Solve the problems involving (HCF) highest common factor for each of the the following

B) A restaurant donated 540 pieces of fried chicken and 360 cups of drink for a gathering event. The restaurant has set the condition the every visitor will receive the portion of food equally. Find :

(1) Find the maximum number of visitors that can be invited to the event.

(2) Find the numbers of pieces of chicken to be received by the visitors who attended the event.

The difference in mail handled between 195 and 1965 is -5.4 x 10

The data on the pieces of mail handled by the United States Postal Service is written in scientific notation. Scientific notation is used to compress larger numbers into smaller numbers.

In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example, 1 x 10² is equivalent to 100

Difference in mail handled = mail handled in 1995 - mail handled in 1965

(1.8 x [tex]10^{11}[/tex]) - (7.2 x [tex]10^{10}[/tex])

(1.8 - 7.2)  x [tex]10^{11 - 10}[/tex]

-5.4 x 10

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Answer:

Work is incorrect

Step-by-step explanation:

I'm assuming this question is asking whether the work is correct or not? In which case the work is not correct.

The Pythagorean Theorem states: [tex]a^2+b^2=c^2[/tex] where c=hypotenuse, and "a" and "b" are the other two sides. The main thing to note here, is that the hypotenuse is the largest side of all three sides.

So the equation Arial set up: [tex]9^2+15^2=12^2[/tex] is incorrect, since the 15 would need to be on the right side. This forms the correct equation: [tex]9^2+12^2=15^2[/tex] which then simplifies to: [tex]81 + 144 =225 \implies 225=225[/tex].

Thus a right triangle can be formed using these side lengths. You can of course set up a similar equation to Ariels, where the "c" or hypotenuse is not isolated,  but you would have to rearrange the equation so that: [tex]a^2+b^2=c^2\implies b^2=c^2-a^2[/tex] but see how "a squared" is being subtracted from "c squared"? So it's a similar equation to Ariels, but not quite the same, and if she set it up like this, then she would reach the same conclussion

Answer:

Allana is 2 1/2 and her mother is 15 years old.

Step-by-step explanation:

Let Allana's age be x years then,

her mother's age is 6x.

Using the given information in ten years time we have the equation:-

6x + 10 = 2(x + 10)

6x + 10 = 2x + 20

6x - 2x = 20 - 10

4x = 10

x = 2 1/2

So 6x = 6 * 2 1/2 = 15.

The minimum number of pounds of mozzarella cheese is necessary to say that your medium pizza ranked in the top 3% of all medium pizzas in terms of cheese content.

P(z < 0.2) = 0.5793

Generally, The normal distribution, also known as the Gaussian distribution, is a kind of probability distribution that is symmetric around the mean. This means that it demonstrates that data that are closer to the mean are more likely to occur than data that are farther away from the mean. When represented graphically, the normal distribution takes the shape of a "bell curve."

In conclusion, To begin, we calculate the z score to determine the crucial value. If

[tex]z =\frac{ (x - u)}{ s}[/tex]

x = critical value = 0.5

u = mean = 0.495

Hence

[tex]z =\frac{ (x - u)}{ s}[/tex]

z= 0.2

Therefore, by making use of a table or some other kind of technology, the left-tailed area of this is

P(z < 0.2) = 0.5793

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Complete Question

A pizza shop advertises that it puts 0.5 pounds of real mozzarella cheese on its medium pizzas. In addition, it is discovered that the quantity of cheese put on the population of all medium pizzas has a Normal distribution with a mean of 0.495 and standard deviation 0.025. The probability that a randomly selected pizza has less than the advertised amount of mozzarella cheese is:

a) 0.2000

b) 0.5793

c) 0.4207

d) 0.800

the solution of the system of linear equations is:

x = 6/11

y = -4/11

Here we have the system of equations:

To solve the system, we can see that y is already isolated in both sides, then we get:

(-5/2)*x + 1 = 3x - 2

Now we can solve this for x:

(-5/2)*x + 1 = 3x - 2

2 + 1 = 3x + (5/2)*x

3 = (6/2)*x + (5/2)*x

3 = (11/2)*x

(2/11)*3 = x

6/11 = x

To get the value of y, we evaluate any of the lines in x = 6/11

y = 3*(6/11) - 2 = 18/11 - 2 = 18/11 - 22/11 = -4/11

Then the solution of the system of linear equations is:

x = 6/11

y = -4/11

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Answer:

Step-by-step explanation:

1144

Answer: [tex]\displaystyle\\\frac{x^3}{y^7}[/tex].

Step-by-step explanation:

[tex]\displaystyle\\x^3y^{-7}=\frac{x^3}{y^7} .[/tex]

Answer:

Domain: (-∞, ∞), Range: [-3, ∞)

Step-by-step explanation:

Domain is all of the possible x-values in a solution set, in this case since the solution extends infinitely horizontally it would be:

(-∞, ∞)

The range is just all of the possible y-values in a solution set, which in this set starts from -3 and proceeds on infinitely, making the range:

[-3, ∞)

Using the given data, the average percent score for the 100 students is 77[tex]\%[/tex].

Average, also known as mean, is one of the measures of central tendency and is the ratio of the sum of all observations to the total number of observations. It is very useful to summarize a probability distribution.

Let the average percent score for the 100 students be N.

As it is known that the average is the ratio of the sum of all observations to the total number of observations, therefore:

[tex]N = \dfrac{100\times7+90\times18+80\times35+70\times25+60\times10+50\times3+40\times2}{100}[/tex]

   [tex]= \dfrac{7700}{100}\\= 77[/tex]

Thus, the average percent score for the 100 students, using the given data is calculated as 77[tex]\%[/tex].

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The complete question is as follows:

Mrs. Riley recorded this information from a recent test taken by all of her students. Using the data, what was the average percent score for these 100 students?

[tex]\%[/tex] Score  Number of students

100                  7

90                   18

80                   35

70                   25

60                   10

50                   3

40                   2

Answer:

0.342

Step-by-step explanation:

round to the given amount of significant figures

Answer:

40° to the left and 3/2 units down

Step-by-step explanation:

See attached image.

The answer of your question is option (B)

Answer:   9

Step-by-step explanation:

assuming that each box is 1 square inch then, you would get 9 square inches.

0,5 go down three to get 0,2

0,2 go left three to get -3,2

-3,2 go up three to get -3,5

-3,5 go right three to get 0,5

so you end up with a 3-by-3 box

Answer:

11%

Step-by-step explanation:

Lets find the new price with the monthly installment.

5+6.50(10)=70

Now the percentage of increase.

Find difference

70-63=7

Divide by original

7/63=0.11

Multiply by 100

0.11*100=11.1

Rounds to approximately 11%

Answer:

Step-by-step explanation:

The volume formula can be used to find the height and width of a box with volume 4368 in³ and height 1 in greater than width.

The volume formula is ...

  V = LWH

Substituting given information, using w for the width, we have ...

  4368 = (24)(w)(w+1)

We want to find the value of w.

  182 = w² +w . . . . . . . . divide by 24

  182.25 = w² +w +0.25 = (w +0.5)² . . . . . . add 0.25 to complete the square

  13.5 = w +0.5 . . . . . . . . take the positive square root

  w = 13 . . . . . . . . . . . . subtract 0.5

  h = w+1 = 14

The height of the box is 14 inches; the width is 13 inches.

__

Additional comment

By "completing the square", we can arrive at the exact dimensions of the box, as we did above. Note that we only added 0.25 to the equation to do this.

For numbers close together, the geometric mean (root of their product) is about the same as the arithmetic mean (half the sum):

  [tex]\sqrt{w(w+1)}\approx\dfrac{w+(w+1)}{2}=w+\dfrac{1}{2}\\\\w\approx\sqrt{182}-\dfrac{1}{2}\approx12.99[/tex]

Using this approximation to arrive at the conclusion w=13 saves the steps of figuring the value necessary to complete the square, then adding that before taking the root.

Using proportions, it is found that Jada drinks more water than Elena, as her proportion is 3/2 of Elena's proportion.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Jada drank 3/4 the amount x that Elena drank, hence:

J = 3x/4.

Lin drank twice as much water as Jada, hence her proportion relative to Elena is given by:

L = 2J = 2 x 3x/4  = 6x/4 = 1.5x.

1.5x = 50% more than Elena.

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This means that after 0.5 hours, 259.81 milligrams of the medicine remain on the patient's body.

We know that the exponential function defined by:

[tex]m(h) = 300*(3/4)^h[/tex]

Represents the amount of a mediciene, in milligrams, after a number of hours h.

We want to see what does m(0.5) represent. This is the exponential function evaluated in h = 0.5

Then, it just represents the amount of medicine, in miligrams, in a patient's body present 0.5 hours after the medicine was administered.

Replacing h = 0.5 we get:

[tex]m(0.5) = 300*(3/4)^{0.5} = 259.81[/tex]

This means that after 0.5 hours, 259.81 milligrams of the medicine remain on the patient's body.

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The approximate values of the solution by Euler's method is y₁=0.65, y₂=0.84, y₃=1.0778, y₄=1.3584, y₅=1.6921, y₆=2.05657.

In this question,

The differential equation is

yʹ=y(3−ty) ------- (1)

Here, y(0)=0. 5,h=0. 1, 0≤t≤0. 5.

By Euler's method,

[tex]y_{n+1}=y_n+hf_n[/tex]

where [tex]f_n=f(t_n,y_n)[/tex]

For, t = 0, y = 0,

[tex]y_{1}=y_0+hf_0[/tex] and

[tex]f_0=f(t_0,y_0)[/tex]

Substitute in equation 1,

⇒ f(0,0.5) = 0.5(3-(0)(0.5))

⇒ f(0,0.5) = 0.5(3-0)

⇒ f(0,0.5) = 0.5(3)

⇒ f(0,0.5) = 1.5

Then, [tex]y_{1}=y_0+hf_0[/tex] becomes,

⇒ y₁ = 0.5 + (0.1)(1.5)

⇒ y₁ = 0.5 + 0.15

⇒ y₁ = 0.65

For, t = 1, y = 1,

[tex]y_{2}=y_1+hf_1[/tex] and

[tex]f_1=f(t_1,y_1)[/tex]

⇒ f(0.1,0.65) = 0.65(3-(0.1)(0.65))

⇒ f(0.1,0.65) = 0.65(3-0.065)

⇒ f(0.1,0.65) = 1.90

Then, [tex]y_{2}=y_1+hf_1[/tex] becomes,

⇒ y₂ = 0.65+(0.1)(1.90)

⇒ y₂ = 0.84

For t = 2, y = 2,

[tex]y_{3}=y_2+hf_2[/tex] and

[tex]f_2=f(t_2,y_2)[/tex]

⇒ f(0.2,0.84) = 0.84(3-(0.2)(0.84))

⇒ f(0.2,0.84) = 0.84(3-0.168)

⇒ f(0.2,0.84) = 2.3788

Then, [tex]y_{3}=y_2+hf_2[/tex]

⇒ y₃ = 0.84+(0.1)(2.3788)

⇒ y₃ = 1.0778

For t = 3, y = 3,

[tex]y_{4}=y_3+hf_3[/tex] and

[tex]f_3=f(t_3,y_3)[/tex]

⇒ f(0.3,1.0778) = 1.0778(3-(0.3)(1.0778))

⇒ f(0.3,1.0778) = 1.0778(3-0.32334)

⇒ f(0.3,1.0778) = 2.8848

Then, [tex]y_{4}=y_3+hf_3[/tex] becomes

⇒ y₄ = 1.0778+(0.1)(2.8848)

⇒ y₄ = 1.3584

For t = 4, y = 4,

[tex]y_{5}=y_4+hf_4[/tex] and

[tex]f_4=f(t_4,y_4)[/tex]

⇒ f(0.4,1.3584) = 1.3584(3-(0.4)(1.3584))

⇒ f(0.4,1.3584) = 1.3584(3-0.5433)

⇒ f(0.4,1.3584) = 3.3372

Then, [tex]y_{5}=y_4+hf_4[/tex] becomes

⇒ y₅ = 1.3584 + (0.1)(3.3372)

⇒ y₅ = 1.6921

For t = 5, y = 5,

[tex]y_{6}=y_5+hf_5[/tex] and

[tex]f_5=f(t_5,y_5)[/tex]

⇒ f(0.5,1.6921) = 1.6921(3-(0.5)(1.6921))

⇒ f(0.5,1.6921) = 1.6921(3-0.84605)

⇒ f(0.5,1.6921) = 3.6447

Then, [tex]y_{6}=y_5+hf_5[/tex] becomes

⇒ y₆ = 1.6921 + (0.1)(3.6447)

⇒ y₆ = 2.05657

Hence we can conclude that the approximate values of the solution by Euler's method is y₁=0.65, y₂=0.84, y₃=1.0778, y₄=1.3584, y₅=1.6921, y₆=2.05657.

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Answer:

○ [tex]h = \frac{2A}{b}[/tex]  

Step-by-step explanation:

We are given:

[tex]A = \frac{1}{2} b h[/tex]

To solve for [tex]h[/tex], we have to rearrange the equation to make [tex]h[/tex] the subject:

[tex]A = \frac{1}{2} b h[/tex]

⇒ [tex]2A = bh[/tex]     [multiplying both sides by 2]

⇒ [tex]\frac{2A}{b} = h[/tex]       [dividing both sides by b]

⇒  [tex]h = \frac{2A}{b}[/tex]      [swapping sides]

Answer:

[tex]\textsf{Midpoint rule}: \quad \dfrac{2\pi}{\sqrt[3]{2}}[/tex]

[tex]\textsf{Trapezium rule}: \quad \pi[/tex]

[tex]\textsf{Simpson's rule}: \quad \dfrac{4 \pi}{3}[/tex]

Step-by-step explanation:

Midpoint rule

[tex]\displaystyle \int_{a}^{b} f(x) \:\:\text{d}x \approx h\left[f(x_{\frac{1}{2}})+f(x_{\frac{3}{2}})+...+f(x_{n-\frac{3}{2}})+f(x_{n-\frac{1}{2}})\right]\\\\ \quad \textsf{where }h=\dfrac{b-a}{n}[/tex]

Trapezium rule

[tex]\displaystyle \int_{a}^{b} y\: \:\text{d}x \approx \dfrac{1}{2}h\left[(y_0+y_n)+2(y_1+y_2+...+y_{n-1})\right] \quad \textsf{where }h=\dfrac{b-a}{n}[/tex]

Simpson's rule

[tex]\displaystyle \int_{a}^{b} y \:\:\text{d}x \approx \dfrac{1}{3}h\left(y_0+4y_1+2y_2+4y_3+2y_4+...+2y_{n-2}+4y_{n-1}+y_n\right)\\\\ \quad \textsf{where }h=\dfrac{b-a}{n}[/tex]

Given definite integral:

[tex]\displaystyle \int^{2 \pi}_0 \sqrt[3]{\sin^2 (x)}\:\:\text{d}x[/tex]

Therefore:

Calculate the subdivisions:

[tex]\implies h=\dfrac{2 \pi - 0}{4}=\dfrac{1}{2}\pi[/tex]

Midpoint rule

Sub-intervals are:

[tex]\left[0, \dfrac{1}{2}\pi \right], \left[\dfrac{1}{2}\pi, \pi \right], \left[\pi , \dfrac{3}{2}\pi \right], \left[\dfrac{3}{2}\pi, 2 \pi \right][/tex]

The midpoints of these sub-intervals are:

[tex]\dfrac{1}{4} \pi, \dfrac{3}{4} \pi, \dfrac{5}{4} \pi, \dfrac{7}{4} \pi[/tex]

Therefore:

[tex]\begin{aligned}\displaystyle \int^{2 \pi}_0 \sqrt[3]{\sin^2 (x)}\:\:\text{d}x & \approx \dfrac{1}{2}\pi \left[f \left(\dfrac{1}{4} \pi \right)+f \left(\dfrac{3}{4} \pi \right)+f \left(\dfrac{5}{4} \pi \right)+f \left(\dfrac{7}{4} \pi \right)\right]\\\\& = \dfrac{1}{2}\pi \left[\sqrt[3]{\dfrac{1}{2}} +\sqrt[3]{\dfrac{1}{2}}+\sqrt[3]{\dfrac{1}{2}}+\sqrt[3]{\dfrac{1}{2}}\right]\\\\ & = \dfrac{2\pi}{\sqrt[3]{2}}\\\\& = 4.986967483...\end{aligned}[/tex]

Trapezium rule

[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} &&&&&\\ x & 0 & \dfrac{1}{2}\pi & \pi & \dfrac{3}{2} \pi & 2 \pi \\ &&&&&\\\cline{1-6} &&&&& \\y & 0 & 1 & 0 & 1 & 0\\ &&&&&\\\cline{1-6}\end{array}[/tex]

[tex]\begin{aligned}\displaystyle \int^{2 \pi}_0 \sqrt[3]{\sin^2 (x)}\:\:\text{d}x & \approx \dfrac{1}{2} \cdot \dfrac{1}{2} \pi \left[(0+0)+2(1+0+1)\right]\\\\& = \dfrac{1}{4} \pi \left[4\right]\\\\& = \pi\end{aligned}[/tex]

Simpson's rule

[tex]\begin{aligned}\displaystyle \int^{2 \pi}_0 \sqrt[3]{\sin^2 (x)}\:\:\text{d}x & \approx \dfrac{1}{3}\cdot \dfrac{1}{2} \pi \left(0+4(1)+2(0)+4(1)+0\right)\\\\& = \dfrac{1}{3}\cdot \dfrac{1}{2} \pi \left(8\right)\\\\& = \dfrac{4}{3} \pi\end{aligned}[/tex]

Expand the binomials.

[tex](x+y)^2 - (x-y)^2 = (x^2 + 2xy + y^2) - (x^2 - 2xy + y^2) = 4xy[/tex]

Now let [tex]x=1[/tex] and [tex]y=\sin(A)[/tex].

Answer:

34

Step-by-step explanation:

(a + [tex]\frac{1}{a}[/tex] ) = 6← square both sides

(a + [tex]\frac{1}{a}[/tex] )² = 6² ← expand left side using FOIL

a² + 1 + 1 + [tex]\frac{1}{a^2}[/tex] = 36

a² + 2 + [tex]\frac{1}{a^2}[/tex] = 36 ( subtract 2 from both sides )

a² + [tex]\frac{1}{a^2}[/tex] = 34

Answer:

Rs 1425

Step-by-step explanation:

=(30×40) + (15×15)

=1425

Answer:

Option A

Step-by-step explanation:

The solution is in the image

Answer:Maria

Step-by-step explanation: Maria uses a cup per 2 gallons while Franco uses a cup for 5 gallons. Maria has a 1:16 ratio while Franco has a ratio of 1: 80 because a gallon is 16 cups. It is clear now that Franco has a smaller ratio so, Maria's sports drink is stronger.

Step-by-step explanation:

The volume of a cube is

[tex]a {}^{3} [/tex]

where a is the side length,

Note: If you want to remember this formula, know that a cube is basically a bunch of squares stacked on one another vertically and horizontally

The area of a square with side length a, is

[tex] {a}^{2} [/tex]

If we multiply that by the height of the cube, which is a.

[tex] {a}^{2} \times a = {a}^{3} [/tex]

That is the easy way to derive the formula of the volume of a cube.

Back on track, we know the volume so we must solve for a.

1.

[tex]125 = {a}^{3} [/tex]

Assuming you took algebra, to isolate the variable a, we must undo it being raised to the third power.

To do this, we take the cube root of both sides

[tex] \sqrt[3]{125} = \sqrt[3]{a {}^{3} } [/tex]

The cube root of 125 is 5 so

[tex]5 = a[/tex]

5 cm

2.

[tex]8 = {a}^{3} [/tex]

[tex] \sqrt[3]{8} = \sqrt[3]{ {a}^{3} } [/tex]

[tex]2 = a[/tex]

2 ft

3.

[tex]343 = {a}^{3} [/tex]

[tex]a = 7[/tex]

7 yd

4.

[tex]1000 = a {}^{3} [/tex]

[tex]10 = a[/tex]

10 mm

5.

[tex]1728 = {a}^{3} [/tex]

[tex]a = 12[/tex]

12 in. or 1 ft

6.

[tex]1 = {a}^{3} [/tex]

[tex]a = 1[/tex]

1 m

Answer:

A cube can be seen as a square that has been 'stretched'. We know that all four sides of a square are equal, thus, the sides of the faces of a cube are also equal.

In order to find the volume of a cube, the formula we apply is length x width x height (lwh).

Since all the sides are the same, another formula for the volume of the cube can be written as volume = x^3 in which x stands for the length of each side. When plugging in the formula:

1) V = 125 cm^3

   125 = x^3

   ∛125 = x

    5 = x

When finding the cube root, you can use a calculator or fingure out the answer yourself by multiplying any number by itself three times.

2) 8 = x^3

   ∛8 = x

      2 = x

3) 343 = x^3

 ∛343 = x

        7 = x

4) 1000 = x^3

 ∛1000 = x

         10 = x

5) 1728 = x^3

  ∛1728 = x

    12 = x

6) 1 = x^3

   ∛1 = x

      1 = x

Make sure to include the appropriate unit for each answer

The vertices of the figure after the transformation: T<−5, −2>; 5 units left and 2 units down is X'(-3, -3), V'(-4, 0), E'(-1, -1), K'(0, -5)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Rigid transformations are transformation that preserve the shape and size of a figure such are reflection, rotation and translation.

The vertices of the figure after the transformation: T<−5, −2>; 5 units left and 2 units down is X'(-3, -3), V'(-4, 0), E'(-1, -1), K'(0, -5)

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the gardener would need (1 + 1/6) liters of water to water the whole garden.

Here we know that the gardener needs 1/3 of a liter of water to water 2/7 of a garden.

Then we have the relation:

1/3 L = 2/7 of a garden.

Now, we want to get a "1 garden" in the right side of the equation, then we can multiply both sides by (7/2), so we get:

(7/2)*(1/3) L = (7/2)*(2/7) of a garden

(7/6)L = 1 garden.

(1 + 1/6) L = 1 garden

This means that the gardener would need (1 + 1/6) liters of water to water the whole garden.

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Answer:

Step-by-step explanation:

20 liters -1 liter = 19 liters of milk

20 liters -1 liter = 19 liters of syrup

This was done twice so therefore;

19 liters  -1 liter = 18 liters of milk

19 liters  -1 liter = 18 liters of syrup

Therefore the ratio comes to 18:18

18 goes into 18 1 and the same for the other 18. Therefore the ratio comes to ;

1:1

Your final answer is 1:1