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Natasha2012 [34]

3 years ago

14

78 students are separated into groups of 8 for a field trip how many groups are there there are many students from a smaller gro

up of how many students

1 answer:

mixas84 [53]3 years ago

5 0

Nine groups of 8 students and one group of 6 students. 9 x 8 = 72. 78 - 72 = 6.

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!!!!!PLEASE HELP!!!!!<br> *30 POINTS PLEASE*

Lelechka [254]

Answer:

Part 1)

Part a) Yes, triangle ABC is congruent with triangle DEC by SAS

Part b) No, triangle ABC is not congruent with triangle DCE

Part 2) No, is not enough information

Part 3) Yes, triangle RST is congruent with triangle VUT by ASA

Part 4) Yes, triangle DEF is congruent with triangle DHG by SAS

Step-by-step explanation:

Part 1) we have two cases

Part a) Is triangle ABC and DEC congruent?

Yes, triangle ABC is congruent with triangle DEC by SAS

we know that

The <u><em>Side Angle Side postulate</em></u> ( SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent

In this problem

AC≅DE

BC≅EC

and

∠ACB≅∠DCE ---> by vertical angles

Part b) Is triangle ABC and DCE congruent?

we know that

If two triangles are congruent, then its corresponding sides and its corresponding angles are congruent

In this problem

the corresponding sides are not congruent

because

AB is not congruent with DC

Part 2) we have that

No, is not enough information

If AC≅XZ then the triangles ABC and XYZ will be congruent by SSS

or

If ∠ABC≅∠XYZ then the triangles ABC and XYZ will be congruent by SAS

Part 3) we have that

Yes, triangle RST is congruent with triangle VUT by ASA

we know that

If any two angles and the included side are the same in both triangles, then the triangles are congruent by Angle -Side-Angle (ASA) postulate

In this problem

ST≅UT

∠RST≅∠VUT ----> is a right angle

∠RTS≅∠VTU ---->by vertical angles

so

Two angles and the included side are the same in both triangles

therefore

triangles RST and VUT are congruent by ASA

Part 4) we have that

Yes, triangle DEF is congruent with triangle DHG by SAS

we know that

The <u><em>Side Angle Side postulate</em></u> ( SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent

In this problem

DE≅DH

DF≅DG

and

∠EDF≅∠HDG ---> by vertical angles

7 0

3 years ago

If R is the midpoint of QS, RS= 2x - 4, ST = 4x-1, and RT = 8x - 43, find QS.

Pepsi [2]

Answer: QS=68 units

Step-by-step explanation:

<em>RT=RS+ST</em>

<em>8x-43=2x-4+4x-1</em>

<em>8x-43=6x-5</em>

<em>8x-43-6x=6x-5-6x</em>

<em>2x-43=-5</em>

<em>2x-43+43=-5+43</em>

<em>2x=38</em>

<em>Divide both parts of the equation by 2:</em>

<em>x=19</em>

<em>QS=RS+RQ</em>

<em>As, RS=RQ</em>

<em>QS=2RS</em>

<em>QS=(2)((2)(19)-4))</em>

<em>QS=(2)(38-4)</em>

<em>QS=(2)(34)</em>

<em>QS=68</em>

6 0

1 year ago

If Consider today’s stock listing for Enam Telecom, shown below.

allsm [11]

The answer is B. $0.72

6 0

3 years ago

Read 2 more answers

Solve the equation x2 – 10x – 8= 0 to the nearest tenth.

4vir4ik [10]

Answer:

x = -0.8 and 10.8

Step-by-step explanation:

Given the equation x2 – 10x – 8= 0

Using the general formula

x = -b±√b²-4ac/2a

x = -(-10)±√(-10)²-4(1)(-8)/2(1)

x = 10±√100+32/2

x =10±√132/2

x = 10±11.489/2

x = 10-11.489/2 and 10+11.489/2

x = -1.489/2 and 21.489/2

x = -0.8 and 10.8

3 0

3 years ago

Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backu

JulsSmile [24]

Answer:

a) There is a 10.24% probability that both generators fail during a power outage.

b) There is an 89.76% probability of having a working generator in the event of a power outage, which is not high enough for the hospital.

Step-by-step explanation:

For each emergency backup generator, there are only two possible outcomes. Either they work correctly, or they fail. So we use the binomial probability distribution to solve this problem.

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.

In this problem we have that:

Assume that emergency backup generators fail 32% of the times when they are needed. So they work correctly 100-32 = 68% of the time. So $p = 0.68$

There are two generators, so $n = 2$

a. Find the probability that both generators fail during a power outage

This is $P(X = 0)$

So

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

$P(X = 0) = C_{2,0}.(0.68)^{0}.(0.32)^{2} = 0.1024$

There is a 10.24% probability that both generators fail during a power outage.

b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the hospital? Assume the hospital needs both generators to fail less than 1% of the time when needed.

Either there are no working generators, or there is at least one working generator. The sum of the probabilities of these events is decimal 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$ . So

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1024 = 0.8976$

There is an 89.76% probability of having a working generator in the event of a power outage, which is not high enough for the hospital.

To be high enough for the hospital, this probability should be at least of 99%.

7 0

4 years ago