The required probability is P(T < 2.669) = 0.995.
For QUESTION 5:
Since the t-distribution is symmetric, we can find the desired t-value by looking up the critical value at the upper tail probability of 0.01666/2 = 0.008333 in a t-table with 24 degrees of freedom.
Looking at the t-table, we can see that the closest probability value to 0.008333 is 0.0082, which corresponds to a t-value of 2.492.
Therefore, the positive t-value such that P(T > t) = 0.01666_ is approximately 2.492.
For QUESTION 6:
We need to find the probability that T is less than 2.669, given that T follows a t-distribution with 28 degrees of freedom.
Using a t-table, we can find that the closest probability value to 2.669 is 0.995, which corresponds to a t-value of 2.048.
Therefore, the required probability is P(T < 2.669) = 0.995.
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Pete's yard is 52.7 feet wide. The length is 30.4 feet greater than the width.
What is the perimeter of Pete's yard in feet?
Answer:166.2 feet^2
Step-by-step explanation:
By assuming that Pete's yard is a rectangle, we can get the perimeter by using an equation that looks like this:
perimeter = l+l+w+w
Where l = length, and w = width.
This is because you are adding the measures of every side together, which is the definition of the value of a perimeter.
Furthermore, to get the area of the figure, you would need to multiply 52.7 by 30.4, which would be 1602.08 feet^2
Evaluate the Expression
You want to hang 6 pictures in a row on a wall. You have 11 pictures from which to choose. How many picture arrangements are possible?
The number of different arrangements that can be formed is 7920
How many different arrangements can be formed?From the question, we have the following parameters that can be used in our computation:
Pictures = 11
Arranged pictures = 6
These can be represented as
n = 11 and r = 6
The number of different arrangements that can be formed is
Number = nPr
So, we have
Number = 11P4
Evaluate
Number = 7920
Hence, the arrangements are 7920
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A scatter plot is shown on the coordinate plane.
scatter plot with points plotted at 1 comma 5, 1 comma 8, 2 comma 4, 3 comma 5, 3 comma 6, 5 comma 6, 6 comma 4, 7 comma 2, 9 comma 1, and 10 comma 1
Which two points would a line of fit go through to best fit the data?
(6, 4) and (9, 1)
(3, 5) and (10, 1)
(1, 8) and (5, 6)
(1, 5) and (7, 3)
Answer:
I believe (3, 5) and (10, 1) is the answer
Step-by-step explanation:
three adults and three children are to be seated at a circular table. in how many different ways can they be seated if each child must be next to two adults? (two seatings are considered the same if one can be rotated to form the other.)
There are 84 different ways to seat three adults and three children at a circular table such that each child must be next to two adults.
To seat three adults and three children at a circular table such that each child must be next to two adults, we can use the following steps:
If adults separate all of the children.Place an adult anywhere:There are 2! options for the other two adults and 3! options for children.
The number of ways for two adults and children:
= 2! × 3!
= 2 × 6
= 12 ways to seat them
If 2 of the children sit together and 2 adults sit together:
There are 3 ways to pick the two children, two ways to seat them, and two ways for them to begin the circle, for a total of six options.
The third child has a pair of choices:
6 × 2 so far
Then, there are 3! =6 ways to seat the adults.
6 × 2 × 6 = 72 ways
Putting it all together, the total number of seating arrangements is:
12+72 = 84 ways
Therefore, there are 84 different ways to seat three adults and three children at a circular table such that each child must be next to two adults.
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Question 2 of 25
On a piece of paper, graph f(x): {
answer choice matches the graph you drew.
O A.
10
107
4 if x < 3
2 xifx > 3
y
X
10-X
Click here for long description
. Then determine which
The choice that matches the graph of the function as is defined to us is: Graph A.
How to explain the graphWe are given a function f(x) as:
f(x)= 2x if x < 3
and 4 if x ≥ 3
This means that in the region (-∞,3) the graph of a function is a straight line that passes through the origin and has a open circle at x=3.
Also, in the region [3,∞) the graph is a straight horizontal line i.e. y=4.
Hence, the graph of this function is Graph A.
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On a piece of paper, graph f(x)={2x if x <3
{4 if x >3. Then determine which answer choice matches the graph you drew
E7.5. Given the variance-covariance matrix of three random variables X1, X2 and X3,∑=
4 1 2
1 9 -3
2 -3 25 a. Find the correlation matrix p. b. Compute the correlation between X1, and i/2X2 + 1/2X3.
a. The correlation matrix p = [tex]\left[\begin{array}{ccc}1&1/3&2/5\\1/3&1&-3/5\\2/5&-3/5&1\end{array}\right][/tex]. b. The correlation between X1, and i/2X2 + 1/2X3 is 0.3.
a. The correlation matrix p can be calculated by dividing the covariance matrix by the product of the standard deviations of the variables:
p = [tex]\left[\begin{array}{ccc}1&1/3&2/5\\1/3&1&-3/5\\2/5&-3/5&1\end{array}\right][/tex]
b. To compute the correlation between X1 and i/2X2 + 1/2X3, we first need to calculate the standard deviations of the variables:
σ1 = sqrt(4) = 2
σ2 = sqrt(9) = 3
σ3 = sqrt(25) = 5
Then, we can calculate the covariance between X1 and i/2X2 + 1/2X3:
cov(X1, i/2X2 + 1/2X3) = cov(X1, i/2X2) + cov(X1, 1/2X3)
= i/2 * cov(X1, X2) + 1/2 * cov(X1, X3)
= i/2 * 1 + 1/2 * 2
= 1.5
Finally, we can compute the correlation using the formula:
corr(X1, i/2X2 + 1/2X3) = cov(X1, i/2X2 + 1/2X3) / (σ1 * σ2/2 + σ3/2)
= 1.5 / (2 * 3/2 + 5/2)
= 0.3
Therefore, the correlation between X1 and i/2X2 + 1/2X3 is 0.3.
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researchers found the demand for cheese in a particular country for a particular year can be estimated by the implicit equation -0.82 Inp where p represents the price of a unit of cheese and D represents a constant that can be calculated uniquely for a particular year. Here q represents the annual per capita cheese demand. Answer parts (a) and (b) below. P do 9 dp (a) Use implicit differentiation to calculate and interpret the elasticity of demand. Recall that elasticity of demand is E- Show the first step of implicit differentiation, the equation that results from differentiating each side of the equation da dp Find the elasticity of demand E =(Simplify your answer) Interpret the elasticity of demand you calculated O A. Demand is inelastic OB. Demand is elastic O C. Demand may be elastic or inelastic, depending on the value of D. OD. Demand has unit elasticity
(b) Solve the equation for then calculate the elasticity of demand q= E=
(Simplify your answer.)
(a) First step of implicit differentiation:
-0.82dP/dt = dq/dt
The equation that results from differentiating each side of the equation with respect to P is:
-0.82 - 0.82P(d^2q/dP^2) = (dQ/dP)(dP/dt)/(dq/dt)
To find the elasticity of demand, we need to use the formula:
E = (dQ/Q)/(dP/P)
We can rewrite this as:
E = (dQ/dP) * (P/Q)
We know that dQ/dP = -0.82P(d^2q/dP^2), so we substitute that into the formula:
E = (-0.82P(d^2q/dP^2)) * (P/q)
Simplifying this expression, we get:
E = -0.82P^2(d^2q/dP^2)/q
(b) We can solve the original equation for q by dividing both sides by -0.82:
q = (-1/0.82)P + D
Taking the derivative of q with respect to P, we get:
dq/dP = -1/0.82
We can use this result to calculate the elasticity of demand using the formula:
E = (dQ/dP) * (P/Q)
Substituting the values we found, we get:
E = (-1/0.82) * (P/((-1/0.82)P + D))
Simplifying this expression, we get:
E = -1/(P/((-1/0.82)P + D))
E = -1/((D/P) - 1.22)
(a) Interpretation: The elasticity of demand is a measure of how much the quantity demanded changes in response to a change in price. If E > 1, demand is considered elastic, meaning that a small change in price will result in a large change in quantity demanded. If E < 1, demand is considered inelastic, meaning that a change in price will result in a small change in quantity demanded. If E = 1, demand is unit elastic, meaning that a change in price will result in an equal proportional change in quantity demanded.
(b) Interpretation: The elasticity of demand in this case depends on the values of D and P. If D is relatively small compared to P, then the elasticity of demand will be close to -1.22, which is the upper limit of the elasticity. If D is relatively large compared to P, then the elasticity of demand will be close to zero, which means that demand is very inelastic.
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Part B What will be the area, in square inches, of the piece of sheet metal after both sections are cut and removed?
The dimensions of section B are 36 inches by 48 inches, and the area of the piece of sheet metal after both sections are cut and removed is 6336 square inches.
Given the width and length of a rectangular piece of sheet metal as 60 inches and 44 inches, we need to find the dimensions of section B and the area of the piece of sheet metal after both sections are cut and removed.
The length of rectangle B can be found as TR = SR - ST = PQ - ST, where SR and PQ are opposite sides of the rectangle. Here, PQ is the length of the rectangular sheet metal, which is 60 inches, and ST is the width of the rectangle WVTX, which is 24 inches. Therefore, the length of rectangle B is:
TR = PQ - ST = 60 - 24 = 36 inches
The breadth of rectangle B can be found as UR = QR - QV - VT - TU. Here, QR and PS are opposite sides of the rectangle PQRS, so QR = PS = 144 inches. Also, QV is the width of rectangle WVTX, which is 36 inches, and VT and TU are the lengths of rectangle WVTX, which are both 24 inches. Therefore, the breadth of rectangle B is:
UR = QR - QV - VT - TU = 144 - 36 - 24 - 36 = 48 inches
So, the dimensions of section B are 36 inches by 48 inches.
Next, we need to find the area of the piece of sheet metal after both sections are cut and removed.
The area of rectangle B is the product of its length and breadth, which is:
Area of rectangle B = length × breadth = 36 × 48 = 1728 square inches
The area of rectangle WVTX is the product of its length and breadth, which is:
Area of rectangle WVTX = length × breadth = 24 × 24 = 576 square inches
The area of rectangle PQRS is the product of its length and breadth, which is:
Area of rectangle PQRS = PQ × PS = 60 × 144 = 8640 square inches
Therefore, the area of the piece of sheet metal after both sections are cut and removed is:
Area of the piece of sheet metal = Area of rectangle PQRS - Area of rectangle B - Area of rectangle WVTX
= 8640 - (1728 + 576)
= 8640 - 2304
= 6336 square inches
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Please help 5 points Question in picture
Identify the type of slope each graph represents
A) Positive
B) Negative
C) Zero
D) Undefined
When reading a graph it’s the same as reading most books from left to right and since the line goes up from left to right it is a positive slope.
Consider the equation y=2x²+4x+26.
Part A. Find the value of the discriminant. Show your work.
Part B. Based on the value of the discriminant found in part A, how many real roots does y=2x³+4x+26 have?
Part C. Use the quadratic formula to find the values of x when y-o. Show each step.
Answer:
A. 4^2 - 4(2)(26) = 16 - 208 = -192
B. This equation has no real roots.
C. (-4 + √-192)/(2×2) = (-4 + 8i√3)/4
= -1 + (2√3)i
Write a Variable equation for each sentence
Danika's new running route is 4 miles longer than
her old route.
Answer:
Let x be the length of Danika's old running route in miles.
Then, her new running route can be represented by x + 4, since it is 4 miles longer than her old route.
Step-by-step explanation:
Use the Intermediate Value Theorem to identify the location of the first positive root in f(x)=x²-3
The first positive root of the function f(x) = x² - 3 is located between x = 1 and x = 2.
The Intermediate Value Theorem states that if a function is continuous on a closed interval [a, b] and takes on values f(a) and f(b) with opposite signs, then there exists at least one root (zero) of the function between a and b.
In this case, we have f(x) = x² - 3. To find the first positive root of the function, we need to look for a positive value of x where f(x) = 0.
We can start by evaluating f(0) and f(2), which are the values of the function at the endpoints of the interval [0, 2]:
f(0) = 0² - 3 = -3
f(2) = 2² - 3 = 1
Since f(0) is negative and f(2) is positive, by the Intermediate Value Theorem, there must be at least one root of the function between x = 0 and x = 2.
To further narrow down the location of the root, we can evaluate f(1), which is the midpoint of the interval [0, 2]:
f(1) = 1² - 3 = -2
Since f(1) is negative, we know that the root is between x = 1 and x = 2.
To summarize, the first positive root of the function f(x) = x² - 3 is located between x = 1 and x = 2.
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What is the cordinate of (-7,-3) after a rotation 90 clockwise about the origin?
The coordinates of the point (-7,-3) after a 90 degree clockwise rotation about the origin are (-3,-7).
To rotate a point 90 degrees clockwise about the origin, we need to swap its x and y coordinates and negate the new x coordinate.
So, starting with point (-7,-3):
Swap the x and y coordinates to get (3,-7)
Negate the new x coordinate to get (-3,-7)
Therefore, the coordinates of the point (-7,-3) after a 90 degree clockwise rotation about the origin are (-3,-7).
In mathematics, coordinates are used to specify the position of a point or an object in a particular space. The number of coordinates needed depends on the dimension of the space in which the point or object exists.
In two-dimensional space (also called the Cartesian plane), a point is located by two coordinates, usually denoted as (x, y), where x represents the horizontal distance from a fixed reference point called the origin, and y represents the vertical distance from the origin.
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I need answers badly.
There is 75% of getting at least two tiles of vowels
Fits, less than two of the tiles are vowels
= 11 + 39
= 50
Now, at least two of tiles are vowels
= 200 - 50/ 200
= 150/200
= 0.75 x 100
= 75%
There is 75% of getting at least two tiles of vowels
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Lisa is packing a set of cubic inch blocks into the box shown below. How many blocks will fit in the box?
A rectangular prism that measures 3 inches by 5 inches by 8 inches.
Answer: 120
Step-by-step explanation:V= 8x5x3 =120 ^3
help me please please
Answer: 11.76
Step-by-step explanation: you have to divide by 12 everything and multiply by 6 and you can get the answer
Let y = 5x2 Find the change in y, Δy when x = 4 and Ax 0. 2 Find the differential dy when x = 4 and dx = 0. 2
The differential [tex]dy=2[/tex] when [tex]x = 4[/tex] and [tex]dx = 0. 2.[/tex]
To find the change in [tex]y,Δy[/tex] , when x changes from, we can use the [tex]4 to 4 +Δx = 4 + 0.2 = 4.2[/tex] formula:
[tex]Δy = y(x + Δx) - y(x)[/tex]
where[tex]y(x) = 5x^2.[/tex]
So, plugging in[tex]x = 4[/tex] and[tex]x + Δx = 4.2[/tex] , we get:
[tex]Δy = y(4.2) - y(4)[/tex]
[tex]= 5(4.2)^2 - 5(4)^2[/tex]
[tex]= 44.2[/tex]
Therefore, the change in y is [tex]44.2[/tex] when x changes from [tex]4 to 4.2.[/tex]
To find the differential dy when [tex]x = 4[/tex] and [tex]dx = 0.2,[/tex] we can use the formula:
[tex]dy = f'(x) × dx[/tex]
where the derivative of y with respect to x, which is:
[tex]f'(x) = 10x[/tex]
Plugging in [tex]x = 4[/tex] we get:
[tex]= 2[/tex]
Therefore, the differential [tex]dy = 2[/tex] when [tex]x = 4[/tex] and [tex]dx = 0.2.[/tex]
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38. A new apartment complex with 90 one-bedroom apartment units and 100 two-bedroom apartment units was built near a lake. Rental prices that will provide full occupancy are estimated at $1200 for one-bedroom units and $1800 for two-bedroom units. A market survey suggests that for every $20 increase in the price of a one-bedroom unit one less customer will sign a lease and for every $60 increase in the price of a two-bedroom unit two less customers will sign a lease. What rental price should the manager charge to maximize revenue?
The required manager should charge $1600 for one-bedroom units and $2250 for two-bedroom units to maximize revenue.
Let x be the number of $20 increases in the price of a one-bedroom unit, and y be the number of $60 increases in the price of a two-bedroom unit. Then the rental prices for one-bedroom and two-bedroom units can be expressed as:
One-bedroom price = $1200 + $20x
Two-bedroom price = $1800 + $60y
The total number of customers for one-bedroom units is 90 minus the number of customers lost due to the price increase, which is x. Similarly, the total number of customers for two-bedroom units is 100 minus the number of customers lost due to the price increase, which is 2y. Therefore, the total revenue can be expressed as:
Revenue = (90 - x) * ($1200 + $20x) + (100 - 2y) * ($1800 + $60y)
Expanding and simplifying this expression, we get:
Revenue = 216000 + 9600x - 240x² + 180000 + 108000y - 7200y²
Collecting like terms, we get:
Revenue = -240x² - 7200y² + 9600x + 108000y + 396000
To find the rental price that maximizes revenue, we need to find the values of x and y that maximize the revenue. We can do this by taking partial derivatives of the revenue function with respect to x and y and setting them equal to zero:
dRevenue/dx = -480x + 9600 = 0
dRevenue/dy = -14400y + 108000 = 0
Solving for x and y, we get:
x = 20
y = 7.5
Therefore, the rental prices that maximize revenue are:
One-bedroom price = $1200 + $20x = $1600
Two-bedroom price = $1800 + $60y = $2250
So the manager should charge $1600 for one-bedroom units and $2250 for two-bedroom units to maximize revenue.
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use the method of your choice to determine the following probability. drawing three sevens in a row from a standard deck of cards when the drawn card is not returned to the deck each time. The probability of drawing three sevens is ______.
The probability of drawing three sevens in a row from a standard deck of cards when the drawn card is not returned to the deck each time is approximately 0.00012, or 0.012%.
To determine the probability of drawing three sevens in a row from a standard deck of cards without replacement, we can use the following method:
Step 1: Identify the total number of cards in a standard deck. A standard deck has 52 cards (13 ranks and 4 suits).
Step 2: Determine the number of sevens in the deck. There are 4 sevens (one from each suit).
The probability of drawing a seven from a standard deck of 52 cards is 4/52 or 1/13, since there are four sevens in the deck. After the first seven is drawn, there are 51 cards left in the deck, of which three are sevens. So the probability of drawing a second seven is 3/51. Similarly, after the second seven is drawn, there are 50 cards left in the deck, of which two are sevens. So the probability of drawing a third seven is 2/50.
Step 3: Calculate the probability of drawing the first seven. This would be the number of sevens divided by the total number of cards:
P(1st Seven) = 4/52
Step 4: After drawing the first seven, there are now 51 cards left in the deck and only 3 sevens remaining. Calculate the probability of drawing the second seven:
P(2nd Seven) = 3/51
Step 5: After drawing the second seven, there are now 50 cards left in the deck and only 2 sevens remaining. Calculate the probability of drawing the third seven:
P(3rd Seven) = 2/50
Step 6: To find the probability of all three events happening in a row, multiply the individual probabilities:
P(Three Sevens) = P(1st Seven) * P(2nd Seven) * P(3rd Seven) = (4/52) * (3/51) * (2/50)
Step 7: Calculate the result:
P(Three Sevens) = (4/52) * (3/51) * (2/50) = 0.0012 (approximately)
The probability of drawing three sevens in a row from a standard deck of cards without replacement is approximately 0.0012, or 0.12%.
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find a polynomial function f(x) of least degree having only real coefficients and zeros of 5 and 2-i
To find a polynomial function f(x) of least degree having only real coefficients and zeros of 5 and 2-i, we know that the complex conjugate of 2-i, which is 2+i, must also be a zero. This is because complex zeros of polynomials always come in conjugate pairs.
So, we can start by using the factored form of a polynomial:
f(x) = a(x - r1)(x - r2)(x - r3)...
where a is a constant and r1, r2, r3, etc. are the zeros of the polynomial. In this case, we have:
f(x) = a(x - 5)(x - (2-i))(x - (2+i))
Multiplying out the factors, we get:
f(x) = a(x - 5)((x - 2) - i)((x - 2) + i)
f(x) = a(x - 5)((x - 2)^2 - i^2)
f(x) = a(x - 5)((x - 2)^2 + 1)
To make sure that f(x) only has real coefficients, we need to get rid of the complex i term. We can do this by multiplying out the squared term and using the fact that i^2 = -1:
f(x) = a(x - 5)((x^2 - 4x + 4) + 1)
f(x) = a(x - 5)(x^2 - 4x + 5)
Now, we just need to find the value of a that makes the degree of f(x) as small as possible. We know that the degree of a polynomial is determined by the highest power of x that appears, so we need to expand the expression and simplify to find the degree:
f(x) = a(x^3 - 9x^2 + 24x - 25)
Degree of f(x) = 3
Since we want the least degree possible, we want the coefficient of the x^3 term to be 1. So, we can choose a = 1:
f(x) = (x - 5)(x^2 - 4x + 5)
Degree of f(x) = 3
Therefore, the polynomial function f(x) of least degree having only real coefficients and zeros of 5 and 2-i is:
f(x) = (x - 5)(x^2 - 4x + 5)
To find a polynomial function f(x) of least degree with real coefficients and zeros of 5 and 2-i, we need to remember that if a polynomial has real coefficients and has a complex zero (in this case, 2-i), its conjugate (2+i) is also a zero.
Step 1: Identify the zeros
Zeros are: 5, 2-i, and 2+i (including the conjugate)
Step 2: Create factors from zeros
Factors are: (x-5), (x-(2-i)), and (x-(2+i))
Step 3: Simplify the factors
Simplified factors are: (x-5), (x-2+i), and (x-2-i)
Step 4: Multiply the factors together
f(x) = (x-5) * (x-2+i) * (x-2-i)
Step 5: Expand the polynomial
f(x) = (x-5) * [(x-2)^2 - (i)^2] (by using (a+b)(a-b) = a^2 - b^2 formula)
f(x) = (x-5) * [(x-2)^2 - (-1)] (since i^2 = -1)
f(x) = (x-5) * [(x-2)^2 + 1]
Now we have a polynomial function f(x) of least degree with real coefficients and zeros of 5, 2-i, and 2+i:
f(x) = (x-5) * [(x-2)^2 + 1]
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can someone please help me with my math work i can’t seem to understand where to go on this maze.
Answer:5
explanation:
you are doing great finding the slopes:
Which number is divisible by both 5 and 6?
A.132.359
B.142.645
C.164.780
D.193.560
The only option that has a number that is divisible by both 5 and 6 is: D.193.560
How to find a divisible number?We want to find a number that is divisible by both 5 and 6.
Now, looking at the options, since they are all decimals, the one that would be the most appropriate is the one that does not contain a recurring decimal.
Thus:
A) 132.359/5 =26.4718
132.359/6 = 22.0598333..
B) 142.645/5 = 28.529
142.645/6 = 23.77416666666..
C) 164.780/5 = 32.956
164.780/6 = 27.46333333
D) 193.560/5 = 38.712
193.560/6 = 32.26
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Answer the question below.
Type your response in the space
provided.
How many numbers are 10 units from 0 on the number line?
Answer:
The answer is 10 and -10
You get this answer because in the middle in a number line is 0 and if it 10 units from 0 then the other side of 0 will be -10 (negative ten) units from 0
hotel A charges $2 per minute plus a $5 connection fee for international phone calls. hotel B charges $4 per minute for international calls with a $3 discount on all calls. determine the length, in minutes of an international phone call that would cost the same at either hotel.
A call that lasts for a length of 4 minutes would cost the same at either hotel.
For Hotel A: Cost = 2(4) + 5 = 13
For Hotel B: Cost = 4(4) - 3 = 13 minutes
How do we determine the length of phone call that would cost the same at either hotel?We can determine the length of phone call that would cost the same at either hotel by the following equations.
Given:
Hotel A, cost of the call:
Cost for Hotel A = 2x + 5
For Hotel B, the cost of the call:
Cost for Hotel B = 4x - 3
For the length of the call that would cost the same at either hotel, we shall set these two equations equal to each other and solve for x:
2x + 5 = 4x - 3
Subtracting 2x from both sides, we get:
5 = 2x - 3
Adding 3 to both sides, we get:
8 = 2x
Dividing both sides by 2, we get:
x = 4
So, a call that lasts 4 minutes would cost the same at either hotel.
We can verify this, let's plug x = 4 into both equations:
For Hotel A: Cost = 2(4) + 5 = 13
For Hotel B: Cost = 4(4) - 3 = 13
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Mr. smith is taking an extravagant trip to Puerto Rico. He knows he can bring 1.5 bags for every $52.50 he pays. If his flight costs $262.50 how many bags can Mr. smith bring?
a. Write in your own words a definition of a complex numbers and Modulusof the complex number. Support your answers with examples. (4 marks) b.Find the modulus of + mi (10 marks) c. Write the complex number 2 = ((2+ m) + 3i)in polar form (13 marks) 100+m
The complex number can be written in polar form as 2 + ((2+m) + 3i) = √(m² + 6m + 25)∠tan⁻¹(3/(2+m)).
What is complex number?
A complex number is obtained by adding real and imaginary numbers. Complex numbers have the formula a + ib and are usually symbolized by the symbol z. Here the numbers a and real are both. The value "a" is known as the real component and is denoted Re(z), while "b" is known as the imaginary part and is denoted Im(z). Also known as imaginary number, ib. Hero of Alexandria, a Greek mathematician, first used the idea of complex numbers in the first century when he tried to calculate the square root of a negative integer.
a. A complex number is a number that consists of a real part and an imaginary part, where the imaginary part is the real number multiplied by the imaginary unit "i", defined as the square root of -1. The modulus of a complex number is the distance between the starting point and the point representing the complex number on the complex plane. This can be calculated using the Pythagorean theorem. For example, the real part of the complex number z = 3 + 4i is 3 and the imaginary part is 4, and its modulus is √(3²+4²)=5.
b. Let z = a + bi be a complex number, where a and b are real numbers. The modulus of z is defined as |z| = √(a² + b²). Therefore, for the complex number z = 1 + 2i, the modulus is |z| = √(1² + 2²) = √5.
c. To write the complex number 2 = ((2+ m) + 3i) in polar form, we need to find the modulus and argument of the complex number. The modulus is |2 + ((2+m) + 3i)| = |4 + mi + 3i| = √(4² + (m+3)²) = √(m² + 6m + 25). The argument is given by tan⁻¹(Im/Re) = tan⁻¹(3/(2+m)), which gives us the angle that the complex number makes with the positive real axis. Therefore, the complex number can be written in polar form as 2 + ((2+m) + 3i) = √(m² + 6m + 25)∠tan⁻¹(3/(2+m)).
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Find f(-3) for the piece-wise function.
The value of function f(- 3) for the piece-wise function is,
⇒ f (- 3) = - 1
We have to given that;
The piece-wise function is,
f (x) = (x + 2) ; if x < 2
= (x + 1) ; if x ≥ 2
Hence, At x = - 3;
Function is,
⇒ f (x) = x + 2
Hence, Substitute x = - 3;
⇒ f (- 3) = - 3 + 2
⇒ f (-3) = - 1
Thus, The value of function f(- 3) for the piece-wise function is,
⇒ f (- 3) = - 1
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26/3 minus 16/9 equals what
Answer:
[tex]\frac{62}{9}[/tex] or 6.8888889
Step-by-step explanation:
The explanation is on the attachment below
Rose works a concession stand at a football game that sells whole pretzels and bottle of water.
Each pretzel sells for $2.50 and each bottle of water sells for $1.00
Rose collected $135 in sales
Rose sold a total of 87 items at the past game
Enter the number of pretzels rose sold at the game
Rose sold 53.6 pretzels.
P x ? + W = 135
2.50 x 53.6 + 1.00 = 135
WHAT IS THE AREA OF A TRAPEZOID WITH COORDINATES (1,4) (1,-3) (6,6) (6,-5)
Answer:
THESE NUTS
Step-by-step explanation:
