Select the correct answer.


In the figure, angle C measures 83°, angle F measures 105°, and angle E measures 37°. What is the measurement of angle I?

A.
37°
B.
45°
C.
51°
D.
76°

Answer:

r = \(\sqrt{11}\)

Step-by-step explanation:

So we need to complete the square for both parts of the equation

First though we can add the 6 to the other side so we have x² + 2x + y² + 4y = 6

So first we can complete the square for x² + 2x

To do so we need to use \((\frac{b}{2} )^{2}\) to figure out the number we need to add to both sides

In this case our b is 2, so substituting this in we get \((\frac{2}{2} )^{2} =(1)^{2} =1\)

Here we add 1 to both sides and now we have x² + 2x + 1 + y² + 4y = 6 + 1

Now we can follow the same steps to complete the square for y² + 4y

Here our b is 4, so substituting this in we get \((\frac{4}{2} )^{2}=(2)^{2} =4\)

Now we add 4 to both sides and now we have x² + 2x + 1 + y² + 4y + 4 = 6 + 1 + 4

Now condensing everything we have (x + 1)² + (y + 2)² = 11

The formula for a circle is (x - h)² + (y - k)² = r²

In our equation we have r² = 11

To find the radius we need to take the square root of both sides \(\sqrt{r^{2}} =\sqrt{11}\) to get r = \(\sqrt{11}\)

The length of one side of the square park is approximately 26.87 meters.

To find the length of one side of the square park, we can use the Pythagorean theorem. In a square, the diagonal walkway forms a right-angled triangle with two equal sides (the sides of the square).

Let the length of one side be x meters. According to the Pythagorean theorem, the sum of the squares of the two shorter sides (x^2 and x^2) equals the square of the longest side (38^2).

x^2 + x^2 = 38^2

Combine the x^2 terms:

2x^2 = 38^2

Divide by 2:

x^2 = (38^2) / 2

Now, take the square root of both sides to find the length of one side:

x = √((38^2) / 2)

x ≈ 26.87 meters

The length of one side of the square park is approximately 26.87 meters.

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Answer:

24

Step-by-step explanation:

Given Information

x = -2

y = -7

___________________

Substitute -2 and -7 with x and y

(6 x -2) - (4 x -7) + 8

= -12 - -28 + 8

= 16 + 8

= 24

Answer: -32

Step-by-step explanation: * Imput your x and y values.

* 6(-2) - 4(7) + 8

* Follow PEMDAS, starting with multiplication. Then add/ subtract.

* (-12) - 28 + 8

= (-12) - 20

=> -32

The work done by a force can be calculated by taking the dot product of the force vector with the displacement vector whether the force and displacement vectors are consecutive or anti-congruent.

The formula of the dot product is-

A ⋅ B = |A| |B| cos(θ)

Here A and B are the vectors  |A| and |B| which represent their magnitudes, and θ is the angle between them.

The angle between the force and displacement vectors is either 0 degrees (cos(0) = 1) or 180 degrees (cos(180) = -1) depending on whether they are parallel or antiparallel. The dot product becomes: in these circumstances.

A ⋅ B = |A| |B| (1) = |A| |B| (cos(0)) = |A| |B|

When the vectors are parallel or antiparallel, the angle is 0 or 180 degrees, respectively, and the cosine term is 1 or -1. This occurs since work done is defined as the dot product of the force and displacement vectors multiplied by the cosine of the angle between them.

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How can a telephone survey of 1000 randomly selected US adults provide evidence that more than 1 in 4 US adults believe in ghosts?The survey results provide evidence that more than one in four US adults believe in ghosts. The telephone survey was conducted on a random sample of 1000 US adults. The survey found that 31 percent of US adults believed in ghosts.

To determine whether more than one in four US adults believe in ghosts, the null and alternative hypotheses will be tested.The null hypothesis in this scenario is that less than or equal to 25% of US adults believe in ghosts. The alternative hypothesis is that more than 25% of US adults believe in ghosts.Therefore, the level of significance (α) will be determined.

The α level is typically set to 0.05. This means that the likelihood of making a type I error is 5%. Then, the z-score will be calculated as follows:z = (0.31 - 0.25) / sqrt[(0.25 x 0.75) / 1000]z = 2.83The obtained z-score will be compared to the critical z-value using a z-distribution table. The critical z-value is 1.96. Since the obtained z-score is greater than the critical z-value, the null hypothesis will be rejected. Therefore, there is evidence to suggest that more than one in four US adults believe in ghosts.

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Answer:

2.80

Step-by-step explanation:

 you want to figure out the unit rate (minute per page) by divideing 26 by 9  

26 wont go into 9 evenly so you will have decimal

The area enclosed by the parametric curve and the y-axis is 0.7542 square units.

The parametric curve is defined by \(\(x = t^2 - 2t\)\) and \(\(y = \sqrt{t}\)\).

Now, let's calculate the area enclosed by the curve and the y-axis:

\(\[ \text{Area} = \int_{0}^{c} |y| \, dt \]\)

Here,  \(\(c\)\)  is the upper bound of the domain, which is the value of \(\(t\)\) where the curve intersects the y-axis.

At the y-axis, the x-coordinate is 0, so we set \(\(x = 0\)\) in the equation for the parametric curve:

\(\[ x = 0\\ t^2 - 2t = 0\]\)

Solving for t:

\(\[ t^2 - 2t = 0 \\ t(t - 2) = 0 \]\)

So, t=0, or t=2. Since we are considering the domain where  \(\(t \geq 0\)\), the upper bound of the domain c is \(\(t = 2\)\).

Now, we'll integrate the absolute value of y with respect to t from 0 to 2:

\(\[ \text{Area} = \int_{0}^{2} |\sqrt{t}| (2t-t)\, dt \]\)

Since \(\(y = \sqrt{t}\)\) is positive in the given domain, the absolute value is not necessary, and we can simplify the integral:

\(\[ \text{Area} = \int_{0}^{2} \sqrt{t} (2t-t)\, dt \]\)

Now, integrate:

\(\[ \text{Area} = [\frac{4}{5}t^{5/2} -\frac{4}{3}t^{3/2} \Big|_{0}^{2} \]\\\)

\(\[ \text{Area} = [\frac{4\times\4\sqrt{2}}{5} -\frac{4\times\2\sqrt{2}}{3}] -0\)

\(\[ \text{Area} = \frac{8\sqrt{2}}{15}\)

\(\[ \text{Area} =0.7542 \ sq\ units\)

So, the area enclosed by the parametric curve and the y-axis is 0.7542 square units.

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The complete question is as follows:

Find the area enclosed by the given parametric curve and the y-axis. x = t² − 2t, y = √(t)

the factors of 8 are as follow:

1,2,4,8

Answer:

Factors of 8 are 1, 2, 4, and 8.

Step-by-step explanation:

hope it is helpful to you ☆☆

Answer:

A

Step-by-step explanation:

z1 = 4 - i

z2 = -3 - 2i

z1 - z2 = 4 - i - (-3 - 2i) = 4 + 3 - i + 2i = 7 + i

Answer: A

The resulting divide-and-conquer algorithm for matrix multiplication using 25 scalar multiplications and a constant number of scalar additions and subtractions is efficient for multiplying two 3 × 3 matrices.

To analyze the divide-and-conquer algorithm for matrix multiplication, let's set up and solve the recurrence relations based on the given conditions.

Let's assume we have two 3 × 3 matrices A and B, and we want to compute their product C = A × B.

According to the given information, we can perform the matrix multiplication using 25 scalar multiplications and a constant number of scalar additions and subtractions.

In a divide-and-conquer algorithm, we can split the matrices into smaller submatrices to simplify the multiplication process. Let's assume we divide the matrices into 2 × 2 submatrices:

A = [A11 A12]

   [A21 A22]

B = [B11 B12]

   [B21 B22]

C = [C11 C12]

   [C21 C22]

The recurrence relation for this algorithm can be expressed as follows:

C11 = A11 × B11 + A12 × B21

C12 = A11 × B12 + A12 × B22

C21 = A21 × B11 + A22 × B21

C22 = A21 × B12 + A22 × B22

Since each entry of matrix C requires a scalar multiplication and there are four entries in total, we have a total of 4 scalar multiplications.

To solve the recurrence relation, we can express the number of scalar multiplications as a function of the subproblem size. In this case, the subproblem size reduces to 2 × 2 matrices, and the number of scalar multiplications can be considered constant.

Therefore, the resulting divide-and-conquer algorithm for matrix multiplication using 25 scalar multiplications and a constant number of scalar additions and subtractions is efficient for multiplying two 3 × 3 matrices.

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Answer: The area, in square feet, of the piece of wood is \(32 ft^{2}\).

Step-by-step explanation:

Give: Length = 8 feet

Width = \(\frac{1}{2} \times 8\) = 4 feet

As piece of wood is similar to that of a rectangle. Hence, formula to calculate area is as follows.

\(Area = length \times width\)

Substitute the values into above formula as follows.

\(Area = length \times width\\= 8 feet \times 4 feet\\= 32 ft^{2}\)

Thus, we can conclude that the area, in square feet, of the piece of wood is \(32 ft^{2}\).

Mean and standard deviation of the height of the population using empirical rule is equal to 65inches and 3 inches.

As given in the question,

Distribution of height in women population:

Percent of women heights less than 62inches = 16%

As per Empirical rule of normal distribution,

It is less than 68% it comes in first standard deviation

μ - σ = 62 __(1)

Percent of women heights less than 71 inches = 97.5%

As per Empirical rule of normal distribution,

It is in the range of  97.5% it comes in second standard deviation

μ +2σ = 71 __(2)

Solve (1) and (2) we get,

μ - σ = 62

μ +2σ = 71

0 - 3σ = -9

⇒ σ = 3inches

⇒ μ = 62 + 3

       = 65inches

Therefore, the using empirical rule the mean and standard deviation to represent the height of population is equal to 65inches and 3 inches respectively.

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Answer:

Length = 4x - 5

Step-by-step explanation:

A = length x width

From the given equation y = 30(0.92)d, she should expect 193 phone calls after a week.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "="..

If the number of phone calls she should expect can be represented by the equation y = 30(0.92)d, where y is the number of phone calls after d days, then we can calculate the expected amount phone calls after a week.

To determine how much phone calls she should expect after a week, substitute the value of d.

y = 30(0.92)d

where d = 1 week = 7 days

y = 30(0.92)(7)

y = 193.2

Rounding off to the nearest whole number,

y = 193

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Answer: b. counterexample

A counterexample contradicts the statement or definition you're trying to set up.

For example, if you said that 2x+3x = 7x was true for all x values, then all you need to do is try something like x = 2 to find the original equation simplifies to 10 = 14, which is false. In this case, the counterexample is x = 2 invalidating the equation 2x+3x = 7x.

Answer:

14 or 0.14

Step-by-step explanation:

3 1/2 ÷ 1/4

1/4 = 25

3 1/2 ÷ 25 = 0.14 or 14

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The equations are :

The given pair of equations have infinitely many solutions.

(because the first equation is the product of second equation with -2)

Answer:

80

Step-by-step explanation:

60/3 becomes 20 and then it says equal to 1/4 x because x divided by 4 so we multiply by 4 to get 80

Answer:

x=0,1,±2

Step-by-step explanation:

x^3(x^2-5)=-4x

x^2(x^2-5)=-4

Take x^2=a, we have

a*(a-5)=-4, a^2-5a+4=0, (a-1)(a-4)=0, a=1,4

x^2=0, 1, 4. x=0,1,±2

Answer:

x = 1 and x = 2

Step-by-step explanation:

\( {x}^{5} - 5 {x}^{3} = - 4x \\ {x}^{4} - 5 {x}^{2} + 4 = 0 \\ ( {x}^{2} - 4)( {x}^{2} - 1)=0\)

x² = 4 or x² = 1

Since x > 0, the negative integers are rejected and the solutions to this equations are x = 1 and x = 2

Answer:

It’s in the attachment

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Answer:

hello!

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Answer:

5

Explanation:

When we divide A by B, we are calculating how many Bs fit into A. So, if we want to know how many 2/5s fit into 2 yds, we need to divide 2 by 2/5. So:

So, 2 yds of rope can be divide into 5 ropes of 2/5 yd.

We can see that the statement is not always true for any vectors u and v in V3.

The statement is not always true.

The cross product of vectors u and v in V3 is a vector that is orthogonal to both u and v. That is,

u x v ⊥ u and u x v ⊥ v

However, this does not necessarily mean that (u x v) * u = 0 for all u and v in V3.

For example, let u = <1, 0, 0> and v = <0, 1, 0>. Then,

u x v = <0, 0, 1>

(u x v) * u = <0, 0, 1> * <1, 0, 0> = 0

So in this case, the statement is true. However, consider the vectors u = <1, 1, 0> and v = <0, 1, 1>. Then,

u x v = <1, -1, 1>

(u x v) * u = <1, -1, 1> * <1, 1, 0> = 0

So in this case, the statement is also true. However, if we take the vector u = <1, 0, 0> and v = <0, 0, 1>, then

u x v = <0, 1, 0>

(u x v) * u = <0, 1, 0> * <1, 0, 0> = 0

So in this case, the statement is true as well.

However, if we take the vector u = <1, 1, 1> and v = <0, 1, 0>, then

u x v = <1, 0, 1>

(u x v) * u = <1, 0, 1> * <1, 1, 1> = 2

So in this case, the statement is not true.

Therefore, we can see that the statement is not always true for any vectors u and v in V3.

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The reason it is not possible to fix the poster on the wall, even though the area of the poster is less than the area of the wall.

Sheela is correct. It is not possible to fix the poster on the wall, even though the area of the poster is less than the area of the wall.

The reason is that the dimensions of the poster are larger than the dimensions of the wall, which means it cannot fit properly.

Let's assume the length and width of the wall are Lw and Ww, respectively, and the length and width of the poster are Lp and Wp, respectively.

Given:

Area of the wall = 64 sq cm

Area of the poster = 48 sq cm

We know that the area of a rectangle is calculated by multiplying its length by its width:

Area of the wall = Lw * Ww

Area of the poster = Lp * Wp

From the given information, we have:

Lw * Ww = 64  ---(Equation 1)

Lp * Wp = 48  ---(Equation 2)

We need to compare the dimensions of the poster (Lp and Wp) with the dimensions of the wall (Lw and Ww).

Let's consider the scenario where the dimensions of the poster are larger than the dimensions of the wall:

Lp > Lw and Wp > Ww

If we substitute these values in Equation 2, we get:

Lw * Ww = 48

Since Lp > Lw and Wp > Ww, the area of the poster (48 sq cm) cannot fit within the area of the wall (64 sq cm).

Therefore, the reason it is not possible to fix the poster on the wall, even though the area of the poster is less than the area of the wall, is that the dimensions of the poster are larger than the dimensions of the wall, making it impossible to fit the entire poster on the wall.

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Answer:

- 3a -16b

Step-by-step explanation:

Answer:

Step-by-step explanation:

The number of children is 198, adults are 99 and students are 88.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Given that, the theatre sitting capacity is 385 and the theatre charges are $5.00 for children $7.00 for students, and $12.00 for adults.

Let the number of children be c, since, there are half as many adults as there are children therefore, number of adults = c/2

The number of students = 385 - c - c/2 = 385 - 3c/2

The total cost  = $2794

Therefore,

2794 = 5c+c/2×12+(385-3c/2)×7

2794 = 5c+6c+2695 - 21c/2

c = 198

Therefore, number of adults = 198/2 = 99

The number of students = 385-3/2×198 = 88

Hence, The number of children is 198, adults are 99 and students are 88.

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Answer:

Possible answers could be that you have 400 adults and no children, or you could have 100 children and 340 adults.

We have to find the circumference

\(\\ \rm\longmapsto C=2\pi r\)

\(\\ \rm\longmapsto C=2\dfrac{22}{7}(14)\)

\(\\ \rm\longmapsto C=44(2)\)

\(\\ \rm\longmapsto C=88cm\)

Answer:

556

Step-by-step explanation:

Surface area of the cuboid = 2*(lb+bh+lh)

Surface area = 2*(80+88+110)=556