Find the distance around each figure. Use 3.14 as an approximation for π

30. The figure is made up of a rectangle and two identical semicircles.

Answer:The least number by which 125 be multiplied to make it a perfect square is 5.125 = 5 × 5 × 5

The question deals with solving an equation pertaining to natural numbers and their squares. The solution involves finding the square root of 125 divided by 5, which gives us 5. Thus, the natural number whose square multiplied by 5 equals 125 is 5.

The subject of this question is Mathematics, specifically working with natural numbers and their squares. Here, you're given that 'when the square of a natural number is multiplied by 5, the product is 125'.

It's a simple application of the basic arithmetic operations. We have to try and find the square root of 125 divided by 5 because multiplication is inverse of division.

The calculation would be: √(125/5) = √25 = 5.

Thus, the natural number in question is 5, as 5 squared (25) times 5 is equal to 125.

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The solution to the equations are

1/3(2x - 3/7) + 1/6x = 4/7 is x = 6/7

7/8 x + 3/4 x + 7/16 x - 1/16 = 5/8 is x = 1/3

1 1/5 y + 3/10 y - 1/2 y = 1/3 y + 2/5 is y = 6/10

3/4 * (1/6 x + 16) = 3/7 * (4 3/8  x - 21) is x = 12

4/3x + 9/2y

1. To solve this equation, we can start by simplifying

1/3(2x - 3/7) + 1/6x = 4/7

2/3x - 1/7 + 1/6x = 4/7

Multiplying both sides by the lcm of the denominators which is 42

28x - 6 + 7x = 24

35x = 30

x = 6/7

2. 7/8x + 3/4x + 7/16x - 1/16 = 5/8

Multiplying both sides by the lcm of the denominators which is 16

14x + 12x + 7x - 1 = 10

33x = 11

x = 1/3

3.

6/5 y + 3/10 y - 1/2 y = 1/3 y + 2/5

2/3 y= 2/5

y = 2/5 * 3/2

y = 6/10

4.

3/4 * (1/6 x + 16) = 3/7 * (4 3/8 x - 21)

opening the parenthesis

1/8 x + 12 = 15/8 x - 9

1/8 x - 15/8 x= -12 - 9

-7/4 x = -21

x = 12

5.

2x - 2/3 x + 3 y + 1 1/2 y

4/3 x + 9/2 y

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Answer:

There are 40 apples in the basket.

This is because 5 apples to 3 pears have a difference of 1.66666667 when dividing 5 by 3 to show the ratio difference. Then, all you do is multiply this number by the number of total pears which would look like 24 x 1.66666667 = 40.

I hope this helped you, have an amazing day! :)

We will use Sine Law to find the third side and then according to measurements we will draw the triangle.

Given that a triangle has two sides of length 5 cm and 7 cm with an angle of 35°, [check the figure attached]

Using the Sine Law,

Sin A / BC = Sin C / AB

Sin 35° / 7 = Sin C / 5

Sin C = Sin 35° / 7 × 5

Sin C = 0.4096

C ≈ 24°

Using the angle sum property of a triangle we get the angle B = 121°.

Again, using the Sine Law,

Sin B / a = Sin C / 5

Sin 121° / a = Sin 24° / 5

a = Sin 121° × 5 / Sin 24°

a = 10.53

Therefore, we get the three sides and the three angles of the triangle so we can draw the triangle using these measurements.

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The greatest number of groups the choir director could make is 12.

To find the greatest number of groups the choir director could make, we need to determine the highest common factor (HCF) of 24 and 36.

First, let's prime factorize both numbers:

[tex]24 = 2^3 \times 3\\36 = 2^2 \times 3^2[/tex]

Next, we identify the common factors between 24 and 36:

The factors common to both numbers are [tex]2^2[/tex]and 3.

To find the HCF, we take the smallest exponent for each common prime factor:

[tex]HCF = 2^2 \times 3 = 12[/tex]

Therefore, the greatest number of groups the choir director could make is 12.

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The logarithm with the common base in this problem is given as follows;

C. log(22)/log(9).

The logarithmic expression used in this problem is given as follows:

[tex]\log_9{22}[/tex]

Which means that the parameters are given as follows:

The common logarithm is found using a common base, that is, we divide the logarithm of the common base of the number by the logarithm of the common base of the base.

The common base is given as follows:

10.

Hence the expression is:

log(22)/log(9).

Hence the correct option is given by the option C in the context of the problem.

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Answer:

the answer was 7.71

Step-by-step explanation:

hope this helps

A fraction is usually split into two parts: the first part is the number on top, called the numerator; and the second part is the number on the bottom, called the denominator. These are both separated by a line called the “divisor line”. We can use the division method help to solve this question: to get a decimal, simply divide the numerator 54 by the denominator 7 (which you can enter in any calculator):

54 (numerator) ÷ 7 (denominator) = 7.71

And finally, you get 7.71 as your answer when you convert 7 5/7 (or 54/7) to a decimal.

Answer:

7.71

Step-by-step explanation:

Step-by-step explanation:

7 yr 11 mos = 95 mos

8 yr 11 mos = 107 mos

(x + y + z) / 3 = 95   mos              z is youngest

(x+y)/2 = 107         or      x+y = 214    <=====sub into first equation

(214  + z ) / 3 = 95      solve for 'z'

214+ z = 285

z = 71 months =  5 yrs 11 months  

Answer:9360 - 9000 - 500 is equal to 860.

Step-by-step explanation:

Burger Quick is able to estimate their wait time more consistently than Fast Chicken because it has a smaller IQR.

Burger Quick is able to estimate their wait time more consistently than Fast Chicken because it has a smaller IQR (interquartile range).

The IQR represents the range of the middle 50% of the data, and a smaller IQR indicates that the data is more tightly clustered around the median.

In this case, the IQR for Burger Quick is 15.5 - 9.5 = 6, while the IQR for Fast Chicken is 14.5 - 10 = 4.5.

This means that the wait times reported by Burger Quick are more consistent and predictable than those reported by Fast Chicken.

The range, on the other hand, represents the difference between the largest and smallest data points and does not provide information about the consistency of the data. Therefore, we cannot use the range to determine which drive-thru estimates their wait time more consistently.

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Answer:

C

Step-by-step explanation:

trust me c is the correct answer

The measure of the arc angles which subtends angles at the center are: MN = 72°, NQR = 180°, NQ = 108°, MRP = 193°, QR = 72, MR = 108, QMR = 288°, PQ = 13°, PRN = 265°, and MQN = 288°.

The angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.

So;

arc angle MN = 72° {vertical angles}

arc angle NQR = 95 + 13 + 72 = 180°

arc angle NQ = 95 + 13 = 108°

arc angle MRP = 108 + 72 + 13 = 193°

arc angle QR = 72

arc angle MR = 95 + 13 = 108 {vertical angles}

arc angle QMR = 180 + 108 = 288°

arc angle PQ = 13° {sum of angles on a straight line}

arc angle PRN = 85 + 108 + 72 = 265°

arc angle MQN = 180 + 12 + 95 = 288°.

Therefore, the following are measures of the arc angles which subtends angles at the center: MN = 72°, NQR = 180°, NQ = 108°, MRP = 193°, QR = 72, MR = 108, QMR = 288°, PQ = 13°, PRN = 265°, and MQN = 288°.

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The solution set for the inequality |x-2|>3 is x < -1 or x > 5, represented by the union of the open intervals (-∞, -1) and (5, ∞) on the number line.

To graph the inequality |x-2| > 3 on a number line, we can start by finding the values of x that satisfy the inequality:

|x-2| > 3

x-2 > 3 or x-2 < -3

x > 5 or x < -1

This means that any value of x that is greater than 5 or less than -1 will satisfy the inequality.

On a number line, we can mark -1 and 5 with open circles to indicate that they are not included in the solution set, and shade the regions to the left of -1 and to the right of 5 to show that any value in those regions satisfies the inequality.

The graph should look like this:

         <=========(================>)=========

         -1       2               5

The open circles at -1 and 5 indicate that those values are not included in the solution set, while the shaded regions to the left of -1 and to the right of 5 indicate that any value in those regions satisfies the inequality.

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a) Note that the concentration after 8 hours is 24mg/l

b) the concentration increases over 0 to 3 hours

c) the concentration decreases over 3 to 20 hours

d) after the drug reaches it's maximum concentration, it takes 8 hours for it to decrease to 16m/L

e) the graph predicts that after 1 week, or 1 month, the drug would have been completely removed from the blood stream.

f) Over the first 20 hours, the drugs concentration increases rapidly over a space of 2 hours, then gradually declines finally reaching about 2m/L over the speace of 18 hours.

In discrete mathematics, and more particularly in graph theory, a graph is a structure consisting of a set of objects, some of which are "related" in some way.

The items correspond to mathematical abstractions known as vertices, and each pair of connected vertices is known as an edge.

Note that all the above observations are arrived at by studying the graph.

One must understand that the time (t) is on the x-axis and the concentration (mg/l) is depicted by the y-axis.

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To solve this problem, we can use Newton's law of cooling, which states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. We can use the formula:

T(t) = T_s + (T_0 - T_s) * e^(-kt)

where:

T(t) is the temperature of the coffee at time t

T_s is the temperature of the surroundings (68F)

T_0 is the initial temperature of the coffee (200F)

k is a constant that depends on the specific heat transfer properties of the coffee and its container

e is the mathematical constant e, approximately 2.71828

We can use the fact that the temperature is 145F after 10 minutes to find the value of k:

145 = 68 + (200 - 68) * e^(-10k)

e^(-10k) = (145 - 68) / (200 - 68) = 77 / 132

-10k = ln(77/132)

k = -ln(77/132) / 10

Now we can use this value of k to find the temperature of the coffee after 15 minutes:

T(15) = 68 + (200 - 68) * e^(-k*15)

T(15) = 68 + (200 - 68) * e^(-15ln(77/132)/10)

T(15) = 111.72

Therefore, the temperature of the coffee 15 minutes after it was poured would be approximately 111.72F.

Answer:

127 F

Step-by-step explanation:

we will use newton's law of cooling to understand the  process. Since the coffee here is losing heat so the heat loss will be proportional to the temperature difference

The surface area of the triangular prism is 313.47 cm².

Given is a triangular prism, we need to find the surface area,

A triangular prism is a 3D shape with two identical faces in the shape of a triangle connected by three rectangular faces. The rectangular faces are referred to as the lateral faces, while the triangular faces are called bases. The bases are also called the top and the bottom (faces) of the prism.

Triangular Prism Meaning: A triangular prism is a 3D polyhedron with three rectangular faces and two triangular faces. The 2 triangular faces are congruent to each other, and the 3 lateral faces which are in the shape of rectangles are also congruent to each other. Thus, a triangular prism has 5 faces, 9 edges, and 6 vertices. Observe the following image of a triangular prism in which l represents the length of the prism, h represents the height of the base triangle, and b represents the bottom edge of the base triangle.

so, the surface area of a triangular prism =

perimeter × length + 2 × base area

So,

SA = (4.5+7.2+9) × 8.1 + 2 × 8.1 × 9

= 167.67 + 145.8

= 313.47

Hence the surface area of the triangular prism is 313.47 cm².

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(a) For right triangles, the following must be true a² = b² + c²

(b) For acute triangles, a² > b² + c²  and For obtuse triangles, a² < b² + c²

(c) The triangle is an obtuse triangle because a² > b² + c²

For a triangle to be a right triangle given the triangle's side lengths.

The square of the largest side must be equal to the sum of the square of the other sides

For a triangle to be a acute triangle given the triangle's side lengths.

The square of the largest side must be less than the sum of the square of the other sides

For a triangle to be an obtuse triangle given the triangle's side lengths.

The square of the largest side must be greater than the sum of the square of the other sides

We have

Lengths = 7.2, 8.3 and 12.4

So, we have

12.4² = 7.2² + 8.3²

Evaluate

153.76 = 120.73

The correct inequality is

153.76 > 120.73

Hence, the triangle is an obtuse triangle

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Under the units-of-activity method, the depreciation expense per mile for Bus #3 is $0.4616.

The units-of-activity method is one of the depreciation methods in use.

Under the units-of-activity method, the depreciation expense per unit is determined by dividing the depreciable amount by the total units of activity.

The depreciation amount (the value of the asset subject to depreciation) is the net of the total cost less the salvage value.

Depreciable amount of Bus #3 = $57,700 ($66,500 - $8,800)

Expected total miles for Bus #3 = 125,000

Depreciation expense per mile for Bus #3 = $0.4616 ($57,700 ÷ 125,000)

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Bus    Acquired    Cost    Salvage    Useful Life     Depreciation
                                          Value         in Years          Method

1          1/1/12      $99,100   $7,900           4             Straight-line

2         1/1/12      128,000     11,000          4             Declining- balance

3         1/1/13       66,350      8,800          5             Unit-of-activity

The lease payment's present value is $258,743.55.

The journal entry for the lease on September 1, 2022, are:

- Lease equipment $258,743.55

- Lease liability $258,743.55

We have,

A.

To calculate the present value of the lease payments, we can use the present value formula:

PV = PMT x [ (1 - (1 + r)^{-n} / r]

where PV is the present value, PMT is the monthly lease payment, r is the monthly interest rate

(which is 8 % / 12 = 0.67%), and n is the number of lease payments

(which is 36 since it's a 3-year lease with monthly payments).

Plugging in the values.

PV = $8,000 x [(1 - (1 + 0.0067)^{-36} / 0.0067]

= $258,743.55

B.

The journal entry for the lease is on September 1, 2022.

i.e

Lease equipment $258,743.55

Lease liability $258,743.55

This records the initial recognition of the lease liability and the right-of-use asset at the present value of the lease payments.

Thus,

The lease payment's present value is $258,743.55.

The journal entry for the lease on September 1, 2022, are:

- Lease equipment $258,743.55

- Lease liability $258,743.55

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Answer:

Sure, I can help you with that.

To calculate the density of Saturn, we can use the following formula:

Density = Mass / Volume

We know the mass of Saturn is 5.68 x 1026 kg, and we can calculate the volume of Saturn using the following formula:

Volume = (4/3)πr³

where π is approximately equal to 3.14159 and r is the radius of Saturn, which is 5.6 x 107 m.

Plugging in these values, we get the following:

Density = 5.68 x 1026 kg / (4/3)π(5.6 x 107 m)³

Density = 0.687 kg/m³

Therefore, the density of Saturn is 0.687 kg/m³, which is less than the density of water (997 kg/m³). This means that Saturn would float on water.

Step-by-step explanation:

The perimeter of the hollow space is 14 cm².

We have,

From the figure,

We see that the hollow space is a rectangle.

Now,

We see that,

The length of the hollow space is the side of one square.

The width of the hollow space is also the side of another square.

So,

The rectangles dimensions:

Length = 3 cm

Width = 4 cm

The perimeter of the hollow space.

= 2 (length + width)

= 2 (3 + 4)

= 2 x 7

= 14 cm²

Thus,

The perimeter of the hollow space is 14 cm².

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625 as a fraction of 1000 in its lowest terms is 5/8.

Express 625 as a fraction of 1000 in its lowest terms. Here's a step-by-step explanation:
1. Write the given numbers as a fraction: 625/1000
2. Find the greatest common divisor (GCD) of the numerator (625) and the denominator (1000). The GCD of 625 and 1000 is 125.
3. Divide both the numerator and the denominator by the GCD: (625 ÷ 125) / (1000 ÷ 125)
4. Simplify the fraction: 5/8
So, 625 as a fraction of 1000 in its lowest terms is 5/8.

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Answer:

Not rational

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

have a great day and thx for your inquiry :)

The amount of the 150 g sample of the strontium-90 that will remain after 116 years, with the half-life of strontium-90 of 29 years, is about 9.375 grams

The half-life of a (radioactive) substance is the duration it takes or required for half of the substance to decay into

The formula for exponential decay indicates that we get;

Amount remaining = Initial amount × (1/2)^(t/h)

Where;

t = The duration that elapses = 116 years

h = The half-life of the substance = 29 years

The initial amount of the strontium-90 = 150 g

Therefore; Amount remaining = 150 × (1/2)^(116/29) = 9.375

The amount of the strontium-90 that will remain after 116 years is 9.375 grams

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The distance of bird away from the tower is  4.04 miles.

Given that,

Distance between A and B = 10 miles

To solve this problem,

Use the law of tangents and basic trigonometry.

Let  the distance from tower A to the bird = x

Then,

tan(180° - 64°) = x / (10 - d)

(where d is the distance from tower B to the bird)

tan(42°) = x / d

We can rearrange the first equation to get,

10 - d = x / tan(116°)

Substituting this into the second equation, we get:

⇒ tan(42°) = x / (x / tan(116°))

⇒ tan(42°) = tan(116°) x / x

⇒  x = 10 tan(42°) / (tan(116°) - tan(42°))

Plugging this into a calculator, we get:

x ≈ 4.04 miles

Therefore,

The exotic bird is approximately 4.04 miles away from tower A.

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To calculate how long it would take to pay off a $1000 balance with an interest rate of 14% APR when making minimum payments of $20 each month, we need to consider the monthly interest and the decreasing balance.

First, let's calculate the monthly interest. The annual interest rate is 14%, so the monthly interest rate would be 14% divided by 12 months, which is approximately 1.167%.

Now, let's determine how much of the minimum payment goes towards interest each month. The remaining amount after deducting the interest is used to decrease the balance.

In the first month, the interest on the $1000 balance would be 1.167% of $1000, which is approximately $11.67. So, after making a $20 minimum payment, $11.67 is subtracted from the balance, resulting in a new balance of $988.33.

In the subsequent months, the same process is repeated. The interest is calculated based on the new balance, and the minimum payment is made. This continues until the balance reaches zero.

Given the small minimum payment of $20 and the interest accumulating on the balance, it would take significantly longer than 3 months, 1 year, or 3 years to pay off the $1000 balance. Therefore, the correct option is 6 years.

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