The scale on a map shows that 2 in = 50 km. If there are 5 inches between two cities, what is the actual distance between them?

Answer:

side 1^2 + side 2 ^2 = hypotenuse ^ 2

18^2 + 20^2 = hypotenuse^2

324 + 400 = 724

hypotenuse^2 = 724

hypotenuse = 26.9072480941474

hypotenuse = 26.9

Step-by-step explanation:

Answer:

34000

Step-by-step explanation:

New Ratio = 40/57

Gap between numerator & denominator = 17

Original Ratio = 2/3

Gap between numerator & denominator = 1

=> Original Ratio can be restated as 34/51 to make gap of both ratios same.

Difference between two numerators OR denominators = 40 - 34 = 6 or 57 - 51 = 6

If gap is 6, sumit’s original salary = 51

If gap = 4000, sumit’s original salary is :

51/6 x 4000 = 34000

The salary of Amma is given as ¢11724.10.

A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

The ratio of the salaries of  Kofi and Ama is given as 3 : 5.

After adding 4000 to each ratio the new ratio becomes as 40 : 57.

Suppose the present salaries of  Kofi and Ama be 3x and 5x respectively.

Then, as per the question following equation can be written as,

(3x + 4000)/(5x + 4000) = 40/57

=> 57(3x + 4000) = 40(5x + 4000)

=> 200x - 171x = 68000

=> 29x = 68000

=> x = 68000/29

       = 2344.82

The Amma's salary is given by,

5x = 5 × 2344.82

    = 11724.10

Hence, Amma's present salary is given as ¢11724.10.

To know more about ratio and proportion click on,

brainly.com/question/14279414

#SPJ2

Given the system of equations, y = x + 7 and y = 11 - x.

Use substitute method to find the value of x and y.

So, y = 2+7 = 9.

Thus, the solution of the system of equation is (2,9).

So, option (2) is correct.

The solution set for the inequality is x < 2. Among the given options, the value that is included in the solution set is 0.

To determine which value is included in the solution set for the inequality statement -3(x-4) > 6(x-1), we need to solve the inequality for x.

Starting with the given inequality:

-3(x - 4) > 6(x - 1)

First, distribute -3 and 6 to the terms inside the parentheses:

-3x + 12 > 6x - 6

Next, combine like terms by subtracting 6x from both sides and adding 6 to both sides:

-3x - 6x > -6 - 12

-9x > -18

To isolate x, divide both sides of the inequality by -9. Remember that when dividing by a negative number, we need to reverse the inequality sign:

x < (-18) / (-9)

x < 2

Therefore, the solution set for the inequality is x < 2. Among the given options, the value that is included in the solution set is 0.

for such more question on inequality

https://brainly.com/question/17448505

#SPJ8

In a hypothetical situation, an incorrect dosage calculation due to an error in metric system to Imperial System conversion could lead to potential harm to the patient. To avoid such errors, it is crucial to ensure accurate and precise conversions between the metric and Imperial systems. As a nurse, I will double-check my calculations, use reliable conversion charts or tools, and consult with colleagues or supervisors when in doubt. Additionally, ongoing education and training on dosage calculations and metric system conversions will be important to maintain proficiency and prevent errors in the future.

~~~Harsha~~~

Answer:

B.

Mean: 16.1

Median: 16

Mode: 16

Step-by-step explanation:

First, order the numbers in the data set from least to greatest:

\(14 , 14 , 14 , 14 , 15 , 15 , 15 , 15 , 15 , 16 , 16 , 16 , 16 , 16 , 16 , 17 , 17 , 17 , 19 , 19 , 19 , 19\)

First, find the mean. The mean of a data set can be found by adding all the numbers together and dividing by the amount of numbers in the set:

\(\frac{14 + 14 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 16 + 16 + 16 + 16 + 17 + 17 + 17 + 19 + 19 + 19 + 19}{22} = \frac{354}{22}\)

Next, simplify by dividing:

\(\frac{354}{22} = \frac{177}{11} = 16 \frac{1}{11} or ~16.1\)

Mean: 16.1

Next, find the median. The median is the number(s) directly in the middle. If there is a even amount of number in the data set, find the mean of the two median numbers:

Median: 16 , 16

Median = \(\frac{16 + 16}{2} = \frac{32}{2} = 16\)

Median = 16

Next, find the mode. The median is the number that shows up the most. In this case, it is 16, which appears 6 times, 1 more time then the next number that appears the most 15, which appears 5 times.

Mode: 16

~

If you are asked about range, range would be the greatest digit value subtracted by the least digit value. In this case, it would be 14 & 19:

19 - 14 = 5

Range: 5

~

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

to know more about unitary method

https://brainly.com/question/28276953

Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

94 cm

Step-by-step explanation:

The formula for finding the circumference of a circle is;

Circumference = 2πr

where π = \(\frac{22}{7}\) or 3.14 and

r = radius

Here radius is 15 cm so;

Circumference = \(2 * \frac{22}{7} * 15\)

                         = \(\frac{660}{7}\)cm

                         = 94.28cm

                         = 94 cm (  rounded to the nearest centimetre )

Solution:

Let (1,8)=(x1,y1)

(-1,-2)=(x2,y2)

D=?

Now,

D=

\( \sqrt{(x2 - x1) ^{2} + (y2 - y1)} ^{2} \)

or, D=

\( \sqrt{( -1 - 1) ^{2} + ( - 2 - 8) ^{2} } \)

\( \sqrt{( -2) ^{2} + ( - 10) ^{2} } \)

\( \sqrt{4 + 100 } \)

\( \sqrt{104} \)

2\( \sqrt{26} \)

Answer:

c)

Step-by-step explanation:

my guess is if she needs 1.04 tablets a day, and 1 tablet is closer to that than any other option listed

Answer:

1) scale factor is 3/4

3/4 × -4 = -3, 3/4 × 8 = 6

2) Yes, scale factor is 2.

AD = 3, DC = 4, A'D' = 6, D'C' = 8

A'D'/AD = 2, D'C'/DC = 2

The proportion is

Caramel to hot pepper corn

So:

Caramel/ hot pepper corn

Simply divide each value:

5 /8 = 0.625

10/16=0.625

15/24=0.625

The constant of proportionality is 0.625

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

To solve the exercise using Polya's four-step problem-solving strategy, we will apply the procedures presented in the lesson.

(a) For the series 1+2+3+4+...+392:

Using the arithmetic series formula Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term, we can substitute the values: Sn = (392/2)(1 + 392) = 196(393) = 77,028.

(b) For the series 1+2+3+4...x:

To find the sum of this series, we need to know the number of terms (n) based on the value of x. Since the series follows a consecutive pattern, the number of terms will be equal to x itself. Thus, the sum of the series would be Sn = (x/2)(1 + x).

(c) For the series 546 + 547 + 548 + 549:

Using the arithmetic series formula Sn = (n/2)(a + l), we can determine the number of terms (n) by subtracting 546 from 549 and then adding 1: n = 549 - 546 + 1 = 4. Substituting the values into the formula: Sn = (4/2)(546 + 549) = 2(1095) = 2,190.

The final answer for each part is:

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

for such more question on series

https://brainly.com/question/29062598

#SPJ8

Answer:

\(2p=348 cm\: S=6726 cm^{2}\)

Step-by-step explanation:

Ciao, come stai?

1) Per prima cosa, dobbiamo trovare la misura della base più grande. Scomponendo la figura possiamo visualizzare un triangolo e un quadrato. Ci sono somiglianze con gli angoli. Quindi è un triangolo rettangolo. Applichiamo il teorema di Pitagora:

\(a^2=b^2+c^2\\95^2=b^2+76^2\\57=b\)

2) Perimetro:

\(2p=60+57+76+60+95\\2p=348 cm\)

3) L' area

\(\frac{(B+b)h}{2} =\frac{(117+60)76}{2} =6726 \:cm^{2}\)

Answer:

A ≈ 102.56

Step-by-step explanation:

The quantity decays continuously at a rate of 0.75% per day, which means that the amount of the quantity remaining after a certain number of days can be calculated using the formula:

A = A0 * e^(-rt)

where:

A0 is the initial value of the quantity

r is the decay rate (expressed as a decimal)

t is the number of days

e is the mathematical constant e (approximately equal to 2.71828)

A is the value of the quantity after t days

Substituting the given values, we get:

A = 170 * e^(-0.0075 * 56)

Using a calculator, we get:

A ≈ 102.56

Therefore, the value of the quantity after 56 days, rounded to the nearest hundredth, is approximately 102.56.

Answer:

D. (x - 2)(x + 15)

Explanation:

To factorize x²+13x-30, we need to find two numbers that add to 13 and multiply to -30.

These numbers are -2 and 15 because

-2 + 15 = 13

-2(15) = -30

Therefore, the factorization is

D. (x - 2)(x + 15)

The triangle gotten from this pattern is an isosceles obtuse triangle.

A pattern is a repeated arrangement of numbers, shapes, colours and other items.

Using the rule, we have two obtuse then one right triangle. Hence the fifth would be an obtuse triangle.

For the second, we have isosceles and scalene changing, hence the fifth would be isosceles.

The triangle gotten from this pattern is an isosceles obtuse triangle.

Find out more on pattern at: https://brainly.com/question/17386984

Answer:

First, we need to calculate the total amount of the pension for the first offer:

$58,000 x 0.016 x 20 = $18,560 per year

Then, we can calculate the monthly pension payment:

$18,560 / 12 = $1,546.67 per month

For the second offer, we need to calculate the annual pension amount:

$64,900 x 0.013 x 20 = $16,828 per year

And then the monthly pension payment:

$16,828 / 12 = $1,402.33 per month

Finally, we can calculate the difference in monthly pension payments:

$1,546.67 - $1,402.33 = $144.34

Therefore, the difference in monthly pension payments is $144.34.

Set up the equation to determine the arc length. Arc length is equal to 2 pi times the arc's radius times (arc's central angle/360), where arc's central angle is expressed in degrees.

To learn more about equation, refer to:

https://brainly.com/question/2972832

#SPJ1

Answer:

560 inches cubed

Step-by-step explanation:

The formula to find the volume is length times width times height, so in this case it would be 14*10 which is 140 and 140*4 is 560.

So your answer is 560 inches cubed

Answer:

-4 , -1 , -2 , 0 , +1 , +3

Step-by-step explanation:

Answer:

the integers -4,-2,-1,0, +1, +3

Step-by-step explanation:

because when you put them in order  you find which pairs are located between -5 and +5

-8,-4,-2,-1,0,+3,+8,+9

which tells you that

-4,-2,-1,0, +1, +3 are between -5 and +5

An equation for the total cars and trucks for dealership A is: x + y = 164.

An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.

The number of cars that dealership A sold is: 98 cars.

The number of trucks that dealership B sold is: 66 trucks.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:

Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;

x + y = 164.

Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;

2x + 0.5y = 229.

By solving the systems of linear equations simultaneously, we have:

2x + 0.5(164 - x) = 229

1.5x + 82 = 229

x = 98 cars.

For the y-value, we have;

2(98) + 0.5y = 229

0.5y = 229 - 196

y = 33/0.5

y = 66 trucks.

Read more on solution and equation here: brainly.com/question/25858757

#SPJ1

Answer:

23

Step-by-step explanation:

The Intel pays $7,760 to Bally Manufacturing on August 14.

The first step in calculating what Intel Corporation pays Bally on August 14 is to determine the net price of the machinery after the trade discount and the return of $100 due to defects.

The trade discount of 40% is calculated as follows:

Discount = List price × Discount rate

Discount = $13,100 × 0.40 = $5,240

So the net price of the machinery after the trade discount is:

Net price = List price - Discount

Net price = $13,100 - $5,240 = $7,860

After Intel returns $100 of machinery, the cost of the machinery is further reduced to:

Net price after return = Net price - Return

Net price after return = $7,860 - $100 = $7,760

Since the payment terms are 3/10 EOM (end of month), Intel receives a discount of 3% if payment is made within 10 days. The 10-day period begins on August 1 and ends on August 10 (the payment due date). Since Intel pays the bill on August 14, payment is late and the 3% discount does not apply.

For such more questions on pays

https://brainly.com/question/25793394

#SPJ8

The total number of college students is 204,700,000.

Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

Here, Percentage of enrolled student for part time = 23%

         Total enrolled students = 8.9 millions

Number of part time student = 23% x 8.9 million

                                              \(= 0.23 \times 8900000\)

                                             \(=204,700,000\)

Thus, the total number of college students is 204,700,000.

Learn more about Percentage from:

brainly.com/question/14979505

Answer:

table d

Step-by-step explanation:

functions can not have the same input twice

Answer:

A B and C repreasent functions

Step-by-step explanation:

The terminal point on the unit circle determined by 5π/6 radians is (-√3/2, 1/2).

To find the terminal point on the unit circle determined by an angle of 5π/6 radians, we need to consider the coordinates of the point (x, y) on the unit circle that corresponds to this angle.

The unit circle has a radius of 1 unit, and the terminal point can be found by using the trigonometric functions cosine and sine.

For the angle 5π/6, the cosine function gives us the x-coordinate, and the sine function gives us the y-coordinate.

Using the exact values of cosine and sine for 5π/6, we have:

cos(5π/6) = -√3/2

sin(5π/6) = 1/2

Therefore, the terminal point on the unit circle determined by 5π/6 radians is (-√3/2, 1/2).

For more such answers on trigonometric functions

https://brainly.com/question/25618616

#SPJ8

Volume

Volume