Using proportions, the expression for the price per person is:
[tex]P = \frac{850}{p}[/tex]
Jordan's expression is wrong because the price per person is inverse proportional to the number of people in the party, not direct proportional.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The cost of renting a bowling alley for a party is $850, hence the cost per person is given by:
[tex]P = \frac{850}{p}[/tex]
Jordan's expression is wrong because the price per person is inverse proportional(that is, the amount is divided by p) to the number of people in the party, not direct proportional.
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The sum of the measures of two exterior angles of a triangle is 264. What is the
measure of the third exterior angle?
Answer: 96 degrees
Step-by-step explanation: Assuming that angle ℒ is the third measure, then angle ℒ is 96 degrees as all exterior angle measures of a triangle are 360 degrees.
360-264 = 96 degrees =
ℒ
Please give brainliest if helpful.
find an equation equivalent to (x-2)^2 + (y + 2)^2 = 8 in polar coordinates
The circle equation in polar coordinates is:
[tex]r - 4*cos(\theta) + 4*sin(\theta) = 0[/tex]
How to change the coordinates of the circle equation?
Here we have the circle equation:
[tex](x - 2)^2 + (y + 2)^2 = 8[/tex]
First, we expand it to:
[tex]x^2 - 4x + 4 + y^2 + 4y + 4 = 8[/tex]
Now we can rewrite it as:
[tex]x^2 + y^2 -4x + 4y + 4 + 4 = 8\\\\x^2 + y^2 - 4x + 4y = 0[/tex]
Remember that:
[tex]x^2 + y^2 = r^2\\\\x = r*cos(\theta)\\y = r*sin(\theta)[/tex]
Replacing that, we get:
[tex]x^2 + y^2 - 4x + 4y = 0\\\\r^2 - 4r*cos(\theta) + 4r*sin(\theta) = 0[/tex]
That is the equation in polar form.
Now, because we can discard the solution r = 0, we can divide both sides by r to get:
[tex]r - 4*cos(\theta) + 4*sin(\theta) = 0[/tex]
To simplify it.
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Evaluate the given function. The values of the independent variable are approximate.
f(x) = 3x² - 3x, find f(3.52) and f(-8.77)
The values of f(3.52)=26.61 and f(-8.77)=257.05
An assignment of an element from set Y to each element of set X constitutes a function from set X to set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The notation f: X→Y denotes a function, its domain, and its codomain. The value of a function at an element x of X, denoted by the symbol f(x), is referred to as the image of x under f or the value of f applied to the argument x.
The given function is f(x) = 3x²-3x =3x(x-1)
f(3.52)=3*(3.52)(3.52-1)
=26.61
f(-8.77)=3*(-8.77)(-8.77-1)
=257.05
Therefore, the values of f(3.52)=26.61 and f(-8.77)=257.05
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This table represents a proportional relationship between x and y.
x 0.2 0.4 0.6 0.8
y 0.25 0.5 0.75 1.0
What is the constant of proportionality?
Enter your answer as a decimal in the box.
Answer:
x
Step-by-step explanation:
I got it right.........
Can someone help me answer fast
Answer:
2x+3+9
because plyer scored 9 points and throw 2point shotand same number 3
find the x and y values of this graph algebra 2
x y
2,0
1,-2
0,-4
-1,-6
-2,-8
Find the equation of the line that
is perpendicular to y = -8x + 2
and contains the point (-4,1).
Answer:
Step-by-step explanation:
slope of line ⊥ to y=-8x+2
is -1/-8=1/8
eq. of line with slope 1/8 thro' (-4,1) is
y-1=1/8 (x+4)
8y-8=x+4
8y=x+4+8
8y=x+12
y=1/8 x+12/8
or
y=1/8 x+3/2
Simplest form of ratio 25g:3kg
Answer:
look at the picture.
Step-by-step explanation:
look at the picture.
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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Between every pair of distinct points, there is a positive unique number called the ??? , which can be determined as the ??? of the corresponding real numbers of the two points.
The positive number between every pair of distinct points is known as the distance and it can be found as the absolute value of the difference between the corresponding real numbers.
How is the distance found?The distance represents the space between a pair of distinct points. This is called the distance postulate.
In order to find the distance, you would need to solve for the absolute value of the difference between the real numbers that are at the two points.
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Answer:
The positive number between every pair of distinct points is known as the distance and it can be found as the absolute value of the difference between the corresponding real numbers.
Step-by-step explanation:
A section of a tessellated plane is shown. Which type of symmetry does the tessellated plane have? translational and rotational rotational and reflectional reflectional and translational glide reflectionalA section of a tessellated plane is shown. Which type of symmetry does the tessellated plane have?
translational and rotational
rotational and reflectional
reflectional and translational
glide reflectional
Answer:
The given tessellated plane has translational and rotational symmetry. From the given options, we find that option A is correct.
Step-by-step explanation:
Concept: The symmetry has to be decided in such a way that when it applies to a figure, we get exactly the next figure. In the given figure, we have translational and rotational symmetries. We can translate the triangles to the next position and get the same triangle. Or we can rotate the triangle about the point of contact and get the same triangle.
For example, take the top left triangle. If it is translated towards approximately 30° direction, then we will get the triangle present at the top.
Or when we turn that triangle about the point of contact of that and the topmost triangle, then we can get the topmost triangle.
But there is no reflectional symmetry due to the absence of symmetry line.
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Factor the binomial 9t to second power,-4 =
Using subtraction of perfect squares, it is found that the factored expression is:
9t² - 4 = (3t - 2)(3t + 2).
What is the subtraction of perfect squares factoring?It is given as follows:
a^2 - b^2 = (a - b)(a + b)
In this problem, the binomial is given as follows:
9t² - 4.
Hence:
a² = 9t² -> a = 3t.b² = 4 -> b = 2.Hence the factored expression is:
9t² - 4 = (3t - 2)(3t + 2).
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Here is the histogram of a data distribution. All class widths are
What is the median of the distribution?
The median of the distribution is 4.
What is the median?
A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.
The median is the number at the center of the data set.
Arranging the numbers in the histogram in ascending order is: 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 8, 9, 10
Total numbers = 21 Median = 1/2 x (n + 1)1/2 x 22 = 11th number 4
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Triangle P Q R is shown. Angle P Q R is a right angle. The length of hypotenuse P R is q, the length of P Q is r, and the length of Q R is p.,
Which cosine ratios are correct for ΔPQR? Check all that apply.
cos (P) = StartFraction r Over q EndFraction
cos (P) = StartFraction p Over q EndFraction
cos (Q) = StartFraction r Over p EndFraction
cos (R) = StartFraction r Over p EndFraction
cos (R) = StartFraction p Over q EndFraction
The cosine ratios which are correct for the ΔPQR are CosineP = r/q and CosineR = p/q.
We have,
Δ PQR,
Length of hypotenuse PR = q
The length of PQ = r,
And the length of QR = p
NOw,
We know that Trigonometric ratios of CosineΘ;
CosineΘ = Base/Hypotenuse
So,
CosineP = r/q
And,
CosineR = p/q
So, from the above find out values we can say that these values are given in option (a) and option (d).
Therefore, the cosine ratios which are correct for the ΔPQR are CosP = r/q and CosR = p/q.
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Circle G is shown. Line segment F G is a radius with length 3.
In circle G, r = 3 units. Maria draws a circle with double the area of circle G.
What is the area of Maria’s circle?
6Pi units squared
9Pi units squared
12Pi units squared
18Pi units squared
By definitions of the area of a circle and area ratios, we conclude that the area of the circle drawn by Maria is equal to a value of 18π units squared.
What is the area of the circle?
In this question we have a circle whose radius (r) is kwown. Besides, we know that Maria draws a circle with double the area of the prior circle. The area of the circle (A) is described by the following formula:
A = π · r² (1)
Then, we have that the area drawn by Maria is:
A = 2 · [π · 3²]
A = 18π
By definitions of the area of a circle and area ratios, we conclude that the area of the circle drawn by Maria is equal to a value of 18π units squared.
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Answer:
18π units squared
Step-by-step explanation:
On edge
Identify the category to which the following statement belongs: Brandon has two weeks to decide on the topic of his research paper.
O Not important - Not Urgent
O Not Important - Urgent
O Important - Not Urgent
O Important-Urgent
Answer:
Important- not urgent
Step-by-step explanation:
The research paper is important but since Brandon has two weeks to decide it is not urgent.
Can u answer fast please
C. e
Step-by-step explanation:
[tex] ln( {e}^{e} ) = e ln(e ) = e(1) = e[/tex]
Rewrite each of the following expressions without using absolute value: |x-5|+|x+5| if x<-5
For [tex]x < -5[/tex]:
[tex]x-5 < 0 \Rightarrow |x-5|=-(x-5)=-x+5\\x+5 < 0\Rightarrow |x+5|=-(x+5)=-x-5[/tex]
So
[tex]|x-5|+|x+5|=-x+5-x-5=-2x[/tex]
Use the parabola tool to graph the quadratic function f(x)=−(x−3)(x+1).
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
The parabola has roots at x=3 and x=-1, so its vertex is halfway between those points, at x=1, and so the y-coordinate of the vertex is -(1-3)(1+1)=4.
Another point that lies on the parabola is (-1, 0).
Which expression is equivalent to...
Step-by-step explanation:
hope you can understand
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
At West Painting, they get about three calls a day asking for an estimate of the cost for having the interior of a house painted. To write up an estimate for the cost of a job, they need to know how much paint a job will take. If they average painting of a room with of a gallon of paint, then they can paint, on average,
rooms per gallon.
Answer:
Using the ratio and proportion method, we find that on an average 1.875 rooms can be painted per gallon.
Step-by-step explanation:
Concept: Use the method of ratio and proportion.
In this method, if a relationship is given between two values, then using that relationship we can find another relationship with respect to another variable.
Given that for 2/5 gallons of paint, we can paint 3/4 of rooms. So, for one gallon of paint, divide 2/5 by 3/4.
2/5 gallons of paint = 3/4 rooms
1 gallon of paint = [tex]\frac{\frac{3}{4} }{\frac{2}{5} } = \frac{15}{8} =1.875[/tex] rooms
So, on an average they can paint 1.875 rooms per gallon.
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25. Which of the following expresses 374,274
in scientific notation?
(1)
(2)
(3)
3.74274 x 105
3.74274 x 106
37.4274 X 106
374.274
x 105
× 103
(4)
(5) 3742.74
Ite
Answer:
3
Step-by-step explanation:
374274 =3.74274 x 100000=3.74272x 10^5
Question
A company is considering producing some new Gameboy electronic games. Based on past records, management believes that there is a 70 percent chance that each of these will be successful and a 30 percent chance of failure. Market research may be used to revise these probabilities. In the past, the successful products were predicted to be successful based on market research 90 percent of the time. However, for products that failed, the market research predicted these would be successes 20 percent of the time. If market research is performed for a new product, what is the probability that the results indicate a successful market for the product and the product is actually not successful?
The probability that the results indicate a successful market for the product and the product is actually not successful is P=0.77.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
Events are given:
S: success
F: failure
MS: market research forecast a success
MF: market research forecast a failure
we have given:
P(S)=0.70
P(F)=0.30
P(S | MS)=0.90
P(F | MS)=0.20
we can derive that P(F | MF)=0.80.
We also can conclude that P(S | MF)=0.10.
We can calculate the probability of having a forecast of a failure,
[tex]P(MF | F) =\dfrac{ P(F | MF)P(F)}{ P(F | MF)P(F) + P(S | MS)P(S) }[/tex]
P (MF | F) = 0.24 / 0.31
P (MF | F) = 0.77
The probability that the results indicate a successful market for the product and the product is actually not successful is P=0.77.
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help fast please
i have no idea what to do in math so i need help
Answer:
see the attachment photo!
The sum of two numbers is ten. One number is twenty less than four times the other. Find the numbers
Answer:
6 and 4
Step-by-step explanation:
Let one number be x.
Then another will be : 4x - 20
In accordance with the question;
x + 4x - 20 = 10
5x = 10 + 20
x = 30/5
= 6
x = 6
4x - 20 = 4×6 - 20 = 4
So, the numbers are 6 and 4.
Help please
charles has $2.90 in coins. if he only has dimes and quarters and a total of 17 coins, how many quarts does he have?
Answer:
8
Step-by-step explanation:
8*25=2.00
2.00+.90=2.90
4. During a camping trip, a group went one-third of the total distance by boat, 10km by foot and One-sixth of it by riding horses. Find the total distance of the trip. Plss answer thiissss
Answer:
20 km
Step-by-step explanation:
So 1/3 = 2/6
2/6 = distance traveled by boat + 1/6 traveled by riding horses = 3/6 = 1/2
Meaning the 10 km by foot left is the other half
The planet Earth is about 193,000,000 miles away from the sun, and the speed of light is approximately 1.86 × 10 5 miles per second. Which expression could you use to figure out how many seconds it takes the light from the sun to reach Earth?
Answer:
Speed of light 186000 miles/second.
it takes 500 seconds (approx 8 minutes) for light from the sun to reach Earth.
Step-by-step explanation:
Earth travels around the sun in a slightly oval-shaped orbit, known as an ellipse. Therefore, the planet's distance from the sun changes throughout the year.
However, the average distance from Earth to the sun is about 93 million miles (150 million kilometres). Scientists also call this distance one astronomical unit (AU).
A universe is a big place, and sometimes researchers use astronomical units to communicate how far celestial objects are separated from one another. For example, Jupiter orbits about 5 AU from the sun.
The distance between the earth and the sun d= velocity of light × time taken to reach light from the sun to earth
Distance from Earth to Sun=93000000 miles.
Speed of light = 186000 miles/second.
=> [tex]\frac{93000,000}{186000}[/tex]
=> 500 seconds.
=> 8.333 minutes
it takes 500 seconds (approx 8 minutes) for light from the sun to reach Earth.
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[tex]3.135x 789[/tex]
Answer:
Step-by-step explanation:
Sum of 1/(1*2*3) + 1/(2*3*4) +....+1/(18*19*20)
Answer: 189/760
Step-by-step explanation:
The series can be represented in sigma notation as:
[tex]\sum^{18}_{n=1} \frac{1}{n(n+1)(n+2)}[/tex]
We can perform partial fraction decomposition as follows:
[tex]\frac{1}{n(n+1)(n+2)}=\frac{A}{n}+\frac{B}{n+1}+\frac{C}{n+2}\\\\ \implies 1=A(n+1)(n+2)+B(n)(n+2)+C(n)(n+1)[/tex]
If n = 0, then [tex]1=A(0+1)(0+2) \implies A=\frac{1}{2}[/tex]
If n = -1, then [tex]1=B(-1)(-1+2) \longrightarrow B=-1[/tex]
If n = -2, then [tex]1=C(-2)(-2+1) \longrightarrow C=\frac{1}{2}[/tex]
This means the series can be expressed as:
[tex]\sum^{k}_{n=1} \left(\frac{1}{2n}-\frac{1}{n+1}+\frac{1}{2(n+2)} \right)=\frac{k(k+3)}{4(k+1)(k+2)}[/tex]
Substituting in k=18,
[tex]\frac{18(21)}{4(19)(20}=\boxed{\frac{189}{760}}[/tex]