Solve the system of equations.
2x+2y+ 6z = 8
5x+6y + 5z = 3
5x + 6y + 3z = 5
a. (x= 34, y =
-27,z = -1)
b. (x= 33, y=-26, z = 0)
c.
d.
(x = 35, y = -28, z = -2)
(x= 36, y=-29, z = 1)

Answer:

x = the unknown number. Its square is x2. The sum of a number and its square is 12:

x + x²= 12

Putting the quadratic into standard form:

x2 + x - 12 = 0

(x+4)(x-3) = 0

x = -4 and 3

Let's check x=-4:

x + x2 = 12

(-4) + (-4)2 = 12

-4 + 16 = 12

12 = 12

Now let's check x= 3:

x + x2 = 12

3 + 32 = 12

3 + 9 = 12

12 = 12

Yup, they both work. There are two answers, x = -4 and x = 3

Step-by-step explanation:

The factors of 9x² +49y² are:

D. (3x + 7y)(3x + 7y) and C. (3x - 7y)(3x - 7y)

We can use the identity:

a² + b² = (a + b)(a - b)

To factor the expression 9x² + 49y², let a = 3x and b = 7y. Then we have:

9x² + 49y² = (3x)² + (7y)² = (3x + 7y)(3x - 7y)

So the factors of 9x² + 49y² are (3x + 7y) and (3x - 7y). We can see that these factors are not prime, as they can be factored further into (3x + 7y)(3x + 7y) and (3x - 7y)(3x - 7y).

The probability that you need to pick 7 students to find 2 students using Chrome is approximately 65%.

To calculate this, we can use the formula P = (n!/r!(n-r)!) * p^r * q^(n-r), where n = 7 (number of students to pick), r = 2 (number of Chrome users to find), p = 0.49 (probability of Chrome user), and q = 0.51 (probability of non-Chrome user). By plugging the numbers into the equation, the probability of finding 2 Chrome users is 0.649.

In other words, if you randomly pick 7 students from the group, there is a 65% chance that you will find 2 students using Chrome.

This is because 49% of the group use Chrome, so if you pick 7 students randomly, the probability of picking 2 Chrome users is high.

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26 * 25 * 24 * 22 = 16,384.

There are 16,384 seven-digit license plates that contain exactly four letters, all of which are distinct. This is because there are 26 possible letters, so the first letter could be any of those letters, and then the second letter has 25 options, and so on until the fourth letter, which has 22 possible letters. So, the total number of combinations is 26 * 25 * 24 * 22 = 16,384.

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Answer:

G (-3,-1)

H (-2,-3)

I (1,1)

Step-by-step explanation:

After a reflection across y=2, the y-coordinates of the vertices will change sign while the x-coordinates remain the same. Thus, the new coordinates of the vertices will be:

G (-3,-1)

H (-2,-3)

I (1,1)

Answer:

G (3,3) , H (2,5), I (-1,1)

Step-by-step explanation:

Since it’s flipped over the Y-Axis, the X-Axis numbers remain the same.

WRONG!!

didnt read the question correctly, so the vertices are incorrect lol.

The average number of customers in the West End Donut Shop simultaneously is 30, which is obtained by using the arrival rate and service rate formulas for a queueing system.

To find the average number of customers in the shop simultaneously, we can use the concept of the arrival rate and the service rate.

The arrival rate is the rate at which customers arrive at the shop, and can be calculated as:

arrival rate = number of customers / time

arrival rate = 2400 customers / 10 hours

arrival rate = 240 customers per hour

The service rate is the rate at which customers are served by the shop, and can be calculated as:

service rate = 60 minutes / 5 minutes per customer

service rate = 12 customers per hour

Using the formula for the average number of customers in a queueing system, we get:

average number of customers = arrival rate / (service rate - arrival rate)

average number of customers = 240 / (12 - 240/60)

average number of customers = 240 / 8

average number of customers = 30

Therefore, on average, there are 30 customers in the West End Donut Shop simultaneously.

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It depends on whether the frustum is formed by slicing a cone or a pyramid. If it is a cone, then the area of frustum consists of two circular bases and a curved surface.

Curved surface area ≈  [tex]81.5 cm^2[/tex] (rounded to one decimal place)

Curved surface area [tex]= (1/2) \times (C1 + C2) \times L[/tex]

Where C1 and C2 are the circumferences of the bases of the frustum, and L is the slant height.

From the diagram, you can see that C1 = 2πr and C2 = 2πR, where r and R are the radii of the bases. You can also see that L = √(H² + (R - r)²), where H is the height of the frustum.

Substituting these values into the formula, you get:

Curved surface area = (1/2) × (2πr + 2πR) × √(H² + (R - r)²)

Simplifying, you get:

Curved surface area = π(r + R) × √(H² + (R - r)²)

Now you just need to plug in the values given in the question. The height of the large cone is 12 cm, so [tex]H = 12 - 6 = 6[/tex] cm. The radius of the small base is 3 cm, so r = 3 cm. The radius of the large base is 4 cm, so [tex]R = 4[/tex] cm.

Curved surface area = π(3 + 4) × √(6² + (4 - 3)²)

Curved surface area ≈ π × 7 × √[tex]37[/tex]

Therefore, Curved surface area ≈  [tex]81.5 cm^2[/tex] (rounded to one decimal place)

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Answer: x = squrt (1/20

Step-by-step explanation:

The maximum number of 12-ton trucks that the cargo ship can carry per trip is 750. This is obtained by solving the linear programming problem subject to the given constraints.

Let's denote the number of 5-ton trucks and 12-ton trucks that the cargo ship carries by x and y, respectively. Then, we can write the following two constraints based on the requirements.

x + y ≥ 750 (constraint 1: the ship must carry at least 750 trucks)

5x + 12y ≤ 5000 (constraint 2: the total weight of the trucks can be at most 5,000 tons)

We want to maximize the number of 12-ton trucks y, subject to these two constraints.

To solve this problem, we can use linear programming techniques.

The feasible region is the set of all (x,y) pairs that satisfy the two constraints

The feasible region is bounded by the x-axis, the y-axis, and the two lines 5x + 12y = 5000 and x + y = 750.

We want to find the point in the feasible region where the number of 12-ton trucks y is maximized. This point will lie on one of the corners of the feasible region.

We can calculate the coordinates of the corners of the feasible region by solving the system of equations formed by the two constraint lines:

x + y = 750      (equation 1)

5x + 12y = 5000      (equation 2)

Multiplying equation 1 by 5, we get:

5x + 5y = 3750        (equation 3)

Subtracting equation 1 from equation 2, we get:

7y = 1250

y = 178.57 (rounded to 2 decimal places)

Substituting this value of y into equation 1, we get:

x = 571.43 (rounded to 2 decimal places)

The coordinates of this corner point are (571.43, 178.57).

Similarly, we can calculate the coordinates of the other corner points:

(750, 0), (500, 250), and (0, 750)

We can now evaluate the objective function (the number of 12-ton trucks y) at each of these corner points:

At (571.43, 178.57), y = 178.57

At (750, 0), y = 0

At (500, 250), y = 250

At (0, 750), y = 750

The maximum value of y is 750, which occurs at the point (0, 750).  

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The perimeter of parallelogram ABCD in which AM ,BN are angle bisector and DM = 4ft and MN = 3ft  is: P = 2(AB + BN) = 2(2 + 2) = 8 ft.

Perimeter is the total length of the boundary or the distance around the edge of a two-dimensional shape such as a polygon or a circle.

To find the perimeter of parallelogram ABCD, we need to find the length of each side of the parallelogram.

Since AM and BN are angle bisectors of parallelogram ABCD, we know that they intersect at the diagonals' midpoint. Therefore, we can say that DM = MB and MN = NA.

Using this information, we can label the sides of the parallelogram as follows:

AB = CD = x (opposite sides of a parallelogram are equal)

AM = MC = BM = MD = x/2 (diagonals of a parallelogram bisect each other)

BN = ND = NA = NC = y (angle bisectors of a parallelogram bisect opposite angles and sides)

DM = 4 ft and MN = 3 ft (given)

Since DM = MB, we can write:

x/2 + 4 = y + 3

x/2 - y = -1

Since BM = MC, we can write:

x/2 + y = x

y = x/2

by substituting-

x/2 + 4 = x/2 + 3

x = 2

Therefore, AB = CD = 2 ft and BN = ND = NA = NC = x/2 = 1 ft.

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Answer:

387.692307692

Step-by-step explanation:

Answer:

To see why, we can compare the graphs of the two functions. The graph of ƒ(x) = e^x is an exponential function that starts at the point (0,1) and increases rapidly as x increases. The graph of g(x) = 5e^x is also an exponential function, but it starts at the point (0,5), which is five times higher than the starting point of ƒ(x). This means that g(x) is a vertical stretch of ƒ(x) by a factor of 5.

Option a) g(x) = e^x + 7 is a vertical shift of ƒ(x) by 7 units, but it does not represent a vertical stretch.

Option b) g(x) = 1/3e^x is a vertical compression of ƒ(x) by a factor of 1/3, rather than a vertical stretch.

Option d) g(x) = e^4x represents a horizontal stretch of ƒ(x) by a factor of 1/4, but it does not represent a vertical stretch.

The independent variable in this hypothesis is the method of studying, specifically whether students engage in spaced learning or cramming.

In the hypothesis that students who study for 7 hours over the course of a week using spaced learning will perform better than students who cram for 7 hours the night before the exam, the independent variable is the method of studying.

This variable is independent because it is being manipulated and controlled by the researcher. In this case, the researcher is comparing two different methods of studying and measuring the effect on exam performance.

Spaced learning involves breaking up the study time into smaller, more manageable chunks over a period of time, such as a week. Cramming, on the other hand, involves trying to learn all the material in a short period of time, such as the night before the exam.

The dependent variable in this hypothesis is exam performance, which is expected to be better for students who engage in spaced learning compared to those who cram.

The hypothesis suggests that the method of studying has a causal relationship with exam performance, but it is the independent variable, the method of studying, that is being manipulated to test this hypothesis.

Therefore the independent variable in the hypothesis that students who study for 7 hours over the course of a week using spaced learning will perform better than students who cram for 7 hours the night before the exam is the method of studying, specifically whether the student engages in spaced learning or cramming.

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Answer:

There are several ways to make 45 cents using different coins:

Nine nickels

Four dimes and one nickel

Three dimes and six nickels

Two dimes and one quarter

One dime, two nickels, and three pennies

One quarter and two dimes

One quarter, one dime, and four nickels

One quarter, three nickels, and five pennies

45 pennies

So there are 9 ways to make 45 cents.

I Hope This Helps!

Answer:

angle "E" =70°

Step-by-step explanation:

<ABC=<ADC

<ADC=<EAD (alternate angles)

<EAD=<DEA (because /DA/=/DE/

and <DEA=angle E, therefore answer=70°

To find the two consecutive odd integers, let's set up an equation using the given information. Let x be the smaller odd integer, then the next consecutive odd integer is x+2.

The problem states that the product of these two integers is 77 more than twice the larger integer. In equation form, this can be written as:

x * (x + 2) = 2(x + 2) + 77

Now, let's solve for x:

x * (x + 2) = 2x + 4 + 77
x^2 + 2x = 2x + 81
x^2 = 81

To find the value of x, take the square root of both sides:

√(x^2) = √81
x = 9

So, the smaller odd integer is 9. The next consecutive odd integer is 9 + 2 = 11.

Therefore, the two consecutive odd integers are 9 and 11.

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The two consecutive odd integers are 9 and 11.

To find the two consecutive odd integers whose product is 77 more than twice the larger, we can set up the following equation:
x * (x + 2) = 2(x + 2) + 77
Here, x represents the first odd integer, and x + 2 represents the second consecutive odd integer. Now, let's solve the equation step by step:
1. Expand the equation: x^2 + 2x = 2x + 4 + 77
2. Simplify the equation: x^2 + 2x = 2x + 81
3. Subtract 2x from both sides: x^2 = 81
4. Take the square root of both sides: x = ±9
Since we're looking for positive integers, x = 9. Therefore, the two consecutive odd integers are 9 and 11.

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If the probability of a breakdown on assembly line 'a' is 12% and probability of a breakdown on assembly line 'b' is 16%, then the probability that assembly line 'a' or assembly line 'b' break down is equals to the 26%, i.e., 0.26.

We have the probability of a breakdown on assembly line 'a' = 12% = 0.12

The probability of a breakdown on assembly line 'b' = 16% = 0.16

The probability that both assembly lines break down = 2% = 0.02

Let's two events a breakdown on assembly line 'a' and a breakdown on assembly line 'b' be 'X' and 'Y' respectively. That is P(X) = 0.12, P(Y) = 0.16,

P(X and Y) = P(X∩Y) = 0.02

we have to calculate the probability that assembly line 'a' or assembly line 'b' break down, P( X or Y) = P(X∪Y). Using addition rule of probability, the probability that event A or event B occurs is equal to the probability that A occurs plus the probability that B occurs minus the probability that both occur. So, P( X or Y) = P(X) + P(Y) - P( X∩Y)

= 0.12 + 0.16 - 0.02

= 0.26

Hence, required probability is 0.26.

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The distance between points B and C on the graph is equal to: D. √34 units.

In Mathematics, Pythagorean's theorem is represented by the following mathematical expression:

c² = a² + b²

Where:

a, b, and c represent the side length of any right-angled triangle.

In order to determine the distance between points B and C in right-angled triangle ABC, we would have to apply Pythagorean's theorem.

BC² = AB² + AC²

BC² = 5² + 3²

BC² = 25 + 9

BC² = 34

BC = √34 units.

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Answer:

domain is [-11 , -3]

Step-by-step explanation:

domain is x

range is y

x values are from -11 to -3

Answer:

Step-by-step explanation:

Three strategies that implement to encourage the use of BEVs are incentives, Infrastructure and Regulations. The cost of gasoline per mile for an ICE vehicle is $0.016 per mile.

Incentives: The federal government could offer financial incentives such as tax credits, rebates, or grants to consumers who purchase BEVs. This would make BEVs more affordable and help to offset the higher upfront cost of these vehicles.

Infrastructure development: The federal government could invest in the development of charging infrastructure for BEVs, such as public charging stations. This would help to alleviate range anxiety and make BEVs more convenient and practical for consumers.

Regulations: The federal government could implement regulations that incentivize or require automakers to produce more BEVs. This could include emissions standards that are more favorable to BEVs, or mandates for automakers to produce a certain percentage of their vehicles as electric.

To calculate the cost of gasoline per mile for an ICE vehicle with fuel efficiency of 235 miles per gallon and gasoline cost of $3.75 per gallon, we divide the cost of gasoline by the fuel efficiency:

Cost per mile = $3.75 / 235 miles per gallon

Cost per mile = $0.016 per mile

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The standard deviation for the number of people with the genetic mutation in a group of 1000 individuals is approximately 4.89.

To find the standard deviation for the number of people with a particular genetic mutation in a group of 1000 individuals, we first need to understand the concept of binomial distribution.

Binomial distribution is a statistical probability distribution that represents the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure).

In this case, the probability of success (having the genetic mutation) is 0.04, and the probability of failure (not having the mutation) is 0.96. Thus, we can model the number of people with the mutation in a group of 1000 individuals using a binomial distribution with n = 1000 and p = 0.04.

The formula for the standard deviation of a binomial distribution is:

σ = √(np(1-p))

Where σ is the standard deviation, n is the number of trials, and p is the probability of success. Plugging in the values, we get:

σ = √(1000 x 0.04 x 0.96) = 4.89

In other words, we can expect that the number of people with the genetic mutation in a group of 1000 individuals will vary around the mean of 40 (1000 x 0.04) by about 4.89, with about 68% of the observations falling within one standard deviation of the mean.

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Answer:

Step-by-step explanation: Its 6x, you add the 6 + 1 then keep the x.

First we have to remember what the perimeter of a rectangle is. The perimeter is the outside edges of the rectangle, think of it as the fence around a yard. This means that the perimeter of a rectangle or a square has four sides: two widths and two lengths.

This problem tells us that the length of this rectangular parking lot is 98m. Since this parking lot is a rectangle, each of the parallel lengths are the same size. Therefore, each length is 98m and that takes care of 196m of the perimeter [tex](98\text{m} \times 2)[/tex].

To find the width, we know that the lengths take up 196m of the total 364m of the perimeter which leaves 168m for the widths. Again, since this parking lot is a rectangle, each parallel width is the same size so we can find one width by dividing the left over perimeter by 2: [tex]168\text{m} \div 2 = \bold{84m}[/tex].

I hope that helps!

The expression -5 + 28p9q5 - 12pq + 7 is equivalent to 7. Since all the terms except the last one contain variables, we can use algebra to solve for the value of the expression.

Algebra is a branch of mathematics which deals with the manipulation of equations, inequalities, and other mathematical expressions. Algebra is used to solve equations, simplify expressions, and model real-world problems.

To begin, we can add -5 and 7 to obtain 2. This means that the expression is now equal to 2 + 28p9q5 - 12pq. We can then simplify this expression by combining like terms.

Since 28p9q5 and -12pq are both products of the same variables, we can add them together. When we do so, we obtain 16p9q5, which means that the expression is now equal to 2 + 16p9q5.

Finally, we can simplify the remaining term by breaking down the product. We can divide 16 by 8 to obtain 2, and then divide 9 by 3 to obtain 3. This means that the expression is now equal to 2 + 2p3q5. Since there are no more terms to simplify, we can conclude that the answer is 2.

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The goal of calculating an acceptance interval is to find the probability that the true mean lies between two values, hence the correct answer is option a.

The acceptance interval is a method for developing a tolerance interval for a specified percentage of future measurements in a distribution. The tolerance interval specifies the interval into which a specified percentage of future measurements will fall.

An acceptance interval is a quality control tool for assessing whether the characteristics of a production lot meet predetermined quality criteria. These predetermined criteria are usually in the form of upper and lower limits for the interval.

The acceptance interval is utilized to detect whether a production lot's results are within the tolerances or specifications of the quality criteria.

The purpose of calculating an acceptance interval is to locate the probability that the true mean falls between two values. In conclusion, the goal of calculating an acceptance interval is to find the probability that the true mean lies between two values.

Therefore, option a is the correct answer.

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Answer:

12x - 6

Step-by-step explanation:

[tex] \rm \: 4 + 5(3x - 2) - 3x[/tex]

[tex] \rm \: = 4 + 15x - 10 - 3x \: \sf (distribute \: the \: 5)[/tex]

[tex] \rm= 12x - 6 \: \sf (combine \: like \: terms)[/tex]

[tex] \rm= 6(2x - 1) \: \sf (factor \: out \: a \: 6)[/tex]

[tex] \rm \: = 6(2x) - 6(1) \: \sf (distribute \: the \: 6)[/tex]

[tex] \rm \:= 12x - 6 \: \sf (simplify)[/tex]