Determine the domain on which the following function is increasing

The value of s - t is 2.

It is given in the question that:-

s = 1/4 and,

t = -1.75

We can convert the decimal form of t in the fractional form.

-1(3/4) = -7/4

Hence, according to the data given in the question we can write,

s - t = (1/4)-(-7/4) = (1+7)/4 = 8/4 = 2.

Decimal

In Algebra, decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point. The dot present between the whole number and fractions part is called the decimal point. For example, 34.5 is a decimal number.

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Answer:  the number that can be placed in the box to make the statement true is 3.

Step-by-step explanation:

To make the statement true, we need to find a number that, when added to 7, equals 10. From the given options, the number that satisfies this condition is 3.

If we substitute 3 for the box in the statement, it becomes:

If +7=10, then 10-7=3.

The diameter of the tin in the picture is  \(3d/5\) where 'd' is the diameter of the tin in reality.

Determining the diameter of tin:

Since there is no indication of dimensions, represent the diameter with a variable 'd' and find the diameter of the tin according to the given condition in the problem.

Here we have assumed that the diameter of the tin is 'd' in reality and the diameter of the tin picture can be calculated as given below.  

Here we have

A ricoffy tin container with no dimensions indicated

Let d and h be the diameter and height of the tin

Given that the container is 2/5 times smaller than d

then the diameter of the tin in the picture \(= d - 2/5(d)\)

\(= [5d - 2d]/5 = 3d/5\)

Therefore, The diameter of the tin in the picture is  \(3d/5\) where 'd' is the diameter of the tin in reality.

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The value of t₀.₀₁ is 3.355. The value 3.355 is rounded to three decimal places.

What is the critical value?

A crucial value is the test statistic's value that establishes a confidence interval's upper and lower boundaries or the level of statistical significance for a given test.

Any member of the family of continuous probability distributions known as the Student's t-distribution in probability and statistics is used to estimate the mean of a normally distributed population when the sample size is small and the population's standard deviation is unknown.

Given the value of v is 8.

Need to find the value of t₀.₀₁ when v = 8.

The value of t₀.₀₁ according to t distribution table is 3.3550.

= 3.355 (nearest to three decimal places)

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Answer:

the answer is 9 square meters

Answer:

a = 0.9

Step-by-step explanation:

For the quadratic equation \(\boxed{ax^2 + bx + c = 0}\) to have exactly one real root, the value of its discriminant, \(\boxed{b^2 - 4ac}\), must be zero.

For the given equation:

\(y = ax^2 - 6x + 10\),

• a = a

• b = -6

• c = 10.

Substituting these values into the formula for discriminant, we get:

\((-6)^2 - 4(a)(10) = 0\)

⇒ \(36 - 40a = 0\)

⇒ \(36 = 40a\)

⇒ \(a = \frac{36}{40}\)

⇒ \(a = \bf 0.9\)

Therefore the value of a is 0.9 when the given quadratic has exactly one root.

6.66 feet/sec

SPEED = 90 / 13.5

             = 6.66 feet/ sec

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Cesar initially had $2,500 in savings.

Let's solve the problem step by step.

Let's assume that the initial amount of money Cesar had is represented by "x" dollars.

According to the problem, Cesar spent 15% of his savings on a cellphone, which means he has 85% of his initial savings left. We can represent this mathematically as:

0.85x = 2,125

To find the initial amount of money Cesar had, we need to solve for x. We can do this by dividing both sides of the equation by 0.85:

x = 2,125 / 0.85

Calculating this value:

x = 2,500

Cesar initially had $2,500 in savings.

Please note that the calculations are done assuming a straightforward interpretation of the problem. If there are additional factors or context that could affect the interpretation, it's important to consider them in order to arrive at an accurate answer.

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If John solved the equation x² - 10x + 8 = 0 by completing the square, one of the steps in his process would be: A. (x - 5)² = 17.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 10x + 8 = 0

x² - 10x = -8

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 10x + (-10/2)² = 8 + (-10/2)²

x² - 10x + 25 = -8 + 25

x² - 10x + 25 = 17

By simplifying, we have;

(x - 5)² = 17

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Answer:

A is -24

B is 0

C is  1

Step-by-step explanation:

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Complete Question

A 95% confidence interval of 19.3 months to 47.5 months has been found for the mean duration of? imprisonment, ??,of political prisoners of a certain country with chronic PTSD.

a. Determine the margin of error, E.

b. Explain the meaning of E in this context in terms of the accuracy of the estimate.

c. Find the sample size required to have a margin of error of 13 months and a 99% confidence level.? (Use 38 months. for standard deviation )

d. Find a 99% confidence interval for the mean duration of? imprisonment, ??, if a sample of the size determined in part? (c) has a mean of 36.5 months.

Answer:

a

 \(E =  14.1 \)

b

In this context  E tell us that the true mean will lie within E = 14.1 of the sample mean

c

  \(n  =57 \)

d

   \( 23.514 < \mu < 49.486\)

Step-by-step explanation:

Considering question a

From the question we are told that

   The upper limit is  U =   47.5 months

    The lower limit is   L = 19.3 months

Generally the margin of error is mathematically represented as

       \(E = \frac{U - L }{2}\)

 =>  \(E = \frac{ 47.5 - 19.3 }{2}\)

 =>  \(E = 14.1 \)

Considering question b

In this context  E tell us that the true mean will lie within E = 14.1 of the sample mean

Considering question c

Generally the sample size is mathematically represented  as

        \(n = [ \frac{ Z_{\frac{\alpha }{2} * \sigma }}{ E} ]^2\)

Here  E is given as  E = 13

Given that the confidence level is  99% then the level of significance is  

      \(\alpha = (100 - 99 )\%\)

=>   \(\alpha = 0.01 \)

From the normal distribution table  the critical value  of  \(\frac{\alpha }{2}\)  is  

      \(Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } = 2.58\)

So

    \( n = [ \frac{2.58 *  38}{13}]^2\)

=>    \(n =57 \)

Considering question d

From the question

   The sample mean is   \(\= x = 36.5\)

Generally the margin of error is mathematically represented as  

         \(E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{n}\)

=>      \(E = 2.58 * \frac{38 }{57}\)

=>      \(E = 12.986 \)    

Generally the 99% confidence interval  for  mean distribution is  mathematically represented as

    \( 36.5 - 12.986 < \mu < 36.5 + 12.986\)

=>     \( 23.514 < \mu < 49.486\)

Answer:

The low tide level is 0, integer as 0

Step-by-step explanation:

The tide is at the numberline point 0, making it at integer 0.

Please let me know if I need to change the answer via comments (pls don't report me)

The class width used for the frequency distribution is 6.

The class midpoint for the class 23-29 is 26.

The class midpoint for the class 30-36 is 33.

The class midpoint for the class 37-43 is 40.

To find the class width of the frequency distribution, we need to determine the range of each age class. The range is the difference between the upper and lower boundaries of each class. Looking at the table, we can see that the class boundaries are as follows:

23-29

30-36

37-43

For the class 23-29, the lower boundary is 23 and the upper boundary is 29. To find the class width, we subtract the lower boundary from the upper boundary:

Class width = 29 - 23 = 6

So, the class width for the frequency distribution is 6.

To find the class midpoint for each class, we take the average of the lower and upper boundaries of each class.

For the class 23-29:

Class midpoint = (23 + 29) / 2 = 52 / 2 = 26

For the class 30-36:

Class midpoint = (30 + 36) / 2 = 66 / 2 = 33

For the class 37-43:

Class midpoint = (37 + 43) / 2 = 80 / 2 = 40

So, the class midpoint for the class 23-29 is 26, for the class 30-36 is 33, and for the class 37-43 is 40.

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The inequality on the graph is the third option:

(2/5)*x - 3/2 ≥ y

Let's analyse the graph if the inequality.

We can see that there is a solid linear equation with a positive slope, and the shaded area is below that line, then the inequality is of the form:

y ≤ linear equation.

We know that the symbol "≤" must be used because of the solid line.

We also can see that when x = 0, y takes a velue between -1 and -2.

With that in mind the correct option is the third one:

(4/5)*x - 2y ≥ 3

Isolating y we get:

(4/5)*x - 3 ≥ 2y

(2/5)*x - 3/2 ≥ y

Changing the order:

y ≤ (2/5)*x - 3/2

That is the graphed inequality.

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To determine the mathematical expression  {x|€N and x < 100}, we can best assign it to be a Finite Set.

A finite set refers to a set that is finite. What this means is that the set has a definite range and can be determined thus. In the above question, we can see a mathematical expression that shows that the set is finite.

The less than sign shows that the numbers in the set are less than a hundred, thus they are finite and have a given range. So, the statement above can be assigned as a finite mathematical set.

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Answer: what

Step-by-step explanation:bye

answer:

does not have enough money

The height, H (in ft), is related to time, T (in seconds), by the next equation:

Substituting with H = 85 ft we get:

Applying the quadratic formula:

The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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Answer:

{7, 9}

(Numbers from 1 to 10 equal to or greater than 7 are 7 and 9)

Step-by-step explanation:

We have to find the set of whole number greater than and equal to 7 from 1 to 10,

Now, From 1 to 10, the odd numbers are, 1,3,5,7,9,

And of these, 7 and 9 are equal to or greater than 7

So, we get the set,

{7, 9}

Answer:

780

Step-by-step explanation:

In this example we will call Original Price = y

72%=0.72

218.40=0.72*y

1-0.72=0.28

218.4÷0.28=780

Answer:

Step-by-step explanation:

2x+3+2x-12+4x-11=180 degree (sum of interior angles of a triangle)

8x-20=180

8x=180+20

x=200/8

x=25

Now , substitute the value of x.

Chicago=2x+3

=2*25+3

=50+3

=53 degree

Austin=2x-12

=2*25-12

=50-12

=38 degree

Atlanta=4x-11

=4*25-11

=100-11

=89 degree

The particle travels approximately 45.63 units along the path. The displacement is the straight-line distance between the initial and final positions of the particle is 2781.

To find the distance the particle travels along the path, we can integrate the speed over the interval of time. The speed of the particle is given by the magnitude of its velocity vector.

The velocity vector is the derivative of the position function r(t):

\(v(t) = (d/dt)(t^3/3, t^2, 2t)\)

\(= (t^2, 2t, 2)\)

The speed of the particle at any given time t is:

|v(t)| = √((t^2)^2 + (2t)^2 + 2^2)

= √(t^4 + 4t^2 + 4)

= √((t^2 + 2)^2)

To find the distance traveled along the path, we integrate the speed function over the given interval of time. The particle travels from t = -1/3 to t = 9.

distance = ∫[from -1/3 to 9] |v(t)| dt

= ∫[from -1/3 to 9] |t^2 + 2| dt

= ∫[from -1/3 to 0] -(t^2 + 2) dt + ∫[from 0 to 9] (t^2 + 2) dt

= [-1/3 * t^3 - 2t] (from -1/3 to 0) + [1/3 * t^3 + 2t] (from 0 to 9)

Evaluating the definite integrals:

distance = [-1/3 * 0^3 - 2 * 0 - (-1/3 * (-1/3)^3 - 2 * (-1/3))] + [1/3 * 9^3 + 2 * 9 - (1/3 * 0^3 + 2 * 0)]

= [0 - (1/3 * (-1/27) + 2/3)] + [1/3 * 729 + 18]

= [1/27 + 2/3] + [729/3 + 18]

= 1/27 + 2/3 + 729/3 + 18

= 1/27 + 18/27 + 729/3 + 18

= (1 + 18 + 729)/27 + 18

= 748/27 + 18

= 27.63 + 18

= 45.63 units (approximately)

Therefore, the particle travels approximately 45.63 units along the path.

To find the average speed, we divide the distance traveled by the time taken. The time taken is 9 - (-1/3) = 9 1/3 = 28/3.

average speed = distance / time

= 45.63 / (28/3)

= 45.63 * (3/28)

= 4.9179 units per unit time (approximately)

The displacement is the straight-line distance between the initial and final positions of the particle.

displacement = |r(9) - r(-1/3)|

= |(9^3/3, 9^2, 2 * 9) - ((-1/3)^3/3, (-1/3)^2, 2 * (-1/3))|

= |(27, 81, 18) - (-1/27, 1/9, -2/3)|

= |(27 + 1/27, 81

= 2781.

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Yes, because for each input there is exactly one output. Therefore, the relation represented by the mapping diagram is a function.

To determine if the relation represented by the given mapping diagram is a function, we need to check if each input (x value) has exactly one output (y value) associated with it.

From the given mapping diagram, we can see that:

The input value -3 is associated with the output value 0.

The input value -1 is associated with the output value 2.

The input value 1 is associated with the output value 0.

The input value 3 is associated with the output value 2.

The input value 5 is associated with the output value 5.

As we can see, each input value has exactly one output value associated with it. Therefore, the relation represented by the mapping diagram is a function.

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