The quotient of a number and 9. Algebraic expression.

Yakvenalex [24]

Answer:

3) 16.2

Step-by-step explanation:

The supplement to the 115° angle on the right is 65°, the same as the angle at upper left. The vertical angles at C are the same measure, so this tells you that the two triangles FCB and ACD are similar by the AA similarity postulate. That being the case, corresponding sides are proportional:

CB/CD = CF/CA

CB = CD·CF/CA = 7.2·21.6/9.6

CB = 16.2

_____

When given two "point-to-point" triangles like this, quite often there is some sort of similarity relationship involved. First, you need to figure out what it is; then you need to make use of it as needed to answer the question being asked.

4 0

3 years ago

If the temperature is -17° F at 8 am, and 23°F at noon, how much did the temperature rise?

dedylja [7]

17 + 23 = 40

The temperature rose 40 degrees.

3 0

3 years ago

Read 2 more answers

Biologists stocked a lake with 80 fish and estimated the carrying capacity (the maximal population for the fish of that species

kotegsom [21]

Answer:

$P(t) = \frac{160000e^{1.36t}}{2000 + 80(e^{1.36t} - 1)}$

Step-by-step explanation:

The logistic equation is the following one:

$P(t) = \frac{KP(0)e^{rt}}{K + P(0)(e^{rt} - 1)}$

In which P(t) is the size of the population after t years, K is the carrying capacity of the population, r is the decimal growth rate of the population and P(0) is the initial population of the lake.

In this problem, we have that:

Biologists stocked a lake with 80 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 2,000. This means that $P(0) = 80, K = 2000$ .

The number of fish tripled in the first year. This means that $P(1) = 3P(0) = 3(80) = 240$ .

Using the equation for P(1), that is, P(t) when $t = 1$ , we find the value of r.

$P(t) = \frac{KP(0)e^{rt}}{K + P(0)(e^{rt} - 1)}$

$240 = \frac{2000*80e^{r}}{2000 + 80(e^{r} - 1)}$

$280*(2000 + 80(e^{r} - 1)) = 160000e^{r}$

$280*(2000 + 80e^{r} - 80) = 160000e^{r}$

$280*(1920 + 80e^{r}) = 160000e^{r}$

$537600 + 22400e^{r} = 160000e^{r}$

$137600e^{r} = 537600$

$e^{r} = \frac{537600}{137600}$

$e^{r} = 3.91$

Applying ln to both sides.

$\ln{e^{r}} = \ln{3.91}$

$r = 1.36$

This means that the expression for the size of the population after t years is:

$P(t) = \frac{160000e^{1.36t}}{2000 + 80(e^{1.36t} - 1)}$

4 0

3 years ago

Write 7/11 as a decimal ( round to three decimal places as needed

Degger [83]

0.636
Add a 0 then a decimal .you will see the number 70 goes with 6 *11=66
then the remainder will be 4 , add a 0 and you will see the number goes with 3*11= 33 then the remainder will be 7 again add a 0 and multiply 6. You will get your answer.

3 0

3 years ago

A newsletter publisher believes that above 78 % of their readers own a personal computer. Is there sufficient evidence at the 0.

GalinKa [24]

Answer:

$h_{0}$ : p= .78

$h_{a}$ : p > .78

Step-by-step explanation:

Determining the null and alternate hypotheses of a scenario require several components. The first is if one should use p or mu. This depends on if they are assessing a proportion or a mean, since the publisher states a percentage, you know that they are asking for a proportion, and therefore should use p. Next, they will need to assess what value to use for the hypothesis statements, here only .78 is provided and therefore should be used in both. Finally, it is time to add in the comparison symbols, the null hypothesis always uses an equals sign so it therefore becomes:

$h_{0}$ : p= .78

The alternate hypothesis then needs to consider if the researchers claim that the new proportion is greater, fewer, or different. In this case it is greater as they think that the ownership is above 78%, so a greater than sign would be used and the final statement would be:

$h_{a}$ : p > .78

5 0

3 years ago