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3 years ago

Which expressions are equivalent to 6^16? Check all that apply.

Mathematics

1 answer:

gayaneshka [121]3 years ago

4 0

Answer: (6^-4)^-4 , (6^-2)^-8, (6^8)^2

Step-by-step explanation:

When there is a number with an exponent in a parenthesis raised to another exponent, you multiply the two exponents together. So, in this case we are looking for 2 exponents that give us a product of 16.

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A simple random sample of size nequals17 is drawn from a population that is normally distributed. The sample mean is found to be

IRINA_888 [86]

Answer:

95% confidence intervals about the population mean is

(51.7656 , 60.2344)

Step-by-step explanation:

Step(i):-

Given random sample of size 'n' =17

Given mean of the sample 'x⁻' = 56

Given standard deviation of sample 's' = 10

95% confidence intervals about the population mean is determined by

$(x^{-} - t_{0.05} \frac{s}{\sqrt{n} } ,x^{-} + t_{0.05} \frac{s}{\sqrt{n} } )$

Degrees of freedom

ν = n-1 = 17-1 =16

t₀.₀₅ = 1.7459 (from t-table)

Step(ii):-

95% confidence intervals about the population mean is determined by

$(x^{-} - t_{0.05} \frac{s}{\sqrt{n} } ,x^{-} + t_{0.05} \frac{s}{\sqrt{n} } )$

$(56 - 1.7459 \frac{10}{\sqrt{17} } ,56 + 1.7459 \frac{10}{\sqrt{17} } )$

( 56 - 4.2344 , 56 + 4.2344)

(51.7656 , 60.2344)

Conclusion:-

95% confidence intervals about the population mean is

(51.7656 , 60.2344)

4 0

3 years ago

A rectangular swimming pool has a perimeter of 96 ft. The area of the pool is 504 ft2. Which system of equations models this sit

gregori [183]

Answer:

2l + 2w = 96 ..... eqn1

lw = 504 ...... eqn2

Step-by-step explanation:

To model this case where we have two unknowns l and w, we need two equations.

Firstly, the perimeter of a rectangle is given by

2l + 2w = p

Where l,w and p are length, width and perimeter of the rectangle respectively.

Hence,

2l + 2w = 96 ... eqn1

Secondly, the area of a rectangle is given by

Length × width = Area

Hence,

l × w = 504

lw = 504 ... eqn2

With these two equations the solutions to the length and width of the rectangular pool can be derived.

3 0

4 years ago

Help please!!! I have a few late assignments and there due tomorrow T^T

vodomira [7]

Answer:

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

The volume of Solid A is 171.5 m and the volume of Solid B is 500 m, If the solids are similar, find the scale factor of Solid A

Bond [772]

Answer:

The scale factor is $1.429$

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z----> the scale factor

x----> volume of solid B

y ----> volume of solid A

$z^{3}=\frac{x}{y}$

we have

$x=500\ m^{3}$

$y=171.5\ m^{3}$

substitute

$z^{3}=\frac{500}{171.5}$

$z=\sqrt[3]{\frac{500}{171.5}}=1.429$

3 0

3 years ago

At the local dairy farm, Kareem buys a 32-oz container of yogurt for $2.56. Jonah buys a 6-oz container of yogurt for $0.48. Are

vodka [1.7K]

Answer:

Yes, the cost $y$ in dollars and the amount of yogurt $x$ are proportional.

The equation is: $y=0.08x$

Step-by-step explanation:

1. If $y$ varies directly as $x$ , you can write it as following:

$y=kx$

Where $k$ is the constant of proportionality.

2. Let's calculate the value of the constant of proportionality. If $y=2.56$ and $x=32$ , you have:

$y=kx\\k=\frac{y}{x}\\k=\frac{2.56}{32}\\k=0.08$

3. Then, the equation is:

$y=0.08x$

4. Let's verify if they are directly proportional. Substitute $x=6$ which is the amount of yogurt bought by Jonah. The result must be $0,48:

$y=0.08(6)\\y=0.48$

5. They are directly proportional.

6 0

4 years ago

Read 2 more answers