The time (in minutes) of waiting for a costumer to be served in a store, it can be modeled as an exponential random vanable, X. with average time E [x] =12 1. Delermien the probability that a chent wart no more than 10 minutes ___________ 2. Determine the probability that the cliet want more then 22 minutes ___________

The solutions to the equation -30x² + 9x + 60 = 0 are x = 5/2 and x = -4/5.

To solve the equation, we can start by bringing all the terms to one side to have a quadratic equation equal to zero. Let's go step by step:

-5/3 x² + 3x + 11 = -9 + 25/3 x²

First, let's simplify the equation by multiplying each term by 3 to eliminate the fractions:

-5x² + 9x + 33 = -27 + 25x²

Next, let's combine like terms:

-5x² - 25x² + 9x + 33 = -27

-30x² + 9x + 33 = -27

Now, let's bring all the terms to one side to have a quadratic equation equal to zero:

-30x² + 9x + 33 + 27 = 0

-30x² + 9x + 60 = 0

Finally, we have the quadratic equation in standard form:

-30x² + 9x + 60 = 0

Dividing each term by 3, we get:

-10x² + 3x + 20 = 0

(-2x + 5)(5x + 4) = -10x² + 3x + 20

So, the factored form of the equation -30x² + 9x + 60 = 0 is:

(-2x + 5)(5x + 4) = 0

Now we can set each factor equal to zero and solve for x:

-2x + 5 = 0 --> x = 5/2

5x + 4 = 0 --> x = -4/5

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Answer:

3

Step-by-step explanation:

The actual prime factors of 60 are 2, 3, and 5.

Answer:

3

Step-by-step explanation:

prime fatorizations are 2, 3, and 5

Answer:

10

Step-by-step explanation:

Use the distance formula to determine the distance between two points.

Answer:

\(-\frac{11}{3} \leq x\leq -1\)

Step-by-step explanation:

Graphed it on Casio fx cg50 Calculator

but desmos also works but may not show the exact values.

Answer:

A single number that estimates the value of an unknown parameter is called a point estimate.

Step-by-step explanation:

Don't see the point (haha) of elaborating

The upper limit for an 89% confidence interval for the average profit per unit is $6.58.

To find the upper limit for an 89% confidence interval for the average profit per unit, you can use the following formula:

Upper limit = sample mean + (critical value x standard error)

The critical value can be found using a t-distribution table with n-1 degrees of freedom and a confidence level of 89%. Since you have 1000 simulation trials, your degrees of freedom will be 1000-1 = 999.

Using the t-distribution table or a calculator, the critical value for an 89% confidence level with 999 degrees of freedom is approximately 1.645.

The standard error can be calculated as the sample standard deviation divided by the square root of the sample size. So:

standard error = sample standard deviation / sqrt(sample size)

standard error = 1.91 / sqrt(1000)

standard error = 0.060

Plugging in the values we have:

Upper limit = 6.48 + (1.645 x 0.060)

Upper limit = 6.5787

Therefore, the upper limit for an 89% confidence interval for the average profit per unit is $6.58.

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Answer:

20

Step-by-step explanation:

The total degrees in a circle is 360 degrees

x+40+2x+110+3x+90 = 360

==> 6x = 120

x = 20

Answer:

The answer would be x=20

Answer:

= 4

or

= −5

Step-by-step explanation:

Answer:

\(x=-5\) and \(x=4\)

Step-by-step explanation:

\(x^2+7x-20=6x\)

\(x^2+7x-20-6x=6x-6x\)

\(x^2+x-20=0\)

\((x+5)(x-4)=0\)

\(x=-5\) and \(x=4\)

The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).

Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.

Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).

Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).

Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).

To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.

(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)

Expanding this expression, you get:

(0+a+b, 1+a+b, 0+a, 0+b)

Simplifying, you obtain the following set of solutions:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Therefore, the correct set of possible results would be:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.

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Answer: the answer is A

Step-by-step explanation:

hope it helps

Answer:

He bought about 176 ounces or 22 cups, or 5.2 liters.

Step-by-step explanation:

1.) 4 * 28 = 112

2.) 112 + 64 = 176 (answer in ounces)

3.) 8 ounces in a cup

4.) 176 ÷ 8 = 22 (answer in cups)

5.) About 4.227 cups in a liter

6.) 22 ÷ 4.227 = 5.204636858

7.) Round to the nearest tenth = 5.2 (answer in liters)

Answer:

Below in bold.

Step-by-step explanation:

Starting height is when t = 0

It is 5 units.

To find the maximum height we convert the equation to vertex form:

h = -t^2 + 4t + 5

h = -(t^2 - 4t - 5)

=  - [(t - 2)^2 - 9]

= -(t - 2)^2 + 9

From this we see that the ball reaches max height after 2.

Maximum height = -2^2 +  4(2) + 5

= 9 units.

Ball reaches the ground after 2*2 = 4 .

Answer: £225

Step-by-step explanation:

Amount shared = £750

Let Sarah's share = y

Therefore,

Caroline's share = 3y

Bridget's share = 2(3y) = 6y

Mathematically,

y + 3y + 6y = £750

10y = £750

y = £750/10

y = £75

Caroline's share = 3y

Caroline's share = 3 × £75 = £225

Caroline's share is £225

The probability that the sample mean will be greater than 57.95 is 0.0495.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.

To solve this question, we need to know the concepts of the normal probability distribution and of the central limit theorem.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).

In this problem, we have that:

The probability that the sample mean will be greater than 57.95

This is 1 subtracted by the p-value of Z when X = 57.95. So

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

By the Central Limit Theorem

\(Z=\dfrac{X-\mu}{\text{s}}\)

\(Z=\dfrac{57.95-53}{3}\)

\(Z=1.65\)

\(Z=1.65\) has a p-value of 0.9505.

Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495

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Answer:

16

Step-by-step explanation:

(fog)x=f{g(x)}

=f(x-2)

=(x-2)^2

So,

(fog)(-2)=(-2-2)^2

=-4^2

=16

Answer:

2/9 , 3/7 , 1/5

Step-by-step explanation:

The pattern in matching the x value / y value, kind of like getting a gradient.

For example: Look at first paragraph, the points it corresponds are on x = 9, and y = 2, y/x = 2/9

The unit rate of first, second and third graph respectively are 2/9, 3/7 , and 1/5.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

To determine unit rate to the graph that represents

The pattern that results from matching the ratio x value to the y value resembles that of a gradient.

According to the first graph,

the points it corresponds are on x = 9, and y = 2, y/x = 2/9

According to the second graph,

the points it corresponds are on x = 7, and y = 3, y/x = 3/7

According to the third graph,

the points it corresponds are on x = 5, and y = 1, y/x = 1/5

Hence, the unit rate of first, second and third graph respectively are 2/9, 3/7 , and 1/5.

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The change in the area of the surface of the cube when its side length triples from s units to 3s units is 52s³.

To quantify the change in the area of the surface of a cube when its side length triples from s units to 3s units, we can set up an integral.

Let's denote the side length of the cube as "x". The initial side length is "s" and the final side length is "3s". We want to find the change in surface area, which is the difference between the final surface area and the initial surface area.

The surface area of a cube with side length "x" is given by 6x², as each face of the cube has an area of x² and there are 6 faces.

The change in surface area can be calculated as:

ΔA = ∫(6x²) dx,

where the integral is taken from the initial side length "s" to the final side length "3s".

Now let's evaluate the integral:

∫(6x²) dx = 2x³ + C,

where C is the constant of integration.

To find the change in surface area, we substitute the limits of integration:

ΔA = [2x³]s to 3s

= 2(3s)³ - 2s³

= 2(27)s³ - 2s³

= 52s³

Therefore, the change in the area of the surface of the cube when its side length triples from s units to 3s units is 52s³.

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Answer:

9

Step-by-step explanation:

Answer:

x = \(\sqrt{53}\)

Step-by-step explanation:

Using Pythagoras' identity on the upper right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

Let the third side be d, then

d² + b² = a² , that is

d² + 8² = 11²

d² + 64 = 121 ( subtract 64 from both sides )

d² = 57

Using Pythagoras' identity on the lower right triangle, then

x² + c² = d²

x² + 2² = 57

x² + 4 = 57 ( subtract 4 from both sides )

x² = 53 ( take the square root of both sides )

x = \(\sqrt{53}\)

The line x=-1 is a vertical line that passes through the point (-1,0).

It means that a line that is vertical to it will be an horizontal line. Since the horizontal line will always have the same y coordinate and one of the points on it is (6,9), the y coordinate of every point on this line is 9.

With this information we can determine that the equation of this line is y=9.

Answer:

The answer to the given question is - ¹/₂

Step-by-step explanation:

Given;

\(\frac{2}{5} \times -\frac{3}{7} - \frac{1}{14} - \frac{3}{7} \times \frac{3}{5}\)

Before we apply the distributive property, perform the multiplication operation.

\((\frac{2}{5} \times -\frac{3}{7}) - \frac{1}{14} - (\frac{3}{7} \times \frac{3}{5} )\\\\\frac{-6}{35} - \frac{1}{14} - \frac{9}{35}\)

Now, apply the distributive property, to obtain the final answer,

In distributive property, the following rule is applied;

ax + ay = a(x + y)

\(\frac{-6}{35} - \frac{1}{14} - \frac{9}{35} = \frac{-1}{7} (\frac{6}{5} + \frac{1}{2} + \frac{9}{5} )= \frac{-1}{7} (\frac{12 + 5+ 18}{10} )= \frac{-1}{7} (\frac{35}{10} ) = \frac{-35}{70} = \frac{-1}{2}\)

Therefore, the answer to the given question is - ¹/₂

You can determine if the inverse of a polynomial function is a function by using the Horizontal Line Test on the inverse.

The Horizontal Line Test is a graphical method that can be used to determine whether a given function is one-to-one, meaning that for each output value, there is at most one input value that maps to it.

If the inverse of a polynomial function is a function, it must pass the Horizontal Line Test, meaning that no horizontal line intersects the graph of the inverse more than once.

In other words, if the inverse of a polynomial function passes the Horizontal Line Test, it is guaranteed to have an inverse, which will be a function itself. If the Horizontal Line Test fails, then the inverse is not a function and does not have an inverse.

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Answer:

m<1=75 degree m<2=105degree

m<3=75 degree m<4=105 degree

Answer:

m∠1 = 75°

m∠2 = 105°

m∠3 = 75°

m∠4 = 105°

Step-by-step explanation:

Angles on a straight line sum to 180°

⇒ m∠1 + m∠2 = 180°

Given:

⇒ m∠2 - m∠1 + m∠1 = 30° + m∠1

⇒ m∠2 = 30° + m∠1

Substitute the found expression for m∠2 into the first equation and solve for m∠1:

⇒ m∠1 + m∠2 = 180°

⇒ m∠1 + 30° + m∠1 = 180°

⇒ m∠1 + 30° + m∠1  - 30° = 180° - 30°

⇒ m∠1 + m∠1 = 150°

⇒ m∠1 = 150° ÷ 2

⇒ m∠1 = 75°

As angles on a straight line sum to 180°, subtract m∠1 from 180° to find m∠2:

⇒ m∠2 = 180° - m∠1

⇒ m∠2 = 180° - 75°

⇒ m∠2 = 105°

Vertical Angles Theorem:  When two straight lines intersect, the opposite vertical angles are the same (congruent).

⇒ m∠3 = m∠1 = 75°

⇒ m∠4 = m∠2 = 105°

Answer:

Step-by-step explanation:

Given that:

The equation of the sphere is = x² + y² + z² = 36;  &

The cone z = \(\sqrt{x^2+y^2}\)

The first process is to evaluate the intersection of these curves.

i.e.

\(x^2 + y^2 + ( \sqrt{x^2 +y^2})^2=36\)

\(x^2 + y^2 + ( {x^2 +y^2})=36\)

2(x² + y²) = 36

Dividing both sides 2, we get;

x² + y² = 36

Suppose the parameterization of x=u, y=v;

Thus, the sphere result to:

x² + y² + z² = 36

Making z² the subject of the formula:

z² = 36 - x² - y²

\(z = \sqrt{36-x^2-y^2}\)

Now, to evaluate z in terms of  u and v, we have:

\(z = \sqrt{36-u^2-v^2}\)

Thus, the expected parametric representation for the surface is:

\(r(u,v) =\bigg \langle u,v, \ \sqrt{36-u^2-v^2} \bigg \rangle, where \ \ u^2 +v^2 = 18\)

Answer:

x=9

Step-by-step explanation:

x+12=21

x=21-12

x=9

x+12=21

Step 1: Subtract 12 from both sides.

x+12−12=21−12

x=9

After analyzing all the critical paths  the maximum possible reduction in the project duration is 1 week. The correct option is d. 1 week.

To determine the maximum possible reduction in the project duration within the given budget, we need to analyze the critical paths and crashing costs.

The crashing cost per week for activity A is $540 in the first week and $1080 per week from the second week onwards. For activity E, it is $545 in the first week and $1350 per week thereafter. For all other activities, the crashing cost is $135 per activity per week in the first week and $405 per activity per week thereafter.

Considering the crashing budget of $2300, let's calculate the maximum reduction for each critical path:

A-B-C-D-E: The total crashing cost for this path is $1350 (for A and E) + $405 (for B, C, and D) = $1755 per week. With a budget of $2300, this path can be crashed for a maximum of $2300 / $1755 = 1.31 weeks. Therefore, the maximum reduction for this path is 1 week.

A-F-E: The total crashing cost for this path is $1350 (for E) + $405 (for F) = $1755 per week. With the given budget, this path can be crashed for a maximum of $2300 / $1755 = 1.31 weeks. Hence, the maximum reduction for this path is 1 week.

A-B-H-J-K-E: The total crashing cost for this path is $1350 (for A and E) + $810 (for B, H, J, and K) = $2160 per week. This path can be crashed for a maximum of $2300 / $2160 = 1.06 weeks. Thus, the maximum reduction for this path is 1 week.

A-S-T-E: The total crashing cost for this path is $1350 (for A and E) + $540 (for S and T) = $1890 per week. This path can be crashed for a maximum of $2300 / $1890 = 1.22 weeks. Hence, the maximum reduction for this path is 1 week.

After analyzing all the critical paths, we observe that the maximum possible reduction in the project duration is 1 week.

The correct option is d. 1 week.

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Here, x value of 8 would be located on the left tail of the normal distribution curve, 3.67 standard deviations below the mean (μ=22.3) and with a very low value in terms of percentile or probability (0.015%).

To indicate where the given x value of 8 would be on the curve, we need to plot it on a normal distribution curve with a mean (μ) of 22.3 and a standard deviation (σ) of 3.9.
First, we need to convert the given x value of 8 into a z-score by using the formula:  z = (x - μ) / σ
Plugging in the values, we get: z = (8 - 22.3) / 3.9 = -3.67
This means that the value of 8 is located 3.67 standard deviations below the mean.
Next, we need to find this point on the normal distribution curve. We can use a z-score table or a graphing calculator to find the corresponding area under the curve.
If we use a z-score table, we can look up the area to the left of -3.67, which is 0.00015. This means that only 0.015% of the data falls below this point.
To plot this on the curve, we can locate the mean (μ) and mark it as the center of the curve. Then, we can count 3.67 standard deviations to the left of the mean and mark this as the point where the value of 8 would be located.

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Step-by-step explanation:

Equation at the end of step 1

(3x2 - 38x) + 24 = 0

STEP2:Trying to factor by splitting the middle term

 2.1     Factoring  3x2-38x+24 

The first term is,  3x2  its coefficient is  3 .

The middle term is,  -38x  its coefficient is  -38 .

The last term, "the constant", is  +24 

Step-1 : Multiply the coefficient of the first term by the constant   3 • 24 = 72 

Step-2 : Find two factors of  72  whose sum equals the coefficient of the middle term, which is   -38 .

     -72   +   -1   =   -73     -36   +   -2   =   -38   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -36  and  -2 

                     3x2 - 36x - 2x - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

                    3x • (x-12)

              Add up the last 2 terms, pulling out common factors :

                    2 • (x-12)

Step-5 : Add up the four terms of step 4 :

                    (3x-2)  •  (x-12)

             Which is the desired factorization

Equation at the end of step2:

(x - 12) • (3x - 2) = 0

STEP3:Theory - Roots of a product

 3.1    A product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

 3.2      Solve  :    x-12 = 0 

 Add  12  to both sides of the equation : 

                      x = 12

Solving a Single Variable Equation:

Step-by-step explanation:

\(if \: (x + 12) = (3x + 2) \\ 12 - 2 = 3x - x \\ 2x = 10 \\ x = 5 \\ \\ \\ if(x + 12)(3x + 2) = 0 \\ x + 12 = 0 \: \: \: or \: \: \: 3x + 2 = 0 \\ x = - 12 \: \: \: or \: \: \: x = - \frac{2}{3} \)