Expand (2x + 3)^5 using the Binomial Theorem and Pascal’s triangle. Show all steps.

To solve the congruence 4x ≡ 5 (mod 9), we need to find the inverse of 4 modulo 9, which we found in part (a) of exercise 5 to be 7.

Multiplying both sides of the congruence by the inverse of 4, we get:

4x * 7 ≡ 5 * 7 (mod 9)

28x ≡ 35 (mod 9)

Since 28 ≡ 1 (mod 9), we can simplify the left side of the congruence:

x ≡ 35 (mod 9)

Now we need to find the smallest non-negative integer solution for x. We can do this by repeatedly subtracting 9 from 35 until we get a number less than 9:

35 - 9 = 26
26 - 9 = 17
17 - 9 = 8

So x ≡ 8 (mod 9) is the smallest non-negative integer solution to the congruence 4x ≡ 5 (mod 9) using the inverse of 4 modulo 9 found in part (a) of exercise 5.

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Answer:

A. 102

B. 78

Step-by-step explanation:

mEG = 360 - 258 = 102°

m∠EFG = 1/2 ( major arc - manor arc) = 1/2 (258 - 102) = 78°

Answer:  1732 feet

Step-by-step explanation:  If each tower is 1152 feet from the end, subtract twice that length from the total.

1152 × 2 = 2304  

4036 - 2304 = 1732

The length of the ladder is 8 meters. The ladder forms a right triangle with the wall and the ground, where the ladder is the hypotenuse. The angle between the ladder and the ground is given as 60°.

Using trigonometric functions, we can determine the length of the ladder. In a right triangle, the cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse. In this case, the adjacent side is the distance between the base of the ladder and the wall, which is 4 meters. Therefore, cos(60°) = 4/ladder length.

Using the trigonometric identity cos(60°) = 1/2, we can solve for the ladder length:

1/2 = 4/ladder length

Multiplying both sides by 2, we get:

1 = 8/ladder length

Rearranging the equation, we find:

ladder length = 8 meters

Therefore, the length of the ladder is 8 meters.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\(y = \stackrel{\stackrel{m}{\downarrow }}{3} x + 3\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{3\implies\cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}\)

so we're really looking for the equation of a line whose slope is -1/3 and that is passes through (3 , 2)

\((\stackrel{x_1}{3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{3}) \\\\\\ y-2=- \cfrac{1}{3}x+1\implies {\Large \begin{array}{llll} y=- \cfrac{1}{3}x+3 \end{array}}\)

Answer:

the 3 pefections

Step-by-step explanation:

took the test

Answer:

the three perfections

Step-by-step explanation:

Answer:

84

Step-by-step explanation:

add em all together

Answer:

£7.3

Step-by-step explanation:

2 x £2=£4

3 x £3 = £6

3 x 90 = 270 = £2.7

£4+£6+£2.7= £12.7

20-12.7=7.3

7 pounds and 3

Answer: 4.3

Step-by-step explanation:

2(2)+3(3)+3(.9)=

4+9+2.7=15.7

20-15.7= 4.3

I'm assuming that 100 p is 1 £, if that's not the case this would be wrong

Answer:

O -x+y=-2

Step-by-step explanation:

-x + y = -5

⇔ y = x - 5

a line parallel to y = x - 5 must have the same slope as the line y = x - 5

Then

The equation of the parallel line is of the form : y = x + p

Finding p :

the point (-6,-8) lies on the parallel line means :

-8 = -6 + p

Then

p = -8 + 6 = -2

Finally :

y = x - 2 ⇔ -x + y = -2

Answer:

A

We are 95 percent confident that the mean increase in the weight of a black bear for each one-year increase in the age of the bear is between 7.0 and 18.4 pounds.

Step-by-step explanation:

The 95 confidence interval given by 1.272±0.570, or (0.702,1.842), estimates the relationship between weight in tens of pounds and age in years. So we are 95 percent confident that the mean increase in the weight of a black bear will be between 7.0 and 18.4 pounds for each one-year increase in the age of the bear.

The correct interpretation of the provided confidence interval is given by:

Option B: We are 95 percent confident that an increase of one year in the age of an individual black bear will result in an increase in the black bear's weight of between 7.0 and 18.4 pounds.

Suppose the confidence interval at P% for some parameter's values is given by \(x \pm y\)

That means, that parameter's estimated value is P% probable to lie in the interval \([x - y, x + y]\)

For this case, the regression line predicts weight in tens of pounds based on the age in years.

The 95% confidence interval for that prediction is given to be: \(1.272 \pm 0.570\)

That means, the predicted value of weight of a black bear (in tens of pounds) when one year age is incremented is 95% probable to lie in the interval \([1.272 - 0.57, 1.272 + 0.57] \approx [0.7, 1.84]\)

That is for weight in tens of pounds. Converting it to pounds gives us the interval \([7.0, 18.4]\) approx.

Note the words "prediction", and "of a bear".

That makes us conclude that:

Option B: We are 95 percent confident that an increase of one year in the age of an individual black bear will result in an increase in the black bear's weight of between 7.0 and 18.4 pounds.

(focus on the "will result in" phrase. It is taking similar to prediction thing. Since we're taking about regression line which tries to fit line for prediction of future output values for input values, thus, we chose second option.)

Thus, the correct interpretation of the provided confidence interval is given by:

Option B: We are 95 percent confident that an increase of one year in the age of an individual black bear will result in an increase in the black bear's weight of between 7.0 and 18.4 pounds.

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Answer:

24

Step-by-step explanation:

4x-6y

substitute:

4x3 - 6x (-2) = 12+12 = 24

Hope this helps

Step-by-step explanation:

A body at rest accelerates to 2.5 meters in 1 second, it then maintains a constant speed for 2 seconds and accelerate 2.5 meters in 2 seconds. It then maintains a constant speed for 2 seconds and finally decelerates for the next eight seconds.

scale = 1cm : 1 unit.

distance axis : 1 to 7.5 meters

Time axis : 1 to 15 seconds

The main goal of data democratization is to make data accessible to all users. Option (a) is correct.

Given the primary goal of data democratization.

Data democratization is the ability to make information in a digital format accessible to the average end user. The goal of data democratization is to allow non-professionals to collect and analyze data without the need for outside help. This requires us to support access with an easy way for people to understand data, so they can use it to accelerate decision-making and uncover opportunities for a business. The goal is for everyone to be able to use the data at any time to make decisions without barriers of access or understanding.

Therefore, the main goal of data democratization is to make data accessible to all users.

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The X value corresponding to z = -2.25 is X = 56.

A z score is a statistical indicator that shows how far a raw score is from a distribution's mean. Give the z-score formula. The z-score is calculated using the formula z = (x -μ)/σ.

To find the corresponding X value for a given z-score, we use the formula:

X = µ + (z * σ)

Given µ = 65, σ = 4, and z = -2.25, we can calculate the X value:

X = 65 + (-2.25 * 4)

X = 65 - 9

X = 56

Therefore, the X value corresponding to z = -2.25 is X = 56.

The correct answer is b. X = 56.

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Answer:

Step-by-step explanation:

Let the height of each kite be h.

The h is opposite to angle of elevation and the sting length is hypotenuse of the formed triangle.

Kattie's kite:

Matt's kite:

Kattie's kite is flying higher as 532 ft > 466 ft

Answer:

No linear relationship between x and y

Step-by-step explanation:

change in y is constant, change in x is increasing not a constant. constant means it remains the same doesnt change.

Equilibrium is the term refers to coordination, balance, and balance in three dimensional space.

The equilibrium condition of an object exists when Newton's first law is valid. An object is in equilibrium in a reference coordinate system when all external forces (including moments) acting on it are balanced. This means that the net result of all the external forces and moments acting on this object is zero.

There are three types of equilibrium: stable, unstable, and neutral.

Examples of equilibrium in everyday life:

A book kept on a table at rest. A car moving with a constant velocity. A chemical reaction where the rates of forward reaction and backward reaction are the same.

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The value of x in the figure is 18

The angle with the measure 9x -12 and the angle with the measure 30 degrees are internal angles of a transversal

This means that

9x -12 + 30 = 180

Evaluate the like terms

9x = 162

Divide by 9

x = 18

Hence, the value of x in the figure is 18

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Answer:

it would be -12

Step-by-step explanation:

Step-by-step explanation:

-10 or -20 satisfies the equation.

But when you substitute 10 in:

30-40<-50+8

-10<-42(wrong)

it's wrong

The solutions are −10 and −20 to the inequality 3n − 40 < −5n + 8 because they satisfy the inequality unlike 10.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The inequality is given in the question as:

3n − 40 < −5n + 8

Rearrange the terms in the above inequality

3n + 5n < 8 + 40

Apply the addition operation in the terms

8n < 48

Divided by 8 into both sides of the inequality

n < 6  ....(i)

Substitute the value of n = 10 in inequality (i),

10 < 6

This is not true, so 10 is not the solution to the given inequality.

Therefore, the solutions are −10 and −20 to the inequality 3n − 40 < −5n + 8 because they satisfy the inequality unlike 10.

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The calculated t-statistic (3.24) is greater than the critical value (1.699), reject the null hypothesis

Since the calculated t-statistic (3.24) is greater than the critical value (1.699), we reject the null hypothesis.
In conclusion, the dentist's claim is supported.

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hope this helps :)

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

Follow these procedures to calculate the mean absolute deviation.

1. Determine the data's mean by adding all of the values and dividing by the number of values in the data set.

2. Subtract the mean from each of the data points.

3. Make each difference a good one.

4. Add up all of the positive differences.

5. Subtract this total from the amount of data values in the collection.

This is the  mean absolute deviation.

A data set's average absolute deviation is the sum of its absolute departures from a central point. It is a statistical dispersion or variability summary statistic.

The average distance between the values in a data collection and the set's mean is described by mean absolute deviation. A data collection with a mean average deviation of 3.2, for example, has values that are 3.2 units away from the mean on average.

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Answer:

  -8748

Step-by-step explanation:

You want the 8th term of the geometric sequence that begins 4, -12, 36, ....

A geometric sequence is characterized by a common ratio r. When the first term is a1, the n-th term is ...

  an = a1×r^(n-1)

Here, the first term is 4, and the common ratio is -12/4 = -3. That means the n-th term is ...

  an = 4×(-3)^(n-1)

and the 8th term is ...

  a8 = 4×(-3)^(7-1) = -8748

The 8th term is -8748.

__

Additional comment

The attachment shows the 8th term and the first 8 terms of the sequence.

<95141404393>

the 8th term of the geometric sequence  4 , − 12 , 36 , . . . 4,−12,36,... is -4374 by using formula of a:an = a1 * rn-1Wherean = nth terma1 = first term r = common ratio

Given the first three terms of a geometric sequence: 4, -12, 36, ...To find the 8th term of the geometric sequence, we need to first find the common ratio of the sequence which can be found using the formula:Common ratio, r = Term 2 / Term 1= -12 / 4= -3The nth term of a geometric sequence is given by the formula:an = a1 * rn-1Wherean = nth terma1 = first term r = common ratio To find the 8th term, we use the formula:a8 = a1 * r8-1= 4 * (-3)7= -4374Therefore, the 8th term of the geometric sequence is -4374.

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Answer:

This is ratio. A:B = 3:5

If the 3 parts of a =90 that means 1 part =30 (90/3=30).

So B =5.

5 parts would equal 30x5= 150

B=150cm

Answer:

Ari has two pieces of ropes, a and b, their lengths are in the ratio 3:5. rope a is 90 cm long. if ari cuts of the ratio of the length of rope a to the remaining length to rope b?​

Step-by-step explanation:

Answer:

an = 196,608 nth term

Hope it's helped

Answer:

an = -3 • 4^(n - 1)

Step-by-step explanation:

In the Histogram the horizontal line (dimension) represents the value of the selected collection plan element. The vertical line (dimension) represents the count or sum of occurrences of the primary collection element on the horizontal line.

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Answer:

4+2x is a sum.

Step-by-step explanation:

It can't be 1, because the coefficient of "x" is 2.

It can't be 2, because there aren't two variables in 4+2x. The only variable is x.

It can't be 4, because 4+2x is ADDING, not multiplying.

There we go!