The exterior circumference of the regular polygon is: 20 x 8.13cm = 162.6cm
What is polygon ?
A polygon is a two-dimensional closed geometric shape made up of three or more straight sides connected by straight line segments. Polygons are named based on the number of sides they have. For example, a polygon with three sides is called a triangle, a polygon with four sides is called a quadrilateral, and so on.
Polygons can be regular or irregular. A regular polygon is a polygon with all sides of equal length and all interior angles of equal measure. An irregular polygon is a polygon with sides of different lengths and/or interior angles of different measures.
Some examples of polygons include:
Triangle: A polygon with three sides.
Square: A regular polygon with four sides of equal length and four interior angles of 90 degrees each.
Pentagon: A polygon with five sides.
Hexagon: A polygon with six sides.
Octagon: A polygon with eight sides.
According to the question:
The sum of the exterior angles of any polygon is always 360 degrees. In a regular polygon, all the exterior angles are equal, so each exterior angle of this regular polygon measures 360° divided by the number of sides.
Let's call the number of sides "n". Then we know that:
n x 18° = 360°
Solving for n, we get:
n = 360° / 18° = 20
So the regular polygon has 20 sides.
To find the exterior circumference of the polygon, we need to find the length of one exterior side. To do this, we can use trigonometry. The exterior angle and the interior angle of a regular polygon are supplementary, so each interior angle of this polygon measures:
180° - 18° = 162°
In a regular polygon, all the interior angles are equal, so we can use the formula for the sum of the interior angles to find the measure of each interior angle:
sum of interior angles = (n - 2) x 180°
20 x 162° = (20 - 2) x 180°
20 x 162° = 3240°
So each interior angle of the polygon measures 3240° / 20 = 162°.
Now, in a right triangle with one leg equal to half the side length (5.75cm) and the other leg equal to the tangent of half the interior angle (tan(81°) ≈ 5.98), the hypotenuse is equal to the length of one exterior side. Using the Pythagorean theorem, we can find the hypotenuse:
h = √(5.75^2 + 5.98^2) ≈ 8.13
Therefore, the exterior circumference of the regular polygon is:
20 x 8.13cm = 162.6cm (rounded to one decimal place)
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How to solve I can’t get the answer when I scan
On solving the given functions, we got the values as follows:
1) (rs)(4) = 8
2) ) [tex]\frac{r}{s}[/tex] (3) = 2
What is a function?
A relation between a set of inputs and a set of allowable outputs is called a function. It has the property that every input is associated with exactly one output. A function from one set X to another allocates precisely one element of the other set Y to each element of X. Both the set X and the set Y are referred to as the function's domain and codomain, respectively. The basic conception of functions was the relationship between fluctuating quantities and other variables. Multiply the outputs of two functions to multiply them. Put the numerator of a fraction with the first function as the numerator and the denominator with the second function as the denominator to divide functions. If you can, simplify.
Given two functions,
r(x) = 2√x
s(x) = √x
Now we have to calculate the following:
1) (rs)(4) = r(4) * s(4)
Multiplying the functions and finding the value when x = 4.
Solving,
= 2√4 * √4 = 2*2 * 2 = 8
2) [tex]\frac{r}{s}[/tex] (3) = [tex]\frac{r(3)}{s(3)}[/tex]
Dividing the functions and finding the value when x = 3.
Solving,
= [tex]\frac{2\sqrt{3} }{\sqrt{3} } = 2[/tex]
Therefore on solving the given functions, we got the values as follows:
1) (rs)(4) = 8
2) ) [tex]\frac{r}{s}[/tex] (3) = 2
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FILL IN THE BLANK. A decision maker has conditions of __________ when all the information needed to make the decision is available.
A decision maker has conditions of certainty when all the information needed to make the decision is available.
In decision making, there are three different conditions: certainty, risk, and uncertainty.
Certainty is when all the information needed to make a decision is available and the decision maker knows the outcome of each alternative.
Risk is when the decision maker has some information but does not know the outcome of each alternative with certainty.
Uncertainty is when the decision maker has little or no information and cannot predict the outcome of each alternative. In the case of the question, the decision maker has conditions of certainty because all the information needed to make the decision is available.
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I’D LIKE HELP AS SOON AS POSSIBLE
3. The measure of side c is 121 inches. The measure of side a is 57 inches. What is the
length of side b? SHOW YOUR WORK
Answer:
C
b
B
Answer:
Step-by-step explanation:
[tex]a^2+b^2=c^2[/tex] (Pythagoras Theorem)
[tex]57^2+b^2=121^2[/tex]
[tex]b^2=121^2-57^2[/tex]
[tex]b^2=11392[/tex]
[tex]b=\sqrt{11392}[/tex]
[tex]=106.73inches[/tex]
Answer:
Step-by-step explanation:
If we assume that the triangle is a right-angled triangle, then we can solve this by using the Pythagoras theorem.
the Pythagoras theorem: a^2+b^2= c^2
We already have a= 57 inches and c= 121 inches
So, putting values in the formula:
57^2+b^2= 121^2
After simplifying we get:
3249 + b^2=14641
b^2= 14641-3249
b^2= 11392
Now, taking the square root of both sides, we would have b as:
b ≈ 106.7 inches
Solve the system of equations.
y = 4x
y = x² +3
O A. (1,4) and (3, 12)
O B. (-3,-12) and (-1,-4)
OC. (0, 3) and (1,4)
OD. (-1,-4) and (3, 12)
SUBMIT
Answer: A. (1,4) and (3,12)
Explanation: These ordered pair are the only ones which fit into the given equations when substituted.
(1,4)
4 = 4(1)
4 = 4
4 = 1^2+3
4 = 4
(3,12)
12 = 4(3)
12 = 12
12 = 3^2+3
12 = 12
Answer:
A. (1, 3) and (3, 12).
Step-by-step explanation:
y = 4x
y = x² +3
As y is common on left side:
x^2 + 3 = 4x
x^2 - 4x + 3 = 0
(x - 1)(x - 3) = 0
x = 1, 3.
When x = 1, y = 4*1 = 4
and when x = 3 , y = 12.
If f (x) = (x + 2)² and g(x) = x +4, find all values of x for which f(x) = g(x).
Answer: g(x)=32
Step-by-step explanation:
4x + 2y = 12
x - y = 3
Step-by-step explanation:
4x+2y= 12 (1)
x-y= 3 (2)
From (2):
x= y+3 (3)
sub (3) into (1):
4(y+3)+2y= 12
4y+12+2y= 12
6y= 0
y=0 (4)
sub (4) into (2):
x-0= 3
x= 3
x= 3 and y= 0
The point P(1, 0) lies on the curve y = sin(14pi/x)
If Q is the point (x, (14pi/x)) find the slope of the secant line PQ (correct to four decimal places) for the following values of x.
(i) 2
(ii) 1.5
(iii) 1.4
(iv) 1.3
(v) 1.2
(vi) 1.1
(vii) 0.5
(viii) 0.6
(ix) 0.7
(x) 0.8
(xi) 0.9
The slopes of the secant lines are listed below:
Case I: m = 0
Case II: m = - √3 (aprox. 1.7321)
Case III: m = 0
Case IV: m = 2.2103
Case V: m = 5√3 / 2 (approx. 4.3301)
Case VI: m = 7.5570
Case VII: m = 0
Case VIII: m = - √3 (aprox. 1.7321)
Case IX: m = 0
Case X: m = 5
Case XI: m = - 9.8480
How to determine the determine the slope of a secant line
In this problem we find eleven cases of two pairs of points lying on a sinusoidal curve, each of which we need to determine the slope of the secant line by means of the following formula:
m = [f(a) - f(b)] / (b - a)
Where the definition of the sinusoidal function is f(x) = sin (14π / x).
Now we proceed to determine the slope of each secant line:
Case I
m = [f(2) - f(1)] / (2 - 1)
m = (0 - 0)
m = 0
Case II
m = [f(1.5) - f(1)] / (1.5 - 1)
m = (- √3 / 2 - 0) / 0.5
m = - √3 (aprox. 1.7321)
Case III
m = [f(1.4) - f(1)] / (1.4 - 1)
m = (0 - 0) / 0.4
m = 0
Case IV
m = [f(1.3) - f(1)] / (1.3 - 1)
m = (0.6631 - 0) / 0.3
m = 2.2103
Case V
m = [f(1.2) - f(1)] / (1.2 - 1)
m = (√3 / 2 - 0) / 0.2
m = 5√3 / 2 (approx. 4.3301)
Case VI
m = [f(1.1) - f(1)] / (1.1 - 1)
m = (0.7557 - 0) / 0.1
m = 7.5570
Case VII
m = [f(0.5) - f(1)] / (0.5 - 1)
m = (0 - 0) / (- 0.5)
m = 0
Case VIII
m = [f(0.6) - f(1)] / (0.6 - 1)
m = (- √3 / 2 - 0) / (- 0. 4)
m = - √3 (aprox. 1.7321)
Case IX
m = [f(0.7) - f(1)] / (0.7 - 1)
m = (0 - 0) / (- 0. 3)
m = 0
Case X
m = [f(0.8) - f(1)] / (0.8 - 1)
m = (- 1 - 0) / (- 0.2)
m = 5
Case XI
m = [f(0.9) - f(1)] / (0.9 - 1)
m = (- 0.9848 - 0) / (- 0.1)
m = - 9.8480
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find the inverse of f(x) = (8x+11)/(15x-3)
The inverse of f(x) = (8x+11)/(15x-3) is = 11 + 3x / 15x-8
What is inverse of a fn?With relation to the original function f, the inverse function is denoted by the symbol f-1, and both the original function's domain and its range are transformed into the inverse function's domain and range, respectively.
Swapping (x, y) with (y, x) with reference to the line y = x yields the graph of the inverse function.
A function's inverse, indicated by the symbol f-1, only exists when the function is both a one-one and an onto function.
Keep in mind that f-1 is NOT f's inverse.
The domain value of x is determined by the combination of the function f and the reciprocal function f-1.
f(x) = (8x+11)/(15x-3)
swapping(x,y)
11 + 3x / 15x-8
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he point (2, 0) lies on a circle with the center at the origin. What is the area of the circle to the nearest hundredth? Use 3.14 for π.
r = 2
Area = πr^2
= π2^2
= π4
= 12.566370
The area of the circle is 12.57 units squared.
You perform an hypothesis test and the null hypothesis was not rejected at an alpha level of 0.05. You want to perform the same test using an alpha of 0.25. What will be your conclusion? a. Fail to reject the null hypothesis b. Accept the alternative hypothesis c. No conclusion can be made
d. Reject the null hypothesis e. Reject the alternative hypothesis
The correct answer is a. Fail to reject the null hypothesis.
Explanation:
When performing a hypothesis test, the alpha level is the probability of rejecting the null hypothesis when it is actually true. A lower alpha level, such as 0.05, means that there is a smaller chance of making a Type I error (rejecting the null hypothesis when it is actually true). If the null hypothesis was not rejected at an alpha level of 0.05, it means that there was not enough evidence to support the alternative hypothesis.
When the alpha level is increased to 0.25, the probability of making a Type I error increases, but it does not change the conclusion of the test. The null hypothesis will still fail to be rejected because there is not enough evidence to support the alternative hypothesis.
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Given the matrix find all values of a that make the |A| = 0. Enter the values of a as a comma-separated list:
The only value of a that makes |A| = 0 is a = 0. there is only one value that satisfies the condition, our answer is: 0.
Here's how to approach it:Given the matrix A, we need to find all values of a that make the determinant of A (denoted |A|) equal to 0. To do this, we will first calculate |A| by multiplying the elements of A in a particular way:|A| = a(2a + 1) - (2a)(a + 3) = 2a² + a - 2a² - 6a = -5aNow, we know that |A| = 0 when -5a = 0, which occurs only when a = 0.
Therefore, the only value of a that makes |A| = 0 is a = 0.
The requested answer is in the form of a comma-separated list. Since there is only one value that satisfies the condition, our answer is: 0.
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A credit card holder has an outstanding balance on four different credit cards. Which method of paying off the credit card will save the most money?
O Snowballing payments according to the highest interest rate
O Snowballing payments according to the lowest balance
O Making fixed payments each month
O Paying the minimum balance each month
Snowballing payments according to the highest interest rate is likely to save the most money in the long run.
Option (A) is correct.
What is the interest rate?
An interest rate is the amount charged, expressed as a percentage of principal, by a lender to a borrower for the use of assets, such as money or property. It is typically calculated as an annual percentage of the principal amount, and represents the cost of borrowing or the reward for saving.
Snowballing payments according to the highest interest rate is likely to save the most money in the long run.
This method involves paying off the credit card with the highest interest rate first, while continuing to make minimum payments on the other cards. Once the card with the highest interest rate is paid off, the next highest interest rate card is tackled, and so on.
By prioritizing the highest interest rate cards, the overall amount of interest paid will be lower than if the payments were made based on the lowest balance or a fixed payment each month. Additionally, paying only the minimum balance each month will result in much higher interest charges and a longer payoff period.
While the snowball method of paying off the lowest balance may provide psychological benefits by creating a sense of progress and momentum, it may not always be the most cost-effective way to pay off debt.
Hence, Snowballing payments according to the highest interest rate is likely to save the most money in the long run.
Option (A) is correct.
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The position of an object moving along a line is given by the function
s(t)=−8t2+24t.
Find the average velocity of the object over the following intervals.
(a) [1,
4]
(b) [1,
3]
(c) [1,
2]
(d) [1,
1+h]
where
h>0
is any real number.
The average velocity of the given following intervals is :
a) 16 m/s
b) 12 m/s
c) 8 m/s
d) (24+16h)/h m/s
The average velocity of an object over a given interval is equal to the change in position (Δs) over the change in time (Δt).
For part (a) of the question, the interval is [1,4] and the change in position is s(4)-s(1). The change in time is 4-1.
Therefore, the average velocity over the interval [1,4] is (s(4)-s(1))/(4-1).
Plugging in the equation given, this is (-8×4×2+24×4)-(-8×1×2+24×1))/(4-1).
The average velocity over the interval [1,4] is 16 m/s.
For part (b) of the question, the interval is [1,3] and the change in position is s(3)-s(1). The change in time is 3-1.
Therefore, the average velocity over the interval [1,3] is (s(3)-s(1))/(3-1).
Plugging in the equation given, this is (-8×3×2+24×3)-(-8×1×2+24×1))/(3-1).
The average velocity over the interval [1,3] is 12 m/s.
For part (c) of the question, the interval is [1,2] and the change in position is s(2)-s(1). The change in time is 2-1.
Therefore, the average velocity over the interval [1,2] is (s(2)-s(1))/(2-1).
Plugging in the equation given, this is (-8×2×2+24×2)-(-8×1×2+24×1))/(2-1).
The average velocity over the interval [1,2] is 8 m/s.
For part (d) of the question, the interval is [1,1+h] and the change in position is s(1+h)-s(1). The change in time is (1+h)-1.
Therefore, the average velocity over the interval [1,1+h] is (s(1+h)-s(1))/((1+h)-1).
Plugging in the equation given, this is (-8×(1+h)2+24×(1+h))-(-8×12+24×1))/((1+h)-1).
The average velocity over the interval [1,1+h] is (24+16h)/h m/s.
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Determine the equation of the circle with center (7, -7) containing the point (11, -3)
The equation of the circle is: [tex](x - 7)^2 + (y + 7)^2 = 32[/tex]. The general equation of a circle with center (h, k) and radius r is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
We are given that the center of the circle is (7, -7) and that it contains the point (11, -3).
Using the formula for the equation of a circle, we can substitute the values of h and k:
[tex](x - 7)^2 + (y + 7)^2 = r^2[/tex]
To find the value of [tex]r^2[/tex], we can substitute the coordinates of the point (11, -3) into the equation and solve for[tex]r^2[/tex]:
[tex](11 - 7)^2 + (-3 + 7)^2 = r^2[/tex]
[tex]4^2 + 4^2 = r^2[/tex]
[tex]16 + 16 = r^2[/tex]
[tex]32 = r^2[/tex]
Therefore, the equation of the circle is: [tex](x - 7)^2 + (y + 7)^2 = 32[/tex]
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For what values of c does the quadratic equation x^2-2x+c=0 have no real roots?
Answer:
c > 1
Step-by-step explanation:
For a quadratic equation of the form ax^2 + bx + c = 0 to have no real roots, its discriminant (b^2 - 4ac) must be negative.
In the given quadratic equation, a = 1, b = -2, and c = c. So the discriminant is:
b^2 - 4ac = (-2)^2 - 4(1)(c) = 4 - 4c
For the equation to have no real roots, we need:
b^2 - 4ac < 0
4 - 4c < 0
Solving for c, we get:
4c > 4
c > 1
Therefore, for c > 1, the quadratic equation x^2 - 2x + c = 0 has no real roots.
Answer:
C<1
Step-by-step explanation:
Im pretty sure
Olivia opens a bank account and deposits $514. During the month, Olivia withdraws $120.00 and deposits $40. What is her new balance at the end of the month
Ben is a computer repair technician. He charges
a fee of $20 to go to a client's home, and $30 for
every hour of work. Ben went to a client's home
and worked for x hours.
Enter an expression that represents the total
amount of money, in dollars, Ben earned.
The expression that represents the total amount of money, in dollars, Ben earned is:
y = 30x + 20
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one maths operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. These are mathematical statements that must have at least two terms with variables or terms with numbers, or both, joined by an operator. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables. Mathematical expressions include constants, variables, terms, and coefficients.
The money charged by Ben to go to the client's home = $20
The money charged by Ben for one hour's work = $30
We are asked to write an expression that represents the total amount of money Ben earned if he worked for x hours.
Let the total money earned by Ben be y.
Now $20 is the fixed amount.
the amount of money earned for x hours work = 30*x = 30x
Therefore the expression that represents the total amount of money, in dollars, Ben earned is:
y = 30x + 20
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find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties: (a) are divisible by 5 and by 7.
The total number of positive integers with exactly four decimal digits that are divisible by 5 and by 7 is 255
There are a total of 12 positive integers with exactly four decimal digits that are divisible by 5 and by 7.
To find these numbers, we can start by finding the smallest and largest four-digit numbers that are divisible by 5 and 7. The smallest four-digit number that is divisible by 5 and 7 is 1050 (5 * 7 * 30) and the largest is 9945 (5 * 7 * 283).
Next, we can find how many multiples of 35 (5 * 7) are between 1050 and 9945. To do this, we can subtract the smallest multiple (1050) from the largest (9945) and divide by 35:
(9945 - 1050) / 35 = 8895 / 35 = 254
This means there are 254 multiples of 35 between 1050 and 9945. However, we need to add 1 to this number to include the smallest multiple (1050), so the total number of positive integers with exactly four decimal digits that are divisible by 5 and by 7 is 254 + 1 = 255.
Therefore, the answer is 255.
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NEED ANSWERS QUICK! This is really tuff for me HELP ME
The value of x for the given equations are: x/2 - 1 = 3; x = 8, 19 - 2x = 7; x = 6, 11x - 21 = 56; x = 7, and (x + 26)/3 = 6; x= -8.
What is equation with one variable?One solution exists for the linear equation with one variable, which is written as ax+b = 0, where a and b are two integers, and x is a variable. A linear equation with a single variable, for instance, is 2x+3=8. As a result, x = 5/2 is the sole answer to this problem. In contrast, a linear equation with two variables has two solutions.
The given equations are:
x/2 - 1 = 3
Take the LCM:
x - 2/2 = 3
x-2 = 6
x = 8
For 19 - 2x = 7
19 - 7 = 2x
2x = 12
x = 6
For 11x - 21 = 56
11x = 56 + 21
11x = 77
x = 7
For (x + 26)/3 = 6
x + 26 = 18
x = 18 - 26
x = -8
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Prove that the following pairs of expressions are not logically equivalent.
(a) p → q and q → p
(b) ¬p → q and ¬p ∨ q
(c) (p → q) ∧ (r → q) and (p ∧ r) → q
(d) p ∧ (p → q) and p ∨ q
The pairs of expressions (a), (b), (c), and (d) are not logically equivalent because they do not yield the same truth value when p and q are assigned certain values.
For (a):
p → q is false if p is true and q is false, but q → p is true in this case. Therefore, these expressions are not logically equivalent.
For (b):
¬p → q is true if p is false and q is true, but ¬p ∨ q is false in this case. Therefore, these expressions are not logically equivalent.
For (c):
(p → q) ∧ (r → q) is false if p is true, q is false, and r is true, but (p ∧ r) → q is true in this case. Therefore, these expressions are not logically equivalent.
For (d):
p ∧ (p → q) is true if p is true and q is true, but p ∨ q is false in this case. Therefore, these expressions are not logically equivalent.
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what is 8 Rounded tl to the nearest tenth. 12 13
The number 8, rounded to the nearest tenth, is given as follows:
8.0.
How to round a number to the nearest tenth?To round a number to the nearest tenth, follow these steps:
Identify the digit in the hundredths place (two digits to the right of the decimal point).If this digit is 5 or greater, add 1 to the tenths place (one digit to the right of the decimal point). If it is less than 5, leave the tenths place as it is.Drop all digits to the right of the tenths place.For example, if you want to round the number 3.56 to the nearest tenth:
The digit in the hundredths place is 6.Since 6 is greater than 5, add 1 to the tenths place, giving 3.6.Drop all digits to the right of the tenths place, leaving you with the rounded number of 3.6.For the number 8, the first and the second decimal digits are of 0, thus the number rounded to the nearest tenth is given as follows:
8.0.
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a restaurant sells a family meal for $22 plus $2 per drink. Another restaurant sells a family meal for $25 plus $1.50 dollars per drink. how many drinks need to be purchased at each restaurant so the total cost for a meal and drinks is the same?
Answer:
6 drinks
Step-by-step explanation:
To find out how many drinks must be purchased for the meal to cost the same amount, we have to set the two expressions equal to each other
22 + 2x = 25 + 1.50x
0.50x + 22 = 25
0.50x = 3
x = 6
Then we can check our answers individually
22 + 2(6) = 34
25 + 1.50(6) = 34
what does it mean if the slope of a line is undefined
The slope of a line is undefined when the line is vertical. In this case, the line does not have a well-defined slope because its rise (change in y) would be infinite while its run (change in x) would be zero.
In general, the slope of a line represents the rate at which the line rises or falls as it moves from left to right. It is defined as the change in y divided by the change in x between any two points on the line.
If the slope of a line is positive, the line is sloping upward from left to right, and if the slope is negative, the line is sloping downward from left to right. If the slope is zero, the line is horizontal. When the slope is undefined, it means that the line is vertical, and it has no well-defined rate of rise or fall as it moves from left to right.
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Giving brainliest need ASAP
Answer:
I can answer this if you can make copyable
a triangle sides of length 16cm,48cm and 50cm is the triangle a right angled triangle?
Yes, the triangle with sides of length 16cm, 48cm, and 50cm is a right angled triangle.
Why it is?
This is because the Pythagorean theorem states that in a right angled triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the longest side (the hypotenuse).
In this case, if we square the lengths of the sides, we get:
16²2 + 48²2 = 256 + 2304 = 2560
50²2 = 2500
Since 16²2 + 48²2 = 2560, which is equal to 50²2, we can see that the lengths of the sides of this triangle satisfy the Pythagorean theorem. Therefore, this triangle is a right angled triangle, where the side with length 50cm is the hypotenuse and the sides with length 16cm and 48cm are the legs.
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help me please, picture below
-5i-6i
picture given
.........
if you roll an 8.5-by-11-inch piece of paper into a cylinder by bringing the two longer sides together, you get a tall, thin cylinder. if you roll an 8.5-by-11-inch piece of paper into a cylinder by bringing the two shorter sides together, you get a short, fat cylinder. which of the two cylinders has the greater volume?
The second cylinder has the greater volume, as it has a greater radius and a greater height than the first cylinder. The volume of the second cylinder is 740π cubic inches, which is 145.75π cubic inches greater than the volume of the first cylinder.
The volume of the two cylinders can be calculated using the formula for the volume of a cylinder, which is V = πr2h, where r is the radius and h is the height of the cylinder.
For the first cylinder, the radius of the cylinder is [tex]8.5/2 = 4.25[/tex] inches, and the height is 11 inches. Therefore, the volume of the first cylinder is V = π(4.25)2 x 11 = 594.25π cubic inches.
For the second cylinder, the radius of the cylinder is 11/2 = 5.5 inches, and the height is 8.5 inches. Therefore, the volume of the second cylinder is V = π(5.5)2 x 8.5 = 740π cubic inches.
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Jia designs a vase in the shape of a triangular prism. She decides
to make a smaller version of the vase. She decreases the area of
the base by 50%. She decreases the height by 50%. By what
percent does the volume of the vase change? Show your work.
Answer:
50%
Step-by-step explanation:
[tex]volume = \frac{area \: of \: base \times \: height}{3} \\ v = \frac{ \frac{1}{2} area \: of \: base \times \frac{1}{2} height}{3} \\ v = \frac{ \frac{1}{2} (area \: of \: base \times heigh)}{3} \\ v = \frac{1}{2} ( \frac{1}{3} area \: of \: base \: \times height) \\ v = \frac{1}{2} (v)because \: v \: = \frac{1}{3} area \: ofbase \times height[/tex]
[tex] \frac{1}{2} \times 100 \\ = 50\%[/tex]
Cleveland woods earns 126,000 per year he is paid monthly how much is deducted in august for social security for medicare
Answer: The amount deducted for Social Security and Medicare for Cleveland Woods for the month of August would be $1,585.30 ($126,000 x 0.01239).
Step-by-step explanation:
7. Elizabeth is trying to determine the best way to invest in her retirement. Retirement Saving Plan #1 will start with $2000 at age 20 and earn 2.8% interest compounded annually. Retirement Saving Plan #2 will start with $2500 at age 25 and earn 5% simple interest every year.
a) Which retirement plan will she earn the most money by age 65?
b) What is the difference in the amount of money earned in both plans?
Part a: The retirement plan Saving Plan #2 will give most money by age 65.
Part b: Difference in amount of money earned in each plans is $1195.21
Explain simple interest and compound interest?Simple interest is computed on a loan's principal, or initial loan amount. Compound interest is often referred to as "interest on interest" since it is calculated using both the principal and the accrued interest from prior periods.Part a: retirement plan will she earn the most money by age 65.
Saving Plan #1 :compounded annually
A = P[tex](1 + \frac{r}{n} )^{nt}[/tex]
Principal P = $2000
Time = 65 - 20 = 45 years.
Interest r = 2.8%.
A = 2000[tex](1 + \frac{0.028}{1} )^{1*45}[/tex]
A = $6929.79
Saving Plan #2 : simple interest
SI = PRT/100
Principal P = $2500
Time = 65 - 20 = 45 years.
Interest r = 5%.
SI = 2500*45*5/100
A = SI + P
A = 2500 + 5625
A = $8125
The retirement plan Saving Plan #2 will give most money by age 65.
Part b: difference in the amount of money earned in both plans.
Difference = A(SI) - A(CI)
Difference = $8125 - $6929.79
Difference = $1195.21
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