there 56 people invited to marks family reunion. each table at the park where the reunion is held can hold 7 people

The slope of the tangent line to the curve at (8, 2) is given by the derivative [tex]\frac{dy}{dx}[/tex] at that point. By the chain rule,

[tex]\dfrac{dy}{dx} = \dfrac{dy}{dt} \times \dfrac{dt}{dx} = \dfrac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]

Differentiate the given parametric equations with respect to [tex]t[/tex] :

[tex]x = 4t \implies \dfrac{dx}{dt} = 4[/tex]

[tex]y = \dfrac4t \implies \dfrac{dy}{dt} = -\dfrac4{t^2}[/tex]

Then

[tex]\dfrac{dy}{dx} = \dfrac{-\frac4{t^2}}4 = -\dfrac1{t^2}[/tex]

We have [tex]x=8[/tex] and [tex]y=2[/tex] when [tex]t=2[/tex], so the slope at the given point is [tex]\frac{dy}{dx} = -\frac14[/tex].

The normal line to the same point is perpendicular to the tangent line, so its slope is +4. Then using the point-slope formula for a line, the normal line has equation

[tex]y - 2 = 4 (x - 8) \implies \boxed{y = 4x - 30}[/tex]

Alternatively, we can eliminate the parameter and express [tex]y[/tex] explicitly in terms of [tex]x[/tex] :

[tex]x = 4t \implies t = \dfrac x4 \implies y = \dfrac4t = \dfrac4{\frac x4} = \dfrac{16}x[/tex]

Then the slope of the tangent line is

[tex]\dfrac{dy}{dx} = -\dfrac{16}{x^2}[/tex]

At [tex]x = 8[/tex], the slope is again [tex]-\frac{16}{64}=-\frac14[/tex], so the normal has slope +4, and so on.

Answer:

(14, -9)

Step-by-step explanation:

So you can solve this using substitution. When you're solving a systems of equations, you're looking for when (x, y) is the same for both equations, or in other words where the two linear equations intersect. Because of this we can solve for x or y in one equation and substitute it into the other equation, since the x and y in one equation should equal the x and y in the other equation.

Original equation:

x + 2y = -4

Subtract 2y from both sides

x = -2y - 4

Original equation:

2x + 3y = 1

Substitute -2y -4 as x

2(-2y - 4) + 3y = 1

Distribute the 2

-4y - 8 + 3y = 1

Combine like terms

-y - 8 = 1

Add 8 to both sides

-y = 9

Multiply both sides by -1

y = -9

So now that you know what y is, you can plug it into either equation to solve for x:

x + 2y = -4

Plug in -9 as y

x + 2(-9) = -4

Multiply

x - 18 = -4

Add 18 to both sides

x = 14

So this gives you the solution (14, -9)

The values of a and b if they are integers are -10 and 3

Surd functions are square root of prime numbers. Given the following equation;

10 - √18 = a +b√2

Equate the real and surd part to form the equation

b√2 = √18

2b² = 18

b² = 9

b = 3

Similarly

a = -10

Hence the values of a and b if they are integers are -10 and 3

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The question is incomplete. Please find the full content below.

Which number produces a rational number multiplied by 0.5

(C) 2.22 produces a rational number multiplied by 0.5.

If a number can be expressed by p/q form where p and q are whole numbers and q does not equal to 0, is called a Rational number.

If a number cannot be expressed as above then that number is called Irrational Number.

In simple term, we can say that the never-ending decimal numbers and square roots of non perfect square numbers are Irrational Numbers.

Product of two rational numbers is always a rational and the product of one rational and one irrational is always an irrational number.

Here given that the number is 0.5 which is clearly a rational number.

In order to get a rational number, we have to multiply another rational number with that.

In the given choices,

[tex]\pi=3.14......[/tex]

is a never-ending decimal number that is irrational.

7 is not a perfect square so

[tex]\sqrt{7}[/tex]

is an irrational number.

2.020020002.... is also a never-ending decimal number hence it is irrational.

Only 2.22 is rational here.

So multiplication of 2.22 and 0.5 produces a rational number since the product of two rational numbers is always a rational number.

Hence option (C) is correct.

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Answer:

[-20.25;+∞).

Step-by-step explanation:

1) according to the properties of the given parabola the minimum is:

[tex]x_0=-\frac{-7}{2}=3.5; \ y_0=-20.25;[/tex]

2) y₀=-20.25 means, the value -20.25 is minimum of the range, the maximum →+∞;

3) finally, the range y≥-20.25.

Answer:

Step-by-step explanation:

Below is the graphs of the given g(x) and p(x)

g(x) is green

p(x) is blue

The graph of g(x) is wider.

The graph of g(x) opens downward

Both have the axis of symmetry x = 0

The vertex of g(x) is (0, 7); the vertex of p(x) is (0, 0).

The graph of g(x) opens downward and the graph of p(x)  opens upward

The graph of g(x) is wider.

Zeros, solutions, roots, x-intercepts, and factors are subjects that reference the same area on a polynomial graph.

A polynomial graph can be defined as a type of graph that can be used to represent only positive (non-negative) integer exponents of a variable in an equation.

This ultimately implies that, a polynomial graph touches the x-axis at zeros, solutions, roots, x-intercepts, and factors with even multiplicities.

In conclusion, we can logically deduce that zeros, solutions, roots, x-intercepts, and factors are subjects that reference the same area on a polynomial graph.

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Answer:

10

Step-by-step explanation:

x = Edith's age = 20 years

y = Ronald's age

x = 20 = y/4

y = 20×4 = 80 years

in z years we have

(x + z) = (y + z)/3

(20 + z) = (80 + z)/3

3(20 + z) = 80 + z

60 + 3z = 80 + z

60 + 2z = 80

2z = 20

z = 10

in 10 years Edith's age will be 1/3 of Ronald's age.

then Edith will be 30, and Ronald will be 90.

30 = 90/3

correct.

Answer:

a=1.5, b= 3

Step-by-step explanation:

sum of all sides will give us perimeter. Therefore

2a+b+6a+2b+1+4a=28

12a+3b+1=28

12a+3b=27....eqn1

since t two sides of this isosceles triangle are equal:

2a+b=4a

2a=b

[tex]a=\frac{b}{2}[/tex]

substituting [tex]\frac{b}{2}[/tex][tex].[/tex] in the first equation whenever we encounter a we will have:

[tex]12(\frac{b}{2})+3b=27\\[/tex]

6b+3b=27

9b=27

b=3

therefore [tex]a= \frac{b}{2} =\frac{3}{2} =1\frac{1}{2} or 1.5[/tex]

Final answer:

Area of tile is 14 cm².

Step-by-step explanation:

Area of triangle is:

[tex]\frac{1}{2} base.height[/tex]

Putting [tex]b=3.5[/tex] and [tex]h=8[/tex] in [tex]\frac{1}{2} base.height[/tex]

[tex]\frac{1}{2}bxh=\frac{1}{2}3.5x8[/tex]

[tex]=3.5x4[/tex]

[tex]=14[/tex]

Answer:  Sample space:  {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG}

1. 8 outcomes in total

2. 1/8 or 0.125

3. 1/2 or 0.5

4. 1/2 or 0.5

5. 3/8 or 0.375

Step-by-step explanation:

1. As shown by the sample space and the tree diagram, there are 8 total possibilities.

2. There is only a 1/8 or 0.125 chance of there being all boys, which is BBB

3. There are 4 outcomes that allow the middle child to be a girl, and 4/8 = 1/2.  There will only be a girl middle child with BGB, GGG, BGG, and GGB.

4. We can think of at least as meaning no less than two boys, which includes two to three boys.  The only outcomes that have either two or three boys is BBB, BBG, BGB, GBB.  4/8 = 1/2.

5. We can think of at most as meaning no more than one girl.  The only outcomes that have only one girl are BBG, BGB, and GBB, which is 3/8.

The number which represent tens digit of a number is twice the ones digit is;

Complete question:

The tens digit of a number is twice the ones digit. The sum of the digits in the number is

12. What is the number?

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Answer:

Yes

Step-by-step explanation:

In mathematics, there are real numbers, imaginary numbers, and complex numbers. Is there any other category? We have infinite Cardinal and Ordinal numbers, not covered above.

Step-by-step explanation:

that is a tricky question.

basically all numbers we know are either a real or an imaginary number.

but there are many sub-types and one super-type that are defined in mathematics.

the superset of real and imaginary numbers is called complex numbers. that means it contains all real and all imaginary numbers.

the real numbers have then many sub-types :

e.g.

natural numbers

whole numbers

integer numbers

rational numbers

irrational numbers

so, you see, if the question means if there are any additional forms of numbers than real and imaginary numbers, then no.

if the question means if there are more number type definitions than just real and imaginary numbers, then yes.

Answer:

  X = 91.50

Step-by-step explanation:

The relation that defines a Z value can be used to find an X value when the appropriate parameters are given.

The equation for finding the Z-score associated with an X-value is ...

  Z = (X -μ)/σ

Solving this for X using the values given, we have ...

  3.15 = (X -60)/10

  31.5 = X -60 . . . . . . . multiply by 10

  91.5 = X . . . . . . . . add 60

The random variable value is ...

  X = 91.50

The correct answers to the question are:

A. b

B. c.

C. (1.486, 1.594)

d. b

This is because it would help to make the mean normal. This is given that the distribution for eating and drinking is not properly skewed.

B. The random sample of 972 is less than the population by 5 percent so it can be said to have satisfied the requirement. option c

C. sample size n = 972

mean = 1.54

sd = 0.65

1 - 0.99 = 0.01

Z0.01/2 = 2.58

The confidence interval would be gotten as

1.54 ± 2.58 ( 0.65/√972)

= 1.54 ± 2.58*0.021

= 1.54 - 0.054 , 1.54 + 0.054

= (1.486, 1.594)

d. The correct answer is b. The mean may differ given that the interval is about those that are 15 or more.

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5. A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 969 people age 15 or older, the mean amount of time spend eating or drinking per day is 1.85 hours with a standard deviation of 0.67 hours. Complete parts (a) through (d) below.

A). A histogram of time spends eating and drinking each day is skewed right. Use this result to explain why a large sample size is needed to construct a confidence interval for the mean time spent eating and drinking each day.

a. The distribution of the sample mean will always be approximately normal.

b. Since the distribution of time spent eating and drinking each day is not normally distributed (skewed right), the sample must be larger so that the distribution of the sample mean will be approximately normal.

c. Since the distribution of time spent eating and drinking each day is normally distributed, the sample must be larger so that the distribution of the sample mean will be approximately normal.

d.The distribution of the sample mean will never be approximately normal.

B). In 2010, there were over 200 million people nationally age 15 or older. Explain why this, along with the fact that the data were obtained using a random sample, satisfies the requirements for constructing a confidence interval.

a. The sample size is less than 10% of the population.

b. The sample size is greater than 5% of the population.

c. The sample size is less than 5% of the population.

d. The sample size is greater than 10% of the population.

C). Determine and interpret a 99% confidence interval for the mean amount of the time Americans age 15 or older spend eating and drinking each day. Select the correct choice and fill in the blanks.

a. There is a 99% probability that the mean amount of time spent eating and drinking per day is between _____ and _____ hours.

b. The nutritionist is 99% confident that the amount of time spent eating and drinking per day for any individual is between _____ and _____ hours.

c. The nutritionist is 99% confident that the mean amount of time spent eating and drinking per day is between _____ and _____ hours.

d. The requirements for conducting a confidence interval are not satisfied.

D). Could the interval be used to estimate the mean amount of time a 9 year old spends eating and drinking each day?

a. Yes; the interval is about the mean amount of time spend eating and drinking per day for people age 15 or older and can be used to find the mean amount of time spent eating and drinking per day for a 9 year olds.

b. No; the interval is about people age 15 or older. The mean amount of time spent eating and drinking per day for 9 years old may differ.

c. No; the interval is about individual time spent eating and drinking per day and cannot be use to fin the mean time spent eating and drinking per day for specific age.

d. Yes; the interval is about individual time spent eating and drinking per day and can be used to find the mean amount of time a 9 year old spends eating and drinking each day.

e. A confidence interval could not be constructed in part (c)

a. The number of shares outstanding after the stock split by Willey’s Grill & Restaurant Corporation is 670,000 (335,000 x 2).

b. If the common stock had a market price of $510 per share before the stock split, the approximate market price per share after the split is $255 ($510/2).

A stock split is a way that a corporation increases the number of its shares by increasing or decreasing the number of shares outstanding.

When a stock split increases the number of outstanding shares, the market price reduces proportionately.

a. What will be the number of shares outstanding after the split? Round your answer to the nearest whole number.

b. If the common stock had a market price of $510 per share before the stock split, what would be an approximate market price per share after the split? Round your answer to the nearest dollar.

Thus, the stock split increased the outstanding shares to 670,000 while reducing the market price to $255.

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In the graph,

Amplitude = 1.5 units

Period = 180°

The x-intercepts are 40°, 140°, 220°, and 320°

From the question, we are to determine the amplitude, period and the x-intercepts of the given graph

Amplitude is the distance from rest to crest.

In the graph,

Amplitude = 1.5 units

Period is how long from crest to crest OR trough to trough

In the graph,

Period = 180°

x-intercepts refers to the points where the graph cuts the x-axis

In the graph,

The x-intercepts are 40°, 140°, 220°, and 320°

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Answer:

C

Step-by-step explanation:

please mark brainliest if correct

The greater unit rate (slope) of the two functions is 2 (of the first function).

The greater y-intercept of the two functions is 6 (of the second function).

The unit rate (slope) of a linear function is the rise (or fall) in the independent variable for a unit change in the dependent variable.

When the linear function goes through the points (x₁, y₁) and (x₂, y₂), then the unit rate (slope) can be calculated as (y₂ - y₁)/(x₂ - x₁).

The first function goes through the points (0, 5) and (5, 15).

Thus unit rate (slope) of the first function = (15 - 5)/(5 - 0) = 2.

The second function goes through the points (0, 6) and (-4, 0).

Thus unit rate (slope) of the second function = (6 - 0)/(0 - (-4)) = 1.5.

Therefore, the greater unit rate (slope) of the two functions is 2 (of the first function).

The y-intercept of a linear function is the y-coordinate of the point at which the graph of the function intersects the y-axis. It is also shown as the point (0, b).

The y-intercept of the first function is 5, as it passes through the point (0, 5).

The y-intercept of the second function is 6, as it passes through the point (0, 6).

Therefore, the greater y-intercept of the two functions is 6 (of the second function).

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Answer:

2 and 6

Source:

Trust me bro

The given statement m<COX = m<COA + <AOX is TRUE

A protractor is a mathematical instrument for measuring angle. From the given protractor, we have that;

The measure of angle COA and angle AOX is equivalent to angle COA. Mathematically;

m<COX = m<COA + <AOX

This shows that the given statement is TRUE

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Hello

42. ?

100 17

We use cross product.

[tex] \frac{42 \times 17}{100} = 7.14[/tex]

42% of 17 => 7.14

Have a nice day ;)

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads....}[/tex]

[tex]\large\textbf{What is 42\% of 17?}[/tex]

[tex]\huge\textbf{Answering your question}[/tex]

[tex]\mathbf{42\% \ of \ 17}[/tex]

[tex]\huge\textbf{Translating it to easier to terms}[/tex]

[tex]\mathbf{42\% \ of \ 17}[/tex]

[tex]\mathbf{= 42\%\times 17}\\[/tex]

[tex]\mathbf{= \dfrac{42}{100}\times 17}[/tex]

[tex]\mathbf{= \dfrac{42\div2}{100\div2}\times17}[/tex]

[tex]\mathbf{= \dfrac{21}{50}\times17}[/tex]

[tex]\mathbf{= \dfrac{21}{50} \times \dfrac{17}{1}}[/tex]

[tex]\mathbf{= \dfrac{21\times17}{50\times1}}[/tex]

[tex]\mathbf{= \dfrac{357}{50}}[/tex]

[tex]\mathbf{= 357 \div 17}[/tex]

[tex]\mathbf{= 7.14}[/tex]

[tex]\huge\textbf{Answer }\bf \huge\boxed{\downarrow}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{7.14}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

All real numbers

Step-by-step explanation:

there arent any domain restrictions

The future value of the amount is $458,083.92.

The formula for calculating future value when there is continuous compounding is :

A x e^r x N

Where:

25,000 x e^0.20 x 15 = $458,083.92

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The subtraction of complex numbers [tex]z_{1} -z_{2}[/tex] is cos(π)+i sin(π).

Given [tex]z_{1} =\sqrt{2}[/tex][cos(3π/4+i sin(3π/4) and [tex]z_{2}[/tex]=cos (π/2) +i sin(π/2)

We have to find the value of [tex]z_{1} -z_{2}[/tex].

A complex number is a number that includes real number as well as a imaginary unit in which [tex]i^{2} =1[/tex]. It looks like a+ bi.

We have to first solve [tex]z_{1} and z_{2}[/tex] and then we will be able to find the difference.

[tex]z_{1} =[/tex][tex]\sqrt{2}[/tex][ cos (3π/4)+i sin (3π/4)]

[tex]=\sqrt{2}[/tex][cos(π-π/4)+ i sin (π-π/4)]

=[tex]\sqrt{2}[/tex] [-cos(π/4)+sin (π/4)]

=[tex]\sqrt{2}[/tex](-1/[tex]\sqrt{2}[/tex]+1/[tex]\sqrt{2}[/tex])

=[tex]\sqrt{2} *0[/tex]

=0

[tex]z_{2} =[/tex]cos(π/2)+i sin (π/2)

=0+i*1

=1

Now putting the values of [tex]z_{1} and z_{2}[/tex],

[tex]z_{1} -z_{2} =0-1[/tex]

=-1

=-1+i*0

=cos (π)+i sin(π)

Hence the value of difference between [tex]z_{1} and z_{2}[/tex] is cos(π)+i sin(π).

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Answer:

I need to see the graph

No explanation

Answer:

18

Step-by-step explanation:

Let x be the unknown number.

Given information:

Factor Pair:  

A pair of numbers that multiply together to give the original number.

We can immediately discount prime numbers since prime numbers only have one factor pair:  itself and one.

Remaining numbers: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18.

Of the remaining numbers, only 12, 16 and 18 have more than 2 pairs of factors:

Factors of 12:   1 and 12, 2 and 6, 3 and 4

Factors of 16:   1 and 16, 2 and 8, 4 and 4

Factors of 18:   1 and 18, 2 and 9, 3 and 6

If the pairs of factors sum to 19, 11 and 9, then the number must be 18.

Answer:

Area = 150 m²

Volume = 125 m³

Step-by-step explanation:

• The surface area of a cube is given by the formula:

[tex]Area = 6r^2[/tex]

where r is the length of an edge of the cube = 5 m.

∴ Area = 6(5)²

           = 6(25)

           = 150 m²

• The volume of a cube is given by the formula:

[tex]Volume = r^3[/tex]

∴ Volume = (5)³

                = 125 m³

[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\large{\textsf{\textbf{\underline{\underline{Answer :}}}}}}[/tex]

We use the formulas for the area and volume of the cube, assuming that the length [tex] \bold{A=5m}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold\red \: \bold \red A \purple = \bold \blue6 \bold \blue a {}^{ \bold \orange2} [/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold \red A \purple= \bold \blue6 \bold \blue \: \: \blue • \: \: \bold \blue5 {}^{ \bold\orange{ 2}} [/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold \red A \purple= \bold \blue 1 \bold \blue5 \bold \blue0 \bold \blue m {}^{ \bold \orange2} [/tex]

Now we will find the volume of the cube :-

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\bold \red V \purple = \bold\blue a {}^{ \bold \orange3} [/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold \red V \purple = \bold \blue 5 {}^{ \bold \orange3} [/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold \red V \purple = \blue{ \bold{125m}} {}^{ \bold \orange3} [/tex]

Answer: The area of the cube is 150 m² and the volume it Equal a 125 m³

I hope I've helped : )

The point F tells us that Marcelina spends the intended amount of money and she buys more than the intended amount of corn.

From the question the entire kg of maize that she buys from what we see in the graph is

50 + 20 = 70kg

But the amount that she was supposed to buy is 50 kg

Hence the point F shows that she spent the money the way she wanted to use in to buy the product.,

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