A square garden is changed into a rectangle, length is doubled and with is 3metres less. Area of the new garden is 25% more than the original area. What was the original area?

The probability that a sample of 81 painkiller pills has a mean weight less than 345 mg can be found using the properties of the normal distribution.

We are given that the weights of painkiller pills are normally distributed with a mean of 350 mg and a standard deviation of 7 mg. Since we are interested in the mean weight of a sample of 81 pills, we can use the Central Limit Theorem, which states that the sample mean of a large enough sample size will be approximately normally distributed, regardless of the underlying distribution.

To calculate the probability, we need to standardize the sample mean using the Z-score formula:

Z = (X - μ) / (σ / sqrt(n))

Where:

X is the sample mean,

μ is the population mean,

σ is the population standard deviation, and

n is the sample size.

In this case, X = 345 mg, μ = 350 mg, σ = 7 mg, and n = 81.

Calculating the Z-score:

Z = (345 - 350) / (7 / sqrt(81))

Z = -5 / (7 / 9)

Z ≈ -5 / 0.777

Z ≈ -6.43

To find the probability corresponding to this Z-score, we can refer to the standard normal distribution table or use statistical software. Looking up the Z-score of -6.43 in the table, we find that the probability is extremely close to 0 (approaching 0 but not exactly 0).

The sketch of the density curve for the normal distribution would show a symmetric, bell-shaped curve centered at the mean of 350 mg. The probability we calculated represents the area under the curve to the left of the Z-score -6.43, which corresponds to the probability of the sample mean weight being less than 345 mg.

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Therefore the values of a and b are 5 and −2 respectively.

The inverse trigοnοmetric functiοns are the trigοnοmetric functiοns' cοunterparts in mathematics. They can be used tο create an angle frοm any οf the angle's trigοnοmetric ratiοs because they are specifically the inverses οf the sine, cοsine, tangent, cοtangent, secant, and cοsecant

Properties of complex number

Let z₁ = a + i b and z₂ =c + i d , where a, b, c, d  are real numbers.

z₁ z₂   = ( a +i  b) ( c + i d)

         \($ = ac + i ad + i bc + i^2 bd\)

         \($= (ac - bd) + i(ad + bd) where i^2= -1\)

Given 7+3i and \((a+i b)(1+i)=7+3 i\)

Now

\(7+3 i = (a + i b) (1+i)\)

\(7+3 i = a + i a + i b + i^2 b\)

\(7+3 i=(a - b)+i(a+b)\)

Equating real and imaginary parts, we get

a − b = 7 → (1)

a + b = 3 → (2)

(1) and (2), we get 2a = 10 implies a = 5.

substitute the value a = 5 in equation (1)

5 − b = 7

−b =7 − 5

−b =2

b =− 2

Therefore the values of a and b are 5 and −2 respectively.

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Each piece of wood will be 6.25 inches long.

To find the length of each piece of wood after it is cut into thirds, we can divide the total length of the original piece of wood by the number of pieces it is being cut into.

So, to find the length of each piece of wood after being cut into thirds, we can use the following formula:

Length of each piece = Total length ÷ Number of pieces

In this case, the total length of the piece of wood is 18.75 inches and it is being cut into 3 pieces.

Therefore, the length of each piece of wood will be:

Length of each piece = 18.75 ÷ 3 = 6.25 inches

So each piece of wood will be 6.25 inches long after Jose cuts the original piece into thirds.

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Answer:

water: sucrose: saline solution: 100:15:60

Step-by-step explanation:

water 1L = 1000ml

sucrose 150ml

saline solution 600ml

so, water: sucrose: saline solution = 1000L: 150L: 600L

1000:150:600

100:15:60

the proportion

Since both partial derivatives exist and are continuous everywhere in ℛ2, we conclude that f possesses first order partial derivatives.

To show that the function f: ℝ² → ℝ, defined by f(x, y) = (xy) / (x² + y⁴) when x² + y⁴ ≠ 0, and f(x, y) = 0 when x = 0 and y = 0, possesses first-order partial derivatives, we need to compute the partial derivatives with respect to x and y and show that they exist.

Let's compute the partial derivatives:

1. Partial derivative with respect to x (∂f/∂x):

For x² + y⁴ ≠ 0, using the quotient rule:
∂f/∂x = [(y)(x² + y⁴) - (xy)(2x)] / (x² + y⁴)²

At x = 0 and y = 0:
∂f/∂x = lim (x -> 0, y -> 0) [(y)(x² + y⁴) - (xy)(2x)] / (x² + y⁴)² = 0

So, the partial derivative ∂f/∂x exists.

2. Partial derivative with respect to y (∂f/∂y):

For x² + y⁴ ≠ 0, using the quotient rule:
∂f/∂y = [(x)(x² + y⁴) - (xy)(4y³)] / (x² + y⁴)²

At x = 0 and y = 0:
∂f/∂y = lim (x -> 0, y -> 0) [(x)(x² + y⁴) - (xy)(4y³)] / (x² + y⁴)² = 0

So, the partial derivative ∂f/∂y exists.
In conclusion, the function f(x, y) possesses first-order partial derivatives since both ∂f/∂x and ∂f/∂y exist.

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Answer:

Step-by-step explanation:

To solve the given equation \(\sf x - y = 4 \\\), we can perform the following calculations:

a) To find the value of \(\sf 3(x - y) \\\):

\(\sf 3(x - y) = 3 \cdot 4 = 12 \\\)

b) To find the value of \(\sf 6x - 6y \\\):

\(\sf 6x - 6y = 6(x - y) = 6 \cdot 4 = 24 \\\)

c) To find the value of \(\sf y - x \\\):

\(\sf y - x = - (x - y) = -4 \\\)

Therefore:

a) The value of \(\sf 3(x - y) \\\) is 12.

b) The value of \(\sf 6x - 6y \\\) is 24.

c) The value of \(\sf y - x \\\) is -4.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

See attached

Step-by-step explanation:

Solution is in the picture

Evaluated the integral along the curve c:  ∫c (y^2 - 2xy) dx = ∫c (y^2 - 2xy) dx.

To evaluate the integral ∫ c 2 x y 2 z d x 2 x 2 y z d y ( x 2 y 2 − 2 z ) d z using Stokes' theorem, we need to follow these steps:

Step 1: Determine the curl of the vector field.

First, let's find the curl of the vector field F = (2xy^2z, x^2yz, x^2y^2 - 2z).

The curl of F can be calculated using the formula:

curl F = (∂Fz/∂y - ∂Fy/∂z, ∂Fx/∂z - ∂Fz/∂x, ∂Fy/∂x - ∂Fx/∂y).

By substituting the components of F, we get:

curl F = (2xz - 0, 0 - yz, y^2 - 2xy).

Therefore, the curl of F is (2xz, -yz, y^2 - 2xy).

Step 2: Determine the surface bounded by the curve.

The curve c is given by x. This means that the curve lies in the xy-plane.

To determine the surface bounded by the curve, we need to find the normal vector to the curve. Since the curve lies in the xy-plane, the normal vector is k (the z-axis).

Step 3: Calculate the dot product between the curl of F and the normal vector.

The dot product between the curl of F and the normal vector is given by:

(2xz, -yz, y^2 - 2xy) · k = y^2 - 2xy.

Step 4: Evaluate the double integral over the region.

Now, we need to evaluate the double integral of y^2 - 2xy over the region D, which is the projection of the curve c onto the xy-plane.

Since the curve is given by x, the projection of the curve onto the xy-plane is simply the curve itself.

Therefore, the double integral becomes:

∫∫D (y^2 - 2xy) dA = ∫c (y^2 - 2xy) dx.

Step 5: Evaluate the line integral.

Using the line integral, we can evaluate the integral along the curve c:

∫c (y^2 - 2xy) dx = ∫c (y^2 - 2xy) dx.

And this is the final step in evaluating the given integral using Stokes' theorem.

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The possible values of X are that if n is even X can takes even integers from [-n, n], and if n is odd, X can takes odd integers from [-n, n]

To solve this question, we can use X to represents the difference between the number of heads and the number of tails obtained when a coin is tossed X times, the possible values of X are now obtained below:

Let H be the no. of heads and T be the no. of tails, since the coin is tossed n times, we have:

H+T=n

now, X = H-T ,

X=H-(n-H)

X=2H-n

Now,

H takes values {0,1,2,3 ......,n-2, n-1,n}

2H takes values {0,2,4,6,.....,2n-4,2n-2,2n}

2H - n takes values {-n,-(n-2),-(n-4), -(n-6),.............,n-4, n-2,n}

X takes values {-n,-(n-2), -(n-4),-(n-6),.............,n-4, n-2, n}

therefore, if n is even X can takes even integers from [-n, n]

and, if n is odd, X can takes odd integers from [-n, n]

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Since PS = RS, the triangle PRS is isosceles. This means the angles SPR and SRP are congruent.

The interior angles of any triangle sum to 180° in measure. So we have

∠SPR + ∠SRP + 90° = 180°

2 ∠SPR + 90° = 180°

2 ∠SPR = 90°

∠SPR = a = 45°

Answer:

9 18 27 36

Step-by-step explanation:

9x(d) each day Im pretty sure its correcr

we need to first find the common ratio (r) of the sequence. We can use the formula for the nth term of a geometric sequence:The 10th term of the geometric sequence is approximately 96.074.

an = a1 * r^(n-1)
where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.
Using the given information, we can find the value of r:
24 = 12 * r^(4-1)
r^3 = 2
r = ∛2
Now that we know the common ratio, we can find the 10th term:
a10 = 12 * (∛2)^(10-1)
a10 = 12 * (∛2)^9
a10 ≈ 72.99
Therefore, the 10th term of the geometric sequence is approximately 72.99.
Hi! To find the 10th term of the geometric sequence, we need to identify the common ratio (r) first. Given the first term (a1) is 12 and the fourth term (a4) is 24, we can set up the following equation:
a1 * r^3 = a4
12 * r^3 = 24
Now, we solve for r:
r^3 = 24 / 12
r^3 = 2
r = ∛2
Now that we have the common ratio, we can find the 10th term (a10) using the formula:
a10 = a1 * r^(10-1)
a10 = 12 * (∛2)^9
a10 ≈ 96.074

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Answer:

78.625

Step-by-step explanation:

629 / 8 =  78.625

Answer:

629/8=78.625

OR

\(\frac{629}{8}=78\frac{5}{8}\)

Answer:

10

Step-by-step explanation:

he can buy 10 because 7×10=70

Answer:

10

Step-by-step explanation:

The function "fig" is not defined in the given information, without its definition, we cannot determine the domain of the function for the given expressions: f(x) = x + 99 & g(x) = x²

(a) (r + g)(x) = r(x) + g(x) = (x - 8) + (x² - 8) = x² + x - 16

(b) (-9)(x) - 8 = - 9x - 8

(c) (f)(x) = f(x) = x + 99(x) = x²(f/g)(x) = f(x) / g(x) = (x + 9) / x

The domain of the given figure is not given, hence we can not find the domain of fig.

f(x) = x + 99

The function f(x) is defined as the sum of x and 99.

g(x) = x²

The function g(x) is defined as the square of x.

(a) (r+g)(x) = ?

The expression (r+g)(x) represents the sum of two functions, r(x) and g(x).

However, the specific definitions of r(x) and the value of x are not provided.

Therefore, we cannot determine the result without more information.

(b) (-9)(x) - ?

The expression (-9)(x) represents the product of -9 and x.

However, a specific value for x is not given, so we cannot compute the result without more information.

(c) (f)(x) = (a)

The expression (f)(x) represents the function f(x).

Since f(x) is defined as x + 99, we have (f)(x) = x + 99.

The result (a) is the same as the function itself, which is x + 99.

(d) (f/g)(x) = ?

The expression (f/g)(x) represents the quotient of two functions, f(x) and g(x).

Therefore, we need to divide f(x) by g(x), which gives us:

(f/g)(x) = (x + 99) / (x²)

(e)The domain of fig:

The function "fig" is not defined in the given information. Without its definition, we cannot determine the domain of the function.

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Answer:

10:12

Step-by-step explanation:

hope it helped!!

xxx me!

Answer:

5:6

Step-by-step explanation:

Chicken : Pasta

10           :  12       (Both divide by 2)

5             :  6        (Simplest form)

Answer:

10ms/2

Step-by-step explanation:

The equation for acceleration

= Final Velocity - Starting Velocity /Time

= 20 (Final Velocity) - 0 (starting velocity) /2

= 10 ms/2

Answer: Filled dot at 22 going to the Left.

Step-by-step explanation:

Let's start with what we know. We have:

34<= 12 + n

When we take the 12 to the other side we get:
22 <= n

When we have a <= that means that there is going to be a filled dot at 22 and the arrow going to the Left.

Answer:

4.8 cm

Step-by-step explanation:

What we know: V= 24 cm3 and b= 5 cm2

Formula: V= bh

24cm3= (5cm2)h

4.8 cm= h

Answer:

Median is 6 Mode is 10

Step-by-step explanation:

Median is the middle number when all the numbers are lined up in order.

Mode is the number that shows up most frequently.

Answer:

Mode: 10

Median: 6

Step-by-step explanation:

Answer:

(2x+3)(3x+2)

Step-by-step explanation:

.....

......

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

Answer:

(2x + 3)(3x + 2)

Step-by-step explanation:

\(6x^2+13x+6 \\ \\ = 6x^2+9x + 4x+6 \\ \\ = 3x(2x + 3) + 2(2x + 3) \\ \\ = (2x + 3)(3x + 2)\)

Answer:

The answer is 133/900

Step-by-step explanation:

BECAUSE I SAID SO LOL

Answer:

To write 14.7 as a fraction you have to write 14.7 as the numerator and put 1 as the denominator. Now you multiply the numerator and denominator by 10 as long as you get in the numerator the whole number.

14.7 = 14.7/1 = 147/10

And finally, we have:

14.7 as a fraction equals 147/10

Step-by-step explanation:

The number of black sweatshirts bought, based on simultaneous equations, is 28.

Simultaneous equations are two or more equations solved simultaneously, concurrently, or at the same time.

Simultaneous equations are also known as a system of equations.

The total number of sweatshirts bought = 50

The unit cost of each white sweatshirt = $10

The unit cost of each black sweatshirt = $12

The total cost for 50 sweatshirts = $556

Let the number of white sweatshirts = x

Let the number of black sweatshirts = y

x + y = 50... Equation 1

10x + 12y = 556... Equation 2

Multiply Equation 1 by 10:

10x + 10y = 500... Equation 3

Subtraction Equation 3 from Equation 2:

10x + 12y = 556

-

10x + 10y = 500

2y = 56

y = 28

x = 50 - y

x = 50 - 28

x = 22

Thus, using a system of equations, you bought 28 black and 22 white sweatshirts for your store.

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A z-score of 2.14 indicates that Katie's score on the test is quite high and unusual, and places her in the top 2% of the scores in the population.

Katie scored a 93 on a test and her calculated z score was 2.14, that means that her score is 2.14 standard deviations above the mean of the test scores.

A z score represents the number of standard deviations a data point is from the mean of the data set.

A positive z score means that the data point is above the mean, while a negative z score means that the data point is below the mean.

The mean of the test scores was, 80 with a standard deviation of 5, then Katie's z score would be calculated as:

z = (x - μ) / σ

= (93 - 80) / 5

= 2.6

Z scores are useful for comparing data points from different data sets or for comparing data points within the same data set that are measured on different scales.

Katie's score is 2.6 standard deviations above the mean.

A z score of 2.14 would mean that Katie's score is slightly below this value, but still significantly above the mean.

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The probability of  number of times we draw a card is 3.

The probability of drawing a heart or a face card on any given draw.

There are 16 such cards in the deck (4 kings, 4 queens, 4 jacks, and 4 hearts), out of a total of 52 cards. So the probability of drawing a heart or a face card on any given draw is 16/52, which simplifies to 4/13.
Now, to calculate the expected number of draws until we get a heart or a face card, we can use the formula:
Expected number of draws = 1/P(event)
where P(event) is the probability of the event happening. In this case, the event is drawing a heart or a face card, so:
Expected number of draws = 1 / (4/13) = 13/4 = 3.25
So on average, we would expect to draw a card 3.25 times before getting a heart or a face card. However, since we cannot draw a fraction of a card, the actual number of draws will either be 3 or 4.

Hence,  the expected number of times we draw a card is 3 (or 4, if the last card drawn is not a heart or a face card).


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The probability of the next coat being sold as a medium navy coat is 11 / 95 when a store sells a coat in three sizes: small, medium, and large. The coat comes in red, navy, and tan.

We need to find the probability that the next coat sold as a medium navy coat. To find the probability we need to find the total number of coats and the number of medium navy coats,

Given data:

Medium navy coat = 22

Total Number of small coats = 18 + 24 +19 = 61

Total Number of medium coats = 21 + 22 + 25 = 68

Total Number of large coats = 19 + 20 + 22 = 61

From the given data the total number of coats is = 61 + 68 + 61 = 190

The probability that the next coat sold as a medium navy coat = a number of medium navy coats / total number of coats.

= 22 / 190

= 11 / 95

Therefore, the probability of the next coat being sold as a medium navy coat is  11 / 95

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Answer:

Tony poured is 9% of the total

Step-by-step explanation:

Given data

The capacity of the container= 60000 liters

Amount of water that tony pours=  5400 liters

Let us compute the percentage to know if it is up to 10%

= 5400/60000*100

=0.09*100

=9%

Hence the amount of water Tony poured is 9% of the total

Answer:

He is wrong

Step-by-step explanation:

60 000 LB=55000

60 000 UB=65000

5400 LB= 5350

5400 UB=5450

65000x0.10=6500

55000x0.10=5500

he is wrong

Answer:

C.it a function ,many to 1 bcz it satisfies the vertical test which the first 1 and the horizontal test which is second 1.B ITS NOT A FUNCTION CUZ IT DOES NOT SATISFY THE FIRST TEST

Step-by-step explanation:

The simplify value of numeric expression, 3 + 2, after adding 3456 then subtracting 45 and then dividing by 20 is equals the 17.8.

We have an expression of numbers, 3 + 2 we have to apply some arithematic operations on it and determine the final simplfy value. Let the expression be x = 3 + 2, add 3456 in it

=> x = 3 + 2 + 3456

Substracts 45 from above expression

=> x = 3 + 2 + 3456 - 45

Dividing the above expression of x by 20

=>

\(\frac{ x } {20} = \frac{ 3 + 2 + 3456 - 45}{20}\)

\(= \frac{3416}{20}\)

= 17.8

Hence, required simplify value is 17.8.

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