What is the explicit formula for this sequence?<br> -6, -2, 2, 6, 10, ...

Given ABCD is a parallelogram ABE equals 180° CBE is congruent to CEB prove DAE is congruent to CEA

katrin2010 [14]

Answer:

The proved is given below.

Step-by-step explanation:

Given ABCD is a parallelogram and also ∠ABE equals 180°, ∠CBE ≅ ∠CEB

We have to prove that ∠DAE ≅ ∠CEA

As ∠CEA=∠CBE → (1)

and given ABCD is a parallelogram implies AD||CB

∴ ∠DAE=∠CBE → (2) as these are corresponding angles.

From equation (1) and (2), we get

∠DAE=∠CEA

Hence, ∠DAE is congruent to ∠CEA

Hence Proved

6 0

3 years ago

How can we use theorems about the angles formed by transversals to help ensure that lines are parallel in the design and constru

ElenaW [278]

Answer:

We can use this knowledge in planning of cities

Step-by-step explanation:

The transversal is a line that intersects two or more parallel lines.Angles with similar characteristics are formed when this occurs.

In city planning, streets can be designed to resemble parallel lines with roads that do not meet.However, other roads can be constructed to allow people on the other street to cross to neighboring streets.Such roads allowing this access can be viewed as transversal.

The areas where street roads meet the transversal roads have similar angle characteristics thus could be used for CCTV cameras for surveillance and traffic lights positioning.

7 0

3 years ago

Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit. Assume that

vivado [14]

The Profit = Revenue - CostP ( x ) = ( 40 x - 0.5 x² ) - ( 5 x + 15 ) = = 40 x - 0.5 x² - 5 x - 15 = - 0.5 x² + 35 x - 15The maximum profit is when: P`( x ) = 0P ` ( x ) = ( - 0.5 x² + 35 x - 15 ) ` = - x + 35- x + 35 = 0x = 35 ( the number of units )P max = - 0.5 · 35² + 35 · 35 - 15 = - 612.5 + 1225 - 15 = 597.5Answer: The maximum profit is 597.5 and the number of units is 35.

7 0

3 years ago

Henry sells apples. The graph shows the relationship

Eddi Din [679]

Answer:

Henry does not make money if he does not sell any apples.

Step-by-step explanation:

Henry sells apples. The graph of the relationship between the price of apples and their total weight passes through the point (0,0) or origin.

Now, we have to clarify the meaning of the point (0,0) on the graph.

We choose from the options that Henry does not make money if he does not sell any apples.

Therefore, option D will be the correct one. (Answer)

8 0

3 years ago

Each person in random samples of 207 male and 253 female working adults living in a certain town in Canada was asked how long, i

Sergeu [11.5K]

Answer:

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the mean daily conmute time for males is significantly bigger than the mean daily conmute time for females (P-value=0.155).

Step-by-step explanation:

The data is:

Males n1=207 M1=31.6 s1=24.0

Females n2=253 M2=29.3 s2=24.3

This is a hypothesis test for the difference between populations means.

The claim is that the mean daily conmute time for males is significantly bigger than the mean daily conmute time for females.

Then, the null and alternative hypothesis are:

$H_0: \mu_m-\mu_f=0\\\\H_a:\mu_m-\mu_f> 0$

The significance level is 0.05.

The sample 1 (males), of size n1=207 has a mean of 31.6 and a standard deviation of 24.

The sample 2 (females), of size n2=253 has a mean of 29.3 and a standard deviation of 24.3.

The difference between sample means is Md=2.3.

$M_d=M_m-M_f=31.6-29.3=2.3$

The estimated standard error of the difference between means is computed using the formula:

$s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{24^2}{207}+\dfrac{24.3^2}{253}}\\\\\\s_{M_d}=\sqrt{2.783+2.334}=\sqrt{5.117}=2.262$

Then, we can calculate the t-statistic as:

$t=\dfrac{M_d-(\mu_m-\mu_f)}{s_{M_d}}=\dfrac{2.3-0}{2.262}=\dfrac{2.3}{2.262}=1.017$

The degrees of freedom for this test are:

$df=n_1+n_2-1=207+253-2=458$

This test is a right-tailed test, with 458 degrees of freedom and t=1.017, so the P-value for this test is calculated as (using a t-table):

$P-value=P(t>1.017)=0.155$

As the P-value (0.155) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the mean daily conmute time for males is significantly bigger than the mean daily conmute time for females.

7 0

3 years ago

What is the explicit formula for this sequence? -6, -2, 2, 6, 10, ...