Find P 20 of the following arithmetic sequence: 206, 212, 218, 224....
State:
Po =
d =
P20 =

Jane received $30025 and Lydia received $60000. Let's assume the amount of money that Jane received as x; then Lydia's share of the money will be twice the share of Jane.

We are to find out the share of each person. Here is the solution in steps:Suppose Jane's share was x dollars, and Lydia's share was y dollars.

Given that the total amount given to the two daughters was $90000. Also, given that Lydia paid off her $75, hence she got $75 less than Jane.

Therefore,  y = 2x - 75; this is because we are given that Lydia got twice the share of Jane, and also, she got $75 less than Jane. Hence, x + y = $90000, this is because the total sum of money shared is $90000.

Substituting y = 2x - 75 into x + y = $90000 gives x + (2x - 75) = $90000.

Simplifying, we have :3x = $90000 + 75 = $90075.

Dividing both sides by 3, we get:x = $30025. Hence, Jane's share is $30025 Lydia's share = 2x - 75 = 2($30025) - $75 = $60075 - $75 = $60000.

Therefore, Jane received $30025 and Lydia received $60000.

For more question on amount

https://brainly.com/question/25720319

#SPJ8

Answer:

the square root of 16 is 4

Answer:

19 miles

Step-by-step explanation:

y = mx + b  

y = the total cost

m = the number of miles

x = the cost per mile

b = pick-up fee

98.20 = m(5) + 3.20   Subtract 3.20 from 98.2

95 = 5m divide both sides by 5

19 = m

If the taxi company charged a pick-up fee of $3.20 plus $5 per mile and the total fare was $98.20 the equation representing the given relation is 98.20 = m(5) + 3.20 and the obtained value of m is 19 miles.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that the taxi company charged a pick-up fee of $3.20 plus $5 per mile and the total fare was $98.20.

If m, is the number of miles in the taxi ride, y represents the total fare, x represents the charge per mile and b represents the pickup charge.

y = mx+ b

98.20 = m(5) + 3.20  

5m = 98.20 - 3.20

95 = 5m

19 = m

Thus, if the taxi company charged a pick-up fee of $3.20 plus $5 per mile. The total fare was $98.20 the equation representing the given relation is 98.20 = m(5) + 3.20 and the obtained value of m is 19 miles.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ2

Answer:

7a + 3 -3 =45 - 3

7a + 0 = 42

7a = 42

7a/7 = 42/7

a = 6

The monthly cell phone bill when shared data equals zero is given as follows:

$26.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The intercept of the line in this problem is given as follows:

b = 26.

Hence $26 is the monthly cell phone bill when shared data equals zero.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.

Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.

Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.

At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.

To learn more about equilibrium of demand and supply:

https://brainly.com/question/30237240

Answer:

Step-by-step explanation:

Let assume that the volume = 88 cubic feet

Then:

\(L = 3w --- (1)volume = l \times w \times h \\ \\ 88 = (3w) \times w \times h \\ \\ 3w^2 h= 88 \\ \\ h = \dfrac{88}{3w^2}--- (2) \\ \\\)

The construction cost now is:

\(C = 4(l \times w) + 2 ( w \times h) + 2(l \times h) \\ \\ C = 4(3w^2) + 2(w \times \dfrac{88}{3w^2}) + 2(3w \times \dfrac{88}{3w^2}) \\\\ C = 12w^2 + \dfrac{176}{3w} + \dfrac{176}{w}\)

Now, to determine the minimum cost:

\(\dfrac{dC}{dw}= 0 \\ \\ \implies 24 w - \dfrac{176}{3w^2}- \dfrac{176}{w^2}=0 \\ \\ 24 w ^3 = \dfrac{176}{w^2}(\dfrac{1}{3}+1) \\ \\ 24 w ^3 = \dfrac{176(4)}{3} \\ \\ w^3 = \dfrac{88}{3(3)}\)

\(w = \dfrac{88}{3(3)}^{1/3} \ feet\)

Now;

\(length = 3 ( \dfrac{88}{3(3)})^{1/3} \ feet\)

\(height = ( 88})^{1/3} (3)^{1/3} \ feet\)

Answer:

105ft per minute

Step-by-step explanation:

well, if he/she walks 7ft in 4s, then you divide 60/4. In which you get 15.

15•7=105

Kala spun the spinner 1000 times and got the following results:

- Yellow: 400 times

- Red: 300 times

- Blue: 300 times

1. Calculate the amount of sales tax:

  - The item costs $350 before tax.

  - The sales tax rate is 14%.

  - To find the sales tax amount, multiply the cost of the item by the tax rate:

    Sales tax = $350 * 0.14 = $49.

2. Determine the total cost of the item including tax:

  - Add the sales tax amount to the original cost of the item:

    Total cost = $350 + $49 = $399.

3. Analyze the spinner results:

  - The spinner has 10 equal-sized slices.

  - There are 4 yellow slices, 3 red slices, and 3 blue slices.

  - Kala spun the dial 1000 times.

4. Calculate the frequency of each color:

  - Yellow: Kala got 400 yellow results out of 1000 spins.

  - Red: Kala got 300 red results out of 1000 spins.

  - Blue: Kala got 300 blue results out of 1000 spins.

5. Calculate the probability of landing on each color:

  - Yellow: Probability = Frequency of yellow / Total spins = 400 / 1000 = 0.4.

  - Red: Probability = Frequency of red / Total spins = 300 / 1000 = 0.3.

  - Blue: Probability = Frequency of blue / Total spins = 300 / 1000 = 0.3.

For more such questions on spinner, click on:

https://brainly.com/question/32737567

#SPJ8

For the forecasting process to be effective, internal data should be highly disaggregated

Predicting the future based on historical and current facts is the forecasting process. The most popular method for doing this is trend analysis. It is typically ideal to use internal data that is significantly disaggregated for forecasting to be successful. This means that rather than aggregating or summarizing the data at a high level, it should be broken down into as much detail as feasible.

Since highly disaggregated data presents a more complete and precise picture of the variables that may impact future events, forecasting can be done more accurately and dependably. This can include information about previous sales, manufacturing rates, inventory levels, costs, and other elements that can be important for forecasting. Whereas, using highly aggregated data can lead to less accurate and reliable forecasts, as it may not capture the full range of factors that may influence future outcomes.

Read more about forecasting on:

https://brainly.com/question/29889592

#SPJ4

If a pole has two wires attached to it, one on each side, forming two right triangles as shown, then the height of the pole is 29.6 feet

Consider the triangle on left hand side

The length of the base = 34 feet

The measure of angle = 41 degrees

Opposite side is the height of the pole

Here we have to use the trigonometric functions

sin θ = Opposite side / Hypotenuse

cos θ = Adjacent side / Hypotenuse

tan θ = Opposite side / Adjacent side

Here we have to use the equation of tan θ

Substitute the values in the equation

tan 41 = Opposite side / 34 feet

Opposite side = 34 × tan 41

= 29.6 feet

Therefore, the height of the pole is 29.6 feet

Learn more about trigonometric functions here

brainly.com/question/25618616

#SPJ4

Answer:

The exponential function is

\(y = {2}^{x} \)

Answer:

148

Step-by-step explanation:

A and B are alternate exterior angles and alternate exterior angles are equal when the lines are parallel

A = B

6x-2 = 4x+48

Subtract 4x from each side

6x-4x-2 = 4x+48-4x

2x-2 = 48

Add 2 to each side

2x-2 +2 = 48+2

2x = 50

Divide by 2

2x/2 = 25

We want to find angle A

A = 6x-2

   = 6*25 -2

    150 -2

  = 148

Answer:

Solution given:

<A=<B{alternate exterior angle are equal}

6x-2=4x+48

6x-4x=48+2

2x=50

x=50/2

x=25

<A=6×25-2=148°

Answer:

Yes, the function f(x) = (x + 2)² is one-to-one.

Answer:

volume is 8 times larger and surface area is about 2.7 times larger

Step-by-step explanation:

a)24 in³ b) 76 in² c) volume is 8 times larger and surface area is about 2.7 times larger.

Answer:

f(-5)=5

Step-by-step explanation:

the "-5" is telling us what to plug in for x. So, the new equation would be:

f(-5)= -(-5)^2-7(-5)-5

if we reduce, the expression would be

-25+35-5

our final answer would be 5.

The system of equations that allows finding the cost of each bag of tulip bulbs (t) and each bag of daffodil bulbs (d) are:

A system of equations refers to simultaneous equations, which are two or more equations that must be solved together.

                           Tulip      Daffodil     Total Sales

Lisa's sales             4              8               $176

Mark's sales           8              6               $192

Lisa's sales, L = 4t + 8d = 176 ... equation 1

Mark's sales, M = 8t + 6d = 192 ... equation 2

Multiply equation 1 by 2:

8t + 16d = 352 ... equation 3

Subtract equation 2 from equation 3:

8t + 16d = 352

- 8t + 6d = 192

= 10d = 160 (352 - 192)

d = 16 (160/10)

Substitute d in either equation 1 or 2, to get t:

8t + 6d = 192

8t + 6(16) = 192

8t + 96 = 192

8t = 96

t = 12 (96/8)

4t + 8d = 176

= 4(12) + 8(16) = 176

= 48 + 128 = 176

176 = 176

Thus, the cost of each bag of tulip bulbs (t) is $12, while the cost of one bag of daffodil bulbs (d) is $16 based on the system of equations above.

Learn more about the system of equations at https://brainly.com/question/13729904

#SPJ1

Answer:

16

Step-by-step explanation:

can't really explain it but it's 16 trust me

Answer:

Step-by-step explanation:

4/7 balls are blue

so 3/7 are red

28/7=4

4 x 3=12

Step-by-step explanation:

To eliminate x in the system of equations:

1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:

Equation 1: 36x -54y = 90

Equation 2: -36x - 8y = -28

2. Add the two equations together to eliminate x:

(36x - 54y) + (-36x - 8y) = 90 - 28

Simplifying, we get:

-62y = 62

3. Solve for y:

y = -1

4. Substitute y = -1 into one of the original equations, say Equation 1:

4x - 6(-1) = 10

Simplifying, we get:

4x + 6 = 10

5. Solve for x:

4x = 4

x = 1

Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.

Answer:

Answer:

The angle D is 64 degrees.

Step-by-step explanation:

This is because they are vertical

Answer:

i think its the yellow square

Step-by-step explanation:

13.13.13.13.13 in exponential form is 13^5

The expression is given as:

13.13.13.13.13

The factors of the above expression are 13.

And each factor is grouped by product

There are five 13s in the expression.

So, we have:

13.13.13.13.13 = 13^5

Hence, 13.13.13.13.13 in exponential form is 13^5

Read more about exponential form at:

https://brainly.com/question/2456547

#SPJ1

Answer:

$2.20

Step-by-step explanation:

Original price (before discount and before tax): $5

Discount is 60%.

Amount of discount is: 60% of $5 = 0.6 × $5 = $3

Price after 60% discount: $5 - $3 = $2

Tax is 10%.

Amount of tax is: 10% of $2 = 0.1 × $2 = $0.20

Final price = price after discount + tax = $2.00 + $0.20 = $2.20

A percentage is a way to describe a part of a whole. The final price of the candy, including the discount and a 10% sales tax is $2.2.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that the cost of the candy is $5 and a 60% discount is given on the candy. Therefore, the price of the candy after the discount will be,

Discounted price = Price - 60% of price

                             = $5 - 0.60($5)

                             = $5 - $3

                             = $2

Now, on the price of the candy 10% sales tax will be added. Therefore, the Price of the candy after adding Tax will be,

Taxed price = Discounted price + 10% of discounted price

                    = $2 + 0.10($2)

                    = $2 + $0.2

                    = $2.02

Hence, the final price of the candy, including the discount and a 10% sales tax is $2.2.

Learn more about Percentages here:

https://brainly.com/question/6972121

#SPJ2

The missing parts of the triangles are found below.

1) Cos 34 = x/13

x = 13Cos 34

= 12.9

2) Sin 43 = x/19

x = 19Sin 43

= 13

3) Cos 65 = 16/x

x = 16/Cos 65

= 38

4) Cos 47 = x/13

x = 13Cos 47

= 9

5) Sin 57 = 20/x

x = 20/Sin57

x = 24

6) Sin 69 = 11/x

x = 11/Sin 69

= 12

7) Cos 22 = 12/x

x = 12/Cos 22

x = 13

8) Sin 26 = 17/x

x = 12/Sin 26

x = 27

9) Sin 38 = 17/x

x = 17/Sin 38

x = 28

These are the parts that we need to find in the triangles above.

Learn more about triangle:https://brainly.com/question/2773823

#SPJ1

The equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

To find an equation in slope-intercept form that passes through the point (1, -2) and is perpendicular to the given equation y = 5x + 4, we need to determine the slope of the perpendicular line.

The given equation y = 5x + 4 is already in slope-intercept form (y = mx + b), where m represents the slope. In this case, the slope of the given line is 5.

To find the slope of a line perpendicular to this, we use the fact that the product of the slopes of two perpendicular lines is -1. So, the slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line.

The negative reciprocal of 5 is -1/5.

Now that we have the slope (-1/5) and a point (1, -2), we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Substituting the values:

y - (-2) = (-1/5)(x - 1)

Simplifying:

y + 2 = (-1/5)(x - 1)

To convert the equation into slope-intercept form (y = mx + b), we need to simplify it further:

y + 2 = (-1/5)x + 1/5

Subtracting 2 from both sides:

y = (-1/5)x + 1/5 - 2

Combining the constants:

y = (-1/5)x - 9/5

Therefore, the equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

For more question on perpendicular visit:

https://brainly.com/question/1202004

#SPJ8

Answer:

\(x = \frac{9}{ \sqrt{2} } = \frac{9 \sqrt{2} }{2} \)

The quadratic equation of the parabola representing the flight of the ball is: y = \(46x^2 - 153x + 170\)

To find the quadratic equation of the parabola representing the flight of the ball, we can use the standard form of a quadratic equation: y = \(ax^2\) + bx + c.

Given the points (1, 63), (2, 48), and (3, 1), we can substitute these values into the equation to form a system of three equations:

Equation 1: 63 =\(a(1^2) + b(1) + c\)

Equation 2: 48 =\(a(2^2) + b(2) + c\)

Equation 3: 1 = \(a(3^2) + b(3) + c\)

We can simplify these equations:

Equation 1: 63 = a + b + c

Equation 2: 48 = 4a + 2b + c

Equation 3: 1 = 9a + 3b + c

Now, we can solve this system of equations to find the values of a, b, and c. Subtracting Equation 1 from Equation 2 and Equation 3, we get:

Equation 4: 48 - 63 = 4a + 2b + c - (a + b + c)

Equation 5: 1 - 63 = 9a + 3b + c - (a + b + c)

Simplifying these equations:

Equation 4: -15 = 3a + b

Equation 5: -62 = 8a + 2b

Now, we have a system of two equations (Equation 4 and Equation 5) with two variables (a and b). Solving this system of equations, we get:

Multiply Equation 4 by 2: -30 = 6a + 2b

Subtract Equation 5 from this result: 30 - (-62) = 6a + 2b - (8a + 2b)

92 = -2a

a = -92 / -2

a = 46

Substituting the value of a into Equation 4:

-15 = 3(46) + b

-15 = 138 + b

b = -15 - 138

b = -153

Now, we have found the values of a and b. To find the value of c, we can substitute any of the given points into the equation y = \(ax^2 + bx + c.\)Let's use the point (1, 63):

63 = \(46(1^2) + (-153)(1) + c\)

63 = 46 - 153 + c

c = 63 - 46 + 153

c = 170

Therefore, the quadratic equation of the parabola representing the flight of the ball is: y =\(46x^2 - 153x + 170\)

For such more questions on quadratic equation

https://brainly.com/question/28038123

#SPJ11

Answer:

the two numbers are x = -81 - 81*sqrt(7) and y = (-1 - sqrt(7)) / 2.

Step-by-step explanation:

To find the two numbers, we can use the formula for the sum of two numbers:

x + y = z

Where x and y are the two numbers and z is their sum.

In this case, we know that the difference between the two numbers is 9, so we can set x to be the larger of the two numbers and y to be the smaller number:

x - y = 9

We can also use the fact that the product of the two numbers is 162 to set up an equation:

xy = 162

Now we can solve for x and y by substituting the second equation into the first and solving for x:

x = 162/y

Substituting this expression for x into the first equation gives us the following:

(162/y) - y = 9

We can simplify this equation to:

162 - y^2 = 9

We can solve for y by completing the square:

y^2 - y + 4.5 = 0

We can use the quadratic formula to find the solutions for y:

y = (1 +/- sqrt(1 - 414.5)) / (2*1)

This simplifies to:

y = (-1 +/- sqrt(7)) / 2

Since y is the smaller number, we need to choose the negative solution:

y = (-1 - sqrt(7)) / 2

We can use this value of y to find the value of x:

x = 162/y = 162/(-1 - sqrt(7))/2

This simplifies to:

x = (-81 - 81*sqrt(7))/2

So the two numbers are x = -81 - 81*sqrt(7) and y = (-1 - sqrt(7)) / 2.

Answer:

9, 18

Step-by-step explanation:

lets say the smaller number is x, then the larger number is x+9

we know x * (x+9) = 162.

expand to get x^2 + 9x - 162 = 0, factor or use the quadratic formula to get x^2 + 9x -162 = (x + 18) (x - 9) = 0, so x = 9 or -18.

I'm assuming the two numbers must be positive, so x = 9, and the larger number is 9+9 = 18.

Answer:

95

Step-by-step explanation:

Take the missing number as x.

Then the required value of x will be,

→ x ÷ 19 = 5

→ x = 5 × 19

→ [ x = 95 ]

Hence, the number is 95.

Answer:

x ÷ 9

= 5

x = 5 × 19

x = 95

Hance,the number is 95