Solve the system of equations without graphing
2y=x-4
4x+3y=5

It will take about 9.5 months (or 10 months rounded up) for the rabbit population to reach 5,800.

Let's use the formula for exponential growth to solve this problem:

N = N0 * 2^(t/k)

Where:

N0 = initial population (8 rabbits)

N = final population (5,800 rabbits)

k = doubling time (1 month)

t = time in months (what we're trying to find)

Substituting the values we have:

5,800 = 8 * 2^(t/1)

Dividing both sides by 8:

725 = 2^(t/1)

Taking the logarithm of both sides (base 2):

log2(725) = t/1

t = log2(725) ≈ 9.515

So it will take about 9.5 months (or 10 months rounded up) for the rabbit population to reach 5,800.

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We have to divide the shape into two

It will give us a Rectangle and a Trapezium

Answer:A.Very Crowded

I am 100% positive

Step-by-step explanation:

The first arrivals were the people who made up Washington society. ... Jackson found himself pressed into a situation with his back to a wall until his people were able to get him away from the crowd, and back to his hotel. The sheer number of people inside the White House led to collisions with furniture and food and yeah.

A scientist can use bootstrap analysis to estimate the strength of evidence that a particular node in a phylogeny exists.

Bootstrap analysis is a statistical method used to determine the reliability and robustness of phylogenetic trees' topologies. In bootstrap analysis, a series of random resampling with replacement is used to assess how well the observed data fit the phylogenetic hypothesis.

Bootstrap values range from 0 to 100 and reflect the proportion of times that a particular node or branch occurs in the bootstrap replicate trees. Bootstrap values greater than 70% are usually considered strong evidence that a particular node or branch exists in the phylogenetic tree.

Bootstrap analysis is an important tool for understanding the reliability of phylogenetic trees and the evolutionary relationships among organisms.

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When the cosine of an angle (0) is 3/5 and the angle lies in quadrant 4, the exact value of the sine of that angle is -4/5.

To find the exact value of sin(0), we can utilize the Pythagorean identity, which states that \(sin^2(x) + cos^2(x) = 1,\) where x is an angle in a right triangle. Since the terminal side of the angle (0) is in quadrant 4, we know that the cosine value will be positive, and the sine value will be negative.

Given that cos(0) = 3/5, we can determine the value of sin(0) using the Pythagorean identity as follows:

\(sin^2(0) + cos^2(0) = 1\\sin^2(0) + (3/5)^2 = 1\\sin^2(0) + 9/25 = 1\\sin^2(0) = 1 - 9/25\\sin^2(0) = 25/25 - 9/25\\sin^2(0) = 16/25\)

Taking the square root of both sides to find sin(0), we have:

sin(0) = ±√(16/25)

Since the terminal side of (0) is in quadrant 4, the y-coordinate, which represents sin(0), will be negative. Therefore, we can conclude:

sin(0) = -√(16/25)

Simplifying further, we get:

sin(0) = -4/5

Hence, the exact value of sin(0) when cos(0) = 3/5 and the terminal side of (0) is in quadrant 4 is -4/5.

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Note the correct and the complete question is

Q- Find the exact value of sin(0) when cos(0) =3/5 and the terminal side of (0) is in quadrant 4​ ?

A triangle can not have three sides whose lengths are 3.2 cm 5.3 cm 9.4 cm

We know that the triangle inequality theorem states that for any triangle the sum of any two sides of a triangle is greater than or equal to the third side.

Here, we have been given the three measurements.

Let a = 3.2 cm, b =  5.3 cm and c = 9.4 cm

Consider the sum of sides a and b,

a + b

= 3.2 + 5.3

= 8.5cm

< 9.4

= c

i.e., a + b < c

Acctording to triangle inequality theorem, a, b, c can not be the sides of triangle, as the sum of two sides that measure 3.2 cm and 5.3 cm is not greater than or equal to the third side which measures 9.4 cm

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1/7 of the animals in the zoo are male monkeys.

To find the fraction of animals in the zoo that are male monkeys, we have to calculate the product of the fractions representing the proportion of monkeys and the proportion of male monkeys among them.

Given that 1/5 of the animals in the zoo are monkeys, we will then represent this as:

= 1/5

= 5/25.

And 5/7 of the monkeys are male which is written as 5/7.

To get fraction of male monkeys, we will multiply these two fractions:

= (5/25) * (5/7)

= 25/175

= 1/7.

Full question:

1/5 of the animals in the zoo are monkeys 5/7 of the monkeys are male. What fraction of the animals in the zoo are male monkeys?

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a) 10x2 = 10

b) 20x2 − 40 = 0

Answer:

Below in bold.

Step-by-step explanation:

We find fg(x) by replacing the x in f(x) by g(x), so:

fg(x) = (4x - 2a)^2 + 4a(4x - 2a) + a^2

fg(3) = 89 so:

(4(3) - 2a)^2 + 4a(4(3) - 2a) + a^2 = 69

(12 - 2a)^2 + 48a - 8a^2 + a^2 - 69 = 0

144 - 48a + 4a^2 + 48a - 8a^2 + a^2 - 69 = 0

-3a^2  + 75 = 0

-3a^2  = -75

a^2 = 25

a = 5.

Now g(x) = 4x - 2(5) = 4x - 10.

Finding g-1(x);

4x = g(x) + 10

x = (g(x) + 10)/4

So g-1(x) = (x + 10)/4

When g-1(x)= x

x = (x +10)/4

4x = x + 10

3x = 10

x = 10/3.

Answer:35

Step-by-step explanation:

The volume of a cylinder is calculated by multiplying the area of its base by its height. The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height.

The volume of a cone is calculated by multiplying the area of its base by its height and then dividing by 3. The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height.

Since Sonequa’s two containers have equal radii and equal heights, it can be concluded that the volume of the cylinder is three times the volume of the cone. This means that if Sonequa fills the cone with water and pours it into the cylinder, she will need to repeat this process three times to fill the cylinder completely.

So, the claim that is most likely to be supported using the result of Sonequa’s investigation is: “The volume of a cylinder with the same radius and height as a cone is three times greater than the volume of the cone.”

Answer:

t=84

Step-by-step explanation:

Malin's answer is $\frac{t-6}{6}$. Shawn's answer is $\frac{t+7}{7}$. We know these are equal, so we have the equation

$$\frac{t-6}{6} = \frac{t+7}{7}.$$

To eliminate denominators from the problem, we multiply both sides by $6\cdot 7$:

$$\frac{6\cdot 7\cdot (t-6)}{6} = \frac{6\cdot 7\cdot (t+7)}{7},$$

then simplify to get

$$7\cdot (t-6) = 6\cdot (t+7).$$

The parentheses are important here! For example, the parentheses on the left side of the equation tell us that it is $t-6$, not just $t$, which is multiplied by $7$.

Now we expand using the distributive property:

7t - 7\cdot 6 &= 6t + 6\cdot 7;\\

7t - 42 &= 6t + 42.

Adding $42$ to both sides gives

$$7t = 6t + 84,$$

then subtracting $6t$ from both sides gives $t=\boxed{84}$.

(We can check that starting from $t=84$, Malin and Shawn do indeed get the same final answer -- namely, $13$.)

The range of the function y = 4x + 1 is {y | 1 ≤ y ≤ 41}.

What is the range of data?

The range of data is defined as a measure of the difference between the maximum value of data and the minimum value of data.

The function is given as y = 4x + 1.

The range of the function y = 4x + 1 is the set of all possible output values that the function can produce.

Given that the domain of the function is 0 ≤ x ≤ 10.

The range of this function is the set of all y-values that can be obtained by plugging in x-values between 0 and 10 into the function.

Plugging in x = 0, the value for y = 4(0) + 1 = 1.

Plugging in x = 10, the value for y = 4(10) + 1 = 41.

The range of the function y = 4x + 1 is the set of all y-values between 1 and 41, inclusive.

Therefore, the range of the function is {y | 1 ≤ y ≤ 41}.

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Pairs of samples in which the selection of people or objects into one sample directly affects or is affected by the selection of people or objects into the other sample are referred to as dependent samples. The correct option is B) dependent samples.

Dependent samples are those where the selection of people or objects in one sample is related to the selection in another sample. For example, a study comparing pre- and post-intervention results of the same group of individuals would have dependent samples.

In statistical analysis, dependent samples require different methods than independent samples, as the relatedness between the samples needs to be taken into account. Understanding the nature of the relationship between the samples is important for drawing accurate conclusions from the data. The correct answers is B).

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Answer:

1,164 in²

Step-by-step explanation:

the area of 1 sofa cushion =

2× ( 10×11 + 10×4 + 11×4)

= 2 × (110+40+44)

= 2×(194)

= 388 in²

the fabrics she needs to cover 3 sofa cushions =

3 × 388 = 1,164 in²

9514 1404 393

Answer:

  J Compound interest; $298.65

Step-by-step explanation:

Interest compounding pays interest on the interest. For the same annual rate, any amount of compounding will earn more interest.

For short time periods, the effect of compounding is not great. In general, it will be a fraction of the equivalent simple interest rate. Here, the effective multiplier for annual compounding is ...

  1.051^4 = 1.22024337

and the effective multiplier for simple interest is ...

  1 +0.051·4 = 1.204

Then the difference in interest rate multiplier for the 4-year period is ...

  1.22024337 -1.204 = 0.01614337

That fraction of the $18500 principal is $298.65.

Compound interest earns $298.65 more than simple interest in this scenario.

Answer:

225

Step-by-step explanation:

(- 15)² = - 15 × - 15 = 225

Answer:

\(2p^2\)

Step-by-step explanation:

Step 1: Apply the exponentiation property:

\((8p^6)^\frac{1}{3} = 8^\frac{1}{3} * (p^6)^\frac{1}{3}\)

Step 2: Simplify the cube root of 8:

The cube root of 8 is 2:

\(8^\frac{1}{3} =2\)

Step 3: Simplify the cube root of \((p^6)\):

The cube root of \((p^6)\) is \(p^\frac{6}{3} =p^2\)

Step 4: Combine the simplified terms:

\(2 * p^2\)

So, the simplified expression is \(2p^2\).

(i) Large Table Required are 3 and Small Table required are 8

(ii) Price of Student Ticket is $5.5 and Adult Ticket is $7.5

What is Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

(i)

Seats in Large Table = 12

Cost of Large Table = $50

Seats in Small Table = 8

Cost of Small Table = $25

Let, Number of Large Tables = x

Number of Small Tables = y

According to the Question:

12x + 8y = 100

50x + 25y = 350

x = 3, y = 8 (refer graph 1)

(ii)

Cost of Student Ticket = x

Cost of Adult Ticket  = y

According to the Question:

16x + 3y = 110.5

12x + 4y = 96

x = $5.5, y = $7.5 (refer graph 2)

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To find the feet of fence needed:

1. Find the perimeter (cirfumference) of the semicircle:

2. Sum the perimeter of the semicircle and the 3 exterior sides of the rectangle to get the total perimeter of the garden:

The monthly rate for the given loan is 1.0118%.The annual rate for this loan is 12.1423%.

Given loan: $150,000

Payment per month: $1,770

Duration of loan: 10 years

Interest = ?

The formula for monthly payment is given by:

\(PV = pmt x (1 - (1 + r)^-n) / r\)

Where, PV is the present value, pmt is the payment per period, r is the interest rate per period and n is the total number of periods.Solving the above formula for r will give us the monthly rate for the loan.

r = 1.0118%The monthly rate for the given loan is 1.0118%.The annual rate can be calculated using the following formula:

Annual rate = \((1 + Monthly rate)^12 - 1\)

Annual rate = 12.1423%

The annual rate for this loan is 12.1423%.The effective annual rate can be calculated using the following formula:

Effective annual rate =\((1 + r/n)^n - 1\)

Where, r is the annual interest rate and n is the number of times interest is compounded per year.If interest is compounded monthly, then n = 12

Effective annual rate = (1 + 1.0118%/12)^12 - 1

Effective annual rate = 12.6801%

The effective annual rate for this loan is 12.6801%.

Total amount paid after 10 years = Monthly payment x Number of payments

Total amount paid after 10 years = $1,770 x 120

Total amount paid after 10 years = $212,400

The total amount paid after 10 years is $212,400.

The future value for this loan can be calculated using the following formula:

FV = PV x (1 + r)^n

Where, PV is the present value, r is the interest rate per period and n is the total number of periods.If the loan is paid off in 10 years, then n = 120 (12 payments per year x 10 years)

FV = $150,000 x (1 + 1.0118%)^120

FV = $259,554.50

The future value for this loan is $259,554.50.

Thus, the monthly rate for the loan is 1.0118%, the annual rate for this loan is 12.1423%, the effective annual rate for this loan is 12.6801%, the total amount paid after 10 years is $212,400 and the future value for this loan is $259,554.50.

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Answer:

3$

Step-by-step explanation:

Your right it is easy 1.50 per pound 1 pound is 16 ounces so to make 32 ounces times it by 2 16 times 2 is 32 you will also times 1.50$ times 2

The probability mass function (PMF) of X can be determined by calculating the probability associated with each possible outcome of the product of two fair dice, plus three. Let's go through the process step by step.

The probability mass function of X is as follows:

P(X = 5) = 1/36

P(X = 6) = 2/36

P(X = 7) = 3/36

P(X = 8) = 4/36

P(X = 9) = 5/36

P(X = 10) = 4/36

P(X = 11) = 3/36

P(X = 12) = 2/36

P(X = 13) = 1/36

To find the probability mass function, we need to determine the probability of each possible outcome of X. The sum of two dice ranges from 2 to 12, which means the product of the two dice ranges from 1 to 36.

To calculate the probabilities, we'll consider each possible outcome:

When X = 5:

There is only one combination of dice that gives a product of 2 (1 × 2) + 3 = 5. Since there are 36 equally likely outcomes, the probability is 1/36.

When X = 6:

The combinations that yield a product of 3 (1 × 3) and 4 (2 × 2) both result in X = 6. Hence, the probability is 2/36.

When X = 7:

The combinations that yield products of 4, 5, and 6 result in X = 7. So, the probability is 3/36.

When X = 8:

The combinations that yield products of 5, 6, 7, and 8 result in X = 8. Thus, the probability is 4/36.

When X = 9:

The combinations that yield products of 6, 7, 8, and 9 result in X = 9. Hence, the probability is 5/36.

When X = 10:

The combinations that yield products of 7, 8, 9, and 10 result in X = 10. So, the probability is 4/36.

When X = 11:

The combinations that yield products of 8, 9, and 10 result in X = 11. The probability is 3/36.

When X = 12:

The combinations that yield products of 9 and 10 result in X = 12. Thus, the probability is 2/36.

When X = 13:

There is only one combination that yields a product of 10, resulting in X = 13. Hence, the probability is 1/36.

The probability mass function of X, denoting the probabilities associated with each possible outcome of X, is calculated as shown above. The PMF allows us to understand the likelihood of each value occurring and is a fundamental tool in probability theory. In this case, the PMF of X provides a clear distribution of probabilities for the product of two dice plus three.

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Answer:

No

Step-by-step explanation:

One way to tell if a number is rational is if it can be written as a fraction. Anything that can be written as a fraction of two integers is rational.

-6/11 is a fraction with integer numerators and denominators.

Therefore it is rational.

There are 10 digits (0-9) that can be used for each of the three digits in the passcode. Since repetition of digits is allowed, there are 10 options for each digit. Therefore, the number of possible three-digit passcodes is 10 x 10 x 10 = 1000.
b) If a person randomly enters 3 digits, the probability of guessing the correct passcode is 1 out of 1000. This can also be written as a decimal fraction: 0.001 or as a percentage: 0.1%.

a) To determine the number of possible three-digit passcodes on a smartphone, we can use the counting principle. Since there are 10 digits (0-9) and repetition is allowed, there are 10 options for each of the 3 digits. So, the total number of possible passcodes is 10 × 10 × 10 = 1000.

b) If a person finds a smartphone and randomly enters 3 digits, the probability of entering the correct passcode can be found by dividing the number of successful outcomes (1 correct passcode) by the total number of possible outcomes (1000 passcodes). So, the probability is 1/1000, or 0.001.

In summary, there are 1000 possible three-digit passcodes, and the probability of randomly entering the correct passcode is 0.001.

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A is an n x n diagonal matrix with rank r , where rsn  and the statement (a)"O is an eigenvalue with algebraic muitiplicity n-r "  about A is true

Since A is an n x n diagonal matrix with rank r, the number of non-zero entries on the diagonal is r. This means that there are n - r zero entries on the diagonal.

For any diagonal matrix, the eigenvalues are simply the entries on the diagonal. Since there are n - r zero entries, the eigenvalue O has a geometric multiplicity of n - r.

Therefore, the correct statement is that O is an eigenvalue with geometric multiplicity n - r.

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The correct order to write and solve an equation is,

1. identify the variable

2. identify the operation

3. write an equation

4. solve the equation

5. check the solution

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

To find the steps to write and solve an equation.

Here, All the steps are,

1. Identify the variable.

2. Identify the operation.

3. Write an equation.

4. Solve the equation.

5. Check the solution.

2. Solve the equation.

3. Check the solution.

Hence, The correct order to write and solve an equation is,

1. identify the variable

2. identify the operation

3. write an equation

4. solve the equation

5. check the solution

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The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

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Raphael could finish the job in 3/2 hr = 90 min. Matilde could finish the job in 3 hr.

Let M denote for matilde

R for Raphael.

I assume they worked on the task together to finish it in 1 hr.

M does 1/M of the job per hr.

R does 1/R of the job per hr.

(1/M + 1/R) * x hr = 1 whole job completed

We are told x = 1 hr, so that's done.

We are told M's rate of work is 1/2 of R's

R's rate of work is 1/R

1/2 * 1/R = 1/2R

substitute 1/2R for 1/M

(1/2R + 1/R) * 1 hr = 1 whole job completed

solve

(R+ 2R)/ 2R^2 = 1

3R /2R^2 = 1

3R = 2R^2

2R^2 -3R = 0

R(2R-3) = 0

R = 0 or 2R = 3

However, if R could do the work in 0 hours, then his rate of work would be undefined.

Therefore, we select 2R = 3, which means R= 3/2.

R can do the whole job in 3/2 hr working alone.

M can do the whole job in 2*3/2 = 3 hr working alone.

We can check this solution to be sure it is correct.

In 1 hr, R can do 2/3 of the job.

In 1 hr, M can do 1/3 of the job

2/3+1/3 = 1.

We also can substitute in the original equation as double-check.

(1/3 + 1/(3/2))*1 = 1 ??

(1/3 + 2/3) = 1

Answer: R could finish the job in 3/2 hr = 90 min. M could finish the job in 3 hr.

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