assume one person out of 10,000 is infected with hiv, and there is a test in which 2.5% of all people test positive for the virus although they do not really have it. if you test negative on this test, then you definitely do not have hiv. what is the chance of having hiv, assuming you test positive for it?

The area of the regular decagon with centre O and apothem 14 units is found as 637 square units

What is an apothem?

An apothem is like a radius for any polygon. It is the perpendicular distance from the centre of any given polygon to any of the opposite sides of that polygon. And polygon is a shape that is a closed two dimensional figure made up of straight lines or line segments. based on the number of sides we have different polygons such as triangle, quadrilateral,pentagon etc.

Here the regular polygon is decagon.

As decagin has 10 sides, number of sides N=10

Given the length of apothem(A) =14 units

Using trigonometric ratios we can find the length of side:

We know that the total angle at the centre=360

angle subtended by each side of decagon at centre=360÷10

                                                                                       =36°

angle bisected by the apothem= 36 ÷ 2

                                                    =18°

Tan18 = [tex]\frac{side opposite to the angle}{side adjacent to the angle}[/tex]

         =   [tex]\frac{half length of side}{apothem}[/tex]

          =[tex]\frac{0.5L}{14}[/tex]

0.325  =[tex]\frac{0.5L}{14}[/tex]

       L = (0.325 x 14)÷ 0.5

       L=9.1 units

The area of a regular polygon using apothem is given by

Area (A) = [number of sides×length of side×apothem] ÷2

             =[tex]\frac{N L A}{2}[/tex]

             =[tex]\frac{10 x 14 x 9.1}{2}[/tex]

             =637 sq. units

The area of given decagon is 637 sq. units

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Refer to the attachement for complete question.

Answer:

An exponential function has the form `f(x) = ab^x`, where `a` and `b` are constants. To find the exponential function that passes through the points `(-2,1)` and `(-1,2)`, we can use these points to set up a system of equations to solve for the values of `a` and `b`.

Substituting the coordinates of the first point into the equation for an exponential function gives us:

`1 = ab^(-2)`

Substituting the coordinates of the second point into the equation for an exponential function gives us:

`2 = ab^(-1)`

Dividing these two equations gives us:

`(2)/(1) = (ab^(-1))/(ab^(-2))`

`2 = b`

Now that we know that `b=2`, we can substitute this value back into either equation to solve for `a`. Substituting into the first equation gives us:

`1 = a(2)^(-2)`

`1 = a(1/4)`

`a = 4`

So, the exponential function that passes through the points `(-2, 1)` and `(-1, 2)` is given by:

`f(x) = 4 * 2^x`.

To find the exponential function for the graph passing through (-2,1) and (-1,2), we need to use the general form of an exponential function, which is:

y = a * b^x

where:

a is the initial value or the y-intercept of the function

b is the base of the exponential function

x is the variable or the exponent

To determine the values of a and b, we need to use the two given points and solve for the corresponding equations. Substituting the first point (-2,1), we get:

1 = a * b^(-2)

Substituting the second point (-1,2), we get:

2 = a * b^(-1)

Now, we can solve for a and b by eliminating one variable. Dividing the second equation by the first equation, we get:

2/1 = a * b^(-1) / (a * b^(-2))

2 = b

Substituting this value of b into the first equation, we get:

1 = a * 2^(-2)

a = 4

Therefore, the exponential function that passes through (-2,1) and (-1,2) is:

y = 4 * 2^x

or

f(x) = 4 * 2^x

The appropriate graph displaying the solution set for 2x 3>-9 is:.

      o====================>

 -2  -1   0   1   2   3   4   5   6

A number line is a straight line that represents the set of real numbers.   It is a graphical representation of numbers in which each point on the line corresponds to a unique number.

To graph the solution set for 2x+3>-9, we need to solve for x and graph the inequality on a number line.

Starting with the given inequality:

2x + 3 > -9

Subtracting 3 from both sides gives:

2x > -12

Dividing both sides by 2 gives:

x > -6

Any value of x greater than -6 will therefore satisfy the inequality.

To graph this on a number line, we can start by marking -6 with an open circle (since x is not equal to -6).

Then, we shade to the right of -6, indicating all values of x that are greater than -6.

where the open circle at -6 indicates that x is not equal to -6, and the arrow pointing to the right indicates that all values of x greater than -6 satisfy the inequality.

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Answer:

Solution- x = 5 Equation- x + 4 = 9

Step-by-step explanation:

I hope this helps you understand.

Therefore, the answer is D. Block 1 IQR: 20; Block 2 IQR: 5. Therefore, the answer is B. Block One: 25, Block Two: 100. Therefore, the answer is B. Block 1 is skewed right, Block 2 is skewed left. Therefore, the answer is option A: mean: 76.5, standard deviation: 21.6.

In statistics, the mean (or arithmetic mean) is a measure of central tendency of a set of numerical data. It is calculated by adding all the values in the dataset and dividing by the number of values. The mean is often used as a representative value for a dataset, as it provides a single value that summarizes the entire dataset. However, it can be affected by extreme values (outliers) in the dataset.

Here,

1. To find the interquartile range (IQR) for each block, we first need to determine the quartiles. We can do this by finding the median (Q2) of each block, and then finding the median of the lower half (Q1) and upper half (Q3) of the data.

For Block 1:

Q1: median of {25, 60, 70, 75, 80} = 70

Q2: median of {85, 85, 90, 95, 100} = 90

Q3: median of {70, 75, 80, 85, 90} = 80

IQR = Q3 - Q1 = 80 - 70 = 10

For Block 2:

Q1: median of {70, 70, 75, 75, 75} = 75

Q2: median of {75, 75, 80, 80, 85} = 80

Q3: median of {80, 85, 100, 75, 75} = 82.5

2. To identify outliers, we can use the 1.5 x IQR rule. Any data point that is more than 1.5 x IQR above Q3 or below Q1 is considered an outlier.

For Block 1:

Q1 = 70

Q3 = 80

IQR = 10

1.5 x IQR = 15

The only data point that is more than 15 above Q3 is 100, so it is an outlier.

For Block 2:

Q1 = 75

Q3 = 82.5

IQR = 8

1.5 x IQR = 12

There are no data points that are more than 12 above Q3 or below Q1, so there are no outliers.

3. To determine if each block's data is symmetric, skewed left, or skewed right, we can examine the shape of the distribution.

For Block 1, the data is:

Highest at 100, with several values clustered around the upper end of the range.

No values below 25, which suggests a lower boundary.

Median is 90.

No values are particularly isolated from the rest of the data.

This suggests that Block 1 is skewed right.

For Block 2, the data is:

Highest at 75, with several values clustered around the middle of the range.

No values below 70, which suggests a lower boundary.

Median is 80.

No values are particularly isolated from the rest of the data.

This suggests that Block 2 is skewed left.

4. To find the mean of Block 1, we add up all the scores and divide by the number of scores:

mean = (25 + 60 + 70 + 75 + 80 + 85 + 85 + 90 + 95 + 100) / 10

mean = 765 / 10

mean = 76.5

To find the standard deviation of Block 1, we need to first calculate the variance.

To do that, we can use the formula:

variance = (sum of (each score - mean)²) / (number of scores - 1)

First, we'll find the sum of (each score - mean)²:

(25 - 76.5)² = 2562.25

(60 - 76.5)² = 270.25

(70 - 76.5)² = 42.25

(75 - 76.5)² = 2.25

(80 - 76.5)² = 12.25

(85 - 76.5)² = 71.25

(85 - 76.5)² = 71.25

(90 - 76.5)² = 182.25

(95 - 76.5)² = 379.25

(100 - 76.5)² = 562.5

Next, we'll add up these values:

2562.25 + 270.25 + 42.25 + 2.25 + 12.25 + 71.25 + 71.25 + 182.25 + 379.25 + 562.5 = 3154.5

Now we can plug this into the variance formula:

variance = 3154.5 / 9

variance = 350.5

Finally, to get the standard deviation, we take the square root of the variance:

standard deviation = √(350.5)

standard deviation = 18.7 (rounded to one decimal place)

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Based on the information, it should be noted that the theorem that is not applicable and doesn't prove the relationship is A. MCA = MCO, CAM = COM

The triangles are congruent if their two sides and included angles are identical to each other, according to the side-angle-side (SAS) theorem.

You cannot use any theorem along with option A. For B, you can use SAS. For option C, you can use SAS. For option D, you can use SSS. For option D, you can use ASA

Therefore, based on the information, the correct option is A.

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I don't think anyone can, that's the wrong pic

put 62  it does have instructions right

h is equal to the sum of f and 3, divided by 3 times g. The given equation is 3gh = f + 3, and we are asked to solve for h. To solve for h, we need to isolate h on one side of the equation.

First, we can simplify the left-hand side of the equation by dividing both sides by 3g:

(3gh)/(3g) = (f + 3)/(3g)

This simplifies to:

h = (f + 3)/(3g)

Now we have isolated h on the left-hand side of the equation. This means that the solution for h is given by the right-hand side of the equation, which is (f + 3)/(3g).

Therefore, h is equal to the sum of f and 3, divided by 3 times g. This is a general formula that will give us the value of h for any given values of f and g, as long as they are not equal to zero.

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The correct graph will display the inequalities with appropriate lines (solid or dashed) and shading that demonstrates the solution set where all inequalities are satisfied simultaneously.

To determine which graph represents the system of inequalities, consider the following steps:

1. Identify the inequalities involved in the system. They typically include one or more linear inequalities, which can be expressed as Ax + By ≤ C, Ax + By ≥ C, Ax + By < C, or Ax + By > C.

2. Graph each inequality separately, using solid lines for "≤" and "≥" inequalities and dashed lines for "<" and ">" inequalities. Solid lines represent the points that satisfy the inequality, while dashed lines indicate that points on the line do not.

3. Shade the regions that satisfy each inequality. For inequalities with "≤" or "<", shade the region below the line, adeterminationnd for those with "≥" or ">", shade the region above the line.

4. Observe the overlapping shaded regions, as this represents the solution set for the system of inequalities.

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Using the area formula, we can find the area of the region to be 24.5 square units.

The total area of a three-dimensional object's faces represents the object's surface. The idea of surface areas has practical implications in wrapping, painting, and ultimately creating things to create the best possible design.

To determine the area of the territory in the above question, we must first calculate the areas of the three shapes.

Triangle 1: The height is equal to the distance between the x-(which axis's is 0) and the (3,6)-axis's (which is 6) y-coordinates.

The triangle's dimensions are as follows:

= 1/2 × base × height

= 1/2 × 3 × 6

= 9

Triangle 2's base is the area between the x-axis and the point where the line y=10-x intersects it (10,0).

Triangle 2:

= 1/2 × base × height

= 1/2 × 4 × 1

= 2

Trapezoid:

The areas of the three forms added together are:

= 9 + 2 + 13.5

= 24.5

The x-axis, lines x=2, x=6, lines y=x+3, and y=10-x surround the region, which is 24.5 square units in size.

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The point of intersection is (6, 6).


To find the point where two lines intersect, we need to solve the system of equations:

y = 2x - 6 (equation 1)

y = 1/2x + 3 (equation 2)

We can solve this system by setting the two expressions for y equal to each other:

2x - 6 = 1/2x + 3

Multiplying both sides by 2 to eliminate the fraction, we get:

4x - 12 = x + 6

Subtracting x and adding 12 to both sides, we get:

3x = 18

Dividing by 3, we get:

x = 6

Now we can plug this value of x into either equation to find the corresponding y-coordinate. Let's use equation 1:

y = 2(6) - 6 = 6

Therefore, the point of intersection is (6, 6).

The assumptions and conditions for inference can be checked by options a, b, c, and d.

The assumptions and conditions for inference are checked while making statistical inferences about a population parameter based on sample statistics. These assumptions are made to ensure that the sample accurately reflects the population from which it was drawn. The correct options from the given alternatives are:

a. The residual plot and the scatterplot show consistent variability.

b.The residuals look random.

c. The scatterplot looks straight enough.

d. The residuals are nearly normal.

A residual plot is a graphical tool used to check the assumptions of a simple linear regression model. The scatterplot is the most common method for visualizing the relationship between two quantitative variables. The assumptions of linear regression are that the residuals are normally distributed, have constant variance (homoscedasticity), and are independent of one another. If the residuals are not normally distributed, have heteroscedasticity or the observations are dependent, then the linear regression model may not provide accurate predictions.

The scatterplot should also show the residual plot as random if we want to make valid inferences from a simple linear regression model. If the scatterplot shows any pattern, it indicates that the model does not capture all of the relationships between the variables, which may result in incorrect conclusions when making inferences from the model.The residuals should also be nearly normal for making valid inferences from a simple linear regression model.

It is possible to check whether the residuals are approximately normal by creating a histogram or a normal probability plot of the residuals. If the distribution of residuals is non-normal, the statistical inference may not be accurate.

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The probability that the sample mean is between 50.9 and 51.5 is approximately 0.0998.

We can use the central limit theorem to find the probabilities of the given events. According to the central limit theorem, if we take random samples of size n from a population with mean μ and standard deviation σ, the sample means will be approximately normally distributed with mean μ and standard deviation σ/√n.

a. To find the probability that the sample mean is greater than 53, we first calculate the z-score of the sample mean:

[tex]$z=(x-\mu) /(\sigma / \sqrt{n})=(53-50) /(19 / \sqrt{ } 64)=1.684$[/tex]

Using a standard normal distribution table or calculator, we find that the probability of a z-score being greater than 1.684 is 0.0455. Therefore, the probability that the sample mean is greater than 53 is approximately 0.0455.

b. To find the probability that the sample mean is less than 53, we use the same formula and calculate the z-score:

[tex]$z=(x-\mu) /(\sigma / \sqrt{ } n)=(53-50) /(19 / \sqrt{ } 64)=1.684$[/tex]

The probability of a z-score being less than 1.684 is 1 - 0.0455 = 0.9545. Therefore, the probability that the sample mean is less than 53 is approximately 0.9545.

c. To find the probability that the sample mean is less than 47, we again use the formula for the z-score:

[tex]$z=(x-\mu) /(\sigma / \sqrt{ } n)=(47-50) /(19 / \sqrt{ } 64)=-1.684$[/tex][tex]$z 1=(47.5-50) /(19 / \sqrt{ } 64)=-0.842$[/tex]

The probability of a z-score being less than -1.684 is the same as the probability of a z-score being greater than 1.684, which we found to be 0.0455. Therefore, the probability that the sample mean is less than 47 is approximately 0.0455.

d. To find the probability that the sample mean is between 47.5 and 51.5, we first calculate the z-scores of the two endpoints:

[tex]z_1[/tex] = (47.5 - 50) / (19/√64) = -0.842

[tex]z_2[/tex]= (51.5 - 50) / (19/√64) = 0.842

Using a standard normal distribution table or calculator, we find that the probability of a z-score being between -0.842 and 0.842 is 0.6603. Therefore, the probability that the sample mean is between 47.5 and 51.5 is approximately 0.6603.

e. To find the probability that the sample mean is between 50.9 and 51.5, we first calculate the z-scores of the two endpoints:

[tex]z_1[/tex]= (50.9 - 50) / (19/√64) = 0.674

[tex]z_2[/tex] = (51.5 - 50) / (19/√64) = 0.842

Using a standard normal distribution table or calculator, we find that the probability of a z-score being between 0.674 and 0.842 is 0.0998. Therefore, the probability that the sample mean is between 50.9 and 51.5 is approximately 0.0998.

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Answer: The composite figure consists of two square pyramids, so we can find the total surface area by adding the surface area of each pyramid. The surface area of a square pyramid is given by:

S = B + (1/2)Pl

where B is the area of the base, P is the perimeter of the base, l is the slant height, and S is the total surface area.

For each pyramid, we have:

B = 24^2 = 576 cm^2

P = 4(24) = 96 cm

l = sqrt(24^2 + 5^2) = 25 cm

So the surface area of each pyramid is:

S = 576 + (1/2)(96)(25)

S = 576 + 1200

S = 1776 cm^2

Therefore, the total surface area of the composite figure is:

2S = 2(1776)

= 3532 cm^2

The expression that represents the total surface area, in square centimeters, of the figure is:

(24) (24) + 8 (one-half (24) (5)) + 8 (one-half (24) (13)) = 576 + 480 + 624 = 1680 cm^2

This expression only accounts for the surface area of the base and the triangular faces, but it does not include the surface area of the pyramid faces. So it is not correct.

The correct answer is:

8 (one-half (24) (5)) + 8 (one-half (24) (13)) = 480 + 624 = 1104 cm^2

which only represents the surface area of the triangular faces of both pyramids. To get the total surface area, we need to add the surface area of the base, which gives:

1104 + 2(576) = 2256 + 1104 = 3360 cm^2

Therefore, the total surface area of the composite figure is 3360 square centimeters.

Step-by-step explanation:

Answer:

[tex]\large\boxed{\tt f(2) = 10}[/tex]

Step-by-step explanation:

[tex]\textsf{For this problem, we are asked to evaluate the function given x.}[/tex]

[tex]\textsf{Note that because x is given, all that's needed to be done is substitution.}[/tex]

[tex]\large\underline{\textsf{Substitute;}}[/tex]

[tex]\tt f(2)= 3x^{3} -5x-4[/tex]

[tex]\tt f(2)= 3(2)^{3} -5(2)-4[/tex]

[tex]\large\underline{\textsf{Evalulate;}}[/tex]

[tex]\tt f(2)= 3(2 \times 2 \times 2) -10-4[/tex]

[tex]\tt f(2)= 3(8) -10-4[/tex]

[tex]\tt f(2)= 24-14[/tex]

[tex]\large\boxed{\tt f(2) = 10}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{f(x) = 3x^3 - 5x - 4}\\\\\mathsf{f(x) = 3(2)^3 - 5(2) - 4}\\\\\mathsf{f(x) = 3(2^3) - 5(2) - 4}\\\\\mathsf{f(x) = 3(2\times2\times2) - 5(2) - 4}\\\\\mathsf{f(x) = 3(4\times2) - 5(2) - 4}\\\\\mathsf{f(x) = 3(8) - 5(2) - 4}\\\\\mathsf{f(x) = 24 - 5(2) - 4}\\\\\mathsf{f(x) = 24 - 10 - 4}\\\\\mathsf{f(x) = 14 - 4}\\\\\mathsf{f(x) = 10}\\\\\\\huge\text{Therefore your answer should be:}\\\\\huge\boxed{\mathtt{f(x) = 10}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

cone’s radius r in terms of y is  r = 2(y + 5).

The quantity of space a cone encloses is referred to as its volume. It is the measure of the three-dimensional space occupied by the cone.

volume of a cone with a height of 9 inches as:

V = 3πy² + 30πy + 75π

Also, we are aware that the formula for a cone's volume with height hand radius r is

V = 1/3πr²h

Since we are looking for the radius of the cone in terms of y, we need to express h in terms of y. We can do this by noting that the height of the cone is 9 inches, and that it is made up of two parts: a smaller cone with height y and a larger frustum with height (9-y). The radius of the smaller cone is r/y times the radius of the larger frustum, so we can write:

h = y + (9 - y) = 9

r/y = r/(r + 3y)

As a result, the cone's volume may be represented as:

V = 1/3πr²(y + (9 - y))

= 1/3πr²(9)

Equating this to the given volume, we get:

1/3πr²(9) = 3πy² + 30πy + 75π

Simplifying and solving for r, we get:

r = √(4(y² + 10y + 25))

r = 2√(y² + 10y + 25)

Therefore, the cone's radius in terms of y is:

r = 2(y + 5)

So the answer is r = 2(y + 5).

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The points (5, 0), (0, 5), (-5, 0) and (0, -5) all lie on a circle with center (0, 0) and radius 5.

The equation of a circle with center (0, 0) and radius 5 can be written as (x - 0)2 + (y - 0)2 = 52.

In Quadrant I, the point (5, 0) lies on the circle. This can be seen by substituting x = 5 and y = 0 in the equation of the circle.

5² + 0² = 25

In Quadrant II, the point (0, 5) lies on the circle. This can be seen by substituting x = 0 and y = 5 in the equation of the circle.

0² + 5² = 25

In Quadrant III, the point (-5, 0) lies on the circle. This can be seen by substituting x = -5 and y = 0 in the equation of the circle.

(-5)² + 0² = 25

In Quadrant IV, the point (0, -5) lies on the circle. This can be seen by substituting x = 0 and y = -5 in the equation of the circle.

0² + (-5)² = 25

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Jimmy's living space really gauges 24 feet by 16 feet in light of the fact that every 2 cm on the size attracting is equal to 8 feet.

We can utilize this scale variable to decide the genuine dimensions of the rectangle room in the event that each 2 cm on the scale attracting relates to 8 feet.

We should initially sort out the number of 2 cm units there that are in the scale drawing's length and expansiveness.

Length: 6 cm ÷ 2 cm = 3 units

Width: 4 cm ÷ 2 cm = 2 units

Thus, the size drawing is 3 by 2 units.

Next, we can interpret the dimensions of the scale bringing into genuine dimensions utilizing the scale variable of 2 cm = 8 feet:

Length: 3 units times 8 feet for every unit approaches 24 feet

Width: 2 units times 8 feet for every unit approaches 16 feet

Jimmy's living space really gauges 24 feet by 16 feet in light of the fact that each 2 centimeters on the size attracting is comparable to 8 feet.

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Answer:2 years

Step-by-step explanation:

Reason being is that 27% is for one year and if you add it on 54% for the second year which mean it will halve in value. I can only give this answer based on the information you have given.

The value of x in the equation (x - m)/(n + m) = (x - n)/(n - m) when solved is x = n²/m

From the figure, the equation is

(x - m)/(n + m) = (x - n)/(n - m)

When cross multiplied, we have

(x - m)(n - m) = (n + m)(x - n)

Opening the bracket, we have

xn - xm - mn + n² = xn + xm - n² - mn

Evaluating the like terms, we have

2xm = 2n²

So, we have

xm = n²

Divide by m

x = n²/m

Hence, the solution is x = n²/m

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Answer:

Step-by-step explanation:

Sup? Pay attention closely (or not XD)

Short answer: 0.0308 or 3.08%

We use the combination formula C = n!/(r! * (n-r)!) for each brand. It basically tells us the number of ways to select a certain number of cars:

1) Fords: C(5, 2) = 5! / (2! * (5 - 2)!) = 10 ways to pick 2 Fords

2) Chevrolets: C(7, 3) = 7! / (3! * (7 - 3)!) = 35 was to pick 3 Chevys

3) Dodges: C(4, 1) = 4! / (1! * (4 - 1)!) = 4 ways to pick 1 Dodge

4) Hondas: C(3, 1) = 3! / (1! * (3 - 1)!) = 3 ways to pick 1 Honda

5) Toyotas: C(4, 2) = 4! / (2! * (4 - 2)!) = 6 ways to pick 2 Toyotas

Then you multiply all them results. Peep this:

10*35*4*3*6 = 25,200 ways to pick your target cars from each brand in total (sheesh)

Now how many ways would it be to pick 9 out of the 23 cars??

Use your best friend combination problem to solve this!

C(23, 9) = 23! / (9! * (23 - 9)!) = 817,190 (sheesh)

Now divide! 25,200/817,190 = 0.0308 or 3.08%

Thanks for listening to my TED talk. Hope this helps.

Answer:

D

Step-by-step explanation:

i did the quiz

Answer:

x = 32°

Step-by-step explanation:

The definition of tangent means that the angle formed by the line and the circle is a 90° angle. We can also see that the two segments connected to the center have equal angles because they are both radii of the circle. They form a triangle and the angle measurements are 61°, 61° and 58°. We have two angle measurements of the overall triangle, 58°, 90° (from the tangent), and x°.

The sum of the angles of any triangle is 180°. Therefore, we can form an equation to calculate the value of x.

58 + 90 + x = 180

x = 180 - 90 - 58

x = 32°

Answer:

x = 32°

Step-by-step explanation:

To find:-

Answer:-

As we know that angle made by tangent on the centre is a right angle . So here [tex]\angle[/tex]OBC will be 90° ( as CB is tangent on the circle.) Again we know that the angles opposite to equal sides are equal . Therefore here OB and OA are radii of the circle which are equal. So we can say that;

[tex]\sf:\implies \red{ \angle OBA = \angle OAB = 61^o}\\[/tex]

Again we know that the angle sum property of a triangle is 180° . Therefore in ∆OBA ,

[tex]\sf:\implies 61^o + 61^o + \angle AOB = 180^o \\[/tex]

[tex]\sf:\implies 122^o + \angle AOB = 180^o \\[/tex]

[tex]\sf:\implies \angle AOB = 180^o - 122^o \\[/tex]

[tex]\sf:\implies \angle AOB = 58^o\\[/tex]

Finally look into the ∆OBC ,

[tex]\sf:\implies \angle BOC + \angle OCB + \angle CBO = 180^o\\[/tex]

[tex]\sf:\implies 58^o + 90^o + x = 180^o \\[/tex]

[tex]\sf:\implies 148^o + x = 180^o \\[/tex]

[tex]\sf:\implies x = 180^o - 148^o \\[/tex]

[tex]\sf:\implies \red{ x = 32^o }\\[/tex]

Hence the value of x is 32°.

More than 1 triangles can be constructed with the angles 110°, 50°, and 20°.

Three non-collinear points are connected with straight line segments to create the two-dimensional geometric shape known as a triangle. The triangle's three points are referred to as its vertices, and the line segments that link them as its sides. Triangles are named based on their sides and angles.  

In the given triangles,

angles are 110, 50 and 20.

we can construct on triangle by using these angles.

Now, 110 angle subtend longest side, 20 subtend shortest side as well as, 50 subtend third side.

Sides length are not mentioned.

So, we can construct one infinite triangle by scaling the length of sides.

Hence, More than 1 triangles can be constructed with the angles 110, 50, and 20.

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Therefore, Conner's starting weight was 3 kg. Therefore, the starting price of the toys was $7.50.

An equation is a mathematical statement that shows that two expressions are equal. It typically contains one or more variables, which are placeholders for unknown or varying quantities. The equation may also contain constants, which are known values that do not change.

Here,

31. Let's assume that Conner's starting weight was x kg. According to the given condition, he lifted 2 more kg each week, which means he lifted (x+2) kg on the second week, (x+4) kg on the third week, and so on. Therefore, he lifted (x+12) kg on the seventh week. We know that Conner lifted 15 kg on the seventh week, so we can set up an equation:

x + 12 = 15

Solving for x, we get:

x = 3

Answer: 3 kg

32. Let's assume that the starting price of the toys was x dollars. According to the given condition, the price of the toys was marked down by $0.25 every hour, which means the price of the toys was (x-0.25) dollars after the first hour, (x-0.5) dollars after the second hour, and so on. Therefore, the price of the toys was (x-2) dollars after the eighth hour. We know that the price of the toys was $5.50 after the eighth hour, so we can set up an equation:

x - 2 = 5.5

Solving for x, we get:

x = 7.5

Answer: $7.50

33.  Let's assume that Grayson started earning at a base hourly rate of x dollars. Then, we can use the given information to form an equation that relates his earnings for one day (in dollars) with his hourly rate (in dollars/hour):

Total earnings for one day = base hourly rate + (number of hours worked) * (hourly increase in rate)

Since we know that Grayson earned $45 in one day and that his hourly rate increases by $3 every hour, we can substitute these values into the equation:

45 = x + (number of hours worked) * 3

Simplifying this equation, we get:

(number of hours worked) * 3 = 45 - x

(number of hours worked) = (45 - x) / 3

We can now use the fact that Grayson worked for a full day (i.e., 24 hours) to solve for the base hourly rate x:

24 * x + 3 * (1 + 2 + ... + 23) = 45

Simplifying the sum of the first 23 integers, we get:

24 * x + 3 * (276) = 45

24 * x + 828 = 45

24 * x = 45 - 828

24 * x = -783

x = -32.625

Since a negative base hourly rate doesn't make sense in this context, we can conclude that there is no solution to this problem. Perhaps there was an error in the given information or assumptions made.

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