There are 50 students in a class. If 14% are absent on a particular day, Find the number of students in the class on that day.

Answer:

a) C) The system has no solutions only when h=3 and k is any real number.

b) D) The system has a unique solution when \(h=(-\infty,3)U(3,\infty)\) and k is any real number.

c) The system has may solutions when h=3 and k=15

Step-by-step explanation:

a) In order to determine when the system will have no solution, we can start by solving the equation by substitution. We can solve the first equation for x1:

\(x_{1}+hx_{2}=3\)

so

\(x_{1}=3-hx_{2}\)

Next we can substitute this into the second equation so we get:

\(5(3-hx_{2})+15x_{2}=k\)

We distribute the 5 into the first parenthesis so we get:

\(15-5hx_{2}+15x_{2}=k\)

and group like terms:

\(-5hx_{2}+15x_{2}=k-15\)

we factor x2 so we get:

\(x_{2}(-5h+15)=k-15\)

and solve for x2:

\(x_{2}=\frac{k-15}{-5h+15}\)

this final answer is important because it tells us what value the system of equations is not valid for. That answer will not ve vallid if the denominator is zero, so we can set the denominator equal to zero and solve for h, so we get:

\(-5h+15= 0\)

and solve for h:

\(-5h= -15\)

\(h=\frac{-15}{-5}\)

\(h= 3\)

so it doesn't really matter what value k gets since all that matters is that the denominator of the answer isn't zero.

b)

For part b we need to know when the system of equations will have infinitely many answers. Generally, this will happen when both equations are basically the same, so we need to make sure to simplify the second equation so it looks like the first equation, compare them and determine the respective coefficients.

So we take the second equation and factor it:

\(5x_{1}+15x_{2}=k\)

we start by factoring a 5 from the left side of the equation so we get:

\(5(x_{1}+3x_{2})=k\)

Next, we divide both sides of the equation into 5 so we get:

\(x_{1}+3x_{2}=\frac{k}{5}\)

we now compare it to the first equation:

\(x_{1}+hx_{2}=3\)

\(x_{1}+3x_{2}=\frac{k}{5}\)

In this case, every coefficient of the two equations must be the same for us to get infinitely many answers, so we can see that h=3 and \(\frac{k}{5}=3\)

when taking the second condition and solving for k we get that:

\(k=3(5)\)

so

k=15

Anything else than the specific combination h=3 and k=15 will give us unique solutions, so for b, the answer is:

D) The system has a unique solution when and k is any real number.

c)

We have already solved part c on the previous part of the problem, so the answer is:

The system has many solutions when h=3 and k=15

Answer: The Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.

Step-by-step explanation:

Answer:

\(\frac{57}{10}\)

Step-by-step explanation:

W=\(6\frac{1}{2} -\frac{4}{5}\)=\(\frac{13}{2} -\frac{4}{5}=\frac{65}{10} -\frac{8}{10} =\frac{57}{10}\)

Answer:

  18 cubic inches

Step-by-step explanation:

The formulas for the volumes of a cone and a cylinder can be used to answer this question.

The volume of a cone is given by ...

  V = 1/3πr²h . . . . . volume of cone with radius r and height h

The volume of a cylinder is given by ...

  V = πr²h . . . . . volume of a cylinder with radius r and height h

Comparing the formulas, we see that the volume of a cone is 1/3 the volume of a cylinder with the same radius and height.

  (cone volume) = 1/3(cylinder volume)

Multiplying this equation by 3 gives ...

  3×(cone volume) = (cylinder volume)

Using the given value for cone volume, we have ...

  cylinder volume = 3×(6 in³) = 18 in³

The volume of the cylinder is 18 cubic inches.

Answer:

184.3448276

Step-by-step explanation:

5346/29

184.3448276

Answer:

594

Step-by-step explanation:

Answer:

244

Step-by-step explanation:

14 x 12 = 244

14 lb 224 oz

hope it helped i just looked it up and this is what i got

Answer:

the numbers are 4 and 7

Step-by-step explanation:

"twice a number added to another number is 15" --- 4(2) + 7 = 15

"the sum of the two numbers is 11" --- 4 + 7 = 11

Answer:

a.

Step-by-step explanation:

The p-value is a measurement of the likelihood that a difference observed is due to a random chance or a sampling error. In an alternative way, the p-value of a study represents the probability or area under distribution for obtaining more radical outcomes whenever the null hypothesis is true.

Any observable change is deemed to be addressed by sampling variability if the P-value is greater than the selected alpha level. A statistical test will nearly always show a substantial difference with a suitably big sample unless there is no impact at all when the effect size is exactly zero.

As a result, simply reporting the P-value alone for a study is insufficient to fully validate the results and findings of scientific publications.

Answer:

The answer for the question is 3/10

Answer:

\(y - 4 = - 3(x - 2)\)

Answer:

11 2/3 or 11.6667

Step-by-step explanation:

Hope this helps and have a great day.

Answer:

im pretty sure its c

Step-by-step explanation:

Answer:

181

Step-by-step explanation:

7× (82 - 60) + 3³

or. 7 × 22 + 27

or 154 + 27

or. 181

9514 1404 393

Answer:

Step-by-step explanation:

The inverse variation described can be either of ...

  c = k/d

or

  d = k/c

Either way, the equation can also be written as ...

  cd = k

For the given values of c and d, the value of k is ...

  (5)(5/3) = k = 25/3

So, the model can be written as ...

  cd = 25/3

or

  d = (25/3)/c

__

For c=10, the value of d is ...

  d = (25/3)/10 = 25/30

  d = 5/6

Answer: 18

Step-by-step explanation:

Multiply number of each item possible

3*2*3=18

Answer: 166.72 \(ft^{2}\)

Step-by-step explanation: math

Step-by-step explanation:

All you have to do here is use the surface area, or SA, equation.

Sa=2lw+2lh+2hw
sa=2(8.5)(3.2)+2(8.5)(4.8)+2(4.8)(3.2)

Sa=54.4+81.6+30.72

Sa=166.72

Hope this helped!

The " Eight  further than the Quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.

The equation 8( x/ 7) =  3 represents the  judgment " Eight  further than the Quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.    

" Eight  further than" implies addition, so we've 8 " The quotient of a number and 7" means dividing a number by 7, so we've x/ 7 " is equal to" means that the expression on the left side is equal to the expression on the right side, so we've =  " 3" is the value to which the expression on the left side is equal, so we've 3  Putting it all together the  judgment " Eight  further than the quotient of a number and 7 is equal to 3" can be  restated into the equation ( x/ 7) =  3  

In this equation, x represents the number we're trying to find. To  break for x, we can manipulate the equation using algebraic operations to  insulate x on one side of the equation.  By abating 8 from both sides of the equation, we get ( x/ 7)- 8 =  3- 8  Simplifying, we have  x/ 7 = -5

To  insulate x, we can multiply both sides of the equation by 7  *( x/ 7) = -5 * 7  This gives us  x = -35  thus, the equation 8( x/ 7) =  3 represents the  judgment " Eight  further than the quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.

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Answer:

3780 different words

Step-by-step explanation:

The number of possible words that can be formed by a word with n letters is given by n! (factorial of n), but when we have repeated letters, we need to divide the result by the factorial of each number of repeated letters.

In this case, we have 9 letters, but we have 4 times A, 2 times B and 2 times C, so the formula to calculate the number of different words is:

\(number = {9!}/(4!2!2!)\)

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

\(number = 3780\ words\)

So we can form 3780 different words.

Answer:

homogeneous Add to list Share. If a group of things are homogeneous, they're all the same or similar, like a room full of identically dressed Elvis impersonators.

Step-by-step explanation:

The height of the cylinder with radius of 7 yards and given volume of 2,923.34 cubic yards is calculated as; h = 19 yards

A cylinder is defined as a 3D solid shape that consists of two identical and parallel bases linked by a curved surface.

Now, the formula to find the volume of a cylinder is;

V = πr²h

where;

r is radius

h is height

V is volume

The parameters are;

Radius; r = 7 yards

Volume; V = 2923.34 cubic yards

Thus;

2923.34 = π * 7² * h

h = 2923.34/(49π)

h = 19 yards

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Answer:

16.41 i think

Answer:

6/25

Step-by-step explanation:

its a probability  out of all the odd numbers such as 1,3,5,7,9,11,13,15,17,19,21,23,25

Alaska occupies 17.22% of the surface area of the United States. Rounding to the nearest whole number, we get 17%. Hence, the answer is:17%

We are given that the surface area of the United States is 3.797 million square miles and the state of Alaska occupies 655,400 square miles. We need to determine what percentage of the surface area of the United States is occupied by Alaska using ratios.To find the percentage, we need to first find the ratio of Alaska's surface area to the surface area of the United States. We can do this by dividing the surface area of Alaska by the surface area of the United States. That is,655,400 / 3,797,000 = 0.1722We can express this ratio as a percentage by multiplying by 100. That is,0.1722 × 100 = 17.22%

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Answer:

They can make 30 Bags total.

Step-by-step explanation:

Jane has $17. There are 12 pencils in each pack for $1.60.

Jane can bay 10 packs of 12 pencils for $16.9 or else she will go over the amount of money she has.

1.69 x 10 = 16.9

Eric has $19. There are 150 cards in one pack for $2.99.

Eric can bay 6 packs of 150 cards for $17.94 or he ill go over the amount of money he has.

2.99 x 6 = 17.94

Eric.

150^6 = 900

900/30 = 30

Jane.

12^10 = 120

120/2 = 60

60/2 = 30

Together.

30 cards can go into 30 bags, and 2 pencils can go into 30 bags

Answer:

50

Step-by-step explanation:

The value of each digit in a number is known as the place value. One of the numbers that can have 5 as 1/10 of the value of 5 in 522.12 is 50.

The value of each digit in a number is known as the place value. The 5 in 350, for example, represents 5 tens, or 50, whereas the 5 in 5,006 represents 5 thousand, or 5,000. It is critical that children that while a digit can be the same, its value is determined by its position in the number.

Identification of the place value of a digit in a number:

Let the unknown number be represented by x.

Given that the value of 5 in the number x is 1/10 of the value of 5 in 522.12. Therefore, we can write,

x = (1/10) of 500

x = (1/10) × 500

x = 50

Hence, one of the numbers that can have 5 as 1/10 of the value of 5 in 522.12 is 50.

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The different group of 2 players that the coach can pick is 45 groups.

The selection of groups of 2 player can be done using the method of combination.

The different group of 2 players that the coach can pick from the 10 players is calculated as follows;

n = 10C2

\(n = \frac{10!}{(10-2)! 2!} = \frac{10 \times 9\times 8!}{8! \times 2} = 45\)

Thus, the different group of 2 players that the coach can pick is 45 groups.

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Answer:

45

Step-by-step explanation:

I hope this helps!

Answer:

The definition of a prime number is a number with only two factors - 1 and itself; 5 is an example. Between 20 and 50 you have 23, 29, 31, 37, 41, 43, and 47. Notice they are all odd numbers.

Step-by-step explanation:

The numbers between 20 and 50 have two factors are 23, 29, 31, 37, 41, 43, 47.

Prime numbers are very special type of numbers they have only two factors 1 and the prime number it self.The smallest and only even prime number is 2.There are infinite no. of prime numbers.

According to the given question we have to find numbers between 20 and 50 which have just two factors.

We know prime numbers have two factors which are 1 and the prime number it self.

∴ The numbers are 23, 29, 31, 37, 41, 43, 47.

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Answer:

C

Step-by-step explanation:

Edge

The required figure has been attached below could be the result of dilating a given triangle with a scale factor greater than 1. The correct answer would be an option (C).

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

The triangle has points (0, 0), (0, 3), and (6, 0) which are given in the question.

As per option (C), we have

On a coordinate plane, a triangle has points (0, 0), (0, 5), and (10, 0).

This result of dilating a given triangle with a scale factor greater than 1.

The required figure has been attached below which represents the dilation.

The correct answer would be an option (C).

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Answer:

Cayley earned per day: 4 x 5 = 20

: Her earning per week-  3 x 20 = 60

: Her earning for 8 weeks- 8 x 60 = 480

Cayley earns $480 per week.