If sqrt(4 + x) + (10 − x) = 6 , then find sqrt(4 + x)(10 − x) algebraically.

Answer:

The point of estimate for the true difference would be:

\( 186-171= 15\)

And the confidence interval is given by:

\( (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753\)

\( (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753\)

Step-by-step explanation:

For this case we have the following info given:

\( \bar X_1 = 186\) the sample mean for the first sample

\( \bar X_2 = 171\) the sample mean for the second sample

\(s_1 =33\) the sample deviation for the first sample

\(s_2 =23\) the sample deviation for the second sample

\(n_1 = 8\) the sample size for the first group

\(n_2 = 7\) the sample size for the second group

The confidence interval for the true difference is given by:

\( (\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}\)

We can find the degrees of freedom are given:

\( df = n_1 +n_2 -2 =8+7-2= 13\)

The confidence level is given by 90% so then the significance would be \(\alpha=1-0.9=0.1\) and \(\alpha/2=0.05\) we can find the critical value with the degrees of freedom given and we got:

\( t_{\alpha/2}= \pm 1.77\)

The point of estimate for the true difference would be:

\( 186-171= 15\)

And replacing into the formula for the confidence interval we got:

\( (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753\)

\( (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753\)

Answer:

heres your answer :)

Step-by-step explanation:

Step 1: Put the numbers in order. ...

Step 2: Find the median. ...

Step 3: Place parentheses around the numbers above and below the median. Not necessary statistically, but it makes Q1 and Q3 easier to spot. ...

Step 4: Find Q1 and Q3. ...

Step 5: Subtract Q1 from Q3 to find the interquartile range.

Answer:

 Planes and circle both have flat surface that extends infinitely in all directions.

By dividing the total cost of the 12 grams of coffee (x) by the quantity of cups the 12 grams produce, one can get the price of a cup of coffee (12y).

The price of the coffee required to create one cup of coffee must be taken into account before attempting to calculate the cost of one cup of coffee. The price for 12 grams of coffee is specified in this instance (x). We also know that x cups of coffee may be made from every gram of coffee. We must divide the total cost of the 12 grams of coffee (x) by the number of cups the 12 grams produce in order to determine the price of one cup of coffee (12y). As a result, we will know how much one cup of coffee will cost in terms of x and y. Knowing this equation can help you estimate your coffee expenses and determine the price per cup.

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Answer..

Q 1, 80 mm

2, 7000

3,

Answer: a) Let the revenue equation be R(x) = mx + b, where m and b are constants. Since the revenue equation is a polynomial of order 1, it can be written in this form.

Let the cost equation be C(x) = ax² + bx + c, where a, b, and c are constants. Since the cost equation is a polynomial of order 2, it can be written in this form.

We know that the graphs of the two equations meet at points A(1,1) and B(5,9). Therefore, we have the following two equations:

R(1) = m(1) + b = 1 (1)

R(5) = m(5) + b = 9 (2)

We can solve for m and b by solving the system of equations (1) and (2):

m = 2

b = -1

Therefore, the revenue equation is R(x) = 2x - 1.

We also know that the third point of the cost function is C(2,0), which gives us:

a(2)² + b(2) + c = 0

4a + 2b + c = 0

Using points A(1,1) and B(5,9), we can set up two more equations:

a(1)² + b(1) + c = 1 (3)

a(5)² + b(5) + c = 9 (4)

Simplifying (3) and (4), we get:

a + b + c = 1 (5)

25a + 5b + c = 9 (6)

Subtracting (5) from (6), we get:

24a + 4b = 8

6a + b = 2

Multiplying (5) by 6 and subtracting it from (6), we get:

19a + 3b = 3

Solving these two equations simultaneously, we get:

a = -1/5

b = 13/5

Substituting these values of a and b into equation (5), we get:

c = 3/5

Therefore, the cost equation is C(x) = (-1/5)x² + (13/5)x + (3/5).

b) The common solutions to the revenue and cost equations are the points where the company breaks even, i.e. where the revenue earned is equal to the cost incurred. These points are important because they represent the minimum amount of sales the company needs to make in order to avoid making a loss. In this case, the common solutions represent the points where the company earns just enough revenue to cover its costs.

Step-by-step explanation:

Answer: 6.5

Step-by-step explanation:

\(|-6.5| = 6.5\)

_________

The total number of students calculated with the method called simplification and who are playing volleyball is 206.

How simplification method work?

In mathematics, the simplification method is used for the equation formation for the problem statements. And it also convert the complicated expression into simpler one to make the calculation easy.

According to the question, the given survey data for the playing volleyball is written below and it is solved by the simplification method:

survey of students: 36

play volleyball: 17

As per question, the simplification expression for the given statement which state that, if the survey of 648 students how many students play volleyball?

Therefore, the required simplified expression can be written as:

Required expression: 648÷36= 18

Now, playing volleyball =18×17=206 students play volleyball

Hence, the total number of students calculated with the method called simplification who are playing volleyball is 206.

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Answer:

5.067 is the correct answer

Answer:

5.067

Step-by-step explanation:

"five and.." , the and=decimal point. (5.)

the 7 is right before the thousandths, so it is in the third row (aka the thousandth spot, or the third 0 away from the decimal point. .000).

The six is in the place before the seven, so it gets placed in the hundreds spot (.007).

There is no number before the sixty, so it is placed as a zero (.067)

So, all together its 5.067

Answer:

x=162

Step-by-step explanation:

101 + 123 + 104 + 112 + 106 + 162 / 6 = 118

Answer:

7x-4y=-11

Step-by-step explanation:

Answer:

Neither in K.A

Step-by-step explanation:

Make sure put some choices before you ask we wouldn't know .

Thank me later !

Answer:

the answers are A and B

Step-by-step explanation:

Answer:

A and A

Step-by-step explanation:

Right on edge 2023

a. About 50% of the students scored less than 78.

b. Approximately 68% of the students scored between 75 and 78.

c. Approximately 95% of the students scored between 72 and 81.

d. Approximately 99.7% of the students scored between 69 and 75.

a) The normal curve is symmetrical, meaning that the area to the left of the mean is equal to the area to the right of the mean. Since the mean score is 78, 50% of the students scored above 78 and 50% scored below 78.

b) To apply the Empirical Rule, we will assume that 68% of the data falls within one standard deviation of the mean, which in this case is 3 points. So, 68% of the students scored between 75 and 81.

c) The percentage of students who scored between 72 and 81 can be found by subtracting the area to the left of 72 from the area to the left of 81. Using the Empirical Rule, we know that 95% of the observations are within two standard deviations of the mean, so the area between 72 and 81 is equal to 95%.

d) The percentage of students who scored between 69 and 75 can be found by subtracting the area to the left of 69 from the area to the left of 75. Using the Empirical Rule, we know that 99.7% of the observations are within three standard deviations of the mean, so the area between 69 and 75 is equal to approximately 99.7%.

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Answer:

  x = (1 +i√83)/6  or  x = (1 -i√83)/6

Step-by-step explanation:

You want the solutions to the quadratic equation 3x² -x +7 = 0.

The solutions to the equation ax² +bx +c = 0 are given by the formula ...

  \(x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)

The given equation has a=3, b=-1, c=7, so the solutions are ...

  \(x=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(3)(7)}}{2(3)}=\dfrac{1\pm\sqrt{-83}}{6}\\\\\\\boxed{x=\dfrac{1+i\sqrt{83}}{6}\quad\text{or}\quad x=\dfrac{1-i\sqrt{83}}{6}}\)

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The shape that can tessellate without leaving gaps is the hexagon (option A).

The shapes that can tessellate without leaving gaps are shapes that can be repeated to completely cover a flat surface without any overlaps or gaps. Among the options provided, the shape that will tessellate without leaving gaps is the hexagon (option A).

A hexagon is a six-sided polygon with equal sides and angles. It is a regular polygon, which means all of its sides and angles are equal. A regular hexagon can be arranged and repeated in a pattern to fill a plane without any gaps or overlaps. Bees' honeycombs are a real-world example of hexagonal tessellation.

On the other hand, octagons (option B) and pentagons (option C) do not tessellate by themselves without gaps. While they can be used in combination with other shapes to create tessellations, they cannot tessellate on their own.

A circle (option D) cannot tessellate without leaving gaps. A circle is a curved shape, and it cannot form a repeating pattern that completely covers a flat surface without overlaps or gaps.

In summary, the shape that can tessellate without leaving gaps is the hexagon (option A).

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Answer:

25 + 9^3

Step-by-step explanation:

Answer:

  x = 5

Step-by-step explanation:

The only thing the circle does for you is tell you that the angle between the lines marked 3 and 4 is a right angle. A tangent line is always at right angles to the radius at that point.

So, you have a 3-4-x right triangle. The Pythagorean theorem applies:

  3² +4² = x²

  9 + 16 = x² = 25

  x = √25

  x = 5

_____

Comment on the answer

This is a 3-4-5 right triangle. You will meet them a lot, so it is useful to remember these side ratios form a right triangle.

Answer:

3mg per BID vistrail

Step-by-step explanation:

The operating income is $800,000.

Operating income is the amount of revenue left after deducting the operational direct and indirect costs from sales revenue.

Given that, Blane Company has the following data: Total sales $800,000 Total variable costs $300,000 Fixed costs $200,000 Units sold 50,000 units

Operating income = sales - variable costs - fixed costs

Selling price per unit = total sales/unit sold

= 800,000/50,000 = $16

Variable cost per unit = total variable costs/unit sold

= 300,000/50,000 = $6

Operating income = (16x100,000) - (6x100,000) - (200,000)

Operating income = $800,000

Hence, the income from operations  is $800,000

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a) The number of bird feeders that the company must sell in a week to obtain the maximum profit = 100

b) Maximum profit = 3800

Maximum profit

Given that ,

f(x)=−0.40\(x^{2}\)+80x−200

f'(x) = -0.40 x \(2x\) + 80

      = - 0.80\(x + 80\)

f''(x) = - 0.80

a) For Maximum and minimum profit

f'(x) = 0

- 0.80\(x\) + 80 = 0

        0.80 \(x\)  = 80

                  \(x\) = 80 / 0.80

                     = 80 /80 x 100

                  \(x\) = 100

for x = 100 , f''(x) = -0.80

                   f''(x) < 0

Therefore, for x = 100 profit is maximum

Number of bird feeders = 100

b)Maximum profit

f(x) = -0.40 \(x^{2}\) + 80 \(x\) - 200

      = -0.40 x 100 x 100 + 8000 - 200

      = - 4000 + 8000 - 200

      = 4000 - 200

      = 3800

Therefore maximum profit = 3800

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Answer:

66.67

Step-by-step explanation:

Answer:

66.67

Step-by-step explanation:

24 / 36 x 100 is 66.67%

We can plοt the pοints (0,1) and (1,-11) οn the line tο graph the functiοn p(x) = 1 - 12x.

A functiοn frοm a set X tο a set Y is an assignment οf an element οf Y tο each element οf X. The set X is called the dοmain οf the functiοn and the set Y is called the cοdοmain οf the functiοn.

A functiοn, its dοmain, and its cοdοmain, are declared by the nοtatiοn f: X→Y, and the value οf a functiοn f at an element x οf X, denοted by f(x), is called the image οf x under f, οr the value οf f applied tο the argument x.

Functiοns are alsο called maps οr mappings, thοugh sοme authοrs make sοme distinctiοn between "maps" and "functiοns" (see § Other terms).

Tο plοt twο pοints οn the line fοr the functiοn p(x) = 1 - 12x, we can chοοse any twο values οf x and find the cοrrespοnding values οf p(x).

Fοr example, if we chοοse x = 0, then p(0) = 1 - 12(0) = 1, sο the pοint (0,1) is οn the line.

If we chοοse x = 1, then p(1) = 1 - 12(1) = -11, sο the pοint (1,-11) is οn the line.

Therefοre, we can plοt the pοints (0,1) and (1,-11) οn the line tο graph the functiοn p(x) = 1 - 12x.

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Answer:

12x/2 or 52/2

Step-by-step explanation:

Ok, perimeter is length+length+width+width. 12x/2 and 52/2 could are probably the answers.

Answer:

a

Step-by-step explanation:

(-1.00000005)^n

as n becomes very large, the function increases in both positive and negative direction.

If n=1, -1.00000005

if n=2, 1.0000001

if n= 3, -1.00000015

if n=20, 1.000001

if n=21, -1.00000105

All three sides are congruent. Option C is correct

According to the given question, the triangle DEF is classified as equilateral. An equilateral triangle is a triangle that has all its sides and angles to be equal as shown:

Hence the statement true about the equilateral triangle is that all three sides are congruent.

Answer: All three sides are congruent......

Step-by-step explanation: pic vvvvvvvvvvvvvvvv

Total number of rabbits produced in 9 years will be 45.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a rabbit can produce 5 new rabbits per year

Total number of rabbits produced in 9 years will be -

n = 5y = 5 x 9 = 45 new rabbits

Therefore, total number of rabbits produced in 9 years will be 45.

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Using the cross product for the proff of Pythagoras theorem, the correct step is

By the cross product property, AB² =  BC multiplied by BD

The cross product property is typically used to solve equations with two values, where the product of the extremes (the outer terms) is equal to the product of the means (the inner terms).

For the similar triangles, the ratio is as follows

BD / BA = BA / BC

BA² = BD * BC

and AB = BA, hence

BA² = BD * BC

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Answer:

4 1/8km

Step-by-step explanation:

if you have done 3 1/4km you can multiply the fraction by 2 so you get 3 2/8.

so now we have 2 5/8km and 3 2/8.

(its always easier to have the fractions the same denominator)

now we add the whole numbers first.

2 km + 3km = 5km.

now the fractions.

5/8 km + 2/8 km = 7/8km.

now add them both together and we get.

5 7/8 km.

take that answer away from 10.

we get 4 1/8km.