For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1 (based on data from the National Health Survey). Hypertension is commonly defined as a systolic blood pressure above 140. If a woman between the ages of 18 and 24 is randomly selected, find the probability that her systolic blood pressure is greater than 140.

Step-by-step explanation:

the average velocity of a car that travels 50 km in 2 hrs = 50/2 = 25 km/hrs

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

WHat is Divisibility?

Divisibility is a mathematical property that describes whether one number can be divided evenly by another number without leaving a remainder. If a number is divisible by another number, it means that the division process results in a whole number without any remainder. For example, 15 is divisible by 3

To prove that 4 evenly divides 11n - 7n for any positive integer n, we can use mathematical induction.

Base Case:

When n = 1, 11n - 7n = 11(1) - 7(1) = 4, which is divisible by 4.

Inductive Step:

Assume that 4 evenly divides 11n - 7n for some positive integer k, i.e., 11k - 7k is divisible by 4.

We need to prove that 4 evenly divides 11(k+1) - 7(k+1), which is (11k + 11) - (7k + 7) = (11k - 7k) + (11 - 7) = 4k + 4.

Since 4 evenly divides 4k, and 4 evenly divides 4, it follows that 4 evenly divides 4k + 4.

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

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Step-by-step explanation:

because when the exponent is an odd number a negative number stays negative

and when the exponent is an even number the sign changes and a negative number becomes positive

Answer:

Angle S

Step-by-step explanation:

The two triangles are similar, with the reason of (corr. angles, similar triangles), we get that angles S = angle N

She can select one freshman and one sophomore in 72 ways.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is Phyllis who wants to select one freshman and one sophomore to attend a conference. She teaches 8 freshman and 9 sophomores

Total number of possible combinations are -

C[8,1] x C[9,1]

8!/(7! x 1!) x 9!/(8! x 1!)

8 x 9

72

Therefore, she can select one freshman and one sophomore in 72 ways.

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Answer:

A. 16.2 cm

Step-by-step explanation:

I took the test

The width of ornament is 16.2 cm.

The formula for the volume of a sphere is V = 4/3 πr³.

As, the ornament is in shape of sphere.

Volume of sphere= 4/3 * π * r³

2226.09 = 4/3* 3.14 *  r³

r³= 2226.09  * 3 / 4*3.14

r³= 6,678.27  / 12.56

r³ = 531.7093949044586

r= 8.101

Hence, width = 2* 8.101= 16.2 cm

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a. The amount of minutes it will take for the two pools to have thesame amount of water is 24 minutes

b. The amount of water in each pool is 1098liters

Simultaneous equations are two or more algebraic equations with the same unknown variables and the same value of the variables satisfies all such equations. This implies that the simultaneous equations have a common solution. Some of the examples of simultaneous equations are: 2x - 4y = 4, 5x + 8y = 3.

Represent the number of minutes it will take the two pool to have thesame amount y be x

therefore ;

y = 654+ 18.5x equation 1

y = 0+ 45.75x equation 2

from equation 2, y = 45.75x

substitute 45.75x for y in equation 1

45.75x = 654+ 18.5x

collect like terms

654 = 45.75x - 18.5x

654 = 27.25x

x = 654/27.25

x= 24minutes

from equation 2,

y = 0 + 45.75 × 24

y = 1098 litres

therefore at 24minutes the first and second pool will have the same volume of water of 1098litres

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The water in each pool when they have the same amount will be 1098 liters.

An equation simply has to do with the statement that illustrates the variables given.

In this case, two pools are being filled with water. To start, the first pool contains 654 liters of water and the second pool is empty. Water is being added to the first pool at arate of 18.5 liters per minute.

Water is being added to the second pool at a rate of 45.75 liters per minute.

Let the minute be represented by m. The equation will be:

653 + 18.5m = 45.75m

Collect the like terms

45.75m - 18.5 m = 654

27.25m = 654

Divide

m = 654 / 27.25

m = 24 minutes

The water in each pool when they have the same amount will be:

= 45.75 × 24

= 1098 liters

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Answer:

It is C

Step-by-step explanation:

To get the new coordinates you would move the shape up the y-axis 8 times, and right on the x-axis 8 times as well.

Answer:

C

Step-by-step explanation:

You can either compare two similar points or just count the units on the graph

Answer:

Alex has twice as much money as Jennifer.

a = 2j

Jennifer has $6 less than Shannon.

j = s-6

j+6 = s

All together the three friends have $54.

a + j + s = 54

Replace a and s

2j + j + (j+6) = 54

4j = 54 - 6

4j = 48

j = 48/4

j = 12  

Jennifer has $12

Alex= 2*12 = $24

Shannon = 24+12+s = 54

= 36+s = 54

s = 18

Shannon has $18

Answer:

1/30

Step-by-step explanation:

P(champion)= 1/30

Answer:

15.45

Step-by-step explanation:

add everything together and divide by ten% and you should get 6.25 then you add 5.00, 2.10, 2.10, and 6.25 together to get 15.45

If the standard deviation of a set of data is 6, then the value of variance is 36

The formula for determining variance is variance = √Standard deviation

Variance of a set of data is equal to square of the standard deviation.

If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula

variance = √Standard deviation

Take square root on both sides

Standard deviation² = 6²

Standard deviation= 36

Hence,  standard deviation of a set of data is 6, then the value of variance is 36

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The breadth of the rectangle is 3.4353 cm

What is rectangle?

A rectangle is a type of quadrilateral with parallel sides equal to each other and four equal 90-degree vertices. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Area, A= 25.25 square cm

length, l = 7.35 cm

let b= breadth

Formula:

Area of a rectangle, A = l * b

                          25.25 = 7.35 * b

                            => b =  25.25 / 7.35   =  3.4353 cm

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Answer:

SLOPE IS = 2

Step-by-step explanation:

to find the slope you should remeber the slope equation:

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

\((x_{1} ,y_{1} )=(-4,-1)\\(x_{2} ,y_{2} )=(-3,1)\)

\(M=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\\M=\frac{1-(-1)}{-3-(-4)}\)

\(M=\frac{2}{1} \\M=2\)

SLOPE IS =2

We can expect 30 guests to receive free admission out of the 1500 guests expected this weekend.

To determine how many guests can be expected to receive free admission, we need to use the given information about the ratio of guests with coupons to guests without coupons. We can do this by setting up a proportion and solving for the unknown variable.

Let x be the number of guests we can expect to receive free admission.
1/50 = x/1500

Cross-multiplying gives us:
50x = 1500

Dividing both sides by 50 gives us:
x = 30

Therefore, we can expect 30 guests to receive free admission out of the 1500 guests expected this weekend.

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Answer:

3/5 cups of sugar

Step-by-step explanation:

If 1/5 of a cup of sugar is used for 1/3 of a gallon of lemonade, 1/5 of a cup will be used in each of the overall three thirds of a gallon.

Answer:

3/5 cup of sugar good luck

Answer:

5.7×-1.2=-7.14

Step-by-step explanation:

+5.7(×)-1.3

+(×)- = -(it gives a negative answer)

so you multiply 5.7 and 1.3= 7.14

you just add a negative sigh to the ans

answer=-7.14

please consider a brainlest question

run towards it and throw stuff at it

Answer: A. run away from it

The African black mamba is the fastest moving land snake at 16-20 km/h. A person—regardless of how scared they are—could easily escape and outpace that snake with no problem. In reality, there's no need to run at all. The snake won't attack you unless you provoke it (i.e., don't do what option B, C, or D suggests), and snakes are probably more scared of us than we are of them. If I could add an option, I'd add: E. Leave it alone or keep still. If it moves towards you, slowly back off, and if it moves again, keep still, and then move slowly. The snake will eventually back off unless you do something to agitate it.

Question 37:  The following is a solution to the differential equation y = t - 1. d.

Question 38:  The tea temperature be after a very long time is dT/dt = k(S - T); T ≈ 20 degrees after a very long time. a.

To determine the solution to the given differential equation: t²(d²y/dt²) - 6t(dy/dt) + 12 = 0, we can solve the equation by assuming a solution in the form of y = tⁿ, where n is a constant.

By differentiating y with respect to t, we can substitute the derivatives into the differential equation to determine the value of n.

Let's differentiate y = tⁿ with respect to t:

dy/dt = n × tⁿ⁻¹

d²y/dt² = n(n-1) × tⁿ⁻²

Substituting these derivatives into the differential equation:

t²(n(n-1)tⁿ⁻²) - 6t(ntⁿ⁻¹) + 12 = 0

Simplifying the equation:

n(n-1)tⁿ - 6ntⁿ + 12 = 0

n(n-1)tⁿ - 6ntⁿ = -12

Since this equation must hold for all values of t, the coefficients of the tⁿ terms on both sides of the equation must be equal.

We can equate the coefficients:

n(n-1) = 0

n = 0 or n = 1

The general solution to the differential equation is y = c₁ + c₂ × t, where c₁ and c₂ are constants.

According to Newton's law of cooling, the rate of change of the temperature T of an object is proportional to the temperature difference between the object's temperature T and the surroundings' temperature S.

We can write the differential equation as follows:

dT/dt = k(S - T)

dT/dt represents the rate of change of temperature, k is the proportionality constant, and (S - T) represents the temperature difference between the object and the surroundings.

The cup of tea starts at 100 degrees and cools to 50 degrees in 3 minutes, with the room temperature at 20 degrees.

We can assume that the temperature of the tea will tend toward the room temperature as time goes to infinity.

This option correctly represents that as time goes to infinity, the temperature T of the tea will approach the temperature S of the surroundings, which is approximately 20 degrees.

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Answer:

original box wasn't given... atleast send original surface area..

Step-by-step explanation:

^^^^^^!!!!!!!!!!^^^^^^

The yy-component of vector a a is -y-direction, which is equal to 0 m/s2.the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.

Given a vector, a⃗ a→ = (5.0 m/s2, −y−direction)Find the yy -component of the given vector a⃗ a→.Solution: The yy-component of the given vector a⃗ a→ = -y-directionTo find the yy-component of the given vector a⃗ a→, we have to take the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.Therefore, the yy-component of vector a⃗ a→ is :a_yy = -y-direction = (-1)(0) = 0 m/s²  Answer: 0 m/s².

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The yy-component of vector a⃗ a→ is -y-direction.

The yy-component of a vector represents the magnitude of the vector in the y-direction.

In this case, the vector a⃗ a→ is given as (5.0 m/s2, −y-direction).

Since the yy-component is the magnitude in the y-direction, the yy-component of the vector a⃗ a→ is -y-direction.

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Answer:

=6

Step-by-step explanation:

\(\huge{\textbf{\textsf{{\color{navy}{An}}{\purple{sw}}{\pink{er}} {\color{pink}{:}}}}}\)

B. 3

The type of order that requires the government to offer specific and articulable facts showing reasonable grounds to believe that the contents of a wire or electronic communication, or the records or other information sought, are relevant and material to an ongoing criminal investigation is a search warrant.

A search warrant is a legal document issued by a court that authorizes law enforcement agencies to search a specific location, such as a person's property, premises, or electronic communication devices, for evidence related to a criminal investigation.

To obtain a search warrant, the government must provide specific and articulable facts to the court, demonstrating reasonable grounds to believe that the requested information or communication contents are relevant and material to the ongoing investigation.

This requirement helps ensure that the government has a valid reason and sufficient evidence to conduct the search and obtain the sought-after information.

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The y-intercept of the sample regression line is approximately 1.9854.

To find the y-intercept of the sample regression line, we can use the following formula:

y-intercept (b₀) = (Σy - b₁ * Σx) / n

where b₁ is the slope of the regression line, n is the number of observations, Σx and Σy are the sums of the x and y values respectively. To find b₁, we use the formula:

b₁ = (n * Σ(xy) - Σx * Σy) / (n * Σ(x²) - (Σx)²)

We are given:
n = 27
Σy = 57.2
Σx = 1253.4
Σ(xy) = 3133.7
Σ(x²) = 73296.4

First, let's find b₁:

b₁ = (27 * 3133.7 - 1253.4 * 57.2) / (27 * 73296.4 - 1253.4²)
b₁ ≈ -0.0236

Now, we can find the y-intercept (b₀):

b₀ = (57.2 - (-0.0236) * 1253.4) / 27
b₀ ≈ 1.9854

Therefore, we can state that the y-intercept of the sample regression line is approximately 1.9854.

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Answer:

1.2 minutes per lap

Step-by-step explanation:

Answer:

See below ↓↓

Step-by-step explanation:

Equation of line k

a. parallel line

b. perpendicular line

Answer:

p=60

Step-by-step explanation:

p=4(15)

p=60