The following data represent the miles per gallon for a particular make and model car for six randomly selected vehicles. Compute the mean, median, and mode miles per gallon 24.2. 22.2. 37.8, 22.7. 35 4. 31.61. Compute the mean miles per gallon. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mean mileage per gallon is _______B. The mean does not exist 2. Compute the median miles per gallon. Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The median mileage per gallon is __________B. The median does not exist. 3. Compute the mode miles per gallon. Select the correct choice below and, if necessary,fill in the answer box to complete your choice. A. The mode is _________B. The mode does not exist.

Answer:

C. y = 66

Step-by-step explanation:

this is a equal triangle so you know you have to find out what that one angle is to get the rest

180 - 114 = 66

Answer:

Step-by-step explanation:

The volume of a cube is given by the formula :

a³ (where a is the side length )

So now we have to cube these lengths :

Part A :

(3x²y)³ =

(3x²y)(3x²y)(3x²y) =

(9x^4y²)(3x²y) =

27x^6y³ (This is now fully simplified so our final answer for a)

Part B:  

(5y²)³ =

(5y²)(5y²)(5y²) =

(25y^4)(5y²) =

125y^6 (This is now fully simplified so our final answer for b)

Hope this helped and have a good day

The property illustrated in equation 4(-8+5) = -32 + 20 is the Distributive Property.

The Distributive Property states that when a number is multiplied by a sum or difference in parentheses, it can be distributed or multiplied by each term inside the parentheses separately, and then the results can be added or subtracted.

In this case, the number 4 is multiplied by the sum (-8 + 5). By applying the Distributive Property, we distribute the 4 to each term inside the parentheses:

4(-8 + 5) = (4 * -8) + (4 * 5)

This simplifies to:

4(-8 + 5) = -32 + 20

Finally, we can perform the addition:

-32 + 20 = -12

Therefore, the equation demonstrates the application of the Distributive Property.

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Answer:

The opposite sides are parallel. AB - CD, AC - BD. Parallelograms are always opposite equal. If not, they are not one.

Proven AB = CD and BC = DA

A parallelogram is a quadrilateral with opposite sides parallel.

Given ABCD is a parallelogram

In parallelogram ABCD, compare triangles ABC and CDA. In these triangles

AC = CA (common side)

∠BAC = ∠DCA (alternate interior angles)

∠BCA = ∠DAC (alternate interior angles)

Hence by the Angle side Angle criterion, both the triangles are congruent and the corresponding sides are equal.

Therefore we have AB = CD, and BC = AD.

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Answer:

no

Step-by-step explanation:

The required by the principle of mathematical induction, the statement is true for all integers n ≥ 0.

Mathematical induction is a method of proof commonly used in mathematics to prove that a statement is true for all positive integers.

The process involves two steps:

Here,
First, we need to prove the statement is true for the base case n=0,

When n=0, we have,

\(\sum_{i=1}^{1} i * 2^i = 1*2^1 = 2\)

and

\(n * 2^{n+2} + 2 = 0*2^{0+2} + 2 = 2\)

Therefore, the statement is true for n=0.

Next, we assume the statement is true for some arbitrary integer k, meaning:

\(\sum_{i=1}^{k+1} i * 2^i = k * 2^{k+2} + 2\)

We want to show that the statement is also true for n=k+1,

\(\sum_{i=1}^{k+2} i * 2^i = (k+1) * 2^{k+3} + 2\)

We can rewrite the left-hand side of the equation as,

\(=\sum_{i=1}^{k+2} i * 2^i \\= \sum_{i=1}^{k+1} i * 2^i + (k+2) * 2^{k+2} \\= k * 2^{k+2} + 2 + (k+2) * 2^{k+2} \\= (k+1) * 2^{k+3} + 2\)

This last step used the assumption that the statement is true for n=k.

Therefore, by the principle of mathematical induction, the statement is true for all integers n ≥ 0.

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The motor oil dealer will have to use both tanks since he needs 15 gallons of oil but will still be short by one gallons.

The motor oil dealer will have to use both tanks since he needs 15 gallons of oil but will still be short by one gallons.

A motor oil store has two tanks: one holds 12 gallons of oil, and the other holds 2 gallons of oil. In order to determine which tank will require to fill the bottles, the following computation must be done:

Quarts to gallons is 4 to 1.

1/4 x 60 = X

60/4 = X

15 = X

Since the motor oil vendor requires 15 gallons of oil, he must use both tanks but will still be short by 1 gallons

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Answer:

Ok simple Algebra Question:

Let "x" be the number of miles she drives.

18.95 + 0.16x = 40.00

Subtract 18.95 from both sides.

0.16x = 21.05

Divide both sides by 0.16

You get:

x = 131.5625

Round to nearest mile:

Answer is: 132

Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

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The equation of the Parabola in vertex form that has a vertex of (4, -2) and a y-intercept of (0, -66) is:y = -4(x - 4)^2 - 2

The vertex form of a parabola is given by:y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola.

We are given that the vertex is (4, -2), so we can substitute these values in the equation to get:y = a(x - 4)^2 - 2

Now, we need to find the value of "a". To do this, we can use the fact that the y-intercept is (0, -66). Since the point (0, -66) lies on the parabola, we can substitute x = 0 and y = -66 in the equation above to get:-66 = a(0 - 4)^2 - 2

Simplifying this, we get:-66 = 16a - 2

Adding 2 to both sides, we get:-64 = 16a

Dividing both sides by 16, we get:a = -4

Substituting this value of "a" in the equation above, we get the equation of the parabola in vertex form:y = -4(x - 4)^2 - 2

Therefore, the equation of the parabola in vertex form that has a vertex of (4, -2) and a y-intercept of (0, -66) is:y = -4(x - 4)^2 - 2

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The probability of rolling a number less than 12 is 91.6%.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

each case in the set is mutually exclusive with the others in the set, the probability that any one of its components will occur is equal to the sum of its component probabilities.

We can have the number 12, the probality will be 1/12

So the probability of rolling a number less than 12 is = (1 -  probability of 12)

=1-1/12

=11/12

=0.916

Hence the probability of rolling a number less than 12 is 91.6%.

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Answer:

2/16

Step-by-step explanation:

1/8 * 2/2 = 2/16

Answer:

2/16

Step-by-step explanation:

Hope this helped!!!

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Answer:

\(\sqrt{4}, \ \sqrt{9} \text{ are rational numbers.}\)

Step-by-step explanation:

Hello,

\(\sqrt{n^2}=n \ for \ n\geq 0\\\\\text{For instance}\\\\\sqrt{2^2}=2=\sqrt{4}\\\\\sqrt{3^2}=3=\sqrt{9}\)

Answer:

all real values of x where x < -1

The correct statement is all real values of x where x < -1.

Option A is the correct answer.

We have,

To determine the values for which the graph of the function

f(x) = (x - 3)(x + 1) is positive and decreasing, we need to analyze the behavior of the function.

Let's consider the factors individually:

(x - 3): This factor is positive for x > 3 and negative for x < 3.

(x + 1): This factor is positive for x > -1 and negative for x < -1.

To determine the overall sign of the function, we need to consider the signs of both factors together.

When both factors are positive or both factors are negative, the function is positive.

When the factors have opposite signs, the function is negative.

From the above analysis, we can conclude the following:

When x > 3, both factors are positive, so the function is positive.

When -1 < x < 3, the factor (x - 3) is negative, while the factor (x + 1) is positive. Therefore, the function is negative.

When x < -1, both factors are negative, so the function is positive again.

Since we are looking for values where the function is positive and decreasing, we can eliminate the options that include positive and increasing regions (such as x > 3).

Thus,

The correct statement is all real values of x where x < -1.

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1598 cm square is the area of the container.

According to the statement

we have given that the container is rectangular prism

And Length of rectangular prism is 34cm

Width of rectangular prism is 17 cm

Height of rectangular prism is 20 cm

we use the below written formula to find the surface area

Surface area formula A=(wl+hl+hw)

To find the surface area of the container.

Substitute the values of Length, width and height in the formula then

A=(wl+hl+hw)

A=((17)(34)+(20)(34)+(20)(17))

After solving the values

A=(578+680+340)

A= 1598

So, 1598 cm square is the area of the container.

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El supplemento y el complemento de cada ángulo son, respectivamente:

Caso A: m ∠ A' = 43°

Caso B: m ∠ A' = 31°

De acuerdo con la geometría, la suma de un ángulo y su complemento es igual a 90° and la suma de un ángulo y su suplemento es igual a 180°. Matemáticamente hablando, cada situación es descrita por las siguientes formulas:

Ángulo y su complemento

m ∠ A + m ∠ A' = 90°

Ángulo y su suplemento

m ∠ A + m ∠ A' = 90°

Donde:

Ahora procedemos a determinar cada ángulo faltante:

Caso A: Complemento

47° + m ∠ A' = 90°

m ∠ A' = 43°

Caso B: Suplemento

149° + m ∠ A' = 180°

m ∠ A' = 31°

El enunciado se encuentra escrito en español y la respuesta está escrita en el mismo idioma.

The statement is written in Spanish and its answer is written in the same language.

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The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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Answer:

73

Step-by-step explanation:

so basically this process is rather easy, okay what u have to do is find the area but since u cant u just have to try your best and go over the answer with a friend, oh you have none? Sorry for assuming, so just ask siri if you have 0 friends, the formula should look a little like this:

A=l*w or A=b*h

which than u would have to add up the circumference (sorry for not mentioning that earlier) so the new formula would be a little like this

A+C=

than thats your answer (it should be 12.)

Answer:

42

Step-by-step explanation:

The correct radical form of b^1/5 is 5^√b.

Square root and nth roots are represented by the symbol "radical," which. a square root is a component of a radical expression, which is an expression.

A number's or an algebraic expression's simplest radical form is referred to as this. When a number or algebraic expression contains no elements that are perfect nth powers under the radical, it is said to have an nth root and is said to be in its simplest radical form.

When a number or algebraic expression contains no elements that are perfect nth powers under the radical, it is said to have an nth root and is said to be in its simplest radical form.

Explanation:

Convert to radical form using the formula

a^x/n=n^√a^x

5^√b.

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Answer:

Quadrant V

Step-by-step explanation:

A co-ordinate graph only has 4 quadrants!

Answer:

The first lower quartile is 15

The median is 25

Step-by-step explanation:

Answer:

modulus just changed negative to positive so 5 minus 3 = 2

The proof that z lies on the x-axis is shown below

For z to lie on the x-axis, then the coordinate must be represented as (x, 0)

Given that

\(\frac{|z - 5i|}{|z + 5i|} = 1\)

We start by simplifying the given expression using the definition of the modulus of a complex number:

So, we have

\(\frac{|z - 5i|}{|z + 5i|} = \frac{\sqrt{(x - 0)^2 + (y - 5)^2}}{\sqrt{(x - 0)^2 + (y + 5)^2}} = 1\)

Where

z = x + yi or z = (x, y)

Squaring both sides of the equation above, we obtain:

\(\frac{(x - 0)^2 + (y - 5)^2}{(x - 0)^2 + (y + 5)^2} = 1\)

This gives

\(\frac{x^2 + (y - 5)^2}{x^2 + (y + 5)^2} = 1\)

By comparison, we have

\((y + 5)^2 = (y - 5)^2\)

Set y = 0 to test the equation

So, we have

\((0 + 5)^2 = (0 - 5)^2\)

25 = 25 --- true

The equation is true for y = 0

This means that

z = (x, 0)

Hence, z lies on the x-axis

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Answer:

Intersecting (fourth answer choice)

Step-by-step explanation:

First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where

Converting y - 3x = 4x to slope-intercept form:

(y - 3x = 4x) + 3x

y = 7x

Thus, the slope of this line is 7 and the y-intercept is 0.

Converting 6 - 2y = 8x to slope-intercept form:

(6 - 2y = 8x) - 6

(-2y = 8x - 6) / -2

y = -4x + 3

Thus, the slope of this line is -4 and the y-intercept is 3.

Checking if y = 7x and y = -4x + 3 are perpendicular lines:

We can show this in the following formula:

m2 = -1 / m1, where

Thus, we only have to plug in one of the slopes for m1.  Let's do -4.  

m2 = -1 / -4

m2 = 1/4

Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.

 Checking if y = 7x and y = -4x + 3 are parallel lines:

The slopes of parallel lines are equal to each other.

Because 7 and -4 are not equal, the two lines are not parallel.

Checking if the lines intersect:

Method to solve the system:  Elimination:

We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:

-1 (y = 7x)

-y = -7x

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

    -y = -7x

+

    y = -4x + 3

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

(0 = -11x + 3) - 3

(-3 = -11x) / 11

3/11 = x

Now we can plug in 3/11 for x in y = 7x to find y:

y = 7(3/11)

y = 21/11

Thus, x = 3/11 and y = 21/11

We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3.  If we get the same answer on both sides of the equation for both equations, the lines intersect:

Checking solutions (x = 3/11 and y = 21/11) for y = 7x:

21/11 = 7(3/11)

21/11 = 21/11

Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:

21/11 = -4(3/11) + 3

21/11 = -12/11 + (3 * 11/11)

21/11 = -12/11 + 33/11

21/11 = 21/11

Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).

This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.

Answer:

three and three ninths plus seven and six-elevenths equals ten and eighty-seven ninety ninths

Step-by-step explanation:

Pls mark me brainliest

Answer:

First and last

Step-by-step explanation:

Answer:

Step-by-step explanation:

fork knife

The Surface Area of cylinders are: 100 yd² , 264 m², 226  mm²

The Surface Area of Can is 219 cm².

We know the formula for Surface Area of Cylinder

= 2πrh

1. Radius = 2 yd

Height = 8 yd

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 2 x 8

= 100 yd²

2. Radius = 7 m

Height = 6 m

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 6 x 7

= 264 m²

3. Radius = 3 mm

Height = 12 mm

So,  Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 3 x 12

= 226  mm²

4. Radius = 3.5 cm

Height = 10 cm

So, Surface Area of Can

= 2πrh

= 2 x 3.14 x 3.5 x 10

= 219 cm²

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