Solve this linear system using determinants: 2x 3y = 6 −8x − 3y = 12.

Answer:

No solution

Step-by-step explanation:

2>1+2x-2x

the two x's would cancel out.

The answer is no solution

Answer:

y = 8 root 2

Step-by-step explanation:

Since it is a 90-45-45 triangle, y is s root 2

s = 8

so, y = 8 root 2

Answer:

y=8√2

Step-by-step explanation:

Because 2 of the angles are the same, the triangle is isosceles (because of base angles theorem). Therefore, x=8. Using Pythagoras theorem, y=8√2.

Answer:

$375.32

Step-by-step explanation:

100% - 40% = 80%

80/100 = 0.8 (multiplier)

521.28 x 0.8 = 417.024

417.024 to 417.02 (2 d.p.)

100 - 10 = (ans)/100 = 0.9

417.02 x 0.9 = 375.318

$375.32

Step 1: Find the sales price

The surfboard was marked down 40% of its original price, $521.28.

0.40(521.28) = 208.512

521.28 - 208.512 = 312.768

Step 2: Find the final price

We add the tax on the sales price, not the original price. The tax is 10% in this case.

0.10(312.768) = 31.2768

312.768 + 31.2768 = 344.0448

Final price = $344.04

---I did not round until the end in this case, but rounding at every step leads to an answer of $344.05

Hope this helps!

To find the point P on the line y=3x that is closest to the point (50,0), we need to use the formula for the distance between a point and a line. This formula is:

distance = |Ax + By + C| / sqrt(A^2 + B^2)

Where A, B, and C are the coefficients of the equation of the line in the form Ax + By + C = 0.

In this case, the equation of the line y=3x can be written as -3x + y = 0. So we have:

A = -3, B = 1, C = 0

Now we can plug in the values of (50,0) and solve for x and y to find the point P that is closest to it:

distance = |-3x + y| / sqrt((-3)^2 + 1^2)
distance = |-3x| / sqrt(10)

To minimize the distance, we need to minimize |-3x|. This occurs when x = 0. So the point P that is closest to (50,0) is the point (0,0).
To find the point P on the line y = 3x that is closest to the point (50, 0), we need to minimize the distance between P and (50, 0).

Let P(x, y) be a point on the line y = 3x. The distance between P and (50, 0) is given by the distance formula:

D = sqrt((x - 50)^2 + (y - 0)^2)

Since y = 3x, we can rewrite the distance formula as:

D = sqrt((x - 50)^2 + (3x)^2)

To minimize the distance, we can minimize the square of the distance (D^2), as it avoids dealing with the square root:

D^2 = (x - 50)^2 + (3x)^2

Now, we can find the derivative of D^2 with respect to x and set it to 0 to find the critical points:

d(D^2)/dx = 2(x - 50) + 2(3x)^2 * 6x = 0

Solve this equation to find the x-coordinate of the point P. Then, use y = 3x to find the corresponding y-coordinate. Finally, you'll have the coordinates of the point P that is closest to (50, 0).

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There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.

To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.

Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.

Therefore, the number of different votes possible is m * (m-1) / 2.

In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.

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\( \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star\)

\(\textsf{ \underline{\underline{Steps to solve the problem} }:}\)

\( \qquad❖ \: \sf \: \sin {}^{4} ( \alpha) + 2 \sin {}^{2} ( \alpha) \cos {}^{2} ( \alpha) + { \cos {}^{4} ( \alpha) }^{} \)

\( \qquad❖ \: \sf \:( \sin {}^{2} ( \alpha) ) {}^{2} + 2( \sin {}^{2} ( \alpha))( \cos {}^{2} ( \alpha)) + {( \cos {}^{2} ( \alpha)) }^{} \)

( use identity a² + 2ab + b² = (a + b)² )

\( \qquad❖ \: \sf \:( {\sin {}^{2}( { \alpha}) + \cos {}^{2} ( \alpha)) }^{2} \)

( sin² x + cos ² x = 1 )

\( \qquad❖ \: \sf \: {1}^{2} \)

\( \qquad❖ \: \sf \: {1}^{} \)

\( \qquad \large \sf {Conclusion} : \)

Value of that expression is 1

The domain of (f/g)(x) in interval notation is [-3, 6].

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

From the graph,

f(x) has x values from x = -1 to x = 6

g(x) has x values from x = -3 to x = 5

The function f(x) is f(x) = mx + c

Find two coordinates from the graph of f(x).

= (-1, 3) and (6, 4)

m = (4 - 3) / (6 + 1) = 1/7

Now,

3 = (1/7) x -1 + c

3 = -1/7 + c
c = 3 + 1/7

c = 22/7

f(x) = (1/7)x + 22/7  _____(1)

The function g(x) is f(x) = mx + c

Find two coordinates from the graph of g(x).

= (-3, 2) and (5, 4)

m = (4 - 2) / (5 +3) = 2/8 = 1/4

Now,

2 = 1/4 x (-3) + c

2 = -3/4 + c
c = 2 + 3/4

c = 11/4

g(x) = (1/4)x + 11/4  _______(2)

Now,

From (1) and (2)

(f/g)(x)

= f(x)/g(x)

= ((1/7)x + 22/7) / ((1/4)x + 11/4)

The domain of f(x) and g(x) will include the domain of both f(x) and g(x).

So,

x = -1 to x = 6 and x = -3 to x = 5

This can be written as,

[-3, 6]

Thus,

The domain of (f/g)(x) is [-3, 6].

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The bicycle manufacturer is studying the reliability of its models and analyzing the probability of defects. They found the probability of a brake defect is 4 percent and the probability of both brake and chain defects is 1 percent.

Given that the probability of a defect with brakes or chain is 6 percent, we can find the probability of a chain defect using the formula: P(A and B) = P(A|B) * P(B), where P(A and B) is the probability of both events A and B occurring, P(A|B) is the probability of event A occurring given that event B has occurred, and P(B) is the probability of event B occurring.

In this case, we want to find the probability of a chain defect given that there is a defect with either the brakes or the chain. Let's use the events: A = brake defect, B = chain defect, From the problem statement, we know that: P(A) = 0.04 (probability of a brake defect), P(A and B) = 0.01 (probability of both a brake defect and a chain defect)
P(A or B) = 0.06 (probability of a defect with the brakes or the chain).

To find P(B|A or B), we can use the formula: P(B|A or B) = P(A and B) / P(A or B) = 0.01 / 0.06, = 1/6, = 0.1667, So the probability of a chain defect given that there is a defect with either the brakes or the chain is 16.67%, or approximately 2/12 or 1/6.

Therefore, the correct answer is option 2: 2%, Solving for the probability of a chain defect, we get: P(chain defect) = 0.06 - 0.04 + 0.01 = 0.03, So, the probability of a chain defect is 3 percent.

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Answer: 25

Step-by-step explanation:

they are corresponding angles

The required answer is area of the forest will be approximately 2209 km².

Explanation:-

To find the area of the forest after 6 years with a 3.5% annual decrease, follow these steps:

1. Convert the percentage decrease to a decimal by dividing by 100: 3.5% / 100 = 0.035
2. Subtract the decimal from 1: 1 - 0.035 = 0.965. This represents the proportion of the forest remaining each year after the decrease.
3. Raise this value to the power of the number of years: 0.965^6 ≈ 0.789
4. Multiply the initial area of the forest by the result: 2800 km² * 0.789 ≈ 2209.2 km²
5. Round the result to the nearest square kilometer: 2209 km²
After 6 years, the area of the forest will be approximately 2209 km².

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The largest figure that Ash can built with 61 toothpicks is of:

A composition of 12 hexagons.

The number of toothpicks needed is modeled with a linear function, defined as follows:

y = mx + b.

The coefficients of the function are given as follows:

The number of toothpicks in each figure is represented by the following sequence:

(6, 11, 16, ...).

Hence the parameters are given as follows:

m = 5, b = 6.

Thus the definition of the function is of:

T(n) = 5(n - 1) + 6. (as the first figure is with n = 1).

T(n) = 5n + 1.

Then the number of hexagons with 61 toothpicks is obtained as follows:

5n + 1 = 61

5n = 60

n = 60/5

n = 12 hexagons.

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Answer:

I'm sorry, but it is not possible to accurately answer your question without more information. In order to determine the number of dragons and unicorns that Isabella can amuse with joke books, we would need to know more about the constraints represented in the graph. Without knowing the specific conditions represented by conditions A and B, it is not possible to determine how many dragons and unicorns Isabella can amuse.

Answer:

Value after:

7 years = $9971.42

8 years = $8176.56

9 years = $6704.78

Rate of decay = 18%

Step-by-step explanation:

A $40,000 car depreciates in value about 18% per year for the life of the car.

Determine the value of the car after 7,8, and 9 years. What is the rate of decay?

The formula for Depreciation is

FV = PV( 1 - r)^t

Where

FV = Future value

PV = Present value = $40,000

r = Depreciation rate = 18% = 0.18

t = time in years

a) After 7 years

$40,000 (1 - 0.18)⁷

= $9971.4188227

= $9971.42

b) After 8 years

$40,000 (1 - 0.18)⁸

= $8176.5634346

= $8176.56

c) After 9 years

$40,000 (1 - 0.18)⁹

= $6704.7820164

≈ $6704.78

= $9971.42

The Rate of decay = 18%

Answer:

17 degrees

Step-by-step explanation:

See attached image.

We conclude that the angle at the top measures 65.8°.

The whole tree measures 117 ft, and it is broken 34 ft above the ground, forming this way a right triangle.

Then one cathetus of the right triangle measures 34ft, and the hypotenuse measures 117ft - 34ft = 83ft

The angle at the top is θ, the adjacent cathetus to it is the one that measures 34 ft, then to get the angle we can use the relation:

cos(θ) = (adjacent cathetus)/(hypotenuse)

Replacing what we know, we get:

cos(θ) = (34 ft)/(83ft) = 34/83

Solving for θ, we get:

θ = Acos( 34/83) = 65.8°

So we conclude that the angle at the top measures 65.8°.

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Answer: Incorrect, 19492.5

Step-by-step explanation:

Given

Jo said 565 times 34 one half  i.e. \(565\times 34\ \dfrac{1}{2}\)   is \(595111\)

Solving for a mixed fraction

\(\Rightarrow 565\times \dfrac{34\times 2+1}{2}\\\\\Rightarrow 565\times \dfrac{69}{2}=\dfrac{38985}{2}=19492.5\)

Clearly, \(19492.5\neq 595111\)

Thus, Jo is wrong

Answer:

Answer:

Step-by-step explanation:

A population parameter describes an entire population; a particular characteristic of an entire population. A value that describes the entire population. In this context, the population parameter is looking into the average ages of fathers when they had their first child, but this value is not given. The mean given here is the sample statistic.

Since, the population studied here is a very large population (all fathers), you have a statistic. But sometimes, if the population is very small and groups are small enough to measure, you have a parameter.

Answer:

D

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

Answer:

Step-by-step explanation:

10² + 2(6 - 3)²

100 + 2 (3)²

100 + 2(9)

100 + 18

118

Answer: 2

Step-by-step explanation:

The slope intercept form states that y=mx+b

M represents the slope.

Answer:

2

Step-by-step explanation:

it is of the form y=mx+c

therefore m= slope

m=2

if my answer helped pls mark me as brainiest:)

a) The probability distribution of X is \((2/3)^k\) * \((1/3)^{2-k\) * C(2, k).

b) Mean number of accidents that A suffered is 2p.

c) The probability that B suffered more accidents than A is P(A = 0, B = 1) + P(A = 0, B = 2) + P(A = 0, B = 3) + P(A = 1, B = 2) + P(A = 1, B = 3) + P(A = 2, B = 3).

To solve this problem, let's consider the following information:

Let X be the number of accidents that befall driver A.

Since driver A drives twice as much as driver B, we can assume that driver B drove half the distance of driver A. Therefore, the ratio of the distances driven by A and B is 2:1.

We are also given that A and B are equally good drivers with the same risk per mile driven.

Now, let's answer the questions:

(a) Probability distribution of X:

To find the probability distribution of X, we can use the binomial distribution. The probability of an accident occurring for each driver remains the same for each mile driven. Let p be the probability of an accident occurring for either driver A or B.

The number of accidents that befall A follows a binomial distribution with parameters n and p, where n is the total number of miles driven by A.

If we assume that driver B drove a distance of 1, then driver A drove a distance of 2.

Therefore, the probability distribution of X, the number of accidents that befall A, is given by:

P(X = k) = \((2/3)^k\) * \((1/3)^{2-k\) * C(2, k)

where C(2, k) represents the binomial coefficient "2 choose k," which is equal to 2! / (k!(2-k)!).

(b) Mean number of accidents that A suffered:

The mean or expected number of accidents that A suffered can be calculated using the formula:

E(X) = n * p

Since driver A drove a distance of 2, we have:

E(X) = 2 * p

(c) Probability that B suffered more accidents than A:

To find the probability that B suffered more accidents than A, we need to consider all the possible values of accidents for A and B and calculate the probabilities for each case.

Let's consider the following scenarios:

A has 0 accidents: B can have 1, 2, or 3 accidents.

A has 1 accident: B can have 2 or 3 accidents.

A has 2 accidents: B can only have 3 accidents.

We calculate the probabilities for each scenario and sum them up to get the final probability:

P(B > A) = P(A = 0, B = 1) + P(A = 0, B = 2) + P(A = 0, B = 3) + P(A = 1, B = 2) + P(A = 1, B = 3) + P(A = 2, B = 3)

Note that P(A = 2, B = 1) is not included because A cannot have more accidents than B.

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Answer:

A real estate agent is someone who helps people to either buy or sell a home or a piece of property. One can work either as a listing agent, to help a client sell a home, or as a buyer's agent, to help the client buy a home.

Step-by-step explanation:

Answer:

Real estate agents assist their clients to rent, buy, or sell their properties. They help clients out by giving them information on the market and guide them through their needs.

The calculated values are:

\(e_{n+1\) = 50

\(h_{n+1\) = 0.9

\(d_{n+1\) = 2.1

To find the formulas for \(e_{n+1\), \(h_{n+1\), and \(d_{n+1\), we can use the given information about the transitions between the different life stages of the ducks.

Given:

\(e_n\) = number of eggs at time t = n

\(h_n\) = number of hatchlings at time t = n

\(d_n\) = number of ducks at time t = n

The formulas for \(e_{n+1\), \(h_{n+1\), and \(d_{n+1\) can be derived as follows:

\(e_{n+1\) = 5 \(d_n\) (Each duck at time t = n lays 5 eggs, which will be eggs at time t = n + 1.)

\(h_{n+1\) = 0.9 * \(e_n\) (90% of the eggs at time t = n hatch into ducklings at time t = n + 1.)

\(d_{n+1\) = 0.7 * \(h_n\) (70% of the ducklings at time t = n become ducks at time t = n + 1.)

Therefore, the formulas for\(e_{n+1\), \(h_{n+1\), and \(d_{n+1\) are:

Using these formulas, we can calculate the values of \(e_{n+1\), \(h_{n+1\), and \(d_{n+1\) based on the given values of en, hn, and dn.

To calculate the values of \(e_{n+1\), \(h_{n+1\), and \(d_{n+1\) based on the given formulas, we substitute the given values of \(e_n\), \(h_n\), and \(d_n\) into the respective formulas. Let's perform the calculations:

Given values:

\(e_n\) = 1

\(h_n\) = 3

\(d_n\) = 10

Using the formulas:

\(e_{n+1\)= 5 \(d_n\)

\(e_{n+1\)= 5 * 10

\(e_{n+1\) = 50

\(h_{n+1\) = 0.9 * \(e_n\)

\(h_{n+1\) = 0.9 * 1

\(h_{n+1\)= 0.9

\(d_{n+1\) = 0.7 * \(h_n\)

\(d_{n+1\)= 0.7 * 3

\(d_{n+1\)= 2.1

Therefore, the calculated values are:

\(e_{n+1\) = 50

\(h_{n+1\) = 0.9

\(d_{n+1\) = 2.1

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Answer:

315

Step-by-step explanation:

You're welcome
Answer above is rounded btw

Full number is:315.24444

Answer:

2 apples

Step-by-step explanation:

he should be more careful next time :)

SI unit is an international system of measurements that are used universally in technical and scientific research to avoid the confusion with the units. Having a standard unit system is important because it helps the entire world to understand the measurements in one set of unit systems.

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The given question is incomplete, complete question is:

What is the SI prefix for each of the following multiples and submultiples of a unit?

\(10^-^9\)