Answer:
1365
Step-by-step explanation:
The number of ways in which you can choose r items as a set from n available items is given by n choose k which can be represented as
Here n = 15, r = 4
C(n, r)
C(n,r) = C(15,4)
The formula is
[tex]C(n,r) = \binom{n}{r} = \dfrac{n!}{( r! (n - r)! )}[/tex]
where ! represents factorial of a number
n! = n x (n-1) x (n-2) x.......x 3 x 2 x 1
So
[tex]C(15,4) = = \dfrac{15!}{( 4! (15 - 4)! )}\\\\ = \dfrac{15!}{4! \times 11! }\\\\\\= 1365[/tex]
Answer: 1365 combinations
Step-by-step explanation:
What you're looking for if the order doesn't matter is the number of combinations.
You can use this formula for it:
[tex]\frac{n!}{r!(n-r)!} \\[/tex]
Where n is the number of objects there are and r is the number of objects you take out.
We'll be using the variables:
n = 15
r = 4
Plug them in and solve:
[tex]\\\frac{15!}{4!(15-4)!} \\\\= \frac{15!}{4!* 11!} \\\\= \frac{1307674368000}{24 * 39916800} \\\\= \frac{1307674368000}{958003200} \\= 1365[/tex]
Is collecting pennies dependent or an independent events?
Collecting pennies can either be a dependent or an independent events based on the scenario.
How to illustrate the information?Events classified as independent do not depend on other events for their occurrence. For instance, if we toss a coin in the air and it lands on head, we can toss it again and this time it will land on tail.
A coin toss is an illustration of an autonomous occurrence. With each toss of the coin, there is an equal probability (0.5) of either heads or tails occurring, presuming that the coin is fair and can only land on heads or tails. It doesn't matter if the coin came up heads on the prior toss.
In conclusion, collecting pennies can either be a dependent or an independent events based on the scenario.
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Solve
4/2x+1 + 1/4x*POWER TO 2*-1=1
show clear algebraic fraction
*sorry for the way I wrote the question its the only way I can possibly write
The solution of the equation will be -7.46 and -0.54.
What are the roots of the equation?Let the equation be ax² + bx + c = 0. Then the roots of the equation will be
[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}[/tex]
The quadratic equation is given below.
(4/2)x + 1 + (1/4)x² - 1 = 1
Simplify the equation, then we have
(4/2)x + 1 + (1/4)x² - 1 = 1
2x + 1 + (1/4)x² = 0
x² + 8x + 4 = 0
Then the solution of the equation is given as,
[tex]\rm x = \dfrac{-8 \pm \sqrt{8^2 - 4 \times 1\times 4 }}{2 \times 1}\\[/tex]
Simplify the equation, then we have
x = [-8 ± √48] / 2
x = [-8 ± 4√3] / 2
x = -4 ± 2√3
x = - 4 ± 3.46
x = -7.46, -0.54
The solution of the equation will be -7.46 and -0.54.
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PLS HELP THIS IS CONFUSING
Answer:you need to show the options at the bottom
Step-by-step explanation:
Find the equation of the line through the points (3/5,2) and (6,−1). Write your answer in the form y=mx+b.
0.48
Step-by-step explanation:
To find the gradient when given points, label one of the x points as X2 and the other x1 ( it could be anyone of them: 3 could be X2 and 6 x1 or vise versa) and do the same with the y points, doesn't matter which one is y2 or y1.
But bare in mind, if you used the first coordinate x as x1 you must used the y coordinate as the y1. you must use the same order. so if you used X2 for second coordinate use y2 for the y point of the second coordinate.
Now set up the formula: x2-x1/y2 -y1
=( 3-6)/((-1)-5.2/
=0.48
Sorin Incorporated, a company that produces and sells a single product, has provided its contribution format income statement for January.
Sales (3,600 units) $ 97,200
Variable expenses 50,544
Contribution margin 46,656
Fixed expenses 37,300
Net operating income $ 9,356
If the company sells 4,100 units, its total contribution margin should be:
$ 53,136 is total contribution margin .
What is contribution format income?
A contribution margin income statement is an income statement in which all variable expenses are deducted from sales to arrive at a contribution margin. Then, all fixed expenses are subtracted to arrive at the net profit or net loss for the period.Requirement of the question is missing which is as follows
"If the company sells 4,100 units, its total contribution margin should be closest to"
Following answer is made accordingly.
Sales ( 97,200 / 3600) * 4100 110700
Variable expenses ( 50,544 / 3600) * 4100 57564
Contribution margin 53136
Fixed expenses 37,300
Net operating income 15836
The revised Contribution margin is $ 53,136 and Net Operating Profit is
$15836 if company sells 4100 units.
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need a bit of help this is confusing me
90 in²
Step-by-step explanation:Area is the amount of space a 2-D shape occupies.
Area Formula
As stated above, the area of a triangle is [tex]\frac{1}{2}bh[/tex]. When solving for area, it doesn't actually matter which side is the base. You just have to remember to take the height perpendicular to the base you use. Since this is a right triangle, the height is the same as one of the legs. For the purpose of this question, I will use 12 as the base and 15 as the height. Because the 12 and 15 sides are perpendicular to each other, we can plug them into the formula for b and h.
Solving For A
Now we can just plug 12 and 15 in and solve.
[tex]\frac{1}{2}*12*15 = 90[/tex]The area of the triangle is 90 in².
I need to answer this is something like a test but it is not just help me please
Perpendicular lines from angles that measure (90) degrees
a family paid $25,200 as a down payment for a home. if this represents 14% of the price of the home, find the price of the home
Answer:
$178571.43
Step-by-step explanation:
14% of a number is 25000
multiply 25000 by 100 and divide the product by 14
you will get 178571.428571
round up the 100ths place and it's 178571.43
Like terms have the same ______, with each variable raised to the same exponent
Answer:
variable
Step-by-step explanation:
Like terms are the terms that contain same variables raised to the same power, the coefficients need not be same. For example, 7x and 2x are like terms because both terms contain same variable "x".
Two triangles are drawn in the coordinate plane. The vertices of the first triangle are (5, 4), (-4, 6), (-8, 9). The vertices of the second triangle are (1, 6), (-8, 8), (x, y). Find the value of x and y that allow these two triangles to be congruent.
The value of x and y that allows these two triangles to be congruent is
(-12, 11)
What are congruent triangles?The congruence of two or more triangles is determined by the measurements of their sides and angles. The three sides of a triangle determine its size, and the three angles determine its shape.
Two triangles are said to be congruent if the pairs of their corresponding sides and angles are equal. They are the same size and shape. Triangles have numerous congruence conditions.
Here we will use translation to find out units of displacements
If the triangle is congruent then vertices are of same shape too which means coordinate of first triangle will give us coordinate of second triangle
The coordinates of 1st vertices of traingle1 = (5, 4), x = 5, y = 4
The coordinates of 1st vertices of traingle2 = (1, 6), x = 1, y = 6
By subtracting,
translation x = 5 - 1 = 4
translation y = 4 - 6 = -2
Thus the vertices of other triangles are translated 4 units left and 2 units up. Same goes for second vertices
-4 - 4 = 8
6 + 2 = 8
And the same will go for the last vertices (-8, 9) that is
-8 - 4 = -12
9 + 2 = 11
The value of x and y that allow these two triangles to be congruent is (-12, 11)
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Consider the following conditional statement and scenario. Is the conditional statement true or false?
Conditional Statement: If I had set my alarm clock, I would have woken up on time.
Scenario: The power went out and reset all the clocks in the house.
We can actually deduce here that considering the conditional statement and scenario, the conditional statement is false.
What is conditional statement?Conditional statement is actually known to be an if-then statement. It is usually used to show and emphasizes the relationship that exists between two ideas. This means that one idea comes as a result of the other.
Conditional statements actually helps one to make proper deductions in a clear and rigorous way.
We see here that considering the scenario that "the power went out and reset all the clocks in the house", even if alarm was set, it wouldn't ring out because all the clocks in the house were reset when the power out.
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π=7x−2y
Solve the equation for y. Leave your answer in terms of π.
y=
If correct Brainliest + 100 points
Answer:
[tex]y=\dfrac{7x}{2}- \dfrac{\pi}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]\pi=7x-2y[/tex]
To isolate y, add 2y to both sides:
[tex]\implies\pi+2y=7x-2y+2y[/tex]
[tex]\implies\pi+2y=7x[/tex]
Subtract π from both sides:
[tex]\implies\pi+2y - \pi=7x- \pi[/tex]
[tex]\implies 2y=7x- \pi[/tex]
Divide both sides by 2:
[tex]\implies \dfrac{2y}{2}=\dfrac{7x}{2}- \dfrac{\pi}{2}[/tex]
[tex]\implies y=\dfrac{7x}{2}- \dfrac{\pi}{2}[/tex]
This can also be written as a rational function:
[tex]\implies y=\dfrac{7x- \pi}{2}[/tex]
Answer:
y = (-π + 7x)/2
Step-by-step explanation:
Now we have to,
→ find the required value of y.
The equation given is,
→ π = 7x - 2y
Then the required value of y will be,
→ π = 7x - 2y
→ -2y = π - 7x
→ y = (π - 7x)/(-2)
→ [ y = (-π + 7x)/2 ]
Hence, the equation is (-π + 7x)/2.
The area of a rectangular parking lot is 7031m? If the with of the parking lot is 79m, what is its length?
Answer:
The length of the parking lot is 89metres
Step-by-step explanation:
Area of a rectangle = Lenght × Breadth
[tex]7031 {m}^{2} = x \times 79m \\ divide \: both \: sides \: by \: 79 \\ x = \frac{7031}{79} \\ x = 89m[/tex]
what are least common multiple and greatest common factor of the numbers 9 and 6
Answer:
LCM=18 and GCF = 3
Step-by-step explanation:
Multiples of 9: 9, 18, 27
Multiples of 6: 6, 12, 18
LCM = 18
Factors of 9: 1, 3, 9
Factors of 6: 1, 2, 3, 6
GCF = 3
A package of 6 water bottles costs $7.74. How much does each water bottle
cost?
A. $0.74
B. $0.80
C. $1.29
D. $1.74
Plsss help
Answer:
1.29 take the cost and divided by each water bottle and that’ll give you how much each water bottle cost in a pack
Step-by-step explanation:
What is the slope of the line x=2
to get the slope of any straight line, we simply need two points off of it, let's use those two points on the picture below.
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{2}}} \implies \cfrac{-3 -4}{2 -2}\implies \cfrac{-7}{0}\implies und efined[/tex]
Find the length of AB.
AC=33
AB=x+5
BC=2x+10
Answer:
Step-by-step explanation:
Write 0.56 as a fraction
Answer:
14/25
Step-by-step explanation:
The heights of women aged 20–29 in the United States are approximately Normal with mean 64.1 inches and standard deviation 3.7 inches. Men the same age have mean height 69.4 inches, with standard deviation 3.1 inches.
Using the normal distribution, it is found that the z-score of the height of a women 5.5 feet tall is 0.51.
What is the missing information?The problem asks for the z-score of the height of a women 5.5 feet tall.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Considering that each feet has 12 inches, the parameters are given as follows:
[tex]X = 5.5 \times 12 = 66, \mu = 64.1, \sigma = 3.7[/tex]
Hence the z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (66 - 64.1)/3.7
Z = 0.51.
The z-score of the height of a women 5.5 feet tall is 0.51.
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Covert 3/7 into percent
The percentage of fraction 3/7 is 42.8571%.
what is percentage?Percentage, a relative value indicating hundredth parts of any quantity. One percent is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.
Given fraction:
3/7
To convert the fraction into percentage we have multiply 100
3/7*100
=300/7
= 42.8571%
Hence, the percentage of fraction 3/7 is 42.8571%.
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What conjecture can you make about backpack sales in June?
The conjecture about the backpack sales in June is that less than 8,000 backpacks were sold
How to make a conjecture about the backpack sales in June?From the graph, the number of backpack sales in June is not represented on the graph
The last month represented on the graph is May
On the vertical axis of the graph, the number of backpack sales that corresponds to the month of May is between 8,000 and 8,5000
By looking at the trend,
This means that the number of backpack sales in the month of June is less than the number of backpack sales in the month of May
Hence, the conjecture about the backpack sales in June is that less than 8,000 backpacks were sold
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The conjecture about backpack sales is that June sales will be less than 8,000 units.
What is a conjecture?
A conjecture is a mathematical statement without proof. Instead, conjectures survive on some existing patterns.
The existing patterns show that backpack sales peaked in November but deteriorated or decreased steadily every month.
For instance, in November, the backpack sales were 11,000 units but 10,250 in January. It reduced to 8,750 in March.
However, following the end of the Easter holidays, backpack sales may increase from May. But this prediction does not agree with the trend.
Thus, the conjecture about backpack sales is that June sales will be less than 8,000 units.
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PLEASE HELP, I WILL GIVE AN EXTRA 20 POINTS TO WHOEVER ANSWERS RIGHT
Answer:
The first choice { (1,2) (2,3) (3,6) (4,5)}
Step-by-step explanation:
A function has each x going to only one y
The first choice has each x going to only one y
Choice two has x=21 going to different y's
Choice 3 has x= 1 going to different y's
Choice 4 has x=2 going to different y's
3x³ = -16x² - 21x
Solve for x
Answer:
x=0, x=-7/3, x=-3
Step-by-step explanation:
I really need someone’s help with this it’s about ratios and proportions
Answer:
different from players, yes
(
2) a) If the function f(x) = |x| is changed to g(x) = 3|x-1| +3,
how is the graph transformed? (left, right, up, down? By how much?)
b) On the blank graph, graph the function g(x) = 3|x-1| +6
The required transformation of graphs are represented and attached below.
Given:
(a) function f(x) = |x| transformed to g(x) = 3 |x ₋ 1 | ₊ 3
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Parent Function : f(x) = |x|
Horizontal Shift: Right 1 Units
Vertical Shift: Up 3 Units
Reflection about the x-axis: None
Vertical Stretch: Stretched
(b) If there is a horizontal or vertical shift, reflection around the x-axis or y-axis, or vertical stretch, the function has undergone transformation. To identify the transformation, compare the function to the parent function.
Parent Function : f(x) = |x|
Horizontal Shift: Right 1 Units
Vertical Shift: Up 6 Units
Reflection about the x-axis: None
Vertical Stretch: Stretched
Hence the required graphs are plotted.
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In a choir of 32 singers, what is the ratio of men to women if there are
18 women in the choir?
Answer: Ratio of men to women is 7: 9
Step-by-step explanation:
Total: 32
Women: 18
Men: 32 - 18 = 14
Ratio of Men to Women would be 14 : 18. That simplified is 7 : 9
Answer:1.7
Step-by-step explanation:
divide 32/18=1.7
Elon’s she’s is 10 feet long 6 feet wide and 8 feet tall what is the volume of the shed?
Answer:
project adam?
Step-by-step explanation:
Answer: 480 cubic ft
Step-by-step explanation:
Elon' s shed is 10ft long 6 ft wide 8 ft tall. The volume of the shed is 10 × 6 × 8 = 480 cubic feet
How do you know that 30 is 1/10 of 300.
Answer: Division
Step-by-step explanation: It's simple. 1/10 = divided by 10. So, all you have to do is divide 10 by 300 and get your answer
Hey there!
1/10 of 300 = 30
1/10 * 300 = 30
1/10 * 300/1 = 30
1(300)/10(1) = 30
300/10 = 30
300 ÷ 10 / 10 ÷ 10 = 30
30 / 1 = 30
30 ÷ 1 = 30
30 = 30
Therefore, your could say you: Simplified your given equation (1/10 * 300) like how I did above and you received the answer (30) & the statement is very much true
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
The number of trees in a forest follows the logistic growth function f(t):
When will the number of trees reach 30,000?
about 81 years
about 69 years
about 65 years
about 60 years
32,000
1+12.8 -0.005
where t is the time in years.
Answer: 60 years
Step-by-step explanation:
ur answer is 60 because it's the same as 3+3 its 6 but it's
kind of the opposite way
A parking lot is 126.1 m long and 38.06 m wide, what is the perimeter of the lot? Express your answer using four significant figures.
