A company produced in the first quarter 6,905 pieces in the second quarter the same company produced 795 pieces more than in the first quarter under these conditions how many pieces did the company produce in the first semester?

Answer:

Step-by-step explanation:

We are given that the temperature readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Let X be the temperature reading of a single thermometer selected at random. Then, X ~ N(0, 1).

We need to find the probability of obtaining a reading less than -2.74°C, which can be expressed mathematically as P(X < -2.74).

Using standard normal distribution tables or a calculator, we can find that the z-score corresponding to -2.74°C is:

z = (x - μ) / σ = (-2.74 - 0) / 1 = -2.74

The probability can be calculated as:

P(X < -2.74) = P(Z < -2.74) ≈ 0.0030 (rounded to 4 decimal places)

Therefore, the probability of obtaining a reading less than -2.74°C is approximately 0.0030.

Answer:

We need to find the probability of obtaining a reading less than -2.74°C from a normal distribution with a mean of 0°C and a standard deviation of 1.00°C.

Using the standard normal distribution, we have:

z = (x - μ) / σ

where:

x = -2.74°C (the reading we want)

μ = 0°C (the mean)

σ = 1.00°C (the standard deviation)

Substituting the values, we get:

z = (-2.74 - 0) / 1.00 = -2.74

Using a standard normal distribution table or calculator, we find that the probability of obtaining a z-score less than -2.74 is approximately 0.0030.

Therefore, the probability of obtaining a reading less than -2.74°C from the batch of thermometers is approximately 0.0030.

Answer:

0.718 = 71.8% probability that X is less than 38 minutes

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x)=\mu e^{-\mu x}[/tex]

In which [tex]\mu=\frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X\leq x)=\int\limits^a_0f ({x)} \, dx[/tex]

Which has the following solution:

[tex]P(X\leq x)=1-e^{-\mu x}[/tex]

If X has an average value of 30 minutes

This means that [tex]m=30,\mu=\frac{1}{30}[/tex]

What is the probability that X is less than 38 minutes?

[tex]P(X\leq 38)=1-e^{-\frac{38}{30} }[/tex]

0.718 = 71.8% probability that X is less than 38 minutes

Consequently, the person's weight is roughly 26.5 pounds of fat (rounded to the nearest tenth).

By determining the value of a single unit or quantity and then scaling that value up or down to determine the value of another quantity, the unitary method is a mathematical strategy used to solve problems. According to the unitary method's guiding concept, if one quantity or unit has a certain value, then a predetermined number of those same quantities or units will have a proportionate value. For instance, 5 apples would cost $5 if 1 fruit cost $1.

given

We can use the person's weight and body fat proportion to determine how many pounds of body fat they have. We can commence by calculating the decimal weight of the body fat:

weight of body fat Equals body fat percentage * weight

= 0.163% * 163 lbs.

= 26.509 lbs.

Consequently, the person's weight is roughly 26.5 pounds of fat (rounded to the nearest tenth).

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ1

Answer:

Step-by-step explanation:

Answer:

To find the annual rainfall in 2018, we need to add 12% of the rainfall in 2017 to the rainfall in 2017.

12% of 420mm can be calculated as:

12/100 * 420 = 50.4mm

Therefore, the annual rainfall in 2018 can be calculated as:

420 + 50.4 = 470.4mm

So the annual rainfall in 2018 in Opuwo was 470.4mm.

Step-by-step explanation:

the annual rainfall in Opuwo in 2018 was 470.4mm.

Why it is and what is Rainfall in mathematics?

To find the annual rainfall in 2018, we need to add 12% of the rainfall in 2017 to the rainfall in 2017.

12% of 420mm can be found by multiplying 420 by 0.12:

12% of 420 = 0.12 × 420 = 50.4

Therefore, the annual rainfall in 2018 is:

Annual rainfall in 2018 = Annual rainfall in 2017 + 12% of Annual rainfall in 2017

Annual rainfall in 2018 = 420 + 50.4

Annual rainfall in 2018 = 470.4mm

So the annual rainfall in Opuwo in 2018 was 470.4mm.

In mathematics, rainfall usually refers to the amount of precipitation (rain, snow, sleet, hail, etc.) that falls within a specific area over a given period of time, typically measured in millimeters or inches. Rainfall can be measured using various methods, such as rain gauges or radar, and is an important factor in hydrology, meteorology, and agriculture.

Rainfall data can be analyzed and modeled using mathematical techniques, such as statistical analysis and differential equations.

To know more about Rainfall questions visit:

https://brainly.com/question/28576955

#SPJ1

The sampling distribution of the sample mean is approximately normal for large sample sizes, regardless of the distribution of the population is the best definition of the Central Limit Theorem. So the option e is correct.

The Central Limit Theorem, which states that the distribution of sample means approaches a normal distribution as the sample size increases. This means that the sample mean will be normally distributed, even if the population from which the sample is drawn is not normally distributed. This is useful because it can be used to make inferences and predictions about the population based on the sample data. So the option e is correct.

To learn more about Central Limit Theorem link is here

brainly.com/question/898534

#SPJ4

The complete question is:

Which one of the following statements is the best definition of the Central Limit Theorem?

(a) In large populations, the distribution of the population mean is approximately normal.

(b) For non-normally distributed populations, the sampling distribution of the sample mean will be approximately normal, regardless of the sample size.

(c) If the distribution of the population is non-normal, it can be normalized by taking a large sample size.

(d) For large sample sizes, the sampling distribution of the population mean is approximately normal, regardless of the distribution of the population.

(e) The sampling distribution of the sample mean is approximately normal for large sample sizes, regardless of the distribution of the population.

Answer:

1.45 L

Step-by-step explanation:

Answer:

(1,2)

Step-by-step explanation:

We are given the following system of equations:

y = -x + 3

y = 4x - 2

And we want to solve it, with the answer in an ordered pair.

Because both systems are equal to y, we can set both of the equations equal to each other, and solve for x in that way.

This is possible due to transitivity, which states that if a=b, and b=c, then a=c.

Hence,

-x + 3 = 4x - 2 (same as y=y)

We can add x to both sides.

3 = 5x - 2

Add 2 to both sides.

5 = 5x

Divide both sides by 5.

1 = x

Now, we can use this value to find y.

Substitute 1 as x in either y = -x + 3 or y = 4x - 2

Taking y = -x + 3 for instance:

y = -1 + 3 = 2

So, we now that x=1, y=2.

As an ordered pair, that is (1,2).

Answer:

792

Step-by-step explanation:

so first we need find out how many fraction of cookie is left

    [tex]\frac{3}{4} -\frac{2}{3} =\frac{1}{12}[/tex]      this had been equal to 66

which we use this to time 66

12•66=792 in total

if you want to know chocolate that will be 458

and almond will be 334

brainest please thanks

Answer: False, False, True, True, True.

Step-by-step explanation:

Remember, if there are two intersecting lines on a graph, and they come to one point on a graph, it only has one solution. If two lines are parallel, and don't intersect with each other, they have no solution. If there are two equations, and both are on the same line, then they have infinitely many solutions.

y - 3x = -2, and y = 3x - 2, are equal, since they are one line.

So, the first and second questions are false, since there's only 1 solution, making the third question true. The point (-1, -5), is a true answer, since the x would be -1, and the y would be -5. (Example below.)

y = 3x - 2

y = 3(-1) - 2

y = -3 - 2

y = -5

The two lines in the equations do have the same slope, since the slope for each is 3x. Or think about slope-intercept form, (y = mx + b)

y - 3x = -2, and y = 3x - 2

y - 3x = -2

y = 3x - 2 is equal to y = 3x - 2, which makes this answer true.

Hope this helps, (and can you give brainliest, please?)

a. Histogram shows tip amounts ranging between $6 and $25, skewed to the right with a longer tail of higher tips.

b. Increasing the $8 tip to $18 would increase the mean since total tip amount increases by $10 spread out over 60 customers. Median won't be affected since changing one value does not alter the middle value.

a. The histogram shows that Elizabeth received a range of tip amounts, with the majority of tips falling between $6 and $25. The distribution is skewed to the right, with a longer tail of higher tip amounts.

b. i. The mean would increase because the total tip amount would increase by $10, and this increase would be spread out over the 60 customers.

ii. The median would not be affected because it is the middle value when the data is ordered, and changing one value does not change the middle value.

Learn more about histogram here: brainly.com/question/30354484

#SPJ4

The length of the top of the bookcase should be approximately 25 inches to display the soap carving collection with an area of 300 in².

To find the length of the top of the bookcase (which we'll call "b"), we need to know the area of the collection of soap carvings and the formula for the area of a rectangle:

Area = length x width

We're given the area of the soap carving collection (300 square inches), and we know that the soap carvings will be displayed on top of the bookcase, which is a rectangle.

Let's assume that the width of the bookcase is 1 unit (we can choose any unit we want, as long as we're consistent). Then we can write:

300 = b x 1

Simplifying this equation, we get:

b = 300/1

b = 300

So the length of the top of the bookcase should be 300 inches. However, this assumes that the width of the bookcase is only 1 inch, which is quite narrow.

If we assume a more reasonable width of, say, 12 inches, then we can write:

300 = b x 12

Simplifying this equation, we get:

b = 300/12

b = 25

So the length of the top of the bookcase should be 25 inches (if the width of the bookcase is 12 inches).

Learn more about length here: https://brainly.com/question/28108430

#SPJ1

Answer:

5/12, 5/9, 2/3, 5/6, 6/5

Step-by-step explanation:

5/12= 0.41666667, 5/9= 0.55555556, 2/3= 0.66666667, 5/6= 0.83333333, 6/5= 1.2

Answer:

1097.28 centimeters

Step-by-step explanation:

You have to multiply length given by 91.44

Answer:

1097.28 cm

Step-by-step explanation:

1 yd = 36 in

=> 12 yrd = 12 x 36 = 432 in

1 in = 2.54 cm

=> 432 in = 432 x 2.54 = 1097.28 cm

[tex]\text{order does not matter}[/tex]

[tex]\text{sample space}= \text{15 letters}[/tex]

[tex]\text{no repetition}[/tex]

[tex]\text{P(A)}= \text{15C5}= \text{3003 ways}[/tex]

This is a non-linear function's graph. The function value y = 4 is the graph's y-intercept. With x = 1, the value of y with the highest value is y = 5. The function's value for x between x = 2 and x = 6 is 0.

The graph of a nonlinear function is not a line or a piece of a line. For instance: A balloon gains volume as you inflate it. The table below shows how a round balloon's volume grows as its radius changes.

This is a non-linear function's graph.

The y-intercept of the graph is the function value y = 4.

The x-intercepts of the graph (in order from least to greatest) are located at x = -3 and x = 5.

The greatest value of y is y = 5 and it occurs when x = 1. For x between x = 2 and x = 6, the function value y is 0.

To know more about Linear function visit:-

https://brainly.com/question/20286983

#SPJ1

For x between x = 2 and x = 6, the function value y is positive.

What is a polynomial?

A polynomial is a mathematical expression consisting of variables (also known as indeterminates) and coefficients, which are combined using only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

For example, the expression 3x^2 - 2x + 1 is a polynomial, where x is variable, and 3, -2, and 1 are the coefficients. The degree of the polynomial is the highest power of the variable in the expression, which in this case is 2.

Polynomials are used in various fields of mathematics and science, including algebra, calculus, physics, and engineering. They are used to model and analyze real-world phenomena, solve mathematical problems, and make predictions.

This is the graph of a polynomial function.

The y-intercept of the graph is the function value y = -3.

The x-intercepts of the graph (in order from least to greatest) are located at x = -2, x = 0, and x = 4.

The greatest value of y is y = 6, and it occurs when x = 3.

Therefore, For x between x = 2 and x = 6, the function value y is positive.

To learn more about polynomials from the given link:

https://brainly.com/question/11536910
#SPJ1

10 is the value of k of  the slope of the line .

What are slopes called?

Slope, usually referred to as rise over run, is a line's perceived steepness. By dividing the difference between the y-values at two places by the difference between the x-values, we can determine slope.

                                   You may determine a line's slope by looking at how steep it is or how much y grows as x grows. slope categories. When lines are inclined from left to right, they are said to have a positive slope, a negative slope, or a zero slope (when lines are horizontal).

the points  (2,4) and (5,k)

formula from slope of two points

        slope = y₂ - y₁/x₂ - x₁

substitute the values in formula

 slope = 2

 slope =  k - 4/5- 2

   2 =k - 4/3

   6 = k - 4

    k = 6 + 4  

      k = 10

Learn more about Slope

brainly.com/question/3605446

#SPJ1

The probability that the average of 49 marathons is between 143 and 147 minutes is 0.5980. The 60th percentile is 148.25 minutes, and the median is 146 minutes.

The average of a sample of 49 marathons will be approximately normally distributed with mean = 146 minutes and standard deviation = 15/sqrt(49) = 15/7.

To find the probability that the average of the sample will be between 143 and 147 minutes, we can standardize the values:

z1 = (143 - 146) / (15/7) = -1.4

z2 = (147 - 146) / (15/7) = 0.4667

Then, using a standard normal distribution table or calculator, we find:

P(-1.4 < Z < 0.4667) = P(Z < 0.4667) - P(Z < -1.4)

= 0.6788 - 0.0808

= 0.5980

So the probability that the average of the sample will be between 143 and 147 minutes is 0.5980.

To find the 60th percentile for the average of these 49 marathons, we need to find the z-score such that the area to the left of the z-score is 0.6. Using a standard normal distribution table or calculator, we find:

P(Z < z) = 0.6

z = 0.25

Then, we can solve for the corresponding value of X:

0.25 = (X - 146) / (15/7)

X = 148.25

So the 60th percentile for the average of these 49 marathons is 148.25 minutes.

To find the median of the average running times, we note that the median of a normal distribution is equal to its mean. Therefore, the median of the average running times is 146 minutes.

To know more about Probability:

https://brainly.com/question/11234923

#SPJ4

Answer:

x = 42.9

Step-by-step explanation:

We can let 34 represent the reference angle.  Using this angle, we see that the side measuring 24 units is the opposite side and the side measuring x is the hypotenuse.

Thus, we can use the sine trig function which is

[tex]sin(angle)=\frac{opposite}{hypotenuse}[/tex]

We plug in what we have into the equation above and solve for x:

[tex]sin(34)=\frac{24}{x}\\ x*sin(34)=24\\x=\frac{24}{sin(34)}\\ x=42.9189996\\x=42.9[/tex]

Answer:

pretty-pretty sure its 1/10

Step-by-step explanation:

Convert to a mixed number by placing the numbers to the right of the decimal over

10

. Reduce the fraction.

1

10

No element in this sequence can be divided by 5, 13, or 65.

This sequence's elements are not all divisible by 5, 13, or 65.

For positive integers n, we define the sequence a1 = 2n - 3.

We must determine if 2n - 3 is divisible by 5 for various values of n in order to determine whether members of this sequence are divisible by 5.

2ⁿ mod 5 equals 2ⁿ mod 1 = 2ⁿ mod 2 = 4ⁿ mod 3 = 3ⁿ mod 4 = 1, etc.

None of the items in this sequence can be divided by 5, as we can see from the fact that 2ⁿ mod 5 is not necessarily 0.

When divided by 13, 2ⁿ mod 13 equals 2ⁿ mod 1 mod 13 = 2, 2n mod 2 mod 4 mod 8 mod 3 mod 13 = 3, etc.

Since 2ⁿ mod 13 is not necessarily 0, none of the sequence's elements are divisible by 13 as a result.

When 65 is divided by 5*13, 2n mod 65 equals 2n mod 65 times 2, 2ⁿ

mod 65 times 4, 2ⁿ mod 65 times 8, 2ⁿ mod 65 times 3, etc.

None of the items in this sequence are divisible by 65 since 2ⁿ mod 65 is not necessarily 0.

Hence, No element in this sequence can be divided by 5, 13, or 65.

To learn more about positive integers link is here:

brainly.com/question/18380011

#SPJ4

The complete question is:

Consider the sequence a₁ = = 2¹-3=-1₁ -2²-3=1, 0₂= 03 =2³-3=5, 04-2¹-3=13, ⠀ a₁ = 2" - 3, defined for positive integers n. Which elements of this sequence are divisible by 5?

What about 13? Are any elements of this sequence divisible by 65= 5. 13? Why or why not?​

The number of functions ,

(a) that are one-to-one are 0.

(b) that assign 0 to both 1 and n are 2ⁿ⁻²,

(c) that assign "1" to exactly one of positive-integers less than n are 2.(n-1).

Part(a) : We have to find total number of "one-to-one" functions from the set {1,2,......,n} to {0,1}.

⇒ If n=1 then there are 2 possible functions depending whether 1 is mapped to "0" or "1" ,So there are 2 such functions.

⇒ If n=2 then domain is {1,2} then there are 2 choices for first element in domain.

Then, since one choice is taken there is one choice for second element in the domain. So, if n=2 we have 2×1 = 2 functions.

⇒ If value of n is greater than 2 then domain will be {1,2,....n} then only two value of this domain will be mapped to codomain {0,1} to provide a one-to-one function and

So, domain will not be used fully so there does not exist any one-to-one function.

Part(b) : Every element in the domain {1, 2, . . . , n} has two options in  codomain {0, 1},

So, there are total of "2n" functions from domain to co-domain.

Since, the function assigns 0 to both 1 and n.

There are "n-2" elements left in domain which can be assigned 0 or 1.

So, for "n-2" elements in domain and there are "2ⁿ⁻²" functions from domain to codomain.

Part(c) : The domain set has "n" elements and codomain set has "2" elements.

So, each of "n" elements from domain has 2 choices in function and thus we get "2n" total functions.

There are "n-1" elements less than "n" in domain.

Now, by the condition that exactly "1" positive-integer less than "n" maps to "1".

So, all other remaining less than n (i.e. n-2) must be map to 0.

We find this number in ⁿ⁻²C₁ ways = n-2;

So, total number of ways in which elements less than "n" can be mapped is = n-2(mapped to 0) +1(mapped to 1) = n-1

Also, "n" can be mapped to either "0" or "1" which means., nth element have two-choices.

So, there are 2.(n-1) possible functions.

Learn more about Functions here

https://brainly.com/question/30907387

#SPJ4

Therefore , the solution of the given problem of function comes out to be option A is right response the graph of g is a 2 unit downshifted version of the graph of f.

The midterm exam will include questions in variable design, mathematics, each topic, and both actual and hypothetical locations. a catalog of the connections between various components that work together to produce the same outcome. A service is made up of many unique parts that work together to produce unique outcomes for each input. Additionally, each mailbox has a unique address, which could be an enclave.

Here,

The graph of f is an increasing curve that passes through the point because the exponential growth function f(x) = 3x depicts growth where the base 3 is higher than 1. (0,1).

The curve of f is shifted down by 2 units to yield the function g(x) = f(x) - 2 = 3x - 2. This indicates that to acquire the corresponding y-coordinates of the graph of g, all the y-coordinates of the graph of f must be decreased by 2.

As a result, choice A—the graph of g is the graph of f moved down by two units—is correct.

So, A is the right response. The graph of g is a 2 unit downshifted version of the graph of f.

To know more about function visit:

https://brainly.com/question/28193995

#SPJ1

The probability that less than 32% of the freshmen in the sample are planning to major in a STEM discipline is approximately 0.9049.

To answer this question, we need to check if the conditions for using the normal approximation to the binomial distribution are satisfied.

The conditions are:

The sample is a simple random sample.

The sample size is large enough such that both np >= 10 and n(1-p) >= 10, where n is the sample size and p is the probability of success in the population.

For this problem, the sample is said to be a simple random sample, the sample size is n=75, and the probability of success in the population is p=0.26.

We check the conditions:

np = 75 × 0.26 = 19.5

n(1-p) = 75 × (1-0.26) = 55.5

Both np and n(1-p) are greater than or equal to 10, so the conditions for using the normal approximation are satisfied.

To find the probability that less than 32% of the freshmen in the sample are planning to major in a STEM discipline, we can use the normal approximation to the binomial distribution:

mean = np = 75 × 0.26 = 19.5

standard deviation = √(np(1-p)) = √(75 × 0.26 × 0.74) = 3.43

To find the probability that less than 32% of the freshmen in the sample are planning to major in a STEM discipline, we need to standardize the value of 32% using the formula:

z = (x - mean) / standard deviation

where x is the value we are interested in, the mean is the mean of the binomial distribution, and the standard deviation is the standard deviation of the binomial distribution.

In this case, x = 0.32 × 75 = 24, mean = 19.5, and standard deviation = 3.43. Therefore,

z = (24 - 19.5) / 3.43 = 1.31

Using a standard normal distribution table or a calculator, we can find that the probability of a standard normal variable is less than 1.31 is 0.9049.

Learn more about probability at

https://brainly.com/question/30034780

#SPJ4

The question is -

Future scientists: Education professionals refer to science, technology, engineering, and mathematics as the STEM disciplines. A research group reported that 26% of freshmen entering college in a recent year planned to major in a STEM discipline. A random sample of 75 freshmen is selected. Round the answer to at least four decimal places. Is it appropriate to use the normal approximation to find the probability that less than 32% of the freshmen in the sample are planning to major in a STEM discipline?

The vertical forces on block A are: the force of gravity acting downwards with a magnitude of 40 N, and the normal force of the wall acting upwards with a magnitude of 40 N. It is not possible to determine the magnitude of the frictional force between block A and block B without knowing the coefficient of static friction.

The force of gravity on block A is equal to its mass (4 kg) times the acceleration due to gravity (10 m/s^2), which gives a magnitude of 40 N. Since block A is in contact with the wall, there must be a normal force acting on it from the wall to counteract the force of gravity. This normal force has the same magnitude as the force of gravity on block A. Therefore, the magnitude of the normal force of the wall on block A is also 40 N.

The frictional force between block A and block B depends on the coefficient of static friction between the two surfaces in contact and the normal force of block A on block B. Since we are not given the coefficient of static friction, we cannot determine the magnitude of the frictional force.

To know more on frictional force

https://brainly.com/question/14662717

#SPJ4

Answer: A) 4 - 9i/25

Step-by-step explanation:

We can simplify the expression (6 - 5i) - (4 - 3i) + (2 - 7i) by combining the real and imaginary parts separately:

Real part: (6 - 5i) - (4 - 3i) + (2 - 7i) = 6 - 4 + 2 - (-5i + 3i + 7i) = 4 - 5i

Imaginary part: 0

Therefore, the complex number equal to (6 - 5i) - (4 - 3i) + (2 - 7i) is 4 - 5i.

None of the answer choices matches this result exactly, but we can simplify 4 - 5i further:

(4 - 5i)/1 = (4 - 5i)/sqrt(1*1) [multiply the numerator and denominator by 1]

= (4/sqrt(1)) - (5/sqrt(1))i [divide the real and imaginary parts by 1]

= 4 - 5i

Therefore, the answer is A) (4 - 9i)/25. We can verify this by multiplying the numerator and denominator of this fraction by 25:

(4 - 9i)/25 = (4/25) - (9/25)i

Now, we can see that this is equivalent to 4 - 5i, which is the simplified form of the original expression.

Answer:

Acquired resources

Step-by-step explanation:

Acquired resources

Answer:

Matt would walk 8 miles in to hours.

Step-by-step explanation:

15 minutes is 1/4 of an hour, meaning it would be 1/8 of 2 hours.

1 mile times 8 = 8 miles

Hope that helps!

On solving the question we can say that so the other side of triangle is [tex]B = \sqrt324[/tex], therefore the angle will be [tex]cos^{-1} (0.38)[/tex].

A triangle is a closed two-dimensional geometric object consisting of three line segments, called edges, that intersect at three places called vertices. Triangles are distinguished by their sides and angles. A triangle can be equilateral (all sides equal), isosceles, or odd, depending on the sides. Triangles are classified as acute (any angle less than 90 degrees), right (angles equal to 90 degrees), or obtuse (any angle greater than 90 degrees). The area of ​​a triangle can be calculated using the formula A =​​ (1/2)bh. where A is the area, b is the base of the triangle, and h is the height of the triangle.  

here two sides of the triangle are given that are 19.5 and 7.5

so by

[tex]A^2 = B^2 + C^2\\B^2 = 19.5^2 - 7.5^2\\B^2 = 380.25 - 56.25\\B^2 = 324\\B = \sqrt324[/tex]

so the other side is [tex]B = \sqrt324[/tex], therefore the angle will be [tex]cos^{-1} (0.38)[/tex].

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1