x - 4y = -8
3x + 8y = 12

Answer:

Step-by-step explanation:

a(n) = a(1) + (n-1)d

a(n) = -9 + (n-1) x (-6-(-9)

a(n) = -9 + (n-1) x (-6 +9)

a(n)=  -9 + (n-1) x 3

a(n) = -9 + 3n - 3

a(n) = 3n - 12

a(30) = 3 x 30 - 12

a(30) = 90 - 12

a(30) = 78

The quadratic function which models the motion of the penny is

h(t) = -4.9t² -0.327761 t + 52.6  

and the maximum height reached is 57.43

h(t) = - 0.5gt² + vt + h

g = 9.8 m/s²

h = 52.6 m

v = ?

For v,

h(t) = -0.5gt² + vt + 52.6

h(t) = - 4.9t² + vt + 52.6

Time when penny hits the ground ; t = 3.31

h(3.31) = 0

0 = -4.9(3.31)² + v(3.31) + 52.6

0 = -53.68489 + 3.31v +52.6

3.31v = -1.08489

v = -1.08489/3.31

v = -0.327761 m/s

Therefore,

h(t) = -4.9t² -0.327761 t + 52.6

2.) Maximum height of the penny above the ground

t = 0.85 seconds

h(0.85) = -4.9(0.85^2)-0.327761 (0.85) + 52.6

Maximum height reached =  57.43 meters

Therefore, the maximum height reached is 57.43 meters.

An object changing its position with regard to time is referred to as motion. Motion is mathematically characterised in terms of displacement, distance, velocity, acceleration, and speed as well as the observer's frame of reference and the measurement of the change in the body's position with respect to that frame over time. Kinematics is the area of physics that studies how motion is affected by forces, whereas dynamics is the area that studies how motion is affected by forces.

To learn more about motions

https://brainly.com/question/18980389

#SPJ4

Consta8of proportionality is 1/9

Answer:

Step-by-step explanation:

Answer= use 2 eggs per 1 cup of flour to make 1 serving.

The probabilty that the first card is 7 and the second card is 6 numbered would be 0.0059.

What is probability?

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.

It is given that there is a deck of 52 cards.

So sample space (n) = 52.

Now in the first draw, 7 numbered card should be drawn

and there are four 7 numbered cards in a deck of 52 cards

so probability of drawing a 7 numbered card will be = 4/52 = 2/26

Now in the second draw, 6 numbered cards should be drawn

and there are four 6 numbered cards in a deck of 52 cards but already one card is drawn so there will be 51 cards remaining in the deck.

so probability of drawing a 6 numbered card will be = 4/51

Hence the probability that the first card is 7 and the second card is 6 numbered will be = 2/26 * 4/51

                             = 0.076 * 0.078

                             = 0.0059

Hence, the probabilty that the first card is 7 and the second card is 6 numbered would be 0.0059.

To learn more about probability in mathematics, visit:

https://brainly.com/question/24756209

#SPJ4

The approximate change per day since the lowest price occurred 35 days ago, is a. $2.08.

The approximate average change can be found by the formula :

= ( Current price of stock - Lowest price ) / Number of days since lowest price

Current price of Dagofi Radar stock = $ 130. 58 closing price

Lowest price = $ 57. 71

The approximate average change is:

= ( 130. 58 - 57. 71) / 35

= 72. 87 / 35

= $ 2.08

Find out more on approximate average change at https://brainly.com/question/22409149

#SPJ1

Missing part of question:
Consider today's stock listing for Dagofi Radar, shown below.

52 wk High

52 wk Low

Symbol

Div.

Close

Net Change

162.22

57.71

DFR

9.75

130.58

-2.64

Answer:

Step-by-step explanation:

You want the acute angles in a right triangle in which the larger is 8 times the smaller.

The ratio of the acute angles in the triangle is 1 : 8, so the smaller one is 1/(1+8) = 1/9 of the sum of the two angles.

The sum of the acute angles in a right triangle is 90°, so the smaller one is ...

  (1/9)(90°) = 10°

The larger is 8 times that:

  8 × 10° = 80°

The smaller angle is 10°; the larger angle is 80°.

<95141404393>

The minimum unit cost is 7738 when the function is C(x)=1.2x²-600x+82,738

A company's unit cost is the cost of producing, storing, and selling one unit of a specific product. Unit costs encompass all fixed and variable production costs. A cost unit is a quantity measuring unit for a product or service.

A unit cost is the overall cost incurred by a business to manufacture, store, and sell one unit of a specific product or service. Unit costs are the same as cost of goods sold (COGS). This accounting metric incorporates all fixed and variable expenses related with the manufacture of a good or service.

Given,

C(x)=1.2x²-600x+82,738

Minimum value [tex]C_{min}[/tex]=c-(b²/4a)

Where a=1.2, b=-600, c=82738

[tex]C(x)_{min}[/tex]=82738-((-600)²/4(1.2))

=82738-(360000/4.8)

=7738

Therefore, the minimum unit cost is 7738.

Hence, the minimum unit cost is 7738 when the function is C(x)=1.2x²-600x+82,738

To know more about variable cost, visit:

https://brainly.com/question/15358722

#SPJ1

Answer:

x^2+16x+64

Step-by-step explanation:

(x+8)^2 is (x+8)(x+8)

This equals x^2+8x+8x+64=x^2+16x+64

Answer:

90°

Step-by-step explanation:

Note that the sum of the exterior angles of an octagon is 360°. Therefore we can say:

x+2x+3x+4x+5x+7x+8x+10x=360

40x=360

x=9

10x° is the largest exterior angle and x=9, so 10x°=90°

Hope this helps :)

Rachel's total income is $13320.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Rachel works at 'Best Price Cars' and earns $9 per hour plus 4% commission on every car she sales.

Commission = 9 x 0.04 = $0.36

Commission on 36000 cars = $12960

By working 40 hours he earn = 9 x 40 = $360

Hence, the total income = 360+ 12960 = $13320

Learn more about Unitary method here:

https://brainly.com/question/22056199

#SPJ1

Number of kids ticket is 40

What do you mean by system of linear equation?

A set of two linear equations with two variables is a system of linear equations. There are infinitely many possible solutions to a linear equation with two variables. There can be a single solution to a system of two linear equations with two variables that satisfies both solutions. It is necessary to combine two equations with two variables into one equation with one variable while solving a system of equations.

Total number of tickets = 60

Cost of 1 kid ticket = $3

Cost of 1 adult ticket = $5

Total profit = $220

Let number of kid tickets = x

number of adult tickets = y

According to question:

x + y = 60 ......(1)

3x + 5y = 220 ........(2)

Substitute the value of x from eq(1) to eq(2)

3(60 - y) + 5y = 220

180 - 3y + 5y = 220

180 + 2y = 220

2y = 220 - 180

2y = 40

y = 40/2

y = 20

Substitute this value of y in eq(1)

x + 20 = 60

x = 60 - 20

x = 40

Therefore, number of kids ticket is 40

To learn more about linear equation from the given link.

https://brainly.com/question/2030026

#SPJ4

The problem is based on laws of exponents and answer to this Question is a = 2 and b = 14

What are laws of exponents?

Laws which are used to solve the problems including the exponents are called laws of exponents

Solution:

As we can clearly see in whole expression 2 is present in every term

By laws of Exponents we can take 2 common out and we can easily express this thing in given form that a multiplied 2 rays to power b

When we solve this expression we get

this expression equal to 2^15

which we can write 2×2^14

hence on comparing we get a = 2 and b = 14

To learn more about Exponent laws

https://brainly.com/question/28966438

#SPJ9

Answer:125

Step-by-step explanation:

At a standard deviation of $15,000, the probability that the condominium will sell at a price below $200,000 is 0.2525 and above $240,000 is 0.02. At a standard deviation of $20,000, the probability that the condominium will sell at a price below $200,000 is 0.3085 and above $240,000 is 0.0668.

From the given question;

Let the average sale price(μ)=210,000

Standard Deviation(σ)=$15,000

(a) We have to find the probability that the condominium will sell at a price.

(i) below $200,000, i.e. P(x<200,000)

Z=(x−μ)/σ

Z=(200,000−210,000)/15,000

Z= −10,000/15000

Z= −0.67

Now finding P(x<200,000) is same as finding P(Z<−0.67) using the standard table of z.

P(Z<−0.67) = 0.2525

(ii) above $240,000, i.e. P(x>240,000)

Z=(x−μ)/σ

Z=(240,000−210,000)/15,000

Z= 30,000/15000

Z= 2

Now finding P(x>240,000) is same as finding P(Z>2) using the standard table of z.

P(Z>240,000)=P(Z>2)

P(Z>240,000)=1−P(Z<2)

P(z>240,000)=1−0.98

P(z>240,000)=0.02

(b) Now the average sale price(μ)=210,000

Standard Deviation(σ)=$20,000

We have to find the probability that the condominium will sell at a price.

(i) below $200,000, i.e. P(x<200,000)

Z=(x−μ)/σ

Z=(200,000−210,000)/20,000

Z= −10,000/20000

Z= −0.5

Now finding P(x<200,000) is same as finding P(Z<−0.5) using the standard table of z.

P(Z<−0.5) = 0.2085

(ii) above $240,000, i.e. P(x>240,000)

Z=(x−μ)/σ

Z=(240,000−210,000)/20,000

Z= 30,000/20000

Z= 1.5

Now finding P(x>240,000) is same as finding P(Z>1.5) using the standard table of z.

P(Z>240,000)=P(Z>1.5)

P(Z>240,000)=1−P(Z<1.5)

P(z>240,000)=1−0.93319

P(z>240,000)=0.0668

To learn more about probability link is here

brainly.com/question/26836799

#SPJ4

The sampling technique used in the given scenario is Systematic sampling technique.

Systematic sampling technique

Systematic sampling is a probability sampling technique in which researchers randomly choose individuals of a population at regular intervals. The sampling interval, or fixed periodic interval, is calculated by dividing the population size by the required sample size.

Types of Systematic sampling technique

A systematic sample can be generated in three ways:

Systematic random sampling: The most common type of systematic sampling in which the subject is chosen at a predefined interval.

Linear systematic sampling: Instead of picking the sample interval at random, a skip pattern is constructed by following a linear path.

Circular systematic sampling: It occurs when a sample begins from the same spot where it ends.

To know more about Systematic sampling technique, check out:

https://brainly.com/question/28505229

#SPJ4

Answer:

hi do you mind making the question a bit clear? where is the table?

Step-by-step explanation:

Answer:

Since the only even prime number is 2, we can say that its reciprocal is 1 2 \dfrac{ 1 }{ 2 } 21​. By checking, we get 2 × 1 2 = 1 2 \times \dfrac{ 1 }{ 2 } = 1 2×21​=1.

Step-by-step explanation:

The third term of the sequence is 3/x+5 when the arithmetic sequence is 1/x+3, 2/x+4,....

Given that,

The first two terms of an arithmetic sequence are given that is

1/x+3, 2/x+4,....

We have to find the third term of this sequence.

We know that,

The arithmetic sequence is the set of terms where the common difference between any two succeeding terms is always the same. Recall the definition of a sequence. A group of integers that follow a pattern is referred to as a sequence.

There are two ways of defining an arithmetic sequence. A "sequence where the differences between each pair of succeeding terms are the same" is what it is. Alternatively, "each term in an arithmetic sequence is obtained by adding a fixed number (positive, negative, or zero) to its preceding term."

The sequence has

n/x+(n+2)

Take n=1 is 1/x+3

Take n=2 is 2/x+4

Take n=3 is 3/x+5

Therefore, The third term of the sequence is 3/x+5 when the arithmetic sequence is 1/x+3, 2/x+4,....

To learn more about sequence visit: https://brainly.com/question/21961097

#SPJ1

From the given Venn diagram, the value of  M∩N={4,7}.

A Venn diagram is a prominent diagram type that depicts the logical relationship between sets. It was popularized in the 1880s by John Venn (1834-1923). The diagrams are used to teach elementary set theory and to show simple set relationships in probability, logic, statistics, linguistics, and computer science. To depict sets, a Venn diagram uses basic closed curves drawn on a plane. These curves are almost often circles or ellipses.

Before Venn, similar concepts had been presented. Similar ideas were proposed by Christian Weise in 1712 and Leonhard Euler (Letters to a German Princess) in 1768. Venn popularized the concept in Symbolic Logic, Chapter V "Diagrammatic Representation," 1881.

The intersection of two sets is the set of all the elements that are shared by both.

M={4,7,9,3}

N={4,7,6}

Because M and N share the numbers 4 and 7, M∩N={4,7}.

To know more about Venn diagram, visit:

https://brainly.com/question/29301560

#SPJ9

If Cary earned $45600 before tax, then she paid $18240 as tax

The amount that Cary earned last year = $45600 before tax

The rate of tax if earning exceed of 43000 and up to 150000 = 40%

Then the amount of tax = The amount that Car earned last year × (The rate of tax if earning exceed of 43000 and up to 150000 / 100)

Substitute the values in the equation to find the tax amount

The amount of tax = 45600 × (40/100)

Divide the numbers first

= 45600 × 0.40

Multiply the numbers

= $18240

Hence, the amount of tax that he paid is $18240

Learn more about rate of tax here

brainly.com/question/13184546

#SPJ4

t approaches infinity then salt is:

[tex]Q(\infty) = 18lb[/tex]

What is volume?

Volume is a mathematical term used to describe how much three-dimensional space an object or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc. Volume is sometimes referred to as capacity.

The amount of salt in the barrel at time t is given by

where Q(t) is in pounds and time t is in minutes.

(a) Salt after 5 minutes i.e. t=5

[tex]Q(5) = 18(1 - e^{-0.08(5)} ) = 18(1 - e^{-0.4})\\\\Q(5) = 18(1 - 0.6703) = 5.93 \\\\Q(5) = 5.93lb[/tex]

(b) Salt after 10 minutes i.e. t=10

[tex]Q(10) = 18(1 - e^{-0.08(10)} ) = 18(1 - e^{-0.8} )\\\\Q(10) = 18(1 - 0.4493 ) = 9.91\\\\Q(10) = 9.91lb[/tex]

(d) When t becomes large, let say when t approaches infinity then salt is

[tex]Q(\infty) = 18(1 - e^{-0.08(\infty)} ) = 18(1- e^{-\infty})\\\\Q(\infty) = 18(1 - 0) = 18\\\\Q(\infty) = 18lb[/tex]

Learn more about volume link below

https://brainly.com/question/463363

#SPJ1

The solution of the equations 3x - 5y = 15 and x - 4y = 12 will be (0, -3).

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of equations is given below.

3x - 5y = 15         ...1

x - 4y = 12          ...2

From equation 2, then we have

x = 4y + 12  

Put in equation 1, then we have

3(4y + 12) - 5y = 15

12y + 36 - 5y = 15

7y = -21

y = - 3

Then the value of the variable 'x' is calculated as,

x = 4(-3) + 12

x = - 12 + 12

x = 0

The solution of the equations 3x - 5y = 15 and x - 4y = 12 will be (0, -3).

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ1

Answer:

Step-by-step explanation:

12 root 6 is the answer because the 3 root 8 can be simplified to 6 root 2, so you when you multiply 2 root 3 with 3 root 8, you get 12 root 6.

Answer:

[tex]12\sqrt{6}[/tex]

Step-by-step explanation:

Given expression:

[tex]2 \sqrt{3} \cdot 3 \sqrt{8}[/tex]

Multiply the numbers 2 and 3:

[tex]\implies 6\sqrt{3}\sqrt{8}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}:[/tex]

[tex]\implies 6\sqrt{3 \cdot 8}[/tex]

Simplify:

[tex]\implies 6\sqrt{24}[/tex]

Rewrite 24 as 4 · 6:

[tex]\implies 6\sqrt{4 \cdot 6}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 6\sqrt{4}\sqrt{6}[/tex]

Rewrite 4 as 2²:

[tex]\implies 6\sqrt{2^2}\sqrt{6}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]

[tex]\implies 6 \cdot 2 \sqrt{6}[/tex]

Multiply the numbers 6 and 2:

[tex]\implies 12 \sqrt{6}[/tex]

The median will be greater than 10 and less than 15.

Given,

The mean of the skewed distribution = 15

The mode of the skewed distribution = 10

We have to find the potential range of the median for a positively skewed distribution;

Here,

The empirical relationship between mean, median, and mode for a frequency distribution that is positively skewed is mean > median > mode. Based on this, the range of the median is 15 > median > 10 if the mean is 15 and the mode is 10.

Therefore,

The median will  be higher than 10 and lower than 15.

Learn more about mean, mode and median here;

https://brainly.com/question/17877219

#SPJ4

Answer:

Step-by-step explanation:

i don't think so

Answer:

Step-by-step explanation:

The area of the part of the plane 2x+y+2z=4 in the first octant is S= [tex]\int_{0}^{2}\int_{0}^{-2x+4}\frac{3}{2}dydx[/tex].

In the given question we have to check which of the following integrals represents the area of the part of the plane in the first octant.

The given plane is 2x+y+2z=4 that lies in the first octant.

In the first octant the all variables are positive.

First we need to find the equation of hypotenuse in the linethat intersects xy plane means z=0. So:

2x+y=4

y=4-2x

Now find the surface area. We need the function in the form of z=f(x,y). So:

2x+y+2z=4

2z=4-2x-y

z=(4-2x-y)/2

On taking the partial derivative we get

f(x) = -1 and f(y) = -1/2

Now the defining the limits will be;

0≤x≤2 and 0≤y≤ (-2x+4)

So the area will be;

S= [tex]\int \int _{D}\sqrt{f(x)^{2}+f(y)^{2}+1}dydx[/tex]

S= [tex]\int_{0}^{2}\int_{0}^{-2x+4}\sqrt{(-1)^{2}+(-1/2)^{2}+1}dydx[/tex]

S= [tex]\int_{0}^{2}\int_{0}^{-2x+4}\sqrt{1+1/4+1}dydx[/tex]

S= [tex]\int_{0}^{2}\int_{0}^{-2x+4}\sqrt{(4+1+4)/4}dydx[/tex]

S= [tex]\int_{0}^{2}\int_{0}^{-2x+4}\sqrt{9/4}dydx[/tex]

S= [tex]\int_{0}^{2}\int_{0}^{-2x+4}\frac{3}{2}dydx[/tex]

To learn more about area of plane link is here

brainly.com/question/28238702

#SPJ4

The least possible area is 0 meter² and the greatest possible area is 49.5metre².

With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object.

A rectangle has equal and parallel opposing sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's length is its longer side, while its width is its shorter side.

A little information

1) Parallelograms are all squares, yet squares are all not parallelograms

2) A rectangle is divided into four triangles by its diagonals.

3) While not all rectangles are squares, all squares are rectangles.

How to solve?

Area of rectangle is given by = length × breadth.

For minimum area, we have one digit whole number.

In whole number smallest digit is 0

so, least possible area =0×breadth=0 metres²,

Now talking about maximum possible area, the greatest one digit whole number is 9.

width of rectangular region is 5.5 meters.

The greatest possible area is =9×5.5=49.5meters².

Hence, the answers are 0 and 49.5 meters².

To know more about area of rectangle, visit here:

brainly.com/question/20693059

#SPJ4

(Complete question) is:

A landscaper digs a rectangular region for a garden. The length is a one digit whole number of meters and width is 5.5 meters. What is the least possible area? What is the greatest possible area?

Answer:

x less than or equal to $75 + $8

Step-by-step explanation:

itll look like this

x <= 75   + 8

x is the price of the hoodie

u can pay for a hoodie that will be under $75 including shipping