express x^2-5x+8 in the form (x-a)^2+b where a and b are top-heavy fractions

Answer:

The median is 21

Step-by-step explanation:

Since you have 12 numbers in order, that's an even number, once you put them in numerical order and start crossing them off on both sides, you'll have 18 and 24 left, add them together and divide them by 2 and you'll have your median 21.

Answer:

\(405 \: {units}^{3} \)

Step-by-step explanation:

Given:

A triangular prism

a (base area) = 45

h (height) = 9

Find: V (volume) - ?

\(v = a(base) \times h\)

\(v = 45 \times 9 = 405\)

We need to solve the next system of linear equations:

Let's pair the equations to eliminate 1 variable.

The first pair, add both equations:

The second pair:

Multiply the first equation by 5 and the second equation by -2:

Then, add both equations:

Now, solve the new system :

Multiply the first equation by 4 and multiply the second equation by -3:

Add both equations:

Solve for z:

To solve for x, replace the z value on one equation:

Finally, replace the z and x values:

Solve for y:

Hence, the result for each variable are:

x= 2

y= 2

z=6

Answer:

they are perpendicular

Step-by-step explanation :

If you graph both equations you will see that they Intersect with each other.

A conclusion which can be inferred about an individual score that corresponds to a z-value of 1.0 is that: c.) it is likely to come from the healthy distribution.

A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:

\(Z=\frac{x\;-\;u}{\delta}\)

Where:

Since the individual score that corresponds to a z-value of 1.0, we can reasonably infer and logically conclude that an individual score is likely to come from the healthy distribution.

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Complete Question:

Scores of healthy adults on a neurological test form a normal distribution with mean = 100 and SD = 15. What conclusion can be inferred about an individual score that corresponds to a z value of 1.0?

a.) it falls in the general region of the population

distribution

b.) it falls in the common region of the distribution

c.) it is likely to come from the healthy distribution

d.) it is unlikely to come from the healthy distribution

The arrow's motion can be described by parametric equations: x = V₀cosθt and y = -4.9t² + V₀sinθt + h, where V₀ is the initial velocity, θ is the launch angle, t is the time, and h is the initial height. To determine the time the arrow is in the air before touching the ground and the maximum height reached, we need to solve for the corresponding values in the equations.

(a) To find the time the arrow is in the air before touching the ground for the final time, we need to determine the value of t when y equals zero (the ground level). We can set the equation -4.9t² + V₀sinθt + h = 0 and solve for t. This equation represents the vertical motion of the arrow. Once we find the value of t, we can round it to the nearest tenth.

(b) To determine the maximum height reached by the arrow, we need to find the vertex of the parabolic equation -4.9t² + V₀sinθt + h. The maximum height occurs at the vertex of the parabola, which corresponds to the highest point of the arrow's trajectory. We can use the formula t = -b/2a, where a = -4.9 and b = V₀sinθ, to find the time at which the maximum height is reached. Once we find the value of t, we can substitute it into the equation y = -4.9t² + V₀sinθt + h to calculate the maximum height, rounding it to the nearest whole number.

By solving for the time when the arrow touches the ground and finding the maximum height, we can better understand the arrow's motion and trajectory.

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When the problem is solved using fraction addition, the answer is 3601/2520 in common fraction.

Subset S has the following values: 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, and 1/10.

The element in subset S product is 3601/2520.

Therefore, we can calculate the product of the elements in S by solving the numbers using fractional addition.

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Answer:

Step-by-step explanation:

The answer should be 8/3.

Answer:

y divided by k

Step-by-step explanation:

Based on the diagram provided, the length of the ramp appears to be approximately 9 feet. Therefore, the closest measurement to the length of the ramp in feet would be 9 ft.

Based on the information provided, it seems you are looking for the length of a ramp used to load and unload a moving van. The side view of the ramp shows a 9 ft height. To find the length of the ramp, we can use the Pythagorean theorem if we have the other leg of the right triangle.
However, you have not provided the length of the other leg (base) of the triangle. If you can provide that information, I can help you find the closest length of the ramp in feet.

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Answer:

1)The probability that the ball drawn is not red is 6 /14

2)Probability of getting either a prime or a multiple of 3 is 7/10

3)Probability of  drawing three balls without replacement such that all three are Same colour  is 0.0747

Probability of drawing three balls without replacement such that all three are different colour is 0.5

Step-by-step explanation:

1) A ball is drawn randomly from a bag containing 8 red, 4 blue and 2 green identical balls. Find the probability that the ball drawn is not red.

No. of red balls = 8

No. of blue balls = 4

No. of green balls = 2

Total no. of balls = 8+4+2=14

P(Getting red bal)=\(\frac{8}{14}\)

P( ball drawn is not red) = \(1 - \frac{8}{14}=\frac{6}{14}\)

So,the probability that the ball drawn is not red is 6 /14

2)What is the probability that a number chosen at random from the integers between 1 and 10 inclusive is either a prime or a multiple of 3?

Numbers : 1 ,2,3,4,5,6,7,8,9,10

Prime numbers: 2,3,5,7 = 4

Multiple of 3 = 3,6,9 =3

So, Probability of getting prime number =\(\frac{4}{10}\)

Probability of getting multiple of 3 =\(\frac{3}{10}\)

So, Probability of getting either a prime or a multiple of 3=\(\frac{4}{10}+\frac{3}{10}=\frac{7}{10}\)

Hence  Probability of getting either a prime or a multiple of 3 is 7/10

3)A bag contains four red balls, five blue balls and six green balls. Three balls are drawn from the bag at random without replacement. What is the probability that all three are:

The same colour

Different colour

No. of red balls = 4

No. of blue balls = 5

No. of green balls = 6

Total balls = 15

Case 1 :all three are Same colour

So, probability of  drawing three balls without replacement such that all three are Same colour = \(\frac{4}{15} \times \frac{3}{14} \times \frac{2}{13}+\frac{5}{15} \times \frac{4}{14} \times \frac{3}{13}+\frac{6}{15} \times \frac{5}{14} \times \frac{4}{13}=0.0747\)

So, probability of drawing three balls without replacement such that all three are different colour =\(\frac{4}{10} \times \frac{5}{9} \times \frac{6}{8}+\frac{5}{10} \times \frac{4}{9} \times \frac{6}{8}+\frac{6}{10} \times \frac{5}{9} \times \frac{4}{8}=0.5\)

So,probability of  drawing three balls without replacement such that all three are Same colour  is 0.0747

So,probability of drawing three balls without replacement such that all three are different colour is 0.5

Skew lines are the lines that are neither parallel nor intersecting.

The above statement is not possible for coplanar lines so it can be concluded that skew lines are non coplanar.

Hence the statement Lines that do not intersect and are not in the same plane which is option D justifies the definition of skew lines.

Hence option D is correct.

9514 1404 393

Answer:

  Item B

Step-by-step explanation:

The mass of platinum with the given volumes would be ...

  A: (2 cm³)(21 g/cm³) = 42 g . . . matches the given mass

  B: (5 cm³)(21 g/cm³) = 105 g . . . greater than the given mass, which is not platinum

  C: (7 cm³)(21 g/cm³) = 147 g . . . matches the given mass

__

Item B is too light to be platinum.

Answer:

Item B

Step-by-step explanation:

item b is too light

The equation that represents the amount of money saved is S = $100 + $20w

The equation that represents the amount of money saved is a linear equation . A linear equation is an equation that has a single variable raised to the power of 1.

The form of the linear equation is:

Total money saved = amount in the bank + (amount that would be saved each week x number of weeks)

S = $100 + ($20 x w)

S = $100 + $20w

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The value of x is 4.8cm.

Here BD // EF and BF // DE

So from this, we have ∠ABF = ∠EFC

Let's take two triangles ΔABC and ΔFCE

∠C =∠C (common angle)

∠ABC = ∠EFC

So ΔABC ≅ ΔEFC

So ∠BAC = ∠FEC

AB/ EF = BC/ FC

AB = 8cm, EF =x, BC = 12cm, FC= 12-x

8/x = 12/ 12-x

2/x = 3/ 12-x

24 - 2x = 3x

5x = 24

x = 4.8cm

Therefore the value of x is 4.8cm.

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Answer:

B. 12cm,7cm,5cm

Step-by-step explanation:

use triangular inequality therom

A+B>C  12+7>5 true

B+C>A 7+5>12 false

A+C>B 12+5>7 true

One of the sides is not complete so it can not be a triangle.

Answer is option-B

Triangle Inequality Theorem :

In Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than the third side; in symbols,

a + b > c.

a + c  > b

b + c  > a

(Here)

For option-B  

let's take a = 12cm, b = 7cm and c = 5cm.

b + c = a.

It violates triangle Inequality property.

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The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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Answer:

Dependent sample

Step-by-step explanation:

The sample: a data set includes the morning and evening temperature for the last 90 days.

The samples are dependent in that they are paired measurements on just one set of item which is the temperature.

These measurements are related in such a way that the each observation in one sample can be paired with an observation in the other sample.

Work Shown:

x = number of miles

Cost of company A = 0.09x+50.50

Cost of company B = 0.14x+60.50

Subtract the two expressions (B-A) to find the difference in price

B-A = (0.14x+60.50)-(0.09x+50.50)

B-A = 0.14x+60.50-0.09x-50.50

B-A = (0.14x-0.09x) + (60.50-50.50)

B-A = 0.05x+10

Answer:

I dont know, check in calculator

Step-by-step explanation:

So the formula is I=p(1+r)t

6300(1+.08)power of 21

Answer:

248

Step-by-step explanation:

Conversion formula

The conversion factor from pounds to ounces is 16, which means that 1 pound is equal to 16 ounces:

1 lb = 16 oz

To convert 15.5 pounds into ounces we have to multiply 15.5 by the conversion factor in order to get the mass amount from pounds to ounces. We can also form a simple proportion to calculate the result:

1 lb → 16 oz

15.5 lb → M(oz)

Solve the above proportion to obtain the mass M in ounces:

M(oz) = 15.5 lb × 16 oz

M(oz) = 248 oz

The final result is:

15.5 lb → 248 oz

We conclude that 15.5 pounds is equivalent to 248 ounces:

15.5 pounds = 248 ounces

Pilot program means  is a small scale, short term experiment that helps an organization or company to learn how a large scale project might work in practice.

Pilot program:

The best  pilot program provides a platform for the organization to test logistics, prove value before spending a significant amount of time, energy or money on a large scale project.

The pilot program is also called as feasibility study or experimental trial.

Steps for pilot program:

1.

set clear goals

2.

Decide on a length of time

3.

Choose your testing group

4.

Develop a plan for on-boarding

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The parallelogram having the sides of length 19 mm 19mm 7mm will have the length of the fourth side to be 7mm.

A parallelogram is a shape which has four sides and the opposite sides of the parallelogram are equal in magnitude.

The sum of the angles present on the opposite sides of one line of the parallelogram makes a sum of 180 degrees.

Here it is given to us that the parallelogram has the side length of 19 mm and 7 mm.

It is making sense that one of the remaining two size is 19 mm because that will be equal in magnitude as well as parallel to the side.

Going by the above mentioned logic we can conclude that the fourth side of the parallelogram will have a length of 7 mm.

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Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

Answer: the answer is b or 6.48

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sorry I can't explain how it is done. It is very difficult to explain on paper.

Answer:

20 percent

Step-by-step explanation:

There are 20 percent of the trees in the forest are the Oak trees.

The percentage of oak trees,  p , in the forest can be calculated using the following formula:

p = Number of oak  trees/ Total number of trees x  100

Given that there are 300 oak trees out of a total of 1,500 trees in the forest.

Plugging these values into the formula:

p = (300)/ (1500) x 100

   = 1/5 x 100

   = 100/5

   = 20

So, 20% of the trees in the forest are oak trees.

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The matching answers and corresponding colors for the holiday lights are: (Slope: 3) Dark Blue, (Slope: -4) Violet, (Slope: 1/4) Red.

To find the slope of a line passing through two points \((x_1, y_1)\ and\ (x_2, y_2)\), we can use the formula:

Slope = \((y_2 - y_1) / (x_2 - x_1)\)

Let's calculate the slopes for each pair of points:

1. (8, 3) and (10, 9):

Slope = (9 - 3) / (10 - 8) = 6 / 2 = 3

2. (2, -3) and (1, 1):

Slope = (1 - (-3)) / (1 - 2) = 4 / (-1) = -4

3. (-4, -8) and (-8, -9):

Slope = (-9 - (-8)) / (-8 - (-4)) = (-9 + 8) / (-8 + 4) = -1 / (-4) = 1/4

Now let's compare the slopes to identify the matching answers:

1. Slope: 3 (Dark Blue)

2. Slope: -4 (Violet)

3. Slope: 1/4 (Red)

Thus, the corresponding colors for the holiday lights would be:

1. Dark Blue

2. Violet

3. Red

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Answer:

D

Step-by-step explanation:

D

Answer: 2.87

Step-by-step explanation:

Answer: can buy (2x³ - 3x² + 4x - 6) reams

\(6x^{4} -17x^{3}+24x^{2} -34x+24\\\\\\=6x^{4}-8x^{3} -9x^{3} +12x^{2} +12x^{2} -16x-18x+24\\\\=2x^{3}(3x-4) -3x^{2} (3x-4)+4x(3x-4)-6(3x-4)\\\\\\=(2x^{3}-3x^{2} +4x-6)(3x-4)\)

Step-by-step explanation:

The number of reams of bondpaper that can be bought from \(6x^4-17x^3+24x^2-34x+24\) pesos are \(2x^3-3x^2+4x-6\).

Cost of a ream of bondpaper is \((3x-4)\) pesos.

The number of reams that can be bought from \(6x^4-17x^3+24x^2-34x+24\) pesos is calculated by following the long division method as-

\(\dfrac{6x^4-17x^3+24x^2-34x+24}{3x-4}=2x^3-3x^2+4x-6\)

So,

The number of reams that can be bought from \(6x^4-17x^3+24x^2-34x+24\) pesos are \(2x^3-3x^2+4x-6\).

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