Needing help with these 2 problems

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:

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]

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]

From the table we can say Srey visited Pittsburgh if the Cory, Srey, Molly, and Mao each visited a different city: Santa Clara, Seattle, Des Moines, and Pittsburgh.

When making a choice or addressing an issue, reasoning is the ability to appraise things rationally by using logic based on new or existing information.

We have:

Cory, Srey, Molly, and Mao each visited a different city: Santa Clara, Seattle, Des Moines, and Pittsburgh. Cory and Molly visited cities with two words in their names.

Mao and Cory visited cities whose names start with an S.

The table can be make to show the information provided:

Cory - city with 2 words

Molly - city with 2 words

Mao - starting with an s

Cory - starting with an s

cities are : Seattle, Santa Clara,Pittsburgh,Des Moines

The table is:

Name            City name

Cory               Santa Clare

Molly              Des Moines

Mao                Seattle

Srey               Pittsburgh

Thus, from the table we can say Srey visited Pittsburgh if the Cory, Srey, Molly, and Mao each visited a different city: Santa Clara, Seattle, Des Moines, and Pittsburgh.

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The area of the triangle is 608 cm².

Area is the region bounded by a plane shape.

To calculate the area of the triangle, we use the formula below.

Formula:

Where:

From the question,

Given:

If

Substitute these values into equation 1

Hence, the area is 608 cm².

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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.

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

Answer:

7

Step-by-step explanation:

350÷50=7

................

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

The simplification of the expression is 28. The mistake in your calculation occurred in step 3.

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]          

= 22 + 6[(9) ÷9]    

= 22 + 6[ 1]

= 22 + 6

= 28

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Step-by-step explanation:

¿qué es eso?¿es esto importante? :)

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 :)

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?

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]

[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]

Answer:

2.65 cm

Step-by-step explanation:

Applied Formula :

Solving :

The coordinate of the point is (6,-2)

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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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.

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.

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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The big arc is 2.09 centimeters longer 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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Answer & Step-by-step explanation:

I have attached two ways you can find the number of green Jolos, by adding and/or subtracting from the other known values. Both ways will give the answer of C. 280 Jolos

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

Answer:

The answer to this question is -11

Answer:

the answer to the question above would be the option 3 (vertex)

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°

Answer:

0.275

Step-by-step explanation:

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.

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.

Note that:

The power of the test shows that:

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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Answer:

-2, 5, 12, 19, 26, 33, 40, 47, 54, 61, 68, 75, 82, 89, 96, 103

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.