Use place value ans distributive property to match each multiplication expression with an equivalent expression.

A converging lens with a focal length of 12 cm forms a real image 24 cm behind the lens when a 2.0 cm tall object is placed 8.0 cm in front of it. The image is inverted and has a height of 6.0 cm.

Part A) To determine the location of the image formed by a converging lens, we can use ray tracing.

1. Draw a ray parallel to the lens axis. This ray will pass through the focal point on the opposite side of the lens.

2. Draw a ray through the center of the lens. This ray will continue undeviated.

3. Draw a ray passing through the focal point on the same side of the lens. This ray will emerge parallel to the lens axis.

4. Where these two rays intersect after refraction is the location of the image.

In this case, the object is 8.0 cm in front of the lens. The ray diagram will show that the refracted rays converge on the opposite side of the lens. By extending the rays backward, the image is formed 24.0 cm behind the lens.

Part B) To determine the height of the image, we measure the height of the object and the height of the image. In this case, the object is 2.0 cm tall.

By measuring the distance from the principal axis to the top of the object and the corresponding distance to the top of the image, we find that the image is 6.0 cm tall.

Part C) The image formed by the converging lens is inverted, as the top of the object is at the bottom of the image. Since the image is formed on the opposite side of the lens from the object, it is a real image.

A real image can be projected onto a screen, indicating that it exists in physical space.

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Answer:

Step-by-step explanation:

the answer is

z=0.625

1. the solutions to the equation are x = π/3 and x = 2π/3.

2. the solutions to the equation are: x = (π/2 + nπ)/6, 2π/3, 4π/3        (n is an integer)

3. Dividing both sides by 3:

x = π/9 + (2nπ)/3, 5π/9 + (2nπ)/3        (n is an integer)

1. Solving the equation 16cos^2(x) - 4 = 0:

Let's rewrite the equation in terms of the double-angle formula for cosine:

16(1 - sin^2(x)) - 4 = 0

Simplifying the equation:

16 - 16sin^2(x) - 4 = 0

12 - 16sin^2(x) = 0

16sin^2(x) = 12

sin^2(x) = 12/16

sin^2(x) = 3/4

Taking the square root of both sides:

sin(x) = ±√(3/4)

sin(x) = ±√3/2

Now, we can find the values of x by considering the unit circle and the quadrants where sin(x) is positive or negative.

In the first quadrant (0 < x < π/2):

sin(x) = √3/2

x = π/3

In the second quadrant (π/2 < x < π):

sin(x) = √3/2

x = π - π/3 = 2π/3

Note: Since we're using radians, we don't need to consider the angles in the third and fourth quadrants.

Therefore, the solutions to the equation are x = π/3 and x = 2π/3.

Answer: π/3, 2π/3

2. Solving the equation cos(6x)(2cos(x) + 1) = 0:

We have two possibilities for this equation to be true:

1) cos(6x) = 0

2) 2cos(x) + 1 = 0

For the first possibility, cos(6x) = 0, we know that cosine is equal to zero at odd multiples of π/2.

6x = π/2 + nπ        (n is an integer)

Solving for x:

x = (π/2 + nπ)/6        (n is an integer)

For the second possibility, 2cos(x) + 1 = 0, we can solve for cos(x):

2cos(x) + 1 = 0

2cos(x) = -1

cos(x) = -1/2

We know that cosine is equal to -1/2 at 2π/3 and 4π/3.

Therefore, the solutions to the equation are:

x = (π/2 + nπ)/6, 2π/3, 4π/3        (n is an integer)

Answer: (π/2 + nπ)/6, 2π/3, 4π/3

3. Solving the multiple-angle equation sec(3x) - 2 = 0:

To solve this equation, we need to isolate the secant function.

sec(3x) - 2 = 0

sec(3x) = 2

Taking the reciprocal of both sides:

1/cos(3x) = 2

Now, we can solve for cos(3x):

cos(3x) = 1/2

We know that cosine is equal to 1/2 at π/3 and 5π/3.

Now, we can solve for x:

3x = π/3 + 2nπ, 5π/3 + 2nπ        (n is an integer)

Dividing both sides by 3:

x = π/9 + (2nπ)/3, 5π/9 + (2nπ)/3        (n is an integer)

Answer: π/9 +(2nπ)/3, 5π/9 + (2nπ)/3 (n is an integer)

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The correct explanation for preferring the mean over the median as a measure of center is option 3: The mean is the same as the median for symmetric data.

The mean over the median as a measure of center is that the mean takes into account all values in a data set, making it more representative of the data as a whole. On the other hand, the median only considers the middle value(s), and is less sensitive to outliers. This means that extreme values in a data set have less impact on the median than they do on the mean. However, if the data set is skewed or has outliers that significantly affect the mean, the median may be a better measure of central tendency. In summary, the choice between the mean and the median depends on the characteristics of the data set being analyzed and the research question being asked.
In symmetric data, the mean and median provide the same central value, giving an accurate representation of the data's center. However, it's important to note that the mean is more sensitive to outliers than the median, which might affect its accuracy in skewed data sets.

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Two parallel lines have the same slopes thus ;

The line which we want should in form like this :

y = - 2 x + h

(( h )) can be any positive and any negative number.

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Answer:

(3*12) 36 Camcorders= $5040

1 Camcorder= $5040/36 = $140

Original= $140/1.03= $135.92

a) The sample mean years to maturity for corporate bonds = 16.9625

and the sample standard deviation =  8.2232

b) A 95% confidence interval for the population mean years to maturity: (14.4141, 19.5112)

c) The sample mean yield on corporate bonds is 4.5405

and the sample standard deviation = 2.3082

d) A 95% confidence interval for the population mean yield on corporate bonds:  (3.825, 5.256)

a) The mean of the sample would be,

\(\bar{x}\) = (10.25 + 28 +  23 + 13.25 + 3, 7.5 + 26.5 + 21.25 + 3.25, 19 + 9.25 + 28.75 + 1.75 + 17 + 8.75 + 24 + 24.5 + 18+ 11.75 + 22 + 22.75 + 27.75 + 16.75 + 12 + 16.5 + 23.75 + 25.25 + 25.75 + 22.5 + 1.25 + 19.5 + 12.5 + 27.25 + 19.5 + 17.75 + 11.5+ 3.5 + 20 + 25.25 + 6.75) / 40

\(\bar{x}\) = 678.5 / 40

\(\bar{x}\) = 16.9625

And  the sample standard deviation would be,

s = √(67.6203)

s =  8.2232

b)

We know that the formula for the confidence interval is,

CI = \(\bar{x}\) ± (z × s/√n)

Here, n = 40, \(\bar{x}\) = 16.9625, s = 8.2232 and z = 1.9600

Using above formula the 95% confidence interval for the population mean years to maturity would be,

CI = 16.9625 ± (1.9600 × 8.2232/√40)

CI = (16.9625 ± 2.548)

CI =  (16.9625 - 2.548,  16.9625 + 2.548)

CI = (14.4141, 19.5112)

c) Consider sample yield on corporate bonds.

The mean would be,

\(\bar{x}\) = 181.62 / 40

\(\bar{x}\) = 4.5405

And the standard deviation would be,

s = √(5.327594)

s = 2.3082

d) Now we construct a 95% confience interval.

Here, n = 40, s = 2.3082, \(\bar{x}\) = 4.4505, and z = 1.9600

Using above formula the 95% confidence interval for the population mean years to maturity would be,

CI =  4.4505 ± (1.9600 × 2.3082/√40)

CI = (4.5405 ± 0.716)

CI = (4.5405 - 0.716, 4.5405 + 0.716)

CI = (3.825, 5.256)

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Find the complete question below.

The radius of the circle is approximately 10.17 units (rounded to two decimal places).

To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:

arc length = radius x central angle

In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:

24.4 = r x 2.4

Solving for r, we get:

r = 24.4 / 2.4

r ≈ 10.17

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The given equation x/4 - y = -2(x/y) can be expressed in a verbal sentence as the difference between the fourth fraction of x and y is equal to minus of twice the fraction of x and y.

How to express the mathematical equation in the form of a verbal sentence?    

To express the mathematical equation in the form of a verbal sentence, we have to express the operations by using sentences.

Let's take an example,

                   x + y = 4.

Then the verbal form will be the sum of two numbers is 4.

Hence, the given expression can be expressed as the difference between the fourth fraction of x and y is equal to minus of twice the fraction of x and y.

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Answer:

1500

1.5 times 10 to the power of three is 1500. Remember, 1.5 times 10 was 15, 15 times 10 was 150, and 150 times 10 is 1500.

Step-by-step explanation:

I hope this helped you sorry if it didn’t

Answer:

150,000,000

Step-by-step explanation:

10^8 = 100000000 (8 zeros)

1.5 x 100000000 (move the decimal point 8 to the right)

150000000.00 = 150,000,000

Answer:

C

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Ok, 60! is a really big number

\(x!=x(x-1)(x-2)...1\)

So we have 60*59*58...*1

2 times 5 is 10 which makes a terminal zero (ending zero)

We need to count how many fives and twos are in 60!

There are 60/5=12 5^1's

There are 60/25=2 5^2's

So 12+2=14

There are way more 2's than fives so we take the lesser number

So the answer is 14

*Note that 60/25 is not 2, we need an integer rounded down

If the solution contains 6 ounces of water, then 1.6 is the amount of salt in ounces.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

The ratio of salt to water in certain solutions is 4 to 15.

If the solution contains 6 ounces of water, then x is the amount of salt in ounces.

So,

x/6 = 4/15

x = 24/15

x = 1.6 ounces of salt.

Therefore, 1.6 ounces of salt.

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Answer:

Step-by-step explanation:

its a real all whole numbers start with real numbers

Answer:

40

Step-by-step explanation:

Given that:

Number of options available for transmission = 2 (Standard or Automatic)

Number of options for doors = 2 (2 doors or 4 doors)

Number of exterior colors available = 10

To find:

Total number of outcomes = ?

Solution:

First of all, let us calculate the number of outcomes for the transmission mode and number of doors options.

1. Standard - 2 doors

2. Standard - 4 doors

3. Automatic - 2 doors

4. Automatic - 4 doors

Number of outcomes possible = 4 (which is equal to number of transmission mode available multiplied by number of doors options i.e. 2\(\times 2\))

Now, these 4 will be mapped with 10 different exterior colors.

Therefore total number of outcomes possible :

Number of transmission modes \(\times\) Number of doors options  \(\times\) Number of exterior colors

2 \(\times\) 2 \(\times\) 10 = 40

The number of possible outcomes of a new car will be 40. Then the correct option is B.

A sample is a collection of well-defined elements. A sample is represented by a capital letter symbol and the number of elements in the finite sample is shown as a curly bracket {..}.

A new car is available with standard or automatic transmission, two or four doors, and it is available in 10 exterior colors.

Then the number of possible outcomes will be

\(\rm Possible \ outcomes = 2*2*10\\\\Possible \ outcomes = 40\)

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Answer: 27

Step-by-step explanation:

If 2 scoops of ice cream cost $6, then 1 scoop of ice cream costs $6/2 = $3.

So, 9 scoops of ice cream would cost 9 x $3 = $27.

Answer:

27$

Step-by-step explanation:

If two wcoops of ice crewm cost 6$ them one scoop would cost 3$ because 6/2 =3. If one scoop costs 3$ then 9 scoops would cost 9x3 so 27$

JL, LK, JK are the smallest angle of a triangle is located across from its smallest side. The biggest side is on the other side of the biggest side.

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Answer:

The answer's the third one listed.

Step-by-step explanation:

The equation to solve for x is:

6x + 16 + 10x - 6 + 90 = 180

16x + 100 = 180

16x = 80

x = 5

To solve for angle BCD, just substitute 5 for x

m = 10(5) - 6

m = 50 - 6

m = 44

The probability that exactly 3 out of the first 11 customers buy a magazine is 2.23%

The proportion of customers that buy a magazine = 8.4%

If 3 out of the first 11 customers buy a magazine, then this proportion is given as; 3/11 or 27.27%

Therefore, the probability that 3 out of the first 11 customers will buy a magazine is calculated as follows;

probability = 8.4% × 27.27%

probability = (8.4/100) × (27.27/100)

probability = 0.084 × 0.2727

probability = 0.0223

Converting it into percentage as follows;

probability = 0.0223 × 100

probability = 2.23%

Therefore, the probability that 3 out of the first 11 customers buy a magazine is calculated to be 2.23%.

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Answer:

\(27\pi\)

Step-by-step explanation:

Since the diameter is 54 cm, and the formula for the circumference(perimeter) of a circle is \(2\pi r\) or \(\pi d\), we can multiply 54 by pi to get the circumference of the entire circle. This is \(54\pi\)

Now, since we are finding the circumference of the semicircle, we just divide this by 2 to get \(27\pi\).

Hope this helped!

Step-by-step explanation:

\( solution \\ diameter = 54cm \\ radius = 54 \div 2 = 27cm \\ now \\ perimeter \: of \: semi \: circle = πr + 2r, \\ = 22 \div 7 \times 27 + 2 \times 27 \\ = 84.85 + 54 \\ =138.85cm\)

we can write 27π also

Answer: (0,-2)

Step-by-step explanation: uhdehdwhehehhH

k is approximately 1.342, such that the probability P(-0.54 ≤ t ≤ k) is 0.3.

To find the value of k in the interval (-0.54 ≤ t ≤ k) such that the probability is 0.3, we need to use the cumulative distribution function (CDF) of the t-distribution.

Given that the random variable t follows a t-distribution with 14 degrees of freedom, we can use statistical software, tables, or calculators to determine the value of k.

Using these tools, we can find the value of k such that the probability P(-0.54 ≤ t ≤ k) is 0.3. This means that the area under the t-distribution curve between -0.54 and k is 0.3.

Since the t-distribution is symmetric, we can find the corresponding area in the upper tail of the distribution by subtracting the given probability (0.3) from 1. Then we can find the corresponding critical t-value for that area.

In this case, we would look for the critical t-value that corresponds to an upper-tail area of 0.7 (1 - 0.3 = 0.7) in the t-distribution with 14 degrees of freedom.

Using statistical software or tables, we can find the value of k to be approximately 1.342.

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Based on the team combination, the number of ways the team can be formed is  861,029,868,672 ways.

For the first team with 9 members, we need to select 9 members out of 32, which can be done in C(32, 9) ways.

Similarly, for the second team with 6 members, we need to select 6 members out of the remaining 32 - 9 = 23 members, which can be done in C(23, 6) ways.

For the third team with 7 members, we need to select 7 members out of the remaining 23 - 6 = 17 members, which can be done in C(17, 7) ways.

Finally, for the fourth team with 10 members, we need to select 10 members out of the remaining 17 - 7 = 10 members, which can be done in C(10, 10) ways.

Total number of ways = C(32, 9) × C(23, 6) × C(17, 7) × C(10, 10)

Using the combination formula C(n, r) = n! / (r! * (n - r)!), we can calculate the combinations:

Evaluating these expressions, we find:

C(32, 9) = 32,468,436

C(23, 6) = 1,352,128

C(17, 7) = 19,448

C(10, 10) = 1

Now, we can calculate the total number of ways:

Total number of ways = 32,468,436 × 1,352, 128 × 19,448 × 1

Total number of ways ≈ 861,029,868,672

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Answer:

x = 2.7

Step-by-step explanation:

5.4 = 2x

2x = 5.4

Divide both sides by 2.

x = 2.7

Answer: x= 2.7

1. Divide 2 on both sides

2. cancel terms who have the same numerator and denominator

the probability that the diameter of a elected bearing is greater than 85 millimeter P(diameter > 85) = P(z > (85-81)/4) = P(z > 1) = 0.1587

The diameter of ball bearings is normally distributed, with a mean of 81 millimeters and a variance of 16.

To calculate the probability that a selected bearing has a diameter greater than 85 millimeters, we first calculate the z-score for 85 millimeters.

We subtract 81 from 85 to get 4, and divide by 4 to get 1 for the z-score.

We the look up the probability for a value of 1 in the z-table, which is 0.1587.

This is the probability that a selected bearing has a diameter greater than 85 millimeters, rounded to four decimal places.

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Answer: -1

Step-by-step explanation:

Answer: -1

Step-by-step explanation: I got it right :))

Answer:

4. D

5. D

Step-by-step explanation:

To subtract Matrices, subtract the numbers that are in the same position.

You can only add or subtract Matrices that have the same order.

Here, both Matrix X and Y, are 2 by 2 matrices.

So let's subtract

\(5 - 6 = - 1\)

\( - 4 - ( - 1) = - 3\)

\(3 - ( - 7) = 10\)

\( - 2 - 4 = - 6\)

The Matrix that matches that is D so the answer to 4 is D.

5. We do the same thing above, but we multiply by 2 first.

\(5 - 2(6 ) = - 7\)

\( - 4 - 2( - 1) = - 2\)

\(3 - 2( - 7) = 17\)

\( - 2 - 2( 4) = - 10\)

The answer here is D as well.

Answer: w = ±7

Step-by-step explanation:

To get rid of the square on w, we square root both sides of the equation.

The square root of w^2 is w, and the square root of 49 is ±7.

±7 is your answer.