Answer:
No, the ribbon would not be long enough to go around the edge of the cake.
Circumference ≈ 81.7 cm
Step-by-step explanation:
1) Calculate the circumference of the cake
Circumference - the length around a circle
[tex]C=2\pi r[/tex] where r is the radius
Plug 13 in as the radius
[tex]C=2\pi (13)\\C=26\pi\\C= 81.7[/tex]
Therefore, the circumference of the cake is approximately 81.7 cm.
Because the ribbon is only 36 cm long, it would not be enough to go around the edge of the cake.
I hope this helps!
16. Use the distributive property of multiplication to find the product of 2x5²
We have:
[tex]2x \cdot (5^2)[/tex]
[tex]= 2x \cdot 25[/tex]
[tex]= \boxed{50x}[/tex]
Given the following utility function:
X: -100 -90 -80 -65 -50 -35 -20 0 20 45 70 110 150
U (X): 0 3 4.5 6 7 8 9 10 11 12 13 14 15
(a) Calculate the probabilities p1 and p2 such that 45 is indifferent to the lotteries: (20, p1; 150, 1 −p1) and (−20, p2; 110, 1 −p2)
(b) Calculate the selling price and risk premiums of the lotteries: (−90, 0.5; −20, 0.5) and (−100, 0.2; −50, 0.3; −20, 0.4; 70, 0.1).
(c) Calculate the buying price for the following lottery (150, 0.4; 45, 0.6).
If utility function is given then we set up U(45) = p2 * U(-20) + (1 - p2) * U(110) and solve for p2.
(a) To find the probabilities p1 and p2, we set up the equation U(45) = p1 * U(20) + (1 - p1) * U(150) and solve for p1. Similarly, we set up U(45) = p2 * U(-20) + (1 - p2) * U(110) and solve for p2.
(b) The selling price of a lottery is the amount at which an individual is willing to sell the lottery. We compare the expected utility of the lottery to the utility of the certain amount. The risk premium is the difference between the selling price and the expected value of the lottery.
(c) The buying price is the amount an individual is willing to pay for a lottery. We set up the equation U(45) = p * U(150) + (1 - p) * U(45) and solve for p to find the buying price.
Note: The specific calculations for parts (a), (b), and (c) require the values of U(X) for each corresponding X value in the utility function.
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Write an equation of the line perpendicular to the given line that contains P.
[tex]\sqrt{x} 196
can someone help me
Answer:
14
Step-by-step explanation:
√196
Calculate the square root of 196 and get 14.
14
jet travelling at 500 km/h for 4 hours.
Answer: jet travels a total of 2000 km in total
Step-by-step explanation:
(help asap) The steps to solving the expression the quantity of the sum of three squared plus four divided by the absolute value of negative 0.25 end quantity minus 10.4 ÷ 4 are listed below.
Part A: Explain what the missing expression should be in Step 3. (6 points)
Part B: Explain what the missing expression should be in Step 6. (6 points)
Step 1 the quantity of the sum of three squared plus four divided by the absolute value of negative 0.25 end quantity minus 10.4 ÷ 4
Step 2 the quantity of the sum of three squared plus four divided by 0.25 end quantity minus 10.4 ÷ 4
Step 3
Step 4 the quotient of quantity 13 divided by 0.25 end quantity minus 10.4 ÷ 4
Step 5 52 − 10.4 ÷ 4
Step 6
Step 7 49.4
The final result of the given expression is 49.4.
Part A: In the missing expression should be the result of squaring three and adding four.
This is because the expression in Step 2 states "the quantity of the sum of three squared plus four divided by 0.25.
" Therefore, to continue simplifying the expression, we need to evaluate the value of the sum of three squared plus four.
The quantity of [tex](3^2 + 4)[/tex] divided by 0.25
To solve Step 3, we first evaluate the expression inside the parentheses:
[tex]3^2 + 4 = 9 + 4 = 13[/tex]
So, Step 3 becomes:
The quantity of 13 divided by 0.25
Part B: In the missing expression should be the result of dividing 13 by 0.25.
This is because in Step 4, the expression is "the quotient of the quantity 13 divided by 0.25 end quantity minus 10.4 divided by 4."
To simplify further, we need to calculate the value of 13 divided by 0.25.
13 divided by 0.25
To solve Step 6, we perform the division:
13 ÷ 0.25 = 52
So, it becomes:
52 minus 10.4 ÷ 4
Following the remaining steps:
52 minus (10.4 ÷ 4) = 52 - 2.6 = 49.4
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What is the area of this
Answer:
area of trapezoid = 1/2×(a+b)×height
area of trapezoid =1/2×(15m+7m)×7m
area of trapezoid =1/2×22m×7
area of trapezoid =77m²
area of trapezoid =1/2×(a+b)×height
area of trapezoid =1/2×(9ft+12ft)×4ft
area of trapezoid =1/2×21ft×4ft
area of trapezoid =42ft²
Let 2 = 3 + 6i and w = a + bi where a, b E R. Without using a calculator (a) determine z/w and hence, b in terms of a such that z/w is real; (b) determine arg{z - 9}; (c) determine =||w/w||
The correct answers for the given data are (a) b = 6, (b) arg(z - 9) = -π/4, and (c) ||w/w|| = 1.
(a) To determine z/w, we first need to express z and w in terms of their real and imaginary parts. Given 2 = 3 + 6i, we can rewrite it as z = 3 + 6i. Similarly, w = a + bi. Now, let's calculate z/w:
z/w = (3 + 6i)/(a + bi)
To make z/w real, the imaginary part of the denominator should cancel out the imaginary part of the numerator. This means 6/a = 6i/b. Simplifying further, we get ab = 6a + 6bi. Since a and b are real numbers, the only way for the equation to hold is if b = 6 and a = 1. Therefore, b = 6.
(b) To determine arg(z - 9), we need to subtract 9 from z = 3 + 6i:
z - 9 = (3 + 6i) - 9 = -6 + 6i
The argument (or angle) of -6 + 6i can be calculated as:
arg(-6 + 6i) = arctan(6/(-6)) = arctan(-1) = -π/4
(c) To determine ||w/w|| (the magnitude of w divided by the magnitude of w), we need to find the magnitude of w. Given w = a + bi, the magnitude of w is given by:
||w|| = √(a^2 + b^2)
Now, substituting a = 1 and b = 6 (from part a):
||w|| = √(1^2 + 6^2) = √37
Therefore, ||w/w|| = ||w||/||w|| = 1.
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can somebody help me first answer gets brainiest pls help
There is a sale on jeans where you will get 20% off the original price. If the jeans cost $65, how much will you SPEND on the jeans?
plzzzz answer
In ΔEFG, the measure of ∠G=90°, GF = 48, EG = 55, and FE = 73. What ratio represents the cosecant of ∠F?
Answer:
Cosec <F = 73/55
Step-by-step explanation:
In ΔEFG, the measure of ∠G=90°, GF = 48, EG = 55, and FE = 73. What ratio represents the cosecant of ∠F?
First you must know that;
Cosecant <F = 1/sin<F
Given
∠G=90°, GF = 48, EG = 55, and FE = 73.
ED ,= hyp = 73
EG = opp = 55*side facing <F
Using DOH CAH TOA
Sin theta = opp/hyp
Sin <F= 55/73
Reciprocate both sides
1/sinF = 73/55
Cosec <F = 73/55
Nicole wants to rent a boat and spend less than $33. The boat costs $6 per hour , and Nicole has a discount coupon for $9 off. What is the answer in inequality
Answer: Nicole can spend up to 7 hours in the boat.
Step-by-step explanation:
Based on the information given in the question, the possible number of hours that can be used will be calculated as thus:
(6 × t) - 9 ≤ 33
6t - 9 ≤ 33
Collect like terms
6t ≤ 33 + 9
6t ≤ 42
Divide both side by the coefficient of t
6t/6 ≤ 42/6
t ≤ 7
Nicole can spend up to 7 hours in the boat.
A certain college graduate borrows $6600 to buy a car. The lender charges interest at an annual rate of 10%. Assuming that interest is compounded continuously and that the borrower makes payments continuously at a constant annual rate k dollars per year, determine the payment rate k that is required to pay off the loan in 5 years. (Round your answer to two decimal places.) k = $ per yr
The borrower would need to make payments of approximately $943.57 per year to pay off the loan in 5 years.
To determine the payment rate required to pay off the loan in 5 years, we can use the continuous compound interest formula:
A = P * [tex]e^{(rt)[/tex],
where A is the final amount, P is the initial principal, e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate, and t is the time in years.
In this case, the initial principal is $6600, the annual interest rate is 10%, and the time is 5 years. We want to find the payment rate, so let's set A equal to zero, indicating that the loan is fully paid off:
0 = 6600 * [tex]e^{(0.10 * 5)[/tex]- k * 5,
Simplifying the equation, we have:
[tex]e^{(0.5)[/tex] = k / 6600.
Now, we can solve for k by multiplying both sides of the equation by 6600:
k = 6600 * [tex]e^{(0.5)[/tex],
Using a calculator or software, we find that k is approximately $943.57 per year.
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What does 5/9 + 1/3 equal to?
Answer:
= 5/9 + 1/3
=5/9 + 3/9
= 5+3/9
=8/9
find the lengths of the sides of the triangle with the indicated vertices, and determine whether the triangle is a right triangle, an isosceles triangle, or neither. a(3, 4, 1), b(0, 6, 2), c(3, 5, 6)
The lengths of the sides of the triangle ABC are √14, √26, and √26, and the triangle is neither a right triangle nor an isosceles triangle.
To find the lengths of the sides of the triangle with vertices A(3, 4, 1), B(0, 6, 2), and C(3, 5, 6), we can use the distance formula.
The distance formula between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) in three-dimensional space is given by:
d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)
Let's calculate the lengths of the sides of the triangle:
Side AB:
d₁ = √((0 - 3)² + (6 - 4)² + (2 - 1)²)
= √((-3)² + 2² + 1²)
= √(9 + 4 + 1)
= √14
Side BC:
d₂ = √((3 - 0)² + (5 - 6)² + (6 - 2)²)
= √(3² + (-1)² + 4²)
= √(9 + 1 + 16)
= √26
Side AC:
d₃ = √((3 - 3)² + (5 - 4)² + (6 - 1)²)
= √(0² + 1² + 5²)
= √(0 + 1 + 25)
= √26
Now, let's analyze the triangle based on the lengths of its sides:
Since all three sides have different lengths (√14, √26, and √26), the triangle is neither an isosceles triangle (which has at least two sides of equal length) nor a right triangle (which satisfies the Pythagorean theorem).
In summary, the lengths of the sides of the triangle ABC are √14, √26, and √26, and the triangle is neither a right triangle nor an isosceles triangle.
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A proton moves along the x-axis with u2 -1.0 x 10⁷ m/s.
As it passes the origin, what are the strength and direction of the magnetic field at the (1 cm, 0 cm, 0 cm) position? Give your answer using unit vectors Express your answer in terms of the unit vectors i, j, and k. Use the 'unit vector button to denote unit vectors in your answer.
The magnetic field using the unit vector notation B = Bx i= [(μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) / 10^-16 m²)] i.
To determine the strength and direction of the magnetic field at the (1 cm, 0 cm, 0 cm) position caused by a moving proton, we can use the formula for the magnetic field produced by a moving charge:
B = (μ₀ / 4π) * (qv × r / r³)
where B is the magnetic field, μ₀ is the permeability of free space (constant), q is the charge of the proton, v is its velocity, × denotes the cross product, r is the position vector, and r³ represents the magnitude cubed of the position vector.
Given information:
u = -1.0 x 10⁷ m/s (velocity of the proton)
Position vector r = 1 cm i
Let's calculate the magnetic field at the given position:
First, we convert the position vector from centimeters to meters:
r = (1 cm, 0 cm, 0 cm) = (0.01 m, 0 m, 0 m)
Next, we substitute the values into the formula and simplify:
B = (μ₀ / 4π) * (qv × r / r³)
= (μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) × (0.01 m i) / (0.01 m)³)
= (μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) × (0.01 m i) / 0.000001 m³)
= (μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) × (0.01 m i) / 10^-18 m³)
= (μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) / 10^-16 m²) i
Now, we can express the magnetic field using the unit vector notation:
B = Bx i
= [(μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) / 10^-16 m²)] i
where Bx represents the magnitude of the magnetic field in the x-direction.
Please note that the direction of the magnetic field will depend on the orientation of the velocity vector of the proton.
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I will mark brainlyist! Can anyone answer and explain how to do these? Thank you!
Answer:
2) $1797
3) $152
4) $5,378
I need help fast and for real no bots
Answer: d. 201.06
Step-by-step explanation:
To find area of a circle we use the equation 2pi(r) or in this case 2*pi(16)= 804.25in^2 but since we are looking for the shaded region which is 1/4 or one-fourth of the circle so divide 804.25/4 to get 201 or specifically 201.06
Jo records the number of text messages she receives each day she uses this information to draw this bar chart write 3 mistakes she has made
Answer:
X axis labels aren't evenly spaces
Y axis has no origin
Missing label
Step-by-step explanation:
Scale of a graph is important when displaying numerical data on a plot.
Based on the bar chart given, it could be seen that the x axis which is labeled days of the week is not adequately spaced. Data on both axis should he a recognizable.
2.)
Taking a look at the graph, it has no origin, the numbering of the vertical axis, number of text messages should start from 0
3.) Also, the x and y axis aren't labeled Hence charts should be well labeled to include x - axis and y-axis.
Answer:
X axis labels aren't evenly spaces
Missing label
there us no scale written starting at 0
Step-by-step explanation:
this will give u 3/3
Find the surface area of a cubical planter
measuring 30 inches on a side.
30 x 30 = 900
This is the surface area of one side
900 x 6
Multiply by 6 to get the surface area of all 6 sides of the cube
900 x 6 = 5400
This is my last question !
Answer:
x=50 degrees
Step-by-step explanation:
I'm not sure but hope this helps and have a wonderful day!!!!
Answer:
x = 48
Step-by-step explanation:
2x + 10 + x + 26 = 180
3x + 36 = 180
3x = 180 - 36
3x = 144
x = 48
Using Substitution, what is the point of intersection of the following
systems? *
3x – ly = 14
y = - 2x + 16
1) (6,4)
2) (-6,-4)
3) (-6, 4)
4) (6,-4)
Answer:
A
Step-by-step explanation:
(6,4)
3x-1y=14
-y= 3x-14
y=-2x+16
sub in first equation
3x-14 =-2x+16
3x+2x= 16 +14
5x = 30
x = 6
plug in x
y=-2x+16
y = -2(6)+16
y = 4
(6,4)
Need help with this question thank you!
Answer:
You asked this question like 4 times
Step-by-step explanation:
The answer is
(5,-1)
(-4,0)
SOMEONE HELP ME ILL GIVE YOU 50 POINTS I AM DESPERATE I AM IN A MATHS TEST!
Answer:
12:2
4:24
6:1
Step-by-step explanation:
those 3 are the correct ones
2x + 7 = 15
What does x equal?
Country Financial, a financial services company, uses surveys of adults age and older to determine if personal financial fitness is changing over time (USA Today, April 4, 2012). In February of 2012, a sample of adults showed indicating that their financial security was more than fair. In February of 2010, a sample of adults showed indicating that their financial security was more than fair. a. State the hypotheses that can be used to test for a significant difference between the population proportions for the two years. - Select your answer - - Select your answer - b. What is the sample proportion indicating that their financial security was more than fair in 2012
Complete question :
Country Financial, a financial services company, uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time (USA Today, April 4, 2012). In February of 2012, a sample of 1000 adults showed 410 indicating that their financial security was more than fair. In February of 2010, a sample of 900 adults showed 315 indicating that their financial security was more than fair. a. State the hypotheses that can be used to test for a significant difference between the population proportions for the two years. H : Pi - P2 - Select your answer HA : P1 P2 - Select your answer - b. What is the sample proportion indicating that their financial security was more than fair in 2012? Round your answer to two decimal places. In 2010?
Answer:
H0 : p1 - p2 = 0
H1 : p1 - p2 ≠ 0
Phat 2010 = 0.35
Phat 2012 = 0.41
Step-by-step explanation:
The null and alternative hypothesis :
H0 : p1 - p2 = 0
H1 : p1 - p2 ≠ 0
The null means there is no difference in proportion for the two years while the alternative claims that there is difference in proportion for the two years.
Sample proportion for 2010:
Phat = x / n
x = 315 ; n = 900
Phat = 315 / 900
Phat = 0.35
Sample proportion for 2012 :
Phat = x / n
x = 410 ; n = 1000
Phat = 410 / 1000
Phat = 0.41
please help asap
which inequality is represented by this graph
Answer:
W is either less than or( less than or equal to)
Step-by-step explanation:
I do not know what shows if something is equal to so the best answer I can think if is less than -2 as it looks like W is everything lower or equal to -2
11. Find the following GCD and LCM. (a) GCD (360, 4000) (c) GCD (627, 205143) (b) LCM (360, 4000) (d) LCM (627, 205143)
The required answers are:
(a) GCD = 40 (b) LCM = 36000 (c) GCD = 33 (d) LCM = 1032933
GCD and LCM of the given numbers are:
(a) Prime factors of 360: 2 x 2 x 2 x 3 x 3 x 5.Prime factors of 4000: 2 x 2 x 2 x 2 x 5 x 5 x 5.GCD = 2 x 2 x 2 x 5 = 40.
(b) LCM = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 = 36000.
(c) Prime factors of 627: 3 x 11 x 19.Prime factors of 205143: 3 x 3 x 7 x 7 x 11.GCD = 3 x 11 = 33.
(d) LCM = 3 x 3 x 7 x 7 x 11 x 19 = 1032933.
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Answer:
C
Step-by-step explanation:
In a study of the accuracy of fast food? drive-through orders, Restaurant A had 239 accurate orders and 70 that were not accurate.
a. Construct a 95?% confidence interval estimate of the percentage of orders that are not accurate
The 95% confidence interval estimate of the percentage of orders that are not accurate is approximately (17.37%, 27.83%)
Let's denote p as the proportion of orders that are not accurate.
The sample proportion of orders that are not accurate is given by:
p(bar) = 70 / (239 + 70)
= 70 / 309
≈ 0.226
The standard error of the proportion is calculated as:
SE = √[(p(bar)(1 - p(bar))) / n]
= √[(0.226(1 - 0.226)) / 309]
≈ √(0.1785 / 309)
≈ 0.0267
To find the margin of error, we need to multiply the standard error by the critical value corresponding to a 95% confidence level. For a 95% confidence level, the critical value is approximately 1.96.
Margin of error = 1.96 × SE
≈ 1.96 × 0.0267
≈ 0.0523
Now we can construct the confidence interval:
Lower limit = p(bar) - Margin of error
= 0.226 - 0.0523
≈ 0.1737
Upper limit = p(bar) + Margin of error
= 0.226 + 0.0523
≈ 0.2783
Therefore, the 95% confidence interval estimate of the percentage of orders that are not accurate is approximately (17.37%, 27.83%).
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