How far did they travel per hour

Using the given information, the percent error is 52%

From the question, we are to calculate the percentage error

From the given information,

Prediction = 23 people

Actual = 48 people

Using the formula,

\(Percent \ error = \frac{|Prediction - Actual|}{|Actual|}\times 100\%\)

\(Percent \ error = \frac{|23 - 48|}{|48|}\times 100\%\)

\(Percent \ error = \frac{|-25|}{|48|}\times 100\%\)

\(Percent \ error = \frac{25}{48}\times 100\%\)

Percent error = 52.083%

Percent error ≈ 52%

Hence, the percent error is 52%

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After solving the given expression, the value obtained will be equal to 7/12.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the given fraction in the question,

4/6 - 1/12

Take LCM as 12 and then solve,

= (8 - 1)/12

= 7/12

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The volume of the solid generated when the region bounded by y = 9x and y = 27x/x is revolved around the x-axis is given by V = 27lnx - 9x + c

To calculate this volume, we need to calculate the area of the cross-section of a shell at x.

The cross-section is found by taking the difference of the two curves, y = 9x and y = 27x/x, at that particular x in the form of a rectangle.

The height of the rectangle is y₂ - y₁ and the width is the interval dx. Therefore, the area of the cross-section is given by

A(x) = (y₂ - y₁)dx = [(27x/x - 9x)dx].

The volume of the solid is then given by the formula

=> V = ∫A(x)dx.

Substituting in the expression for A(x), we have

=>  V = ∫(27x/x - 9x)dx.

Integrating this expression, we get V = 27lnx - 9x + c, where c is an arbitrary constant.

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The volume of the solid is 1.5 cubic units. From the solid in the first octant under the plane z = x + y, above the surface z = xy, and enclosed by the surfaces x = 0, y = 0, and x2 + y2 = 4

To find the volume of the solid by subtracting two volumes, we need to find the limits of integration for x, y, and z.

From the given information, we know that the solid is in the first octant and is enclosed by the surfaces x = 0, y = 0, and x2 + y2 = 4. Thus, the limits of integration for x and y are 0 to 2 since the radius of the circle x2 + y2 = 4 is 2.

Next, we need to find the limits of integration for z. To do this, we need to set the two given equations equal to each other:

xy = x + y

xy - x - y = 0

Using partial fraction decomposition:

xy - x - y = (x - 1)(y - 1) - 1

So, we have:

(x - 1)(y - 1) = z - 1

Thus, the limits of integration for z are 1 to 3.

Now, we can set up the integral to find the volume:

V = ∫∫∫ dV

V = ∫0^2 ∫0^(2 - x) ∫1^(x + y) dz dy dx

Evaluating this integral, we get the volume of the solid as 1.5 cubic units.

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Answer:

See below ~

Step-by-step explanation:

We need to prove that the figures are similar by applying the various kinds of transformations.

===============================================================

Question A :

⇒ Compare the side lengths of A and B

⇒ 2 : 5 (for all sides)

⇒ 1 : 2.5

⇒ Hence, Shape A has been dilated with a scale factor of 2.5 to form Shape B

=============================================================

Question B :

⇒ Compare the side lengths of A and B

⇒ A : B = 2 : 6

⇒ A : B = 1 : 3

⇒ Shape A has been dilated with a scale factor of 1/3 to form Shape B

The evaluation of the details in the question to obtain the equation and the amount earned is presented as follows;

11. Part A

The required equation for determining the amount Stephany earned for mowing her neighbors grass is; Equation: 20 = 8.75 + 3.5 + x

x = The amount Stephany earned for mowing her neighbors grass

Part B

The amount Stephany earned for mowing her neighbors grass is; $7.75

An equation expresses an equivalence between a mathematical expression and other mathematical expressions or numbers.

11. Part A

The amount Stephane earned for baby sitting = $8.75

The amount Stephane earned for doing her chores = $3.5

The total amount Stephane earned in total = $20.00

The amount she earned for mowing her neighbors grass = x

An equation that can be used to determine the amount Stephane earned for mowing her neighbors grass can be presented as follows;

The total money she earned = Amount she earned baby sitting + Amount she earned doing her chores + The amount she earned mowing her neighbors grass, from which we get;

The variable x in the equation is the amount Stephany earned for mowing her neighbors grass

Part B

The equation can be solved as follows;

20 = 8.75 + 3.5 + x

Making x the subject of the equation by subtracting 8.75 + 3.5 from both sides, we get;

20 - (8.75 + 3.5) = 8.75 + 3.5 + x - (8.75 + 3.5)

20 - (8.75 + 3.5) = 7.75 = 8.75 + 3.5 - (8.75 + 3.5) + x = x

7.75 = x

The symmetric property, indicates that we get;

x = 7.75

The amount Stephany earned for mowing her neighbors grass is; $7.75

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Answer:

62

Step-by-step explanation:

find the area of each side

(3 * 5) + (2 * 3) + (2 * 5) + (2 * 5) + (2 * 3) + (3 * 5)

add them all

15 + 6 + 10 + 10 + 6 + 15 = 62

The quantity of thermal energy gained by the water is 0.836 J while the quantity of thermal energy lost by the metal is -24.94 J. The difference between the two values shows that the thermal energy lost by the metal is much more than the thermal energy gained by the water.

D. Sources of experimental error and how to improve the investigation:
Sources of experimental error include loss of heat to the surrounding, inaccuracy in temperature measurement, and incomplete mixing of the metal and water.

E. Differences between coffee cup calorimetry and bomb calorimetry:
Coffee cup calorimetry is used to determine the heat absorbed or released in chemical reactions taking place in a solution while bomb calorimetry is used to determine the heat of combustion of organic compounds.

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Answer:

D is on the number line, which point is closest to /-/

Answer:

It well be D

Step-by-step explanation:

Answer:

30000

Step-by-step explanation:

200x10x15=30000

Answer:

7. ) 3 3/4   9.) 3 1/8  11.) 7/16  13.) 5 13/15  15.) 7 1/2

Step-by-step explanation:

Number 7, first make 4 1/6 into an improper fraction.

6x4+1= 25/6

25/6x9/10

225/60

Simplified- 3 3/4

Number 9, make 4 3/8 into an improper fraction.

4x8+3= 35/8

35/8x5/7

175/56

Simplified- 3 1/8

Number 11, make 2 5/8 into an improper fraction.

2x8+5= 21/8

21/8x1/6

21/48

Simplified- 7/16

Number 13, make 1 3/5 and 3 2/3 into an improper fraction.

1x5+3= 8/5,   3x3+2=11/3

8/5x11/3

88/15

Simplified- 5 13/15

Number 15, make 3 1/3 and 2 1/4 into an improper fraction.

3x3+1= 10/3,   2x4+1=9/4

10/3x9/4

90/12

Simplified- 7 1/2

Hope that helped! :D

Answer:

                     .                           .                                       .

_________-16____-14____-12____-10____-8____-6____-4____-2____0

Answer:

6 3/5 points

Step-by-step explanation:

Steve is creating a web page.

Step 1

He starts with a font of 5 9/10 points and decreases it by 1/2.

Hence: Current font

= 5 9/10 - 1/2

= 5 + ( 9/10 - 1/2)

Lowest common denominator

= 10

= 5 + (9 - 5/10)

= 5 + 4/10

= 5 + 2/5

= 5 2/5 points

Step 2

He decreases it again by 6/10 points.

Current fonts

= 5 2/5 - 6/10

= 5 + ( 2/5 - 6/10)

Lowest common denominator

= 10

= 5 + (4 - 6/10)

= 5 + (-2/10)

= 5 - 1/5

= 4 4/5 points

Step 3

Steve then realizes that the font is to small to read easily and increases it by 1 4/5 points.

New font

= 4 4/5 points + 1 4/5 points

Lowest common denominator = 5

= 4 + 1 + (4/5 + 4/5)

= 5+ ( 4 + 4/5)

= 5 +(8/5)

= 6 3/5 points

The best estimate of the font's final size is 6 3/5 points

The volume of the remaining piece of ice cube is 6911.5 cubic cm

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

The figure

Where, we have

Radius, r = 20/2  = 10 cm

Height, h = 33 cm

The volume of the remaining piece is calculated is

V = 2/3πr²h

Substitute the known values in the above equation, so, we have the following representation

V = 2/3 * 22/7 * 10² * 33

Evaluate

V = 6911.5

Hence, the volume of the remaining piece is 6911.5 cubic cm

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Answer:

-57

Step-by-step explanation:

If he had an 8 ft board and cut 65 ft off it would be -57.

Answer:

\( \frac{4}{1} \times \frac{4}{1} \times \frac{4}{1} \times \frac{4}{1} = \frac{256}{1} = - 256\)

Step-by-step explanation:

I dont know if I'm right or not

but this is how I learned it

0.123 < 2 > 0.1002, is the true statement after inserting symbols.

What is greater than symbol refer?

What is lesser than symbol refer?

What is equal to symbol refer?

Hence, 0.123 < 2 > 0.1002, is the true statement after inserting symbols.

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Answer:

replace r with t

Step-by-step explanation:

correct on plato

The correct equation for the area of the triangle is A= 1/2st sin(R).

The total area that is bounded by a triangle's three sides is referred to as the triangle's area. In essence, it is equal to the base times the height divided by half.

Area = (1/2)×Base×Height

Correct calculation for the area of the triangle.

A = (1/2)×Base×Height

Base = s

height = h

A = 1/2 hs

Sine (R) = Base/Hypotenuses

sin(R) = h/t

h = tsin(R)

A = 1/2(t)(s)sin(R)

Therefore, the correct area of the triangle is A = 1/2(t)(s)sin(R).

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Answer: When combining like terms, add or subtract the coefficients. Keep the exponents as they are.

Step-by-step explanation:

You can combine 2x^2 + 3x^2 to get 5x^2. If x =3, 3^2=9 So 2(3)^2 is 18 and 3(3)^2 is 27. 18+27=45 And 5(3)^2= 45. Same result!

You can not combine 2x^2 and 2x^3. If the value of x is 3, 2(3)^2 this term works out to =18 and 2(3)^3 =54

If you add the exponents x^5 becomes 2(3)^5 or 2×243=486. Vastly different values! Don't add exponents unless you are multiplying terms.

Yes, when combining like terms with exponents, you add the exponents only if the terms have the same base.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

When combining like terms with exponents, you add the exponents only if the terms have the same base.

For example,

3x² + 9x²

= (3 + 9)x²

= 12x²

And,

2² x 2³

= \(2^{2 + 3}\)

= \(2^5\)

Thus,

Yes, we add the exponents.

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The equation of line in slope-intercept form is,

Here, m is slope of line and c is y-intercept.

Simplify the equation to obtain the slope-intercept form.

The size of the the matrix B if a matrix A is 5x3 and the product AB is 5x7 is B =[3x7].

Two matrices can only be multiplied if the first matrix has the same number of columns as the second matrix has. If the first matrix has dimensions of a x b and the second matrix has dimensions of c x d, then b = c and their product will have dimensions of a x d.

Let A is a 3 x 5 matrix and B is a 5 x 7 matrix

We know that matrix multiplication of A and B is possible if

Number of columns of A = Number of rows of B

Since in the given problem

Number of columns of A = Number of rows of B = 5

So the product is possible

Now the product AB is a matrix of order 3 × 7

Now the order of the product AB is 3 × 7

If a 3 x 5 matrix is multiplied by a 5 x 7 matrix then their product is a matrix of order 3 × 7.

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There are 16 different answer combinations possible for the three questions.

For each question, there are a certain number of answer choices available. Let's analyze each question separately:

Were you born before 1990?" - This question has 2 answer choices: yes or no.

b) "What is your favorite color?" - This question has 4 answer choices: red, green, blue, or other.

c) "Do you play a musical instrument?" - This question has 2 answer choices: yes or no.

To find the total number of answer combinations, we multiply the number of choices for each question. Therefore, we have 2 * 4 * 2 = 16 different answer combinations.

For question a, there are 2 choices. For each choice in question a, there are 4 choices in question b, resulting in 2 * 4 = 8 combinations. For each of these 8 combinations, there are 2 choices in question c, resulting in a total of 8 * 2 = 16 different answer combinations.

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Answer:

Next 2 terms: 0, 3

Step-by-step explanation:

The patter in +3, +3, -3, -3

-3 + 3 = 0

0 + 3 = 3

3 - 3 = 0

0 - 3 = -3

-3 + 3 = 0

0 + 3 = 3

Answer:

-7

Step-by-step explanation:

The sum of interior Angles of Hexagon is always 720°

Any hexagon's internal angles add up to 720° in all cases. By dividing 720° by 6, we may get the size of each interior angle of a regular hexagon. As a result, we have:

720°÷6 = 120°

In a regular hexagon, each inside angle is 120°.

An example of a regular hexagon with equal-length sides and angles is shown in the diagram below. By multiplying the six 120° angles together, we can demonstrate that the result is 720°.

Therefore, the interior angles of a hexagon are always added up to 720°.

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PLEASE GIVE ME BRAINIEST IF I HELPED YOU!!! THANKS!! HAVE A GOOD DAY/NIGHT!!!

also......

X=5

The lengths of the diagonals are:

GE = 8√5 units

DE = 4√5 Units

Area = 80 sq. units

We have been given an image of a kite on coordinate plane.

To find the length of GE we will use distance formula:

Distance = √[x₂ - x₁)² + (y₂ - y₁)²]

Substituting coordinates of point G and E in above formula we will get,  

GE = √[16 - 0)² + (8 - 0)²]

GE = √(256 + 64)

GE = √320

GE = 8√5 units

Similarly we will find the length of diagonal DF using distance formula.

DF = √[14 - 10)² + (2 - 10)²]

DE = √(16 + 64)

DE = √80

DE = 4√5 Units

Area of kite is given by the formula:

Area = (p * q)/2

where p and q are diagonals of kite.

Thus:

Area = ( 8√5 *  4√5)/2

Area = 80 sq. units

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Here is my answer for you:

Graph each equation, until you find the one that lines up.

Below is a picture of all the equations on a graph.

Your answer is already in standard form, x-6y=-9.

Answer:

x−6y=−9

Step-by-step explanation:

10. To find the eigenvalues and eigenvectors of the linear transformation T(X1, X2, X3, ..., Xn) = (X1, 2X2, 3X3, ..., nXn), we need to solve the equation T(X) = λX, where λ is the eigenvalue and X is the eigenvector.

(a) Let's find the eigenvalues first:

T(X) = λX

(X1, 2X2, 3X3, ..., nXn) = λ(X1, X2, X3, ..., Xn)

By comparing corresponding components, we get:

X1 = λX1

2X2 = λX2

3X3 = λX3

...

nXn = λXn

From these equations, we can see that λ must be equal to 1, and the eigenvectors are of the form X = (X1, X2, X3, ..., Xn), where X1, X2, X3, ..., Xn are arbitrary real numbers.

Therefore, the eigenvalues are λ = 1, and the corresponding eigenvectors are of the form X = (X1, X2, X3, ..., Xn), where X1, X2, X3, ..., Xn are arbitrary real numbers.

(b) To find the invariant subspaces of T, we need to determine the subspaces of R^n that are mapped into themselves by T. In this case, any subspace spanned by the eigenvectors is an invariant subspace, since multiplying the eigenvectors by the transformation T will still result in a scalar multiple of the same eigenvector.

So, the invariant subspaces of T are the subspaces spanned by the eigenvectors (X1, X2, X3, ..., Xn), where X1, X2, X3, ..., Xn are arbitrary real numbers.

11. The linear transformation T: P(R) -> P(R), defined as T(p) = p, where P(R) represents the set of all polynomials with real coefficients.

To find the eigenvalues and eigenvectors of T, we need to solve the equation T(p) = λp, where λ is the eigenvalue and p is the eigenvector.

T(p) = p

λp = p

This equation implies that any non-zero polynomial p is an eigenvector with eigenvalue λ = 1. Therefore, the eigenvalues are λ = 1, and the corresponding eigenvectors are all non-zero polynomials.

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