What is the measure of each angle in a regular polygon with 14 sides? If necessary, round your answer to the nearest tenth.

Equivalence means to be same, whether it be value, temperature, size, etc.

Let's make an equation to solve this problem. We first would need to take the total (12 pounds) and divide that total by the amount each slice must weigh (1.5 pounds) to get an equal number of slices.

To check our work, we can take number of slices (8), and multiply that by the weight of each slice (1.5 pounds) to get the original weight of the watermelon.

Now, we know for sure that Mr. Ramirez can make 8 watermelon slices each weighing 1.5 pounds if he has a 12-pound watermelon.

Answer:

20%

Step-by-step explanation:

1 + r = 1.2 = 1 + 0.2 = 1 + 20%

r = 20%

The percent growth is 20%.

Answer:

Larger number: 29

Smaller number: 13

Step-by-step explanation:

29 + 13 = 42

29 - 16 = 13

Answer:

Larger number: 29

Smaller number: 13

Step-by-step explanation:

x = larger number

y = smaller number

x+y=42

29-13 = 16

29+13=42

a) Standard factored form is 2^4 × 3^2 × 5.

b) Standard factored form is 2^18 × 5^8.

c) There are 6 zeros at the end of (20!)^2

If n is an integer and n > 1, then  factorial of n is the product of n and every other positive integer that is less than n.

We have to find the standard factor form of 6!

6! = 6 × 5 × 4 × 3 × 2 × 1

Then, we can simplify by grouping the factors of 6! into pairs that multiply to 10:

6! = 2 × 3 × 2 × 2 × 5 × 1 × 3 × 2 × 1 = 2^4 × 3^2 × 5

Therefore, 6! in standard factored form is 2^4 × 3^2 × 5.

Part b

To write 20! in standard factored form, we start with 20 and multiply by every positive integer less than 20:

20! = 20 × 19 × 18 × ... × 3 × 2 × 1

To simplify this expression, we can group the factors into pairs that multiply to 10

20! = (2 × 10) × (2 × 9) × (2 × 8) × ... × (2 × 1) × (5 × 3) × (5 × 2) × 5

We can then combine the factors of 2 and the factors of 5:

20! = 2^18 × 5^8

Therefore, 20! in standard factored form is 2^18 × 5^8.

Part C

The number of zeros at the end of (20!)^2 in decimal form is equal to the number of factors of 10 in (20!)^2. Since 10 = 2 × 5, we need to count the number of factors of 2 and 5 in (20!)^2.

The number of factors of 2 in (20!)^2 is the number of even integers less than or equal to 20, which is 10.

The number of factors of 5 in (20!)^2 is the number of multiples of 5 less than or equal to 20, which is

5, 10, 15, and 20.

However, since we are squaring (20!), we also need to count the number of factors of 25, which is 2:

5^2 and 10^2.

There are 6 zeros at the end of (20!)^2 when it is written in decimal form.

Therefore, each part has been solved

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Refer to the attached images.

**Should be arctan(tanx)=x on the last page**

The explanation 3 is the path that tells us that the interlopers would have to come between the men in the story.

The summary here is that the men are faced with a face off. That is they were to fight themselves till they killed themselves.

But while they were to fight they are met with the interloper which is a more ferocious danger that they are facing.

This tells us that they both have more on their plate at the moment.

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The frequency table is completed and the percent of the people who have exactly one sibling is 20.48%.

Relative frequency is found by dividing the frequency with the total number of values.

Cumulative frequency is calculated by adding the previous frequencies together.

(a) From the table,

Total number of people = 210

So, Total frequency = 210

Frequency of number of siblings as 4 = 210 - (43 + 43 + 41 + 43) = 40

Relative frequency = Frequency / Total frequency

Relative frequency of number of siblings as 2 = 0.1952

Cumulative frequency of number of siblings as 3 = 127 + 43 = 170

(b) Percent of people having exactly 1 sibling = (43 / 210) × 100

                                                                           = 20.48%

Hence the percent of people having exactly 1 sibling is 20.48%.

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Answer:

x = 16

Step-by-step explanation:

subtract 12 from both sides to isolate the variable and its coefficient

4x = 64

divide both sides by 4 to get x

x = 16

Answer:

x = 16

Step-by-step explanation:

4x+12=76

Step 1: Subtract 12 from both sides.

4x + 12 - 12 = 76 - 12

4x = 64

Step 2: Divide both sides by 4.

[tex]\frac{4x}{4} = \frac{64}{4}[/tex]

x = 16

The correct answers are given below:

(a) 1 to 55

(b) 40%

Since Mansour scores 55% of his kicks, we'd want exactly 55% of the simulated numbers to denote Mansour scoring a penalty, thus, 1 to 5 is a possible range.

To find the percentage of trials where Mansour scored exactly one penalty, we have to count the trials where one of the simulated numbers is in the range of 1 to 5 (denoting Mansour scoring the penalty) and the other is in the range of 56 to 100 (denoting Mansour missing the penalty)

Trails 1, 3, and 4, 6 are such trials. Thus, Mansour scored exactly one penalty kick in 40% of the trials.

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Answer:

64 is not divisible by 6 because although it is divisible by 2, it is not divisible by 3 so it is not divisible by 6.

Step-by-step explanation:

The length of f to the nearest 10th of an inch is 308.8 inches.

A trigonometric rule known as the Law of Sines connects any triangle's sides and angles. It claims that for all three sides of a triangle, the ratio of the length of one side to the sine of the angle opposite that side is the same. To put it another way, we may write: If we have a triangle with sides a, b, and c, and opposing angles A, B, and C:

Sin(A) / a = b / a sin(B) / c / sin (C)

Using the Law of Sines we have:

f / sin(89°) = e / sin(27°)

f = sin(89°) * 310 / sin(27°)

f ≈ 308.8 inches

Hence, the length of f to the nearest 10th of an inch is 308.8 inches.

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Answer:

  613.7 in

Step-by-step explanation:

You want the length of side f in ∆EFG with e = 310 in, E = 27°, G = 89°.

The law of sines tells you ...

  f/sin(F) = e/sin(E)

Angle F is the third angle in the triangle, so its measure is ...

  F = 180° - 89° -27° = 64°

Then the length of f is ...

  f = e·sin(F)/sin(E) = (310 in)·sin(64°)/sin(27°) ≈ 613.7 in

The length of f is about 613.7 inches.

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Answer:

Step-by-step explanation:

The cost of renting a car for "d" days can be represented by the following function:

c(d) = 75d + 30

where "c" is the total cost of the car rental and "d" is the number of days the car is rented for. The first term, 75d, represents the daily rental fee of $75 per day. The second term, 30, represents the flat fee for the full tank of gas that can be returned either full or close to empty.

Answer:

Below

Step-by-step explanation:

So you have this:

4x + 16 = 35       subtract 16 from both sides of the equation

4x = 19   Divide by 4

x = 19/4

Answer:

The value of x is

[tex]x = 4.75[/tex]

Step-by-step explanation:

Greetings!!!

Thus, the value of y is given as 35, substitute known value of y in expression and solve for x.

[tex]4x + 16 = 35[/tex]

Move the constant to the right

[tex]4x = 35 - 16 \\ 4x = 19[/tex]

Divide both sides of the expression by 4

[tex] \frac{4x}{4} = \frac{19}{4} [/tex]

solve

[tex]x = \frac{19}{4} [/tex]

or

[tex]x = 4 \frac{3}{4} [/tex]

or

[tex]x = 4.75[/tex]

Hope it helps!!!

The equation for option 1 is y = 3.5x + 7.5 and option 2 is y = 5.5x. Option 1 will be the least expensive. The solution has been obtained by using the slope-intercept form.

What is slope-intercept form?

The graph of the equation y = mx + b is represented by a line with a slope of m and a y-intercept of b. The slope-intercept representation of the linear equation is employed, and the values of m and b are real numbers.

We are given two options.

Using slope-intercept form, we get the equations as

Option 1

It requires monthly fee of $7.50 which means this is the y-intercept and $3.50 per game which means this is the slope.

So, the equation is y = 3.5x + 7.5

Option 2

Slope = (33 - 16.5)/ (6 - 3)

Slope = 16.5/ 3

Slope = 5.5

The y-intercept for this is 0.

So, we get the equation as y = 5.5x.

Fee for renting 5 games

As per option 1: y = 3.5(5) + 7.5 = $25

As per option 2: y = 5.5(5) = $27.5

Hence, option 1 will be the least expensive.

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We can form 15 different 4-digit numbers using the digits 1, 2, 3, 7, 8, and 9, without repetition. Out of these, 30 are even numbers. We used the concept of combination to find these numbers.

Combination is a mathematical technique used to calculate the number of ways in which a group of objects can be selected from a larger set, without considering their order.

We can use the combination formula to find the total number of possible combinations:

C(4, 3) = 4! / (3! * 1!) = 4

This means that we can form four different 3-digit numbers using the digits 1, 2, 3, and 4, without repetition.

Now, coming back to our original problem, we need to form 4-digit numbers using the digits 1, 2, 3, 7, 8, and 9, without repetition. Using the same combination formula, we can find the total number of possible combinations:

C(6, 4) = 6! / (4! * 2!) = 15

This means that we can form a total of 15 different 4-digit numbers using the given digits.

Next, we need to find out how many of these numbers are even. An even number is a number that is divisible by 2, and in our case, this means that the last digit of the number must be either 2, 8, or a combination of 1 and 7.

To find the number of even 4-digit numbers, we can use the same combination formula, but this time we have to consider only 3 digits (2, 8, and a combination of 1 and 7) for the last digit:

C(3, 1) * C(5, 3) = 3 * 10 = 30

This means that we can form a total of 30 different 4-digit even numbers using the given digits.

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Answer:

75a%

or

3/4a

or

0.75a

Step-by-step explanation:

I answer for what I understand, a number a is reduced by 50% and the result increased by 50%

a - 50% = 50% or 1/2 or 0.5

    2. increase

50 + 50% = 75% or 3/4 or 0.75

Answer:

0.392 < p < 0.508

Step-by-step explanation:

[tex]\displaystyle CI=\hat{p}\pm z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\CI_{90\%}=0.45\pm 1.645\sqrt{\frac{0.45(1-0.45)}{200}}\\\\CI_{90\%}\approx0.45\pm0.058\\\\CI_{90\%}=\{0.392,0.508\}[/tex]

Thus, we are 90% confident that the true population proportion [tex]\hat{p}[/tex] is between 0.392 and 0.508, assuming conditions are met.

Answer:B

Step-by-step explanation:

Answer:

Step-by-step explanation:

The tide over a 24-hour period can be modeled by a sinusoidal function of the form:

f(x) = A * sin(Bx) + C

where A is the amplitude, B is the frequency, and C is the vertical shift.

To determine the values of A, B, and C, we need three points. Let's use the following points:

(0, 5): This is the value of the tide at midnight, 5 ft.

(12, 9.5): This is the value of the tide at its high, 9.5 ft.

(6, 0.5): This is the value of the tide at its low, 0.5 ft.

Using the first point (0, 5), we can calculate the vertical shift, C:

C = 5

Using the second point (12, 9.5), we can calculate the amplitude, A:

A = (9.5 - 5) / 2 = 2.25

Using the third point (6, 0.5), we can calculate the frequency, B:

0.5 = 2.25 * sin(B * 6) + 5

4.5 = 2.25 * sin(B * 6)

2 = sin(B * 6)

B * 6 = sin^-1(2)

B * 6 = pi / 2

B = pi / (2 * 6) = pi / 12

So, the final equation is:

f(x) = 2.25 * sin(pi * x / 12) + 5

This represents one period of the sinusoidal function that models the tide over a 24-hour period, with time x measured in hours since midnight.

The value of x for the given expression will be 22/3.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that the expression is triple x less by 10 is at least 12. The mathematical form of the expression can be written as below:-

3x - 10 = 12

3x = 10 + 12

3x = 22

x = 22 / 3

Hence, the value of x for the expression 3x - 10 = 12 is x = 22 / 3.

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a) The value of z-score is -0.299.

c) The IQR value is measure of spread of data,  IQR = 4.25.

d) There is outliers since observations are not less than 30.375 and greater than 47.375.

The z-score is an example of a standardised score. The standard deviation of a data point's divergence from the mean of the distribution is calculated using a z-score.

Given:

Sample Data = 31.5, 36.0, 37.8, 38.5, 40.1, 42.2, 34.2, 36.2, 38.1, 38.7, 40.6, 42.5, 34.7, 37.3, 38.2, 39.5, 41.4, 43.4, 35.6, 37.6, 38.4, 39.6, 41.7, 49.3

(a) The value of z-score is calculated as follows,

μ = [tex]\sum _{i=1}^n[/tex]/ n = 933.1 /24 = 38.88

σ = 3.61

So, z = X - μ / σ  

 = 37.8 - 38.88/3.61

 = −  0.299

(b) Quartile:

Q₁ = ( n+1/4)th value

= (24+1/4)th

= 6.25th

=  36.2 + 0.25 x ( 37.3 −  36.2 )  

= 36.47

and, M = ( n+1/2)th value

= (24+1/2)th

= (24+1/4)th

=  12.5 t h

= 38.4 + 38.5/2

= 38.45

Q₃ = 3( n+1/4)th

= 3(24+1/4)th

= 18.75 t h  

= 40.6 + 0.75 x ( 41.4  −  40.6 )  

= 41.2

(c) Interquartile​ range

=  Q ₃ −  Q ₁  

= 41.2  −  36.47  

= 4.25

(d) Lower fences =  Q₁− 1.5 ( I Q R )  

                           =  36.75 −  1.5  ( 4.25 )  

                           =   30.375  

Upper fences = Q ₃+1.5

                      =  41 + 1.5( 4.25 )  

                      = 47.375

Hence, there is outliers since observations are not less than 30.375 and greater than 47.375.

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The annual percentage rate is 19.59%.

An expression contains terms with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Repayment months =  48

Interest rate = 10%

The annual percentage rate.

=  (2 x repayment months x interest rate) ÷ (repayment months + 1)

= (2 x 48 x 10/100) / (48 + 1) x 100

= (2 x 48 x 0.10) / 49 x 100

= 9.6/49 x 100

= 0.1959 x 100

= 19.59%

Thus,

The annual percentage rate is 19.59%.

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Blake needs a wooden dowel that is 2 1/6 feet long. Blake needs to cut off 7.4167 feet from the dowel.

What are arithmatic operations?

Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.

To find out how much Blake should cut off the dowel, we need to subtract the length of the dowel from the required length.

The length of the dowel is -5 1/4 feet, which can be written as -5.25 feet.

The required length is 2 1/6 feet, which can be written as 2.1667 feet (rounded to four decimal places).

To find out how much needs to be cut off, we can subtract the length of the dowel from the required length:

2.1667 ft - (-5.25 ft) = 7.4167 ft

Therefore, Blake needs to cut off 7.4167 feet from the dowel.

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The permutation formula is used when the order matters as it does not remove the combinations with the same elements and different order from the equation.

For the combination formula, the term x! is removed, as it removes all the combinations with the same elements but different order.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

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The ratio of the areas of the quadrilaterals is 1:2. Option A

Let's assume that the two similar quadrilaterals have side lengths of x and 2x, respectively. The ratio of their perimeters is then 2x + 2x + 2x + 2x = 8x : 2 * (2x + 2x + 2x + 2x) = 4 * 8x = 32x. The ratio of the perimeters is 2:4, so we can write the equation:

8x/32x = 2/4

Solving for x, we find that x = 4.

So the ratio of the areas of the two similar quadrilaterals is (x^2)/(2x)^2 = (4^2)/(2 * 4^2) = 16/32 = 1/2.

Therefore, the ratio of the areas of the two similar quadrilaterals is 1:2.

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Explanation:

Spreadsheet software is strongly recommended. If you have excel, then it's best to use it since it's used practically everywhere. If you don't have excel, then there are tons of free alternatives such as OpenOffice or LibreOffice.

Enter the data as shown. Then form a third column labeled xy which represents multiplying each x and y pair for any given row. Eg: Tom = xy = 7*2 = 14. Use cell references to quickly compute this new column. I don't recommend manually multiplying each pair of items.

Once the xy column is formed, add up everything in it since [tex]\Sigma[/tex] represents summations. The command called "Sum" or "SUM" does this very quickly. In a cell off to the side type in [tex]=Sum(C2:C10)[/tex] which will add up the elements in cell C2, C3, ... all the way up to C10. Don't forget about the equal sign up front. That's needed to execute the command rather than print out text.

The result of the command should be 350

To verify you can manually add up the values to check the answer is correct.

Answer:

X = 7+2+5+9+6+10+9+8+4

X= 50

Y = 2+5+7+4+2+9+9+4+10

Y = 52

Now ,

Σ(xy)= 50×52

= 2600

Hope it helpful to you

The values of f(-1) , f(0) and f(2) are 0, 8 , 16 .

What is a function ?

Function can be defined in which it relates an input to output.

Given function ,

f ( x ) =  4x + 4 when x < 0

= 4x + 8 when x >= 0

f(-1) = 4x + 4

= 4 ( -1 ) + 4

= 0

f(0) = 4x + 8

= 4*0 + 8

= 8

f(2) = 4x + 8

= 4*2 + 8

= 8 + 8

= 16

Therefore, The value of f(-1) , f(0) and f(2) are 0, 8 , 16 .

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Answer:

A nonlinear function is a function in which the rate of change of the output (y) is not proportional to the rate of change of the input (x). In other words, a nonlinear function is a function where the graph of the function is not a straight line.

Here are a few examples of equations that represent nonlinear functions:

y = x^2: This is the equation for a parabolic function, which is a classic example of a nonlinear function.

y = sin(x): This is the equation for the sine function, which is periodic and nonlinear.

y = |x|: This is the equation for the absolute value function, which is nonlinear and has a "kink" at x = 0.

y = log(x): This is the equation for the natural logarithmic function, which is also nonlinear.

These are just a few examples of nonlinear functions. There are many other types of nonlinear functions, including polynomial, exponential, and trigonometric functions.