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Answer: Mean = 23

Step-by-step explanation:

Given information:

35, 40, 12, 16, 25, 10

Given formula:

[tex]Mean~=~\frac{Sum~of~terms}{Number~of~terms}[/tex]

Substitute values into the formula

[tex]Mean~=~\frac{35~+~40~+~12~+~16~+~25~+~10}{6}[/tex]

Combine like terms

[tex]Mean~=~\frac{75~+~28~+~35}{6}[/tex]

[tex]Mean~=~\frac{103~+~35}{6}[/tex]

[tex]Mean~=~\frac{138}{6}[/tex]

Simplify the fraction

[tex]\Large\boxed{Mean=23}[/tex]

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Answer:

22, 23

Step-by-step explanation:

4x + 3(x + 1) = 157

4x + 3x + 3 = 157

7x + 3 = 157

7x = 154

x = 22

To estimate that table given in Option (4) will define the quadratic relationship.

Therefore, the table of Option (5) will describe the quadratic relationship.

By estimating the second difference, if the second difference in a table exists equivalent, the table will define the quadratic relationship.

In the given option, we estimate that table given in Option (4) will define the quadratic relationship.

x       y      I st difference       II nd difference

0      4           -                               -

1      -4      -4 - (4) = -8                    -  

2     -4      -4 - (-4) = 0                0 - (-8) = 8

3      4       4 - (-4) = 8                 8 - 0 = 8

The second difference between the terms in y exists exactly as 8.

Therefore, the table of Option (4) means the quadratic relationship.

Similarly, in Option (5) we will estimate the second distinction of y terms.

x        y             I st difference       II nd difference

0      -4                     -                          -

1       -8               -8 - (-4) = -4              -

2     -10             -10 - (-8) = -2      -2 - (-4) = 2  

3     -10             -10 - (-10) = 0       0 - (-2) = 2

Here the second difference exists identical to 2.

Therefore, the table of Option (5) will describe the quadratic relationship.

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Answer:

90ft

Step-by-step explanation:

43,560ft² = L × l

43,560ft² = 484ft × l

43,560ft² ÷ 484ft = l

l = 90ft

The unit rate of 1/4 book 1/3 hour in books per hour is 3/4 books per hour.

Unit rate is the rate of a quantity in terms of another quantity per unit.

Unit rate(books per hour) = Number of books / Number of hours

= 1/4 ÷ 1/3

= 1/4 × 3/1

= (1×3) / (4×1)

= 3/4 books per hour

Therefore, the unit rate of 1/4 book 1/3 hour in books per hour is 3/4 books per hour.

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The linear function of best fit for the information on the graph is:

f(x) = 200x + 100.

A linear function is modeled by:

y = mx + b

In which:

The function on the graph goes through points (3,700) and (4,900), that is, when x changes by 1, y changes by 200, which means that the slope is of 200 and the function is:

f(x) = 200x + b.

When x = 3, f(x) = 700, hence we use it to find b.

700 = 200(3) + b

b = 100.

Hence the function is:

f(x) = 200x + 100.

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Answer:

4/9

Step-by-step explanation:

.44444.. = 4/9

0.nnnnnnnn.... = n/9

0.mnmnmnmnmn.... = mn/99

and so on

Her business will break even when she contains sold 1740 bottles of her lotion.

Given: She invests $15,225 in equipment to manufacture and package her lotion each bottle costs $3.25 to manufacture and sells for $12.

"Break even" occurs when Revenue = Costs.

($12/bottle)x = $15225 + ($3.25)x

Simplifying the above equation, we get

$8.75x = $15225

Diving both sides of the equation by 8.75, we get

$8.75x/8.75 = $15225/8.75

x = 1740 bottles

Therefore, the value of x = 1740 bottles.

Her business will break even when she contains sold 1740 bottles of her lotion.

Therefore, the correct answer is option b. 1740 bottles.

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The new mixture exists 56.5% peanuts.

The first batch of 9 lb of mixed nuts possesses 40% peanuts.

This means the quantity of peanuts exists:

9 [tex]*[/tex] 40/100 = 3.6 lb

The second batch of 9 lb of mixed nuts possesses 73% peanuts.

This means the quantity of peanuts exists:

9 [tex]*[/tex] 73/100 = 6.57 lb

The total quantity of peanuts in the mix exists

3.6 lb + 6.57 lb = 10.17 lb

There exist 9 lb + 9 lb = 18 lb of mix.

Therefore, the percent of peanuts in the mix exists:

10.17 / 18 [tex]*[/tex] 100 = 56.5%

The new mixture exists 56.5% peanuts.

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The matrix for the linear transformation for which rotates every vector in r2 is [tex]\left[\begin{array}{cc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right][/tex].

In this question,

The angle is -π/3 = -60°

Clockwise rotations are denoted by negative numbers.

Matrix for counter-clockwise direction for an angle α is

[tex]\left[\begin{array}{cc}cos\alpha &-sin\alpha \\-sin\alpha &cos\alpha \end{array}\right][/tex]

Then, matrix for clockwise direction for an angle α

Put α = -α in the above matrix,

⇒ [tex]\left[\begin{array}{cc}cos(-\alpha) &-sin(-\alpha) \\-sin(-\alpha) &cos(-\alpha) \end{array}\right][/tex]

⇒ [tex]\left[\begin{array}{cc}cos\alpha &sin\alpha \\sin\alpha &cos\alpha \end{array}\right][/tex]

Now substitute α = 60°

Then matrix becomes,

⇒ [tex]\left[\begin{array}{cc}cos60 &sin60 \\sin60 &cos60 \end{array}\right][/tex]

⇒ [tex]\left[\begin{array}{cc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right][/tex]

Hence we can conclude that the matrix for the linear transformation for which rotates every vector in r2 is [tex]\left[\begin{array}{cc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right][/tex].

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The dimensions of a rectangle with area 1728 square meter whose perimeter is as small(minimum) as possible are 41.57m and 41.56m.

Let the dimension of the rectangle be x and y m.

According to the given question.

The area of the rectangle is 1728 square meter.

⇒ x × y = 1728

⇒ x = 1728/y

Since, the perimeter of the rectangle is the sum of the length of its boundary.

Therefore,

Perimeter of the recatngle with dimensions x and y is given by

Perimeter of the rectangle, P = 2(x + y)

⇒ P = 2(1728/y + y)

⇒ P = 3456/y + 2y

Differentiate the above equation with respect to y

⇒ [tex]P^{'} = -\frac{3456}{y^{2} } + 2[/tex]

For the minimum(small) perimeter equate the above equation to 0.

⇒ [tex]-\frac{3456}{y^{2} } + 2 = 0[/tex]

⇒ [tex]2y^{2} =3456[/tex]

⇒ [tex]y^{2} = \frac{3456}{2}[/tex]

⇒ y^2 = 1728

⇒ y = √1728

⇒ y = 41.56 m

Therefore,

x = 1728/41.56

⇒ x = 41.57 m

Hence, the dimensions of a rectangle with area 1728 square meter whose perimeter is as small(minimum) as possible are 41.57m and 41.56m.

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The complete proofs are:

Proof 1

Proof 2

Proof 1

Lines a & b and c and d are given as parallel lines.

So, we have

a || b; c || d ⇒ Given

From the question, we have:

∠5 is supplementary to ∠4

So, we have

∠5 + ∠4 = 180

This is so because supplementary angles add up to 180

Corresponding angles are equal.

So, we have:

∠2 = ∠4

By the substituting ∠2 for ∠4 in ∠5 + ∠4 = 180, we have

∠5 + ∠2 = 180

Hence, angles ∠5 and ∠2 are supplementary angles

Proof 2

Line BD bisects angle ABC; lines AD & BC and AB & CD are given as parallel lines.

So, we have

BD bisects ∠ABC; AD || BC; AB || CD ⇒ Given

From the question, we have:

∠3 ≅ ∠4 ⇒ Definition of congruent angles

∠1 ≅ ∠3 ⇒ Definition of corresponding angles

Substitute ∠1 ≅ ∠3 in ∠3 ≅ ∠4

∠1 ≅ ∠4

Hence, the angles 1 and 4 are congruent

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0.0016

reduce expression if possible by canceling the common factors

Answer:

cot x

Step-by-step explanation:

using the identities

csc x = [tex]\frac{1}{sinx}[/tex]

sin([tex]\frac{\pi }{2}[/tex] - x) = cos x

then

csc x × sin ([tex]\frac{\pi }{2}[/tex] - x)

= [tex]\frac{1}{sinx}[/tex] × cosx

= [tex]\frac{cosx}{sinx}[/tex]

= cot x

The equivalent expression to [tex](k o h)(x)[/tex]is [tex]\frac{1}{5 + x}[/tex]

Therefore  [tex](k o h)(x) = \frac{1}{5 + x}[/tex]

Given that the functions h is defined by h(x)=5+x

and k is defined by k (x) = [tex]\frac{1}{x}[/tex]

To find the composition of k and h that is: (k o h) (x)

Therefore

k (h(x)) = k (5+x)

k (h(x)) = [tex]\frac{1}{5+ x}[/tex]

The equivalent expression to is [tex]\frac{1}{5+ x}[/tex]

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Based on the orbital period of the planet in earth years, and the distance it is rotating, the mass of the star that the planet is orbiting is 3 solar masses.

Because the sun is so heavy, it needed to have a special unit that could adequately reflect this mass.

Solar masses was the term that scientists came up with. In terms of the Earth's mass, a single solar mass means that the body is 333,000 times the mass of the Earth.

When given the orbital period of a planet, and the distance it is orbiting around a sun, you can find the solar mass by the formula:

= Distance planet is rotating³ - Orbital period²

Solving gives:

= 1.2³ / 0.76²

= 2.99

= 3 solar masses

In conclusion the mass of the star is 3 solar masses

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Answer:

3 solar masses

Step-by-step explanation:

just did it and got it right

Step-by-step explanation:

x^2 +4x +4 -7 is

y=x^2+4x-3

Answer: g(x)=(x+2)²-4.

Step-by-step explanation:

g(x)=f(x)+3

g(x)=(x+2)²-7+3

g(x)=(x+2)²-4.

By direct comparison and definition of line segment  we notice that the point (x, y) = (- 6, 0) lies on the line segment AB as each AP is a multiple of former. (Correct choice: C)

According to linear algebra, a point lies in a line segment if its vector is a multiple of the vector that generates the line segment itself, that is:

AB = k · AP        (1)

The vector that generates the line segment is:

AB = (2, 6) - (- 2, 3)

AB = (4, 3)

And the vectors related to each point are:

Case A

AP = (- 2, 12) - (- 2, 3)

AP = (0, 9)

Case B

AP = (6, 12) - (- 2, 3)

AP = (8, 9)

Case C

AP = (- 6, 0) - (- 2, 3)

AP = (- 4, - 3)

Case D

AP = (- 6, 6) - (- 2, 3)

AP = (- 4, 3)

By direct comparison and definition of line segment  we notice that the point (x, y) = (- 6, 0) lies on the line segment AB as each AP is a multiple of former. (Correct choice: C)

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The area of a rectangle is the amount of space it would cover on a 2-Dimensional plane. The required value of the width is 25 feet.

A rectangle is a plane shape with equal opposite sides. Its area can be determined by;

Area of a rectangle = length x width

Considering the given question, let the length of the plot be represented by l and its width as w. Given that the width of the plot should be longer than its length by 5, then we have;

w = l + 5

But,

Area of the plot = length x width

500 = l x (l + 5)

       = [tex]l^{2}[/tex] + 5l

This implies that,

500 = [tex]l^{2}[/tex] + 5l

[tex]l^{2}[/tex] + 5l - 500 = 0

Applying the quadratic formula, we have;

l = (-b  ± [tex]\sqrt{b^{2} - 4ac}[/tex]) / 2a

a = 1, b = 5, c = -500

= (-5  ±  [tex]\sqrt{5^{2} - (4*1*-500)}[/tex]/ 2

 = (-5  ± 45) / 2

l =   (40) / 2 OR l =  (-50) / 2

l = 20 OR l = - 25.5

So that,

l = 20

Therefore, the length of the plot is 20 feet.

Thus the width of the plot can be determined as;

w = l + 5

   = 20 + 5

w = 25

The width of the plot is 25 feet.

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Explanation:

To go from gallons to fluid ounces (abbreviation fl oz), we multiply by 128

For example, 2 gallons becomes 2*128 = 256 fl oz as shown in the table.

Another example: 3 gallons = 3*128 = 384 fl oz.

Therefore, 6 gallons would be 6*128 = 768 fl oz.

To go in reverse, from fl oz to gallons, we divide by 128.

Using proportions, the value of y is of 100º.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In a circle, the measure of an arc is twice the measure of it's equivalent internal angle. The internal angle is of 50º, hence the measure of the arc, given by y, is found as follows:

y = 2 x 50º = 100º.

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Using proportions, it is found that 68 more people prefer vanilla than do strawberry.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Researching this problem on the internet, it is found that, out of 400 people:

Hence the amounts are:

The difference is:

140 - 72 = 68.

68 more people prefer vanilla than do strawberry.

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Step-by-step explanation:

1st : Vector translation.

a vector -8j ( 0 , -8 ) helped translate (x , y) => (x , y - 8)

2nd : rotation.

The only rotation that results in (-x , -y) is pi rotation.

formula : (x , y -8) => ( xcos(pi) - ysin(pi) , xsin(pi) + ycos(pi) )

substitute x & y-8 into x & y respectively of the formula above.

Answer:

Step-by-step explanation:

Comment

The sum of the remote interior angles = The exterior angle not connected to them

What that means is that

<C + <D = <KEB

Givens

<C = 60

<KED = <C + <D

Solution and answer

<KED = <C + <D                      Substitute the givens into this equation

100 = 60 + <D                         Turn this around

<60 + <D = <100                     Answer first equation

Subtract 60 from both sides

<60-<60 + <D = <100 - 60

<D = <40                                   Answer second Equation

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

Given:

▪ [tex]\longrightarrow \sf{KED = 100^\circ}[/tex]

▪ [tex]\longrightarrow \sf{\angle ECD = 60^\circ}[/tex]

[tex]\leadsto[/tex] According to the triangle angle sum theorem, the sum of interior angles of a triangle is 180°.

[tex]\leadsto[/tex] We can find the value of ∠E if we know the sum of two supplementary angles is equal to 180°

[tex]\longrightarrow \sf{m \angle E+ m \angle K=180^\circ}[/tex]

[tex]\longrightarrow \sf{m \angle E+ 100^\circ =180^\circ}[/tex]

[tex]\longrightarrow \sf{m \angle E= 80^\circ}[/tex]

As we find the value of ∠E, we can replace it in the initial formula. [tex]\downarrow[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex]\bm{m \angle C + m \angle \boxed{\bm D} = m \angle \boxed{\bm E}}[/tex]

[tex]\bm{m \angle D= \boxed{\bm{ 40^\circ}}}[/tex]

Step-by-step explanation:

....................

Answer:

2√(133)

Step-by-step explanation:

Triangle 1 = 8, 12, ?

triangle 2 = 18, x, ?

we have to find value of x which is a hypotenuse

a² + b² = c²

8² + 12² = 64 + 144 = √208 = 14.4222051019

x = 14.4222051019² + 18²

= 208 + 324

= 532

x = √532 = 2√(133)

Using the normal distribution, it is found that:

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given, respectively, by:

[tex]\mu = 83, \sigma = 6[/tex]

The proportion of students, with a grade of at least 70 is one subtracted by the p-value of Z when X = 70, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{70 - 83}{6}[/tex]

Z = -2.17

Z = -2.17 has a p-value of 0.015.

1 - 0.015 = 0.985 = 98.5% of students have at least a 70.

The proportion of students, with a grade of at least 80 is one subtracted by the p-value of Z when X = 80, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{80 - 83}{6}[/tex]

Z = -0.5

Z = -0.5 has a p-value of 0.3085.

1 - 0.3085 = 0.6915 = 69.15% of students have an 80 or above.

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Answer: H

Step-by-step explanation:

[tex]9(-3)=-27[/tex], which is an integer.

The power output is  = 5W

Correct option is B.

Power is the quantity of energy that is transferred or transformed in a certain length of time. The unit of power is the watt, which in the International System of Units is equivalent to one joule per second.. Power may also be referred to as activity in earlier writings. The scalar property of power

Power is characterized as the rate at which a thing performs labor.

P = W/T ..... (1)

Work is calculated as the product of force applied to an item and the distance that object has traveled.

W = F.s

When we plug this value into the equation above, we get:

P = (F. s)/t

where,

power = P =?W

F = 10N Force Exercised

s = Displacement = 400cm = 4m  (1 meter = 100 centimeters).

t = Time required = 8s

Using the values in the equation above, we obtain

P = (10 x 4)/8

P = 5W

Hence, the correct option is Option b.

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I understand that the question you are looking for is :

Den pushes a desk 400 cm across the floor. He exerts a force of 10 N for 8 s to move the desk.

What is his power output? (Power: P = W/t)

a. 1.25 W

b. 5 W

c. 40 W

d.500 W