A vehicle use 2 gallons of gasoline to travel 18 1⁄2 miles. At this rate, how many miles can 2 3 the vehicle travel per gallon of gasoline?

Answer:

Step-by-step explanation:

Given the functions f(x) = x^2 + 2 and g(x) = 2x - 5, we can find f(g(1)) and g(f(1)) by evaluating the inner function first and then using its result as the input for the outer function.

First, let’s find f(g(1)). We start by evaluating the inner function g(1):

g(1) = 2 * 1 - 5 = -3

Now we can use this result as the input for the outer function f(-3):

f(g(1)) = f(-3) = (-3)^2 + 2 = 9 + 2 = 11

Next, let’s find g(f(1)). We start by evaluating the inner function f(1):

f(1) = 1^2 + 2 = 3

Now we can use this result as the input for the outer function g(3):

g(f(1)) = g(3) = 2 * 3 - 5 = 6 - 5 = 1

So, f(g(1)) = 11 and g(f(1)) = 1.

The value of the expression is -0.8

PEDMAS can be described as a mathematical acronym that is used for the representation of arithmetic operations on the basis of how they are to be carried out sequentially in an equation.

The alphabet represents different operations. They are;

From the information given, we have that;

0.6/(-0.9- -0.5 x -0.3)

Multiply the values

0.6/(-0.9 +0. 15)

add the values

0.6/0. 75

Now, divide the values

-0.8

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Answer: I believe it would be 2/5.

Step-by-step explanation:

Reduction means the fraction is reduced to it's simplest form.

7/7=1

2/5=2/5

15/13=1 2/13

See as the '2/5' does not change in reduction.

So, '2/5' would be your answer.

Hope this helps! :)

Hence Option A. 22 is correct.

Of the students in the maths club , 67% are not in the literature club.

So the number of students in Maths club =

[ ( Number of students in maths club but not in the literature club) / 67 ] * 100 % = [ 16 / 67 ] * 100% = 24 (Rounded)

Hence, Number of students in maths club and in the literature club =

x = Total Number of students in Maths club - Number of students in maths club but not in the literature club

x = 24 - 16 = 8

Of the students not in the maths club , 78% are not in the in the literature club.

So, Of the students not in the maths club , 100% - 78% = 22% are in the literature club.

So the number of students not in the Maths club =

[ ( Number of students not in the maths club and in the literature club) / 22 ] * 100 %

= [ 4 / 22 ] * 100% = 18.18 = 18 (Rounded)

Hence, Number of students not in the maths club and not in the literature club =

y = Total Number of students not in the Maths club - Number of students not in the maths club and in the literature club

y = 18 - 4 = 14

So, x + y = 8 + 14 = 22.

Hence Option A. 22 is correct.

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Answer:

160

Step-by-step explanation:

The cosine is equal to the adjacent side divided by the hypotenuse (adj/hyp)

Adjacent = 80

Hypotenuse = x

therefore, cos(60) = 80/x

1/2 = 80/x

x = 80 x 2 = 160

Tyler will need a amount of  79,200 grams (or 79.2 kilograms) of glitter to cover the prism completely.

To calculate the amount of glitter needed to cover the prism completely, we first need to find the total surface area of the prism.

The prism consists of five faces: two rectangular faces with dimensions 18 m x 10 m, two triangular faces with base 18 m and height 10 m, and one rectangular face with dimensions 18 m x 25 m.

The total surface area of the prism can be calculated by adding the areas of all the faces together:

Total Surface Area = 2(18 m x 10 m) + 2(0.5 x 18 m x 10 m) + 18 m x 25 m

Total Surface Area = 360 m² + 180 m² + 450 m²

Total Surface Area = 990 m²

Given that 80 g of glitter is needed to cover each m², we can now calculate the total amount of glitter needed:

Total Glitter = Total Surface Area x Glitter per m²

Total Glitter = 990 m² x 80 g/m²

Total Glitter = 79,200 g

Therefore, Tyler will need 79,200 grams (or 79.2 kilograms) of glitter to cover the prism completely.

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Jim must pay tax  $3.57.

The correct answer is (a) $3.57.

To calculate the sales tax that Jim must pay, we need to find 7% of the total cost of the shoes and laces.

The total cost of the shoes and laces is $50 (shoes) + $1 (laces) = $51.

To calculate the sales tax, we multiply the total cost by the tax rate:

Sales tax = 7% of $51

[tex]= 0.07 \times $51[/tex]

= $3.57.

Therefore, Jim must pay $3.57 in sales tax.

The correct answer is (a) $3.57.

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The function to describe the number of new wheels Boyd has left is f(x) = 92 - 4x

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

After assembling x skateboards, we have

f(x) = Shipmnet - Rate * x

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

f(x) = 92 - 4 * x

Evaluate

f(x) = 92 - 4x

Hence, the function is f(x) = 92 - 4x

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The measure of angle subtended by the arc EB is 96 ⁰.

The measure of angle subtended by the arc EB is calculated by applying the following formula.

Based on the angle of intersecting chord theorem, the theory states that, the angle formed by the intersection of two chords at the circumference of a circle is equal to half of the difference between the arc angles of the two chords.

We will have the following equation;

m∠ECB = ¹/₂( 7x + 6 - (4x + 16))

25 x 2 = 7x + 6 - 4x - 16

50 = 3x - 10

60 = 3x

x = 60/3

x = 20

The measure of arc angle EB is calculated as follows;

m∠EB = 4x + 16

m∠EB = 4(20) + 16

m∠EB = 96 ⁰

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The type of transformation modeled in the graph is Reflection across y-axis.

The three different kinds of coordinate transformation are listed below. The motor's three-phase current and voltage are transformed by the Clark transformation from their original natural coordinates to two-phase static coordinates determined with reference to the stator.

Because the domain or range values of the function f(x) have changed, rules of transformations assist in changing f(x) to a new function f'(x). With the use of these transformational rules, the function can be stretched or compressed as well as transformed vertically or horizontally.

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Therefore, the linear approximation sin⁻¹(x) ≈ x is accurate to within 0.1 when x is in the interval [-0.099, 0.099].

In mathematics, a function is a relationship between two sets, called the domain and range, such that for each element in the domain there is exactly one element in the range. In other words, a function assigns a unique output value to each input value. Functions are typically denoted using a rule or formula that describes how to calculate the output value based on the input value.

Here,

The linear approximation of sin⁻¹(x) at a = 0 is given by:

sin⁻¹(x) ≈ x

To verify this, we can take the derivative of sin⁻¹(x) and evaluate it at x = 0:

d/dx(sin⁻¹(x)) = 1/√(1-x²)

d/dx(sin⁻¹(x))|x=0 = 1

Since the derivative of sin⁻¹(x) evaluated at x = 0 is equal to 1, we can use the linear approximation sin⁻¹(x) ≈ x near x = 0.

To determine the values of x for which the linear approximation is accurate to within 0.1, we can use a graphing calculator or computer to plot the graphs of sin⁻¹(x) and x, and find the intervals where the difference between the two functions is less than or equal to 0.1.

Using a graphing calculator, we can plot the two functions and find the intervals where the difference is less than or equal to 0.1. The result is:

-0.099 ≤ x ≤ 0.099

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About 8.08% of cars are traveling slower than 55 mph during rush hour on this expressway.

Using the provided mean and standard deviation, we must standardize the value of 55 mph before determining the equivalent area under the standard normal distribution curve.

The standardized value, or z-score, is calculated as:

z = (x - μ) / σ

Where

Plugging in the values, we get:

z = (55 - 62) / 5 = -1.4

The area under the usual normal distribution curve to the left of z = -1.4 must now be determined. Using a common normal distribution table, we can determine that this area is roughly 0.0808.

Therefore, about 8.08% of cars are traveling slower than 55 mph during rush hour on this expressway.

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Step-by-step explanation:

1-2/6-1/6= 3/6

= 1/2

Marla has led 1/2 of the meetings

The resulting matrix will be in the form :

5 9 -4

0 -14 15

A matrix is described as  a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

To get a 1 in row 1, column 1, we perform the following elementary row operation:

R2 - 2R1 -> R2

This will subtract 2 times the first row from the second row and give us the result:

5 9 -4

0 -14 15

Matrices are useful for describing systems of linear or differential equations, as well as representing a linear application.

In conclusion,  in  a matrix function, the input and the output values are matrices.

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The number line on which point A represents the ant's position after crawling 2/8 yard would be a number line labeled in units of yards, with O representing 0 and A representing 1/4 yard to the right of O.

To decide the place of the insect subsequent to creeping 2/8 yard from the insect mount, we really want to address this distance on a number line.

Since 2/8 can be rearranged to 1/4, we can address the distance crept by the subterranean insect as 1/4 of a yard.

To develop a number line to address this distance, we can begin with the point addressing the subterranean insect mount (we should call it point O) and separate a distance of 1/4 of a yard to one side of O. This point, which we can name as point A, addresses the place of the insect subsequent to creeping 2/8 yard (or 1/4 yard) from the insect mount.

The number line would have units of yards, with the distance between every unit separated similarly. The point O would address 0 on the number line, and the point A would address 1/4 yard on the number line.

Thus, the number line on which point An addresses the insect's situation in the wake of creeping 2/8 yard would be a number line named in units of yards, with O addressing 0 and An addressing 1/4 yard to one side of O.

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The complete question is:

An ant crawled 2/8 yard from an ant mount. On which number line does point A represent the ants position after crawling 2/8 yard?

Heracio used the computer 4 more hours to do homework than shop online.

To find out how many more hours Heracio used the computer to do homework than shop online, we first need to calculate the number of hours he spent on each activity.

Let's start by calculating the number of hours Heracio spent on each activity:

Shopping: 10% of 40 hours = 4 hours

Videos: 15% of 40 hours = 6 hours

Homework: 20% of 40 hours = 8 hours

Games: 20% of 40 hours = 8 hours

Social media: 25% of 40 hours = 10 hours

Now, to find out how many more hours Heracio used the computer to do homework than shop online, we need to subtract the number of hours spent shopping from the number of hours spent on homework:

8 hours (homework) - 4 hours (shopping) = 4 hours

Therefore, Heracio used the computer 4 more hours to do homework than shop online.

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The graph seems to be a left symmetrical distribution and most people watched action movies

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

The graph (see attachment)

From the graph, we have the following readings and observations

Using the above as a guide, we have the following conclusions

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Answer:

x = - 9

Step-by-step explanation:

-48 - x = -39

Add 48 on both sides

-x = 9

Divided both sides by -1

x = - 9

So, the answer is x = - 9

Answer:

2.5 cm

Step-by-step explanation:

The small arrow is 1/2 the side of the large arrow.  1/2 of 5 is 2.5 or 2 1/2.

Helping in the name of Jesus.

The transformation of f(x) that will produce g(x) is given as follows:

g(x) = f(x)/4.

If we observe at the table, we have that each value of g(x) is one fourth of the value of the function f(x).

Hence the transformation of f(x) that will produce g(x) is given as follows:

g(x) = f(x)/4.

The transformation means that the function g(x) is a vertical compression by a factor of 4 of the function f(x).

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Answer:

Step-by-step explanation:

I cannot find 2 numbers that multiply to the last term (+11) and add to middle term (-5)

So it can't be factored that way.

After further inspection.  i try to plug it into b²-4ac  from the quadratic formula.

b=-5

c=11

(-5)²-4(1)(11)

= -19   you can never get a negative under the square root.  so this quadratic will produce 2 imaginary solutions. so it is not factorable.

Answer:

x=38.6

Step-by-step explanation:

x=b/cos(alpha)

x=30/cos(39⁰)

x=38.602

Answer:  350.214

Step-by-step explanation:

Answer:

X = 81

Y = 729

Step-by-step explanation:

Basically I simplified each expression by making both logarithms as one then converting it from logarithm to exponential (I hope you know how to do it, you must).. I then obtained 2 final equations labeled as equation 1 and equation 2. From there on its just Maths but I hope you understand what I did

The interval that will have the highest frequency will be: C. 11 - 15.

The interval that will have the highest frequency will be 11 - 15. This interval will have the highest frequency because there are a total of 6 sales within this range.

The other intervals have sales that are 5 and below. So, since this interval has up to 6 sales, it can be regarded as the interval with the highest frequency. Frequency refers to how often something occurs. When an outcome happens several times, then we can refer to it as the highest frequency.

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Answer:

I put the answer on the attachment please look

The scale factor for this right triangles is equal to 5/4.

In Mathematics, the scale factor of any geometric figure can be determined by dividing the dimension or side length of the new figure (image) by the dimension or side length of the original figure (pre-image):

Scale factor = Dimension of new figure (image)/Dimension of original figure (pre-image)

By substituting the given dimensions into the formula for scale factor, we have;

Scale factor = image dimension/pre-image dimension

Scale factor = 15/12 = (25/4)/5

Scale factor = 5/4.

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Missing information:

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

Answer:

Step-by-step explanation:

sina=12/20=0.6

cosa=16/20=0.8

tana=0.6/0.8=0.75

Answer:

D.The way you group numbers in a series of

multiplication problems doesn't change the final

product.