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choli [55]
2 years ago
11

According to wildlife experts, the rate at which crickets chirp per minute is a function of the temperature in degrees Fahrenhei

t. James observed that when the temp was 60 degrees, there were 84 chirps and when the temp was 85 degrees, there were 184 chirps. Write a linear function to model the relationship between the number of chirps and the temperature.
Mathematics
1 answer:
ozzi2 years ago
5 0

Answer:

Step-by-step explanation:

We will let the x coordinates be the temp and the y coordinates by the number of chirps. Our coordinates then will look like this:

(60, 84) and (85, 184). If this is linear, then first we will find the slope of the line which will tell us, in the context of this problem, how many chirps a cricket gives per 1 degree of temp increase.

The slope formula is:

m=\frac{y_2-y_1}{x_2-x_1} and filling in our numbers:

m=\frac{184-84}{85-60}=\frac{100}{25}= 4

This means that for every 1 degree temp increase, a cricket will give 4 chirps. That's the m value in y = mx + b. Now we will pick one of the coordinates, doesn't matter which one, and use those x and y values in the point-slope form of a line to get the equation. I will choose (60, 85), just because. Using the other point will give you the exact same line equation, I PROMISE!

Using 85 as y1 and 60 as x1 in

y - y1 = m(x - x1) gives us

y - 85 = 4(x - 60) and

y - 85 = 4x - 240 and

y = 4x - 240 + 85 and

y = 4x - 155

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OlgaM077 [116]

We need to find the center and the radius of

-10x\: =\: -121\: -\: y^2\: -\: x^2\: -22y

The general circle equation is the following

(x-h)^2+(y-k)^2=r^2

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(h,k) is the center and

r is the radius

1. rearrange the equation

(x^2-10x)+(y^2+22y+121)=0

2. Add 25 on both sides

(x^2-10x+25)+(y^2+22y+121)=25

3. Factor

(x-5)^2+(y+11)^2=5^2

Now we have an equation that is very similar to the circle equation, so let's compare them

Center -> (h,k) = (5,-11)

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8 0
1 year ago
Given the matrices: 1 2 A= 1 -1 2 1 1 B= 3 4 Calculate AB: C11 C12 [2.1] х 1 2 3 4 C21 C22 C11 = C12 = -2 C22 - C215 DONE​
eduard

Answer:

\:c_{11}=-2,\:\:\:c_{12}=-2

\:c_{21}=5,\:\:\:c_{22}=8

Step-by-step explanation:

Given the matrices

A=\begin{pmatrix}1&-1\\ 2&1\end{pmatrix}

B=\begin{pmatrix}1&2\\ \:3&4\end{pmatrix}

Calculating AB:

\begin{pmatrix}1&-1\\ \:\:2&1\end{pmatrix}\times \:\begin{pmatrix}1&2\\ \:\:3&4\end{pmatrix}=\begin{pmatrix}c_{11}&c_{12}\\ \:\:\:c_{21}&c_{22}\end{pmatrix}

Multiply the rows of the first matrix by the columns of the second matrix

                                   =\begin{pmatrix}1\cdot \:1+\left(-1\right)\cdot \:3&1\cdot \:2+\left(-1\right)\cdot \:4\\ 2\cdot \:1+1\cdot \:3&2\cdot \:2+1\cdot \:4\end{pmatrix}

                                   =\begin{pmatrix}-2&-2\\ 5&8\end{pmatrix}

Hence,

\begin{pmatrix}c_{11}&c_{12}\\ \:\:\:c_{21}&c_{22}\end{pmatrix}=\begin{pmatrix}-2&-2\\ \:5&8\end{pmatrix}

Therefore,

\:c_{11}=-2,\:\:\:c_{12}=-2

\:c_{21}=5,\:\:\:c_{22}=8

5 0
2 years ago
Read 2 more answers
150 parents were surveyed. 26% said that the kids were noddy and 70% said their kids were nice. How many parents didn't answer w
alexandr1967 [171]

Answer:

The parents who didn't answer with either naughty and nice are <u>6</u>.

Step-by-step explanation:

Given:

150 parents were surveyed. 26% said that the kids were naughty and 70% said their kids were nice.

Now, to find parents who didn't answer with either naughty and nice.

<em>So, as given in question:</em>

<em>70% said that their kids are naughty.</em>

<em>26% said that their kids are nice.</em>

So, to get the percentage of parents who didn't answer we subtract.

<em>Thus, the percentage of  parents who didn't answer with either naughty and nice:</em>

100% - (70% + 26%)

100% - 96% = 4%.

Hence, 4% of parents didn't answer.

Now, to get how many  parents didn't answer we calculate the percentage of the total who didn't answer:

<em>Total parents surveyed = 150.</em>

<em>Parents who didn't answer =  4% of the total parents surveyed.</em>

Parents\ who\ didn't\ answer = 4\% of 150.

Parents\ who\ didn't\ answer = \frac{4}{100}\times 150.

Parents\ who\ didn't\ answer = \frac{600}{100}.

Parents\ who\ didn't\ answer = 6.

Therefore, the parents who didn't answer with either naughty and nice are 6.

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Answer:

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If the jars of peanut butter were 15, then the cans of soup would be (7/5 × 15) = 21

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877.71=877.7
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