A circle has a circumference of 145 units. Find the length of the arc intercepted by a central angle of 125°.
Round to the nearest tenth.

By using the properties of triangles and straight lines we get the values of x as 65° and the value of y as 115°

A) In the given triangles we know that the sum of all the angles is 180 .

Hence :

60 + 55 + c = 180

or, c = 180° - 115°

or, c = 65°

Now the angle marked x is vertical angle to the angle c , hence the value of x is also 65°.

B) Now we know that the value of x is 65°

Again  x + y = 180°

Therefore : 65° + y = 180°  or, y = 180° - 65° or, y = 115°

Three vertices, three sides, and three angles make up a closed triangle. PQR serves as the symbol for a triangle with the vertices P, Q, and R.

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Answer:

The area is 1,014 cm^2

Step-by-step explanation:

Here, we want to find the total surface area of a cube with side length of 13 cm

what we shall do here is to apply the formula to get the total surface area

Mathematically, that will be

A = 6L^2

so we have

Area = 6 * 13^2

Area = 1,014 square cm

The double integral of 2x+1 over the region R={(x,y):0≤x≤2,0≤y≤1} is equal to the volume of the solid bounded by the graph of the function and the region R, which is 6 cubic units

To identify the given double integral as the volume of a solid, we can think of the integrand, 2x+1, as representing the height of the solid at each point (x,y) in the rectangular region R.

Thus, the double integral can be written as:
∫∫ 2x+1 dA = ∫0¹ ∫0² (2x+1) dxdy
This integral represents the volume of a solid that extends from the xy-plane up to the height of 2x+1 at each point (x,y) in the region R.
To evaluate the integral, we can first integrate with respect to x, treating y as a constant:
∫0² (2x+1) dx = [x²+ x] from x=0 to x=2
= (2² + 2) - (0² + 0)
= 4 + 2
= 6
Then, we integrate the resulting expression with respect to y, treating x as a constant:
∫0¹ 6 dy = 6[y] from y=0 to y=1
= 6(1-0)
= 6
Therefore, the double integral ∫∫ 2x+1 dA over the region R = { (x,y): 0≤x≤2 , 0≤y≤1 } represents the volume of a solid, and its value is 6.

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The expected number of flips until the first time that your previous 2012 flips are HTHT is = 4096

According to the information given in the question,

Now to calculate the chances of getting HTHT for the first time will be,

E(x) = n × p

Where E(x) = the expected number of flips.

n = number of flips.

p = Probability of getting HTHT

Given,

n = 2012

p = ( \(\frac{1}{4096}\) )

E(x) = 4096

Therefore, the expected number of flips until the first time that your previous 2012 flips are HTHT is = 4096

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You are repeatedly flipping a fair coin. what is the expected number of flips until the first time that your previous 2012 flips are HTHT ...?you are repeatedly flipping a fair coin. what is the expected number of flips until the first time that your previous 2012 flips are HTHT ...?

We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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Answer:

the answer would be 4 cm i think

Answer:

the answer is 5.

you need to use the volume formula of the prism and you will get the answer.that is 5

Answer:

I think the answer is 2.) p^q

Step-by-step explanation:

hope this helps if it is wrong let me know have a blessed day

p → q represents “if p then q" represents "If x = 4, then y = −2”

Therefore, the correct representation is:

Thus Option 3 is correct. 3.) p → q

Given :Let p: x = 4 Let q: y = −2

To Find Which represents "If x = 4, then y = −2”?

we know that:

1. p ∧ q represents “p and q”

2.p ∨ q represents “p or q (or both)

3.p → q represents “if p then q”

4. p ↔ q represents “p if and only if q"

The statement "If x = 4, then y = -2" can be represented by the conditional statement "p → q" which reads "p implies q" or "if p, then q."

In the given representation:

p: x = 4

q: y = −2

The conditional statement "p → q" means that if x is equal to 4 (p is true), then y is equal to -2 (q is true).

So, we can see that p → q represents “if p then q" represents "If x = 4, then y = −2”

Therefore, the correct representation is:

Thus Option 3 is correct. 3.) p → q

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A good sampling method for this scenario would be a probability-based method called Simple Random Sampling.

In Simple Random Sampling, each individual from the population of individuals who have high cholesterol has an equal chance of being selected for the sample. This ensures that the sample is representative of the population and that each individual in the population has a known non-zero probability of being selected.

This method can be supported by the fact that it is easy to implement, and it does not require any prior knowledge of the population characteristics. It also ensures that the sample is unbiased and has a good chance of being representative of the population.

Additionally, Simple Random Sampling is also a cost-effective sampling method as it is less expensive and time-consuming than other sampling methods such as stratified random sampling or cluster sampling.

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Answer:

c = 3/4 j your welcome hope this helps

Answer:

x = 8

Step-by-step explanation:

Hope this helps have a great day

Allan would need to sell 427 boxes to make 1600 dollars in total sales. The number line representation of the number of boxes sold is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ..............., 1600].

A pair of coordinates’ vertical value. How high or low the point is. In an ordered pair of coordinates (x,y), the Y Coordinate is always written second, as in (12,5). In this case, the Y Coordinate is “5”. Also known as “Ordinate” Pick x and solve the equation for y to locate points on the line y = mx + b, or choose y and solve for x.

When you know the slope of the line to be investigated and the point supplied is also the y intercept, you may utilize the slope intercept formula y = mx + b. (0, b). The y value of the y intercept point is represented by b in the formula. Exemplification 2: Determine the equation.

In the given question,

a. The point on the graph that represents 1600 dollars in total sales is (427, 1600).

b. Allan would have to sell 427 boxes to make 1600 dollars in total sales.

c. The number line representation of the number of boxes sold when the total sales is equal to 1600 dollars would be:

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ................., 1600].

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The negative correlation coefficient of -0.73 between consumption of vitamin A and the cancer rate of a particular type of cancer suggests that as vitamin A consumption increases, the cancer rate tends to decrease.

A correlation coefficient measures the strength and direction of the linear relationship between two variables.

In this case, a correlation coefficient of -0.73 indicates a negative correlation between consumption of vitamin A and the cancer rate.

Interpreting this correlation, it can be inferred that there is an inverse relationship between the two variables. As consumption of vitamin A increases, the cancer rate tends to decrease.

However, it is important to note that correlation does not imply causation.

It would be incorrect to conclude that consuming more vitamin A causes this type of cancer. Correlation does not provide information about the direction of causality.

Other factors and confounding variables may be involved in the relationship between vitamin A consumption and cancer rate.

To establish a causal relationship, further research, such as experimental studies or controlled trials, would be necessary. These types of studies can help determine whether there is a causal link between vitamin A consumption and the occurrence of this particular cancer.

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Answer:

13

Step-by-step explanation:

b2-12a

2(8)-12(1/4)

16-12/4

16-3

13

Answer: They are all symmetry :)

Step-by-step explanation:

Divide all the shapes with a straight line

−196,16

.....................

Answer:

The Median is 75

Step-by-step explanation:

median is the middle number in a set of given numbers

arranging in order will be

30,64,70,80,90,110

the middle numbers are 70 and 80

Median=80+70/2

=150/2

Median=75

The algebraic expression for "The product of 9 and two more than a number" is 9(x + 2).

In the given word phrase, "a number" is represented by the variable x. The phrase "two more than a number" can be translated as x + 2 since we add 2 to the number x. The phrase "the product of 9 and two more than a number" indicates that we need to multiply 9 by the value obtained from x + 2. Therefore, the algebraic expression for this word phrase is 9(x + 2).

"A number": This is represented by the variable x, which can take any value.

"Two more than a number": This means adding 2 to the number represented by x. So, we have x + 2.

"The product of 9 and two more than a number": This indicates that we need to multiply 9 by the value obtained from step 2, which is x + 2. Therefore, the algebraic expression becomes 9(x + 2).

In summary, the phrase "The product of 9 and two more than a number" can be algebraically expressed as 9(x + 2), where x represents the number.

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The critical value to be used in constructing the 99% confidence interval is 2.576.

Step 1: Finding the Critical Value

To determine the critical value for constructing a 99% confidence interval, we need to refer to the z-table or use a statistical calculator. The critical value corresponds to the desired level of confidence and takes into account the sample size.

Since the sample size is large (n = 77) and the population is assumed to be approximately normal, we can use the z-distribution to find the critical value. For a 99% confidence interval, the critical value is found by subtracting half of the desired confidence level from 1 and dividing the result by 2.

In this case, the calculation would be:

(1 - 0.99) / 2 = 0.005

The corresponding critical value is then determined by finding the z-score that has an area of 0.005 in the upper tail of the standard normal distribution. Consulting a z-table or using a statistical calculator, the critical value is approximately 2.576 (rounded to three decimal places).

Therefore, the critical value to be used in constructing the 99% confidence interval is 2.576.

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Finding the midpoint of a line segment is easy.

In a two-dimensional Cartesian plane with known endpoints, the abscissa value of the midpoint is half the sum of the abscissa values of the endpoints, and the ordinate value is half the sum of the ordinate values of the endpoints.

Based on this information, we can comfortably say that the midpoint of this line segment is as follows;

Let the midpoint of this segment is \(M(x_{1},y_{1})\).

Hence, the midpoint of this segment is \((6,4)\).

Answer:

D is correct!

Step-by-step explanation:

Remember that the equation of a line in slope-intercept form, is:

Where m is the slope of the line and b is the y-intercept.

First, write the equation 3x-y=8 in slope-intercept form to find its slope:

Answer:

\(\frac{15}{28}\)  is the required probability.

Step-by-step explanation:

Total number of Marbles = Blue + Red \(= 3 + 5 = 8\)

Probability of getting blue \(= \frac{3}{8}\)

Probability of not getting a blue \(=\frac{5}{8}\)

To get exactly one blue in two draws, we either get a blue, not blue, or a not blue, blue.

First Draw Blue, Second Draw Not Blue:

1st Draw: \(P(Blue) = \frac{3}{8}\)

2nd Draw: \(P(Not\:Blue)=\frac{5}{7}\)  (since we did not replace the first marble)

To get the probability of the event, since each draw is independent, we multiply both probabilities.

\(P(Event)=\frac{3}{8}\cdot \frac{5}{7}=\frac{15}{56}\)

First Draw Not Blue, Second Draw Not Blue:

1st Draw: \(P(Not\:Blue)=\frac{5}{8}\)

2nd Draw: \(P(Not\:Blue)=\frac{3}{7}\)  (since we did not replace the first marble)

To get the probability of the event, since each draw is independent, we multiply both probabilities.

\(P(Event)=\frac{5}{8}\cdot \frac{3}{7}=\frac{15}{56}\)

To get the probability of exactly one blue, we add both of the events:

\(\frac{15}{56}+\frac{15}{56}=\frac{15}{28}\)

I substituted x' value as square numbers so we don't get irrational or decimal number as y's value.

Now,

plot (9,3) , (4,2), (36,6), (25,5) and (49,7) in the graph and join them.

The population is increasing for values of P greater than 4100, and it is decreasing for values of P less than 4100. The equilibrium solution occurs when the population remains constant at P = 4100.

The given differential equation is dp/dt = P/4100. To determine when the population is increasing or decreasing, we need to consider the sign of dp/dt.

If dp/dt is positive, then the population is increasing, and if dp/dt is negative, then the population is decreasing.

In this case, dp/dt = P/4100. Since 4100 is a positive constant, the sign of dp/dt depends on the sign of P.

If P > 4100, then dp/dt is positive, indicating that the population is increasing.

Therefore, the population is increasing for values of P greater than 4100.

Similarly, if P < 4100, then dp/dt is negative, indicating that the population is decreasing.

Therefore, the population is decreasing for values of P less than 4100.

Finally, the equilibrium solution occurs when dp/dt = 0, which means that the population is neither increasing nor decreasing.

In this case, when P = 4100, dp/dt = 4100/4100 = 1, and thus the population remains constant.

Hence, the equilibrium solution is p = 4100.

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Answer:

Yes

Step-by-step explanation:

the x has different numbers each time

Answer:

1.) 54.6

2.) 61.4

(props to aeh589)

Explanation:

The expected population proportion that prefers to shop at places with loyalty cards is between 54.6% to 61.4% if, in a survey conducted by a retail store, 58% of the sampled respondents said they prefer to shop at places with loyalty cards. If the margin of error is 3.4%

It is defined as an error that gives an idea about the percentage of errors that exist in the real statistical data.

The formula for finding the MOE:

\(\rm Z{score}= \frac{s}{\sqrt{n} }\)

Where    is the z score at the confidence interval

            s is the standard deviation

            n is the number of samples.

The percent of sample respondents = 58%

Margin of error = 3.4%

The expected population that prefers to shop at places with loyalty cards is:

= (58±3.4%)

Take minus sign:

= 54.6%

Take plus sign:

= 61.4%

Thus, the expected population proportion that prefers to shop at places with loyalty cards is between 54.6% to 61.4% if, in a survey conducted by a retail store, 58% of the sampled respondents said they prefer to shop at places with loyalty cards. If the margin of error is 3.4%

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Answer:

X(4x+x^2)

Step-by-step explanation:

First the LCM is x

Now just distribute

Answer: 3623.75

Step-by-step explanation:

We can solve this problem by using casework on the number of collinear points in each triangle.

If all three points are collinear, the triangle has zero area, so we want to count triangles with no more than two collinear points.

Case 1: Three points in a row (horizontal)

There are $4$ rows of points, and each row has $\binom{3}{1} = 3$ ways to choose a set of $3$ points. Therefore, there are $4 \cdot 3 = 12$ triangles with three points in a row.

Case 2: Three points in a column (vertical)

This case is the same as Case 1, so there are also $12$ triangles with three points in a column.

Case 3: Two points in a row, one point in a different row

There are $4$ rows of points, and each row has $\binom{3}{2} = 3$ ways to choose a set of $2$ points. For each choice of two points, there are two other rows that contain the third point of the triangle. Therefore, there are $4 \cdot 3 \cdot 2 = 24$ triangles in this case.

Case 4: Two points in a column, one point in a different column

This case is the same as Case 3, so there are also $24$ triangles with two points in a column.

Case 5: Two points in a diagonal, one point not on the diagonal

There are two diagonals that contain $4$ points each. Each diagonal has $\binom{4}{2} = 6$ ways to choose a set of $2$ points. For each choice of two points, there are $2$ other points that can be paired with it to form a triangle. Therefore, there are $2 \cdot 6 \cdot 2 = 24$ triangles in this case.

Case 6: All other triangles

All other triangles have one point in each of three different rows, or one point in each of three different columns. There are $\binom{4}{3} = 4$ ways to choose $3$ rows, and each row has $4$ points, so there are $4^3 = 64$ triangles with one point in each of three different rows. The same is true for triangles with one point in each of three different columns. Therefore, there are $2 \cdot 64 = 128$ triangles in this case.

Putting it all together, the total number of triangles with positive area is $12+12+24+24+128=\boxed{200}$.

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