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We are given the following information:

• 174 paving stones total (examined)

• 16, paving stones ,cracked

• 21, paving stones ,discolored

• 3, paving stones ,both cracked and discolored

We are trying to find the probability of paving stones that are not cracked.

Since we know from our given that 16 paving stones were cracked plus an additional 3 paving stones were both cracked and discolored, the total amount of cracked stones out of the 174 paving stones is equal to 19.

Therefore, we know that there will be 155 paving stones that aren't cracked. In order to find the probability, we will need to divide this number over the total amount of stones present:

If we evaluate this fraction, we should obtain our answer.

The probability that a paving stone isn't cracked is equal to 0.890805.

Answer:

[tex] \frac{1}{10000} [/tex]

or Decimal

[tex]0.0001[/tex]

Step-by-step explanation:

Greetings !

look at the figure i have attached above

Hope it helps !!

A golf lesson lasts from 10:00 am - 11:15 am and includes a 15 minutes break with equal lengths of time before and after the break is at 10:30 am.

Total lesson time is 1 hour and 15 minutes (10:00 - 11:15)

There is 15 minutes break with equal lengths of time before and after break.

The lesson before the break is from 10 - 10:30

Therefore , break is at 10:30 am

Lesson resumes at 10:45 when break is over then lesson runs another 30 minutes until 11:15 am (10:45 - 11:15).

Therefore, the break is at 10:30 am in mid of 10:00 am - 11:15 am.

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Answer:

r=32

Step-by-step explanation:

when DM=35

then. 35=r+3

35-3=r

r=32 therefore, substitute into

second equation to solve GM

GM=4r-28

GM=128-28

GM=100

13/20 cups

The recipe makes 10 Pancakes with 13/4 cups of milk

The recipe will make 1 pancake with x cups of milk

The recipe will make 1 pancake with 13/40 cups of milk

The recipe will make 2 pancakes with (2 x 13/40) cups of milk

= 26 / 40

= 13 / 20

The recipe will make 2 pancakes with 13/20 cups of milk

Answer:

Concept:

To figure out the measure of angle A, we will use the sine rule below

By substituting the values, we will have

Cross multiply, we will have

Hence,

The measure of angle A to the nearest whole number is

Answer:

Exponential

Step-by-step explanation:

If the initial difference has the same value, the model will be linear.

If the value of the second difference is the same, the model will be quadratic.

If the difference has been calculated more than five times before duplicate values are discovered, the model might be exponential or involve another unique equation.

Hope this helps!

Given the equation:

Using the Pythagorean identities

so,

so, the equation will be:

Given : a tree in your yard that is 60 inches around

60 inches represents the circumference of the tree

The circumference =

Where d is the diameter of the tree

so,

So, the answer is : the diameter of the tree is a bout 19.1 inches

Average rate of change = -2 celcius / hour

Interpretation: For every unit change in the time (x), there is a change of -2 celcius in the temperature

The average rate of change is to be found for the interval:

From the interval, we can deduce that:

Know the corresponding value of y for each value of x shown above:

The average rate of cgange is given by the formula:

The rate of change for the interval is -2 celcius/hour

This can be interpreted as for every unit change in the time (x), there is a change of -2 celcius in the temperature

Answer:

es 1 1/4 + 2/4 +3 2/4 = 5 1/4

5 1/4

Given data:

The numbers given are 12 and 3.

The 12 and 3 are both positive integers in which 12 is greater than 3.

The 12 and 3 both lie on the right side of the number line in which 12 comes after 3, so 12 is bigger number than 3.

The 12 and 3 are both natural as well as rational number, 12 is nine more than 3.

We will determine the arch lenght (In radians) as follows:

*First: We transform the measure of the angle from degrees to radians, that is:

*Second: We find the arc length:

So, the arc length for CT is 88pi/15 radians.

*Third: We find its measure in feet:

So, the arch length for CT in feet is approximately 18.43 feet.

Applying the two-tangent theorem, the length of LM is: A. 18.

The two-tangent theorem states that if two tangents are drawn from a circle to meet at a point outside the circle, then the tangent segments are congruent to each other, that is they have equal lengths.

Segments LK and LM are tangent segments drawn to meet at the external point L. This means, the length of Lk and the length of LM would be equal to each other.

LK = 4x - 2

LM = 3x + 3

LK = LM

Substitute

4x - 2 = 3x + 3

Combine like terms

4x - 3x = 2 + 3

x = 5

LM = 3x + 3

Plug in the value of x

LM = 3(5) + 3

LM = 15 + 3

LM = 18

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The measure of GH is 4 units.

The correct option is (B)

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.

Given:

FG = 2 units, FI = 7 units, and HI = 1 unit

Now,

FI = FG+ GH +HI

7= 2 + GH + 1

7= 3 + GH

GH = 7-3

GH = 4 units

Hence, the measure of GH is 4 units.

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The value of the mutual fund of Tom after 15 deposits will be $5197.320   .

In the question ,

it is given that , Tom invested $2500 in mutual fund for 15 years ,

So,

the investment amount(P) = $2500 .

time for investment(x) = 15 years

rate of increase(r) = 5% = 0.05

The amount of fund  after 15 deposits can be calculated using the formula

amount = P*(1+r)ˣ

Substituting the values of  P, x and r , we get

amount = 2500*(1 + 0.05)¹⁵

= 2500*(1.05)¹⁵

= 5197.320

Therefore , The value of the mutual fund of Tom after 15 deposits will be $5197.320   .

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1. Calculating the marginal cost per day yields the following results:

Air conditioners  Total cost    Marginal cost

    per day          ($ per day)      ($ per day)

      1                          100                  100

      2                         150                   50

      3                        220                   70

      4                         310                   90

      5                        405                   95

      6                         510                  105

      7                        650                  140

      8                       800                   150

2. To maximize profits, the price-taking firm should produce 6 air conditioners per day.

The profit-maximizing point or units is the output and price interaction that ensures that the marginal revenue equals the marginal cost.

The marginal revenue (MR) is the revenue earned from an additional unit. The marginal cost (MC) is the production cost per additional unit.

For price-taking firms, the maximum profit is achieved at the level of output where MC equals MR.

Market Price for one unit = $125

Air conditioners  Total cost    Marginal cost

    per day          ($ per day)      ($ per day)

      1                          100              100 (100 - 0)

      2                         150               50 (150 - 100)

      3                        220               70 (220 - 150)

      4                         310              90 (310 - 220)

      5                        405              95 (405 - 310)

      6                         510            105 (510 - 405)

      7                        650             140 (650 - 510)

      8                       800              150 (800 - 650)

Thus, profit is not maximized where the MC exceeds the MR. Instead producing at that unit reduces profit.

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Total Cost Information

Air conditioners  Total cost

    per day          ($ per day)

      1                          100

      2                         150

      3                        220

      4                         310

      5                        405

      6                         510

      7                        650

      8                       800

1. Calculate marginal cost per day, and enter your responses as whole numbers.

2. How many air conditioners should the firm produce per day if its goal is to maximize its profit? air conditioners per day.

Given that

a) The formula for the test statistics for this sample is,

Therefore,

Hence, the test statistic for this sample is

b)

The markup percentage was

The markup percentage was 30%.

Answer:

[tex]f(x) = $\begin{cases}3x-4 & -2\le x < 1\\x + 3 & 1 \le x \le 5\\8 & 5 \le x \le 8 \end{cases}$[/tex]

Step-by-step explanation:

The permissible values of x for a function is called the domain of the function. Permissible values mean that the function is real and defined.

The range of a function is the set of all y values for the domain

If a point on a graph is a filled circle, that point is included in the domain(x-value) and represents a ≤ or a ≥ inequality

If a point on a graph is an unfilled or hollow circle, that point is not included in the domain(x-value) and represents a < or a >inequality

Let's look at the three parts of the given piecewise graph

Piecewise part A

We see that the minimum and maximum values of x for this function are x = -2 and x = 1 respectively. The point corresponding to x= 1 is a hollow circle so it is not included in the domain whereas the point corresponding to x = -2 is included

Let's find the equation of this line:
Take 2 points on the line. We choose points (0, -4) and (1, -1)

Slope of this line is -1 -(-4)/(1-0) = (-1 + 4)/1 = 3
The y-intercept is -4

So equation of the line is y = 3x -4  for -2 ≤ x < 1

Proceeding in a similar manner we can determine the domain and function equation for the other two pieces, B and C

Piecewise part B

Domain of x : 1 ≤ x ≤5
Slope = (8-4)/(5-1) = 4/4 = 1

Equation is of the form y = 1x + b
To calculate b, plug in values of x = 1, y = 4 to get
4 = 1(1) + b

b = 3

Equation of this piecewise function is
y = x + 3    for 1 ≤ x ≤ 5

Piecewise Part C

This is a flat horizontal line at y = 8
So that is the equation of the line
The domain of this piece is 5 ≤ x ≤ 8  
So we get y = 8 for [tex]$\begin{cases}3x-4 & -2\le x < 1\\x + 3 & 1 \le x \le 5\\8 & 5 \le x \le 8 \end{cases}$[/tex]

Normally, instead of using y we use f(x)

Putting all this together we get the piecewise function defined as

[tex]f(x) = $\begin{cases}3x-4 & -2\le x < 1\\x + 3 & 1 \le x \le 5\\8 & 5 \le x \le 8 \end{cases}$[/tex]

The most appropriate choice for binomial distribution will be given by-

Mean of binomial distribution= 20

Standard deviation of binomial distribution = 16

What is binomial distribution?

Let there are n number of success or failure experiment called Bernouli trial and let p be the probability of success. Binomial distribution with parameters n and p is the probability distribution of p successes in n number of Bernouli trials.

Probability mass function of Binomial distribution

P(x = k) = [tex]n \choose k[/tex][tex]p^k(1-p)^k[/tex]

Here,

n = 100,

p = [tex]\frac{1}{5}\\[/tex]

1 - p = [tex]1 - \frac{1}{5}[/tex]

       = [tex]\frac{5-1}{5}[/tex]

       = [tex]\frac{4}{5}[/tex]

Mean of binomial distribution = np

                                                 = [tex]100 \times \frac{1}{5}\\[/tex]

                                                 =20

Standard deviation of binomial distribution  =

                                                                          [tex]100 \times \frac{1}{5}(1- \frac{1}{5})\\100 \times \frac{1}{5} \times \frac{4}{5}\\16[/tex]

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The equation of the line with coordinate (0, -2) that goes through y = -²/₃x + 5 is; y = -²/₃x - 2

We know that the general formula for an equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, from the given equation of y = -²/₃x + 5, we can say that;

Slope; m = -²/₃

y-intercept = 5

Thus, equation of the new line would be;

y - (-2) = -²/₃(x - 0)

y + 2 = -²/₃x

y = -²/₃x - 2

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Answer: t = 820

Step-by-step explanation:

1) Set up the equation

369 + 55%t = t

2) Simplify the percentage

369+ 0.55t = t

3) Minus 0.55 t on both sides

369 = 0.45t

4) Set t by itself.

t = 820

Answer:15

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

If there is a negative sign just add a positive sign or remove the sign. And if it's a positive number add a negative sign.

Easy There we go!

The given function is a rational function

We will find the zeros of the denominator

The end behavior of the function will be as follows:

The graph of the function is as follows:

Answer:

Explanation:

a)

The formula for calculating the length of an arc is expressed as

Length of arc = θ/360 x 2πr

where

θ is the angle subtended at the center of the circle.

r is the radius of the circle

From the information given,

diameter = 5(length of each metal spoke)

r =diameter/2 = 5/2 = 2.5

Recall, the total angle in the circle is 360 degrees. There are 8 partitions. Angle between consecutive spokes is

360/8 = 45. Thus,

θ = 45

Length of are between consecutive spokes = 45//360 x 2 x π x 2.5

Length of are between consecutive spokes = 5π/8

b) The formula for calculating the area of a sector is expressed as

area of a sector = θ/360 x πr^2

By substituting the values,

area of a sector = 45/360 x π x 2.5^2

Area of sector = 25π/32 square inches

The area of the shaded region can determined by substracting the area of rectangle from the area of triangle,

Thus, the area of the shaded region is 212.5 square centimeters.

First, find the z-score of 86

Rounding to the nearest hundredth, that is 0.26

Next, find z = 0.26 to the left of z in the z-table and we have the following

Multiply by 100%, and we have

Therefore, the percentage of students who scored lower than 86 is 60.257%.

The answer is d. 82.1

Explanation:

Tan 75 = x/22

It's important to know that empty circles refer to open intervals or parenthesis.

In this case, we observe that the first interval of the domain is (-1, 1) and the second interval of the domain is (2, 5), so the whole domain would be the union of these two intervals.

To obtain the range, let's observe the y-values. The function goes from y = -5 to y = 3, so the range would be