if two positive integers p & q are written as p = a^2b^3 and q=a^4b; a,b are prime numbers, then HCF(p,q) is

Answer:

2 feet 3 inches

Step-by-step explanation:

So we know there are 12 inches in one foot. so 27/3= 2 remainder 3. So the answer is 2 feet 3 inches

The coordinates of I ( x, y) = ( 6, 11 )

What is coordinate in math?

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).

The coordinates of the  G = (2,7)

The coordinates of the  H = (11,16)

Point I is on GH and divides it such that GI:HI is 4:5.

the coordinates of I ( x, y)

                      \(x = \frac{m_{1}x_{2} + m_{2} x_{1} }{m_{1} + m_{2} }\)

                      \(x = \frac{4 * 11 + 5 * 2}{ 4 + 5}\)

                   x = 6

\(y = \frac{m_{1}y_{2}+ m_{2}y_{1} }{m_{1} + m_{2} }\)

\(y = \frac{4 * 16 + 5 * 7}{9}\)

y = 11

the coordinates of I ( x, y) = ( 6, 11 )

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Answer:

She can decompose it into two rectangles or a triangle

Step-by-step explanation:

I just did this on EDMENTUM its right!

Answer:

1 13/ 24

Step-by-step explanation:

2-1=1

5/8 - 1/12=26/48 =13/24

Thanh's cost per month (four weeks) will be $300.00.The given fixed rate for Thanh is $49.00 per week. Thanh also pays $14.00 per week for the optional insurance and $12.00 weekly on gas.

To find Thanh's cost per month (four weeks), we need to multiply his weekly cost by 4.We can use the formula below to calculate Thanh's monthly cost.

Total weekly cost = Fixed rate + Insurance cost + Gas cost

Total weekly cost = $49.00 + $14.00 + $12.00

Total weekly cost = $75.00

The cost for Thanh per month (four weeks) = Total weekly cost × 4

Cost for Thanh per month (four weeks) = $75.00 × 4

Cost for Thanh per month (four weeks) = $300.00

Therefore, Thanh's cost per month (four weeks) will be $300.00.

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Hey there! I'm happy to help!

Let's call the hamburgers h and the cheeseburgers c.

h+c=810

c=h+60

Let's plug this value of c into the first equation to solve for h.

h+h+60=810

2h+60=810

Subtract 60 from both sides.

2h=750

Divide both sides by 2.

h=375

Therefore, 375 hamburgers were sold on Wednesday.

Have a wonderful day! :D

Answer:

321.50 dollars.

Step-by-step explanation:

Dena is buying wallpaper. It costs $8.79 per meter. She needs 120 feet. How much will the wallpaper cost? Round to the nearest half dollar.

This is a tricky math problem that requires some conversions and calculations. First, we need to convert feet to meters, because Dena lives in a country that uses the metric system. According to the search results   , one foot is equal to 0.3048 meters. So, 120 feet is equal to 120 x 0.3048 = 36.576 meters.

Next, we need to multiply the length of the wallpaper by the price per meter to get the total cost. The total cost is 36.576 x 8.79 = $321.38.

Finally, we need to round the total cost to the nearest half dollar. This means we need to look at the cents part of the cost and see if it is closer to 0, 50 or 100. In this case, 38 cents is closer to 50 than to 0 or 100, so we round up the cost to $321.50.

Therefore, Dena will have to pay $321.50 for the wallpaper. That's a lot of money for some paper that will probably peel off in a few years! Maybe she should consider painting her walls instead.

Yes, the additional education costing $36,000 will pay for itself in less than 2 years based on the increased earning potential.

To determine whether the additional education costing $36,000 will pay for itself, we need to consider the time it takes to recover the investment through the increased earning potential.

The additional yearly earning potential is the difference between the post-education income ($39,746) and the pre-education income ($21,484), which is $18,262.

To calculate the payback period, we divide the cost of education ($36,000) by the annual increase in earning potential ($18,262).

Payback Period = Cost of Education / Annual Increase in Earning Potential

Payback Period = $36,000 / $18,262

The payback period is approximately 1.97 years, meaning that it would take approximately 1.97 years to recover the cost of education through the increased earning potential.

If the time required to recover the cost is less than the time in which the increased earning potential will be realized, then the additional education would be considered to have paid for itself.

In this case, since the payback period is less than 2 years and the increased earning potential will continue for subsequent years, it can be concluded that the additional education costing $36,000 will pay for itself over time.

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Answer:

26.67% to nearest hundredth.

Step-by-step explanation:

Write it as a fraction and multiply by 100>

= 120/ 449.99  * 100

= 12000/449.99

= 26.667 %.

When the unit digits are the same , we have to look at the decimal places . Since the unit digits in 5.7 and 5.89 are same , which is 5 , let us look at the decimals . As 5.89 has more decimal digits when compared with 5.7 , we say that the measurement 5.89 has more precision .

Therefore , 5.89 us has more precision .

Answer:

A. $147.67

B. $26,581.49

C.  Principal: 65.8352%

C.  Interest: 34.1647%

The values:

a) PMT = $147.67.

b) $26580.6

c) Of the total amount paid, 65.84 percentage is paid toward the principal and 34.16 percentage is paid for the interest.

The formula:

PV = PMT/i[1 - {1/(1+i)ⁿ]

PV denotes the loan sum.

PMT stands for "monthly payment," I for "interest rate" (interest rate % divided by 12), and "n" for the number of months (term of the loan in months)

Given:

Consider a student loan of $17,500 at a fixed APR of 6% for 15 years.

PV is the loan amount = 17500

PMT is the monthly payment .

i is the interest rate per month in decimal form (interest rate percentage divided by 12)

i = 0.06/12 = 0.005

n is the number of months (term of the loan in months)

n = 180 months.

The monthly payment,

PMT = PV i(1+i)ⁿ/{(1+i)ⁿ-1}

PMT = 17500(0.005)(1.005)⁴⁸/{(1.005)⁴⁸-1}

PMT = $147.67.

The total amount paid over the term of the loan,

= 147.67 x 180 = $26580.6

Of the total amount paid, 65.84 percentage is paid toward the principal and 34.16 percentage is paid for the interest.

Therefore, all the required values are given above.

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Answer:

1) 30 pounds is the weight of the bag all together

2) science book is the heaviest book

Step-by-step explanation:

bag=4 pounds

library book=2 pounds

maths book=2×4=8 pounds

science book=8×2=16 pounds

4+2+8+16=30 pounds all together

heaviest book= science book (16 pounds)

Answer:

-1.125

Step-by-step explanation:

The specific measure of the given geometric figure in the image is: C. a 165° angle.

A geometric figure can be defined as a combination of lines or points.

The geometric figure shown is a combination of two rays that forms an angle.

The specific angle measure in the geometric figure is 165°.

Therefore, the specific measure of the given geometric figure in the image is: C. a 165° angle.

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Therefore, **x < 7** is the inequality that may be utilized to find x

A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).

For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".

Let x represent how many days the client paid for pet sitting.

$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.

We are aware that the customer's purchase was under $125. Consequently, we can write:

20 + 15x < 125

Putting this disparity simply:

15x < 105

x < 7

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Step-by-step explanation:

A) A school hall has 456 seats.

If you round is as per rules, you will round it up to get 460.

Now, if the number of tickets is 460 and all tickets are sold out, what problem will you have?

B) A bridge can safely carry a weight of 15.75 tonnes.

Same as above, rounding up will make the sign with 16 tonnes, but the bridge is not designed to handle this weight!

In both cases above you would round the numbers down to be in safer place.

450 seats or 15 tonnes are better numbers.

Answer:

=15.4

Step-by-step explanation:

6^2+(3.4)-24 = 36+3.4−24

36+3.4−24

39.4−24

=15.4

The length of the rectangle is 19.25 cm when it is 2 more than three times the width of 5.75 cm.

A perimeter is a closed path that encompasses, surrounds, or outlines a two-dimensional shape or length in one dimension. A circle's or an ellipse's circumference is its perimeter. There are several applications for calculating the perimeter. The length of fence required to encircle a yard or garden is known as the calculated perimeter.  

The perimeter (circumference) of a wheel/circle describes how far it can roll in one revolution.  Similarly, the amount of string wound around a spool is proportional to the perimeter of the spool; if the length of the string were exact, it would equal the perimeter.

Given that,

Perimeter = 2(l + b) = 50cm

And also given that,

l = 2 + 3b

Substituting the value of l in perimeter we get

2((2 + 3b) + b) = 50cm

2(2 + 4b) = 50cm

4 + 8b) = 50cm

8b = 50 - 4

b = 46/8

b = 5.75

Substituting the value of b in l, we get

l = 2 + 3(5.75)

l = 19.25

Therefore, the length of the rectangle is 19.25 cm when it is 2 more than three times the width of 5.75 cm.

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Answer:

Mean = 59

Median = 56.5

Step-by-step explanation:

56 + 57 + 53 + 63 + 68 + 52 + 55 + 65 + 62 = 531

531 / 9 = 59

Mean = 59

52, 53, 55, 56, 57, 62, 63, 65, 68

Num between 56 and 57

56.5

Median = 56.5

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-Lil G

Answer:

Polygon D is similar to polygon ABCD.

Answer:

2546

Step-by-step explanation:

Q is a stochastic matrix, with dynamics related to a Markov chain, where the transition probabilities are increased by p.

A stochastic matrix is a matrix whose entries are all non-negative and whose rows sum to 1. A Markov chain is a stochastic process in which the probability of transitioning from one state to another depends only on the current state. The transition matrix P of a Markov chain on k states is a stochastic matrix. Now consider the matrix Q = (1 − p)I + pP, for 0 < p < 1. Since the identity matrix I is itself a stochastic matrix and the entries of P are all non-negative, all the entries of Q are non-negative. Furthermore, since each row of P sums to 1 and each row of I sums to 1, the sum of each row of Q is (1 − p) + p = 1, meaning that Q is a stochastic matrix. The dynamics of a Markov chain governed by the Q matrix are related to the original Markov chain, as the probability of transitioning to any other state is increased by p compared to the P matrix. Therefore, the Q matrix provides a probabilistic interpretation for the dynamics of the original Markov chain.

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Answer:

2(x + 6)

Step-by-step explanation:

If we let the number be "x", then the sum of the number and six is x + 6. To find twice the sum, we multiply this expression by 2:

2(x + 6)

Therefore, the expression that represents twice the sum of a number and six is 2(x + 6)

If the two stations have the same bit rate, they will both have to be on air for the same amount of time to broadcast 4 minutes of news, regardless of the specific bit rate

What is time in maths ?

In mathematics, time is often thought of as a dimension, similar to length, width, and height. However, time is unique in that it only moves in one direction, from the past to the future. Time can be measured in various units such as seconds, minutes, hours, days, weeks, months, and years.

The length of time a station will have to be on air to broadcast 4 minutes of news depends on the bit rate of the broadcast.

The bit rate is the amount of data transmitted per second in a digital signal. The higher the bit rate, the more data can be transmitted per second, resulting in higher audio or video quality but also a larger file size.

Assuming the two stations have different bit rates, the station with the lower bit rate will have to be on air longer to broadcast the same 4 minutes of news than the station with the higher bit rate. This is because the station with the lower bit rate can transmit less data per second, so it will take longer to transmit the same amount of information.

For example, if Station A has a bit rate of 128 kbps (kilobits per second) and Station B has a bit rate of 256 kbps, Station A will have to be on air for twice as long as Station B to transmit the same 4 minutes of news, as it can transmit only half as much data per second as Station B.

Hence, If the two stations have the same bit rate, they will both have to be on air for the same amount of time to broadcast 4 minutes of news, regardless of the specific bit rate

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Answer:

\(\huge\boxed{\sf 1}\)

Step-by-step explanation:

Given the expression:

= 9 - b

Given that b = 8

= 9 - 8

= 1

\(\rule[225]{225}{2}\)

Hope this helped!

Okay so we are asked to solve 9 - b, and we are told that b=8

Therefore this is just a matter of substitution:

9 - b

Substitute 8 for b:

9 - 8

Now just finish solving:

1

Therefore, the answer is 1

Hope this helped :)

Create a new post where you analyze two functions of maximum and minimum values are,

Maximum is at (-2.0801 , 0.203)

Minimum is at (0.0801 , -5)

Function,

\(f_{1} (x) = x^{3} +3x^{2} -\frac{1}{2} - 5\)

X              -3         -2       -1       0        1       2       3

\(f_{2} (x)\)          21        4        -1       0        1       -4      -21

\(f_{2} (x)\) = \(-x^{3} +2x\)

At maximum and minimum \(f^{1} (x)\) = 0

At \(f^{1} (x) = 3x^{2} +6x-\frac{1}{2} =0\)

Common factor,

1/2 (6\(x^{2}\) + 12x - 1) = 0

Divide both sides by the same factor

(6\(x^{2}\) + 12x - 1) = 0

The polynomial equation whose highest degree is two is called a quadratic equation. The equation is given by ax² + bx + c = 0, where a ≠ 0.

Use the quadratic formula to find the solutions.

x = [-b ± \(\sqrt{b^{2} -4ac}\) ]/2a

Substitute the values a=6, b=12, and c=−1 into the quadratic formula and solve for x,

x = [-12 ± \(\sqrt{12^{2}-4*6*(-1) }\) ] /2*6

Evaluate the exponent,

x = [-12 ± \(\sqrt{144-4*6*(-1)}\) ] /2*6

Multiply the numbers,

x = [-12 ± \(\sqrt{144+24}\) ] /2*6

Add the numbers,

x = [-12 ± \(\sqrt{168}\) ] /2*6

Evaluate the square root

x = [-12 ± \(2\sqrt{2*3*7}\) ] /2*6

Multiply the numbers

x = [-12 ± \(2\sqrt{42}\) ] /12

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

x1 = [-12 + \(2\sqrt{42}\) ] /12   and     x2 = [-12 - \(2\sqrt{42}\) ] /12

Rearrange and isolate the variable to find each solution

x1 = [-6 + \(\sqrt{42}\) ] /12     and      x2 = [-6 - \(\sqrt{42}\) ] /12

x1 = 0.0801

x2 = -2.0801

             -3        -2.0801          0         0.0801          1

\(f^{1} (x)\)        /               -                \               _               /

Therefore,

Maximum is at (-2.0801 , 0.203)

Minimum is at (0.0801 , -5)

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Answer:

Step-by-step explanation:

If the order you select them is important

nmber of ways = 9! / (9-7)!

= (9*8*7*6*5*4*3*2*1) / (2*1)

= 9*8*7*6*5*4*3

= 181,440.

If the order does not matter:

nmber of ways = 9! / ((9-7)! * 7!)

= 9*8 / 2*1

= 36.

Answer: x>0

X is greater than 0 but isn’t greater than or equal to because the circle is open.

Hope this helps :D

Answer:

Step-by-step explanation:

x>0

x is all real numbers greater than zero, in interval notation this is

x=(0,+oo)

Answer:

1 out of 6

Step-by-step explanation:

Each roll of the die is an independent event. This means that the second roll does not rely on the first roll. The probability of rolling a six is one out of six. The probability of rolling a two is also one out of six. Since the two events are independent of each other, you would take the average of the two probabilities, which since they are both one out of six, the probability of rolling a six and then a two is one out of six.