A student was asked to find a 95% confidence interval for widget width using data from a random sample of size n = 21. Which of the following is a correct interpretation of the interval 10.6 < μ < 29.1? Check all that are correct.

A. With 95% confidence, the mean width of all widgets is between 10.6 and 29.1.
B. With 95% confidence, the mean width of a randomly selected widget will be between 10.6 and 29.1.
C. The mean width of all widgets is between 10.6 and 29.1, 95% of the time.
D. We know this is true because the mean of our sample is between 10.6 and 29.1.
E. There is a 95% chance that the mean of the population is between 10.6 and 29.1.
F. There is a 95% chance that the mean of a sample of 21 widgets will be between 10.6 and 29.1.

Answer:

y=8

Step-by-step explanation:

y=3(4)-4

y=12-4

y=8

Answer:

1. Parametrization: [tex](2\cos(t), 2\sin(t))[/tex] and [tex]t\in [0,\pi][/tex]

2. In case that [tex]t\in [0,4\pi][/tex], the desired parametrization is [tex](2\cos(\frac{t}{4}), 2\sin(\frac{t}{4}))[/tex]

Step-by-step explanation:

Consider the particle at the point (2,0) and the circle of equation [tex]x^2+y^2=4[/tex]. Recall that the general equation of a circle of radius r is given by [tex]x^2+y^2=r^2[/tex]. Then, in our case, we know that the circle has radius 2.

One classic way to parametrize the movement of a particle that starts at point (r,0) and moves in a counterclockwise manner over a circular path of radius r is given by the following parametrization [tex](r\cos(t),r\sen(t)), t\in [0, 2\pi][/tex]. Since, for all t we have that

[tex](r\cos(t))^2+(r\sin(t))^2 = r^2(\cos^2(t)+\sin^2(t)) = r^2[/tex]

If we want to draw only the upper half of the circle, we must have [tex] t\in[0,\pi][/tex].

So, with r=2 the desired parametrization is [tex](2\cos(t), 2\sin(t))[/tex] and [tex]t\in [0,\pi][/tex]. Recall that in this parametrization when t=0 the particle is at (2,0) and when t=pi the particle is at (-2,0).

In the case that we want the parameter s [tex]\in[0,4\pi][/tex] but keeping the same particle's motion, we must do a transformation. We know that if parameter t is in the interval[tex][0,\pi][/tex] we get the desired motion. Note that in this case we are multiplying this interval by 4. So, we have that s = 4t.  If we solve for the parameter t, we get that t=s/4. Then, with the parameter s in the interval [tex][0,4\pi][/tex] we get the parametrization [tex](2\cos(\frac{s}{4}), 2\sin(\frac{s}{4}))[/tex] which is obtained by replacing t in the previous parametrization.

Note that since when [tex]s=4\pi[/tex] we have that [tex]t=\pi[/tex] and that when s=0, we have t=0, then the motion of the particle is the same (it changes only the velocity in which the particle moves a cross the path).

Parametric equations for the particle's motion are x(t) = 2cos(t) and y(t) = 2sin(t), with a parameter interval from 0 to 4π radians to trace the top half of the circle x2 + y2 = 4 four times.

To find the parametric equations that describe the motion of a particle tracing the top half of the circle x2 + y2 = 4 four times, we start from the standard parametric equations for a circle with radius 2 centered at the origin: x(t) = 2cos(t) and y(t) = 2sin(t). Since the problem specifies the top half of the circle and repeats this motion four times, we adjust our parameter t to cover the desired motion from 0 ≤ t ≤ 4π.

The parametric equations for the particle's motion are then: x(t) = 2cos(t) and y(t) = 2sin(t) with the parameter interval of 0 ≤ t ≤ 4π. Here, the parameter t represents the angle of rotation in radians, where the values of t from 0 to π cover the upper semicircle and the values of t from π to 2π would cover the lower semicircle, which we're ignoring in this case. Our chosen interval ensures that the top half is traced four times.

:D XD :D XD :D XD :D XD :D XD XD XD

Answer:

[tex]36+15+15+15+15[/tex]

Step-by-step explanation:

For the surface area we need to add up all the areas in the pyramid:

Area of the base:

the base is a square, and the area of a square is given by:

[tex]a_{base}=l^2[/tex]

where [tex]l[/tex] is the length of the side: [tex]l=6[/tex], thus:

[tex]a_{base}=(6)^2\\a_{base}=36[/tex]

Area of the triangles:

one triangle has the area given by the formula:

[tex]a_{triangle}=\frac{b*h}{2}[/tex]

where [tex]b[/tex] is the base of the triangle: [tex]b=6[/tex]

and [tex]h[/tex] is the height of the triangle: [tex]h=5[/tex], thus we have the following:

[tex]a_{triangle}=\frac{6*5}{2} \\\\a_{triangle}=\frac{30}{2} \\\\a_{triangle}=15[/tex]

the expression that represents the surface area of the pyramid is:

[tex]a_{base}+area_{triangle}+area_{triangle}+area_{triangle}+area_{triangle}[/tex]

substituting our values:

[tex]36+15+15+15+15[/tex]

which is option B

Answer:

Its Option C

Step-by-step explanation:

Answer:

1,031

Step-by-step explanation:

you divide 491,787 divided into 477, you get 1,031

491,787 divided into 477 would be 1031

Answer:

80% probability of not choosing a multiple of five

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes:

In this problem, we have that:

There are 40 numbers between 1 and 40.

Multiples of 5 are: 5,10,15,20,25,30,35,40

So there are 8 numbers that are multiple of 4 and 40-32 = 8 which are not multiples of five.

So

32/40 = 0.8

80% probability of not choosing a multiple of five

Answer: the probability of not choosing a multiple of five is 0.8

Step-by-step explanation:

Probability is expressed as the ratio of the number of favorable outcomes to the total number of outcomes.

In this scenario, the total number of outcomes is 40. The multiple of 5 between 1 to 40 are 5, 10, 15, 20, 25, 30, 35, 40. The total numbers that are multiples of 5 is 8. The total numbers that are not multiples of 5 is 40 - 8 = 32

Therefore, the number of favorable outcomes is 32

Probability = 32/40 = 0.8

To find the measure of an unknown angle like angle D without a protractor, one must apply geometric or trigonometric principles based on the angle's context, such as its relation to other angles and its placement within shapes. The original question lacks specific details about angle D, making it impossible to provide a precise method for its calculation.

To find the measure of angle D without a protractor involves understanding the geometric or trigonometric principles applicable to the given situation. For instance, if angle D forms part of a straight line with another angle, the sum of both should be 180° due to the Linear Pair Postulate. In a triangle, knowing the measurements of two angles allows us to find the third, as the interior angles of a triangle always sum up to 180°. Additionally, if angle D is part of more complex figures like parallelograms, circles, or involves trigonometric functions, equations and properties specific to those shapes or functions can be used. For example, in trigonometry, the sine and cosine rules could help find unknown angles given certain side lengths or other angles.

Unfortunately, the original question does not provide enough context or specific details about angle D, such as its relation to other angles, its placement within geometric shapes, or any other condition that could determine its calculation method. Without this information, we cannot provide a step-by-step method to calculate angle D specifically.

a. As all the angles are 60° So, It is an equilateral triangle.

b. As all the angles are 30°, 60° and 90° So, It is an equilateral triangle.

Given:

Two figures are given with some given angle x and y

To find:

The measure of the unknown angles

Let the points are A B and C in this given figure

At point, A of the triangle exterior angle of the triangle is equal to the

       the interior angle which is equal to x  [by the vertically

        opposite angle]

        ∴ ∠BAC =  x

At point B of the triangle also exterior angle of the triangle is equal to the interior angle which is equal to x  [by the vertically opposite angle]

∴ ∠ABC =  x

At point C angle Y is equal to Angle X by the property of vertically  opposite angle

       ∴ ∠ACB = x

By the sum of angle of triangle property

       ∠ACB+∠ABC+∠BAC = 180°

                        x+x+x = 180°

                             3x = 180°

                                  x = 60°

As all the angles are 60° So, It is an equilateral triangle

In part b

2x +3x +x = 180 °     [angle of a straight line is 180°]

                  6x = 180 °

                  x  =  30°

By x=30 placing find all the angles

2x= 2 x 30 = 60°

3x= 3 x 30 = 90°

Answer:

6/17

Step-by-step explanation:

Answer:

The value of x is -1/2 .

Step-by-step explanation:

You have to use Logarithm Law,

[tex] {a}^{x} = y => log_{a}(y) = x[/tex]

So for this question :

[tex] log_{7}(7) = 2x + 2[/tex]

[tex]1 = 2x + 2[/tex]

[tex]2x = - 1[/tex]

[tex]x = - \frac{1}{2} [/tex]

Answer:

Negative correlation

Step-by-step explanation:

In a negative correlation, as one variable increases, the other variable decreases, and as one variable decreases, the other variable increases. In positive correlation, as one variable increases, so does the other and as one variable decreases, so does the other.

In the given question, as the number of student interruptions during class decreases, student scores on in-class quizzes increase. So, this an example of a negative correlation.

Answer:

x-coordinate of the circle's center = -2

y-coordinate of the circle's center = 5

Radius = 3

Step-by-step explanation:

Look at the picture

Answer:

What is the radius of the circle? 3

What is the x-coordinate of the circle’s center? -2

What is the y-coordinate of the circle’s center? 5

Step-by-step explanation:

Answer:

The standard deviation of the number of people who believe that the product is in fact improved is 1.50.

Step-by-step explanation:

The random variable X can be defined as the number of people who believe that a product is improved when they are told so.

The probability of a person believing that a product is improved is, p = 0.25.

A random sample of n = 8 people who are given a sales talk about a new, improved product are selected.

The event of a person believing that the product is improved is independent of others.

The random variable X follows a Binomial distribution with parameters n = 8 and p = 0.25.

The success is defined as a person believing that a product is improved.

The mean and standard deviation of a Binomial distribution is given by:

μ = n × p

σ = √[n × p × (1 - p)]

Compute the standard deviation as follows:

σ = √[n × p × (1 - p)]

  = √[8 × 0.25 × (1 - 0.25)]

  = √(2.25)

  = 1.50

Thus, the standard deviation of the number of people who believe that the product is in fact improved is 1.50.

Answer:

Check the explanation

Step-by-step explanation:

1)  The null and alternative hypothesis is ,

[tex]H_0 : \mu = 0.35[/tex]

[tex]H_a : \mu \neq 0.35[/tex]

Test statistic = t =

= [tex](T - \mu ) / s / \sqrt n[/tex]

= [tex](0.30 - 0.35 ) / 0.03 / \sqrt 20[/tex]

Test statistic = t = - 7.45

2) Solution :

The null and alternative hypothesis is

[tex]H_0[/tex] : p = 0.60

[tex]H_a[/tex] : p > 0.60

[tex]\hat p[/tex] = x / n = 25 / 60 = 0.417

P0 = 0.60

1 - P0 = 1 - 0.60 = 0.40

Test statistic = z = 0.417

= [tex]\hat p - P0 / [\sqrtP0 * (1 - P0 ) / n][/tex]

= [tex]0.417 - 0.60/ [\sqrt(0.60 *(1 - 0.60) / 80 ][/tex]

Test statistic = z = -3.34

Answer:

There is enough evidence to support the claim that the zinc concentration is higher on the bottom than the surface of the water source.

Step-by-step explanation:

We have the data

Zinc conc. bottom water (X)  | Zinc conc. in surface water (Y)

1 .430 .415

2 .266 .238

3 .567 .390

4 .531 .410

5 .707 .605

6 .716 .609

7 .651 .632

8 .589 .523

9 .469 .411

10 .723 .612

We can calculate the difference Di=(Xi-Yi) for each pair and calculate the mean and standard deviation of D.

If we calculate Di for each pair, we get the sample:

D=[0.015 0.028 0.177 0.121 0.102 0.107 0.019 0.066 0.058 0.111 ]

This sample, of size n=10, has a mean M=0.0804 and a standard deviation s=0.0523.

All the values are positive, what shows that the concentration water appearse to be higher than the concentration on the bottom.

We can test this with a t-model.

The claim is that the zinc concentration is greater on the bottom than the surface of the water source.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=0\\\\H_a:\mu> 0[/tex]

The significance level is 0.01.

The sample has a size n=10.

The sample mean is M=0.0804.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.0523.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.0523}{\sqrt{10}}=0.017[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{0.0804-0}{0.017}=\dfrac{0.08}{0.017}=4.861[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=10-1=9[/tex]

This test is a right-tailed test, with 9 degrees of freedom and t=4.861, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=P(t>4.861)=0.00045[/tex]

As the P-value (0.00045) is smaller than the significance level (0.01), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the zinc concentration is greater on the bottom than the surface of the water source.

To determine if the zinc concentration is less on the bottom than the surface of the water source, a paired t-test can be performed. The t-test helps to compare the mean difference in zinc concentrations between the bottom and surface water. By comparing the calculated t-value with the critical t-value at the α = 0.1 level of significance, we can determine if the data supports the hypothesis.

To determine if the zinc concentration is less on the bottom than the surface of the water source, we can perform a hypothesis test. We'll use a paired t-test since we have paired data. We want to test if there is a significant difference between the bottom and surface zinc concentrations.

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Answer:

The equation of the line is [tex]f\left(x\right)=-\frac{1}{9}x^{2}+1.8[/tex]

Step-by-step explanation:

I graphed the equation on the graph below and found the equation of the line.

If this answer is correct, please make me Brainliest!

Graphing the function [tex]\(f(x) = -\frac{1}{9}x^2 + 1.8\)[/tex] involves identifying the vertex, axis of symmetry, and plotting key points by selecting suitable x-values.

To graph the quadratic function [tex]\(f(x) = -\frac{1}{9}x^2 + 1.8\)[/tex], start by finding the vertex.

The vertex form [tex]\(f(x) = a(x - h)^2 + k\)[/tex] helps identify it, where \((h, k)\) is the vertex.

Here, [tex]\(a = -\frac{1}{9}\)[/tex].

The x-coordinate of the vertex is given by [tex]\(h = -\frac{b}{2a}\)[/tex] from the standard quadratic form [tex]\(ax^2 + bx + c\)[/tex], and [tex]\(b = 0\)[/tex] here since [tex]\(f(x)\)[/tex] has no linear term. So, [tex]\(h = 0\)[/tex]. Thus, the vertex is at [tex]\((0, 1.8)\)[/tex].

Next, find the axis of symmetry, which passes through the vertex. The axis of symmetry is the vertical line [tex]\(x = h\)[/tex], so in this case, [tex]\(x = 0\)[/tex].

To plot additional points, choose x-values on either side of the axis. Calculate corresponding y-values using the function.

For instance, when [tex]\(x = 3\)[/tex], [tex]\(f(3) = -\frac{1}{9}(3)^2 + 1.8\)[/tex], which equals [tex]\(1.3\)[/tex]. Repeat this process for a few more x-values.

Plot the vertex, axis of symmetry, and other points on a coordinate plane.

The resulting graph is a downward-opening parabola with the vertex as the highest point.

Label the axes, points, and use arrows to indicate the direction of opening.

This visual representation provides insight into the behavior of the function for different x-values.

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Answer:

240 ft^2

Step-by-step explanation:

area: (24+16)12/2=240 ft^2

(the area of a trapezoid is the sum of the bases multiplied by the height over 2.)

Answer:

b 24

Step-by-step explanation:

The measure of angle 3 is 24 degrees. The correct answer would be an option (B).

The complementary angles are defined as when pairing of angles addition to 90° then they are called complementary angles. There are two types of supplementary angles.

Given that the measure of angle 4 is (11 x) degrees and angle 3 is (4 x) degrees

Here, the pairing of angles sums up to 90° then they are called complementary angles.

11x + 4x = 90

15x = 90

x = 90/15

Apply the division operation, and we get

x = 6

So, angle 3 is 4 × 6 = 24 degrees

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Answer:

x=-7, x=6

Step-by-step explanation:

[tex]3x^{2} +x-14=0\\(x+7)(x-6)=0\\x=-7, x=6[/tex]

Answer:

Failure

Step-by-step explanation:

A synonym is a word that has a similar or exact same meaning as another given word. The synonym for malfunction, would therefore, be failure.

Answer:

It is failure

Step-by-step explanation:

a malfunction is a computer error. also known as a failure

Answer:

  x = 16

Step-by-step explanation:

We assume that ray BF lies between BA and BC, so that ...

  ∠ABF +∠FBC = ∠ABC

  (7x +20) +(2x -5) = 159

  9x +15 = 159 . . . .collect terms

  9x = 144 . . . . . . . subtract 15

  x = 16 . . . . . . . . . .divide by 9

Answer:

14.29% probability that Marlon's friend will think of the number 9

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that:

There are 7 numbers from 5 to 11(5,6,7,8,9,10,11)

9 is one of them

So

[tex]p = \frac{1}{7} = 0.1429[/tex]

14.29% probability that Marlon's friend will think of the number 9

9514 1404 393

Answer:

  67 cm

Step-by-step explanation:

Put 15 where m is and do the arithmetic.

  H(15) = 52 +15 = 67

The plant's height in 15 months is modeled as being 67 cm.

Answer:

5

Step-by-step explanation:

To find the Calorie content of a serving of cereal with 3 g protein, 18 g carbohydrates, and 6 g fat, multiply each by their Caloric values (4.1 Cal/g for protein and carbohydrates, 9.1 Cal/g for fat) and sum the results to get 140.7 Calories.

Calculating Calories in Breakfast Cereal

To calculate the Calorie content of a serving of the breakfast cereal described, we need to multiply the mass of each macronutrient by its respective Caloric value per gram and sum them up. The given macronutrient values per serving of the cereal are 3 grams of protein, 18 grams of carbohydrates, and 6 grams of fat. Below are the calculations:

Calories from protein = 3 g × 4.1 Cal/g = 12.3 Cal

Calories from carbohydrates = 18 g × 4.1 Cal/g = 73.8 Cal

Calories from fat = 6 g × 9.1 Cal/g = 54.6 Cal

The total Calorie content for a serving of this breakfast cereal is obtained by adding the individual Calorie contributions from proteins, carbohydrates, and fat:

Total Calorie content = 12.3 Cal + 73.8 Cal + 54.6 Cal = 140.7 Calories

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Answer: 1 .9 kilograms

Step-by-step explanation:

9.5/5=1.9

since the apples account for 4 parts, we multiply 4 times the value of 1 of the 5 parts

4x1.9=7.6

Now we subtract from the original weight of everything.

9.5-7.6=1.9

Final answer:

To calculate the weight of pears sold, subtract the weight of apples (three-fifths of the total) from the total weight of 9.2 kg, resulting in 3.68 kg of pears sold at the market.

Explanation:

The farmer sells 9.2 kilograms of apples and pears in total. To find out the weight of the pears sold, we need to first calculate the weight of the apples, which is three-fifths (3/5) of the total weight, and subtract that from the total weight.

First, calculate the weight of apples:

Then, to find the weight of the pears sold, subtract the weight of the apples from the total weight:

Therefore, the farmer sold 3.68 kilograms of pears at the farmer's market.

Answer:

20,880 x 2/5

= (20,880 x 2)/5

= (41,760)/5

= 8,352

Final answer:

To determine the acreage needed for the soccer field and facility, the fraction 2/8 is simplified to 1/4, and then 1/4 of the total land (16 acres) is calculated, resulting in 4 acres required for the soccer field and facility.

Explanation:

The question asks about a professional soccer player who has purchased 16 acres of land and wishes to use 2/8 of the land for a soccer field and facility. To find out how many acres will be needed for the soccer field and facility, we perform a simple calculation:

First, reduce the fraction 2/8 to its simplest form, which is 1/4. Then, multiply the total acreage by this fraction to determine the acreage for soccer use:

16 acres × 1/4 = 4 acres

Therefore, the soccer player will need 4 acres of land for his soccer field and facility.

Answer: your age

Step-by-step explanation:

An item which is not a factor that affects a person's automobile insurance premiums is: c. the color of your car.

An insurance company is a business firm that is establish to collect premium from all of the insured for losses which may or may not occur, so they can easily use this cash to compensate or indemnify for losses incurred by those having high risk.

here, we have,

Generally, some examples of the factors that typically determines and affects a person's automobile insurance premiums include the following;

Driving record.

Duration of car usage.

Owner's age

Location

Gender

Where owner lives.

Credit score

Year, make, and model of car.

Overall value of the car.

In conclusion, we can infer and logically deduce that the color of a car is not a factor that affects a person's automobile insurance premiums.

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Complete Question:

Which of the following is not a factor that affects your auto insurance premiums?

a year, make, and model of your car

b. where you live

c. the color of your car

d. overall value of your car