When a number is put into a machine, a different number comes out. If 5 goes in, 2 comes out. If 7 goes in, 4 comes out. If 8 goes in, 5 comes out. If 10 goes in, what number should come out? A 3 B 7 C 9 D 10​

The magnitude and direction of vector <4, 2> are 2√5 and 26.6°, respectively.

In this problem we find the representation of a two-dimension vector, that is, a vector of the form <x, y>. Vectors are described both by magnitude and direction:

Magnitude - This can be found by Pythagorean theorem:

r = √(x² + y²)

Direction - This can be determined by following inverse trigonometric function:

θ = tan⁻¹ (y / x)

Where θ is expressed in degrees.

If we know that x = 4 and y = 2, then the magnitude and direction of the vector <4, 2> are, respectively:

r = √(4² + 2²)

r = √20

r = 2√5

θ = tan⁻¹ (2 / 4)

θ = tan⁻¹ (1 / 2)

θ ≈ 26.565°

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The coordinates of the vertex of the function y = -3x² -12x + 3 is (-2,15) and the graph of the function is attached below.

Vertex in math is known as a point on a polygon where the sides or edges of the object meet or where two rays or line segments meet.

Here we have given that the function y = -3x² - 12x + 3 and we have to find the coordinates of the vertex.

As we all know that for any equation of the type y = ax² + bx + c the vertex is given by (h, k)

And the value of the vertex is calculated by using the formula  h = -b/2a and k = (4ac - b2)/4a.

From the given question we have identified the value of  a = -3, b = -12 and c = 3

Then the value of h is calculated as,

=> h = -(-12)/2(-3)

When we simplify this one then we get the value of h as -2

Similarly the value of k is calculated as,

=> 4ac = 4(-3)(3) = -36

Then the equation is written as,

=> k = [-36 - (-12)2]/4(-3)

When we simplify this one then we get

=> k = -180/-12

Therefore, the value of k is 15

Hence the coordinates of the vertex is (h, k) = (-2, 15).

Complete Question:

What are the coordinates of the vertex of the graph of the function y = -3x² -12x + 3?

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The two boys are far away from the resort and distance measured about 35.81m.

The Pythagoras theorem equation is written as c² = a² + b², with c denoting the hypotenuse of the right triangle and a and b denoting the other two legs. So, any triangle that has a 90° angle creates a Pythagoras triangle, which can then be solved using the Pythagoras equation.

We must first use the Pythagoras theorem to determine how far the resort is from Manuel's home.

S₁ = √50²+20²

S₁ = √2500+400

S₁ = √2900

S₁ = 53.85m.

The distance between Manuel's house and his friend's house must then be calculated.

S₂ = √15²+10²

S₂ = √225+100

S₂ = √325

S₂ = 18.03m.

The displacement of the two boys will be,

∆S = S₁-S₂

∆S =  53.84-18.03

∆S = 35.81m.

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The two boys are far away from the resort and the distance measured about 35.81 m.

The Pythagoras theorem equation is written as c² = a² + b², with c denoting the hypotenuse of the right triangle and a and b denoting the other two legs. So, any triangle that has a 90° angle creates a Pythagoras triangle, which can then be solved using the Pythagoras equation.

We must first use the Pythagoras theorem to determine how far the resort is from Manuel's home.

S₁ = √50²+20²

S₁ = √2500+400

S₁ = √2900

S₁ = 53.85m.

The distance between Manuel's house and his friend's house must then be calculated.

S₂ = √15²+10²

S₂ = √225+100

S₂ = √325

S₂ = 18.03m.

The displacement of the two boys will be,

∆S = S₁-S₂

∆S =  53.84-18.03

∆S = 35.81m.

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The experimental probability of getting a cinnamon jelly bean is P = 2/11

Suppose that we have an experiment with some given number of outputs, and we perform that experiment N times.

The experimental probability of a given outcome is equal to the quotient between the number of times that we got that outcome and the total number of times we performed the experiment.

Here we have the data:

root beer = 5

licorice = 22

cinnamon = 6

For a total of 5 + 22 + 6 = 33 tries.

Then the probability of getting a cinnamon jelly bean is:

P = 6/33 = 2/11

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Thus, position 26 would have 1378 tiles.

Pattern rule equation:

A pattern rule equation is a mathematical formula that describes how a pattern is created. It defines the relationship between the position number (p) and the number of tiles (n) in the pattern.

The pattern rule equation is a useful tool to predict the number of tiles in a certain position, for example, position 26 as I mentioned in my previous answer.

It's also useful to predict the total number of tiles in a pattern or to identify the position number of a specific number of tiles.

In the pattern rule equation n = 53p, n is the number of tiles and p is the position number. To find the number of tiles in position 26, we can substitute 26 for p in the equation:

n = 53p

n = 53(26)

n = 1378

So there would be 1378 tiles in position 26.

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All the required values are given below.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

To find the percentages:

12 is 150% of,

= 12 x 100/ 150

= 8.

5 is 50% of,

= 5 x 100/50

= 10

10% of m number is 300,

m = 300 x 100/ 10

m = 3000

5% of k number is 72,

k = 72 x 100/5

k = 1440

20 is 80% of,

= 20 x 100/80

= 25

Therefore, all the required values are given above.

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Each ticket cost 54$.

$332 (the total cost of the tickets) less $5 (the service charge) equals the cost of 9 tickets.

Round your estimate to the nearest even number: If you want it to be an even $100, deduct $4 rather than $5. Then multiply by a whole number to get 9 + 2 = 10. You now have simple numbers. $10 is equivalent to $100 divided by 10 tickets.

3. $104 (the total cost of the tickets) less $5 (the service charge) equals the cost of 8 tickets.

STEP 1: $5 off of $104 equals $99

$99.00 is equal to the cost of 9 tickets.

Step 2: Divide $99 by 9 to get $11.

Consequently: The Price/Ticket is $54.

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The solution of pair of equation 2x + y = 5 and 3x - 2y = 4 is x = 2 and y = 1.

The set of equations given is linear equations that can be solved simultaneously to find the values of variables x and y.

2x + y = 5------->(1)

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

Multiply equation (1) by 2 and then add it to equation (2)

4x + 2y = 10

3x -  2y =   4

7x + 0  = 14

7x = 14

x = 2

Putting x = 2 in (1),

2(2) + y = 5 

y = 5 - 4 = 1

Therefore, the values of x and y obtained are 2 and 1, respectively. 

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The tan function is referred to as the ratio of a right-angled triangle's opposite side to its neighbouring side.

The length of the neighbouring side to the angle and the opposite side to the angle are compared using the Tan formula. If we know the angle and either side of the triangle.

The six inverse trigonometric ratios are as follows: sin-1 (opposite)/(hypotenuse) = cos-1 (base)/(hypotenuse) = tan-1 (opposite)/(hypotenuse)=θ

we can also use the tan formula to determine the lengths of the triangle's sides. Tan Formula is formally defined as

tan⁡Ф = Opposite SideAdjacent Side

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Step-by-step explanation:

[tex]volume \: of \: cyinder = \pi{r}^{2}h \\ \pi {r}^{2} \times 120cm = 2880\pi {cm}^{3} \\ {r}^{2} = 24 \: {cm}^{2} \\ r = \sqrt{24} \: = 4.899 \: cm[/tex]

The number in question is 4*20 = 80.

The factors of 80 are:

1, 2, 4, 5, 8, 10, 16, 20, 40 and 80

A factor of a number is an integer that divides the number completely without leaving a remainder. To find the factors of 80, we can start with 1 and divide 80 by each number up to 80. Any number that divides 80 without leaving a remainder is a factor of 80.

1, 2, 4, 5, 8, 10, 16, 20, 40 and 80 are the factors of 80.

The answers are 1.67 glucose molecules, 36 glucose molecules, 15 glucose molecules and 8400 times.

When two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Given are some questions regarding production of glucose molecules during aerobic metabolism.

1) 1 glucose molecules produces 30 ATP molecules, how many for 50 ATP molecules :-

Using proportionality, let there be x glucose molecules required to produce 50 ATP molecules,

1 / 30 = x / 50

x = 5/3

x = 1.67

Therefore, there are 1.67 glucose molecules required to produce 50 ATP molecules.

2) 1 glucose molecules produces 6 ATP molecules, how many for 216 ATP molecules :-

Using proportionality, let there be x glucose molecules required to produce 216 ATP molecules,

1 / 6 = x / 216

x = 36

Therefore, there are 36 glucose molecules required to produce 216 ATP molecules.

3) 1 glucose molecules produces 30 ATP molecules, how many for 450 ATP molecules :-

Using proportionality, let there be x glucose molecules required to produce 450 ATP molecules,

1 / 30 = x / 450

x = 15

Therefore, there are 15 glucose molecules required to produce 450 ATP molecules.

4) Since, in one day it's 1200 times an ATP molecule is reused in a human body,

We need to find for a week, there are 7 days in a week,

Therefore, an ATP molecule is reused in a human body for a week = 1200 x 7 = 8400 times.

Hence, the answers are 1.67 glucose molecules, 36 glucose molecules, 15 glucose molecules and 8400 times.

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Answer:

a = 97° , b = 19°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

(a)

a is an exterior angle of the triangle , then

a = 40° + 57° = 97°

(b)

57° is an exterior angle of the triangle , then

b + 38° = 57° ( subtract 38° from both sides )

b = 19°

Using subtraction, weight put on by kitten is 1,298.43.

When we subtract from the group, the total number of items falls or gets less. The minuend, subtrahend, and difference are the elements of a subtraction problem.

It involves calculating the difference between two numbers. The icon looks like this: (minus). In this operation, we take a number and divide it by a smaller number. In other words, we divide one integer by another.

Weight of kitten when Madison brought her = 787.37 grams

Current weight of Madison = 2085.8 grams

Using subtraction,

Total weight Kitten put on = (2085.8 - 787.37)grams

= 1,298.43

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Answer:

use symbolab it will give you the answer

Step-by-step explanation:

The simplified expression of 2(5+3x)+(x+10) is 7x + 20

From the question, we have the following parameters that can be used in our computation:

2(5+3x)+(x+10)

Open the brackets

so, we have

10 + 6x + x + 10

Evaluate the like terms

7x + 20

Hence, the expression is 7x + 20

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No, â =1 is not equals to ¾. Since ¾ is written as 0.75 in fractional notation.

The fraction ¾, which is equivalent to 0.75, is shown by the fractional notation "â...". The bottom number, or denominator, must be multiplied by the top number in order to comprehend this fraction (top number). 4 times 3 in this instance equals 12, which is true. Find the fractional value by first dividing the numerator by the denominator. In this case, the result of 3 divided by 4 is 0.75, or 3/4.

To calculate a fractional value, use the following formula:

Fractional Value: Numerator / Denominator

The numerator is multiplied by the denominator to arrive at 12 when calculating the fractional value of 3/4. Following that, the fractional value is obtained by dividing the numerator by the denominator:

Fractional value equals 3 / 4 = 0.75

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The 2 real solutions are rational and irrational solutions.

Quadratic Formula is the simplest method to find the roots of a quadratic equation. There are particular quadratic equations that cannot be easily factorized, and here we use this quadratic formula to find the roots in the quickest possible way.

Quadratic Formula: The roots of a quadratic equation ax² + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.

The value b² - 4ac is called the discriminant of a quadratic equation and is represented as 'D'. The nature of the roots of the quadratic equation can be predicted based on the discriminant value.

If D > 0, the roots are real and distinct (two real solutions).

If D = 0, the roots are real and equal (one real solution).

If D < 0, the roots do not exist, or they are imaginary (two imaginary solutions).

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The substitution that should be used to rewrite  x⁸ + 3x⁴ + 2 = 0, as a quadratic equation is U = x⁴ .

The equation is called as quadratic if the equation has the highest degree  as 2 , it can also be called as an algebraic equation that is second degree in x .

The equation to make a quadratic is  x⁸ + 3x⁴ + 2 = 0 ;  

we have to make this given equation a quadratic equation ,

So , we substitute U = x⁴  ,  in equation ,

we get ;

⇒  (x⁴)² + 3x⁴ + 2 = 0 ;

⇒  (U)² + 3U + 2 = 0;

the equation becomes ⇒ U₂ + 3U + 2 = 0 , which is an quadratic equation,

Therefore , the substitution that should be used is U = x⁴  .

The given question is incomplete , the complete question is

What substitution should be used to rewrite  x⁸ + 3x⁴ + 2 = 0  as a quadratic equation ?

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congrats man!!

good job!! you did great on it

The complete table is answered along with solutions is given above.

Given is the table as shown in the image.

{ 1 } -

D = 4

R = D/2 = 2

H = 10

Area = πR² = 4π

Volume = πR²h = 40π

D = 6

R = D/2 = 3

H = 10

Volume = πR²h = 63π

Area = πR² = 9π

Therefore, the complete table is answered along with solutions is given above.

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On a graph, indicate the coordinate plane point (3,4). It's  contains of two coordinate are x , y coordinate

Identify the first four positive units and draw the y-axis.

The x-axis is then drawn, and the first four positive units are labeled.

The x-coordinate is 3, thus.

The y-coordinate is 4, thus.

Plotting (3,4) requires us to start at the beginning.

The x-coordinate being positive 3, we shift 3 units to the right.

The y-coordinate being positive 4, we shift 4 units to the right .

The point's x-value indicates how it travels to the right or left along the x-axis. The rectangular axis, often known as the Cartesian plane, has this axis as its major horizontal line.

The point's y-value indicates how it goes up or down along the y-axis. The rectangular axis, often known as the Cartesian plane, is centered on this axis.

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It would take the automated car wash 20 hours to wash 120 cars.

What is rate ?

In general, a rate is a measure of how much of something happens within a certain period of time. It can be thought of as a ratio that compares two different units of measurement.

In the context of the problem, the rate at which the automated car wash can wash cars is the number of cars that it can wash per unit of time.

The rate at which the automated car wash can wash cars is 30 cars per 5 hours. To find out how long it would take to wash 120 cars, we can use the formula:

Time = (Number of cars / Rate)

Time = (120 cars / 30 cars per 5 hours)

Time = (120/30) * 5 hours

Time = 20 hours

So it would take the automated car wash 20 hours to wash 120 cars.

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The rate at which the automated car wash can wash cars is 30 cars per 5 hours. To find out how long it would take to wash 120 cars, we can use the formula:

Time = (Number of cars / Rate)

Time = (120 cars / 30 cars per 5 hours)

Time = (120/30) * 5 hours

Time = 20 hours

So it would take the automated car wash 20 hours to wash 120 cars.

Value of log 1 is 0 for base 10.

In mathematics, logarithmic functions, also referred to as log functions, are the inverse function of exponentiation. A logarithm, by definition, is a measurement that shows how much a base (fixed number) is raised to get a given number.

The two different kinds of logarithmic functions, in general. The base of the logarithmic function in common logarithmic functions is 10. The base of the logarithmic function in a natural logarithmic function is e.

Hence, the value of log 1 is 0 for base 10.

Correct question :

What is the value of log 1 for base 10?

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Answer:

2.6

Step-by-step explanation:

260÷x=100

260/x=100

260=100x

x=2.6

95% of toy eskimo dogs have weight between 6.04 and 9.96 pounds assuming normal distribution.

What is weight ?

Weight is a measure of the force exerted on an object due to gravity. It is typically measured in units of mass such as kilograms (kg) or pounds (lbs). The weight of an object can be determined by multiplying its mass by the acceleration due to gravity.

Assuming the weights of toy eskimo dogs are normally distributed, we can use the standard normal distribution table to find the range of weights that would include 95% of the dogs.

The standard normal distribution table gives the proportion of data within a given number of standard deviations from the mean. Since the standard deviation of the toy eskimo dog's weight is 1 pound, we can use this table to find the range of weights that are within 1.96 standard deviations from the mean.

Using this method, we can find that 95% of the toy eskimo dogs will have a weight that is between 6.04 pounds (8 - 1.96) and 9.96 pounds (8 + 1.96).

95% of toy eskimo dogs have weight between 6.04 and 9.96 pounds assuming normal distribution.

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Answer:

[tex] \sf \: 4x + 3 [/tex]

Step-by-step explanation:

Given expression,

→ (-3x + 5) - (-7x + 2)

Let's simplify the expression,

→ (-3x + 5) - (-7x + 2)

→ -3x + 5 + 7x - 2

→ (-3x + 7x) + (5 - 2)

→ (4x) + (3)

→ 4x + 3

Hence, the answer is 4x + 3.

10x +7

because minus and minus equals plus 7x + 3x equals 10x and 2 plus 5 is 7