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8 months ago

The wavelength of ultraviolet light is about 0.00000003 inches. Which number best approximates this length as a power of 10?

Mathematics

1 answer:

Phantasy [73]8 months ago

4 0

Letter C is the answer

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Luka's weekly earnings of $475 are increased by 6% calculate his new weekly earnings

KengaRu [80]

He earns 28.5. (475•0.06)

6 0

3 years ago

REWARD: 50 points + Brainly to the best answer.<br> Check the file.

Debora [2.8K]

Answer:

a) No because the gallons and quarts of oil you and your friend bought is proportional.

b) Yes because the gallons and quarts of oil are no longer proportional.

c) 1 gallon of gasoline = $3.55

1 quart of oil = $5.00

Step-by-step explanation:

Let g = cost per gallon of gasoline

Let q = cost per quart of oil

a) Creating expressions from the given information:

10g + 2q = 45.50

5g + q = 22.75

From inspection, we can see that if we multiply the second equation by 2, it will give us the first equation. Therefore, they are proportional and we cannot determine the variables.

b) Creating expressions from the given information:

10g + 2q = 45.50

5g + q = 22.75

8g + 2q = 38.40

From inspection, we can see that the third equation is not proportional to equations 1 and 2. Therefore, we can use this equation with either of the other equations to determine the variables.

Using equations 2 and 3 from the previous part (b):

5g + q = 22.75

8g + 2q = 38.40

Rewrite 5g + q = 22.75 to make q the subject:

⇒ q = 22.75 - 5g

Substitute into 8g + 2q = 38.40 and solve for g:

⇒ 8g + 2(22.75 - 5g) = 38.40

⇒ 8g + 45.5 - 10g = 38.40

⇒ 2g = 7.1

⇒ g = 3.55

Substitute found value for g into q = 22.75 - 5g and solve for q:

⇒ q = 22.75 - (5 x 3.55)

⇒ q = 5

3 0

1 year ago

A circle passes through points A(7,4), B(10,6), C(12,3). Show that AC must be the diameter of the circle.

Artist 52 [7]

so we have three points, A, B and C, if indeed AC is the diameter of the circle, then half the distance of AC is its radius, and the midpoint of AC is the center of the circle, morever, since B is also on the circle, the distance from B to the center must be the same radius distance.

in short, half the distance of AC must be equals to the distance of B to the midpoint of AC, if indeed AC is the diameter.

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{12}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{12+7}{2}~~,~~\cfrac{3+4}{2} \right)\implies \left( \cfrac{19}{2}~~,~~\cfrac{7}{2} \right)=M\impliedby \textit{center of the circle}$

now, let's check the distance from say A to the center, and check the distance of B to the center, if it's indeed the center, they'll be the same and thus AC its diameter.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AM=\sqrt{\left( \frac{19}{2}-7 \right)^2+\left( \frac{7}{2}-4 \right)^2} \\\\\\ AM=\sqrt{\left( \frac{5}{2}\right)^2+\left( -\frac{1}{2} \right)^2}\implies \boxed{AM\approx 2.549509756796392} \\\\[-0.35em] ~\dotfill$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{10}~,~\stackrel{y_1}{6})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}}) \\\\\\ BM=\sqrt{\left( \frac{19}{2}-10 \right)^2+\left( \frac{7}{2}-6 \right)^2} \\\\\\ BM=\sqrt{\left( -\frac{1}{2}\right)^2+\left( -\frac{5}{2} \right)^2}\implies \boxed{BM\approx 2.549509756796392}$

6 0

2 years ago

In a sample of 1000 randomly selected consumers who had opportunities to send in a rebate claim form after purchasing a product,

Vadim26 [7]

Answer: 0.2872

Step-by-step explanation:

Given : In a sample of 1000 randomly selected consumers who had opportunities to send in a rebate claim form after purchasing a product, 260 of these people said they never did so.

i.e. n= 1000 and x= 260

⇒ Sample proportion : $\hat{p}=\dfrac{260}{1000}=0.26$