The thief stole 22 oranges using algebraic equations.
To solve this problem, we need to use algebra. Let x be the number of oranges the thief stole.
According to the problem, the thief gave the guard half of the stolen oranges and two more. This means that he gave away (1/2)x + 2 oranges.
We also know that the thief was left with only 9 oranges. So we can set up the equation:
x - [(1/2)x + 2] = 9
Simplifying this equation:
(1/2)x - 2 = 9
(1/2)x = 11
x = 22
Therefore, the thief stole 22 oranges.
The problem presents us with a scenario where a thief entered an orange garden and stole some oranges. However, he was caught by the guard. In order to get rid of the guard, the thief decided to give him half of the stolen oranges and two more. As a result, the thief was left with only 9 oranges.
To solve this problem, we used algebraic equations. We let x be the number of oranges the thief stole. We also knew that the thief gave away (1/2)x + 2 oranges to the guard. Using this information, we were able to set up an equation where x - [(1/2)x + 2] = 9. Simplifying the equation, we were left with (1/2)x - 2 = 9. Solving for x, we found that the thief had stolen 22 oranges.
In conclusion, algebraic equations are a useful tool in solving mathematical problems. By setting up an equation and simplifying it, we were able to determine the number of oranges that the thief had stolen.
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The slope at [1,pi/2] from -8x^3/siny
As a result, the function's slope at [1, pi/2] is [-24] as where the derivative of y with respect to x is denoted by y'.
what is slope ?The slope of a line in mathematics serves as a gauge for how steep it is. Between any two locations on the line, it is the proportion of the shift in the vertical motion (y) to the shift in the horizontal position (x). If we take into account two points on a line, (x1, y1) and (x2, y2), we can use the following formula to get the slope of the line: slope equals (y2 - y1)/. (x2 - x1) . Depending on the line's direction, the inclination can be zero, positive, or negative. A line with a positive slope is moving upward from left to right, whereas one with a negative slope is moving downward.
given
Finding the derivative of the given function with respect to x can be our first step. By applying the quotient rule, we get:
F(x) = 8x 3 sin (y)
[tex][(sin(y))(-24x2)] = f'(x) - (-8x^3) (cos(y))(y')] / (sin(y))^2[/tex]
where the derivative of y with respect to x is denoted by y'.
We can change x=1 and y=pi/2 in the equation above since we are interested in the slope at the position [1, pi/2].
Due to the fact that cos(pi/2) = 0 and sin(pi/2) = 1, we can write:
[tex]f'(1) = [(1)(-24) (-24) - (-8)(1)(0)(y')] / (1)^2[/tex]
f'(1) = -24 + 0
f'(1) = -24
As a result, the function's slope at [1, pi/2] is [-24] as where the derivative of y with respect to x is denoted by y'.
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What is the mean of this data set?
Please help ASAP giving Brainlyist (I don’t know how to spell it) it is not 24 cm
The closest option is (b) 23 12/15.
What are mean in statistics?
Mean: The average of a set of values, is calculated by adding up all the values in the set and dividing by the total number of values.
To find the mean (average) of the data set, we need to first find the sum of all the lengths of roses multiplied by their respective frequencies, and then divide by the total number of roses:
(22 x 2) + (23 x 4) + (24 x 5) + (25 x 3) + (26 x 1) = 344
Total number of roses = 2 + 4 + 5 + 3 + 1 = 15
Mean = Sum of all lengths / Total number of roses = 344 / 15 ≈ 22.93 cm
Rounding to the nearest whole number, the mean length of roses in this data set is 23 cm. Therefore, the closest option is (b) 23 12/15.
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Convert the following decimals to percents.
1.37 =_%
Answer:
137%
Step-by-step explanation:
1.37 x 100 = 137%
What is 2^6*2^5 is other exponent?
Answer:
below
Step-by-step explanation:
Yes, there is another exponent.
When you are multiplying exponents, you add the exponents.
So from the equation 2^6 x 2^5, you can keep the 2 the same, as this is the base:
2^11
and add the exponents (6+5)
To check:
2^6=64
2^5=32
64x32=2048
2^11=2048
So, 2^11 is equivalent to your equation. Hope this helps ;)
the table below shows the summary for weights of 7 people before a diet program and after. the weight lost by each person was also recorded and summarized in the table below. mean standard deviation before 204.71 18.117 after 189.71 18.273 weight loss 15 3.786 find a 95% confidence interval for the true mean weights loss.
The 95% confidence interval for the true mean weight loss is (11.168, 18.832).
To find the 95% confidence interval for the true mean weight loss, we can use the formula:
CI = x(bar) ± t*(s/√n)
where:
x(bar) = sample mean weight loss
s = sample standard deviation of weight loss
n = sample size
t = t-value from the t-distribution table with (n-1) degrees of freedom and a 95% confidence level
Using the values given in the table, we have:
x(bar) = 15
s = 3.786
n = 7
The t-value for a 95% confidence level with 6 degrees of freedom (n-1) is 2.447.
Substituting these values into the formula, we get:
CI = 15 ± 2.447*(3.786/√7)
CI = 15 ± 3.832
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on aurora ave the distance between thomas st to denny way is 0.2 miles. what is the distance between these two streets on broad st? show your work below and round your answer to the nearest tenth of a mile.
The distance between Thomas St and Denny Way on Broad St is approximately 0.2 miles (rounded to the nearest tenth of a mile).
To determine the distance between Thomas St and Denny Way on Broad St, we can use the Pythagorean theorem.
Let x be the distance between Thomas St and Denny Way on Broad St. We can draw a right triangle where the hypotenuse is 0.2 miles (the distance between Thomas St and Denny Way on Aurora Ave), and one leg is x (the distance between Thomas St and Denny Way on Broad St). The other leg is the distance between Aurora Ave and Broad St.
Using the Pythagorean theorem, we have:
[tex]0.2^2 = x^2 + d^2[/tex]
where d is the distance between Aurora Ave and Broad St.
Assuming d is negligible, we can solve for x:
[tex]x^2 = 0.2^2 - d^2x^2 = 0.2^2x = sqrt(0.2^2) = 0.2[/tex]
Therefore, the distance between Thomas St and Denny Way on Broad St is approximately 0.2 miles (rounded to the nearest tenth of a mile).
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Find the value of x. If a segment looks like a tangent, it is a tangent.
We got x = 84.50 by using Pythagorean theorem.
What is the Pythagorean theorem in plain English?According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides.Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.angle of semicircle is always be 90°.
[tex]115^2 = 78^2 + x^2[/tex]
[tex]13225 = 6084 + x^2[/tex]
[tex]x^2 = 13225- 6084[/tex]
[tex]= 7141[/tex]
[tex]x = \sqrt{7141}[/tex]
[tex]x = 84.50[/tex]
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PLSSSSSSSSSSSSSSSS HELP I WILL MARK YOU BRAINLYEST
Evaluate (-25)^1/2
Answers:
a) 625
b)-625
c) not a real number
Then the answer is C. not a real number
How to evaluate that?
An exponent of 1/2 is equivalent to the square root, so we can write:
√-25
That is the square root of a negative number, so we will get the complex numbers ±i
Then the answer is C.
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WILL MARK AS BRAINLEIST!! ASAP PLEASE!!
Question in picture
I have more questions on my account if u can help me out!!
For the region above x + 3y = 9 and below x + 9 = y², we have:
a = 18, b = -9, f(x) = (y² - 9)/3, and g(x) = (9 - x)/3.
For single integration: α = -6, β = 3 and h(y) = [(9 - y²)/3 - (y² - 9)].
What is the area bounded by the curves?To solve this problem, we first need to find the intersection points of the two curves x + 3y = 9 and x + 9 = y². We can do this by solving the system of equations:
x + 3y = 9
x + 9 = y²
Rearranging the first equation, we get:
x = 9 - 3y
Substituting this expression for x into the second equation, we get:
9 - 3y + 9 = y²
Simplifying, we get:
y² - 3y - 18 = 0
Factorizing, we get:
(y - 6)(y + 3) = 0
So the solutions are:
y = 6 or y = -3
Substituting these values of y into the equation x + 3y = 9, we get:
When y = 6, x = -9
When y = -3, x = 18
So the intersection points of the two curves are (-9, 6) and (18, -3).
Now we can find the area between the two curves by splitting it into two regions: the region above the curve x + 3y = 9 and below the curve x + 9 = y², and the region below the curve x + 3y = 9 and above the curve x + 9 = y².
For the region above x + 3y = 9 and below x + 9 = y², we have:
a = 18
b = -9
f(x) = (y² - 9)/3
g(x) = (9 - x)/3
Alternatively, to compute the area between the two curves x + 3y = 9 and x + 9 = y² using a single integral, we need to express the area as a function of y instead of x.
We can rearrange the equations x + 3y = 9 and x + 9 = y² to get:
x = 9 - 3y
x = y² - 9
Setting these two expressions equal to each other, we get:
9 - 3y = y² - 9
Simplifying, we get:
y² + 3y - 18 = 0
Factorizing, we get:
(y + 6)(y - 3) = 0
So the solutions are:
y = -6 or y = 3
Substituting these values of y into the equation x + 3y = 9, we get:
When y = -6, x = 27
When y = 3, x = 0
So the intersection points of the two curves are (27, -6) and (0, 3).
The area between the curves can be expressed as the difference between the integrals of the curves' respective functions with respect to y, since the curves are better expressed in terms of y.
The function representing the curve x + 3y = 9 in terms of y is:
x = 9 - 3y
We can rearrange this equation to get:
y = (9 - x)/3
Substituting x = y² - 9, we get:
y = (9 - y² + 9)/3
Simplifying, we get:
y² + 3y - 18 = 0
This is the same equation we obtained before, so we know that the bounds of integration are -6 and 3.
The function representing the curve x + 9 = y² in terms of y is:
x = y² - 9
Substituting this expression into the formula for the area of a region between two curves, we get:
Area = ∫(y=α)^(y=β) [(9 - y²)/3 - (y² - 9)] dy
Where;
α = -6 and β = 3 are the bounds of integration, and
the integrand [(9 - y²)/3 - (y² - 9)] represents the difference between the y-values of the two curves at a given x-value.
Simplifying the integrand, we get:
Area = ∫(y=-6)^(y=3) (18 - 2y²)/3 dy
Integrating, we get:
Area = [(6y - (2/3)y³)/3] |(y=-6)^(y=3)
Plugging in the limits of integration, we get:
Area = [(18 - 216)/3] - [(-36 + 216)/3]
Simplifying, we get:
Area = 66
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What is 4.5621 rounded to the nearest tenth?
least common multiple of 43 24 17
the least common multiple of 43, 24, and 17 is 87,672.To find the least common multiple (LCM) of three numbers, we first need to find their prime factorization.
what is prime factorization ?
Prime factorization is the process of finding the prime numbers that multiply together to give a given composite number. A composite number is any positive integer greater than 1 that is not itself a prime number.
In the given question,
To find the least common multiple (LCM) of three numbers, we first need to find their prime factorization.
Prime factorization of 43: 43 is a prime number, so its prime factorization is simply 43.
Prime factorization of 24: 24 can be factored as 2 × 2 × 2 × 3.
Prime factorization of 17: 17 is a prime number, so its prime factorization is simply 17.
Next, we find the highest power of each prime factor that appears in any of the three factorizations:
The prime factor 2 appears to the third power in the factorization of 24, and to the first power in the factorizations of 43 and 17.
The prime factor 3 appears to the first power in the factorization of 24, and to the zero power in the factorizations of 43 and 17.
The prime factor 17 appears to the first power in the factorization of 17, and to the zero power in the factorizations of 43 and 24.
The prime factor 43 appears to the first power in the factorization of 43, and to the zero power in the factorizations of 24 and 17.
Therefore, the LCM of 43, 24, and 17 is:
2³ × 3¹ × 17¹ × 43¹ = 87,672
Hence, the least common multiple of 43, 24, and 17 is 87,672.
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On Ernest Airlines, baggage cannot weigh more than 40 pounds. Devin packed 21 pounds of clothes and four packages which weighed a total of 7 pounds. Write an inequality for this scenario. Then solve and determine the weight that each package must be less
Inequality for this scenario
x ≤ 4.75
So, each package must weigh less than or equal to 4.75 pounds in order for Devin to stay within the weight limit of 40 pounds on Ernest Airlines.
HOW TO SOLVE AN INEQUALITY?Let x be the weight of each package (in pounds).
The inequality for the scenario can be written as:
21 + 4x ≤ 40
This represents the total weight of Devin's clothes (21 pounds) plus the total weight of the four packages (4x pounds) cannot exceed the weight limit of 40 pounds on Ernest Airlines.
To solve for x, we can subtract 21 from both sides of the inequality:
4x ≤ 40 - 21
4x ≤ 19
Finally, we divide both sides by 4 to isolate x:
x ≤ 19 / 4
Let x be the weight of each package (in pounds).
The inequality for the scenario can be written as:
21 + 4x ≤ 40
This represents the total weight of Devin's clothes (21 pounds) plus the total weight of the four packages (4x pounds) cannot exceed the weight limit of 40 pounds on Ernest Airlines.
To solve for x, we can subtract 21 from both sides of the inequality:
4x ≤ 40 - 21
4x ≤ 19
Finally, we divide both sides by 4 to isolate x:
x ≤ 19 / 4
x ≤ 4.75
So, each package must weigh less than or equal to 4.75 pounds in order for Devin to stay within the weight limit of 40 pounds on Ernest Airlines.
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there was no red arc. so please help me on this. its for geometry
Answer:
21. x=70
22. x=15
*Not sure what the red arc is, but I found the value of x for both 21 and 22*
Step-by-step explanation:
Let's start with 21 first.
Line AB is a straight line, meaning the arc length of AB is 180 degrees. So,
(2x-30)+x=180
let's solve:
3x-30=180
3x=210
x=70
I'm not sure what the red arc is, so I can't help you there.
Next, 22.
All the arcs in a complete circle need to add up to 360 degrees, so:
4x+6x+7x+7x=360
simplify first:
24x=360
let's solve:
x=15
Again, not sure where or what the red arc is, so can't help again. I hope that the x values help.
PLEASE HELP I have no idea how to do this.. our teacher hasnt been here all week.. and I have no clue what this is..
solve for the value of V (9v+3)° 60°
The value of v is 13 degrees.
What are supplementary angles?Supplementary angles are a set of given measure of angles which add up to 180 degrees. Thus producing a measure of the sum of angles on a straight line.
To determine the value of v in the given diagram, we have;
60 + (9v + 3) = 180 (sum of angles on a straight line)
So that;
9v + 3 = 1890 - 60
9v + 3 = 120
9v = 120 - 3
= 117
v = 117/ 9
= 13
v = 13^o
The value of v in the question is 13 degrees.
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assume that the hourly cost to operate a commercial airplane follows the normal distribution with a mean of $3,403 per hour and a standard deviation of $398.what is the operating cost for the lowest 2% of the airplanes?
Answer:
$2,611.9.
Step-by-step explanation:
To find the operating cost for the lowest 2% of the airplanes, we need to find the corresponding z-score from the standard normal distribution using a z-table.
Using the formula:
z = (x - μ) / σ
where x is the cost we are interested in, μ is the mean cost, and σ is the standard deviation.
For the lowest 2% of airplanes, the z-score can be found by looking up the area to the left of z in the z-table. This area is 0.02.
Looking up 0.02 in the z-table gives a z-score of approximately -2.05.
So we have:
-2.05 = (x - 3403) / 398
Solving for x, we get:
x = -2.05 * 398 + 3403 = $2,611.9
Therefore, the operating cost for the lowest 2% of the airplanes is approximately $2,611.9.
How many planes of symmetry does a right pyramid with an isosceles triangle base have?
A right pyramid with an isosceles triangle base has one plane of symmetry.
How many planes of symmetry does a right pyramid with an isosceles triangle base have?A plane of symmetry is a plane that can be passed through an object such that the object is divided into two halves that are mirror images of each other.
In the case of a right pyramid with an isosceles triangle base, if a plane passes through the apex (the top point) of the pyramid and is perpendicular to the base, it will bisect the base into two halves that are mirror images of each other. This is the only plane of symmetry that exists for this particular pyramid.
Thus, the right pyramid with isosceles triangle base has one plane of symmetry.
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Find the mean of the following data 0,5,30,25,16,18,19,26,0,20,28 A. 0 B. 18 C. 19 D. 17
The mean of the following data 0,5,30,25,16,18,19,26,0,20,28 is 17.
Hence option D is the correct option.
Mean is the average value of a given set of data. It is calculated by the formula,
Mean = {Summation of all the values in the data set} / {Number of observations is the data set}
That is, Mean = {Σ all values in the data set} / {number of observations}
The given data set is as follows,
0,5,30,25,16,18,19,26,0,20,28
The number of observations in the data set is 11.
The summation of all the values in the data set is = {0 + 5 + 30 + 25 +
16 + 18 + 19 +26 + 0 + 20 + 28} = 187
Therefore, by applying the formula of Mean we get
Mean = 187/ 11 = 17
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a continuous random variable x has a uniform distribution between 5 and 25 (inclusive), then p(x = 15) = 0.05. a. true b. false
Answer:
Step-by-step explanation:
The probability of a continuous random variable taking any specific value is always zero, so the statement p(x = 15) = 0.05 is false.
True or False : The environmental lapse rate is usually the same as the dry adiabatic rate
False. The environmental lapse rate, which changes based on various variables like humidity and atmospheric stability, is the real rate at which temperature decreases with increasing altitude in the atmosphere.
The pace at which a parcel of dry air cools as it ascends in the atmosphere, on the other hand, is known as the dry adiabatic rate and is set at around 9.8 degrees Celsius per 1000 meters of ascension.
Although it is not often the same, the environmental lapse rate can occasionally be comparable to the dry adiabatic rate. The environmental lapse rate can differ from the dry adiabatic rate due to things like the presence of moisture or atmospheric instability.
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A coin is flipped at the start of every game to determine if Team A (heads) or Team B (tails) will get the ball first.
Part A: Find the theoretical probability of a fair coin landing on heads.
Part B: Flip a coin 14 times and record the frequency of each outcome. Be sure to include the frequency of each outcome in your answer. Then, determine the experimental probability of landing on heads and compare it to the theoretical probability.
The theoretical probability of a fair coin landing on heads is 1/2 or 0.5. The experimental probability of landing on heads is also 0.5, which matches the theoretical probability.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.
According to the given condition:Part A: The theoretical probability of a fair coin landing on heads is 1/2 or 0.5.
Part B: Let's record the outcomes of flipping a coin 14 times and count the frequency of each outcome:
HHHHHHHHHHHHHH - 14 heads
TTTTTTTTTTTTTT - 14 tails
The frequency of heads is 14, and the frequency of tails is also 14.
To find the experimental probability of landing on heads, we divide the frequency of heads by the total number of flips:
experimental probability of heads = frequency of heads / total number of flips = 14 / 28 = 0.5
The experimental probability of landing on heads is the same as the theoretical probability. This is not surprising since the number of trials is large enough to approach the theoretical probability.
Therefore,The theoretical probability of a fair coin landing on heads is 1/2 or 0.5. The experimental probability of landing on heads is also 0.5, which matches the theoretical probability.
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A. Draw and write the correct answer in each letters. (3 points each)
A={ pink, brown, white, blue}
B={ pink, yellow, red, green}
C={ pink, red, yellow, brown, white, purple}
A. Find AUB
B. Find AnB
C. Find AnBnc
D. Find AUBUC
E. Find (AUB)'
F. Find (ANB)'
G. Venn diagram (Draw
Word Problem: The company For The Ocean has already cleared the earth's oceans of 125 million pounds of trash. They are committed to picking up exactly 550 pounds of trash per day. Write an equation to represent total "p" pounds of trash removed as a function of number of "d" days passed.
A(n) ______ design compares different independent variable levels by using homogeneous groups of experimental units.
A blocked design compares different independent variable levels by using homogeneous groups of experimental units.
In this type of experimental design, subjects are divided into homogeneous groups, or blocks, based on similar characteristics or traits. These blocks help to control or account for potential confounding variables that may affect the outcome of the experiment.
By grouping subjects into blocks, researchers can reduce the variability within each group and increase the accuracy of the experimental results. This allows for a more precise comparison of the effects of different levels of the independent variable on the dependent variable. Blocked designs are particularly useful when there are natural groupings within the experimental units or when the variability between units is high.
In summary, a blocked design is a powerful experimental tool that can help researchers account for potential confounding factors and reduce variability among experimental units. By doing so, it enables the accurate comparison of different levels of the independent variable, ultimately leading to more reliable and valid results.
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Simplify. 4 2/5 x 3 = ?
Answer:
66/5 or 13.2
Step-by-step explanation:
..........
Isaiah is trying to find the height of a radio antenna on the roof of a local building. He stands at a horizontal distance of 20 meters from the building. The angle of elevation from his eyes to the roof ( (point � A ) ) is 32 ∘ ∘ , and the angle of elevation from his eyes to the top of the antenna ( (point � B ) ) is 43 ∘ ∘ . If his eyes are 1.62 meters from the ground, find the height of the antenna ( (the distance from point � A to point � B ) ). Round your answer to the nearest meter if necessary.
The height of the antenna is approximately 29 meters.
What is the angle of elevation?
The point of rise is a point that is framed between the even line and the view. An angle of elevation is formed when the line of sight extends upward from the horizontal line.
We should refer to the level of the structure as "h" and the level of the receiving wire "x". Two equations can be created with the help of the tangent function:
Since the elevation angle to the roof is 32 degrees,
tan(32) = h/20, and
tan(43) = (h+x)/20
because the elevation angle to the antenna's peak is 43 degrees.
We can solve for "h" in the first equation by multiplying both sides by 20:
h = 20 tan(32)
We can substitute this expression for "h" into the second equation:
tan(43) = (20 tan(32) + x)/20
Now we can solve for "x":
x = 20 tan(43) - 20 tan(32)
We can then add the height of Isaiah's eyes (1.62 meters) to get the total height of the antenna:
height = x + 1.62
Plugging in the values and using a calculator, we get:
height ≈ 28.7 meters
As a result, the antenna stands about 28.7 meters tall. The answer is 29 meters when rounded to the nearest meter.
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How do you express 0.000 000 000 000 1 in exponential form.
Answer:
1 x 10^-12
Step-by-step explanation:
....
Question 10(Multiple Choice Worth 5 points)
(Identifying Functions LC)
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
a graph with points plotted at negative 5 comma 1, at negative 2 comma 0, at negative 1 comma 3, at negative 1 comma negative 2, at 0 comma 2, and at 5 comma 1
Is the relation a function? Explain.
No, because for each input there is not exactly one output.
No, because for each output there is not exactly one input.
Yes, because for each input there is exactly one output.
Yes, because for each output there is exactly one input.
Is the relation a function:
No, because for each input there is not exactly one output.How to know if the relation is a functionTo determine if the relation is a function, we need to check if there is exactly one output for each input.
Looking at the given set of points, we see that there are two points with an x-coordinate of -1: (-1, 3) and (-1, -2).
This means that there are two outputs for the same input, so the relation is not a function.
Therefore, the correct answer is: "No, because for each input there is not exactly one output."
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Question 9(Multiple Choice Worth 2 points)
(Creating Graphical Representations LC)
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
The most useful visual representation of the teacher's data on the preferred subjects of 100 kids at the school would be a histogram. answer is option (a).
What is a histogram?In a histogram, which is a graphical depiction of the distribution of a set of continuous or discrete data, the height of a bar above the bin on the x-axis represents the frequency or count of the data falling within each bin. On the y-axis of the histogram, the frequency or count of the data points that fall into each bin is displayed.
The most useful visual representation of the teacher's data on the preferred subjects of 100 kids at the school would be a histogram. In a histogram, bars are used to illustrate the frequency distribution of a group of continuous or discrete data points.
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Choose ALL answers that describe the quadrilateral
Answer:
All of the above.
Quadrilateral's must have at the maximum 4 equal sides, or the minimum 2 equal sides.
a square has 4 equal sides.
a rectangle has 2 equal side. (that add up to 4 because each side is a pair of 2)
a rhombus can be a quadrlaterial depending on the shape.
a parrellelogram mostly have atleast 2 equal sides.
and a trapezoid mostly has atleast 2 equal sides.
Hope this helps!