The charge-to tap time (m) for carbon steel in one type of open-hearth furnace is to be determined for each heat in a sample n. If the investigator believes that almost all times in the distribution are between 320 and 440, what sample size would be appropriate for estimating the true time to within 5 min confidence level of 95%

The functions g(x) = x² - 4x + 3 and f(x) = x² - 4x are:

The functions have the same range.

The functions have the same domain.

The functions have the same x-intercepts.

Let's analyze the given functions g(x) = x² - 4x + 3 and f(x) = x² - 4x and determine which statements about them are true.

Here are the options:

The functions have the same graph.

The functions have the same range.

The functions have the same domain.

The functions have the same vertex.

The functions have the same y-intercept.

The functions have the same x-intercepts.

The functions have the same graph:

This statement is false. While both functions are quadratic functions, their additional terms make them different. g(x) has an additional constant term (+3) compared to f(x).

Their graphs will be different, with g(x) being shifted upward by 3 units compared to f(x).

The functions have the same range:

This statement is true.

Both functions are quadratic functions, and their range will be the same. The range of a quadratic function is either all real numbers (if the parabola opens upward) or the set of real numbers greater than or equal to (or less than or equal to) the vertex of the parabola.

The functions have the same domain:

This statement is true.

The domain of both functions, unless restricted by any other factors, is all real numbers.

Quadratic functions have a domain of (-∞, ∞).

The functions have the same vertex:

This statement is false.

The vertex of a quadratic function is determined by the values of "a," "b," and "c" in the general form of the quadratic function (ax^2 + bx + c).

Since g(x) has an additional constant term, its vertex will be different from the vertex of f(x).

The functions have the same y-intercept:

This statement is false.

The y-intercept of a function is the value of y when x = 0.

For f(x), when x = 0, we have f(0) = (0)² - 4(0) = 0.

For g(x), when x = 0, we have g(0) = (0)² - 4(0) + 3

= 3.

Their y-intercepts are different.

The functions have the same x-intercepts:

This statement is true.

To find the x-intercepts of both functions, we set y (or f(x) and g(x)) equal to zero and solve for x.

The quadratic equation x² - 4x + 3 = 0 can be factored as (x - 1)(x - 3) = 0, giving x = 1 and x = 3 as the x-intercepts.

Both functions have the same x-intercepts.

For similar questions on functions

https://brainly.com/question/11624077

#SPJ8

Answer:

\(P(Red) = \frac{3}{20}\)

Step-by-step explanation:

Given

\(Red = 3\)

\(Trials = 20\)

Required

Determine the experimental probability of next marble being red

This is calculated as:

\(P(Red) = \frac{n(Red)}{Trials}\)

Substitute values for n(Red) and Trials

\(P(Red) = \frac{3}{20}\)

Answer:

x = 9.9 in.

Step-by-step explanation:

area of triangle = base * height /2

49 = x*x /2

49*2 = x^2

98 = x^2

\(\sqrt{98}\) = x

\(7\sqrt{2}\) = x

9.9 = x

Answer:  9 boys

Reason:

The multiples of 13 are

13, 26, 39, 52, ...

We only need to focus on the first two since they are smaller than 35

So we focus on 13 and 26

The second option has more girls than boys, so that must mean there are 26 girls and 9 boys.

According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

For more questions on algebraic expression:

https://brainly.com/question/29333936

#SPJ8

Answer:

hiro ..................

Using the pattern, n can represent the the increase of dots according to step.

In the given question we have to find what values make sense for n in this situation.

n is representing the number.

As we can see that there is a pattern given.

In the step 1 have 1 dot, in step 2 have 3 dots, in step 3 have 6 dots and in step 4 have 10 dots.

So if we see the pattern then according to number of step the dots increasing accordingly.

As In step 1 have 1 dot, in step 2, 2 dots increase, in step 3, 3 dots increase and in step 4, 4 dots increase.

So, n can represent the the increase of dots according to step.

To learn more about pattern link is here

brainly.com/question/23136125

#SPJ1

Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

(-1, 6), (1, -6), (-2, 3), (2, -3)

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

Answer:

a) CI = (113,637.5  ,  124,672.5)

b) CI = (112,581  ,  125,729)

c) CI = (110,501.4  ,  127,808.6)

Step-by-step explanation:

You have the following information:

\(\overline{x}\): mean annual household income = 119,155

σ: standard deviation = 30,000

n: sample = 80

The interval of confidence is given by the following expression:

\(\overline{x}\pm Z_{\alpha/s}(\frac{\sigma}{\sqrt{n}})\)

Z_α/2: distribution density factor

where α and Z_α/2 are given by the range of the confidence interval.

a) For a 90% confidence interval you have:

α = 1 - 0.9 = 0.1

Z_0.1/2 = Z_0.05 = 1.645   (found in a table of normal distribution)

You replace in the equation (1) to obtain the confidence interval:

\(119,155\pm (1.645)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm5,517.5\)

Then, the confidence interval is (119,155 + 5,517.5 , 119,155 - 5,517.5  )

= (113,637.5  ,  124,672.5)

b) For a 95% confidence interval you have:

α = 1 - 0.95 = 0.05

Z_0.05/2 = Z_0.025 = 1.96

\(119,155\pm (1.96)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm 6,574.0\)

The confidence interval is (112,581  ,  125,729)

c) For a 99% confidence interval:

α = 1 - 0.99 = 0.01

Z_0.01/2 = Z_0.005 = 2.58

\(119,155\pm (2.58)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm 8,653.6\)

The confidence interval is (110,501.4  ,  127,808.6)

d) When the confidence level increases the width of the confidence increases too. This can be noticed in the normal distribution, when the confidence level is higher, the area of the tails is reduced, and so, the confidence interval is higher.

Answer:

Brief description of the functions of brain cells, blood cells, and muscle cells.

Brain cell (Neuron):

Blood cell (Erythrocyte, Leukocyte, and Platelet):

Muscle cell (Myocyte):

Answer:

Step-by-step explanation:

Answer:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

Step-by-step explanation:

To solve this problem, we'll consider the velocities of the cruise ship and the Gulf Stream as vectors and calculate their components and resultant vector. Then we'll find the magnitude (resultant velocity) and direction (resultant direction) of the resultant vector.

Given:

Cruise ship velocity (south): 22 mph

Gulf Stream velocity (east): 4 mph

A) Vector component for the cruise ship:

The cruise ship is traveling south, so its velocity vector is (0, -22).

B) Vector component for the Gulf Stream:

The Gulf Stream is flowing east, so its velocity vector is (4, 0).

C) Resultant vector:

To find the resultant vector, we'll add the two velocity vectors together:

Resultant vector = Cruise ship velocity + Gulf Stream velocity

Resultant vector = (0, -22) + (4, 0)

Resultant vector = (0 + 4, -22 + 0)

Resultant vector = (4, -22)

D) Resultant velocity:

The magnitude of the resultant vector gives us the resultant velocity. We can use the Pythagorean theorem to calculate it:

Resultant velocity = sqrt((x-component)^2 + (y-component)^2)

Resultant velocity = sqrt((4)^2 + (-22)^2)

Resultant velocity = sqrt(16 + 484)

Resultant velocity = sqrt(500)

Resultant velocity ≈ 22.4 mph (rounded to the nearest tenth)

E) Resultant direction:

The direction of the resultant vector can be found using trigonometry. We'll use the inverse tangent function (arctan) to find the angle between the resultant vector and the positive x-axis.

Resultant direction = arctan(y-component / x-component)

Resultant direction = arctan(-22 / 4)

Resultant direction ≈ -1.405 radians or -80.5 degrees (rounded to the nearest tenth)

Therefore, the answers are:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

Use the FOIL method to solve.

(3 + 4i)(3 - 4i)

(3 * 3) + (3 * -4i) + (4i * 3) + (4i * -4i)

9 - 12i + 12i - 16i

9 - 16i

Best of Luck!

If the initial time was 60 seconds and 18 seconds have passed,

There would be 42 seconds left.

The critical value of tα/2 for a 90% confidence interval for the sample size 15 is 1.761.

Given, sample size=15

Confidence interval= 90%.

To find the critical value we have to first find alpha, by subtracting 90 from 100.

= 100%-90%

=1-0.9

=0.1

α=0.1

α/2=0.05

Next, we have to find the degrees of freedom(df) by using the formula n-1.

=15-1

df=14

Calculate tα/2 by using t-distribution with degrees of freedom 14 and α/2 = 0.05 as right-tailed area.

From the table we get the critical value for tα/2 as 1.761.

Therefore, the critical value for a 90% confidence interval with sample size 15 is 1.761.

To know more about confidence interval here

https://brainly.com/question/24131141#

#SPJ1

9x +4 = 3x+16

6x=12 X=2........

Answer:

D

Step-by-step explanation:

There isn't enough information to find a y-intercept.

The surface area of the figure is approximately 997.5π cm².

We have,

The figure has two shapes:

Cone and a semicircle

Now,

The surface area of a cone:

= πr (r + l)

where r is the radius of the base and l is the slant height.

Given that

r = 15 cm and l = 19 cm, we can substitute these values into the formula:

= π(15)(15 + 19) = 885π cm² (rounded to the nearest whole number)

The surface area of a semicircle:

= (πr²) / 2

Given that r = 15 cm, we can substitute this value into the formula:

= (π(15)²) / 2

= 112.5π cm² (rounded to one decimal place)

The surface area of the figure:

To find the total surface area of the figure, we add the surface area of the cone and the surface area of the semicircle:

Now,

Total surface area

= 885π + 112.5π

= 997.5π cm² (rounded to one decimal place)

Therefore,

The surface area of the figure is approximately 997.5π cm².

Learn more about cones here:

https://brainly.com/question/13798146

#SPJ1

Answer:

254in^2

Step-by-step explanation:

(SA)=2lw+2lh+2hw

L -> 9 W ->4 H -> 7

2(9)(4)+2(9)(7)+2(7)(4)

18*4+18*7+14*

72+126+56

198+56

254

Answer:

Yes

Step-by-step explanation:

To know if a table is a function or not, we have to see if 1 input only has 1 output.

Looking at the table each input only has 1 output, so it is a function.

Answer:

So, about 2.28% of men in the country are no more than 64 inches tall.

Step-by-step explanation:

First, we need to standardize the value of 64 inches to a z-score:

z = (64 - 68) / 2 = -2

We can use a standard normal distribution table or a calculator to find the percentage of men who are no more than 64 inches tall:

P(Z ≤ -2) = 0.0228

Answer:

60818

Step-by-step explanation:

well you do this by adding each term in the sequence

Answer:

18

Step-by-step explanation:

She won 75% of 24 matches.

75% of 24 = 0.75 × 24 = 18

Answer: 18

Tennis player will win 18 matches as a required percentage of total matches.

"Percentage is defined as the hundredth part of a given quantity."

According to the question,

Percentage of tennis player won the matches = 75%

Total number of matches played by player = 24

x represents the number of matches she win

Therefore,

   x = 75% of 24

⇒ x = (75 / 100) × 24

⇒ x = 18 matches

Hence, tennis player will win 18 matches.

Learn more about percentage here

https://brainly.com/question/14979505

#SPJ2

7√10+2√10-√10

Every square root has the same radicand, which is 10. So, simply combine terms.

7 + 2 - 1 = 9 - 1 = 8

Answer: 8√10

Answer:

The one with the better deal would be 30 ride tickets for $22.50 this is because you pay less money for more rides.

Step-by-step explanation:

First you divide 20 by 14. Doing this will give you the cost of a ride per ticket.

20/14 = 1.42

Then you do the same thing to 30 and 22.50.

30/22.50 = 1.30

Last you compare which deal has less money per ride.

1.42 > 1.30

The solution of the inequality expression in interval notation is;

-1/2 < x < 2/3 and the number line is attached

We are given the Inequality expression  as;

6x² - x  < 2

To express the function in quadratic form, we subtract 2 from both sides to get;

6x² - x - 2 < 0

We now factorize this expression to get;

(2x +1)(3x - 2) < 0

This means that we have two inequalities solution which are expressed as; (2x + 1) < 0 and (3x - 2) < 0

For (2x + 1) < 0, add 1 to both sides to get;

2x < 1

divide both sides by 2 to get;

x < 1/2

Similarly, for (3x - 2) < 0;

Add 2 to both sides and then divide by 3 to get;

x < 3/2

Thus, the solution to the inequality is x = -1/2 and x = 3/2

Read more about Inequalities at; https://brainly.com/question/25275758

#SPJ1