does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = x/ x + 2 , [1, 4]
Yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem. No, f is continuous on [1,4] but not differentiable on (1,4). There is not enough information to verify if this function satisfies the mean value theorem. No, f is not continuous on [1,4]. Yes, f is continuous on [1,4] and differentiable on (1,4).

Step-by-step explanation:

$9.99 + $0.35t <= $12

$0.35t <= $2.01

t <= 5.74

The most number of toppings would be 5.

Answer:

9.99 + 0.35t ≤ 12

5 toppings

Step-by-step explanation:

First part of question:

9.99 + 0.35t ≤ 12

"At most" means you use ≤.

Second part of question:

Take the inequality and solve for t:

9.99 + 0.35t ≤ 12

0.35t ≤ 2.01

t ≤ 5.74

So, the most number of toppings that a pizza can have and still be at most $12 is 5 toppings. You have to round down 5.74 to 5 otherwise the cost will exceed $12.

The probability that it has a hairline crack is 19/27.

Given that;

In a shipment of 54 vials, only 16 do not have hairline cracks.

Let shipment of 54 Vials;

x(s) = 54

Let,' A ' be the event that selects 16

x(A) = 16

P(A) = x(A) / x(s)

       = 16/54

But only 16 don't have hairline Crakes;

To solve a given case;

The probability that it has a hairline crack is:

P(A') = 1 - P(A)

       = 1- 16/54

P(A') = 19/27

Hence, the probability that it has a hairline crack is 19/27.

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Answer:

360,450

Step-by-step explanation:

First find 19 percent of 455,000

19*445000= 8455000

8455000/100= 84550

Then subtract:

445,000-84,550= 360,450

Hope this helps! :) Pls mark brainliest if correct :)

Answer:

Hey there!

Step-by-step explanation:

This is ur answer...

Hope it helps!

Brainliest pls!

Have a good day!^^

❄ Hi there,

the coefficient of a variable is a number multiplied by that variable; it can be any real number.

∴,

\(\hfill\stackrel{\textbf{coefficient of x}}{5}\)

\(\hfill\stackrel{\textbf{coefficient of y}} {-3}\)

That's it.                              

❄                                                                                                   \(\small\pmb{Frozen \ melody}\)

Answer:

No.

Step-by-step explanation:

This is not a right triangle. Use the Pythagorean Theorem, \(a^{2} + b^{2}=c^{2} \\\), but write it as \(c^{2}= a^{2}+b^{2}\). The hypotenuse would be 17 feet, so you can insert 17 as \(c^{2}\). \(a\) and \(b\) could be 6 or 16. It can be written either way. The simplified equation would be:

\(c^{2}=a^{2} +b^{2} \\17^{2} = 6^{2} + 16^{2} \\17^{2} = 36+ 256\\17^{2}= 292\\289\neq 292\)

This isn't a right triangle.

I hope this helped :)

The maximum value of the function on the closed interval is 11

Given  the function

f(x) = 2x + 5, with interval [-10, 3].

First need to find the critical points of the function within the interval and compare their values. The critical points occur when the derivative of the function is equal to zero or undefined.

first order derivative of f(x):

f'(x) = 2 ≠ 0 (no critical points)

Since the interval is bounded, the maximum value of the function occurs at either one of the endpoints or at a critical point outside the interval.

At x = -10,

f(-10) = 2(-10) + 5 = -15

At x = 3,

f(3) = 2(3) + 5 = 11

Therefore, the maximum value of f(x) on the closed interval [-10, 3] is 11, which occurs at x = 3.

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Answer:

(x+8)

Step-by-step explanation:

Answer:

x2 + 8x + 12

Step-by-step explanation:

(x + 2) (x + 6) = x (x + 6) + 2 (x + 6)

= x * x + 6x + 2 (x + 6)

= x2 + 6x + 2 (x + 6)

= x2 + 6x + 2x + 2 * 6

= x2 +6x + 2x + 12

= x2 + 8x + 12

Answer: $4,000

Step-by-step explanation:

If you have $1,000 dollars, and take ad ten percent ($100) interest you would get $1,100. But If you take away 30 percent ($300) away from 1,100 dollars you would get $800 dollars. The over all balance on the account after five years is, $4,000.

Hope this answer helps! :)

Answer: Try A; 13 units

Step-by-step explanation:

count the number of units

Answer:

Are you doing monarch?

If so I do too!

Answer:

2/10

you have to match the bottom number on both fractions then do what ever you did to the top number

so with this to get the 5 to a 10 you have to times it by 2

so you do the same to the 1

Step-by-step explanation:

Rewrite the expression using the definition of base of a log:

Answer:

a = 27

The infinite series ax/a+x can be expressed as a geometric series with the sum being a/a-x.

The infinite series for ax/a+x can be represented as a geometric series. The first five terms can be expressed as:

\(Term 1: ax/(a+x)\\Term 2: (ax)^2/(a+x)^2\\Term 3: (ax)^3/(a+x)^3\\Term 4: (ax)^4/(a+x)^4\\Term 5: (ax)^5/(a+x)^5\)

The infinite series can be expressed using summation notation as:

\(∑_(n=1)^∞ (ax)^n / (a+x)^n\)

Using the formula for a geometric series, the sum of the infinite series can be calculated as:

\(S = ax/(a+x) * 1/(1-ax/(a+x)) \\ = ax/(a+x) * (a+x)/(a-ax) \\ = ax/(a-ax) \\ = a/a-x\)

Therefore, the infinite series ax/a+x can be expressed as a geometric series with the sum being a/a-x.

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Answer:10

Step-by-step explanation:

10

Answer:

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

2x - y = 4

y = -2x + 8

-y = -2x + 4

y = -2x + 8

0 = -4x + 12

-4x = -12

x = 3

The null hypothesis is based on the idea that there is no relationship between the variables.

What is null hypothesis?

The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable. The null hypothesis can be evaluated to determine whether or not there is a relationship between two measured phenomena, which makes it valuable. It can let the user know if the outcomes are the product of random chance or deliberate manipulation of a phenomenon.

The null hypothesis states that there is no relationship between two population parameters, i.e., an independent variable and a dependent variable. Therefore, the null hypothesis is based on the idea that there is no relationship between the variables.

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Answer:

----------------------

Find the hypotenuse c of the base using Pythagorean theorem:

Lateral surface area, three rectangular faces, is:

Find base area, the area of two right triangles:

Find total surface area:

There is a 0.25 and a 0.5 chance that the flight will arrive no more than 5 and 10 minutes late, respectively. 130 minutes is the estimated flight time.

Probability density function: It can take on any value and is used to define the random unknown probability falling inside a specific range of values.

For its flights from Cincinnati to Tampa, Delta Airlines reports a flight duration of 2 hours and 5 minutes.

Let's say we think the range of real flight timings is 2 hours to 2 hours and 20 minutes.

a)Between 120 and 140 minutes, the probability density function for a continuous uniform random variable is given as

\(f(x)=\left \{ {{\frac{1}{140-120},120 \leq x\leq 140}\\ \atop {0.o.e}} \right.\)

b)The likelihood that the flight will arrive no later than five minutes late is

integration from 130 to 125 of 1/20dx=5/20=1/4=0.25

c)There is a 10% chance that the flight will arrive no more than 10 minutes late.

integration from 135 to 125 of 1/20dx=10/20=0.5

d)The anticipated duration of the flight, in minutes, is

integration from 140 to 120 of x/20dx=(5200*5)/(2*20)=130

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On solving the provided question, we can say that Area of the rectangle2 = L X B = 9*6 = 54 ft sq.

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

here,

Area of the rectangle1 = L X B

27 = 3 X B
B = 27/3 = 9 ft

Area of the rectangle2 = L X B = 9*6 = 54 ft sq.

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9514 1404 393

Answer:

{2, 2, 2}, {2, 3, 3}, {2, 4, 4}, {3, 2, 3}, {3, 3, 2}, {3, 3, 4}, {3, 4, 3}, {4, 2, 4}, {4, 3, 3}, {4, 4, 2}, {5, 2, 5}, {6, 2, 6}

Step-by-step explanation:

The requirement that side lengths be greater than 0 means that ...

  y > x > 0

  y > z > 0

Then possible values for x and z are 1, 2, 3, and possible values for y are 3, 4, 5, 6, 7.

When we list the possibilities, and exclude those that do not give isosceles triangles, we find the values of {a, b, c} can be those listed above.

Answer:

He is wrong by 7.14%

Answer:

7.14

Step-by-step explanation:

The absolute maximum value of f(x, y) is √13, and the absolute minimum value is -√13.

To find the absolute maximum and minimum values of the function f(x, y) = 2x - 3y subject to the constraint \(x^{2}\) + \(y^{2}\) = 1, we can use the method of Lagrange multipliers. Let's set up the following system of equations:

∇f = λ∇g

g(x, y) =  \(x^{2}\) + \(y^{2}\)  - 1

where ∇f and ∇g are the gradients of f and g, respectively, and λ is the Lagrange multiplier.

The partial derivatives are:

∂f/∂x = 2

∂f/∂y = -3

∂g/∂x = 2x

∂g/∂y = 2y

Setting up the system of equations:

2 = λ(2x)

-3 = λ(2y)

\(x^{2}\) + \(y^{2}\) = 1

From the first equation, we have x = λ.

From the second equation, we have y = -3λ/2.

Substituting these values into the third equation:

(λ\()^{2}\) + (-3λ/2\()^{2}\) = 1

(λ\()^{2}\)  + (9(λ\()^{2}\) /4) = 1

(13(λ\()^{2}\) )/4 = 1

(λ\()^{2}\)  = 4/13

λ = ±2/√13

Now, we can find the corresponding values of x and y:

For λ = 2/√13:

x = 2/√13

y = -3(2/√13)/2 = -3/√13

For λ = -2/√13:

x = -2/√13

y = -3(-2/√13)/2 = 3/√13

Now, we evaluate the function f(x, y) at these points:

f(2/√13, -3/√13) = 2(2/√13) - 3(-3/√13) = (4 + 9)/√13 = 13/√13 = √13

f(-2/√13, 3/√13) = 2(-2/√13) - 3(3/√13) = (-4 - 9)/√13 = -13/√13 = -√13

Therefore, the absolute maximum value of f(x, y) = 2x - 3y subject to the constraint  \(x^{2}\) + \(y^{2}\) = 1 is √13, and the absolute minimum value is -√13.

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Answer:

20°

Step-by-step explanation:

Exterior angle property: The exterior angle of a triangle equals the sum of opposite interior angles.

  ∠XYZ  = ∠YWX + ∠WXY

10x - 5   = 3x + 17 + 3x + 2

 10x - 5  = 3x + 3x + 17 + 2

  10x - 5 = 6x + 19

        10x = 6x + 19 + 5

        10x = 6x + 24

10x - 6x  = 24

        4x  = 24

         x   = 24÷ 4

           \(\sf \boxed{x = 6}\)

∠WXY =  3x + 2

           = 3*6 + 2

          = 18 + 2

          = 20°

When x = -2:

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

f(-2) = 6 +1

f(-2) = 7

y = 7

When x = 0:

f(0) = -3 (0) + 1

f(0) = 0 +1

f(0) = 1

y = 1

When x = 3:

f(3) = -3 (3) +1

f(3) = -3 (3) + 1

f(3) = -9 +1

f(3) = -8

y = -8

So, the Range is {7, 1, -8}

From the deposit slip

The amount on each check is

Check #162 = $123.51

Check #234 = $211.00

Check #521 = $214.14

The summation of the amount on each check is\

T

Answer: $521.24

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's call the two angles in the ratio of 4:13 "x" and "y".

We know that the sum of all three angles in a triangle is always 180 degrees.

So, we can set up an equation:

10 + x + y = 180

We also know that x and y are in a ratio of 4:13, which means we can write:

x = 4k

y = 13k

where "k" is a constant that we need to find.

Substituting these expressions for x and y into the equation, we get:

10 + 4k + 13k = 180

17k = 170

k = 10

Now we can find the values of x and y:

x = 4k = 4(10) = 40

y = 13k = 13(10) = 130

Therefore, the measures of the two angles in the ratio of 4:13 are 40 degrees and 130 degrees, respectively.

Answer:

13%

Step-by-step explanation:

C(n, x) • \(p^{x}\) • \(q^{n-x}\)

x = number of successes = 2

p = probability of success = 3/7

q = probability of failure = 1 = 3/7

n = number of games

(3/7)^2 x (4/7)^(9-2) = 13%