To answer this question, we're going to use some important properties of the Pascal's triangle.
1) If we number the rows starting at zero, then the kth row has k + 1 elements.
2) If we number the elements on the kth row starting with zero, then the mth element of row k is given by
[tex]\begin{pmatrix}{k} \\ {m}\end{pmatrix}=\frac{k!}{m!(k-m)!}[/tex]Using those two properties, we can answer our question.
We want to know the numbers that will fill in the eighth row, this means our k = 8.
From the first property, we know that we have 9 elements on this row, and they are given by
[tex]\begin{pmatrix}{8} \\ {m}\end{pmatrix}=\frac{8!}{m!(8-m)!},m=0,1,2,\ldots,8[/tex]Plugging each m value on this equation, we have
[tex]\begin{gathered} \begin{pmatrix}{8} \\ {0}\end{pmatrix}=\frac{8!}{0!(8-0)!}=\frac{8!}{8!}=1 \\ \begin{pmatrix}{8} \\ {1}\end{pmatrix}=\frac{8!}{1!(8-1)!}=\frac{8!}{7!}=8 \\ \begin{pmatrix}{8} \\ {2}\end{pmatrix}=\frac{8!}{2!(8-2)!}=\frac{8\cdot7}{2}=28 \\ \begin{pmatrix}{8} \\ {3}\end{pmatrix}=56 \\ \begin{pmatrix}{8} \\ {4}\end{pmatrix}=70 \\ \begin{pmatrix}{8} \\ {5}\end{pmatrix}=56 \\ \begin{pmatrix}{8} \\ {6}\end{pmatrix}=28 \\ \begin{pmatrix}{8} \\ {7}\end{pmatrix}=8 \\ \begin{pmatrix}{8} \\ {8}\end{pmatrix}=1 \end{gathered}[/tex]And those are the values on the eighth row.
Question 13(Multiple Choice Worth 4 points)(06.04 MC)The function f(x) = 4x + 30 represents the length of a rectangle. The function g(x) = x - 1 represents the width of the rectangle. Use (f•g)(5) to determine the area of the rectangle.44650200
From the problem, the length of the rectangle is f(x) = 4x + 30 and the width is g(x) = x - 1.
To find the area, use (f · g)(5)
That will be :
[tex]\begin{gathered} (f\cdot g)(x)=(4x+30)(x-1) \\ (f\cdot g)(5)=(4\times5+30)(5-1) \\ (f\cdot g)(5)=50(4) \\ (f\cdot g)(5)=200 \end{gathered}[/tex]ANSWER :
The area is 200
What is the scale factor for AMNP ~ AQRSk=type your answer...
Given
Graph
Procedure
[tex]\begin{gathered} \frac{RS}{NP}=\frac{15}{10} \\ \frac{RS}{NP}=1.5 \end{gathered}[/tex]
T
Write 12.4% as a decimal and simplified fraction
Given the following question:
We are given 12.4%
[tex]undefined[/tex]Which statement must be true if ARST = AXYZ?
OA LT = LX
OB. RS=XY
OC. RT = XY
OD. ZS = LX
The correct option is (B) RS = XY.
What are congruence rules of triangles?
If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. "≅" is the congruence symbol. When two figures resemble one another in terms of size and shape, this is what mathematics refers to as congruence.
Given, the two congruent triangles are ΔRST and ΔXYZ.
Thus corresponding sides and angles must be equal.
Therefore, ∠R = ∠X, ∠S = ∠Y, ∠T = ∠Z and RS = XY, RT = XZ, TS = ZY
Comparing this to the options in question, only (B) RS = XY is correct.
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What is the slope and y intercept of
-5-y=-3x
Answer:
Slope: 3
y-int: 5
Step-by-step explanation:
Isolate y:
-y = -3x + 5
y = 3x - 5
y = mx + b where x and y are variables, m is the slope and b is the y-int
Hope that helps
Answer:
slope is -3 and y-intercept is -5!
If ST = 11 and RT = 41, find RS. Use the number line below.RRS =(Type an integer or a decimal.)
1) Let's draw the line to better understand this
2) In this case, let's use the Segment Addition Postulate.
Since RT = 41 and ST=11
41 -11=30
So RS = 30
need help with this question Determine the points, if any, at which the graph R intersects the horizontal or oblique asymptote, if one exist.
The graph has a horizontal asymptote given by y = 0.
We can check that R(-3) = 0
Therefore, the graph of R intersects the horizontal asymptote at (-3,0)
Answer: A
help meeee pleasee!!!
thank youu
Answer:
Domain: A, [1, 7]
Range: [-4, 2]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Simply qqqqqqqqqqqqqqqqqqqqqqqqq hurry plsss
Answer:
6.) =37/36 mixed form is 1 1/36 decimal form 1.027 repeating the 7
6.) = 11/35 decimal form 0.3142857repeating
9.) = 23/60 decimal form 0.383 repeating 3
11.) = 11/56 decimal form 0.19642857.....
12.) = 13/45 decimal form 0.28 repeating 8
11.) = 5/6 decimal form 0.83 repeating 3
12.) = 17/48 decimal form 0.35416 repeating 6
Answer:
number 1 is 13/18 number 2 is 19/28 number 3 is 1 5/24 number 4 is 1/2 number 5 is 1 7/40 number 6 is 1 1/36 number 1 on the 2 page is 1 7/12
number 2 is 1 1/8 number 3 is 32/63 number 4 is 1 3/40 number 5 is 31/60 number 6 is 11/35 number 1 is 7/8 number 9 is 23/60 number 11 is 11/56 numbers 11 and 12 are 5/6 and 17/48 numbers 4 5 and 6 are 2/3 43/60 numbers 4 5 6 are 1 1/24 19/56 17/45
Step-by-step explanation:
You randomly observe purchases at a candy store and record the weight of each bag of candy with 100 different customers. You find the proportion of weights greater than 2 pounds. Is investigating this sample proportion the same as investigating the sampling distribution of the proportion?No, the sample comes from only one store. The sample needs to be expanded to multiple candy stores.Yes, the customers will most likely purchase different weights of candy, and the different amounts will be evenly distributed.No, the sampling distribution of the proportion is the distribution of the proportions from all samples, not just one.Yes, at least 100 customers were observed.
Solution
No, the sampling distribution of the proportion is the distribution of the proportions from all samples, not just one.
Two lines that have a point in common are calledlines.
When a line shares a common point with another line, they are callled intersection lines. In some cases, the lines may be on top of each other, thus describing as collinear or on the same line. Lines can also be parallel, coplane (located in the same plane), congruent, etc. Howerer, the best answer for your question is the intersection of the lines.
The answer is intersection lines
How do I do c? I can’t seem to figure these ones out
c) For this expression, let's start by rewriting it as a rational function:
[tex]\begin{gathered} y=\frac{x}{x+4}\cdot\frac{x+2}{x-5} \\ y=\frac{x(x+2)_{}}{(x+4)(x-5)} \end{gathered}[/tex]So to find out the Domain, we need to determine for which values do this function is defined. So looking at the denominator we can write out:
[tex]\begin{gathered} x+4\ne0 \\ x\ne-4 \\ x-5\ne0 \\ x\ne5 \\ D=(-\infty,-4)U(-4,5)U(5,\infty) \end{gathered}[/tex]Note that if we plug into the denominator x=5 or x=-4 the function becomes undefined for the denominator would become equal to 0. For all values but -4, and 5 this function is defined.
We could draw the diagram to check the intersections.
2) Now, let's perform the product of that ratios, as indicated.
[tex]\frac{x}{x-4}\cdot\frac{x+2}{x-5}=\frac{x(x+2)}{(x-4)(x-5)}=\frac{x^2+2x}{x^2-5x-4x+20}=\frac{x^2+2x}{x^2-9x+20}[/tex]Note that when we multiply ratios we multiply both numerator and denominator simultaneously. We can leave it in its factored form as well.
3) Hence, the answer is:
[tex]\begin{gathered} D=(-\infty,-4)U(-4,5)U(5,\infty) \\ \frac{x^2+2x}{x^2-9x+20} \end{gathered}[/tex]the graph shows the profit, y, of a community fundraiser, with respect to the number of tickets sold, x.use the graph to determine the y-intercept and what it represents A) the y-intercept = 35 and represents the number of tickets sold B) the y-intercept = -700 and represents the number of tickets sold C) the y-intercept = -700 and represents the initial amount of expensesD) the y-intercept = 35 and represents the initial amount of expenses
we have that
x -----> number of tickets sold
y ----> profit
Remember that
the y-intercept is the value of y, when the value of x is zero
in this context
the y-intercept is the profit when the number of tickets sold is zero (initial value of profit)
Looking at the graph
the y-intercept is $-700
therefore
the answer is option Cy=-5x - 13,7x+2y=-23*Different / Different(-1,-8)(4.10)One PointAl PointsSame/ differentInfinite Solutions
1) Let's solve this Linear System of equations
y=-5x-13
x+2y=-23
2) Using the method of Substitution on the 2nd equation
x +2(-5x-13) = -23
x -10x -26= -23
-9x -26 =-23 Add 26 to both sides
9x=-23+26
9x = 3
x= 3/9
x= 1/3
y=-5(1/3) -13
y=-5/3 -13
y=-44/3
3) So there is one solution to that Linear System, different than those points (-1,-8) (4,10).
Rearrange the equation
a = 1/2(b- c)
to make b the subject.
Answer:
subject b = 2a + c
Step-by-step explanation:
Given
a = (b - c)
Multiply both sides by 2 to clear the fraction
2a = b - c ( add c to both sides )
2a + c = b
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what is the solution of 3+ x-2÷x-3<=4
3 + x - 2/x - 3 =< 4
Post the picture please of the problem
(3 + x - 2) / (x - 3) =< 4
3 + x - 2 =< 4(x - 3)
3 + x - 2 = < 4x - 12
x - 4x =< -12 - 3 + 2
- 3x = -15 + 2
-3x =< -13
x >= -13/-3
x >=13/3
6. Find (G + G) then subtract H from the result H = (2x^2 + 6x + 5) and G = (6x^2 + 3x + 5)
ANSWER
[tex]10x^2\text{ + 5}[/tex]EXPLANATION
We have that:
[tex]\begin{gathered} G=6x^2\text{ + 3x + 5} \\ \text{and} \\ H=2x^2\text{ + 6x + 5} \end{gathered}[/tex]Let us find G + G:
[tex]\begin{gathered} 6x^2\text{ + 3x + 5 + }6x^2\text{ + 3x + 5} \\ 6x^2+6x^2\text{ + 3x + 3x + 5 + 5 } \\ 12x^2\text{ + 6x + 10} \end{gathered}[/tex]Now, let us subtract H:
[tex]\begin{gathered} 12x^2+6x+10-(2x^2\text{ + 6x + 5)} \\ 12x^2+6x+10-2x^2\text{ - 6x - 5} \\ 12x^2-2x^2\text{ + 6x - 6x + 10 - 5} \\ \Rightarrow10x^2\text{ }+\text{ 5} \end{gathered}[/tex]That is the answer
KE= 1/2 mv^2 solve for v
Step-by-step explanation:
[tex]KE = \frac{1}{2} mv^{2}[/tex] solve for v
multiply both sides by 2:
[tex]2(KE) = 2(\frac{1}{2} mv^{2})\\2KE = mv^{2}[/tex]
divide both sides by m:
[tex]2KE = mv^{2}\\\frac{2KE}{m} = \frac{mv^{2}}{m} \\[/tex]
[tex]v^{2} = \frac{2KE}{m}[/tex]
take the sqrt of both sides:
[tex]\sqrt{v^{2}} = \sqrt{\frac{2KE}{m}}\\[/tex]
so:
[tex]v = \sqrt{\frac{2KE}{m}}\\ OR\\ v = -\sqrt{\frac{2KE}{m}}\\[/tex]
Domain and range of this graph.
Thanks for any help :).
uh hey can you help me with my hw if you help send me your snap and if you want I will send pics
The question says 900,000 /556040 x 190600
[tex]\begin{gathered} \frac{900,000}{556040}\text{ x 190600 } \\ \text{cancel the zero in the denominator and one zero above, then divide by 4 } \\ \frac{900000}{13901}\text{ x 47650} \\ \text{divide the dirst expression into decimal, that gives } \\ 64.74\text{ x 47650 = 3085029.85} \end{gathered}[/tex]Hence, 3085029.85 isthe solution to the question.
Answer: why
Step-by-step explanation: help me
can I get help please
we have the equation
y=-4x+4
step 1
Find the x-intercept (value of x when the value of y is zero)
so
For y=0
0=-4x+4
4x=4
x=4/4
x=1
x-intercept is (1,0)step 2
Find the y-intercept (value of y when the value of x is zero)
so
For x=0
y=-4(0)+4
y=4
y-intercept is (0,4)Rita has a circular hot tub . The hot tub has a circumference of 25.12 feet . It is 3.5 feet deep. c. The hot tub manual recommends filling the hot tub to 80% of its full capacity. Howmuch water should Rita put in the hot tub in order to follow the recommendation?
Step 1
The circular hot tube is in the shape of a cylinder. Therefore its volume will be;
[tex]v=\pi\times r^2\times h[/tex]where;
[tex]\begin{gathered} circumference=2\times\pi\times r=25.12ft \\ h=3.5feet \end{gathered}[/tex]Find r, using the circumference
[tex]\begin{gathered} 2\times\pi\times r=25.12 \\ \pi r=\frac{25.12}{2} \\ r=\frac{25.12}{2\pi} \\ \end{gathered}[/tex]Step 2
Find the volume of the hot tube at 100%
[tex]\begin{gathered} v=\pi\times(\frac{25.12}{2\pi})^2\times3.5 \\ v=3.5\pi\frac{25.12^2}{2^2\pi^2} \\ v=3.5\times\:50.21453046 \\ v=175.7508566ft^3 \end{gathered}[/tex]Step 3
Find the recommended capacity which is 80% full
[tex]\begin{gathered} \frac{175.7508566}{x}=\frac{100}{80} \\ x=140.6006853ft^3 \\ \end{gathered}[/tex]Note; 1 Cubic foot=7.48052 gallons of water. Therefore, the water Rita should put in the hot tub will be;
[tex]\begin{gathered} \frac{140.6006853ft^3}{1ft^3}=\frac{y}{7.48052} \\ y=1051.766238\text{ gallons of water} \\ \approx1051.77\text{ gallons of water} \end{gathered}[/tex]Answer;
[tex]1051.77\text{ gallons of water}[/tex]you put $939 into an investment at 8% annual interest for 6 years what will your balance be at the end of 6 years
The amount put into the investment which is 939 is the principal, P.
The annual interest is 8% (or 0.08) while the duration in years is 6, that is T.
The simple interest formula is given as;
[tex]\begin{gathered} I=\text{PRT} \\ I=939\times0.08\times6 \\ I=450.72 \\ \text{The balance at the end of 6 years will be;} \\ A=P+I \\ A=939+450.72 \\ A=1389.72 \end{gathered}[/tex]The balance at the end of 6 years will be $1,389.72
which of these points is the closest to the y-axis
A.(-6,0)
B.(-2,12)
C.(4,2)
D.(5,1)
Nathan receives a lump sum inheritance of $55 000 and invests the money into a savings account with an annual interest rate of 7.5%, compounded quarterly.(a) Calculate the value of Nathan's investment after 5 years, rounding your answer to thenearest dollar. After m months, the amount in the savings account has increased to more than $70000.(b) Find the minimum value of m, where me N.Nathan is saving to purchase a property. The price of the property is $150 000. Nathan puts down a 15% deposit and takes out a loan for the remaining amount.(c) Write down the loan amount.The loan duration is for eight years, compounded monthly, with equal monthly payments of$1500 made by Nathan at the end of each month.(d) For this lonn, find(i) the amount of interest paid by Nathan over the life of the loan.(i) the annual interest rate of the loan, correct to two decimal places After 5 years of paying this locu, Nathan decides to pay the outstanding loan amount in onefinal payment. (e) Find the amount of the final payment after 5 years, rounding your answer to the nearestdollarif Find the amount Nathan saved by making this final payment after 5 years, roundingyour answer to the nearst dollar.
The Solution:
Given:
[tex]\begin{gathered} P=\text{ \$}55000 \\ r=7.5\text{ \% compounded quarterly}=\frac{7.5}{400}=0.01875 \\ t=5\text{ years}=5\times4=20\text{ periods} \end{gathered}[/tex]Required:
Find the value of the investment after 5 years.
The Formula:
[tex]V=P(1+\frac{r}{n})^{nt}[/tex]In this case,
[tex]\begin{gathered} V=Value\text{ of the investment}=? \\ P=\text{ \$55000} \\ r=0.075 \\ n=\text{ number of periods in a year}=4 \\ t=5\text{ years} \end{gathered}[/tex]Substitute:
[tex]V=55000(1+\frac{0.075}{4})^{(5\times4)}[/tex][tex]V=55000(1+0.01875)^{20}=55000(1.01875)^{20}[/tex][tex]V=79747.1414\approx\text{ \$}79747.14[/tex]Answer:
(a) $79,747.14
Find the number of months it will take the account to increase to more than $70,000
Solve for n in the equation below:
[tex]55000(1.01875)^n>70000[/tex][tex]\begin{gathered} (1.01875)^n>\frac{70000}{55000} \\ \\ (1.01875)^n>\frac{14}{11} \end{gathered}[/tex][tex]ln(1.01875)^n>ln(\frac{14}{11})[/tex][tex]n=\frac{ln(\frac{14}{11})}{ln(1.01875)}>12.982\approx13\text{ months}[/tex]Answer:
13 months or more
You told your friend that you could eat 7/8 of a large pizza. If you only ate 2/3 of what you said you could eat, what fraction of a large pizza did you eat?
The fraction of the large pizza that you were supposed to eat is 7/8. You could only eat 2/3 of 7/8. Thus, the fraction that you ate would be
(2/3) / (7/8)
If we flip 7/8 such that it becomes 8/7, the division sign would change to multiplication sign. Thus, we have
2/3 * 8/7
= 16/21
The fraction of the large pizza pizza that you ate is 16/21
Ava has $14. She earns $8 each hour she spent babysitting. She now has $78. Write and solve an equation to find the number of hours Chloe spent babysitting
Answer:
8 hours.
Step-by-step explanation:
Hello there! Let's help you with your question here!
To always begin questions, let's start with what we know! So, we know that Ava has a total of $14 and that she earns $8 each hour she spends babysitting and now her new total is $78. Alright! So, what do we have here? Here, we're solving for how much money Ava will earn in total. When being asked to write and solve an equation, we always look for what's known as fixed value and a variable value. And what do this mean?
A fixed value is something that can't really be changed under any circumstances. In the question we have here, we are looking for a number that does not change at all and that would be $14. Why? Because no matter what the new total amount of money being made, she'll always start with $14.
A variable value is something that can be changed based on a quantity. In the question we have here, we are looking for a number that follows up with something that we are unsure of but necessary. In this case, that would be $8 each hour. The reason we use this is because we don't know how many hours Ava's going to work. It can be anything and the total amount of money she earns depends on how many hours she worked.
So, now that we have all of our information, we can start by creating a formula! Let y be the new total amount of money that Ava has and let x be how many hours Ava has spent babysitting. And that would be as such:
[tex]y=8x+14[/tex]
Now that we have our formula, we can now begin to solve. We are looking for how many hours Ava spent babysitting to get her new total value up to $78. We substitute y and then solve for x. It would be as such:
[tex]78=8x+14[/tex]
[tex]64=8x[/tex] - Subtracting 14 from both sides.
[tex]8=x[/tex] - Dividing both sides by 8 to isolate x.
Therefore, in order for Ava to get $78 in total, she would need to spend 8 hours of babysitting, if she started out with $14.
Hello I need help with question 6! I will give you a great rating! Please help, I’m not sure how to do this. Also this is not a quiz this is practice
6.
cos a = adjacent side / hypotenuse
Replacing with the values given:
Cos 45 = 13 / y
y= 13/cos45
y= 13/ (1 /√2 )
Y= 13√2
For x apply the Pythagorean theorem
c^2 = a^2 + b^2
Where:
c= hypotenuse
a & b = the other 2 legs
(13 √2 )^2 = x^2 + 13^2
338 = x^2 + 169
338 - 169 = x^2
169 =x^2
√169 = x
x = 13
Show your work PLEASE HELP DUE TODAY (if you show your work and answer all you get BRAINLIEST)
Answer:
1) = x = 20/6 or x = 6 2/3 (for the alternative form) since x/2 =10/3 = 3x = 20 when you do cross multiplication, then divide both sides of the equation by 3 giving x = 20/3 also giving you x= 6 2/3.
2) Solve for v:
2/3 = v/4
2/3 = v/4 is equivalent to v/4 = 2/3:
v/4 = 2/3
Multiply both sides of v/4 = 2/3 by 4:
(4 v)/4 = 4×2/3
4×2/3 = (4×2)/3:
(4 v)/4 = (4×2)/3
(4 v)/4 = 4/4×v = v:
v = (4×2)/3
4×2 = 8:
Answer: |
| v = 8/3
3) Solve for n over the real numbers:
4/9 = 2/n
4/9 = 2/n is equivalent to 2/n = 4/9:
2/n = 4/9
Take the reciprocal of both sides:
n/2 = 9/4
Multiply both sides by 2:
Answer: |
| n = 9/2
4) Solve for x:
x/7 = 8/3
Multiply both sides of x/7 = 8/3 by 7:
(7 x)/7 = 7×8/3
7×8/3 = (7×8)/3:
(7 x)/7 = (7×8)/3
(7 x)/7 = 7/7×x = x:
x = (7×8)/3
7×8 = 56:
Answer: |
| x = 56/3
5)
1 2/5 and a percent nnnnnn
Answer:
what does that even mean
Step-by-step explanation:
