What is the measure of angle JFL?

The interest rate that would be earned each month on the amount invested is 0.47%.

When the money invested in an account earns a compound interest, it means that both the amount invested and the interest that has already being earned increases 12 times in a year. When an investment earns at a compound interest, it grows exponentially.

The formula that can be used to determine the interest rate is :

Interest rate = [(future value / amount invested)^(1/n)] - 1

Where n is the number of periods

Number of periods = number of years x compounding period

Number of periods = 13 x 12 = 156

Number of periods = [(6200 / 3000)^(1/156) ] - 1 = 0.47%

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The Perimeter of the Pentagon is 15 cm

A pentagon is a geometrical shape, which has five sides and five angles

The equation P=5s represents the perimeter P of a regular pentagon with side length s.

We are to find the perimeter of a regular pentagon with side length of 3 cm.

To find it, put s = 3 cm in the given equation.

P = 5(3) cm

P = 15 cm

Hence, the perimeter of the regular pentagon of side length 3 cm is 15 cm.

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The perimeter of a regular pentagon with side length of 3 cm is 15 cm.

A pentagon is a polygon with 5 sides. A regular pentagon is a pentagon with all sides and angles equal to each other.

The Equation P = 5s represents the perimeter P of a regular pentagon with side length s.

The perimeter of a regular pentagon with side length of 3 centimetres can be calculated as follows:
P = 5s

where

Therefore,

P = 5(3)

Perimeter of the regular pentagon = 15 cm.

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Answer:

11,520

Step-by-step explanation:

If the cost of carpeting 1 sq.m of floor is Rs 120 , what is the cost of carpeting 96 sq. m of floor​?

120 * 96 = 11,520

When there is relationship between two variable is in table it represents a function.

A function assigns only output to each input. The value that is put into a function is the input. The result is the output.

Relationships between input values and output values can also be represented using tables. The values in the first column are the input values. The values in the second column are the output values. The relationship represents a function if each input value is paired with only one output value.

For examples :

In Given table below , Since each input value is paired with only one output value, the relationship given in the above table is a function.

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We can reject the null hypothesis at the 0.05 level and accept the alternative hypothesis.

A one-sided test will test using the full alpha to test whether the result is far enough in one direction. A two-sided test will split the alpha in half to test whether the result is too big or too small.

The null hypothesis is:

[tex]\mathit{H}_{0}: \mu= 2.5[/tex]

The alternative hypothesis is:

[tex]\mathit{H}_{1}: \mu > 2.5[/tex]

The z-score for a mean of 3 is:

[tex]z = (x- \mu)/ (\sigma/ \sqrt{n})) \\ = (3-2.5)/(1.8/\sqrt{n})) \\ = (.5)/(1.8/6)) \\ = (.5)/(.3)) \\ = 1.666666667[/tex]

The z-score for the 0.05 significance level is 1.645, which is less than the mean of 3 z score of 1.67.

Hence, we can go ahead and reject the null hypothesis

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Answer:

D). x+17=32

Step-by-step explanation:

32 is the total

and Geraldine and Felicia together would get 32

so, Felicia ran D). x+17=32 in an equation

Answer:

36√3

Step-by-step explanation:

Given a=36 and ∠α=30°,

b = √c^2 - a^2

= √72^2 - 36^2

= √3888

= 62.35383 = 36√3

Thanks.

The solution to the given system of equations y=-3x-2 and 5x+2y=15  is given by the coordinates as [tex](-19,55)[/tex]

What is a System Of Equations ?

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Define Subsitution Method .

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

Define Elimination Method.

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.

The solution to the system of equations y = -3x - 2 and 5x + 2y = 15

Given:

[tex]y=-3x-2[/tex]       - (1)

[tex]5x+2y=15[/tex]       - (2)

Here we are using substitution method to proceed with the given problem ,

So,

⇒[tex]5x+2(-3x-2)=15[/tex]

⇒[tex]5x-6x-4=15[/tex]

By further calculation

⇒[tex]-x=15+4[/tex]

⇒[tex]x=-19[/tex]

Substituting x value in (1)

⇒[tex]y=(-3)(-19)-2[/tex]

By further calculation

⇒[tex]y=57-2[/tex]

⇒[tex]y=55[/tex]

Therefore, the solution is [tex](-19,55)[/tex].

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Inequality is use when we are not sure about the exact date of a given sample.

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

For example:

If the cost of a Jersy = $40

Cost of Hat = $15

The softball team has a total of $1,200 to spend.

Let x equal the number of jerseys the team orders and y equal the number of hats the team orders.

So the total money will be spent within the budget will be

40*x + 15*y ≤ $1200

Hence, the inequality model will be 40*x + 15*y ≤ $1200.

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Boxes used in one month is 221/8 as fraction.

What is mixed fraction?

A fraction portrayed with its quotient and remainder may be a mixed fraction. as an example, two 1/3 may be a mixed fraction, wherever two is that the quotient, one is that the remainder. So, a mixed fraction may be a combination of a full range and a correct fraction.

Main body:

Initial boxes with kevin = 55 1/4

converting mixed fraction in simple fraction = 55[tex]\frac{1}{4}[/tex]

= 221/4

Total boxes left = 27[tex]\frac{5}{8}[/tex]

converting it ,

=27 [tex]\frac{5}{8}[/tex] = (27*8+5)/8

=221/8

Total boxes used = 221/4 - 221/8

taking L.C.M , we get

=442-221/8

= 221/8

Hence total boxes used = 221/8

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40 x 7 = _________ x 10 x 7

280 = ? x 70

280 = 4 x 70

check: 280 = 280

4 goes in the blank

Answer:

4

Step-by-step explanation:

40×7=280

10×7=70

280:70=4

The height of the cylinder is 10.81 cm and the radius of the cylinder is 5.41 cm

The volume of the cylinder can = 1000 cubic cm

Consider the height of the cylinder as h and the radius of the base is r

Volume of the cylinder = π[tex]r^2[/tex]h = 1000

h = 1000 / π[tex]r^2[/tex]

The surface area of the cylinder

A = 2π[tex]r^2[/tex] + 2πrh

A = 2π[tex]r^2[/tex] + 2πr(1000 / π[tex]r^2[/tex] )

A = 2π ( [tex]r^2[/tex] + 1000 / π[tex]r^2[/tex])

Differentiate the terms

A' =  2π (2r + 1000 / π[tex]r^3[/tex])

When the minimum surface area

2π (2r + 1000 / π[tex]r^3[/tex]) = 0

r = [tex](1000/2\pi )^\frac{1}{3}[/tex]

r = 5.41 cm

Then,

h =  1000 / π[tex]r^2[/tex]

= 1000 / (π × 5.41 × 5.41)

= 1000 / 91.94

= 10.87 cm

Hence, the height of the cylinder is 10.81 cm and the radius of the cylinder is 5.41 cm

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The only price at which consumer and producer plans can be reconciled is the equilibrium price, which is reached when the quantity of the good that consumers wish to purchase, or quantity demanded, equals the quantity that producers wish to sell, or quantity supplied. The equilibrium quantity is the name given to this common quantity..

What is  equilibrium quantity?

What are the equilibrium quantity and price?

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The congruent postulate in which two corresponding angles and non-Included side of the two triangles are congruent is AAS. AAS is an abbreviation of angle angle side postulate.

Triangles are said to be congruent if they are of  identical sides and angles. The three sides of first triangle are exactly equal in measure to the three sides of second triangle. The three angles of first are each the same angle as the second triangle.

Triangles are said to be congruent when all corresponding sides and interior angles are congruent. The triangles will have same shape and size, but the first triangle may be a mirror image of the other triangle.  

The definition of Angle Angle Side Theorem also states that-

If two angles and the non-included side of first triangle are congruent to the corresponding parts of second triangle, then the  triangles are said to be congruent.

Other theorems which triangles follow are Side Angle Side, Side Side Angle, Angle Side Side, Side Side Side, Angle Angle Angle etc.

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In general, 62% of the values in a data set lie at or below the 62th percentile. 76% of the values in a data set lie at or above the 76th percentile. If a sample consists of 900 test scores, 504 of them would be at or below the 56th percentile. If a sample consists of 900 test scores, 540 of them would be at or above the 40th percentile.

A percentile is a comparison score among a particular score and the scores of the rest of a group. It presents the percentage of scores which a particular score surpassed. For example, if you score 85 points on a test, and are ranked in the 75th percentile, this means that the score 85 is higher than 75% of the scores. In general, percentile defines the percentage of a data set which is below or at a value which is being considered.

Thus, the percentage of the values of a data set that lies below or at the 62th percentile is 62%.

And also, the values of a data set that lies below or at the 76th percentile is 76%.

Given a sample of 900 test scores, the number of test scores that will be at or below the 56th percentile is 56% of 900 which is mathematically represented as:

n = 56% x 900

n = 56/100 x 900

n = 504 test scores

Given a sample of 900 test scores, the number of test scores that will be above the 40th percentile is (100 - 40 = 60) % of 900 which is mathematically represented as:

n = 60% x 900

n = 60/100 x 900

n = 540 test scores

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The development of information applicable to activity that upholds by the fundamental elements of scientific inquiry is referred to as practical research.

In the given question we have to define practical in research.

The development of information applicable to activity that upholds by the fundamental elements of scientific inquiry—clearly specified research questions, reliable patterns of thought, methodical data collecting and analysis, and acceptable conclusions—is referred to as practical research.

Practical research aims to advance knowledge through scientific theories, concepts, and ideas in order to benefit society. Establishing hypotheses, gathering data, evaluating, etc. all serve practical research purposes.

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After 33 minutes the diver reenter the water for a dive to 50 feet for 38 minutes.

What is eRDPML?

The Electronic Recreational Dive Planner Multi Level, or simply eRDPml, is a novel programme created by PADI to help you correctly plan your dives. FOR MANY. An electronic version of the PADI dive tables may be more convenient for certain divers than having to recall how to use them.

If a diver exits the water at 1:30 pm after a 35-minute dive to 19 metres utilising the eRDPML, he will be in pressure group P.

At 2:20 PM, he returns to the ocean. His surface interval is 50 minutes, according to this. A diver in pressure group P switches to pressure group G after 50 minutes.

He will then be in pressure group S if he stays at 17 metres for another 25 minutes. Go to the Surface Interval Mode to find out how long must be spent above the surface before the third dive.

After the second dive, join the pressure group S and start the third dive at a depth of -15 metres for 38 minutes.

33 minutes are determined to be the necessary surface interval. A 33 minute surface interval after the second dive places the diver in pressure group K before the third dive, completing the dive profile.

Hence, after 33 minutes the diver reenter the water for a dive to 50 feet for 38 minutes.

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The steps for solving inequality is consisting of four  steps which are elaborated  below :

The first step of solving an inequality is to Eliminate divisions by multiplying all terms by the slightest common denominator of all fractions, then the next step is to Simplify by combining like terms on each side of the inequality, then subtract or add quantities to get the unknown on one side and the numbers on the other, the next step is to divide each term of the inequality by the coefficient of the unknown, just  In case the coefficient is positive, the inequality will stay the same or if the coefficient is negative, the inequality will be reversed.

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Total subscribers that Netflix must sample to obtain the interval to estimate the proportion of their current subscribers who would pay extra for a premium membership including access to more movies and TV shows are 385 subscribers.

For the Wald-type confidence interval, the confidence limits are:

[tex]p-[/tex][tex]z_{\alpha /2}[/tex][tex]\sqrt{\frac{p(1-p)}{n} }[/tex] , [tex]p+[/tex][tex]z_{\alpha /2}[/tex][tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

Where p is the sample proportion attended, n is the sample size, and z∗α/2 is the upper α/2 quantile of the standard normal distribution for a 100 (1−α) % confidence interval. If a 95% CI is needed, this corresponds to α = 0.05, thus

[tex]z_{\alpha /2}[/tex] ≈ 1.96

And, the quantity

ME = [tex]z_{\alpha /2}[/tex][tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

is studied as the margin of error. Since we also need ME ≤ 0.05, we solve for n to acquire

n ≥ p (1 − p) [tex](\frac{z \alpha /2}{ME} )^{2}[/tex]

The only undetermined quantity is p; but since p (1 − p) ≤ 1/4 for all p ∈ [0,1], we identify that a sample size of at least

n ≥ [tex](\frac{z \alpha /2}{2ME} )^{2}[/tex]

undertakes the Wald interval will have a margin of error less than the needed margin no matter the sample proportion checked. Alternating the given values results in

n ≥ [tex](\frac{1.96}{2(0.05} )^{2}[/tex] = 384.16

for that we need to round up to guarantee the sample size is enough, thus n = 385.

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The company fails to reject H0, making a Type II error. So the option B is correct.

In the given question,

Mars candy company is testing one of its machines in the factory to make sure it is producing more than 98% high-quality candy (H0: p = 0.98; Ha: p > 0.98; α = 0.05).

The test results in a p-value of 0.15.

However, the company is unaware that it is actually producing 99% high-quality candy.

We have to find MOST likely happens as a result of the testing.

The given options are:

A. The company rejects H0, making a Type I error.

B. The company fails to reject H0, making a Type II error.

C. The company rejects H0, making a Type II error.

D. The company fails to reject H0, making a Type I error.

E. The company rejects H0 correctly.

The company will not be rejecting the null hypothesis when it should have been, given the P-value is approaching 0.05.

Hence, the business commits a Type II error by failing to reject H0.

So the option B is correct.

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A treaty is a series of higher-level business agreements or contracts involving two or more corporations, governments, royalty, or organizations of any kind.

Contract Basics :

To understand the basics of contracts, it is important to first know what a treaty is. Firstly, it is the first stage of a treaty, treaty, alliance, or agreement. It consists of the agreements, rights and obligations between two or more parties and the terms and conditions mutually agreed upon by all parties.

Treaties as a source of International law . The treaties are considered one of the most important sources of international law. If there is a treaty between two countries, the rights and obligations under that treaty become the laws of both countries.

The sources of international law are:

International treaty law derives from the 1969 Vienna Convention on the Law of Treaties. Treaties and their enforceability. The contract will be interpreted in accordance with international law. Types of Treaties : The treaties are classified into two he following types

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This circular swimming pool has 4595  ft³ of water in it.

According to what is said, the depth grows linearly from 2 feet at the south end to 7 feet at the north end and remains constant along east-west lines.

The given data in the question-

Diameter of  circular swimming Pool; d = 30 ft

Radius r = d/2 = 30/2 = 15 ft

The average depth is given as;

avg (h) = (4 + 9)/2

avg (h) = 6.5 ft

Formula for circular area is;

A = πr²

Put the values;

A = π × 15²

A = 225π

Formula for circular volume is;

Volume = Area × depth

Volume = 225π × 6.5

Volume = 4594.57 ft³

Rounding to a whole number;

Volume =  4595 ft³

Thus, this circular swimming pool has 4595  ft³ of water in it.

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The translation rule, T₋₃,₅ (x,y) for a given triangle on the coordinate plane can be written as

(x, y) → (x – 3, y + 5)

that is x-coordinate shifts to left on x-axis and y-coordinate shifts upward on y-axis. So, the correct option is option ( A).

Translation:

Figure translation is horizontal, vertical, or both movement of the graph or figure. Figures can be moved left, right, up, or down.

Steps to Perform a Translation on the Coordinate Plane are :

We have given that

A triangle say ABC is translated on coordinate plane according to following rule, T₋₃,₅ (x, y)

Another way to wright this is explained below. As we know that translation is represented

Tₕ,ₖ(x,y) = (x+h, y+k) which implies that x coordinate shifts to left h point and new coordinate is x+h.

Similarly, new y corrdinate will be y+k

Now, for our point ,

T₋₃,₅ (x,y) ---shifted---> ( x-3 , y+5)

=> (x, y) → (x – 3, y + 5)

Hence , the coordinates of new trangle say A'B'C' which is translation of triangle ABC with coordinates (x,y) are ( x-3 , y+5).

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Answer:

144

Step-by-step explanation:

This is the counting principle.

Multiply the numbers of the items together.

6 × 4 × 3 × 2 = 144

The point estimator for the difference between two populations proportion in favor of this product is 0.09.

In the given question, the results of a recent poll on the preference of shoppers regarding two products are shown below.

Product             Shoppers Surveyed        Shoppers Favoring this Product               a                                       800                                          560

b                                       900                                          549

We have to find the point estimate for the difference between the two population proportions in favor of this product.

n(1)=800, x(1)=560

n(2)=900, x(2)=549

P(1)=x(1)/n(1)

P(1)=0.7

P(2)=x(2)/n(2)

P(2)=0.61

The point estimator for the difference between two populations proportion in favor of this product is

P(1) - P(2)=0.7-0.61

P(1) - P(2)=0.09

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The consumer surplus is $5.

Consumer surplus is defined as the amount saved based on the estimated value and actual paid price. It is the difference between the amount that customer wants to pay and the amount that customer has to pay based on the final price.

Leon is willing to pay $10. The discount offered of $10 item is 50%. Hence, the final price will be -

Final price = 10 - 50%×10

Final price = 10 - 5

Final price = 5

Surplus amount = 10 - 5

Surplus amount = $5

Thus, the surplus amount for Leon is $5.

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The complete question is -

Determine the amount of consumer surplus generated: Leon goes to the clothing store to buy a new T-shirt, for which he is willing to pay up to $10. He picks out one he likes with a price tag of exactly $10. When he is paying for it he learns that the T-shirt has been discounted by 50%

well, clearly is 4 :).

now, if we take 25 to be the 100%, what is 4 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 25 & 100\\ 4& x \end{array} \implies \cfrac{25}{4}~~=~~\cfrac{100}{x} \implies 25x=400\implies x=\cfrac{400}{25}\implies x=16[/tex]

The array formulas are (r³ - 3) × 1 = 24, (r² + 3) × 2 = 24, (r² - 1 ) × 3 = 24, (r² - 3 ) × 4 = 24, (r) × 8 = 24, (r - 1 ) × 12 = 24, and (r - 2) × 12 = 24 where, r = 3.

The array can be taken as rows.

If we take the first side as the length denoted by L and the second side as the width indicated by W.

Then the area can be given as;

Area = length * width

Area = L * W

The total area of the quilt is 24 squares which can be obtained as;

24 × 1 = 24

All squares are arranged in a single row.

(r³ - 3) × 1 = 24

12 × 2 = 24

12 squares arranged in 2 rows.

(r² + 3) × 2 = 24

8 × 3 = 24

8 squares arranged in 3 rows.

(r² - 1 ) × 3 = 24

6 × 4 = 24

6 squares arranged in 4 rows.

(r² - 3 ) × 4 = 24

3 × 8 = 24

3 squares arranged in 8 rows.

(r) × 8 = 24

2 × 12 = 24

2 squares arranged in 12 rows.

(r - 1 ) × 12 = 24

1 × 24 = 24

1 square arranged in 24 rows.

(r - 2) × 12 = 24

In all of the above r = 3.

Thus, the array formulas are (r³ - 3) × 1 = 24, (r² + 3) × 2 = 24, (r² - 1 ) × 3 = 24, (r² - 3 ) × 4 = 24, (r) × 8 = 24, (r - 1 ) × 12 = 24, and (r - 2) × 12 = 24 where, r = 3.

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3750 tons of SO₂ are produced for one million tons of coal burned.

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