The distribution of the sample​ mean, ​, will be normally distributed if the sample is obtained from a p+opulation that is normally​ distributed, regardless of the sample size.

The quotient of x⁴ – 3x³ – 7x + 1 ÷ x + 2 is x³ - 5x² + 3x and the remainder is 5

From the question, we have the following parameters that can be used in our computation:

x^4 – 3x^3 – 7x + 1 ÷ x + 2

Rewrite as

x⁴ – 3x³ – 7x + 1 ÷ x + 2

This means that

Divisor = x + 2

Dividend = x⁴ – 3x³ – 7x + 1

Using the synthetic division, we have the following setup

-2 |    1     -3    -7     1

Bring down the first factor

-2 |    1     -3    -7     1

        1

Multiply by -2

-2 |    1     -3    -7     1

              -2

        1

Repeat the above steps as follows

So, we have

-2 |    1     -3    -7     1

              -2    10    -6

        1      -5    3    5

The last number represents the remainder of the division

This means that

Remainder = 5

Quotient = x³ - 5x² + 3x

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Answer:

  24 years

Step-by-step explanation:

You want to know the number of years it will take an account's value to exceed $300, given it was opened with $100 and earns 4.8% interest compounded annually.

The value of the account earning compound interest is ...

  A = P(1 +r)^t

where principal P is earning interest at rate r for t years.

Solving for t, we get ...

  A/P = (1 +r)^t

  log(A/P) = t·log(1+r)

  t = log(A/P)/log(1 +r) = log(300/100)/log(1 +0.048)

  t = log(3)/log(1.048) ≈ 23.433

For the value to exceed $300, it will take 24 years.

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Therefore , the solution of the given problem comes out to be that one statement is true other than else are false.

In mathematics, inequalities describe the connection between two variables that are not equal. Equal implies to be equal, not. The "not equal symbol ()" is typically used to indicate that two values are not equaivalent. But different inequalities are used to compare the data to see if one is more or less than the other.

Here,

0 < a<1<b

Multiply all terms by b since b>1

0 < ab < b < [tex]b^{2}[/tex]

Since

b > 1 , then ab > a so then ,

0 < a<ab <  b < [tex]b^{2}[/tex]  

Given that,

F. 0< ab<a, Never true

G. 0< ab<1, Not always true

H. a< ab<1, Not always true

J. a< ab<b, True

K. b< ab, Never true

Therefore , the solution of the given problem comes out to be that one statement is true other than else are false.

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On solving the provided question, we can say that - by equation, total amount of water removed was  = 1.R(0) + 2.R(1) + 3.R(3) = 1(1340) + 2(1190) + 3(950) + 2(740) = 8050 liters

An equation is a mathematical formula that expresses equality by joining two expressions together with the equal symbol =. A formula that claims two formulae are equal is the definition of an equation in algebra in its most basic form. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. An equal sign is a part of all mathematical formulas, including equations. Often, algebra is used in equations. In mathematics, algebra is employed when we don't know the precise quantity to calculate.

R'(2) = R(3) - R(1) /3-1 = 950-1190/2 = /120L/hr

total amount of water removed was  = 1.R(0) + 2.R(1) + 3.R(3) = 1(1340) + 2(1190) + 3(950) + 2(740) = 8050 liters

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Answer:

Step-by-step explanation:

Let's call the two numbers x and y. We can set up the following equation to represent the problem:x + y = 679y = x + 431Substituting the second equation into the first equation, we get:x + (x + 431) = 679Combining like terms, we get:2x + 431 = 679Subtracting 431 from both sides, we get:2x = 248Dividing both sides by 2, we get:x = 124Substituting this value back into the equation y = x + 431, we get:y = 124 + 431 = 555Therefore, the two numbers are 124 and 555.

The solutions to the equation word problems are as follows;

1) Amount jane will have is 50 + 2d

2) Amount Elis will have = 24 + 6d

3) The equation is; 50 + 2d = 24 + 6d

4) Amount each has saved = $63

We are given that;

Amount Jane has = $50

Amount Elis has = $24

Amount saved by Jane each day = $2

Amount saved by Elis each day = $6

1) After d days of saving, amount jane will have is;

A = 50 + 2d

2) After d days of saving, amount Elis will have is;

A = 24 + 6d

3) The equation that will be used to show when Joan and Elis would have saved same amount is;

50 + 2d = 24 + 6d

4) 50 + 2d = 24 + 6d

26 = 4d

d = 26/4

d = 6.5 days

Amount each has saved = 50 + 2(6.5) = $63

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Answer:

The surface area of a sphere is 2461.76 units.

Step-by-step explanation:

where,

π = 3.14 or 22/7

r = radius of sphere

Here, we know that

radius = diameter ÷ 2 = 28/2 = 14 units

So,

A = 4 π r²

A = 4 × 3.14 × (14)² units

A = 12.56 × 196 units

A = 2461.76 units

Thus, The surface area of a sphere is 2461.76 units.

Answer:  the surface area of the sphere of diameter 28cm is 2464 cm²

Step-by-step explanation:

     Given, diameter = 28 cm

      hence, radius of the sphere = d/2 = 28/2 =14 cm

 Therefore, the surface area of a sphere of radius (r) = 4пr²

                 where п= 22/7= 3.14

                                            = 4×3.14×14×14

                                            = 2464 cm²

Answer:
You sold 15 vegetarian sandwiches and 10 turkey sandwiches.

Step-by-step explanation:

First, let's call the number of vegetarian sandwiches sold "V" and the number of turkey sandwiches sold "T".

We can set up the following equation: 3V + 4T = 85

Next, we need to find the values of V and T that satisfy this equation. To do this, we can use the fact that V and T must be whole numbers since we cannot sell a fraction of a sandwich.

We can start by trying V = 1 and T = 6. Plugging these values into the equation, we get: 3(1) + 4(6) = 18 + 24 = 42

Since 42 is not equal to 85, this means that V and T cannot both be 1 and 6.

We can try other values of V and T that are whole numbers until we find a combination that satisfies the equation. One way to do this is to use trial and error.

For example, we can try V = 2 and T = 5, which gives us: 3(2) + 4(5) = 6 + 20 = 26 This is still not equal to 85, so we can try other values. We can also use the fact that V + T = 25 (since we sold a total of 25 sandwiches) to help us solve the equation.

If we set V + T = 25, then we can rewrite the original equation as: 3V + 4(25 - V) = 85 Solving for V, we get: 3V + 100 - 4V = 85 Combining like terms, we get: -V = 15 Dividing both sides by -1, we get: V = 15

Since V + T = 25, this means that T = 25 - 15 = 10

Therefore, we sold 15 vegetarian sandwiches and 10 turkey sandwiches.

Answer:

Below

Step-by-step explanation:

All of the  angles are the same (their opposite sides are =)....it is an equilateral triangle

 all of the angles sum to 180°

  each angle is then 60°

    5y+10 = 60

       5y = 50

          y = 10 °

The Ancient Egyptians were the first to invent a dish close to what we know as a pie today. They had a honey filling covered in a crusty cake made from oats,

And cost of one pumpkin pie = $8

Let the cost of one apple pie be $x

And cost of one pumpkin pie be $ y.

According to given problem,

For Lisa :  sold 8 apple pies and 4 pumpkin pies for a total of $80

8x + 4y = 80   ------------(1)

For Shreya :  sold 8 apple pies and 3 pumpkin pies for a total of $72

8x + 3y = 72    ---------------(2)

Solving equation (1) and (2), to get x and y.

Subtract equation (2) from equation (1)

i.e 8x + 4y - (8x +3y) = 80 - 72

or 8x - 8x + 4y - 3y = 8

or  y = 8

And x = 6   { 8x + 4×8 = 80   or x = (80 - 32)/8  = 48/8 = 6 }

Hence, the cost of one apple pie = x = $6

And cost of one pumpkin pie = y =$8

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Answer:

Step-by-step explanation:

Step-by-step explanation: the original weight of a cereals is ounces. Now according to question, new weight of cereals is more of original weight of cereals. Therefore, New weight of cereals will be formulated as Hence, the new weight of cereals is ounces.

Answer:

c = 5

Step-by-step explanation:

The slope is the change in y over the change in x. Or as I memorized RISE OVER RUN. Also in physics, you can write ∆y/∆x. Delta (∆) just means change.

Using this equation we have

The slope = m = 3 = ∆y/∆x

m = (-1 - c)/(-8 - -6) = (-1 - c)/(-8+6) = (-1 - c)/(-2) = 3

Now multiply both sides of the equation by -2 and you get

(-1 - c) = 3•(-2) = -6

Almost there!

Now we have the equation

-1 - c = -6

Add one to both sides and you get

-1+1-c = -6 +1

Simplified that equals

-c = -5

Then to get our answer we have to go from negative to positive.

Multiplying both sides by -1 we get

-1 • -c = -1 • -5

c = 5

Now CHECK!

Plug c into the equation ∆y/∆x and you get a slope of 3 which proves the answer is right.

Answer:

0.0086

Step-by-step explanation:

Answer:The Flemish giant rabbit weighs 32 pounds.

Step-by-step explanation:

Solving a system of equations we can see that the length is 22 feet and the width is 16 feet.

For a rectangle of length L and width W, the area is given by the formula:

A = L*W

Here we know that the rectangular room has an area of 352 square feet, and we also know that the length of the room is 6 feet mroe than the width of the room, then we can write a system of equations:

352 = L*W

L = W + 6

To solve that system, we can substitute the second equation in the first one, we will get:

352 = (W + 6)* W

352 = W^2 + 6W

W^2 + 6W - 352 = 0

So we have a quadratic equation, the solutions give:

[tex]W = \frac{-6 \pm \sqrt{6^2 - 4*1*(-352)} }{2} \\\\W = \frac{-6 \pm 38 }{2}[/tex]

We take the positive value as the with, so:

W = (-6 + 38)/2

W = 16

And the length is 6 feet longer than that, so:

L = 16 + 6 = 22

Then the length is 22 feet, and the width is 16 feet.

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The exponent [tex]3^{21}[/tex] is 9 times greater than the exponent [tex]3^{19}[/tex]

What are Exponents?

Exponentiation is the process of expressing huge numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself.

Solution:

To solve this type of question all we need to know are the Rules of Exponents with their help any question of this type can be solved

Since we are required to find the number of times the value os greater so we will divide the numbers

3^21 / 3^19

By rule of exponents if a^b/a^c then we can write it as a^(b-c)

Similarly 3^21 / 3^19 = 3^(21 - 19) = 3^2 = 9

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Answer:

The total cost for the three buildings was $6,034,250.

Step-by-step explanation:

Given,

The first sold for $1,259,300,

the second sold for $2,839,750,

the third sold for $1,935,200.

We add these three sold cost of apartment buildings

$1,259,300 + $2,839,750 +  $1,935,200 = $6,034,250.

To calculate the total cost of three things, you will need to add the individual costs of each item together.

1. Determine the cost of each item. Add together the cost of all three items. This total is the cost of the three items.

2. If the items are sold as a package, determine the cost of the package. This is the cost of the three items.

3. If the items are sold at a discounted rate, calculate the total cost of each item after the discount has been applied. Add together the costs of the three items after the discount has been applied. This total is the cost of the three items.

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Answer: -27

Step-by-step explanation:

To solve for x, we have to make f alone.

f+24=-3       [subtract both sides by 24]

f=-27

The answer is -27.

Answer: -27

Step-by-step explanation: f+24+-3 to find f subtract 24 from -3. which equals -27 it might not be the proper way but it works. :)

The simplest form of  [tex]2\sqrt{3} + 3\sqrt{3}[/tex] is found to be  8.66025403784 .

A fraction is  in  its  simplest form   when   the    numerator   and   the denominator have  no common factors besides one.

Reducing equation is a method of rewriting the equation in a simpler form. Certain equations in mathematics are not in the form of linear equations but they can be put in the form of linear equations by performing some mathematical operations on them. After reduction of these equations in linear form they can be solved and the value of unknown can be calculated easily.

Given the equation is;

[tex]2\sqrt{3} + 3\sqrt{3}[/tex]

Now solving it ,

[tex]2\sqrt{3} + 3\sqrt{3}[/tex]

By adding this we get,

[tex]5\sqrt{3}[/tex]  (∵ [tex]\sqrt{3}[/tex] is common in both )

= 8.66025403784

The decimal (or) simplified value of [tex]2\sqrt{3} + 3\sqrt{3}[/tex] is  8.66025403784.

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The speed of car is 50 miles per hour and the speed of the motorcycle is 40 miles per hour.

Let M = speed of the motorcycle.

Hence, speed of the car = 2M - 30.

Distance covered = Time taken x Speed.

Hence in 2 hours,

Distance covered by motorcycle = 2M

Distance covered by car = 2(2M-30).

Given, the car is 20 miles ahead of the motorcycle.

Hence,

2(2M-30) = 2M + 20

4M-60 = 2M + 20

2M = 80

M = 40

2M-30 = 2(40)-30 = 80-30 = 50

Therefore, speed of motorcycle is 40 miles per hour and speed of car is 50 miles per hour.

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Answer:

Axis of Symmetry: x = 1

Vertex: (1,7)

Step-by-step explanation:

The standard form of an equation for a parabola is

ax² + bx + c

So converted to standard form, the equation is

y = -x² + 2x + 6,

where

a = -1,  b = 2, and c = 6

The axis of symmetry of a parabola follows the formula

x = -b/(2a)

--> x = -2/(2*(-1))

--> x = 1

This is also the x-coordinate of the vertex.

To get the y-coordinates of the vertex, substitute 1 into x:

y=6+2x-x²

y=6+2(1)-(1)²

y = 7

So the coordinates of the vertex is (1,7)

The value of x is 12 .

Given ,

angle DEH as exterior angle and angle  E, C, D as interior angles .

What is the relation between interior & exterior angles of a triangle ?

Interior angle refer to all those angles that are inside a shape. On the other hand, the exterior angle is an angle that is made by the side of the shape and a line drawn out from an adjacent side.

Furthermore, the exterior angle is equal to the sum of the non-adjacent interior angles .

Calculations

angle  DEH = angle C + angle D

9x + 22 = 5x + 10 + 60

9x - 5x = 70 - 22

   4x     = 48

     x      = 12

The value of x is 12 .

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If Tommy is flying his kite one afternoon and notices that he has let out

the entire 130 ft of string.  The height , to the nearest foot, is his kite at this time is : 144 ft.

Given data:

String = 130 ft

Angle =  48°

Let h represent the height

Hence,

Tan48° = h/130

h= 130 tan48°

h = 130 (1.11061251483)

h = 144 ft

Therefore we can conclude that the height is 144ft.

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Answer: In order to describe a translation using arrow notation, we need to specify the direction and distance of the translation. In the case of the given translation, point P is translated to point P' by moving 6 units to the left and 2 units down. This can be represented using arrow notation as follows:

P' = P ← 6 ↓ 2

Here, the symbol ← represents a leftward movement, and the symbol ↓ represents a downward movement. The numbers 6 and 2 indicate the distance of the movement in the respective directions. This means that point P is translated to point P' by moving 6 units to the left and 2 units down from its original position.

Since the probability is less than equal to 0.8907, then the value of x is 0.9750.

Given, the random variable is from of a normal distribution with

μ = 4 and  σ = 1.37

.where, μ  is the mean value and σ  is the standard deviation.

According to the Question:

P(X≤8.907) = P( X−μ/σ ≤ 0.8907 - 4.00/ 1.37)

                  = P ( Z ≤ -29196.43)

​                  

Using Z-table we get a value of x which is 0.9750

So,

P(X ≤ 0.8907) = 97.50%

According to the calculations, the required value of x is 97.50%.

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The equation of the line is (b) y = 2.25x - 6.25

From the question, we have the following parameters that can be used in our computation:

Points = (3, 1/2) and (5, 5)

A linear equation can be represented as

y = mx + c

Substitute the known values in the above equation, so, we have the following representation

1/2 = 3m + c

5 = 5m + c

Subtract the equations

2m = 4.5

Divide by 2

m = 2.25

Substitute m = 2.25 in 5 = 5m + c

5 = 5 * 2.25 + c

So, we have

c = 5 - 5 * 2.25

Evaluate

c = -6.25

Recall that

y = mx + c

So, we have

y = 2.25x - 6.25

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Complete question

Select the equation for the line crossing the points (3,1/2) and (5,5).​

(a) y = 5x + 2

(b) y = 2.25x - 6.25

(c) y = 2.25x + 6.25

(d) y = -5x - 2

y = 2.115 + 0.842

= 2.957

no explanation

If the line y=-x+4 is tangent to the graph of f(x) = x^2 - 5x + a, it means that the line and the graph of the function are just touching at a single point, and are not intersecting at any other points.

To find the value of a, we can start by setting the equation for the line and the equation for the function equal to each other:

y = -x + 4

f(x) = x^2 - 5x + a

Then, we can substitute the equation for the function into the equation for the line:

-x + 4 = x^2 - 5x + a

We can then solve this equation for a by moving all the terms to one side:

-x + 4 - x^2 + 5x = a

-x^2 + 6x - 4 = a

We can see that the left-hand side of this equation is a quadratic expression in x, and we know that a quadratic function is tangent to a line when the line is a horizontal tangent. This occurs when the derivative of the function is equal to the slope of the line.

The derivative of f(x) = x^2 - 5x + a is 2x - 5, so we can set this equal to the slope of the line, which is -1:

2x - 5 = -1

2x = -6

x = -3

Now that we know the value of x, we can substitute it back into the equation for the function to find the value of a:

f(-3) = (-3)^2 - 5(-3) + a

f(-3) = 9 + 15 + a

f(-3) = 24 + a

Since the line and the function are just touching at this point, the y-value of the function at x=-3 must be equal to the y-value of the line at x=-3. We can substitute these values into the equation for the line to find the value of a:

y = -(-3) + 4

y = 3 + 4

y = 7

Substituting this back into the equation for the function, we get:

f(-3) = 24 + a = 7

a = 7 - 24

a = -17

Therefore, the value of a is -17.

what do you mean by tangent?

A tangent is a line that touches a curve at a single point, but does not intersect the curve at any other points. In other words, it is a line that is just "skimming" the curve, rather than crossing it.

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Answer:

To graph the relationship between the pool's water level and time, we can start by creating a table of values for the water level at different times. Here is an example of such a table:

Time (minutes) Water Level (centimeters)

0 0

1 6

2 12

3 18

4 24

5 30

6 36

7 42

8 48

9 54

10 60

11 66

12 72

13 78

14 84

15 90

16 96

17 102

18 108

19 114

20 120

We can then plot these values on a graph, with the time on the x-axis and the water level on the y-axis. The resulting graph would be a straight line that slopes upwards, starting at the origin (0, 0) and ending at (20, 120).

The graph shows that the water level in the pool increases linearly with time. The slope of the line represents the rate at which the water level is increasing, which in this case is 6 centimeters per minute.

Step-by-step explanation: