Bob wants to catch an elevator before the door closes. He is 32ft
away when the door starts to close.
The door has to travel 4.3ft to fully close, and is closing at a rate of
1.2ft/s. Bob needs to get to the door while it is at least 0.6ft open.
How fast does he have to run in order to catch the elevator?
Give your answer in feet per second, and round to the nearest
hundredth.

I can only draw the conclusion that if a triangle is equilateral, then it is describing various based on the previous statement, "If a triangle is isosceles, it is then equilateral."

Equilateral describes a triangle that has three equal sides. A triangle is referred to as isosceles if two of its sides are equal.

An equilateral triangle in geometry is a triangle whose sides are all of the same length. Since the three sides are equal, the three angles that are opposite the equal sides are also equal. As a result, it is also known as an equiangular triangle because each angle is 60 degrees.

The length of each side is the same. Two sides of an isosceles triangle are of equal length. Scalene triangle: Each side measures a different distance.

A triangle with two equal sides is called an isosceles triangle. Additionally, the two angles that face the two equal sides are also equal. To put it another way, "An isosceles triangle is a triangle with two congruent sides."

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We can use the distributive property to expand the left side of the equation, which will give us YZ + XY.

Property is a term used to describe an individual's ownership of something tangible or intangible. Property can include real estate, such as a house or land, or personal property, such as furniture, vehicles, and jewelry. Property can also include intangible items such as copyrights, patents, trademarks, and trade secrets. When property is owned, it is the responsibility of the owner to protect it from damage, destruction, theft, or other losses.

We can then use the given equation to substitute WX for YZ on the right side, which will give us WY. Therefore, YZ + XY = WY.

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Effect of switching the explanatory response variables have on the regression line is E) The sign and value of m and the value of b all change.

The y-axis dependent variables and x-axis independent variables are shown as a regression line to show their linear relationship. By examining the data pattern the variables' effects have created, the correlation is established.

In a regression graph, the line closest to the data points is shown. By changing the value of x in the regression equation, his statistical tool assists in analyzing the behavior's of a dependent variable y when there is a change in the independent variable x.

Hence, The sign and value of m and the value of b all change.

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The area bounded by the curve y = sin(x) and y = cos(x) for sin(x) = cos(x) as point of intersection is equal to 2√2.

Area bounded by the curve y = sin(x) and y = cos(x).

Point of intersection for sinx = cosx

⇒  x = π/4 and 5π/4

Required area

= [tex]\int_{\frac{\pi }{4} }^{\frac{5\pi }{4}}[/tex]( sinx - cosx)dx

= ( -cosx - sinx ) [tex]|_ {\frac{\pi}{4} }^ {\frac{5\pi}{4} }[/tex]

= [ -cos(5π/4) - sin(5π/4) ] - [ -cos(π/4) - sin(π/4) ]

= [ -( -1 / √2 ) - (-1 / √2 ) ] - [ -1 /√2 - 1 /√2 ]

= ( 1 + 1 ) / √2 + ( 1 + 1 ) / √2

=  ( 2 + 2 ) / √2

= 4 /√2

= 2√2

Therefore, the area bounded by the given curve is equal to  2√2.

The given question is incomplete, I answer the question in general according to my knowledge:

find the area of the region bounded by the curves y = sin(x), y = cos(x), where solution the points of intersection occur when sin(x) = cos(x), that is, when x = π/4 and 5π/4.

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Answer: There are 850 students total

Step-by-step explanation: First step is to analyze, 34 brought lunch which makes up 4% so to find total we will divide because dividing percentages gives you bigger numbers.

We will do 34/4%= 850

Therefore there are 850 students attending Ridgewood Junior High School

Answer:

136

Step-by-step explanation:

calculating each area as shown in the picture above

Answer:

(f•g)(-4) = f(g(-4)) = f(-21) = -43

Answer:

This time, ratio is 4:1 for you and 24:5 for your friend

Step-by-step explanation:

For You: Using the same method, join (4,1) and (8,2) with a line and extend it
For your friend: Take (24,5) and (48,10), extend line joining them
Done!

Edit: I took the time variable for the y axis, here's the right graph

Answer: in the graph.

Step-by-step explanation:

When you look at the graph you see time is the x axis and cubes are on the y axis. So your first point is (2, 8) for two hours:8 cubes. From zero, go right 2 and up 8 and place your point. From there go right 2 and up another 8 for your 2nd point. Draw your line. For your second line, 5 hours: 24 cubes, so your first point is right 5 and up 24, place your dot. From there, go right 5 and up 24, draw your dot. Now draw your second line. Graph attached.

Answer:

The product of (px + qy)(ax − by) is pax^2 + qaxby - pbx^2 - qby^2.

Step-by-step explanation:

Answer: apx^2-bpxy+aqxy-bqy^2

Step-by-step explanation: (px+qy)x(ax-by) Multiply each term in the first parenthesis by each term in the second parenthesis (FOIL). That would give you pxax-bpxy+aqxy-qyby. Then calculate the product pxax which would give you apx^2-bpxy+aqxy-qyby. Calculate the other product qyby which would give you apx^2-bpxy+aqxy-bqy^2.  

Using right triangle properties, The length of the guy wire, to the nearest foot is 11√(37) ft.

A triangle in which one of the interior angles is 90° is called a right triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the height and the base.

Here, 2 right triangles are formed. One between stake and pole and second between stake and cell tower.

The height of pole = 12 ft.

The distance between stake and pole = 2 ft.

The distance between pole and tower = 9 ft. so the The distance between stake and tower = 2 + 9 = 11 ft.

Let x is the angle between wire and ground.

from first right angled triangle,

tan x = 12/2

tan x = 6

from second right angled triangle

tan x = height of tower/(11)

6 = height of tower/11

height of tower = 66 ft

So, length of wire = √(66² + 11²)

⇒ length of wire = √[(11*6)² + 11²]

⇒ length of wire = √[11²(6²+1)]

⇒ length of wire = √[11²(36+1)]

⇒ length of wire = 11√(37) ft.

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Answer:

Lin originally had 4 bags * the same amount of apples per bag = 4 * x apples.

After eating 1 apple from each bag, she was left with 4 * x - 4 apples = 28 apples.

Therefore, each bag originally contained x = 28 + 4 = 32 apples.

1)  The number of gallons of soapy water that are in Elianni's bucket are; 1.5 gallons

2) The number of more quarts that it can hold is; 14 more quarts

Elianni puts 12 pints of soapy water in the bucket to wash her blue Hondi. From conversion factors, we know that;

1 pint = 1/8 gallon

Thus;

12 pints = 12 * (1/8)

12 pints =  (12/8) gallons

= 3/2 = 1.5 gallons.

Due to the fact that the bucket is 5 gallon capacity, It can hold:

5 - 1.5 = 3.5 gallons more.

But from conversion factors, we know that;

1 gallon = 4 quarts.

Thus;

3.5 gallons = 3.5 * 4

= 14 quarts more.

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Answer: Using the distributive property, an expression equivalent to 34 + 16 is

2 (17 + 8)

Answer:

Step-by-step explanation:

A. 96 hotdogs is 12 packs of hot dogs because 96/8 = 12

so 12 x 3.96 is $47.52 which is the amount for 96 hot dogs

B. 96 hotdogs is 12 packs of hotdogs

12 * 4.49 = $53.88

Answer: 10 for A

Step-by-step explanation: Because I know

The volume of paper in the recycling bin is 6800 cubic inches.

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same. Volume of a rectangular prism = Area of a base × Height.

Given that, the area of the bottom of the bin is 400 square inches. Paper completely fills the bin to a height of 17 inches.

So, the volume of recycling bin is 400×17

= 6800 cubic inches

Therefore, the volume of paper in the recycling bin is 6800 cubic inches.

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Answer:

10

Step-by-step explanation:

You need to use the Pythagorean Theorem for this problem since you're solving for the lengths of a right triangle:

A right triangle is a triangle that has a 90-degree angle.

Let's say the side lengths are a, b, and c.

According to the Pythagorean Theorem, the way to relate a, b, and c is:

a^2 + b^2 = c^2   ==> c is the hypotenuse (the diagonal line on the triangle)

We already know a and b since they're given:

a=6 and b=8

Just apply these known values to the Pythagorean theorem:

6^2 + 8^2 = c^2  ==> solve for c

36 + 64 = c^2  ==> simplify

100 = c^2

c = 10  ==> take the square root on both sides

Answer: 10

The slope intercept forms of the values are: 1) y--10x -3 (2) y7x+5 (3) y =9/5-4 (4) -5x/4 +5

The slope or gradient of a line is a number that describes both the direction and the steepness of the line. Slope is often denoted by the letter m; there is no clear answer to the question why the letter m is used for slope,

The slope-intercept forms of the values are

1) y--10x -3

2) y7x+5

3) y-9/5-4

4) -5x/4 +5

5) Slope is determined by:

a) (7+6)/(-11-17) =13/-18

b) (-5-4) / (-4-3) = -9/-7 = 9/7

c) (15-14) / (11+20) = 1/31

d) (-7+18) / (-1-11) =11/-12

The slopes of the equations are 1) y=2/3x -2 The slope is 2/3

2) y = 9/5x -5 = The slope is 9/5

3) y = -1/2x -2 the slope is -1/2

4) y = -x -1:  the slope is -1

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Answer:

The equation that describes the relationship between the distance below ground and the time for the drone's descent is: Distance = -250m - 500m(Time-1).

The amount compounded after 16 years is $641.88. Therefore, option D is the correct answer.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].

Given that, principal =$400, time period = 16 years and the rate of interest = 3%.

Here, Amount =400(1+3/100)¹⁶

= 400(1.03)¹⁶

= 400×1.605

= $641.88

Therefore, option D is the correct answer.

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The probability of drawing a total of 3 orange balls and 2 green balls = 5/2(0.6)sqaure*(1-0.6)cube

What is Probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

here we will use binomial distribution formuale

p(x)= (n/x) px.qn-x

where , p = probability of success in a single trail

q = 1-p probability of failure in one trail

n = total number of trail or number of total sample

x= number of success desired

now total number of ball contain =5

and let define probability of success is drawing 2 green ball

so probability of drawing a green ball (p) =3/5

=0.6

and we need this favouable results 2 times

so x = 2

and q = 1- p = (1-0.6)

so putting value of p, q ,x,m,n above formula we get

(n/x) px.qn-x

5/2(0.6)sqaure*(1-0.6)cube

The possibility of getting all three orange balls and two green balls in a row

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Answer:

Below

Step-by-step explanation:

G = 11  + 2w   <===== 11 passed + 2 more per week

P = 8 + 5w     <====== 8 passed and 5 more per week

  When are they equal ?

     Equate   G and P equations:

  11+ 2w = 8 + 5w

   3 = 3w

    w =1     after ONE week they will have the same  G = 13 = P

The equation that represents the given sitution is 3a-6 = 69. Rita saved $25.

What is an epression?

A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.

Assume that Rita saved $a.

Given that the cost of a skateboard is $6 less than three times what she has saved.

The mathematical expression of $6 less than three times what she has saved is 3a-6

The actual cost is $69.

According to the question,

3a-6 = 69

Add 6 on both sides:

3a = 69 + 6

3a = 75

Divide both sides by 3:

a = 75/3

a = 25

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The populations of interest are the 30 patients in the treatment group and the 30 patients in the control group. The parameter of interest is the pulse rate at a critical point during the operation

a. Identify the populations and parameters of interest. Then state hypotheses.

The populations of interest are the 30 patients in the treatment group and the 30 patients in the control group. The parameter of interest is the pulse rate at a critical point during the operation. The null hypothesis is that beta-blockers do not reduce the pulse rate, while the alternative hypothesis is that beta-blockers do reduce the pulse rate.

b. State and verify conditions for carrying out a significance test.

The conditions for carrying out a significance test are that the data must be sampled randomly, the samples must be independent, the data must be normally distributed, and the sample sizes must be equal. The data in this study was randomly sampled, the samples are independent, and the sample sizes are both 30. However, we cannot assume that the data is normally distributed without testing.

c. Calculate the test statistic and the P-value.

The test statistic is calculated using the formula t = (x1 - x2) / sqrt(s1^2/n1 + s2^2/n2), where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes. In this case, t = (65.2 - 70.3) / sqrt(7.8^2/30 + 8.3^2/30) = -5.45. The P-value is calculated by finding the probability of obtaining a result at least as extreme as the observed one if the null hypothesis is true. In this case, the P-value is 0.000003.

The populations of interest are the 30 patients in the treatment group and the 30 patients in the control group. The parameter of interest is the pulse rate at a critical point during the operation

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Answer:

Graph B represents an increasing function

Step-by-step explanation:

If you look at the other graphs, they are either stagnant on one line or going downwards.

Graph B, on the other hand, is growing on both the x and y axis.

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y = x + 1,If you know the value of x, you can solve for y by plugging the value of x into the equation and then solving for y. if x = 4,y = 4 + 1y = 5.

The equation is a mathematical expression that consists of symbols and numbers, and is used to calculate a numerical value or result. The symbols in the equation represent variables or constants, which are either given values or unknowns that need to be solved. An equation can also be used to describe relationships between different concepts, such as physical laws or chemical reactions.

y = 2x - 5

To solve for y, rearrange the equation to isolate y on one side. Subtract 2x from both sides to isolate y on the left side:

y - 2x = -5

Now add 2x to both sides to get y by itself on the left side:

y = 2x - 5

Therefore, the solution for y is 2x - 5.

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The relative frequency of class D is 0.35.

The number of times an event occurs is called a frequency. Relative frequency is an experimental one, but not a theoretical one. Since it is an experimental one, it is possible to obtain different relative frequencies when we repeat the experiments.

The ratio of the number of times a value of the data occurs in the set of all outcomes to the number of all outcomes gives the value of relative frequency.

Consider the given partial relative frequency distribution.

  Class            Relative frequency

    A                         0.22

    B                         0.18

    C                         0.43

    D                            

Then,

We need to find the relative frequency of class D

We know that,

Sum of relative frequency is equal to one.

that is.

[tex]$0.22+0.18+0.25+$[/tex] relative frequency of class D=1

0.65 + relative frequency of class [tex]$\mathrm{D}=1$[/tex]

relative frequency of class D=1-0.65

=0.35

We get,

Relative frequency of class D Is 0.35

Therefore, the relative frequency of class D is 0.35

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I would implement a random sampling approach to determine the rate of smoking among teenagers.

Simple random sampling is a form of probability sampling in which a selection of participants is chosen at random from a population. Each person in the population has an equal probability of getting chosen. The data is then collected from as big a percentage of this random selection as feasible.

The Simple Random Sampling method is a dependable way of gathering information in which every member of a population is picked at random, purely by chance.

Random sampling guarantees that the findings received from your sample are close to those obtained if the full population was surveyed. The simplest random sample gives each unit in the population an equal probability of being chosen.

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The probability of rain in a place during a long weekend (Friday, Saturday, and Sunday) is 65% . The risk of rain is between 10% and 30% on all three days.

a) The risk of rain in the destination throughout the long weekend may be calculated by adding the chance of rain on each day, which is 10% + 25% + 30% = 65%. As a result, the probability of rain at the destination throughout the long weekend is 65%.

b) The notion of conditional probability may be used to calculate the likelihood that it will rain in the destination on all three days of the long weekend. It is the likelihood of rain on Sunday given that it has already rained on:

Friday and Saturday × (the probability of rain on Saturday given that it has already rained on Friday) × (probability of rain on Friday) ×( the probability of rain on Friday).

The best lower bound for this probability is the 10% chance of rain on any given day, and the best upper bound is the 30% chance of rain on any given day.

As a result, the likelihood of rain at the destination on all three days of the long weekend is between 10% and 30%.

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Answer:

The constant of variation for direct variation is k = y/x.

So we have k = y/x = 5/8

To find y when x = 4, we can use the equation y = kx.

y = kx = (5/8) * 4 = 5

So when x = 4, y = 5