All categories

3 years ago

Find two consecutive even integers such that four times the first plus three times the second is 20

1 answer:

8 0

2 consecutive even integers : x and x + 2

4(x) + 3(x + 2) = 20
4x + 3x + 6 = 20
7x + 6 = 20
7x = 20 - 6
7x = 14
x = 14/7
x = 2

x + 2 = 2 + 2 = 4

so ur first number (x) = 2 and ur second number (x + 2) = 4

You might be interested in

In 2017 the Gallup poll surveyed 1021 adults in the United States and found that 57% supported a ban on smoking in public places

maria [59]

Answer:

Explained below.

Step-by-step explanation:

(a)

A population is the set of all the data that can be collected and from which a smaller set of data is drawn for further examination. A population may denote to a group of individuals, articles, trials or measurements. A population can thus be called as a collection of information regarding subjects combined together by a common characteristic.

The population is adults in the United States.

A sample denotes a smaller, controllable form of a larger cluster. It is a subset comprising of the characteristics of a bigger population. Samples are used in statistical experiments when the population under consideration is too large for the test to include all the members.

The sample is the 021 adults surveyed.

(b)

A parameter is a valuable element of statistical analysis. It denotes the characteristics that are used to define a given population. It is used to define a particular attribute of the population. For instance, population mean, population standard deviation, population proportion and so on.

The parameter of interest is population proportion of adults in the United States who support smoking bans.

While making a statistical conclusion about the population under study, the parameter value is unknown. This is because it would not be possible to gather data from every single member of the population. So a sample is selected from the population to derive a conclusion about the parameter.

A statistic is the value of the characteristics that are computed using this sample. For instance, sample mean, sample standard deviation, sample proportion and so on.

The statistic is the 57% of adults who support smoking bans.

6 0

3 years ago

Write 5,806 in scientific notation

aalyn [17]

Answer:

5.806 x 10^3

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Find the solution to the differential equation dB/dt+4B=20 with B(1)=30

natita [175]

Answer:

The solution of the differential equation is $B=5+25e^{-4t+4}$

Step-by-step explanation:

The differential equation $\frac{dB}{dt}+4B=20$ is a first order separable ordinary differential equation (ODE). We know this because a separable first-order ODE has the form:

$y'(t)=g(t)\cdot h(y)$

where g(t) and h(y) are given functions.

We can rewrite our differential equation in the form of a first-order separable ODE in this way:

$\frac{dB}{dt}+4B=20\\\frac{dB}{dt}=20-4B\\\frac{dB}{dt}=4(5-B)\\\frac{1}{5-B}\frac{dB}{dt}=4$

Integrating both sides

$\frac{1}{5-B}\frac{dB}{dt}=4\\\frac{1}{5-B}\cdot dB=4\cdot dt\\\\\int\limits {\frac{1}{5-B}} \, dB=\int\limits {4} \, dt$

The integral of left-side is:

$\int\limits {\frac{1}{5-B}} \, dB\\\mathrm{Apply\:u-substitution:}\:u=5-B\\\int\limits {\frac{1}{5-B}} \, dB=\int\limits {\frac{1}{u}} \, dB\\\mathrm{du=-dB}\\-\int\limits {\frac{1}{u}} \,du\\\mathrm{Use\:the\:common\:integral}:\quad \int \frac{1}{u}du=\ln \left(\left|u\right|\right)\\-\int\limits {\frac{1}{u}} \,du =-\ln \left|u\right|\\\mathrm{Substitute\:back}\:u=5-B\\-\ln \left|5-B\right|\\\mathrm{Add\:a\:constant\:to\:the\:solution}\\-\ln \left|5-B\right|+C$

The integral of right-side is:

$\int\limits {4} \, dt = 4t + C$

We can join the constants, and this is the implicit general solution

$-\ln \left|5-B\right|+C=4t + C\\-\ln \left|5-B\right|=4t + D$

If we want to find the explicit general solution of the differential equation

We isolate B

$-\ln \left|5-B\right|=4t + D\\\ln \left|5-B\right|=-4t+D\\\left|5-B\right|=e^{-4t+D}$

Recall the definition of |x|

$|x|=\left \{ {{x, \:if \>x\geq \>0 } \atop {-x, \:if \>x0}} \right.$

$\left|5-B\right|=e^{-4t+D}\\5-B= \pm \:e^{-4t+D}\\B=5 \pm \:e^{-4t+D}\\B=5\pm \:e^{-4t}\cdot e^{D}\\B=5+Ae^{-4t}$

where $A=\pm e^{D}$

Now B(1) =30 implies

$B=5+Ae^{-4t}\\30=5+Ae^{-4}\\30-5=Ae^{-4}\\25e^{4}=A$

And the solution is

$B=5+(25e^{4})e^{-4t}\\B=5+25e^{-4t+4}$

8 0

4 years ago

How would you do 13 as a exponential

Ksenya-84 [330]

Hello! Welcome to Brainly! Let's solve together. :)

To put a number into scientific notation, you multiply it by a power of 10 that will make it a digit 1-10.

As you can see, we can divide by 10, or multiply by 1/10 to get us to 1.3, which is between 1 and 10. How would we get 1.3 to 13? We would multiply by 10!

This gives us our answer below.

1.3(10 $^{1}$ )

I hope this helps!

6 0

3 years ago

Read 2 more answers

Find the sum or difference. Round your answer appropriately. 11.7 qt + 2 qt

qwelly [4]

Add 11.7 and 2. The answer is 13.7 (quarts).

4 0

3 years ago