ladders can be extremely dangerous if not used correctly. a 20 ft. extension ladder is played on a wall making and angle 85° with the ground. if a person at top of the ladder leaned back, rotating the ladder away from the wall, how far to the nearest foot would the person fall before he hit the ground?

Answer:

The angle is 84 degrees

Step-by-step explanation:

Let's call the angle by 'x'.

the supplement of x is equal to 180-x, and the complement of x is equal to 90-x.

If the supplement is sixteen times the complement, we can write the following equation:

(180 - x) = 16 * (90 - x)

180 - x = 1440 - 16x

16x - x = 1440 - 180

15x = 1260

x = 84

The angle is 84 degrees.

Answer:

84⁰

Step-by-step explanation:

Complement = 90 - x

Supplement = 180 - x

Given:

180 - x = 16(90 - x)

180 - x = 1440 - 16x

15x = 1260

x = 84

Answer:

b

Step-by-step explanation:

The square root of b times the square root of b is simply b.

b^(1/2)*b^(1/2) = b^1 = b

Answer: The volume is 40 cubic inches

Step-by-step explanation: Each toy block is 1 cubic inch, which means each toy block is a cube with all sides (Length, width and height) measuring 1 inch. That makes the volume of each cube or block to be derived as;

Volume = L x W x H

Volume = 1 x 1 x 1

Volume = 1 cubic inch

The first 3 floors are made up of six rows of four blocks. This means, the first 3 floors has six by four blocks, that is, six times four blocks and that gives us 24 blocks.

The fourth to eighth floors are made up of four rows of four blocks. This also means four by four blocks, that is, four times four blocks and that gives us 16 blocks.

Having determined the amount of blocks used in the total model building as

1st - 3rd = 24 blocks

4th - 8th = 16 blocks

The total number of blocks used is 24 plus 16 which equals 40. Having been told that each block has a volume of 1 cubic inch, the volume of the model building equals 40 cubic inches.

Answer:

Shelly paid $215 for the desk

Step-by-step explanation:

In this question, we are asked to calculate the price a particular desk was bought given the price at which it was sold and the percentage of profit associated with the sales of the desk. In other words, we are calculating the cost price

Mathematically,

% profit = (selling price - cost price)/cost price * 100%

Our percentage profit here is 35% and our selling price is $290.25, we are left with calculating the selling price. let’s input these values into the equation;

Before that, let’s say the cost price is $x

35 = (290.25-x)/x * 100

100(290.25-x) = 35x

29025 -100x = 35x

135x = 29025

x = 29025/135

x = $215

Answer:

0.65 kilograms

Step-by-step explanation:

Answer:

0.65 kg

Step-by-step explanation:

[tex] \because \: 1 \: gram = \frac{1}{1000} kg \\ \\ \therefore \: 650 \: grams = \frac{650}{1000} \\ \\ \red{ \boxed{\bold {\therefore \: 650 \: grams =0.65 \: kg} }}[/tex]

Using normal distribution concepts, we can conclude that the correct statement is:

B. Use t when the population is normal and the population standard deviation is not known

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Answer: 408/x

Step-by-step explanation:

Total number of people = 816

after 1 song = 816/2 people remained

after 2 songs = 816/4 people remained

after 3 songs = 816/8 people remained

after x songs = 816/x*2 people remained

People that remained = 816/2x

where x is the number of songs

Simplified = 408/x

Final answer:

The probability of selecting a red marble followed by a yellow marble from a bag, without replacement, is 1/5. Option B)  1/5 is correct.

Explanation:

The probability of selecting a red marble and then a yellow marble without replacement from a bag is determined by multiplying the probability of the first event by the probability of the second event, given the first has occurred.

First, calculate the probability of drawing a red marble (P(red)). With 3 red marbles out of 6 total marbles, that probability is 3/6 or 1/2.

Next, calculate the probability of drawing a yellow marble after a red one has been drawn (P(yellow | red)). Now there are only 5 marbles left in the bag, 2 of which are yellow, so that probability is 2/5.

Finally, multiply these two probabilities to find the probability of both events occurring in sequence: P(red then yellow) = P(red) × P(yellow | red) = (1/2) × (2/5) = 2/10 or 1/5.

The probability of selecting a red and then a yellow marble from a bag containing 3 red, 1 blue, and 2 yellow marbles, without replacement, is 1/5.

Therefore, the probability of selecting a red marble and then a yellow marble without replacement is 1/5, which corresponds to option b).

Answer:

1. 2a

2. Vertex

3. Center

4. (c-a)

Step-by-step explanation:

The missing black in the paragraph will be 2a, vertex, center, and (c – a).

The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.

In the derivation, the difference between the distances from any point P on a branch of the hyperbola to foci of the hyperbola is set equal to the constant value of 2a.

2a is used in the equation because the Vertex is a point on the hyperbola, and it is the difference in the distances from this point to the foci.

This can be shown algebraically if we let a be the distance from the Center to the vertex. Then, the difference of the distances is (c + a) – (c – a).

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Answer:

C. 100 cm

Step-by-step explanation:

2x-15=185

+15      +15

2x=200

/2    /2

x=100

Answer:

0.2x

Step-by-step explanation:

Answer:

0.2x---------------------------------------------------------------------------------------

Answer:

Voluntary response sample

Step-by-step explanation:

They constitute voluntary response sample. Voluntary response sample is a sample that is made up of volunteers.

Apart from voluntary response sample, it can also be called or known as self-selected sample.

A good example of this sample is the typical phone in polls u can witness on radio or tv stations where people call to air their views or make their stands known.

The voluntary response sample is most times chosen or selected by the people that will respond rather than the administrator of the survey.

One of the standout advantages or benefit of the voluntary response sampling is the convenience and probably the ethical considerations as well. The demerit is that this self-selected samples are sometimes subject to bias.

The one that is an the inverse of y = 3 Superscript x is y = 3x is f-1(x) = 1/3x.

The use of the idea of inverse function to look for the solution is given below:

Note that, y = 3x

Then let f(x) = y = 3x

One will need to Switch x and y and as such, x = 3y

Then one should express y in terms of x and as such, y = 1/3 x

Since f(x) = y ⇒ x = f-1(y)

Then f-1(y) = 1/3x

Therefore, the inverse of y = 3x is f-1(x) = 1/3x.

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Answer:

80 minutes

Step-by-step explanation

24/3=8

8mins/1 mile

8 minsx10 miles= 80 mins for 10 miles

Answer:

The hourly rate she worked to pay for the new bike is $18.84.

Step-by-step explanation:

Given:

Sis worked 14.4 hours and saved $271.30 for a new bike.

The equation 14.4x=271.30 could be used to represent how much she earned per hour.

Now, to find the hourly rate she worked to pay for the new bike.

The hourly rate = [tex]x[/tex].

Number of hours = 14.4.

Money she saved = $271.30.

According to the question, the equation used to represent she earned per hour is:

[tex]14.4x=271.30[/tex]

Now, to solve the equation to get the hourly rate:

[tex]14.4x=271.30[/tex]

Dividing both sides by 14.4 we get:

[tex]x=\$18.840.[/tex]

Thus, the hourly rate rounding to the nearest hundredths place is $18.84.

Hence, the hourly rate she worked to pay for the new bike is $18.84.

Step-by-step explanation:

Given

f(x) = 3x - 5

f(-2) = 3 * (-2) - 5

= -6 -5

= - 11

Answer:

f(×)=

Step-by-step explanation:

[tex] f(- 2 )= 3( - 2) - 5 [/tex]

[tex] - 2 = - 6 - 5[/tex]

[tex] - 2 = - 11[/tex]

Answer:

19.20 seconds.

Step-by-step explanation:

Given:

She invited 150 friends.

But she only had 5 activities for her friends and her party only lasted 4 hours.

Question asked:

How much time will each friend get on each activity ?

Solution:

First of all convert 4 hours into seconds:-

1 hour = 3600 seconds

4 hours = 3600 [tex]\times[/tex] 4 = 14400 seconds

By unitary method:

150 friends get time in 5 activities = 14400

1 friend get time in 5 activities = 14400 [tex]\div[/tex] 150 = 96 seconds

That means each friend get 96 seconds in all 5 activities.

Each friend get time on each activity = ?

Each friend get time on 5 activities = 96

Each friend get time on 1 activity = 96 [tex]\div[/tex] 5 = 19.20 seconds

Thus, each friend will get 19.20 seconds on each activity.

The volume of rotation of region R is [tex]192\pi[/tex] cubic units.

Given information:

Region R is bounded by the lines y=4, x=6, the y-axis and the x-axis.

Region R is rotated about the line y=-2.

So, the region R is a rectangle with length 6 units (x=0 to x=6), and the height of the rectangle is 4 units (y=0 to y=4).

After rotating this rectangle about y=-2, we will get a hollow cylinder.

The outer radius of the cylinder will be,

[tex]R=4-(-2)=6[/tex]

The inner radius of the cylinder will be,

[tex]r=0-(-2)=2[/tex]

And the length of the cylinder is 6 units.

So, the volume of the solid formed after the rotation will be,

[tex]V=\pi R^2L-\pi r^2L\\V=\pi L(R^2-r^2)\\V=\pi \times 6(6^2-2^2)\\V=\pi\times 6 \times 32\\V=192\pi[/tex]

Therefore, the volume of rotation of region R is [tex]192\pi[/tex] cubic units.

For more details about Volume after rotation, refer to the link:

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To find the volume of the solid formed by rotating region R about the line y=-2, we use the washer method which results in a volume of 216π cubic units.

The problem involves calculating the volume of a solid of revolution, which is formed when a two-dimensional region is rotated around a line that does not intersect the region.

Region R is defined as the area bounded by y=4, x=6, the y-axis, and the x-axis. The volume of the solid formed by rotating this region around the line y=-2 can be calculated using the washer method, which involves integrating over the area of concentric washers.

The general formula for the volume V of a washer is given by V = π∫[R2(x) - r2(x)]dx , where R(x) and r(x) are the outer and inner radii of the washers, respectively. In this case, the outer radius is R(x) = 4 - (-2) = 6 and the inner radius is r(x) = -2 - (-2) = 0.

Therefore, the volume V is:

V = π∫06[62 - 02 ]dx = π∫0636dx = 36π∫06dx = 36π[6] = 216π cubic units.

Write it as an equation:

X - 10 = 6x + 3

Now solve for x:

Subtract 3 from both sides:

x-13 = 6x

Subtract 1 x from both sides:

-13 = 5x

Divide both sides by 5:

x = -13/5

Answer:

x = -2.6.

Step-by-step explanation:

Let the number be x, then:

x - 10 = 6x + 3

x - 6x = 3 + 10

-5x = 13

x = -13/5

= -2.6.

Answer:

Sales Price = $21.00

New Price = $39.00

Step-by-step explanation:

Convert 35% into a decimal and multiply that with the $60.00. After you get the product, which is $21.00, you then need to subtract $21.00 from $60.00 and that gets you $39.00.

Answer:

-0.95

Step-by-step explanation:

cos(theta) = sqrt(1 - sin²(theta))

= sqrt(1 - 0.312²)

= sqrt(0.902656)

= +/- 0.9500821017

Since cos is negative in quadrant 2,

cos(theta) = -0.95

To approximate the value of cos0, we can use the given value of sin0 and the Pythagorean identity. The approximate value of cos0 is -0.95022.

Since the given angle 0 lies in Quadrant II where cos0 is negative, we can approximate the value of cos0 using the given value of sin0.

Using the Pythagorean identity sin^2(0) + cos^2(0) = 1, we can find cos0.

sin^2(0) + cos^2(0) = 1

0.312^2 + cos^2(0) = 1

0.097344 + cos^2(0) = 1

cos^2(0) = 1 - 0.097344

cos^2(0) = 0.902656

cos0 = √0.902656

cos0 ≈ -0.95022

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Answer:

B

Step-by-step explanation:

I got it correct

Answer:

38.2º

hope you have a good day!

Answer:

A) (x²/127806.25) + (y²/76956) = 1

B) 451 miles

C) 715 miles

Step-by-step explanation:

Center is at (0,0) and focus is at (c,0) while vertex is at (a,0)

Thus, a - c = 132 miles

and a + c=583 miles

Adding both equations together, we have;

2a= 715 miles

Thus, a = 715/2

a = 357.5 miles

Since a+c=583

Thus, c = 583-357.5 = 225.5 miles

Now, for an ellipse it is defined by; a² = b² + c²

a² = 357.5² = 127806.25

c² = 225.5² = 50850.25

So, b² = 127806.25 - 50850.25

b² = 76956

b = √76956

b = 277.409

A) Equation of tangent to ellipse which is equation of orbit would be;

(x²/a²) + (y²/b²) = 1

Thus,

(x²/127806.25) + (y²/76956) = 1

B) distance between the earth and the other focus is = 2c = 2 x 225.5 = 451 miles

C) Length of other major axis = 2a = 2 x 357.5 = 715 miles

a) The equation of the orbit is \(\frac{x^2}{(583+3963)^2}+\frac{y^2}{132^2} = 1\). b) The distance from the center to the other focus is calculated using the formula \(c = \sqrt{(583+3963)^2 - 132^2}\). c) The length of the major axis is \(2(583+3963)\).

a) To find an equation of the orbit, we can use the standard form equation for an ellipse:
\[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1\] where \((h,k)\) represents the center of the ellipse, \(a\) represents the distance from the center to the vertices along the major axis, and \(b\) represents the distance from the center to the co-vertices along the minor axis. In this case, the center of the ellipse is the Earth's center, which is at the origin \((0,0)\). The highest point of the orbit is 583 miles above the Earth's surface, so the distance from the center to the vertices along the major axis is 583 miles + the radius of the Earth. The radius of the Earth is approximately 3963 miles. The lowest point of the orbit is 132 miles above the Earth's surface, so the distance from the center to the co-vertices along the minor axis is 132 miles. Substituting the values into the equation:
\[\frac{x^2}{(583+3963)^2}+\frac{y^2}{132^2} = 1\]

b) The distance from the center to the other focus can be found using the relationship \(c = \sqrt{a^2 - b^2}\), where \(c\) represents the distance from the center to the foci. Substituting the values into the equation:
\[c = \sqrt{(583+3963)^2 - 132^2}\]

c) The length of the major axis can be found using the formula \(2a\), where \(a\) represents the distance from the center to the vertices along the major axis. Substituting the values into the equation:
\[2a = 2(583+3963)\]

Answer: r=0.8

Step-by-step explanation:

4r + 8 = 7.2 + 5r

-4r             -4r

8=7.2+r

8-7.2=r

0.8=r

Answer: [tex]r=0.8[/tex]

Step-by-step explanation:

-Solve:

[tex]4r+8=7.2+5r[/tex]

-Subtract [tex]5r[/tex] from both sides:

[tex]4r+8-5r=7.2[/tex]

Combine [tex]4r[/tex] and [tex]5r[/tex] to get [tex]-r[/tex]:

[tex]-r+8=7.2[/tex]

-Subtract [tex]8[/tex] from [tex]7.2[/tex] to get [tex]-0.8[/tex]:

[tex]-r=7.2-8[/tex]

[tex]-r=-0.8[/tex]

-Multiply both sides by [tex]-1[/tex]:

[tex]r=0.8[/tex]

-Result:

[tex]r=0.8[/tex]

Answer:

I think it is 38 centimeters.

Step-by-step explanation:

Answer:

t = 3 seconds

Step-by-step explanation:

This is a quadratic equation. First set it up and set it equal to 0 (the ground).

-16t² + 46t + 6 = 0

The quadratic formula is (-b ± √(b² - 4ac))/2a

a= -16

b = 46

c = 6

Plug those numbers into the equation and solve which will result in -.125 or 3.

The time of course can not be negative in this case. Therefore, t=3 seconds.

The ball will hit the ground after 3 seconds.

The problem deals with the quadratic equation representing the motion of the ball. When the ball hits the ground, the height (h) is 0. So, we need to solve the equation -16t^2 + 46t + 6 = 0 for (t). The roots of this quadratic equation can be found using the quadratic formula, t = [-b ± sqrt(b^2 - 4ac)]/2a. Substituting a=-16, b=46, and c=6 into the formula, you will find the solutions are t = 3 seconds and t = -0.375 seconds. Therefore, the ball will hit the ground after 3 seconds. The correct choice is A. 3.

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Answer:

try using this it might help out with the question

Step-by-step explanation:

Y=2x+3

Answer:

About 29

Step-by-step explanation:

575 cans of food / 20 days = About 28.75 cans a day, rounded to 29.

Answer:

28.7 cans

Step-by-step explanation:

We want to find the unit rate for cans per day

To find this, divide the number of cans by the number of days

cans/days

574/20

28.7

About 28.7 cans per day