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Answer:

10 1/8 or 81/8

Step-by-step explanation:

Considering the dot plot, the tallest conifer is 3.25 inches taller than the shortest conifer.

This shows, with dots, the number of times that each of the measures appears in a data set.

For finding the dot plot, we have that:

The shortest conifer measures 6 and 1/4

= 6.25 inches.

The tallest conifer measures 9.5 inches.

The difference is:

9.5 - 6.25 = 3.25 inches.

Therefore the tallest conifer is 3.25 inches taller than the shortest conifer.

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Answer:

Enter each answer as a fraction in simplest form, as a decimal, and as a percent. You draw one card at random from a shuffled deck of 52 playing ...

-by-step explanation:

The total time for the trip is:

T =  3mi*( 3/2x).

Where x is the rate at which she comes home.

Remember the relation:

distance = rate*time.

We know that the distance is 3 miles (done twice).

First, the rate is 2x and then the rate is x, then the time it took the first half is:

t = 3mi/2x

And for the coming back:

t = 3mi/x

Then the total time for the trip is:

T =  3mi/2x +  3mi/x = 3mi( 1/2x + 1/x) = 3mi*( 3/2x).

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Answer:

32

Step-by-step explanation:

66 2/3% = 2/3 of 1

so 48*2/3=32

Answer:

7⁷¹

Step-by-step explanation:

Let's do it this way

7⁴^³ × 7⁷

Let's firstly apply indices since the base is the same

7⁴^³+ (⁷)

(4³ = 4×4×4 can be rewrite)

7⁴×⁴×⁴ + ⁷

7⁶⁴+⁷

= 7⁷¹

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Answer:

Raise 7 to the power of 4

Step-by-step explanation:

2401

The sum of the geometric progression is the sum S₃ = 32

The sum of terms of a geometric progression is given by

Sₙ = a(rⁿ - 1)/(r - 1) where

Given the geometric progression, aₙ = 4(2)ⁿ⁻¹ comparng it with the general term of a geometric sequence aₙ = arⁿ⁻¹, then

Now, we desire S₃, that is Sₙ when n = 3.

So, S₃ = a(r³ - 1)/(r - 1)

= 4(2³ - 1)/(2 - 1)

= 4(8 - 1)/1

= 4(8)

= 32

So, the sum S₃ = 32

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Answer:

Step-by-step explanation:

base area=41.57 in²

height=9 in

volume=41.57×9=374.13 in³

Step-by-step explanation:

1/2 = 6/12

3/4 = 9/12

5/6 = 10/12

So the order is 1/2,3/4,5/6

The surface area of the wooden structure is approximately 1012 cm².

To calculate the surface area of the wooden structure, we need to find the surface area of the cone and the surface area of the hemispherical base, and then add them together.

Surface Area of the Cone:

The surface area of a cone is given by the formula:

A_{cone = \(\pi \times r_{cone} \times (r_{cone} + s_{cone})\), \(r_{cone\) is the radius of the base of the cone and \(s_{cone\) is the slant height of the cone.

The vertical height of the cone is 24 cm, and the base radius is 7 cm, we can calculate the slant height using the Pythagorean theorem:

\(s_{cone\) = \(\sqrt{(r_{cone}^2 + h_{cone}^2).\)

Using the given measurements:

\(s_{cone\) = √(7² + 24²) cm

\(s_{cone\) ≈ √(49 + 576) cm

\(s_{cone\) ≈ √625 cm

\(s_{cone\) ≈ 25 cm

Now, we can calculate the surface area of the cone:

\(A_{cone\) = π × 7 cm × (7 cm + 25 cm)

\(A_{cone\) = (22/7) × 7 cm × 32 cm

\(A_{cone\) = 704 cm²

Surface Area of the Hemispherical Base:

The surface area of a hemisphere is given by the formula:

\(A_{hemisphere\) = \(2 \times \pi \times r_{base}^2\), \(r_{base\) is the radius of the base of the hemisphere.

Given that the base radius is 7 cm, we can calculate the surface area of the hemispherical base:

\(A_{hemisphere\) = 2 × (22/7) × (7 cm)²

\(A_{hemisphere\) = (22/7) × 2 × 49 cm²

\(A_{hemisphere\) = 308 cm²

Total Surface Area:

To calculate the total surface area, we add the surface area of the cone and the surface area of the hemispherical base:

Total Surface Area = \(A_{cone} + A_{hemisphere}\)

Total Surface Area = 704 cm² + 308 cm²

Total Surface Area = 1012 cm²

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Answer:

It's A, D, and F

Step-by-step explanation:

The answer to the question is 8a+26 so everything else that equals that is the answer.

Answer: 17 square units

Step-by-step explanation:

There are two rectangles

One has the dimensions

5 by 3, A = 5 * 3 = 15

The other has the dimensions 3-2 or 1 by 7-5 or 2, A = 1 * 2 = 2

Add the areas:

15 + 2 = 17

The entire area is 17 square units

The base protonation constant Kb of allantoin (C4H4N3O3NH2) is ×9.1210−6. The pH of a 1.1M solution of allantoin at 25°C is :

pH value = 1.15.

To the calculation of the pH value, we need to write the ionization equation first. Then using the ICE table and the information given by the problem we can set up the problem:

\(C_4H_4N_3O_3NH_2 + H_2O^{-} > C_4H_4N_3O_3NH_2^{+} + OH^{-}\)

I                   1.1 M                          Zero                             Zero              

C                   -X                            +X                                 +X

E                  1.1-X                           X                                   X

As next step, using the equilibrium expression for Kb we can replace the terms find in the ICE table and then solve for X, so:

     \(Kb= \frac{C_4H_4N_3O_3NH_2}{C_4H_4N_3O_3NH_2}\)

⇒ \(9.2x10^{-6} = \frac{[x][x]}{[1.1-x]}\)

⇒ \(9.2x10^{-6}-[1.1-x] = x^2\)

⇒ \(1.10x10^{-5}-9.2x10^{-6} - x^2 = 0\)

⇒ X = 0.003173

With the value of X we can find the pOH (lets remember that X is the concentration of OH-), so:

   \(pOH = -Log(0.00313)\)

⇒  \(pOH= 2.50\)

Finally, we can find the pH value with the equation:

   \(14= pH + pOH\)

⇒ 14 - 2.5 = pOH

⇒ pH = 11.5

The 1.1 M allantoin solution have a pH value of 11.5

Complete Question:

The base protonation constant Kb of allantoin (C4H4N3O3NH2) is ×9.1210−6. Calculate the pH of a 1.1M solution of allantoin at 25°C. Round your answer to 1 decimal pl.

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Answer:

This is indeed a function

The value of a3 is 30.

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

We are given that a_1 = 6 and \(a_n = n_a(n-1) + 2\)

Then Substitute as needed and do the arithmetic;

a_1 = 6

\(a_n = n_a(n-1) + 2\)

\(a_2 = -5a_1 +2 \\a_2= -5(6) +2 =-28\)

 \(a_ 3 = -5a_2 +2 = -(-28) +2 = 30\)

The value of a3 is 30.

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Answer:

.988  or 98.8%

Step-by-step explanation:

Answer:

A. r²

Step-by-step explanation:

The formula for the area of a circle is π r²,

thus the π is multiplied by the r²

The solutions are: x = ln(2) for 2eˣ = 4,  x = ln(25)/4 for e⁴ˣ = 25, x = ln(72) for eˣ = 72 and x = ln(124)/3 for e³ˣ = 124.

To solve these equations using natural logarithm, we can use the following rules:

Using these rules, we can solve the given equations as follows:

2eˣ = 4

Divide both sides by 2 to get

eˣ = 2.

Take the natural logarithm of both sides to get

ln(eˣ) = ln(2).

Using rule 1 above, we can simplify ln(eˣ) to x, and we get

x = ln(2).

e⁴ˣ = 25

4x = ln(25).

Divide both sides by 4 to get

x = ln(25)/4.

eˣ = 72

Take the natural logarithm of both sides to get

x = ln(72).

e³ˣ = 124

Take the natural logarithm of both sides to get

3x = ln(124).

Divide both sides by 3 to get

x = ln(124)/3.

For the second set of equations, we use the same rule as above

So, we have

ln(x - 3) = 2

x - 3 = e²

x = e² + 3.

x ≈ 10.389.

Therefore, the solution is x ≈ 10.389.

ln(2t) = 4

2t = e⁴

t = 0.5 * e⁴

t ≈ 27.299.

Therefore, the solution is t ≈ 27.299.

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There are 120 different ways to create a path to 3 different roller coasters at Six Flags.

There are a total of 10 choose 3 ways (120) to choose 3 roller coasters out of the 10 available at Six Flags. To calculate this, we can use the combination formula.

The combination formula is:

In this case, n is 10 and r is 3, so the total number of possible combinations is

To calculate the number of combinations without using a formula, we can use the following method: Start with the first roller coaster, then add a second roller coaster, then a third. There are 10 choices for the first roller coaster, then 9 for the second, and 8 for the third. This results in:

which is 6 times more than the 120 calculated by the combination formula. This is because the combinations ABC and CBA are the same, and so are other combinations that are just permutations of each other.

Therefore, there are 120 different ways to create a path to 3 different roller coasters at Six Flags.

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The thermometer reading would be 73.48°C.

The boiling point of water is generally considered to be 100°C. According to the given information, the temperature of the liquid in the thermometer is 26.52°C lower than the boiling point of water. Therefore, to find the thermometer reading, we subtract 26.52 from 100.

100 - 26.52 = 73.48

Hence, the thermometer reading would be 73.48°C.

In this scenario, we are assuming that the thermometer is calibrated to measure temperature in Celsius. The boiling point of water at standard atmospheric pressure is 100°C, and the given information states that the liquid in the thermometer is 26.52°C lower than the boiling point.

By subtracting 26.52 from 100, we obtain a reading of 73.48°C.

Thermometers work by utilizing the principle that certain substances, such as mercury or alcohol, expand or contract with changes in temperature. The expansion or contraction is measured using a scale, which is marked with various temperature values.

In this case, the thermometer is calibrated in Celsius, so we refer to the Celsius scale. By subtracting 26.52 from 100, we find the temperature at which the liquid in the thermometer is settled, which is 73.48°C.

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Answer:

4

Step-by-step explanation:

A mode is the number having the highest frequency, that is, the number which occurs the most times. (The number which occurs the most here is 4, there are two 4s. You only have one of the rest of the numbers.)

Answer:

-2.75

Step-by-step explanation:

Subtract 7 by both sides to get -22 = 8z. Divide 8 on both sides. You get -2.75

It will take 150 minutes for the two containers to have the same amount of water.

To find the number of minutes it will take for the two containers to have the same amount of water, we need to use the following formula:

m = |A - B| / (a - b)

where m is the number of minutes, A is the initial amount of water in Container A, B is the initial amount of water in Container B, a is the rate at which water is being added to Container A, and b is the rate at which water is being drained from Container B.

In this case, the initial amount of water in Container A is 300 liters, the initial amount of water in Container B is 900 liters, the rate at which water is being added to Container A is 6 liters per minute, and the rate at which water is being drained from Container B is 2 liters per minute. Substituting these values into the formula, we get:

m = |300 - 900| / (6 - 2)

m = |-600| / 4

m = 600 / 4

m = 150 minutes

Therefore, it will take 150 minutes for the two containers to have the same amount of water.

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Answer: B

Step-by-step explanation:

Add 47.6 and 7.32 to get 54.92.

Add 54.92 and 0.0574 to get 54.9774.

Add 54.9774 and 6 to get 60.9774.

We conclude that the correct option is alternative "B".

The relationship between equality and congruence is established by three key theorems. If and only if two angles have equal measurements, they are said to be congruent. If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.

In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle.

All triangles are contained in a single plane if all geometry is on the Euclidean plane, but in higher-dimensional Euclidean spaces, this is no longer the case.

The definition of the terminology used to classify triangles can be found on the first page of Euclid's Elements, which dates back more than two thousand years. In modern classification, names are either directly transliterated from Euclid's Greek or translated from Latin.

hence, The relationship between equality and congruence is established by three key theorems. If and only if two angles have equal measurements, they are said to be congruent. If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.

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Answer:

1.97497

Step-by-step explanation:

Using my calculator, I just put in log(94.4).

Answer:

d = sqrt(17)

Step-by-step explanation:

d = sqrt( x2 - x1)^2 + (y2 - y1)^2  )

d = sqrt( (4 - 5)^2 + (-3 - 1)^2 )

d = sqrt( (-1)^2 + (-4)^2  )

d = sqrt ( 1 + 16)

d = sqrt(17)