Answer:
1707
Step-by-step explanation:
Let's designate the three sets of collinear points, A, B, C, having 4, 6, 7 points, respectively.
Since there are 3 sets of collinear points, exactly two of the vertices must come from the same set.
For two vertices from set A, the remaining two must come from the 13 members of sets B and C. There are a total of (4C2)(13C2) = 468 such quadrilaterals.
For two vertices from set B, we have already counted the quadrilaterals that result when the remaining two are from set A. There are 4·7 = 28 ways to have one each from sets A and C, and 7C2 = 21 ways to have two from set C. Thus, the additional number of quadrilaterals having 2 vertices in set B is ...
(6C2)(28 +21) = 735
For two vertices from set C, we have already counted the cases where two are from A or two are from B. There are 4·6 = 24 ways to have one each of the remaining vertices from sets A and B. Then the number of additional quadrilaterals having two points from set C is ...
(7C2)(4)(6) = 504
So, the total number of unique quadrilaterals is ...
468 +735 +504 = 1707
__
nCk means "the number of ways to choose k from n"
nCk = n!/(k!(n-k)!)
Select the correct answer.
The numbers of pages in the books in a library follow a normal distribution. If the mean number of pages is 180 and the standard deviation is 30
pages, what can you conclude?
What’s the correct answer for this?
Answer:
B:
Step-by-step explanation:
IN THE ATTACHED FILE
What’s the correct answer for this?
Answer:
what is this it is not understand able
Answer:
11
Step-by-step explanation:
<TKF = 90° ( BECAUSE OF THE BISECTOR)
BUT
<TKF = 5(x+7)
So
5(x+7) = 90
5x+35 = 90
5x = 90-35
5x = 55
Dividing by 5(both sides)
x = 11
A company makes two types of biscuits: Jumbo and Regular. The oven can cook at most 400 biscuits per day. Each jumbo biscuit requires 2 oz of flour, each regular biscuit requires 1 oz of flour, and there is 600 oz of flour available. The income from each jumbo biscuit is $0.08 and from each regular biscuit is $0.11. How many of each size biscuit should be made to maximize income? What is the maximum income?
Answer:
$ 44
Step-by-step explanation:
If we analyze the statement well, we can observe something very crucial to solve it, the jumbo biscuits require 2 oz of flour and give a profit of $ 0.08, the Regular one that only requires 1 oz of flour leaves a profit of $ 0.11, which means that requiring a smaller quantity of flour leaves a greater profit, so in terms of profit it is not profitable to make Jumbo, only Regular.
Therefore, since you can make 400 biscuits, they would all be regular since there are 600 oz of flour available, it is enough to make 400, therefore the maximum profit would be:
$ 0.11 * 400 = 44
The maximum possible profit is $ 44
How do I write the formula?
Answer:
1/5x = h(x)
Step-by-step explanation:
6x+y = 4x+ 11y
Subtract y from each side
6x+y -y = 4x+ 11y-y
6x = 4x+10y
Subtract 4x from each side
6x-4x = 4x+10y-4x
2x = 10y
Divide each side by 10
2x/10 = 10y/10
1/5x = y
1/5x = h(x)
Round 4/7 to the nearest tenth.
Answer:
0.6
Step-by-step explanation:
4/7 can be considered a suspended division problem. To find the answer, 4 must be divided by 7. This yields the result 0.57142, which can be rounded to 0.6.
Factor 4x^2+12x+5 by applying the distributive property
Answer:
(2x + 5)(2x + 1)
Step-by-step explanation:
4x^2 + 12x + 5
=4x^2 + 2x + 10x + 5
=2x(2x + 1) + 5(2x + 1)
=(2x + 5)(2x + 1)
Hope this helps!
Four interior angles of a pentagon measure 88°, 118, 132, and 100°. What is the measure of the fifth interior angle?
82
92
102
112
Answer:
fifth angle = 102°
Step-by-step explanation:
A pentagon is a polygon that have 5 sides. A pentagon can be divided into 3 triangles .And the sum of angle in a triangle is 180°. Therefore the sum of interior angle in a pentagon will be 180 × 3 = 540°. The sum of interior angles of a pentagon = 540°.
The general rule for calculating sum of the interior angles of a polygon is
sum of interior angle = (n−2) × 180°
where
n = number of sides
n = 5 since we are dealing with a pentagon.
sum of interior angle of a pentagon = 540°
The fifth angle can be computed when you subtract the sum of the 4 angles from 540°.
fifth angle = 540 - (88 + 118 + 132 + 100)
fifth angle = 540 - 438
fifth angle = 102°
Answer:
its C on edg
Step-by-step explanation:
What’s the correct answer for this?
Answer:
(AE )(EB)=(CE)(ED)
Step-by-step explanation:
The lines (AE )(EB)=(CE)(ED)
Line AE is congruent with line CE and Line EB is congruent with ED
A line is congruent when they assume the same shape and form but only they can be flipped;
AB and CD are both line segments.
Answer:
fourth option
Step-by-step explanation:
Given two intersecting chords, then
The product of the parts of one chord is equal to the product of the parts of the other chord, that is
AE(EB) = CE(ED)
The volume of a cube is 343 cubic feet. What is the side length of the cube
A. 12 feet
B. 23 feet
C. 7 feet
D. 2 feet
Steps:
Shape: Cube
Solved for side length of the cube
Volume: 343 cubic feet
Formula: a=V⅓
Description:
Using the formula for the volume of the cube a=V⅓. We are going to calculate the side length of the cube. Your answer will be 7 feet. Meaning the correct answer for this question is C.
Answer: a≈7ft
Please mark brainliest
Hope this helps.
At a fundraiser, a school group charges $8 for tickets for a "grab bag." You choose one bill at random from a bag that contains 38 $1 bills, 20 $5 bills, 7 $10 bills, 5 $20 bills, and 1 $100 bill. Is it likely that you will win enough to pay for your ticket?
It is that you will win enough to pay for your ticket because the probability of winning enough to pay for your ticket as a simplified fraction is
Answer:
a. It is not likely that a winning ticket will be selected
b. The probability of winning enough to pay for the ticket expressed as a simplified fraction is 13/71
Step-by-step explanation:
To answer this question, there are some important notes to know.
1. The selection is only once
2. To win, you have to select a note which has a greater value than $8
Now, the total number of notes that we have = 38 + 20 + 7 + 5 + 1 = 71
The number of bills present that are greater than $8 are; 7 $10 bills , 5 $20 bills and 1 $100 bill
This makes a total of 7 + 5 + 1 = 13
Thus, the probability of selecting a bill which would pay for the charges is 13/71
Now, the probability of not selecting is 1- probability of selecting = 1-13/71 = 58/71
Since the probability of not selecting is greater than the probability of selecting, it means that it is not likely that a winning ticket will be selected
What is the solution to the equation below?
Answer:
A
Step-by-step explanation:
2/3x=1-5
2/3x=-4
x=-4/2/3
x=-6
On your second day of measuring living trees you find a tree with a diameter of 24 inches! Should you predict the volume of this tree? Why or why not? Group of answer choices Yes! Extrapolation is fine. Don't worry about it. No! That would be extrapolation, and extrapolation is bad. (Notice in the plot that we only collected date for diameters between 8 and 22 inches).
Answer:
Yes! Extrapolation is fine. Don't worry about it.
Step-by-step explanation:
Because the data we have ranges from 8 to 22 inches, an extrapolation should be made, which is the process of estimating beyond the original observation interval, the value of the variable based on its relationship to another variable. It is similar to interpolation, which produces estimates between known observations, unlike this, extrapolation is subject to greater uncertainty and a higher risk of producing insignificant results, but because the value is 24 inches, it is not too far away. of the upper limit which is 22, the error should not be very big, therefore the answer is: Yes! Extrapolation is fine. Don't worry about it.
A map has a scale of 3cm 7km if two cities was 8 cm on the nearest tenth of a kilometer
Answer:
18.7 km
Step-by-step explanation:
3 cm >>> 7 km
1 cm >>> 7/3 km
8 cm >>> 8*7/3 km= 18.7 km
Answer:
18.7
Step-by-step explanation:
Find the missing side length. Show all of your work. *
Find the distance between the points (6,-4) and (-3,-4) .
The right answer is 9 units.
please see the attached picture for full solution
Hope it helps
Good luck on your assignment:)
A rectangular swimming pool is 17 meters long, 13 1/2 meters wide, and 2 1/2 meters deep. What is its volume?
Answer: 573.75 meters^3
Step-by-step explanation:
Volume = Length x width x height
Volume = 17 x 13.5 x 2.5
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
The requried equations that are equivalent to each other are,
(A) 2 + x = 5 (B) x + 1 = 4 (E) -5 + x = -2.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Given equations,
(A) 2 + x = 5
Simplifying the above expression,
x = 5 - 2
x = 3
Similarly, simplify all the equations,
(B) x = 3
(C) x = -3
(D) x = 11
(E) x = 3
Therefore, equations that give x = 3, after simplification is equivalent equations.
Thus, the requried equations that are equivalent to each other are,
(A) 2 + x = 5 (B) x + 1 = 4 (E) -5 + x = -2.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ2
In microbiology, colony-forming units (CFUs) are used to measure the number of microorganisms present in a sample. To determine the number of CFUs, the sample is prepared, spread uniformly on an agar plate, and then incubated at some suitable temperature. Suppose that the number of CFUs that appear after incubation follows a Poisson distribution with μ = 15.
(a) If the area of the agar plate is 75 square centimeters (cm2), what is the probability of observing fewer than 4 CFUs in a 25 cm2 area of the plate? (Round your answer to four decimal places.)
(b) If you were to count the total number of CFUs in 5 plates, what is the probability you would observe more than 95 CFUs? Use the Poisson distribution to obtain this probability. (Round your answer to four decimal places.)
(c) Repeat the probability calculation in part (b) but now use the normal approximation. (Round your answer to four decimal )
(d) Find the difference between this value and your answer in part (b). (Round your answer to four decimal places.)
Answer:
(a) 0.2650
(b) 0.0111
(c) 0.0105
(d) 0.0006
Step-by-step explanation:
Given that:
In microbiology, colony-forming units (CFUs) are used to measure the number of microorganisms present in a sample.
Suppose that the number of CFUs that appear after incubation follows a Poisson distribution with mean μ = 15. &;
If the area of the agar plate is 75cm²;
what is the probability of observing fewer than 4 CFUs in a 25 cm² area of the plate.
We can determine the mean number of CFUs that appear on a 25cm² area of the plate as follows;
75cm²/25cm² = 3
Since;
mean μ = 15
mean number of CFUs that appear on a 25cm² = 15/3 = 5 CFUs
Thus ; the probability of observing fewer than 4 CFUs in a 25 cm² area of the plate is estimated as:
= P(X < 4)
Using the EXCEL FUNCTION ( = poisson.dist(3, 5, TRUE) )
we have ;
P(X < 4) = 0.2650
b) If you were to count the total number of CFUs in 5 plates, what is the probability you would observe more than 95 CFUs?
Given that the total number of CFUs = 5 plates; then the mean number of CFUs in 5 plates = 15×5 = 75 CFUs
The probability is therefore = P( X > 95 )
= 1 - P(X ≤ 95)
= 1 - poisson.dist(95,75,TRUE) ( by using the excel function)
= 0.0111
c) Repeat the probability calculation in part (b) but now use the normal approximation.
Let assume that the mean and the variance of the poisson distribution are equal
Then;
[tex]X \sim N (\mu = 75 , \sigma^2 = 75)[/tex]
We are to repeated the probability calculation in part (b) from above;
So:
P( X > 95 )
use the normal approximation
From standard normal variable table:
P(Z > 2.3094)
Using normal table
P(Z > 2.3094) = 0.0105
(d) Find the difference between this value and your answer in part (b).
So;
the difference between the value in part c and part b is;
= 0.0111 - 0.0105
[tex]= 6*10^{-4}[/tex]
= 0.0006 to four decimal places
1. In an AP, the ratio of the 2nd term to the 7th term is 1/3. If the 5th term is
11, what is the 15th term?
Answer:
T15 = 31
Step-by-step explanation:
Its in the picture
I hope it helps :)
If you roll two fair dice how many different ways can you obtain a different number on each side
Answer:
30
Step-by-step explanation:
You can have any number on the first die, and any number besides the first one on the second. 6*5=30
¿Qué es y para que nos sirve la jerarquía de operaciones en la vida cotidiana?
for example, si te pones los zapatos antes que los pantalones, te costará mucho vestirte
can someone help me?
Answer: 26
Step-by-step explanation:
32-6 = 26
A homeowner finds that there is a 0.15 probability that a flashlight does not work when turned on. If she has three flashlights, find the probability that at least one of them works when there is a power failure. Find the probability that the second flashlight works given that the first flashlight works.
Answer:
A) 0.386
B).0.325
Step-by-step explanation:
probability p will not work = 0.15
Q probability w5ill work = 0.85
Number of flashlight = 3
Probabilty of at least one=
1- probability of none
But probability of none= 3C0(p)^0(q)^3
= 1*(0.15)^0(0.85)^3
= 1*1*(0.614)
= 0.614
Probability of at least one=1-0.614
= 0.386
Probability of two flashlight work
= 3C1(0.15)^1(0.85)^2
= 3*(0.15)*(0.7225)
= 0.325
If f(x)= 5x + 40, what is f(x) when x = -5?
Answer:
f(x) = 15
Step-by-step explanation:
"If f(x)= 5x + 40, what is f(x) when x = -5?"
Substitute x for -5:
f(x) = 5x + 40
f(x) = 5(-5) + 40
f(x) = -25 + 40
f(x) = 15
Which of the following is the solution to 3x - 1>=12
Answer:
The solution to [tex]3x\:-\:1\ge 12[/tex] is [tex]x\ge \frac{13}{3}[/tex].
Step-by-step explanation:
An inequality is a mathematical relationship between two expressions and is represented using one of the following symbols: inequalities involving "<", "≠" or ">" are referred to as "strict inequalities", while inequalities involving "≤" or "≥" are not.
Solving an inequality means finding all of its solutions. A solution of an inequality is a number which when substituted for the variable makes the inequality a true statement.
To find the solution to [tex]3x\:-\:1\ge 12[/tex]
[tex]\mathrm{Add\:}1\mathrm{\:to\:both\:sides}\\\\3x-1+1\ge \:12+1\\\\\mathrm{Simplify}\\\\3x\ge \:13\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\\\frac{3x}{3}\ge \frac{13}{3}\\\\\mathrm{Simplify}\\\\x\ge \frac{13}{3}[/tex]
Who knows the answer to the picture?
Step-by-step explanation:
The way i like to remember it is that the exponent inside of the radical will be the numerator of the fraction and the index of the radical will be the denominator so the answer is 2^(-5/3).
While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning to the
United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have?
Round to the nearest cent.
1 European euro = 1.3687 US dollars
44.70 US dollars
73.06 US dollars
136.87 US dollars
140.41 US dollars
Answer:
44.70 USD
Step-by-step explanation:
250÷1.3687
=182.655074158
182.655074158-150
=32.655074158
32.655074158×1.3687
=44.6950000001
The 44.70 US dollars Phelan now has if Phelan exchanged 250 US dollars for euros option (A) is correct.
What is unit conversion?It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.
It is given that:
While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip.
After returning to the United States he converts his money back to US dollars. H
Let x be the total original 250 US dollars Phelan now have:
The value of x can be found as follows:
x = (250/1.3687 - 150)x1.3687
After simplification:
x = 44.69 ≈ 44.70 US dollars
Thus, the 44.70 US dollars Phelan now has if Phelan exchanged 250 US dollars for euros option (A) is correct.
Learn more about the unit conversion here:
https://brainly.com/question/11543684
#SPJ2
Find the value of a in the equation below
2sin(1÷4a+20)=√3
Step-by-step explanation:
[tex]sin(1 \div 4a + 20) = \sqrt{3} \div 2 \\ sin(1 \div 4a + 20) =sin 60[/tex]
1÷4a+20=60
1÷4a=4
a=1/160
Each side of a square piece of confetti is 12 millimeters long. What is the piece of confetti's perimeter?
Answer:
P=48 millimeters
Step-by-step explanation:
p=4l
p=4 x 12
p=48 mm
