What is 5÷2(mod 6)
What is 9÷7(mod 7)
What is 6÷5(mod7)

solve the following equations
a) 3 + x =4(mod 5)
b) x² + 1 = 2(mod 7)
c)x² + 1 = 2(mod 4)
d) 2(x - 5) = 2(mod 8)​

The height and radius of the cup are 4.41 cm and 2.07 cm respectively

To minimize the amount of paper used, we need to minimize the surface area of the cup. Let h be the height and r be the radius of the cone. Then we have:
\(Volume of cone = \frac{1}{3}  πr^{2} h = 36 cm^{3}\)

Solving for h, we get:
\(h = \frac{108}{(πr^2)}\)

Now we can express the surface area of the cone as:
\(Surface area = πr^2+ πr\sqrt{r^{2}+h^{2}  }\)

Substituting the expression for h, we get:

\(Surface area = πr^2+πr \sqrt{(r^{2} +(\frac{108}{(πr^2)^{2}) } )}\)

To minimize this function, we take its derivative with respect to r and set it equal to zero:
\(\frac{d}{dx} (Surface area) =  \frac{2πr - 108r }{[(r^2+(\frac{108}{πr^2}))^{0.5}  }] - \frac{108π}{r^2 }  = 0\)

Simplifying, we get:
\(2r^3 - \frac{108^2}{π} = 0\)

Solving for r, we get:
\(r = (\frac{54}{π})^{\frac{1}{3} }\)

Substituting this value into the expression for h, we get:
\(h = \frac{108}{\frac{54}{π} ^{(\frac{2}{3}π )} }\)

Thus, the height and radius of the cup that will use the smallest amount of paper are:
height = 4.41 cm
radius = 2.07 cm (rounded to two decimal places)

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Answer:

I believe the answer is "6 quarts of blue paint for every 9 quarts of purple paint."

Step-by-step explanation:

r(b) = the number of quarts of purple paint, with "b" representing the number of quarts of blue paint, and "r" representing the number of quarts of red paint. The "6" in "r(6) = 9" substitutes the "b", which means there are 6 quarts of blue paint. The "9" substitutes the amount of purple paint, which means there are 9 quarts of purple paint.

Answer:

9 quarts of blue paint for every 6 quarts of red paint

Step-by-step explanation:

in the paragraph thing above the equation says r=red paint. and to make a certain shade of purple you need to mix red and blue paint.

in the equation it says r(6) and I know r is red to red=6 quarts. since r=6 quarts of red paint I know that 9 is the amount of quarts of blue paint. and then I looked at the answer choices.

A) 9 quarts of blue paint for every 6 quarts of purple paint

I immediately knew that A is wrong because to get purple paint you need to mix red and blue not purple

B) 9 quarts of blue paint for ever 6 quarts of red paint

I know that it said in the paragraph thing above the equation that the relationship between the number of quarts of blue paint in the mix,b, and the number of quarts of red paint,r, is represented by the function r(b). and I knew that it was saying for every 9 quarts of blue paint for every 6 quarts of red paint.

(sorry but this is all I can pretty much write down for ya so...) Hope this helped!

The area of pentagon ABCDE is 36 times the area of pentagon PQRST.

Any five-sided polygon or 5-gon is referred to as a pentagon. The area of pentagon ABCDE is 36 times the area of pentagon PQRST.

We have,

Any five-sided polygon or 5-gon is referred to as a pentagon. A basic pentagon's interior angles add up to 540°. A pentagon might be straightforward or self-intersecting.

We know the formula for the area of a pentagon, therefore, the area of the pentagon PQRST can be written as,

A = 1/4 * √5(5+25)*a²

Given that the side of the side length of pentagon ABCDE is 6 times the side length of pentagon PQRST, therefore, the area of the pentagon ABCDE can be written as,

ABCDE = 1/4 * √5(5+25)* 6a²

ABCDE = 36 * A

Hence, The area of pentagon ABCDE is 36 times the area of pentagon PQRST.

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complete question:

Pentagon ABCDE is similar to pentagon PQRST. If the side length of pentagon ABCDE is 6 times the side length of pentagon PQRST, which

statement is true?

A.

The area of pentagon ABCDE IS 6 times the area of pentagon PQRST.

B.

The area of pentagon ABCDE is 12 times the area of pentagon PQRST.

C.

The area of pentagon ABCDE is 36 times the area of pentagon PQRST.

D.

The area of pentagon ABCDE IS 216 times the area of pentagon PQRST.​

When the pile is 22 feet high, the height of the pile changes to 20/1089π.

Given (dV)/(dt) = 20, h = 22 feet , dh /dt =?

The volume of cone is V = 1/3 * pi * r ^ 2 * h

d=3h

2r = 3h

r = (3h)/2

V = 1/3 * pi * r ^ 2 * h

= 1/3 * pi * ((3h)/2) ^ 2 * h

= 1/3 * pi((9 * H ^ 2 )/4) * h

= (9pi)/12 * h ^ 3

Differentiate w.r.to t

(dV)/(dt) = (3pi)/4 * (3h * h^ 2) * (dh)/(dt)

(dV)/(dt) = (9pi)/4 * (h ^ 2) * (dh)/(dt)

(dV)/(dt)=20, h=22 feet

20 = (9pi)/4 * (22 ^ 2) * (dh)/(dt)

(dh)/(dt) = 80/ (9pi * (22^ 2))

h^ t = 20/ 1089 *pi   ft / min

Therefore, The height of the pile changing when the pile is 22 feet high is 20/1089π

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After answering the provided question, we can conclude that Mason inequality believes the solutions are x 12. The graph shows a shaded region to the left of 12.

In mathematics, an inequality is a non-equal relationship between two expressions or values. As a result, imbalance leads to inequality. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal sign is commonly used (). Different inequalities, no matter how small or large, are used to contrast values. Many simple inequalities can be solved by modifying the two sides until only the variables remain. However, a number of factors contribute to inequality: Negative values are divided or added on both sides. Exchange left and right.

To solve the x517 inequality, first add 5 to both sides to get:

x - 5 + 5 ≤ 17 + 5

When we simplify, we get:

x ≤ 22

As a result, the correct solution to the inequality is x 22.

Now consider Mason's solution. He stated that the solutions are x 12 and graphed them as shown below.

  |

   |

   |

   |

   |

   |

----|------------

  -5|4  9   12

Mason believes the solutions are x 12. The graph shows a shaded region to the left of 12.

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Answer: C or $256

You will also save $64

Answer:

The cost of the stereo system is $256.

Step-by-step explanation:

What we know:

The cost of the stereo system is $320.

Zenaida is getting the stereo system 20% off.

We can set our equation up like this:

Stereo System = 320-320*20%

(to find the cost of the stereo system, we have to subtract 20% of the original price)

1. Multiply 20 by 100 to change 20% into a decimal

20*100=0.2

2. Plug into the equation and solve

320-320*0.2

= 320-64

= 256

I hope this helped!

Answer:

12

Step-by-step explanation:

I am not sure what you mean by "opposite", but the result of that operation is -12, and the opposite is 12

Answer:

The answer is 7,540 to the nearest tenth. If I'm wrong put it in the comments olease

The radius of the toy ball is 24.5 millimeter (to nearest tenth)

Let, r be the radius of the sphere.

Then the surface area of the sphere = \(4\pi r^{2}\) sq. unit

The structure of the toy ball is sphere.

Given, Surface area of the toy ball = 7543 square millimeter

Let, the radius be r millimeter

∴  \(4\pi r^{2}\) = 7543

⇒ \(r^{2}\) = \(\frac{7543}{4*3.14}\)  , where \(\pi\) = 3.14

⇒  \(r^{2}\) = \(\frac{7543}{12.56}\)

⇒  \(r^{2}\) = 600.56

⇒ r = \(\sqrt{600.56}\)

⇒ r = 24.5 (approx)

Radius = 24.5 millimeter (to nearest tenth)

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Answer:

50 feet per second

Step-by-step explanation:

500 / 10 = 50

divide feet by seconds to find feet per second ratio

Answer:

15

Step-by-step explanation:

1, 3. 5, 7. 9, 11. 13, 15.

Consider the given expression,

Consider the formulae,

Then the expression is transformed as,

Consider another formula,

This will give the other value of 'x',

Thus, the given trigonometric equation has two solutions 8 and -6.4

Solve for the first angle as,

Solve for the other angle as,

Answer:

Control: No music

Step-by-step explanation:

A control group is the group that receives no changes in a experiment and is used as a benchmark. For example, a experiment where you wanted to know if plants can live without water, one of the treatments would be not giving them water. The control group would be the group that received water, like normal. Back to the question: Usually, music isn't played. Therefore no music would be the control group.

*Since you forgot to put the options, I can't be 100% sure, but I'm almost positive that this should be the answer.*

I hope this helped!

Answer:

Try 150

Step-by-step explanation:

I'm not sure but it might work.

Answer:

150

Step-by-step explanation:

180-30 = 150 degrees

Answer:

56.8 m²

Step-by-step explanation:

This shape is clearly a trapezium / trapezoid. So :  

Area of a trapezium is given by the formula :

\(\frac{a+b}{2} h\)

Substitute values given in diagram :

a = 4.2

b = 10

h = 8

\((\frac{4.2+10}{2} )8\)

7.1 × 8 = 56.8

Units will be m² as this is area

Giving us our final answer of 56.8 m²

Answer:

\(\frac{-7}{10}\ or \ 0.7\)

Step-by-step explanation:

step 1.

\(\frac{1}{3} (\frac{-6}{4}-\frac{1}{2}(\frac{6}{5}))\)

step 2.

put it in a calculator

step 3

=\(\frac{-7}{10}\ or \ 0.7\)

Answer:2

Step-by-step explanation:

You need to remember these 3 rules when working with multiplication:

Negative number x Negative number = positive number

Negative number x Positive number = Negative number

Positive Number x Positive Number = Positive Number

With that in mind, we see in this equation we are multiplying negative number x positive number = negative number

And we also know 7*2=14 so we know A = 2 and we also know (since A is a positive number) 2 will be postitive:

So the equation will look like this:

-7 x 2 = -14

Therefore A = 2

Hope this helps :D

The inequality that describes this situation will be 6x + 2s ≤ 76

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

x = number of group dance numbers

s = number of solo performances

The inequality will be 6x + 2s ≤ 76

This inequality can be read as "the total duration of the group dance numbers (6 minutes per group dance number) plus the total duration of the solo performances (2 minutes per solo performance) is less than or equal to 76 minutes."

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Answer:

1. 31.3%

2. 34.35%

3.62.6%

Step-by-step explanation:

There were 131 acoustic guitars, and 41 of them needed neck repair.

41/131 = 0.3130 = 31.3%

There were 262 total guitars serviced by Emely. 60 of them were acoustic and needed a string repaired, and 30 of them ere acoustic and needed repair, so 90 of them were acoustic and did not need neck repair.

90/262 = 0.3435 = 34.35%

There were 131 electric guitars. 48 of them had a broken string and 34 of them needed body repairs. So 82 of them needed either string or body repairs.

82/131 = 0.6260 = 62.6%

Answer:

Step-by-step explanation:

The equation format of the circle is \((x-x_{0} )^2 +(y-y_{0} )^2 = r ^2\)

In this case, r is the radius and \(r^{2}\) is equal to 16

Thus the radius is 4. The diameter is double the radius so the diameter is 8

When the probability of paying the claim is 5%, the chance the insurance company must pay for (a) exactly two claims is 31.51%, (b) two or more claims is 8.62%, and (c) four or fewer claims is 98.22%.

To calculate the probability of these scenarios, we will use the binomial probability formula:

P(x) = C(n, x) * p^x * (1-p)^(n-x),

where n is the number of trials (projects), x is the number of successes (claims), p is the probability of success (5%), and C(n, x) is the number of combinations of n items taken x at a time.

a) For exactly two claims:

P(2) = C(10, 2) * (0.05)^2 * (0.95)^8

P(2) ≈ 0.3151

So, the chance the insurance company must pay for exactly two claims is approximately 31.51%.

b) For two or more claims:

P(2 or more) = 1 - P(0) - P(1)

P(0) = C(10, 0) * (0.05)^0 * (0.95)^10 ≈ 0.5987

P(1) = C(10, 1) * (0.05)^1 * (0.95)^9 ≈ 0.3151

P(2 or more) ≈ 1 - 0.5987 - 0.3151 ≈ 0.0862

So, the chance the insurance company must pay for two or more claims is approximately 8.62%.

c) For four or fewer claims:

P(4 or fewer) = P(0) + P(1) + P(2) + P(3) + P(4)

P(3) = C(10, 3) * (0.05)^3 * (0.95)^7 ≈ 0.0573

P(4) = C(10, 4) * (0.05)^4 * (0.95)^6 ≈ 0.0111

P(4 or fewer) ≈ 0.5987 + 0.3151 + 0.0573 + 0.0111 ≈ 0.9822

So, the chance the insurance company must pay for four or fewer claims is approximately 98.22%.

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Answer:

133°

Step-by-step explanation:

 supplementary angeles sum 180°

a = 3b - 8. Eq. 1

a + b = 180. Eq. 2

Replacing Eq.1 in Eq.2

(3b - 8) + b = 180

3b + b = 180 + 8.

4b = 188

b = 188/4.

b = 47°

From Eq. 1:

a = 3b - 8.

a = 3*47 - 8.

a = 141 - 8.

a = 133°

then:

133>47

The larger anglel is:

133°

Sam will earn $99 for 12 hours of babysitting.

Two or more expressions with an equal sign are defined as an equation.

Given that, Sam earns $33 for babysitting for 4 hours.

4 hours = $33

4 ×3 hours = $33×3

12 hours = $99

Hence, Sam will earn $99 for 12 hours of babysitting.

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Answer:

78

Step-by-step explanation:

The radius of the cone is 783.84/√h

A cone is the surface traced by a moving straight line (the generatrix) that always passes through a fixed point (the vertex).

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

The volume of a cone is expressed as;

V = 1/3πr²h

643072 × 3 = 3.14 × r²h

r²h = 614400

r² = 614400/h

r = 783.84/√h

therefore the radius of the cone is 783.84/√h

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Answer:

117 units

Step-by-step explanation:

39/(x+10)=15/10

(a) 52.475nm many nautical miles south and 29.09nm many nautical miles west will the ship have traveled by 6:00 p.m.

(b) at 6:00pm the ship changes course to due west when 36.68° the ship's bearing and distance from port at 7:00 p.m.

Given that,

A ship sets out from port at noon with a bearing of s 23° west and a speed of 10 knots.

We have to find

(a) By the time it gets dark at six o'clock, how far south and west will the ship have sailed? The ship alters its course to head due west at 6:00 p.m. miles south miles west

(b). at 7:00 p.m., determine the ship's bearing and distance from the port. nautical miles in s.

We know that,

(a) For 6:00 p.m

Sin(θ)=opposite/ hypothesis

θ=29

Opposite=west

Hypothesis =60

Sin(29°)=w/60

w=29.09nm

West= 29.09nm

Cos(θ)=adjacent/ hypothesis

θ=29

Adjacent= south

Hypothesis =60

Cos(29°)= south/60

south=52.475nm

Therefore, 52.475nm many nautical miles south and 29.09nm many nautical miles west will the ship have traveled by 6:00 p.m.

(b) tan(θ)=opposite/adjacent

Opposite=29.09nm

Adjacent= 52.475nm

Tan(θ)=29.09nm/52.475nm

θ=36.68°

Therefore, at 6:00pm the ship changes course to due west when 36.68° the ship's bearing and distance from port at 7:00 p.m.

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