calculate the unit rate of change for each linear function using the formula. (4,9) (8,12) (16,18) (32,30)

It would take 21 weeks for the population to surpass 16,000.

The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.

For the population to surpass 16,000, we can set up the following equation:

15,000 + 2500 sin(πt/52) = 16,000

Subtracting 15,000 from both sides, we get:

2500 sin(πt/52) = 1000

Dividing both sides by 2500, we get:

sin(πt/52) = 0.4

We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:

πt/52 = sin⁻¹(0.4)

Multiplying both sides by 52/π, we get:

t = (52/π) sin⁻¹(0.4)

Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.

t = (52/π) (0.4115)

t = 21.02

Therefore, it would take 21 weeks for the population to surpass 16,000.

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Answer: The area of the floor can be found by multiplying the width and the length.

Area of the floor = (6x - 9)(6x + 9) = 36x^2 - 63x - 81

The area of each tile can be found by evaluating the expression 24x^2 - 12x - 36.

Area of each tile = 24x^2 - 12x - 36

To find out how many tiles are needed to cover the floor we need to divide the area of the floor by the area of each tile.

Number of tiles needed = (36x^2 - 63x - 81) / (24x^2 - 12x - 36)

The division is simplified by canceling out common factors between the numerator and denominator, the number of tiles is a fraction that can't be simplified any further.

So the answer is (36x^2 - 63x - 81) / (24x^2 - 12x - 36) tiles are needed to cover the floor.

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

15 x 20%=18

Answer:

138

Step-by-step explanation:

because when you add 18 to 120 it is 138

The value of m ∠ABC=86° ,because of the cyclic quadrilaterals.

Hence, Option (B) is correct.

Since, We know that,

A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a common circle.

The opposite angles of a cyclic quadrilateral have a total of 180°.

Hence, We can formulate;

m ∠ABC +  m ∠ADC  = 180°

m ∠ABC + 94° = 180°

m ∠ABC = 180° - 94°

m ∠ABC = 86°

Similarly, one can find m∠DCB

m∠DAB +  m∠DCB  = 180°

99° + m∠DCB = 180°

m∠DCB = 180° - 99°

m∠DCB = 81°

Hence, m∠ABC = 86°

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Answer:

slope (m) = 2/3

Step-by-step explanation:

slope = change in x /change in y

Also, slope is y2 - y1 / x2 -x1. That is what I apply for this activity, hence:

slope = 3 - (-1) / 0 - (-6)

         = 3 + 1 / 0 + 6

         = 4 / 6

         = 2/3

∴ slope(m) = 2/3

The dimensions of the smaller rectangle are 13 centimeters by 52 centimeters.

Let's assume the dimensions of the smaller rectangle are length L and width W (in centimeters).

We know that the area of the smaller rectangle is 676 square centimeters:

L * W = 676    ----(1)

We also know that the larger rectangle has a shorter side of 41 centimeters. Let's say the corresponding longer side of the larger rectangle is H centimeters.

The area of the larger rectangle is 3457 square centimeters:

41 * H = 3457    ----(2)

Our current set of equations contains two unknowns. In order to get the smaller rectangle's dimensions, we can simultaneously solve these equations.

In order to find H, we can use equation (2):

H = 3457 / 41

H ≈ 84.22

Now we can substitute this value of H into equation (1):

L * W = 676

We need to find the dimensions (L and W) that multiply to give 676. We can start by looking for factors of 676.

Factors of 676: 1, 2, 4, 13, 26, 52, 169, 338, 676

By trial and error, we can see that the factors that give a close match to the dimensions of the larger rectangle (41 and 84.22) are 13 and 52:

L = 13

W = 52

Therefore, the smaller rectangle has measurements of 13 by 52 centimetres.

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Answer:

A = 18

B = 88

C = 74

Step-by-step explanation:

Givens

B = 3*A + 34

C = A + 56

Equation

A + B + C = 180

Solution

A + 3A + 34 + A +56 = 180   Collect like terms

5A + 90 = 180                  Subtract 90 from both sides

5A = 180 - 90

5A = 90                            Divide by 4

A = 90 / 5

A = 18

Answer

B = 18*3 + 34 = 54 + 34 = 88

C = 74

Check

A + B + C = 18 + 88 + 74

A + B + C = 180 as it should.

The given equation is expressed as

5x - 9 = - 8y - 3

Rearranging the equation, it becomes

8y = - 3 + 9 - 5x

8y = 6 - 5x

The x intercept is the value of x when y = 0. Substituting y = 0 into the equation, we have

0 * 8 = 6 - 5x

0 = 6 - 5x

5x = 6

x = 6/5

The x intercept is 6/5

The y intercept is the value of y when x = 0. Substituting x = 0 into the equation, we have

8y = 6 - 5 * 0

8y = 6

y = 6/8

y = 3/4

X intercept = 6/5

y intervept = 3/4

The time taken to reaches its maximum height is 3s.

In the question,

It is given that,

Height, h(t) = \(96t - 16t^{2}\)

The maximum value of the function is obtained if the first derivative of the function h (t) = 0.

\(\frac{dh(t)}{dt} = 96 - 32t = 0\)

⇒ \(t = 3\)

So, time taken to reach its max height is 3 seconds.

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Answer:   Number 5 is 60%

Step-by-step explanation:

Answer:

\(y = -3/2x + 4\)

Step-by-step explanation:

\((2,1) and (6,-5).\\x_1 = 2\\x_2 = 6\\y_1 =1\\y_2 =-5\\\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}\\ \\\frac{y-1}{x-2} = \frac{-5-1}{6-2}\\\\\frac{y-1}{x-2} = \frac{-6}{4} \\Cross-Multiply\\4(y-1) = -6(x-2)\\4y-4=-6x+12\\4y =-6x+12+4\\4y = -6x+16\\Divide through-by ; 4\\\frac{4y = -6x+16}{4} \\\\y = -\frac{3}{2} x +4\)

Answer:

At least 3/4 of the proportion of cell phones that will have talk time between 2.4 hours and 5.6 hours.

Step-by-step explanation:

Chebyshev's Theorem states that:

1) at least 3/4 of the data lie within two standard deviations of the mean, that is, in the interval with endpoints x bar ±2s for samples and with endpoints μ±2σ for populations;

2) at least 8/9 of the data lie within three standard deviations of the mean, that is, in the interval with endpoints x bar ±3s for samples and with endpoints μ ± 3σ for populations;

3) at least 1−1/k² of the data lie within k standard deviations of the mean, that is, in the interval with endpoints x bar ± ks for samples and with endpoints μ ± kσ for populations, where k is any positive whole number that is greater than 1.

1) endpoints μ ± 2σ for populations;

μ = mean = 4

σ = standard deviation = 0.8

= 4 ± 2(0.8)

= 4 ± 1.6

= 4+ 1.6 = 5.6

= 4 - 1.6 = 2.4

Therefore, the proportion of cell phones that will have talk time between 2.4 hours and 5.6 hours is at least 3/4

Answer:

3/4

Step-by-step explanation:

The inference is that the author suggest that looking at birds is silly A. to create a sense of doubt in the reader.

It should be noted that that an inference simply means the conclusion that can be deduced based on the information given in a story.

In this case, A Big Year" is a year in which a person attempts to see as many different species of birds as possible within a particular region. For most in North America who participate in a "Big Year," this region is the lower 48 American states, plus Alaska, Canada, and a couple of French islands off the Canadian coast.

The inference is that the author suggest that looking at birds is silly is to create a sense of doubt in the reader. Therefore, the correct option is A.

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Answer:

Step-by-step explanation:

The given equations are ...

  4a +5s = 87

  2a +2s = 40

We observe that the coefficient of 'a' in the first equation is 2 times that in the second equation. We can multiply the second equation by -2 and add it to the first to eliminate 'a' terms.

  (4a +5s) -2(2a +2s) = (87) -2(40)

  4a +5s -4a -4s = 87 -80 . . . . . . . . . eliminate parentheses

  s = 7 . . . . . . . . . . . . . . . . . .simplify

  2a +2(7) = 40 . . . substitute for s in the second equation

  2a = 26 . . . . . . subtract 14

  a = 13 . . . . . . . divide by 2

Adult tickets cost $13; student tickets cost $7.

Answer:

9/41

Step-by-step explanation:

Draw a right triangle in quadrant 2 and label your opposite (40) and hypotenuse (41) sides then use the pythagorean theorem to find the missing side (the adjacent side)  which is equal to 9. Then since cosine is adjacent/hypotenuse and you get 9/41.

The difference between the observed and expected number of late departures is statistically significant, we need to perform a binomial test by calculating the probability of observing 16 or more late departures out of 300 flights assuming the null hypothesis is true. If the resulting p-value is less than 0.05, we can conclude that the difference is statistically significant.

Based on the given information, an airline with a 95% on-time departure rate has 16 out of 300 flights with late departures. The question asks whether the difference between what occurred (16 late departures) and what you would expect by chance is statistically significant.
To determine if the difference is statistically significant, we need to conduct a hypothesis test. In this case, we can use a binomial test since we are dealing with two possible outcomes: on-time departure or late departure.
The null hypothesis (H0) assumes that the observed number of late departures is equal to what would be expected by chance. The alternative hypothesis (Ha) assumes that there is a significant difference between the observed and expected values.
In this case, the expected number of late departures can be calculated by multiplying the total number of flights (300) by the expected on-time departure rate (95%). This gives us an expected value of 300 * 0.05 = 15.
To perform the binomial test, we can calculate the probability of observing 16 or more late departures out of 300 flights, assuming the null hypothesis is true. This probability can be calculated using the binomial probability formula or by using statistical software.
If the resulting probability (also known as the p-value) is less than the significance level (usually 0.05), we can reject the null hypothesis and conclude that the difference between what occurred and what would be expected by chance is statistically significant. Otherwise, if the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that the difference is not statistically significant.
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As previously solved, the y-intercept is 26 and the slope is 4. To get -13/2 as the previous x intercept, substitute 0 for y.

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). So, the slope of a line is tan.

A line's slope often indicates the steepness and direction of the line. By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them.

Given,

y-6 = 4(x+5)

is in point slope form, (y-y1) = m(x - 1), where m = slope = 4 and (x1,y1) = (6,-5) is a point on the line

the y-intercept is when x = 0:

y - 6 = 4(0 + 5)

y = 26

the x-intercept is when y = 0:

0 - 6 = 4(x+5)

-6 = 4x + 20

-26 = 4x

-26/4 = x

-13/2 = x

in trying to change the equation to y = mx + b (slope-intercept form), you shouldn't have divided both sides by 6.

y - 6 = 4(x+5)

first distribute right side:

y - 6 = 4x + 20

solve for y by adding 6 to both sides:

y = 4x + 26

so slope is 4 and y-intercept is 26 as solved before.

Therefore, plug in 0 for y to get -13/2 as x intercept as before

The complete question is:

MY question is how can I find the X-intercept, and the Y-intercept of the equation: y - 6 = 4(x + 5)?

I solved what I could like this....

y - 6 = 4(x+5) equals

-6y   = 4x + 20

-6       -6     -6

y = -2/3x + 20/6

Slope: -2/3

Y-intercept: (0,20/6)

X-intercept: ?

I cannot remember how to find the X-intercept, once I have gotten to this point.

Could you explain it to me?

I use khan Academy, if that helps.

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The series appears to be     166, 199, 232, 265, 298, 331

With examples, define sequence?

A list of numbers in a certain order is known as a sequence. A term is the name given to each number in a sequence.

                                      In a series, each term has a place (first, second, third and so on). Take the sequence 5, 15, 25, 35, as an example. Each number is referred to as a word in the sequence.

The last number of the common difference must end in 3

And this must be a 2 digit number

So....the first number must end in 6

The the 4th number must be 265

So..... the 5th number  must end in 8

And the last digit  of the last term must end in  1  [ and begin with 3 ]

Putting all this together  we have that

265  + 2d  =  331

2d  = 66   ⇒  d = 33

So  the first term must be  265 - 3 (66)  =  166

the series appears to be     166, 199, 232, 265, 298, 331

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The day, from the following two days, which would be the best to sell both stocks with the closing price is day 3 by an amount of $2.45.

Given are the closing prices of two stocks in three days.

If you purchase 65 shares of Metropolis stock and 50 shares of Suburbia stock on Day 1 at the closing price,

Amount invested = (65 × 17.95) + (50 × 5.63) = $1448.25

If the stock is sold in day 2,

Amount received = (65 × 18.25) + (50 × 4.98) = $1435.25

Profit = $1435.25 - $1448.25 = -$13

If the stock is sold in day 3,

Amount received = (65 × 18.28) + (50 × 5.25) = $1450.7

Profit = $1450.7 - $1448.25 = $2.45

The profit is more for day 3 than day 2.

Hence it is best to sell on day 3 by $2.45.

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Using the concept of ratio and Pythagoras theorem on the similar triangle, the distance from the library to the park is 4√2 miles and the distance of the park from the football field is 4√6 miles

Similar triangles are triangles that have the same shape but not necessarily the same size. Two triangles are similar if and only if their corresponding angles are congruent (equal in measure) or in other words, if the ratio of any two corresponding sides of the triangles is equal.

In this problem, using ratios;

a.

Let the distance from the library to the park be represented by x.

8 / x = x / 4

Cross multiply both sides

x² = 8 * 4

x² = 32

x = √32

x = 4√2 miles

b. The distance of the park from the football field?

Using Pythagoras theorem, the distance from the park to the football field can be calculated as the hypothenuse

y² = (4√2)² + 8²

y² = 96

y = 4√6 miles

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Answer: 7.5

Step-by-step explanation:

5x3 = 15 A = 1 half L x H

A = (3)(5)

A = 15

A =  15 x 1 half = 7.5

correct me if i am wrong.

Answer:

Opal saves more

Step-by-step explanation: