5 points


You need to change a blown outdoor lightbulb on your house. The bulb is 5m up, but you have a 1m reach when you are on the top rung of the ladder. If you need 3m of


space off the house for the ladder's base for stability, what is the minimum height of the ladder in meters?

The positive value of z indicates option e) the value z is to the right of the mean.

A standard normal random variable has a mean of 0 and a standard deviation of 1. Positive values of z represent values above the mean, while negative values of z represent values below the mean.

The probability associated with a value of z is always positive since it represents the likelihood of observing a certain value. The area between zero and z is also always positive since it represents the probability of observing a value between 0 and z.

Therefore, option e) is the correct answer as it reflects the relationship between positive values of z and their location relative to the mean.

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Answer:

( 5 , 5½ )

Step-by-step explanation:

It's simple actually, use the midpoint formula,

[tex] \frac{x1 + x2}{2} ... \frac{y1 + y2}{2} = ( \frac{8 + 2}{2} ... \frac{4 + 7}{2} ) = (5..5 \frac{1}{2} )[/tex]

Take the ... as a comma.

So the final answer is ( 5 , 5.5 )

Answer:

Step-by-step explanation:

If I'm wrong, write and I'll correct it. Because I don't know how to proceed

Answer :

Step-by-step explanation:

60 minutes = 1 hour

1 minute = 1/60

1 minute = 0.016666666666667 hours

1.47 minutes = 0.016666666666667 × 1.47

1.47 minute = 0.0245 hours

Therefore, 1.47 Minutes is equal to 0.0245 Hours.

Answer:

2x + 3x = 475

= 5x = 475

= x = 475/5

= x = 95

Answer:

285 boys

Step-by-step explanation:

2 + 3 = 5

475/5=95

Girls: 2 x 95= 190

Boys: 3 x 95 = 285

Check

285 + 190= 475

a) We can use the formula for the volume of a cylinder to relate the given liquid volume to the dimensions of the can: πr^2h = 2500, Solving for h, we get: h = 2500/(πr^2)

b) The surface area of the can consists of the area of the circular top and bottom, as well as the area of the cylindrical side. The area of the top and bottom is 2πr^2 each, and the area of the side is 2πrh. Therefore, the total surface area is: Surface area = 2πr^2 + 2πrh

Substituting the expression for h in terms of r that we found in part (a), we get:

Surface area = 2πr^2 + 2πr(2500/(πr^2))

Simplifying, we get:

Surface area = 2πr^2 + 5000/r

c) To minimize the surface area, we need to find the value of r that makes the derivative of the surface area with respect to r equal to zero. So we differentiate the expression we found in part (b) with respect to r: d(Surface area)/dr = 4πr - 5000/r^2

Setting this equal to zero and solving for r, we get:

4πr = 5000/r^2

r^3 = 1250/π

r ≈ 6.17 (rounded to two decimal places)

Substituting this value of r into the expression we found for h in part (a), we get: h ≈ 10.55 (rounded to two decimal places)
Therefore, the aluminum can should have a radius of approximately 6.17 cm and a height of approximately 10.55 cm in order to minimize the surface area and conserve material.

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Let's use the method of setting up a system of equations to solve this problem.

Let x be the number of pints of the first type of fruit drink (30% pure), and y be the number of pints of the second type of fruit drink (55% pure). We want to find the values of x and y that will produce 60 pints of a mixture that is 40% pure.

We can start by setting up two equations based on the information given:

Equation 1: x + y = 60 (since we want to produce 60 pints of the mixture)

Equation 2: 0.3x + 0.55y = 0.4(60) (since we want the mixture to be 40% pure)

Simplifying Equation 2, we get:

0.3x + 0.55y = 24

Now we have a system of two equations with two unknowns:

x + y = 60

0.3x + 0.55y = 24

We can solve this system using substitution or elimination. Here, we'll use substitution:

Solving Equation 1 for x, we get x = 60 - y. Substituting this expression for x in Equation 2, we get:

0.3(60 - y) + 0.55y = 24

Expanding and simplifying, we get:

18 - 0.3y + 0.55y = 24

Combining like terms, we get:

0.25y = 6

Dividing by 0.25, we get:

y = 24

Substituting this value of y back into x + y = 60, we get:

x + 24 = 60

Solving for x, we get:

x = 36

Therefore, we need 36 pints of the 30% pure fruit drink and 24 pints of the 55% pure fruit drink to make 60 pints of a mixture that is 40% pure.

To find dy/dx implicitly, we need to differentiate both sides of the equation with respect to x, treating y as a function of x and using the chain rule.

In this problem, we are given the equation X^2e^{-x} + 3y^2 - xy = 0, and we need to find dy/dx. To do this, we first differentiate each term with respect to x, using the product rule for the xy term and the chain rule for the y^2 term. Then we can solve for dy/dx by isolating the derivative term on one side of the equation. Implicit differentiation is a powerful technique used in calculus to find derivatives of functions that are not easily expressed in terms of a single variable. This technique is used extensively in many areas of mathematics, science, and engineering, including optimization, physics, and economics.

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Each rectangle is 1/3 of the area of the complete design.

A fraction represents the parts of a whole or collection of objects e.g. 3/4 shows that out of 4 equal parts, we are referring to 3 parts.

Looking at the design, you will be notice that the main (bigger) rectangle is divided to three smaller rectangles. Thus, each rectangle is one out of three  rectangles i.e. 1/3.

Therefore, each rectangle is 1/3 of the area of the complete design.

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Complete Question

Check attached image

The final answer to this limit question is 1/4.

a function from a set X to a set Y assigns to each element of X exactly one element of Y.[1] The set X is called the domain of the function[2] and the set Y is called the codomain of the function.

Given that lim f(x) = 3 and lim g(x) = 12, we want to find the limit:
lim (f(x) / g(x)) as x approaches -5.
Using the limit rules, specifically the quotient rule, we have:
lim (f(x) / g(x)) = lim f(x) / lim g(x)

Now, substituting the given limits:
lim (f(x) / g(x)) = 3 / 12

Simplifying the fraction:

lim (f(x) / g(x)) = 1/4

So, the answer is 1/4.

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The direction of the vector is (-5, -8).

To find the direction in which the function is increasing most rapidly at point P(2, -1),

we need to find the gradient vector of the function at that point.

The gradient vector of the function f(x, y) = xy^2 - yx^2 is given by:

∇f(x, y) = ( ∂f/∂x , ∂f/∂y ) = ( y^2 - 2xy , 2xy - x^2 )

So, at point P(2, -1), we have:

∇f(2, -1) = ( (-1)^2 - 2(2)(-1) , 2(2)(-1) - 2^2 ) = (-5, -8)

The direction of greatest increase is in the direction of the gradient vector.

So, the direction in which the function is increasing most rapidly at point P(2, -1) is in the direction of the vector (-5, -8).

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The combined time if Mike and Nancy worked together is approximately 1.71 hours.

To answer your question, we can use the concept of work rates. Mike can mop McDonald's in 3 hours and Nancy can do it in 4 hours. To find the combined work rate, we can use the formula:

1/Mike's rate + 1/Nancy's rate = 1/combined rate

1/3 + 1/4 = 1/combined rate

To solve for the combined rate, we can find a common denominator for the fractions:

(4 + 3) / (3 × 4) = 1/combined rate

7/12 = 1/combined rate

Now we can find the combined time by inverting the combined rate:

Combined time = 12/7

So, if Mike and Nancy worked together, they would mop McDonald's in 12/7 hours, which is approximately 1.71 hours.

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Main answer:

Working together, Mike and Nancy can mop the McDonald's in 12/7 hours or approximately 1.71 hours (rounded to two decimal places).

Explanation:

To solve the problem, we can use the following formula:

time = work / rate

where time is the time it takes to complete the job, work is the amount of work to be done (which in this case is mopping the McDonald's), and rate is the rate of work, or the amount of work done per unit of time.

Let's let x be the time it takes for Mike and Nancy to mop the McDonald's together. Then, we can set up two equations based on the given information:

x = work / (Mike's rate of work)

x = work / (Nancy's rate of work)

To solve for x, we can use the fact that the amount of work to be done is the same in both equations. So we can set the two equations equal to each other:

work / (Mike's rate of work) = work / (Nancy's rate of work)

Simplifying this equation by multiplying both sides by (Mike's rate of work)*(Nancy's rate of work), we get:

work * (Nancy's rate of work) = work * (Mike's rate of work)

We can cancel out the work on both sides, and then solve for x:

x = 1 / [(1/Mike's rate of work) + (1/Nancy's rate of work)]

Substituting in the given rates of work, we get:

x = 1 / [(1/3) + (1/4)] = 12/7

Therefore, it takes Mike and Nancy 12/7 hours, or approximately 1.71 hours (rounded to two decimal places), to mop the McDonald's together.

To find the arc length between each car on the Ferris Wheel, we need to first find the measure of the central angle formed by each car.

The Ferris Wheel has a diameter of 150 ft, which means its radius is half that of 75 ft. We can use the formula s = rθ, where s is the arc length, r is the radius, and θ is the central angle in radians.

Since we have 25 cars on the Ferris Wheel, we can divide the circle into 25 equal parts, each representing the central angle formed by each car.

The total central angle of the circle is 2π radians (or 360 degrees), so each central angle formed by each car is:

(2π radians) / 25 = 0.2513 radians (rounded to four decimal places)

Now we can use this central angle and the radius of the Ferris Wheel to find the arc length between each car:

s = rθ
s = 75 ft * 0.2513
s = 18.8475 ft (rounded to four decimal places)

Therefore, the approximate arc length between each car on the Ferris Wheel is approximately 18.85 ft.

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To find the approximate area of the shaded region in this figure, we need to subtract the area of the smaller circle from the area of the larger circle. The radius of the larger circle is 6 feet and the radius of the smaller circle is 3 feet.

The formula for the area of a circle is A = πr^2, where π is approximately 3.14 and r is the radius.

So, the area of the larger circle is A = 3.14 x 6^2 = 113.04 square feet.
The area of the smaller circle is A = 3.14 x 3^2 = 28.26 square feet.

To find the area of the shaded region, we subtract the area of the smaller circle from the area of the larger circle:

Area of shaded region = 113.04 - 28.26 = 84.78 square feet (rounded to two decimal places).

Therefore, the approximate area of the shaded region in this figure is 84.78 square feet.

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The Uncle Richard's phone number contains 8 different digits which are given by 67935421.

The term "numerical digit" refers to a single sign that is used to represent numbers in a positional numeral system, either by itself (as in "2") or in conjunction with other symbols (as in "25"). The term "digit" refers to the ten digits (Latin digiti meaning fingers) of the hands, which are the decimal (old Latin adjective decem meaning ten) digits. These digits correspond to the ten symbols of the conventional base 10 numeral system.

Let the number with eight different digits be a, b, c, d, e, f, g, h

So sum of the numbers formed by the first 5 digits and the number formed by the last 3 digits is 68427

     a b c d e                                                d e f g h

+           f g h                                           +         a b c

    6 8 4 2 7                                                3 6 0 9 0

So, a = 6 and d = 3

Hence by calculating in such way we get,

b = 7, c = 9  , e = 6 , f = 4  , g = 9 , h = 1    

Therefore, number with eight different digits be a, b, c, d, e, f, g, h

67935421  

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For the given function y = 126 \sqrt(x), dy is 3.57 if x = 9 and Δx = dx = 0.17.

To find the change in y (or dy), we need to use the formula:

dy = f'(x) * dx

where f'(x) is the derivative of y with respect to x.

The given function is y = 126 \sqrt(x).

To find the derivative, we can use the power rule and chain rule of differentiation.

y = 126x^{1/2}

Taking the derivative of y with respect to x:

dy/dx = 1/2 * 126x^(-1/2)

Simplifying, we get:

dy/dx = 63/(\sqrt(x))

Now, we can substitute x = 9 into this expression to get the value of the derivative at that point:

dy/dx = 63/(\sqrt(9)) = 63/3 = 21

Next, we can use the given value of dx, which is 0.17, to find the change in y or dy.

dy = f'(x) * dx ≈ 21 * 0.17 ≈ 3.57

Therefore, the change in y or dy is approximately 3.57.

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The width of the toy train track is 4 cm.

To find the width of the toy train track, we need to consider the inner radius, the arc length of the inner sector, and the arc length of the outer sector.

Given:
Inner radius (r1) = 6 cm
Inner arc length (s1) = 33 cm
Outer arc length (s2) = 55 cm

Step 1: Find the central angle (θ) using the inner arc length and inner radius.
θ = s1/r1 = 33 cm / 6 cm = 5.5 radians

Step 2: Find the outer radius (r2) using the central angle and the outer arc length.
s2 = r2 × θ
55 cm = r2 × 5.5 radians
r2 = 55 cm / 5.5 radians = 10 cm

Step 3: Calculate the width of the track.
Width = Outer radius - Inner radius
Width = r2 - r1 = 10 cm - 6 cm = 4 cm

The width of the toy train track is 4 cm.

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Answer:

Step-by-step explanation:

false i think

Answer:

True

Step-by-step explanation:

The article red was titled "sense of emotion of dog and cat to humans"

To visualize the differences in feeling between Dogs and cats towards people, I would think of a dog swaying its tail and hopping up with fervor upon seeing its owner, whereas a cat may approach its owner more calmly and gradually with a loose tail.

I might picture the puppy gasping and looking for physical fondness, whereas the cat may lean toward to be petted or rubbed under the chin.

Dogs show enthusiasm and affection towards owners, while cats exhibit different behaviors. Dogs show excitement through body language like wagging tails, jumping, seeking affection, and vocalizing.

Pets express joy and eagerness to be around humans, with cats being more reserved towards humans. Although affectionate, cats express emotions subtly such as calm body posture and soft chirping.

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Answer:

[tex]h = \sqrt{ {21}^{2} - {19}^{2} } = \sqrt{441 - 361} = \sqrt{80} = 4 \sqrt{5} [/tex]

h = 4√5 feet = 8.9 feet

He will have $566 in this account if he keeps it for 5 years.

To determine how much money he will have in this account if he keeps it for 5 years, we can use the compound interest formula:

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

Where:

A = the final amount

P = the principal, $500

r = the interest rate, 2.5% = 0.025

n = the number of times the interest is compounded per year, in this case quarterly (n = 4)

t = the time period in years, 5

Substituting the values :

A = 500(1 + 0.025/4)^(4 * 5)

A = 500(1 + 0.00625)²⁰

A = 500(1 .00625)²⁰

A = $566

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This is just a rough estimate, and the actual number of pumpkins that weigh less than 15.5 pounds could be slightly higher or lower.

What is the median?

The median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude.

Assuming that the quartiles divide the pumpkins' weights into four equal parts, we can use the value of the second quartile (Q2) to estimate the median weight of the pumpkins. Since there are 80 pumpkins, Q2 would be the average of the 40th and 41st heaviest pumpkins.

We don't know the exact values of the quartiles, but we can make some reasonable assumptions. For example, if we assume that the first quartile (Q1) is around 12 pounds and the third quartile (Q3) is around 20 pounds, then we can estimate the median weight as follows:

Median = (Q2) = (Q1 + Q3)/2 = (12 + 20)/2 = 16 pounds

Based on this estimate, we can expect that roughly half of the 80 pumpkins (i.e., 40 pumpkins) weigh less than 16 pounds. Therefore, we might expect that slightly fewer than 40 pumpkins would weigh less than 15.5 pounds.

However, this is just a rough estimate, and the actual number of pumpkins that weigh less than 15.5 pounds could be slightly higher or lower depending on the distribution of the pumpkin weights.

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Answer:

y = -6/7x - 3/7 or 7y = -6x - 3

Step-by-step explanation:

I'm guessing you mean line c: y = -6/7x - 1

Parallel lines have same slope => line d will have slope = -6/7

y = mx + b

-9 = -6/7(10) + b

-9 = -60/7 + b

b = 60/7 - 9 = 60/7 - 63/7 = -3/7

y = -6/7x - 3/7

or 7y = -6x - 3

The measure of in quadrilateral GERA ∠GAR = 102° , ∠TAR = 23°, ∠GAN = 55° , m AG = 110° , m RE = 110° , m GE = 94°

∠REG = 78° , m AR = 46

The sum of the opposite angle of the quadrilateral is equal to 180°

∠REG + ∠GAR = 180°

∠GAR = 180 - ∠REG

∠GAR = 180 - 78

∠GAR = 102°

The tangent chord angle is half the intercept arc

∠TAR = 1/2 m AR

∠TAR = 1/2 ×46

∠TAR = 23°

The sum of straight angles is 180

m ∠GAN = 180 - (m ∠TAR + m ∠GAR )

m ∠GAN =  180 - (23 + 120)

m ∠GAN = 55°

The tangent chord angle is half the intercept arc

m AG = 2 m ∠GAN

m AG = 2(55)

m AG = 110°

as EG = GA

m RE = m GA

m RE = 110°

Complete angle sum = 360°

m GE = 360 - (m AG + m AR + m RE)

m GE = 360 - (110 + 46 + 110 )

m GE = 94°

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The 95% confidence interval is (0.56, 0.62). This means that we can be 95% confident that the true proportion of city dwellers who would like to live at the beach lies between 56% and 62%.

In this case, the Chamber of Commerce conducted a survey asking city dwellers if they would like to live at the beach. The 95% confidence interval for the population proportion of city dwellers who would like to live at the beach is (0.56, 0.62).

To break this down:
1. Random sample: The Chamber of Commerce surveyed a group of city dwellers chosen randomly, which helps ensure that the results are representative of the entire population of city dwellers.
2. Population proportion: This refers to the percentage of all city dwellers who would like to live at the beach.
3. 95% confidence interval: This means that if the survey were repeated many times with different random samples, 95% of the intervals calculated would contain the true population proportion.

In this case, the 95% confidence interval is (0.56, 0.62). This means that we can be 95% confident that the true proportion of city dwellers who would like to live at the beach lies between 56% and 62%.

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If a couple of two-way radios were purchased from different stores. The  number of square miles does two-way radio A cover. 154 square miles.

Part A:

Radius of two-way radio A = 7 miles

Area of circle = πr^2 = 3.14 x 7^2 = 153.86 square miles

Rounding to the nearest whole number, two-way radio A covers 154 square miles.

Part B:

Radius of two-way radio B = 9.66 kilometers

Area of circle = πr^2 = 3.14 x 9.66^2 = 293.15 square kilometers

Rounding to the nearest whole number, two-way radio B covers 293 square kilometers.

Part C:

1 mile = 1.61 kilometers

Area covered by two-way radio A = π(7)^2 = 153.86 square miles

Converting square miles to square kilometers:

153.86 x 1.61^2 = 393.73 square kilometers

Area covered by two-way radio B = π(9.66)^2 = 293.15 square kilometers

Comparing the areas, we can see that two-way radio A covers the larger area.

Part D:

The scale factor relationship between the radio coverages can be determined by comparing their radii.

Radius of two-way radio A = 7 miles

Radius of two-way radio B = 9.66 kilometers = 6 miles (rounded to two decimal places)

Therefore, the scale factor relationship between the radio coverages is 7:6 or 1.17:1 (rounded to two decimal places).

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In the given ratio problem, Eli gets 21 sweets.

Let's assume that Dylan gets 7x sweets, Eli gets 3x sweets, and Fabian gets 5y sweets.

From the given information, we know that:

[tex]5y = 7x + 21[/tex] (since Fabian gets 21 more sweets than Dylan)

We can simplify this expression by dividing both sides by 5:

[tex]y = (7/5)x + 21/5[/tex]

We can also express the ratio of the amount of sweets that Dylan gets to the amount that Fabian gets as [tex]4:5[/tex], which means that:

[tex]4x = (5/1)y[/tex]

Substituting y from the first equation, we get:

[tex]4x = (5/1)*[(7/5)x + 21/5][/tex]

Simplifying this equation, we get:

[tex]4x = 7x + 21[/tex]

[tex]3x = 21[/tex]

[tex]x = 7[/tex]

Therefore, Dylan gets [tex]7x = 49[/tex] sweets, Eli gets [tex]3x = 21[/tex] sweets, and Fabian gets [tex]5y = 70[/tex] sweets.

Hence, Eli gets [tex]21[/tex] sweets.

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R1 and R2 are relations on a set A, which means they define a set of ordered pairs of elements in A. The matrices that represent R1 and R2 can be thought of as a way to visualize these ordered pairs.

Each row and column of the matrix corresponds to an element in A. If there is a 1 in the ith row and jth column of the matrix for R1, then (i,j) is an ordered pair in R1. Similarly, if there is a 1 in the ith row and jth column of the matrix for R2, then (i,j) is an ordered pair in R2.

If there is a 0 in a particular position in the matrix, then the corresponding pair is not in the relation.

Let R1 and R2 be relations on a set A. These relations can be represented by matrices M1 and M2, respectively, with dimensions |A|x|A|, where |A| is the cardinality of set A. The elements of the matrices M1 and M2 are binary, indicating whether there is a relation between the corresponding elements of set A in R1 and R2, respectively. If there is a relation, the matrix element will be 1, and if there is no relation, the matrix element will be 0.

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The volume of the fish tank is approximately 3,693,142,608 cubic inches

To find the volume of the rectangular prism-shaped fish tank, we need to multiply its width, length, and height.

Given the dimensions are 2014 inches wide, 1012 inches long, and 1812 inches tall, the calculation is as follows:

Volume = Width × Length × Height

Volume = 2014 in × 1012 in × 1812 in

Upon calculating the product, we get:

Volume ≈ 3,693,142,608 cubic inches

The volume of the fish tank is approximately 3,693,142,608 cubic inches

N.B: None of the answer choices has the correct answer.

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