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3 years ago

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Triangle D E F is shown. The length of E F is 3, the length of F D is 6, and the length of D E is 5. Heron’s formula: Area = Sta

rtRoot s (s minus a) (s minus b) (s minus c) EndRoot What is the area of triangle DEF? 2 StartRoot 2 EndRoot square units 2 StartRoot 14 EndRoot square units 6 StartRoot 22 EndRoot square units 12 StartRoot 77 EndRoot square units

2 answers:

Galina-37 [17]3 years ago

6 0

Answer:

2 radical 14

Step-by-step

square root of 7(7-3)(7-5)(7-6)

which is the square root of 56

which is about 7.5 or 2 radical 14

lora16 [44]3 years ago

5 0

Answer:

2 radical 14

Step-by-step explanation:

just took the test :)

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One environmental group did a study of recycling habits in a California community. It found that 75% of the aluminum cans sold i

AysviL [449]

Answer:

a

$P( \^ p > 0.775 ) = 0.12798$

b

$P( 0.6718 < p < 0.775 ) =0.87183$

Step-by-step explanation:

From the question we are told that

The population proportion is $p = 0.75$

Considering question a

The sample size is $n = 387$

Generally the standard deviation of this sampling distribution is

$\sigma = \sqrt{ \frac{p(1 - p)}{ n } }$

=> $\sigma = \sqrt{ \frac{0.75(1 - 0.75)}{ 387 } }$

=> $\sigma = 0.022$

The sample proportion of cans that are recycled is

$\^ p = \frac{ 300}{387 }$

=> $\^ p = 0.775$

Generally the probability that 300 or more will be recycled is mathematically represented as

$P( \^ p > 0.775 ) = P( \frac{\^ p - p }{ \sigma } > \frac{0.775 - 0.75 }{ 0.022} )$

$\frac{\^ p - p }{\sigma } = Z (The \ standardized \ value\ of \ \^ p )$

$P( \^ p > 0.775 ) = P( Z > 1.136 )$

From the z table the area under the normal curve to the left corresponding to 1.591 is

$P( Z > 1.136) = 0.12798$

=> $P( \^ p > 0.775 ) = 0.12798$

Considering question b

Generally the lower limit of sample proportion of cans that are recycled is

$\^ p_1 = \frac{ 260 }{387 }$

=> $\^ p_1 = 0.6718$

Generally the upper limit of sample proportion of cans that are recycled is

$\^ p_2 = \frac{ 300}{387 }$

=> $\^ p_2 = 0.775$

Generally probability that between 260 and 300 will be recycled is mathematically represented as

$P( 0.6718 < p < 0.775 ) = P( \frac{0.6718 - 0.75 }{ 0.022}< \frac{\^ p - p }{ \sigma }$

=> $P( 0.6718 < p < 0.775 ) = P( -3.55 < Z < 1.136 )$

=> $P( 0.6718 < p < 0.775 ) = P(Z < 1.136 ) - P( Z < -3.55 )$

From the z table the area under the normal curve to the left corresponding to 1.136 and -3.55 is

$P( Z < -3.55 ) = 0.00019262$

and

$P(Z < 1.136 ) = 0.87202$

So

$P( 0.6718 < p < 0.775 ) = 0.87202- 0.00019262$

=> $P( 0.6718 < p < 0.775 ) =0.87183$

4 0

3 years ago

Sara's savings account balance changed by -$34 one week and by -$67 the next week .Which amount represents the greater change?

fomenos

<u />The greater change is represented by the absolute magnitude

|-34| = 34
|-67| = 67

67 > 34

<u><em>-67 represents the greater change</em></u>

4 0

3 years ago

Read 2 more answers

The height of the pyramid in the diagram is three times the radius of the cone. The base area of the pyramid is the same as the

Brut [27]

Answer:

jhhfhgk

Step-by-step explanation:

7 0

3 years ago

the ratio of red marbles to blue marbles in a bag is 3:4. if there are 42 marbles in the bag, how many of the marbles are red?

AlexFokin [52]

Answer:

18

Step-by-step explanation:

Sum the parts of the ratio, 3 + 4 = 7

Divide the amount of marbles by 7 to find the value of one part of the ratio

42 ÷ 7 = 6 ← value of 1 part of the ratio, thus

red marbles = 3 × 6 = 18

8 0

3 years ago

A factory sells backpacks for $35 each. The cost to make 1 backpack is $15. In addition to the cost of making backpacks, the fac

Otrada [13]

Answer:9400 backpacks

$\geq$ Step-by-step explanation

since the number of packs to be sold in a is represented by x,

selling price for 1 week = 35x

cost price for 1 week = 15x

profit = 35x-15x = 20x

additional cost of production = 11,000

this implies that 20x - 11,000 $\geq$ 7800

20x - 11,000 $\geq$ 7,800

20x $\geq$ 7800+ 11000

20x $\geq$ 18,800

x $\geq$ 18800/2

x $\geq$ 9,400

at least 9,400 packs have to be sold each week to make a profit of $7800

7 0

3 years ago