Since the maximum height of the ball above the ground is 28 ft, the ball will never reach a height of 30 ft.
How to determine if the ball will ever reach a height of 30 ft?To determine if the ball will ever reach a hgeight of 30 ft, we need to determine the maximum height of the ball.
What is the maximum height of the ball?Using the equation of motion, v² = u² - 2gh where
v = speed of ball at maximum height = 0 ft/s(since it stops momentarily), u = initial vertical velocity of ball = 40 ft/s, g = acceleration due to gravity = 32 ft/s² and h = maximum height of ball from starting point.So, making h subject of the formula, we have
h = (v² - u²)/-2g
Substituting the values of the variables into the equation, we have
h = (v² - u²)/-2g
h = ((0 ft/s)² - (40 ft/s)²)/-(2 × 32 ft/s²)
h = (0 ft²/s² - 1600 ft²/s²)/-(64 ft/s²)
h = - 1600 ft²/s²/-64 ft/s²
h = 25 ft
Since the ball is released from a height of 3 ft, its maximum height above the ground is H = 3 ft + h
= 3f + 25 ft
= 28 ft
So, we see that H = 28 ft < 30 ft.
Since the maximum height of the ball above the ground is 28 ft, the ball will never reach a height of 30 ft.
Learn more about maximum height here:
https://brainly.com/question/28225946
#SPJ1
7th-grade easy math PLEASE Answer correctly this is for a grade
SHOW YOUR WORK AND TAKE A PICTURE
PLS
PLEASE Answer correctly this is for a grade
SHOW YOUR WORK AND TAKE A PICTURE
PLS
Answer:
4 lemons per pitcher basically by looking at the graph you can determine each pitcher increased by a steady pattern of 4 lemons per pitcher.
Example: 2x=8, x=4, 2(4)=8, 8=8 true, the x and y value is cannot be 0 for this equation since no workers means no lemons. If I subtract back by -4 the graph would look like: 1 4, 0 0. Proving this. Also another example I can do is 3x=12, divide 3 by both side x=4, plug them in, 12=12 which is true. Keep in mind X means Pitcher so 4 is correct.
Oh yea less compilcated way is to just look a graph I did all those step to prove to you. Good luck!
Step-by-step explanation:
Your friend's averages 56 miles per hour while driving to a college. On the return trip, your friend averages 48 miles per hour due to construction. The total driving time is 6 hours and and 30 minutes. How long does each trip take?
the first trip takes 3 hours
and the second one takes 3 hours and 30 minute
Do the numbers in the perimeter row form an arithmetic sequence? If so, what is the common difference, and what is the recursive formula for the perimeter of a square of side n(the nth perimeter) using the first number(perimeter) in the pattern?
Answer:
Common difference d = 4Recursive formula Pₙ₊₁ = Pₙ+ 4Step-by-step explanation:
Let the perimeter of the square with length of n be Pₙ.
According to given table we have:
P₁ = 4, P₂= 8, P₃ = 12, P₄= 16, P₅= 20We can put this as a sequence:
4, 8, 12, 16, 20Common difference is:
d = 8 - 4 = 12 - 8 = 16 - 12 = 20 - 16 = 4The recursive formula for this sequence is:
Pₙ₊₁ = Pₙ+ 4WHAT IS THE PATTERN IN 9:47, 10:21, 10:57, ?, 12:15
11:35 will be the omitted number in the supplied sequence.
Describe a series.A list of components that have been arranged in a sequential fashion, with members coming either before or after, is referred to as a sequence.
The order will be provided as
9:47, 10:21, 10:57, ?, 12:15
The two increases the gap between the two numbers.
Consequently, there will be a 36-second gap between 10:57 and 10:21.
The distance between the following number and 10:57 will then be 38. The following number will be
→ 10: 57 + 00:38
→ 11: 35
Thus, 11:35 will be the following number.
To learn more about sequence from given link
https://brainly.com/question/26748083
#SPJ9
What is the missing number in this sequence 6, 7, 9, 12, 17, ?
Chris saved x dollars and spent half of his savings buying video games. After earning an additional $20 cutting grass, he had $60. If the equation 1/2bh represents the scenario, how much did he start with in his savings?
Answer:
80
Step-by-step explanation:
Simply reverse the steps.
In the end he has 60, before that he got 20 dollars for cutting grass, so subtract 20.
Now he has 40, which is after he spent half of his money on games, so multiply it by 2.
This is where he started, and he has 80 dollars saved.
(2-I)(3+5i) multiple
Answer:
ii-7i
Step-by-step explanation:
These can be multiplied in a manner similar to expanding brackets:
(
2
+
i
)
(
3
−
5
i
)
=
6
+
3
i
−
10
i
−
5
i
2
Remember that
i
=
√
−
1
so
i
2
=
−
1
This will in turn allow us to gather the like terms like so:
6
+
5
+
3
i
−
10
i
=
11
−
7
i
10. Find the conditions on m and b such that the linear function y = mx + b is its own inverse. Prove this using algebraic techniques only.
The conditions on m and b such that the linear function y = mx + b is its own inverse is 1 and 0 respectively.
What is Linear Function ?A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. It's look like the slope-intercept form of a line which is expressed as y = mx + b.
Or, it is a function that represents a straight line on the coordinate plane.
It is given that the linear is b,
y = mx + b
So, inverse of this function will be :
x = my + b
my = x - b
y = (1/m)x - b/m
Then, for both functions equal
m = 1/m and -b = b
So, m must be 1 and b must be 0.
Therefore, the value is of the m and b of the given equation y = mx + b is its own inverse will be 1 and 0 respectively.
To learn more about Linear Function visit :
https://brainly.com/question/14695009
#SPJ1
Which word not be a step in solving 18=2(4+x)
The correct option is B) Collect variables terms on one side because there is one value for the variable.
What is defined as the variables?In the perspective of a math concept or experiment, a variable is a quantity that really can change. A variable is typically represented by a single letter. Variables are commonly represented by the alphabets x, y, and z. We will sometimes select a letter which further tells us of the quantity this represents, including such t for time, v voltage, and any b for bacteria.The given equation in this case is,
18 = 2(4+x)
By using the Distributive property on the right side,
18 = 8 + 2x
After subtracting 8 from both sides ( Isolating variable x )
18 - 8 = 8 + 2x - 8
Compile similar terms,
10 = 2x
By dividing both sides by two ( Isolating variable x )
x = 5
As a result of the preceding explanation, it is completely obvious that we utilized all options but apart from option B.
To know more about the variables, here
https://brainly.com/question/2804470
#SPJ9
The complete question is-
Which would not be a step in solving 18=2(4+x)?
A) Use the distributive property.
B) Collect variables terms on one side.
C) Collect like terms.
D) Isolate the variable.
Yumi takes 5/12 hour to complete 50 math problems Eric is able to complete 48 math problems in 2/5 hour which student can complete math problems at a greater rate of problems per hour
If Yumi takes 5/12 hour to complete 50 math problems Eric is able to complete 48 math problems in 2/5 hour the student that can complete math problems at a greater rate of problems per hour is: They solve the same number of problems per hour.
RateCalculation for the rate of Yumi
Yumi=5/12×60
Yumi=25 minutes
Rate=50/25
Rate=2
Calculation for the rate of Eric
Eric=2/5×60
Eric=24 minutes
Rate=48/24
Rate=2
Hence, Both Yumi and Eric has the same rate which is 2.
Therefore If Yumi takes 5/12 hour to complete 50 math problems Eric is able to complete 48 math problems in 2/5 hour the student that can complete math problems at a greater rate of problems per hour is: They solve the same number of problems per hour.
Learn more about rate here: https://brainly.com/question/11416162
#SPJ1
Select all sets that √7 belong to.
Onatural numbers
Owhole numbers
O integers
O rational numbers
Oirrational numbers
Oreal numbers
All sets that √7 belong to irrational numbers
The number √7 is a number inside a square root. Also, note that the number 7 is a whole number, but not a perfect square. Therefore, by our rule, we have that √7 belongs to the set of real numbers and to the set of irrational numbers.
In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the important numbers that are not rational numbers.
That is, irrational numbers can't be expressed as the ratio of two integers. When the ratio of lengths of two line segments is a real number, the road segments are also described as being incommensurable, meaning that they share no "measure" in common, that is, there's no length ("the measure"), regardless of how short, that would be used to express the lengths of both of the two given segments as integer multiples of itself.
Among irrational numbers are the ratio π of a circle's circumference to its diameter, Euler's number e, the golden ratio φ, and therefore the square root of two. In fact, all square roots of natural numbers, aside from perfect squares, are irrational.
Like all real numbers, irrational numbers are often expressed in positional notation, notably as decimal numbers. within the case of irrational numbers, the decimal expansion doesn't terminate, nor end with a repeating sequence.
for instance, the decimal representation of π starts with 3.14159, but no finite number of digits can represent π exactly, nor does it repeat.
Conversely, a decimal expansion that terminates or repeats must be a real number. These are provable properties of rational numbers and positional number systems and aren't used as definitions in mathematics.
To learn more about irrational numbers from the given link:
brainly.com/question/17450097
#SPJ9
Simplify the given algebraic expression.
9{9b-[2-3(9b-5)]}
Please I need an answer for this
Thanks!!!
After simplifying the algebraic expression 9 { 9 b - [ 2 - 3 ( 9 b - 5 ) ] }, we get the result as 324 b - 153.
We are given the algebraic expression:
9 { 9 b - [ 2 - 3 ( 9 b - 5 ) ] }
We need to simplify the expression.
For this, we will use the BODMAS rule.
B - Brackets
O - Of
D - Division
M - Multiplication
A - Addition
S - Subtraction
So, simplifying the expression, we get that:
9 { 9 b - [ 2 - 3 ( 9 b - 5 ) ] }
= 9 { 9 b - [ 2 - 27 b + 15 ] }
= 9 { 9 b - 2 + 27 b - 15 }
= 9 { 9 b - 2 + 27 b - 15 }
= 81 b - 18 + 243 b - 135
= 324 b - 153
Therefore, after simplifying the algebraic expression 9 { 9 b - [ 2 - 3 ( 9 b - 5 ) ] }, we get the result as 324 b - 153.
Learn more about algebraic expression here:
https://brainly.com/question/4344214
#SPJ9
m< 1=3x° and m2 = (x+48)°
If the two angles are supplementary then the value of x is 33°.
Two angles that sum to a straight angle or 180° are called supplementary angles.
The non-shared sides of two supplementary angles that are nearby create a straight line if they share just one side and have a common vertex. A linear pair of angles is the name given to such angles. However, extra angles might be spaced apart and need not be on the same line. For instance, opposite angles of a cyclic quadrilateral (one whose vertices all fall on a single circle) and adjacent angles of a parallelogram are supplementary.If the two given angles are supplementary then we can create a linear equation in x of the form:
m∠1+m∠2=180°
Substituting the values we get:
3x°+(x+48)°=180°
or, 4x°+48°=180°
or, 4x°=180°-48°
or,4x°=132°
or, x°=33°
Hence the value of x is 33°.
Disclaimer: The complete question should be: if m< 1=3x° and m2 = (x+48)° are supplementary find the value of x.
To learn more about supplementary angles visit:
https://brainly.com/question/13045673
#SPJ9
Determine all the unknown values of the figure Devon is hired by the city to create a scale mural of a local park. Devon is exactly 6 feet tall but in the mural, he is 4.5 feet tall. If the tree in the park is 30 feet tall, how tall should the tree be in the mural?
The tree will be feet tall in the mural.
Answer:
F=10, S=26
Step-by-step explanation:
We know that the base is 24. Using that information, 10^2+24^2=26^2 which is a pythagorean triple
The height of the tree in the mural should be 22.5 feet.To determine the height of the tree in the mural, we can set up a proportion using the given information:
Devon's height in the mural: 4.5 feet
Devon's actual height: 6 feet
Tree's height in the mural: Unknown (let's denote it as x)
Tree's actual height: 30 feet
The proportion can be set up as follows:
(Devon's height in the mural) / (Devon's actual height) = (Tree's height in the mural) / (Tree's actual height)
(4.5 feet) / (6 feet) = x / (30 feet)
Now, let's solve for x by cross-multiplying:
4.5 feet * 30 feet = 6 feet * x
135 feet = 6x
Now, divide both sides of the equation by 6 to find x:
x = 135 feet / 6
x = 22.5 feet
So, the height of the tree in the mural should be 22.5 feet.
To know more about tree:
https://brainly.com/question/33583331
#SPJ2
help pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
f(x) = 4x³ - 7x + 5
f(x) = 4x³ - 7x + 5(a). f(0) = 5
f(x) = 4x³ - 7x + 5(a). f(0) = 5 Check
f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,
f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula above
f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5
f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5
f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓
f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) =
f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) = Using the formula above,
f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) = Using the formula above, f(7) = 4(7)³ - 7(7) + 5
f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) = Using the formula above, f(7) = 4(7)³ - 7(7) + 5 = 4(343) - 49 + 5
f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) = Using the formula above, f(7) = 4(7)³ - 7(7) + 5 = 4(343) - 49 + 5 =1372 - 54
f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) = Using the formula above, f(7) = 4(7)³ - 7(7) + 5 = 4(343) - 49 + 5 =1372 - 54 = 1318
f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) = Using the formula above, f(7) = 4(7)³ - 7(7) + 5 = 4(343) - 49 + 5 =1372 - 54 = 1318
(c). f(-5) =
Using the formula above
f(-5) = 4(-5)³ - 7(-5) + 5
= 4(-125) + 35 + 5
= -500 + 40
= -460
*remember to use a calculator to check the answers
Hope this helps xoxo....
Answer: 1328
Step-by-step explanation:
4*7^3 - 7*7 + 5 = 1328
A rectangular lawn is 20 yards by 28 yards. It would cost $4.80 per yard to install a fence around the lawn. How much would it cost to put a fence around the lawn?
HELLO CAN SOMEONE PLEASE ANSWER THIS MATH QUESTION ASAP I WILL MARK YOU THE BRAINLIEST
The expression for one fifth the difference of a number and 17 is B. 1/5( n - 17).
How to illustrate the information?It should be noted that an expression is used to show the relationship between the variables.
In this case, the information is to find the expression for one fifth the difference of a number and 17.
Let the number be n. The expression will be:
1/5( n - 17).
In conclusion, the correct option is B.
Learn more about expressions on:
brainly.com/question/25968875
#SPJ1
1. Han's teacher asked him to draw a polygon similar to polygon A. Here is his work.
Which explanation shows that polygons A and C are similar to each other?
A. Use a protractor to measure all four angles in polygon A and all four angles in
polygon C. Since each angle in polygon A has a matching angle measure in
polygon C, the polygons are similar.
Since each side in polygon C is three times as long as the corresponding side in
polygon A, the figures are similar.
C. Dilate polygon C with center at the upper-left vertex and a scale factor of
Then, translate 7 units to the left. Since polygon C can be taken to polygon A
with a dilation followed by a translation, the figures are similar.
D. Dilate polygon C with center at the upper-right corner and a scale factor of 3.
Since polygon C can be taken to polygon A with a dilation, the polygons are
similar.
Difference between a Keynesian economists and classical economists and their views on how they would respond to an economy falling into a recession
Classical economics emphasizes that unfastened markets provide efficient results and are self-regulating.
Classical economics means that the long time mixture deliver curve is inelastic, therefore any divergence from complete employment is most effective transitory. The Classical version emphasizes the want of minimizing authorities interference and operating to preserve markets freed from any impediments to effective functioning.
Keynesians declare that because of imperfect markets, the economic system can function at less than full potential for an extended period of time.
Keynesians consider that expansionary economic policy (authorities intervention) has a larger role in overcoming recession.
The Keynesian angle on lengthy-run mixture deliver differs.
To learn more about Keynesian economists and classical economists from the given link:
https://brainly.com/question/27961496
#SPJ9
How do you find out how many times a number goes into another number? What math do you do?
Answer:
Divide one number by the other, your quotient is the answer.
K
A certain group of test subjects had pulse rates with a mean of 78.9 beats per minute and a standard deviation of 11.7 beats per minute. Use the range rule of thumb for identifying
significant values to identify the limits separating values that are significantly low or significantly high. Is a pulse rate of 92.3 beats per minute significantly low or significantly high?
Significantly low values are beats per minute or lower
(Type an integer or a decimal.
Do not round)
Significantly high values are
(Type an integer or a decimal. Do not round)
Is a pulse rate of 92.3 beats per minute significantly low or significantly high?
beats per minute or higher.
OA. Significantly low, because it is more than two standard deviations below the mean
OB. Neither, because it is within two standard deviations of the mean
OC. Significantly high, because it is more than two standard deviations above the mean
OD. It is impossible to determine with the information given
B. Neither, because it is within two standard deviations of the mean.
Given; A certain group of test subjects had pulse rates with a mean of 78.9 beats per minutes.
Standard deviation of 11.7 beats per minute.
Range Rule of Thumb:
Standard deviation = Range/4.
Range = 4×SD.
= 4×11.7
= 46.8
The "usual" range for this situation is,
78.9-2(11.7) to 78.9+2(11.7) = 55.5 to 102.3
Significantly low will be less than 55.5
Sig high will be greater than 102.3
Pulse rate - Mean = 92.3 - 78.9 = 13.4
This value below mean
Then check 2×Standard deviation = 2×11.7= 23.4
This value is also below the mean value.
Significantly low values are 55.5 beats per minute or lower.
Significantly high values are 102.3 beats per minute or higher.
Hence it is within two standard deviations of the mean.
Therefore, the answer is B Neither, because it is within two standard deviations of the mean.
To learn more about Standard deviation visit:
https://brainly.com/question/14747159
#SPJ1
What is the slope of a line that is parallel to –x + 3y = 6 Responses 1/3 StartFragment, 1/3, -1 StartFragment, -1, 3 StartFragment, 3, 6
The slope of the line parallel to the line –x + 3y = 6 is a 1/3 option (A) 1/3 is correct.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that:
The equation of the line:
–x + 3y = 6
Write the equation in standard form:
y = x/3 + 6/3
y = x/3 + 2
m = 1/3
The slope of the line parallel to the line –x + 3y = 6
M = 1/3
Thus, the slope of the line parallel to the line –x + 3y = 6 is a 1/3 option (A) 1/3 is correct.
Learn more about the slope here:
brainly.com/question/3605446
#SPJ1
Marie sells outdoor grills. She knows she earns a 10% commission on the first $10,000 and 12% on the next $15,000. She does not remember the rate on the sales of more than $25,000 but her total sales for the month are $29,665, and her total commission is $4,891. What is her rate of commission for the sales over $25,000?
The commission rate is 44.8%.
What is the commission rate?The first step is to determine the commission on the first $10,000 : 0.1 x 10,000 = 1,000
The second step is to determine the commission on the next $15,000: 0.12 x $15,000 = $1,800
The third step to determine the commission on amounts more than $25,000 : x%(29,665 - 25,000)
x%(4,665)
Total commissions earned on amount more than $25,000 : $4,891 - (1,800 + 1,000) = $2091
Now, determine the commission rate : $2091 / $4,665 = 0.448 = 44.8%
To learn more about commissions, please check: https://brainly.com/question/20987196
#SPJ1
Jordan and Ellen recycle cans. Jordan recycles 7 cans for every 12 cans Ellen recycles. Last week, Jordan recycled 42 cans.
What number, c , can be multiplied by 12 to determine the number of cans Ellen recycled last week? How many total cans did Jordan and Ellen recycle last week?
Answer:
c = 6
Total: 114
Step-by-step explanation:
The ratio of the number of cans Jordan recycles to the number Ellen recycles is 7:12.
The ratio of the number of cans Ellen recycles to the number of cans Jordan recycles is 12:7.
Jordan recycled 42 cans.
Ellen recycled 42 × 12/7 = 6 × 12
c × 12 = 6 × 12
c = 6
Total: 42 + 72 = 114
Can someone explain please?
sketch the graphs 3y+2x=1
Answer: y= -2/3 x + 1/3
Step-by-step explanation:
The first thing you need to do is but it into standard y = mx + b form, where m is the slope of the line and b is the y-intercept. Using algebra, we can turn 3y + 2x = 1 into y = -2/3x + 1/3. the slope is -2/3 which means you start at the y-intercept (0,1/3) and go down 2 and to the right 3. Putting it on paper or in a graphing simulator will give you this line. The point on the y-axis is the y-intercept and the point on the x-axis is the x-intercept.
Answer:
make 3y subjet of the fomulae then subtract 2x then divide by 3 both sides then the ans will be y= -2x+1/3
a bag contains 2 green, 4 blue, and 3 yellow disks. alana selects 4 disks from the bag at random, one at a time, without replacing them. what is the probability that she selects all 4 blue disks?
The probability that she selects all 4 blue disks is 0.0317.
What is probability?The probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Now, according to the question;
There is a total of 2 green disks.
There is a total of 4 blue disks.
There is a total of 3 yellow disks.
The formula for selecting the combination of 4 blue disks are
Probability = (combination for 4 blue)/ Total combination for 9.
The combination is given by the relation;
ⁿCₓ = n!/{x!(n-x)!}
The combination for getting 4 blues is-
n is the total blue disks = 9
x is the selected blue disks = 4
⁹C₄ = 9!/{4!(9-4)!} = 126
The required probability = 4/126
The required probability = 0.0317
Thus, the probability that she selects all 4 blue disks is 0.0317.
Learn more about the probability here:
brainly.com/question/11234923
#SPJ1
if x=-5,0,4,8,13 and y=-7,3,11,19,29 what is the slope of the line
The slope of the line is 1/2.
What is slope?The slope is a measure of the steepness of a line, or a section of a line, connecting two points.
Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.
For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).
Given:
x=-5,0,4,8,13 and y=-7,3,11,19,29
To find the slope
m= (0-(-5))/(3-(-7))
m=0+5/ 3+7
m=5/10
m= 1/2
Hence, the slope is 1/2.
Learn more about slope here:
https://brainly.com/question/14548961
#SPJ1
A box has 15 ping pong balls in it, numbered 1 through 15. How many distinct sets of four different numbers can be chosen from the box of ping pong balls if the order in which the numbers are chosen is not important?
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]
Which of the following could be a real-world description of the quantity two times x end quantity divided by 2x/10?
The real-world description of the expression could be: John's age is one-fifth of his sister's age
How to determine the real-world description of the expression?The expression is given as:
2x/10
To determine the real-world description of the expression, we simply represent the variable x with a real-world expression
Take for instance:
x represents the age of a boy
So, the real-world description of the expression could be:
John's age is one-fifth of his sister's age
Read more about expressions at:
https://brainly.com/question/723406
#SPJ1
