write four times the sum of a number and one-fourth is less than or equal to nine more the product of two and the number as an inequality

Therefore, based on the given information, the estimated age of the tomb is approximately 3,970 years.

To estimate the age of the tomb based on the radioactive carbon-14 (C-14) content in the cypress beam, we can use the decay equation:

A = A₀ * e*(kt)

Where:

A = Final amount of radioactive substance (55% of the original C-14 content)

A₀ = Initial amount of radioactive substance (100% of the original C-14 content)

k = Decay constant (ln(2) / half-life of C-14)

t = Time (age of the tomb)

Given that the half-life of C-14 is approximately 5600 years, we can calculate the decay constant:

k = ln(2) / 5600 years

Now we can plug in the values:

0.55A₀ = A₀ * e*((ln(2) / 5600 years) * t)

Dividing both sides by A₀:

0.55 = e*((ln(2) / 5600 years) * t)

Taking the natural logarithm of both sides:

ln(0.55) = (ln(2) / 5600 years) * t

Now we can solve for t, the age of the tomb:

t = (ln(0.55) * 5600 years) / ln(2)

Evaluating the expression:

t ≈ 3,970 years

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Main Answer:The approximate probability is 0.033

Supporting Question and Answer:

How do we calculate the expected average and standard deviation for a sample?

To calculate the expected average and standard deviation for a sample, we need to consider the characteristics of the population and the sample size.

Body of the Solution:

a) To find the expected average amount of the waiter's tips, we can use the fact that the mean of the sample means is equal to the population mean. Since the mean of the tips is given as 7 dollars, the expected average amount of his tips is also 7 dollars.

b) The standard deviation for the average amount of the waiter's tips, also known as the standard error of the mean, can be calculated using the formula:

Standard deviation of the sample means

= (Standard deviation of the population) / sqrt(sample size)

In this case, the standard deviation of the population is given as 2 dollars, and the sample size is 30. Plugging these values into the formula, we have:

Standard deviation of the sample means = 2 / sqrt(30) ≈ 0.365

Therefore, the standard deviation for the average amount of the waiter's tips is approximately 0.365 dollars.

c) To find the approximate probability that the average amount of the waiter's tips is less than 6 dollars, we can use the Central Limit Theorem, which states that for a large sample size, the distribution of sample means will be approximately normal regardless of the shape of the population distribution.

Since the sample size is 30, which is considered relatively large, we can approximate the distribution of the sample means to be normal.

To calculate the probability, we need to standardize the value 6 using the formula:

Z = (X - μ) / (σ / sqrt(n))

where X is the value we want to standardize, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we have:

Z = (6 - 7) / (2 / sqrt(30)) ≈ -1825

Using a standard normal distribution table or a calculator, we can find the probability associated with this z-score. The approximate probability that the average amount of the waiter's tips is less than 6 dollars is approximately 0.033.

Final Answer:Therefore, the approximate probability is 0.033, accurate to three decimal places.

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The approximate probability is 0.033

To calculate the expected average and standard deviation for a sample, we need to consider the characteristics of the population and the sample size.

a) To find the expected average amount of the waiter's tips, we can use the fact that the mean of the sample means is equal to the population mean. Since the mean of the tips is given as 7 dollars, the expected average amount of his tips is also 7 dollars.

b) The standard deviation for the average amount of the waiter's tips, also known as the standard error of the mean, can be calculated using the formula:

Standard deviation of the sample means

= (Standard deviation of the population) / sqrt(sample size)

In this case, the standard deviation of the population is given as 2 dollars, and the sample size is 30. Plugging these values into the formula, we have:

Standard deviation of the sample means = 2 / sqrt(30) ≈ 0.365

Therefore, the standard deviation for the average amount of the waiter's tips is approximately 0.365 dollars.

c) To find the approximate probability that the average amount of the waiter's tips is less than 6 dollars, we can use the Central Limit Theorem, which states that for a large sample size, the distribution of sample means will be approximately normal regardless of the shape of the population distribution.

Since the sample size is 30, which is considered relatively large, we can approximate the distribution of the sample means to be normal.

To calculate the probability, we need to standardize the value 6 using the formula:

Z = (X - μ) / (σ / sqrt(n))

where X is the value we want to standardize, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we have:

Z = (6 - 7) / (2 / sqrt(30)) ≈ -1825

Using a standard normal distribution table or a calculator, we can find the probability associated with this z-score. The approximate probability that the average amount of the waiter's tips is less than 6 dollars is approximately 0.033.

Therefore, the approximate probability is 0.033, accurate to three decimal places.

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At the bicycle manufacturer, the average cost per bicycle is $77.

To find the average cost per bicycle, we need to find the total cost of making all three bicycles and divide that by the number of bicycles.

The total cost is of the bicycles is given by -

$72 (cost of first bicycle) + $83 (cost of second bicycle) + $77 (cost of third bicycle) = $232

Now to find the average cost per bicycle, we will divide the total cost by the number of bicycles.

Hence, $232 ÷ 3 = $77

Therefore, the average cost per bicycle is $77.

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sample consists of 87 subjects, with 71 successes.the test statistic, rounded to 2 decimal places ,Test statistic = (71/87) = 0.81

To calculate the test statistic, you need to divide the number of successes by the total number of subjects in the sample.

In this case, the number of successes is 71 and the total number of subjects is 87.

Therefore, the test statistic is calculated a

s 71/87 = 0.81

which can be rounded to two decimal places. The result of the calculation is that the test statistic is 0.81.

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Answer:

Answer D is correct

Step-by-step explanation:

Let us solve this now.

58

× 100

      000

      00

+   58

= 5800

------------------------------------------------------------------------------------------

Let us solve this sum in a different way.

If there's a number to multiply by 100 you can simply put 2 zeros to the other number like this.

58 × 100 = 5800

The linear equation represents the total number of visits Jackson must make to earn a free movie ticket is 9.5x + 45 = 102 and the total number of visits to the movie theater he must make is 6.

Given :

The following steps can be used in order to determine the number of visits Jackson must make to earn a free movie ticket:

Step 1 - Let the total number of visits to the movie theater be 'x'.

Step 2 - So, the linear equation represents the total number of visits Jackson must make to earn a free movie ticket is:

9.5x + 45 = 102

Step 3 - Simplify the above linear equation.

9.5x = 57

x = 6

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The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. We are given that the line passes through the point (0,9) and has a slope of -3, so we can substitute these values into the equation to find the y-intercept:

y = mx + b

9 = (-3)(0) + b

b = 9

Now we know that the y-intercept is 9, so we can write the equation of the line:

y = -3x + 9

Therefore, the equation of the graph that passes through (0,9) and has a slope of -3 is y = -3x + 9.

Hope this helps <3

Please give me Brainliest :)

Answer:

correct answer would be S. A. S,

Answer:

I believe the answer is alternate interior :^))

Answer:

Step-by-step explanation:

We'll look for an equation with the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0.

A line parallel to y=3x+6 will have the same slope, 3.

We can write y=3x+b.  Any value of b can be used to generate a parallel line.  

If we want that line to go through a specific point, such as (0,-2), we need to find a value of b that shifts the line so that it includes (0,-2).  This can be done by using that point in the equation y=3x+b:

y=3x+b

-2=3*(0)+b  for point (0,-2)

b = -2

The equation becomes y=3x-2

See the attached plot.

===========================

Do that same thing for the remaining two points.  

For B:  (2,5) The equation is y=3x-1

For C:   (4,1) The equation is y=3x-11

Answer:

75 coloured pencils

Step-by-step explanation:

Let's say Jordon has x total pencils.

We know that 20% of these x pencils is 15, so we have:

20% * x = 15

Remember that % is just "out of 100", so 20% = 20/100 = 0.20. Then:

0.20x = 15

x = 15 / 0.20 = 75

Jordon has 75 coloured pencils.

Answer:

75 pencils

Step-by-step explanation:

Let the total no. of pencils be T

20% of T = 15

20/100 × T = 15

T = 15 × 100/20

T = 15 × 5

T = 75

Answer:

212586955997.2

Step-by-step explanation:

90^5x36-(35+60)÷25+57^4

36x90^5-95÷25+57^4

36x90^5-3.8+57^4

Solution

36x90^-3.8+57^4

Alternate form

212586955997.2

Answer:90^5x36-(35+60)÷25+57^4=? Please help quickly, show your work

Step-by-step explanation:

Answer:

y=-4x-3

Step-by-step explanation:

y=mx+b

y=b=-3 ( y intercept is when x=0, then y=b=-3)

y=-4x-3

Answer:

Step-by-step explanation:

Defining CB

CB is not the hypotenuse of triangle ABC. The hypotenuse is the longest side of any right triangle. CB is the other side other than the hypotenuse that makes up <C. It is the adjacent side because AC and CB make up angle C.

Defining Cos(C)

All of this makes up what you need to know to define the Cos(C)

Cos (C) = adjacent side / hypotenuse.

adjacent side = 6

Hypotenuse = 10

Cos(C) = 6/10

Answer: B

Answer:

19

Step-by-step explanation:

Answer:

2061.9\(mm^{3}\)

Step-by-step explanation:

We can see the original shape of the gold block is a cuboid.

Volume of Cuboid = Length x Width x Height

Volume of Original Gold Block = 27mm x 8mm x 12mm = \(2592mm^{3}\)

Next, we can see the shape of the cut-out hole is a cylinder.

Volume of Cylinder = \(\pi r^{2} h\)

We know that r = 0.5 x diameter = 0.5 x 5 = 2.5mm

Volume of cut-out hole = \(\pi (2.5)^{2} (27)\\\) = \(168.75\pi mm^{3}\)

Volume of Remaining Gold Block = Volume of Original Gold block - Volume of cut-out hole

= \(2592mm^{3} -168.75\pi mm^{3}\)

= 2061.9\(mm^{3}\)

I would like to construct a 95% confidence interval with a 4% margin of error. We don't have an estimate for the percentage, so we use a conservative estimate.

This is the minimum sample size, so we need to round up to 601. The larger the sample, the more confident the responses truly represent the population.

This shows that for a given confidence level, the confidence interval gets smaller as the sample size increases. At least 1450 samples from each group are required.

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y = e is the equation of the tangent line to the given curve at the specified point , y = \(e^{x}\) / x , (1, e)

Through the coordinate geometry formal of point-slope form, the equation of tangent and normal can be calculated.

The tangent has the equation (y - y1) = m(x - x1), and a normal travelling through this point and perpendicular to the tangent has the equation (y - y1) = -1/m (x - x1).

thus , y' =  \(\frac{e^{x}-xe^{x} }{x^{2} }\)

y'(1) = 0 = m

Our slope is indicated by the horizontal line.

y−\(y_{1}\)=m(x−\(x_{1}\))

Our line will simply be our y-coordinate because our slope(m) is 0:

e

Therefore:

The tangent line's equation is y=e.

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Answer:

27

Step-by-step explanation:

The measure of segment YX is 27 units, the correct option is C.

Trigonometric Ratios are ratios of the side of a right angled triangle. These are used to find the missing sides and angles of a right angled triangle.

A right angled triangle is a triangle with measure of one of the angle as 90 degree.

The triangle  XYW is a right triangle, with right angle at W.

The measure of angle X is f degrees and the measure of angle Y is d degrees.

The value of the trigonometric ratio sin f = 8/9

The measure of segment YW is 24 units,

The sin of an angle is the ratio of Perpendicular to the angle and the hypotenuse of the triangle.

sin f = YW / XY

8/9 = 24 / XY

XY = 24 * 9/8

XY = 27 °

The value of YX has been determined.

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The required solution for the hypothesis testing is shown.

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here,
Part A:

The null hypothesis (H0) is that the company's claim is true, and the proportion of defective batteries is 5% or less.

The alternative hypothesis (Ha) is that the company's claim is false, and the proportion of defective batteries is greater than 5%.

H0: p ≤ 0.05

Ha: p > 0.05

where p represents the proportion of defective batteries.

Part B:

A Type I error in this context would be rejecting the null hypothesis (i.e., finding significant evidence that the proportion of defective batteries is greater than 5%) when it is actually true (i.e., the proportion of defective batteries is 5% or less). This would be a false positive result.

A Type II error would be failing to reject the null hypothesis (i.e., not finding significant evidence that the proportion of defective batteries is greater than 5%) when it is actually false (i.e., the proportion of defective batteries is greater than 5%). This would be a false negative result.

Part C:

If the hypothesis is tested at a 5% level of significance instead of 1%, this means that the criteria for rejecting the null hypothesis will be less stringent. In other words, it will be easier to find significant evidence that the company's claim is false. Therefore, increasing the level of significance from 1% to 5% will increase the power of the test.

Part D:

If the hypothesis is tested based on the sampling of 500 boxes of batteries rather than 100 boxes of batteries, this means that the sample size is larger. As a result, the standard error of the estimate will be smaller, and the test will be more precise. This increased precision will increase the power of the test.

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The maximum is the highest point in a graph.

A maximum cannot occur at (a) an intersection of constraints

The point of intersection of constraints, is simply the point where the lines or curves of more than one equationequations meet.

The maximum cannot occur at this point, because at least one of the functions that meet at that point would extend past the point of intersection.

However, other options may or may not be the maximum; but, they can possibly be the maximum point.

See attachment for illustration of maximum point

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Answer:

5.7

Step-by-step explanation:

How this helps

Answer:

\(5\frac{7}{10}\)

Step-by-step explanation:

\(\frac{19}{5} *\frac{3}{2} = \frac{57}{10}\)

\(\frac{57}{10}= 5\frac{7}{10}\)

Hope this helps, have a great day:)

The principle can makes 4 groups with 7 girls and 8 boys.

The biggest number that divides each of the two or more numbers is known as the HCF, or highest common factor. The Greatest Common Measure (GCM) and Greatest Common Divisor are further names for HCF (GCD). The least common multiple, or LCM, is used to determine the smallest common multiple of any two or more numbers. LCM and HCM are two separate approaches.

According to the given statement ;

We are given that 28 girls and 32 boys volunteer to plant at a school.

The principle divided the girls and boys into identical groups that have girls and boys in each group.

We have to find that how much the principle can make greatest number of groups.

We will find HCF of 28 and 32

28= 2X2X7

32= 2X2X2X2X2

Highest common factor of 28 and 32 =2X2=4

Therefore, the principle can makes 4 groups with 7 girls and 8 boys.

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Answer:

4

5(2)+5(7)

Step-by-step explanation:

Answer:

Explicit formula *******