What is the length of /AB?

\(\\ \sf\longmapsto tan(270+\theta)=1-\dfrac{sin\theta}{cos\theta}\)

\(\\ \sf\longmapsto \dfrac{sin(270+\theta)}{cos(270+\theta)}=1-\dfrac{sin\theta}{cos\theta}\)

\(\\ \sf\longmapsto \dfrac{-cos\theta}{sin\theta}=1-\dfrac{sin\theta}{cos\theta}\)

\(\\ \sf\longmapsto\dfrac{sin\theta}{cos\theta} \dfrac{-cos\theta}{sin\theta}=1\)

\(\\ \sf\longmapsto \dfrac{sin^2\theta-cos^2\theta}{-cos\theta sin\theta}=1\)

\(\\ \sf\longmapsto \dfrac{-2cos\theta}{-cos\theta sin\theta}\)

\(\\ \sf\longmapsto \dfrac{2}{sin\theta}=1\)

\(\\ \sf\longmapsto 2cosec\theta=1\)

\(\\ \sf\longmapsto cosec\theta=\dfrac{1}{2}\)

\(\\ \sf\longmapsto \theta=cosec^{-1}\left(\dfrac{1}{2}\right)\)

If the initial population is 3800. The population of cockroaches after 3 years will be 1603.

Consider the function:

y = a(1 ± r)ⁿ

where n is the number of times growth/decay, a = initial amount, and r = fraction by which this growth/decay occurs.

If there is a plus sign, there is exponential growth happening by r fraction or r%.

If there is a minus sign, there is exponential decay happening by r fraction or r%.

If the population is currently 3,800 cockroaches.

The expression is given as

y = 3800(0.75)ⁿ

The population of cockroaches after 3 years will be

y = 3800(0.75)³

y = 3800 x 0.4218

y = 1603.125

y ≅ 1603

Hence, the population of cockroaches after 3 years will be 1603.

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The complete question is:

Colette has an exterminator visit regularly to control an ongoing cockroach problem. it's been working, and the population has declined by 15% every year. if the population is currently 3,800 cockroaches, how many will there be in 3 years? if necessary, round your answer to the nearest whole number.

Answer:

Measure of the arc = 14.32°

Step-by-step explanation:

Radius of a circle = 4 cm²

Area of the circle = πr²

Here, r = radius of the circle

Area of the circle = π(4)²

                             = 16π cm²

                             = 50.265 cm²

Since, area of a sector = \(\frac{\theta}{360}(\text{Area of the circle})\)

Here, θ = Central angle subtended by the arc Or measure of arc

Area of the sector given as 2 cm²

2 = \(\frac{\theta}{360}(50.265)\)

θ = 14.32°

Therefore, measure of the arc = 14.32°.

The length of the base is 22 feet, and its height is 6 feet, given the area is 66 square feet.

The area of a triangle is given by the formula, area = (1/2)*base*height.

In the question, we are given that the cross-section of a lean-to shelter is in the shape of a triangle. Also, we are told that the base of the triangle is 10 feet more than twice its height.

We are asked to determine the length of the base and the height of the triangle in feet if the area of the triangle is 66 square feet.

We assume the height of the triangle to be x feet.

Thus, the base of the triangle is 10 feet more than twice its height, that is, base = 10 + 2x feet.

Now, the area of the triangle, using the formula, area = (1/2)*base*height can be shown as:

area = (1/2)(10 + 2x)x square feet.

But, the area of the triangle is given to be 66 square feet.

Equating these values, we get:

(1/2)(10 + 2x)x = 66,

or, x(5 + x) - 66 = 0,

or, x² + 5x - 66 = 0,

or, x² + 11x - 6x - 66 = 0,

or, x(x + 11) - 6(x + 11) = 0,

or, (x - 6)(x + 11) = 0, which implies that:

Either x - 6 = 0, or, x = 6,

Or, x + 11 = 0, or, x = -11, which is not possible since x is the height of a triangle which cannot be negative.

Thus, the height of the triangle, x = 6 feet.

The base of the triangle, 10 + 2x = 22 feet.

Thus, the length of the base is 22 feet, and its height is 6 feet, given the area is 66 square feet.

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Answer:

10 yrs old and 35 yrs old

Step-by-step explanation:

I figured it out by trial and error but here's the thinking process.

10 + 35= 45

Son becomes dad's age so 35-10=25, so plus 25 year to each age.

10+25=35

35+25= 60

35+60=95

I hope that makes enough sense!

The required area of the shaded portion is given as 248.54 cm².

As mentioned, in the diagram below a circle is inscribed in a square. The radius of the circle is 17 cm.

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

here,
The area of the shaded portion is given as,
= area of the square - an area of the circle
= [side]² - πr²
= [2r]²- πr²
Substitute the values,
= [2×17]² - 3.14 × 17²
= 284.54

Thus, the required area of the shaded portion is given as 248.54 cm².

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Answer:false

Step-by-step explanation:

Answer:

2 2/5 hours

Step-by-step explanation:

If Marcus takes 4/5 an hour to paint 1/3 of the room, then you have to multiply 4/5 times 3 for every 1/3 of the room.

Sorry if this is hard to understand, this is my first time answering.

Answer:

5/12

Step-by-step explanation:

I think

The value of the square root of 140 lies between 11 and 12. The square root of 140 is 11.83

The last score of Carter will cause the display to be skewed to the right. Option D.

A distribution is considered skewed when the data is not evenly spread out around the average or median.

In this case, Carter's scores were 113, 117, 101, 97, 104, and 110. These scores are relatively close to each other, forming a distribution that is somewhat centered around a typical range.

However, when Carter played the game again and achieved a score of 198, this score is significantly higher than the previous scores. As a result, the overall distribution of scores will be affected.

Since the last score is much higher than the previous scores, it will cause the data to skew toward the right side of the distribution. The previous scores will be closer together on the left side of the distribution, and the high score of 198 will pull the distribution towards the right, causing it to skew in that direction.

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The sine function, y = 2sin(x), has an amplitude of 2 and a period of π.

The amplitude of a function represents the maximum displacement of the function from its mean or average value. In the case of the sine function, the amplitude determines the vertical distance between the peak and trough of the wave. Therefore, when the amplitude is 2, it means that the function oscillates between +2 and -2.

The period of a function refers to the length of one complete cycle of the function. For the sine function, the period is the distance between two consecutive peaks or troughs. A period of π corresponds to half of the full wave, meaning that the function completes one full cycle in the interval from 0 to π.

Combining these properties, the function y = 2sin(x) has an amplitude of 2, which stretches the sine curve vertically by a factor of 2, and a period of π, which compresses the curve horizontally, resulting in one complete cycle from 0 to π.

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Step-by-step explanation:

Since it is a regular pentagon, all five sides are equal and you know one side is x-3. Thus the equation would be: x-3 = 18.8/5

x - 3 = 18.8/5

       = 3.76

x = 3.76 + 3

x = 6.76

The point estimate of the population mean, based on the given sample data, is 10.375.

To find the point estimate of the population mean, we calculate the mean of the sample data. The sample mean is found by summing up all the values in the sample and dividing it by the number of observations. In this case, the sum of the sample data is 10 + 8 + 12 + 15 + 13 + 11 + 6 + 5 = 80. Since there are 8 observations in the sample, we divide the sum by 8 to get the sample mean: 80/8 = 10. The sample mean of 10 indicates that, on average, the observed values in the sample tend to cluster around 10. Thus, 10.375 can be considered as the point estimate for the population mean based on the given sample data. It's important to note that this point estimate is only an approximation and may not be exactly equal to the true population mean. To make more accurate inferences about the population, a larger sample or additional statistical methods would be necessary.

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The area of triangle PQR is 25/2 * √(5).

In geometry, a triangle is a two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and has many important properties and applications.

The sum of the interior angles of a triangle is always 180 degrees, and the exterior angles sum to 360 degrees. The three sides of a triangle can be classified according to their lengths and their angles.

To find the area of triangle PQR, we can use the formula:

Area = (1/2) * base * height

where the base and height are the lengths of two sides of the right triangle that meet at a 90-degree angle.

We can use the distance formula to find the lengths of the sides of triangle PQR:

PQ = √[(x_Q - x_P)² + (y_Q - y_P)²] = √[(-1 - (-6))² + ((-1) - 9)²] = √[25 + 100] = 5√(5)

PR = √[(x_R - x_P)² + (y_R - y_P)²] = √[(-9 - (-6))² + (5 - 9)²] = √[9 + 16] = 5

QR = √[(x_R - x_Q)² + (y_R - y_Q)²] = √[(-9 - (-1))² + (5 - (-1))²] = √[64 + 36] = 2√20) = 4√(5)

Since triangle PQR is a right triangle, the base and height are PQ and PR, respectively. Therefore, the area of triangle PQR is:

Area = (1/2) * PQ * PR = (1/2) * 5√(5) * 5 = 25/2 * √(5)

So the area of triangle PQR is 25/2 * √(5).

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The given point were reflected about the line y = x and the coordinates the reflected point (-5 , 3)  is (3, - 5)

According to the question, given that

point reflected line y =x,

Reflected point coordinates of (-5, 3), then find the coordinates of the point after in the line of symmetry :

(-5, 3) →  (3, - 5)

A reflection is referred to as a twist in geometry. A reflection is the mirror image of shape . A line, called the line of reflection, will agree an image to reflect without change it. When all of the points in a figure are evenly spaced apart from one another, the two figures are said to reflect each other. The reflected picture should have the same size and shape as the original, but it faces the opposite way. Changes in position during contemplation may also result in translation. Pre-image and image are terms used to refer to the same thing in this context. ABC and A'B'C are used to represent the pre-image and image, respectively.

A reflection point is similar to staring at a flipped mirror picture of yourself.

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Answer:

A community is a social unit (a group of living things) with commonality such as norms, religion, values, customs, or identity. pls Mark me branilest

Answer:

-11a

Step-by-step explanation:

To get the answer, you must combine these terms because they are like terms. -5a+a = -4a, and -4a-7a = -11a. Therefore, the answer is -11a.

The experimental probability of rolling a number less than 3 is 0.11 or 11% when rolling a 12-sided solid numbered from 1 to 12, based on the provided data.

The number of faces that are numbered less than 3 on a 12-sided solid is 2, i.e., 1 and 2. Therefore, the probability of rolling a number less than 3 can be calculated by adding the frequencies of rolls that resulted in 1 and 2, and then dividing the sum by the total number of rolls.

From the table, we can see that the frequency of rolling a 1 is 10 and the frequency of rolling a 2 is 12. Therefore, the total frequency of rolling a number less than 3 is 10 + 12 = 22.

The total number of rolls is 200.

The experimental probability of rolling a number less than 3 is the frequency of rolling a number less than 3 divided by the total number of rolls:

Experimental probability = Frequency of rolling a number less than 3 / Total number of rolls

Experimental probability = 22 / 200

Experimental probability = 0.11

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Answer:

291

Step-by-step explanation:

2x2x2=8

8x2=16

5x5x11=275

275+16=291

Answer:

1/5 of 10 is 2

Step-by-step explanation:

you divide ten by the denominator (5) and multiply the answer (2) by the numerator (1), giving you 2.

hope this helps :) !!!

The calculated correlation coefficient (r) is approximately -0.291.

To calculate the correlation coefficient between telomere length and chronicity, we can utilize the given summary data. The correlation coefficient, often denoted as r, measures the strength and direction of the linear relationship between two variables.

Let's denote the sum of products as Σxy, the sum of squares for chronicity as Σx², the sum of squares for telomere length as Σy², and the total sample size as n.

From the given data, we have the following values:

Σxy = -8.822

Σx² = 318.817

Σy² = 2.868

n = 38

The correlation coefficient (r) can be calculated using the following formula:

r = Σxy / √(Σx² * Σy²)

Substituting the given values into the formula:

r = -8.822 / √(318.817 * 2.868)

Now, let's solve this equation step by step:

First, multiply the values inside the square root:

r = -8.822 / √(913.350956)

Next, calculate the square root:

r = -8.822 / 30.219307

Finally, divide Σxy by the square root of the product of Σx² and Σy²:

r ≈ -0.291

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Answer:

-38,

Step-by-step explanation:

1. 9x-11=-27-11=-38

2. 9x-11=63-11=52

The answers are in order.

1. x=-3

2. x=7

Answer:

Step-by-step explanation:

-4

Work Shown:

\(a_1 = -1 = \text{ first term} \\\\d = 0.5 = \text{ common difference} \\\\a_n = a_1 + d(n-1)\\\\a_n = -1 + 0.5(n-1)\\\\a_6 = -1 + 0.5(6-1)\\\\a_6 = -1 + 0.5(5)\\\\a_6 = -1 + 2.5\\\\a_6 = 1.5\\\\\)

Answer:

\( 94.2 -0.994*3.1 = 91.1186\)

\( 94.2 +0.994*3.1 = 97.2814\)

And the 68% confidence interval is given by (91.1186, 97.2814)

Step-by-step explanation:

For this case we know that mean time that visitors stay at a museum is given by:

\( \bar X = 94.2 \)

The standard deviation is given by:

\( s= 15.5\)

And the standard error is given by:

\( SE = \frac{s}{\sqrt{n}} =3.1 \)

And we want to interval captures 68% of the means for random samples of 25 scores and for this case the critical value can be founded like this using the normal standard distribution or excel:

\( z_{\alpha/2}= \pm 0.994\)

We can find the interval like this:

\( \bar X \pm ME\)

And replacing we got:

\( 94.2 -0.994*3.1 = 91.1186\)

\( 94.2 +0.994*3.1 = 97.2814\)

And the 68% confidence interval is given by (91.1186, 97.2814)

The value of the inverse of the function f(x) = x +3 is,

⇒ h (x) = x - 3

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

Function is,

f (x) = x + 3

Now, We can find the inverse of the function f(x) = x +3 as,

f (x) = x + 3

y = x + 3

x = y - 3

h (x) = x - 3

Thus, The value of the inverse of the function f(x) = x +3 is,

⇒ h (x) = x - 3

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To find the two numbers, we can set up a system of equations based on the given information.

Let's use the variables x and y to represent the two integers. The sum of the two numbers is 11, which can be represented as x + y = 11. The difference between the two numbers is 19, which can be represented as x - y = 19. By solving this system of equations, we can determine the values of x and y.

Let x and y represent the two integers. We can set up the following system of equations based on the given information:

Equation 1: x + y = 11 (sum of the two numbers)

Equation 2: x - y = 19 (difference between the two numbers)

We can solve this system of equations using various methods such as substitution, elimination, or matrix methods. Here, we'll solve it using the elimination method.

Add Equation 1 and Equation 2:

(x + y) + (x - y) = 11 + 19

2x = 30

x = 15

Substitute the value of x into Equation 1:

15 + y = 11

y = 11 - 15

y = -4

Therefore, the two numbers are 15 and -4.

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Answer:

here (edit I made a mistake)

Step-by-step explanation:

9) \(y=\frac{3}{5} x +5\)

10) y = x - 3

11)  \(y=-\frac{3}{5} x - 3\)

12) \(y=\frac{5}{4} x + 2\)

these are the slop int forms, my bad...

sorry

Answer:

9) -3/5x + y = 5

10) -x + y = -3

11) 3/5x + y = -3

12) -5/4x + y = 2

Step-by-step explanation:

Answer:

see explaination

Step-by-step explanation:

area of rectangle =l×b