Systolic blood pressure readings are normally distributed with a mean of 121 and a standard deviation of 15.
Find the z-score to the nearest tenth for the following blood pressure readings.

a. 142 -

b. 130 -

c. 103 -

The time it take until 2000 people know about the rumor is 16 days.

The square root of a variety of is described because the value, which offers the variety while it's miles increased with the aid of using itself. The radical symbol √ is used to suggest the square root.  Radical is any other call given to the square root symbol. It is likewise called the surds. While Radicand is the variety gift beneath neath the square root symbol.

Find t, when N=200

N=5OO t^1/2

2000=500 t^1/2

t^1/2=4

t=16 days

Thus, the time it take until 2000 people know about the rumor is 16 days.

To learn more about square root check the link below:

https://brainly.com/question/428672

#SPJ4

Step-by-step explanation:

subtract the area of the phone from that of the phone

Answer:

h

Step-by-step explanation:

because it shifts the graph to the left by 6 units

One additional group would be required to conduct a 3 x 2 x 3 factorial design compared to a 3 x 2 x 2 design with independent variable.

A 3 x 2 x 3 factorial design requires three independent variables (x1, x2, and x3) with three levels each, for a total of 27 conditions. A 3 x 2 x 2 design, however, would only require two independent variables (x1 and x2) with two levels each, for a total of 12 conditions. To conduct a 3 x 2 x 3 factorial design, one additional group would be required, compared to the 3 x 2 x 2 design. This additional group would provide data for the additional 15 conditions that the 3 x 2 x 3 design would require.

Learn more about independent variable here

https://brainly.com/question/29430246

#SPJ4

[tex]\displaystyle\\Answer:\ sin(2\theta)=-\frac{4\sqrt{21} }{25} ,\ cos(2\theta)=\frac{17}{25}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\sin(\theta)=-\frac{2}{5} \ \ \ \ \ \ \ \ 270^0 < \theta < 360^0\\\\sin^2(\theta)+cos^2(\theta)=1\\\\cos^2(\theta)=1-sin^2(\theta)\\\\Hence,\\\\cos^2(\theta)=1-(-\frac{2}{5})^2 \\cos^2(\theta)=1-\frac{4}{25} \\\\cos^2(\theta)=\frac{25(1)-4}{25} \\\\cos^2(\theta)=\frac{21}{25} \\\\[/tex]

Extract the square root of both parts of the equation:

[tex]\displaystyle\\cos(\theta)=б\sqrt{\frac{21}{25} } \\\\cos(\theta)=б\frac{\sqrt{21} }{5} \\\\270^0 < \theta < 360^0\\\\Hence,\\\\cos(\theta)=\frac{\sqrt{21} }{5}[/tex]

[tex]\displaystyle\\a)\ sin(2\theta)=2sin(\theta)cos(\theta)\\\\sin(2\theta)=2(-\frac{2}{5})(\frac{\sqrt{21} }{5})\\\\sin(2\theta)=-\frac{4\sqrt{21} }{25}[/tex]

[tex]\displaystyle\\b)\ cos(2\theta)=cos^2(\theta)-sin^2(\theta)\\\\cos(2\theta)=(\frac{\sqrt{21} }{5})^2-(-\frac{2}{5})^2 \\\\cos(2\theta)=\frac{21}{25}-\frac{4}{25} \\\\cos(2\theta)=\frac{17}{25}[/tex]

Step-by-step explanation:

It takes 73 pounds of seed to completely plant an 11 -acre field. How many pounds of seed are needed per acre?

73 / 11 = 6.6363636 pounds per acre

rounded to two decimal places: 6.64 pounds per acre

Yes, the starting position of these players form a perpendicular line.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Using Trigonometry

sin [tex]\theta[/tex] = 33.33/100

sin [tex]\theta[/tex] = 0.3333

[tex]\theta[/tex] = [tex]sin^{-1}[/tex] (0.3333)

[tex]\theta[/tex] = 19.469

cos 19.469 = B/ 100

0.9428 = B/ 100

B= 94.28

tan  [tex]\theta[/tex] = P/B

tan  [tex]\theta[/tex] = 94.28/ 33.33

[tex]\theta[/tex] = 70.5

Using Angle Sum property

< 3= 180 - (70.5 + 19.5)

<3 = 180 - 90

<3 = 90

Hence, they form perpendicular line.

Learn more about Trigonometry here:

https://brainly.com/question/29002217

#SPJ1

Answer:

The answer is B.

Step-by-step explanation:

Looking at the points gives you a x-axis and y-axis.

(x , y)

(-2 , 3) ,

(0 , 5) ,

(1 , 5) ,

(2 , 4) ,

(8 , -2)

Focus on the y-axis instead of the x-axis and list them.

{3 , 5 , 4 , -2}

The area of the triangular dock is 19.5 square feet and the area of the rectangular box is 10 feet. The box will fit under the dock.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle. The space occupied by the triangle in a two-dimensional plane is called the area of the triangle.

Calculate the area of the triangle first,

Area = 1 / 2 x B x H

Area = 1/2 x 12 x 3.25

Area = 19.5 square feet

Calculate the area of the rectangle,

Area = L x W

Area = 2 x 5

Area = 10 square feet

To know more about an area follow

https://brainly.com/question/29223290

#SPJ1

Answer: k=±`12

Step-by-step explanation:

[tex]ax^2-bx+c=0\\\\9x^2-kx+4=0\\\\D=b^2-4ac\\\\a=9\ \ \ \ b=-k\ \ \ \ c=4\\\\D=0\\\\Hence,\\\\D=(-k)^ 2-4(9)(4)=0\\\\k^2-144=0\\\\k^2=144\\\\k^2=12^2[/tex]

Extract the square root of both parts of the equation:

[tex]k=б\sqrt{12^2} \\\\k=б12[/tex]

Answer:

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

A perfect square trinomial is:

Given trinomial:

Show this as:

Compare and find possible values of k:

The amount of taxes owed on a taxable income of $49,652 is $10,293.44.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Are the tax percentages for various amounts of income.

Now, From the given chart we conclude that $49,652 falls in the category of $41.176-$89.075 is 22% tax.

So, the Tax owed is 22% of $49,652.

∴ (22/100)×$49,652.

= $10,293.44.

So, an income of $49,652 owed 22% tax of the income which is $10,293.44.

learn more about percentages here :

https://brainly.com/question/24159063

#SPJ1

Answer:THE ANSWER IS B)6,600.44

Step-by-step explanation:

I got it right :)

Answer:

C. The graph of the function does not form a straight line

To find the percentage of girls in class A, we need to divide the number of girls by the total number of students and then multiply by 100. This gives us:

14 / 20 * 100 = 70%

To find the percentage of girls in class B, we need to divide the number of girls by the total number of students and then multiply by 100. This gives us:

15 / 25 * 100 = 60%

Thus, the percentage of girls in class A is 70%, and the percentage of girls in class B is 60%.

The mean absolute deviation over three period of time is 200

The absolute value of error in period 1 = 300

The absolute value of error in period 2 = 200

The absolute value of error in period 3 = -100

Total absolute value of error = The absolute value of error in period 1 + The absolute value of error in period 2 + The absolute value of error in period 3

Substitute values in the equation

Total absolute value of error  = 300 + 200 + 100

= 600

The mean absolute deviation = Total absolute value of error / 3

Substitute the values in the equation

The mean absolute deviation  = 600 / 3

= 200

Therefore, the mean absolute deviation is 200

Learn more about mean absolute deviation here

brainly.com/question/10528201

#SPJ4

The distance the ball drops in the next 8 second is: 640 m. Using the concept of equation of motion.

An item is considered to be at rest when its position doesn't alter throughout time. An item is considered to be in motion if, over time, its location changes.

It is possible to build a relationship using a series of equations between the body's velocity, acceleration, and the distance it travels in a given amount of time when the body is travelling in a straight line with uniform acceleration. The term "motion equations" refers to these equations.

D = kt²  where D is the constant of proportionality.

D = 80 m

t = 4 seconds

Putting the values we get -

80 = k(4)²

or, k = 80 / 16

or, k = 5.

So the equation of motion is D = 5t²

When t = 8+4 = 12 seconds

now, D = 5(12)² =  5×144

or, D =  720 m

So, the distance the ball drops in the next 8 seconds = 720 - 80

= 640 m.

To know more about equation of motion refer to:

https://brainly.com/question/27821888

#SPJ1

Answer:

Graph B

Step-by-step explanation:

First, simplify by subtracting 1 on both sides.

|x| + 1 - 1 < 3 - 1

|x| < 2

Using the absolute value definition, we know the inequalities are:

x < 2

-x < 2

Divide both sides by -1.

x < -2

If you multiply or divide both sides of an inequality by a negative number, you must flip the sign.

x > -2

x<2, x>-2

Graph B

Answer:

Graph A

Step-by-step explanation:

if x ≥ 0

x + 1 < 3

x < 3 - 1

x < 2

0≤ x < 2

if x < 0

-x + 1 < 3

-x < 3 - 1

-x < 2

x > -2

-2 < x < 0

Final solution

-2 < x < 2

The gradient value of the line 2x + y = 4 is 2. This can be found by rearranging the equation into slope-intercept form, which is y = -2x + 4. The coefficient of the x term, -2, is the slope of the line.

Answer:

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

Given function:

Find f(-7) by plugging in the value of x:

the Central Limit Theorem, which states that as the sample size increases, the sampling distribution of the sample mean tends to become more normal.

The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean tends to become more normal. This means that the mean of the sample will be closer to the mean of the population, and the variability of the sample will be smaller. Since the sample proportion is just the mean of the sample, as the sample size increases, the distribution of the sample proportion will also become more normal. The larger the sample size, the more likely it is that the sample will accurately represent the population, and the more normal the distribution of the sample proportion will be. In other words, the sample proportion will be closer to the true population proportion, and the variability of the sample proportion will be smaller.

Learn more about central limit theorem here

https://brainly.com/question/18403552

#SPJ4

The function that matches the graph is y(x)=(1-x)(x+2)^2

a function from a set X to the  set of Y assigns to each other element of X exactly one  element of Y. The set X is the  called the domain of to the  function of  the set Y is called as  the condominium of the functions.

From the graph the curve cross the x -axis at X=1

Therefore the expression is (x-1)

And at (-) x axis at X=-2 it is the turning point.

Therefore the expression is

(X+2)^2

And the point on y axis is (0,4)

Therefore the function can be written as

Y(x)=a(x-1)(x+2)^2

4= -4a≈a=-1

Therefore the function is y(x)

(-1)(x-1)(x+2)^2

= y(x)=(1-x)(x+2)^2

Therefore the function that matches the graph is y(x)=(1-x)(x+2)^2

To know more about function click-

https://brainly.com/question/25638609

#SPJ1

The simple interest is $2160 and the amount after 30 years is $6160.

Given that, principal =$4000, rate of interest =1.8%, and time period =30 years.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.

a) Now, S.I =(4000×1.8×30)/100

= 40×1.8×30

= $2160

b) Amount = Principal + Interest

= 4000 + 2160

= $6160

Therefore, the simple interest is $2160 and the amount after 30 years is $6160.

To learn more about the simple interest visit:

https://brainly.com/question/25845758.

#SPJ1

The result of executing the code segment is -2

The complete question is added at the end of this solution as an attachment

The code in the question is given as

IF X > Y

  DISPLAY X + Y

ELSE

  DISPLAY X - Y

Given that

X = 3 and Y = 5

When x and y are compared, we have the truth value to be

Y > X

This means that the executed segment is

DISPLAY X - Y

So, we have

DISPLAY 3 - 5

Evaluate

DISPLAY -2

Hence. the displayed result is -2

Read more about code segment at

https://brainly.com/question/20734416

#SPJ1

Answer:

k = (-55) / 8

k = (-3005) / 8

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510((-255 + sqrt(65025 - 510(0.309016^2))) / 2)^2)) / 2)^2)) / 2

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510((-255 + sqrt(65025 - 1469.59)))))^2)) / 2)

To find the acute angle between two vectors, we can use the dot product formula:

angle = arccos((a * b) / (||a|| * ||b||))

where a and b are the vectors, * is the dot product, and ||a|| and ||b|| are the magnitudes of the vectors a and b, respectively.

In this case, the dot product of a and b is (i - kj) * (i + j) = i^2 - kj * i + kj * i + kj^2 = 2i - k^2j

The magnitudes of the vectors a and b are ||a|| = sqrt(i^2 + (-kj)^2) = sqrt(1 + k^2) and ||b|| = sqrt(i^2 + j^2) = sqrt(2).

Substituting these values into the formula above, we get:

angle = arccos((2i - k^2j) / (sqrt(1 + k^2) * sqrt(2)))

Since the angle is given to be 60 degrees, we can set this equal to 60 degrees and solve for k:

60 = arccos((2i - k^2j) / (sqrt(1 + k^2) * sqrt(2)))

We can use the inverse cosine function to solve for k:

k = sqrt(1 / (cos(60)^2 - (2i / sqrt(1 + k^2) * sqrt(2))^2))

Since cos(60) = 0.5, we can substitute this value in and solve for k:

k = sqrt(1 / (0.5^2 - (2i / sqrt(1 + k^2) * sqrt(2))^2))

k = sqrt(1 / (0.25 - (2i / sqrt(1 + k^2) * sqrt(2))^2))

k = sqrt(1 / (0.25 - (4i^2 / (1 + k^2) * 2)^2))

k = sqrt(1 / (0.25 - (16 / (1 + k^2))^2))

k = sqrt(1 / (0.25 - 256 / (1 + k^2)^2))

k = sqrt((1 + k^2)^2 / (256 - (1 + k^2)^2))

k = sqrt((1 + k^4) / (256 - 1 - 2k^2 - k^4))

k = sqrt((k^4 + 1) / (255 - 2k^2))

We can then solve for the roots of this equation to find the possible values of k:

k = sqrt((k^4 + 1) / (255 - 2k^2))

k^4 - (255 - 2k^2)k^2 + 1 = 0

This is a quartic equation and can be solved using the quartic formula:

k = sqrt((-b +- sqrt(b^2 - 4ac)) / 2a)

where a, b, and c are the coefficients of the polynomial. In this case, a = 1, b = -(255 - 2k^2), and c = 1.

Substituting these values into the quartic formula, we get:

k = sqrt((-(-(255 - 2k^2)) +- sqrt((-(255 - 2k^2))^2 - 4 * 1 * 1)) / 2 * 1)

k = sqrt((255 - 2k^2 +- sqrt((255 - 2k^2)^2 - 4)) / 2)

k = sqrt((255 - 2k^2 +- sqrt(255^2 - 510k^2 + 4k^4)) / 2)

k = sqrt((255 - 2k^2 +- sqrt(255^2 - 510k^2)) / 2)

k = sqrt((255 - 2k^2 +- sqrt(65025 - 510k^2)) / 2)

Solving for the roots of this equation gives us the possible values of k:

k = (-255 + sqrt(65025 - 510k^2)) / 2

k = (-255 - sqrt(65025 - 510k^2)) / 2

The first equation gives us one possible value of k:

k = (-255 + sqrt(65025 - 510k^2)) / 2

Substituting k = (-255 + sqrt(65025 - 510k^2)) / 2 into the second equation gives us the second possible value of k:

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510k^2)) / 2)^2)) / 2

Simplifying this expression gives us the final possible value of k:

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510((-255 + sqrt(65025 - 510k^2)) / 2)^2)) / 2)^2)) / 2

Therefore, the possible values of k are:

k = (-255 + sqrt(65025 - 510k^2)) / 2

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510k^2)) / 2)^2)) / 2

solve for k in each

To solve for k in the first equation, we can isolate k by moving everything else to the right side of the equation:

k = (-255 + sqrt(65025 - 510k^2)) / 2

2k = -255 + sqrt(65025 - 510k^2)

2k + 255 = sqrt(65025 - 510k^2)

(2k + 255)^2 = 65025 - 510k^2

4k^2 + 1020k + 65025 = 65025 - 510k^2

4k^2 + 1530k + 65025 = 0

This is a quadratic equation, and we can use the quadratic formula to solve for k:

k = (-b +- sqrt(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the polynomial. In this case, a = 4, b = 1530, and c = 65025.

Substituting these values into the quadratic formula gives us:

k = (-1530 +- sqrt(1530^2 - 4 * 4 * 65025)) / 2 * 4

k = (-1530 +- sqrt(3080400 - 2601000)) / 8

k = (-1530 +- sqrt(477900)) / 8

k = (-1530 +- sqrt(222725)) / 8

k = (-1530 + 1475) / 8

k = (-55) / 8

k = (-1530 - 1475) / 8

k = (-3005) / 8

Therefore, the solutions to the first equation are:

k = (-55) / 8

k = (-3005) / 8

IT is found that the value of x is 4 and value of y is 5.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The given system of equations are

2x-6y=22

-5x+y=1

The matrix form is

[tex]\left[\begin{array}{ccc}2&-6\\-5&1\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}22\\1\end{array}\right][/tex]

Let as assume

[tex]A = \left[\begin{array}{ccc}2&-6\\-5&1\end{array}\right]\\ \\X = \left[\begin{array}{ccc}x\\y\end{array}\right] \\B = \left[\begin{array}{ccc}22\\1\end{array}\right][/tex]

WE know that AX = B

Then we have;

[tex]\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}4\\5\end{array}\right][/tex]

Therefore, the value of x is 4 and value of y is 5.

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ1

Answer:

y = 4

Step-by-step explanation:

substitute x = 3 into the equation

y = 6(3) - (9 + 5) = 18 - 14 = 4

Answer: y=4

Step-by-step explanation:

y=6(3)-(9+5)

y=18-14

y=4

The equation of function for the given problem is y = 3x + 12.

What is point slope form of the line?

For linear equations, the general form is y - y1 = m(x - x1).

It draws attention to the line's slope and one of the line's points (that is not the y-intercept).

Given:

A bathtub has some water in it. Mia turns on the faucet to add more water.

The total amount of water in gallons, y, is a function of the time in minutes since Mia turns on the faucet, a.

The graph of the linear function passes through the points (4, 24) and

(6, 30).

We have to find the equation of function.

Let the linear function passes through the points (4, 24) and (6, 30).

First to find the slope of equation using given points.

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{30-24}{6-4} = \frac{6}{2} = 3[/tex]

Now to find the equation of function.

Consider the point slope form of the line,

[tex]y-y_1=m(x-x_1)[/tex]

Plug the values of m = 3 and [tex](x_1,, y_1) = (4, 24)[/tex]

⇒

[tex]y-24=3(x-4)\\y-24=3x-12\\y=3x-12+24\\y=3x+12[/tex]

Hence, the equation of function for the given problem is y = 3x + 12.

To know more about point slope form of line, click on the link

https://brainly.com/question/29797287

#SPJ1

P(n) = 1³ +2³ +···+n³ = (n(n+1)/2)²

P(1) = 1³ = 1

According to statement P(n) = (n(n+1)/2)²

Checking for n = 1,

(n(n+1)/ 2)² = (1(1+1)/ 2)²

P(1) = (1 × 2/ 2)²

P(1) = 1² = 1

P(1) = 1³ = 1

So P(n) holds for n = 1.

The inductive hypothesis is that the statement holds for P(n). To prove this the inductive step under the assumption that the inductive hypothesis is true, we prove it is true for P(n + 1)

Let us assume P(n) = 1³ + 2³ + ... + n³ = (n(n+1)/ 2)²

Then P(n + 1) = 1³ + 2³ + ... + n³ + (n + 1)³ = (n(n+1)/ 2)² + (n + 1)³

P(n + 1) = (n(n+1)/ 2)² + n³ + 3n² + 3n + 1

P(n + 1) = ((n + 1)((n + 1) + 1)/ 2)²

As assuming P(n) holds, it is also true for P(n + 1) so it will be true for all values of n as it is proved already that P(1) is true.

To know more mathematical induction

https://brainly.com/question/29503103

#SPJ4

Answer:

215

Step-by-step explanation:

218+212/2

Answer:

Answer. it is -111 because it is greater than 112 and in positive form it is smaller and in negative it is bigger .