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Suppose that people’s heights (in centimeters) are normally distributed with a mean of 170 and a standard deviation of 5. We find the heights of 50 people.

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We have
mean=mu=170
standard deviation=sigma=5

can now calculate the Zmin and Zmax using Z=(X-mean)/standard deviation
Zmin=(165-170)/5=-1
Zmax=(175-170)/5=+1
From normal probability tables, 
P(z<Zmin)=P(z<-1)=0.15866
P(z<Zmax)=P(z<+1)=0.84134
P(165<x<175)=P(Zmin<z<Zmax)=0.84134-0.15866= 0.68269

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The table shows conversions of common units of length. Unit of Length Customary System Units Metric System Units 1 inch 2.54 centimeters 1 foot 0.3048 meters 1 mile 1.61 kilometers How many miles are equivalent to 800 meters? Round answer to the nearest hundredth. 0.50 miles 1.29 miles 2.62 miles 4.97 miles

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The table shows conversions of common units of length. Unit of Length Customary System Units Metric System Units 1 inch 2.54 centimeters 1 foot 0.3048 meters 1 mile 1.61 kilometers How many miles are equivalent to 800 meters? Round answer to the nearest hundredth. 0.50 miles 1.29 miles 2.62 miles 4.97 miles

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Find a model for simple harmonic motion if the position at t=0 is 0 the amplitude is 5 centimeters and the period is 4 seconds

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Answer:

y = 5sin(frac{x}{2})

Step-by-step explanation:

Since harmonic motion is represented by the sine wave equation.

y = a sin (bx)

where a = amplitude

period = frac{2pi}{b}

Amplitude of the harmonic motion is given as 5 and period is 4 seconds.

so a = 5

and 4 = frac{2pi}{b} ⇒ b = frac{2pi}{4}

b = frac{pi}{2}

Now we replace the values of a and b in the sine equation

y = 5sin(frac{x}{2})

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An accelerometer is a device that uses the extension of a spring to measure acceleration in terms of Earth's gravitational acceleration (g). What is the approximate acceleration if this accelerometer spring is extended just 0.43 centimeters?

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An accelerometer is a device that uses the extension of a spring to measure acceleration in terms of Earth’s gravitational acceleration (g). What is the approximate acceleration if this accelerometer spring is extended just 0.43 centimeters?

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Help asap To measure the thickness of a dime, you would use meters centimeters kilometers millimeters

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Help asap To measure the thickness of a dime, you would use meters centimeters kilometers millimeters

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How many years would it take the Atlantic Ocean to grow 500 centimeters

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How many years would it take the Atlantic Ocean to grow 500 centimeters

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If the side of a cube is 5xy centimeters in length, what is the volume of the cube?

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If the side of a cube is 5xy centimeters in length, what is the volume of the cube?

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If the side of a cube is 5xy centimeters in length, what is the volume of the cube?

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If the side of a cube is 5xy centimeters in length, what is the volume of the cube?

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In a right triangle, angle a measures 20°. the side opposite angle a is 10 centimeters long. approximately how long is the hypotenuse of the triangle? 3.4 centimeters 10.6 centimeters 27.5 centimeters 29.2 centimeters

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In a right triangle, angle a measures 20°. the side opposite angle a is 10 centimeters long. approximately how long is the hypotenuse of the triangle? 3.4 centimeters 10.6 centimeters 27.5 centimeters 29.2 centimeters

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The area of a circle is 78.5 square centimeters, and a subtending arc on the circle has an arc length of 6. The estimated value of is 3.14. The measure of the angle subtended by the arc is __ degrees

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Answer:  The correct option is (C). 10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared

Step-by-step explanation:  Given that the segment AB has point A located at (8, 9). The distance from A to B is 10 units.

We are to select the correct option that could be used to calculate the coordinates for point B.

Let, (x, y) be the co-ordinates of point B.

According to distance formula, the distance between two points (a, b) and (c, d) is given by

d=sqrt{(c-a)^2+(d-b)^2}.

Therefore, the distance between the points A(8, 9) and B(x, y) is given by

d=sqrt{(x-8)^2+(y-9)^2}.

Since, distance between A and B is 10 units, so

d = 10.

Therefore,

10=sqrt{(x-8)^2+(y-9)^2}.

Thus, the correct statement is

10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared.

Option (C) is correct.

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A funnel is made up of a partial cone and a cylinder as shown in the figure. The maximum amount of liquid that can be in the funnel at any given time is 16.59375π cubic centimeters. Given this information, what is the volume of the partial cone that makes up the top part of the funnel?

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A funnel is made up of a partial cone and a cylinder as shown in the figure. The maximum amount of liquid that can be in the funnel at any given time is 16.59375π cubic centimeters. Given this information, what is the volume of the partial cone that makes up the top part of the funnel?

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A woman rides a bicycle for 3 hours and travels 51 kilometers. Find the angular velocity of the wheel if the radius is 30 centimeters

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A woman rides a bicycle for 3 hours and travels 51 kilometers. Find the angular velocity of the wheel if the radius is 30 centimeters

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The area of a triangle is found by multiplying half of the measure of its base by its height. The area of the following right triangle is 18 square centimeters. A. Write and solve an equation to find the value of h. Include all of your work in your answer. B. In two or more complete sentences, verify your answer using mental math.

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Answer:

3 hours.          

Step-by-step explanation:

Let x be the time taken by shoe repairman to repair one pair.

We have been given that his assistant, who takes twice as long to repair a pair of shoes. So time taken by his assistant to repair one pair of shoes would be 2x.

The number of pair of shoes repaired by repairman in one hour would be frac{1}{x}.

The number of pair of shoes repaired by assistant in one hour would be frac{1}{2x}.

We have been given that together they can fix 16 pairs of shoes in an eight-hour day. We can represent this information in an equation as:

frac{1}{x}+frac{1}{2x}=frac{8}{16}

frac{1}{x}+frac{1}{2x}=frac{1}{2}

Let us have a common denominator.

frac{2*1}{2*x}+frac{1}{2x}=frac{1}{2}

frac{2}{2x}+frac{1}{2x}=frac{1}{2}

frac{2+1}{2x}=frac{1}{2}

frac{3}{2x}=frac{1}{2}  

Upon cross multiplying our equation we will get,

2x*1=3*2

2x=3*2

frac{2x}{2}=frac{3*2}{2}

x=3

Therefore, it take 3 hours for the repairman to fix one pair of shoes by himself.

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Determine the linear velocity of an object with an angular velocity of 5.9 radians per second at a distance of 12 centimeters from the center. use . round the answer to the nearest tenth.

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Answer:

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²    

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

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The altitude to the hypotenuse of a right triangle divides the hypotenuse into two segments measuring 11 centimeters and 5 centimeters. to the nearest tenth, what is the length of the shorter leg of the triangle?

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The altitude to the hypotenuse of a right triangle divides the hypotenuse into two segments measuring 11 centimeters and 5 centimeters. to the nearest tenth, what is the length of the shorter leg of the triangle?

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You’re given two side lengths of 10 centimeters and 8 centimeters. The angle between the sides measures 40°. How many triangles can you construct using these measurements? Answers= 0, 1, 2, infinitely many

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127=7 (mod n) means when 127 is divided by n, the division leaves a remainder of 7.

The statement is equivalent to
120=0 (mod n), meaning that n divides 120.

All divisors of 120 will satisfy the statement because 120 divided by a divisor (factor) will leave a remainder of 0.

Factors of 120 are:
n={1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120}, |n|=16.
You can count how many such values of n there are, and try to check that each one satisfies 127=7 mod n.

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A substance with a density of 1.0 gram per cubic centimeter has a mass of 1.0 kilogram if its volume is 100 cubic centimeters. True or false ? Please answer with explanation

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Answer:  The correct option is (C). 10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared

Step-by-step explanation:  Given that the segment AB has point A located at (8, 9). The distance from A to B is 10 units.

We are to select the correct option that could be used to calculate the coordinates for point B.

Let, (x, y) be the co-ordinates of point B.

According to distance formula, the distance between two points (a, b) and (c, d) is given by

d=sqrt{(c-a)^2+(d-b)^2}.

Therefore, the distance between the points A(8, 9) and B(x, y) is given by

d=sqrt{(x-8)^2+(y-9)^2}.

Since, distance between A and B is 10 units, so

d = 10.

Therefore,

10=sqrt{(x-8)^2+(y-9)^2}.

Thus, the correct statement is

10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared.

Option (C) is correct.

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A large diamond with a mass of 2138.7 grams was recently discovered in a mine. If the density of the diamond is 3.51 grams over centimeters cubed, what is the volume? Round your answer to the nearest hundredth. 141.84 cm3 609.3 cm3 717.06 cm3 8169.8 cm3

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The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is – 1.

So, from that basic knowledge you can analyze each option:

a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.

So, the right choices are a, c and g.

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In a triangle whose perimeter is 44 centimeters, the length of the longest side is 4 cm less than the sum of the lengths of the other sides. Twice the length of the shortest side is 9 cm more than the difference between the lengths of the other sides. How long is each side of the triangle?

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Answer:

The length of the rectangle is 64 cm.

The area of the square is 100 cm. sq.          

Step-by-step explanation:

Given : The length of a rectangle is 4 times than its width. The area of the rectangle is 1024 cm sq.

The perimeter of the rectangle 4 square has the same perimeter as that its rectangle.

To find : The length of the rectangle  and Find the area of the square?

Solution :

Let l be the length of the rectangle.

Let w be the width of the rectangle.

The length of a rectangle is 4 times than its width i.e l=4w

The area of the rectangle is

A=ltimes w

1024=4wtimes w

256=w^2

w=pm 16

Reject negative value.

The width of the rectangle is w=16 cm.

The length of the rectangle is

l=4w\l=4times 16\l=64cm

Therefore, The length of the rectangle is 64 cm.

Now, The perimeter of the rectangle 4 square has the same perimeter as that its rectangle.

Perimeter of the rectangle is P=2(l+b)

P=2(64+16)

P=2(80)

P=160  

Perimeter of rectangle divides into 4 squares.

i.e. Perimeter of one square is P=frac{160}{4}=40

Now, The side of the square is

P=4s

40=4s

s=10

The area of the square is A=stimes s

A=10times 10

A=100cm^2

Therefore, The area of the square is 100 cm. sq.

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48 centimeters equals how many deckmeters

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48 centimeters equals how many deckmeters
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A rectangle has a width that is 7 centimeters less than its length, and it's area is 330 square centimeters. what are the dimensions?length = _____ centimeterswidth = _____ centimeters

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A rectangle has a width that is 7 centimeters less than its length, and it’s area is 330 square centimeters. what are the dimensions?length = _____ centimeterswidth = _____ centimeters
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Given 1 inch = 2.54 centimeters, enter the value that will complete this expression for converting 2.5 feet to centimeters. ~ Someone please answer ASAP Last question

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Answer:

The yearly payment is $ 10047.60 ( approx )

Step-by-step explanation:

Since, the yearly payment of a loan is,

P=frac{R(P.V.)}{1-(1+R)^{-n}}

Where, R is the annual rate of interest ( in decimals ),

P is the present value of the loan,

n is the time ( in years ),

Given,

A home is bought for $140,000 at 20 % down payment,

Thus, the present value of the loan, P.V. = 140000(100-20)%

= 140000 × 80 %

= 140000 × 0.8

= $ 112,000

Annual rate of interest, R = 7.5 % = 0.075,

n = 25 years,

Hence, the annual payment is,

P=frac{112000(0.075)}{1-(1+0.075)^{-25}}

=$ 10047.5952247approx $ 10047.60

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The perimeter of a square is 1/5 meters. (A) Find the length of each side in meters. Draw a picture to support your response. (B) Another question how long is each side in centimeters. (C) A few more questions a pallet holding 5 identical crates weigh 1/4 ton. How many tons does each crate weigh? Draw a picture to support your response. (D) How many pounds do each crate weigh?

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The perimeter of a square is 1/5 meters. (A) Find the length of each side in meters. Draw a picture to support your response. (B) Another question how long is each side in centimeters. (C) A few more questions a pallet holding 5 identical crates weigh 1/4 ton. How many tons does each crate weigh? Draw a picture to support your response. (D) How many pounds do each crate weigh?

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