In a test of the effectiveness of garlic for lowering​ cholesterol, 4545 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes ​(beforeminus−​after) in their levels of LDL cholesterol​ (in mg/dL) have a mean of 5.15.1 and a standard deviation of 19.119.1. Construct a 9090​% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL​ cholesterol?

Answer:

42

Step-by-step explanation:

7/8 = x / 48

We need to get a common denominator

Multiply the left side by 6

7/8 *6/6 = x/48

42/48 = x/48

Since the denominators are equal, the numerators must be equal

42 =x

Answer:

42

Step-by-step explanation:

7/8=42/48

Cross products: 7(48)=8x

Answer:

p+2p+3p=180degree(sum of angle of triangle)

6p=180degree

p=180degree/6

p=30degree

here your answer and please support me

Answer:

30, 60, 90

Step-by-step explanation:

p+2p+3p= 180

6p= 180

p=30, 2p= 60, 3p= 90

Answer:

P = 0.5

Step-by-step explanation:

Let's call A the event that the second card is red suit and B the event that the second card is a heart.

So, the probability that the second card is a heart given that is a red suit is calculated as:

P(B/A) = P(A∩B)/P(A)

Additionally, the probability P(A∩B) that the second card is a red suit and is a heart is equal to the probability P(B) that the second card is a heart. So,

P(B/A) = P(B)/P(A)

Then, P(A) is equal to 0.5 because half of the cards are red cards and P(B) is equal to 0.25 because a quarter of the cards are red. Finally, P(B/A) is equal to:

P(B/A) = 0.25/0.5 = 0.5

Answer:

A. System of equations:

[tex]3.2C+3P=48.5\\C+P=15.5[/tex]

B. 5.5 pounds of peanut butter fudge were sold.

Step-by-step explanation:

Given:

Cost of chocolate fudge = $3.20

Cost of peanut butter fudge = $3.00

Total pounds sold = 15.5

Total gross profit = $48.50

C is the number of pounds of chocolate fudge sold.

P is the number of pounds of peanut butter fudge sold.

To find:

System of equations and number of pounds of peanut butter fudge sold = ?

Solution:

As per given conditions:

1. [tex]C+P=15.5[/tex]

Gross profit from Chocolate fudge: [tex]3.20 \times C[/tex]

Gross profit from Peanut Butter fudge: [tex]3.00 \times P[/tex]

Total gross profit = [tex]3.20C+3.00P = 48.50[/tex]

So, the system of equations is:

[tex]3.2C+3P=48.5\\C+P=15.5[/tex]

2. To find P.

Let us solve the equations.

Multiply 2nd equation with 3 and subtracting from 1st equation:

[tex]0.2C = 48.5- 3 \times 15.5\\\Rightarrow 0.2C = 48.5- 46.5\\\Rightarrow C = 10\ pounds[/tex]

Putting in 2nd equation:

[tex]10+P=15.5\\\Rightarrow P =5.5\ pounds[/tex]

So, the answer is:

5.5 pounds of peanut butter fudge were sold.

Answer:

a) 0.0498

b) 0.1489

c) 0.1818

Step-by-step explanation:

Given:

Number of telephones = 6+6+6= 18

6 cellular, 6 cordless, and 6 corded.

a) Probability that all the cordless phones are among the first twelve to be serviced:

12 are selected from 18 telephones, possible number of ways of selection = ¹⁸C₁₂

Then 6 cordless telephones are serviced, the remaining telephones are: 12 - 6 = 6.

The possible ways of selecting thr remaining 6 telephones = ¹²C₆

Probability of servicing all cordless phones among the first twelve:

= (⁶C₆) (⁶C₁₂) / (¹⁸C₁₂)

[tex] = \frac{1 * 924}{18564} [/tex]

[tex] = 0.0498 [/tex]

b) Probability that after servicing twelve of these phones, phones of only two of the three types remain to be serviced:

Here,

One type must be serviced first

The 6 remaining to be serviced can be a combination of the remaining two types.

Since there a 3 ways to select one type to be serviced, the probability will be:

= 3 [(⁶C₁)(⁶C₅) + (⁶C₂)(⁶C₄) + (⁶C₃)(⁶C₃) + (⁶C₄)(⁶C₂) + (⁶C₅)(⁶C₁)] / ¹⁸C₁₂

[tex] = \frac{3 * [(6)(6) + (15)(15) + (20)(20) + (15)(15) + (6)(6)]}{18564}[/tex]

[tex] = \frac{2766}{18564} [/tex]

[tex] = 0.1489 [/tex]

c) probability that two phones of each type are among the first six:

(⁶C₂)³/¹⁸C₆

[tex] \frac{3375}{18564}[/tex]

[tex] =0.1818 [/tex]

Answer:

Tan B = 24/10 = 12/5

Step-by-step explanation:

Tangent is opposite/adjacent. The side opposite of B is 24 and adjacent to that is 10.

Answer:

[tex]\boxed{Larger \ Number = -7}[/tex]

Step-by-step explanation:

Let the consecutive numbers be x and x+1 (Since they are coming one after another)

So, Given Condition is:

x+1 = 9 + 2(x)

x+1 = 9 +2x

Subtracting -2x to both sides

x+1-2x = 9

-x+1 = 9

Subtracting 1 from both sides

-x = 9-1

-x = 8

=> x = -8

The larger number is:

=> x+1 = -8+1 = -7

Answer:

The dimensions are x = 23 and y = 23

The maximum area of the rectangle  A = 529

Step-by-step explanation:

Step(i):-

Let given function area of the rectangle

                                    A = x y ....(i)

Given Perimeter of rectangle

                          2 ( x + y ) = 92

                               (x +y ) = 46

                                y = 46 - x ....(ii)

Substitute y = 46 - x in equation (i)

                             A = x (46 - x)

                            A = 46 x - x²  ....(iii)

Differentiating equation (iii) with respective to 'x'

                            [tex]\frac{dA}{dx} = 46(1) - 2 x[/tex]  ...(iv)

Step(ii):-

              [tex]\frac{dA}{dx} = 46(1) - 2 x = 0[/tex]

                       46 - 2 x = 0

                             46  = 2 x

                              x  = 23

Again Differentiating equation (iv) with respective to 'x'

                      [tex]\frac{d^{2} A}{dx^{2} } = - 2 (1) = -2 < 0[/tex]

The maximum value at x = 23

Step(iii):-

From(ii)

                      y = 46 - x

                     y   = 46 - 23

                   y    = 2 3

The dimensions are x = 23 and y = 23

Final answer :-

The dimensions are x = 23 and y = 23

The maximum area of the rectangle

                        A = x y

                      A = 23 ×23

                     A = 529

The maximum area of the rectangle  = 529

The dimension of the rectangle with perimeter 92 m whose area is as large as possible is 23m by 23m

If the perimeter of a rectangle is 92m, hence;

2(x+y) = 92

x is the length

y is the width

x + y = 46 ....... 1

If the area is as large as possible, hence;

xy = maximum .........2

From equation 1, x = 46 - y

Substitute into the second equation

(46-y)y = P(y)

P(y) = 46y - y²

If the product is at the maximum, hence;

dP/dy = 46 - 2y = 0

46 - 2y = 0]

2y = 46

y = 23

Since x + y = 46

x = 46 - y

x = 46 - 23

x = 23

Hence the dimension of the rectangle with perimeter 92 m whose area is as large as possible is 23m by 23m

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Answer:

see below

Step-by-step explanation:

9 x 8 = (10 x 8) - ( blank x 8) =80 - blank = blank

We are replacing 9 with 10 minus something

9 = 10 -1

9 x 8 = (10 x 8) - ( 1 x 8)

           80 - 8

             72

Answer:

a.) dx3x² + 2

Use the properties of integrals

That's

integral 3x² + integral 2

= 3x^2+1/3 + 2x + c

= 3x³/3 + 2x + c

= x³ + 2x + C

where C is the constant of integration

b.) x³ + 2x

Use the properties of integrals

That's

integral x³ + integral 2x

= x^3+1/4 + 2x^1+1/2

= x⁴/4 + 2x²/2 + c

= x⁴/4 + x² + C

c.) dx6x 5 + 5

Use the properties of integrals

That's

integral 6x^5 + integral 5

= 6x^5+1/6 + 5x

= 6x^6/6 + 5x

= x^6 + 5x + C

d.) x^6 + 5x

integral x^6 + integral 5x

= x^6+1/7 + 5x^1+1/2

= x^7/7 + 5/2x² + C

Hope this helps

Answer:

1/7

Step-by-step explanation:

y=-7X

The slope of this line is -7

Perpendicular lines have slopes that multiply to -1

-7 * m = -1

Divide each side by -7

m = -1 / -7

m = 1/7

The slope of the perpendicular line is 1/7

Answer:

1/7

Step-by-step explanation:

Perpendicular slope can be calculated by take the opposite/negative reciprocal of the given slope. This means multiply the given slope by -1 (so if it is negative it becomes positive and if it is positive then becomes negative) and then flip the numerator and denominator.

So -7 is the slope of the given equation (y = mx + b where is m is slope and b is the y-intercept).

to find perpendicular slope..

Step 1. Multiple -7 by -1 = 7

Step 2. Flip 7/1 to 1/7

Answer: 1/7 is perpendicular slope

Answer:

7.2 times

Step-by-step explanation:

There are 36 possible outcomes when rolling a die twice and adding the results. The outcomes for which the sum is 6 are:

Sum = 6: {1,5; 2,4; 3,3; 4,2; 5,1}

Therefore there is a 5 in 36 chance that the sum will be 6.

The expected number of trials to achieve that result is given by:

[tex]E = \frac{36}{5}\\E=7.2\ times[/tex]

On average, it would take 7.2 trials to achieve a sum of 6.

Answer: 57 degrees

Step-by-step explanation: We can use our knowledge of knowing the sum of the interior angles of a triangle to be 180 degrees, to find the measure of the angle. So we can do 90 degrees plus 33 degrees, and then subtract the sum from 180 to find the measure of the angle. So we get 123 degrees when we add up 90 and 33 and when we subtract 123 degrees from 180 we get, 57 degrees as the answer.

Answer:

57 degrees

Step-by-step explanation:

We can use our knowledge of knowing the sum of the interior angles of a triangle to be 180 degrees, to find the measure of the angle. So we can do 90 degrees plus 33 degrees, and then subtract the sum from 180 to find the measure of the angle. So we get 123 degrees when we add up 90 and 33 and when we subtract 123 degrees from 180 we get, 57 degrees as the answer.

Answer:

$2,160 is what he need for both daughters for 1 year

Step-by-step explanation:

90 x 2 = 180

180 x 12 = 2,160

Dominic need to budget a total of 2160 for a year of gymnastics for both daughters.

Multiplication is one of the basic mathematical operations which includes a number added repeatedly to times of the other number. The final answer is called the product of the numbers.

Multiplication is usually denoted as '×' sign.

a × b indicates that a is added repeatedly upto b times.

Cost for the gymnastics per month per child = 90

In order to find the cost per month for both daughters, we need to multiply 90 with 2.

Cost for the gymnastics per month for 2 daughters = 2 × 90 = 180

To find the total cost for an year, we need to multiply 180 with 12.

Total cost for the year = 180 × 12 = 2160

Hence the total budget for Dominic to send both the daughter in a year is 260.

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Answer:

[tex]\int \int \bigtriangledown F\ X\ dS = \int F\cdot dr[/tex] = 12π

Step-by-step explanation:

The field F is given by:

[tex]F = 3y\hat{i} + y\hat{j}+z\hat{k}[/tex]      (1)

The curve C is the ellipse:

[tex]\frac{x^2}{4}+\frac{y^2}{64}=1\\\\(\frac{x}{2})^2+(\frac{y}{8})^2=1[/tex]

In order to calculate the circulation of F around the curve C, you first find the parametric equation for the given ellipse.

The general form of an ellipse equation is:

[tex](\frac{x}{a})^2+(\frac{y}{b})^2=1[/tex]

The parametric equation is:

[tex]r(t)=acost \hat{i} + bsint\hat{j}=2cost\hat{i}+8sint\hat{j}[/tex]      (2)

The Stokes's theorem is given by the following identity:

[tex]\int \int \bigtriangledown F\ X\ dS = \int F\cdot dr[/tex]    

The path integral is also:

[tex]\int F\cdot dr=\int F(r(t))\cdot dr(t)[/tex]      (3)

For F(r(t)) and dr(t) you obtain:

[tex]F(r(t))=3(8sint)\hat{j}+(8sint)\hat{j}+(z)\hat{k}\\\\dr(t)=(-2sint\hat{i}+8cost\hat{j}+0\hat{k})dt\\\\F(r(t))\cdot dr(t)=(-48sin^2t+64cos^2t)dt[/tex]

Next, in the equation (3) you obtain:

[tex]\int_0^{2\pi} (-48sin^2t+64cos^2t)dt=\int_0^{2\pi}(-\frac{48}{2}(1-cos2t)+\frac{64}{2}(1+cos2t))dt\\\\=\int_0^{2\pi}(-24+24cos2t+32+32cos2t)dt\\\\=\int_0^{2\pi}(6+56cos2t)dt\\\\=[6t+56sin2t]_0^{2\pi}=[6(2\pi)-0]=12\pi[/tex]

The circulation of the field around C is 12π

x+-2*2-3x-7

x+4-3x-7

x+1.x-7

x.x-7

2x-7

Answer:

The shape of the graph of f(x)=x is that of a linear function.

Step-by-step explanation:

The graph f(x)=x is the parent function of the linear function.  It is a positive function since it goes upward from left to right, and it passes through the point of (0,0).  It also has a slope of 1, which is the slope of the parent function, or the graph of f(x)=x.  Note once again: The parent linear function and the graph of f(x)=x are the exact same graph.

The shape of the graph of function f(x) = x is that of a linear function.

There are many tools we can use to find the information of the relation which was used to form the graph. A graph contains data of which input maps to which output. Analysis of this leads to the relations which were used to make it.

The graph of a function f(x)=x is the parent function of the linear function.  

This is a positive function since it goes upward from left to right, and it passes through the point of (0,0).  

And also has a slope of 1, which is the slope of the parent function, or the graph of f(x)=x.  

Hence, the parent linear function and the graph of f(x)=x are the exact same graph.

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Answer:

Greatest number = 9867

Smallest number = 1027

Step-by-step explanation:

Greatest number:

- - - 7

In order to form the greatest number, we should simply put the greatest available digit at the thousands place, the second greatest at the hundreds place and the third greatest at the tens place (which would be 9, 8, and 6 respectively).

9867

Smallest number:

- - - 7

In order to form the greatest number, we should simply put the lowest available digit at the thousands place (excluding zero since a number can't start with a zero), put zero at the hundreds place and the third lowest at the tens place (which would be 1, 0, and 2 respectively).

1027

Answer:

39

Step-by-step explanation:

Angle AQC, AQB and BQC are 120deg. (360/3=120). Therefore, Angle BZC, CXA and AYB are 60deg. Because, angle BZC is half of angle BQC. same for the other three angles. As, all 3 angles are 60deg, it is an equilateral triangle. So, YZ is 13 therefore as all 3 sides are equal its 13*3=39.

The solution is: 39 is the perimeter of XYZ.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

Here, we have,

Angle AQC, AQB and BQC are 120deg.

(360/3=120).

Therefore, Angle BZC, CXA and AYB are 60deg.

Because, angle BZC is half of angle BQC.

same for the other three angles.

As, all 3 angles are 60deg, it is an equilateral triangle.

So, YZ is 13

therefore as all 3 sides are equal

its 13*3=39.

Hence, 39 is the perimeter of XYZ.

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Answer:

22.62°

Step-by-step explanation:

tan x = 5/12

tan x = 0.416666667

x = arctan(0.416666667)

x = 22.61986983

x = 22.62°

x = +7 or -7

a = +3 or -3

x = +19 or -5

n = -5 or -7

p = +4 or -2

x = +11 or +1

a = -11 or -7

k = +16 or 0

m = -1 or 0

r = +6 or +1    

: Answer:

Step-by-step explanation:

|3a|=9

a=3

2- |x–7|=12

For the Negative case we'll use -(x-7)  

For the Positive case we'll use (x-7)  

Solve the Negative Case

     -(x-7) = 12  

 Multiply

     -x+7 = 12  

    rearrange and Add up

     -x = 5  

    Multiply both sides by (-1)

     x = -5  (for negative)

Solve the Positive Case

     (x-7) = 12  

     x = 19  

 Which is the solution for the Positive Case

Wrap up the solution

x=-5             ,x=19

 4- |n+6|=1

The Absolute Value term is |n+6|

 For the Negative case we'll use -(n+6)  

For the Positive case we'll use (n+6)  

Solve the Negative Case

     -(n+6) = 1  

    Multiply

   -n-6 = 1  

  -n = 7  

  Multiply both sides by (-1)

     n = -7  

  Which is the solution for the Negative Case

Solve the Positive Case

     (n+6) = 1  

     n = -5  

Which is the solution for the Positive Case

Wrap up the solution

n=-7

n=-5

5-   |1–p|=3

The Absolute Value term is |-p+1|

 For the Negative case we'll use -(-p+1)  

For the Positive case we'll use (-p+1)  

Solve the Negative Case

     -(-p+1) = 3  

  Multiply

   p-1 = 3  

   Rearrange and Add up

     p = 4  

Solve the Positive Case

     (-p+1) = 3

Rearrange and Add up

   -p = 2  

 Multiply both sides by (-1)

p = -2

Which is the solution for the Positive Case

Wrap up the solution

p=4                             , p=-2

6 - |6–x|=5    

The Absolute Value term is |-x+6|

For the Negative case we'll use -(-x+6)  

For the Positive case we'll use (-x+6)  

Solve the Negative Case

   -(-x+6) = 5  

  Multiply

   x-6 = 5

 Rearrange and Add up

     x = 11  

Solve the Positive Case

     (-x+6) = 5  

 Rearrange and Add up

     -x = -1

  Multiply both sides by (-1)

  x = 1  

   Which is the solution for the Positive Case

Wrap up the solution

x=11              ,   x=1

7-

The Absolute Value term is |a+9|

 For the Negative case we'll use -(a+9)  

For the Positive case we'll use (a+9)  

Solve the Negative Case

     -(a+9) = 2  

  Multiply

     -a-9 = 2  

    Rearrange and Add up

     -a = 11  

  Multiply both sides by (-1)

   a = -11  

   Which is the solution for the Negative Case

Solve the Positive Case

     (a+9) = 2  

    Rearrange and Add up      a = -7  

 Which is the solution for the Positive Case

Wrap up the solution

a=-11    a=-7

8-  |k–8|=8

The Absolute Value term is |k-8|

For the Negative case we'll use -(k-8)  

For the Positive case we'll use (k-8)  

Solve the Negative Case

     -(k-8) = 8  

    Multiply

     -k+8 = 8  

    Rearrange and Add up

     -k = 0  

    Multiply both sides by (-1)

   k = 0  

  Which is the solution for the Negative Case

Solve the Positive Case

     (k-8) = 8  

  Rearrange and Add up

     k = 16  

    Which is the solution for the Positive Case

Wrap up the solution

k=0  k=16

Solutions on the Number Line

Two solutions were found :

k=16

k=0

9-|2m+1|=1

The Absolute Value term is |2m+1|  

For the Negative case we'll use -(2m+1)  

For the Positive case we'll use (2m+1)  

Solve the Negative Case

     -(2m+1) = 1  

    Multiply

     -2m-1 = 1  

Rearrange and Add up

     -2m = 2  

    Divide both sides by 2

     -m = 1  

    Multiply both sides by (-1)

     m = -1  

    Which is the solution for the Negative Case

Solve the Positive Case

     (2m+1) = 1  

Rearrange and Add up

  2m = 0  

  Divide both sides by 2

   m = 0  

 Which is the solution for the Positive Case

Wrap up the solution

m=-1

m=0

Solutions on the Number Line

Two solutions were found :

m=0

m=-1

9- |7–2r|=5

The Absolute Value term is |-2r+7|

For the Negative case we'll use -(-2r+7)  

Solve the Negative Case

     -(-2r+7) = 5  

    Multiply

     2r-7 = 5  

    Rearrange and Add up

     2r = 12  

    Divide both sides by 2

     r = 6  

Solve the Positive Case

     (-2r+7) = 5  

   Rearrange and Add up

   -2r = -2  

  Divide both sides by 2

   -r = -1  

 Multiply both sides by (-1)

   r = 1  

  Which is the solution for the Positive Case

Wrap up the solution

r=6

r=1

Answer:

B. 3x+15 / 4x+10

Step-by-step explanation:

[tex]\frac{3x+}{2x+5}[/tex] X [tex]\frac{x+5}{2x}[/tex]  -> multiply by the reciprocal

[tex]\frac{3x}{2x+5}[/tex] X [tex]\frac{x+5}{2x}[/tex]  -> reduce the expression

[tex]\frac{3}{2x+5}[/tex] X [tex]\frac{x+5}{2}[/tex] -> multiply the fractions

[tex]\frac{3(x+5)}{2(2x+5)}[/tex]       -> remove parenthesis

and you get:

[tex]\frac{3x+15}{4x+10}[/tex]

-Hope this helps :)

Answer:

[tex]V=\frac{4}{3}\pi r^{2}[/tex]

=[tex]\frac{4}{3}[/tex] x [tex]\pi[/tex] x [tex]7^3[/tex]

= 1436.755040

Volume = 1436.755040

Step-by-step explanation:

Answer:

1436.03 in³

Step-by-step explanation:

We can use the formula V = [tex]\frac{4}{3}[/tex][tex]\pi[/tex]r³

Plug in 7 for r:

V = [tex]\frac{4}{3}[/tex][tex]\pi[/tex](7)³

Plug in 3.14 for pi:

V = [tex]\frac{4}{3}[/tex](3.14)(343)

V = 1436.03 in³

Answer:

There are 0.01 meters in a centimeter.

Step-by-step explanation:

cent means 100th

Hope this helps :)

Answer:

1. A resposta é a opção C.

2. ( a +b )² = a² + 2ab + b² Verdade

( a - b )² = a² - 2ab + b² Verdade

( a + b ) .( a – b) = a² + b² Falso

( a +b)³ = a³ + 3a²b + 3ab² + b³ Verdade

( a -b)³ = a³ - 3a²b + 3ab² - b³ Verdade

3. a.) m² - 14am + 49a² = ( m - 7a)²

b) m2 – 9n² = m² - (3n)² = (m + 3n)(m - 3n)

c) 30+ 5xy + 12a +2axy = (6 + xy)(5 + 2a)

d) 8a²b + 10ab² = 2ab( 4a + 5b)

Espero que isso ajude você

Answer:

The picture on the bottom right.

Step-by-step explanation:

There are eight compartments and seven of it is shaded and the other one five of the eight compartments are shaped.

I hope this helps :)

It is D.

you must multiply the second equation by 3, so that the +3y in the first equation can cancel out the (now) -3y in the second equation.

Answer:

6 ounces of red beads

6 ounces of gold beads

Step-by-step explanation:

x + y = 12

x + 3y = 24

We can solve this with substitution or elimination.  In this case, I would suggest elimination.  Subtract the first equation from the second:

2y = 12

y = 6

Plug back into either equation to find x.

x = 6

Answer:

How many ounces of red beads will Juanita buy to break even?

6

How many ounces of gold beads will she buy?

6

Step-by-step explanation:

Because I got 100 percent on EDG 2020

Answer:

y= -3.7x+100.94

Step-by-step explanation:

Generally this type of problems is solved by using a calculator or a spreadsheet. Now, getting the final equation depends on the model of calculator you are using, so I will suggest you look for the instructions on your calculator's instruction manual. I'll provide indications for using excel.

So first you need to input the table on an excel sheet. You can input them just the same way they were given to you. (See attached picture)

Once you inputed them, you can highlight them and go to the insert tab. There you can pick the scattering plot option. Once the scatterplot is graphed, you can right-click on the graph and a menu should appear. Pick the option add tendency line. Choose the line option and below, you can mark the option present equation on the graph and present the value of R. And that will be it! Excel will automatically provide you with the equation of the regression line you need.

Most scientific calculators nowaday can provide you with the equation, you just need to input the data and they will return the slope and y-intercept of the line.

There are other formulas you can use to find this regression by hand, but they are generally used in statistics courses.