(b) Each unit on the grid repreent 25 feet. Find the perimeter of the factory. Show your work

Using the parameters associated with the parabola and the formula for the equation using the focus and the focal diameter, The required equation is

[tex]x = \frac{-1}{62} (y+5)^{2}+ \frac{9}{2}[/tex] .

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

All points in a plane that are equally spaced out from a given point and a given line make up a parabola. The line is known as the directrix, and the point is known as the parabola's focus. The parabola's axis of symmetry is the subject of attention.

focus = (-11,5)

focal diameter =20

Required equation of parabola,

[tex]x = \frac{-1}{62} (y+5)^{2}+ \frac{9}{2}[/tex]

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Answer:

write the equation in slope intercept form. Write the numbers in the equation as simplified proper fraction improper fraction or integer

The equation of the parallel line t is y = -4x  - 9.

The equation of line s is given as

y = -4x - 5/3

Also, from the question, the point on line t is given as Point = (-3, 3)

The equation of a line can be represented as

y = m x + c-------(1)

Where m represents the slope

c is the constant value

By comparing the equations, we have the following

m = -4

This means that the slope of y = -4x - 5/3 is -4

The slopes of parallel lines are equal

This means that the slope of the line t is -4

The equation of the parallel line is then calculated as:

y = m(x - x₁) +y₁

Where m = -4

(x₁, y₁) = (-3, 3)

Now, we should substitute the known values in the above equation(1)

y = -4(x + 3) + 3

By Evaluating we get

y = -4x - 12 + 3

y = -4x  - 9

Hence, the parallel line has an equation of y = -4x  - 9.

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Answer:

ANS:- 2439

Step-by-step explanation:

2439/3 = 813

2439/9 = 271

Answer:

20%

Step-by-step explanation:

2 x 10 = 20

20%

To find the sum of vectors u and v, we can add their components separately:

(u + v)x = (7cos 310° + 2cos 115°)

(u + v)y = (7sin 310° + 2sin 115°)

Using a calculator to evaluate these expressions, we get:

(u + v)x = -2.16

(u + v)y = 8.48

The magnitude of the sum vector u + v can be found using the Pythagorean theorem:

|u + v| = √((u + v)x^2 + (u + v)y^2)

= √(-2.16^2 + 8.48^2)

= √(72.3584)

= 8.51

The direction of the sum vector u + v can be found using the inverse tangent function:

θ = tan^(-1)((u + v)y / (u + v)x)

= tan^(-1)(8.48 / -2.16)

= tan^(-1)(-3.928571428571429)

= 143.13°

Rounding the magnitude to the nearest tenth and the direction to the nearest degree, we get:

u + v = 8.5 (cos 143°, sin 143°)

Therefore, the sum of vectors u and v is equal to 8.5 (cos 143°, sin 143°).

Answer:

To write √73 in exponential form, we can use the fact that the square root of a number is the same as that number to the power of 1/2. Thus, we can write √73 as 73^(1/2).

Here's how we can show this using algebraic steps:

First, we can write the square root as a fractional exponent:

√73 = 73^(1/2)

Next, we can rewrite the fractional exponent using the rule that says that a^(m/n) = (a^m)^(1/n):

√73 = (73^1)^(1/2)

Finally, we can simplify the expression by evaluating the power of 1:

√73 = (73)^(1/2) = 73^(1/2)

Therefore, √73 can be written in exponential form as 73^(1/2).

Answer: To find the x-intercept of a line, we set y equal to 0 and solve for x. To find the y-intercept of a line, we set x equal to 0 and solve for y.

For the line 5x + 17y = -25, we set y equal to 0 to find the x-intercept:

0 + 17y = -25

17y = -25

y = -25/17

Since we set y equal to 0, the x-intercept is (0, 0).

For the line 6x - 7y = -21, we set x equal to 0 to find the y-intercept:

6x - 7y = -21

-7y = -21

y = 21/7

Since we set x equal to 0, the y-intercept is (0, 21/7).

Therefore, the x-intercept of the line 5x + 17y = -25 is (0, 0) and the y-intercept of the line 6x - 7y = -21 is (0, 21/7).

Answer:

Biotic factors of a marine ecosystem typically include algae, plankton, bacteria, seaweed, corals, fish, sharks, seals, whales, penguins and jellyfish.

Step-by-step explanation:

i hope this answer helped

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Reflection of point 1 over X axis is (-4, -2)

Reflection of point 2 over Y axis is (2, 3)

Reflection of point 3 over x = 1 is (2, 1)

Reflection of point 4 over y = x is  (2, -1)

What is Reflection of a point?

A reflection point occurs when a figure is constructed around a single point known as the point of reflection or center of the figure. For every point in the figure, another point is found directly opposite to it on the other side.

According to the given question:

1. Reflection of point 1 over X axis (x, -y) ⇔ (x, y)

 ∴ Reflection of (-4, 2) over X axis is (-4, -2)

2. Reflection of point 2 over Y axis (x, y) ⇔ (-x, y)

 ∴ Reflection of (-2, 3) over Y axis is (2, 3)

3. Reflection of point 3 over x = 1

 ∴ Reflection of (-2, 1) over x = 1 axis is (2, 1)

4. Reflection of point 4 over y = x is  (x, y) ⇔ (y, x)

 ∴ Reflection of (-1, 2) over X axis is (2, -1)

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The distance Alex jumped and the distance Eric jumped compared with the state records indicates that the magnitude of Eric's score was closer to their grades state  record

The magnitude of a value is the value itself, indicating the distance of the number from zero.

Alex is an eight grader

Eric is a seventh grader

The distance Alex jumped = 39.75  feet

The distance Eric jumped = 37 feet 11 inches

The eight grade record = 42.25 feet

The seventh grade record = 39 feet 3 inches

Each athlete distance  jumped is compared with  the record for the grade at which they jumped

The deviation of the distance  jumped from the record scores are;

Alex's difference between distance jumped  and the record = 39.75 - 42.25 =  -2.5

The difference between the distance Eric jumped and the record =  37 feet + 11 inches - (39 feet + 3 inches)  =  -(1 feet + 4 inches)

-(1 feet + 4 inches) = -1.[tex]\overline 3[/tex] inches

The magnitude of the difference between the distance Eric jumped and the state record is smaller, therefore, Eric was closer to the state record

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Answer: I can confirm that Eric is closer!

Step-by-step explanation:

Answer: 35%

Step-by-step explanation:

Answer:

5f + 4s

Step-by-step explanation:

Third option

Answer:

y =5x

Step-by-step explanation:

y = 5x

Because the slope is 5 and the y-intercept is 0.

The number of days to rent a car at either place and pay thesame amount is 11 days

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time.

Let the number of days to repay after a down payment be x and the y represent the total payment.

Therefore 61+24x= y equation 1

105+ 20x = y equation 2

subtract equation 1 from 2

105-61+20x-24x= 0

44-4x= 0

4x = 44

divide both sides by 4

x= 44/4

x= 11 days

therefore the number of days to rent a car at either places and pay thesame amount is 11 days

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Answer:

  0.1220

Step-by-step explanation:

You want the probability that greater than 90 out of 149 software users will not call tech support, given that the probability a given user will not call is 56%. You want the value using the normal approximation to the binomial distribution.

For a sample size of n, and probability p of "success", the normal approximation to the binomial distribution can be used if ...

  min(pn, (1-p)n) > 5

Here, that is ...

  min(0.56·149, 0.44·149) > 5

  65.6 > 5 . . . . . . . . true, the normal approximation is appropriate

Then the parameters of the normal distribution are ...

  µ = pn = 0.56·149 = 83.44

  σ = √((1-p)µ) = √(0.44·83.44) ≈ 6.0592

The probability that X = N will occur can be considered to be ...

  P(N -0.5 < X < N +0.5)

Then the probability that X > N will be modeled using the normal distribution as ...

  P(X > N +0.5)

For this problem, we want ...

  P(X > 90.5) . . . . using the normal distribution with µ = 83.44, σ = 6.0592

The attached calculator shows that value to be ...

  P(>90) ≈ 0.1220 . . . . . . rounded to 4 decimal places

__

Additional comment

A probability calculator says the actual binomial distribution result for this problem is 0.1217.

Answer:

-5x+9y=-18

Dividing both sides by -18

-5x/-18+9y/-18=-18/-18

5x/18-y/2=1

x/(18/5)-y/2=1. eqn(i)

eqn (i) is comparing with x/a+y/b=1, we get

x - intercept (a) =18/5

y-intercept (b) = -2

Using proportions, James need 750ml for 24 pancakes

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

To find the amount of milk James need, we need to use proportions.

8 pancakes = 250ml milk

24 pancakes = x

cross multiply both side and make x the subject of formula

8 × x = 24 × 250

8x = 6000

Divide both sides by coefficient of x

8x / 8 = 6000 / 8

x = 750

He needs 750 ml of milk

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Graph (D) represented the inequality solution of 5+x<3(2x+4).

The set of ordered pairs is the graph of a function f in mathematics, where These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.

To develop a graph is to make a diagram that depicts the relationship between two or more objects.

Make a sequence of bars on graph paper as an example of a graph.

So, we have the inequality:

5 + 8x < 3 (2x+4)

Now, we need to plot this on the graph:

(Refer to the graph attached below)

We can easily tell that this is identical to graph sin option (D).


Therefore, graph (D) represented the inequality solution of 5+x<3(2x+4).

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Circumference of the circle is 37.68 feet

A circle's diameter is multiplied by to determine its circumference (pi). You can also determine the circumference by multiplying 2radius by pi (=3.14).

R is specified as 6 feet, with a diameter of 12 feet (2 x 6).

Circumference: 12 feet times 3.14 inches, or 37.68 feet

If r is equal to 6 cm, the circumference is given by c = 2 (6) = 12 cm. If you'd rather have a number, the solution is 37.7 cm, rounded to the closest tenth.

D is the diameter, which is equal to 2 times r in the circumference formula ( r is the radius).

The distance between the center of the sphere and any plane passing through it is known as the circumference. 

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Answer:

She bought 3 large frames and 8 small frames.

Step-by-step explanation:

X= Large frames = $19

Y= Small frames  = $ 9

Total Frames Cost = $129

Total Frames = 11

Then, costs formula:

1) 19X + 9Y = 129

2) X + Y = 11

So here you have a equation system and we will solve it by substituion method:

2) Y = 11-X

replace Y in 1)

1) 19X + 9(11-X) = 129

19X +99 -9X = 129

10X = 129-99

10X = 30

X = 30/10

X = 3

Then

Y = 11-3

Y = 8

Answer:

x=2.5, 5/2

y=1.5, 3/2

Step-by-step explanation:

2x-2(-5x+14)=2

2x+10x-28=2

12x=30

x=2.5

y=-5(2.5)+14

y=-12.5+14

y=1.5

The statistician model makes sense to predict the calories in food items.

A mathematical model called a statistical model contains a collection of statistical presumptions about how sample data are produced (and similar data from a larger population). A statistical model simulates the process of creating data, frequently in a highly idealised form.

Yes it makes sense to use the statistician model to predict calories calories in food items because the test of the overall model I.e F test is significant at any level of significance because the p value (2.2 e^-16)  is approximately zero which indicates that the model Is significant.

And also the individual test of each variable are all significant at any significance level (alpha) with p values ( 2e^-16, 2e^-16, 1.36e^-6).

Thirdly we can say of the strength of the relationship between calories and the independent variable through the R value = √R square = √0.929 = 0.9638 which indicates a strong relationship between them.

Therefore, the statistician model makes sense to predict the calories in food items.

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The 90% confidence interval's margin of error is 0.0183, and its success probability is 0.546.

The term "margin of error" refers to the probability or "chances of error" when selecting or computing a sample in a survey.

Jamie works as an analyst for a provider of educational technologies. She gathered information on the outcomes of a particular kind of query. 1,092 of the 2,000 replies she examined were accurate.

Here,

Number of samples, N=2000

Probability of responding correctly,

=1092/2000

=0.546

Z-score at 90% confidence level,

=1.645

Margin of Error ME,

=z*√(p*(1-p)/N)

=1.645*√(0.546*(1-0.546)/2000)

=1.645*√(0.546*0.454)/2000

=1.645*√(0.248/2000)

=1.645*√0.000124

=1.645*0.011

=0.0180

With a success rate of 0.546 percent, the margin of error for the 90% confidence interval is 0.0183.

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The factory produces 72 bottles of juice per minute.

What is the rate?

A rate is a special ratio in which the two terms are in different units. If a 12-ounce can of corn costs $69, the rate is $69 for 12 ounces. This is not a proportion of two comparable units, such as shirts. This is a proportion of two dissimilar units: cents and ounces.

To find the factory's production rate in bottles per minute, we need to divide the number of bottles produced by the time it took to produce them. In this case, the factory produced 360 bottles in 5 minutes, so the production rate is:

360 bottles / 5 minutes = 72 bottles/minute

This means that the factory produces 72 bottles of juice per minute.

Hence, the factory produces 72 bottles of juice per minute.

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Answer:

C

Step-by-step explanation:

A line perpendicular to the y-axis is a horizontal line

  Horizontal lines have  slope = 0

       answer C    y = 3   slope = 0

Simple random sampling is a sort of probability sampling in which a selection of participants is randomly chosen from a population by the researcher.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

Hence, In probability sampling, a sample is chosen from a population based on the randomization principle, also known as chance or random selection.

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Answer: 240

Step-by-step explanation: you take 10 times 12 and you get 140

Answer:

$240

Step-by-step explanation:

If ten friends went out and each was $24 it’s 10x24 which is equal to $240

From the equation, the value of m is 4

The given parameter is

0.m1+ 0.m2 + 0.m3 = 11/14

Simplify this to have

m1 / 99 + m2 / 99 + m3 / 99 = 11/14

Simplify the equation further

( m1 + m2 + m3 ) / 99 = 11/14

⇒( m1 + m2 + m3 ) = 126

By multiplication we have

( 10 * m + 1 ) + ( 10 * m + 2 ) + ( 10 * m + ) = 126

Simplify to get

30 * m + 6 = 126

30 * m = 120

m = 4

Therefore the value of m is 4

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Translated question:

Please help, given that 0.m1 +0.m2 +0.m3 = 14/11, Find the value of m

The value of P(A and B)  is 1/5.

What is Sample Space?

The set of all potential outcomes or results of an experiment or random trial is referred to as the sample space in probability theory. The sample points, or potential ordered outcomes, are listed as elements in the set notation used to represent a sample space.

Here, we have

Given

Sample Space = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {1, 2, 3, 4}

B={1, 3, 5, 7, 9}

We have to find P(A and B).

First, we will find A and B i.e A∩B

A∩B = {1,3}

Now, we will find P(A and B).

P(A and B) = n(A∩B)/n(S)

P(A and B) = 2/10

P(A and B)  = 1/5

Hence, the value of P(A and B)  is 1/5.

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True, In a paired test, a factor is what you are testing to see the effect of because its effect is unknown.

The paired t-test is a technique for determining whether or not the mean difference between two measurement pairs is zero. When your data values are paired measurements, you can apply the test.

The dependent samples t-test, paired difference t-test, matched pairs t-test, and repeated-samples t-test are other names for the paired t-test. You might not be able to test for normality if your sample sizes are too small. You might have to rely on your comprehension of the information. You might also do a nonparametric test that doesn't make the assumption of normality.

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