2. An escalator was built with an angle of depression of 30°. It descends at a rate of 100 feet per
minute. If the vertical rise of the escalator is 60 feet, how many seconds does it take for a
person riding the escalator to travel its full length? (sin 30° = 0.5; cos 30°= 0.866;
tan 30°=0.577)
A. 1.3 min
B. 1.2 min
C. 1.03 min
D. 0.7 min

The 4 tests for similar triangles are:-

AAA: Three pairs of equal angles.

SSS: Three pairs of sides in the same ratio.

SAS: Two pairs of sides in the same ratio and an equal included angle.

ASA: Two angles and the side included between the angles of one triangle are equal

What is AAA,SAS,ASA,SSS?

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle. 

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

According to the  AAA rule, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."

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There are 24 possible outcomes when rolling a number cube and picking a cube from 4 colored cubes.

To determine the number of possible outcomes when rolling a number cube and picking a cube from 4 colored cubes,

we need to multiply the number of outcomes for each event.

For rolling a number cube (assuming it has 6 sides), there are 6 possible outcomes (1, 2, 3, 4, 5, and 6).

For picking a cube from 4 colored cubes, there are 4 possible outcomes (one for each color).

Now, to calculate the total number of outcomes, multiply the outcomes of each event:

6 (number cube outcomes) x 4 (colored cube outcomes) = 24 possible outcomes.

So, there are 24 possible outcomes when rolling a number cube and picking a cube from 4 colored cubes.

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There are 24 possible outcomes when rolling a number cube and picking a cube from 4 colored cubes.

When rolling a number cube, there are six possible outcomes (numbers 1-6). When picking a cube from four colored cubes, there are four possible outcomes. Therefore, the total number of possible outcomes is the product of the number of outcomes from each event: 6 x 4 = 24 possible outcomes.

When rolling a number cube, there are 6 possible outcomes (1, 2, 3, 4, 5, or 6), since a standard number cube has 6 faces, each with a different number.

When picking a cube from 4 colored cubes, there are 4 possible outcomes, one for each color.

To find the total number of outcomes when performing both actions, you can multiply the number of outcomes for each individual action:

Total outcomes = outcomes from rolling a number cube × outcomes from picking a colored cube
Total outcomes = 6 × 4
Total outcomes = 24

So, there are 24 possible outcomes when rolling a number cube and picking a cube from 4 colored cubes.

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Answer: y^18

Step-by-step explanation:

(y²)⁵ · y⁸

Using exponent rules, you would multiply the exponents, 2 * 5 to get y^10

Now you have y^10 * y^8  

This is another rule, you will add 10+8 because they are exponents

This leads to our answer y to the power of 18

Hope this helped

1.5·10⁸ kilometers

As a result, the Earth Sun distance is 150 million kilometers. To use scientific notation, pick a value between 1 and 10, then multiply it by 10ˣ.

So the number between 1 and 10 in 150,000,000 is 1.5, with 8 decimal points.

As a result, the solution is 1.5·10⁸

The benefits of Earth's prime placement in the solar system are numerous. We are just far enough away from the Sun for life to thrive.

Venus is excessively hot. Mars is quite chilly. Scientists refer to our region of space as the "Goldilocks Zone" because it looks to be ideal for life.

As previously stated, Earth's average distance from the Sun is around 93 million miles (150 million kilometers). That's one AU.

On this hypothetical scale, these so-called "linebackers" resemble minuscule specks rather than the massive linebackers of the NFL.

If all of the known asteroids in our solar system were combined, their total mass would be less than 10% that of Earth's moon.

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It would take approximately 4.7 years for the investment to reach R30,000 using continuous compounding. The answer is option B.

To determine the time it would take for an investment to reach a specific goal, we can use the formula for compound interest:

A = P(1 + r/n)^(n*t)

Where:

A is the desired goal amount

P is the initial principal (R20,000 in this case)

r is the interest rate (9% or 0.09)

n is the number of compounding periods per year (1 for simple interest, infinite for continuously compounding)

t is the time in years

Question 21: Simple Interest

Given P = R20,000 and A = R30,000, we need to find t.

30000 = 20000(1 + 0.09*t)

Dividing both sides by 20000 and rearranging the equation, we get:

1.5 = 1 + 0.09*t

0.5 = 0.09*t

t = 0.5 / 0.09

t ≈ 5.56 years

Therefore, it would take approximately 5.6 years for the investment to reach R30,000 using simple interest. The answer is option A.

Question 22: Continuous Compounding

Given P = R20,000 and A = R30,000, we need to find t.

30000 = 20000 * e^(0.09*t)

Dividing both sides by 20000 and rearranging the equation, we get:

1.5 = e^(0.09*t)

Taking the natural logarithm of both sides, we have:

ln(1.5) = 0.09*t

t = ln(1.5) / 0.09

t ≈ 4.73 years

Therefore, it would take approximately 4.7 years for the investment to reach R30,000 using continuous compounding. The answer is option B.

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Answer:

15g+16n=294

Step-by-step explanation:

15g=15*12=180

16n=16*9=114

total=g+n=180+114=294

Answer:

please provide better chart / context.

Step-by-step explanation:

Answer:

the unit rate would be 66 units per minute

Step-by-step explanation:

2,046/31 = 66

Answer:

65.974 Square-miles

Step-by-step explanation:

We do 3.14*2^2=12.566

We then do 3.14*5^2=78.54

78.54-12.566=65.974

The change in the area of the circular oil spill is given by the equation

A = 65.973 miles²

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The perimeter of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle

Given data ,

Let the change in area of circular oil spill be A

Now , the equation will be

The initial radius of the circular oil spill r = 2 miles

The increased radius of the circular oil spill R = r + 3

R = 5 miles

Now , the initial area of the circular oil spill = πr²

Substituting the values in the equation , we get

The initial area of the circular oil spill = 4π miles²

Now ,

The increased area of the circular oil spill = πR²

Substituting the values in the equation , we get

The increased area of the circular oil spill = 25π miles²

And , change in area of circular oil spill A = 25π miles² - 4π miles²

On simplifying the equation , we get

The change in area of circular oil spill A = 21π miles²

The change in area of circular oil spill A = 65.973 miles²

Therefore , the value of A is 65.973 miles²

Hence , the change in circular area is 65.973 miles²

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Answer:

$6455.

Step-by-step explanation:

The formula for this investment is:

A = P(1 + r/4)^4t      where P = amount deposited ,  A amount after t years,

                                r = rate (as a decimal fraction).

So we have:

7160.06 = P(1 + 0.026/4)^16

7160.06 = P * 1.109227

P = 7160.06 / 1.109227

  =  $6455.

Answer:

If you divide 32.4 by 6, then you get 5.4 as an answer

Answer:

1

Step-by-step explanation:

Add teh exponents.

9^c * 9^-c = 9^(c - c) = 9^0 = 1

Answer:

67,500 men

Step-by-step explanation:

Percent of children = 20% (.2)

30,000 x 5 = 150,000 (Total pop.)

150,000-30,000 = 120,000 (Pop. minus children)

.35 (Percent of women) x 150,000 =52,500

120,000-52,500 = 67,500

Answer:

67,500

Step-by-step explanation:

20 percent of the population is children. 45 percent is men. If children population is 30000, you multiply by 2 to get 40 percent. That means that if men were 40 percent, men population would be 60000. When you add another 5 percent to get 45 percent, it makes 67500 men.

Answer:

1,1.1,1.25,1.5,1.7,9

Answer:

64 lb

Step-by-step explanation:

you can solve this problem by using a proportion, then cross multiply and divide. (better explained in yt videos).

The value of x which is the length of the base of the triangle in the question is; 29 meters

A triangle is a three sided polygon, with three interior angles.

Please find attached the possible diagram in the figure, (created with MS Word), which is a question from a mathematics textbook posted on the internet

The diagram indicates that the altitude or height of the triangle = 8 meters

The specified area of the triangle is; A = 261 square meters

The base length of the triangle = x

The formula for the area of a triangle, A, is; A = (1/2) ×Base length × Height

Therefore;

A = 261 m² = (1/2) × x × 18 m

x = 261 m² ÷ ((1/2) × 18 m) = 29 m

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The distance Hailey and Levi are from the stadium as they drive, can be  

shown using a graph.

Reasons:

The given information are;

Distance of Hailey from the stadium at noon = 300 miles

Distance of Levi from the stadium at noon = 450 miles

Hailey's speed = 25 mph

Levi's speed = 50 mph

Required:

(a) Draw the graph of the function of their distance from the stadium

(b) Determine the distance how far from the stadium at which they are at an equal distance from the stadium.

Solution:

Based on the question, the required function are;

Hailey's distance from the stadium, H = 300 - 25·t

Levi's distance from the stadium, L = 450 - 50·t

The graph of the distance of Hailey and Levi can be plotted on MS Excel using the above functions.

At the time they are equal distance from the stadium, we have;

H = L

Which gives;

300 - 25·t = 450 - 50·t

50·t - 25·t = 450 - 300 = 150

25·t = 150

\(\displaystyle t = \frac{150}{25} = 6\)

Therefore, after 6 hours, Hailey and Levi are at an equal distance from the stadium.

The distance from the stadium, d = 300 - 25 × 6 = 150

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Answer:

1.2m

Step-by-step explanation:

1 meter = 100 cm

120cm * (1m/100cm)  = 1.2m

Answer:

A

.....

....

....

...

...

...

Answer:

1000 m

Step-by-step explanation:

Tom's distance = 400 m

Sophie's distance = 600 m

Hence. Distance per day = 600 - 400 = 200 m per days

In 5 days ;

200 m * 5 = 1000 m

Sophie travels 1000 m more

Answer:

16 inches/2 feet

Step-by-step explanation:

We already have our ratio of 8:1, so we can multiply this ratio by any number of out choosing and the ratio will still be the same.

Answer: No

Step-by-step explanation: A isosceles triangle is a triangle that has 2 sides of equal length. If you take just two lines from the triangle and just draw a straight line from the ends of them if the lines line up then they are equal if they don't they aren't equal.

===================================================

Explanation:

Each point listed is of the form (x,y)

The input x is fed into the f(x) function to get a y = f(x) output.

Recall that the inverse function undoes everything the original function does.

This means that when we determine the inverse function for a list of points like this, we just swap each x and y.

So if

\(f = \{ (3.5, 2), (0,4), (1,5), (6,1) \}\)

then,

\(f^{-1} = \{ (2,3.5), (4,0), (5,1), (1,6) \}\)

Again all I've done is swap each x and y value.

From here, we look through the inverse function set and look for the point when x = 1. We see the point (1,6) is in the set.

Therefore, \(f^{-1}(1) = 6\)

Answer: n - 6

Step-by-step explanation:

Multiply -3 and 2.

-3 x 2 = -6

n -6

sorry if this is incorrect

Answer:

24

Step-by-step explanation:

-3N^2=24

Move all terms to the left:

-3N^2-(24)=0

a = -3; b = 0; c = -24;

Δ = b2-4ac

Δ = 02-4·(-3)·(-24)

Δ = -288

Delta is less than zero, so there is no solution for the equation!Q

Hope this helps You! :D

Answer:

I'm not completely sure but I beileve Jackie less than 4

Step-by-step explanation:

good luck tho

Answer:

D

(i scored 100 on the quiz)

Answer:

$24.60

Step-by-step explanation:

First, you need to find 20% of $30.75.

To do this, we need to divide $30.75 by 5.

20% og $30.75 is $6.15.

$30.75 - $6.15 = $24.60

I hope that this helps! :)

The measures of the angles are v = 80°, y = 100°, w = 45°, and x = 55°.

An inscribed four-sided polygon in a circle is known as a cyclic quadrilateral. With the specified side lengths, it has the largest area feasible.

Given the quadrilateral inside a circle.

The angle v is given by:

45° +v + 55°=180°

v + 100° = 180°

v = 180° - 100°

v = 80°

Since the quadrilateral is cyclic, the sum of its opposite angle is 180°.

Therefore,

y + v = 180°

y + 80° = 180°

y = 100°

Using the property of cyclic quadrilateral, it follows:

w = 45° and x = 55°

Hence, the measures of the angles are v = 80°, y = 100°, w = 45°, and x = 55°.

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The complement of selecting a grape candy is D. 7:8.

The complement of a choice is the ratio of not choosing the specified item in preference to others.

The chance of choosing a grape candy is 1/8 or 1:8.  The complement of choosing a grape candy is 7:8 or (1 - 1/8).

The complement of a choice is the opposite probability of choosing an event.

Items          Number    Ratio

Cherry               4         4/16

Lemon               3         3/16

Watermelon      7         7/16

Grape candies  2        2/16

Total                 16

The ratio of grape candies = 2/16 or 1:8

The ratio of not choosing grape candies = 14/16 or 7/8

Thus, the likelihood of failing to choose a grape candy is Option D.

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A. 1:8

B. 4:6

C. 13:16

D. 7:8

The function  in which the table is provided is an exponential function because it generates a growing curve.

The exponential function is a mathematical function of the form:

f(x) = \(a^{x}\),

where:

a is the base constant  

x is the variable.

In this function, the base, a, is a positive real number and is typically greater than 1, although it can also be between 0 and 1.

Properties

Exponential Growth: When the base, a, is greater than 1, the function exhibits exponential growth.

That is, as "x" increases, the function values increase at an increasingly rapid rate.

Exponential Decay: When the base, a, is between 0 and 1, the function exhibits exponential decay.

That is, as "x" increases, the function values decrease, approaching zero but never actually reaching it.

Constant Base: If the base "a" is equal to 1, the exponential function becomes f(x) = \(1^{x}\) = 1, resulting in a constant function.

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The area of the composite solid is 602.88m²

A composite solid is a solid that is composed, or made up of, two or more solids.

The solid consist of two cones. one big and one small cone

Area of a cone can be expressed as;

A = πr² + πrl

A = πr(r+l)

For the Big cone

A = πr(r+l)

A = 3.14 × 8 ( 8+10)

A = 25.12 × 18

A = 452.16m²

Area of the small cone

A = 3.14 × 4( 4 + 8)

A = 12.56 × 12

A = 150.72m²

Therefore the area of the composite solid

= 452.16 + 150.72

= 602.88 m²

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