[tex]\displaystyle\\\binom{52}{3}=\dfrac{52!}{3!49!}=\dfrac{50\cdot51\cdot52}{2\cdot3}=22100[/tex]
Divide: StartFraction 5 Over 8 EndFraction divided by three-fourths
The value gotten when 5/8 is divided by 3/4 is 5/6.
What is the value gotten from the division?A fraction is a non-integer that is made up of numerator and a denominator. An example is 5/8. Division is the process of grouping a number into equal parts using another number.
5/8 ÷ 3/4
5/8 × 4/3 = 5/6
To learn more about the division of fractions, please check: https://brainly.com/question/25779356
#SPJ1
The function f(x) is graphed. It represents a translation of the square root function g(x) = . What equation represents the graph of f(x)? f(x) = f(x) = f(x) = – 1 f(x) = + 1
Using translation concepts, the equation of the graph of f(x) is given as follows:
[tex]f(x) = \sqrt{x - 1}[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Function f(x) is a shift right of one unit of the square root function, hence x -> x - 1 and the equation is given by:
[tex]f(x) = \sqrt{x - 1}[/tex]
More can be learned about translation concepts at https://brainly.com/question/4521517
#SPJ1
who knows how to sketch this kind of graph
The graph of f(x) = 0.5sin(4x) is sketched below
Graph of trigonometric functionsFrom the question, we are to sketch the graph of the given trigonometric function.
The given trigonometric function is
f(x) = 0.5sin(4x)
The graph of f(x) = 0.5sin(4x) is sketched below
Learn more on Graph of trigonometric functions here: https://brainly.com/question/4987799
#SPJ1
what is the equation of the line that is paralle to y=3x-8 and passes thur the point (4,-5)
⊰_________________________________________________________⊱
Answer:
The equation is-: y=3xStep-by-step explanation:
[tex]\large\displaystyle\text{$\begin{gathered} \sf{Substitute \ the \ values \ into \ the \ formula \ y-y_1=m(x-x_1)} \\ \sf {parallel \ lines \ have \ same \ slopes, \ thus} \\ \sf{slope \ of \ the \ 2nd \ line = 3}\\ \sf{now \ substitute \ the \ values} \\ \sf {y-(-5)=3(x-4)}\\ \sf{y+5=3(x-4) (It's \ Point-Slope\;Form, \ see \ below \ for \ slope-intercept)}\\ \sf {y+5=3x-12} \\ \sf{y=3x-12-5} \\ \sf{y-3x-17} \end{gathered}$}}[/tex]
[tex]\pmb{\tt{done \ !!}}[/tex]
⊱_________________________________________________________⊰
A trader sold an article for N150 and
made a profit of 20%. What was the
cost price of the article?
Answer:
125
Step-by-step explanation:
N150=120%
? =100
150×100/120
=125
The cost price of the good is $125.
What is cost price?Cost price is the total amount of money that it costs a manufacturer to produce a given product or provide a given service.
Given that a good has been sold for $150 which made a profit of 20% we need to find the cost price of the good,
Let the cost price be x,
So,
x × 120% = 150
x = 150 × 100 / 120
x = 125
Hence the cost price of the good is $125.
Learn more about cost price click;
https://brainly.com/question/30175345
#SPJ2
Please answer all parts as I know the answers but need the work to go with them. Thus, I believe the answers are correct. Thank you!
t+b = 41
t = 2b+2
Solve for t and b
Answer: b=13, t=29
Step-by-step explanation:
Substituting the first equation into the second,
[tex]2b+2+b=41\\\\3b+2=41\\\\3b=39\\\\b=13\\\\\implies t=2(13)+2=29[/tex]
Which point is a solution to the system?
Answer:
what solution bc i could answer this pls let me know the equation but......
Step-by-step explanation:
to find a solution you can add divide or subtract to find the solution like x=2
Complete the sentence.
The amount of time it takes to eat an apple is most likely to be a function of
the
OA. size of the apple
B. orchard where the apple was harvested
O C. store where the apple was purchased
OD. color of the apple
Set up an algebraic equation and then solve.
The width of a rectangle is 14 units less than the length. If the area is 120 square
units, then find the dimensions of the rectangle.
Length:
Width:
Answer:
Width: 6
Length: 20
Step-by-step explanation:
So the area of a rectangle can be defined as: [tex]A=wl[/tex] where w=width and l=length.
In this case we don't know what the length is, so let's just say the length is the variable l, and since the width is 14 units less than the length, we can express it as (l-14). this gives us the equation: [tex]A=l(l-14)=l^2-14l[/tex]. We can solve for l, since we're given the area which is 120. So let's set the equation equal to that:
Original Equation:
[tex]A=l^2-14l[/tex]
Substitute 120 as A (given)
[tex]120=l^2-14l[/tex]
There is many ways to solve this equation: factoring, quadratic equation, completing the square etc... but in this case I'll just complete the square
Add (b/2)^2 to both sides to complete the square
[tex]120+(\frac{-14}{2})^2=l^2-14l+(\frac{-14}{2})^2[/tex]
Simplify
[tex]169=l^2-14l+49[/tex]
Rewrite right side a square binomial
[tex]169=(l-7)^2[/tex]
Take the square root of both sides
[tex]13=l-7\\[/tex]
Add 7 to both sides
[tex]20=l[/tex]
to solve for width simply subtract 14 from the length which is 20, so the width is 6
Width: 6
L: 20
giving brainliest to first person who answers correctly
Using it's concept, the domain and the range of the function are given as follows:
Domain: [tex]x \leq 4[/tex].Range: [tex]y \geq 0[/tex]What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.The function for this problem is:
[tex]y = \sqrt{4 - x}[/tex]
The square root is defined only for non-negative numbers, hence the domain is given as follows:
[tex]4 - x \geq 0 \rightarrow x \leq 4[/tex]
The outputs of the square root function are also non-negative numbers, hence the range is given as follows:
[tex]y \geq 0[/tex].
More can be learned about the domain and the range of a function at https://brainly.com/question/10891721
#SPJ1
Based on the diagram, which is a true statement?
- If a student plays in the band, then he/she is an honor student.
- If a student is an honor student, then he/she plays in the band.
- If a student is not an honor student, then he/she cannot play in the band.
- If a student is an honor student, then he/she may also be a band member.
Based on the diagram, the true statement is "If a student is an honor student, then he/she may also be a band member."
What does the diagram show?It shows the intersection between two groups:
Honor studentsBand membersThis intersection implies some band members are honor students and vice versa. However, not all band members are honor students and not all honor students are band members.
What can be concluded?A correct conclusion is that an honor student may also belong to the band.
Learn more about venn diagrams in https://brainly.com/question/1605100
#SPJ1
Given f(x)-3x-1 and g(x)-2x-3, for which value of x does g(x)=f(2)?
Answer:
x = 4
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=3x-1\\g(x)=2x-3\end{cases}[/tex]
f(2) means substitute x = 2 into function f(x):
[tex]\begin{aligned}g(x) & = f(2)\\ \implies 2x-3 & = 3(2)-1\\2x-3 & = 6-1\\2x - 3 & = 5\\2x - 3 + 3 & = 5 + 3\\2x & = 8\\\dfrac{2x}{2} & = \dfrac{8}{2}\\x & = 4\end{aligned}[/tex]
Therefore, g(4) = f(2).
f(2)
3(2)-16-15so
g(x)=52x-3=52x=8x=4Complete the equation: x2−4x+−−=(−−)2
The complete equation is x^2 - 4x + (-2) = (-2)^2
How to complete the equation?The equation is given as:
x^2 - 4x + __ = (__)^2
_____________________________
Take the coefficient of x
k = -4
Divide by 2
k/2 = -4/2
k/2 = -2
Square both sides
(k/2)^2 = (-2)^2
_____________________________
Add the result of the above computation to both sides of x^2 - 4x + __ = (__)^2
So, we have:
x^2 - 4x + (-2) = (-2)^2
Hence, the complete equation is x^2 - 4x + (-2) = (-2)^2
Read more about completing the square at:
https://brainly.com/question/16483306
#SPJ1
A suitcase measures 18 inches long and 12 inches high. What is the diagonal length of the suitcase?
Answer:
21.6 in
Step-by-step explanation:
Imagine the suitcase as a rectangle, with length of 18 in and width of 12 in. In order to find the diagonal length, simply use the Pythagorean Formula, a^2 + b^2 = c^2, and solve for c!
In this case, a = 18 and b = 12.
Please give Brainliest if this was helpful!
Select each graph that shows a function and it’s inverse
Answer:
First option
Explanation:
The inverse of a graph is its reflection on the line y = x.
This means that it is the graph that you get by reflecting the original graph on a line with the equation y = x.
In the picture below, we can see a function (red graph), its inverse (blue graph) and the line (green) that the two graphs are reflected on.
From the picture below, we can see that the shapes of the graph of a function and its inverse is similar and correspond to the shape given as the first option in the question. Therefore, the first option is the answer.
ram takes 20 minutes to inspect a car, while robert takes only 18 minutes.if both start inspecting car at 8.00 hours what is the first time at which both will have finished inspecting a car at the same point time
Answer:
11:00
Step-by-step explanation:
here we have to calculate the LCM of 20 and 18
20 = 2² × 5
18 = 2 × 3²
Then
LCM(20 , 18) = 2² × 5 × 3² = 20 × 9 = 180
The
After 180 minutes (3 hours) they will have finished inspecting a car at the same point time.
Then
At 8:00 + 3 = 11:00 Ram and Robert will have finished inspecting a car at the same point time.
Suppose that poaching reduces the population of an endangered animal by 6% per year. Further suppose that when the population of this animal falls below 20, its extinction is inevitable (owing to the lack of reproductive options without severe in-breeding). If the current population of the animal is 1500, when will it face extinction? Comment on the validity of this exponential model.
If poaching reduces the population of an endangered animal by 6% and the criteria of population extinction is 20 with present population 1500 then it will take 3.62 years to reach to the mark of extinction.
Given Poaching reduces the population of endangered animals by 6% per year. The criteria of population extinction is 20. Present population being 1500.
Number of years taken by the population of endangered animals to reach to 20 mark can be calculated as under:
20=1500*[tex](1-0.06)^{n}[/tex]
20=1500*[tex]0.94^{n}[/tex]
20/1500=[tex]0.94^{n}[/tex]
0.133=[tex]0.94^{n}[/tex]
take log both sides
log(0.133)=log[tex]0.94^{n}[/tex]-------1
log(0.133)=nlog (0.94)
put the values log values:
log(0.133)=-0.8761
log(0.94)=-0.0268
Taking 1
-0.8761=n*(-0.0268)
n=0.8761/0.0268
n=3.269
Hence to reach level of 20 the population takes 3.2 years.
Learn more about logarithm at https://brainly.com/question/25710806
#SPJ10
Seriation can be described as a series or a growing pattern, i.e. arranged by an attribute such as height, length, or weight. Which of the following activities would be the best way to help children understand seriation?
a. Read the story of the Three Billy Goats Gruff and discuss the little, medium and great big billy goat gruff brothers.
b. Have children put the pictures in order according to their size on a worksheet.
C. This book would not be used because it isn't a math concept book.
The best way to help them understand Seriation is; A: Read the story of the Three Billy Goats Gruff and discuss the little, medium and great big billy goat gruff brothers.
How to Identify growth patterns in Seriation?We are told that;
Seriation is a series or a growing pattern. This means arranged by an attribute such as height, length, or weight.
Now, we want to find the option that is the best way to help children understand Seriation. Looking at the options, the best option would be option A. This is because by reading the story of the three Billy Goats Gruff, we can be able to arrange them by little, medium and great big billy goat gruff brothers.
Read more about Seriation at; https://brainly.com/question/15754340
#SPJ1
A random variable is not normally distributed, but it is mound shaped. It has a mean of 11 and a standard deviation of 4.
If you take a sample of size 14, can you say what the shape of the sampling distribution for the sample mean is? Why?
Using the Central Limit Theorem, nothing can be stated about the shape of the sampling distribution for the sample mean, as the sample size is less than 30.
What does the Central Limit Theorem state?It states that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.
In this problem, we have a skewed variable and n < 30, hence nothing can be stated about the shape of the sampling distribution for the sample mean.
More can be learned about the Central Limit Theorem at https://brainly.com/question/16695444
#SPJ1
the objective function of linear programming model should be
The objective function of a linear programming model should be to maximize or minimize the numerical value.
What is the objective function?The objective function consists of linear functions which are subjected to constraints in the form of linear equations or in the form of inequalities.
The objective function is always stated as z = ax + by.
The numerical value may be the:
Cost of a projectProduction quantityProfit valueMaterials savings.Thus, the objective function of a linear programming model, which is always linear, is to maximize or minimize a numerical value.
Learn more about the objective function of a linear programming at https://brainly.com/question/25828237
#SPJ1
PLEASE HELP ! Determine f of the quantity 2 plus h end quantity minus f of 2 all over h if f (x) = 5x − 6.
4
4h
5
5h
The value of the function is 5
What is function?A function is defined as a relation between a set of inputs having one output each.
Given function:
f(x) = 5x − 6
Now f(2+h) - f(2) /h
= 5(2+h)-6 - 10+6/h
=10+ 5h -10/h
=5h/h
=5
Learn more about this concept here:
https://brainly.com/question/26102243
#SPJ1
MATH: EXPONENTIAL WORK PROBLEM 1. HELP PLEASE! 13 pts
The amount of the radioactive substance is 374.6 g
How to determine the amount of radioactive substance?The given parameters are:
Initial, a = 424 mgRate, r = 6%Time, t = 2 hoursThe amount of the radioactive substance is calculated as:
A(t) = a(1 - r)^t
This gives
A(t) = 424 * (1 - 6%)^t
At 2 hours, we have:
A(2) = 424 * (1 - 6%)^2
Evaluate
A(2) = 374.6
Hence, the amount of the radioactive substance is 374.6 g
Read more about exponential functions at:
https://brainly.com/question/2456547
#SPJ1
Find the 8th term of the sequence with formula tn= 7+2 (n-1)
Answer:
Your answer is 71
Step-by-step explanation:
7+2(n-1)
we have our n as 8
so,7+2(8-1)
9(7)=63
Let t be the number of weeks Dr. Elder is on his diet and D(t) be a linear equation that models his weight in pounds. At the beginning of his diet, t=0, Dr. Elder weighs 265 pounds, D(0)=265. After nine weeks, t=9, he now weighs 229 pounds, D(9)=229. Find the slope
Using it's concept, it is found that the slope of the function is of -4.
What is the slope of a function?The slope of a function is given by the change in the output of the function divided by the change in the input.
For this problem, in 9 months, his weight changed from 265 pounds to 229 pounds, hence it changed -36 pounds, which means that the slope is of:
m = -36/9 = -4.
More can be learned about the slope of a function at https://brainly.com/question/24808124
#SPJ1
Pamela is 7 years younger than Jiri. The sum of their ages is 39. What is Jiri ‘s age?
Based on the task given, Pamela's age and juri's age is 16 and 23 years respectively.
EquationJuri's age = xPamela's age = x - 7Their total age = 39x + (x - 7) = 39
x + x - 7 = 39
2x = 39 + 7
2x = 46
x = 46/2
x = 23
Therefore,
Juri's age = x
= 23 years
Pamela's age = x - 7
23 - 7
= 16 years
Learn more about equation:
https://brainly.com/question/2972832
#SPJ1
Which of the following has a slope of –2 and a y-intercept of 4?
y = 2x – 4
y = –2x – 4
y = –2x + 4
y = 2x + 4
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Which equation has a slope of -2 and a y-intercept of 4?
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
All of these equations are in [tex]\bf{y=Mx+b}[/tex] form.
The y-int. is b. The slope is M.
[tex]\bf{y\!=\!\!-2x+\!4}[/tex] | put in the values
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=\!\!y=-2x+4}[/tex]
[tex]\LARGE\boxed{\bf{aesthetics\not1\theta l}}[/tex]
Find the sum of s = 1 - (1)/(4) + (1)/(6)-(1)/(9)+ (1)/(11)- (1)/(14)...
The sum of the equation is
[tex] \frac{859}{2772} [/tex]
How to find the sum
Given the expression
s = 1 - (1)/(4) + (1)/(6)-(1)/(9)+ (1)/(11)- (1)/(14)
Let's find the LCM, which is 2772
s =
[tex] \frac{2772 - 693 + 462 - 308 +252 - 198}{2772} [/tex]
Add the numerators, do the addition before the substraction
s =
[tex] \frac{859}{2772} [/tex]
Thus, the sum of the equation is
[tex] \frac{859}{2772} [/tex]
Learn more about BODMAS here:
https://brainly.com/question/16788360
#SPJ1
The length of a rectangle is five times the width. If the area of the rectangle is 45
square inches, then find the length and width.
Step-by-step explanation:
sol;
l=5w
area=l*w
or,45=5w*w
or,45=5w2
or,45\5=w2
0r[tex]\sqrt{9}[/tex]=w
or,3=w
again,
l=5w
l=5*3
l=15
Therefore, length is 15 inch and width is 3 inch.
Which of the following shows that the two composite figures cover the same area?
The area of a 2D form is the amount of space within its perimeter. It is measured in square units. The correct option is 9 units².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The area of the different figures will be shown below.
Thus, the expression that shows that the two composite figures cover the same area is A = 4 + 3 + 2 = 9 units².
Hence, the correct option is 9 units².
Learn more about the Area:
https://brainly.com/question/1631786
#SPJ1