Find the measure of the exterior angle 1
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This interval is wider than the confidence interval in part (a) and the prediction interval in part (b) because it is based on the entire population of metal pieces, not just a sample.

(a) To find a 99% confidence interval on the mean diameter, we can use the t-distribution with n-1 degrees of freedom since the population standard deviation is not known. The formula for the confidence interval is:

CI = x ± tα/2,s/√n

where x is the sample mean, s is the sample standard deviation, n is the sample size, and tα/2 is the t-value with (n-1) degrees of freedom for the desired level of confidence α.

Plugging in the values, we get:

CI = 1.0056 ± t0.005/2,0.0246/√9

= 1.0056 ± 0.025

= (0.9806, 1.0306)

Therefore, we can be 99% confident that the true mean diameter of the metal pieces produced by the machine is between 0.9806 and 1.0306 centimeters.

(b) To compute a 99% prediction interval on a measured diameter of a single metal piece taken from the machine, we can use the formula:

PI = x ± tα/2,s(1 + 1/n)√(1 + 1/n)

where x is the point estimate of the diameter (in this case, the sample mean), s is the sample standard deviation, n is the sample size, and tα/2 is the t-value with (n-1) degrees of freedom for the desired level of confidence α.

Plugging in the values, we get:

PI = 1.0056 ± t0.005/2,0.0246(1 + 1/9)√(1 + 1/9)

= 1.0056 ± 0.052

= (0.9536, 1.0576)

Therefore, we can be 99% confident that a single metal piece produced by the machine will have a diameter between 0.9536 and 1.0576 centimeters.

(c) To find the 99% tolerance limits that will contain 95% of the metal pieces produced by this machine, we can use the formula:

TL = x ± kσ

where x is the sample mean, σ is the population standard deviation (which is estimated by the sample standard deviation s), k is the number of standard deviations from the mean that will contain the desired percentage of the population (in this case, 95% or 1.96 standard deviations for a normal distribution).

Plugging in the values, we get:

TL = 1.0056 ± 1.96(0.0246)

= (0.9573, 1.0539)

Therefore, we can be 99% confident that 95% of the metal pieces produced by the machine will have diameters between 0.9573 and 1.0539 centimeters. This interval is wider than the confidence interval in part (a) and the prediction interval in part (b) because it is based on the entire population of metal pieces, not just a sample.

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Answer:

Step-by-step explanation:

A = length x width = (2w + 5)(w) = 2w² + 5w

P = 2(2w + 5) + 2w = 6w + 10

To graph:  sorry, Brainly doesn't have graphing tools so I'll just have to describe it

A:  parabola, opens up, vertex at (-1.25, -3,124), crosses x axis at (-2.5, 0) and (0,0)

P:  straight line, slants up, with a slope of 6, y-intercept of 10, crosses x axis at (-1.667, 0)

FYI, the 2 graphs intersect at 2 points:  (-2, 2) and (2.5, 25)

There were 3097 6th-grade students who went on the field trip to see the play at the theater.

We have,

If 95% of the 3260 seats in the theater were filled by the 6th-grade students,

We can find the total number of students by multiplying the total number of seats by the fill percentage as a decimal:

Number of 6th graders = 3260 x 0.95

Number of 6th graders = 3097

Therefore,

There were 3097 6th-grade students who went on the field trip to see the play at the theater.

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Answer:

Colbie did not complete the square correctly.

Colbie failed to add the square of half the coefficient of the term in x to both sides of the equation. She only added 25 to the left side of the equation. She also factored x² + 10x + 25 incorrectly by using a subtraction sign in the binomial rather than an addition sign.

Step-by-step explanation:

Given quadratic equation:

[tex]2x^2+20x-48=0[/tex]

As the leading coefficient is not one, to complete the square we must first divide both sides of the equation by the leading coefficient, 2:

[tex]\dfrac{2x^2+20x-48}{2}=\dfrac{0}{2}[/tex]

[tex]x^2+10x-24=0[/tex]

Now move the constant to the right side of the equation by adding 24 to both sides of the equation:

[tex]\begin{array}{rcr}x^2+10x-24&=&0\\\vphantom{\dfrac12}+24 & &+24\\\cline{1-3}\vphantom{\dfrac12}x^2+10x\phantom{-24.}&=&24\end{array}[/tex]

We need to make the left side of the equation a perfect square trinomial. To do this, add the square of half the coefficient of the term in x to both sides of the equation.

The coefficient of the term in x is 10. Therefore, the square of half of this is 25:

[tex]\left(\dfrac{10}{2}\right)^2=5^2=25[/tex]

This is the point at which Colbie made her first mistake. She didn't add the square of half the coefficient of the term in x to both sides of the equation - she only added it to the left side.

Add 25 to both sides of the equation:

[tex]x^2+10x+25=24+25[/tex]

[tex]x^2+10x+25=49[/tex]

To continue to solve the equation, factor the perfect square trinomial on the left side of the equation:

[tex](x+5)^2=49[/tex]

↑ Colbie made her second mistake here. She factored x² + 10x + 25 incorrectly by using a subtraction sign in the binomial rather than an addition sign.

Square root both sides:

[tex]\sqrt{(x+5)^2}=\sqrt{49}[/tex]

[tex]x+5=\pm7[/tex]

Subtract 5 from both sides:

[tex]x+5-5=-5\pm7[/tex]

[tex]x=-5\pm7[/tex]

Therefore, the solutions are:

[tex]x=-5+7=2[/tex]

[tex]x=-5-7=-12[/tex]

A linear equation which shows a proportional relationship include the following: A. y = 2x.

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 2/1 = 4/2 = 6/3 = 8/4

Constant of proportionality, k = 2.

Therefore, the required linear equation is given by;

y = kx

y = 2x

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The probability that the randomly selected point is in the bullseye = 15/16.

To calculate the probability that the randomly selected point is in the bullseye, we shall first evaluate the area of each of the circles:

The area of the larger circle (outer circle) with radius 8 cm is given:

A_outer = πr² = π(8)² = 64π

The area of the smaller circle (inner circle) with radius 2 cm is given:

A_inner = πr² = π(2)² = 4π

The area of the bullseye (the region between the two circles) = the difference between the areas of the two circles:

A_bullseye = A_outer - A_inner

= 64π - 4π = 60π

Therefore, the probability that a randomly selected point is in the bullseye:

P = A_bullseye / A_outer

= (60π) / (64π)

P = 15/16

x

Therefore, the probability that the randomly selected point is in the bullseye = 15/16.

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Check the picture below.

The velocity of the meteorite is 4 km per sec.

Given that, a meteorite is approaching the earth and is 10000 km away from earth,

we need to find the velocity,

v = k / √d

v = 400 / √10000

v = 400 / 100

v = 4 km per sec.

Hence, the velocity of the meteorite is 4 km per sec.

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The velocity at a distance of 6,889 kilometers is 6.795 Km/ sec.

We have,

The velocity v of a meteorite approaching earth is V = k/√d.

The distance from center of Earth = 8836

and, Velocity = 6 Km/ s

So, using the formula for velocity

6 = k/√8836

6 = k/94

k= 564 Km

Now, velocity at 6689 Km

V = 564/ √6889

V =6.795 km/sec

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Answer:

Step-by-step explanation:

1. The line of best fit must have an equal number of points above and below the line

2. The line of best fit could be used as a predictions showing a trend in data

The point that satisfies y = -3-x is (0,-3), the point that satisfies y = x-3 is (0,-3), the point that satisfies y = 3x+2 is (0,2), the point that satisfies y = 3x -2 is (0,-2), the point that satisfies y = -3x+2 is (0,2). The graph is shown below.

To find the points that satisfy the equation y = -3 - x, we can substitute different values of x and solve for y.

When x = 0, y = -3 - 0 = -3, so one point is (0, -3).

When x = 1, y = -3 - 1 = -4, so another point is (1, -4).

When x = -1, y = -3 - (-1) = -2, so another point is (-1, -2).

By repeating this process for different values of x, we can find more points that satisfy the equation.

To find the points that satisfy the equation y = x - 3, we can again substitute different values of x and solve for y.

When x = 0, y = 0 - 3 = -3, so one point is (0, -3).

When x = 1, y = 1 - 3 = -2, so another point is (1, -2).

When x = -1, y = -1 - 3 = -4, so another point is (-1, -4).

To find the points that satisfy the equation y = 3x + 2, we can once again substitute different values of x and solve for y.

When x = 0, y = 3(0) + 2 = 2, so one point is (0, 2).

When x = 1, y = 3(1) + 2 = 5, so another point is (1, 5).

When x = -1, y = 3(-1) + 2 = -1, so another point is (-1, -1).

To find the points that satisfy the equation y = 3x - 2, we can once again substitute different values of x and solve for y.

When x = 0, y = 3(0) - 2 = -2, so one point is (0, -2).

When x = 1, y = 3(1) - 2 = 1, so another point is (1, 1).

When x = -1, y = 3(-1) - 2 = -5, so another point is (-1, -5).

To find the points that satisfy the equation y = -3x + 2, we can once again substitute different values of x and solve for y.

When x = 0, y = -3(0) + 2 = 2, so one point is (0, 2).

When x = 1, y = -3(1) + 2 = -1, so another point is (1, -1).

When x = -1, y = -3(-1) + 2 = 5, so another point is (-1, 5).

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Based on the information, we are 90% confident that the true mean birth weight of boys is between 2.956 and 3.124 kilograms.

standard error will be:

= 0.71 / ✓(195) = 0.051 kilograms

Substituting these values into the formula, we will then get:

Confidence interval = 3.04 ± (1.645) × (0.051)

Confidence interval = 3.04 ± 0.084

Confidence interval = (2.956, 3.124)

Therefore, we are 90% confident that the true mean birth weight of boys is between 2.956 and 3.124 kilograms.

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The J curve impact is an financial wonder that happens when domestic currency  increases in value in esteem relative to other monetary forms within the remote trade advertise. The J curve impact is named for the shape of the bend that's made when the adjust of exchange and the esteem of a country's currency are plotted against time.

Within the brief run, when a country's money increases in value, its sends out ended up more costly and imports ended up cheaper. This implies that the request for a country's sends out will diminish, whereas the request for imports will increase. As a result, the adjust of exchange will at first

compound, which implies that the nation will have a exchange shortfall.

Be that as it may, within the long run, the J curve impact predicts that the adjust of exchange will in the long run progress, and the exchange shortage will turn into a exchange overflow. This happens because the increment within the cost of sends out due to the appreciation of the currency will in the long run lead to a diminish within the amount of trades requested. At the same time, the diminish within the price of imports due to the appreciation of the money will in the long run lead to an increment within the amount of imports requested. Over time, these changes in request will cause a move within the adjust of exchange, coming about in a exchange excess.

In this manner, the Jcurve impact portrays the short-term weakening within the adjust of exchange that happens when a money increases in value, taken after by a long-term enhancement within the adjust of exchange. This impact is named after the shape of the bend that's shaped when the adjust of exchange and the esteem of a country's cash are plotted against time, which looks like a "J" shape.

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Step-by-step explanation:

the volume of a sphere is

4/3 × pi × r³

the original sphere had a radius of 3.

now, after a dilation of factor 4 the radius is 3×4 = 12.

the volume of that sphere is then

4/3 × pi × 12³ = 4/3 × pi × 1728 = 2304pi

When distributed directly proportionally among the people, using age, the result would be b) 3 years = 6,000, 7 years = 14,000, 10 years = 20,000.

First, find the total age of the people give :

= 10 + 7 + 3

= 20

To amount that would go to 10 as a directly proportional measure is:

= 10 / 20 x 40, 000

= 20, 000

The amount to 7 as a directly proportional value would be:

= 7 / 20 x 40, 000

= 14, 000

The amount to 3 would follow the same pattern :

= 3 / 20 x 40, 000

= 6, 000

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The following statements are always true regarding the given diagram having angles: m<3+m<4+m<5=180, m<5+m<6=180, m<2+m<3=m<6.

Statement 2 is always true because the sum of the three angles in a triangle is always 180 degrees.

Statement 3 is always true because the sum of the angles on a straight line is 180 degrees.

Statement 4 is always true because angles 2, 3, and 6 are opposite angles, which means they are congruent.

Thus, statements 1 and 5 are not always true. The sum of angles 3, 4, and 5 could be greater or less than the measure of angle 5. The sum of angles 2, 3, and 5 could be greater or less than the measure of angle 3.

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The unknown angle in the cyclic quadrilateral is as follows:

m∠DGF = 75 degrees

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle.

The sum of angles in a cyclic quadrilateral is 360 degrees.

Therefore, let's the angle m∠DGF as follows:

The opposite angles of a cyclic quadrilateral have a total of 180°.

4x + 7 + 8x - 31 = 180

12x  - 24 = 180

12x = 180 + 24

12x = 204

divide both sides by 12

x = 204 / 12

x = 17

Hence,

m∠DGF = 4x + 7 = 4(17) + 7 = 68 + 7 = 75 degrees

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Answer:

Carlos did 49 more jumping jacks than John.

Step-by-step explanation:

Carlos = 138

John = 89

138 - 89 = 49

Answer:-30c

Step-by-step explanation:

you subtract 8 from 3c which is -5c than multiply by 6 which is -30c

Answer: B) 1/2

Step-by-step explanation: Hope this helps! :)

The answer is 1/3. I looked it up on gpt and also got a 100 on this quiz

1.) [tex]6p=30[/tex]

2.) Sebastian bought a pack of 30 mechanical pencils and plans to give the same number of pencils each to 6 friends.

Let a varible such as p be the number of pencils given by him to each students.

Now we need to find p we need to divide 30 by 6, we get

[tex]p = \frac{30}{6}[/tex]    

 [tex]to[/tex]

[tex]6p = 30[/tex]

Thus, the equation can he use to find p, the number of pencils each friend will receive is: [tex]6p = 30[/tex]

Answer:

[tex]6p = 30[/tex]

Step-by-step explanation:

3dxnn have's the explanation.

The original sample box had a volume of 343 cubic cm, which is half the volume of the new sample box.

Since the height of the new sample box is twice as long as the original box, its height will be 2×7=14 cm.

The length and width remain the same at 7 cm.

The volume of the new sample box is given by the formula:

V = lwh

Substituting the values, we get:

V = (7)(7)(14) = 686 cubic cm

Therefore, the volume of the new sample box is 686 cubic cm.

Comparing the volumes of the two boxes, we see that the new sample box has a larger volume than the original sample box.

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The perimeter of the shape above is 22.22 units

the area of the shape above is 26 square units

We can see from the diagram shown, that the shape is made up of a semicircle below and a triangle above.

Now, the formula for calculating the area of a triangle is expressed as;

A = 1/2bh

Such that the parameters are;

Now, substitute the values

Area = 1/2 × 7 ×6

Multiply the values

Area = 42/2

Area = 26 square units

The formula for perimeter of a triangle is;

Perimeter = (a + b + c)

Perimeter = 6 + 7 + 9. 22

Add the values

Perimeter = 22. 22 units

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Answer: the visitor would save $8 with the coupon.

Step-by-step explanation: 10% of $80 = 0.1 x $80 = $8

The data presented shows the growth of the Javanese gibbon population on three different islands over time.

Data trends must be analyzed to determine the type of function that is modeling population growth. A common way to do this is to plot the data points and observe the shape of the curve. However, since the table only contains data, you can analyze trends by looking at the differences between consecutive terms.

To do this, we can calculate the first difference and the second difference in the population data.

The first difference:

- Swing: 40 - 30 = 10, 50 - 40 = 10, 60 - 50 = 10

Example: 60 - 50 = 10, 75 - 60 = 15, 90 - 75 = 15

- Salavati: 80 - 60 = 20, 100 - 80 = 20, 120 - 100 = 20

The second difference:

- Batanta: 10 - 10 = 0, 10 - 10 = 0

- Example: 15 - 10 = 5, 15 - 15 = 0

- Salavati: 20 - 20 = 0, 20 - 20 = 0

The first difference is constant for each island and shows a linear relationship between time and population growth. Also, the second difference is zero, indicating a constant rate of change.

Therefore, we can conclude that the population growth modeling function is a linear function that can be written as

M(x) = mx + b

where x is the time in years, m is the slope (population growth rate), and b is the y-intercept (initial population).

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The solution to the multiplication of both functions is:

2x³ - x² - 4x + 3

To multiply a function by another function, multiply their outputs. For example, if f (x) = 2x and g(x) = x + 1, then fg(3) = f (3) × g(3) = 6 × 4 = 24. fg(x) = 2x(x + 1) = 2x² + x.

We are told that the domain for f(x) and g(x) is the set of all real numbers.

The functions are given as:

f(x) = 2x² + x - 3

g(x) = x - 1

Thus:

f(x) · g(x) = (2x² + x - 3) * (x - 1)

= 2x³ + x² - 3x - 2x² - x + 3

= 2x³ - x² - 4x + 3

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The total number of employees in the company is 297 if  ratio of union members to nonunion members working for a company is 4 to 7

The given ratio of union members to nonunion members, which is 4 to 7. This means that for every 4 union members, there are 7 nonunion members.

We are also given that there are 108 union members working for the company.

The total number of employees in the company be "x".

Let us from a proportional equation

4/11 = 108/x

To solve for x, we can cross-multiply and simplify:

4x = 1188

x = 297

Therefore, the total number of employees in the company is 297.

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The x-intercepts represent a zero profit.

The maximum value of the graph represents the maximum profit.

The function increases up till the vertex and decreases after it.

This means that the profit increases as it reaches the peak at the vertex.

It decreases after the vertex up till it reaches zero.

On the left of the first zero and on the right of the second zero, the profits are negative.

An approximate average rate of change of the graph from x = 3 to x =5 represents the reduction in profit from 3 to 5

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Answer: See attached.

Step-by-step explanation:

     First, we will create an equation with the slope given.

y = [tex]\frac{3}{4}[/tex]x + b

     Then, we will substitute this value in and solve for b (our y-intercept). Then we will graph the equation.

y = [tex]\frac{3}{4}[/tex]x + b

(-1) = [tex]\frac{3}{4}[/tex](-4) + b

-1 = -3 + b

b = 2

     Our final equation:

           y = [tex]\frac{3}{4}[/tex]x  + 2

     See attached for the graph. We will plot the point (0, 2) for our y-intercept and then move 3 units up for every four units right, according to the slope.

Answer:

cmon man

Step-by-step explanation:

We want to show that sinθ cosθ = cotθ is not true for all values of θ. To do this, we just need to find one counterexample, i.e., one value of θ for which the equation is not true.

Recall that cotθ = cosθ/sinθ. So, the equation sinθ cosθ = cotθ can be rewritten as sinθ cosθ = cosθ/sinθ.

Multiplying both sides by sinθ, we get:

sin^2θ cosθ = cosθ

Dividing both sides by cosθ, we get:

sin^2θ = 1

Taking the square root of both sides, we get:

sinθ = ±1

So, we need to find a value of θ such that sinθ is equal to ±1. This occurs when θ = π/2 + kπ, where k is an integer.

Now, let's check whether sinθ cosθ = cotθ is true for this value of θ. We have:

sin(π/2 + kπ) = ±1

cos(π/2 + kπ) = 0

cot(π/2 + kπ) = undefined (since cos(π/2 + kπ) = 0)

Therefore, sinθ cosθ = cotθ is not true for θ = π/2 + kπ, and we have found a counterexample. This shows that sinθ cosθ = cotθ is not a trigonometric identity.

The figure that has two more faces than a rectangular prism is a Square pyramid.

There are precisely six faces that a rectangular prism contains, which consists of a pair of identical rectangles for its top and bottom planes as well as four lateral faces consisting of corresponding right-angled, congruent rectangles. Hence, a solid figure that has two more sides than the aforementioned rectangular prism could only have eight total faces without exception.

An example of such an entity is a square pyramid whose base constitutes of four equal-length sides with four corresponding triangular surfaces converging at one single vertex on the summit's tip. Within this context, it possesses five faces (one square and four isosceles triangles), thus exceeding by two faces compared to the former geometric model.

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