Answer:
48 adult tickets were sold.
Step-by-step explanation:
Let's use algebra to solve this problem:
Let's define:
x: the number of student tickets soldy: the number of adult tickets soldFrom the problem statement, we know:
x + y = 320 (the total number of tickets sold is 320)3x + 8y = 1200 (the total revenue from ticket sales is $1200)We can use the first equation to solve for x in terms of y:
x = 320 - y
Substituting this expression for x into the second equation, we get:
3(320 - y) + 8y = 1200
Expanding the left side, we get:
960 - 3y + 8y = 1200
Simplifying, we get:
5y = 240
Solving for y, we get:
y = 48
Therefore, 48 adult tickets were sold.
Additional:
To find the number of student tickets sold, we can substitute y=48 into the first equation:
x + 48 = 320
x = 272
Therefore, 272 student tickets were sold.
Tell whether the angles are adjacent or vertical. Then find the value of x. Please help with this question
Make a number line and mark all the points that represent the following values of x. X < -1 and x > 1
To make a number line for the values of x that are less than -1 and greater than 1, we can start by drawing a horizontal line and marking a point at 0. Then, we can label the left side of the line with negative numbers and the right side with positive numbers.
Next, we need to mark all the points that represent the values of x that satisfy the condition X < -1 and x > 1. This means we are looking for all the numbers that are less than -1 and greater than 1 at the same time. However, there are no numbers that satisfy this condition since a number cannot be both less than -1 and greater than 1 simultaneously.
Therefore, there are no points to mark on the number line for this condition.
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Find f'(4) for f(x) 8/In(3x^2) Round to 3 decimal places, if necessary.
To find f'(4), we need to take the derivative of f(x) with respect to x and then evaluate it at x=4. Using the chain rule, we get:
f'(x) = -16x/(ln(3x^2))^2
So, f'(4) = -16(4)/(ln(3(4)^2))^2 = -64/(ln(48))^2
Rounding to 3 decimal places, we get f'(4) = -0.019.
To find f'(4) for f(x) = 8/ln(3x^2), we first need to differentiate f(x) with respect to x. We will use the quotient rule and the chain rule for this purpose.
The quotient rule states: (u/v)' = (u'v - uv')/v^2, where u = 8 and v = ln(3x^2).
Now, differentiate u and v with respect to x:
u' = 0 (since 8 is a constant)
v' = d(ln(3x^2))/dx = (1/(3x^2)) * d(3x^2)/dx (using chain rule)
Now, differentiate 3x^2 with respect to x:
d(3x^2)/dx = 6x
So, v' = (1/(3x^2)) * (6x) = 2/x
Now, apply the quotient rule for f'(x):
f'(x) = (0 - 8 * (2/x))/(ln(3x^2))^2 = -16/(x * (ln(3x^2))^2)
Now, plug in x = 4 to find f'(4):
f'(4) = -16/(4 * (ln(3*(4^2)))^2) = -16/(4 * (ln(48))^2)
Rounded to 3 decimal places, f'(4) ≈ -0.171.
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In an effort to eat healthier, Bridget is tracking her food intake by using an application on her phone. She records what she eats, and then the
application indicates how many calories she has consumed. One Monday, Bridget eats 10 medium strawberries and 8 vanilla wafer cookies as an
after-school snack. The caloric intake from these items is 192 calories. The next day, she eats 20 medium strawberries and 1 vanilla wafer cookie as an after-school snack. The caloric intake from these items is 99 calories.
a. Write a system of equations for this problem situation. Let S represent the number of calories in one strawberry and let W represent the number of calories in one vanilla wafer cookie.
The equation _____ represents the calories Bridget ate on Monday and the equation _____ represents the calories she ate the next day.
b. Solve the system of equations using the substitution method. Check your work.
The number of calories in each strawberry is ____
And the number of calories in each vanilla wafer cookie is ____. The solution is ____.
PLEASE HELP ME
The equation 10S + 8W = 192 represents the calories Bridget ate on Monday and the equation 20S + 1W = 99 represents the calories she ate the next day.
The number of calories in each strawberry is 4, and the number of calories in each vanilla wafer cookie is 19.
a. We have two equations for the two days, using S for the number of calories in a strawberry and W for the number of calories in a vanilla wafer cookie:
On Monday:
10S + 8W = 192
On Tuesday:
20S + 1W = 99
b. To solve the system of equations using the substitution method, first solve one of the equations for one of the variables. We'll choose the second equation and solve for W:
W = 99 - 20S
Now substitute this expression for W in the first equation:
10S + 8(99 - 20S) = 192
Expand and simplify:
10S + 792 - 160S = 192
Combine like terms:
-150S = -600
Now divide by -150:
S = 4
Now that we have the value for S, substitute it back into the expression for W:
W = 99 - 20(4)
W = 99 - 80
W = 19
So the number of calories in each strawberry is 4, and the number of calories in each vanilla wafer cookie is 19. The solution is (S, W) = (4, 19).
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A line includes the points (0,-7) and (n, -8) has a slope of -1/6. What is the value of n?
Answer:
n = 6.
Step-by-step explanation:
The slope of the line = (y2 - y1) / (x2 - x1) where the 2 points are (x1, y1) and (x2, y2).
So, (-8 - (-7)) / (n - 0) = -1/6
-1/n = -1/6
n = 6.
A dth tv connection provides channels in english and other languages in the ratio 7:13. what percentage of the channels are in english
A DTH TV connection provides channels in English and other languages in the ratio 7:13. To find out what percentage of the channels are in English, you need to divide the number of English channels by the total number of channels and then multiply the result by 100.
Let's assume that there are a total of 100 channels available on this DTH TV connection. According to the given ratio, 7 out of every 20 channels will be in English. So, the percentage of channels in English will be:
(7/20) x 100 = 35%
Therefore, 35% of the channels on this DTH TV connection are in English.
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Compound Interest:
In March 2003, Natalie invested $800 in an account that earns 4. 8% interest compounded monthly. After 5 years, she withdrew all the money and reinvested it in a new account that earns 6% interest compounded semiannually. Assuming there were no other deposits or withdrawals, how much total interest will she have earned by March 2025?
I NEED HELP, CAN SOMEONE HELP ME, PLEASE?
Natalie will have earned a total of $488.97 in interest by March 2025.
"What is compound interest formula?To solve this problem, we can use the formula for compound interest:
A = [tex]P(1 + r/n)^(nt)[/tex]
where A is the total amount, P is the principal amount, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.
First, let's find out how much money Natalie will have in her first account after 5 years:
P = $800
r = 4.8% per year = 0.048
n = 12 (compounded monthly)
t = 5 years
A = [tex]800(1 + 0.048/12)^(12*5)[/tex]
A = $995.08
So after 5 years, Natalie will have $995.08 in her first account.
Next, let's find out how much money Natalie will have in her second account:
P = $995.08
r = 6% per year = 0.06
n = 2 (compounded semiannually)
t = 5 years
A = [tex]995.08(1 + 0.06/2)^(2*5)[/tex]
A = $1,288.97
So after reinvesting her money in the second account, Natalie will have $1,288.97 after 5 years.
Finally, let's calculate the total interest earned:
Total interest = A - P
Total interest = $1,288.97 - $800
Total interest = $488.97
Therefore, Natalie will have earned a total of $488.97 in interest by March 2025.
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Resume the totat revenue from the sale of them is given by R(x) * 25 1n (6x + 1), while the total cost to produce x items is C(x)=ſ. Find the approximate number of items that should be manufactured so that profit, RIX-C) is maximum G A 143 Rems OB. 84 items C. 47 items OD 114 items
The approximate number of items that should be manufactured so that the profit, P(x) = R(x) - C(x), is maximum is 47 items (option C).
To find the approximate number of items that should be manufactured to maximize profit, we need to first find the profit function P(x) by subtracting the total cost, C(x), from the total revenue, R(x). Then, we need to find the critical points of P(x) and determine which one corresponds to the maximum profit.
process of finding profit:Step 1: Find the profit function P(x) = R(x) - C(x)
Given R(x) = 25 ln(6x + 1) and C(x) = ∫x, let's find P(x):
P(x) = R(x) - C(x)
P(x) = 25 ln(6x + 1) - ∫x
Step 2: Find the critical points of P(x)
To find the critical points, we need to take the derivative of P(x) and set it equal to 0:
P'(x) = d/dx [25 ln(6x + 1) - ∫x]
Since the derivative of ln(6x + 1) is (6/(6x + 1)), and the derivative of ∫x is x:
P'(x) = 25 [tex]\times[/tex] (6/(6x + 1)) - x
Now, set P'(x) = 0 and solve for x:
25 [tex]\times[/tex] (6/(6x + 1)) - x = 0
Step 3: Determine which critical point corresponds to the maximum profit
The approximate number of items that should be manufactured so that the profit, P(x) = R(x) - C(x), is maximum is 47 items (option C).
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find the critical numbers of f(x)=4−5x/4 + x and classify any local extrema.
The function has a global maximum at the vertex (2/5, 41/25), and there are no local maxima or minima.
To find the critical numbers of the function f(x) = 4 - 5x/4 + x, we first need to find its derivative:
f'(x) = -5/4 + 1
f'(x) = -1/4
To find the critical numbers, we set f'(x) equal to zero and solve for x:
-1/4 = 0
This is never true, so there are no critical numbers for f(x).
Since there are no critical numbers, there are no local maxima or minima for the function. Instead, we can analyze the behavior of the function to determine if it has any extrema.
One way to do this is to examine the end behavior of the function. As x approaches positive or negative infinity, the leading term of the function is -5x/4, which dominates the constant term. Therefore, as x becomes large in either direction, the function approaches negative infinity. This suggests that the function has a global maximum at its vertex.
To find the vertex, we can complete the square:
f(x) = 4 - 5x/4 + x
[tex]f(x) = -(5/4)x^2 + x + 4[/tex]
[tex]f(x) = -(5/4)(x^2 - (4/5)x) + 4[/tex]
[tex]f(x) = -(5/4)(x - 2/5)^2 + 4 + (5/4)(2/5)^2\\f(x) = -(5/4)(x - 2/5)^2 + 41/25[/tex]
Therefore, the function has a global maximum at the vertex (2/5, 41/25), and there are no local maxima or minima.
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Recent studies show that the number of three-legged frogs in a particular area is increasing due to exposure to chemical pollutants. The first set of data reported in 2000 estimates a population of 5000 three-legged frogs. Statistics show an annual increase of 15%. Let denote the number of three-legged frogs projected to inhabit this area in the year 2000N. How many three-legged frogs are projected to inhabit this area by 2009? Round to the nearest whole number
By 2009, it is projected that approximately 13,956 three-legged frogs will inhabit the area.
Recent studies have indicated a growing concern for the population of three-legged frogs in a specific area, as they have been exposed to chemical pollutants. In the year 2000, data estimated that there were about 5,000 three-legged frogs (N) in this area. With an annual increase of 15%, we can project the number of frogs in future years using the formula:
Future population = N * (1 + growth rate) ^ number of years
In this case, we want to determine the number of three-legged frogs in the area by 2009. To calculate this, we will use the given values:
Future population = 5,000 * (1 + 0.15) ^ (2009 - 2000)
Future population = 5,000 * (1.15)⁹
Future population ≈ 13,956
Therefore, by 2009, it is projected that approximately 13,956 three-legged frogs will inhabit the area, rounding to the nearest whole number. This increase in population highlights the potential ecological consequences of chemical pollutants on the environment and the need for further investigation and mitigation measures.
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Find the error & explain why it is wrong:
megan solved the following problem. what did she do wrong?
what is (f - g)(2)?
f(x) = 3x2 – 2x + 4
g(x) = x2 – 5x + 2
The value of (f-g)(2) is 16, provided that Megan has made no mistakes in the calculation.
Find the error in the given problem solved by Megan?The problem asks us to compute the value of (f - g)(2) where f(x) = 3x^2 - 2x + 4 and g(x) = x^2 - 5x + 2.
The notation (f - g)(2) means that we need to subtract g(x) from f(x) and then evaluate the result at x = 2. We can do this as follows:
(f - g)(x) = f(x) - g(x) = (3x^2 - 2x + 4) - (x^2 - 5x + 2) = 2x^2 + 3x + 2
Substituting x = 2, we get:
(f - g)(2) = 2(2)^2 + 3(2) + 2 = 16
Therefore, the value of (f - g)(2) is 16.
It's worth noting that the problem statement mentions "what did she do wrong?" without providing any context or information about what Megan did or didn't do. So, it's not possible to identify any error in Megan's solution based on the given information. However, based on the correct computation above, we can be sure that (f - g)(2) is indeed equal to 16.
In other words, it can be described as,
The error in Megan's solution is not clear from the given statement. However, it seems that she may have made an error while computing (f-g)(2).
To compute (f-g)(2), we need to subtract g(2) from f(2) as follows:
f(2) = 3(2)^2 - 2(2) + 4 = 12
g(2) = (2)^2 - 5(2) + 2 = -4
Therefore, (f-g)(2) = f(2) - g(2) = 12 - (-4) = 16. is the final conclusion.
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What is the median of the lower half of data
We can see here that in order to find the median of the lower half of data, one will have to sort out the data in an ascending order. Then take the lower half of the data (i.e., the first half of the sorted data) and find its median.
What is median?The median, which is used to measure central tendency in statistics, is the point at which a dataset may be divided into two equal parts. If a dataset has an even number of values, it is the average of the two middle values or the middle value in a sorted dataset.
The values in the dataset must first be arranged from lowest to highest in order to determine the median. The median is the middle value if the dataset has an odd number of values.
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A force of 80 pounds on a rope is used to pull a box up a ramp inclined at 10 degrees from the horizontal. The rope forms an angle of 33 degrees with the horizontal. How much work is done pulling the box 26 feet along the ramp?
The work done on the displacement is 301.95J
What is the work done in pulling the boxTo determine the work done, we need to find the displacement in which the box moved.
cos θ = adjacent / hypothenuse
cos 33 = adjacent / 80
adjacent = 80 * cos 33
adjacent = 67.1 lbs
The force applied is 67.1lbs
The displacement on the ramp;
sin θ = opposite / hypothenuse
sin 10 = opposite / 26
opposite = 26 * sin 10
opposite = 4.5 ft
The work done in moving the object can be calculated as;
work done = force * displacement
work done = 67.1 * 4.5
work done = 301.95 J
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Solve each system by substitution
Y=-7x-24
Y=-2x-4
Answer:
(- 4, 4 )
Step-by-step explanation:
y = - 7x - 24 → (1)
y = - 2x - 4 → (2)
substitute y = - 2x - 4 into (1)
- 2x - 4 = - 7x - 24 ( add 7x to both sides )
5x - 4 = - 24 ( add 4 to both sides )
5x = - 20 ( divide both sides by 5 )
x = - 4
substitute x = - 4 into either of the 2 equations and evaluate for y
substituting into (1)
y = - 7(- 4) - 24 = 28 - 24 = 4
solution is (- 4, 4 )
3. The scale of a room in a blueprint is 2 inches : 1 foot. A window in the same blueprint is 12 inches. Complete the table. Blueprint Length (in.) Actual Length (ft) a. How long is the actual window? 2 1 4 3 4 10 12 5 6 b. A mantel in the room has an actual width of 8 feet. What is the width of the mantel in the blueprint?
Therefor, the length of mantel in blueprint is > 30 ft
width of the mantel in the blueprint 8ft×2inc/1ft=16inch
what is width?The term "width" refers to the length from side to side of anything. For instance, the shorter side of a rectangle would be the width.
we know that
[scale]=[blueprint]/[actual]-------> [actual]=[blueprint]/[scale]
[scale]=3/5 in/ft
for [wall blueprint]=18 in
[wall actual]=[wall blueprint]/[scale]-------> 18/(3/5)----> 30 ft
Part A)
the actual wall is 30 ft long
Part B) window has actual width of 2.5 ft
[ window blueprint]=[scale]*[actual window]-----> (3/5)*2.5----> 1.5 in
the width of the window in the blueprint is 1.5 in
Part C) Complete the table
For [blueprint length]=4 in
[actual length]=[blueprint length]/[scale]-------> 4/(3/5)----> 20/3 ft
For [blueprint length]=5 in
[actual length]=[blueprint length]/[scale]-------> 5/(3/5)----> 25/3 ft
For [blueprint length]=6 in
[actual length]=[blueprint length]/[scale]-------> 6/(3/5)----> 30/3=10 ft
For [blueprint length]=7 in
[actual length]=[blueprint length]/[scale]-------> 7/(3/5)----> 35/3 ft
For [actual length]=6 ft
[blueprint length]=[actual length]*[scale]-------> 6*(3/5)----> 18/5 in
For [actual length]=7 ft
[blueprint length]=[actual length]*[scale]-------> 7*(3/5)----> 21/5 in
For [actual length]=8 ft
[blueprint length]=[actual length]*[scale]-------> 8*(3/5)----> 24/5 in
For [actual length]=9 ft
[blueprint length]=[actual length]*[scale]-------> 9*(3/5)----> 27/5 in
B) width of the mantel in the blueprint 8ft×2inc/1ft=16inch
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Which expressions represent the length of side MN?
Choose 2 answers:
A. 4 • sin (65)
B. 1. 9 • cos (65)
C. 4/sin (65)
D. 1. 9/cos (65)
PLEASE HELP!!
Expressions A and B represent the length of side MN.
How can the length of side MN be expressed?The two expressions that represent the length of side MN are A) 4•sin(65) and B) 1.9•cos(65). The length of side MN can be found using the trigonometric ratios of sine and cosine in a right triangle.
The angle of 65 degrees is opposite to side MN and the hypotenuse of the triangle is given as 4 units. Using the sine ratio, we can find the length of MN as 4•sin(65). Similarly, using the cosine ratio, we can find the length of MN as 1.9•cos(65).
Therefore, expressions A and B both represent the length of side MN, and they have been obtained by using different trigonometric ratios.
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expand and simplify(2w-3)3
Answer:
6w-9
Step-by-step explanation:
2w×3=6w
-3×3=-9
=6w-9
If a point is randomly located on an interval (a, b) and if y denotes the location of the point, then y is assumed to have a uniform distribution over (a, b). a plant efficiency expert randomly selects a location along a 500-foot assembly line from which to observe the work habits of the workers on the line. what is the probability that the point she selects is:closer to the beginning of the line than to the end of the line
The probability that the point she selects is closer to the beginning of the line than to the end of the line is 0.5 or 50%.
If a point is randomly located on an interval (a, b), and y denotes the location of the point, then y is assumed to have a uniform distribution over (a, b). In this case, the interval is the assembly line of length 500 feet, where a is the beginning and b is the end of the line.
The question asks for the probability that the point she selects is closer to the beginning of the line than to the end of the line. For the point to be closer to the beginning, it must be located in the first half of the line, which is an interval of length 250 feet (500/2).
Since the point has a uniform distribution, the probability of the point being within any sub-interval is equal to the length of the sub-interval divided by the total length of the interval (500 feet).
So, the probability that the point she selects is closer to the beginning of the line than to the end of the line is the length of the first half (250 feet) divided by the total length (500 feet).
Probability = (Length of the first half) / (Total length)
Probability = (250 feet) / (500 feet)
Probability = 0.5 or 50%
There is a 50% chance that the place she chooses will be closer to the line's beginning than its finish.
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Consider the function f(x) = 2x³ + 6x² – 144x + 4, -6 ≤ x ≤ 5. Find the absolute minimum value of this function. Answer: Find the absolute maximum value of this function. Answer:
The absolute maximum value of the function f(x) is 222.
To find the absolute minimum value of the function f(x), we need to first find the critical points within the given interval -6 ≤ x ≤ 5. To do this, we take the derivative of f(x) and set it equal to zero:
f'(x) = 6x² + 12x - 144
0 = 6(x² + 2x - 24)
0 = 6(x+6)(x-4)
The critical points are x=-6, x=-4, and x=4. To determine which of these points correspond to a minimum value, we evaluate f(x) at each of these points and at the endpoints of the interval:
f(-6) = -880, f(-4) = -184, f(4) = -136, f(-6) = -880, f(5) = 222
Therefore, the absolute minimum value of the function f(x) is -880.
To find the absolute maximum value of the function f(x), we follow the same process. The critical points are still x=-6, x=-4, and x=4, but now we need to evaluate f(x) at each of these points and at the endpoints of the interval to determine which corresponds to a maximum value:
f(-6) = -880, f(-4) = -184, f(4) = -136, f(-6) = -880, f(5) = 222
Therefore, the absolute maximum value of the function f(x) is 222.
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How many 4-digit numbers have the second digit even and the fourth digit at least twice the second digit?
There are 1350 4-digit numbers that have the second digit even and the fourth digit at least twice the second digit.
To form a 4-digit number, we have 10 choices for each digit, except the first digit, which can't be 0. Hence, there are 9 choices for the first digit.
For the second digit, there are 5 even digits (0, 2, 4, 6, 8) to choose from.
For the third digit, there are 10 choices.
For the fourth digit, we can choose any of the even digits we picked for the second digit, or any of the larger odd digits 4, 6, 8.
Hence, the number of 4-digit numbers that meet the given criteria is
9 × 5 × 10 × 3 = 1350.
Therefore, there are 1,350 4-digit numbers that have the second digit even and the fourth digit at least twice the second digit.
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What is -2(x + 12y - 5 - 17x - 16y + 4) simplified?
-40x + 8y + 2
28x + 8y +2
28x + 6y + 2
-28x - 8y + 2
Answer:
Step-by-step explanation:
First, we can simplify the expression inside the parentheses by combining like terms:
-2(x + 12y - 5 - 17x - 16y + 4) = -2(-16x - 4y - 1)
Next, we can distribute the -2 to each term inside the parentheses:
-2(-16x - 4y - 1) = 32x + 8y + 2
Therefore, -2(x + 12y - 5 - 17x - 16y + 4) simplified is 32x + 8y + 2.
The simplified expression is 32x + 8y + 2.
Simplification of an algebrai expression can be defined as the process of writing an expression in the most efficient and compact form without affecting the value of the original expression.
The process entails collecting like terms, which implies adding or subtracting terms in an expression.
Simplify the expression -2(x + 12y - 5 - 17x - 16y + 4).
First, let's distribute the -2 to each term inside the parentheses:
-2(x) + (-2)(12y) - (-2)(5) - (-2)(17x) - (-2)(16y) + (-2)(4)
Now we'll multiply: -2x - 24y + 10 + 34x + 32y - 8
Next, we'll combine like terms:
(-2x + 34x) + (-24y + 32y) + (10 - 8)
The result is 32x + 8y + 2
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help i need this done pls 50 points
The length of the diagonal is 12. 7in
How to determine the lengthTo determine the length of the diagonal, we need to know the Pythagorean theorem.
The Pythagorean theorem states that the square of the hypotenuse side is equal to the sum of the squares of the other two sides of a triangle.
The other two sides are the opposite and the adjacent sides.
From the information given in the diagram, we have that;
The opposite side = 12in
The adjacent side = 4in
Substitute the values
x² = 12² + 4²
find the squares
x² = 160
find the square root
x = 12. 7 in
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Hannah has an offer from a credit card issuer for 0% APR for the first 30 days
and 12. 22% APR afterwards, compounded daily. What effective interest rate
is Hannah being offered?
To find the effective interest rate that Hannah is being offered, we need to take into account the compounding period, which is daily in this case. The effective annual interest rate (EAR) can be calculated using the formula:
EAR = (1 + APR/n)^n - 1
where APR is the annual percentage rate, and n is the number of compounding periods per year.
For the first 30 days, Hannah is offered a 0% APR, so the EAR for this period is simply 0.
After 30 days, Hannah is offered a 12.22% APR compounded daily, which means that there are 365 compounding periods per year. Therefore, the EAR for this period can be calculated as follows:
EAR = (1 + 0.1222/365)^365 - 1
≈ 0.1267
So the effective interest rate that Hannah is being offered is approximately 12.67%.
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James says the fraction 3 4 has the same value as the expression 4 ÷ 3. Use the drop-down menus to state whether you agree or not, and why. James is Choose. . A fraction can be interpreted as division of the Choose. By the Choose.
James says the fraction 3/4 has the same value as the expression 4 ÷ 3. I disagree with James' statement.
The fraction 3/4 is not the same as the expression 4 ÷ 3. A fraction can be interpreted as division of the numerator (top number) by the denominator (bottom number). In this case, 3/4 represents the division of 3 by 4, whereas 4 ÷ 3 represents the division of 4 by 3. These two expressions have different values and are not equal.
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
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Consider the circle centered at the origin and passing through the point (0, 4)
Equation of the circle: x^2 + (y - 2)^2 = 4
How to find the equation of the circle?
The circle centered at the origin and passing through the point (0, 4) can be represented by the equation of a circle. The general equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius.
Since the center is at the origin (0, 0), the equation simplifies to x^2 + y^2 = r^2. To determine the radius, we can use the point (0, 4) that lies on the circle. Substituting these coordinates into the equation, we get 0^2 + 4^2 = r^2. Simplifying, we find that 16 = r^2.
Therefore, the equation of the circle centered at the origin and passing through the point (0, 4) is x^2 + y^2 = 16.
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The box plot displays the number of push-ups completed by 9 students in a PE class.
A box plot uses a number line from 12 to 58 with tick marks every 2 units. The box extends from 27.5 to 42.5 on the number line. A line in the box is at 37. The lines outside the box end at 15 and 55. The graph is titled Push-Ups In PE and the line is labeled Number of Push-Ups.
Which of the following represents the value of the lower quartile of the data?
27.5
37
42.5
55
Given that 27.5 is the bottom end of the box, the lower quartile's value equation (Q1) must fall between 27.5 and 30. Hence, the appropriate response is 37.
Since, A mathematical equation links two statements and utilizes the equals sign (=) to indicate equality.
In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions.
For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
Here, 25% of the data fall inside the lower quartile (Q1), which is represented by that number. Q1 is situated near the bottom of the box in the box plot.
According to the description, the box's boundary is at 30, and its size ranges from 27.5 to 42.5 on the number line. As a result, the median value of the middle 50% of the data is 37, with a range of 27.5 to 42.5.
There are some data points outside the middle 50% since the lines outside the box finish at 15 and 55.
Hence; 27.5 is the bottom end of the box, the lower quartile's value (Q1) must fall between 27.5 and 42.5.
Hence, the appropriate response is,
= 37
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Pedro is walking down the longest staircase ever, which contains 4000 steps. She
starts from the top and is walking down the staircase at 150 steps a minute. Hal is
walking up the staircase, starting at the bottom, at 80 steps a minute. After how
many minutes will they meet?
Pedro and Hal will walk 1800 steps staircase and meet after 25 minutes.
Pedro is walking down the longest staircase ever, which contains 4000 steps. She starts from the top and is walking down the staircase at 150 steps a minute. Hal is walking up the staircase, starting at the bottom, at 80 steps a minute. After how many minutes will they meet?
Let's assume that they will meet at point X, which is y steps away from the top and z steps away from the bottom. As Pedro is walking down the staircase, she will cover a distance of y steps, while Hal is walking up the staircase, he will cover a distance of (4000-z) steps.
The time taken by Pedro to cover a distance of y steps is y/150 minutes, while the time taken by Hal to cover a distance of (4000-z) steps is (4000-z)/80 minutes. Since they will meet at the same point X, we can set these two times equal to each other and solve for y and z.
y/150 = (4000-z)/80
Solving this equation, we get y = 1800 and z = 2200. This means that Pedro will have covered 1800 steps in y/150 = 12 minutes and Hal will have covered (4000-2200) = 1800 steps in (4000-2200)/80 = 25 minutes.
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In the diagram shown, segments AE and CF are both perpendicular to DB.
DE=FB, AE=CF. Prove that ABCD is a parallelogram.
Answer:
Step-by-step explanation:
Given:- ABCD is a parallelogram, and AE and CF bisect ∠A and ∠C respectively. To prove:- AE∥CF Proof:- Since in a parallelogram, opposite angles are equal.
what are the coefficients in the expression (2x+15)(9x-3) need it asap
Answer:
2x and 9x are the coefficients.
Step-by-step explanation:
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression (including variables such as a, b and c ).
How many hours is 1,000,00 minutes
Answer:
16.6666 hours.
Step-by-step explanation:
This conversion of 1,000 minutes to hours has been calculated by multiplying 1,000 minutes by 0.0166 and the result is 16.6666 hours.
Answer:
16,666.67 hours
Step-by-step explanation:
A minute is a unit of time equal to 60 seconds.