What is the solution of log2x + 6 to the power of 8 = 3? x = −2 x = 2 x = −3 x = 3

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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The values of x for which f(x) = 7 are x = 61 and x = 21.

To find the values of x for which f(x) = 7, we can set up the equation and solve for x.

The given function is f(x) = 0.5|x - 41| - 3.

Setting f(x) equal to 7, we have:

0.5|x - 41| - 3 = 7.

First, let's isolate the absolute value term:

0.5|x - 41| = 7 + 3.

0.5|x - 41| = 10.

To remove the absolute value, we can consider two cases:

Case: (x - 41) is positive or zero:

0.5(x - 41) = 10.

Multiplying both sides by 2 to get rid of the fraction:

x - 41 = 20.

Adding 41 to both sides:

x = 61.

So x = 61 is a solution for this case.

Case: (x - 41) is negative:

0.5(-x + 41) = 10.

Multiplying both sides by 2:

-x + 41 = 20.

Subtracting 41 from both sides:

-x = -21.

Multiplying both sides by -1 to solve for x:

x = 21.

So x = 21 is a solution for this case.

Therefore, the values of x for which f(x) = 7 are x = 61 and x = 21.

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Step-by-step explanation:

a) 11*5=55

15*5=75

8*5+5=45

b) No, because (55+75+45=175°) and the perimeter of a triangle is 180°

The expansion of (3x-4y)¹¹ using Pascal's Triangle is:

177147x¹¹ - 2598156x¹⁰y - 17321040x⁹y² - 69284160x⁸y³ - 184757760x⁷y⁴ -  344881152x⁶y⁵ - 458941536x⁵y⁶ - 437944320 x⁴y⁷ - 291962880x³y⁸ - 129761280x²y⁹ + 34603008xy¹⁰ - 4194304y¹¹.

So, the expression is:

Now, use Pascal's Triangle to expand as follows:

Therefore, the expansion of (3x-4y)¹¹ using Pascal's Triangle is:

177147x¹¹ - 2598156x¹⁰y - 17321040x⁹y² - 69284160x⁸y³ - 184757760x⁷y⁴ -  344881152x⁶y⁵ - 458941536x⁵y⁶ - 437944320 x⁴y⁷ - 291962880x³y⁸ - 129761280x²y⁹ + 34603008xy¹⁰ - 4194304y¹¹.

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Answer:

The growth model that represents the population of this city is not linear--it is exponential:

\(f(t) = 10000( {1.025}^{t} )\)

\(t = 0 \: represents \: 2010\)

Answer:

answer is D

x = -4±√4^2 - 4(3)(5)

               2(3)

Step-by-step explanation:

ax^2 + bx + c = 0

3x^2 + 4x + 5 = 0

x = -b ±√b^2 - 4ac

             2(a)

x = -4±√4^2 - 4(3)(5)

               2(3)

Answer:

The last choice is correct.

Step-by-step explanation:

Use only the coefficients and the constant, a, b & c. not the variable x.

When it comes to arrays in mathematics, it usually involves objects or numbers that are arranged in rows and columns.In order for a set of squares to be considered an array, it must meet certain requirements. These requirements are:All rows must have the same number of squares. All columns must have the same number of squares. Squares must be organized in an orderly manner. A set of squares that does not meet these requirements is not an array.

An array is a set of objects or values that are organized in a specific order. It is used in programming, mathematics, and other fields to make data manipulation and analysis easier.

When it comes to arrays in mathematics, it usually involves objects or numbers that are arranged in rows and columns.In order for a set of squares to be considered an array, it must meet certain requirements. These requirements are:All rows must have the same number of squares. All columns must have the same number of squares. Squares must be organized in an orderly manner. A set of squares that does not meet these requirements is not an array.

For example, if a set of squares is arranged in a random or disorganized manner, it cannot be considered an array because it does not meet the orderly requirement. Additionally, if the number of squares in each row or column is different, it cannot be considered an array because it does not meet the uniformity requirement.

Overall, it is important to remember that an array is a specific type of organization and cannot be applied to any random set of objects or values.

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Answer:

wacha le vas a hacer x-3+21=67

Answer:

The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of \(Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\), in which \(\mu\) is mean amount of inches of rain and \(\sigma\) is the standard deviation.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

Mean \(\mu\), standard deviation \(\sigma\)

n days:

This means that \(s = \frac{\sigma}{\sqrt{n}}\)

Applying the Central Limit Theorem to the z-score formula.

\(Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

What is the probability that the mean daily precipitation will be of X inches or less for a random sample of November days?

The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of \(Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\), in which \(\mu\) is mean amount of inches of rain and \(\sigma\) is the standard deviation.

Answer:

\(x = \frac{-6y+7}{5}\)

Step-by-step explanation:

\(6y + 5x = 7\)

Isolate x ;

\(5x = 7-6y\\\\5x =-6y+7\)

Divide both sides of the equation by 5

\(\frac{5x}{5} = \frac{-6y+7}{5} \\\\x = \frac{-6y +7}{5}\)

Answer:

20%

Step-by-step explanation:

if zero toppings is an option, then there would be 5 possibilities for toppings

0,1,2,3,or 4

the server randomly chose 3 toppings so that would be one out of 5 or 20%.

(If the server did not have the option to put zero toppings on then there would be only 4 options 1,2,3, or 4 toppings and the correct answer would be one out of 4 or 25%.)

Answer:

Step-by-step explanation:

1 find out what kind of  its is

if its equivelent you might use 60 as thee angles then find out

Answer:

A.35°, 114°, 31°.

B.61°,119°,153°,27° and 92°

A. alternates angles are equal;

35°=35°

Vertically opposites angles are equal;

114°=114°

Sum of interior angles of a triangle is 180;

114+35+x=180

x=180-(114+35)

x=31

Picture B.

Corresponding angles are equal;

61°=61°

Sum of angles on a straight line is 180°

61+x=180

x=180-61

x=119°

Corresponding angles are equal;

153°=153°

Sum of angle on straight line is 180;

153+x=180

x=180-153

x=27

Sum of interior angle of a triangle is 180;

27+61+X=180

x=180-(27+61)

x=92

Step 1:

Write the parent function

Step 2:

The parent function y = In(x) is shifted 3 units down to get y = In(x) - 3

Final answer

Option B

It is shifted 3 units down.

Answer:

m=-9

Step-by-step explanation:

The approximate margin of error for a survey based on 2,700 adults, when rounded to nearest thousand is 0.021.

In statistical surveys, the margin of error is a measure of the expected amount of random sampling error that is present in a survey's results. It is a range of values that is likely to contain the true value of the population parameter being estimated, with a certain degree of confidence.

In other words, the margin of error is the amount by which the sample estimate may differ from the true value of the population parameter.

The margin of error is affected by several factors, such as the size of the sample and the level of confidence. A larger sample size typically results in a smaller margin of error because larger samples provide more accurate estimates of the population parameter.

Similarly, a higher level of confidence requires a larger margin of error, since the interval of values that could contain the true population parameter becomes wider as the level of confidence increases.

Assuming a 95% level of confidence, the formula for calculating the margin of error is:

Margin of error = z * sqrt(p * (1 - p) / n)

where:

z is the z-score for the desired level of confidence (1.96 for 95%)

p is the sample proportion, which is the proportion of the sample that exhibits a particular characteristic of interest (e.g., the proportion of respondents who support a certain political candidate)

n is the sample size, which is the number of observations in the sample.

If the sample proportion is not known, it is common to use a value of 0.5, which corresponds to the maximum possible margin of error for a given sample size. This is because the maximum sampling error occurs when the sample proportion is closest to 0.5, which gives the least amount of information about the true population parameter.

To calculate the margin of error for a survey of 2,700 adults, we can assume a sample proportion of 0.5 and a 95% level of confidence. Plugging these values into the formula, we get:

Margin of error = 1.96 * sqrt(0.5 * (1 - 0.5) / 2700)

= 1.96 * sqrt(0.25 / 2700)

= 1.96 * 0.008

= 0.016

Rounding to the nearest thousandth, the approximate margin of error is 0.021. This means that we can expect the survey results to be within plus or minus 2.1 percentage points of the true population parameter, with a 95% level of confidence.

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Answer:

4x+8=54 this is the correct answer

Answer: See image

Step-by-step explanation:

The bases are 5cm times 3cm, meaning that 2 parallel sides have to be 5cm by 3cm, 2 other parallel sides have to 2cm by 3cm, and the 2 other parallel sides have to be 5cm by 2cm.

Answer:

Step-by-step explanation:

2x^2 + 9x + 4=0

2x^2+8x+x+4=0

2x(x+4) +1 (x+4) =0

2x+1 = 0

x+ 4 =0

2x= -1

x= -1/2

x=-4

Therefore x = -4 and x = -1/2

The matching of items and their corresponding descriptions are 1. Domain, 2.Output, 3. Input, 4. Relation, 5. Function, and 6. Range.

1. Domain - the first element of a relation or function; also known as the input value.

3. Input - the x-value of a function.

6. Range - the second element of a relation or function; also known as the output value.

4. Relation - any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane.

2. Output - a relation in which every input value has exactly one output value.

5. Function - the y-value of a function.

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Answer:

3 =x

Step-by-step explanation:

(segment piece) x (segment piece) =   (segment piece) x (segment piece)

3x(x+1) = 4x*x

Divide each side by x

3(x+1) = 4x

Distribute

3x+3 = 4x

Subtract 3x from each side

3x-3x +3 = 4x-3x

3 =x

The x-intercepts will be at x = 0 , -2 A line crosses the x-axis at the x-intercept, and the y-intercept is where the line crosses the y-axis.

Given

f(x) = x²(x+2)

To find the x-intercepts ⇒ f(x) = 0

∴ x²(x+2) = 0

∴ x² = 0  OR   x+ 2 = 0

∴ x = 0  or   x = -2

So, the x-intercepts will be at x = 0 , -2

We must graph the function f in order to determine whether the graph crosses the x-axis, hits the x-axis, and then reverses at each intercept (x)

The attached figure represents the graph of f(x)

As shown in the figure:

1)  The graph crosses the x-axis at x = -2

2) The graph touches the x-axis and turns around at x = 0

The complete question is,

Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis and turns around at each intercept. Show your work.

f(x) = x2(x + 2)

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The  answer of this queation :∫ (4 + √x + x/x) dx = 4x + 2/3 x^(3/2) + x + C

where C = C1 + C2 + C3 is the constant of integration for the entire expression.

eparate integrals:

∫ 4 dx + ∫√x dx + ∫ x/x dx

The first two integrals can be easily integrated as follows:

∫ 4 dx = 4x + C1, where C1 is a constant of integration.

∫√x dx = 2/3 x^(3/2) + C2, where C2 is a constant of integration.

For the third integral, note that x/x simplifies to 1 for all nonzero x.

∫ x/x dx = ∫ 1 dx = x + C3, where C3 is a constant of integration.

Putting it all together, we have:

∫ (4 + √x + x/x) dx = 4x + 2/3 x^(3/2) + x + C

where the integration constant for the entire statement is C = C1 + C2 + C3.

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n+5

Subtract 4.2n and 3.2n

Answer:

4/6

Step-by-step explanation:

there are three even numbers (3/6) and 3 odd numbers but you are only looking for 5 (1/6) so the answer is 4/6

hopefully this helps you :)

pls mark my answer brainlest I need it ;)

Answer:

Thats not possible

Step-by-step explanation:

There is no:

Answer:

i cant rlly see the question bc its cut out but i yhink its 8

Step-by-step explanation:

total Amount of Marbles in the bag is:

5 + 3 = 8

So, since there are 5 Red marbles, the probability of drawing one is 5 / 8.

Now that you pulled that marble out, you have 7 marbles total left in the bag, 4 of those are read (5 originally, minus the one you took out.

So, the probability of the second round is 4/7.

To find the overall probability, you multiply those probabilities together:

4/7*5/8 = 20/56

Answer:

The second one

O (1-6) (2-5) (3-4) (4-3) (5-2) (6-1)

Step-by-step explanation:

Favorable outcome is the outcome that we are looking for

The outcome that we are looking for when rolling two = die is a sum of 7

The set (1-6) (2-5) (3-4) (4-3) (5-2) (6-1) all add up to equal 7

( 1 , 6 ) 1 + 6 = 7

( 2 , 5 ) 2 + 5 = 7

( 3 , 4 ) 3 + 4 = 7

etc.

Which means that they are the favorable outcomes for rolling a seven

In June, A.B.C company invested $20,000, purchased equipment, paid insurance premium, bought office supplies, billed students for tutorial services, received cash, paid for supplies, withdrew personal funds.

Accounting Cycles:

1. June 1:

  - A.B.C company invests $20,000 in the business.

  - Prepare the journal entry:

    - Debit: Cash ($20,000)

    - Credit: Capital ($20,000)

2. June 3:

  - Purchased equipment for $12,100.

  - Prepare the journal entry:

    - Debit: Equipment ($12,100)

    - Credit: Cash ($12,100)

3. June 4:

  - Paid $220 premium for an insurance policy.

  - Prepare the journal entry:

    - Debit: Insurance Expense ($220)

    - Credit: Cash ($220)

4. June 6:

  - Purchased office supplies on account for $140.

  - Prepare the journal entry:

    - Debit: Office Supplies ($140)

    - Credit: Accounts Payable ($140)

5. June 9:

  - Purchased a new computer for $9,000. Paid 40% in cash and agreed to pay the remainder later.

  - Prepare the journal entry for the cash payment:

    - Debit: Computer ($3,600) [40% of $9,000]

    - Credit: Cash ($3,600)

  - Prepare the journal entry for the remaining amount:

    - Debit: Computer ($5,400)

    - Credit: Accounts Payable ($5,400)

6. June 10:

  - Billed student Omar $58 for tutorial services performed.

  - Prepare the journal entry:

    - Debit: Accounts Receivable ($58)

    - Credit: Tutorial Services Revenue ($58)

7. June 14:

  - Paid for the supplies purchased on June 6th ($140).

  - Prepare the journal entry:

    - Debit: Accounts Payable ($140)

    - Credit: Cash ($140)

8. June 15:

  - The owner suggested purchasing a new building for the company for $22,000.

  - No journal entry is required at this point. It is a decision made by the owner.

9. June 25:

  - Received $85 cash from student Salim Ali for tutorial services performed.

  - Prepare the journal entry:

    - Debit: Cash ($85)

    - Credit: Accounts Receivable ($85)

10. June 30:

   - Student billed on June 10 pays the amount due ($58).

   - Prepare the journal entry:

     - Debit: Cash ($58)

     - Credit: Accounts Receivable ($58)

11. June 30:

   - A.B.C company withdraws $60 for personal use.

   - Prepare the journal entry:

     - Debit: Withdrawals ($60)

     - Credit: Cash ($60)

These transactions represent the accounting cycles for the given period.

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