To test the effect of a new exercise routine on muscle growth, a researcher sets up the following experiment: 60 volunteers subjects (40 men and 20 women) of average build are selected to participate in the study. Their body mass and muscle sizes (biceps, thighs, etc.) are measured. The researcher gives all the men a DVD with the new exercise routine, and the women a DVD with a standard routine, but only the researcher knows this.
The results of the experiment are likely to be invalid mostly because .
The treatment group and control group were not the same size.
The subjects were volunteers.
The subjects did not know if they were getting the real treatment.
The gender of the subject is a confounding variable in this situation.

a)  The inverse function is obtained by rearranging the variables for temperature and height in the  given equation.

b)   T⁻¹(x) =41-x/1.25

c)  T⁻¹(30) =8.8

The given function is T(h)=41- 1.25h, so the inverse of a function is just obtained by rearranging the variables for height and temperature,  the variable of temperature is replaced by height and vice versa. for the second

T(h)=41- 1.25h,  considering h= x

=>T(x)=41- 1.25x

setting T(x)=x and x= T(x), we get  

41- 1.25T(x) =x

=>1.25T(x) =x -41

=>T(x) =x- 41/ 1.25

now setting T(x)= T⁻¹ (x) we get  : T⁻¹ (x) =41-x/1.25

For  T⁻¹(30) =41-30/1.25= 11/1.25 =8.8

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Answer:

24π m

Step-by-step explanation:

r = 12 m

C = 2πr

C = 2 × π × 12 m

C = 24π m

The sample proportion of defective item is 0.184

What is proportion ?

A part, share, or number that is measured in comparison to a whole is referred to as a proportion in general. When two ratios are equal, according to the definition of proportion, they are in proportion. It is a formula or claim that shows that two ratios or fractions are equal.

let x = number of defective items

       = 46

Let n = sample size

        = 250

Therefore , sample proportion of defective items given by

p = x / n

  = 46 / 250

  = 0.184

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The value of the standard deviation of the variance S is equivalent to 250 and the value of the variance (S) is equivalent to 62500.

Given that:

2Ax = 0.08

Ax = 0.2

A fully discrete whole life insurance issued to (x) is 1000.

Firstly we have to find out the value of variance S.

Variance S = (insurance issued)^2 * [2Ax - Ax^2]/(1- Ax)^2

Variance S = (1000)^2 * [0.08 -  0.2^2]/(1- 0.2)^2

Variance S = (1000)^2 * [0.04]/.64

Variance S = (1000)^2 * .0625

Variance S = 62500

Standard deviation of S = (insurance issued) * [[tex]\sqrt{2Ax - Ax^2}[/tex]]/(1- Ax)

Standard deviation = 1000 * [[tex]\sqrt{0.08 - 0.2^2}[/tex]]/(1- 0.2)

Standard deviation = 1000 * 0.2/0.8

Standard deviation = 1000 * 1/4 = 250

The value of the standard deviation of the variance S is equivalent to 250 and the value of the variance (S) is equivalent to 62500.

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The equation of the line is y = -1/4x + 15/4

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

Slope = -1/4

Point = (3, 3)

The equation of a line is calculated using

y = m(x - X) + Y

Where

m = Slope = -1/4

(x, y) = Point = (3, 3)

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

y = -1/4(x - 3) + 3

So, we have

y = -1/4x + 3/4 + 3

Evaluate

y = -1/4x + 15/4

Hence, the equation is y = -1/4x + 15/4

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1.239x10²⁴ different ways can the 26 different letters be arranged so that either the word "the" or the word "aid" are present.

Given that,

We have to find how many different ways can the 26 different letters be arranged so that either the word "the" or the word "aid" are present.

We know that,

Total number of arrangements of 26 different letters= 26!

Let A be the number of arrangements that contains 'the' = 24! ( Total no. Of alphabet= 26 subtract the number That contains 'the' i.e, 3 and add one for 'the' 26-23+1=24)

Let B be the number of arrangements that contains 'aid' = 24! (Total no. Of alphabet minus number of letter in 'aid' and add 'aid' as an alphabet i.e, 26-23+1= 24)

Total no. Of arrangements that contains either sequence 'the' or 'aid'

A or B= (A)+(B)- (A intersection B)

24! +24! -22! = 1.239x10²⁴

Therefore, 1.239x10²⁴ different ways can the 26 different letters be arranged so that either the word "the" or the word "aid" are present.

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Answer: I need the Problem?

Step-by-step explanation:

The amount of $34.65 is deducted from Ron’s gross wages for social security at 6.2% and Medicare at 1.5% .

Percentage means one part of every cent or hundred. And it is represented by symbol '%'.

Given that Ron earns $450 in gross wages on January 10.

To find deduction amount from Ron’s gross wages for social security at 6.2% ;

Firstly, we find  6.2% of $450 that is $450 x 6.2 / 100 = $27.9 and then we substract to the gross wages.

$450 - $27.9 = $422.1

Now to find 1.5 % of $450 that is 450 x 1.5/ 100 = $6.75 and then we substract to the gross wages.

$450 - $6.75 = $443.25

total deduction amount is $6.75 + $27.9 = $34.65

Therefore, $34.65 is deducted from Ron’s gross wages for social security at 6.2% and Medicare at 1.5%

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Answer:

Step-by-step explanation:

do 21 ÷ 4 = 5.25

Now we have 5.25 miles for each inch. So all we have to do is multiply 5.25 by 13 to find the answer:

5.25 × 13 = 68.25

Let me know if this helped!

Boxplot tells whether a quantitative variable and a categorical variable are associated.

The distributions of one or more sets of numerical data are shown using boxes and lines in a box plot (also known as a box and whisker plot).

With a centre line designating the median value, box limitations show the range of the centre 50% of the data. From each box, lines extend to represent the range of the remaining data, and dots are positioned beyond the line's margins to represent outliers.

Box plots are used to display the distributions of numerical data values, particularly when comparing them across various groups.

They provide a broad overview of the symmetry, skew, variance, and outliers in a set of data. It is simple to determine where the primary concentration of the data is and to compare different groups.

I've answered the question in general as the question is incorrect

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Using the table the quadratic equation is y = x² - 2

from the curve the quadratic equation is y = x² + 1

Quadratic equation is written of the form

y = a(x - h)² + k

from the table the vertex is

v(h, k) = v(0, -2)

substituting the values to the formula

y = a(x - 0)² - 2

y = ax² - 2

Using the point (2, 2) from the table

y = ax² - 2

2 = a * 2² - 2

2 = 4a - 2

4a = 2 + 2

4a = 4

a = 1

The equation of the curve is

y = x² - 2

from the graph the vertex is

v(h, k) = v(0, 1)

substituting the values to the formula

y = a(x - 0)² + 1

y = ax² + 1

Assuming a unit on the graph is a unit we take point (1, 2) where the curve passed

y = ax² + 1

2 = a * 1² + 1

2 = a + 1

a = 2 - 1

a = 1

The equation of the curve is

y = x² + 1

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The area of the polygons sorted in ascending order of area is:

Rectangle  = 4

Triangle = 12

Square = 13

In geometry, a polygon is a planar shape defined by a restricted number of straight line segments linked to form a closed polygonal chain.

Area of the triangle is:

[Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)]/2

Where Ax and Ay are the x and y coordinates of A's vertex. The same is true for the x and y notations of the B and C vertices.

Given,

A(-4-3), B(1, -3), C(-1,2)

We have

[-4(-3-2) + (1(2-(-3)) + (-1(-2-(-3))]/2

= 24/2

= 12

As a result, the area of the triangle is 12.

We use the distance formula to calculate the area of the rectangle. The equation is as follows:

d² = (x₂ - x₁)² + (y₂-y₁)²

Where (x₁, x₂) are the first point's coordinates and (y₁, y₂) are the coordinates of the second point.

Assuming that the vertices are labeled as follows:

A(7,9), B(6,9), C(6,5), D(7,5), then

AB² = (6-7)² + (9-9)²

AB² = 1 + 0

AB = 1

BC² = (6-6)² + (5-9)²

BC² = 0² + -4²

BC = 4

CD² = (7-6)² +(5-5)²

CD² = 1² + 0²

CD = 1

DA² = (7-7)² + (9-5)²

DA² = 0² +4²

DA = 4

As is typical of a rectangle, we can deduce that AB = CD and BC = DA

Since the Area of the rectangle is AB x CD OR BC x DA

The area of the rectangle =4 x 1 = 4

We may also calculate the length of the square's sides using distance methods.

We only need the length of one side because the area of a square is provided as L2.

Hence,

AB = 3.60555

Hence the area of the square =3.60555²

= 12.9999908025

Area of the square is 13

Thus, the polygons are placed in increasing area order as follows:

Rectangle = 4

Triangle = 12

Square = 13

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If a jar contains 15 red marbles and 14 blue marbles. If you reach in the jar and pull out 2 marbles at random, the probability that both are red is: 2/812.

Probability

Total marbles:

Total marbles=15+14

Total marbles = 29

Chance that a red will be pulled=2/29

Chance that the second marble will be red =1/28

Hence,

Probability :

Probability = 2/29*1/28

Probability = 0.00246

Therefore  If a jar contains 15 red marbles and 14 blue marbles. If you reach in the jar and pull out 2 marbles at random, the probability that both are red is: 2/812

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The fourth figure is a function as it passes the vertical line test.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

By vertical line test which is drawing a vertical line anywhere in a graph of a function if it only intersects only at one point, it is a function.

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Answer:

8 - 1/3x = 16

8-8 - 1/3x = 16-8

-1/3x=8

8/-(1/3)= -24

x= -24

Step-by-step explanation:

8- 1/3(-24)=16

Answer:

7

Step-by-step explanation:

if he gets $35 in 5 hours then he gets $7 an hour, and 7*7=49.

Answer: 7 hours

Step-by-step explanation:

$35/5 hours=$7 an hour

$49/$7 an hour=7 hours of mowing

P(4, 7.25) are the coordinates of circumcentre of the triangle

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of that particular triangle intersect

Given: The vertices R(-2,5), S(-6, 5), T(-2,-1)​

Let P(x,y) be the circumcentre of triangle. Then,

PR = PS = PT

PR² = PS²

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

(x+2)² + (y-5)² = (x+6)² + (y-5)²

x²+4x+4 + y²-10y+25 = x²+12x+36 + y²-10y+25

12x-4x = 36 -4

8x = 32

x = 32/8 = 4

Also, PS² = PT²

(x-(-6))² + (y-5)² = (x-(-2))² + (y-(-1))²

(x+6)² + (y-5)² = (x+2)² + (y+1)²

x²+12x+36 + y²-10y+25 = x²+4x+4 + y²+2y+2

12x-4x-10y-2y = 4+2-36-25

8x-12y = -55 .......(1)

put x= 4 into (1):

8x-12y = -55

8(4)-12y = -55

32 -12y = -55

-12y = -55-32

-12y = -87

y = 7.25

Therefore, the coordinates of circumcentre of the triangle are P(4, 7.25)

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Answer:

15. x = 4

16. x = 7

Step-by-step explanation:

15.

CD/ ED = DG / DF

48 / (5x - 2) = 40 / (2x + 7)

48 (2x + 7) = 40 (5x - 2)

96x + 336 = 200x - 80

200x - 96x = 336 + 80

104x = 416

x = 4

16.

ST / PL = TU / LM

(x + 1) / 72 = (2x - 3) / 99

99 (x + 1) = 72 (2x - 3)

99x + 99 = 144x - 216

144x - 99x = 99 + 216

45x = 315

x = 7

Answer:

15.  x = 4

16.  x = 7

Step-by-step explanation:

Similar Triangles

In similar triangles, corresponding sides are always in the same ratio.

If ΔCDG ~ ΔEDF then:

From inspection of the given diagram:

Therefore:

[tex]\implies \sf CD : ED = DG : DF[/tex]

[tex]\implies 48 : (5x-2) = 40 : (2x+7)[/tex]

[tex]\implies \dfrac{48}{(5x-2)} = \dfrac{40}{(2x+7)}[/tex]

[tex]\implies 48(2x+7)=40(5x-2)[/tex]

[tex]\implies 96x+336=200x-80[/tex]

[tex]\implies 416=104x[/tex]

[tex]\implies x=\dfrac{416}{104}[/tex]

[tex]\implies x=4[/tex]

If ΔSTU ~ ΔPLM then:

From inspection of the given diagram:

Therefore:

[tex]\implies \sf ST : PL = TU : LM[/tex]

[tex]\implies (x+1) : 72 = (2x-3) : 99[/tex]

[tex]\implies \dfrac{(x+1)}{72}= \dfrac{(2x-3)}{99}[/tex]

[tex]\implies 99(x+1)=72(2x-3)[/tex]

[tex]\implies 99x+99=144x-216[/tex]

[tex]\implies 315=45x[/tex]

[tex]\implies x=\dfrac{315}{45}[/tex]

[tex]\implies x=7[/tex]

True, With an 80-person sample size, we are selecting from a skewed-right distribution, hence the sampling distribution mean should likewise be skewed-right.

80 people make up the sample that was taken from the population distribution with a right skew. We may infer that the sampling distribution of the sample means would be close to normalcy given the size of the sample.

In general, the distribution is normal.

The central limit theorem states that as sample size increases, the sample mean distributions become normal, with standard deviations equaling n and mean values approximating the population mean, regardless of the underlying distribution's form. In other words, the sample means sampling distribution turns roughly normal.

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The predetermined overhead rate for the recently completed year was closest to $28.56 par labor - hour.

What is Labor - hour?

4 to 8 hours or more are typical for active labor. Your cervix will expand on average at a rate of 1 cm per hour. What you can do: Seek encouragement and support from your labor partner and your medical team. To ease your discomfort, try deep breathing and relaxation exercises.

Given:

Longobardi corporation bases its predetermined overhead rate on the estimated labor- hours for the upcoming year.

At the beginning of the most recently completed year, the corporation estimated the labor-hours for the upcoming year at 46,000 labor- hours.

The estimated variable manufacturing overhead was $6.25 per labor-hour and the estimated total fixed manufacturing overhead was $1,026,260.

The actual labor- hours for the year turned out to be 41,200 labor-hours.

Estimated total manufacturing overhead

= $1,026,260 + ($6.25 per labor- hour X 46,000 labor - hours)

= $1,313,760

Predetermined overhead rate

= $1,313,760 / 46,000 labor-hours

= $28.56 per labor-hour

Hence, the predetermined overhead rate for the recently completed year was closest to $28.56 par labor - hour.

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The expression to find out the total length of its beak and tongue that sticks out is b+t.

When Rufous-tailed hummingbird’s beak is 20 millimeters long and its tongue sticks out 8 millimeters, the length is 28 millimeters.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

From the information illustrated, Guevara’s feeders take pictures of the birds’ tongues sticking out as they sip nectar.

A hummingbird’s beak is b millimeters long and its tongue sticks out t millimeters past its beak.

The expression to find out the total length will be:

= Length of beak + Length of tongue

= b + t

The length when the hummingbird’s beak is 20 millimeters long and its tongue sticks out 8 millimeters is:

= 20 + 8

= 28 millimeters

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Cara has a 25/216 chance of waiting until her third throw before throwing a six.

for the stated question-

Total times the dice is thrown = 3.

Total number of sample space = 6 x 6 x 6 = 216.

The probability of coming six = 1/6

The probability of not coming six = 1 - 1/6 = 5/6.

Probability of getting 6 in third throw = 5/6 x 5/6 x 1/6

Probability of getting 6 in third throw = 25/216

Thus, Cara has a 25/216 chance of waiting until her third throw before throwing a six.

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A manager be interested in analyzing risk to determine a range of outcomes.

Project managers and their teams undertake risk analysis, such as calculating the likelihood of various undesirable outcomes affecting a project, to avoid or minimize their impacts. The process can help reduce exposure, time, and budget overruns and keep businesses in compliance.

Analyzing risk can help to uncover threats to the success of the projects or business operations, such as: vulnerabilities in security; potential litigations, penalties and non-compliance issues; and, mistakes in budget or scheduling.

In general, there are 4 accepted ways to respond to risks, those are: avoidance, mitigation, acceptance, and transfer.

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Answer:

log 58.875/ log 13

Step-by-step explanation:

log 58.875/ log 13

Answer:

i need points

Step-by-step explanation:

Answer:

y - 9 = -18/13(x + 5)

Step-by-step explanation:

Answer: $1.05 per orange

Step-by-step explanation:

12.33 - 2.88 = 9.45

9.45 ÷ 9 = 1.05

A shooter has a 27.92% chance of hitting the target at least 13 times.

This probability mass function in this type of binomial distribution is the quantity of successes ("x").

P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ

The required number of wins is five since we are concerned with the likelihood that target will be hit exactly five times.(i.e., x = 13).

P(X = 13) =  ¹⁵C₁₃. (0.89)¹³ (0.11)²

P(X = 13) = 0.2792

P(X = 13) = 27.92%

Therefore, there is a 27.92% chance that a shooter will hit its target at the very most 13 times.

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The required linear function in slope intercept form is C = 5x + 20

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan \theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here,

Let Chandler uses x gigabytes of data and let Chandler's monthly cell phone plan cost be C

Chandler's monthly cell phone plan costs $20 plus $5 per gigabyte of data that he uses

So,

C = 20 + 5x

C = 5x + 20

This is the required linear function in slope intercept form

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