The effectiveness of a blood pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 42.2 for a sample of size 309 and standard deviation 10.7. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 99% confidence level) Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

The value of function, f(t) for L⁻¹ ( e−s /(s²+ 1)) is equals to sin( t - π ) u(t-π) .

The Laplace transform is the essential term of the given derivative function. Moreover, it comes with a real variable (t) for converting into complex function with variable (s). For ‘t’ ≥ 0, let ‘f(t)’ be given, the Laplace transform of ‘f(t)’, denoted by 'L{f(t)}' or ‘F(s)’ is definable with the equation:

\( L(f(t)) = F(s) = ₀∫^{ \infty } e⁻ˢᵗ f(t)dt\)

we have L⁻¹ ( e−s /(s²+ 1))

Now, L⁻¹ (1 /(s²+ 1)) = sin(t)

so, L⁻¹ ( e−s /(s²+ 1)) = sin( t - π ) u(t-π)

where u(t-π) is unit of step function.

so, required function f(t) is sin( t - π ) u(t-π).

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Complete question:

Find f(t) ℒ−1 (e−s /(s²+ 1))

f(t)=? + (?) (t - ?)

Answer:

$63

Step-by-step explanation:

The store is 20% off, Jessica has a coupon that is 5% off add that together and it's 25% off. $84 - 25% = $63

The arc angle x in the circle is 38 degrees.

An inscribed angle in a circle is formed by two chords that have a common end point on the circle.

The inscribed angle A is half of the arc angle x of the circle.

Therefore,

51 + 53 + ∠A = 180

∠A = 180 - 51 - 53

∠A = 76 degrees

Therefore,

x = 1 / 2∠A

Hence,

x = 1 / 2 × 76

x = 38 degrees

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The actual height of the rocket is 576 inches.

Cross multiply is to multiply the numerator of each side of a proportion by the denominator of the other side.

A ratio box is a visual tool that can be used to solve proportion problems. To use a ratio box to solve this problem, we can set up the following ratio:

1/12 : 48 inches : : x : actual height

where x is the unknown value that we want to find.

To solve for x, we can cross-multiply and simplify the equation:

1/12 * actual height = 48 inches

actual height = 48 inches * 12/1

actual height = 576 inches

So the actual height of the rocket is 576 inches.

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An expression for the number of bracelets of n beads, where rotations.

Whats an expression for the bracelets?

In mathematics, the term "bracelets" can refer to a type of combinatorial object, specifically, a set of beads arranged in a circular pattern. An expression for the number of bracelets of n beads, where rotations and reflections are considered identical, can be given as follows:

B(n) = (1/n) * (2raise to the power (n-1) + Σ(d|n, d<n) μ((n/d)) * 2 raise to the power ((n/d)-1))

Here, B(n) represents the number of distinct bracelets of n beads, Σ denotes the summation, d|n denotes "d divides n", and μ is the Möbius function.

The first term in the expression, (1/n) * (2 raise to the power (n-1)), represents the number of bracelets that are invariant under rotation. The second term takes into account the bracelets that are not invariant under rotation, but are invariant under reflection, and involves the Möbius function.

This expression can be used to calculate the number of bracelets for any value of n, by plugging in the value of n and evaluating the expression.

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Answer:

30

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

i really don't have a method for this, just try a number you think is close, go up, or down depending on the number

Answer:

27

Step-by-step explanation:

\(3^{3}\) is basically just multiplying the number 3, three times. So 3x3x3. 3x3 is 9, and when you multiply 3 more, it is 27.

Answer:

Step-by-step explanation: 3, because when 3 is cubed you get 27.

Answer:

1. (any number less than 10) < 10

2. 520 (division)

   520

➗     2

   260

3. (any number less than 3 *1 or 2*) < 3

4. (any number greater than 1) > 1

5. (Subtraction - A number subtracting two and the result is less than 10) < 10  

Step-by-step explanation:

1. The symbol "<" shows greater than. It is facing the number "10",

So, we need to get any number below 10. As example: 1 ; 2 ; 3 ; 4 ; 5 ; 6 ; 7 ; 8 ; 9. The numbers I mentioned there are what you can use for question 1.

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

2. The number 520' is what I find to be multi-result but I would do division. Number 520 is part of the addition, subtraction, multiplication, and division but I am doing division.

Divison:

   520

➗     2

   260

Multiplication:

    260

  x     2

    520

Addition:

  500

+  20

  520

Subtraction:

 550

-   30

 520

These are the examples that you can try for number 2.

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

3. First, you can see that there is the greater symbol here again, "<".

But this time, it's pointing to 3. Which means the number is less than 3.

The only numbers that are less than 3 is 1 and 2 so those are the 2 options you can choose.

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

4. This time, the symbol is less. It's now pointing at 1, so you can pick any number that is greater than 1.

Example:

5 > 1

Like that! You can pick any number that is greater than 1 for this question!

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

5. the equation "-2 < 10" is about a number subtracting 2 but than the results come in being less than 10. Since we have spotted the greater symbol as "<", and the subtraction symbol as "-".

Now, first we find a number that can subtract 2 but less than 10 in the result.

The options we have are:

1. 2 (2-2=0 ; 0 < 10)

2. 3 (3-2=1 ; 1 < 10 )

3. 4 (4-2=2 ; 2 < 10 )

4. 5 (5-2=3 ; 3 < 10 )

And so on until you reach number 9 as the result!

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

Hope this helped you! I tried my best to help you. But have a good day!

The function C(F) to calculate the temperature in degrees Celsius for a given temperature in degrees Fahrenheit will be equal to \([(\frac{5}{9}F) -\frac{160}{9}]\)

As per the question statement,  the formula [F(C) = 9/5C + 32] is to calculate the temperature in degrees Fahrenheit for a given a temperature in degrees Celsius.

We are required to determine the function to calculate the temperature in degrees Celsius for a given temperature in degrees Fahrenheit.

Since, [F(C) = 9/5C + 32],

\(or, [F = \frac{9}{5} C + 32]\\or, (F-32)= \frac{9}{5} C\\or, \frac{9}{5} C=(F-32)\\or,C=\frac{5}{9} (F-32)\\or,C=\frac{5}{9}F-\frac{160}{9}\)

That is, the function to calculate the temperature in degrees Celsius for a given temperature in degrees Fahrenheit is \(C(F)=[(\frac{5}{9}F) -\frac{160}{9}]\).

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Answer:

inverse

C(F)=5/9F-106/9

check all

Step-by-step explanation:

23

Answer:

picture #1 - 50.27 square units

picture #2 - 113.10 square units

picture #3 - 380.13 square units

Step-by-step explanation:

picture #1 - area = πr^2 -> π*4^2 = 50.27 square units

picture #2 - area = πr^2 -> π*6^2 = 113.10

picture #3 - area = πr^2 -> π*11^2 = 380.13

Answer:

B

Step-by-step explanation:

Answer:

15) Quadratic Function : The 3x is squared

16) Linear Function : It is a straight line

17) Quadratic Function : The line is a U shape

18) Linear Function : There is one y value for every x value, and the points form a straight line

Step-by-step explanation:

Done

Starting off we just need to divide the numbers by each other to see how they are increasing.

20÷8 = 2.5

50÷20 = 2.5

Seeing that our answer is 2.5 we need to multiply several times to reach our 10th term.

8, 20, 50, 125, 312.5, 781.25, 1953.125, 4882.8125, 12207.03125, 30517.578125

Meaning the 10th term is 30517.578125 or when rounded to a whole number 30,518  

Checking

To check if the term is right you just need to keep dividing the numbers until your back at the starting number.

ex.

30517.578125 ÷ 2.5 = 12207.03125 (Which is the 9th term)

Answer:-5/4

Step-by-step explanation:

Answer:

C) 12.2 cm

Step-by-step explanation:

To find the area of a square, you multiply length and width, which for a square, are the same. So to find the length of one of its sides, you have to take the square root of the area.

\(L^{2} = 150\\\\L=\sqrt{150} \\L= 12.2\\\)

Answer and Step-by-step explanation:

These triangles are similar by AA......

This is because the point that connects the triangles together have the same angle value. We also see that they both have 90 degrees as an angle, making it similar by AA~.

The other angle that shows the 38 in it is 52, so it is definitely proven by AA~.

#teamtrees #PAW (Plant And Water)

The online retailer will make $4 on a sale of $80. This is calculated by multiplying the cost of the sale ($80) by the retailer's percentage (5%).

The first step in calculating the retailer's profit is to identify the cost of the sale. In this case, the cost of the sale is $80.

The next step is to identify the percentage of the cost that the retailer will receive. In this case, the retailer will receive 5% of the cost of the sale.

The third step is to calculate the retailer's profit. This can be done by multiplying the cost of the sale ($80) by the retailer's percentage (5%). This calculation results in $4, which is the retailer's profit for this sale. Hence, the online retailer will make $4 on a sale of $80.

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Answer:

-13

Step-by-step explanation:

expression =4a-|3b+2c|

subtitute all values in the expression:

=4(-2) -|3(-3)+2(2)|

=-8-|-9+4|

=-8-|-5|

=-8-(5)

=-8-5

=-13

Note:if you need to ask any question please let me know.

The value of the expression from the variables  is -13

From the question, we have the following parameters that can be used in our computation:

4a - |3b + 2cl

Also, we have

a = - 2, b = -3, c = 2, x = 2.1, y = 3, and z = - 4.2.

substitute the known values in the above equation, so, we have the following representation

4a - |3b + 2cl = 4 * -2 - |3 * -3 + 2 * 2|

Evaluate

4a - |3b + 2cl = -13

Hence, the expression from the variables  is -13

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Answer:

x = 52

y = 19

Step-by-step explanation:

The degree measure of a straight line is (180) degrees. One can use this to find the measure of the angle that is adjacent to the angle with a measure of (142) degrees. Form an equation and solve for the unknown,

142 + (unknown angle) = 180

unknown angle = 38

The inscribed angle theorem states that twice the measure of an angle with its vertex of the circumference (outer edge) of a circle is equal to the measure of the surrounding arc. Therefore, one can state the following:

(2)(unknown angle) = (surrounding arc)

(2)(38) = (surrounding arc)

76 = surrounding arc

The central angles theorem states that the measure of an angle whose vertex is the center of the circle is equal to the measure of the surrounding arc. Therefore, one can state the following:

m<O = (surrounding arc)

m<O = 76

The radius is the distance from the center of the circle to the circumference of the circle. All radii in a circle are congrunet. Therefore the triangle with angle (x) and vertex (O) is an isosceles triangle, as two of its sides are radii, and are thus congruent. One property of an isosceles triangle is the base angles theorem. This theorem states that the angles opposite the congruent sides in an isosceles triangle are congruent. Moreover, the sum of angles in any triangle is (180) degrees. Therefore, one can make the following statement:

m<O + x + x = 180

76 + 2x = 180

x = 52

Finally, one can use the property that the sum of angles in any triangle is (180) degrees to make the following statement:

(x + 19) + (x + y) + (38) = 180

52 + 19 + 52 + y + 38 = 180

161 + y = 180

y = 19

x=52°

y=19°

Answer:

Solution given:

<OCA=19°[base angle of isosceles triangle]

Since ∆AOC is similar to ∆ BOC

y=19°[corresponding angle of a similar triangle are equal]

<OAB=<OBA=x[base angle of isosceles triangle]

again

<A+<B=180°[exterior angle of a triangle is equal to the sum of two opposite interior angle]

x+19+x+19=142°

2x=142°-38°

x=104/2

x=52°

Answer: 12.2

Step-by-step explanation:

Answer:

Step-by-step explanation:

a + b)^6 will have 7 terms so you want row 6 of the triangle 1 6 15 20 15 6 1

so (a + b)^6 = a^6 + 6a^(5)b + 15a^(4)b^2 + 20a^(3)b^3 + 15a^(2)b^4 + 6ab^5 + b^6

given a = d and b = -5y

∴ (d − 5y)^6 = d^6 + 6d^(5)(-5y) + 15d^(4)(-5y)^2 + 20d^(3)(-5y)^3 + 15d^(2)(-5y)^4 +

Answer:

\(3^{14}\) or 4,782,969

Step-by-step explanation:

Note that the base are the same (3). In this case, when you are multiplying, add the powers together:

\(3^9 * 3^5 = 3^{9 + 5} = 3^{14}\).

~

The phrase "a of 1:2" refers to the scale factor between the length of the scale drawing and the actual length of the patio.

It means that the length on the scale drawing is half of the actual length of the patio.

The scale is used to represent the object's size proportionally.

The scale shows the ratio of the size of the drawing to the actual size of the object.

A scale of 1:2 means that one unit on the drawing represents two units in real life.

The patio, if the length on the scale drawing and the actual length of the patio can be written as a ratio of 1:2, it means that the length of the patio on the drawing is half the length of the actual patio.

This scale can be used to determine the actual length of the patio if the length on the scale drawing is known.

If the length of the patio on the scale drawing is 4 inches, then the actual length of the patio can be found by multiplying the length on the drawing by the scale factor:

Actual length of the patio = 4 inches × 2 = 8 inches

Conversely, if the actual length of the patio is known, the length on the scale drawing can be found by dividing the actual length by the scale factor:

Length on the scale drawing = Actual length of the patio / 2

The actual length of the patio is 16 feet, then the length on the scale drawing would be:

Length on the scale drawing = 16 feet / 2 = 8 feet

The scale ratio of 1:2 allows us to represent the actual size of the patio in a smaller size on a drawing, while maintaining the correct proportions. This can be useful for architectural plans, blueprints, or any other situation where a representation of an object needs to be made in a smaller size.

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The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

where c is a constant.

The solution to the question is shown below.

Step 1: We have given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

We have to find the number of words we have to write to express this function in words.

Step 2: Solution

f(t) = et5+4t + ln(t²+3c)⁷ +te-1+5e⁶

Where,

et5+4t = exponential function

ln(t²+3c)⁷ = natural logarithmic function

te-1 = linear function

e⁶ = exponential function

Therefore, f(t) can be expressed in words as:

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Step 3: Conclusion

Hence, the function f(t) can be expressed in words with:The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

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Answer:

hope this helps

Step-by-step explanation:

The value of the given integral is 15/4 - 5z.The given integral represents the volume integral of the function f(x,y,z) = 5r - 3y over the region R bounded by the coordinate planes and the plane 2 + y + z = 1.

To evaluate the given integral, we need to determine the limits of integration for x, y, and z. The region R is bounded by the coordinate planes, so the limits of integration for x, y, and z are simply 0 to 1.

The plane 2 + y + z = 1 intersects the coordinate planes at the points (1,0,0), (0,1,0), and (0,0,-1), so this plane divides the region R into two parts. To determine the limits of integration for z, we need to find the equation of the plane in terms of z:

2 + y + z = 1

y + z = -1

So, the limits of integration for z are -1 to 0 for the part of R below the plane, and 0 to 1 for the part of R above the plane.

Now we can write the given integral as:

∫∫∫R (5x - 3y) dV

= ∫0^1 ∫0^1 ∫-1^0 (5x - 3y) dz dy dx + ∫0^1 ∫0^1 ∫0^1 (5x - 3y) dz dy dx

= ∫0^1 ∫0^1 [-z(5x - 3y)]|z=-1^0 dy dx + ∫0^1 ∫0^1 [(1-z)(5x - 3y)]|z=0^1 dy dx

= ∫0^1 ∫0^1 (3y - 5x) dy dx + ∫0^1 ∫0^1 (4-5z)(5x - 3y) dy dx

= ∫0^1 ∫0^1 (3y - 5x) dy dx + ∫0^1 [(4-5z)(5/2 - 3)] dx

= ∫0^1 ∫0^1 (3y - 5x) dy dx + 5/2 ∫0^1 (4-5z) dx

= ∫0^1 ∫0^1 (3y - 5x) dy dx + 5/2 (4-5z)

= ∫0^1 [-5x/2 + (3/2)y]|y=0^1 dx + 5/2 (4-5z)

= ∫0^1 (-5x/2 + 3/2) dx + 5/2 (4-5z)

= [-5x^2/4 + (3/2)x]|x=0^1 + 5/2 (4-5z)

= -5/4 + 3/2 + 5/2 (4-5z)

= 15/4 - 5z

Therefore, the value of the given integral is 15/4 - 5z.

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The simple interest on a principal of $7,600 at a rate of 7% for 9 months is $399.

To determine the simple interest, we can use the formula:

Simple Interest = Principal x Rate x Time

Principal = $7,600

Rate = 7% (which can be expressed as 0.07 in decimal form)

Time = 9 months (which can be expressed as 9/12 or 0.75 in years)

Let's substitute these values into the formula:

Simple Interest = $7,600 x 0.07 x 0.75

Calculating this expression, we have:

Simple Interest = $7,600 x 0.0525

Simple Interest = $399

Therefore, the simple interest on a principal of $7,600 at a rate of 7% for 9 months is $399.

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Answer:

15/50×100=30%

Step-by-step explanation:

Answer:

5,424 ft.

Step-by-step explanation:

For every 1 foot the ski lift goes up by, it travels west 4 feet. So, because we know that the lift will be 1,356 feet higher at the top of the mountain, all we have to do is multiple 1,356 by 4.

1,356 * 4 = 5,424 ft.

I hope this helps. :)