A water tank contains 1,250 gallons of water. The water is used to fill some 30 gallon barrels. What is the number of the barrels that can be completely filled and how much water is left?

Answer:

[tex]8\frac{1}{8}[/tex] L

Step-by-step explanation:

A recipe of chicken soup calls for chicken stocks = [tex]2\frac{1}{2}[/tex] L

Josh makes [tex]3\frac{1}{4}[/tex] times the recipe

= [tex]3\frac{1}{4}[/tex] × [tex]2\frac{1}{2}[/tex]

= [tex]\frac{13}{4}[/tex] × [tex]\frac{5}{2}[/tex]

= [tex]\frac{65}{8}[/tex]

= [tex]8\frac{1}{8}[/tex]

Josh would use [tex]8\frac{1}{8}[/tex] L of chicken stocks.

Final answer:

To find the formula for f(q), solve the equation 11q-4=3r-6 for r. The steps include adding 6 to both sides and then dividing by 3, resulting in f(q) = (11q + 2) / 3.

Explanation:

To write a formula for f(q) in terms of q, we need to solve the equation 11q - 4 = 3r - 6 for r, the output of the function f. First, we add 6 to both sides to isolate the terms with r on the right side of the equation:

11q - 4 + 6 = 3r - 6 + 6

11q + 2 = 3r

Next, we divide both sides by 3 to solve for r:

(11q + 2) / 3 = 3r / 3

(11q + 2) / 3 = r

Therefore, the formula for f(q) is:

f(q) = (11q + 2) / 3

Answer:

A strong positive correlation

Step-by-step explanation:

Since the dependent variable increases as the independent variable increases, this is a positive correlation.

Plotting these points, we can see that they form a nearly straight line.  This makes it a strong correlation.

A strong positive correlation best describes the strength of the given model. So, option B is correct.

The correlation coefficient is used to measure the strong relationship between the two variables.

The formula for the correlation coefficient

[tex]r= \frac{n(\sum xy)-(\sum x)(\sum y)} {\sqrt{ {[n\sum x^2-(x)^2] [n\sum y^2-(\sum y)^2]}}}[/tex]

We need to calculate the correlation coefficient and then make a conclusion about its value.

Form a table as shown where x is the cost of items and y is the shipping cost. The table becomes

x               y              XY               x²              y²

25           5.99        149.8          625         35.9

45            8.99       404.6         2025       80.8

50            8.99       449.5         2500       80.8

70            10.99      769.3         4900       120.8

190          34.96      1773.2        10050      318.3

The formula for the correlation coefficient

[tex]r= \frac{n(\sum xy)-(\sum x)(\sum y)} {\sqrt{ {[n\sum x^2-(x)^2] [n\sum y^2-(\sum y)^2]}}}[/tex]

where n=4

[tex]= \frac{ 4(1773.2)-(190)(34.96)} {\sqrt{{[4(10050)-190^2] [4(318.3)-34.96^2]}} }[/tex]

r[tex]=\frac{450}{4100\times51}[/tex]

r = 450 / √209100

r = 450/457.3

r = 0.98409

Thus, The value of r indicates a stronger positive correlation.

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The Area of Florida is 65,754.6

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

Given that Florida is 65,754.59 square miles

rounding this nearest to tenth will be  65,754.6  square miles

Therefore, Area of Florida is 65,754.6 square miles

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The two stacks will be the same height when stacked to a height of 6 inches.

To find the shortest height at which two stacks of boxes, one measuring 12 inches tall and the other measuring 18 inches tall, will be the same height, we need to find the least common multiple (LCM) of the two heights. Since 12 and 18 are both divisible by 6, the LCM is 6 inches. Therefore, the two stacks will be the same height when stacked to a height of 6 inches.

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Answer:

reapeating and terminating

Step-by-step explanation:

Answer: its c

Step-by-step explanation:

5+4=9 9+8=17

The equations of the graph after respective transformations are;

13) f(x) = a(x + 2) - 7

14) f(x) = 3(x - 5) + 2

13) In transformations, when we translate a function to the left, it means we will add the number of units it is translated to the left to f(x).

Thus, if we translate 2 units to the left, then using the form f(x) = a(x - h) + k, we will have;

f(x) = a(x + 2) + k

This is because;

h = horizontal shift

k = the vertical shift

a = the factor of stretch.

Now, we are told that it is translated 7 units down.

Downward translation denotes subtraction. Thus, k = -7 and our final translated function is;

f(x) = a(x + 2) - 7

14) Using the same concept above;

Translation of 5 units to the left means h = -5

Also, translation of 2 units up means that k = +2

Stretching by a factor of 3 means that a = 3.

Thus, from the form; f(x) = a(x + h) + k, we have;

f(x) = 3(x - 5) + 2

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Final answer:

To calculate 0.279 times 53, multiply 279 by 53 and then place the decimal point three places from the right of the product, resulting in 14.787. If rounding to two decimal places, the answer is 14.79.

Explanation:

To find the product of 0.279 times 53, we can follow the usual multiplication process. We multiply as if there were no decimal places, and then we count the total number of decimal places in both numbers to place the decimal in the correct position in the final answer.

0.279 has three decimal places, and 53 has none. After you multiply 279 by 53, count three places from the right of the resulting number to place the decimal point. So, if 279 times 53 equals 14787, then 0.279 times 53 equals 14.787.

Applying the rules of rounding, if we wanted to round the result to two decimal places we would get 14.79 since the third decimal place is a 7 which rounds up the second decimal place from 8 to 9.

Answer:

a y=  -x+9

Step-by-step explanation:

Answer:

[tex]3y-x<6[/tex]

[tex]2x+y\leq2[/tex]

Step-by-step explanation:

Equation of line that passes two points (a,b) and (c,d) :

[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]

Dotted line passes through (0,2) and (-3,1).

Equation of Dotted line :

[tex](y-2)=\dfrac{1-2}{-3-0}(x-0)[/tex]

[tex](y-2)=\dfrac{-1}{-3}x[/tex]

[tex]3(y-2)=x[/tex]

[tex]3y-6=x[/tex]

[tex]3y-x=6[/tex]

Inequality for dotted line (values on line is not included for dotted)

[tex]3y-x<6[/tex]  (shaded below )

Solid line passes through (0,2) and (1,0)

[tex](y-2)=\dfrac{0-2}{1-0}(x-0)[/tex]

[tex]y-2=-2x[/tex]

[tex]2x+y=2[/tex]

Inequality for dotted line (values on line is included for solid line)

[tex]2x+y\leq2[/tex] (shaded leftwards )

∴ System of linear inequalities is shown on the graph:

[tex]3y-x<6[/tex]

[tex]2x+y\leq2[/tex]

Answer:

$9.1 per kg of sliced salami.

Step-by-step explanation:

We are supposed to find unit rate for the given scenario.

Hailey paid $13 dollars for 1 3/7 kg of sliced salami.

To find unit rate, we will divide total price by total weight.

[tex]\text{Unit rate}=\$13\div 1\frac{3}{7}\text{ kg}[/tex]

Convert mixed fraction to improper fraction:

[tex]\text{Unit rate}=\$13\div \frac{10}{7}\text{ kg}[/tex]

Convert to division problem by flipping the fraction as:

[tex]\text{Unit rate}=\$13\times\frac{7}{10}\text{ kg}[/tex]

[tex]\text{Unit rate}=\frac{\$13\times7}{10\text{ kg}}[/tex]

[tex]\text{Unit rate}=\frac{\$91}{10\text{ kg}}[/tex]

[tex]\text{Unit rate}=\frac{\$9.1}{\text{ kg}}[/tex]

Therefore, unit rate is $9.1 per kg of sliced salami.

Answer: She cuts 2 pieces

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

So, to calculate the number of pieces we have to divide the length of the board (3/4) by the length of each piece (3/8)

Mathematically speaking:

3/4 ÷ 3/8 = (3x8) /(4x3)=24/12= 2  pieces

Feel free to ask for more if needed or if you did not understand something.

The scientific notation of the given number is 3.708 × [tex]10^9[/tex]. Therefore, option B is the correct answer.

The given number is 3,708,000,000.

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

If the given number is multiples of 10 then the decimal point has to move to the left, and the power of 10 will be positive.

Now, 3,708,000,000 can be written in scientific notation as 3.708 × [tex]10^9[/tex].

The scientific notation of the given number is 3.708 × [tex]10^9[/tex]. Therefore, option B is the correct answer.

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The initial amount given is $10, this represents a constant

Now another friends is willing to give an amount which is not fixed, hence it is dependent on the amount if miles we walk

Let this variable amount be x

We have walks 5 miles in total

We have raid is 13.5 total amount

Therefore he expression to represent the total amount we have made is given as

10+5x= 13.50

Let us solve for x

subtract 10 from both sides we have

5x= 13.5-10

5x= 3.50

divide both sides by 5 we have

x = 3.5/5

x= 0.7

Hence our friend gives us $0.7 per mile

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Answer:  The correct option is

(A) x < 3.

Step-by-step explanation:  Given that one-third of a number is greater than five less than twice the number.

We are to select the inequality that is TRUE.

Let the required number be represented by x.

Then, according to the given information,we have

[tex]\dfrac{1}{3}x>2x-5\\\\\\\Rightarrow x>3(2x-5)\\\\\Rightarrow x>6x-15\\\\\Rightarrow x-6x>-15\\\\\Rightarrow -5x>-15\\\\\Rightarrow 5x<15~~~~~~~~~~[\textup{since }-a>-b~~~\Rightarrow a<b]\\\\\Rightarrow x<\dfrac{15}{5}\\\\\Rightarrow x<3.[/tex]

Thus, the true statement is x < 3.

Option (A) is CORRECT.

he was right, the answer is just flipped, so it's 18≤x≤20