Help please and show work if possible!

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 charge nurse is reviewing orthostatic hypotension with a group of newly licensed nurses. the statements should the charge nurse make is c) a decrease of 20 mm of Hg in the diastolic pressure with a position change indicates orthostatic hypotension.

Orthostatic hypotension — also called postural hypotension — is a form of low blood pressure that happens when standing after sitting or lying down. Orthostatic hypotension can cause dizziness or lightheadedness and possibly fainting.

Orthostatic hypotension can be mild. Episodes might be brief. However, long-lasting orthostatic hypotension can signal more-serious problems. It's important to see a health care provider if you frequently feel lightheaded when standing up.

Occasional orthostatic hypotension is usually caused by something obvious, such as dehydration or lengthy bed rest. The condition is easily treated. Chronic orthostatic hypotension is usually a sign of another health problem, so treatment depends on the cause.

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If Florida had the same number of hospitals per million people as Texas, it would have 558 hospitals in 2009. This is slightly higher than the actual number of hospitals in Florida in 2009 (343).

Proportional reasoning is a mathematical process used to compare the ratios of two or more similar quantities.

This question uses the theory of proportional reasoning.

In this case, we are comparing the ratio of the number of hospitals per million people in Texas to the ratio of the number of hospitals per million people in Florida.

By comparing these two ratios, we can estimate the number of hospitals in Florida given the same ratio as Texas.

1. Calculate the number of hospitals per million people in Texas: 428 hospitals / 26.4 million people = 16.2 hospitals per million people.

2. Calculate the number of hospitals per million people in Florida: 343 hospitals / 19.5 million people = 17.6 hospitals per million people.

3. Multiply the number of people in Florida (19.5 million) by the number of hospitals per million people in Texas (16.2): 19.5 million people x 16.2 hospitals per million people = 315.3 hospitals.

4. Round the result to the nearest whole number: 315.3 hospitals = 315 hospitals.

5. Compare the estimated number of hospitals in Florida (315) to the actual number of hospitals in Florida in 2009 (343).

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Answer:

False

Step-by-step explanation:

If the card is removed after it is picked, the number of cards in the deck decreases. For example, if you pick the first card remove it. The cards available decreases to 51, so the probability becomes 1/51 for the next draw. This is dependant probability.

Answer: The last three digits are 201.

Step-by-step explanation: Hope this helps

Expected values are = 150/7 .Ci-square distribution is Day of the week observed count Expected Chi-square = O E (O -E )2/E

testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis. Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Statistical hypothesis: A statement about the nature of a population. It is often stated in terms of a population parameter.

Null hypothesis: A statistical hypothesis that is to be tested. : The alternative to the null hypothesis.

Test statistic: A function of the sample data.

The critical value for the chi-square statistic is determined by the level of significance (typically . 05) and the degrees of freedom. The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) where r is the number of rows and c is the number of columns.

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Expected values are = 150/7 .Ci-square distribution is Day of the week observed count Expected Chi-square = O E (O -E )2/E

testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis. Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Statistical hypothesis: A statement about the nature of a population. It is often stated in terms of a population parameter.

Null hypothesis: A statistical hypothesis that is to be tested. : The alternative to the null hypothesis.

Test statistic: A function of the sample data.

The critical value for the chi-square statistic is determined by the level of significance (typically . 05) and the degrees of freedom. The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) where r is the number of rows and c is the number of columns.

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Answer:

The statement that is true is:

All the equal parts must have the same area.

This is true because when a rectangle is divided into equal parts, it means that the area of each part is the same. The lines dividing the shape can be drawn in any direction (top to bottom, left to right, diagonal, etc.) and the shape of the parts can also be different( rectangles, squares or any shape).

A recycling truck that feeds on petroleum is would not be an application of Stuart Wilkinson's theory.

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Answer:

Step-by-step explanation:

Answer:

24 waffles

Step-by-step explanation:

16÷6=2.66 so she can make that many waffles per egg

9x2.66= 23.94 which would round up to 24 waffles

The answer to this question is determined on the volume of water coming from the faucet. When the tap is switched on but no water flows out, the tank can retain 275 gallons eternally. Yet, if water flows out of the tap at a constant pace, the tank will take a given period of time to empty.

A gallon is a volume unit used mostly in the United States, equivalent to 128 US fluid ounces or 3.785 liters.

To establish how long it will take to empty the tank, we must first know the flow rate of the tap, which is normally measured in gallons per minute (GPM). We may use the following calculation to calculate the time it will take to empty the tank once we have known the GPM:

Time (minutes) = 275 gallons per minute / GPM

For example, if the tap is running at a rate of 10 GPM, the time required to empty the tank is:

Time (minutes) = 275 gallons /10 GPM = 27.5 minutes

As a result, if the tap is set at 10 GPM, it will take 27.5 minutes for the tank to empty before Angel can turn off the water.

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Answer:
f(6) = -22
g(-2) = -10

Step-by-step explanation:
Plug in 6 into f(x) = -4x + 2
f(6) = -4(6) + 2
f(6) = -24 + 2
f(6) = -22

Plug in -2 into g(x) = 2x^3 + 6
g(-2) = 2(-2)^3 + 6
g(-2) = 2(-8) + 6
g(-2) = -16 + 6
g(-2) = -10

I hope this was able to help you :D

The water content of the cylindrical sample of saturated sandy clay is 2.54%.

To determine the water content of the sample, we have to calculate the mass of water present in the sample before oven-drying, next divide that value by the total mass of the sample.

Firstly, we have to calculate the mass of water present in the sample before oven-drying. We already know that the mass of the sample before oven-drying is 182g and the mass after oven-drying is 151.7g.

So the mass of water present in the sample is:

mass of water = mass before oven-drying - mass after oven-drying

mass of water = 182g - 151.7g = 30.3g

Next, divide the mass of water by the total mass of the sample and multiply by 100 to get the water content as a percentage:

water content (w%) = (mass of water / total mass of sample) * 100

water content (w%) = (30.3g / 1192.0g) * 100 = 2.54%

So, the water content of the cylindrical sample of saturated sandy clay is 2.54%.

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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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Hey there!

Answer:

In the expression, 23 is the constant.

Hope this helps!

Answer:

not e

Step-by-step explanation:

A common aspect ratio for computer screens is 16:9, which means that for every 16 units of width, there are 9 units of height. This aspect ratio is also used on many televisions and mobile devices.

If a screen has an aspect ratio of 16:9, the width and height will be similar on all screens with this aspect ratio. However, the diagonal measurement will vary depending on the size of the screen.

Congruent screens are two or more screens that have the same dimensions. Two screens are congruent if and only if corresponding sides are equal and corresponding angles are equal. This can be proven using the postulates of congruence, such as the SSS (Side-Side-Side) postulate or the SAS (Side-Angle-Side) postulate.

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The trigonometric form of complex number -6√3 + 6i will be option a. 12(cos150 + isin150)

We are given z = -6√3 + 6i

Now the polar form of a complex number is given by r(cosx + isiny)

We first need the modulus which for a complex number a + bi

r = √(a² + b²)

Hence r = √(108+36)

= √(144)

= 12

Now we need to find the angle x such that

tan x' = |b/a|

or, tan x' = |-1/√3|

or, tan x' = 1/√3

or, tan x' = tan(π/6)

or, x' = π/6

Now since a < 0 and b > 0 x will lie in Quadrant 2

Hence x = π - π/6

= 5π/6 =

Hence we get the trigonometric form to be

12(cos5π/6 + isin5π/6)

= 12(cos150 + isin150)

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Answer:

D. x = 12

Step-by-step explanation:

8 x 4 = 32

3 x 4 = 12

x = -2 and x = -3 are the two values of x that are roots of the equation x^2 + 3x - 6 = 0

What is the root of the equation?

A root of an equation is a value of the variable that makes the equation true. An equation is a statement that asserts the equality of two expressions. A root of an equation is also known as a solution or a zero of the equation.

The two values of x that are roots of the equation x^2 + 3x - 6 = 0 are x = -2 and x = -3.

To find the roots of the equation, we can use the factoring method, which consists of factoring the polynomial on the left side of the equation.

x^2 + 3x - 6 = 0

(x-2)(x+3) = 0

So, x - 2 = 0, x = 2 and x + 3 = 0, x = -3

Alternatively, we can use the Quadratic formula, which states that for any quadratic equation in the form ax^2 + bx + c = 0, the roots are given by:

x = (-b ± √(b^2 - 4ac))/ 2a

So, by plugging in the values of a, b and c we have:

x = (-3 ± √(3^2 - 41-6))/ 2*1 = (-3 ± √(9+24))/2 = (-3 ± √33)/2 = (-3 ± √33)/2 = -2, -3

Hence, x = -2 and x = -3 are the two values of x that are roots of the equation x^2 + 3x - 6 = 0

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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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The 10% condition when constructing a confidence interval for a population proportion states that the sample size should be less than 10% of the population size.

This is expressed mathematically as follows:

n/N < 0.10

Where n is the sample size and N is the population size. For example, if the population size is 500, then we must ensure that the sample size is less than 50 (500 x 0.10 = 50). This is because if the sample size is larger than 10% of the population size, then the confidence interval will not be reliable. In other words, the results of the confidence interval may be inaccurate and biased.

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The exponential model for the population can be written as P(t) = 11,000(1.163)t, where P(t) represents the population size in t years and 1.163 is the growth rate.

We can calculate the population size at any time t by multiplying the initial population size (11,000) by the growth rate (1.163) raised to the power of t. For example, after 10 years the population size would be P(10) = 11,000(1.163)10 = 22,906.7. We can also use the model to predict the population size in future years. For example, the population size in 20 years will be P(20) = 11,000(1.163)20 = 40,803.7. For example, if the population is measured after 10 years, the equation would be P(10) = 11,000(1.163)^10. Solving for P(10) yields a population of 21,945 organisms. Thus, the population has grown by 16.3% per year over the 10-year period and has increased by 10,945 organisms.

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The list of items that shows what Elena could buy is the list for which the sum of all prices is at most 10.

The maximum amount that Elena can spend is given as follows:

$10.

Hence, for each list, the sum is calculated for the prices of all the items, giving the total price.

The list with a sum of at most $10 is the list that shows what Elena can buy.

The problem is incomplete, hence the general procedure needed to solve it is presented.

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The net profit of the company this year is $729,000

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

Given;

Last year small manufacturing company netted $540,000

The net profit increased this year by 135%

Now, to find 135% of $540,000

Let the profit this year be x

x*100/$540,000=135

x=135*5400

x=729000

Therefore, net profit by 135% will be $729,000

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The best way to improve the running speed of the game is to use an algorithm which can quickly evaluate potential moves and select the best one.

For example, alpha-beta pruning is an algorithm which is used for game tree search. It prunes the search tree and eliminates the branches which are not likely to contain the optimal solution. Alpha-beta pruning uses the following formula to evaluate positions:

Max(α, Min(β, v))

Where α is the best value that the maximizing player can guarantee at the current branch of the tree, β is the best value that the minimizing player can guarantee at the current branch of the tree and v is the value of the current position. The evaluation of the position helps to quickly identify the best move. This reduces the time taken to evaluate the potential moves and thus improves the running speed of the game.

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The solution to the system of equations include the following: B. (6, 3).

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

By critically observing the graph of the lines representing the system of equations, we can reasonably infer and logically deduce that the correct solution set lies in Quadrant I and it is denoted by the point of intersection of both the x-axis and y-axis, which is given by the ordered pair (6, 3).

In conclusion, the ordered pair (6, 3) is a solution to the system of equations represented by the given graph.

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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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