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2 years ago

Kayla determines the remainder of 4x37+12x15−2x4−28x+1 , using the remainder theorem.

Mathematics

1 answer:

Luden [163]2 years ago

5 0

The answer to the equation is -25

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Jim is assessing the popularity of his high school football team's website for the first 5 weeks after the season ends. The aver

Maksim231197 [3]

Hey!

There are three sentences in this problem that require us to fill in the blanks with the correct number. Let's start by filling in the first sentence.

SENTENCE #1

The initial number of visits to the website was _____.

Before we being placing numbers in the blank, I would like to make sure you know the meaning of the terms in this sentence that you may not understand. I'm talking about the word initial. The term initial means the first or beginning of something. So, to simplify, the sentence is basically asking us for the first number of visits to the football team's website. It does not directly state that it wants the first number of visits in the first day or the first hour or first five hours, so we'll just assume it wants the first number of visits in the week 0.

To find the number of visits in week 0 all we have to do is review the chart and locate week 0. The number of visits to the website on week 0 is 48,000. So, the sentence completed should look something like this...

The initial number of visits to the website was 48,000.

SENTENCE #2

The percent decrease from the $4^{th}$ week to the $5^{th}$ week was ____ %.

Before we fill in the blank, I want to make sure you understand how to calculate a percentage decrease. The first step is to work out the difference (or the decrease) between the two numbers you are comparing. To do that, you can write your equation that looks something like this...

$decrease = original$ $number-new$ $number$

Then we would have to divide the decrease by the original number and multiply that answer by 100. So your new equation would have to look something like this...

% $decrease=decrease$ ÷ $original$ $number$ · $100$

***Note: If your answer ends up being a negative number, then this is a percentage increase.

So, now that we understand that let's move on the finding the percentage decrease in both the weeks.

The percentage decrease between both the weeks is 50%. So this means the new sentence should look something like this...

The percent decrease from week 4 to week 5 was 50%.

SENTENCE #3

The minimum number of visits on the website in the first 5 weeks since Jim began his assessment was _____ .

Solving this part of the sentence will be simple. All we have to do is take a look at the last week, which is week 5. This will give us the minimum number of visits to the football website.

So, your completed sentence should look something like this...

The minimum number of visits on the website in the first 5 weeks since Jim began his assessment was 1,500.

Hope this helps!

- Lindsey Frazier ♥

5 0

2 years ago

Read 2 more answers

The truth table represents statements p, q, and r. p q r p ∧ q p ∧ r A T T T T T B T T F T F C T F T F T D T F F F F E F T T F F

maksim [4K]

The table shows the results of (p ^ q) and results of (p ^ r) for all possible outcomes. We have to tell which of the outcomes of union of both these events will always be true.

(p ^ q) V (p ^ r) means Union of (p ^ q) and (p ^ r). The property of Union of two sets/events is that it will be true if either one of the event or both the events are true i.e. there must be atleast one True(T) to make the Union of two sets to be True.

So, (p ^ q) V (p ^ r) will be TRUE, if either one of (p ^ q) and (p ^ r) or both are true. From the given table we can see that only the outcomes A, B and C will result is TRUE. The rest of the outcomes will all result in FALSE.

Therefore, the answer to this question is option 2nd

5 0

2 years ago

Find the missing length of the triangle. 7.8 ft b 17.8 ft

riadik2000 [5.3K]

What is the perimeter?

4 0

2 years ago

A 400 gallon tank initially contains 100 gal of brine containing 50 pounds of salt. Brine containing 1 pound of salt per gallon

posledela

Answer:

The amount of salt in the tank when it is full of brine is 393.75 pounds.

Step-by-step explanation:

This is a mixing problem. In these problems we will start with a substance that is dissolved in a liquid. Liquid will be entering and leaving a holding tank. The liquid entering the tank may or may not contain more of the substance dissolved in it. Liquid leaving the tank will of course contain the substance dissolved in it. If Q(t) gives the amount of the substance dissolved in the liquid in the tank at any time t we want to develop a differential equation that, when solved, will give us an expression for Q(t).

The main equation that we’ll be using to model this situation is:

Rate of change of Q(t) = Rate at which Q(t) enters the tank – Rate at which Q(t) exits the tank

where,

Rate at which Q(t) enters the tank = (flow rate of liquid entering) x

(concentration of substance in liquid entering)

Rate at which Q(t) exits the tank = (flow rate of liquid exiting) x

(concentration of substance in liquid exiting)

Let y(t) be the amount of salt (in pounds) in the tank at time t (in seconds). Then we can represent the situation with the below picture.

Then the differential equation we’re after is

$\frac{dy}{dt} = (Rate \:in)- (Rate \:out)\\\\\frac{dy}{dt} = 5 \:\frac{gal}{s} \cdot 1 \:\frac{pound}{gal}-3 \:\frac{gal}{s}\cdot \frac{y(t)}{V(t)} \:\frac{pound}{gal}\\\\\frac{dy}{dt} =5\:\frac{pound}{s}-3 \frac{y(t)}{V(t)} \:\frac{pound}{s}$

$V(t)$ is the volume of brine in the tank at time t. To find it we know that at time 0 there were 100 gallons, 5 gallons are added and 3 are drained, and the net increase is 2 gallons per second. So,

$V(t)=100 + 2t$

We can then write the initial value problem:

$\frac{dy}{dt} =5-\frac{3y}{100+2t} , \quad y(0)=50$

We have a linear differential equation. A first-order linear differential equation is one that can be put into the form

$\frac{dy}{dx}+P(x)y =Q(x)$

where P and Q are continuous functions on a given interval.

In our case, we have that

$\frac{dy}{dt}+\frac{3y}{100+2t} =5 , \quad y(0)=50$

The solution process for a first order linear differential equation is as follows.

Step 1: Find the integrating factor, $\mu \left( x \right)$ , using $\mu \left( x \right) = \,{{\bf{e}}^{\int{{P\left( x \right)\,dx}}}$

$\mu \left( t \right) = \,{{e}}^{\int{{\frac{3}{100+2t}\,dt}}}\\\int \frac{3}{100+2t}dt=\frac{3}{2}\ln \left|100+2t\right|\\\\\mu \left( t \right) =e^{\frac{3}{2}\ln \left|100+2t\right|}\\\\\mu \left( t \right) =(100+2t)^{\frac{3}{2}$

Step 2: Multiply everything in the differential equation by $\mu \left( x \right)$ and verify that the left side becomes the product rule $\left( {\mu \left( t \right)y\left( t \right)} \right)'$ and write it as such.

$\frac{dy}{dt}\cdot \left(100+2t\right)^{\frac{3}{2}}+\frac{3y}{100+2t}\cdot \left(100+2t\right)^{\frac{3}{2}}=5 \left(100+2t\right)^{\frac{3}{2}}\\\\\frac{dy}{dt}\cdot \left(100+2t\right)^{\frac{3}{2}}+3y\cdot \left(100+2t\right)^{\frac{1}{2}}=5 \left(100+2t\right)^{\frac{3}{2}}\\\\\frac{dy}{dt}(y \left(100+2t\right)^{\frac{3}{2}})=5\left(100+2t\right)^{\frac{3}{2}}$

Step 3: Integrate both sides.

$\int \frac{dy}{dt}(y \left(100+2t\right)^{\frac{3}{2}})dt=\int 5\left(100+2t\right)^{\frac{3}{2}}dt\\\\y \left(100+2t\right)^{\frac{3}{2}}=(100+2t)^{\frac{5}{2} }+ C$