Given m∠B = 62, m∠C = 54 and line AD bisects ∠BAC, find m∠ADB

Answer:

7

Step-by-step explanation:

since 3x-6 and x+8 are congruent x had to make both the equations equal eachother. 7 is the only number that does that

Answer:

A right triangle.

Step-by-step explanation:

A right triangle (triangle with one right angle) can also be scalene if each of its sides are a different length, which is the definition of a scalene triangle.

Reason:

Vertical angles form after intersecting two lines in an X shape. The vertical angles are opposite one another. They do not have to be vertically aligned.

The other pair of vertical angles are ADB and XDF.

Vertical angles are always congruent.

Answer: 40

Step-by-step explanation: Subtract 16 from 36 and you get 20. It says half so you multiply by 2 and get 40.

The results obtained using the algebraic approach and the matrix approach should be the same. Both methods are mathematically equivalent and provide the most probable values of A and B that minimize the sum of squared weighted residuals.

To solve the system of equations using the weighted least squares method, we need to minimize the sum of the squared weighted residuals. Let's solve the problem using both the algebraic approach and matrices.

Algebraic Approach:

We have the following equations:

A + 2B = 10.50 + V1 ... (1)

2A - 3B = 5.55 + V2 ... (2)

2A - B = -10.50 + V3 ... (3)

To minimize the sum of squared weighted residuals, we square each equation and multiply them by their respective weights:

\(2^2 * (A + 2B - 10.50 - V1)^2\)

\(3^2 * (2A - 3B - 5.55 - V2)^2\\1^2 * (2A - B + 10.50 + V3)^2\)

Expanding and simplifying these equations, we get:

\(4(A^2 + 4B^2 + 10.50^2 + V1^2 + 2AB - 21A - 42B + 21V1)\\9(4A^2 + 9B^2 + 5.55^2 + V2^2 + 12AB - 33A + 16.65B - 11.1V2)\\(A^2 + B^2 + 10.50^2 + V3^2 + 2AB + 21A - 21B + 21V3)\\\)

Now, let's sum up these equations:

\(4(A^2 + 4B^2 + 10.50^2 + V1^2 + 2AB - 21A - 42B + 21V1) +\\9(4A^2 + 9B^2 + 5.55^2 + V2^2 + 12AB - 33A + 16.65B - 11.1V2) +\\(A^2 + B^2 + 10.50^2 + V3^2 + 2AB + 21A - 21B + 21V3)\int\limits^a_b {x} \, dx\)

Simplifying further, we obtain:

\(14A^2 + 31B^2 + 1113 + 14V1^2 + 33V2^2 + 14V3^2 + 14AB - 231A - 246B + 21V1 - 11.1V2 + 21V3 = 0\)

Now, we have a single equation with two unknowns, A and B. We can use various methods, such as substitution or elimination, to solve for A and B. Once the values of A and B are determined, we can substitute them back into the original equations to find the most probable values of A and B.

Matrix Approach:

We can rewrite the system of equations in matrix form as follows:

| 1 2 | | A | | 10.50 + V1 |

| 2 -3 | | B | = | 5.55 + V2 |

| 2 -1 | | -10.50 + V3 |

Let's denote the coefficient matrix as X, the variable matrix as Y, and the constant matrix as Z. Then the equation becomes:

X * Y = Z

To solve for Y, we can multiply both sides of the equation by the inverse of X:

X^(-1) * (X * Y) = X^(-1) * Z

Y = X^(-1) * Z

By calculating the inverse of X and multiplying it by Z, we can find the values of A and B.

Comparing Results:

The results obtained using the algebraic approach and the matrix approach should be the same. Both methods are mathematically equivalent and provide the most probable values of A and B that minimize the sum of squared weighted residuals.

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Answer:

199.5

Step-by-step explanation:

3 is not greater than 5

Answer:

199.5

Step-by-step explanation:

The tenth place is the first number to the right of the decimal, in this case, it is 5. In order to know whether or not to raise it to 6 or keep it as 5, we have to look at the hundredth's value. If the number is 5 or higher, we change 5 to 6. If the number is 4 or lower, we keep the 5. In this case, the number is 3, which is 4 or lower. We keep the 5 as it is and get rid off all the numbers behind it. Resulting in:

199.5

There are 11 red skittles and 8 orange skittles, giving a total of 19 skittles that are either orange or red. Therefore, the probability of selecting an orange or red skittle is 19/50, which simplifies to 0.38 or 38%.

To find the probability of selecting an orange or red skittle, we need to determine the number of skittles that fall into those categories and divide it by the total number of skittles in the bowl. In this scenario, there are 11 red skittles and 8 orange skittles. Adding these together, we get a total of 19 skittles that are either orange or red.

Next, we divide this number by the total number of skittles in the bowl, which is 50. So, the probability can be calculated as 19/50. This fraction cannot be simplified further, so the probability of selecting an orange or red skittle is 19/50.

Converting this fraction to a decimal or percentage, we find that the probability is 0.38 or 38%. Therefore, if you randomly pick a skittle from the bowl, there is a 38% chance that it will be either orange or red.

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The degree by (a) are definition and (b) chord definition of standard length 30 m, the length of the curve, tangent length, livili length of long chord, mid-ordinate, and apex distance are calculated.

A circular curve has a 300 m radius and 60 degrees deflection angle. The degree by (a) are definition and (b) chord definition of standard length 30 m are given as follows:

(a) Degree by definition:

Degree by definition is defined as the central angle subtended by an arc of the circle equal in length to the radius of the circle.The radius of the circle is 300m.

So, the degree by definition is:

Degree = Length of arc / Radius of the circle

The length of the arc can be calculated as follows:

Length of arc = (Degree / 360) x 2 x π x Radius of the circle

Length of arc = (60 / 360) x 2 x π x 300

Length of arc = 314.16 m

Degree by definition = Length of arc / Radius of the circle

= 314.16 / 300

= 1.05 radian (approx)

1 radian = 57.3 degrees

Degree by definition = 1.05 x 57.3

= 60 degrees (approx)

(b) Degree by chord definition:

Degree by chord definition is defined as the central angle subtended at the center of the circle by a chord of a circle, which is equal in length to the chord definition standard length.

The chord definition standard length is 30 m.

So, the degree by chord definition is given by:

Degree = (Length of chord / 2 x Radius) x 180 / π

The length of the chord can be calculated as follows:

Length of chord = 2 x Radius x sin (Degree / 2)

Length of chord = 2 x 300 x sin (60 / 2)

Length of chord = 346.41 m

Degree by chord definition = (Length of chord / 2 x Radius) x 180 / π

= ((346.41 / 2 x 300) x 180) / π

= 34.15 degrees (approx)

The lengths of the curve, tangent length, livili length of long chord, mid-ordinate, and apex distance are given as follows:

(i) Length of curve:

Length of curve = Degree by definition / 360 x 2 x π x Radius of the circle

Length of curve = 60 / 360 x 2 x π x 300

= 314.16 m

(ii) Tangent length:

Tangent length = Radius of the circle x tan (Degree by definition / 2)

Tangent length = 300 x tan (60 / 2)

Tangent length = 173.21 m

(iii) Livili length of long chord:

Livili length of long chord = 2 x Radius x sin (Degree by definition / 2)

Livili length of long chord = 2 x 300 x sin (60 / 2)

Livili length of long chord = 346.41 m

(iv) Mid-ordinate: Mid-ordinate = Radius of the circle x (1 - cos (Degree by definition / 2))

Mid-ordinate = 300 x (1 - cos (60 / 2))

Mid-ordinate = 150 m

(v) Apex distance: Apex distance = Radius of the circle - Mid-ordinate

Apex distance = 300 - 150= 150 m

Therefore, the degree by (a) are definition and (b) chord definition of standard length 30 m, the length of the curve, tangent length, livili length of long chord, mid-ordinate, and apex distance are calculated.

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Step-by-step explanation:

y = mx + c

m before x = slope

C. y = 3x - 1

slope = 3

select C

Answer:

c) y=3x-1

Step-by-step explanation:

y=mx+b

Answer: 1

Step-by-step explanation:

Change in y/change in x

starting at y intercept. up 1 unit (change in y) and over 1 unit (change in x) to get to next point on line.

slope is 1/1 which reduces to 1.

Answer:

AB=24.5

Step-by-step explanation:

5x+7=7x

7=2x

x=3.5

7(3.5)=24.5

Answer:

Please check the attached file.

Hope this helps!

:)

Answer:

the side opposite to right angle is hypotenuse ,AB is side opposite to thita nd BC is the side adjacent to thita.

The quadratic regression equation that best fits the data is:

y = 32.86x² - 379.14x + 1229.14.

Regression equations are obtained inserting the points of a table or of a scatter plot into a calculator.

The choice of calculator is relevant to the type of regression equation desired. For this problem, it is stated that a quadratic regression equation is desired, hence the calculator used is for quadratic regression.

From the table given on the right side of the image, the points that will be used to build the quadratic regression equation are given by the ordered pairs presented as follows:

(3, 330), (4, 276), (5, 263), (6, 86), (7, 174), (8, 198), (9, 553).

Inserting these points into a calculator, the quadratic regression equation that best fits the data from the table is given below:

y = 32.86x² - 379.14x + 1229.14.

The concave up parabola is expected, as the measures in the table start decreasing and after the vertex they increase.

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The Probability that 2 or fewer will withdraw without completing the introductory statistics course is 0.4547  .

The Binomial  Distribution formula is

P(X=x) = C(n,x)*pˣ*qⁿ⁻ˣ

where ,

n is the number of trials

x is the number of times success occurs

p is the probability of success

q is the probability of failure .

In the given question ;

it is given that

students that are registered for the course = 20

so , n=20

Let x denote the number of students that withdraw without completing the course .

given that 14 % students  withdraw without completing the course ,

hence p = 14% = 0.14

So , q= 1-p = 1-0.14 = 0.86

the probability that 2 or fewer will withdraw from the course is denoted by P(X ≤ 2) and  is calculated using

the formula , P(X≤2)=P(X=0)+P(X=1)+P(X=2)        ...(i)

using Binomial Probability we get

P(X=x) = C(n,x)*pˣ*qⁿ⁻ˣ

P(X=0) = C(20,0)*(0.14)⁰*(0.86)²⁰⁻⁰

= C(20,0)*(0.14)⁰*(0.86)²⁰

= 1*1*(0.0489)

= 0.0489

So , P(X=0)=0.0489        ...(ii)

P(X=1) = C(20,1)*(0.14)¹*(0.86)¹⁹

= 20*0.14*0.0569

= 0.1593

So , P(X=1)=0.1593        ...(iii)

P(X=2) = C(20,2)*(0.14)²*(0.86)¹⁸

= 190*0.0196*0.0662

= 0.2465    

So , P(X=2)=0.2465        ...(iv)

Substituting the values of (ii) , (iii) and (iv) in (i) , we get

P(X≤2)=P(X=0)+P(X=1)+P(X=2)

P(X ≤ 2) = 0.0489 + 0.1593 + 0.2465

= 0.4547

Therefore , the Probability that 2 or fewer will withdraw without completing the introductory statistics course is 0.4547   .

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If the null hypothesis is rejected, and the proportion of customers willing to pay more is significantly different from 10%, this would support my hypothesis that customers are willing to pay more for eco-friendly packaging.

Let's say you work for a company that has been using a certain type of packaging material for their products. However, there have been concerns raised about the environmental impact of this material, and the company is considering switching to a more eco-friendly option. You believe that customers would be willing to pay more for products that are packaged with the eco-friendly material, but you need to test this hypothesis.

Variable: The variable that would be tested is whether customers are willing to pay more for products that are packaged with the eco-friendly material.

Guess of value: I would guess that customers would be willing to pay more for eco-friendly packaging, but I'm not sure how much more. Let's say my guess is that customers would be willing to pay 10% more for products packaged with the eco-friendly material.

Hypothesis test: To test this hypothesis, I would conduct a survey where I randomly select a sample of customers and ask them if they would be willing to pay more for products packaged with the eco-friendly material. I would then compare the proportion of customers who are willing to pay more to my guess of the value (10%).

Null hypothesis: The null hypothesis would be that the proportion of customers willing to pay more for eco-friendly packaging is not significantly different from 10%.

Alternative hypothesis: The alternative hypothesis would be that the proportion of customers willing to pay more for eco-friendly packaging is significantly different from 10%.

 If the null hypothesis is not rejected, this would suggest that customers are not willing to pay more for eco-friendly packaging, and the company may need to reconsider their decision to switch to the more expensive material.

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The normalized wavefunction for an electron in a region of length L is given by sin(42π⋅x) multiplied by N, where N is sqrt(2/(L - (1/π)⋅sin(L))).



To normalize the wavefunction, we want to find the value of N that ensures the integral of the squared wavefunction over the region from x = 0 to x = L is equal to 1. The given wavefunction is sin(42π⋅x).We start by calculating the integral of (N⋅sin(L/2π⋅x))^2 from 0 to L. Simplifying the expression, we have N^2 times the integral of sin^2(L/2π⋅x) dx.Using the identity sin^2θ = (1 - cos(2θ))/2, we rewrite the integral as N^2/2 times the integral of (1 - cos(L/π⋅x)) dx.



Evaluating the integral, we get N^2/2 times (L - (1/π)⋅sin(L)). Setting this equal to 1, we have N^2 = 2/(L - (1/π)⋅sin(L)).Taking the square root of both sides, we find the value of N: N = sqrt(2/(L - (1/π)⋅sin(L))).

Therefore, the normalized wavefunction for the electron in the given region is sin(42π⋅x) multiplied by N, where N is sqrt(2/(L - (1/π)⋅sin(L))).

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Using the Pigeonhole Principle, it can be shown that in a set of n positive integers, none exceeding 2n, there is at least one integer that divides another integer.

We can prove this statement by contradiction using the Pigeonhole Principle.

Suppose we have a set of n positive integers, none of which exceed 2n, and assume that no integer in the set divides another integer.

Consider the prime factorization of each integer in the set. Since each integer is at most 2n, the largest prime factor in the prime factorization of any integer is at most 2n.

Now, let's consider the possible prime factors of the integers in the set. There are only n possible prime factors, namely 2, 3, 5, ..., and 2n (the largest prime factor).

By the Pigeonhole Principle, if we have n+1 distinct integers, and we distribute them into n pigeonholes (corresponding to the n possible prime factors), at least two integers must share the same pigeonhole (prime factor).

This means that there exist two integers in the set with the same prime factor. Let's call these integers a and b, where a ≠ b. Since they have the same prime factor, one integer must divide the other.

This contradicts our initial assumption that no integer in the set divides another integer.

Therefore, our assumption must be false, and there must be at least one integer in the set that divides another integer.

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The probability of the data vale more extreme than 3.65 is 0.000131.

First of all given that x(value) = μ+3.65σ , where μ is the mean and σ is the standard deviation.

we know that z-score = (x - μ)/σ

z-score = (μ+3.65σ - μ)/σ

z = 3.65σ/σ

z = 3.65

From the normal distribution table,

P(z>3.65) = 0.000131

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Answer:

Step-by-step explanation:

In order to prove the triangles are similar, you have to use SAS, SSS and AA rule.

In triangle, the similarity theorem states that if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Here we have to find the 3 shortcuts to prove the triangles are similar.

According to the similarity theorem, here we have triangle that is similar to other if two pairs of angles are congruent (AA) or if two pairs of sides are proportional and the included angles are congruent whereas if three pairs of sides are proportional (SSS).

Here we must know that the term similarity and congruent are similar terms.

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12/35 fraction of the total number is unused from two different cards.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Assuming the total first kind of card form is 1 and the total second kind of card form is also one.

Given, a company buys equal numbers of two different card forms. it utilizes 4/5 of one kind and 6/7 of the other.

∴ The total unused card form is,

= (1 + 1) - (4/5 + 6/7).

= 2 - (28 + 30)/35.

= 2 - 58/35.

= (70 - 58)/35.

= 12/35.

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The m variable is the slope of the line and controls its 'steepness'. A positive value has the slope going up to the right. A negative slope goes down to the right. The b variable is the y intercept - the point where the line crosses the y axis.

example 1                                                    

y = mx + b

m = slope b = y-intercept

y = 3x - 1

m = 3 and b = -1

example 2

y = b + mx

b = y-intercept m = slope

y = 5 - 1/2x

m =- 1/2 and b = 5

(hope this helped!!)

can i have brainliest?

\(625=5^{7x-3}\implies 5^4=5^{7x-3}\implies 4=7x-3 \\\\\\ 7=7x\implies \cfrac{7}{7}=x\implies 1=x\)

Answer:

1) x=1/2-y/2-3z

2)x= 16/3- 2y/3- 5z/3

3)x= 11/7- 3y/7+ 4z/7

Step-by-step explanation:

isolate the variable, to do that divide each side by the factors that don't contain the variable

To calculate the relative vector of B we have to:

\(P_B=\left[\begin{array}{ccc}3\\3\\-2\\3/2\end{array}\right]\)

The coordenates of:

\(p(t)= 12t^3-8t^2-12t+7\), with respect to B satisfy:

\(C_1(1)+C_2(2t)+C_3(-2+4t^2)+C_4(-12t+8t^3)= 7-12t-8t^2+12t^3\)

Equating coefficients of like powers of t produces the system of equation:

\(\left \{ {C_1-2C_3=7} \atop {2C_2-12C_4=-12} \right. \\\left \{ {{4C_3=-8} \atop {8C_4=12}} \right.\)

After solving this system, we have to:

\(C_1=3\\C_2= 3\\C_3= -2\\C_4= \frac{3}{2}\)

And the result is:

\(P_B=\left[\begin{array}{ccc}3\\3\\-2\\3/2\end{array}\right]\)

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By comparing the responses across the three groups, the researcher can identify potential variations in opinions based on educational background. This information can provide valuable insights into how different types of schooling may shape perspectives on civic policies like curfews.

That's an interesting research approach!  By gathering opinions from different groups of children, specifically home-schooled, private school attendees, and public school attendees, the researcher can gain insights into how various educational backgrounds might influence their opinions on the new town curfew.

Collecting a simple random sample from each group ensures that every child within the respective groups has an equal chance of being selected for the survey. This helps in minimizing bias and increasing the generalizability of the findings to the larger population of home-schooled, private school, and public school children.

Once the samples are obtained, the researcher can administer a survey or questionnaire to collect the children's opinions on the new town curfew. The survey may include questions related to their awareness of the curfew, their understanding of its purpose, and their personal opinions on whether they support or oppose it.

By comparing the responses across the three groups, the researcher can identify potential variations in opinions based on educational background. This information can provide valuable insights into how different types of schooling may shape perspectives on civic policies like curfews.

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