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solniwko [45]
3 years ago
6

-7–5(3g+8)<10g–7+g help me please!

Mathematics
1 answer:
Ede4ka [16]3 years ago
8 0

Answer:

-20/13 <g

Step-by-step explanation:

-7–5(3g+8)<10g–7+g

Distribute

-7–15g-40<10g–7+g

Combine like terms

-15g - 47 < 11g -7

Add 15 g to each side

-15g+15g -47< 11g+15g -7

-47 < 26g -7

Add 7 to each side

-47+7 < 26g-7+7

-40 < 26g

Divide each side by 26

-40/26 <26g/26

-40/26 <g

Divide top and bottom by 2

-20/13 <g

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127

Step-by-step explanation:

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672 - 545 = 127

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Lisa went to the hardware store and bought 12 pieces rope. Each rope was 3/4 of a meter long. If the rope cost $3.50 a meter, ho
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Mark wants to fence 4 rectangular gardens, each with a length of 9 1/4 feet and a width of 4 1/2 feet. What is the total length
juin [17]

Answer:

110 feet

Step-by-step explanation:

Given that,

Length of the rectangular garden = 9 1/4 feet = 37/4 feet

Width of the rectangular garden = 4 1/2 feet = 9/4 feet

We need to find the total length of fencing Mark needs to surround all 4 gardens.

The length for 1 garden = perimeter of the garden

The length for 4 garden = 4×perimeter of the garden

= 4×2(l+b)

=8(l+b)\\\\=8(\dfrac{37}{4}+\dfrac{9}{2})\\\\=8\times 13.75\\\\=110\ \text{feet}

Hence, 110 feet is the total length of the fencing Mark needs to surround all 4 gardens.

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Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorab
Katyanochek1 [597]

Answer:

(a) Customer will not purchase the light bulbs at significance level of 0.05

(b) Customer will purchase the light bulbs at significance level of 0.01 .

Step-by-step explanation:

We are given that Light bulbs of a certain type are advertised as having an average lifetime of 750 hours. A random sample of 50 bulbs was selected,  and the following information obtained:

Average lifetime = 738.44 hours and a standard deviation of lifetimes = 38.2 hours.

Let Null hypothesis, H_0 : \mu = 750 {means that the true average lifetime is same as what is advertised}

Alternate Hypothesis, H_1 : \mu < 750 {means that the true average lifetime is smaller than what is advertised}

Now, the test statistics is given by;

       T.S. = \frac{Xbar-\mu}{\frac{s}{\sqrt{n} } } ~ t_n_-_1

where, X bar = sample mean = 738.44 hours

               s  = sample standard deviation = 38.2 hours

               n = sample size = 50

So, test statistics = \frac{738.44-750}{\frac{38.2}{\sqrt{50} } } ~ t_4_9

                            = -2.14

(a) Now, at 5% significance level, t table gives critical value of -1.6768 at 49 degree of freedom. Since our test statistics is less than the critical value of t, so which means our test statistics will lie in the rejection region and we have sufficient evidence to reject null hypothesis.

Therefore, we conclude that the true average lifetime is smaller than what is advertised and so consumer will not purchase the light bulbs.

(b) Now, at 1% significance level, t table gives critical value of -2.405 at 49 degree of freedom. Since our test statistics is higher than the critical value of t, so which means our test statistics will not lie in the rejection region and we have insufficient evidence to reject null hypothesis.

Therefore, we conclude that the true average lifetime is same as what it has been advertised and so consumer will purchase the light bulbs.

6 0
3 years ago
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