A movie theater sells popcorn in bags of different sizes. The table shows the volume of popcorn and the price of the bag. If the theater wanted to offer a 60-ounce bag of popcorn, what would be a good price? Explain your reasoning
Answers
Answer:
For a volume of 60 ounces, the appropriate price is $16
Step-by-step explanation:
Firstly, we need to determine the relationship between volume of popcorn and the price of bag.
Let us try and see if there is a linear relationship
A linear model is of the form ;
y = mx + b
where m is the slope and b is the y intercept
While the price represents the y axis values, the volume represents the x axis values
For the slope;
m = (y2-y1)/(x2-x1)
m = (13.6-11)/(48-35) = 2.6/13 = 0.2
So we have the slope value as 0.2
the equation is;
y = 0.2x + b
to get b, substitute any value of (x,y)
6 = 0.2(10) + b
6 = 2 + b
b = 6-2 = 4
If we had substituted (20,8)
8 = 0.2(20) + b
8 = 4 + b
b = 4
if (48,13.6)
13.6 = 48(0.2) + b
13.6 = 9.6 + b
b = 13.6-9.6
b = 4
Hence we have established linear relationship between the volume in ounces and the price in $
So we have this as
Price = 0.2(volume) + 4
So for volume of 60 ounces;
Price = 0.2(60) + 4
price = 12 + 4
price = $16
The reason why this is appropriate is because it follows the rule of the established linear relationship
Answer:
$16
Step-by-step explanation:
Related Questions
An amusement park sells adult tickets and children’s tickets, with adults tickets costing $5 and children’s tickets costing $3. If Ed bought 15 tickets and spent a total of $57, how many children’s tickets did he buy?
Answers
Answer:
9 children tickets
Check:
adult is 5$
child3$
6×5=30
9×3=27
30+27=57
Step by step in photo
Answer:
the answer is 6
Step-by-step explanation:
Answer please i need help
Answers
separation of powers
freedom of speech, religion, and the press
the right to life, liberty, and the pursuit of happiness
universal voting rights
(2x - 24) + (5x - 27) = 180
7x -51 = 180
7x = 231
x = 33
mB = 5x - 27 = 5(33) - 27 = 138
The measure of angle B is 138 degrees.
There are 3 green apples and 8 red apples in a basket what is the ratio of the red apples and the green to all the apples in the basket a. ratio for red b. ratio for green
Answers
Answer:
The answer is 3:8 or 3 to 8
Step-by-step explanation:
What is the mean for this set of data? {3, 5, 8, 11, 11, 12} question 4 options:
a. 8
b. 8.33
c. 11
d. 9.5
Answers
Answer:
b. 8.33
Step-by-step explanation:
"mean" is the math word for what non-math people call average. This is where you add up all the numbers and divide by however many there are.
3+5+8+11+11+12 is 50
There are 6 numbers in the data set. So 50/6 is 8.3333...
b. 8.33 is the correct answer.
Mean means add and divide.
2. The perimeter of a rectangular park is 640 yards. The length of the rectangle is 40 yards less than twice the width. What are the dimensions of the park?
Answers
The dimensions of the park are obtained as 180 yards and 140yards respectively.
What is a Linear equation?A linear equation is a equation that has degree as one.
To find the solution of n unknown quantities n number of equations with n number of variables are required.
Suppose the width of the rectangle be x yards.
Then, its length is given as x - 40 yards.
Since, the perimeter of a rectangle is given as 2(l + b).
Substitute the corresponding values to get the equation as follows,
640 = 2(x - 40 + x)
=> 640 = 2(2x - 40)
=> 2x - 40 = 640/2
=> 2x - 40 = 320
=> x = 360/2 = 180
Then, the length is given as 180 - 40 = 140 yards.
Hence, the dimensions of the park are obtained as 180 yards and 140 yards respectively.
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Last year, Jora spent
30% of his salary on rent
2⁄5 of his salary on entertainment
¼ of his salary on living expenses.
He saved the rest of his salary.
Jora spent £3600 on living expenses.
Work out how much money he saved.
Answers
Answer:
Saved Money = 189.47
Step-by-step explanation:
find the sum percent of how much he spent:
30% + 40%+ 25% = 95%
Given That:
95% = 3600
So, he saved only 5%
5% = 3600/19 = 189 pounds
Hope this helps
14. The dimensions of a fish tank are x-3, x-4, and x-2. The fish tank has a volume of
23x + 3 cubic units.
a. C2P1: Write a polynomial equation in standard form to represent the volume of
the tank.
b. C2P2: Solve your equation for x.
C. C2P2: What are the dimensions of the fish tank?
Answers
The polynomial equation in standard form representing the volume of the fish tank is \(V = x^3 - 9x^2 + 26x - 24\). Solving the equation gives x = 3 or x = 3 ± √6. The dimensions of the tank are √6, √6 - 1, and √6 - 3 for x = 3 + √6, and -√6, -√6 - 1, and -√6 + 3 for x = 3 - √6.
Given dimensions of a fish tank: x-3, x-4, and x-2. Volume of the tank: 23x+3 cubic units.
We need to write a polynomial equation in standard form to represent the volume of the tank.
Also, we need to solve that equation to get the value of x.
Finally, we will find the dimensions of the fish tank.
a) Volume of the tank is given by: V = l × w × h.
Here, l = x-3, w = x-4, and h = x-2.
So, V = (x-3) × (x-4) × (x-2)
Simplifying this expression, we get \(V = x^3 - 9x^2 + 26x - 24\).
Now, we can write the equation in the standard form: \(V = x^3 - 9x^2 + 26x - 24\).
b) We have to solve the equation \(V = x^3 - 9x^2 + 26x - 24\) to get the value of x.
We have \(V = 23x + 3.\\So, x^3 - 9x^2 + 26x - 24 = 23x + 3 x^3 - 9x^2 + 3x - 27 = 0\)
We can see that x = 3 is a root of this equation.
Using synthetic division, we can factorize the equation as:\((x-3)(x^2 - 6x + 9) = 0x = 3, or x = 3 \pm \sqrt6\)
The value of x is either 3 or 3 ± √6.
c) The dimensions of the tank are (x-3), (x-4), and (x-2).
We have to substitute the value of x in these dimensions. We have two values of x: x=3 and x = 3 ± √6
When x = 3, the dimensions are: 0, -1, and 1.
But these are not possible as dimensions cannot be negative.
When x = 3 + √6, the dimensions are: √6, √6 - 1, and √6 - 3
When x = 3 - √6, the dimensions are: -√6, -√6 - 1, and -√6 + 3
We can see that the dimensions of the fish tank are √6, √6 - 1, and √6 - 3 when x = 3 + √6, and -√6, -√6 - 1, and -√6 + 3 when x = 3 - √6.
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Find the values of x and y in parallelogram PQRS. PTy, TRx1, QTy, TSx = 7x+ 11
Answers
The values of x and y of the parallelogram PQRS are x = 2 and y = 11
What is the side length of the parallelogram?We're given the dimensions of parallelogram PQRS as;
PT = y
TR = 5x + 1
QT = 2y
TS = 6x + 10
T is the intersection of the two diagonals PR and QS and so the diagonals bisect each other.
The diagonal PR is cut into PT and TR, both of which are congruent or equal. Thus, PT = TR.
Similarly, the other diagonal QS is split in half as well. The two equal pieces are QT and TS. So QT = TS.
PT = TR
y = 5x + 1
and
QT = TS
2y = 6x + 10
Plugging the values gives;
2y = 6x + 10
2(y) = 6x + 10
2(5x + 1) = 6x + 10
2*5x + 2*1 = 6x + 10
10x + 2 = 6x + 10
10x + 2 - 6x = 6x + 10 - 6x
4x + 2 = 10
4x + 2 - 2 = 10 - 2
4x = 8
4x/4 = 8/4
x = 2
If x = 2, then y is...
y = 5x+1
y = 5*x+1
y = 5*2+1
y = 10+1
y = 11
Thus, the values of x and y of the parallelogram PQRS are x = 2 and y = 11
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please help if u can like fast too
Answers
Answer:
-3-x=27
Step-by-step explanation:
Answer:
x= -30
Step-by-step explanation:
Multiply both sides of the equation by -1
Move the constant to the right
Now calculate x= -27-3
:)
Find an expression to represent the area
of the trapezoid below.
Answers
1. Compute the following sums.
a) $1+3+5+7+\ldots+999$
b) $\sum_{i=4}^n 1$
c) $\sum_{i=4}^{n+1} i$
2. Use the Euclid's algorithm to find gcd between 46415 and 13142 (10)
3. Write a pseudocode for an algorithm for finding real roots of equation $a x^2+b x+c=0$ for arbitrary real coefficients $a, b$, and $c$. (You may assume the availability of the square root function $\operatorname{sqrt}(x)$.)
(10)
4. Describe the algorithm used by your favorite ATM machine in dispensing ca Give your description in a pseudocode.
$(10$
5. Analyse the following algorithm,
Answers
The ATM machine uses a predefined set of denominations. It then updates the remaining amount and moves to the next lower denomination until the remaining amount becomes zero. Finally, it dispenses the required number of notes for each denomination.
1. Compute the following sums:
a) To find the sum of the odd numbers from 1 to 999, we can observe that these numbers form an arithmetic sequence with a common difference of 2. The formula for the sum of an arithmetic sequence can be used to calculate the sum:
\[S = \frac{n}{2}(a + l)\]
where \(n\) is the number of terms, \(a\) is the first term, and \(l\) is the last term.
In this case, \(n = \frac{999-1}{2} + 1 = 500\), \(a = 1\), and \(l = 999\).
Plugging these values into the formula:
\[S = \frac{500}{2}(1 + 999) = 250(1000) = 250,000\]
b) The sum \(\sum_{i=4}^n 1\) represents adding 1, \(n-3\) times. Therefore, the sum is equal to \(n-3\).
c) The sum \(\sum_{i=4}^{n+1} i\) represents adding the numbers from 4 to \(n+1\). This can be computed using the sum formula for an arithmetic sequence:
\[S = \frac{n}{2}(a + l)\]
where \(n\) is the number of terms, \(a\) is the first term, and \(l\) is the last term.
In this case, \(n = (n+1) - 4 + 1 = n - 2\), \(a = 4\), and \(l = n+1\).
Plugging these values into the formula:
\[S = \frac{n-2}{2}(4 + n+1) = \frac{n-2}{2}(n+5)\]
2. Euclid's algorithm to find the greatest common divisor (gcd) between 46415 and 13142:
The algorithm repeatedly divides the larger number by the smaller number and replaces the larger number with the remainder until the remainder is 0. The last non-zero remainder is the gcd.
Pseudocode:
```
function gcd(a, b):
while b ≠ 0:
temp = b
b = a mod b
a = temp
return a
```
Applying Euclid's algorithm to the given numbers:
\[
\begin{align*}
a & = 46415, \\
b & = 13142.
\end{align*}
\]
Iteration 1:
\[
\begin{align*}
a & = 13142, \\
b & = 46415 \mod 13142 = 6341.
\end{align*}
\]
Iteration 2:
\[
\begin{align*}
a & = 6341, \\
b & = 13142 \mod 6341 = 474.
\end{align*}
\]
Iteration 3:
\[
\begin{align*}
a & = 474, \\
b & = 6341 \mod 474 = 37.
\end{align*}
\]
Iteration 4:
\[
\begin{align*}
a & = 37, \\
b & = 474 \mod 37 = 29.
\end{align*}
\]
Iteration 5:
\[
\begin{align*
}
a & = 29, \\
b & = 37 \mod 29 = 8.
\end{align*}
\]
Iteration 6:
\[
\begin{align*}
a & = 8, \\
b & = 29 \mod 8 = 5.
\end{align*}
\]
Iteration 7:
\[
\begin{align*}
a & = 5, \\
b & = 8 \mod 5 = 3.
\end{align*}
\]
Iteration 8:
\[
\begin{align*}
a & = 3, \\
b & = 5 \mod 3 = 2.
\end{align*}
\]
Iteration 9:
\[
\begin{align*}
a & = 2, \\
b & = 3 \mod 2 = 1.
\end{align*}
\]
Iteration 10:
\[
\begin{align*}
a & = 1, \\
b & = 2 \mod 1 = 0.
\end{align*}
\]
The gcd is the last non-zero remainder: gcd(46415, 13142) = 1.
3. Pseudocode for finding real roots of a quadratic equation \(a x^2 + b x + c = 0\):
```
function findRealRoots(a, b, c):
discriminant = b^2 - 4*a*c
if discriminant < 0:
print "No real roots"
else if discriminant == 0:
root = -b / (2*a)
print "One real root:", root
else:
root1 = (-b + sqrt(discriminant)) / (2*a)
root2 = (-b - sqrt(discriminant)) / (2*a)
print "Two real roots:", root1, root2
```
4. Description of the algorithm used by an ATM machine for dispensing cash:
Pseudocode:
```
function dispenseCash(amount):
denominations = [100, 50, 20, 10, 5, 1] // available denominations
remainingAmount = amount
for denomination in denominations:
count = remainingAmount / denomination // number of notes of the current denomination
remainingAmount = remainingAmount % denomination // remaining amount to be dispensed
print "Dispense", count, "notes of", denomination
```
The ATM machine uses a predefined set of denominations. It starts with the highest denomination and calculates the number of notes of that denomination required to dispense the amount. It then updates the remaining amount and moves to the next lower denomination until the remaining amount becomes zero. Finally, it dispenses the required number of notes for each denomination.
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1. Find the length of the missing side. Leave your answer in simplest radical form (1 point)
The triangle is not drawn to scale.
025
0144
05
3
√√5
Answers
The missing side of the given triangle is 5 units.
Given, a right angled triangle with height and base 3 and 4 respectively.
So, Height = 3 units and Base = 4 units
Let the hypotenuse or the missing side be h,
On applying the Pythagoras Theorem, we get
h² = (Height)² + (Base)²
h² = 3² + 4²
h² = 9 + 16
h² = 25
h = √25
h = 5
Hence, the missing side of the given triangle is 5 units.
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15
Find the values of x in this equation: x-
-= 2.
х
A.
-7,3
B.
-5, 2
C.
-7,5
D.
-2,5
E.
-3,5
Reset
Next
Answers
Answer:
Option (E)
Step-by-step explanation:
Expression given in the attachment,
\(x-\frac{15}{x}=2\)
By multiplying with x on both the sides of the given equation,
x² - 15 = 2x
x² - 2x - 15 = 0
x² - 5x + 3x - 15 = 0
x(x - 5) + 3(x - 5) = 0
(x + 3)(x - 5) = 0
(x + 3) = 0
x = -3
And (x - 5) = 0
x = 5
Therefore, x = -3, 5 are the solutions of the given equation.
Option (E) will be the answer.
Find the 16th term of the arithmetic sequence whose common difference is d=9 and whose first term is a, = 1.
Answers
Answer: 136
Step-by-step explanation:
a + ( 16 - 1 ) da + 15 d( 1 )
a = 1
d = 9
1 + 15 ( 9 )
1 + 135
136
Answer:
a₁₆ = 136
Step-by-step explanation:
the nth term of an arithmetic sequence is
\(a_{n}\) = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 1 and d = 9 , then
a₁₆ = 1 + (15 × 9) = 1 + 135 = 136
Please answer it in two minutes
Answers
Answer:
cot B = 48/55
Step-by-step explanation:
cot B = 48/55
what is the difference between the points (-3,4) and (-3,-5)?
Answers
The difference between the points (-3, 4) and (-3, -5) is (0, 9)
Brainliest?? ;D
A company expects that the number N(x) of a product sold during a week is related to the amount spent on advertising by the function N(x)=-6x3+180x²+2250x + 13,000, where x (with 0 ≤x≤25) is the amount spent on advertising in thousands of dollars. What is the point of diminishing returns?
The point of diminishing returns is
(Simplify your answer. Type an ordered pair. Do not use commas in the individual coordinates.)
Answers
The point of diminishing returns is (20.98, 21247.3).
The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.
Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.
The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:
0 = -18x² + 360x + 2250
Dividing by -18 simplifies the equation:
0 = x² - 20x - 125
Using the quadratic formula, we find the solutions to the equation:
x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)
x₁,₂ = 10 ± 5√5
Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.
To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:
N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8
N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8
From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.
To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).
Hence, the point of diminishing returns is approximately (20.98, 21247.3).
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PLZ PLZ PLZ I NEED HELP!!!!
Answers
Answer:
The answer is B
Step-by-step explanation:
Divide the distance by the time.
A box is to be made out of a 10 cm by 20 cm piece of cardboard. Squares of side length cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top. (a) Express the volume V of the box as a function of x. V = cm^3 (b) Give the domain of V in interval notation. (Use the fact that length and volume must be positive.) = ? (c) Find the length L , width W, and height H of the resulting box that maximizes the volume. (Assume that W < or = to L ) L= ?cm W= ?cm H= ? cm (d) The maximum volume of the box is ? cm^3.
Answers
(a) The volume V of the box as a function of x is V = 4x^3-60x^2+200x
(b) The domain of V in interval notation is 0<x<5,
(c) The length L , width W, and height H of the resulting box that maximizes the volume is H = 2.113, W = 5.773, L= 15.773
(d) The maximum volume of the box is 192.421 cm^2.
In the given question,
A box is to be made out of a 10 cm by 20 cm piece of cardboard. Squares of side length cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top.
(a) We have to express the volume V of the box as a function of x.
If we cut out the squares, we'll have a length and width of 10-2x, 20-2x respectively and height of x.
So V = x(10-2x) (20-2x)
V = x(10(20-2x)-2x(20-2x))
V = x(200-20x-40x+4x^2)
V = x ( 200 - 60 x + 4x^2)
V = 4x^3-60x^2+200x
(b) Now we have to give the domain of V in interval notation.
Since the lengths must all be positive,
10-2x > 0 ≥ x < 5 and x> 0
So 0 < x < 5
(c) Now we have to find the length L , width W, and height H of the resulting box that maximizes the volume.
We take the derivative of V:
V'(x) = 12x^2-120x+200
Taking V'(x)=0
0 = 4 (3x^2-30x+50)
3x^2-30x+50=0
Now using the quadratic formula:
x=\(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
From the equationl a=3, b=-30, c=50
Putting the value
x=\(\frac{30\pm\sqrt{(-30)^2-4\times3\times50}}{2\times3}\)
x= \(\frac{30\pm\sqrt{900-600}}{6}\)
x= \(\frac{30\pm\sqrt{300}}{6}\)
x= \(\frac{30\pm17.321}{6}\)
Since x<5,
So x= \(\frac{30-17.321}{6}\)
x= 2.113
So H = 2.113, W = 5.773, L= 15.773.
d) Now we have to find the maximum volume of the box.
V = HWL
V= 2.113*5.773*15.773
V = 192.421 cm^3
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What is a requirement of the data in order for us to be allowed to control for individual variability?.
Answers
Statistics help present data precisely and draw meaningful conclusions. While presenting data, one should be aware of using adequate statistical measures.
Readers are generally interested in knowing the variability within the sample, descriptive data should be precisely summarized with SD. The use of SEM should be limited to computing CI which measures the precision of population estimate. Journals can avoid such errors by requiring authors to adhere to their guidelines.
Studying the entire population is time and resource-intensive and not always feasible; therefore studies are often done on the sample, and data are summarized using descriptive statistics. These findings are further generalized to the larger, unobserved population using inferential statistics.
For example, to understand the cholesterol levels of the population, the cholesterol levels of the study sample, drawn from the same population are measured.
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the coordinate plane, we can calculate the slope of the line through these points using the following formula. Slope = Δy Δx = b2 − b1 a2 − a1 Find the point where the line through (5, 2) with slope 4 crosses the vertical axis. (x, y) =
Answers
The point where the line through (5, 2) with slope 4 crosses the vertical axis is (0, -18).
To do this, we can use the point-slope form of a line equation:
y - y1 = m(x - x1)
Here, (x1, y1) is the given point (5, 2) and m is the slope, which is 4. Let's plug in these values:
y - 2 = 4(x - 5)
Now, we need to find the point where the line crosses the vertical axis (y-axis). When a point is on the y-axis, its x-coordinate is 0. So, we will substitute 0 for x and solve for y:
y - 2 = 4(0 - 5)
y - 2 = -20
y = -20 + 2
y = -18
Therefore, the point where the line through (5, 2) with slope 4 crosses the vertical axis is (0, -18).
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Simplify 5^2 • 5^4
O A. 5^8
O B. 5^6
O C. 5•8
O D. 5^2
Answers
Work:
You add 2 and 4 and get 6. Thus your answer is 5^6
Match each pair of inverse operations.
1. cubing
subtraction
2. multiplication
division
3. squaring
taking the square root
4. addition
taking the cube root
Answers
squaring- taking the square root
addition- subtraction
multiplication- division
Find the critical values, absolute maximum and absolute minimum values off on the given
interval.
a5(a)=3x^4-4x^3-12x^2+1,[-2,3]
Answers
To find the critical values, we first take the derivative of the function:
a5'(x) = 12x^3 - 12x^2 - 24x
Then, we set this equal to 0 and solve for x:
12x^3 - 12x^2 - 24x = 0
Simplifying this equation, we get:
12x(x^2 - x - 2) = 0
Using the zero product property, we can solve for x:
x = 0, x = -1, x = 2
These are our critical values.
Next, we need to evaluate the function at these critical values and the endpoints of the given interval:
a5(-2) = 113, a5(0) = 1, a5(-1) = 8, a5(2) = -35, a5(3) = 316
Therefore, the absolute maximum value of the function on the given interval is 316, and it occurs at x = 3. The absolute minimum value of the function on the given interval is -35, and it occurs at x = 2.
To find the critical values, absolute maximum, and absolute minimum of the function f(x) = 3x^4 - 4x^3 - 12x^2 + 1 on the interval [-2, 3], we first need to find the critical points by taking the derivative of the function and setting it to zero.
f'(x) = 12x^3 - 12x^2 - 24x (by differentiating f(x))
Now, set f'(x) to zero and solve for x:
12x^3 - 12x^2 - 24x = 0
x(12x^2 - 12x - 24) = 0
x(2x^2 - 2x - 4) = 0
To find the critical points, solve for x in the equation above. After that, evaluate the original function f(x) at each critical point and the endpoints of the interval, -2 and 3. Compare the function values to determine the absolute maximum and minimum.
Please note that without the exact solutions for x, I can't provide the absolute maximum and minimum values.
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what is the perpendicular slope of y=4x-6 ?
Answers
Answer:
-1/4
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals of each other.
Simplify the following expression.
2x + 3x³ -5x² + x² +7x+1+7x5 -3x³-4
A. 9x - 4x +7x+5
B. 9x5 +6x +7x+3
C. 5x5 +5x +7x-3
D. 9x - 4x +7x-3
Answers
Answer:
c
Step-by-step explanation:
The answer is 9x⁵+7x-4x²-3
What is a polynomial expression?Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial.
Given here: The polynomial expression 2x⁵ + 3x³ -5x² + x² +7x+1+7x⁵ -3x³-4
On simplifying we get 2x⁵ + 3x³ -5x² + x² +7x+1+7x5 -3x³-4= 9x⁵+7x-4x²-3
Hence, The answer is 9x⁵+7x-4x²-3
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Assume that police estimate that 23% of drivers do not wear their seatbelts. They set up a safety roadblock, stopping cars to check for seatbelt use. They stop 20 cars during the first hour a. Find the mean, variance, and standard deviation of the number of drivers expected not to be wearing seatbelts. Use the fact that the mean of a geometric distribution is pi = 1/p and the variance is ohm^2 = p/q^2? b. How many cars do they expect to stop before finding a driver whose seatbelt is not buckled?
Answers
The mean of the number of drivers expected not to be wearing seatbelts is approximately 4.35, the variance is approximately 15.62, and the standard deviation is approximately 3.95 and they expect to stop approximately 4.35 cars before finding a driver whose seatbelt is not buckled.
a. To find the mean, variance, and standard deviation of the number of drivers expected not to be wearing seatbelts, we can model the situation using a geometric distribution.
Let's define a random variable X that represents the number of cars stopped until the first driver without a seatbelt is found. The probability of a driver not wearing a seatbelt is given as p = 0.23.
The mean (μ) of a geometric distribution is given by μ = 1/p.
μ = 1/0.23 ≈ 4.35
The variance (σ^2) of a geometric distribution is given by σ^2 = q/p^2, where q = 1 - p.
σ^2 = (0.77)/(0.23^2) ≈ 15.62
The standard deviation (σ) is the square root of the variance.
σ = √(15.62) ≈ 3.95
b. The expected number of cars they expect to stop before finding a driver whose seatbelt is not buckled is equal to the reciprocal of the probability of success (finding a driver without a seatbelt) in one trial. In this case, the probability of success is p = 0.23.
Expected number of cars = 1/p = 1/0.23 ≈ 4.35
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The wholesale price for a shirt is $3.50 . A certain department store marks up the wholesale price by 90 %. Find the price of the shirt in the department store.
Answers
Answer: $6.65
Step-by-step explanation:
The price of the shirt in the department store = wholesale price + 90% of wholesale price
= 3.50 + (3.50*90)/100
= 3.50 + 3.15
= 6.65
Therefore, the price of the shirt is $6.65
suppose a female fruit fly heterozygous for the white (w) gene is mated to a male with wild type red eye color. the white gene is x-linked, so the cross can be written as: xw xw x xw y. what is the the probability of getting a fly that is white-eyed and male?
Answers
The probability of getting a fly that is white-eyed and male from the given cross is 25%.
Let's see how: The cross of a female fruit fly heterozygous for the white (w) gene with a male having the wild type red eye color can be written as: xw, xw, x, xw, y.
As per the given cross, the female parent can have two types of gametes, i.e., xw and x. The male parent can have two types of gametes, i.e., xw and y.
The possible offsprings are:xw, x (white-eyed female)
xw ,y (red-eyed male)
x ,xw (white-eyed female)
y, xw (red-eyed male)
So, there are two white-eyed females and two red-eyed males in the offspring. Out of these four, only one is a white-eyed male.
Hence, the probability of getting a fly that is white-eyed and male is 1/4, or 25%.
Therefore, the probability of getting a fly that is white-eyed and male from the given cross is 25%.
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Find the domain of the vector functions, r(t), listed below.
You may use "-INF" for ?? and use "INF" for ? as necessary, and use "U" for a union symbol if a union of intervals is needed.
a) r(t)=?ln(6t),?t+16,1/?10?t?
b) r(t)=??t?9,sin(6t),t^2?
c) r(t)=? e^?9t,t/?t^2?36,t^1/3?
Answers
The domain of r(t) is (-INF, INF). a) The domain of r(t) = [ln(6t), -t + 16, 1/(10t)] is t > 0. a) The domain of the vector function r(t) = [ln(6t), -t + 16, 1/(10t)] can be determined by considering the individual components.
The natural logarithm, ln(6t), is defined only for positive values of 6t, so we need 6t > 0. This implies that t > 0.
The second component, -t + 16, is defined for all real values of t.
The third component, 1/(10t), is defined as long as 10t ≠ 0, which means t ≠ 0.
Putting these conditions together, we find that the domain of r(t) is t > 0.
b) The vector function r(t) = [t - 9, sin(6t), t^2] does not have any explicit restrictions on its domain.
The first component, t - 9, is defined for all real values of t.
The second component, sin(6t), is also defined for all real values of t.
The third component, t^2, is defined for all real values of t.
Therefore, the domain of r(t) is (-INF, INF). a) The domain of r(t) = [ln(6t), -t + 16, 1/(10t)] is t > 0.
b) The domain of r(t) = [t - 9, sin(6t), t^2] is (-INF, INF).
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The domains of the vector functions r(t) are respectively: for the first one t > 0, for the second one t >= 9 and for the third one it is a union of intervals, t < -6 U t > 6.
Explanation:The domain of a vector function r(t) is defined as the set of all t-values for which the function is defined.
r(t) = ln(6t), t+16, 1/10t: The domain for this function is all values for which the natural logarithm ln(6t) is defined, which means the inside of the logarithm must be greater than zero. As a result, the domain is t > 0.r(t) = root(t-9), sin(6t), t^2: The domain is all real values of t for both the second and third functions. For the first function, to be defined, the inside of the square root, t-9, must be greater than or equal to zero. As a result, the domain is t >= 9.r(t) = e^(-9t), t/root(t^2-36), t^1/3: Again, the third function has domain for all real values. The exponential function is also defined for all real numbers. However, the second function t/root(t^2-36) is undefined where root(t^2-36) = 0, which makes the domain to be a union of intervals, t < -6 U t > 6.Learn more about Vector Functions here:https://brainly.com/question/31672931
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