The following are the lengths of stay (in days) for a random sample of 20 patients discharged from a particular hospital 13,9,5,11,6,3,12,10,11,7,4,4,2,2,2,10,10,10,12,12Draw the histogram for these data using an initial class boundary of 1.5 and a class width of 2 you can add or remove classes from the figure. Label each class with its endpoints.

answer is 7.5

\( {9}^{2} = {5}^{2} + {x}^{2} \\ 81 = 25 + {x}^{2} \\ - 25 \: \:- 25 \\ 56 = {x}^{2} \\ \sqrt{56} = \sqrt{x} \\ 7 .4833... \\ 7.5\)

Answer:

  x < -3 or x > 4

Step-by-step explanation:

The product of the factors is 4th-degree, and the leading coefficient is 1 (positive).

The factors tell you the following about the zeros:

  x = -3 . . . sign change from + to -

  x = -1 . . . graph touches, but no sign change. - on either side of x=-1

  x = 4 . . . sign change from - to +

__

The function will be positive for x < -3 and for x > +4.

_____

Additional comments

The value of the function is zero when any of its factors is zero. The value of a factor changes sign when the value of x changes from one side of the 0 to the other. For example, here, we have x+1 as a factor, so x=-1 is a zero. When x = -0.9, the factor is positive (-0.9 +1 = 0.1). When x = -1.1, the factor is negative (-1.1 +1 = -0.1). If this factor were to the first power, it would cause the value of the function to change sign at x=-1.

However, the factor (x+1) has an even power: (x+1)^2. That means when the factor is negative, its square is positive, and when the factor is positive, its square is positive. In short, the factor (x+1)^2 causes the function to be zero at x=-1, but does not make the function change sign there.

The product of all of these factors will result in a polynomial with x^4 as the highest-degree term. That means the function is of even degree. The leading coefficient is 1, so is positive, and the function will generally have a U-shape. The left-most (odd-degree) zero will be where the function changes sign from positive to negative. The right-most (odd-degree) zero will be where the function changes sign from negative to positive. Those zeros are x=-3 and x=+4, respectively. There are no places between these where the function changes sign, so these zeros are the ends of the regions where the function is positive (>0).

Answer:

1. diameter=8 kilometres

2. area=98.96 inches

3. 37m

Step-by-step explanation:

1. diameter= 2*radius

2. area of sector=θ out of 360*π\(r^{2}\) where θ is the angle

3. area of garden=π\(r^{2}\)

        706.5=π\(r^{2}\)

     \(r^{2}\)=706.5/π

        = 225(nearest whole)

     r=\(\sqrt{225}\)=15m

we now use Pythagoras theorem to find length of each pathway

\(40^{2} =15^{2} +x^{2}\)

1600=225+\(x^{2}\)

\(x^{2}\)=1600-225=1375

x=\(\sqrt{1375}\)=37 m (to nearest whole)

The tangent pathways from the entrance form right triangles from which

the length of the pathway which are the sides of the triangle, can be found.

Reasons:

1. The radius of the particle accelerator = 4 kilometers

The diameter of the particle accelerator = 2 × The radius

Therefore;

The diameter = 2 × 4 km = 8 km

The accelerator's diameter is 8 kilometers

2. The area of a sector of a circle is A = \(\displaystyle \frac{\theta}{360^{\circ}} \times \pi \cdot r^2\)

The angle subtended by the sector, θ = 140°

The radius of the sector, r = 9 inches

Therefore;

\(\displaystyle A = \frac{140^{\circ}}{360^{\circ}} \times \pi \times 9^2 = \mathbf{ 31.5 \cdot \pi}\)

The area of the shaded sector, A = 31.5·π in.² ≈ 98.96 in.²

3. The distance from the center to the main entrance, d = 40 m

Area of the circular garden, A = 706.5 m²

Solution:

The radius of the garden, r = √(A ÷ (π))

Therefore;

r = √(706.5 ÷ (π)) ≈ 15

The tangent pathways are perpendicular to the radius of the circular garden.

Therefore, the pathway from the entrance, the 40 m. distance from the center to the entrance and the radius form a right triangle.

Where;

The 40 m. distance = The hypotenuse side

By Pythagorean theorem, we have;

40² = r² + (Length of the pathway)²

Which gives;

40² = 15² + (Length of the pathway)²

Length of the pathway ≈ √(40² - 15²) ≈ 37.1

The length of each pathway is approximately 37.1 m.

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Answer:

100 ^2

10000

Step-by-step explanation:

100^100 / 100^98

We know that a^b / a^c = a^(b-c)

100 ^ (100-98)

100 ^2

10000

Answer:

100

Step-by-step explanation:

Answer: infinitely many solutions

Answer:

All real numbers are solutions

Step-by-step explanation:

2x+4x-6x=7-19+12

0=0

Answer:

12

Step-by-step explanation:

With PEMDAS you could know to do parentheses FIRST

6 x (10 - 2^3)

6 x (2)

12

Answer:

your answer would be 12

Step-by-step explanation:

Incordding to math this dot is mutpcation

but next to it is is a bracket in math a bracket me you need to add or subtrack evrything  in it  then multpliy the answer with the the number in it

so we just need simplfy what in the bracket

so the equation is actaliy 6x2.Hence the answer is 12

Answer:

see explanation

Step-by-step explanation:

let s be the second side then the first side is s - 5 and the third side is

s - 5 + 3 = s - 2

-------------------------

the perimeter (P) is the sum of the 3 sides of the triangle.

given P = 17 , then

s - 5 + s + s - 2 = 17

3s - 7 = 17 ( add 7 to both sides )

3s = 24 ( divide both sides by 3 )

s = 8

third side = s - 2 = 8 - 2 = 6 in

hmmmmmmmmmm the. answer. is 9/7

The product 3 x 3/7 as a fraction can be written as 9/7.

Given are two numbers 3 and 3/7.

We have to find the product of these numbers.

These numbers has to written as the product as a fraction.

When a fraction is multiplied by a whole number, the whole number is multiplied with the numerator of the fraction by keeping the denominator same.

Here whole number is 3 and the fraction is 3/7

3 x 3/7 = (3 x 3) / 7

           = 9/7

Hence the product is 9/7.

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Answer:

I may be wrong but I think it's c

The roots of the quadratic equation are x = (3±2i)/2

The meaning of quadratic formula is a formula that gives the solutions of the general quadratic equation ax² + bx + c = 0

Given a quadratic equation, 4x²+13 = 12x

4x²-12x + 13 = 0

Quadratic formula =

x = [-b ± (√b²-4ac)]/2a

a = 4, b = -12 and c = 13

x = [12 ± (√(-12)² - 4*4*13)]/2*4

x = (12 ± 8i)/8

x = (3 ± 2i)/2

Hence, The roots of the quadratic equation are x = (3±2i)/2

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Answer:

quantity of 16 plus 18 i over 145

Step-by-step explanation:

Answer:

sqrt(-49) / [ (7-2i) - (4+9i) ]

= 7i / (3 - 11i)

= 7i (3+11i) / [ (3 - 11i) (3 + 11i) ]

= (21 i - 77) / (9 + 121) = choice (d), (-77 + 21i) / 130

Step-by-step explanation:

:) hope i helped

Answer:

The answer is b

Step-by-step explanation:

Answer:

the answer is B

Step-by-step explanation:

Answer:

2 1/3

Step-by-step explanation:

8-1=7

9-6=3

7/3= 2 1/3

Answer:

y = 7

Step-by-step explanation:

y-4 = 3

Add 4 to both sides of the equation so the y is 'isolated' (alone).

y - 4 + 4 = 3 + 4

Now simplify

y-0 = 7

y = 7

Answer: y = 7

Step-by-step explanation:

y - 4 = 3

add 4 to both sides.

this becomes y - 4 + 4 = 3 +4

                       y + 0 = 7

                       y = 7

If Leyanna choose one marble at random, the chances that it is yellow is 4/9 that is 0.44.

Total number of marbles in bag are 9

There are 5 red marbles and 4 yellow marbles

Total number of marbles = 5 + 4 = 9.

Therefore total number of cases is 9

Since there are 4 yellow marbles, the number of favorable outcomes is 4.

So P ( a yellow marble) =Number of favorable cases/ Total number of cases

= 4/9

So probability of choosing a yellow marble is 4/9.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

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​

The contract between Gene and Hollis regarding the trail bike is most likely voidable due to the non-disclosure of the disconnected odometer.

Gene's failure to disclose that the odometer on the trail bike was disconnected 90,000 miles ago raises concerns of misrepresentation and fraud. Generally, when a seller fails to disclose material information that would significantly impact a buyer's decision-making process, it can render the contract voidable. In this case, the disconnection of the odometer and the significant difference between the displayed mileage and the actual mileage could be considered material information.

The non-disclosure of the disconnected odometer could be seen as a fraudulent act, as it involves intentional deception or misrepresentation. Fraudulent misrepresentation can provide grounds for the affected party (in this case, Hollis) to seek remedies such as rescission of the contract, seeking damages, or demanding a refund. The misrepresented mileage could significantly affect the value and condition of the trail bike, as well as Hollis' decision to purchase it.

It is important to note that contract laws can vary across jurisdictions, and specific circumstances may influence the legal outcome. Consulting with a legal professional familiar with the applicable laws and regulations in the relevant jurisdiction would provide the most accurate advice regarding the contract's enforceability and potential remedies available to Hollis.

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Answer:

Step-by-step explanation:

38 -$2 per ride = 36/2 per mile driven=18 miles

The central limit theorem states that if we draw a simple random sample (SRS) from any population, regardless of the shape of the population distribution.

The sampling distribution of the sample mean will be approximately normal if the sample size is large enough. This means that the mean of the sampling distribution will be the same as the mean of the population, and the standard deviation of the sampling distribution will be the standard error of the mean, which is equal to the standard deviation of the population divided by the square root of the sample size. Therefore, the central limit theorem allows us to make inferences about the population mean based on the sample mean, as long as we have a large enough sample size.
According to the Central Limit Theorem, if we draw a Simple Random Sample (SRS) from any population, the sampling distribution of the sample mean will APPROXIMATELY be normal, not exactly normal. This approximation improves as the sample size increases, especially when the sample size is large (usually n ≥ 30). The Central Limit Theorem allows us to make inferences about the population based on the sampling distribution.

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The factored form of the given trinomial is (x -7)(x +1)

From the question, we are to factor the given trinomials

The given trinomial is

x² + 6x - 7

The trinomial is a quadratic expression. The trinomial/ quadratic expression can be factored as a product of two binomial. When factored, the trinomial will take the form (x + a)(x + b)

Where are a and b are integers.

Factoring the trinomial

x² + 6x - 7

To factor the trinomial, we will find two numbers such that when added, we get the middle term; and when these numbers are multiplied we get the constant term.

The numbers that satisfy this condition are +1x and -7x

x² +x -7x - 7

x (x + 1) -7(x +1)

(x -7)(x +1)

Hence, the factored form of the given trinomial is (x -7)(x +1)

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Answer:10

Step-by-step explanation:

Answer:

3,250

Step-by-step explanation:

Let's go from left to right, using multiple of 12 times a power of 10 in the process.

What is the closest multiple of 12,000 (12 * 10^3) to 39,000 without going over? That's 3 (36,000). That's the thousands digit in this answer.

12,000 * 3 = 36000

39000 - 36000 = 3000

What's the closest multiple of 1,200 (12 * 10^2) to 3,000 without going over? That's 2 (2,400). That's the hundreds digit.

1,200 * 2 = 2,400

3,000 - 2,400 = 600

What is the multiple of 120 (12 * 10) closest to 600 without going over? That's 5 (600, it's even!). That's the tens digit. Since it goes evenly, 0 is the ones digit.

120 * 5 = 600

600 - 600 = 0.

The answer to 39,000 over 12 is 3,250.

Answer:

1000

Step-by-step explanation:

when rounding a number to the nearest 100 we used the tents place to decide whether he will raise a score or keep it the same.

remember five or more raise the score, seven is greater than 5 so we raise the score by 1 so 976 rounded to the nearest 100 is 1000

Answer:

D. 5x 2+12x−7

Step-by-step explanation:

(0-(2•(x2)+8x)-9)+4x)+7x2)+2

(0-2x2)+8x)-9)+4x)+7x2)+2

Factoring  5x2+12x-7

The first term is,  5x2  its coefficient is  5 .

The middle term is,  +12x  its coefficient is  12 .

The last term, "the constant", is  -7

Step-1 : Multiply the coefficient of the first term by the constant   5 • -7 = -35

Step-2 : Find two factors of  -35  whose sum equals the coefficient of the middle term, which is   12 .

     -35 +   1 =   -34

     -7+   5 =   -2

     -5+   7 =   2

     -1+   35=   34

No two such factors can be found

Trinomial can not be factored

Answer:

see image,

Area = 5 units^2

Step-by-step explanation:

Graph three points to make a triangle.

Use

Area = 1/2•b•h

to find the area.

Fortunately, the base is horizontal and the height is vertical, so we can just count the squares to find those lengths. (If they aren't horizontal and vertical, then you need distance formulas)

see image.

Total time for whole journey can be calculated by adding the three parts of the journey which would give answer as 2.5 hours.

What is a fraction?

The components of an entire or group of items are represented by fractions. A fraction consists of two components. The numerator is that the figure at the top of the line. It details the amount of equal portions that were taken from the total or collection. The denominator is that the figure that appears below the line.

Main Body:

total time = 20 minutes + 40 minutes + 1 hour 30 minutes

                = 2.5 hours or 5/2 hours.

Hence total time for journey is 2.5 hours.

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The value in radians of cos⁻¹0.98 is 0.2003 (rounded to four decimal places).

Step-by-step explanation: We are given the expression cos⁻¹0.98. We have to find the value in radians of this expression.

Let us solve this expression as follows: We know that cos is a trigonometric function and has an inverse cos⁻¹, which means cosine inverse, or arc cosine.

Let us use the calculator to solve this expression as follows: Click on the cos⁻¹ button.

Enter 0.98. Press the enter button to get the solution. The calculator shows that cos⁻¹0.98 is 0.2003 (rounded to four decimal places). Therefore, the value in radians of cos⁻¹0.98 is 0.2003 (rounded to four decimal places).

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Answer:

The slope is 30, and the y-intercept is 75.

Step-by-step explanation:

Use two points from the table, and find the equation of a line given two points.

Point 1: (1, 105)

Point 2: (3, 165)

y = mx + b

slope = m = (y_1 - y_1)/(x_2 - x_1)

m = (165 - 105)/(3 - 1) = 60/2 = 30

y = 30x + b

Use point (1, 105) for x and y.

105 = 30(1) + b

105 = 30 + b

b = 75

y = 30x + 75

The slope is 30, and the y-intercept is 75.

The values of c for which y = C is a constant solution of y' = y² + 5y - 6 are 1 and -6.

Option d is the correct answer.

To find out the constant solutions of the equation (1), we need to first solve it. Let's solve equation (1) using separation of variables.

Separating variables in equation (1), we get:

dy / dx = y² + 5y - 6Now, multiplying both sides by dx, we get:

dy = (y² + 5y - 6) dxIntegrating both sides, we get:

∫ dy = ∫ (y² + 5y - 6) dxy = (y³ / 3) + (5y² / 2) - 6y + C1... (2)

where C1 is the constant of integration.

We can see that equation (2) is not in the form of y = f(x), which means we can't use it to find the values of c for which y = c is a constant solution of equation (1).

To convert equation (2) into the required form, we need to first simplify it.

Let's do that.Simplifying equation (2), we get:

y (y² + 5y - 12 / 3) + C1y (y² + 5y - 12) / 3 + C1

Now, for y = c to be a constant solution of equation (1), we have:

y (y² + 5y - 12) / 3 + C1 = c

Multiplying both sides by 3, we get:

y (y² + 5y - 12) + 3C1 = 3c

Rearranging, we get:y³ + 5y² - 12y - 3c + 3C1 = 0

Now, if y = c is a constant solution of equation (1), it means that equation (1) should be equal to 0.

So, we have:

y' = 0

On substituting y = c in equation (1), we get:(dy / dx) = c² + 5c - 6= 0

Solving the above equation, we get:

c = 1 and -6

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The company is deploying chargeback type of IT funding model where the IT department charges her department for actual usage of a SharePoint server, determining how often users log in and how much storage space her department consumes.

Traditional IT and project finance methods offer a key business risk and, if not modified, jeopardize the future of technology-based enterprises.

This excerpt from the whitepaper Changing the Finance Method by Keanen Wold, Levi Geinert, Shaun Norris, Charles Betz, Beth Dumke, Sam Guckenheimer, and Troy Magennis discusses that contradiction over how traditional financing methods handle ethical concerns and also what Agile and DevOps teams require to execute successfully.

Balancing the high-risk investment in innovation (research and development department) with regular business-as-usual responsibilities has always been difficult for organizations. Too much risk might, in the case of an unexpected failure, result in a business's dissolution; too little innovation could ultimately cause the company to be overtaken and lose market share to rivals and new upstarts.

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The value of k from the equation is k = -20

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = kx   be equation (1)

Let the first point be P ( 4 , -80 )

Substituting the values in the equation , we get

-80 = 4k

Divide by 4 on both sides of the equation , we get

k = - ( 80/4 )

On simplifying the equation , we get

k = -20

Hence , the equation is k = -20

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