Using graphing, what are the approximate solutions to this equation?
|2x - 3|= log(2x - 3) + 2

The recurrence relation for an is an = an-1 + an-2.  the number of ways to climb n stairs is equal to the sum of the number of ways to climb (n-1) stairs and the number of ways to climb (n-2) stairs.

To find a recurrence relation for an, the number of ways to climb n stairs if a person can take one stair or two stairs at a time, we can break it down into smaller subproblems.

Consider the last step taken to reach the nth stair. If the person took one step, there are an-1 ways to reach the (n-1)th stair. If the person took two steps, there are an-2 ways to reach the (n-2)th stair.

Since the person can only take one or two steps at a time, these are the only two possibilities.

Therefore, the recurrence relation for an is an = an-1 + an-2.

This means that the number of ways to climb n stairs is equal to the sum of the number of ways to climb (n-1) stairs and the number of ways to climb (n-2) stairs.

Note: This recurrence relation is based on the assumption that there are no other constraints or conditions given in the problem statement.

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Answer:

1.4 my guyyyyyyyyyyyyyyy

Answer:

0.708

Step-by-step explanation:

Change the divisor 2.1 to a whole number by moving the decimal point 1 places to the right. Then move the decimal point in the dividend the same, 1 places to the right.

We then have the equations:

14.88 ÷ 21 = 0.708

and therefore:

1.488 ÷ 2.1 = 0.708

Both calculated to 3 decimal places.

Answer:

It is 0.00231481481

Hope it helped :3

Answer:

No its not a function

Step-by-step explanation:

Brainliest pls?

Answer:

301,250,000

I'm pretty sure that's it.

Using the given ANOVA table, the treatment SS value is calculated. That is the amount of the squared sum of treatments of fertilizer is 1500.2. So option a is correct.

The ANOVA table is a statistical tool used to display how the sum of squares is spread according to variation.

Given that the number of treatments of fertilizer brands is 3 and the total number of observations/tree samples is 68. To calculate the treatment SS, we have to calculate the total SS and error SS.

First, let's calculate the degree of freedom for error, treatment, and total,

\(\begin{aligned}\text{treatment df}&=\text{number of fertilizer brands - 1}\\&=3-2\\&=2\\\text{total df}&=\text{number of trees - 1}\\&=68-1\\&=67\\\text{error df}&=\text{total df - treatment df}\\&=67-2\\&=65\end{aligned}\)

Then, the MS error is calculated as follows,

\(\begin{aligned}\text{MS error}&=\frac{\text{Error SS}}{\text{Error df}}\\33.4247&=\frac{\text{Error SS}}{65}\\\text{Error SS}&=65\times 33.4247\\&=2172.6055\end{aligned}\)

Now, the amount squared sum of treatments (Treatment SS) is given by,

\(\begin{aligned}\text{Treatment SS}&=\text{Total SS - Error SS}\\&=3672.8-2172.6055\\&=1500.2\end{aligned}\)

The required option is option a.

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The complete question is -

Three different brands of fertilizer used in the orange orchards are believed to deliver the same results. A farmer is skeptical about this and runs a test to prove crop amounts differ for different brands. In a specific plant, three samples of orange trees (a total of 68 trees) are treated with different brands. The following table is the partial ANOVA output.

\(F_{2,65,0.025}=3.906\), \(F_{2,65,0.05}=3.138\),  \(F_{65,2,0.025}=39.482\), \(F_{65,2,0.05}=19.48\)

What is the amount of the squared sum of treatments? Select one:

a. 1500.2

b. 2172.6

c. 750.1

d. 22.44

e. 3672.8

The value of x from the shape is 5.6

Since the shapes are similar, hence the ratio of the sides is equal to a constant. Mathematically;

10/14 = 4/x

10x = 14 * 4

10x = 56

Divide both sides by 10

10x/10 = 56/10

x = 5.6

Hence the value of x is 5.6

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Answer:

X=5.6

Step-by-step explanation:

The degree measure of the sector is θ = 180°

We know that the area of a sector is nothing but the area inside the section of the circle created by two radii and an arc.

The formula for the area of a sector of the circle is:

area of a sector = \(\frac{\theta}{360} \times \pi \times r^2\)

where θ is the central angle measure in degrees

And πr² is the area of the circle

Here, the area of a sector of the circle A = 32π cm²

and the area of a circle (πr²) =  64π cm²

Using above formula of the area of a sector of the circle,

\(A=\frac{\theta}{360} \times \pi \times r^2\\\\32\pi=\frac{\theta}{360} \times \pi \times r^2\\\\32\pi=\frac{\theta}{360} \times 64\times \pi\\\\\theta=\frac{360}{2}\\\\ \theta=180^{\circ}\)

Therefore, the central angle associated to that sector is 180°

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Answer:

(-3,-6)

Step-by-step explanation:

I can't really explain it, sorry about that.

To determine which sets of ingredients are in a proportional relationship with the given recipe, we need to compare the ratios of the ingredients to the given ratio of 12 parts oil, 3 parts vinegar, and 2 parts honey.

For example, if we take the first set of ingredients: 16 parts oil, 4 parts vinegar, and 2 parts honey, we can calculate the ratios:

Oil: 16 parts / 4 = 4 parts

Vinegar: 4 parts / 4 = 1 part

Honey: 2 parts / 4 = 0.5 parts

Comparing these ratios to the original recipe, we can see that they are proportional, as each ratio is a multiple of the original ratio:

Oil: 4 / 12 = 1/3

Vinegar: 1 / 3 = 1/3

Honey: 0.5 / 2 = 1/4

Therefore, the first set of ingredients is in a proportional relationship with the recipe. We can apply the same process to the other sets of ingredients to see if they are proportional as well.

Answer:

-6.318

Step-by-step explanation:

(14) × (5/11) - 13 + (7/22) = -6.318

First compute everything in the parenthesis.

The continue with multiplication.

Finally, proceed with the addition / subtraction of 13 and the value for (7/22).

By taking advantage of proportional line segments, we conclude that the coordinates of the point E inside the line segment CD is (1, 0). (Correct choice: C)

In this question we have a line segment whose ends and partition ratio are known. Hence, the point E can be located in the line segment by applying the following equation:

E(x, y) = C(x, y) + r · [D(x, y) - C(x, y)]      

Where r is the partition ratio.

If we know that C(x, y) = (- 1, - 3), D(x, y) = (5, 6) and r = 1/3, then the coordinates of the missing point is:

E(x, y) = (- 1, - 3) + (1/3) · [(5, 6) - (- 1, - 3)]

E(x, y) = (- 1, - 3) + (1/3) · (6, 9)

E(x, y) = (- 1, - 3) + (2, 3)

E(x, y) = (1, 0)

By taking advantage of proportional line segments, we conclude that the coordinates of the point E inside the line segment CD is (1, 0). (Correct choice: C)

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Answer:

Step-by-step explanation:

this is a positive slope, since it goes up from left...

vertical distance           rise         3

_______________ = _____ = ____  

horizontal distance       run         5

Answer:

25% decrease

Step-by-step explanation:

=(60−80)|80|×100

=−2080×100

=−0.25×100

=−25%change

=25%decrease

Answer:

25% decrease

Step-by-step explanation:

Answer:

cos B = 8/17

tan B = 15/8

sin B = 15/17

Step-by-step explanation:

sin = opposite side / hypotenuse

cos = adjacent / hypotenuse

tan = opposite / adjacent

Remember: Some old hippie, caught another hippie, tripping on acid.

Answer:

We know that one pair of sides and one pair of angles are congruent from the diagram. In order to know that the triangles are congruent by SAS we need to know that the pair of sides on the other side of the angle are congruent.

Step-by-step explanation:

HOPE IT HELPS :)

Answer:B

Step-by-step explanation:

R^2=Q^2-P^2

R^2=2025

R=45

Answer:

b) 45cm

Step-by-step explanation:

by pythagoras theorem:

R² = P² - Q²

R² = 53² - 28² = 2809 - 784

R² = 2025

R = √2025

R = 45cm

Hope this helps!

Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

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Main Answer: The slope of a steep upward-sloping line will be a positive.

Supporting Question and Answer:

How is the slope of a line calculated?

The slope of a line is calculated by dividing the change in the y-coordinate (vertical change) between any two points on the line by the change in the x-coordinate(horizontal change)between the same two points.This is represented by the formula:

slope= \(\frac{(y_2-y_1)}{(x_2-x_1)}\) ,where \((x_1,y_1)\) and \((x_2,y_2)\) are two points on the line.

Body of the Solution:In mathematics, the slope of a line is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line. A positive slope indicates that the line is increasing in the y-direction as the x-coordinate increases.

A steep upward-sloping line means that the line is increasing rapidly in the y-direction as the x-coordinate increases, and therefore the slope of the line will be a large positive number. Conversely, a steep downward-sloping line will have a large negative slope, indicating that the line is decreasing rapidly in the y-direction as the x-coordinate increases.

Therefore, the slope of a steep upward-sloping line will be a positive.

Final Answer:The slope of a steep upward-sloping line will be a positive.

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We have a function, f(x) = 2x^2 to be revolved about the x-axis over the interval [2, 3].

We know that the volume of the solid obtained by revolving the region under the graph of f(x) = 2x^2 about the x-axis is given by the\(integral V= π ∫_a^b (f(x))^2 where [a, b] is the interval of rotation.\)

In this case, the interval of rotation is [2, 3].

\(Therefore, we need to compute the integral given by V = π ∫_2^3 (2x^2)^2 dxNow, V = π ∫_2^3 4x^4 dxV = π [4/5 (3^5 - 2^5)]V = π [4/5 (243 - 32)]V = 802.94 cubic units (rounded to 2 decimal places)\)

Therefore, the volume of the solid obtained by revolving the region under the graph of\(f(x) = 2x^2 a\)bout the x-axis over the interval [2, 3] is 802.94 cubic units.

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The volume of the solid obtained by revolving the region under the graph of f(x) = 2x^2 about the x-axis over the interval [2, 3] is approximately 203.74 cubic units.

To calculate the volume of the solid obtained by revolving the region under the graph of f(x) = 2x^2 about the x-axis over the interval [2, 3], we can use the method of cylindrical shells.

The volume of the solid can be found using the integral:

V = ∫(2πxf(x)) dx

where V is the volume, x is the variable of integration, and f(x) is the function being revolved.

In this case, we have f(x) = 2x^2 and the interval of integration is [2, 3].

Therefore, the volume V can be calculated as follows:

V = ∫(2πx(2x^2)) dx

 = 4π ∫(x^3) dx

 = 4π * (1/4) * x^4 | [2, 3]

 = π * (3^4 - 2^4)

 = π * (81 - 16)

 = π * 65

 ≈ 203.74

Thus, the volume of the solid obtained by revolving the region under the graph of f(x) = 2x^2 about the x-axis over the interval [2, 3] is approximately 203.74 cubic units.

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Answer:

y-intercept: (0, 5)

Step-by-step explanation:

This parabola has an equation of -x² + 4x + 5.

It's y-intercept is (0, 5).

It's x-intercepts or roots are (-1, 0) and (5, 0).

It's vertex is (2, 9).

___________________________________

Keep in mind that the y-intercept is when x = 0.

The surface with the given vector equation, r(s, t) = (s cos(t), s sin(t), s), is a circular cone.

The vector equation r(s, t) = (s cos(t), s sin(t), s) represents a surface in three-dimensional space. Let's analyze the equation to determine the nature of the surface.

In the equation, we have three components: s, cos(t), and sin(t). The presence of s indicates that the surface expands or contracts radially from a central point. The trigonometric functions cos(t) and sin(t) determine the angle at which the surface extends in the x and y directions.

By observing the equation closely, we can see that as s increases, the radius of the surface expands uniformly in all directions, while the height remains constant. This behavior is characteristic of a circular cone. The circular base of the cone is defined by s cos(t) and s sin(t), and the vertical component is determined by s.

Therefore, the surface described by the vector equation r(s, t) = (s cos(t), s sin(t), s) is a circular cone.

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Answer:

The difference in price between a small pizza and a medium pizza is $0.81

Step-by-step explanation:

Small pizza

Side = 5inch

Area =  25 sq.in

Cost = $4 +0.04*25

        = 4 + 1.25  = $5.25

Medium pizza

Side = 8inche

Area = 64 sq.in

Cost = 3.50 + 0.04*64 = $6.06

Difference = Medium pizza - small pizza

                  = 6.06 - 5.25

                   = $0.81

The area of the windshield swept by the wiper blade, found using the formula for finding the area of a sector of a circle is 1470·π cm²

A sector of a circle is a part of a circle surrounded by two radius and part of the circumference.

The length of the wiper = 60 cm

The length of swing arm from the pivot to the wiper-blade tip = 72 cm

The area the length of the swing arm to the wiper-blade tip sweeps can be obtained from the area of a sector of a circle as follows;

The area swept by the circle with a radius of 72 cm = (105/360) × π × 72² cm²

(105/360) × π × 72² cm² = 1512·π cm²

The area of the not swept by the wiper blade =  (105/360) × π × (72 - 60)² cm²

(105/360) × π × (72 - 60)² cm² = (105/360) × π × 12² cm² = 42·π cm²

The area swept by the wiper blade is therefore;

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(a) The probability that someone who has traveled to Mexico has also visited Canada can be calculated using conditional probability. Let's denote the event of traveling to Mexico as event M, and the event of traveling to Canada as event C.

Given that the probability of traveling to Canada is 0.18, the probability of traveling to Mexico is 0.09, and the probability of traveling to both countries is 0.04, we can use conditional probability formula:

P(C | M) = P(C ∩ M) / P(M)

where P(C | M) represents the probability of traveling to Canada given that someone has traveled to Mexico, P(C ∩ M) represents the probability of traveling to both countries, and P(M) represents the probability of traveling to Mexico.

Plugging in the given values:

P(C | M) = 0.04 / 0.09 ≈ 0.4444

So, the probability that someone who has traveled to Mexico has also visited Canada is approximately 0.4444 or 44.44%.

(b) No, traveling to Mexico and traveling to Canada are not disjoint events. Disjoint events are events that cannot happen at the same time, meaning if one event occurs, the other cannot. However, in this case, the given information states that the probability of traveling to both Mexico and Canada is 0.04, which means it is possible for someone to have traveled to both countries.

(c) The events of traveling to Mexico and traveling to Canada are not necessarily independent events. Independent events are events where the occurrence of one event does not affect the occurrence of another event.

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Answer:

127x1

Step-by-step explanation:

127 is prime, so there are only 2 factors

Answer:

\(x=\frac{1}{7}\)

Step-by-step explanation:

\(3x-4x-4-x+65=83x-8x+50\)

\(3x-4x-x-4+65=83x-8x+50\)

\(-2x-4+65=83x-8x+50\)

\(-2x+61=83x-8x+50\)

\(-2x+61=75x+50\)

\(-2x+61-61=75x+50-61\)

\(-2x=75x-11\)

\(-2x-75x=75x-11-75x\)

\(-77x=-11\)

\(\frac{-77x}{-77}=\frac{-11}{-77}\)

\(x=\frac{1}{7}\)

Answer:

x=1/7

Step-by-step explanation:

3x-4x-4-x+65=83x-8x+50

Solving the right side of equation we have;

83x-8x+50 = 75x +50

Solving the left side of the equation we have;

3x-4x-4-x+65= -2x +61

Equating left side and right side.

-2x +61= 75x +50

by grouping terms with x , we have :

-2x- 75x = -61+50

-77x= -11

x= -11/ -77 = 1/7