Find the area under the standard normal curve more than 3.2. Give your answer to 4 decimal places.

Answer: x = -2, \(\frac{2 }{3}\)

Step-by-step explanation:

     Given:

0 = –3x² – 4x + 4

    The quadratic formula:

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

    Substitute known values:

* a = -3, b = -4, c = 4

\(\displaystyle x=\frac{-(-4)\pm\sqrt{(-4)^2-4(-3)(4)} }{2(-3)}\)

    Simplify with multiplication:

\(\displaystyle x=\frac{4\pm\sqrt{16+48} }{-6}\)

    Simplify:

\(\displaystyle x=\frac{4\pm\sqrt{64} }{-6}\)

\(\displaystyle x=\frac{4+8 }{-6}\),    \(\displaystyle x=\frac{4-8 }{-6}\)

\(\displaystyle x=\frac{12 }{-6}\),    \(\displaystyle x=\frac{-4 }{-6}\)

The value of x is 9 cm, and angle O is 0 degrees.

To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:

(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:

LN = 12 cm

NK = 6 cm

KM = 8 cm

Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.

Using the Law of Cosines, we can write the equation for side NM (x):

x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)

We don't know the value of angle N yet, so we need to find it using the Law of Sines.

(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:

sin(A) / a = sin(B) / b = sin(C) / c

In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.

We can write the equation for angle O:

sin(O) / 8 = sin(N) / 6

Now, let's solve these equations step by step to find the values of x and angle O.

To find angle N, we can use the Law of Sines:

sin(N) / 12 = sin(180 - N - O) / x

Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:

sin(N) / 12 = sin(O) / x

Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):

sin(N) / 12 = (6 / 8) * sin(N) / x

Now, we can solve this equation for x:

x = (12 * 6) / 8 = 9 cm

So, the value of x is 9 cm.

To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:

sin(O) / 8 = sin(N) / 6

sin(O) / 8 = sin(O) / 9

9 * sin(O) = 8 * sin(O)

sin(O) = 0

This implies that angle O is 0 degrees.

Therefore, the value of x is 9 cm, and angle O is 0 degrees.

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The figure for the given question is provided here :

Answer:

B) \(4i\sqrt{2}\)

Step-by-step explanation:

\(\sqrt{-2}=i\sqrt{2}\\\sqrt{-18}=i\sqrt{18}=i\sqrt{9*2}=3i\sqrt{2}\\\\\sqrt{-2}+\sqrt{-18}=i\sqrt{2}+3i\sqrt{2}=4i\sqrt{2}\)

Step-by-step explanation:

Hey there!!!

1. Ans.

The formula for quadratic equation,

\(x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a} \)

2. Ans.

When, the quadratic equation is given, in the form of;

\(a {x}^{2} + bx + c = 0\)

Then, "a" is the coefficient of x "b" is the coefficient of y. and c is the constant value.

3.Ans.

\( \sqrt{ {b}^{2} - 4ac } \: tells \: us \: the \: type \: of \: solutions.\)

Hope it helps..

The answer would be (C) 20.

Answer:

The 2nd quartile, also known as the median, is the middle value of a dataset, or the value that separates the lower half of the data from the upper half. In a box-and-whisker plot, the 2nd quartile is represented by the line in the middle of the box.

In the given box-and-whisker plot, the 2nd quartile is 12.5, which is the middle value of the data set. This can be determined by looking at the scale on the x-axis and finding the value that is in the middle of the box.

Option B, 12.5, is the correct answer.

Step-by-step explanation:

The smallest number that will make it divisible by 11 is n = 2 and the number is A = 7,01,69,302

Given data ,

Let the missing number be represented as n

Now , the value of the original number is A = 7,01,69,30*​

where * represents = n

To make a number divisible by 11, the difference between the sum of the digits in the odd-numbered positions and the sum of the digits in the even-numbered positions must be a multiple of 11.

On simplifying the equation , we get

To make the difference between the sums a multiple of 11, we need to add the smallest digit to the end. The smallest digit is 8

Hence , the number that is divisible by 11 is 7,01,69,302

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Chandler ended up 8 feet below sea level. The negative sign indicates that his final position is below sea level. This means that he has descended further into the lake compared to the starting point on the cliff.

Chandler started on the cliff at 32 feet above sea level. When he jumped for 40 feet, we need to determine the final position in relation to sea level.

Since Chandler jumped down, the distance below sea level will be calculated as a negative value. To find how far below sea level Chandler ended up, we subtract the jump distance (40 feet) from the starting height (32 feet above sea level):

32 feet - 40 feet = -8 feet

It's important to note that negative values are used here to represent the direction and magnitude of Chandler's descent relative to sea level

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Answer:

-8 feet

Step-by-step explanation:

The value of ∂x/∂s is  4s^2 * t^6.

To find ∂x/∂s, we need to differentiate x with respect to s while treating t as a constant. Let's begin by substituting the given expressions for x, y, and z into the function f(x, y, z):

f(x, y, z) = (x^2)(y^3) + z^3

Substituting x, y, and z:

f(s, t) = ((s^2)(t^3))^2 * (s*t)^3 + ((s^2)*t)^3

Expanding the expression:

f(s, t) = (s^4 * t^6) * (s^3 * t^3) + (s^6 * t^3)

Now, let's differentiate x with respect to s:

∂x/∂s = ∂/∂s [(s^2)(t^3)]^2

Using the chain rule, we can differentiate each term separately:

∂x/∂s = 2 * (s^2 * t^3)^1 * ∂/∂s [(s^2)(t^3)]

Differentiating (s^2)(t^3) with respect to s:

∂/∂s [(s^2)(t^3)] = 2s * t^3

Substituting back into the expression for ∂x/∂s:

∂x/∂s = 2 * (s^2 * t^3)^1 * 2s * t^3

Simplifying:

∂x/∂s = 4s^2 * t^6

Therefore, ∂x/∂s = 4s^2 * t^6.

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To find the volume of the object we need to notice that is is made from two rectangular prisms:

• A prism with length 8 cm, width 6 cm and height 13 cm.

• A prism with length 3 cm, width 4 cm and height 7 cm.

Hence the volume is the sum of the volumes of the prisms.

The volume of a rectangular prims is given by:

Hence the volume of the object is:

Therefore, the volume of the object is 708 cubic cm.

When a mass of 3 kg is hanged to it, the string will stretch 7.5 cm.

Given,

The length of the spring attached to the ceiling = 10 cm

The quantity of the mass hanged in the spring = 2 kg

The amount of stretching happened in the spring = 15 cm

We have to find the stretching of string when a mass of 3 kg is hanged to it;

Here,

Given that the force applied to the spring by the 2.0 kg is equal to the mass's weight:

F = mg = 2 kg × 9.8 m/s² = 19.6 N

Additionally, the stretching of:

Δx = 15 cm - 10 cm = 5 cm

So, applying Hooke's law:

F = kΔx

To determine the spring constant, k;

k = F/Δx = 19.6/5 = 3.92  N/ cm

The spring is now coupled to a new mass of m = 3.0 kg; the force this mass exerts on the spring equals

F = mg = 3 kg × 9.8 m/s² = 29.4 N

Thus, we may apply Hooke's law once more to determine the new stretching:

Δx = F/k = 29.4/3.92 = 7.5 cm

Therefore,

The string will be stretched 7.5 cm when a mass of 3 kg is hanged to it.

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3. The volume of the Pringle Chips container is approximately 2034.72 cubic inches.

4. The cake takes up approximately 7317 cubic inches of space.

5. The volume of foam in the model of the volcano is approximately 7234.08 cubic centimeters.

1. The units for Volume are always cubed.

2. Volume is the amount of space an object takes up. True.

3. To calculate the volume of the Pringle Chips container, we need to find the volume of a cylinder. The formula for the volume of a cylinder is V = πr^2h, where π is a constant (approximately 3.14), r is the radius, and h is the height. Given that the diameter is 9 inches, the radius would be half of that, which is 4.5 inches. Substituting the values into the formula, we have:

V = 3.14 * (4.5)^2 * 32

V = 3.14 * 20.25 * 32

V ≈ 2034.72 cubic inches

4. To find the volume of the 3-tier cake, we need to find the volume of each tier separately and then add them together. Since all the tiers are cylinders, we can use the formula V = πr^2h.

Tier 1:

V1 = 3.14 * (12)^2 * 10 = 4521.6 cubic inches

Tier 2:

V2 = 3.14 * (8)^2 * 10 = 2010.4 cubic inches

Tier 3:

V3 = 3.14 * (5)^2 * 10 = 785 cubic inches

Total volume:

Total V = V1 + V2 + V3

Total V = 4521.6 + 2010.4 + 785

Total V ≈ 7317 cubic inches

5. To find the volume of the Styrofoam model of the volcano, we can use the formula for the volume of a cone, V = (1/3)πr^2h. Given that the diameter is 48 centimeters, the radius would be half of that, which is 24 centimeters. Substituting the values into the formula, we have:

V = (1/3) * 3.14 * (24)^2 * 12

V = (1/3) * 3.14 * 576 * 12

V ≈ 7234.08 cubic centimeters

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Given:

The horizontal component of velocity is 5 ft/s.

To find the rate of change,

So, the rate of chnage of elevation is -2 ft/s.

That means decreasing by 2 ft/s.

Stokes' theorem relates the surface integral of the curl of \(\vec F\) across \(S\) to the line integral of \(\vec F\) along the boundary of \(S\).

The boundary of \(S\) is a circle with radius 7 centered at the origin in the \(x,y\)-plane. Parameterize this path by

\(\vec r(t) = 7\cos(t)\,\vec\imath + 7\sin(t)\,\vec\jmath\)

with \(0\le t\le2\pi\). Observe that \(z=0\), so \(\cos(z) = 1\) and the \(\vec\jmath\)-component of \(\vec F\) contributes nothing. The double integral then reduces to

\(\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec S = \int_0^{2\pi} \vec F(\vec r(t)) \cdot \frac{d\vec r}{dt} \, dt \\\\ ~~~~~~~~ = \int_0^{2\pi} \left(e^{49\cos(t)\sin(t)}\,\vec\imath + 49\cos(t)\sin(t)\,\vec\jmath\right) \cdot \left(-7\sin(t)\,\vec\imath + 7\cos(t)\,\vec\jmath\right) \, dt \\\\ ~~~~~~~~ = -7 \int_0^{2\pi} e^{49\cos(t)\sin(t)} \sin(t) \, dt\)

Observe that by substituting \(t=u+\pi\), we have

\(\sin(t) = \sin(u+\pi) = \sin(u)\cos(\pi) + \cos(u)\sin(\pi) = -\sin(u)\)

so that the integral over \([\pi,2\pi]\) can be expressed in terms of the integral over \([0,\pi]\) as

\(\displaystyle \int_\pi^{2\pi} e^{49\cos(t)\sin(t)} \sin(t) \, dt = \int_0^\pi -e^{49\cos(t)\sin(t)} \sin(t) \, dt\)

Then the integrals over \([0,\pi]\) and \([\pi,2\pi]\) cancel each other and integral of the curl of \(\vec F\) is

\(\displaystyle -7 \int_0^{2\pi} e^{49\cos(t)\sin(t)} \sin(t) \, dt = -7 \int_0^\pi 0 \, dt = \boxed{0}\)

Answer:

\(\theta =135\)

Step-by-step explanation:

Required

Interior of a regular octagon

This is calculated using:

\(\theta =\frac{180(n-2)}{n}\)

Where

\(n = 8\)

So:

\(\theta =\frac{180(8-2)}{8}\)

\(\theta =\frac{180*6}{8}\)

\(\theta =135\)

Let's assume x gallons of milk containing 8% butterfat and y gallons of milk containing 2% butterfat are used.

The total amount of milk is x + y gallons, and we want it to be equal to 258 gallons.

To determine the amount of butterfat in the mixture, we can multiply the volume of each type of milk by its respective butterfat percentage and sum them up.

For milk containing 8% butterfat, the amount of butterfat is 0.08x (8% is equivalent to 0.08 as a decimal).

For milk containing 2% butterfat, the amount of butterfat is 0.02y (2% is equivalent to 0.02 as a decimal).

Since we want the final mixture to contain 7% butterfat, we can set up the following equation:

0.08x + 0.02y = 0.07(258)

Simplifying the equation, we have:

0.08x + 0.02y = 18.06

To solve for x and y, we need another equation. Since the total amount of milk is x + y = 258, we can rearrange it to y = 258 - x.

Substituting this value into the equation above, we get:

0.08x + 0.02(258 - x) = 18.06

Solving this equation will give us the values of x and y, which represent the gallons of milk containing 8% butterfat and 2% butterfat, respectively, needed to obtain the desired 258 gallons.

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The ratios will be equal if the theorem that the product of the extremes equals the product means follows.

Let us understand the equality of ratios through example. The example ratio will be -

7:10 = 21:30

In this ratio, 7 and 30 are first and last numbers and hence they are extremes. The number 10 and 21 are in middle and hence considered mean. Now, we will perform multiplication to if the ratios are equal or not.

Product of extremes = 7 × 30

Extremes product = 210

Product of means = 21 × 10

Means product = 210

Since the products are equal, the ratios are also equal.

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The complete question is -

Are the following ratios equal? write yes or no. use the theroem that the product of the extremes equals the product means.

Ratio = 7:10 and 21:30.

The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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the equation of the line that passes through the points (2, 4) and (6, 2) is y = - 0.5x + 6.

The standard equation of a straight line is -

Ax + By + C = 0

Given is to find the equation of the line that passes through the points (2, 4) and (6, 2).

We can write the slope as -

{m} = (2 - 4)/(6 - 2)

{m} = -2/4

{m} = -1/2

{m} = -0.5

The slope - intercept form would become -

y = - 0.5x + c

For the point (2, 4), we can write the {y} - intercept as -

4 = - 0.5 x 2 + c

c = 6

Therefore, the equation of the line that passes through the points (2, 4) and (6, 2) is y = - 0.5x + 6.

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Answer:

x = -1

Step-by-step explanation:

-8x - 28 = 2x - 18

      +28  +28

-8x = 2x + 10

  -2x  -2x

-10x = 10

÷-10 ÷-10

x = -1

Answer:

1.Distribute

2.Add 28 to both sides

3.Simplify

4.Subtract 2x from both sides

5.Simplify

6.Divide both sides by the same factor

7.Simplify

x =-1

Answer: $2.75

Step-by-step explanation:

2) Judy spent 3*5.25 = 15.75 on popcorn bags, 13.60 on a jumbo bag of chips and 7.90 for a dip. This means that overall she spent $37.25. If she had $40, this means that she have left $40 - $37.25 = $2.75.

1) Your answer is right.

Step-by-step explanation:

OK, 'Brainless'....  the triangle side length rule states that any two sides of a triangle must sum to greater than the remaining side length...

42 + 20 > x        then  12 , 20, 22, 32, 42, 50     will work here

42+x > 20            all of the possibles work here

20 + x > 42         32, 42, 50, 62 and 70 work here

   so   32 and 42 are in all of the lists ....that is your answer

Answer:

Variable terms: 4a and 6a

Constant terms: 4 and 11

Step-by-step explanation:

A constant term is one that is NOT multiplied by any variables.

At this level of math, think of constants as terms that are only numbers.

(for example: 1, 68.9, -42, etc.)

Note that a term in « a + bi » form can also be a constant.

A variable term is a one that IS multiplied by a variable.

(for example x, -3y, 8z, etc.)

In question 1, the variable terms are:

4a and 6a because they are multiplied by the variable a

The constant terms are:

4 and 11 because they are simply integers

Note that the constant terms could also be written as -4 and -11 depending on how the operations are viewed (subtracting vs adding a negative)

The equivalent expression to  4√3 is  √48 or 6.928.

An equivalent expression is an expression that has equal value to the original given expression.

From the given expression, we can determine its equivalent expression as follows;

The given expression = 4√3

We can square 4 and multiply it by 3 and enclose all with the square root.

4√3 = √(4² x 3 )

= √ ( 16 x 3 )

= √ ( 48 )

= 6.928

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Answer:

If each book cost $20.45 then you times it by 21 and the answer you would get is 429.45

Step-by-step explanation:

im 99% that its correct

Answer:

He should expect to spend as much as 429.45 (to be exact)

Step-by-step explanation:

It's really just simple math $20.45 multiplied by 21 is 429.45 (:

I'm sorry if I'm wrong. Have a great day and good luck!

Answer:

70 percent?

Step-by-step explanation:

I hope this helps:)

Here is the attached image for the answer. If you write it in in slope-intercept form, y=mx+b. You will get the answer below in the attached image.

Answer:

Since you state that capitalization is important, then we can see that it is not possible to solve the equation for F.

If that's correct, then the only point of this was that we need to pay attention to symbols when dealing with equations or expressions

Step-by-step explanation:

happy to help have a bless day or night:)

Answer:

no question

Step-by-step explanation:

Answer:

there is no question

Step-by-step explanation:

Answer:

EF

Because if line EF continued on, it would go across line DE.

Answer:

AD is the answer i would go with but it could be CF or BE

Step-by-step explanation: