Answer:
Circumference is 12.56 km
Explanation:
C = 2πr (with radius)
C = 2(3.14)(2)
C = 12.56 km
The circumference of a circle with a radius of 2 km is calculated using the formula C = 2πr. Using π ≈ 3.14159, the circumference is approximately 12.57 km.
The circumference of a circle is calculated using the formula C = 2πr, where C is the circumference and r is the radius of the circle. Given the radius (r) of 2 km, we can substitute this value into the formula to find the circumference:
C = 2π(2 km)
C = 4π km
By using the approximation π ≈ 3.14159, we can calculate the circumference as:
C = 4 × 3.14159 km
C ≈ 12.56636 km
Therefore, the circumference of the circle is approximately 12.57 kilometers.
Expand and simplify (x- 3)(x + 5)
Answer:
[tex] {x}^{2} + 2x - 15[/tex]
Step-by-step explanation:
[tex]x(x + 5) - 3(x + 5) \\ = \times {x}^{2} + 5x - 3x - 15 \\ = {x}^{2} + 2x - 15[/tex]
Final answer:
To expand and simplify (x - 3)(x + 5), we use the FOIL method, resulting in [tex]x^2 + 5x - 3x - 15[/tex]. Combining like terms, we get the simplified form [tex]x^2 + 2x - 15.[/tex]
Explanation:
To expand and simplify the expression (x - 3)(x + 5), we use the distributive property, also known as the FOIL method, which stands for First, Outer, Inner, and Last. This refers to the terms you multiply together in a binomial multiplication:
First: Multiply the first terms in each binomial: x* x = [tex]x^2[/tex]
Outer: Multiply the outer terms in the binomials: x *5 = 5x
Inner: Multiply the inner terms in the binomials: -3 * x = -3x
Last: Multiply the last terms in each binomial: -3 * 5 = -15
Combining these products gives us: [tex]x^2 + 5x - 3x - 15.[/tex] We then combine like terms, which in this case are 5x and -3x:
[tex]x^2 + 2x - 15.[/tex]
So, the expanded and simplified form of (x - 3)(x + 5) is [tex]x^2 + 2x - 15.[/tex]
Kara and Lindsey both hike in separate directions from their campsite, with Kara hiking straight to the east and Lindsey hiking straight north. At
2:00 p.m., Kara hiked twice as far to the east as Lindsey hiked to the north. At 2:30 p.m., Kara had covered another mile, while Lindsey had
covered another half of a mile. If x represents Lindsey's distance, in miles, from the campsite at 2:00p.m., what function could be used to
represent the area of the triangular region formed by the girls' locations and the campsite at 2:30 p.m.?
Answer:
A. f(x)=x^2+x+0.25
Step-by-step explanation:
If x represents Lindsey's distance at 2:00 PM, then 2x represents Kara's distance at 2:00 PM because she walked twice as far as Lindsey. Then adding on the values we got for 2:30 PM, we get that Kara walked a distance of 2x+1 and Lindsey walked a distance of x+0.5 at the time of 2:30 PM. Now, we know that they have formed a right triangle because we are given the directions they walked in; east and north. This allows us to use a formula for the area of a right triangle: 1/2(L x W). Plugging in our values, we get...
1/2(2x+1)(x+0.5)
which simplifies to...
1/2(2x^2+2x+0.5)
which further simplifies to...
x^2+x+0.25
which is our answer.
Answer:
A. f(x) = x^2 + x + 0.25
Step-by-step explanation:
Factor completely: 2x4 − 32.
a 2(x2 − 4)(x2 + 4)
b 2(x − 2)(x + 2)(x2 + 4)
c 2(x − 2)(x + 2)(x + 2)(x + 2)
d 2(x − 2)(x + 2)(x2 − 4)
Answer:
Option b) is correct.
The completed factor of given expression is [tex]2(x-2)(x+2)(x^2+4)[/tex]
Step-by-step explanation:
Given expression is [tex]2x^4-32[/tex]
To find the completed factor for the given expression:
[tex]2x^4-32[/tex]:
Taking the common number "2" outside to the above expression we get
[tex]2x^4-32=2(x^4-16)[/tex]
Now rewritting the above expression as below
[tex]=2(x^4-2^4)[/tex] (since 16 can be written as the number 2 to the power of 4)
[tex]=2((x^2)^2-(2^2)^2)[/tex]
The above expression is of the form [tex]a^2-b^2=(a+b)(a-b)[/tex]
Here [tex]a=x^2[/tex] and [tex]b=2^2[/tex]
Therefore it becomes
[tex]=2(x^2+2^2)(x^2-2^2)[/tex]
[tex]=2(x^2+4)(x^2-2^2)[/tex]
The above expression is of the form [tex]a^2-b^2=(a+b)(a-b)[/tex]
Here [tex]a=x[/tex] and [tex]b=2[/tex]
Therefore it becomes
[tex]=2(x^2+4)(x+2)(x-2)[/tex]
[tex]=2(x+2)(x-2)(x^2+4)[/tex]
Therefore [tex]=2(x+2)(x-2)(x^2+4)[/tex]
[tex]2x^4-32=2(x-2)(x+2)(x^2+4)[/tex]
Option b) is correct.
The completed factor of given expression is [tex]2(x-2)(x+2)(x^2+4)[/tex]
Answer:
b
Step-by-step explanation:
find the sum of the following gp:6,12,24,......to 10term and 1,-1/2,1/4,1/8,1/16.........to 20term
Answer:
Sₙ = 6 x (1 - 2¹⁰) / (1 - p) = 6 x 1023 = 6138
S'ₙ =2.52
Step-by-step explanation:
sum of this sequence: Sₙ = A₁ x (1 - pⁿ) / (1 - p)
Sₙ: sum of n terms
A₁: initial value 6
p: common ratio 2
n: terms 10
Sₙ = 6 x (1 - 2¹⁰) / (1 - p) = 6 x 1023 = 6138
Is there any mistake in the 2nd question - about the common ratio (-1/2)?
S'ₙ =1 + (-1/2) + 1 x (1 - (1/2)¹⁸)) / (1 - (1/2)) = 1/2 + 2 x (1 - (1/2)¹⁸)
S'ₙ = 1/2 + 2 x (1 - 1/262144) = 1/2 + 262143/130072= 0.5 +2.02 = 2.52
PLEASE HELP!!!!!!! CORRECT GETS BRAINLIEST!!!!!!
Answer:
Step-by-step explanation:
If angle STU is given as 82 degrees, then arc SVU is twice the measure of its inscribed angle. That means that arc SVU is 164 degrees.
arc SVU = arc SV + arc VU. By substitution,
164 = 120 + arc VU so
arc VU = 44 degrees
Jennifer wants to rent a car for 5 days, and she's interested in the loss
damage waiver but not the collision damage waiver. If the daily rate is $45
and LDW is $65, what is her total rental cost?
Answer:
290
Step-by-step explanation:
Which of the following is not a way to determine if a relation is a function?
A.
Use the vertical line test on a graph of the relation.
B.
Check to see if each input maps to only one output.
C.
There should be no duplicated x-coordinates in the ordered pair set.
D.
Determine if the relations’ graph forms a line.
D. Determine if the relations’ graph forms a line.
Step-by-step explanation:
A function is a relation if the input values lead to only one output value.The input values, normally x values make up the domain, where as the output values form the domain.A function is a relation where the input values are associated with a single output.The vertical test is used to determine if a curve is a function.The line graph should only hit a single point on the curve.
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A phone survey has a margin error of +/– 4%. What is the range of number of people who will vote for the other candidate if 87 of 114 people said they would vote for the other person and there are 9918 people in the district?
A. 7266 to 7872
B. 7266 to 7827
C. 7222 to 7872
D. 7296 to 7872
Answer:
The range of people who voted for other person = 7266 to 7872
Step-by-step explanation:
A phone survey has a margin error of +/– 4%. The range of number of people who will vote for the other candidate if 87 of 114 people said they would vote for the other person.
We get the percentage from this ,
Percentage = [tex]\frac{87}{114} \times 100[/tex] = 76.3 %
Border percentages = 72.3 and 80.3% (Since error = 4%)
We have already taken vote of 114 people so remaining = 9804
Lower end = 0.723 [tex]\times[/tex] 9804 = 7266
Upper end = 0.803[tex]\times[/tex] 9804 = 7872
Hence the range = 7266 to 7872
Katy makes 48 cookies an hour. If she has 24 alr, how long would it take her to make 120?
Question:
Katy makes 48 cookies an hour. If she has 24 already, how long would it take her to make 120?
Answer:
It takes 2.5 hours for Katy to make 120 cookies
Step-by-step explanation:
Given:
Time taken to make 48 cookies = 1 hour
To Find:
Time taken to make 120 cookies = ?
Solution:
Time taken to make 48 cookies = i hour
So now time taken to make 1 cookie = [tex]\frac{1}{48} hour[/tex]
So time taken to make 120 cookies
= Number of cookies X time taken to make one cookie
=>[tex]120 \times \frac{1}{48}[/tex]
=>[tex] \frac{120}{48}[/tex]
=> 2.5 hours
Find the unit rate. Please and thank you.
Answer:
(20-10)/(4-2)= 10/2= 5 miles/day
The unit rate in this case is the miles travelled per day.
2 days = 10 miles
1 day = 5 miles
answer: 5 miles/day
What is the effect on the graph of the function f(x)=c^2 when f(x) is changed to 3f(x-2)
The graph of f(x) is stretched vertically by scale factor 3 and translated 2 units to the right to give the graph of 3f(x - 2)²
Step-by-step explanation:
Let us revise the vertical stretch and the horizontal translation
A vertical stretching is the stretching of the graph away from the x-axis If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched by multiplying each of its y-coordinates by k.If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h) If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)∵ f(x) = x²
∵ f(x) is multiplied by 3
- 3 is greater than 1, then the graph of f(x) is stretched vertically
by scale factor 3
∴ The graph of f(x) is stretched vertically by scale factor 3
∵ x² is changed to (x - 2)²
- That means the graph of f(x) translated 2 units to the right
∴ The graph of f(x) is translated 2 units to the right
The graph of f(x) is stretched vertically by scale factor 3 and translated 2 units to the right to give the graph of 3f(x - 2)²
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Which of the following uses the reciprocal property to rewrite x/5=72/4
Answer:
x=90
Step-by-step explanation:
x/5=72/4
simplify 72/4 into 18
x/5=18
x=18*5
x=90
The reciprocal of x/5=72/4 is 5/x = 4/72.
Given,
Which of the following uses the reciprocal property to rewrite x/5 = 72/4?
A. 5/x = 4/72
B. x/4 = 5/72
C. x/5 = 72/4
What is a reciprocal of a number?We denote the reciprocal of a number M by 1/M.
Example: 1, 1/2, 2/3,
The reciprocal is:
1 = 1/1 = 1
1/2 = 1/(1/2) = 2
2/3 = 1/(2/3) = 3/2
We have,
x/5 = 72/4
If we apply reciprocal property here we get,
1/(x/5) = 1/(72/4)
5/x = 4/72
Thus the reciprocal of x/5=72/4 is 5/x = 4/72.
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Mr. Babe used to work at a local furniture store.
This is what my answers were for these questions(If it is correct, just write a comment. But if it is incorrect, explain why in the answers box)
A. While he worked there, Mr. Babe earned 3% on how much he sells. If he sold $495 couch, how much commission did he make?
What I did:
495 x 3 = 1485
1485/100 = 14.85
B. On top of his commission, Mr. Babe made $15 per hour. He eventually got a raise with an increase of 5% per hour. After the raise, how much did he make per hour?
What I did:
495 x 5 = 2475
2475/100 = 24.75
A. Mr. Babe made a commission of $14.85
B. He makes $15.75 per hour after the raise.
Step-by-step explanation:
A. While he worked there, Mr. Babe earned 3% on how much he sells. If he sold $495 couch, how much commission did he make?
Worth of sold couch = $495
Commission = 3%
Amount of commission = 3% of total worth sold
Amount of commission = [tex]\frac{3}{100}*495[/tex]
Amount of commission = [tex]\frac{1485}{100}=\$14.85[/tex]
Mr. Babe made a commission of $14.85
B. On top of his commission, Mr. Babe made $15 per hour. He eventually got a raise with an increase of 5% per hour. After the raise, how much did he make per hour?
Amount earned per hour = $15
Increase = 5%
As the increment is on per hour amount, therefore,
Amount of increase = 5% of per hour amount
Amount of increase = [tex]\frac{5}{100}*15=\frac{75}{100} = \$0.75[/tex]
New amount per hour = Per hour amount + amount of increase
New amount per hour = 15+0.75 = $15.75
He makes $15.75 per hour after the raise.
Keywords: percent, addition
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ALGEBRA 24 POINTS
simplify?
Answer:
1200
Step-by-step explanation:
its just common sense that 2*2=4 and 10*4=40 so now all you have to do is 40*30 which its just common knowledge that 4*3=12 now just add the zeros 1200
a line with a slope of 10 passes through the point 0,2. what is the equation in slope intercept form
Answer:
y=10x+2
Step-by-step explanation:
y-y1=m(x-x1)
y-2=10(x-0)
y-2=10(x)
y-2=10x
y=10x+2
for events A and B, P(A)= 3/14 and P(B)= 1/5. Also, P(A and B)= 3/65. Are A and B independent events?
No, A and B are not independent events
Step-by-step explanation:
Let us study the meaning independent probability
Two events are independent if the result of the second event is not affected by the result of the first eventIf A and B are independent events, the probability of both events is the product of the probabilities of the both events P (A and B) = P(A) · P(B)∵ P(A) = [tex]\frac{3}{14}[/tex]
∵ P(B) = [tex]\frac{1}{5}[/tex]
∴ P(A) . P(B) = [tex]\frac{3}{14}[/tex] × [tex]\frac{1}{5}[/tex]
∴ P(A) . P(B) = [tex]\frac{3(1)}{14(5)}[/tex]
∴ P(A) . P(B) = [tex]\frac{3}{70}[/tex]
∵ P(A and B) = [tex]\frac{3}{65}[/tex]
∵ P(A) . P(B) = [tex]\frac{3}{70}[/tex]
- The two answers are not equal
∴ P (A and B) ≠ P(A) · P(B)
- In independent events P (A and B) = P(A) · P(B)
∴ A and B are not independent events
No, A and B are not independent events
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Events A and B are not independent.
The events A and B are independent given that P(A) = 3/14, P(B) = 1/5, and P(A AND B) = 3/65. To determine if two events are independent, the product of their individual probabilities, P(A) and P(B), should equal the probability of both events occurring together, P(A and B).
Let's calculate this:
P(A) × P(B) = (3/14) × (1/5) = 3/70
Since P(A AND B) = 3/65, we compare it to the calculated product of P(A)P(B).
P(A AND B) is not equal to P(A)P(B). Therefore, events A and B are not independent because their joint probability is not the product of their individual probabilities.
a bedroom measures 13.62 feet long and 11.5 feet wide. what is the most accurate measure of the area of the bedroom, in square feet?
Answer:
156.63 Square feet
Step-by-step explanation:
Final answer:
The area of a bedroom that is 13.62 feet by 11.5 feet is 156.63 square feet, found by multiplying the length by the width.
Explanation:
The most accurate measure of the area of a bedroom that measures 13.62 feet long and 11.5 feet wide is calculated by multiplying the length by the width. The formula for the area of a rectangle is:
Area = length × width
Thus, the area is:
Area = 13.62 feet × 11.5 feet = 156.63 square feet
This calculation ensures that you have the most accurate measure of the square footage necessary, for example, if you are planning to replace the carpet or perform other renovations that require an accurate measure of the room's floor space.
What is the result when 8x^3+6x^2+15x+7 divides by 2x + 1
Answer:
Step-by-step explanation:
the hypotenuse longest side of similar triangles ABC and DFA both lie on line k, as shown below. Demonstrate whether the slope of line k is constant(same) between C and D. Use the leg length short sides of triangles ABC and DFA in your answer
Answer:
Yes, The slope of the line k between C and D is constant
Step-by-step explanation:
Lets find the slope of the line K from the points AC and AD
Step1:
Slope of line K from AC (point C)
= [tex]\frac{AB}{BC}[/tex]
= [tex]\frac{1}{3}[/tex]
Step 2:
Slope of line k from AD (point D)
= [tex]\frac{DF}{A F}[/tex]
= [tex]\frac{2}{3}[/tex]
=[tex]\frac{1}{3}[/tex]
The slope of the line K from the points AC and AD are equal
. Sabrina jogged 54 laps around the
football field. Harry ran 9 laps. How
many times as many laps did Sabrina
run than Harry?
Ⓡ 3 times
® 6 times
© 8 times
O 9 times
Answer:
B) 6 times
Step-by-step explanation:
54/9=6
What is the simplified form of 100x36 ?
Answer:
36
100x
Step-by-step explanation:
Answer: I believe 1036 ur welcome :)
kylie has a rectangular poster that has an area of 2/3 square meters. the width of the poster is 3/5 meter. what is the length of the poster?
Answer:
1 1/9 (10/9) meter
Step-by-step explanation:
area of rectangle = width x length
2/3 m² = 3/5 m x Length
Length = (2/3) / (3/5) = 10/9 = 1 1/9
Answer:
10/9
Step-by-step explanation:
Paul is looking at two vacation packages while planning a trip to Cancun, Mexico. In the first vacation package, round-trip airfare costs $799, and it costs $139 per night to stay at the resort. In the second vacation package, it costs $587 per night to stay in the resort and $285 for round-trip airfare. Let x represent the number of nights spent at the resort, and let y represent the total cost of the trip. Which system of equations could be used to find how many nights Paul needs to stay at either resort so that both vacation packages have the same cost? A. B. C. D.
Answer:
y = 139x + $ 799
y = 587x + $ 285
Step-by-step explanation:
Let x represent the number of days spent at the resort and y represent the total cost.
for the first option
y = 139x + $799 since $ 139 is the amount per night at the resort, $139x must be the cost for x number of days
y = 587x + $285 similarly x number of days should equal $587x
Does anyone know this?
Answer:
59°
Step-by-step explanation:
Since the triangle is isosceles then the base angles are congruent.
Subtract the vertex angle from 180° and divide the result by 2, that is
base angle = [tex]\frac{180-62}{2}[/tex] = 59°
John weighs three times as much as Karen. Two times John’s weight plus Karen’s weight is 875 pounds. How much does John weigh? How much does Karen weigh?
Answer: Karen's weight = 125 pounds
Step-by-step explanation:
Let Karen's weight be x , this means that John's weight is 3x.
Two times John’s weight = 2(3x)
Two times John’s weight plus Karen’s weight is 875 pounds implies;
2(3x) + x = 875
6x + x = 875
7x = 875
divide through by 7
x = 125
Therefore Karen's weight = 125 pounds
John's weight = 3 x 125 = 375 pounds
Answer:
John weighs 375 pounds, and Karen weighs 125 pounds.
Step-by-step explanation:
The best way to solve this question is to assign the weights to variables.
Let's give variable j to John's weight and k to Karen's.
If John weighs 3 times as much as Karen, j=3k.
If 2x John's weight plus 1x Karen's weight = 875, then 2j + k = 875,
which can also be written as 6k + k = 875 since we established that j=3k and 2*3=6.
Now all we need to do to find k is solve the equation:
6k + k = 875 combine common factors
7k = 875 divide both sides by 7
k = 875/7
k = 125
Now that we know Karen's weight, we can find John's weight by using j=3k.
Plug the now known value of k in:
j=3k
j=3(125)
j=375
Now you have your pair:
j=375, k = 125.
The midpoint of AB is (3,-5).
A = (9,4)
What are the coordinates of point B?
Give your answer in the form (x,y).
Answer:
(-3, -14)
Step-by-step explanation:
the difference between 9 and 3 is 6 so subtract 6 from 3 to get negative 3. the difference between 4 and - 5 is 9 so subtract 9 from -5
make b the subject of this equation A = 1/2 x b x h
The equation is [tex]b=\frac{2A}{h}[/tex]
Step-by-step explanation:
Let us revise how to make a variable subject of an equation
Write the equation and circle the variable you want to make it subjectKeep it in one side and move all other in the other sideMake the coefficient of the subject 1∵ A = [tex]\frac{1}{2}[/tex] × b × h
∵ b is the subject
∴ Multiply the two sides by 2
∴ 2A = b × h
- Divide both sides by h
∴ [tex]\frac{2A}{h}= b[/tex]
- Switch the two sides
∴ [tex]b=\frac{2A}{h}[/tex]
The equation is [tex]b=\frac{2A}{h}[/tex]
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a 45-45-90 right triangle is formed when a ____ is cut in half
A 45-45-90 right triangle is formed when a square is cut in half diagonally. This forms two such right triangles, where the sides are in a specific ratio, with the length of the hypotenuse being root 2 times the length of each leg.
Explanation:A 45-45-90 right triangle is formed when a square is cut in half. This is because when you draw a diagonal on a square, the angles it forms with the sides are all 45 degrees, and the angles at the vertices remain 90 degrees. Therefore, it forms two 45-45-90 right triangles.
In a 45-45-90 triangle, the sides are in a specific ratio. The length of the hypotenuse is root 2 times the length of each leg, which are equal in measure because it is an isosceles triangle. These properties are unique to 45-45-90 right triangles.
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Dear Ms. Meyer:
Laura Yin suggested I contact you concerning the Marketing position available at Eastern Arbor. I am inspired to
pursue my marketing interests at Eastern Arbor due to its reputation as a prestigious, innovative and growing
company in liability policies.
Which type of cover letter would the above excerpt come from?
a. Prospecting cover letter
b. Networking cover letter
c. Application cover letter
d. Follow up cover letter
Please select the best answer from the choices provided
Answer:
a, Prospecting cover letter
Step-by-step explanation:
Given:
Dear Ms. Meyer:
Laura Yin suggested I contact you concerning the Marketing position available at Eastern Arbor. I am inspired to pursue my marketing interests at Eastern Arbor due to its reputation as a prestigious, innovative and growing company in liability policies.
From the given data;
We can say that it is an E-mail which has been sent to Ms. Meyer regarding the Job opening of Marketing position available at Eastern Arbor.
It was been suggested by Laura Yin to the writing person that there is a Job opening at Eastern Arbor.
The writing person has a marketing interest which he wanted to pursue at Eastern Arbor as it is a reputed company with prestigious, innovative and growing company in liability policies.
A Prospecting cover letters are introductory in nature. Rather than focusing on your skills and experiences that are related to a job listing (since there is no job listing), a letter of interest should highlight your marketable qualifications and skills that would be easily transferable between a number of positions.
Hence we can say that it is an Prospecting Cover letter.
Answer:
Your answer is A! Prospecting cover letter
Step-by-step explanation:
did the test
Which of the following could be a solution to a system of linear equations including the line graphed below?
Select one:
A. (-2, 3)
B. (1,4)
OC. (3,0)
D.(-5,-4)
Correct answer:
D. (-5,-4)
Explanation:In order to solve this problem, let's plot each point. So, see the attached file below and keep in mind the following:
Point (-2, 3) is the red one.Point (1, 4) is the blue one.Point (3, 0) is the orange one.Point (-5, 4) is the yellow one.As you can see on the graph, only point (-5, -4) lies on the given line. Therefore, the conclusion is that this point could be a solution to a system of linear equations including the line graphed below.
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