A kite flying in the air has a 78-string attached to it, and the string is pulled taut. The angle of elevation of the kite is 52°. Find the height of the kite. Round
your answer to the nearest tenth.

The value of x is 4.

To determine the value of x, we can use the concept of similarity between shapes.

Similar shapes have corresponding sides that are proportional to each other.

Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:

5/x = 30/24

To solve for x, we can cross-multiply:

30 · x = 5 · 24

30x = 120

Dividing both sides of the equation by 30:

x = 120 / 30

x = 4

Therefore, the value of x is 4.

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The reasonable estimate would be 25

We have to solve this using the rule of 3

9 out of 30 members said that they run more than 5 days a week.

We will form the equations

when 9 ran = 30 menbers

when n ran = 84 members

we will then cross multiply

84 x 9 = 30 x n

n = 25.2

When we round this, the reasonable estimate would be 25

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Complete question

Freemont Run Club surveyed a random sample of 30 of their members about their running habits. Of the members surveyed, 9 said that they run more than 5 days a week.

There are 84 Freemont Run Club members.

Based on the data, what is the most reasonable estimate for the number of Freemont Run Club members who run more than 5 days a week?

The graph of the function f(x) = 5(2)^x is an upward-sloping exponential curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing the x-axis.

The function f(x) = 5(2)^x represents exponential growth. Let's analyze its graph.

As x increases, the value of 2^x grows exponentially. Multiplying it by 5 further amplifies the growth. Here are a few key points to consider:

When x = 0, 2^0 = 1, so f(0) = 5(1) = 5. This is the y-intercept of the graph, meaning the function passes through the point (0, 5).

As x increases, 2^x grows rapidly. For positive values of x, the function will increase quickly. As x approaches positive infinity, 2^x grows without bound, resulting in the function also growing without bound.

For negative values of x, 2^x approaches zero. However, the function is multiplied by 5, so it will not reach zero. Instead, it will approach y = 0, but the graph will never touch or cross the x-axis.

The function is always positive since 2^x is positive for any value of x, and multiplying by 5 does not change the sign.

Based on these observations, we can conclude that the graph of f(x) = 5(2)^x will be an exponential growth curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing or touching the x-axis.

The graph will have a smooth curve that rises steeply as x increases. The rate of growth will be determined by the base, in this case, 2. The larger the base, the steeper the curve. The function will approach but never reach the x-axis as x approaches negative infinity.

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The percentage of the sample selected at random that would be expected to be afflicted by stress would also be = 80%

The percentage of a data set is when part of the data is represented per 100 with a symbol of %.

It was stated in the question that 80% of Americans report being afflicted by stress.

Therefore when a sample is randomly selected from an American population, the percentage that is expected to be afflicted by stress should also be 80%.

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Answer:

it would be 2

Step-by-step explanation:

Answer:

smaller than the sum of the other two sides

In this case less than 21

Step-by-step explanation:

Triangle Inequality Theorem

Answer:

balls

Step-by-step explanation:

lol hahahahahahahahhahahahahahhahahahahahahahahhahah

Answer:

two balls for every one paddle

Step-by-step explanation:

why are there two of these?
Answer:

53.9

Step-by-step explanation:

89% of all houses have garages and 48% have garages and pools. We try to find houses with a pool that have a garage. Let's assume that there are 100 houses in her neighborhood. then 89 of them have garages and 48 of them have garages and pools. 48 / 89 = about 0.5393. Conver this to percent and we get 53.9

You have the following expression:

(5x + 7) - (x + 2)

in order to simplify the previous expression, eliminate parenthesis and take into account that if a parenthesis is preceeded by a minus sign, when you elminate th eparenthesis the sign inside change to the opposite, just as follow:

(5x + 7) - (x + 2) =

5x + 7 - x - 2 =

5x - x + 7 - 2 =

4x + 5

Hence, the simplified expression is 4x + 5

When x = 13, the equation that is true is option D) 5(x - 9) = 20.

To determine which equation is true when x = 13, we can substitute the value of x into each equation and see which equation holds true. Let's go through each option:

A) 3(18 - x) = 67

Substituting x = 13:

3(18 - 13) = 67

3(5) = 67

15 = 67

The equation is not true when x = 13. Therefore, option A is false.

B) 4(9x) = 23

Substituting x = 13:

4(9*13) = 23

4(117) = 23

468 = 23

Again, the equation is not true when x = 13. Therefore, option B is also false.

C) 2(x - 3) = 7

Substituting x = 13:

2(13 - 3) = 7

2(10) = 7

20 = 7

Once again, the equation is not true when x = 13. Therefore, option C is false as well.

D) 5(x - 9) = 20

Substituting x = 13:

5(13 - 9) = 20

5(4) = 20

20 = 20

Finally, the equation is true when x = 13. Therefore, option D is true.

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Note: the translated questions is

X = 13, which equation is true?

Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

(-1, 6), (1, -6), (-2, 3), (2, -3)

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

Answer:

14

Step-by-step explanation:

cuz that's the answer and I'm the smartest person on urt

The key here is to not worry too much and just follow PEMDAS.

Here we have the expression \((5\cdot 7)^2\).  Following PEMDAS, we complete the expression inside the parentheses first, or \(5\cdot 7 = 35\). This gives us \((35)^2\) or just \(35^2.\)

Hope this helps.

Answer:

0-3=-3

Step-by-step explanation:

The factors of the polynomial function f(x) must be x, x + 6  and x + 3

From the question, we have the following parameters that can be used in our computation:

The graph (see attachment)

On the graph, we have the zeros of the function to be

x = -6, x = -3 and x = 0

Set the equations to 0

So, we have the following representation

x + 6 = 0, x + 3 = 0 and x = 0

This means that the factors are

x, x + 6  and x + 3

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Answer:

y = 4\(\sqrt{5}\) , ? = 10

Step-by-step explanation:

using Pythagoras' identity on the smallest right triangle

x² = 4² + 2² = 16 + 4 = 20 ( take square root of both sides )

x = \(\sqrt{20}\) = \(\sqrt{4(5)}\) = \(\sqrt{4}\) × \(\sqrt{5}\) = 2\(\sqrt{5}\)

using Pythagoras' identity on the middle right triangle

y² = 8² + 4² = 64 + 16 = 80 ( take square root of both sides )

y = \(\sqrt{80}\) = \(\sqrt{16(5)}\) = \(\sqrt{16}\) × \(\sqrt{5}\) = 4\(\sqrt{5}\)

using Pythagoras' identity on the largest right triangle

?² = x² + y² = (2\(\sqrt{5}\) )² + (4\(\sqrt{5}\) )² = 20 + 80 = 100

Take square root of both sides

? = \(\sqrt{100}\) = 10

Answer:

C) More than 1 solution

Step-by-step explanation:

\(3y-12x=18\\2y-8x=12\\\\3(y-4x)=18\\2(y-4x)=12\\\\y-4x=6\\y-4x=6\\\\6=6\)

Therefore, since both sides will always be equal to each other, then there are infinitely many solutions (so C is the best choice)

\(\sf\sin^2 150^\circ + \sin^2 60^\circ = 1 \\\)

Step 1: Convert degrees to radians:

\(\sf\sin^2 \left(\frac{150\pi}{180}\right) + \sin^2 \left(\frac{60\pi}{180}\right) = 1 \\\)

Step 2: Simplify the expressions using the trigonometric identity:

\(\sf\sin^2 \left(\frac{\pi}{6}\right) + \sin^2 \left(\frac{\pi}{3}\right) = 1 \\\)

Step 3: Recall the values of sine for angles \(\sf \frac{\pi}{6} \\\) and \(\sf \frac{\pi}{3} \\\):

\(\sf\left(\frac{1}{2}\right)^2 + \left(\frac{\sqrt{3}}{2}\right)^2 = 1 \\\)

Step 4: Evaluate the squares and simplify further:

\(\sf\frac{1}{4} + \frac{3}{4} = 1 \\\)

Step 5: Combine the fractions:

\(\sf\frac{4}{4} = 1 \\\)

Step 6: Simplify the fraction:

\(\sf1 = 1 \\\)

Thus, the equation \(\sf \sin^2 150^\circ + \sin^2 60^\circ = 1 \\\) is verified and true.

\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

For p(x<62) and p(x>68), we can use the z-score formula to calculate the probability.

p(x<62), the z-score formula is (62-64)/18 = -0.11.

p(x>68), the z-score formula is (68-64)/18 = 0.22.

The rest answer are mentioned below with calculation.

It is (X-μ)/σ, where X is the value we are evaluating, μ is the mean of the population, and σ is the standard deviation of the population.

For the first two questions, p(x<62) and p(x>68), we can use the z-score formula to calculate the probability. The z-score formula is (X-μ)/σ, where X is the value we are evaluating, μ is the mean of the population, and σ is the standard deviation of the population.

For the first question, p(x<62), the z-score formula is (62-64)/18 = -0.11. This means that the probability of x being less than 62 is 0.3767 (from the z-score table).

For the second question, p(x>68), the z-score formula is

(68-64)/18 = 0.22.

This means that the probability of x being greater than 68 is 0.5987 (from the z-score table).

For the third question, the probability that a randomly selected pregnancy lasts less than 260 days can be calculated using the z-score formula.

The z-score formula is (260-266)/16 = -0.375. This means that the probability of a randomly selected pregnancy lasting less than 260 days is 0.3296 (from the z-score table).

For the fourth question, the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less can be calculated using the Central Limit Theorem.

Since the sample size is 20, the standard deviation of the sample is

16/√(20) = 4.

The z-score formula is (260-266)/4 = -1.5.

This means that the probability of a random sample of 20 pregnancies having a mean gestation period of 260 days or less is 0.0668 (from the z-score table).

For the fifth question, the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less can be calculated using the Central Limit Theorem.

Since the sample size is 50, the standard deviation of the sample is

16/√(50) = 1.83

The z-score formula is (260-266)/1.8 = -3.3.

This means that the probability of a random sample of 50 pregnancies having a mean gestation period of 260 days or less is 0.0062 (from the z-score table).

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Quartic equations are equations that have an highest exponent of 4

The table entries are given as:

Year 2001 2002 2003 2004 2006 2007

Cars 705 1716 2803 3515 2742 1081

Represent the table as:

Year 1       2       3      4       6         7

Cars 705 1716 2803 3515 2742 1081

A quartic equation is represented as:

\(y = ax^4 + bx^3 + cx + d\)

Using a graphing calculator; we plot the table entries on a graph.

From the graphing calculator, the quartic equation that represents the table is:

\(y = 6.04x^4 - 135.32x^3 + 698.78x^2- 228.48x + 363.95\)

Rewrite as a function

\(P(x) = 6.04x^4 - 135.32x^3 + 698.78x^2- 228.48x + 363.95\)

Hence, the equation that represents the table is:

(c) \(P(x) = 6.04x^4 - 135.32x^3 + 698.78x^2- 228.48x + 363.95\)

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Answer

(5/2, 9/2)

Step-by-step explanation

We need to use the midpoint formula.

The formula is: (x1+x2) / 2 , (y1+y2) / 2

Answer:

(2.5, 4.5)

Step-by-step explanation:

Midpoint of (4, 6) and (1, 3):

(x1+x2/2 , y1+y2/2)

(4+1/2 , 6+3/2)

(5/2 , 9/2)

(2.5, 4.5)

Hope it helps! May I please have a brainliest for this? Thanks!

The two numbers are 1 and 1.

Let the non-negative number be x and its reciprocal be y = 1/x

The sum of the two numbers is f(x,y) = x + y

= x + 1/x

= f(x)

For f(x) to be minimum, we differentiate it with respect to x and equate it to zero to find the value of x at which irt is minimum.

So, df(x)/dx = d(x + 1/x)/dx

= dx/dx + d(1/x)/dx

= 1 - 1/x²

Equating it to zero, we have

1 - 1/x² = 0

1 = 1/x²

x² = 1

Taking square-root of both sides, we have

x = ±√1

x = ±1

Since x is non-negative x = + 1

We differentiate f(x) again to determine if this value gives a minimum for f(x).

So, d²f(x)/dx² = d(1 - 1/x²)/dx

= d1/dx - d(1/x²)/dx

= 0 - × (-2/x³)

= 2/x³

Substituting x = 1 into the equation,

d²f(x)/dx² = 2/x³

= 2/1³

= 2 > 0.

So x = 1 is a minimum point for f(x)

Since x = 1 and y = 1/x, y = 1/1 = 1

So, the two numbers are 1 and 1.

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Answer:

24 1/4 lbs

Step-by-step explanation:

She starts off with 32 1/2 lbs.

She then gives 8 1/4 to her friend.

To find how much she has left, we subtract 8 1/4 from 32 1/2.

To make this easier, lets make them both have a common denominator:

32 2/4 - 8 1/4 = 24 1/4

I hope this helped, please mark Brainliest, thank you so much!

Answer:

ez

Step-by-step explanation:

ezz

Answer:

Step-by-step explanation:

The nomebers are equivalent (true)

opposites. (true)

produt 1 (false)

a positive value (false)

last on don't now but I think it's (false)

Rollaway Skates is cheaper when the number of people is less than or equal to 4. For example, the cost for 2 people at Rollaway Skates is $10, while the cost for 2 people at Wheelie's Skates and Stuff is $106.

Wheelie's Skates and Stuff is cheaper when the number of people is greater than or equal to 5. For example, the cost for 6 people at Rollaway Skates is $30, while the cost for 6 people at Wheelie's Skates and Stuff is $118.

I hope this helps! Do you have any other questions?

Answer:Write x² + 10x + 29 in the form (x + c)² + d, where c

Step-by-step explanation:

Answer:

(x+5)² + 4, so c is 5 and d is 4

Step-by-step explanation:

x² + 10x + 29 is a quadratic equation which can be witten as x² + bx + c, where b is 10 and c is 29.

We need to complete the square to get it in the form

(x + c)² + d

Completing the square uses the form:

\((x + \frac{b}{2} ) {}^{2} - ( \frac{b}{2} ) {}^{2} + c\)

substitute b = 10 and c = 29 in this form:

\((x + \frac{10}{2}) {}^{2} - ( \frac{10}{2} ) {}^{2} + 29\)

Simplify further:

\((x + 5) {}^{2} - 25 + 29\)

\((x + 5) {}^{2} + 4\)

c = 5, d = 4