Find the length of side a. 13, 5 B on a right triangle​

Answers

Answer 1

In a right triangle, the length of side "a" is 12.

The Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, can be used to find the length of side "a" in a right triangle with sides of 13 and 5 units.

Let's assign "a" as the unknown side. According to the Pythagorean theorem, we have the equation: [tex]a^{2}[/tex] = [tex]13^{2}[/tex] - [tex]5^{2}[/tex].

Simplifying the equation, we get [tex]a^{2}[/tex] = 169 - 25, which becomes [tex]a^{2}[/tex] = 144.

To solve for "a," we take the square root of both sides: a = √144.

The square root of 144 is 12. Therefore, side "a" has a length of 12 units.

In summary, using the Pythagorean theorem, we determined that side "a" in the right triangle with side lengths 13 and 5 units has a length of 12 units.

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Related Questions

help me please.. please

Answers

Step-by-step explanation:

Parallel to the x-axis means it is just a horizontal line with the value being the y-coordinate of the point:

y = -2

Answer:

y=-2

and m=0 must be your answer

Step-by-step explanation:

as line is parallel to x axis its slope will be zero as it does not have any definite x coordinate

so

equation of line is y-y'=m(x-x')

so m=0 m is slope

y'=-2 and x'=4

so by substituting the values

y+2=0

so y=-2

and m=0 is your answer

Michelle had 5 paperback books and 3 hardcover books on the shelf by her bed. Write a ratio to represent the ratio of paperback books to hardcover books.

3:5
five over three
3 to 8
5:8

Answers

The correct ratio to represent the ratio of paperback books to hardcover books is 5:3.

Answer: The correct ratio to represent the ratio of paperback books to hardcover books is 5:3.

(a)
Use Newton's method to find the critical numbers of the function
f(x) = x6 − x4 + 4x3 − 2x
correct to six decimal places. (Enter your answers as a comma-separated list.)
x =
Incorrect: Your answer is incorrect.
(b)
Find the absolute minimum value of f correct to four decimal places.

Answers

(a) Using Newton's method, the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] correct to six decimal places, are approximately -1.084, -0.581, -0.214, 0.580, and 1.279.

(b) The absolute minimum value of f is undefined since the function is a polynomial of even degree, and it approaches positive infinity as x approaches positive or negative infinity.

(a) To find the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex]  we can use Newton's method by finding the derivative of the function and solving for the values of x where the derivative is equal to zero.

First, let's find the derivative of f(x):

f[tex]'(x) = 6x^5 - 4x^3 + 12x^2 - 2[/tex]

Now, let's apply Newton's method to find the critical numbers. We start with an initial guess, x_0, and use the formula:

[tex]x_{(n+1)} = x_n - (f(x_n) / f'(x_n))[/tex]

Iterating this process, we can approximate the values of x where f'(x) = 0.

Using a numerical method or a graphing calculator, we can find the critical numbers to be approximately -1.084, -0.581, -0.214, 0.580, and 1.279.

Therefore, the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] correct to six decimal places, are approximately -1.084, -0.581, -0.214, 0.580, and 1.279,

(b) To find the absolute minimum value of f(x), we need to analyze the behavior of the function at the critical numbers and the endpoints of the interval.

Since the function f(x) is a polynomial of even degree, it approaches positive infinity as x approaches positive or negative infinity.

Therefore, there is no absolute minimum value for the function.

Hence, the absolute minimum value of f is undefined.

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given f(x) = x^3 - 10x + k, and the remainder when f(x) is divided by x + 3 is 6, then what is the value of K?

Answers

Answer:

Step-by-step explanation:

(x^3 - 10x + K)/(X+3) = 6 GIVEN

for different values of x there are many possible values of k some i will show

when we substitute x=1

we get k=33

at x=2

weget k=42

so many values are possible for k

because there is no intervel in question which restrics us from taking different values of x or k so you take any value of x you will get different values of k

The ratio of the length to the width of a rectangle is 3:2. If the perimeter of the rectangle is 40, what is the length of the rectangle?

Answers

Answer:

Step-by-step explanation:

Let's denote the length of the rectangle as 3x and the width as 2x, based on the given ratio.

The perimeter of a rectangle is given by the formula P = 2(length + width). In this case, we have:

P = 2(3x + 2x)

40 = 2(5x)

Now, let's solve for x:

40 = 10x

x = 40/10

x = 4

Now that we have the value of x, we can find the length of the rectangle:

Length = 3x = 3(4) = 12

Therefore, the length of the rectangle is 12.

Determine the measure of the interior angle at vertex F.
A. 54
B. 108
C. 36
D. 72

Answers

The measure of the interior angle at vertex F is 72 degrees.

How to find the interior angle at vertex F

A hexagon is a polygon with six sides. The sum of the interior angles of a hexagon is equal to 720 degrees.

The angle of the hexagon is given in terms of x,

The sum of the angle is equal to 720 degrees

[tex]4\text{x}+4\text{x}+4\text{x}+4\text{x}+2\text{x}+2\text{x} = 720[/tex]

[tex]20\text{x} = 720[/tex]

[tex]\text{x} = 36[/tex]

[tex]\bold{2x = 72^\circ}[/tex]

Therefore, the measure of interior angle at vertex F is equal to 72 degrees.

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A newly hired lawyer receives a $15,000 signing bonus from a law firm and invests the money in a savings account at 4.75% interest. After 42 months, the lawyer checks the account balance.

Part A: Calculate the interest earned if the interest is compounded quarterly. Show all work. (2 points)

Part B: Calculate the interest earned if the interest is compounded continuously. Show all work. (2 points)

Part C: Using the values from Part A and Part B, compare the interest earned for each account by finding the difference in the amount of interest earned. (1 point)

Answers

Part A: The interest earned if the interest is compounded quarterly is $2,768.40.

Part B: The interest earned if the interest is compounded continuously is $2,695.92.

Part C: The difference in the amount of interest earned is approximately $72.48.

Part A: To calculate the interest earned when the interest is compounded quarterly, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^(^n^t^)[/tex]

Where:

A = the final account balance

P = the principal amount (initial investment)

r = the annual interest rate (4.75% or 0.0475 as a decimal)

n = the number of times the interest is compounded per year (4 times for quarterly)

t = the number of years (42 months divided by 12 to convert to years)

Plugging in the values:

A = $15,000(1 + 0.0475/4)^(4 * (42/12))

A = $15,000(1.011875)^(14)

A ≈ $15,000(1.18456005)

A ≈ $17,768.40

The interest earned is the difference between the final account balance and the principal amount:

Interest earned = $17,768.40 - $15,000

Interest earned ≈ $2,768.40

Part B: When the interest is compounded continuously, we can use the formula:

[tex]A = Pe^(^r^t^)[/tex]

Where:

A = the final account balance

P = the principal amount (initial investment)

e = the mathematical constant approximately equal to 2.71828

r = the annual interest rate (4.75% or 0.0475 as a decimal)

t = the number of years (42 months divided by 12 to convert to years)

Plugging in the values:

A = $15,000 * e^(0.0475 * 42/12)

A ≈ $15,000 * e^(0.165625)

A ≈ $15,000 * 1.179727849

A ≈ $17,695.92

The interest earned is the difference between the final account balance and the principal amount:

Interest earned = $17,695.92 - $15,000

Interest earned ≈ $2,695.92

Part C: Comparing the interest earned for each account, we find that the interest earned when the interest is compounded quarterly is approximately $2,768.40, while the interest earned when the interest is compounded continuously is approximately $2,695.92.

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Find the value of x.

Answers

At least 4 probably

50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answers

Answer:   D

Step-by-step explanation:

Similar means that if you multiplied all of the sides by the same number it would proportionally be that much larger.

D)    4x2=8

       12x2=24

       15x2=30      All sides were multiplied by 2 so D is similar

Answer:

D)

Step-by-step explanation:

Figure D is similar in all mesurements .

...

Five years older than Mukhari. Find the value of the expression if Mukhari is 43 years old.

Answers

If x is Mukhari’s age, then
x + 5
(43) + 5 = 48

Show that y₁(t) = e^ãt cos(μt) and
y₂(t) = e^ãt sin(μt)
are a fundamental set of solutions and state the general solution.​

Answers

The functions y₁(t) = e^ãt cos(μt) and y₂(t) = e^ãt sin(μt) are a fundamental set of solutions because they are linearly independent and satisfy the given homogeneous linear differential equation, allowing for the formation of the general solution.

To show that y₁(t) = e^ãt cos(μt) and y₂(t) = e^ãt sin(μt) are a fundamental set of solutions, we need to demonstrate two things: linear independence and satisfaction of the given homogeneous linear differential equation.

First, let's consider linear independence. We can prove it by showing that there is no constant c₁ and c₂, not both zero, such that c₁y₁(t) + c₂y₂(t) = 0 for all t.

Now, let's verify that y₁(t) and y₂(t) satisfy the homogeneous linear differential equation. If the given differential equation is of the form ay''(t) + by'(t) + cy(t) = 0, we can substitute y₁(t) and y₂(t) into the equation and verify that it holds true.

Once we have established linear independence and satisfaction of the differential equation, we can state that the general solution to the homogeneous linear differential equation is given by y(t) = c₁y₁(t) + c₂y₂(t), where c₁ and c₂ are arbitrary constants. This general solution represents the linear combination of the fundamental set of solutions.

In summary, y₁(t) = e^ãt cos(μt) and y₂(t) = e^ãt sin(μt) form a fundamental set of solutions for the given differential equation, and the general solution is given by y(t) = c₁y₁(t) + c₂y₂(t).

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Assume a class has 26 members.
a. In how many ways can a president, a vice president, and a secretary be selected?
b. How many committees of 4 people can be chosen?
a. The number of ways to select a president, a vice president, and a secretary is
b. The number of ways to form a 4-person committee is
$0.

Answers

a. There are 15,600 ways to select a president, a vice president, and a secretary from a class of 26 members.

b. There are 14,950 ways to form a 4-person committee from a class of 26 members.

a. To select a president, a vice president, and a secretary from a class of 26 members, we can use the concept of permutations.

For the president position, we have 26 choices. After selecting the president, we have 25 choices remaining for the vice president position. Finally, for the secretary position, we have 24 choices left.

The total number of ways to select a president, a vice president, and a secretary is obtained by multiplying the number of choices for each position:

Number of ways = 26 * 25 * 24 = 15,600

Therefore, there are 15,600 ways to select a president, a vice president, and a secretary from a class of 26 members.

b. To form a 4-person committee from a class of 26 members, we can use the concept of combinations.

The number of ways to choose a committee of 4 people can be calculated using the formula for combinations:

Number of ways = C(n, r) = n! / (r!(n-r)!)

where n is the total number of members (26 in this case) and r is the number of people in the committee (4 in this case).

Plugging in the values, we have:

Number of ways = C(26, 4) = 26! / (4!(26-4)!)

Calculating this expression, we get:

Number of ways = 26! / (4! * 22!)

Using factorials, we simplify further:

Number of ways = (26 * 25 * 24 * 23) / (4 * 3 * 2 * 1) = 14,950

Therefore, there are 14,950 ways to form a 4-person committee from a class of 26 members.

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the peterson family and the stewart family each used their sprinklers last summer. the water output rate for the peterson family’s sprinkler was 35 L per hour. the water output rate for the stewart family’s sprinkler was 40 L per hour. the families used their sprinklers for a combined total of 45 hours, resulting in a total water output of 1,650 L. how long was each sprinkler used?

Answers

The Peterson family used their sprinkler for 30 hours, while the Stewart family used theirs for 15 hours.

Let's assume that the Peterson family used their sprinkler for a certain number of hours, which we'll denote as x, and the Stewart family used their sprinkler for the remaining hours, which would be 45 - x.

The water output rate for the Peterson family's sprinkler is given as 35 L per hour. Therefore, the total water output for the Peterson family can be calculated by multiplying the water output rate (35 L/h) by the number of hours they used the sprinkler (x): 35x.

Similarly, for the Stewart family, with a water output rate of 40 L per hour, the total water output for their sprinkler is given by 40(45 - x).

According to the problem, the combined total water output for both families is 1,650 L. Therefore, we can write the equation:

35x + 40(45 - x) = 1,650.

Simplifying the equation, we get:

35x + 1,800 - 40x = 1,650,

-5x = 1,650 - 1,800,

-5x = -150.

Dividing both sides of the equation by -5, we find:

x = -150 / -5 = 30.

So, the Peterson family used their sprinkler for 30 hours, and the Stewart family used theirs for 45 - 30 = 15 hours.

Therefore, the Peterson family used their sprinkler for 30 hours, while the Stewart family used theirs for 15 hours.

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Which type of conic section is defined by the equation:... 100pts

Answers

Answer:

This is an equation of a parabola.

[tex](y+6)^2=4(x+1)[/tex]

Step-by-step explanation:

A conic section is a curve obtained by the intersection of a plane and a cone. The three major conic sections are parabola, hyperbola and ellipse (the circle is a special type of ellipse).

The standard equations for hyperbolas and ellipses all include x² and y² terms. The standard equation for a parabola includes the square of only one of the two variables.

Therefore, the equation y² - 4x + 12y + 32 = 0 represents a parabola, as there is no x² term.

As the y-variable is squared, the parabola is horizontal (sideways), and has an axis of symmetry parallel to the x-axis.

The conic form of a sideways parabola is:

[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]

where:

(h, k) is the vertex.(h+p, k) is the focus.x = h-p is the directrix.

To write the given equation in conic form, we need to complete the square for the y-variable.

Rearrange the equation so that the y-terms are on the left side:

[tex]y^2 + 12y = 4x - 32[/tex]

Add the square of half the coefficient of the y-term to both sides of the equation:

[tex]y^2 + 12y+\left(\dfrac{-12}{2}\right)^2 = 4x - 32+\left(\dfrac{-12}{2}\right)^2[/tex]

    [tex]y^2 + 12y+\left(-6\right)^2 = 4x - 32+\left(-6\right)^2[/tex]

         [tex]y^2 + 12y+36 = 4x - 32+36[/tex]

         [tex]y^2 + 12y+36 = 4x +4[/tex]

Factor the perfect square trinomial on the left side of the equation:

[tex](y+6)^2=4x+4[/tex]

Factor out the coefficient of the x-term from the right side of the equation:

[tex](y+6)^2=4(x+1)[/tex]

Therefore, the equation of the given conic section in conic form is:

[tex]\boxed{(y+6)^2=4(x+1)}[/tex]

where:

(-1, -6) is the vertex.(0, -6) is the focus.x = -2 is the directrix.

The conic section of the equation y² - 9x + 12y + 32 = 0 is a parabola

Selecting the conic section of the equation

The given equation is

y² - 9x + 12y + 32 = 0

The above equation is an illustration of a parabola equation

The standard form of a parabola is

(x - h)² = 4a(y - k)²

Where

(h, k) is the center

While the general form of the equation is

Ax² + Dx + Ey + F = 0

In this case, the equation y² - 9x + 12y + 32 = 0 takes the general form

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A city currently has 2.08 thousand residents. Each year the city's population grows by around 420 persons.

After 14 years what will the approximate population of the city be? Round to three significant digits.

Approximately
thousand residents.

Answers

Answer:

the approximate population of the city after 14 years will be 7.96 thousand residents.

Step-by-step explanation:

to calculate the approximate population of the city after 14 years, we need to take into account the annual growth rate.

Given that the city's population grows by around 420 persons each year, we can calculate the total growth over 14 years by multiplying the annual growth rate by the number of years:

14 years × 420 persons/year = 5,880 persons

To find the approximate population after 14 years, we add the total growth to the current population:

2.08 thousand + 5.88 thousand = 7.96 thousand

3. Determine whether the triangles are similar. If they are, write a similarity statement.
Look at picture for reference
Please show work

Answers

The triangles DEF and SRQ are not similar triangles

Identifying the similar triangles in the figure.

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

The triangles in this figure are

DEF and SRQ

These triangles are not similar

This is because:

The corresponding angles in the triangles are not equal

For DEF, the angles are

50, 90 and 40

For SRQ, the angles are

51, 90 and 39

This means that they are not similar by any similarity statement

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√7
7. Given that the sin(E)= 4 and TE = 4, determine the
remaining sides of A THE. Give exact answers.
E

Answers

Answer:

Step-by-step explanation:

To determine the remaining sides of triangle THE given that sin(E) = 4 and TE = 4, we can use the sine ratio.

The sine ratio is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.

In this case, sin(E) = 4/TE, which means the side opposite angle E is 4 and the hypotenuse TE is 4.

Using the Pythagorean theorem, we can find the length of the remaining side TH:

TH^2 = TE^2 - HE^2

TH^2 = 4^2 - 4^2

TH^2 = 16 - 16

TH^2 = 0

TH = 0

Therefore, the length of side TH is 0.

Find the midpoint of WZ of WXYZ with the vertices W(0, 0), X(h, 0), Y(h,b), and Z(0, b).

(0, h/2)
(h/2, b/2)
(0, b/2)
(h/2, 0)

Answers

Third option is correct.The midpoint of WZ of WXYZ with the vertices W(0, 0), X(h, 0), Y(h,b), and Z(0, b) is (0, b/2).

To find the midpoint of segment WZ, we need to average the x-coordinates and the y-coordinates of the endpoints.

The coordinates of point W are (0, 0), and the coordinates of point Z are (0, b).

To find the x-coordinate of the midpoint, we average the x-coordinates of W and Z:

(x-coordinate of W + x-coordinate of Z) / 2 = (0 + 0) / 2 = 0 / 2 = 0

To find the y-coordinate of the midpoint, we average the y-coordinates of W and Z:

(y-coordinate of W + y-coordinate of Z) / 2 = (0 + b) / 2 = b / 2

Therefore, the midpoint of segment WZ is (0, b/2).

So, the correct answer is (0, b/2).

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number 33!!!! this is a test !!!

Answers

33.) The volume of the given triangular prism would be= 36. That is option E.(NOTA)

How to calculate the volume of a triangular prism?

To calculate the volume of a triangular prism, the formula that should be used is given as follows;

Volume= BH

where;

B= area of base = 1/2 × base×height

= 1/2×4×3

= 6

H= 6

Volume= 6×6= 36.

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find the surface area of the composite figure 12cm x 2cm x 10cm x 3cm x 6cm x 8cm SA=

Answers

Answer:

If you are in Acellus trust me the answer is 394

Step-by-step explanation:

SA = 2 ( 2 x 12 ) + 2 ( 2 x 10 ) + ( 8 x 6 ) + 2 ( 3 x 8 ) + ( 3 x 6 ) + ( 12 x 16 )

SA = 48 + 40 + 48 + 48 + 18 + 192

SA = 394 square cm.

Team A and Team B together won 50% more games than Team C did. Team A won 50% as many games as Team B did. The three teams won 60 games in all. How many games did each team win?

Answers

Let's assign variables to represent the number of games won by each team:

Let x be the number of games won by Team A.
Let y be the number of games won by Team B.
Let z be the number of games won by Team C.

From the given information, we can form the following equations:

Equation 1: x + y + z = 60 (The total number of games won by the three teams is 60.)

Equation 2: x = (1/2)y (Team A won 50% as many games as Team B.)

Equation 3: x + y = 1.5z (Team A and Team B together won 50% more games than Team C.)

Now, let's solve this system of equations:

Substituting Equation 2 into Equation 3, we get:

(1/2)y + y = 1.5z
(3/2)y = 1.5z
y = (1.5z) * (2/3)
y = z

Substituting y = z into Equation 1, we have:

x + y + z = 60
x + y + y = 60
x + 2y = 60

Substituting y = z into Equation 3, we have:

x + y = 1.5z
x + y = 1.5y
x = 0.5y

Now, we can substitute x = 0.5y and y = z into Equation 1:

0.5y + 2y = 60
2.5y = 60
y = 60 / 2.5
y = 24

Substituting y = 24 into x = 0.5y:

x = 0.5 * 24
x = 12

Substituting y = 24 into the equation y = z:

z = 24

Therefore, Team A won 12 games, Team B won 24 games, and Team C won 24 games as well.

In circle M below, diameter AC, chords AB and BC, and radius MB
are drawn.



Answers

The statement which is not true about the circle M is ∆ABM is isosceles.

The correct answer choice is option 2.

Which statement is not true?

Based on the circle M;

diameter AC,

chords AB and BC,

radius MB

Isosceles triangle: This is a type of triangle which has two equal sides and angles.

Equilateral triangle is a triangle which has three equal sides and angles.

Hence, ∆ABM is equilateral triangle.

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Un objeto que se hace girar, se desplaza 25 radianes en 0.8 segundos. ¿cuál es la velocidad angular de dicho objeto?

Answers

The angular velocity of the object is 31.25 radians/second.

Angular velocity is defined as the change in angular displacement per unit of time. In this case, the object rotates a total of 25 radians in 0.8 seconds. Therefore, the angular velocity can be calculated by dividing the total angular displacement by the time taken.

Angular velocity (ω) = Total angular displacement / Time taken

Given that the object rotates 25 radians and the time taken is 0.8 seconds, we can substitute these values into the formula:

ω = 25 radians / 0.8 seconds

Simplifying the equation gives:

ω = 31.25 radians/second

So, the angular velocity of the object is 31.25 radians/second.

Angular velocity measures how fast an object is rotating and is typically expressed in radians per second. It represents the rate at which the object's angular position changes with respect to time.

In this case, the object completes a rotation of 25 radians in 0.8 seconds, resulting in an angular velocity of 31.25 radians per second. This means that the object rotates at a rate of 31.25 radians for every second of time.

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Note the translated question is:

An object that is rotated moves 25 radians in 0.8 seconds. what is the angular velocity of said object?

The points A, B and C have position vectors a, b, c, referred to an origin O. i. Given that the point X lies on AB produced so that AB : BX = 2 : 1, find x, the position vector of X, in terms of a and b. ii. If Y lies on BC, between B and C so that BY : Y C = 1 : 3, find y, the position vector of Y, in terms of a and b iii. Given that Z is the midpoint of AC, Calculate the ratio XY : Y Z.

Answers

i.  The position vector of X is 2b - a.

ii.  The position vector of Y is (3b + c)/4.

iii.  The ratio XY : Y Z is [tex]|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|[/tex]. Simplifying this expression will give us the final ratio.

i. To find the position vector x of point X, we can use the concept of vector addition. Since AB : BX = 2 : 1, we can express AB as a vector from A to B, which is given by (b - a). To find BX, we can use the fact that BX is twice as long as AB, so BX = 2 * (b - a). Adding this to the vector AB will give us the position vector of X: x = a + 2 * (b - a) = 2b - a.

ii. Similar to the previous part, we can express BC as a vector from B to C, which is given by (c - b). Since BY : YC = 1 : 3, we can find BY by dividing the vector BC into four equal parts and taking one part, so BY = (1/4) * (c - b). Adding this to the vector BY will give us the position vector of Y: y = b + (1/4) * (c - b) = (3b + c)/4.

iii. Z is the midpoint of AC, so we can find Z by taking the average of the vectors a and c: z = (a + c)/2. The ratio XY : YZ can be calculated by finding the lengths of the vectors XY and YZ and taking their ratio. Since XY = |x - y| and YZ = |y - z|, we have XY : YZ = |x - y|/|y - z|. Plugging in the values of x, y, and z we found earlier, we get XY : YZ =[tex]|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|[/tex].

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Please look at photo. Thank you. If you get it right I’ll give you a good rating!

Answers

a. The absolute maximum of g is 4.

The absolute minimum of g is -4.

b. The absolute maximum of h is 3.

The absolute minimum of h is -4.

What is a vertical asymptote?

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the graph of the polynomial function g shown above, we can logically deduce that its vertical asymptote is at x = 3. Furthermore, the absolute maximum of the polynomial function g is 4 while the absolute minimum of g is -4.

In conclusion, the absolute maximum of the polynomial function h is 3 while the absolute minimum of h is -4.

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Answer this question based on the table above. Choose the right answer.

Is the statement true that between 1966 and 1976 the average number of miles flown per passenger increased by one-third. (Yes or no)

Answers

Answer:

No

Step-by-step explanation:

To determine if the average number of miles flown per passenger increased by one-third between 1966 and 1976, we need to compare the increase in miles flown during that period.

According to the given table:

In 1966, the average number of miles flown per passenger was 711 miles.In 1976, the average number of miles flown per passenger was 831 miles.

To find the increase in miles flown, subtract the 1966 value from the 1976 value:

[tex]\begin{aligned}\sf Increase\; in\; miles\; flown &= \sf 831 \;miles - 711\; miles\\&= \sf 120\; miles\end{aligned}[/tex]

Therefore, the average number of miles flown per passenger between 1966 and 1976 increased by 120 miles.

To check if the increase is one-third of the initial value, we need to calculate one-third of the 1966 value:

[tex]\begin{aligned}\sf One\;third \;of \;711 \;miles &= \sf \dfrac{1}{3} \times 711\; miles\\\\ &= \sf \dfrac{711}{3} \; miles\\\\&=\sf 237\;miles\end{aligned}[/tex]

Since the increase in miles flown (120 miles) is not equal to one-third of the initial 1966 value (237 miles), the statement that the average number of miles flown per passenger increased by one-third between 1966 and 1976 is not true.

What are the dimensions of the rectangle shown on the coordinate plane?


The base is 5 units and the height is 3 units.
The base is 4 units and the height is 7 units.
The base is 7 units and the height is 5 units.
The base is 7 units and the height is 3 units.

Answers

Answer:

D The base is 7 units and the height is 3 units.

Step-by-step explanation:

The answer is d I counted the width/base then the height/length and found answer.

A restaurant offers 10 appetizers and 7 main courses. In how many ways can a person order a two-course meal?
There are
ways a person can order a two-course meal.

Answers

There are 70 ways a person can order a two-course meal from the given restaurant.

To determine the number of ways a person can order a two-course meal from a restaurant that offers 10 appetizers and 7 main courses, we can use the concept of combinations.

First, we need to select one appetizer from the 10 available options.

This can be done in 10 different ways.

Next, we need to select one main course from the 7 available options. This can be done in 7 different ways.

Since the two courses are independent choices, we can multiply the number of options for each course to find the total number of combinations.

Therefore, the number of ways a person can order a two-course meal is 10 [tex]\times[/tex] 7 = 70.

So, there are 70 ways a person can order a two-course meal from the given restaurant.

It's important to note that this calculation assumes that a person can choose any combination of appetizer and main course.

If there are any restrictions or limitations on the choices, the number of combinations may vary.

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9.
Find the volume of the cylinder. All measurements are in
centimeters. Keep your answer exact.
5

Answers

Answer:

The volume of the cylinder is 628.318530718

Step-by-step explanation:

The formula used to find the volume of a cylinder (v) is [tex]v = \pi r^2h[/tex], where r = radius and h = height. As the question says to keep the answer exact, we will be using pi as opposed to 3.14.

The radius is 5, and the height is 8. Plug these values into the equation and solve:

[tex]v =\pi *5^2*8[/tex]

[tex]v = 628.318530718[/tex]

So, the exact volume of the cylinder is 628.318530718. Rounded is 628.32

Answer:

200π or 628

Step-by-step explanation:

Note: your picture is not clear so I am assuming the height to be 8.

r = 5

h = 8

Volume = πr²h

= π * 5² * 8

= (25*8) π

= 200π

= 200*3.14

= 628

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Answers

Basketballs: 18

8 (footballs) x 2 = 16
16 + 2 = 18

Baseballs: 36

8 (footballs) x 5 = 40
40 - 4 = 36

Softballs: 24

36 (baseballs) / 2 = 18
18 + 6 = 24
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