1) Given the area of a Football field (57,600 sqft), and the dimensions of a

Basketball court(84ft x 50ft), what fraction of the football crowd would fit

on the court?"

Set up a ratio. Basketball / Football (Area)

a half (1/2)

a quarter (1/4)

a tenth (1/10)

or less than a tenth (< 1/10)

Answer:

16.5 units square

Step-by-step explanation:

The area of a triangle is 1/2bh

To find the base and heights

We use the formula above

Using the formula for my x.-axis I got 11

From 14 - 3

And for the y-axis, I got 3

From 8-5

Then using the formula 1/2bh

The area of the triangle is 1/2 ×11×3

=16.5

Answer:

6/35

Step-by-step explanation:

\(\frac{2}{5} *\frac{3}{7} =\frac{2*3}{5*7} =\frac{6}{35}\)

Answer:

6/35

Step-by-step explanation:

2/5x3/7=

6/35

Does not simplify. Multiply straight across..

Hope this helps!

Answer:

its 5/4! haha i used to be good at this when i was in 6th grade:)

Answer :-

Step by step explanation :-

1#

Profit on 3000 bags of white cement sold = 3000 × 8 = 24000

loss on 5000 bags of grey cement sold = 5000 × 5 = 25000

Alternatively:

As the result of transaction is negative/ loss

2#

In order to have no profit, profit from the Cello white cement should be 32000.

4000 why cement bags and 6400 grey cement bags are sold in order to have no profit and no loss

Hope it helps ~

The total loss is $-1000.

The Number of white cement to be sold is 4000.

A profit is earned when total revenue is greater than total cost. A loss occurs when  total revenue is less than total cost.

Total profit or loss of selling white and grey cement = (8 x 3000) - (5 x 5000)

24,000 - 25,000 = $-1,000

Number of white cement to be sold: (8 x w) = (6400 x -5)

8w = -32,000

w = 4000

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If the line and curve intersect, it happens when

\(mx + 2 = x^2-5x+18\)

or

\(x^2-(m+5)x + 16 = 0\)

Recall the discriminant (denoted by ∆) of a quadratic expression:

\(\Delta (ax^2+bx+c) = b^2 - 4ac\)

If the discriminant is positive, then the quadratic has two real roots. If it's zero, it has only one real root. If it's negative, it has two complex roots. We're interested in the third case, because that would make it so the above equation has no real roots corresponding to points of intersection in the x,y-plane.

The discriminant here is

\((-(m+5))^2 - 4\cdot16 = (m+5)^2-64\)

Find all m such that this quantity is negative:

\((m+5)^2-64 < 0 \\\\ \implies (m+5)^2 < 64 \\\\ \implies \sqrt{(m+5)^2} < \sqrt{64} \\\\ \implies |m+5| < 8 \\\\ \implies -8 < m + 5 < 8 \\\\ \implies \boxed{-13 < m < 3}\)

The upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

To determine the upper bound of the 95% confidence interval for the average age in the U.S., we can use the sample data from the survey. The sample size is 1072 people, randomly selected from the U.S. population, with a minimum age of 12. By calculating the average age of the respondents, we can estimate the average age of the entire U.S. population.

Using the given information that the average age of the respondents is 43.56 years, and assuming that the sample is representative of the population, we can calculate the standard error. The standard error measures the variability of the sample mean and indicates how much the sample mean might deviate from the population mean.

Using statistical methods, we can calculate the standard error and construct a confidence interval around the sample mean. The upper bound of the 95% confidence interval represents the highest plausible value for the population average age based on the sample data.

Therefore, based on the provided information and calculations, the upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

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f(x) = -1, f(x) = 0,No Fourier series expansion, No Fourier series expansion f(x) = (4/π) * (sin(x) - (1/3) * sin(3x) + (1/5) * sin(5x) - ...)f(x) = (a₀/2) + Σ(an * cos(n#x) + bn * sin(n#x))

Fourier series expansion represents a periodic function as a sum of sine and cosine functions. Let's find the Fourier series expansions for the given functions:

For the function f(x) = -1, the Fourier series expansion will have only a constant term. The expansion is f(x) = -1.

For the function f(x) = 0, which is a constant function, the Fourier series expansion will also have only a constant term. The expansion is f(x) = 0.

For the function f(x) = x², the Fourier series expansion can be found by calculating the coefficients. However, since the function is not periodic with a period of 21, it does not have a Fourier series expansion.

For the function f(x) = x³/2, similar to the previous function, it is not periodic with a period of 21, so it does not have a Fourier series expansion.

For the function f(x) = sin(x), which is periodic with a period of 2π, we can express it as a Fourier series expansion with coefficients of sin(nx) and cos(nx). In this case, the expansion is f(x) = (4/π) * (sin(x) - (1/3) * sin(3x) + (1/5) * sin(5x) - ...).

For the function f(x) = cos(#x), where "#" represents a constant, the Fourier series expansion will also have coefficients of sin(nx) and cos(nx). The expansion is f(x) = (a₀/2) + Σ(an * cos(n#x) + bn * sin(n#x)), where a₀ is the average value of f(x) over a period and an, bn are the Fourier coefficients.

For the function f(x) = |x|, which is an absolute value function, the Fourier series expansion can be calculated piecewise for different intervals. However, since the function is not periodic with a period of 21, it does not have a simple Fourier series expansion.

For the function f(x) = (1 + x)^(if-1), the Fourier series expansion depends on the specific value of "if." Without knowing the value, it is not possible to determine the exact Fourier series expansion.

For the function f(x) = 1/x², similar to the previous cases, it is not periodic with a period of 21, so it does not have a Fourier series expansion.

For the function f(x) = 0, which is a constant function, the Fourier series expansion will have only a constant term. The expansion is f(x) = 0.

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Thus, the probability that it will rain on exactly one of the five days during the Hiking Club's camping trip in the State park is approximately 4.38%.

We can use the binomial probability formula to calculate the probability of rain on exactly one of the five days during the Hiking Club's camping trip in the State park. The formula is:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:
- P(X = k) is the probability of k successes (rain) in n trials (days)
- C(n, k) is the number of combinations of n items taken k at a time
- p is the probability of success (rain) on any given day (66% or 0.66)
- n is the number of trials (5 days)
- k is the number of successes (1 day with rain)

Plugging the values into the formula, we get:

P(X = 1) = C(5, 1) * 0.66^1 * (1 - 0.66)^(5 - 1)

First, we find the number of combinations C(5, 1) which is 5.

Next, we calculate the probabilities:
0.66^1 = 0.66
(1 - 0.66)^4 = 0.34^4 = 0.0133

Now, we multiply everything together:

P(X = 1) = 5 * 0.66 * 0.0133 ≈ 0.0438

So, the probability that it will rain on exactly one of the five days during the Hiking Club's camping trip in the State park is approximately 4.38%.

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Step-by-step explanation:

perimeter = 2* ( length + width)

Length = 4 + Width = 4+x

Equation is,

2* (4+x+x) = 48

2* (4+2x) = 48

4+2x = 48/2 = 24

4+2x=24

2x = 24-4 = 20

2x = 20

x = 10

Answer:

x=39.76693372

Step-by-step explanation:

Subtract 2187 from 3.

54.92x−2184=0

Add 2184

to both sides of the equation.

54.92x=2184

Divide each term by 54.92

and simplify.

x=39.76693372

The statistical decision based on the reported results of the hypothesis test is that the null hypothesis was rejected at the α = .05 significance level.

The t-value reported is 2.38, and the degrees of freedom are 21. This suggests that the test was likely a t-test with an independent samples design, where the sample size was n = 22 (since df = n - 1).

The p-value reported is less than .05, which indicates that the probability of obtaining the observed results, or results more extreme, under the assumption that the null hypothesis is true, is less than .05. Therefore, the null hypothesis is rejected at the .05 significance level in favor of the alternative hypothesis.

In conclusion, the statistical decision is that there is sufficient evidence to suggest that the population means are not equal, and the sample size was 22. However, we do not have information about the direction of the effect (i.e., whether the difference was positive or negative).

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A firm experiences increasing returns to scale if inputs are doubled and output more than doubles.

When the firm's output grows at a faster rate than the growth in inputs, increasing returns to scale result. In this case, the company experiences economies of scale, which makes it more effective as it grows its production.

The firm is able to boost productivity and efficiency as it expands its scale of operations if inputs are doubled and output more than doubles.

This can be ascribed to a number of things, including specialisation, labour division, the use of capital-intensive technology, discounts for bulk purchases, and spreading fixed costs over a higher output. Lower average costs per unit of output result in higher profitability and competitiveness for the company.

The firm gains a number of benefits from growing returns to scale. First off, it lets the company to benefit from cost savings brought about by economies of scale, allowing it to manufacture goods or services for less money per unit. This may enable more competitive pricing on the market or result in larger profit margins.

Second, raising returns to scale can result in better operational effectiveness and resource utilisation. As the company grows in size, it will be able to use resources more wisely and profit from production volume-related synergies.market prices that are competitive.

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Answer:

1) x < -1

2) x ≥ -1

3) x ≤ -1

4) x < -1 and x > 0

5) -1 < x < 0

Explanation:

(1) f(x) > 0

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x-2 > \:0\)

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x > \:2\)

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x > \:2^{-1}\)

\(\sf \rightarrow x < -1\)

(2) f(x) ≤ 0

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x-2 \leq \:0\)

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x \leq \:2\)

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x \leq \:2^{-1}\)

\(\sf \rightarrow x\geq -1\)

(3) g(x) ≥ 0

\(\sf \rightarrow -\dfrac{2}{x}-2 \:\geq \:0\)

\(\sf \rightarrow -\dfrac{2}{x} \:\geq \:2\)

\(\sf \rightarrow \dfrac{1}{x} \:\geq \:-1\)

\(\sf \rightarrow x \: \leq \:-1\)

(4) g(x) < 0

\(\sf \rightarrow -\dfrac{2}{x}-2 \: < \: 0\)

\(\sf \rightarrow x < -1 \ or \ x > 0\)

Observe the graphs a find solution for g(x) < 0

(5) f(x) < g(x)

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x-2 < -\dfrac{2}{x}-2\)

\(\sf \rightarrow -1 < x < 0\)

Answer:

n = 2

Step-by-step explanation:

Expand the brackets.

1/2n - 2 - 3 = 3 - 2n - 3

Add or subtract terms.

1/2n - 5 = -2n

Add 5 and 2n on both sides.

1/2n + 2n = 5

5/2n = 5

Multiply both sides by 2/5.

n = 5 × 2/5

n = 10/5

n = 2

As a result, 210 gallons of oil are thought to have been present in the lake at time 12 (t=12).

A polynomial is a mathematical equation that only uses addition, subtraction, multiplication, and non-negative integer exponents and is made up of variables and coefficients. To put it another way, a polynomial is an algebraic expression made up of terms that are sums, products, and/or products of variables and coefficients. The leading coefficient is the coefficient of the term with the highest degree, while the degree of a polynomial is the maximum power of the variable in the expression.

given

(a) We need to determine Q(10), Q'(10), and Q" in order to determine the second degree Taylor polynomial for Q(t) with a center at t=10 (10).

As we are aware, Q(10) = 200. (given in the problem statement).

We must take the derivative of Q(t) with respect to t in order to determine Q'(10):

Q'(t) = -5t + 250

Q'(10) = -5(10) + 250 = 200

We must take the derivative of Q'(t) with respect to t in order to determine Q"(10):

Q''(t) = -5

Q''(10) = -5

The second degree Taylor polynomial can now be calculated using the following formula: P2(t) = Q(10) + Q'(10)(t-10) + (1/2)Q"(10)(t-10)2.

With the numbers we discovered, we can calculate P2(t) as 200 + 200(t-10) + (1/2)(-5)(t-10)2.

\(P2(t) = 200 + 200(t-10) - (5/2)(t-10)^2\)

(b) We must assess the second degree Taylor polynomial at t=12 in order to determine how much oil is in the lake at that time.

P2(12) = 210 gallons because P2(12) = 200 + 200(12-10) - (5/2)(12-10)2. (rounded to the nearest gallon)

As a result, 210 gallons of oil are thought to have been present in the lake at time 12 (t=12).

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A linear recurrence relation is a function or sequence in which each term is a linear combination of the terms that came before it.

The recurrence relation exists \($T(n)=\Theta\left(3^n\right)$\).

Recurrence relations are used to simplify complex problems by reducing them to an iterative process based on simpler versions of the problem.

Using the substitution method, we find out that

\(T(n) &=n+3 T(n-1) \\\)

\(&=n+3(n-1)+3^2 T(n-2) \\\)

\(&=n+3(n-1)+3^2(n-2)+3^3 T(n-3) \\\)

\(&=\cdots \\\)

\(&=n+3(n-1)+3^2(n-2)+\cdots+3^{n-1}(n-(n-1))+3^n T(0) \\\)

simplifying the above equation, we get

\($&=\frac{3^{n+1}-2 n-3}{4}+3^n T(0) \\\)

\(&=\Theta\left(3^n\right)\)

Even without doing the full calculation it is not hard to check that \($T(n) \geq 3^{n-1}+3^n T(0)$\), and so \($T(n)=\Omega\left(3^n\right)$\).

A cheap way to obtain the corresponding upper bound is by considering

\($S(n)=T(n) / 3^n$\), which satisfies the recurrence relation  

\($S(n)=S(n-1)+n / 3^n$\).

Repeated substitution then gives

\($\frac{T(n)}{3^n}=\sum_{m=1}^n \frac{m}{3^m}+T(0)\)

Since the infinite series \($\sum_{m=1}^{\infty} \frac{m}{3^m}$\) converges, this implies that \($\frac{T(n)}{3^n}=\Theta(1)$\) and so \($T(n)=\Theta\left(3^n\right)$\)

Therefore, the recurrence relation exists \($T(n)=\Theta\left(3^n\right)$\).

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Answer:

y = x - 2

Step-by-step explanation:

points: (3, 1) and (0, -2)

slope = m = (-2 - 1)/(0 - 3) = 1

y-intercept = b = -2

y = x - 2

Answer:

The best chart to show how your department's expenses compare to the total company's expenses, and hopefully save employee jobs, would be:

Pie Chart

Step-by-step explanation:

The image is formed behind the mirror, and the image is upright.

Given data: Object height, h = 3.0 cm Image distance, v = ? Object distance, u = -20.0 cmFocal length, f = -60.0 cmUsing the lens formula, the image distance is given by;1/f = 1/v - 1/u

Putting the values in the above equation, we get;1/-60 = 1/v - 1/-20

Simplifying the above equation, we get;v = -40 cm

This negative sign indicates that the image is formed behind the mirror, as the object is placed in front of the mirror.

Hence, the image is virtual and erect. Using magnification formula;M = -v/uWe get;M = -(-40) / -20M = 2Hence, the height of the image is twice the height of the object.

The height of the image is given by;h' = M × hh' = 2 × 3h' = 6 cm Now, let's draw the ray diagram:

Thus, the position of the image is -40.0 cm and the height of the image is 6 cm.

The image is formed behind the mirror, and the image is upright.

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Answer:

Step-by-step explanation:

25% commission equals 180.00

Total sales amount is x:

Answer:

C) -9

Step-by-step explanation:

x + 19 must be half x + 29 because triangles RBC and RST are similar by SAS and RB is half of RS and RC is half of RT.

2(x + 19) = x + 29

2x + 38 = x + 29

x + 38 = 29

x = -9

The differences between the annual interest and semi-annual interest will be Rs 435.78.

Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

The same of annual interest and semi-annual compound interest on a same of money for 2 years at the interest rate of 20% per annum is Rs. 18082.

The annual interest will be

⇒ 18082(1.2)² – 18082

⇒ Rs 7956.08

The semi-annual interest will be

⇒ 18082(1.1)⁴ – 18082

⇒ Rs 8391.86

Then the differences between the annual interest and semi-annual interest will be

⇒ 8391.86 – 7956.08

⇒ Rs 435.78

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Blaise Pascal invented the statistical method known as regression. False. The author learned through the reading that adding a bathroom increases home prices more than adding a bedroom does.

What does a statistical regression mean?

What does regression mean?

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By using first principle, the value of Dy/Dx is,

⇒ Dy/Dx = - 7 / x²

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ y = 7 / x

Now, Differentiate the function with respect to x, we get;

⇒ y = 7 / x

⇒ Dy/ Dx = D / Dx (7 / x)

                = 7 D/Dx (1/x)

                = 7 (- 1 × x⁻¹⁻¹ )

                = 7 (- x⁻²)

                = - 7 / x²

⇒ Dy/Dx = - 7 / x²

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By answering the presented question, we may conclude that 1.1.5: A inequality factor of 51 - 25 is a factor of 51 since 51 can be written as 25 x 2 + 1.

An inequality in mathematics is a link between two expressions or values that is not equal. As a result, inequality results from imbalance. An inequality in mathematics is a relationship between two values that are not equal. Equality and inequality are not the same thing. The not equal sign is often used to indicate that two values are not equal (). To contrast values, various disparities—no matter how small or large—are used. By changing the two sides until just the variables are left, many fundamental inequalities can be resolved. Yet, a variety of causes fuel inequality: On both sides, negative values are divided or added. Trade right and left.

1.1.1: Irrational number - 2.13131.... is a non-repeating, non-terminating decimal, which is a characteristic of irrational numbers.

1.1.2: Recurring decimal - None of the given numbers have a repeating decimal pattern, so this option is not applicable.

1.1.3: An uneven square number - None of the given numbers are perfect squares, so this option is not applicable.

1.1.4: An even prime number - The only even prime number is 2, which is not in the list. Therefore, this option is not applicable.

1.1.5: A factor of 51 - 25 is a factor of 51 since 51 can be written as 25 x 2 + 1.

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If the "arithmetic-sequence" which has "first-term" as 25, then it's 13th term will be -71.

The first-term of the "arithmetic-sequence" is denoted as "a₁" is 25,

The common-difference denoted as "d" is -8,

We can use the formula for the nth term of an arithmetic sequence to find the 13th term. The formula is : aₙ = a₁ + (n - 1)d;

where, n is = number of the term we want to find,

We have to find the 13th term, so, n is = 13,

Substituting the values,

We get;

a₁₃ = 25 + (13 - 1)(-8)

a₁₃ = 25 + 12(-8)

a₁₃ = 25 - 96

a₁₃ = -71

Therefore, the 13th term of arithmetic sequence is -71.

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Answer:

5^-4

1/-625

Step-by-step explanation:

5^3 x 5^-7

They have the same base is 5, which means we just need to add the root, so 3 + (-7) = -4, so the answer is 5^-4

5^ -4

5 times 5 times 5 times 5 = -625

Because it is a negative exponent, means it is a fraction. So, the answer is

1/ -625

The value of x in the model expression is x = 10/8

From the question, we have the following parameters that can be used in our computation:

The model

When represented as an equation, we have

4x - 4 = -4x + 6

Collect the like terms

So, we have

4x + 4x - 4 + 6

Evaluate the like terms

8x = 10

Divide by 8

x = 10/8

Hence, the solution is x = 10/8

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Answer:

2/3 and -4

Step-by-step explanation:

using the quadratic formula,

-b +_root(b squared - 4(3)(-8) the whole divided by 2a

Step-by-step explanation:

hope this will help you.