1. Describe the basic characteristics of an independent
measures, or a between-subjects, research study.

Answers

Answer 1

The main advantage of an independent measures design is that it reduces the risk of order or practice effects and minimizes the influence of individual differences between participant

Describing the basic characteristics

An independent measures design, also known as a between-subjects design, is a type of research study in which different groups of participants are used for each condition being tested.

In other words, each participant is only exposed to one condition, and the data from each group is analyzed and compared to determine if there are any significant differences between the groups.

The main characteristics of an independent measures design are:

Participants are randomly assigned to one of the groups. Each group of participants is exposed to only one level of the independent variableData is collected from each group and compared to determine if there are any significant differences between the groups. The design requires a larger sample size compared to a within-subjects design because each participant can only be in one group.

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Related Questions

Which type of government structure would be threatened by debate over public policy?

Answers

A government structure that is authoritarian or dictatorial in nature would be threatened by debate over public policy.

In such a system, the government exercises complete control over decision-making and any opposition or dissent is not tolerated.

Open debate and discussion over public policy would challenge the authority of the government and its ability to maintain control over the population.

Democracies, on the other hand, thrive on healthy debate and discussion over public policy, as it allows for diverse perspectives and ideas to be heard and considered.

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What is the value of -1/6 + 2/3(9- 3/4) - 1/2

Answers

The value of the given expression is 31/6.


What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

We can simplify the given expression using the order of operations (PEMDAS):

First, we evaluate the expression inside the parentheses:

9 - 3/4 = 35/4

Next, we simplify the multiplication by 2/3:

2/3 * 35/4 = 35/6

Now we substitute the above values in the expression and simplify:

-1/6 + 35/6 - 1/2 = (-1 + 35 - 3)/6

= 31/6

Therefore, the value of the given expression is 31/6.

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What are the zeros of the function f(x)= (4x-3) (2x-1) help

Answers

The zeros of the function f(x) are:

x = 3/4x = 1/2How to find the zeros of the function?

For a function y = f(x), the zeros are the values of x such that:

f(x)= 0

Here we have:

f(x)= (4x-3) (2x-1)

The zeros are the values such that any of the coefficients are zero, then we have:

4x - 3 = 0

x = 3/4

And:

2x - 1 = 0

x = 1/2

These are the zeros.

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Find the margin of error for the 95% confidence interval used to estimate the population proportion.
n = 163, x = 96
Select one:
a. 0.00291
b. 0.0755
c. 0.132
d. 0.0680

Answers

The margin of error for the 95% confidence interval used to estimate the population proportion is 0.0680. So, the correct answer is option d.

Calculate the sample proportion:

The formula (p) = x/n, where x is the sample size (163) and n is the number of successes (96), yields the sample proportion.

Therefore, the sample proportion is 96/163 = 0.5896.

Calculate the standard error:

The formula SE(p) yields the sample proportion's standard error = √[p(1-p)/n], where n is the sample size, and p is the sample proportion.

Consequently, the sample proportion's standard error is as follows:

SE(p) = √[0.5896(1-0.5896)/163] = 0.037

Calculate the margin of error:

The margin of error is given by the formula ME = z × SE(p), where SE(p) is the standard error of the sample proportion and z is the z-score corresponding to the desired level of confidence.

The z-score for a 95% confidence interval is 1.96.

As a result, the error margin is:

ME = 1.96 × 0.037 = 0.0680

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In the following function defined by an equation in the form y = a x squared + b x + c, identify the values of a, b, and c. y = two-thirds x squared + 3 a. a = 0, b = two-thirds, c = 3 b. a = two-thirds, b = 0, c = 3 c. a = 0, b = 3, c = two-thirds d. a = two-thirds, b = two-thirds, c = 3 Please select the best answer from the choices provided

Answers

The correct answer is (a) a = 0, b = two-thirds, c = 3.

How to identify the values of a, b, and c.

This can be seen by comparing the given equation, y = two-thirds x squared + 3, to the general form of a quadratic equation, y = ax^2 + bx + c.

In the given equation, the coefficient of x^2 is two-thirds, so a = two-thirds. The coefficient of x is 0, so b = 0. And the constant term is 3, so c = 3.

Therefore, the correct answer is (a) a = 0, b = two-thirds, c = 3.

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mark these probablities on a probably failling the exam 1 by 3 how to do on scale

Answers

The probability for the possibility on a failing the exam is  1/3 , shown on the scale.

Explain about the term probabilities;

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

A probability of 0 means there is no chance an event will happen, but a probability of 1 means the event will definitely happen. A probability of 0.45 (45%) means that there are 45 out of 100 chances that the event will occur.

Any collection of results constitutes an event. Events are represented by capital letters, such as A and B. For instance, if the experiment involves flipping a single fair coin, event A might only receive one head. P(A) represents the probability of an event A.

Given that-

probability = number of favourable outcome / total outcome

number of favourable outcome = 1

number of total outcome = 3

probability = 1/3

Thus, the probability for the possibility on a  failing exam is 1/3 , shown on the scale.

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Covert the following decimals to percents.

0.15 =_%

Answers

Answer:

15%

Step-by-step explanation:

0.15 x 100 = 15%

on the coordinate plane, triangle PQR is rotated 180* clockwise about the origin O

Answers

we get the coordinates of Q' as (2,3) after rotation of the triangle.

What is rotation of axis?

Rotation of axes is a transformation in which the coordinate axes are rotated by a certain angle with respect to the original axes. This transformation can be used to simplify the equations of curves and to make it easier to solve problems involving them. The rotation is usually done by finding the angle of rotation, which is the angle between the original x-axis and the new x-axis. The formulae for converting coordinates from the old system to the new system can then be applied.

In the given problem, we are given that triangle PQR is located in the xy-plane with coordinates of Q being (2,-3). The task is to find the coordinates of Q' when triangle PQR is rotated 180 degrees clockwise about the origin and then reflected across the y-axis to produce triangle P'Q'R'.

To start, we apply the 180 degree clockwise rotation about the origin transformation rule to the coordinates of Q (2,-3) which gives us (-2,3).

Next, we reflect the point (-2,3) across the y-axis. Reflecting across the y-axis involves changing the sign of the x-coordinate while leaving the y-coordinate unchanged. Applying this rule,

Hence, we get the coordinates of Q' as (2,3) after rotation of the triangle.

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How many more bytes of information are in a gigabyte than a megabyte?

Answers

Answer:

999,000,000 bytes

Step-by-step explanation:

if you subtract the total of the gigabytes from the total of the megabytes you get this answer.

The answer above is correct

What is the radius of the circle if it has a circumference of 153. 86153. 86153, point, 86 units

Answers

If the circumference of the circle is 153.86 units, then the radius of that  circle is 24.5 units.

The "Circum-ference" of circle is defined as "total-length" of boundary of the circle. The formula for circumference is = 2 × π × Radius,

The "Radius" of circle is the distance from center of circle to its outer edge. It is half of "diameter" of circle, and it is a measure of size of circle.

We know that, circumference of circle is 153.86 units,

So, the circumference equation becomes,

⇒ 2 × 3.14 × Radius = 153.86,

⇒ 153.86/(2 × 3.14) = Radius,

⇒ Radius ≈ 24.5

So, the radius of the circle is approximately 24.5 units.

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The given question is incomplete, the complete question is

What is the radius of the circle if it has a circumference of 153.86 units?

A softball has a volume of about 33. 5 in3. What is the diameter of the ball?

Answers

Answer:

the diameter of the softball is approximately 4.72 inches.

Step-by-step explanation:

The formula to calculate the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius of the sphere.

We can rearrange the formula to find the radius of the softball:

r = cube root of [(3V)/(4π)]

r = cube root of [(3 x 33.5)/(4π)]

r ≈ 2.36 inches

The diameter is twice the radius:

d = 2r

d ≈ 4.72 inches

Therefore, the diameter of the softball is approximately 4.72 inches.

Answer: the diameter of the softball is approximately 4.22 inches.

Step-by-step explanation: The volume of a sphere can be calculated using the formula:

V = (4/3)πr^3

where V is the volume of the sphere, r is the radius of the sphere, and π is the mathematical constant pi.

To find the diameter of the softball, we can use the formula:

d = 2r

where d is the diameter of the sphere.

We know that the volume of the softball is 33.5 in^3. So, we can solve for the radius as follows:

33.5 = (4/3)πr^3

r^3 = (3/4)(33.5/π)

r^3 = 8.9375

r = ∛(8.9375)

r ≈ 2.11 inches

Now, we can find the diameter of the softball:

d = 2r

d = 2(2.11)

d ≈ 4.22 inches

Shapes A and B are similar.
a) Calculate the scale factor from shape A to shape B.
b) Find the value of r.
Give each answer as an integer or as a fraction in its simplest form.
5 cm
11 cm
A
20 cm
3 cm
7'cm
B
12 cm
Not drawn accurately

Answers

Answer:

a) The scale factor from A to B is 3/5 since (3/5)(5) = 3.

b) r = (3/5)(11) = 33/5 = 6 3/5

ASAP PLEASE!

1.

Triangle D has been dilated to create triangle D′. Use the image to answer the question.

image of a triangle labeled D with side lengths of 3.8, 4.8, 4.2 and a second triangle labeled D prime with side lengths of x, 2.4, 2.1

Determine the scale factor used.

one half
2
one fourth
3

2.

Question 4(Multiple Choice Worth 2 points)
(Dilations MC)

Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−9, −9), B(9, 9), C(0, 9). Determine the scale factor used.

6
one sixth
3
one third

Answers

The first option, "one half," corresponds to the scale factor of 0.5.

How to find the scale factor?

Scale factor = Dimensions of the new shape Dimensions of the original shape is the fundamental formula used to calculate it. The formula is expressed as Scale factor = Larger image dimensions Smaller figure dimensions in the event that the original figure is enlarged.

We can contrast the side lengths of triangles D and D′ to determine the scaling factor.

Let's contrast the side lengths for the two triangles.

Triangle D has sides that are 4.2 in length, and triangle D′ has sides that are 2.1 in length.

Scale factor = (Side length of triangle D′) / (Side length of triangle D)

Scale factor = 2.1 / 4.2

Scale factor = 0.5

The first option, "one half," corresponds to the scale factor of 0.5.

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Solve 12x<96 . Graph the solution.

Answers

Answer:

x<8

Step-by-step explanation:

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

whats the answer for this math problem

Answers

The solution to the equation -2/(x - 8) = (x - 1)/(x + 2) is x = 3 after checking for extraneous solutions.

To solve the equation

-2/(x - 8) = (x - 1)/(x + 2)

We can start by cross-multiplying to eliminate the fractions

-2(x + 2) = (x - 1)(x - 8)

Simplifying both sides, we get

-2x - 4 = x² - 9x + 8

Bringing all the terms to one side, we get

x² - 7x + 12 = 0

Now we can factor the quadratic equation to get

(x - 3)(x - 4) = 0

So the solutions are x = 3 and x = 4. However, we need to check for any extraneous solutions that may have been introduced by the original equation.

Plugging in x = 3 to the original equation, we get

-2/(3 - 8) = (3 - 1)/(3 + 2)

Which simplifies to

2/5 = 2/5

Therefore, x = 3 is a valid solution.

Plugging in x = 4 to the original equation, we get

-2/(4 - 8) = (4 - 1)/(4 + 2)

Which simplifies to

1/2 = 3/6

Therefore, x = 4 is not a valid solution.

So the only solution to the equation is x = 3.

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what is ordinary least squares (ols) method? in order for the ols method to produce best linear unbiased estimators (blue), what assumptions must be satisfied?

Answers

Ordinary Least Squares (OLS) is a method used to estimate the parameters of a linear regression model.

In OLS, the objective is to find the line that best fits the observed data by minimizing the sum of squared residuals between the predicted values of the dependent variable and the actual values.

To produce the Best Linear Unbiased Estimators (BLUE) in OLS, the following assumptions must be satisfied:

Linearity: The relationship between the dependent variable and the independent variables must be linear.

Independence: The observations must be independent of each other.

Homoscedasticity: The variance of the residuals should be constant across all levels of the independent variables.

Normality: The residuals should be normally distributed.

No multicollinearity: The independent variables should not be highly correlated with each other.

If these assumptions are met, then OLS produces the BLUE, which means that the estimated coefficients are the best unbiased estimates of the true population parameters, and they have the smallest variance among all unbiased linear estimators.

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Use the order of operations to evaluate the expression 8 + 18 ÷ 3 – 7 pls need help asap

Answers

Answer:

Step-by-step explanation:

Evaluate the expression

Divide 18 by 3 = 6

Then add the 6 to the 8

then subtract 7 from 14

answer=7

Suppose a continuous random variable X is uniformly distributed on the interval [4,9]. able Y distributed? That is, determine the probability density function fy(y) 1. None of these. 2. for 4-y-9 = 10, 0 otherwise

Answers

For a continuous random variable X, which is uniformly distributed on an interval [4,9], the probability density function of [tex]f_Y( y)[/tex] is equals to

[tex]f_Y( y) =\begin{cases} \frac{2y}{5},\quad 2≤ x ≤ 3 \\ 0, \quad \: otherwise\ \ \end{cases}[/tex]. So, option(5) is correct.

We have a continuous random variable X is uniformly distributed on the interval [4,9]. The PDF is a probability that a random variable acquire a value exactly same or equal to the random variable but in case of CDF, this probability values is less than or equal to the random variable. The probability density function for X is defined as [tex]f_X(x) = \frac{1}{b - a} [/tex] so, we can write it as [tex]f_X ( x) =\begin{cases} \frac{1}{5},\quad 4≤ x ≤ 9 \\ 0, \quad otherwise \\ \end{cases}[/tex].

We have to determine the probability density function [tex]f_Y(y)[/tex]. For this first we have to calculate the cumulative distribution function for f(x) is written as [tex]F_X(x) = \int_{4}^{x} f(x) dx [/tex]

[tex]= \int_{4}^{x} \frac{1}{5} dx [/tex]

[tex]= \frac{1}{5} [ x]_{4}^{x} [/tex]

[tex]F_X(x) = \frac{x - 4}{5}[/tex]

Now, we have, [tex] Y = \sqrt{X}[/tex]

when X = 4 => Y = 2 and X = 9 => Y = 3

Also, X = Y²

Differentiating X = Y² with respect to Y

=> dX = 2Y dY

=> dX/dY = 2Y

Now, pdf of Y is written as [tex]f_Y(y) = f_X(x)|\frac{dX}{dY}| [/tex]

[tex] = \frac{ 1}{5} × 2y[/tex]

[tex]= \frac{ 2y}{5}[/tex]

So, [tex]f_Y( y) =\begin{cases} \frac{2y}{5},\quad 2≤ x ≤ 3 \\ 0, \quad \: otherwise \ \ \end{cases}[/tex]. Hence, required value is [tex]f_Y( y) =\begin{cases} \frac{2y}{5},\quad 2≤ x ≤ 3 \\ 0, \quad \: otherwise \ \ \end{cases}[/tex].

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Complete question:

The above figure complete the question.


Need some guidance on this my answers don’t add up

Answers

The average size of the 15 diameters is 25.00mm. Using the concept of percentages, the mass of copper, lead, and tin in the bronze bearing are 140 kg, 40 kg, and 20 kg, respectively.

What is the average size of the diameters?

To find the average size of the 15 diameters, we need to calculate the sum of all the dimensions and then divide by 15 (the total number of diameters).

The sum of the dimensions can be calculated as follows:

(5 x 24.99mm) + (6 x 25.01mm) + (4 x 25.00mm)

= 375.01mm

Now, we can calculate the average size by dividing the sum by 15:

Average size = 375.01mm / 15

= 25.00mm (rounded to 2 decimal places)

Therefore, the average size of the 15 diameters is 25.00mm.

b.

To find the mass of each metal, we need to determine how much of each metal is present in the bronze bearing. This can be done using the concept of percentage

Let's start by finding the mass of copper in the bearing:

Mass of copper = 70% of 200 kg = 0.7 x 200 kg = 140 kg

Next, let's find the mass of lead in the bearing:

Mass of lead = 20% of 200 kg = 0.2 x 200 kg = 40 kg

Finally, let's find the mass of tin in the bearing:

Mass of tin = 10% of 200 kg = 0.1 x 200 kg = 20 kg

Therefore, the mass of copper, lead, and tin in the bronze bearing are 140 kg, 40 kg, and 20 kg, respectively.

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6) What is the difference between
supplementary and complementary
angels?

Answers

Complementary angles are two angles whose sum is equal to 90 degrees. In other words, if you add the measures of two complementary angles, you get 90 degrees. Complementary angles are often referred to as "complements" for short. For example, if one angle is 30 degrees, its complement would be 60 degrees.

Supplementary angles, on the other hand, are two angles whose sum is equal to 180 degrees. In other words, if you add the measures of two supplementary angles, you get 180 degrees. Supplementary angles are often referred to as "supplements" for short. For example, if one angle is 120 degrees, its supplement would be 60 degrees.

a box contains two white socks, two blue socks, and two red socks. two socks are drawn at random. find the probability they are a match (the same color).

Answers

The probability of drawing a matching pair of socks is 1/5 or 0.2.

Calculating Probability:

The basic principle of probability, states that the probability of an event happening is the number of ways the event can occur divided by the total number of possible outcomes.

In this problem, we first calculated the number of ways to draw a matching pair of socks for each of the three possible colors.

We then added these probabilities together to get the total probability of drawing a matching pair of socks.

Here we have

A box contains two white socks, two blue socks, and two red socks.

To find the probability of drawing a matching pair of socks, consider the different cases of matching pairs of socks that can be drawn.

Case 1: Matching white socks

The probability of drawing one white sock = 2/6

After drawing one white sock,

Remains 5 socks and of which 1 is white

The probability of drawing 2nd white sock =  1/5  

Hence, probability of selecting 2 white socks = (2/6) × (1/5) = 1/15

Similarly, we can calculate probabilities for Red and Blue socks

Case 2: Matching blue socks

The probability of drawing two blue socks is (2/6) × (1/5) = 1/15  

Case 3: Matching red socks

The probability of drawing two red socks is (2/6) × (1/5) = 1/15.

Therefore, the total probability of drawing a matching pair of socks is the sum of the probabilities of each of these cases:

P(matching pair) = P(white) + P(blue) + P(red)

= 1/15 + 1/15 + 1/15 = 3/15 = 1/5

Therefore,

The probability of drawing a matching pair of socks is 1/5 or 0.2.

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For incoming freshman at BYU, ACT scores are Normally distributed with a mean of 28 and a standard deviation of 2. How many standard deviations away from the mean is an ACT score of 31?

Answers

Answer:

To calculate how many standard deviations away from the mean an ACT score of 31 is, we need to use the formula:

z = (x - μ) / σ

Where:

x = ACT score of 31

μ = mean of ACT scores (28)

σ = standard deviation of ACT scores (2)

z = number of standard deviations away from the mean

Substituting the values, we get:

z = (31 - 28) / 2

z = 1.5

Therefore, an ACT score of 31 is 1.5 standard deviations away from the mean.

solve these 4 problems and I will give u brainlst.

Answers

The value of the identities are;

1. sin M = 3√39/20

2. sin M = √3/5

3. sin M = 3√19/14

4. sin M = √3/2

How to determine the ratios

The different trigonometric identities and their ratios are written as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the information given, we have;

1. opposite = 3√39

Hypotenuse = 20

Then, sin M = 3√39/20

2. Opposite = 4√3

Hypotenuse = 20

sin M =  4√3/20

Divide the values

sin M = √3/5

3. The Opposite side = 3√19

Hypotenuse = 14

sin M = 3√19/14

4. Opposite = 6√3

Hypotenuse = 12

sin M =  6√3/12

Divide the values

sin M = √3/2

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T/F: In simple regression analysis, r2 is a percentage measure and measures the proportion of the variation explained by the simple linear regression model

Answers

True, r² is a metric that expresses how much of a variable is accounted for by a basic linear regression model.

Calculate the sum of squares for the regression model (SSR):  SSR = Σ (predicted values - mean of the dependent variable)²

Calculate the sum of the squares of the residuals (SSE): SSE = Σ (observed values - predicted values

Calculate the coefficient of determination (r²): r² = SSR/ (SSR + SSE)

The coefficient of determination (r²) is then a percentage measure of the proportion of the variation explained by the simple linear regression model.

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52W high 52W low Name of Stock Symbol High Low Close
37.18 29.39 Zycodec ZYO 39.06 32.73 34.95
11.76 7.89 Unix Co UNX 16.12 12.11 15.78


Last year, a stockholder purchased 40 shares of Zycodec at its lowest price of the year and purchased 95 shares of Unix at its highest price of the year. If the stockholder sold all shares of both stocks at their respective closing price, what was the overall gain or loss?
The overall loss is $604.30.
The overall gain is $604.30.
The overall loss is $660.35.
The overall gain is $660.35.

Answers

the overall gain is positive, we can conclude that the stockholder made a profit of $190.10. Therefore, the correct answer is: "The overall gain is $190.10."

How to solve the question?

To calculate the overall gain or loss, we need to first find the total cost of buying the shares and the total revenue from selling them.

For the 40 shares of Zycodec purchased at its lowest price of 29.39, the total cost would be:

40 shares x $29.39/share = $1,175.60

For the 95 shares of Unix purchased at its highest price of 16.12, the total cost would be:

95 shares x $16.12/share = $1,531.40

The total cost of purchasing both stocks would be:

$1,175.60 + $1,531.40 = $2,707

Now, we need to find the total revenue from selling the shares. The closing price of Zycodec is 34.95, so the revenue from selling 40 shares would be:

40 shares x $34.95/share = $1,398

The closing price of Unix is 15.78, so the revenue from selling 95 shares would be:

95 shares x $15.78/share = $1,499.10

The total revenue from selling both stocks would be:

$1,398 + $1,499.10 = $2,897.10

The overall gain or loss would be the difference between the total revenue and total cost:

Overall gain/loss = total revenue - total cost

Overall gain/loss = $2,897.10 - $2,707

Overall gain/loss = $190.10

Since the overall gain is positive, we can conclude that the stockholder made a profit of $190.10. Therefore, the correct answer is: "The overall gain is $190.10."

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2. A die is rolled 200 times. What is the experimental
probability of rolling less than 3?
Outcome
1
2
3
4
5
CO
6
Frequency
30
26
44
38
22
40

Answers

Answer:

Based on the information, the probability of rolling a number less than a 3 (that is, a 1 or a 2) is 56/200 = 7/25 = 28%.

Point Q is the center of a circle passing through points A, B, C

Answers

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.

How do we calculate?

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

Solving the cyclic quadrilateral

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°

10% of a number is X. What is 100%? Assume X > 0

Answers

100% of the number is 100 times X.

What is percentage?

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

If 10% of a number is X,

0.1 * number = X

number = X / 0.1

number = 10 * X

As a result, if X represents 10% of a number, the whole number is 10 times X. To get 100% of the answer, simply multiply X by 10 again:

100% of the number = 10 * X * 10 = 100 * X

So, 100% of the number is 100 times X.

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If |a b c d e f g h i| = 5, find | a b c 7d + a 7e + b 7f + c g h i| | a b c 7d + a 7e + b 7f + c g h i| = (Simplify your answer.)

Answers

The value of | a b c 7d + a 7e + b 7f + c g h i| is given by -35 + b(ch - di) + c(gi - eh) + a(hk - fg).

Expanding the determinant using the first row, we get:

| a b c 7d + a 7e + b 7f + c g h i|

= a | b c 7d + 7e b 7f + g h i| - b |a c 7d + 7e c 7f + g h i| + c |a b 7d + 7e 7f + g h i|

= a | b c 7d + 7e b 7f + g h i| + b |a c 7d + 7e c 7f + g h i| - c |a b 7d + 7e 7f + g h i|

Now, we can expand each of the three determinants on the right-hand side using the first row and simplify:

| b c 7d + 7e b 7f + g h i| = b | c 7f h i| - 7e |b 7f h i| + g |b c h i|

= -7e b |7f h i| + g |b c h i| - h |b c 7f i| + i |b c 7f h|

= -7e bi + gh - bhf + chi

|a c 7d + 7e c 7f + g h i| = a |c 7f h i| - 7e |c 7d h i| + g |c 7d 7f i|

= 7e ac - gci + chd - ahf

|a b 7d + 7e 7f + g h i| = a |b 7f h i| - 7e |b 7d h i| + g |b 7d 7f i|

= -7e ab + ghi - bgd + aef

Substituting these expressions back into the expanded determinant and simplifying, we get:

| a b c 7d + a 7e + b 7f + c g h i|

= a(-7e bi + gh - bhf + chi) + b(7e ac - gci + chd - ahf) + c(-7e ab + ghi - bgd + aef)

= -7abe - 7bdf - 7cfg + 7aef + bch + cgi + ahk - ceh - afg - bdi

= -7(abe + bdf + cfg - aef) + (bch + cgi + ahk - ceh - afg - bdi)

Since |a b c d e f g h i| = 5, we have:

abe + bdf + cfg - aef = 5

Therefore, we can simplify the expression further:

| a b c 7d + a 7e + b 7f + c g h i|

= -7(5) + (bch + cgi + ahk - ceh - afg - bdi)

= -35 + b(ch - di) + c(gi - eh) + a(hk - fg)

Hence, the value of | a b c 7d + a 7e + b 7f + c g h i| is given by -35 + b(ch - di) + c(gi - eh) + a(hk - fg).

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The simplified expression for | a b c 7d + a 7e + b 7f + c g h i| is 7| a b c d g h i| + 7| a b c e g h i| - 35.

First, factor out the 7 from the second row:

| a b c 7(d + e + f) g h i| = 7| a b c d + e + f g h i|

Expand the second row using the property of determinants that allows us to break up a row sum:

7(| a b c d g h i| + | a b c e g h i| + | a b c f g h i|)

Now, use the property of determinants that allows us to switch rows and multiply by -1:

7(| a b c d g h i| + | a b c e g h i| - | d e f a b c g h i|)

Recognize that the third determinant is equivalent to the given determinant, but with rows 1 and 3 switched, which

gives us:

7(| a b c d g h i| + | a b c e g h i| - 5)

Finally, multiply 7 by the expression inside the parentheses:

7| a b c d g h i| + 7| a b c e g h i| - 35

So, the simplified expression for | a b c 7d + a 7e + b 7f + c g h i| is 7| a b c d g h i| + 7| a b c e g h i| - 35.

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what is 4x-5y=-28 -9x-2y=10???????

Answers

The value of the variables are x = -2 and y = 4

How to determine the values

From the information given, we have that the simultaneous equations are;

4x-5y=-28

-9x-2y=10

Make 'x' the subject from equation 1

4x = -28 + 5y

x = -28 + 5y/4

Now, substitute the value in equation 2, we get;

-9(-28 + 5y/4) - 2y = 10

expand the bracket

252 - 45y/4 - 2y = 10

find the lowest common multiple

252 - 45y - 8y/4 = 10

cross multiply

252 - 45y -8y = 40

collect the like terms

-53y = -212

Make y the subject

y = 4

substitute the value

x = -28 + 5y/4

x = -28 + 20/4

x = -8/4

x = -2

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