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2 years ago

Which exponent makes this statement true? 1/5^9= 5^?

Mathematics

1 answer:

Aleks04 [339]2 years ago

5 0

Answer:

The exponent -9 makes the given statement true.

Step-by-step explanation:

We have been given an incomplete mathematical statement and we need to figure out the exponent for 5 on the right hand side to complete the statement.

The given incomplete statement is $\frac{1}{5^{9}}=5^{?}$ .

Let us rewrite the left hand side of the expression by moving the exponential term to the numerator using exponent property. As per this property, if we shift an exponential term from denominator to numerator (or vice versa), the sign of exponent changes.

Therefore, we get:

$5^{-9}=5^{?}$

Now that we have common bases on both the sides, we can equate the exponents. And upon equating the exponents, we can see that the 'question mark' should be replaced by -9 in order for statement to be true.

Therefore, exponent -9 on the right hand side will make the statement true.

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2 years ago

Find the slope of (-6,2) and (-4,13)

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2 years ago

Find the area of the rhombus.<br> 4.32 m2<br> 2.16 m2<br> 1.08 m2<br> 1.05 m2

S_A_V [24]

Answer:

Step-by-step explanation:

Alright, lets get started.

The part of the diagonals are given as 0.9 m and 1.2 m.

The diagonals of rhombus intersect each other.

Hence the length of diagonals will be : $0.9*2=1.8$ and $1.2*2=2.4$

The formula of area of rhombus is : $\frac{pq}{2}$ where p and q are the length of diagonals.

So plugging the values of diagonals in formula, the area will be :

Area = $\frac{1.8*2.4}{2}$

Area = $\frac{4.32}{2}$

Area = $2.16 \ m^2$ ................. Answer

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6 0

2 years ago

Two researchers, Jaime and Mariya, are each constructing confidence intervals for the proportion of a population who is left-

soldi70 [24.7K]

Answer:

Jaime's. Interval not centered around the point estimate.

Step-by-step explanation:

When constructing a confidence interval based on a point estimate, the obtained point estimate must be the central value of the interval.

For Jaime's interval

Lower bound = 0.078

Upper Bound = 0.193

$Central = \frac{0.078+0.193}{2} =0.1355$

For Mariya's interval

Lower bound = 0.051

Upper Bound = 0.189

$Central = \frac{0.051+0.189}{2} =0.12$

For a point estimate of 0.12, only Mariya's interval is adequate since Jaime's is not centered around the point estimate.

4 0

2 years ago

EMERGENCY HELP! A steady stream of water flows into a partially-filled rectangular tank. After 6 minutes, there are 87 gallons o

german

Answer:

$y=9x+33$

33 gallons of water to begin with.

Step-by-step explanation:

So we essentially are given two coordinates: (6,87) and (21,222). To find an equation, we simply need to find the slope and y-intercept. We know it's a linear equation because it's a steady stream, meaning a constant slope.

The slope is:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{222-87}{21-6}=135/15=9$

So, the rate at which the stream flows is 9 gallons per minute.

Now, let's find the initial amount of water. To do this, we can use point-slope form. Pick either of the two points. I'm going to use (6,87).

$y-y_1=m(x-x_1)\\y-87=9(x-6)\\y-87=19-54\\y=9x+33$

So, there were 33 gallons of water in the tank to begin with.

3 0

2 years ago