solve the systemof linear equations -3x+y=2 -x+y-4=0​

Answer:

She would have $1,126.16 in 3 years.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

\(A(t) = P(1 + \frac{r}{n})^{nt}\)

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.

In this question:

Invested 1000, which means that \(P = 1000\).

Interest of 4%, so \(r = 0.04\)

Semianually is twice a year, so \(n = 2\)

How much money would she have in 3 years?

This is A(3).

\(A(t) = P(1 + \frac{r}{n})^{nt}\)

\(A(3) = 1000(1 + \frac{0.04}{2})^{6} = 1,126.16\)

She would have $1,126.16 in 3 years.

a. Own Price Elasticity of Demand = (-30) / (0) = undefined. Since the own price elasticity of demand is undefined, we cannot determine if the demand is elastic, inelastic, or unitary elastic based on this information.

b. Cross-Price Elasticity of Demand = (12/7) / 0 = undefined. Since the cross-price elasticity of demand is undefined, we cannot determine if goods X and Y are substitutes or complements based on this information.

c. Income Elasticity of Demand = (-2860.71) / (0) = undefined. Since the income elasticity of demand is undefined, we cannot determine if good X is a normal or inferior good based on this information.

d. We cannot calculate the own advertising elasticity of demand with the provided data.

a. To determine the own price elasticity of demand, we need to use the formula:

Own Price Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Price)

Given the demand equation OX​d​ = 7−15PX​+2Py​+0.5M+A, we can calculate the derivative of demand with respect to price:

d(OX​d​) / d(PX​) = -15

Now, let's plug in the values:

% Change in Quantity Demanded = (d(OX​d​) / d(PX​)) * (PX​ / OX​d​) = (-15) * (15 / 7) = -30

% Change in Price = (ΔPX​ / PX​) = (15 - 15) / 15 = 0

b. To determine the cross-price elasticity of demand between goods X and Y, we use the formula:

Cross-Price Elasticity of Demand = (% Change in Quantity Demanded of Good X) / (% Change in Price of Good Y)

Using the same demand equation, we calculate the derivative of demand with respect to the price of good Y:

d(OX​d​) / d(Py​) = 2

Now, let's plug in the values:

% Change in Quantity Demanded of Good X = (d(OX​d​) / d(Py​)) * (Py​ / OX​d​) = (2) * (6 / 7) = 12/7

% Change in Price of Good Y = (ΔPy​ / Py​) = (6 - 6) / 6 = 0

c. To determine the income elasticity of demand, we use the formula:

Income Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Income)

Using the same demand equation, we calculate the derivative of demand with respect to income:

d(OX​d​) / d(M) = 0.5

Now, let's plug in the values:

% Change in Quantity Demanded = (d(OX​d​) / d(M)) * (M / OX​d​) = (0.5) * (-40000 / 7) = -2860.71

% Change in Income = (ΔM / M) = (-40000 - (-40000)) / (-40000) = 0

d. The own advertising elasticity of demand measures the responsiveness of quantity demanded to changes in advertising expenditure. Unfortunately, the given demand equation does not provide any information about advertising expenditure or its impact on quantity demanded.

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Answer:

Train A = 403

Train B = 48

Step-by-step explanation:

A + B = 451

A - B = 355

Solve by adding the equations together.

2A = 806

806 / 2 = A

A = 403

Plug in 403 for A

403 + B = 451

451 - 403 = B

B = 48

The expected value of the uniform variable x is of 101.

The uniform probability distribution is a distribution with two bounds, given by a and b, in which each possible outcome is equally as likely.

The expected value of the uniform probability distribution is given by the mean of the two bounds, as follows:

E(X) = (a + b)/2.

The chips are labeled with the integers 1 through 100, hence the bounds are given as follows:

a = 1, b = 100.

In this problem, we have two trials, each with a = 1 and b = 100, hence the expected value of x is obtained as follows:

E2(x) = 2E(X) = 2(a + b)/2 = a + b = 1 + 100 = 101.

As the mean of the two trials is calculated as the sum of the means of each trial.

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Answer:

10.

Step-by-step explanation:

Lets define a square root.  A square root is a number multiplied by itself.        10 x 10 = 100, this is the closest we can get to 105, therefore 10 is the answer.

Answer:

h = 5 feet

Step-by-step explanation:

V = lwh

40 = 4 x 2 x h

40 = 8h

h = 5

Answer:

X=5/16                    

Explaination:

Answer:

Step-by-step explanation:

\(\frac{2}{9}=\frac{2*3}{9*3}=\frac{6}{27}\\\\\frac{2}{9}=\frac{2*4}{9*4}=\frac{8}{36}\\\\\frac{2/2}{9/2}=\frac{1}{4.5}\)

Answer:

B. 24700

Step-by-step explanation:

Answer:

b. 24700 cm³

Step-by-step explanation:

\(\frac{lwh}{3} \\\\65*30*38/3 = 24700 cm^3\)

Hope this helps! :)

The length of the longer base of the trapezoid is TP = 13 units

The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

The area of the Trapezoid is given by

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

Given data ,

Let the area of the trapezoid be A = 100 units²

Now , the length of the longer base b = 32 units

The length of the shorter base a = 8 units

Let the height of the trapezium be = h

Area of Trapezoid = ( ( a + b ) h ) / 2

Substituting the values in the equation , we get

100 = ( 32 + 8 ) x h / 2

200 = 40h

Divide by 40 on both sides of the equation , we get

h = 5 units

Now , the height be PE , where E lies 12 units from T

Now , from the Pythagoras equation , we get

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Substituting the values in the equation , we get

TP² = PE² + TE² , where PE is the height of the triangle

TP² = 5² + 12²

TP² = 169

Taking square roots on both sides of the equation , we get

TP = 13 units

Hence , the length of the trapezium is 13 units

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The given statement if f(x) is a differentiable function on (a, b) and f'(c) = 0 for a number c in (a, b), then f(x) has a local maximum or minimum value at x = c is true

1. Since f(x) is differentiable on (a, b), it is also continuous on (a, b).
2. If f'(c) = 0, it indicates that the tangent line to the curve at x = c is horizontal.
3. To determine if it is a local maximum or minimum, we can use the First Derivative Test:
  a. If f'(x) changes from positive to negative as x increases through c, then f(x) has a local maximum at x = c.
  b. If f'(x) changes from negative to positive as x increases through c, then f(x) has a local minimum at x = c.
  c. If f'(x) does not change sign around c, then there is no local extremum at x = c.
4. Since f'(c) = 0 and f(x) is differentiable, there must be a local maximum or minimum at x = c, unless f'(x) does not change sign around c.

Hence, the given statement is true.

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a) The rate of people leaving the health club, L(t), can be calculated as:

L(11) = 0.013(11)^2 - 0.25(11) + 8

b) To find the number of people, we integrate the net rate of change over the time interval:

Number of People at t=20 = Integral of (E(t) - L(t)) dt, from t=0 to t=20

c) This can be done by finding the critical points of the net rate of change and evaluating them to determine whether they correspond to maximum or minimum values.

To determine whether the number of people in the facility is increasing or decreasing at time t=11, we need to compare the rates of people entering and leaving the health club at that time.

a) At time t=11 hours:

The rate of people entering the health club, E(t), can be calculated as:

E(11) = -0.018(11)^2 + 11

Similarly, the rate of people leaving the health club, L(t), can be calculated as:

L(11) = 0.013(11)^2 - 0.25(11) + 8

By comparing the rates of people entering and leaving, we can determine if the number of people in the facility is increasing or decreasing. If E(t) is greater than L(t), the number of people is increasing; otherwise, it is decreasing.

b) To find the number of people in the health club at time t=20, we need to integrate the net rate of change of people over the time interval 0≤t≤20 hours.

The net rate of change of people can be calculated as:

Net Rate = E(t) - L(t)

To find the number of people, we integrate the net rate of change over the time interval:

Number of People at t=20 = Integral of (E(t) - L(t)) dt, from t=0 to t=20

c) To determine the time t at which the number of people in the health club is a maximum, we need to find the maximum value of the number of people over the interval 0≤t≤20.

This can be done by finding the critical points of the net rate of change and evaluating them to determine whether they correspond to maximum or minimum values.

Let's calculate these values and solve the problem.

Note: Since the calculations involve a series of mathematical steps, it would be best to perform them offline or using appropriate computational tools.

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Answer:

I think its 5 to the third (the second option). but I'm not sure. Im not the best with exponents.

The equation represented by Ms. Wilson's model is n² + 13n + 40 = (n + 8)(n + 5)

The partially completed model is given as:

    |  n

    |  n²

5   | 5n  |  40

By dividing the rows and columns, the complete model is:

    |  n    | 8

n   |  n²  |  8n

5   | 5n  |  40

Add the cells, and multiply the leading  row and columns

n² + 8n + 5n + 40 = (n + 8)(n + 5)

This gives

n² + 13n + 40 = (n + 8)(n + 5)

Hence, the equation represented by Ms. Wilson's model is n² + 13n + 40 = (n + 8)(n + 5)

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The equation that models the height, y, x seconds after firing is: y = -10(x)(x - 5).

Let's break down the equation and explain its components:

The equation is: y = -10(x)(x - 5)

-10: The coefficient -10 represents the effect of gravity on the projectile's height. It indicates that the height decreases at a rate of 10 units per second squared.

(x): The first term (x) represents the time (in seconds) since the projectile was fired.

It is squared, indicating that the height is influenced by the square of the time.

(x - 5): The term (x - 5) represents the time difference between the current time (x) and the time at which the projectile was fired (5 seconds ago).

It determines how long the projectile has been in the air since it was launched.

By multiplying these components together, we calculate the height (y) of the projectile at a given time (x) after firing.

The equation represents a quadratic function, as indicated by the squared term (x) and the presence of a variable with a coefficient of -10.

The resulting graph of this equation would depict the parabolic trajectory of the projectile's height over time.

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a) The confidence interval is (0.13, 0.35) for the males who have this blood disorder.

b) The number of African males or the sample size is 88 for the value of P to be 0.20

It is mentioned that a geneticist is interested in the proportion of the African males who have a certain minor blood disorder. In a random sample of 100 males, 24 were found to be afflicted.

So we have,

n (total males) = 100

X (afflicted males)= 24

Let P be the sample porportion,

P = X/ n

∴ P = 24 / 100 = 0.24

a) Here it is given to find the confidence interval if the proportion of males is 99% who have this blood disorder so,

c = 99 % = 0.99

∴ α = \(1 -\) c = 1 - 0.99 = 0.01

⇒ α/2 = 0.01/2 = 0.005

Using Z table,

Z of α/2 = \(Z_{0.005}\) = 2.576

Margin of error E = \(Z_{0.005}\sqrt[2]{\frac{P(1-P)}{n} }\)

                            = 2.576 x \(\sqrt{\frac{0.24(1-0.24)}{100} }\)

                            = 0.11

Now, 99 % confidence interval is P ± E

P-E < P < P +E

0.24 - 0.11 < P' < 0.24 + 0.11

P' = (0.13, 0.35) is the required confidence interval.

b) It is given to find the the number of African males when

P = 0.20

Z = 2.576

E = 0.11

Now E = \(Z_{0.005}\sqrt[2]{\frac{P(1-P)}{n} }\)

⇒ 0.11 = 2.576 x \(\sqrt[2]{\frac{0.20(1-0.20)}{n} }\)

⇒ 0.0427 = \(\frac{0.4}{\sqrt{n} }\)

⇒ \(\sqrt{n}\) = 9.37

⇒ n = \((9.37)^{2}\)

⇒ n = 87.7969

Hence the approximate number of males is 88 for the proportion of males with this blood disorder to be 0.20

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Answer:

it would take 20 miles and cost 10 dollars.

Step-by-step explanation: Like up the equations so that 50x=40x+200. When you solve for x (number of miles) you find that x=20. Use 20 in either equation (0.5x or 0.4x+2) to get 10 (total cost).

The probability that a given student is called upon j times during the term

b(32,j,1/80) = (32/j)∗(1/80)j∗(79/80)(32−j)

Probability:

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).

given that

In a class of 80 students, the professor calls on 1 at random for a recitation in each class period

there are 32 class periods in a term

the probability that a given student is called upon j times during the term

b(32,j,1/80) = (32/j)∗(1/80)j∗(79/80)(32−j)

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Answer:

x2

Step-by-step explanation:

you multiply 1x2 to get 2 and multiple 3x2 to get 6

pls mark brainly :)) hope you have a good day

Answer:

x = 146

Step-by-step explanation:

x - 62 = 84

 + 62 = + 62   <-- inverse operation on both sides

      x = 146

Answer:

x= 146

Step-by-step explanation:

x-62=84

x=84+62

x=146

add 62 to 84 to isolate x while getting the answer

Answer:

Step-by-step explanation:

3. If x + 7 = 23, then x = 16

7. If x - 24 = 25, then x = 49.

When performing a statistical analysis, we work with sample rather than the entire population because, we often lack manpower or resources to gather data. So option D is correct.

Statistical work is usually done with a sample. This is done because, if we try to include and collect data from the whole population, it will be very time consuming and need more manpower and resources. It will become a much tedious process.

So a sample which is representative of the whole population is needed. Selecting a sample size and determining the sample must follow certain criteria. They are population parameters we want to estimate, Cost of sampling, Variability of the population, how hard is it to collect data and how precise we want the final estimates to be. All these are taken into consideration and a sample that properly represent the population is determined without bias.

So, option D is the correct answer.

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Answer:

the option 3 says that the volume of box is true.as volume of box is calculated by (v)= l×b×h

Answer:

Step-by-step explanation:

Volume is a cubic measure. That means that the label you get for volume is the length cubed. For example, if the sides of that box were meaured in inches, your label would be in inches cubed. To get a length cubed, you would multiply. If each of the length, width, and height all measured x, then our volume expression would be x*x*x which is x-cubed.

That should tell you that to find the volume of the box shown, you have to multiply the length, width, and height together. The option you want is C. The word "product" means to multiply, in case that was an issue with determining the correct answer.

We will see that the path should be 4 feet wide.

For a rectangle of length L and width W, the area is:

A = L*W

In this case, we know that the dimensions of the garden are:

Now if we add a path of width x that surrounds it, the new length and width will be:

And the area of this rectangle must be 4524 ft^2, then we have:

(50 ft + 2x)*(70 ft + 2x) = 4524 ft^2

Now we can solve this for x.

Ignoring the units, so the math is easier to read, we have:

(50 + 2x)*(70  + 2x) = 4524

50*70 + 50*2x + 2x*70 + 2x*2x = 4524

3500 + 240x + 4x^2 = 4524

4x^2 + 240x + 3500 - 4524 = 0

4x^2 + 240x - 1024 = 0

Now to simplify the quadratic equation, we can divide both sides by 4 to get:

x^2 + 60x  + 256 = 0

The solutions of the quadratic equation are given by Bhaskara's formula:

\(x = \frac{-60 \pm \sqrt{60^2 - 4*1*(-256)} }{2*1} \\\\x = \frac{-60 \pm 68 }{2}\)

We only care for the positive solution (the negative one does not make physical sense).

x = (-60 + 68)/2 = 4

So the width of the path must be 4 ft.

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Answer: D 7/13

Step-by-step explanation:

4+3=7

7+6=13

P(not white)=7/13

Answer:

See image

Step-by-step explanation:

Plato

Answer: The recursive formula for the sequence 2, -6, 18, -54 is given by the following:

a(n) = (-3) * a(n-1)

where a(n) is the nth term of the sequence and a(n-1) is the previous term in the sequence.

This means that each term in the sequence is equal to -3 times the previous term, with the first term being 2. For example, the third term of the sequence (a(3)) would be equal to (-3) * a(2), which is (-3) * (-6) = 18. The fourth term of the sequence (a(4)) would be equal to (-3) * a(3), which is (-3) * 18 = -54. And so on.

This recursive formula can be used to calculate the nth term of the sequence for any value of n.

Answer:

4.24

Step-by-step explanation:

3.64 + 3/5

3.64 + 0.6 <--- 3/5 = 0.6 as a decimal

= 4.24 <--- Final answer

Answer:

5^x - 5^-x

Step-by-step explanation:

g(x) = 5^-x

h(x) = 5^x

We want h(x) - g(x)

h(x) - g(x) = 5^x - 5^-x

This cannot be simplified

Assuming 100% efficiency, the current in the secondary coil will be the same as the current in the primary coil.

The current in the secondary coil is dependent on the voltage ratio of the primary and secondary coils. If the voltage ratio of the coils is the same as the turns ratio, then the current in the secondary coil will be identical to that in the primary coil. Therefore, assuming 100% efficiency, the current in the secondary coil will be the same as the current in the primary coil.

The current in the secondary coil is determined by the voltage ratio of the primary and secondary coils. The voltage ratio is equal to the turns ratio, which is the ratio of the number of turns in the secondary coil to the number of turns in the primary coil. In an ideal transformer with 100% efficiency, the power output in the secondary coil will be equal to the power input in the primary coil. Since power is equal to voltage multiplied by current, and the voltage ratio is equal to the turns ratio, the current in the secondary coil will be the same as the current in the primary coil.

Therefore, assuming 100% efficiency, the current in the secondary coil will be the same as the current in the primary coil.

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