Answer: 60 oranges
Step-by-step explanation:
Given information
Weight = 75 g / orange
Total = 4.5 kg
Given formula
Total = Number of oranges × Average weight
Convert Kilogram unit to Gram
1 kg = 1000 g
4.5 kg = 4.5 × 1000 = 4500 g
Substitute values into the given formula
Total = Number of oranges × Average weight
Number of oranges = Total / Average weight
Number of oranges = 4500 / 75
Simplify by division
[tex]\Large\boxed{Number~of~oranges~=~60}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
60 oranges
Step-by-step explanation:
Let the unknown number of oranges be x.Given that,The average weight of an orange ⇒ 75g
Total weight of oranges ⇒ 4.5 kg
Therefore,Number of oranges Weight ( in grams)
1 75 g
x (4.5 × 1000) g
To find the number of oranges we can make an expression like this.1 ⇒ 75
x ⇒ 4500
Use cross multiplication and find the value of x.
75x = 4500 × 1
75x = 4500
Divide both sides by 75.
x = 60
Therefore, 60 oranges would weight 4.5kgA softball pitcher has a 0. 431 probability of throwing a strike for each pitch. if the softball pitcher throws 22 pitches, what is the probability that exactly 12 of them are strikes?
The probability that exactly 12 of them are strikes is 0.09.
In this question,
Number of pitches, n = 22
Probability of throwing a strike for each pitch, p = 0.431
Then, q = 1 - p
⇒ q = 1 - 0.431
⇒ q = 0.569
Number of strikes, x = 12
The probability that exactly 12 of them are strikes can be calculated using Binomial expansion,
[tex]P(X=x)=nC_xP^{x}q^{(n-x)}[/tex]
⇒ [tex]P(X=12)=22C_{12}(0.431)^{12}(0.569)^{(22-12)}[/tex]
⇒ [tex]P(X=12)=22C_{12}(0.431)^{12}(0.569)^{10}[/tex]
⇒ [tex]P(X=12)=(\frac{22!}{12!10!} )(0.431)^{12}(0.569)^{10}[/tex]
⇒ P(X=12) = (646646)(0.000041)(0.00355)
⇒ P(X=12) = 0.09431 ≈ 0.09
Hence we can conclude that the probability that exactly 12 of them are strikes is 0.09.
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A train to new york city leaves every 7 minutes. another train to boston leaves the station every 6 minutes. suppose it is 6:30 am right now. at what time will both trains leave the station together again if both of them left the station together at 6:30 am?
Both trains will leave the station together again at 7:12 am if both of them left the station together at 6:30 am.
What is LCM?The lowest integer that is a multiple of two or more numbers is known as the LCM. For instance, the LCM of 4 and 6 is 12, and the LCM of 10 and 15 is 30. There are numerous ways for determining the least common multiples, just as there are for computing the greatest common divisors. One approach is to divide both numbers by their primes.To find at what time will both trains leave the station together again if both of them left the station together at 6:30 am:
If a train to New York City departs every 7 minutes and another to Boston departs every 6 minutes,The two trains then depart together after a time equal to the LCM of their individual intervalsLCM (7,6) = 42As a result, if they begin at the same time, they will depart at the same time every 42 minutes.If both trains left the station at 6.30 a.m., they will leave together again 42 minutes later, at 7.12 am.
Therefore, both trains will leave the station together again at 7:12 am if both of them left the station together at 6:30 am.
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HELPPPP (x-y)^3-(y-x)^2
Answer:
(x-y)(x-y)(x-y)= x²-yx+x²-yx-yx+y²-yx+y²
2x²-4yx+2y²
(y-x)(y-x)= y²-yx-yx+x²
y²-2yx+x²
-(y²-2yx+x²) = -y²+2yx-x²
2x²-4yx+2y²-y²+2yx-x²= x²-2yx+y²
or
(x−y−1)(x−y)² ≡ x³−x²+3xy²+2xy−y³−y²−3yx³
What is the probability that the battery life for an ipad mini will be at least 11 hours?
Answer:
0.2857
Step-by-step explanation:
We want to determine,
The probability that the battery life is at least 11 hours is 0.2857.
Roger owns a one-acre piece of land. the length of the land is 484 feet. what is the width of his property? (hint: one acre = 43,560 square feet)
Answer:
90ft
Step-by-step explanation:
43,560ft² = L × l
43,560ft² = 484ft × l
43,560ft² ÷ 484ft = l
l = 90ft
Please help and explain.
Answer:
B
Step-by-step explanation:
It's B
Answer:
Option B
Step-by-step explanation:
The equation is:
[tex]y=10-2x[/tex]
when x=2
[tex]y=10-2(2)010-4=6[/tex]
When x = 3
[tex]y=10-2(3)=10-6=4[/tex]
When x=4
[tex]y=10-2(4)=10-8=2[/tex]
Hope this helps
Solve for P : p/10 = 7.2/3
P/10 = 7.2/3
P = 7.2x10/3
P=72/3
P= 24
a) The line y = 4 meets the line 2x + y = 8 at the point A
Fins the co-ordinates of A
b) The line 3x + y = 18 meets the x axis at the point B
Find the co-ordiantes of B
c) (i) Find the co-ordiantes of the mid-point M of the line joining A to B
(ii) Find the equation of the line through M parallel to 3x + y =18
answers :
a.
coordinates of A are (2,4)
b.
coordinates of B are (6,0)
i.
(4,2) is the midpoint
ii.
y = -3x + 18 is the parallel line
Step-by-step explanation:
a.
if two things are equal to the same thing then they are equal to each other
y = 4
2x + y = 8 is y = -2x +8 so
-2x +8 = 4
-2x = -4
x = 2
coordinates of A are (2,4)
b.
if two things are equal to the same thing then they are equal to each other
y=0
3x+y=18 is y = -3x+18 so
-3x+18=0
x = 6
coordinates of B are (6,0)
midpoint formula is
(X1+X2)/2 , (Y1+Y2)/2
(2,4) (6,0)
(X1+X2)/2 , (Y1+Y2)/2
(2+6)/2 , (4+0)/2
(4,2) is the midpoint
parallel line has the same x value
so for a line parallel to 3x+y=18 or y = -3x+18
the parallel line would be
y = -3x
point slope formula
point slope formulay - y1 = m (x - x1)
3x+y=18 or y = -3x+18 was 6,0 at y = 0
y - y1 = m (x - x1)
y - 0 = m (x - x1)
since it's a parallel line the m has to be the same
(6,0)
y - 0 = -3 (x - 6)
y = -3x + 18 is the parallel line
Use the function, f(x)=50(1.02)^x to identify if it's growth or decay & the percentage of the growth or decay.
The exponential function illustrated as f(x)=50(1.02)^x has a growth rate of 2%.
What is the growth rate in the function?The exponential function is a mathematical function that is represented by e^x. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.
In this case, the function is given as:
f(x)=50(1.02)^x
It should be noted 1 + 2% = 1.02 which us the value in the parentheses.
In conclusion, the growth rate is 2%.
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Select all the correct answers. If the measure of angle 0 is 5(pi)/4, which statements are true?
The Measure of the reference angle is 45
cos(0)= √ 2/2
tan(0)=1
sin(0)=√ 2/2
the measure of the referance angle is 30
the measure of the referance angle is 60
Finding the equivalent angle of [tex]\theta[/tex], the correct statements are given as follows:
The Measure of the reference angle is 45.[tex]\cos{\theta} = \frac{\sqrt{2}{2}}[/tex].[tex]\tan{\theta} = 1[/tex][tex]\sin{\theta} = \frac{\sqrt{2}{2}}[/tex].What are equivalent angles?Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.
In this problem, the given angle is as follows:
[tex]\theta = \frac{5\pi}{4}[/tex]
It is on the third quadrant, as it is between pi and 1.5 pi, hence the equivalent on the first quadrant, also known as the reference angle, is given by:
[tex]\frac{5\pi}{4} - \pi = \frac{5\pi}{4} - \frac{4\pi}{4} = \frac{\pi}{4}[/tex]
The angle of 45º has equal sine and cosine, and tangent of 1, hence the correct statements are:
The Measure of the reference angle is 45.[tex]\cos{\theta} = \frac{\sqrt{2}{2}}[/tex].[tex]\tan{\theta} = 1[/tex][tex]\sin{\theta} = \frac{\sqrt{2}{2}}[/tex].More can be learned about equivalent angles at https://brainly.com/question/24787111
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Answer:
The measure of the reference angle is 45 degrees
tan(theta) = 1
Step-by-step explanation:
Charles used a chain which was 12.5 metres long, 12 times to measure the breadth of his garden. Stephen used a chain of different length 10 times to cover the breadth of Charles' garden and 18 times to cover its length. What is the area of Charles' garden to the nearest one tenth of a hectare?
A. 4.05 m^2
B. 5.4 m^2
C. 3.6 m^2
D. 4.1 m^2
The function [tex]B(t) = 182(1.065)^t[/tex] represents the annual population of bees in a county park, the growth rate is 6.5%.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
Length of Charles garden = 12.5 m * 12 = 150 m
Length of Stephen chain = 150 m /18 = 25/3 m
Breadth of Charles garden - 25/3 * 10 = 250/3 m
Area of Charles garden = 150 m * 250/3 m = 12500 m =
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18 times the quantity g plus 5
Comparing it to a system of equations, the expression is represented as follows:
18g + 5.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, we consider g as the variable. Then:
18 times the quantity g is 18g.Adding 5 to the expression, we have that 18g + 5.More can be learned about a system of equations at https://brainly.com/question/24342899
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16. a) In the given figure, OB bisects ABC and OC bisects ACB, prove that BOC - BAC = ABO+ACO.
Answer:
Points ABC and points OBC form two separate triangles. Triangle ABC is made up of angles BAC, ABC, ACB, while triangle OBC is made up of angles BOC, OBC, OCB. Since interior angles of triangles add up to 180 degrees, m<BAC + m<ABC + m<ACB = 180 and m<BOC + m<OBC + m<OCB = 180. 180 is equal to 180, so m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB.
Since OB bisects <ABC and OC bisects <ACB, m<ABO = m<OBC and m<ACO = m<OCB. We can also say that m<ABC = 2m<ABO and m<ACB = 2m<ACO. Substitute and simplify the equation.
m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB
m<BAC + 2m<ABO + 2m<ACO = m<BOC + m<ABO + m<ACO
m<ABO + m<ACO = m<BOC - m<BAC
Which expression is equivalent to x^2 + 5x - 6? Explain how.
(1) (x + 3) (x - 2)
(2) (x + 2) (x - 3)
(3) (x - 6) (x + 1)
(4) (x + 6) (x - 1)
Answer:
(4) (x + 6)(x - 1)
Step-by-step explanation:
Hello!Given expression
[tex]x { }^{2} + 5x - 6[/tex]
Find numbers when they are multiplied gives 6 and when they are added which gives 5.
Thus, these numbers are -1 & 6.
[tex]x {}^{2} + 6x - x - 6 \\ x(x + 6) - 1(x + 6) \\ (x + 6) \: \: (x -1 )[/tex]
Can also check the multiplied values of these two values.
Hope it helps!
Answer:
(4)
Step-by-step explanation:
Determine two multiples which when multiplied gives - 6(the last term in the equation), when added, gives +5 (the middle term in the equation).
Multiples are: +6 and -1
input the two multiples in place of the middle term (+5x)
=x^2+6x-1x-6
Collect like terms
=x(x+6)-1((x+6)
Answer= (x+6)(x-1)
Confirm answer above:
Open bracket
x(x-1)+6(x-1)
x^2-x+6x-6
x^2+5x-6 (initial equation).
Identify the factors of x2 − 4x − 21. (x − 7)(x 3) (x 7)(x − 3) (x 21)(x − 1) (x − 21)(x 1)
The factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.
A quadratic expression is of the form ax² + bx + c, which can be factorized using the mid-term factorization method, where b is shown as the sum or difference of two such numbers, whose product is equal to the product of a and c.
In the question, we are asked to factorize the quadratic expression, x² - 4x - 21.
In the given expression, a = 1, b = -4, and c = -21.
Thus, ac = -21.
The numbers having a product 21 are:
1*21 = 21,
3*7 = 21.
Since, 3 - 7 = -4 (That is b), we break b into 3 and -7.
Thus, the expression can now be shown as:
x² - 4x - 21
= x² + (3 - 7)x - 21
= x² + 3x - 7x - 21
= x(x + 3) - 7(x + 3) {By taking common}
= (x - 7)(x + 3) {By taking common}.
Thus, the factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.
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The odds of rolling a die and getting an even number is 50%. Write out the success set and the sample set to use the definition of probability to show that this is true.
Answer:
It gets more complicated with a six-sided die. In this case if you roll the die, there are 6 possible outcomes (1, 2, 3, 4, 5 or 6). Can you figure out what the theoretical probability for each number is? It is 1/6 or 0.17 (or 17 percent).
Use a left-hand sum with 4
intervals to approximate the area
under f(x) = 4 - x² between
x = 0 and x = 2.
Answer:
25 / 4
Step-by-step explanation:
To find the left sum, you need to....
1.) Find Δx
2.) Find [tex]x_{k-1}[/tex]
3.) Find ∑[tex]^n_{k=1}f(x_{k-1})[/tex]Δx
4.) Solve for the left sum
What does the point (1, 2) represent? parking costs $1 per hour for the entire day. parking costs $2 per hour for the entire day. the total cost of 2 hours of parking is $1. the total cost of 1 hour of parking is $2.
The point which is indicated in the task content; (1, 2) represents; parking costs $2 per hour for the entire day.
What is the interpretation of the point given in the task content; (1,2)?
It follows from convention that the coordinate systems are structured such that the independent variable, x be placed 1st and the dependent variable, y be placed second.
Consequently, since the cost of parking is dependent on the time for which the car is parked, then, it represents parking costs 2 per hour for the entire day.
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Find the slope of the line shown below
Answer:
[tex] \frac{3}{2} [/tex]
Step-by-step explanation:
From the attached photo, we can deduce:
(2,2) as (x1,y1)
(-2,-4) as (x2,y2)
Slope Formula =
[tex] \frac{y1 - y2}{x1 - x2} [/tex]
Now we can substitute these values into the formula to find the slope.
Slope of line =
[tex] \frac{2 - ( - 4)}{2 - ( - 2)} \\ = \frac{2 + 4}{2 + 2} \\ = \frac{6}{4} \\ = \frac{3}{2} (reduced \: to \: simplest \: form)[/tex]
HELP!!! MATH!!! 100 PTS !!!
Suppose f is a one-to-one, differentiable function and its inverse function f−1 is also differentiable. One can show, using implicit differentiation (do it!), that
(f^−1)′(x)=1/(f′(f^−1(x)))
Find (f^−1)′(6) if f(−1)=6 and f′(−1)=3/7.
Answer:
(f^−1)′(6)=1/(f'(f^-1(6)))
(f^−1)′(6)=1/(f'(f^-6)))
I hope this helps.
Could I get some help with this?
Answer:
Step-by-step explanation:
base=b=7.2yd
height =h=7yd
area of parallelogram = b x h
. =7.2yd x 7yd
=50.49[tex]yd^{2}[/tex]
A bin in the school gymnasium holds different colored balls. a ball is picked at random and then replaced. the probability of picking a green ball is 0.5, the probability of picking a blue ball is 0.4, and the probability of picking a red ball is 0.1. if a ball is picked and replaced 140 times, how many times should you expect a blue ball to be picked? a. 14 b. 48 c. 56 d. 70
Correct answer is C. the number of times blue ball appears is 56
Given,
probability of picking a green ball is 0.5,
the probability of picking a blue ball is 0.4,
the probability of picking a red ball is 0.1.
a ball is picked and replaced = 140
Probability = (the number of ways of achieving success) / (the total number of possible outcomes)
Probability provides information about the likelihood that something will happen. Meteorologists, for instance, use weather patterns to predict the probability of rain. In epidemiology, probability theory is used to understand the relationship between exposures and the risk of health effects.
For this item, the number of times that we should expect that a blue ball is picked should be the product of the number of times and the probability of picking a blue ball (which is equal to 0.4)
= (140)(0.4) = 56
Therefore, we should expect that the blue ball will be picked 56 times.
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A box is to constructed with a rectangular base and a height of 5cm. if the rectangular base must have a perimeter of 28cm, which quadratic equation best models the volume of the box ? a. y=5(28-8)(x) b.y=5(28-2x)(x) c. y=5(14-x)(x) d. y=5(14-2x)(x)
y=5(14-x)(x) quadratic equation best models the volume of the box .
What is volume of cuboid?
Perimeter is the distance around the outside of a shape. Area measures the space inside a shape. The volume of a cuboid is found by multiplying the length by the breadth by the height.Perimeter = 2(width + length) =28
Let x=width of base, then length of base = (28/2)-x = 14-x
Volume of box = length*width*height
=x(14-x)*5 ⇒ 5x(14-x)(x)
Therefore, y=5(14-x)(x) quadratic equation best models the volume of the box .
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What is the range of the function f(x) = |x + 4| + 2?
R: {f(x) ∈ ℝ | f(x) ≤ 2}
R: {f(x) ∈ ℝ | f(x) ≥ 2}
R: {f(x) ∈ ℝ | f(x) > 6}
R: {f(x) ∈ ℝ | f(x) < 6}
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Given:▪ [tex]\longrightarrow \sf{f(x) = |x + 4| + 2}[/tex]
You need to remember that the form of an Absolute Value Function is:
• For the vertex:
[tex]\small\longrightarrow \sf{H= \: \: x -coordinate}[/tex]
[tex]\small\longrightarrow \sf{K= y-coordinate}[/tex]
• For the definition:
If "a" is positive (+) , then the range of the function is:
[tex]\small\longrightarrow \sf{R:y \: \underline > \: k}[/tex]
If "a" is negative (-), the range of the function is:
[tex]\small\longrightarrow \sf{R: y \: \underline < \: k}[/tex]
In this case we can identify that:
[tex]\small\longrightarrow \sf{a = 1}[/tex]
[tex] \small\longrightarrow\sf{a = 2}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex] \large \bm{R: {f(x) \in ℝ | f(x) \underline > 2}}[/tex]
Csn u please help me o have no idea
Answer:
D.= √29
Step-by-step explanation:
Greetings!The distance between the two complex numbers,
Z₁=a+bi and Z₂=c+di in the complex plane is
[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]
In the Cartesian plane, the distance between, one point and other is (x₁,y₁) and (x₂,y₂) is the distance formula is
[tex]d = \sqrt{(X₂-X₁)² + (Y₂-Y₁)²} [/tex]
To find the distance between the two complex numbers using the formula
[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]
where,
a=4b=3c=6d=-2[tex]d = \sqrt{(a - b) {}^{2} + (d - b) {}^{2} } \\ d = \sqrt{(6 - 4) {}^{2} + ( - 2 - 3) {}^{2} } \\ d = \sqrt{(2) {}^{2} + ( - 5) {}^{2} } \\ d = \sqrt{4 + 25} = \sqrt{29 \\ } [/tex]
What is the area of the shape?
The area of the shape is 35 square units
How to determine the area of the shape?The given shape is a trapezoid, and it has the following side lengths
Parallel bases = 6 and 8
Height = 5
The area of the shape is then calculated as:
A = 0.5 * (sum of parallel bases) * height
Substitute the known values in the above equation
A = 0.5 * (6 + 8) * 5
Evaluate the product
A = 35
Hence, the area of the shape is 35 square units
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The area of the given trapezoid is given as 35 square units
How to determine the area of a trapezoid?The given shape is quadrilateral known s a trapezoid. The formula for calculating the are of the trapezoid is expressed as;
A = 1/2(a+b)*h
where
a and b are parallel sides
h is the height of the trapezoid.
Given the following parameters
a =6units
b = 8 units
h - 5 units
Substitute to have:
A = 1/2(6 + 8) * 5
A = 1/2(14) *5
A = 7 * 5
A = 35 square units
Hence the area of the given trapezoid is given as 35 square units
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Need this soon please -
Select the correct answer.
What is the inverse of function
f(x)=√x + 7
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Option A is correct[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Find inverse of given function :
[tex]\qquad❖ \: \sf \:y = \sqrt{x} + 7[/tex]
[tex]\qquad❖ \: \sf \: \sqrt{x} = y - 7[/tex]
[tex]\qquad❖ \: \sf \:x = (y - 7) {}^{2} [/tex]
Next, replace x with f-¹(x) and y with x ~
[tex]\qquad❖ \: \sf \:f {}^{ - 1} (x) = (x - 7) {}^{2} [/tex]
we got our inverse function.
Condition : x should be greater or equal to 7
because we will get same value of y for different x if we also include values less than 7.
[tex] \qquad \large \sf {Conclusion} : [/tex]
Correct option is A[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]
Given:[tex]\longrightarrow\bold{f(x)= \sqrt{7}}[/tex]
To solve for the inverse of a function we begin by re-writing the function as an equation in terms of y.
[tex]\bold{Becomes,}[/tex]
Next step we switch sides for x and y variables and then solve for the y variable as shown below,
[tex]\longrightarrow\sf{y= \sqrt{x}+7}[/tex]
[tex]\bold{Then,}[/tex]
[tex]\longrightarrow\sf{x= \sqrt{y}+7}[/tex]
[tex]\small\bold{Solve \: for \: y \: and \: subtract \: 7 \: from \: the \: both \: }[/tex] [tex]\bold{sides,}[/tex]
[tex]\longrightarrow\sf{x-7= \sqrt{y}}[/tex]
[tex]\small\bold{Square \: both \: sides }[/tex]
[tex]\sf{(x-7)^2=(\sqrt{y})^2}[/tex]
[tex]\sf{(x-7)^2=y}[/tex]
We now re-write in function notation. Take note however that this is the inverse:
[tex]\bold{Where \: y}[/tex] [tex]\sf{=(x-7)^2 }[/tex]
[tex]\longrightarrow\sf{y= (x-7)^2 }[/tex]
[tex]\huge\mathbb{ \underline{ANSWER:}}[/tex]
[tex]\large\boxed{\sf A. \: \: f^{-1}(x)= (x − 7)^2 , \: for \: \underline > 7 }[/tex]
Write as a single term from Pascal's Triangle in the form t_nr(1 mark)
t_13,8 + t_13,9
¹³C₈ + ¹³C₉ as a single term from Pascal's Triangle is ¹⁴C₉
What is Pascal's triangle?
Pascal's triangle is a triangle written in such a way that it forms the coefficients of a binomial expansion. The coefficients of the terms are gotten through combination.
What is combination?Combination is the number of ways r in which n objects can be selected. It is given by ⁿCₓ = n!/x!(n - x)!
How to write a single term from Pascal's Triangle in the form t_nr = t_13,8 + t_13,9.Since we have ¹³C₈ + ¹³C₉ and we want to write it as a single term, we have that
¹³C₈ = 13!/8!(13 - 8)! = 13!/8!5! and ¹³C₉ = 13!/9!(13 - 9)! = 13!/9!4!So, ¹³C₈ + ¹³C₉ = 13!/8!5! + 13!/9!4!
= 13!/(8! × 5 × 4!) + 13!/(9 × 8! × 4!)
= 13!/8!4![1/5 + 1/9]
= 13!/8!4! × [(9 + 5)/45]
= 13!/8!4! × 14/45]
= 13!/8!4! × 14/(9 × 5)]
= 14 × 13!/8! × 9 × 4! × 5)]
= 14!/9!5!
= 14!/9!(14 - 9)!
= ¹⁴C₉
So, ¹³C₈ + ¹³C₉ as a single term from Pascal's Triangle is ¹⁴C₉
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Need this quick ! Correct answers appreciated
(Selected answer is not known to be correct it just won’t let me un select an answer)
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\qquad❖ \: \sf \:g(f( - 5)) = 5[/tex]
[tex]\textsf{\underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:f(x) = |2x + 9| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = |2( - 5) + 9| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = | - 10+ 9| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = | - 1| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = 1[/tex]
next,
g(f(-5)) represents value of y at x = f(-5) = 1
hence,
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\sf \:g(f( - 5)) = 5[/tex]Pick the correct answer
Thanks so much :)
The linear functions with their slopes ranked from least to greatest are given as follows:
E. I, K, J.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, we have that:
Line I is decreasing, hence it has a negative slope.Line K is constant, hence it has a slope of zero.Line J is increasing, hence it has a positive slope.Hence the linear functions with their slopes ranked from least to greatest are given as follows:
E. I, K, J.
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