The bars in this graph represent the favorite sport listed
by teenagers in a random sample.
Is this graph misleading?
Favorite Sports
O Yes, because the scale does not start at 0
Yes, because the bars are not the same height
O No, because the bars are all the same width
O No, because the scale starts at 0
20
18
16
Frequency
14
12
10
Basketball Football Lacrosse Soccer Volleyball
Favorite Sport

Answer: $1159.42

Step-by-step explanation:

A simple rule to remember
Specific Currency to Dollars ----> Divide
Dollars to Specific Currency ----> Multiply
R20,000/17.25

=$1159.42

Ryan will get 1160 dollars if he exchanges 20,000 into dollars.

The study and use of numbers, their relationships, and mathematical observations are topics covered by the area of mathematics known as arithmetic. The term "arithmetic" (which originates from the Greek word "arithmos," "number") often refers to the fundamental principles in number theory, measurement, and calculation (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).

As per the given data:

We are given the amount of money that Ryan had saved for a holiday in America.

We have to find out how much money in dollars Ryan will have after converting his money into dollars.

Money Ryan saved for the holiday (M) = 20,000

Conversion rate to dollar = 17.25 per dollar

Money Ryan have after converting into dollars:

= M / 17.25 dollars

= 20,000 / 17.25

= 1160 dollars

Ryan will get 1160 dollars if he exchanges 20,000 into dollars.

Hence, Ryan will get 1160 dollars if he exchanges 20,000 into dollars.

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Step-by-step explanation:

To find the greatest common factor (GCF) of 8, 16, and 40, we can determine the largest number that evenly divides all three of them.

Let's first find the prime factorization of each number:

- 8 = 2 * 2 * 2

- 16 = 2 * 2 * 2 * 2

- 40 = 2 * 2 * 2 * 5

Now, let's identify the common factors by finding the minimum exponent for each prime factor:

- 2 is a common factor with an exponent of 2 (appearing twice in the prime factorization of 8 and 16).

- 5 is not a common factor since it appears only in the prime factorization of 40.

The GCF is obtained by multiplying the common factors with their respective minimum exponents:

GCF = 2^2 = 4

Therefore, the greatest common factor of 8, 16, and 40 is 4.

Answer: \(y=Ce^(^3^t^{^9}^)\)

Step-by-step explanation:

Beginning with the first differential equation:

\(\frac{dy}{dt} =27t^8y\)

This differential equation is denoted as a separable differential equation due to us having the ability to separate the variables. Divide both sides by 'y' to get:

\(\frac{1}{y} \frac{dy}{dt} =27t^8\)

Multiply both sides by 'dt' to get:

\(\frac{1}{y}dy =27t^8dt\)

Integrate both sides. Both sides will produce an integration constant, but I will merge them together into a single integration constant on the right side:

\(\int\limits {\frac{1}{y} } \, dy=\int\limits {27t^8} \, dt\)

\(ln(y)=27(\frac{1}{9} t^9)+C\)

\(ln(y)=3t^9+C\)

We want to cancel the natural log in order to isolate our function 'y'. We can do this by using 'e' since it is the inverse of the natural log:

\(e^l^n^(^y^)=e^(^3^t^{^9} ^+^C^)\)

\(y=e^(^3^t^{^9} ^+^C^)\)

We can take out the 'C' of the exponential using a rule of exponents. Addition in an exponent can be broken up into a product of their bases:

\(y=e^(^3^t^{^9}^)e^C\)

The term e^C is just another constant, so with impunity, I can absorb everything into a single constant:

\(y=Ce^(^3^t^{^9}^)\)

To check the answer by differentiation, you require the chain rule. Differentiating an exponential gives back the exponential, but you must multiply by the derivative of the inside. We get:

\(\frac{d}{dx} (y)=\frac{d}{dx}(Ce^(^3^t^{^9}^))\)

\(\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*\frac{d}{dx}(3t^9)\)

\(\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*27t^8\)

Now check if the derivative equals the right side of the original differential equation:

\((Ce^(^3^t^{^9}^))*27t^8=27t^8*y(t)\)

\(Ce^(^3^t^{^9}^)*27t^8=27t^8*Ce^(^3^t^{^9}^)\)

QED

I unfortunately do not have enough room for your second question. It is the exact same type of differential equation as the one solved above. The only difference is the fractional exponent, which would make the problem slightly more involved. If you ask your second question again on a different problem, I'd be glad to help you solve it.

Answer:

m+2m-s

Step-by-step explanation:

Answer:

A: M + 2m - s

Step-by-step explanation:

Answer:

i think its 116

Step-by-step explanation:

Answer:

  96°

Step-by-step explanation:

You want the value of angle C in the diagram with two parallel lines and a triangle between them.

The sum of angles in a triangle is 180°, so the missing angle in the triangle is ...

  180° -60° -24° = 96°

Angle C and the one we just found are alternate interior angles with respect to the parallel lines and the transversal that forms those angles. As such, they are congruent:

  C = 96°

<95141404393>

Answer:

$93.74

Step-by-step explanation:

5/5-1/5=4/5

4u=74.99

1u=74.99÷4=18.7475

5u=18.7475x5=93.7375

93.7375=93.74

Hope this helps! Thanks.

The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:

Step 1: Divide the coefficient of x by 2 and square the result.

  (Coefficient of x) / 2 = -28/2 = -14

  (-14)² = 196

Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.

  g(x) = 4x² - 28x + 49

  = 4x² - 28x + 196 - 196 + 49

Step 3: Rearrange the terms and factor the perfect square trinomial.

  g(x) = (4x² - 28x + 196) - 196 + 49

  = 4(x² - 7x + 49) - 147

  = 4(x² - 7x + 49) - 147

Step 4: Write the perfect square trinomial as the square of a binomial.

  g(x) = 4(x - 7/2)² - 147

Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

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The probable question may be:

Rewrite the function by completing the square.

g(x)=4x²-28x +49

g(x)= ____  (x+___ )²+____.

Answer:

Y=x-5

2x+y=4

Step-by-step explanation:

Answer:

Plot these points:

For the line y = x - 5:

(0, -5)

(1, -4)

For the line 2x + y = 4:

(0, 4)

(1, 2)

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

The length of the third side of the triangle, to the nearest hundredth, is approximately 54.75 units.

1. We have a triangle with two known side lengths: 43 and 67 units.

2. The angle included between these sides measures 27 degrees.

3. To find the length of the third side, we can use the Law of Cosines, which states that \(c^2 = a^2 + b^2\) - 2ab * cos(C), where c is the third side and C is the included angle.

4. Plugging in the known values, we get \(c^2 = 43^2 + 67^2\) - 2 * 43 * 67 * cos(27).

5. Evaluating the expression on the right side, we get \(c^2\) ≈ 1849 + 4489 - 2 * 43 * 67 * 0.891007.

6. Simplifying further, we have \(c^2\) ≈ 6338 - 5156.898.

7. Calculating \(c^2\), we find \(c^2\) ≈ 1181.102.

8. Finally, taking the square root of \(c^2\), we get c ≈ √1181.102 ≈ 34.32.

9. Rounding to the nearest hundredth, the length of the third side is approximately 34.32 units.

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Answer:

Problem  says that the number line shows the graph of an inequality: A number line is shown from negative 5 to positive 5 with increments of 0.5. All the whole numbers are labeled on the number line. An empty circle is shown on the third mark to the left of 0. The region to the left of the empty circle is shaded. Graph is not given so I have created graph as per given description.

Now we have to select correct choice.

From graph we can easily see that third statement

"Yes it can, because −3.5 lies to the left of −1.5. " is correct.

Step-by-step explanation:

The answer is D

Answer:

\(\huge\boxed{(-19)^{-8}=19^{-8}}\)

Step-by-step explanation:

Use

\(a^n\times a^m=a^{n+m}\)

\((-19)^{-12}\times(-19)^4=(-19)^{-12+4}=(-19)^{-8}\)

Answer:

They r correct lol

Step-by-step explanation:

Hello!

x = the intersection

5x + 3 = 2x + 15

5x - 2x = 15 - 3

3x = 12

x = 12/3

x = 4

Answer: X=4

Step-by-step explanation: 5x + 3 and 2x + 15 are congruent. sub tract 3 from each side, 5x and 2x + 12 are equal. Subtract 2x from each side, 3x and 12 are equal. Divide each side by 3 and get X=4

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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The final answer for the surface area of the prism is 32 m^2 + 16h m^2.

To find the surface area of the prism, we need to calculate the area of each face and sum them up.

The prism has two identical square faces and four rectangular faces. The square face has a side length of 4 m. The area of one square face is given by:

Area of square face = side length^2 = 4^2 = 16 m^2

Since there are two square faces, the total area of the square faces is:

Total area of square faces = \(2 * 16 = 32 m^2\)

The rectangular faces have a length equal to the side length of the square face (4 m) and a width equal to the height of the prism. Let's assume the height of the prism is h. The area of one rectangular face is given by:

Area of rectangular face = length * width = \(4 * h = 4h m^2\)

Since there are four rectangular faces, the total area of the rectangular faces is:

Total area of rectangular faces = \(4 * 4h = 16h m^2\)

Therefore, the surface area of the prism is the sum of the areas of the square and rectangular faces:

Surface area of prism = Total area of square faces + Total area of rectangular faces

                          = \(32 m^2 + 16h m^2\)

                          = \(32 m^2 + 16h m^2\)

The answer for the surface area of the prism is 32 m^2 + 16h m^2.

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Answer:

\(x^2-x-3+\frac{5}{x+6}\)

Step-by-step explanation:

\(\frac{x^3+5x^2-9x-13}{x+6} \\ \\ =\frac{x^2(x+6)-x^2-9x-13}{x+6} \\ \\ =\frac{x^2(x+6)-x(x+6)-3x-13}{x+6} \\ \\ =\frac{x^2(x+6)-x(x+6)-3(x+6)+5}{x+6} \\ \\ =x^2-x-3+\frac{5}{x+6}\)

Answer: -15'5

it is very simple all you gotta do is times  6 x + 59 and thats your anwser

Answer:

1 hour and 15 min

Step-by-step explanation:

I think this is right but look it up just to be sure

Step-by-step explanation:48miles in 60 min. 1/4 of 60 is 1so 60 +15 = 1hr 15 min.

Answer:

\(\%Change = 58.33\%\)

Step-by-step explanation:

Given

\(Initial = 12\)

\(Final = 19\)

Required

Determine the percentage change

Percentage change is calculated as thus:

\(\%Change = \frac{|FInal - Initial|}{Initial} * 100\%\)

\(\%Change = \frac{|19 - 12|}{12} * 100\%\)

\(\%Change = \frac{|7|}{12} * 100\%\)

\(\%Change = \frac{7}{12} * 100\%\)

\(\%Change = \frac{7* 100\%}{12}\)

\(\%Change = \frac{700\%}{12}\)

\(\%Change = 58.33\%\)

Answer:

6.27 lbs

Step-by-step explanation:

Answer:

43.6 has 3 significant figures.

Answer:

y=-4x-4

Step-by-step explanation:

y=-4x-4

y=mx+b where m=slope and b=y-intercept.

Answer:

Anna had $125 in her account before the deposit. Here's the math:

$150 (current balance) - $25 (deposit) = $125 (previous balance)

angle E= 48° Angle W= 32°

from the first triangle,

calculating for the measure of E

32°+100° +m<E= 180° (sum of angle in a triangle equal 180°)

132°+m<E= 180

M<E= 180- 132= 48°

for the second triangle

calculating for the measure of W

48°+100°+m<W= 180°(sum of angle in a triangle equal 180°)

148° + W = 180°

W = 180-148= 32°

Answer:

-40x

Step-by-step explanation:

f(x) =-3x-5

g(x) =4x-2

(f+g)(x) =?

now,

f(g(x))

=f(4x-2)

=-3×4x-2-5

=-10×4x

=-40x

The values of f(0) that can be read from (a similar question in part (a) and (c)) the table, functions, and graph in the question are;

(a) f(0) = 1

(b) f(0) = 12

(c) f(0) = -2

Part of the question appears missing. From a similar question online, we have;

(a) A table of values;

x: -1, 0, 1, 2, 3

y: 7, 1, 6, -3, -4

Taking the function, f(x) = y, we have;

From the above values in the table, when x = 0, y = f(0) = 1

Therefore;

(b) y = 12 - 2•x²

Taking the function, f(x) = y, we have;

At x = 0, y = f(0) = 12 - 2 × 0² = 12

Therefore;

(c) A graph of a parabola passing through the points (-1, 3), (2, -6), (5, 3)

Let f(x) = a•x² + b•x + c, represent the function, we have;

f(-1) = 3 = a•(-1)² + b•(-1) + c = a - b + c

f(2) = -6 = a•(2)² + b•(2) + c = 4•a + 2•b + c

f(5) = 3 = a•(5)² + b•(5) + c = 25•a + 5•b + c

Solving the system of linear equations, (1), (2), (3) using a graphing calculator gives;

a = 1, b = -4, c = -2

Which gives;

f(x) = x² - 4•x - 2

Therefore;

f(0) = 0² + 4×0 - 2 = -2

Which gives;

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Answer:

A.

Step-by-step explanation:

The vertical line test is a way of finding out if a relation is a function.

Graph the relation.

Then imagine a vertical line moving from left to right over the graph of the relation.

If the vertical line intersects at most one point of the graph in any position you place the vertical line, then the relation is a function.

This function passes the vertical test since it never intersects more than one point on the vertical line at a time.

Answer: A.