Mr. beasley 's science class wants to decorate one wall in the classroom like an underwater scene. They use sheets of blue poster board that are 2 feet long and 2 feet wide. How many sheets of blue poster board are used to cover the entire area of the wall? use math words and symbols to explain how you solve

Answer:

27.6%

Step-by-step explanation:

See the attached worksheet. Find the total number of marbles (29) and then take the green marbles and divide by the total and multiply by 100%.  (8/29)*(100%) = 27.6% to the nearest tenth.

In a case whereby Mai poured 2.4 L into a partilly filled water now there is 10.4 the best figure that represent this is the second fiqure.

Based on the given information it can be seen that the total volume of the figure is 10.4 which implies that it will take the total volume of of water of 10.4

Considering the second fiqure , it can be deduced that the total volume is 10.4, where one part of the fiqure is X and other bis 2.4, which impies that 10.4 = X + 2.4 which is the expression for the fiqure.

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Answer:

4r to the power of 2 - 3r +1

Answer:  

Letter D

Step-by-step explanation:

not always zero

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Functions g(x) = 2x² - 72 and f(x) = 2x² are graphed below g(x) is graphed by shifting f(x) downwards 72 units.

A quadratic function is a polynomial function with one or more variables whose highest exponent is 2. It is also called a quadratic polynomial because the highest order term of  a quadratic function is quadratic. A quadratic function has at least one quadratic term. It's an algebraic function.

Given functions,

g(x) = 2x² - 72

f(x) = 2x²

Graph of the functions are drawn as follows:

f(x) is the parent function of g(x)

f(x) is shifted 72 unit down to get g(x)

Table for points of function g(x)

vertex is at (0, -72)

x  y

1   -70

2  -64

Table for points of function f(x)

vertex is at (0, 0)

x  y

1   2

2  8

3  18

Hence, graphs of the function g(x) = 2x² - 72 and f(x) = 2x² are attached below. f(x) is shifted 72 unit downwards to get g(x).

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The probability of either event E or event F occurring, when E and F are mutually exclusive, is 0.85.

If E and F are mutually exclusive events, it means that they cannot occur simultaneously. In such cases, the probability of either event E or event F occurring is the sum of their individual probabilities.

Given that P(E) = 0.34 and P(F) = 0.51, we can calculate the probability of E or F, denoted as P(E or F), as:

P(E or F) = P(E) + P(F)

Substituting the given values, we have:

P(E or F) = 0.34 + 0.51

Calculating the sum, we find:

P(E or F) = 0.85

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The required  vector v that solves the given vector equation\(2v + (7, - 6, 5) = (1, 4, 5)\) is  \(v = (-3, 5, 0)\).

Given that the vector equation \(2v + (7, - 6, 5) = (1, 4, 5)\)

To solve for vector v, and isolate v by subtracting the constant vector  \((7, -6, 5)\) from both sides of the equation:

\(2v = (1, 4, 5) - (7, -6, 5)\).

\(2v = (-6, 10, 0)\).

Solve for \(v\) by dividing both sides of the equation by 2:

\(v = (-6/2, 10/2, 0/2)\)

\(v = (-3, 5, 0)\)

Therefore, the vector v that solves the given vector equation is                \(v = (-3, 5, 0)\).

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To test the claim that workplace accidents are distributed on workdays as stated, we can use the p-value method of hypothesis testing with a significance level of 0.01.

Step 1: State the null and alternative hypotheses:
- Null hypothesis (H0): The distribution of workplace accidents is as claimed.
- Alternative hypothesis (Ha): The distribution of workplace accidents is not as claimed.

Step 2: Calculate the expected frequencies for each day based on the claimed distribution. Assuming a total of 112 accidents occurred (46 + 3 + 10 + 5 + 48):
- Monday: (25% of 112) = 28 accidents
- Tuesday: (15% of 112) = 16.8 accidents (rounded to 17)
- Wednesday: (15% of 112) = 16.8 accidents (rounded to 17)
- Thursday: (15% of 112) = 16.8 accidents (rounded to 17)
- Friday: (30% of 112) = 33.6 accidents (rounded to 34)

Step 3: Calculate the test statistic:
- Use the chi-squared test statistic formula: X^2

= Σ((O - E)^2 / E), where O is the observed frequency and E is the expected frequency.
- For each day, calculate (O - E)^2 / E and sum the values.

Step 4: Determine the degrees of freedom:
- Degrees of freedom = number of categories - 1 = 5 - 1 = 4

Step 5: Find the p-value:
- Use the chi-squared distribution table with 4 degrees of freedom to find the critical value at a significance level of 0.01.
- Compare the test statistic to the critical value to determine if we reject or fail to reject the null hypothesis.
- If the test statistic is greater than the critical value, reject the null hypothesis.

Step 6: State the conclusion:
- If the p-value is less than 0.01, reject the null hypothesis and conclude that the workplace accidents are not distributed as claimed.

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A type of research study that applies statistical analysis to generalize findings from a smaller sample to a larger population is considered inferential research.

A type of research study that derives meaning from statistical analysis and aims to apply or generalize knowledge from a smaller sample of subjects to a larger population is typically considered inferential research.

Inferential research involves making inferences or drawing conclusions about a population based on data collected from a sample. It uses statistical techniques to analyze the sample data and make inferences or predictions about the larger population. The goal is to generalize the findings from the sample to the broader population from which it was drawn.

Inferential research often involves hypothesis testing, where researchers formulate hypotheses about the population and collect sample data to determine whether the data supports or rejects the hypotheses. Statistical analysis plays a crucial role in inferential research by providing methods to estimate population parameters, test hypotheses, calculate confidence intervals, and assess the significance of findings.

The purpose of inferential research is to make valid and reliable inferences about the population based on the sample data, allowing researchers to draw meaningful conclusions and apply the findings to a larger context. It helps researchers gain insights into the underlying relationships, patterns, or effects within the population they are studying, even when they are unable to collect data from the entire population.

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Answer:  20 and 28 years old

Step-by-step explanation:

The interest estimated by compounding methods are-

(a) Annual: n = 1; CI = $860

(b) Semiannual: n = 2; CI = $862.

(c) Monthly: n = 12; CI = $865

(d) Daily: n = 365; CI = $855

The formula for computing the compound interest is -

CI = A - P

A = P(1 + r/100nt)∧rt

In which,

(a) Annual: n = 1

A = 10,400(1 + 8/500)∧5

A = 10,400 x 1.08

A = 11,260

CI = 11,260 - 10,400

CI = $860

(b) Semiannual: n = 2

A = 10,400(1 + 8/1000)∧10

A = 10,400 x 1.089

A = 11,262

CI = $862.

(c) Monthly: n = 12

A = 10,400(1 + 8/6000)∧60

A = 10,400 x 1.083

A = 11,265

CI = $865

(d) Daily: n = 365

A = 10,400(1 + 8/182500)∧1825

A = 10,400 x 1.0832

A = 11,255

CI = $855

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The sample standard deviation is approximately 0.83.

Sample size \(($n$)\) = 36

Population mean \(($\mu$)\) = 50

Population standard deviation \(($\sigma$)\) = 5

The sample standard deviation, denoted as \($s$\) can be estimated using the formula:

\(\[ s = \sqrt{\frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n-1}} \]\)

where:

\($x_i$\) represents the individual data points in the sample

\($\bar{x}$\) is the sample mean

In this case, since we don't have individual data points, we can use the population standard deviation as an estimate for the sample standard deviation when the sample size is relatively large (as in this case \($n = 36$\)). This approximation is known as the standard error of the mean.

Therefore, the sample standard deviation can be approximated as:

\(\[ s \approx \frac{\sigma}{\sqrt{n}} \]\)

Substituting the given values:

\(\[ s \approx \frac{5}{\sqrt{36}} = \frac{5}{6} \] = 0.83\)

Hence, the sample standard deviation is approximately 0.83.

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(1) Using the Black/Scholes Option Pricing Model, the value of the call option is $7.70.

(2) The intrinsic value of the call is the difference between the stock price and the strike price of the option. Therefore, it is $4.

(3) The stock price required to break-even is the sum of the strike price and the option premium. Therefore, it is $74.

(4) If volatility were to decrease, the value of the call would decrease.

(5) If the exercise price would increase, the value of the call would decrease.

(6) If the time to maturity were 3-months, the value of the call would decrease.

(7) If the stock price were $62, the value of the call would be zero.

(8) The maximum value that a call option can take is unlimited.

In the Black/Scholes option pricing model, the value of a call option can be calculated using the formula:

C = S*N(d1) - X*e^(-rT)*N(d2)

where S is the stock price, X is the exercise price, r is the risk-free rate, T is the time to maturity, and σ2 is the variance of the stock's return.

Using the given values, we can calculate d1 and d2:

d1 = [ln(S/X) + (r + σ2/2)T]/(σ2T^(1/2))

   = [ln(74/70) + (0.10 + 0.50/2)*0.5]/(0.50*0.5^(1/2))

   = 0.9827

d2 = d1 - σ2T^(1/2) = 0.7327

Using these values, we can calculate the value of the call option:

C = S*N(d1) - X*e^(-rT)*N(d2)

= 74*N(0.9827) - 70*e^(-0.10*0.5)*N(0.7327)

= $7.70

The intrinsic value of the call is the difference between the stock price and the strike price of the option. Therefore, it is $4.

The stock price required to break-even is the sum of the strike price and the option premium. Therefore, it is $74.If volatility were to decrease, the value of the call would decrease. This is because the option's value is directly proportional to the volatility of the stock.

If the exercise price would increase, the value of the call would decrease. This is because the option's value is inversely proportional to the exercise price of the option.

If the time to maturity were 3-months, the value of the call would decrease. This is because the option's value is inversely proportional to the time to maturity of the option.If the stock price were $62, the value of the call would be zero. This is because the intrinsic value of the call is zero when the stock price is less than the strike price.

The maximum value that a call option can take is unlimited. This is because the value of a call option is directly proportional to the stock price. As the stock price increases, the value of the call option also increases.

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The solution set of the given equation is x = 8.39 or x = -12.39

\( \frac{1}{4} {{(x + 2} )}^{2} = 27\)

cross product

\( {1} {{(x + 2}^{} )}^{2} = 27 \times 4\)

(x + 2²) = 108

find the square root of both sides

\( \sqrt{ ({x + 2)}^{2} } = ± \sqrt{108}\)

x + 2 = ± 10.39

So,

x = 10.39 - 2 or x = -10.39 - 2

x = 8.39 or x = -12.39

Therefore, the equation has a solution set of x = 8.39 or x = -12.39

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The weights are within 2 standard deviations of the mean are 8.9 lbs, 9.5 lbs and 10.4 lbs

The given parameters are:

The weights within 2 standard deviation is represented as:

μ - 2σ ≤ x ≤ μ + 2σ

Substitute known values

9.5 - 2(0.5) ≤ x ≤ 9.5 + 2(0.5)

Evaluate the product

9.5 - 1 ≤ x ≤ 9.5 + 1

Evaluate the sum

8.5 ≤ x ≤ 10.5

This means that the weights are between 8.5 and 10.5 (inclusive)

Hence, the weights are within 2 standard deviations of the mean are 8.9 lbs, 9.5 lbs and 10.4 lbs

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Answer:

B C D

Step-by-step explanation:

I got it right on the quiz. :)

Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 1 = 5(x - (-5))

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

According to the Ratio Test, if the limit of the ratio of consecutive terms is less than 1, the series converges. In this case, the limit is 0, which is less than 1. Therefore, the series ∑(n^3/n!) from n=1 to infinity converges.

To determine the convergence or divergence of the series ∑(n^3/n!) from n=1 to infinity, we can use the Ratio Test.

Step 1: Calculate the ratio of consecutive terms, a_n+1/a_n:
a_n+1/a_n = ((n+1)^3/(n+1)!)/(n^3/n!)

Step 2: Simplify the expression:
a_n+1/a_n = ((n+1)^3/(n+1)!)*(n!/(n^3)) = ((n+1)^3/((n+1)(n!))) * (n!/(n^3)) = ((n+1)^3/(n^3(n+1)))

Step 3: Further simplify the expression:
a_n+1/a_n = (n+1)^2/(n^3)

Step 4: Find the limit as n approaches infinity:
lim (n→∞) (n+1)^2/(n^3) = 0

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Answer C

Step-by-step explanation:.

Answer:

The answer is 3 2/5 hope this helps :)

Step-by-step explanation:

Answer:

7. 78

8. 169

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

(2, 5)

Step-by-step explanation:

The x coordinate is the number inside the parentheses, but with the opposite sign, 2

The y coordinate is the number at the end

Answer:

vertex: (2, 5)

Step-by-step explanation:

y=3(x−2)2+5

this is a parabola because of one variable squared and the other one is not so now write it in the standard form of parabolas which it is = to

______

Vertical :

(x−h)2=4p(y−k)

Horizontal:

(y−k)2=4p(x−h)2

vertex = (h, k)

______

this y=3(x−2)2+5 equation is vertical since x is squared

subtract 5 from both sides:

y−5=3(x−2)2

divide both sides by 3:

(y−5)13=(x−2)2

vertex:

(2,5)

Dan suzy and aaron share 16 slices of pizza in ratio 1:2:5 aaron get 10 clicks of pizza out of the total.

To break it down further, we can first find the portion size (x) by dividing the total number of slices (16) by the sum of the ratios (1 + 2 + 5 = 8).

So, x = 16 / 8 = 2.

This means that each portion represents 2 slices of pizza.

Next, we can use the ratio to find how many portions each person received. We know that Dan received 1 portion, Suzy received 2 portions, and Aaron received 5 portions. So, to find the number of slices each person received, we just need to multiply their portion size (2 slices) by the number of portions they received.

For Dan, it's 1 portion * 2 slices/portion = 2 slices.

For Suzy, it's 2 portions * 2 slices/portion = 4 slices.

And for Aaron, it's 5 portions * 2 slices/portion = 10 slices.

So, in total, Aaron received 10 slices of pizza.

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To prove the relationship between the illumination at two different distances from a lamp, we can use the inverse square law of light propagation. According to this law, the intensity or illumination of light decreases as the distance from the source increases.

The inverse square law states that the intensity of light is inversely proportional to the square of the distance from the source. Mathematically, it can be expressed as:

I1 / I2 = (D2 / D1)^2 where I1 and I2 are the illuminations at distances D1 and D2, respectively. In this case, we are given that the illumination from the lamp at a distance of 1 m is 10 m/m^2 (meters per square meter). Let's assume that the illumination at a distance of 0.5 m is I2.

Using the inverse square law, we can write the equation as:

10 / I2 = (1 / 0.5)^2

Simplifying the equation, we have:

10 / I2 = 4

Cross-multiplying, we get:

I2 = 10 / 4 = 2.5 m/m^2

Therefore, we have proven that the illumination at a point 0.5 m away from the lamp is 2.5 m/m^2, not 40 m/m^2 as stated in the question. It seems there may be an error or inconsistency in the given values.

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a. The solutions to the equation 1.2x² = 45 are x = √37.5 and x = -√37.5.

b. The solution to the equation 3x + 122.5 = 465.5 is x ≈ 114.333.

c. The solutions to the equation 8x² - 2x = 1 are x = 0.5 and x = -0.25.

a. 1.2x² = 45

To solve this equation, we can start by dividing both sides by 1.2:

1.2x² / 1.2 = 45 / 1.2

x² = 37.5

Next, we take the square root of both sides to isolate x:

√(x²) = √37.5

x = ±√37.5

Therefore, the solutions to the equation 1.2x² = 45 are x = √37.5 and x = -√37.5.

b. 3x + 122.5 = 465.5

To solve this equation, we can start by subtracting 122.5 from both sides:

3x + 122.5 - 122.5 = 465.5 - 122.5

3x = 343

Next, we divide both sides by 3 to isolate x:

3x / 3 = 343 / 3

x = 114.333...

Therefore, the solution to the equation 3x + 122.5 = 465.5 is x ≈ 114.333.

c. 8x² - 2x = 1

To solve this equation, we can rearrange it to a quadratic form:

8x² - 2x - 1 = 0

To solve the quadratic equation, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 8, b = -2, and c = -1.

x = (-(-2) ± √((-2)² - 4(8)(-1))) / (2(8))

x = (2 ± √(4 + 32)) / 16

x = (2 ± √36) / 16

x = (2 ± 6) / 16

x = (2 + 6) / 16 or x = (2 - 6) / 16

x = 8 / 16 or x = -4 / 16

x = 0.5 or x = -0.25

Therefore, the solutions to the equation 8x² - 2x = 1 are x = 0.5 and x = -0.25.

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Answer:

\( \frac{x}{4} + \frac{1}{2} = \frac{1}{8} \)

\( \frac{x}{4} = - \frac{3}{8} \)

\(x = - \frac{3}{2} = - 1 \frac{1}{2} \)

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

Consider the equation, we have only one x term, so taking all the terms without x to the other side and terms with x on one side.

x/4 + 1/2 = 1/8

Take the 1/2 term on the other side,

x/4=1/8 - 1/2

Taking the LCM on the Right side,

x/4 = (1-4) / 8

x/4 = -3/8

Now, we have x/4 so what we can do is, shift the 4 to the other side too, we get,

x = ( -3/8) * 4

x = -3/2

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

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All members of set S can be expressed as numbers of the form 2ᵃ3ᵇ, where a and b are non-negative integers.

We will prove by structural induction that all members of set S can be expressed as numbers of the form 2ᵃ3ᵇ, where a and b are non-negative integers.

Base Case:

We start with the base case, where n = 1. In this case, 1∈ S, and we can see that 1 can be expressed as 2⁰3⁰, which is of the desired form.

Inductive Step:

Now, assume that for some positive integer k, if n = k, then k∈ S can be expressed as 2ᵃ3ᵇ for non-negative integers a and b.

We will show that if n = k + 1, then k + 1 can also be expressed as 2ᵃ3ᵇ for non-negative integers a and b.

Case 1: If n = 2k, then we know that 2k∈ S. By the induction hypothesis, we can express 2k as 2ᵃ3ᵇ for some non-negative integers a and b. Now, we can observe that 2k+1 = 2(2k) = 2ᵃ₊₁3ᵇ, which is still of the desired form.

Case 2: If n = 3k, then we know that 3k∈ S. By the induction hypothesis, we can express 3k as 2ᵃ3ᵇ for some non-negative integers a and b. Now, we can observe that 3k+1 = 3(3k) = 2ᵃ3ᵇ₊₁, which is still of the desired form.

Since we have shown that if n = k + 1, then k + 1 can be expressed as 2ᵃ3ᵇ, the proof by structural induction is complete.

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Answer:

110 minutes

Step-by-step explanation:

This is a volume question where we find the volume of each aquarium and work out per minute rate, here we can either divide the time amount given for per volume of the smaller tank back into the volume of the larger aquarium

- or find per minute first as shown below and divide per minute into total volume.

v / u  = t  

where v is volume

where u is our multiplier  one part and time found ie) 1 minute)

where t is total time

Smaller Tank

Volume = 8 x 9 x 14 = 1008 inch cube

Per minute rate = 1008/4 = 252 inch p/m

Larger Tank

Volume 29 x 30 x 32 = 27840 inch cube

Total minutes  27840 / 252 = 110.476190476 = 110 minutes 28 seconds.

or 110.47 minutes to 2 dp.

Answer:

-21 r^5

Step-by-step explanation:

(7r) (-3r^4)

Multiply the coefficients

7*(-3)

-21

Multiply the variables

r * r^4 = r^(4+1) = r^5

-21 r^5

The distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

We can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the coordinates of M(6, 16) and Z(-1, 14), we get:

d = √((-1 - 6)² + (14 - 16)²) = √(49 + 4) = √53 ≈ 7.1

Therefore, the distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

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