is √2/3 a rational or irrational

The value of k is 0.05.

The exponential growth function is: A = 28e^kt

Where

A = future value of population

e = 2.718

k = growth rate

t = time

The  exponential growth function can be written as:

36 = 28 x e^k 5

log(36/28) ÷ log(e) ÷ 5 = 0.05

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25 x 2 = 50

140-50 = 90 dollars left

Answer:

its the last one number 4

Step-by-step explanation:

The system of linear inequalities that includes the point (2, 1) in its solution set is y ≥ 2x - 3 and y ≤ -2x + 5.

The system of linear inequalities that has the point (2, 1) in its solution set can be represented by the inequalities:

To determine if the point (2, 1) satisfies these inequalities, we can substitute the x and y values into each inequality and check if the resulting statements are true. In this case, 1 is indeed greater than or equal to 2(2) - 3, and 1 is also less than or equal to -2(2) + 5, so the point (2, 1) is indeed in the solution set of this system of linear inequalities.

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Answer:  The correct option is

[tex](A)~~x+y=90,~~x-y=8.[/tex]

Step-by-step explanation:  Given that one of the two complementary angles is 8 degrees less than the other.

We are to select the correct system of equations represents the given word problem.

Let x and y represents the two complementary angles where y is less than x.

Since one angle is 8 degrees less than the other and y is less than x, so we have

[tex]x-y=8.[/tex]

We know that the sum of two complementary angles is 90 degrees, so we get

[tex]x+y=90.[/tex]

Thus, the required system of equations representing the given word problem will be

[tex]x+y=90,\\\\x-y=8.[/tex]

Option (A) is CORRECT.

Answer:

first one is (constant)

second answer is (slope)

the third answer is 2

Step-by-step explanation:

First, you add 8 and 6 which will be 14. Since it's asking for the first four, it would be 4 over 14.

You can reduce that which is always a good idea and it comes out to be 2 over 7. That because you would divide both the top and bottom (like usual) by 2 each.

If you would want it as a percent, you would turn it into a decimal first. The decimal would be .02857. That's of course if you divide 2 and 7 like normal.

From there you would move the decimal point over two places making it 28.57 percent.

Hope this helps!!

Let us say that,

X = the number of residents in the sample who favor annexation.
X has a distribution which follows a binomial curve with parameters:

 n=50 and p=0.29

Calculating for mean:
Mean of X = n * p = 50 * 0.29

Mean of X = 14.5

Calculating for standard deviation:
Standard deviation of X = sqrt(n * p * (1 - p))

Standard deviation of X = 3.2086

Now we are to find the probability that at least 35% favour annexation:
35% * 50 = 17.5 residents

Normal approximation can be applied in this case since sample size is greater than 31. Therefore,

 Required Probability:

P(X>=17.5) = 1 - P(X<17.5)

1 - P(z<(17.5-14.5)/3.2086) = 1 - P(z<0.9350) = 1- 0.825106 = 0.174894

Answer:

0.175 or 17.5%

The probability that at least 35% of a sample of 50 residents favor annexation is approximately 0.1469.

To solve this problem, we are dealing with a situation where we need to find the probability that at least 35% of a random sample of 50 residents favor annexation, given that the true population proportion is 29%.

Let's denote:

- ( p = 0.29 ) as the population proportion favoring annexation.

- ( n = 50 ) as the sample size.

We are interested in finding [tex]\( P(X \geq 0.35 \times 50) \),[/tex] where ( X ) follows a binomial distribution[tex]\( X \sim \text{Binomial}(n=50, p=0.29) \).[/tex]

First, calculate [tex]\( 0.35 \times 50 \):[/tex]

[tex]\[ 0.35 \times 50 = 17.5 \][/tex]

Since we can't have half a person favoring annexation, we take the ceiling of 17.5, which is 18. So, we need to find [tex]\( P(X \geq 18) \).[/tex]

To find this probability, we can use the cumulative distribution function (CDF) of the binomial distribution or an appropriate normal approximation. Here, due to large ( n ) and ( p), we can use the normal approximation to the binomial distribution.

1. **Calculate mean and standard deviation for normal approximation:**

  - Mean (( mu )) of the binomial distribution: ( mu = np = 50 x 0.29 = 14.5 )

  - Standard deviation[tex](\( \sigma \)) of the binomial distribution: \( \sigma = \sqrt{np(1-p)} = \sqrt{50 \times 0.29 \times 0.71} \approx 3.34 \)[/tex]

2. **Approximate using normal distribution:**

  Convert [tex]\( X \geq 18 \)[/tex]  to the corresponding normal distribution:

[tex]\[ Z = \frac{18 - 14.5}{3.34} \approx 1.05 \][/tex]

3. **Find the probability using the standard normal distribution:**

[tex]\[ P(X \geq 18) \approx P\left(Z \geq \frac{18 - 14.5}{3.34}\right) = P(Z \geq 1.05) \][/tex]

  Using standard normal distribution table or calculator,

[tex]\[ P(Z \geq 1.05) \approx 0.1469 \][/tex]

Therefore, the probability that in a random sample of 50 residents at least 35% will favor annexation is approximately [tex]\( \boxed{0.1469} \).[/tex]

An expression is defined as a set of numbers, variables, and mathematical operations. The value of the expression 30 divide -6 will be -5.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that we need to divide the integer 30 with a negative integer, therefore, -6. If the given condition is written in the form of an expression then we can write it as,

30 ÷ (-6)

Writing the expression in the form of a fraction,

= 30/(-6)

Break 30 into factors to cancel it out,

= (6 × 5) / (-6)

Cancelling 6 from both the numerator and the denominator

= 5/-1

= -5

Hence, the value of the expression 30 divide -6 will be -5.

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Final answer:

The correct option is (B) -5. The expression 30 divide -6 results in -5 after dividing the absolute values and applying the negative sign from the original divisor.

Explanation:

The value of the expression 30 divide -6 is obtained by performing the division of 30 by -6. Division by a negative number yields a negative result. Therefore, the calculation would be:

Take the absolute value of both numbers: 30 (positive) and 6 (positive).

Divide the absolute values: 30 \/ 6 = 5.

Attach the negative sign to the result because the original divisor was negative: -5.

The correct answer is -5, which corresponds to option B.

Answer:

61.4%

Step-by-step explanation:

There are a total of 43+27 = 70 students that like sandwiches.

Out of these, 43 also like tacos; this is

43/70 = 0.614 = 61.4%

A. The distance around a closed figure is the correct answer.

Explanation:

The definition of perimeter is : The summation of the outer sides of any closed figure. Like in a rectangle, its the sum of all the four sides. In a circle, its the measure of the outline of the circle also called the circumference.

Hence, the distance around a closed figure is called its perimeter.

Answer:

you can make 12 bouquets...each containing 5 roses, 7 daisies, and 2 lilies

Step-by-step explanation:

Answer:

63,360 ft/h

Step-by-step explanation:

Answer:

B I took the test and got it right

Step-by-step explanation:

Answer:

D=(-∞,∞) Range = [0, ∞)

Step-by-step explanation:

V(r) =5πr²

Firstly we have to work with π as ≈ 3.14 so that we can make it better, by doing this we reveal it more clearly its quadratic form

V(r)= 15.71r²

As there is no restriction algebraically speaking. The Domain is all the Real Line. This is a Total Function.

As for the Range, since any negative value plugged into x² will turn into a positive one we'll only have positive results for y to each entry of x. So the Range is f(x) ≥0

As you can check it below.

Final answer:

a. The equation for the line in point-slope form is y + 9 = 4(x - 9), with a slope of 4.

b. The equation can be rewritten in standard form as 4x - y = 45.

Explanation:

a. To write the equation for the line in point-slope form, we need to determine the slope (m) and one point on the line (x1, y1).

The slope can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Taking the points (9, -9) and (10, -5), we can substitute the values into the formula to get m = (-5 - (-9)) / (10 - 9) = 4 / 1 = 4.

Now we can use the formula y - y1 = m(x - x1) with the point (9, -9) to get y - (-9) = 4(x - 9). Simplifying, we have y + 9 = 4x - 36.

b. To rewrite the equation in standard form, we need to bring the equation to the form Ax + By = C, where A, B, and C are integers.

Starting from the point-slope form, we can expand and simplify the equation to get y + 9 = 4x - 36 becomes y = 4x - 45.

To make all the coefficients integers, we can multiply the equation by 5 to get 5y = 20x - 225, rearrange the terms as -20x + 5y = -225, and divide every term by -5 to get the standard form 4x - y = 45.

To get an A in the course, you need to score at least 97 on the last test.

To find the range of scores needed on the last test to get an A in the course, we need to set up and solve an inequality. Let's assume that the score on the last test is x. The average of the four tests must be at least 90, so the sum of the scores on the first three tests (263) plus the score on the last test (x) divided by 4 must be greater than or equal to 90.

(87 + 92 + 84 + x)/4 ≥ 90

Combine like terms: (263 + x)/4 ≥ 90

Multiply both sides of the inequality by 4: 263 + x ≥ 360

Subtract 263 from both sides of the inequality: x ≥ 97

Therefore, you need to score at least 97 on the last test to get a course grade of 'A'.