Genevieve has $9000 to invest. She invests some at 6% annual interest and the rest at 4% annual interest. After one year, her total interest from both accounts is $444. How much did she invest in each account? (Clearly label which amount is for which account in your answer. Hint: Over a one year period, annual interest is the same as simple interest.)

The solution to the equation sqrt 2-3x / sqrt 4x = 2 is x = -2/3.

To solve the equation, we must first clear the denominators and simplify the equation. We can do this by multiplying both sides by sqrt(4x) and then squaring both sides. This gives us:
sqrt 2-3x = 4sqrt x
2 - 6x + 9x² = 16x
9x² - 22x + 2 = 0
Using the quadratic formula, we can find that x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in a = 9, b = -22, and c = 2, we get:
x = (-(-22) ± sqrt((-22)² - 4(9)(2))) / 2(9)
x = (22 ± sqrt(352)) / 18
x = (22 ± 4sqrt22) / 18
Simplifying this expression, we get:
x = (11 ± 2sqrt22) / 9
Therefore, the solution to the equation is x = -2/3.
To solve the equation sqrt 2-3x / sqrt 4x = 2, we must clear the denominators and simplify the equation. This involves multiplying both sides by sqrt(4x) and then squaring both sides.

After simplifying, we end up with a quadratic equation. Using the quadratic formula, we can find that the solutions are x = (11 ± 2sqrt22) / 9.

However, we must check that these solutions do not result in a division by zero, as the original equation involves square roots. It turns out that the only valid solution is x = -2/3.

Therefore, this is the solution to the equation.

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On solving the provided question, we can say that The number of hours he has to work since he earns $12 per hour would be 480/12 = 40 hours of work.

Along with addition, subtraction, and division, multiplication is one of the four arithmetic operations. Multiplication in math refers to regularly adding groups of the same size. The formula for multiplication is multiplicand multiplier Equals product. Specifically, multiplicand: First number (factor). divider: Second number (factor). After multiplying the multiplicand and the multiplier, the result is known as the product. Multiple additions are made while adding numerals. as in 5 times 4 Equals 5 + 5 + 5 + 5 = 20. I multiplied 5 by 4 times. Multiplication is frequently referred to as "doubling" because of this.

$500

8% tax = 8/100 * 500 = $40

He is paying 2 bills of $35 each making a total of 2 * $35 = $70

The total amount he is to pay is thus; 500 + 40 + 70 = $610

Bonus $45

Birthday gift $85

The total amount of money he has asides his salary to offset the bill is 45 + 85 = $130

The balance to pay from his salary would be $610 - $130 = $480

The number of hours he has to work since he earns $12 per hour would be 480/12 = 40 hours of work

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Answer:

Theta = 0, 60 degrees.

Step-by-step explanation:

2 sin^2 theta + 3 cos theta = 3​

Using the identity sin ^2 theta = 1 - cos^2 theta :

2(1 - cos^2 theta) + 3 cos theta  = 3

2 - 2cos^2 theta) + 3 cos theta  = 3

2 cos^2 theta - 3 cos theta   + 3 - 2 = 0

2 cos^2 theta - 3 cos theta   + 1 = 0

(2 cos theta - 1)(cos theta - 1) = 0

cos theta = 1/2 , cos theta = 1

Theta = 60 degrees or theta = 0

Answer:

33 units³

Step-by-step explanation:

Volume of a rectangular prism

\(\sf Volume = Area\:of\:base \times height\)

From inspection of the given diagram:

Substitute the given values into the formula and solve for volume:

\(\begin{aligned}\sf \implies Volume & = \sf 9 \times 3 \dfrac{2}{3}\\\\& = \sf 9 \times \dfrac{3 \times 3+2}{3}\\\\& = \sf 9 \times \dfrac{11}{3}\\\\& = \sf \dfrac{9 \times 11}{3}\\\\& = \sf \dfrac{99}{3}\\\\& = \sf \dfrac{33 \times \diagup\!\!\!\!3}{\diagup\!\!\!\!3}\\\\& = \sf 33\:units^3 \end{aligned}\)

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\(\boxed{\sf Volume=Area\:of\:base\times Height}\)

\(\\ \tt\dashrightarrow Volume=9\times3 \dfrac{2}{3}\)

\(\\ \tt\dashrightarrow Volume=9\times \dfrac{11}{3}\)

\(\\ \tt\dashrightarrow Volume=3(11)\)

\(\\ \tt\dashrightarrow Volume=33units³\)

In linear equation, 432 milliliters of water does he use .

What are a definition and an example of a linear equation?

Nick bakes 3 dozen cookies for the bake sale.

1 cookie  requires 12 milliliters of water.

water does he use = 3 × 12 × 12

                                = 432 milliliters of water

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Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

Answer:

6,791,240>6,781,204

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

a prime polynomial is one which does not factor into 2 binomials.

its only factors are 1 and itself

attempt to factorise the given polynomials

3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )

= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(3x² - 2) ← in factored form

--------------------------------------------------

3x³ - 2x² + 3x - 4 ( factor the first/second terms

= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored

thus this polynomial is prime

----------------------------------------------------

4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )

= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term

= (2x + 1)(2x² + 3) ← in factored form

-------------------------------------------------

4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )

= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(4x² - 3) ← in factored form

--------------------------------------------------

the only polynomial which does not factorise is

3x³ - 2x² + 3x - 4

Each number should be dragged to a box to complete the table as follows;

Kilometers     Meters

1                        1,000

2                       2,000

3                       3,000

5                       5,000

8                       8,000

In Science and Mathematics, a conversion factor can be defined as a number that is used to convert a number in one set of units to another, either by dividing or multiplying.

Generally speaking, there are one (1) kilometer in one thousand (1,000) meters. This ultimately implies that, a proportion or ratio for the conversion of kilometer to meters would be written as follows;

Conversion:

1 kilometer = 1,000 meters

2 kilometer = 2,000 meters

3 kilometer = 3,000 meters

4 kilometer = 4,000 meters

5 kilometer = 5,000 meters

6 kilometer = 6,000 meters

7 kilometer = 7,000 meters

8 kilometer = 8,000 meters

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

59

Step-by-step explanation:

6 plus 4 equals 8 plus 9

Answer:

Step-by-step explanation:

(x-2)(x-2)(x-4)

Answer:

31.4

Step-by-step explanation:

d = 10

radius times 2 = d

multiply the circle's diameter by pi (3.14).

31.4

Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment

We see here that new thousand is actually liken to be the result in thousand that is gotten after carrying out an operation.

A thousand is a number that denotes the sum of 1,000 units or ten hundreds.

The word "thousand" is frequently used in daily speech to denote a significant but limited amount, such as a thousand money, a thousand individuals, or a thousand pages. Alternatively, it can be used as a round number to denote an approximation, as in "a thousand times" or "a thousand and one nights."

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Answer:

An hour and 30 minutes.

Step-by-step explanation:

In one hour, they travel 8 kilometers. They then have 4 kilometers left. 4 is half. of 8, so I would possibly take half the time it would to travel 8, making it 30 minutes for the other 4 kilometers.

Answer:

where is the square at I cannot see it

Answer: C

Step-by-step explanation:

why are there two of these?
Answer:

53.9

Step-by-step explanation:

89% of all houses have garages and 48% have garages and pools. We try to find houses with a pool that have a garage. Let's assume that there are 100 houses in her neighborhood. then 89 of them have garages and 48 of them have garages and pools. 48 / 89 = about 0.5393. Conver this to percent and we get 53.9

Consider the triangle ABX.

Determine the length of AX by using the pythagoras theorem.

The length of XY is twice of side AX. So XY = 36

Consider trinagle XYZ.

Detertmine the length of side YZ by using pythagoras theorem.

The length of side YC is half of YZ so YC = 24.

Determine the length of side AC by using pyhtagras theorem in triangle AYC.

So length of AC is 30.

Answer: 30

Answer:

0.7

Step-by-step explanation:

Answer:

0.35

Step-by-step explanation:

Answer:

3 in 730500

tens of thousands

3 in 73050

thousands

Answer:

10 times

Step-by-step explanation:

the value of the digit 3 in 730,500 is 10 times the value of the digit 3 in 73,050

730,500 (digit 3) = 30,000

73,050 (digit 3) = 3,000

30,000/3,000 = 10

The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:

πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:

A = (πr^2)/2 + rh

To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:

r = (9 - 2h)/(π)

Now we can rewrite the area function in terms of h only:

A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)

Simplifying this equation, we get:

A = (1/2)(9h - h^2/π)

To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:

dA/dh = 9/2 - h/π = 0

Solving this equation, we find:h = 9π/2

Substituting this value of h back into the area function, we get:

A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4

Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

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Step-by-step explanation:

867.5x ×2.8

is is equal to 2429x

Unless we restrict its domain, a quadratic function doesn't have the inverse.

Answer:

Since the calculated value of z= 1.869 does not fall in the critical region we accept the null hypothesis H0: p1≠ p2  the data provides evidence that the proportion of high school students in metropolitan areas who have internet access during school hours is different than the proportion of rural high school students who have internet access during school hours.

Step-by-step explanation:

Let p1= proportion of the high school students having internet access

p2= proportion of the rural school students having internet access

1) The null and alternate hypothesis are

H0: p1≠ p2  against the claim   Ha: p1= p2

2) We choose significance level ∝ =0.05

3) The test statistic under H0 is

z= p1^- p2^/√ p^q^( 1/n1 + 1/n2)

Now

p1^= 768/850= 0.9035

p2^= 308/355= 0.8670

p^= 768+ 308/850+ 355= 1076/1205

p^= 0.8929

q^= 1-p^= 0.1070

Putting the values

z= p1^- p2^/ √p^q^( 1/n1 + 1/n2)

Z= 0.9035-0.8670/sqrt [0.8929*0.1070( 1/850 + 1/355)]

z= 0.0365/ sqrt [ 0.0955403 (0.001176 + 0.002816)]

z= 0.0365/ 0.019531

z= 1.8688

The critical region is  z∝/2 = ± 1.96

The value of z is 1.8666. The value of p is 0.06148 which is greater than 0.05

Conclusion:

Since the calculated value of z= 1.869 does not fall in the critical region we accept the null hypothesis H0: p1≠ p2  the data provides evidence that the proportion of high school students in metropolitan areas who have internet access during school hours is different than the proportion of rural high school students who have internet access during school hours.

Answer:

22 cents per mile

Step-by-step explanation:

to get this answer, divide 17.60 by 4 to get the unit rate, or the rate when x=1.