Answer:
28
Step-by-step explanation:
7C2
The 3rd term of 7th row of the Pascals triangle is 21.
We have a Pascal's triangle.
We have to determine the 3rd term of 7th row of this triangle.
What is Pascal's triangle ?A pascal's triangle is an arrangement of numbers in a triangular array such that the numbers at the end of each row are 1 and the remaining numbers are the sum of the nearest two numbers in the above row. The pascals triangle is shown below -
[tex]\begin{tabular}{rccccccccc}$n=0$:& & & & & 1\\\noalign{\smallskip\smallskip}$n=1$:& & & & 1 & & 1\\\noalign{\smallskip\smallskip}$n=2$:& & & 1 & & 2 & & 1\\\noalign{\smallskip\smallskip}$n=3$:& & 1 & & 3 & & 3 & & 1\\\noalign{\smallskip\smallskip}$n=4$:& 1 & & 4 & & 6 & & 4 & & 1\\\noalign{\smallskip\smallskip}\end{tabular}[/tex]
If we have to find the element or term at position - m in row number - n, than the element will be -
[n] C [m-1] = [n-1] C [m-2] + [n-1] C [m-1]
According to the question, we have to find the 3rd term of 7th row of this triangle. It can be found out using the formula -
[n] C [m-1] = [n-1] C [m-2] + [n-1] C [m-1]
We have - n = 7 and m = 3
[7] C [2] = [6] C [1] + [6] C [2]
[tex]$\frac{7!}{(7-2)!2!} = \frac{6!}{(6-1)!1!} + \frac{6!}{(6-2)!2!} = 6 + 15 = 21[/tex]
Hence, the 3rd term of 7th row of the Pascals triangle is 21.
To solve more questions on Pascals Triangle, visit the link below-
https://brainly.com/question/15655806
#SPJ2
The slope through (3, 5) and (1. y) is 3. Find y.
Really need this answer!
Step-by-step explanation:
y2 - y1 / x2 - x1
2 = 5 - y / (3 - 1)
4 = 5 - y
y = 1
So the line with slope 2 passes through the points (1,1) and (3,5).
Hope this helps!
An electrical completes 1/6 of job in 2/3 hours At this rate how many hours does it take the electrician to complete the job
Answer:
4 hours
Step-by-step explanation:
6 × 2 = 12
12 ÷ 3 = 4
4 hours is the correct answer
Glad I could help:)
PLEASE HELP I WILL MARK BRAINLY IF THE ANSWER IS CORRECT
Answer:
I think it is B.
Step-by-step explanation:
Hope this helps.
Evaluate the expression below.\
(4.4+7.6)x-(24/12)x
Answer:
10x
Step-by-step explanation:
Answer:
10x
Step-by-step explanation:
Suppose that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked. (Round your answers to four decimal places.) (a) What is the (approximate) probability that X is at most 30
Answer:
0.9726 = 97.26% approximate probability that X is at most 30
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
11% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped).
This means that [tex]p = 0.11[/tex]
Random sample of 200 shafts
This means that [tex]n = 200[/tex]
Mean and Standard deviation:
[tex]\mu = E(x) = np = 200*0.11 = 22[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.11*0.89} = 4.42[/tex]
(a) What is the (approximate) probability that X is at most 30
Using continuity correction, this is [tex]P(X \leq 30 + 0.5) = P(X \leq 30.5)[/tex], which is the pvalue of Z when X = 30.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30.5 - 22}{4.42}[/tex]
[tex]Z = 1.92[/tex]
[tex]Z = 1.92[/tex] has a pvalue of 0.9726.
0.9726 = 97.26% approximate probability that X is at most 30
The perimeter of the square is 36. What is the length of the diagonal, x? HELPNPLZ FOR THE LOVE OF GOD
Answer:
D. [tex] 9 \sqrt{2} [/tex]
Step-by-step explanation:
Side length of square = Perimeter/4 = 36/4 = 9
Length of diagonal (x)
[tex] = length \: of \: side \sqrt{2} \\ \\ = 9 \sqrt{2} [/tex]
What is the largest of three consecutive odd integers whose sum is 105.
I need help to find the range
Answer:
algebraic terms = 4- -4 = 8
Step-by-step explanation:
-4 is our lowest value as 5 is not equal or counted
4 is our highest value and is counted.
(x - 5)2 + (y-(-3))2 = 34 (x - 5)2 + ( + 3)2 = 34 Exercises 12.2 Complete the following: 1. Find the equation of the circle having the given center and ra (a) C(0,0), r= 3 (c) C(4, 3), r = 5 (d) C(2, (b) C(-2.
Answer:
Step-by-step explanation:
The general equation of the circle
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Center = c = (h,k) , radius = r
if C = (0,0) , r = 3
The equation will be :
(x-0)^2+(y-0)^2=3^2
[tex]x^2+y^2=9[/tex]
50 POINTS AND MARKED BRAINLIEST IF U DO THIS ASAP!
LOOK AT PICTURE
Answer:
Diagram 2, 12 foul balls
Step-by-step explanation:
12/3=4
12-4=8
Is height always a statistical subject
Answer:
It Is!
Step-by-step explanation:
"For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students' ages."
Which triangles are similar to AABC?
A
5
B
11
8
A . it is increasing and linear
B. it is decreasing and linear
C. it is increasing and non linear
D. It is decreasing and non linear
Answer:
The answer is B.
Step-by-step explanation:
From the interval -6 < x < 0, the line is straight which is linear equation. The line shows its going down so it will be decreasing gradient.
At the end of August, a store is
trying to get rid of their swimsuits to
make room for fall clothes The
price of a swimsuit is reduced $5
each week for 6 weeks By how
much did the price of the swimsuit
change during this time?
Answer:
Week one: 5$ off
Week two: 10$ off
Week three: 15$ off
Week four: 20$ off
Week five: 25$ off
Week six: 30$ off
30-5=25 There is a 25 dollar difference from week one and week six
Step-by-step explanation:
Combine like terms 3x^2 + 4x^3 + 6x^2
Answer:
3x^2+6x^2= 9x^2
9x^2+4x^2
Step-by-step explanation:
LOOK AT PIC, ASAP, ROGHT ANSWER GETS BRAINLIEST !
Answer:
Step-by-step explanation:
The teacher has 7/8 pounds of clay given.
gives out 1/16 per station
7/8= 0.875 pound
7/8 / 1/16 pound= 14 maximum stations
14 stations divided by 2 classes = 7 in each room
HELP I’m being timed!!!
line segment AB is perpendicular to line segment CD . How many 90° angles are formed by the intersection?
Answer:
4 90 degree angles
rewrite 4.4.6.4.4.6 using exponents
Answer:
[tex]4^{4}[/tex]×[tex]6^{2}[/tex]
Step-by-step explanation:
There is 2 of the same number 6 and there is 4 of the number 4
I hope this helps
What is the image of (-10,-6) after dilation by a scale factor of 1/2 centered at the origin?
The coordinate of resulting image after dilation is (-5, -3)
Dilation and scale factorsGiven the coordinate of an image (-10,-6), dilating the coordinate by 1/2 means reducing the image by multiplying each coordinate by the factor of 1/2.
Image = (1/2(-10), 1/2(-6))Image = (-5, -3)From the calculation above, you can see that the coordinate of resulting image after dilation is (-5, -3)
learn more on dilation here: https://brainly.com/question/3457976
sorry i answerd the wrong question.
the verified answer is correct
5-3can you please help me with this?
A) 29
B) 15
C) 45
D) 8
Answer:
A) 29
Step-by-step explanation:
Step 1: Find angle G
Since Sin(θ) = Opposite over Hypotenuse:
[tex]sin^{-1} ( 58 / (52+52) )[/tex] = θ
θ = 33.896°
Now repeat for just the smaller triangle:
[tex]sin(33.896) = Opposite/Hypotenuse\\sin(33.896) = Opposite/52\\Opposite = sin(33.896) * 52\\Opposite = 29[/tex]
BRAINLIEST Write an equation that represents the line
Use exact numbers
Answer: Steep. Its 50% steep.
in which table is y a linear near function of x will mark brainest
possibly c, I'm not that good with math
pls give brainliest
Pls help me this is 7th grade (ADVANCED)
Answer:
Step-by-step explanation:
Any line will add up to 180 degrees. If you subtract the 165 degrees from 180 (total), you will get the x value.
180 - 165 = 15 degrees
please help me with this please
Answer:
4 feet
Step-by-step explanation:
Let x be the height of the tower when finished.
We have been given that Priya takes a break when the tower is 2 and 1/2 feet tall, which is 5/8 of the height of the tower she wants to build.
This means that 5/8 of x equals 2 and 1/2. Let us represent this information in an equation.
5/8*x=2 and 1/2
Let us convert our given mixed fraction into an improper fraction.
5/8*x=5/2
Let us multiply both sides of our equation by 8/5.
8/5*5/8*x=5/2*8/5
x=8/2
x=4
What is the volume of the triangular prism shown below?
8 cm
3 cm
13 cm
Answer:
312
Step-by-step explanation:
8 x 3 = 24
24 x 13 = 312
3k - 14 = 3(k – 5) +1 one solution, no solution, or infinite solution
Complete the tables of values?
Plz help I’m so stuck on this
Answer:
d=1
e=4/9
f=16/81
Step-by-step explanation:
Substitute x in the right column with the values in the left column to find d, e, and f.
Answer:
d = 1
e = 4/9
f = 16/81
Step-by-step explanation:
d is 1 because any term raised to the power of zero equals one
e: (2/3)² = 2²/3² = 4/9
f: (2/3)^4 = 2^4/3^4 = 16/81
HELP PLEASE!!
100 POINTS!!
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
We are given:
[tex]\displaystyle \frac{w^{-x+4}}{w^{-3}}=w^{2x+1}[/tex]
First, by the quotient property:
[tex]w^{(-x+4)-(-3)}=w^{2x+1}[/tex]
Since they both have the same base, their exponents must be equivalent:
[tex](-x+4)-(-3)=2x+1[/tex]
Solve for x. Simplify:
[tex]-x+7=2x+1[/tex]
Therefore:
[tex]3x=6\Rightarrow x=2[/tex]
Answer:
x=2
Step-by-step explanation:
:]
which of the following graphs describes the solution set of -4/5x-13/5>=-9?
Answer:
Hey Bud
your answer is x ≤ 8
Step-by-step explanation:
should be closed dot pointing to the negative numbers
Let's solve your inequality step-by-step
Step 1: Simplify both sides of the inequality.
Step 2: Add 13/5 to both sides.
Step 3: Multiply both sides by 5/(-4).