Triangle G E F is shown with its exterior angles. Line G F extends through point B. Line F E extends through point A. Line E G extends through point C. Angles F E G and E G F are congruent. Sides E F and G F are congruent. Angle E F G is 50 degrees.
What is the measure of ∠EGF?


°

What is the measure of ∠CGF?


°

The total amount payable at the end of 4 years is 406

In this given sum we are provided with the values of principal , rate of interest , and the number of years , we are asked to calculate the amount payable after 4 years that is the matured amount which is calculated with the addition of the principal amount and the simple interest. For that we had to first find out the amount of interest and then we need to add that with the principal amount to get the matured amount or the amount that is payable at the end of 4 years.

here we have to apply the formulla of simmple interest :

(principal × rate of interest × no. of years )/ 100

In the given sum principal (p) = 350 , rate of interest (r) = 4% pa , no. of years (n) = 4

Simple interest = pnr/100

= (350 × 4 × 4)/100  = 56

Matured Amount = Principal + Interest

= 350 + 56 = 406

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The percent decrease in the number of ponds that support brook trout would be approximately 47.37%.

To calculate the percent decrease in the number of ponds that support brook trout, we need to determine the difference between the initial number of ponds and the final number of ponds, and then express that difference as a percentage of the initial number of ponds.

Initial number of ponds: 19

Final number of ponds: 10

To calculate the percent decrease, we can use the following formula:

Percent Decrease = (Difference / Initial Value) * 100

Let's apply this formula to the given data:

Difference = Initial number of ponds - Final number of ponds

Difference = 19 - 10

Difference = 9

Percent Decrease = (9 / 19) * 100

Now, let's calculate the percent decrease:

Percent Decrease = (9 / 19) * 100

Percent Decrease ≈ 47.37%

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Answer:

1. 392

2. 75

3. \(12x^{2} - 5x -2\)

Step-by-step explanation:

1. 7×8 + 3×8×14 = 56 + 336 = 392

2. 675 ÷ (6 + 3) = 675 ÷ 9 = 75

3. \(12\)\(x^{2}\) + \(3x -\) \(8x - 2\) = \(12x^{2} -5x-2\)

Step-by-step explanation:

length = 8×width - 30

length × width = 3542

(8×width - 30)×width = 3542

8width² - 30width - 3542 = 0

4width² - 15width - 1771 = 0

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = width

a = 4

b = -15

c = -1771

width = (15 ± sqrt((-15)² - 4×4×-1771))/(2×4) =

= (15 ± sqrt(225 + 28336))/8 =

= (15 ± sqrt(28561))/8 = (15 ± 169)/8

width1 = (15 + 169)/8 = 184/8 = 23 ft

width2 = (15 - 169)/8 = -154/8 = -19.25 ft

a negative number for an actual length does not make any sense, so, only width = 23 ft is a valid solution.

length = 8×width - 30 = 8×23 - 30 = 184 - 30 = 154 ft

Answer:

The p-value of the test is 0.004 < 0.02, which means that there is sufficient evidence at the 0.02 level to support the company's claim.

Step-by-step explanation:

The company's promotional literature claimed that over 32% do not fail in the first 1000 hours of their use.

At the null hypothesis, we test if the proportion is of at most 32%, that is:

\(H_0: p \leq 0.32\)

At the alternative hypothesis, we test if the proportion is more than 32%, that is:

\(H_1: p > 0.32\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

0.32 is tested at the null hypothesis:

This means that \(\mu = 0.32 \sigma = \sqrt{0.32*0.68}\)

A sample of 1700 computer chips revealed that 35% of the chips do not fail in the first 1000 hours of their use.

This means that \(n = 1700, X = 0.35\)

Value of the test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{0.35 - 0.32}{\frac{\sqrt{0.32*0.68}}{\sqrt{1700}}}\)

\(z = 2.65\)

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion above 0.35, which is 1 subtracted by the p-value of z = 2.65.

Looking at the z-table, z = 2.65 has a p-value of 0.9960.

1 - 0.9960 = 0.004.

The p-value of the test is 0.004 < 0.02, which means that there is sufficient evidence at the 0.02 level to support the company's claim.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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The correct matches are: 4 in. → 10.2 cm   ,   7 kg → 15.4 lb

6 gal → 22.7 L   and  65 ft → 19.8 m.

Conversions refer to the process of changing a measurement from one unit to another unit that measures the same quantity.

For example, converting distance from miles to kilometers, or converting weight from pounds to kilograms.

Here are the conversions:

1 inch = 2.54 cm (approx.)

1 kg = 2.205 lb (approx.)

1 gal = 3.785 L (approx.)

1 ft = 0.3048 m (approx.)

Using these conversions, we can find the equivalent measures:

4 in. → 4 × 2.54 = 10.16 ≈ 10.2 cm

7 kg → 7 × 2.205 = 15.435 ≈ 15.4 lb

6 gal → 6 × 3.785 = 22.71 ≈ 22.7 L

65 ft → 65 × 0.3048 = 19.812 ≈ 19.8 m

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Answer:

x = 18.5 - 7.3

x = 11.2

Step-by-step explanation:

Answer:

The scatterplot that shows the strongest negative linear association would have the points on the plot in a downward slope from left to right. The closer the points are to forming a straight line going from the upper left to the lower right, the stronger the negative linear association is. The points on the scatterplot with the strongest negative linear association will be closely clustered along a line, indicating a clear and strong relationship between the two variables being plotted.

Answer:

Σ( xi ) / n ; $29

Step-by-step explanation:

Given the following data:

X= $27, $31, $30, $26, $25, $27, $37, $33, $32, $28, $26, $26

Number of observations (n) = 12

Mean formula (m) = ( Σ xi ) / n

Where i = each individual value in X

Mean water bill for the years is thus :

m = Σ [(27 + 31 + 30 + 26 + 25 + 27 + 37 + 33 + 32 + 28 + 26 + 26)] / 12

m = 348 / 12

m = 29

Hence, the mean water bill for the year is $29

Answer:

It should be 42.4

Answer:

7

Step-by-step explanation:

Since the smaller triangle is similar to the larger, then its' sides are in the same proportion. So:

1/2=2x-6/16

Then:

4x-12=16

4x=28

x=7 ........................

The solution of the expression, \(x^{\frac{9}{7} }\) is \(\sqrt[7]{x^{9} }\).

An expression is a combination of numbers, variables, functions such as addition, subtraction, multiplication or division etc.

Therefore, let's rewrite the expression to it's equivalent expression.

An equivalent expression is an expression that has the same value or worth as another expression, but does not look the same.

Therefore, using indices rule

\(x^{\frac{9}{7} }\) = \(\sqrt[7]{x^{9} }\)

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Using simple interest, it is found that the monthly payments are of $739.00.

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

\(A(t) = A(0)(1 + rt)\)

In which:

In this problem:

Then, the total amount will be of:

\(A(t) = A(0)(1 + rt)\)

\(A(t) = 85000[1 + 30(0.071)]\)

\(A(t) = 266050\)

In 30 x 12 = 360 monthly payments, hence:

266050/360 = 739.

The monthly payments are of $739.00.

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If the end behavior is decreasing to the left, then the function or leading coefficient of the function will be negative and the degree of the function will be Odd.

Leading coefficients are the number numerals that are written in front of a variable that has the biggest exponent.

Similar to other coefficients that are regular, they can be:

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Answer:

0.111

Step-by-step explanation:

I used a calculator :)

The solution of number 1/9 as a decimal form and Round it to the nearest thousandth is,

⇒ 0.111

We have to given that,

Write 1/9 as a decimal and Round it to the nearest thousandth.

We can divide it as,

⇒ 1 / 9

⇒ 1 ÷ 9

⇒ 0.111111....

Round it to the nearest thousandth,

⇒ 0.111

Thus, The solution of number 1/9 as a decimal form and Round it to the nearest thousandth is,

⇒ 0.111

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Answer: m Spt upt

Step-by-step explanation: big brain

The bank reconciliation reveals various errors and discrepancies between ABC Company's records and the bank statement, including missing deposits, incorrect check charges, outstanding checks, unrecorded interest proceeds, fees, NSF charges, and recording errors.

Upon analyzing the bank reconciliation for ABC Company, several discrepancies between the company's records and the bank statement are identified:

A deposit of Br. 410.90 made after banking hours does not appear on the bank statement. This indicates that the deposit was not processed by the bank before the statement was generated.

A check drawn for Br. 79 was charged by the bank as Br. 973. This suggests an error by the bank in processing the check, resulting in an incorrect charge to ABC Company.

Outstanding checks are checks issued in July but have not yet been paid by the bank. The checks include check numbers 801, 888, 890, and 891, with respective amounts of Br. 100.00, Br. 10.25, Br. 294.50, and Br. 205.00.

A check written for Br. 210 was charged by the bank as Br. 120, indicating an error in the bank's recording.

The proceeds from the collection of an interest-bearing note receivable from David, with a face amount of Br. 500, are not reflected in the bank statement.

A Br. 24.75 interest earned on the average account balance during July is included in the bank statement.

A check for Br. 10, which was recorded in the check register as Br. 100, was returned with the statement. This discrepancy could be due to an error in recording the check amount.

A Br. 5.00 fee was charged by the bank for handling the collection of a note receivable.

A Br. 50.25 check from customer John, deposited by ABC Company, was charged by the bank as Non-Sufficient Funds (NSF), indicating that the customer's check bounced.

A Br. 12.70 service charge was imposed by the bank for the month of July.

Check number 875 was issued on July 20 for Br. 85 but was erroneously recorded in the cash payment journal as Br. 58 for the payment of telephone expenses.

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The statements that are true regarding the expression with the exponents -1, -3, and 1 are;

An exponent is a quantity or power to which a value, expression or number is to be raised.

The specified expression can be presented as follows;

8⁻¹ × 8⁻³ × 8

Therefore; 8⁻¹ × 8⁻³ × 8 = 8⁽⁻¹ ⁺ ⁻³ ⁺ ¹⁾ = 8⁻³ = 1/8³

1/8³ = 1/512

Similarly, we get; 8⁷ × 8⁻¹⁰ = 8⁽⁷ ⁻ ¹⁰⁾ = 8⁻³ = 1/8³

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Answer:

\(620x+72y\)

Step-by-step explanation:

\(310x+16y+310x+56y \\ \\ =310x+310x+16y+56y \\ \\ =620x+72y\)

Solution:

The functions are given below as

Step 1:

Using a graphing calculator, we will have

Step 2:

The second function is given below as

Step 3:

The third function is given below as

Hence,

By combining the functions, we will have

Hence,

The arrangement from widest to narrowest is given below as

Answer:

y = 7

Step-by-step explanation:

y = 3(2-1) 2 + 1

y = 3(1)(2) + 1

y = 6 + 1

y = 7

Answer:

  96°

Step-by-step explanation:

You want the value of angle C in the diagram with two parallel lines and a triangle between them.

The sum of angles in a triangle is 180°, so the missing angle in the triangle is ...

  180° -60° -24° = 96°

Angle C and the one we just found are alternate interior angles with respect to the parallel lines and the transversal that forms those angles. As such, they are congruent:

  C = 96°

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Considering the data we have been provided, we can build a multiple regression model as follows.

a.) In MS Excel, we enter the data set and utilize the "Correlation" option under Data > Data Analysis to create the correlation matrix and answer the question. The correlation matrix may be seen below.

[Fig. 1]

Correlation coefficients for at least one of the independent variables are larger than 0.7.

b.) We must look at the column labeled "Won" in the correlation matrix. The variables are Runs, Hits, Earned Run Average (ERA) and Walks if the criteria are 0.4.

c.) In MS Excel, we enter the data set and utilize the "Regression" option under Data > Data Analysis to create the regression model and answer the question. The result is shown below.

[Fig. 2,3,4]

Runs, ERA, and SO are all significant, with p-values less than 0.05. As a result, we recreate the regression model with these three independent variables.

[Fig. 5,6,7]

The right answer is Won = 80.321 + (0.101) X1 + (-14.276) X3 + (-0.011) X4.

The R2 value of the model is 0.948. This suggests that these factors can predict 94.8% of the number of victories. This model does not make use of the same variables as the previous one (b).

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Answer:

Step-by-step explanation:look it up

The actual distance between the road intersections is 120000 inches.

Scaling is the process in which the size of a figure or object is either increased or decreased by a factor k so as to create an image.

Let y represent the size in actuality and x represent the size in the map. Given that the scale used is 1:24000.

Hence for a map size of 5 inches:

y = 1/(1/24000) * 5 = 24000 * 5 = 120000 inches

The actual distance between the road intersections is 120000 inches.

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The lengths equal to 3 yards 16 inches are 3 yards, 108 inches, 3.44 yards (approximately), and 108.44 inches (approximately).

To determine the lengths that are equal to 3 yards 16 inches, we need to convert the measurements into a consistent unit. Since both yards and inches are units of length, we can convert the inches into yards or the yards into inches to find the equivalent lengths.

1 yard is equal to 36 inches (since 1 yard = 3 feet and 1 foot = 12 inches).

Therefore, 3 yards is equal to 3 * 36 = 108 inches.

Now, we can compare 108 inches to 3 yards 16 inches.

108 inches is equal to 3 yards, so it matches the given length.

To convert 16 inches into yards, we divide it by 36 since 1 yard = 36 inches. 16 inches / 36 = 0.44 yards.

Therefore, 3 yards 16 inches is equivalent to:

3 yards

108 inches

3 yards 0.44 yards (or approximately 3.44 yards)

108 inches 0.44 yards (or approximately 108.44 inches)

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The average amount of time it takes Bob to get his goods and pay if when he comes in there is one customer named Al with server 1 and no one at server 2 will be 16 minutes.

Let us assume that, T = the total amount of time Bob spends in the hardware store.

Let us assume that, T1 = the amount of time Bob spends waiting in line for Al to get his goods from server 1

Let us assume that, T2 = the amount of time it takes for Bob to get his goods from server 1

Let us assume that, T3 = the amount of time Bob spends waiting in line for Al to pay server 2 for his goods

Let us assume that,  T4 = the amount of time it takes for Bob to pay server 2 for his goods

So, the value of total time T will be

T = T1 + T2 + T3 + T4 and E[T] = E[T1] + E[T2] + E[T3] + E[T4]

Now, E[T1] = 6 min. because of the memoryless property of the exponential distribution

E[T2] = 6 min.

To find E[T3], the condition on the availability of server 2 after Bob is done with server 1

So, the value of E[T3] will be

E[T3] = E[T3 | Server 2 is free] P(​Server 2 is free) + E[T3 | Server 2 is not free] P(​Server 2 is not free)

= 0 + 3 . P(Bob is done with server 1 before AI is done with server 2)

\($$=3 \cdot \frac{1 / 6}{1 / 6+1 / 3}$$\)= 3(1/3) = 1 min. and E[T4] = 3 min.

So, E[T] = E[T1] + E[T2] + E[T3] + E[T4]

or, E[T] = 6+6+1+3= 16 minutes

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