Athena was completing a puzzle picture by connecting ordered pairs of points. Her next point is described below:

In the picture below, ABCD is a rectangle. If the area of triangle ABE is 40, what is the area of the triangle?

MariettaO [177]

Area of the rectangle: 112

Step-by-step explanation:

Picture is missing: find it in attachment.

The area of a triangle is given by

$A=\frac{1}{2}bh$

where

b is the length of the base

h is the height

For triangle ABE, we know that

A = 40 (area)

h = 8 (height)

So we can find the length of the base AE:

$AE=b=\frac{2A}{h}=\frac{2(40)}{8}=10$

Now we observe that the base of the rectangle, AD, is the sum of AE and DE, therefore:

$AD=AE+DE=10+4=14$

We also know the height of the rectangle AB is 8, and that the area of a rectangle is

$A=bh$

where b is the base and h the height. Therefore, the area of this rectangle is

$A=bh=(AD)(AB)=(14)(8)=112$

Learn more about area of figures:

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7 0

4 years ago

Some transportation experts claim that it is the variability of speeds, rather than the level of speeds, that is a critical fact

scZoUnD [109]

Answer:

Explained below.

Step-by-step explanation:

The claim made by an expert is that driving conditions are dangerous if the variance of speeds exceeds 75 (mph)².

(1)

The hypothesis for both the test can be defined as:

H₀: The variance of speeds does not exceeds 75 (mph)², i.e. σ² ≤ 75.

Hₐ: The variance of speeds exceeds 75 (mph)², i.e. σ² > 75.

(2)

A Chi-square test will be used to perform the test.

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

The degrees of freedom of the test is,

df = n - 1 = 55 - 1 = 54

Compute the critical value as follows:

$\chi^{2}_{\alpha, (n-1)}=\chi^{2}_{0.05, 54}=72.153$

Decision rule:

If the test statistic value is more than the critical value then the null hypothesis will be rejected and vice-versa.

(3)

Compute the test statistic as follows:

$\chi^{2}=\frac{(n-1)\times s^{2}}{\sigma^{2}}$

$=\frac{(55-1)\times 94.7}{75}\\\\=68.184$

The test statistic value is, 68.184.

Decision:

$cal.\chi^{2}=68.184$

The null hypothesis will not be rejected at 5% level of significance.

Conclusion:

The variance of speeds does not exceeds 75 (mph)². Thus, concluding that driving conditions are not dangerous on this highway.

7 0

3 years ago

Find the volume of a right circular cone that has a height of 10.7 in and a base with a diameter of 8.1 in. Round your answer to

scoundrel [369]

Answer:

$V = \pi r^2 h$

And for this case the value for the height is $h = 10.7 in$ the diameter is provided $D = 2r = 8.1 in$ so then the radius is given by:

$r = \frac{D}{2}=\frac{8.1 in}{2}= 4.05 in$

Then we can find the volume with the first formula and replacing we got:

$V = \pi (4.05in)^2 (10.7 in)= 551.4 in ^3$

The final answer for this case would be 551.4 cubic inches

Step-by-step explanation:

The volume for a right circular cone is given by this formula:

$V = \pi r^2 h$

And for this case the value for the height is $h = 10.7 in$ the diameter is provided $D = 2r = 8.1 in$ so then the radius is given by:

$r = \frac{D}{2}=\frac{8.1 in}{2}= 4.05 in$

Then we can find the volume with the first formula and replacing we got:

$V = \pi (4.05in)^2 (10.7 in)= 551.4 in ^3$

The final answer for this case would be 551.4 cubic inches

7 0

3 years ago

Read 2 more answers

A right rectangular prism has a side height of 4 cm and a volume of 48 cm cubed.

MrRissso [65]

Answer:

15cm^2

Step-by-step explanation:

it is basic math to me.

3 0

3 years ago

How many do all triangles equal

Ratling [72]

If we are talking about degrees they should equal 180

8 0

2 years ago