A container releases fuel at a rate of 5 gallons per second. If y represents the amount of fuel remaining in the container and represents the number of seconds that have passed since the fuel started
dispensing, then x and y satisfy a linear relationship.
If the tank begins with 103 gallons, how many gallons will remain after 2 seconds?

Answer:

A ≈ 6538.35 cm²

Step-by-step explanation:

Calculating the area (A) using Heron's formula

A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

where s is the semi perimeter and a, b, c the 3 sides

here

s = 380 ÷ 2 = 190

given perimeter = 380 and unequal side is 150 , then

equal sides = (380 - 150) ÷ 2 = 230 ÷ 2 = 115 cm

then a = 150, b = 115 , c = 115

A = [tex]\sqrt{190(190-150)(190-115)(190-115)}[/tex]

   = [tex]\sqrt{190(40)(75)(75)}[/tex]

   = [tex]\sqrt{42750000}[/tex]

   ≈ 6538.35 cm² ( to 2 dec. places )

The probability that the mean number of hours spent playing video games is less than 42.8 hours  is   0.15866

we are  given the  mean of ( m )= 43 hours and the standard deviations (s) of  2 hours, where the sample size (n) =  100.

Obtain the Zscore ;

Z = (x - m) ÷s/sqrt(n)

Z = (42.8 - 43) ÷ 2/sqrt(100)

Z = - 0. 2 ÷ 0.2

Z = - 1

so we need the probability of P(Z < - 1), from the  table  of  z-score  the probability of a z-score of -1  is   0.15866.Hence, the probability that the mean number of hours spent playing video games is less than 42.8 hours is 0.15866

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The distance on the map, in cm, given the real distances, and the scale of the map are:

A scale of 1 : 200, 000 means that every 1 cm on the map is 200, 000 cm on the ground.

To find the distance on the map of 10 km, first convert it to cm:
= 10 km x 100, 000 cm per km

= 1, 000, 000 cm

The distance on the map is therefore:

= 1, 000, 000 / 200, 000 cm scale

= 5 cm on map

The distance of 15 km on the map is:

= (15 km x 100, 000) / 200, 000

= 7.5 cm

The distance of 4 km is:

= (4 x 100, 000) / 200, 000

= 2 cm

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The number that will be next in the series will  be  63 .

In the question ,

a recurrence relation is given that is  0, 3, 8, 15, 24, 35, 48, ? .

we have to find the number that will come in place of question mark .

On carefully examining the series , we can see that

3 - 0 = 3

8 - 3 = 5

15 - 8 = 7

24 - 15 = 9

35 - 24 = 11

48 - 35 = 13

we can se that increments 3,5,7,9,11,13,... form an Arithmetic Progression

with first term as 3 and common difference as 2 ,

So ,the next increment will be 13+2 = 15

let the next term be "x" .

x - 48 = 15

x = 15 + 48 = 63

the number in place of ? is 63 .

Therefore , The number that will be next in the series will  be  63 .

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Explanation:

In 1 month, 1.27cm grows.

So, multiply 1.27cm by 4 months to get 5.08cm

Let's set "a number" to "x":

7*6 - x

This can be simplified to:

42 - x

Answer:

480 lbs

Step-by-step explanation:

First, find the ratio of weight on the moon to weight on the earth. I will put the two known values in a fraction like this:

[tex]\frac{25}{150}[/tex]

Now, I can create a proportion, making sure to keep the same types of measurements in the numerator and denominator. I will use w for the unknown weight on earth.

[tex]\frac{25}{150}=\frac{80}{m}[/tex]

Now, I will simplify the fractions as much as I can.
[tex]\frac{1}{6}=\frac{80}{m}[/tex]

Now, I can see a correlation. 1 times 80 is 80, so 6 times 80 is m. Simplified, here is the answer!

[tex]6*80=m\\480=m\\m=480[/tex]

Answer:

480 pounds

Step-by-step explanation:

we times for objects on earth and divide for objects on the moon by the same number

150

[tex]150 \div x = 25[/tex]

150/-25=-x

-6/-1= -x/-1

6=x

[tex]150 \div 6 = 25[/tex]

so when in object is on earth you multiple by x Wich 6

[tex]80 \times 6 = 480[/tex]

you can also cross multiply

The coordinates of each base is listed below

preimage     image

1 (3, 3)         1. (3, -3)

2 (13, 3)       2' (3, -13)

3 (3, 13)       3' (13, -3)

Rotation is one of  the numerous types of transformation. it involves circular movement about an axis

The transformation rule for 270° counterclockwise rotation

(x, y) → (y, -x)

The preimage coordinates of the base field and the image coordinates

Applying the transformation rule  rule gives

preimage      image

1 (3, 3)    →      1. (3, -3)

2 (13, 3)  →      2' (3, -13)

3 (3, 13)  →      3' (13, -3)

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The Y-intercept, or b is -3 because it is where the line touches the Y-axis. The slope, or m is 1/2 because from -3, the line goes up one, and right two. Therefore, the equation is y=1/2-3.

The graph of the image of the triangle in the question following the dilation by a scale factor of (5/3) with vertices (10, 15), (10, 10), (15, 10) created with MS Excel is attached.

In a dilation transformation, the dimensions of the original figure is changed by multiplying the lengths by a scale factor.

The coordinates of the vertices of the triangle in the are (6, 9), (6, 6), and (9, 6)

The coordinate of a point (x, y) following a dilation by a scale factor of k, centered at the origin is the point (k·x, k·y)

The coordinates of the vertices of the image of the triangle in the question following a dilation of 5/3 centered at the origin, are therefore;

(6, 9)      [tex]\overset{R_{5/3}}\longrightarrow[/tex]  ((5/3)×6, (5/3)×9) = (10, 15)

(6, 6)      [tex]\overset{R_{5/3}}\longrightarrow[/tex]  ((5/3)×6, (5/3)×6) = (10, 10)

6(9, 6)      [tex]\overset{R_{5/3}}\longrightarrow[/tex]  ((5/3)×9, (5/3)×6) = (15, 10)

The graph of the image of the triangle following a dilation by a scale factor of 5/3) can therefore be plotted using points (10, 15), (10, 10), and (15, 10) and the plot function on MS Excel

Please find attached the graph of the image of the triangle following a dilation by a scale factor of (5/3) about the origin.

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Answer:

  -6, 1

Step-by-step explanation:

You want the real roots of the quadratic x^2 + 5x = 6.

The roots are easily identified from the factored form of the equation. The factors will involve the constants that have a sum of +5 and a product of -6.

  -6 = 6·(-1) = 3·(-2)

Sums of the factor pairs are 5 and 1. We will use the constants that have a sum of 5.

  x^2 +5x = 6 . . . . . . given

  x^2 +5x -6 = 0 . . . . . standard form

  (x +6)(x -1) = 0 . . . . . . . factored form

The zero product rule tells us that a product will be zero if and only if at least one of the factors is zero. To find the values of x, we set the factors equal to zero and solve for x.

  (x +6) = 0   ⇒   x = -6

  (x -1) = 0   ⇒   x = 1

  x = -6, or x = 1 . . . . . . . . roots of the quadratic

Answer:20%

Step-by-step explanation: Since 2% of x = 4, that would mean 1% would equal 2. So 2 times 100 equals 200, making 20 10% of 200

The price of one sweater is $15 and the price of one shirt is $10.

The first step is to form a set of linear equations using the information provided in the question:

s + 4p = $55 equation 1

4s + 5p = $110 equation 2

Where:

In order to determine the value of p, take the following steps:

Multiply equation 1 by 4

4s + 16p = 220 equation 3

Subtract equation 2 from equation 3:

11p = 110

Divide both sides of the equation by 11

p  = 110 / 11

p = 10

In order to determine the value of s, substitute for p in equation 1:

s + 4(10) = $55

s + 40 = 55

s = 55 - 40

s = 15

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You got to set it up to boys to girls

Answer:

0,1

Step-by-step explanation:

simplest form

A student skipped the step  (1 minute / 60 seconds).

The time in seconds divided by 3,600 results in the time in hours.

Given:

A student skipped a step when he tried to convert 720 seconds into hours, and he got the following incorrect result;

720 seconds (1 hour / 60 minutes) = 12 hours.

In order to convert the seconds to hours:

First, we should convert the seconds to minutes.

And the rate of conversion is 1 minute per 60 seconds.

720 / 60 = 12 minutes.

Now, converting minutes to hours.

And the rate of conversion is 60 minutes per hour.

12/60 = 1/5 hours.

Therefore, student skipped the step where rate of conversion is (1 minute / 60 seconds).

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Answer:

x = 1/8

Step-by-step explanation:

divide the two from both both sides

1/4 = 2x

(1/4)/2 = x/2

1/8 = x

Answer: x = -2

Step-by-step explanation:

X is -2 because whenever you get a negative exponent you gotta make it into a fraction which is [tex]\frac{1}{4}[/tex] because I ignored the negative sign for a second and did it normally so 2 to the power of 2 is 4 put it as a fraction 1 over 4.

Normally it doesn’t happen to every problem you get. Most of the time you gotta divide the numerator by the denominator which will give you .25 in this case scenario, .25 converted to a fraction would be 1/4.

- Your Welcome.

That would be x+4=2x+3, so we must use substitution. Making x=1, hope that helps.

The fourth option D is a function of the form of f(x) = ax(x-2)(x+2) where a is a constant.

We know that any function of the form y = f(x) will pass through the x axis at points such that there is only 1 value of x for a value of y.

Of all the options given the option D is in the form of polynomial expression which crosses the x-axis at points (-2,0 ) ,  (0,0) and (0,2).

The graph of the function at D will be of the form:

f(x) = ax(x-2)(x+2) a is a constant.

At y = 0 , x =-2 ,0 and 2.

Therefore for one value of y there are 3 values of x. but every value of x is mapped into one single value of y only.

For option A at x = 2 , y ahs two values -2 and 2 so it is not a function of x.

For option B  the graph is not differentiable at certain points, hence it is not a function.

For option C again y has 2 values for a single x.

The values of x are used to denote the roots and zeros of the expression, which are also on the left side of the equation, and to satisfy the equation. A quadratic problem should only have two possible solutions. One contends that if there is just one solution, the problem has numerous causes.

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To generate the overall equation A → 2C, should be B → 2C added to  

A → B gives the equation A + B → B + 2C.  

In mathematics, an equation is a method that expresses the equality of two expressions, by using connecting them with the equals signal =. The phrase equation and its cognates in other languages may also have subtly exclusive meanings; for example, in French, an equation is described as containing one or more variables, at the same time as in English, any nicely shaped formula together with expressions associated with an equal’s signal is an equation.

Solving an equation containing variables includes determining which values of the variables make the equality actual. The variables for which the equation must be solved are also known as unknowns, and the values of the unknowns that satisfy the equality are referred to as solutions of the equation. Equations come in two varieties: identities and conditional equations. An identification is actual for all values of the variables. A conditional equation is handiest genuine for unique values of the variables.

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Answer:

9

Step-by-step explanation:

guess

The total number of toys is 45 Samuel if Samuel has a collection of toy cars. His favorites are the 27 red ones.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

Samuel has a collection of toy cars. His favorites are the 27 red ones.

Let Samuel has x number of toys:

From the equation:

60% of x = 27

(60/100)x = 27

0.6x = 27

x = 27/0.6

x = 45

Thus, the total number of toys is 45 Samuel if Samuel has a collection of toy cars. His favorites are the 27 red ones.

The complete question is:

Samuel has a collection of toy cars. His favorites are the 27 red ones which make up 60% of his collection. How many toy cars does Samuel have?

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Answer: 163$

Step-by-step explanation:

Measures which examine the spread of different values around the measures of central tendency is measures of variability.

A central tendency in statistics is a typical or characteristic value for a probability distribution. Measures of central tendency are commonly referred to as averages in everyday speech. In the late 1920s, the phrase "central tendency" first appeared. The arithmetic mean, the median, and the mode are the three most popular ways to measure central tendency. The number used to represent the center or middle of a set of data values is known as the central tendency measure.

Given,

Measures which examine the spread of different values around the measures of central tendency:

B. Measures of variability

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Answer:

The voltage in an electrical circuit is multiplied by itself each time it is reduced. The voltage is 27 /125 of a volt and has been reduced 3 times.

Write the voltage in exponential form.

What was the original voltage in the circuit?

Step-by-step explanation:

voltage = v

v³ - exponential form

v³ = 27/125

make v³ a fraction so v³/1 then cross multiply

so... 125v³ = 27 then v³ = 27/125 or v³ = 0.216 if you like decimals better then to get v by it self you cube root mean v = ∛27/125

original voltage in circuit - v = ∛27/125

Answer:108x10 to the 2nd power

Step-by-step explanation: Given, the diameter of the Sun is 1.4 × 10⁹ m. The diameter of the Earth is 1.2756 × 10⁷ m. We have to compare the diameters by division. Therefore, the diameter of the Sun is nearly 110 times the diameter of the Earth, So i would say 108x10 squared

Answer:

Math = 63

Step-by-step explanation:

Math = x

Eng = Math + 8

Geo = Math + 3

Math + Eng + Geo = 200

Substitute Eng and Geo with information above

Math + (Math + 8) + (Math + 3) = 200

3Math + 8 + 3 = 200

3Math + 11 = 200

3Math = 200 - 11

3Math = 189

Math = 189 ÷ 3

Math = 63

Answer:

D

Step-by-step explanation:

D) 1755 yards is the closest amount to 1760 yards, which is how much is in a mile

Answer:

(i)15v=10r

Step-by-step explanation:

let no. of rice=r

let stir fry=s

let no. of veggies=v

6r=4v

then if,  v=15, r=?

if 6r=4v, then v=6/4r

v=2/3r,

1X v= 1X2/3 r

15 X v= 15X2/3r

25v=5X2r=10r