Factorise
8 a ² b ²-
64 ab​

\(P(490 < X < 560)\)= 0.3133

Given: μ = 560

σ = 90  

To find: P (490 < X < 560)

Normal distributions are symmetric, unimodal, and asymptotic. A normal distribution is determined by two parameters the mean and the variance. A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. It's always easy to solve questions in terms to standard normal

Hence, converting normal distribution to standard normal gives:

P(490 < X < 560)  = \(P(\frac{560-560}{90}\)≤ \(\frac{X-\mu}{\sigma} < \frac{640-560}{90})\)

                              = P(0 ≤ Z < 0.888)

                               = P (z<0.89) - P(z  ≤ 0)

Using standard normal table,

= 0.8133 - 0.5

P(490 < X < 560) = 0.3133

To learn more about Normal Distribution, visit:

https://brainly.com/question/4079902

#SPJ4

Equation of the line is y = -(1/3)x+5

The figure shows a straight line of which two points and thereby the slope can be found out.

Equation of a line is in the slope-intercept form is,

y = mx +c,

where m is the slope of the line and c is the y-intercept of the line.

From the figure, two points on the line are, (0,5) and (3,4).

Then slope = (4-5)/(3-0)

                  = -1/3

Now y-intercept, c is the y-co-ordinate when x = 0.

From the figure, when x = 0, y = 5

So y-intercept, c = 5.

Thus the equation of the line is, y = -(1/3)x+5

Learn more about slope-intercept form at https://brainly.com/question/16975427

#SPJ1

Answer:

y + 9 ≤ -30

Step-by-step explanation:

If the skill builder has a total of 40 questions, and the maximum percent grade is 100%, we can use a rule of three to determine the relation between the percent grade y and the number of correct answers x:

So the equation is y = 2.5x + 0.

(Each correct answer is worth 2.5% of the grade)

The charge q is ±7.46 × 10⁻⁷C.

Give:

Take a look at the charge on the left. The following forces are at work in response to this charge:

(Refer to the diagram below)

Because the charge is in equilibrium, the charge's vertical and horizontal forces must be zero.

We have the following in the vertical direction:

\(\begin{aligned}T \cos 20^{\circ} &=W \\\Rightarrow T &=\frac{m g}{\cos 20^{\circ}} \\&=\frac{3.0 \times 10^{-3} \mathrm{~kg} \times 9.8 \mathrm{~m} / \mathrm{s}^2}{\cos 20^{\circ}} \\&=3.13 \times 10^{-2} \mathrm{~N}\end{aligned}\)

Coulomb's Law states that the electrostatic force between two point charges, q₁, and q₂, separated by r is given by the equation:

\(\begin{aligned}F &=\frac{q_1 q_2}{4 \pi \epsilon_0 r^2} \\&=\frac{K q_1 q_2}{r^2}\end{aligned}\)

Here,

Using trigonometric personalities, the distance between any two charges is:

\(\begin{aligned}r &=2 l \sin 20^{\circ} \\&=2 \times 1.0 \mathrm{~m} \times 0.342 \\&=0.684 \mathrm{~m}\end{aligned}\)

We have the following in the vertical direction:

\(\begin{aligned}F_e &=T \sin 20^{\circ} \\\Rightarrow \frac{K q_1 q_2}{r^2} &=T \sin 20^{\circ} \\\Rightarrow \frac{K q^2}{r^2} &=T \sin 20^{\circ} \\\Rightarrow q^2 &=\frac{r^2 T \sin 20^{\circ}}{K} \\&=\frac{(0.684 \mathrm{~m})^2 \times 3.13 \times 10^{-2} \mathrm{~N} \times \sin 20^{\circ}}{9 \times 10^9 \mathrm{~N} \cdot \mathrm{m}^2 / \mathrm{C}^2} \\&=55.65 \times 10^{-14} \mathrm{C}^2 \\\Rightarrow q &=\pm 7.46 \times 10^{-7} \mathrm{C}\end{aligned}\)

Therefore, the charge q is ±7.46 × 10⁻⁷C.

Know more about the charge here:

https://brainly.com/question/25922783

#SPJ4

The correct question is given below:
Two 3.0g point charges on 1.0m - long threads repel each other after being equally charged, as shown in the figure. What is the charge q?

Answer:

x-intercept is x = -4; y-intercept is y = -2

Step-by-step explanation:

1.

The zero or x-intercept is when the line touches the x-axis or horizontal line axis or is when y = 0.

x = -4

2.

The y-intercept is when the line touches the y-axis or vertical line axis or is when x = 0.

y = -2

The probability of event A and event B is 6.

Given that, P(A)=6, P(B)=20 and P(A∩B)=6.

P(A/B) Formula is given as, P(A/B) = P(A∩B) / P(B), where, P(A) is probability of event A happening, P(B) is the probability of event B.

P(A/B) = P(A∩B) / P(B) = 6/20 = 3/10

We know that, P(A and B)=P(A/B)×P(B)

= 3/10 × 20

= 3×2

= 6

Therefore, the probability of event A and event B is 6.

To learn more about the probability visit:

https://brainly.com/question/11234923.

#SPJ1

The cost of the utility pole is approximately $1273.99 when rounded to the nearest cent.

To calculate the cost of the utility pole, we need to find its volume first. The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the base of the cylinder and h is its height.

Here, the diameter of the utility pole is given as 1.5 ft. We need to find the radius, which is half of the diameter, so r = 0.75 ft. The height is given as 30 ft.

Using the formula, we get:

V = πr^2h = π(0.75 ft)^2(30 ft) = 53.36 ft^3

Now, we can calculate the cost of the utility pole by multiplying its volume by the cost of wood per cubic foot, which is $23.89 per cubic foot.

Cost = 53.36 ft^3 x $23.89/ft^3 ≈ $1273.99

To learn more about Cost click on,

https://brainly.com/question/29020588

#SPJ4

Answer:

∠CED = 58°

Step-by-step explanation:

Clearly, we can see that ∠AED and ∠CED are a linear pair. Therefore:

Definition of Linear pair: A linear pair is two angles that form a 180 angle.

We are given that:

Therefore, when we substitute the measure of ∠AED, we get;

This problem is now an algebraic problem. Simply isolate ∠CED on one side of the equation to determine the measure of ∠CED. This can be done by subtracting 122 both sides of the equation.

Therefore, the measure of ∠CED is 58°.

The measure of angle CED is 58° adjacent to the angle AED.

A pair of linear angles are adjacent to each other whose sum is 180°.

Given, a measure of the angle AED is 122°

We know the measure of linear pair of angles is 180°.

∴ m∠AED + m∠CED = 180°.

122° + m∠CED = 180°.

m∠CED = 180° - 122°.

m∠CED = 58°.

learn more about linear pairs of angles here :

https://brainly.com/question/17525542

#SPJ2

Answer:

45t+250

Step-by-step explanation:

Given that the box contains 46 red marbles, 58 white marbles, and 51 blue marbles, you know that the total number of marbles the box contains is:

In this case, let be A the event in which the randomly selected marble from the box is white, and B the event in which the randomly selected marble from the box is blue.

Since those events are independent, you can set up that the probability of randomly selecting a white marble or blue marble from the box is:

Knowing that there are 58 white marbles, you can determine that:

And knowing that there are 51 blue marbles, you can determine that:

Therefore:

Hence, the answer is:

Answer:x=4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

4−3x=8−4x

4+−3x=8+−4x

−3x+4=−4x+8

Step 2: Add 4x to both sides.

−3x+4+4x=−4x+8+4x

x+4=8

Step 3: Subtract 4 from both sides.

x+4−4=8−4

x=4

Answer:

x=4

Step-by-step explanation:

4-3×=8-4x

4-8=-4x+3x

-4=-×

x=4

(both side have negative so you just cancel out the negative sign)

Answer:

There are no factors of 3 that add up to -15

Step-by-step explanation:

the only factors of 3 is, 1 and 3.

The minim she can get for a score is a 90%

Based on the given simple statements, "The scroll is open" and "The writings are visible," we can determine which compound statements would also be true.

The scroll is not open or the writings are visible.

This compound statement would be true. Since the first simple statement states that the scroll is open, the negation of this statement would be that the scroll is not open. The second simple statement states that the writings are visible, which aligns with this compound statement. Therefore, this compound statement is true.

The scroll is open or the writings are not visible.

This compound statement would not be true. Both simple statements state that the scroll is open and the writings are visible. So, the second part of this compound statement contradicts the given information.

The scroll is open or the writings are visible.

This compound statement would be true. It directly matches the given simple statements, where both the scroll being open and the writings being visible are mentioned. Therefore, this compound statement is true.

The scroll is not open or the writings are not visible.

This compound statement would not be true. Both simple statements state that the scroll is open and the writings are visible. So, neither part of this compound statement aligns with the given information.

The compound statements that would be true are:

The scroll is not open or the writings are visible.

The scroll is open or the writings are visible.

To know more about compound statements , visit;
https://brainly.com/question/29098482?referrer=searchResult
#SPJ11

Answer: To determine the number of liters of oxygen needed to produce a given number of water molecules, we need to use the concept of stoichiometry and the Avogadro's number.

First, let's find the number of oxygen molecules required to produce 6.518 × 10^22 molecules of water. The balanced chemical equation for the production of water is:

2 H2 + O2 -> 2 H2O

From the equation, we can see that 2 molecules of H2O are produced for every 1 molecule of O2. Therefore, the number of O2 molecules needed is half the number of water molecules:

Number of O2 molecules = (6.518 × 10^22 molecules of water) / 2

Next, we'll use Avogadro's number, which states that 1 mole of any substance contains 6.022 × 10^23 particles (atoms, molecules, etc.). Since we have the number of oxygen molecules, we can calculate the number of moles of oxygen:

Number of moles of O2 = (Number of O2 molecules) / (Avogadro's number)

Finally, we'll convert the number of moles to liters using the ideal gas law, assuming standard temperature and pressure (STP), where 1 mole of any ideal gas occupies 22.4 liters:

Number of liters of O2 = (Number of moles of O2) * (22.4 liters/mole)

Let's calculate the number of liters of oxygen needed:

Number of O2 molecules = (6.518 × 10^22 molecules of water) / 2

Number of moles of O2 = (Number of O2 molecules) / (Avogadro's number)

Number of liters of O2 = (Number of moles of O2) * (22.4 liters/mole)

Plug in the values to calculate the number of liters of oxygen needed.

Answer:

10

Step-by-step explanation:

i dont know because this is a guess

Answer:

y^2

step-by-step-explanation:

Answer:

Step-by-step explanation:

84 cents divided by 14 inches = 6 cents per inch

48 cents divided by 6 cents = 8 inches

8 inches of wire can be bought for 48 cents

The ratios for sin A, cos A, and tan A are,

sin A = 12/13

cos A = 5/13

tan A = 12/5

We have,

A triangle ABC is shown in image.

Now,

By given figure,

sin A= BC/AC

sin A = 24/26

sin A = 12/13

And,

cos A= AC/AB

cos A = 10/26

cos A = 5/13

And,

tan A = BC/AC

tan A = 24/10

tan A = 12/5

Thus, The ratios for sin A, cos A, and tan A are,

sin A = 12/13

cos A = 5/13

tan A = 12/5

Learn more about trigonometric ratios at:

brainly.com/question/1836193

#SPJ4

Fabiana's average velocity is 19 km/h.

Instantaneous Velocity:

Instantaneous velocity is the velocity of an object at a specific point in time. It is calculated by taking the derivative of the position function with respect to time. The position function of Fabiana's bicycle ride is s(t) = 19t + 17, where s is the position in km and t is the time in hours.

To find the instantaneous velocity, we need to take the derivative of s(t) with respect to t:

s'(t) = 19

This means that Fabiana's instantaneous velocity is constant at 19 km/h.

Average Velocity:

Average velocity is the total displacement of an object divided by the total time taken. In this case, Fabiana's total displacement is s(1) - s(0) = (19*1 + 17) - (19*0 + 17) = 19 km, and her total time taken is 1 hour.

Therefore, her average velocity is 19 km/h.

Know more about average velocity here:

https://brainly.com/question/28512079

#SPJ11

70.8 mins - 90 mins = 19.2  minutes

ANSWER

(5, 4)

EXPLANATION

We are given that C is the midpoint from A to B.

First, we have to find the coordinates of point C.

To do that, we apply the formula for midpoint of two points:

where (x1, y1) and (x2, y2) are the two points.

The coordinates of A and B are (-3, 8) and (9, 2)

Therefore, the coordinate of C is:

Point D is given to be one-third the distance between C and B.

This means that we want to partition the distance between C and B into 3, where D is the point 1/3 that distance away from C.

To find D, we have to find the difference between the coordinate points of C and B, find 1/3 of that, then, add that to the coordinate of C:

Adding that to the coordinates of C:

That is the coordinate of D.

A triangle (Option B)

If you cut it perpendicular to its base and through its vertex, the cross-section would be shaped like an isosceles triangle. The base of the triangle will be the base of the cone. The cone would create a circle shape if the plane sliced it parallel to its base

Answer:

the second

Step-by-step explanation:

refers to well-founded standards of right and wrong that prescribe what humans should do, usually in terms of rights, obligations, benefits to society, justice