arc length of AB
angle ab=115
radius bc=13

Answer:

The correct answer is 7.

Step-by-step explanation:

The sum of 2 and 5 is 7, not 8. Addition is a basic arithmetic operation that combines two numbers to find their total or sum. In this case, when we add 2 and 5 together, we count a total of 7. It's important to carefully perform calculations to ensure accuracy and obtain the correct result.

The z-score of a time of 44 minutes is 1.2

From the question, we have the following parameters that can be used in our computation:

Normally distributed mean = 38 minutes

Normally distributed standard deviation = 5 minutes.​

Also, we have

Score = 44 miniues

The z-score of a time of 44 minutes is calculated as

z = (Score - Mean)/standard deviation

substitute the known values in the above equation, so, we have the following representation

z = (44 - 38)/5

Evaluate

z = 1.2

Hence, the z-score of a time of 44 minutes is 1.2

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Answer:

net salary = 8047.5

Step-by-step explanation:

his basic salary is 8700

7.5% of that is (8700)(0.075) = 652.5

He gives this away, so his net salary will become

8700 - 652.5 = 8047.5 = net salary

Answer:

0.63

Step-by-step explanation:

We have the following information:

The probability of a student being male is 0.45.

The probability of a student having a job off-campus is 0.33.

The probability of a student being male and having a job off-campus is 0.15.

Now, we want to find the probability that a student is either male or has an off-campus job.

To do this, we add the probability of being male (0.45) to the probability of having an off-campus job (0.33). However, we need to be careful not to count the students who are both male and have an off-campus job twice. So, we subtract the probability of being male and having an off-campus job (0.15) once.

By doing this, we account for all the possible cases and get the probability that a student is either male or has an off-campus job.

Calculating the values:

P(Male or Off-campus job) = P(Male) + P(Off-campus job) - P(Male and Off-campus job)

= 0.45 + 0.33 - 0.15

= 0.63

Therefore, the probability that a student chosen at random from the college is male or has an off-campus job is 0.63.

Hope this helps!

Step-by-step explanation:

therefore, the correct option is option number 1.

Al the nth term are,

1) a (n) = 6 + 4n

2) a (n) = 26 + 8n

3) a (n) = 23 - n

4) a (n) = 7n - 3

5) a (n) = 8n - 43

We have to given that;

All the sequence are,

1.10,14,18,22..

2.34,26,18,10,..

3.17;11;5;-1;-7;..

4.4;11;18;25;..

5.-35;-27;-19;-11;..​

Now, WE can find the nth term as;

1) 10,14,18,22..

Here, a = 10

Common difference = 14 - 10 = 4

Hence, The nth term is,

a (n) = a + (n - 1) d

a (n) = 10 + (n - 1)4

a (n) = 10 + 4n - 4

a (n) = 6 + 4n

2) 34,26,18,10,..

Here, a = 34

Common difference = 26 - 34 = 8

Hence, The nth term is,

a (n) = a + (n - 1) d

a (n) = 34 + (n - 1)8

a (n) = 34 + 8n - 8

a (n) = 26 + 8n

3) 17;11;5;-1;-7;..

Here, a = 17

Common difference = 11 - 17 = - 6

Hence, The nth term is,

a (n) = a + (n - 1) d

a (n) = 17 + (n - 1) (- 6)

a (n) = 17 - 6n + 6

a (n) = 23 - n

4) 4;11;18;25;..

Here, a = 4

Common difference = 11 - 4 = 7

Hence, The nth term is,

a (n) = a + (n - 1) d

a (n) = 4 + (n - 1) (7)

a (n) = 4 + 7n - 7

a (n) = 7n - 3

5) -35;-27;-19;-11;..​

Here, a = - 35

Common difference = - 27 + 35 = 8

Hence, The nth term is,

a (n) = a + (n - 1) d

a (n) = - 35 + (n - 1) (8)

a (n) = - 35 + 8n - 8

a (n) = 8n - 43

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Step-by-step explanation:

Let the boys be x

Girls = x - 14 (number of females is 14 less than the number of males)

x + x - 14 = 32

2x - 14 = 32

2x = 32 + 14 (add 14 to both sides or if 14 crosses over the bracket. The sign changes to plus or positive)

2x = 46

Divide both sides by 2

x = 23

Girls = x - 14 = 23 - 14

=9

Therefore, The boys are 23, while the girls are 9

The perimeter of this parallelogram is equal to 32.4 units.

In Mathematics and Geometry, the perimeter of a parallelogram can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

For the length, we have:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(-5 + 4)² + (-3 - 2)²]

Distance = √26

Distance = 5.1 units

For the width, we have:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(7 + 4)² + (3 - 2)²]

Distance = √122

Distance = 11.1 units.

P = 2(5.1 + 11.1)

P = 2(16.2)

P = 32.4 units.

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Step-by-step explanation:

If the sin 0° = 0, then which statement is true?

1) cos 90° = 0, because the cosine and sine are complements

2) cos 180° = 1, because the cosine and sine are supplements

3) cos 90° = 1, because the cosine and sine are complements

4) cos 180° = 0, because the cosine and sine are supplementscc

Answer:

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

Let it be x years after that Jack's mother will be 3 times as old as Jack.

Set up equation and solve for x:

After 15 years Jack will be 20 and his mother will be 60 years old.

Answer:

55

Step-by-step explanation:

You just need to divide 220 ÷ 4 = 55

Hope this helps :)

Pls brainliest...

Answer:

Step-by-step explanation:

[tex]a+b=(3i+4j)+(-2i+5j)[/tex]

        [tex]=3i+4j-2i+5j[/tex]

        [tex]=1i+9j[/tex]

The final simplified expression: 30 + 20 = 50 the Simplified form of the expression 18 - 9 × (-4) ÷ 3 + 10 × 2 is 50.

The expression 18 - 9 × (-4) ÷ 3 + 10 × 2, we follow the order of operations (also known as PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) to perform the operations in the correct order.

First, we simplify the multiplication and division from left to right:

9 × (-4) ÷ 3 = -36 ÷ 3 = -12

Now we have the expression: 18 - (-12) + 10 × 2

Next, we perform the subtraction and addition from left to right:

18 - (-12) = 18 + 12 = 30

Now we have the expression: 30 + 10 × 2

Finally, we perform the multiplication:

10 × 2 = 20

Now we have the final simplified expression: 30 + 20 = 50 the simplified form of the expression 18 - 9 × (-4) ÷ 3 + 10 × 2 is 50.

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Answer: 19:30 is the current time as per the 24-hour time format

Step-by-step explanation: We know that a day has 24 hours. The time can be shown in two different formats- the 12-hour format and the 24-hour format. 12 hour format ranges only from 1-12 on the hour while 24-hour format varies from 1-24 representing the hour.

      The 24 hour time format is quite simple- marks one number each for one hour. If the Reading says 19:30, it simply means hour 19 of that day. 12-hour time format is different since it makes use of A.M. (Ante Meridiem) and P.M. (Post Meridiem).

Answer:

Rate of slower train: 110 km/h

Rate of faster train: 122 km/h

Step-by-step explanation:

The explanation is attached below.

If she decides to trade her in her car 8 years from now then the car will be worth of $8,782.52.

To estimate the future value of Tara's car 8 years from now, we can consider the average depreciation rate of vehicles and assume it applies to her car.

On average, cars tend to depreciate around 15-20% per year.

Let's assume a conservative depreciation rate of 15% per year for Tara's car. We can calculate the future value using the following formula:

Future Value = Current Value× (1 - Depreciation Rate)^Number of Years

Suppose the current value of Tara's car is $20,000.

Plugging in the values, we get:

Future Value = $20,000(1 - 0.15)⁸

Future Value = $20,000(0.85)⁸

Calculating this, we find:

Future Value = $8,782.52

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The linear combination of the standard unit vectors i and j for the given initial and terminal points is 9i + 20j.

To find the linear combination of the standard unit vectors i and j, we need to determine the components of the vector that connects the initial point to the terminal point.

Given:

Initial Point: (0, -8)

Terminal Point: (9, 12)

To find the linear combination, we subtract the coordinates of the initial point from the coordinates of the terminal point:

So, Terminal Point - Initial Point

= (9, 12) - (0, -8)

= (9 - 0, 12 - (-8))

= (9, 20)

Therefore, the linear combination of the standard unit vectors i and j for the given initial and terminal points is 9i + 20j.

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Answer:

≈0.71441

Step-by-step explanation:

1. to calculate the area of the given circle;

2. to calculate the area of the rectangle ABCD;

3. to divide the area of the circle by the area of the rectangle ABCD

and to calculate the rest part.

All the details are in the attachment.

Answer: 5.4

Step-by-step explanation:

First, start with adding the two given sides, then take that sum and subtract it from the perimeter, then after that, divide by two

1 + 3.8= 4.8  

15.6 - 4.8=10.8

10.8 / 2 = 5.4

Answer:

[tex]\huge\boxed{\sf x = 130\°}[/tex]

Step-by-step explanation:

So,

90 + 90 + 50 + x = 360

230 + x = 360

x = 360 - 230

[tex]\rule[225]{225}{2}[/tex]

The volume of the given triangular pyramid is 59.2 feet³.

Given figure is that of a triangular pyramid.

We have to find the volume of the pyramid.

Volume of a pyramid = 1/3 × base area × height

Here base is triangular.

Base area = 1/2 × 12 × 3.7

                  = 22.2 feet²

Height of the pyramid = 8 feet

Volume = 1/3 × 22.2 × 8

             = 59.2 feet³

Hence the volume is 59.2 feet³.

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Answer:

The first one is g(x)=1/4x-7

Step-by-step explanation:

Answer:

156.76 days (approx.)

Step-by-step explanation:

To calculate the Cash Cycle, we need to consider the time it takes for a company to convert its investment in inventory and receivables back into cash. The formula for Cash Cycle is as follows:

Cash Cycle = Inventory Conversion Period + Receivables Collection Period - Payables Deferral Period

Now, let's calculate each component of the Cash Cycle using the given information.

1. Inventory Conversion Period:

Inventory Conversion Period measures the average number of days it takes to convert raw materials into finished goods.

Average Inventory = (Opening Raw Material + Closing Raw Material) / 2

= (4,00,000 + 5,00,000) / 2

= 4,50,000

Manufacturing Costs per day = Manufacturing Costs / 360 days

= 10,45,000 / 360

= 2,902.77 (approx.)

Inventory Conversion Period = Average Inventory / Manufacturing Costs per day

= 4,50,000 / 2,902.77

≈ 155 days

2. Receivables Collection Period:

Receivables Collection Period measures the average number of days it takes to collect payments from customers.

Average Receivables = (Opening Debtors + Closing Debtors) / 2

= (2,50,000 + 3,15,000) / 2

= 2,82,500

Sales per day = Total Sales / 360 days

= 4,20,00,500 / 360

= 1,16,666.67 (approx.)

Receivables Collection Period = Average Receivables / Sales per day

= 2,82,500 / 1,16,666.67

≈ 2.42 days

3. Payables Deferral Period:

Payables Deferral Period measures the average number of days the company takes to pay its suppliers.

Average Payables = (Opening Creditors + Closing Creditors) / 2

= (5,60,000 + 6,25,000) / 2

= 5,92,500

Purchases per day = Total Purchases / 360 days

= 3,23,00,000 / 360

= 8,97,222.22 (approx.)

Payables Deferral Period = Average Payables / Purchases per day

= 5,92,500 / 8,97,222.22

≈ 0.66 days

Now, we can calculate the Cash Cycle using the formula mentioned earlier:

Cash Cycle = Inventory Conversion Period + Receivables Collection Period - Payables Deferral Period

= 155 days + 2.42 days - 0.66 days

≈ 156.76 days (approx.)

Therefore, the Cash Cycle is approximately 156.76 days based on the given information.

The solution is: The arc length SR is 52.12ft.

We have,

Arc length is the distance between two points along a section of a curve. An arc is a cut out section of a circumference of a circle.

The arc angle = sector angle in the diagram

The length of an arc is expressed as;

l = tetha/360 × 2πr

where r is the radius and tetha is the angle between the two radii.

l = 332/360 × 2 × 9 × 3.14

l = 1042.48 × 18/360

l = 18764.64/360

l = 52.12( nearest hundredth)

therefore the length of the arc is 52.12 ft

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The 19  tykes  given away by the Shelter, that have room for only 4  tykes  per family.        

The number of different canine families that could be created from the 19  tykes  given away by the  sanctum, we need to calculate the number of combinations. room for only 4  tykes , we need to choose 4  tykes  from the aggregate of 19  tykes . The order of the  tykes  in the family doesn't count, as long as we choose different  tykes  for each family.  The number of combinations can be calculated using the formula for combinations  C( n, r) =  n!/( r!( n- r)!)  Where C( n, r) represents the number of combinations of choosing r  particulars from a set of n  particulars.  In this case, we've n =  19( total number of  tykes ) and r =  4( number of  tykes  per family).  Plugging these values into the formula, we get  C( 19, 4) =  19!/( 4!( 19- 4)!)  Calculating the factorial values  19! =  19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 =  ! =  4 × 3 × 2 × 1 =  24  15! =  15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 =   Substituting these values into the formula  C( 19, 4) = /( 24 ×)  ≈ 91,390  The 19  tykes  given away by the  sanctum, considering that you have room for only 4  tykes  per family.

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Answer:

The statement that is NOT always true about matrices A, B, and C is:

C. If A is singular, then its transpose is also singular.

Step-by-step explanation:

A matrix A is singular if and only if its determinant is zero. However, the transpose of a matrix does not necessarily have the same determinant as the original matrix. So, it is possible for a matrix A to be singular while its transpose is non-singular. Therefore, statement C is not always true.

The correct statement that F: "I agree. The ratios of consecutive x-values are constant, and the y-values are increasing at a constant rate."

To determine whether the function shown in the table is exponential, we need to analyze the relationship between the x-values and y-values.

The table shows x-values that are increasing by a power of 2 (1, 2, 4, 8, 16, 32, 64) and y-values that are increasing by a constant rate of 1 (0, 1, 2, 3, 4, 5, 6).

The constant ratio between consecutive x-values indicates exponential growth or decay.

In this case, the function is growing exponentially because the y-values are increasing at a constant rate.

Based on this information, we can conclude that the function is exponential.

Therefore, we agree with statement F: "I agree. The ratios of consecutive x-values are constant, and the y-values are increasing at a constant rate."

The other statements are incorrect because they do not accurately describe the relationship between the x-values and y-values in an exponential function.

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The scale factor of the perimeters from figure A to figure B is 1.5. Scale factor is the ratio of any two corresponding lengths in two similar figures.

Here, the two figures are similar, that is why we can find the scale factor by dividing corresponding sides of one figure by the corresponding sides of another figure. We will find the scale factor for the perimeter of figures A and B below:Perimeter of figure A = 12 + 10 + 18 = 40 unitsPerimeter of figure B = 15 + 15 + 15 = 45 unitsTo find the scale factor of the perimeters, we divide the perimeter of figure B by the perimeter of figure

A:Scale factor of the perimeters = (Perimeter of figure B)/(Perimeter of figure A) = 45/40 = 1.125To simplify any fractional answer, we have to convert it to the lowest terms, which is 9/8. The decimal answer 1.125, when rounded to the nearest tenth is 1.1. Therefore, the scale factor of the perimeters from figure A to figure B is 1.5.

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