[tex]|\Omega|=10^2=100\\|A|=2\cdot3=6\\\\P(A)=\dfrac{6}{100}=6\%[/tex]
Write down the first three and last two terms of the binomial expansion of:
a) (3x+(2/x))^15
b) (2x-(3/x))^20
Answer:
a) [tex](3x)^{15} + 15(3x)^{14}(\frac{2}{x}) + 105(3x)^{13}(\frac{2}{x})^2 + ... + 15(3x)(\frac{2}{x})^{14} + (\frac{2}{x})^{15}[/tex]
b) [tex](2x)^{20} + 20(2x)^{19}(-\frac{3}{x}) + 190(2x)^{18}(-\frac{3}{x})^2 + ... + 20(2x)(-\frac{3}{x})^{19} + (-\frac{3}{x})^{20}[/tex]
Step-by-step explanation:
The binomial expansion formula is:
[tex](a + b)^n = a^n + \binom{n}{1}a^{n-1} b + \binom{n}{2}a^{n-2}b^2 + ... + \binom{n}{r}a^{n-r}b^{r} + ... + b^n[/tex]
The (n r) in front of each term is the binomial coefficient. This can be calculated on a calculator using the nCr button (in this case, you'd put 15C1 for (n 1), 15C2 for (n 2), etc). This can be calculated without a calculator using this formula:
[tex]\binom{n}{r} = \frac{{n!}}{{r!\left( {n - r} \right)!}}[/tex]
In a), a = 3x, b = 2/x and n = 15.
You can plug these into the formula above to get:
[tex](3x)^{15} + 15(3x)^{14}(\frac{2}{x}) + 105(3x)^{13}(\frac{2}{x})^2 + ... + 15(3x)(\frac{2}{x})^{14} + (\frac{2}{x})^{15}[/tex]
Here's how to do this without the formula:
Start with the a^nIn the second term, you subtract 1 from a's power (in this case, 15 to 14) and add 1 to b's power (0 to 1). Then you multiply it by nCr.This keeps going until you get to b^n. To check you've done it correctly, the powers of a and b in each term should add up to n. For example, in term 3 above, a's power is 13 and b's power is 2. These add to make 15.Remember, a's power goes down by 1 each time, and b's power goes up by 1 each time. There is no b in the first term because b^0 = 1.You could 'simplify' this by expanding the brackets, but this gives you massive numbers so it's probably best to leave it like this.
Applying this to b):
a = 2x, b = -3/x, n = 20
[tex](2x)^{20} + 20(2x)^{19}(-\frac{3}{x}) + 190(2x)^{18}(-\frac{3}{x})^2 + ... + 20(2x)(-\frac{3}{x})^{19} + (-\frac{3}{x})^{20}[/tex]
please help me
i need this for my homework
Answer:
As ΔABC is an isosceles triangle:
⇒ BA = BC
(the dashes on the line segments indicate they are of equal measure)
⇒ ∠BAC = ∠BCA = 55°
⇒ ∠BCA = ∠BAD = 55°
Angles on a straight line sum to 180°
⇒ ∠ADE + ∠EDC = 180°
⇒ 98° + ∠EDC = 180°
⇒ ∠EDC = 82°
As BE intersects AC, the vertically opposite angles are equal:
⇒ ∠BDC = ∠ADE = 98°
⇒ ∠ADB = ∠EDC = 82°
Interior angles in a triangle sum to 180°
⇒ ∠BAD + ∠ADB + ∠ABD = 180°
⇒ 55° + 82° + ∠ABD= 180°
⇒ ∠ABD = 180° - 55° - 82°
⇒ ∠ABD = 43°
Answer:
∠ABD = 43°
Step-by-step explanation:
Let's solve !
⇒ ∠BAC = ∠BCA = 55° (Angles opposing equal sides)
⇒ ∠BDA = 180° - 98° (Linear pair)
⇒ ∠BDA = 82°
⇒ ∠BAC + ∠BDA + ∠ABD = 180° (Angle Sum Property)
⇒ ∠ABD + 82° + 55° = 180°
⇒ ∠ABD + 137° = 180°
⇒ ∠ABD = 43°
The quadrilaterals JKLM and PQRS are similar.
Find the length x of QR.
K
Q
7
M
2
Z
3.6
S
1.8
A
X
3.6
R
Answer:
x = 6.3
Step-by-step explanation:
since the quadrilaterals are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{QR}{KL}[/tex] = [tex]\frac{RS}{LM}[/tex] ( substitute values )
[tex]\frac{x}{7}[/tex] = [tex]\frac{3.6}{4}[/tex] ( cross- multiply )
4x = 7 × 3.6 = 35.2 ( divide both sides by 4 )
x = 6.3
Q1.Simplify:
(I) {1³+2³}×(1/3) ²
(II) {5^-1×4^-1}²
(III) {(1/3) ^-1×(1/2)^-2}÷(1/4) ^-3
Give correct answer I will mark as brianlist. It wrong will deleated.
[tex]\textbf{(i)}\\\\\{1^3 +2^3 \} \times \left(\dfrac 13 \right)^2\\\\=(1+8) \left(\dfrac 19 \right)\\\\=9\left(\dfrac 19 \right)\\\\=1\\\\[/tex]
[tex]\textbf{(ii)}\\\\\{5^{-1}\times 4^{-1}\}^2\\\\=\left(5^{-1} \right)^2 \times \left(4^{-1} \right)^2~~~~~~~~~~~;[(ab)^m = a^mb^m]\\\\=5^{-2}\times 4^{-2}~~~~~~~~~~~~~~~~~~~~;[(a^m)^n = a^{mn}]\\\\=\dfrac 1{5^2} \times \dfrac 1{4^2}~~~~~~~~~~~~~~~~~~~~~~;\left[a^{-m} = \dfrac 1{a^m},~ a\neq 0 \right]\\\\=\dfrac{1}{400}\\\\=0.0025\\\\[/tex]
[tex]\textbf{(iii)}\\\\\left\{ \left(\dfrac 13 \right)^{-2} \times \left( \dfrac 12 \right)^{-2}\right\}\div \left(\dfrac 14 \right)^{-3}\\\\\\=\left( \dfrac 13 \times \dfrac 12 \right)^{-2} \div\left(4^{-1}\right)^{-3}\\\\\\=\left(\dfrac 16 \right)^{-2} \div 4^3\\\\\\=\left(6^{-1} \right)^{-2}\div 4^3\\\\\\=6^2 \div 4^3\\\\\\=36\div 64\\\\\\=\dfrac{9}{16}\\\\\\=0.5625[/tex]
An angle of measure to the angle opposite it is a right angle. True or false
Answer:
True
Step-by-step explanation:
22+6[(14-5)÷3(17-14)]
I got 76 and every calculator I use says 76 but in the back of the book it says the answer is 28. Am I missing something or could it be a typo?
My work:
22+6[(14-5)÷3(17-14)]
22+6[(9)÷3(3)]
22+6 [(3)(3)]
22+6(9)
22+54 = 76
The simplification of the expression is 28. The mistake in your calculation occurred in step 3.
What is the process involved in simplifying expression involving brackets?TO simplify expressions involving brackets, we use a common method called BODMAS (Brackets, Of, Division, Multiplication, Addition, and Subtraction).
This means that we will first solve the expression in brackets first, followed by division, multiplication, addition, and subtraction as the case may be.
Now, from the given information, we have:
= 22+6[(14-5)÷3(17-14)]
solving parameters in the bracket first, we have:
= 22 + 6[(9) ÷3(3)]
= 22 + 6[(9) ÷9]
The above step is where you missed it from your calculation, you must first open all brackets within brackets before solving them.= 22 + 6[(9) ÷9]
= 22 + 6[ 1]
= 22 + 6
= 28
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Look at the dot plots below. Compare the shapes of the distributions of the results from the two experiments.
The shape of experiment 1 is roughly bell shaped. This indicates that it is normally distributed. The shape of experiment 2 is asymmetrical. This indicates that it is not normally distributed.
What is a dot plot?
A dot plot is a graph that is used to represent the frequency of a data set using dots. The dots represents the frequency of a number. The results from experiment 1 is more spread out over the numbers compared to experiment 2 which is concentrated around the center.
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Line segment AB has endpoints A(1,8) and B(7,−4). What are the coordinates of the point located 5/6 of the way from A to B?
O (-4, 11 1/3)
O (3, -2 1/3)
O (6, -2)
O (12, -14)
The coordinate of the point is (6,-2)
How to determine the coordinate of the point?The given parameters are:
A = (1,8)
B = (7,-4)
The location of the point (i.e 5/6) means that the ratio is:
m :n = 5 : (6 - 5)
m : n = 5 : 1
The coordinate of the point is then calculated as:
[tex](x,y) = \frac{1}{m + n}* (mx_2 + nx_1,my_2 + ny_1)[/tex]
So, we have:
[tex](x,y) = \frac{1}{5 + 1}* (5 * 7 + 1 * 1 , 5 * -4 + 1 * 8)[/tex]
Evaluate
[tex](x,y) = \frac{1}{6}* (36 , -12)[/tex]
Evaluate the product
(x,y) = (6,-2)
Hence, the coordinate of the point is (6,-2)
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- 34+(- 23) please fast
Answer:
The answer to this question is -11
A soccer player stands at a point that is modeled by (0, 0) on the coordinate plane.
he then kicks a soccer ball that is modeled by a quadratic equation.
select all key features that help determine the vertical height that the soccer ball
traveled from when it left the ground to when it reached its maximum height.
- y-intercept
- zeros
- vertex
- end behavior
Answer:
the answer to the question above would be the option 3 (vertex)
could someone please help will give brainliest
Answer:
A - x = 4
Step-by-step explanation:
According to The Midsegment Trapezoid Theorem the length of the midsegment is the sum of both bases divided by 2.
So to find the value of x:
x + 3 + 4x 7 = 15*2 add like terms
5x + 10 = 30 subtract 10 from both sides
5x = 20 divide both sides by 5
x = 4
Is believed that 80% of adults are honest an honesty experiment was conducted on a random sample of 50 adultsit was discovered that 42 of the adults were honestthe researcher would like to know if the data provide convincing evidence that more than 80% of adults are honest are the conditions for inference met? yesthe conditions for inference are met no, the 10% condition is not met no, the large counts condition is not met no, the randomness condition is not met
The first option, “yes, the conditions for inference are met” is correct.
What are population and sample?It is described as a collection of data with the same entity that is linked to a problem. The sample is a subset of the population, yet it is still a part of it.
Lets you're conducting an experiment on the honesty of a random sample of 50 persons. A total of 42 adults were assessed to be trustworthy.
It has to be determined whether the conditions of inference are satisfied.
A) The randomness of the sample.
The sample is given to be randomly selected. So, this condition is satisfied.
B) The number of success and failures must be at least 10.
The success rate is 0.80, and the sample size is 50. As a result, the following conditions must be met:
[tex]\rm n_p\geq 10 \ and \ n\left ( 1-p \right )\geq 10[/tex]
[tex]\rm 50\left ( 0.80 \right )=40 > 10[/tex]
[tex]\rm 50\left ( 1-0.80 \right )=10=10[/tex]
As a result, the sample size is sufficient, and the big numbers requirement is met.
C) 10% condition:
The sample size is modest, at 50 people, and hence represents less than 10% of the population.
As a result, the inference requirements are met.
Thus, the first option “yes, the conditions for inference are met” is correct.
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fractions and decimals
T_T
1. 0.0563
2. 0.05
3. 0.008
4. 0.6
5. eight tenths
6. six tenths three hundredths
7. eight five thousandth
8. six hundredths
what is a good approximating for 4pi^3
Answer: 123.84
Step-by-step explanation: You can set pi as 3.14. Then, you get 123.836576. Round to the nearest hundredth to get 123.84.
Which table represents a function?
Answer:
The one on the top left
Step-by-step explanation:
What makes a function, a function is that the x coordinate (x,y), cannot be repeated in the tables. The y coordinate can though.
1/4 of the players on every team are girls. Write 3 fractions equivalent to 1/4
Answer:
2/8, 3/12 and 4/16
Step-by-step explaination:
All these fractions are equivalent to 1/4 as the numerator is a multiple of 1, the denominator is a multiple of 4, and the numerators are all a quarter of their respective denominators.
What is the measure of USQ⌢
A triangle has a base length of 2ac2 and a height 6 centimeters more than the base length. Find the area of the triangle if a = 4 and c = 2.
The area of the triangle is 608 cm².
What is area?Area is the region bounded by a plane shape.
To calculate the area of the triangle, we use the formula below.
Formula:
A = bh/2............................ Equation 1Where:
A = Area of the triangleb = Base of the triangleh = Height of the triangleFrom the question,
Given:
b = 2ac²If
a = 4, c = 2b = (2×4×2²) = 32 cmh = (32+6) = 38 cmSubstitute these values into equation 1
A = (32×38)/2A = 608 cm²Hence, the area is 608 cm².
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need help with this ASAP: methods for solving right triangles.
Explanation:
1) sin(37º)=x/10.3————>trigonometric ratio (sine)
2)7²+10²=c²—————-> pythagorean theorem
3) using sine—————> sin(51º)=9/x
using tangent —————> tan(51º)=9/x and x = 7.3 (rounded)
4)using pythagorean theorem————> 6²+7²=c²
angle b is tanx=6/7 where x = 40.6 degrees, angle a is tanx=7/6 where x = 49.4
Answers:
1)x= 6.2
2)x= 12.2
3)x= 11.6 (rounded)
4)x= 9.2
credit to genan for question 3 and 4
ur welcome :)
correct me if im wrong
brainliest please?
1. There are 10 cards. 4 of them are of green color and another 6 are of
orange color. Steve picks a card at random. What is the
probability of green?
did I solve this problem right?
Step-by-step explanation:
¿qué es eso?¿es esto importante? :)
5. Find the value of the 11th term of the arithmetic sequence
-2, 5, 12, 19, 26, ...(11th term)
Answer:
-2, 5, 12, 19, 26, 33, 40, 47, 54, 61, 68, 75, 82, 89, 96, 103
10 A group of young men decided to raise sh 480 000 to start a business.. Before the actual payment was made, four of the members pulled out and each of those remaining had to pay an additional sh 20 000. Determine the original number of members.
A group of young men decided to raise Ksh.480000 to start a business. Before actual payment was made four members pulled out and each of the remaining had to pay an additional Ksh.20000. Write an expression in terms of P for.
(a) (i) Original contribution of each member.
(ii) Contribution after withdrawal of four members.
(b) Form an equation in P and hence determine the number of initial members.
(c) Three men Kamau, James and Hassan shared Shs.480000 such that Kamau: James is 3: 2 and James: Hassan is 4: 2. Find how much each got.
A runner runs a distance of 350 metres in a time of 50 seconds.
What is his average speed?
Answer:
7
Step-by-step explanation:
350÷50=7
................
if abcd is a parallelogram with AB=3x-4 , BC= 2x+7 and CD = x+18 what type of paralleogram is ABCD
Answer:
rhombus
Step-by-step explanation:
If ABCD is a parallelogram, then AB and CD are opposite sides and should be equal
3x - 4 = x + 18
subtract x.
2x - 4 = 18
add 4.
2x = 22
divide by 2.
x = 11
Find the lengths of the sides.
AB= 3(11)-4 = 29
BC= 2(11)+7 = 29
CD = 11+18 = 29
If BC is 29, then DA must also be 29. So all four sides are the same, it is a rhombus.
Suppose you have the following null and alternative hypothesis
A type I error takes place if a given null hypothesis is rejected but is said to be true in the population such as the forecast shows it is snowing outside but actually it is isn't.
What is type 11 error?A type II error is known to be a statistical term that tells the error that takes place when one fails not to accept a null hypothesis that is said to be really false. A type II error create a false negative.
It known is known also as an error of omission. Example is the forecast shows that It is not snowing but it is actually snowing.Note that:
Type I error is false positive.Type II error is false negative.The power of the test shows that:
The Power is the likelihood of rejecting the null hypothesis even if it is false.Power is the likelihood of making the right decision that is to reject the null hypothesis even if the null hypothesis is false.Power is the likelihood of not making a Type II error and others.See full question below
Suppose you have the following null and alternative hypothesis:
H o: it is snowing.
H a: It is not snowing
(A) in the context of this problem, describe a Type-1 error
(B) Describe Type II error
(C)Describe power of the test
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Mark is a professional race car driver. He has competed in 15 races and won 40% of them. How many races has Mark won?
3 races
6 races
9 races
37 races
Answer:
6 races
Step-by-step explanation:
If he won 40% of the races he competed in, and he raced 15 times, this means that he won roughly 4/10 races.
4/10= ?/15
cross multiply 4 and 15 = 60
60/10 = 6
He won 6 races
Give brainliest please!
hope this helps :)
nich
2. What quantity should be added to both sides of
this equation to complete the square?
x² - 8x = 5
Answer:
[tex]16[/tex]
Step-by-step explanation:
[tex]~~~~~~x^2 -8x = 5 \\\\\implies x^2 -2\cdot 4 \cdot x+ 4^2 = 5+ 4^2~~~~~~~~~~~~;[\text{Add}~ 4^2 = 16 ~ \text{to both sides }]\\\\\implies (x-4)^2 = 21[/tex]
Rewrite as a simplified fraction. 3.16 (6 is repeating)
0.16 (with 6 repeating) = 1/6
3.16 = 3 1/6
Mixed Number = 3 1/6
Improper Fraction = 19/6
Hope this helps!
Answer:
3 4/25
Step-by-step explanation:
[tex]\frac{3.16}{1} \cdot \frac{100}{100} = \frac{316}{100}[/tex]
[tex]\frac{316 \div 4}{100 \div 4} = \frac{79}{25}[/tex]
[tex]= 3\frac{4}{25}[/tex]
sectors of circle. east points, this is due tomorrow help is appreciated
The big arc is 2.09 centimeters longer than the small arc.
How much longer is the big arc than the small arc?For a circle of radius R, if we define an arc with an angle θ, the length of that arc will be:
L = (θ/360°)*2πR
Where π = 3.14
in this case, for both arcs, we have θ = 120°.
For the smaller arc, the radius is R = 5cm, so we get:
L = (120°/360°)*2*3.14*5cm = 10.47 cm
For the larger arc, the radius is R = 5cm, so we get:
L' = (120°/360°)*2*3.14*6cm = 12.56 cm
Then we can see that:
L' - L = 12.56 cm - 10.47 cm = 2.09 cm
So the largest arc is 2.09 centimeters longer than the smaller arc.
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