Answer: [tex]\frac{2}{35}[/tex] hour
Step-by-step explanation:
We will divide the time it takes it to do 7 tasks (⅖ hour) by the number of tasks it does in that time frame (7 tasks) to find the time per task.
[tex]\frac{2}{5}[/tex] hour / 7 tasks = [tex]\frac{2}{5} *\frac{1}{7}[/tex] = [tex]\frac{2}{35}[/tex] hour or about 3.43 minutes
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In the diagram below line MN is parallel to line JK. If KN=12, MN=25, and JK=40 find the length of line LN
The length of line LN is 25.
What is Similarity of Triangles?
Two triangles are similar if they have the same shape but possibly different sizes. This means that their corresponding angles are congruent and their corresponding sides are proportional.
Since line MN is parallel to line JK, we can use the property that corresponding angles are congruent to set up the following proportion:
LN/KJ = NM/JK
Substituting the given values, we have:
LN/40 = 25/40
Multiplying both sides by 40, we get:
LN = 25
Therefore, the length of line LN is 25.
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A dog's body temperature (t), in degrees Fahrenheit (°F), is considered normal when the value of the expression below is no more than 0.75.
|t - 101.75|
A dog's body temperature is 101.2°F. Based on the expression, which statement about the dog's body temperature is true?
A. Since normal body temperature is from 100.25°F to 103.25°F, the dog's body temperature is considered normal.
B. Since normal body temperature is from 100.25°F to 103.25°F, the dog's body temperature is not considered normal.
C. Since normal body temperature is from 101°F to 102.5°F, the dog's body temperature is considered normal.
D. Since normal body temperature is from 101°F to 102.5°F, the dog's body temperature is not considered normal.
C. The dog's body temperature is regarded normal because the range for a healthy adult is 101°F to 102.5°F.
What exactly is value?
Value is the appraised, monetary, or material worth of a good, service, or asset. Several ideas are associated with the word "value," including shareholder value, company value, fair value, and selling price.
The phrase to assess whether a dog's body temperature is acceptable or not is:
|t - 101.75| ≤ 0.75
When we replace the specified value for the dog's body temperature, we obtain:
|101.2 - 101.75| = |-0.55| = 0.55
The body temperature of the dog is regarded as normal because 0.55 is less than 0.75.
Option C, however, is the one that accurately depicts the dog's core body temperature:
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Answer the next 2 questions
16) Matthew owns a tent company and is canvassing an A-Frame tent for a customer. The tent is eight feet high
and has a rectangular bottom that measures 12 feet wide by 10 feet. The sides of the tent are 10 feet long.
What is the area of the surface that he plans to canvass?
17) when filled to maximum capacity, a silo can hold about 4,000 cubic meters of corn. The radius of the silo is 8 meters. To the nearest meter, what is the approximate height (h) of the silo?
16) The area of the surface area of the canvass is 240 feet²
17) The approximate height of the silo is 24 meters.
What is the rationale for the above response?16) The A-Frame tent has two identical triangles as its sides and a rectangle as its base.
The area of each triangle is
(1/2)bh
= (1/2)10(12)
= 60 square feet.
The area of the rectangle is
lw = 12(10)
= 120 square feet.
Therefore, the total area that he plans to canvass is
2(60) + 120
= 240feet²
17) The volume of the silo is given by
V = (1/3)πr²h, where r is the radius of the base and h is the height. Solving for h,
we get
h = 3V/πr².
Substituting V = 4000 cubic meters and r = 8 meters, we get
h = 3(4000)/(π(8)²)
≈ 24 meters approximately.
Therefore, the approximate height of the silo is 24 meters.
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The population of the United States was 328.2 million people in 2019. The total healthcare costs for the country at that time amounted to $3.6 trillion. Calculate the average amount spent per person on healthcare in 2019. Round the answer in standard form to the nearest cent.
The average amount spent per person on healthcare in 2019 in the United States of America is $1.09×10⁴.
What is average in mathematics?
The average can be defined as the sum of all numbers divided by the total number of values. The mean can be defined as the mean of the values of a sample of data. That is, the average is also called the arithmetic mean.
Solution according to the information given in the question:
Given, Population of USA = 328.2 million = 3282 × 10⁵
Total Healthcare costs = $3.6 trillion = 3.6 × 10¹²
∴ Average amount spent = Total Healthcare costs/Population of USA
= (3.6 × 10¹²)/(3282 × 10⁵)
= (36 × 10¹¹)/ (3282 × 10⁵)
= (36/3282) × (10¹¹/10⁵)
= 0.0109 × 10⁶
= $1.09 × 10⁴
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The average amount spent per person on healthcare in the United States in 2019 was $10,918.98.
What is average in mathematics?
Average in mathematics is a measure of the central or typical value in a set of numbers. It is computed by adding all the values together and dividing the total by the number of values in the set. In statistics, the average is the most commonly used measure of central tendency.
The average amount spent per person on healthcare in the United States in 2019 was $10,918.98. This figure is calculated by taking the total healthcare costs of $3.6 trillion and dividing it by the population of 328.2 million people. This figure represents the amount of money each person in the country spent on healthcare in 2019, ranging from medical services and prescriptions to insurance premiums and other costs. It is important to note that this figure does not take into account any out-of-pocket expenses that individuals may have incurred during the year.
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Identify the FALSE statement about the equation below:
12/20=6/10
This is a proportion because the cross-products both equal 120
This is a proportion because when simplified both fractions are equal.
This is a proportion because the both sides are equal to 0.6 in decimal form.
This is a proportion because the cross-products both equal 200
Similarly, the fact that the cross-products both equal 120 and 200 is further evidence that the equation is a proportion.
What does an equation in math mean?A relationship between two expressions in mathematics is known as an equation, and it is written as an equality on both sides of the equal to sign. An example of an equation is 3y = 16.
The false statement is: "This is a proportion because the both sides are equal to 0.6 in decimal form."
While both sides of the equation do indeed equal 0.6 when simplified, this is not the definition of a proportion.
A proportion is an equation that states that two ratios are equal. In this case, the equation is a proportion because the ratio of 12 to 20 is equal to the ratio of 6 to 10. Specifically,
12/20 = 6/10
3/5 = 3/5
which is true, indicating that the two ratios are indeed equal.
Similarly, the fact that the cross-products both equal 120 and 200 is further evidence that the equation is a proportion.
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write and solve a proportion to find the perimeter of a square when its side length is 12
Therefore, the perimeter of the square when its side length is 12 is 48 units.
What, for example, is a perimeter?The perimeter of an object is the space surrounding it. For instance, the yard around your house is fenced in. The perimeter of the barrier is its length. If the yard is 50 by 50 feet, your fence is 200 feet long.
Since a square has all equal sides, the perimeter of a square is just four times the length of one side. Therefore, the perimeter of the square when its side length is 12 is:
Perimeter = 4 x 12 = 48
To write a proportion to solve for the perimeter of a square when its side length is x, we can set up the following ratio:
12/x = 48/p
where p represents the perimeter of the square. We can cross-multiply to get:
12p = 48x
p = 4x
Now we can substitute 12 for x to find the perimeter when the side length is 12:
p = 4(12) = 48
Therefore, the perimeter of the square when its side length is 12 is 48 units.
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Halla el valor de la cofunción de sec(y−π ). Recuerda que p = 180° y π/2
= 90°
Answer:
La cofunción del seno de un ángulo es igual al coseno de su complemento. Similarmente, la cofunción del coseno de un ángulo es igual al seno de su complemento.
Entonces, para encontrar la cofunción de sec(y-π), primero encontramos el complemento de (y-π), que es (π/2 - (y-π)) = (π/2 - y + π) = (3π/2 - y).
Por lo tanto, la cofunción de sec(y-π) es igual al coseno de su complemento, que es el coseno de (3π/2 - y):
cos(3π/2 - y) = -sin(y)
Entonces, la cofunción de sec(y-π) es igual a -sin(y).
All Il of the following are reasons that you might receive a 1099 statement EXCEPT....
Working as an independent contractor
b. Receiving unemployment benefits
c. Earning interest or dividends
d. Working as a post office clerk
Answer:
File Form 1099-MISC for each person to whom you have paid during the year:
At least $10 in royalties or broker payments in lieu of dividends or tax-exempt interest.
At least $600 in:
Rents.
Prizes and awards.
Other income payments.
Medical and health care payments.
Crop insurance proceeds.
Cash payments for fish (or other aquatic life) you purchase from anyone engaged in the trade or business of catching fish.
Generally, the cash paid from a notional principal contract to an individual, partnership, or estate.
Payments to an attorney.
Any fishing boat proceeds.
Step-by-step explanation:
In addition, use Form 1099-MISC to report that you made direct sales of at least $5,000 of consumer products to a buyer for resale anywhere other than a permanent retail establishment.
In Jack's basement, there's an area that is 6 feet long and 5 1/2 feet wide for the kids to play ping pong. In Mike's basement, there is an area that is 12 feet long and 5 1/2 other games. How many times larger is the area of Mike's basement?
Answer:
2 times larger
Step-by-step explanation:
Mikes basement is 2 time larger then Jacks base meant because jacks basement area is 33 ft and mikes is 66 ft.
33 x 2 = 66
find the sum ( please help i need this done by tmrw!!)
Answer:
I CANT SEE THE OTHER NUMBER OML
Step-by-step explanation:
Valeria ordered a set of beads. She received 25 beads in all. 17 of the beads were green. What percentage of the beads were green?
7/25 = x/100 17•100= 1700÷25=
60 answer is 68%
Can you solve the inequality 2 ( x − 3 ) ≤ 10 2(x−3)≤10 without using the Distributive Property? Explain.
Answer:
X is Greater than or equal to 31/10
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 10 N acts on a certain object, the acceleration of the object is 5 /ms2. If the force is changed to 14 N, what will be the acceleration of the object?
The acceleration of the object when a force of 14 N acts on it will be 7 m/s².
We can use the proportionality relationship between force and acceleration to solve this problem. The relationship can be expressed as:
F = k a
where F is the force, a is the acceleration, and k is a constant of proportionality.
We are given that the force and acceleration are directly proportional, so we can set up a proportion using the given information:
10 N / 5 m/s² = 14 N / a
Solving for a, we can cross-multiply and simplify:
10 N * a = 5 m/s² * 14 N
a = (5 m/s² * 14 N) / 10 N
a = 7 m/s²
Therefore, the acceleration of the object when a force of 14 N acts on it will be 7 m/s².
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At an ice cream shop, the cost of 4 milkshakes and 2 ice cream sundaes is $23.50. The cost of 8 milkshakes and 6 ice cream sundaes is $56.50.
A milkshake costs $3.50 and an ice cream sundae costs $4.75.
What is a system of linear equations?
A system of linear equations is a set of two or more linear equations that contain the same variables. A linear equation is an equation of a straight line and has the form ax + by = c, where a, b, and c are constants and x and y are variables.
The goal of a system of linear equations is to find the values of the variables that satisfy all the equations in the system simultaneously. This can be done by different methods, such as substitution, elimination, or matrix methods.
Systems of linear equations are widely used in mathematics, science, engineering, and economics to model and solve real-world problems involving multiple unknowns. They are a fundamental concept in algebra and linear algebra.
Using this information, we can set up a system of equations to find the cost of a milkshake and the cost of an ice cream sundae. Let's use x to represent the cost of a milkshake and y to represent the cost of an ice cream sundae.
From the first sentence, we can write the equation:
[tex]4x + 2y = 23.5[/tex]
From the second sentence, we can write the equation:
[tex]8x + 6y = 56.5[/tex]
Now we can solve for x and y using any method of solving systems of equations, such as substitution or elimination.
Let's use elimination. Multiplying the first equation by -3 and adding it to the second equation, we get:
[tex]-12x - 6y = -70.5[/tex]
[tex]8x + 6y = 56.5[/tex]
[tex]-4x = -14[/tex]
Dividing both sides by -4, we get:
[tex]x = 3.5[/tex]
Now we can substitute x = 3.5 into one of the original equations to solve for y. Let's use the first equation:
[tex]4x + 2y = 23.5[/tex]
[tex]4(3.5) + 2y = 23.5[/tex]
[tex]14 + 2y = 23.5[/tex]
[tex]2y = 9.5[/tex]
[tex]y = 4.75[/tex]
Therefore, a milkshake costs $3.50 and an ice cream sundae costs $4.75.
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The sum of the first 3 terms of a geometric sequence
is 30 1/2. The sum of the 4th, 5th and 6th term is 3 15/16.
Determine the value of r.
The value of r is approximately 0.62.
The sum of the first 3 terms of a geometric sequence is 30 1/2 and the sum of the 4th, 5th, and 6th term is 3 15/16. To determine the value of r, we can use the formula for the sum of a geometric sequence:
S_n = a_1 (1 - r^n) / (1 - r)
Where S_n is the sum of the first n terms, a_1 is the first term, and r is the common ratio.
For the first 3 terms, we have:
30 1/2 = a_1 (1 - r^3) / (1 - r)
For the 4th, 5th, and 6th terms, we can use the formula for the nth term of a geometric sequence:
a_n = a_1 r^(n-1)
So the 4th term is a_1 r^3, the 5th term is a_1 r^4, and the 6th term is a_1 r^5. The sum of these terms is:
3 15/16 = a_1 r^3 + a_1 r^4 + a_1 r^5
We can factor out a_1 r^3 to get:
3 15/16 = a_1 r^3 (1 + r + r^2)
Now we can substitute the expression for a_1 r^3 from the first equation into the second equation:
3 15/16 = (30 1/2) (1 - r) (1 + r + r^2)
Simplifying and rearranging terms, we get:
r^5 - 8r^4 + 15r^3 - 8r^2 + r = 0
This is a quintic equation, which cannot be solved algebraically. However, we can use numerical methods to find an approximate value of r. Using a graphing calculator, we find that r ≈ 0.62.
Therefore, the value of r is approximately 0.62.
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i need help with this questchin
The triangle in this problem is classified as follows:
Scalene obtude triangle.
How to classify the triangle?According to the largest angle measure, the triangle is classified as follows:
Less than 90º: acute.90º: straight = right.Greater than 90º: obtuse.The largest angle measure in this problem is of 102º > 90º, hence the triangle is an obtuse triangle.
The triangle is also classified as scalene, isosceles or equilateral as follows:
Scalene: 3 different angle measures.Isosceles: 2 equal and 1 different angle measure.Equilateral: 3 equal angle measures.The three angle measures for this problem are different, hence the triangle is scalene.
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Hi! Question is attached ty!
The rate of interest per annum when he invested £6,500 and got £6,838 will be 5.2%.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
The amount after one year is £6838 if he invested £6,500. Then the rate of interest is given as,
£6,838 = £6,500 × (1 + r)¹
1 + r = 1.052
r = 0.052 or 5.2%
The rate of interest per annum when he invested £6,500 and got £6,838 will be 5.2%.
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A rectangular box with a volume of 60x^(6)y^(6)z^(10) width of 2x^(2)y^(3)z^(4) length of 10x^(3)y^(4)z^(5) units and a height, 2x^(2)y^(3)z^(4) units. Write an expression for its height
The expression for the height of the box is 3x^(1)y^(-1)z^(1) units.
The volume of a rectangular box is given by the formula V = lwh, where l is the length, w is the width, and h is the height. We are given the volume, width, and length of the box and we are asked to find the expression for its height.
Volume = 60x^(6)y^(6)z^(10)
Width = 2x^(2)y^(3)z^(4)
Length = 10x^(3)y^(4)z^(5)
Substituting the given values into the formula for volume, we get:
[tex]60x^{(6)}y^{(6)}z^{(10)} = (2x^{(2)}y^{(3)}z^{(4))}(10x^{(3)}y^{(4)}z^{(5))(h)[/tex]
Simplifying the right side of the equation, we get:
60x^(6)y^(6)z^(10) = 20x^(5)y^(7)z^(9)(h)
Dividing both sides of the equation by 20x^(5)y^(7)z^(9), we get:
h = (60x^(6)y^(6)z^(10))/(20x^(5)y^(7)z^(9))
Simplifying the fraction, we get:
h = 3x^(1)y^(-1)z^(1)
Therefore, the expression for the height of the box is 3x^(1)y^(-1)z^(1) units.
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helppppppp
Find the final amount for an investment of $5,000 over 5 years at an annual interest rate of 6% if the interest is compounded quarterly.
The final amount for the investment of $5,000 is $ 6,749.29.
Compound interest:Compound interest is a type of interest calculation in which the interest earned on an initial principal amount is added to the principal, and the new total amount earns interest in subsequent periods.
This means that the interest earned in each period is based on the total amount, which includes both the principal and the accumulated interest from previous periods.
The formula used for compound interest:
[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]Where:
P = Initial investment
r = Rate of interest (as a decimal)
n = Number of compounds
t = Time period in years
Here we have
P = $5,000,
r = 6% = 0.06,
n = 4 (since the interest is compounded quarterly), and
t = 5 years.
Using the above formula
[tex]A = 5000(1 + 0.06/4)^{(4*5)[/tex]
[tex]A = 5000(1.015)^{20[/tex]
[tex]A = 5000(1.34985711)[/tex]
[tex]A =\$6,749.29[/tex]
Therefore,
The final amount for the investment of $5,000 is $ 6,749.29.
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The value of stocks in a certain new startup company is being modeled by the function S(t)S(t), where tt is in years since the company going public in 2015. How would you best interpret the following information about the value of the company's stocks?
S′(5)=0S′(5)=0 and S′′(t)>0S″(t)>0 for 5 ≤ t ≤ 65 ≤ t ≤6.
The best interpretation of the given information about the value of the company's stocks is that the value of the company's stocks has reached a local minimum at t=5 and is increasing at an increasing rate for 5 ≤ t ≤ 6.
The value of stocks in a certain new startup company is being modeled by the function S(t), where t is in years since the company going public in 2015. The given information about the value of the company's stocks is S′(5)=0 and S′′(t)>0 for 5 ≤ t ≤ 6.
The derivative S′(t) represents the rate of change of the value of the company's stocks with respect to time. Therefore, S′(5)=0 means that the rate of change of the value of the company's stocks at t=5 is zero, or in other words, the value of the company's stocks is not changing at t=5. This indicates that the value of the company's stocks has reached a local maximum or minimum at t=5.
The second derivative S′′(t) represents the rate of change of the first derivative S′(t) with respect to time. Therefore, S′′(t)>0 for 5 ≤ t ≤ 6 means that the rate of change of the first derivative S′(t) is positive for 5 ≤ t ≤ 6, or in other words, the first derivative S′(t) is increasing for 5 ≤ t ≤ 6. This indicates that the value of the company's stocks is increasing at an increasing rate for 5 ≤ t ≤ 6.
the best interpretation of the given information about the value of the company's stocks is that the value of the company's stocks has reached a local minimum at t=5 and is increasing at an increasing rate for 5 ≤ t ≤ 6.
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Can someone please help me with these and a tip on how to solve em step by step please
Applying the definition of complementary angles, the measures are:
7. m<DBE = 64°; m<CBE = 26°
8. m<WVZ = 84°; m<XVW = 96°
9. m<RTS = 63°; m<PTQ = 27°
10. m<EFG = 139°
m<IFH = 49°
What are Complementary Angles?Complementary angles are two angles whose sum is equal to 90 degrees. In other words, when two angles are placed side by side, forming a right angle, they are said to be complementary.
7. Angles DBE and CBE are complementary angles, therefore:
17x + 13 + 32 - 2x = 90
15x + 45 = 90
15x = 90 - 45
15x = 45
x = 3
m<DBE = 17x + 13 = 17(3) + 13 = 64°
m<CBE = 32 - 2x = 32 - 2(3) = 26°
8. 5x + 29 = 9x - 15 [vertical angles are equal]
5x - 9x = -29 - 15
-4x = -44
x = 11
m<WVZ = 9x - 15 = 9(11) - 15 = 84°
m<XVW = 180 - 84 = 96° [linear pair]
9. 8x - 17 = 5x + 13 [vertical angles]
8x - 5x = 17 + 13
3x = 30
x = 10
m<RTS = 5x + 13 = 5(10) + 13 = 63°
m<PTQ = 180 - 90 - 63 = 27°
10. (2x + 3) + (6x + 25) = 180 [linear pair]
8x + 28 = 180
8x = 180 - 28
8x = 152
x = 19
m<EFG = 6x + 25 = 6(19) + 25 = 139°
m<IFH = 90 - (2x + 3) = 90 - (2(19) + 3)
m<IFH = 49°
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a Warm-Up Select all the fractions that are equivalent to (2)/(3). (4)/(6)(8)/(15)(12)/(13),(20)/(30)
The fractions that are equivalent to 2/3 are 4/6 and 20/30.
To determine if two fractions are equivalent, you can cross multiply the numerator and denominator of one fraction with the denominator and numerator of the other fraction, respectively. If the products are equal, then the fractions are equivalent.
For example, to determine if 2/3 and 4/6 are equivalent, you would cross multiply as follows:
2 x 6 = 12
3 x 4 = 12
Since the products are equal, 2/3 and 4/6 are equivalent fractions.
Similarly, you can cross multiply 2/3 and 20/30 to determine if they are equivalent:
2 x 30 = 60
3 x 20 = 60
Since the products are equal, 2/3 and 20/30 are equivalent fractions.
Therefore, the fractions that are equivalent to 2/3 are 4/6 and 20/30.
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The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 80.2° is added to the data, how does the range change?
The range stays 47°.
The range decreases to 47°.
The range stays 48°.
The range increases to 50°.
Answer:
The range stays 48°
Step-by-step explanation:
The range is the difference between the highest and lowest values in the data set. Before adding 80.2°, the highest temperature is 105° and the lowest temperature is 57°, so the range is 105° - 57° = 48°.
After adding 80.2°, the highest temperature becomes 105° + 80.2° = 185.2° and the lowest temperature becomes 57° + 80.2° = 137.2°. So the new range is 185.2° - 137.2° = 48°.
Therefore, the range stays the same at 48°. The answer is: The range stays 48°.
Answer:
The range stays 48°
Step-by-step explanation:
Which of the equation choices could represent the circle shown on the graph?
The equation that represents the circle shown in the graph is:[tex](x - 2)^2 + (y + 1)^2 = 9.[/tex]
What is circle ?
A circle is a shape in geometry that is defined as a closed curve that is formed by a set of points that are equidistant from a single fixed point called the center. The distance between any point on the circle and the center is called the radius of the circle.
The center of the circle appears to be at the point (2, -1) and the radius seems to be approximately 3 units.
Using the values of the center and radius, we can plug them into the general equation of a circle to obtain the equation that represents the circle:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Substituting h = 2, k = -1, and r = 3, we get:
[tex](x - 2)^2 + (y + 1)^2 = 9[/tex]
Therefore, the equation that represents the circle shown in the graph is:[tex](x - 2)^2 + (y + 1)^2 = 9.[/tex]
Option D is the equation that represents the circle, which is[tex](x - 2)^2 + (y + 1)^2 = 9.[/tex]
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PLEASE HELP I WILL MARK BRAINLIEST
The measure of arc ED is 78.7°
How to find the measure of an arc?An arc of a circle is a portion of the circumference of a circle. It is defined by two endpoints and the arc itself.
The measure of an arc is given in degrees or radians, and it is determined by the angle that it subtends at the center of the circle.
Since FC is the diameter and arc FB is equivalent to arc BC. We can say:
arc FB + arc BC = 180°
arc FB = arc FB = 90°
Also, arc ED is twice the measure of arc CD. We can write:
arc ED = 2 * arc CD
arc CD = (arc ED)/2
Since the sum arc FB and arc BC is 180°. We can say:
arc FE + arc ED + 0.5(arc ED) = 180°
62° + arc ED + 0.5(arc ED) = 180°
62° + 1.5(arc ED) = 180°
1.5(arc ED) = 180 - 62
1.5(arc ED) = 118
arc ED = 118/3
arc ED =78.7°
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(Algebraic and graphical modelling)
please help
Ben's ball lands approximately 2.5 seconds after Andrew's ball.
How long after Andrew's does Ben's ball land?Since the value of parameter a is -5 for both balls, the height of each ball follows the equation:
h(t) = -5t² + vt + h0
where;
h(t) is the height of the ball at time t, v is the initial velocity of the ball (in meters per second), and h0 is the initial height of the ball (in meters).Let's assume that Andrew's ball is hit with an initial velocity of v1, and Ben's ball is hit with an initial velocity of v₂. We also know that Ben's ball reaches a maximum height 50% greater than Andrew's, which means that:
h_max₂ = 1.5h_max₁
At the maximum height, the velocity of the ball is zero, so we can find the time it takes for each ball to reach the maximum height by setting v = 0 in the equation for h(t):
t_max1 = v₁ / (2 x 5)
t_max2 = v₂ / (2 x 5)
Since Ben's ball reaches a maximum height that is 50% greater than Andrew's, we can write:
h_max2 = 1.5h_max1
-5(t_max2)² + v₂t_max2 + h0 = 1.5(-5(t_max1)² + v1 * t_max1 + h0)
Simplifying this equation, we get:
-5(t_max2)² + v₂t_max2 = -7.5(t_max1)² + 1.5v₁t_max1
We also know that Andrew's ball lands after 4 seconds, which means that h(4) = 0:
h(4) = -5(4)² + v1 * 4 = 0
-80 + 4v1 = 0
v1 = 80/4
v1 = 20 m/s
Solving these equations for t_max2 and v2, we get:
t_max1 = v1 / (2 x 5)
t_max1 = 20 / (2 x 5) = 2 s
t_max2 = 1.5 * t_max1 = 3 s
v2 = 1.5 * v1 = 30 m/s
To find the time it takes for Ben's ball to land, we need to find the time t2 when h(t2) = 0.
We can use the equation for h(t) with v = v2, h0 = 0, and solve for t:
-5t² + v₂t = 0
-5t² + 30 = 0
5t² = 30
t² = 30/5
t² = 6
t = √6
t = 2.5 s
Therefore, Ben's ball lands approximately 2.5 seconds after Andrew's ball.
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The variance of a sample of 169 observations equals 576. The standard deviation of the sample equals:
a. 13
b. 24
c. 576
d. 28,461
The standard deviation of the sample is 24. Therefore the correct option is, option b. 24.
The variance of a sample is the square of the standard deviation. In other words, the standard deviation is the square root of the variance. Therefore, to find the standard deviation of the sample, we need to take the square root of the variance:
√576 = 24
Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.
Like the variance, if the data points are close to the mean, there is a small variation whereas the data points are highly spread out from the mean, then it has a high variance.
So, the standard deviation of the sample of 169 observations and variance 576 equals 24. The correct option is b.
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5) Practice: Organizing Information
Fill in the blanks.
The first step in solving this system of linear equations is to multiply both sides of the bottom equation by 2.
5x + 2y = 14
3x – y = 4
This works because of the__________________________.
The next step is to add the two equations together.
5x+2y=14
+ 6x-2y=8
11x=22
This works because of the__________________________.
Answer: Distributive Property!
Step-by-step explanation:
The answer is the Distributive Property. The Distributive Property states that for any numbers a, b, and c, a(b + c) = ab + ac. In this case, the Distributive Property is being applied to the equations, so 2(3x - y) = 6x - 2y. This allows us to add the two equations together.
there are 3242 candies in a jar. 7 candies are kept in each pack what fraction of candies is left behind
The fraction of candies left behind is 3/7.
To find the fraction of candies left behind, we need to divide the total number of candies by the number of candies in each pack and find the remainder. This remainder will be the numerator of the fraction and the number of candies in each pack will be the denominator.
Step 1: Divide the total number of candies by the number of candies in each pack: 3242 ÷ 7 = 463 with a remainder of 3
Step 2: The remainder, 3, is the numerator of the fraction and the number of candies in each pack, 7, is the denominator. So the fraction of candies left behind is 3/7.
The fraction of candies left behind is 3/7.
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What is the magnitude and direction of MN with tail and head points M(-3, -2) and N(4, 0)? Please choose answer choices and give explanation.
A) 7.3 units, 15.9° south of west
B) 6.4 units, 74.1° north of east
C) 6.4 units, 74.1° south of west
D) 7.3 units, 15.9° north of east
Its direction is south of east which is 49.56° east of south, the answer is not listed among the answer choices provided.
What is magnitude ?Magnitude refers to the size or amount of something, often measured numerically or on a scale. In mathematics, it is commonly used to describe the absolute value of a number or the length of a vector in a geometric space. Magnitude can also be used to describe the intensity or strength of physical phenomena, such as the magnitude of an earthquake or the magnitude of a force.
According to given information :To find the magnitude and direction of MN with tail and head points M(-3, -2) and N(4, 0), we can use the distance formula and trigonometry.
First, we can find the coordinates of MN by subtracting the coordinates of M from those of N:
MN = (4 - (-3), 0 - (-2)) = (7, 2)
The magnitude of MN is the distance between M and N, which can be found using the distance formula:
|MN| = √((7 - (-3))² + (2 - (-2))²) = √(10² + 4²) = √116 ≈ 10.77
Next, we can find the direction of MN by using trigonometry. The angle between MN and the positive x-axis (east) is:
θ = arctan(2/7) ≈ 16.26°
The direction of MN is 180° + θ (measured counterclockwise from the positive x-axis) because the tail point M is to the left of the head point N:
Direction of MN = 180° + 16.26° ≈ 196.26°
To convert this direction to a compass direction, we can subtract it from 360° and then divide by 4, rounding to the nearest degree. This gives:
Compass direction of MN = (360° - 196.26°)/4 ≈ 40.44°
Since MN is to the right of the y-axis (north-south), its direction is south of east, which is 90° - 40.44° = 49.56° east of south.
Therefore, its direction is south of east which is 49.56° east of south, the answer is not listed among the answer choices provided.
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