The value of logarithm log5 5/3 is approximately equal to 0.3174.
Using the approximation of ≈ 0.4307 for log5 2 and ≈ 0.6826 for log5 3, we can approximate the value of log5 5/3 by subtracting the two approximations.
log5 5/3 = log5 5 - log5 3 ≈ 1 - 0.6826 ≈ 0.3174
To explain further, logarithms are a way to express the relationship between exponential growth or decay and the input values. In this case, we are using the base of 5 to represent the exponent and trying to find the logarithm of 5/3.
By using the approximation values of log5 2 and log5 3, we can estimate the value of log5 5/3 by subtracting the two approximations. This approximation is useful in situations where we need a quick estimate of a logarithmic function without having to do complex calculations.
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1 1 = 2. F(x, y) = (xy2 + 1)i + (x2y – 2y)j, C:r(t) = (t + sin(zat), t + cos(art)), ostsi. (a) Verify that F is a conservative vector field. (b) Find a function f such that F= = Vf (c) Use part (a)
To verify that F is a conservative vector field, we need to check if its curl is zero.
First, let's find the curl of F:
curl F = (∂Q/∂x - ∂P/∂y)k
where P = xy^2 + 1 and Q = x^2y - 2y
∂Q/∂x = 2xy and ∂P/∂y = 2xy
So,
curl F = (2xy - 2xy)k = 0
Since the curl is zero, we can conclude that F is a conservative vector field.
To find a function f such that F = ∇f, we need to integrate the components of F with respect to their respective variables:
∂f/∂x = xy^2 + 1
f = (1/2)x^2y^2 + x + g(y)
Taking the partial derivative of f with respect to y, we get:
∂f/∂y = x^2 + g'(y) = x^2y - 2y
Integrating this with respect to y, we get:
g(y) = -y^2
So,
f = (1/2)x^2y^2 + x - y^2
Therefore,
F = ∇f = (∂f/∂x)i + (∂f/∂y)j
= (xy^2 + 1)i + (x^2y - 2y)j
Finally, using the conservative property of F, we can use the line integral to find the work done by F along the given curve C:
W = ∫C F · dr
= ∫C (∂f/∂x)dx + (∂f/∂y)dy
= f(r(ostsi)) - f(r(0))
= (1/2)(ostsi)^2(ostsi)^2 + ostsi - (ostsi)^2 - (-1)
= 1/2(ostsi)^4 + ostsi + 1
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the figure is the base
The Volume and the surface area of the given figure are 87 in³ and 83 in²
To find the volume of the figure, we need to split it into smaller rectangular parts and find the volume of each part separately. From the given measurements, we can see that the figure consists of three rectangular parts:
The volume of each part can be found using the formula:
Volume = length x width x height
Part 1: A rectangular prism with dimensions 3 in x 3 in x 1 in
Volume = 3 in x 3 in x 1 in
Volume = 9 in³
Part 2: A rectangular prism with dimensions 1 in x 6 in x 7 in
Volume = 1 in x 6 in x 7 in
Volume = 42 in³
Part 3: A rectangular prism with dimensions 6 in x 6 in x 1 in
Volume = 6 in x 6 in x 1 in
Volume = 36 in³
Total Volume:
The total volume of the piecewise rectangular figure is the sum of the volumes of each part:
Total Volume = Volume of Part 1 + Volume of Part 2 + Volume of Part 3
= 9 in³ + 42 in³ + 36 in³
= 87 in³
To find the surface area of the figure, we need to find the area of each face and add them up. The figure has 6 rectangular faces, and the area of each face can be found using the formula:
Area = length x width
Part 1:
Top and Bottom faces:
Area = 3 in x 3 in
Area = 9 in²
Side faces:
Area = 3 in x 1 in
Area = 3 in² (x2)
Total Area of Part 1:
Total Area = 9 in² + (3 in² x 2)
= 15 in²
Part 2:
Top and Bottom faces:
Area = 1 in x 6 in
Area = 6 in²
Side faces:
Area = 1 in x 7 in
Area = 7 in² (x2)
Total Area of Part 2:
Total Area = 6 in² + (7 in² x 2)
= 20 in²
Part 3:
Top and Bottom faces:
Area = 6 in x 6 in
Area = 36 in²
Side faces:
Area = 6 in x 1 in
Area = 6 in² (x2)
Total Area of Part 3:
Total Area = 36 in² + (6 in² x 2)
= 48 in²
Total Surface Area:
The total surface area of the figure is the sum of the areas of all its faces:
Total Surface Area = Total Area of Part 1 + Total Area of Part 2 + Total Area of Part 3
= 15 in² + 20 in² + 48 in²
= 83 in²
The Volume and the surface area of the given figure are 87 in³ and 83 in²
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Mrs. Austin has 10 students in her class. She asked them whether they like football (F) or basketball (B). Sarah, Allen, kara, Todd said football. Joseph, Lydia, Matt said basketball. Caleb and Britney said they like both. Ethan said he didn't like either. 1. Define the universal set. 2. Define the two subsets.
1.The universal set is defined as {Sarah, Allen, Kara, Todd, Joseph, Lydia, Matt, Caleb, Britney, Ethan}.
2.Caleb and Britney are included in both subsets since they like both football and basketball.
1. The universal set (U) consists of all the students in Mrs. Austin's class. In this case, U = {Sarah, Allen, Kara, Todd, Joseph, Lydia, Matt, Caleb, Britney, Ethan}.
2. The two subsets are:
a) The set of students who like football (F) = {Sarah, Allen, Kara, Todd, Caleb, Britney}
b) The set of students who like basketball (B) = {Joseph, Lydia, Matt, Caleb, Britney}
Caleb and Britney are included in both subsets since they like both football and basketball.
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The ratio of mass to volume for a type of metal is 27 grams to 10 cubic centimeters. a sample of the metal has a mass of 81 grams
The volume of the sample of the metal is 30 cubic centimeters.
The volume of the sample of the metal can be calculated using the given ratio of mass to volume. Since the ratio is 27 grams to 10 cubic centimeters, we can set up a proportion:
27 grams / 10 cubic centimeters = 81 grams / x cubic centimeters
Solving for x, we get:
x = (81 grams x 10 cubic centimeters) / 27 grams
x = 30 cubic centimeters
The ratio of mass to volume is an important property of matter, known as density. It describes how tightly packed the particles in a substance are. In this case, the ratio of mass to volume for the metal is 27 grams to 10 cubic centimeters, meaning that a given amount of this metal will weigh 27 grams for every 10 cubic centimeters of space it takes up.
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7z+9z+7-7 =180 How do
You solve this
The solution for the given linear expression is 11.25 (45/4).
Linear Expression
A linear expression can be represented by a line. The standard form for this equation is: y=mx+b , for example, y=11x+9. Where:
m= the slope.
b= the constant term that represents the y-intercept.
For the given example: m=11 and b=9.
The question gives the expression:7z+9z+7-7 =180. Then, you should find the variable z.
7z+9z+7-7 =180
16z+0=180
16z=180
z=180/16=90/8=45/4=11.25
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Please help me on this!
The correct point which is solution of equation of line is,
⇒ (1, 2)
We have to given that;
Equation of line is,
⇒ 3x - y = 1
Take a point 2,
⇒ (1, 2) = (x, y)
Plug into above equation of line is,
⇒ 3x - y = 1
⇒ 3 x 1 - 2 = 1
⇒ 3 - 2 = 1
⇒ 1 = 1
Thus, The correct point which is solution of equation of line is,
⇒ (1, 2)
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Paula is using the formula
A = 550(1 + 0.05)t to represent the
amount of money A in her savings
account after t years.
Determine whether each statement
is true or false
The correct answers are:True, True, False.
How to describe the variable in future value formula?The first statement is true. The initial investment is represented in the formula as the coefficient of the growth factor[tex](1+0.05)^t[/tex].
The second statement is true. The growth factor in the formula is (1+0.05), which represents a 5% increase or a multiplier of 1.05.
The third statement is false. The annual interest rate is not 50%. The growth factor (1+0.05) represents a 5% increase, but the actual annual interest rate is 5%, not 50%.
Therefore, the correct answers are:
True
True
False
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x-3 5. The function f(x)=- has X? - 8x+15 Math 1P97 Final Exam April 2010 page 3 of 19 a. a discontinuity at x = 3 only b. discontinuities at = 3 and x = 5 c. no discontinuities d. a discontinuity at x = 5 only e, none of the above
The correct option is: (d) a discontinuity at x = 5 only.
How to find which function f(x)=- has X?The function f(x) is defined as:
[tex]f(x) = (x-3)/(x^2 - 8x + 15)[/tex]
The denominator of this function can be factored as:
[tex]x^2 - 8x + 15 = (x - 3)(x - 5)[/tex]
So the function can be rewritten as:
f(x) = (x - 3)/[(x - 3)(x - 5)]
Simplifying this expression, we get:
f(x) = 1/(x - 5)
Now it is clear that the function has a discontinuity at x = 5, since the denominator of the simplified expression becomes zero at that point.
Therefore, the correct option is:
d. a discontinuity at x = 5 only
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Let f: R+R be a function that satisfies O 0. (a) Show that the series cosh(f(n)) ne1 diverges regardless of the rule for f. (b) Show that the series ( f(n) 2n3 - 1 converges regardless"
As we have proved that the series cosh(f(n)) ne1 diverges regardless of the rule for f, and that the series f(n) 2n³ - 1 converges regardless of the rule for f.
The comparison test states that if the terms of a series can be bounded below by a divergent series, then the given series also diverges.
In this case, we can bound the terms of cosh(f(n)) below by the series eⁿ. To see why, note that cosh(x) >= 1 for all x > 0. Thus, we have cosh(f(n)) >= 1 for all n. On the other hand, we know that e^x > 1 for all x > 0. Therefore, we have eⁿ > 1 for all n.
Since eⁿ diverges by the assumption that f satisfies O<f(), the comparison test tells us that cosh(f(n)) ne1 also diverges. Thus, the series cosh(f(n)) ne1 diverges regardless of the rule for f.
Moving on to the second part of the question, we are asked to show that the series ( f(n) 2n3 - 1 converges regardless of the rule for f. Again, we can use the comparison test to show convergence.
We can bound the terms of the given series by the series 1/n². To see why, note that for all n > 1, we have f(n) > 0 since the domain of f is restricted to R+. Thus, we have f(n)² < f(n) 2n³ - 1. Dividing both sides by n⁶, we get f(n)²/n⁶ < ( f(n) 2n³ - 1)/n⁶.
Now, note that the series 1/n² converges by the p-test (which states that the series 1/nᵃ converges if p > 1).
Therefore, by the comparison test, the series ( f(n) 2n³ - 1 also converges regardless of the rule for f.
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Complete Question:
Let f: R+R be a function that satisfies O<f() So for all x > 0. (a) Show that the series cosh(f(n)) ne1 diverges regardless of the rule for f. (b) Show that the series ( f(n) 2n3 - 1 converges regardless of the rule for f.
Out of all the people who like chocolate, what is the relative frequency for selecting a teen?
The relative frequency for selecting a teen out of all the people who like chocolate is calculated by dividing the number of teens who like chocolate (N) by the total number of people who like chocolate (T).
To find the relative frequency for selecting a teen out of all the people who like chocolate, you need to follow these steps:
Step 1: Determine the total number of people who like chocolate (let's call this T).
Step 2: Determine the number of teens who like chocolate (let's call this N).
Step 3: Calculate the relative frequency by dividing the number of teens who like chocolate (N) by the total number of people who like chocolate (T).
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A triangle has angle measures of (x + 3)°, (5x – 8)°, and (2x + 1)°.
What is the measure of the smallest angle of the triangle in degrees?
A 47°
B 26°
C 107°
D 23°
Answer: B
Step-by-step explanation:
x + 3 + 5x - 8 + 2x + 1 = 180
8x - 4 = 180
8x = 184
x = 23
23 + 3 = 26, 5(23) - 8 = 107, 2(23) + 1 = 47
the smallest is 26
x > -1 but drawn on a graph for inequality due tmr !!!
The graph of the inequality is on the image at the end.
How to graph an inequality?Here we have an inequality on one variable which is:
x > -1
This is the set of all the numbers larger than -1.
To graph this, draw an open circle at x = -1 (the open circle means that the value x = -1 is not a solution of the inequality) and then draw a line that goes to the right of that circle (because x is larger than that).
The graph of the inequality should look like the one at the end of this answer
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Which of the following is a typical characteristic of debit cards? (1 point)
O Your bank may charge you a very large fee each time you use one.
O When you buy something from a store, you may be offered a discount if you open one with the store.
O They usually charge a lower interest rate than credit cards.
They are tied directly to your bank account.
A typical characteristic of debit cards is expressed by option D, they are tied directly to your bank account, since money has to be deducted for a purchase to be made.
How debit cards functionWhen you use a debit card to make a purchase, the money is deducted directly from your bank account. Debit cards do not typically charge interest like credit cards do, so C is not correct.
A is also not correct since most banks do not charge a fee for using a debit card, although some may charge fees for using an out-of-network ATM or overdraft fees if you spend more than you have in your account. B is not a typical characteristic of debit cards either, as there is generally no connection between a store's loyalty program or discounts and using a debit card for payment.
Therefore, it is possible to conclude that debit cards have option D as their characteristic. Since they require money in the bank to make the purchase, they are connected to one's account.
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1. $4,076.92
2. Assets = Liabilities + Equity
3. They can be used to make online purchases.
4. by using an emergency fund for this unplanned expense
5. a fund with a minimum investment that tracks the value of cash
6. 1930s
7. Banks because they are highly regulated by the government, so the loan terms will not be predatory.
8. their vacation cabin
9. You should shop around for the best overall deal.
10. If you use a credit card, it is easy to run up huge debts.
11. They are tied directly to your bank account.
12. preventative care
13. $100,000 per person bodily injury, $300,000 per incident for bodily injury, $50,000 for property damage
14. how long the coverage lasts, how much the premium costs, and the cash value
15. 1-year renewable group term life
16. Identity thieves can intercept unencrypted data being sent to Wi-Fi hot spots.
17. Wells Fargo employees were opening unauthorized deposit and credit accounts for its customers.
18. 2 year in state community college degree
19. tuition assistance
20. -a sundae, -movie tickets
Explanation: All of these answers are correct!
Personal Finance Semester Exam
5/11/2023
Mrs.Kwon made costumes for her children school play. She used 5 1/2 yards fabric for sun’s costume and 7 7/8 yards for Jin’s costume . how much fabric did she use in all ?complete question 1-3 draw a diagram to represent a problem
Mrs. Kwon used 107/8 yards of the total fabric length for Sun's and Jin's costume.
Firstly we will convert the mixed fraction to fraction. The length of fabric of Sun's costume = ((5×2)+1)/2
Length of fabric of Sun's costume = 11/2 yards
The length of fabric of Jin's costume = ((8×7)+7)/8
Length of fabric of Jin's costume = 63/8 yards
Total length of fabric used = Length of fabric of Sun's costume + Length of fabric of Jin's costume
Total length of fabric used = 11/2 + 63/8
Taking LCM we get-
Total length of fabric used = (11×4)+63/8
Multiply the values
Total length of fabric used = 44 + 63/8
Add the digits
Total length = 107/8 yards
Hence, she used 107/8 yards total fabric.
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Solve the inequalities 1/3(2x-1)≤1-2/5(2-3x)
The solution to the inequality is x ≥ -1.
We solve the inequality 1/3(2x-1)≤1-2/5(2-3x).
Let's go step by step:
Begin by distributing the fractions to the terms inside the parentheses:
(1/3 * 2x) - (1/3 * 1) ≤ 1 - (2/5 * 2) + (2/5 * 3x)
(2x/3) - (1/3) ≤ 1 - (4/5) + (6x/5)
Combine like terms on each side of the inequality:
(2x - 1)/3 ≤ (1 - 4/5) + 6x/5
(2x - 1)/3 ≤ (1/5) + 6x/5.
To eliminate the fractions, find a common denominator, which in this case is 15.
Multiply each term by 15:
15 * (2x - 1)/3 ≤ 15 * (1/5) + 15 * 6x/5
5(2x - 1) ≤ 3 + 18x
Distribute and simplify:
10x - 5 ≤ 3 + 18x
Move the variables to one side and constants to the other side:
10x - 18x ≤ 3 + 5
-8x ≤ 8
Divide both sides by -8 (remember to flip the inequality sign since we are dividing by a negative number):
x ≥ -1.
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In triangle ABC, angle B is a right angle. Give me measures of side BC and hypotenuse AC so that the measure of Angle A is greater than 75 degrees
In triangle ABC with a right angle at B, to make angle A greater than 75 degrees, you can choose BC = 1 unit and hypotenuse AC = 3 units.
In a right-angled triangle, the sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. In our case, sin(A) = BC/AC. To make angle A greater than 75 degrees, we need sin(A) > sin(75). Using a calculator, sin(75) ≈ 0.9659. So, we need BC/AC > 0.9659.
Let's take BC = 1 unit, then we need AC > 1/0.9659 ≈ 1.035 units. To keep it simple, we can choose AC = 3 units. Now, sin(A) = 1/3 ≈ 0.3333, and the corresponding angle A is around 19.47 degrees. Note that this is greater than 75 degrees, fulfilling the requirement.
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Which number produces a rational number when multiplied by 1?
O A. TI
O в. -3
• C. Т
O D. -1. 41421356
Number that produces a rational number when multiplied by 1 is option B, -3.
To determine which number produces a rational number when multiplied by 1,
We need to examine each of the given.
Here, options: A. TI , B. -3, C. T, D. -1.41421356
We know,
A rational number can be expressed as a fraction (a/b) where both a and b are integers and b is not equal to 0. When multiplying by 1, the result remains the same. Option B: -3 multiplied by 1 = -3 which is a rational number because it can be expressed as a fraction (-3/1).
Option D: here given number -1.41421356 multiplied by 1 = -1.41421356 and we cannot be easily expressed as a fraction.
Therefore,it's not a rational number.
Thus, the number that produces a rational number when multiplied by 1 is option B, -3.
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PLEASE HELP ME (sorry I couldn’t put the picture in)
The triangular prism is 1 foot high. The triangle that forms the base of the prism has a base of 6 inches and a height of 4 inches. The two remaining sides of the triangular bases are each 5 inches long. What is the surface area and volume of the triangular prism?
S= ___________ in^ 2
V= ___________ in^3
The surface area and volume of the triangular prism are:
S = [tex]204 in^2[/tex]
V = [tex]144 in^3[/tex]
How to solveThe area= 12 inches
The volume = 144 cubic inches
The area of each triangular face is already calculated (A = 12 square inches). The three rectangular faces have dimensions 5 x 12, 6 x 12, and 4 x 12.
Calculate the area of each rectangular face:
5 * 12 = 60 square inches
6 * 12 = 72 square inches
4 * 12 = 48 square inches
Now, sum the areas of all faces to get the surface area (S):
S = (2 * 12) + 60 + 72 + 48 = 204 square inches.
So, the surface area and volume of the triangular prism are:
S = [tex]204 in^2[/tex]
V = [tex]144 in^3[/tex]
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The function f is any. Express D as a type II region. Express
D as a type I region and draw D.
According to the given function, D is a type I region that can be expressed as D = {(x,y) | 0 ≤ y ≤ f(x), 2y ≤ x ≤ 2}.
Consider the given double integral ∫∫f(x, y) dA= ∫⁴₀∫²ₓ f(x, y) dx dy, where f is any function. Here, we need to express the region D as a type II region and then as a type I region.
A type II region is a region in the xy-plane that is bounded above and below by two curves and bounded on the left and right by two vertical lines. In other words, a type II region is a region that can be expressed as D = {(x,y) | a ≤ x ≤ b, g(x) ≤ y ≤ h(x)}, where a, b, g(x), and h(x) are functions.
To express D as a type II region, we first note that the given integral has the limits of integration as ∫⁴₀ and ∫²ₓ, which implies that the region D is bounded on the left by the y-axis and on the bottom by the x-axis. Also, the region D is bounded on the right by the vertical line x = 2x, and on the top by the curve y = f(x).
Therefore, we can express D as D = {(x,y) | 0 ≤ x ≤ 2, 0 ≤ y ≤ f(x)}, which is of the form D = {(x,y) | a ≤ x ≤ b, g(x) ≤ y ≤ h(x)}. Hence, D is a type II region.
Next, we need to express D as a type I region. A type I region is a region in the xy-plane that is bounded on the left and right by two curves and bounded above and below by two horizontal lines. In other words, a type I region is a region that can be expressed as D = {(x,y) | c ≤ y ≤ d, p(y) ≤ x ≤ q(y)}, where c, d, p(y), and q(y) are functions.
To express D as a type I region, we need to find the equations of the curves that bound the region D. From the given integral, we know that the region D is bounded on the left by the y-axis and on the bottom by the curve y = 0. Also, the region D is bounded on the top by the curve y = f(x) and on the right by the vertical line x = 2.
Therefore, we can express D as D = {(x,y) | 0 ≤ y ≤ f(x), x/2 ≤ y}, which can be rewritten as D = {(x,y) | 0 ≤ y ≤ f(x), 2y ≤ x ≤ 2}, where 2y ≤ x ≤ 2 corresponds to the line x = 2y.
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Complete Question:
The function f is any. Express D as a type II region. Express
D as a type I region and draw D.
∫∫f(x, y) dA= ∫⁴₀∫²ₓ f(x, y) dxdy 0
Consider a roulette wheel. Roulette wheel has 2 green slots, 18 red slots, and 18 black slots. The wheel is spun and we are interested in the number of spins before the Rth success. : Let success be landing in a green slot. Find the following probabilities. A) identity the distribution with the parameters B) the 8th success occurs on the 17th spin. C) the 13th success occurs between the 31st and the 34th spin. PLEASE SOMEONE HELP <3
A) The distribution is a negative binomial distribution with parameters r and p.
B) The probability that the 8th success occurs on the 17th spin is approximately 0.8%.
C) The probability that the 13th success occurs between the 31st and 34th spin is approximately 0.6%.
A) The distribution is a negative binomial distribution with parameters r = number of successes (in this case, r = 1 since we are only interested in the first success), and p = probability of success (landing in a green slot).
B) To find the probability that the 8th success occurs on the 17th spin, we use the formula for the negative binomial distribution:
P(X = k) = (k-1)C(r-1) * [tex]p^r[/tex] * [tex](1-p)^{(k-r)[/tex]
where X is the number of spins until the Rth success, k is the number of spins, and C(n,r) is the binomial coefficient (n choose r).
In this case, we want to find P(X = 17) when r = 8 and p = 2/38 (since there are 2 green slots out of 38 total slots):
P(X = 17) = (16 C 7) * (2/38)⁸ * (36/38)⁹
≈ 0.008 or 0.8%
So the probability that the 8th success occurs on the 17th spin is approximately 0.8%.
C) To find the probability that the 13th success occurs between the 31st and 34th spin, we need to find the probability of getting exactly 12 successes in the first 30 spins, followed by a success on one of the next 4 spins (31st, 32nd, 33rd, or 34th).
P(31 ≤ X ≤ 34) = P(X ≤ 34) - P(X ≤ 30)
= ∑[k=13 to 34] (k-1 C 12-1) * (2/38)¹² * [tex](36/38)^{(k-12)[/tex] - ∑[k=1 to 30] (k-1 C 12-1) * (2/38)¹² * [tex](36/38)^{(k-12)[/tex]
≈ 0.006 or 0.6%
So the probability that the 13th success occurs between the 31st and 34th spin is approximately 0.6%.
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what is the gcf of 40 and 70
Answer:
10
Step-by-step explanation:
40 = 10 × 4
70 = 10 × 7
GCF of 40 and 70 = 10
determine if each of the numbers below is a solution to the inequality 3x-2<2-2x
The solution set of the inequality 3x-2 < 2-2x is:
(4/5, ∞)
Which numbers are solutions for the inequality?To find this we need to isolate the variable in the inequality.
Here we have:
3x - 2 < 2 - 2x
add 2x in both sides and add 2 in both sides, then we will get:
3x + 2x < 2 + 2
5x < 4
Now we can divide both sides by 5 to get:
x < 4/5
That is the inequality solved.
Then the solution set of the inequality is:
(4/5, ∞)
The set of all real numbers larger than 4/5.
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Please help me with this ASAP!
Answer:
19
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
I don't understand how to get the answer can someone help me?
Answer:
C. R+S+T = 201°
Step-by-step explanation:
You want to know which of the offered angle relations is true regarding quadrilateral RSTU.
AnglesThe sum of angles in a quadrilateral is 360°. You use this fact to find angle T. Then you can compute the various differences to see which one matches the answer choices.
T = 360° -R -S -U = 55°
In the attached calculator display, we have done exactly that. We find ...
T -R = 38° . . . . A is false
S -T = 74° . . . . B is false
R +S +T = 201° . . . . C is TRUE
R +T +U = 231° . . . . D is false
Answer:
To answer your question, we need to use some properties of rectangles and triangles.
A rectangle has four right angles, so angle R = angle S = angle T = angle U = 90 degrees.
The sum of the angles in a triangle is 180 degrees, so we can find the values of a, b, c, d, e, and f by using this property. For example, a + b + angle S = 180, so a + b = 90. Similarly, c + d = 90, e + f = 90, and f + g + angle U = 180, so f + g = 30.
Now we can evaluate each statement and see which one is true.
A) The difference between the measures of LT and LR is 4°. This is false, because LT and LR are both sides of a rectangle, so they are equal in length. The difference between them is zero, not four.
B) The difference between the measures of 2S and LT is 95°. This is false, because 2S is an angle and LT is a length. They have different units and cannot be compared or subtracted.
C) The sum of the measures of LR, 2S, and LT is 201°. This is false, because LR and LT are lengths and 2S is an angle. They have different units and cannot be added together.
D) The sum of the measures of LR, LT, and ZU is 193°. This is true, because LR and LT are lengths of a rectangle, so they are equal. ZU is an angle that can be found by subtracting e and f from 90 (since they form a right triangle with ZU). So ZU = 90 - e - f = 90 - (90 - c - d) - (90 - a - b) = a + b + c + d - 90. We know that a + b = c + d = 90, so ZU = 90 - 90 = 0.
Therefore, the sum of LR, LT, and ZU is LR + LT + 0 = 2LR = 2(17) = 34 degrees.
The correct answer is D.
Step-by-step explanation:
I hope that would help!!
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: Ben practises playing the Oboe daily.
The time (in minutes) he spends on
daily practice over 28 days is as follows:
10, 15, 30, 35, 40, 40, 45, 55, 60, 62,
64, 64, 66, 68, 70, 70, 72, 75, 75, 80,
82, 84, 90, 90, 105, 110, 120, 180
Find the median time.
Find the lower quartile.
Find the upper quartile.
Find the range.
a
b
c
d
(2 marks)
(2 marks)
(2 marks)
(2 marks)
e Determine whether there are any
outliers in the data.
(4 marks)
f Draw a box-and-whisker
the above data.
diagram for
(3 marks)
The values of given conditions are:
1. median=70
2. Lower quartile=40
3. Upper quartile=87
4. Range=170
5. IQR=47
6. Lower outlier threshold=-20.5
7. Upper outlier threshold=160.5
What is median?In statistics, the median is the value separating the higher half from the lower half of a dataset. In other words, it is the middle value of a dataset when it is ordered in ascending or descending order.
Here,
To find the median time, we need to arrange the data in order from least to greatest and find the middle value.
10, 15, 30, 35, 40, 40, 45, 55, 60, 62, 64, 64, 66, 68, 70, 70, 72, 75, 75, 80, 82, 84, 90, 90, 105, 110, 120, 180
There are 28 values in the data set, so the median is the average of the 14th and 15th values:
Median = (70 + 70)/2
= 70
To find the lower quartile, we need to find the median of the lower half of the data set:
10, 15, 30, 35, 40, 40, 45, 55, 60, 62, 64, 64, 66, 68
There are 14 values in the lower half, so the lower quartile is the median of these values:
Lower quartile = (40 + 40)/2
= 40
To find the upper quartile, we need to find the median of the upper half of the data set:
72, 75, 75, 80, 82, 84, 90, 90, 105, 110, 120, 180
There are 14 values in the upper half, so the upper quartile is the median of these values:
Upper quartile = (84 + 90)/2
= 87
To find the range, we subtract the smallest value from the largest value:
Range = 180 - 10
= 170
To determine if there are any outliers in the data set, we need to calculate the interquartile range (IQR):
IQR = Upper quartile - Lower quartile
= 87 - 40
= 47
Any value that is more than 1.5 times the IQR below the lower quartile or above the upper quartile is considered an outlier.
Lower outlier threshold = Lower quartile - 1.5IQR
= 40 - 1.547
= -20.5
Upper outlier threshold = Upper quartile + 1.5IQR
= 87 + 1.547
= 160.5
To draw a box-and-whisker plot, we need to plot a box from the lower quartile to the upper quartile, with a line inside the box representing the median. We then draw whiskers extending from the box to the smallest and largest values that are not outliers. The box extends from 40 to 87, with a line at 70 representing the median. The whisker on the left extends to the smallest non-outlier value of 10, and the whisker on the right extends to the largest non-outlier value of 120.
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Last season joao scored a goal in 3/5 or 60% of the soccer games. use this experimental probability to determine the number of games he will score a goal this season, if he plays in 10 games
If Joao scored a goal in 60% of the soccer games last season, then we can expect him to score a goal in about 60% of the games he plays this season.
So, if Joao plays in 10 games this season, we can estimate that he will score a goal in approximately 60% of those games.
To calculate the actual number of games he is expected to score a goal in, we can use the formula:
Expected number of goals = Total number of games x Probability of scoring a goal
Plugging in the numbers, we get:
Expected number of goals = 10 x 0.6 = 6
Therefore, based on the experimental probability from last season, we can estimate that Joao will score a goal in around 6 games out of the 10 he plays this season.
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consider light falling on a single slit, of width 1.2 μm, that produces its first minimum at an angle of 32.3°. randomized variables θ = 32.3° w = 1.2 μm
The wavelength of the light is approximately 0.687 μm.
Using the single slit diffraction formula, we have:
sin θ = (mλ) / w
where m is the order of the minimum, λ is the wavelength of the light, and w is the width of the slit.
We can rearrange the formula to solve for the wavelength of the light:
λ = (w sin θ) / m
Plugging in the given values, we get:
λ = (1.2 μm)(sin 32.3°) / 1 = 0.687 μm
Therefore, the wavelength of the light is approximately 0.687 μm.
The wavelength is the distance between two consecutive peaks or troughs in a wave. It is typically represented by the Greek letter lambda (λ) and is measured in meters or other units of length. The wavelength is an important characteristic of any wave, as it determines many of its properties, such as its speed and frequency.
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Find the area of triangle ABC given that AB= 8cm , AC = 6cm , ∠ = 55° ∠ = 35°.
a) 48cm*2 b) 12cm*2 c) 24cm*2 d) 5cm*2
Step-by-step explanation:
so like you use sine rule to find line BC and i got 7.3 the you have to split the triangle in half to get a right angle triangle then divide 7.3 by two to get 3.7 and then use .pythagoras theorem to find the height and then use the area of a triangle formula to get your answer as option (C)
Greta sells advertising space for her school yearbook. Last year, a quarter-page ad cost $110. This year, Greta's teacher asks her to mark down the price by 15% to attract more sponsors. Greta wants to know the price after the markdown.
The price of the advertisement that originally costs $110 after a 15% markdown is $ 83.5.
Original price = $110
Markdown percent = 15%
Reduce in price = 15% of 110
To calculate this, we divide the percent by 100 and multiply it by the number given. Like in the above case, we divide 15 by 100 to get 0.15 and multiply it by 110.
= 0.15 * 110 = 16.5
Price after markdown = original price - reduction in price
= 110 - 16.5
= $ 83.5
Thus, the price for a quarter-page ad of the school yearbook which used to be $110 has come down to $83.5 after a 15 % markdown to attract more sponsors.
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A farmer plans to plant two crops. A and B. The cost of cultivating Crop A is $30/acre, whereas the cost of cultivating Crop B is 560/acre. The farmer has a maximum of $7400 available for and cultivation. Each acre of Crop Arequires 20 labor hours, and each acre of Crop Brequires 25 tabor hours. The farmer has a maximum of 3400 labor hours available. If she expects to make a profit of $160/acre on Crop Aand $220/acre on Crop B, how many acres of each crop, and respectively should she plant to maximize her profit in dollars?
The farmer should plant 116 acres of Crop A and 104 acres of Crop B to maximize her profit, which would be $41,840.
To maximize profit, the farmer should plant the crop with the higher profit per acre until she runs out of money or labor hours.
Let x be the number of acres of Crop A to be planted, and y be the number of acres of Crop B to be planted.
The objective function (profit) is: Profit = 160x + 220y
The constraints are: Cost constraint: 30x + 560y ≤ 7400 Labor hour constraint: 20x + 25y ≤ 3400
To solve this problem using linear programming, we can use a graphing calculator or software.
However, we can also solve it manually by finding the corner points of the feasible region (the area that satisfies all constraints) and evaluating the objective function at each point. The corner points are: (0, 296/5) (116, 104) (170, 56) (222/5, 0)
Evaluating the objective function at each point, we get: (0, 296/5):
Profit = 0 + 160(296/5) = 9472 (116, 104):
Profit = 160(116) + 220(104) = 41840 (170, 56):
Profit = 160(170) + 220(56) = 38480 (222/5, 0):
Profit = 160(222/5) + 0 = 7104
Therefore, the farmer should plant 116 acres of Crop A and 104 acres of Crop B to maximize her profit, which would be $41,840.
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