answer:
x=-13
Step-by-step explanation:
Since the two angles given are equivalent, you set up the equation as 7x+205=114.
7x+205=114
7x=114-205
7x=-91
7x/7=-91/7
x=-13
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Plot and connect the points in the order listed below. When you are done, find the area of the resulting figure.
A(-5,4)A(−5,4), B(4,4)B(4,4), C(4,1)C(4,1), D(1,1)D(1,1), E(4,-3)E(4,−3), F(4,-6)F(4,−6), G(-5, -6)G(−5,−6)
The total area of the figure with points A(-5,4), B(4,4), C(4,1), D(1,1), E(4,-3) F(4,-6), G(-5, -6) is 51 square units.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Divide the figure is into two rectangles and a triangle.
The points B, C, E, and F form a rectangle with base BC and height 7 units.
The points A, D, and G form a rectangle with base AG and height 5 units. The points C, D, and E form a triangle with base CE and height 4 units.
The length of BC is 4 - 4 = 0, so the area of the rectangle with base BC is 0.
The area of the rectangle with base AG is (4 - (-5)) x 5 = 45 square units. The area of the triangle with base CE is (4 - 1) x 4 / 2 = 6 square units.
Therefore, the total area of the figure with points A(-5,4), B(4,4), C(4,1), D(1,1), E(4,-3) F(4,-6), G(-5, -6) is 45 + 6 = 51 square units.
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Use the data in the table below, which shows the employment status of individuals in a particular town by age group.
Age
0-17
18-25
26-34
35-49
50 +
Full-time
21
267
492
535
520
Part-time
187
200
67
195
166
Unemployed
356
135
28
133
231
If a person is randomly chosen from the town's population, what is the probability that the person is under 18 or employed part-time?
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The probability that the person is under 18 or employed part-time is 179/864.
What is experimental probability?Experimental probability calculates the probability of some event from the results of experiments.
For an event E, we get the experimental probability of that event
[tex]P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}}[/tex]
where,[tex]P_e(E)[/tex] is denoting experimental probability of occurrence of E.
Given that;
The table of age, full time, part time, unemployed
Now,
Total number of people who are between the age group 35-49
= 581+179+104
= 864
Number of people who are employed part time= 179
Number of people employed part time in age group 35-49/ Total people in age group 35-49
= 179/864
Therefore, the probability will be 179/864.
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