The percent of the front page taken up by the prom story is 20%
Calculating the percent of the front page taken up by the prom storyFrom the question, we have the following parameters that can be used in our computation:
The front page
From the front page, we have
Area front page = 5 * 4
Area front page = 20
Also, we have
Prom = 2 * 2
Prom = 4
So, we have
Percentage = 4/20 * 100%
Evaluate
Percentage = 20%
Hence, the percent of the front page taken up by the prom story is 20%
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Natalie borrowed money from her parents to pay for a trip.
Natalie will pay her parents in equal amounts every week until she pays back the entire amount she borrowed.
The table below shows the amount of money Natalie still owes her parents at the end of every two weeks for the first eight weeks.
Number of Weeks Natalie Has Paid,
�
w
Amount Natalie Still Owes,
�
d
0
0
$
180
$180
2
2
$
162
$162
4
4
$
144
$144
6
6
$
126
$126
8
8
$
108
$108
Part A
How much does Natalie pay her parents each week?
$
per week
Part B
Write a function that shows the relationship between the amount Natalie still owes,
�
d, and the number of weeks she has paid,
�
w.
Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.
We can see that Natalie is reducing the amount she owes by $18 every two weeks.
Therefore, the amount she owes after 2 weeks is $180 - $18 = $162, after 4 weeks is $144, after 6 weeks is $126, and after 8 weeks is $108.
This means that after n weeks, the amount she still owes is:
$180 - $18n
Since she will pay the same amount each week, let's call the weekly payment P. After one week, she will owe:
$180 - P
After two weeks, she will owe:
($180 - P) - P = $180 - 2P
After four weeks, she will owe:
($180 - 2P) - P - P = $180 - 4P
After six weeks, she will owe:
($180 - 4P) - P - P = $180 - 6P
And after eight weeks, she will owe:
($180 - 6P) - P - P = $180 - 8P
We can set up an equation using the information we have:
$180 - 8P = $108
Solving for P, we get:
P = $9
Therefore, Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.
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The complete question:
Natalie borrowed money from her parents to pay for a trip. Natalie will pay her parents in equal amounts every week until she pays back the entire amount she borrowed. The table below shows the amount of money Natalie still owes her parents at the end of every two weeks for the first eight weeks. How much does Natalie pay her parents each week? What is the initial amount Natalie still owes?
Week 0 = $180
Week 2 = $162
Weeks 4 = $144
Week 6 = $126
Week 8 = $108
A family is planning their vacation to Disney World. They will drive from a small town outside New Orleans,
Louisiana, to Orlando, Florida, a distance of 700 miles. They plan to average a rate of 55 mph. How long will this
trip take?
The time taken for the trip will be 12.7 hours.
How to calculate the value?It should be noted that time taken is calculated as:
Time = Distance / Speed
Distance = 700 miles
Speed = 55 mph
Time = 700/55
Time = 12.7 hours.
Therefore, the time taken for the trip will be 12.7 hours.
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The weights X of an animal are distributed according to the
probability distribution shown.
What is the probability that the animal's weight will be less than
151 pounds?
O 0.25
O 0.50
O 0.60
O 0.75
The probability that the animal's weight will be less than 151 pounds is 0.50.
The correct option is B.
What is the probability that the animal's weight will be less than 151 pounds?Since the given probability distribution ranges from 148 to 152, and we need to find the probability that the animal's weight will be less than 151 pounds, we can add the probabilities corresponding to the weights less than 151.
From the distribution, we see that the probability of the animal's weight being less than 151 pounds is 0.2 + 0.3 = 0.5.
Therefore, the answer is O 0.50.
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solve the triangle for which angle a =30\degree, angle b=45\degree, and a=20
The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636
Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.
Here, it is given that,
angle a = 30 degrees
angle b = 45 degrees
side a = 20
angle c = 180 - (angle a + angle b)
angle c = 180 - (30 + 45)
angle c = 180 - 75
angle c = 105 degrees
We know that, a/sin(A) = b/sin(B) = c/sin(C)
a/sin(A) = b/sin(B) = c/sin(C)
20/sin(30) = b/sin(45) = c/sin(105)
b/sin(45) = 20/sin(30)
b = (sin(45) * 20) / sin(30)
b ≈ (0.7071 * 20) / 0.5
b ≈ 14.142 / 0.5
b ≈ 28.284
Now,
c/sin(105) = 20/sin(30)
c = (sin(105) * 20) / sin(30)
c ≈ (0.9659 * 20) / 0.5
c ≈ 19.318 / 0.5
c ≈ 38.636
Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.
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A transformation maps A(-3, 5), B(0, 5), and c(-4, 5) onto A'(-5, 9),B'(-2, 8), and c'(-6, 1). Determine if the transformation is a translation.Choose all that apply.Yes, all pairs of corresponding points have moved in the same directionby the same distance.No, one or more pairs of corresponding points have not moved thesame distance.No, one or more pairs of corresponding points have not moved in thesame direction.
As we can see in the drawing, A and B moves very similary whereas C has moved in a very different direction and magnitude. Therefore, the answers are:
-No, one or more pairs of corresponding points have not moved the
same distance.
-No, one or more pairs of corresponding points have not moved in the
same direction.
Use the function f(x) to answer the questions:
f(x) = 2x2 − 5x + 3
Part A: What are the x-intercepts of the graph of f(x)? Show your work.
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work.
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph.
The x-intercepts of the graph of f(x) are x = 3/2 and x = 1,the Vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point, The vertex is at (5/4, 3/8). This is the minimum point of the graph.
Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.
2x^2 - 5x + 3 = 0
To factor this quadratic equation, we look for two numbers that multiply to give 3 (the coefficient of the constant term) and add up to -5 (the coefficient of the linear term). These numbers are -3 and -1.
2x^2 - 3x - 2x + 3 = 0
x(2x - 3) - 1(2x - 3) = 0
(2x - 3)(x - 1) = 0
Setting each factor equal to zero, we get:
2x - 3 = 0 --> x = 3/2
x - 1 = 0 --> x = 1
Therefore, the x-intercepts of the graph of f(x) are x = 3/2 and x = 1.
Part B: To determine whether the vertex of the graph of f(x) is a maximum or a minimum, we look at the coefficient of the x^2 term, which is positive (2 in this case). A positive coefficient indicates that the parabola opens upwards, so the vertex will be a minimum.
To find the coordinates of the vertex, we can use the formula x = -b/2a. In the equation f(x) = 2x^2 - 5x + 3, the coefficient of the x term is -5, and the coefficient of the x^2 term is 2.
x = -(-5) / (2*2) = 5/4
Substituting this value of x back into the equation, we can find the y-coordinate:
f(5/4) = 2(5/4)^2 - 5(5/4) + 3 = 25/8 - 25/4 + 3 = 3/8
Therefore, the vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point.
Part C: To graph f(x), we can use the information obtained in Part A and Part B.
- The x-intercepts are x = 3/2 and x = 1. These are the points where the graph intersects the x-axis.
- The vertex is at (5/4, 3/8). This is the minimum point of the graph.
We can plot these points on a coordinate plane and draw a smooth curve passing through the x-intercepts and the vertex. Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the graph will be concave up.
Additionally, we can consider the symmetry of the graph. Since the coefficient of the linear term is -5, the line of symmetry is given by x = -(-5) / (2*2) = 5/4, which is the x-coordinate of the vertex. The graph will be symmetric with respect to this line.
By connecting the plotted points and sketching the curve smoothly, we can accurately graph the function f(x).
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simplify using distributive law ;
1.) X n ( X n Y )
2.) ( X n Y ) u ( X n Y )
Answer:
X n Y , X n Y
Step-by-step explanation:
1) Use Associative law:
X n (X n Y) = (X n X) n Y
Idempotent law:
= X n Y
2) it is in the 'distributed' form, thus we need to reverse the distribution,
akin to 'factorization':
(X n Y) u (X n Y) = (X n (Y u Y))
which can be further simplified using idempotent law:
= X n Y
What is a hand drawn picture or design of a 3D object
Answer:
hello
Step-by-step explanation:
i think it is modelling
hope it helps
have a nice day
I am pretty sure it's modeling!
I need help with 1456 dived by 45
Given the expression:
1456 divided by 45
Let's perform the division.
To divide, let's use the long division method.
We have:
After dividing 1456 by 45 the quotient is:
32 remainder 16
As a mixed fraction, the quotient is:
\(32\frac{16}{45}\)As a decimal, the quotient is:
\(32.35\)Determine all minors and cofactors of the matrix A given below (5)
2 −1 1 3
0 1 1 3
2 1 1 0
2 0 −1 −2
How many times smaller is the value of 3 in 53075 than the 3 in 38499
Answer:
10 times smaller
Step-by-step explanation:
the first one the 3 is in the thousands place. in the second one, the 3 is in the ten thousands place.
kathy runs a 26.2-mi;e marathon at an average pace of 6.2 minutes per mile how long will it take her to finish the marathon round your answer to the nearest minute
Answer:
162 minutes
Step-by-step explanation:
Since she takes 6.2 minutes a mile, you multiply it by 26.2 for every mile. 6.2x26.2= 162.44, then round it to 162
A figure shows a trapezoid drawn inside a triangle. The area of the trapezoid is 96 mm², and the area of the triangle is 125 mm². A point on the figure is randomly selected, and its location recorded.
After 250 trials, the randomly selected point was in the trapezoid 154 times.
How does the experimental probability of a randomly selected point being in the trapezoid compare to the theoretical probability of the event?
The experimental probability of the event is
Choose...
and the theoretical probability of the event is
Choose...
. Therefore, the experimental probability is
Choose...
the theoretical probability.
Answer:
1 61.6 2 76.8 3 less than
Step-by-step explanation:
Took k-12 quiz
Total Assets
Sales
Task 3: Preparing a Cash Flow Statement
Nikea Inc.'s income statement for the year 2013 is shown below:
During the year, the balances for the sales account, cost of goods sold, and gross profit
increased. This information is provided to you. Prepare the cash flow for operating activities,
using both the direct method and the indirect method.
Accounts
Nikea's income statement for the year 2013 is shown below.
Cost of Goods Sold
Gross Profit
Operating Expenses
Deprecation
Styles
Net Income
934,000 Total Liability & Stockholders Equity
Type your response here:
Amount ($)
600,000
14
(400,000)
200,000
(30,000)
(20,000)
150,000
934,000
4
Editin
The preparation of the Cash Flow Statement for Nikea Inc. for the year ended December 31, 2013, is as follows:
Direct Method:
Nikea Inc.
Cash Flow StatementCash received from customers $600,000
Cash paid to suppliers of goods (400,000)
Cash paid to vendors of servides (30,000)
Cash from operating activities $170,000
Indirect Method:
Nikea Inc.
Cash Flow StatementFor the year ended December 31, 2013
Net income $150,000
Add non-cash expenses:
Depreciation 20,000
Cash from operating activities $170,000
What is the difference between the direct method and the indirect method of Cash Flow Statement?The direct method of preparing the Cash Flow Statement starts with the operating income and adds the non-cash expenses to obtain the cash flow from operating activities.
On the other hand, the indirect method reconciles the accounts receivable and payable to extract the exact cash flows received from customers or paid to suppliers of goods and services.
Both methods of determining the cash flow from operating activities yield the same result.
Data and Calculations:Nikea’s income statement for the year 2013
Sales $600,000
Cost of Goods Sold (400,000)
Gross Profit 200,000
Operating Expenses (30,000)
Deprecation (20,000)
Net Income 150,000
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A box contains 16 square chips, 12 triangular chips, and 4 circular chips. Identify the ratio of circular chips to square chips in all three forms.
The ratio of circular chips to square chips is 1:4.
What is a ratio?The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
Given:
A box contains 16 square chips, 12 triangular chips, and 4 circular chips.
The ratio of circular chips to square chips,
= Circular chips / square chips
= 4 / 16
= 1/4
= 1: 4
Therefore, the ratio is 1:4.
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(8,3) (5,6) what is slope??
Answer:
-1
Step-by-step explanation:
what are exchange rates?
Answer:
Step-by-step explanation:
Exchange rates are the rates at which one currency can be exchanged for another currency. They represent the value of one currency relative to another currency.
Is the relation shown in
the table a function?
Explain.
The inputs 4 and 8 have more than one out, the relation is not a function.
Is the relation shown in the table a function?A relation is said to be a function if one input is mapped to one output.
that is, each x-value can only have one y-value.
From the table;
Input, output
4 ----- 1
8 ----- 3
4 ------5
8 ----- 4
4 is an input, it has an output of 1.
4 appeared again as input but this time has an output of 5.
This means one input has more than one output.
Also, 8 is an input, it has an output of 3.
8 appeared again as input but this time has an output of 4.
Which also means one input has more than one output.
Therefore, the relation is not a function.
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k= y/x (3x-1)-2.75(x+2)
Answer:
k=
−2.75x2+3xy−5.5x−y/x
Step-by-step explanation:
Hi! so i see you need help with this problem let me help you and guide you through the steps :]
Let's solve for k.
k= y/x
(3x−1)−2.75(x+2)
Step 1: Multiply both sides by x.
kx=−2.75x2+3xy−5.5x−y
Step 2: Divide both sides by x.
kx/x
=
−2.75x2+3xy−5.5x−y/x
k=
−2.75x2+3xy−5.5x−y/x
Answer:
k=
−2.75x2+3xy−5.5x−y/x
Write equations for the horizontal and vertical lines passing through the point (4,-3)
The equations for the horizontal line and the vertical line are y = - 3 and x = 4, respectively.
How to determine the equation of a horizontal line and a vertical line
Herein we find the case of a point (x, y) = (a, b), from which we must derive the equations for the horizontal line and the vertical line, whose forms are described below:
Horizontal line
y = b
Vertical line
x = a
If we know that (x, y) = (4, - 3), then the equations for the horizontal and vertical lines are, respectivelly:
Horizontal line
y = - 3
Vertical line
x = 4
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find the positive suare root of the following number 57.27
The positive square root of 57.27 is approximately 7.5726, with further decimal places available through iterative approximation methods.
To find the positive square root of the number 57.27, we can use a calculator or mathematical operations.
Taking the square root of a number involves finding a value that, when multiplied by itself, gives the original number. In this case, we want to find the value that, when squared, equals 57.27.
Using a calculator, we can find the square root of 57.27 as approximately 7.5726. However, it's important to note that this is an approximation and may not be completely accurate due to rounding errors.
If we want to find a more precise answer manually, we can use iterative approximation methods. One such method is the Newton-Raphson method, which involves repeatedly refining an initial guess.
Starting with an initial guess of, let's say, 7, we can use the formula:
x(n+1) = (x(n) + (57.27/x(n)))/2,
where x(n) is the current approximation and x(n+1) is the next approximation. Iterating this formula a few times will converge to a more accurate value.
After a few iterations, we find that the positive square root of 57.27 is approximately 7.572615. This value can be further refined by performing more iterations or using more advanced numerical methods.
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NEED IN 2 MINUTES An isosceles trapezoid has a perimeter of 15.6 feet. Its shorter base measures 1 foot and its longer base measures 3.8 feet. The two remaining sides have the same length; what is that length?
Answer: 5.4
Step-by-step explanation:
First, start with adding the two given sides, then take that sum and subtract it from the perimeter, then after that, divide by two
1 + 3.8= 4.8
15.6 - 4.8=10.8
10.8 / 2 = 5.4
i need help answering this question
Answer:
Step-by-step explanation:
there is no question?
The area of a triangle is 105 square inches. The base is 15 inches. What is the height in inches?
Step-by-step explanation:
Area of triangle=1/2×base×Height
105=1/2×15×h
210=15×h
h=14inches
Drag each equation to the correct location on the table.
Match the equations with the value of x that makes them true.
5x - 2x - 4 = 5
5x - (3x - 1) = 7
x + 2x + 3 = 9
2(2x - 3) = 6
4x - (2x + 1) = 3
5(x + 3) = 25
x = 2
X = 3
Answer:
The answer to your questions are given below.
Step-by-step explanation:
To answer the question given above, we shall determine the value of x in each equation. This can be obtained as follow:
5x - 2x - 4 = 5
3x - 4 = 5
Collect like terms
3x = 5 + 4
3x = 9
Divide both side by 3
x = 9/3
x = 3
5x - (3x - 1) = 7
Clear the bracket
5x - 3x + 1 = 7
2x + 1 = 7
Collect like terms
2x = 7 - 1
2x = 6
Divide both side by 2
x = 6/2
x = 3
x + 2x + 3 = 9
3x + 3 = 9
Collect like terms
3x = 9 - 3
3x = 6
Divide both side by 3
x = 6/3
x = 2
2(2x - 3) = 6
Clear the bracket
4x - 6 = 6
Collect like terms
4x = 6 + 6
4x = 12
Divide both side by 4
x = 12/4
x = 3
4x - (2x + 1) = 3
Clear the bracket
4x - 2x - 1 = 3
2x - 1 = 3
Collect like terms
2x = 3 + 1
2x = 4
Divide both side by 2
x = 4/2
x = 2
5(x + 3) = 25
Clear the bracket
5x + 15 = 25
Collect like terms
5x = 25 - 15
5x = 10
Divide both side by 5
x = 10/5
x = 2
SUMMARY:
x = 2
x + 2x + 3 = 9
4x - (2x + 1) = 3
5(x + 3) = 25
x = 3
5x - 2x - 4 = 5
5x - (3x - 1) = 7
2(2x - 3) = 6
Find the greatest common factor of 9n3 and 8n4.
Answer:
9 and 3 GCF is 3
8 and 4 GCF is 4
the GCF of 8,3,4,9 = 1
Step-by-step explanation:
andy’s saving account pays 0.3% more interest then marty’s. martys account earns 200 in interest. how much does interest does andy’s account earn?
1. 200.60
2. 203.00
3. 206.00
4. 230.00
200.60 interest does andy’s account earn.
Let x be the amount of interest earned by Andy's account.
According to the problem, Andy's account earns 0.3% more interest than Marty's account, which means that Andy's account earns the same amount plus an additional 0.3% of that amount. Mathematically, we can express this as:
x = 200 + 0.3% of 200
Simplifying the right-hand side of the equation, we get:
x = 200 + 0.003 × 200
x = 200.60
Therefore, the answer is option 1: 200.60.
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A student is graduating from college in 18 months but will need a loan in the amount of $6,720 for the last three semesters. The student may receive either an unsubsidized Stafford Loan or
a PLUS Loan. The terms of each loan are:
Unsubsidized Stafford Loan: annual interest rate of 3.99%, compounded monthly, and a grace period of six months from time of graduation.
PLUS loan: annual interest rate of 4.99%, compounded monthly, with a balance of $7,241.17 at graduation
Which loan will have a higher balance and by how much at the time of repayment?
O The Stafford loan will have a higher balance by $107.41 at the time of repayment.
O The PLUS loan will have a higher balance by $107.41 at the time of repayment.
O The Stafford loan will have a higher balance by $36.53 at the time of repayment.
O The PLUS loan will have a higher balance by $36.53 at the time of repayment.
The Stafford loan will have a higher balance of $36.53 at the time of repayment.
The correct option is C.
What is a loan calculation formula?The formula:
PV = PMT/i[1 - {1/(1+i)ⁿ]
PV denotes the loan sum.
PMT stands for "monthly payment," I for "interest rate" (interest rate % divided by 12), and "n" for the number of months (term of the loan in months)
To compare the balances of the two loans at the time of repayment, we need to calculate the total amount owed for each loan.
For the Unsubsidized Stafford Loan:
The total loan amount is $6,720, and the annual interest rate is 3.99%, compounded monthly.
Therefore, the monthly interest rate is 3.99% / 12 = 0.3325%. The loan has a grace period of 6 months, so interest will not start accruing until 6 months after graduation.
The loan will be repaid over a period of 10 years, or 120 months.
Using the formula for the future value of an annuity, the total amount owed for the Unsubsidized Stafford Loan is:
FV = PMT x [(1 + r)ⁿ - 1] / r
where PMT is the monthly payment, r is the monthly interest rate, and n is the number of months.
We can solve PMT using a loan repayment calculator, such as the one found on bankrate.com, and we get a monthly payment of $73.80. Plugging this into the formula, we get:
FV = $73.80 x [(1 + 0.003325)¹¹⁴ - 1] / 0.003325
FV = $9,222.41
Therefore, the total amount owed for the Unsubsidized Stafford Loan at the time of repayment is $9,222.41.
For the PLUS Loan:
The loan amount is $7,241.17, and the annual interest rate is 4.99%, compounded monthly. Therefore, the monthly interest rate is 4.99% / 12 = 0.4158%. Interest starts accruing immediately, and the loan will be repaid over a period of 10 years, or 120 months.
Using the same formula, the total amount owed for the PLUS Loan is:
FV = PMT x [(1 + r)ⁿ- 1] / r
Again, using a loan repayment calculator, we get a monthly payment of $78.93. Plugging this into the formula, we get:
FV = $78.93 x [(1 + 0.004158)^120 - 1] / 0.004158
FV = $9,258.94
Therefore, the total amount owed for the PLUS Loan at the time of repayment is $9,258.94.
Comparing the two loan amounts, we see that the Unsubsidized Stafford Loan will have a higher balance of $36.53 ($9,222.41 - $9,258.94) at the time of repayment.
Therefore, the answer is:
The Stafford loan will have a higher balance of $36.53 at the time of repayment.
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Φ1 = ∬S1 (-2u^6cos(v) - 2u^3sin(v)) du dv
= ∫(0->1) ∫(0->2π) (-2u^6cos(v) - 2u^3sin(v)) dv du
\(\begin{align}\sf\:\Phi_1 &= \iint_{S_1} (-2u^6\cos(v) - 2u^3\sin(v)) \, du \, dv \\ &= \int_{0}^{1} \int_{0}^{2\pi} (-2u^6\cos(v) - 2u^3\sin(v)) \, dv \, du \end{align} \\\)
If p2-8 = 17, which of the following
is a possible value of P
Answer:
+ 5, - 5
Step-by-step explanation:
p^2 - 8 = 17
p^2 = 17 + 8
p^2 = 25
= 5 x 5
p^2 = 5^2
p = ± 5