A little help? the question is attached

Answer:

35) 352.14

36) 329.8

37) 339.4

38) 319.4

It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of compounding periods per year

t = Number of years

In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.

We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.

Let's substitute the given values into the formula and solve for t:

56,398.43 = 500(1 + 0.06/2)^(2t)

Divide both sides by 500:

112.79686 = (1 + 0.03)^(2t)

Take the natural logarithm of both sides to eliminate the exponent:

ln(112.79686) = ln(1.03)^(2t)

Using the property of logarithms, we can bring down the exponent:

ln(112.79686) = 2t * ln(1.03)

Now, divide both sides by 2 * ln(1.03):

t = ln(112.79686) / (2 * ln(1.03))

Using a calculator, we find t ≈ 17.12.

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The fox population after 30 years is 675

From the question, we have the following parameters that can be used in our computation:

Initial population =75

Rate of growth = Triples every 15 years

Year = 30 years

The equation of the function can be represented as

y = 75 * 3^x

So, we have

x = 30/15

Evaluate

x = 2

Substitute the known values in the above equation, so, we have the following representation

y = 75 * 3^2

Evaluate

y = 675

Hence, the population is 675

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a) The statement " The intersection of two events A and B can be larger than the union of the same two events A and B" is False.

b) The statement " The probability of a single event A must be smaller than or equal to the union of two events A and B" is False.

c) The statement " The condition probability of A given B must be smaller than the intersection of the same two events A and B"  is False.

(a) False. The intersection of two events A and B represents the set of outcomes that are common to both A and B, while the union of the same two events A and B represents the set of outcomes that belong to either A or B or both. Hence, it cannot be larger than the union of A and B.

(b) False. The probability of an event A must be between 0 and 1 (inclusive), while the union of two events A and B represents the set of outcomes that belong to either A or B or both. The probability of the union of A and B is the sum of the probabilities of A and B, which can be larger than the probability of A.

(c) False. The conditional probability of A given B, denoted as P(A|B), represents the probability of event A occurring given that event B has already occurred.  Since the intersection of A and B must be less than or equal to 1, the conditional probability of A given B must also be less than or equal to 1.

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Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

The dimensions of the pool are 27 feet by 10 feet, and the area is indeed 270 square feet.

Let's assume that the width of the rectangular pool is x feet. According to the problem, the length of the pool is 7 feet more than twice the width, so we can write:

Length = 2x + 7

The area of a rectangle is given by the formula:

Area = Length x Width

Substituting the expression for length in terms of width in the above equation, we get:

Area = (2x + 7) x x

Simplifying the above equation, we get:

Area = 2x^2 + 7x

We are given that the area of the pool is 270 square feet. So, we can set up an equation:

2x^2 + 7x = 270

Rearranging the terms, we get a quadratic equation:

2x^2 + 7x - 270 = 0

We can solve this quadratic equation using the quadratic formula:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

where a = 2, b = 7, and c = -270.

Solving this equation, we get two values of x: x = 10 and x = -13.5.

Since the width of the pool cannot be negative, we reject the value x = -13.5. Therefore, the width of the pool is 10 feet.

Using the expression for the length of the pool in terms of the width, we get:

Length = 2x + 7 = 2(10) + 7 = 27 feet

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The Principal when calculated quarterly will give a sum of 2900 + (2.525)^4t at a rate of 6.1% interest

What is Compound Interest?

Compound interest is usually referred to as "interest on interest." Compound interest can work in your favour as your assets increase over time, but it can also work against you if you're paying off debt, such as credit cards. A calculator can assist in estimating how much money compound interest will generate over time.

Given that the Principal amount is $2900

and the Rate of Interest is 6.1%

Since, the interest is calculated quarterly

Amount = Principal * (1 + Rate/4)^4*Time

Amount = 2900 + (1 + 6.1/4)^4t

Amount = 2900 + (10.1/4)^4t

Amount = 2900 + (2.525)^4t

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The smallest integer that Pearl wrote down is -12.Let's assume the smallest integer that Pearl wrote down is represented by the variable "x."

According to the given information, the sum of the seven consecutive integers is equal to $\frac{21}{4}$ times the largest integer.

The sum of consecutive integers can be expressed as the sum of an arithmetic series. The sum of an arithmetic series can be calculated using the formula:

Sum = (n/2)(first term + last term)

In this case, the first term is x and the last term is x + 6 (since there are seven consecutive integers). Therefore, the sum of the integers can be written as:

Sum = (7/2)(x + (x + 6))

Simplifying the equation:

(7/2)(2x + 6) = (21/4)(x + 6)

Multiplying both sides by 4 to eliminate the fractions:

14x + 42 = 21x + 126

Subtracting 14x from both sides:

42 = 7x + 126

Subtracting 126 from both sides:

-84 = 7x

Dividing both sides by 7:

-12 = x.

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Answer:

  B.  A point

Step-by-step explanation:

You want a description of the intersection between a plane and a cone given that the plane is parallel to the base and passes through the vertex of the cone.

The vertex of a cone is a single point. If a plane passes through that, but does not intersect the base of the cone, it will not intersect anywhere else.

The intersection is one point.

__

Additional comment

Figure f in the attachment illustrates this case.

This statement in the article is wrong because $2.69 is not the mean price ($2.81)

The prices from 5 gas stations surveyed are given as:

$2.79, $2.99, $2.69, $2.89, and $2.69.

There are no outliers in the dataset

So, the dataset can be summarized by the mean

The mean is

Mean = Sum/Count

So, we have

Mean = ($2.79+ $2.99+ $2.69+ $2.89+$2.69)/5

Evaluate

Mean = 2.81

The article quoted $2.69 as the typical price

This statement in the article is wrong because $2.69 is not the mean price ($2.81)

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First let's start with A

All the sides in a hexagon add up to 720

do 720/6

720/6=120

A=120

Each angle in that hexagon adds up to 120

Then B

The triangle is equilateral, so 180/3=60

B would be 60

C would also be 60

D is = to a, so D=120

A:120

B:60

C:60

D:120

Step-by-step explanation:

1. 1/9 of 450

of is multiply

1/9 × 450

= ???

2. 15/60 = decimal number

change number to percentage = ???

I dont know what 3 is

put answers to 1 and 2 in comments i will mark if u don't understand comment

please mark brainiest

1 day = 1 hour

1 year = 365 days

365 x 1 = 365

= 365 hours

Answer:

if one day equals one hour then a year is equal to 365 hours

The total volume of the air space of spherical ball is A = 12.265625 inches³

Given data ,

Since each tennis ball has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.

The air space around the balls can be thought of as a cylinder with a height equal to the diameter of one ball and a radius equal to the radius of one ball.

The height of the cylinder is 2.5 inches, and the radius is 1.25 inches.

The formula for the volume of a cylinder is:

V = πr²h

V = ( 3.14 ) ( 1.25 )² ( 7.5 )

V = 36.796875 inches³

where V is the volume, r is the radius, and h is the height.

So, the volume of the one ball is:

V₁ = ( 4/3 )π(1.25)³

V₁ = 8.177083 inches³

The total volume of three balls is = volume of 3 spherical balls

V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches

Therefore, the total volume of the air space around the three tennis balls is approximately A = 36.796875 inches³ - 24.53125 inches³

A = 12.265625 inches³

Hence , the volume of air space is A = 12.265625 inches³

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Answer:

C

Step-by-step explanation:

The Interquartile range determines how consistence Annie and Ellen are. The greater the IQR, the less the consistency, while the lesser the IQR, the more consistency.

The IQR for Annie is lesser than that of Ellen because the rectangular box is smaller for Annie's than that of Ellen.

Therefore, Annie is more consistent.

Answer:

x = 145

Step-by-step explanation:

x and 35° lie on a straight line and are supplementary angles , sum to 180°

x + 35 = 180 ( subtract 35 from both sides )

x = 145

Answer:

Step-by-step explanation:

2.1 so a

The loss on selling 50 shares of stock would be 87.50.

To calculate the loss on selling 50 shares of stock originally bought at

\(13\frac{3}{4}\) and sold at 12, we need to determine the difference between the purchase price and the selling price, and then multiply it by the number of shares sold.

First, let's convert the purchase price from a mixed fraction to a decimal. \(13\frac{3}{4}\) can be expressed as 13.75.

Next, we calculate the difference between the purchase price and the selling price:

\(13.75 - 12 = 1.75.\)

Finally, we multiply the difference by the number of shares sold:

\(1.75 \times50 = 87.50.\)

Therefore, the loss on selling 50 shares of stock would be 87.50.

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The calculated vertex of the point C is (b) (-7, 3.5)

From the question, we have the following parameters that can be used in our computation:

ABC with vertices at A(3, 2), B(2, -1), C(-2, 1)

The scale factor is 3.5

The vertex of point C is calculated as

C' = C * Scale factor

Substitute the known values in the above equation, so, we have the following representation

C = (-2, 1) * 3.5

Evaluate

C = (-7, 3.5)

Hence, the vertex of point C is (b) (-7, 3.5)

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The velocity of the ball in ft/sec, when t = 1 second is equal to -12 ft/sec.

Given the following data:

To calculate the velocity of the ball in ft/sec, when t = 1 second:

Mathematically, the velocity of an object or physical body is equal to the differentiation of it's position function.

Velocity = s'(t)

Velocity = \(s(t) = -16t^2 + 20t + 100\)

\(Velocity = -32t + 20\)

Substituting the value of time (t), we have:

\(Velocity = -32(1) +20\\\\Velocity =-32+20\)

Velocity = -12 ft/sec

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Answer:

The opposite of 1/2 is -2/1, which can also be written as -2.

Answer:

x = 2

Step-by-step explanation:

P = \(\frac{x-2}{x+1}\)

P will equal zero when the numerator is equal to zero , that is

x - 2 = 0 ( add 2 to both sides )

x = 2

P = 0 when x = 2

The correct expression is 5/a = 1. There is no need to introduce an additional variable "x".

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.

The error in the reasoning is that it assumes that multiplying the second fraction by "x" will result in an equivalent expression to 5/a. However, this is not necessarily true.

To correct the error, we can use the property of reciprocals, which states that if a/b = c/d, then b/a = d/c. Using this property, we can rewrite the given equation as:

a/5 = b/3

5/a = 3/b (multiplying both sides by 5/a)

5/a = (b/3) * (3/b) (multiplying both sides by the reciprocal of b/3)

5/a = 1

Therefore, the correct expression is 5/a = 1. There is no need to introduce an additional variable "x".

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Answer:

1 and 4

Step-by-step explanation:

Answer:

(-3, 8)

Step-by-step explanation:

\(7x-14y=-133\\35x+14y=7\)

\(42x=-126\)

\(x=-126/42=-3\)

\(5(-3)+2y=1\\-15+2y=1\)

\(2y=1+15\\2y=16\\y=16/2=8\)

I hope this help you

Answer:

1 , 4 , and 6

Step-by-step explanation:

so , in a 45 45 90 triangle , the lines that are the same length are x . the hypotenuse ( the long diagonal line ) is gonna be \(x\sqrt{2}\) . so using that i got the answers . :)

The three pairs are (AB = 6, BC = 6) (AB = 4, AC = 4√2) and (BC = 2√2, AC = 4). So, First option, Option 5. and Option 6 are correct answers.

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

here, we have,

The formula for a 30-60-90 triangle is this:

1) Side opposite to 30 will be value a.

2) Side opposite to 60 will be value a√3

3) Hypotenuse will be 2a.

AB is opposite of the angle with 30 degree measurement.

BC is opposite of the angle with 60 degree measurement.

The sides of an isosceles right triangle are in the ratio,

1:1:√2

where √2 is the hypotenuse.

For the example, BC = 2√2, then AC = 2√2  x √2 = 4.

Therefore, the three pairs are;

1. (AB = 6, BC = 6)

5. (AB = 4, AC = 4√2)

6.(BC = 2√2, AC = 4).

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1.- Get rid of the parenthesis

3 + 2(3x - 2)

3 + 6x - 4

2.- Simplify like terms.

In this expression, like terms are only 3 and -4

(3 - 4) + 6x

-1 + 6x

3.- Write the result

6x - 1

Answer:

Step-by-step explanation:

Length of each part of the ruler will be

8x and 7x

. Hence, 8x+7x=30 => 15x=30 =>x=2

Hence, the lengths will be

8x=8×2=16

7x=7×2=14

Answer:

The solutions are not viable because the amount of the sale cannot be negative

Step-by-step explanation:

We are told that;

Let A be the amount of the sale in dollars and C be the charge of the online auction

This means that both values of A and B should be non-negative integers.

Now, we are also told that An online auction charges sellers a flat fee of $1.20 and 2% of the amount of the sale.

We can conclude that the solution is not viable because the amount of sale of -1.1 cannot be negative.