A van travels 150 miles on 6 gallons of gas.How many gallons will it need to travel 325 miles?

............, .......

Answer:

1/15

Step-by-step explanation:

2/3*5/5 - 3/5*3/3( we are multiplying and dividing by the same number in order to get the same denominator. as 5/5 = 1 and 3/3= 1)

2/3*5/5 - 3/5*3/3

= 10/15-9/15

= 1/15

Answer:

124 students

Step-by-step explanation:

Girls participating in the exercise

4/15 x 285 = 76

Boys participating in the exercise

3/20 x 320 = 48

Total students participating

76 + 48 = 124

Answer:

Triangle F G E is similar to Triangle J K L

Step-by-step explanation:

I AM A GOAT

Answer:

F G E  J K L

Step-by-step explanation:

To find the combined rate of all the individuals working together, you must add the individual rates.

When calculating the combined rate of individuals working together, you need to add up the individual rates. Each worker contributes their own rate of work or productivity, and by adding these rates together, you can determine the combined rate at which they are working collectively.

This allows you to assess the overall efficiency and output of the team or group. By summing up the individual rates, we have better understanding of the overall productivity and performance of the group.

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Answer:130

Step-by-step explanation:13 tenths as a Decimal. If you divide 13 by ten you get 13 tenths as a decimal which is 1.30. 13 tenths as a Percent. To get 13 tenths as a Percent, you multiply the decimal with 100 to get the answer of 130 percent. 13 tenths of a dollar.

The recursive sequence that represents the sequence defined by the following explicit formula is given as follows:

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term.

The first term and the common ratio for this problem is given as follows:

\(a_1 = -32, q = -\frac{1}{4}\)

The common ratio means that each term is the previous term multiplied by -1/4, hence the recursive formula is given as follows:

\(a_{n + 1} = -\frac{1}{4}a_n\)

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Answer:

\(n =26\)

Step-by-step explanation:

Given

\(f(n) = (2n - 2) + 2\)

Required

Find n when \(f(n) = 52\)

Substitute 52 for f(n) in \(f(n) = (2n - 2) + 2\)

\(52 = (2n - 2) + 2\)

Remove bracket

\(52 = 2n - 2 + 2\)

\(52 = 2n\)

Make n the subject

\(n = \frac{52}{2}\)

\(n =26\)

The position is 26

c'mon bro you can't be this helpless

odd, even, even, even, even

Answer:

63 is odd

30 is even

434 is even

898 is even

96 is even

Step-by-step explanation:

Any numbers that end in 0, 2, 4, 6, 8 are even.

Any numbers that end in 1, 3, 5, 7, 9 are odd.

Answer:

110 kobo

Step-by-step explanation:

first 18 = 35 kobo

48-18 = 30 words left

30x2.5  = 75 kobo

35 + 75 = 110 kobo

The values of x and y for the given logarithmic function, 2 log (x²y) = 3 + logx - logy are respectively, 13/2 and 7/2

The logarithmic function is an expression which we can write as, y = logₐx, where a>0 & x>0, It is the inverse of exponential function.

Formulae for logarithmic function are,

LogAB = LogA + LogB

Logₐaᵇ = b

Given that,

the logarithmic function,

2 log (x²y) = 3 + logx - logy

x - y = 3                .....................(i)

2 log (x²y) = 3 + logx - logy

2[ logx² + logy] = 3 + logx - logy

2[ 2logx + logy] = 3 + logx - logy

4logx + 2logy   = 3 + logx - logy

3logx + 3logy = 3

logx + logy = 1

logx + logy = log10

x  +  y  = 10          .............(ii)

By solving the equation (i) & (ii)

x - y = 3

x + y = 10

2x     =  13

x  = 13/2

13/2 - y = 3

y  = 7/2

Hence, the values of x and y is, 13/2 and 7/2

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The difference in volume between the two boxes would be = 156in³

To calculate the difference in volume between the boxes is the find the individual volume of the boxes using the formula ;

Volume = length×width×height.

For box 1 = length = 12in, width = 7¾in, height= 2in

Vol = 12×7¾×2 = 186in³

For box 2; length = 3⅔in, width = 3½in, height= 2⅓in

Volume = 3⅔×3½×2⅓ = 30

The difference = 186-30 = 156in³

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The correct order of functions, in increasing order of growth rate, is g1, g4, g3, g5, g2, g7, and g6.

A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions are everywhere, and they are crucial for constructing physical relationships in the sciences. A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Here,

The list of function is attached in image.

g1, g4, g3, g5, g2, g7, g6 is the correct sequence of functions in increasing order of growth rate.

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Answer:Una cámara de televisión está a 30 pies de uno de los lados de 94 pies de una cancha, y está a 7 pies del centro. Determinar qué ángulo debe barrer.

Step-by-step explanation:

Answer:

\(\frac{1}{3}(p-2)\) ,    1/3(p-2)

Step-by-step explanation:

\(\frac{1}{3} p-\frac{2}{3}\)

\(\frac{1}{3}(p-2)\)

The equation to show the perimeter of the rectangle is P = 2(2w + 5)

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

Length = 5 more than the width

Also, we have

Perimeter = 58

This means that

P = 2(w + 5 + w)

P = 2(2w + 5)

In (a), we have

P = 2(2w + 5)

This gives

2(2w + 5) = 58

So, we have

2w + 5 = 29

2w = 24

w = 12

Next, we have

l = 12 + 5

l = 17

Lastly, we have

Area = 17 * 12

Area = 204

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Therefore, the end behavior of the function f(x) is: f(x) → 0- as x → -∞ and f(x) → 1 as x → ∞.

In mathematics, a function is a rule that assigns a unique output value to each input value. Functions are often represented as equations or graphs that relate the input (also known as the independent variable) to the output (also known as the dependent variable). The input is usually denoted by the variable x, and the output is usually denoted by the variable y. Functions can be used to model relationships between different quantities, such as time and distance, or temperature and pressure. They are a fundamental concept in mathematics and are used in many fields, including physics, engineering, economics, and computer science.

Here,

To determine the end behavior of the function f(x) = (-4x³+ 7x + 9)/(8x⁶ - 9x⁴ - 2x), we need to consider the limit of the function as x approaches positive or negative infinity.

As x approaches negative infinity, the highest power of x in the numerator is -4x³, which will dominate the function. The highest power of x in the denominator is 8x⁶, which will also dominate the function. Therefore, we can simplify the function to:

f(x) ≈ (-4x³)/(8x⁶) = -1/(2x³)

As x approaches negative infinity, the denominator of this simplified function will become very large (since x³ becomes very negative), causing the function to approach 0 from the negative side:

f(x) → 0- as x → -∞

As x approaches positive infinity, the highest power of x in the numerator and denominator are both 8x⁶. Therefore, we can simplify the function to:

f(x) ≈ (8x⁶)/(8x⁶) = 1

As x approaches positive infinity, the function will approach 1 from the positive side:

f(x) → 1 as x → ∞

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Complete question:

Consider the following rational function fff. f(x)=\dfrac{-4x^3+7x+9}{8x^6-9x^4-2x}f(x)= 8x 6 −9x 4 −2x −4x 3 +7x+9 ​ f, left parenthesis, x, right parenthesis, equals, start fraction, minus, 4, x, cubed, plus, 7, x, plus, 9, divided by, 8, x, start superscript, 6, end superscript, minus, 9, x, start superscript, 4, end superscript, minus, 2, x, end fraction Determine fff's end behavior. f(x)\tof(x)→f, left parenthesis, x, right parenthesis, \to as x\to -\inftyx→−∞x, \to, minus, infinity. f(x)\tof(x)→f, left parenthesis, x, right parenthesis, \to as x\to \inftyx→∞x, \to, infinity.

Answer:

38.81 pounds

Step-by-step explanation:

Considering the definition of right rectangular prism and its volume,  the total weight of the contents is 38.81 pounds.

Right rectangular prism

A right rectangular prism (or cuboid) is a polyhedron whose surface is formed by two equal and parallel rectangles called bases and by four lateral faces that are also parallel rectangles and equal two to two.

Volume of right rectangular prism

To calculate the volume of the rectangular prism, it is necessary to find the product of its dimensions, or of the three edges that converge at a certain vertex.

That is, to calculate the volume of a rectangular prism, multiply its 3 dimensions: length×width×height.

Volume of the container

In this case, you know that:

the dimensions of the container built are 7.5 ft by 11.5 ft by 3 ft.

the container is entirely full and, on average, its contents weigh 0.15 pounds per cubic foot.

So, the volume of the container is calculated as:

7.5 ft× 11.5 ft× 3 ft= 258.75 ft³

Then, the total weight of the contents is calculated as:

258.75 ft³×  0.15 pounds per cubic foot= 38.8125 pounds≅ 38.81 pounds

Finally, the total weight of the contents is 38.81 pounds.

An equation of the line that goes through the point (-1, -3) and (3, 5) is y = 2x - 1.

An equation of the line in slope-intercept form that is perpendicular to the equation for obstacle 1 is y = -x/2 + 3.

In Mathematics, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁) or \(y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\)

Where:

At data point (-1, -3), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

\(y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - (-3) = \frac{(5- (-3))}{(3-(-1))}(x -(-1))\\\\y +3 = \frac{(5+3)}{(3+1)}(x +1)\)

y + 3 = 2(x + 1)

y = 2x + 2 - 3

y = 2x - 1

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

2 × m₂ = -1

m₂ = -1/2.

At point (-4, 5), an equation of the line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -1/2(x + 4)

y = -x/2 - 2 + 5

y = -x/2 + 3

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the final result of the double integral is `(4/3)*a. we have to Integrate the inner integral with respect to z.

what is inner integral ?

An inner integral is a mathematical term that refers to the integral function that is evaluated first in a double integral.

In the given question,

To solve this double integral, we will use the following steps:

Integrate the inner integral with respect to z.

Evaluate the result of the inner integral at  upper and lower limits of z.

Substitute the result of the inner integral into the outer integral and integrate with respect to y.

Evaluate the result of the outer integral at the upper and lower limits of y.

Simplify the expression.

Now, let's apply these steps to solve the given double integral:

Integrate the inner integral with respect to z:

∫(x²*z + y²*z + z³) dz = x²/2*z² + y²/2*z² + z^4/4 + C

where C is the constant of integration.

Evaluate the result of the inner integral at the upper and lower limits of z:

(x²/2*(a²-x²-y²)¹⁵ + y²/2*(a²-x²-y²)¹⁵ + (a²-x²-y²)²/4)

- (x²/2*(-a²+x²+y²)¹⁵ + y²/2*(-a²+x²+y²)¹⁵ + (-a²+x²+y²)²/4)

Substitute the result of the inner integral into the outer integral and integrate with respect to y:

markdown

∫[(x²/2*(a²-x²-y²)¹⁵ + y²/2*(a²-x²-y²)¹⁵ + (a²-x²-y²)²/4)

- (x²/2*(-a²+x²+y²)¹⁵ + y²/2*(-a²+x²+y²)¹⁵ + (-a²+x²+y²)²/4)] dy

Evaluate the result of the outer integral at the upper and lower limits of y:

= ∫[(x²/2*(a²-x²-y²)¹⁵ + y²/2*(a²-x²-y²)¹⁵ + (a²-x²-y²)²/4)- (x²/2*(-a²+x²+y²)¹⁵ + y²/2*(-a²+x²+y²)¹⁵ + (-a²+x²+y²)²/4)] dy

from y = -sqrt(a²-x²) to y = sqrt(a²-x²)

= (2/3)*x²*(a²-x²)¹⁵ + (2/3)*(a²-x²)²⁵

- (2/3)*x²*(-a²+x²)¹⁵ + (2/3)*(-a²+x²)²⁵

Simplify the expression:

= (4/3)*a³ - (4/3)*a*x²

Therefore, the final result of the double integral is `(4/3)*a

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Answer:

Step-by-step explanation:

372 Millimeters

Answer:

2,300 millimeters

Step-by-step explanation:

when you convert 30 centimeters it’s 300 millimeters. When you convert 2 meters it’s 2,000 millimeters so…. That is the correct answer plus I just did the quiz and got it correct with that answer.

Answer:

Step-by-step explanation:

(3x - 1)(3x - 4) = 9x^2 - 15x + 4

(x + 2)(9x^2 - 15x + 4) = 9x^3 - 15x^2 + 4x + 18x^2 - 30x + 8

9x^3 + 3x^2 -26x + 8 is the solution

Explanation:

If the grasshopper travels a distance of 5 feet in 9 equal hops, then in each hops it travels 5/9 feet.

Now we want to know how many feet does it travel after 2 hops. It will be twice one hop:

Answer:

The grasshopper traveled 1 1/9 feet after hopping twice

Answer:

\(\huge\boxed{a=\frac{bc}{d}}\)

Step-by-step explanation:

In order to find the value of a when we have the equation \(bc=ad\), our goal is to isolate a on one side.

The key question here is: what's stopping a from being alone on one side? That would be it being multiplied by \(d\). If we were able to remove the d, we would have a by itself.

Since we are multiplying a and d, we can get rid of the d by dividing both sides by d.

We have to divide both sides of the equation by the same value in order to keep it equal.

\(bc \div d = ad \div d\\\\\frac{bc}{d}=a\\\\a = \frac{bc}{d}\)

Hope this helped!

Answer:

\(A=\left[\begin{array}{ccc}1&1&0\\0&0&0\\\end{array}\right]\)

Step-by-step explanation:

We have a linear transformation L mapping R3 into R2 ⇒

\(L:\) \(IR^{3}\) ⇒ \(IR^{2}\)

We need to find a matrix A such that \(L(x)=Ax\) for every \(x\) in R3

We have the formula of \(L(x)\) ⇒

\(L(x)=L(\left[\begin{array}{c}x1&x2&x3\end{array}\right])=\left[\begin{array}{c}x1+x2&0\end{array}\right]\)

We must notice that \(x\) is a vector in R3 and the image of L is a vector in R2.

Given that L is define as \(L:\) \(IR^{3}\) ⇒ \(IR^{2}\) , the matrix that defines the linear transformation L will be a matrix A ∈ \(IR^{2x3}\)

How can we find this matrix A? One way is to apply L to a base from the domain of L (R3) and putting that result as the columns of the matrix A.

Let's work with the cannonic base of R3  :

\(B_{IR^{3}}=\) { \(\left[\begin{array}{c}1&0&0\end{array}\right],\left[\begin{array}{c}0&1&0\end{array}\right],\left[\begin{array}{c}0&0&1\end{array}\right]\)}

Now if we transform each vector of the base :

\(L(\left[\begin{array}{c}1&0&0\end{array}\right])=\left[\begin{array}{c}1&0\end{array}\right]\)

\(L(\left[\begin{array}{c}0&1&0\end{array}\right])=\left[\begin{array}{c}1&0\end{array}\right]\)

\(L(\left[\begin{array}{c}0&0&1\end{array}\right])=\left[\begin{array}{c}0&0\end{array}\right]\)

The final step is to put the result of each vector as the columns of the matrix A :

\(A=\left[\begin{array}{ccc}1&1&0\\0&0&0\\\end{array}\right]\) ⇒

\(L(x)=Ax\) being A the matrix calculated. It is important to remark that the transformation L is defined in the cannonic base.

We can verify the matrix A by performing the transformation into any vector of R3. For example, let's calculate :

\(L(\left[\begin{array}{c}1&2&3\\\end{array}\right])=\left[\begin{array}{c}3&0\end{array}\right]\)

If we use the equation and :

\(A\left[\begin{array}{c}1&2&3\end{array}\right]=\left[\begin{array}{ccc}1&1&0\\0&0&0\end{array}\right]\left[\begin{array}{c}1&2&3\end{array}\right]=\left[\begin{array}{c}3&0\end{array}\right]\)  

If we use the matrix A calculated.

Based on the arithmetic sequence, the sum of the first 19 terms is 532.

1, 4, 7, 10, 13, 16...

Sn = n/2{2a + (n - 1)d}

= 19/2{2×1 + (19 - 1)3}

= 9.5{2 + (18)3}

= 9.5(2 + 54)

= 9.5(56)

Sn = 532

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Answer: 8

Step-by-step explanation: 8 minus 3 would be 5, subtracting 10 would then get to -5 (simplified)

For the function: y = √(x - 7) - 1

The domain is D: [7, ∞) and the range is R: [1, ∞)

Remember that the for a function y = f(x), the domain is the set of the possible inputs (possible values of x) while the range is the set of the possible outputs (possible values of y).

Here we want to find the domain and range of the function:

y = √(x - 7) - 1

First, we will find the domain, remember that the argument of a square root must be zero or larger, then the minimum of the domain is the value of x such that:

x - 7 = 0

x = 7

The domain is:

D: [7, ∞)

The square root is an increasing function, then the minimum of the range is given by evaluating the function in the minimum of the domain:

f(7) = √(7 - 7) - 1

f(7) = 1

Then the range is:

R: [1, ∞)

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