Question 3(Multiple Choice Worth 5 points) (01.06) Jack and Jill had 5 pails of water. Each trip up the hill, Jack and Jill obtained 2 more buckets of water. Which of the graphs below represents Jack and Jill's number of pails over time? graph of line going through 1, 7 and 2, 12 graph of line going through 1, 7 and 3, 11 graph of line going through 2, 6 and 4, 7 graph of line going through 0, 2 and 6, 3

Answer:

C) 89 degrees

Step-by-step explanation:

Given:

The given angle is -271. which is standard position

We have to subtract 271 from 360 to find the required angle.

= 360 -271

= 89 degrees.

The answer is C) 89 degrees

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Humans can hear up to 20,000 Hz, written as 2.0 x 10⁴ Hz in scientific notation, while dolphins can hear up to 150,000 Hz, written as 1.5 x 10⁵ Hz.

Humans can hear sounds with frequencies up to 20,000 Hz, while dolphins can hear sounds as high as 150,000 Hz. These numbers can be written in scientific notation as follows:

20,000 Hz = 2.0 x 10⁴ Hz

150,000 Hz = 1.5 x 10⁵ Hz

Writing these frequencies in scientific notation helps simplify and understand large numbers easily.

The y - intercept of the line is 0.

We have f(x) = 3x

We have to find the y - intercept of this function f(x).

The general equation of a straight line is as follows -

y = mx + c

where -

m - slope of line

c - intercept of line on y - axis.

According to question, we have -

f(x) = 3x

or

f(x) = 3x + 0

Comparing it with the general equation of a straight line, we get -

y = f(x)

m = 3

c = 0

Here, c is the y - intercept of the line f(x) = 3x.

Hence, the y - intercept of the line is 0.

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Answer: After 24 minutes Chris begins riding so, he catch up to Samir.

Step-by-step explanation:

Since we have given that

Speed of Samir riding his bike = 6mph

Speed of Chris riding his bike = 9 mph

Time taken by Chris be x

Time taken by Samir be x+12

AS we have given that at any given time ,t, the distance traveled can be using the formula " d=rt "

where d means distance and r represents rate.

So, our equation becomes,

[tex]9x=6(x+12)\\\\9x=6x+72\\\\9x-6x=72\\\\3x=72\\\\x=\frac{72}{3}=24\ minutes[/tex]

As there is no need to change mph into miles per minutes as applying both will nullify the effect.

Hence, after 24 minutes Chris begins riding so, he catch up to Samir.

since gecko is 1/ the length of an iguana,

 that would mean iguanas are twice as long as geckos

 so 4*2 = 8 inches for iguanas 

The value of the expression is 25

An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.

Given is an expression, 8√8.41 +1.8

8√8.41 +1.8

= 8×2.9 + 1.8

= 23.2 + 1.8

= 25

Hence,  the value of the expression is 25

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The approximate value of the expression [tex]\( 8\sqrt{8.41} + 1.8 \)[/tex] is 25.016.

To evaluate the expression [tex]\( 8\sqrt{8.41} + 1.8 \)[/tex], follow these steps:

1. First, approximate the square root of 8.41. The square root of 8.41 is approximately 2.902, because [tex]\( 2.902^2 \approx 8.41 \)[/tex].

2. Now, multiply this approximate square root by 8:

[tex]\[ 8 \times 2.902 \approx 23.216 \][/tex]

3. Finally, add 1.8 to this result:

[tex]\[ 23.216 + 1.8 \approx 25.016 \][/tex]

Therefore, the approximate value of the expression [tex]\( 8\sqrt{8.41} + 1.8 \)[/tex] is 25.016.

The answer is: 25.016.

To encode a separate x and y coordinate on a 96 x 96 grid, you would need a minimum of 7 bits to represent each coordinate. This is because the nearest power of 2 above 96 is 128, which is 2^7.

The subject of this question deals with using binary numbers, or bits, to store data in two-dimensional space, such as with a coordinate grid or a digital image. In this specific case, a coordinate grid with a size of 96 by 96. When encoding the x and y coordinate as separate numbers, we are trying to represent numbers from 0 to 96, so we have 97 different values to represent.

To calculate how many bits you need to store an integer, the question becomes: how many powers of 2 (bits) does it take to store that many different values? The closest power of 2 greater than 96 is 128, which is 2 to the seventh power (2^7). Therefore, you would need a minimum of 7 bits to store a coordinate in that space.

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5 1/6 - 2 2/3

 convert to improper fractions:

5 1/6 = 31/6

2 2/3 = 8/3

find common denominator:

8/3 = 16/6

31/6 - 16/6 = 15/6

15/6 = 2 3/6 = 2 1/2

The solution of an equation 1/r =1/r1+1/r2 for R is r = r1 r2/(r1 + r2).

The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.

We have been given a equation as

1/r = 1/r1 + 1/r2

Let r1 = x and r2 = y for an instance, then solve for equivalent r.

Therefore,

1/r = 1/x + 1/y

Solving further;

1/r = (y + x)/xy

Or

r = xy/(x +y)

Now substitute the real values of x and y, we get;

r = xy/(x +y)

r = r1 r2/(r1 + r2)

Hence, The solution of an equation 1/r =1/r1+1/r2 for R is r = r1 r2/(r1 + r2).

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If the length of a rectangle is 6 ft greater than the width and the perimeter is 40 ft , then the dimensions of the rectangle will be 6ft x 7ft.

What is the Area of Rectangle?

The area of the rectangle is length times of width.

Let the Length and Width of the rectangle be 'L' and 'B' , then the dimensions of the rectangle will be L x B

Given data , we have L = 6 + B

The perimeter of the rectangle = 40 ft

= 2 x ( L + B ) = 40 ft

= 2 x ( 6 + B + B ) = 40 ft  

= ( 6 + 2B ) =  20 ft

Substract both sides by 6

2B = 14 ft

Divide both sides by 2

B = 7 ft

Now , Length of the rectangle will be L = 6 + 7 = 13 ft

Hence, the dimensions of the rectangle is Length x Width = 13 ft x 7 ft

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Two or more expressions with an Equal sign is called as Equation. The number is 16 in sentence one-half of the number is 2 less than two-thirds of the number

Two or more expressions with an Equal sign is called as Equation.

We x be the unknown number which we have to find.

Given,

one-half of the number is 2 less than two-thirds of the number

Which is one-half of the number is x/2

2 less than two-thirds of the number is 2/3 x-2

So let us form a equation

x/2 = 2x/3-2

x/2=(2x-6)/3

Apply cross multiplication

3x=2(2x-6)

Use distributive law on RHS

3x=4x-16

16=4x-3x

16=x

Hence the number is 16 in sentence one-half of the number is 2 less than two-thirds of the number

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Answer:

3x + 8

Step-by-step explanation:

We have to find the sum of (x+5)and(2x+3).

Write it in sum form

x+5+2x+3

Group the like terms first.

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

Combine the like terms

(1+2)x+8

= 3x +8

Therefore, the sum is 3x + 8

The sum of (x+5) and (2x+3) is calculated by adding the coefficients of like terms, which results in 3x + 8.

To find the sum of (x+5) and (2x+3), you simply need to add the like terms. The first step is to add the terms that contain the variable x, and then add the constant terms.

Step 1: Add the x terms together: x + 2x = 3x.

Step 2: Add the constant terms together: 5 + 3 = 8.

Step 3: Combine the results from step 1 and step 2 to get the final sum: 3x + 8.

Therefore, the sum of (x+5) and (2x+3) is 3x + 8.

By setting up two equations based on the total number of tickets and the difference in the number of student and adult tickets, we find that 225 adult tickets were sold for the school play.

To determine the number of adult tickets sold, we can set up two equations based on the information provided. Let A represent the number of adult tickets and S represent the number of student tickets.

The first equation comes from the total number of tickets sold: A + S = 518.

The second equation comes from the additional information about the number of student tickets being greater than adult tickets: S = A + 68.

We can substitute the second equation into the first to solve for A:

Therefore, 225 adult tickets were sold for the school play.

For  A(5, 3) and B(7, -4), the distance is is mathematically given as

Generally, the equation for distance is mathematically given as

[tex]D=\sqrt{(x')^2+(y')^2)}[/tex]

Therefore

[tex]D=\sqrt((7-5)^2+(-4-3)^2)[/tex]

[tex]D=\sqrt{2^2+(-7)^2) }[/tex]

[tex]D=\sqrt(53)[/tex]

D=7.28 units

In conclusion, the distance  is

D=7.28 units

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