Whenever Marlon and her classmates finished reading a book, they wrote the title on a 1/3 ft by 1/3 ft piece of paper. Each piece of paper was stapled to the bulletin board, side by side, without overlapping. By the end of the school year, the entire bulletin board was covered with book titles. How many pieces of paper were on the bulletin board?

Area of bulletin board: 34 2/3 Number model:__________________

The value of

1. BC = 12.04

2. angle B = 50°

3. angle C = 50°

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse

c² = a² + b²

BC is the hypotenuse

c² = 8² + 9²

c² = 64+81

c² = 145

c = √145

= 12.04

TanB = opp/adj

tanB = 6/8

tanB = 0.75

B = 40( nearest degree)

angle C = 90- 40

C = 50°

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The 95% confidence interval for the population mean μ is (18.3, 21.7).

Given: n = 100, σ2 = 64, X-bar = 20, and the desired level of confidence is 95%.

We can use the formula for the confidence interval for the population mean when the population standard deviation is known:

CI = X-bar ± Zα/2 * σ/√n

where CI is the confidence interval, Zα/2 is the critical value from the standard normal distribution for the given level of confidence, σ is the population standard deviation, and n is the sample size.

Since the level of confidence is 95%, we have α = 0.05 and Zα/2 = 1.96.

Substituting the given values, we get:

CI = 20 ± 1.96 * 8/√100

Simplifying the expression, we get:

CI = (18.3, 21.7)

Therefore, we can be 95% confident that the true population mean μ lies between 18.3 and 21.7 based on the given sample data.

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Tanisha would expect to earn 180 on a day when she waits on 10 tables.

Tanisha's guaranteed wage is 40 per day. This means that no matter what happens during her shift, she will earn at least 40.

In addition to her guaranteed wage, Tanisha earns money from tips. She earns about 14 in tips for each table she waits on. If Tanisha waits on 10 tables in a day, she can expect to earn:

14 x 10 = 140

Therefore, her total earnings for the day would be:

40 (guaranteed wage) + 140 (tips) = 180

So Tanisha would expect to earn 180 on a day when she waits on 10 tables.

It's important to note that Tanisha's tips may vary from day to day depending on factors such as the size of the party, the generosity of the customers, and the overall volume of business at the restaurant. However, based on past experience, she can reasonably expect to earn around 14 in tips for each table she waits on.

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The given waveform is λ(t) = 100 cos (2π x 10^5 t + 35 cos (100 πf)). The frequency band occupied by the waveform can be approximated as twice the maximum deviation from the carrier frequency due to the modulating function.

The given waveform λ(t) can be written as:

λ(t) = 100 cos (2π x 10^5 t + 35 cos (100 πf))

The inner function, 35 cos (100 πf), is a modulating function that varies slowly compared to the carrier wave at 2π x 10^5 t. The modulating function is the cosine of a rapidly varying frequency, 100 πf, and it will produce sidebands around the carrier frequency of 2π x 10^5 t.

The sidebands will occur at frequencies of 2π x 10^5 t ± 100 πf. The width of the frequency band occupied by the waveform can be approximated as twice the maximum deviation from the carrier frequency due to the modulating function. In this case, the maximum deviation occurs when cos (100 πf) = ±1, which gives a frequency deviation of 35 x 100 = 3500 Hz.

Therefore, the approximate band of frequencies occupied by the waveform is 2 x 3500 = 7000 Hz, centered around the carrier frequency of 2π x 10^5 t.

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The area of the rectangular farm is 197,600 square meters.

Let's assume the breadth of the rectangular farm is x meters. According to the given information, the length of the farm is 140 meters longer than its breadth, so the length would be (x + 140) meters.

The perimeter of a rectangle is given by the formula P = 2(length + breadth). We can set up the equation as follows:

2(length + breadth) = 1800

Substituting the values, we get:

2((x + 140) + x) = 1800

Simplifying the equation:

2(2x + 140) = 1800

4x + 280 = 1800

4x = 1800 - 280

4x = 1520

x = 1520 / 4

x = 380

Therefore, the breadth of the farm is 380 meters.

Using this value, we can find the length:

Length = x + 140 = 380 + 140 = 520 meters.

The area of a rectangle is given by the formula A = length * breadth. Substituting the values, we have:

Area = 520 * 380 = 197,600 square meters.

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A tax rate of $0.0711 per $1,000 of assessed valuation in decimal form is 0.00711% and in fractional form is $0.0000711 .

Given, that tax rate of $.0711 .

First, divide the tax rate by 1,000 to determine the rate per dollar:

$0.0711 / 1,000 = $0.0000711.

This represents the decimal equivalent of the tax rate per dollar.

To express it as a percentage, multiply the decimal value by 100: $0.0000711 × 100 = 0.00711%.

Therefore, a tax rate of $0.0711 per $1,000 of assessed valuation is equal to 0.00711% in decimal form.

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A tax rate of $.0711 per dollar is equivalent to $71.1 per $1000 when expressed in terms of assessed valuation.

A tax rate of $.0711 in decimal form expresses a tax of 7.11 cents per dollar. However, the question asks for the tax rate expressed per $1000. Therefore, to find this, we need to multiply the tax rate per $1 by 1000. Thus, $.0711 per $1 x 1,000 = $71.1 per $1000 of assessed valuation.

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Answer:

[tex]5 + 2\sqrt{3}[/tex]

    &          

[tex]5-2\sqrt{3}[/tex]

Step-by-step explanation:

Okay! The equation is : 2x²+26=20x

Right off the bat we notice that this can be simplified. We divide all numbers by a common multiple: 2.

Our resulting equation is [tex]x^2 + 13= 10x[/tex]

Now, in order to plug this equation into our quadratic formula, we need to rearrange this equation into the [tex]ax^2 + bx +c = 0[/tex] format.

In order to do that, we simply move the 10x to the left side of the equation, resulting in this: [tex]x^2 - 10x + 13[/tex]

Here is the quadratic formula:

(-b±√(b²-4ac))/ 2a

I will include a picture of the quadratic equation at the bottom (because the typed equation is strange).

So looking at our previously found formula, x^2 - 10x + 13, we know that a: 1

b: -10

c: 13

Now, we plug in our values!

(-(-10) ± √((-10)²-(4(1)(13))) / 2(1)

Simplify! (10 ± √(100-52)) / 2

Simplify again! (10 ± √48) / 2

Now we must simplify the square root. If we try to find the square root of 48, it comes out to 6.92820323, which is a very messy number. We will NOT be using this number. We will instead find the factors of 48.

2·2·2·2·3 = 48

So it looks like this: √2·2·2·2·3

We can pair up the similar numbers, so it looks like: √(2·2)(2·2)·3

Now, we move the pairs of twos to the front of the equation (but only one two from each pair is represented because they've been square-rooted) , and out of the square root, to get us: 2·2 √3, which equals 4√3

Now that we have the square root figured out, we re-enter the square root into the equation we had before (replacing the un-simplified version with the simplified version), which was (10 ± √48) / 2.

Here is the equation with the simplified root:  (10 ± 4√3) / 2

Now we notice that 10 and 4 are divisible by 2, so the equation becomes: (5 ± 2√3), which is 5+2√3, AND 5-2√3

Hope that helped!!!!

Answer:

Step-by-step explanation:

We must divide the frequency of F grades by the total number of pupils in the class to get the likelihood that a student would receive an F.

The frequency distribution being what it is:

Level: A B C D F

28 35 56 14 7 times each year

You can determine the total number of pupils by adding the frequencies:

Students total: 28 + 35 + 56 + 14 + 7 = 140.

We can now determine the probability:

P(F) = Number of students overall / Frequency of F grades

P(F) = 7 / 140 P(F) = 0.05

As a result, the likelihood that a student will receive a F is 0.05, or 5%.

(a) To calculate the probability of the first miss occurring after 12 attempts, we need to consider the scenario in which the shooter makes the first 11 shots and then misses the 12th shot. The probability of making a free throw is given as p = 0.9.

The probability of making a shot is 0.9, so the probability of missing a shot is 1 - 0.9 = 0.1. Therefore, the probability of making 11 shots in a row is (0.9)^11.

The probability of missing the 12th shot is 0.1. Since these events are independent, we can multiply the probabilities together. Therefore, the probability of making the first 11 shots and missing the 12th shot is (0.9)^11 * 0.1.

Therefore, the probability of having the first miss after 12 attempts is (0.9)^11 * 0.1.

(b) To calculate the probability that the third miss occurs on the 30th attempt, we need to consider the scenario in which the shooter makes the first 29 shots and then misses the 30th shot.

The probability of making a shot is 0.9, so the probability of missing a shot is 1 - 0.9 = 0.1. Therefore, the probability of making 29 shots in a row is (0.9)^29.

The probability of missing the 30th shot is 0.1. Since these events are independent, we can multiply the probabilities together. Therefore, the probability of making the first 29 shots and missing the 30th shot is (0.9)^29 * 0.1.

However, we also need to consider that the shooter must miss the first two shots before reaching the 30th attempt. The probability of missing two shots in a row is (0.1)^2.

Therefore, the probability that the third miss occurs on the 30th attempt is (0.9)^29 * 0.1 * (0.1)^2.

Note that these calculations assume that each shot is independent of the others and that the shooter's probability of making a shot remains constant throughout the attempts.

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The critical numbers of the function f(theta) = 18 cos(theta) + 9 sin^2(theta) need to be found.

To find the critical numbers, we need to first take the derivative of the function.

f'(theta) = -18 sin(theta) + 18 sin(theta) cos(theta)

Setting f'(theta) equal to zero and solving for theta, we get:

-18 sin(theta) + 18 sin(theta) cos(theta) = 0

simplifying, we get:

sin(theta) (cos(theta) - 1) = 0

So, the critical numbers occur when sin(theta) = 0 or cos(theta) = 1.

Therefore, the critical numbers of the function are: theta = npi, where n is an integer, and theta = 2npi, where n is an integer.

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The approximate area bounded by the curve is 57.96 square units.

The given equation is a polar equation of a cardioid. To find the area enclosed by the curve, we can use the formula for the area of a polar region:

A = (1/2)∫(b,a) r(θ)² dθ

where 'a' and 'b' are the values of θ that define the region.

In this case, the cardioid is symmetric about the x-axis, so we only need to consider the area in the first quadrant, where 0 ≤ θ ≤ π/2.

Thus, we have:

So the area enclosed by the curve is approximately 57.96 square units.

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In diagram A, the axis of symmetry will be vertical and has rotational asymmetry. In diagram D, the axis of symmetry will be horizontal.

Axial symmetrical is similarity around an axis; an item is internally symmetric if it retains its appearance when turned around an axis.

Rotational symmetry is a property of an object or a figure that remains unchanged when it is rotated about a fixed point by an angle less than 360 degrees.

In diagram A, the axis of symmetry will be vertical and has rotational asymmetry.

In diagram D, the axis of symmetry will be horizontal.

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Answer:

B is 41 × 1/2

Step-by-step explanation:

A is 18 × 1/2 so that is your answer

The area of a triangle with sides A=18, B=41, and C=41 is 360cm^2(assuming sides are given in "cm").

By using Heron's formula to calculate the area of a triangle from the sides,

Just use this two-step process:

Step 1: Calculate "s" (half of the perimeter of the triangle):

s =  a+b+c/2

Step 2: Then calculate the Area:

A = \sqrt{s(s−a)(s−b)(s−c)}

Here, a=18,b=41,c=41

so,s=50 and A=360.

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Answer:

4.695

Step-by-step explanation:

multiply top and bottom by 100, 000 to clear any decimal places

now we have 78, 000 / 16,614

= 4.695 (3 decimal places).

Answer:

(X+8) (x+5)

Step-by-step explanation:

factorise it

The null hypothesis for this test is that the mean weight of adult cats of the same breed is equal to 9.0 lb, while the alternative hypothesis is that it is different from 9.0 lb.

In statistical hypothesis testing, the null hypothesis is a statement that is assumed to be true unless there is sufficient evidence to reject it in favor of an alternative hypothesis. In this case, the null hypothesis is that the mean weight of adult cats of the same breed is equal to 9.0 lb, which is what we are trying to test. The alternative hypothesis, on the other hand, is that the mean weight of adult cats of the same breed is different from 9.0 lb, which could be either higher or lower. This is the hypothesis that we would accept if there is sufficient evidence to reject the null hypothesis.

To test these hypotheses, we would need to collect a sample of adult cats of the same breed, measure their weights, and calculate the sample mean. We could then use statistical methods to determine whether the sample mean is significantly different from the hypothesized value of 9.0 lb. If it is, we would reject the null hypothesis in favor of the alternative hypothesis.

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The approximate value of the irrational number in the set is 7.1 (rounded to one decimal place).

To find the irrational number in the set, we need to check which of these numbers are perfect squares. The perfect squares in the set are 9 and 36. The other two numbers, 50 and 121, are not perfect squares.

Since the set includes two perfect squares, the irrational number must be the positive square root of one of the non-perfect square numbers. We can eliminate 121 since it is a perfect square, so the only option left is 50.

The positive square root of 50 is an irrational number, which is approximately 7.071. Therefore, the approximate value of the irrational number in the set is 7.1 (rounded to one decimal place).

So the answer is: 7.1.

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The rule for the translated function is:

g(x) = log(x) + 2

We know that the function f(x) is the parent logarithmic function, it can be written as.

f(x) = log(x)

We know that g(x) is a translation of f(x), and we can see that the graph of g(x) is 2 units above the graph of f(x), then we can write:

g(x) = f(x) + 2

Now we can replace the function f(x) there to get:

g(x) = log(x) + 2

That is the translated function.

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Complete question:

"Which of the following functions describes g?

g(x) = log(x) + 2

g(x) = log(x + 2)

g(x) = log(x) - 2"

The equation of the line in the graph is:

y = 2

A general linear equation can be written as:

y = ax + b

Where a is the slope and b is the y-intercept.

Particularly, in this case we can see that the line intercepts the y-axis at the value y = 2, then we have that b = 2

y = ax + 2

Now we can see that the line also passes through the point (5, 2), replacing these values in the equation we get:

2 = a*5 + 2

2 - 2 = a*5

0 = a*5

0/5 = a

0 = a

Then the equation of the line is:

y = 2

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The required value of the account after 2 years is $337.08.

The equation below represents the value V of a bank account in which $300 is invested at 6.00% interest compounded yearly:

[tex]V = 300 \times (1.06)^t[/tex]    .....(i)

where t is the period in years.

It is required to find the value of the account after 2 years.

The value of the bank account after 2 years can be found by substituting t = 2 into the given equation (i):

V = 300 × (1.06)²

V = 300 × 1.1236

Apply the multiplication operation to get

V = 337.08

Therefore, the value of the account after 2 years is $337.08.

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The volume of the sphere is  0. 52 ft³

To determine the volume, we need to know the formula

Hence, the formula that is used for calculating the volume of a sphere is expressed as;

V = 4/3 πr³

Such that the parameters of the formula are;

Substitute the values, we have that;

Volume = 4/3 ×3.14 × 0.5³

Find the cube value

Volume = 4/3 × 3.14 × 0.125

Multiply the values

Volume = 1.57/3

Divide the values

Volume = 0. 52 ft³

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a) H is a subgroup of G. b) H is not a subgroup of G. c) H is a subgroup of G. d) H is a subgroup of G. e) H is not a subgroup of G. f) H is a subgroup of G. g) H is not a subgroup of G. h) H is a subgroup of G.

(a) H = {0, 1, -1}, G = Z:

H is a subgroup of G since it is closed under addition, inverse and contains the identity element.

(b) H = {1, 3}, G = Zs:

H is not a subgroup of G since it is not closed under addition. For example, 1 + 3 = 4 is not in H.

(c) H = {1, 3}, G = Z*_15:

H is a subgroup of G since it is closed under multiplication, inverse and contains the identity element.

(d) H = {element_1 (1, 2) (3 4), (1, 2)(2, 4)}, G = S_3:

H is a subgroup of G since it is closed under composition, inverse and contains the identity element.

(e) H = {[1 0 0 1], [-1 0 0 -1], [0 1 -1 0], [0 -1 1 0]}, G = GL_1(z):

H is not a subgroup of G since it is not closed under matrix multiplication. For example, [1 0 0 1] * [0 1 -1 0] = [0 1 -1 0] is not in H.

(f) H = {2, 4, 6}, G = Z_6:

H is a subgroup of G since it is closed under addition, inverse and contains the identity element.

(g) H = N, G = Z:

H is not a subgroup of G since it does not contain the identity element.

(h) H = {(m, k)|m + k is even}, G = Z x Z:

H is a subgroup of G since it is closed under addition, inverse and contains the identity element.

"Z" refers to the integers and "Z*_15" refers to the integers modulo 15. "GL_1(z)" refers to the set of invertible 1x1 matrices with integer entries.

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Answer:

2x² + 7x - 13

Step-by-step explanation:

so the equation is 3(x² - 1) - (x² -7x + 10).

let’s say x=3.

3(3² - 1) - (3² - 7 • 3 + 10) = 26

now we have to find which equation is equivalent to 26, because now this will be much easier as we substituted x for 3.

after doing all the math, i found out that 2x²+ 7x - 13 is equivalent to the expression. this is because both equations share the answer of 26, which makes them equivalent. hope this helped!

Answer: 60

Step-by-step explanation:

you just take the value of the number your looking at and turn it into its original whole number. e.g. the value of 2 in that equation would be 200

The scenario that the sample means differ more is Scenario 1 because the mean seems to be very far from each other.

The scenario that there is a larger variation in the distribution of data within each sample is Secnario 2

The f statistics is larger for Scenario 1 as the Means are far and the spread is less so the F statistic will be larger.

Scenario 1 as F statistic will be larger. So chances of Rejecting H0 is more.

The F statistic is a statistical measure used to determine if there is a significant difference between the means of two or more groups. It is calculated by dividing the between-group variability (also known as the mean square between) by the within-group variability (also known as the mean square error).

The scenario that there is a larger variation in the distribution of data within each sample is Secnario 2 because for this scenario there seems to be more spread within each sample.

Lastly,  Scenario 1 as F statistic will be larger. So chances of Rejecting H0 is more.

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Answer: Correct.

Step-by-step explanation:

2.8 Kg is 2800 grams

Each day birds eat 125 grams, 125x7 = 875 grams in a week.

If we divide the 875 grams which is that total feed in a week to 2800 our total feed, we will find the argument is correct or not.

2800/875 = 3,2

So it is correct.

To prove the equation [tex]\frac{1}{\tan(2\theta) - \tan(\theta)} - \frac{1}{\cot(2\theta) - \cot(\theta)} = \cot(\theta)[/tex] we'll simplify the left side, this is shown below:

Using the trigonometric identities [tex]\tan(2\theta) = \frac{2\tan(\theta)}{1 - \tan^2(\theta)}[/tex] and [tex]\cot(\theta) = \frac{1}{\tan(\theta)}[/tex]

We can rewrite the expression as [tex]\frac{1}{\tan(\theta)(1 - \tan(\theta))} - \frac{\tan(\theta)}{\tan(\theta)(1 - \tan^2(\theta))}[/tex]

Combining the fractions with a common denominator, we obtain [tex]\frac{1 - \tan(\theta)}{\tan(\theta)(1 - \tan(\theta))}[/tex]

Simplifying further, we cancel out the [tex](1 - tan(\theta))[/tex] terms, leaving us with [tex]\frac{1}{\tan(\theta)}[/tex] = [tex]\cot(\theta)[/tex], which is equivalent to the right side of the equation.

Thus, the equation is proven.

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The range of the graphed exponential function is b . y < -1.

The function which is best represented by the graph is f(x) = -x² + 1.

1) Given an exponential function.

We have to find the range of the function.

The range of the function is the set of all the y values for the x values where the function is defined.

From the graph, it is clear that for any x values, the y values are all either -1 or numbers less than -1.

So the range is y < -1.

2) Given a graph of a parabola opens downwards.

So the function will be quadratic. That is, the highest degree of the variable will be 2.

For a function of the form, (parent function), y = -x², the parabola passes through the point (0, 0), which will be the vertex and the parabola is opened downwards.

Here vertex is (0, 1).

That is the parabola is shifted up to 1 unit.

A function f(x) after the translation to k units up becomes f(x) + d.

So here since the original function is shifted up 1 units, it becomes,

f(x) = -x² + 1

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The null hypothesis is that the proportion of residents in favor of annexation is equal to or greater than 44%, while the alternative hypothesis is that the proportion is less than 44%. A significance level of 0.02 will be used to determine if there is sufficient evidence to support the mayor's claim.

The null hypothesis (H0) is a statement of no difference or no effect, while the alternative hypothesis (H1) is a statement of the expected difference or effect. In this case, the null hypothesis is that p >= 0.44, where p is the proportion of residents in favor of annexation. The alternative hypothesis is that p < 0.44.

To test the hypothesis, a sample of residents can be taken and the proportion of those in favor of annexation can be calculated. Then, a hypothesis test can be performed using the sample proportion and the null hypothesis to determine if there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis. A significance level of 0.02 means that if the p-value (the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true) is less than 0.02, then the null hypothesis will be rejected in favor of the alternative hypothesis.

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