Boris invests $280 for 2 years at a rate of 3% per year compound interest. Calculate the interest Boris receives at the end of the 2 years. Give your answer correct to 2 decimal places.

Thee values of the functions are;

(f . g)(x) = √(-2x + 3)

(g . f)(x) = - 2√x + 3

A function can simply be defined as a law, rule or expression showing the  relationship between two variables in an equation or expression.

The two variables are given;

Given the functions;

To determine the function (f . g)(x), substitute the value of x as g(x) in the function, we have;

(f . g)(x) = √(-2x + 3)

To determine the function  (g . f)(x), substitute the values of x  in the function g(x), we have;

(g . f)(x) = - 2√x + 3

Hence, the functions are √(-2x + 3) and  - 2√x + 3

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The ways to pack are

This is further explained below.

Generally, The science, art, and technology of packaging involves confining or safeguarding goods for distribution, storage, sale, and usage. The process of creating, analyzing, and designing packages is sometimes referred to as packaging.

In conclusion,

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Answer:

câu này là 500 nhen

Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

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Answer:

Step-by-step explanation:

The least common multiple of 3 and 4 is 12. Divide the rectangle in twelfths.

⅓ = 4/12

¼ = 3/12

Answer:

haha lol

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

ok

The measure of the central angle θ in degrees and then multiply by 1/(2π). Then that result by πr²

We will use the following points to find the area of the sector;

First of all, the angle that is formed in a full rotation is 2π.

The area of a circle is given by the formula; A = πr²

The central angle is given by the angle symbol θ. Thus, we have to multiply the area of the circle by a factor θ/2π

Thus, the area of a sector is given by the formula;

A = (θ/2π) * πr²

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Answer:

$432

Step-by-step explanation:

60*6=360

They paid $360 for the first 6 months.

20%*60=.2*60

0.2*60=12

12*6=72

They paid $72 for the last 6 months.

360+72=432

They paid $432

$648 is the total amount the customer will pay for the 1-year plan

percentage, a relative value indicating hundredth parts of any quantity.

Given that a customer enrolled in a 1-year product purchase plan that costs $60 per month.

After 6 months, the customer received a monthly discount of 20%.

We need to find the total amount the customer will pay for the 1-year plan.

Product Plan = $60 per month

Money he pay for 1 month = $ 60

Money He pay for first 6 month = 6 × 60 = $ 360

after 6 month he receives 20% discount monthly,

So, Now he pay for 1 month = 60 - 20% × 60

=60-20/100×60

=60-12=48

Money he pay for last 6 month = 6 × 48 = 288

Total Money he  pay in a year = 360 + 288 = $ 648

Hence, $648 is the total amount the customer will pay for the 1-year plan

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The total area from the graph is 2.737.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

First of all, lets calculate the points of intersection (P, Q, R)

x²+3=(x+2) +5

x²-2=√(x+2)

x⁴+4-4x²=x+2

x⁴-4x²-x+2=0

(x-2)(x³+2x²-1)=0

(x-2)(x+1)(x²+x-1)=0

x=2, -1, -1±√(1+4)/2

Clearly, the x-coordinate of Q is -1, P is -1-√5/2, R is -1+√5/2, S is 2

So the limit of integration will be

P( (-1-√5)/2, (-1-√5/2)² +3)=P((-1-√5)/2, (3+√5/2))

Q(-1, (-1)²+3)=Q(-1, 4)

Area A:

\(\int\limits^\frac{3+\sqrt{5} }{2} _4 {-\sqrt{-y-3}-((y-5)^2 -2)} \, dx\)

= \([\frac{-(y-3)^\frac{3}{2} }{\frac{3}{2} }-\frac{(y-5)^3}{3}+3y]^{\frac{3+\sqrt{5} }{2} }_4\)

= 2.07

Area B:

\(\int\limits^\frac{-1+\sqrt{5} }{2} _4 {-\sqrt{x+2}+5-(x^2+3)} \, dx\)

= \([\frac{-(x+2)^\frac{3}{2} }{\frac{3}{2} }+5x-\frac{x^3}{3}-3x]^{\frac{-1+\sqrt{5} }{2} }_{-1}\)

= 0.667

Total area = 2.07+0.667

= 2.737

Therefore, the total area from the graph is 2.737.

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The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm

To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.

The formula for a confidence interval for the population mean (μ) is:

Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

For the first situation:

n = 15

Confidence level is 95% (which corresponds to an alpha level of 0.05)

x = 35 (sample mean)

s = 2.7 (sample standard deviation)

Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.

The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.

Plugging the values into the formula:

Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))

Calculating the confidence interval:

Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)

Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.

For the second situation:

n = 37

Confidence level is 99% (which corresponds to an alpha level of 0.01)

x = 82 (sample mean)

s = 5.9 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.

The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.

Plugging the values into the formula:

Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))

Calculating the confidence interval:

Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)

Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.

For the third situation:

n = 1009

Confidence level is 90% (which corresponds to an alpha level of 0.10)

x = 0.9 (sample mean)

s = 0.04 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.

The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.

Plugging the values into the formula:

Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))

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Answer:

The triangles are similar.

Explanation:

Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.

The final answer is (f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

To find the composite functions (f o g)(x) and (g o f)(x), we need to substitute one function into the other.

(f o g)(x):

To find (f o g)(x), we substitute g(x) into f(x):

(f o g)(x) = f(g(x))

Let's substitute g(x) = x^2 - 8 into f(x) = x^2 + 8:

(f o g)(x) = f(g(x)) = f(x^2 - 8)

Now we replace x in f(x^2 - 8) with x^2 - 8:

(f o g)(x) = (x^2 - 8)^2 + 8

Simplifying further:

(f o g)(x) = x^4 - 16x^2 + 64 + 8

(f o g)(x) = x^4 - 16x^2 + 72

Therefore, (f o g)(x) = x^4 - 16x^2 + 72.

(g o f)(x):

To find (g o f)(x), we substitute f(x) into g(x):

(g o f)(x) = g(f(x))

Let's substitute f(x) = x^2 + 8 into g(x) = x^2 - 8:

(g o f)(x) = g(f(x)) = g(x^2 + 8)

Now we replace x in g(x^2 + 8) with x^2 + 8:

(g o f)(x) = (x^2 + 8)^2 - 8

Simplifying further:

(g o f)(x) = x^4 + 16x^2 + 64 - 8

(g o f)(x) = x^4 + 16x^2 + 56

Therefore, (g o f)(x) = x^4 + 16x^2 + 56.

(f o g)(2):

To find (f o g)(2), we substitute x = 2 into the expression (f o g)(x) = x^4 - 16x^2 + 72:

(f o g)(2) = 2^4 - 16(2)^2 + 72

(f o g)(2) = 16 - 64 + 72

(f o g)(2) = 24

Therefore, (f o g)(2) = 24.

In summary:

(f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

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Answer:

182sq.in.

Step-by-step explanation:

base = 14in

height = 13in

Area of a parallelogram = base × height

Area = 14 × 13

= 182 sq.in.

The width of the field is 230 feet and the length is 310 feet.

Let's denote the width of the field as "x" feet.

The length of the field is 80 feet longer than the width, so it can be represented as "x + 80" feet.

To find the total amount of fencing material needed, we sum up the lengths of all four sides of the rectangular field:

2(length) + 2(width) = perimeter

Substituting the given values:

2(x + 80) + 2(x) = 1080

2x + 160 + 2x = 1080

4x + 160 = 1080

4x = 920

x = 920/4

x = 230

Therefore, the width of the field is 230 feet.

Now we can find the length by adding 80 feet to the width:

Length = Width + 80 = 230 + 80 = 310 feet.

So, the width of the field is 230 feet and the length is 310 feet.

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Answer: 4 ways to pick a king, 13 ways to pick a heart, and 4 ways to pick a five. Given the cards are returned to the deck, there are no special cases such as picking the King of Hearts and/or the Five of Hearts that affect the count. 208 ways.

Step-by-step explanation:

The angles in the parallel lines are as follows;

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, vertically opposite angles etc.

Therefore, let's find the angles m∠1 and m∠2.

Hence,

138 + m∠1 = 180(angles on a straight line)

The sum of angles on a straight line is 180 degrees.

m∠1 = 180 - 138

m∠1 = 42 degrees

Therefore,

m∠1 =  m∠2 (alternate exterior angles)

Alternate exterior angles are the pair of angles that are formed on th outer side of the parallel lines but on the opposite side of the transversal.

Alternate exterior angles are congruent.

Therefore,

m∠1 =  m∠2 = 42 degrees.

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Answer:

Two examples of points that satisfy this condition is (0,5) and (0,-5).

Step-by-step explanation:

Suppose we have two points:

\(A = (x_{1}, y_{1})\)

\(B = (x_{2}, y_{2})\)

The distance between these points is:

\(D = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}\)

In this question:

B(0,0)

A(x,y)

We have to find x and y.

We have that:

\(\sqrt{(x-0)^{2} + (y-0)^{2}} = 5\)

\(\sqrt{x^{2} + y^{2}} = 5\)

\((\sqrt{x^{2} + y^{2}})^{2} = 25\)

\(x^{2} + y^{2} = 25\)

One example of a point:

I will say that x = 0. So

\(0^{2} + y^{2} = 25\)

\(y = \pm \sqrt{25}\)

\(y = \pm 5\)

So two examples of points that satisfy this condition is (0,5) and (0,-5).

The distance formula is a formula that is used to find the distance between two points.

The coordinate of point A is (0, 5)  or   (0, -5).

Let us consider that, coordinate of point A is (x, y).

The distance between (0,0) and (x, y) is computed as by using distance formula.

                 \(Distance=\sqrt{(x-0)^{2}+(y-0)^{2} } \\\\5=\sqrt{(x-0)^{2}+(y-0)^{2} } \\\\x^{2} +y^{2}=25\)

All values that satisfies above equation, will be the coordinate of point A.

When x = 0,  

                \(y=\sqrt{25} =\pm 5\)

The coordinate of point A is (0, 5)  or   (0, -5).

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The correct answer is A. a characteristic of the population.

A population parameter refers to a specific characteristic

A population parameter refers to a specific characteristic or numerical value that describes the entire population being studied. It is a fixed value that is typically unknown and estimated using sample data. Examples of population parameters include the population mean, population standard deviation, population proportion, etc.

The volume of the tower is 224 in³, which is not listed among the given options.

To find the volume of the rectangular block, we need to multiply its length, width, and height. Therefore, the volume of the single block is:
8 x 3.5 x 2 = 56 cubic inches.
Since we are stacking four blocks to create a tower, we need to multiply the volume of a single block by 4.

Thus, the volume of the tower is:
56 x 4 = 224 cubic inches.
The volume of a rectangular block can be found using the formula,

V = length × width × height.

In this case, the length is 8 inches, the width is 3.5 inches, and the height is 2 inches.

V = 8 × 3.5 × 2 V

= 28 × 2 V

= 56 in³

Now that we know the volume of one block, we can find the volume of the tower created by stacking four blocks. Tower volume = block volume × number of blocks Tower volume = 56 in³ × 4 Tower volume = 224 in³

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Answer:

A

Step-by-step explanation:

consider the coordinates of points C and A

C (4, - 1 ) and A (- 3, 2 )

4 → - 3 in the x- direction is - 7

- 1 → 2 in the y- direction is + 3

then the translation rule is

(x, y ) → (x - 7, y + 3 )

Answer

Explanation

The total charge on the car = (Charge based on number of days) + (Charge based on the number of miles)

Charge based on number of days = (23.95) (x) = (23.95x) dollars

Charge based on the number of miles = (0.08) (400) = 32 dollars

(The total charge on the car) ≤ 440

23.95x + 32 ≤ 440

23.95x + 32 - 32 ≤ 440 - 32

23.95x ≤ 408

Divide both sides by 23.95

(23.95x/23.95) ≤ (408/23.95)

x ≤ 17.04

Hope this Helps!!!

Given:

Area of rectangle = 8613 cm²

Length = 99 cm

Find-:

The width of the rectangle

Explanation-:

The area of a rectangle is:

Given data is:

So, the width of the rectangle is:

The width of the rectangle is 87 cm

9514 1404 393

Answer:

  ∠G ≅ ∠U

Step-by-step explanation:

G is the 3rd letter in the triangle name on the left side of the congruence statement.

U is the 3rd letter in the triangle name on the right side of the congruence statement.

  ∠G ≅ ∠U

_____

Corresponding parts are listed in the same order in congruence and similarity statements.

Step-by-step explanation:

✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️

Answer:

The 2nd and the 4thᕕ( ᐛ )ᕗ

Answer:

the second [2ǹd] & the fourth [4th]

Answer: B.

x ≈2.5

Step-by-step explanation:

\(-\left(u\right)^{-1}-6=-u+10\)

\(u=8-\sqrt{65},\:u=8+\sqrt{65}\)

\(x=\frac{\ln \left(8+\sqrt{65}\right)}{\ln \left(3\right)}\)

x=2.52...

Answer:

x=2.5

Step-by-step explanation:

The total cost for the family of four is $944

Cost denotes the amount of money that a company or a person spends on the creation or production or acquiring of goods or services.

Here the family needs the service if transportation.

The cost of adult is $280. Out of four members , two are under 3years. This means the total cost for adult is 2 × 280 = $560

The cost of under 3 is ⅔ of the cost of adult.

= ⅔ × 280= $192

The cost of the two under 3 = 2 × $192 = $384

therefore the total cost for the family is $560 +$384 = $944

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Answer:

52

Step-by-step explanation:

RTQ is 52 because if PTR is a right angle, right angles equal 90 degrees. So if PTQ is 38 degrees, we subtract 38 from 90 to get RTQ. 90-38 equals 52.

Answer:

52 degrees

Step-by-step explanation:

right angle = 90

90-38=52

So RTQ = 52 degrees