Keep in mind that if Lourdes is able to pay off her credit card balance at the end of the month, she won't be charged any interest, making the credit card the better option in that case.
To determine whether Lourdes should use a debit card or credit card, we need to consider the ATM fee and the potential interest charges from the credit card.
Step 1: Determine the ATM fee
Find out how much Lourdes would be charged for using the ATM to withdraw cash.
Step 2: Determine the interest rate on the credit card
Check the credit card's terms and conditions to find the annual percentage rate (APR). This will help us calculate the potential interest charges.
Step 3: Calculate the potential interest charges
Assuming Lourdes doesn't pay off the credit card balance by the end of the month, divide the APR by 12 to get the monthly interest rate. Multiply this rate by the $48 grocery cost to find the potential interest charges.
Step 4: Compare costs
Compare the ATM fee and potential interest charges to determine the cheaper option. If the ATM fee is less than the potential interest charges, Lourdes should use her debit card. If the potential interest charges are less than the ATM fee, she should use her credit card.
Keep in mind that if Lourdes is able to pay off her credit card balance at the end of the month, she won't be charged any interest, making the credit card the better option in that case.
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I MAKE U BRAINLIEST solve for x
Answer: 9
Step-by-step explanation:
The angle is 1/2 of the arc angle
Since the tangent line is a line, I know the angle on the other side of 78 is
180-78 = 102
That angle, 102, is 1/2 the arc angle
102 = 1/2 (23x -3) > multiply both sides by 2
204 = 23x -3 > add 3 to both sides
207 = 23x >divide both sides by 23
x=9
What is the difference in minutes between the shortest collection.
The difference in the shortest collection times before and after the well installation is 20 minutes, calculated by subtracting the shortest time after installation (25 minutes) from before (45 minutes), as shown in the box and whiskers plot.
This is calculated by subtracting the shortest collection time after well installation (25 minutes) from the shortest collection time before well installation (45 minutes):
45 - 25 = 20 minutes.
This can be seen in the box and whiskers plot provided, where the lowest value for each distribution is denoted by the beginning of the whiskers.
So, the difference is before and after the well installation is 20 minutes.
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--The given question is incomplete, the complete question is given
" What is the difference in minutes between the shortest collection times before and after the well was installed"--
The snow globe below is formed by a hemisphere and a cylinder on a cylindrical
base. The dimensions are shown below. The base is slightly wider than the globe
with a diameter of 10cm and height of 1cm.
10 cm
4cm
3cm
Part C: If each globe is individually packaged into a box, what are the minimum
dimensions of the box?
The minimum dimensions of the box will be 7 cm × 6 cm × 6 cm
What do we by dimension?A dimension is described as the measurement of something in physical space such as length, width, or height.
We know that the there will be maximum dimension when the height of the cylinder and the radius of the hemisphere are aligned together.
Maximum height = 4 cm + 3 cm = 7 cm
Maximum diameter = 2 × 3 cm = 6 cm
Therefore, we can see that the minimum dimensions of the box are :
7 cm × 6 cm × 6 cm.
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PLEASE HELP!! How can you find the annual percentage rate (APR) of a loan if you know the number of monthly payments and the finance charge per $100? What does knowing the APR allow you to do?
APR is obtained by dividing the finance charge for the loan by the total amount borrowed, given by this formula APR = ((F / P) x 12) x 100
What is the annual percentage rate?The formula for APR (annual percentage rate) is given as;
APR = ((F / P) x 12) x 100
Where;
F is the finance charge for the loanP is the total amount borrowed12 represents the number of months in a yearThe annual percentage rate (APR) of a loan if you know the number of monthly payments and the finance charge per $100, is calculated as follows;
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Aria ate the pictured slice of pizza. If the original
pizza was 8 inches in diameter, what is the area
of the slice she ate?
Answer:
Step-by-step explanation:
50.24n2
The height of the storage space is 6 feet. The length is 2 times the width. The volume of the storage is 48 cubic feet. What is the width and length of the storage space
Step-by-step explanation:
Let's use the formula for the volume of a rectangular prism, which is:
V = lwh
where V is the volume, l is the length, w is the width, and h is the height.
We are given that the height is 6 feet, and the volume is 48 cubic feet. Therefore, we can solve for the product of the length and width:
lw = V / h = 48 / 6 = 8
We are also given that the length is twice the width, so we can substitute 2w for l:
(2w)w = 8
Simplifying this equation, we get:
2w^2 = 8
Dividing both sides by 2, we get:
w^2 = 4
Taking the square root of both sides, we get:
w = 2
Therefore, the width of the storage space is 2 feet. Since the length is twice the width, the length is:
l = 2w = 2(2) = 4
So the length of the storage space is 4 feet.
Mrs Gibson is sending a package to her son through the mail the package is a rectangular prism is 12 inches long,12 inches wide and 48 inches high what is the volume in cubic feet
The volume of the package which is 12 inches long, 12 inches wide, and 48 inches high is 6912 inches³ or 4 cubic feet.
Given length of the package which is in rectangular prism shape (L) = 12 inches
similarly, width of the package (W) = 12 inches
height of the package (H) = 48 inches
To know the volume of the package which is in the rectangular prism shape the formula is V= L x W x H
The substituting the given values in the above equation, we can obtain the volume of the package.
So,
L x W x H = 12 x 12 x 48 = 6912 inches³
To convert the cubic inches into the cubic feet we have to divide the obtained value by 1728.
So, [tex]\frac{6912}{1728}[/tex] = 4 feet³
From the above explanation, we can conclude that the volume of the given package of rectangular prism shape is 4 feet³.
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Dina has a mass of 50 kilograms and is waiting at the top of a ski slope that’s 5 meters high. the maximum kinetic energy she can reach when she skis to the bottom of the slope is joules. use pe = m × g × h and g = 9.8 m/s2. ignore air resistance and friction.
Dina can reach a maximum kinetic energy of 2450 Joules when she skis to the bottom of the slope.
How much kinetic energy can Dina reach?Potential energy (PE) = m x g x h
where m = mass, g = acceleration due to gravity, and h = height
Here, Dina's mass (m) = 50 kg, height (h) = 5 m, and acceleration due to gravity (g) = 9.8 m/s².
So, PE = 50 x 9.8 x 5
PE = 2450 Joules
When Dina skis down the slope, all of her potential energy will be converted into kinetic energy (KE) at the bottom of the slope, neglecting any losses due to friction and air resistance.
Thus, the maximum kinetic energy (KE) Dina can reach at the bottom of the slope is also 2450 Joules.
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The maximum kinetic energy she can reach when she skis to the bottom of the slope is 2452 joules
To find the maximum kinetic energy that Dina can reach when she skis to the bottom of the slope, we need to use the principle of conservation of energy, which states that the total energy of a system remains constant.
At the top of the slope, Dina has potential energy due to her position relative to the ground. This potential energy is given by:
PE = m × g × h
where m is Dina's mass (50 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the slope (5 m).
PE = 50 kg × 9.8 m/s^2 × 5 m = 2450 J
When Dina skis to the bottom of the slope, all of her potential energy is converted into kinetic energy, which is given by:
KE = 1/2 × m × v^2
where v is her velocity at the bottom of the slope.
To find the maximum velocity, we can use the fact that the total energy of the system remains constant:
PE = KE
2450 J = 1/2 × 50 kg × v^2
v^2 = 98 m^2/s^2
v = sqrt(98) = 9.90 m/s
Finally, we can substitute this velocity into the kinetic energy equation to find the maximum kinetic energy that Dina can reach:
KE = 1/2 × 50 kg × (9.90 m/s)^2 = 2452 J
Therefore, Dina can reach a maximum kinetic energy of 2452 Joules when she skis to the bottom of the slope.
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HELP PLS & THANK YOU
Answer:
Step-by-step explanation:
6 Moses makes a school spirit flag. He has as many yards of red fabric as blue
fabric. He buys 2 yards more red fabric. Now he has equal amounts of red and
blue fabric. Use x to represent the amount of blue fabric. Which equations could
you use to find the amount of red fabric Moses has? Select all that apply.
A X =
B x= x + 2?
x = 2
1/x + 273
x= 1/3x - 223
E x + 2 2 2 = 1/3 x + 2 2 3
C X=
D x- 27 28 = 1/3 x
F * = }}x+ 2
2 2 3
The equations to find the amount of red fabric Moses has are X = x + 2 and X + 222 = 1/3x + 223. These equations are obtained by using x as the amount of blue fabric and setting up equations based on the given information. So, the correct answer is A) and E).
There are two equations that can be used to find the amount of red fabric Moses has
X = x + 2, This equation represents the fact that Moses bought 2 more yards of red fabric than he originally had of blue fabric. So, the amount of red fabric (X) is equal to the amount of blue fabric (x) plus 2.
X + 222 = 1/3x + 223, This equation represents the fact that after buying 2 more yards of red fabric, Moses has equal amounts of red and blue fabric.
So, the amount of red fabric (X) plus 222 (the additional 2 yards he bought) is equal to one-third of the amount of blue fabric (1/3x) plus 223 (the original 2 yards of red fabric he had).
Therefore, the equations that could be used to find the amount of red fabric Moses has are A) and E).
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--The given question is incomplete, the complete question is given
" 6 Moses makes a school spirit flag. He has as many yards of red fabric as blue fabric. He buys 2 yards more red fabric. Now he has equal amounts of red and blue fabric. Use x to represent the amount of blue fabric. Which equations could you use to find the amount of red fabric Moses has? Select all that apply.
A X = x + 2
B x = 2
C 1/x + 273
D x= 1/3x - 223
E x + 2 2 2 = 1/3 x + 2 2 3
F x- 27 28 = 1/3 x
G = x+ {{22}*2}^3 "--
Complete the following statement. Use the integers that are closest to the number in the
middle.
44
The closest integers to 44 are 43 and 45.
How to find the integers closest to 44?To complete the statement using the integers closest to the number in the middle, we need to determine the middle number in a sequence or set of numbers. However, the given prompt only provides the number "44" without any context or additional information.
If we assume that the number "44" is part of a sequence or set, we would need more information to determine the middle number and complete the statement accurately.
Without additional context or information, it is not possible to provide a specific answer or complete the statement. Please provide more details or clarify the question to assist further.
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John has $23. 65 spend on a book and magazines. The book costs $5. 95z the magazines cost $2. 95 each. A) write an equation that models the number of magazines that John can afford. B) solve the equation
John can afford approximately 6 magazines.
A) To write an equation that models the number of magazines John can afford, let's denote the number of magazines as 'm'. Since each magazine costs $2.95 and John has a total of $23.65 to spend, the equation can be expressed as:
2.95m + 5.95 = 23.65
B) To solve the equation, we can isolate the variable 'm' by subtracting 5.95 from both sides:
2.95m = 23.65 - 5.95
2.95m = 17.70
Then, divide both sides by 2.95:
m = 17.70 / 2.95
m ≈ 6
Therefore, John can afford approximately 6 magazines.
In conclusion, the equation 2.95m + 5.95 = 23.65 models the number of magazines John can afford, and by solving it, we find that he can purchase approximately 6 magazines with the given amount of money.
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f(x,y)-x' + y -6y? - 3x + 9 a. To find the critical points, you must first use calculus to set up a system of equations. Show how you would derive the system of equations, and then write the system in the box provided. Write system of equations in this box. . Solve the system of equations. Show all of your work. No calculators please. List all of the critical points in this box
To find the critical points of the function f(x,y) = x' + y - 6y - 3x + 9, we need to take the partial derivatives with respect to x and y and set them equal to zero.
∂f/∂x = -3 = 0
∂f/∂y = 1 - 6 = -5 = 0
So the system of equations is:
-3 = 0
-5 = 0
These equations have no solutions, which means there are no critical points for this function.
Therefore, the list of critical points is empty.
Hello! I'd be happy to help you find the critical points of the given function. The function is:
f(x,y) = x' + y - 6y? - 3x + 9
To find the critical points, we need to find the partial derivatives of the function with respect to x and y, and then set them equal to zero:
∂f/∂x = ∂(x' + y - 6y? - 3x + 9)/∂x
∂f/∂y = ∂(x' + y - 6y? - 3x + 9)/∂y
Now, let's calculate the partial derivatives:
∂f/∂x = 1 - 3
∂f/∂y = 1 - 12y
The system of equations is:
1. ∂f/∂x = 1 - 3 = 0
2. ∂f/∂y = 1 - 12y = 0
Now let's solve the system of equations:
1. 1 - 3 = 0 → -2 = 0 (this equation cannot be satisfied)
Since the first equation cannot be satisfied, there are no critical points for the given function.
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Find f'(-2) for f(x) = ln(5x² + 20x + 1). Round to 3 decimal places, if necessary.
To find f'(-2), we need to first find the derivative of f(x) using the chain rule.
f'(x) = (1/(5x² + 20x + 1)) * (10x + 20)
Then, we can plug in x = -2 to get f'(-2):
f'(-2) = (1/(5(-2)² + 20(-2) + 1)) * (10(-2) + 20)
f'(-2) = (1/(20 - 40 + 1)) * (-20 + 20)
f'(-2) = 0
Therefore, f'(-2) is equal to 0.
To find f'(-2) for f(x) = ln(5x² + 20x + 1), we first need to find the derivative of f(x) using the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.
1. Let u = 5x² + 20x + 1. Then, f(x) = ln(u).
2. Find the derivative of f(x) with respect to u: f'(x) = d[ln(u)]/du = 1/u.
3. Find the derivative of u with respect to x: du/dx = d(5x² + 20x + 1)/dx = 10x + 20.
4. Apply the chain rule: f'(x) = (1/u) * (du/dx) = (1/(5x² + 20x + 1)) * (10x + 20).
Now, to find f'(-2), simply substitute -2 for x in the derivative:
f'(-2) = (1/(5(-2)² + 20(-2) + 1)) * (10(-2) + 20)
f'(-2) = (1/(20 - 40 + 1)) * (-20 + 20)
f'(-2) = (1/(-19)) * 0
Since any number multiplied by 0 is 0, we have:
f'(-2) = 0.000
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During their team meeting, both managers shared their findings. Complete the statement describing their combined results.
Select the correct answer from each drop-down menu.
The initial number of video views was (more than, fewer than, the same as,)the initial number of site visits, and the number of video views grew by (a smaller factor, the same factor, a larger factor) the number of site visits.
The difference between the total number of site visits and the video views after 5 weeks is(15,625, 20,825, 36,450, 52,075)
The initial number of video views was (fewer than) the initial number of site visits, and the number of video views grew by (a larger factor) the number of site visits. The difference between the total number of site visits and the video views after 5 weeks is (20,825).
Video views refer to the number of times a video has been watched or viewed by viewers.
A site visit refers to a visit or session by a user to a website. It occurs when a user accesses and interacts with webpages or content on a particular website.
The initial number of video views was (fewer than) the initial number of site visits, and the number of video views grew by (a larger factor) the number of site visits. The difference between the total number of site visits and the video views after 5 weeks is (20,825).
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Suppose that you measure the flow rate of blood in an artery. You find that your measurements are well-fit be the equation dᏙ /dt =10 - 2 cos(120t)
in units of milliliters per second.
a) What volume of blood flows through the artery in 10 seconds? (include units)
b) What volume of blood flows through the artery in one minute? (include units)
The volume of blood flow through the artery in one minute is 600 milliliters.
We can integrate the given equation to get the volume of blood flow.
a) Integrating both sides of the equation with respect to time from 0 to 10 seconds, we get:
∫dᏙ = ∫(10 - 2cos(120t)) dt
ΔᏙ = [10t - (1/60)sin(120t)] from 0 to 10
ΔᏙ = [(10 x 10) - (1/60)sin(1200)] - [(10 x 0) - (1/60)sin(0)]
ΔᏙ ≈ 100 - 0
So, the volume of blood flow through the artery in 10 seconds is 100 milliliters.
b) To find the volume of blood flow through the artery in one minute, we need to integrate the given equation from 0 to 60 seconds:
∫dᏙ = ∫(10 - 2cos(120t)) dt
ΔᏙ = [10t - (1/60)sin(120t)] from 0 to 60
ΔᏙ = [(10 x 60) - (1/60)sin(7200)] - [(10 x 0) - (1/60)sin(0)]
ΔᏙ ≈ 600 - 0
So, the volume of blood flow through the artery in one minute is 600 milliliters.
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A.
kyle swam 4 laps in the pool on monday. he swam
6 times as many laps on tuesday. choose true or false
for each statement.
a. the expression 6 x 4 represents the number of
x
laps kyle swam on tuesday.
b. the words 6 times as many as 4 represents the
number of laps kyle swam on tuesday.
c. the number of laps kyle swam on tuesday can be
found by solving the equation ? = 6 x 4.
d. kyle swam 10 laps on tuesday.
A. Kyle swam 4 laps in the pool on Monday. He swam 6 times as many laps on Tuesday.
a. The expression 6 x 4 represents the number of laps Kyle swam on Tuesday.
b. The words "6 times as many as 4" represent the number of laps Kyle swam on Tuesday.
c. The number of laps Kyle swam on Tuesday can be found by solving the equation x = 6 x 4.
d. Kyle swam 10 laps on Tuesday.
a) True. Since Kyle swam 6 times as many laps on Tuesday as he did on Monday (4 laps), you would multiply 6 by 4 to find the number of laps he swam on Tuesday.
b) True. This phrase means that Kyle swam 6 times the number of laps he swam on Monday (4 laps), which gives you the number of laps he swam on Tuesday.
c) True. This equation represents the total number of laps Kyle swam on Tuesday. By solving the equation, you can determine that Kyle swam 24 laps on Tuesday.
d) False. Based on the information given and the calculations made, Kyle actually swam 24 laps on Tuesday, not 10.
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A resale store is having a sale on DVDs and CDs. DVDs cost $7 and CDs cost $4. On one day, the store made $211 from DVD and CD sales and sold a total of 40 items. Write a system of equations, then solve to find how many DVDs and CDs were sold
Answer:
17 DVDs and 23 CDs
Step-by-step explanation:
x is the number of DVDs
y is the number of CDs
7x + 4y = $211
x + y = 40 ----(x4)----> 4x + 4y = 160
3x = 51
x = 17
x + y = 40
17 + y = 40
y = 23
In conclusion, 17 DVDs and 23 CDs were sold.
(1 point) Find the maximal area of a right triangle with hypotenuse of length 3.
The maximal area of a right triangle with hypotenuse of length 3 is 0.
How to calculate the maximal area?Let's call the legs of the right triangle a and b.
Since the hypotenuse has length 3, we know that a² + b² = 3² = 9
The area of the triangle is given by A = 1/2 ab.
We want to maximize A subject to the constraint a² + b²= 9.
One way to do this is to use the method of Lagrange multipliers.
We want to maximize the function f(a, b) = 1/2 ab subject to the constraint g(a, b) = a²+ b² - 9= 0. The Lagrangian is then:
L(a, b, λ) = f(a, b) - λg(a, b) = 1/2 ab - λ(a² + b² - 9)
To find the maximum, we need to solve the system of equations:
∂L/∂a = 0∂L/∂b = 0∂L/∂λ = 0Taking the partial derivatives and setting them equal to zero, we get:
b/2 - 2λa = 0a/2 - 2λb = 0a² + b²- 9 = 0Solving the first two equations for a and b in terms of λ and plugging them into the third equation,
we get:
4λ² + 1 = 0
Then from the constraint a² + b² = 9, we have a = ±3.
The area of the triangle in this case is A = 1/2 ab = 0.
Therefore, the maximal area of a right triangle with hypotenuse of length 3 is 0, and it is achieved when one of the legs has length 0.
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1. What is the probability of rolling a # larger than 2 and drawing an Ace or 4? A 2 3 4 5
The probability of rolling a number larger than 2 and drawing an Ace or 4 is 2/39. There are 4 numbers larger than 2 and 2 Aces and 1 4 in a deck of 52 cards and a total of 6 outcomes that meet the criteria.
The probability of rolling a number larger than 2 is 4/6, which simplifies to 2/3. The probability of drawing an Ace or 4 is 4/52, which simplifies to 1/13. To find the probability of both events happening, you multiply the probabilities
P(rolling a number larger than 2 and drawing an Ace or 4) = P(rolling a number larger than 2) x P(drawing an Ace or 4)
= (2/3) x (1/13)
= 2/39
Therefore, the probability of number larger than 2 and drawing an Ace or 4 is 2/39.
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SOMEONE HELP PLS, giving brainlist to anyone who answers
Answer:
[tex]s = \frac{3(1 - {6}^{9}) }{1 - 6} = 6046617[/tex]
The sum of this finite geometric series is 6,046,617.
the graph of a sinosudial function has a maximum point at (0,5) and then has a minimum point at (2pi, -5)
The equation of the sinusoidal function is y = 5sin(x).
How to graph sinusoidal function?
To solve this, we need to find the equation of the sinusoidal function that has a maximum point at (0,5) and a minimum point at (2π,-5).
First, we know that the function is a sine function because it has a maximum at (0,5) and a minimum at (2π,-5).
Second, we can find the amplitude of the function by taking half the difference between the maximum and minimum values. In this case, the amplitude is (5-(-5))/2 = 5.
Third, we can find the vertical shift of the function by taking the average of the maximum and minimum values. In this case, the vertical shift is (5+(-5))/2 = 0.
Finally, we can find the period of the function by using the formula T=2π/b, where b is the coefficient of x in the equation of the function. In this case, we know that the function completes one cycle from x=0 to x=2π, so the period is 2π.
Putting it all together, the equation of the function is y = 5sin(x)
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Find the perimeter of the semicircular region. Round your answer to the nearest hundredth
9 m
The perimeter is about
meters
The perimeter of the semicircular region is about 28.27 meters.
We know that the semicircular region is half of a circle.
Let's assume that the radius of the circle is r meters. Then the circumference of the circle is 2πr meters, and the perimeter of the semicircular region is half of that, which is πr meters.
We are given that the radius of the circle is 9 meters, so we can plug that in to get:
The perimeter of the semicircular region = πr
= π(9)
≈ 28.27
Rounding to the nearest hundredth, the perimeter of the semicircular region is about 28.27 meters.
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what is the area of each student's photo?
The area of students photo with sides 10cm by 8cm is 80cm².
How to calculate the areaOn order to calculate the area of a student's photo, one can use the formula for the area of a rectangle, which is:
Area = length x width. You can simply multiply the two numbers together to get the area of the photo in that unit squared (e.g. square centimeters).
If a student's photo has a length of 10 centimeters and a width of 8 centimeters, the area of the photo would be:
Area = 10 cm x 8 cm = 80 cm²
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What is the area of students photo with sides 10cm by 8cm
The solution of a quadratic equation are x=-7 and 5. Which could represent the quadratic equation, and why?
An answer option that could represent the quadratic equation, and why is: B. x² + 2x - 35 = 0, the factors are (x + 7) and (x - 5) and (x + 7)(x - 5) = x² + 2x - 35.
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Next, we would solve the quadratic function by using the factors (zeros or roots) provided as follows;
y = (x + 7)(x - 5)
y = x² + 2x - 35
x² + 2x - 35 = 0
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
The double dot plot shows the values in two data sets. express the difference in the measures of center as a multiple of the measure of variation.
no troll comments or i will hack ur device and find out where u live ! okay :)
The difference in measures of center as a multiple of the measure of variation can be expressed using the coefficient of variation.
How to express difference in data?To express the difference in measures of center as a multiple of the measure of variation, you can use the coefficient of variation (CV).
The CV is calculated by dividing the standard deviation (measure of variation) by the mean (measure of center), and then multiplying by 100 to express the result as a percentage.
For example, if the standard deviation of one dataset is 5 and the mean is 10, the CV would be 50%. If the standard deviation of another dataset is 2 and the mean is 8, the CV would be 25%.
To express the difference in measures of center as a multiple of the measure of variation between these two datasets, you would calculate the difference in their means (10-8=2) and divide it by the CV of the combined dataset ((5/10 + 2/8)/2 = 47.5%).
Therefore, the difference in measures of center is approximately 0.042 times the measure of variation (2/47.5%).
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A group of students were surveyed about what they want to be when they grow up. The table provided shows the choices that the students made. Use the information in the table to answer the following questions. Round all answers to the nearest whole number.
Teacher Doctor Athlete
Boys 24 28 56
Girls 45 31 26
The marginal relative frequency of boys and girls who want to be a teacher is
%.
The joint relative frequency of girls who want to be an athlete is
%.
The conditional relative frequency of students that selected doctor, given that those students are boys is
%
The marginal relative frequency of boys and girls who want to be a teacher is 32.86%.
The joint relative frequency of girls who want to be an athlete is 12.38%.
The conditional relative frequency of students that selected doctor, given that those students are boys is 25.93%.
We'll use the terms marginal relative frequency, joint relative frequency, and conditional relative frequency to analyze the data in the table.
1. The marginal relative frequency of boys and girls who want to be a teacher is:
First, find the total number of students who want to be a teacher (boys + girls):
24 (boys) + 45 (girls) = 69 (total students)
Next, find the total number of students surveyed (sum of all entries in the table):
24 + 28 + 56 + 45 + 31 + 26 = 210
Now, calculate the marginal relative frequency of boys and girls who want to be a teacher (total students who want to be a teacher / total students surveyed):
69 / 210 ≈ 0.3286
Multiply by 100 to get the percentage:
0.3286 * 100 ≈ 32.86%
2. The joint relative frequency of girls who want to be an athlete is:
Find the number of girls who want to be an athlete: 26
Calculate the joint relative frequency (number of girls who want to be an athlete / total students surveyed):
26 / 210 ≈ 0.1238
Multiply by 100 to get the percentage:
0.1238 * 100 ≈ 12.38%
3. The conditional relative frequency of students that selected doctor, given that those students are boys:
Find the total number of boys surveyed (sum of boys row):
24 + 28 + 56 = 108
Calculate the conditional relative frequency (number of boys who want to be a doctor / total boys surveyed):
28 / 108 ≈ 0.2593
Multiply by 100 to get the percentage:
0.2593 * 100 ≈ 25.93%
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Find the area of the region bounded by the
curves:
y = 10 - x^2
y = x^2 + 8
The area of the region bounded by the curves is 4/3 square units.
To find the area of the region bounded by the curves y = 10 - [tex]x^2[/tex] and y = [tex]x^2[/tex] + 8, we need to find the points of intersection between the two curves.
Setting the two equations equal to each other, we have:
10 - [tex]x^2[/tex] = [tex]x^2[/tex] + 8
Simplifying, we get:
[tex]2x^2[/tex] = 2
[tex]x^2[/tex] = 1
x = ±1
Substituting x = 1 into either equation gives us:
y = 10 - [tex]1^2[/tex] = 9
And substituting x = -1 gives us:
y = 10 - [tex](-1)^2[/tex] = 10
So the two curves intersect at the points (1, 9) and (-1, 10).
To find the area of the region bounded by the curves, we need to integrate the difference between the two equations with respect to x, from x = -1 to x = 1:
∫[10 - [tex]x^2[/tex]] - [[tex]x^2[/tex] + 8] dx, from x = -1 to x = 1
= ∫(2 - 2[tex]x^2[/tex]) dx, from x = -1 to x = 1
= [2x - (2/3)[tex]x^3[/tex]] from x = -1 to x = 1
= 4/3
So
The area of the region bounded by the curves y = 10 - [tex]x^2[/tex] and y = [tex]x^2[/tex] + 8 is 4/3 square units.
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A bag contains five red socks and eight blue socks. Lucky reaches into the bag and randomly selects two socks without replacement. What is the probability that Lucky will get different colored socks? Express your answer as a common fraction. I will give brainliest if you give a full explanation, I have the answer but I need to know HOW to solve the problem!!!
The probability that Lucky will get different colored socks is 1/6 or 1 out of 6.
To solve this problem, we can use the concept of probability and combinations.
Step 1: Determine the total number of possible outcomes.
When Lucky selects two socks without replacement, there are a total of 13 socks in the bag (5 red + 8 blue). So, the total number of possible outcomes is given by selecting 2 socks out of 13, which is represented as C(13, 2) or 13 choose 2.
C(13, 2) = (13!)/(2!(13-2)!) = (13 * 12)/(2 * 1) = 78
Step 2: Determine the number of favorable outcomes.
For Lucky to get different colored socks, there are two cases to consider: selecting a red sock first and a blue sock second, or selecting a blue sock first and a red sock second.
Case 1: Red sock first, then blue sock:
The number of ways to select one red sock out of five is C(5, 1) = 5. After selecting one red sock, there are eight blue socks remaining, and Lucky needs to select one blue sock out of eight, which is C(8, 1) = 8.
Case 2: Blue sock first, then red sock:
The number of ways to select one blue sock out of eight is C(8, 1) = 8. After selecting one blue sock, there are five red socks remaining, and Lucky needs to select one red sock out of five, which is C(5, 1) = 5.
So, the total number of favorable outcomes is 5 + 8 = 13.
Step 3: Calculate the probability.
The probability of getting different colored socks is the ratio of the number of favorable outcomes to the total number of possible outcomes:
P(Different Colored Socks) = Number of Favorable Outcomes / Total Number of Possible Outcomes
= 13 / 78
= 1/6
Therefore, the probability that Lucky will get different colored socks is 1/6 or 1 out of 6.
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Arrange the following assets and liabilities and construct a net worth statement. Assets and Liabilities Amount Checking account $14,532 Student Loan $1,225 Retirement Savings $43,675 Credit Card Debt $3,876 Car (paid off) $12,225 Home Loan Balance $65,225 Create a table or list for assets and another for liabilities. Find the total amount for all assets and the total amount of liabilities. What is the net worth?
The net worth is about $106.
This can be calculated by the addition of liabilities and assets amount
Assets - Amount
Checking amount - $14,532
Retirement savings- $43,675
Car - $12,225
Therefore total assets equal to: $70,432
Now, for liabilities
Liabilities - Amount
Student loan $1,225
Credit card debt $3,876
Home loan balance $65,225
Therefore total liabilities equals to: $70,326
The net worth can be find out by subtracting the total liabilities from the total assets:
Hence Net worth = Total assets- Total liabilities
= $70,432- $70,326
= $106
Therefore the total net worth is about $106.
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