For a given function y = f(x), the domain is the set of the possible values of x that we can use in the function, and the range is the set of the possible values of y that the function can return.
We will find that the range is: {3, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63}
And the domain is: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Here the function is:
f(x) = 6*x + 3
Where x is the number of boxes sold.
We know that only 10 students bought popcorn, so what is reasonable domain and range?
Knowing that 10 students bought popcorn, we know that the maximum value that x can take is 10.
Then the domain will be:
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
These are the possible values of x that makes sense to use in our function.
We only use whole numbers as you can not buy a rational number of boxes.
To get the range we just need to evaluate the function in these values (the ones from the domain):
f(0) = 6*0 + 3 = 3
f(1) = 6*1 + 3 = 9
f(2) = 6*2 + 3 = 15
f(3) = 6*3 + 3 = 21
f(4) = 6*4 + 3 = 27
f(5) = 6*5 + 3 = 33
f(6) = 6*6 + 3 = 39
f(7) = 6*7 + 3 = 45
f(8) = 6*8 + 3 = 51
f(9) = 6*9 + 3 = 57
f(10) = 6*10 + 3 = 63
Then the range is just:
{3, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63}
If you want to learn more, you can read:
https://brainly.com/question/1632425
A rocket is stopped 34 feet from a satellite when it begins accelerating away from the satellite at a constant rate of 18 feet per second per second. The distance between the rocket and the satellite is given by the polynomial P(t) = 9t2 + 34. Find the distance between the rocket and the satellite 10 seconds after the rocket started moving.
Answer:
The distance between the rocket and the satellite 10 seconds after the rocket started moving is of 934 feet.
Step-by-step explanation:
The distance between the rocket and the satellite, in feet, after t seconds, is given by the following equation:
\(P(t) = 9t^{2} + 34\)
Find the distance between the rocket and the satellite 10 seconds after the rocket started moving.
This is P(10).
\(P(t) = 9t^{2} + 34\)
\(P(10) = 9*(10)^{2} + 34 = 934\)
The distance between the rocket and the satellite 10 seconds after the rocket started moving is of 934 feet.
Carlos has a box of coins that he uses when playing poker
with friends. The box currently contains 33 coins,
consisting of pennies, dimes, and quarters. The number of
pennies is equal to the number of dimes, and the total
value is $3.18. How many of each denomination of coin
does he have?
Number
Denomination of Coins Value
0.01
х 0.01x
х
0.25
33 3.18
The number of quarters is
The number of pennies, which is also equal to the number of dimes, is
(Simplify your answers.)
Answer:
so far i got 8 quarters 14 dimes and 13 pennies
Step-by-step explanation:
ill update you if i got any closer
=please finish this
Answer: 38
Step-by-step explanation:
Please answer this correctly
Answer:
24.99
Step-by-step explanation:
If the area of the quarter circle is 38.465, then the equation to find this would be
3.14*r^2 / 4 = 38.465. we solve for r, the radius, and get two solutions. 7 and -7. Obviously the length of the radius can't be -7, so we know the radius is 7.
Now we must solve for the perimeter. The perimeter is equal to 2r + (2*3.14*r)/4
Plugging 7 in as the radius, r, we get 24.99 as our final answer.
2(3x + 5) − 4(x − 1)
8,900 incoming freshman to a university take an entrance exam, with the top 10% being offered admission to the university's honors program. The average test score is 78%, with a standard deviation of 11%. Use a calculator to find what the student must score to be invited to join the honors program if only 65 scores are looked at to determine the honors admissions requirement.
Answer:
The student must score 79.75% to be invited to join the honors program.
Step-by-step explanation:
Let X denote the score of a freshman in the entrance exam.
It is provided that the average test score is 78%, with a standard deviation of 11%.
It is provided that the top 10% being offered admission to the university's honors program.
Let x denote the score eligible for being offered admission to the university's honors program.
Then, P (X ≤ x) = 0.90.
Then P (Z < z) = 0.90.
The corresponding z-score is, 1.28.
*Use a z-table.
Compute the value of x as follows:
\(z=\frac{x-\mu}{\sigma/\sqrt{n}}\\\\1.28=\frac{x-78}{11/\sqrt{65}}\\\\x=78+(1.28\times \frac{11}{\sqrt{65}})\\\\x=79.75\%\)
Thus, the student must score 79.75% to be invited to join the honors program.
2 over 3 divided by 6
Answer:
1/9
Step-by-step explanation: This is because 2/3 then you divide by 6 to get 1/6.
A historian wonders why an ancient civilization disappeared. He suggests that a natural disaster might have destroyed it thousands of years ago. What step should the historian take next?
Ask a question
Test the hypothesis
Draw a conclusion
Make an educated guess about what happened
ik its not math btw
Answer:
aaaaaaaaaaaaaaa
Step-by-step explanation:
it A
Answer:
A?
Step-by-step explanation:
What are some important features of a prism? In other words, what makes a prism a prism?
Answer:
A solid figure whose bases or ends have the same size and shape and are parallel to one another, and each of whose sides is a parallelogram.
Step-by-step explanation:
Answer:
I d k... give other guy brainiest though
At the tree farm, 9 rows of trees with 24 trees in each row were planted how many trees?
Answer:
24 times 9
Step-by-step explanation:
216 trees were planted
What is the square root of five
Answer:
2.24
Step-by-step explanation:
that's the square root of 5
Determine whether or not the given set is (a) open, (b) connected, and (c) simply-connected. 31. {(x, y) | 0
This set {(x, y) | 0 is (a) open, (b) connected, and (c) not simply-connected.
(a) Open: This set is open because all points within the set have a neighborhood that is also within the set.
(b) Connected: This set is connected because there is a path between any two points in the set that does not leave the set.
(c) Not simply-connected: This set is not simply-connected because it contains a hole in the center, which is not a simply-connected space.
Learn more about set here
https://brainly.com/question/12979762
#SPJ4
What is the intermediate step in the form (x+a)^2=b as a result of complementing the square for the following equations
The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.
To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.
Add the square of half of the coefficient of x to both sides of the equation:
x² + 2x + (2/2)² = 319 + (2/2)²
x² + 2x + 1 = 320
The left-hand side of the equation can now be factored as a perfect square:
(x+1)² = 320
This is the equation in the form (x+a)²=b, where a=1 and b=320.
Learn more about the perfect square here:
https://brainly.com/question/385286
#SPJ1
The complete question is as follows:
What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?
x² + 2x = 319
Is the formula V=LWH or V=BH or A=BH
PLEASE HELP!
Answer:
It's A=BH
Step-by-step explanation:
In the story the key words are there: Area, base/length, height
Answer:
It's A=BH
Step-by-step explanation:
The vector ⇀
= ⟨2, 3⟩ is multiplied by the scalar –4. Which statements about the components, magnitude, and direction of the scalar product –4⇀
are true? Select all that apply.
A. The component form of −4⇀
is ⟨–8, –12⟩.
B. The magnitude of −4⇀
is 4 times the magnitude of ⇀
.
C. The direction of −4⇀
is the same as the direction of ⇀
.
D. The vector −4⇀
is in the fourth quadrant.
E. The direction of −4⇀
is 180° greater than the inverse tangent of its components.
Answer:
Therefore, the correct statements are A, B, and E.
Explanation:
Based on my knowledge, a vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude. When a vector is multiplied by a scalar, the magnitude of the vector is multiplied by the absolute value of the scalar, and the direction of the vector is either preserved or reversed depending on the sign of the scalar.
To answer your question, we need to find the component form, magnitude, and direction of the scalar product –4⇀
.
- The component form of −4⇀
is obtained by multiplying each component of ⇀
by –4. Therefore, −4⇀
= ⟨–8, –12⟩. This means that statement A is true.
- The magnitude of −4⇀
is obtained by multiplying the magnitude of ⇀
by 4. The magnitude of ⇀
is √(2^2 + 3^2) = √13. Therefore, the magnitude of −4⇀
is 4√13. This means that statement B is true.
- The direction of −4⇀
is opposite to the direction of ⇀
because the scalar –4 is negative. This means that statement C is false.
- The vector −4⇀
is in the third quadrant because its components are both negative. This means that statement D is false.
- The direction of −4⇀
is 180° greater than the inverse tangent of its components because it is opposite to ⇀
. The inverse tangent of its components is tan^(-1)(–12/–8) = tan^(-1)(3/2). Therefore, the direction of −4⇀
is 180° + tan^(-1)(3/2). This means that statement E is true.
Therefore, the correct statements are A, B, and E.
Write the expression using only positive exponents. Assume no denominator equals zero. (-2m^3n^7)^-5
We can rewrite the expression with positive exponents:\((-2m^3n^7)^{-5} = 1 / (-32m^15n^{35})\)
How to Write the expression using only positive exponents.To rewrite the expression\((-2m^3n^7)^{-5}\) using only positive exponents, we can apply the rule of negative exponents:
\((-2m^3n^7)^{-5} = 1 / (-2m^3n^7)^5\)
To convert the negative exponent to a positive exponent, we take the reciprocal of the base and change the sign of the exponent:
\(1 / (-2m^3n^7)^5 = 1 / ((-2)^5 * (m^3)^5 * (n^7)^5)\)
Now, we can simplify further:
\(1 / ((-2)^5 * (m^3)^5 * (n^7)^5) = 1 / (-32 * m^{15} * n^{35})\)
Finally, we can rewrite the expression with positive exponents: \((-2m^3n^7)^{-5} = 1 / (-32m^{15n}^{35})\)
Learn more about expression at https://brainly.com/question/1859113
#SPJ9
50 - [ 7 + ( 3^(2) / 2 ) ]
Step by step please
Answer:
evaluation : 38.5 38.5 is the answer because you simplify this term
Step-by-step explanation:
the home plate in baseball which is a Pentagon has three right angle. the other two angles are equal. find the measure of each missing angle.
Answer:
Missing angle = 135°
Step-by-step explanation:
Given:
Pentagon shape
Number of right angle = 3
Remain two angles are equal
Computation:
Sum of Pentagon angles = 540°
So,
90 + 90 + 90 + a +a = 540
270 + 2a = 540
a = 135°
Missing angle = 135°
Plz help and explain if this is a parallelogram
Answer:
It is a parallelogram!
Step-by-step explanation:
This is because it has four sides and all the sides have parallel lines if that makes sence.
Find the measure of the following numbered angles and the reason: Measure Reason 1 1 3 1 m
Student unresponsive. Information incomplete.
x + 20 ≤ -10 please help progress leraning
The value of x for the given expression, x + 20 ≤ -10 will be -30. The value of x is obtained by applying the arithmetic operation.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.
It is given that the expression is,
x + 20 ≤ -10
Rearrange the expression as
x≤ -10-20
x≤ -30
Thus, the value of x for the given expression, x + 20 ≤ -10 will be -30. The value of x is obtained by applying the arithmetic operation.
Learn more about inequality here:
brainly.com/question/19491153
#SPJ1
A research company desires to know the mean consumption of meat per week among people over age 32
. They believe that the meat consumption has a mean of 3
pounds, and want to construct a 80%
confidence interval with a maximum error of 0.09
pounds. Assuming a standard deviation of 1
pounds, what is the minimum number of people over age 32
they must include in their sample? Round your answer up to the next integer.
The minimum number οf peοple οver age 32 they must include in their sample is 225.
What is Standard deviatiοn?The definition of standard deviation is: A measure of how widely spaced out numbers are. The Variance, which is the average of the squared deviations from the Mean, determines what it is square root of.
The following formula can be used to determine the minimal sample size required to construct an 80% confidence interval with a maximum error of 0.09 pounds and a population standard deviation of 1 pounds:
n = (Z * σ / E)²
First, we need tο find the value οf Z.
Next, we can plug in the values we have intο the fοrmula and sοlve fοr n:
n = (1.28 * 1 / 0.09)²
n ≈ 224.6
Therefοre, the minimum number οf peοple οver age 32 they must include in their sample is 225.
To know more about Standard deviation visit,
https://brainly.com/question/475676
#SPJ1
Convert the following equation into
standard form.
y = -5x + 2
5x + [?]y = [ ]
Answer:
standard form is Ax + by + c = 0
Step-by-step explanation:
add 5x to each side to get 5x + y - 2 = 0
PLS HELP FAST I NEED HELP
Answer:
50 snail shells
Step-by-step explanation:
Which expression would be easier to simplify if you used the associative
property to change the grouping?
A. 0.85+ (0.15 +(-3)
B. [(-3)+(-3)] +(-3)
C. (160 + 40 + 27
O D. 1+*+(-))
SUBMIT
P
Answer:
A . 0.85 + (0.15 +(-3)) = -2
B . [(-3)+(-3)]+(-3) = - 9
Step-by-step explanation:
Explanation:-
Associative property with addition
(a+(b+c)) = (a+b) + c
A)
Given 0.85 + (0.15 +(-3)) = (0.85 +0.15)+(-3)
= 1 - 3
= -2
B) Given [(-3)+(-3)]+(-3) = ( (-3)+[( -3)+(-3))]
= ( -3 +[-3-3]
= -3 -6
= -9
Final answer:-
A . 0.85 + (0.15 +(-3)) = -2
B . [(-3)+(-3)]+(-3) = - 9
x + 7 -3 = 1 A) -10 B) - 22 3 C) - 3 7 D) 4
The answer would be x = -3
Find the approximate side length of a square game board with an area of 173in
Answer:
It's 13.15
I don't really have a explanaton sorry.
So
Area=side²side²=173side=√173side=13.15inwhat is 38-12x3 equal
Answer: 2
Step-by-step explanation: 12 x 3 first becuase pemdas
A store has clearance items that have been marked down by 50%. They are having a sale, advertising an additional 45% off clearance items. What percent of the original price do you end up paying?
bTo determine the percent of the original price you end up paying after the discounts, we can calculate the final price as a percentage of the original price.
Let's assume the original price of an item is $100.
The first discount reduces the price by 50%, so the price after the first discount is 50% of the original price, which is $100 * 0.5 = $50.
The second discount of 45% is applied to the price after the first discount. The price after the second discount is 45% of $50, which is $50 * 0.45 = $22.50.
Therefore, the final price you end up paying after both discounts is $22.50.\
To find the percent of the original price you end up paying, we divide the final price by the original price and multiply by 100:
Percent of original price = (final price / original price) * 100
In this case, the final price is $22.50 and the original price is $100:
Percent of original price = ($22.50 / $100) * 100
= 0.225 * 100
= 22.5%
Therefore, you end up paying 22.5% of the original price after the discounts.
It's important to note that the percent of the original price you end up paying will depend on the original price of the item. The calculations above were based on the assumption that the original price was $100. If the original price is different, the resulting percentage will vary accordingly.
For more such questions on discounts
https://brainly.com/question/28420607
#SPJ8
in the form, y=a(1+r)^t PLEASEEEEEE
Answer:
y
a= ——
(r + 1 )t
Step-by-step explanation:
divide both sides