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DerKrebs [107]
2 years ago
8

Henry has a wooden chest that has a length of 312 ft, a width of 114 ft and a height of 2 ft. Henry sands the entire outside of

the chest with sandpaper. How many square feet of wood does Henry sand?
Mathematics
1 answer:
timurjin [86]2 years ago
4 0
The surface area of a rectangular prism is:

A=2(xy+xz+yz)  where x,y, and z are the dimensions, in this case:

A=2(312*114+312*2+114*2)

A=2(35568+624+228)

A=2(36420)

A=72840 ft^2
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You have been doing research for your statistics class on the prevalence of severe binge drinking among teens. You have decided
Serggg [28]

Answer:

(1.218 ; 1.322)

the confidence interval is appropriate

Step-by-step explanation:

The confidence interval :

Mean ± margin of error

Sample mean = 1.27

Sample standard deviation, s = 0.80

Sample size, n = 914

Since we are using tbe sample standard deviation, we use the T table ;

Margin of Error = Tcritical * s/√n

Tcritical at 95% ; df = 914 - 1 = 913

Tcritical(0.05, 913) = 1.96

Margin of Error = 1.96 * 0.80/√914 = 0.05186

Mean ± margin of error

1.27 ± 0.05186

Lower boundary = 1.27 - 0.05186 = 1.218

Upper boundary = 1.27 + 0.05186 = 1.322

(1.218 ; 1.322)

According to the central limit theorem, sample means will approach a normal distribution as the sample size increases. Hence, the confidence interval is valid, the sample size of 914 gave a critical value at 0.05 which is only marginally different from that will obtained using a normal distribution table. Hence, the confidence interval is appropriate

8 0
3 years ago
Write the equation of the conic section with the given properties:
timurjin [86]

Answer:

\frac{x^2}{64} + \frac{y^2}{25} =1

Step-by-step explanation:

An ellipse with vertices (-8, 0) and (8, 0)

Distance between two vertices = 2a

Distance between (-8,0) and (8,0) = 16

2a= 16

so a= 8

Vertex is (h+a,k)

we know a=8, so vertex is (h+8,k)

Now compare (h+8,k) with vertex (8,0) and find out h and k

h+8 =8, h=0

k =0  

a minor axis of length 10.

Length of minor axis = 2b

2b = 10

so b = 5

General formula for the equation of horizontal ellipse is

\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b} =1

a= 8 , b=5 , h=0,k=0. equation becomes

\frac{(x-0)^2}{8^2} + \frac{(y-0)^2}{5} =1

\frac{x^2}{64} + \frac{y^2}{25} =1

5 0
3 years ago
Genius question: A long level railway bridge passes over a railroad track, which is 100 feet below it and at right angles to it.
nataly862011 [7]

Answer: <u>110 feet per second</u>

Step-by-step explanation:

In this problem we will assume that the car at 45 miles per hour is moving into the x direction with a high of 100 feet, and the train is going in the y direction, so they trajectories will made an angle of 90º.

Now we can calculate the speed of the trains in feet per second so:

S1=\frac{45*5280}{3600}=66

S2=\frac{60*5280}{3600}=88

So we can make a right triangle with sides 66 and 88 and the hypotenuse will be the rate that the trains will separate per second so:

h=\sqrt{66^{2} +88^{2} } =\sqrt{4356+7744}

h=\sqrt{12100}=110

Is important to have in mind that the initial high is not going to change how fast the trains will separate, however, if we are going to calculate the distance we should have it in the calculations.

7 0
2 years ago
Please help with this 2+4(5-8). step by step
igor_vitrenko [27]
NAMASTE

HERE IS YOUR ANSWER:

2+4(5-8)
We know, the BODMAS (bar, order, multiply, add, subtract) rule. so we will solve it as follows:


➡2+4(-3) (✔ 5-8= -3)

➡2+(-12) (✔ 4(-3)= -12)

➡2-12 (✔ +(-12) = -12)

➡ \boxed{-10}
8 0
3 years ago
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Write an expression that is equivalent to 2/3 (4x + 9)
prohojiy [21]

Answer:

8x/3 + 6

Step-by-step explanation:

3 0
3 years ago
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