Can someone help me with this please? Question and possible answers down below

Answer:

a. 30 meters per second

b. -10 meters per second

Step-by-step explanation:

a. Average rate of change for the height from 0 to 6.6 secs can be calculated using the formula, [tex] m = \frac{H(b) - H(a)}{b - a} [/tex]

Thus,

Where,

[tex] a = 0, H(0) = 0 [/tex]

[tex] b = 6.6, H(6.6) = 198 [/tex]

Plug in the values into the formula:

[tex] m = \frac{198 - 0}{6.6 - 0} [/tex]

[tex] m = \frac{198}{6.6} [/tex]

[tex] m = 30 [/tex]

b. Average rate of change for the height from 8.8 to 13.2 secs = tex] m = \frac{H(b) - H(a)}{b - a} [/tex]

Where,

[tex] a = 8.8, H(8.8) = 44 [/tex]

[tex] b = 13.2, H(13.2) = 0 [/tex]

Plug in the values:

[tex] m = \frac{0 - 44}{13.2 - 8.8} [/tex]

[tex] m = \frac{-44}{4.4} [/tex]

[tex] m = -10 [/tex]

Answer:

Sum of two rational numbers-

-10 = -5+-5

0= -5+5

15= 10+5

Step-by-step explanation:

Answer:

[tex]h=30[/tex]

Step-by-step explanation:

Volume of a cone=1540[tex]cm^{3}[/tex], Radius=7cm.

The height of a cone=h

When we need to find the height of a cone, we can use the formula of the volume of a cone, which is [tex]\frac{1}{3} \pi r^{2} h[/tex] to find the height of a cone.

[tex]1540cm^{3} =\frac{1}{3}\pi r^{2} h[/tex]

Put the pi value=22/7 and the value of radius which is 7 cm into the formula.

[tex]1540cm^{3}=\frac{1}{3}*\frac{22}{7} 7^{2}h[/tex]

[tex]1540cm^{3} =\frac{154}{3}h[/tex]

Move [tex]\frac{154}{3}[/tex] to another side. 1540 divided by  [tex]\frac{154}{3}[/tex] to calculate what is the value of h, h is the height of a cone. Like this.

[tex]\frac{1540cm^{3} }{\frac{154}{3} } =h[/tex]

[tex]30=h[/tex]

Rearrange the h.

[tex]h=30[/tex]

I hope you will understand my solution and explanation. If you still cannot get the point, you can ask me anytime! Thank you!

Answer:

The height of the cone is h = 30 cm.

Step-by-step explanation:

The formula for a cone is:

[tex] \\ V = \frac{1}{3}*\pi*r^2*h[/tex]

We have (without using units) and using pi = 22/7:

[tex] \\ 1540 = \frac{1}{3}*\frac{22}{7}*(7)^2*h[/tex]

Which is equals to:

[tex] \\ 1540 = \frac{1}{3}*\frac{22}{7}*(7)*h[/tex]

[tex] \\ 1540 = \frac{1}{3}*22*7*h[/tex]

Well, we have to solve the equation for h:

[tex] \\ \frac{1540*3}{22*7} = h[/tex]

[tex] \\ 30 = h[/tex]

Therefore, the height of the cone is 30 cm.

Answer:

Hey there!

You would use the HL theorem, because these are both right triangles, and have two lengths congruent to each other.

Hope this helps :)

Answer:

[tex]\sqrt[5]{x^7}[/tex]

or (x ^ 1/5) ^7

or ([tex]\sqrt[5]{x}[/tex])^7

Step-by-step explanation:

x ^ 1.4

Rewriting the decimal as an improper fraction

x ^ 14/10

x ^ 7/5

The top is the power and the bottom is the root

[tex]\sqrt[5]{x^7}[/tex]

or (x ^ 1/5) ^7

or ([tex]\sqrt[5]{x}[/tex])^7

Answer:

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).

Step-by-step explanation:

Hope you understand

Answer:

1.63

HOPE THIS WILL HELP..............!

Answer:

The equation is true

Step-by-step explanation:

The best way to check if this equate is true is to convert the pi in radians to degree and actually evaluate the trigonometric terms.

Mathematically we know that pi = 180 degrees

So pi/8 = 22.5

and pi/4 = 180/4 = 45

So let’s make our check.

Insert pi = 22.5 and pi = 45

So we have;

tan 22/5 = √(1-cos45)/(1+cos45)

Now let’s evaluate this using a calculator.

tan 22/5 = 0.414213562373

The term in the root; 0.171572875254

The square root of this number is

0.41421356237

This is exactly as what is obtained with the tan 22.5

So we conclude that what we have is true

Answer:

48 degrees

Step-by-step explanation:

A straight line measures up to 180 degrees so take what we know which is 138 and subtract that from 180 to get your answer 48

Answer:

48

Step-by-step explanation:

Sum of angles On a straight line = 180

Given angle = 132

O, x is the remaining angle that must join 132 to form 180, which is

180-132 = 48 degrees.

Hope this helps

Good luck

Answer:

Ram therefore has more amount in his account at the end of the month, and the balances in their bank accounts at the end of the month are arranged in ascending order, i.e. from the smallest to the largest, as follows:

Rahul – Debits AED 200; Rohit – Credits AED 200; and Ram – Credits AED 500.

Step-by-step explanation:

In banking and finance, a credit transaction on a bank account indicates that an additional amount of money has been added to the bank account and the balance has increased. This gives a positive balance in the account

On the other hand, a debit transaction on a bank account indicates that an amount of money has been deducted or withdrawn from the bank account and the balance has therefore reduced. This gives a negative balance in the account.

Based on the above, we have:

a. Ram – Credits AED 500 on 12th May 2020

Since there is no any other credit or debit transaction during the month, this implies that Ram still has Credits AED 500 in his account at the end of the month.

The Credits AED 500 indicates that Ram has a positive balance of AED 500 in his account at the end of the month.

b. Rahul – Debits AED 700 on 12th May 2020 and Credits AED 500 on 15th May 2020.

The balance in the account of Rahul gives Debits of AED 200 as follows:

Debits AED 700 - Credits AED 500 = Debits AED 200

The Debits AED 200 indicates that Rahul has a negative balance of AED 200 in his account at the end of the month.

c. Rohit – Credits AED 700 on 12th May 2002 and Debits AED 500 on 15th May 2020.

The balance in the account of Rohit gives Credits of AED 200 as follows:

Credits AED 700 - Dedits AED 500 = Credits AED 200

The Credits AED 200 indicates that Rohit has a positive balance of AED 200 in his account at the end of the month.

Conclusion

Arrangement of numbers or amounts of money in ascending order implies that they are arranged from the smallest to the largest number or amount.

Since Credits implies positive amount and Debits implies negative amount, Ram therefore has more amount in his account at the end of the month, and the balances in their bank accounts at the end of the month are arranged in ascending order, i.e. from the smallest to the largest, as follows:

Rahul – Debits AED 200; Rohit – Credits AED 200; and Ram – Credits AED 500.

Answer:

a

Step-by-step explanation:

Since the graph intersects the x-axis at 2 points, it has 2 solutions which means that the discriminant is greater than 0. The only option that satisfies this is 10.

Answer:

10  option a)

Step-by-step explanation:

The discriminant has to be a number greater than zero, since we clearly see two solutions (crossings of the x axis) of the curve. So, the only option larger than zero among the possible answers is 10 (option a)

Answer:

SOLUTION SET ={a/a≥20}

Step-by-step explanation:

[tex]\frac{2a}{5}-2\geq\frac{a}{4}+1[/tex]

[tex]adding 2 on both sides[/tex]

[tex]\frac{2a}{5}-2+2\geq \frac{a}{4}+1+2[/tex]

[tex]now subtracting \frac{a}{4} on both sides[/tex]

[tex]\frac{2a}{5}-\frac{a}{4}\geq 3[/tex]

[tex]takig LCM as 20\\\frac{8a}{20}-\frac{5a}{20}\geq 3[/tex]

[tex]\frac{3a}{20}\geq 3[/tex]

[tex]by cross-multiplication[/tex]

3a≥3×20

3a≥60

dividing 3 on both sides

3a/3≥60/3

a≥20

SOLUTION SET ={a/a≥20} is the answer

i hope this will help you :)

Answer:

C. The interquartile range is 55

Step-by-step explanation:

When you want to find the interquartile range you look at the box plot to see that it is everything from the upper interquartile range to the lower interquartile range is the interquartile range. So from 40 to 65. So there for the answer C. is incorrect.  

Answer:

A.

Step-by-step explanation:

Answer:

(a) The point estimate for the population mean travel tax is $ 83.36.

(b) The lower bound is $73.70 and the upper bound is $93.02 One can be [95]% confident that the mean travel tax for all cities is between these values.

(c) The researcher could decrease the level of confidence.

Step-by-step explanation:

We are given that a normal probability plot suggests the data could come from a population that is normally distributed.

X: 68.87, 78.25, 70.44, 84.67, 79.79, 86.33, 100.24, 98.26.

(a) A point estimate for the population mean travel tax is the sample mean of the data. i.e;

      Point estimate, [tex]\bar X[/tex] =  [tex]\frac{\sum X}{n}[/tex]

                                     =  [tex]\frac{68.87+ 78.25+ 70.44+ 84.67+ 79.79+ 86.33+ 100.24+ 98.26}{8}[/tex]

                                     =  [tex]\frac{666.85}{8}[/tex]  = $83.36

So, the point estimate for the population mean travel tax is $ 83.36.

(b) Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean travel tax = $83.36

             s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex]  = $11.55

             n = sample size = 8

             [tex]\mu[/tex] = population mean travel tax

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.365 < N(0,1) < 2.365) = 0.95  {As the critical value of t at 7 degrees of

                                                 freedom are -2.365 & 2.365 with P = 2.5%}  

P(-2.365 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.365) = 0.95

P( [tex]-2.365 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.365 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.365 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.365 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.365 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.365 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                        = [ [tex]\$83.36-2.365 \times {\frac{\$11.55}{\sqrt{8} } }[/tex] , [tex]\$83.36+2.365 \times {\frac{\$11.55}{\sqrt{8} } }[/tex] ]

                        = [$73.70, $93.02]

Therefore, a 95% confidence interval for the population average debt load of graduating students with a bachelor's degree is [$73.70, $93.02].

The lower bound is $73.70 and the upper bound is $93.02 One can be [95]% confident that the mean travel tax for all cities is between these values.

(c) The researcher could decrease the level of confidence who wants to increase the precision of the interval but does not have access to additional data.

Answer:

The volume is

Step-by-step explanation:

Volume of a sphere is given by

[tex]V = \frac{4}{3} \pi {r}^{ 3} [/tex]

where r is the radius

π = 3.14

From the question we were given the diameter and

radius = diameter/ 2

diameter = 2 feet

radius = 2/2 = 1 feet

So the volume of the sphere is

[tex]V = \frac{4}{3} (3.14)(1) ^{3} [/tex]

[tex] = \frac{4}{3} \times 3.14[/tex]

V = 4.186

We have the final answer as

V = 4 ft³ to the nearest hundredth

Hope this helps you

Answer:

0.60

Step-by-step explanation:

find the probability it is a 2:

0.40 / 1 = 0.4 or 40%

find the probability it isn't a 2:

1 - 0.4 = 0.6

Answer:

A. 0.60

Step-by-step explanation:

I did geometry last year. My teacher assigned it to us.

Hope this helps :)

Answer:

I believe the median is 6.5

Step-by-step explanation:

Answer:

52 students

Step-by-step explanation:

From the question above, we have the following information:

a) Vidya ranks 7th from the top.

Mathematically,

Vidya = 7th student

b) Divya 3 ranks behind Vidya.

Divya = Vidya + 3

Hence, Mathematically:

Divya = 7 + 3 = 10

Divya = 10th student

c) Also, Divya is 7 ranks ahead of Medha.

Mathematically,

Medha = 10 + 7= 17

Medha= 17th student

d)Sushma is 32 ranks behind Medha

Mathematically,

Sushma = Medha + 32

= 17 + 32 = 49

Sushma is the 49th student

Therefore, since, Sushma is 4th from the bottom, total number of students is:

49 + 3 = 52 students

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

           Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

                    [tex]\boxed{x = 7}[/tex]

Move 1 to the left side of the equation by subtracting it from both sides.

[tex]\sqrt{2x -5 - 2 - 1 = 0 }[/tex]

Subtract 1 from -2.

[tex]\sqrt{2x -5 - 3 = 0 }[/tex]

Add 3 to both sides of the equation.

[tex]\sqrt{2x - 5 = 3}[/tex]

To remove the radical on the left side of the equation, square both sides of the equation.

[tex]\sqrt{2x - 5^3 = 3^2}[/tex]

Simplify each side of the equation.

Multiply the exponents in [tex](( 2x - 5) ^\frac{1}{2})^2[/tex] .

Apply the power rule and multiply exponents, [tex](a^m)^n = a^mn[/tex]

[tex](2x -5)^\frac{1}{2}.2 = 3^2[/tex]

Cancel the common factor of 2.

[tex](2x - 5)^1 = 3^2[/tex]

Simplify.

[tex]2x - 5 = 3^2[/tex]

Raise 3 to the power of 2.

[tex]2x - 5 = 9[/tex]

Solve for x

Move all terms not containing x to the right side of the equation.

Add 5  to both sides of the equation.

[tex]2x = 9 + 5[/tex]

Add 9 and 5.

[tex]2x = 14[/tex]

Divide each term by 2  and simplify.

Divide each term in 2x = 14 by 2.

[tex]\frac{2x}{2} = \frac{14}{2}[/tex]

Cancel the common factor of 2.

[tex]x = \frac{14}{2}[/tex]

Divide 14 by 2.

[tex]x = 7[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

root of f(x) =  -0.7419124700395855 to about 16 figures

Step-by-step explanation:

given

f(x) = 2x^5-x^2+1 = 0

The polynomial is prime, so cannot solve by factoring.

Since it is a 5th degree polynomial, it has at least one real root.

Graphing helps locate where roots are, if more than one.

(refer to first graph)

So there is a real root between -1 and 0.

We will use numerical methods to find the root to a good degree of accuracy.  The technique applies to any univariable function which is differentiable and continuous near the roots.  This requirement is true for all polynomials.

However, we must know approximately where the root is, usually found by graphing.

The formula used is a recursive one, which gives a better approximation (x1) from the initial (x0) one , and can be repeated until the required accuracy is reached.

Here, we see that the slope of the function at the root is quite steep, so convergence will be rapid.

The formula is

x1 = x0 - f(x0) / f'(x0), where

x1 = new approximation

x0 = initial (or previous) approximation

f(x0) = value of function when x=x0

f'(x0) = value of derivative of function when x=x0

For the given function

f(x) = 2x^5-x^2+1 = 0

f'(x) = 10x^4-2x = 2x(5x^3-1)

From the graph of f(x), we can take an initial approximation as

x0 = -1

x1 = -1 - (-2)/12 = -5/6

Repeat using x0=-5/6

x1 = -5/6 - ( 2(-5/6)^5 - (-5/6)^2 + 1 ) / (2(-5/6(5(-5/6)^3-1))

= 0.7565596512088784

Repeat again, multiple times

x1 = -0.7423377914518363

x1 = -0.7419128371988212

x1 = -0.7419124700398593

x1 = -0.7419124700395855

x1 = -0.7419124700395855

So we see that the root of f(x) = x1 = -0.7419124700395855 to about 16 figures

Note that the accuracy of the iterations approximately doubles every time.

The average cost of weekly groceries is $124.50."  The statistical measurement are they most likely claiming is Mean

The correct option is (B)

The arithmetic mean of a given data is the sum of all observations divided by the number of observations.

For example, a cricketer's scores in five ODI matches are as follows: 12, 34, 45, 50, 24. To find his average score in a match, we calculate the arithmetic mean of data using the mean formula:

Mean = Sum of all observations/Number of observations

The value of the middlemost observation, obtained after arranging the data in ascending or descending order, is called the median of the data.

For example, consider the data: 4, 4, 6, 3, 2. Let's arrange this data in ascending order: 2, 3, 4, 4, 6. There are 5 observations. Thus, median = middle value i.e. 4.

The value which appears most often in the given data i.e. the observation with the highest frequency is called a mode of data.

As per the situation we have given average cost of groceries.

The mean is also the average sum of data divided by total number of data.

Hence, The statistical measurement is Mean.

Learn more about mean here:

https://brainly.com/question/15323584

#SPJ2

━━━━━━━☆☆━━━━━━━

▹ Answer

You can use a graphing calculator. Attached is a picture of it graphed.

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

The five number summary are;

The minimum is 198

The 1st quartile, Q₁, is 205

The 2nd quartile, Q₂, or  median is 214

The 3rd quartile, Q₃, is 228

The Maximum is 237

Step-by-step explanation:

The numbers are;

232, 198, 214, 205, 222, 228, 208, 237, 217, 199, 213, 208, 228, 224, 203

Which can be rearranged in increasing order as follows;

198, 199, 203, 205, 208, 208, 213, 214, 217, 222, 224, 228, 228, 232, 237

The five number summary are;

The minimum = The lowest number in the list = 198

The 1st quartile, Q₁,  is the (n + 1)/4 th term which is (15 + 1)/4 = 4th term = 205

The 2nd quartile, Q₂, or  median is the (n + 1)/2 th term which is (15 + 1)/2 = 8th term = 214

The 3rd quartile, Q₃, is the 3×(n + 1)/4 th term which is 3×(15 + 1)/4 = 12th term = 228

The Maximum = The highest number in the list = 237.

Answer:

6 i

Step-by-step explanation:

The imaginary number "6 i" when squared gives :[tex](6\,i)^2=36\,(i)^2=36 (-1) = -36[/tex]

Answer:

Step-by-step explanation:

[tex]\\ \sqrt{-36 }=\sqrt{36 \times -1} =\sqrt{36 \times \iota^2}=\pm 6 \iota\\so~ 0+6 \iota\\and~0-6 \iota[/tex]

Answer:

Step-by-step explanation:

[tex]tan^{-1} (\frac{\sqrt{3} }{3} )=x\\tan x=\frac{\sqrt{3} }{3} =tan (\frac{\pi}{6} )\\x=\frac{\pi}{6}[/tex]

Answer:900

Step-by-step explanation:

Answer:

960 cm.

Step-by-step explanation:

For the first day:

Subtract the primary level of water by the 20% of it. 20% of 1500 is:

[tex]0.2*1500=300[/tex] (Convert the percent to decimal)

Then subtract 1500 to 300. That would become 1200cm for the first day.

For the second day:

Subtract the level of water from the first day by 20% of it. 20% of 1200 is:

[tex]0.2*1200= 240[/tex]

Then subtract 1200 to 240. That would become 960 for the second day.

The level of the water after 2 days is 960 cm.

Answer:

[tex]\boxed{\±\sqrt{x+4}}[/tex]

Step-by-step explanation:

The inverse of a function is the reverse of the function.

[tex]f(x)=x^2 -4[/tex]

[tex]y=x^2-4[/tex]

Switch variables.

[tex]x=y^2-4[/tex]

Make y as subject.

Add 4 to both sides.

[tex]x+4=y^2[/tex]

Take the square root on both sides.

[tex]\±\sqrt{x+4} =y[/tex]

Answer:

[tex]f^{-1}[/tex] = ± [tex]\sqrt{x+4}[/tex]

Step-by-step explanation:

[tex]f(x) = x^2-4[/tex]

Replace f(x) by y

[tex]y = x^2-4[/tex]

Exchange x and y

[tex]x = y^2-4[/tex]

Solve for y

[tex]x = y^2-4\\[/tex]

Adding 4 to both sides

[tex]y ^2 = x+4[/tex]

Taking sqrt on both sides

y = ±[tex]\sqrt{x+4}[/tex]

Replacing y by [tex]f^{-1}[/tex]

[tex]f^{-1}[/tex] = ± [tex]\sqrt{x+4}[/tex]

Answer:

For two polygons to be similar, both of the following must be true: Corresponding angles are congruent. Corresponding sides are proportional.

Step-by-step explanation:

HOPE THIS HELPS AND PLSSS MARK AS BRAINLIEST]

THNXX :)

What must be true for two polygons to be similar?

Similar polygons: For two polygons to be similar, both of the following must be true: Corresponding angles are congruent. Corresponding sides are proportional.

Answer:

Step-by-step explanation:

18/60-12/60= 4 miles

just my guess

Answer:

A

Step-by-step explanation:

The blue graph, g(x), is shifted down 8 units.

So the answer is f(x)-8 which is A

Answer:  C. g(x) = eˣ⁻¹ - 3

Step-by-step explanation:

g(x) is a vertical shift 8 units down (-8) from f(x)

f(x) = eˣ⁻¹ + 5

g(x) = (eˣ⁻¹ + 5) - 8

      = eˣ⁻¹ - 3

Answer:

sqroot 16/49 A

Step-by-step explanation:

The expression  [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] is equivalent to expression [tex]\sqrt{\frac{16}{49}}[/tex] because by property  [tex]\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b} }[/tex].

The expression [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] can be simplified by taking the square root of 16 and the square root of 49 separately.

√16 equals 4 because the square root of 16 is the number that, when multiplied by itself, gives 16.

Similarly, √49 equals 7 because the square root of 49 is the number that, when multiplied by itself, gives 49.

So, the expression [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] simplifies to 4/7.

and we know that [tex]\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b} }[/tex]

[tex]\sqrt{\frac{16}{49}}[/tex] is equivalent to  [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] , which simplifies to 4/7.

Therefore, [tex]\sqrt{\frac{16}{49}}[/tex] is equivalent to  [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] .

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPj4