Answer:
40 meters
Step-by-step explanation:
The maximum distance between the runners at any given time 40 meters. Therefore, option C is the correct answer.
Given that, Addison and Kelsey are running on a path modeled by x² + y² - 14x - 16y - 287 = 0.
What is a circle equation?The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle. The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.
The standard equation of a circle with center at (x1,y1) and radius r is (x-x1)²+(y-y1)²=r²
Here, the circular path is modeled by x² + y² - 14x - 16y - 287 = 0
We complete the squares to place it in the standard format, thus:
x² - 14x + 49 + y² - 16y +64 = 287+49+64
⇒ (x-7)² + (y-8)² = 400
⇒ (x-7)² + (y-8)² = 20²
So, r² = 20²
⇒ r = 20 meters
Maximum distance = d = 2r
= 40 meters
The maximum distance between the runners at any given time 40 meters. Therefore, option C is the correct answer.
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The graph of the function f(x) = -(x+3)(x-1) is
shown below.
-6
-4 -2
6
A
2
-2
4
-6
2
4
6 X
What is true about the domain and range of the
function?
O The domain is all real numbers less than or equali
to 4, and the range is all real numbers such that -31
≤x≤ 1.
The domain is all real numbers such that-3≤x≤
1, and the range is all real numbers less than or
equal to 4.
The domain is all real numbers, and the range is all
real numbers less than or equal to 4.
The domain is all real numbers less than or equal
to 4, and the range is all real numbers.
Using the concepts of domain and range of a function, the correct statement regarding the graph of the function f(x) = -(x + 3)(x - 1) is given by:
The domain is all real numbers, and the range is all real numbers less than or equal to 4.
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.In a graph:
The domain is given by the x-values, the horizontal axis.The range is given by the y-values, the vertical axis.The graph of f(x) = -(x + 3)(x - 1) is given at the end of the answer, hence:
The domain is all real values, as the function keeps going to infinity.The range is all values of y that are less than or equal to 4.Hence the correct statement is:
The domain is all real numbers, and the range is all real numbers less than or equal to 4.
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There is a 50% chance of rain here and a 25% chance of rain on Mars. Therefore, there is a 75%
chance that it will rain here or on Mars. Explain why this is a false statement.
There is a 75% chance that it will rain here or on Mars is false because there is a 25% chance that it will rain here and not on Mars.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
There is a 50% chance of rain here and a 25% chance of rain on Mars. Therefore, there is a 75% chance that it will rain here or on Mars.
The probability that it will rain here:
P(rain here) = 50%
P(rain on mars) 50%
P(not rain here) = 100 - 50 = 50%
P(not rain on mars) = 100 - 50 = 50%
P(rain here and not on mars) = 0.5×0.5 = 0.25 or 25%
Thus, there is a 75% chance that it will rain here or on Mars is false because there is a 25% chance that it will rain here and not on Mars.
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5
14
6
3
1
2
Two friends, Andrew and Liz, are playing a game using this spinner. If the
spinner lands on region 2 or 3, Andrew wins. If it lands on region 4, Liz wins. If
it lands on any other region, neither wins. Is this a fair game?
A. Yes. Each friend has a
probability of winning.
B. Yes. Each friend has a
probability of winning.
C. No. Andrew has a probability of winning and Liz has a
probability of winning.
D. No. Andrew has a probability of winning and Liz has a
probability of winning.
The question is incomplete. Below you will find the missing figure.
Two friends, Andrew and Liz, are playing a game using this spinner. If the
spinner lands on region 2 or 3, Andrew wins. If it lands on region 4, Liz wins. If it lands on any other region, neither wins. Is this a fair game?
A. Yes. Each friend has a 1/4 probability of winning.
B. Yes. Each friend has a 1/6 probability of winning.
C. No. Andrew has a probability of 1/4 winning and Liz has a probability of 1/6 winning.
D. No. Andrew has a probability of 1/3 winning and Liz has a probability of 1/4 winning.
The correct option is Option A: Yes. Each friend has 1/4 probability of winning.
Probability is the possibility of an event to happen which is the ratio of no. favorable outcomes and no. of total outcomes.
P = no. of favorable outcome/ total no. of outcome
Here given in the question,
If the spinner touches region 2 or 3, Andrew wins
If the spinner touches region 4, Liz wins.
This is fair play because both have the same size of region for winning.
If we cut the circle into 8 pieces,
as region 1 is the sum of 2 sub-parts of the circle,
possibility of spinner touching region 1= 2/8= 1/4
possibility of spinner touching the small region = 1/8
So the possibility of the spinner touching the region 2or 3= 1/8+1/8= 2/8= 1/4
Hence the possibility of Andrew wins= possibility of the spinner touching region 1= 1/4
possibility of Liz wins= possibility of the spinner touching the region 2 or 3= 1/4
Therefore the correct option is Option A: Yes. Each friend has 1/4 probability of winning.
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solve for x for this problem
Answer:
x = 5 and 6
Step-by-step explanation:
1. Square both sides
x - 5 = (x - 5)(x - 5)
2. Simplify the right side
x - 5 = x^2 - 10x + 25
3. Add 5 to both sides
x = x^2 - 10x + 30
4. Subtract x from both sides
0 = x^2 - 11x + 30
5. Factor
0 = (x-5)(x-6)
x = 5,6
Answer:
x = 5 , x = 6
Step-by-step explanation:
[tex]\sqrt{x-5}[/tex] = x - 5 ( square both sides )
x - 5 = (x - 5)² ← expand using FOIL
x - 5 = x² - 10x + 25 ← subtract x - 5 from both sides
0 = x² - 11x + 30 ← in standard form
0 = (x - 5)(x - 6) ← in factored form
equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x - 6 = 0 ⇒ x = 6
As a check
substitute these values into the equation and if both sides are equal then these values are the solutions.
x = 5
left side = [tex]\sqrt{5-5}[/tex] = [tex]\sqrt{0}[/tex] = 0
right side = 5 - 5 = 0
then x = 5 is a solution
----------------------------------
x = 6
left side = [tex]\sqrt{6-5}[/tex] = [tex]\sqrt{1}[/tex] = 1
right side = 6 - 5 = 1
then x = 6 is a solution
SUPER URGENT AND EASY FOR MOST- 30 PTS
factorise
10x + 300
Answer:
10(x + 30)
Step-by-step explanation:
10x + 300
Both terms have 10 in common, so you can factor out 10.
10x + 300 = 10(x + 30)
1 (c)
Gavin goes to Joti's shop.
He is making a circular blanket.
The finished blanket will have a radius of 0.325 m
It will have ribbon all around the edge.
He thinks he will need 2.5 m of ribbon.
Gavin knows that is about 3.1416
Round to 1 decimal place and use this value to work out how much ribbon
Gavin will have left if he buys 2.5 m
[4 marks]
Answer: 0.5m
Hope this helps!
What is f(0)?
O 0 only
O -6 only
O -2, -1, 1, and 3 only
O -6, -2, -1, 1, and 3 only
A function assigns the values. The correct option is C.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
For the given graph, the value of f(0) means the value of function when the value of x is 0. Thus, when the graph intersect with the x-axis is the value of f(0), therefore,the values of f(0) are -2, -1, 1, and 3 only.
Hence, the correct option is C.
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simplify 1 1 3 - 4 1 3 =
Answer:
-300
Step-by-step explanation:
113-413=-300
Solve by applying the counting principle. James is choosing a Four-digit Passcode for his smartphone. How many different Passcodes are possible? There are Ten digits that James can choose from. Enter Solve by applying the counting principle . James is choosing a Four - digit Passcode for his smartphone . How many different Passcodes are possible ? There are Ten digits that James can choose from.
Answer:
10k.
Step-by-step explanation:
1) if for the 1st position can be used 0-9 digits (10 digits), for the 2d - 0-9 digits, for the 3d - 0-9 digits and for the 4th - 0-9 digits, then
2) the required number of pwd is: 10*10*10*10=10⁴=10000.
What is the partial fraction decomposition of StartFraction 7 x squared + 14 Over (x squared + 3) squared EndFraction?
The final decomposition of the given partial fraction is; 7 + (-7/(x² + 3))
How to decompose partial fractions?We are given the polynomial fraction (7x² + 14)/(x² + 3) to decompose.
Now, due to the fact that the degree of the numerator is not less than the degree of the denominator, we will perform polynomial long division to get;
(7x² + 14)/(x² + 3) = 7 + (-7/(x² + 3))
Now, the second term (-7/(x² + 3)) cannot be decomposed further and as such, we say that our final decomposition of the given partial fraction is;
7 + (-7/(x² + 3))
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HELP PLEASE!!!!!! AND TYYY
Answer:
17cm Squared
Step-by-step explanation:
Get the area of the whole triangle, then the area of the white part. Then subtract the white from the whole area
A snack bar offers chili and/or cheese on its hot dogs for an additional fee.
The owner kept track of the hot dog orders over the course of a week. His
data are shown in a relative frequency table.
A relative frequency table is a chart that depicts the popularity or pattern of a specific piece of data based on the population sampled. The correct option is D.
What is a relative frequency table?A relative frequency table is a chart that depicts the popularity or pattern of a specific piece of data based on the population sampled. When we look at relative frequency, we are comparing the number of times a given event occurs to the overall number of events.
The complete question is mentioned in the below image with the relative frequency table.
As per the relative frequency table, the value 0.2 highlighted in the table represents that 20% of his customers ordered cheese but no chili on their hot dogs.
Hence, the correct option is D.
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Help will give br brainlesssssss
Answer:
i think the answer is the second one D and A
In the equation 3y = 21, what is the next step in the equation solving sequence
Answer:
divide both sides by 3
Step-by-step explanation:
Solving the equation means to have y alone on the left side equaling a number.
Since the variable y is being multiplied by 3, the next step is to do the opposite operation to "multiplying by 3" which is "dividing by 3." Since the rule in algebra is that you must do the same operation to both sides of an equation, the next step is:
divide both sides by 3
manual spent 4.56 on a sandwich and 2.98 on a drink How much did he spend in all? If he paid with a 10$ bill how much change did he get
Manual paid with a $10 bill and he got $2.46 as a change.
What is subtraction?Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, −.
Money spent on sandwich=$4.56 and money spent on drink=$2.98.
We need to find out how much did he spend in all.
That is, the total money spent=4.56+2.98=$7.54
He paid with a $10 bill, he gets change as 10-7.54=$2.46
Hence, he paid with a $10 bill and he got $2.46 as a change.
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Need number 11 please!!!
The coordinates of the inverse function f⁻¹(x) will be swapped of the coordinates of the function f(x).
The complete question is attached below.
What is inverse of a function?Let the function will be
f: X → Y
Then the inverse function will be
f⁻¹: Y → X
If the coordinates of the function f(x) are given.
Then the coordinates of the inverse function f⁻¹(x) will be swapped of the coordinates of the function f(x).
f(x) f⁻¹(x)
(33, 40) (40, 33)
(-19, -15) (-15, -19)
(-28, 47) (47, -28)
(-15, -34) (-34, -15)
(50, 0) (0, 50)
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Can u answer fast please
C. e
Step-by-step explanation:
[tex] ln( {e}^{e} ) = e ln(e ) = e(1) = e[/tex]
Analia is a school district manager. Here are some details about two schools in her district for the last school year:
School A School B
Number of students 300030003000 400040004000
Number of teachers 190190190 380380380
Graduation rate 86\%86%86, percent 90\%90%90, percent
Budget per student \$10{,}500$10,500dollar sign, 10, comma, 500 \$10{,}000$10,000dollar sign, 10, comma, 000
% of students in sports club 62\%62%62, percent 68\%68%68, percent
Number of sports medals won 999 777
SAT average 120012001200 105010501050
SAT range (max-min) 900900900 700700700
Analia wants to know which school has higher athletic achievements relative to the SAT average.
1) Analia thought of two different ways to define this quantity. Identify these two definitions among the following options.
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
% of students in sports club divided by SAT average
(Choice B)
B
Graduation rate divided by SAT average
(Choice C)
C
Number of sports medals won
(Choice D)
D
Number of sports medals won divided by SAT average
2) Determine which school has higher athletic achievements relative to the SAT average, according to the two definitions. Did you get the same result for both definitions?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Yes. According to both definitions, School A has higher athletic achievements relative to the SAT average.
(Choice B)
B
Yes. According to both definitions, School B has higher athletic achievements relative to the SAT average.
(Choice C)
C
No. The definitions have opposite results.
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pls help i forgot how to do this :)
Answer:
in picture
Step-by-step explanation:
added in the picture
Kubin Company's relevant range of production is 29,000 to 33,000 units. When it produces and sells 31,000 units, its average costs per unit are as follows:
Direct materials $8.90
Direct labor $5.90
Variable manufacturing overhead $3.40
Fixed manufacturing overhead $6.90
Fixed selling expense $5.40
Fixed administrative expense $4.40
Sales commissions $2.90
Variable administrative expense $2.40
1. If 29,000 units are produced and sold , what is the variable cost per unit produced and sold ?
2. If 33,000 units are produced and sold , what is the variable cost per unit produced and sold ?
3. If 29,000 units are produced and sold , what is the total amount of variable cost related to the units produced and sold ?
4. If 33,000 units are produced and sold , what is the total amount of variable cost related to the units produced and sold ?
5. If 29,000 units are produced , what is the average fixed manufacturing cost per unit produced ?
6. If 33,000 units are produced , what is the average fixed manufacturing cost per unit produced ?
7. If 29,000 units are produced , what is the total amount of fixed manufacturing overhead incurred to support this level of production ?
8. If 33,000 units are produced , what is the total amount of fixed manufacturing overhead incurred to support this level of production ?
A table is in the shape of a regular
hexagon. The perimeter of the table is 12
feet. What is the length of each side of
the table?
A 1 ft
B 2 ft
C 3 ft
D 4 ft
Answer:
B
Step-by-step explanation:
A hexagon has 6 sides. If you divide the perimeter(12) by the number of sides(6), you get the length of one side(2).
In AABC, a = 13, b = 14, and c = 18. Find m/A.
B
A
39.5
с
b
a
Answer:
Step-by-step explanation:
Using the Law of Cosines,
[tex]a^{2}=b^2 + c^2 - 2bc \cos A\\\\13^{2}=14^{2}+18^{2}-2(14)(18) \cos A\\\\-351=-504 \cos A\\\\\cos A=\frac{351}{504}\\\\A=\boxed{\cos^{-1} \left(\frac{351}{504} \right)}[/tex]
12. A bag contains 12 red, 9 green and 5 black markers. If Cooper randomly selects 7 markers, how many
ways could this be done if EXACTLY 6 are to be the same color?
Answer:
Step-by-step explanation:
7 marks
6 same colors
from 12 red 6 same exactly the same
12 x 11 x 10 x 9 x7 x6
1 remainig
from 9 green 6 saem exactly the same
9 x 8 x 7 x 6 x5 x4
1 remaining
add the results above to get your final answer
26 markers in total
6 to be chosen of the same color from 7
Is 3^20 times 2^14 a factor of 3^22 Times 2^12
Answer:
no
Step-by-step explanation:
In order for one number (A) to be a factor of another (B), the exponents of the primes in the prime factorization of A cannot exceed those of the prime factorization of B.
__
A = 2^14 × 3^20
B = 2^12 × 3^22
The exponent of the factor 2 in A is 14, which exceeds the exponent of the factor 2 in B (12). Therefore, A cannot be a factor of B.
(3^20)(2^14) is not a factor of (3^22)(2^12)
No Question, this account was set up in error.
Answer:
is the question no questions question ❓
What 2 numbers add up to 37 and multiply to 210?
Answer: 30 and 7
Step-by-step explanation: 30 plus 7 is 37, 30 times 7 is 210
Look at the photo and answer it pls
Answer:
There isn't a photo
Step-by-step explanation:
There is no photo
Large eggs weigh 1/1/2 pounds per dozen. Dawn bought eight large eggs. How much did the eggs weigh
Answer: 1 pound
Step-by-step explanation:
Because 12 eggs= 1.5 pounds. So, you divide 1.5/12 = 0.125. And the 0.125 times 8 = 1 pound
Answer:
1 lb
Step-by-step explanation:
Since 1 dozen(12) eggs weigh 1 1/2 or 3/2 lbs, each egg weights 3/2 ÷ 12 = 3/24 lb
So 8 eggs would weight 8 x 3/24 = 1 lb
which system of the equation is represents by the graph?
Each statement describes a transformation of the graph of y = log2x. Which statement correctly describes the graph of y = log2(x + 3) - 9?
The transformation of a function may involve any change in the initial function. The correct option is C.
The complete question is:
Each statement describes a transformation of the graph of y = log2x.
Which statement correctly describes the graph of y = log2(x + 3) - 9?
It is the graph of y = log2x translated 3 units down and 9 units to the left.It is the graph of y = log2x translated 9 units down and 3 units to the right.It is the graph of y = log2x translated 9 units down and 3 units to the left.It is the graph of y = log2x translated 3 units up and 9 units to the left.How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]Horizontal stretch by a factor k: [tex]y = f(\dfrac{x}{k})[/tex]Given the initial function y = log2x, now if the function is needed to be transformed to y = log2(x + 3) - 9, then the function is needed to be shifted left by 3 units and down by 9 units.
Hence, the correct option is C.
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