There are 130 people in a sport centre.
73 people use the gym.
62 people use the swimming pool.
58 people use the track.
22 people use the gym and the pool.
29 people use the pool and the track.
25 people use the gym and the track.
11 people use all three facilities.
A person is selected at random.
What is the probability that the person uses exactly one of the facilities?

The spring constant of the spring is 11.092N/m

given that

a 180 g air-track glider is attached to a spring

the glider is pushed in 10.2 cm and released.

a student with a stopwatch finds that 12.0 oscillations take 15.0 s

The formula for calculating the period of oscillation is

T = 2\(\pi\)\(\sqrt{\frac{m}{k} }\)

m is the mass of the spring

k is the spring constant

Making the spring constant "k" the subject of the formula will give

k = 4\(\pi ^{2}\)\(\frac{m}{T^{2} }\)

the period of oscillation "T"

T = \(\frac{1}{f}\)

frequency "f" is the number of oscillations completed in one second.

a student with a stopwatch finds that 12.0 oscillations take 15.0 s

number of oscillations in one sec will be 15/12 = 1.25 osc.

Period T = 1/1.25 = 0.8sec

the required spring constant;

k = 4\(\pi ^{2}\)\(\frac{m}{T^{2} }\)

k = 4\((3.14)^{2}\)\(\frac{0.18}{(0.8)^{2} }\)

k = 11.092N/m

Therefore, the spring constant of the spring is 11.092N/m

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There exists a value c in the interval (2, 4) such that f(c) = 15.

Given that f is a function that is continuous on the closed interval [2, 4] and f(2) = 10 and f(4) = 20, we can use the Intermediate Value Theorem to show that there exists a value c in the interval (2, 4) such that f(c) = 15.

The Intermediate Value Theorem states that if a function f is continuous on a closed interval [a, b], and if M is any value between f(a) and f(b) (inclusive), then there exists at least one value c in the interval (a, b) such that f(c) = M.

In this case, f(2) = 10 and f(4) = 20, and we are interested in finding a value c such that f(c) = 15, which is between f(2) and f(4). Since f is continuous on the interval [2, 4], the Intermediate Value Theorem guarantees that such a value c exists.

Therefore, there exists a value c in the interval (2, 4) such that f(c) = 15.

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A factorization of the quadratic function 81x² - 36x + 4 is (9x - 2)².

First of all, we would rearrange the given quadratic function as follows;

4 - 36x + 81x²

81x² - 36x + 4

By using the sum-product pattern, we have the following:

81x² - 18x - 18x + 4

By writing the common factor from the two pairs, we have the following:

(81x² - 18x) + (-18x + 4)

9x(9x - 2) - 2(9x - 2)

By rewriting in factored form, we have the following:

(9x - 2)(9x - 2)

Lastly, we would combine to a square as follows;

81x² - 36x + 4 = (9x - 2)².

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Complete Question:

Factorize each of the following expressions completely.

(a) 4 - 36x + 81x²

Answer:  2

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

Explanation:

r/t means we are dividing r over t

r and t are placeholders for numbers. In this case, 6 and 3 in that order.

So,

r/t = 6/3 = 6 ÷ 3 = 2

Answer:

x = log 10/log 3

Step-by-step explanation:

3^x - 4 = 6

3^x = 10

We take log base 3 of both sides since log_3 3^x is simply x.

log_3 3^x = log_3 10

x = log_3 10

We have an answer for x, but it is a log base 3. We want log base 10.

Now we use the change of base formula.

log_b y = log y/log b

x = log 10/log 3

Answer:

its not 1, its the second one (B)

Step-by-step explanation:

Answer:

I know I'm 1 year late but B is the correct answer choice. I just did it on edge 2021.

Answer:

M= 1.4

Step-by-step explanation:

i'll be honest I just slapped into google and a Quizlet popped up

Answer:

x = 11

Step-by-step explanation:

12x - 3x + 90 = 12x + 57

simplify both sides

12x - 3x + 90 = 12x + 57

9x + 90 = 12x + 57

inverse operations

9x + 90 = 12x + 57

-9x            -9x

90 = 3x + 57

-57         -57

33 = 3x

/3     /3

11 = x

Answer:

x = 11

General Formulas and Concepts:

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Write equation

12x - 3x + 90 = 12x + 57

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

The rational root theorem is the representation of the finding rational solution of the given polynomial function.

As given in the question,

Therefore, the rational root theorem is the representation of the finding rational solution of the given polynomial function.

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Answer:

1. Create a three-dimensional figure net.

2. Determine the area of each net face.

3. To calculate the surface area of the cube, add the areas of all the net's faces.

Answer:

2. 216cm3

3. 748.75

Step-by-step explanation:

Cube v=Bh

To get Base area 9cm x 4cm=36cm2

36cm2 x 6cm=216cm3

Answer:

C

Step-by-step explanation:

A 1 2-liter bottle for $0.89

1 liter = .89 /2 = $0.445

B 3 1-liter bottles for $1.50

1 liter = $1.50/3 = $0.50

C 24 0.5-liter bottles for $5.25

1 liter = 5.25 / 12  = $0.4375

D 36 0.25-liter bottles for $4.75

1 liter = $4.75 / 9  = $0.53

Give me brainllest

Answer:

C is the best buy

Step-by-step explanation:

0.89/2 = 0.445

3 * 1 litre bottles = 3 litres

1.50/3 = 0.5

24 * 0.5 litres = 12 litres

5.25/12 = 0.4375

36 * 0.25 liters = 9 liters

4.75/9 = 0.52777777

Using the normal distribution, the probabilities are given as follows:

a. Between 8 and 12 cases with side effects: 0.582 = 58.2%.

b. More than 16 cases with side effects: 0.0174 = 1.74%.

The z-score of a measure X of a normally distributed variable that has mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is given by the equation presented below:

\(Z = \frac{X - \mu}{\sigma}\)

The parameters for the binomial distribution in this problem are given as follows:

p = 0.05, n = 200.

Hence the mean and the standard deviation of the approximation are given as follows:

For item a, using continuity correction, the probability of between 8 and 12 cases with side effects is the p-value of Z when X = 12.5 subtracted by the p-value of Z when X = 7.5, hence:

X = 12.5:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (12.5 - 10)/3.08

Z = 0.81

Z = 0.81 has a p-value of 0.7910

X = 7.5:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (7.5 - 10)/3.08

Z = -0.81

Z = -0.81 has a p-value of 0.2090.

0.7910 - 0.2090 = 0.582 probability.

For item b, the probability of finding more than 16 cases with side effects is one subtracted by the p-value of Z when X = 16.5, hence:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (16.5 - 10)/3.08

Z = 2.11

Z = 2.11 has a probability of 0.9826.

1 - 0.9826 = 0.0174 = 1.74% probability.

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Answer:

the value of x is twenty nine

Answer:

The mass of 3.5 moles of Ca (Sodium)  is 140 g to two significant figures.

To prove that f is one-to-one function, it must be proven that f(x1)=f(x2) and x1=x2.

What is a one to one function?

The mapping of two sets is essentially what a one to one function refers to. When every element in a function's range and domain match exactly one another, the function is said to be one-to-one.

The one-to-one function, also known as an injective function, is one of the many different types of functions.

A function that transfers different components of its domain to different elements of its codomain is known as a one-to-one function.

For example, a function  f:A→B  is said to be one-to-one if -

f(x1)=f(x2)⇒x1=x2

for all elements x1,x2∈A.

To prove  f:A→B  is one-to-one -

Consider the fact that f(x1)=f(x2).  

Then it must be true that x1=x2.

Therefore, it is now understood that f is one-to-one by definition if f(x1)=f(x2) and x1=x2.

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a. There is a 0.6827 percent chance that the random variable will take on a value between 45 and 55. b. There is a 0.9545 percent chance that the random variable will take on a value between 40 and 60.

a. To find the probability that the random variable will assume a value between 45 and 55, we need to calculate the z-scores for each value and then use a standard normal distribution table or calculator.

The z-score for 45 is:

\(z = (45 - 50) / 5 = -1\)

The z-score for 55 is:

\(z = (55 - 50) / 5 = 1\)

Using a standard normal distribution table or calculator, we find the probability of the random variable assuming a value between 45 and 55 is:

P(-1 < Z < 1) = 0.6827 (to 4 decimals)

As a result, there is a 0.6827 percent chance that the random variable will take a value between 45 and 55.

b. To find the probability that the random variable will assume a value between 40 and 60, we again need to calculate the z-scores for each value and then use a standard normal distribution table or calculator.

The z-score for 40 is:

\(z = (40 - 50) / 5 = -2\)

The z-score for 60 is:

\(z = (60 - 50) / 5 = 2\)

Using a standard normal distribution table or calculator, we find the probability of the random variable assuming a value between 40 and 60 is:

P(-2 < Z < 2) = 0.9545 (to 4 decimals)

Hence, there is a 0.9545 percent chance that the random variable will take on a value between 40 and 60.

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Answer:

68.3%

Step-by-step explanation:

Using the relation :

Zscore = (x - Mean) / standard deviation

For, x between 46 and 54

Zscore = ((54 - 50) / 4) - ((46 - 50) / 4)

P(Z < 4/4) - P(Z < -4/4)

P(Z < 1) - P(Z <-1)

0.84134 - 0.15866

= 0.68268

= 0.68268 * 100%

= 68.3%

Answer:

A standardized test is designed so that scores have a mean of 50 and a standard deviation of 4. What percent of scores are between 42 and 58?

Step-by-step explanation:

about 95.4%

The value of y when x = 17 based on y=156 when x=39 is 68

Based on the given task content; the value of y can be determined by using ratio

y = 156 when x = 39

y = ? when x = 17

Equate the ratio of y to x

156 : 39 = y : 17

156/39 = y / 17

cross product

156 × 17 = y × 39

2,652 = 39y

divide both sides by 39

y = 2,652 / 39

= 68

In conclusion, y is 68 when x = 17 when solved with ratio.

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Answer:

259.5

Step-by-step explanation:

8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5

The number of possible license plates is  2,176,782,336

To calculate the number of possible Nebraska license plates with 6 characters, we will use the counting principle.

Each character can either be a number (0-9) or a letter (A-Z). There are 10 possible numbers and 26 possible letters. So, for each character,

there are \(36 (10 + 26)\)possibilities.
Now, we will apply the counting principle to find the total number of combinations. The counting principle states that if there are n ways to do one thing and m ways to do another, there are n * m ways to do both.
In our case, there are 6 characters on the license plate, and each character has 36 possible options.

Therefore, the number of possible license plates is:
\(36 * 36 * 36 * 36 * 36 * 36 = 36^6 = 2,176,782,336\)
There are 2,176,782,336 possible Nebraska license plates with 6 characters, each filled with a number (0-9) or a letter (A-Z).
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Answer:

above sea level

Step-by-step explanation:

Answer:

The answer would be B

Answer:

-2

Step-by-step explanation:

We know that the object is at 12 on a horizontal line.

The horizontal line of a graph is the x axis, so lets think of 12 as 12x

On a graph, left is negative, and right is postive.

In this case we need to move 14x to the right, or -14x.

We start at 12x, so its going to be:

12x-14x=-2x

So -2 is the postition of the object on the x axis.

This is answer B.

Hope this helps!

In linear equation, 3437.5  feet - lbs is the work done to haul the anchor .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Anchor  weighing = 100 lbs

   given 3  lb/ft

  the combined weight  = 3( 25 -y ) + 100

                                 = 175 - 3y

    the workdone on small solution is = (175 - 3y)Δy

                      w = ∫₀²⁵ (175 - 3y) dy

                        = 175[y]²⁵₀- 3/2[y²]²⁵₀

                       = 175 [ 25 - 0 ] - 3/2 [ 25²- 0²]

                       = 3437.5  feet - lbs

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The expected value of the number of patients that will be cured is 2.78 which has been obtained by using probability.

It is feasible to determine the expected value of the number of patients who will be cured by multiplying each potential result by the appropriate probability and adding the results. The following probability and outcomes are:

0 patients cured: P(X=0) = 0.01

1 patient cured: P(X=1) = 0.08

2 patients cured: P(X=2) = 0.27

3 patients cured: P(X=3) = 0.40

4 patients cured: P(X=4) = 0.24

To calculate the expected value, we multiply each outcome by its probability and sum them up:

E(X) = (0 * 0.01) + (1 * 0.08) + (2 * 0.27) + (3 * 0.40) + (4 * 0.24)

Simplifying the calculation, we find:

E(X) = 0 + 0.08 + 0.54 + 1.20 + 0.96

E(X) = 2.78

Therefore, the expected value of the number of patients that will be cured is 2.78, rounded to two decimal places.

The expected value represents the average number of patients that would be cured if the treatment is repeated many times. In this case, based on the given probabilities, we can expect that, on average, approximately 2.78 patients out of four will be successfully cured with chemotherapy for this particular type of cancer.

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The complete question has been attached below.

The solution for b of the equation A(2 + b) = -12 is given as follows:

b = (-12 - 2A)/A.

The equation in the context of this problem is given as follows:

A(2 + b) = -12.

The variable of interest for this problem is given as follows:

b.

Applying the distributive property on the left side of the equality, we have that:

2A + Ab = -12.

Now, to obtain the solution for the variable of interest b, we simply isolate the variable, as follows:

Ab = -12 - 2A

b = (-12 - 2A)/A.

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Answer:

Step-by-step explanation:

f(x)=a(x+2)(x+7)=a(x²+2x+7x+14)

or f(x)=a(x²+9x+14)

it has zeros as -2 and -7.