==========================================
Explanation:
Let's start off counting the number of ways to form the panel that doesn't have Allen or Joe on it. In other words, both are not on the panel.
There are 22 students, but we want to exclude 2 of them (Allen and Joe) from the panel. So in reality, we only have 20 students to pick from. There are 6 slots to fill.
The first slot has 20 choices
The second slot has 19 choices
The third has 18 choices
And so on. We count our way down until all six slots are filled. We'll have this sequence of six values: 20, 19, 18, 17, 16, 15
They multiply out to 20*19*18*17*16*15 = 27,907,200
This is the number of permutations where we choose 6 from a pool of 20.
With permutations, order matters; however, order doesn't matter on this panel. All we care about is the group overall.
So we must divide by 6! = 6*5*4*3*2*1 = 720 and we get
(27,907,200)/(720) = 38,760
There are 38,760 different combinations, so there are 38,760 different panels where neither Allen nor Joe are selected.
We'll use this later later, so let A = 38,760
------------------------------------------------------
Now onto the next part. We need to count the total number of possible panels, and this time we're including Allen and Joe.
We have our original total of 22 students. There are still 6 seats to fill.
We could follow the same steps as the prior section, but I'll use a different route.
Let n = 22 and r = 6. Plug these values into the nCr combination formula below
[tex]_n C_r = \frac{n!}{r!*(n-r)!}\\\\_{22} C_6 = \frac{22!}{6!*(22-6)!}\\\\_{22} C_6 = \frac{22!}{6!*16!}\\\\_{22} C_6 = \frac{22*21*20*19*18*17*16!}{6!*16!}\\\\_{22} C_6 = \frac{22*21*20*19*18*17}{6!}\\\\_{22} C_6 = \frac{22*21*20*19*18*17}{6*5*4*3*2*1}\\\\_{22} C_6 = \frac{53721360}{720}\\\\_{22} C_6 = 74613\\\\[/tex]
There are exactly 74,613 ways to form a committee of 6 people from a pool of 22 total.
Let B = 74,613
------------------------------------------------------
To find the probability of neither Allen or Joe are on the committee, we divide the values of A and B found earlier
A/B = (38,760)/(74,613) = 0.5194805
This value is approximate.
Rounding to three decimal places, or rounding to the nearest thousandth, leads to the final answer 0.519
There's roughly a 51.9% chance of forming a panel where neither Allen nor Joe are members.
How far does the tip of the minute hand of a clock move in 20 minutes if the hand is 10 inches long?
Answer:
20.95 inches
Step-by-step explanation:
The complete revolution of the minute hand forms a circle in 60 minutes.
circumference of a circle = 2[tex]\pi[/tex] radius
i.e C = 2[tex]\pi[/tex]r
But from the question, r = length of the minute hand = 10 inches
⇒ C = 2[tex]\pi[/tex] x 10
= 20[tex]\pi[/tex]
C = 20[tex]\pi[/tex] inches
Also, 20 minutes = [tex]\frac{20 minutes}{60 minutes}[/tex] = [tex]\frac{1}{3}[/tex] of the circumference.
So that,
the distance of the tip of the minute hand = [tex]\frac{1}{3}[/tex] x C
= [tex]\frac{1}{3}[/tex] x 20[tex]\pi[/tex]
= [tex]\frac{1}{3}[/tex] x 20 x [tex]\frac{22}{7}[/tex]
= 20.9524
= 20.95 inches
Thus, the distance of the tip of the minute hand is 20.95 inches
499 to the nearest hundred
Answer:
the correct answer would be 500
Step-by-step explanation:
Answer:
500
Step-by-step explanation:
hope this helps
What is the distance between 0.6 and 0
Answer:
on the number its between 0 and 1
Step-by-step explanation:
if you jump from 0 to 6 you would have 6 jumps, so it would be 6.
0.6 equals 0.60 so it could ALSO be 60 jumps. (incase u needed that)
Solve for y
3(7y + 4) = 15y + 6y +4+8
Answer: the are no values of y that make it true
Step-by-step explanation: no solution
Answer:
-4/7
Step-by-step explanation:
Can someone please help me it's slope
Answer:
-0.04
Step-by-step explanation:
The sum of the 112th term of the geometric series is 256 and the common ratio is 3/4. Find the first term of the first geometric series.
Answer:
First term = 64
Step-by-step explanation:
We are given the formula for the nth term of a geometric series to be;
S_n = (a1(1 - rⁿ))/(1 - r)
Where:
S_n is the sum of n terms
A1 is first term
r is common ratio
We are given;
S_112 = 256
r = ¾
Thus;
256 = a1(1 - ¾^(112))/(1 - ¾)
256 = a1(4)
a1 = 256/4
a1 = 64
In the diagram below, BC is an altitude of AABD. To the nearest whole unit, what is the length of CD?
Answer:
C
Step-by-step explanation:
Using the Pythagorean theorem, find BA: [tex]\sqrt{37^{2}+53^{2} } = \sqrt{4178}[/tex]
Making BC = x, find the lenth of BD: [tex]\sqrt{x^{2} +37^{2} }[/tex]
Since DBA is a right triangle, this follows: [tex]DA^{2}=BD^{2}+BA^{2}[/tex]
Substitute: [tex](x+53)^{2} =\sqrt{4178} ^{2} +\sqrt{x^2+37^2} ^{2}[/tex]
Expand: [tex]x^{2} +106x+2809=x^{2} +5547[/tex]
Solve: 106x = 2736
Finally: x ≈ 25.8 ≈ 26
Therefore: C
Malcolm and Theo's families are both traveling to the same vacation resort.
The equation d=65t models the distance, d, that Malcolm's family travels after t hours.
The graph below shows the relationship between the distance and the amount of time that Theo's family traveled.
How much faster did Malcolm's family travel than Theo's family
10 miles per hour
15 miles per hour
30 miles per hour
65 miles per hour
Graph is missing, so i have attached it.
Answer:
15 miles per hour
Step-by-step explanation:
We are given that d = 65t models the distance, d, that Malcolm's family travels after t hours.
Since we are comparing speed of both families, then we will find the speed here.
Formula for speed is;. Speed = distance/time
d = 65t and we know that d is distance and t is time. Thus, d/t = 65 m/hr = speed.
For Theo's family, looking at the image attached;
At a distance of 50 miles, time spent is 1 hr
At a distance of 100 miles, time spent is 2 hrs
At a distance of 150 miles, time spent is 3 hrs
At a distance of 200 miles, time spent is 4 hrs
Thus, speed = 200/4 or 150/3 or 100/2 or 50/1.
They all give a constant value of 50 m/hr.
Thus, speed of Theo's family = 50 mi/hr
Comparing this to that of Malcolm's family,we can see that Malcolm's family were faster by 65 - 50 = 15 mi/hr
Answer:
15
Step-by-step explanation:
Farmers market Sells grapefruit strawberries and avocado they each have a different cost and are price per box Alyssa Buys two boxes of strawberries and three boxes of avocados and spent $23 London by three boxes of grapefruit and four boxes of strawberries in Spain $19 Tina by seven boxes of grapefruit and five boxes of avocados in Spencer $51 find the missing quantity below
Answer:
The cost of grapefruits per box is $3, The cost of strawberries per box is $2.5
The cost of avocados per box is $6
Step-by-step explanation:
Let us represent the price of Grapefruits per box = g
Strawberries per box = s
Avocados per box = a
Alyssa buys two boxes of strawberries and three boxes of avocados and spent $23
2s + 3a = 23 ....... Equation 1
a = 23 - 2s
London buys three boxes of grapefruit and four boxes of strawberries in Spain $19
3g + 4s = 19 ....... Equation 2
Tina buys seven boxes of grapefruit and five boxes of avocados in Spencer $51
7g + 5a = 51..... Equation 3
2s + 3a = 23 ....... Equation 1
3g + 4s = 19 ....... Equation 2
7g + 5a = 51..... Equation 3
Substituting 3a = 23 - 2s in Equation 3
a = 23 - 2s/3
7g + 5(23 - 2s/3) = 51
7g +( 115 - 10s/3) = 51
Multiply through by 3
7g × 3 + ( 115 - 10s/3) × 3 = 51 × 3
21g + 115 - 10s = 153
21g -10s = 38 ........ Equation 4
Combining Equation 2 and 4
3g + 4s = 19 ....... Equation 2 × 10
21g -10s = 38 ........ Equation 4 × 4
30 + 40s = 190.. Equation 5
84g - 40s = 152 .... Equation 6
We Add Equation 5 and Equation 6 to eliminate s
114g = 342
g = 342/114
g = $3
To find s, cost 0f straw berries
g = $3
3g + 4s = 19 ....... Equation 2
3(3) + 4s = 19
9 + 4s = 19
4s = 19 -9
4s = 10
s = 10/4
s = $2.5
For find a, the cost of avocados.
7g + 5a = 51..... Equation 3
g = $3
7(3) + 5a = 51
21 + 5a = 51
5a = 51 - 21
5a = 30
a = 30/5
a = $6
g =$ 3, s =$ 2.5 and a = $6.
Therefore:
The cost of grapefruits per box is $3.
The cost of strawberries per box is $2.5 and
The cost of avocados per box is $6
James ran 25/100 of a mile yesterday. His friend, Natasha, ran 4/10 of a mile. Who ran farther and how do you know?
Answer:
James ran faster
Step-by-step explanation:
Help please and thank you
Answer:
1. 22
2. 8
3. 31
4. 20
5. 38
6. 22
7. 26
8. 16
9. 14
10. 28
Step-by-step explanation:
USE PEMDAS
P: Parantheses
E: exponents
D: division
A: addition
S: subtraction
and ywww
I need your knowledge.
Answer:
det(2*3) also det(6)
Step-by-step explanation:
this is just filler so I can send it
x + 8x + 15 help me out with this plz
Answer:
3(3x + 5)
Step-by-step explanation:
x + 8x + 15 Combine liked terms
9x + 15
GCF: 3
3(3x +5) Factor
James determined that these two expressions were equivalent expressions using the values of x - 4 and x - .6
Which statements are true? Check all that apply.
7x+4 and 3x+5+4x-1
When x = 2, both expressions have a value of 18.
The expressions are only equivalent for x = 4 and x = 6.
The expressions are only equivalent when evaluated with even values.
The expressions have equivalent values for any value of x.
The expressions should have been evaluated with one odd value and one even value.
When x = 0, the first expression has a value of 4 and the second expression has a value of 5.
The expressions have equivalent values if x = 8.
Answer:2 4 and 5
Step-by-step explanation:
Misty correctly determined the equation of the linear function represented by the table of values below to be y = negative 2 x + 9 in slope-intercept form by using the ordered pairs (1, 7) and (2, 5).
x
y
1
7
2
5
3
3
4
1
What would she have gotten for the equation of the linear function if she had used the ordered pairs (2, 5) and (4, 1) instead?
y = negative 4 x + 9
y = negative 4 x + 18
y = negative 2 x + 9
y = negative 2 x + 18
Answer:
C
Step-by-step explanation:
y = mx + c
m = (y2 - y1 )/ (x2 - x1)
using (1 , 7) & (2,5)
y2 = 5 y1 = 7 so y2 -y1 = -2
x2 = 2 x1 = 1 so x2 - x1 = 1
m - -2/1 = -2
y = -2x + c
when x =1 y = 7
so 7 = -2 + c
=> c =9
y = -2x + 9
if ordered pairs (2, 5) and (4, 1) used
m = (1-5)/(4-2)
=> m = -4/2
=> m = -2
y = -2x + c
for x =2 y =5
5 = -2*2 + c
=> c = 9
y = -2x + 9
she would have got same equation
Answer:
The person above is correct ! :))
Step-by-step explanation:
This is an confirmation :))
Carmine and Hiram are solving the following word problem.
Gina is training for a marathon. She ran 6.75 miles on Saturday. On Sunday, she ran 7.20 miles. How far did she run on Saturday and Sunday combined?
Carmine sets up his problem as 6.75 + 7.20
Hiram sets up his problem as 7.20 + 6.75
Who is correct? Carmine, Hiram, or both
Answer:
Both is the anwser.
Step-by-step explanation:
Look it this way its simple 7.20 plus 6.75 equals 13.95
6.75 plus 7.20 is 13.95 theres no decimals changing in this problem meaning that both of them are correct.
Determine the range of the function graphed above.
OA. (-4, 0]
OB. [0, 4]
Oc. (-00, 4]
OD. [4, 00)
Answer:
Step-by-step explanation:
the range are the y values so must be [4,-∞) because if you look at the y-axis the highest value is 4 and the lowest goes to -∞
Kira skied at a steady speed in a 2 mile cross country ski race her finished time was 5/12 hour Kira wants to know her speed miles per hour
Answer: The purpose of this task is to give students experience in reasoning with equivalent ratios and unit rates from both sides of the ratio. This prepares for studying proportional relationships in Grade 7, and in Grade 8 for understanding that a proportional relationship can be viewed as a function in two different ways, depending on which variable is regarded as the input variable and which as the output variable. The values in column B were found by dividing both values in column A by 10. The values in column C were found by dividing both values in column B by 2. The other columns contain multiples of the values in column B.
If we look in column E, we can see that it would take her 45 minutes to run 6 miles.
If we look in column B, we can see that she could run 2 miles in 15 minutes.
If we look in column F, we can see that she is running 8 miles every 60 minutes (which is 1 hour), so she is running 8 miles per hour.
If we look in column C, we can see that her pace is 7.5 minutes per mile.
If we divide 150 by 20, we get the unit rate for the ratio 150 minutes for every 20 miles.
150÷20=7.5
So the runner is running 7.5 minutes per mile. We can multiply this unit rate by the number of miles:
7.5minute mile×6 miles=45 minutes
Thus it will take her 45 minutes to run 6 miles at this pace.
If it takes her 45 minutes to run 6 miles, it will take her 45÷3=15 minutes to run 6÷3=2 miles at the same pace.
If it takes her 15 minutes to run 2 miles, it will take her 4×15=60 minutes to run 4×2=8 miles at the same pace. Since 60 minutes is 1 hour, she is running at a speed of 8 miles per hour.
We found her pace in minutes per miles in part (a).
Using the speed - distance relationship, kira's speed in miles per hour would be 4.8 miles per hour.
Given the Parameters :
Speed = 5/12 hours = 0.416666 hour Distance = 2 miles Speed = distance / timeHence,
Speed = (2 ÷ 0.416666) = 4.8 miles per hour.
Therefore, Kira's speed is 4.8 miles per hour.
Learn more : https://brainly.com/question/13816092
Billy and Joe go to McDonalds for lunch. They order 2 burgers, 3 fries, and 2 sodas. The mom
bugers cost $3.50 each. The sodas cost $1.00 each. If the total was $16.29 how much was
each fry. Write and solve an equation to represent this situation. Round your answer to
the nearest tenth
Answer:
2.43 and rounded it is 2 dollars
Step-by-step explanation:
2 burger-$7.00
3 Fries-
2 Sodas- $2.00
7+2=9
$16.29-9.00=7.29
$7.29/3=2.43
33. The distance d in miles that a car travels in t
hours at a rate of 58 miles per hour is given by
the equation d = 581. What is the best estimate
of how far a car travels in 7 hours?
Answer:
406 miles
Step-by-step explanation:
You would simply multiply 7 by 58.
Hope this helps...... Hisoka
You are redecorating your room and the only thing left to paint is your door. You’re only going to paint the side that faces the inside of your room. The door is 6 feet 8 inches tall and 30 inches wide. You need to know the surface area of the side of the door to determine how much paint to buy. The hardware store sells paint by how much covers a square foot. What is the surface area you should report to the hardware store? (Hint: First find the number of square inches in 1 square foot.)
Answer: Then the surface area that you should report to the hardware store is 15 ft^2.
Step-by-step explanation:
Remember that the area of a rectangle of length L and width W is
A = L*W
In this case, we can think in the door as a rectangle, where:
L = 6ft + 8in
W = 30in
Now, we know that in the hardware store they sell paint by how much covers a square foot, then we must calculate the area of the door in square feet.
Then the first step would be to replace all the units by ft.
We know that:
1ft = 12in.
Then we have that:
(1ft/12in) = 1
Then we have that:
8in = 8in*1 = (8in/12in)*1ft = 0.6... ft
(the 3 dots means that the 6 repeats infinitely)
And;
30in = 30in*1 = 30in*(1ft/12in) = 2.5ft
Then the measures of the door are:
L = 6ft + 0.6...ft = 6.6...ft
W = 2.5ft
The area will be:
A = L*W = 6.6...ft*2.5ft = 15 ft^2
Then the surface area that you should report to the hardware store is 15 ft^2.
Classify the equation 5 (2x + 3) = 3(3x + 12) as having one solution, no solution, or infinitely many solutions.
Answer: one solution I believe
Step-by-step explanation: I got 21 as my answer and that is one solution
-6p + 4p > 12
( please look at picture instead )
Answer:
the asnwer is p is less than or equal to -6.
Step-by-step explanation:
The reasonfro that is becuase when u have a negative variable you have to divide both sides by a negative, which will flip the symbol making it less than in this case rather than greater than. Hope this works mark as brainliest pls
that what i got but check the sign well
Question #3: Can you add the following terms? Why or why not?
3V2 + 2V2
whats the rate if 13 inches of snow in 7 hours
Answer:
1.86 (rounded to nearest hundredth) inches of snow in 1 hour
Step-by-step explanation:
Divide 13 inches of snow by 7 hours
The answer is 1.8571428571428571428571428571429
Round to the nearest hundredth
1.86
Hope this helped :)
[tex]\textsf{Hey there!}[/tex]
[tex]\textsf{What's the rate of 13 inches of snow in 7 hours?}[/tex]
[tex]\mathsf{\dfrac{13\leftarrow \bf{inches}}{7\leftarrow{hours}}} \\\\\mathsf{\dfrac{13\div7\leftarrow inches}{7\div7\leftarrow hours}}\\\\\mathsf{7\div7=1}\\\\\mathsf{\dfrac{13\div7\leftarrow\underline{ inches}}{1\leftarrow \underline{hour(s)}}}\\\\\mathsf{13\div7=1.857143}\\\\\mathsf{\dfrac{1.857143\leftarrow \frak{inches}}{1\leftarrow\frak{hour(s)}}}}}}\\\\\mathsf{1.85714\div1=\bf{ANSWER}}\\\\\textsf{Solve above and you have your answer.}[/tex]
[tex]\lhuge\text{Note: We're rounding our answer because the actual answer will take some time}[/tex]
[tex]\boxed{\boxed{\textsf{Thus, your answer is: \boxed{\boxed{\large\textsf{\bf1.86 inches per hour}}}}}}\checkmark[/tex]
[tex]\textsf{Good luck on your assignment and enjoy your day!}\\\\\frak{LoveYourselfFirst}[/tex]
Rewrite 14/32 in simplest form.
Answer:
7/16
Step-by-step explanation:
Answer:
14/32 = 7/16
Step-by-step explanation:
You divide each number by two
Help me please please
Answer:
Hold a sec I got this
what do expressions (3^3) and (3^4) have in common?
Answer:
they are both 3 with different powers
Step-by-step explanation:
A loaf of sandwich bread contains 24 slices. Which of these tables correctly shows the ratios of different numbers of loaves of bread to the numbers of total slices they contain?
Answer:
which table?
Step-by-step explanation:
im assuming it would look like this
1 24
2 48
3 72
4 96
5 120
6 144
7 168
8 192
9 216
10 240
just multiply the number of loaves to 24
Hope this helped :)
Evaluate the given integral by making an appropriate change of variables.
The integrand and given boundary for R suggests we should use
u = x - 4y
v = 5x - y
with 0 ≤ u ≤ 3 and 6 ≤ v ≤ 9.
Then
x = (4v - u)/19
y = (v - 5u)/19
and the Jacobian for this transformation is
[tex]J=\begin{bmatrix}x_u&x_v\\y_u&y_v\end{bmatrix}=\dfrac1{19}\begin{bmatrix}-1&4\\-5&1\end{bmatrix}\implies|\det J|=\left|\dfrac1{19}\right|=\dfrac1{19}[/tex]
The integral is then
[tex]\displaystyle\iint_R 2\frac{x-4y}{5x-y}\,\mathrm dA = \frac1{19} \int_6^9 \int_0^3 \frac{2u}v\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle \frac2{19} \int_6^9 \frac{3^2-0^2}{2v}\,\mathrm dv[/tex]
[tex]=\displaystyle \frac9{19} \int_6^9 \frac{\mathrm dv}v[/tex]
[tex]=\dfrac9{19}(\ln9-\ln6)=\dfrac9{19}\ln\dfrac96=\boxed{\dfrac9{19}\ln\dfrac32}[/tex]