If a ping-pong ball were tossed randomly on the board shown below, what is
true about the probability of the ball landing on a square located on the
border?

Answer:

Let p = the speed of the plane

and w = the speed of the wind

It takes the plane 3 hours to go 600 miles when against the headwind and 2 hours to go 600 miles with the headwind. So we set up a system of equations.

600mi3hr=p−w600mi2hr=p+w

Solving for the left sides we get:

200mph = p - w

300mph = p + w

Now solve for one variable in either equation. I'll solve for x in the first equation:

200mph = p - w

Add w to both sides:

p = 200mph + w

Now we can substitute the x that we found in the first equation into the second equation so we can solve for w:

300mph = (200mph + w) + w

Combine like terms:

300mph = 200mph + 2w

Subtract 200mph on both sides:

100mph = 2w

Divide by 2:

50mph = w

So the speed of the wind is 50mph.

Now plug the value we just found back in to either equation to find the speed of the plane, I'll plug it into the first equation:

200mph = p - 50mph

Add 50mph on both sides:

250mph = p

So the speed of the plane in still air is 250mph.

Answer:

140miles/hour

Step-by-step explanation:

Speed of airplane + speed of wind

=240miles/3 hours + 240miles/4 hours

=80miles/hour +60miles/hour

= 140miles/hour

I'm assuming all the numbers here mistakenly got copied twice.

Let A(t) denote the amount (in kg) of salt in the tank at time t. The solution starts with 70 kg of salt, so (a) A(0) = 70.

I also assume there is more to the question, so I'll just go ahead and build the differential equation to model this situation, and solve it.

Pure water is flowing into the tank, so no salt is being introduced. The concentration of salt at time t is A(t)/2000 kg/L, and solution is drained from the tank at a rate of 4 L/min, which means salt is being removed at a rate of

(4 L/min) (A(t)/2000 kg/L) = A(t)/500 kg/min = 0.002 A(t) kg/min

Thus the amount of salt (ignoring units now) in the tank changes according to the DE,

dA(t)/dt = -0.002 A(t)

which is easy to solve because it's linear with constant coefficients.

Without going into too much detail:

dA(t)/dt + 0.002 A(t) = 0

exp(0.002t ) dA(t)/dt + 0.002 exp(0.002t ) A(t) = 0

d/dt [exp(0.002t ) A(t)] = 0

exp(0.002t ) A(t) = C

A(t) = C exp(-0.002t )

Given A(0) = 70, solve for C :

70 = C exp(0) = C

Hence

A(t) = 70 exp(-0.002t )

Answer:

Step-by-step explanation:

1) the triangle on the right is half of an equilateral one, so the minor leg is 9

the left one has the two legs congruent

so we have

2x^2 = 81

x^2 = 81/2

x = 9/√2 = 9/2 √2 (at the numerator)

2) the top triangle has the congruents leg

hypotenuse^2 = 2(6√6)^2

hypotenuse^2 = 2(216)

hypotneuse^2 = 432

hypotenuse = √2^4 * 3^2 * 3

hypotenuse = 12√3

the triangle in the bottom is half of the an equilateral one, so

x = 12√3 * 2 = 24√3

3) the left triangle has congruent legs

7^2 = leg^2 + leg^2

49 = 2leg^2

leg^2 = 49/2

leg = 7/√2 = (7√2)/2

the right triangle is half of an equilateral one

x = 7√2/2 * √3 =  7/2 √6 (at the numerator)

4) the rifht triangle has two congruent legs

hy^2= 2(7√6)^2

hy^2 = 2(294)

hy^2 = 588

hy = √2^2 * 7^2* 3

hy = 14√3

the triangle on the left is half of an equilteral one: so

x = 14

Answer:

i dont know hun i am very sorry

Step-by-step explanation:

SOLUTION

• -4 = 5(p -2)

 -4 = (5)(p) + (5)(-2)   • Distribute

 -4 = 5p + (-10)

 -4 = 5p - 10

• 5p - 10 = -4

• 5p - 10 + 10 = -4 + 10

  5p = 6

• [tex]\frac{5p}{5} = \frac{6}{5}[/tex]

  p = [tex]\frac{6}{5}[/tex]

Answer:

6

Step-by-step explanation:

.....................

Answer:

6

Step-by-step explanation:

pecentage calculator.what is 75 percent of 8?=6

Answer:

2 hours and 30 minutes

Step-by-step explanation:

25/5 = 5 Divide to find out how many fives are there in 25.

5 x 30 = 150 minutes (multiply 5 by 30 to find out how many minutes)

150/60 = 2.5 hours or in other words, 2 hours and 30 minutes ( Convert the minutes into hours by dividing by 60)

9514 1404 393

Answer:

  D

Step-by-step explanation:

The first equation of System 2 is the first equation of System 1.

The second equation has an x-coefficient of (A-L). The coefficients of x in System 1 are A and L, so (A-L) is their difference. The second equation of System 2 is the difference of the equations in System 1.

__

This is described by Choice D:

The second equation in System 2 is the difference of the equations in System 1. The first equation in System 2 is the first equation in System 1.

Answer:

1

Step-by-step explanation:

When you multiply two quantities under a root, it is just like normal multiplication. 2*18 is 36, which is the perfect square of six. Since this number can be expressed as p/q (where p and q are integers; the values here are 6 and 1), it is rational.

Answer: x=3

Step-by-step explanation:

from figure

=>tan45= x/3

=>x= 3tan45

=>x=3

Answer:

Step-by-step explanation:

here hypotenuse is x

since it is an isosceles triangle the other side of the triangle also must 3.

using pythagoras theorem

a^2 + b^2 = c^2

3^2 + 3^2 = x^2

9 + 9 = x^2

18 = x^2

[tex]\sqrt{18} = x[/tex]

Answer:

Sn=−6650

Step-by-step explanation:

Answers:

=================================================

Explanation:

Any conditional statement is of the form "If P, then Q"

P is the hypothesis, which is the initial set up to lead to the conclusion Q

As an example, the sentence "If it rains, then it gets wet on the road" has P = "it rains" as the hypothesis and Q = "it gets wet on the road" as the conclusion.

-------------

In short, the format is "If hypothesis, then conclusion".

Answer:

He should have subtracted 2 from each side to find the solution for x+2 =0

Step-by-step explanation:

(x + 2)(x - 7) = 0

Using the zero product property

x+2 = 0   x-7=0

x+2-2=0-2    x-7+7=0+7

x = -2            x=7

He should have subtracted 2 from each side to find the solution for x+2 =0

Step-by-step explanation:

the steps he took are correct but the answer of x is somehow wrong because

(x+2)=0

x = -2

and not x = 2

Answer:

OMGGGG wanna work on this together I need this question too

Answer:

Directions: Write the new coordinates for each point or figure.

Sample Question:

Point F has the coordinates (-9,6). What are the coordinates of its image point after the translation of six units down and three units to the left?

Answer:

The coordinates of its image point after the translation are (-12, 0).

Explanation: When you look at an ordered pair the x number comes first, followed by the y number (x,y). Moving a point left or right changes the x number. Moving a point up or down changes the y number. Left and down require subtraction, while right and up require addition. In the sample, we had to go 3 units to the left, -9 - 3 = -12. We also had to go 6 units down, so 6 - 6 = 0.

Point Q has the coordinates (9,5). What are the coordinates of its image point after a translation of six units up and three units to the right?

Point P has the coordinates (3,4). What are the coordinates of its image point after a translation of 8 units down and 5 units to the left?

Point Z has the coordinates (10,7). What are the coordinates of its image point after a translation of six units down and three units to the right?

Point Y has the coordinates (0,-4). What are the coordinates of its image point after a translation of 10 units up and 3 units to the left?

Point X has the coordinates (3,-8). What are the coordinates of its image points after a translation of 11 units down and 10 units to the right?

Answer:

(-10,5)

Step-by-step explanation:

Answer:

Step-by-step explanation:

either do 23 x23

or

23 x 16 ( do this first )

Answer:

Step-by-step explanation:

The number of sandwiches sold: 73

The cost to make one sandwich: S

The profit the band earns from one sandwich: 0.2S

The amount of money that the band recieves for selling one sandwich:

S + 0.2S

The scale is 5/4

Because:

Let's take

20/16 = 5/4

20/16 = 5/4

15/12 = 5/4

Answer:

5/2 or 5:2 ratio is the reduced fraction from the scale factor A to B.

Answer:

54√2

Step-by-step explanation:

3√3 * 6√6

number x number = 6 * 3 = 18

root * root = √18 = √3^2 *.2 = 3√2

18 * 3 = 54

54√2

Answer:

6: 15

Step-by-step explanation:

When finding the ratio of anything, you must count each side.

x + 2 1/2 = 10

x + 0.5 = 10

x = 9.5

Someone donated 2 toys and one-half of a toy. Someone donated a random out of toys and we had 10 toys in total.

x equal that mystery amount of toys that were dontated.

Answer:

0.8612 = 86.12% probability that the sample proportion will differ from the population proportion by less than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose a large consignment of televisions contained 11% defectives.

This means that [tex]p = 0.11[/tex]

Sample of size 237

This means that [tex]n = 237[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.11[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.11*0.89}{237}} = 0.0203[/tex]

What is the probability that the sample proportion will differ from the population proportion by less than 3%?

P-value of Z when X = 0.11 + 0.03 = 0.14 subtracted by the p-value of Z when X = 0.11 - 0.03 = 0.08. So

X = 0.14

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.14 - 0.11}{0.0203}[/tex]

[tex]Z = 1.48[/tex]

[tex]Z = 1.48[/tex] has a p-value of 0.9306

X = 0.08

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.08 - 0.11}{0.0203}[/tex]

[tex]Z = -1.48[/tex]

[tex]Z = -1.48[/tex] has a p-value of 0.0694

0.9306 - 0.0694 = 0.8612

0.8612 = 86.12% probability that the sample proportion will differ from the population proportion by less than 3%

Answer:

b/2 + 8 = 86

b = 156

Step-by-step explanation:

Half the comics is b/2

b/2 + 8 = 86

Subtract 8 from both sides

b/2 = 78

multiply both sides by 2

b = 156

Answer:

Step-by-step explanation:

[tex]sin({\alpha\over{2}})=\pm\sqrt{{1-cos(\alpha)\over{2}}}\Rightarrow sin({30\over{2}})=+\sqrt{{1-{\sqrt{3}\over{2}}\over{2}}}={\sqrt{{2-\sqrt{3}}}\over{2}}[/tex]

[tex]cos({\alpha\over{2}})=\pm\sqrt{{1+cos(\alpha)}\over{2}}=+\sqrt{{1+{\sqrt{3}\over{2}}\over{2}}}={\sqrt{{2+\sqrt{3}}}\over{2}}[/tex]

substituting we get:

[tex]tg(15)=\sqrt{{2-\sqrt{3}}\over{2+\sqrt{3}}}[/tex]

the answer is 2,0

Step-by-step explanation:

i got it right according to my teacher

The x-intercept of the continuous function shown in the table is, (2, 0)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Slope = -7+8/1

slope=1

You can see the values of x and f(x) from the given table.

An ordered pairs is in the form of (x, f(x)).

By x-intercept definition;

at x =2

⇒ f(x) = 0

Therefore,  the x-intercept of the continuous function shown in the table is, (2, 0)

To learn more on slope of line click:

https://brainly.com/question/16180119

#SPJ7

Answer:

The answer is "choice c".

Step-by-step explanation:

Below, we shall find the line equation, dissociation for both the management's behavior and achievement.

Here, attitudes are the response variable while performance seems to be the predictor as attitude is achievement dependant.

If Y indicates the attitude while X relates to workers' performance.

Let's describe the data like:

[tex]y=a+bx+e[/tex]

Now we get the estimates of e via the least quadratic method, – i.e., by reducing the number of segments.

[tex]S=\sum e_{i}^{2}=\sum {(y_{i}-a-bx_{i})^{2}}[/tex]

minimize S to obtain the estimates of a and b as:

[tex]\hat{b}=\frac{\sum{(y_{i}-\bar{y})(x_{i}-\bar{x})}}{\sum{(x_{i}-\bar{x})^{2}}}\\\\\hat{a}=\bar{y}-\hat{b}\bar{x}[/tex]

So,

[tex]a=11.7b=1.02[/tex]

Equation:

[tex]Y=11.7+1.02x[/tex]