peter sets up a neurological study in which he wants to investigate three pre-defined groups of patients. each group of patients is already diagnosed with the same neurological syndrome. peter not only examines the average score for each group of patients, but also the scores for each individual patient. peter's study is an example of...

Answer:

first remove the parentheses on both sides by distributing the multiplication. Then collect all the terms involving

y

on one side (say the left) and the terms without

y

on the right. Finally, divide both sides by the coefficient of

y

. (the number in front of

y

).

It looks like this:

4

(

2

y

−

1

)

=

4

(

y

+

3

)

8

y

−

4

=

4

y

+

12

8

y

−

4

y

=

12

+

4

(subtract

4

y

from both sides and add

4

to both sides)

4

y

=

16

4

y

4

=

16

4

y

=

4

Check your answer.

More thought, looking at the equation:

Instead of distributing the

4

's on both sides, you could start by dividing both sides by

4

(multiplying by

1

4

. This keeps the numbers smaller. It looks like this:

4

(

2

y

−

1

)

=

4

(

y

+

3

)

1

4

[

4

(

2

y

−

1

)

]

=

1

4

[

4

(

y

+

3

]

)

#1/4*4 = [1/4 *4] (y+3)

2

y

−

1

=

y

+

3

2

y

−

y

=

3

+

1

(subtract

y

and add

1

on both sides)

y

=

4

Check your answer.

Answer link

Gió

Mar 25, 2015

First multiply

4

to get rid of the brackets:

8

y

−

4

=

4

y

+

12

Now, isolate the

y

s on one side and numbers on the other of the

=

sign (remembering to change sign in crossing the

=

sign);

8

y

−

4

y

=

+

4

+

12

Notice the change of sign of

4

y

and

−

4

;

now we can add and subtract:

4

y

=

16

The

4

is multiplying the

x

and can go to the right dividing to get:

x

=

16

4

=

4

hope it helps!

Answer: x = 22

Step-by-step explanation:

Subtract 34 from both sides.
x + 34 - 34 = 56-34 --> x = 22

The total cost to operate 5 fluorescent 40w light bulbs for the months of April and May if they are on for 3 hours/day is given as follows:

$1,830.

The total cost is obtained applying the proportions in the context of the problem.

The number of kilowatt hours is given as follows:

Hence:

200 x 61 x 3 = 36,600 kwh.

The cost is of $0.05 per kwh, hence the total cost is given as follows:

0.05 x 36600 = $1,830.

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4 3/4 pounds amount of sugar were left after Garth used 9 1/2 pounds for the lemonade.

9 1/2 pounds of sugar were used from 14 1/4 minus 4 3/4.

Garth needed 14 1/4 pounds of sugar to make lemonade for the school carnival, so he purchased them. He had 4 3/4 pounds of sugar left over when he had done preparing the lemonade. This indicates that he made the lemonade using 9 1/2 pounds of sugar. He took the 14 1/4 pounds of sugar he purchased and subtracted the 4 3/4 pounds that were leftover to get at the amount of sugar he utilised, or 9 1/2 pounds. This indicates that the correct response is D: The lemonade required 9 1/2 pounds of sugar.

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Answer:

3w² = 243

Step-by-step explanation:

The surface area of the given cylinder is 602.88 square centimeters.

The surface area of the cylinder is: A = 2πr(r+h)

where 'r' is the radius of the base (circle) of the cylinder

'h' is the height of the cylinder

The cylinder with a height of 10 cm and a radius of 6 cm.

⇒ A = 2πr(r+h)

Here h = 10 cm and r = 6 cm

Substitute the known values in the above formula,

⇒ A = 2(3.14)(6)(6+10)

⇒ A = (12.56)(6)(16)

Apply the multiplication operation, and we get

⇒ A = 602.88

Therefore, the surface area of the given cylinder is 602.88 cm².

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Answer:

Below

Step-by-step explanation:

Go to   x = 1 on the x axis number line.....go UP to where the graph crosses x = 1  to find   y = 1    <====this is your answer for f(1)

for f(-)   go to x = 3 then go UP to the graph crossing at y = 1   <--answer

A. Circle

B. Ellipse (which can resemble an oval)

The following are the area of the sectors:

6a). π square inches

6b). 24π square centimeters

7a). 9 square centimeters

7b). 16.7 square inches

The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.

For question 6:

a). (40/360) × π × 3 in × 3 in = π in²

b). (135/360) × π × 8 cm × 8 cm = 24π cm²

For question 7:

a). (90/360) × π × 6 cm × 6 cm = 9 cm²

b). (60/360) × π × 10 in × 10 in = 16.7π in²

Therefore, the following are the area of the sectors:

6a). π square inches

6b). 24π square centimeters

7a). 9 square centimeters

7b). 16.7 square inches

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Answer:

the answer is a=15cm

Step-by-step explanation:

c²=a²+b²

where c=Hypothenuse,a=adjacent, b=opposite

a²=c²-b²

a²=39²-36²

a²=1521-1296

a²=225

take Square root of both sides

a=15cm

When the dimension of height is doubled, the volume of the cone also gets doubled.

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc. The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. We will discover how to find the volume for each of these shapes.

Volume of a cone is given by,

V = πr²h/3

Where,

V = Volume,

r = radius of the base,

h = height of the cone.

Let, height at first be x, then volume would be,

V1 = πr²x/3

As the height is doubled, so height = 2x, then volume would be,

V2= πr²(2x)/3

We observe that:

V2 = 2(πr²x/3)

V2 = 2V1

Therefore, when the height is doubled, the volume of the cone also gets doubled.

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The mass of the roller coaster is 800.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

PE = 235,200

Height = h = 30 m

Now,

PE = mhg

We use g = 9.8

So,

Substituting the values.

235,200 = m x 30 x 9.8

m = 235200 / (9.8 x 30)

m = 235200 / 294

m = 800

Thus,

The mass of the roller coaster is 800.

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The shape of the sampling distribution will be approximately normal, with a center at 40 inches and a standard deviation of 1.645 inches.

The mean of the sampling distribution of the sample mean height for samples of size 10 will also be 40 inches.

The standard deviation of the sampling distribution of the sample mean height can be calculated as:

σ/sqrt(n) = 5.2/sqrt(10) = 1.645

So, the shape of the sampling distribution will be approximately normal, with a center at 40 inches and a standard deviation of 1.645 inches.

The variability of the sampling distribution is smaller than the variability of the population distribution, because the standard error is smaller than the population standard deviation. This means that the sample means are more likely to be closer to the population mean than the individual heights in the population.

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The Average daily balance of the given scenario is $2083.

Suppose we're given that:

P_v = Present value of the loan amount

r = rate of interest (compound interest) per period of time

n = number of period of time in which loan is to be paid off

P = A fixed period payment needed to be done for paying off the loan in n number of periods.

Then, we get:

[tex]P = \dfrac{r\times P_v}{1 - (1 + r)^{-n}}[/tex]

Given;

APR= 25%

Cost of wheels and tires= $1500

Time=14days

Cost of brake calipers and leaking= $500

Time=30days

Now,

P= 25x2000/1-(1+25)^-30

P=50000/24

P=2083

Therefore, the monthly balance of loan will be $2083.

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Multiplying the total number of children by the fraction that like chocolate yields [tex]32(3/8)=12[/tex]

Answer:

-2a-2

Step-by-step explanation:

We can start solving this expression by combining like terms: Constants, or the number values, and Variables(the letters)

We can combine -6, 4, and 0 to get -2.

We can combine 3a and -5a to get -2a.

-2a + (-2) is the expression we are left with.

We can simplify this to

-2a - 2.

It can't be simplified further, so our answer is

-2a-2.

The solution of the expression x²-8x = 24 will be x = 4+√40. The correct option is D.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that the quadratic expression is, x²-8x = 24. The expression will be solved as below,

x²-8x = 24

Solve the above expression by completing the square method.

x²-8x = 24

( x - 4 )² - 24 - 16 = 0

( x - 4)² =40

x - 4 = √40

x = √40 + 4

Therefore, the correct option is D.

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the angle between the vectors is: θ = cos⁻¹ (- 12 / √145)

A quantity or phenomena with independent directions and magnitudes is called a vector. The word can also refer to a quantity's mathematical or geometrical representation. Science uses vectors to express everything with a direction and a magnitude. They are typically shown as pointed arrows, with the length of the arrow representing the magnitude of the vector.

Let, a(vector) = < -1, -2 >

a(vector) = -i -2j

||a(vector)|| = √(-1)² + (-2)² = √5

b(vector) = < -2, 5 >

b(vector) = -2i + 5j

||b(vector)|| = √(-2)² + (5)² = √29

Next, a(vector) . b(vector) = (-i -2j) . ( -2i + 5j)

a(vector) . b(vector) = (1 × (-2)) + (-2 × 5) = - 12

Thus, angle between these two vectors:

cosθ = a(vector) . b(vector) / ||a(vector)|| . ||b(vector)||

cosθ = - 12 / (√5 . √29)

cosθ = - 12 / √145

θ = cos⁻¹ (- 12 / √145)

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Answer: C= 24-4t

Step-by-step explanation: Since four were eaten each dat the blue is getting lower, use -4t to represent it. 24 is the total amount gotten by substitution.

Answer:

(a) P(A ∩ E) = 0.03

(b) P(A) = 0.39

(c) P(A | E) = 0.1

Step-by-step explanation:

The first level of the tree gives the following probabilities

P(E) = 0.1

P(E') = 1 - P(E) = 0.9

The second level gives conditional probabilities

P(A|E) = 0.3  this is the top most branch from the root

P(A ∩ E) = P(A|E) P(E) = 0.3 x 0.1 = 0.03      Answer(a)

To find P(A) we find all routes that will end in A, compute each probability and add up the individual probabilities

For event E happening, P(A ∩ E) = 0.03 which is computed in A

However A can also happen when the complement event E' happens
P(A ∩ E') = P(A | E') P(E') = 0.4 x 0.9 = 0.36

Add these two together to get 0.03 + 0.36 = 0.39 Answer (b)

P(A|E) is nothing but the probability value when we follow the E branch first followed by the A branch

This is 0.1   answer (c)

Answer:

Below

Step-by-step explanation:

Second choice      at x = 0     it is = 6

  and as the exponent (x) gets more negative it gets larger meaning it has a coefficient of < 1     ( it is 3/4)

Answer:

x = 20

Step-by-step explanation:

since the 3 sides of the triangle are congruent then it is equilateral with 3 congruent angles, each of 60° , then

3x = 60 ( divide both sides by 3 )

x = 20

Answer:

20

Step-by-step explanation:

We know that sum of corner of a triangle is 180° and if the triangle is equilateral, the corners are same

180:3=3x

60=3x

x=20

100%

You calculate the increase, which is the final amount minus the initial amount.

You then divide the value of increase by the original amount (in our case, this was 8÷8).

You then multiply that amount by 100 to put it into a percentage.

Hope this helps!

Quadrilateral FGHI is a scalene quadrilateral as none of the sides equal to each other from calculated slopes and lengths.

Coordinates of the quadrilateral FGHI are,

F (-1,-8), G(-3,2), H(0,1) and I(2,7)

Slope of side lengths of FGHI are:

Slope FG = ( 2 + 8)/ (-3 + 1)

               = -5

Slope GH = ( 1 -2)/ (0 + 3)

                = -1/3

Slope HI = ( 7 -1)/ ( 2 -0)

              = 3

Slope IF = ( 7 + 8 )/ (2 + 1)

              = 5

Product of slopes of perpendicular lines = -1

FG is perpendicular to IF

GH is perpendicular to HI

Measure of side lengths are:

FG = √(2+8)² + (-3+1)²

     = √104

     = 2√26

GH =√(1-2)² + (0 +3)²

     = √10

HI = √(7-1)² + (2-0)²

    = √40

    =2√10

IF = √(7+8)² + (2+1)²

   = √234

   = 9√26

Therefore, the given quadrilateral is scalene quadrilateral concluded using slopes and lengths.

The above question is incomplete, the complete question is:

The points F (-1,-8), G(-3,2), H(0,1) and I(2,7) form a quadrilateral. Find the desired slopes and lengths, then fill in the words that BEST identifies the type of quadrilateral.

Slope of FG = __                            Length of FG = __

Slope of GH = __                            Length of GH = ___

Slope of HI= __                               Length of HI = ____

Slope of IF = __                               Length of IF = ____

Quadrilateral FGHI is ______

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For the two given graphs, the value for vector equation is obtained as [tex]\vec{w} = 2\vec{u} + \vec{v}[/tex].

What is a vector?

A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.

From first graph it is seen that -

[tex]\vec{u}= < 1,1 >[/tex] and [tex]\vec{v}= < -1,2 >[/tex]

From second graph it is seen that -

[tex]\vec{w}= < 1,4 >[/tex]

So, it is obtained that -

[tex]a\vec{v}+b\vec{u}=\vec{w}[/tex]

Substitute all the values in the equation -

a<-1,2> + b<1,1> = <1,4>

<-a,2a> + <b,b> = <1,4>

<-a+b,2a+b> = <1,4>

The two equation obtained are -

-a + b = 1

2a + b = 4

Subtracting the equation 1 from 2 -

2a + b - (-a + b) = 4 - 1

2a + b + a - b = 3

3a = 3

a = 1

Substitute the value of a in equation 1 -

-1 + b = 1

b = 1 + 1

b = 2

So, the equation [tex]a\vec{v}+b\vec{u}=\vec{w}[/tex] becomes -

[tex]\vec{v} + 2\vec{u} = \vec{w}[/tex]

Therefore, the vector is obtained as [tex]\vec{w} = 2\vec{u} + \vec{v}[/tex].

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The value of the expression when evaluated is -15

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

The table of values for the function f(x)

The expression to evaluate is given as

f-1(3) - 4 * f(6)

Using the above as a guide, we have the following:

f-1(3) = 5

f(6) = 5

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

f-1(3) - 4 * f(6) = 5 - 4 * 5

Evaluate

f-1(3) - 4 * f(6) = -15

Hence, the solution is -15

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The correct option is E, another rule that takes a line to a perpendicular line (x,y)→(4y,-4x) A B C D OE.

(x,y)→(y,-x)

E:(x,y)→(4y,-4x)→4(y,-x)

So E = (x,y)→(4y,-4x) A B C D OE.

Perpendicular lines play an important role in geometry and trigonometry. They are used to construct right angles, which are essential in measuring angles and finding distances between points. In construction, perpendicular lines are often used to ensure accuracy when building structures, such as walls or flooring.

Perpendicular lines also have real-world applications in navigation, surveying, and astronomy. For instance, in navigation, perpendicular lines are used to calculate a ship's course and location. In surveying, perpendicular lines are used to create precise measurements of land plots, while in astronomy, they are used to calculate distances between celestial objects.The slope of a perpendicular line is the negative reciprocal of the slope of the other line.

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Complete Question: -

The rule (x,y)→(y,-x) takes a line to a perpendicular line. Select all the rules that take a line to a perpendicular line.

A. (x,y)→(2y,-x)

B. (x,y)→(-y,-x)

C. (x,y)→(-y,-x)

D. (x,y)→(0.5y,-2x)

E.  (x,y)→(4y,-4x) A B C D OE

The value of P(-3) is -12, Quotient is (-2x² + x - 3) and Remainder is 6.

Remainder Theorem is a method for dividing polynomials according to Euclidean geometry. This theorem states that a polynomial P(x) divided by a factor (x - a) is not really an element of the polynomial.

Given:

P(x) = -2x³-5x²-3.

Using the remainder theorem, the value of P(3) is given by:

P(-3)=  -2x³-5x²-3.

P(-3) =  -2(-3)³-5(-3)²-3

P(-3) = -2(-27) -5(-9) -3

P(-3) = -54 + 45 - 3

P(-3) = -12

As, the divisor of P(x) is (x+3).

so, the division is

                                  (x+3) | -2x³-5x²-3 | -2x² + x - 3

                                             -2x³-6x²

                                          __________

                                                        x² - 3

                                                        x² + 3x

                                                     ________

                                                               -3x - 3

                                                               -3x - 9

                                                              _______

                                                                      6

So, the Quotient is (-2x² + x - 3) and Remainder is 6.

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