Write 512 as a product of primes.

Use index notation when giving your answer.

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Answer:

63°

Step-by-step explanation:

[tex]m\angle OZQ=m\angle OZP+m\angle PZQ \\ \\ 125^{\circ}=62^{\circ}+m\angle PZQ \\ \\ m\angle PZQ=63^{\circ}[/tex]

We take the value 2 for which y(2)=4 and [tex]y^{2}[/tex]=2 and see that y(x)=[tex]x^{2}[/tex] is a function and [tex]y^{2}[/tex]=x is a relation.

Domain is the set of values that a variable can take in an algebraic expression.For the equation y(x)=[tex]x^{2}[/tex], x can take any value from negative infinity to positive infinity so we can say that the domain for x is (-∞,∞). For the equation [tex]y^{2}[/tex]=x, x can take any value greater than or equal to zero. Since x=[tex]y^{2}[/tex] we can't take a negative value for x because squared numbers are always positive, so the domain of x will be [0,∞). The common domain for both the equations is [0,∞). Let us choose a value from this common domain,let's say 2. Then for

y(x)=[tex]x^{2}[/tex]⇒y(2)=4 ...(i)

[tex]y^{2} =x[/tex]=2 then y=±[tex]\sqrt{2}[/tex]...(ii)

A function always has an output variable and one or more input variables.For first equation, y is the output variable and x is the input variable. A relation states that two expressions are equal and one is not dependant on another. For equation (i) y is dependant on x but in equation (ii) both the variables are independant.

Thus we can conclude that y(x)=[tex]x^{2}[/tex] is a function and [tex]y^{2}[/tex]=x is a realtion.

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Step-by-step explanation:

the second equation gives us right away

y = 4 - 3x

we can use that now in the 3rd equation :

-2(4 - 3x) + 2z = 4

-8 + 6x + 2z = 4

6x + 2z = 12

3x + z = 6

z = 6 - 3x

now we use both in the 1st equation :

-2x + 3(4 - 3x) - (6 - 3x) = -2

-2x + 12 - 9x - 6 + 3x = -2

-8x + 6 = -2

-8x = -8

x = 1

y = 4 - 3x = 4 - 3×1 = 4 - 3 = 1

z = 6 - 3x = 6 - 3×1 = 6 - 3 = 3

so,

(1, 1, 3)

The ending number is related to the starting number by n + 9.

To start with this magic number puzzle, let us take a positive number and a negative number. After that we have to perform some simple mathematical operations,

Taking positive number as 10 and negative number as -8.

Now, performing the mathematical operations as described in the next steps.

First starting with positive number which is 10.

Step-1. Add 10

So, 10+10 = 20

Step-2. Multiply by 2

So, 20×2 = 40

Step-3. Subtract 2,

So, 40 - 2 = 38

Step-4. Divide by 2,

So, 38/2= 19

Number chosen in the starting was 10 and at the end it became 19. The number 9 got added to 10.

Now, performing the steps on our negative number which is -8,

Step-1. Add 10

So, 10-8=2

Step-2. Multiply by 2

So, 2×2 = 4

Step-3. Subtract 2

So, 4-2 = 2

Step-4. Divide by 2

So, 2/2 = 1.

Number chosen in the starting was -8 and after performing the steps it became 1.

Now, for any number 'n',

Step-1. Adding 10

So, n+10

Step-2. Multiply by 2

So, 2(n-10) = 2n+20

Step-3. Subtract 2

So, 2n+20-2 = 2n+18

Step-4. Divide by 2.

So, (2n+18)/2 = n+9

The number taken in the starting was n and now it became n+9.

So the ending number becomes 9 times more in the end then the starting number.

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The number √60 - 11 will be plotted between -3 and -4, but closer to -3 (Option A), as seen by number system.

Given: √60 - 11

The value of √60 - 11 is given as: √60 - 11 = 7.2 (approx.) - 11 = -3.2

Thus, as seen from the calculation of the value of the given number, √60 - 11 will lie between -3 and -4, but closer to -3 as -3.2 is closer to -3 than to -4.

Hence, The number √60 - 11 will be plotted between -3 and -4, but closer to -3 (Option A), as seen by number system.

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The expression two less than four times a number is represented as 4x - 2

An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as the addition, subtraction, division and multiplication.

According to the question, we are to transform two less than four times a number into expression

Let the unknown number be x such that

four times a number = 4x

two less than four times a number = 4x - 2

Hence the expression two less than four times a number is represented as 4x - 2

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The probability is  [tex]\frac{1}{2}[/tex].

To solve this problem we need to recognize the idea of probability.

To calculate the probability we need to divide the desired final results with the aid of the overall number of consequences.

here, it is asked to locate the chance of having all even numbers earlier than getting an strange variety.

We know that the whole number of results when we roll a dice is 6.

We realize there are three odds and three even in the cube. So, the required

probability of getting even = [tex]\frac{3}{6}[/tex]

                                             = [tex]\frac{1}{2}[/tex]

The required probability is equals to [tex]\frac{1}{2}[/tex].

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Answer: 3/7

Step-by-step explanation:

You would divide this by the number 8.

8*3 = 24

8*7 = 56

Therefore the answer is 3/7

Hey there!

24/56

= 24 ÷ 8 / 56 ÷ 8

= 3/7

Therefore, your answer should be:

3/7

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The value of b in the equation of common external tangent to both the given circles is 3.75.

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The LCM of 34 using prime factorisation method is 2 and 17

The equation that represents the line that passes through the point (6, −3) and has a slope of one half is 2y - x = 13.

The equation of a line is represented as,

y = mx + c                                       equation1

x and y are the coordinates of the point from where the line is passing and m is the slope of the line.

As per the question the line is passing from the point (6, -3). This means value of x = 6 and that of y = -3. The slope of line is (1/2), means m = (1/2).

The slope of the line through the point (-1,6) can also be written as   (y - 6)/(x - (-1))  =  (y-6)/(x+1).

i.e., m = (y-6)/(x+1)

On equating both the values of m, we will get

(y-6)/(x+1) = 1/2

On simplifying, we get

2y - 12 = x +1

or  2y - x = 13

The equation that represents the line that passes through the point (6, −3) and has a slope of one half is 2y - x = 13.

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Step-by-step explanation:

THE POINT OF INTERSECTION IS WHERE F(x) = G(x)

[tex](x + 3)(x - 1) = (x + 1)(x - 3) \\ {x}^{2} + 2x - 3 = {x}^{2} - 2x - 3 \\ \\ {x}^{2} - {x}^{2} + 2x + 2x - 3 + 3 = 0 \\ 4x = 0 \\ \frac{4x}{4} = \frac{0}{4} \\ x = 0[/tex]

find the y coordinate by plugging in the value of c in any of the function.You will get thw same value

[tex]g(0) = (0 + 1)(0 - 3) \\ g(0) = 1( - 3) \\ g(0) = y = - 3[/tex]

The point of intersection is (0,-3)

The probability that they are both left-handed is 0.01

Probability is the number of ways of achieving success.

the total number of possible outcomes.

Probability takes values between 0 (no chance) and 1 (certain) inclusive.

Complement Rule (probability that an event doesn't occur): P(A') = 1 - P(A) .

Addition rule: P(A ∪ B) = P(A) + P(B) – P(A ∩ B) .

Multiplication rule: P(A ∩ B) = P(A) × P(B) for independent events. P(A ∩ B)

For both, the persons selected at random are left-handed

10 % out of 100 % are left-handed.

Hence the probability that the person is left-handed

P(L) = 10 /100 = 1 / 10 = 0.1

where P(L) is the probability that the person is left-handed.

Therefore both the persons selected are left-handed

= 0.1 * 0.1

= (0.1)^2

= 0.01

Hence the probability that they are both left-handed is 0.01.

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Answer:

x =52

Step-by-step explanation:

The angles shown are same side interior angles, and when the lines are parallel, same side interior angles add to 180 degrees

< 1 + <2 = 180

x+23    + x+53   = 180

Combine like terms

2x+ 76 = 180

Subtract 76 from each side

2x+76-76 = 180 -76

2x = 104

Divide by 2

2x/2 = 104/2

x =52

Answer:

x = 52

Step-by-step explanation:

Angle 1 and angle 2 are on the same side, and on the inside of the interior. This means that when added together they = 180

We can set up an equation

x+23+x+53 = 180

Simplify: 2x + 76 = 180

Subtract 76 from both sides

2x = 104

Now divide by 2

x = 52

The required code for the pedometer is illustrated below:

steps_per_mile=2000

def steps_to_miles(steps, inches_per_step):

   distance = steps * inches_per_step

   miles = distance / (steps_per_mile * inches_per_step)

   return miles

if __name__ == '__main__':

   steps = int(input())

   inches_per_step=float(input())

   miles_in_pedometer = steps_to_miles(steps,inches_per_step)

   print(f"You walked {steps} steps which are about {miles_in_pedometer:.2f} miles.")

what is a pedometer?

The required code for the pedometer is illustrated below:

steps_per_mile=2000

def steps_to_miles(steps, inches_per_step):

   distance = steps * inches_per_step

   miles = distance / (steps_per_mile * inches_per_step)

   return miles

if __name__ == '__main__':

   steps = int(input())

   inches_per_step=float(input())

   miles_in_pedometer = steps_to_miles(steps,inches_per_step)

   print(f"You walked {steps} steps which are about {miles_in_pedometer:.2f} miles.")

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Answer:

3⁹

Step-by-step explanation:

you can use a calculater and it will give 19683 and 3⁹ gives 19683

The equation of line passing through (1, -17) with slope 4 will be y = 4x - 21 .

What is the slope intercept form of a line ?

The equation of line that can be written as y = mx + c, where m is the slope and c is the line's y-intercept, is known as a slope intercept form.

The equation of a line which is passing through point (1 , -17) with slope m = 4 can be found by using the slope intercept form which is given by :

y = mx + c

Here ; m is the slope and c is the y - intercept of the line.

So ;

The point given is (x , y) = (1, -17) and slope m = 4. Let's use these values to find out the equation of the line. But before that let's find out the value of y-intercept (c).

-17 = (4 × 1) + c

c = - 17 - 4

c = -21

Hence , the equation of line passing through (1, -17) will be :

y = 4 ×  x + (-21)

or

y = 4x - 21

Therefore , the equation of line passing through (1, -17) with slope 4 will be y = 4x - 21 .

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Avani needs 6 cups of yogurt.

To find the amount of yogurt required for specified number of smoothies, simple multiplication operation needs to be performed.

For 1 smoothie, the required amount of yogurt = 3/8 cups

So, the required amount of yogurt for 17 smoothies = (3/8) × 17

Performing multiplication and division to find the amount of yogurt required

Amount of yogurt required = 51/8 cups

Converting the fraction into fraction into decimal -

Amount of yogurt required = 6.375 cups

Rounding off the number of cups to convert it in simplest form -

Number of cups of yogurt required = 6 cups

Hence, the amount of yogurt for making 17 smoothies is 6 cups.

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The complete question is -

Avani is making smoothies. Each smoothie uses 3/8 cups of yogurt. How many cups of yogurt does she need to make 17 smoothies? Express your answer in simplest form.

Using proportions, it is found that Kurt spent $22.68 a month on movie streaming services.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, or operations such as multiplication and division.

These operations are used from the unit rates, as for example, when we have an amount over a period of time, the amount per unit of time is the total amount divided by the total time.

For this problem, we have that the important parameters are found as follows:

Hence his monthly spending is given by the unit rate as follows:

96.39/4.25 = $22.68 a month.

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Answer:

No 3

2x+4x+3x+12=0

9x+12=0

9x=0_12

9x=-12

divide by 9

x=1.333

The rate of change of the surface area of the cylinder is approximately to 18.473 square meters per second.

In this question we find a formula for the surface area of a cone, of which we must estimate its rate of change by applying derivative rules and the concept of rate of change. The rate of change is the first derivative of the equation:

ds / dt = 2π · r · (dr / dt) + π · √(r² + h²) · (dr / dt) + π · r · [0.5 / √(r² + h²)] · [2 · r · (dr / dt) + 2 · h · (dh / dt)]

If we know that r = 3 m, h = 4 m, dr / dt = 0.5 m / s and dh / dt = 0.2 m / s, then the rate of change of the surface area of the cone is:

ds / dt = 2π · (3 m) · (0.5 m / s) + π · √[(3 m)² + (4 m)²] · (0.5 m / s) + π · (3 m) · [0.5 / √[(3 m)² + (4 m)²] · [2 · (3 m) · (0.5 m / s) + 2 · (4 m) · (0.2 m / s)]

ds / dt ≈ 18.473 m² /s

The rate of change of the surface area of the cylinder is approximately to 18.473 square meters per second.

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Answer:

Choice 1: ∠CFG = ∠FCB

Step-by-step explanation:

∠CFG and  ∠FCB are interior alternate angles and equal only if ABCD||EFG

Answer:

your mixed fraction would be 12 37/100

Step-by-step explanation:

The number has two parts the whole number part is 12, and the decimal part is .37, 12 would be the whole number part of your mixed fraction and we will convert the .37 to become the fraction part of your mixed fraction.

You have to convert the decimal part into a fraction since there are two decimal places you will have 100 in the denominator .37 becomes 37/100 simplify this fraction if possible.

Using the ratio given in the question,

The relation between the quantities of two or more objects—referred to as a ratio—indicates how much of one object is contained in the other. The ratio formula can be used to represent a ratio as a fraction. The ratio formula is given as, for any two quantities, let's assume a and b.

a:b = a/b

Given that James, Fay and Sal share 160 apples.

Total number of apples =  160

Hence, apples received by James = 1/4(160)

= 40 apples

Remaining apples = 160 - 40 = 120 apples

It is also given that the remainder is shared by Fay and Sal in the ratio 3:2.

Hence, the total share will be 3+2=5

So, we can write that Fay's share will be 3/5 of total apples and Sal's share will be 2/5 of the total apples.

Fay's share = 3/5(120)

=3(24)

=72 apples

Sal's share = 2/5(120)

=2(24)

=48 apples

Therefore, the number of apples with Fay is 72.

The number of apples with Sal is 48.

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the probability is pinapple 53/58

lemon 2/58

watermelon 3/58

The given values are

A pineapple chew was selected 53 Times

A lemon chew was selected 2 times

A watermelon chew was selected 3 times

The probability that you Bella remove from the bag is pineapple chew.

Probability is which we can't predict actual it is usually about the prediction

As we know

Probability - expected outcome/total outcome

The question Bela perform experiment 58 times then the total outcome will be 58 if you pineapple was selected 53 times the probability of the chew Bella pick of pineapple is 53/58

The probability of Bella pick chew of lemon -2/58

The probability of Bella pick watermelon is - 3/58

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The area of the circle with the radius is 192 square feet

The figure represents the given parameter

On the figure, we have the radius (r) to be

r = 8 ft

The area of a circle is calculated as

A = πr^2

Where π is given as

π = 3

So, we have

A = 3 * 8^2

Evaluate the exponent

A = 3 * 64

Evaluate the product

A = 192

Hence, the area of the circle with the radius is 192 square feet

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the area of the circle is 201.06