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3 years ago

1/3 + (3x+12) = 6x -11

Mathematics

2 answers:

Lerok [7]3 years ago

6 0

Answer:

x = 70/9

Step-by-step explanation:

Pavel [41]3 years ago

6 0

Answer:

70/9

Step-by-step explanation:

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Sonja [21]

Answer:

Step-by-step explanation:

4 0

3 years ago

poll finds that 54% of the 600 people polled favor the incumbent. Shortly after the poll is taken, it is disclosed that he had a

Paha777 [63]

Answer: A. z = -2.57

Step-by-step explanation:

Let p be the population proportion of people polled favor the incumbent.

As per given , we have

$H_0: p=0.54\\\ H_a: p$

Sample size : n= 1030

sample proportion : $\hat{p}=0.50$

Test statistic for proportion : $z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

$z=\dfrac{0.50-0.54}{\sqrt{\dfrac{0.54(1-0.54)}{1030}}}\\\\= \dfrac{-0.04}{\sqrt{\dfrac{0.2484}{1030}}}\\\\=\dfrac{-0.04}{0.015529488}\approx-2.57$

Hence, the test statistic is z = -2.57 .

Thus , the correct answer is A. z = -2.57 .

7 0

3 years ago

A contaminant is leaking into a lake at a rate of R(t) = 1700e^0.06t gal/h. Enzymes that neutralize the contaminant have been ad

olasank [31]

Answer:

16,460 gallons

Step-by-step explanation:

This is a differential equation problem, we have a constant flow of contaminant into the lake, but also we know that only a fraction of that quantity of contaminant remains because of the enzymes. For that reason, the differential equation of contaminant's flow into the lake would be:

$\frac{dQ}{dt} =1700exp(0.06t)*exp(-0.32t)\\\frac{dQ}{dt} =1700exp(-0.26t)\\$

Then, we have to integrate in order to find the equation for Q(t), as the quantity of contaminant in the lake, in function of time.

$\int\limits^0_t {dQ}=\int\limits^0_t {1700exp(-0.26t)dt}\\Q(t)=\frac{1700}{-0.26} exp(-0.26t)+C \\$

Now, we use the given conditions to replace them in the equation, in order to solve for $C$

$t_{0} =0\\Q_{0}=10,000\\Q_{0}=-6538exp(-0.26*0)+C\\C=10,000+6538=16538$

Then, we reorganize the equation and we replace t for 17 hours, in order to determine the quantity of contaminant at that time:

$Q_{t} =-6538exp(-0.26t)+16538\\Q_{17} =-6538exp(-0.26*17)+16538\\Q_{17} =16460 gallons$

3 0

3 years ago

B. Write an equation that matches the situation.

baherus [9]

Zsjdjdjjfjfnfnfnfnfnnfnfmf

6 0

4 years ago

Claudio needs to buy gifts for 8 friends. He wants to give the same gift to all his friends and he plans to have the gifts wrapp

Blizzard [7]

Answer:

7.25

Step-by-step explanation:

In the question, the term at least means less than or equal to is represented by ≥

Let the cost of each gift = c

He is buying gifts for 8 friends = 8 gifts

Hence, our Inequality equation is written as:

(c + $1.50)× 8 ≥ $70

8c + 12 ≥ 70

8c ≥70 - 12

c ≥ 58/8

c≥ 7.25

Therefore, the amount Claudio needs to spend on each gift in order to receive free shipping is 7.25

6 0

3 years ago