Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

= 6; = 2
P(5 ≤ x ≤ 9) =

The maximum volume of the box is 54 cm³ .

To obtain the largest volume feasible, multiply each measurement by the largest possible error. To find the least volume that may be created, multiply after subtracting the biggest possible error from each measurement.

Given :

a box is to be constructed from a sheet of cardboard that is 10 cm by 60 cm

cutting out squares of length x by x from each corner and bending up the sides

⇒ (50-2x)(10-2x)(x)

⇒ 500-100x-20x+4x^2) (x)

⇒ 4x^3-120x^2+500x

⇒ dv/dx     12x^2-240x+500=0

⇒ 3x^2-60x+125=0

⇒ Quadratic formula x=[60 ± √2100]/6

⇒ x= 2.36 or 17.64

volume max: 45.28 x 5.28 x 2.36= 564 cm^3

Hence The maximum volume of the box is 54 cm³

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Using simple linear equation we calculate the cost of a sweater as $35 .

A linear polynomial over a field, from which the coefficients are taken, can be equalised to zero to produce a linear equation.

Let the cost of each sweater be x.

Cost of the skirt = $20

Let us form a linear equation to calculate the required cost

4x + 20 = 160

solving we get :

x = 35

Therefore the cost of a skirt is $35.

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Answer:

see explanation

Step-by-step explanation:

f(3) means what is the value of f(x) when x = 3

substitute x = 3 into f(x)

f(3) = 10(3) + 13 = 30 + 13 = 43

similarly for x = - 8

f(- 8) = 10(- 8) + 13 = - 80 + 13 = - 67

given f(x) = 10x + 13 and f(x) = 53 , equate the right sides

10x + 13 = 53 ( subtract 13 from both sides )

10x = 40 ( divide both sides by 10 )

x = 4

The degrees to radians conversion is given as 1° = π/180 radian thus the conversion of 310° is (31/18)π.

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

It is known that π radian = 180°.

1° = (π/180) radian.

Multiply both sides by 310

310° = (π/180)310

310° = (31/18)π

Hence "The degrees to radians conversion is given as 1° = π/180 radian thus the conversion of 310° is (31/18)π".

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1 1/2 : 1/2 is the rario of wayer to milk

The ratio of water to milk is 3:1.

The quantitative relation between two amounts showing the number of times one value contains or is contained within the other is called ratio.

Water = 1½ cups

         = 3/2 cups

Milk =  1/2 cup

Ratio of Water to milk

= 3/2 : 1/2

= 3/2 ÷ 1/2

= 3/2 x 2/1

= 3/1

so, the ratio of water to milk is 3:1.

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The equation of line is y = -9.

These lines are written in the form y = mx + b, where m is the slope and b is the y-intercept. We know from the question that our slope is 3 and our y-intercept is –5, so plugging these values in we get the equation of our line to be y = 3x – 5.

Given that,

(1, -9) = ( [tex]x_{1}, y_{1}[/tex])

(-3, -9) = [tex](x_{2},y_{2})[/tex]

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

         = [tex]\frac{-9+9}{-3-1}[/tex]

Slope = 0

Then the equation of line

[tex]y-y_{1} = m(x-x_{1})[/tex]

y+9 = 0

y = -9

Hence, The equation of line is y = -9.

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Answer:

i will answer in 2050 my bad

i just need the points rq

Step-by-step explanation:

n/a

Step-by-step explanation:

5,15 can accord to be an sciencetistic teachers, the 15,11 which means you can appear to combine them together and be an 100 then you do the abcd and boom

yes thank you very muchGiven: Measure of angle D E G equals 51 degrees. Measure of angle G E F equals 39 degrees. Prove: Triangle D E F is a right triangle. Art: A right angle triangle D E F. Angle D E F is a right angle. Point G is on segment D F, and segment E G is drawn.

An expression, in terms of n, for the nth term of this arithmetic sequence is aₙ = 23 - 4n.

An arithmetic sequence can be defined as a series of real and natural numbers in which each term differs from the preceding term by a constant numerical quantity.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ = a₁ + (n - 1)d

Where:

For the second term, we have:

a₂ = a₃ - d

a₂ = 11 - (-4)

a₂ = 11 + 4

a₂ = 15.

For the first term, we have:

a₁ = 4 + second term

a₁ = 4 + 15

a₁ = 19

Substituting the given parameters into the formula, we have;

aₙ = a₁ + (n - 1)d

aₙ = 19 + (n - 1)(-4)

aₙ = 19 - 4n + 4

aₙ = 23 - 4n

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The set of numbers from least to greatest is-

5×10⁻², 6%, 2/5, 4/9, 2⁻¹, √3.

For the given numbers;

The given number are-

2/5, 5×10⁻², √3, 6%, 4/9, 2⁻¹.

These number can be written in the decimal form as;

Now arrange the number from least to greatest.

0.058, 0.06, 0.40, 0.44, 0.5, 1.73

Convert the number in given form.

5×10⁻², 6%, 2/5, 4/9, 2⁻¹, √3.

Thus, the number represented in the ascending order are-

5×10⁻², 6%, 2/5, 4/9, 2⁻¹, √3.

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For a Simple Interest of $160, the amount that he invested is $2000.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

Given:

Simple Interest (S.I.) = $160

Rate of Interest (R) = 2%

Time Period (T) = 4 Years

Let the Principal Amount be $P

We know,

[tex]S.I. =\frac{P*R*T}{100}[/tex]

Putting the given values in the formula, we get:

[tex]S.I. =\frac{P*R*T}{100}\\S.I. =\frac{P*2*4}{100} =\frac{P*8}{100}\\ 160 =\frac{P*8}{100} \\P = \frac{160*100}{8} =\frac{16000}{8} = 2000[/tex]

Hence, He Invested $2000

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Answer:

$2,000

Step-by-step explanation:

Simple Interest Formula

[tex]\large\boxed{\sf I = Prt}[/tex]

where:

Given values:

Substitute the given values into the formula and solve for P:

[tex]\implies \sf 160=P \cdot 4 \cdot 0.02[/tex]

[tex]\implies \sf 160=0.08P[/tex]

[tex]\implies \sf P=\dfrac{160}{0.08}[/tex]

[tex]\implies \sf P=2000[/tex]

Therefore, the amount Deshaun invested was $2,000.

Answer:

Step-by-step explanation:

49 = 7/6u

49 * 6/7 = 7/6u * 6/7

42 = u

The continuous growth rate per year of the world population is 0.664%.

We've been told to assume that population is growing at an exponential rate. As a result, we can employ the population model shown below.

N(t) = N₀ e∧(kt)

Here, N(t) represents the population after t years, N₀ represents the initial population, and k represents the continuous growth rate.

We've been told that initial population of 6.9 billion will increase to 9 billion in 40 years (2050-2010).

To use this information, we calculate the growth rate using the model described below.

N(40) = 6.9 e∧(40k)

N(40) = 9 (given)

9 =  6.9 e∧(40k)

Taking ㏑ both side

㏑ 9 = ㏑ 6.9 e∧(40k)

40k = ㏑(9/6.9)

k = 0.00664

k = 0.664%

Thus, the continuous growth rate per year of the world population is 0.664%.

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Answer:

Step-by-step explanation:

Yes

Answer:

1b) in first image

1c) in second image

Answer:

Is y3 supposed to be y^3?  Is so, the answer is 1.  

Step-by-step explanation:

If the equation is correct as written, 3y = 1, then y = 1/3

y^3 = 1

This can also be written as y^2*y = 1

1.  If y = -1, then y^2y would be (1)*(-1) = -1

2. If y = 1, then (1)^3 * (1) = 1  This works.

3.  If y = ±1, then -1 is a possible answer and -1 does not work as per #1

4.  3^3 = 27

Answer:

54 + (7x + 1) + 90 = 180° (sum of angles in triangle=180)

7x = 35

x = 5

Answer:

x = 5

Step-by-step explanation:

This question deals with a right-angled triangle. The sum of the angles in a  triangle is equal to 180 degrees. A right angle is equal to 90 degrees which means that the other two angles must equal to 90 degrees as well.

Form the equation.

( 7x + 1 ) + 54 + 90 = 180;

Subtract 90 from both sides.

7x + 1 + 54 + 90 - 90 = 180 - 90;

7x + 1 + 54 = 90;

Simplify left-hand side.

7x + 55 = 90;

Subtract 55 from both sides.

7x + 55 - 55 = 90 - 55;

7x = 35;

Divide both sides by 7.

x = 35 / 7;

x = 5;

Answer:

B Description is in the picture

Answer:

[tex]2^2*3^2[/tex]

Step-by-step explanation:

By definition of a negative exponent: [tex](\frac{a}{b})^{-x}=(\frac{b}{a})^x=\frac{b^x}{a^x}[/tex]

In the last step I simply distributed the exponent, but this actually goes both ways! So we can do: [tex]\frac{b^x}{a^x}\implies(\frac{b}{a})^x[/tex]

The next thing you need to know is that: [tex](ab)^x=a^x*b^x[/tex]

and like the previous statement, it works both ways! So this means: [tex]a^x*b^x\implies (ab)^x[/tex]

So the denominator of the expression given can be expressed as:

[tex](2^{-2}*3^{-2})\implies (2*3)^{-2}[/tex]

Lastly you need to understand: [tex]1^x[/tex] just simplifies to one, because [tex]1*1*1*1...\text{ x amount of times}[/tex] will stay equal to one. So we can thing of 1 as being raised to some number, even if not explicitly stated.

This helps because we can write one as: [tex]1^{-2}[/tex]

so now we have the expression:
[tex]\frac{1^{-2}}{(3*2)^{-2}}[/tex]

Well this can because now we can "factor" out this exponent just like how it was demonstrated in the beginning

We get the expression: [tex](\frac{1}{3*2})^{-2}[/tex]

Now we use the definition of a negative exponent, to get the reciprocal giving us the expression

[tex](\frac{3*2}{1})^{2}[/tex]

We can now "distribute" this exponent across the division to get

[tex]\frac{(3*2)^2}{1^2}[/tex]

Well 1 squared just simplifies to 1, so it's redundant to write.

This gives us the expression:
[tex](3*2)^2[/tex]

and as stated before we can distribute this across multiplication, and another way to think of it is:

[tex](3*2)^2\implies (3^2*2^2)\\\\\\text{because } (3*2)^2\implies (3*2)*(3*2)\implies(3*3)*(2*2)[/tex]

we're just grouping the like terms, so we can write them as an exponent.

So this gives us our final expression:
[tex]3^2*2^2[/tex]

or

[tex]2^2*3^2[/tex]

which is the option B, since the order in which we multiply does not matter.

The solution to the given inequality expression is g <3

Inequality are expressions not separated by an equal sign. They are separated by a less than, greater than, less than or equal to and greater than or equal to.

Given the linear equation below:

g + 3 < 6

We are determine the unknown variable "g"

First, we need to subtract 3 from both sides to have;

g + 3 - 3 <  6-3

g < 6 - 3

g < 3

Hence the solution to the given inequality expression is g < 3

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Answer:

2/3

Step-by-step explanation:

If 1/3 rd of the fence can be built in 1/2 hr then in 1 hour which is 1/2 x 2 the fraction of the fence that can be built is 1/3 x 2 = 2/3

The measure of center that is a better indication of a "typical” salary at this business is A. The mean is better because it is not affected by the high salaries.

When the majority of the data are gathered on the left of the distribution curve or the histogram, the distribution is said to be positively skewed, or skewed to the right.

If the majority of the data are gathered on the right side of the distribution curve or the histogram, the distribution is said to be negatively skewed, or to the left. It is assumed that many employees at tiny businesses earn extremely low pay while a select few earn very high salaries. In this case, the mean gives between information about the data.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - 6x+ 6[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The given equation is :

[tex]\qquad\displaystyle \tt \rightarrow \: 24x + 4y = 24[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 4y =24 - 24x [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{ 24}{4} - \frac{24x}{4} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - 6x + 6[/tex]

And this the equation of same line in its slope intercept form, where slope (m) = -6 and y - intercept = +6

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Given:

The geometric sequence is

To find the common ratio,

Hence the common ratio, r is 14/35.

Answer:

i think is (a)

because i zay do

Step-by-step explanation:

anyways...... i want more pictures of math problems

Answer:

3.6*10³

Step-by-step explanation:

Jack cannot add the powers of 10 because they are in addition. We can apply the exponent rule only when they are in multiplication.

[tex]\sf 6 *10^2 + 3*10^3= 6*100 + 3*1000\\[/tex]                          

                         = 600 + 3000

                         = 3600

                          [tex]\sf = 3.6 * 10^3[/tex]

Answer: x^2 + y^2 - 4x + 18y = 76 = 0

The center of the circle given is (2, 9)

radius = r

The equation of a circle for a given point is

(x - h)^2 + (y - k)^2 = r^2

Where h = 2, and y = 9

(x - 2)^2 + (y - 9)^2 = 3^2

Expand the parentheses

(x - 2) (x - 2) + (y - 9) (y - 9) = 9

(x - 2) (x - 2 ) = x* x - 2*x - 2*x + 2* 2

= x^2 - 4x + 4

(x - 2) (x - 2) = x^2 - 4x + 4

(y - 9) (y - 9) = y*y - y*9 - 9*y + 9*9

= y^2 - 18y + 81

(y - 9) (y - 9)= y^2 - 18y + 81

Therefore, the equation becomes

x^2 - 4x + 4 + y^2 - 18y + 81 = 9

Re-arrange the equation

x^2 + y^2 - 4x - 18y + 4 + 81 = 9

x^2 + y^2 - 4x - 18y = 9 - 81 - 4

x^2 + y^2 - 4x - 18y = -76

x^2 + y^2 - 4x - 18y + 76 = 0

The equation of a circle given the center (2, 9) and radius 3 is x^2 + y^2 - 4x + 18y = 76 = 0

Answer:

The equation of a circle given the center (2, 9) and radius 3 is x^2 + y^2 - 4x + 18y = 76 = 0

Step-by-step explanation:

I can buy 75 latex balloons and 50 mylar balloons.

This is a problem from an algebraic equation. We can solve this problem by following a few steps.

We need 125 balloons. Let's assume we have to purchase x latex balloons.

So, mylar balloons are ( 125 - x ).

Our total budget is $32.50.

The cost of x latex balloons is ($.10 × x) = $.10x , as the latex balloons cost $.10 each.

The cost of ( 125- x)  mylar balloons is $[( 125- x) × 0.50] , as the mylar balloons cost $.50 each.

So the total cost is,

$[( 125- x) × 0.50] + $.10x  = 32.50

Now, we have to solve this equation, Let's simplify it.

62.50 - 0.50x + .10x = 32.50

Or, 62.50 - 0.40x = 32.50

Or, -0.40x =  32.50 - 62.50       [ deduce 62.50 from both side ]

Or, -0.40x =  -30                 [ we should devide both sides 0.40 ]

Or, x = 30/0.40 = 75

So, the number of latex balloons is 75. Therefore, the number of remaining mylar balloons is ( 125 - 75) = 50

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