Step-by-step explanation:
(1) Factor the GCF out of the trinomial on the left side of the equation. (2 points: 1 for the GCF, 1 for the trinomial) 2x²+6x-20=0
2x²+6x-20
2(x²+3x-10)
the factors are 2 and (x²+3x-10)
(2) Factor the polynomial completely. (4 points: 2 point for each factor)
2(x²+3x-10)
2(x²-2x+5x-10)
2(x(x-2) + 5(x-2)) group like terms
2(x+5)(x-2)
(3) If a product is equal to zero, we know at least one of the factors must be zero. And the constant factor cannot be zero. So set each binomial factor equal to 0 and solve for x, the width of your project. (2 points: 1 point for each factor)
constant = 2 cannot be zero
the other factors are (x+5) and (x-2)
(x+5)=0 => x= -5
or
(x-2)=0 => x=2
(4) What are the dimensions of your project? Remember that the width of your project is represented by x. (2 points: 1 point for each dimension)
thank you so much, sorry if it's a little confusing!!
(it is indeed confusing, because physical dimensions cannot be negative)
The dimensions of the project (assumed a rectangle) are +2 and -5
What is the slope of the line represented by the equation y = 5 x – 3?
0-3
4
o
5
tln m
O 3
Answer:
the slope is 5
Step-by-step explanation:
y = 5 x – 3
This equation is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
the slope is 5 and the y intercept is -3
Answer:
The Slope is 5
Step-by-step explanation:
As seen in the y-intercept equation, 5x is shown as the slope of the line.
PLEASE ANSWER THIS GEOMETRY QUESTIONS ASAP FOR ME PLEASE!!
Answer:
x = 12.5
Step-by-step explanation:
Since measure of 4th arc is not given (measure of 3 arcs have been given), we will apply the following theorem.
By the intersecting chords theorem,
"If two chords intersecting inside a circle, measure of the angle between these chords will measure the half the sum of measures of arcs intercepted by the angle and its vertical angle."
Here intercepted arcs are (2x)° and 155°. Angel between the chords measure 90°.
By the theorem,
90° = [tex]\frac{1}{2}(2x + 155)[/tex]°
180° = (2x + 155)°
2x = 180 - 155
2x = 25
x = 12.5
What percent of the players finished the walk in less than 2 hours? Show your work.
What is the probability that two randomly chosen players completed the walk in 2.9 hours or more? Show your work.
What is the probability that four randomly chosen players completed the walk between 1.7 and 2.9 hours? Show your work.
What observations can you make about the number of participants who complete the walk in more than 3.5 hours, given that there are 1,200 participants?
What might you observe if the number of participants increased or decreased?
Answer:
I also need the same help :(((
Step-by-step explanation:
1. The percentage of the players who finished the walk in less than 2 hours will be 2.28%
2. The probability that two randomly chosen players completed the walk in 2.9 hours or more was 15.87%
3. The probability that four randomly chosen players completed the walk was between 1.7 and 2.9 hours 84%
4. The number of participants who complete the walk in more than 3.5 hours, given that there are 1,200 participants 0
5. if the number of participants increased, the probability would increase while if they decreased, the probability would decrease
What is Z-score?The z score is a measure used in probability to determine the number of standard deviations the raw score is above or below the mean, it is given by the equation:
[tex]Z=\dfrac{x-\mu}{\sigma}[/tex]
Given that:
the mean μ = 2.6 hours and a standard deviation(σ) of 0.3 hours.
[tex]Z=\dfrac{x-\mu}{\sigma}[/tex]
1) What percent of the players finished the walk in less than 2 hours.
To calculate this, we use x as 2 hours and then find the z score.
[tex]Z=\dfrac{x-\mu}{\sigma}=\dfrac{2-2.6}{0.3}=-2[/tex]
From the normal probability distribution table, P(x < 2) = P(z < -2) = 0.0228 = 2.28%
2) What is the probability that two randomly chosen players completed the walk in 2.9 hours or more
To calculate this, we use x as 2.9 hours and then find the z score.
[tex]Z=\dfrac{x-\mu}{\sigma}=\dfrac{2.9-2.6}{0.3}=1[/tex]
From the normal probability distribution table, P(x > 2.9) = P(z > 1) = 1-P(z<1) = 1 - 0.8413 = 0.1587
3. What is the probability that four randomly chosen players completed the walk between 1.7 and 2.9 hours
To calculate this, we first use x as 1.7 hours and then find the z score.
[tex]Z=\dfrac{x-\mu}{\sigma}=\dfrac{1.7-2.6}{0.3}=-3[/tex]
For x as 2.9 hours and then find the z score.
[tex]Z=\dfrac{x-\mu}{\sigma}=\dfrac{2.9-2.6}{0.3}=1[/tex]
From the normal probability distribution table, P(1.7 < x < 2.9) = P(-3 < z < 1) = P(z<1) - P(z < -3) = 0.8413 - 0.0013 = 0.84
4. What observations can you make about the number of participants who complete the walk in more than 3.5 hours, given that there are 1,200 participants?
To calculate this, we use x as 3.5 hours, a number of samples (n) = 1200, and then find the z score.
[tex]Z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}=\dfrac{3.5-2.6}{\dfrac{0.3}{\sqrt{1200}}}=104[/tex]
From the normal probability distribution table, P(x > 3.5) = P(z > 104) = 1-P(z<104) = 1 - 1 = 0
5. What might you observe if the number of participants increased or decreased?
if the number of participants increased, the probability would increase while if they decreased, the probability would decrease
To know more about Z-scores follow
https://brainly.com/question/25638875
Please answer this question fast in two minutes
Answer:
4
Step-by-step explanation:
Angle 2 and angle 4 are vertically opposite angles.
Vertically opposite angles are equal.
Answer:
the angle that is congruent to <2 is <4.
Step-by-step explanation:
They are vertical angles, therefore congruent
If the variance of 3 4 6 y (y+3) and 9 is 21.6 what is the standard deviation of 6 8 12 2y (2y+6) and 18
Answer:
The standard deviation of second data set is 9.2952.
Step-by-step explanation:
The variance of a random variable is independent of change of origin but not of scale.
That is if any value is added or subtracted from the random variable then the variance of the random variable will not change.
[tex]V(X+a)=V(X)+V(a)=V(X)[/tex]
And if any value is multiplied or divided by the random variable then the variance of the random variable will change.
[tex]V(aX)=a^{2}V(X)[/tex]
The first set of data is:
S₁ = {3, 4, 6, y, (y+3) and 9}
The variance of S₁ is,
V (S₁) = 21.6
The second set of data is:
S₂ = {6, 8, 12, 2y, (2y+6) and 18}
On comparing the two sets of data, it can be concluded that:
S₂ = 2 × S₁
Compute the variance of S₂ as follows:
[tex]V(S_{2})=V(2\times S_{1})[/tex]
[tex]=2^{2}\times V(S_{1})\\\\=4\times 21.6\\\\=86.4[/tex]
Then the standard deviation of S₂ is:
[tex]SD(S_{2})=\sqrt{V(S_{2})}[/tex]
[tex]=\sqrt{86.4}\\=9.2952[/tex]
Thus, the standard deviation of second data set is 9.2952.
Write down the integer values satisfied by this diagram
Answer:
0,1,2,3
Step-by-step explanation:
There is an open circle at -1 so it is not included
There is a closed circle at 3 so it is included
The integers between and including 3 are good
0,1,2,3
Answer:
-1,3
Step-by-step explanation:
Joseph and Isabelle left Omyra’s house at the same time. Joseph jogged north at 8 kilometers per hour, while Isabelle rode her bike west at 12 kilometers per hour. Omyra tried to figure out how far apart they were after 1.5 hours. Her work is shown below. Which statements describe her errors? Check all that apply.
A. She did not find the full distance each traveled in 1.5 hours. She should have used 12 km for Joseph’s distance and 8 km for Isabelle’s distance.
B. She did not square the 12 in the problem. She should have used 12 squared = 144.
C. She did not evaluate 8 squared correctly. She should have used 8 squared = 8 (2) = 16.
D. She did not evaluate StartRoot 88 EndRoot correctly. She should have used StartRoot 88 EndRoot almost-equals 44.
E. She should not have taken the square root of each side when solving. She should have just divided each side by 2.
F. She should not have added the squares in the first step. She should have used 12 squared minus 8 squared = d squared.
Answer:
A and B
Step-by-step explanation:
A) because what Omyra found is the distance for an hour and what she should have found is the distance for an hour and a half.
B) because the pythagorean theorem is a^2+b^2=c^2. The legs of an triangle should always be squared before being added.
Answer:
For this case the distance will be given by:
d ^ 2 = (12 * 1.5) ^ 2 + (8 * 1.5) ^ 2
Rewriting we have:
d ^ 2 = (18) ^ 2 + (12) ^ 2
d ^ 2 = 324 + 144
d ^ 2 = 468
d = root (468)
d = 21.63 Km
Answer:
1) She did not find the full distance each traveled in 1.5 hours.
2) She should have used 12 km for Joseph's distance and 18 km for Isabelle's distance.
Step-by-step explanation:
Can someone help me with this question please.
Answer:
a. +3
b. -12a
Step-by-step explanation:
Here, we want to know the steps that are involved in those unoccupied segments
let’s start with the output
6a + 18
So what turned a to 6a + 18
Let’s call that output x
Let’s reverse the last step that multiplied that term and a
Thus (6a + 18)/6 = a + 3
Thus the x-term we are looking for is + 3 before the multiplication by 6
Now for the second part;
a * 4 -3 = -12a
find the equation of the line
Answer: y=1/2x
Step-by-step explanation:
The equation we can use is slope-intercept form. The formula is y=mx+b. The m represents the slope, and b is the y-intercept. The line passes through the y-axis at (0,0). therefore, the y-intercept is 0.
To find the slope, we can take any two points and use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] to solve for slope. Let's use (2,1) and (4,2).
[tex]m=\frac{2-1}{4-2} =\frac{1}{2}[/tex]
The slope is 1/2. Our equation is y=1/2x+0 or y=1/2x.
Answer:
y=1/2x+0
Step-by-step explanation:
slope : 1/2
y=mx+b is the equation
y-intercept is 0 therefore the equation becomes:
y=1/2x+0
HURRY I NEED HELP PLEASE IM STUCK! :(
Answer:
0.6 then calculate which expression is equal to that
Step-by-step explanation:
arccos = cos^-1
Put that in calculator
what is the measure of ∠x
Answer:
see below
Step-by-step explanation:
If we look at ∠CBA and ∠BAE, we notice that they must be supplementary because they are same side interior angles, therefore:
41 + 102 + x = 180
143 + x = 180
x = 37°
Answer:
x = 37°
Step-by-step explanation:
→ First, we need to remember 2 important angle facts
Angles in a triangle add up to 180°Alternate angles are equal→ The first thing we want to do is find BCA because it's alternate to CAE or angle x, so let's set up an equation
BCA + 41° + 102° = 180°
→ Add the whole number together
BCA + 143° = 180°
→ Minus 143° from both sides to isolate BCA
BCA = 37°
→ Using the second angle fact, that alternate angles are equal, we can confirm that angle 'x' and angle BCA are alternate therefore equal
x = 37°
A tank is 4 feet long, 6 feet wide and 10 feet
tall. How much water can that tank hold?
Answer:
Volume = 240 feet³
Step-by-step explanation:
We'll find it's volume
Volume = [tex]Lenth *Width*Height[/tex]
Where Length = 4, Width = 6, Height = 10
Volume = 4 * 6 * 10
Volume = 240 feet³
Using side lengths only, could the triangles be similar? Triangle X Y Z. Side X Y is 1.5, X Z is 1, Z Y is 2. Triangle Q S R. Side Q R is 1, R S is 1.5, S Q is 0.5.
Answer:
no
Step-by-step explanation:
In ∆XYZ, we can write the ratios of the sides from shortest to longest as ...
y : z : x = 1 : 1.5 : 2 = 2 : 3 : 4
In ∆QSR, we can write the ratios of the side lengths from shortest to longest as ...
r : s : q = 0.5 : 1 : 1.5 = 1 : 2 : 3
Based on side lengths only, the triangles cannot be similar.
__
Additional note
Even if shortest-to-longest side ratios were the same, the triangle naming is incorrect for them to be similar.
The value that satisfies the equation 7/n=8/7 is
Answer:
n= 35/8
Step-by-step explanation:
7/n= 8/7
7/8 = n/7
7²/8 = n
n = 49/8
Answer:
n = 49/8Step-by-step explanation:
[tex] \frac{7}{n} = \frac{8}{7} [/tex]
Cross multiply
We have
49 = 8n
Divide both sides by 8
n = 49/8Hope this helps you
complete both I will give brainliest question if answer correct
Answer:
1. 5 3/4 - 2 1/4 = 3 1/12 2. 7 2/3 + 2 1/5 = 9 13/15
Step-by-step explanation:
1. 5 3/4 - 2 1/4
subtract the numbers on the side 5-2=3
subtract the fraction 3/4-1/4=2/4
reduce 2/4=1/2
add them together 3+1/2=3 1/2
2. 7 2/3 + 2 1/5
subtract the numbers on the side 7+2=9
find LCD of 2/3 and 1/5=
10/15+3/15=13/15
add them together 9+13/15=9 13/15
Answer: [tex]a)\ 3\dfrac{1}{2}[/tex]
[tex]b)\ 9\dfrac{13}{15}[/tex]
Step-by-step explanation:
a)
[tex].\quad 5\dfrac{3}{4}\\-\\.\quad\underline{ 2\dfrac{1}{4}}\\\\.\quad 3\dfrac{2}{4}\div\dfrac{2}{2}\quad =\quad \large\boxed{3\dfrac{1}{2}}[/tex]
b)
[tex].\quad 7\dfrac{2}{3}\times \dfrac{5}{5}=7\dfrac{10}{15}\\+\\.\quad 2\dfrac{1}{5}\times \dfrac{3}{3}=\underline{2\dfrac{3}{15}}\\\\.\qquad \qquad \quad \ \large\boxed{9\dfrac{13}{15}}[/tex]
Simplify this expression: 19 - (-8) - (-14) = ? A. 41 B. 25 C. -7 D. -3
Answer:
A. 41
Step-by-step explanation:
19 - (-8) - (-14) =
19+8+14
Remember: Two negatives=One positive ;)
27+14
41
A. 41
Answer:
[tex]\mathrm{A.} \: 41[/tex]
Step-by-step explanation:
[tex]19 - (-8) - (-14)[/tex]
[tex]\mathrm{Apply \: rule:} \: -(-a)=a[/tex]
[tex]19+8+14[/tex]
[tex]\mathrm{Add \: the \: numbers.}[/tex]
[tex]=41[/tex]
PLEASE HELP WILL GIVE EXTRA POINTS For a hypothesis test of H0: p = 0.40 against the alternative Ha: p > 0.40, the z test statistic is found to be 2.25. What can be said about this finding? The finding is significant at both α = 0.05 and α = 0.01. The finding is significant at α = 0.05 but not at α = 0.01. The finding is significant at α = 0.01 but not at α = 0.05. The finding is not significant at α = 0.05 and α = 0.01.
Answer:
The finding is significant at α = 0.05 but not at α = 0.01.
Step-by-step explanation:
We are given with the following hypothesis below;
Null Hypothesis, [tex]H_0[/tex] : p = 0.40 {means that the population proportion is equal to 40%}
Alternate Hypothesis, [tex]H_A[/tex] : p > 0.40 {means that the population proportion is greater than 40%}
The z-test statistics given to us is 2.25.
Now, at 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.
Since the value of our test statistics is more than the critical value of z as 2.25 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Now, at 0.01 level of significance, the z table gives a critical value of 2.33 for the right-tailed test.
Since the value of our test statistics is less than the critical value of z as 2.25 < 2.33, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
This means that the finding is significant at α = 0.05 but not at α = 0.01.
x-5=11-3x solve for x
Answer:
4
Step-by-step explanation:
x-5=11-3x
+5 +5
x=16-3x
+3x +3x
4x=16
--- ----
4 4
//x= 4//
// have a great day //
Solve for x 5 x − 1 = 6 x − 9
Answer:
The value of x in this equation is 8.
Step-by-step explanation:
5x - 1 = 6x - 9
Subtract 6x on both sides.
-x - 1 = -9
Add 1 to both sides.
-x = -8
Divide by -1 on both sides.
x = 8
Inga can earn $375 per week in a plant store, or she can earn 3% of total sales. How much would Inga have to sell to earn more in commission than in salary?
Answer:
Inga will have to sell $12,533 to earn more in commission than in salary.
Step-by-step explanation:
As the commission is the percentage of sales amount so, need to calculate the minimum sales value required.
Igna's salary = $375
Commission rate = 3%
Sale to earn more than salary = $376 / 3% = $12,533.33
Igna has to make a minimum sale of $12,533 per week in order to earn more commission than her salary.
BRAINLIEST AND 20 POINTS!! PLEASE PLEASE PLEASe HELP ASAP!!!
Answer:
Option 2 and 4
Step-by-step explanation:
Area of the big rectangle to fit small ones:
15*11= 165Area of small rectangles:
A= 11*7=77B=2*11=22C=6*6=36D=6*5=30E=13*4=52Now, the answer options:
3E+2B= 3*52+2*22= 200 > 165 ⇒ noA+B+C+D= 77+22+36+30= 165 ⇒ yes2C+2D+2B= 2(36+30+22)=176 > 165 ⇒ noA+4B= 77+4*22= 165 ⇒ yesE+C+D+3B= 52+36+30+22= 140 < 165 ⇒ noAn arrow on a spinner is spun 250 times. Some of the results are shown below. The relative frequency of landing on a 4 is the same as the relative frequency of landing on a 5 Work out the relative frequency of landing on a 4
Answer:
11/50
Step-by-step explanation:
The frequency numbers for landing on 1, 2, and 3 are:
25, 53, 62.
We add them up to get: 25 + 53 + 62 = 140
Since 250 spins were made, and 140 of them landed on 1, 2, or 3, then
250 - 140 = 110,
so 110 landed on 4 or 5.
We are told the numbers of spins landing on 4 and 5 are equal, so
110/2 = 55,
so the spinner landed 55 times on 4 and 55 times on 5.
relative frequency = 55/250 = 11/50
helpzies again lollll
Answer:
2nd Graph
Step-by-step explanation:
If it's a direct proportional relationship, the the 2nd graph is your best choice. Usually renting stuff keeps increasing in price (like a linear graph) as businesses want to make money continuously. Besides, it's charged by the hour, with an increase of price proportional to the amount of hours, so it is a linear equation.
82 Find the circumference
of a circle with a radius
of 10cm.
A. 6.28 m
B. 62.8m
C. 628m
D. 6280m
Answer:
0.628 m (This is the correct answer but I cant find it in your options)
Step-by-step explanation:
Radius = 10 cm = 0.1 m
Now, The circumference:
=> Circumference = [tex]2\pi r[/tex]
=> C = 2(3.14)(0.1)
=> C = 0.628 m
Answer:
B. 62.8m
Step-by-step explanation:
C= 2πr= 2*3.14* 10 m= 62.8 m
Assumed radius is 10 m as the answer options are in metre
Which of these equations have no solution? Check all that apply.
0 26x + 2) + 2 =2(x+3)+1
0 2x + 3(x+5)= 5(x-3)
4x + 3) = x + 12
4 - (2x + 5) = {(-4x - 2)
5(x + 4) - X= 4(x + 5) - 1
Answer:
B and E
Step-by-step explanation:
(26x+2)+2=2(x+3)+1 - solution = 1/8
2x+3(x+5)=5(x-3) - NO SOLUTION
4x+3=x+12 - solution = 3
4 - (2x + 5) = {(-4x - 2) - solution = -1/2
5(x + 4) - X= 4(x + 5) - 1 - NO SOLUTION
Use the distributive property to multiply -3(-28)
Answer:
84
Step-by-step explanation:
-3 multiplied by -28 equals 84. The two negatives cancel out.
Answer: ur answer would be 84
-3*-28
84
Please answer this in two minutes
Answer:
WX = 7.9
Step-by-step explanation:
By applying tangent rule (law of tan) in the given right triangle WXY.
tan(W) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
tan(27)° = [tex]\frac{\text{XY}}{\text{WX}}[/tex]
0.509525 = [tex]\frac{4}{\text{WX}}[/tex]
WX = [tex]\frac{4}{0.509525}[/tex]
WX = 7.85
WX ≈ 7.9
Therefore, length of side WX is 7.9 units.
Which of the following choices translates the sentence “the difference of three times a number and 20 is 13”?
Answer:
3x - 20 = 13
Step-by-step explanation:
1. The word is signals the equal sign.
The difference of three times a number and 20 = 13
2. The word difference signals subtraction.
3. The phrase a number sigals that the number is unknown, so a variable should be used. In this case, I'll use x.
4. Three times that number = 3x.
The difference = subtraction.
3x-20=13
Answer: the number is 11
3 times a number becomes 3x. is becomes an = sign rhen the given amount, 13
3x - 20 = 13
Step-by-step explanation:
3x - 20 =13
3x = 13 + 20
3x =33
x= 11
Los datos siguientes corresponden a los tiempos de reacción de una muestra de 33 sujetos, medidos en centésimas de segundo(Inventar los dos últimos datos, reemplazando las x por un número): 55, 51, 60, 56, 64, 56, 63, 63, 61, 57, 62, 50, 49, 70, 72, 54, 48, 53, 58, 66, 68, 45, 74, 65, 58, 61, 62, 59, 64, 57, 63, xx, xx. 1. Calcular los cuartiles de los 33 sujetos 2. Calcular el decil 5 y el decil 7 3. Calcular el percentil 13 y el percentil 76
Responder:
Compruebe amablemente la explicación
Explicación paso a paso:
Dados los datos: 55, 51, 60, 56, 64, 56, 63, 63, 61, 57, 62, 50, 49, 70, 72, 54, 48, 53, 58, 66, 68, 45, 74, 65, 58, 61, 62, 59, 64, 57, 63, xx, xx
Los dos valores faltantes podrían ingresarse utilizando varios métodos, incluyendo la mediana, modal y el valor medio de los datos dados en la distribución.
Aquí usaremos el valor medio.
Media (m) de los datos = suma de la observación / número de observaciones Media =
(55 + 51 + 60 + 56 + 64 + 56 + 63 + 63 + 61 + 57 + 62 + 50 + 49 + 70 + 72 + 54 + 48 + 53 + 58 + 66 + 68 + 45 + 74 + 65 + 58 + 61 + 62 + 59 + 64 + 57 + 63) / 31 = 1844/31 = 59.4 = 59 (al número entero más cercano) Entonces reemplace los valores faltantes con 59.
En otro para hacer cálculos sobre los datos, hay que reorganizarlos.
Datos ordenados: 45,48,49,50,51,53,54,55,56,56,57,57,58,58,59,59,59,60,61,61,62,62,63,63,63, 64,64,65,66,68,70,72,74
Los cuartiles de datos:
Primer cuartil (Q1) = 1/4 (33 + 1) = 1/4 (34) = 8.5
Q1 = (8º + 9º) / 2 = (55 + 56) = 111/2 = 55,5
Segundo cuartil (Q2) = Q3 - Q1 = (25.5 - 8.5) = 17th = 59
Tercer cuartil (Q3) = 3/4 (33 + 1) = 3/4 (34) = 25.5 Q3 = (25 + 26) = (63 + 64) = 127/2 = 63.5
Rango intercuartil (IQR) = 63.5 - 55.5 = 8
Mediana = Q2 = 59
Mínimo = 45
Máximo = 74
Rango = 74-45 = 29
El quinto decil:
D5 = [5 (33 +1)] / 10 = 5 (34) / 10
D5 = 170/10 = 17º valor = 59
7mo decil: D7 = [7 (33 + 1)] / 10 = 7 (34) / 10
D7 = 238/10 = 23.8 ° término D7 = 63
Percentil:
Percentil 13 (13% × 33) = 0.13 × 33 = 4.29
4to término = 50
Percentil 76: (76% × 33) = 0.76 × 33 = 25.08
25 ° término = 63
Kate wants to buy a new sled. She has already saved 35% of the amount she needs. What fraction (in the simplest form) describes this percent?
Answer:
7/20.
Step-by-step explanation:
Simply convert 35% to a fraction. You get 35/100. Then, you are expected to leave your fraction in its simplest form. Do the simplification, and you will derive 7/20.