Joshua was trying to calculate the mean of his test scores. He did not know what he had scored on each of the first 4 tests but knew that the sum of his scores was 370. If Joshua scored an 85 on his fifth test, then what was the mean of all 5 scores?

The measure of the smaller angle of the complementary angles is: 36 degrees.

If the sum of two angles equals 90 degrees, then they are complementary angles.

Given that the ratio of two complementary angles is 3:2, therefor:

3x + 2x = 90

5x = 90

5x/5 = 90/5

x = 18

The smaller angle = 2x = 2(18) = 36 degrees.

The larger angle = 3x = 3(18) = 54 degrees.

Therefore, the measure of the smaller angle of the complementary angles is: 36 degrees.

Learn more about on:

https://brainly.com/question/16281260

#SPJ4

The length of apothem for a regular hexagon with radius of 18 cm and side of 18 cm is 15.6 cm

The apothem of a regular polygon is a line segment from the center to the midpoint of one of its sides.

Let a represent the length of the apothem. Hence half of the side = 18/2 = 9 cm.

Using Pythagoras:

18² = a² + 9²

The length of apothem for a regular hexagon with radius of 18 cm and side of 18 cm is 15.6 cm

Find out more on apothem at: https://brainly.com/question/369332

Check the picture below.

In the triangles, the values of x are 25,  14.9,  70, 8, 50, 6 respectively

A triangle is a three-sided polygon that consists of three edges and three vertices.  The sum of angles of a triangle is equal to 180 degrees

1) 2x = 20+30

2x = 50

x = 25 degrees

2)  2x +6+8x +25 = 180

10x = 180-31

10x = 149

x = 14.9

3) 4x -5+40+3x+5 = 180

7x=180-40

7x = 140

x = 70

4)  8x +40+60=180

8x = 180-100

8x = 80

x = 8

5) m<R = 50 corresponding angles

6)  XY = 6 units      Corresponding sides

m<X = 55     corresponding angles

7) m<S = 75     (sum of angles of a triangle)

Learn more about angles of a triangle on https://brainly.com/question/19976619

#SPJ1

Answer:

Taylor will earn $27.60 after the raise.

Step-by-step explanation:

If you take $24.00 and multiply it by $1.15, your answer should be $27.60. Therefore, this is the answer to your question.

Hopefully this helps, did the best I could!

Answer:

1/2

Step-by-step explanation:

3/8 + 1/8 = 4/8 = 1/2

As groups grow in size, their structure and function tend to change. The larger the group, the more complex its structure becomes. For example, there may be more formal roles and responsibilities, as well as more rules and regulations to manage the larger number of individuals involved.

The function of the group may also change as it grows in size. In smaller groups, there may be more flexibility and autonomy for each member, with a greater emphasis on collaboration and shared decision-making. However, in larger groups, there may be a need for more hierarchical structures and centralized decision-making processes to manage the increased complexity and diversity of perspectives. Overall, the size of a group can have a significant impact on its structure and function, with larger groups often requiring more formalized and hierarchical structures to manage their complexity and diversity of perspectives. Generally, larger groups require more complex structures and may have more specialized functions.
1. Structure: As groups grow in size, they often transition from informal, loosely organized structures to more formal, hierarchical structures. This may involve the establishment of distinct roles, responsibilities, and communication channels to ensure effective coordination among group members.
2. Function: The functions of a group often become more specialized and diverse as the group grows. Smaller groups may have members with overlapping roles and responsibilities, whereas larger groups may divide tasks among members, allowing for increased specialization and expertise in specific areas.

Learn more about structure here: https://brainly.com/question/30942627

#SPJ11

Answer:

9^(x)=(1)/(27)

Step-by-step explanation:

Answer:

UP=78

Step-by-step explanation:

TP=TU+UP

103=2x+3+6x+12

103=8x+15

103-15=8x

8x=88

x=11

UP=6x+12

UP=6(11)+12

UP=66+12

UP=78

Answer:

UP = 78

Step-by-step explanation:

TU + UP = TP, substitute values

2x + 3 + 6x + 12 = 103, that is

8x + 15 = 103 ( subtract 15 from both sides )

8x = 88 ( divide both sides by 8 )

x = 11

Thus

UP = 6x + 12 = 6(11) + 12 = 66 + 12 = 78

Answer:

each ribbon should be 3.5(3 and a half or 3 1/2) feet long

Step-by-step explanation:

i divided 14 by 4

Answer:

it is A

Step-by-step explanation:

you line up the numbers and the horizonal line first

The total number of registered doctors is roughly 183,156 + 52,600 = 235,756 when rounded to the nearest whole number.

In a recent year, 52,600 female registered doctors accounted for 28.7 percent of all registered doctors. The total number of registered physicians, rounded to the nearest whole number,

To begin, calculate the percentage of male registered doctors: 100 percent - 28.7 percent = 71.3 percent, which represents the percentage of male registered doctors.

Find the number of male registered doctors: 0.713 × x = (male registered doctors) 0.713 × x = x - 52,600 0.287 × x = 52,600x = 183,156.42 ≈ 183,156 .
In order to calculate the total number of registered doctors, it is necessary to first find the number of male registered doctors.

The number of female registered doctors has already been provided, which is 52,600. Let x be the total number of registered physicians, then the percentage of female registered doctors can be expressed as:

0.287x = 52,600. Solving for x, we get x = 183,156.42, but this is not a whole number.

To round this to the nearest whole number, we add 0.5 to it (since the decimal is greater than or equal to 0.5), and then take the integer part of the result.

This gives us 183,156 + 0.5 = 183,156.5.

Since this is halfway between 183,156 and 183,157, we round up to 183,157.

Adding the number of female registered doctors to this, we get: 183,157 + 52,600 = 235,757.

So the total number of registered doctors is approximately 235,757 when rounded to the nearest whole number.

for such more questions on number

https://brainly.com/question/24644930

#SPJ8

Answer:

You are simply dividing a by 3 to reach y each time!

Step-by-step explanation:

Answer:

The correct option is;

1, 6, 11, 15

Step-by-step explanation:

The given information are;

The function that defines the terms of the sequence is f(n) = f(n - 1) + 5

Where;

n = The number of the term

For n = 1, we have, f(1) = -4

The first four terms are therefore;

f(2) = f(2 - 1) + 5 = f(1) + 5 = - 4 + 5 = 1

f(3) = f(3 - 1) + 5 = f(2) + 5 = 1 + 5 = 6

f(4) = f(4 - 1) + 5 = f(3) + 5 = 6 + 5 = 11

f(5) = f(5 - 1) + 5 = f(4) + 5 = 11 + 5 = 15

The first four terms are; 1, 6, 11, 15

Answer:

14.9

Step-by-step explanation:

Hope this helps!

The Accounting project for Grade 12 in Term 2 of 2022 in the Eastern Cape was a comprehensive assessment of students' accounting knowledge and skills.

The accounting project for Grade 12 in Term 2 of 2022 in the Eastern Cape served as a crucial assessment tool for evaluating students' understanding and application of accounting principles and concepts. This project aimed to assess their ability to analyze financial transactions, prepare financial statements, and apply accounting standards and procedures accurately.

During this project, students were typically required to complete a series of tasks that simulated real-world accounting scenarios. They were given a set of financial data, such as invoices, receipts, bank statements, and purchase orders, and were expected to record and process these transactions in appropriate accounting journals and ledgers. Students also had to prepare financial statements, including income statements, balance sheets, and cash flow statements, based on the given data.

The evaluation of the accounting project involved assessing various aspects of students' work. The accuracy and completeness of the recorded transactions, adherence to accounting principles, and the presentation and interpretation of financial information were all crucial factors in determining the final grade. Teachers assessed students' ability to demonstrate critical thinking, problem-solving skills, and attention to detail in their accounting work.

Overall, the accounting project for Grade 12 in Term 2 of 2022 in the Eastern Cape provided students with an opportunity to apply their theoretical knowledge to practical accounting scenarios. It served as a comprehensive assessment that tested their understanding of accounting principles, their proficiency in using accounting software and tools, and their ability to communicate financial information effectively.

Learn more about the Accounting project

brainly.com/question/32049046

#SPJ11

To determine if the linear system corresponding to an augmented matrix [a1 a2 a3 b] has a solution, we can check whether the vector b is in the span of the vectors {a1, a2, a3}.

In linear algebra, the augmented matrix represents a system of linear equations. The columns a1, a2, and a3 correspond to the coefficients of the variables in the system, while the column b represents the constants on the right-hand side of the equations. To check if the system has a solution, we need to determine if the vector b is a linear combination of the vectors a1, a2, and a3.

If the vector b lies in the span of the vectors {a1, a2, a3}, it means that b can be expressed as a linear combination of a1, a2, and a3. In other words, there exist scalars (coefficients) that can be multiplied with a1, a2, and a3 to obtain the vector b. This indicates that there is a solution to the linear system.

On the other hand, if b is not in the span of {a1, a2, a3}, it implies that there is no linear combination of a1, a2, and a3 that can yield the vector b. In this case, the linear system does not have a solution.

Therefore, determining whether the vector b is in the span of {a1, a2, a3} allows us to determine if the linear system corresponding to the augmented matrix [a1 a2 a3 b] has a solution or not.

Learn more about matrix here:

https://brainly.com/question/29132693

#SPJ11

Congruent triangles are also frequently employed in architectural designs, carpet patterns, stepping stone patterns, and geometric art.

The following are the two most typical instances of this: Equilateral triangles are used to make truss bridges, which are built on both sides.

Congruence :

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. A term used to describe an object and its mirror counterpart is congruence. If two things or shapes superimpose on one another, they are said to be congruent. They are identical in terms of size and shape. Line segments having the same length and angles with the same measure are congruent in the context of geometric figures.

To learn more about Congruence visit: brainly.com/question/12413243

#SPJ4

Answer:

8

Step-by-step explanation:

8/7  x 7 = 56/7 = 8

Answer:

8 days

Step-by-step explanation:

All you have to do is 8/7 multiplied by 7. Then you'll get your answer of 8 days.

Answer:

x=-7

Step-by-step explanation:

Brain-list?

Answer:

x= -7

Step-by-step explanation:

8x-2=-9+7x

7x-8x=x

x-2=-9

+2 to -9

x=-7

Frequency Distribution of data is an arrangement of data into groups called classes along with their corresponding frequencies or counts.

The sample mean is the arithmetic average of a sample and is one of the most commonly used measures of central tendency.

Then the arithmetic mean of the given distribution can be found out as follows:

Given frequency distribution: Class Interval (X)  Frequency (f) 40-46  11 47-53  21 54-60  10 61-67  11 68-74  8 75-81  7Sample mean = \(\frac{\sum fx}{\sum f}\)

we need to calculate mid-points of the given intervals;

Mid-point of 40-46 = (40+46)/2 = 43Mid-point of 47-53 = (47+53)/2 = 50Mid-point of 54-60 = (54+60)/2 = 57Mid-point of 61-67 = (61+67)/2 = 64Mid-point of 68-74 = (68+74)/2 = 71Mid-point of 75-81 = (75+81)/2 = 78

Now, we need to calculate the product of mid-point and frequency and sum it up.

Let us tabulate the values:Frequencies(X)  Frequency (f)  FX  43  11  473  50  21  1050  57  10  570  64  11  704  71  8  568  78  7  546Total  68  3911

Now, Sample Mean = \(\frac{\sum fx}{\sum f}\)= \(\frac{3911}{68}\)= 57.515Hence, the Sample mean of the given frequency distribution is 57.515.

To know more about Frequency Distribution visit

 https://brainly.com/question/30371143

 #SPJ11

Answer:

Option A, \(0.71\ d\)

Step-by-step explanation:

Step 1:  Determine the correct expression

If an item is discounted 29 percent that means that the item is now priced at the following:  (1 - 0.29) * d

This would mean that the item costs 71% of the original value or 0.71d.

Answer: Option A, \(0.71\ d\)

Answer: XYW = 32, WYZ = 85

Step-by-step explanation:

We are looking for what x is, which we can find with the formula:

117 = (6x+44) + (-10x+65)

117 = -4x + 109

8 = -4x

x = -2

We can verify this is correct by plugging it in and seeing if they add up to 117.

6x + 44 (XYW)

= 6(-2) + 44

= -12 + 44

= 32

-10x + 65 (WYZ)

= -10(-2) + 65

= 20 + 65

= 85

32 + 85 = 117

Answer:

See below

Step-by-step explanation:

The first one 'cubes' the denominator AND the numerator:

(-2/5)^3  = -2/5  * -2/5  * -2/5 =  -8/125

The second one 'cubes' only the denominator:

-2/5^3  = -2 / (5 * 5 * 5) =  - 2 / 125

Step 3 is unnecessary (the statement is already given, plus you haven't proven the triangle is isosceles anyway).

After, omit step 5 and jump straight to 6.

After this, step 6 is the statement that used to be step 5, which is true by CPCTC.

Then, you can prove the required statement by definition from this.

If two polygons are similar, then they have the same shape but not necessarily the same size.

They can be either enlarged or reduced in size or reflected. Hence, even though the polygons are similar, they do not have to be drawn to scale.

The term scale refers to the ratio of any two corresponding lengths in two geometric figures, so if two figures are drawn to scale, the ratio of their corresponding lengths in the drawing is the same as the ratio of their corresponding lengths in the actual figures.

Therefore, if two polygons are similar but not drawn to scale, the drawing may not be an accurate representation of the actual figures, as the scaling information may not be consistent.

Know more about polygons here:

https://brainly.com/question/26583264

#SPJ11