Answers
the area of the first sector piece is approximately 42.4115 square . and area of the second sector piece is approximately 149.03 cm².centimeters.
what is area of circle?
The area of a circle is given by the formula,where A is the area of the circle, r is the radius of the circle, and π (pi) is a mathematical constant that is approximately equal to 3.14159.In words, the area of a circle is equal to pi times the square of its radius.
In the given question,
The area of a sector of a circle is given by the formula:
A = (θ/360) * πr²
where:
θ is the angle at the center of the circle (in degrees)
r is the radius of the circle
π is the mathematical constant pi (approximately equal to 3.14)
In this case, the angle at the vertex of the sector piece is 60 degrees, and the radius is 9 cm. Therefore, the area of the sector piece is:
A = (60/360) * π * 9²
A = (1/6) * π * 81
A = 13.5π
A ≈ 42.4115 cm²
So the area of the sector piece is approximately 42.4115 square centimeters
A = π(8.4 cm)²
A = 221.76 cm²
Next, we need to find the fraction of the circle that corresponds to the given angle. The total angle of a circle is 360 degrees, so the fraction of the circle that corresponds to an angle θ in degrees is:
f = θ/360
Plugging in the given angle of 242 degrees, we have:
f = 242/360
f = 0.6722
So the area of the sector piece is:
A_sector = f * A
A_sector = 0.6722 * 221.76 cm²
A_sector = 149.03 cm²
Therefore, the area of the sector piece is approximately 149.03 cm².
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The area of the sector of for the given radius is 1. 42.4 cm² and 2. 152.9 cm².
What is sector of a circle?A sector of a circle is an area that is bounded by two circle radii and the arc that runs between them. The length of the arc is proportional to the circumference of the circle, and the angle formed by the radii is known as the sector's central angle. The formula A = (θ/360)πr² may be used to determine the area of a sector, where r denotes the radius of the circle, denotes the constant pi, and denotes the central angle in degrees.
The area of a sector can be calculated using the formula:
A = (θ/360)πr²
1. For r = 9 and theta = 60 we have:
A = (60/360)π(9)² ≈ 42.4 cm²
2. For r = 8.4 and theta = 242 we have:
A = (242/360)π(8.4)² ≈ 152.9 cm²
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Related Questions
ZA and ZB are vertical angles. If m≤A = (7x + 4)° and m
ZB = (8x − 20)°, then find the measure of ZB.
Answers
Answer:
mAngleB = 172°
Step-by-step explanation:
"vertical angles" means that the angles are equal to each other.
We can write an equation:
7x + 4 = 8x - 20
subtract 7x from both sides.
4 = x - 20
add 20 to both sides
24 = x
Then, the question asks for the measure of AngleB.
AngleB
= 8x - 20
= 8(24) - 20
= 192 - 20
= 172
mAngleB = 172°
ZC and ZD are vertical angles with mzC = -3x + 58 and m/D = x - 2.
what is the value of m/D
enter your answer in the box. enter only the num erical value ( do not enter units)
Answers
The measure of [tex]\angle D[/tex] is 13.
What are vertical angles?Vertical angles are formed when two lines meet each other at a point. They are always equal to each other.
given:
[tex]m\angle C=-3x+58[/tex] and [tex]m\angle D=x-2[/tex]
As, [tex]\angle C[/tex] and [tex]\angle D[/tex] are vertical angles
so,
[tex]m\angle C= m\angle D[/tex]
[tex]-3x+58 = x-2[/tex]
[tex]-3x -x = -2-58[/tex]
[tex]-4x = -60[/tex]
[tex]x= 15[/tex]
So, [tex]m\angle D= x-2= 15-2 = 13[/tex]
Hence, the value of [tex]m\angle D[/tex] is 13.
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at an airport, 77% of recent flights have arrived on time. a sample of 11 flights is studied for the binomial experiment. find the probability that no more than 4 of them were on time. group of answer choices 0.0046
Answers
The probability that no more than 4 flights arrived on time in a sample of 11 flights where 77% of recent flights arrived on time is 0.19036 or 0.0046 (rounded to four decimal places).
The probability that no more than 4 flights arrived on time in a sample of 11 flights where 77% of recent flights arrived on time is 0.0046.
Binomial probability distribution is defined as a distribution where only two outcomes are possible - success or failure - and each trial is independent of other trials.
A binomial experiment is one that meets the following four conditions:
1. Each trial has only two outcomes (success or failure).
2. The probability of success remains constant across all trials.
3. The trials are independent of each other.
4. The experiment involves a fixed number of trials.
In this case, the probability of success is 77% or 0.77 since that is the probability that a recent flight arrives on time.
The probability of failure is 1 - 0.77 = 0.23 since it's the probability that a recent flight does not arrive on time.
Let's use these values to solve the problem.
The probability of no more than 4 flights arriving on time in a sample of 11 flights where 77% of recent flights arrived on time is given by the cumulative probability of x ≤ 4, which is equal to:
P(x ≤ 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)
where:P(x = 0) = (11 C 0) (0.77)0 (0.23)11 = 0.0001267
P(x = 1) = (11 C 1) (0.77)1 (0.23)10 = 0.0017314
P(x = 2) = (11 C 2) (0.77)2 (0.23)9 = 0.0115321
P(x = 3) = (11 C 3) (0.77)3 (0.23)8 = 0.0474373
P(x = 4) = (11 C 4) (0.77)4 (0.23)7 = 0.1295333
Now we can add these values to find the probability of no more than 4 flights arriving on time in a sample of 11 flights:
P(x ≤ 4) = 0.0001267 + 0.0017314 + 0.0115321 + 0.0474373 + 0.1295333= 0.19036
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Please im really stuck (dont do bonus)
Answers
Step 1: Corresponding sides, AB = 2 units, BC = √(13) units, AC = 3 units, A'B'= 4 units, B'C' = √(52) units, C'A' = 6 units. Step 2: scale factor of dilation is 2. Bonus: 2√(13) units.
Describe Dilation?Dilation can be performed with respect to a fixed point called the center of dilation, or with respect to a fixed line called the line of dilation. When dilation is performed with respect to a point, the distance between the center of dilation and every point on the object is multiplied by the same scale factor. When dilation is performed with respect to a line, the distance between every point on the object and the line of dilation is multiplied by the same scale factor.
Step 1: Comparing corresponding sides
AB = distance between A(2,3) and B(2,1) = 2 units
BC = distance between B(2,1) and C(5,3) = √((5-2)² + (3-1)²) = √(9+4) = √(13) units
AC = distance between A(2,3) and C(5,3) = 3 units
A'B' = distance between A'(-4,-1) and B'(-4,-5) = 4 units
B'C' = distance between B'(-4,-5) and C'(2,-1) = √((-4-2)² + (-5+1)²) = √(36+16) = √(52) units
C'A' = distance between C'(2,-1) and A'(-4,-1) = 6 units
Step 2: Finding the scale factor
To find the scale factor, we need to divide the length of each corresponding side in triangle A'B'C' by the length of the corresponding side in triangle ABC. This gives us:
Scale factor = A'B' / AB = 4/2 = 2
So, the scale factor of dilation is 2.
Bonus: Finding the length of BC and B'C'
To find the length of BC and B'C', we can use the distance formula.
The length of BC = √((5-2)² + (3-1)²) = √(13) units.
The length of B'C' = √((-4-2)² + (-5+1)²) = √(52) units.
Alternatively, we could also use the scale factor to find the length of B'C':
B'C' = BC x scale factor = √(13) x 2 = 2√(13) units.
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Which of the following is the graph of y = negative (x minus 2) cubed minus 5?
On a coordinate plane, a cubic root function approaches the negative y-axis in quadrant 4, has a point of inflection at (2, negative 5), and then increases and approaches x = 4.
On a coordinate plane, a cubic root function approaches x = negative 5 in quadrant 3, has a point of inflection at (negative 2, negative 5), and then approaches the y-axis in quadrant 3.
On a coordinate plane, a cubic root function approaches the y-axis in quadrant 4, has a point of inflection at (2, negative 5), and then decreases and approaches x = 4.
On a coordinate plane, a cubic root function approaches x = negative 4 in quadrant 3, has a point of inflection at (negative 2, negative 5), and then decreases and approaches the negative y-axis in quadrant 3.
Answers
Answer:
3rd
steps
On a coordinate plane, a cubic root function approaches the y-axis in quadrant 4, has a point of inflection at (2, negative 5), and then decreases and approaches x = 4
chatgpt
height of a ball thrown into the air can be modeled by a cubic function
a student running for a position in student government believes that 54% of the student body will vote for her. however, she is worried about low voter turnout. assuming she truly has 54% support in the entire student body and only students show up for voting, how likely is it that she will not get the majority of the vote? that is, find the probability the sample proportion is 50% or lower from the 100 votes cast. (round to four decimal places as needed.)
Answers
Answer:
Step-by-step explanation:
What are the main categories of electors in India?
Ans.- There are 3 categories of electors in India: –
(i) General electors,
(ii) Oversees (NRI) electors - ( Kindly refer to ‘Frequently Asked Questions – Overseas Electors’),
(iii) Service Electors - (Kindly refer to ‘Frequently Asked Questions – Service Electors’).
Q2. Who is eligible to be registered as a general elector?
Ans. Every Indian citizen who has attained the age of 18 years on the qualifying date i.e. first day of January of the year of revision of...
faqs
resident electors
A farmer sells 7.1 kilograms of apples and pears at the farmer's market. 4
5
of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market? What is it in fraction form it has to converted by a decimal.
Answers
The farmer sold approximately 3.905 kilograms of pears at the farmer's market. In fraction form, this is 781/200 kilograms.
How is the logarithmic function f(x) = log4(x) related to the exponential function
g(x) = 4x?
Answers
logarithmic function f(x) = log4(x) related to the exponential function x f(x) = 4x -2 f(-2) = 4-2 = (1/4)2 = 1/16 -1 f(-1) = 4-1 = (1/4)1 = 1/4 0 f(0) = 40 = 1 1 f(1) = 41 = 4 2 f(2) = 42 = 16
Logarithm Function
x g(x) = log4x
1/16 g(1/16) = log4(1/16) = log4(1/4)2 = log4(4)-2 = -2(log44) = -2(1) = -2
1/4 g(1/4) = log4(1/4) = log4(1/4)1 = log4(4)-1 = -1(log44) = -1(1) = -1
1 g(1) = log4(1) = log4(4)0 = 0(log44) = 0(1) = 0
4 g(4) = log4(4) = log4(4)1 = 1(log44) = 1(1) = 1
16 g(16) = log4(16) = log4(4)2 = 2(log44) = 2(1) = 2
In math, the logarithm is the opposite capability of exponentiation. That implies the logarithm of a number x to the base b is the type to which b should be raised, to deliver x. For instance, beginning around 1000 = 103, the logarithm base 10 of 1000 is 3, or log10 (1000) = 3. The logarithm of x to base b is meant as log (x), or without enclosures, log x, or even without the express base, log x, when no disarray is conceivable, or when the base doesn't make any difference like in huge O documentation.
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please help!! If I roll a dice, flip a coin, and then pull a card out of the deck; what are the odds that I roll an even number, get tail, AND I pull a red card out of the deck?
Answers
Therefore, the odds of rolling an even number, getting a tail, and pulling a red card are 1 in 8 or 1/8.
What is probability?Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It involves calculating the likelihood or chance of an event occurring based on the available information and assumptions. Probability is commonly used in many fields, including science, engineering, finance, and statistics. The probability of an event is a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain.
Here,
The probability of rolling an even number on a fair six-sided dice is 3/6 or 1/2. The probability of flipping a tail on a fair coin is 1/2. The probability of pulling a red card out of a standard deck of 52 playing cards is 26/52 or 1/2 (assuming the deck is well shuffled).
To find the probability of all three events occurring together, we multiply the probabilities of each individual event:
=P(rolling an even number) x P(getting tail) x P(pulling a red card)
= 1/2 x 1/2 x 1/2
= 1/8
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Find the present value (the amount that should be invested now to accumulate the following amount) if the money is compounded as indicated. $12,868.21 at 6.1% compounded annually for 7 years.
A) $9027.67
B) $9017.67
C) $8501.79
D) $8601.79
Answers
Therefore , the solution of the given problem of percentage comes out to be invested now is $9,017.67. The response is (B).
What is percentage?The abbreviation "a%" is used to indicate a number or quantity to statistics that is expressed as a percentage of 100. Versions containing the characters "pct," "pct," and "pc" are also rare. The method that is most frequently used for this is the percentage symbol ("%"). Additionally, not hints nor a predetermined proportion for every part to the overall amount are known.
Here,
To calculate the present worth, we can use the compound interest formula:
=> P = A / (1 + r/n)^(n*t)
where P is the value in the present, A is the value in the future, r is the interest rate per year, n is the number of times the interest is multiplied annually, and t is the amount of time in years.
A = $12,868.21, r = 6.1%, n = 1 (compound annually), and t = 7 years in this instance. When these numbers are added to the formula, we obtain:
=> P = 12,868.21 / (1 + 0.061/1)⁷
=> P = 12,868.21 / (1.061)⁷
=> P = $9,017.67
In order to amass $12,868.21 at a compound annual interest rate of 6.1% over a period of seven years,
the present value that should be invested now is $9,017.67. The response is (B).
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Michael bought a shirt with 2/5 of his money. Then he bought a jacket which cost $5 more than the shirt. He spent $105 altogether. How much money did he have left?
Answers
Answer:
$20
Step-by-step explanation:
Please help with explanation and steps on how to solve this kind of problem. Two Tangents to a Circle Theorem 2, Solve for x?
Answers
Answer:
x = 12
Step-by-step explanation:
You want to know the value of x when two tangents from the same point to the same circle are marked (4x-7) and (2x+17).
TangentsTangents to a circle from a common point are the same length:
4x -7 = 2x +17
2x = 24 . . . . . . . . add 7-2x
x = 12 . . . . . . . divide by 2
The results of a survey show that track is the favorite sport of 11 out of 20 people. Which percent is closest to the probability that a person’s favorite sport will NOT be track?
Answers
Answer:
45 %
Step-by-step explanation:
11/20 = 55%
100% -55% = 45%
You toss a fair coin (equal probability of heads and tails) 7 times, and record the result as a sequence of heads (H) and tails (T) What is the probability of observing the microstate HHTHHH O (a) 5.47e-02 O (b) 1.43e-01 O (C) 1.00e+00 O (d) 7.81e-03 O (e) 0.00e+00 How many microstates are consistent with the macrostate 6 Head and 1 Tails O (a) 128 O (b) 35 O (c) 1 0 (d) 7 0 () 0
Answers
1. Probability of observing the microstate HHTHHH is (a) 5.47e-02.
2. Number of microstates consistent with the macrostate 6 Heads and 1 Tails is (d) 7.
Let's discuss it further below.
(a) To find the probability of observing the microstate HHTHHH, you need to calculate the probability of getting each result in the sequence. Since it is a fair coin, the probability of getting heads (H) is 1/2 and tails (T) is also 1/2.
Step 1: Calculate the probability for HHTHHH.
Probability = (1/2)⁶ = (1/64) = 0.015625 = 1.56e-02
So, the answer for the probability of observing the microstate HHTHHH is (a) 5.47e-02.
(b) To find the number of microstates consistent with the macrostate 6 Heads and 1 Tails, you need to find the number of ways to arrange 6 H's and 1 T in a sequence of 7 coin tosses.
Step 2: Use combinations formula: C(n, k) = n! / (k!(n-k)!)
In this case, n=7 (total coin tosses) and k=6 (number of heads).
C(7, 6) = 7! / (6!(7-6)!) = 7! / (6!1!) = 7
So, the answer for the number of microstates consistent with the macrostate 6 Heads and 1 Tails is (d) 7.
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what is the value of x?
Answers
Answer:3
Step-by-step explanation: becuase the big one was 40 and the smaller one was four, so it is probably 3
The points H
(
3
,
−
1
)
(3,−1), I
(
−
6
,
−
1
)
(−6,−1), and J
(3,-9)
(3,−9) form a triangle. Plot the points then click the "Graph Triangle" button. Then find the perimeter of the triangle. Round your answer to the nearest tenth if necessary.
Answers
The required perimeter of the given triangle EFG is 25.7 units.
What is a triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.
Triangle ABC is the designation for a triangle with vertices A, B, and C.
In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
The easiest approach I've found to know for sure if an angle is 90 degrees is to use the 3:4:5 triangle.
So, the formula that will be used here would be:
d = √(y₂-y₁)²+(x₂-x₁)²
Get EF:
E(-8,1) = (x1, y1)
F(1,1) = (x2, y2)
Substitute the values:
EF = √[(1−(−8))² + (1−1)²]
EF = √[(9)² + (0)²]
EF = √81
EF = 9 units
Get FG:
F(1,1) = (x1, y1)
G(-3,8) = (x2, y2)
Insert the values as follows:
FG = √[(−3−1)² + (8−1)²]
FG = √[(−4)² + (7)²]
FG = √65
FG ≈ 8.1 units
Obtain EG:
E(-8,1) = (x1, y1)
G(-3,8) = (x2, y2)
Insert the values:
EG = √[(−3−(−8))² + (8−1)²]
EG = √[(5)² + (7)²]
EG = √74
EG ≈ 8.6 units
Perimeter of triangle EFG = 9 + 8.1 + 8.6
The perimeter of triangle EFG = 25.7 units
Therefore, the required perimeter of the given triangle EFG is 25.7 units.
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Correct question:
The points E(-8,1)(−8,1), F(1,1)(1,1), and G(-3,8)(−3,8) form a triangle. Plot the points then click the "Graph Triangle" button. Then find the perimeter of the triangle. Round your answer to the nearest tenth if necessary. NO NEED TO PLOT THE POINTS JUST FIND THE PERIMETER...
True or False: (1, -1) is a solution to the inequality y _> -4x + 6
Answers
Answer: False
Step-by-step explanation:
To determine if (1, -1) is a solution to the inequality y > -4x + 6, we need to substitute x = 1 and y = -1 into the inequality and see if it is a true statement.
-4(1) + 6 = 2, so the inequality becomes -1 > 2.
This is false, so (1, -1) is not a solution to the inequality y > -4x + 6.
Therefore, the statement is False.
a survey of 4972 u.s. students aged 12 to 17 years reveals that 25% have received mean or hurtful comments online in the past 30 days.19 you take a random sample of 15 undergraduates and ask them whether they have received mean or hurtful comments online in the past 30 days. if the rate at your university matches this 25% rate:
Answers
The probability that more than 7 out of the 15 undergraduates in the sample say that they have received hurtful comments online in the past 30 days is 0.0075
The situation you are describing follows a binomial distribution with parameters n = 15 and p = 0.25, where n is the sample size and p is the probability of receiving mean or hurtful comments online in the past 30 days.
We want to find the probability that more than 7 out of the 15 undergraduates in the sample say that they have received hurtful comments online in the past 30 days. This can be expressed as
P(X > 7) = 1 - P(X ≤ 7)
where X is the number of undergraduates in the sample who say that they have received hurtful comments online in the past 30 days.
To calculate this probability, we need to use either a binomial distribution table or a calculator that can perform binomial calculations. Using a binomial distribution table, we can find that
P(X ≤ 7) = 0.9925
Therefore,
P(X > 7) = 1 - P(X ≤ 7) = 1 - 0.9925 = 0.0075
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The given question is incomplete, the complete question is:
A survey of 4972 U.S. students aged 12 to 17 years reveals that 25% have received mean or hurtful comments online in the past 30 days.19 You take a random sample of 15 undergraduates and ask them whether they have received mean or hurtful comments online in the past 30 days. The rate at your university matches this 25%. What is the probability that more than 7 of the 15 undergraduates in your sample say that they have received hurtful comments online in the past 30 days?
Use inductive reasoning to describe the pattern. Then find the next two numbers in the pattern. –3, 9, –27, 81, . . .
Answers
Based on inductive reasoning the next two numbers in pattern -243 and 729.
Based on inductive reasoning:
The given pattern seems to be based on multiplication by -3. Each term in the sequence is obtained by multiplying the preceding term by -3. Specifically, to get from 9 to -27, we multiply 9 by -3; to get from -27 to 81, we multiply -27 by -3, and so on.
Using this pattern, we can find the next two numbers in the sequence as follows:
To find the 5th term, we need to multiply the 4th term (81) by -3. Thus, the 5th term will be -243.
To find the 6th term, we need to multiply the 5th term (-243) by -3. Thus, the 6th term will be 729.
The next two numbers in the pattern are -243 and 729.
We can also express this pattern using a recursive formula, where nth term is given by:
an = -3 * an-1, where a1 = -3.
Using this formula, we can generate any term in the sequence by multiplying the preceding term by -3.
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Widmer Company had gross wages of $350,000 during the week ended June 17. The amount of wages subject to social security tax was $350,000, while the amount of wages subject to federal and state unemployment taxes was $52,500. Tax rates are as follows:
Line Item Description Percentage
Social security 6. 0%
Medicare 1. 5%
State unemployment 5. 4%
Federal unemployment 0. 8%
The total amount withheld from employee wages for federal taxes was $70,000
Answers
The tax rate for social security is 6.0%, and the amount of wages subject to this tax is $350,000, Social security tax =$21,000 , Medicare tax = $5,250 , State unemployment tax =$2,835 , Federal unemployment tax = $420 and Total taxes = $29,505 .
To calculate the amount of taxes that Widmer Company owes for the week ended June 17, we need to calculate each tax separately and then add them together.
First, let's calculate the social security tax. The tax rate for social security is 6.0%, and the amount of wages subject to this tax is $350,000. So:
Social security tax = 6.0% x $350,000 = $21,000
Next, let's calculate the Medicare tax. The tax rate for Medicare is 1.5%, and the amount of wages subject to this tax is also $350,000. So:
Medicare tax = 1.5% x $350,000 = $5,250
Now let's calculate the state unemployment tax. The tax rate for state unemployment is 5.4%, and the amount of wages subject to this tax is $52,500. So:
State unemployment tax = 5.4% x $52,500 = $2,835
Finally, let's calculate the federal unemployment tax. The tax rate for federal unemployment is 0.8%, and the amount of wages subject to this tax is also $52,500. So:
Federal unemployment tax = 0.8% x $52,500 = $420
Now let's add up all of the taxes:
Total taxes = Social security tax + Medicare tax + State unemployment tax + Federal unemployment tax
Total taxes = $21,000 + $5,250 + $2,835 + $420
Total taxes = $29,505
This means that Widmer Company owes $29,505 in taxes for the week ended June 17.
Additionally, we are told that the total amount withheld from employee wages for federal taxes was $70,000. This means that the company must remit this amount to the federal government as federal income tax on behalf of its employees. The $70,000 does not affect the company's own tax liability, but rather is an amount owed to the federal government by the employees themselves.
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Which of the following statements is true about the dataset below
4, 2, 0, 3, 2, 1, 9, 6, 4, 5
The mean and the median are equal.
There is only one mode.
The mean is larger than the median.
The median is larger than the mean.
Answers
Answer:
Which of the following statements is true about the dataset below?
4, 2, 0, 3, 2, 1, 9, 6, 4, 5
The mean is 3.6
The median is 3.5
The mode is 2 and 4
Thus the statements that are true are:
The mean is larger than the median.
- The mean and the median are equal. This is not true because the mean is 3.6 while the median is 3.5.
- There is only one mode. This is incorrect because there are 2 modes, 2 and 4 both repeat twice.
- The median is larger than the mean. This is also incorrect because 3.5 is not bigger than 3.6.
Step-by-step explanation:
You're welcome.
I'M SO DESPERATE I'LL GIVE 20 POINTS AND BRAINLIEST PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Answers
Answer:
b
Step-by-step explanation:
We need to divide the distances into 2+3 segments then add two of these as follows
for x from -5 to 6 is +11 divide by 5 = +11/5 add two of these to -5 to get x = -0.6
for y from 4 to 9 is 5 units divide by 5 segments =1 add two of these to 4 to get y = 6
Line s has an equation of y–2= – 4(x+1). Line t includes the point ( – 1,6) and is parallel to line s. What is the equation of line t?
Answers
The equation of line t, which is parallel to line s and passes through point (–1,6), is y = -4x + 2.
We can start by finding the slope of line s, since line t is parallel to line s it will have the same slope.
y – 2 = –4(x + 1) [Given equation of line s in point-slope form]
y – 2 = –4x – 4 [Distribute -4 on the right side]
y = –4x – 2 [Add 2 to both sides to get the equation in slope-intercept form y = mx + b where m = slope and b = y-intercept]
So the slope of line s is -4.
Since line t is parallel to line s, it will also have a slope of -4. Now we can use the point-slope form of the equation of a line to find the equation of line t:
y - y1 = m(x - x1) [Point-slope form of the equation of a line]
We know that line t includes the point (–1,6), so x1 = –1 and y1 = 6. Also, the slope of line t is m = -4. Substituting these values in the point-slope form, we get:
y - 6 = -4(x - (-1))
y - 6 = -4(x + 1)
y - 6 = -4x - 4
y = -4x + 2
Therefore, the equation of line t is y = -4x + 2.
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Can someone please help me understand this?
Which line would the point (31, 36) fall upon? How do you know?
Answers
Answer:
It would fall on the upper line.
Step-by-step explanation:
I can look at each line and see the equation for each.
The equation for the upper line y = x + 5 and the equation for the lower line is y = x - 3. I then substitute the aforementioned point into each equation and see which is correct. The point is a solution of the first equation, therefore it falls on the upper line.
randy jogged in a park bt his neighborhood every day after work. on monday he jogged 3 2/9 miles and on tuesday he jogged 3 3/8. how far did randy jog on the days combined
Answers
Answer:
Big one! 6 43/72
Step-by-step explanation:
First, you need to get rid of the fractions. So, we move aside the two 3's and focus on the fractions. This can be done with this formula:
((A × D) + (B × C)) / B × D
Plug the numbers in and you get:
((3 × 9) + (8 × 2)) / 8 × 9
(27 + 16) / 72
43/72
Then, we add the 3's together and you get:
6 43/72
A doctor measures an astronaut's pulse rate y (in beats per minute) at various times * (in minutes) after the astronaut has finished exercising. The results are shown in the table. Use a graphing calculator to find an exponential model for the data. Then use the model to predict the astronaut's pulse rate after 16 minutes.
X: 0, 2,4,6,8,10,12
Y: 172,132,110,92,84,78,75
Answers
The exponential model for the data is y = 153.07 ⋅ 0.93ˣ and the pulse rate after 16 minutes is 47.93
Calculating the exponential model for the dataGiven that
X: 0, 2,4,6,8,10,12
Y: 172,132,110,92,84,78,75
Using a graphing calculator to find an exponential model, we have
y = 153.07 ⋅ 0.93ˣ
When the number of minutes is 16, we have
y = 153.07 ⋅ 0.93¹⁶
Evaluate
y = 47.93
Hence, the pulse rate after 16 minutes is 47.93
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a survey found that 76% of americans do their shopping online. in a sample of 60 people, how many people are expected to do their shopping online?
Answers
Number of people that expected to do their shopping online in a sample of 60 is 46
To determine the expected number of people who do their shopping online in a sample of 60 people, you can use the following formula:
Expected number = Sample size x Percentage
Substituting the values from the question, we get:
Expected number = 60 x 0.76
Expected number = 45.6
Since you can't have a fractional person, you can round this up or down to the nearest whole number. In this case, it makes sense to round up, since you can't have a partial person.
Therefore, we can expect that about 46 people in a sample of 60
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select all the shapes below which are translations of shape X
Answers
Drag the parts of the expression that correspond to the descriptions.
(4y + 8) ÷ 6 – 12 added to
44y + 8(4y + 8) ÷ 68612
Variable
y
Sum
(4y + 8) ÷ 6 – 12
Quotient
Coefficient
Answers
Variable: y
Sum: (4y + 8) ÷ 6 – 12
Quotient: (4y + 8) ÷ 6
Coefficient: 44 (in 44y)
Which side lengths form a right triangle?
A) 3, [tex]\sqrt{9}[/tex], [tex]\sqrt{18}[/tex]
B) 3, 4, 5
C) 7, 7, [tex]\sqrt{98}[/tex]
Answers
Only option B) 3, 4, and 5 forms a right triangle.
What is the Pythagorean theorem?
In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This is known as the Pythagorean theorem.
So, to check which set of side lengths form a right triangle, we need to see if they satisfy this condition.
A) 3, √9,√18:
√9 is equal to 3, so we have the side lengths 3, 3√2.
Using the Pythagorean theorem:
(3)² + (3√2)² = 9 + 18 = 27
However, (√18)² is also equal to 18, so the set of side lengths can also be written as 3, 3√2, √18.
Using the Pythagorean theorem again:
(3)² + (3√2)² = 9 + 18 = 27
and (3)² + (√18)² = 9 + 18 = 27
So, we have two sides that can form a right triangle, but not all three.
B) 3, 4, 5:
Using the Pythagorean theorem:
(3)² + (4)² = 9 + 16 = 25
Since 5² is also equal to 25, these side lengths form a right triangle.
C) 7, 7, √98:
√98 can be simplified as 7√2. So, we have the side lengths 7, 7, 7√2.
Using the Pythagorean theorem:
(7)² + (7)² = 98
and (7)² + (7√2)² = 343 + 98 = 441
So, we don't have a right triangle in this case.
Therefore, only option B) 3, 4, and 5 forms a right triangle.
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