Which function family is represented by the table?
x -5 0 5 10 15 20 y 3 4 5 6 7 8
Answers
Domain ( Inputs ) Range (Outputs)
2, 5, 10. 6, 15 , 30
X Y
2. 6
5. 15
10. 30
Related Questions
a bus is full of passengers. if you count them by either twos, threes, or fives, there is one left. if you count them by seven there will be none left. find the least number of passengers in the bus?
Answers
The lowest multiple of 7 that is not a multiple of 2, 3 or 5 is 7
The next multiple after 7 that is not a multiple of 2, 3 or 5 is 49
7 x 1 = 7
7 x 2 = 14 ( can be divided by 2 )
7 x 3 = 21 ( can be divided by 3 )
7 x 4 = 28 ( can be divided by 2 )
7 x 5 = 35 ( can be divided by 5 )
7 x 6 = 42 ( can be divided by 2 )
7 x 7 = 49
In a sale, all normal prices are reduced by 15%
The normal price of a mixer is reduced by 22.50 dollars.
Work out the normal price of the mixer.
Answers
Answer:
The normal price of mixer is $150.
Step-by-step explanation:
Given that:
Normal prices are reduced by 15% in sale.
The normal price of mixer is reduced by $22.50
It means that it is the amount of discount.
Let,
x be the normal price of the mixer.
15% of x = 22.50
\(\frac{15}{100}x=22.50\\0.15x=22.50\)
Dividing both sides by 0.15
\(\frac{0.15x}{0.15}=\frac{22.50}{0.15}\\x=150\)
Hence,
The normal price of mixer is $150.
The normal price of the mixer is $150.
Given that,
In a sale, all normal prices are reduced by 15% The normal price of a mixer is reduced by 22.50 dollars.Based on the above information, the calculation is as follows;
Let us assume the normal price be x
15%x = 22.50
0.15x = 22.50
x = $150
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Write the slope-intercept form of the equation.Passes through (-1,-2) and parallel to y=-2x-1
Answers
Answer:
The slope-intercept form of the equation is;
\(y=-2x-4\)Explanation:
Given that the equation passes through;
\((-1,-2)\)And is parallel to the equation;
\(y=-2x-1\)We can derive the slope from the equation parallel to it;
\(m=-2\)Using the point-slope formula;
\(y=m(x-x_1)+y_1\)Substituting the point and the slope;
\(\begin{gathered} y=-2(x+1)-2 \\ y=-2x-2-2 \\ y=-2x-4 \end{gathered}\)Therefore, the slope-intercept form of the equation is;
\(y=-2x-4\)2+3×9+3×5=
help me..
Answers
Answer:
44
Step-by-step explanation:
2 + 3 * 9 + 3 * 5
=> 2 + 27 + 15
=> 29 +15
=> 44
Answer:
\(2 + 3 \times 9 + 3 \times 5 \\ = 2 + 27 + 15 \\ = 44 \\ thank \: you\)
a country's census lists the population of the country as 250 million in 1990, 282 million in 2000, and 310 million in 2010. fit a second-degree polynomial passing through these three points. (let the year 2000 be x = 0 and let p(x) represent the population in millions.)
Answers
The second-degree polynomial passing through these three points,
⇒ \(-0.02x^{2} + 3x + 282\)
According to the data given in the question,
Year Population
1990 250
2000 282
2010 310
According to the question let the year 2000,
⇒ x = 0
If 2000 = x,
Then,
1990 could be = -10
2010 could be = 10
As a coordinate, we could write them as:
(-10,250) (0,282) (10,310)
According to the equation,
y = \(ax^{2} + bx + c\)
Taking the coordinate with x = 0,
282 = \(a(0)^{2} + b(0) + c\)
282 = c
Taking the coordinate with x = +10
310 = \(a(10)^{2} + b(10) + c\)
310 = 100a + 10b + 282
100a + 10b = 28 ------- equation 1
Taking the coordinate with x = -10
250 = \(a(-10)^{2} + b(-10) + c\)
250 = 100a - 10b + 282
100a - 10b = -32 ------- equation 2
Solving the equations 1 and 2 for values of a and b,
Consider equation 1,
100a = 28 - 10b
a = \(\frac{28 - 10b}{100}\) -------- equation 3
Putting the value of an in equation 2,
10b = 100a + 32
10b = 100 ( \(\frac{28 - 10b}{100}\) ) + 32
10b = 28 - 10b + 32
b = \(\frac{28 + 32}{20}\)
b = 3
Putting the value of b in equation 3,
a = \(\frac{28 - (10 * 3)}{100}\)
a = -0.02
Quadratic equation = \(-0.02x^{2} + 3x + 282\)
Therefore, the second-degree polynomial passing through these three points,
⇒ \(-0.02x^{2} + 3x + 282\)
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The following probability distribution represents the payout for a certain dice game
x P(x)
−5 0.17
−3 0.21
−1 0.09
3 0.23
5 0.23
7 0.07
a.) What is the expected payout?
b.) Is it expected that a person playing this particular game will win money or lose money?
win money since the expected value is positive
lose money since the expected value is negative
c.) What is the standard deviation (round to four decimal places)?
Answers
The standard deviation by the given probability distribution is 3.3412.
What do you mean by standard deviation?In statistics, Standard deviation is a measure of the variation of a set of values.
σ = standard deviation of population
N = number of observation of population
X = mean
μ = population mean
We are given that;
x P(x)
−5 0.17
−3 0.21
−1 0.09
3 0.23
5 0.23
7 0.07
Now,
To find the standard deviation, we need to use the formula:
standard deviation = sqrt[∑(x - μ)²P(x)]
where μ is the expected payout.
We have already calculated μ to be 0.76. Using this value and the given probabilities, we can calculate the standard deviation as:
standard deviation = sqrt[( (-5 - 0.76)² * 0.17) + ((-3 - 0.76)² * 0.21) + ((-1 - 0.76)² * 0.09) + ((3 - 0.76)² * 0.23) + ((5 - 0.76)² * 0.23) + ((7 - 0.76)² * 0.07)]
=3.3412
Therefore, by the given data the standard deviation will be 3.3412.
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Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.
Answers
The general formula for quadractic expression is given as,
\(ax^2+bx+c\)The expression given is,
\(w^2-20w\)Comparing the two expressions.
where,
\(\begin{gathered} a=1 \\ b=-20 \\ c=\text{?} \end{gathered}\)To solve for c, which is the value that will be added to the expression to make it a perfect trinomial. We will apply discriminant formula.
\(b^2-4ac=0\)\(\begin{gathered} (-20)^2-4(1)c=0 \\ 400-4c=0 \\ 400=4c \\ \text{divide both sides by 4,} \\ \frac{400}{4}=\frac{4c}{4} \\ 100=c \\ \Rightarrow c=100 \end{gathered}\)The trinomial expression will now be,
\(\begin{gathered} w^2-20w+c \\ \text{where c=100} \\ w^2-20w+100 \end{gathered}\)Let us now factorize the expression inorder to write it as a binomial squared,
\(\begin{gathered} w^2-20w+100 \\ w^2-10w-10w+100 \\ w(w-10)-10(w-10) \\ (w-10)(w-10)=(w-10)^2_{} \end{gathered}\)Hence, the result as a binomial squared is,
\((w-10)^2_{}\)
The straight line shown below passes through the points (3, 1) and (8,36).
What is the gradient of this line?
Answers
Answer:
Step-by-step explanation: The gradient(slope) y-axis intercept form of a straight line is = mx +b, where m is the gradient(slope), b is the y-axis intercept we are given a gradient of -3, Therefore = -3x +buse the given point (-3, 5) to solve for b5 = -3(-3) + b5 = 9 +bb = -4 Therefore,y = -3x -4or3x +y +4 = 0
The spreadsheet shows exam scores for one class.
Find the mean for all Exam 2 scores. (Round to one decimal place.)
The mean for all Exam 2 scores, rounded to one decimal place, is approximately %.
Answers
Answer:
29.8%
Step-by-step explanation:
\(\frac{3+19+46+23+52+6+11+47+51+32+1+15+82}{13} \approx 29.8\%\)
Polygon ABCD is drawn with vertices A(−4, −4), B(−4, −6), C(−1, −6), D(−1, −4). Determine the image coordinates of B′ if the preimage is reflected across y = 3.
B′(−4, 6)
B′(−4, 12)
B′(−1, −3)
B′(10, −6)
Answers
To reflect a point across the line y=3, we find the point that is the same distance from y=3 as the original point, but on the opposite side of the line. In this case, the original point is B(−4,−6), which is 9 units below y=3. The image point will be 9 units above y=3, so it will have a y-coordinate of 3+9=12. The x-coordinate remains the same, so the image point is B
′
(−4,12).
PLEASE HELP ME PLEASE!!
Answers
Step-by-step explanation:
in such a case, where we have all the sides and need angles, the best tool is the extended Pythagoras (for general triangles and not just for right-angled ones) :
c² = a² + b² - 2ab×cos(C)
c is the side opposite of angle C.
the side opposite of B is CA.
so, we have
220² = 100² + 160² - 2×100×160×cos(B)
48,400 = 10,000 + 25,600 - 32,000×cos(B)
12,800 = -32,000×cos(B)
cos(B) = -12,800/32,000 = -0.4
B = 113.5781785...° ≈ 114°
Evaluate.
Remember Order of Operations!
(PEMDAS)
3+ 6 x 4 - 2
Answers
Answer:
25
Step-by-step explanation:
3+6×4-2
6×4=24
3+24-2
3+24=27
27-2=25
One half of 96 is equal to 80% of what number?
(A) 35
(B) 60
(C) 76
(D) 84
(E) 90
Answers
B
48=60x80%
Which is the following closet to 1/2+1/3
Answers
Answer:
0.5
Step-by-step explanation:
you have 1/2+1/3 so you take the numerator of the first fraction and multiply it, and do the same for the numerator of the second fraction. you should be left with 2 & 3. you add those two together and there is your answer. if i am wrong please tell me so i can find the mistake.
A 20-kilogram mass is attached to a spring. If the frequency of simple harmonic motion is 2/p cycles/s, what is the spring constant k? What is the frequency of simple harmonic motion if the original mass is replaced with an 80-kilogram mass?
Answers
Step-by-step explanation:
Frequency of a mass-spring system is:
f = √(k/m) / (2π)
Given f = 2/π Hz and m = 20 kg:
2/π Hz = √(k / 20 kg) / (2π)
4 Hz = √(k / 20 kg)
16 s⁻² = k / 20 kg
k = 320 kg/s²
k = 320 N/m
If the 20 kg mass is replaced with an 80 kg mass, the frequency is:
f = √(320 kg/s² / 80 kg) / (2π)
f = √(4 s⁻²) / (2π)
f = 2 Hz / (2π)
f = 1/π Hz
The sprint constant is 320 N/m
And, the frequency is \(1\div \pi Hz\)
Calculation of the spring constant & the frequency:Since A 20-kilogram mass is attached to a spring. And, the frequency of simple harmonic motion is 2/p cycles/s.
Now we know that
\(f = \sqrt (k\div m) \div (2\pi)\)
Here
\(f = 2\div \pi Hz\)
and m = 20 kg:
So,
\(2\div \pi Hz = \sqrt (k \div 20 kg) / (2\pi)\\\\4 Hz = \sqrt(k \div 20 kg)\\\\16 s^{-2} = k \div 20 kg\)
k = 320 kg/s²
k = 320 N/m
Now the frequency is:
\(f = \sqrt(320 kg/s^2 \div 80 kg) \div (2\pi)\\\\f = √(4 s^{-2}) \div (2\pi )\\\\f = 2 Hz \div (2\pi)\)
\(f = 1\div \pi Hz\)
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The local government is concerned with the population of a new predatory fish, the tiger gar, which was first observed in Lake Richmond about 5 years ago. The following table shows the approximate number of tiger gars living in the lake since 2016:
2016 2017 2018 2019 2020 2021
322 399 507 618 785 975
Using the TI-nspire calculator, write an exponential function that models the population of tiger gar in the lake. (Round all numbers to the nearest hundredth.)
y=blank(blank)x
Answers
The exponential function that models the population of tiger gar in the lake is given as follows:
\(y = 322.63(1.25)^x\)
How to define an exponential function?An exponential function has the definition presented as follows:
\(y = ab^x\)
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.Considering x as the number of years since 2016, the points are given as follows:
(0, 322), (1, 399), (2, 507), (3, 618), (4, 785), (5, 957).
Inserting these points into an exponential regression calculator, the equation is given as follows:
\(y = 322.63(1.25)^x\)
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Which equation is equivalent to this equation and written with the same base?
4x+1=16x−1
Answers
Answer:
\( 2^{2x + 2} = 2^{4x - 4} \)
Step-by-step explanation:
\( 4^{x + 1} = 16^{x - 1} \)
\( 2^{2(x + 1)} = 2^{4(x - 1)} \)
\( 2^{2x + 2} = 2^{4x - 4} \)
The function G(m) = 49.5m + 89.75 represents the cost of joining the gym in addition to the one time membership fee. The cost, G, is measured in dollars for m months. 1. Find the value of G(6).
Answers
Answer:
386.75
Step-by-step explanation:
added in the picture
The cost of joining the gym for 6 months is 386.75.
Given,
The function G(m) = 49.5m + 89.75 represents the cost of joining the gym in addition to the one-time membership fee.
The cost, G, is measured in dollars for m months.
We need to find the value of G(6).
Here,
The one-time membership = 89.75.
Now,
Putting m = 6 months in:
G(m) = 49.5m + 89.75
G(6) = 49.5 x 6 + 89.75
= 297 + 89.75
= 386.75
Thus the cost of joining the gym for 6 months is G(6) = 386.75.
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A competitor moved into your area in late April this year. Based on percent change, which location's volume has been most negatively impacted?
Location 21
Location 34
Location 57
Location 63
Answers
The location's volume has been most negatively impacted is Location 63: option D
What is volume of returns?The volume of returns display low extreme correlation, meaning that a stock market crash or a stock market boom can be associated with both large and small volumes.
The given table shows
Volume over time
Locations May April May
last year This year this year
location 21 296 278 248
location 34 376 324 336
location57 354 328 314
location 63 226 186 198
Totals 1252 1116 1096
Based on this table, the volume of returns from last year may to this year April, the location that has least volume is location 63 option D
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this question confuses me so much helpppppp
Answers
Answer:
-11°C or 1°C
Step-by-step explanation:
The question said that, by the noon, the temperature changes by 6°C, but it doesn't tell you if it changes for a hotter or colder temperature, so its possible the temperature at the noon to be:
-5 -6 = -11°C
or
-5 +6 = 1°C
To graph the possible temperatures, you have to draw a dot at the numbers -11 and 1
If f(x)=3x-1 find the following f(3) f(2)
Answers
Answer:
(4(f(2)
Step-by-step explanation:
If f(x(=3x-1 then f(3)f(2)
What’s the answers to this problem?
Answers
\(f(g(2))=f(2)=3 \\ \\ g(f(1))=g(2)=2 \\ \\ f(f(4))=f(2)=3\)
Question 1 of 5
The two best runners, Imani and Jack finished first and second. (20 points)
Extra Content
In each of the following sentences, exactly one comma is missing. Determine where the missing comma should be placed, and choose the correct answer.
A after best
B. after Jack
C. after first
Answers
"After first" will be the one comma that is lacking in this sentence. Imani and Jack, the two best runners, came in first and second, so that is the perfect phrase.
what is comma ?In order to create equilibrium, add a comma after a conjunction. We drove to the beach but turned around since there was no more space in the parking lot. The placement of a comma after a conjunction as opposed to before is one of the most frequent mistakes with commas: Nancy always found time despite having a busy schedule to visit the gym.
explanation :
If any of these seven coordinating conjunctions—and, but, for, or, nor, so, yet—are used to unite independent sentences, you should use commas to separate them.
Place commas after the preceding opening (a) sentences, (b) phrases, or (c) words.
"After first" will be the one comma that is lacking in this sentence. Imani and Jack, the two best runners, came in first and second, so that is the perfect phrase.
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given the quadratic function, find the x value of the vertex of y=x2=4x-8
Answers
Answer:
27x^2−9y^2=81
5. Given the right triangle JKL, identify the locations of sides j, k, and I in relation to angle L
in terms of opposite, adjacent, and hypotenuse.
HELP
Answers
In relation to the angle L of the right triangle the sides are as follows:
l = opposite sidek = hypotenusej = adjacentHow to name the side of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sides of a right angle triangle can be named according to the position of the angles in the right angle triangle.
The sides of a right triangle can also be solved by using Pythagoras's theorem or trigonometric ratios.
Let's identify the sides j, k, and I in relation to angle L in terms of opposite, adjacent, and hypotenuse.
Therefore,
l = opposite sidek = hypotenusej = adjacentThe hypotenuse side is the longest side of a right triangle.
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5. The denominator of a rational number is greater than its numerator by 7. If the numerator is increased by 17 and the denominator is decreased by 6, the new number becomes 2. find the original number.
Answers
Answer:
Let the fraction be qp
So q=p+7
q−6p+17=2
⇒p+7−6p+17=2
⇒p+1p+17=2
⇒p+17=2p+2
⇒p=15
q=15+7=22
So qp=2215.
Step-by-step explanation:
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Answer:
15/22.
Step-by-step explanation:
Let the denominator of original number be x.
Then the fraction is written as x/(x+7).
From the given info:-
(x+17)/ (x + 7 - 6) = 2
(x+17)/(x+1) = 2
2(x+1) = x+ 17
2x + 2 = x + 17
x = 17-2 = 15.
So the original number = x/x+7
= 15/22.
1. write a set of even numbers .
2. write a set of counting numbers.
3. write a set of odd number.
4. what is the length of the table .
5. what is the area of the table
Answers
1,2,3,4,5
6 foot
9 foot
cupcakes for $1.59 each. Last month they sold 24 less than the previous month. How much money did they lose?
Answers
Answer:
Calculate the loss which is 24 cupcakes:
Find the total price of the 24 cupcakes:
24 x 1.59 = 38.16
They incurred $38.16 in losses.
Perform the following mathematical operation and report the answer to the appropriate number of significant figures.
We know the least precise place value is in the 10's place.
67.4 +43 +30 + 42.10 = [?]
it's not 182.5 / 137.9 / 182
Answers
Answer:
200
Step-by-step explanation:
The sum is 182.5, which is 200 to 1 significant figure.
what should be added to 7 3/5 to get 18 (Step explanation )
Answers
