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marin [14]
1 year ago
11

Identify all pairs of congruent corresponding parts. Then write another congruence statement for the triangles.

Mathematics
1 answer:
astra-53 [7]1 year ago
4 0

..

SOLUTION

\begin{gathered} \Delta FED\cong\Delta CBA \\ \angle F\cong\angle C \end{gathered}\begin{gathered} \Delta EFD\cong BCA \\ \angle E\cong\angle B \\ \bar{DE}\cong\bar{AB} \end{gathered}\begin{gathered} \bar{EF}=\bar{BC} \\ \angle D=\angle A \\ \bar{DF}=\bar{AC} \end{gathered}

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A 20% apple juice drink is mixed with a 100% apple juice drink. The function f(x)=(2)(1.0)+x(0.2)2+x models the concentration of
luda_lava [24]

Answer:

17.5

Step-by-step explanation:

Given that:

20% apple juice drink is mixed with a 100% apple juice drink.

f(x)=\dfrac{(2)(0.1)+x(0.2)}{2+x}

represents the concentration of apple juice in the drink when x gallons of 20% drink are added to 2 gallons of pure juice.

Also, given that 6 gallons of 20% drink are added to the 2 gallons of pure juice.

To find:

The concentration of apple juice in the drink = ?

Solution:

Given the function:

f(x)=\dfrac{(2)(0.1)+x(0.2)}{2+x}

and

x=6\ gallons

f(x)=\dfrac{(2)(0.1)+6(0.2)}{2+6}\\\Rightarrow f(x)=\dfrac{0.2+1.2}{8}\\\Rightarrow f(x)=\dfrac{1.4}{8}\\\Rightarrow f(x)=\bold{0.175}

In percentage, the concentration 17.5.

7 0
3 years ago
Many utility companies promote energy conservation by offering discount rates to consumers who keep their energy usage below cer
aleksley [76]

Answer:

a. 0.1681 = 16.81% probability that all five qualify for the favorable rate.

b. 0.5283 = 52.83% probability that at least four qualify for the favorable rates

Step-by-step explanation:

For each Puerto Rico resident, there are only two possible outcomes. Either they qualify for discounted rates, or they do not. The probability of a person in the sample qualifying for discounted rates is independent of any other person in the sample. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

70% of the island residents of Puerto Rico have reduced their electricity usage sufficiently to qualify for discounted rates.

This means that p = 0.7

Five residential subscribers are randomly selected from San Juan, Puerto Rico

This means that n = 5

a. All five qualify for the favorable rate

This is P(X = 5). So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 5) = C_{5,5}.(0.7)^{5}.(0.3)^{0} = 0.1681

0.1681 = 16.81% probability that all five qualify for the favorable rate.

b. At least four qualify for the favorable rates

This is

P(X \geq 4) = P(X = 4) + P(X = 5)

So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 4) = C_{5,4}.(0.7)^{4}.(0.3)^{1} = 0.3602

P(X = 5) = C_{5,5}.(0.7)^{5}.(0.3)^{0} = 0.1681

P(X \geq 4) = P(X = 4) + P(X = 5) = 0.3602 + 0.1681 = 0.5283

0.5283 = 52.83% probability that at least four qualify for the favorable rates

5 0
3 years ago
find the measure of the arc or angle indicated. assume that lines which appear to be diameters are actual diameters just enter t
konstantin123 [22]

Answer:

I think D

if wrong correct me plssssssss

have a nice day

And good luck if you have exam

#Captainpower

8 0
3 years ago
L.c.m of 84 ,27,35,45 <br>please help​
den301095 [7]

Answer:

3780

Step-by-step explanation:

84 = 2^2 * 3 * 7

27 = 3^3

35 = 5 * 7

45 = 3^2 * 5

lcm = 2^2 * 3^3 * 5 * 7 = 3780

8 0
3 years ago
If the lateral area of a right rectangular prism is 384 cm^2, its length twice its width, and its height is twice its length, fi
Katen [24]
Width = w
Length = 2w
Height = 4w
w \times 2w  = 384 \\  {2w}^{2}  = 384 \\  {w}^{2}  = 192 \\ w = 13.86cm
Width = 13.86cm

Hope this helps. - M
7 0
4 years ago
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