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Anastaziya [24]
2 years ago
13

please help !! A safety regulation states that the height h of a guardrail should be 106 centimeters with an absolute deviation

of no more than 7 centimeters. Write and solve an absolute value inequality that represents the acceptable heights of a guardrail. The absolute value inequality is_ . The acceptable range of heights of a guardrail are _cm to _cm.
Mathematics
2 answers:
babymother [125]2 years ago
8 0

The absolute value is the mean value itself therefore the absolute value is 106 centimeters.

The acceptable range can be obtained by adding and subtracting the absolute deviation on the mean, that is:

106 cm ± 7 cm so that:

<span>The acceptable range of heights are 99 cm to 113 cm.</span>

Zepler [3.9K]2 years ago
3 0

The height h of a guardrail = 106 centimeters

absolute deviation =  7 centimeters

To find the acceptable heights of a guardrail , we add and subtract absolute deviation(7) from the mean height(106)

The acceptable range of height is 7 cm away from 106 to the left and then to the right.

106 + 7 = 113

106 - 7 = 99

acceptable heights are defined by

99 <=h<=113

The absolute value inequality is |x-106|<=7

The acceptable range of heights of a guardrail are 99 cm to 113 cm.


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A village was founded four hundred years ago by a group of 20 people. In this village, the population triples every one hundred
Paha777 [63]

Answer:

Step-by-step explanation:

Treat this like compound interest:  Use A = P(1 + r)^t.

Here, P is the initial population and A is 3 times that, or 3P.  Since P = 20 people, 3P = 60 people,

and this population is reached after 100 years.

We need to determine r, substitute its value into the formula A = P(1 + r)^t, and then determine the population of the village after 400 years.

60 = 20(1 + r)^100

Simplifying, 3 = (1 + r)^100.

Taking the natural log of both sides,

ln 3 = 100 ln (1 + r), or

                   ln 3

ln (1 + r) = ---------------

                    100

              = 1.0986 / 100 = 0.01986

We must solve this for r.  Raising e to the power ln (1 + r), on the left side of an equation, and raising e to the power 0. 01986 on the right side, we get:

1 + r = 3, so r must = 2.

Now find the pop of the village today.  Use the same equation:  A = P (1+r)^t.

A = 20(1 +2)^4 (hundreds),

or

A = 20(3)^4, or

A = 81

The population after 400 years is 81.

8 0
2 years ago
"A consultant compiled the following data set that shows" the number of visits made to the National Museum of American History f
aalyn [17]

Answer:

Step-by-step explanation:

The best option is for the consultant to remove these data points because they are outliers.  Unusual data points which are located far from rest of the data points are known as outliers.

3 0
2 years ago
Triangle ABC was dilated and translated to form similar triangle A'B'C'.
Hunter-Best [27]
Dilation refers to a non rigid motion where a figure is transform and its image has the same form but a different size measure.

On this exercise is asked to find the scale factor by which the triangle ABC was 
dilated to produce the triangle A'B'C'. 
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As can be see on the picture the dilation produce was an enlargement meaning that the image is larger that the preimage.
Of this form you can discard the choices A and B as possible solutions.

Lets try 5/2 as the possible scale factor:
(x,y)-- (kx, ky)
A(0,2)--(5/2(0),5/2(2))=A'(0,5)
B(2,2)--(5/2(2),5/2(2))=B'(5,5)
C(2,0)--(5/2(2),5/2(0))=C'(5,0)

Lets try 5/1 or 5 as the scale factor:
A(0,2)--(5(0),5(2))=A'(0,10)
B(2,2)--(5(2),5(2))=B'(10,10)
C(2,0)--(5(2),5(0))=C'(10,0)

As said at the beginning of the question the triangle was not only dilated.
After a dilation and a translation, the scale factor of the dilation is letter C or 5/2.  

3 0
2 years ago
Read 2 more answers
Jarvis works in a garage £6 an hour. If he works on Saturday, he is paid time and a quarter. If he works on Sunday, he is paid t
ruslelena [56]

Answer: He is paid $90 last weekend.

Step-by-step explanation:

Since we have given that

Amount he earns per hour = $6

If he works on Saturday, he is paid time and a quarter .

Amount would be

6\times 1.25=\$7.5

If he works on Sunday, he is paid time and a half.

Amount would be

6\times 1.5=\$9

Number of hours he worked on Saturday = 6 hours

Number of hours he worked on Sunday = 5 hours

So, Total amount he is paid last weekend altogether is given by

6\times 7.5+5\times 9\\\\=\$90

Hence, he is paid $90 last weekend.

4 0
2 years ago
Line segment JL is an altitude in triangle JKM. Which statement explains whether JKM is a right triangle? Round measures to the
natulia [17]

Answer:

C. JKM is not a right triangle because KM ≠ 15.3.

Step-by-step explanation:

We can see from our diagram that triangle JKM is divided into right triangles JLM and JLK.  

In order to triangle JKM be a right triangle KM^{2}=JK^{2}+JM^{2}.

We will find length of side KM using our right triangles JLM and JLK as KM=KL+LM.  

Using Pythagorean theorem in triangle JLM we will get,

LM=\sqrt{JM^{2}-JL^{2}}

LM=\sqrt{8^{2}-5^{2}}

LM=\sqrt{64-25}

LM=\sqrt{39}=6.244997998\approx 6.24

Now let us find length of side KL.

KL=\sqrt{JK^{2}-JL^{2}}  

KL=\sqrt{13^{2}-5^{2}}

KL=\sqrt{169-25}

KL=\sqrt{144}=12

Now let us find length of KM by adding lengths of KL and LM.

KM=12+6.24=18.24

Now let us find whether JKM is right triangle or not using Pythagorean theorem.

KM^{2}=JK^{2}+JM^{2}  

18.24^{2}=13^{2}+8^{2}

18.24^{2}=169+64

18.24^{2}=233

Upon taking square root of both sides of equation we will get,

18.24\neq 15.264337522473748

18.2\neq 15.3  

We have seen that KM equals 18.2 and in order to JKM be a right triangle KM must be equal to 15.3, therefore, JKM is not a right triangle and option C is the correct choice.    

6 0
2 years ago
Read 2 more answers
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