ROLLER COASTERS The height of a roller coaster is 157.5 feet. If the roller
coaster's shadow is 60 feet long, how long will a person's shadow be if the
person is 5 feet 3 inches tall?

Answer:

acute

Step-by-step explanation:

this is an acute triangle because all angles are less than 90 degrees

it is not obtuse because no angle is over 90 degrees

it is not equiangular because the angles are not equal to each other

and it is not right because there is no right angle

Acute

Triangles can be classified by the size of their angles.

Angle Classification

Angles can be classified into 3 sizes: acute, right, and obtuse.

Triangle Classification

Triangles are classified by their largest angle. If the largest angle is obtuse, then it is an obtuse triangle. If there is a right angle, then it is a right triangle. If the largest angle is an acute angle, then it is an acute triangle. Finally, there is one special classification that technical falls under acute angles. If all of the angles are equal (meaning they are all 60°), then it is an equiangular triangle.

The triangle in the picture has 3 angles that are all under 90°. The largest angle is 76°. Since this is an acute angle, it is an acute triangle.

On solving the provided question, we can say that 1 degree = 3600 arc seconds and 1 degree = 60 arc minutes.

A 160 degree angle is measured in arc minutes, often known as arcmin, arcmin, arcmin, or arc minutes (represented by the sign '). One minute is equal to 121600 revolutions, or one degree, hence one degree equals 1360 revolutions (or one complete revolution). A degree, also known as a complete angle of arc, angle of arc, or angle of arc, is a unit of measurement for plane angles in which a full rotation equals 360 degrees. A degree is sometimes referred to as an arc degree if it has an arc of 60 minutes. Since there are 360 degrees in a circle, an arc's angles make up 1/360 of its circumference.

1 degree = 3600 arc seconds

1 degree = 60 arc minutes

A. 2 degree 18'36 = 2 + 18/60 + 36 / 2600 = 231 / 100 degree

B. 36 ′ 18 ′′ = 36/60 + 18/2600 = 121 / 200 degree

C. 7 degrees 59′ 59′′ = 7 + 59 / 60 + 59 / 3600 = 28799 / 3600 degree

D. 1' = 1/60 degree

F. 1" = 1/3600 degree

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Length + width = half the perimeter

66/2 = 33 feet

Length  +  width = 33 feet

List the factors of 260: 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130 and 260.

Find the two factors that when added together equal 33:

13 + 20 = 33

The dimensions are 13 feet by 20 feet

Answer:

v = \(\frac{600-60t}{t}\)

Step-by-step explanation:

Let the trains A and B meet each other after t hours after the departure of a train A.

Distance traveled by train A in t hours \((d_1)\) = Speed × time

                                                                      = 60 × t

Distance traveled by train B \((d_2)\) = v × t

Since, Distance between the cities A and B = 600 km

\(d_1+d_2=600\)

60t + vt = 600

vt = 600 - 60t

v = \(\frac{600-60t}{t}\)

Therefore, expression that the represents the relation between v and t will be,

v = \(\frac{600-60t}{t}\)

Answer:

96% percent and fraction is 24/25

Answer: Down below

Step-by-step explanation:

64 % = 16 / 25

21 / 50 = 0. 42

9 / 25 = 36 %

2 / 5 = 40 %

/ = divide okay

The present value of the installment plan is approximately $2,939,487.33. The winner should choose the one-time payment of $1,800,000 instead.

The present value of the installment plan, we need to determine the current value of the future cash flows, taking into account the 8% annual interest rate. Each annual installment of $200,000 is received over a period of 20 years.

Using the formula for calculating the present value of an ordinary annuity, we have:

Present Value = Annual Payment × [1 - (1 + interest rate)^(-number of periods)] / interest rate

Plugging in the values, we get:

Present Value = $200,000 × [1 - (1 + 0.08)^(-20)] / 0.08

Present Value ≈ $2,939,487.33

The present value of the installment plan is approximately $2,939,487.33.

In this case, the one-time payment option is $1,800,000. Comparing this amount to the present value of the installment plan, we can see that the present value is significantly higher. Therefore, the winner should choose the one-time payment of $1,800,000 instead of the installment plan. By choosing the one-time payment, the winner can immediately receive a larger sum of money and potentially invest it at a higher rate of return than the estimated 8% annual interest rate.

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The expected count of women who ranked the dark-skinned model as the most beautiful is 100.

Since there are three models, we would expect 100/3 = 33.33% of the women to have ranked each model as the most beautiful if there were no relationship between skin color and beauty judgements. Thus, we can calculate the expected count of women who ranked the dark-skinned model as the most beautiful as follows:

Expected count = 300 * 33.33% = 100

Therefore, we can expect that 100 women out of the 300 sampled would have ranked the dark-skinned model as the most beautiful if there were no relationship between skin color and beauty judgements. The observed count of 55 women who ranked the dark-skinned model as the most beautiful is higher than the expected count, which suggests that there may be a relationship between skin color and beauty judgements. However, further statistical tests would be needed to confirm this.

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Answer:

The histogram is presented in the second attached image to this solution.

Step-by-step explanation:

Histogram is a representation that uses bars to represent numerical distribution. It is similar to the bar chart but it is the histogram's area that corresponds to the frequency of the distribution instead of just the heights of the bars.

In constructing a histogram, we first divide the entire range of values into a series of intervals (called bins) and then count how many values fall into each interval, that is, the frequench of the variables in each range of values.

This question asks us to use 10 bins for this question.

The table of range of variables and frequencies used in the plotting of the histogram is presented in the first attached image to this solution and the histogram is presented in the second attached image to this solution.

Hope this Helps!!!

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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Answer:

let,

x=ky

y=39 when x=7 so,

7=39k

or, k=7/39

now, when x=22

22=7y/39

or, y=39×22/7

or, y=858/7

or, y=122.57 (rounded to the nearest hundredth)

Answer:

3.

C. The domain is (1,+[infinity]) and the range is (-1,+[infinity])

4.

B. 6

5.

A. (-[infinity], 3)

Step-by-step explanation:

The Linear function has one independent and one dependent variable. The value of dependent variable can be found by taking the equation equals to 0. The domain function is set to analyse the range. The range can be set as -1 to 1. Any number between this is acceptable but outside this is not considered in the domain.

Answer:

Answer:

lol

Step-by-step explanation:

The simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is 729x^6 - V^2.

In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.

To simplify the expression using the given values, we substitute \(U = 3x^3\)and V = y + 1 into the original expression:

\(81x^6 - (y + 1)^2\)

Replacing U and V:

\(81(3x^3)^2 - (V)^2\)

Simplifying:

\(81 \times 9x^6 - V^2\)

\(729x^6 - V^2\)

Therefore, the simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is\(729x^6 - V^2.\)

In this way, we can represent the original expression in a simplified form using the assigned values for U and V.

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Consider the expression: \(81x^6 - (y + 1)^2\)

If\(U = 3x^3\) and V = y + 1, what is the simplified form of the expression in terms of U and V?

In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.

The derivative dy/dx can be found by implicitly differentiating the equation cot(y) = 8x - 5y. The result is dy/dx = (8 + 5cot(y))/(5 + 8xcsc^2(y)).

To find the derivative dy/dx using implicit differentiation, we differentiate both sides of the equation cot(y) = 8x - 5y with respect to x. The left side of the equation involves the function cot(y), which is the cotangent of y. The right side involves the variables x and y.

Differentiating cot(y) with respect to x requires the use of the chain rule. The derivative of cot(y) is -csc^2(y) * dy/dx. Differentiating 8x with respect to x gives 8, and differentiating -5y with respect to x gives -5 * dy/dx.

Combining these results, we have -csc^2(y) * dy/dx = 8 - 5 * dy/dx.

Next, we rearrange the equation to solve for dy/dx:

dy/dx + 5 * dy/dx = 8 + csc^2(y).

Factoring out dy/dx on the left side of the equation gives us:

(1 + 5) * dy/dx = 8 + csc^2(y).

Simplifying further, we have:

6 * dy/dx = 8 + csc^2(y).

Finally, we can solve for dy/dx:

dy/dx = (8 + csc^2(y))/6.

This is the derivative dy/dx obtained through implicit differentiation of the given equation cot(y) = 8x - 5y. The resulting derivative involves both x and y variables, and the trigonometric function csc(y) (the cosecant of y).

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Geometric series is convergent if the |r|<1 where r is the common ratio.

Let Sn=∑ni=0(−3/4)i then

Sn=(−3/4)n+1−1(−3/4)−1

Now take n→∞ then

Sn→0−1(−3/4)−1=4/7

because |−3/4|<1 and so (−3/4)n→0. Now note that your sum is

lim ∑i=1n+1(−3)i−14i=lim 14∑i=1n+1(−3)i−14i−1=1/4.lim Sn=1/7.

Geometric series: A geometric series is the result of adding together geometric sequences indefinitely. Depending on the sequence given to us, such infinite sums can either be finite or infinite. A series is considered to be convergent if the partial sums gravitate to a certain value, also known as a limit. In contrast, a divergent series is one whose partial sums do not reach a limit. Divergent series frequently reach, reach, or avoid a particular number.

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Answers:

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

Explanation:

A function has any given input lead to exactly one output.

Relation 1 has the input "paper" lead to more than one output, which are the values 9 and -3. Therefore, relation 1 is not a function.

Relations 2 and 4 are similar stories.

---------

In contrast, relation 3 has each input lead to exactly one output, which is why we have a function here.

Put another way: a function cannot have the x coordinates repeat, but the y coordinates can repeat.

Yes, 1212 divided by 3 = 404.

Answer:

Step-by-step explanation:

Sum the digits. The result must be divisible by 3.

1+2+1+2=6

6:3=2

YES

Answer:

Step-by-step explanation:

h(x) = 2

Look at the picture.

h(-1) = 2 and h(-3) = 2

Answer:

The lines on the graph are too faint to read.  But the question wants to know what value of x is required for the function to return a 2 in the calculation.  We don't have the equation, but the graph will tell us those points.  Find all cases in which the graph passes through a line drawn horizontally through the y = 2 mark.  I can't read the graph to find them.

Step-by-step explanation:

Answer:

181

Step-by-step explanation:

62+61+58=181

The Estimation is 62, 61 and 58 is 181.

In order to avoid complex calculations, estimation of numbers refers to the process of estimating/approximating or rounding down the numbers when the value is used for some other purpose. The words accurate and estimation have different meanings.

Given:

62, 61, and 58.

Now, the sum is found by adding the three number

= 62 + 61 + 58

= (60+ 2) + (60+ 1) + (50+ 8)

= 60+ 60 + 50 + 2 + 1 + 8

= 170 + 11

= 181

Hence, the estimation is 181.

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There are 72 different sums that can be obtained by rolling the die, spinning the spinner, and picking a card.

To determine the number of different sums possible, we need to consider the outcomes of rolling the die, spinning the spinner, and picking a card.

Let's analyze each component separately:

1. Rolling the die: The die has 6 sides, numbered 1 to 6. Therefore, there are 6 possible outcomes when rolling the die.

2. Spinning the spinner: The spinner has 6 sections labeled 1 to 6. Again, there are 6 possible outcomes when spinning the spinner.

3. Picking a card: The card has two options, either 6 or 7. Thus, there are 2 possible outcomes when picking a card.

To find the total number of different sums, we need to multiply the number of outcomes for each component. Therefore, the total number of different sums is obtained by multiplying 6 (die outcomes) by 6 (spinner outcomes) by 2 (card outcomes), resulting in 6 * 6 * 2 = 72 different possible sums.

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Answer:

Hey there!

Angela will have 7+2, or 9 cups of rice.

Let me know if this helps :)

Answer:

7/2

Step-by-step explanation:

Answer:

m/2 or 1/2m

Step-by-step explanation:

Let's call the numbers x and y.
The ratio is x:y

Now, if we multiply them by the same number (let's call it z), we have :

zx:zy

And since they are both multiplied by z, we can simplify it and get x:y (basically reversing the step) and the ratio will stay the same

So no matter what number you multiply, as long as both of them are multiplied to the same number, you will be able to get an equivalent ratio. (Apologies if it doesn't make any sense..)

Answer:

\(130.2845\leq h\leq 137.7245\)

Step-by-step explanation:

Given an inequality that relates the height h, in centimeters, of an adult female and the length f, in centimeters, of her femur by the equation

\(|h - (2.47f + 54.10)| \leq 3.72\)

If an adult female measures her femur as 32.25 centimeters, we can determine the possible range of her height by plugging f = 32.25cm into the modelled equation as shown:

\(|h - (2.47(32.25) + 54.10)| \leq 3.72\\|h - (79.9045 + 54.10)| \leq 3.72\\|h - (134.0045)| \leq 3.72\\\)

If the modulus function is positive then:

\(h - 134.0045 \leq 3.72\\h \leq 3.71+134.0045\\h\leq 137.7245\)

If the modulus function is negative then:

\(-(h - 134.0045) \leq 3.72\\-h+134.0045 \leq 3.72\\-h\leq 3.72-134.0045\\-h\leq -130.2845\\\)

multiply through by -1

\(-(-h)\geq -(-130.2845)\\h\geq 130.2845\\130.2845\leq h\)

combining the resulting inequalities, the estimate of the possible range of heights will be \(130.2845\leq h\leq 137.7245\)

Answer:

$3 because if they are having a product at 4 dollars and lose a Dollar for ever one sold then $4-$1 = $3

Answer:

a. 9m3n3

b. 8k3m2n

c. km2n

d. 5k3n

Step-by-step explanation:

Terms are just the things you multiply and add in an equation.

Answer:

True

Step-by-step explanation:

Parallel line do not touch, perpendicular are ones that intersect

Answer:

True

Step-by-step explanation:

These are what parallel lines would look like: l   l

Answer:

Step-by-step explanation:

\(7x=4x^{2} -1\)

\(7x - (4x^{2} -1)= 0\)

\(7x - 4x^{2} +1 = 0\)

\(-4x^{2} +7x+1=0\)

\(4x^{2} -7x-1=0\)

use the quadratic formula: \(x = \frac{ -b \frac{+}{-} \sqrt{b^{2} -4ac }}{2a}\)

a = 4  b = -7  c = -1

·\(x = \frac{-(-7)\frac{+}{-} \sqrt{(-7)^{2}-4 times 4(-1)} }{2 times 4}\)

\(x = \frac{7\frac{+}{-} \sqrt{49-16} }{8}\)

\(x = \frac{7\frac{+}{-} \sqrt{65} }{8}\)

hope this helped!

mark me brainliest :D

Answer:15

Step-by-step explanation:

A ladder is resting against a wall.The top of the ladder touches the wall at a height of 9 feet.Find the length of the ladder if the length is 3 feet more than its distance from the wall.

Let the distance of the ladder from the wall be x

The length of the ladder = x+3

The ladder touches the wall at a vertical height of 9 feet.

(x+3)^2 = x^2 + 9^2 ( using the pythagoras theorem

x^2 + 6x+ 9 = x^2 + 81

x^2- x^2 +6x = 81-9

6x= 72

x= 12

Therefore the length of the ladder will be x+3 = 12 + 3 =15 Answer.

Answer: He sold 19 cars last month

Step-by-step explanation:

set up the equasion: 1352.35 + 133.04x = 2880.11

x is the number of cars sold

solve: 2880.11 - 1352.35 is 2527.76

133.04x = 2527.75

2527.75 divided by 133.04 is 19

x = 19