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2 years ago

14

In a period of 2 and one-fourth hours, 5 and one-half gallons of water leaked from a water tank. How much water did the tank los

e per hour?
Which division problem represents the problem?

1 answer:

pantera1 [17]2 years ago

7 0

Answer:

-11/2 divided by 9/4

You might be interested in

Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 60 miles in the same time that Dana travels 52 miles. If

Alex Ar [27]

30 mph, because Chuck travels 8 miles more, 8 divided bz 4 is two, so thez both travel for two hours, 60 divided bz 2 is 30 and thats the answer

8 0

3 years ago

During April of 2013, Gallup randomly surveyed 500 adults in the US, and 47% said that they were happy, and without a lot of str

Brilliant_brown [7]

Answer:

number of successes

$k = 235$

number of failure

$y = 265$

The criteria are met

A

The sample proportion is $\r p = 0.47$

B

$E =4.4 \%$

C

What this mean is that for N number of times the survey is carried out that the which sample proportion obtain will differ from the true population proportion will not more than 4.4%

Ci

$r = 0.514 = 51.4 \%$

$v = 0.426 = 42.6 \%$

D

This 95% confidence interval mean that the the chance of the true population proportion of those that are happy to be exist within the upper and the lower limit is 95%

E

Given that 50% of the population proportion lie with the 95% confidence interval the it correct to say that it is reasonably likely that a majority of U.S. adults were happy at that time

F

Yes our result would support the claim because

$\frac{1}{3 } \ of N < \frac{1}{2} (50\%) \ of \ N , \ Where\ N \ is \ the \ population\ size$

Step-by-step explanation:

From the question we are told that

The sample size is $n = 500$

The sample proportion is $\r p = 0.47$

Generally the number of successes is mathematical represented as

$k = n * \r p$

substituting values

$k = 500 * 0.47$

$k = 235$

Generally the number of failure is mathematical represented as

$y = n * (1 -\r p )$

substituting values

$y = 500 * (1 - 0.47 )$

$y = 265$

for approximate normality for a confidence interval criteria to be satisfied

$np > 5 \ and \ n(1- p ) \ >5$

Given that the above is true for this survey then we can say that the criteria are met

Given that the confidence level is 95% then the level of confidence is mathematically evaluated as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha =0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table, the value is

$Z_{\frac{ \alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p (1- \r p}{n} }$

substituting values

$E = 1.96 * \sqrt{ \frac{0.47 (1- 0.47}{500} }$

$E = 0.044$

=> $E =4.4 \%$

What this mean is that for N number of times the survey is carried out that the proportion obtain will differ from the true population proportion of those that are happy by more than 4.4%

The 95% confidence interval is mathematically represented as

$\r p - E < p < \r p + E$

substituting values

$0.47 - 0.044 < p < 0.47 + 0.044$

$0.426 < p < 0.514$

The upper limit of the 95% confidence interval is $r = 0.514 = 51.4 \%$

The lower limit of the 95% confidence interval is $v = 0.426 = 42.6 \%$

This 95% confidence interval mean that the the chance of the true population proportion of those that are happy to be exist within the upper and the lower limit is 95%

Given that 50% of the population proportion lie with the 95% confidence interval the it correct to say that it is reasonably likely that a majority of U.S. adults were happy at that time

Yes our result would support the claim because

$\frac{1}{3 } < \frac{1}{2} (50\%)$

3 0

2 years ago

Given the graph below, answer the following questions

Anton [14]

Y=-2x-6
reflect over the y axis
down one
to the left 4

4 0

2 years ago

What is the solution set of (x-2)(x-3)=3

natali 33 [55]

Answer:

x =(5-√13)/2= 0.697

x =(5+√13)/2= 4.303

Step-by-step explanation:

Step 1 :

Equation at the end of step 1 :

(x - 2) • (x - 3) - 3 = 0

Step 2 :

Trying to factor by splitting the middle term

2.1 Factoring x2-5x+3

The first term is, x2 its coefficient is 1 .

The middle term is, -5x its coefficient is -5 .

The last term, "the constant", is +3

Step-1 : Multiply the coefficient of the first term by the constant 1 • 3 = 3

Step-2 : Find two factors of 3 whose sum equals the coefficient of the middle term, which is -5 .

-3 + -1 = -4

-1 + -3 = -4

1 + 3 = 4

3 + 1 = 4

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step 2 :

x2 - 5x + 3 = 0

Step 3 :

Parabola, Finding the Vertex :

3.1 Find the Vertex of y = x2-5x+3

Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 2.5000

Plugging into the parabola formula 2.5000 for x we can calculate the y -coordinate :

y = 1.0 * 2.50 * 2.50 - 5.0 * 2.50 + 3.0

or y = -3.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = x2-5x+3

Axis of Symmetry (dashed) {x}={ 2.50}

Vertex at {x,y} = { 2.50,-3.25}

x -Intercepts (Roots) :

Root 1 at {x,y} = { 0.70, 0.00}

Root 2 at {x,y} = { 4.30, 0.00}

Solve Quadratic Equation by Completing The Square

3.2 Solving x2-5x+3 = 0 by Completing The Square .

Subtract 3 from both side of the equation :

x2-5x = -3

Now the clever bit: Take the coefficient of x , which is 5 , divide by two, giving 5/2 , and finally square it giving 25/4

Add 25/4 to both sides of the equation :

On the right hand side we have :

-3 + 25/4 or, (-3/1)+(25/4)

The common denominator of the two fractions is 4 Adding (-12/4)+(25/4) gives 13/4

So adding to both sides we finally get :

x2-5x+(25/4) = 13/4

Adding 25/4 has completed the left hand side into a perfect square :

x2-5x+(25/4) =

(x-(5/2)) • (x-(5/2)) =

(x-(5/2))2

Things which are equal to the same thing are also equal to one another. Since

x2-5x+(25/4) = 13/4 and

x2-5x+(25/4) = (x-(5/2))2

then, according to the law of transitivity,

(x-(5/2))2 = 13/4

We'll refer to this Equation as Eq. #3.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

(x-(5/2))2 is

(x-(5/2))2/2 =

(x-(5/2))1 =

x-(5/2)

Now, applying the Square Root Principle to Eq. #3.2.1 we get:

x-(5/2) = √ 13/4

Add 5/2 to both sides to obtain:

x = 5/2 + √ 13/4

Since a square root has two values, one positive and the other negative

x2 - 5x + 3 = 0

has two solutions:

x = 5/2 + √ 13/4

or

x = 5/2 - √ 13/4

Note that √ 13/4 can be written as

√ 13 / √ 4 which is √ 13 / 2

Solve Quadratic Equation using the Quadratic Formula

3.3 Solving x2-5x+3 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

2A

In our case, A = 1

B = -5

C = 3

Accordingly, B2 - 4AC =

25 - 12 =

13

Applying the quadratic formula :

5 ± √ 13

x = —————

2

√ 13 , rounded to 4 decimal digits, is 3.6056

So now we are looking at:

x = ( 5 ± 3.606 ) / 2

Two real solutions:

x =(5+√13)/2= 4.303

or:

x =(5-√13)/2= 0.697

4 0

3 years ago

Read 2 more answers

Find the next term in the sequence 1, 4, 9, 16, 25, ….

Agata [3.3K]

The next is 36!!!! If you notice each time, you are adding by two more than what you were adding before. Like, 1+3=4 4+5=9 9+7=16 See?

So, 25+11=36

7 0

2 years ago