can someone show me how to do this?

The length of the side P is 15 cm. And the right option is C.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides.

To calculate the length of side P we use Pythagoras theorem's formula

Pythagoras formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the right option is C 15 cm.

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Trigonometry

We are given the following condition:

sin (a) = cos (b)

Since both angles are acute, the following relationship must apply:

a = 90° - b

Both angles must be complementary

Substituting the values for each angle:

a = 5x - 2

b = 5x - 22

We have:

5x - 2 = 90 - (5x - 22)

Removing brackets:

5x - 2 = 90 - 5x + 22

Adding 5x:

5x - 2 + 5x = 90 + 22

Adding 2:

5x + 5x = 90 + 22 + 2

Simplifying:

10x = 114

Dividing by 10:

x = 114/10

x = 11.4

Correct choice: C)

The height of the sand in the display container is 12 inches when the display container is right triangular prism.

What is right triangular prism ?

A right triangular prism is a three-dimensional geometric shape with two parallel triangular bases and three rectangular faces. The rectangular faces connect the corresponding vertices of the triangular bases.

To find the height of the sand in the display container, we need to use the fact that the volume of sand in the storage container is equal to the volume of sand in the display container.

The storage container has a length, width, and height of 6 inch, 6 inch, and 6inche, respectively. Then, the volume of the storage container is:

\(V_{storage} = L * W * H = 6 * 6 * 6 = 216 inch^3\)

Similarly, let's assume that the display container has a base of length 4 inch and height 9 inches and height of sand be H.

Then, the volume of the display container is:

\(V_{display} = (1/2) * b * h * H = (1/2) * 4 * 9 * H = 18H\)

where (1/2) is the area of the triangle base of the display container.

Since the volumes of sand in both containers are equal, we can set these expressions equal to each other and solve for h:

216 = 18H

H = 12 inches

Therefore, the height of the sand in the display container is 12 inches.

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Answer:

x = 2

Step-by-step explanation:

The denominator of the rational function cannot be zero as this would make it undefined.

Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non zero for this value then it is a vertical asymptote.

5x - 10 = 0 ⇒ 5x = 10 ⇒ x = 2 ← excluded value

Thus x = 2 is the vertical asymptote

Note that the probabilities are given below.

a) the probability of a randomly selected catch being a mouse caught by Cyd

p(Catching a mount) x p(Cyd made the catch)

= 0.5x .2

= 0.1

b) the   probability of a bird not caught by Cyd is 0.5 x 0.8 = 0.4.

Thus

P(that a catch is a bird) x p(the Cyd didn't make the catch)

= 0.3 x 0.8

=0.24

c) The probability of a randomly selected catch being caught by Greg is 0.45

To calculate, we say

(0.5   x0.45) + (0.3 x 0.45) + (0.2 x .45)

= 0.45.

d)

P (mouse caught by Greg) = (0.45 x 0.5) / 1

= 0.225.

e) P(catch is a mouse caught by Ken and catch is a mouse)

= P(catch is a mouse | catch is made by Ken) x P(catch is made by Ken)

= 0.05 x 0.1

= 0.005

f)

P (catch made by Cyd | catch is a mouse)

= 0.1    x 0.2 / 0.5

= 0.04

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Answer:

After 10 weeks, Susan will have $295 and CiCi will have $259.

Step-by-step explanation:

Susan: y= 65+23x

CiCi: y = 119+14x

65+23(6)=203

119+14(6)=203

After 6 weeks, Susan and CiCi will both have $203 in their accounts.

65+23(10)=295

119+(14)(10)=259

Therefore, After 10 weeks, Susan will have $295 and CiCi will have $259.

We have to solve the system of equations

by substitution.

This method requieres to solve one of the equations for one of the variables and then plugging this value in the other equation. Since in this case the second equation is already solve for y, we plug this value in the first equation to get an equation of only the x variable.

Since this equation is always true, no matter the value of x, the system of equations has an infinite number of solutions.

Answer:

1. 3,077.2 cm³

2. 1,808.6 ft³

3. 602.9 in.³

4. 230.8 yd³

5. 191.8 m³

6. 70.3 in.³

Step-by-step explanation:

Recall: Volume of cylinder = πr²h

1. r = 7 cm

h = 20 cm

π = 3.14

Volume = 3.14*7²*20 = 3,077.2 cm³

2. r = 8 ft

h = 9 ft

π = 3.14

Volume = 3.14*8²*9 ≈ 1,808.6 ft³

3. r = ½(8) = 4 in.

h = 12 in.

π = 3.14

Volume = 3.14*4²*12 ≈ 602.9 in.³

4. r = 3½ yd = 3.5 yd

h = 6 yd

π = 3.14

Volume = 3.14*3.5²*6 ≈ 230.8 yd³

5. r = ½(5.3) = 2.65 m

h = 8.7 m

π = 3.14

Volume = 3.14*2.65²*8.7 ≈ 191.8 m³

6. r = 1.9 in.

h = 6.2 in.

π = 3.14

Volume = 3.14*1.9²*6.2 ≈ 70.3 in.³

Answer: the answer is 1

Answer:

Step-by-step explanation:

one

The only really certain way of getting an odd integer is to do 2k + 1. Therefore the answer should be something like 2k+1, 2k+3, 2k + 5

The best I can do for the first one is to assume that k is odd and that the answer is k + 10, k+12, k+14, but I would ask your instructor if this is merely the best answer out of a poor lot or if the question really has no answer.

Two things should be noted.

1. k has to be odd.

2. The first choice has to give consecutive integers because what is added on is 2 3 and 4. Those numbers are consecutive.

Two

k+1, k+2, k+3. See point 2 above. k is a constant and any number. 1,2,3 are consecutive so the results are consecutive. Even if k < 0 the numbers will be consecutive.

k= - 10

k+1 = - 9

k+2 = -8

k+3 = - 7

These are consecutive.

Your first choice will give either consecutive odd or even numbers depending on what k is.

If k = even, then k+6, k+ 8, k+10 will all be even.

If k = odd then the givens will be odd.

2k+9, 2k+11, 2k+13 will yield consecutive odd integers.

k+6, k+8, k+10 will yield consecutive integers.

The mean is 0.477514 (rounded to 6 decimal places).

The standard deviation is 0.288919 (rounded to 6 decimal places).

To calculate the mean and standard deviation, we will use the following formulas:

Mean = (sum of all values) / (number of values)

Standard deviation = sqrt[(sum of (value - mean)^2) / (number of values)]

Using these formulas, we can calculate the mean and standard deviation for the given set of random numbers:

Mean = (0.937776 + 0.270012 + 0.243785 + 0.590701 + 0.824982 + 0.131805 + 0.879337 + 0.741998 + 0.254683 + 0.080259 + 0.419321 + 0.928220 + 0.958430 + 0.980182 + 0.263900 + 0.063119 + 0.762096 + 0.485612 + 0.662900 + 0.362242 + 0.724796 + 0.307736 + 0.305021 + 0.417052 + 0.054337 + 0.323357 + 0.069662 + 0.843387 + 0.353107 + 0.074262 + 0.735596 + 0.175095 + 0.390508 + 0.668932 + 0.029861 + 0.205228 + 0.387740 + 0.962169 + 0.646565 + 0.423914 + 0.754782 + 0.156719 + 0.773113 + 0.546335 + 0.323573 + 0.649740 + 0.214082 + 0.382383 + 0.383982 + 0.030539) / 50 = 0.477514

Therefore, the mean is 0.477514 (rounded to 6 decimal places).

Now we will calculate the standard deviation:

Standard deviation = sqrt[((0.937776 - 0.477514)^2 + (0.270012 - 0.477514)^2 + (0.243785 - 0.477514)^2 + ... + (0.382383 - 0.477514)^2 + (0.383982 - 0.477514)^2 + (0.030539 - 0.477514)^2) / 50] = 0.288919

Therefore, the standard deviation is 0.288919 (rounded to 6 decimal places).

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Answer:

8 in the thousandths and 2 in the hundreths

Step-by-step explanation:

ur in colledge u stupid idiot, or as your profile puts it.

Answer:

Solving gives us the result, x = 2, y = -1

Step-by-step explanation:

The system of equations is,

y = 2x-5

y=-2x+3

equating the two equations, we get,

(since y = y)

\(2x-5 = -2x + 3\\4x -5 = 3\\4x = 3+5\\4x=8\\x=8/4\\x=2\)

and then since y = 2x-5

\(y=2(2)-5\\y=-1\)

so, x =2, y = -1

Answer:

a) (0,-2)

b) \(\frac{1-(-2)}{3-0}\)= 1

c) -3  or 9

Step-by-step explanation:

Answer:

2/5    or 0.4

Step-by-step explanation:   i'm smart

Answer:

0.0283642

Step-by-step explanation:

Number of uppercase letters = 26

Number of lowercas = 26 alphabets = 10

Number of password characters = 10

Hence total number of passwords with exactly 10 characters (26 + 26 + 10) ^10 = 62^10 = 839299365868340224 passwords

Password with 10 strings, and having atleast one upper, lower and digit character :

26^1 * 26^1 * 10^1 * (26+26+10)^7 = 23806114737966080 (1 upper, lower and digit character, the remaining 7 could be any of them)

Probability = required outcome / Total possible outcomes

P(password with atleast 1 upper, lower and digit character) = 23806114737966080 / 839299365868340224

= 0.0283642

The results show that the most common response was access, with 27% of the respondents choosing it as the most urgent health problem.

Cost came in second place, with 20% of the respondents choosing it. Obesity and cancer followed closely behind, with 14% and 13% of the respondents choosing them, respectively. Government interference and the flu were the least common responses, with only 3% and less than 0.5% of the respondents choosing them, respectively.

The margin of sampling error for the poll is ±4 percentage points, which means that if the poll was conducted multiple times, 95% of the time, the results would be within 4 percentage points of the actual population values.

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Answer:

y=−x2+8x−7

Step-by-step explanation:

Answer:

The answer to your question is A. Yes, because the total will be $3.27

0.35(2)+0.99(2)+0.59≤4.

Then you multiply: .35(2)=.70. .99(2)=1.98.

Then add: .70+1.98+.59=3.27, so yes she can since 3.27 is less than 4 :)

Step-by-step explanation:

I hope this helps and have a good day!

You have the following expression:

The previous expression can be written as follow:

The derivative of the previous expression is the derivative of a product:

by factorizing the numerator of the second term, you obtain:

Answer:

The question is not complete

Answer:

the experimental probability of being struck by lightning in this city is approximately 0.56667%.

Step-by-step explanation:

The experimental probability of an event happening is calculated by dividing the number of times the event occurred by the total number of trials or observations. In this case, the event is being struck by lightning, and the trials are the total number of people in the city.

The number of people struck by lightning is given as 85, and the total population of the city is 1.5 million. To find the experimental probability of being struck by lightning in this city, we can divide the number of people struck by lightning by the total population and multiply by 100% to express the answer as a percentage:

Experimental probability = (number of people struck by lightning / total population) * 100%

Experimental probability = (85 / 1,500,000) * 100%

Experimental probability = 0.0056667 * 100%

Experimental probability = 0.56667%

Therefore, the experimental probability of being struck by lightning in this city is approximately 0.56667%.

Check the picture below.

Make sure your calculator is in Degree mode.

\(\cos(25^o )=\cfrac{\stackrel{adjacent}{x}}{\underset{hypotenuse}{12}}\implies 12\cos(25^o)=x\implies \boxed{10.876\approx x} \\\\[-0.35em] ~\dotfill\\\\ \sin(25^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{12}}\implies 12\sin(25^o)=z \\\\[-0.35em] ~\dotfill\\\\ \sin(50^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{y}}\implies y=\cfrac{z}{\sin(50^o)}\implies y=\cfrac{12\sin(25^o)}{\sin(50^o)}\implies \boxed{y\approx 6.62}\)

Li Ming can paint the whole house in 10 hours

The absolute minimum of the function is f ( -10 ) = -1

Given data ,

Let the function be represented as f ( x )

Now , the function f ( x ) is plotted on the graph

where the minimum of a function is the smallest value that the function takes on over its entire domain.

It is the point on the graph of the function that is the lowest possible point

So , the function has the minimum value of - 1 at the point x = -10

Hence , the minimum of function is f ( -10 ) = -1

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The only solution for log₂(x-1)+log₂(x+5) is x = 3 using logarithms.

Logarithmic properties are rules that allow us to simplify and manipulate logarithmic expressions. They are based on the properties of exponents and are essential in solving logarithmic equations and evaluating logarithmic expressions.

Using the logarithmic property that log a + log b = log ab, we can simplify the left-hand side of the equation to:

log₂((x-1)(x+5)) = 4

2⁴ = (x-1)(x+5)

Simplifying:

16 = x² + 4x - 5

Rearranging:

x² + 4x - 21 = 0

Factorizing:

(x + 7)(x - 3) = 0

Therefore, either x + 7 = 0 or x - 3 = 0. Solving for x in each case:

x + 7 = 0 → x = -7

x - 3 = 0 → x = 3

However, we need to check whether these solutions are valid in the original equation. We cannot take the logarithm of a negative number, so x = -7 is not a valid solution.

Therefore, the only solution is x = 3.

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Answer:

a) 0.11 =  11% probability that the car needs work on either the engine, the transmission, or both.

b) 0.9 = 90% probability that the car needs no work on the engine.

Step-by-step explanation:

P(E) = 0.10 , P(T) = 0.02 and P(E,T) = 0.01 .

This means that:

Only engine: 0.1 - 0.01 = 0.09

Only transmission: 0.02 - 0.01 = 0.01

Both engine and transmission: 0.01

(a) Find the probability that the car needs work on either the engine, the transmission, or both.

0.09 + 0.01 + 0.01 = 0.11

0.11 =  11% probability that the car needs work on either the engine, the transmission, or both.

(b) Find the probability that the car needs no work on the engine.

Probability of needing work on engine:

0.09 + 0.01 = 0.1

Not needing:

1 - 0.1 = 0.9

0.9 = 90% probability that the car needs no work on the engine.

The radius of the gear should be approximately 2.8644 inches.It is important to note that when making calculations involving units, we need to make sure that all units are consistent and convert them when necessary. In this case, we converted the answer from feet to inches to match the given unit.

To find the radius of the gear that will pull a chain at 60 ft/min when rotating at 40 rev/min, we can use the formula:

chain speed = 2 x pi x radius x rotational speed

where pi is a mathematical constant approximately equal to 3.14.

We know that the chain speed is 60 ft/min and the rotational speed is 40 rev/min, so we can substitute those values into the formula:

60 = 2 x 3.14 x radius x 40

Simplifying the equation, we get:

radius = 60 / (2 x 3.14 x 40)

radius = 0.2387 ft

To convert feet to inches, we can multiply the answer by 12:

radius = 0.2387 x 12 = 2.8644 inches.

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Answer:

x = 58 degrees

Step-by-step explanation:

Using the SOH CAH TOA trigonometry identity

hypotenuse =99

adjacent = 52

angle of elevation  = x

cos theta = adj/hyp

cos x = 52/99

x = arccos (52/99)

x = arccos(0.5253)

x = 58 degrees ( to the nearest degree)