Fine Angle R using law of cosines. Round to the nearest tenth

Answer: Decreased 40%

Step-by-step explanation:

Alright, we know they reduced $10.00 (25-15)

Now all we have to do is find the percentage, 10 is how much of 25?

10/25 =0.4

(to get 0.4 to a percentage multiply by 100)

The price was decreased by 40%

Answer:

Alright, so we want to know how much that can be earned in one year. So that's going to be 3000. And this is simple interest. So this is one plus 0.011, which equals $3,033. And that's the solution to this exercise.

Answer:

$3,036

Step-by-step explanation:

The new customer can open a money market account. The bank will deposit $3,000 into the account.

The bank will pay 1.2% (0.012) in interest every year. This interest will increase the original amount to $3,036.

Step-by-step explanation:

answer is in the picture

6,000 grams is equivalent to 6 kilograms.

The problem is solved by converting the given dimensions from grams to kilograms. The conversion is from a smaller metric unit to a larger metric unit.

A kilogram is a larger unit of measurement for mass or weight compared to a gram.

The prefix kilo in kilogram means 1000, so one kilogram is equal to 1000 grams.

Therefore, to convert from grams to kilograms, you simply divide the number of grams by 1000.

In this case, 6,000 grams divided by 1000 equals 6 kilograms.

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Answer:

              The area of the quadrilateral is C: 12 square feet.

Step-by-step explanation:

               In the photo, the quadrilateral is divided into two triangles, both having a base length of 4 feet and a height of 3 feet. Therefore, we can find the area of the entire quadrilateral by adding the areas of the two triangles together. Since the triangles have a base length of 4 feet and a height of 3 feet, their individual areas will be [tex]4*3*\frac{1}{2} =12*\frac{1}{2} = 6[/tex] square feet. As there are two triangles, we need to multiply the area of one triangle by 2 to get the total area of the quadrilateral, which would be [tex]6 * 2=12[/tex] square feet. Hence, we can conclude that the correct answer will be C.

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Answer:

He will need 64 ft of fencing

Step-by-step explanation:

To determine the amount of fencing, we need to find the perimeter.

P = 2 (l+w)  where l is the length and w is the width

P = 2(22+10)

P = 2(32)

P = 64

He will need 64 ft of fencing

Answer:

16 years old

Step-by-step explanation:

Let's call Mikhail's age "x". Gabrielle's age is 3 times that, so her age is 3x. The sum of their ages is 64, so:

x + 3x = 64

4x = 64

x = 16

So, Mikhail's age is 16 years old.

It looks like 1) adjacent angles.

The constant of proportionality is 0.60

The equation is y = $0.60x.

Here is the completed table

Number of lemons  Total cost

4                                  $2.40

7                                 $4.20

15                                 $9

18                                  $10.80

Direct variation is when two variables move in the same direction. As the number of lemons bought increases, the total cost increases.

The equation that represents direct variation is:

y = kx

Where:

$1.80 = 3k

k = $1.80 / 3

k = $0.60

y = $0.60x

Total cost of 4 lemons=  $0.60 x 4 = $2.40

Total cost of 18 lemons=  $0.60 x 18 = $10.80

Number of lemons that cost $4.20 : 4.20 / 0.6 = 7

Number of lemons that cost $9 : 9 / 0.60 = 15

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The average rate of change over the interval (-1, 2) is; 3

The formula for the average rate of change over an interval (a, b) is expressed as;

f'(x) = [f(b) - f(a)]/[b - a]

We want to find the average rate of change over the interval (-1, 2). Thus;

a = -1 and b = 2

Thus;

f(-1) = -4

f(2) = 5

Thus;

f'(x) = (5 - (-4))/(2 - (-1))

f'(x) = 9/3

f'(x) = 3

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The statement describes the solutions of this equation is

The Equation have two valid solution and No Extraneous solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

x/3 + (x-1)/ (x+ 4)= (x+3)/ (x+4)

Now, simplifying the above Expression

(x² + 4x + 3x - 3) / 3(x+4) = (x+3)/ (x+4)

(x² + 4x + 3x - 3) / 3 = (x+3)

x² + 7x -3 = 3(x+3)

x² + 7x -3 - 3x - 9 = 0

x² + 4x - 12 = 0

Solving the above Quadratic Equation

x² + 6x- 2x - 12 = 0

x(x+6)- 2(x+6)= 0

(x-2)(x+6)= 0

x= 2, -6.

So, the Equation have two valid solution and No Extraneous solution.

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Answer:

295>_ 39x+11.50

Step-by-step explanation:

the >_ means less than or equal to.

Answer:a rectangular prism has  height  4m, length 6m & width 5m

thus the surface consist of two  4*6 vertical surfaces

                                          two 4*5 vertical surfaces

                                        & two 6*5 top & bottom surfaces

that is

            2(4*6) =  48

            2(4*5) =  40

            2(6*5) =  60

total surface area =  48+40+60 = 148m²

Step-by-step explanation:

On solving the provided question, we can say that  In decimals r = 3.8799 and d = 7.7598

Integer and non-integer numbers are οften expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded tο include non-integer values. Decimal notation is the name fοr the method used to represent numbers in the decimal system.

A decimal is a number with a whοle and a fractional component. Decimal numbers, which are in between integers, are used tο express the numerical value οf full and partially whole amounts.

the lengths (in inches) οf the radius and the diameter οf a circle with area 47.25 in'.

Area  = πr²

47.25 = 3.14 × r × r

r × r = 15.0541401274

In decimals

r = 3.8799

d = 7.7598

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Answer:

Step-by-step explanation:

To solve this problem, we must first use an equation that reflects the amount of acid in each solution and its relationship to the total volume of the resulting solution. We can use the following equation:

(C1 * V1) + (C2 * V2) = (C3 * V3)

Where:

C1 = concentration of the acid solution at 60% (in percent)

V1 = volume of the acid solution at 60% (in ml)

C2 = concentration of the acid solution at 30% (in percent)

V2 = volume of the 30% acid solution (in ml)

C3 = concentration of the resulting 50% acid solution (in percent)

V3 = volume of the resulting 50% acid solution (in ml)

In this case, we know the total volume of the resulting solution (V3 = 300 ml) and the desired concentration (C3 = 50%). We also know the concentration of one of the original solutions (C1 = 60%). So we can plug the known values ​​into the equation:

(60 * V1) + (30 * V2) = (50 * 300)

Clearing V1:

V1 = (300 * 50 - 30 * V2) / 60

Now that we have V1 as a function of V2, we can solve the problem to find the volume of the 60% acid solution to mix with the 30% solution. Substitute the known values ​​into the equation:

V1 = (300 * 50 - 30 * V2) / 60

V1 = (15000 - 30 * V2) / 60

V1 = 250 - (V2 / 2)

We can use this last equation to find the volume of the 30% solution that we must mix with the 60% solution:

V2 = 2 * (250 - V1)

Clearing V1:

V1 = 250 - (V2 / 2)

V1 = 250 - (2 * (250 - V1) / 2)

V1 = 250 - 250 + V1

V1 = 250

Therefore, we must mix 250 ml of 60% acid solution with 250 ml of 30% solution to produce 300 ml of 50% solution.

Answer:

Step-by-step explanation:

Calculate the total hours used: We add up the hours used each year to find the total hours used:

2,800 + 1,400 + 1,500 + 2,500 + 2,300 + 2,000 = 12,500

Calculate the total depreciation: We subtract the residual value from the cost to find the total depreciation:

$219,000 - $19,500 = $199,500

Calculate the annual depreciation expense: We divide the total depreciation by the number of years to find the annual depreciation expense:

$199,500 / 6 = $33,250

Calculate the depreciation expense per hour: We divide the annual depreciation expense by the estimated total hours to find the depreciation expense per hour:

$33,250 / 12,500 = $2.66

So the depreciation expense per hour is $2.66.

Calculate the depreciation expense for each year: We multiply the hours used each year by the depreciation expense per hour to find the depreciation expense for each year:

Year 1: 2,800 * $2.66 = $7,448

Year 2: 1,400 * $2.66 = $3,724

Year 3: 1,500 * $2.66 = $3,990

Year 4: 2,500 * $2.66 = $6,650

Year 5: 2,300 * $2.66 = $6,118

Year 6: 2,000 * $2.66 = $5,320

So the depreciation expense for each year is:

Year 1: $7,448

Year 2: $3,724

Year 3: $3,990

Year 4: $6,650

Year 5: $6,118

Year 6: $5,320

The value of x in the trapezoid is 12

It is important to note that the properties of a trapezoid are;

Now, let's equate the angles, we getl

7x + 21 = 105

collect the like terms, we get;

7x = 105 - 21

subtract the like terms

7x = 84

Make 'x' the subject of formula

x = 84/7

Divide the values

x = 12

Hence, the value is 12

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The value of x is given as follows:

x = 9.

The sum of the interior angle measures of a polygon with n sides is given by the equation presented as follows:

S(n) = 180 x (n - 2).

The figure for this problem has four sides, hence the sum of the internal angle measures is given as follows:

S(4) = 180 x (4 x 2)

S(4) = 360º.

Adding the four angle measures and equaling them to 360º, the value of x is obtained as follows:

117 + 93 + 87 + 6x + 9 = 360

306 + 6x = 360

6x = 54

x = 54/6

x = 9.

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The probability that the sample proportion exceeds 0.12 is given as follows:

0.6103 = 61.03%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters of the binomial distribution are given as follows:

n = 90, p = 0.13.

Hence the mean and the standard error are given as follows:

The probability that the sample proportion exceeds 0.12 is one subtracted by the p-value of Z when X = 0.12, hence:

Z = (0.12 - 0.13)/0.0354

Z = -0.28

Z = -0.28 has a p-value of 0.3897.

Hence:

1 - 0.3897 = 0.6103.

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Answer:

  -5x⁵ +2x² -3/x³

Step-by-step explanation:

You want the quotient and remainder of (-15x⁸ +6x⁵ -9)/(3x³).

The quotient and remainder can be found by dividing term by term.

  [tex]\dfrac{-15x^8+6x^5-9}{3x^3}=\dfrac{-15x^8}{3x^3}+\dfrac{6x^5}{3x^3}-\dfrac{9}{3x^3}\\\\\\=\boxed{-5x^5+2x^2-\dfrac{3}{x^3}}[/tex]

__

Additional comment

The exponent rule is (a^b)/(a^c) = a^(b-c).

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Total 105 of the 420 vehicles contained at least 3 people. Therefore , option C is correct.

Given :

percent distribution : 40% , 35% , 15% , 7% , 3%

Vehicles : 420

First, add the percentage of cars containing 3 people, 4 people, and 5 or more people:

15% + 7% + 3% = 25%

Thus, 25% of the cars contained at least 3 people, so use that to calculate the number of cars:

420 × 0.25 = 105 cars.

Hence , Total 105 of the 420 vehicles contained at least 3 people. Therefore , option C is correct.

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Complete question:

A researcher recorded the number of people in each vehicle that passed through a checkpoint. The table above shows the percent distribution for the 420 vehicles that passed through the checkpoint yesterday morning.

How many of the 420 vehicles contained at least 3 people?

A. 42

B. 63

C. 105

D. 315

The system of equations which represents this

situation is 3x+4y= 32 and 5x + 5y = 18.

The correct answer choice is option B

Amount with Maya = $32

Amount spent on each notebook = x

Number of notebook = 3

Amount spent on each pack of index cards = y

Number of index cards = 4

Maya bought 5 notebooks and 5 packs of

index cards

$18 short = $32 - $18

= $14

3x + 4y = 32

5x + 5y = 14

In conclusion, the system of equation is 3x+4y= 32 and 5x + 5y = 18.

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Area of desert 1 is 18,000,000 square miles and area of desert 2 is 3,000,000 square miles.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Let A₁ and A₂ be the area of Desert 1 and Desert 2 respectively.

Given,

Area of a Desert 1 is six times the area of Desert 2.

A₁ = 6 A₂

The sum of their areas is 21,000,000 square miles.

A₁ + A₂ = 21,000,000

Substituting A₁ = 6 A₂ in A₁ + A₂ = 21,000,000 ,

6 A₂ + A₂ = 21,000,000

7 A₂ = 21,000,000

A₂ = 21,000,000 / 7

A₂ = 3,000,000 square miles

A₁ = 6 A₂

   = 6 × 3,000,000

   = 18,000,000 square miles

Hence the areas of each desert is 18,000,000 square miles and 3,000,000 square miles.

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The equations used are:

Longest side = a

Shortest side = 1/2 x a = 1/2a

Third side = a - 1

The shortest side is 8 inches, the longest side is 16 inches and the third side is 15 inches.

The perimeter of a triangle is the sum of the length of the three sides of the triangle.

Let the following expressions represent the lengths of the sides of the triangle:

Longest side = a

Shortest side = 1/2 x a = 1/2a

Third side = a - 1

Perimeter = a + 1/2a + a - 1 = 39

a + 1/2a + a = 39 + 1

2a + 1/2a = 40

2 1/2a = 40

5/2a = 40

a = 40 x 2/5

a = 16 inches

Shortest side = 1/2 x 16 = 8 inches

Third side = 16 - 1 = 15 inches

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The number of monthly payments required to pay off the loan of $128,000 at 4% interest is 232.48 which is equivalent to approximately 232 payments.

To determine the number of monthly payments required to pay off a loan, you can use the formula for loan amortization: n = (-log(1 - B/A * r)) / log(1 + r)

Where: n = number of monthly payments, A = loan amount ($128,000), B = monthly payment ($611.09), r = monthly interest rate (4% / 12 months = 0.0033)

The number of monthly payments for the loan is plugged and computed as:

n = (-log(1 - $128,000/$611.09 * 0.0033)) / log(1 + 0.0033)

n = (-log(1 - 0.0208)) / log(1.0033)

n = (-log(0.9792)) / log(1.0033)

n = 21.8068 / 0.093984

n = 232.48 payment.

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The solution to the equation "negative x = 9" is "x = -9". There is no invisible number in front of "x" in this equation.

To solve the equation "negative x = 9" algebraically, we want to isolate the variable "x" on one side of the equation.

First, we notice that "negative x" means "-x", so we can rewrite the equation as:

-x = 9

To isolate "x", we need to perform an inverse operation on both sides of the equation. Since "-x" means the opposite of "x", we need to perform the opposite operation, which is to add "x" to both sides:

-x + x = 9 + x

Simplifying the left-hand side by canceling out the "-x" and "+x", we get:

0 = 9 + x

We can further simplify this equation by subtracting 9 from both sides:

0 - 9 = 9 + x - 9

-9 = x

So the solution to the equation "negative x = 9" is "x = -9".

There is no invisible number in front of "x" in this equation, so we don't need to worry about any additional steps or calculations.

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From unit prices gotten, the price of one feet of annel fabric is cheaper than the price of one feet of fleece fabric.

A unit price is defined as the price for one item or measurement, such as a pound, a kilogram, or a pint. This can be used to compare the same type of goods sold in varying weights and amounts.

The parameters are;

3 yards of annel fabric costs $12.60

5 feet of fleece fabric costs $8.75.

From conversion units;

1 yard =  3 feet

Thus;

3 yards = 3 * 3 = 9 ft

Thus;

Unit price of Annel fabric = 12.6/9 = $1.4 per ft

Unit price of fleece fabric = 8.75/5 = $1.75 per ft

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The area of the given composite shape with two rectangles is 68 m²

What is a rectangle?

There are four right angles on the quadrilateral that forms the rectangle. Every corner or vertex has a right angle where the two sides meet. It differs from a square, which has all of its sides of equal length, in that the opposite sides of the rectangle are equal in length. Two dimensions and flatness combine to make a rectangle.

The figure can be divided into a rectangle with a length of 8m and breadth of 6m and another rectangle of length 5m and breadth = (10-6) = 4m.

To find the area of the whole figure, we first find the areas of small and big rectangles and sum their areas.

Area of small rectangle = length * breadth = 5*4 = 20 m²

Area of big rectangle = length * breadth  = 8 * 6 = 48 m²

Therefore the area of the given composite shape with two rectangles is 20+48 = 68 m².

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