The largest size of the square that can be embroidered within the 6 inch hoop is 4.2 inches per side (rounded to the nearest tenth). This is found using geometry principles involving squares and circles.
Explanation:This question is asking for the side length of a square that will fit within a circle, or in this case, an embroidery hoop, with a certain diameter. This is a concept from geometry that involves the relationship between squares and circles. Essentially, the diameter of the circle becomes the diagonal of the square.
To calculate the side length (x) of the square, we'll use the formula for the diagonal (d) of a square divided by the square root of 2 (d = √2 * x). Since the diameter of the hoop is 6 inches, rearranging the equation gives us x = d / √2 which results in x = 6 / √2 = 4.2 inches (rounded to the nearest tenth)
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Can you create a rule relating library fines for new books to the number of days the book is kept? Write your rule in symbolic form, using F for the fine and d for number of days the book is kept.
total of the fine = C
you would need to multiply the amount of the fine by the number of days
so the equation would be C=Fd
What is the value of X? Make sure to show all of your work!
Which graph represents the division of -12 / 4 ?
First step to solve the equation 9h-21=99
You make skateboard ramps by cutting pieces from a board that is 12 1/2 feet long.
a. your friend estimates you can cut 6 ramps from the board. is her estimate reasonable? explain. how many ramps can you cut from the board? how much wood is left over?
The estimate of cutting 6 ramps from a 12 1/2 feet long board is reasonable. Each ramp will have a length of 2 1/12 feet, and no wood will be left over.
Explanation:To determine if the estimate of cutting 6 ramps from a 12 1/2 feet long board is reasonable, we can calculate the length of each ramp by dividing the total length of the board by the number of ramps.
12 1/2 feet is equivalent to 12 + 1/2 feet. To divide by a fraction, we can multiply by the reciprocal. So, when we divide 12 1/2 by 6, we get (12 + 1/2) / 6 = 12/6 + 1/2 / 6 = 2 feet + 1/12 feet = 2 1/12 feet.
Therefore, each ramp will have a length of 2 1/12 feet. Since 6 ramps multiplied by 2 1/12 feet is 12 1/2 feet, the estimate is reasonable. No wood will be left over.
This figure is a rectangle Select the three statements that describe all rectangles.
Megan is checking her tax bill for the last year.
The tax rates were as follows;
-no tax on the first £11 000 of earnings
Final answer:
Marginal tax rate refers to the tax rate applied to each additional dollar of income. Individuals pay according to the bracket their income falls into, with higher rates applying only to income that exceeds certain thresholds. An example includes a single taxpayer earning $35,000 a year being in the 15% marginal tax rate bracket.
Explanation:
The student's question relates to understanding marginal tax rates and how they apply to an individual's income. Marginal tax rate is the tax rate incurred on each additional dollar of income, meaning as you earn more, you generally pay a higher tax rate on your incremental earnings beyond certain thresholds. However, it's important to note that lower tax rates apply to lower income brackets, meaning individuals pay progressively more only on the income that falls within higher brackets.
For instance, consider the marginal tax rate structure where the first $9,075 of income is taxed at 10%, the income from $9,075 to $36,900 at 15%, and income beyond $36,900 at 25%. If a single taxpayer earns $35,000 a year, their marginal tax rate is 15% because their last dollar earned falls into the 15% tax bracket. However, not all their income is taxed at 15%; the income up to $9,075 is taxed at 10%, and only the income over $9,075 up to $35,000 is taxed at 15%.
The cube of a positive number divided by the square of the same positive number
The cube of a positive number divided by its square simplifies to the number itself, based on the exponent subtraction rule in algebra.
Explanation:The question involves a mathematical concept where the cube of a positive number is divided by the square of the same number. Mathematically, if we denote the positive number as 'x', then the expression would be x3/x2. According to the laws of exponents, when we divide two powers with the same base, we subtract the exponents. Thus, x3/x2 = x3-2 = x. This implies that the cube of 'x' divided by the square of 'x' simplifies to just 'x'. This is a fundamental mathematical operation under the topic of exponentiation and simplification of algebraic expressions.
According to one web page on the resale value of cars, a BMW that cost $71,000 in 2003 depreciates in value about 15% a year. How much was it worth in 2013?
71,000 *(1-0.15)^10 =
71,000*0.85^10 =
$13,978.08
we apply the exponential decay formula leading to an estimated worth of approximately $13,978.37 in 2013.
To calculate the value of a BMW that cost $71,000 in 2003 and depreciates at a rate of about 15% per year for 10 years, we will use the formula for exponential decay, which is:
V = [tex]P(1 - r)^t[/tex]
Where:
V is the final value after depreciation
P is the principal amount ($71,000)
r is the rate of depreciation (15%, or 0.15)
t is the time in years (2013 - 2003 = 10 years)
So, our calculation will be:
V = $71,000 *[tex](1 - 0.15)^{10}[/tex]
V = $71,000 * [tex](0.85)^{10}[/tex]
V = $71,000 * 0.19687
V ≈ $13,978.37
Therefore, the BMW would be worth approximately $13,978.37 in 2013.
If you are given the height and base of a pyramid, how would you get the slope of one of the triangular faces?
by using the Pythagorean theorem
use the height and half the base dimension for the 2 edges of a triangle and the slope ( slant height) would be the hypotenuse
so: SQRT(height ^2 + half of base^2) = hypotenuse ( Slant height)
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The function graphed is f(x). What is f(2)?
when x is on 2
y is on -3
answer is y=-3
If the measure of cae is 95° what is the measure of cba
Answer:
The measure of the arc CBA is equal to 190°
Step-by-step explanation:
95 x 2 = 190
Suppose that a department contains 8 men and 16 women. how many different committees of 6 members are possible if the committee must have strictly more women than men
Mazie Invested $4500 in an account earning 4.3% interest compounded continuously. After how many years will she have $7400 in her account
The question is about continuous compound interest in finance. Given initial investment, final amount, and interest rate, we utilize the formula for continuous compound interest to calculate how many years it will take for the investment to reach a certain value.
Explanation:The subject in this question is interest compounding in mathematics, specifically in the field of finance. Compounding continuously involves the application of the formula for continuous compound interest, which is A = P*e^(rt), where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).e is the base of the natural logarithm, approximately equal to 2.71828.r is the annual interest rate (in decimal).t is the time the money is invested or borrowed for, in years.In Mazie's case, we have P=$4500, A=$7400, and r=4.3% or 0.043 in decimal form. We're solving for t, the time. Therefore, by substitution, we have 7400=4500*e^(0.043t). Solving for 't' will provide us the number of years it takes for the account to grow to $7400.
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what is the greatest possible whole number remainder if you divide any number by 41?
what is the numerical sum of angle DEA (X+25) and angle AEB (9x+10) ?
Draw the image of ∆PQR after a rotation of 180° about the origin. Label the image ∆P'Q'R'.
Draw the image of ∆PQR after a reflection across the x-axis. Label the image ∆P"Q"R".
To obtain the image of triangle ∆PQR after a 180° rotation about the origin, we applied the rotation formula to each vertex, resulting in the new coordinates P'(-1, 1), Q'(-3, 2), and R'(-3, 4). Connecting these points forms the rotated triangle ∆P'Q'R'.
To draw the image of triangle ∆PQR after a 180° rotation about the origin, we'll need to find the new coordinates of the vertices P', Q', and R'. The general formula for rotating a point (x, y) by 180° about the origin is to negate both the x and y coordinates, resulting in the point (-x, -y). Let's apply this formula to each vertex:
Vertex P(1, -1) is rotated to P'(-1, 1).
Vertex Q(3, -2) is rotated to Q'(-3, 2).
Vertex R(3, -4) is rotated to R'(-3, 4).
Now, we have the new coordinates for the vertices of the rotated triangle ∆P'Q'R'. Let's plot these points on a coordinate plane:
P'(-1, 1)
|
|
| Q'(-3, 2)
| /
|/
R'(-3, 4)
The triangle ∆P'Q'R' is formed by connecting these three points, and it is the image of ∆PQR after a 180° rotation about the origin.
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how to simplify 6/35
Evaluate f(x)= 1.8 X 2^x for x=6
A: 115.2
B: 2176.78
C: 21.6
Question:
Evaluate f(x)= 1.8 X 2^x for x=6
Answer choices:
A: 115.2
B: 2176.78
C: 21.6
Answer:
A:115.2
Step-by-step explanation:
F(x) F(6)
=1 . 8 • 2 • 1
=1 . 8 • 261
=1 . 8 • 64115.2
=115.2
Hence, your answer is A:
suppose you roll a red number cube and a blue number cube. what is the probability that you will roll a 5 on the red cube and a 1 or a 2 on the blue cube?
The probability that you will roll a 5 on the red cube and a 1 or a 2 on the blue cube will be 1/18.
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
You will roll a 5 on the red cube and a 1 or a 2 on the blue cube.
Now,
Sides of cube dice = 6
Hence, For red cube;
P (r) = 1/6
And, For blue red;
P (B₁ or B₂) = P(B₁) + P (B₂)
= 1/6 + 1/6
= 1/3
Thus, The probability that you will roll a 5 on the red cube and a 1 or a 2 on the blue cube = 1/6 x 1/3
= 1/18
Therefore, The probability that you will roll a 5 on the red cube and a 1 or a 2 on the blue cube will be 1/18.
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2/3 + y - 1/9 = 7/9 Solve for Y
2 1/2x - 3/4(2x + 5) = 3/8 Solve for X
0.9 (x + 1.4) - 2.3 + 0.1x = 1.6 Solve for X
Answer:
A. Y = 2/9
B. X = 11/24
C. X = 2.64
The graph of y=f(x) is given above. For what value of x is y=f(x-4) undefined?
Answers to question 5 and 6 please xx
In the xy-plane, if the parabola wiry equation y=ax^2+bx+c, where a, b, and c are constants, passes through the point (-1,1), which of the following must be true?
in order to have reflection symmetry must a polygon have at least two sides that are the same length ?
A population grows with an annual growth rate of 16.5 % per year. (a) what is the monthly growth rate
Why did Benjamin Franklin use the pseudonym “Richard Saunders” when writing Poor Richards Almanac?
how do you solve this equation?
216=-4(8n-6)
Bill spends two days driving from point a to point
b. on the first day, he drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. if during the two days he drove a total of 680 miles over the course of 18 hours, what was his average speed on the second day, in miles per hour?
Answer: his average speed on the second day is 35 miles per hour
Step-by-step explanation:
Bill spends two days driving from point a to point b
Let x = his speed on the first day.
Let y = his speed on the second day
Speed = distance / time
Time = distance / speed
Total time spent on the trip is 18 hours
Let time that he spent on the first day be t hours
Time that he spent on the second day will be 18 - t
Bill drove 2 hours longer on the second day than on the first day. This means
t = 18 - t + 2
t+t = 18+2
2t = 20
t = 10
He spent 10 hours on the first day.
He spent 18-10 = 8hours on the second day.
Bill drove at an average speed of 5 miles per hour faster than he drove on the second day. This means that
x = y + 5 - - - - - - - -- 1
Distance travelled on the first day = speed on the first day × time spent. This becomes
10 × x = 10x miles
Distance travelled on the second day = speed on the second day × time spent. This becomes
8 × y = 8y miles
He drove a total of 680 miles over the course of the 18 hours. This means that
10x + 8y = 680 - - - - - - - - 2
Substituting equation 1 into equation 2, it becomes
10(y + 5) + 8y = 680
10y + 50 + 8y = 680
10y + 8y = 680 - 50
18y = 630
y = 630/18 = 35 miles per hour
x = y + 5 = 35 + 5
x = 40 miles per hour
Identify the function that has a vertex of (2,-1) and is stretched vertically by a factor of 3.
f(x) = ⅓|x - 2| - 1
f(x) = |x - 2| + 4
f(x) = ⅓|x + 2| - 1
f(x) = 3|x - 2| - 1
Answer:
[tex]f(x)=3|x-2|-1[/tex]
Step-by-step explanation:
Identify the function that has a vertex of (2,-1) and is stretched vertically by a factor of 3.
The option are absolute function, So the parent function is y=|x|
Vertex form of absolute function is
[tex]y=|x-h|+ k[/tex] where (h,k) is the vertex
vertex of (2,-1) h=2, k =-1
the function becomes
[tex]f(x)=|x-2|-1[/tex]
function is stretched vertically by a factor of 3
when f(x) is vertically stretched by a factor of 'a'.We multiply the factor with f(x)
[tex]f(x)=3|x-2|-1[/tex]