Find the value of x. Round to the nearest degree.

SOMEONE, PLEASE HELP ME!!

The function f(x) = x + 10√(9 - x) is increasing on the interval (-∞, 9) and decreasing on the interval (9, ∞).

To determine the intervals on which the function is increasing or decreasing, we need to find the derivative of the function and analyze its sign.

Let's find the derivative of the function f(x) = x + 10√(9 - x) with respect to x.

f'(x) = 1 + 10 * (1/2) * (9 - x)^(-1/2) * (-1)

= 1 - 5√(9 - x) / √(9 - x)

= 1 - 5 / √(9 - x).

To analyze the sign of the derivative, we need to find the critical points where the derivative is equal to zero or undefined.

Setting f'(x) = 0:

1 - 5 / √(9 - x) = 0

5 / √(9 - x) = 1

(√(9 - x))^2 = 5^2

9 - x = 25

x = 9 - 25

x = -16.

The critical point is x = -16.

We can see that the derivative f'(x) is defined for all x values except x = 9, where the function is not differentiable due to the square root term.

Now, let's analyze the sign of the derivative f'(x) in the intervals (-∞, -16), (-16, 9), and (9, ∞).

For x < -16:

Plugging in a test value, let's say x = -17, into the derivative:

f'(-17) = 1 - 5 / √(9 - (-17))

= 1 - 5 / √(9 + 17)

= 1 - 5 / √26

≈ 1 - 0.97

≈ 0.03.

Since f'(-17) is positive, the function is increasing in the interval (-∞, -16).

For -16 < x < 9:

Plugging in a test value, let's say x = 0, into the derivative:

f'(0) = 1 - 5 / √(9 - 0)

= 1 - 5 / √9

= 1 - 5 / 3

≈ 1 - 1.67

≈ -0.67.

Since f'(0) is negative, the function is decreasing in the interval (-16, 9).

For x > 9:

Plugging in a test value, let's say x = 10, into the derivative:

f'(10) = 1 - 5 / √(9 - 10)

= 1 - 5 / √(-1)

= 1 - 5i,

where i is the imaginary unit.

Since the derivative is not a real number for x > 9, we cannot determine the sign.

Combining the information, we conclude that the function f(x) = x + 10√(9 - x) is increasing on the interval (-∞, 9) and decreasing on the interval (9, ∞).

For more such questions on function, click on:

https://brainly.com/question/11624077

#SPJ8

Answer:

Undefined

Step-by-step explanation:

yep, it was right

The tangent of the given angle is undefined, so the correct option is C.

We know that the terminal point of θ is (0, 1).

Now, the tangent of an angle is equal to the quotient between the y-component and the x-component of the terminal point, then we have:

tan(θ) = 1/0

And we can't divide by zero, so it is undefined, then the correct option is C.

If you want to learn more about the tangent function:

https://brainly.com/question/6904750

#SPJ2

Answer:

-15

Step-by-step explanation:

The solution of expression for x = - 4 is,

⇒ - 15

We have to given that,

An expression is,

⇒ 2x - 7

Now, We can simplify the expression for x = - 4 as,

An expression is,

⇒ 2x - 7

Plug x = - 4;

⇒ 2 × - 4 - 7

⇒ - 8 - 7

⇒ - 15

Thus, The solution of expression for x = - 4 is,

⇒ - 15

Learn more about the equation visit:

brainly.com/question/28871326

#SPJ6

Answer:

B) SA = 984 cm²

Step-by-step explanation:

SA = (2 x 13 x 24) + (10 x 24) + (10 x 12) = 984 cm²

Answer:

4=11

$19.25=15

30=$38.75

Answer:

3 divided by (1+2)=1

Step-by-step explanation:

bc u do parthensis first so 1+2 is 3 therfore if u divide 3 by 3 gives u one

The probability of getting a Z-score of 2.44 or higher is approximately 0.0148. Therefore, the answer is (c) 0.0148.

Probability refers to the likelihood or chance of an event occurring, expressed as a number between 0 and 1.

A probability of 0 indicates that an event is impossible, while a probability of 1 indicates that an event is certain to occur. For example, the probability of rolling a 7 on a fair six-sided die is 0, while the probability of rolling a 1, 2, 3, 4, 5, or 6 is 1/6.

Probabilities can also be expressed as percentages, with a probability of 0.5 (or 50%) indicating an even chance of an event occurring.

To find the P-value for the hypothesis test, we can use the formula:

P-value = P(Z ≥ Z-score) or P(Z ≤ Z-score)

where Z-score is given by:

Z-score = (X'1 - X'2) / (s1²/n1 + s2²/n2)¹/²

and X'1 - X'2 is the difference in sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, and the formula assumes that the population variances are equal.

Substituting the given values, we get:

Z-score = (8 - 7) / ((2.5²/50) + (2²/50))¹/² = 2.44

Using a standard normal distribution table, we can find that the probability of getting a Z-score of 2.44 or higher is approximately 0.0148. Therefore, the answer is (c) 0.0148.

To know more about Z-score visit:

https://brainly.com/question/28979122

#SPJ1

The complete question is:

Assume that you plan to use a significance level of α = 0.05 to test the claim that µ1 = µ2. Use the given sample sizes and numbers of successes to find the P-value for the hypothesis test. n1 = 50 n2 = 50 µ1 = 8 µ2 = 7 s1 = 2.5 s2 = 2

a. 0.0295

b. 0.9852

c. 0.0148

d. 0.0500

Answer:

Because the product is always a non-terminating, non-repeating decimal.

The product of a rational number and an irrational number will always be an irrational number. Then the correct option is A.

If the value of a numerical expression is terminating then they are the rational number then they are called the rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.

The product of a rational number and an irrational number will always be an irrational number.

Because the product is always a non-terminating, non-repeating decimal number.

Then the correct option is A.

More about the rational number link is given below.

https://brainly.com/question/9466779

#SPJ2

Answer:

sept one

Step-by-step explanation:

By using the Unitary Method we get the number of children who went on an excursion was 63. Thus, the total number of children at school is 90.

We are given that,

No. of children who stayed at school is 27,

Also, 70% of the children went on an excursion.

Suppose, the total number of children in percentage is 100%

Out of which 70% went on an excursion

Thus, the children who stayed at school is 100% - 70% = 30%

By using the Unitary method, we can find out the number of 70% of children.

If 30% of the children are 27

Then 70% of the children are = 27 × 100

                                                        30

                                                 = 63

∴ the total no. of children in the school = 27 + 63

                                                                 = 90

To learn more about the Unitary method refer to the link below:

https://brainly.com/question/8083231

Answer:

Step-by-step explanation:

66

Answer:

The non-negative zero of the function f(x) is x = 2.

Step-by-step explanation:

For a given function f(x), the "zeros" of the function are the values of x such that:

f(x) = 0

In this case, we have the function:

f(x) = 6*x^2 - 9*x - 6

If we want to find the zeros of this function, we need to solve:

f(x) = 0 =  6*x^2 - 9*x - 6

To solve this, we can use the Bhaskara's formula, which says that for a general quadratic equation:

0 = a*x^2 + b*x + c

The zeros are:

\(x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}\)

In this case our equation is:

0 =  6*x^2 - 9*x - 6

then, in the above notation, we have:

a = 6

b = -9

c = -6

Replacing these in our general formula, we get:

\(x = \frac{-(-9) \pm \sqrt{(-9)^2 - 4*6*(-6)} }{2*6} = \frac{9 \pm 15 }{12}\)

Then we have two zeros:

x = (9 + 15)/12 = 24/12 = 2

x = (9 - 15)/12 = -6/12 = -1/2

But we want only the non-negative, so we can discard the second one.

Concluding, the non-negative zero of the function f(x) is x = 2.

Answer:

x intercept= (11.429,0) and it doesn't have an y intercept

Step-by-step explanation:

No y intercept because it is parallel to the y axis

The rate at which the volume of the cylinder is changing at that moment is 1200π mm³/min.

The rate at which the surface area of the cylinder is changing at that moment is 240π mm²/min.

The rate at which the volume and surface area of a cylinder are changing, we can use the given information and the formulas for volume and surface area.

Given:

Rate of change of the radius, dr/dt = 3 mm/min

Height, h = 20 mm

Radius at the moment of interest, r = 10 mm

Rate of change of volume (dV/dt):

The formula for the volume of a cylinder is V = πr²h.

Differentiating both sides with respect to time (t), we get:

dV/dt = 2πrh(dr/dt) + πr²(dh/dt)

Since the height (h) is constant, dh/dt = 0.

Substituting the given values:

dV/dt = 2π(10)(20)(3) + π(10)²(0)

dV/dt = 1200π + 0

dV/dt = 1200π mm³/min

Rate of change of surface area (dA/dt):

The formula for the surface area of a cylinder is A = 2πrh + 2πr².

Differentiating both sides with respect to time (t), we get:

dA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)

Again, since the height (h) is constant, dh/dt = 0.

Substituting the given values:

dA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)

dA/dt = 0 + 120π + 120π

dA/dt = 240π mm²/min

Your calculations were correct.

The rate of change of volume is 1200π mm³/min, and the rate of change of surface area is 240π mm²/min.

For similar questions on cylinder

https://brainly.com/question/23935577

#SPJ8

a. The rate at which the volume of the cylinder is changing when the radius is 10 mm is 1200π mm³/min.

b. The rate at which the surface area of the cylinder is changing when the radius is 10 mm is 120π mm²/min.

To find the rate at which the volume and surface area of the cylinder are changing, we can use the formulas for volume and surface area of a cylinder and apply the chain rule of differentiation.

Given:

Rate of change of radius (dr/dt) = 3 mm/min

Height (h) = 20 mm

Radius (r) = 10 mm

1. Rate of change of volume (dV/dt):

Volume (V) = πr²h

Differentiating both sides with respect to time (t):

dV/dt = d/dt (πr²h)

Using the chain rule:

dV/dt = 2πrh(dr/dt) + πr²(dh/dt)

Substituting the given values:

dV/dt = 2π(10)(20)(3) + π(10²)(0)

dV/dt = 1200π + 0

dV/dt = 1200π mm³/min

Therefore, the rate at which the volume of the cylinder is changing when the radius is 10 mm is 1200π mm³/min.

2. Rate of change of surface area (dSA/dt):

Surface Area (SA) = 2πrh + 2πr²

Differentiating both sides with respect to time (t):

dSA/dt = d/dt (2πrh + 2πr²)

Using the chain rule:

dSA/dt = 2πh(dr/dt) + 2πr(dh/dt)

Substituting the given values:

dSA/dt = 2π(20)(3) + 2π(10)(0)

dSA/dt = 120π + 0

dSA/dt = 120π mm²/min

Therefore, the rate at which the surface area of the cylinder is changing when the radius is 10 mm is 120π mm²/min.

Learn more on rate of change of volume of cylinder here;

https://brainly.com/question/9408912

#SPJ4

Answer:

p=9

Step-by-step explanation:

6(2p+2)=120

6(2p)+6(2)=120

12p+12=120       1. subtract 12 on both sides

12p=108            2. divide 12 on both sides

p=9

Answer:

p=9

Step-by-step explanation:

Here is the most simple way to solve:

Instead of distributing the 6 into the parenthesis, you can simply divide both sides by 6:

\(6(2p+2)=120\\\frac{6(2p+2)}{6} =\frac{120}{6}\)

\(2p+2=120\)

Subtract each side by 2 to isolate the variable:

\(2p+2=20\\2p+2-2=20-2\)

\(2p=18\)

Divide both sides by 2 to have the coefficient of the variable be 1 (Because thats how we solve these kinds of equations!)

\(2p=18\\\frac{2p}{2} =\frac{18}{2} \\p=9\)

Have a good day! :)

Answer:

To find 29% of 150, we can first express 29% as a decimal by dividing 29 by 100. 29% is the same as 0.29.

Then, we multiply 0.29 by 150 to find the answer:

0.29 * 150 = 43.5

So, 29% of 150 is equal to 43.5.

Here's the work:

29% * 150 = 0.29 * 150 = 43.5

\(\huge\text{Hey there!}\)

\(\mathsf{29\%\ of \ 150}\)

\(\mathsf{= \dfrac{29}{100} \ of \ 150}\)

\(\mathsf{= \dfrac{29}{100} \times 150}\)

\(\mathsf{= \dfrac{29}{100} \times \dfrac{150}{1}}\)

\(\mathsf{= \dfrac{29(150)}{100(1)}}\)

\(\mathsf{= \dfrac{4,350}{100}}\)

\(\mathsf{= \dfrac{4,350 \div 50}{100 \div 50}}\)

\(\mathsf{= \dfrac{87}{2}}\)

\(\mathsf{= 43 \dfrac{1}{2}}\)

\(\mathsf{= 43.5}\)

\(\huge\text{Therefore, your answer should be:}\)

\(\huge\boxed{\mathsf{\dfrac{87}{2}}}\huge\checkmark\)

\(\huge\boxed{\mathsf{43 \dfrac{1}{2}}}\huge\checkmark\)

\(\huge\boxed{\mathsf{43.5}}\huge\checkmark\)

\(\large\text{Either of those should work because they are all equivalent to each}\\\large\text{other}\uparrow\)

\(\huge\text{Good luck on your assignment \& enjoy your day! }\)

The statement that describes the distribution based on the given information is:

A) The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 98 messages.

The graph shows a normal distribution, as indicated by the shape of the curve. The highest point of the curve (the peak) is at 128, which represents the mean of the distribution.

The standard deviation measures the spread of the data, and based on the information given, it is 98. Therefore, option A accurately describes the distribution.

Learn more about standard deviation at https://brainly.com/question/475676

#SPJ1

(a) The leading coefficient is positive and the degree is odd, so:

(b) The leading coefficient is negative and the degree is even, so:

Answer: No

Step-by-step explanation:

to be proportional, both numbers have to increase by the same number

because if u multiply 6 by 2 you get 12, but when you multiply 10 by 2 you get 20, not 60 it would be proportional if you said 6 and 10 in to 12 and 20 in

Answer:

lim as x---->0 of (x²-5) = -5 which is D

The radius of the volleyball to the nearest tenth of an inch is 8.3

The formula is

= √ 3v/4π

volume(v) = 288

π = 3.142

= √ 3×288/4×3.142

= √ 864/12.6

Next step is to get the square root of 68.6

= √ 68.6

= 8.29

Hence the radius of the volley ball is 8.3 inches

Read more on Radius here

https://brainly.com/question/17405190

#SPJ1

Option D, For a standard normal distribution, the expression that is always equal to 1 is P(z ≤ -a) + P(-a≤z≤a) + P(Z≥a).

A standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1.

For a standard normal distribution, the total area of a curve is always equal to 1.

total area = P(z≤-a)+P(-a≤z≤a)+P(Z≥a) = 1

Thus, for a standard normal distribution, the expression that is always equal to 1 is P(z ≤ -a) + P(-a≤z≤a) + P(Z≥a).

Learn more about standard normal distribution here: https://brainly.com/question/4079902

#SPJ1

Step-by-step explanation:

\Given :

x^{3} +x^{2} -20x

Solution:

x^{3} +x^{2} -20x

taking x common from the given polynomial

⇒x(x^{2} +x-20)=0

⇒x(x(x+5)-4(x+5))=0

⇒x(x+5)(x-4)=0

⇒ x=0 , x+5=0 , x-4=0

⇒x = 0 , x = -5 , x = 4

Answer:

0, x = 4, and x = -3.

Step-by-step explanation:

he zeros of the polynomial function f(x) = x3 − x2 − 12x are x = 0, x = 4, and x = -3. To find these, we can factor the polynomial and set each factor equal to zero. Since x = 0 is already given as a zero, we can factor out x from the polynomial to get f(x) = x(x^2 - x - 12) = x(x - 4)(x + 3) = 0. Thus, the other zeros are x = 4 and x = -3.

Answer:

5 ft

Step-by-step explanation:

The formula for Volume is V=lwh, or Volume = length x width x height.

The equation would be:

\(180=l(4)(9)\)

or

\(180=36l\)

To find the answer, divide by 36.

\(\frac{180}{36} =\frac{36l}{36}\)

\(5=l\)

Answer:

Step-by-step explanation:

it would be "c" because the question asks for the number that makes the inequality true

4x≤ x+3

the graph in c is saying that every number that is 1 or less than 1 makes the inequality true. so lets take -7 as an example

4 x -7=-28

-28+3=-25

-25 is greater than -28 so the inequality is true. the reason why graph d doesnt work is because if we plug in 2 into the equation, then 4x =8 and x+3=5

5 is not greater than 8 so it doesnt work

A salary slip for the month of March 2023 with information given below.

Salary Slip - March 2023

Employee Details:

Name: [Employee Name]

Employee ID: [Employee ID]

Designation: [Employee Designation]

Earnings:

Basic Salary: [Basic Salary]

House Rent Allowance (HRA): [HRA]

Dearness Allowance (DA): [DA]

Incentive: [Incentive]

Total Earnings: [Total Earnings]

Deductions:

Provident Fund (PF): [PF]

Insurance: [Insurance]

Loss of Pay (LOP): [LOP]

Total Deductions: [Total Deductions]

Net Pay: [Net Pay]

Breakdown:

Basic Salary: 50% of CTC (18L) = [Basic Salary]

HRA: 20% of Basic Salary = [HRA]

DA: 12% of Basic Salary = [DA]

Incentive: 75% of target completion = [Incentive]

Total Earnings = Basic Salary + HRA + DA + Incentive = [Total Earnings]

PF: 12% of Basic Salary = [PF]

Insurance: Rs. 2500 = [Insurance]

LOP: [LOP]

Total Deductions = PF + Insurance + LOP = [Total Deductions]

Net Pay = Total Earnings - Total Deductions = [Net Pay]

For such more question on salary slip

https://brainly.com/question/30318240

#SPJ8