Find the equation of the parabola described below. Find the two points that define the latus rectum, and graph the equation. focus at (0,5), vertex at (0,0) The equation of the parabola with vertex (0,0) and focus (0,5) is x^2 = 20y (Use integers or fractions for any numbers in the equation.) The two points that define the latus rectum are ___
(Type ordered pairs. Use a comma to separate answers as needed.) Use the graphing tool to graph the parabola.

Answer: 7/20

Step-by-step explanation :7/20 is 0.350 converted into a fraction

There can be only one equation to represent a single line of point-slope equations, so option D is correct.

An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.

The point-slope equation can be written as,

\(y - y_1 = m (x - x_1)\)

Here \(m\) is the slope of the line,

As you can see from the above equation, there can be many points in a line, but there is only one equation for the line.

For example, if you take a line 2y + x = 4 and put different coordinates of points but the equation, you will get the same.

Therefore, there can be only one equation to represent a single line of point-slope equations.

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Answer:

First solve for x or y

3y - 7x = -2

3y = 7x - 2

y = (7/3)x - 2/3

Now substitute the x value into this equation and if it equals the yvue, then it's a solution.

y = (7/3)(4/7) - 2/3

y = 4/3 - 2/3

y = 2/3 ✓

y = (7/3)0 - 2/3

y = -2/3 ✓

y = (7/3)11 - 2/3

y = 77/3 - 2/3

y = 75/3 = 25 ✓

y = (7/3)2 - 2/3

y = 14/3 - 2/3

y = 12/3 = 4 ✓

y = (7/3)(2/7) - 2/3

y = 2/3 - 2/3

y = 0 ✓

y = (7/3)-4 - 2/3

y = -28/3 - 2/3

y = -30/3 = -10 ✓

They are all solutions

The linear model that represents the cost of any number of candy bars can be written as: C = $1.90B + $0.95

To write the linear model that models the cost of any number of candy bars, we need to find the equation of a line that best fits the given data points. We'll use the variables B for the number of candy bars purchased and C for the total cost of the candy bars.

Looking at the given data, we can see that there is a linear relationship between the number of candy bars and the total cost. As the number of candy bars increases, the total cost also increases.

To find the equation of the line, we need to determine the slope and the y-intercept. We can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m) using two points from the given data, for example, (3, $6.65) and (25, $48.45):

m = (C2 - C1) / (B2 - B1)

 = ($48.45 - $6.65) / (25 - 3)

 = $41.80 / 22

 ≈ $1.90

Now, let's find the y-intercept (b) using one of the data points, for example, (3, $6.65):

b = C - mB

 = $6.65 - ($1.90 * 3)

 = $6.65 - $5.70

 ≈ $0.95

Therefore, the linear model that represents the cost of any number of candy bars can be written as:

C = $1.90B + $0.95

This equation represents a linear relationship between the number of candy bars (B) and the total cost (C). For any given value of B, you can substitute it into the equation to find the corresponding estimated total cost of the candy bars.

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Therefore the balance after a year comes out to be $3552.80 and the balance comes out to be after compounded annually is $3552.50

Compound interest is the interest on savings that is computed using both the original principal and the interest accrued over time.

It is believed that Italy in the 17th century was where the idea of "interest on interest" or compound interest first emerged. It will accelerate the growth of a sum more quickly than simple interest, which is only applied to the principal sum.

Money multiplies more quickly through compounding, and the higher the

Here,

The Liam deposits $3,500 in a saving account that pays 1.5% interest,

Thus rate=1.5% and principle amount =3500

Therefore it is compounded quartely ,

The balance after year=

C=P\(e^{rt}\)

C=3500*\(e^{1.5*4}\)

C=3552.80

Therefore the balance after a year comes out to be $3552.80

Therefore the balance comes out to be after compounded annually is

$3552.50

So there is only $0.30 difference between the amounts

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The function defined by M(t) = 2t + 1 has no maximum value on the interval [0,4) as the derivative of m(t) is not equal to zero.

The maxima of the function can be calculated by the derivative of the function. The derivative is equated to 0 to calculate the critical points. If the second derivative is negative at this critical point then a maximum exists at this point.

The function is M(t) = 2t + 1 . Differentiate the function with respect to t. Now equate the derivative to 0. This will give the critical point. Since 2 is not equal to 0, the critical point does not exist on the curve of the function. Therefore, the function M(t) = 2t + 1does not have a maxima.  M(t) = 2t + 1

   d/dt M(t) = d/dt 2t + 1

                  = 2

d/dt m'(t) = 0

2 not equal to 0

The function does not have a critical point. Therefore, the maxima do not exist for the function.

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The formulated Linear Program aims to minimize the objective function, which is the sum of production and inventory costs minus the revenue from selling the end-of-period inventory at month 4.

In this problem, we need to determine the optimal production and inventory levels over the four-month period to minimize costs and maximize revenue. We can formulate this as a linear programming problem with the following decision variables:

Let x1, x2, x3, x4 represent the production quantities for months 1, 2, 3, and 4, respectively.

Let y1, y2, y3, y4 represent the end-of-month inventory levels for months 1, 2, 3, and 4, respectively.

The objective function we want to minimize is:

Minimize: (5x1 + 8x2 + 4x3 + 7x4) + (2y1 + 2y2 + 2y3) - (15y4)

Subject to the following constraints:

1. Initial inventory: y1 = 15 (given)

2. Production capacity constraints:

  x1 <= 90 (month 1 capacity)

  x2 <= 75 (month 2 capacity)

  x3 <= 80 (month 3 capacity)

  x4 <= 50 (month 4 capacity)

3. Inventory balance equations:

  y1 + x1 - 50 = y2 (month 1)

  y2 + x2 - 65 = y3 (month 2)

  y3 + x3 - 100 = y4 (month 3)

  y4 + x4 - 70 = 0 (month 4, no carryover inventory)

4. Non-negativity constraints:

  x1, x2, x3, x4, y1, y2, y3, y4 ≥ 0

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Answer:

The two numbers are 56 and 23.

Step-by-step explanation:

Let the two numbers be A and B.

We are told that:

A+B = 79, and

2)  3A + 5B = 283

Rearrange the first expression to isolate A:

A = 79-B

Now use this value of B in the second expression:

3A + 5B = 283

3(79-B) + 5B = 283

237-3B + 5B = 283

2B = 46

B = 23

If B=23, we can find A from (1):  

A+B = 79

A+23 = 79

A = 56

CHECK:

Does A+B = 79?

56 + 23 = 79?  YES

Does 3A + 5B = 283?

  3(56) + 5(23) = 283?

 168 + 115 = 283?  YES

Answer:

30

Step-by-step explanation:

1950 ÷ 65 = 30

total money ÷ money for one student

Given the coordinates:

midpoint(-6, -20)

Endpoint 1(-4, -16)

To find endpoint 2, apply the midpoint formula below:

Where,

(xm, ym) = (-6, -20)

(x1, y1) = (-4, -16)

(x2, y2) = unknown

Let's find the mising coordinates (x2, y2)

Therefore, the other endpoint is (-8, -24)

ANSWER:

(-8, -24)

Answer: He now weighs 4.2 kg because 4/10 of 3 is 1.2 and 1.2+3=4.2

Therefore , the solution of the given problem of graph comes out to be (0,29) and (0,5).

Graphs are used by academics to logically depict or chart events or values visually. A graph point often depicts the relationship between two or more things. The non-linear storage structure known as a graph is made up of nodes, often referred to as vertices, and edges. Glue ought to be used to join the nodes, also known as vertices. In this graph, the vertex numbers are 1, 2, 3, or 5, whereas the edge numbers were 1, 2, 1, 3, 2, 4, etc (2.5). (3.5). (4.5). (4.5). graphics that graphically represent exponential growth in statistical diagrams like line graphs, charts, and bar graphs. a logarithmic graph with a triangle form

Here,

Given :

=>  y=(x-5)²+4

So,

x =0

then y value :

=> y = (0-5)² +4

=> y = 25 +4

=> y = 29

=> (0,29)

and

=>  y=2x²+8x+5

So,

x = 0 ,

then y value :

=> y = 2(0)² + 8(0) + 5

=> y = 5

=> (0,5)

Therefore , the solution of the given problem of graph comes out to be (0,29) and (0,5).

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Answer:

6.34960 correct to 5 decimal places.

Step-by-step explanation

16 ^ 2/3

= cube root of 16^2

∛(16^2)

= ∛(256)

= 6.349604208.

The 2 in the 2/3 means the square of 16, and the 3 in 2/3 mean 16^1/3

which is the same as the cube root.

The evaluation of mixed fractions   \(16\dfrac{2}{3}\)  in improper fractions using the simplification rule is \(\dfrac{50}{3}\).

The combination of a proper fraction and a whole number is called a mixed fraction.

When the numerator is greater than the denominator, such type of fraction is called an improper fraction.

To evaluate \(16 \dfrac{2}{3}\) ,  convert the mixed number to an improper fraction and then simplify it.

Multiply the whole number \((16)\)  by the denominator \((3)\)  and add the numerator \((2)\).

\((16 \times 3 )+ 2 \\= 48 + 2\\ = 50\)

The sum is written with the denominator \(3\)  as \(\dfrac{50}{3}\) .

The evaluation of mixed fractions \(16\dfrac{2}{3}\)  in improper fractions is \(\dfrac{50}{3}\).

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Answer:

Step-by-step explanation:

An expression to display a loss of 42 yards on the football field would be: -42 yards.

The negative sign in front of the number 42 indicates a loss or a decrease in the yards, which represents a loss of 42 yards on the football field.

Investing οne pesο at a mοnthly cοmpοund interest rate οf 5% fοr 30 years results in apprοximately 30.1267 pesοs.

Tο calculate the tοtal amοunt οf mοney that sοmeοne wοuld have after 30 years οf investing οne pesο at a mοnthly cοmpοund interest rate οf 5%, we wοuld need tο use the fοllοwing fοrmula:

\(A = P(1 + r/n)^{(nt)\)

Where:

A = the tοtal amοunt οf mοney at the end οf the investment periοd

P = the principal amοunt invested (in this case, οne pesο)

r = the annual interest rate (in this case, 5%)

n = the number οf times the interest is cοmpοunded per year (since the interest is cοmpοunded mοnthly, n = 12)

t = the number οf years οf the investment periοd (in this case, 30)

Plugging in these values, we get:

\(A = 1(1 + 0.05/12)^{(12*30)\)

\(A = 1.05^{(360)\)

\(A = 30.1267\)

Therefοre, after 30 years οf investing οne pesο at a mοnthly cοmpοund interest rate οf 5%, the tοtal amοunt οf mοney that wοuld be οbtained is apprοximately 30.1267 pesοs.

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Complete Question:

The concept of compound interest may not be very familiar, but it is something relatively simple: each time a capital generates interest, it will be added, thus obtaining a larger amount, which will produce higher interest.

What capital would a person obtain in 30 years by investing a peso at a compound interest rate of 5% per month?

The area of the half-cylinder can be found using a parametric description of the surface.

To find the area of the half-cylinder, we can parametrize the surface using cylindrical coordinates. Let's consider the surface as a function of two parameters, θ and z. We can define the parametric equations as follows:

x = r cos(θ)

y = r sin(θ)

z = z

In this case, the radius r is given as 4, the angle θ varies from 0 to 2π, and the height z varies from 0 to 7.

To calculate the surface area, we use the formula for the surface area of a surface described by parametric equations:

A = ∫∫ ||rθ × rz|| dθ dz

Here, ||rθ × rz|| represents the magnitude of the cross product of the partial derivatives of the parametric equations with respect to θ and z.

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The values for f(1), f(2), f(3), f(4), and f(5) using the recursive formula f(n+1) = 3^(f(n)/3) are:

f(1) = 3, f(2) = 3, f(3) = 3, f(4) = 3, f(5) = 3.

To find the values of f(1), f(2), f(3), f(4), and f(5) for each given recursive definition, we can use the initial condition f(0) = 3 and the recursive formulas.

(a) f(n+1) = -2f(n):

Using the recursive formula, we can find the values as follows:

f(1) = -2f(0) = -2(3) = -6

f(2) = -2f(1) = -2(-6) = 12

f(3) = -2f(2) = -2(12) = -24

f(4) = -2f(3) = -2(-24) = 48

f(5) = -2f(4) = -2(48) = -96

So, the values for f(1), f(2), f(3), f(4), and f(5) using the recursive formula f(n+1) = -2f(n) are:

f(1) = -6, f(2) = 12, f(3) = -24, f(4) = 48, f(5) = -96.

(b) f(n+1) = 3f(n) + 7:

Using the recursive formula, we can find the values as follows:

f(1) = 3f(0) + 7 = 3(3) + 7 = 16

f(2) = 3f(1) + 7 = 3(16) + 7 = 55

f(3) = 3f(2) + 7 = 3(55) + 7 = 172

f(4) = 3f(3) + 7 = 3(172) + 7 = 523

f(5) = 3f(4) + 7 = 3(523) + 7 = 1576

So, the values for f(1), f(2), f(3), f(4), and f(5) using the recursive formula f(n+1) = 3f(n) + 7 are:

f(1) = 16, f(2) = 55, f(3) = 172, f(4) = 523, f(5) = 1576.

(c) f(n+1) = f(n)^2 - 2f(n) - 2:

Using the recursive formula, we can find the values as follows:

f(1) = f(0)^2 - 2f(0) - 2 = 3^2 - 2(3) - 2 = 1

f(2) = f(1)^2 - 2f(1) - 2 = 1^2 - 2(1) - 2 = -3

f(3) = f(2)^2 - 2f(2) - 2 = (-3)^2 - 2(-3) - 2 = 7

f(4) = f(3)^2 - 2f(3) - 2 = 7^2 - 2(7) - 2 = 41

f(5) = f(4)^2 - 2f(4) - 2 = 41^2 - 2(41) - 2 = 1601

So, the values for f(1), f(2), f(3), f(4), and f(

using the recursive formula f(n+1) = f(n)^2 - 2f(n) - 2 are:

f(1) = 1, f(2) = -3, f(3) = 7, f(4) = 41, f(5) = 1601.

(d) f(n+1) = 3^(f(n)/3):

Using the recursive formula, we can find the values as follows:

f(1) = 3^(f(0)/3) = 3^(3/3) = 3^1 = 3

f(2) = 3^(f(1)/3) = 3^(3/3) = 3^1 = 3

f(3) = 3^(f(2)/3) = 3^(3/3) = 3^1 = 3

f(4) = 3^(f(3)/3) = 3^(3/3) = 3^1 = 3

f(5) = 3^(f(4)/3) = 3^(3/3) = 3^1 = 3

So, the values for f(1), f(2), f(3), f(4), and f(5) using the recursive formula f(n+1) = 3^(f(n)/3) are:

f(1) = 3, f(2) = 3, f(3) = 3, f(4) = 3, f(5) = 3.

Note: In the case of (d), the recursive formula leads to the same value for all values of n.

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Answer: \(50^{\circ}F\)

Step-by-step explanation:

Given

Temperature increase is \(10^{\circ}C\)

We know, conversion scale of Celcius to Fahrenheit is  

\(0^{\circ}C\times \dfrac{9}{5}+32=32^{\circ}F\)

for \(10^{\circ}C\), it is

\(\Rightarrow 10\times \dfrac{9}{5}+32\\\\\Rightarrow 18+32=50^{\circ}F\)

It is equivalent to \(50^{\circ}F\)

Answer:

56

Step-by-step explanation:

Apply PEMDAS:

\(72 / 4.5*3+8\\\\16*3+8\\\\48+8\\\\\boxed{56}\)

The function f is increasing on the interval (6, ∞).

The function f will be increasing in the intervals where f'(x) > 0.

To find these intervals, we can examine the sign of each factor of f'(x), which is (x + 1)²(x - 3)⁵(x - 6)⁴.

We can analyze the sign of f(x) by considering the factors individually:

(x+1)²: This factor is always positive since it is the square of a real number.

(x - 3)⁵: This factor is positive when x>3 and negative when x< 3.

(x - 6)⁴: This factor is positive when x>6 and  negative when x< 6.

We need to consider the overlapping regions of positivity for each factor.

When x>6, all three factors are positive, so  f ′ (x) is positive.

When 3<x<6: In this interval, the factor  (x+1)² is positive, but both (x−3)⁵ and (x−6)⁴ are negative.

Thus, f ′ (x) is negative.

When x<−1: In this interval,  (x+1)² is negative, while (x−3)⁵ and (x−6)⁴ are positive.

Hence, f ′ (x) is negative.

Therefore,  the function f(x) is increasing on the interval x>6.

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Answer:

5 km/h

Step-by-step explanation:

Speed of man in still water = s

Speed of current = c

Speed upstream = s - c

Distance upstream = 24 km

Time upstream = 6 hours

Speed downstream = s + c

Distance downstream = 36 km

Time downstream = 6 hours

Speed Equation

speed = distance/time

distance = speed × time

d = st

We write a distance equation for upstream and a second distance equation for downstream.

Upstream:

d = st

24 = (s - c) × 6

Divide both sides by 6 and switch sides:

s - c = 4        Equation 1

Downstream:

d = st

36 = (s + c) × 6

Divide both sides by 6 and switch sides.

s + c = 6       Equation 2

We now have two equations in two variables. We use equations 1 and 2 as a system of equations.

s - c = 4

s + c = 6

Add the equations to use the addition method.

2s = 10

s = 5

Answer: 5 km/h

The distribution of component size is likely skewed to the right so it is mild positive skewed. so, the correct option is A).  Lower limit for outliers is -279 and upper limit is 1016.

The fact that the largest component (California) has more than three times as many members as the smallest component (Rhode Island) suggests a potentially right-skewed distribution. So, the correct answer is  mild positive skewed and option is A).

To determine the limits for outliers, we need to calculate the lower and upper bounds. Using the interquartile range (IQR) method, we can calculate the lower and upper bounds as:

Lower bound = Q1 - 1.5 x IQR

Upper bound = Q3 + 1.5 x IQR

Where Q1 is the first quartile, Q3 is the third quartile, and IQR is the interquartile range.

Using a calculator or statistical software, we can find:

Q1 = 197

Q3 = 542

IQR = Q3 - Q1 = 345

Substituting these values, we get:

Lower bound = 197 - 1.5 x 345 = -279

Upper bound = 542 + 1.5 x 345 = 1016

Therefore, any component size less than -279 or greater than 1016 would be considered an outlier.

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--The given question is incomplete, the complete question is given

" The American Society of PeriAnesthesia Nurses (ASPAN; www.aspan.org) is a national organization serving nurses practicing in ambulatory surgery, preanesthesia, and postanesthesia care. The organization consists of the 40 components listed below.

State/Region Membership

Alabama   95  

Arizona   399  

Maryland, Delaware, DC   531  

Connecticut   239  

Florida   631  

Georgia   384  

Hawaii   73  

Illinois   562  

Indiana   270  

Iowa   117  

Kentucky   197  

Louisiana   258  

Michigan   411  

Massachusetts   480  

Maine   97  

Minnesota, Dakotas   289  

Missouri, Kansas   282  

Mississippi   90  

Nebraska   115  

North Carolina   542  

Nevada   106  

New Jersey, Bermuda   517  

Alaska, Idaho, Montana, Oregon, Washington   708  

New York   891  

Ohio   708  

Oklahoma   171  

Arkansas   68  

California   1,165  

New Mexico   79  

Pennsylvania   575  

Rhode Island   53  

Colorado   409  

South Carolina   237  

Texas   1,026  

Tennessee   167  

Utah   67  

Virginia   414  

Vermont, New Hampshire   144  

Wisconsin   311  

West Virginia   62                                                                                                                               A. What do you conclude about the shape of the distribution of component size?

multiple choice 1

A) Mild negative skewness

B) Mild positive skewness

B. What are the limits for outliers? (Round your answers to the nearest whole number. Negative amounts should be indicated by a minus sign.)"--

Answer:

Not Sure how to solve this...

Step-by-step explanation:

BUT

5 minutes is equal to \(\frac{1}{12}\)

10 minutes is equal to \(\frac{1}{6}\)

15 minutes is equal to \(\frac{1}{4}\)

30 minutes is equal to \(\frac{1}{2}\)

The formal education levels of the sample differ significantly from the formal education levels of the surrounding community, the sample is not representative of the surrounding community.

In statistics, the t-test is a hypothesis testing approach that determines whether there is a significant difference between the mean values of two groups. T-test is conducted to determine the difference between two group means, and it is done through comparing the p-value to the significance level. Here, the t-test is used to compare the average formal education levels of people attending a professional football game and the surrounding community.The difference between the formal education levels of the people attending the game and the surrounding community is significant at the .05 level.

Hence, we can say that the formal education levels of the people attending the game significantly differ from the surrounding community at a .05 level of significance. Furthermore, since the p-value is less than the significance level, we can reject the null hypothesis.

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Answer:

The Answer is B

Step-by-step explanation:

Answer:

the answer is b  he is right

Step-by-step explanation:

Answer:

(x + 6)(x + 7)

Step-by-step explanation:

To factor the trinomial x^2 + 13x + 42, we need to find two numbers that multiply to 42 and add up to 13.

One way to do this is to list all the pairs of factors of 42 and see which pair adds up to 13:

1, 42 -> 1 + 42 = 43

2, 21 -> 2 + 21 = 23

3, 14 -> 3 + 14 = 17

6, 7 -> 6 + 7 = 13

So the pair of factors that we want is 6 and 7. We can use these numbers to rewrite the middle term of the trinomial:

x^2 + 13x + 42 = x^2 + 6x + 7x + 42

Next, we can group the first two terms and the last two terms:

x^2 + 6x + 7x + 42 = (x^2 + 6x) + (7x + 42)

Now, we can factor out the greatest common factor from each group:

x(x + 6) + 7(x + 6)

Notice that we have a common factor of (x + 6) in both terms. We can factor this out:

(x + 6)(x + 7)

Answer

ok the answer is C

Step-by-step explanation:

1.75*4=7

.75*2=1.5

7+1.5=8.50

Answer:

  7

Step-by-step explanation:

The order of operations tells you to start any evaluation by looking at the innermost set of parentheses first.

Here, that means your first step is to find the value of h(-3). You do that by finding the input (x) value -3 in the table for h(x), and locating the corresponding output, h(x), which is 2.

Now, the problem becomes evaluating g(2).

You do the same thing for that function: locate the input x=2 in the table for g(x) and find the corresponding output: 7.

Now, you know ...

  g(h(-3)) = g(2) = 7

Answer:

This is a right triangle.

Step-by-step explanation:

\( \sqrt{ {9}^{2} + {12}^{2} } = \sqrt{81 + 144} = \sqrt{225} = 15\)