Answers
The area of the shade region is 24π unit squared.
How to find the area of a sector?The radius of the circle is 6 units and the length DE is 4π. Therefore, the
area of the shaded portion can be found as follows:
Hence, let's find the angles using the length DE
length of arc = ∅ / 360 × 2πr
4π = ∅ / 360 × 12π
4π = π∅ / 30
cross multiply
120π = π∅
∅ = 120 degrees
Therefore, let's find area of the shaded region
area of the sector = ∅/ 360 × πr²
area of the shaded region = 240 / 360 × π 36
area of the shaded region = 8640 / 360 π
area of the shaded region = 24π units²
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Related Questions
A. complementary
B. supplementary
C. vertical
D. no relationship
Answers
Answer:
d I believe have a goood day
Question 5: Write each of the following in the form 9^n
(a) 81
(b) 3
(C) 27
Answers
Answer:
a) 9^2
b) 9^(1/2)
c) 9^(3/2)
Step-by-step explanation:
It is perhaps easier to start by using 3^n.
3 = 3^1
27 = 3^3
81 = 3^4
Recognize that 3 = 9^(1/2) and replace 3 in each of the above. The applicable rule of exponents is (a^b)^c = a^(bc).
a) 81 = (9^(1/2))^4 = 9^2
b) 3 = 9^(1/2)
c) 27 = (9^(1/2))^3 = 9^(3/2)
Answer:
(a) 9^2
(b) 9^0.5
(c) 9^1.5
Step-by-step explanation:
We need to find n such that 9^n = value indicated.
Recall that n=2 is a square, so
(a) 9^2=9*9=81
Recall that n=0.5 (or 1/2) is a square root, because 9^0.5 * 9^0.5 = 9^1 = 9, so
(b) 9^0.5 = 3, because 3*3 = 9
Recall that multiplication of two powers with the same base is the sum of the exponents, e.g. 9^a * 9^b = 9^(a+b).
Therefore,
(c) 27 = 9*3 = 9^1 * 9^0.5 = 9^(1+0.5) = 9^1.5
amber wants to have $300,000
Answers
Answer:
i hope i can answer your question
Step-by-step explanation:
Amber wants to have $300,000 so i don't see another number that you can solve on maybe type that first so i can answer please
We just purchased some sweet tea concentrate (we're being adventurous). It's supplied as a 90% solution. We need 5 L of 40% sweet tea concentrate for the cookout later (it'll make some great tea). How would we make this solution (note: we'll need to add water to our concentrate to make the sweet tea)? 2. The molecular weight of anhydrous calcium chloride is 110.99grams/mol. How many grams do we need for 400ml of 790mM calcium chloride? 3. We have 10 mL of cells to treat with Hydrogen Peroxide (H
2
O
2
), such that the final concentration of H
2
O
2
is 20μM. How much of a 30mM stock solution of H
2
O
2
would we add to our cells? 4. We need to prepare a stock solution of medium for your culture cells, which usually includes liquid salt solution and bovine serum. Our liquid salt solution is supplied in a 50X concentration, and we need to dilute it to 1X for use. We also need to add 75% fetal bovine serum for a final concentration of 15%. How would we make up 0.80 liters of this culture media using water as our solvent?
Answers
1. To make 5 L of a 40% sweet tea concentrate, you need to mix approximately 2.22 L of the 90% sweet tea concentrate with 2.78 L of water.
2. For 400 ml of 790 mM calcium chloride, you would need approximately 34.97 grams of anhydrous calcium chloride.
3. To achieve a final concentration of 20 μM hydrogen peroxide in 10 ml of cells, you would need to add approximately 6.67 μL of a 30 mM stock solution of hydrogen peroxide.
4. To prepare 0.80 liters of culture media, you would need to mix 16 ml of the 50X liquid salt solution with 784 ml of water.
C1V1 = C2V2 where C1 is the initial concentration (90%), V1 is the initial volume (unknown), C2 is the desired concentration (40%), and V2 is the final volume (5 L). Rearranging the equation, we have:
V1 = (C2V2) / C1
Plugging in the values, we get:
V1 = (0.4 * 5 L) / 0.9
V1 ≈ 2.22 L
So, you'll need to mix approximately 2.22 L of the 90% sweet tea concentrate with 2.78 L of water to obtain 5 L of a 40% sweet tea concentrate for your cookout.
To calculate the amount of anhydrous calcium chloride needed for 400 ml of 790 mM calcium chloride, you can use the formula:
mass = molarity × volume × molecular weight
First, convert the molarity from mM to M (mol/L):
790 mM = 0.79 M
Then, calculate the mass using the formula:
mass = 0.79 M × 0.4 L × 110.99 g/mol
mass ≈ 34.97 g
Therefore, you would need approximately 34.97 grams of anhydrous calcium chloride for 400 ml of 790 mM calcium chloride solution.
To determine the amount of a 30 mM stock solution of hydrogen peroxide (H2O2) needed to achieve a final concentration of 20 μM in 10 ml of cells, you can use the formula:
C1V1 = C2V2
Where C1 is the initial concentration (30 mM), V1 is the initial volume (unknown), C2 is the desired concentration (20 μM), and V2 is the final volume (10 ml). Rearranging the equation, we have:
V1 = (C2V2) / C1
Plugging in the values, we get:
V1 = (20 μM × 10 ml) / 30 mM
V1 ≈ 6.67 μL
Therefore, you would need to add approximately 6.67 μL of the 30 mM stock solution of hydrogen peroxide to your 10 ml of cells to achieve a final concentration of 20 μM.
To prepare a stock solution of medium for your culture cells, you'll need to dilute the liquid salt solution and add the required amount of fetal bovine serum (FBS). Since the liquid salt solution is supplied at a 50X concentration and you need a 1X concentration, you'll need to dilute it 50-fold. For a final volume of 0.80 liters, you'll need to mix 0.016 liters (or 16 ml) of the 50X liquid salt solution with 0.784 liters (or 784 ml) of water.
Next, you'll need to calculate the volume of FBS required to achieve a final concentration of 15%. To calculate this, you can use the equation:
V_FBS = (C_FBS × V_total) / C_FBS%
Where V_FBS is the volume of FBS, C_FBS is the desired concentration (15%), V_total is the final volume (0.80 liters), and C_FBS% is the concentration of the supplied FBS (75%). Plugging in the values, we get:
V_FBS = (0.15 × 0.80 liters)
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6) Bill is three times older than Kevin. He is also 28 years older than Kevin. How old are they?
Answers
Answer:
If bill is 28 years older than him, but also 3 times older than him, then you divide 28 by 3, which gives you 9.3. So that means kevin is around 9 1/4 years old and bill is around 37 and 1/4 years old, but you dont ahve to count the fraction if you dont want to, all that matters is the whole number.
Step-by-step explanation:
Bill is 42, while Kevin is 14 years old
Represent Bill's age with B, and Kevin's age with K.
So, we have the following equations
B = 3K and B = 28 + K
Substitute 3K for B in the second equation
\(3K = 28 + K\)
Collect like terms
\(-K + 3K = 28\)
\(2K = 28\)
Divide both sides by 2
\(K = 14\)
Substitute 14 for K in the first equation
\(B =3 \times 14\)
\(B =42\)
Hence, Bill is 42, while Kevin is 14 years old
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Problem:
The pile of blocks above weighs 2 pounds. How many ounces do the blocks weigh?
A
32 ounces
B
16 ounces
C
1 ounce
D
64 ounces
End
Session
Answers
the answer is 32 ounces this same queston is in my notes
hope it likes you...
Plzzzzz helpppppppppppp meeeeeee
Answers
Which one is a proportional relationship between x and y
Answers
Answer: C
Step-by-step explanation: A proportional relationship between two variables x and y is when one variable is always some constant value multiplied by the other. The “constant of proportionality” is the name given to this constant. All proportional relationships can be represented by the equation y =kx , where k is the proportionality constant.
Which inequality describes the graph below?
Answers
Answer:
X>_1 and x<_7
Step-by-step explanation:
Which set of ordered pairs (x,y) could represent a linear function
Answers
Inside both the cylinder x^2 + y^2 = 4 and the ellipsoid 4x^2 + 4y^2 + z^2 = 64
Answers
The region common to both the cylinder x^2 + y^2 = 4 and the ellipsoid 4x^2 + 4y^2 + z^2 = 64 is an ellipse centered at the origin in the xy-plane.
The given cylinder x^2 + y^2 = 4 represents a circular cross-section in the xy-plane with radius 2. The equation of the ellipsoid 4x^2 + 4y^2 + z^2 = 64 describes a three-dimensional surface centered at the origin, with its major axes along the x, y, and z directions. By intersecting the cylinder and the ellipsoid, we find the common region between them.
To determine the intersection, we substitute x^2 + y^2 = 4 into the equation of the ellipsoid. This gives us 4(4) + z^2 = 64, which simplifies to z^2 = 48 and z = ±√48. However, since we are looking for the region inside both surfaces, we take z = -√48.
Thus, the common region lies in the xy-plane (z = 0) and is given by the equation x^2 + y^2 = 4. This equation represents an ellipse centered at the origin, with its major axis along the x-axis and a radius of 2. Therefore, the region common to both the cylinder and the ellipsoid is an ellipse centered at the origin in the xy-plane.
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a cookie recipe calls for 2 and 1/2 cups of sugar. Damian needs to make only two thirds of the recipe. How much sugar will he need?
Answers
Answer:
5/3 or 1 2/3 cups of sugar.
Step-by-step explanation:
First, divide by 3 to find the amount of sugar per third.
2 1/2 ÷ 3
5/2 * 1/3
5/6
Second, multiply by two.
5/6 * 2
5/6 * 2/1
10/6
5/3 or 1 2/3
Best of Luck!
F is inversely proportional to d^2.
When F = 5, d = 9
Work out d (positive value rounded to 2 DP) when F = 3
Answers
Answer:
11.6
Step-by-step explanation:
F = k/ d^2
where k = proportionality constant
k = Fd^2
k = 5 * 9^2
k = 5*81 = 405
d = (K/F)^1/2
d = (405/3)^1/2
d = 11.62 =11.6
Answer:
11.62
Step-by-step explanation:
F is inversely proportional to d^2, so
\(F=\frac{k}{d^2}\)
for some constant k. To find k plug in given values for F and d.
\(5=\frac{k}{9^2}\\5=\frac{k}{81}\\k=405\)
Now you can find d for F = 3.
\(3=\frac{405}{d^2}\\\\3d^2=405\\\\d^2=135\\d=\sqrt{135}\approx 11.62\)
find the length of the curve. r(t) = cos(7t) i + sin(7t) j + 7 ln(cos(t)) k, 0 ≤ t ≤ π/4
Answers
To find the length of the curve given by r(t) = cos(7t) i + sin(7t) j + 7 ln(cos(t)) k, 0 ≤ t ≤ π/4, we need to use the formula for arc length:
L = ∫[a,b] √[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 dt
In this case, we have:
dx/dt = -7 sin(7t)
dy/dt = 7 cos(7t)
dz/dt = -7 sin(t) / cos(t)
So,
[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 = 49 sin^2(7t) + 49 cos^2(7t) + 49 sin^2(t) / cos^2(t)
= 49 [sin^2(7t) + cos^2(7t) + sin^2(t) / cos^2(t)]
= 49 [1 + sin^2(t) / cos^2(t)]
Now, using the identity sin^2(t) + cos^2(t) = 1, we can rewrite this as:
[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 = 49 cos^2(t)
Therefore, the length of the curve is:
L = ∫[0,π/4] √[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 dt
= ∫[0,π/4] 7 cos(t) dt
= 7 [sin(t)]|[0,π/4]
= 7 sin(π/4) - 7 sin(0)
= 7 (√2/2)
= 7√2/2
So the length of the curve is 7√2/2.
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Gina can trade empty bottles for money at the grocery store. She returned a few bottles worth $0.10 each and 6 bottles with $0.05 each. The clerk paid Gina $0.80 for all the bottles
How man bottles worth $0.10 did Gina return
A.4
B.5
C.6
D.8
Answers
Answer:
Step-by-step explanation:
Oct 03, 1:51:41 PM
Noah is a high school basketball player. In a particular game, he made some two
point shots and some three point shots. Noah made a total of 11 shots altogether and
scored a total of 29 points. Write a system of equations that could be used to
determine the number of two point shots Noah made and the number of three point
shots he made. Define the variables that you use to write the system.
Let
Let
=
System of Equations:
Answers
Let
x = no of two point shorts
y = no of three point shorts
System of Equations:
x + y = 11 (Noah made a total of 11 shots altogether)
2x + 3y = 29 ( scored a total of 29 points.)
No. of Two point short Noah Made = 4;
No. of Three Point short Noah Made = 7;
Define System of linear equations?A collection of one or more linear equations involving the same variables is known as a system of linear equations (or linear system) in mathematics.The subject of linear algebra, which is employed in most areas of contemporary mathematics, is based on the theory of linear systems. Numerical linear algebra includes computational strategies for obtaining the solutions, which are crucial to the fields of engineering, physics, chemistry, computer science, and economics. A helpful strategy when creating a mathematical model or computer simulation of a relatively complex system is to approximate a system of non-linear equations by a linear system.To learn more about : System of linear equations
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Evelyn, Neil, and Leilani swim laps at constant rates.
Answers
Answer: Leilani swam the fastest, but next time give the full question.
Step-by-step explanation:
Arjun and Mei each improved their yards by planting rose bushes and ivy. They bought their supplies from the same store. Arjun spent $198 on 7 rose bushes and 13 pots of ivy. Mei spent $204 on 14 rose bushes and 10 pots of ivy. what is the cost of one rose bush and the cost of one pot of ivy?
Answers
The cost of one rose bush is $5 and the cost of one pot of ivy is $ 14.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Arjun spent $198 on 7 rose bushes and 13 pots of ivy.
Mei spent $204 on 14 rose bushes and 10 pots of ivy.
let the cost of rose bushes be x and cost of ivy pots be y.
So, 7x+ 12y = 198.....(1)
14x+ 10y = 204........(2)
Now solving above equation
x = 234/49
≈ 4.77551
y = 96/7
≈ 13.714286
Hence, cost of one rose bush is $5 and the cost of one pot of ivy is $ 14.
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The sides of a rectangle are in a ratio of 7 : 4. If the perimeter of the rectangle is 176 ft, what is the area of the rectangle? The area of the rectangle is
Answers
Answer:
1792
Step-by-step explanation:
The sides of the rectangle is 7 and 4
7x, 4x
2(7x+4x) = 176
14x + 8x= 176
22x= 176
Divide both sides by the coefficient if x which is 22
x= 176/22
x= 8
7x
= 7(8)
= 56
4x
= 4(8)
= 32
Area of the rectangle
= 56×32
= 1792
I NEED HELP. PLEASE, THANKS! :)
a. Find the amplitude of a sinusoidal function that models this temperature variation.
b. Find the vertical shift of a sinusoidal function that models this temperature variation.
c. What is the period of a sinusoidal function that models this temperature variation?
d. Use t = 0 at 5 P.M. to write a sinusoidal function that models this temp. variation.
e. What is the model’s temperature at 10 A.M.? Compare this to the actual value?
Answers
Answer: (a) Amplitude = 19
(b) Vertical Shift = 59
(c) Period = 24
\(\bold{(d)\quad y=19\cos\bigg(\dfrac{\pi}{12}x\bigg)+59}\)
(e) The model = 50°, the actual value = 52°
Step-by-step explanation:
The equation of a cosine function is: y = A cos (Bx - C) + D where
Amplitude (A) is the distance from the center to the maximumPeriod (P) = 2π/B --> B = 2π/PPhase Shift = C/BCenter (D) is the vertical shift(a) Amplitude (A) = (Max - Min)/2
= (77 - 40)/2
= 37/2
= 18.5 (I rounded it up to 19)
(b) Vertical Shift (aka Center) (D)= (Max + Min)/2
= (77 + 40)/2
= 117/2
= 58.5 (I rounded it up to 59)
(c) Period (P) = 24
B = 2π/P
= 2π/24
= π/12
(d) There is no Phase Shift because the max is on the y-axis.
A = 19, B = π/12, C = 0, D = 59
⇒ y = 19 cos(π/12)x + 59
(e) let x = -2 (-2 represents 10 am on the graph)
⇒ y = 19 cos(π/12)(-2) + 59
= 19 cos (-π/6) + 59
= 19(-1/2) + 59
= -9.5 + 59
= 49.5
The model estimates the temperature at 10 am to be ≈ 50°
The actual temperature from the table is 52°
suppose a 3 x 5 coefficient matrix for a system has three pi vot columns. is the system consistent? why or why not?
Answers
No, the system is inconsistant because there are only three equations, as opposed to the required minimum for a system of equations with three pivot columns, which is implied by the stated coefficient matrix's size of 3x5.
No, Since a system of equations with three pivot columns requires the presence of three equations, the system is since there must be three equations in a system of equations with three pivot columns. The columns of the coefficient matrix that have non-zero entries make up the pivot columns. A row of the coefficient matrix corresponds to each equation in the system. There are therefore insufficient equations for a system of equations with three pivot columns based on the supplied coefficient matrix, which is 3x5. The system is inconsistent if there aren't at least three equations since there wouldn't be enough data to find a singular solution.
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A function follows the rule y = -75 - 5 x . When the function's output is 25, the equation is 25 = -75 - 5 x .
What is the function input when the output is 25?
10
20
-20
-10
Answers
Answer:
same here idek tbh
Step-by-step explanation:
.......
an investment project offers $4,350 per year forever, with the first payment occurring one year from now. if the interest rate is 6%, what would you pay to participate in this project?
Answers
The present value of this investment project is $72,500. This can be solved by the concept of Compound interest.
The perpetual cash flow of $4,350 per year can be considered as an annuity perpetuity, where the cash flow is constant forever. To calculate the present value of this perpetuity, we can use the formula:
Present Value = Annual Cash Flow / Discount Rate
Here, the annual cash flow is $4,350, and the discount rate is the interest rate of 6%. Thus, we can calculate the present value as:
Present Value = $4,350 / 0.06
Present Value = $72,500
Therefore, to participate in this investment project, you would need to pay $72,500 today to receive $4,350 per year forever, starting from one year from now
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A train leaves at 11:32 and arrives at 13:24. It travelled at an average speed of 85 km/h. How far did it travel? Give your answer in km to 1DP
Answers
Answer: 158.7 km
two friends washed 18 cars in 2 hours. then they worked more slowly and washed 2 cars fewer per hour. how many cars did they wash each hour at the new slower rate?
pls help idk how to solve it
Answers
Answer:
They washed 18 cars in 2 hours, and each hour they washed 2 fewer.
16 cars in 4 hours,
14 cars in 6 hours,
12 in 8 hours, etc.
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
doin it rn
For which of the following series is the Ratio Test inconclusive(that is, it fails to give a definite answer)? (a)sum_(n=2)^infinity 6/n^3Inconclusive Conclusive(convergent) Conclusive(divergent)
Answers
The Ratio Test is inconclusive for the series sum_(n=2)^infinity 6/n^3.
What is ratio ?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.
The Ratio Test is given by:
lim_(n->infinity) |a_n+1 / a_n| = L
If L < 1, then the series converges. If L > 1, then the series diverges. If the limit L does not exist or is equal to 1, then the test is inconclusive.
Consider the series sum_(n=2)^infinity 6/n^3. We have:
|a_n+1 / a_n| = |6 / (n + 1)^3 / (6 / n^3)| = |n^3 / (n + 1)^3| = n^3 / (n + 1)^3
As n approaches infinity, n^3 / (n + 1)^3 approaches 1, so the limit of |a_n+1 / a_n| does not exist or is equal to,
Hence, The Ratio Test is inconclusive for the series sum_(n=2)^infinity 6/n^3.
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What value of z should we use when making a 98% confidence interval for p?.
Answers
The z-score that The z-score that corresponds to the desired level of confidence is often used when creating a confidence interval for a proportion (p).
The crucial z-value for a 98% confidence interval can be calculated by subtracting the confidence level from 1 to obtain the area in the tail and dividing it by 2 to divide the tail area equally. In this instance, (1 - 0.98), / 2, equals 0.01 / 2, or 0.005.We can find the z-score for a cumulative chance of 0.005 in the lower tail using a calculator or a conventional normal distribution table. It is estimated that the z-score is -2.33.
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I'll mark brainliest pls help!
im stuppid
Answers
Answer:
c
Step-by-step explanation:
a shipment to a warehouse consists of 4,000 MP3 players. The manager chooses a random sample of 50 MP3 players and finds 4 that are defective. How many MP3 players in the shipment are likely to be defective?
Answers
Answer:
320
Step-by-step explanation:
Answer:
320 MP3 players
Step-by-step explanation:
4/50 MP3 players are defective
Multiply by 80 to get the whole shipment
4/50 x 80 = 320/4000
What is the end behavior of the function f of x equals 3 times the cube root of x?
As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞
As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞
As x → –∞, f(x) → 0, and as x → ∞, f(x) → 0
As x → 0, f(x) → –∞, and as x → ∞, f(x) → 0
Answers
\(f(x) = 3 \sqrt[3]{x} \)
\(lim f(x) = 3 \sqrt[3]{ - \infty } = - \infty \\ x = > - \infty \)
\(limf(x) = 3 \sqrt[3]{ \infty } = \infty \\ x = > \infty \)
Answer:
As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.
Step-by-step explanation:
I got it right on the test.