Given logs 2 0.4308 and logs 27 ≈ 2.0478, evaluate the expressions. Note: you must use the given values
and not values obtained from a calculator for those logarithms.
(a) log, 3
(b) logs (7)
show your work.

If a bungee jumper free falls for 6 seconds, the bungee jumper falls 576 feet.

We are given that the amount of time it takes for a bungee jumper to free fall is given by the function t = √(d/16), where d represents the distance that the object falls in feet. We are also told that the bungee jumper free falls for 6 seconds.

To find the distance that the bungee jumper falls, we can plug in the value of t = 6 into the equation t = √(d/16) and solve for d.

t = √(d/16)

6 = √(d/16)

Square both sides to eliminate the square root:

36 = d/16

Multiply both sides by 16 to isolate d:

d = 36 x 16

d = 576 feet

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Complete question is:

The amount of time in seconds, t, it takes for a bungee jumper to free fall is given by the function t = √(d/16)  where d represents the distance that the object falls, in feet. if a bungee jumper free falls for 6 seconds, how far does the jumper fall?

The volume of water in the cone-shaped paper cup is 25.12 cubic centimeters.

To calculate the volume of water in the cone-shaped paper cup, we can use the formula for the volume of a cone:

V = (1/3) * π * r^2 * h

Given:

Height of water (h) = 6 cm

Diameter of the top surface of water (2r) = 4 cm

First, we need to find the radius (r) of the top surface of the water. Since the diameter is given as 4 cm, the radius is half of that:

r = 4 cm / 2 = 2 cm

Now we can substitute the values into the volume formula and calculate the volume of water:

V = (1/3) * 3.14 * (2 cm)^2 * 6 cm

V = (1/3) * 3.14 * 4 cm^2 * 6 cm

V = (1/3) * 3.14 * 24 cm^3

V = 25.12 cm^3.

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Answer:

Store A

Step-by-step explanation:

25$ is less than 39$

but if they are asking for a different amount of sweatshirts then the answer would be depending on the number of sweatshirts.

Answer:

The masses of the oranges on sale at a farm stand are normally distributed with a mean of 239 grams and a standard deviation of 25 grams.

Enter the z-score of an orange that has a mass of 259 grams.

.8 is the correct answer.

Step-by-step explanation:

I took the test.

Answer: x=-3 can you mark me brainlyest thanks

Step-by-step explanation:

3(x-6)=2x(x+3)

3x-18=3x+6x

3x-18=9x

-3x      -3x

-18=6x

__   __

6      6

x=-3

Answer:

Part 1)

a=3; BC=10; AC=10

Part 2)

Isosceles Triangle

Step-by-step explanation:

Part 1)

We know that AC=BC.

Therefore, their lengths are equivalent.

So, we can write the following equation:

\(6a-8=4a-2\)

Let’s solve for a. Subtract 4a from both sides:

\(2a-8=-2\)

Add 8 to both sides:

\(2a=6\)

Divide both sides by 2. Therefore, the value of a is:

\(a=3\)

Now, we can substitute the value back to find AC and BC.

For AC, we have:

\(AC=6a-8\\\)

Substitute 3 for a:

\(AC=6(3)-8=18-8=10\)

So, the value of AC is 10.

For BC, we have:

\(BC=4a-2\)

Substitute 3 for a:

\(BC=4(3)-2=12-2=10\)

Therefore, both AC and BC measure 10 units, which was expected.

Part 2)

Remember that:

We know that AC is equal to BC. So, two sides are equal.

We don’t know anything about AB. AB could or could not be equal.

Therefore, the best answer is that Triangle ABC is an isosceles triangle.

Answer:

No

7x7=49 and 8x8=64, 56 does not have an exact square root

Answer:

Step-by-step explanation:

x + 25 + 4x + 10 = 180

5x + 35 = 180

5x = 145

x = 29

<1 = 29 + 25 = 54

<2= 4(29) + 10 = 116 + 10 = 126

Answer:

63

Step-by-step explanation:

add the given then subtract from 180

If m∠1 = 98° and m∠2 = 19°, the value of m∠3 will be 63°.

It should be noted that the sum of the angles that are in a triangle is 180°. Based on the information given, we've been given two angles to be 98° and 19°.

Therefore, the value of the third angle will be:

= 180° - (19° + 98°)

= 180° - 1117°

= 63°

Therefore, the third angle is 63°.

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Answer:

B

Step-by-step explanation:

Cube root of 27 is 3, which is in integer

Answer:

$110

Step-by-step explanation:

If her art book costs $26.62 less than her math book, and her math book costs $83.38, then all you have to do is add 26.62 to 83.28. Then the answer would be 110.

Answer:

Domain: [-6, 6]

Step-by-step explanation:

Domain is the set of x-values that can be inputted into function g.

We see from the graph that our x-values span from -6 to 6. We also see that both points are also closed dots, so we use brackets to denote that they are included. Therefore, [-6, 6] would be our domain.

His monthly payment to the nearest dollar of the loan taken over 25 years = $4,391.67

The mortgage capital = $620,000

The rate of payment of interest= 4.5%

The period for the payment = 25 years.

Simple interest

= p×T×R/100

= $620,000 × 25 × 4.5/100

= 69750000/100

= $697,500

Therefore the total amount of money that will be generated = $620,000 + $697,500 = $1,317,500

Therefore the monthly payment,

= $1,317,500/12×25

= $4,391.67

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Answer:

cd

Step-by-step explanation:

Answer:

CD?

Step-by-step explanation:

If boat is heading towards a lighthouse, whose beacon-light is 142 feet above the water, the distance from point A to point B is approximately 226.6 feet.

To find the distance from point A to point B, we can use the tangent function. Let x be the distance between point A and the lighthouse, and let y be the distance between point B and the lighthouse. We can then set up two equations based on the angles of elevation:

tan(13°) = 142/x

tan(20°) = 142/y

Solving for x and y, we get:

x = 142/tan(13°) ≈ 627.8 feet

y = 142/tan(20°) ≈ 401.2 feet

The distance between point A and point B is the difference between x and y:

x - y ≈ 226.6 feet

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Complete question is:

A boat is heading towards a lighthouse, whose beacon-light is 142 feet above the water. From point A, the boat’s crew measures the angle of elevation to the beacon, 13 degree, before they draw closer. They measure the angle of elevation a second time from point B at some later time to be 20 degrees . Find the distance from point A to point B. Round your answer to the nearest foot if necessary.

For the given problem:

Let the number = x

Two less than the quotient of a number and 8 is 1/4

so, we can write the following expression:

Now, solve the equation to find (x)

Multiplying by (8) to eliminate the denominators:

Add (6) to both sides:

So, the answer will be the number is 18

To change 3 stones to kilograms, we need to know the conversion rate between these two units of measurement. One stone is equal to 6.35 kilograms. Therefore, to convert 3 stones to kilograms, we simply multiply 3 by 6.35. This gives us: 3 stones x 6.35 kilograms/stone = 19.05 kilograms So, 3 stones is equal to 19.05 kilograms.

In summary, to change 3 stones to kilograms, we use the conversion rate of 1 stone = 6.35 kilograms and multiply the number of stones by this rate. The result is the equivalent weight in kilograms, which is 19.05 kilograms in this case.

To convert 3 stones to kilograms, you can use the conversion factor: 1 stone = 6.35029 kilograms.

Your answer: 3 stones * 6.35029 kg/stone ≈ 19.051 kg
So, 3 stones are approximately equal to 19.051 kilograms.

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The solution to the system of equations is x = 8/3 and y = 41/43.

To find the solution for the given system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:

Given equations:

3x + 2y = 22 ---(1)

-x + 15y = 21 ---(2)

To eliminate one variable, we can multiply equation (2) by 3 and equation (1) by -1, then add the resulting equations:

-3x + 45y = 63 ---(3) (multiplying equation (2) by 3)

-3x - 2y = -22 ---(4) (multiplying equation (1) by -1)

Adding equations (3) and (4) eliminates the x variable:

43y = 41

Dividing both sides by 43 gives us:

y = 41/43

Now we can substitute this value of y into either equation (1) or (2). Let's use equation (1):

3x + 2(41/43) = 22

Multiplying both sides by 43 to eliminate the fraction:

129x + 82 = 946

Subtracting 82 from both sides:

129x = 864

Dividing both sides by 129:

x = 864/129

Simplifying:

x = 8/3

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SOLUTION

Given:

Given the formula C = ph, solve for p.

Final answer:

a) The value of p₀=1

b)  The population in the year 2020 is 1.3 billion.

c)  The function f(x)=1.5 billion reaches India's population in the year 2030.

A function is a relationship between two or more inputs, each of which corresponds to exactly one output. A domain and a codomain or range are assigned to each function.

a) Given, The population of India after x years is f(x)=p₀(1.01355)ˣ⁻²⁰⁰⁰

Also in 2000, the population reached 1 billion.

That is when x=2000, f(x)=1

f(2000)=1

p₀(1.01355)ˣ⁻²⁰⁰⁰⁻²⁰⁰⁰=1

p₀×1=1

p₀=1

Hence p₀=1

b) Here the objective is we have to find the population in the year 2020

Then the value of f(x) when x=2020

Hence,

f(2020)=p₀(1.01355)ˣ⁻²⁰²⁰⁻²⁰²⁰

f(2020)=1(1.01355)²⁰

f(2020)=1.3

Therefore, the population in the year 2020 is 1.3 billion.

c) f(x)=1.5

p₀(1.01355)ˣ⁻²⁰⁰⁰=1.5

1×p₀(1.01355)ˣ⁻²⁰⁰⁰=1.5

p₀(1.01355)ˣ⁻²⁰⁰⁰=1.5

ln(p₀(1.01355)ˣ⁻²⁰⁰⁰)=ln(1.5)

(x-2000)ln(1.01355)=ln(1.5)

x-2000=ln(1.5)/ln(1.01355)

x=(ln(1.5)/ln(1.01355))+2000

x=30.12+2000

x=2030.12

Hence in the year 2030, the population might reaches to 1.5 billion.

Therefore, f(x)=1.5 billion

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The complete question is:

In 2000 , India's population reached 1 billion, and its projected to be \( 1.45 \) billion in 2025 . Use the function \( f(x

Show transcribed data

In 2000 , India's population reached 1 billion, and it's projected to be

1.45

billion in 2025 . Use the function

f(x)=P0(1.01355)

x−2000

find the help find the following a) What is p₀

​? billion b) Predict India's population in 2020 to the nearest tenth of a billion. billion c) Use the function to determine the year when India's population might reach

1.5

billion. (Round to the nearest year) Question 21 Out of pocket spending for healthcare in the United States increased between 2000 and 2008 . The function

f(x)=2572e

0.0359x

models the average annual expenditures per household, dollars, In this model,

x

represents the year,

x=0"

To calculate the probability of both cards being Kings, we need to determine the number of favorable outcomes (drawing two Kings) and the total number of possible outcomes.

The number of favorable outcomes is the number of ways we can choose two Kings from a pack of four Kings, which is given by the combination formula:

C(n, r) = n! / (r!(n-r)!)

In this case, n = 4 (four Kings) and r = 2 (we want to choose two Kings). So, the number of favorable outcomes is:

\(C(4, 2) = 4! / (2!(4-2)!) = 6\)

The total number of possible outcomes is the number of ways we can choose any two cards from a pack of 52 cards, which is given by the combination formula:

\(C(n, r) = n! / (r!(n-r)!)\)

In this case, n = 52 (total number of cards) and r = 2 (we want to choose two cards). So, the total number of possible outcomes is:

\(C(52, 2) = 52! / (2!(52-2)!) = 1326\)

Therefore, the probability of both cards being Kings is:

Probability = Favorable outcomes / Total outcomes = 6 / 1326 = 1/221

None of the given options match the calculated probability of 1/221, so the correct answer would be "None of the Above."

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The quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

To solve the quadratic equation 2a^2 = -6 + 8a, we need to rearrange it into standard quadratic form, which is ax^2 + bx + c = 0, where a, b, and c are coefficients.

Step 1: Move all the terms to one side of the equation to set it equal to zero:

2a^2 - 8a + 6 = 0

Step 2: The equation is now in standard quadratic form, so we can apply the quadratic formula to find the solutions for 'a':

a = (-b ± √(b^2 - 4ac))/(2a)

Comparing with our equation, we have:

a = (-(-8) ± √((-8)^2 - 4(2)(6)))/(2(2))

Simplifying further:

a = (8 ± √(64 - 48))/(4)

a = (8 ± √16)/(4)

a = (8 ± 4)/(4)

Now, we can calculate the two possible solutions:

a1 = (8 + 4)/(4) = 12/4 = 3

a2 = (8 - 4)/(4) = 4/4 = 1

Therefore, the quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

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Answer:

i love ur art its amazeballs and an asteroid thing

Step-by-step explanation:

As a result, the 15 cartons of creamer will last for 1,350 days, or nearly 3.7  expression years. This implies the consumer drinks one serving of creamer per day at a weight of 5 grammes per serving.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

(Total amount of creamer in grammes) / number of days (Amount of creamer consumed per day in grams)

Let's start by calculating the entire amount of creamer in grammes:

(Number of cartons) x (Total quantity of creamer) (Amount of creamer per box)

15 boxes x 450 grammes each box = total quantity of creamer

Total creamer weight = 6,750 g

(Total amount of creamer in grammes) / number of days (Amount of creamer consumed per day in grams)

The number of days is 6,750 grammes divided by 5 grammes each day.

The number of days is 1,350.

As a result, the 15 cartons of creamer will last for 1,350 days, or nearly 3.7 years. This implies the consumer drinks one serving of creamer per day at a weight of 5 grammes per serving.

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83 boxes are required to carry 800 books.

According to the question:

One Box can hold weight = 30 pounds

We know that ,  1 pound= 0.45 kg

hence, 30 pounds = 30 x 0.45 = 13.5kg  

hence,  one box can carry 13.5 kg of weight.

Now,

Weight of 1 book = 1.4 kg

So, Total Weight of 800 books= 1.4 x 800 kg

And , No. of boxes required to carry 800 books = (1.4 x 800)/13.5 = 82.96

                                                                             or approximately 83 boxes

Hence, 83 boxes are required to carry 800 books.

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Answer:

-262

Step-by-step explanation:

Given sequence is: 33, 28, 23, 18...

First term a = 33

Common Difference d = 28 - 33 = - 5

To find: \( t_{60}\)

By nth term of an AP.

\(t_n = a + (n - 1)d \\ t_{60} = 33 + (60- 1)( - 5) \\ t_{60} = 33 + 59( - 5) \\ t_{60} = 33 - 295\\ t_{60} = - 262\\ \)

Answer:

86

Step-by-step explanation:

Given, x = 5

length of a rectangle = 6x-4 = 6 * 5 - 4 = 30-4 = 26

width of a rectangle = 3x + 2 = 3 * 5 + 2 = 15 + 2 = 17

Now , finding the perimeter of the rectangle :

Perimeter of a rectangle = 2 ( length + width )

                                          = 2 ( 26 + 17 )

                                          = 2 * 43

                                         = 86

Hope I helped!

Best regards !

- TheAnimeGirl

The optimal clutch size is 1.

a)The survivorship of an offspring, S, decreases with the clutch size, C.

Therefore, the formula is given as:

S = 0.5 - 0.1C

We need to find the optimal clutch size for this bird species.

We can do this by differentiating S with respect to C, and equating the result to zero.

That is:S = 0.5 - 0.1C => dS/dC = -0.1

Equating dS/dC to zero gives:-0.1 = 0 => C = 0

This implies that there is no optimal clutch size for this species.

However, since C represents clutch size, it must be a positive integer.

Therefore, we can choose a clutch size of 1, which will result in the highest survivorship of offspring. Hence, the optimal clutch size is

1.b)The optimal clutch size for a species with a survivorship-clutch size relationship of the form S = a - bC can be obtained by following the same procedure as above.

We can differentiate S with respect to C, and equate the result to zero.

That is:S = a - bC => dS/dC = -b

Equating dS/dC to zero gives:-b = 0 => C = 0

This implies that there is no optimal clutch size for this species. However, since C represents clutch size, it must be a positive integer. Therefore, we can choose a clutch size of 1, which will result in the highest survivorship of offspring. Hence, the optimal clutch size is 1.

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Answer:

240 :)

Step-by-step explanation:

easy all u have to do is just add all the sides together but the empty sides with no number u have to try to figure out how much meters that is.

they're both 36 because they're the same size as the meters on the other side.

so its going to be

60+36+36+36+36+36

hope this helps

good luck!