The term containing b^6 in the expansion of (a + b2)10

In each diagram, line f is parallel to line g, and line t intersects both lines f and g. The given information suggests the application of certain geometric properties and relationships.

Firstly, when a transversal line (line t) intersects two parallel lines (lines f and g), it creates several pairs of corresponding angles.

Corresponding angles are congruent, meaning they have equal measures. This property can be used to determine the measures of specific angles in the diagram.

Secondly, when a transversal intersects parallel lines, it also creates alternate interior angles and alternate exterior angles.

Alternate interior angles are congruent, as well as alternate exterior angles.

By utilizing these properties and relationships, one can analyze the diagram and determine the measures of various angles.

It is important to measure angles systematically and compare them to find congruent or equal measures.

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Answer:

(a)2030

Step-by-step explanation:

I'm assuming the 100 at the end of the question is a typo.
In 2040, the son's age can be written as \(\frac{x}{3}\), where x equals the age of his father. In 2050, the son's age can be written as \(\frac{x-10}{2}\) (as ten years is added between 2040 and 2050). When equated to each other--> \(\frac{x-10}{2}\) = \(\frac{x}{3}\), we can first simplify by multiplying both sides to reach the least common denomination 6, giving us 3(x-10)=2x --->3x-30=2x--->x=30 is the dad's age. The son's age in 2040, 30/3, is equal to 10 years, meaning he was born in the year 2030 (a).

Answer:

When a 3D figure is cut to create a cross-section parallel to the base, the direction of the perpendicular is vertical. This means that the cross-section will be perpendicular to the base and will have a vertical orientation.

The method that determines the volume of the prism is simply multiply the area of the base by the height, and the result is 12.5 cm³. (option-a)

To determine the volume of the prism shown in the diagram, we need to multiply the area of the base by the height.

The base of the prism is a rectangle with dimensions 5 cm by 2 cm. Therefore, the area of the base is:

A = length x width = 5 cm x 2 cm = 10 cm²

The height of the prism is 2-¹ cm, which is equivalent to 5/4 cm.

Therefore, the volume of the prism is:

V = A x h = 10 cm² x 5/4 cm = 12.5 cm³

The expressions involving unit cubes and one-quarter cubes are not relevant to this problem and do not provide a method for finding the volume of the prism.

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Answer: In decimal form, 14.85

Answer in fraction form: 297/20

Step-by-step explanation:

Answer:

0 = 0 means that there are infinite solutions.

Step-by-step explanation:

Equation is -5(-4+2n)=-10(n-2)

1. Distribute the -5 and -10

20 -10n = -10n + 20

2. Subtract 20 from one side to the other to get only 1 variable on 1 side.

-10n = -10n

3. divide -10 to separate the variable from the constant.

n = n

This means there are infinite solutions.

The total distance covered by Jeremy is 1320 m

What is a line segment ?

A line segment in geometry is bounded by two separate points on a line. Another way to describe a line segment is as a piece of the line that joins two points. A line segment has two fixed or distinct endpoints while a line has no endpoints and can stretch in both directions indefinitely.

For sapling 1 = No distance is covered.

For sapling 2, distance covered = 10 m

Return distance=10 m

For sapling 3, distance covered =20 m

Return distance=20 m and so on

Thus the distances covered for saplings can be represented as : 0,2(10), 2(20),...i.e. 0,20, 40,...

Therefore total distance covered by Jeremy for planting 12 saplings and coming back to original position = S 12

Total distance covered = 122 [2(0) + (12 − 1) 20 ]

Total distance covered = 6 (11)(20) = 1320 m

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Complete question:

There are 12 saplings to be planted in a straight line at an interval of 10 m between

two consecutive saplings. Jeremy can carry only one sapling at a time and he has to

come back to the original point to take the next sapling. He plants 12 saplings in this

manner, planting the first sapling at the original point. After planting all the saplings,

he comes back at the original point,

In the process, what is the total distance that Jeremy covers?

​

Answer:

First number: 30

Second number: 22

Third number: 88

Step-by-step explanation:

22 is 8 less than 30

88 is four times more than 22

30 + 22 + 88 = 140

Answer:

28.07°

Step-by-step explanation:

use SohCahToa

in this case we use tan^-1 to get the angle x°

tan^-1(8/15)=28.07248694

to the nearest hundredth

=28.07°

Answer:

he can buy 7 for 14 dollars

Step-by-step explanation:

Answer:

Javier can by 8 action figures breasted if each figure cost $2.

Answer: -30

Step-by-step explanation:

Answer:

the answer would be -30!!!

Step-by-step explanation:

i took the quiz.

Answer:

8 quarts

Step-by-step explanation:

no explanation needed this should be correct.

The numerical value of x in the similar pair of triangle is 10.

A ratio is simply the relation between two amounts showing how many times a value is contained within another value.

From the diagram,

Side A of the small triangle = 10

Side B of the small triangle = x + 2

Side A of the Big triangle = 10 + x

Side B of the big triangle = x + 14

Hence;

Ratio of Side A to Side B of the small triangle = 10 / x + 2

Ratio of Side A to Side B of the Big triangle = 10 + x / x + 14

Since the triangle area similar, equate the two ratio and solve for x.

10 / ( x + 2 ) = ( 10 + x ) / ( x + 14 )

Cross multiply

10( x + 14 ) = ( 10 + x )( x + 2 )

Expand using FOIL method

10x + 140 = 10x + 20 + x² + 2x

10x + 140 = x² + 12x + 20

x² + 12x + 20 = 10x + 140

x² + 12x + 20 - 10x - 140 = 0

x² + 2x - 120 = 0

Factor the left side of the equation

( x - 10 )( x + 12 ) = 0

Hence;

x - 10 = 0 and x + 12 = 0

x = 10 and x = -12

Since the dimension of the triangle cannot be negative,

x = 10

Therefore, the value of x is 10.

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The correlation coefficient between X and Y is Corr(X, Y) = 0.

To calculate the marginal distribution of X and Y, we need to integrate the joint probability density function (PDF) over the appropriate ranges.

a. Marginal distribution of X:

To find the marginal distribution of X, we integrate the joint PDF over the range of Y:

∫[0, 1] J(x, y) dy

Since the joint PDF is defined as J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1 and J(x, y) = 0 otherwise, the integral becomes:

∫[0, x] 1 dy = x, for 0 ≤ x ≤ 1

So, the marginal distribution of X is simply X(x) = x for 0 ≤ x ≤ 1.

b. Expectation of X:

The expectation (mean) of X can be calculated as the integral of x times the marginal PDF of X:

\(E(X) = ∫[0, 1] x * X(x) dx = ∫[0, 1] x^2 dx = [x^3/3] from 0 to 1 = 1/3\)

Therefore, the expectation of X is E(X) = 1/3.

c. Variance of X:

The variance of X can be calculated using the formula:

\(Var(X) = E(X^2) - (E(X))^2E(X^2) = ∫[0, 1] x^2 * X(x) dx = ∫[0, 1] x^3 dx = [x^4/4] from 0 to 1 = 1/4Var(X) = 1/4 - (1/3)^2 = 1/4 - 1/9 = 5/36\)

Therefore, the variance of X is Var(X) = 5/36.

d. Covariance of X and Y:

The covariance of X and Y can be calculated as:

Cov(X, Y) = E(XY) - E(X)E(Y)

Since the joint PDF J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1, the integral becomes:

\(E(XY) = ∫[0, 1] ∫[0, x] xy dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

\(E(X) = 1/3 (from part b)E(Y) = ∫[0, 1] ∫[0, x] y J(x, y) dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

Cov(X, Y) = 1/6 - (1/3)(1/6) = 0

Therefore, the covariance of X and Y is Cov(X, Y) = 0.

e. Correlation coefficient between X and Y:

The correlation coefficient can be calculated using the formula:

Corr(X, Y) = Cov(X, Y) / √(Var(X) * Var(Y))

Since the covariance of X and Y is 0, the correlation coefficient will also be 0.

Therefore, the correlation coefficient between X and Y is Corr(X, Y) = 0.

f. Conclusion based on the correlation coefficient:

The correlation coefficient of 0 indicates that there is no linear relationship between X and Y. In this case, the fraction of male runners (X) and the

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Answer:

$880

Step-by-step explanation:

Use the equation:

\(P=(1-d)x\) with d being the discount in a decimal form, and P being the price that was bought at.

220=(1-0.75)x

simplify parenthesis terms

220=0.25x

divide both sides by 0.25

880=x

So, the original price was $880.

Hope this helps! :)

Answer: x= -1

Step-by-step explanation:

4(x-1)=-8

First distribute

4x-4=-8

Now add 4 to -8

4x=-4

Now divide by 4

X=-1

The answer is x = -1

Step-by-step explanation: When it comes to solving for a variable (x) you have to distribute if there is parenthesis and then use inverse operations to get the answer.

4(x-1)=-8 Distribute

4x - 4 = -8 Subtract 4 from both sides

4x = -4 Divide 4 on both sides

x = - 1 and that is your answer

Answer: well solve what's in the parentheses first

Step-by-step explanation: that is the first step

Answer:

y = x + 5

Step-by-step explanation:

We need to find the inverse of the given relation . Firstly replace x with y and then solve for y to get the inverse . We have ,

=> y = x - 5

=> x = y - 5

=> y = x + 5

The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

To solve this problem, we can use the concept of radioactive decay and the decay factor. Here's how we can calculate the required volume to correct the dose:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = Initial activity * Decay factor

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = Initial activity - 20 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = Remaining activity * Decay factor

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = Desired activity at 9:30 / Remaining activity at 9:30 * Volume at 9:30

Calculate the remaining volume at 9:30:

Remaining volume = Volume at 8 am - Volume withdrawn - Volume accidentally discharged

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume

Let's perform the calculations step by step:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = 180 mCi * 0.841 = 151.38 mCi

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = 180 mCi - 20 mCi = 160 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = 160 mCi * 0.841 = 134.56 mCi

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = (Desired activity at 9:30 / Remaining activity at 9:30) * Volume at 9:30

Volume at 9:30 = Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Volume needed = (20 mCi / 134.56 mCi) * 15 ml = 2.236 ml

Calculate the remaining volume at 9:30:

Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume = 2.236 ml - 15 ml = -12.764 ml

Since the calculated volume to be added is negative, it means that no additional volume is required. The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

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Answer:

\((2 x 10^1^7)^2\) is 4×\(10^3^4\)

Step-by-step explanation:

Standard Form is 4×\(10^3^4\)

Answer: Number 2

Step-by-step explanation: yes

The circumference of a circle with a radius of 14 feet is 88 feet.

Every point in the surface of a circle, which is a circular, two-dimensional object, is evenly separated from the centre. All lines that cross the circle join together to produce the line of reflected symmetry. Each angle has axis of symmetry around the centre, in addition. Monitoring a linear interpolation in a surface while keeping a fixed distance from some other point will result in the closed shape of a circle. The English term circle derives from the Greek word curriculum provides students, which also means hoop or ring.

When we find the circumference, we obtain:

The  circumference( C) of a circle is 2πr.

C=2πr

⇒C=2×\(\frac{22}{7}\)×14=88 feet.

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(x - 4y) / w = 9

Multiply both sides by w

x - 4y = 9w

Add 4y to both sides

x = 9w + 4y

Answer:

48.459 second

Step-by-step explanation:

all you do is align the decimals and add it.

The answer to 21.261+27.98 is 48.459

All you have to do is line the numbers up and the decimals up and add :)

\((2x-y)(3x+y)\\\\=2x(3x+y) -y(3x+y)\\\\=6x^2 +2xy - 3xy -y^2\\\\=6x^2 -xy -y^2\)