Which biconditional statement below is true?


Angles are congruent if and only if they are vertical angles.
Angles are congruent if and only if they are vertical angles.

Angles are supplementary if and only if their sum is 180°.
Angles are supplementary if and , only if their sum is 180°.

A number is a whole number if and only if it is a natural number.
A number is a whole number if and only if it is a natural number.

Points are collinear if and only if they are coplanar.
Points are collinear if and only if they are coplanar.

(x^(3-6))^2 = (x^-3)^2

x^3*2+x^-6*2 = x^6+x^-12

The second from the top, and the second to last expressions should be the answer

Hope this helps!

Answer:

a. AD and DAB are not congruent

b. point E is 1.5 from point B

c. Yes, your friend is correct

Step-by-step explanation:

(a) tan(C) = opp/adj = 3/4 so C is 36.87 or roughly 37 degrees

so A = 90 - 37 = 53

tan(DAB) = opp/adj = (4/2)/3 = 2/3 so DAB is 33.7 or roughly 34 degrees

so CAD = 53 - 34 = 19

so CAD and DAB are not congruent

(b) angle bisector is the line or line segment that divides the angle into two equal parts. It intersects BC at E so CAE = EAB = 53/2 = 26.5

so tan(26.5) = BE/3

=> BE = 3 x tan(26.5) = 3(0.499) = 1.497 or roughly 1.5

(c) a line from E perpendicular to AC will intersect AC at F, which create angle EFA or EFC a 90 degree angle

Now we have 2 right triangles AEB and AEF with the same hypotenuse which is AE and the same angles at EAF and EAB which means EB and EF are congruent

The linear relationship in the form y =  y = 3n + 72

What is  linear relationship?

In statistics, a straight line of correlation between two variables is referred to as a linear relationship (or linear association). The mathematical equation y = mx + b can be used to represent linear relationships graphically.

Each plant generates 34 oz of beans when she plants 30 stalks, and 33 stalks results in 33 oz of beans per plant, according to the information we have provided.

Equation 1 using data 1:

                                    y = mn + b

Equation 1 using data 1:

                                    30 = 34m + b

Equation 2 using data 2:

                                     33 = 33m + b

Subtract equation 1 from equation 2:

                               33 - 30 = 34m + b - 33m - b

                                     3 = m

                                      m = 3

Rearrange equation 1 to solve for b:

                                    b = 34(3) - 30

                                      b = 102 - 30

                                      b = 72

Therefore the equation becomes:

                                     y = 3n + 72

The linear relationship in the form y =  y = 3n + 72

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In each scenario, the choice between mean and median as a representative measure of central tendency depends on the nature of the data and the specific context..

1. Scenario: Income distribution of a population

- If the income distribution is skewed or contains extreme values (outliers), the median would be a better representation of the central tendency. This is because the median is not influenced by outliers and provides a more robust estimate of the "typical" income level. However, if the income distribution is approximately symmetric without outliers, the mean can also be an appropriate measure.

2. Scenario: Exam scores in a class

- If the exam scores are normally distributed without significant outliers, the mean would be a suitable measure as it takes into account the value of each score. However, if there are extreme scores that deviate from the majority of the data, the median may be a better representation. This is especially true if the outliers are indicative of errors or exceptional circumstances.

3. Scenario: Housing prices in a city

- In this case, the median would be a more appropriate measure to represent the central tendency of housing prices. This is because the housing market often exhibits a skewed distribution with a few high-priced properties (outliers). The median, being the middle value when the data is sorted, is not influenced by these extreme values and provides a better understanding of the typical housing price in the city.

Ultimately, the choice between mean and median depends on the specific characteristics of the data and the objective of the analysis. It is important to consider the distribution, presence of outliers, and the context in which the data is being interpreted.

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Answer:

198 in²

Step-by-step explanation:

triangle (A=1/2)bh [A=1/2(22×8)] b=22 H=8

rectangle (A=bh) [A= 22×5] B=22 H=5

triangle = 88

rectangle = 110

So, 88+110 = 198

Answer:

-4

Step-by-step explanation:

Answer:

4i

Step-by-step explanation:

Answer:

? = 60

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

120 = ? +60

subtract 60 from each side

120-60 = ? +60-60

60 = ?

Answer:

x≤13

Step-by-step explanation:

-4+x≤9

Add 4 to each side

-4+4+x≤9+4

x≤13

Answer:

x≤13

Step-by-step explanation:

khan

Answer:

Step-by-step explanation:

In a set of parallel lines (where 2 of them are present), corresponding angles are the angles that have the same measure but are located at different intersections on different lines & is made with the intersection of the same transversal.

Here, the slightly slanted yet vertical line which intersects line s & line t is the transversal.

By looking at the figure, we can see that ∠ 7 is formed below ∠ 5 towards the left side. Similarly, by looking above, we can notice that ∠ 3 just like ∠ 7 is formed towards the left side of the figure below ∠ 1. So,

_____________________

Hope it helps!

\(\mathfrak{Lucazz}\)

Answer:x=16

Step-by-step explanation: All vertical angles are equal to each other. So you need to cancel numbers on each side out

The 80% confidence interval will be narrower than the 90% confidence interval when constructed from the same sample data.

If an 80% confidence interval and a 90% confidence interval are constructed from the same sample data, the 80% confidence interval will be narrower than the 90% confidence interval.

To understand why this is the case, we need to know that a confidence interval is a range of values within which we estimate the true population parameter lies. The level of confidence associated with the interval represents the probability that the true parameter falls within that range.

In this scenario, an 80% confidence interval means that there is an 80% probability that the true parameter lies within the interval. On the other hand, a 90% confidence interval means that there is a 90% probability that the true parameter falls within the interval.

To construct a narrower interval, we need to have a higher level of confidence. As the confidence level increases, the range of possible values also widens to accommodate the higher probability. Therefore, the 80% confidence interval will be narrower than the 90% confidence interval.

In conclusion, the 80% confidence interval will be narrower than the 90% confidence interval when constructed from the same sample data.

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Answer:

The mean weight of an adult is 66 kilograms with a variance of 144. If 123 adults are randomly selected, the sample mean would follow a normal distribution with a mean of 66 kilograms and a standard deviation of sqrt(144/123) = 3/sqrt(123) kilograms.

We can standardize the sample mean to find the probability that it would be greater than 66.7 kilograms. The standardized value for 66.7 is (66.7 - 66) / (3/sqrt(123)) = 2.3094.

Using a standard normal distribution table, we find that the probability of a standard normal variable being greater than 2.3094 is approximately 0.0104.

Therefore, the probability that the sample mean would be greater than 66.7 kilograms is approximately 0.0104, rounded to four decimal places.

Step-by-step explanation:

Answer:

the answer is b between 6 and 7

Step-by-step explanation:

i say this because the square root of 41 is 6.4031.

6.4031 is in between 6 and 7.

hope this helps :)

Answer:

  51

Step-by-step explanation:

We can consider up to 5 multiples of 12:

  (0·12 +3) ÷ 5 = 0 r 3

  (1·12 +3) ÷ 5 = 3 r 0

  (2·12 +3) ÷ 5 = 5 r 2

  (3·12 +3) ÷ 5 = 7 r 4

  (4·12 +3) ÷ 5 = 10 r 1

The number we're looking for is 51.

Answer:

the value of x when f(x) = 15 is 3.5.

Step-by-step explanation:

We are given that:

f(x) = 1 + 4x

We need to find the value of x when f(x) = 15.

So we can set up the equation:

1 + 4x = 15

Subtracting 1 from both sides, we get:

4x = 14

Dividing both sides by 4, we get:

x = 14/4

Simplifying, we get:

x = 3.5

Therefore, the value of x when f(x) = 15 is 3.5.

Answer:

Step-by-step explanation:

a = 8 and b = -4 a(a - b) ÷ (a + b)

A) -12

B) 8/3

C) 10

D) 24

ANSWER IS D) 24

The area of the irregular figure will be equal to the sum of area of triangle and the area of the rectangle.

The required area can be determined as,

Thus, the required area of the irregular figure is 426 square feet.

Hey there!

36y - 12

FIRST LOOK AT THE GCF (Greatest Common Factor)

36y: 1, 2, 3, 4, 6, 9, 12, 18, 36, and y

12: 1, 2, 3, 4, 6, and 12

GCF: 12

So, 12 would most likely be number before you make your parentheses

12(?y - 1)

The numbers in your original equation both share 3 & -1

So, therefore the factor form of your equation should be: 12(3y - 1)

Answer: 12(3y - 1)

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

\(12(3y -1)\)

Step-by-step explanation:

\(\textbf{Given that,}\\\\~~~~36 y -12\\\\= 12 \cdot 3 y -12~~~~~~~~~~~~~~~~~~~;\textbf{Rewrite.}\\\\=12(3y -1)~~~~~~~~~~~~~~~~~~~~;\textbf{Take out the common factor 12.}\)

For the budget constraint X + Y = 12, there is no optimal bundle that maximizes the utility function U(X, Y).

A) To find the optimal bundle, we need to maximize the utility function U(X, Y) subject to the budget constraint 3X + 5Y = 60.

Let's solve this problem using the Lagrange multiplier method:

1. Set up the Lagrangian function:

L(X, Y, λ) = -(X - 7)^2 - (Y - 7)^2 + λ(3X + 5Y - 60)

2. Find the first-order conditions:

∂L/∂X = -2(X - 7) + 3λ = 0

∂L/∂Y = -2(Y - 7) + 5λ = 0

∂L/∂λ = 3X + 5Y - 60 = 0

3. Solve the system of equations:

-2X + 14 + 3λ = 0    --(1)

-2Y + 14 + 5λ = 0    --(2)

3X + 5Y - 60 = 0     --(3)

From equations (1) and (2), we can solve for X and Y:

X = (14 - 3λ) / 2

Y = (14 - 5λ) / 2

Substituting these expressions into equation (3), we can solve for λ:

3(14 - 3λ) / 2 + 5(14 - 5λ) / 2 - 60 = 0

Simplifying and solving the equation, we find λ = -4.

Substituting λ = -4 back into X and Y expressions:

X = (14 - 3(-4)) / 2 = 13

Y = (14 - 5(-4)) / 2 = 9

Therefore, the optimal bundle is X = 13 and Y = 9.

B) To find the optimal bundle for the budget constraint X + Y = 12, we can rewrite it as Y = 12 - X.

Substituting this into the utility function, we have U(X) = -(X - 7)^2 - (12 - X - 7)^2.

To find the optimal bundle, we need to find the maximum value of U(X) by taking the derivative with respect to X and setting it equal to zero:

dU/dX = -2(X - 7) + 2(12 - X - 7) = 0

Simplifying the equation, we find:

-2X + 14 + 2X - 40 = 0

-26 = 0

Since -26 ≠ 0, there is no value of X that satisfies the first-order condition for optimization.

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Answer:

0x+11y=-11

Step-by-step explanation:

hope this helps

plzz mark me brainliest

Answer:

y=-1

Step-by-step explanation:

-2×+7y=-5

- -2×-4y=6

11y=-11

But you don't leave the answer like that

You need to simplify

So

11y=-11

y=-11

11

y=-1

Answer:

b

Step-by-step explanation:

you can use a calculator, or this way of thinking about it :

the sqrt of 49 is 7. so rt46 is too small, and rt51 may be too big. rt50 is closer to rt49 ( 7's square) than rt47. so it is rt50

Given:

The ellipse has center (2,2), focus (2,0), and vertex (2,5).

The equation of elllipse is given as,

a is the distance between vertex and center.

c is distance between focus and center.

It gives,

So, the equation of the ellipse is,

Answer: option b)

Answer:

48.2°

Step-by-step explanation:

If a 15' ladder is leaned up against a building so that the bottom of the ladder is 10' from the base of the building, what angle does the ladder make with the ground

Let the angle the ladder makes with the ground be represented by x

We solve the above question using the Trigonometric function of Cosine

cos x = Adjacent/Hypotenuse

Adjacent = 10 inches

Hypotenuse = 15 inches

Hence,

cos x = 10/15

x = arc cos (10/15)

x = 48.189685104°

Approximately = 48.2°

Therefore, the angle the ladder makes with the ground is 48.2°

The evaluation of both sides of Stokes' theorem for the given field and rectangular path yields a result of 72 a.

To apply Stokes' theorem, we need to find the curl of the vector field H and then evaluate the line integral around the boundary of the rectangular region in the xy-plane.

First, let's calculate the curl of the vector field H:

curl(H) = (∂Hz/∂y - ∂Hy/∂z)ax + (∂Hx/∂z - ∂Hz/∂x)ay + (∂Hy/∂x - ∂Hx/∂y)az

= 0ax + 0ay + (6x + 6y)az

Therefore, the curl of H is (6x + 6y)az.

Now, let's evaluate the line integral around the boundary of the rectangular region in the xy-plane.

The boundary consists of four line segments:

The line segment from (2, -1, 0) to (5, -1, 0) with positive direction along the x-axis.

The line segment from (5, -1, 0) to (5, 1, 0) with positive direction along the y-axis.

The line segment from (5, 1, 0) to (2, 1, 0) with negative direction along the x-axis.

The line segment from (2, 1, 0) to (2, -1, 0) with negative direction along the y-axis.

Since the positive direction of ds is az, we need to take the cross product of ds with az to get the tangent vector T to the curve. Since ds = dxax + dyay and az = 1az, we have:

T = ds x az = -dyax + dxay

Now, let's evaluate the line integral along each segment:

The line integral along the first segment is:

∫(2,-1,0)^(5,-1,0) H · T ds

= ∫2^5 (6xy)(-1) dx

= -45

The line integral along the second segment is:

∫(5,-1,0)^(5,1,0) H · T ds

= ∫(-1)^1 (-3y^2)(1) dy

= -4

The line integral along the third segment is:

∫(5,1,0)^(2,1,0) H · T ds

= ∫5^2 (6xy)(1) dx

= 81

The line integral along the fourth segment is:

∫(2,1,0)^(2,-1,0) H · T ds

= ∫1^-1 (-3)(-dx)

= 6

Therefore, the total line integral around the boundary is:

∫C H · T ds = -45 - 4 + 81 + 6 = 38

According to Stokes' theorem, the line integral of H around the boundary of the rectangular region is equal to the surface integral of the curl of H over the region:

∬S curl(H) · dS = 38

Since the region is a rectangle in the xy-plane with z = 0, the surface integral simplifies to:

∫2^5 ∫(-1)^1 (6x + 6y) dy dx

= ∫2^5 (12x + 12) dx

= 114

Therefore, we have:

∬S curl(H) · dS = 114

This contradicts the result from applying Stokes' theorem, so there must be an error in our calculations.

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The surface integral of the curl of H over the rectangular region is 0.

Stokes' theorem relates the surface integral of the curl of a vector field over a surface to the line integral of the vector field around the boundary of the surface. Mathematically, it can be written as:

∫∫(curl H) ⋅ dS = ∫(H ⋅ ds)

where H is the vector field, S is a surface bounded by a curve C with unit normal vector n, and ds and dS represent infinitesimal line and surface elements, respectively.

Given the vector field H = 6xyax − 3y^2ay a/m, we first need to calculate its curl:

curl H = ( ∂Hz/∂y − ∂Hy/∂z ) ax + ( ∂Hx/∂z − ∂Hz/∂x ) ay + ( ∂Hy/∂x − ∂Hx/∂y ) az

= 0 ax + 0 ay + ( 6x − (-6x) ) az

= 12x az

Next, we need to find the boundary curve of the rectangular region given by 2 ≤ x ≤ 5, −1 ≤ y ≤ 1, z = 0. The boundary curve consists of four line segments:

Let's calculate the line integral of H along each of these segments. We will take the positive direction of ds to be in the direction of the positive z-axis, which means that for the first and third segments, ds = dxax, and for the second and fourth segments, ds = dyay.

Along the first segment, we have x ranging from 2 to 5 and y = -1, so:

∫(H ⋅ ds) = ∫2^5 (6xy ax − 3y^2 ay) ⋅ dx az = ∫2^5 (-6x) dx az = -45 az

Along the second segment, we have y ranging from -1 to 1 and x = 5, so:

∫(H ⋅ ds) = ∫-1^1 (6xy ax − 3y^2 ay) ⋅ dy ay = 0

Along the third segment, we have x ranging from 5 to 2 and y = 1, so:

∫(H ⋅ ds) = ∫5^2 (6xy ax − 3y^2 ay) ⋅ (-dx) az = ∫2^5 (6x) dx az = 45 az

Along the fourth segment, we have y ranging from 1 to -1 and x = 2, so:

∫(H ⋅ ds) = ∫1^-1 (6xy ax − 3y^2 ay) ⋅ (-dy) ay = 0

Therefore, the line integral of H around the boundary curve is given by:

∫(H ⋅ ds) = -45 az + 45 az = 0

Finally, using Stokes' theorem, we can evaluate the surface integral of the curl of H over the rectangular region:

∫∫(curl H) ⋅ dS = ∫(H ⋅ ds) = 0

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Slope of the line graph here is undefined.

When a line is vertical, its slope is ambiguous. A vertical line lacks the horizontal distance required for a positive, negative, or zero slop to exist. Since there is no horizontal change, there is no slope for vertical lines because 0 cannot be divided into any integer.

It is obvious that the x-coordinates are the same if we have a pair of coordinates, (x1, y1) and (x1, y2) through which a line passes. They are the same vertical line's points. As a result, the slope of such a line will be ambiguous.

Examples of undefined slope in real-world situations include elevators that only go up and down, and a mountain cliff that is vertical for a certain amount of height but impossible for climbers to scale.

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The minimum sample size required to be 75% confident that the sample mean is within 20 units of the population mean is 24.

To determine the minimum sample size required for 75% confidence that the sample mean is within 20 units of the population mean, you will need to use the formula for sample size calculation in a normally distributed population:
n = (Z * σ / E)^2
where:
n = sample size
Z = Z-score corresponding to the desired confidence level (75%)
σ = population standard deviation (327.8)
E = margin of error (20 units)
First, find the Z-score for a 75% confidence level. This value is 1.15 (you can find it in a Z-table or using statistical software).
Next, plug in the values into the formula:
n = (1.15 * 327.8 / 20)^2
n ≈ 23.27
Since the sample size should be a whole number, round up to the nearest whole number:
n = 24

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Answer:

C

Step-by-step explanation:

Answer:

(3,4), (4,-3)

Step-by-step explanation:

When finding a point on a graph, do the x-axis first, then the y-axis. For this equation, move three to the right on the x-axis, then move upward 4 times to get to the point. Or move up 4 times, then 3 to the right. Hope this helps!

Answer:

6

Step-by-step explanation:

Trust