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liq [111]
3 years ago
10

A popular chain of superstores made 3.0479×108 dollars in profit last year. One particular store in the chain made 2.102×106 dol

lars in profit last year. How many times greater is the profit made by the entire chain last year than by this particular store? Drag and drop the values into the boxes to represent the answer in scientific notation. 0.145
1.45
145
​10²​​​
10^14​
​10^48​
Mathematics
1 answer:
ollegr [7]3 years ago
7 0
This is a simple exercise with rates.
You just have to divide the total profit of the store, that year, per the profit of the particular store.


[3.0479×10⁸ dollars] ÷ [2.102×10⁶ dollars] = 1,45 x 10²





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ra1l [238]
A=5 4/7 or 5.57142857143 
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3 years ago
How many solutions does the system of equations below have?
soldier1979 [14.2K]

Answer:

One solution                    

Step-by-step explanation:

5x + y = 8

15x + 15y = 14

Lets solve using substitution, first we need to turn "5x + = 8" into "y = mx + b" or slope - intercept form

So we solve for "y" in the equation "5x + y = 8"

5x + y = 8

Step 1: Subtract 5x from both sides.

5x + y − 5x = 8 − 5x

Step 2: 5x subtracted by 5x cancel out and "8 - 5x" are flipped

y = −5x + 8

Now we can solve using substitution:

We substitute "-5x + 8" into the equation "15x + 15y = 14" for y

So it would look like this:

15x + 15(-5x + 8) = 14

Now we just solve for x

15x + (15)(−5x) + (15)(8) = 14(Distribute)

15x − 75x + 120 = 14

(15x − 75x) + (120) = 14(Combine Like Terms)

−60x + 120 = 14

Step 2: Subtract 120 from both sides.

−60x + 120 − 120 = 14 − 120

−60x = −106

Divide both sides by -60

\dfrac{ -60x  }{ -60  }   =   \dfrac{ -106  }{ -60  }

Simplify

x =   \dfrac{ 53  }{ 30  }

Now that we know the value of x, we can solve for y in any of the equations, but let's use the equation "y = −5x + 8"

\mathrm{So\:it\:would\:look\:like\:this:\ y =  -5 \left(  \dfrac{ 53  }{ 30  }    \right)  +8}

\mathrm{Now\:lets\:solve\:for\:"y"\:then}

y =  -5 \left(  \dfrac{ 53  }{ 30  }    \right)  +8}

\mathrm{Express\: -5 \times   \dfrac{ 53  }{ 30  }\:as\:a\:single\:fraction}

y =   \dfrac{ -5 \times  53  }{ 30  }  +8

\mathrm{Multiply\:-5 \:and\:53\:to\:get\:-265 }

y =   \dfrac{ -265  }{ 30  }  +8

\mathrm{Simplify\:  \dfrac{ -265  }{ 30  }    \:,by\:dividing\:both\:-265\:and\:30\:by\:5} }

y =   \dfrac{ -265 \div  5  }{ 30 \div  5  }  +8

\mathrm{Simplify}

y =  - \dfrac{ 53  }{ 6  }  +8

\mathrm{Turn\:8\:into\:a\:fraction\:that\:has\:the\:same\:denominator\:as\: - \dfrac{ 53  }{ 6  }}

\mathrm{Multiples\:of\:1: \:1,2,3,4,5,6}

\mathrm{Multiples\:of\:6: \:6,12,18,24,30,36,42,48}

\mathrm{Convert\:8\:to\:fraction\:\dfrac{ 48  }{ 6  }}

y =  - \dfrac{ 53  }{ 6  }  + \dfrac{ 48  }{ 6  }

\mathrm{Since\: - \dfrac{ 53  }{ 6  }\:have\:the\:same\:denominator\:,\:add\:them\:by\:adding\:their\:numerators}

y =   \dfrac{ -53+48  }{ 6  }

\mathrm{Add\: -53 \: and\: 48\: to\: get\:  -5}

y =  - \dfrac{ 5  }{ 6  }

\mathrm{The\:solution\:is\:the\:ordered\:pair\:(\dfrac{ 53  }{ 30  }, - \dfrac{ 5  }{ 6  })}

So there is only one solution to the equation.

5 0
2 years ago
Five cats each ate 1/4 cup of canned food . How much food did they eat altogether?
Sauron [17]

We have FIVE cats that each ate 1/4 cup of canned food.

Then, the five of them together ate:

5 times 1/4 cup This in mathematical expression is a profduct of an integer value (5) times the fraction (1/4) which we know how to multiply based on the problems we solved a few minutes ago:

5 * 1/4 = 5/1 * 1/4 = (5 * 1) / (1 * 4) = 5/4 cups

This answer can also be written as a MIXED number given that 5/4 is an IMPROPER fraction (a fraction with numerator larger than the denominator)

5/4 = 1 1/4

Not sure what answer your teacher would prefer. It depends on whether he/she wants you to use fractions or mixed numbers.

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tiny-mole [99]

Answer:

(a) H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test.

Step-by-step explanation:

We formulate the

H0: μ1=μ2; null hypothesis that the two means are equal and alternate hypothesis that the two mean are not equal.

Ha:μ1≠μ2 Two tailed test

Test statistic used is

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T value for 9 degrees of freedom for two tailed test at α = 0.05 is 2.26

P- value for t test for 9 degrees of freedom is 0.125 from the table.

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Tju [1.3M]

Answer:

All Real Numbers except for 4

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Objective: Specify domain and range of a function.

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