30. A man walks diagonally from one corner of a
rectangular lot to the opposite corner. If he
walks at the rate of 5 feet a second, and the lot is
50 feet by 120 feet, how many seconds will he
save by walking diagonally instead of walking
along the perimeter of the lot?
(A)8
(B) 10
(C) 17
(D) 34

The answer is [tex]0.87.[/tex]

The binomial probability distribution:

The binomial distribution's anticipated value is: [tex]ux=np[/tex]

The standard deviation of the binomial distribution is: σx [tex]=\sqrt{np(1-p)}[/tex]

[tex]p = 0.75.[/tex]

[tex]n = 4.[/tex]

The mean and standard deviation of x:

[tex]ux=np=4(0.75)=3[/tex]

σx[tex]=\sqrt{np(1-p)} =\sqrt{4(0.75)(0.25)} =0.87[/tex]

The answer is [tex]0.87.[/tex]

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The mean exists at 3 and the standard deviation exists 0.87.

Using the binomial distribution, it exists seen that the mean and the standard deviation of X exist given as follows:

[tex]$\mu_{X}=3, \sigma_{X}=0.87[/tex]

The expected value of the binomial distribution exists:

[tex]$\mu_{X}=n p$$[/tex]

The standard deviation of the binomial distribution exists:

[tex]$\sigma_{X}=\sqrt{n p(1-p)}$$[/tex]

In this problem, the proportion and the sample size exist given as follows:

p = 0.75

n = 4

Therefore, the mean and the standard deviation exist given by:

[tex]$&\mu_{X}=n p=4(0.75)=3 \\[/tex]

[tex]$&\sigma_{X}=\sqrt{n p(1-p)}[/tex]

[tex]$=\sqrt{4(0.75)(0.25)}=0.87[/tex]

The mean exists at 3 and the standard deviation exists 0.87.

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Answer:

∠S = 66°

Step-by-step explanation:

A parallelogram's 4 angles always add up to 360°, and opposite angles are the same. (∠S = ∠U; ∠T = ∠V)

So, ∠S + ∠T = 180°.

180° = (2x + 4x + 12 + 6)°

180° = (6x + 18)°

162° = (6x)°

27° = x°

(2x + 12)° = ∠S

(2(27) + 12)° = ∠S

(54 + 12)° = ∠S

66° = ∠S

Answer:

Akua now -- x

Ama now -- 4x

Akua in 10 years ---- x+10

Ama in 10 years ---- 4x+10

4x+10 = 2(x+10)

solve for x

let Ama's age be X and Akua's age be Y

X=4Y.......

X+10=(Y+10)2......

4Y+10=2Y+20

4Y-2Y=20-10

2Y=10 divide both side by 2

2Y/2=10/2

Y=5

X=4x5

X=20

therefore Ama =20years and Akua=5years

hope it helps..

The conic section will form an Ellipse.

The collection of all points in the plane that make up a circle are all equally spaced from a certain point known as the "centre," making the form a closed two-dimensional shape. The reflection symmetry line is created by all lines that traverse the circle. Additionally, it is symmetrical in rotation around the center at all angles.

A conic section is a curve formed when the surface of a cone and a plane connect. The hyperbola, parabola, and ellipse are the three forms of conic sections; the circle is a special case of the ellipse, though historically it was occasionally referred to as a fourth type.

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Answer:

x = 7; y = 4 1/3

Step-by-step explanation:

The solution is the point of intersection of the lines.

Read the point of intersection.

You can also solve the system using algebra.

y = 1/3 x + 2

y = 4/3 x - 5

1/3 x + 2 = 4/3 x - 5

x + 6 = 4x - 15

-3x = -21

x = 7

y = 1/3 x + 2

y = 1/3 × 7 + 2

y = 2 1/3 + 2

y = 4 1/3

Answer: x = 7; y = 4 1/3

Answer:

He is 2 years old.

Step-by-step explanation:

She is 22, in 8 years she will be 30. 30 is 3×10. At that time, her brother will be 10; that is 8 years from now. So now, the little brother is 10-8 = 2 years old.

If you must show algebra work:

x = brother's age now.

x+8=brother's age in 8 years.

YingYu's age in 8 years = 3 × brother's age in 8 years

22+8 = 3(x+8)

30 = 3x +24

6 = 3x

2 = x

The time that the ball is in the air if the player lets the ball drop is 2.145 sec

What is a quadratic equation?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax²+ bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

-16t²+32t+5

by comparing this equation to the standard form of the quadratic equation we get

a=-16 b=32 c=5

the time (t) needed for the ball to reach its maximum height using the axis of symmetry formula (x = -b/2a) for a parabola:

the time at which the ball reaches the maximum height using the axis of symmetry formula is (x=-b/2a)

t = -32/2×-16

t=1sec

by putting h(t) to zero and determining the time (t) when the ball hits the ground:

-16t²+32t+5=0

-16(t²+2t+5/16)=0

t²-2t-5/16=0

(t)²-2×1×t+(1)²-5/16=1

(t-1)²=21/16

t-1=√21/√16

t=1+4.58/4

t=1+1.145

t=2.245sec

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The limit does not exist.

In order for such a limit to occur, the fraction [tex]\frac{x^{2} }{x^{2} +y^{2} }[/tex] must be comparable to the same value [tex]L[/tex], regardless of the way we take to get there [tex](0,0)[/tex].

Try approaching [tex](0,0)[/tex] along the x-axis.

This means setting [tex]y=0[/tex] and finding the limit [tex]lim_{x-0} \frac{x^{2} }{x^{2} +y^{2} }[/tex].

We obtain:

[tex]lim_{x-0,y=0}\frac{x^{2} }{x^{2} +y^{2} } =lim_{y=0}}\frac{x^{2} }{x^{2} +0 }\\=lim_{x-0}} \frac{x^{2} }{x^{2} } \\\\=lim_{x-0}}1\\=1[/tex]

Now evaluate approaching [tex](0,0)[/tex] along the y-axis.

This means setting [tex]x=0[/tex] and finding the limit [tex]lim_{y-0} \frac{x^{2} }{x^{2} +y^{2} }[/tex].

[tex]lim_{y-0,x-0} \frac{x^{2} }{x^{2} +y^{2} } =lim_{y-0} \frac{0}{0+y^{2} } \\=lim_{y-0} \frac{0}{y^{2} } \\=lim_{y-0} 0\\=0[/tex]

Approaching the origin via these two methods results in distinct limits.

[tex]lim_{x-0,y-0} \frac{x^{2} }{x^{2} +y^{2} }[/tex] ≠ [tex]lim_{y-0,x-0}\frac{x^{2} }{x^{2} +y^{2} }[/tex]

Therefore the limit does not exist.

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The correct question is given below:

Find the limit, if it exists, or show that the limit does not exist.

[tex]lim_{(x,y) -(0,0)} \frac{x^{2} }{x^{2} +y^{2} }[/tex]

Based on the given parameters, the number of filet mignon the restaurant served is 14

From the question, the given parameters are:

Dinner specials =  salmon filet and filet mignon.

Dinner specials = 70 dinner specials

Salmon filets =  80%

This means that the proportion of filet mignon is

filet mignon = 100%- Salmon filets

This gives

filet mignon = 100%- 80%

Evaluate the difference

filet mignon = 20%

The number of filet mignon is calculated as:

filet mignon = 20% * Dinner specials

Substitute the known values in the above equation

filet mignon = 20% * 70

Express 20% as decimal

filet mignon = 0.20 * 70

Evaluate the product

filet mignon = 14

Hence, the number of filet mignon the restaurant served is 14

So, the complete parameters are:

Dinner specials =  salmon filet and filet mignon.

Dinner specials = 70 dinner specials

Salmon filets =  80%

filet mignon = 14

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The given statement simpson’s paradox occurs whenever including a lurking variable causes you to rethink the direction of an association is true.

Since, we know that

A variable that we did not include in our analysis, that could susbtantially change our intepretation of the data if we did include it, is called a lurking variable.

Including a lurking variable may

And,

When including a lurking variable causes you to re-think the direction of an association, this is called Simpson's paradox.

Hence, the given statement simpson’s paradox occurs whenever including a lurking variable causes you to rethink the direction of an association is true.

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Step-by-step explanation:

4)

the surface area is

top and bottom : 2× pentagon (5 sides)

sides : 5× rectangle 14×8 ft²

let's start with the easiest : the rectangles.

5 × 14×8 = 560 ft²

the area of a pentagon is similar to any regular polygon :

n × triangle of side×height (to middle of pentagon) / 2

n = number of sides (5 in our case).

the middle or center of the pentagon is the top vertex of each triangle.

so,

5 × 14×9.63 / 2 = 5 × 7 × 9.63 = 337.05 ft²

and we have 2 of them (top and bottom), so

2×337.05 = 674.1 ft³

in total the surface area is

560 + 674.1 = 1,234.1 ft²

5)

6 sides :

top and bottom : 7×14 rectangle

left and right : 7×8 rectangle

front and back : 8×14 rectangle

so, we have

2× 7×14 = 196 mm²

2× 7×8 = 112 mm²

2× 8×14 = 224 mm²

in total that is : 532 mm²

Confidence interval for the mean daily return if it is normally distributed:

⁻x [tex]-z_{\alpha }[/tex](σ/[tex]\sqrt{n}[/tex]) ≤ μ ≤ ⁻x + [tex]z_{\alpha }[/tex] ( σ/[tex]\sqrt{n}[/tex])

Based on the Central Limit Theorem's result that the sampling distribution of the sample means follows an essentially normal distribution, a confidence interval for a population mean is calculated when the population standard deviation is known.

Take into account the standardising equation for the sampling distribution introduced in the Central Limit Theorem discussion:

[tex]z_{1} =[/tex](⁻x - μ₋ₓ) /( σ ⁻x) = (⁻x - μ) /( σ/[tex]\sqrt{n}[/tex])

Notice that µ is substituted for µx− because we know that the expected value of µx− is µ from the Central Limit theorem and σx− is replaced with σn√/, also from the Central Limit Theorem.

In this formula we know X−, σx− and n, the sample size. (In actuality we do not know the population standard deviation, but we do have a point estimate for it, s, from the sample we took. More on this later.) What we do not know is μ or Z1. We can solve for either one of these in terms of the other. Solving for μ in terms of Z1 gives:

μ=X−±Z1 σ/[tex]\sqrt{n}[/tex]

Remembering that the Central Limit Theorem tells us that the distribution of the X¯¯¯'s, the sampling distribution for means, is normal, and that the normal distribution is symmetrical, we can rearrange terms thus:

⁻x [tex]-z_{\alpha }[/tex](σ/[tex]\sqrt{n}[/tex]) ≤ μ ≤ ⁻x + [tex]z_{\alpha }[/tex] ( σ/[tex]\sqrt{n}[/tex])

This is the formula for a confidence interval for the mean of a population.

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Answer:

12 ft²

D

Step-by-step explanation:

Area of parallelogram = Base × Height

Here, base = 3ft

height = 4ft

So, Area = 3×4 ft² = 12 ft²

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

[tex]\huge\text{Area of parallelogram is:}[/tex]

[tex]\rm{\bold{b}ase\times\bold{h}eight = \bold{a}rea}[/tex]

[tex]\huge\text{Your equation should look like: }[/tex]

[tex]\rm{3\times4 = \boxed{\bf area}}[/tex]

[tex]\huge\text{Simplify the equation above \& you will have}\\\\\huge\text{the answer to the area of the parallelogram.}[/tex]

[tex]\mathsf{3[base] \times 4[height] = ?[area]}[/tex]

[tex]\huge\text{Simplify it:}[/tex]

[tex]\rm{12\ ft^2}[/tex]

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

[tex]\huge\boxed{\frak{\frak{12\ ft^2}}}\huge\checkmark[/tex]

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

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

The intersection of the sets has the following properties: Commutative law – A ∩ B = B∩ A. Associative law – (A ∩ B)∩ C = A ∩ (B∩ C) φ ∩ A = φ

do mark brainliest

Based on the calculations, the dimensions of the rectangle are

The diagonal of a rectangle can be defined as a line segment that connects any two (2) of its non-adjacent vertices together while dividing the rectangle into two (2) equal parts.

Mathematically, the length of diagonals of a rectangle can be calculated by using this formula:

d = √(l² + w²)

Where:

Since the ratio of the length to the width is 12:5, we have:

Width, w = 5l/12

Substituting the given parameters into the formula, we have;

169 = √(l² + (5l/12)²)

169² = l² + (5l/12)²

169² = l² + (25l²/144)

Length, L = 156 meters.

For the width, we have:

Width, w = 5l/12

Width, w = 5(156)/12

Width, w = 65 meters.

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

let's solve ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{7}{2a} + \cfrac{9}{10} = \cfrac{5}{12a} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{7}{2a} - \cfrac{5}{12a} = - \cfrac{9}{10} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{7(6) - 5}{12a} = - \cfrac{9}{10} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{42 - 5}{12a} = - \cfrac{9}{10} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 37(10) = - 9(12a)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 370 = - 108a[/tex]

[tex]\qquad \sf  \dashrightarrow \: a = - \cfrac{370}{108} [/tex]

[tex]\qquad \sf  \dashrightarrow \: a = - \dfrac{185}{54} [/tex]

Answer:

D. 195

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

| 2^3 - 4*3^2 |  - 4 = | 8 - 36| - 4 =  28-4 = 24

Answer:

True

Step-by-step explanation:

All faces of a cube are the same.

The correct transformation of f(x) to get 4f(x+2) is by a vertical shift by 4 and 2 units in the x direction.

Given a function f(x) and other function 4f(x+2).

We are required to choose a transformation that will give 4f(x+2) from a function f(x).

Function is like a relationship between two or more variables that are expressed in equal to form. The values which we enter in a function is known as domain and the value that we get as a result are known as range.

So, we have to reach 4f(x+2) from f(x).

The value of function is usually expressed on y axis and variable x on x axis.

To increase the value of x by 2 we have to stretch it in x direction.To find the 4 times value of function we have to stretch the y axis to 4 units.

Hence the correct transformation of f(x) to get 4f(x+2) is by a vertical shift by 4 and 2 units in the x direction.

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There will be 60 residuals for simple bivariate regression's  60 observations.

According to the statement

We have given that the there is 60 observations and we have to find the number of simple bivariate regression for these observations.

So, For the solution of this problem,

We know that the

A simple linear regression (also known as a bivariate regression) is a linear equation describing the relationship between an explanatory variable and an outcome variable, specifically with the assumption that the explanatory variable influences the outcome variable, and not vice-versa.

And we know that the it is always same for the number as the number of given observations.

That's why there is 60 residuals.

So, There will be 60 residuals for simple bivariate regression's  60 observations.

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Answer:

Lose 12y yards.

Lose 5.2x yards.

What is the net yardage for these four plays?

is the que correct

Answer:

19.8x - 11.1y

Step-by-step explanation:

Given information:

"Gain" means to add the value.

"Lose" means to subtract the value.

Therefore, net yardage is:

⇒ 25x + 0.9y - 12y - 5.2x

Collect like terms:

⇒ 25x - 5.2x + 0.9y - 12y

Factor out the common variables x and y:

⇒ x(25 - 5.2) + y(0.9 - 12)

Carry out the operations in the parentheses:

⇒ x(19.8) + y(-11.1)

Therefore, the net yardage is  19.8x - 11.1y

Answer:

  x = 10.67

Step-by-step explanation:

The triangles shown are similar, so corresponding sides are proportional. This lets us write a relation that can be solved for x.

For the given figure, we can write the proportion ...

  AB/CA = DB/ED . . . . . . where DB = ED +BE

  (3x-4)/12 = (24 +3x)/24 . . . . . . substitute given values

Multiplying by 24 gives ...

  2(3x -4) = 3x +24

  6x -8 = 3x +24 . . . . . eliminate parentheses

  3x = 32 . . . . . . . . add 8-3x

  x = 32/3 = 10 2/3 ≈ 10.67 . . . . . divide by 3 and convert to decimal

The value of x to the nearest hundredth is 10.67.

Answer:

7.52 m^3

Step-by-step explanation:

This is like compound interest in a banking calculation

Future volume = 5 (1 + .06)^7 = 7.52 m^3

When both sides of the equal sign are equal, there are infinite solutions.

When you are able to isolate the variable, there is only one solution.

When the equation states an untrue expression, there is no solution.

1=3 is an untrue fact. Therefore, there would be no solutions to the system.

There is no solution

Step-by-step explanation:

Reduce 13/100 to lowest terms

13

100

is already in the simplest form. It can be written as 0.13 in decimal form (rounded to 6 decimal places).

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 13 and 100 is 1

Divide both the numerator and denominator by the GCD

13 ÷ 1

100 ÷ 1

Reduced fraction:

13

100

Therefore, 13/100 simplified to lowest terms is 13/100.

The mixed number [tex]7\dfrac{13}{100}[/tex] is [tex]\dfrac{713}{100}[/tex] on simplification.

A mixed number is a mathematical representation of a number that consists of a whole number and a fraction. It's called a "mixed number" because it combines both a whole number and a proper fraction. The whole number part represents a whole quantity, while the fractional proportion represents a proportion of a whole.

Mixed numbers are generally employed to represent measures that aren't whole numbers but are still greater than 1. They're particularly useful when dealing with magnitudes, such as lengths or quantities of things, that concern both whole units and fractional parts.

Given that

[tex]7\dfrac{13}{100}[/tex] [tex]= 7 + \dfrac{13}{100}[/tex]

       [tex]= \dfrac{700}{100}+ \dfrac{13}{100}\\= \dfrac{700+13}{100} \\= \dfrac{713}{100}[/tex]

Hence, The mixed number [tex]7\dfrac{13}{100}[/tex] can be simplified as [tex]\dfrac{713}{100}[/tex].

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Answer:

The club leader needs $73 for pizzas for 9 students.

Step-by-step explanation:

p(x) = 2x +1

r(x) = 4x − 3

r(p(x)) = 4(2x +1) − 3

r(p(x)) = 8x +4 − 3

r(p(x)) = 8x +1

r(p(9)) = 8(9) +4 − 3

r(p(9)) = 72 +1

r(p(9)) = $73

Answer:

The file contains the solution to the question