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3 years ago

1. Find f(x) if it is known that f(x+5)=x+12.

Mathematics

1 answer:

uranmaximum [27]3 years ago

7 0

Answer:

1. f(x)=x+7

2. f(x)=1.2x

Step-by-step explanation:

1. If f(x+5)=x+12, then substitute

$t=x+5\Rightarrow x=t-5$

Hence,

$f(t)=(t-5)+12\\ \\f(t)=t+7$

Now change t into x:

$f(x)=x+7$

2. If f(x-5)=1.2x-6, then substitute

$t=x-5\Rightarrow x=t+5$

Hence,

$f(t)=1.2(t+5)-6\\ \\f(t)=1.2t+6-6\\ \\f(t)=1.2t$

Now change t into x:

$f(x)=1.2x$

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Mr. Acosta, a sociologist, is doing a study to see if there is a relationship between the age of a young adult (18 to 35 years o

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Answer:

There is a relationship between the age of a young adult and the type of movie preferred.

Step-by-step explanation:

In this case we need to test whether there is a significance relationship between the age of a young adult and the type of movie preferred.

The hypothesis can be defined as:

H₀: Age of a young adult and movie preference are independent.

Hₐ: Age of a young adult and movie preference are not independent.

The test statistic is given as follows:

$\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}$

Consider the table below.

The formula to compute the expected frequencies is:

$E_{i}=\frac{\text{Row Total}\times \text{Column Total}}{\text{Total}}$

The Chi-square test statistic value is:

$\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}=2.6013$

The significance level of the test is, α = 0.05.

The degrees of freedom of the test is,

df = (r - 1)(c - 1)

= (3 - 1)(3 - 1)

= 2 × 2

= 4

Compute the p-value as follows:

p-value = 0.6266

*Use a Chi square table.

As the p-value is more than the significance level the null hypothesis was failed to be rejected.

Thus, concluding that there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred.

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2 years ago

Every summer Kendra plants a vegetable garden in her yard last year she planted six rows of tomatoes eight rows of peppers Kendr

Alenkasestr [34]

Answer: Ratio's 3:5

Step-by-step explanation:

Ratio of last year 6:8 Now this year since she wants to only plant 3 rows of tomatoes there would be five rows of tomatoes cuz ur taking away three rows form each typa veggie so the new ratio is now 3:5

((Hope it Helps))

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3 years ago

X^2 - y^2 = 100

luda_lava [24]

Answer:

Step-by-step explanation:

Let's start by rewriting the second equation in terms of "x":

$x+y=5$

Subtract y from both sides:

$x=5-y$

Now, substitute "5-y" for "x" in the first equation:

$(5-y)^2-y^2=100$

Note that:

$(a-b)^2=a^2-2ab+b^2$

$25-10y+y^2-y^2=100$

Cancel out like terms:

$25-10y=100$

Subtract 25 from both sides:

$-10y=75$

Divide both sides by -10

$y=\frac{75}{-10}=\frac{15}{-2}=-\frac{15}{2}$

Now, substitute this value back into either of the equations to solve for x.

$x+y=5\\x-\frac{15}{2}=5\\$

Add 15/2 to both sides:

$x=5+\frac{15}{2}\\x=\frac{10}{2}+\frac{15}{2}\\x=\frac{25}{2}$

Now, find the difference:

$x-y=\frac{25}{2}-(-\frac{15}{2})=\frac{25}{2}+\frac{15}{2}=\frac{40}{2}=20$

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2 years ago

Train A and train B leave the station at 2 pm. The graph below shows the distance covered by the two trains. Compare the two spe

jarptica [38.1K]

Both trains travel for 7 time units.

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$\dfrac{577.5}{7}=82.5$

Note that the units are not specified, but considering that we're talking about trains, the graph is likely to be showing distance in km (or miles) and time in hours.

Also, the distance traveled by train B is not perfectly aligned with the grid, so I assumed that it was the average between the two ticks of 550 and 605.

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2 years ago

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xeze [42]

Answer:

Step-by-step explanation:

3 0

2 years ago

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