The designers of a water park have sketched a preliminary drawing of a new slide. The length of the ladder is I - 40 feet, and its angle of elevation is 60 (segure). 60 (a) Find the height of the slide. (Round your answer to two decimal places) - (b) Find the angle of depression from the top of the slide to the end of the slide at the ground in terms of the horizontal distance ander travels (c) Safety restrictions require the angle of depression of the slide to be no less than 25 and no more than 30°. Find an interval for how far ander travels hortzontally (round me values to one decimal place. Enter your answer using interval notation

d= -16.

[tex]-10=-2+\frac{1}{2}d[/tex]

[tex]-10+2=-2+\frac{1}{2}d+2\neq \\\\ -8=\frac{1}{2}d[/tex]

[tex]\frac{-8}{\frac{1}{2}} =\frac{\frac{1}{2}d}{\frac{1}{2}} \\ \\-8*2=d\\ \\-16=d\\ \\d=-16[/tex]

[tex]-10=-2+\frac{1}{2}(-16)\\ \\-10=-2-8\\ \\-10=-10[/tex]

That's correct! The answer is d= -16.

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The image's distance from the mirror is -1.87, by using the mirror equation.

Note:-  Although the question is missing, I believe the issue is asking where the image is located.

To find the solution to the problem, the mirror equation can be used:

Mirror equation =  [tex]\frac{1}{f}+\frac{1}{d_{o} }+\frac{1}{d_{i} }[/tex]

Where,

f = mirror's focal length

[tex]d_{o}[/tex] = object's distance from the mirror

[tex]d_{i}[/tex] =  image's distance from the mirror

The focal length is assumed to be negative for a convex mirror in our problem.

f = -2.8 m

The object's distance (do) = 5.6m

By using the mirror equation, the image's distance from the mirror can be determined

[tex]\frac{1}{f}+\frac{1}{d_{o} }+\frac{1}{d_{i} }[/tex]

i.e, [tex]\frac{1}{d_{i} } = \frac{1}{f} -\frac{1}{d_{o} }[/tex]

= [tex]-\frac{1}{2.8} -\frac{1}{5.6}[/tex] =  [tex]-\frac{3}{5.6}[/tex]

= - 0.5357

[tex]d_{i} =[/tex] [tex]-\frac{5.6}{3}[/tex]

= -1.87 m

The virtual nature of the image is indicated by the negative sign (located behind the mirror)

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y= - x + 2.

The slope of any linear equation will always be the coefficient of the "x" variable when the equation is solved for "y". Since there isn't any number written to the left of "x", the slope of the line is 1.

When looking for the slope of a line perpendicular do another, take the value of the slope and find its multiplicative inverse and change the sign of this value as well. This is how you do it:

Original slope value: 1.

Multiplicative inverse: 1/1= 1

Changing the sign: -1

Using the calculated value of the slope "m", which is -1, use the formula for calculating linear equations with both the slope and the values of the ordered pair:

[tex]y-y_{1} =m(x-x_{1} )[/tex]

Substitute the values and simplify.

[tex]y-(-3) =(-1)(x-(5) )\\ \\y+3=(-1)(x)-(-1)(5)\\ \\y+3=(-1x)-(-5)\\ \\y+3=-1x+5\\ \\y=-1x+2\\ \\y=-x+2[/tex]

A line that passes through point (5, –3) and is perpendicular to the equation y = x is y= - x + 2.

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Answer:

0.875

Step-by-step explanation:

7/8 in decimal form is 0.875.

The linear correlation coefficient of the data is calculated to be -0.911 as the slope of the regression line is -1.38

As the coefficient of determination that is (R^2) = 0.83 and the slope of the regression line = - 1.38, we can determine the linear correlation coefficient of the data as follows;

The Coefficient of determination (R^2) is the square of the linear correlation Coefficient (R) and is used to acquire the proportion of explained variance of the regression line.

Hence. To get the linear correlation Coefficient (R) from the Coefficient of determination (R^2); we take the square root of R^2 as follows;

R = √R^2

R = √0.83

R = 0.91104335791

R = 0.911

As the value of the slope is negative, therefore this represents a negative relationship between the variables, hence R will also be negative ;

Therefore, R = -0.911

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Answer:

[tex]\left(-\frac{1}{3},\:\frac{130}{27}\right) \:\mathrm{Maximum}\left(1,\:6\right)\\\\\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \: < x < \infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\\\\\\Not sure if I did it right[/tex]

Answer:

  x ≥ 0

Step-by-step explanation:

You want to know an appropriate limit on the domain of f(x) = 3 -x² so the function is one-to-one.

A function is one-to-one if it passes the "horizontal line test." That is, a horizontal line can intersect its graph in at most one place.

The function f(x) = 3-x² has a turning point at x=0 and is symmetrical about that line. In order to make the function be one-to-one, the domain must be restricted to one of ...

or any subset of either of those domains.

When you add one-digit number to a decade number, you will notice that the ones place digit sum is interchanged in their positions

You should know the word decade means ten. so a decade number is a number with ten digits. The digits of the decade number are

1,2,3,4,5,6,7,8,9

So write the number as

12345679

A digit number is  say 9

123456789+9

= 123456798

Therefore when a digit number is added to a decade number, the last digits interchange their positions

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The point (x, y) where the lines intersect is (0, 0).

What is lines intersect?

The empty set, a point, or another line can cross another line in Euclidean geometry. Examples of applications for identifying these circumstances and locating the intersection include computer graphics, motion planning, and collision detection.

We have the linear system:

y = r[tex]\times[/tex]x

y = s[tex]\times[/tex]x

We want to find the point where the lines intersect,

We know that

r[tex]\times[/tex]x = y = s[tex]\times[/tex]x

r[tex]\times[/tex]x = s[tex]\times[/tex]x

if r and s are different numbers (if r = s, this means that the two lines are the same line)

Then we have that the equality is only true when x = 0.

this means that the value of y is.

y = s[tex]\times[/tex]0 = r[tex]\times[/tex]0 = 0

So the point (x, y) where the lines intersect is (0, 0).

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Interest morgan will pay is $1560.

Compound interest, also known as interest on principle and interest, is the practice of adding interest to the principal amount of a loan or deposit.

Given, Morgan used a payment plan to purchase brand-new living room furnishings for $6,500. He put down $500, and over the following three years, he must pay a monthly payment of $210.00.

Hence he has to total pay = 500 + 210*12*3

The total money morgan has to pay is $8060.

Therefore total interest morgan has to pay is 8060-6500 = $1560.

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Answer:

   Domain: -∞ < x < ∞

   Range: y ≥ -2

Step-by-step explanation:

The domain of a parabola graph is all real numbers, this is written as;

      -∞ < x < ∞

The range of this parabola graph is all numbers greater than and equal to -2, since the parabola opens up and the vertex is at (-4, -2). This is written as;

      y ≥ -2

Answer:

x ≤ 14

Step-by-step explanation:

x = age of Sis

x - 6 = Martin's age

x + (x-6) ≤ 22

2x - 6 ≤ 22

2x ≤ 28

x ≤ 28/2

x ≤ 14

Answer:

4 11/12

Step-by-step explanation:

2 1/4 + 8/3

9/4 + 8/3

23/12 + 32/12

59/12

4 11/12

The equation of the tangent line to the ellipse 9x^2 + xy + 9y^2 = 19 at the point (1, 1) is y = -18x + 19, which can be found using implicit differentiation.

We can find the equation of the tangent line to the ellipse 9x^2 + xy + 9y^2 = 19 at the point (1, 1) using implicit differentiation. Firstly, we take the partial derivatives of both sides of the equation with respect to x and y, which gives us y' = (9x + y)/(9y +x). Then, we plug in the given point (1,1) into the equation for y' and solve for y'. This gives us y' = (9 + 1)/(9 + 1) = 10/10 = 1. This means that the slope of the tangent line at this point is 1. We can then use the point-slope form of a line equation, y - 1 = 1(x - 1), to find the equation for the tangent line at this point, which is y = -18x + 19.

y' = (9x + y)/(9y +x)

At the given point (1,1):

y' = (9 + 1)/(9 + 1) = 10/10 = 1

Equation of the tangent line:

y - 1 = 1(x - 1)

y = -18x + 19

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In a table of values for a pattern, P=3 when n=1; the equations P=3n and 2n+1 might represent the pattern. So the option d "Both A and C" is correct option.

In the given question, In a table of values for a pattern, P=3 when n=1; which of the following equations might represent the pattern.

a) P=3n

b) P = n+3

c) P = 2n+1

d) P = 3-n

We find the pattern we firstly observe the given diagram closely.

We firstly check which option can given P=3 when n=1.

Firstly taking the option a.

P = 3n

Now put n=1, so

P = 3

Hence, the option one is following the condition.

Now taking the option b.

P = n+3

Now put n=1, so

P = 1+3

P = 4

Hence, the option b is not following the condition.

Now taking the option c.

P = 2n+1

Now put n=1, so

P = 2(1)+1

P = 2+1

P = 3

Hence, the option c is following the condition.

Now taking the option d.

P = 3-n

Now put n=1, so

P = 3-1

P = 2

Hence, the option d is not following the condition.

Hence, the option a and c is following the condition. So the option d "Both A and C" is correct option.

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Using the Central Limit Theorem, it is found that the correct option is

a. The expected values of R and S will be equal, and the variability of R will be less than the variability of S.

What is the Central Limit Theorem?

A sufficiently high sample size from a population with a finite level of variance will result in a mean of all samples from that population that is roughly equal to the population mean, according to the CLT, a statistical theory.

                             According to the central limit theorem, the distribution of the sample means will be roughly normally distributed if you take sufficiently large random samples from a population with mean and standard deviation and replacement.

The samples in this issue were drawn from the same population, thus they all had the same expected value.

R has less variability because there are more samples available.

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Answer:

(9.22 x 10⁻⁵) + (1.078 x 10⁻⁵)

You can take 10⁻⁵ as common from both terms and add the remaining ones.

(9.22 + 1.078) x 10⁻⁵

10.298 x 10⁻⁵

Step-by-step explanation:

remember the priorities of doing the calculation operations :

1. brackets

2. exponents

3. multiplications and division

4. addition and subtraction

so,

(22 + 5) / (12 - 9) × 6

(27) / (3) × 6

and to write it without any doubt :

(27 / 3) × 6

9 × 6 = 54

why is

(27 / 3) × 6

better than

(27) / (3) × 6 ?

because if you are really taking it literally, you could understand

27 / 3 × 6

as

27 / (3 × 6)

and then the result is different.

so, many greetings to your teacher ! if what your write here was really what your teacher gave you, he/she was sloppy. in real math documentation people would write that as

((22 + 5) / (12 - 9)) × 6

our leave extra space like

(22 + 5) / (12 - 9) × 6

Answer:

Step-by-step explanation:

You just have to recall those rules  in geometry.  :/

for 1  RU =  QT

the red single marks on the segment mean those are the same length

for 2 ∠T = ∠U

the red arc means they are the same angle

for 3  QT is parallel to RU

because  of both red marks,  same length, and same angles

for 4  RQT = SRU

because both of these angles come from the same line, and have the same length and angle below

for 5  triangle QRT = RSU

because of both red marks and starting from the same line.

Answer:

hush Nikki

nnnnmm

nnnnn

The cone will fit in 4 times and the volume of the cone is 535.89 in³

A cone is a pyramid with a circular cross-section. A right cone is a cone with its vertex above the center of the base. It is also called right circular cone.

The formula of volume of a cone is given as;

V = 1/3πr²h

However, we have to calculate the volume of the sphere which is given as

V = 4/3 πr³

The volume of the ball = 4/3 * 3.14 * 8³ = 2143.57in³

The volume of the cone = 1/3 * 3.14 * 8² * 8 = 535.89 in³

The number of times it will fit into will be 2143.57 / 535.89 = 4

It will fit in 4 times

b)

The volume of the cone is 535.89in³

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On solving the provided question, Since rate multiplied by time gives output, 1/5+1/7 (t-1)=1

A formula is a statement that the values ​​of two expressions are equal. The formula essentially says that two things are equal. An equals sign or '=' indicates that. 8+2=12-2 is an example equation. According to the above formula, the left side of the formula is equal to the right side. So the equation is the statement "this is equal to that".

Doug can paint 1/5 of a room per hour, Dave can paint 1/7 of a room per hour, and the time they spend working together is t-1.

Since rate multiplied by time gives output, 1/5+1/7 (t-1)=1

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Answer:

To find the fourth term in the given sequence, we can use the formula for the nth term, which is a^n = 2 (a^n-1) + 4. We can then plug in the value of a^1, which is 3, and the value of n, which is 4, to find the fourth term:

a^4 = 2 (a^3) + 4

= 2 [2 (a^2) + 4] + 4

= 2 [2 [2 (a^1) + 4] + 4] + 4

= 2 [2 [2 (3) + 4] + 4] + 4

= 2 [2 [10] + 4] + 4

= 2 [24] + 4

= 52

Therefore, the fourth term in the sequence is 52.

Answer:

[tex]a_4 = 52\\[/tex]

Step-by-step explanation:

There is no way around this one. You just had to calculate each term until you got the fourth term.

[tex]a_2 = 2(a_1) + 4 = 2(3) + 4 = 10[/tex]

[tex]a_3 = 2(a_2) + 4 = 2(10) + 4 = 24[/tex]

[tex]a_4 = 2(a_3) + 4 = 2(24) + 4 = 52[/tex]

Using the Z- Distribution table, The answer is c) that is 0.7929.

A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions.

A normal distribution with a mean of zero and a standard deviation of one is known as the standard normal distribution. The standard normal distribution is centered at zero, and the standard deviation indicates how much a specific measurement deviates from the mean.

Following the Z-table,

P(-0.86<x<2.25) = 0.79288

The answer is c) 0.7929

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Let us answer the individual questions as per the given conditions:

1. Since the area of the bulletin board is meant to be exactly 12 square feet, the 2 pairs for length and width would be 4feet and 3feet(first pair), 6 feet and 2 feet(second pair) respectively.

2. The possible length and width of the board were determined using trial and error method to find two numbers whose product equal to 12.

3. If width of the board were to be x , and the length be 1 greater than width, we can represent the length as x+1.

4. Given the area of illustration board as 12 sq ft. the equation that represents the given situation is :  

5. The equation can be described as quadratic equation.

6. Yes, I think we can use the equation formulated to find the length and width of the bulletin board.

What is rectangle?

A quadrilateral with equal angles and parallel opposing sides is referred to as a rectangle. Around us, there are a lot of rectangle items. Two dimensions, the length and breadth, define any rectangle form.

What is the formula for calculating area of rectangle?

The formula for calculating the area of rectangle is given by:

A = L * B

where A - area of rectangle

          L - Length of the rectangle

          B - Width of the rectangle

According to the given question:

1. Using the formula for area of rectangle(length * width) , the two pairs of length and breadth can be found by finding two real positive numbers whose product equals to 12. Hence , we get 4 feet and 3 feet as first pair and 6 feet and 2 feet as second pair for length and width respectively.

2. The possible length and width pairs were determined by using the equation of area, A = L*B which is equal to 12 sq ft.

3. Since the width is given to be x by the question and x is mentioned to be    1  greater than width, hence length will be equal to x+1.

4. Using the equation for area of rectangle:

A = L * B

substituting the values as per the given conditions,

12 = x(x+1)

or, x2 + x = 12

or, x2+x-12 =0

Which is the required equation.

5. Since the highest power in the equation is 2. Hence the equation is described as quadratic equation.

6. Yes , we can use the equation formulated to find the length and width of the bulletin word, Simply solving the quadratic equation given above.

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The particle's velocity at time t = 1 seconds is equal to 3 meters per seconds.

In Mathematics, a position vs time graph can be defined as a type of graph that is used to graphically represent the distance traveled (covered) by an object from its starting position with respect to the time when it is started moving.

Generally speaking, the position of a physical object (body) in a position vs time graph is always plotted on the y-coordinate (y-axis) while time is always plotted on the x-coordinate (x-axis).

From the information provided about this particle on a position vs time graph, we have;

s =√(3 + 6t)

Where:

Substituting the given parameters into the formula, we have;

s =√(3 + 6(1))

s =√(3 + 6)

s =√9

Distance, s = 3 meters.

Now, we can determine the velocity as follows;

Velocity = distance/time

Velocity = 3/1

Velocity = 3 meters per seconds.

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