the mean systolic blood pressure of all healthy adults is less than 122 mm Hg. Simple data for 281 healthy adults, the mean systolic blood pressure level is 119.87 mm Hg and the standard deviation is 15.21 mm Hg. Complete part a and b. express the original claim in symbolic form. Let the parameter represent a value with respect to systolic blood pressure for a healthy adult

Answer:

A

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 6, - 6) and (x₂, y₂ ) = (6, 0) ← 2 points on the line

m = \(\frac{0-(-6)}{6-(-6)}\)= \(\frac{0+6}{6+6}\) = \(\frac{6}{12}\) = \(\frac{1}{2}\)

Answer:

We use the rule,

\((a^b)^c = a^{bc}\)

a. (10^7)²

\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)

10^14

b. (10^9)³

\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)

10^27

c. (10^6)³

\(10^{(6)(3)}= 10^{18}\)

10^18

d. (10^2)³

\(10^{(2)(3)} = 10^{6}\)

10^6

e. (10³)²

\(10^{(3)(2)}=10^{6}\)

10^6

f. (10^5)^7

\(10^{(5)(7)} = 10^{35}\)

10^35

Step-by-step explanation:

The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

= (x + 2) (x + 3) (x - 1)

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

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Answer:

Step-by-step explanation:

Given that Ruben's distance from Barstow is d = |210 -60t|, you want to know the time t when he is exactly 90 miles from Barstow.

The absolute value will be 90 when the argument of the function is either -90 or +90.

The question resolves to two equations:

These two-step linear equations can be solved in the usual way:

Then ...

Ruben is 90 miles from Barstow after driving 2 hours, and again after driving 5 hours.

We can write k(x) as the composition of g(x) and f(x).

k(x) = g(f(x))

A composition of two functions means that we need to evaluate one function in the other one.

Here we have the functions:

f(x)=  x²

g(x) = √(x - 1)

h(x) = 2x + 3

And we know that:

k(x) = √(x² - 1)

So we have a square root, then we need to evaluate g(x), and the argument is a square, then we need to evaluate in f(x), the composition is:

k(x) = g(f(x))

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Answer:

380 seconds

Step-by-step explanation:

Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360

Now add the 20 seconds.
360 + 20 = 380

6 minutes and 20 seconds are equal to 380 seconds.

log₂ 24 can be expressed as 3 + log₂ 3 in terms of prime factors, using the properties of logarithms.

To express log₂ 24 in terms of prime factors, we can use the properties of logarithms and the fact that any positive integer can be expressed as a product of prime factors.

First, let's find the prime factorization of 24.

24 can be divided by 2, so we have 24 = 2 × 12.

12 can be divided by 2, so we have 12 = 2 × 6.

6 can be divided by 2, so we have 6 = 2 × 3.

Therefore, the prime factorization of 24 is 2 × 2 × 2 × 3, or 2³ × 3.

Now, using the properties of logarithms, we can express log₂ 24 as the sum of logarithms of its prime factors.

log₂ 24 = log₂ (2³ × 3)

According to the properties of logarithms, we can separate the factors inside the logarithm as individual terms:

log₂ (2³ × 3) = log₂ 2³ + log₂ 3

Since log₂ 2³ is equal to 3, we can simplify the expression further:

log₂ (2³ × 3) = 3 + log₂ 3

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The property illustrated in equation 4(-8+5) = -32 + 20 is the Distributive Property.

The Distributive Property states that when a number is multiplied by a sum or difference in parentheses, it can be distributed or multiplied by each term inside the parentheses separately, and then the results can be added or subtracted.

In this case, the number 4 is multiplied by the sum (-8 + 5). By applying the Distributive Property, we distribute the 4 to each term inside the parentheses:

4(-8 + 5) = (4 * -8) + (4 * 5)

This simplifies to:

4(-8 + 5) = -32 + 20

Finally, we can perform the addition:

-32 + 20 = -12

Therefore, the equation demonstrates the application of the Distributive Property.

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Answer:

A and C

Step-by-step explanation:

A. Like terms have the same variable like -6y and 7y. If it was -6y squared and 7y, they would NOT be like terms.

B. 6 is a coefficient (number), not a variable.

C.  5 is the coeffecient (it 's being multiplied by x)

D. A constant term is a number.

An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

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Answer:

x = 7

Step-by-step explanation:

yeah

Answer:

x = 7

Step-by-step explanation:

-4x - 3 = -3x - 10\\ \\

      +3           +3

-4x = -3x + 7

+3x    +3x

-x = 7

/-1  /-1

x = 7

Using translation concepts, we have that:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For function f(x), the multiplication by -1 of the function is in the output, meaning that it was a reflection over the y-axis. For function g(x), the multiplication is in the input, the domain, hence the reflection was over the x-axis.

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Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

1 + 1 ÷ 10 - 20

1 + 0.1 - 20 (Starting with

Answer: -24

Step-by-step explanation:

I am assuming you want the value of (f × g)(-2)

\(f(-2)=(-2)^2+4\\f(-2) = 4+4\\f(-2)=8\)

\(g(-2)=2(-2)+1\\g(-2)=-4+1\\g(-2)=-3\)

8 × -3 = -24

Answer:

14+22i

Step-by-step explanation:

We multiply and simplify (3-5i)(-2+4i)​ to get:

14 + 22i

A complex number is a number of the form a + bi, where a and b are real numbers, and i is an imaginary unit satisfying i² = -1. For example, 2 + 3i is a complex number.

Complex numbers can be multiplied using the following rules:

(a + bi)(c + di) = (ac - bd) + (ad + bc)i

Thus, the two complex numbers can be multiplied and simplified as follow:

(3-5i)(-2+4i)​ = 3(-2+4i)​ -5i(-2+4i)​

                    = 3(-2) + 3(4i) -5i(-2) -5i(4i)

                    = -6 + 12i + 10i -20i²

                   = -6 + 22i + 20    (Note: i² = -1)

                   = -6 + 20 + 22i

                   = 14 + 22i

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Answer:

Step-by-step explanation:x=3 y=-1

Answer:

8x - 2

Step-by-step explanation:

2x + 3 - (5 - 6x) ← distribute parenthesis by - 1

= 2x + 3 - 5 + 6x ← collect like terms

= (2x + 6x) + (3 - 5)

= 8x + (- 2)

= 8x - 2

The estimated arrival time of the train in San Diego is 4:16 PM.

To find the arrival time, we must add the length of the trip to the starting time.

The trip is 4 hours and 26 minutes long, so we must add 4 hours, which is equivalent to 240 minutes, and 26 minutes to the starting time of 11:50 AM.

This results in a final time of 4:16 PM.

The drawing that shows the line segments ab, ac, bd is attached.

A point in used to represent a location, it has no size i.e. no magnitude. A line is defined as a straight path that connects points that extends infinitely in two directions.

A ray is a line with a single endpoint that extends infinitely in one direction.

The drawing that shows the line segments ab, ac, bd is attached.

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Answer:

12 units?

Step-by-step explanation:

Answer:

y = \(\sqrt{55}\)

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(altitude)² = product of parts of hypotenuse

then

y² = 11 × 5 = 55 ( take square root of both sides )

y = \(\sqrt{55}\)

Answer:

D) any number that isn't a perfect square is irrational

Step-by-step explanation:

Answer:

D                              PLEASE MARK BRANLIEST

Answer:

5 years : 1781.52

20 years: 2984.68

Answer:

\(\frac{1}{x^21y^12}\)

Step-by-step explanation:

The total wage bill for hiring 3 students to deliver the catalogues and leaflets will be 3 x £51.30 = £153.90.

Number is an abstract concept used to count, measure and identify a quantity. It is a fundamental part of mathematics, and is also used in many other fields, such as physics and computing. Numbers can represent both discrete, such as the number of people in a room, and continuous, such as the temperature outside. Numbers are also used to represent abstract ideas, such as the amount of money in a bank account.

In order to calculate the minimum number of students needed to deliver the catalogues and leaflets, we need to calculate how many catalogues and leaflets can be delivered in 8 hours by one student.

16 catalogues and 90 leaflets can be delivered in 1 hour by one student. Therefore, 128 catalogues and 720 leaflets can be delivered in 8 hours by one student.

Therefore, the total number of catalogues and leaflets that can be delivered in 8 hours by one student is 848 (128 + 720).

Since the total number of catalogues and leaflets to be delivered is 384 + 1890 = 2274, the minimum number of students required to deliver all the catalogues and leaflets is 3 (2274 / 848 = 2.67).

Therefore, the total wage bill for hiring 3 students to deliver the catalogues and leaflets will be 3 x £51.30 = £153.90.

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Answer:

During the first four minutes, the temperature of the chicken soup is decreasing at a faster average rate than the temperature of the clam chowder.

Step-by-step explanation:

A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.

Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.

Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.

Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of

To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).

First, let's convert the fractions 1/5 and 2/3 to fifteenths:

\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)

\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)

Now we can rewrite the expression using the common denominator:

\(3 + \frac{3}{15}+\frac{10}{15}\)

Answer:

Angle C =  45°

Step-by-step explanation:

Hello There!

If you didn't know opposite angles are congruent in parallelograms

So ∠A≅∠C and ∠B≅∠D

So if ∠A = 45° then ∠C also equals 45°

As it is a parallelogram

\(\\ \sf\longmapsto <B\cong <D\)

\(\\ \sf\longmapsto <A\cong <C\)

\(\\ \sf\longmapsto <C=<A=45°\)