Could I get some assistance with this one? I'm a little stuck. Thank you so much! C:

ΔLMJ and ΔLKN are congruent by SAS congruence postulate.

What is SAS and ASA congruence rule for triangles?

SAS : If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

ASA : If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

According to the given question:

The pair of overlapping congruent triangles in the diagram are:

ΔLMJ and ΔLKN

Now,

LM ≅ LK (Given)

LN ≅ LJ (Given)

∠LJM = ∠LNK (Angles opposite to equal sides are equal)

∴ ΔLMJ ≅ ΔLKN by SAS congruence of triangles

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After 8 years, the amount of money which Carl would have in the bank account is equal to $620.

Mathematically, simple interest can be calculated by using this formula:

S.I = PRT or S.I = A - P

Where:

Substituting the given parameters into the simple interest formula, we have the following;

S.I = 500 × 3/100 × 8

S.I = $120.

Now, we can calculate the future value (A) as follows;

Future value (A) = P + S.1

Future value (A) = 500 + 120

Future value (A) = $620.

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Answer:

24 sides

Step-by-step explanation:

The interior angles of a polygon add up to 180(n-2) degrees, where n is the number of sides the polygon has. This means that to find the number of sides a polygon has, we can set up the following equation:

180(n-2) = 4320

Solving for n, we get:

n = (4320 + 360) / 180 = 24

Therefore, the polygon has 24 sides.

The number a has to be greater than or equal to 1000.

As per the given data we have to determine that how large the number a has to be so that [tex]$$\int_a^{\infty} \frac{1}{1+x^2} \cdot d x < 0.001$$[/tex]

[tex]$$\Rightarrow \quad\left[\tan ^{-1}(x)\right]_a^{\infty} < 0.001$$[/tex]

[tex]$\Rightarrow \quad \tan ^{-1}(x)-\tan ^{-1}(a) < 0.001$[/tex]

[tex]$$\begin{array}{ll}\Rightarrow & \frac{\pi}{2}-0.001 < \tan ^{-1}(a) \\\\\Rightarrow & 1.5698 < \tan ^{-1}(a)\end{array}$$[/tex]

[tex]$$\begin{aligned}& \Rightarrow \quad \tan ^{-1}(a) > 1.5698 \\& \Rightarrow \quad a > \tan (1.5698)\end{aligned}$$[/tex]

[tex]$$\begin{aligned}& \Rightarrow \quad a > 999.999 \\& \Rightarrow \quad a \geqslant 1000\end{aligned}$$[/tex]

Therefore the answer is [tex]\quad a \geqslant 1000[/tex]

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The value of y in the given inequality 4y + 1/5 ≤ 4/5 is: y ≤ 3/20.

To solve any inequalities, apply the same knowledge used to solve a normal algebraic equation by isolating the value of the variable.

The given inequality is 4y + 1/5 ≤ 4/5. To solve for the value of y, follow the steps below:

4y + 1/5 ≤ 4/5 [given]

Subtract 1/5 from both sides of the inequality:

4y ≤ 4/5 - 1/5 [subtraction property of equality]

4y ≤ 3/5

Multiply both sides by 1/4:

4y × 1/4 ≤ 3/5 × 1/4

y ≤ (3 × 1) / (5 × 4)

y ≤ 3/20

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Answer:

it would be C

hope this helps

Step-by-step explanation:

The area of circle when π is 3.14 is 1017.36 inches².

What is the area of circle?

Area of the circle = πr²

= 3.14 * 18 * 18

= 3.14 * 324

= 1017.36 inches²

Hence, the area of circle when π is 3.14 is 1017.36 inches².

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The dimension of the eigenspace corresponding to an eigenvalue is the number of linearly independent eigenvectors associated with that eigenvalue

What is Eigen Value?

Eigenvalues are a unique set of scalar values connected to a set of linear equations that are most likely seen in matrix equations. The characteristic roots are another name for the eigenvectors. It is a non-zero vector that, after applying linear transformations, can only be altered by its scalar factor.

It is not possible to determine the eigenvalues, their multiplicities, and the dimensions of the corresponding eigenspaces of the matrix g without more information about the matrix itself.

In order to find the eigenvalues of a matrix, you need to determine the values of the variables in the matrix and then solve the characteristic equation, which is obtained by setting the determinant of the matrix equal to zero.

The eigenvalues are the roots of the characteristic equation, and the multiplicity of an eigenvalue is the number of times it appears as a root.

The dimension of the eigenspace corresponding to an eigenvalue is the number of linearly independent eigenvectors associated with that eigenvalue.

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Monica was wrong she will get less interest than Paul as Paul has invested a higher Principal amount than Monica.

What is simple interest?

Simple interest is based on the principal amount of a loan or the first deposit in a savings account.

                         [tex]A = P (1 + rt)\\\\A $ = final amount$\\P $ = initial principal balance$\\r $ = annual interest rate$\\t $ = time (in years)$[/tex]

Given that:

For Monica:

Principal (p) = $400

Rate (r) = 4.3% = 0.043

Year (t) = 1 year

Deposit Paul:

Principal = $500

Rate (r) = 4.2%  = 0.042

Year (t) = 1 year

Now calculate the interest amount for Monica and Paul, we get

For Monica:

             A = P(1 + rt)

             A = 400(1 + (0.043 × 1))

             A = 417.2

             A = $417.20

Now for Monica, Interest will be

           I = A - P

             = 417.20 - 400

           I = 17.20 dollars -----------(II)

For Paul:

             A = P(1 + rt)

             A = 500(1 + (0.042 × 1))

             A = 521

             A = $521 dollars

Now for Paul, Interest will be

           I = A - P

             = 521 - 500

           I = 21 dollars ---------------(II)

From (I) and (II), we can say that Paul will earn more interest than Monica.

Hence, Monica was wrong she will get less interest than Paul as Paul has invested a higher Principal amount than Monica.

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If the regular box has dimensions l, w, and h, then the dimensions of the family value box would be 1.25l, 1.25w, and 1.25h. This means that the volume of the family value box would be 1.25 * 1.25 * 1.25 = 1.953125 times the volume of the regular box. Since the family value box is 25% larger in each dimension, its volume is nearly double the volume of the regular box.

The population percentage of candies that are red: (0.141,0.447)

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The formula for the population proportion's confidence interval is: pz/2[p (1-p)/n]

Given:

- Number of samples: 34

10 red candies total.

The formula for the population proportion's confidence interval is: pz/2[p (1-p)/n]

Given:

- Number of samples: 34

10 red candies total.

Red candy prevalence in sample: p = 10/340.294

Level of significance: =1-0.95=0.05

Critical value: 1.96 for z / 2

The population percentage of red candies will now have the following 95% confidence interval estimate: 0.294 (1.96) [0.294(1-0.294)/34] 0.294 0.153, 0.294+0.153) (0.141.0. 447)

The population percentage of candies that are red: (0.141,0.447)

The complete question is : The data given to the right includes data from 34 ​candies, and 10 of them are red. The company that makes the candy claims that 29​% of its candies are red. Use the sample data to construct a 95​% confidence interval estimate of the percentage of red candies. What do you conclude about the claim of 29​%? Construct a 95 % confidence interval estimate of the population percentage of candies that are red.

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The cost per ounce is $0.156

An ounce is a unit of weight and mass in the Imperial and United States customary systems of measurement. It is commonly used to measure the weight of precious metals such as gold, silver, and platinum. In the US, the ounce is equal to 28.35 grams. The ounce is also used to measure the weight of food items, liquids, and other substances. In the UK, the ounce is equal to 28.4 grams. The ounce is also used to measure the weight of postage stamps, coins, and other small items. The ounce can also be used to measure the volume of a liquid. One fluid ounce is equal to 29.57 milliliters. A dry ounce is equal to 28.35 grams. An ounce is also one-sixteenth of a pound.

Solution:

1 pound is equal to 16 ounce

6 pounds of coffee = 6 x 16 = 96 ounce

So take $14.99 and divided it into 96

the cost of per ounce is equal to 14.99 / 96 = 0.156

The cost of one ounce is $0.156

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Answer: 170678

Step-by-step explanation:

try it and you'll see.

The sales price for the shirts in different countries are the following

Country. Price of shirt

4. European Union, is the best market for Mariee Josee’s shirts and this country also gives her most revenue.

We have given that,

Marie Josee makes famous custom shirts and sold it in Canada. The currency of Canada , CAD.

The price of shirt = $45 CAD

Now, we should find out the price of shirt in different countries.

Country Currency

Canada CAD

European Union EUR

Japan JPY

Australia AUD

1. one CAD = 1.3882 EUR

=> price of shirt in European Union = 45× 1.3882

= 62.469 EUR

2. one CAD = 0.0106 JPY

=> price of shirt in Japan = 45× 0.0106 =0.477 JPY

3. one CAD = 0.9314 AUD

=> price of shirt in Australia = 45× 0.9314

= 41.913 AUD

4. The country Currency which gives highest price of shirt in above list is better option for selling it. So, we see that the European Union country would it be the best market for Mariee Josee’s shirts. It gives best selling price for shirt

i.e 62.469 EUR.

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Thus ,the statement about overhead expenses which is true is option (B). .

In the business world, an ongoing expense of operating a business is known as overhead or an overhead charge .In contrast to operating costs like raw material and labor, overheads are expenses that cannot easily be connected to or associated with any one revenue unit.

Here,

the statement about overhead expenses  which is true is option (B).

Explanation :The costs of operating a firm that aren't directly connected to providing an item or service are referred to as overhead. These expenses might be either fixed, like rent, or variable, like transportation expenditures. Additionally, they may be semi-variable, like utilities. Thus contribute directly to the running of a business.

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Answer:

Savings Account

Investment Account

The expression that represents the number of snow cones is 6/s.

An algebraic expression is an expression that is made up of variables and constants by operations like addition, subtraction, etc. We use Algebraic Expressions to find unknown values or numbers.

Here we have

Jamal spent 6 dollars on snow cones last week  

Each snow cone costs s dollars

Let Jamal bought y snow cones

=> Cost of y cones = ys dollars

Given that Jamal spent 6 dollars

=> ys = 6  

=> y = 6/s

Therefore,

The expression that represents the number of snow cones is 6/s.

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The number of possible outcomes that do not show 1 on the first spinner and 4 on the second spinner is 2.

It is the total number of possible outcomes from a given set.

We have,

The sample space for when both the spinners are spun once.

S = {(1, 2, 3) x (3, 4, 5, 6)}

S = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 4), (3, 5), (3, 6)}

Now,

The number of total outcomes = 12

The number of outcomes that do not show 1 on the first spinner and 4 on the second spinner.

= {(2, 4), (3, 4)}

= 2

Thus,

The number of required possible outcomes is 2.

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PA BRAINLIEST

Answer:

Step-by-step explanation:

To calculate the original price of the sweater, we first need to determine the amount of the discount. Since the sweater was 40% off, the discount was 40/100 * $21 = $8.40.

To find the original price of the sweater, we then need to subtract the discount from the sales price. Since the sales price was $21 and the discount was $8.40, the original price of the sweater was $21 - $8.40 = $<<21-8.4=12.60>>12.60.

However, since the problem states that the original price of the sweater was $35, we can conclude that the calculation above must be incorrect. To find the correct original price of the sweater, we need to divide the sales price by the discount percentage, rather than subtracting the discount amount from the sales price.

Using this method, we can calculate the original price of the sweater by dividing the sales price of $21 by the discount percentage of 40/100, which gives us $21 / (40/100) = $35. This is the correct original price of the sweater

Answer:

d=c/pi

Step-by-step explanation

divide by pi then d=c/pi

Answer:

C / pi = d

Step-by-step explanation:

The formula for circumference is

C = pi * d

To solve for d, divide each side by pi

C / pi = d

the ratio of is x: yin reverse

The cost of one ft² of grass sod is $3 and the cost of one shrub is $10.

Let the cost of grass be g and the cost of shrubs be s.

Pranav spent $90 on 10 ft² of grass sod and 5 shrubs. Thus, the equation that portrays this is;

10g + 5s = 90   -----(1)

Paul spent $50 on 5 ft² of grass sod and 3 shrubs. Thus, the equation that portrays this is;

5g + 3s = 50   ------(2)

Multiply eq 2 by 2 to get;

10g + 6s = 100   -----(3)

Subtract eq 1 from eq 2 to get;

s = 10

Put 10 for s in eq 1 to get;

10g + 5(10) = 90

10g = 40

g = 4

Thus, we conclude that the cost of grass sod and shrubs are the values of s and g above.

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Answer:

-5/6

Step-by-step explanation:

By the application of Analytical geometry the rate of change of y with respect to x is -5/6.

what is Analytical geometry?

Analytical geometry is a branch of mathematics that studies geometric shapes and figures using analytical methods. It is a branch of mathematics that uses algebraic techniques to describe geometric shapes and figures. It involves the use of analytical equations and formulas to study geometric concepts. Analytical geometry is used to study the properties of points, lines, angles, circles, and other geometric shapes. It can also be used to solve problems involving angles, distances, and areas of figures. In addition, analytical geometry can be used to find the intersection of two lines, calculate the area of a circle, and calculate the volume of a cylinder. Analytical geometry is a powerful tool used in many scientific and engineering fields.

The rate of change of y with respect to x for this line is -5/6
Therefore -5/6 is rate of change in this graph.

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The equation of the line is y = x + 7

The equation of a line is an equation that describes the line. It is given by y = mx + c where

Since the equation of a line is given by y = mx + c and we have the points from the table (-5, 2) and (0, 7)

Substituting these evalues into the equation, we have

y = mx + c

2 = m(-5) + c

2 = -5m + c  (1)

Also, the point (0,7),we have

y = mx + c

7 = m(0) + c

7 = 0 + c

c = 7

Substituting c = 7 into equation (1), we have that

2 = -5m + c

2 = -5m + 7

2 - 7 = -5m

-5 = -5m

m = -5/-5

m = 1

Substituting m = 1 and c = 7 into the equation for the line, we have

y = mx + c

y = (1)x + 7

y = x + 7

So, the equation is y = x + 7

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In the early 1900s, many people in the United States were concerned that drinking alcoholic beverages was causing many problems in society. This concern led to the passage of the Eighteenth Amendment.

An unintended effect of the enactment of this amendment was an increase in The amount of organized crime.

The temperance movement, which believed that prohibiting the sale of alcohol would help alleviate poverty and other societal issues, worked for decades to create the Eighteenth Amendment.

Sadly, there was an unintended effect with the Eighteenth Amendment which was a rise in organized crime. This was because criminal gangs became obscenely rich and powerful from the sale of alcohol on the Black Market.

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Answer: b includes only rational numbers

Step-by-step explanation:

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer.

b.

By solving a system of equations we will see that they sold 35 advanced tickets and 30 same-day ones.

Let's define the variables we will be using for this problem, these are:

x = number of same advance tickets.

y = number of same-day tickets.

With the given information we can write a system of equations:

x*$25 + y*$20 =  $1,450

x + y = 65

To solve the system we can isolate x on the second equation:

x = 65 - y

Now let's replace that in the other equation:

(65 - y)*$25 + y*$20 =  $1,450

$1,625 - y*$5 =  $1,450

$1,625 - $1,450 = $5*y

$175/$5 = y

35 = y

Then the value of x is:

x = 65 - 35 = 30

So they sold 35 advanced tickets and 30 same-day ones.

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Answer:

Step-by-step explanation:

Given that $6000 is deposited into an account earning 5.9% compounded quarterly, you want the values of P, r, n used in the future-value formula, and you want the value after 9 years.

The problem statement tells you the values:

  amount deposited = P = 6000

  interest rate = r = 5.9% = 0.059

  compounding periods in a year = n = 4

Using these numbers in the formula, you find (with t=9) ...

  S(9) = 6000(1 +0.059/4)^(4·9) ≈ $10164.30