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In rectangle ABCD, what is the length of BD¯?
Answers
Answer:
BD = √97 cm ≈ 9.849 cm
Step-by-step explanation:
Diagonal BD of rectangle ABCD is the hypotenuse of right triangle ABD. Opposite sides of the rectangle are the same length, so we have ...
AB = 4 cm
AD = 9 cm
The sides are related to the diagonals by the Pythagorean theorem.
Pythagorean theoremThe Pythagorean theorem tells you the relation between sides and hypotenuse of a right triangle:
AB² +AD² = BD²
4² +9² = BD² = 16 +81 . . . . . evaluating the squares
BD = √97 . . . . . take the square root
The length of BD is √97 cm, about 9.849 cm.
Related Questions
PLease helppppppppp!!!
Answers
Answer:
437.068 28.019
Step-by-step explanation:
Not sure how to explain this one....it is what it is
7 ones = 7
3 tens = 30
4 hundreds = 400 added = 437
No tenths = 0
6 hudredths = .06
8 thousandths = .008 added to = 437.068
280 tenths = 280 * 1/10 = 28
19 thousandths = .019 summed = 28.019
Find the third order maclaurin polynomial. Use it to estimate the value of sqrt1.3
Answers
You can use the well-known binomial series,
[tex]\displaystyle (1+x)^\alpha = \sum_{k=0}^\infty \binom \alpha k x^k[/tex]
where
[tex]\dbinom \alpha k = \dfrac{\alpha(\alpha-1)(\alpha-2)\cdots(\alpha-(k-1))}{k!} \text{ and } \dbinom \alpha0 = 1[/tex]
Let [tex]\alpha=\frac12[/tex] and replace [tex]x[/tex] with [tex]3x[/tex]; then the series expansion is
[tex]\displaystyle (1+3x)^{1/2} = \sum_{k=0}^\infty \binom{\frac12}k (3x)^k[/tex]
and the first 4 terms in the expansion are
[tex]\sqrt{1+3x} \approx 1 + \dfrac{\frac12}{1!}(3x) + \dfrac{\frac12\cdot\left(-\frac12\right)}{2!}(3x)^2 + \dfrac{\frac12\cdot\left(-\frac12\right)\cdot\left(-\frac32\right)}{3!}(3x)^3[/tex]
which simplify to
[tex]\sqrt{1+3x} \approx \boxed{1 + \dfrac32 x - \dfrac98 x^2 + \dfrac{27}{16} x^3}[/tex]
You can also use the standard Maclaurin coefficient derivation by differentiating [tex]f[/tex] a few times.
[tex]f(x) = (1+3x)^{1/2} \implies f(0) = 1[/tex]
[tex]f'(x) = \dfrac32 (1+3x)^{-1/2} \implies f'(0) = \dfrac32[/tex]
[tex]f''(x) = -\dfrac94 (1+3x)^{-3/2} \implies f''(0) = -\dfrac94[/tex]
[tex]f'''(x) = \dfrac{81}8 (1+3x)^{-5/2} \implies f'''(0) = \dfrac{81}8[/tex]
Then the 3rd order Maclaurin polynomial is the same as before,
[tex]\sqrt{1+3x} \approx f(0) + \dfrac{f'(0)}{1!} x + \dfrac{f''(0)}{2!} x^2 + \dfrac{f'''(0)}{3!} x^3 = 1 + \dfrac32 x - \dfrac98 x^2 + \dfrac{27}{16} x^3[/tex]
Now,
[tex]\sqrt{1.3} = \sqrt{1+3x} \bigg|_{x=\frac1{10}} \\\\ ~~~~~~~~ \approx 1 + \dfrac32 \left(\dfrac1{10}\right) - \dfrac98 \left(\dfrac1{10}\right)^2 + \dfrac{27}{16} \left(\dfrac1{10}\right)^3 \\\\ ~~~~~~~~ = \dfrac{18,247}{16,000} \approx \boxed{1.14044}[/tex]
Compare to the actual value which is closer to 1.14018.
[tex]\sqrt{1+3x}=1+\frac{3}{2} x-\frac{9}{8} x^{2} + \frac{81}{8}x^{3}[/tex] is the maclaurin polynomial and estimate value of [tex]\sqrt{1.3}[/tex] is 1.14. This can be obtained by using the formula to find the maclaurin polynomial.
Find the third order maclaurin polynomial:Given the polynomial,
[tex]f(x)=\sqrt{1+3x}=(1+3x)^{\frac{1}{2} }[/tex]
The formula to find the maclaurin polynomial,
[tex]f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} + \frac{f'''(0)}{3!}x^{3}[/tex]
Next we have to find f'(x), f''(x) and f'''(x),
[tex]f'(x) = \frac{3}{2}(1+3x)^{-\frac{1}{2} }[/tex] [tex]f''(x) =-\frac{9}{4}(1+3x)^{-\frac{3}{2} }[/tex][tex]f'''(x) = \frac{81}{8}(1+3x)^{-\frac{5}{2} }[/tex]By putting x = 0 , we get,
[tex]f(0)=(1+3(0))^{\frac{1}{2} }=1[/tex] [tex]f'(0) = \frac{3}{2}(1+3(0))^{-\frac{1}{2} }=\frac{3}{2}[/tex][tex]f''(0) =-\frac{9}{4}(1+3(0))^{-\frac{3}{2} }=-\frac{9}{4}[/tex][tex]f'''(0) = \frac{81}{8}(1+3(0))^{-\frac{5}{2} }=\frac{81}{8}[/tex]Therefore the maclaurin polynomial by using the formula will be,
[tex]\sqrt{1+3x}=f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} + \frac{f'''(0)}{3!}x^{3}[/tex]
[tex]\sqrt{1+3x}=1+\frac{3}{2} x-\frac{9}{8} x^{2} + \frac{81}{8}x^{3}[/tex]
To find the value of [tex]\sqrt{1.3}[/tex] we can use the maclaurin polynomial,
[tex]\sqrt{1.3}[/tex] is [tex]\sqrt{1+3x}[/tex] with x = 1/10,
[tex]\sqrt{1+3(1/10)}=1+\frac{3}{2} (1/10)-\frac{9}{8} (1/10)^{2} + \frac{81}{8}(1/10)^{3}[/tex]
[tex]\sqrt{1+3(1/10)}=\frac{18247}{16000} = 1.14[/tex]
Hence [tex]\sqrt{1+3x}=1+\frac{3}{2} x-\frac{9}{8} x^{2} + \frac{81}{8}x^{3}[/tex] is the maclaurin polynomial and estimate value of [tex]\sqrt{1.3}[/tex] is 1.14.
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In one afternoon's shopping Seedevi spent half as much money as Georgia, but $6 more than Amy. If the three of them spent a total of $258, how much did Seedevi spend?
Answers
The amount spent by Seedevi is $66
How to determine the amount spent by Seedevi?From the question, the given parameters are:
Seedevi = half as much money as Georgia,
Seedevi = $6 more than Amy
The three of them = $258
To solve this question, we use the following representations
x = Seedevi
y = Georgia
z = Amy
So, we have the following equations
x = 0.5y
x = 6 + z
x + y + z = 258
Make y and z the subjects
y = 2x
z = x - 6
Substitute y = 2x and z = x - 6 in x + y + z = 258
x + 2x + x - 6 = 258
Evaluate the like terms
4x = 264
Divide by 4
x = 66
Hence, the amount spent by Seedevi is $66
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Express graph in slope intercept form
Answers
Answer:
2/6
Step-by-step explanation:
Count up and over going from one point to the next and you get slope intercept. This one is up 2 over 6
Answer:
y = 1/3x - 3
Step-by-step explanation:
Slope-intercept form follows the format y = mx + b, where m is the slope of the line, and b is the y-intercept.
First let's find the slope. The slope is the amount the graph rises/runs. From point (0,-3), it rises by 1, and runs to the right by 3 where it meets the next point on the graph, meaning that the slope is 1/3.
Now, let's find the y-intercept. The y-intercept is the point on the graph where the line touches the y-axis. In this line, we can clearly see that the line touches (0,-3), therefore, the y-intercept is -3.
Using this information, we can construct the equation y = 1/3x - 3
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.
Answers
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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5. In one game, the final score was Falcons 3, Hawks 1. What fraction and
percent of the total goals did the Falcons score? Show your work in the space
below. Remember to check your solution.
Answers
Answer:
3/4 or 75%
Step-by-step explanation:
Falcons scored 3 and Hawks scored 1, so in total 4 points were scored during the game. Falcons scored 3 out of 4 points, so they scored 3/4 of the points scored in the game.
To convert 3/4 to percentage, divide 3 by 4, multiply the quotient (result after division calculation) by 100, and add % sign after the number.
3/4 = 0.75
Therefore 3/4 is equivalent to 75%.
Answer:
[tex] \frac{3}{4} [/tex]
[tex]75\%[/tex]
Step-by-step explanation:
From the information given from the question, we can deduce:
Total goals scored by both teams = 3 + 1 = 4
Fraction of Goals Scored by Falcons =
[tex] \frac{goals \: scored \: by \: falcons}{total \: goals \: scored \: by \: both \: teams} \\ = \frac{3}{4} [/tex]
To get the percentage, we have to make sure the denominator is 100.
[tex] \frac{3}{4} \\ = \frac{3 \times 25}{4 \times 25} \\ = \frac{75}{100} \\ = 75\%[/tex]
Simplify.
2[(8 ÷ 4)-(-5)] + 6
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{Equation:}[/tex]
[tex]\mathsf{2[(8 \div 4)-(-5)] + 6}[/tex]
[tex]\huge\textsf{Solving:}[/tex]
[tex]\mathsf{2[(8 \div 4)-(-5)] + 6}[/tex]
[tex]\mathsf{= 2[((2 - (-5)] + 6}[/tex]
[tex]\mathsf{= 2(7) + 6}[/tex]
[tex]\mathsf{= 2 \times 7 + 6}[/tex]
[tex]\mathsf{= 14 + 6}[/tex]
[tex]\mathsf{= 20}[/tex]
[tex]\huge\textbf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\frak{20}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Given:▪ [tex] \sf{2[(8 ÷ 4)-(-5)] + 6}[/tex]
First, we will start with the division:
[tex]\longrightarrow \sf{2[(2) − (−5)] +6}[/tex]
Now we will resolve what is inside the bracket:
[tex]\longrightarrow \sf{2[2+5] +6}[/tex]
[tex]\longrightarrow \sf{2 \times 7 +6}[/tex]
Now we will solve the multiplication:
[tex]\longrightarrow \sf{14 +6= 20}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex] \bm{2[(8 ÷ 4)-(-5)] + 6 = \boxed{\bm {20}}}[/tex]
id love the help! (im not great at math)
Answers
Calculate the radius : 12 divided by 2 is 6 inches
Then calculate the area : 6 squared is 36, then mutiply by 3.14. Equals 113.04 inches². I think that’s the answer !
Answer:
Area = 113.04 in^2
Step-by-step explanation:
you have the diameter which is twice the radius, the formula is in the question:
Area = πr^2
so
12: 2 = 6 (RADIUS)
Area = π6 ^ 2 =
Area = π 36 in^2
Area = 3.14 * 36
Area = 113.04 in^2
A container contains 20 liters of milk and another container contains 20 liters of syrup. One liter was taken from each vessel and poured into another vessel. After doing this twice, determine the ratio of milk and syrup in the two types of mixture.
Answers
Answer:
Step-by-step explanation:
20 liters -1 liter = 19 liters of milk
20 liters -1 liter = 19 liters of syrup
This was done twice so therefore;
19 liters -1 liter = 18 liters of milk
19 liters -1 liter = 18 liters of syrup
Therefore the ratio comes to 18:18
18 goes into 18 1 and the same for the other 18. Therefore the ratio comes to ;
1:1
Your final answer is 1:1
-7(-w-1)-2 simplest form
Answers
You can distribute or combine like terms and both work to get the answer
Which statement describes independent events?
A. You write the numbers 1 through 10 on
index cards. You randomly draw two
cards without replacement: a 6 and an 8.
C. You randomly draw a blue marble from a
bag, return the marble, and then
randomly draw a yellow marble.
B. A President and Vice President are
randomly selected from a group of 24
students.
D. You randomly draw four cards from a
standard deck of cards without
replacement. You draw a King, then a
Queen, then a Jack, and then an Ace.
Answers
The statement that describes independent events is:
C. You randomly draw a blue marble from a bag, return the marble, and then randomly draw a yellow marble.
How to determine the statement describes independent eventsIn this case, the events of drawing a blue marble and drawing a yellow marble are independent because the first draw does not affect the probability or outcome of the second draw.
Returning the marble to the bag ensures that each draw is independent of the previous one.
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3
Anastacio distributed 4 4/5 kg of seed among several bird feeders. He put = 3/5 kg of seed in each
feeder. Let f represent the number of bird feeders that Anastacio filled.
Select 1 multiplication and 1 division equation to represent the relationship.
Choose 2 answers:
ƒx3/5=4 4/5
fx 4 4/5=3/5
3/5 divided 4 4/5=f
4 4/5 divided 3/5 =f
Answers
The equations to represent the relationship are ƒx3/5=4 4/5 and 4 4/5 divided 3/5 =f
Ratio and proportionFractions are written as a ratio of two integers. For instance a/b is a fraction.
If Anastacio distributed 4 4/5 kg of seed among several bird feeders and put 3/5 kg of seed in each feeder, the expression that represents the number of bird feeders that Anastacio filled is given as;
Number of bird feeder = 4 4/5 ÷ 3/5
f = 4 4/5 ÷ 3/5
Multiply both sides by
f * 3/5 = 4 4/5 ÷ 3/5 * 3/5
f * 3/5 = 4 4/5
Hence the equations to represent the relationship are ƒx3/5=4 4/5 and 4 4/5 divided 3/5 =f
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What is the quotient of the rational expression below?
3x+1 x-7
x+8 5x
O A.
O B.
O C.
O D.
3x² + x
x²+x-56
15x² +5x
x² +15x-56
15x² +5x
x²+x-56
15x² +1
x²+x-56
Answers
Answer: C
Step-by-step explanation:
[tex]\frac{3x+1}{x+8} \div \frac{x-7}{5x}\\\\=\frac{3x+1}{x+8} \times \frac{5x}{x-7}\\\\=\frac{5x(3x+1)}{(x+8)(x-7)}\\\\=\frac{15x^2 +5x}{x^2 +x-56}[/tex]
Marty went on a bike ride to the store 8 miles away. If it
took Marty 3/4 of an hour to get there and 1/2 of an hour
to get back, what was his average rate of speed (miles
per hour) for the entire trip?
Answers
His average rate of speed for the entire trip is 12.8 miles per hour.
How do you calculate the average rate of speed?The most popular formula for calculating average speed is the distance traveled divided by the time taken.If you know how far something has traveled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time.The overall distance the object covers in a given time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.Average speed is a scalar quantity defined as the average distance traveled by the body in the total amount of time. It measures in m/s.Marty's speed is =V
[tex]\frac{3}{4} V+\frac{1}{2} V=8*2[/tex]
[tex]\frac{5}{4} V=16[/tex]
[tex]V=12.8[/tex]
The average rate of speed for the entire trip is 12.8 miles per hour.
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Solve this system of equations by using the elimination method. x+4y=9 2x-4y=-6
Answers
Answer:
[tex]x=6[/tex]
[tex]y=\frac{3}{4}[/tex]
Step-by-step explanation:
Given the following question:
[tex]x+4y=9[/tex]
[tex]2x-4y=9[/tex]
To solve using the elimination method we will add the two equations together to find the two individual values.
[tex]x+2x=3x[/tex]
[tex]4y-4y=0[/tex]
[tex]9+9=18[/tex]
[tex]3x=18[/tex]
[tex]\frac{3x}{3} =x[/tex]
[tex]18\div3=6[/tex]
[tex]x=6[/tex]
[tex]x+4y=9[/tex]
Substitute six in for x:
[tex]x=6[/tex]
[tex]6+4y=9[/tex]
Solve for y:
[tex]6-6=0[/tex]
[tex]9-6=3[/tex]
[tex]\frac{4y}{4} =y[/tex]
[tex]3=\frac{3}{4}[/tex]
[tex]y=\frac{3}{4}[/tex]
x is equal to 6, and y is equal to 3/4.
Hope this helps.
quien me hace una canción de ley de los cosenos de C por favor le doy 100 estrellas y corona
Answers
Answer:
Step-by-step explanation: all oof it equals to = 2c c2 = b1
Please help me solve this problem with work
Answers
Answer:
m∠B ≈ 51.5°
Step-by-step explanation:
A triangle solver can find this answer simply by entering the data. If you do this "by hand," you need to first find length BC using the Law of Cosines. Then angle B can be found using the Law of Sines.
Length BCThe Law of Cosines tells us ...
a² = b² +c² -2bc·cos(A)
a² = 21² +13² -2(21)(13)cos(91°) ≈ 619.529
a ≈ 24.8903
Angle BThe Law of Sines tells us ...
sin(B)/b = sin(A)/a
B = arcsin(sin(A)×b/a) = arcsin(sin(91°)×21/24.8903)
B ≈ 57.519°
The measure of angle B is about 57.5°.
simplify (b^9)^3
A b^9
B b^6
C b^24
D b^27
Answers
Apply the exponent rule (x^a)^b= x^ab.
(b^9)^3= b^9*3= b^27
Answer this question please
NO FAKE ANSWERS OR I WILL REPORT
Answers
Answer:
D
Step-by-step explanation:
the figure is composed of a rectangle and a right triangle ( top )
calculate the hypotenuse h of the right triangle using Pythagoras' identity
h² = 6² + 8² = 36 + 64 = 100 ( take square root of both sides )
h = [tex]\sqrt{100}[/tex] = 10
the base of the rectangle is equal to h , then perimeter (P) of pentagon is
P = 10 + 4 + 6 + 8 + 4 = 32 cm
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
What does the problem want:
⇒ the dimensions or the perimeter of the pentagon
What information do we need to find the perimeter:
⇒ the unknown side length
Let's find the unknown side length:
[tex]\hookrightarrow \text{split the pentagon into two shapes as shown in the image below}\\\hookrightarrow \text{the hypotenuse of the right triangle is equal to the length of the unknown side}\\\hookrightarrow\text{hypotenuse}=\sqrt{6^2+8^2}= \sqrt{36+64}=\sqrt{100}=10\\[/tex][tex]\hookrightarrow \text{the unknown side length is 10}[/tex]
Perimeter = 6 + 8 + 4 + 4 + 10 = 32
Answer: 32 or (D)
Hope that helps!
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a writer wrote 10,010 words for his book on the first day of writing. he wrote 9,760 words on the second day, 9,510 words on the third day, and continued this way in an arithmetic sequence. write an explicit rule showing the equation for the number of words the writer would write on the 14th day, and solve.
Answers
Answer:
rule: an = 10010 -250(n -1)day 14: 6760 wordsStep-by-step explanation:
The first three terms of the arithmetic sequence for the number of words written are 10010, 9760, 9510. These have a common difference of 9760-10010 = -250. The first term and common difference can be used to make the explicit equation for the words written on the n-th day.
Formula for Arithmetic SequenceThe explicit formula for the n-th term of an arithmetic sequence with first term a₁ and common difference d is ...
[tex]a_n=a_1+d(n-1)[/tex]
ApplicationFor first term a₁ = 10010 and common difference d = -250, the explicit rule is ...
[tex]a_n=10010-250(n-1)[/tex]
On day 14, n=14, and the number of words written is ...
[tex]a_{14}=10010-250(14-1)\\\\a_{14}=10010-250(13)=10010-3250\\\\a_{14}=6760[/tex]
The writer would write 6760 words on the 14th day.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
ABIs parallel to CD, and EFis perpendicular to AB.
The number of 90° angles formed by the intersections of EFand the two parallel lines ABand CDis
Answers
Answer:
8
Step-by-step explanation:
The four angles formed at each intersection of lines are all 90°.
The total number of 90° angles at the two intersections is 2×4 = 8 90° angles.
The square below has an area of x2 + 4x + 4 square meters.
What expression represents the length of one side of the square?
Perfect Squares
Write your answer without any spaces. Ex. x+3
Answers
Answer:
The side length of a square is the square root of its area. We know that:
x2 + 4x + 4 = (x + 2)2
Therefore, the side length of the square is x + 2
What's the circumference of a
circle with a diameter of 31 inches?
Use 3.14 for I.
C = [?] inches
Enter the number that belongs in the green
box. Do not round your answer.
Hint: C = nd
Answers
Answer: C = 97.34 inches
Step-by-step explanation:
C = πd
= 3.14(31)
= 97.34
HELPPP There are 30 pencils in a box (15 pairs). 2 pair(s) are yellow,
3 pairs are brown, and the rest are tan. What is the probability of
pulling out a brown pencil on the first draw?
Write your answer as a reduced fraction.
Answers
Answer:
1/10
Step-by-step explanation:
Probability= number of brown pencil/number of pencil in the box
3/30
=1/10
Answer: 1/5
Step-by-step explanation:
30/15 pairs is 2 pencils per pair. That means there are 4 yellow pencils, 6 brown pencils, and the rest are tan.
30-10=20. There are 20 tan pencils.
6/30 is the probability of a brown pencil being pulled out.
This simplifies to 1/5.
A model train has a scale of 1 in : 3in. if the real train is 12ft tall then how tall is the model train
Answers
If the ratio of a model train to a real train exists 1:3 and the real train exists 12 feet then the model train exists 3 feet long.
How to estimate the ratio of the model train?Given that the model train contains a scale of 1: 3 and the real train exists 12 feet tall.
The ratio indicates how many times one number has another number.
A ratio exists as the relationship in quantity between two things.
It conveys the quantity of one thing in words of another.
The ratio of a model train to a real train exists at 1 inch :3 inches.
Height of model train = 12 [tex]*[/tex] 1/4
Height of model train = 3 inches
Therefore, the ratio of a model train to a real train exists 1: 3 and if the real train exists 12 feet then the model train exists 3 feet long.
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What is the simplified form of the following expression?
2√27+√12-3√3-2√12
O√3
O 9√3
O 11 √3
O 15√3
Answers
Answer:
[tex] \sqrt{3} [/tex]
Step-by-step explanation:
27 is 3×3×3 from square root we can take 3 out as 3^2 elimate square root and remaining 3 is under root
Translate the phrase into a variable expression. Use the letter d to name the
variable. If necessary, use the asterisk (*) for multiplication and the slash
(/) for division.
the number of dollars Paul owes minus 18...
Answer here
Answers
Answer:
d - 18
Step-by-step explanation:
The question said to use d as the variable. We do not know the number of dollars Paul owes. So we put d for that amount.
Then "minus" means to subtract 18.
Writing the expression is all that is being asked for. Translating the words into algebra. We aren't solving anything. Not even writing an entire equation, just an expression, so it has no equals sign.
What equation can be used to find the sum of 4/10 and 7/100
Answers
Answer:
47/100
Step-by-step explanation:
First you have to make the denominators equal.
4/10 * 10/10 = 40/100
40/100 + 7/100 = 47/100
In a grade 11 class there are 30 learners. 16 of them are girls. there are 7 girls and 6 boys with blue eyes. a student is selected at random tone the class monitor what is the probability that the class monitor is a girl
Answers
Answer:
8/15
Step-by-step explanation:
possibilities/ sample size=16 girls/30 "learners"=8/15
30. You want to simulate an experiment to draw cards out of a deck. You
plan to draw 35 cards (with replacement), and list which card you drew. How
many times would you expect to draw a face card?
6
8
12
10
Answers
Using the binomial distribution, you would expected to draw a face card 8 times.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
For this problem, the parameters are given as follows:
n = 35, as the experiment will be repeated 35 times.p = 12/52, as of the 52 cards, there are 12 faces, hence this is the probability of a success on a single trial.Then the expected value is found as follows:
E(X) = np = 35 x 12/52 = 420/52 = 8.
Thus, you would expected to draw a face card 8 times.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
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