an electronics company is designing a watch with a face that is in the shape of a hexagon and two congruent trapezoids attached. the heights of the trapezoids and the apothem of the hexagon measure 2 centimeters each, and the legnth of the shorter base of each trapezoid is 1.5 centimeters. what is the total area of the face of the watch to the nearest tenth of a square centimemter?

Answer:

28

Step-by-step explanation:

21^2+28^2=35^2

The third number of the Pythagorean triplet as c = 40.82.

Given is that 21 and 35 are two members of a Pythagorean triplet.

We can write the Pythagorean triplet as -

a² + b² = c²

c² = a² + b²

c² = (21 x 21) + (35 x 35)

c² = 441 + 1225

c² = 1666

c = √1666

c = 40.82

Therefore, the third number of the Pythagorean triplet as c = 40.82.

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Answer:

Step-by-step explanation:

The first one is Crosses the axis at (1, 0). The second one is Crosses the axis at (−4, 0). The third one is touching the axis at (−5, 0).

To graph the function g(x) = (x - 5)² - 9, shift the graph of f(x) = x²

5 units right and 9 units down

Step-by-step explanation:

Let us revise the translation

1. If the function f(x) translated horizontally to the right by h units, then

   its image is g(x) = f(x - h)

2. If the function f(x) translated horizontally to the left by h units, then

   its image is g(x) = f(x + h)

3. If the function f(x) translated vertically up by k units, then its image

   is g(x) = f(x) + k

4. If the function f(x) translated vertically down by k units, then its image

   is g(x) = f(x) - k

∵ f(x) = x²

∵ g(x) = (x - 5)² - 9

∴ g(x) = f(x - 5)² - 9

∴ h = 5 ⇒ 5 units right

∴ k = -9 ⇒ 9 units down

∴ f(x) translated 5 units to the right

∴ f(x) translated 9 units down

To graph the function g(x) = (x - 5)² - 9, shift the graph of f(x) = x²

5 units right and 9 units down

The graph of g(x) = -1/5(x + 5)² - 2 is plotted making use of the points it passes.

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

The given function is g(x) = -1/5(x + 5)² - 2.

In order to plot its graph, consider following values of x and y as follows,

For x = 0,

g(x) = -1/5(0 + 5)² - 2

      = -7

For x = -5,

g(x) = -1/5(-5 + 5)² - 2

      = -2

Now as the given function has its degree as 2, it is parabolic.

Thus, its graph can be drawn as follows,

Hence, the graph of the given function is drawn clearly.

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The difference in the amount of interest is $847.36. The Option B is correct.

For the 3-year loan at 6.00% interest. We need to first find the amount with the formula A = P(1 + r/n)^(nt).

Plugging in the values, we get:

A = $5,000(1 + 0.06/1)^(1*3)

A = $5,000(1.191016)

A = $5,955.08

The total interest paid is:

I = A - P

I = $5,955.08 - $5,000

I = $955.08

For the 4-year loan at 8.00% interest:

A = $5,000(1 + 0.08/1)^(1*4)

A = $5,000(1.36048896)

A = $6,802.44

The total interest paid is:

I = A - P

I = $6,802.44 - $5,000

I = $1,802.44

Difference in amount of interest for these two loans is:

= $1,802.44 - $955.08

= $847.36

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Answer:

Point B is located where x is negative and y is positive.

Hope this helps!!

Answer:

The length is 15.71 feet.

Step-by-step explanation:

Answer:

Using the order of operations, the expression can be simplified as  

9 + 1.34 + 62.88 = 73.22

The order of operations instructs us on how to solve steps in multi-step expressions. Any operations contained within parenthesis or brackets are first solved. After that, we handle any exponents. Third, we perform all division and multiplication operations from left to right. Fourth, all addition and subtraction problems are solved from left to right.

Remember PEMDAS when simplifying multi-step expressions, i.e.:

P (Parentheses)

E (Exponents, Powers and Square Roots)

MD (Multiplication and Division, left-to-right)

AS (Addition and Subtraction, left-to-right)

The expression given in the problem is:  9 + 1.34 + 1 2 (3.50 +1.74)

Apply the above operation order:

Step 1: solve the addition inside the parenthesis

9 + 1.34 + 1 2 (3.50 +1.74)  =  9 + 1.34 + 1 2 (5.24)

Step 2: Multiply the result by 12

9 + 1.34 + 1 2 (5.24) = 9 + 1.34 + 62.88

Step 3: Apply addition from left to right

9 + 1.34 + 62.88 = 73.22

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the given expression is

so the answer is - 141/4

The probability of selecting an orange marble is 0.33.

Option B is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of times each marble is selected.

Green = 4

Black = 6

Orange = 5

Total number of times all marbles are selected.

= 4 + 6 + 5

= 15

Now,

The probability of selecting an orange marble.

= 5/15

= 1/3

= 0.33

Thus,

The probability of selecting an orange marble is 0.33.

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You can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

To calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation with 10% interest compounded monthly, we can break down the problem into two parts:

Calculate the accumulated balance after 15 years of regular deposits:

We can use the formula for the future value of a regular deposit:

FV = P * ((1 + r/n)^(nt) - 1) / (r/n)

where:

FV is the future value (accumulated balance)

P is the regular deposit amount

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

P = $125.00 (regular deposit amount)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 15 (number of years)

Plugging the values into the formula:

FV = $125 * ((1 + 0.10/12)^(12*15) - 1) / (0.10/12)

Calculating the expression on the right-hand side gives us the accumulated balance after 15 years of regular deposits.

Calculate the balance after an additional 5 years of accumulation:

To calculate the balance after 5 years of accumulation with monthly compounding, we can use the compound interest formula:

FV = P * (1 + r/n)^(nt)

where:

FV is the future value (balance after accumulation)

P is the initial principal (accumulated balance after 15 years)

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

Given the accumulated balance after 15 years from the previous calculation, we can plug in the values:

P = (accumulated balance after 15 years)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 5 (number of years)

Plugging the values into the formula, we can calculate the balance after an additional 5 years of accumulation.

By following these steps, you can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

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this is the answer I hope it helps you

-17 19 55 91 127 163

36 36 36 36 36

6^2 6^2 6^2 6^2 6^2

It's a second degree sequence

After reducing all the book prices by 50%, the new median price is determined to be $7.70 (B)

To find the new median price after reducing all the book prices by 50%, we first need to calculate the reduced prices. By reducing each given price by 50%, we get $6.375, $7.40, $9.995, $4.975, $8.00, and $8.975 respectively.

Next, we arrange these reduced prices in ascending order: $4.975, $6.375, $7.40, $8.00, $8.975, and $9.995. The median is the middle value in this ordered list. Since there are six prices, the middle two values are $7.40 and $8.00.

To find the median, we take the average of these two values, which gives us ($7.40 + $8.00) / 2 = $7.70.

Therefore, the new median price, after reducing all the book prices by 50%, is $7.70 (B). This means that the median price of the books, after the reduction, is $7.70.

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The vector equation of the line passing through points P(1, -4) and Q(5, 0) can be expressed as x = [1, -4] + t[1, 4], where t is a scalar parameter.

To find the vector equation of the line passing through points P(1, -4) and Q(5, 0), we first need to find the direction vector of the line. The direction vector is obtained by subtracting the coordinates of one point from the coordinates of the other point.

Let's calculate the direction vector:

Direction vector = Q - P = [5, 0] - [1, -4] = [4, 4] = 4[1, 1].

Now, we can write the vector equation of the line as:

x = P + t * Direction vector,

where x is a position vector representing any point on the line, P is the position vector of point P, t is a scalar parameter, and Direction vector is the vector obtained earlier.

Substituting the values, we have:

x = [1, -4] + t * [4, 4].

This equation represents the line passing through P(1, -4) and Q(5, 0) in vector form. By varying the parameter t, we can obtain different points on the line.

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Answer:

3: equally likely

4: likely

Step-by-step explanation:

Question 3:

the spinner has 1, 2, 3, 4, 5, 6

2, 4, 6 are all even number which is 3 / 6 = 1 / 2

so half a chance can be odd or half even possibility of landing

Question 4:

- 13 yellow

- 4 green

- 3 blue

total marbles: 13 + 4 + 3 = 20

yellow / total = 13 / 20

which is more than half of the marbles are yellow

Step-by-step explanation:

Formula

\(p = \frac{si \times 100}{t \times r} \)

Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. The principal amount that was invested is $5576.65.

Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.

\(A = P(1+ \dfrac{r}{n})^{nt}\)

where A is the final amount

P is the principal amount

r is the rate of interest

n is the number of times interest is charged in a year

t is the number of years

Given the compound interest is $2,500, while the interest rate is 5% compounded semi-annually for 7.5 years, therefore, the principal amount is,

\(A = P(1+\dfrac{r}{n})^{(n \times t)} - P\\\\2500 = P[(1+\dfrac{0.05}{2})^{(2 \times 15)} -1]\\\\P = 5576.65\)

Hence, the principal amount that was invested is $5576.65.

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There are 84 ways to buy two objects of different types.

To choose two objects of different types, we can choose one type of object first and then choose one object from that type and one object from the other two types.

The number of ways to choose one type of object is 3 (cups, saucers, or spoons). For each type of object, there are different numbers of objects to choose from:

So, the total number of ways to choose two objects of different types is:

3 x (5 x 4 + 5 x 2 + 4 x 2) = 3 x 28 = 84

Therefore, there are 84 ways to buy two objects of different types.

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Answer:

-33.

Step-by-step explanation:

[12 -5 x 9]

= 12 - 45

= -33.

Answer:

-36

Step-by-step explanation:

[12-45]=3

-33=3

-33-3=-36

Answer:(1x2)+(4divided by 2)

Step-by-step explanation:

Answer:

50.40 is the answer.

Step-by-step explanation:

Here, we have been given damping ratio values for different period values. Our objective is to compare the correlation coefficient values of the three regression models and determine the best one.

We will do this by using Excel or Matlab's analysis tools. Here, we can clearly see that the damping ratio is non-linearly related to the period. In this case, we will fit a non-linear model which is capable of predicting the damping ratio for given period values. We will start by plotting a scatter plot of the given data. Based on the scatter plot, we can conclude that a non-linear model will be the best fit.  

From the given table, we will first plot a scatter plot for the given damping ratio values against their corresponding period values. This will help us visualize the relationship between the two variables and select the best regression model. Here, we can clearly see that the damping ratio is non-linearly related to the period. In this case, we will fit a non-linear model which is capable of predicting the damping ratio for given period values.

We will start by plotting a scatter plot of the given data.Based on the scatter plot, we can conclude that a non-linear model will be the best fit. The correlation coefficient values for the three regression models are as follows:Linear regression model: r = -0.9441Non-linear regression model: r = -0.9992Polynomial regression model: r = -0.9984 From the above values, we can conclude that the non-linear regression model has the highest correlation coefficient value and is the best fit for the given data. We can now use this model to predict the damping ratio for any given period values.

Based on the given data and analysis, we have concluded that the non-linear regression model is the best fit for the given data. This model is capable of predicting the damping ratio for any given period values. The correlation coefficient value for this model is the highest among the three regression models considered.

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Use the formula:

Radio= r, Height= h

V= 3.14xrx2h

r =25, h=31

V= 3.14 x 25 x 2 (31) =. 4867

V= 4867 cubic inches

Step-by-step explanation:

Answer: 7

Step-by-step explanation:

\frac{-14}{-2}

Both 14 and 2 are divisible by 2, so we can divide both of these numbers by 2.

\frac{-7}{-1}

Both numbers are negative, so we can divide both of these numbers by -1.

\frac{7}{1}

This gives us 7.

Answer:

Step-by-step explanation:

=14 / -2 = 7

-14 / -2 = 14/2 = 7

Answer:

Step-by-step explanation:

        630 miles        

 21 miles per gallons

= 30 gallons were used,

All the situation are Exponential relationship accept the last one.

A linear function is modeled by the following rule:

y = mx + b

In which: m is the slope, which is the rate of change, that is, the change in y divided by the change in x. b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.

Given that "you work as a taxi driver. you earn an average of $75 in tips each day".

That is, 75^x

This is a Exponential equation.

2. The number of visitors to the eiffel tower in paris increases by 1.5% each year.

This is a Exponential equation.

The number of tadpoles in the pond triples each day.

This is a Exponential equation.

Also, every year 39 million cars cross the golden gate bridge in san francisco.

This is a Linear equation.

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The probability that a green marble is randomly drawn will be 2% if 50 blue marbles are removed. The probability of randomly picking a green marble will be greater if there are fewer marbles.

The probability of an event can be expressed as

P(A) = n(A) / n(S)

Where

We must find the value of n(S) (the total number of marbles) so that we know how many marbles that must be removed.

Hence, the probability of randomly drawn green marble will be 2% if there are 50 marbles. So, 50 blue marbles should be removed.

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