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bagirrra123 [75]
3 years ago
7

Andre is preparing for the school play and needs to paint the rectangular cardboard castle backdrop that measures LaTeX: 14\frac

{1}{4}14 1 4feet by 6 feet. If one bottle of paint covers an area of 40 square feet, how many bottles of paint does Andre need for his backdrop? Enter your numerical answer with no label.
Group of answer choices
Mathematics
1 answer:
Genrish500 [490]3 years ago
6 0

Answer:

2.1375 bottles of paint

Step-by-step explanation:

cardboard length = 14 1/4 ft, which is equivalent to (4*14 + 1)/4 = 57/4 ft

cardboard width = 6 ft

Rectangular cardboard area = length * width = 57/4 * 6 = (57*6)/4 = 342/4 ft²,  which can be simplified dividing numerator and denominator by 2: 171/2 ft²

If 1 bottle of paint covers an area of 40 square feet, then to paint 171/2 square feet the following proportion must be satisfied:

1  bottle of paint / 40 square feet = x bottles of paint / (171/2) square feet

x = (1/40) * (171/2) = (1*171)/(40*2) = 171/80 or (160 + 11)/80 = 160/80 + 11/80 = 2 11/80 or 2.1375 bottles of paint

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Marks test scores for this semester were 83,80,91,74,66,95,87,72,95,97 what is the mode of his test scores
Vlada [557]

Answer:

95

Step-by-step explanation:

Mode is what is the most frequent number that occurred; 95 occurred the most from the data.

3 0
3 years ago
How do i factor s^2+9s=-20
Talja [164]
To factor you have to do this: 

s^2 + 9s = -20
      + 20    +20

s^2 + 9s + 20 = 0

now you need to numbers that multiplied give you 20 
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5+ 4 = 9

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3 years ago
g An irate student complained that the cost of textbooks was too high. He randomly surveyed 36 other students and found that the
blagie [28]

Answer:

A 90% confidence interval of the true mean is [$119.86, $123.34].

Step-by-step explanation:

We are given that an irate student complained that the cost of textbooks was too high. He randomly surveyed 36 other students and found that the mean amount of money spent on textbooks was $121.60.

Also, the standard deviation of the population was $6.36.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                              P.Q.  =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean amount of money spent on textbooks = $121.60

            \sigma = population standard deviation = $6.36

            n = sample of students = 36

            \mu = population mean

<em>Here for constructing a 90% confidence interval we have used One-sample z-test statistics as we know about population standard deviation.</em>

<em />

So, 95% confidence interval for the population mean, \mu is ;

P(-1.645 < N(0,1) < 1.645) = 0.90  {As the critical value of z at 5% level

                                                      of significance are -1.645 & 1.645}  

P(-1.645 < \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < 1.645) = 0.90

P( -1.645 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X-\mu} < 1.645 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.90

P( \bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.90

<u>90% confidence interval for</u> \mu = [ \bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } } , \bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } } ]

                                      = [ 121.60-1.645 \times {\frac{6.36}{\sqrt{36} } } , 121.60+1.645 \times {\frac{6.36}{\sqrt{36} } } ]

                                      = [$119.86, $123.34]

Therefore, a 90% confidence interval of the true mean is [$119.86, $123.34].

5 0
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Write the quadratic equation whose roots are −6 and 4, and whose leading coefficient is 3.
marshall27 [118]

Answer:

The quadratic equation is  ( 3x^{2} +6x -72)

Step-by-step explanation:

The quadratic equation form f(x) = a ( x- α) (x-β)

The roots are −6 and 4 and whose leading coefficient is 3.

the quadratic equation is f(x) = 3 ( x- (-6)) (x-4) = 3( x^{2} -4x +6x-24)

The quadratic equation is 3( x^{2} +2 x -24)

<u>Final answer</u>:-

The quadratic equation is  ( 3x^{2} +6x -72)

8 0
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