The price of sweaters starts at Pa= $120 each and a quantity supplied of Qa= 40 sweaters. If the price falls to Pb= $12 each, what is the new quantity supplied (Qb) if the slope of the supply curve is m=3 Round your answer to nearest whole number of sweaters.

The area of the pool given by the expression, ∆ × 102 + ∆ × 101 + 6, gives;

A) The whole number x = 33

B) The perfect square number closest to 33 is 36

The side length of a square pool with an area of 36 square units is 6 units

C) The side length of a square pool with the area chosen in part A is 33•√33

An expression is a mathematical statement which consists of 2 or more numbers and, or variables joined together by mathematical operators.

A) The given equations for the pool is presented as follows;

Area of the pool = ∆ × 102 + ∆ × 101 + 6

Area of the pool = x³

x = A whole number

Expressing the word problem mathematically gives;

∆ × 102 + ∆ × 101 + 6 = x³

203•∆ + 6 = x³

Which gives;

[tex] \displaystyle{ \triangle = \frac{ {x}^{3} - 6}{203} }[/tex]

Using a graphing calculator, when x = 33, we get;

[tex] \displaystyle{ \triangle = \frac{ {33}^{3} - 6}{203} = 177 }[/tex]

The value of the number is x = 33 and ∆ = 177

B) The perfect square that is closest to x = 33 is 36

The side length of a square pool with an area of 36 is √(36) = 6

C).The area of the pool chosen is 33³ = 35937

The side length of a square pool with an area of 35937 is √(35937) = 33•√(33)

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The length of each side is less than sum of the lengths of the other two sides and greater than the difference between these lengths.

2s is not less than 1/2s+ 2/3s

A triangle is polygon with the three edges and three vertices. It is one of the basic shapes in the geometry. A triangle with the vertices A, B, and C is denoted Δ ABC.

In the Euclidean geometry, any three points, when the non-collinear, determine a unique triangle and simultaneously, a unique plane (i.e. two-dimensional Euclidean space). In the other words, there is the only one plane that contains that triangle, and every triangle is contained in some plane. If the entire geometry is only  Euclidean plane, there is only one plane and all triangles are contained in it; however, in the higher-dimensional Euclidean spaces, this is no longer true. This article is about triangles in the Euclidean geometry, and in the particular, the Euclidean plane, except where otherwise noted.

new triangle perimeter is = 2s + 1/2s + 2/3s

This new triangle, however, cannot be created physically because

The length of each side is less than sum of the lengths of the other two sides and greater than the difference between these lengths.

2s is not less than 1/2s+ 2/3s

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A situation in which positive and negative numbers are used to describe values that have opposite meaning is that John is on top of a mountain that is 2000 above sea level and his friend is diving and is below 2000 feet.

The thing that 0 represents is the addition in the sea level.

Based on the information illustrated, the situation will be that John is on top of a mountain that is 2000 above sea level and his friend is diving and is below 2000 feet.

Therefore, the addition will be:

= 2000 + (-2000)

= 2000 - 2000

= 0

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[tex] = x \times 2 + 15 \\ = 2x + 15[/tex]

DOUBLING IT MEANS MULTIPLYING IT BY 2

THEN ADD 15 AS SHOWN ABOVE.

HOPE THIS HELPS

The values are as follows:

center:  y²/25-x²/25 = 1

transverse axis : b = 5

Vertices:  (0,5) and (0,-5)

Foci: (0,5√2) and (0,-5√2)

Asymptotes: y = x and y = -x

An asymptote is a line being approached by a curve but never touching the curve. i.e., an asymptote is a line to which the graph of a function converges. We usually do not need to draw asymptotes while graphing functions.

Types of Asymptotes:

1) Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k.

2) Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k.

3) Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b.

y² -x² =25 up down hyperbola with (h,k) = (0,0) a = 5 and b = 5

(y-k)²/a²-(x-h)²/b² = 1 is the standard equation of up-down hyperbola.

With semi-axis is a and semi-conjugate axis is b.

and centre (h,k).

Center = (y-0)²/5²-(y-0)²/5² = 1

= y²/25-x²/25 = 1

The axes are a = 5 and b = 5

transverse axis is b = 5

The foci are given by (h, k+c) and (h, k-c), where c = √a²+b²

c = √5²+5² = 5√2

therefore, the foci are (0,5√2) and (0,-5√2).

The vertices are (h, k+a) and (h, k-a)

(h,k) = (0,0) and a = 5 and b = 5

vertices are (0,5) and (0,-5)

Asymptotes are y = x and y = -x.

Therefore, the summary is as follows:

center:  y²/25-x²/25 = 1

transverse axis : b = 5

Vertices:  (0,5) and (0,-5)

Foci: (0,5√2) and (0,-5√2)

Asymptotes: y = x and y = -x

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the height and width of her scale drawing is respectively:

height = 1*1/2inch

width = 3/4 inch

Dimension are the measure of the size or distance of an object or region or space in one direction.

so, all we needs to do is multiply is dimension of the original door image by the scale factor , to get the height and width of the scale drawing.

height:   3 inch x 1/2 =3x1/2=3/2=1x1/2 inch

width: 1x 1/2 inch x 1/2 =3/2 x 1/2= 3x1/2x2=3/4 inch

hence , the height and width of the scale drawing is respectively= 1x 1/2 inch ,3/4 inch

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This necklace sold at auction for $11,379,600 in 2011. The percentage of the initial purchase price was represented by the auction price is 2.1%.

Given that,

For $54,000, an actor purchased a pearl, diamond, and ruby necklace for his well-known wife. This necklace sold at auction for $11,379,600 in 2011.

We have to find what percentage of the initial purchase price was represented by the auction price.

Let us take the percentage as x%.

Necklace sold at auction=the percentage multiplied by the actual price

We get,

$11,379,600 =x%($54,000)

x%=$11,379,600/$54,000

x%=2.1%

Therefore, the percentage of the initial purchase price was represented by the auction price is 2.1%.

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Answer:

1/5,1/6,2/9,3/10

Step-by-step explanation:

hope it helps helps and have a nice day! :)

To find the x-intercepts of the function g(x), we must set it equal to 0 and solve for x.

We have the following:

we can use the quadratic formula to get the roots of the polynomial:

therefore, the x-intercepts of the function g(x) are the points (3/4,0) and (-1/4,0)

Answer:

C) 0.1666

Step-by-step explanation:

The probability of selecting a calculator that is defective can be defined as: [tex]\frac{46}{46+26}[/tex]

The 46 in the numerator is the number of calculators that are defective in the group. The 46 + 26 represents the total amount of calculators since 46 are defective and 26 are not defective and assuming a calculator can only be defective or not defective then these are the total number of calculators in the group.

This gives you a probability of approximately: [tex]\frac{46}{72}[/tex] or approximately 0.638889

We can multiply independent events to find the combined probability of these events occurring. So we have to assume you put the calculator back into group after selecting one.

If this is the case we simply multiply 46/72 * 46/72 * 46/72 * 46/72 or (46/72)^4 to get an approximate probability of: 0.1666

Answer: 6x8

Ur answers should be 48 and again we did repeated addition so

6+6+6+6+6+6+6+6 or we can do 12+12+12+12 or 24+24 which we should know use 48

Step-by-step explanation:

Step-by-step explanation:

a)

[tex]f(x+h) = 4(x+h)+4[/tex]

[tex]f(x+h)=4x+4h+4[/tex]

b)

[tex]f(x+h)-f(x)=4x+4h+4-(4x+4)[/tex]

[tex]f(x+h)-f(x)=4x+4h+4-4x-4[/tex]

[tex]f(x+h)-f(x)=4h[/tex]

c)

[tex]f(x+h)-f(x)h=4x+4h+4-h(4x+4)[/tex]

[tex]f(x+h)-f(x)h=4x+4h+4-4hx+4h[/tex]

[tex]f(x+h)-f(x)h=-4hx+8h+4x+4[/tex]

[tex](5x - 23) + (7x - 1) = 180 \\ 5x + 7x - 23 - 1 = 180 \\ 12x - 24 = 180 \\ 12x = 180 + 24 \\ 12x = 204 \\ \frac{12x}{12} = \frac{204}{12} \\ x = 17[/tex]

x=17°

Angles opposite to shorter sides are shorter. Then, the shortest angle is opposed to the shortest side.

Since the shortest side has a length 2.8 and is opposed to the angle A, then the shortes angle is A.

The next shortest side is that opposite to B, which has a length of 3.4.

And finally, the largest side has a length of 4.7 and it's opposite to the angle C.

Therefore, the list of angles from largest to smallest, is:

Answer:

55

Step-by-step explanation:

First solve for f(-3):

[tex]f(-3) = 3(-3)^2-(-3)+5[/tex]

[tex]f(-3)=3(9)+3+5[/tex]

[tex]f(-3)=27+3+5[/tex]

[tex]f(-3) = 35[/tex]

Second solve for f(2):

[tex]f(2) = 3(2)^2-(2)+5[/tex]

[tex]f(2) = 3(4)-(2)+5[/tex]

[tex]f(2) = 12-2+5[/tex]

[tex]f(2) = 15[/tex]

Now plug in f(-3) and f(2) to the expression:

[tex]2(f(-3))-(f(2)) =[/tex]

[tex]2(35)-(15)=[/tex]

[tex]70-15=55[/tex]

The parabolic equation that passes through the points is y = 29/7x^2 + -27/7x - 342/7

Parabolic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The given parameters are

x-intercepts (-3,0) and (4,0)

Point = (2,-40)

From the definition above, we have the form to be

y = ax^2 + bx + c

Substitute (-3,0) and (4,0)  in the above equation

So, we have

0 = a(-3)^2 + b(-3) + c

0 = a(4)^2 + b(4) + c

This gives

9a -3b + c = 0

16a + 4b + c = 0

Substitute (2,-40) in the above equation y = ax^2 + bx + c

a(2)^2 + b(2) + c = -40

So, we have

4a + 2b + c = -40

The equations become

9a -3b + c = 0

16a + 4b + c = 0

4a + 2b + c = -40

Using a graphing tool, we have

a = 29/7, b = -27/7 and c = -342/7

So, we have

y = ax^2 + bx + c

This gives

y = 29/7x^2 + -27/7x - 342/7

Hence, the equation is y = 29/7x^2 + -27/7x - 342/7

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Using the probability concept, we have that:

a) The probability is of 0.244.

b) The probability is of 0.756.

c) A student given a $1 bill is more likely to have kept the money.

A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.

For item a, we have that out of 11 + 34 = 45 students who were given a $1 bill, 11 spent the money, hence the probability is given as follows:

p = 11/45 = 0.244.

For item b, we have that out of 11 + 34 = 45 students who were given a $1 bill, 34 kept the money, hence the probability is given as follows:

p = 34/45 = 0.756.

For item c, we have that a student given a $1 bill is more likely to have kept the money, as 0.756(kept) > 0.244(spent), which are the two probabilities we found in the previous items.

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Answer:

t > -2/3

Step-by-step explanation:

−8>−3t−10

Step 1: Flip the equation.

−3t−10<−8

Step 2: Add 10 to both sides.

−3t−10+10<−8+10

−3t<2

Step 3: Divide both sides by -3.

−3t/−3 < 2/−3

t > −2/3

He must save 21 dollars per week to meet the goal.

Given,

Katie wants to save at least $280

He currently has $112 saved.

If he has 8 weeks left to save.

Solution:

The amount to be saved is $280 - $112 = $168

If he has 8 weeks left to save,

Per week he must save = $168/8

= $21

He must save 21 dollars per week to meet the goal.

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The result of the multiplication operation yields 7 7/12

From the question, we are to multiply the given fractions. The given fractions are

1 3/4 and 4 2/6

First, we will convert the fractions to improper fractions

Converting 1 3/4 to an improper fraction

1 3/4 = 7/4

Converting 4 2/6 to an improper fraction

4 2/6 = 26/6

Thus,

The multiplication operation becomes

7/4 × 26/6

= 7/4 × 13/3

= 91/12

= 7 7/12

Hence, the product of the given numbers is 7 1/12

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Answer:

3:7

Step-by-step explanation:

Given:

To Find:

Formula used:

Using the formula, we have

No. of boys = 28 - 16 = 12

Proportion of boys = 12/28 = 3/7

So, proportion of boys = 3:7.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

angle = 26 degress

complement angle = ?

Step 02:

26 + x = 90

x = 90 - 26

x = 64

The answer is:

The complement angle is 64 degrees

The group of restrictions used to simulate the issue includes

The issue includes the following information.

The following are the restrictions for modeling the issue: There is a maximum of a five-fold difference between the number of hours Savanah has booked and that John has.

Savanah will provide childcare for at least 40 hours, with no more than meaning it is not larger than that which suggests it is less than, Hence, y<5x

Meaning "at least 40 hours" is "at least 40 hours." 40 hours or more may be expressed as

y ≥ 40 hours

The two necessary restrictions are represented as y< 5x and y=> 40 hours in an inequality model.

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We are asked to find the simple interest associated with a principal of 5480 , an annual rate of 0.04 (4%) and at the end of 7 years:

We use the simple interest formula:

I = P r t

in our case: I = (5480) (0.04) (7) = 1534.4

So the interest is: 1534.40

We answer using two decimal places because this is refering to cents of a dollar.

Given:

v is the given vector.

To find:

Find the direction angle of v.

Formula to find the direction:

From the given vector x and y are:

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

he deatails of the solution are as follows:

rom tjhe triangle, we can see that Traingle KLM is an isosceles triangle, such that Angle J = 52.3 degrees suchn that:

Now, we have that:

ONCLSUSION:

The measure of Angle L =

Answer:

  C.  One solution

Step-by-step explanation:

You want to know the number of solutions of a system of equation such that the graph of the linear function touches the graph of the quadratic function at its minimum.

The number of real solutions of the system of equations is equal to the number of points of intersection of their graphs. The problem statement tells you the graphs intersect at one point, so there is one solution.

__

Additional comment

The linear function can only touch the minimum of a quadratic if its graph is a horizontal line.

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The distance between MO is 9.

From the question MP is straight line and O & N is points between M & P.

so the total length of line is 15

Need to find MO , To find  MO = MP - (NP - NO)

                                                   = 15 - (8 -2)

                                                  = 15 - 6 = 9

The MO is 9.

To find points in graph :

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The midpoint of the given points (11, 3) and (4, 3) on the coordinate plane is ( 15/2, 3 ).

A midpoint is simply a point that divides a line segment into two equal halves.

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Given the data in the question;

Point 1( 11, 3 )

Point 2( 4, 3 )

Midpoint = ?

To find the midpoint, plug the given points into the midpoint formula above and simplify.

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

M = ( ( 11 + 4 )/2, ( 3 + 3 )/2 )

M = ( ( 15 )/2, ( 6 )/2 )

Midpoint M = ( 15/2, 3 )

Therefore, the midpoint of the given coordinates is ( 15/2, 3 ).

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