Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answe f(x) = 2x3 + x2 + 4x x =

The average speed of NFL players varies by position and other factors, and while the forty-yard dash is a common measure of speed, it's important to consider other factors and potential biases when comparing average times between different years.

The average speed of NFL players can vary depending on their position and other factors such as age, height, and weight. The forty-yard dash is a common measure of speed and agility for NFL players.

Regarding the question about whether NFL players were significantly faster between 2012-2014 compared to previous years, we would need to compare the average forty-yard dash times for running backs and wide receivers from 2012-2014 to the average times from prior years to determine if there was a significant difference.

However, it's worth noting that the average forty-yard dash time can be influenced by a variety of factors, including changes in the testing conditions, differences in the player population being tested, and changes in training and coaching techniques. Therefore, we cannot make any definitive conclusions about changes in player speed based solely on this one measure.

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If an employee is selected at random, the probability that you will select a person who uses a suv or sedan is 85%.

Given data: Primary vehicles to commute to work :

Percentage of employees who use a boat = 10%

Percentage of employees who use a Sedan = 35%

Percentage of employees who use a SUV = 50%

Percentage of employees who use a Bicycle = 5%

Probability of selecting a person who uses a SUV or Sedan can be calculated as follows:

Probability of selecting a person who uses a SUV or Sedan= Probability of selecting a person who uses a SUV + Probability of selecting a person who uses a Sedan

Probability of selecting a person who uses a SUV or Sedan= 50% + 35%= 85%

Hence, the probability of selecting a person who uses a SUV or Sedan is 85%.

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(a) The number of ways the books can be arranged in any order is 362880,

(b) The number of ways the mathematics books must be together and the novels must be together is 4320.

Part(a) :

The number of mathematics-book is = 3,

The number of novels is = 5,

The number of biology books is = 1,

So, there are total of (5+3+1) = 9 books

These 9 books can be arranged in 9! = 362880 ways.

Part(b) :

If the mathematics book are together we can consider the mathematics books as 1 book and

if the novels are together then these 5 novels can be considered as one.

So, there are total 3 books which can be arranged in 3! Ways.

And these 5 novels can be arranged in themselves in 5! Ways and

these 3 mathematics books can be arranged in themselves in 3! ways.

So, total number of ways = 3!×3!×5! =6×6×120 = 4320 ways.

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Answer:

C. 13,200 mm²

Step-by-step explanation:

Overall, we have area of a rectangle which is 12000 and the area of the two triangles are 1200.

We both add them to get the area of the irregular shape.

12000 + 1200 = 13,200 mm²

AE and CD intersect at point B then angle ABD = 152°

A straight angle in mathematics is one with a degree value of 180. Because it resembles a straight line, it is called straight. Essentially, two rays linked end to end create an angle according to the definition of angles in mathematics. As a result, where the rays are linked at endpoints, the two 180-degree angle rays are subtended in the opposite direction.

AE and CD intersect at point B,

angle DBE = 48,

and AE is a straight line,

So the sum of angles on a straight line is 180,

We have to find the angle ABD,

∠DBE+∠ABD=180

∠ABD=180-48

∠ABD=152°

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The height of the plane is about 3855 feet and the distance from the nearer end of the runway is about 13580 feet.

To find out the height of the plane and the distance of it from the nearer end of the runway, we have to use trigonometry.

Let's start by finding the height of the plane, h.

Using the angle of depression of 12.5 degrees, we can write this equation:

tan 12.5 = h/d

Where d is the distance from the nearer end of the runway. If we cross-multiply, we get:

d = h/tan 12.5

We can use the equation from the other angle of depression to eliminate the distance,

d.tan 17.0 = h/(d + 10,000)

By substituting the previous equation in for d, we get:

tan 17.0 = h/(h/tan 12.5 + 10,000)

Simplifying: tan 17.0 = h(tan 12.5)/(h/tan 12.5 + 10,000)

Multiplying both sides by h/tan 12.5 + 10,000:

tan 17.0 (h/tan 12.5 + 10,000) = h tan 12.5

Expanding the left side: distributed = h + 10,000 tan 17.0 tan 12.5

Simplifying and isolating h: h = 10,000 tan 17.0 tan 12.5/(tan 12.5 - tan 17.0) ≈ 3855 ft

Therefore, the height of the plane is about 3855 feet. To find the distance from the nearer end of the runway, we use the previous equation:d = h/tan 12.5 ≈ 13580 ft

Therefore, the distance from the nearer end of the runway is about 13580 feet.

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Anna's monthly Salary in June was $3600 as she received a 20% rate and her monthly Salary in July was $2880 as she received a 20% pay cut from June.

It is given to us that: Ana's salary in May =3000$

in June she received 20% raise

the amount she received in June after 20% raise = 3000 x 20/100

= 30 x 20 = 600

we have to first find Ana's salary at the end of June month with 20% raise. and then her salary after the end of July month with the pay cut of 20%.

Ana's salary after June month when she got 20% raise in his salary after May:

= 3000 + (20% x 3000)

= 3000 + (20/100 x 3000)

= $3600

her new salary after June will be 3600$.

therefore, she received 3600 in June.

in July she received 20% pay cut.

To find Ana's monthly salary after the two changes in June and July.

Ana's salary after June month when she got 20% raise in his salary after May = $3600

now she got a pay cut of 20% on his new salary from July month,

= 3600 - (20% x 3600)

= 3600 + (20/100 x 3600)

= 3600 - 720

= $2880

so, her salary after that would be equal to $2880.

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5y+15

I think this is correct. Hope this helps:)

Answer: 5y + 15

Step-by-step explanation: 5(y+3)

                                            = 5(y) + 5(3)

                                            = 5y + 15

The correct statement regarding the solution of the system of equations is given as follows:

A. The solution to the system is viable.

The situation is modeled by a system of equations, for which the variables are given as follows:

From each row of the table, the equations are given as follows:

Subtracting the third equation by the second, the value of x is given as follows:

2x = 178

x = 178/2

x = 89.

From the first equation, the value of y is given as follows:

y = [614 - 4 x 89]/2

y = 129.

From the second equation, the value of z is given as follows:

z = 555 - 3 x 89 - 129

z = 159.

Hence the system has a viable solution.

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The probability that each of you orders a different type of sandwich is 72%.

To find the probability that each of you orders a different type of sandwich, we can use the counting principle.
Step 1: Determine the total number of ways you and your friends can order sandwiches.

Since there are 10 types and each of you can choose any type, there are 10 * 10 * 10 = 1000 possible ways to order.
Step 2: Calculate the number of ways you can order different types of sandwiches.

For the first person, there are 10 choices.

For the second person, there are 9 remaining choices (since their sandwich must be different from the first person's). For the third person, there are 8 remaining choices (different from both the first and second person's choices). So there are 10 * 9 * 8 = 720 ways to order different types of sandwiches.
Step 3: Calculate the probability of ordering different types of sandwiches.

Divide the number of ways to order different sandwiches by the total number of ways to order:
Probability = (Number of ways to order different sandwiches) / (Total number of ways to order)
Probability = 720 / 1000 = 0.72 or 72%.

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The rectangular bird sanctuary has dimensions of  12 km by 6 km in size to reduce the amount of fencing required to enclose the other three sides.

   The given rectangular bird sanctuary has a side along a straight river. To minimize the amount of fence necessary to enclose the remaining three sides, we need to find the dimensions of the rectangle.

  Therefore, let us consider that the width of the rectangular bird sanctuary is x and the length is y.

  The area of the given bird sanctuary is given as,

                A = xy= 72 km²

   The amount of fence required for the bird sanctuary can be written as,

                 F = 2x + since we are looking to minimize the amount of fence necessary to enclose the remaining three sides, we need to differentiate the expression for a fence with respect to x and equate it to zero to obtain the value of x that will minimize the fence.

              dF/dx = 2 - 0 (since dy/dx = 0)

     Therefore, dF/dx = 2 Let us consider this to be equation (1) Differentiating the expression for a fence with respect to y and equating it to zero to obtain the value of y that will minimize the fence.

             dF/dy = 0 + 1 (since dx/dy = 0)

      Therefore, dF/dy = 1

Let us consider this to be equation (2)

      Now, we can solve equations (1) and (2) to obtain the values of x and y that will minimize the fence.

            dF/dx = 2 ⇒ 2x + y

                       = 0dF/dy

                       = 1 ⇒ 2y + x

                      = 0

       Solving the above two equations for x and y, we get x = 12 km and y = 6 km

       Therefore, the dimensions of the rectangular bird sanctuary are 12 km and 6 km to minimize the amount of fence necessary to enclose the remaining three sides.

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The expression that makes the equation true is: (4 x 3) ÷ 2.

option 1 is the correct answer.

In mathematics, an expression is a combination of symbols and/or values that represents a quantity or a relationship between quantities. It can include variables, constants, mathematical operations, and functions.

first, let's simplify the expression within the parentheses:

3 x 5 + 1 = 15 + 1 = 16

Now, we can simplify the entire expression:

1/2 x (3 x 5 + 1) - 2 = 1/2 x 16 - 2 = 8 - 2 = 6

So, we need to select the expression that equals 6:

6 ÷ 3 + 2 = 4

6 + 8 ÷ 4 = 8

(4 x 3) ÷ 2 = 6

Therefore, the expression that makes the equation true is: (4 x 3) ÷ 2.

option 1 is the correct answer.

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Answer:

        .

(4x3)---- 2

         .

B

Step-by-step explanation:

hope this help!

Answer:

I just had to say those numbers because of so I can send it like I'm about

To find the lower bound and upper bound of the difference m-n, we need to first find the possible range of values for m and n.

• For m rounded to 1 decimal place, the actual value could be anywhere between 48.15 and 48.25 (since the digit in the second decimal place could be anything from 0 to 9, and we round to the nearest 0.1).

• For n rounded to 1 decimal place, the actual value could be anywhere between 6.65 and 6.75.

Now, we can calculate the lower bound and upper bound of m-n:

Lower bound of m-n = (48.15 - 6.75) = 41.4

Upper bound of m-n = (48.25 - 6.65) = 41.6

Therefore, the lower and upper bounds of m-n are 41.4 and 41.6, respectively.

Answer:-1.5

Step-by-step explanation:

first distribute 3

to get 6x + 3= 4x

then -6x on right side to get

3= -2x

then divide by -2

3/-2= x

x= -1.5

Hello !

Answer:

[tex]\Large \boxed{\sf x=-\frac{3}{2}}[/tex]

Step-by-step explanation:

We're looking for the value of x that satisfies the following equation :

[tex]\sf 3 (2x+1) = 4x[/tex]

We need to isolate x.

First, let's expand left side :

[tex]\sf 3\times 2x+3\times1=4x\\6x+3=4x[/tex]

Now let's substract 4x from both sides :

[tex]\sf 6x+3-4x=4x-4x\\2x+3=0[/tex]

Substract 3 from both sides :

[tex]\sf 2x+3-3=0-3\\2x=-3[/tex]

Finally, let's divide both sides by 2 :

[tex]\sf \frac{2x}{2} =-\frac{3}{2} \\\boxed{\sf x=-\frac{3}{2}}[/tex]

Have a nice day ;)

Answer:

Step-by-step explanation:

The distributive property of multiplication over addition can be used when you multiply a number by a sum. For example, suppose you want to multiply 3 by the sum of 10 + 2. 3(10 + 2) = ? According to this property, you can add the numbers and then multiply by 3.

Rounding to the nearest whole number, Dr. Powell can expect about 16 micrograms of medication to be remaining in Ruby's body after 4 hours.

In mathematics, an equation is a statement that two expressions are equal. It typically consists of two sides, a left-hand side and a right-hand side, separated by an equal sign (=). Equations are used to represent relationships between variables or to solve for unknown values. They are an important tool in algebra, calculus, and other areas of mathematics and science.

Here,

The exponential equation in the form y = a(b)^x that can model the amount of medication in Ruby's body, y, x hours after it was administered is:

y = 40(0.8)ˣ

where:

a = 40, the initial amount of medication given to Ruby

b = 0.8, the factor by which the medication decreases each hour

To find the amount of medication remaining in Ruby's body after 4 hours, we can substitute x = 4 into the equation and evaluate:

y = 40(0.8)⁴

y = 40(0.4096)

y = 16.384

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Answer:

(-2/5, 11/5)

Step-by-step explanation:

We can use the formula for finding a point that divides a line segment into a given ratio. Let P be the point on the line segment QR that partitions it in the ratio 2:3. Then we have:

P = ( (3x2 + 2x1)/(3+2), (3y2 + 2y1)/(3+2) )

where (x1, y1) = (-8, -8) is the coordinates of Q and (x2, y2) = (2, 7) is the coordinates of R.

Substituting the values, we get:

P = ( (32 + 2(-8))/(3+2), (37 + 2(-8))/(3+2) )

P = ( (-2/5), (11/5) )

Therefore, the coordinates of the point P on the directed line segment QR that partitions it in the ratio 2:3 are (-2/5, 11/5).

Answer:

y = - [tex]\frac{1}{2}[/tex] (x + 3)² + 4

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here (h, k ) = (- 3, 4 ) , then

y = a(x - (- 3) )² + 4 , that is

y = a(x + 3)² + 4

to ind a substitute the point (1, - 4 ) into the equation

- 4 = a(1 + 3)² + 4

- 4 = a(4)² + 4 ( subtract 4 from both sides )

- 8 = 16a ( divide both sides by 16 )

- [tex]\frac{8}{16}[/tex] = a , that is

a = - [tex]\frac{1}{2}[/tex]

y = - [tex]\frac{1}{2}[/tex] (x + 3)² + 4 ← equation of parabola

Answer: 59.02 square inches

Step-by-step explanation:

We can use the formulas for the volume and surface area of a sphere to solve this problem.

The formula for the volume of a sphere is:

V = (4/3)πr^3

Where V is the volume, r is the radius, and π is pi (approximately equal to 3.14159).

We know that the volume of the sphere is 33.51 cubic inches, so we can plug that in and solve for the radius:

33.51 = (4/3)πr^3

r^3 = (3/4) * (33.51/π)

r^3 = 10.56

r ≈ 2.17

Now that we know the radius is approximately 2.17 inches, we can use the formula for the surface area of a sphere to find the surface area:

A = 4πr^2

A = 4π(2.17)^2

A ≈ 59.02 square inches

Therefore, the surface area of the sphere is approximately 59.02 square inches.

Answer: The nth term of the sequence is given by the formula 2n + 11

Step-by-step explanation:

The given sequence is an arithmetic sequence because the difference between each pair of consecutive terms is the same. In this case, the common difference is 2, because:

15 - 13 = 2

17 - 15 = 2

and so on

The formula for the nth term of an arithmetic sequence is:

an = a1 + (n-1)d

where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.

For this sequence, the first term (a1) is 13 and the common difference (d) is 2. Therefore, the formula for the nth term is:

an = 13 + (n-1)2

Simplifying this expression, we get:

an = 2n + 11

Answer: To solve this problem, we can start by drawing a diagram of the two triangles and the line connecting their hypotenuses. Let's label the height of the first triangle as h1, the width of the second triangle as w2, and the slope of the line as m.

We know that the hypotenuse of a right triangle is always longer than either of its legs, so we can conclude that h1 < w2. We also know that the height of the second triangle is 12 units, so we can label that as h2 = 12.

Using the Pythagorean theorem, we can express the lengths of the hypotenuses in terms of their legs:

h1^2 + 3^2 = L^2, where L is the length of the first hypotenuse

w2^2 + 12^2 = L^2, where L is the length of the second hypotenuse

Setting these two expressions equal to each other, we can solve for h1 in terms of w2:

h1^2 + 3^2 = w2^2 + 12^2

h1^2 = w2^2 + 12^2 - 3^2

h1^2 = w2^2 + 141

h1 = sqrt(w2^2 + 141)

Now, we can use the fact that the hypotenuses lie on the same line to write an equation for that line:

y = mx + b

where b is the y-intercept of the line. Since the hypotenuses intersect the y-axis at the points (0,h1) and (0,12), we know that b = (h1 + 12)/2. Therefore, our equation becomes:

y = mx + (h1 + 12)/2

To find the slope of the line, we can use the fact that the rise (change in y) over run (change in x) is the same for both triangles. We can express this as:

(h1 - 12) / 3 = 12 / w2

Solving for h1 in terms of w2 and simplifying, we get:

h1 = (36/w2) + 12

Substituting this expression for h1 into our equation for the line, we get:

y = mx + ((36/w2) + 24)/2

y = mx + (18/w2) + 12

Comparing this to the general form of the equation for a line, y = mx + b, we see that the slope is simply:

m = 18/w2

Substituting w2 = 3 (since we were given that the width of the second triangle is 3 units), we get:

m = 18/3 = 6

Therefore, the slope of the line is 6.

Step-by-step explanation:

Answer:

3x + 12

Step-by-step explanation:

3(x + 4) ​

3x + 12

So, the expand is 3x + 12

Answer:

3x + 12

Step-by-step explanation:

You multiply the outside of the perentheses by everything inside, and 3(x) + 3(4) = 3x + 12

Answer:

A=1 B=2 C=3   Domain: [2, infinity) Range: (neg. infinity, 3]

Step-by-step explanation:

a is rate B is Horitzontal shift C is vertical shift

Answer:

(x-2.5)^2 + 1.75

Step-by-step explanation:

To write that as an equation, we get x^2 - 5x + 8.

now, we need to complete the square:

x^2 - 5x + 6.25 + 1.75 =

(x-2.5)^2 + 1.75.

Real number that is greater than or equal to zero. The only number that is both positive and negative is the number 0.

Answer:

Step-by-step explanation:

I have two questions; One, are you the student? Two, is this a trick question because if it is it's freaking hilarious