Paul split an inheritance between two investments, one paying 7% annual interest and the other 10%. He invested twice as much in the 10% investment as he did in the 7% investment. If his combined annual income from the two investments was $4050, how much did he inherit?

Answer: The skis cost $117.60.

Step-by-step explanation:

A pair of skis costing $210 is 30% off.

30% of $210 is $147

Then two weeks later, it will be 20% off THAT price.

20% of $147 is $117.60

Therefore, $117.60 is the clearence price of the skis. Hope this helps!

Answer + Step-by-step explanation:

The effect of the “-“ when y = (x+3) is changed to y = -(x+3) is creating a negative slope and y-intercept,

y = -(x+3) distributed is y = -x - 3

Visual representation:

The red line: y = (x+3)

The blue line: y = -(x+3)

The dimensions of the poster with the smallest area are; 27.75 cm x 27.75 cm

Let "x" and "y" denote the length and the width of the poster.

We are told that the margin of a poster are 4 cm and the side margins are 4 cm.

The length of the print = x - 2(4) = x - 8

The width of the print = y - 2(4) = y - 8

The area of the print = length * width = (x - 8)(y - 8)

The area of the print is given as 390 square inches. Thus;

(x - 8)(y - 8) = 390

Making y the subject gives;

y = (390/(x - 8)) + 8

The area of the poster is; A = xy

Thus;

A = x[(390/(x - 8)) + 8]

A =  (390x/(x - 8)) + 8x

Minimizing the area gives;

A' = 8 - (3120/(x - 8)²)

Equating to zero gives;

8 - (3120/(x - 8)²) = 0

8(x - 8)² = 3120

(x - 8)² = 3120/8

(x - 8)² = 390

x = 27.75 cm

y = (390/(27.75 - 8)) + 8

y = 27.75 cm

Read more about Algebra Word Problems at; https://brainly.com/question/21405634

#SPJ1

The reasonable range for the total cost of the tickets the groups

would pay  is {84, 126, 2163}.

The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation.

A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values.

Given:

The Function modeled for the situation is

f(x) = 21 x where x is the number of tickets sold.

So, For x= 4 Tickets

Fare, F(x) = 21 x 4= $84

and, For x= 6 Tickets

Fare, F(x) = 21 x 6 = $126

and, For x= 103 Tickets

Fare, F(x) = 21 x 103 = $2163.

Hence, the range is {84, 126, 2163}.

Learn more about Domain and Range here:

https://brainly.com/question/28135761

#SPJ1

The number of ways to pick a digit, a lowercase letter, an uppercase letter, or one of eight allowable punctuation marks is 70.

The total number of digits (0-9) = 10.

Thus, the number of ways to pick a digit = 10.

The total number of lowercase letters (a - z) = 26

Thus, the number of ways to pick a lowercase letter = 26.

The total number of uppercase letters (A - Z) = 26

Thus, the number of ways to pick an uppercase letter = 26.

The total number of allowable punctuation marks = 8

Thus, the number of ways to pick a punctuation = 8.

Hence, the total number of ways to pick a digit, a lowercase letter, an uppercase letter, or one of eight allowable punctuation marks is -

10 + 26 + 26 + 8 = 70.

Read more about Permutations and combinations:

brainly.com/question/25966410

#SPJ4

Answer:

m=50

General Formulas and Concepts:

Pre-Alg

Order of Operations: BPEMDAS

Algebra I

Slope Formula:

Step-by-step explanation:

Step 1: Define

Point (40, 3000)

Point (60, 4000)

Step 2: Find slope m

Answer:

5-4=12x+x

1=13x

1/13=×

The function operation (f + g)(x) of the functions f(x) = √( 16x⁴ ) and g(x) = 3x² - 3x - 5 is -5x² + 5x - 7.

A function is simply a relationship that maps one input to one output.

Given the functions in the question;

To determine the function operation (f + g)(x), replace the function designators with the functions and simplify.

(f + g)(x) = f(x) + g(x)

(f + g)(x) = √( 16x⁴ ) + ( 3x² - 3x - 5 )

Replace √( 16x⁴ ) with 4x²

(f + g)(x) = 4x² +  3x² - 3x - 5

Collect and add like terms

(f + g)(x) = 7x² - 3x - 5

Therefore, the function operation (f + g)(x) is 7x² - 3x - 5.

Option A is the correct answer.

Learn more about functions here: brainly.com/question/2541698

#SPJ1

Answer:

B

Step-by-step explanation:

12: 2 2 3

36: 2 2 3 3

GCF 223

The GCF is 2x2x3=12

Answer:

(1, -4)

Step-by-step explanation:

With what you gave, that's the reduction.

Answer:

Each pizza cost $8.50

Step-by-step explanation:

Answer:

simple interest=$97.50.

compound interest= $100.668

Step-by-step explanation:

Given:

Principal (P) = $750

Rate (R) = 6.5% (in decimal form, 0.065)

Time (T) = 2 years

Simple Interest = Principal*Rate*Time

Using the formula, the simple interest is calculated as follows:

Simple Interest = $750*0.065*2 = $97.50

Therefore, the simple interest for $750 with a 6.5% interest rate over 2 years is $97.50.

Again:

Compound Interest = Principal*(1 + Rate)^(Time)-Principal

Using the same values as above, the compound interest can be calculated as follows:

Compound Interest = $750*(1+0.065)^(2)-$750

= $750*1.065^2 -$750

= $750 × 1.134225 - $750

= $850.66875-$750

= $100.668

Therefore, the compound interest for $750 with a 6.5% interest rate over 2 years is $100.668

Answer:

It is also 124 degrees.

Step-by-step explanation:

Answer:

  5 months

Step-by-step explanation:

We assume that y represents production capacity, rather than increase in production capacity. Then we want to solve the 6th-degree equation ...

  x^6 -25x^4 +199x^2 -4975 = 0

This can be factored in groups as ...

  x^4(x^2 -25) + 199(x^2 -25) = 0

  (x^4 +199)(x^2 -25) = 0

This has 4 complex solutions and 2 real solutions.

  x^2 = 25

  x = ±5

The duration required for capacity to reach 4975 units is 5 months.

Answer:

Car A gets 19 miles per gallon while Car B gets ~17.8 miles per gallon. Car A gets better mileage.

Step-by-step explanation:

Answer:

Try A

Step-by-step explanation:

382.4cm

Answer:

E[N] = 1

Step-by-step explanation:

Here is the hint we are given on this problem - " Write N = \(1_{A_1}\) + \(1_{A_2}\) + · · · + \(1_{A_{ 13}\)where \(A_k\) is the event that a match occurs on deal k. "

_____

Now the standard thing is to do is let \(X_i\) = 1, if there is a match on the \(i\)-th pick and 0 otherwise. The number of matches is given to be \(X_1\) + \(X_2\) . . . + \(X_{13}\). Knowing that, we can use the linearity of expectation -

There are 13 cards and for \(i\)-th pick, the probability of having a card with \(i\) number is 1 / 13. Therefore, E[N] = E[\(X_1\) + \(X_2\) . . . + \(X_{13}\)] = 1

_____

Solution: E[N] = 1

Answer:

The x side is multiplying four each time to get the y side example 2x4=8 and so on

The equation would be x x 4= y

So hope this helps

The equation that represents the proportional relationship from the table is y=4x.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

The given table is

x     y

2    8

3    12

7    28

Here, we can see when x increases y value also increases.

So, x and y are directly varies

Now, y∝x

y=kx -----(i)

k=y/x

k=8/2

k=4

Substitute k=4 in equation (i), we get

y=4x

Therefore, the equation that represents the proportional relationship from the table is y=4x.

To learn more about the proportional relationship visit:

brainly.com/question/12917806.

#SPJ2

Answer: x = 8

BC = 13

AB = 13

AD = 10

Step-by-step explanation:

The figure shows that AB = BC so:

x+5 = 2x-3

2x-x = 5+3

x = 8

Hence we have:

BC = 2(8)-3 = 13

AB = 8+5 = 13

AD = 8+2 = 10

Answer:

\(30.3 + 40.8 + m = 180\)

Step-by-step explanation:

\(30.3° + 40.8° + m° = 180° \\m = 180 - 30.3 - 40.8 \\ m = 108.9\)

Answer:

1650 Cubic Centimeters

Step-by-step explanation:

To get the volume of the cereal boxes, you must multiply their 3 dimensions together.

Box A:

25×20=500

500×9=4500

Box B:

25×19=475

475×6=2850

Now, to find the difference of these volumes, you want to subtract the smaller volume from the larger volume.

4500-2850=1650

The answer is 1650 cubic centimeters.

The exact solutions of the given equation in the interval are;

A: x = 0, π/2, π, ³/₂π

We are given the equation as;

sin 4x = –2sin 2x

Writing the equation in standard form gives;

sin 4x + 2sin 2x = 0

Using trigonometric Identity, substitute (sin 4x) with (2sin 2x.cos 2x) to get;

2sin 2x cos 2x + 2sin 2x = 0

Factorize to get;

2sin 2x(cos 2x + 1) = 0

A. sin 2x = 0

The unit circle will give us 3 solutions for 2x as follows;

2x = 0

Thus; x = 0

2x = π

Thus; x = π/2

2x = 2π

Thus; x = π

B. cos 2x = - 1

The unit circle gives 2 solutions for 2x as;

2x = π

Thus; x = π/2

2x = 3π

Thus; x = ³/₂π

Read more about solutions of trigonometric equations at; https://brainly.com/question/28921050?source=archive

#SPJ1

Complete question is;

How do you find the exact solutions of the equation sin4x = −2sin2x in the interval [0, 2π)?

Answer:

8.8 pounds

Step-by-step explanation:

Given the following :

Combined weight loss which occurred within a week = 28 kg

Number of days in a week = 7 days

1 kilogram (kg) = 2.2 pounds

Combined weight loss in pounds that occurs within a week:

Weight loss in kg × 2.2

28kg * 2.2 = 61.6 pounds

Assume weight loss occurred at a constant rate :

Weight lost by the group per day :

(Total weight loss / number of days in a week)

(61.6 pounds / 7)

= 8.8 pounds daily

Answer:

88

Step-by-step explanation:

Found the answer and I am doing the quiz rn lel

Answer:

48 miles

Step-by-step explanation:

i think thats it.

Answer: 4.

Step-by-step explanation: 8+8=16. count how many more until you get to 24, that is 8. Split 8 in half. We get 4.

                                Hope this helps!

Answer:

look at analysis

Step-by-step explanation:

11. 23.81

12.

part A

y is 12 and x is 4

part B

4

part C

5×12×4

240

Answer:

7.5 pounds

Step-by-step explanation:

How much orange pekoe tea costing $6.00 per pound should be mixed with green tea costing $5.00 per pound to get a mixture of 30 pounds costing $5.25 per pound?

We have two systems of equations

Let the number of pounds of pekoe tea be represented by p

The number of pounds of green tea be represented by g

Hence:

p + g = 30 ...... Equation 1

p = 30 - g

$6 × p + $5 × g = 30 × $5.25

6p + 5g = 157.5.........Equation 2

We substitute 30 - g for p in Equation 2

6(30 - g) + 5g = 157.5

180 - 6g + 5g = 157.5

-6g + 5g = 157.5 - 180

-g = -22.5

g = 22.5 pounds

Solving for p

p = 30 - g

p = 30 - 22.5

p = 7.5 pounds

Hence, the number of pounds of pekoe tea = 7.5 pounds

The Division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

To find the division of the sum of (7/8), (15/4), and (1/12) by their multiplication, we first need to calculate the sum and multiplication of the given fractions.

The sum of the fractions is:

(7/8) + (15/4) + (1/12)

To add these fractions, we need a common denominator. The least common multiple of 8, 4, and 12 is 24. Let's convert each fraction to have a denominator of 24:

(7/8) = (21/24)

(15/4) = (90/24)

(1/12) = (2/24)

Now we can add the fractions:

(21/24) + (90/24) + (2/24) = (113/24)

The multiplication of the fractions is:

(7/8) * (15/4) * (1/12)

To multiply fractions, we multiply the numerators and denominators:

(7*15*1) / (8*4*12) = (7/96)

Now we can divide the sum of the fractions by their multiplication:

(113/24) / (7/96)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

(113/24) * (96/7) = (2712/168)

Therefore, the division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

For more questions on Division .

https://brainly.com/question/30340100

#SPJ8

-2x – (-6x) + 4 = 3x – (-2) +1-(-3)

= -2x + 6x + 4 = 3x + 2 + 1 + 3

= -2x + 6x - 3x = 2 + 1 + 3 - 4

= 4x - 3x = 3 - 1

= x = 2 ANSWER

HOPE THIS HELPS :)

The interest rate is given as follows:

5%.

The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are explained as follows:

The interest accrued is given as follows:

I(t) = Prt.

For each case, the interest accrued is given as follows:

The total interest was of 13,500, hence:

I(3) + I(5) = 13500.

Meaning that the interest rate is obtained as follows:

120,000r + 150,000r = 13500

r = 13500/270000

r = 0.05.

r = 5%.

More can be learned about simple interest at https://brainly.com/question/20690803

#SPJ1