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3 years ago

CD is the perpendicular bisector of both XY and ST and CY=20.

Mathematics

2 answers:

agasfer [191]3 years ago

8 0

Is a 5 percent effective

xenn [34]3 years ago

3 0

Answer:

The correct option is C.

Step-by-step explanation:

It is given that CD is the perpendicular bisector of both XY and ST, and CY=20.

In triangle XCD and YCD,

$CD=CD$ (Common sides)

$\angle XDC=\angle YDC=90^{\circ}$ (Definition of perpendicular bisector)

$\angle XD=\angle YD$ (Definition of perpendicular bisector)

By SAS postulate of congruent triangles,

$\triangle XCD=\triangle YCD$

The corresponding parts of congruent triangle are congruent,

$CX=CY$ (CPCTC)

$XC=20$ (CY=20)

The length of CX is 20 units. Therefore the correct option is C.

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In 1998 the average income for middle class families in the US was $37,100 with a population standard deviation of $6362. We wan

sammy [17]

Answer:

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

The best answer would be:

A. Z test

Step-by-step explanation:

Data given and notation

$\bar X=36670$ represent the mean average

$\sigma=6362$ represent the population standard deviation for the sample

$n=1225$ sample size

$\mu_o =37100$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal or not to 37100, the system of hypothesis would be:

Null hypothesis: $\mu =37100$

Alternative hypothesis: $\mu \neq 37100$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

The best answer would be:

A. Z test

5 0

3 years ago

F is a twice differentiable function that is defined for all reals. The value of f "(x) is given for several values of x in the

nadezda [96]

The correct answer is actually the last one.

The second derivative $f''(x)$ gives us information about the concavity of a function: if $f''(x)$ then the function is concave downwards in that point, whereas if $f''(x)>0$ then the function is concave upwards in that point.

This already shows why the first option is wrong - if the function was concave downwards for all x, then the second derivate would have been negative for all x, which isn't the case, because we have, for example, $f''(8)=5$

Also, the second derivative gives no information about specific points of the function. Suppose, in fact, that $f(x)$ passes through the origin, so $f(0)=0$ . Now translate the function upwards, for example. we have that $f(x)+k$ doesn't pass through the origin, but the second derivative is always $f''(x)$ . So, the second option is wrong as well.

Now, about the last two. The answer you chose would be correct if the exercise was about the first derivative $f'(x)$ . In fact, the first derivative gives information about the increasing or decreasing behaviour of the function - positive and negative derivative, respectively. So, if the first derivative is negative before a certain point and positive after that point. It means that the function is decreasing before that point, and increasing after. So, that point is a relative minimum.

But in this exercise we're dealing with second derivative, so we don't have information about the increasing/decreasing behaviour. Instead, we know that the second derivative is negative before zero - which means that the function is concave downwards before zero - and positive after zero - which means that the function is concave upwards after zero.

A point where the function changes its concavity is called a point of inflection, which is the correct answer.

7 0

3 years ago

Travis earned 92 bonus points. Zoe earned b more bonus points than Travis. Write an expression that shows how many bonus points

Serga [27]

92 + b= the amount of points Zoe earned

7 0

3 years ago

Read 2 more answers

use this information for items 1-3. Aaron has $65 to rent a bike in the city . It costs $15 per hour to rent a bike. The additio

marissa [1.9K]

Answer:

Step-by-step explanation:

What we are expected to solve for that the problem did not expressly state is most likely the number of hours that you could ride for an amount of $65.

firstly we need to model the inequality (equation) for this scenario.

the constant fee= $3 additional fee for helmet

$3+15n\leq 65\\\\$