Trapezoid ABCD is similar to trapezoid GFHE, with DA = 12, BC = 8, and FH = 4.
What is EG?

The amount that will accumulate by the end of the sixth and final payment is approximately $41,666.60.

To calculate the accumulated amount by the end of the sixth and final payment, we can use the future value of an ordinary annuity formula:

Future Value = Payment × Future Value of an Ordinary Annuity Factor

The payment is $5,800, and the interest rate is 9%. Since the payments are made at the end of each year, we can use the future value table for an ordinary annuity at 9%.

Looking up the factor for 6 years at 9% in the future value table, we find it to be 7.169858.

Now we can calculate the accumulated amount:

Future Value = $5,800 × 7.169858 = $41,666.60

Therefore, the amount that will accumulate by the end of the sixth and final payment is approximately $41,666.60. The correct answer is not among the options provided.

Learn more about approximately from

https://brainly.com/question/27894163

#SPJ11

We would need 168 square inches of Teflon to completely cover the triangular prism machinery.

To calculate the surface area of a triangular prism, we need to find the area of each face and then add them up. Let's assume that the triangular bases of the prism have base b and height h, and that the length of the prism is l.

The surface area of the triangular bases is (1/2)bh for each base, so the total area is (1/2)bh + (1/2)bh = bh.

The lateral surface area of the prism is the area of the three rectangular faces. Each rectangular face has length l and height h, so the total lateral surface area is 3lh.

Therefore, the total surface area of the triangular prism is

bh + 3lh

To determine how much Teflon is needed to cover the machinery, we need to know the dimensions of the triangular prism. Once we have those dimensions, we can calculate the surface area using the formula above and then use that value to determine the amount of Teflon required.

Let's say the base of the triangular prism is 4 inches and the height is 6 inches, and the length of the prism is 8 inches. Then the surface area of the triangular prism is

bh + 3lh

= (4 in. x 6 in.) + 3(8 in. x 6 in.)

= 24 in² + 144 in²

= 168 in²

To know more about triangular prism here

https://brainly.com/question/17286531

#SPJ4

a) G(t) = 685.4 * (1 + 0.04)^t, b) G(t) = 685.4 + 4t.

(a) If the gross domestic product (G) of Switzerland increases by 4% per year, we can express it as a function of time (t) in years after 2013. The initial GDP in 2013 is given as 685.4 billion dollars. Since it increases by 4% per year, we can use the following formula: G(t) = 685.4 * (1 + 0.04)^t. Here, (1 + 0.04) represents the growth factor of 4% per year, and t represents the number of years after 2013. (b) If the gross domestic product (G) of Switzerland increases by 4 billion dollars per year, we can express it as a function of time (t) in years after 2013. The initial GDP in 2013 is given as 685.4 billion dollars. Since it increases by 4 billion dollars per year, we can use the following formula: G(t) = 685.4 + 4t. Here, 685.4 represents the initial GDP in 2013, and 4t represents the increase of 4 billion dollars per year.

Learn more about GDP and economic growth here:

https://brainly.com/question/28722559

#SPJ11

Answer:

aw hope he gets better tell him I said hi

Answer:

Stay strong! I am praying for all of you and your family!

The amount of a) interest is $114.82 , b) final payment is $3,714.82  and c) savings by paying the loan off early is $173.18.

a. Interest

Interest = [ ($313.20 × 6) + $1,835.62] -  $3,600

Interest = ( $1,879.2 +  $1,835.62) -  $3,600

Interest = $3,714.82 -$3,600

Interest = $114.82

b. Final payment

Final payment = [ ($313.20 × 6) + $1,835.62]

Final payment = ( $1,879.2 +  $1,835.62)

Final payment =  $3,714.82

c. Saving:

Savings = [ ( 8% × $3,600) + $3,600] - $3,714.82

Savings = ($288 + $3,600) - $3,714.82

Savings = $3,888 - $3,714.82

Savings = $173.18

Therefore the interest is the amount of $114.8.

Learn more about interest here: https://brainly.com/question/16134508

#SPJ1

Answer:

y = -x - 14

Step-by-step explanation:

The independent variable of interest in an ANOVA procedure is called a factor. Hence (d).

The independent variable of interest in an ANOVA procedure is referred to as the factor. The factor represents the different categories or levels being compared to assess their impact on a dependent variable. It is the variable that is manipulated or controlled by the researcher to determine its effect on the outcome. In the context of ANOVA, the factor is typically a categorical variable that divides the data into distinct groups or treatments. These groups are compared to evaluate if there are statistically significant differences in the means of the dependent variable across the different levels of the factor. Therefore, the correct answer is factor(d).

Read more about ANOVA here: https://brainly.com/question/30459773

#SPJ11

The exercise involves finding the product C = AB, where matrix A is given by [2 9] and matrix B is given by [3 6 1]. We need to perform the matrix multiplication to obtain the resulting matrix C.

Let's calculate the matrix product C = AB step by step:

Matrix A has dimensions 2x1, and matrix B has dimensions 1x3. To perform the multiplication, the number of columns in A must match the number of rows in B.

In this case, both matrices satisfy this condition, so the product C = AB is defined.

Calculating AB:

AB = [23 + 912 26 + 94 21 + 95]

[103 + 612 106 + 64 101 + 65]

Simplifying the calculations:

AB = [6 + 108 12 + 36 2 + 45]

[30 + 72 60 + 24 10 + 30]

AB = [114 48 47]

[102 84 40]

Therefore, the product C = AB is:

C = [114 48 47]

[102 84 40]

In summary, the matrix product C = AB, where A = [2 9] and B = [3 6 1], is given by:

C = [114 48 47]

[102 84 40]

To learn more about matrix visit:

brainly.com/question/29239316

#SPJ11

The Domain of the function is : (−∞,∞).

A relation is any subset of a Cartesian product.

As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."

A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.

Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).

A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).

Every function, as you can see from these definitions, is a relation from X .

Hence, The Domain of the function is : (−∞,∞).

Learn more about function here:

brainly.com/question/2253924

#SPJ1

Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

Answer

Slope of the line is 2/3

Step-by-step explanation:

Given the slope-intercept equation

2x - 3y = 5

The standard form of the slope-intercept equation is

y = mx + b

where m = slope of the line

b = intercept of the y-axis

Rearrange the above equation

2x - 3y = 5

-3y = 5 - 2x

-3y = -2x + 5

Divide through by -3

-3y/-3 =-2x/-3 + (5/-3)

y = 2x/3 - 5/3

Hence, the slope of the line is 2/3

The rounded number to two decimal places is 95.89.

Rounding is a common mathematical operation used to approximate a number to a specified degree of accuracy. It involves determining the closest value to the original number based on a predetermined set of rules. In this case, we are asked to round the number 95.8937 to two decimal places.

To perform rounding, we first identify the digit in the third decimal place, which is 3 in this case. The digit immediately to the right of the third decimal place is 7. According to the rules of rounding, if the digit in the third decimal place is less than 5, we simply truncate all the digits after the second decimal place.

In this case, since 3 is less than 5, we round down and remove the digits after the second decimal place. As a result, the rounded number to two decimal places is 95.89.

Rounding serves various purposes, such as simplifying numbers for easier comprehension, providing a more practical representation of measurements, and ensuring the desired level of precision in calculations. It is commonly used in fields such as mathematics, finance, engineering, and statistics.

However, it's important to note that rounding introduces a level of approximation, and the rounded value may not be an exact representation of the original number. The degree of accuracy and the specific rounding method chosen depend on the context and requirements of the problem at hand.

In conclusion, rounding is a useful mathematical technique that allows us to simplify and approximate numbers to a desired level of precision. The rules of rounding, such as those outlined in textbooks, provide guidelines for determining the appropriate rounded value based on the digit in question and the context of the problem.

Learn more about Common Mathematical Operation at

brainly.com/question/15388527

#SPJ4

Based on the chi-square test, there is no significant evidence to suggest that the die is not balanced.

We have,

To determine if the die is balanced, we can perform a chi-square test of goodness of fit.

The null hypothesis is that the die is balanced, and the alternative hypothesis is that the die is not balanced.

First, let's calculate the expected frequencies for each outcome assuming the die is balanced. Since there are 180 tosses in total, each outcome is expected to have an equal probability of 1/6.

Expected frequency for each outcome

= (Total tosses) x (Probability of each outcome)

Expected frequency for each outcome = (180) x (1/6)

Expected frequency for each outcome = 30

Now, we can calculate the chi-square test statistic using the formula:

χ² = Σ [(Observed frequency - Expected frequency)² / Expected frequency]

Let's calculate the chi-square test statistic:

χ² = [(28 - 30)² / 30] + [(36 - 30)² / 30] + [(36 - 30)² / 30] + [(30 - 30)² / 30] + [(27 - 30)² / 30] + [(23 - 30)² / 30]

χ² = [(-2)² / 30] + [(6)² / 30] + [(6)² / 30] + [(0)² / 30] + [(-3)² / 30] + [(7)² / 30]

χ² = 4/30 + 36/30 + 36/30 + 0/30 + 9/30 + 49/30

χ² = 134/30

χ² ≈ 4.467

Next, we need to compare the calculated chi-square value to the critical chi-square value at a significance level of 0.01 and degrees of freedom equal to the number of outcomes minus 1 (6 - 1 = 5).

Looking up the critical chi-square value in a chi-square distribution table with 5 degrees of freedom and a significance level of 0.01, we find it to be approximately 15.086.

Since the calculated chi-square value (4.467) is less than the critical chi-square value (15.086), we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to conclude that the die is not balanced at a 0.01 level of significance.

Thus,

Based on the chi-square test, there is no significant evidence to suggest that the die is not balanced.

Learn more about the chi-square test here:

https://brainly.com/question/30760432

#SPJ1

Answer:

The slope of the dotted line is -1. The slope of the solid line is 4.

Answer:

C) 26

Step-by-step explanation:

a + 32 + 85 = 180   {Sum of all angles of triangle}

a + 117 = 180

a = 180 - 117

a = 63

b = a   {Vertically opposite angles}

b = 63

91 + 63 + c = 180  {Angle sum property of triangle}

154 + c = 180

c = 180 - 154

c = 26

Answer:

d = \(\frac{11}{12}\)

Step-by-step explanation:

1) To solve for d, isolate it in the equation. So, to get rid of the \(-\frac{1}{2}\) with the d, add \(\frac{1}{2}\) to both sides.

\(d-\frac{1}{2} = \frac{5}{12} \\d - \frac{1}{2} +\frac{1}{2} = \frac{5}{12} + \frac{6}{12} \\d = \frac{11}{12}\)

Thus, d = \(\frac{11}{12}\).

Answer:

Step-by-step explanation:

Given,

Two positive number whose squares have a sum of 74 and a difference of 24

To Find:

The two positive number.

Explanation

Let the two positive numbers be x and y.

Then according to the question, we have two equations:

\(x^2 + y^2 = 74\)                   (equation 1)

\(x^2 - y^2 = 24\)                   (equation 2)

Now, use equation 2 to solve for one of the variables in terms of the other.

Adding \(y^2\) to both sides gives:

\(x^2 = y^2 + 24\)

Taking the square root of both sides gives:

\(x = \sqrt{(y^2 + 24)}\)

Now substitute this expression for x into equation 1 and solve for y:

\((y^2 + 24) + y^2 = 74\)

\(2y^2 + 24 = 74\)

\(2y^2 = 50\)

\(y^2 = 25\)

\(y = 5\)        (since we're looking for a positive number)

Now we can use the expression we found for x to get:

\(x = \sqrt{(y^2 + 24)} = \sqrt{25 + 24} = \sqrt{49} = 7\)

So the two positive numbers are x = 7 and y = 5.

Therefore, the solution is x = 7 and y = 5.

Answer:

7 and 5

Step-by-step explanation:

Let x and y be the two unknown positive numbers.

Set up a system of equations using the defined variables and the given information:

\(\begin{cases}x^2 + y^2 = 74\\x^2 - y^2 = 24 \end{cases}\)

Solve the system of equations by the method of elimination.

Add the two equations to eliminate the terms in y:

\(\begin{array}{crcccc}&x^2&+&y^2&=&74\\\vphantom{\dfrac12}+&x^2&-&y^2&=&24\\\cline{2-6}\vphantom{\dfrac12}&2x^2&&&=&98\end{array}\)

Solve for x:

\(\begin{aligned}2x^2&=98\\2x^2 \div 2&=98 \div 2\\x^2&=49\\\sqrt{x^2}&=\sqrt{49}\\x&=\pm7\end{aligned}\)

As x is positive, x = 7 only.

To find the value of y, substitute x = 7 into one of the equations:

\(\begin{aligned}x^2+y^2&=74\\(7)^2+y^2&=74\\49+y^2&=74\\49+y^2-49&=74-49\\y^2&=25\\\sqrt{y^2}&=\sqrt{25}\\y&=\pm 5\end{aligned}\)

As y is positive, y = 5 only.

Therefore, the two positive numbers whose squares have a sum of 74 and a difference of 24 are 7 and 5.

Answer:

6x: 312

x: 52

Step-by-step explanation:

Let the deck be denoted by x then

6x:  312

There are 312 cards in 6x decks

In 1 deck x there are 312/6= 52 cards

6x: 312

6x/6: 312/6        Cancelling both sides by 6

x: 52

In ratio both the sides are divided by the same number to get equivalent fractions.

In 1 deck there are 52 cards

Answer:

=========================

The triangle is isosceles as marked.

The two opposite angles of equal sides are equal, one of them is x and the angle in between them is 28°.

Use angle sum of the triangle:

Same as previous question, we have an isosceles triangle. Equal sides are:

Find the perimeter by substituting the value of x:

The value of cos θ is equal to 1/3 when sec θ= √6/2.

Since we are given the value of secant of theta, we can use the relationship between secant and cosine to find the value of cosine of theta.

Let's start by recalling the definitions of secant and cosine functions. The secant of an angle is defined as the reciprocal of the cosine of that angle.

In other words, secθ = 1/cosθ

Conversely, the cosine of an angle is defined as the reciprocal of the secant of that angle.

cosθ = 1/secθ

We are given that secθ= √6/2

We can use this value to find cosθ= 1/secθ

cosθ = 1 / (√6/2)

To simplify this expression, we can multiply both the numerator and denominator by 2/sqrt(6).

cosθ = ((2/√6) / (√6/2) * (2/√6))

cosθ = (2/√6) / 1

cosθ = (2/√6 * √6/√6)

cosθ = 2/6 = 1/3

Therefore, the value of cosθ is equal to 1/3 when secθ = sqrt(6)/2.

For more such questions on cos θ  visit:

https://brainly.com/question/21867305

#SPJ8

The slope of the situation is determined as: A 0.95.

The slope of a situation is always the unit rate. And it is represented in a linear equation as m in y = mx + b.

In the linear equation above, the value of b is the initial value or additional value.

Interpreting the situation given, we have the following:

The y-intercept, b, is the additional cost = $7.25

The cost of 1 bagel = the slope / unit rate

12 bagels costs $11.40

Slope (m) = $11.40 / 12 = $0.95

This means that the slope of the situation is represented as: A. 0.95.

Learn more about the slope of a situation on:

https://brainly.com/question/27506916

#SPJ1

Step-by-step explanation:

To dilate the figure by a factor of 2, I will multiply the x and y-value of each point by 2. I plotted all the new points to find the new triangle. To dilate the figure by a factor of 2, I will multiply the x-value of each point by 2.

Approximately 0.99% of the days the bank will be notified because the amount dispensed is very low (less than $2500).

To determine the percentage of days the bank will be notified because the amount dispensed is very low (less than $2500), we need to calculate the cumulative probability up to that threshold using the normal distribution.

Given:

Mean (μ) = $4200 per day

Standard deviation (σ) = $720 per day

We can use the Z-score formula to standardize the value:

Z = (X - μ) / σ

For X = $2500:

Z = (2500 - 4200) / 720

Z = -1700 / 720

Z ≈ -2.36

Using a standard normal distribution table or calculator, we can find the cumulative probability associated with Z = -2.36. This probability represents the percentage of days the amount dispensed will be less than $2500.

Looking up the Z-score of -2.36 in the standard normal distribution table, we find that the cumulative probability is approximately 0.0099.

Therefore, approximately 0.99% of the days the bank will be notified because the amount dispensed is very low (less than $2500).

To know more about Z-score:

https://brainly.com/question/31871890

#SPJ11

Answer:

Step-by-step explanation:

Its 140 minutes because thats when the both meet up cause 35x4 is 140 and 20 x 7 is 140 too so thats the answer.

Answer: B?

Step-by-step explanation:

Answer:

Go for B

Step-by-step explanation:

The required explanation for log of base 10 is described.

The ability of logarithms to solve exponential problems is a large part of their strength. Examples of this include sound (measured in decibels), earthquakes (measured on the Richter scale), starlight brightness, and chemistry (pH balance, a measure of acidity and alkalinity).

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

The logarithm can be rewritten using the general rule. The common logarithm, which has a base of 10 always, is what you're dealing with when the log has no base.

To know more about logarithmic function visit:

brainly.com/question/3181916

#SPJ4

Could you possibly repost your question with a clear image?

The details on this image are unreadable and, therefore, make it difficult to help.

Will bookmark this question so I can find your new post if posted again.

Answer:

difference = \(x^2-12x\)

Step-by-step explanation:

hope this helps :)