Find the percent change from the first value to the second 50;31

The center will be on the line segment CA because, as we already know, a circle's diameter is a chord that passes through its center.

Therefore, the answers are CA and diameter.

we have that in the question, a circle with center 'O' is passing through three A, B and C, where ∠B is a right angle.

In the circumscribed circle, we have the converse of the Thales' theorem, which states that -

if A, B, and C are distinct points on a circle where angle ∠ABC is a right-angle, then the line AC will be a diameter of the circle.

The given information is drawn in the attached figure.

Applying the converse of Thales' Theorem, we have AC will be a diameter of the circle.

As the longest side (hypotenuse) of a right-angled triangle is the opposite side of the right-angle, CA is the longest side of ABC.

The longest side of the triangle equals the diameter of the circle because CA is likewise a diameter of the circle.

Thus, the center will lie on the line segment CA and the longest side of the triangle is equal to the diameter of the circle.

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#complete question:

Point O is the center of a circle passing through points A, B, and C. ∠B is a right angle.

The center of the circumscribed circle lies on line segment, (options: AB,BC, or CA) and the longest side of the triangle is equal to the (options: radius, diameter, or circumference) of the circle.

From the cyclic quadrilateral, If ∠ADC=120° and AB is a diameter, then ∠BAC=30°

Correct option is A

Given that:  ∠ADC=120

                  ∠ACB=90° (Diameter of the circle subtends an angle of 90°)

Consider  cyclic quadrilateral ABCD:

                  ∠ADC+∠ABC=180°   (sum of opposite angles of a cyclic quadrilateral is 180°)

        Thus, ∠ABC=180°−120°=60°

In △ABC:

                  ∠BAC=180°−∠ACB−∠ABC .....(Sum of three angles of a triangle is 180°)

                  ∠BAC=180°−90°−60°=30°

Answer:     ∠BAC=30°

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Point Q is the centre of a circle passing through the points A, B, C and D taken in order. If ∠ADC=120° and AB is a diameter, then ∠BAC=

A 30°

B 40°

C 45°

D50°

Title: Analysis of Gasoline Prices in Pennsylvania During Memorial Day Weekend

Introduction and Problem Background:

This report analyzes the prices of regular gasoline in Pennsylvania during Memorial Day weekend in 2010. The average price reported by AAA is $2.65 per gallon. The purpose of this analysis is to determine if the prices observed in a sample of 15 randomly selected stations differ significantly from AAA's findings.

Data Description:

The prices per gallon of regular gasoline for 15 randomly selected stations are as follows: $2.73, $2.59, $2.74, $2.65, $2.71, $2.73, $2.51, $2.71, $2.61, $2.64, $2.58, $2.46, $2.64, $2.74, and $2.58.

Calculate the mean:

The mean price of regular gasoline for the sample is $2.64 per gallon. This means that the average price of gasoline for the 15 stations is slightly lower than the average reported by AAA.

Calculate the upper and lower limits of the box-plot:

The lower limit is $2.46 per gallon, and the upper limit is $2.74 per gallon. This means that 50% of the prices fall within this range.

Construct the 95% confidence interval:

The 95% confidence interval is ($2.54, $2.74) per gallon. This means that we are 95% confident that the true population mean falls within this range.

Analyses:

The box-plot shows that the prices are fairly consistent with the majority of the stations falling within the interquartile range. The confidence interval is narrow and does not include the AAA reported mean price of $2.65 per gallon.

Interpretation of Results and Conclusion:

Based on the analysis, we cannot validate AAA's findings. The mean price of gasoline in the sample is slightly lower than the reported mean. The confidence interval does not include the reported mean, and the box-plot shows that the prices are fairly consistent across the 15 stations. Overall, we can conclude that the prices of regular gasoline in Pennsylvania during Memorial Day weekend in 2010 did not significantly differ from the AAA reported average price.

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The ground speed of the plane is 402 mph

We have given,

A plane leaves an airport traveling at 400 mph in the direction n 45° e. a wind is blowing at 40 mph in the direction n 45° w.

Now, Draw a right triangle with 400 and 40 as the two legs.

This is a right angle because 45 degrees NE is perpendicular to 45 degrees NW.

So, the two side lengths are 400 and 40

Using the Pythagorean theorem,

(a^2 + b^2 = c^2)

\(400^2+40^2=c^2\\\\c^2=160000+1600\\c^2=161600\\c=401.99\)

Therefore the answer is 401.995, or 402mph.

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Answer:

-87

Step-by-step explanation:

f(x) = —x^2 + 6x + 4

Let x = -7

f(-7) = —(-7)^2 + 6(-7) + 4

Exponents first

     = -49 + 6(-7) + 4

Multiply

     = -49-42+4

Add

   = -87

-87

Answer:

Solution given:

f(x) = —x2 + 6x + 4

Substituting value of x and solve

f(-7)=-(-7)²+6*-7+4=-49-42+4=-87

Greetings from Brasil...

Here we don't have much to go

∛Y = A.(C + 1/X)

∛Y = (AC + A/X)

raising both members to the cube.....

(∛Y)³ = (AC + A/X)³

from Notable Products: (a + b)³ = a³ + 3a²b + 3ab² + b³

Y = (AC)³ + 3(AC)².(A/X) + 3AC(A/X)² + (A/X)³

Y = A³[C³ + (3C²/X) + (3C/X²) + (1/X³)]

The weighted weekly mean of t-shirt sales is 5.6.

The total number of weeks reported is the sum of the frequency column.

1+4+7+3 = 15 weeks

The total number of t-shirts sold is calculated as the product of the quantity of t-shirts sold and the number of weeks during which those t-shirts were sold.

2*1 + 4*4 + 6*7 + 8*3 = 2 + 16 + 42 + 24 = 84

The weighted mean, which is the product of the total quantity of t-shirts and the total number of weeks, represents the average number of T-shirts sold every week:

84/15 = 5.6

Response: 5.6

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The probability that a randomly selected gas station in Russia charges more than the mean price in the United States is approximately 0.0495 or 4.95%.

For the United States:

Mean price (μ) = $3.73

Standard deviation (σ) = $0.25

Probability that a randomly selected gas station in the United States charges less than $3.50 per gallon:

To find this probability, we need to standardize the value $3.50 using the z-score formula: z = (x - μ) / σ

z = ($3.50 - $3.73) / $0.25

z = -0.23 / $0.25

z = -0.92

Now, we can use a standard normal distribution table or calculator to find the probability associated with a z-score of -0.92. The probability is the area under the standard normal curve to the left of -0.92.

Using the standard normal distribution table or calculator, we find that the probability is approximately 0.179.

Therefore, the probability that a randomly selected gas station in the United States charges less than $3.50 per gallon is approximately 0.179 or 17.9%.

For Russia:

Mean price (μ) = $3.40

Standard deviation (σ) = $0.20

Percentage of gas stations in Russia that charge less than $3.50 per gallon:

We'll follow the same approach as before and standardize the value $3.50 using the z-score formula: z = (x - μ) / σ

z = ($3.50 - $3.40) / $0.20

z = 0.10 / $0.20

z = 0.50

Now, we can use a standard normal distribution table or calculator to find the probability associated with a z-score of 0.50. The probability is the area under the standard normal curve to the left of 0.50.

Using the standard normal distribution table or calculator, we find that the probability is approximately 0.6915.

Therefore, the percentage of gas stations in Russia that charge less than $3.50 per gallon is approximately 0.6915 or 69.15%.

Probability that a randomly selected gas station in Russia charges more than the mean price in the United States:

To find this probability, we need to standardize the mean price in the United States using the z-score formula: z = (x - μ) / σ

z = ($3.73 - $3.40) / $0.20

z = 0.33 / $0.20

z = 1.65

Now, we can use a standard normal distribution table or calculator to find the probability associated with a z-score of 1.65. The probability is the area under the standard normal curve to the right of 1.65.

Using the standard normal distribution table or calculator, we find that the probability is approximately 0.0495.

Therefore, the probability that a randomly selected gas station in Russia charges more than the mean price in the United States is approximately 0.0495 or 4.95%.

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Volunteer/voluntary response bias, also known as self-selection bias, occurs when research participants exert control over the decision to engage in the study.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

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The expected total number of heads in the experiment, consisting of 30 flips of a fair coin and 59 flips of an unfair coin, can be calculated as 20.9.

To calculate the expected total number of heads, we need to find the expected number of heads for each coin and then sum them up. For the fair coin, since it is unbiased, the expected number of heads is equal to half the number of flips. Thus, the expected number of heads for the fair coin is (30 / 2) = 15. For the unfair coin, the probability of landing heads up is 1/10. So, the expected number of heads for the unfair coin is (59 × 1/10) = 5.9.

To find the expected total number of heads, we add the expected number of heads for each coin: 15 + 5.9 = 20.9. Therefore, the expected total number of heads in the experiment is approximately 20.9.

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Answer:

Step-by-step explanation:

Answer:

the answer is C

Step-by-step explanation:

hope it helped!!!

Answer:

All of the above

Step-by-step explanation:

Let's assume that Horacio collected x dollars. Then Jack's collection was x+15.75 dollars. Rashad collected (1/3) x dollars. Thus, we can come up with the equation:

x + (x + 15.75) + (1/3)x = 126.35(5/3) x = 110.60x = $66Horacio collected 66 dollars Jack collected $81.75Rashad collected 1/3 of Horacio's amount which is $22Please note that the equation is used in order to find out the unknown values, it is a representation of the given information in a mathematical form. If-then moves are used to solve the equation. It is important to be familiar with these moves as they simplify and make the solution more manageable.

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Answer:

x = -3/4

Step-by-step explanation:

Because you have the variable x and you do not know the number of fruit snacks he ate and you need to have the same variables to properly find the answer.

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well, since the y-intercept is at -5, or namely when the line hits the y-axis is at -5, that's when x = 0, so the point is really (0 , -5), and we also know another point on the line, that is (-1 ,6), to get the equation of any straight line, we simply need two points off of it, so let's use those two

\(\stackrel{y-intercept}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{0}}} \implies \cfrac{6 +5}{-1} \implies \cfrac{ 11 }{ -1 } \implies - 11\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- 11}(x-\stackrel{x_1}{0}) \implies y +5 = - 11 ( x -0) \\\\\\ y+5=-11x\implies {\Large \begin{array}{llll} y=-11x-5 \end{array}}\)

If the budget were to increase to $3000, allowing us to survey many more people from a simple random sample, the test statistic would likely be more accurate and reliable.

As per the given scenario,

if we have a limited budget of $500, we can only survey 50 people from a simple random sample. In order to study the relationship between social class and voting preferences, the budget must be increased to $3000.

On increasing the budget, we can survey more people from a simple random sample, which would lead to a better representation of the population.
Due to the small budget, the test statistic would be less accurate as only a small number of people are being surveyed. However, if the budget increases to $3000, it would allow for a larger sample size and therefore the test statistic would be more accurate.

This would result in a narrower confidence interval and a higher level of confidence in the accuracy of the results.
Moreover, with a larger budget, it would be possible to use more sophisticated sampling techniques such as stratified random sampling, which could further increase the accuracy of the test statistic.

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The total cost of mower is $10,228.48. The correct option from the following option given is D.

A down payment on a cottage is the money paid in advance by the buyer in a real estate transaction or other large purchase. Down payments are typically a portion of the sales price and can range from 3% to 20% for a primary residence.

The total cost of the mower will be the sum of the down payment and the total amount paid through the loan:

Down payment = $1,000

Total amount paid through the loan = (monthly payment) x (number of months) = $192.26 x 48 = $9,228.48

The total cost of the mower is:

Total cost = Down payment + Total amount paid through the loan

Total cost = $1,000 + $9,228.48

Total cost = $10,228.48

Therefore, the total cost of the mower is $10,228.48.

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Using the proportional rule of Similar Triangles, the length of SD is 12 m.

Given a truss bridge.

From it,

The triangles BCD and RSD are similar.

For similar triangles, corresponding sides are proportional.

Corresponding sides are,

BC and RS, CD and SD, BD and RD.

BC / RS = CD / SD = BD / RD.

Consider BC / RS = CD / SD.

2 / 1 = 24 / SD

2 (SD) = 24

SD = 12

Hence the length of SD is 12 m.

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3 (hight) × 8 (base) = 24

24 ÷ 2 = 12 (area of triangle)

12 × 2 = 24 (because there are 2 triangles)

5 × 7 = 35 (because length times width)

35 × 2 = 70 (because there are 2 rectangles)

8 × 7 = 56 (because of the base)

24 + 12 + 24 + 35 + 70 + 56 = 221

Describe four common ways in which individuals respond to perceived inequity are -

Equity, also known as shareholders' equity (or shareholders' equity for private companies), is the sum of money which would be handed back to a company ’s creditors if each of its assets have been liquidated and all of its debt was paid off in the event of liquidation.

Some key features regarding the equity are-

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Answer:

3 + 5i

Step-by-step explanation:

Given

- 2i + (9 - 3i) - (6 - 10i) ← distribute parenthesis

= - 2i + 9 - 3i - 6 + 10i ← collect like terms

= 3 + 5i

Answer:

\(\displaystyle y=-\frac{1}{4}\ x\)

Step-by-step explanation:

Proportions

A direct proportion is a relation between variables where their ratio is a constant value. This means that if y and x are proportional, then:

y = kx

Where k is the constant of proportionality.

The value of k can be calculated if we know a point (x,y) that belongs to the graph. Substituting the point (-12,3):

3 = -12k

Solving for k:

\(k=-\frac{3}{12}=-\frac{1}{4}\)

Thus, the corresponding equation is:

\(\boxed{\displaystyle y=-\frac{1}{4}\ x}\)

Answer:

Ricky it is 1,202

And for Pedro 1202 + 276 = 1478

Step-by-step explanation:

The computation is shown below:

Let us assume the ricky be x,

So, pedro be x + 276

Now the equation is,

x + x + 276 = 2680

2x + 276 = 2680

2x = 2680-276

2x = 2404

x = 1,202

For Ricky it is 1,202

And for Pedro 1202 + 276=1478

Answer:

Option A

Step-by-step explanation:

Dennis made an extra $245.00 for selling furniture. The extra $245.00 was 7% of the total value of the furniture he sold. What was the total value of the furniture Dennis sold?

245 = 0.07x

divide both sides by 0.07:

245/0.07 = 0.07x/0.07

x = $3,500

Option A

Answer: Probability = 44%

Step-by-step explanation:

To find the probability of finding 2 black balls in a row, we first need to find the probability of finding 1 black ball at a time.

To do that, we need to divide the amount of total black balls by the number of total balls.

Black balls = 6

Total balls = 3 + 6 = 9

6 divided by 9 = 0.(6)

If you multiply 0,(6) by 100%, it will give you 66% (rounded) of getting a black ball.

Now, to find the chances of getting 2 black balls in a row, we need to multiply \(\frac{6}{9}\) by \(\frac{6}{9}\). What we are doing is squaring the chances of getting one black ball, by the number of times we want to get it.

That is equal to 0,(4)

Multiply 0,(4) by 100%, and it will give you 44%(rounded) chances to get a black ball 2 times in a row.

Probability = 44%

Hope I Helped!

Answer:

\(\boxed{\sf n= \dfrac{2}{5} ,\: n=1}\)

Step-by-step explanation:

\(\rightarrow 5n^2 = 7n -2\)

\(\rightarrow 5n^2 - 7n +2=0\)

\(\rightarrow 5n^2 - 5n -2n+2=0\)

\(\rightarrow 5n(n - 1) -2(n-1)=0\)

\(\rightarrow (5n-2)(n-1)=0\)

\(\rightarrow 5n-2= 0,\: n-1=0\)

\(\rightarrow 5n= 2,\: n=1\)

\(\rightarrow n= \dfrac{2}{5} ,\: n=1\)

Step-by-step explanation:

\(\hookrightarrow\sf{5n^2 = 7n -2}\\\\\hookrightarrow\sf{5n^2 - 7n +2=0}\\\\\hookrightarrow\sf{5n^2 - (5+2)n +2=0}\\\\\hookrightarrow\sf{5n^2 - 5n -2n+2=0}\\\\\hookrightarrow\sf{ 5n(n - 1) -2(n-1)=0}\\\\\hookrightarrow\sf{ (5n-2)(n-1)=0}\\\\\hookrightarrow\sf{ 5n-2= 0\:or~ n-1=0}\\\\\hookrightarrow\sf{ 5n= 2\:or~n=1}\\\\\hookrightarrow\bold{ n= \dfrac{2}{5} \:or~ n=1}\)

Without knowing the specific values of A, A1, A2, and A3, it is not possible to determine whether A belongs to the span of {A1, A2, A3}.

I assume that M22 refers to the set of 2x2 matrices.

To determine whether the given vector A belongs to the span of {A1, A2, A3}, we need to see if we can find scalars c1, c2, and c3 such that:

A = c1*A1 + c2*A2 + c3*A3

If we can find such scalars, then A is in the span of {A1, A2, A3}. Otherwise, it is not.

Without knowing the specific values of A, A1, A2, and A3, it is not possible to determine whether A belongs to the span of {A1, A2, A3}.

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To find the point on the surface 6x = y^2 + z^2 where its tangent plane is parallel to a given plane, we need to find a point on the surface and determine the normal vector of the surface at that point.

Then, we can compare the normal vector of the surface to the normal vector of the given plane to check if they are parallel.

Let's first find a point on the surface by substituting a value for either y or z and solving for x. Let's choose y = 0:

6x = 0^2 + z^2

6x = z^2

x = z^2/6

So, one point on the surface is (z^2/6, 0, z).

To find the normal vector of the surface at this point, we can calculate the partial derivatives with respect to x, y, and z:

∂/∂x (6x) = 6

∂/∂y (y^2 + z^2) = 0

∂/∂z (y^2 + z^2) = 2z

The normal vector is then N = (6, 0, 2z) = (6, 0, 2z) / ||(6, 0, 2z)||, where ||N|| represents the magnitude of N.

To determine if the tangent plane is parallel to a given plane, we compare the normal vector of the surface to the normal vector of the given plane. If they are parallel, their direction vectors should be proportional.

If the given plane is parallel to the xy-plane and has a normal vector N_1 = (0, 0, 1), we can compare it to the normal vector of the surface. In this case, we see that the z-component of N (2z) is not proportional to the z-component of N_1 (1). Therefore, the tangent plane of the surface at the chosen point is not parallel to the given plane.

To find a point on the surface where its tangent plane is parallel to the given plane, we would need to choose a different point on the surface such that the normal vector of the surface at that point is parallel to the given plane's normal vector.

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