<7 is a complement of <8 and m<7 = 18 degrees. Find m<8.

Answer:

D. \(10^{\circ}\)

Step-by-step explanation:

Let the measure of minor arc \(AE\) be \(\alpha\) and the measure of minor arc \(BD\) be \(\beta\).

Using the secant-secant theorem, \(\frac{\alpha-\beta}{2}=32 \implies \alpha-\beta=64^{\circ}\).

By the inscribed angle theorem, \(\alpha=84^{\circ}\).

Thus, \(\beta=20^{\circ}\).

By the inscribed angle theorem, \(x=10^{\circ}\).

Answer:

A. AB = AC because of the definition of an isosceles triangle

B. ∠B = ∠C because corresponding parts of congruent triangles are congruent.

D. BM = CM because of the definition of a midpoint

Step-by-step explanation:

A. An isosceles triangle is a triangle with two equal sides, hence:

AB = AC because of the definition of an isosceles triangle. option A is correct.

D. Since Point M is drawn as the midpoint of BC, hence:

BM = CM because of the definition of a midpoint. Option D is correct.

E. Reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself. hence AM ≈ AM because of reflexive property.

AM ≈ AM because of the Symmetric Property is wrong. Option E is wrong.

C) The side - side - side (SSS) triangle congruence theorem states that if all the sides of two triangles are equal, then they are congruent triangles.

Since BM = CM, AM = AM and AB = AC, hence ΔABM = ΔACM because of the SSS triangle congruence criterion

ΔABM = ΔACM because of the SAS triangle congruence criterion is wrong. Option C is wrong.

D. Corresponding parts of congruent triangles are congruent. hence:

∠B = ∠C because corresponding parts of congruent triangles are congruent. Option B is correct

Answer: 1/2

Step-by-step explanation:

Kim ate 2/5 which is also equal to 4/10 and Courtney has eaten 1/10

4/10 + 1/10 = 5/10 = 1/2

The possible dimensions of the rectangular plot are 13 m by 13 m (a square) or 26 m by 6.5 m.

Perimeter is the total distance around the edge of a two-dimensional shape, such as a polygon or a circle. It is calculated by adding up the lengths of all the sides of the shape. The perimeter is a measure of the distance that must be covered to go around the shape, and is typically expressed in units of length, such as meters or feet.

Let the length of the rectangular plot be L and the width be W.

We know that the perimeter of the rectangular plot is equal to the sum of the lengths of the three sides of the fence:

2L + W = 39

Also, the area of the plot is LW = 169.

From the second equation, we can solve for L or W in terms of the other variable:

L = 169/W or W = 169/L.

Substitute these expressions into the first equation:

2(169/W) + W = 39

Simplify and rearrange:

2(169) + W² = 39W

W² - 39W + 338 = 0

Solve for W using the quadratic formula:

W = (39 ± √(39² - 4(1)(338))) / 2

W = (39 ± 13) / 2

W = 26 or 13.

If W = 26, then L = (39 - 2W)/2 = -6, which is not possible. So, we can discard this solution.

If W = 13, then L = (39 - 2W)/2 = 13.

Therefore, the possible dimensions of the rectangular plot are 13 m by 13 m (a square) or 26 m by 6.5 m.

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The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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Answer:

q = M - 3p

Step-by-step explanation:

M = q+3p

to isolate q on one side, we need to remove 3p with subtraction, since it is the opposite of addition.

M-3p = q

Answer:

q=m-3p

Step-by-step explanation:

m=q+3p

-3p. -3p

-3p+m=q

Answer:

4

Step-by-step explanation:

2/3 • 6

*Multiply 2 and 6 by 3.

= (2 × 6) / 3

= 12/3

*12 divided by 3 is equal to 4.

= 4

___________

hope it helps!

Answer:

There were 30 people attending at the start of the concert

Step-by-step explanation:

The coefficient of the value raised to an exponent in these types of functions is always the "starting" value. In your case, '30' is the coefficient, so it is the starting value. FYI: 1.10 is the rate at which the people increase, t is time passed, 20 is a constant, and P is the total number of people after the time goes by.

Answer:

There were 30 people attending at the start of the concert.

Step-by-step explanation:

30 is the coefficient, so that's your starting point, basically.

Let's begin by identifying key information given to us:

To know if the vertex is the maximum or minimum point, we will follow this below:

Hence, the answer is B.(0,4); minimum

Answer:

336,000

Step-by-step explanation:

2 × 2 = 4 x 4 = 16 × 5 = 80 × 6 = 480 x 2 = 960 x 2 = 1920 × 5 = 9600 x 7 = 62700 × 5 = 336,000

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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The value of integral is 3.

Let's evaluate the integral over the positive half of the interval:

∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx

Let u = 4 + 3sin(x), then du = 3cos(x) dx.

Substituting these expressions into the integral, we have:

∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du

Using the power rule of integration, the integral becomes:

∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]

Evaluating the definite integral at the limits of integration:

(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))

(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0

So, the value of integral is

= 3-0

= 3

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Answer:

\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)

Step-by-step explanation:

First, compute the indefinite integral:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)

To evaluate the indefinite integral, use the method of substitution.

\(\textsf{Let} \;\;u = 4 + 3 \sin x\)

Find du/dx and rewrite it so that dx is on its own:

\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)

Rewrite the original integral in terms of u and du, and evaluate:

\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)

Substitute back u = 4 + 3 sin x:

                            \(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

Therefore:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.

Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.

\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)

Therefore, the curve of the function is:

So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.

Integrate the function between -π and -π/2.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)

Integrate the function between -π/2 and π/2:

\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)

Integrate the function between π/2 and π.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)

To evaluate the definite integral, sum A₁, A₂ and A₃:

\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)

Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:

\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)

Therefore, the given expression cannot be zero.

Answer: 2 sides

Step-by-step explanation:

you need 2 diagonals and 2 sides for it to make a quadilateral

Answer:

2 diagonals and 2 sides

Step-by-step explanation:

quadilaterals don't need to have diagonals to make it a quadilateral.

Answer:

\(28km\)

Step-by-step explanation:

\(5miles = 8km\)

\(17.8miles = x\)

\( \frac{17.8}{5} \times 8km\)

\(x = 28km\)

Answer:

x=52.5

Step-by-step explanation:

2/3x-5=30

2/3x=35

x=52.5

Answer:

Hey it’s C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

wwwuhwhwuiwhwhwhshss

Answer:x=1

Step-by-step explanation:

Given

\(F(x)=\dfrac{x^2+x-2}{x-1}\)

F(x) will be discontinuous at x=1 because value of f(x) is undefined at that point.

F(x) is defined for all values of x except at x=1

If you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

To calculate the Social Security tax, we need to know the tax rate for Social Security and the taxable wages. Let's assume the Social Security tax rate is 6.2% for both the employee and the employer.

Given that your taxable wages for Social Security purposes are $1,100, and your previous taxable wages are $102,000, we can determine the Social Security tax amount.

First, we need to calculate the Social Security tax on the previous taxable wages of $102,000. Multiply $102,000 by 6.2% (0.062) to find the Social Security tax for that amount:

Social Security tax = $102,000 x 0.062 = $6,324

Next, we calculate the Social Security tax on the current taxable wages of $1,100. Multiply $1,100 by 6.2% to find the tax amount:

Social Security tax = $1,100 x 0.062 = $68.20

Therefore, if you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

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Answer:

B) 50cm^2

Step-by-step explanation:

The frequency table for the given data using 4 classes with class internval size of 5, which gives us the following class limits:

Class 1: 1-5

Class 2: 6-10

Class 3: 11-15

Class 4: 16-20

One method to display data is in a frequency table. To summarise bigger sets of data, the data are ordered and counted. You can examine the distribution of the data across various numbers using a frequency table.

To construct a frequency table for grouped data using 4 classes, we need to first determine the range of the data and the size of each class interval.

Range = Maximum value - Minimum value = 20 - 1 = 19

We can choose a class interval size of 5, which gives us the following class limits:

Class 1: 1-5

Class 2: 6-10

Class 3: 11-15

Class 4: 16-20

Next, we count the number of data points that fall into each class interval and record them in the table:

Class Interval                      Tally                               Frequency

1-5  

6-10  

11-15  

16-20  

The tally marks in the second column represent the number of data points in each class interval, and the frequency in the last column is the total count of data points for each class interval.

Therefore, the frequency table for the given data using 4 classes is as shown above.

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Answer:

chisquare = 31.667

degree of freedom = 2

Step-by-step explanation:

Formula for chisquare test =  (O-E)²/E

total number observations= 60 + 25 + 15 = 100                  

Estimated E,

80% x 100 = 80

15%x100 = 15

5% x 100 = 5

chisquare =

\(\frac{(60-80)^{2} }{80} +\frac{(25-15)^{2} }{15}+\frac{(15-5)^{2} }{5}\\\)

= 5 + 6.67 + 20

= 31.667

from the calculation above the value of the chisquare statistic = 31.67

the degree of freedom is the number of samples in the test  n - 1

= 3-1

= 2

I have solve this question also in a tabular form to aid understanding in the file i uploaded.

thank you and good luck!

Answer:

It is a false statement

The correct statement is -The margin of error from the smaller sample will be \(\sqrt{2}\)  times the margin of error from the larger sample.

Step-by-step explanation:

P.S - The exact question is -

Given - A large restaurant chain is curious what proportion of their

            customers in a given day are new customers. They  are thinking  

            of taking a sample of either n = 50 or nº= 100 customers and

            building a one-sample z interval for  a proportion using the data

            from the sample.

To find - The margin of error from the smaller sample will be 2 times

               the margin of error from the larger sample.

Proof -

We know that

E ∝ \(\frac{1}{\sqrt{n} }\)

For smaller margin, E₁ = \(\frac{1}{\sqrt{50} }\)

For larger margin , E₂ = \(\frac{1}{\sqrt{100} }\)

Now,

\(\frac{E_{1} }{E_{2} } = \frac{\sqrt{100} }{\sqrt{50} } = \sqrt{\frac{100}{50} } = \sqrt{2}\\\)

⇒E₁ = \(\sqrt{2}\) E₂

⇒The margin of error from the smaller sample will be \(\sqrt{2}\)  times the margin of error from the larger sample.

So,

It is a false statement.

Answer:

4.5255

Step-by-step explanation:

Use the Pythagorean theorem (a²+b²=c²) where A and B are equal to 3.2