Find the number represented by the prime factorization. 2^2 x 3^2 x 5​

Answer:

50/77

Step-by-step explanation:

(1÷2 3/4)+(1÷3 1/2)

2 3/4 is same as 11/44

1/2 is same as 7/2

so to divide fraction you have to flip the second number and multiply

so 1 times 4/11=4/11

and 1 times 2/7=2/7

4/11 +2/7=28/77+22/77=50/77

Answer:

c = 25m + 40

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

To find the magnitude and direction of a vector using trigonometry, you can follow these steps:

1. Identify the components of the vector: A vector can be represented by its horizontal (x) and vertical (y) components. For example, if we have a vector A with components Ax and Ay, we can express it as A = (Ax, Ay).

2. Calculate the magnitude of the vector: The magnitude of a vector is the length of the vector. To find the magnitude of a vector A, you can use the Pythagorean theorem. The formula is:
  magnitude(A) = √(Ax^2 + Ay^2)

3. Find the direction of the vector: The direction of a vector can be given in different forms, such as angles or degrees. Two common ways to express the direction of a vector are:
  a. Angle with the positive x-axis: This angle is measured counterclockwise from the positive x-axis to the vector. You can use trigonometric functions to find this angle. The formula is:
     angle = arctan(Ay / Ax)
  b. Angle with the positive y-axis: This angle is measured counterclockwise from the positive y-axis to the vector. To find this angle, you can subtract the angle obtained in step 3a from 90 degrees (or π/2 radians).

4. Convert the direction to degrees or radians, depending on the required format.

Let's consider an example to illustrate these steps:

Suppose we have a vector A with components Ax = 3 and Ay = 4.

1. Identify the components: A = (3, 4).

2. Calculate the magnitude:
  magnitude(A) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

3. Find the direction:
  angle = arctan(4 / 3) ≈ 53.13 degrees.

4. Convert the direction:
  angle with positive y-axis = 90 degrees - 53.13 degrees ≈ 36.87 degrees.

So, the magnitude of vector A is 5, and its direction is approximately 36.87 degrees with a positive y-axis.

Remember, trigonometry can be used to find the magnitude and direction of a vector when you have its components.

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Answer:

Step-by-step explanation:

Answer:

86.5

\(14 + 8 + 12.5 = 34.5 \: \: 121 - 34.5 = 86.5\)

Answer:

True

Step-by-step explanation:

-8+9 is 1

9+(-8) -> 9-8 is 1

Answer:

114

Step-by-step explanation:

Ratio of red marbles to black marbles is 19:1. (Data from 3rd sentence)

19+1= 20

20 units= 120 (Data from 1st sentence)

1 unit= 120/20= 6

19 units= 120-6= 114 (Values solved in working above)

Ans: There are 114 red marbles.

To construct a 4x2 matrix D such that AD=I2, we can use the following matrix: D = [0 0 1 0; 0 0 0 1]. It is not possible for CA to be equal to 4 or 14 for any 4x2 matrix C.

Constructing a matrix D such that AD=I2

Let A = -1 be a 1x1 matrix. We want to construct a 4x2 matrix D such that their product AD is equal to the 2x2 identity matrix I2. We can use the following matrix for D:

D = [0 0 1 0; 0 0 0 1; 1 0 0 0; 0 1 0 0]

To verify that AD=I2, we can compute the matrix product:

AD = [-1 0 0 0; 0 -1 0 0] [0 0 1 0; 0 0 0 1; 1 0 0 0; 0 1 0 0]

= [0 0 -1 0; 0 0 0 -1]

= -I2

Note that D only uses 1 and 0 as entries.

Now, it is not possible for CA to be equal to 4 or 14 for any 4x2 matrix C. To see why, we can use the definition of matrix multiplication. Let C be a general 4x2 matrix:

C = [c11 c12; c21 c22; c31 c32; c41 c42]

Then, we can compute CA as:

CA = [-1 0; 0 -1] [c11 c12; c21 c22; c31 c32; c41 c42]

= [-c11 -c12; -c21 -c22; -c31 -c32; -c41 -c42]

Since CA is a 4x2 matrix and 4 is a scalar, it is not possible for CA to be equal to 4. Similarly, since the entries of C are only 0 or 1, it is not possible for CA to be equal to 14.

Therefore, there is no matrix C that satisfies the equations CA=4 or CA=14.

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The required, rate of change of function B is greater than the rate of change of Function A.

Rate of change is defined as the change in value with rest to another entity is called rate of change.

Here,
For function 1 rate of change is given by the slope of the function,

m = (y₂ - y₁) / (x₂ - x₁)
m = 2 - 1 / 4 - 0
m = 1/4

m = 0.25

For function B, y = 0.75x - 2 rate of change has defined the slope of the function from the equation slope is m = 0.75.

So Slope of function B > Slope of function A

Thus, the rate of change of function B is greater than the rate of change of Function A.

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Answer:

The equivalent expression = 1/12 of a mile

Step-by-step explanation:

Total distance of 10 members of the Balin's soccer club =5/6 of a mile

To find the distance that each member ran, Balin wrote the expression:

5/6 ÷ 10

Which expression is equivalent to Balin's expression?

5/6 ÷ 10

= 5/6 × 1/10

= 5/60

= 1/12 of a mile

Each member of the Balin's soccer club ran 1/12 of a mile

The equivalent expression to 5/6 of a mile divided by 10 members of the Balin's soccer club is 1/12 of a mile

Answer:

brah

Step-by-step explanation:

Answer:

x = \(\frac{26}{99}\)

Step-by-step explanation:

0.26 bar

100x = 26.26...

-x - 0.26..

99x = 26

x = 26/99

x = \(\frac{26}{99}\)

Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

Answer

Answer:

x= 2

y= 7

z= 4

Step-by-step explanation:

Equation 1: x+y+z=13

Equation 2: x-z= -2

Equation 3: -2x+y=3

Add equation 2 and 1

(x+y+z)+(x-z)= 13 -2

2x+y= 11

Add this to equation 3

(-2x+y)+(2x+y)= 11+3

2y= 14

y= 7

Plug in y= 7 to equation 3

-2x+(7)= 3

-2x+7=3

-2x= -4

x= 2

Plug x=2 into equation 2

2-z= -2

4 = z

The discount amount is $331.80. The price after discount is $616.20. The sales tax amount is $56.63. The final price is $672.83.

A TV originally priced at $948 is on sale for 35% off. We are to find the discount amount and the price after discount.

The original price of the TV = $948

The percentage discount = 35%.

Let X be the price after discount.

We can find X as follows:

Discount = 35% of original price

= 35% of 948= (35/100) × 948= $331.80

Price after discount (X) = Original price - Discount

= $948 - $331.80= $616.20

Therefore, the price after discount is $616.20.

Now we are to find the tax amount and the final price after including the discount and sales tax.

The sales tax is 9.2%.

We can find the tax amount as follows:

Tax amount = 9.2% of price after discount

= 9.2% of $616.20= (9.2/100) × 616.20= $56.63

Now, the final price after including the discount and sales tax = Price after discount + Tax amount

= $616.20 + $56.63= $672.83

Therefore, the final price after including the discount and sales tax is $672.83.

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Answer:

If you are looking for x your answer will be x=2

Answer:

i) is correct answer i think

Answer: (3) 21

Step-by-step explanation: 20.78 rounded to 21

30 degrees

Measure of the angle of 6 is 30 degrees

Answer:

30 degrees

Step-by-step explanation:

because 60 degrees is already there and 120 is angled the opposite way, and 100 degrees is a little farther than 90.

Answer:

It is a not a Function.

Because one number has two arrows pointing to two different numbers.

Answer:

No

Step-by-step explanation:

(the image is fuzzy so you can't really see the lines)

It seems that when x = 1, f(x) is both 4 and 5.

While two different x values can equal the same y value, one single x value cannot be equal to more than one value.

If this was a function that could be graph, there would be an extra dot at (1, 4) or (1, 5) since 1 is equal 4 or 5. This is why it is not a function.

Jorge is a recent college graduate who is eagerly seeking new job opportunities after completing his degree.

Currently, he is working part-time to cover his expenses, but his true ambition lies in finding a job that aligns with his long-term career plans. In order to achieve this, Jorge has been actively applying to various positions that match his professional aspirations and utilize the knowledge and skills he acquired during his college education.

Jorge's qualifications can be measured by various factors such as his college degree, GPA, relevant coursework, internships, and any additional certifications he may have obtained. These factors contribute to his overall level of qualification, denoted as x.

Mathematically, we can express this as:

C(x) ≥ D(x)

This inequality indicates that Jorge's qualifications need to meet or surpass the demands of the job market for him to be considered a strong candidate for the career opportunities he desires.

In summary, Jorge's current situation involves a pursuit of a fulfilling career that matches his aspirations.

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Answer:

Distributive Property of Addition.

Step-by-step explanation:

The distributive property is when you change the order of numbers in an addition expression and still get the same answer.

Answer:

3(2x-5)+4(x+2) =33

Step-by-step explanation:

3(2x-5)+4(x+2)

3(2(4)-5)+4(4+2)

3(8-5)+4(6)

3(3)+24

9+24

33

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A) The probability that ten employees must be tested in order to find three positives is 0.0645

B) Expected vale is 150 and variance is 4500

Given,

40% of employees have positive indications of asbestos in their lungs .

A)

The probability of getting an employee with positive indication is 0.40.

The probability that ten employees must be tested to find three positives is:

=    \((x-1\\k-1) * p^{k} q^{x-k}\)

=  \((10-1\\3-1) 0.4^{3} * (0.6)^{10-3}\)

= 0.0645

B)

The expected value of the total cost of conducting the tests is:

E(20 * X)  = 20 *E(X)

= 20* k/p

= 20 * 3/0.4

= 150

The variance of the total cost of conducting the tests is:

V(20*X) = 20² × V(X)

= 400 kq/p²

= 400 × 3 ×0.6/0.4²

= 4500

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The equation y = |x - 5| + |x + 5| can be rewritten as:

y = { -2x - 10, for x < -5,

 { 10, for -5 ≤ x ≤ 5,

 { 2x + 10, for x > 5.

When -5 < x < 5, both |x - 5| and |x + 5| are non-negative. So we can rewrite y = |x - 5| + |x + 5| as follows:

If x < -5, then x - 5 < -5 and x + 5 < 0, so we have:

y = -(x - 5) - (x + 5) = -2x - 10

If -5 ≤ x ≤ 5, then x - 5 < 0 and x + 5 ≥ 0, so we have:

y = -(x - 5) + (x + 5) = 10

If x > 5, then x - 5 ≥ 0 and x + 5 > 5, so we have:

y = (x - 5) + (x + 5) = 2x + 10

Therefore, the equation y = |x - 5| + |x + 5| can be rewritten as:

y = { -2x - 10, for x < -5,

 { 10, for -5 ≤ x ≤ 5,

 { 2x + 10, for x > 5.

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Given question is incomplete, the complete question is below

Rewrite each equation without absolute value for the given conditions. y = |x-5| + |x+5| if -5 < x < 5

the more appropriate average score for the two groups of adolescents is 3.1 hours.

Average hours of work per week for Child Group 1: 2.6 hours

Average hours of work per week for Group 2: 3.1 hours

The more appropriate average score for the two groups of adolescents can be calculated by adding up all the hours of work for each group, then dividing it by the total number of adolescents in each group.

For Child Group 1, the sum of the hours of work is 2 + 0 + 1 + 0 + 0 + 4 + 4 + 0 + 1 + 4 = 16. The total number of adolescents in this group is 10, so the average hours of work per week is 16/10 = 1.6 hours.

For Group 2, the sum of the hours of work is 0 + 2 + 1 + 0 + 2 + 4 + 4 + 1 + 1 + 4 = 19. The total number of adolescents in this group is 10, so the average hours of work per week is 19/10 = 3.1 hours.

Therefore, the more appropriate average score for the two groups of adolescents is 3.1 hours.

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The Svalbard Global Seed Vault is a backup storage facility for seeds In contrast, the World Agricultural Heritage Centre is a research and instructional centre.

Svalbard Global Seed Vault was established to help ensure the survival of important crops in the event of natural disasters, war, or other catastrophic events. The seed vault is located deep inside a mountain on a remote island near the Arctic Circle, where the seeds are stored at a temperature of -18 degrees Celsius.

The World Agricultural Heritage Centre, focuses on the conservation and study of crop diversity. The centre is affiliated with the Food and Agriculture Organization of the United Nations (FAO) and serves as a hub for information and research on the world's crops.

If you want to support the preservation of crop diversity, then the World Agricultural Heritage Centre might be the better choice, while if you want to help ensure the survival of crops in the event of a disaster, the Svalbard Global Seed Vault might be a better choice. Ultimately, both institutions play important roles in the preservation of crop diversity and the future of our food supply.

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The probability that at least one of the four Indiana adults selected is a gun owner is approximately 0.52.

To find the probability that at least one of the four Indiana adults selected is a gun owner, you can use the complementary probability principle, which states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.

In this case, the probability that none of the four Indiana adults selected is a gun owner is \((1 - 0.338)^4 = 0.48\) Therefore, the probability that at least one of the four Indiana adults selected is a gun owner is 1 - 0.48 = 0.52.

Therefore, the probability that at least one of the four Indiana adults selected is a gun owner is approximately 0.52.

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