Find the vertex, focus, directrix, and focal width of the parabola -1/20x^2=y

Answer:

P=4/250=0.016

nearest tenth=0.02

1.6%

Answer:

1/8 for each friend.

Step-by-step explanation:

1/8 + 1/8 + 1/8 + 1/8 = 1/2

Answer:

Umm i dont know if this is the right answer but its saying what fraction will the 4 friends get if they shared the pizza whole. So i just took 1/2 and mult. it by 2 to get 3/3 but i am not to sure on this one.

Step-by-step explanation:

Answer:

not completely sure this is the answer: 2/3 square meters

Step-by-step explanation:

i'm sorry if i got this wrong, i didn't understand really. did you mean 1 m x 2/3 m? if you did the answer is 2/3 sq m :)

The estimated sum of 7 83/84 is 8 to the nearest whole number.

Mixed fractions are fraction that has a whole number attached to an improper fraction. A mixed fraction can be added by first adding the real whole numbers together, then adding their improper fraction counterparts with it.

Also, we can add two mixed fractions together by first converting all the mixed fractions to improper fractions before adding them together.

Using the first process:

= 4 5/12 + 3 8/14

The whole number are 4 and 3, adding those two together, we have:

= 7 (5/12 + 8/14)

The L.C.M of 12 and 14 is 84.

= 7( (7×5)+ (6*8) )  /84

= 7 (35+ 48/84)

= 7 (83/84)

To decimal, we get 7.988. Therefore, the estimated sum of 7 83/84 is 8 to the nearest whole number.

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After answering the provided question, we can state that As a result, 145.62 square feet of glass are required to cover the entire pyramid.

A pyramid is a polygon formed by connecting points known as bases and polygonal vertices. For each hace and vertex, a triangle known as a face is formed. A cone with a polygonal shape. A pyramid with a floor and n pyramids has n+1 vertices, n+1 vertices, and 2n edges. Every pyramid is dual in nature. A pyramid contains three dimensions. A pyramid is made up of a flat tri face and a polygonal base that come together at a single point known as the vertex. A pyramid is formed by connecting the base and peak. The base's edges form triangle faces known as sides that connect to the top.

To determine how much glass is required to cover the entire pyramid, we must first determine the total surface area of the pyramid, including the base.

The formula for calculating the surface area of each triangular face is:

(1/2) x width x height

27.31 square feet = (1/2) x 7 feet x 7.79 feet

24 square feet = (1/2) x 6 feet x 8 feet

Simply multiply the length and width to find the area of the rectangular base:

7 feet by 6 feet equals 42 square feet

As a result, the total surface area of the pyramid is:

145.62 square feet = 2 (27.31 square feet) + 2 (24 square feet) + 42 square feet

As a result, 145.62 square feet of glass are required to cover the entire pyramid.

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Answer: 102.53

Step-by-step explanation:  I calculated all the numbers you gave me and then added them to get 102.53

Answer:

x = 17

Step-by-step explanation:

(5x - 23) and (7x - 1) are same- side interior angles and sum to 180° , so

5x - 23 + 7x - 1 = 180

12x - 24 = 180 ( add 24 to both sides )

12x = 204 ( divide both sides by 12 )

x = 17

The length of PQ is 3√5 and its slope is -2

The length of SR is 3√5 and its slope is -2

The length of SP is 5√2 and its slope is -7

The length of RQ is 5√2 and its slope is -1

So PQ ≅ SR and SP ≅ RQ. By the Perpendicular Bisector theorem, adjacent sides are perpendicular. By the selection of  side, ∠PSR, ∠SRQ, ∠RQP and ∠QPS are right angles. So, the quadrilateral is a rectangle.

To find the lengths and slopes of the sides of the quadrilateral PQRS, we apply the distance formula:

D = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)  

and the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

1. Length PQ:

Using the distance formula, the length PQ can be calculated as follows:

PQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((3 - 0)² + (-4 - 2)²)

  = √(3² + (-6)²)

  = √(9 + 36)

  = √45

  = 3√5

2. Length SR:

Using the distance formula, the length SR can be calculated as follows:

SR = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - (-2))² + (-5 - 1)²)

  = √((1 + 2)² + (-6)²)

  = √(3² + 36)

  = √(9 + 36)

  = √45

  = 3√5

3. Length SP:

Using the distance formula, the length SP can be calculated as follows:

SP = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - 0)² + (-5 - 2)²)

  = √(1² + (-7)²)

  = √(1 + 49)

  = √50

  = 5√2

4. Length RQ:

Using the distance formula, the length RQ can be calculated as follows:

RQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((-2 - 3)² + (1 - (-4))²)

  = √((-2 - 3)² + (1 + 4)²)

  = √((-5)² + 5²)

  = √(25 + 25)

  = √50

  = 5√2

Now, let's calculate the slopes of the sides:

1. Slope PQ:

The slope of PQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-4 - 2) / (3 - 0)

  = -6 / 3

  = -2

2. Slope SR:

The slope of SR can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 1) / (1 - (-2))

  = -6 / 3

  = -2

3. Slope SP:

The slope of SP can be calculated using the slope formula:

m =\(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 2) / (1 - 0)

  = -7 / 1

  = -7

4. Slope RQ:

The slope of RQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (1 - (-4)) / (-2 - 3)

  = 5 / (-5)

  = -1

Therefore, the lengths and slopes of the sides of the quadrilateral PQRS are:

Length PQ: 3√5

Length SR: 3√5

Length SP: 5√2

Length RQ: 5√2

Slope PQ: -2

Slope SR: -2

Slope SP: -7

Slope RQ: -1

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Answer:

x = 2.4

Step-by-step explanation:

4x + 5 / x + 7
combine like terms

X + 4x = 5x

5 + 7= 12

12/ 5x

Divide

12 /5= 2.4

X= 2.4

The scale factor is 1/3.

What is the scale factor?

The difference in scale between an original object's scale and a new object that is its representation but is larger or smaller is known as a scale factor. For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.

Here, we have

Given: Triangle D has been dilated to create triangle D′.

To find the scalar value, simply choose one side of D and one did of D’ and divide them to find the scalar. We can verify that we have the correct scalar by performing this division on each related edge. Below I will do D to D’ represented like D/D’:

4.8 / 1.6 = 3

4.2 / 1.4 = 3

2.7 / x = 3

Knowing that the scaling for each edge is 3, we can solve for x.

2.7 / 3 = x

0.9 = x

The edges for D are 4.8, 4.2, and 2.7 respectively to D’ scaled by 1/3. So we can determine that the edges for D’ are 1.6, 1.4, and 0.9 respectively to D scaled by 3.

So if we go D’ to D, we scale by 3. If we go D to D’, we scale by 1/3.

Hence, the scale factor is 1/3.

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Answer:

0 = 0 means that there are infinite solutions.

Step-by-step explanation:

Equation is -5(-4+2n)=-10(n-2)

1. Distribute the -5 and -10

20 -10n = -10n + 20

2. Subtract 20 from one side to the other to get only 1 variable on 1 side.

-10n = -10n

3. divide -10 to separate the variable from the constant.

n = n

This means there are infinite solutions.

Using the pattern, n can represent the the increase of dots according to step.

In the given question we have to find what values make sense for n in this situation.

n is representing the number.

As we can see that there is a pattern given.

In the step 1 have 1 dot, in step 2 have 3 dots, in step 3 have 6 dots and in step 4 have 10 dots.

So if we see the pattern then according to number of step the dots increasing accordingly.

As In step 1 have 1 dot, in step 2, 2 dots increase, in step 3, 3 dots increase and in step 4, 4 dots increase.

So, n can represent the the increase of dots according to step.

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Answer:

(3x+2)(x-5)

Step-by-step explanation:

Factor by grouping

\(3x^2-13x-10\\=3x^2-15x+2x-10\\=3x(x-5)+2(x-5)\\=(3x+2)(x-5)\)

it has the correct conditions and the correct formula for calculating the cost. \(C(x) = 3.25x + 5 if x > = 6\) Thus, option C is correct.

The correct function that models this scenario is:

\(C(x) = 3.75x if x < 6\)

\(C(x) = 3.25x + 5 if x > = 6\)

This is because for rentals less than 6 hours, the cost is simply $3.75 per hour, so the function is  \(C(x) = 3.75x\)  . For rentals of 6 hours or more, there is a discounted hourly rate of $\(3.25\) per hour, but there is also a $5 processing fee, so the function is \(C(x) = 3.25x + 5\)  .

Option (a) is incorrect because it does not include the $5 processing fee for rentals of 6 hours or more.

Option (b) is incorrect because it has the wrong conditions for the hourly rate discounts. It specifies that the discount starts at x = 6, but the correct condition is \(x > = 6.\)

Option (c) is correct, as it has the correct conditions and the correct formula for calculating the cost.

Option (d) is incorrect because it has the wrong condition for the hourly rate discounts (x < 5 instead of x < 6), and it does not include the $5 processing fee for rentals of 6 hours or more.

Therefore, it has the correct conditions and the correct formula for calculating the cost. \(C(x) = 3.25x + 5 if x > = 6\)

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Answer: 8.06 Inches

The area of the circle is 28.26 ft². 3. The diameter of the circle is 8.06 inches.

Answer:

C and E

Step-by-step explanation:

23 > 16 and \(23\geq 16\) are both true statements since the quantity of 23 is greater than that of 16.

Answer:

y=-5x+12

Step-by-step explanation:

just use a graphing calculator and basic knowledge of slope intercept form

Answer:

Step-by-step explanation:

I think 4f + 10

Answer: C 0.22,

Step-by-step explanation:

We have a normal sampling distribution because we expect at least 10 successes and 10 failures per sample

Using the Central Limit Theorem, it is found that the best approximation of the sampling distribution of p is that it is approximately normal, with mean of 0.22 and standard deviation of 0.0586.

In this problem:

Then, \(s = \sqrt{\frac{0.22(0.78)}{50}} = 0.0586\)

The sampling distribution of p is approximately normal, with mean of 0.22 and standard deviation of 0.0586.

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Applying the Pithagorean Theorem

we have

solve for x

Answer:

A, B, and E. Hope this helps!

Answer:

x - -5.78526086, -1.50769051, 2.29295138

Step-by-step explanation:

Try to graph each side of the equation. The solution Is probably the x-value of the point of intersection. Sorry if this is wrong I tried my best!

For the given two - dimensional function, we can write -

In mathematical analysis, the maximum and minimum of a function, known generically as extremum are the largest and smallest value of the function, either within a given range (the local or relative extrema), or on the entire domain.

Given is calculate the relative maxima and minima for the function -

2x⁴ + y² - 3yx²

For the given two - dimensional function, we can write -

Relative Maxima  →  No relative maxima.

Relative Minima  →  No relative minima.

Saddle Points  →  No saddle points.

Therefore, for the given two - dimensional function, we can write -

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{Question in english -

Calculate the relative maxima and minima of the function.

f(x, y)=2x^4+y^2-3yx^2}

The delivery person will use 6 gallons of gasoline

The function to determine the number of miles in x hours is:

f(x)  =  x²  +  3x

The number of gallons of gasoline used for driving y miles is:

g(y) = y/18

For a delivery person that works a 9-hour shift:

x  =  9

f(9)  =  9²  +  3(9)

f(9)  =  81  +  27

f(9)  =  108

That is, the number of miles, y = 108 miles

The number of gallons of gasoline used:

g(y)  =  y/18

g(108)  =  108/18

g(108)  =  6

The delivery person will use 6 gallons of gasoline

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Answer:

A

Step-by-step explanation:

22.5 times 3.32 results in 74.7, or A.

Answer:

the rate / speed of the boat is 10 miles per hour.

the rate / speed of the current is 2 miles per hour.

Step-by-step explanation:

r = rate of boat (speed of boat)

t = time

d = distance.

c = rate of current (speed of current)

with the current, the formula becomes (r + c) * t = d

against the current, the formula becomes (r - c) * t = d

going with the current, the boat takes 1 hour to travel 12 miles.

therefore:

(r + c) * t = d becomes (r + c) * 1 = 12

going against the current, the boat takes 1.5 hour to travel the same 12 miles.

therefore:

(r - c) * t = d becomes (r - c) * 1.5 = 12.

your two equations that need to be solved simultancously are:

(r + c) * 1 = 12

(r - c) * 1.5 = 12

divide both sides of the second equation by 1.5 and leave the first equaion as is to get:

r + c = 12

r - c = 8

add the equations together to get:

2 * r = 20

solve for r to get:

r = 20 / 2 = 10

(r + c) * 1 = 12 becomes (10 + c) * 1 = 12

simplify to get 10 + c = 12

solve for c to get c = 12 - 10 = 2

(r - c) * 1 = 8 becomes (10 - c) * 1 = 8

simplify to get 10 - c = 8

solve for c to get c = 10 - 8 = 2

you have:

r = 10

c = 2

that's your solution.

the rate / speed of the boat is 10 miles per hour.

the rate / speed of the current is 2 miles per hour.

Answer:

the height of the triangle is 4

Step-by-step explanation:

2a/b

2(10/5)

2*2

=4

Answer:

The answer is 50.

Step-by-step explanation:

As per the given confidence interval, the given statement "in forming a 95% confidence interval for a population mean from a sample size of 20, we can proceed with large sample inference" is false.

Confidence interval,

in probability , confidence interval refers the probability that a population parameter will fall between a set of values for a certain proportion of times.

Given,

in forming a 95% confidence interval for a population mean from a sample size of 20, we can proceed with large sample inference.

Here we need to find the given statement is true or false.

While we looking into the given question, we have identified that the value of

Confidence interval = 95%

Sample size = 20

Then the sample inference is calculated as, if we were to take 20 different samples and compute a 95% confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true mean value (μ).

Therefore, the statement is in correct.

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Answer:

\(P(X = 5) = 0.166\)

Step-by-step explanation:

Given

\(Mean = 4.3\)

\(x = 5\)

Required

Determine the probability that the order is 5

This question can be answered using Poisson distribution.

\(P(X = x) = \frac{\alpha ^x e^{-\alpha}}{x!}\)

Where

\(\alpha\) is used to represent the mean

and

\(\alpha = 4.3\)

\(x = 5\)

\(e = 2.71828\) ---- Euler's constant

So, we have:

\(P(X = x) = \frac{\alpha ^x e^{-\alpha}}{x!}\)

\(P(X = 5) = \frac{4.3^5 * 2.71828^{-4.3}}{5!}\)

\(P(X = 5) = \frac{4.3^5 * 2.71828^{-4.3}}{5* 4 * 3 * 2 *1}\)

\(P(X = 5) = \frac{4.3^5 * 2.71828^{-4.3}}{120}\)

\(P(X = 5) = \frac{1470.08443 * 0.01356859825}{120}\)

\(P(X = 5) = \frac{19.9469850243}{120}\)

\(P(X = 5) = 0.1662248752\)

\(P(X = 5) = 0.166\) Approximated