Simplify. Need ASAP. show work

The row in Pascal's triangle where three consecutive entries are in the ratio 3:4:5 is the 62nd row.

To find the row in Pascal's triangle where three consecutive entries are in the ratio 3:4:5, we will use the concept of binomial coefficients.

The binomial coefficient C(n, k) represents the number of ways to choose k items from a set of n items, and is given by the formula -

C(n, k) = n! / (k! (n-k)!).

In Pascal's triangle, the entries are arranged such that the nth row contains n+1 entries, and the kth entry in that row is given by C(n, k).

We can determine the ratio of three consecutive entries in Pascal's triangle by looking at the binomial coefficients C(n, k), C(n, k+1), and C(n, k+2) in a particular row.

In order to find the row where the ratio of these three consecutive entries is 3:4:5, we will set up the following equation:

C(n, k) / C(n, k+1) = 3/4 and C(n, k+1) / C(n, k+2) = 4/5

We will now use the formula for binomial coefficients to simplify these equations as follows -

(n! / (k! (n-k)!) ) / (n! / ((k+1)! (n-(k+1))!)) = 3/4

Similarly,

(n! / ((k+1)! (n-(k+1))!)) / (n! / ((k+2)! (n-(k+2))!)) = 4/5

Solving for n, we can get n = 62

Therefore, the row in Pascal's triangle where three consecutive entries are in the ratio 3:4:5 is the 62nd row.

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A possible equation to express the situation described is 2x + 4y = 110.

The word equation can be defined as a mathematical expression that uses numbers, symbols, and even letters to mathematically represent a situation.

Consider the variables:

Now relate these variables using letters and symbols

2x (number of tables that can fit two people) + 4y (number of tables that can fit four people) = 110

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The integral of k*f(x) equals the integral of f(x) multiplied by k because the total of k*f(x) equals the sum of f(x) multiplied by k.

K*F(x) Integral = K*Fintegral (x). This is inferred from the description of a definite integral as the upper limit of a term sum. The area under the curve can be divided into a number of rectangles and their areas added if we are taking the integral of a function from a to b. The integral then equals the maximum value of this total. The result is identical to the original sum increased by k if we multiply each term of the sum by a constant called k. as a result, the maximum allowed f(x) multiplied by k because the total of k*f(x) equals the sum of f(x) multiplied by k.

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The cost of one belt is $53 and the cost of one wallet is $ 73.

The first step is to set up a system of equation using the information in the question:

20w + 14b = 2202 equation 1

20w + 83b = 5859 equation 2

Where:

b= number of belts sold

w = number of wallets sold

In order to determine the value of b, take the following steps:

Subtract equation 2 from equation 1 :

69b = 3657

Divide both sides of the equation by 69

b = 3657 / 69

b = 53

Substitute for b in equation 1:

20w + 14(53) = 2202

20w + 742 = 2202

20w = 2202 - 742

20w = 1460

w = 1460 / 20

w = 73

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The value of the expression 14.5 * 35 is 507.5

From the question, we have the following parameters that can be used in our computation:

14.5 * 35

The given expression is a simple expression that can be solved using a calculator

Using a calculator, we have the following solution

14.5 * 35 = 507.5

Hence, the solution is 507.5

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The number which must be a factor of 247247 is 11.

Given integer = 247247

To find the factor, we can add and minus signs alternately in front of each digit to determine whether a number is divisible by any of the given options. and then compute the answer. For example: If the integer is divisible by 11 if this result is divisible by 11 (including 0), if not, the number is not divisible by 11.

As per the question, and given integer -

+2 - 4 + 7  -2 + 4 - 7

= 0

Since the outcome is 0, the number 247247 can be divided by 11.

Complete Question:

Let Z be a 6-digit positive integer, such as 247247, whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must also be a factor of Z$

a) 11

b) 19

c) 101

d) 111

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Answer:

6 divided by 2/3 = 9

Step-by-step explanation:

because it is mathematically correct (can check via calculator)

and the question includes the fact that S cut the rope into 9 sections from 6.

Dion will make $16381.2 in a year.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

The formula for simple interest is:

S = p*t*r/100

where P is the principal amount of money, R is the interest rate as a decimal, T is the time.

Dion gave $12, 848 to his local church

which he calculated as 27.5 % of his yearly salary.

S = 12, 848 * 1*27.5 /100 = 3533.2

Total = 3533.2+12, 848 = $16381.2

Hence Dion will make $16381.2 in a year.

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By  polynomial equation, 7i , −7i this we get  1, y = x²  + 49 .

The x-axis and the graph's intersection points, or the places where y = 0, are known as the roots.

The roots of y equal 0

By figuring out what x is when x ( 7 I ) = y and y = 0 we can find the root at x = 7 i.

x 7 I is the factor.

By determining the value of x at the point where x ( 7 I ) = y and y = 0, the root at x = 7 I was discovered.

x + 7 I is the factor.

One equation can be created by combining all the variables.

y = ( x − 7 i ) ( x + 7 i)

To make the equation y = (x 7 I (x + 7 I easier to understand, multiply all the elements.

Use the FOIL Method to extend (x 7 I ) (x + 7 I

Put the distributive property to use.

y =  x ( x + 7 i ) − 7 i ( x + 7 i )

Put the distributive property to use.

y = x ⋅ x + x ( 7 i ) − 7 i ( x + 7 i )

Put the distributive property to use.

y = x ⋅ x + x ( 7 i ) − 7 i x − 7 i ( 7 i )

Clarify terminology.

x x + x ( 7 I ) x 7 I x ( 7 I ) is the result of combining the opposing terms.

y = x x + 7 I x + 7 I x 7 I ( 7 I ) Rearrange the elements in the terms x ( 7 I ) and 7 I x.

To get y = x x + 0 7 I ( 7 I ), subtract 7 I x from 7 I x.

y = x x 7 I ( 7 I ) is the result of adding x x and 0.

Condense each phrase.

Divide x by x to get y: x 2 7 I (7 I

7 I ( 7 I times itself..

Calculate y = x 2 49 I I by multiplying 7 by 7.

Raising I to the power of 1, y = x²- 49 ( I I

I must be raised to the strength of

1 . y = x 2 − 49 ( i i )

Raise I to the power of 1 and then find y as y = x 2 49 ( I I )

When combining exponents, use the power rule a m a n = a m + n.

y = x ² − 49 i1 + 1

To get y = x ²-  49 I ² ,add 1 and 1.

I ² should be rewritten as 1; y = x ² -  49. -  1

y = x ² + 49 multiplied by 49 by 1.

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Answer:

9 cm

Step-by-step explanation:

cos B = adj/hyp

cos B = BC/AB

cos 25° = 8 m / AB

AB = 8 m / cos 25°

AB = 9 cm

Answer:

Step-by-step explanation:

The measure of angle K and L in the first figure is ∠L = 23 degrees and ∠K = 157. Second figure, the measure of ∠K = ∠L = 70 degrees.

A polygon's interior angle is the angle created between its two adjacent sides. Alternately, we may state that the internal angle of a polygon refers to the angle measured at the interior portion of a polygon.

For figure 2 the two lines are parallel to each other, and the line that meets the parallel line at points at M and L are from two equal lines.

Hence, the angle suspended by both are equal, that is:

∠L = ∠M

∠L = 23 degrees.

Now, the ∠K and ∠J are created by two parallel lines; hence they are equal:

∠K = ∠J = x

The sum of interior angles of a quadrilateral is 360, so:

∠L + ∠M + ∠J + ∠K = 360

23 + 23 + x + x = 360

46 + 2x = 360

2x = 360 - 46

x = 157

Hence, the measure of angle K and L is 157 and 23 respectively.

For the second figure, the angle K and L are created by equal length of segments.

∠K = ∠L = x

The sum of interior angles of a quadrilateral is 360, so:

∠L + ∠M + ∠J + ∠K = 360

x + 90 + 130 + x = 360

2x + 220 = 360

2x= 360 - 220

x = 70

Hence, the angle of K and L is 70 degrees.

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You can only convert 1/6 to a decimal probability and round to 2 decimal places if you include the percentage sign (%) at the end.

When converting fractions to decimal probabilities, it is important to include the percentage sign (%) at the end. This is because when converting a fraction to a decimal, the result is not a whole number, but a decimal probability. For example, 1/6 can be written as a decimal probability of 0.17, but it is usually written as 0.17% to indicate the probability of an event occurring. The percentage sign is essential for students to understand that the decimal is a probability, rather than an incorrect answer. Percentage sign also allows the decimal to be rounded to two decimal places, giving a more precise answer. Without the percentage sign, the decimal will appear to be a whole number, which is not the correct answer.

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Answer:

p(a black sock and then a green sock)

The probability of drawing a black sock first is 2/8=1/4, and then the probability of drawing a green sock next is 2/7=2/14 since we have one less sock left. So the overall probability is (1/4) * (2/14) = 1/7

p(two blue socks)

The probability of drawing a blue sock first is 3/8, and then the probability of drawing another blue sock next is 2/7 since we have one less sock left. So the overall probability is (3/8) * (2/7) = 6/56 = 3/28

p(a green sock and then a red sock)

The probability of drawing a green sock first is 2/8, and then the probability of drawing a red sock next is 1/7 since we have one less sock left. So the overall probability is (2/8) * (1/7) = 2/56 = 1/28

4.p(two green socks)

The probability of drawing a green sock first is 2/8, and then the probability of drawing another green sock next is 1/7 since we have one less sock left. So the overall probability is (2/8) * (1/7) = 2/56 = 1/28

Note that these are the theoretical probabilities, and in reality, drawing a sock and not replacing it will change the number of socks left, so the probability of the next draw will change accordingly.

Step-by-step explanation:

The best approximation for the area of this figure is A = 12+9.125π units²in the given figure.

What is the diameter of triangle?

In a triangle, the diameter is a line segment that passes through the midpoint of one side of the triangle and is perpendicular to that side. It is also the longest chord of the triangle. The length of the diameter is called the diameter of the triangle.

Draw the diameter from point (-1, -5) to point (2, 3).

The triangle has base 3 and height 8.

The diameter of the semicircle is the hypotenuse of the triangle.

d = root(3² + 8²)

d = 8.544

The radius is half the diameter.

r = d/2 = 8.544/2 = 4.272

The total area is the area of the triangle plus the area of the semicircle.

A = 3*8/2 + π*4.272²/2

A = 12+9.125pi units²

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The number of hours that Alonso would have to work to earn $ 554. 40, given the same hourly wage, is 37.9 hours

To find the number of hours that Alonso needs to work in the week to make $ 554. 40, you first need to find the hourly wage :

= Amount earned / Hours worked

= 204. 40 / 14

= $ 14. 60 per hour

If Alonso wants to earn $ 554 .40 then the number of hours he would need to work is:

= Amount to be earned / Hourly wage

= 554. 40 / 14. 60

= 37.9 hours

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Whatever 18x+1 equals is what it equals

Answer:

3 3

Step-by-step explanation:

graph of a line passing through the points 0 comma 3 and 3 comma 1

The initial velocity is related to the maximum height by the relation [tex]v_{0}=\sqrt{\frac{2gH}{3} }[/tex]

The initial velocity (v0) is the velocity of an object at the beginning of its motion. In the scenario you described, the initial velocity of the rock is the velocity at which it is thrown upward from the edge of the roof of a building.

Without any information about the velocity at which the rock is thrown, it is not possible to determine the initial velocity.

Using the fact that the velocity at maximum height is zero, we can write the following:

      [tex]v_{y}=v_{y_{0,t} }+ a_{y}t[/tex]

at maximum height, the equation becomes

[tex]0=v_{0}-gT_{max}[/tex]

=> [tex]T_{max}=\frac{v_{0} }{g}[/tex]

Now, the displacement is (-H)−H) when the rock hits the ground, so we can use one of the kinematic equations to write the following

[tex]y-y_{0}=v_{0}t+\frac{1}{2}a_{y}t^{2}[/tex]

where [tex]y_{0} =0 and y=-H[/tex]

On substituting the values and rearranging we get:

[tex]v_{0}=\sqrt{\frac{2gH}{3} }[/tex]

Therefore, The initial velocity is related to the maximum height by the relation [tex]v_{0}=\sqrt{\frac{2gH}{3} }[/tex].

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The value of x is 10.79

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

sin (tetha) = opp/ hyp

cos ( tetha) = adj/ hyp

tan ( tetha) = opp/ adj

tetha = 26

hyp = 12

adj = x

cos 26 = x/12

cos 26 × 12 = x

x = 0.899 × 12

x= 10.79

Therefore the value if x is 10.79

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Sarah and Winston buy the same brand of T-shirts from different stores. Sarah pays $8 and Winston pays $4.The simplest way of writing this as a ratio 2:1.

What is Ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.

The relationship between the amounts of two or more objects—referred to as a ratio—indicates how much of one object is contained in the other. The ratio formula can be used to represent a ratio as a fraction. The ratio formula is given as a:b = a/b for any two quantities, let's say a and b.

Two quantities are compared to form a ratio. An equality of two ratios is a proportion. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.

We are given;

Sarah pays $8 for t shirt

Winston Pays $4 for t shirt

So, Simplest way of writing this as in ratio is ;

Sarah/Winston = 8/4=2/1

Hence , this is written in ratio as 2:1.

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The exact length (in inches) of the arc of a circle formed by given angle (in radians) and radius  is 5.233 inches.

The radius of a circle and the central angle determine the length of an arc. We are aware that given an angle of 360 degrees, the arc length corresponds to the circumference. Thus, the arc length is determined by multiplying the radius by the Centre angle (in radians).

Arc length = radius x angle(in radians)

Radius = 2 inches

Angle = 5pi/6 radians

Arc length = 2 x (5pi/6)

                = 5.233

Hence, the arc length is 5.233 inches.

Correct question :

find the exact length (in inches) of the arc of a circle formed by an angle that measures 5pi/6 radians if the circle has radius 2 inches. (round you answer to two decimal places.)

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Event A has the highest probability, which is "at least one 6 appears when 6 fair dice are rolled.

Event A: At least one 6 appears when 6 fair dice are rolled has the highest probability. The probability of rolling at least one 6 with a fair die is 5/6, and the probability of rolling at least one 6 with 6 fair dice is (5/6)^6.

Event B: At least two 6's appear when 12 fair dice are rolled has a lower probability than A.

Event C: At least three 6's appear when 18 fair dice are rolled has a lower probability than B.

So among these three events, this is event A with the highest probability.

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The dimension of the largest possible rectangular area that can be fenced for $4800 is 300 yard × 150 yard. The area, A of the rectangle as a function of its width, w is A = 300w - 1.5w².

Let the width of the rectangular area be "w" and its length be "l".

The cost of the east-west direction fencing is

2w * 12 = 24w

and the cost of the north-south direction fencing is

2l * 8 = 16l

Since the rancher wants to spend exactly $4800 on fencing, we can write an equation to represent the cost:

24w + 16l = 4800

Divide by 8

3w + 2l = 600

Therefore, l = 300 - 1.5w

The area of the rectangle is given by "lw", so

A = lw

Substituting the value of "l" from the first equation into this second equation:

A = (300 - 1.5w)w

A = 300w - 1.5w²

Thus, the area of the rectangle is a function of its width and can be expressed as Area = 300w - 1.5w².

To find value of w with maximum area, dA/ dw = 0

300 - 3w = 0

w = 100

Therefore, l = 300 - 1.5*100

l = 150

--The question is incomplete, answering to the question below--

"A rancher who wishes to fence off a rectangular area finds that the fencing in the east-west direction will require extra reinforcement due to strong prevailing winds. Because of this, the cost of fencing in the east-west direction will be $12 per (linear) yard, as opposed to a cost of $8 per yard for fencing in the north-south direction. Find the dimensions of the largest possible rectangular area that can be fenced for $4800, express the area of the rectangle as a function of its width."

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Answer:  To find the surface area of the figure, we need to add up the areas of all the individual faces. The triangular prism has three rectangular faces and three triangular faces, and the rectangular prism has six rectangular faces.

The triangular prism:

The area of one of the rectangular faces is (x * z)/2 = (5 * 8.75)/2 = 21.875 inches^2

The area of one of the triangular faces is (x * W)/2 = (5 * 6.2)/2 = 15.5 inches^2

The rectangular prism:

The area of one of the rectangular faces is x * y = 5 * 20 = 100 inches^2

So, the total surface area of the figure is

(3 * 21.875) + (3 * 15.5) + (6 * 100) = 65.625 + 46.5 + 600 = 712.125 inches^2

So the surface area of the figure is 712.125 inches^2

Step-by-step explanation:

The answer is the same i. e., 4.375 in all the cases as shown

There are two terms which describe the three numbers in a multiplication problem. The factors are the numbers that are being multiplied together. The product is the result or answer of multiplying the multiplicand by the multiplier.

= 3/7 x 5/6 x1/4

=  38/8

= 3/7 x 1/4 x 5/6

= 5/6 x 1/4 x3/7

= 5/6 x 3/7 x 1/4

= 1/4 x 5/6 x 3/7

=1/4 x 3/7 x 56

= 4.375

The answer is the same i. e., 4.375 in all the cases as shown.

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The statement is true about the home appliances sales is "Home appliances sales increased profits by 8 percentage points".

Given that ,

The right answer is that 90% of all random samples of 50 students from this high school would produce a 90% confidence interval that contains the actual mean amount of money students spend on lunch.

an appliance store manager noted that the sales of home appliances contributed

74 % of the store profits in the year 2010, and 82 % in the year 2011.

Thus, the profit in the year 2010 is 74 %.

The profit in the year 2011 is 82 %.

The increased profit from year 2010 to 2011 is ( 82-74 ) % = 8%

Hence, the statement true about the home appliances sales is "Home appliances sales increased profits by 8 percentage points".

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The value of each variable in the parallelogram is h = 9 and g = 59.

A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has neighboring angles that add up to 180 degrees. Angles on either side are equal.

We know that the opposite sides of a parallelogram and the opposite angles of a parallelogram are equal.

Using the above statement, we can write:

16 - h = 7

16 - 7 = h

h = 9

g + 4 = 63

g = 63 - 4

g = 59

Hence, the value of each variable in the parallelogram is h = 9 and g = 59.

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Hey there!

Answer:

In the expression, 23 is the constant.

Hope this helps!

Answer:

No, these ratios are not equivalent.

Step-by-step explanation: