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ivolga24 [154]
3 years ago
7

A rectangular garden has an area of 24 square meters. The width is 8 meters less than twice the length. Find the dimensions of t

he garden
The garden is
meters long by
meters wide.
Mathematics
1 answer:
OLEGan [10]3 years ago
3 0

Answer:

Length: 6 m

Width: 4 m

Step-by-step explanation:

Area: 24 m^{2}

Width: 2L - 8 m

Length: ?

Formula: A = W * L

Replace the variables:

24 = (2L - 8) * L

24 = 2L^{2} - 8L

0 = 2L^{2} - 8L - 24

or

2L^{2} - 8L - 24 = 0

Solve; if you don't know how to solve it using this method, let me know. It's the expression Ax^{2} +Bx+C

1. 2 (\frac{(2L^2 - 8L - 24)}{2})

2. \frac{(2L)^2 - 8(2L) - 48}{2}

3. \frac{(2L - 12)(2L + 4)}{2}

4. 2(\frac{(L - 6)(2L + 4)}{2})

5. (L-6) (2L+4)

6. L-6 = 0 AND 2L+4 = 0

L - 6 =0

L = 6

---------------------------------

2L = -4

L = \frac{-4}{2}

L = -2

Since the length cannot be negative, the only real value is 6.

Area: 24 m^{2}

Width: 2L - 8 m

Length: 6 m

Calculate width:

W = 2L - 8

W = 2(6) - 8

W = 12 - 8

W = 4 m

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"A manufacturer of automobile batteries claims that the average length of life for its grade A battery is 55 months. Suppose the
STALIN [3.7K]

Answer:

\\ P(z>-2) = 0.97725 or P(x>49) is about 97.725% (or being less precise 97.5% using the <em>empirical rule</em>).

Step-by-step explanation:

We solve this question using the following information:

  1. We are dealing here with <em>normally distributed data</em>, that is "<em>the frequency distribution of the life length data is known to be mound-shaped</em>".
  2. The normal distribution is defined by two parameters: the population mean (\\ \mu) and the population standard deviation (\\ \sigma). In this case, we have that \\ \mu = 55 months, and \\ \sigma = 3 months.
  3. To find the probabilities, we have to use the <em>standard normal distribution</em>, which has \\ \mu = 0 and \\ \sigma = 1. The probabilities for this distribution are collected in the <em>standard normal table</em>, available in Statistics books or on the Internet. We can also use statistics programs to find these probabilities.
  4. For most cases, we need to use the <em>cumulative standard normal table, </em>and for this we have to previously "transform" a raw score (x) into a z-score using the next formula: \\ z = \frac{x - \mu}{\sigma} [1]. A z-score tells us the distance from the mean that a raw score is from it in <em>standard deviations units</em>. If this value is <em>negative</em>, the raw score is <em>below</em> the mean. Conversely, a <em>positive</em> value indicates that it is <em>above</em> the mean.
  5. The <em>cumulative standard normal table </em>is made for positive values of z. Since the normal distribution is <em>symmetrical</em> around the mean, we can find the negative values of z using this formula: \\ P(z [2].

Having all this information, we can solve the question.

<h3>The percentage of the manufacturer's grade A batteries that will last more than 49 months</h3>

<em>First Step: Use formula [1] to find the z-score of the raw score x = 49 months</em>.

\\ z = \frac{49 - 55}{3}

\\ z = \frac{-6}{3}

\\ z = -2

This means that the raw score is represented by a z-score of \\ z = -2, which tells us that it is<em> two standard deviations below</em> the population mean.

<em>Second Step: Consult this value in the cumulative standard normal table for z = 2 and apply the formula [2] to find the corresponding probability.</em>

For a z = 2, the probability is 0.97725.  

Then

\\ P(z

\\ P(z2)

\\ P(z2)

But we <em>are not asked</em> for P(z<-2) but for P(z>-2) = P(x>49). This probability is the <em>complement</em> of the previous result, that is

\\ P(z>-2) = 1 - P(z

\\ P(z>-2) = 1 - 0.02275

\\ P(z>-2) = 0.97725

That is, the "<em>percentage of the manufacturer's grade A batteries will last more than 49 months</em>" is

\\ P(z>-2) = 0.97725 or about 97.725%

A graph below shows this result.

Notice that if we had used the <em>68-95-99.7 rule</em> (also known as the <em>empirical rule</em>), that is, in a normal distribution, the interval between <em>one standard deviation below and above the mean</em> contains, approximately, 68% of the observations; the interval between <em>two standard deviations below and above the mean</em> contains, approximately, 95% of the observations; and the interval between <em>three standard deviations</em> below and above the mean contains, approximately, 99.7% of the observations, we could have concluded that 2.5 % of the manufacturer's grade A batteries will last <em>less</em> than 49 months, and, as a result, 1 - 0.025 = 0.975 or 97.5% will last more than 49 months.

We can conclude that with a less precise answer (but faster) because of the <em>symmetry of the normal distribution</em>, that is, 1 - 0.95 = 0.05. At both extremes we have 0.05/2 = 0.025 or 2.5% and we were asked for P(x>49) = P(z>-2) (see the graph below).

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Area of a triangle with verticals of (-4,1),(-7,5),(0,1)
Lynna [10]

Answer:

8 ft^2

Step-by-step explanation:

I assume that the three points given are the vertices of the triangle. So the three points are:

A (-4,1)

B (-7,5)

C (0,1)

The area of a triangle is given by:

A=\frac{1}{2}bh

where b is the base and h is the height.

Here we can take as follows:

- We can take the base to be the side AC, so that its length is equal to the distance between the two points:

AC=\sqrt{(0-(-4))^2+(1-1)^2}=4

- The height of the triangle is therefore the perpendicular distance between AC and point B. This is equivalent the difference in the x-coordinate between any point on AC and B, so:

h=(5-1)=4 ft

Therefore, the area of the triangle is:

A=\frac{1}{2}(4)(4)=8 ft^2

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2 years ago
How many months are in 59 days???
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1 month 29 days but if the month have 29 days each then the it will be 2 months

7 0
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island rentals charges a $50 base fee plus $25 per hour to rent and electric boat that can carry six people . Thomas and his fri
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225=50+25x
175=25x
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Answer: They can rent the boat for up to 7hrs

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2 years ago
Read 2 more answers
confirm or disprove ernest's work by selecting two different points and applying the slope formula. be sure to identify the poin
yan [13]

Answer:

Part a) Ernest's calculation was correct

Part b) Ernest's calculation was correct

Step-by-step explanation:

The picture of the question in the attached figure

<u><em>The complete question is</em></u>

Ernest calculated the slope of the graph during the uphill climb to be 10. His work is shown below.

Points: (60.900). (15, 450)

Slope : 900-450/60-15=450/45=10

Part a) Determine whether his calculation was correct or incorrect, and then explain why.

Part b) Confirm or disprove Ernest's work by selecting two different points and applying the slope formula. be sure to identify the points you chose

Part a)

we know that

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

we have the points

A(60,900),B(15,450)

Remember that

m_A_B=m_B_A

step 1

Find m_A_B

substitute in the formula

m_A_B=\frac{450-900}{15-60}\\\\m_A_B=\frac{-450}{-45}=10

step 2

Find m_B_A

substitute in the formula

m_B_A=\frac{900-450}{60-15}\\\\m_B_A=\frac{450}{45}=10

therefore

Ernest's calculation was correct, because m_A_B=m_B_A

Part b) selecting two different points

we take the points

(0,300) and (50,800) -----> see the attached figure

substitute in the formula of slope

m=\frac{800-300}{50-0}

m=\frac{500}{50}

m=10

therefore

Ernest's calculation was correct

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