Which expression is equivalent to (7^-8)(7^3)

If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when x is 2?

sertanlavr [38]

y = ( 48 *2 ) / 6

Step-by-step explanation:

If y varies directly as x they are directly proportional, which means they relate to each other in the same way....

2 : y = 6: 48

what is y if x = 2?

The value of y can be found if you write it a two fracrions

2 : y = 6 : 48

2 / y = 6 / 48

cross multiply the fractions gives

6*y = 48 *2

divide left and right of the = sign by 6 gives the answer:

y = ( 48 *2 ) / 6

(if you solve it you get y = 12 but that was not the question).

Other method:

multiply left and right of the = sign by y

2 * y/y = y *6 / 48

6y / 48 = 2 * 1

multiply left and right of the = sign by 48

6y * 48/48 = ( 48 *2 )

6y = ( 48 *2 )

divide left and right of the = sign by 6

6/6* y = ( 48 *2 )/6

y = ( 48 *2 ) / 6

(if you solve it you get y = 12 but that was not the question).

4 0

3 years ago

What is a sum of 1/2 and 3/10 in simplest from

Dahasolnce [82]

Answer:

4/5

Step-by-step explanation:

1/2=5/10

5/10+3/10=8/10

simplified or 8/10 divided by 2 =4/5 and u cant simplify it anymore

4 0

3 years ago

Read 2 more answers

A vial contains 80 mg of drug in 2 mL of injection. How many milliliters of the injection should be administered to obtain 0.02

Marina CMI [18]

Answer:

0.5mL of the injection should be administered to obtain 0.02 g of the drug.

Step-by-step explanation:

First step: The first step of this problem is the conversion of 0.02g to mg.

Each gram has 1000 miligrams. So:

1g - 1000mg

0.02g - xmg

x = 1000*0.02

x = 20mg

Final step:

A vial contains 80 mg of drug in 2 mL of injection. How many mL should be administered to obtain 0.02 g = 20mg of the drug.

This can be solved as a rule of three problem.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

In this step, as the dose of the injection increases, so the quantity of the drug. So the relationship between the measures is direct. So:

80 mg - 2mL

20 mg - xmL

80x = 40

$x = \frac{40}{80}$

x = 0.5mL

0.5mL of the injection should be administered to obtain 0.02 g of the drug.

3 0

3 years ago

Calculate the sample variance and sample standard deviation for the following frequency distribution of heights in centimeters f

Zolol [24]

Answer:

$\bar X = \frac{\sum_{i=1}^n X_i f_i}{n}= \frac{22026.1}{171}=128.81$

$s^2 = \frac{2839948.85- \frac{(22026.1)^2}{171}}{171-1}= 16.59$

$s= \sqrt{16.587}=4.07$

Step-by-step explanation:

For this case we can calculate the sample variance and deviation with the following table

Class Midpoint (Xi) fi Xi*fi Xi^2 *fi

120.6-123.6 122.1 17 2075.7 253443

123.7-126.7 125.2 49 6134.8 768077

126.8-129.8 128.3 29 3720.7 477365.8

129.9-132.9 131.4 41 5387.4 707904.4

133.0-136.0 134.5 35 4007.5 633158.8

___________________________________________

Total 171 22026.1 2839948.85

For this case we can calculate the mean or expected value with the following formula:

$\bar X = \frac{\sum_{i=1}^n X_i f_i}{n}= \frac{22026.1}{171}=128.81$

Now we can calculate the sample variance with the following formula:

$s^2 =\frac{\sum f_i X^2_i -[\frac{(\sum X_i f_i)}{n}]^2}{n-1}$

And if we replace we got:

$s^2 = \frac{2839948.85- \frac{(22026.1)^2}{171}}{171-1}= 16.59$

And the standard deviation would be the square root of the variance and we got:

$s= \sqrt{16.59}=4.07$

7 0

4 years ago

Solve the equation, x^2+3x+1=0, using the quadratic formula.

kari74 [83]

Answer:

x = (-3±√5)/2

Step-by-step explanation:

Matching the given equation to the pattern ...

... ax² +bx +c = 0

we see that a=1, b=3, c=1.

The solution to the above pattern is given by the quadratic formula ...

... x = (-b±√(b²-4ac))/(2a)

Substituting the values of a, b, c that we found, the formula gives ...

... x = (-3±√(3²-4·1·1))/(2·1)

... x = (-3±√5)/2

7 0

4 years ago