to investigate whether the consumption of beetroot juice enhances exercise performance, a researcher selected a random sample of 50 student athletes from all the student athletes at a college. the athletes in the sample were randomly assigned to one of two groups. in one group, 25 athletes were given a daily dose of beetroot juice, and in the other group, the remaining athletes were given a daily dose of a placebo. at the end of six weeks of exercise training, the researcher compared the performances of the two groups. based on the design of the investigation, which of the following is the largest population to which the results can be generalized?
(A) The 25 student athletes assigned to the beetroot juice group (B) The 50 student athletes in the sample (C) All student athletes at the college (D) All students at the college (E) All people who exercise

Answer:

c) 27.9

Step-by-step explanation:

Since MN is the midsegment ,

MN = (AB + CD)/2

21.1 = (AB + 14.3)/2

21.1*2 = AB + 14.2

AB = 42.2 - 14.2

AB = 27.9

Answer:

C

Step-by-step explanation:

the midsegment is equal to half the sum of the parallel bases, that is

\(\frac{1}{2}\) (AB + CD) = MN ( substitute values )

\(\frac{1}{2}\) (AB + 14.3) = 21.1 ( multiply both sides by 2 to clear the fraction )

AB + 14.3 = 42.2 ( subtract 14.3 from both sides )

AB = 27.9 cm

Answer:

100/250*100= 40%

Step-by-step explanation:

40%

2 1/2m = 250 cm

250cm .............100%

100cm ..................x%

x = 100cmx100%/250 cm

= 10000%/250

= 40%

The area of triangle is 460.89 unit square.

Given:

lengths of rod, a = 29 and b = 36 ,

angle between them (θ) = 62

We know that in a general triangle of side a,b,c and angles A,B,C ,

we can write area of triangle (Δ) is

 Δ = absinθ/2

Δ =  29*36sin62/2

Δ = 460.89 unit square.

hence, the area of triangle is 460.89 unit square.

#123

The area of the SAS triangle is 460.89 cm³.

Given data;

Side length (a) = 29

Side length (b) = 36

With an angle of Ф = 62°

Here, it is stated that the triangle is a SAS triangle which is known as the Side Angle Side triangle.

Now, to calculate the area of a given triangle, we use the formula as;

Area = a*b*sinФ/2

From the above formula;

Area of the SAS triangle = a*b*sinФ/2

                                         = [29*36*sin(62°)]/2

                                         = 460.89 cm³

Hence, the area of the SAS triangle is 460.89 cm³.

To learn more about Area click here:

brainly.com/question/27683633

#SPJ4

Answer:

6 hours

Step-by-step explanation:

In one trip, the plane will fly 51 minutes (510:10=51).

In seven trips, the plane will fly 357 minutes (51.7=357)

1 hour=60 minutes

357:60=5.95

5.95 rounded to the nearest whole hour is 6 hours.

Answer: D. -1(3x+2)(x+1)

Step-by-step explanation: First, use the F.O.I.L. method (First, Outer, Inner, Last). Then combine all your like terms. After, multiply the whole outcome by negative one. So, 3\(x^{2}\) turns into -3\(x^{2}\); 5x turns into -5x; and 2 is -2. BOOM! you got the exact right answer.

Answer:

D. 1/5^15

Step-by-step explanation:

When an exponent is negative you need to get the reciprocal to make it positive.

Answer: you chose the correct answer, d, if the exponent is negative you need to find it’s reciprocal

Step-by-step explanation: 5 is a positive number but the exponent is not, in order for it to be positive the reciprocal is 1/5 because you are basically flipping the number 5 (which is equal to 5/1)

a) The work done by the force F = 5i + 3j + 2k on a body moving from the origin to the point (3, -1, 2) is 13 units.

b) A vector that is perpendicular to both u = -i + 2j - k and v = 2i - j + 3k is -6i - 7j - 3k.

a) The work done by a force F = 5i + 3j + 2k acting on a body that moves from the origin to the point (3, -1, 2) can be determined using the formula:

Work done = ∫F · ds

Where F is the force and ds is the displacement of the body. Displacement is defined as the change in the position vector of the body, which is given by the difference in the position vectors of the final point and the initial point:

s = rf - ri

In this case, s = (3i - j + 2k) - (0i + 0j + 0k) = 3i - j + 2k

Therefore, the work done is:

Work done = ∫F · ds = ∫₀ˢ (5i + 3j + 2k) · (ds)

Simplifying further:

Work done = ∫₀ˢ (5dx + 3dy + 2dz)

Evaluating the integral:

Work done = [5x + 3y + 2z]₀ˢ

Substituting the values:

Work done = [5(3) + 3(-1) + 2(2)] - [5(0) + 3(0) + 2(0)]

Therefore, the work done = 13 units.

b) To find a vector that is perpendicular to both u = -i + 2j - k and v = 2i - j + 3k, we can use the cross product of the two vectors:

u × v = |i j k|

|-1 2 -1|

|2 -1 3|

Expanding the determinant:

u × v = (-6)i - 7j - 3k

Therefore, a vector that is perpendicular to both u and v is given by:

u × v = -6i - 7j - 3k.

Learn more about force

https://brainly.com/question/30507236

#SPJ11

The improper fraction is 81/10.

Mixed number:

To convert a decimal to a mixed number, the whole number part of the decimal is written as the integer part of the mixed number, and the decimal part is written as the fraction part of the mixed number.

Therefore, to convert 8.1 to a mixed number, it will be written as

8.1 = 8 + 0.1

Thus, 8.1 as a mixed number is 8 1/10.

Improper fraction:

To convert a mixed number to an improper fraction, the following steps are taken:

a) The denominator of the fraction part is retained as the denominator of the improper fraction.

b) The numerator of the fraction part is added to the product of the integer part and the denominator.

c) The sum obtained in step b is the new numerator of the improper fraction.

Therefore,to convert 8 1/10 to an

improper fraction = (10 × 8) + 1/10

improper fraction = 80/10 + 1/10= 81/10

Thus, 8.1 as an improper fraction is 81/10.

For such more questions on improper fraction

https://brainly.com/question/19318336

#SPJ8

The hypotheses of Theorem 2.4.2 are satisfied when the points lie on the ty-plane. Specifically, the points should be in the region bounded by the inequality |ty| <=1.

Theorem 2.4.2 is also known as the Mean Value Theorem. It states that if a function f is continuous on a closed interval [a, b] and differentiable on an open interval (a, b), then there exists a number c in the interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a).

The hypotheses of the Mean Value Theorem are satisfied in the ty-plane at any point where the function is continuous and differentiable. This means that the function must have no breaks or sharp turns at that point. Additionally, the function must be defined at the endpoints of the interval [a, b] and must be differentiable on the open interval (a, b).

In the ty-plane, the hypotheses of the Mean Value Theorem are satisfied at any point that meets these conditions. For example, if the function f(t) = t^2 is graphed in the ty-plane, the hypotheses of the Mean Value Theorem are satisfied at any point on the curve because the function is continuous and differentiable at all points.

You can read more about hypotheses of Theorem at https://brainly.com/question/12446464

#SPJ11

Answer:

50°

Step-by-step explanation:

BC⊥CD

Sum of interior angles of ΔABC = 180

Therefore, m∠BAC = 180 - 90 - 40 = 50

Answer:

The answer is B

Step-by-step explanation:

I took the test.

As per the divisibility rule, the number is 6552

In math, the divisibility rule states that one to check whether a number is divisible by another number without the actual method of division here if a number is completely divisible by another number then the quotient will be a whole number and the remainder will be zero.

Here we have given that 655Δ i a 4-digit number with one of it digit represented by Δ. 655Δ is divisible by 3.

Here we have to find the missing digit in the given number.

Here we have given that the number is 655Δ.

And we have also given that the given number is divisible y 3.

So, here we must know the divisibility rule of 3.

The divisibility rule of 3 states that a number is completely divisible by 3 if the sum of its digits is divisible by 3.

So, based on these rules let us consider that x be the missing digit.

Then it can be written as.

=> [6 + 5 + 5 + x]/3

=> 16 + x/3

Here we put the value of x as 2, then we get 18, that is divisible by 3.

To know more about Divisibility rule here,

https://brainly.com/question/10703980

#SPJ4

When slave starting a disabled vehicle, the term that serves an important safety consideration is c. The slaving vehicle engine must be running while connecting the slave cable

The dead car is started while the live vehicle's engine is running by inserting a slave cable into the receptacle on each vehicle.

Vehicles with manual transmissions rely heavily on the clutch slave cylinder. When the pedal is depressed, the clutch is disengaged and the transmission is shifted thanks to the slave and clutch master cylinders.

Read more on vehicle here

https://brainly.com/question/30094730

#SPJ4

The set {a, b, c, d, e, f} has 2⁶ = 64 distinct subsets and 2⁶ - 1 = 63 distinct proper subsets.

A subset is any set of elements taken from a larger set. For example, {a, b} is a subset of {a, b, c}. A proper subset is any subset which does not contain all elements from the original set. For example, {a, b} is a proper subset of {a, b, c}, but {a, b, c} is not a proper subset of {a, b, c}.

To calculate the number of distinct subsets and proper subsets of a given set, we first need to determine the cardinality of the set (i.e. the number of elements it contains). In this case, the set contains 6 elements, so its cardinality is 6.

The number of distinct subsets for a given set is 2ⁿ, where n is the cardinality of the set. Thus, for our given set {a, b, c, d, e, f}, the number of distinct subsets is 2⁶ = 64.

The number of distinct proper subsets for a given set is 2ⁿ - 1, where n is the cardinality of the set. Thus, for our given set {a, b, c, d, e, f}, the number of distinct proper subsets is 2⁶ - 1 = 63.

To know more about proper subsets click on below link:

https://brainly.com/question/28705656#

#SPJ11

Answer:

Ray ZV and Ray WV

Step-by-step explanation:

The turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

Part A:
The radius of the turntable is half of the diameter, which is 6.0 in. The ladybug crawls in a straight radial line to the edge, which means its displacement vector is equal to the radius of the turntable. Therefore, the magnitude of the ladybug's displacement vector is 6.0 in.

Part B:
The direction of the ladybug's displacement vector is the same as the direction of the radial line from the center of the turntable to the edge. This direction can be described by the angle between the positive x-axis and the radial line.

Since the turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

Visit here to learn more about displacement vector  :  https://brainly.com/question/30466999
#SPJ11

Answer:

0.0275

Step-by-step explanation:

Linear Approximation:

L(x) ≈ 3 - 3x

A linear approximation is an estimation of a function using a tangent line at a specific point. In this case, we are given the function g(x) = 3/(1 + x) and we need to find its linear approximation, L(x), at a = 0.

To obtain the linear approximation, we first find the derivative of g(x) with respect to x. Taking the derivative of g(x) using the quotient rule, we get:

g'(x) = (-3)/(1 + x)²

Next, we evaluate g'(x) at x = 0 to find the slope of the tangent line at that point:

g'(0) = (-3)/(1 + 0)² = -3

The linear approximation, L(x), is given by the equation of the tangent line, which has the form y = mx + b, where m is the slope and b is the y-intercept. Plugging in the values we have:

L(x) = -3x + b

To find the y-intercept, we substitute x = 0 into the original function:

g(0) = 3/(1 + 0) = 3

Since the y-intercept of the tangent line matches the y-value of the function at that point, we have b = 3. Thus, the linear approximation is:

L(x) ≈ 3 - 3x

Learn more about: Linear Approximation:

brainly.com/question/30403460

#SPJ11

Answer:

-4

Step-by-step explanation:

Rearranging the terms of this polynomial in descending order by powers of x, we get 3x2 + 5x3 − 4x4 − 7x => -4x^4 + 5x^3 + 3x^2 - 7x.

-4x^4 is the leading power of x, and -4 is the "leading coefficient" of the polynomial.

Answer:

14x14 is 196

Step-by-step explanation:

Use a calculator lol 14x14 is simple

The product of the 14 x 14 is 196.

Given that we need to calculate 14 x 14,

To calculate 14 multiplied by 14, you simply multiply the two numbers together.

Here's the step-by-step process:

Start by multiplying the ones digit of the first number (4) by the ones digit of the second number (also 4).

4 x 4 = 16

Write down the ones digit of the result (6) and carry over the tens digit (1).

Next, multiply the tens digit of the first number (1) by the ones digit of the second number (4).

1 x 4 = 4

Add the carried over tens digit (1) to the result.

4 + 1 = 5

Write down the tens digit of the result (5) and carry over any remaining digits (none in this case).

Finally, multiply the tens digit of the first number (1) by the tens digit of the second number (1).

1 x 1 = 1

Write down the tens digit of the result (1).

Putting it all together, we get:

14 x 14 = 196

Operation:

   14

×  14

------

  56   (4 × 14)

+140  (10 × 14)

------

 196

Therefore, 14 multiplied by 14 equals 196.

Learn more about Multiplication click;

https://brainly.com/question/11527721

#SPJ6

Answer:

Step-by-step explanation:

The probability that the balls are both white be 1/7.

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.

Number of black balls = 4

Number of white balls = 3

Total number of balls = 7

Number of ways of picking up a white ball out of 7 balls, P(W) = 3/7

Number of ways of picking up a second white ball ,P(W) = 2/6

Therefore, the probability of picking up 2 white balls

P(WW) = 3/7 \(*\) 2/6 = 1/7

To learn more about probability, refer to:

https://brainly.com/question/7965468

#SPJ4

The fractional equivalent of the repeating decimal 0.2 is 2/9

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

Repeating decimal = 0.2

Represent properly

So, we have

Repeating decimal = 0.2222

Express as fraction

So, we have

Fraction = 2/(10 - n)

In this case

n = 1

So, we have

Fraction = 2/(10 - 1)

Evaluate

Fraction = 2/9

Hence, the fractional equivalent is 2/9

Read more about repeating decimal at

https://brainly.com/question/12407250

#SPJ1

The graph of f(x) = sin(x + 1/x^2) does not have horizontal asymptotes at y = 0 or y = 1, and it does not have a vertical asymptote at x = 0. Hence none of the statements are true.

To determine the properties of the function f(x) = sin(x + 1/x^2), let's analyze each statement individually:

1. The graph of f has a horizontal asymptote at y = 0:

To check if there is a horizontal asymptote at y = 0, we need to evaluate the limit of f(x) as x approaches positive or negative infinity.

lim(x→∞) sin(x + 1/x^2) = sin(∞) (which is undefined).

lim(x→-∞) sin(x + 1/x^2) = sin(-∞) (which is undefined).

Since the limits are undefined, we cannot conclude that there is a horizontal asymptote at y = 0.

2. The graph of f has a horizontal asymptote at y = 1:

We need to evaluate the limit of f(x) as x approaches positive or negative infinity.

lim(x→∞) sin(x + 1/x^2) = sin(∞) (which is undefined).

lim(x→-∞) sin(x + 1/x^2) = sin(-∞) (which is undefined).

The limits are undefined, so there is no horizontal asymptote at y = 1 either.

3. The graph of f has a vertical asymptote at x = 0:

A vertical asymptote occurs when the function approaches infinity or negative infinity as x approaches a particular value.

To check if there is a vertical asymptote at x = 0, we examine the behavior of f(x) as x approaches 0 from both the positive and negative sides:

lim(x→0+) sin(x + 1/x^2) = sin(∞) (which is undefined).

lim(x→0-) sin(x + 1/x^2) = sin(-∞) (which is undefined).

Since the limits are undefined, there is no vertical asymptote at x = 0.

To know more about horizontal asymptotes refer here:

https://brainly.com/question/4084552#

#SPJ11

Answer:

This population, the population is 45 fish.

Step-by-step explanation:

This problem can be solved by a rule of three.

Last year there were 60 fish in the lake. That was 100, that is, decimal 1.

This year it decreased 25%. So there 100%-25% = 75%, that is decimal 0.75. So

60 fish - 1

x fish - 0.75

x= 60*0.75

x=45

This population, the population is 45 fish. Please make the brainliest.

60-25% of 60 =number of fish this year

60-25/100 x 60

60-15

45 fish are present in the lake

Answer:

27 students

Step-by-step explanation:

b/c 1/4×60=15 students

3/10×60=18

18+15=33

60-33=27

brainlist please

The probability that the sum of the numbers rolled is either even or a multiple of 5 is 22/36 or 11/18.

The probability that the sum of the numbers rolled is either a multiple of 3 or a multiple of 4 is 20/36 or 5/9.

The outcomes of rolling two dices together are:

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6).

The sum of the outcomes on the dice are:

2, 3, 4, 5, 6, 7,

3, 4, 5, 6, 7, 8,

4, 5, 6, 7, 8, 9,

5, 6, 7, 8, 9, 10,

6, 7, 8, 9, 10, 11,

7, 8, 9, 10, 11, 12.

Now, we are asked for the probability that the sum of the numbers rolled is either even or a multiple of 5.

Favorable outcomes = 2, 4, 5, 6, 4, 5, 6, 8, 4, 5, 6, 8, 5, 6, 8, 10, 6, 8, 10, 8, 10, 12.

Thus, the number of favorable outcomes = 22.

The total number of outcomes = 36.

Thus, the probability that the sum of the numbers rolled is either even or a multiple of 5 is 22/36 or 11/18.

Now, we are asked for the probability that the sum of the numbers rolled is either a multiple of 3 or a multiple of 4.

Favorable outcomes = 3, 4, 6, 3, 4, 6, 8, 4, 6, 8, 9, 6, 8, 9, 6, 8, 9, 8, 9, 12.

Thus, the number of favorable outcomes = 20.

The total number of outcomes = 36.

Thus, the probability that the sum of the numbers rolled is either a multiple of 3 or a multiple of 4 is 20/36 or 5/9.

Learn more about the probability at

https://brainly.com/question/23955312

#SPJ4

The binomial 2a-1 smaller than the value of the binomial 7-1.2a by 7 for a =

What is binomial?

A mathematical expression consisting of two terms connected by a plus sign or minus sign.

According to the question

the value of binomial 2a-1 smaller than the value of 7-1.2a by 7

translating the statement into mathematical notation

we have

⇒ (7 - 1.2a) - ( 2a -1  )=7

⇒ 7 - 1.2a - 2a + 1 = 7

⇒ 8 - 3.2a = 7

⇒  3.2a = 8 - 7

⇒  3.2a = 1

⇒ a =    (dividing the above expression both the sides by 3.2)

Hence, value of a will be .

A  value of a equal to 0.25, the value of the binomial 2a-1 is seven less than the value of the binomial 7-1.2a.

To solve this problem, we need to set up an equation using the given information. The value of the binomial 2a-1 can be written as (2a-1)C(0) or simply (2a-1), since we are choosing 0 objects from the binomial. Similarly, the value of the binomial 7-1.2a can be written as (7-1.2a)C(0) or simply (7-1.2a).

We know that the value of (2a-1) is seven less than the value of (7-1.2a). In equation form, this is:

(7-1.2a) - (2a-1) = 7

Simplifying this equation gives:

8 - 3.2a = 7

Subtracting 8 from both sides and dividing by -3.2, we get:

a = 0.25

To learn more about : binomial

https://brainly.com/question/12336181

#SPJ11

Answer:

5/13

Step-by-step explanation:

CosineФ=Adj/H

=5/13