QT = 36
Step-by-step explanation:
Step 1 :
Lines RT and SV are the diagonals of the parallelogram RSTV.
Step 2 :
The diagonals of a parallelogram bisect each other . (Properties of a parallelogram)
Step 3 :
Given that the diagonals RT and SV intersect at Q, we have QT = RQ.
=> 5 x + 1 = 3 x + 15
=> 5 x - 3 x = 15 -1
=> 2 x = 14
= > x = 7
Step 4:
QT = 3 x + 15
=> QT = 3 * 7 + 15
=> QT = 21 + 15 = 36
Applying the properties of the diagonal of a parallelogram, the length of QT = 36 units.
Diagonals of a ParallelogramThe diagonals of a parallelogram are always congruent to each other.When the diagonals intersect, they bisect each other, that is, they cut each other into equal segments.Therefore,
RQ = QT
Substitute5x + 1 = 3x + 15
Add like terms5x - 3x = -1 + 15
2x = 14
x = 7
QT = 3x + 15
Plug in the value of xQT = 3(7) + 15
QT = 36
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Joe, John and Jason are each a year apart in age. If the
sum of their ages i 39, how old is Jason?
equality
Substitute and Check (Answer in a Complete Sentence
HELP PLEASE!!!
Answer:
Jason is 14 year old.
Step-by-step explanation:
Given: Joe, John and Jason are each a year apart in age.
Sum of their age is 39.
Lets assume the age of Joe be x
∴ Age of Jahn will be [tex](x+1)[/tex]
And age of Jason will be [tex](x+2)[/tex]
Now, putting up an equation for the sum of their age.
∴ [tex]x+(x+1)+(x+2)= 39[/tex]
Opening the parenthesis.
⇒[tex]x+x+1+x+2= 39[/tex]
⇒[tex]3x+3= 39[/tex]
Subtracting both side by 3
⇒ [tex]3x= 36[/tex]
Dividing both side by 3
⇒[tex]x= \frac{36}{3}[/tex]
∴ [tex]x= 12\ years[/tex]
Hence, Joe is 12 year old.
Next subtituting the value of x to find age of Jason and John.
Jason= [tex](x+2)= 12+2[/tex]
∴Jason= 14 years.
John age= [tex](x+1)= 12+1[/tex]
∴ John Age= 13 years.
Hence, Jason is 14 year of age.
Lauryn grew p tomato plants. Padma grew 5 fewer than 3 times the number Lauryn grew. Kent grew 6 more than 4 times the number Lauryn grew. Choose an expression and a simplified expression to represent the total number of tomato plants that Lauryn, Padma, and Kent grew. Select all that apply.
A. p + (3p – 5) + (4p + 6)
B. p + (5 – 3p) + (6 + 4p)
C. p + 11
D. 8p + 1
E. 7p – 1
Answer:
the anwser is a
Step-by-step explanation:
The expression represents the total number of tomato plants is [tex]\rm p + (3p - 5) + (4p + 6)[/tex].
Given that
Lauryn grew p tomato plants.
The Padma grew 5 fewer than 3 times the number Lauryn grew.
Kent grew 6 more than 4 times the number Lauryn grew.
We have to determine
Choose an expression and a simplified expression to represent the total number of tomato plants that Lauryn, Padma, and Kent grew.
According to the question
Let the number of tomato plants be p.
Lauryn grew p tomato plants.
[tex]\rm = p[/tex]
The Padma grew 5 fewer than 3 times the number Lauryn grew.
[tex]\rm= 3p-5[/tex]
Kent grew 6 more than 4 times the number Lauryn grew.
[tex]\rm = 4p+6[/tex]
Therefore,
An expression to represent the total number of tomato plants = Lauryn + Padma + and Kent grew.
[tex]\rm p + (5 - 3p) + (6 + 4p)[/tex]
Hence, the expression represents the total number of tomato plants is [tex]\rm p + (3p - 5) + (4p + 6)[/tex].
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3. (3x + 4) - (x + 2)
I don't understand plz help
Step-by-step explanation:
Perhaps you want to simplify the given expression: Let's do it.
[tex](3x + 4) - (x + 2) \\ \\ = 3x + 4 - x - 2 \\ \\ = 3x - x + 4 - 2 \\ \\ = 2x + 2 \\ this \: is \: the \: simplest \: form \: of \: the \: \\ given \: expression.[/tex]
Answer:
2(x + 1)
Step-by-step explanation:
(3x + 4) - (x + 2)
3x + 4 - x - 2
3x - x + 4 - 2
2x + 2
2(x + 1)
Are 10(e+0.5g) and 10e+5g not equivalent or equivalent?
Are 6(p+q) and 6p+q not equivalent or equivalent?
Are 7y-15+2y and 9y-15 not equivalent or equivalent?
Are 1+(8r+9) and (2+8)+8r not equivalent or equivalent?
Are 0x11+5n and 5n not equivalent or equivalent?
Are 16s-4+s and 12s not equivalent or equivalent?
Are 11dx2 and 22d not equivalent or equivalent?
Are 8m+(9m-1) and 8m-8 not equivalent or equivalent?
Please help me...
(1) 10(e + 0.5)g
Using distributive property, a × (b + c) = a × b + a × c
10(e + 0.5)g = 10 eg + 10 × 0.5g
Therefore, 10(e + 0.5g) and 10e + 5g are not equivalent.
(2) 6(p + q)
Using distributive property,
6(p + q) = 6p + 6q
Therefore, 6(p + q) and 6p + q are not equivalent.
(3) 7y – 15 + 2y
Using commutative property, a + b = b + a
7y – 15 + 2y = 7y + 2y – 15
= 9y – 15
Therefore 7y – 15 + 2y and 9y – 15 are equivalent.
(4) 1 + (8r + 9)
Using associative property, a + (b + c) = (a + b) + c
1 + (8r + 9) = (1 + 9) + 8r
= 10 + 8r
= (2 + 8) + 8r
Therefore 1 + (8r + 9) and (2 + 8) + 8r are equivalent.
(5) 0 × 11 + 5n
Using multiplicative identity property: a × 0 = 0
0 × 11 + 5n = 0 + 5n
= 5n
Therefore, 0 × 11 + 5n and 5n are equivalent.
(6) 16s – 4 + s
Using associative property, a + (b + c) = (a + b) + c
16s – 4 + s = 16s + s – 4
= 17s – 4
Therefore, 16s – 4 + s and 12s not equivalent.
(7) 11d × 2 = 22d
Therefore, 11d × 2 and 22d are equivalent.
(8) 8m + (9m – 1)
Using associative property, a + (b + c) = (a + b) + c
8m + (9m – 1) = (8m + 9m) – 1
= 17m – 1
Therefore, 8m + (9m – 1) and 8m – 8 not equivalent.
Where will her cut be located? Round to the nearest tenth. Genevieve is cutting a 60-inch piece of ribbon into a ratio of 2:3. Since 2 inches are frayed at one end of the ribbon, she will need to start 2 inches in. This is indicated as 2 on the number line. 25.2 in. 29.4 in. 35.1 in. 40.7 in.
Answer:
25.2 in
Step-by-step explanation:
The short piece will have a length that is 2/(2+3) = 2/5 of the entire usable length. The usable length is 60-2 = 58 inches long, so the cut will be ...
(2/5)(58 in) = 23 1/5 in
from the beginning of the usable part. Since the usable part of the ribbon starts 2 inches in, the cut will be 23 1/5 + 2 = 25 1/5 inches from the frayed end of the ribbon.
Answer:
25.2
Step-by-step explanation:
Correct on Edge 2020
A square plot of land has a side length of 50 meters.
It is surrounded by a footpath that is 3 meters wide.
What is the area of the footpath?
50 m
3 m
Your answer
Answer:
636
Step-by-step explanation:
the area of the footpath=
(50m+3m+3m)^2-50^2
What is the radius of a circle whose equation is x2 + y2 + 8x - 6y + 21 = 0?
units
Answer:r=2
Step-by-step explanation:
Answer:
A) 2
Step-by-step explanation:
I got it right on edge 2020.
Hope it helps :)
I purple you have a good year, stay safe.
What is the decimal from of 12%
Answer:
0.12
Step-by-step explanation:
12/100
There can be many based on what the total amount of the number is.
But in this case I'll say 0.12
the numerator of a fraction is 12 the gcf witch stand for great common factor of the numerator and denominator is 4. what is the denominator
Answer:
16.
Step-by-step explanation:
The denominator could be 16.
The GCF of 12 and 16 is 4.
Final answer:
The denominator of the fraction with a numerator of 12 and a GCF of 4 with the denominator is 12. You divide the numerator by the GCF and then multiply the result by the GCF to get the denominator.
Explanation:
The student is asking for the denominator of a fraction when the numerator is 12 and the greatest common factor (GCF) of the numerator and the denominator is 4. To find the denominator, you would divide the numerator (12) by the GCF (4). This gives us 12 ÷ 4, which equals 3. Therefore, the denominator of the fraction must be a number that when divided by the GCF (4) will give us a quotient of 3. Since the denominator is 4 times larger than this quotient, we multiply 3 by 4 to find the denominator. Therefore, the denominator is 3 × 4, which equals 12.
FLAGPOLE Julie is 6 feet tall. If she stands 15 feet from the flagpole and holds a cardboard square, the edges of the square line up with the top and bottom of the flagpole. Approximate the height of the flagpole
Answer:
44 ft
Step-by-step explanation:
Given: Julie is 6 feet tall
She stands 15 feet from the flagpole.
The edges of the square line up with the top and bottom of the flagpole.
Lets assume the height of flagpole be "h".
As given, the edges of the square line up with the top and bottom of the flagpole.
∴ Angle and base of triangle are same then ratio of corresponding sides are also equal.
Now, finding the height of flagpole by using tangent rule.
we know, [tex]tan\theta= \frac{Opposite}{adjacent}[/tex]
Remember, both the angle are equal.
∴ Ratio of opposite and adjacent leg for both right angle triangle= [tex]\frac{6}{15} : \frac{h-6}{15}[/tex]
We can put it; [tex]\frac{6}{15} = \frac{15}{h-6}[/tex]
Solving the equation now
⇒ [tex]\frac{6}{15} = \frac{15}{h-6}[/tex]
Multiplying both side by 15
⇒[tex]6 = \frac{15\times 15}{h-6}[/tex]
Multiplying both side by (h-6)
⇒ [tex]6\times (h-6) = 15\times 15[/tex]
Distributive property of multiplication
⇒ [tex]6h-36= 225[/tex]
Adding both side by 36
⇒[tex]6h= 225+36[/tex]
Dividing both side by 6
⇒[tex]h= \frac{261}{6}[/tex]
∴ [tex]h= 43.5\ feet[/tex] [tex]\approx 44 feet[/tex]
Hence, the height of flagpole is 44 feet.
Final answer:
To approximate the height of a flagpole given that Julie, who is 6 feet tall, lines up a cardboard square with the top and bottom of the flagpole while standing 15 feet away, we can use the principles of similar triangles. This results in a calculation showing that the flagpole is approximately 6 feet tall, the same as Julie's height.
Explanation:
The height of the flagpole can be approximated using similar triangles. Julie is 6 feet tall and stands 15 feet from the flagpole. Using the cardboard square, we understand that the triangle formed by Julie and her shadow is similar to the triangle formed by the flagpole and its shadow. Therefore, we can set up a proportion:
Julie's height / Julie's distance from flagpole = Flagpole's height / Flagpole's distance from cardboard.
If we assume that the cardboard square is held adjacent to Julie, the flagpole's distance from the cardboard is also 15 feet. The proportion simplifies to:
6 feet / 15 feet = Flagpole's height / 15 feet
Cross-multiplying to solve for the flagpole's height gives us:
Flagpole's height = 6 feet × (15 feet / 15 feet) = 6 feet
Therefore, the flagpole is approximately 6 feet tall.
A certain television is advertised as a 29-inch TV (the diagonal length). If the width of
the TV is 20 inches, how many inches tall is the TV?
Answer:
21 inches
Step-by-step explanation:
refer to attached graphics
we can find the height by the Pythagorean theorem.
diagonal² = width² + height²
height² = diagonal² - width²
we are given that diagonal = 29" and width = 20", hence
height² = 29² - 20²
height² = 841 - 400
height² = 441
height = √441 = 21 inches
Convert the complex number z = -7 - 8i from rectangular form to polar form.
The polar form of z = -7 - 8i is:
z = 3√13 (cos 230.2° + i sin 230.2°)
Converting -7 - 8i to polar form:
The rectangular form of a complex number is given by z = a + bi, where a is the real part and b is the imaginary part. In this case, a = -7 and b = -8.
The polar form of a complex number is given by z = r(cos θ + i sin θ), where:
r is the modulus (or absolute value), which represents the distance of the complex number from the origin in the complex plane.
θ is the argument (or angle), which represents the direction of the complex number relative to the positive real axis.
1. Finding modulus (r):
r = √(a² + b²) = √((-7)² + (-8)²) = √(113) = √(13 * 9) = √13 * 3 (using factorization and perfect squares)
Therefore, r = 3√13.
2. Finding argument (θ):
θ = arctan(b/a) = arctan((-8)/(-7)) ≈ 50.2° (using the arctangent function on a calculator). However, this only gives one possible angle for the complex number.
Note: The arctangent function typically outputs values between -90° and 90°, which corresponds to Quadrant 1 or 4 in the complex plane. Since -7 - 8i lies in Quadrant 3, we need to add 180° to get the correct angle:
θ = 50.2° + 180° = 230.2°
Therefore, the polar form of z = -7 - 8i is:
z = 3√13 (cos 230.2° + i sin 230.2°)
Two numbers are respectively twenty percent and ten percent more than the third number. How many percent is the first number more than the second ?
Answer:
10%
Step-by-step explanation:
Let the third number is X.
then first number = (100-30)% of X
= 70% of X = 7X/10
Second number is (63X/100)
Difference = 7X/10 - 63X/100 = 7X/10
So required percentage is, difference is what percent of first number
=> (7X/100 * 10/7X * 100 )% = 10%
5f + 3s +6
use f= 6 and s = 7
Which of the following equations can be a harmonic on a string that is 10 cm long? Select all that apply. (three correct answers)
A.) y=2sin(pi/5 x)
B.) y=2sin(2pi/7 x)
C.) y=2sin(pi/10 x)
D.) y=2sin(10pi x)
E.) y=2sin (5/2pi x)
Answer:
The options are: A, C and D
Step-by-step explanation:
The sine wave has a general form : y = A sin (BX)
Where A is the amplitude and B = 2π/period
So, we will check which of the options will be a harmonic on a string that is 10 cm long.
A.) y=2sin(pi/5 x)
B = π/5 ⇒ period = 2π/B = 2π ÷ π/5 = 2π * 5/π = 10
So, one cycle of y=2sin(pi/5 x) will be a harmonic on a string that is 10 cm long.
B.) y=2sin(2pi/7 x)
B = 2π/7 ⇒ period = 2π/B = 2π ÷ 2π/7 = 7
C.) y=2sin(pi/10 x)
B = π/10 ⇒ period = 2π/B = 2π ÷ π/10 = 20 = 2 * 10
So, half a cycle of y=2sin(pi/10 x) will be a harmonic on a string that is 10 cm long.
D.) y=2sin(10pi x)
B = 10π ⇒ period = 2π/B = 2π ÷ 10π = 1/5 = 10/50
So, 50 cycles of y=2sin(10pi x) will be a harmonic on a string that is 10 cm long.
E.) y=2sin (5/2pi x)
B = 5/2π ⇒ period = 2π/B = 2π ÷ (5/2π) = 4π²/5
So, options A, C and D can be a harmonic on a string that is 10 cm long.
Answer:
A. y=2sin(pi/5x)
C. y=2sin(pi/10x)
D. y=2sin(10pix)
Step-by-step explanation:
A play train travels around a Christmas
tree in a circle. The train track measures 6
feet in diameter. What is the distance that
the train travels?
The distance that the train travels is 18.84 feet
Solution:
Given that,
A play train travels around a Christmas tree in a circle
The train track measures 6 feet in diameter
To find: distance that the train travels
The distance the train travels is equal to the circumference of circle
The circumference of circle is given as:
[tex]C = \pi d[/tex]
Where, "d" is the diameter of circle
From given,
d = 6 feet
[tex]C = 3.14 \times 6\\\\C = 18.84[/tex]
Thus the train travels 18.84 feet
In circle A, ∠BAE ≅ ∠DAE. Circle A is shown. Line segments A B, A E, and A D are radii. Lines are drawn from point B to point E and from point E to point D to form secants B E and E D. Angles B A E and E A D are congruent. The length of B E is 3 x minus 24 and the length of E D is x + 10. What is the length of BE? 14 units 17 units 27 units 34 units
Answer:
The missing figure is attached down
The length of BE is 27 units ⇒ 3rd answer
Step-by-step explanation:
In circle A:
∠BAE ≅ ∠DAELine segments A B, A E, and A D are radiiLines are drawn from point B to point E and from point E to point D to form secants B E and E DThe length of B E is 3 x minus 24 and the length of E D is x + 10We need to find the length of BE
∵ AB and AD are radii in circle A
∴ AB ≅ AD
In Δs EAB and EAD
∵ ∠BAE ≅ ∠DAE ⇒ given
∵ AB = AD ⇒ proved
∵ EA = EA ⇒ common side in the two triangles
- Two triangles have two corresponding sides equal and the
including angles between them are equal, then the two
triangles are congruent by SAS postulate of congruence
∴ Δ EAB ≅ Δ EAD ⇒ SAS postulate of congruence
By using the result of congruence
∴ EB ≅ ED
∵ EB = 3 x - 24
∵ ED = x + 10
- Equate the two expressions to find x
∴ 3 x - 24 = x + 10
- Add 24 to both sides
∴ 3 x = x + 34
- Subtract x from both sides
∴ 2 x = 34
- Divide both sides by 2
∴ x = 17
Substitute the value of x in the expression of the length of BE to find its length
∵ BE = 3 x - 24
∵ x = 17
∴ BE = 3(17) - 24
∴ BE = 51 - 24
∴ BE = 27
The length of BE is 27 units
Answer:
27
Step-by-step explanation:
I TOOK THE QUIZ, AND GOT 100%
The volume of a box is 39.375 inches³. What is the volume of the box if it is scaled down by a factor of 1/10?
The volume of scaled object is 0.039375 cubic inches
Solution:
Given that,
Volume of box = 39.375 cubic inches
Scaled down by a factor = [tex]\frac{1}{10}[/tex]
The volume of a scaled object will be equal to the volume of object times scale factor cubed
Therefore,
Volume of scaled object = Volume of box x scale factor cubed
[tex]Volume\ of\ scaled\ object = 39.375 \times (\frac{1}{10})^3\\\\Volume\ of\ scaled\ object = 39.375 \times \frac{1}{1000}\\\\Volume\ of\ scaled\ object = 0.039375[/tex]
Thus volume of scaled object is 0.039375 cubic inches
One positive number is three larger than another positive number. If sixteen times the reciprocal of the smaller number is added to nine times the reciprocal of the larger number, the sum is one. Find the two number.
Answer: = [tex]\frac{25+\sqrt{949} }{6}[/tex] and y = \frac{25+\sqrt{949} }{6} - 3.
Step-by-step explanation:
Take x as the larger number and y as the smaller number.
x + 3 = y
[tex]\frac{16}{y}[/tex]+ [tex]\frac{9}{x}[/tex] = 1
Substitute x + 3 for y in the second equation.
[tex]\frac{16}{x+3}[/tex]+ [tex]\frac{9}{x}[/tex] = 1
Make a common denominator.
[tex]\frac{16(x) + 9(x+3)}{(x+3)(x)} =1[/tex]
Simplify and get rid of that fraction.
[tex]16x + 9x + 27 = x^{2} + 3x[/tex]
[tex]x^{2} + 3x - 25x - 27 = 0[/tex]
[tex]x^{2} -22x - 27 = 0[/tex]
By quadratic formula (and because they must be positive), x = [tex]\frac{25+\sqrt{949} }{6}[/tex] and then y = \frac{25+\sqrt{949} }{6} - 3.
To solve for the two positive numbers, we can set up an equation and solve for x.
Explanation:Let's call the smaller number x and the larger number x + 3.
From the given information, we can write the following equation:
16(1/x) + 9(1/(x + 3)) = 1
To solve this equation, we can find a common denominator and then simplify:
16(x + 3)/(x(x + 3)) + 9x/(x(x + 3)) = 1
After simplifying and solving for x, we find that the smaller number is 4 and the larger number is 7.
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Expressions 5* 10 product
Answer:
50
Step-by-step explanation:
Expression 5*10 is also known as 5 x 10 which is indeed 50.
Or if 5 is to the power of 10 (5^10) the answer would be 9765625
Hope this helped!
When Sabine set off to climb Mt. Marcy, she had 18 gummi bears in her bag.
When she returned to the lodge, she had 6 gummi bears left. How many
gummi bears did she eat during her hike?
Write a function that gives the car’s value, V(t), t years after it is sold.
Seven divided by four hundred ninety three
Seven divided by four hundred ninety three
Answer:
0.0141987829615
Step-by-step explanation:
Eva and her children went into a restaurant and where they sell hotdogs for $5 each and tacos for $2.50 each. Eva has $30 to spend and must buy at least 7 hotdogs and tacos altogether. If Eva decided to buy 2 hotdogs, determine the maximum number of tacos that she could buy.
Answer: 8 tacos
Step-by-step explanation: 2 hotdogs are $10 as they are $5 each. Tacos are $2.50 each. $2.50 x 8 equals $20. $20 + 10 = $30. Eva can buy 8 tacos.
After buying 2 hotdogs with $10, Eva will have $20 left. With the remaining $20, she can buy a maximum of 8 tacos at $2.50 each.
Explanation:Since Eva is determined to buy 2 hotdogs at $5 each, she will spend $10 on hotdogs. She has a total of $30 to spend, meaning she will have $20 left after purchasing the hotdogs. Tacos cost $2.50 each. Therefore, with the remaining $20, Eva can afford to buy a maximum of 8 tacos (since $20 divided by $2.50 equals 8). This will also meet the condition of purchasing at least 7 hotdogs and tacos in total.
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Every day, Bert spends an hour commuting to and from his office, driving at an average speed of 50 mph and taking the same route each way. How far does Bert live from his office?
When speed and time are known, distance can be calculated using the formula 'distance = speed x time'. Given Bert's speed of 50 mph and travel time of 0.5 hours each way, the distance from his home to the office is calculated to be 25 miles.
Explanation:The subject of this problem is fundamentally about understanding the relationship between speed, time, and distance. In this particular case, Bert is spending a total of an hour commuting to and from office. However, this total time includes both the journey to work and the journey back home so each journey takes half an hour or 0.5 hours. Given that his average speed is 50 mph, we can calculate the distance he travels one way using the formula "Distance = Speed x Time."
So, for Bert:
Distance = 50 mph x 0.5 hours = 25 miles
Therefore, "Bert lives 25 miles from his office."
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Are the magnetic North Pole and the geographic North Pole always the same distance apart
james says that 5 fithes is greater than 9 tenthes is he correct?
Answer:
yes
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
9 tenths is 90. 5 fifths is 25.
How many different ways can 5 baseball players and 4 basketball players be selected from 12 baseball players and 13 basketball players
1507 are the different ways can 5 baseball players and 4 basketball players be selected from 12 baseball players and 13 basketball players
Solution:
Given that,
5 baseball players and 4 basketball players be selected from 12 baseball players and 13 basketball players
This is a combination problem
Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter
The formula is given as:
[tex]n C_{r}=\frac{n !}{r !(n-r) !}[/tex]
Where n represents the total number of items, and r represents the number of items being chosen at a time
Let us first calculate 5 baseball players from 12 baseball players
Here, n = 12 and r = 5
[tex]\begin{array}{l}{12 C_{5}=\frac{12 !}{5 !(12-5) !}} \\\\{12 C_{5}=\frac{12 !}{5 ! \times 7 !}}\end{array}[/tex]
For a number n, the factorial of n can be written as:
[tex]n !=n \times(n-1) \times(n-2) \times \ldots . \times 2 \times 1[/tex]
Therefore,
[tex]\begin{aligned}12 C_{5} &=\frac{12 \times 11 \times 10 \times \ldots \ldots \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} \\\\12 C_{5} &=\frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2} \\\\12 C_{5} &=792\end{aligned}[/tex]
Similarly, 4 basketball players be selected 13 basketball players
n = 13 and r = 4
Similarly we get,
[tex]\begin{aligned}&13 C_{4}=\frac{13 !}{4 !(13-4) !}\\\\&13 C_{4}=\frac{13 !}{4 ! \times 9 !}\end{aligned}[/tex]
[tex]13C_4 = 715[/tex]
Thus total number of ways are:
[tex]12C_5 + 13C_4 = 792 + 715 = 1507[/tex]
Thus there are 1507 different ways
To determine the number of ways to select 5 baseball players from 12, and 4 basketball players from 13, we use the combination formula for both and multiply the results, applying the Counting Principle.
Explanation:The question asks how many different ways can 5 baseball players and 4 basketball players be selected from 12 baseball players and 13 basketball players. This is a problem of combinatorics, specifically the use of combinations, since the order of selection does not matter.
To find the number of ways to select the baseball players, we use the combination formula C(n, k) = n! / (k! * (n-k)!), where 'n' is the total number to choose from, 'k' is the number to choose, and '!' denotes factorial. For the 5 baseball players from 12, it is C(12, 5).
For the basketball players, it's C(13, 4), as we are choosing 4 out of 13. To find the total number of ways to form the group, we multiply these two values together, because each combination of baseball players can be paired with each combination of basketball players, which is an example of the Counting Principle.
So, the calculation is C(12, 5) * C(13, 4).
The ratio of boys to girls in a class is 2 to 3. There are 12 boys in the class. How many girls are in the class?
Answer:
18
you do 2/3=12/n. and find out n (im to lazy to explain sorry)
how would I find x?
Step-by-step explanation:
In the question figure,
∠ 1 = 115 °, ∠ 2 = 115 °, ∠ 3 = 120 °, ∠ 4 = 14x °, ∠ 5 = 133 °, ∠ 6 = 167 °, ∠ 7 = 138° and ∠ 8 = 18x °
To find, the value of x = ?
We know that,
The sum of all angles of heptagon = 1080°
∴ ∠ 1 + ∠ 2 + ∠ 3 + ∠ 4 + ∠ 5 + ∠ 6 + ∠ 7 + ∠ 8 = 1080°
⇒ 115 ° + 115 ° + 120 ° + 14x ° + 133 ° + 167 ° + 138° + 18x ° = 1080°
⇒ 32x ° + 788° = 1080°
⇒ 32x ° = 1080° - 788° = 292°
⇒ x ° = 9.125°
∴ x ° = 9.125°