The standard error of the mean for a sample of size 153 is 25. in order to cut the standard error of the mean in half (to 12.5) we must select a sample size of?

Answer:

If a tangent segment and a secant segment intersect outside a circle, then the square of the measure of the tangent segment equals the product of the measures of the secant segment and its external portion.

6^2 = (x + 4)(4)

36 = 4x + 16

4x = 20, so x = 5

Answer: y = 3x

Step-by-step explanation:

In order to solve this particular question, we're first just going to look at the differences between the x and y values.

2 x 3 = 6

3 x 3 = 9

4 x 3 = 12

5 x 3 = 15

Therefore y = 3x

Answer:

SSS, SAS, ASA, AAS, and HL are valid and sufficient criteria to prove that two triangles are congruent.

This is called a variable or a symbol. In mathematics, letters or symbols are often used to represent numbers or other mathematical objects.

  The letter or symbol that represents a number is called a "variable". Variables are often used in algebra and mathematics to represent an unknown or uncertain quantity.

  In computer programming, a variable is a symbol or name used to represent a variable value or quantity. In programming, variables are used to store and manipulate data. 

For example, in the equation "y = 2x + 3", "y" and "x" are variables.

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The correct question is :

What is it called if It is a letter or symbol which represents a number?

Step-by-step explanation:

Angle 6 is equal to angle 2

  angle 2 and angle 3 form a straight line = 180 degrees

         so angle 2 = 60 degrees

  angle 6 = 60 degrees

Since sum of interior angles is equal to 180°, we get

<3 + <6 = 180°

120° + <6 = 180° since <3 = 120°

<6 = 180° - 120°

<6 = 60°

You can also prove this by measuring the angle with a protector:)

The solution is: a) 1,2,6,24,120 are the first five terms of the sequence in which the nth term is a_n=(n+1)!/n+1.

Here, we have,

The formula for the nth term of the sequence is expressed as

n=(n+1)!/n+1

For the first term, n = 1.

Therefore,

(1+1)!/(1+1)

= 2!/2

= (2×1)/2

= 1

For the second tern, n = 2.

Therefore,

(2+1)!/2+1

= 3! /3

= (3×2×1)/3

= 6/3

= 2

For the third term, n = 3,

therefore

(3+1)!/3+1

= 4!/4

=(4×3×2×1)/4

= 6

For the fourth term, n = 4.

Therefore

(4+1)!/4+1

= 5!/5

= (5×4×3×2×1)/5

= 24

For the fifth term, n = 5.

Therefore

(5+1)!/5+1

= 6!/6

= 6× 5×4×3×2×1)/6

= 120

Hence, The solution is: a) 1,2,6,24,120 are the first five terms of the sequence in which the nth term is a_n=(n+1)!/n+1.

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complete question:

Write the first five terms of the sequence in which the nth term is a_n=(n+1)!/n+1.

a) 1,2,6,24,120

b) 1,2,3,4,5

c) 1,1,3,12,60

d) 1,1,1,1,1

The university grew at an average percentage rate of approximately 15.36% per year.

1. In order to find the average percentage growth rate, we will use the formula for geometric mean growth rate:
Growth Rate = ((Ending Value / Starting Value)^(1 / Number of Years)) - 1
2. In this case, the starting value is 1,200 students, the ending value is 5,200 students, and the number of years is 10.
Growth Rate = ((5,200 / 1,200)^(1 / 10)) - 1
3. Calculate the values:
Growth Rate = (4.3333^(1 / 10)) - 1
Growth Rate = 1.1536 - 1
Growth Rate = 0.1536
4. Convert the decimal to a percentage:
Growth Rate = 0.1536 * 100 = 15.36%

Hence, Based on the geometric mean, the local university grew at an average percentage rate of approximately 15.36% per year over the 10-year period.

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Answer: x=92

Step-by-step explanation: the total degrees in a triangle is 180 so add the two angles you already have and subtract that number from 180

The graph of the equation is g ( x ) = 3 | x |

Given data ,

Step 1:

Let the equation be g(x) = kf(x)

Substitute the known point (2, 6) and solve for k

Given that the vertex of g(x) is at (0, 0) and it passes through the point (2, 6) in quadrant 1, we can substitute these values into the equation g(x) = k • f(x).

Plugging in the point (2, 6)

6 = k|2|

Since the absolute value of 2 is 2, we can rewrite the equation as:

6 = 2k

Now, solving for k by dividing both sides by 2:

k = 6/2

k = 3

So, the value of k is 3

Step 2: Use the value of k that you found in Step 1 to write an equation for g(x)

Using the value of k = 3, we can write the equation for g(x) as:

g(x) = 3f(x)

Since f(x) is given as f(x) = |x|, we can substitute it into the equation for g(x):

g(x) = 3|x|

Hence , the equation for the stretched graph g(x) is g(x) = 3 |x|

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Answer:

Step-by-step explanation:

Given lengths (in feet) of 1, 3, 5, 6, you want to know which three of them will form a triangle.

The differences between adjacent lengths are 3-1 = 2, 5-3 = 2, 6-5 = 1. The shortest side must be longer than the difference in lengths between the other two sides. Hence the 1 foot plank cannot be used. (It is not longer than either 1 or 2 feet.)

The remaining three planks satisfy the triangle inequality:

  3 + 5 > 6

  3 + 6 > 5

  5 + 6 > 3

Amanda should use the planks that are 3 feet, 5 feet, and 6 feet long.

The combined area of the mirror and the frame is equal to  π(r+2)² square inches.

Width of circular frame surrounds the mirror = 2 inches

Let us denote the radius of the circular mirror by r.

Then, the radius of the circular frame that surrounds the mirror is 'r + 2'.

The combined area of the mirror and the frame is the sum of the areas of the mirror and the frame.

The area of the mirror is πr²,

And the area of the frame

= Area of the larger circle with radius r+2  - Area of the smaller circle with radius r

⇒ Area of frame = π(r+2)² - πr²

Simplifying this expression, we get,

⇒ Area of frame = π(r² + 4r + 4) - πr²

⇒ Area of frame = πr² + 4πr + 4π - πr²

⇒ Area of frame = 4πr + 4π

The combined area of the mirror and the frame is,

πr² + 4πr + 4π

There is no specific value for r.

So we cannot calculate the exact area.

Simplify the expression by factoring out π,

=πr² + 4πr + 4π

= π(r² + 4r + 4)

= π(r+2)² square inches.

Therefore, the combined area of the mirror and the frame is π times the square of the sum of the radii of the mirror and the frame, which is (r+2)².

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In radical form, the rational exponent can be written as  [tex]m ^\frac{32}{3}[/tex]

Given rational exponent function is [tex]3^\frac{5}{4}[/tex]

Rational exponents are fractional exponents with power as the numerator and a root as the denominator.

We can write the Rational exponent function into radical form as follow

To write a rational exponent in radical form, keep in mind that it represents a power that can be written as a fraction, with the numerator being the power to which the base is raised and the denominator being the root to which the base is taken.

[tex]3^\frac{5}{4}[/tex] = [tex]3^{5\times\frac{1}{4}[/tex]

= [tex](3^5)^\frac{1}{4}[/tex]

= [tex]\sqrt[4]{3^5}[/tex]

Therefore, in radical form, the rational exponent can be written as [tex]\sqrt[4]{3^5}[/tex]

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Given question is incomplete, the complete question is given below

Rational exponents write the final answer in radical form

[tex]3^\frac{5}{4}[/tex]

Answer:

Step-by-step explanation:

To calculate the amount Fred paid for Social Security and Medicare taxes in 2020, we first need to calculate the amount of income subject to Social Security tax.

Since Fred earned $125,000, which is less than $157,700, all of his income is subject to Social Security tax.

Therefore, the amount of Social Security tax Fred paid in 2020 is:

$125,000 x 8.25% = $10,312.50

To calculate the amount of Medicare tax Fred paid in 2020, we simply multiply his income by the Medicare tax rate:

$125,000 x 1.5% = $1,875

Therefore, Fred paid a total of $10,312.50 + $1,875 = $12,187.50 for Social Security and Medicare taxes in 2020.

Answer:

1/3

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

A) The value of period of f (t) is, 2.5 seconds

B) The period of the function represents the time it takes for the height of the nail above the ground to complete one full cycle.

C) The graph is shown in figure.

Now,

A) To find the period of the function f(t), we need to identify the coefficient of the variable "t" inside the cosine function.

Hence, In this case, the coefficient is 0.8pi.

So, The period of the function is given by the formula;

T = 2π / |0.8π|,

T = 2.5 seconds.

B) The period of the function represents the time it takes for the height of the nail above the ground to complete one full cycle.

This means that every 2.5 seconds, the nail will reach its maximum height of 13 inches, before descending to its minimum height of 0 inches, and then rising again to its maximum height.

C) Here is a graph of one cycle of the function f(t), including the y-intercept:

Hence, From the graph, the function starts at a height of 0 inches, reaches its maximum height of 13 inches at t = 1.25 seconds, descends back to a height of 0 inches at t = 2.5 seconds, and then rises again to its maximum height at t = 3.75 seconds.

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The probability of people earning between $45,000 and $65,000 in this large company is approximately 29.46%.

We need to use the standard normal distribution formula, where we standardize the original distribution with mean and standard deviation to a standard normal distribution with mean 0 and standard deviation 1. We can then use a Z-table to find the probability.

First, we calculate the Z-scores for the lower and upper limits of the range of interest:

Z1 = (45,000 - 50,000) / 20,000 = -0.25

Z2 = (65,000 - 50,000) / 20,000 = 0.75

We can then look up the probabilities associated with these Z-scores in a standard normal distribution table. From the table, we find that the probability of a Z-score between -0.25 and 0.75 is 0.2946. To convert this back to the original units, we need to multiply the probability by 100 to get a percentage:0.2946 x 100 = 29.46%.

The normal distribution is a continuous probability distribution, so the probability of exact values is zero. We are calculating the probability of a range of values.

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If there is sufficient evidence exist to conclude the mean amount of milk in cartons is less than 32 ounces, then we have to use one sample t test (option b).

In this case, we have a sample of 22 cartons and we want to determine if the mean amount of milk in the cartons is less than 32 ounces. Since we are only dealing with one sample and comparing its mean to a known population mean of 32 ounces, we can use a one sample t test. This test will help us determine if the sample mean is significantly different from 32 ounces.

To perform a one sample t test, we need to calculate the sample mean and sample standard deviation of the amount of milk in the 22 quart cartons. We can then use these values, along with the known population mean of 32 ounces, to calculate the t statistic. This t statistic will tell us how many standard errors the sample mean is away from the hypothesized population mean of 32 ounces.

We can then calculate the p-value, which is the probability of getting a t statistic as extreme as the one we calculated, assuming the null hypothesis is true.

If the p-value is less than our chosen significance level (usually 0.05), we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the mean amount of milk in the cartons is less than 32 ounces.

Hence the correct option s (b).

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Answer:

Step-by-step explanation:

67

Answer:

Rather than doing the easy way do it the common way

Answer:

Step-by-step explanation:

5/6

Answer:

5/6 or approximately 0.8333 (83.33%)

Step-by-step explanation:

This is because there are five possible outcomes that are not a 3 (1, 2, 4, 5, 6) out of a total of six possible outcomes.

3,638 more votes were cast by people in the 56 and up age group than by people in the 18 to 35 and 36 to 55 age groups combined.

From the table, the amount of votes for each age range is given as follows:

The combined amount of votes of people in the 18 to 35 and 36 to 55 age groups is given as follows:

10673 + 21372 = 32,045 votes.

Then the difference in the number of votes of people in the 56 and up age range is given as follows:

35683 - 32045 = 3,638.

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Answer:

3,638 votes more than 18 to 35 and 36 to 55.

Step-by-step explanation:

you subtract and you add

Roger received £97.50. after converting $130 at the premium rate. If Roger had chosen the standard rate, he would have received £5.20 less than what he received with the premium rate. To receive the same amount in pounds regardless of the exchange rate, Roger would need to return with $173.33.

Using the premium rate, Roger would receive $130 x £0.75 = £97.50.

If Roger had chosen the standard rate, he would have received $130 x £0.71 = £92.30. Therefore, he would have received £97.50 - £92.30 = £5.20 less if he had chosen the standard rate.

Let x be the number of dollars Roger would need to return to receive the same amount in pounds, regardless of the exchange rate he chose.

Using the premium rate, he received £97.50 - £3.20 (charge) = £94.30.

Using the standard rate, he would have received x x £0.71 - £3.20 (charge) = £94.30.

Simplifying the equation, we get

x x £0.71 = £97.50

x = £97.50 / £0.71

x ≈ $137.32

Therefore, Roger would need to return $137.32 to receive the same amount, in pounds, regardless of which exchange rate he chose.

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The pressure per square inch at a depth of 25 feet is approximately 10.9 pounds per square inch.

We have,

We can use the point-slope form of a linear equation to model the pressure as a function of depth.

Let (x1, y1) = (9, 18.7) be a point on the line, and let (x2, y2) = (14, 20.9) be another point on the line.

Then the slope of the line is:

slope = (y2 - y1) / (x2 - x1)

= (20.9 - 18.7) / (14 - 9)

= 0.44

Using the point-slope form with the point (x1, y1):

y - y1 = m(x - x1)

y - 18.7 = 0.44(x - 9)

y = 0.44x - 0.08

So the function that models the amount of pressure as a function of depth is:

y = 0.44x - 0.08

To find the pressure at a depth of 25 feet,

we substitute x = 25 into the equation:

y = 0.44(25) - 0.08

= 10.92

Therefore,

The pressure per square inch at a depth of 25 feet is approximately 10.9 pounds per square inch.

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The required roots of the equation f(x)=x³+2x²-11x-12  are  -1, -4, and 3 and the value of the largest root is 3.

The given polynomial is f(x)=x³+2x²-11x-12

We have to find the roots of the given polynomial f(x), we can use a method called "factoring by grouping"

The equation can be written as x³+2x²-11x-12

x(x²+2x-11)-12=0

x(x²+2x+1-1-11)-12=0

x((x+1)²-12)-12=0

x(x+1)² - 12x - 12 =0

(x+1)(x²+x-12)=0

(x+1)(x+4)(x-3)=0

x+1 = 0 ---->x=-1

x+4 = 0---->x=-4

x-3=0---->x=3

Hence, the required roots of the equation f(x)=x³+2x²-11x-12  are  -1, -4, and 3 and the value of the largest root is 3.

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The surface area of the sphere is 1519.76 mm² and the volume is 5575.87 mm³.

Given that the diameter of the sphere is 22 mm, we can find the radius (r) by dividing the diameter by 2:

Radius (r) = 22 mm / 2 = 11 mm

The surface area (A) and volume (V) of a sphere can be calculated using the formulas:

Surface area (A) = 4πr²

Volume (V) = (4/3)πr³

Now we can substitute the value of the radius into the formulas to calculate the surface area and volume:

Surface area (A) = 4 x 3.14 x (11 mm)²

Volume (V) = (4/3) x 3.14 x (11 mm)³

Calculating the values:

Surface area (A) = 4 x 3.14 x (11 mm)²

= 4 x 3.14 x 121 mm²

= 1519.76 mm²

Volume (V) = (4/3) x 3.14 x (11 mm)³

= (4/3) x 3.14 x 1331 mm³

= 5575.87 mm³

Therefore, the surface area of the sphere is 1519.76 mm² and the volume is 5575.87 mm³.

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Answer:

Step-by-step explanation: