Use mathematical induction to prove that the statement is true for all positive integers: 30 + 138 + 318...

Answer:

True, a cone has an apex which is the point where the sides of the cone meet to form a tip.

Step-by-step explanation:

The hypotenuse of each of these right triangles can be found using Pythagorean theorem....the hypotenuse is also the DIAMETER of the circle

   diamter * pi = circumference

First one:

  Hypot^2 = 13^2 + 13^2

    hypot ^2 = 338

     hypot = diameter = sqrt (338)

   circumference = diamter * pi  =  sqrt 338 pi   ft   ( or 13 sqrt(2) pi   ft )  

The second one is the same with slightly different numbers...you try it ...

Answer:[tex]\sqrt{338}\pi[/tex], [tex]25\pi[/tex]

Step-by-step explanation:

I will start with the second one, since it will be easier. Because this is a right triangle, you can use the given side lengths of the triangle to find the hypotenuse, which is also equal to the diameter of the triangle. Since the pythagorean theorem states that a^2(the shorter leg, squared) + b^2 (the longer leg, squared) = c^2 (the hypotenuse, squared) we can turn it into an equation like this:

[tex]7^{2\ }+\ 24^{2}\ =\ c^{2}[/tex]

(lets use x in place of c in the next few equations, for algebraic simplicity)

Simplify

[tex]49+\ 576\ =x^{2}[/tex]

[tex]625=x^{2}[/tex]

Get the square roots

[tex]\sqrt{625}=\sqrt{x^{2}}[/tex]

[tex]x=25[/tex]

Since x is equal to the hypotenuse, we know that the hypotenuse is also 25. This means the diameter of the second circle is 25, and we can now find the circumference. The EXACT circumference of the second circle is 25π, but a simplified version can be created by calculating it as if it were an equation. This comes out to around 78.5398163397, which would trail for infinity. which is why to get an exact measurement of the diameter, the most simplified exact version is displayed by multiplying the diameter by the pi symbol, because it is impossible to fit an infinite number in a finite space.

Now for the first circle, which I am now realising is no more difficult than the last one. We can do the same thing in this case, using pythagorean theorem, because there are two dash lines marking two of the lines on the circle to be equal to one another, we know that the two marked lines are equal to 13, despite not appearing to be.

We can use the same equation as we did before, but slightly modified.

[tex]13^{2}+13^{2}=x^{2}[/tex]

Simplify:

[tex]169+169=x^{2}[/tex]

[tex]338=x^{2}[/tex]

Now we can take the square roots of both sides of the equation.

[tex]\sqrt{338}=\sqrt{x^{2}}[/tex]

This is where we come to a bit of a pause. Because the square root of 338 is an irrational constant number, we have to use the unsimplified square root in our answer for the circumference, otherwise, our answer would not be exact.

The diameter of our circle is [tex]\sqrt{338}[/tex], which means that we can use an equation like this to find the circumference:

[tex]\sqrt{338}\pi[/tex]

But since we cannot simplify this any further without it not being exact, we must leave it as is.

2. The side AC corresponds to side AE of the other triangle.

3. The length of side BC is 15.

Two or more triangles are said to be similar if on comparing their properties, there exist some common relations. Some of the common relations are; measure of internal angles, scale factor etc.

From the diagram given, we have;

2. Given that the triangles are similar, thus:

The side AC corresponds to side AE of the other triangle.

3. On comparing the corresponding length of the triangles, we have;

15/ 25 = 9/ BC

15BC = 9 x 25

         = 225

BC = 225/ 15

     = 15

The length of side BC is 15.

Learn more about similar triangles at https://brainly.com/question/29782809

#SPJ1

You need 9 years to buy the car.

Given that, you need to $160,000, you have $58,000, the bank pays 6 % annual interest on its accounts. we need to find the number of years will it be before you have enough to buy the car,

A = P(1+r)ᵇ

102000 = 58000(1+0.06)ᵇ

1.75 = 1.06ᵇ

log 1.75 = b log 1.06

b = 9.6

Hence, you need 9 years to buy the car.

Learn more about compound interest, click;

https://brainly.com/question/14295570

#SPJ1

Answer: 75%

Step-by-step explanation:

     We will divide the wanted outcome by the total number of possible outcomes. Note that a decimal times 100 becomes a percentage.

[tex]\displaystyle \frac{\text{not picking a diamond card}}{\text{cards in the deck}} =\frac{39}{\text{52}} =0.75\;\;\;0.75*100=75\%[/tex]

Answer:

-24√35

Step-by-step explanation:

Mark Brainliest!!

The sketches of the graphs are added as an attachment and the gradient of the perpendicular line l₂ is 1

Given that

3x + 4y + 12 = 0

Set x = 0 to determine the y-intercept

4y + 12 = 0

So, we have

y-intercept = -3

Set y = 0 to determine the x-intercept

3x + 12 = 0

So, we have

x-intercept = -4

For the gradient, we make y the subject in 3x + 4y + 12 = 0.

y = -3/4x - 12/4

y = -3/4x - 3

So, the gradient is -3/4

The sketch of the graph is attached.

Here, we have the points P (-1,4) and Q (3,0).

The gradient is

gradient = (0 - 4)/(3 + 1)

gradient = -1

From the point, we have

x-intercept = 3

For the y-intercept, we have

(0 - 4)/(3 + 1) = (y - 4)/(0 + 1)

(y - 4)/(0 + 1) = -1

y - 4 = -1

y-intercept = 3

So, the equation is

y = -x + 3

The sketch of the graph is attached.

We understand that l₂ is perpendicular to l

The gradients of perpendicular lines are

Gradient 1 = -1/Gradient 2

So, we have

l₂ = -1/-1

Evaluate

l₂ = 1

Hence, the gradient of line l₂ is 1

Read more about linear relation at

https://brainly.com/question/30318449

#SPJ1

The rate of each bus which leave a station at the same time are 76 mi/h and 68 mi/h respectively.

Given that,

Two buses leave a station at the same time and travel in opposite directions.

Let x be the distance travelled by the the first bus in 3 hours.

Then the distance travelled by the other bus in 3 hours = 432 - x

Rate of first bus = x/3 miles per hour

Rate of second bus = (432 - x) / 3 miles per hour

One bus travels 8 mi/h slower than the other bus.

x/3 - (432 - x) / 3 = 8

(x - 432 + x) / 3 = 8

2x - 432 = 24

2x = 456

x = 228

Rate of one bus = 228/3 = 76 mi/h

Rate of second bus = (432 - 228)/3 = 68 mi/h

Hence the rate of each bus are 76 mi/h and 68 mi/h respectively.

Learn more about Rate here :

https://brainly.com/question/16604920

#SPJ1

Answer:

16.5 = 6

Step-by-step explanation:

The equation given is (+25)-5x5:2+2² = 27-5×5=2+2². When calculating, we first simplify the division to get (+25)-12.5+4 = 27-25+4. Then we add and subtract the values on either side to get 16.5 = 6. Finally, as the equation is incorrect, we can conclude that the initial assertion is false. It is important to carefully follow the order of operations and simplify expressions correctly to avoid errors in equations.

Answer:

V = (1/2)(4/3)π(6.5^3) = 575.17 cubic inches

V = (1/2)(4/3)(3.14)(6.5^3) =

574.88 cubic inches

The correct answer is 574.9 cubic inches.

a) The exponential growth function for a city's population that was 6.53 million in 2012 with an exponential growth rate of 2.79% per year is y = 6.53(1.0279)^t.

b) Based on the exponential growth function y = 6.53(1.0279)^t the population of the city in 2018 is 7.7 million.

c) The population of the city will be 10 million in 2028.

d) The doubling time for the population is 25 years.

An exponential growth function is one of the two exponential functions, including an exponential decay function.

An exponential growth function shows the relationship between two variables with an exponent and exhibits a constant rate of growth per period.

Population of the city in 2012 = 6.53million

Exponential growth rate = 2.79% per year

Let the number of growth years = t

a) y = 6.53(1.0279)^t

b) From 2012 to 2018, the number of years = 6 years

Population in 2018, y = 6.53(1.0279)^6

= 7.7 million

c) When the population will be 10 million = 15.5 years

10 = 6.53(1.0279)t

t = 15.5 years

= 16 years

= 2028

d) 13.06 = 6.53(1.0279)t

t = 25.189 years

= 25 years

Learn more about exponential growth functions at https://brainly.com/question/13223520.

#SPJ1

The term that refers to the basic characteristics of a population segment such as gender, age, and income is demographics.

We have,

Demographics refers to statistical data that describes a population and its characteristics, such as age, gender, income, education level, marital status, and other relevant factors.

Demographic information is commonly used by businesses and organizations to analyze consumer behavior, market trends, and patterns in the population.

By understanding the demographics of a particular population segment, businesses can tailor their products and services to better meet the needs and preferences of their target audience.

Demographic information is also used by government agencies and policymakers to allocate resources, plan for future development, and assess the needs of the population.

Thus,

The term that refers to the basic characteristics of a population segment such as gender, age, and income is demographics.

Learn more about demographics here:

https://brainly.com/question/13146758

#SPJ1

Answer:

90 degrees counterclockwise

Examining the graph, it can be deduced that the graph is not a function.

Domain and range are mathematical notation utilized to define the spectrum of possible accepted input values (domain) as well as the corresponding output values (range) in a given function or relation.

A definitive domain correspondingly denotes the compilations of all plausible inputs that generate a valid result when put essentially into the relation or operation.

Conversely, the range defines the plethora of conceivable outputs that this very same function or relation can devise, considering its specified domain.

Learn more about domain and range at\

https://brainly.com/question/26098895

#SPJ1

The Equation based on the function will be: t = (1/0.07) * ln(P/1,500,000)

Initially, the exponential expression is extracted and formulated as follows:

It should be noted that to obtain e^(0.07t) = P/1,500,000

Secondly, in order to determine the value of t, take the natural logarithm of both sides of the equation such that:

Take ln(e^(0.07t)) = ln(P/1500000)

It can now be represented by 0.07t = ln(P/1500000)

Finally, on dividing both components of the term through 0.07, it results in the isolation of t where:

Equation: t = (1/0.07) * ln(P/1,500,000)

In conclusion, this function's inverse describes the number of years, since the year 1990, for a determined population figure, P - its formation being previously outlined above.

Learn more about functions on

https://brainly.com/question/11624077

#SPJ1

Answer:

A

Step-by-step explanation:

4x - 2y = 8

x - int y = 0

4x = 8

x = 2

(2, 0)

y-int, x = 0

-2y = 8

y = -4

Answer:

<HAG

Step-by-step explanation:
Two angles are adjacent when they have a common side and common vertex, and they do not overlap one another. In this case, <EAG, A is the vertex. <HAG has the same vertex, A, and it shares side AG.

This statement defines the concept of left and right sets of elements x of G with respect to the subgroup H of G.

The left set of x in G, denoted by xH, is the set of all elements of G obtained by multiplying x to the left by all elements of H. Formally xH = {xh: h ∈ H}, where "xh" denotes the product of x and h in G.

Similarly, the right-hand set of x in G, denoted Hx, is the set of all elements of G obtained by multiplying x on the right by all elements of H. Formally Hx = {hx: h ∈ H}, where "hx" denotes the product of h and x in G.

Generally, left and right sets are different sets and may contain different numbers of elements. However, if the group G is commutative (ie the order of multiplication does not matter), then the left and right sets are equal.

learn more about left and right cosets: https://brainly.com/question/29585253

#SPJ1

The test score for Jason will be 55% for answering 11 questions right.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Jason is taking a multiple-choice test with a total of 20 points available. Each question is worth exactly 1 point.

The test score will be calculated as,

[tex]\text{Test score} =\dfrac{\text{Total questions - wrong answers}}{\text{Total questions}} \times100[/tex]

[tex]\text{Test Score}=\huge \text[\dfrac{(20-9)}{20}\huge \text] \times100[/tex]

[tex]\text{Test Score}=0.55\times100[/tex]

[tex]\text{Test Score}=0.55\%[/tex]

To know more about percentages follow

brainly.com/question/24304697

The surface area of the composite figure is about 98.56 sq.cm

The composite figure is made up of a cylinder and a cuboid.

The formula for surface area of a cylinder is:

A = 2πr² + 2πrh

In this case, we only have top and not bottom. Thus:

A = πr² + 2πrh

A = π(1)² + 2π(1 * 6)

A = 37.7 sq.cm

Surface area of cuboid is:

A = 2(4 * 4) + 4(2 * 4) - π(1)²

A = 32 + 32 - π

A = 60.86 sq.cm

Total surface area = 37.7 sq.cm + 60.86 sq.cm

= 98.56 sq.cm

Read more about surface area at: https://brainly.com/question/16519513

#SPJ1

The given images shows us that we have a total of two lines

In mathematics, a point is referred to as the particular location on a plane. A point is identified by a dot.  It has no length, shape or size.

A line is straight, without any type of thickness and it is the shortest distance that exists between 2 points. It has only length. It is without width.

A line segment has two end points. The difference that a line segment has with a line is that a line is extensive while the line segment has two end points.

Ray is defined as a line that has only one endpoint. The other end of the line just goes on. It has one start point and one end point.

From the attached image, it is vert clear that we have two lines which are the horizontal line and the line that divides it.

Read more about lines at: https://brainly.com/question/280216

#SPJ1

The measure of  each interior angle of a regular 16-sided polygon is 157.5 degrees

To determine the value of the interior angle, we need to note that;

The formula for calculating the sum of the interior angles of a polygon is expressed with the expression;

(n -2)180

Such that the variable n in the expression represents the number of sides of the polygon

From the information given, we have that;

(16- 2)180

expand the bracket

14(180)

multiply the values

2520 degrees

Then, we have;

16x = 2520

Make 'x' the subject

x= 157. 5 degrees

Learn more about angles at: https://brainly.com/question/25716982

#SPJ1

1. Using the formula for Pearson correlation coefficient, we have:

x y xy x^2 y^2

1 3 3 1 9

1 1 1 1 1

2 3 6 4 9

3 7 21 9 49

3 9 27 9 81

4 5 20 16 25

6 8 48 36 64

6 7 42 36 49

7 10 70 49 100

7 7 49 49 49

n = 10

sum(x) = 40, sum(y) = 53, sum(xy) = 286, sum(x^2) = 214, sum(y^2) = 506

r = [n(sum(xy)) - sum(x)sum(y)] / sqrt{ [n(sum(x^2)) - sum(x)^2][n(sum(y^2)) - sum(y)^2] }

r = [10(286) - (40)(53)] / sqrt{ [10(214) - (40)^2][10(506) - (53)^2] }

r = 0.832 (rounded to 3 decimal places)

2. The critical value (rcrit) for a 2-tailed test with a 0.05 alpha level and 8 degrees of freedom is 0.632 (using a t-distribution table or calculator).

3. The calculated correlation coefficient (r = 0.832) is greater than the critical value (rcrit = 0.632), which means that the correlation is statistically significant. We would reject the null hypothesis and conclude that there is a significant positive correlation between client expectations and satisfaction with therapy sessions.

The completed calculation with regards to the area of the congruent triangles can be presented as follows;

The distance formula indicates;

AM = √((x₂ - x₁)² + (y₂ - y₁)²)

Therefore, we get;

AM = √((4 - 0)² + (0 - 0)²) = √(4²)

AM = √(4²) = 4

BM = √((x₂ - x₁)² + (y₂ - y₁)²)

BM = √((4 - 4)² + (6 - 0)²) = √(6²)

BM = √(6²) = 6

AM ≅ CM Definition of the midpoint of AC

AM = CM Definition of congruent segments

CM = 4 Substitution property

Area ΔABM

A = (1/2)·b·h

= (1/2) × 4 × 6

= 12

Area ΔCBM

A = (1/2)·b·h

= (1/2) × 4 × 6

= 12

Therefore Area ΔABM = area ΔCBM by congruence

Triangles are congruent if they have the same size and shape.

The details of the reasons for the calculation steps and values are presented as follows;

Definition of midpoint of a segment

The midpoint of a line segment is the point that divides the segment into two parts of the same length

Definition of congruence?

Congruence refers to the existence of compatibility or harmony between objects, which in geometry indicates that the two geometric figures have the same measurement

Learn more on congruent triangles here: https://brainly.com/question/2938476

#SPJ1

The value of the term a5 is 39

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

{3, 12, 21, 30, 39, 48, 57}

The expression a5 means the 5th term of the sequence

In {3, 12, 21, 30, 39, 48, 57} , the fifth eterm is 39

Hence, a5 = 39

Read sequence at

https://brainly.com/question/30499691

#SPJ1

Answer: 28.3

Step-by-step explanation:

The question is just asking for the area of a circle with a diameter of 6. The equation for that is [tex]A = \pi r^{2[/tex].

Since the Radius (r) is half the diameter, your equation will look like this: [tex]A=\pi 3^2[/tex].

When plugged into a calculator, 28.27443 is the answer. Rounded to the nearest tenth would be 28.3. Hope this helps!

The values of the trigonometric ratios for the given triangle are sinθ = 8/17, cosθ = 15/17 and tanθ = 8/15.

From the given right triangle hypotenuse= 17 units and legs of triangle are 15 units and 8 units.

We know that, sinθ = Opposite/Hypotenuse

sinθ = 8/17

We know that, cosθ = Adjacent/Hypotenuse

cosθ = 15/17

We know that, tanθ = Opposite/Adjacent

tanθ = 8/15

Therefore, the values of the trigonometric ratios for the given triangle are sinθ = 8/17, cosθ = 15/17 and tanθ = 8/15.

Learn more about the trigonometric ratios here:

brainly.com/question/25122825.

#SPJ1

Answer:

2.38888

Step-by-step explanation:

That's what is says hope this helps

The statements that defines the term resources is A. materials that help you achieve your goals.

Resource  can be described as all the materials available  that is available in individual environment  and can be seen as one that is  technologically accessible.

It should be noted that resources do help us to achieve most of our goals and can be seen as one that is economically feasible  as welll as culturally sustainable and they serves as things that can help us and thjat can  satisfy our needs and wants which is needed on daily basis.

Learn more about resources at:

https://brainly.com/question/1290230

#SPJ1

Based on the information, we cannot reject the null hypothesis because our calculated phi coefficient (0.245) is smaller than the critical value (3.84).

It should be noted that to establish whether the phi coefficient is statistically significant, we can compare it to a crucial value. However, the significance level (i.e., alpha) must be specified ahead of time.

Assume a 0.05 level of significance. We calculate the crucial value for a 2x2 contingency table with 1 degree of freedom and a significance level of 0.05 using a phi coefficient table or calculator.

We cannot reject the null hypothesis because our calculated phi coefficient (0.245) is smaller than the critical value (3.84). As a result, we find that there is no statistically significant relationship between the therapist's method and client satisfaction.

Learn more about coefficient on

https://brainly.com/question/1038771

#SPJ1