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3 years ago

7

Benjamin has completed 78 of his sixth-grade final exam. What percentage is equivalent to the fraction of the final exam that Be

njamin has completed?
A 87.5%

B 7.8%

C 8.75%

D 56%

1 answer:

Gre4nikov [31]3 years ago

3 0

I pretty sure it’s A

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The combined volume of all the tanks at an aquarium is 1.25 X 106 gallons. The aquarium plans to install a new dolphin tank with

DaniilM [7]

1. The combined volume of all the tanks at the aquarium is written in Scientific notation. Keeping this on mind, you can write it as following:

$(1.25)(10^{6})=1,250,000gallons$

2. Now, you must sum the combined volume of all the tanks and the volume of the new tank to calculate the total volume of all of them: $Vt=1,250,000gallons+250,000gallons\\Vt= 1,500,000gallons$

3. Now, you can write the result in Scientific notation, as following:

$Vt=(1.5)(10^{6}) gallons$

The answer is: $(1.5)(10^{6}) gallons$

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3 years ago

I can't figure out how to do (i + j) x (i x j)for vector calc

Vinil7 [7]

In three dimensions, the cross product of two vectors is defined as shown below

$\begin{gathered} \vec{A}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k} \\ \vec{B}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k} \\ \Rightarrow\vec{A}\times\vec{B}=\det (\begin{bmatrix}{\hat{i}} & {\hat{j}} & {\hat{k}} \\ {a_1} & {a_2} & {a_3} \\ {b_1} & {b_2} & {b_3}\end{bmatrix}) \end{gathered}$

Then, solving the determinant

$\Rightarrow\vec{A}\times\vec{B}=(a_2b_3-b_2a_3)\hat{i}+(b_1a_3+a_1b_3)\hat{j}+(a_1b_2-b_1a_2)\hat{k}$

In our case,

$\begin{gathered} (\hat{i}+\hat{j})=1\hat{i}+1\hat{j}+0\hat{k} \\ \text{and} \\ (\hat{i}\times\hat{j})=(1,0,0)\times(0,1,0)=(0)\hat{i}+(0)\hat{j}+(1-0)\hat{k}=\hat{k} \\ \Rightarrow(\hat{i}\times\hat{j})=\hat{k} \end{gathered}$

Where we used the formula for AxB to calculate ixj.

Finally,

$\begin{gathered} (\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=(1,1,0)\times(0,0,1) \\ =(1\cdot1-0\cdot0)\hat{i}+(0\cdot0-1\cdot1)\hat{j}+(1\cdot0-0\cdot1)\hat{k} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=1\hat{i}-1\hat{j} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=\hat{i}-\hat{j} \end{gathered}$

Thus, (i+j)x(ixj)=i-j

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1 year ago

A caterer charger $120 to carter a party for 15 people and $200 for 25 people

Luba_88 [7]

Answer:

y = 8x

Step-by-step explanation:

When the number of people increased by 10, the caterer charged an additional $80. Therefore, we estimate that the cost per person is $8. In order to verify:

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Therefore, if we let x represent the number of people being cater for and y represent the cost, the equation to model the situation is simply y = 8x.

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3 years ago

Are 4/16 and 0.25/2 equivalent numbers? If so, explain how they are.

Aleksandr-060686 [28]

Two fractions are equivalent if the product of the numerator of the first and the denominator of the second is equal to the product of the numerator of the second and the denominator of the first.
4 x 2 ___ 16 x 0.25
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3 years ago

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Answer:

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Step-by-step explanation:

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4 years ago