Answer:
B. r = 4cosθStep-by-step explanation:
Given the expression in rectangular coordinate as x²+y²−4x=0, in order to write the given expression in polar coordinates, we need to write the value of x and y as a function of (r, θ).
x = rcosθ and y = rsinθ.
Substituting the value of x and y in their polar form into the given expression we have;
x²+y²−4x=0
( rcosθ)²+( rsinθ)²-4( rcosθ) = 0
Expand the expressions in parenthesis
r²cos²θ+r²sin²θ-4rcosθ = 0
r²(cos²θ+sin²θ)-4rcosθ = 0
From trigonometry identity, cos²θ+sin²θ =1
The resulting equation becomes;
r²(1)-4rcosθ = 0
r²-4rcosθ = 0
Add 4rcosθ to both sides of the equation
r²-4rcosθ+4rcosθ = 0+4rcosθ
r² = 4rcosθ
Dividing both sides by r
r²/r = 4rcosθ/r
r = 4cosθ
Hence the correct equation in polar coordinates is r = 4cosθ
Luke owns a trucking company. For every truck that goes out, Luke must pay the driver $17 per hour of driving and also has an expense of $1.75 per mile driven for gas and maintenance. On one particular day, the driver drove an average of 40 miles per hour and Luke's total expenses for the driver, gas and truck maintenance were $522. Write a system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove. Define the variables that you use to write the system.
Answer:
17h+1.75m=522 m=40h
Step-by-step explanation:
Let h= {the number of hours the driver drove}
Let m= the number of miles driven
The driver makes $17 for each hour working, so if the driver worked for hh hours, Luke would have to pay him 17h17h dollars. The cost of gas and maintenance is $1.75 per mile, so for mm miles Luke's costs would be 1.75m1.75m dollars. The total cost of the route 17h+1.75m17h+1.75m equals \$522:$522:
17h+1.75m=522
17h+1.75m=522
Since the driver drove an avearge of 40 miles per hour, if the driver drove hour, he would have driven 40 miles, and if the driver drove hh hours, he would have driven 40h40h miles, therefore mm equals 40h:40h:
m=40h
m=40h
Write System of Equations:
17h+1.75m= 522
m=40h
The truck is going for a run for 6 hours and the system of the equation to solve a further problem related to this is [tex]\rm{Cost}=17x+1.75y[/tex]
The following are the different costs of the truck that Luke must be pay while running a truck:
Luke must pay the driver $17 per hour of driving.A truck has an expense of $1.75 per mile driven for gas and maintenance.Let ' x ' be the total time of driving a truck in hours.
and ' y ' be the total mile distance that is covered by the truck.
Therefore, the system of the equation for the overall running cost for a truck is given below.
[tex]\rm{Cost}=17x+1.75y[/tex]
Now, On one particular day, the driver drove an average of 40 miles per hour, and Luke's total expenses for the driver, gas and truck maintenance were $522.
Thus,
The total distance traveled by truck is 40x.
That is,
[tex]y=40x[/tex]
Substitute the values and solve them further.
[tex]522=17x+1.75y\\522=17x+1.75 \times 40x\\522=17x+70x\\522=87x\\x=6[/tex]
Thus, the truck is going for a run for 6 hours and the system of the equation to solve the further problems related to this is [tex]\rm{Cost}=17x+1.75y[/tex]
To know more about variables, please refer to the link:
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Answer using the graph
Answer:
8
Step-by-step explanation:
f(x)=x²+4 ( find quadratic equation: given vertex)
g(x)=x+2 ( find linear equation : given 2 points)
(f-g)(-2)
(x²+4-x-2)of (-2)
x²-x+2 now find (f-g)(-2)
-2²-(-2)+2=4+2+2=8
Greg is 10 years older than his brother gabe. He is also 3 times as old as gabe. How old is Greg?
Answer: 30 i think 10x3=30
Step-by-step explanation:
Please tell me the answer ASAP Lynette's average score on five tests is 18. If she scores 24 points on her sixth test, what is her average score on all six tests? Show Your Work
Answer:
The average score of 6 tests is 19.
Step-by-step explanation:
Given that the average score of 5 tests is 18. So first, we have to find the total number of scores for 5 tests :
[tex]let \: x = total \: no. \: of \: scores[/tex]
[tex] \frac{x}{5} = 18[/tex]
[tex]x = 18 \times 5[/tex]
[tex]x = 90[/tex]
We have found out that the total scores for 5 tests is 90. So we have to find the average of 6 scores :
[tex] \frac{x + 24}{5 + 1} = \frac{90 + 24}{6} = \frac{114}{6} = 19[/tex]
[tex] \LARGE{ \boxed{ \rm{ \pink{Solution : )}}}}[/tex]
Given:Average score in 5 tests = 18He scored 24 points in 6th pointTo FinD:Find the average score in all six tests?How to find?We need to know how to find the average
☄ For this case, We are gonna find average score...!
[tex] \large{ \boxed{ \sf{Avg. \: score = \frac{Total \: score}{No. \: of \: tests} }}}[/tex]
So, Let's proceed further towards solution....
Solution:We have,
Avg. score = 18No. of tests = 5Finding total score in 5 tests,
⇛ Total score = Avg. score × No. of tests
⇛ Total score = 18 × 5
⇛ Total score = 90
According to question,
He scored 24 marks in 6th test⇛ Total score now = 90 + 24 = 114
No. of tests = 6Finding the average score of 6 tests,
⇛ Avg. score = 114 / 6
⇛ Avg. score = 19 points
☄ Avg. score of lynette in 6 tests = 19
━━━━━━━━━━━━━━━━━━━━
graph the linear equation. Find three points that solve the equation, the plot them on the graph. -2y= 5x +11
Answer:
Three points are (0,-5.5), (-1,-3), (-2.2,0) and graph is shown below.
Step-by-step explanation:
The given equation is
[tex]-2y=5x+11[/tex]
We need to find three points that solve the equation.
Put x=0,
[tex]-2y=5(0)+11[/tex]
[tex]-2y=11[/tex]
[tex]y=-5.5[/tex]
Put x=-1,
[tex]-2y=5(-1)+11[/tex]
[tex]-2y=6[/tex]
[tex]y=-3[/tex]
Put y=0,
[tex]-2(0)=5x+11[/tex]
[tex]5x=-11[/tex]
[tex]x=-2.2[/tex]
So, three points (0,-5.5), (-1,-3) and (-2.2,0) are the solutions of the given equation.
Plot these points on a coordinate plane and connect them by a straight line as shown below.
Alonso brings $21 to the market to buy eggs and avocados. He gets eggs that cost $2.50. Then, he notices
that the store only sells avocados in bags of 3 for $5. He wants to buy as many avocados as he can with his
remaining money.
Let B represent the number of bags of avocados that Alonso buys.
1) Which inequality describes this scenario?
Answer:
Step-by-step explanation:
The money Alonso has is $21 which he wants to use to buy eggs and Avocados. The eggs he bought costs $2.50. Therefore the money remaining after the egg is bought is $18.50 (21 - 2.50)
Each bag of avocado cost $5, therefore the number of bags that can be bought with $18.50 is:
Bags of Avocado = $18.50 / $5 = 3.7 = 3 (to the previous whole number).
This means that the maximum number of bags of Avocado that can be bought is 3 bags. It can be represented by the inequality:
Bags ≤ 3
Answer:
2.50 + 5B ≤ 21;
Step-by-step explanation:
Cost of eggs = $2.50
Cost of avocado = $5 (bag of 3)
Total budgeted amount = $21
Bags of avocado = B
Therefore :
(Cost of eggs + cost of avocado) ≤ total budgeted amount
($2.50 + $5(B)) ≤ 21
2.50 + 5B ≤ 21
5B ≤ 21 - 2.50
5B ≤ 18.50
B ≤ 18.50 / 5
B ≤ 3.7
Therefore the maximum number of bags can purchase is 3(whole number without exceeding $21)
Which statements about the sum of the interior angle measures of a triangle in Euclidean and non-Euclidean geometries are true? A. In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is less than 180 degrees. B. In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is greater than 180 degrees. C. In Euclidian geometry the sum of the interior angle measures of a triangle is less than 180 degrees, but in hyperbolic geometry the sum is equal to 180 degrees. D. In Euclidian geometry the sum of the interior angle measures of a triangle is greater than 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees. E. In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.
Answer:
its b and e
Step-by-step explanation:
The statements given in options B and E are true so options B and E are right options.
Given some statements we have to determine that which of the following statements are true
The given statements are as follows
A. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is less than 180 degrees.
B. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is greater than 180 degrees.
C. In Euclidean geometry the sum of the interior angle measures of a triangle is less than 180 degrees, but in hyperbolic geometry the sum is equal to 180 degrees.
D. In Euclidean geometry the sum of the interior angle measures of a triangle is greater than 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.
E. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.
We know some facts about each type of geometry
In Euclidean geometry plane is used to plot the points and line.
In spherical geometry uses the sphere to plot the points and circles
Elliptical geometry is such a geometry where no parallel lines exists.
The sum of interior angles of a triangle is dependent on the type of geometry we are dealing with and they can be written down in the following points
In Euclidean geometry the sum of interior angles of a triangle is 180° In spherical or elliptical geometry the sum of interior angles of a triangle is more than 180° In hyperbolic geometry the sum of interior angles of a triangle is less than 180°So from the above observations we can conclude that statements given in options B and E are true so options B and E are right options.
For more information please refer to the link given below
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Write an equation showing the relationship between the lengths of the three sides of a right triangle.
Answer:
Below
Step-by-step explanation:
First triangle)
This triangle is a right one so we will apply the pythagorian theorem.
● 25 is the hypotenus
● 25^2 = b^2 + 24^2
■■■■■■■■■■■■■■■■■■■■■■■■■■
Seconde triangle)
Again it's a right triangle
x is the hypotenus.
● x^2 = 12^2 +5^2
● 12^2 = x^2-5^2
■■■■■■■■■■■■■■■■■■■■■■■■■■
This is a right triangle
AC is the hypotenus.
● AC^2 = BC^2 + BA^2
Notice that: BC = BE+EC and BA=BD+DA
● AC^2 = (BE+EC)^2 + (BD+DA)^2
Answer: 2) b = 7 3) x = [tex]\sqrt{119}[/tex]
Step-by-step explanation:
Use Pythagorean Theorem: (leg₁)² + (leg₂)² = hypotenuse²
2) b² + 24² = 25²
b² + 576 = 625
b² = 49
[tex]\sqrt{b^2}=\sqrt{49}[/tex]
b = 7
3) 5² + x² = 12²
25 + x² = 144
x² = 119
[tex]\sqrt{x^2}=\sqrt{119}[/tex]
[tex]x=\sqrt{119}[/tex]
What is the answer, what are the steps to solve this, and what do the parts of the equation represent?
Answer:
[tex]\sum_{a=1}^{7}(500-a)=3472[/tex]
Step-by-step explanation:
[tex]\sum_{a=1}^{7}(500-a)[/tex] will form a sequence as,
499, 498, 497.......7 terms
Since there is a common difference between successive and previous term,
d = 498 - 499 = -1
This sequence is an arithmetic sequence.
Sum of n terms of an arithmetic sequence is,
[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex]
where a = first term of the sequence
n = number of term
d = common difference
For the given given sequence,
[tex]S_{7}=\frac{7}{2}[2(499)+(7-1)(-1)][/tex]
= [tex]\frac{7}{2}[998-6][/tex]
= [tex]\frac{7}{2}(992)[/tex]
= 3472
Therefore, sum of seven terms of the given sequence will be 3472.
Determine the equation of the exponantial function with a common ratio of 2, a horizontal asymptote at y=4 and passin through the point (2,10).
Answer:
Step-by-step explanation:
Suppose that you are standing 150 feet from a building and the angle of elevation to the top of the building is 42°. What is the building's height?
Answer:
135.06 feet
Step-by-step explanation:
Since the side of the building makes a right triangle with the ground and you know one side length and the degree angle between you and the top of the building we can use trigonometric function to find the height of the building. So since we know one side other than the hypotenuse we can use tangent to solve. Tangent is the opposite side over the adjacent side of the known angle.
opposite side = x
adjacent side = 150 feet
angle = 42°
tan(42°) = x/150 feet
150 feet * tan(42°) = x
x = 135.06 feet
According to the U.S. Energy Information Administration the average number of televisions per household in the United States was 2.3. A college student claims the average number of TV’s per household in the United States is different. He obtains a random sample of 73 households and finds the mean number of TV’s to be 2.1 with a standard deviation of 0.84. Test the student’s claim at the 0.01 significance level.
Let [tex]\mu[/tex] be the average number of televisions per household in the United States .
As per given ,
[tex]H_0:\mu =2.3\\\\ H_a:\mu\neq2.3[/tex]
Since [tex]H_a[/tex] is two-tailed and population standard deviation is unknown, so the test is two-tailed t-test.
For sample : Sample size : n= 73, sample mean: [tex]\overline{x}[/tex] = 2.1, sample standard deviation : s= 0.84.
[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]
[tex]t=\dfrac{2.1-2.3}{\dfrac{0.84}{\sqrt{73}}}\\\\ t=-2.034[/tex]
T-critical value for degree of freedom n-1 = 73-1=72 and 0.01 significance level is 2.646 . [By students' t-distribution table]
Since, [tex]|2.034|<2.646[/tex] i.e. [tex]|T_{cal}|<|T_{crit}|[/tex]
This means we cannot reject null hypothesis.
We conclude that the average number of televisions per household in the United States is 2.3 at the 0.01 significance level.
rational number between 2 and 3 ?
Answer:
2:3
Step-by-step explanation:
It’s easy
Answer:
2.5
Step-by-step explanation:
i think
The admission to a local carnival ride is $8.25 per person and $1.50 for each ride.
Answer:
You would multiply 8.25 by 3 which equals 24.75. Then multiply 1.50 by 8 which is 12.00.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Which represents a measure of volume?
O 5 cm
O 5 square cm
05 cm
05 cm
Answer:
a) 5[tex]cm^{3}[/tex]
Step-by-step explanation:
Bodies have three dimensions (width, height and depth). Measuring volume is calculating the number of cubic units that can fit inside.
When raising to 3, these dimensions are included and therefore 5[tex]cm^{3}[/tex] is a measure of volume.
Answer:
5cm^3
Step-by-step explanation:
Volume for a form will always be in cubic units.
Area of a shape will always be in squared units.
Length will not be in cubic or squared units.
Hence, the first option is a measure for volume.
The second option is equal to 5cm^2 which represents a measure for area, as does the fourth option.
The third option represents a measurement of length, for example the length of a line segment or the height of a figure.
Find the interquartile range of the following data set.
Number of Points Scored at Ten Basketball Games
57 63 44 29 36 62 48 50 42 34
A.21
B.28
C.6
D.34
Answer:
[tex]\huge\boxed{IQR = 21}[/tex]
Step-by-step explanation:
The data set given is:
57,63,44,29,36,62,48,50,42,34
Arrange in ascending order:
29,34,36,42,44,48,50,57,62,63
Place parenthesis around the number making two equal sets.
(29,34,36,42,44) | (48,50,57,62,63)
↑ ↑
Q1 Q3
Q1 = 36 , Q3 = 57
So, IQR = Q3-Q1
IQR = 57-36
IQR = 21
Answer:
[tex]\huge \boxed{\sf A. \ 21}[/tex]
Step-by-step explanation:
The data set is given,
[tex]\sf 57 \ 63 \ 44 \ 29 \ 36 \ 62 \ 48 \ 50 \ 42 \ 34[/tex]
Arrange the data set in ascending order.
[tex]\sf 29 \ 34 \ 36 \ 42 \ 44 \ 48 \ 50 \ 57 \ 62 \ 63[/tex]
Split the data set into two equal sets.
[tex]\sf 29 \ 34 \ 36 \ 42 \ 44 \ \ \ 48 \ 50 \ 57 \ 62 \ 63[/tex]
Find the median of the lower half and upper half.
[tex]\sf Median \ of \ lower \ half = 36[/tex]
[tex]\sf Median \ of \ upper \ half = 57[/tex]
Interquartile range = median of upper half - median of lower half
[tex]\sf IQR = 57 - 36[/tex]
[tex]\sf IQR = 21[/tex]
The interquartile range for the number of points scored at ten basketball games is 21.
A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) f(t) = t3 − 8t2 + 27t
The question is not clear, but it is possible to obtain distance, s, from the given function. This, I would show.
Answer:
s = 17 units
Step-by-step explanation:
Given f(t) = t³ - 8t² + 27t
Differentiating f(t), we have
f'(t) = 3t² - 16 t + 27
At t = 0
f'(t) = 27
This is the required obtainaible distance, s.
Claire has to go to the movie theater the movie starts at 4:15 pm it is a 25min walk to the theater from her home what time dose the have to leave the house to get there on time
Answer:
3:50 pm
Step-by-step explanation:
Count backwards with the 25 min.
4:15 - 15 min >
25 - 15 = 10 >
4:00 - 10 = 3:50
Answer:
3:50 pm
Step-by-step explanation:
Starting Time + Time Interval = Ending Time
=> Ending Time - Time Interval = Starting Time
Ending Time = 4:15 pm
Time Interval = 25 minutes
Starting Time = x
=> 4:15 - 25 = x
=> 4:15 - 15 - 10 = x
=> (4:15 - 15) - 10 = x
=> 4:00 - 10 = x
=> 3:50 pm = x
So, she needs to leave the house at 3:50 pm to get to the movie theater on time.
round 1,965 to the nearest tenth
Step-by-step explanation:
1965 round to the nearest tenth is 1970
Answer:
1965.0
Step-by-step explanation:
Describe all numbers x that are at a distance of 2 from the number 8. Express this using absolute value notation.
Answer:
The numbers that are at a distance of 2 from the number 8 can be expressed using absolute value notation as:
|x - 8| = 2
Step-by-step explanation:
The numbers that are at a distance of 2 from the number 8 are the numbers that are satisfied by the equation:
|x - 8| = 2
The equation is written in the notation of absolute value as required.
Write as an equation: The sum of a number and 12 is 78.
Answer:
x+12=78
Step-by-step explanation:
like that? x because its an unknown number but if you actually want to know the number just subtract 78-12 equals 66.
Answer:
n + 12 = 78
Step-by-step explanation:
Let n = number.
n + 12 = 78
3.24 (4 being repeated) to a fraction
Answer:
146/45
Step-by-step explanation:
Let x represent the value of the number of interest. Then we can do the following math to find its representation as a fraction.
[tex]x=3.2\overline{4}\\10x=32.4\overline{4}\\10x-x=9x=32.4\overline{4}-3.2\overline{4}=29.2\\\\x=\dfrac{29.2}{9}=\boxed{\dfrac{146}{45}}[/tex]
__
Comment on procedure
The power of 10 that we multiply by (10x) is the number of repeated digits. Here, there is a 1-digit repeat, so we multiply by 10^1. If there were a 2-digit repeat, we would compute 10^2x -x = 99x to rationalize the number.
10) An amount of $1500.00 is invested for 3 years at rate of 2% for the first year and 5%, for
the 2nd year and 6% for the 3rd year.
a) Calculate the interest amount you will get if this is simple interest?
b) How much more or less you will get if this is compound interest?
Answer:
the interest is 195dollars
Solve x/5 - 1/2 = x/6 (make sure to type the number only)
X/5 -1/2 = x/6
Find the least common denominator of the 3 denominators:5,2,6
The limited is 30
Multiply all 3 fractions by 30:
6x -15 = 5x
Subtract 6x from both sides:
-15 = -x
Multiply both sides by -1:
X = 15
Help please!!! Thank you
Answer:
Option (G)
Step-by-step explanation:
Let the length of the race = a miles
Since, Speed = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]
Time taken to cover 'a' miles with the speed = 12 mph,
Time taken '[tex]t_1[/tex]' = [tex]\frac{a}{12}[/tex]
Time taken to cover 'a' miles with the speed = 11 mph,
Time taken '[tex]t_2[/tex]' = [tex]\frac{a}{11}[/tex]
Since the time taken by David to cover 'a' miles was 10 minutes Or [tex]\frac{1}{6}[/tex] hours more than the time he expected.
So, [tex]t_2=t_1+\frac{1}{6}[/tex]
[tex]\frac{a}{11}=\frac{a}{12}+\frac{1}{6}[/tex]
[tex]\frac{a}{11}-\frac{a}{12}=\frac{1}{6}[/tex]
[tex]\frac{12a-11a}{132}=\frac{1}{6}[/tex]
a = 22 mi
Therefore, distance of the race = 22 mi
Option (G) is the correct option.
Using the distributive property, Marta multiplied the binomial (2x + 3) by the trinomial (x2 + x – 2) and got the expression below.
Answer:
The resultant expression is [tex]2x^{2}+5x^{2}-x-6[/tex].
Step-by-step explanation:
The distributive property of multiplication is:
[tex]a\times (b+c)=(a\times b)+(a\times c)[/tex]
The two polynomials provided are:
[tex](2x+3)\\(x^{2}+x-2)[/tex]
Determine the final expression by multiplying the two polynomials as follows:
[tex](2x+3)\times (x^{2}+x-2)=[2x\times(x^{2}+x-2)]+[3\times(x^{2}+x-2)][/tex]
[tex]=[(2x\times x^{2})+(2x\times x)-(2x\times 2)]+[(3\times x^{2})+(3\times x)-(3\times 2)]\\\\=[2x^{3}+2x^{2}-4x]+[3x^{2}+3x-6]\\\\=2x^{3}+2x^{2}+3x^{2}-4x+3x-6\\\\=2x^{3}+5x^{2}-x-6[/tex]
Thus, the resultant expression is [tex]2x^{2}+5x^{2}-x-6[/tex].
graph the linear equation using the slope and y-intercept y=1/9x+5
Answer:
Slope= 1/9
Y-Intercept= 5
PLEASE HELP !! (4/5) -50 POINTS-
Answer:
2 -7 6 7
1 3 -4 5
1 6 -15 -6
Step-by-step explanation:
An augmented matrix is the coefficients of the variables and then the solution in rows
Rewriting the equations
2x -7y +6x = 7
x +3y -4z = 5
x +6y -15z = -6
The matrix is
2 -7 6 7
1 3 -4 5
1 6 -15 -6
Two trains are moving towards each other on the same railroad track. From this track there's an offshoot piece of railroad − the length of which is shorter than the length of the train but longer than the length of one train car. How can the trains pass each other?
Answer:
one car at a time
Step-by-step explanation:
For each car in the shorter train* (A) ...
train A leaves one of its cars on the offshootboth trains move until train B can move the car from the offshoot to the portion of track away from train Atrain B moves to allow the cycle to repeatWhen there are no more train A cars in front of train B, both trains can continue on their journey.
We assume cars can be decoupled at any point in the train, so that any required order of cars can be preserved. We further assume that train B can move any one of train A's cars in addition to all of its own.
_____
* The total number of car lengths that must pass the offshoot is (at least) the product of the number of cars in both trains, so it doesn't seem to matter which train makes use of the offshoot. We choose to decouple the cars of train A so that the minimum number of cycles is required--even though each cycle is longer.
Simplify -12w + 7w - 3 - 6
Answer: Hi!
We can simplify this by combining like terms:
-12w + 7w - 3 - 6
-12w + 7w = -5w
-3 - 6 = -9
Out equation now looks like this:
-5w - 9
There's nothing left to simplify, so we're done!
Hope this helps!
