Graph the solution to the following system of inequalities.
y≤2x+3
y> -3x+5

The long-term probability that a given marked rat is in room 4 is 1/3

What is meant by probability?

In statistics, probability is defined as the measure of the likelihood of an event to happen and it measures the certainty of the event.

Here we have given that Forty rats are placed at random in a house having 4 rooms. There is one door between rooms 1 and 2, one door between rooms 1 and 4, one door between rooms 2 and 4, one door between rooms 2 and 3, and two doors between rooms 3 and 4 see the book for a picture). There are no doors between rooms 1 and 3. After each minute, a rat may change rooms, or stay still.

And we need to find the  the long-term probability that a given marked rat is in room 4.

By using the eigenvalues method, we know that

Room 4 has the 3 exits that is from Room 1, Room 2 and Room 3.

So, here we have 3 possibilities for the exit so, the rat can choose any one these three ways,

So, the probability can be written as,

=> 1/3

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Step-by-step explanation:

is it like this ? no diagrams ?

The variable t becomes the subject of the equation c=t³ - 8v by adding 8v to both sides and taking the cube root, giving t = ∛(c + 8v).

We need to make t the subject of the equation c=t³ - 8v. To do this, we first add 8v to both sides of the equation to isolate t³ on one side, giving us t³ = c + 8v. We then need to take the cube root of both sides to solve for t. Hence, t = ∛(c + 8v). Now, t is the subject of the equation.

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Answer:

y= -1

Step-by-step explanation:

divide both side by 3

then you'll get -5+2=7

subtract 2 from both sides to get

-5y=5

divide -5 on both sides and you'll get y= -1

(hope my explanation made sense to you)

Answer: 2096 work hours per year

Answer:

y maximum is at 1 for both the points (4,1) and (-4,1)

Step-by-step explanation:

Answer:

plot the following points:

(-1, 1/2) (0, 1) (1, 2) (2, 4) (3,8)

Step-by-step explanation:

Answer:

The temperature went up by 29 degrees.

Step-by-step explanation:

Since -24 is negative,

Add 5 to 24 = 29.

a. The number of red roses left t hours after the store opens \(R(t) = 400/2^{t/2}\)    

b. The number of boxes of chocolate left t hours C(t) = 200 - 0.15t

c. One possible solution is t ≈ 7.546 hours after the store opens.

d. there are 194 boxes of chocolates left.

e. you need to arrive at the store no later than 7.504 hours after it opens.

a. The proportion (relative frequency) of times an event is anticipated to occur when an experiment is repeated a large number of times under identical conditions is known as the probability of the event.:

\(R(t) = 400/2^{t/2}\)

b. Let C(t) be the quantity of boxes of chocolate left t hours after the store opens. At first, there are 200 boxes, of which 15% are purchased every hour. We can therefore write:

C(t) = 200 - 0.15t

c. We must solve the equation R(t) = C(t) in order to determine the time at which the number of boxes of chocolates and the number of roses are equal. We obtain: by substituting the formulas we discovered in parts a and b:

\(400/2^{t/2} = 200 - 0.15t\)

Simplifying this equation, we get:

\(2^{t/2 + 1} + 0.15t - 400 = 0\)

We can solve this equation numerically, using a calculator or a computer program. One possible solution is t ≈ 7.546 hours after the store opens.

d. At 12:30 in the early evening, which is 3.5 hours after the store opens, we can utilize the recipe we tracked down to some extent b to work out the quantity of boxes of chocolates left:

C(3.5) = 200 - 0.15(3.5) = 194.25

We ought to adjust this solution to appear to be legit with regards to the issue. Since we cannot have a fraction of a box, we can round to the nearest integer and state that there are 194 chocolate boxes remaining.

e. To buy 36 red roses, we need to solve the equation R(t) = 36. Substituting the formula we found in part a, we get:

\(400/2^{t/2}= 36\)

Simplifying this equation, we get:

2^(t/2) ≈ 11.111

Taking the logarithm of both sides, we get:

t/2 ≈ log2(11.111)

t ≈ 2 log2(11.111)

Using a calculator, we get:

t ≈ 7.504 hours after the store opens.

Therefore, you must arrive at the store no later than 7.504 hours after it opens in order to purchase 36 red roses.

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Answer:

120,000 ft^3

Step-by-step explanation:

step 1: 20ft times 150ft is 3000ft.

step 2: 3000ft times 40ft^3 is 120,000ft^3

The P-value for the hypothesis test is 0.1034 .Round to two decimal places, the P-value is 0.10

To find the P-value for this hypothesis test, we need to use the sample proportion of on the road cars that are 10 years or older, which is the number of cars in the sample that are 10 years or older divided by the total number of cars in the sample. In this case, the sample proportion is \(\frac{357}{1500}= 0.238.\)

We can then use this sample proportion to calculate the P-value, which is the probability of observing a sample proportion as extreme as the one we have seen, or even more extreme, given that the null hypothesis is true. In this case, the null hypothesis states that the true proportion of on the road cars that are 10 years or older is 0.25, so we need to calculate the probability of seeing a sample proportion as low as 0.238, or lower, if the true proportion is actually 0.25.

To do this, we can use a one-sided test, since we are only interested in the probability of seeing a sample proportion lower than 0.25. We can use a normal approximation to the binomial distribution to calculate the P-value.

The standard error of the sample proportion is given by the formula:

SE \(= \sqrt\frac {p \ * (1 - p)}{n}\)

Where p is the null hypothesis value for the proportion (0.25 in this case) and n is the sample size (1500 in this case). Plugging these values into the formula gives us:

SE = \(\sqrt\frac{0.25 * (1 - 0.25)}{1500}= 0.0158\)

The z-score for the sample proportion is then given by the formula:

z =\(\frac{ (p - p_0)}{SE}\)

Where p is the sample proportion (0.238 in this case) and p0 is the null hypothesis value for the proportion (0.25 in this case). Plugging these values into the formula gives us:

\(z = \frac{(0.238 - 0.25)}{0.0158} = -1.27\)

We can then use the z-score to calculate the P-value. Since we are performing a one-sided test, we only need to consider the probability of seeing a sample proportion lower than 0.25. This is given by the area under the normal curve to the left of the z-score. We can use a z-table or a calculator to find this probability.

The probability for a z-score of -1.27 is about 0.1034. This is the P-value for the hypothesis test.

Round to two decimal places, the P-value is 0.10

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The Minimum sample size table is attached below

Answer:

\(X=173\)

Step-by-step explanation:

From the question we are told that:

Confidence Interval \(CI=99\%\)

Variance \(\sigma^2=30\%\)

Generally going through the table the

Minimum sample size is

\(X=173\)

Answer:

5.1 can be written as 51/10 (the quotient of the integers 51 and 10. So it is a rational number

Step-by-step explanation:

Recall that a rational number is a number that can be written as the quotient of two integer numbers.

In particular the number 5.1 can be written as 51/10 (the quotient of the integers 51 and 10. So it is a rational number.

The correct option of system of equations that can be used to find the temperature at which the degrees Celsius and the degrees Fahrenheit would be equivalent is the option;

5·F - 9·C = 160

F - C = 0

A system of equation, is a set of equation that have common variables.

The equation for conversion of the temperature in degrees Celsius to the temperature in degrees Fahrenheit is; 9·C = 5·F - 160

When the temperature in degrees Celsius is equivalent to the temperature in degrees Fahrenheit, we get;

F = C

Therefore;

F - C = 0

Similarly, from the specified equation, we get;

9·C = 5·F - 160

5·F - 9·C = 160

The system of equation that would give the temperature where the degrees Celsius and degrees Fahrenheit are equivalent is therefore;

5·F - 9·C = 160

F - C = 0

(Which yields a temperature of 40°)

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w=0

Step-by-step explanation:

-1.01=1.4(w+2)-2.41

-1.01=1.4w+2.8-2.41

-1.01=1.4w+0.39

-1.01-0.39=1.4w

+1.4=1.4w

1.4/1.4=w

0=w

So,the answer is w=O

I hope it is very helpful

Answer:

-8

Step-by-step explanation:

i feel its correct

Answer:

w = 9

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

:)

Answer:

Step-by-step explanation:

the dot would either (1,4) or (4,1)

a squared+ b squared= c squared

the length of the sides are 3

3 squared + 3 squared= c squared

9+9 =c squared

18= c squared

square root of 18 rounded to the nearest tenth is 4.2

Answer:

y + 3 = 2(x - 4)

Step-by-step explanation:

Use the equation of a line format y - k = m(x - h), where m is the given slope and (h, k) is the given point.  Here (h, k) is (4, -3) and m is 2.

Then y + 3 = 2(x - 4) (point-slope form)

Answer:

wait I will edit and answer it in a few minutes

Step-by-step explanation:

For this problem, we need to focus on the exponent rule for multiplying.

Rule:

\(x^{a} \times {x}^{b} = {x}^{a + b} \)

In words:

When multiplying with exponents, the exponents add.

For this problem, we'll be adding the exponents of 7 and 4.

Solve:

\({x}^{7} \times {x}^{4} = {x}^{7 + 4} = {x}^{11} \)

Your product is x^11 (x to the 11th power)

Step-by-step explanation:

(A) x ≤ 3

4 + 6x ≤ 22

collect like terms

6x ≤ 22 - 4

6x ≤ 18

divide both sides by the coeficient of x[6]

x ≤ 3

$2010.458 is her new balance after she makes one new transaction for $51.

What does a credit balance mean?

The amount that the credit card company owes you is shown as a credit balance on your billing statement. Each payment you make results in credits being added to your account.

                                   When you return something you purchased with your credit card, you can receive an additional credit.

Credit balance  = $1,603

   APR = 28.6%

        = 28.6%  * $1,603

         =   458.458

Credit balance  = $1,603 + 458.458

                        = $2061.458

  net balance =  $2061.458 - 51

                      = $2010.458

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According to this partial W-2 form, the amount of money paid in FICA taxes is 3274.66.

Option D is the correct answer.

We have,

FICA taxes refer to the Federal Insurance Contributions Act taxes.  

FICA taxes consist of two components:

- Social Security tax:

- Medicare tax:

Now,

According to this partial W-2 form, the amount of money paid in FICA taxes.

= Social security tax withheld + Medicare tax withheld

= 2653.97 + 620.69

= 3274.66

Thus,

According to this partial W-2 form, the amount of money paid in FICA taxes is 3274.66.

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