Compute P9,2. (Enter an exact number.) Compute C7,5. (Enter an exact number.)
Answers
The Exact number of \($$P_{9,2}$$\) is \(72\)
The Exact number of \($$C_{7,5} $$\) is \(21\)
An exact number is a value that is known with complete certainty. In other words, an exact number has zero uncertainty and an infinite number of significant figures. An exact number cannot be simplified or reduced.
Examples of exact numbers included counted numbers, defined units, and defined unit conversions. Many exact numbers are integers, but some are decimals. Here are specific examples.
Number of protons in a carbon atom (6)Minutes in one hour (60)Avogadro’s number (6.02214076 × 1023)ZeroThe number of centimeters in one inch (exactly 2.54)Number of pages in a bookHere we have to compute \($P_{9,2}$\) means
\(P_{1,5} & =\frac{7 !}{(7-5) !}\)
\(P_{9,2} & =\frac{9 !}{(9-2) !}\)
\(=\frac{9 !}{7 !}=\frac{9 \times 8 \times 7 !}{7 !}\)
\(P_{9,2} & =7 \times 8=72\)
Hence \($P_{9,2}$\) \(=72\)
Here we have to compute \($C_{7,5}$\) means
Combination \($(7,5)$\)
\($$\begin{aligned}& \left(\begin{array}{l}7 \\5\end{array}\right)=\frac{7 !}{(7-5) ! 5 !}=\frac{7 * 6 * 5 !}{2 ! * 5 !} \\& =\frac{7 * 6}{2 * 1}=21\end{aligned}$$\)
Hence
\($$C_{7,5}=21$$\)
Therefore, the Exact number of P9,2. is 72 and C7,5. is 21.
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Related Questions
I need help with this problem I cant figure it out.
Answers
Answer:
DFG= 52
JKL=38
Step-by-step explanation:
complementary angle means that the sum of the two angles are equal to 90° so
(x+5)+(x-9)=90
= x+5+x-9=90
= 2x-4=90
= 2x=94
= x= 94÷2=47
DFG= x+5= 47+5=52
JKL= x-9= 47-9=38
hope it helps
Draw a sketch of y = x2 - x - 3for values of x in the domain -3 <=x<= 3. Write down the coordinates of the turning point in your solution. Hence, from your sketch, find approximate solutions to:x2 – X – 3 = 0.
Answers
The sketch of the function y = \(x^{2}\) - x - 3 for -3 <= x <= 3 reveals a parabolic curve that opens upwards. The turning point of the parabola, also known as the vertex, can be identified as (-0.5, -3.25).
To sketch the graph of y = \(x^{2}\) - x - 3, we consider the given domain of -3 <= x <= 3. The function represents a parabola that opens upwards. By calculating the coordinates of the turning point, we can locate the vertex of the parabola.
To find the x-coordinate of the turning point, we use the formula x = -b/2a, where a and b are the coefficients of the quadratic equation. In this case, a = 1 and b = -1. Substituting these values, we have x = -(-1)/2(1) = -0.5.
To find the y-coordinate of the turning point, we substitute the x-coordinate (-0.5) into the equation y = \(x^{2}\) - x - 3. Evaluating this expression, we get y = \(-0.5^{2}\) - (-0.5) - 3 = -3.25.
Therefore, the turning point of the parabola is approximately (-0.5, -3.25).
From the sketch, we can estimate the approximate solutions to the equation \(x^{2}\)- x - 3 = 0 by identifying the x-values where the graph intersects the x-axis. These solutions are approximately x ≈ -2.5 and x ≈ 1.5.
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Lana had 475 Pokemon cards. She gave her little brother 125 of her cards. What percentage of her cards did Lana give away?
Answers
So, Lana gave away 26.32% of he Pokemon cards to her little brother.
To find the percentage of cards Lana gave away, we can use the formula:(Quantity given away / Total quantity) * 100.
In this case, Lana gave away 125 cards out of her total collection of 475 cards.Plugging these values into the formula, we have:
(125 / 475) * 100 = 0.2632 * 100 = 26.32%.
Lana gave away 26.32% of her Pokemon cards to her little brother.
Alternatively, we can calculate the percentage by subtracting the remaining cards from the total and finding the ratio:
Percentage given away
= (Cards given away / Total cards) * 100
= (125 / 475) * 100
= 26.32%.
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chris has been given a list of bands and asked to place a vote. his vote must have the names of his favorite and second favorite bands from the list. how many different votes are possible?
Answers
There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.
To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.
Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.
Therefore, the number of different votes possible is m * (m-1) / 2.
In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.
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What is the equation of the graphed line written in standard form?
2x + 3y = -6
2x + 3y = 6
y=-2/3x-2
y= 2/3x-2
Answers
Answer:
What is the equation of the graphed line written in standard form?" has four options: 2x + 3y = -6, 2x + 3y = 6, y=-2/3x-2, and y= 2/3x-2. The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. In this case, the first two options, 2x + 3y = -6 and 2x + 3y = 6 are already in standard form. The last two options, y=-2/3x-2 and y= 2/3x-2 are not in standard form. However, without additional information such as a graph or coordinates of points on the line, it is not possible to determine which of these options is the correct equation for the graphed line.
MARK AS BRAINLIEST!!!
HELP ME PLS ITS 3AM IM TIRED // geometry HL AND CPCTC
Answers
Answer:
b
Step-by-step explanation:
angle b = angle e = 90 (given) R
if ac = df H
bc = ef (given) S
A crew lays 100 bricks per hour. The crew's job requires them to lay 950 bricks, and 200 have already
been laid. In which equation does h represent the number of hours needed to finish the job?
A. 100h + 200 = 950
R
B. 100h - 200 = 950
C. 100 + 200h = 950
D. 100 - 200h = 950
Answers
On May 1, 2016, a firm purchased a 1-year insurance policy for $3,600 and paid the full premium in advance. The insurance expense associated with this policy for 2016 is:
Answers
The insurance expense associated with the policy purchased by the firm on May 1, 2016, for 2016 is $2,400.
The insurance policy purchased by the firm on May 1, 2016, is for a period of one year. Since the full premium of $3,600 was paid in advance, the expense for 2016 will be the portion of the premium that relates to the current year.
To calculate the insurance expense for 2016, we need to determine the portion of the premium that applies to this year. Since the policy is for one year, we can allocate the premium equally to each month. Therefore, the monthly premium will be $3,600/12 = $300.
The firm purchased the insurance policy on May 1, which means that only eight months of coverage remain in 2016 (May to December). Therefore, the insurance expense for 2016 will be $300 x 8 = $2,400. This amount represents the portion of the premium that relates to the current year, and it will be recognized as an expense on the firm's income statement for 2016.
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A company estimates that it will need $126,000.00 in 10 years to replace a computer. If it establishes a sinking fund by making fixed monthly payments into an account paying 3.9% compounded monthly how much should each payment be
Answers
The company should make fixed monthly payments of $847.89 with 3.9% compound interest into the sinking fund to fulfill the need of $126,000.00 in 10 years to replace a computer.
To calculate the monthly payments needed for the sinking fund, we can use the formula:
P = (A/i) * [1 - (1 + i)^(-n)]
where P is the monthly payment, A is the future value of the investment, i is the interest rate per period (in this case, monthly), and n is the total number of periods (in this case, 10 years * 12 months/year = 120 months).
First, we need to find the future value of the investment, A. The problem tells us that we need $126,000 in 10 years, so we can use the formula for future value with monthly compounding:
A = P * [(1 + i)^n - 1]/i
where P is the monthly payment, i is the interest rate per period (in this case, 3.9%/12 = 0.00325), and n is the total number of periods (in this case, 10 years * 12 months/year = 120 months).
Substituting the given values, we get:
126,000 = P * [(1 + 0.00325)^120 - 1]/0.00325
Solving for P, we get:
P = 126,000 / [(1 + 0.00325)^120 - 1]/0.00325
P = $847.89 (rounded to the nearest cent)
Therefore, the company should make fixed monthly payments of $847.89 into the sinking fund.
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how many terms are in the following expression?
Answers
The number of terms in the expression, 6 + 2 x - 4 y + 5 z is 4 terms.
How to find the number of terms ?In the expression 6 + 2x - 4y + 5z, the number of terms is four, not the number of signs. The terms in this expression are:
62 x- 4 y 5 zEach term is separated by an operator (either addition or subtraction), which is represented by a sign. Therefore, the expression contains three addition signs and one subtraction sign.
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The full question is:
How many terms are in the following expression 6 + 2 x - 4 y + 5 z
Nora was offered a job that paid a salary of $40,000 in its first year. The salary was set to increase by 3% per year every year. If Nora worked at the job for 21 years, what was the total amount of money earned over the 21 years, to the nearest whole number?
Answers
The total amount of money earned by Nora salary over the 21 years is approximately $1,848,000.
To find the total amount of money earned by Nora over 21 years, we need to calculate the salary for each year and then sum them up.
In the first year, Nora's salary is $40,000.
In the second year, her salary will be increased by 3%, so it will be:
$40,000 + 3% of $40,000 = $40,000 + $1,200 = $41,200.
In the third year, her salary will again increase by 3%, so it will be:
$41,200 + 3% of $41,200 = $41,200 + $1,236 = $42,436.
We can continue this process for each year, adding 3% of the previous year's salary to calculate the next year's salary.
To calculate the total amount of money earned over the 21 years, we need to sum up the salaries for each year. Here's the calculation:
Total = $40,000 + $41,200 + $42,436 + ... (21 terms)
To simplify the calculation, we can use the formula for the sum of an arithmetic series:
Total = (n/2) * (2a + (n - 1)d)
where:
n = number of terms (21 in this case)
a = first term ($40,000)
d = common difference (3% of the previous year's salary)
Plugging in the values:
Total = (21/2) * [2(40,000) + (21 - 1)(0.03)(40,000)]
Simplifying further:
Total = (21/2) * [80,000 + 20(0.03)(40,000)]
= (21/2) * [80,000 + 2,400(40,000)]
= (21/2) * [80,000 + 96,000]
= (21/2) * 176,000
= 21 * 88,000
= 1,848,000
Therefore, the total amount of money earned by Nora salary over the 21 years is approximately $1,848,000.
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What is the y-intercept of the line perpendicular to (1,1) and (-3,-1) and passes through (-3,-2)
The y-intercept is
Answers
Answer:
-8
Step-by-step explanation:
Let's first establish the reference line (the one that the second line will be perpendicular to). We are told that this line passes through two points:
(1,1) and (-3,-1).
We'll find a line equation using the point slope form format to start:
(y - y1) = m * (x - x1), where m is the slope and the x and y are from two points.
(x,y) = (1,1)
(x1,y1) = (-3,-1)
Rearrange the equation:
(y - y1) = m * (x - x1)
m = (y - y1)/ (x - x1)
m = (1-(-1))/(1-(-3))
m = 2/4, or 1/2: The slope is 1/2. [This is "m."]
We can use the slope-intercept form for this line (y=mx + b) and then calculate b, the y-intercept:
y = (1/2)x + b
Use either of the two given points. I'll use (1,1) since I have memorized the "1" math tables.
y = (1/2)x + b
1 = (1/2)(1) + b for (1,1)
b = 1/2
This makes the reference line: y = (1/2)x+(1/2)
===
The line perpendicular must have a slope that is the negative inverse of (1/2). This would be -(2/1), or -2.
We can then write y = -2x + b
To find be, enter the one given point for this line: (-3,-2)
y = -2x + b
-2 = -2(-3) + b
-2 = 6 + b
b = -8
The perpendicular line is thus:
y = -2x - 8
It has a y-intercept of -8
Help me solve these equations by graphing please
Answers
Answer:
5, 6, and 8 don’t have solutions because they are parallel / have the same slope. 7 has a solution outside of the domain and range of this graph.
Step-by-step explanation:
I’m honestly not sure about 7, it seems like it should be parallel as well. tell me if I should redo it lol.
PLEASE HELP ME I WILL GIVE BRAINLY TO THE BEST.
Just fill in those blanks and for the explanation question it doesn't have to be long 1 sentence will be alr
Answers
1. A = 45° B = 110°
2. B = 88° C = 44°
3. A = 59° B = 48° C= 73°
4. The measure of the exterior angle is 108°
5. The tornado's direction needs to change by 30°
The sum of interior angles of triangle is always equal to 180°.
Now let's apply it in the given questions.
1. A = x
B = x + 65
C = 25
So, x + x + 65 + 25 = 180
2x = 180 - 90
x = 90/2
x = 45°
2. x + 48 + x - 44 = 180
2x = 180 - 4
x = 176/2
x = 88°
3. x + 73 + x - 11 = 180
2x = 180 - 62
x = 118/2
x = 59°
4. Let the third interior angle be b.
2a + b = 180
b = 180 - 2a
now by applying angle sum property
a + 10 + 44 + 180 - 2a = 180
2a - a = 54
a = 54°
the exterior angle is 2a that is 54*2 = 108°
5. For the tornado to deviate and pass through radar station instead of cell phone tower the angle that needs to be made will be nothing but the third interior angle of the triangle as the tornado is at the vertex.
Let us suppose the angle to be y
so y + 75 + 75 = 180
y = 180 - 150
y = 30°
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Find the length of each segment. Tell whether the segments are congruent. (1,2,3,4 only)
Answers
Answer: 1 & 2 are congruent
Step-by-step explanation:
They both have the same amount of space to get to the other point .
1. AC is congruent to BD.
2. BD and CE are not congruent.
3. AD and BE are not congruent.
4. BC and CE are not congruent.
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
1. The segment AC is (1 - (-8)) = 9 units, and the line segment
BD is (3 -(-6)) = 9 units.
So, AC ≅ BD.
2. Line segment BD is 9 units and line segment CE is (7 - 1) = 6 units.
So, BD and CE are not congruent.
3. Line segment AD is (3 - (-8)) = 12 units and line segment BE is (7 - (-6)) = 13 units. (not congruent)
So, line segment AD and BE are not congruent.
4. Line segment BC is (1 - (-6)) = 7 units and line segment CE is (7 - 1) = 6 units.
So, Line segments BC and CE are not congruent.
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A camera has a listed price of $ 870. 98 870. 98 before tax. If the sales tax rate is 9. 25 % , 9. 25 % , find the total cost of the camera with sales tax included. Round your answer to the nearest cent, as necessary
Answers
Answer:
$951.55
Step-by-step explanation:
Original Camera Price (before tax): $870.98
Tax Rate: 9.25%
Calculation: Original Price x (1 + tax rate as a decimal)
$870.98 x (1+0.0925) = $951.54565--> $951.55 (2dp)Step-by-step explanation:
9.25% of 870.98 is 80 dollars
870.98+80 is 950
Anybody know the answer?
Answers
Answer:
\(2x + {y}^{2} \)
11. There is a $10 monthly membership fee to download music. There is
a $0.50 fee for each song downloaded.
a. Write a linear equation that models the cost of downloading x songs
per month.
b. Graph the equation.
c. What is the cost of downloading 15 songs?
Answers
Answer:
A) y=0.5x+10 C) 17.5 dollars (don't forget your units)
Step-by-step explanation:
a) 0.5 is the price paid per song, or x, and 10 is the price that does not change for a month, so we can say that y=0.5x+10
c) to download 15 songs, we substitute x by 15
y=0.5(15)+10
y=7.5 + 10
y=17.5
and for b, im sorry but I cannot graph here.
A circle has a diameter of 4 inches. Which statement about the area and circumference of the circle is true?
Answers
The numerical values of the circumference and area are equal.
Answer:
To simplify it a
Step-by-step explanation:
7th grade math
Look at photo.
Answers
Answer:
10/z = 15/6
Step-by-step explanation:
Two shapes are similar so their side lengths are proportional, and the correct proportion to find the missing measurements is 10/z = 15/6
Every 7 days plant grows 4 centimeters. Complete the table.
Number of Growth (cm)
days
7 4
_ 8
_ 12
_ 16
_ 20
Answers
Answer:
7,14,21,28,35
Step-by-step explanation:
If the plant grows 7cm every 7 days then you simply have to add 7 for each time it goes up 4. For example from 4-8 it went up 4 therefore you add 7. 7+7= 14. Then you repeat the process for all other numbers
Solve the triangle. ... Question content area top right Part 1 c 76° a=13.2 74° γ b
Answers
Answer:
The missing angle γ=17.97°.
Let's have detailed explanation:
Since the information given includes the angles of the triangle (76°, 74°, and γ), and the lengths of two sides (a=13.2 and b), we can use the Law of Cosines formula to solve for the missing side (b): b^2 = a^2 + c^2 − 2ac cos(γ).
Therefore, b = sqrt(13.2^2 + 76^2 - 2(13.2)(76) * cos(γ)).
To solve for the value of γ, we can use the Law of Cosines formula once again: cos(γ) = (a^2+b^2-c^2)/2ab.
Substituting in the values for a, b, and c then gives us:
cos(γ) = (13.2^2+sqrt(13.2^2 + 76^2 - 2(13.2)(76) * cos(γ))-76^2)/(2*13.2*sqrt(13.2^2 + 76^2 - 2(13.2)(76) * cos(γ))).
Using the cosine inverse function, we then find that
γ=17.97°.
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The possible solutions from the triangle are c = 25.6 units, b = 25.4 units and A = 30 degrees
How to determine the possible solutions from the triangleFrom the question, we have the following parameters that can be used in our computation:
C = 76 degrees
a = 13.2 units
B = 74 degrees
The sum of angles in a triangle is 180 degrees
So, we have
A = 180 - 76 - 74
Evaluate
A = 30
Using the law of sines, the length b is calculated as
b/sin(B) = a/sin(A)
So, we have
b/sin(74) = 13.2/sin(30)
This gives
b = sin(74 deg) * 13.2/sin(30 deg)
Evaluate
b = 25.4
For segment c, we have
c = sin(76 deg) * 13.2/sin(30 deg)
Evaluate
c = 25.6
Hence, the length of the side c is 25.6 units
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Question
Solve the triangle.
c = 76°
a = 13.2
b = 74°
For the given differential equation, (a) Determine the roots of the characteristic equation. (b) Obtain the general solution as a linear combination of real-valued solutions. (c) Impose the initial conditions and solve the initial value problem. 3. y" + 4y = 0, y(f/4) = -2, y'(f/4) = 1
Answers
(a) The roots of the characteristic equation r = ±2i.
The characteristic equation for the differential equation y'' + 4y = 0 is r^2 + 4 = 0. Solving this quadratic equation, we obtain the roots r = ±2i.
(b) The general solution of the differential equation is given by y(t) = c1 cos(2t) + c2 sin(2t), where c1 and c2 are constants determined by the initial conditions.
(c) To solve the initial value problem y(f/4) = -2 and y'(f/4) = 1, we first need to find the values of c1 and c2 that satisfy the conditions. Using the first initial condition, we have -2 = c1 cos(2f/4) + c2 sin(2f/4), which simplifies to -2 = c1 cos(f) + c2 sin(f).
Differentiating this equation with respect to t and using the second initial condition, we get 1 = -2c1 sin(f) + 2c2 cos(f). Solving these two equations simultaneously, we obtain c1 = -2sin(f)/5 and c2 = (2cos(f)+5)/5. Thus, the solution to the initial value problem is y(t) = -2/5 sin(2t+f) + (2cos(f)+5)/5 cos(2t+f).
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solve 2/x-1=16/x^2+3x-4
Answers
The solutions to the equation \(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)
To solve the equation \(2/x - 1 = 16/(x^2 + 3x - 4),\) we'll simplify and rearrange the equation to isolate the variable x. Here's the step-by-step solution:
1. Start with the given equation: 2/x - 1 = 16/(x^2 + 3x - 4)
2. Multiply both sides of the equation by x(x^2 + 3x - 4) to eliminate the denominators:
\(2(x^2 + 3x - 4) - x(x^2 + 3x - 4) = 16x\)
3. Simplify the equation:
\(2x^2 + 6x - 8 - x^3 - 3x^2 + 4x - 16x = 16x\)
4. Combine like terms:
-x^3 - x^2 + 14x - 8 = 16x
5. Move all terms to one side of the equation:
\(-x^3 - x^2 - 2x - 8 = 0\)
6. Rearrange the equation in descending order:
-x^3 - x^2 - 2x + 8 = 0
7. Try to find a factor of the equation. By trial and error, we find that x = 2 is a root of the equation.
8. Divide the equation by (x - 2):
\(-(x - 2)(x^2 + x - 4) = 0\)
9. Apply the zero product property:
x - 2 = 0 or x^2 + x - 4 = 0
10. Solve each equation separately:
x = 2
11. Solve the quadratic equation:
For x^2 + x - 4 = 0, you can use the quadratic formula or factoring to solve it. The quadratic formula gives:
\(x = (-1 ± √(1^2 - 4(1)(-4))) / (2(1)) x = (-1 ± √(1 + 16)) / 2 x = (-1 ± √17) / 2\)
Therefore, the solutions to the equation\(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)
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An envelope contains three cards: a black card that is black on both sides, a white card that is white on both sides, and a mixed card that is black on one side and white on the other. You select one card at random and note that the side facing up is white. What is the probability that the other side is black?
Answers
The probability that the other side is black, given that the side facing up is white, is 1.
Let's denote the events as follows: A: The selected card has a black side facing up. B: The selected card has a white side facing up. We are interested in finding P(A|B), the probability that the other side of the card is black given that the side facing up is white.
We know that there are three possible cases when we select a card: black-black (BB), white-white (WW), and black-white (BW). Since we have selected a card with a white side facing up, we can eliminate the WW case as it is not possible. Out of the two remaining cases (BB and BW), only one has a white side facing up, which is the BW case. Therefore, the other side of the card must be black.
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If we have : y = - √(−x-6) -2
This is a square root graph and I have attached what it looks like below.
I know that it doesn't have a x-int, however, if I do it by hand it seems like it has one.
I have attached my working out below.
Can someone please help?
Thank you!
Answers
The explanation is given below:
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
The graph you have plotted is correct.
But it hasn't been consider the x- integer.
By looking the graph closely,
the graph is in III quadrant, in III quadrant x and y both are negative.
Let us take the first point (-6, -2).
So, here x is (-6) and y is (-2).
Hence, there are both integers are located in the graph.
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Round 21,357 to the nearest ten thousand.
Answers
Answer:
21,000
Step-by-step explanation:
you would round up if it was 21,500 that would round up t0 22,000
there is a population of 15,500 bacteria in a colony. if the number of bacteria doubles every 234 hours, what will the population be 936 hours from now?
Answers
If the number of bacteria doubles every 234 hours, we can use the exponential growth formula to find the population at a future time t:
N(t) = N0 * 2^(t/T)
where N(t) is the population at time t, N0 is the initial population, T is the doubling time (234 hours in this case), and t is the time elapsed.
We are given that the initial population is 15,500 bacteria. We want to find the population 936 hours from now. Therefore, we can substitute the values into the formula:
N(936) = 15,500 * 2^(936/234)
N(936) = 15,500 * 2^4
N(936) = 15,500 * 16
N(936) = 248,000
Therefore, the population of bacteria in the colony will be 248,000 after 936 hours.
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I need help please! It would mean a lot (:
Answers
Answer:
1. x=22 2. x= 28
Step-by-step explanation:
1. The total of angles in a triangle add up to 180˚.
93+65= 158
180-158=22
This means that x = 22
2. Angles on a straight line add up to 180.
180-125=55
180-83=97
55+97=152
180-152=28
This means that x = 28
Hope that this helps you.
9. Felicia works for a furniture company. She earns a base salary of $300
per week, then 4% commission on sales. How much will she make in total
for one week if her sales totaled $7,268? *
O A) $590.72
B) $290.72
C) $2,907.20
D) $3,207.20
I WILL GIVE BRAIN :)
Answers
$590.72/week
Explanation
Felicia earns a base salary of $300 before any sales. To find how much she makes in total you have to find her total sales and multiply that by 4%. When you do that you get $290.72. You then add $290.72 to $300 to get her total earnings for the week.
Hope this helped!!