4.5 over what number equals 3?

The slope of the ramp is approximately 0.2, which is less than 10. Therefore, the access ramp meets the requirements of the code since the slope does not exceed the maximum allowable slope of 10.

To determine if the access ramp meets the requirements of the code, we need to calculate the slope of the ramp and compare it to the maximum allowable slope of 10.

The slope of a ramp can be calculated using the formula:

Slope = Rise / Run

Given:

Rise = 11 feet

Run = 55 feet

Plugging in the values:

Slope = 11 / 55 ≈ 0.2

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The number of integers N less than 1000 that can be written as the sum of j consecutive positive odd integers from exactly 5 values of j ≥ 1 is 15.

Arithmetic sequence is a sequence of numbers/terms that has a fixed pattern, based on the operation of subtraction or addition. Thus, each sequence of numbers will have a common difference.

Formula: aₙ = a₁ + (a - 1)d,

where aₙ is the nᵗʰ term and a₁ is the first term in the sequence, and d is the common difference between terms

Sum of n terms = n (a₁ + aₙ) / 2

We want to know the number of integers N less than 1000 that can be written as the sum of j consecutive positive odd integers from exactly 5 values of j ≥ 1

First, we determine:

- the first odd integer in the list: 2n + 1, where n ≥ 1

- the last odd integer in the list: 2n + 1 + 2(j - 1) = 2(n + j) - 1

These odd integers form a sequence with the following sum:

N = n (a₁ + aₙ) / 2

   = j (2n + 1 + 2(n + j) - 1) / 2

   = j (2n + 1 + 2n + 2j - 1) / 2

   = j (4n + 2j) / 2

   = j (2n + j)

We also know that there are exactly 5 values of j that satisfy the equation, there must be either 9 or 10 factors of N.

This means N = p₁².p₂² or N = p₁.p₂⁴

If N is odd, then j is also odd, which means that 2n+j is also odd. It is valid for all odd j.  Given the boundary of 1000, the possibilities of odd N are (3².5²), (3².7²), (3⁴.5), (3⁴.7), and (3⁴.11) ---> 5 possibilities

If N is even, then j is also even. If we substitute j = 2k into the N, we get:

  N = j (2n + j)

      = 2k (2n + k)

      = 4k (n + k)

N/4 = k (n + k)

This formula implies that the new upper bound is 250. So the possibilities of even N are (2².3²), (2².5²), (2².7²), (3².5²), (2⁴.3), (2⁴.5), (2⁴.7), (2⁴.11), (2⁴.13), and (3⁴.2) ---> 10 possibilities

Thus, the total number of integer N is 5 + 10 = 15

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Answer:

52+74=126

126÷9=14

so u would need at least 14 shelves

To find a ratio in 8th grade math, you need to divide one number by another number to get the ratio. For example, if you want to find the ratio of 10 to 8, you would divide 10 by 8 to get a ratio of 1.25.

1. Identify the two numbers you want to compare as the numerator and denominator

2. Divide the numerator by the denominator

3. The resulting answer is the ratio of the two numbers

To find a ratio in 8th grade math, divide the numerator by the denominator to get the ratio.

To find a ratio in 8th grade math, you need to divide one number by another number to get the ratio. For example, if you want to find the ratio of 10 to 8, you would divide 10 by 8 to get a ratio of 1.25.

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Answer:

-1

Step-by-step explanation:

Step-by-step explanation:

Given by your question

2(3x-1)≥4x-6

Distributive property to take off the parentheses

2×3x-2×1≥4x-6

6x-2≥4x-6

Subtract 4x on both sides (Subtractive property of equality)

6x-2-4x≥4x-6-4x

2x-2≥-6

Add 2 on both sides (Addition property of equality)

2x-2+2≥-6+2

2x≥-4

Divide 2 on both sides (Division property of equality)

2/2 x≥-4/2

x≥-2

----------------------------------------------------------------------------

Looking at the options you've provided.

-10 INCORRECT, it is not greater or equal to -2

-5 INCORRECT, it is not greater or equal to -2

-3 INCORRECT, it is not greater or equal to -2

-1 CORRECT, it is greater than -2

Answer:

2(3x -1) = 4x - 6

6x - 2 = 4x - 6

6x -2+2 = 4x -6 + 2

6x - 4x = 4x - 4x -6 + 2

6x - 4x = -6 + 2

2x = -4

2 2

x = -2

Answer:

Where is M??

Step-by-step explanation:

Answer:

8

Explaining :

4/12 is 8

8+4=12

12-4=8

I hope it work :)

The sum of the first five terms of a geometric series is 242/27

The given parameters are

a1 = 6

r = 1/3

The sum of the first five terms of a geometric series is represented as;

Sn =a * (1 - r^n)/(1 - r)

This gives

S5 = 6 * (1 - (1/3)^5)/(1 - 1/3)

Evaluate the exponent

S5 = 6 * (1 - 1/243)/(2/3)

Evaluate the difference

S5 = 6 * (242/243)/(2/3)

This gives

S5 = 2 * (242/81)/(2/3)

So, we have:

S5 = 2 * (242/81) * 3/2

Evaluate the product

S5 = 242/27

Hence. the sum of the first five terms of a geometric series is 242/27

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Answer:

5700

Step-by-step explanation:

5 percent is the same as 0.05 so we can say 0.05s (5% of s for salary) is equal to 285. so 0.05s=285 and divide both sides by 0.05 (which is the same as multiplying by 20) to get 5700

Answer:

The answer would be $5700

Step-by-step explanation:

If Catherine donates $285 as 5% then since 5*20=100 you could multiply 285 times 20 to get 5700. To check just take 5700 times 0.05 (5%) and you will get $285.

A sample of bacteria is decaying according to a half-life model. After approximately 27 minutes, there will be 15 bacteria remaining.

The time at which there will be 15 bacteria remaining can be found by using the half-life model equation.

The half-life model equation is given by: N(t) = N₀ * \(e^(-kt)\), where N(t) is the number of bacteria at time t, N₀ is the initial number of bacteria, k is the decay constant, and e is the base of the natural logarithm.

Given that the sample begins with 600 bacteria (N₀ = 600) and after 10 minutes there are 420 bacteria (N(10) = 420), we can set up the following equation:

420 = 600 * \(e^(-k*10)\)

To solve for k, we can divide both sides of the equation by 600 and take the natural logarithm of both sides:

ln(420/600) = -10k

Simplifying further:

ln(7/10) = -10k

Now, we can solve for k by dividing both sides by -10:

k = ln(7/10) / -10

Using a calculator, we find that k is approximately -0.0247 (rounded to four decimal places).

To find the time when there will be 15 bacteria remaining (N(t) = 15), we can substitute the values into the equation and solve for t:

15 = 600 * \(e^(-0.0247t)\)

Dividing both sides by 600 and taking the natural logarithm:

ln(15/600) = -0.0247t

Simplifying further:

ln(1/40) = -0.0247t

Now, we can solve for t by dividing both sides by -0.0247:

t = ln(1/40) / -0.0247

Using a calculator, we find that t is approximately 27.7 minutes. Rounding to the nearest whole number, the answer is 28 minutes.

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Answer:

327.6 Euros

Step-by-step explanation:

The exchange rate is 1 = 1.17 so to find euros multiply the total pounds by 1.17

280 * 1.17 =

327.6

Answer:

47°

Step-by-step explanation:

The given angle and its complement sum to 90°, thus

complement = 90° - 43° = 47°

The 15th term of the geometric progression is 9,565,94.

A geometric progression can be expressed as an = a1rn-1 for some a1 and r. You are told that a2 * a4 = 2a5 and a1 + a2 + a3 + a4 = 80.

From the first equation, a2 = a1 r, a4 = a1 r3, and a5 = a1 r4. This tells us that

a1 r a1 r3 = 2 a1 r4

The r's and one a1 cancel leaving a1 = 2.

Now, plugging similarly into a1 + a2 + a3 + a4 = 80,

2 + 2r + 2r2 + 2r3 = 80

r3 + r2 + r + 1 = 40

In general, the easiest way to solve a cubic is by graphing, but here you know the answer will be a small integer, so just try a few. If we try r=3, we get 27 + 9 + 3 + 1 = 40 so r = 3.

So the geometric sequence here is an = 2 3n-1. The 15th term is then:

a15 = 2*3^14

a15 = 9,565,938.

Full question:

A G.P, the product of the 2nd and the 4th term is double the 5th term, and the sum of the first 4th terms is 80. find the 15th term.

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Answer:

x = 100

Step-by-step explanation:

You have to use the equation 15x + 10 = 6x - 6 + 70. This equation finds out that x = 6. Then, you would multiply 6 by 15. This gets 90. Finally, add 10 to that.

Two similar figures have a ratio of areas 72:32. The ratio of similarity between the two figures is 3:2.

The ratio of areas of two similar figures is equal to the square of the ratio of their corresponding side lengths. Let's assume the ratio of side lengths is a:b.

Given: Ratio of areas = 72:32

The ratio of areas is the square of the ratio of side lengths. So, we have:

(a/b)^2 = 72/32

Simplifying the equation:

(a/b)^2 = 9/4

Taking the square root of both sides:

a/b = √(9/4)

a/b = 3/2

Hence, the ratio of side lengths of the two similar figures is 3:2.

Since similarity is based on corresponding side lengths, the ratio of similarity is the same as the ratio of side lengths. Therefore, the ratio of similarity between the two figures is 3:2.

This means that for every unit increase in the length of the corresponding side in the smaller figure, the corresponding side in the larger figure increases by 1.5 units.

In summary, the ratio of similarity between the two figures is 3:2, indicating that they are scaled versions of each other with the smaller figure being 3/2 times smaller in each dimension compared to the larger figure.

Hence, the ratio of similarity is 3:2.

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Answer:

12. yes 13. yes 14. no 15. yes 16. no

Step-by-step explanation:

no explanation since your desperate on time rn

The p-value can be found with the F-distribution table or statistical software. If the p-value is less than or equal to α, then answer is option (a),If the p-value is greater than α, then answer is option (b).

To determine the correct statistical decision based on the given F-statistic, F (3, 12) = 2.72, we need additional information such as the significance level (α) of the hypothesis test. The significance level is a predetermined threshold that is used to assess the statistical significance of the results.

The correct decision depends on whether the calculated p-value, which quantifies the strength of evidence against the null hypothesis, is less than or equal to the significance level (α).

To find the p-value, you would need the F-distribution table or statistical software.

Once you have the p-value, you can compare it to the significance level (α) to make a decision:

If the p-value is less than or equal to α, you would reject the null hypothesis, indicating a statistically significant mean difference.

If the p-value is greater than α, you would fail to reject the null hypothesis, suggesting that there is not a statistically significant mean difference.

Therefore, without the significance level or the p-value, it is not possible to determine the correct statistical decision.

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The expression which is not equivalent to 24 is 2(12 + 10)

To determine which expression isn't equivalent to 24, we need to simplify each expression and test if it equals 24.

Let's start with every expression:

2(12 + 10) = 44

3(8 + 4) = 36

2(12 + 6) = 36

6(4 + 2) = 36

Out of these four expressions, the expression that isn't equivalent to 24 is 2(12 + 10), which simplifies to 44, not 24.

Consequently, the answer is: 2(12 + 10)

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The two most generic and widely used valuation multiples in finance and investment analysis are the price-to-earnings (P/E) ratio and the enterprise value-to-earnings before interest, taxes, depreciation, and amortization (EV/EBITDA) multiple.

1. Price-to-Earnings (P/E) Ratio: The P/E ratio is calculated by dividing the market price per share of a company's stock by its earnings per share (EPS). It provides a measure of how much investors are willing to pay for each dollar of earnings generated by the company.

A high P/E ratio suggests that investors have high expectations for future growth and are willing to pay a premium for the stock. On the other hand, a low P/E ratio may indicate that the stock is undervalued or that investors have low expectations for future growth.

2. Enterprise Value-to-EBITDA (EV/EBITDA) Multiple: The EV/EBITDA multiple is calculated by dividing the enterprise value (EV) of a company by its earnings before interest, taxes, depreciation, and amortization (EBITDA).

The EV is the total market value of a company's equity and debt, minus its cash and cash equivalents. EBITDA represents the company's operating earnings before accounting for interest, taxes, depreciation, and amortization.

The EV/EBITDA multiple is commonly used in evaluating the valuation of companies, especially in the context of mergers and acquisitions. It provides a measure of a company's overall value relative to its earnings, without being affected by capital structure or tax considerations.

Both the P/E ratio and EV/EBITDA multiple are widely used because they are relatively easy to calculate and understand. However, it's important to note that these multiples have limitations and should be used in conjunction with other valuation methods and qualitative analysis to make informed investment decisions.

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let angle=X

(sin x + cos x)/(sin x - cos x) = 3/2

cross multiply

Answer:

-5 1/2

i hope this helps <3

Answer:

\(-\frac{11}{2}\) is the number which represents the expression \(-2+\left(\frac{-7}{2}\right)\).

i.e.

\(-2+\left(\frac{-7}{2}\right)=-\frac{11}{2}\)

Step-by-step explanation:

Given the expression

\(-2+\left(\frac{-7}{2}\right)\)

\(\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\)

\(=-2+\frac{-7}{2}\)

\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}\)

\(=-2-\frac{7}{2}\)

\(\mathrm{Convert\:element\:to\:fraction}:\quad \:2=\frac{2\cdot \:2}{2}\)

\(=-\frac{2\cdot \:2}{2}-\frac{7}{2}\)

\(\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\)

\(=-\frac{2\cdot \:2}{2}-\frac{7}{2}\)

\(=\frac{-2\cdot \:2-7}{2}\)

\(=\frac{-11}{2}\)

\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}\)

\(=-\frac{11}{2}\)

Therefore, \(-\frac{11}{2}\) is the number which represents the expression \(-2+\left(\frac{-7}{2}\right)\).

i.e.

\(-2+\left(\frac{-7}{2}\right)=-\frac{11}{2}\)

The volume and surface area of a pentagonal pyramid with an apothem of 3√2 and a height of 3 are:

   Volume:

The formula for the volume of a pyramid is:

V = (1/3) × A × h

where A is the base area of the pyramid and h is the height of the pyramid.

To find the base area of the pentagonal pyramid, we need to find the length of one side of the pentagon. The apothem of the pentagon is given as 3√2, so we can find the length of one side using the formula for the apothem of a regular pentagon:

a = s / (2√(5-2√5))

3√2 = s / (2√(5-2√5))

s = 6√(5-2√5)

The base area of the pyramid is the area of a regular pentagon with side length s and apothem 3√2, which is given by the formula:

A = (5/2) × s × a

Substituting the given values, we get:

A = (5/2) × 6√(5-2√5) × 3√2

A ≈ 31.18

Therefore, the volume of the pentagonal pyramid is:

V = (1/3) × A × h

V = (1/3) × 31.18 × 3

V ≈ 31.18 cubic units

   Surface Area:

To find the surface area of the pentagonal pyramid, we need to find the area of each of the five triangular faces. Each face has the same base area A and the same slant height l, so we can use the formula for the area of a triangle:

A = (1/2) × b × h

where b is the length of the base and h is the height of the triangle (which is the slant height of the pyramid).

The slant height of the pentagonal pyramid can be found using the Pythagorean theorem:

l = √(h^2 + a^2)

where h is the height of the pyramid and a is the apothem of the base.

Substituting the given values, we get:

l = √(3^2 + (3√2)^2)

l = √(9 + 18)

l = √27

l = 3√3

Substituting the values of A and l into the formula for the area of a triangle, we get:

A = (1/2) × A × l

A = (1/2) × 31.18 × 3√3

A ≈ 26.83

Since there are five triangular faces, the total surface area of the pentagonal pyramid is:

S = 5 × A

S ≈ 134.13 square units

Therefore, the volume of the pentagonal pyramid is approximately 31.18 cubic units, and the surface area is approximately 134.13 square units.

Answer:

could you provide an image and translation please?

Step-by-step explanation:

Temperature change for water due to sheer drop is approximately 0.7 °C when Multnomah Falls in the Columbia River has a sheer drop of 543 ft.

Given that,

Multnomah Falls in the Columbia River Gorge has a sheer drop of 543 feet.

We have to find estimate the water temperature change in °F caused by this drop using the steady flow energy equation.

We know that,

Sheer drop is z₁ - z₂ = 543 feet

We required to calculate temperature change that is ∆T caused by this drop using steady flow energy equation says SFEE.

Assuming

Adiabatic flow i.e. Q =0

No work done, i.e. W=0

Neglecting kinetic energies.

Steady flow energy equation is a mathematical expression that states that for a steady flow the net energy at the inlet of control volume is equal to the net energy at the exit of of the control volume.

SFEE is given as,

h₁ + \(\frac{(v_1)^2}{2}\) + gz₁ + Q = h₂ + \(\frac{(v_2)^2}{2}\) + gz₂ + Q -------> equation(1)

Where, h₁ and h₂ enthalpies at inlet and exit of control volume,

v₁ and v₂ are velocities at inlet and exit of control volume (kinetic energies),

z₁ and z₂ are elevation at inlet and exit of control volume (potential energies),  

Q is energy flow into the control volume and

W is work done by control volume.

Neglecting change in kinetic energies ; Q=0; W=0

Then equation (1) will be,

h₁ - h₂ = g(z₂ - z₁)

Cp(ΔT) =  g(z₂ - z₁)

ΔT = \(\frac{g(z_2-z_1)}{Cp}\)

Here,

Value of g is 32.2 feet per second square and value of Cp for water is 25100 feet

Substituting all values we get,

ΔT = \(\frac{32.2(543)}{25000}\)

ΔT = 0.69°C

ΔT = 0.7°C (approximately)

Therefore, Temperature change for water due to sheer drop is approximately 0.7 °C.

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The perimeter of the triangle is 21

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

The perimeter of the triangle is found by adding all the sides

The vertices of the triangle ABC are (-1,1), (-3, -4), and (5,-2). let A be (-1,1), B be (-3, -4) and C be (5,-2).

The distance between And B = √ (-3-(-1))²+( -4-1)²

Line AB = √ 2²+-5²

AB = √ 4+25

AB =√29 = 5.4

line AC = √5-(-1)² + (-2-1)²

AC = √ 6²+3²

AC = √ 36+9

AC = √ 45

AC = 6.7

The distance between B and C = √( -3-5)² + (-4-(-2)²

BC = √ 8²+4²

BC =✓64+16

BC = √80

BC = 8.9

Therefore the perimeter of the triangle is AB+ BC + AC = 5.4+6.7+8.9 = 21

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a. the sum of the first 200 natural numbers is 20,100. b. when the ball hits the pavement for the 6th time, it will have traveled approximately 104 feet in total (up and down).

(a) To find the sum of the first 200 natural numbers, we can use the formula for the sum of an arithmetic series.

The sum of the first n natural numbers is given by the formula: Sn = (n/2)(a + l), where Sn represents the sum, n is the number of terms, a is the first term, and l is the last term.

In this case, we want to find the sum of the first 200 natural numbers, so n = 200, a = 1 (the first natural number), and l = 200 (the last natural number).

Substituting these values into the formula, we have:

Sn = (200/2)(1 + 200)

  = 100(201)

  = 20,100

Therefore, the sum of the first 200 natural numbers is 20,100.

(b) The ball rebounds three-fourths of the distance it drops, so each time it hits the pavement, it travels a total distance of 1 + (3/4) = 1.75 times the distance it dropped.

For the 6th rebound, we need to find the distance the ball traveled when it hits the pavement.

Let's represent the initial drop distance as h (30 ft).

The total distance traveled after the 6th rebound is given by the sum of a geometric series:

Distance = h + h(3/4) + h(3/4)^2 + h(3/4)^3 + ... + h(3/4)^5 + h(3/4)^6

Using the formula for the sum of a geometric series, we can simplify this expression:

Distance = h * (1 - (3/4)^7) / (1 - 3/4)

Simplifying further:

Distance = h * (1 - (3/4)^7) / (1/4)

        = 4h * (1 - (3/4)^7)

        = 4 * 30 * (1 - (3/4)^7)

Calculating the value:

Distance ≈ 4 * 30 * (1 - 0.1335)

        ≈ 4 * 30 * 0.8665

        ≈ 104 ft

Therefore, when the ball hits the pavement for the 6th time, it will have traveled approximately 104 feet in total (up and down).

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Answer:  1,200  

Step-by-step explanation:

Answer:

I need to see the graph. Can you take a picture of the graph?

Step-by-step explanation: