what is the equation based on the focus and vertex

Probability - The answer to the problem is P(Y = 4) = 3/32

What is Probability?

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Solution:

Mean = 120

Standard Deviation = 5

Z = (X - Mean)/Standard Deviation

Z = 1/2

(i) P(Y = 4) = 6/4 * (1/2)^2 * (1-1/2)^6-4

P(Y = 4) = 3/2 * 1/4 * 1/4

P(Y = 4) = 3/32

(ii)P(X > 500) = 1 - P(X ≤ 500)
= 1 - Φ(500; 480, 10)
= 1 - 0.9772
= 0.0228

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Answer:

Step-by-step explanation:

12.50

Answer:

B

Step-by-step explanation:

constant of proportionality = 10/20 = 1/2

y/x = 1/2

y = 1/2x

y = 1/2 * 25

y = 25/2

y = 12.5

The  sketching of the vector field is attached herewith.

Since we know  the formula for the vector field is :

F(x, y, z) = -yi+ xj = xj -yi, where  x and y are the magnitude and i and j are the unit vectors for the x and y - axis .Since we the  points we are given with are:(-2, -2, -2) ,(-2, -2, 2) ,(-2, 2, -2),(-2, 2, 2),(2, -2, -2) ,(2, -2, 2),(2, 2, -2) , (2, 2, 2). So the  filed vectors  for individual points will be just substituting the magnitude of  the individual axis :

F(-2, -2, -2)   =  -2j +2i

F(-2, -2, 2)  =   -2j +2i

F(-2, 2, -2) =  -2j -2i

F(-2, 2, 2)  =   2j +2i

F(2, -2, -2)  =  -2j-2i

F(2, -2, 2)  =  -2j -2i

F(2, 2, -2)   =  2j -2i

F(2, 2, 2)    =  2j -2i

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Answer:

Point on the line: (0, 15)

Slope: 3

Step-by-step explanation:

Step 1: Put the equation in slope-intercept form

    The slope-intercept form is written like this: y = mx + b

    m = slope

    b = y-intercept

    1. y = 3 + 3(x + 4) → y = 3x + 15

Step 2: Retrieve the values from the equation

    y-intercept = 15

    slope = 3

Angles 1 and 2 are neighboring, hence the fourth choice is accurate. Angles 1 and 2 are adjacent.

The term "Angle" refers to the separation between line segments or rays that converge at a single point.

The following may be said about angles 1 & 2:

In a line that proceeds from left to right, there is a ray in the middle that forms a right angle, a second ray between the two right angles, and one light that labels both the left angle and the right angle.

We can draw just as in the image.

Angles 1 and 2 are neighboring because they share a vertex, as seen in the image.

Angle 2 equals 90 degrees

Angle 1 equals 45 degrees

Angles 1 and 2 are adjacent, so option 4 is correct because it describes the relationship between them.

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The percent markup price is equivalent to 42.86%.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a department store buys 200 shirts at a cost of ​$1400 and sells them at a selling price of ​$10 each

Cost price of 200 shirts = C.P. = $1400

Selling price of 200 shirts = S.P = $(10 x 200) = $2000

Percentage markup = [(2000 - 1400)/1400] x 100 = (600/1400) x 100 = 600/14 = 42.86%.

Therefore, the percent markup price is equivalent to 42.86%.

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Answer: the answer would round up to 43

Step-by-step explanation:

The largest number of bouquet are 9

What is Highest Common Factor?

The greatest common factor is the biggest whole number shared by the supplied numbers. For example, the common factors of 10 and 20 are 1, 2, 5, and 10, with 10 being the greatest; so, the highest common factor of 10 and 20 is 10.

Solution:

Total Red Roses = 18

Total Tulip = 27

Toal White Gardenia = 36

To find the largest number of bouquet we need to use Highest Common Factor

HCF of (18, 27, 36) = 9

The largest number of bouquet are 9

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a) The expected value for distribution A is equal to 1 and expected value for distribution B is equal to 3. b) The value of standard deviation of two distributions is same. c)  A is less than the expected value for the distribution B.

The calculation for expected value of distribution of A is given as,

E(X) = ∑[tex]^{n}[/tex][tex]_{i=1}[/tex]= [tex]X_{i}[/tex]. P (X=x)

       =0⋅ (0.50 )+1⋅(0.20)+....+4⋅0.05=1

E(X) = ∑i=1nXi.P(X=x)=0⋅(0.50)+1⋅(0.20)+....+4⋅(0.05)=1

The calculation for expected value of distribution of B is given as,

E(X)=n∑i=1 Xi.P(X=x)

      =0⋅(0.05)+1⋅(0.1)+....+4⋅(0.50)=3

E(X)=∑i=1nXi.P(X=x)=0⋅(0.05)+1⋅(0.10)+....+4⋅(0.50)

     =3

Therefore, the expected value for distribution A is equal to 1 and expected value for distribution B is equal to 3.

(b) The formula for standard deviation is given as,

σ=√E(X2)−E(X))2

The calculation for the E(X2) of distribution A is given as,

E(X2)=n∑i=1 X2i⋅P(X=x)

        =02⋅(0.50)+12⋅(0.20)2+.....+42⋅(0.05)=2.5

The calculation for the E(X2) of distribution B is given as,

E(X2)=n∑i=1 X2i⋅P(X=x)

        =02⋅ 0.05)+12⋅(0.10)+......+42⋅(0.50)

        =10.5

E(X2)=∑i=1nXi2⋅P(X=x)=02⋅(0.05)+12⋅(0.10)2+......+42⋅(0.50)

       =10.5

The value of standard deviation for the distribution A is given as,

σA=√2.5−12

   =1.225

The value of standard deviation for the distribution B is given as,

σB=√10.5−32

   = 1.225

Therefore, the value of standard deviation of two distributions is same.

(c) The expected value for distribution A is less than the expected value for the distribution B. The standard deviation is same for both distributions; the spread between both the distributions is same. Therefore, the distribution B is better than distribution A.

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The length of the 3rd side of the given triangle with 6 units and 9 units being the length of the 1st and 2nd side can be:

(B) 4 units

(C) 7 units

(F) 10 units

(E) 12 units

A triangle is a polygon with three vertices and three sides.

The angles of the triangle are formed by the connection of the three sides end to end at a point.

The triangle's three angles add up to 180 degrees in total.

So, knowing that the third side of a triangle must be longer than the sum of the first two sides and shorter than the difference between the first two sides allows us to obtain:

x > (9-6) so x > 3 and x < (9+6) so x < 15

Based on these findings, the third side length can be chosen from B. 4, C. 7, F. 10, and E. 12.

Therefore, the length of the 3rd side of the given triangle with 6 units and 9 units being the length of the 1st and 2nd side can be:

(B) 4 units

(C) 7 units

(F) 10 units

(E) 12 units

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Complete question:
A triangle has two sides of lengths 6 and 9. What value could the length of the third side be? Check all that apply

A.15

B.4

C.7

D.2

E.12

F.10

Answer:

-2, -6

-1, -3

0,0

1,3

2,6

Step-by-step explanation:

nsd fbvdvjben ebtv

Step-by-step explanation:

when x is -2 y is y=3x

y=3×-2

y=-6 do that for all

The equation to determine the number of players is (x-y)/z and there are 11 players in total.

Given: Lacrosse players raised $1581.75 to attend a tournament. They allocated $968.50 for the bus rental and $55.75 for each player's meals.

Let,

x = amount raised to attend a tournament.

y = amount allocated for bus rental

z = amount for each player's meals

Number of players = (x-y)/z

                               = (1581.75-968.50)/55.75

                               = 613.25/55.75

                               = 11

Therefore, the equation to determine the number of players is (x-y)/z and there are 11 players in total.

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Answer: 1x

Step-by-step explanation:-3+4=1 and then add a x

Answer:

(-3.4,2.7)

Step-by-step explanation:

The reason it's asking for an estimate, is because the intersection point is not on exact integer coordinates.

Start with the x-value of the intersection point. All options contain either -3.4 or -3.7. The x-value of the intersection point is closer to -3 than -4, so -3.4 is a better estimate.

Do the same with the y-value. Since the intersection point is closer to 3 than 2, 2.7 is the best estimate here.

Answer:

Last choice:  (-3.4, 2.7)

Step-by-step explanation:

Well, you could actually solve the two line equations and arrive at the answer but that is not the intent of the question.

The solution of the two line equations is the point at which the two lines intersect

At this point the x value is closer to -3 than to -4. So the x value from the choices would be -3.4 rather than -3.7

We can eliminate 1st and 3rd choices

The y value is closer to 3 than it is to 2 so the y-value estimate would be 2.7

Correct choice: (-3.4, 2.7)

I have marked the solution point with an X in the attached image

"The scatter plot shows a linear association."  

What is scatter plot ?

Several dots are plotted on horizontal and vertical axes to form a scatter plot. In statistics, scatter plots are crucial because they can demonstrate the degree of correlation, if any, between the values of observed quantities or occurrences (called variables).

But how?  Well, linear means: "arranged in or extending along a straight or nearly straight line." Which if you didn't notice.. All the points on the graph, make up a generally straight line.

"No association" means there is no line or association with any of the points.  So, you'd pick that if the points were all over the graph in no order, line or combination; which isn't the case.  

"Negative association" is when the top of the points come from the left of the graph lowering into the right. While Positive association would be from right to left.  So, it couldn't be choice "Negative Association" since it's coming from right to the left of the graph.

"The point  (2, 14) is an outlier."  If you didn't know, an outlier is one dot out of a whole group.  Think of it as if EVERYONE was wearing pink except one; who wore black.  It's just the out of placed kind of dot; but it's supposed to be there.  When you look at the graph, there is no dot or outlier at point (2,14) so, that's automatically out as well.

Ending with the last choice "The scatter plot shows a linear association." which is not just true but is the only one that'd make since.

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a. test statistic =  1.35

p-value =  0.198439

b. Support the null hypothesis.

So you have the hypothesis:

H₀:μ=4

H₁:μ≠4

with the sample information you calculate the statistic using the t-distribution with 14 (n-1) degrees of freedom:

t=x[bar] - μ ⇒ t=  4.8 - 4    =  0.8   = 1.347≅ 1.35

   s/√n               2.3/√15     0.59

The p-value is defined as the probability corresponding to the calculated statistic (or of obtaining a value as extreme as the value of the statistic) if possible under the null hypothesis.

p-value: 0.198439

b.

Since the calculated p-value is greater than the significance level, you don't reject the null hypothesis.

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 The height of the top change when the lower end is feet from the wall by -4.5 ft/sec.

Given,

Assume that the horizontal floor is x and the vertical wall is y in distance (6 ft).

This creates a triangle, with the ladder serving as the 10 foot hypotenuse.

dy/dt = 6 feet per second.

Pythagoras' law states that there is a link between x and y.

(x²) + (y²) = (hypothenus²) = 10².

When both sides of the equation are distinct,

0 = 2x(dx/dt) + 2y(dy/dt)

(x/y) × (dx/dt) = dy/dt

y = √(10²) - (6²) = 8ft

Consequently, dy/dt = (6/8) × (6/1)= -4.5 ft/sec.

The rate is negative.

That is,

When the lower end is feet from the wall, the height of the top changes by -4.5 feet per second.

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As the sample size increases the mean is 100 , if n = 1000 , the mean of the sample means will be unchanged  .

In the question ,

from the table we can observe that ,

if n = 1 , the mean is 97.656 ,

if n = 5 , the mean is 100.101 ,

if n = 10 , the mean is 100.006 ,

if n = 100 , the mean is 100.341 ,

from the table we notice that as the sample size increases from 1 to 100 , the means of the sample means are same that is 100 .

we can see that for every n , the mean is approximately equal to 100 ,

So , if n = 1000 , then the mean will also be approximately equal to  100 .

Therefore , the mean of the sample means will be unchanged .

The given question is incomplete , the complete question  is

Focus on the means. What do you notice about the means of the sample means as the sample size increases from 1 to 100? What would you expect the mean of the sample means to equal if n = 1000 ?

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The probability that headway is within 1 standard deviation of the mean value is 0.890.

What is mean value?

By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.

The mean of a discrete probability distribution of a random variable X is equal to the sum over all possible values weighted by the likelihood of each value. To calculate the mean, one must multiply each potential value of X by its probability P(x), then add all of these products.

Given mean value is P( 0.995 ≤ x ≤ 1.445) = F(1.445) - F(0.995).

The cdf for the distribution is

[tex]F(x)=\left \{ {{1 -\frac{1}{x^6} ,x > 1} \atop {0,x\le 1}} \right.[/tex]

Now calculate the value of F(1.445) and F(0.995).

F(1.445) = 1 - (1/(1.445)⁶)

F(0.995) = 0

Now putting the value of F(1.445) and F(0.995) in  P( 0.995 ≤ x ≤ 1.445) = F(1.445) - F(0.995):

P( 0.995 ≤ x ≤ 1.445)

=1 - (1/(1.445)⁶)  - 0

=0.890

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Hence, he sum of a number and [tex]18.4[/tex] is at least [tex]-3.8[/tex] as an inequality is [tex](b+18.4)\geq -3.8[/tex].

What is the inequality?

An inequality is said to be sharp if it cannot be relaxed and still be valid in general.

Here given that,

The sum of a number and [tex]18.4[/tex] is at least [tex]-3.8[/tex] as an inequality.

Let [tex]b[/tex] be the number

As it is mentioned that the sum of [tex]x[/tex] and [tex]18.4[/tex] is at least [tex]-3.8[/tex].

Hence, the sum is greater or equal to [tex]-3.8[/tex]

i.e., [tex](b+18.4)\geq -3.8[/tex]

Hence, he sum of a number and [tex]18.4[/tex] is at least [tex]-3.8[/tex] as an inequality is [tex](b+18.4)\geq -3.8[/tex].

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The expected value and the standard deviation of the points per game for the player is -6.5 and 65.43 respectively.

Given:

In a certain computer card game, the player is awarded 5 points for each card that is moved to a correct position. The player is penalized 10 points for each minute the game is played. Let the random variable X represent the number of cards moved to a correct position, and let the random variable Y represent the number of minutes the game is played.

From the given table:

E ( X ) = 9.5 * 5 points

= 47.5

E ( Y ) = 5.4 * - 10

= -54

E ( X + Y ) = 47.5 + ( -54 )

= 47.5 - 54

= -6.5

SD ( X ) = 12.5 * 5

= 64.5

SD ( Y ) = - 11

SD ( X + Y ) = [tex]\sqrt{64.5^2 + (-11)^2}[/tex]

= 65.43

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Full question:

Is in the image uploaded.

The pounds of raisins will there be in 7 pounds of this mixture is 49/10 pounds.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

It is given that:

In a mixture of raisins and dates, the ratio by weight of raisins to dates is 7 to 3

Let the common factor be x:

7x = raising

3x = dates

7x + 3x = 7

10x = 7

x = 7/10

7x = 7(7/10)

Raisin =  49/10 pounds

Thus, the pounds of raisins will there be in 7 pounds of this mixture is 49/10 pounds.

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Variable, x, represents the independent variable and the dependent variable is the distance, because the distance depends on the time. A function relating these variables is R(x) = 60x. So R(3) = 180 miles, meaning after 3, a distance of 180 miles was covered.

The dependent variable is the outcome or result that is being measured or observed, while the independent variable is the factor that is manipulated or changed to see its effect on the dependent variable.

Therefore, we can say that: the independent variable, x, represents the time and the dependent variable is the distance, because the distance depends on the time.

A function relating these variables is R(x) = 60x, representing the distance covered as a function of time at a constant speed of 60 miles per hour.

So, R(3) = 60 * 3 = 180 miles, meaning after 3 hours of driving, Hannah will have covered a distance of 180 miles.

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The independent variable x represents time in hours and the dependent variable R(x) represents distance in miles. The relationship between these variables is expressed by the function R(x) = 60x, signifying the distance (in miles) Hannah would have driven after x hours. For instance, R(3) equals 180, implying that after 3 hours, Hannah would have driven 180 miles.

In this context, the independent variable, x, represents the time in hours and the dependent variable, R(x), is the distance in miles, because the distance depends on the time. A function relating these variables is R(x) = 60x. This is because Hannah's speed is 60 miles per hour, so the formula for distance (Rate x Time) becomes 60 times the number of hours (x). So R(3) equals 180, meaning after 3 hours, Hannah would have driven 180 miles.

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the limit of f (x) g(x) exists as x!0 is exist.

what is function existance ?

The EXISTS function returns a Boolean value to indicate whether a list contains at least one element.

let,

f(x)  =  1    at x=Q

also, f(x)  = -1  at x=Q'

now, g(x)  = -1  at x = Q

also, g(x) = 1 at x = Q'

Here,

[tex]\lim_{n \to \infty} f(x)[/tex]      and [tex]\lim_{n \to \infty} g(x)[/tex]   does not exist.

but,    f(x) + g(x)  =  (f+g)(x) = 0 at x = Q and also at x = Q'

⇒  (f+g)(x) = 0 ∀ x∈IR

⇒   [tex]\lim_{n \to \infty} (f+g)(x)[/tex]  = 0 exist.

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Answer:

-5/6=-1/4-7/10 x /×60

60×(-5/6)=60×(-1/4)+60(-7/10 x)

-50=-15-42 x

-50+15=-42 x

-35=-42 x

35=42 x

x=35/42

x=5/6

The confidence interval of two populations means a) it must pool the sample variances

A confidence interval provides a range of possible values ​​for the difference between two population means. For example, a 95% confidence level indicates that given 100 random samples from the population, you can expect about 95 samples to yield intervals that include the population difference.

If the confidence interval for the between-groups difference contains zero, it means that if you run the experiment again, it is likely that you will not find a difference between the groups. Two populations from which two independent samples are selected are known to have the same variance.

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Answer:

Step-by-step explanation:

apples=$2 per pound

oranges=$3 per pound

If Ben bought x pounds of oranges and five pounds of fruit in total, then he bought 5-x pounds of apples.

oranges price: 3x

apples price: 2(5-x)

Final Equation: 3x+2(5-x)=12

3x+10-2x=12

x+10=12

x=2 -> amount of oranges

input in apples equation

apples= (5-x)->(5-2)=3

Final answer: 2 pounds of oranges, 3 pounds of apples

The average commute for 95% of the students is between 19.0 and 4.2 miles.

The average distance is 19 miles.

Therefore, the standard deviation is 4.2 miles.

A) 2.7 = 19 - a(4.2)

where;

a deviates from the mean by a certain number of standard deviations. Thus;

a = (19 - 2.7) ÷ 4.2

a = 3

In a normal distribution, 3 standard deviations from the mean indicate that 95% of the data falls within that range.

B) The data are 2 standard deviations apart from the mean at the 95% confidence level. Thus;

CI = 19 ± 2(4.2)

CI = (18 - 10.2) OR (18 + 10.2)

CI = (7.8, 28.2)

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Answer:

Part A: The LSRL is y^ = 7.76 + 0.6x.

Part B: y^ = 7.76 + 0.6(19.5) = 19.46

y^ = 19.46%

Part C: 22.7 - 19.46 = 3.24. The residual is 3.24. This means that the value was underpredicted. 

Step-by-step explanation:

well, we know that it was 195 in 1992, so "t" years later that'd be

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &195\\ r=rate\to 1.2\%\to \frac{1.2}{100}\dotfill &0.012\\ t=years\dotfill &t\\ \end{cases} \\\\\\ A=195(1 + 0.012)^{t} \implies A =195(1.012)^t[/tex]

Answer: The at home printer prints faster, and you can print 6 more photos with it than the office printer.

Step-by-step explanation:

25 ÷ 12.5 = 2
15 ÷ 6 = 2.5

2 x 12 = 24
2.5 x 12 = 30