At a school, 460 of the students walk to school. The number of students who bike to school is 5% of the number of students who walk. How many students bike to school?
students

Answer:

5

Step-by-step explanation:

Answer:65miles

Step-by-step explanation:

Let the needed miles be x

(67+62+59+47+x)/5=60

235+x=60×5

235+x=300

x=300-235

x=65miles

Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

A mixed number is simply a whole number and a fraction written together.

The mixed numbers between 1 and 2 on the number line can be any range of fractions written along with 1 as the whole. It cannot include the number 2, because if that happens, then the number has crossed beyond 2 on the number line.

An example of a mixed number that comes between 1 and 2 on the number line is

(a) To find the equation for the line tangent to the graph of f at the point with an x-coordinate of 4, we need to find the slope of the tangent line and the point of tangency.

First, we find the derivative of f(x):

f'(x) = (k - 2x) / (x² - kx)²

Substituting k = 3 into f'(x):

f'(x) = (3 - 2x) / (x² - 3x)²Now, let's find the slope at x = 4:

slope = f'(4) = (3 - 2(4)) / (4² - 3(4))²

= (3 - 8) / (16 - 12)²

= -5 / 4²

= -5 / 16

So, the slope of the tangent line is -5/16.

Now, let's find the y-coordinate of the point of tangency. Substituting x = 4 into f(x):

f(4) = 1 / (4² - 3(4))

= 1 / (16 - 12)

= 1 / 4

= 1/4

So, the point of tangency is (4, 1/4).

Using the point-slope form of a line, we can write the equation of thetangent line:

y - y₁ = m(x - x₁)

where (x₁, y₁) is the point of tangency and m is the slope:

y - 1/4 = (-5/16)(x - 4)

Simplifying:

y - 1/4 = (-5/16)x + 5/4

y = (-5/16)x + 5/4 + 1/4

y = (-5/16)x + 6/4

y = (-5/16)x + 3/2

Therefore, the equation for the line tangent to the graph of f(x) = 1/x² - 3x at the point with an x-coordinate of 4 is y = (-5/16)x + 3/2.

(b) To determine where f(x) = 1/x² - 4x has a relative minimum, a relative maximum, or neither at x = 2, we can analyze the behavior of the derivative f'(x) in the vicinity of x = 2.First, let's find the derivative of f(x):

f'(x) = (k - 2x) / (x² - kx)²

Substituting k = 4 into f'(x):

f'(x) = (4 - 2x) / (x² - 4x)²

Now, let's find the critical points by setting f'(x) = 0:

(4 - 2x) / (x² - 4x)² = 0The numerator can never be zero since 4 - 2x is always nonzero. Therefore, there are no critical points.

To determine whether f(x) has a relative minimum, relative maximum, or neither at x = 2, we can examine the behavior of f'(x) on both sides of x = 2.

For x < 2, let's consider the behavior of f'(x):

f'(x) = (4 - 2x) / (x² - 4x)²

When x is very close to 2 from the left side (x < 2), the denominator (x² - 4x)² is positive and close to zero, while the numerator (4 - 2x) is negative. Therefore, f'(x) is negative for x < 2, indicating a decreasing slope.

For x > 2, let's consider the behavior of f'(x):

f'(x) = (4 - 2x) / (x² - 4x)²When x is very close to 2 from the right side (x > 2), the denominator (x² - 4x)² is positive and close to zero, while the numerator (4 - 2x) is positive. Therefore, f'(x) is positive for x > 2, indicating an increasing slope.

Based on the behavior of the derivative, f'(x), we can conclude that f(x) = 1/x² - 4x has neither a relative minimum nor a relative maximum at x = 2. Instead, it has an inflection point at x = 2.

(c) To find the value of k for which f has a critical point at x = -5, we need to set the derivative f'(x) equal to zero and solve for k.

f'(x) = (k - 2x) / (x² - kx)²

Setting f'(x) = 0:

(k - 2x) / (x² - kx)² = 0

The numerator (k - 2x) can only be zero when k = 2x. Therefore, to find the value of k for which f has a critical point at x = -5, we substitute x = -5 into the equation k = 2x:k = 2(-5)

k = -10Thus, the value of k for which f has a critical point at x = -5 is k = -10.

(d) Given f(x) = 1/x² - 6x, we can find the partial fraction decomposition of f by expressing it as a sum of simpler fractions.

First, let's rewrite f(x) with a common denominator:

f(x) = 1/x² - 6x = (1 - 6x²) / x²

Now, let's perform the partial fraction decomposition by expressing the numerator as a sum of two terms:

f(x) = (1 - 6x²) / x² = A/x + B/x²

To determine the values of A and B, we can multiply both sides of the equation by x²:

1 - 6x² = Ax + B

Now, let's solve for A and B by comparing coefficients:Coefficients of x²:

-6 = 0

Coefficients of x:

0 = A

Constant terms:

1 = B

Therefore, A = 0 and B = 1. Substituting these values back into the partial fraction decomposition:f(x) = 0/x + 1/x²

= 1/x²

So, the partial fraction decomposition of f(x) = 1/x² - 6x is 1/x².

To find ∫f(x) dx, we can integrate each term separately:

∫(1/x²) dx = -1/x

Therefore, the integral of f(x) = 1/x² - 6x is given by:

∫f(x) dx = -1/x - 3x² + Cwhere C is the constant of integration.

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Answer:

I think you would be right.

Answer:\(- \frac{5}{12}\)

Step-by-step explanation:

https://www.symbolab.com/

Answer:

Okay so you are going to get -5/12

Step-by-step explanation:

what you are going to do first is look at your signs the plus and minus signs are there to try and mix you up. What you are doing is subtracting all three of these fractions... Okay?

3/4 - 1/2 - 2/3

What you need to do is turn 1/2 into 1/4 because when adding or subtracting fractions you need to have the same denominator.

Subtract:

3/4 - 2/4 = 1/4

Now you are going to have to multiply the tops and the bottom of 2/3 by four (you should get 8/12) and multiply 1/4 (top and bottom) by three (you should get 3/12). This allows you to subtract 2/3 and 1/4 to get a product of 5/12. You can not simplify this fraction any further so you have your answer!

-5/12

*EDIT

Don't forget the minus sign.

Answer:

sorry i wasnt gonna type it out. im on phone

Answer: x=3

Step-by-step explanation:

3x-7=17-5x

-7=17-8x (subtract both sides by 3x)

-24=-8x (subtract both sides by 17)

3=x (divide both sides by -24)

As per the concept of Combinations, there are 24 different are available to arrange the 4 different novels, 3 different mathematics books, and 1 biology book on a bookshelf if the novels cannot be together.

Combinations:

Combination refers the way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter.

Given,

Here we need to find the number of ways can 4 different novels, 3 different mathematics books, and 1 biology book be arranged on a bookshelf if the novels cannot be together.

Let us consider x be the number of ways those book can be arranged according to the given condition.

Here we know that the total number of book is

=>  4 + 3 + 1

=> 8

But the four novel can be placed together, so it can be placed as in between the books,

=> 4 x 3 x 3 x 2 x 2 x 1 x 1 x 1

=> 12 x 12

=> 24

Therefore, there are 24 ways to arrange the books in that given order.

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Step-by-step explanation:

the slope-intercept form is

y = ax + b

"a" is the slope (the slope is in all forms the factor of x). and "b" is the y-intercept (the y value when x = 0).

so the first equation is

y = -5x + b

b we get by using the point coordinates :

-22 = -5×5 + b = -25 + b

b = 3

so, the full equation is

y = -5x + 3

for the second equation we need to calculate the slope first. remember, it is the ratio "y coordinate change / x coordinate change" :

x changes by +1 (from -4 to -3).

y changes by +7 (from -2 to 5).

the slope is +7/+1 = 7/1 = 7.

the equation looks like

y = 7x + b

again, we use the coordinates of a point to get b. I picked (-4, -2) :

-2 = 7×-4 + b = -28 + b

b = 26

and the full equation is

y = 7x + 26

Answer:

6 Inches

Step-by-step explanation:

Per the above, we were given that;

1/4 inch = 5 feet

But,

X inch = 120 feet

We would represent the above as a ratio

1/4 inch / X inch = 5 feet / 120 feet

1/4 inch / X inch = 1 feet / 24 feet

When we cross multiply, we'll have

1/4 inch × 24 feet = X inch × 1 feet

X = 6 inches

Answer:

6 inches

Step-by-step explanation:

Answer:

it can written as 7(a×b)

The area of one base of the triangular prism is given as 16√3 square cm, and since the base is equilateral, the sides of the triangle are of equal length.

The formula to calculate the area of an equilateral triangle is (sqrt(3)/4) * s^2 where s is the length of a side of the triangle.

So, plugging in the given area of base, 16√3, we can find the length of a side of the equilateral triangle, s.

16√3 = (sqrt(3)/4) * s^2

s = (4*16√3)/sqrt(3) = 16√3 cm

Now we can use the height of the prism, which is given as 30 cm, to find the area of the rectangular surface.

Area of the rectangular surface = 2 * base area * height = 2 * 16√3 * 30 cm²

This simplifies to:

960√3 cm²

So the total area of the rectangular surface of the prism is 960√3 square cm.

Once we have identified these lines, we can add up their corresponding thickness values to find the thickness of the pile.

Therefore, the answer to the question is dependent on the specific thickness values of the four thinnest books on the line plot.

Maria has books of varying thicknesses, and a line plot has been provided to show the thickness of each book.

The question asks how thick the pile of the four thinnest books will be when they are stacked on top of each other.

To determine the thickness of the pile, we will need to find the total thickness of the four thinnest books on the line plot. We can do this by adding up the thicknesses of each of these four books.

Then, we will have the total thickness of the pile.

To make sure we have the correct four books, we will need to start from the left side of the line plot and select the four shortest lines.

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Answer:

D is not a function

Step-by-step explanation:

A function is a relation where the x values or domain do not repeat in this case the d repeats itself so it would be D

Answer:

the answer to your question is 61

Step-by-step explanation:

54+7=61

Answer:

47

Step-by-step explanation:

54-7=47

I'm assuming we are trying to find Rita's score. We know that the total is 54. "The sum" refers to addition, so we must reverse the problem to find her score

54- 7= 47

Total - 7 = her score

Answer:

Obtuse

Step-by-step explanation:

It's definitely not a right triangle.

And one angle is greater than 90 degrees.

The formula for dy/dx is the derivative of y with respect to x. It represents the rate of change of y with respect to x.

In calculus, the derivative of a function with respect to a variable x is a measure of how much the function changes as the variable x changes. The notation for the derivative of a function y with respect to x is dy/dx, read as "delta y over delta x". This notation is called a "derivative" and it represents the rate of change of the function y with respect to x.

The derivative of a function can be calculated using the limit definition of the derivative or with the use of different rules such as power rule, product rule, quotient rule, chain rule, and more. The derivative can also be represented graphically as the slope of a tangent line to the function's graph.

Derivatives are widely used in mathematics, physics, engineering, and other sciences to model various phenomena.

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Answer:

See below.

Step-by-step explanation:

The answer is each figure in group 2 has one face.

-hope it helps

The law of exponential change states that when a quantity grows or decays at a rate proportional to its size, then the quantity changes exponentially over time. In other words, it follows an exponential function as opposed to a linear function.

The law of exponential change describes the phenomenon of a quantity changing exponentially over time. This means that the rate of change is proportional to the quantity itself. For example, if a quantity increases by 10% each minute, then the quantity will double every 7.2 minutes. This is because each time the quantity increases by 10%, it is multiplying by 1.1. This process is ongoing and the rate of growth or decay will continue to increase exponentially.

The law of exponential change is used in many areas of science and mathematics, such as population growth and radioactive decay. It is also an important concept in economics, as it can be used to measure the growth of money over time.

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Answer:

-0.53

Step-by-step explanation:

5/4 *x -1/9 = 6x

-1/9 = (6-5/4) x

x = -4.75/9

x=-0.53

Answer:

980

Step-by-step explanation:

because the quotient of 2800 divided by 100 gives you the answer for 1% but then you multiply that answer by 35 and you get 980

980

35 percent of 2800 is 980

Perimeter = Sum of the sides measures

Perimeter = | AB | + | AT | + | BT |

Perimeter = ( x + 3 ) + ( 4x ) + ( 2x + 2 )

40 = x + 4x + 2x + 3 + 2

Colect like terms

40 = ( 1 + 4 + 2 )x + ( 3 + 2 )

40 = 7x + 5

Subtract both sides - 5

40 - 5 = 7x + 5 - 5

35 = 7x

Switch sides

7x = 35

Divide both sides by 7

7x ÷ 7 = 35 ÷ 7

x = 5

_____________________________

AB = x + 3 = 5 + 3 ======》 AB = 8

AT = 4x = 4 × 5 =========》 AT = 20

BT = 2x + 2 = 2(5) + 2 ===》 BT = 12

According to the law of inequality in a triangle, the sum of any two random sides must be greater than the size of the other side which means :

AB + AT > BT

&

AB + BT > AT

&

AT + BT > AB

If the sides is true in the above inequalities, then those sides are able to form a triangle ;

But if even one of the above inequalities is violated, those sides will not be able to form a triangle.

8 + 20 > 12 ( Check )

8 + 12 > 20 ( Nope this inequlity violated )

Thus the measures of the sides can not represent the measures of the sides of a triangle .

And we're done ...

The statement is generally true.

In materials science, the close-packing of atoms in crystal structures can affect the mechanical properties of the material, such as its ductility and ability to undergo plastic deformation.

In general, structures with closely packed planes (i.e., structures with a higher atomic packing factor) are more likely to undergo plastic deformation because the closely packed planes allow for more slip planes for atoms to move along without disrupting the overall crystal structure.

This means that when a force is applied to the material, the planes can slide more easily past one another, leading to plastic deformation.

In contrast, structures that are not closely packed (i.e., structures with a lower atomic packing factor) have fewer slip planes and are less likely to undergo plastic deformation. Instead, they may experience brittle fracture or other types of failure when subjected to stress.

However, it is important to note that the relationship between atomic packing and plastic deformation is complex and depends on a variety of factors, including the type of crystal structure, the presence of defects or impurities in the material, and the conditions under which the material is being deformed.

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Answer:

Point Form:  ( 4 , − 5 )

Equation Form:  x  =  4 ,  y  =  - 5

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:  ( 4 , − 5 )

Equation Form:  x  =  4 ,  y  =  - 5

Answer:

(4, - 5)

Step-by-step explanation:

3x - 4y = 32 ........ (1)

5x + 2y = 10 ....... (2)

(2) × 2 + (1)

13x = 52 ⇒ x = 4

3(4) - 4y = 32 ⇒ y = - 5

(4, - 5)

Answer:

The answer is 6.035%. Brainest, please

Step-by-step explanation: