There are 135 people in a sport centre. 73 people use the gym. 59 people use the swimming pool. 31 people use the track. 19 people use the gym and the pool. 9 people use the pool and the track. 16 people use the gym and the track. 4 people use all three facilities. A person is selected at random. What is the probability that the person uses exactly one of the facilities?

Answer:

$0.70 per letter, $1.50 flat fee

Step-by-step explanation:

Let x be the flat fee.

Let y be the cost of sending 1 letter.

Lets create 2 equations from those 2 instances.

First Instance: x + 35y = 26 - Equation 1

Second Instance: x + 18y = 14.1 - Equation 2

To find x and y , we can use elimination method in solving simultaneous equations.

Equation 1 - Equation 2

x - x + 35y - 18y = 26 - 14.1

17y = 11.9

y = [tex]\frac{11.9}{17} \\[/tex]

= $0.70

Now we substitute y into equation 1.

x + 35(0.70) = 26

x + 24.50 = 26

x = 26 - 24.50

= $1.50

From the above we know the post charges $0.70 per letter sent and charges $1.50 flat fee.

Answer:

The y-intercept is 25000 . The intercept is the fixed cost of the doughnut selling company.

Step-by-step explanation:

In the question, it is given that the fixed cost is $25000 and the expense to produce each doughnut is $0.25.

It is required to find and identify the y intercept.

To do so, use the equation derived in previous part of the exercise to interpret the slope. Compare the equation with standard equation of the line.

Step 1 of 1

The total cost of the company is the sum of fixed cost and the expenses for the doughnut, C=0.25x+25000.

Compare the equation with general linear equation y=mx+c.

The y-intercept is 25000 .

The intercept is the fixed cost of the doughnut selling company.

Si cada jugador tiene un total de 2 canicas y hay 5 jugadores, se espera que el número total de canicas sea 10.

Multiplica el número de canicas por el de jugadores:

Este factor se puede descomponer así:

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The value of the 1 mile is equal to 5280 feet

We have given that,

The problem involves a conversion from feet to miles.

We have to determine how many feet are in one mile.

Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

1 mile is equal to 5280 feet

Therefore we get,

1mile=5280 feet.

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We can solve this graphically, we will see that f(x) = g(x) when x = -2, so the solution is x = -2.

We want to solve the system:

f(x) = g(x)

Where:

[tex]f(x) = 2x + 24\\\\g(x) = 5*(0.5)^x[/tex]

Replacing the functions, we get:

[tex]2x + 24 = 5*(0.5)^x[/tex]

Notice that on the left side x is a coefficient, while on the right side, it is an exponent, so this is really hard to solve with algebra.

But what we can do, is graph both functions, and see for which value of x the graphs do intersect.

Below you can see the graphs, the green one is f(x), the blue one is g(x).

There you can see that the graphs intersect at x = -2

This means that f(x) = g(x) only for x = -2.

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The intermediate step of x² - 4x = 45 is (x- 2)² = 49

The equation is given as:

x² - 4x = 45

Take the coefficient of x

k = -4

Divide by 2

k/2 = -2

Square both sides

(k/2)^2 = 4

Add 4 to both sides of x² - 4x = 45

x² - 4x + 4= 45 + 4

This gives

x² - 4x + 4= 49

Express as perfect square

(x- 2)² = 49

Hence, the intermediate step of x² - 4x = 45 is (x- 2)² = 49

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To calculate the area of a circle, we use the formula : [tex]\pi r^{2}[/tex], where r is radius.

We replace the numebrs : 144[tex]\pi[/tex] = 452,389342.... = 452 (rounded)

So, the area of this circle is 452 (and whatever units)

Answer:

Area of circle = 452 units²

Step-by-step explanation:

We can use the following formula to calculate the area of a circle:

Area = π r²

where r = radius of circle (12 units)

Substituting into the formula:
Area = π × (12)²

        = π × 144

        = 452.39

        = 452 units²       (rounded to the nearest whole number)

Answer:

C

Step-by-step explanation:

The exact point should be (0, 4) if you're looking for the Y intercept. I'm assuming that each square represents one unit. Hope I could help.

Answer:

c)4

Step-by-step explanation:

Hope it helps!!!

y= 4

x= 0

Answer:

4Hz

Step-by-step explanation:

Standard form of a sine or cosine function,

y = acos(b(x+c))

where a is the amplitude, b is the value to find the period. and c is the phase shift.

Period = \frac{2\pi}{b}

From the equation given in the question,

[tex]y = 3cos(8\pi \: t + \frac{\pi}{2} ) \\ y = 3cos(8\pi(t + \frac{1}{16} )) \: \: (factorising \: 8\pi \: out)[/tex]

We can see:

Amplitude = 3,

Period = \frac{2\pi}{8\pi} = 1 / 4

Phase Shift = 1 / 16

Now we want to find the frequency.

Frequency = 1 / Period

= 1 / (1/4)

= 4Hz

Answer:

[tex]\displaystyle 4[/tex]

Step-by-step explanation:

[tex]\displaystyle y = Acos(Bx - C) + D[/tex]

When working with a trigonometric equation like this, always remember the information below:

[tex]\displaystyle Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A|[/tex]

So, the first procedure is to find the period of this graph, and when calculated, you should arrive at this:

[tex]\displaystyle \boxed{\frac{1}{4}} = \frac{2}{8\pi}\pi[/tex]

You will then plug this into the frequency formula, [tex]\displaystyle T^{-1} = F.[/tex] Look below:

[tex]\displaystyle \frac{1}{4}^{-1} = F \\ \\ \boxed{4 = F}[/tex]

Therefore, the frequency of motion is four hertz.

I am delighted to assist you at any time.

The preference is that ✓5 should be left in radical form as an irrational number.

It should be noted that a radical form is illustrated when n is a positive integer that is greater than 1.

Here, a rational number is a number that can be represented in the form of p/q where p and q are integers. In this case, ✓5 will nvwe give a perfect number in decimal form. Hence, it's better to leave it radical form.

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The line with an equation of y = x have a slope of 1 and y intercept of 0.

An equation is an expression that shows the relationship between two or more variables and numbers.

The standard equation of a line is given as:

y = mx + b

Where m is the slope of the line and b is the y intercept.

The line with an equation of y = x have a slope of 1 and y intercept of 0.

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This distance can be expressed as 3.84× [tex]10^{8}[/tex] m.

What is distance with example?

Given the distance between the earth and the moon is 384000km

Representing in exponential notation,

=384000×1000m  [∵1km=1000m]

=384× [tex]10^{6}[/tex] m

=3.84× [tex]10^{8}[/tex] m

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The correct question is -

The distance between the Earth and the moon is approximately 384000 km.  this distance can be expressed as ____m.

Answer:

C. 6.9

Step-by-step explanation:

Pretend this is a 2-d diagram and use the Pythagorean theorem.

Pythagorean theorem: a^2 + b^2 = c^2

a = 6 mm

b = 7/2 = 3.5 mm

c = x

6^2 + 3.5^2 = x^2

36 + 12.25 = x^2

48.25 = x^2

[tex]\sqrt{48.25} = \sqrt{x^2}[/tex]

x = 6.9

The difference between the retail and wholesale unit price is $ 0.99.

The retail price is the price that the item is sold for to the customer.

Here,

Coordinates extracted from the graph;

(4, 1)     (12, 3)

Equation of straight line (Whole sale price)

(y - y₁) = m(x - x₁)                  

where, m = (y₂-y₁)/(x₂-x₁)

then, m = (3-1) / (12-4)

            = 2/8

           = 1/4

Now,   (y - 1) = 1/4 (x - 4)

           4y - 4 = x - 4

            x = 4y

            x - 4y = 0

Now, whole sale price for 24 boxes; x = 24

           24 - 4y = 0

            4y = 24

             y = 24/4

             y = 6

The wholesale price = $ 6

The retail price = $ 6.99

The difference between retail and wholesale = Retail - Wholesale

                                                                            = 6.99 - 6

                                                                            = $ 0.99

Thus, the difference between the retail and wholesale unit price is $ 0.99.

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The percentage of unemployed women from the total percentage of unemployed is 60%

Percentage of the unemployed women from the total unemployed = 15% / 25% × 100

= 0.60 × 100

= 60%

Therefore, the percentage of unemployed women from the total percentage of unemployed is 60%

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The length of one of the legs says line AC is 58.31.

A figure can be placed in a coordinate plane on the graph by determining the coordinate of the vertices.

For the given isosceles triangle with:

The coordinate of the vertices are:

The length of one leg is calculated as follows:

[tex]\mathbf{AC= \sqrt{(50-0)^2+(30-0)^2}}}[/tex]

AC = [tex]\mathbf{\sqrt{2500+900}}[/tex]

AC = [tex]\mathbf{\sqrt{3400}}[/tex]

AC = 58.31

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The volume of the box is 216 ft cube.

He filled a box with 4 layers of cubes that measured one foot on each side

The bottom of the box fit 6 cubes,

1 cube length = 1 ft.

Therefore,

volume of the box = 6³

Therefore,

volume of the box = 216 ft³

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Answer:

D

Step-by-step explanation:

quadratic formula

Answer:

I hope this is helpful. I had done my calculations and got the answer. The last part in orange is the answer. Your going to have to simplify.

The probability that both sides of the card is red is 0.33

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that both sides of the card is red = total number of cards in which both sides are red / total number of cards

2/6 = 1/3 = 0.33

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The complete statements for the angles as in the task content are:

It follows from the task content that the arrangement involves two parallel lines q and s which are cut by transversal line r.

On this note, according to the description in the task content, the angles formed at the intersections are related as follows;

Angles 1 and 5 are congruent because they are

corresponding angles.

Angles 4 and 6 are congruent because they are alternate angles.

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The order of steps to solve the equation are;

x^2 − 15 = 2x

(x − 5)(x + 3) = 0

x − 5 = 0 or x + 3 = 0

Potential solutions are −3 and 5

Logarithm expressions are inverse of an exponential function. Given the logarithm expression shown below:

log(x^2 − 15) = log(2x)

Cancel the log on both sides

x^2-15 = 2x

Equate to zero

x^2-2x-15 = 0

Factorize

x^2 -5x + 3x -15 = 0

x(x-5)+3(x-5) = 0

(x-5)(x+3) = 0

Find the solution

x - 5 = 0 or x + 3 = 0

Potential solution are 5 and -3

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Answer: [tex]g(x)=(x-5)^2[/tex]

Step-by-step explanation:

The graph of g is the graph of f translated 2 units to the right, so its equation is [tex]g(x)=(x-5)^2[/tex]

the probability of making a Type I error is equal to the significance level of power. To increase the probability of a Type I error, increase the significance level. Changing the sample size has no effect on the probability of a Type I error.

The electricity of a take a look at can be expanded in a number of methods, for example increasing the pattern length, reducing the standard errors, increasing the difference between the pattern statistic and the hypothesized parameter, or growing the alpha degree.

The chance of creating a kind I mistakes is α, that's the extent of importance you put for your hypothesis check. An α of 0.05 indicates which you are inclined to accept a five% chance which you are incorrect whilst you reject the null hypothesis. To lower this risk, you have to use a decrease cost for α

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Answer:

Step-by-step explanation:

This looks like it is intended to represent two equations. They can be solved as a system in any of the usual ways.

The two equations seem to be ...

Adding 4y to the second equation gives ...

  x -4y +4y = -3y +4y

  x = y . . . . . . . . simplify

Substituting for y in the first equation gives ...

  4x -x = 3

  3x = 3 . . . . simplify

  x = 1 . . . . . divide by 3

  y = 1 . . . . . same as x

The variables x and y both have a value of 1.

__

The attachment shows a graphical solution to these equations.

The required inequality is 3x + 2y > 390 and two possibilities is given by (100,45) and (80,75).

Student Council is selling t-shirts and hats for $21 and $14, respectively. The club needs to raise at least $2730.

Inequality can be define as the relation of equation contains the symbol of ( ≤, ≥, <, >) instead of equal sign in an equation.

Let x for the number of t-shirts and y for the number of hats.

Now,
equation for to raise at least $2730.
21x + 14y > 2730
3x + 2y > 390

Two possibility can be caroled out from the graph i,e.  (100,45) and (80,75).

Thus, the required inequality is 3x + 2y > 390 and two possibilities is given by (100,45) and (80,75).  

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Answer: 94

Step-by-step explanation:

The area of each of the top and bottom face is [tex](4)(6)-(2)(2)=20[/tex].

The area of each of the side faces is 12.

The area of each of the faces facing out is 6.

The area of each of the 3 'inner' faces is also 6.

Adding these together,

[tex]20(2)+12(2)+6(2)+6(3)=94[/tex]

These are the expected numbers of spins that is P(N=n)=n−1/n!

According to the statement

Let N is the number of spins AND

Let S is the sums of spins until the sum is greater than one.

we know that the For N=1, P(S) = 0.

The value of expected random variables are

E(X)=μ=∑xP(x).

Put all the integers values in it and integrate.

According to statement condition the expected number of variables become

P(N=n)=P(Sn−1<1≤Sn)

P(N=n)= P(Sn−1 < 1) - P(Sn <1)

P(N=n)=1/(n−1)!−1/n!

P(N=n)=n−1/n!

So, these are the expected numbers of spins that is P(N=n)=n−1/n!

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The true statements about the function are:

The complete question is in the image

From the table, the function values do not exceed 0 at the interval 0 to 2.

This means that f(x) ≤ 0 over the interval [0, 2].

Also from the table, the function values exceeds 0 at the intervals greater than -2 but less than 0

This means that f(x)>0 over the interval (-2,0)

Also from the table, the function values are at least 0 at the intervals greater than 2

This means that f(x) ≥ 0 over the interval [2,∞)

Hence, the true statements are (b), (d) and (e)

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x = -2.5 is a vertical line. The vertical graph of the equation is shown in the image attached below.

The slope of a vertical line is undefined, therefore, the equation of a vertical line is expressed as x = a, where a is the x-intercept.

Given x = -2.5, the equation suggests it is a vertical line, where the line intercepts the x-axis at -2.5, which is the x-intercepts.

Thus, the graph for x = 2.5 is shown in the diagram below.

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