Solve for u. u/7 - 1 < 1

\(67.21^0\) is the angle with the transmission axis of the sheet make with the horizontal when its intensity is 15% of incident light .

The term intensity is used to describe the rate at which light spreads over a surface of a given area which is at some distance from a source.

the formula of intensity of light is

   \(i = i_0 cos^2 (\alpha )\)

where is the intensity at the given angle \(\alpha\)

given that only 15% of the intensity of the incident light is transmitted through the sheet.

 so   \(\frac{i}{i_0} * 100\)  =15 so i/i0 = 0.15

so \(cos^2 (\alpha ) = 0.15 , cos (\alpha ) = 0.38729\)

\(\alpha\)  =  67.21 degree is requied answer of this question

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Answer:

A. The absolute function is negative since the negative sign outside of |x| reflects the function downward. The +4 translates the absolute value function up 4 units, making the vertex be at (0,4) instead of the origin.

B. The vertex is at (0,4), and two other points are (5,-1) and (-1,3).

C. Since the vertex of the function is (0,4), the range of the function can only go from -∞ to 4; the range is (-∞,4]. The domain is still all real numbers, so it is still (-∞,∞).

Step-by-step explanation:

Answer:

x=11

Step-by-step explanation:

Answer:

x=11

Step-by-step explanation:

10x-4+5x+19=180

Combine like terms

15x+15=180

      -15    -15

15x=165

divide by 15

x=11

Answer:

             The x intercept:    (1.5, 0)

The slope intercept form:   y = 2x - 3

                      The slope:    m = 2

Step-by-step explanation:

x intercept means y=0

4x - 2y = 6

4x - 2·0 = 6

4x = 6

x = 1.5

The slope intercept form is:  y = mx + b

4x - 2y = 6            {subtract 4x from both sides}

- 2y = - 4x + 6       {dividing both sides by (-2)}

y = 2x - 3            ← slope intercept form

Slope is the number by x, in slope intercept form of line's equation

Answer:

\(f(x) = - 8 \\ \\ - 7x - 1 = - 8 \\ \\ - 7x = - 8 + 1 \\ \\ - 7x = - 7 \\ \\ 7x = 7 \\ \\ x = \frac{7}{7} \\ \\ x = 1\)

Answer:

72°

Step-by-step explanation:

→ Recall how many degrees are within an interior angle

180

→ Minus the angle from 180

180 - 108 = 72°

Answer: 3480 seconds and 5420 feet

Step-by-step explanation:

We can set an equation for both Keith and Erica. Let t = time in seconds.

Keith's BalloonHeight = 1.5*t+200ft

Erica's Balloon Height = 1.4*t+548ft

We want to know when E=K (same height)

1.4*t+548ft = 1.5*t+200ft

348 = 0.1t

t = 3480 seconds

Use this time in either Keith's or Erica's Height formula:

Keith Balloon Height: 1.5*t+200ft for t=3480

1.5*(3480)+548

Keith's Height in 3460 sec: 5420 feet

Erik's Balloon Height: = 1.4*t+548ft

= 1.4*(3480)+548ft

Erik's Height in 3480 sec: 5420 feet

The two lines intersect at (3460,5420). At 3460 seconds both balloons will be at 5420 feet.

This triangle is an isosceles triangle because it has two congruent sides. Therefore, the two bottom angles are also congruent. And, the sum of the interior angles of a triangle is 180 degrees.

180 = 104 + (9x - 25) + (9x - 25)

180 = 104 + 18x - 50

180 = 54 + 18x

126 = 18x

x = 7

Hope this helps!

Answer:

First blank: 10

Second blank: 1

Step-by-step explanation:

For both i used an online converter:

Please check attachments

So, y = (1/2)(x + 8) is the equation of the linear function.

To write the equation of a linear function with a given x-intercept and y-intercept, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

In this case, we are given that the x-intercept is (-8, 0) and the y-intercept is (0, 4). We can use the coordinates of the x-intercept as (x1, y1) and the slope of the line as m to write the equation:

y - 0 = m(x - (-8))

y = m(x + 8)

We can then substitute the y-intercept into this equation to find the value of m:

4 = m(0 + 8)

4 = 8m

m = 1/2

Substituting the value of m back into the equation, we get:

y = (1/2)(x + 8)

This is the equation of the linear function.

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y - y1 = m(x - x1)

y - 0 = m(x - (-8))

y = m(x + 8)

We can then substitute the y-intercept into this equation to find the value of m:

4 = m(0 + 8)

4 = 8m

m = 1/2

Substituting the value of m back into the equation, we get:

y = (1/2)(x + 8)

The statement implies that the current rate of change of the average revenue per store per month is -$250,000, which means that the average revenue per store is decreasing by $250,000 per month

We can start by differentiating the given expression for revenue with respect to time t:

dR/dt = d(N(t)S(t))/dt

= N(t)dS/dt + S(t)dN/dt

The statement tells us that dN/dt = 2 (the number of stores is increasing by 2 per month) and dR/dt = $250,000 (the total revenue is increasing by $250,000 per month). We also know that at the current time t, N(t) = 50 and R(t) = $7,500,000.

Substituting these values into the above expression, we get:

$250,000 = 50 dS/dt + $7,500,000 × 2

Simplify this equation, we can solve for dS/dt:

dS/dt = ($250,000 - $15,000,000) / 50

= -$250,000

So the current rate of change of the average revenue per store per month is -$250,000, which means that the average revenue per store is decreasing by $250,000 per month. This could be due to various factors such as increased competition, changes in consumer preferences, or changes in pricing strategies.

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After 9 years Rasheed be closest to doubling his initial investment.

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

Given that;

The principal amount which Rasheed invested ‘P’ = $1000

Rate of interest ‘r’ =  8%

                            = 0.08

Compounding annually; then n = 1

Now,

The doubling amount is ‘A’ = 2xP = $2000

Since we know the compound interest year formula;

⇒ A = P (1+r/n)^nt

Where t represents the time in year.

Now substituting the values we get;

⇒ 2000 = 1000 (1+0.08/1)^t

⇒ 2 = (1.08)^t

Taking log both sides

⇒ t =  0.3010/0.0334

⇒ t = 9.01

Thus, it takes 9 years to double.

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We have proven that if the inequality holds true for k, it also holds true for k + 1. By the principle of mathematical induction, the inequality 2^n > n^2 holds true for all n > 4.

To prove the inequality 2^n > n^2 using induction with a basis greater than 4, we will use n=5 as the basis.

Basis: n = 5
2^5 = 32 and 5^2 = 25. Since 32 > 25, the inequality holds true for n = 5.

Now, we need to assume that the inequality holds true for an arbitrary positive integer k > 4, and then prove that it holds true for k + 1.

Assume: 2^k > k^2 for k > 4.

Prove: 2^(k + 1) > (k + 1)^2

Step 1: Multiply both sides of the assumption by 2.
2 * (2^k) > 2 * (k^2)

Step 2: Simplify the left side of the inequality.
2^(k + 1) > 2k^2

Step 3: Show that 2k^2 is greater than (k + 1)^2 for k > 4.
2k^2 > (k + 1)^2
2k^2 > k^2 + 2k + 1

Step 4: Rearrange the inequality to show that it holds true for k > 4.
k^2 - 2k - 1 > 0

Since k > 4, it is clear that k^2 - 2k - 1 > 0, as the left side increases as k increases.

Therefore, we have proven that if the inequality holds true for k, it also holds true for k + 1. By the principle of mathematical induction, the inequality 2^n > n^2 holds true for all n > 4.

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Answer:

A.

Step-by-step explanation:

Answer:

The answer is a.

Step-by-step explanation:

When you plug in 2 for n, 2 - 1  1, so we put 5 for a (because a superscript 1 = 5) and evaluate. This number then become a superscript 2.

Answer:

x = 2.75

Step-by-step explanation:

6x - 2 (x - 5) = 22

6x -2x + 10 = 22

4x + 10 = 22

     - 10    - 10

4x = 11

11/4 = 2.75

x = 2.75

Let me know if you need any more help!

Answer:

6

Step-by-step explanation:

Answer:I am not sure about the answer but when 2 multipled by 3 X 2 equals to 4/3

Answer:

becuz they look the same, theyre the same shape, AND size.. thats what makes to shapes congruent.

Step-by-step explanation:

Brainliest, pretty please? hee hee

Answer:

All three pairs of corresponding sides are equal, have the same shape and dimensions.

Step-by-step explanation:

the answer is a or b I am not sure

As σx (standard deviation) remains unchanged, the value of x alone cannot determine the effect on sample mean. It depends on the value of x relative to the values in original sample and sample size.

If one new person is added to the sample and the standard deviation (σx) remains unchanged, the effect on the sample mean (m) can be determined as follows:

Let's denote the original sample size as n and the sum of the sample values as Σx.

Original sample mean:

m = Σx / n

After adding the new person, the new sample size becomes n + 1, and the sum of the sample values becomes Σx + x_new (x_new represents the value of the new person).

New sample mean:

m' = (Σx + x_new) / (n + 1)

To analyze the effect, we can express the difference in means:

Δm = m' - m = ((Σx + x_new) / (n + 1)) - (Σx / n)

Simplifying this expression, we get:

Δm = (x_new - (Σx / n)) / (n + 1)

Therefore, the effect of adding the new person on the sample mean (m) is determined by the difference between the value of the new person (x_new) and the original mean (Σx / n), divided by the increased sample size (n + 1).

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Answer:

Rational because it isn't a repeating decimal

Step-by-step explanation:

Answer: $7.65 for a dozen/12

Step-by-step explanation: 2.55 x 3

Answer:

2 3/4 = 11/4 :)

Step-by-step explanation:

Whole number times denominator then add the numerator!

Hope this helps, marks as brainliest please!

I have nothing to go off on, but an equation that would fit for (1,2) is y=2x.

---

hope it helps

Answer:

1

Step-by-step explanation:

Answer:

4cm

Step-by-step explanation:

Volume of a rectangular prism is V = L x W x H

plug in what we know:

192 = 8 x 6 x H

192 = 48H

divide both sides by 48

H = 4

Answer:

22 cm

Step-by-step explanation:

A hexagon has six sides. Since it is a regular hexagon, all of the sides have equal length, so we can multiply the length of one side, 3.6 by 6 to get the perimeter. 3.6 x 6 = 21.6. To the nearest centimeter, the upper bound is 22.

The given connected planar graph has 15 edges and 8 faces.

To find the number of edges in a connected planar graph with the given degrees of vertices, we can use the formula known as Euler's formula. Euler's formula states that for a connected planar graph, the number of vertices (V), edges (E), and faces (F) are related by the equation V-E+F=2.

Using the given information, we can calculate the total number of vertices as 9. The sum of the degrees of these vertices is 30, which means the total number of edges can be calculated as (30/2) = 15.

To find the number of faces, we can use another formula: F = E - V + 2. Substituting the values we know, we get F = 15 - 9 + 2 = 8. Therefore, the given connected planar graph has 15 edges and 8 faces.

It's worth noting that the degrees of the vertices play an important role in determining the structure of a planar graph. In particular, the fact that all the vertices in this graph have low degree means that it is likely to have a simple and straightforward structure. By contrast, if the degrees were all high, the graph would be more complex and harder to visualize.

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The integral of\(3e^(2t) + e^(4t)\) with respect to t is evaluated as \(3/2 e^(2t) + 1/4 e^(4t) + C\) using u-substitution and then adding the constants of integration. Absolute values were not necessary.

The integral of \(3e^(2t) + e^(4t)\) with respect to t is evaluated as shown below:

\(∫ (3e^(2t) + e^(4t)) dt= 3 ∫e^(2t)dt + ∫e^(4t)dt\)

Using u-substitution, we can integrate each term separately as follows:Let u = 2t, then du/dt = 2, which implies du = 2dt and

\(dt = du/2∫e^(2t)dt\)

\(= ∫(e^u) (du/2)\)

\(= 1/2 ∫e^udu\)

\(= 1/2 e^u+ C1\)

\(= 1/2 e^(2t) + C1\)

Let u = 4t, then du/dt = 4, which implies du = 4dt and

\(dt = du/4∫e^(4t)dt\)

\(= ∫(e^u) (du/4)\)

\(= 1/4 ∫e^udu\)

\(= 1/4 e^u + C2\)

\(= 1/4 e^(4t) + C2\)

The integral of \(3e^(2t) + e^(4t)\) with respect to t is then given by:\(∫ (3e^(2t) + e^(4t)) dt= 3/2 e^(2t) + 1/4 e^(4t) + C\)

where C = C1 + C2 is the constant of integration.

The above solution shows that the integral of\(3e^(2t) + e^(4t)\) with respect to t is evaluated to be \(3/2 e^(2t) + 1/4 e^(4t) + C\) using u-substitution and then adding the constants of integration. The absolute values were not necessary in this case.

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The distance Jon travels to work is 472.5 miles.

Let d be the distance Jon travels to work.

The time it takes to drive is 20 minutes and the time it takes to bike is 45 minutes.

The difference in speed between driving and biking is 14.5 mph.

We can set up the following equation:

20min * (14.5mph + x) = 45min * x

Solving for x gives us the average speed of Jon on the bike, which is 10.5 mph.

Now we can use the distance formula to solve for d:

d = rate * time

d = 10.5mph * 45min

d = 472.5 miles

Therefore, the distance Jon travels to work is 472.5 miles.

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The solution of the quadratic equation is x = 2. Therefore, \(\frac{4+\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)  or \(\frac{4-\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)

The quadratic formula can be use to solve the quadratic equation as follows:

x² - 4x + 4 = 0

Modelling it to quadratic equation, ax² + bx + c

Hence,

using quadratic formula,

\(\frac{-b+\sqrt{b^{2}-4ac } }{2a}\) or \(\frac{-b-\sqrt{b^{2}-4ac } }{2a}\)

where

Hence,

a = 1

b = -4

c = 4

Therefore,

\(\frac{4+\sqrt{-4^{2}-4(1)(4) } }{2(1)}\) or \(\frac{4-\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)

Finally

x = 2

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