A 4 m ladder leans against a
building. If the bottom of the
ladder is 1.3 m from the bottom of
the building, how far up the wall
will the ladder reach? Round your
answer to one decimal place.

Answer:

about like 4-5

Step-by-step explanation:

its 4 or 5

the proof by mathematical induction involves establishing the basis step, proving the inductive step, and using mathematical induction to show that the formula holds true for all non-negative integers.

The problem asks us to determine whether each of the proposed recursive definitions is a valid definition of a function f from the set of non-negative integers to the set of integers. If it is well defined, we are asked to find a formula for f(n) when n is a non-negative integer and to prove that the formula is valid.    

After finding the formula for f(n), we are asked to prove its validity using mathematical induction. To do this, we first need to establish the basis step and the inductive step.

The basis step is the first step in the proof by mathematical induction. We need to prove that the formula holds true for the smallest value of n, which is usually 0 or 1. In this case, we need to prove that P(0) and P(1) are true.

Next, we need to prove the inductive step. This involves assuming that the formula holds true for some arbitrary value of n and using that assumption to prove that the formula also holds true for n+1.

To prove that the formula holds true for all non-negative integers, we need to show that the basis step and inductive step are both true. We can then conclude that the formula is valid for all non-negative integers by mathematical induction.

The proof of the inductive step can be completed by assuming that P(1) ∧ P(2) ∧ ... ∧ P(k) is true, and then using this assumption to prove that P(k + 1) is true. This is usually done by manipulating the formula for f(n) and using algebraic properties to show that the formula holds true for n+1.

In summary, the proof by mathematical induction involves establishing the basis step, proving the inductive step, and using mathematical induction to show that the formula holds true for all non-negative integers.

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The pressure exerted (in N/m²) by the box on the shelf given that the bottom of the box has an area of 0.30 m² and weighs 60 N, is 200 N/m²

Pressure is defined a force per unit area. Mathematically, it is written as

Pressure (P) = force (F) / area (A)

P = F / A

With the above formular, we can obtain the pressure exerted by the box as follow:

Pressure exerted (P) = Weight of box (W) / Area of box (A)

Pressure exerted = 60 / 0.30

Pressure exerted = 200 N/m²

Thus, we can conclude that the pressure exerted is 200 N/m²

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Complete question:

The area of the bottom of a tiffin box is 0.30 sq. m and weight is 60 N, Calculate the pressure exerted by the box on the shelf in N/sq. m *​

Answer:

3. 211.6 feet

4. 59.04 degrees.

Step-by-step explanation:

3.

To find how much wire Mark Wolfman needs for the tallest tower in the park, we can use trigonometry. Let's call the height of the tower "h". We know that the wire is attached to the top of the tower and to a stake in the ground that is 44 feet away from the base of the tower. The wire makes a 78 degree angle with the flat ground.

We can use the tangent function to find the height of the tower:

tan(78) = h / 44

Multiplying both sides by 44, we get:

h = 44 * tan(78)

So the height of the tower is approximately 207 feet.

To find how much wire is needed, we can use the Pythagorean theorem:

wire length = sqrt(h^2 + 44^2)

Substituting the value we found for "h", we get:

wire length = sqrt(207^2 + 44^2)

Simplifying, we get:

wire length = 211.6

So Mark Wolfman needs approximately 211.6 feet of wire.

4.

To find the angle of depression of the swimmer's dive, we need to consider the triangle formed by the swimmer, the buoy, and the point on the lake bottom directly below the buoy. We know that the buoy is 30 feet away from the swimmer and the chain connecting it to the bottom of the lake is 50 feet down.

The angle of depression is the angle between the swimmer's line of sight and the horizontal. Since the swimmer is looking downward toward the chain, the angle of depression is the same as the angle formed by the horizontal and the line connecting the swimmer to the chain.

Using trigonometry, we can find the tangent of this angle:

tan(angle of depression) = opposite / adjacent

tan(angle of depression) = 50 / 30

tan(angle of depression) = 5/3

Taking the arctangent of both sides, we get:

angle of depression = arctan(5/3)

Using a calculator, we find that the angle of depression is approximately 59.04 degrees.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{59\% of 640}}{\left( \cfrac{59}{100} \right)640}\implies 377.6[/tex]

Answer:

377.6

Step-by-step explanation:

640÷10=64 to find 10%

64×5=320 to find 50%

640÷100=6.4 to find 1%

6.4×9=57.6 to find 9%

320+57.6=377.6

answer: 377.6

So, we have an equation relating the volume of the prism to the dimensions of the base. However, we still need more information to solve for x. Then x is 2.5 xyxx

Height generally refers to the distance from the base of an object, such as a person or a building, to the highest point of that object. In the case of a person, height is typically measured in feet and inches or centimeters and is a measurement of how tall someone is from the top of their head to the soles of their feet. In the case of a building or structure, height is typically measured in meters or feet and is a measurement of how tall the structure is from its base to its highest point, such as its roof or antenna. Height can also refer to the vertical distance between two points, such as the height of a mountain or the height of a wave in the ocean.

by the question.

Volume = base area x height

Since the bases of the prism are right triangles, we can calculate their area using the formula:

base area = 1/2 x base x height

where base is the length of the base of the triangle and height is the height of the triangle.

Let's assume that the length of the base of each right triangle is x, and that the height of each right triangle is y. Then we can write:

base area = 1/2 x y

The total volume of the prism is given as So. Therefore, we can write:

So = base area x height

Substituting the expression for base area and the given value for height, we get:

So = 1/2 x y x 5

Simplifying this equation, we get:

So = 2.5 x y x x

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Answer:☠️☠️☠️☠️do ur hw lil bro u actually need to learn this fr fr dont let me catch u slippin on foenem

Step-by-step explanation:

b. 650 because in the directions it says for groups of more than ( > ) 8 people they charge a FIXED fee of 650 so it's not 75 times 9 which would have been 675

Step-by-step explanation:

C(n) = {

75n, if n <= 8

650, if n > 8 and n <= 12

}

This function states that for groups of 8 people or fewer, the total cost is 75n, while for groups of 9 to 12 people, the total cost is a fixed $650.

b. To determine the total cost of a 1-hour private guided tour with 9 people, we can simply plug n = 9 into the equation we derived in part a:

C(9) = {

75*9, if 9 <= 8

650, if 9 > 8 and 9 <= 12

}

Since 9 is greater than 8 but less than or equal to 12, we use the second case:

C(9) = 650

Therefore, the total cost of a 1-hour private guided tour with 9 people is $650.

ChatGPT

Answer:

A fast and easy surface area of a rectangular prism calculator to find just what its name suggests.

Step-by-step explanation:

l=13in

w=7

h=6

A=422in squared

The quadratic equation is:

y = (149/1,800)*(x + 1)² + 2

Remember that if the parabola has a vertex (h, k) and a leading coefficient a can be written as:

y = a*(x - h)² + k

Here we know that the vertex is (-1, 2), then we will get the following equation:

y = a*(x + 1)² + 2

And we know it passes through (-14, - 153/8), then we will get:

-153/8 = a*(14 + 1)² + 2

-153/8 = a*225 + 2

a = (153/8 - 2)/225 =

a = 149/1,800

The quadratic is:

y = (149/1,800)*(x + 1)² + 2

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Answer:

The volume of the sphere is 2304π ft³.

Step-by-step explanation:

The formula for the volume of a sphere is:

[tex]\boxed{V=\dfrac{4}{3}\pi r^3}[/tex]

where r is the radius of the sphere.

Given the radius of the sphere is 12 feet, substitute r = 12 into the formula and solve for V:

[tex]\begin{aligned}\implies V&=\dfrac{4}{3} \cdot \pi \cdot 12^3\\\\&=\dfrac{4}{3} \cdot \pi \cdot 1728\\\\&=\dfrac{6912}{3} \cdot \pi \\\\&=2304\pi\; \sf ft^3 \end{aligned}[/tex]

Therefore, the volume of the sphere in terms of π is 2304π ft³.

It takes 11.52 years for a population that is growing with a constant relative growth rate of 10% per year to triple.

The formula for calculating the time it takes a population to triple with a constant relative growth rate of 10% per year is:

Time (in years) = ln(3) / ln(1.10)

The natural logarithm of 3 (ln(3)) is 1.09861228866811, and the natural logarithm of 1.10 (ln(1.10)) is 0.095310179804325.

Therefore, the calculation of the time it takes a population to triple with a constant relative growth rate of 10% per year is:

Time (in years) = 1.09861228866811 / 0.095310179804325 = 11.52

It takes 11.52 years for a population that is growing with a constant relative growth rate of 10% per year to triple.

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Answer:

Raul is 15 years old.

Step-by-step explanation:

The number of years from the start of the Great Depression to Nixon's election is six years less than three times Raul's age: 3r-6

If then Nixon's first election happened 39 years after the Great Depression, then: 3r-6=39

3r-6=39    Add six to both sides so the 6 on the left side gets canceled out (positive and negative cancel each other out) so the equation will now look like this: 3r=45

Then divide 3 on both sides (multiplication and division also cancel each other out), then the equation looks like this: r=15

And so, Raul is 15 years old.

Answer:

x = 26

Step-by-step explanation:

the 3 angles lie on the straight line DAC and sum to 180° , that is

4x - 8 + 34 + 76 - x = 180

3x + 102 = 180 ( subtract 102 from both sides )

3x = 78 ( divide both sides by 3 )

x = 26

The area of the given figures is 1) 4 sq. units; 2) 16 sq units; 3) 6 sq units.

Define area and perimeter.

The distance around a closed figure is its perimeter, while the area is the portion of the surface that it occupies. The size of a plane or the space it encloses is expressed in square meters.

1. In this figure, the longest side has 4 units and the smallest one has 1 unit.

   Area of the rectangular figure(A) = 4 * 1 = 4 sq units

   Perimeter(P) = 4 + 1 + 4 + 1 = 10 units.

2. In this figure, the longest side has 4 units and the smallest one has 4 units.

   Area of the rectangular figure(A) = 4 * 4 = 16 sq units

   Perimeter(P) = 4 + 4 + 4 + 4 = 16 units.

3. In this figure, the longest side has 4 units, 3 units, then 2 units the smallest one has 1 unit.

   Area of the rectangular figures combinely (A) = 4 * 1 + 2 * 1= 6 sq units

   Perimeter(P) = 4 + 3 + 2 + 2 + 1 = 12 units.

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Answer:

The tangent line is:  y = 8x - 58

The tangent point is at  (7, -2)

===================================================

Explanation:

One of the definitions of derivatives is

[tex]\displaystyle f'(a) = \lim_{x\to a} \frac{f(x)-f(a)}{x-a}[/tex]

where f ' (a) represents the derivative evaluated at x = a.

The value of f ' (a) will get us the slope of the tangent at x = a.

The idea is that x is getting closer and closer to 'a'. In doing so, the secant lines slowly approach the tangent line.

Keep in mind that x will never reach 'a' itself (if it did, then we'd have a division by zero error).

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

The given limit we have is

[tex]\displaystyle \lim_{x\to 7} \frac{f(x)+2}{x-7} = 8[/tex]

and that is equivalent to

[tex]\displaystyle \lim_{x\to 7} \frac{f(x)-(-2)}{x-7} = 8[/tex]

and also equivalent to

[tex]\displaystyle \lim_{x\to 7} \frac{f(x)-f(7)}{x-7} = 8[/tex]

Compare that to the template I mentioned at the top to see that

Therefore, we can say the tangent slope is 8 and the tangent touches the f(x) curve at (x,y) = (a, f(a)) = (7,f(7)) = (7,-2)

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

[tex]m = 8 = \text{slope}\\\\(x_1,y_1) = (7,-2) = \text{tangent point}\\\\[/tex]

Let's use that info to determine the equation of the tangent line.

I'll use point-slope form to isolate y.

[tex]y-y_1 = m(x-x_1)\\\\y-(-2) = 8(x-7)\\\\y+2 = 8x-56\\\\y = 8x-56-2\\\\y = 8x-58\\\\[/tex]

That's the equation of the tangent line to the point (7,-2).

Answer:

Step-by-step explanation:

In conclusion, the probability of selecting a Democrat or a business major is 11/15.

How to solve?

To find the probability of selecting a Democrat or a business major, we need to add the probabilities of selecting a Democrat and selecting a business major, and then subtract the probability of selecting a student who is both a Democrat and a business major (since we would be double counting this student).

So, let's calculate each of these probabilities:

Probability of selecting a Democrat: There are 40 Democrats out of 60 students, so the probability of selecting a Democrat is 40/60 = 2/3.

Probability of selecting a business major: There are 10 business majors out of 60 students, so the probability of selecting a business major is 10/60 = 1/6.

Probability of selecting a student who is both a Democrat and a business major: We know that there are 4 business majors who are also Democrats, so the probability of selecting one of these students is 4/60 = 1/15.

Now we can calculate the probability of selecting a Democrat or a business major:

P(Democrat or business major) = P(Democrat) + P(business major) - P(Democrat and business major)

= 2/3 + 1/6 - 1/15

= 11/15

Therefore, the probability of selecting a Democrat or a business major is 11/15.

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Therefore , the solution of the given problem of unitary method comes out to be  able to afford the festival because 120 is larger than 70.

To accomplish the task, one may use this generally accepted ease, preexisting variables, as well as any significant components from the original Diocesan customizable query. If so, there might be an opportunity to interact with the item once more. Otherwise, every significant factor that affects how algorithmic evidence behaves will be gone.

Here,

The following chart allows us to determine each person's earnings:

=> Person 1: 2 hours times $8 per hour  =  $16

=>  Person 2: $4 hours x $8 per hour  =  $32 per person

=>Person  3: 3 hours x $8 per hour = $24 per person.

=> Person 4: 5 hours x $8 per hour  =  $40.

=> Person 5: One hour times $8 per hour equals $8.

Each person needs to bring at least $70 in order to join the festival. As a result, the disparity shown below can be used to describe this circumstance:

=> 16 + 32 + 24 + 40 + 8 ≥ 70

Simplifying the inequality's left side, we obtain:

=> 120 ≥ 70

We can infer that all of the friends were able to afford the festival because 120 is larger than 70.

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Answer:

Step-by-step explanation: ??? There is no picture

Answer:

6 quarts

Step-by-step explanation:

2 pints = 1 quart

4 cups = 1 quart

• 5 pints of orange juice

5 pints = 5/2 =>2.5 quarts

• 6 cups of grape juice

6 cups = 6/4 => 1.5 quarts

• 8 cups of apple juice

8 cups = 2 quarts

2.5 + 1.5 + 2 = 6 quarts

The numbers chosen by the Anjali, which when rounded off to 1 decimal place , becomes equal are: 987.47 and 987.53.

The act of rounding off is merely an estimation. Rounding off is the process of estimating an actual number to a close number.

Here is the general rounding rule:

Consider these two numbers:

987.47 and 987.53.

rounded off to 1 decimal place, they becomes:

987.5 (as 7 is greater than 5, it will get rounded off and 1 is added to previous number of 7).

and 987.5 (as is less than 5 , so 53 will be taken as 5 only)

Thus, the numbers chosen by the Anjali, which when rounded off to 1 decimal place , becomes equal are: 987.47 and 987.53.

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Answer:

ion kno fr

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's say the two numbers are x and y.

From the first statement "twice the difference between two numbers is 44", we can set up the equation:

2(x-y) = 44

Simplifying this equation, we get:

x - y = 22 (dividing both sides by 2)

From the second statement "three times their sum is 96", we can set up the equation:

3(x+y) = 96

Simplifying this equation, we get:

x + y = 32 (dividing both sides by 3)

Now we have two equations:

x - y = 22

x + y = 32

We can solve for x and y by adding the two equations together:

2x = 54

x = 27

Substituting x = 27 in either of the two equations, we get:

y = 5

Therefore, the two numbers are 27 and 5.

x = 27;

y = 5.

Say "x" is the first number.

Say "y" is the second number.

First statement: "twice the difference between two numbers is 44".

Difference of the numbers:[tex]x-y[/tex]

Twice the difference: [tex]2(x-y)[/tex]

Twice the difference between two numbers is 44: [tex]2(x-y)=44[/tex]

Second statement: "three times their sum is 96".

Sum of the numbers: [tex](x+y)[/tex]

3 times the sum: [tex]3(x+y)[/tex]

3 times the sum is 96: [tex]3(x+y)=96[/tex]

Use the distributive property of multiplication to simplify each equation as follows (check this property in the attached image).

[tex]2(x-y)=44\\ \\2x-2y=44[/tex]

[tex]3(x+y)=96\\ \\3x+3y=96[/tex]

Let's solve the second equation for "x".

[tex]3x+3y-3y=96-3y\\ \\3x=96-3y\\ \\x=\frac{96-3y}{3} \\ \\x=\frac{96}{3} -\frac{3y}{3} \\ \\x=32-y[/tex]

[tex]2((32-y)-y)=44\\ \\2(32-y-y)=44\\ \\2(32-2y)=44\\ \\(2)(32)+(2)(-2y)=44\\ \\64+(-4y)=44\\ \\64-4y=44\\ \\-4y=44-64\\ \\-4y=-20\\ \\y=\frac{-20}{-4} \\ \\y=5[/tex]

Use any equation to find a value for "x" by substituting "y" by "5" and solving for "x".

[tex]3(x+(5))=96\\ \\3(x+5)=96\\ \\3x+15=96\\ \\3x=96-15\\ \\3x=81\\ \\x=\frac{81}{3} \\ \\x=27[/tex]

To see if the answers are correct, plug in the values of "x" and "y" on each formula and see if they return the correct values (44 and 96).

[tex]2(x-y)=44\\ \\2((27)-(5))=44\\ \\2(22)=44\\ \\44=44[/tex]

Correct.

[tex]3((27)+(5))=96\\ \\3(32)=96\\ \\96=96[/tex]

Correct.

The numbers returned the correct values when evaluated in both opf the equation. Therefore, they are the correct answers.

x = 27;

y = 5.

See the graphic solution to this problem in the second attached image.

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

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Answer:

85.6 cm²

Step-by-step explanation:

You can divide this shape with a horizontal line:  trapezoid and a rectangle

Total Area = Area of trapezoid + Area of rectangle

                  = (1/2)(b₁ + b₂)(h) + (b)(h)

                  = (1/2)(6+10)(7.2) + (10)(2.8)

                  = 57.6 + 28

                  = 85.6 cm²

The answer is no. As the p-value is more than 0.01, evidence does not support Annie's claim that the chances of getting married for this group is greater than 3.4%.

It assumes that the observed result is due to chance and there is not any difference between specified populations.

To determine this, we must calculate the p-value.

The number of successes in the sample is 20 and the number of observations is 407.

The sample proportion = 0.049. (20/407)

The hypothesis is that the percentage of women who got married is greater than 3.4%.

The null hypothesis is that the percentage is 3.4%.

We can use the z-test statistic to test this hypothesis.

The z-test statistic is calculated as:

z = (0.049-0.034)/(√(0.034(1-0.034)/407))

= 1.66.

The p-value is calculated as:

p-value = Φ/(1.66)

= 0.97.

This is more than 0.01 ,so we can not reject the null hypothesis.

This evidence does not support Annie's claim that the chances of getting married for this group is greater than 3.4%.

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Answer:

The range of the stock prices is from $10.82 to $33.17. To find the upper quartile, we need to find the value of the stock price that is greater than 75% of the data.

The distance between the minimum value and the maximum value is:

$33.17 - $10.82 = $22.35

To find the upper quartile, we need to find the value that is three-quarters of the distance above the minimum value:

$10.82 + 0.75($22.35) = $26.69

Therefore, the upper quartile of the stock price is $26.69.

To find the value above which the stock price is higher 25% of the time, we need to find the value that is 75% of the distance above the minimum value:

$10.82 + 0.25($22.35) = $15.62

Therefore, 25% of the time, the stock price is above $15.62.

To find the upper quartile, we need to first find the median of the stock prices, which is the value that divides the distribution into two equal parts. The midpoint of the distribution is:

Midpoint = (10.82 + 33.17) / 2 = 22.995

Now, we can find the upper quartile, which is the median of the upper half of the distribution. The upper half of the distribution ranges from the midpoint to the highest value of 33.17. Therefore, we calculate the median of this range as follows:

Upper quartile = (22.995 + 33.17) / 2 = 28.0825

So, the upper quartile of the stock prices is $28.08.

To find the value above which the stock is priced 25% of the time, we need to find the 75th percentile of the distribution. Since the distribution is uniform, we can use the formula for the percentile as follows:

Percentile rank = (percentile / 100) = (value - minimum) / (maximum - minimum)

Solving for the value, we get:

value = minimum + percentile rank x (maximum - minimum)

For the 75th percentile, we have:

value = 10.82 + 0.75 x (33.17 - 10.82) = 28.49

Therefore, the stock is priced above $28.49 on 25% of all days.

Answer:

Each apple is worth $0.12

Step-by-step explanation:

Total of 12 apples ÷ Quantity of Apples = Cost of each apple

1.44 ÷ 12 = 0.12

The correct answers for the equation of parabola with  (3,5) are:

A. True

B. False

C. True

D. True

E. True

Using the vertex form equation of the parabola with vertex (h, k) and p = 2,

[tex](y-4)^{2}[/tex] = 8(x - 3)

[tex]y^{2}-10y+25[/tex] = 8x - 24

[tex]y^{2}-10y+49[/tex] = 8x

A. (-1, 5): Substitute x = -1 and y = 5 into the equation:

25 - 10(5) + 49 = 8(-1)

-16 = -16

This is true, so the point (-1, 5) is on the parabola.

B. (3, 3): Substitute x = 3 and y = 3 into the equation:

9 - 10(3) + 49 = 8(3)

-8 = 8

This is false, so the point (3, 3) is not on the parabola.

C. (5, 5): Substitute x = 5 and y = 5 into the equation:

25 - 10(5) + 49 = 8(5)

9 = 9

This is true, so the point (5, 5) is on the parabola.

D. (7, 5): Substitute x = 7 and y = 5 into the equation:

25 - 10(5) + 49 = 8(7)

25 = 25

This is true, so the point (7, 5) is on the parabola.

E. (3, 9): Substitute x = 3 and y = 9 into the equation:

81 - 10(9) + 49 = 8(3)

1 = 1

This is true, so the point (3, 9) is on the parabola.

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The angles of the given Rhombus are:

The above are arrived at using the qualities of a Rhombus and the theorem of alternate angles.

A rhombus is a quadrilateral with certain properties that distinguish it from other types of quadrilaterals. The key properties of a rhombus are:

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