i) Find the first 4 terms in the expansion of
[tex](2 + x ^{2})^{6}[/tex]
in ascending powers of x.
ii) Find the term independent of x in the expansion of
[tex](2 + x ^{2})^{6}(1 - \frac{3}{x {}^{2} } ) {}^{2} [/tex]
​

Answer:

A

Step-by-step explanation:

If the mean of a standardized test with a normal distribution is 54.3 and the standard deviation is 4.6. what is the best approximation of the percent of the scores

that fall between 54.3 and 63.5?

Answer:

volume = 33.5 in³

Step-by-step explanation:

Formula:

[tex]\sf volume \ of \ a \ cone=\dfrac13\pi r^2h[/tex]

Given:

Substituting the given values into the formula:

[tex]\sf \implies volume=\dfrac13 \times 3.14 \times 2^2 \times 8[/tex]

                  [tex]=\dfrac13 \times 3.14 \times 4 \times 8[/tex]

                  [tex]\sf =33.49333333...[/tex]

                  [tex]\sf =33.5 \ in^3 \ (nearest \ tenth)[/tex]

Answer:

7.B

9.A

Step-by-step explanation:

Gcf of 24 and 36

is 12

a^2 and a is a

180-50

=130

acute mean less than 90 degrees

180-89=41

89 and 41 are acute

1 is also wrong

Answer:

  7.  B 2·2·3·a

  9.  B 41°

Step-by-step explanation:

You want the greatest common factor of 24a² and 36ab, and you want the smallest integer-valued angle in an acute triangle with one angle 50 degrees.

The factors of 24a² are 2·2·2·3·a·a.

The factors of 36ab are 2·2·3·3·a·b.

The factors these lists have in common are 2·2·3·a, matching choice B.

If one angle of a triangle is 50°, the sum of the other two angles must be ...

  180° -50° = 130° . . . . . . sum of angles B and C

One of these angles will be the smallest it can be only if the other is the largest it can be. The largest integer acute angle is 89°, so the smaller angle will be ...

  130° -89° = 41°

The smallest possible angle in the acute triangle is 41°.

__

Additional comment

8. A dodecagon has 12 lines of symmetry, 6 through opposite vertices, and 6 through opposite sides. The correct choice for 8 is A.

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Answer:

The correct answer is B: 3 cubic feet.

Step-by-step explanation:

If you want to find the volume of a rectangular prism, you need to know the length, width, and height. The first rectangular prism is a cube with a length of 3 feet, so the volume of the figure would be [tex]3^{3}=27 ft^{3}[/tex]. The second rectangular prism has a length of 3 feet, a width of 2 feet, and a height of 4 feet, so the volume of the prism would be 3 × 2 × 4 = [tex]24 ft^{3}[/tex]. Now that you know the 2 volumes, you need to subtract the volumes in order to find the difference, which is 27 - 24 = 3 [tex]ft^{3}[/tex].

Answer:

Step-by-step explanation:

According to coordinates on the graphs and numbers in the tables we have the following relationship:

As we see B, C and E have same relationship, matching the target.

Step-by-step explanation:

hope it's help you this answer

Answer:

5sqroot3

Step-by-step explanation:

see image.

An integer is just a whole positive or negative (positive in this case) number that's not a fraction or decimal or mixed number. In the answer that is the 5.

To simplify a radical, look for a factor that is a perfect square. Radicals and multiplying are very friendly to each other and you can separate the "radicand" (the inside number) into factors inside the radical also into separate radicals to simplify. See image

Answer:

well i wrote it in paper nothing to explain it's ez

Based on the calculations, the radius of this right cone is equal to 6 units.

Given the following data:

Mathematically, the volume of a cone is given by this formula:

[tex]V = \frac{1}{3} \pi r^2h[/tex]

Where:

Making r the subject of formula, we have:

[tex]r=\sqrt{\frac{3V}{\pi h} } \\\\[/tex]

Substituting the given parameters into the formula, we have;

[tex]r=\sqrt{\frac{3\times 252\pi}{\pi \times 21} } \\\\r=\sqrt{\frac{756}{21} }\\\\r=\sqrt{36}[/tex]

r = 6 units.

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Answer:

Length = 42, Width = 14

Step-by-step explanation:

Say width = x

3x + x = 56

4x = 56

x = 14

14 x 3 = 42.

Answer:

width = 7

length = 21

Step-by-step explanation:

x + 3x = 56/2

4x = 28

x = 7

Volume of a Square Pyramid: 1/3 x length x width x height

Length = 2

Width = 2

Height = 3

Volume = 1/3 x 2 x 2 x 3

Volume = 1/3 x 4 x 3

Volume = 1/3 x 12

Volume = 4

Volume = 4 cm^3

Hope this helps!

Answer:

Step-by-step explanation:

First, calculate the angle of FDE (assume it as α) by:

[tex]EF=\frac{\alpha}{360}\times(2\pi)(DE) \rightarrow 2\pi = \frac{\alpha}{360}(2\pi)(6)[/tex]

[tex]\alpha=60^{0}[/tex]

So, use this angle to calculate the area of FDE (unshaded region):

[tex]A_{US}=\frac{\alpha}{360}\times(\pi)(DE)^{2}=\frac{60}{360}(\pi)(6^{2})=6\pi[/tex]

So, the shaded region can be determined by:

[tex]A_{S}=A-A_{US}=\pi(DE)^{2}-6\pi=36\pi-6\pi=30\pi=\frac{60}{2}\pi[/tex]

Answer:

1.True

2.false

3.True

4.True

5.false

6.false

7.false

8.True

9.True

10.false

Step-by-step explanation:

10,000cm^2=1m^2

she spends 68 minutes at the gym on Thursday in order to average 65 minutes a day for four days.

The mean (also known as the arithmetic mean, which varies from the geometric mean) of a dataset is calculated as the sum of all values divided by the total number of values. This measure of central tendency is usually referred to as the "average".

Granted, Laura recorded how long she spent at the gym each day this week.

Let "x" represent the time she spent working out on Thursday.

Since,

Average = (sum of values)/ count of values

Thus, in our case

Average = (60 +70 +62 +x)/4

average is 65 minutes a day for four days.

65 = 192 +x)/4

192 +x = 260

x = 260-192

x = 68

Therefore, she spends 68 minutes at the gym on Thursday in order to average 65 minutes a day for four days.

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#SPJ6

Answer; 60

Step-by-step explanation:

solution:

here,

4 cars = 12 marbles

1 car = 12/4. = 3 marbles

then,

20 cars = 3(20) marbles

= 60 marbles

We can make this into a fraction  4/12 = 20/x

Then, we will solve for x

4x = 240    cross multiply

x = 60

Joe collects 60 marbles after collecting 20 cars.

The Multiplicative Inverse Property is being used.

Answer: 18:4

Step-by-step explanation:

Ez

Answer:

9 : 2

Step-by-step explanation:

length : Width = 18 : 4

                       [tex]\sf = \dfrac{18 \ \div \ 2}{4 \ \div \ 2}\\\\=\dfrac{9}{2}[/tex]

                       = 9 : 2

Answer:

I think its 5 consecutive zeros.

Step-by-step explanation:

This would be a guess but I think you would need two numbers in the hundreds that also have 2 parts of which have a product of a number ending in 0, like 4 and 5.

So my guess would be

400 * 500 * 39

= 7800000

Your net income/take-home would be 84.6 percent of the gross amount.

Your net income is the amount of money left after payroll deductions in the form of taxes and other charges on the gross amount of your paycheck.

If we deduct federal and state taxes, 10 percent and 6 percent respectively, we would charge 10 percent and 6 percent of 100 and have 84.6 percent of your original(gross) income left.

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Answer:

Non-linear equations:

[tex]y=x^2 +2x-3[/tex]

[tex]3y=2^x[/tex]

Step-by-step explanation:

Linear equation: y = mx + b

Therefore, a linear equation has 2 variables that have no exponents.

So the non-linear equations are:

[tex]y=x^2 +2x-3[/tex]  (this is a quadratic equation - polynomial with degree 2)

[tex]3y=2^x[/tex] (this is an exponential equation)

Answer:

C. where the start point is on (3,0) and goes up and to the right

Step-by-step explanation:

y= √x−3

Swap sides so that all variable terms are on the left hand side.

√x−3 =y

Square both sides of the equation.

x−3=y^2

Add 3 to both sides of the equation.

x−3−(−3)=y^2 −(−3)

Subtracting −3 from itself leaves 0.

x=y^2 −(−3)

Subtract −3 from y^2.

x=y^2 +3

Step-by-step explanation:

please mark me as brainlest

Answer:

[tex]\red{ \rule{10pt}{999999pt}} \pink{ \rule{10pt}{999999pt}} \blue{ \rule{10pt}{999999pt}} \purple{ \rule{10pt}{999999pt}} \\ \red{ \rule{10pt}{999999pt}} \pink{ \rule{10pt}{999999pt}} \blue{ \rule{10pt}{999999pt}} \purple{ \rule{10pt}{999999pt}} \\ \red{ \rule{10pt}{999999pt}} \pink{ \rule{10pt}{999999pt}} \blue{ \rule{10pt}{999999pt}} \purple{ \rule{10pt}{999999pt}}[/tex]

Answer:

Putanginaaaaaaaaaaaaaaaaaaaaa

#a

#b

That be x and y

So

So

from eq(1)

Put in second one

Put in third one

Take it positive

Answer:

(a) (i)  Factorize [tex]\sf 4p-6pq+9q-6[/tex]

Rewrite by swapping the order of the first two terms:

⇒ -6pq + 4p + 9q - 6

Factorize the first two terms and the last two terms separately:

⇒ -2p(3q - 2) + 3(3q - 2)

Factor out the common term (3q - 2):

⇒ (3q - 2)(-2p + 3)

(ii)

Square of the binomial: [tex](a+b)^2=a^2+2ab+b^2[/tex]

Rewrite [tex]9.9[/tex] as [tex]10 - 0.1[/tex]

Therefore, [tex]a = 10[/tex] and [tex]b = -0.1[/tex]

Also, remember that multiplying a number by 0.1 is the same as dividing it by 10.  (when dividing a decimal number by 10, simply move the decimal point 1 place to the left).

[tex]\begin{aligned}\implies 9.9^2 & =(10-0.1)^2\\ & =10^2-2 \cdot 10 \cdot 0.1+0.1^2\\& = 100-\dfrac{2 \cdot 10}{10}+\dfrac{0.1}{10}\\& =100-2+0.01\\ & =98 + 0.01\\ & = 98.01\end{aligned}[/tex]

(b) (i)

Let x = number of motor bicycles

Let y = number of cars

Given:

⇒ x + y = 15

Given:

⇒ 2x + 4y = 64

(ii)  Rewrite   x + y = 15  to make x the subject:

⇒ x = 15 - y

Substitute into 2x + 4y = 64  and solve for y:

⇒ 2(15 - y) + 4y = 64

⇒ 30 - 2y + 4y = 64

⇒ 30 + 2y = 64

⇒ 2y = 34

⇒ y = 17 cars

Substitute found value of y into  x = 15 - y  to find x:

⇒ x = 15 - 17 = -2 motorbikes

**There must be an error in the question, as with the given information, the number of motorbikes is -2, which is impossible.**

Here are the possible combinations of number of motorbikes (M) and number of cars (C) whose sum of tires is 64.  As you can see, there is no combination that sums to 15 vehicles:

0 M +  16 C = 16 vehicles

2 M +  15 C = 17 vehicles

4 M +  14 C = 18 vehicles

6 M +  13 C = 19 vehicles

8 M +  12 C = 20 vehicles

10 M +  11 C = 21 vehicles

12 M +  10 C = 22 vehicles

14 M +  9 C = 23 vehicles

16 M +  8 C = 24 vehicles

18 M +  7 C = 25 vehicles

20 M +  6 C = 26 vehicles

22 M +  5 C = 27 vehicles

24 M +  4 C = 28 vehicles

26 M +  3 C = 29 vehicles

28 M +  2 C = 30 vehicles

30 M +  1 C = 31 vehicles

32 M +  0 C = 32 vehicles

The shape in the figure has 6 sides

The choice that describes the group the shape belongs to is (a) parallel sides, acute angles

From the figure, we have the following highlights

The above highlight mean that:

The shape belongs to parallel sides, acute angles group of shapes

Hence, Angela's conclusion is correct

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The polynomials in factored form are listed below:

In this question we must factor polynomials as there are both numerical and analytical methods. Mathematically speaking, factoring polynomials is represented by the following formula:

[tex]\sum^{n}_{i = 0} \,c_{i}\cdot x^{i} = \prod^{n}_{i=1}(x-r_{i})[/tex], [tex]\forall\,x, r_{i}\in \mathbb{C}[/tex]   (1)

Where:

Regarding fourth order polynomials we can solve them by Ferrari's method and third order polynomials by Descartes' method. Then, the solutions of each polynomials are given below:

f(x) = (x - 4) · (x - 3) · (x - 1) · x

f(x) = (x - 2.236) · (x - 2) · (x + 2.236) · (x + 4)

f(x) = (x + 3) · (x - 5) · (x - 1)

f(x) = (x - 4) · (x - 3) · (x - 1) · x

To learn more on polynomials, we kindly invite to check this verified question: https://brainly.com/question/17822016