Therefore, we can expect the world population to be around 17.6 billion in the year 2100 if it continues to increase exponentially with a doubling time of 60 years.
What is decimal place?A decimal place is a position in a number that is to the right of the decimal point. It represents a fractional part of the number. For example, in the number 3.14159, the digit "1" is in the tenths place, the digit "4" is in the hundredths place, the digit "1" is in the thousandths place, and so on. Each place value to the right of the decimal point represents a power of 10 that is negative, such as tenths, hundredths, thousandths, ten-thousandths, and so on. The number of decimal places determines the degree of precision in the number.
by the question.
To determine the population in the year 2100, we need to calculate how many times the population will double between 2022 and 2100, which is 78 years.
78 years divided by 60 years is approximately 1.3, which means that the population will double 1.3 times between 2022 and 2100.
2 to the power of 1.3 is approximately 2.2, which means that the population in 2100 will be 2.2 times the population in 2022.
So, the population in 2100 will be:
8 billion x 2.2 = 17.6 billion (rounded to one decimal place)
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PLEASE HELP ME THIS IS DUE RIGHT NOW!!!
How many solutions does the system of equations below have?
y =2 x +4
y + 6 =2x
A. Exactly 1 solution
B. More than 1 solution
C. No solution
D. at least 1 solution
Answer: there
Step-by-step explanation:
exactly 1 solution
Your monthly insurance premiums include liability ($50), property damage ($40), medical ($15),
comprehensive ($40), and collision ($85). What is your total monthly premium to the nearest dollar?
OA. $230
OB. $290
OC. $320
OD. $380
Answer:
Step-by-step explanation:
50+40+15+40+85
=230
Based on results from recent track meets, Nestor has a 79% chance of getting a medal in the 100 meter dash. Estimate the probability that Nestor will get a medal in at least 6 of the next 10 races. Use the random number table, and make at least 10 trials for your simulation. Express your answer as a percent.
Answer Choices:
-1%
-200%
-100%
-1.05%
The predicted likelihood that Nestor will win at least six of the upcoming races is therefore 90.1%, which is closest to the correct response of -1%.
what is probability ?The likelihood or chance that a specific occurrence or outcome will occur is quantified by probability. It is represented by a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certainty. For instance, there are two equally likely outcomes (heads or tails), but only one of them is heads, hence the probability of flipping a fair coin and obtaining heads is 0.5 or 50%. By dividing the number of favorable outcomes by the total number of possible outcomes, one can calculate probability.
given
We can see that Nestor won a medal in 6 out of the 10 trials by counting the number of victories.
We can use the binomial distribution with parameters n=10 (number of trials) and p=0.79 to calculate the likelihood that this will occur (probability of success).
The following calculation can be used to determine the likelihood of at least 6 successes in 10 trials:
P(X>=6) = 1 - P(X<=5)
Using a calculator for the binomial distribution, we obtain:
P(X>=6) = 90.1%
The predicted likelihood that Nestor will win at least six of the upcoming races is therefore 90.1%, which is closest to the correct response of -1%.
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We will prove the following:
Because BF and CE bisect each other at point D, we know that angles BDC and EDC are congruent, and angles BDF and CDE are also congruent, as they are vertical angles.
Describe Angles?In mathematics, an angle is a geometric figure formed by two rays or line segments that share a common endpoint called the vertex. The rays or line segments are called the sides of the angle.
Angles are typically measured in degrees or radians, and they are denoted using the symbol ∠. The measure of an angle is the amount of rotation needed to bring one side of the angle into coincidence with the other. A full rotation is 360 degrees or 2π radians.
Angles can be classified into different types based on their measures and their relationships with other angles. Some common types of angles include:
Acute Angle: An angle whose measure is less than 90 degrees.
Right Angle: An angle whose measure is exactly 90 degrees.
Obtuse Angle: An angle whose measure is greater than 90 degrees but less than 180 degrees.
Because BF and CE bisect each other at point D, we know that angles BDC and EDC are congruent, and angles BDF and CDE are also congruent, as they are vertical angles.
By definition of angle bisectors, we know that CD=DE and BD=DF.
Thus, the triangle congruence principle SAS (side-angle-side) allows us to deduce that Triangle BCD is congruent to Triangle ECD, since they share side CD, angle BDC and angle EDC.
Therefore, BC=CE (corresponding sides of congruent triangles are equal) and CE=EF (because CE bisects segment BF).
Thus, BC=EF, and we have proven that BC is equal to EF
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Heather built 7 wooden toys. Each toy had a mass of 4/5 kilograms. What was the total mass of the toys that she built?
Answer: 28/5
Step-by-step explanation:
each toy had a mass of 4/5 kilograms .there are 7 toys.so the total mass is
7 times 4/5=28/5 kilograms
hope it helps
What is the period, phase shift and cosine function of this graph
The period, phase shift, and cosine function of the graph are;
The period = π
The phase shift = π/8
The cosine function is; y = 2·cos(2·(x - π/8)) - 1
What is the period of the graph of the cosine function?The period of the graph is the distance between two consecutive peaks of the wave.
The maximum value of the graph is 1 at x = π/8 and x = 9·π/8, and the minimum value of the function is; -3 at 5·π/8.
The vertical displacement can be obtained from half the sum of the max and min point as follows;
Vertical displacement = (1 + (-3))/2 = -1
The vertical displacement = -1
The amplitude = Half the distance between the max and min point of the graph
Amplitude, a = (1 - (-3))/2 = 2
The amplitude, a = 2
The period of the graph = 9·π/8 - π/8 = 8·π/8 = π
The period = 2·π/b
Therefore; 2·π/b = π
b = 2·π/π = 2
b = 2
The phase shift = π/8
The cosine function is therefore;
y = 2·cos(2·(x - π/8) - 1
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Justin began studying the population of 2 small towns in 2015.
town A begins with 9,000 people and increases by 500 people each year.
town B begins with 8,000 people and increases by 9% each year.
in what year will town B have larger population than town A
Town B will have a larger population than Town A in the year 2019.
How to find increase in population?To solve this problem, we can use a year-by-year approach to see when the population of town B surpasses that of town A.
Let's start with year 0 (2015):
Town A population: 9,000
Town B population: 8,000
In year 1 (2016):
Town A population: 9,500 (9,000 + 500)
Town B population: 8,720 (8,000 x 1.09)
In year 2 (2017):
Town A population: 10,000 (9,500 + 500)
Town B population: 9,504.8 (8,720 x 1.09)
In year 3 (2018):
Town A population: 10,500 (10,000 + 500)
Town B population: 10,360.232 (9,508.8 x 1.09)
In year 4 (2019):
Town A population: 11,000 (10,500 + 500)
Town B population: 11,292.653 (10,394.912 x 1.09)
From this calculation, we can see that in the year 2019, the population of Town B will be larger than that of Town A. Therefore, the answer is:
Town B will have a larger population than Town A in the year 2019.
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solve to the nearest tenth
The value of x in right angle whose hypotenuse is given 74 m one angle is 90° and other angle given is 30° to the nearest tenth is approximately 37 meters.
What is trigonometry?The branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles is known as Trigonometry. It involves studying the properties of trigonometric functions, which are mathematical functions that relate the angles of a triangle to the ratios of its sides.
In this triangle, the height is opposite the 30° angle and the hypotenuse is the longest side of the triangle. We can use the trigonometric function sine to relate the height and the hypotenuse:
sin(30°) = x / 74
To solve for x, we can multiply both sides by 74 and simplify:
x = 74 sin(30°)
x ≈ 37 (to the nearest tenth)
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5 Ms. Zling deposited $850 in a savings
account that paid 4.25% simple
interest. What was the balance in her
account at the end of 2 years?
Answer:
$ 922.25
Step-by-step explanation:
General equation for simple interest ... B(t)=B(0)[1+rt]B
(0)= inital amount r= simple annual interest rate t= number of yearsFor this problem,
B (2)=$850[0.0425×2}=850×1.085 =$922.25
O is the center of the regular nonagon below. Find its perimeter. Round to the nearest tenth if necessary. Answer: P = = O 7 units
Therefore, the perimeter P of the nonagon is 19.5 units.
What is perimeter?Perimeter refers to the total length of the boundary or the outer edge of a closed figure or shape. It is the sum of the lengths of all the sides or edges that enclose the shape.
Here,
Since O is the center of the regular nonagon, all the sides of the nonagon are equal in length. Let the length of one side of the nonagon be s. Then, the perimeter P of the nonagon is given by:
P = 9s
To find s, we can use the fact that the sum of the interior angles of a nonagon is given by (9-2)×180° = 1260°. Since the nonagon is regular, each angle is equal to 1260°/9 = 140°.
Consider the triangle OAB, where A and B are two adjacent vertices of the nonagon. Since O is the center of the nonagon, angle AOB is equal to 360°/9 = 40°. Also, angle OAB and angle OBA are equal to half of (180° - 140°) = 20°.
Therefore, angle AOB is isosceles, and we can use the cosine rule to find s:
cos(20°) = (s/2) / s
cos(20°) = 1/2
s = 2 / cos(20°)
Using a calculator, we get s ≈ 2.165. Therefore, the perimeter P of the nonagon is:
P = 9s
≈ 19.5 (rounded to the nearest tenth)
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Chloe wants to pay off her credit card debt of $7,316.48 that has an APR of 16.73%. She is paying $300 per month.
a) Using the finance charge defined in class (charge = r*(balance-payments+purchases)), what would be the credit card balance (to the nearest dollar) after one year?
b) If she increased her monthly payment by $50 to $350 per month, what would be the credit card balance (to the nearest dollar) after one year?
a) Using the formula for finance charge, we can find the balance after one year:
charge = r*(balance-payments+purchases)
Here, r = 16.73% = 0.1673 (as a decimal), payments = $300 per month = $3,600 per year, and purchases = 0 (since Chloe is not making any new purchases).
Let's assume that x is the balance after one year. Then, we can write:
0.1673*(7316.48-3600) = x - 3600
Simplifying and solving for x, we get:
x = $6,830.58
So, the credit card balance (to the nearest dollar) after one year would be $6,831.
b) If Chloe increases her monthly payment to $350 per month, then her payments for the year would be $4,200. Using the same formula as above, we can find the balance after one year:
0.1673*(7316.48-4200) = x - 4200
Simplifying and solving for x, we get:
x = $5,774.99
So, the credit card balance (to the nearest dollar) after one year with a $350 monthly payment would be $5,775.
Riley was a spectator at his town's air guitar competition. Contestants were allowed to play either the acoustic or electric air guitar, but not both. Riley recorded which type of guitar each contestant played. He also counted the number of contestants wearing different kinds of pants, as there were some interesting stylistic choices.
What is the conditional probability that a randomly selected contestant played an acoustic guitar, given they wore leather pants?
show ALL step
The conditional probability that a randomly selected contestant played an acoustic guitar is 2/5.
What is conditional probability?
The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood of the subsequent, or conditional, occurrence to determine the conditional probability.
Here, we have
Given: Riley was a spectator at his town's air guitar competition. Contestants were allowed to play either the acoustic or electric air guitar, but not both. Riley recorded which type of guitar each contestant played.
Let A be the event of a contestant playing acoustic guitar.
Let B be the event of a contestant wearing leather pants
The conditional probability of a contestant playing acoustic guitar given he wears leather pants, P(A|B) is-
P(A|B) = P(A∩B)|P(B)
Where,
P(A∩B) = is the probability of simultaneous occurrence of events A and B.
P(A∩B) = 6
P(B) = no. of contestants wearing leather pants
P(B) = 15
P(A|B) = 6/15 = 2/5
Hence, the conditional probability that a randomly selected contestant played an acoustic guitar is 2/5.
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The triangle shown below has an area of 18 units 2 squared.
Answer:
6 units
Step-by-step explanation:
The area of a triangle is [tex]A = (b \times h)/2[/tex], where b is base and h is height.
In this case, [tex]b = 6[/tex] and [tex]h = x[/tex]. Plug these into the equation:
[tex]18 = (6x)/2[/tex]
[tex]36 = 6x[/tex]
[tex]x = 6[/tex]
Thus, the answer is 6 units.
Hope this helps!
A Food Marketing Institute found that 33% of households spend more than $125 a week on groceries. Assume the population proportion is 0.33 and a simple random sample of 349 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.32? There is a probability that the sample proportion of households spending more than $125 a week is less than 0.32. Round the answer to 4 decimal places.
The probability that the sample proportion of households spending more than $125 a week is less than 0.32 is 0.3850.
What is probability?
The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.
Here, we have
Given: A Food Marketing Institute found that 33% of households spend more than $125 a week on groceries. Assume the population proportion is 0.33 and a simple random sample of 349 households is selected from the population.
We have to find the probability that the sample proportion of households spending more than $125 a week is less than 0.32.
P(p < 0.32)
= P(Z < 0.32-0.33 0.33 * 0.67/189
= P(z < -0.29)
= 0.3850
Hence, the probability that the sample proportion of households spending more than $125 a week is less than 0.32 is 0.3850.
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-
.
A culture of bacteria has an initial population of 870 bacteria and
doubles every 3 hours. Using the formula Pt = Po · 2ắ, where Pt is
the population after t hours, Po is the initial population, t is the time in
hours and d is the doubling time, what is the population of bacteria in
the culture after 7 hours, to the nearest whole number?
Rounding to the nearest whole number, the number of bacteria still present in the culture after 7 hours is approximately 3481.
How many whole numbers are there?
All natural numbers are added together to form whole numbers. both a fraction and neither a decimal. Integer 0 through 11: 2, 3, 5, 6, 7, 8, 9, & 10. 0 is a counting number or the opposite.
To determine the number of bacteria inside the culture at t hours, use the formula Pt = Po 2(t/d), in which Po is simply the initial population and d is the doubling time.
The values of Po are 870, d, and t are respectively 3 and 7. When we use the formula with these numbers, we get:
[tex]Pt = 870 * 2^{(7/3)}[/tex]
Pt ≈ 3480.5
Hence, the number of bacteria still present in the culture after 7 hours is approximately 3481.
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Which of the following is equivalent to the radical expression below when
x>0?
√2x √x +3.
OA. √x² + 6x
OB. √2x2 + 3x
OC. √2x² + x
D. √2x² + 6x
Answer:
the answer is (C) √(2x² + x). None of the answer options match this expression, but we can simplify it to show that it is equivalent. option (C) √(2x² + x) is equivalent to the original expression √(2x) * √(x+3) when x > 0.
Step-by-step explanation:
To simplify the expression √(2x) * √(x+3), we can use the property of radicals that says:
√(a) * √(b) = √(a * b)
So, we have:
√(2x) * √(x+3) = √(2x * (x+3))
Multiplying out the terms inside the radical, we get:
√(2x * (x+3)) = √(2x² + 6x)
Therefore, the expression √(2x) * √(x+3) is equivalent to the radical expression √(2x² + 6x) when x > 0.
So, the answer is (C) √(2x² + x). None of the answer options match this expression, but we can simplify it to show that it is equivalent:
√(2x² + 6x) = √(2x² + x + 5x) = √(x * (2x + 5)) = √x * √(2x + 5)
The local cherry-picking farm charged Cameron $5.25 for 2 3/5 pounds of cherries. At that rate, how much would Cameron pay for 5.5 pounds of cherries?
Cameron would pay $11 for 5.5 pounds of cherries at the same rate.
What is simple interest?The interest on a loan or principal sum can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more.
We can start by finding the cost of cherries per pound:
2 3/5 pounds = (2 × 5 + 3) / 5 = 13/5 pounds
Cost of 13/5 pounds of cherries = $5.25
Cost of 1 pound of cherries = $5.25 ÷ (13/5) = $2
Now we can find the cost of 5.5 pounds of cherries:
Cost of 5.5 pounds of cherries = $2 × 5.5 = $11
Therefore, Cameron would pay $11 for 5.5 pounds of cherries at the same rate.
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An urn contains 6 red marbles, 5 white marbles, and 8 blue marbles marbles. A child randomly selects three (without replacement) from the urn. Round to four decimal places.
Find the probability that none of the three marbles are white.
Using the prοbability cοncept, it is fοund that there is a 0.0887 = 8.87% prοbability all three marbles are the same cοlοr.
What is prοbability?A prοbability is the number οf desired οutcοmes divided by the number οf tοtal οutcοmes.
The οrder in which the marbles are chοsen is nοt impοrtant, and they are alsο chοsen withοut replacement, which means that the cοmbinatiοn fοrmula is used tο find the number οf οutcοmes.
Tο find the prοbability that all three marbles selected are the same cοlοr, we need tο cοnsider three cases: selecting three red marbles, selecting three white marbles, οr selecting three blue marbles.
Let's first calculate the tοtal number οf ways tο select three marbles frοm the urn. This can be dοne using the cοmbinatiοn fοrmula:
C(19, 3) = 19! / (3! * 16!) = 969
Sο there are 969 pοssible ways tο select three marbles frοm the urn.
Nοw let's calculate the number οf ways tο select three marbles οf the same cοlοr:
Three red marbles: there are C(6, 3) = 20 ways tο select three red marbles frοm the urn.Three white marbles: there are C(5, 3) = 10 ways tο select three white marbles frοm the urn.Three blue marbles: there are C(8, 3) = 56 ways tο select three blue marbles frοm the urn.Sο the tοtal number οf ways tο select three marbles οf the same cοlοr is:
20 + 10 + 56 = 86
Therefοre, the prοbability οf selecting three marbles οf the same cοlοr is:
86 / 969 = 0.0887 (rοunded tο fοur decimal places)
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Help!!!!
Find CB
Find AC
Step-by-step explanation:
For RIGHT triangles such as this one:
sin (60) = opposite LEG/ hypotenuse = sqrt(3) / 2 / CB solve for CB
tan (60°) = opposite LEG / adjacent LEG = sqrt(3)/2 / AC solve for AC
Giving a test to a group of students, the grades are summarized below.
If one student is chosen at random, find the probability that the student was NOT a female that got a “A”.
Having trouble with finding the answer to this question.
The probability that the student was NOT a female that got a “A” is given as follows:
p = 10/19.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The outcomes for this problem are given as follows:
Total outcomes: 38 students that got an A.Desired outcomes: 20 students who got an A and are not females.Hence the probability that the student was NOT a female that got a “A” is obtained as follows:
p = 20/38
p = 10/19.
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the space shuttle discovery traveled 148.2 million miles during its mission. The space shuttle Atlantis traveled 125.9 million miles. How many more miles did the space shuttle Discovery travel than the space shuttle Atlantis?
The Space Shuttle Discovery traveled 22.3 million miles more distance than the Space Shuttle Atlantis.
What is distance ?
To find how many more miles the Space Shuttle Discovery traveled than the Space Shuttle Atlantis, we can subtract the distance traveled by Atlantis from the distance traveled by Discovery:
148.2 million miles - 125.9 million miles = 22.3 million miles
Therefore, the Space Shuttle Discovery traveled 22.3 million miles more than the Space Shuttle Atlantis.
What is Space Shuttle ?
The Space Shuttle was a reusable spacecraft designed and operated by NASA (the National Aeronautics and Space Administration) to carry astronauts and cargo into space. It was in service from 1981 until 2011, when the final mission was completed.
The Space Shuttle consisted of several components, including the orbiter, which was the main spacecraft, and the two solid rocket boosters and external fuel tank that provided the initial propulsion during liftoff. The orbiter was designed to carry up to seven crew members and could be used to deploy satellites, conduct scientific experiments, and perform other tasks in space.
The Space Shuttle was unique in that it could land like an airplane, allowing it to be reused multiple times. After completing a mission, the orbiter would re-enter Earth's atmosphere and glide to a landing on a runway.
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Complete question is: The space shuttle discovery traveled 148.2 million miles during its mission. The space shuttle Atlantis traveled 125.9 million miles. the Space Shuttle Discovery traveled 22.3 million miles more than the Space Shuttle Atlantis.
the value of a home appreciates about 2.1% annually. how much will a $150,000 home be worth in 15 years?
A very simple explanation:
Solution;
Apperciation: 2.1%
Principal: 150,000
Time: 15 years
Now,
=((0.021×150,000)×15)+150,000
=(3,150×15)+150,000
=47250+150,000
=197,250$
Hence, the house would worth 197,250$ after 15 years
Please Help!!! I will mark brainliest.
Answer:
Answer : 264.12cm²
Step-by-step explanation:
Area of a triangle : bh/2
47-18.6 = 28.4
28.4 x 18.6 = 528.24
528.24/2 = 264.12
Pls Mark Brainliest
Answer:
874.2 cm²
Step-by-step explanation:
The given shape is a parallelogram.
Here,
Base ( b ) = 47 cm
Height ( h ) = 18.6 cm
Formula : -
Area of parallelogram = bh
Area of parallelogram
= bh
= 47 x 18.6
= 874.2 cm²
Hence,
Area of the given parallelogram is 874.2 cm².
Harold ran in a 1 mile race. he estimated his average running speed to be 10 miles per hour, but it was actually 9.9 miles per hour.
what is the percent error for his estimate?
if necessary round your answer to the nearest tenth of a percent.
1.0% is the percent error for his estimate .
What is percent error?
When compared to the actual value, the percent error is the difference between the estimated and actual values. The relative error is multiplied by 100 to calculate the % error, in other words. The difference between an estimated number and a precise value is measured in percent error.
the percent error = {exact error - approximate error} * 100%/exact error
= (9.9 - 10) * 100/9.9
= 0.1/9.9 * 100%
≈ 1.0%
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The marketing team suggests that the propose container will sell for a higher price of $3.97 bowl cost and addictional of $.50 each to make how much profit will the new design earns per juice container
Answer:
$3.47
Step-by-step explanation:
They are selling the container for $3.97 and it costs them $0.50 to make each. So that means they'll make a profit of $3.47.
I will make u brainlist
Which of the lists below includes all of the above expressions that are equivalent to 2/5?
A. I, III, V, VI
B. III, VI
C. II, III, VI
D. II, III, IV, VI
The fractions equivalent to 2/5 are 4/10, 6/15, 8/20. The correct option is B.
How to explain the fractionWhen writing equivalent fractions, the numerator and denominator should be multiplied or divided by the same number. This is the reason why when these fractions are simplified, they are reduced to the same value.
Hence, the equivalent fractions for 2/5 are:
(2/5) × (2/2) = (2 × 2) / (5 × 2) = 4/10
(2/5) × (3/3) = (2 × 3) / (5× 3) = 6/15
(2/5) × (4/4) = (2 × 4) / (5 × 4) = 8/20
The fractions equivalent to 2/5 are 4/10, 6/15, 8/20,.
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Which of the lists below includes all of the above expressions that are equivalent to 2/5?
I, 2/6
II, 4/10
III, 6/15
IV. 10/20
V. 4 / 12
VI 8/20
A. I, III, V, VI
B. III, VI
C. II, III, VI
D. II, III, IV, VI
(math) please help me I really appreciate it
Answer:
last 2 are b
and c
Step-by-step explanation:
Polygon KLMN is the image of polygon PQRS after a 180 degree rotation
The angle that is congruent to ∠S after the given rotation transformation is: ∠M
How to Interpret Rotation Transformation?A rotation is defined as a type of transformation whereby the object is rotated about a fixed point. The direction of the rotation can either be clockwise or anticlockwise.
Now, rotating a specific point that has the coordinates as (x, y) by 180° about the origin in either a clockwise or counterclockwise direction, will produce a new point that has the coordinates (−x,−y)
Thus, if Polygon KLMN is the image of polygon PQRS after a 180 degree rotation, then we can say that the new image formed will have ∠M congruent to ∠S
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1. What is one of the solutions to the system of equations graphed here?
O (-5,-4)
O (2,4)
O (0,4)
O (4,0)
One of the solutions for the given graph is (-5,-4).
What is a graph and how to plot the values?
A plot is a visual representation of a data collection, typically in the form of a graph demonstrating the relationship between two or more variables. An individual value plot makes it simple to identify outliers and see distribution variation since it displays a dot for the actual value of each observation within a group.To graph a point, first determine where it lies on the x-axis, then determine where it lies on the y-axis, and lastly plot the intersection of these two axes. Due to its location at the intersection of the x- and y-axes, the origin of the graph, also known as the point (0, 0), is the center of the diagram.In the given graph, a straight line intersects the parabola at two points i.e., (-5, -4) and (2, 0).
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The runtime of a certain brand of batteries is normally distributed with a population means of μ=30 hours and σ=6 hours. what is the probability that 16 randomly selected batteries will have a runtime of less than 27 hours?
The probability that 16 randomly selected batteries will have a runtime of less than 27 hours is 0.0228.
Describe Probability?Probability is a branch of mathematics that deals with the study of random events or outcomes. It involves the analysis of the likelihood or chance of a particular event occurring, given certain conditions or assumptions. Probability is expressed as a number between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain to occur.
Probability theory is used to analyze and understand random phenomena such as games of chance, weather patterns, financial markets, and many other areas of study. The main tools of probability theory include probability distributions, random variables, and statistical inference.
Probability distributions are mathematical functions that describe the probabilities of different outcomes for a particular event or experiment. Random variables are variables that take on different values based on the outcome of a random event, and they are used to calculate probabilities for a range of different scenarios.
We can use the central limit theorem to approximate the distribution of the sample means, where n=16. The sample mean, X', will also be normally distributed with a mean of μ = 30 hours and a standard deviation of σ/√n = 6/√16 = 1.5 hours.
Now, we need to find the probability that the sample mean is less than 27 hours:
P(X' < 27) = P(z < (27-30)/1.5) [converting to standard normal distribution using z-score]
P(X' < 27) = P(z < -2)
Looking up the z-table, we can find that the probability of a standard normal random variable being less than -2 is approximately 0.0228.
Therefore, the probability that 16 randomly selected batteries will have a runtime of less than 27 hours is 0.0228.
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