You’re baking a circular cake for a party. Your cake can be any size you want. What will the radius of your cake be and how many slices will you be able to cut?
Answers
This is a problem of geometry. Given that the cake is circular, the greater the cake the greater the radius of it. So, as shown in the figure 1, the radius will be the distance from the center to any extreme point of the circle.
How many slices will you be able to cut?
The total area of a circle is given by:
[tex]A= \pi r^{2}[/tex]
We need to fin how many slices will be cut, so let's calculate the area of the circular sector which can be obtained simply applying rule of three, so:
[tex]A_{cs}= \pi r^{2}( \frac{\theta}{2\pi})= \frac{r^{2}\theta}{2}[/tex]
Let's name n the number of slices, if we divide the total area by n this result, each area must equal, then:
[tex] \frac{\pi r^{2}}{n}=\frac{r^{2}\theta}{n}[/tex]
Finally, we will be able to cut:
[tex]n= \frac{2\pi}{\theta}[/tex] Slices
Related Questions
What is the measure of ∠F, to the nearest degree?
44°
57°
71°
78°
Answers
Answer:
Option A. 44°
Step-by-step explanation:
In a given triangle FGH sides have been given as FG = 7 yards, FH = 6 yards, and GH = 5 yards.
We have to calculate the approximate value of ∠F.
We apply the cosine rule in the given triangle.
5² = 7² + 6² - 2×7×6×cosF
25 = 49 + 36 - 84× cosF
25 = 85 - 84 cosF
84cosF = 85 - 25 = 60
[tex]cosF=\frac{60}{84}=0.71428[/tex]
[tex]F=cos^{-1}( 0.71428) = 44.4[/tex]
F = 44°
Therefore option A. 44° is the correct answer.
A rectangular plot of land that contains 1500 square meters will be fenced and divided into two equal portions by an additional fence parallel to two sides. find the dimensions of the land that require the least amount of fencing.
Answers
The perimeter will be:
2x+3w=1500
thus
3w=(1500-2x)
w=(1500-2x)/3
w=500-2/3x
The area will be:
A=x*w
A=x(500-2/3x)
A=500x-(2/3)x²
The above is a quadratic equation; thus finding the axis of symmetry we will evaluate for the value of x that will give us maximum area.
Axis of symmetry:
x=-b/(2a)
from our equation:
a=(-2/3) and b=500
thus
x=-500/[2(-2/3)]
x=375
the length will be 375 m
The width will be 250 m
You travel 5 miles downstream in a kayak at a speed of r miles per hour. You turn around and travel 6 miles upstream at a speed of 0.6r miles per hour. Finally, you turn around and return to your original starting point at a speed of r+1 miles per hour.
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This high school physics problem deals with relative velocity and vector addition by describing a journey in a kayak under varying speeds amidst a river current. To solve such a problem, the total time taken is found by adding the individual times for each part of the journey, each calculated by dividing the distance by the speed of the kayak.
Explanation:The subject matter of this question involves understanding of the concept of relative velocity, a topic usually taught in high school physics. The student is navigating a kayak in the river with varying speeds relative to different sections of the journey, demonstrating the behavior of an object in a current or wind. In essence, the motion of the kayak is a combination of its own propelled movement and the movement of the river current.
To solve the mathematical aspect of such a problem, you would typically find the total time taken for each segment of the journey by dividing the distance of that segment by the speed at which the kayak is moving. Adding these times together will give the total time taken for the whole journey. Finally, you should understand this as an example of vector addition, where the total velocity of the kayak is the vector sum of its velocity relative to the water and the water's velocity relative to the riverbank.
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Justin is a musician. For eight months a year, he teaches school and is paid $34,780 annually. During the summer months, he teaches private students and plays in clubs, earning another $5,700. What is his average monthly salary, based on his yearly earnings?
Answers
First, we'll need to add the two values together. This gives us $40,480. Then, since we know that there are 12 months in a year, we need to divide the total amount by 12. This gives us, on average, $3373.33 each month.
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
How do I factorise
6-42x
Answers
FACTORING: 6 - 42x
STEPS:
6 - 42x
-42x + 6
= -6(7x - 1)
FINAL ANSWER: -6(7x - 1)
Answer:
[tex]6(-7x+1)[/tex]
Step-by-step explanation:
Given: The equation [tex]6-42x[/tex].
To find: Factorize the given equation.
Solution:
The given expression is:
[tex]6-42x[/tex]
which can be rewritten as:
[tex]-42x+6[/tex]
Upon solving the above expression and Taking 6 common from both the terms of the expression ,we get
[tex]6(-7x+1)[/tex]
which is the required factorized form of the given expression.
what is 3x times x???
Answers
3x × x = 3x²
Hope I helped! :3
3 x squared:) hope this helps
shirts are onsale at 3 for $15.50. how many shirts can you buy with $139.50.
Answers
Multiply 9 by 3 and you get your answer: 27 Shirts
First you take the $139.50 and divide it by $15.50
139.50 / 15.50 = 9
Then you take the 9 and multiply it by 3, be cause there are 3 shirts per $15.50
9 x 3 = 27
You can buy a total of 27 shirts with $139.50
The sum of two consecutive numbers is 131 .What are the two numbers ?
Answers
n + (n + 1) = 131n + n + 1 = 1312n + 1 = 131 |-12n = 130 |:2n = 65n+1 = 66
Answer: 65 and 66.
The sum of two consecutive numbers is 131. What are the two numbers?
Answer is provided in the image attached.
Consider the multiple regression model with two regressors x1 and x2, where both variables are determinants of the dependent variable. when omitting x2 from the regression, there will be omitted variable bias for modifyingabove beta with caret 1:
a. if upper x 2 is measured in percentages.
b. only if upper x 2 is a dummy variable.
c. if upper x 1 and upper x 2 are correlated.
d. always.
Answers
(5x^2+38x+18) divided (x+7) what is the quotient and the remainder
Answers
To determine the quotient and remainder for (5x^2+38x+18) divided by (x+7), polynomial long division must be used, involving dividing terms, multiplying and subtracting until the remainder is obtained.
Explanation:To find the quotient and remainder of the division of polynomials (5x2+38x+18) by (x+7), we can use polynomial long division.
Divide the first term of the dividend, 5x2, by the first term of the divisor, x, to get the first term of the quotient, which is 5x. Multiply the entire divisor (x+7) by 5x and subtract from the dividend. Bring down the next term from the dividend and repeat the process until there are no more terms to bring down. The last line after the subtraction will be the remainder.
By doing this, you will obtain the quotient and the specific remainder for this division.
Bill buys a red marble and a blue marble. If the total weight of 3 such red marbles and 2 such blue marbles is 84g, and the total weight of 12 such red marbles and 5 such blue marbles is 282g, what is weight of the red marble and the blue marble respectively?
Answers
Final answer:
The weight of the red marble is 16 grams, and the weight of the blue marble is 18 grams, based on the solution of the system of linear equations derived from the given total weights of the marbles.
Explanation:
To solve the problem of determining the weight of each marble, we can set up a system of linear equations based on the given information:
Let r be the weight of a red marble in grams.
Let b be the weight of a blue marble in grams.
The total weight of 3 red marbles and 2 blue marbles is 84g.
The total weight of 12 red marbles and 5 blue marbles is 282g.
Based on these statements, we can write two equations:
3r + 2b = 84 (1)
12r + 5b = 282 (2)
We can solve this system of equations by multiplying equation (1) by 4 to eliminate variable b.
(4)(3r + 2b) = (4)(84)
12r + 8b = 336 (3)
Subtract equation (2) from equation (3) to solve for r:
(12r + 8b) - (12r + 5b) = 336 - 282
3b = 54
b = 18 (weight of blue marble)
Substitute value of b in equation (1) to solve for r:
3r + 2(18) = 84
3r + 36 = 84
3r = 48
r = 16 (weight of red marble)
Therefore, the weight of the red marble is 16 grams and the weight of the blue marble is 18 grams.
Find the quotient of 3/5 and 9/10 . Express your answer in simplest form.
Answers
Short answer: 2/3
Why?
When dividing two fractions, you don't divide, you find the reciprocal of the second fraction (9/10) and multiply. So, it's 3*10/9*5. Simplify. {3 * 10 => 30} ~ {9 * 5 => 45} Now we have 30/45. This can be simplified. Simplified, 30/45 reduces down to 2/3.
Hope this helped you! ♥
The quotient of 3/5 and 9/10 is the value obtained by dividing both values, Hence, the quotient of the division is 2/3
The numerator = 3/5 The denominator = 9/10The division operation can be expressed thus :
3/5 ÷ 9/10
Take the reciprocal of the denominator and change the sign to multiplication ;
Reciprocal of 9/10 = 10/9
Hence, we have ;
3/5 × 10/9 = 30/45
In simplest form ; 30/45 = 10/15 = 2/3Therefore, the quotient is 2/3
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Identify intervals on which the function is increasing, decreasing, or constant.
g(x) = 1 - (x - 7)^2
Select one:
a. Increasing: x < 7; decreasing: x > 7
b. Increasing: x < -7; decreasing: x > -7
c. Increasing: x > 1; decreasing: x < 1
d. Increasing: x < 1; decreasing: x > 1
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How many of the first 1992 prime numbers have reciprocals less tahn 0.05?
Answers
In March, a family starts saving for a vacation they are planning for the end of August. The family expects the vacation to cost $1327. They start with $120. At the beginning of each month they plan to deposit 20% more than the previous month. Will they have enough money for their trip? If not, how much more do they need? Select the correct answer below and, if necessary, fill in the answer box within your choice.
Answers
March: 120
April: 120+(120×20)/100=120+24=144
May: 144+(144×20)/100=144+18,8=162,8
June: 162,8+(162.8×20)/100=162,8+32.56=195.36
July: 195.36+(195.36×20)/100=195.36+23.87=219.23
August: 219.23+(219.23×20)/100=219.23+43.85=263.08
120+144+162.8+195.36+219.23+263.08=1105.19
So the answer is no.
The radius of this ball is 24 inches. Which equation gives the ball's surface area, in square inches?
Answers
A boy spent 2/3 money on book store,1/3 money on craft store and has left $8. How much money he has at first?
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2/3s of 26 is 24 minus 36 is 12
so at first He would have to have $36
Drag and drop the symbols to enter the equation of the circle in standard form with center and radius given. Center (-8, -3), radius = 2 times the square root
please answer before 1:00
Answers
(x-a)²+(y-b)²=r²
where:
(a,b) is the center and r is the radius.
Given that (a,b) is (-8,-3) and r=2 units
then the equation of the circle will be:
(x-(-8))²+(y-(-3))²=2²
simplifying the above we get:
(x+8)²+(y+3)²=4
What is the correct order of operations for simplifying the expression (x+3)^2-(x^2+9)/2x^2
Answers
The correct order of operations for simplifying the expression (x+3)^2 - [tex](x^2+9)/2x^2[/tex] is as follows:
1. Square the binomial (x+3) to get x^2 + 6x + 9.
2. Divide each term in (x^2+9) by [tex]2x^2[/tex] to get [tex]1/2 + 9/2x^2[/tex].
3. Substitute the simplified expressions back into the original expression: [tex]x^2 + 6x + 9 - (1/2 + 9/2x^2).[/tex]
The correct order of operations for simplifying the expression (x+3)^2 - (x^2+9)/2x^2 is as follows:
1. Start by simplifying the expression within the parentheses: (x+3)^2. This means squaring the binomial (x+3). To do this, you multiply the binomial by itself: (x+3) * (x+3). This results in [tex]x^2 + 6x + 9.[/tex]
2. Next, simplify the expression within the second set of parentheses: (x^2+9).
3. Now, divide [tex](x^2+9)[/tex] by 2x^2. To do this, divide each term in (x^2+9) by 2x^2. This gives us [tex](x^2/2x^2)[/tex] [tex]+ (9/2x^2)[/tex]. Simplifying further, we get 1/2 + [tex]9/2x^2[/tex].
4. Finally, substitute the simplified expressions back into the original expression: [tex]x^2 + 6x + 9 - (1/2 + 9/2x^2).[/tex]
PLEASE HELP!!! The question is in the picture!
Answers
vertical component=110 N*sin 25°-----> -46.5 N (down)
horizontal component=110 N *cos 25°----> -99.7 N (left)
the vector diagram in the attached figure
A coffee machine can be adjusted to deliver any fixed number of ounces of coffee. if the machine has a standard deviation in delivery equal to 0.4 ounce, what should be the mean setting so that an 8-ounce cup will overflow only 0.5% of the time?
Answers
The question can be addressed using the principles of Normal Distribution. Given the z-chart, 8 ounces is the observed value for the 99.5th percentile, which equates to approximately 2.58 standard deviations. Therefore, the mean setting of the coffee machine should be set around 8 ounces for the cup to overflow only 0.5% of the time.
Explanation:The situation described in the question is a typical case of application of Normal Distribution. As a reminder, in a Normal Distribution, 99.7% of the values lie within 3 standard deviations of the mean. The question states that the cup should overflow only 0.5% of the time. Therefore, we need to consider the 99.5% of the left side under the normal curve (as we're considering the upper limit), which corresponds to around 2.58 standard deviations under the normal curve.
Given that the standard deviation (σ) is 0.4 ounces, using the formula X = μ + Zσ (where Z is the Z-score corresponding to the desired percentile, μ is the mean we want to find, and X is the threshold value where the cup overflows at 8 ounces), we can substitute the known values and solve for μ.
Therefore, 8 = μ + 2.58 * 0.4 Solving for μ gives us around μ = 7.966, or about 8 ounces. Hence, the mean setting of the coffee machine should be set around 8 ounces to ensure that the cup will overflow only 0.5% of the time.
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Without graphing, classify the following system as independent, dependent, or inconsistent. y=-3x+4 and 6x+2y=8
a. independent
b. dependent
c. inconsistent
please help
Answers
Answer:
Dependent
Step-by-step explanation:
[tex]y=-3x+4[/tex] and [tex]6x+2y=8[/tex]
Lets solve the second equation for y and then substitute it in first equation
[tex]6x+2y=8[/tex]
Subtract 6x on both sides
[tex]2y=-6x+8[/tex]
Divide by 2 on both sides
[tex]y=-3x+4[/tex]
Now we plug it in first equation for y
[tex]-3x+4=-3x+4[/tex]
Add 3x on both sides
[tex]4=4[/tex]
Both sides are same, they are equal. the system has infinite solutions.
They are said to be dependent
the dimensions of a rectangle can be expressed as x-3 and x+8. If the area of the rectangle is 42 square feet. Find the dimensions of the rectangle.
Answers
the area of a rectangle=length*width
let
length=x-3
width=x+8
area=42 ft²
so
42=(x-3)*(x+8)----------> x²+8x-3x-24=42--------> x²+5x-66=0
using a graph tool-------> to resolve the second order equation
see the attached figure
the solution is
x=6
hence
length=x-3------> 6-3-----> 3 ft
width=x+8 ------> 6+8----> 14 ft
the answer is
the dimensions of the rectangle are 3 ft x 14 ft
One thousand tickets were sold for a baseball game there were one hundred more adult tickets sold than student tickets, and there were fou times as many tickets sold to students as to children. how many of each type of ticket were sold.
Answers
400 Student tickets
100 Children tickets
Let x = adults
Let y = Students
Let z = children
Then set up this system of equations
x +y + z = 100
y - 4z = 0
x - y = 100
Solve using elimination and combination.
A jacket is discounted 40% the jacket is now 38.70 dollars what was the original price
Answers
To find the original price, you'll first need to convert 40% into a decimal. You can do this by moving the decimal point twice to the left. So now you have 0.40. Now you'll need to divide 38.70 by 0.40. Once you've done that, you'll get the original price
The original price of the jacket was $96.75
I hope this helps!
PLEASE HELP!!! BRAINLIEST! 20 POINTS!
A rectangle has a width of 3 cm and a length of 10 cm.
What is the effect on the perimeter when the dimensions are multiplied by 10?
A) The perimeter is increased by a factor of 10.
B) The perimeter is increased by a factor of 40.
C) The perimeter is increased by a factor of 100.
D) The perimeter is increased by a factor of 400.
THANK YOU SO MUCH!!!! <333
Answers
A 9.5-foot pole casts a shadow that is 29 feet long. What is the approximate measure of angle L? The triangle is JKL and K=90 degrees.
Answers
Answer:
A. 0.32 rad
Step-by-step explanation:
Final answer:
To find the angle L in a triangle where a 9.5-foot pole casts a 29-foot shadow, calculate the angle using the tangent function, yielding an approximate angle of 72.8 degrees.
Explanation:
A 9.5-foot pole casts a shadow that is 29 feet long. What is the approximate measure of angle L?
First, determine the scale factor between the pole and its shadow: 29 feet (length of shadow) ÷ 9.5 feet (length of pole) = 3.05.
Next, calculate the angle L using the tangent function: tan(L) = opposite/adjacent = 29/9.5 ≈ 3.05. Taking the inverse tangent gives L ≈ 72.8 degrees.
What is the middle term of the product of (x - 4)(x - 3)?
Answers
Answer:
The middle term of the product of (x - 4)(x - 3) is -7
Step-by-step explanation:
Consider the given expression (x - 4)(x - 3)
We have to find the middle term of the product of (x - 4)(x - 3).
First multiply the given terms, we get,
[tex](x - 4)(x - 3)=x(x-3)-4(x-3)[/tex]
Simplify, we get,
[tex]x(x-3)-4(x-3)=x^2-3x-4x+12[/tex]
Simplify further, we get,
[tex]x^2-3x-4x+12=x^2-7x+12[/tex]
Thus, the middle term of the product of (x - 4)(x - 3) is -7
Solve for v in the formula v = u + 10t when u = 16 and t = 4. a. v = -22 c. v = 56 b. v = 3 d. v = 40
Answers
You put 16 in for u and 4 in for t
v = (16) + 10(4)
Multiply
v = 16 + 40
Add
v = 56
The answer is v = 56
Hope this helps!
Write an equation of the line with the given slope and containing the given point. write the equation in the slope-intercept form yequals=mxplus+b. slope negative 3−3; through (22,negative 10−10)
Answers
m=-3
y=-3x+b
(22,-10), To find b substitute x=22, and y=-10 into y=-3x+b.
-10=-3*22+b
-10+66=b
b=56
y= - 3x+56