Suppose y varies directly as x, if y = 15 when x = 12, find x when y = 21.

Answer:

A

Step-by-step explanation:

imagine the shape is flipped and standing up. that's how you can compare both images.

The length of the diagonal of Stacy's ceiling using the Pythagorean Theorem and trigonometry is 35.36 ft.

(a) Using the Pythagorean Theorem:

Since the ceiling is a square, we can treat it as two right triangles. Let's call the length of the diagonal 'd'. Now, we can apply the Pythagorean Theorem (a² + b² = c²) to one of the right triangles:

a² + b² = d²
25² + 25² = d²
625 + 625 = d²
1250 = d²

Now, take the square root of both sides:

√1250 = d
d ≈ 35.36 ft

(b) Using trigonometry:

In one of the right triangles, the angle between the two sides of the square (25 ft each) is 45 degrees. We can use the tangent function (tan) to relate the angle to the side lengths:

tan(45) = opposite side / adjacent side
tan(45) = 25 / 25

Since tan(45) = 1, we have 1 = 1, which confirms the angle is 45 degrees. Now, we can use the sine or cosine function to find the diagonal:

sin(45) = opposite side / hypotenuse
sin(45) = 25 / d

OR

cos(45) = adjacent side / hypotenuse
cos(45) = 25 / d

Both functions give us the same result since the angles are 45 degrees. Solving for 'd':

d = 25 / sin(45)
d ≈ 35.36 ft

So, the length of the diagonal of Stacy's ceiling is approximately 35.36 ft using both methods.

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Answer:

wrdfrdfrDFDFDFzfsdfffq

Step-by-step explanation:

dfdfgdf d f df

Answer:

4 feet

Step-by-step explanation:

2 feet = 24 inches

6 inches = 1/2 foot

There are 12 months in a year.

12*(1/2) = 6 feet (72 inches)

OR

12*6 = 72 inches (6 feet)

If it rained 6 inches or 1/2 foot every month of a year, it would rain 6 feet or 72 inches that year.

6-2 = 4 feet

This would be 4 feet of rain more than Springfield's world record.

Answer:

For part A the answer is B (the second one)

For part B I would say there is a 50 percent chance for the chip to land on red so the students should have the last chip land on red on the 9th trial because there would be a more than fifty percent chance for the chip to land on red.

first trial 128/2 = 64,

second trial 64/2 = 32,

third trial 32/2 = 16,

fourth trial 16/2 = 8,

fifth trial 8/2 = 4,

sixth trial 4/2 = 2,

seventh trial 2/2 = 1,

eighth trial 1 chip 50/50 chance,

9th trial 1 chip 75/25 chance for the chip to land on red.

Let's check

See the word off side so it is deducted ,

General formula is ar^n-1

So correct answer is

By using function notation, you should write an equation or expression for each statement as follows;

The temperature at 12 p.m ⇒ f(12).

The temperature was the same at 9 a.m. and at 4 p.m ⇒ f(9) = f(16).

It was warmer at 9 a.m. than at 6 a.m ⇒ f(9) > f(6).

Some time after midnight, the temperature was 24 degrees Celsius. ⇒ f(t) = 24.

In Mathematics, a function simply refers to a mathematical expression which can be used for defining and showing the relationship that exist between two or more variables in a data set.

This ultimately implies that, a function typically shows the relationship between input values (x-values or domain) and output values (y-values or range) of a data set, as well as showing how the elements in a table are uniquely paired (mapped).

For the statement, "The temperature was the same at 9 a.m. and at 4 p.m." we have:

4 p.m = 12 + 4 = 16

In function notation, we have:

f(9) = f(16) or f(16) = f(9)

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Answer:

Triangle: True

Parallelogram: False, area is 63cm^2

Trapezoid: True

Step-by-step explanation:

Use area calculators on the internet to find the area of shapes.

Answer:

The last one,  14 3/4

Step-by-step explanation:

I hope this helped :)

By saving $4,000 per year for 40 years in an IRA with an 8% interest rate, you would accumulate approximately $1,031,250.

To calculate the amount you will have in 40 years, you can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value
P = Annual deposit
r = Interest rate per period
n = Number of periods

In this case, P = $4,000,
                    r = 0.08 (8%), and
                    n = 40.
Plugging in these values, the formula becomes:
FV = 4000 * [(1 + 0.08)^40 - 1] / 0.08
Calculating the expression within the brackets:
(1 + 0.08)^40 = 21.725

Now, substituting this value into the formula:
FV = 4000 * (21.725 - 1) / 0.08
FV = 4000 * 20.725 / 0.08
FV = $1,031,250
Therefore, after 40 years of saving $4,000 annually with an interest rate of 8%, you will have approximately $1,031,250 in your IRA.

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After 40 years of saving $4,000 per year with an 8% interest rate, you will have approximately $459,625.60 in your retirement account.

To calculate the future value of your retirement savings after 40 years, you can use the formula for the future value of an ordinary annuity:

\(FV = P * [(1 + r)^n - 1] / r\)

Where:

FV = Future value

P = Annual deposit

r = Interest rate per period

n = Number of periods

In this case, P = $4,000, r = 0.08 (8%), and n = 40 years.

Plugging these values into the formula:

\(FV = 4000 * [(1 + 0.08)^40 - 1] / 0.08\)

Calculating this expression will give you the future value of your retirement savings after 40 years. Let's calculate it step by step:

\(FV = 4000 * [(1.08)^40 - 1] / 0.08\)

FV = 4000 * [9.6464 - 1] / 0.08

FV = 4000 * 8.6464 / 0.08

FV = 459,625.60

Therefore, after 40 years of saving $4,000 per year with an 8% interest rate, you will have approximately $459,625.60 in your retirement account.

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Answer:

270 is the answer

-Sumin <3

Answer:

SU = 5

SYW = 39°

WXY = 24°

Step-by-step explanation:

The measurements are SU = 5 units, m ∠ SYW = 39° and m ∠ WXY = 24°

A triangle is defined as a two-dimensional shape with three sides, three interior angles, and three vertices.

Given that ΔWXY is shown, all angles have different measures. Point S is equidistant from each side of the triangle. Lines are drawn from each point of the triangle to Point S. Congruent lines are also drawn from each side to the point to form right angles and form lines segments V S, T S, and U S. Angle S Y U is 39°, point S is equidistant from the sides of ΔWXY

According to question,

m ∠ SYW = m ∠ SYX

So, m ∠ SYW = 39°

Also, m ∠ WXT = m ∠ YXT

So, m ∠ WXY = m ∠ WXT + m ∠ YXT

m ∠ WXY = 24°

And, SU = ST = SV

So, SU = 5 units

Hence, The measurements are SU = 5 units, m ∠ SYW = 39° and m ∠ WXY = 24°

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Answer:

Y=(-1/2)x+9/2

Step-by-step explanation:

For straight lines y=mx+c

m=gradient

Find the gradient first-m=(y2-y1) /(x2-x1)

Take the points M and N and substitute in the equation

m=(5-2)/(-1-5)

m=-1/2

Gradient of line MN×gradient of perp line =-1

There fore gradient of perp line =2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the function

f(x) = 2x³ -3x²+ 7

putting x=-1 to find f(-1)

f(-1) =  2(-1)³ -3(-1)²+ 7

      = -2 + 3 + 7

      = 8

putting x=1 to find f(1)

f(1) =  2(1)³ -3(1)²+ 7

      = 2 - 3 + 7

      = 6

putting x=2 to find f(2)

f(2) =  2(2)³ -3(2)²+ 7

      = 16 - 12 + 7

      = 11

Therefore,

(a) The package takes approximately 4.47 seconds to reach the ground.(b) The package hits the ground with a speed of approximately 43.81 m/s downward.(a) The average acceleration of the ball during the time it is in contact with the ground is 0 m/s². (b) The average acceleration is neither up nor down; it is zero.

(a) To solve part (a), we can use the equation of motion for free fall:

\(\[s = ut + \frac{1}{2}gt^2\]\)

where:

- s is the vertical displacement (distance) covered by the package (98 m in this case)

- u is the initial vertical velocity (0 m/s for the package at the moment it is dropped)

- g is the acceleration due to gravity (-9.8 m/s^2, assuming we're near the surface of the Earth)

- t is the time taken for the package to reach the ground (what we're trying to find)

Plugging in the values, we get:

\(\[98 = 0 \times t + \frac{1}{2}(-9.8) t^2\]\)

Simplifying the equation, we have:

\(\[4.9t^2 = 98\]\)

Dividing both sides by 4.9, we get: \(\[t^2 = 20\]\)

Taking the square root of both sides, we find: \(\[t = \sqrt{20} \approx 4.47 \, \text{s}\]\)

Therefore, the package takes approximately 4.47 seconds to reach the ground.

(b) To calculate the speed at which the package hits the ground, we can use the equation:

\(\[v = u + gt\]\)

where:

- v is the final velocity (what we're trying to find)

- u is the initial velocity (0 m/s, as the package was dropped from rest)

- g is the acceleration due to gravity (-9.8 m/s²)

- t is the time taken for the package to reach the ground (4.47 s, as calculated in part a)

Plugging in the values, we get: \(\[v = 0 + (-9.8) \times 4.47\]\)

Simplifying the equation, we find:\(\[v \approx -43.81 \, \text{m/s}\]\)

The negative sign indicates that the package is moving downward. So, the package hits the ground with a speed of approximately 43.81 m/s in the downward direction.

Note: The units for time (a) are seconds, and the units for speed (b) are meters per second.

(a) The average acceleration of the ball during the time it is in contact with the ground can be determined using the following equation:

\(\[a = \frac{{\Delta v}}{{\Delta t}}\]\)

where:

- a represents the average acceleration

- \(\(\Delta v\)\) is the change in velocity

- \(\(\Delta t\)\) is the time interval

In this case, the ball falls to the ground, so its initial velocity \((\(v_i\))\) is 0 m/s. The final velocity \((\(v_f\))\) can be calculated using the equation of motion:\(\[v_f = v_i + at\]\)

Since the ball stops upon hitting the ground, the final velocity is also 0 m/s. Therefore, we have:

\(\[0 = 0 + a \times 0.019\]\)

Simplifying the equation, we find that the average acceleration is:

\(\[a = \frac{0}{0.019} = 0 \, \text{m/s}^2\]\)

(b) The average acceleration of the ball is 0 m/s^2. Since it is in contact with the ground for a very short time before stopping, the ball's acceleration can be considered negligible or zero.

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Answer:

Yes

Step-by-step explanation:

We have two properties for our question :

(4, 27)

y = 3x + 15

We are being asked whether the point (4, 27) is a solution of y = 3x + 15

So how do we figure this out? Well, what we have to know first that (4, 27)  represents a variable, 4 which is the run on the graph, represents x in a solution. And 27 which is the rise on the graph, represents y in the solution. So when asking for a solution with two points, all we must do is substitute x and y for the two coordinates.

y = 3x + 15

y = 27 and x = 4

27 = 3(4) + 15

27 = 12 + 15

27 = 27

Since this equation is true with the respected variables, therefore signifies that (4,27) is a solution of y = 3x + 15

Answer:

yeee

Step-by-step explanation:

Answer: 24/35

Step-by-step explanation:

8/7 x 3/5 = 24/35

THIS IS THE MOST SIMPLIFIED FORM!

HOPE IT HELPS!

Answer:

-7x² + x + 3

I do not know if you need to show work but I just knew this

Answer:

2x^2-4x+2

Step-by-step explanation:

depends what the question is telling you to do

if its askin you to simplify this is the answer

Answer:

this is impossible

Step-by-step explanation:

Answer:

The answer is 64 degrees

Step-by-step explanation:

D on edg

Answer:

D- 64 degrees

Step-by-step explanation:

Since the probability is less than 5%, which is the conventional threshold for unusual results, we can conclude that the time of 14.5 seconds is unusual for this school's 100 meter sprint. Therefore, the correct answer is D) −1.5; unusual.

To solve this question, we need to calculate the z-score using the formula:

z = (x - μ) / σ

Where x is the individual time, μ is the mean time, and σ is the standard deviation.

Substituting the given values, we get:

z = (14.5 - 17.6) / 2.1 = -1.48

Since the calculated z-score is negative, we need to refer to the standard normal distribution table to find the corresponding probability. Looking up the z-score -1.48 in the table, we find that the probability is 0.0694 or approximately 6.94%.

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\(y \geqslant - x + 3\)

\(y < \frac{1}{2} x + 3 \\ \)

now just put the coordinates of point ( 1 , 1 ) in the above inequalities and check if they correct or wrong :

\(1 \geqslant - 1 + 3\)

\(1 < \frac{1}{2} (1) + 3 \\ \)

So :

\(1 \geqslant 2\)

\(1 < 3.5\)

1 is lower than 3.5 of course but geuss what ?

Is 1 higher than 2 or equal to 2 ? Nope not at all

Thus the correct answer would be :

" no , it is not a solution "

(4) The series diverges by the Comparison Test. Each term is greater than that of a divergent geometric series.

To determine whether the series converges or diverges, we can use the Comparison Test.
First, we can simplify the series by dividing both the numerator and denominator by n:
[Infinity] (4 + 1/n) / (3 - 5/n)

As n approaches infinity, both the numerator and denominator approach 4/3, so we can write:
[Infinity] (4 + 1/n) / (3 - 5/n) = [Infinity] 4/3

Since the harmonic series [Infinity] 1/n diverges, we can conclude that the original series diverges as well.
Therefore, the correct answer is:
4. The series diverges by the Comparison Test. Each term is greater than that of a divergent geometric series.

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For a continuous random variable x, the probability of x taking on a specific value a is zero. This is due to the infinite number of possible values that x can take on within its range.

In the case of a continuous random variable, the probability density function (PDF) describes the likelihood of x taking on different values. Unlike discrete random variables, which can only take on specific values with non-zero probabilities, a continuous random variable can take on an infinite number of values within a given range. Therefore, the probability of x being equal to any specific value, such as a, is infinitesimally small, or mathematically speaking, it is equal to zero.

To understand this concept, consider a simple example of a continuous random variable like the height of individuals in a population. The height can take on any value within a certain range, such as between 150 cm and 200 cm. The probability of an individual having exactly a height of, say, 175 cm is extremely low, as there are infinitely many possible heights between 150 cm and 200 cm.

Instead, the probability is associated with ranges or intervals of values. For example, the probability of an individual's height being between 170 cm and 180 cm might be nonzero and can be calculated using integration over that interval. However, the probability of having an exact height of 175 cm, as a single point on the continuous scale, is zero.

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The length of top enclose r s end enclose = √(4² + 5²) = √(16 + 25) = √(41) = approximately 6.4 inches.

The length of top enclose r s end enclose can be determined using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Since top enclose p s end enclose is a diameter of the circle, it is the hypotenuse of a right triangle formed by top enclose p s end enclose, top enclose p q end enclose and top enclose p r end enclose. Thus, the length of top enclose r s end enclose is the square root of the sum of the squares of the lengths of the other two sides, which are 4 inches and 5 inches.

In other words, the length of top enclose r s end enclose = √(4² + 5²) = √(16 + 25) = √(41) = approximately 6.4 inches.

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Answer:

  x = -1, 1

Step-by-step explanation:

The solutions to f(x) = g(x) are the x-values where the two functions have the same value.

The functions are both 1 when x = -1.

The functions are both -7 when x = 1.

The two solutions are x = -1, x = 1.

Answer:

y = 28

Step-by-step explanation:

0.5y + y/ 3 = 0.25y + 7

1.5y / 3 = 0.25y + 7

y/2 = 0.25y + 7

y = ( 0.25y + 7)*2

y = 0.5y + 14

y - 0.5y = 14

0.5y = 14

y = 14/0.5

y = 28

Answer:

(5+3) times 2 then that would be 16

Step-by-step explanation:

You are just multiplying everything inside of the Parentheses after you add them together.

Here is an easy way to remember the order of operation:

PEMDAS

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Hope that helps

The domain of the relation in the graph is:

{-2, -1, 0, 2, 5}

A relation maps elements from one set (the domain) into elements from another set (the range).

Such that the domain is represented in the horizontal axis.

In the graph, we can see the points:

{(-2, -3), (-1, -1), (0, 3), (2, 1), (5, 2)}

The domain is the set of the first values of these points, then the domain is:

{-2, -1, 0, 2, 5}

The correct option is the first one.

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The value of a = 3

The value of b = 5

The Riemann sum becomes more accurate as the number of subintervals increases and the width of each subinterval decreases. In the limit as the number of subintervals goes to infinity and the width of each subinterval goes to zero, the Riemann sum converges to the exact value of the integral.

we have Δx = 2 / n

then from formula

2 / n = b - a / n

a = 3

b = 3 + 2

= 5

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