Question 1 (Essay Worth 10 points)
(01.02 MC)
Part A: Solve the equation 7x + 3x - 18 = 6(x+3), and show your work. (5 points)
Part B: Use this list of properties to justify each step of your math work. Justifications may be used more than once if needed. (5 points)
Distributive Property
Subtraction Property of Equality
Combine Like Terms
Multiplication Property of Equality
Division Property of Equality
Given
Addition Property of Equality

The unknown angle x in the triangle is 80 degrees

From the question, we have the following parameters that can be used in our computation:

The triangle

The unknown angle x is calculated using the sum of angles in a triangle theorem

So, we have

x + 60 + 40 = 180

Evaluate the like terms

x + 100 = 180

So, we have

x = 80

Hence, the unknown angle x is 80 degrees

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Expected completion time of the path other than the critical path is 18.16 weeks.

a) The expected times and variances for each of the activities are as follows:

Activity 1:

Expected Time = 9.83 weeks

Variance = 0.69 weeks

Activity 2:

Expected Time = 10.33 weeks

Variance = 2.78 weeks

Activity 3:

Expected Time = 9.83 weeks

Variance = 0.69 weeks

Activity 4:

Expected Time = 7.83 weeks

Variance = 1.36 weeks

b) The expected completion time of the critical path is 19.66 weeks.

The expected completion time of the path other than the critical path is 18.16 weeks.

c) The variance of the critical path is 1.38 weeks.

The variance of the path other than the critical path is 4.14 weeks.

d) If the time to complete the activities on the critical path is normally distributed, the probability that the critical path will be finished in 22 weeks or less is -98.

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Answer:

B is the correct answer.

because Cos = Adj / Hyp

so it is Cos B = 8 / 17

Answer:

x = 55°

Step-by-step explanation:

Hello!

The sum of angles in a triangle is 180°.

To solve for x, we have to subtract the given angles from 180°.

The value of x is 55°.

Angle sum property of a triangle

∠A + ∠B + ∠C = 180°

We need to find the value of ∠A

According to the angle sum property of a triangle

⇢∠A + ∠B + ∠C = 180°

⇢∠A + 75° + 50° = 180°

⇢∠A + 125° = 180°

⇢∠A = 180° - 125°

⇢∠A = 55°

The simplified expression is 1.5 / 0.134, which can be further simplified to approximately 11.19.

To simplify the expression (cos(-60) - tan135) / (tan315 - cos660), we can break it down into two steps.

Step 1: Calculate the values inside the expression.

cos(-60) is equal to cos(60), which is 0.5.

tan135 is equal to -1, as tangent is negative in the second quadrant.

tan315 is equal to 1, as tangent is positive in the fourth quadrant.

cos660 is equal to cos(660-360) which is cos(300), and cos(300) is equal to 0.866.

Step 2: Substitute the calculated values into the expression.

The numerator becomes (0.5 - (-1)) = (0.5 + 1) = 1.5.

The denominator becomes (1 - 0.866) = 0.134.

Therefore, the simplified expression is 1.5 / 0.134, which can be further simplified to approximately 11.19.

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The equation to model the population is P = \(\frac{1}{40}\) \(e^{0.05t}\) + 30

Here the population P of a small town, measured in hundreds, is modeled by the inverse of the function,P−1(t) = 20ln(40t − 1200)

where t is measured in years.

We need to find an equation to model the population.

let y = \(p^{-1}\)(t)

where t is measured in years.

We need to find an equation to model the population.

20\(ln\)(40y - 1200) = t

\(ln\)(40y - 1200) = t/20

\(e^{ln(40y - 1200)}\) = \(e^{0.05t}\)

(40y - 1200) = \(e^{0.05t}\)

40y = \(e^{0.05t}\) + 1200

y = \(\frac{1}{40}\) \(e^{0.05t}\) + 30

Now, we determine the initial value.

P(0) = \(\frac{1}{40}\) + 30

P(0) = 30

The equation to model the population is P = \(\frac{1}{40}\) \(e^{0.05t}\) + 30

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The ratio strength of the final product is 1:0.4.

One technique to indicate concentration is through ratio strength, which uses a ratio to characterize drug concentration. In this context, concentration is defined as the quantity of a solute that makes up one unit in the whole volume of a solution or combination. You should be an expert in ratio strength calculations as a pharmacy student. Ratio strength uses a ratio to describe the medication concentration. So, what it implies is, you have one unit of solute contained in the complete amount of preparation and so generally your ratio strength is expressed as one is to something. In the case of a weight-in-weight, volume-in-volume, or weight-in-volume situation, you would interpret a ratio of 1:2,000 differently.

Drug strength = 800mg

whole volume =2ltrs

The ratio of the solution in 1 ltr is = 400 mg

The ratio strength of the solutions is = 1:0.4

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Answer:

The space NOT occupied by the tennis balls is 12.26 cube inches.

Step-by-step explanation:

The space NOT occupied = volume of cylinder - total volume of spheres

The can is cylinder with volume = \(\pi\)\(r^{2}\)h

where r is the radius and h the height of the cylinder

With the given condition,

r = \(\frac{diameter}{2}\) = \(\frac{2.5}{2}\)

                 = 1.25 inches

h = 3 x diameter = 3 x 2.5

                     = 7.5 inches

So that,

Volume of the can = \(\frac{22}{7}\) x \((1.25)^{2}\) x 7.5

                               = 36.830

Volume of can is 36.83 cube inches.

The tennis ball is a sphere with volume = \(\frac{4}{3}\)\(\pi\)\(r^{3}\)

                                = \(\frac{4}{3}\) x \(\frac{22}{7}\) x \((1.25)^{3}\)

                                = 8.185

Volume of the tennis ball is 8.19 cube inches.

Since they are sold in three's, then;

total volume of the tennis balls = 3 x 8.19

                                     = 24.57

Volume of the tennis balls is 24.57 cube inches.

Thus,

The space NOT occupied = 36.83 - 24.57

                                           = 12.26

The space NOT occupied by the tennis balls is 12.26 cube inches.

Answer:

7/-3

Step-by-step explanation:

6--1=7

-2-1=-3

Answer:

The slope is m=-7/3

m=y²-y¹/x²-x¹

m=(-1)-6/1-(-2)

m=-7/3

refer to the image given below:

Hi!

I can help you with joy!

First of all, the ≥ sign means "greater than or equal to"

So, numbers that are greater than or equal to 4 will make this inequality true.

Now, let's think of the number line.

Numbers that are greater than 4 are to the right of 4:

---------------------------------------------------->

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Note: I can't attach the graph :(

Hope it helps...

~Silent~

The minimum probability of performance needed by each of the individual components is approximately 0.976.

Since the system consists of 5 components that must all perform for the system to work, the probability of the system performing can be expressed as the product of the probability of each component performing:

P(system performs) = P(component 1 performs) x P(component 2 performs) x ... x P(component 5 performs)

Since all components are identical, we can express the probability of each component performing as x, and the probability of the system performing as:

We want the probability of the system performing to be at least 0.91. Therefore, we can set up the following equation:

Taking the fifth root of both sides gives us:

Therefore, the minimum probability of performance needed by each of the individual components is approximately 0.976.

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The value of the expression (2/3)4 is 8/3.

Expression:

An expression also known as algebraic expression consists of unknown variables, numbers and arithmetic operators. And it does not contain any equality or inequality symbols.

Given,

Here we have the expression (2/3)4

Now, we have to evaluate the expression to find the solution for this one.

In order to get the solution for this expression,

We have to rewrite the given expression like the following form,

=> (2/3) x 4

Now, we have to multiply 4 with the numerator, then we get,

=> 8/3

Therefore, the solution of this expression is 8/3.

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Answer:

A. {(-4,-6), (-3,-2), (1,-2), (1,0)}

Step-by-step explanation:

Ans .: The dimensions of the container that will minimize the cost are a base with sides of length 16.7 cm and a height of 8.35 cm.

To minimize the cost of the container, we need to find the dimensions that will use the least amount of material. Let's call the length of one side of the square base "x" and the height of the container "h".

The volume of the container is given as 2000 cm^3, so we can write:

V = x^2h = 2000

We need to find the dimensions that will minimize the cost, which is determined by the amount of material used. We know that it costs twice as much per square centimeter to make the top and bottom as it does the sides.

Let's call the cost per square centimeter of the sides "c", so the cost per square centimeter of the top and bottom is "2c". The total cost of the container can then be expressed as:

Cost = 2c(x^2) + 4(2c)(xh)

The first term represents the cost of the top and bottom, which is twice as much as the cost of the sides. The second term represents the cost of the four sides.

To minimize the cost, we can take the derivative of the cost function with respect to "x" and set it equal to zero:

dCost/dx = 4cx + 8ch = 0

Solving for "h", we get:

h = -0.5x

Substituting this into the volume equation, we get:

x^2(-0.5x) = 2000

Simplifying, we get:

x^3 = -4000

Taking the cube root of both sides, we get:

x = -16.7

Since we can't have a negative length, we take the absolute value of x and get:

x = 16.7 cm

Substituting this into the equation for "h", we get:

h = -0.5(16.7) = -8.35

Again, we can't have a negative height, so we take the absolute value of "h" and get:

h = 8.35 cm

Therefore, the dimensions of the container that will minimize the cost are a base with sides of length 16.7 cm and a height of 8.35 cm.

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The relative frequency of heads is reasonably close to 40%.Mr. Clark's claim about the theoretical probability is likely to be false. This means that the theoretical probability of tails is most likely 0.60.

The relative frequency is the ratio of the number of times an event occurred to the total number of trials. In this case, the relative frequency of heads is 0.38 and tails is 0.62.The theoretical probability of an event is the number of favorable outcomes divided by the total number of possible outcomes.

Here, Mr. Clark claims that the coin is weighted so that the probability of heads is 40%. Therefore, the theoretical probability of heads is 0.40.However, the relative frequency of heads after 200 trials is only 0.38, which is reasonably close to 0.40. Hence, the relative frequency of heads is reasonably close to 40%.

Mr. Clark's claim about the theoretical probability of heads is likely to be false because the relative frequency of heads is less than the theoretical probability of heads (0.38 < 0.40).Therefore, the theoretical probability of tails is 1 - 0.40 = 0.60 because the coin is fair, so the probabilities of heads and tails should add up to 1. Thus, the theoretical probability of tails is most likely 0.60.

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Answer: 64 d^4 - 24 d^2

Factor 8 d^2 out of 64 d^4 - 24 d^2:

Answer:  8 d^2 (8 d^2 - 3)

Answer:

D

Step-by-step explanation:

-1,3

4,-7

-7-3=-10

4--1=5

-10/5=-2

Answer:

5

Step-by-step explanation:

This is quite some trial and error question.

Based on the question, the numbers we can use are 1,3,5,7 and 9.

We will start with the middle digit first.

Since the question has stated it is 3 times the last digit, the number has to be in multiples of 3.

So we are left with: 3 and 9.

Then, the question also states the middle digit is 4 more than the first digit. See, its a digit, so the value cannot be less than 1 (odd numbers only and no negative values), so if we subtract 4 to the middle digit to find the first, it should still be a Positive Single numerical value.

3 - 4 = -1

9 - 4 = 5

Therefore, this middle digit is = 9.

Since we know the middle digit = 9

The first digit will be 9 - 4 = 5

The whole value is now 593.

Answer:

distance = 7.07 units

Step-by-step explanation:

x difference = 7

y difference = -1

using the Pythagorean theorem:

7² + -1² = d²

d² = 49 + 1 = 50

d = 7.07

Answer:

7.1

Step-by-step explanation:

distance between the x is 7 and y is 1

And to find the hypotenuse, you use the quadratic formula, 7^2 + 1^2 = c^2

c=50

and take the square root, which is 7.071, rounds to 7.1

The expression that replaces the heights of the tallest mountain in each continent with the values 8850, 6963, and 6192 is a table with three rows and two columns, containing the continent and its corresponding mountain height in meters.

To replace the heights of the tallest mountain in each continent with the values 8850, 6963, and 6192, an expression is required that can facilitate this transformation.

Which provides a flexible and powerful way to create dynamic web pages.

Language and is used to create web pages that can be displayed on the internet.

To replace the heights of the tallest mountain in each continent with the values 8850, 6963, and 6192, the following expression can be used:

Continent Tallest Mountain Africa 8850 Antarctica 6963 Asia 6192

Here, a table is used to store the data for each continent and its tallest mountain.

The  tag is used to indicate the start of the table, and the  tag is used to indicate the start of a row.

The  tag is used to indicate the header row, while the  tag is used to indicate a data cell.

The data is then entered into the table using the appropriate tags to create the desired layout.

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A 2x3x2 factorial design has three independent variables. What is a factorial design? A factorial design is an experimental design that studies the impact of two or more independent variables on a dependent variable.

The notation of a factorial design specifies how many independent variables are used and how many levels each independent variable has. In a 2x3x2 factorial design, there are three independent variables, with the first variable having two levels, the second variable having three levels, and the third variable having two levels.

The number of treatments or conditions required to create all feasible combinations of the independent variables is equal to the total number of cells in the design matrix, which can be computed as the product of the levels for each factor.

In this case, the number of cells would be 2x3x2=12.Therefore, a 2x3x2 factorial design has three independent variables and 12 treatment groups..

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The math fact that 4 x 6 = 24 helps Matt remember that 6 x 4 = 24, and Sadie arrived at the answer 10 for 6 + 4 by incorrectly adding the numbers in reverse order.

Matt knows that 6 x 4 = 24. This helps him remember that 4 x 6 and 6 x 4 are both equal to 24.

The math fact that Matt can remember based on 4 x 6 = 24 is that multiplication is commutative. This means that the order of the numbers being multiplied doesn't affect the result. So, if 4 multiplied by 6 equals 24, it also implies that 6 multiplied by 4 would give the same result of 24.

Sadie arrived at the answer 10 for 6 + 4 by mistakenly swapping the order of the numbers and performing the addition incorrectly. The correct sum for 6 + 4 is indeed 10. Sadie's error demonstrates the importance of following the correct order of operations, where addition should be performed after ensuring the numbers are in the correct order.

As for Sadie's answer of 6 + 4 = 10, it is not directly related to the multiplication fact that Matt knows.

It is possible that Sadie used a different math fact or strategy to arrive at that answer.

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Answer:

Just add up the fractions and you get your answer. This is because they are quantities of each fruit used.

The formula is weight of object = mass x gravity

if you punch the numbers in the formula correctly the mass in kg is 875.634 kg x 9.8 m/s =  8,581.2132

Hi there!

\(\large\boxed{x = 2.5}\)

y = x² - 5x - 6

Rewrite into factored form by finding two numbers that sum up to -5 and multiply into -6. We can use the numbers -6 and 1:

y = (x - 6)(x + 1) is the equation in factored form.

There are zeroes at:

0 = x - 6

x = 6

0 = x + 1

x = -1

Find the x-value exactly half-way between the two zeroes to find the axis of symmetry:

(-1 + 6) / 2 = 5 / 2 = 2.5

Therefore, the equation for the line of symmetry is:

x = 2.5

The total number of times 7 can occur as the sum on rolling two cubes for 180 times is 30. It is gained by applying the knowledge of probability to the given problem.

What is probability?

Probability depicts the number of possibilities of how many times an event can occur. The probability of happening of an event invariably lies between 0 and 1. For a sure event, it is always 1. Its formula is given as P(E) = No. of favourable outcomes / Total no. of outcomes

Calculation of the total number of times 7 can appear as a sum on rolling two cubes for 180 times

Number of cubes rolled = 2

Total number of outcomes on rolling two cubes = 36

Total possibility of getting 7 as sum = 6

The probability of getting 7 as a sum on rolling two dice only once is given by P(E1)

P(E1) = 6 / 36

         = 1 / 6

She repeated the process 180 times  so the needed probability, P(E) is obtained by multiplying 180 by P(E1)

P(E) = 180 × (1 / 6)

P(E) = 30

Hence, the required probability of getting 7 as the sum is given by 30.

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Done!

Answer:

50 out of 100 or 50%

Step-by-step explanation:

the data represents between quartile 3 and quartile 1 (known as the Inter-Quartile Range, IQR) is, theoretically, supposed to represent 50% of all data items