What is the value of y?

Using the formula of Simple Interest, the value for the principal amount is obtained to be P = $1333.33.

What is Simple Interest?

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

The value for Simple Interest is given as = $180

The value for rate is given as = 4.5%

The value for time is given as = 3 years

To find the value for Principal amount, follow the formula for Simple Interest -

SI = P R T/100

Where P is the principal amount, R is the rate and T is the time.

Substitute the values in the equation -

180 = (P × 4.5 × 3)/100

180 = 13.5P / 100

P = (180 × 100) / 13.5

P = 18000 / 13.5

P = 1333.33

Therefore, the value for principal amount is $1333.33.

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Answer:

A. 54 minutes

Step-by-step explanation:

Given that:

Number of people working together to clean = 3

Time taken for cleaning when 3 people are working = 90 minutes

To find:

If the number of people are increased to 5, what will be the total time taken ?

Solution:

Formula for Total work is given as following:

Total work = Total men working multiplied with Time for which they work.

i.e.

\(W = M \times T\)

Here, we are given two situations:

\(M_1\) = 3

\(T_1\) = 90 minutes

\(M_2\) = 5

\(T_2\) = ?

Here, Total work in the two situations is same.

i.e. \(W_1 = W_2\)

\(3\times 90 = 5 \times T_2\\\Rightarrow T_2 = \dfrac{270}{5}\\\Rightarrow \bold{T_2 = 54\ min}\)

Therefore, the answer is:

A. 54 minutes

The time taken for 5 people to clean the same house working at the same rate is 54 minutes.

The given parameters:

The time taken for 5 people to clean the same house working at the same rate is calculated as follows.

\(no . \ of \ people = \frac{k}{t} \\\\n = \frac{k}{t} \\\\k = nt\\\\n_1 t_1 = n_2t_2\)

where;

n₁ = 3 people

n₂ = 5 people

t₁ = 90 mins

t₂ = ?

\(t_2 = \frac{n_1t_1}{n_2} \\\\t_2 = \frac{3 \times 90 \min}{5} \\\\t_2 = 54 \min\)

Thus, the time taken for 5 people to clean the same house working at the same rate is 54 minutes.

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Answer:

1). g(-9) = -81.914

2). Last option

Step-by-step explanation:

1). f(x) = x²

   For x = -9

   f(-9) = (-9)² = 81

   g(x) = \(\frac{32}{2x-17}\)

   g(-9) = \(\frac{32}{[2(-9)-17]}\)

           = \(\frac{32}{-35}\)

           = - \(\frac{32}{35}\)    

   (g - f)(-9) = g(-9) - f(-9)

                  = \(-\frac{32}{35}-81\)

                  = \(\frac{-32-2835}{35}\)

                  = \(-\frac{2867}{35}\)

                  = -81.914

2). The relation is not a function because this function doesn't passes a vertical line test.

Last option will be the answer.

Answer:

Step-by-step explanation:

196 = 14 x 14

The correct answer is A) smaller than.

The statement refers to the concept of the Central Limit Theorem (CLT). According to the CLT, when random samples are drawn from a population, the distribution of sample means will tend to follow a normal distribution, regardless of the shape of the population distribution, given that the sample size is sufficiently large. This means that as the number of samples increases, the variability of the distribution of sample means will decrease.

In this case, drawing 1,000 samples of size 100 from a population and computing the mean of each sample implies that we have a large number of sample means. Due to the CLT, the distribution of these sample means will have less variability (smaller standard deviation) compared to the variability of the raw scores in any one sample. Thus, the variability of the distribution of sample means will tend to be smaller than the variability of the raw scores in any one sample.

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Answer:

It's 21

Step-by-step explanation:

Multiply the base and the height

Answer:

x₁(2x₁x₂² - x₂ - 3) - 3x₂

Step-by-step explanation:

The expression you provided is a polynomial in two variables, x₁ and x₂. Let's simplify it step by step:

2x₁²x₂² - x₁x₂ - 3x₁ - 3x₂

To simplify, we can look for common terms that can be factored out:

x₁(2x₁x₂² - x₂ - 3) - 3x₂

Now let's simplify the expression inside the parentheses:

2x₁x₂² - x₂ - 3

The arc from B to D passing through C measures 70 degrees.

Angle CDA measures 100 degrees.

The sum of the measures of the arcs from A to C, one passing through B and the other passing through D, is 360 degrees.

quadrilateral inscribed in a circle. Let's go through each statement and determine if it is true or false:

a. The arc from B to D passing through C measures 70 degrees.

This statement is true. The arc from B to D passing through C does measure 70 degrees.

b. Angle BCD measures 140 degrees.

We don't have enough information to determine the measure of angle BCD. This statement cannot be determined as true or false based on the given information.

c. The arc from A to C passing through D measures 200 degrees.

We don't have enough information to determine the measure of the arc from A to C passing through D. This statement cannot be determined as true or false based on the given information.

d. Angle CDA measures 80 degrees.

This statement is false. We can see that angle CDA measures 100 degrees in the diagram, not 80 degrees.

e. Angle CDA measures 100 degrees.

This statement is true. Angle CDA does measure 100 degrees according to the diagram.

f. The sum of the measures of the arcs from A to C, one passing through B and the other passing through D, is 360 degrees.

This statement is true. In a circle, the sum of the measures of the arcs formed by two intersecting chords is equal to 360 degrees. In this case, the arcs from A to C passing through B and D add up to 360 degrees.

To summarize, the true statements are:

The arc from B to D passing through C measures 70 degrees.

Angle CDA measures 100 degrees.

The sum of the measures of the arcs from A to C, one passing through B and the other passing through D, is 360 degrees.

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The kind of sample that is described is a random sample. A random sample is a type of probability sampling method where every member of the population has an equal chance of being selected for the sample.

In this case, the news reporter selected a random sample of kids and a random sample of adults at the family amusement park, which means that every kid and every adult had an equal chance of being selected to participate in the survey. Random sampling is important because it ensures that the sample is representative of the population, which allows for more accurate and generalizable conclusions to be drawn from the results.

By selecting a random sample, the news reporter can report on the experiences of a diverse group of individuals at the amusement park.

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Answer:

C

Step-by-step explanation:

We'll have to use trigonometry for this.

First, note that in right triangle ABC, if we look from the perspective of angle A, the opposite side is x, the adjacent side is y, and the hypotenuse is 18.

In order to find x, then, we must use sine, which is opposite/hypotenuse. So:

sin(A) = sin(60) = opposite/hypotenuse = x/18

sin(60) is equal to (√3)/2, so multiplying both sides by 18 gives:

[(√3)/2] * 18 = 9√3

Already, we can tell that the answer is likely C, but let's find y to make sure.

We will use cosine to find y because cos = adjacent/hypotenuse.

cos(A) = cos(60) = adjacent/hypotenuse = y/18

cos(60) = 0.5, so multiplying both sides by 18 gives:

0.5 * 18 = 9

So, y = 9.

Thus, C is our answer.

~ an aesthetics lover

Answer:

C

Step-by-step explanation:

Using the cosine/ sine ratio in the right triangle and the exact values

cos30° = \(\frac{\sqrt{3} }{2}\) and sin30° = \(\frac{1}{2}\) , then

cos30° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{BC}{AC}\) = \(\frac{x}{18}\) = \(\frac{\sqrt{3} }{2}\) ( cross- multiply )

2x = 18\(\sqrt{3}\) ( divide both sides by 2 )

x = 9\(\sqrt{3}\)

----------------------------------------------------------

sin30° = \(\frac{opposite}{hypotenuse}\) = \(\frac{AB}{AC}\) = \(\frac{y}{18}\) = \(\frac{1}{2}\) ( cross- multiply )

2y = 18 ( divide both sides by 2 )

y = 9

Thus

x = 9\(\sqrt{3}\) and y = 9 → C

Answer:

The Area of the regular polygon=65.35 inches²

Step-by-step explanation:

We are given:

Length of side of polygon = 10 inches

Apothem = 13.07

We need to find area of the regular polygon.

The formula used is: \(Area \of \ the \ regular \ polygon=\frac{1}{2}\times (apothem) \times(Perimeter) \\\)

\(Perimeter = Sum \ of \ length \ of \ all \ sides\)

The polygon has 8 sides. so,

\(Perimeter = 10+10+10+10+10+10+10+10\\Perimeter = 80\)

Now, finding area of Polygon

\(Area \of \ the \ regular \ polygon=\frac{1}{2}\times (apothem) \times(Perimeter) \\\\Area \of \ the \ regular \ polygon=\frac{1}{2}\times (13.07) \times(10)\\Area \of \ the \ regular \ polygon=\frac{1}{2}\times (130.7)\\Area \of \ the \ regular \ polygon=65.35 \ inches^2\)

So, the Area of the regular polygon=65.35 inches²

Answer:

\(V=210\ cm^3\)

Step-by-step explanation:

The legs measuring 10 cm and 14 cm.

The height of the pyramid is 9 cm.

We need to find the volume of the pyramid. The formula for the volume of a right pyramid is given by :

\(V=\dfrac{1}{3}Bh\)

Where

B is area of base,

\(B=\dfrac{1}{2}\times 10\times 14=70\ cm^2\)

Put all the values,

\(V=\dfrac{1}{3}\times 70\times 9\\\\V=210\ cm^3\)

So, the volume of the right pyramid is equal to \(210\ cm^3\).

The ratio of successive terms in the sequence is 1/2, 6, 4. Hence, this sequence does not have a common difference/ratio. Sequence refers to a set of numbers in a particular order with a rule governing the manner in which the numbers appear.

The sequence given is {1/6, 1/12, 1/2, 2}. Since this sequence is not consecutive, we cannot use the common difference. We can, however, use the ratio to determine the next terms in the sequence. Let us determine the ratio of successive terms in the sequence: {(1/12) / (1/6)} = 1/2{(1/2) / (1/12)} = 6{(2) / (1/2)} = 4

The ratio of successive terms in the sequence is 1/2, 6, 4. Hence, this sequence does not have a common difference/ratio. Sequence refers to a set of numbers in a particular order with a rule governing the manner in which the numbers appear. A sequence is a group of things, events, or numbers that are arranged in a specific order or following a definite rule. A sequence can be made up of numbers, letters, or any other things that follow a pattern. The ratio of a sequence refers to the quotient of successive terms in the sequence. The ratio of successive terms is constant for a geometric sequence while the difference is constant for an arithmetic sequence.

A common difference is a constant difference between successive terms in an arithmetic sequence. This means that the common difference is the number you add or subtract to get to the next term in the sequence. An example of an arithmetic sequence is {1, 3, 5, 7, 9} where the common difference is 2. This means that you add 2 to the previous term to get to the next term in the sequence. A common ratio, on the other hand, is the quotient of successive terms in a geometric sequence. The common ratio is the number that you multiply or divide by to get to the next term in the sequence. For example, {2, 4, 8, 16, 32} is a geometric sequence with a common ratio of 2. This means that you multiply each term by 2 to get to the next term in the sequence. In the given sequence {1/6, 1/12, 1/2, 2}, since the sequence is not consecutive, we cannot use the common difference. We can, however, use the ratio to determine the next terms in the sequence. The ratio of successive terms in the sequence is 1/2, 6, 4. Hence, this sequence does not have a common difference/ratio.

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Solution

We can create the following plot:

Part 1

From this case we can see in the figure that the maxium number of circular rugs are 6

The total area is given by:

A= 12ft * 18 ft= 216 ft2

And the area for a single rug is:

Then the area for the 6 rugs is:

And rounding to the nearest square foot we got:

170 ft2

Part 2

The remaining space would be given by:

R= 216-170 ft2= 46ft

Step-by-step explanation:

m<1=41

m <2=85

m<3=95

m<4=85

m<5=36

m<6=49

m <7=106

Answer:

It should be 49.7 degrees F.

Step-by-step explanation:

Thank you and have a great day too. Also really its just 58.1 minus 1.2 7 times or 58.1 minus 1.2 times 7

1

Câu

2.

A. Soccer

B notice

C. photo

D. grocery

Math question not inserted. Cannot answer.

Step-by-step explanation:

The required answer are according to the following order,

a) France;

25/60 × 360/1 = 150°

b) Spain;

18/60 × 360/1 = 108°

c) Greece;

15/60 × 360/1 = 90°

d) Other;

2/60 × 360/1 = 12°

What do you mean by sum of angles?

We know that the sum of angles in a triangle is 360°. The question requires us to find the angle that corresponds to each of the given holiday destinations. We shall now proceed as follows:

The angle subtended is obtained from number of people that chose a particular location.

a) France;

25/60 × 360/1 = 150°

b) Spain;

18/60 × 360/1 = 108°

c) Greece;

15/60 × 360/1 = 90°

d) Other;

2/60 × 360/1 = 12°

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Answer:

<1=33, <2=90, <3=57

Step-by-step explanation:

Lines A and B are parallel lines. Find the measures of angles 1,2, and 3.

The volume of a cone with the same radius and height as the cylinder is 26 cm³.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

Its volume is expressed as;

V = πr²h

Also, the volume of cone is expressed as;

V = (1/3)πr²h

Hence;

Volume of a cone = (1/3) × Volume of cylinder.

Given the data in the question;

Volume of a cone = (1/3) × Volume of cylinder

Volume of a cone = (1/3) × 78 cm³

Volume of a cone = 26 cm³.

The volume of the cone is 26 cubic centimeters.

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Answer:

Parentheses

Step-by-step explanation:

These are used to single out a part of an equation, and most times you solve the equation in these before you solve anything else.

Answer:

4k - 12

Step-by-step explanation:

k + k + k + k - 12

4k - 12

It's 4k because you're adding and not multiplying

If you were multiplying it would be k^4

Using Simpson's rule with 4 subintervals, the length of the curve is approximately 4.2011 units.

Using Simpson's rule, the formula for approximating the length of each subinterval.

Divide the interval [1, 2] into smaller subintervals. Let's choose a value of n = 4, which means we will have 4 subintervals.

The subinterval width, h, is calculated as (2 - 1) / n = 1/4 = 0.25.

The subinterval endpoints will be:

x0 = 1.00

x1 = 1.25

x2 = 1.50

x3 = 1.75

x4 = 2.00

Calculate the function values for each endpoint. Substituting the x-values into the equation y = (x³)/3 + (1/4x), we get:

y0 = (1³)/3 + (1/(41)) = 1.0833

y1 = (1.25³)/3 + (1/(41.25)) = 2.0156

y2 = (1.50³)/3 + (1/(41.50)) = 3.6250

y3 = (1.75³)/3 + (1/(41.75)) = 6.2530

y4 = (2³)/3 + (1/(4 × 2)) = 9.0000

Apply Simpson's rule to approximate the length:

L ≈ (h/3) × [y0 + 4y1 + 2y2 + 4y3 + y4]

L ≈ (0.25/3) × [1.0833 + 4(2.0156) + 2(3.6250) + 4(6.2530) + 9.0000]

L ≈ (0.25/3) × [1.0833 + 8.0624 + 7.2500 + 25.0120 + 9.0000]

L ≈ (0.25/3) × [50.4077]

L ≈ 0.0833 × 50.4077

L ≈ 4.2011

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a. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores. b. The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

(a) To find the probability that the sample mean will be within ±5 of the population mean, we can use the Central Limit Theorem (CLT) and the properties of a normal distribution.

The sample mean, is an unbiased estimator of the population mean, μ. According to the CLT, the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

     = 200 / √400

     = 200 / 20

     = 10

To find the probability that the sample mean will be within ±5 of the population mean, we can standardize the interval using the z-score:

For the lower bound (-5), the z-score is (-5 - 0) / 10 = -0.5.

For the upper bound (+5), the z-score is (5 - 0) / 10 = 0.5.

We can now use a standard normal distribution table or technology (such as a calculator or statistical software) to find the probability associated with the z-scores -0.5 and 0.5. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores.

(b) To find the probability that the sample mean will be within ±10 of the population mean, we follow the same steps as in part (a).

The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

Note: Since the question mentions rounding answers to four decimal places, please use the appropriate table or technology to obtain the precise probabilities for parts (a) and (b).

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The items in order from the greatest thickness to the least is

Item                    Thickness

Folder                 1.9 * 10⁻²

Ruler                   1.2 * 10⁻²

Dollar bill            1.0 * 10⁻⁴

Sheet of paper   8.0 * 10⁻⁵

From the question, we have the following parameters that can be used in our computation:

Item                    Thickness

Sheet of paper   8.0 * 10⁻⁵

Folder                 1.9 * 10⁻²

Dollar bill            1.0 * 10⁻⁴

Ruler                   1.2 * 10⁻²

By definition, the smaller the power; the smaller the thickness

Since -5 is less than -4, then -4 is thicker than -5

So, we have the following order

Item                    Thickness

Folder                 1.9 * 10⁻²

Ruler                   1.2 * 10⁻²

Dollar bill            1.0 * 10⁻⁴

Sheet of paper   8.0 * 10⁻⁵

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Answer: The answer would be

B. 1/2

C. 1/3

Step-by-step explanation:

The solution of the equation 6x² - x - 1 = 0 are x = 1/2 and x = -1/3 after using the quadratic formula.

Answer:

Choice 4^th

Step-by-step explanation:

Given:

1/2+3/4+7/16 = __

To Solve:

Addition equation by finding a common multiple.

Solution:

Let the blank _ be x.

Then,

1/2+3/4+7/16 = x

Flip this equation:

Now solve for x.

Hence,

1/2+3/4+7/16 = 27/16

4^th Choice is accurate.