if four out of every nine trick-or-treaters that came to your house last Halloween were dressed as Snow White, what proportion of trick-or-treaters were not dressed as Snow White?

Answer:

3√7 /7

Step-by-step explanation:

The rental car is getting approximately 37.56 miles per gallon.

To convert kilometers per liter (km/l) to miles per gallon (mpg), you can use the following conversion factor:

1 km/l ≈ 2.82475 mpg

Therefore, if your rental car is getting 13.3 km/l of gasoline, the equivalent value in miles per gallon would be:

13.3 km/l x 2.82475 mpg ≈ 37.56 mpg

So, your rental car is getting approximately 37.56 miles per gallon.

Learn more about conversion factor click;

https://brainly.com/question/30567263

#SPJ1

The range of this quadratic function y = x² - 2x - 3 is all real numbers greater than 2.

Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x  is defined.

We know a quadratic function y = ax² + bx + c is a graph of a parabola that opens upwards as the coefficient of x² is positive.

Given,  y = x² - 2x - 3.

y = x² - 3x + x - 3.

y = x(x - 3) + 1(x - 3).

y = (x - 3)(x + 1).

Now the x-intercepts are at 3 and -1 so the vertex is located at (3 - 1)/2 = 2.

So the range of this function is all real numbers greater than 2 as the parabola opens upwards.

learn more about the domain and range here :

https://brainly.com/question/28135761

#SPJ1

Answer:

Step-by-step explanation:

You can  calculate the length of side a using the Cosine Rule:

a^2 = 32.6^2 + 41.4^2 - 2.32.6.42.4 cos pi/6

a^2 = 456.01

a = √456.01

a = 21.35

By the Sine Rule:

32.6 / sin B = 21.35 / sin pi/6

sin B =  (32.6 * sin pi/6) / 21.35

sin B = 0.76347

B = 0.869 radians.

C = pi - pi/6 - 0.869 = 1.749 radians.

ANSWER

EXPLANATION

We want to find the number of different combinations of colors possible if both spinners are spun at once.

To do this, we have to find the product of the number of colors on each spinner.

That is:

The answer is option B.

Here proof i.e. ∠1=∠3 is also given in the image for the given geometric shape.

What are geometric shapes?

In Mathematics, Geometric shapes are the figures which demonstrate the shape of the objects we see in our everyday life. In geometry, shapes are the forms of objects which have boundary lines, angles and surfaces. There are different types of 2d shapes and 3d shapes.

Shapes are also classified with respect to their regularity or uniformity. A regular shape is usually symmetrical such as a square, circle, etc. Irregular shapes are asymmetrical. They are also called freeform shapes or organic shapes. For example, the shape of a tree is irregular or organic.

In plane geometry, the two-dimensional shapes are flat shapes and closed figures such as circles, squares, rectangles, rhombus, etc.  In solid geometry, the three-dimensional shapes are cube, cuboid, cone, sphere and cylinder. We can observe all these shapes in our daily existence also. For example books (cuboid shape), glasses (cylindrical shape), traffic cones (conical shape) and so on.

Now

To prove   ∠1=∠3

Here as given ∠1+∠4=180°

and also ∠2+∠3=180°    (supplementary angles)

therefore,

∠1+∠4=∠2+∠3

and also ∠2=∠4  ( complementary angles)

Hence,

          ∠1=∠3

To know more about geometric shapes visit the link

brainly.com/question/10059415?referrer=searchResults

#SPJ1

Answer:

The solution to the equation system given is:

Step-by-step explanation:

First, we must know the equations given:

Following Crammer's Rule, we have the matrix form:

\(\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] =\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]\)

Now we solve using the determinants:

\(x=\frac{\left[\begin{array}{ccc}1&3\\5&1\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(1*1)-(5*3)}{(2*1)-(3*3)} = \frac{1-15}{2-9} =\frac{-14}{-7} = 2\)

\(y=\frac{\left[\begin{array}{ccc}2&1\\3&5\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(2*5)-(3*1)}{(2*1)-(3*3)}=\frac{10-3}{2-9} =\frac{7}{-7}=-1\)

Now, we can find the answer which is x= 2 and y= -1, we can replace these values in the equation to confirm the results are right, with the first equation:

And, with the second equation:

The outcome of multiplying by 8/3 is the same as multiplying with 8 and then by 1/3.

The two fractions that want to multiply come first when multiplying fractions.

For the stated number.

The number given is 8/3.

Other set of numbers are-

Multiplying 1/3 with 8.

= 1/3*8

= (1*8)/3

= 8/3, which is equal to the stated number.

Thus, the outcome of multiplying by 8/3 is the same as multiplying with 8 and then by 1/3.

To know more about the multiplication of fraction, here

https://brainly.com/question/869839

#SPJ1

Answer:

see image.

Step-by-step explanation:

The first step is to convert the equation into slope-intercept form

2x - 4y = 6

2x - 6 = 4y

(2x - 6) / 4 = y

y = 1/2x - 6/4

The next step is to highlight the area where x is less than y.

Answer:

\(x < 3 + 2y\)

Step-by-step explanation:

\(1. \: 2(x - 2y) < 6 \\ 2. \: x - 2y < \frac{6}{2} \\ 3. \: x - 2y < 3 \\ 4. \: x < 3 + 2y\)

Answer:

8

Step-by-step explanation:

i guessed

Answer:

x=16 because the proportional size, this also means that if the -84 becomes 16 in proportion size.

The detailed definition of binary operation is given below.

Binary operations are the operations which are performed on a specific set.

If the operation is defined on a set X, then binary operation can be defined as,

* : X * X → X.

Given statement is

A binary operation on a set S is a mapping of the Cartesian product S × S into S.

Cartesian product is the ordered set of a given set.

Cartesian product of a set S is defined as,

S × S = { (s₁, s₂) | s₁ ∈ S and s₂ ∈ S}

For example S = {1, 2, 3, ......., 10}

Then S × S will consist of ordered pairs of the form (x, y) such that x and y belongs to the set S = {1, 2, 3, ......., 10}.

That is  S × S = {(1, 1), (1, 2), ......, (1, 10), (2, 1), ....., (2, 10),(3, 1), ......,......,(10, 10)}

Let the binary operation defined is multiplication from S × S to S.

1 × 1 = 1 ∈ S

2 × 4 = 8 ∈ S

But 3 × 10 = 30 ∉ S

Hence the binary operation is defined .

Learn more about Binary Operations here :

https://brainly.com/question/26216148

#SPJ1

An equation of the new graph is: A. y = ∣x - 4∣ - 9.

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) + N

Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:

y = ∣x - 4∣ - 9

Read more on function and translation here: brainly.com/question/31559256

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

x

Step-by-step explanation:

the figure always contains an x!;)

Answer:

To answer these, we can use the standard normal distribution & z-scores. A z-score represents the number of standard deviations a value is from the mean. The formula to calculate a z-score is: z = (x - μ) / σ, where x is the value, μ is the mean and σ is the standard deviation.

A) To find the proportion of pregnancies that last more than 278 days, we first calculate the z-score for 278 days: z = (278 - 272) / 12 = 0.5. Using a standard normal distribution table, we find that the proportion of values above a z-score of 0.5 is approximately 0.3085. So, about 30.85% of pregnancies last more than 278 days.

B) To find the proportion of pregnancies that last between 257 and 275 days, we first calculate the z-scores for both values: z1 = (257 - 272) / 12 = -1.25 and z2 = (275 - 272) / 12 = 0.25. Using a standard normal distribution table, we find that the proportion of values between z-scores of -1.25 and 0.25 is approximately 0.3944. So, about 39.44% of pregnancies last between 257 and 275 days.

C) To find the probability that a randomly selected pregnancy lasts no more than 266 days, we first calculate the z-score for 266 days: z = (266 - 272) / 12 = -0.5. Using a standard normal distribution table, we find that the proportion of values below a z-score of -0.5 is approximately 0.3085. So, there is about a 30.85% chance that a randomly selected pregnancy lasts no more than 266 days.

D) To determine if very preterm babies are unusual, we first calculate the z-score for 242 days: z = (242 - 272) / 12 = -2.5. Using a standard normal distribution table, we find that the proportion of values below a z-score of -2.5 is approximately 0.0062. Since this value is less than 0.05, we can conclude that very preterm babies are unusual.

Answer:

Y=KX so its 10=K2

Step-by-step explanation:

Plug in the Number OR K=y/x

The second number in the ordered pair is the y coordinate.

The second value of an ordered pair is the y-value.

It signifies how far above (or below) the x axis o (horizontal axis) that a point is. If the y value is positive, then the point is above the x-axis, but if it is negative it is below the x axis (when it's 0, the point is on the x-axis)

**NOTE** the x and y axes are on the Cartesian plane

The exact value of the specified trigonometric identity found using the the trigonometric identity for tan(A - B) and tan(arccos(x)) and tanarcsin(x)) is presented as follows;

\(tan\left(sin^{-1}\left(\dfrac{3}{4} \right) - cos^{-1}\left(\dfrac{1}{5}\right) \right) =\dfrac{32\cdot \sqrt{6}- 75\cdot \sqrt{7} }{209}\)

A trigonometric identity is an equality that involves trigonometric functions that is valid for all values of the arguments of the equation

The required trigonometric identities are;

\(tan (A - B) = \dfrac{tan(A) -tan(B)}{1-tan(A)\cdot tan(B)}\)

\(tan(sin^{-1}(x)) = \dfrac{x}{\sqrt{1-x^2} }\)

\(tan(cos^{-1}(x)) = \dfrac{\sqrt{1-x^2}}{x }\)

Therefore;

\(tan\left(sin^{-1}\left(\dfrac{3}{4} \right) - cos^{-1}\left(\dfrac{1}{5}\right) \right) = \dfrac{tan\left(sin^{-1}\left(\dfrac{3}{4} \right)\right)-tan\left(cos^{-1}\left(\dfrac{1}{5} \right)\right)}{1-tan\left(sin^{-1}\left(\dfrac{3}{4} \right)\right)\times tan\left(cos^{-1}\left(\dfrac{1}{5} \right)\right)}\)

Which gives;

\(\dfrac{\dfrac{\frac{3}{4} }{\sqrt{1-\left(\frac{3}{4} \right)^2} } -\dfrac{\sqrt{1-\left(\frac{1}{5} \right)^2}}{\frac{1}{5} } }{1+\dfrac{\frac{3}{4} }{\sqrt{1-\left(\frac{3}{4} \right)^2} } \times \dfrac{\sqrt{1-\left(\frac{1}{5} \right)^2}}{\frac{1}{5} }}=\dfrac{\dfrac{3\cdot \sqrt{7}-14\cdot \sqrt{6} }{7} }{\dfrac{7+6\cdot \sqrt{42} }{7} }\)

\(\dfrac{\dfrac{3\cdot \sqrt{7}-14\cdot \sqrt{6} }{7} }{\dfrac{7+6\cdot \sqrt{42} }{7} }=\dfrac{32\cdot \sqrt{6}- 75\cdot \sqrt{7} }{209}\)

Which indicates that we have;

\(tan\left(sin^{-1}\left(\dfrac{3}{4} \right) - cos^{-1}\left(\dfrac{1}{5}\right) \right) =\dfrac{32\cdot \sqrt{6}- 75\cdot \sqrt{7} }{209}\)

Learn more about trigonometric identity here:

https://brainly.com/question/24496175

#SPJ1

Answer:

Step-by-step explanation:

equation perpendicular to y = 6x + 3 is y = (-1/6)x + k

the line passes through (-6,4)

putting the value we get, 4 = 1 + k

                                           k = 3

So equation is y = (-1/6)x + 3

Answer:

Point A is at (0, –4).

Point B is at (–8, –7).

Step-by-step explanation:

point A is 4 units down : y = –4

Point B is 8 units to the left : x = –8

and 7 units down: y = –7

A : (0, –4)

B : ( –8, –7)

Answer:

2 units

Step-by-step explanation:

vertical distance will be the magnitude of the difference in the 'y' coordinates

| -.8 - 1.2| = 2 units

The numbers 0, 1, and -1 are zeros of multiplicity 1.

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

To find the zeros of the function \(y=7x^3-7x\), we can set y equal to zero and solve for x:

\(7x^3 - 7x = 0\)

Factor out 7x:

\(7x(x^2 - 1) = 0\)

Factor the quadratic expression:

7x(x - 1)(x + 1) = 0

The zeros of the function are the values of x that make y equal to zero. From the factored expression, we see that the zeros are:

x = 0 (with multiplicity 1)

x = 1 (with multiplicity 1)

x = -1 (with multiplicity 1)

Therefore, the correct choice is: The numbers 0, 1, and -1 are zeros of multiplicity 1.

Learn more about quadratic equation , by the following link.

https://brainly.com/question/1214333

#SPJ1

Answer:

x < -3 or x > 2

Step-by-step explanation:

x² + x - 6 > 0

Convert the inequality to an equation.

x² + x - 6 = 0

Factor using the AC method and get:

(x - 2) (x + 3) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x - 2 = 0

x = 2

x + 3 = 0

x = -3

So, the solution is x < -3 or x > 2

Answer:

Step-by-step explanation:

The zeros of the function defined by

h(x) = x³ – 4x² – 5x are x = 0, x = 5 and x = -1

The zeros of a function, also referred to as roots or x-intercepts, occur at x-values where the value of the function is 0. It is simply the values of x when f(x) is equal to 0.

For x = 0, we substitute 0 for x in the function h(x);

h(0) = (0)³ - 4(0)² - 5(0)

h(0) = 0

For x = 1, we substitute 1 for x in the function h(x);

h(1) = (1)³ - 4(1)² - 5(1)

h(1) = 1 - 4 - 5

h(1) = -8

For x = -5, we substitute -5 for x in the function h(x);

h(-5) = (-5)³ - 4(-5)² - 5(-5)

h(-5) = -125 - 100 +25

h(-5) = -200

For x = 5, we substitute 5 for x in the function h(x);

h(5) = (5)³ - 4(5)² - 5(5)

h(5) = 125 - 100 - 25

h(5) = 0

For x = -1, we substitute -1 for x in the function h(x);

h(-1) = (-1)³ - 4(-1)² - 5(-1)

h(-1) = -1 - 4 + 5

h(-1) = 0

Therefore, the values of x that makes the function h(x) = x³ – 4x² – 5x equal to zero are; 0, 5, and -1, they are the zeros of the function h(x).

Know more about zeros of a function here: https://brainly.com/question/16550963

#SPJ1

Answer: 0.05

Step-by-step explanation:

Since 95 out of 100 were closed, the closed window is 95% = 0.95.

5 open windows = 5% = 0.05

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Step-by-step explanation:

The roots are equal, so the discriminant equals 0.

b² − 4ac = 0

(2k)² − 4 (k²−1) (3k+1) = 0

4k² − 4 (3k³ + k² − 3k − 1) = 0

k² − (3k³ + k² − 3k − 1) = 0

k² = 3k³ + k² − 3k − 1

0 = 3k³ − 3k − 1

Answer:

49

Step-by-step explanation:

Work is shown in the image

Answer:

  y = (-1/80)x^2 +2x

Step-by-step explanation:

The graph of the equation for the arch will go through the points ...

  (0, 0), (160, 0), (80, 80)

We can start by making use of the zeros to write the function ...

  y = a(x -0)(x -160)

To make the graph go through the point (80, 80), we must have ...

  80 = a(80 -0)(80 -160) = (-80^2)a

  -1/80 = a . . . . . . divide by the coefficient of "a"

So, our equation is ...

  y = (-1/80)x(x -160)

  y = (-1/80)x^2 +2x