The measure of central angle XYZ is 1.25 radians.

Circle Y is shown. Line segments X Y and Z Y are radii. The length of X Y is 8. The major angle of X Y Z is shaded.

What is the area of the shaded sector?

10 units2
20 units2
40 units2
80 unit

Answer:

Step-by-step explanation:

\(a_1=2\\a_2=9\\d=a_2-a_1=7\\\\a_n=a_1+d(n-1)\\\\a_{63}=2+7(63-1)=2+7(62)=2+434=436\)

The 63rd term of the given  arithmetic progression is 436.

An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant. A sequence -

a₁ , a₂, a₃ , a₄ ...... aₙ

will be an arithmetic progression if -

a₂ - a₁ = a₃ - a₂ = a₄ -  a₃ = d (constant) is called common difference of A.P. and a₁ = 'a' as the first term.

Given is the following sequence -

2, 9, 16, ..... nth term

First term [a] = 2

common difference [d] = 9 - 2 = 7

We can calculate the nth term of an A.P. using the formula -

a[n] = a + (n - 1)d

a[63] = a + (63 - 1) d

a[63] = 2 + 62 x 7

a[63] = 2 + 434

a[63] = 436

Therefore, the 63rd term of the given  arithmetic progression is 436.

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Answer:

above sea level

Step-by-step explanation:

The correct answer is 0.391747. To find the probability that 18 or fewer seeds germinate, we can use the binomial distribution formula.

In this case, the probability of germination of a single seed is 0.9, and we are planting 20 seeds.

Let X be the random variable representing the number of seeds that germinate. We want to find P(X ≤ 18).

First, let's calculate the probability of exactly k seeds germinating, denoted as P(X = k), using the binomial distribution formula:

P(X = k) = C(n, k) * p^k * q^(n-k)

where n is the total number of trials (20 seeds), k is the number of successful trials (germinated seeds), p is the probability of success (0.9), and q is the probability of failure (1 - p).

Now, we want to find P(X ≤ 18), which is the sum of the probabilities of 0, 1, 2, ..., 18 seeds germinating:

P(X ≤ 18) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 18)

Calculating each individual probability and summing them up will give us the desired result.

Using a calculator or statistical software, we find that the probability P(X ≤ 18) is approximately 0.391747.

Therefore, the correct answer is 0.391747.

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Quota sampling is a method used in research to ensure that a sample represents the target population accurately and is free from bias. In quota sampling, researchers determine in advance how many individuals from certain groups or characteristics they need to include in the survey.

The main goal of quota sampling is to ensure that every person in the target population has an equal chance of being selected for the sample. This is achieved by selecting individuals based on specific characteristics or demographics that are representative of the population being studied.

For example, let's say a researcher wants to conduct a survey about favorite ice cream flavors among teenagers. They may decide that they need an equal number of male and female participants and an equal representation from different age groups within the teenage population. The researcher would then set quotas for each of these groups and select participants accordingly.

It's important to note that quota sampling does not involve pre-planning or random selection. Instead, researchers use their judgment to select individuals who meet the predetermined quotas as they encounter them in the target population.

By using quota sampling, researchers can ensure that their sample is diverse and representative of the population they are studying. This method helps reduce bias and provides a more accurate understanding of the target population's opinions or behaviors.

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Answer:

you need to subtract 23 from 33 to find x

Step-by-step explanation:

for this question your answer is D

The expression for area of the rectangles are obtained as x² + 10x + 21 and  x² - 9x + 8 respectively. The correct options for both parts are (C) and (B) respectively.

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The dimension of both the rectangles are given as,

First rectangle : (x + 3) and (x + 7)

Second rectangle : (x - 1) and (x - 8)

Since, the area of a rectangle is product of its dimensions.

It can be obtained as,

Area of first rectangle is given as,

⇒ (x + 3) × (x + 7)

⇒ x² + 10x + 21

Area of second rectangle is given as,

⇒ (x - 1) × (x - 8)

⇒ x² - 9x + 8

Hence, the area of both the rectangles are obtained as  x² + 10x + 21 and  x² - 9x + 8 respectively.

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Answer:

A)  y= -x+2

B) ( 2, 1)

Answer:

D, C

Step-by-step explanation:

1) y= -x+2

2) (2,1)

The measures for a = 10 cm , b = 12cm, and acute angle b =30°

A degree, is always denoted by ° (the degree symbol), known as a measurement of a plane angle in which one full rotation is 360 degrees.

Angle is the measure of the degree with which two lines are intersecting each other to form an orientation.

Acute angle is the measure of an angle which is greater than 0° and less than 90°. For example - 25°, 45° etc.

Triangle is the geometrical figure which is always made up of three sides aligning together to form a closed figure. There are various types of triangles like Acute angle triangle, Right angles Triangle, Obtuse angles triangle, etc.

Acute Angles Triangle is the triangle which consists of al three angles less than 90° but greater than 0°. And it can have any length of sides but the bar minimum condition is to have all three angles in acute form.

We need to find the measures of a, b, acute angle b to make exactly one triangle

As it is the necessary observation that, for one measurement there is only one and only one figure exists which is unique in nature.

Hence, the measure of a, b, c are a = 10 cm , b = 12cm, and acute angle b =30°

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Answer:

d) y = -3x-3

e) y = -3x - 1

f) y = -3x + 2

Step-by-step explanation:

Knowledge Needed:

Slope-Intercept Form: y = mx + b

y and x stay as variables so you can solve for the intercepts and graph.

m is the slope, or the constant amount that the y-value on a line changes when the x-value increases by 1.

b is the y-intercept, or when t he line has an x-value of 0.

When lines are parallel, they have the same slope.

Question

d)

Examine the line: At what y-value does the line have a x-value of 0?

y-value: -3

Alternatively, you could also solve be getting a set of points on the line and plugging in.

(1,0)

Our equation for line d:

y = -3x - b

0 = -3(1)  - b

0 = -3 - b

0 + 3 = -3 + 3 - b

3 = -b

b = -3

d) y = -3x-3

e)

Repeat the same steps.

y-intercept: -1

Because they are parallel, they have the same slope.

e) y = -3x - 1

f)

Repeat the same steps.

y-intercept: 2

Because they are parallel, they have the same slope.

f) y = -3x + 2

The estimated equation for these data is: Y= 6.47 + 1.013x

When x = 6, the estimated value of y is approximately 12.55.

To compute the estimated regression equation and predict the value of y when x = 6, we'll follow these steps:

Given data:

xi: 2, 6, 9, 13, 20

yi: 7, 18, 9, 26, 23

a. Compute b0 and b1 and develop the estimated equation for these data.

Step 1: Calculate the means of x and y:

x = (2 + 6 + 9 + 13 + 20) / 5 = 10

y = (7 + 18 + 9 + 26 + 23) / 5 = 16.6

Step 2: Calculate the deviations from the means:

xi - x: -8, -4, -1, 3, 10

yi - y: -9.6, 1.4, -7.6, 9.4, 6.4

Step 3: Calculate the sum of squared deviations:

Σ(xi - x): 180

Σ(yi - y)²: 316.8

Step 4: Calculate the sum of cross-products:

Σ(xi - x)(yi - y): 182.4

Step 5: Calculate the slope (b1):

b1 = Σ(xi - x)(yi - y) / Σ(xi - x)² = 182.4 / 180 ≈ 1.013

Step 6: Calculate the intercept (b0):

b0 = y - b1 * x = 16.6 - 1.013 * 10 ≈ 6.47

Therefore, the estimated equation for these data is:

Y = 6.47 + 1.013x

b. Use the estimated regression equation to predict the value of y when x = 6.

To predict the value of y when x = 6, substitute x = 6 into the estimated equation:

y = 6.47 + 1.013 * 6

y ≈ 6.47 + 6.078

y ≈ 12.55

Thus, when x = 6, the estimated value of y is approximately 12.55.

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The solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

As per data the system of linear equations,

\(\[ \left\{\begin{array}{c} x+2 y+3 z=9 \\ 2 x-y+z=8 \\ 3 x-z=3 \end{array}\right. \] 1)\)

Write the system in the matrix form \(\( A . X=B \)\)

We know that the matrix form of the system of linear equations is as follows.

\(\[A. X = B\]\)

Where

\(\[A=\begin{pmatrix} 1 & 2 & 3 \\ 2 & -1 & 1 \\ 3 & 0 & -1 \end{pmatrix}\[X=\begin{pmatrix} x \\ y \\ z \end{pmatrix}\]\)

and

\(\[B=\begin{pmatrix} 9 \\ 8 \\ 3 \end{pmatrix}\]2)\)

To solve the system, we can use row reduction method.

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 2 & -1 & 1 & 8 \\ 3 & 0 & -1 & 3 \end{pmatrix}\]\)

Applying the elementary row operations

\(\[R_{2}\to R_{2}-2R_{1}\]\)

and

\(\[R_{3}\to R_{3}-3R_{1}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & -6 & -10 & -24 \end{pmatrix}\]\)

Now applying the elementary row operations

\(\[R_{3}\to R_{3}-(6/5)R_{2}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & 0 & -1 & -2 \end{pmatrix}\]\)

Now, we need to apply back substitution method. Using the third row, we can get the value of z as z = 2.

Now, using the second row,

\(\[-5y - 5z = -10\]\\\-5y - 5(2) = -10\]\)

Solving this equation, we get y = 0.

Finally, using the first row, we can get the value of x as

\(\[x + 2y + 3z = 9\]\\x = 3\]\)

Hence, the solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

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Answer:

Step-by-step explanation:

Solving

5x + -2y = 12

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2y' to each side of the equation.

5x + -2y + 2y = 12 + 2y

Combine like terms: -2y + 2y = 0

5x + 0 = 12 + 2y

5x = 12 + 2y

Divide each side by '5'.

x = 2.4 + 0.4y

Simplifying

x = 2.4 + 0.4y

Answer:

B.) \(6^{\frac{1}{2}}\)

Step-by-step explanation:

Use the exponent rule that states \(a^{\frac{1}{m}}=\sqrt[m]{a}\).  For this problem, let

a=6

m=2

So,

\(\sqrt6=6^{\frac{1}{2}}\)

Answer:

x = 16

4x = 64

Step-by-step explanation:

The sum of the exterior angles of any polygon is 360°

Add the given angles and solve for x

93 + 46+ 3x + 62 + 4x +47 = 360

7x + 248 = 360

7x = 360 –248

x = 16

4(16) = 64

Answer: red hot= $4

gummies=$9

Step-by-step explanation:

3r+1g=21

-(3r+3g=39)

3r+1g=21

-3r-3g=-39

-2g=-18

g=9

3r+1(9)=21

3r=12

r=4

According to Sturge's rule, number of classes or bins recommended to construct a frequency distribution is k ≈ 7

Sturge's Rule: There are no hard and fast guidelines for the size of a class interval or bin when building a frequency distribution table. However, Sturge's rule offers advice on how many intervals one can make if one is genuinely unable to choose a class width. Sturge's rule advises that the class interval number be for a set of n observations.

Given,

n = 66

We know that,

According to Sturge's rule, the optimal number of class intervals can be determined by using the equation:

\(k=1+log_{2} n\)

Here, n is equal to 66 and by substituting the value to the equation we get:

\(k=1+log_{2} (66)\)

k = 7.0444

k ≈ 7

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The solution to the inequality are the region in the shaded area and the graph is attached

From the question, we have the following parameters that can be used in our computation:

y ≥3(0.8)^x

y ≥ x² - 5

Represent properly

y ≥ 3(0.8)^x

y ≥ x² - 5

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, one of the coordinates in the shaded area has a coordinate of (0, 5)

None of the options represent the shaded area (see attachment)

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So, the area of the shape is 164.4 square meters.

In geometry, area is the measure of the size of a two-dimensional surface or region. It is the amount of space inside the boundaries of a flat object such as a polygon, circle, or rectangle. Area is measured in square units, such as square meters (m²), square centimeters (cm²), square feet (ft²), square inches (in²), and so on. To calculate the area of a shape, you typically need to use a specific formula depending on the type of shape, such as base times height for a triangle, or length times width for a rectangle.

Here,

The area of the shape is equal to the sum of the areas of these smaller pieces. We can calculate each area as follows:

The area of the rectangle on the left is 4m x 8.4m = 33.6 square meters.

The area of the rectangle on the right is 8m x 11.4m = 91.2 square meters.

The area of the triangle on the top is (8.4m x 4m) / 2 = 16.8 square meters.

The area of the triangle on the bottom is (11.4m x 4m) / 2 = 22.8 square meters.

Therefore, the total area of the shape is:

33.6 + 91.2 + 16.8 + 22.8 = 164.4 square meters

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The system of equations has exactly one real solution , Option A is the correct answer.

The missing point of the line is (13,1)

An Equation is defined as the mathematical statement that is formed when algebraic expression is linked with an equal sign .

The lines are plot on the graph , The lines intersect at only one point which means

The system of equations has exactly one real solution

Option A is the correct answer.

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Answer:

a coin tossed twice in the following week what is the out come

We can use the binomial distribution to solve this problem.

Let X be the number of people out of 15 who used an online travel website to book their hotel. Then, X follows a binomial distribution with n = 15 and p = 0.7.

The expected value of X is given by:

E(X) = n × p

Substituting the values given in the problem, we get:

E(X) = 15 × 0.7 = 10.5

Therefore, we would expect 10 people (rounding down 10.5 to the nearest whole person) out of 15 to use an online travel website to book their hotel.

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the vector (2, -17, 13) is a nonzero vector orthogonal to the plane through the points P, Q, and R.

To find a nonzero vector orthogonal to the plane through the points P(3, 0, 3), Q(-2, 1, 4), and R(6, 2, 5), we can use the cross product of two vectors in the plane.

Let's first find two vectors in the plane. We can use the vectors PQ and PR.

PQ = Q - P = (-2, 1, 4) - (3, 0, 3) = (-5, 1, 1)

PR = R - P = (6, 2, 5) - (3, 0, 3) = (3, 2, 2)

Now we can take the cross product of PQ and PR to get a vector orthogonal to the plane:

N = PQ x PR

N = (-5, 1, 1) x (3, 2, 2)

N = (2, -17, 13)

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5 rules of scientific notation which helps us to represent the numbers which are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent.

The exponent is either positive or negative depending on how big or little the number is. Learn about power and exponents to have a deeper understanding. The five golden rules of the scientific notation:

Hence there are the rules of the the scientific notation.

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Given the figure, we can deduce the following information:

1. Point A lies in the upper left side of the Cartesian Plane.

Based on the given figure, we must note that if the point lies in the upper left side of the Cartesian Plane or the x-coordinate is negative but the y-coordinate is positive, it should be in the Quadrant II.

Therefore, the answer is B. Quadrant II.

Answer:

x=-1.837 or 1.837

Step by Step explanation:

Use the standard form,ax²+bx+c=0 , to find the coefficients of our equation, :

q = 32

b= 0

c= -108

x=-1.837 or x=1.837

I hope this is helpful

pls tag brainliest answer

The probability that he or she actually used steroids is 0.779.

The test is accurate 95% of the time when an athlete has taken steroids. It is 97% accurate when an athlete hasn't taken steroids. Suppose that the drug test will be used in a population of athletes in which 10% have actually taken steroids. Let's choose an athlete at random and administer the drug test.

Based on prior knowledge of conditions that might be related to the event, Bayes' theorem, which is named after Thomas Bayes and is used in probability theory and statistics, describes the probability of an event.

Using Baye's theorem:

P(steroids | positive) = P(steroids)*P(positive|steroids) / P(positive) = (0.10*0.95)/0.122 = 0.779

If the selected athlete passes the test, the probability that they used steroids: 0.779

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(complete question)

A company has developed a drug test to detect steroid use by athletes. The test is accurate 95% of the time when an athlete has taken steroids. It is 97% accurate when an athlete hasn’t taken steroids. Suppose that the drug test will be used in a population of athletes in which 10% have taken steroids. Let’s choose an athlete at random and administer the drug test.

Suppose that the chosen athlete tests positive. What’s the probability that he or she used steroids?

Answer:

C

Step-by-step explanation:

fits the the graph

Answer:

r=30

Step-by-step explanation:

r/30=-2+3

r/30=1

r=1×30

r=30