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ycow [4]
3 years ago
12

The load that can be supported by a rectangular beam there is jointly as the width of the beam in the square of its height and i

nversely as the length of the beam a been 14 feet long with the width of 4 inches and the height of 6 inches can support a maximum load of 800 pounds if a similar board has a width of 9 inches and the height of 5 inches how long must be to support 1400 pounds
Mathematics
1 answer:
g100num [7]3 years ago
5 0

Answer:

  12.5 feet

Step-by-step explanation:

The description of the load-carrying capacity of the beam translates as ...

  load = k·w·h²/l

Filling in the numbers, we can find the constant k:

  800 lb = k·(4 in)(6 in)²/(14 ft)

  k = (800·14 lb·ft)/(144 in³) = 700/9 lb·ft/in³

__

Then the length to support 1400 lb with the other given dimensions will be ...

  1400 lb = (700/9) lb·ft/in³ × (9 in)(5 in)²/l

  l = 700·25/1400 ft = 12.5 ft

The beam must be at most 12.5 ft long to support 1400 pounds.

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One angle of a right triangle measures 61°. What is the measure of the other acute angle?
svetlana [45]
The other answer is 29 degrees because 90 for right angle and 61 for one angle is 151 then subtract 180 (for the Triangle Sum theory) minus 151 then it’s 29 degrees
8 0
2 years ago
A high school principal wishes to estimate how well his students are doing in math. Using 40 randomly chosen tests, he finds tha
ollegr [7]

Answer:

99% confidence interval for the population proportion of passing test scores is [0.5986 , 0.9414].

Step-by-step explanation:

We are given that a high school principal wishes to estimate how well his students are doing in math.

Using 40 randomly chosen tests, he finds that 77% of them received a passing grade.

Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;

                          P.Q. = \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where, \hat p = sample proportion of students received a passing grade = 77%

           n = sample of tests = 40

           p = population proportion

<em>Here for constructing 99% confidence interval we have used One-sample z proportion test statistics.</em>

So, 99% confidence interval for the population proportion, p is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99  {As the critical value of z at 0.5%

                                           level of significance are -2.5758 & 2.5758}  

P(-2.5758 < \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } < 2.5758) = 0.99

P( -2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < {\hat p-p} < 2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.99

P( \hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < p < \hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.99

<u>99% confidence interval for p</u> = [\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } , \hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }]

 = [ 0.77-2.5758 \times {\sqrt{\frac{0.77(1-0.77)}{40} } } , 0.77+2.5758 \times {\sqrt{\frac{0.77(1-0.77)}{40} } } ]

 = [0.5986 , 0.9414]

Therefore, 99% confidence interval for the population proportion of passing test scores is [0.5986 , 0.9414].

Lower bound of interval = 0.5986

Upper bound of interval = 0.9414

6 0
2 years ago
Solve the equation for x. 2 3 x −1 9 x + 5 = 20 x =
zubka84 [21]

Answer:

5/2

Step-by-step explanation:

23x-19x+5=2x

23x-19x-2x=5

2x/2=5/2

x=5/2

3 0
2 years ago
Read 2 more answers
Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Vladimir79 [104]
Understand the problem
Gather your resources
Come to an answering
Check your answer and present the solution
3 0
2 years ago
Read 2 more answers
57.
barxatty [35]

Answer:

$5.70

Step-by-step explanation:

→ Find the total amount they needed to pay

11.40 × 2 = 22.80

→ Divide the total by 4

22.80 ÷ 4 = $5.70

6 0
2 years ago
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