find the mean of the data set down below. 7, -3, 6, -2, 8, 7, -4, 5, 3

Given:

Parallel lines p and q are cut by transversal r.

m∠3=(3x + 4)° and m∠5=(2x + 11)°.

To find:

The relation between ∠3 and ∠5, then find the measure of angle 5.

Solution:

Parallel lines p and q are cut by transversal r as shown in the below figure.

From the figure it is clear that ∠3 and ∠5 are alternate interior angle. So, the values of these angles are equal.

\(m\angle 3=m\angle 5\)

\((3x+4)^\circ=(2x+11)^\circ\)

\(3x+4=2x+11\)

Therefore, the required equation to solve for x is \(3x+4=2x+11\).

Isolate variable terms.

\(3x-2x=11-4\)

\(x=7\)

The value of x is 7.

Now,

\(\angle 5=(2x+11)^\circ\)

\(\angle 5=(2(7)+11)^\circ\)

\(\angle 5=(14+11)^\circ\)

\(\angle 5=25^\circ\)

Therefore, the measure of angle 5 is 25°.

Answer:

Step-by-step explanation:

That'd be (1/4)x or x/4.

Answer:

The answer is A on edg 2020

Step-by-step explanation:

i got it right.

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The value of 0.0062 is less that our significance level of 0.1, we reject the null hypothesis at the 0.1 level of significance and conclude with sufficient evidence that the manufacturer's MPG rating is incorrect.

To answer the question, we will conduct a hypothesis test to at the 0.1 level to ascertain whether or not the manufacturer's MPG rating is incorrect.

We start by stating the null and alternative hypotheses:

\($H_0$\): The mean miles/gallon for the vans is 53.8

\($H_A$\): The mean miles/gallon for the vans is not 53.8

We choose a significance level $\alpha = 0.1$ and calculate the following test statistic:

\($z = \frac{\bar{x}-\mu}{\sigma/\sqrt{n}} = \frac{53.4-53.8}{1/\sqrt{16}} = -2.5$\)

With a standard normal table, we look for the area to the left of -2.5, which is 0.0062. Because this value of 0.0062 is less that our significance level of 0.1, we reject the null hypothesis at the 0.1 level of significance and conclude with sufficient evidence that the manufacturer's MPG rating is incorrect.

Therefore, the value of 0.0062 is less that our significance level of 0.1, we reject the null hypothesis at the 0.1 level of significance and conclude with sufficient evidence that the manufacturer's MPG rating is incorrect.

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The limit, if it exists, or show that the limit does not exist is to be found using the function Lim(x,y,z) → (0,0,0) xy+yz+xz / x²+y²+z².

The given function can be simplified as shown below: xy+yz+xz / x²+y²+z²= x(y+z)/x²+y²+z²+ y(x+z)/x²+y²+z²+ z(x+y)/x²+y²+z²

Now, we'll use the squeeze theorem to find the limit:

0 ≤ |x(y+z)/x²+y²+z²| ≤ |x|/√(x²+y²+z²) (since |y+z| ≤ |y|+|z| ≤ √(y²+z²+2yz))

Similarly, 0 ≤ |y(x+z)/x²+y²+z²| ≤ |y|/√(x²+y²+z²) and 0 ≤ |z(x+y)/x²+y²+z²| ≤ |z|/√(x²+y²+z²)

So, we have: 0 ≤ |xy+yz+xz|/x²+y²+z² ≤ (√(x²+y²+z²)/√(x²+y²+z²)) (|x|+|y|+|z|)0 ≤ |xy+yz+xz|/x²+y²+z² ≤ (|x|+|y|+|z|)

And now we'll apply the squeeze theorem.

Let L = lim(x,y,z) → (0,0,0) xy+yz+xz / x²+y²+z²

Thus,0 ≤ |xy+yz+xz|/x²+y²+z² ≤ (|x|+|y|+|z|) → 0 as (x,y,z) → (0,0,0)

Therefore, by squeeze theorem, lim(x,y,z) → (0,0,0) xy+yz+xz / x²+y²+z² = 0

Hence, the given limit exists and is equal to 0.

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The value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

The history of pi dates back thousands of years, and over time, various civilizations have attempted to calculate its value with varying degrees of accuracy. One of the most inaccurate versions of pi was recorded by the ancient Babylonians around 2000 BC.

The Babylonians calculated the value of pi as 3.125, which is off by more than 6% from the actual value. It is believed that the Babylonians arrived at this value by using a rough approximation of a circle as a hexagon. They measured the perimeter of the hexagon and divided it by the diameter to get their approximation of pi.

This value was later refined by the ancient Egyptians and Greeks, who were able to calculate pi with greater accuracy. The Greek mathematician Archimedes, for instance, was able to calculate pi to within 1% accuracy by using a method of exhaustion.

It wasn't until the development of calculus in the 17th century that mathematicians were able to derive an exact formula for pi. Today, the value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

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The amount of iodine-124 left after 16 days when the technician measured the original sample will be a/16.

Let a be the initial value and x be the number of days, 1/2 be the half-life factor, and y be the amount left after x days.

The exponent is given as,

\(\rm y = a \left ( \dfrac{1}{2} \right )^{\dfrac{x}{4}}\)

Chemistry Iodine-124 has a half-life of four days. Iodine-124 sample of 40 mCi is measured by a technician.

The amount of iodine-124 left after 16 days when the technician measured the original sample will be

\(\rm y = a \left ( \dfrac{1}{2} \right )^{\dfrac{16}{4}}\\\\\rm y = a \left ( \dfrac{1}{2} \right )^{4}\\\\\rm y = a \left ( \dfrac{1}{16} \right )\\\\\rm y = \dfrac{a}{16}\)

The amount of iodine-124 left after 16 days when the technician measured the original sample will be a/16.

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Answer:

81

Step-by-step explanation:

3*3=9

9*3=27

27*3=81

brainliest?

Answer:

22

Step-by-step explanation:

F(5)= 5(5) -3 (Replace x by 5)

F(5)= 25-3 (Solve for 5 and 5)

F(5)= 22 (Simplify)

22 (Answer)

The p-value accurate to 4 decimal places is 0.0191.

To find the p-value for the given test statistic t=2.56, we need to determine the probability of obtaining a test statistic as extreme or more extreme than the observed value under the null hypothesis.

Since the sample size is small (n=15) and the population standard deviation is unknown, we will use a t-distribution for hypothesis testing.

The null hypothesis (H0) states that the typical doctor's salary is not significantly different from 92, and the alternative hypothesis (H1) suggests a significant difference.

To find the p-value, we can use a t-distribution table or statistical software. However, since you requested the p-value accurate to 4 decimal places, it would be best to use statistical software for precise calculations.

Given the test statistic t=2.56 and the degrees of freedom (df = n - 1 = 15 - 1 = 14), the p-value can be calculated as the probability of obtaining a more extreme t-value in either tail of the t-distribution.

Using statistical software, the p-value corresponding to t=2.56 with 14 degrees of freedom is approximately 0.0191.

Therefore, the p-value accurate to 4 decimal places is 0.0191.

The p-value represents the probability of observing a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. In this case, since the p-value (0.0191) is less than the significance level (commonly 0.05), we would reject the null hypothesis. This suggests that there is evidence of a significant difference between the typical doctor's salary and 92.

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a) The SQL query for this would be:
```sql
USE sakila;
SELECT f.film_id, f.title, c.name AS category_name

FROM film f
JOIN film_category fc ON f.film_id = fc.film_id
JOIN category c ON fc.category_id = c.category_id
WHERE c.name IN ('Action', 'Horror') AND f.film_id BETWEEN 200 AND 300
ORDER BY f.film_id;
```b) I'm an AI language model and cannot run the query in MySQL directly. However, you can copy and paste the query above into your MySQL client to execute it and see the results.
c) After executing the query in your MySQL client, please refer to the first 2 rows of the results. Since I cannot run the query directly, I cannot provide the exact result.

Your question is about an SQL query in the MySQL sakila database, to display film id, title, and category name for films with category names "Action" or "Horror", and film ids between 200 and 300, sorted by film id

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1) We can find algebraically the vertex of that Absolute Value inequality, by doing this procedure:

2) Since the vertex is where the absolute value is equal to zero, let's solve as an equation, and then treat it back as an inequality to write the answer:

Now let's plug the quantity of "x" we just found to find the y-coordinate:

So the answer is:

Holly would need one piece of string to go around the outside of her bicycle wheel.

To determine the number of pieces of string Holly would need to go around the outside of her bicycle wheel, we need to consider the circumference of the wheel.

The circumference of a circle is given by the formula: C = πd, where C is the circumference and d is the diameter.

Since Holly cuts the string to be the diameter of her bicycle wheel, the string's length is equal to the diameter of the wheel. Therefore, the circumference of the wheel is also equal to the length of the string.

Hence, Holly would need one piece of string to go around the outside of her bicycle wheel.

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Answer: 13x - 14

Step-by-step explanation:

3x + 10x - 14

13x -14

Answer:

13x-14

Step-by-step explanation:

Answer:

8:31

Step-by-step explanation:

all of them are equal with 1:4 except 8:31

Here the population growth is as per the Malthusian model. As per the calculations, the bacterial population will reach 10000 after 33 days.

Here the bacterial growth is as per the exponential growth curve. So the equation is,

   \(P_{t} = P_{0} e^{rt}\)

\(P_{t}\) is the population at n

\(P_{0}\) is the initial population

r is the time

t is the rate

Population doubles after 10 days.

So,  \(2000 = 1000e^{r*10} \\\\\frac{2000}{1000} = e^{10r}\\\\ 2 = e^{10r\\}\\\\\)

Taking logarithms on both sides

\(ln(2) = lne^{10r}\\\\10r = 0.693\\ \\r = 0.0693\)

So the rate is 0.0693.

When population reaches 10000,

\(10000 =1000e^{0.0693t}\)

\(\frac{10000}{1000} =e^{0.0693n}\)

\(10 = e^{0.0693*t}\\ \\ln(10) = ln(e^{0.0693t}\\ \\2.3 = 0.0693t\\\\t = 2.3/0.0693\\= 33.18\)

So the number of days to reach population of 10000 is 33.18≈ 33 days.

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The area of the paperboard that remains is 613.92 square inches.

To find the area of the paperboard that remains after a semicircle is cut out, we need to calculate the area of the rectangular paperboard and subtract the area of the semicircle.

The rectangular paperboard has dimensions of 35 inches long and 24 inches wide. Therefore, the area of the rectangular paperboard is:

Area_rectangular = length * width = 35 in * 24 in = 840 in²

Now, let's calculate the area of the semicircle. The semicircle is cut out of the rectangular paperboard, and the diameter of the semicircle is equal to the width of the rectangular paperboard (24 inches).

The formula to calculate the area of a semicircle is:

Area semicircle = (π * r²) / 2

where r is the radius of the semicircle.

Since the diameter of the semicircle is 24 inches, the radius is half of that, which is 12 inches.

Plugging in the values into the formula, we get:

Area_semicircle = (3.14 * 12²) / 2 = (3.14 * 144) / 2 = 226.08 in²

Finally, to find the area of the paperboard that remains, we subtract the area of the semicircle from the area of the rectangular paperboard:

Area remaining = Area rectangular - Area semicircle = 840 in² - 226.08 in² = 613.92 in²

Therefore, the area of the paperboard that remains is 613.92 square inches.

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Critical angle for the total internal reflection icrit, β =  78.28⁰

Critical angle for the total internal reflection crit, α = 17,22⁰

We have the refractive index of core, \(n_c_o_r_e\) = 1.46

We have the refractive index of clad , \(n_c_l_a_d\) = 1.4

Critical angle can be defined as the incidence angle which results in the refraction angle being equal to  at that angle of incidence.

For Total Internal Reflection to occur, the incidence angle must be greater than the critical angle.

We know that the critical angle, θ is given by:

sinθ = \(\frac{n_c_l_a_d}{n_c_o_r_e}\)

sinθ = \(\frac{1.4}{1.46}\)

sinθ = 0.959 = sin⁻¹(0.979) = 78.28⁰

β = θ = 78.28⁰

Now, for α:

\(\frac{sin(90-\alpha )}{sin\alpha } = \frac{1}{n_c_o_r_e}\)

sinα = sin(90⁰-78.28⁰) × 1.46

sinα = sin(11.72⁰) × 1.46

α = sin⁻¹(0.296)

α = 17,22⁰

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Critical angle for total internal reflection icrit β = 78.28⁰

Critical angle for total internal reflection crit, α = 17.22⁰

The refractive index of the core is ncore = 1.46.

The refractive index of clad is nclad = 1.4.

We know that the critical angle, θ is given by:

sinθ = nclad/ ncore

sinθ = 1.4/1.46

sinθ = 0.959

sin⁻¹(0.979) = 78.28⁰

β = θ = 78.28⁰

Now, for α:

sin(90- α) / sin α = 1 / ncore

sinα = sin(90⁰-78.28⁰) × 1.46

sinα = sin(11.72⁰) × 1.46

α = sin⁻¹(0.296)

α = 17.22⁰

Critical angle for icrit β = 78.28⁰

Critical angle for crit α = 17.22⁰

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Answer:

let'ssssssssss gooooooooooooooooooooooooooooooooooooooooooooooooo

Step-by-step explanation:

Answer:

3783

Step-by-step explanation:

The terms that explains the value of Sin(pi/3) on the unit circle would be Sin(pi/3) = Opposite side of angle.

According to the statement

we have to give the terms which explain the sin (pi/3) perfectly.

And we have choose these terms from the these below written conditions like From Right Triangle, Hypotenuse, and unit circle.

And Now we explain all terms below

So,

"Right Triangle is a triangle whose one of the angle measures 90° "

And "The hypotenuse is a longest side of the right triangle.

And"Unit Circle is a circle with radius 1."

For given question,

We have been  given a unit circle.

So, We need to find the sin (pi/3)

We know, in a right triangle for any angle , θ

Sinθ = Opposite side of angle / Hypotenuse

So, for , Sin(pi/3) = Opposite side of angle / 1

Sin(pi/3) = Opposite side of angle

Therefore, The terms that explains the value of Sin(pi/3) on the unit circle would be Sin(pi/3) = Opposite side of angle.

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The coffee shop charge for her purchase $46.

The slope of the line and a point on the line can be used to create the equation of a line. To better comprehend how the equation for a line is formed, let's learn more about the line's slope and the necessary point on the line. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis.

The slope intercept form of equation is

y= mx+ b

As, we know the slope intercept form

y= mx + b

Now, we have the points (0, 26) and (4, 52)

So, the y- intercept is 26.

and, slope= (52- 26)/ (4- 0)

                 = 26/4

                 = 6.5

So, coffee shop charge for her purchase is

= 6.5 x 3 +26

= 46

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Answer:

3.5 inches by 4 inches

Step-by-step explanation:

The divergence of the vector field F is positive for y > -1/3 and negative for y <  -1/3.

To plot the vector field F(x, y) = (xy, x + y^2), we can first visualize the vectors at various points in the xy-plane. Let's choose a range of values for x and y and calculate the corresponding vectors. We'll use a step size of 1 for simplicity.

Here is a sample grid of points and their corresponding vectors:

(x, y) = (-2, -2) -> F(-2, -2) = (4, 2)

(x, y) = (-1, -2) -> F(-1, -2) = (2, 2)

(x, y) = (0, -2) -> F(0, -2) = (0, 2)

(x, y) = (1, -2) -> F(1, -2) = (0, 2)

(x, y) = (2, -2) -> F(2, -2) = (4, 2)

(x, y) = (-2, -1) -> F(-2, -1) = (2, 1)

(x, y) = (-1, -1) -> F(-1, -1) = (1, 1)

(x, y) = (0, -1) -> F(0, -1) = (0, 1)

(x, y) = (1, -1) -> F(1, -1) = (0, 1)

(x, y) = (2, -1) -> F(2, -1) = (2, 1)

... and so on for other values of y and for positive values of y.

To calculate the divergence (divF) of the vector field, we need to find the partial derivatives of the components of F with respect to x and y. Then we sum these partial derivatives.

F(x, y) = (xy, x + y^2)

∂F/∂x = y

∂F/∂y = 1 + 2y

divF = ∂F/∂x + ∂F/∂y = y + (1 + 2y) = 3y + 1

Now, we can analyze where the divergence is positive (divF > 0) and where it is negative (divF < 0).

For divF > 0:

If y > -1/3, then divF > 0.

For divF < 0:

If y < -1/3, then divF < 0.

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The distance Chyna ran is 7 1 / 2 kilometres.

Ronaldo ran 9 / 10 fewer kilometres than Chyna ran. Ronaldo ran 6 3 / 5

kilometres

Therefore, the distance Chyna ran in kilometres can be calculated as follows:

Therefore,

Distance Ronaldo ran = 6 3 / 5  = 33 / 5 kilometres

Hence,

Distance Chyna ran = 33 / 5 + 9 / 10

Distance Chyna ran = 66 + 9 / 10

Distance Chyna ran = 75 / 10

Therefore,

Distance Chyna ran = 7 5 / 10

Distance Chyna ran = 7 1 / 2 kilometres

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Answer:

3

Step-by-step explanation:

Find the prime factors of each term in order to find the greatest common factor (GCF).

So the greatest number of both is 3

Hope this helps

Answer:

x= 10

Step-by-step explanation:

hope i help youuuuu :)

ANSWER:

7.5 hours

Step-by-step explanation:

5x6=30

then

4xx=30

x=30÷4

x=7.5