Greg is making dessert for his family. Each serving requires ⅕ tablespoon of vanilla. Greg needs to make 6 servings. How many tablespoons of vanilla does he need?

The probability that 9% or less of the people sampled are left-handed is 0.377.

Using the terms proportion, probability, and considering the constraint of 200 words, I'll provide you with an answer to your question.
The proportion of left-handed people worldwide is believed to be 10%. In a random sample of 128 Americans, you want to find the probability that 9% or less of them are left-handed.
To calculate this probability, we can use the normal approximation to the binomial distribution. First, we find the mean (μ) and standard deviation (σ) for a binomial distribution:
μ = n * p = 128 * 0.1 = 12.8
σ = √(n * p * (1-p)) = √(128 * 0.1 * 0.9) ≈ 3.24
Next, we convert the desired proportion of 9% to the number of people, which is 0.09 * 128 ≈ 11.52. Now, we'll find the z-score:
z = (x - μ) / σ = (11.52 - 12.8) / 3.24 ≈ -0.396
Finally, we use the standard normal distribution table or a calculator to find the probability associated with this z-score. The probability of having 9% or less left-handed people in the sample is approximately 0.346 or 34.6% when rounded to 3 decimal places.

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Answer:

d

Step-by-step explanation:

Identify the slope of the line given in the table: -3/2

Identify the slipe of the line given in the graph: 2/3

Which linear function has a negative slope? Table

Which linear function has the steeper slope? Table

The average of any two numbers always falls between those two numbers.

So one number between 0.65340 and 0.65345 could be

(0.65340 + 0.65345)/2 = 1.30685/2 = 0.653425

You can also compare the first several digits of the two numbers:

0.65340

0.65345

They both have the same digits up to the 5th digit after the decimal point. So you can get any number between them by incrementing (increasing by 1) the last digit to get e.g. 0.65341, or tack on any number of more digits to get a number larger than 0.65340, like 0.635401 or 0.63540000123, etc.

The probability that the X is between 72 and 84 is 0.340 , the correct option is (d) .

In the question ,

it is given that ,

The random variable X is said to be normally distributed  ,

the mean is given as , μ = 70 , and

standard deviation of normal distribution is  (σ) = 10

probability that X is between 72 and 84 is written as P(72 < X < 84)

= P((72 - 70)/10 \(<\) Z \(<\) (84 - 70)/10)

= P(0.2 < Z < 1.4)

= P(0 \(<\) Z \(<\) 1.4) – P(0 \(<\) Z \(<\) 0.2)

From the z table , we get the values as

= 0.4192 – 0.0793

= 0.3399

≈ 0.340

Therefore , The probability that the X is between 72 and 84 is 0.340 , the correct option is (d) .

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Answer:

163.5 meters in one second

Step-by-step explanation:

54.5 = 1/3m

multiply both sides by 3:

163.5 = m

If we take a sample of 50 students from your school and measure their height , then (c) The mean of the sample data. will be a Random Variable .

A Random Variable is a defined as a variable whose value depends on the outcome of a random event.

Option (c) : the random event is the selection of 50 students from the school to measure their height. The mean height of this sample of 50 students is a random variable because it can vary depending on the specific students who are selected.

Option (a) : The true mean height of all students from your school is a population parameter and is a fixed value, so it cannot be called as a random variable.

Option (b) : The mean of the sampling distribution of mean heights for samples of size 50 is a population parameter as well, and it represents the average of all possible sample means of size 50 taken from the population. So,  it is a fixed value and not a random variable.

Therefore , The mean of the sample data will be a random variable .

The given question is incomplete , the complete question is

Suppose you take a sample of 50 students from your school and measure their height.  Which one of the following is a random variable?

(a) The true mean height of all students from your school.

(b) The mean of the sampling distribution of mean heights for samples of size 50.

(c) The mean of the sample data.

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The Solution:

Representing the problem in a diagram:

We are asked to find the length a.

Applying the Pythagorean Theorem, we get

Taking the square root of both sides, we get

Therefore, the correct answer is 7

The domain of the function is given as follows:

x > 0.

The function in this problem is defined for values of x to the right of x = 0, hence the domain is given as follows:

x > 0.

The graph is given by the image presented at the end of the answer.

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Answer:

\(\huge\boxed{\sf Option \ D}\)

Step-by-step explanation:

\(\displaystyle =\frac{36}{25} \\\\\)

36 and 25 have no common factor as:

and

So, No factor can be cancelled out and thus, the expression can not be simplified further. So, It will remain the same.

\(\rule[225]{225}{2}\)

Answer:

d

Step-by-step explanation:

i did it

The radius of convergence is 1.

The interval of convergence is [8, 10).

We can use the ratio test to find the radius of convergence, r:

The series converges if the limit is less than 1, which gives us:

|x - 9| < 1

So, the radius of convergence is 1.

To find the interval of convergence, we need to test the endpoints of the interval [8, 10].

For x = 8, the series becomes:

∑ (8 - 9)^n = ∑ (-1)^n

which is an alternating series that converges by the alternating series test.

For x = 10, the series becomes:

∑ (10 - 9)^n = ∑ 1^n

which is a divergent series.

Therefore, the interval of convergence is [8, 10), which includes the endpoint x = 8 and excludes the endpoint x = 10. In interval notation, this can be written as [8, 10).

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Answer:

  ia) center: (0, 0), the origin

  ib) angle: 90°

  ic) direction: CCW

  ii) LM ≅ L'M', ∠L ≅ ∠L'

  iii) (2, 1)

Step-by-step explanation:

A rigid transformation preserves size and shape of a figure, so the image is congruent to the original. The rigid transformations are rotation, reflection, and translation. Each has characteristics that allow one to determine the nature of the transformation(s) involved.

__

angle and direction

One way to determine the angle and direction of rotation of a figure is to compare a horizontal segment on the original with the corresponding segment on the image. Here, a convenient segment is NM, which is horizontal and points to the right. Its angle relative to the direction of the +x axis is 0°.

The transformed segment N'M' points upward, at an angle relative to the +x axis of 90°. This tells you the figure was rotated 90° in the CCW direction. (This is fully equivalent to a rotation of 270° in the CW direction.)

center

Points in a rotated image always remain at the same distance from the center of rotation as the original points. In most cases, the center of rotation is the origin. We can check to see if that is the case by looking at the distances of a couple of points from the origin.

  N is at coordinates (1, 1), so is √(1² +1²) = √2 from the origin

  N' is at coordinates (-1, 1), so is √((-1)² +1²) = √2 from the origin

  L is at coordinates (1, 3), so is √(1² +3²) = √10 from the origin

  L' is at coordinates (-3, 1) so is √((-3)² +1²) = √10 from the origin

This confirms that the origin is the center of rotation.

__

Since each point and its image are on a circle centered at the center of rotation, the line between them is a chord of that circle. The perpendicular bisector of that chord goes through the center of rotation. Here, we observe that the perpendicular bisector of NN' is the y-axis. The perpendicular bisector of LL' is a line with slope -2 through (-1, 2). It will intersect the y-axis at the origin, confirming the origin as the center of rotation.

__

A rigid transformation preserves lengths and angles, so any length or angle on the rotated figure is congruent to the original:

 LM ≅ L'M', MN ≅ M'N', NL ≅ N'L'

  ∠L ≡ ∠L', ∠M ≡ ∠M', ∠N ≡ ∠N'

__

The components of a translation vector add to the corresponding coordinates of a point.

  L +v = L'

  (1, 3) +(1, -2) = (2, 1) . . . image of point L

Angles TRS and TRV are supplementary, that is,

m∠TRS + m∠TRV = 180°

(25x + 30) + (5x) = 180

(25x + 5x) + 30 = 180

30x = 180 - 30

x = 150/30

x = 5

Angles TRV and WRS are vertical angles, then they are congruent, that is,

m∠TRV = m∠WRS

5x = m∠WRS

5*5 = m∠WRS

25° = m∠WRS

Answer:

The independent variable is m (the number of miles driven), and the dependent variable is "e" (the cost)

Step-by-step explanation:

Notice that the cost "depends" upon the number of miles driven, therefore, the cost (identified with the letter "e") is the dependent variable which depends upon the number of miles driven (and which is the independent variable identified with the letter "m")

Answer: The independent variable is m (number of miles) and the dependent variable is e (the cost).

Step-by-step explanation:

In this situation, if you were to graph the equation on the number line ,

M will be the x and e will be the y.And we know most of the time that x is independent in that situations and y is dependent.

The cost of depends on how many miles travelled.If the cost will go up it depends on how many miles.

The broadcasters sold 68 ad slots for $152 million, resulting in a total revenue of $152 million. To find the mean price per ad slot, divide the total revenue by the number of ad slots sold. The formula is μ = Total Revenue / Number of Ad Slots sold, resulting in a mean price of $2.2 million.

For a large sporting event, the broadcasters sold 68 ad slots for a total revenue of $152 million. The task is to find the mean price per ad slot. The mean price per ad slot was $2.2 million. (Round to one decimal place as needed.)The formula for the mean of a sample is given below:

μ = (Σ xi) / n

Where,μ represents the mean of the sample.Σ xi represents the summation of values from i = 1 to i = n.n represents the total number of values in the sample.

The mean price per ad slot can be found by dividing the total revenue by the number of ad slots sold. We are given that the number of ad slots sold is 68 and the total revenue is $152 million.

Let's put these values in the formula.

μ = Total Revenue / Number of Ad Slots sold

μ = $152 million / 68= $2.23529411764

The mean price per ad slot is $2.2 million. (Round to one decimal place as needed.)

Therefore, the mean price per ad slot is $2.2 million.

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Answer:

1 is m and b

2 is two order pars

3 is one set of ordered pars

Step-by-step explanation:

Answer:

Use the two ordered pairs to find the slope, m . Then substitute the slope, and one set of ordered pairs into y = mx + b to solve for b.

Step-by-step explanation:

Slope is m in the equation.

You need one set of ordered pairs to solve for the y-intercept.

The y-intercept is b in the equation.

Hope it helps!

Answer:distributive

Step-by-step explanation:

Question 13. The exact answer of the congruent angle of ∠4 is ∠3, ∠7, ∠8 so the option d is correct.

Question 14. y-coordinate of the mid point of WU is b. -1.5

Congruent angles are angles that have the same measure or degree of opening. Two angles are said to be congruent if they have the same size and shape, regardless of their orientation or position.

Congruent angles are important in geometry because they can be used to prove that two shapes are similar or congruent. When two triangles have congruent angles, their corresponding sides are proportional, and the triangles are similar. When two polygons have congruent angles and sides, they are congruent.

The symbol used to represent congruent angles is ≅, which means "is congruent to"

For example, if angle A is congruent to angle B, it can be written as ∠A ≅ ∠B.

The congruent angle of ∠4 is the same angle as ∠3, ∠7, ∠8 so the option d is correct.

Describe question 14.

In a plane, the point that is exactly halfway between two points is the midpoint of a line segment. It is the same distance from each straight line segment's endpoints.

The y-coordinate of the mid point of WU is b. -1.5

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Answer:

A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle.

Step-by-step explanation:

Hope this helps

Have a nice day :)

Answer:

A 3-4-5 right triangle is a triangle whose side lengths are in the ratio of 3:4:5. In other words, a 3-4-5 triangle has the ratio of the sides in whole numbers called Pythagorean Triples.

Step-by-step explanation:

Hope that this helps! :)

The capacity of the smaller container is 352 ml. Their volumes are related by the cube of their corresponding linear dimensions.

Since the two containers are mathematically similar, their volumes are related by the cube of their corresponding linear dimensions. Let V1 be the volume of the smaller container and V2 be the volume of the larger container. Let h1 and h2 be the heights of the smaller and larger containers, respectively. Then we have:

V1/V2 = (h1/h2)^3

We know that h1 = 30cm and h2 = 75cm, and V2 = 5.5 litres = 5500 ml. Substituting these values, we get:

V1/5500 = (30/75)^3

V1/5500 = 0.064

Multiplying both sides by 5500, we get:

V1 = 352 ml

Therefore, the capacity of the smaller container is 352 ml.

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Answer:

Step-by-step explanation:

13. 2/3

14. 0

15. 5/2

The expression to represent the cost for any number of people is  $50 + ($9 × x)

The trampoline park charges a fee of $50 to reserve the place. This means that, no matter how many people are going to visit the park, you will have to pay this flat fee of $50 to reserve the place. This fee is fixed and doesn't change with the number of people who will be visiting the park.

In addition to the reservation fee, the park charges $9 per person. So, if there is only one person visiting the park, you will have to pay $50 + $9 = $59. If there are two people visiting the park, you will have to pay $50 + ($9 × 2) = $68. If there are three people visiting the park, you will have to pay $50 + ($9 × 3) = $77, and so on.

To represent the total cost for any number of people, we can use the variable "x" to represent the number of people visiting the park. Then, we can express the total cost as:

Total Cost = Reservation Fee + (Cost per person × Number of people)

Total Cost = $50 + ($9 × x)

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The given question is incomplete, the complete question is:

The trampoline park charges for $50 to reserve the place and then $9 per person. Write an expression to represent the cost for any number of people.

Answer:

70 degrees

Step-by-step explanation:

there are multiple ways, as all the trigonometric functions are related.

let's try it this way :

consider the missing side to be the radius of a circle.

then 41 would be the cos value of the angle (multiplied by that radius, of course).

so, let's calculate the missing side per Pythagoras

c² = a² + b² = 113² + 41² = 12769 + 1681 = 14450

c = 120.21

and now

41 = cos(?) × 120.21

cos(?) = 41/120.21 = 0.341...

? = 70.0576... ≈ 70 degrees

Answer:

70°

Step-by-step explanation:

tangent θ = (opposite side / adjacent side)

tangent θ = (113 / 41)

θ = arctan (113 / 41)

θ = 70.0576°

*Note: "arctan" is the same as "inverse tangent"

**Note: "soh-cah-toa" (and "cho-sha-cao" for sec, csc, & cot) is an easy mnemonic device to remember the trig functions (sin, cos, & tan) and their relations to the sides of a given angle.

The first four terms of the sequence are:

a1 = 2

a2 = 2 - 3 = -1

a3 = -1 - 3 = -4

a4 = -4 - 3 = -7

The sequence defined by the rule an = 2, if n = 1; an-1-3, if n > 1, starts with the first term being 2. For all subsequent terms, the value of the previous term is subtracted by 3. Therefore, the second term of the sequence is -1 (2-3), the third term is -4 (-1-3) and fourth term is -7 (-4-3). This pattern of subtracting 3 from the previous term will continue for all subsequent terms in the sequence. The sequence can be represented by the function an = 2 - 3(n-1) for any natural number n.

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Answer:

HCl + CsOH --> CsCl + H2O

So the ions making up the salt: Cl- and Cs+

Answer:

H+

H3O+

C. Cl-

D.Cs+

OH-