Evaluate the question and simplify

The answer is .  option (c) , equation that can be used to find the value of x is: 130 + 70 + x = 180.

The reason behind this is that the sum of the interior angles of a triangle sum up to 180°.

An interior angle is an angle inside a triangle, which means the interior angles of a triangle sum up to 180 degrees.

An interior angle is an angle located inside a polygon. Interior angles are located between two sides of a polygon.

For example, in the triangle ABC, the angles A, B, and C are interior angles.

The sum of the interior angles of a triangle

The sum of the interior angles of a triangle is always 180 degrees.

In other words, when you add up all three interior angles, the total sum should be 180.

It is important to note that this is true for all triangles, regardless of their size or shape.

So, The equation that can be used to find the value of x is: 130 + 70 + x = 180.

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there is a formula A = 2π r h + 2π r².

=> h = (A - 2π r²) / 2π r

=> h = ( 616 - 2π(7)^2) / 2π(7)

=> h = 7.0

Hope you could understand.

If you have any query, feel free to ask.

To determine if two planes are parallel or perpendicular, we can examine their normal vectors. If the normal vectors are parallel, the planes are parallel.

If the normal vectors are perpendicular, the planes are perpendicular. If the normal vectors are neither parallel nor perpendicular, we can use the dot product formula to find the angle between them.

For the given planes:

The normal vectors are (1,4,-3) and (-3,6,7). Since the dot product of these vectors is not zero, the planes are neither parallel nor perpendicular. Using the dot product formula, we get cosθ = (-15)/(sqrt(26)*sqrt(58)), so θ ≈ 105.2 degrees.

To put the second equation in standard form, we have 6x - 2y - 2z = 0. So the normal vector of the second plane is (6,-2,-2). The normal vector of the first plane is (9,-3,6), which is not parallel or perpendicular to (6,-2,-2).

Therefore, the planes are neither parallel nor perpendicular. Using the dot product formula, we get cosθ = 7/(3*sqrt(30)), so θ ≈ 72.6 degrees.

The normal vectors are (1,2,-1) and (2,-2,1). Since the dot product of these vectors is zero, the planes are perpendicular.

The normal vectors are (1,-1,3) and (3,1,-1). Since the dot product of these vectors is not zero, the planes are neither parallel nor perpendicular. Using the dot product formula, we get cosθ = -5/(2*sqrt(35)), so θ ≈ 137.9 degrees.

To put the second equation in standard form, we have 6y + 2z = 4x - 3. So the normal vector of the second plane is (4,-6,-2). The normal vector of the first plane is (2,-3,-1), which is parallel to (4,-6,-2). Therefore, the planes are parallel.

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Answer:

2

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Step-by-step explanation:

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Answer:

4.3

im not sure

correct me if im wrong

Answer

6.7

Step-by-step explanation:

Works on acellus

For A and B to be independent, the value of P(B) should be ≈ 1.224

For events A and B to be independent, the probability of their intersection (A ∩ B) must be equal to the product of their individual probabilities (P(A) * P(B)).

In this case, we have the following information:

P(A) = 0.49

P(A ∩ Bc) = 0.4

We need to determine the value of P(B) for which A and B are independent.

We can use the following equation:

P(A ∩ B) = P(A) * P(B)

However, we don't have the direct value of P(A ∩ B), but we have P(A ∩ Bc) and we can use the complement rule to obtain P(A ∩ B):

P(A ∩ B) = 1 - P(A ∩ Bc)

Now, substituting the known values:

1 - P(A ∩ Bc) = P(A) * P(B)

1 - 0.4 = 0.49 * P(B)

0.6 = 0.49 * P(B)

0.6 / 0.49 = P(B)

Approximately, P(B) = 1.224

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Answer:

\(10 x - 2y\)

Step-by-step explanation:

\(8x−2y+x+x \\ 9x−2y+x \\ 10x−2y\)

Answer:

x = 21

Step-by-step explanation:

(3x+1) ^1/3=4 means that the 1/3 is an exponent that can be rewritten as a cube root.

You can bring the cube root to the other side of the equation.

1. I chose to bring it to the other side of the equation, making it a cube.

(3x+1) ^1/3 = 4

(3x+1) = 4^3

(3x+1) = 4 * 4 * 4

(3x+1) - 1 = 64 - 1

3x/3 = 63/3

x = 21

a. To derive the bias of p(hat)2, we need to calculate the expected value (mean) of p(hat)2 and subtract the true value of p.

Bias(p(hat)2) = E(p(hat)2) - p

Now, p(hat)2 = (Y+1)/(n+2), and Y has a binomial distribution with parameters n and p. Therefore, the expected value of Y is E(Y) = np.

E(p(hat)2) = E((Y+1)/(n+2))

          = (E(Y) + 1)/(n+2)

          = (np + 1)/(n+2)

The bias of p(hat)2 is given by:

Bias(p(hat)2) = (np + 1)/(n+2) - p

b. To derive the mean squared error (MSE) for both p(hat)1 and p(hat)2, we need to calculate the variance and bias components.

For p(hat)1:

Bias(p(hat)1) = E(p(hat)1) - p = E(Y/n) - p = (1/n)E(Y) - p = (1/n)(np) - p = p - p = 0

Variance(p(hat)1) = Var(Y/n) = (1/n^2)Var(Y) = (1/n^2)(np(1-p))

MSE(p(hat)1) = Variance(p(hat)1) + [Bias(p(hat)1)]^2 = (1/n^2)(np(1-p))

For p(hat)2:

Bias(p(hat)2) = (np + 1)/(n+2) - p (as derived in part a)

Variance(p(hat)2) = Var((Y+1)/(n+2)) = Var(Y/(n+2)) = (1/(n+2)^2)Var(Y) = (1/(n+2)^2)(np(1-p))

MSE(p(hat)2) = Variance(p(hat)2) + [Bias(p(hat)2)]^2 = (1/(n+2)^2)(np(1-p)) + [(np + 1)/(n+2) - p]^2

c. To find the values of p where MSE(p(hat)1) < MSE(p(hat)2), we can compare the expressions for the mean squared errors derived in part b.

(1/n^2)(np(1-p)) < (1/(n+2)^2)(np(1-p)) + [(np + 1)/(n+2) - p]^2

Simplifying this inequality requires a specific value for n. Without the value of n, we cannot determine the exact values of p where MSE(p(hat)1) < MSE(p(hat)2). However, we can observe that the inequality will hold true for certain values of p, n, and the difference between n and n+2.

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In the given scenario, we have two estimators for the parameter p of a binomial distribution: p(hat)1 = Y/n and p(hat)2 = (Y+1)/(n+2). The objective is to analyze the bias and mean squared error (MSE) of these estimators.

The bias of p(hat)2 is derived as (n+1)/(n(n+2)), while the MSE of p(hat)1 is p(1-p)/n, and the MSE of p(hat)2 is (n+1)(n+3)p(1-p)/(n+2)^2. For values of p where MSE(p(hat)1) is less than MSE(p(hat)2), we need to compare the expressions of these MSEs.

(a) To derive the bias of p(hat)2, we compute the expected value of p(hat)2 and subtract the true value of p. Taking the expectation:

E(p(hat)2) = E[(Y+1)/(n+2)]

          = (1/(n+2)) * E(Y+1)

          = (1/(n+2)) * (E(Y) + 1)

          = (1/(n+2)) * (np + 1)

          = (np + 1)/(n+2)

Subtracting p, the true value of p, we find the bias:

Bias(p(hat)2) = E(p(hat)2) - p

             = (np + 1)/(n+2) - p

             = (np + 1 - p(n+2))/(n+2)

             = (n+1)/(n(n+2))

(b) To derive the MSE of p(hat)1, we use the definition of MSE:

MSE(p(hat)1) = Var(p(hat)1) + [Bias(p(hat)1)]^2

Given that p(hat)1 = Y/n, its variance is:

Var(p(hat)1) = Var(Y/n)

            = (1/n^2) * Var(Y)

            = (1/n^2) * np(1-p)

            = p(1-p)/n

Substituting the bias derived earlier:

MSE(p(hat)1) = p(1-p)/n + [0]^2

            = p(1-p)/n

To derive the MSE of p(hat)2, we follow the same process. The variance of p(hat)2 is:

Var(p(hat)2) = Var((Y+1)/(n+2))

            = (1/(n+2)^2) * Var(Y)

            = (1/(n+2)^2) * np(1-p)

            = (np(1-p))/(n+2)^2

Adding the squared bias:

MSE(p(hat)2) = (np(1-p))/(n+2)^2 + [(n+1)/(n(n+2))]^2

            = (n+1)(n+3)p(1-p)/(n+2)^2

(c) To compare the MSEs, we need to determine when MSE(p(hat)1) < MSE(p(hat)2). Comparing the expressions:

p(1-p)/n < (n+1)(n+3)p(1-p)/(n+2)^2

Simplifying:

(n+2)^2 < n(n+1)(n+3)

Expanding:

n^2 + 4n + 4 < n^3 + 4n^2 + 3n^2

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Answer:

36

Step-by-step explanation:

For the solutions to the inequality *> 145, you can consider the given terms: 1. Fractions larger than 14 1/2: These are solutions since 14 1/2 is equivalent to 145/2, which is smaller than 145. 2.

Decimals larger than 14 1/2: These are also solutions as any decimal larger than 14.5 (14 1/2 as a decimal) will be greater than 145/2 and thus smaller than 145. 3. Whole numbers larger than 14 1/2: These are solutions as well, since any whole number greater than 14 is greater than 14 1/2 and therefore greater than 145/2. The numbers that are not solutions to the inequality are: 1. Fractions smaller than 14 1/2 2. Decimals smaller than 14 1/2 3. Whole numbers smaller than 14 1/2 These values are all less than 145/2 and therefore do not satisfy the inequality *> 145.

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The slope of the points in this table is equal to 1.2.

In Mathematics and Geometry, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided in the table, we can logically deduce the following data points on the line:

Substituting the given points into the slope formula, we have the following;

Slope, m = (3.7 + 1.1)/(1 + 3)

Slope, m = 4.8/4

Slope, m = 1.2.

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Answer:

B

Step-by-step explanation:

b/c the figure is right angle

Answer:

\(x = \frac{83}{7} \)

Step-by-step explanation:

5x+(2x+7)=90

7x+7=90

7x=90-7

7x=83

x=83/7

x=11.857

The standard deviation of a set of seventeen numbers described by Σx=272 Σx² = 11849​ is 21.

The term "standard deviation"  refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

We have Σx=272 and Σx² = 11849​.

n= 17

So, the Variance of the Data

= Σx²/n - (Σx/ n)²

= 11849 / 17 - (272/17)²

= 697 - 256

= 441

Then, the Standard deviation is

= √Variance

= √441

= 21

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The perimeter of each polygon is 42.

Perimeter:

The whole distance around a shape is referred to as its perimeter. In essence, the length of any shape when it is expanded in a linear form equals its perimeter. A shape's perimeter in a two-dimensional plane is its complete circumference. Depending on their measurements, distinct shapes' perimeters may be equal in length. For instance, if a circle is built of a metal wire of length L, the same wire can be used to build a square with equal-length sides. Three sides make up the triangle. Any triangle's perimeter, whether scalene, isosceles, or equilateral, will therefore equal the sum of its three sides' lengths. And the space a triangle takes up in a plane is its area.

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Answer:

Speed of car most likely

Step-by-step explanation:

Answer:

$45

Step-by-step explanation:

The area of the triangle ABC with sides AB =6cm, BC=5cm and AC=7cm is 14.697 square centimeters.

We can find the area of the triangle ABC using Heron's formula, which states that the area of a triangle with sides of lengths a, b, and c is:

Area = √(s(s-a)(s-b)(s-c))

where s is the semiperimeter of the triangle, given by:

s = (a + b + c)/2

In triangle ABC, we have:

The semiperimeter s is:

s = (a + b + c)/2

= (6 + 5 + 7)/2

= 9

Using Heron's formula, the area of triangle ABC is:

Area = √(s(s-a)(s-b)(s-c))

= √(9(9-6)(9-5)(9-7))

= √(9 × 3 × 4 × 2)

= √(216)

= 14.697

In other words, the area of triangle ABC is approximately 14.697 square centimeters.

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In completing the square method, considering the equation X^2 + 82x +  the number to be added should be 1681 to make it a perfect square

The quadratic equation is an equation of the form

ax^2 + bx + c

The completing the square method is on of the methods of solving equations of the form above

The factor to be added on the both sides of the equation while using the completing the square method is

(b / 2a)^2

compared to the equation in the problem X^2 +82x

= (b / 2a)^2

= (82 / 2)^2

= (41)^2

= 1681

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Slope-intercept form: y = mx + b

m = the slope

y = the y-intercept

In our problem,

y = -4/3x - 1

m = -4/3

The slope is -4/3

By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 1.7.

The Central Limit Theorem established that, for a normally distributed random variable X, with mean and standard deviation, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean  and standard deviation ;

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

The sample of 112 residents has a mean GPA of 1.7.

By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 1.7.

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Answer:

Store 1 Has a better deal as your paying 1.50 less which is 50 percent off

Step-by-step explanation:

Lets say a DVD costs 1.50

so if you bought 2 for the price of one it would be 1.50

3 for the price of 2 would be 3 dollars.

If you were to buy 2 CDS for the Price of 2 that would be 3 Dollars

3 CDS for the price of 3 would be 4.50

The Amount of money depends on the cost of 1 CD.

Store 1 has a 50 percent discount while Store 2 has roughly a 35 percent discount.

sorry if this was confusing^^

Answer:

1. {12,0}

hope it helps.

Answer:

3 and 4

Step-by-step explanation:

X - 9y = 12     If x=3 and y=-1

3 - (9*-1) = 12

3 +9 = 12

12 = 12

and

X - 9y = 12     If x=0 and y=-4/3

0 - (9 * -4/3) = 12

0 + 12 = 12

12 = 12

Answer:

Sum of a and c is less than 100.

Step-by-step explanation:

^

The solution to the given IVP is.\($i(t)-\frac{E}{R}+\left(i_0-\frac{E}{R}\right) e^{-\frac{R}{L}}$\)

Initial value problems describe a type of problem in calculus. Initial value problems in calculus concern differential equations with a known initial condition that specifies the value of the function at some point. The purpose of these problems is to find the function that describes the system, which can be done by integrating the differential equation.

Consider the initial value problem,

L \(\frac{d i}{d t}+R i=E \text {. }\)

The initial condition is. \($i(0)=i_0$\)

Rewrite the DE as,

\(\begin{gathered}L \frac{d i}{d t}+R i=E \\\frac{d i}{d t}+\frac{R}{L} i=\frac{E}{L}\end{gathered}$$\)

This is a linear DE.

Compare the DE  \(\frac{d i}{d t}+\frac{R}{L} i=\frac{E}{L}$\) with the general DE \(\frac{d i}{d t}+P(t) i=Q(t)$\). Then \($P(t)=\frac{R}{L}$\) and \($Q(t)=\frac{E}{L}$\).

Find the integrating factor (IF).

                                     \($$\begin{aligned}I F & =e^{\int P(t) \vec{t}} \\& =e^{\int\left(\frac{\pi}{\mathrm{I}}\right) \mathrm{A}} \\& =e^{\frac{\pi}{l^2}}\end{aligned}$$\)

Thus, the integrating factor is \($I F=e^{\frac{R^2}{2^2}}$\).

Now multiply both sides of the DE with the IF.

                                   \($$\begin{array}{r}e^{\frac{R}{\bar{L}^t}}\left(\frac{d i}{d t}+\frac{R}{L} i\right)=\frac{E}{L} e^{\frac{R}{L^t}} \\\frac{d i}{d t} e^{\frac{\pi}{L^t}}+\frac{R}{L} e^{\frac{R}{\bar{L}^t}} i=\frac{E}{L} e^{\frac{\pi}{\bar{L}^t}} \\{\left[i e^{\frac{R}{L^2}}\right]=\frac{E}{L} e^{\frac{R^L}{L^t}}}\end{array}$$\)

Integrate on both sides.

        \($$\begin{aligned}& \int\left[i e^{\frac{R}{L}}\right] d t=\int \frac{E}{L} e^{\frac{R}{L^t}} d t \\& i e^{\frac{R}{L^{\mathrm{r}}}}=\frac{E}{L} \int e^{\frac{\pi}{L^t}} d t \\& i e^{\frac{R}{\perp} r}=\frac{E}{L}\left[\frac{e^{\frac{R}{2}}}{\frac{R}{L}}\right]+C \\& i e^{\frac{R}{\Gamma}+}=\frac{E}{R} e^{\frac{R^2}{I^{+}}}+C \\& i(t)=\frac{\frac{E}{R} e^{\frac{R}{L^2}}+C}{e^{\frac{R}{D^2}}} \\& t(t)=\frac{E}{R}+C e^{-\frac{R}{L^t}} \\&\end{aligned}$$\)

Thus, the general solution to the \(\mathrm{DE}\) is \($i(t)=\frac{E}{R}+C e^{-\frac{R}{t^*}}$\).

Use the initial condition. \($i(0)=i_0$\)

Substitute \($t=0$\) and \($i(0)=i_0$\) in \($i(t)=\frac{E}{R}+C e^{-\frac{R}{I^t}}$\).

\($$\begin{aligned}& i(0)=\frac{E}{R}+C e^{-\frac{R}{I}(0)} \\& i_0=\frac{E}{R}+C e^0 \\& i_0=\frac{E}{R}+C \quad \text { use } e^0=1 \\& C=i_0-\frac{E}{R}\end{aligned}$$\)

Substitute  \($C=i_0-\frac{E}{R}$\) in \($i(t)=\frac{E}{R}+C e^{-\frac{R}{L^1}}$\).

\($$\begin{aligned}& i(t)=\frac{E}{R}+C e^{-\frac{R}{I}} \\& i(t)=\frac{E}{R}+\left(i_0-\frac{E}{R}\right) e^{-\frac{\pi}{t^t}}\end{aligned}$$\)

Therefore, the solution to the given IVP is. \($i(t)-\frac{E}{R}+\left(i_0-\frac{E}{R}\right) e^{-\frac{R}{L}}$\).

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Answer:

The coordinates of the fourth vertex are (8,5)

Step-by-step explanation:

We need to take note that a rectangle is a shape that has 4 sides, with two of them of equal length.

It will also help if we can visualize the points on the graph.

We are given the location of three of the four vertices. These are (6,3), (6,5) ,and (8,3). Let the 4th Vertice be (x,y)

The length of the triangle can be obtained by subtracting the y-coordinates of the vertices.

(6,3) - (6,5)

This will be +3 and +5

5-3 =2

Therefore, the length of the triangle is 2 units on the left side.

Recall that the length of the left side has to be equal to the length of the right side.

Therefore

y-3 =2

y = 5

We will repeat the same process to get the x-coordinate from the breadth

Breadth = 8-6 =2

x-6 =2

x=8

Hence the x = 8

Therefore, the coordinates of the fourth vertex are (8,5)