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1 year ago

What value of n makes the statement true? 6xn · 4x2 = 24x6

2 answers:

8 0

We check first the numerical coefficients of both sides of the equation if they match if we perform the operation.
(6)(4) = 24
Then, the variables. For multiplication with the same variables, the exponents are added. In the given above,
n + 2 = 6
The value of n should be 4.

snow_tiger [21]1 year ago

6 0

Answer:

n = 4

Explanation :

1. You have the following expression given in the problem above:

(6x^n)(4x^2)=24x^6

2. By the exponents properties, when you multiply powers with the same base, you must sum the exponents. In this case the base is , therefore, you must sum the exponents.

3. The result of the sum is 6, therefore, must be 4:

(6x^4)(4x^2)=24x^6

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The Unique Glass Company reported sales of $24 million in 1995, and sales increased by 15% each year for the next 10 years.

Dimas [21]

Answer:

n + 1 = 24 million x 1.15

Step-by-step explanation:

The sales is increased 15 percent, so every year 24million is multiplyed with 1.15 to get the result... so yea

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1 year ago

A turtle and a rabbit engage in a footrace over a distance of 4.00 km. The rabbit runs 0.500 km and then stops for a 90.0-min na

Oxana [17]

Answer:

(a) 2.29 km/h

(b) 9 km/h

Step-by-step explanation:

For part (a) you have to apply<em> the average speed formula</em>, which is defined by:

$v=\frac{d}{t}$

where d is the total distance traveled and t is the total time needed.

$d=\frac{4.00}{1.75}=2.29$ km/h

For part (b) you have to calculate the running time (T) , which is the total time of the race minus the nap time:

The nap time in hours is:

90/60 = 1.5 h (because there are 60 minutes in one hour)

The running time is:

T= 1.75 - 1.5 = 0.25 h

Let t1 represent the time before the nap and t2 the time after the nap:

t1+t2 = T

t1+t2 = 0.25

You have to apply the formula d=vt before and after the nap:

-Before the nap, the distance traveled was 0.50 km

0.50 = v1t1

-Afer the nap, the distance traveled was 3.50 km

3.50=v2t2

But v2=2v1 (because after the nap the rabbit runs twice as fast)

You have to solve the system of equations:

t1=0.25-t2 (I)

v1t1=0.50 (II)

2v1t2=3.50 (III)

Replacing (I) in (II)

v1(0.25-t2)=0.50

Applying distributive property and solving:

0.25v1-v1t2=.050

For (III) you have that v1t2=3.50/2=1.75. Hence:

0.25v1-1.75=0.50

Solving for v1:

v1 = 9 km/h

7 0

1 year ago

What is the following product? (StartRoot 12 EndRoot + StartRoot 6 EndRoot) (StartRoot 6 EndRoot minus StartRoot 10 EndRoot)

Crank

Answer:

The product results in: $6\,\sqrt{2} -2\,\sqrt{30} +6-2\,\sqrt{15}$ , which agrees with answer A of the given choices.

Step-by-step explanation:

We need to apply distributive property for the product of two expressions each consisting of two terms, and also use the properties of products of radicals of the same root:

$(\sqrt{12} +\sqrt{6} )(\sqrt{6} -\sqrt{10} )=\\=\sqrt{12*6} -\sqrt{12*10} +\sqrt{6*6} -\sqrt{6*10} =\\=\sqrt{72} -\sqrt{120} +\sqrt{36} -\sqrt{60}$

and now, we extract as many factors we can from the roots to reduce them:

$\sqrt{72} -\sqrt{120} +\sqrt{36} -\sqrt{60} =\\=6\,\sqrt{2} -2\,\sqrt{30} +6-2\,\sqrt{15}$

5 0

1 year ago

Read 2 more answers

For ΔABC, ∠A = 4x - 10, ∠B = 5x + 10, and ∠C = 7x + 20. If ΔABC undergoes a dilation by a scale factor of 1 3 to create ΔA'B'C'

VLD [36.1K]

We know that the angles of a triangle sum to 180°. For ΔABC, this means we have:
(4x-10)+(5x+10)+(7x+20)=180

Combining like terms,
16x+20=180

Subtracting 20 from both sides:
16x=160

Dividing both sides by 16:
x=10
This means ∠A=4*10-10=40-10=30°; ∠B=5*10+10=50+10=60°; and ∠C=7*10+20=70+20=90.

For ΔA'B'C', we have
(2x+10)+(8x-20)+(10x-10)=180

Combining like terms,
20x-20=180

Adding 20 to both sides:
20x=200

Dividing both sides by 20:
x=10

This gives us ∠A'=2*10+10=20+10=30°; ∠B'=8*10-20=80-20=60°; and ∠C'=10*10-10=100-10=90°.

Since the angle are all congruent, ΔABC~ΔA'B'C' by AAA.

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1 year ago

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A sample with a sample proportion of 0.4 and which of the following sizes will produce the widest 95% confidence interval when e

Fed [463]

Answer:

C. 50

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

The higher the margin of error, the wider an interval is.

As the sample size increases, the margin of error decreases. If we want a widest possible interval, we should select the smallest possible confidence interval.

So the correct answer is:

C. 50

6 0

2 years ago