What is the area of the trapezoid shown below??

An article gave the following summary information for fracture strengths (MPa) of n = 196 ceramic bars fired in a particular kil

Oliga [24]

Answer:

54.80 MPa to 55.92 MPa

Step-by-step explanation:

Sample mean fracture strength (x) = 55.36 MPa

Sample standard deviation (s) = 3.99 MPa

Sample size (n) = 196.

The upper and lower bounds for a 95% confidence interval are given by:

$U=x+1.960*\frac{s}{\sqrt{n}} \\L=x-1.960*\frac{s}{\sqrt{n}}$

The upper and lower bounds of the confidence interval are;

$U=55.36+1.960*\frac{3.99}{\sqrt{196}}\\U= 55.92\\L=55.36-1.960*\frac{3.99}{\sqrt{196}}\\L= 54.80\\$

The 95% confidence interval for true average fracture strength is 54.80 MPa to 55.92 MPa

4 0

3 years ago

A fireman's ladder leaning against a house makes an angle of 50° with the ground. How long is the ladder if the ladder is 8 feet

antoniya [11.8K]

The ladder would be 12.4 feet hope that helps

5 0

3 years ago

The seventh term of an arithmetic progression is equal to twice the fifth term. The sum

mario62 [17]

Answer:

a₁ = - 24

Step-by-step explanation:

The n th term of an AP is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₇ = 2a₅ , then

a₁ + 6d = 2(a₁ + 4d) = 2a₁ + 8d ( subtract 2a₁ + 8d from both sides )

- a₁ - 2d = 0 → (1)

The sum to n terms of an AP is

$S_{n}$ = $\frac{n}{2}$ [ 2a₁ + (n - 1)d ]

Given $S_{7}$ = 84 , then

$\frac{7}{2}$ (2a₁ + 6d) = 84

3.5(2a₁ + 6d) = 84 ( divide both sides by 3.5 )

2a₁ + 6d = 24 → (2)

Thus we have 2 equations

- a₁ - 2d = 0 → (1)

2a₁ + 6d = 24 → (2)

Multiplying (1) by 3 and adding to (2) will eliminate d

- 3a₁ - 6d = 0 → (3)

Add (2) and (3) term by term to eliminate d

- a₁ = 24 ( multiply both sides by - 1 )

a₁ = - 24

6 0

3 years ago

Solve.<br> x^2+9x+2=0<br> thanks!

shtirl [24]

Step one:
ALWAYS set equation equal to zero, which in this case has already been done for us.

Step two:
Figure out what formula you need to use in order to solve in this case I'd use the Quadratic formula.

a=1
b=9
c=2

Quadratic formula:
$x = \frac{ - b + - \sqrt{(b) ^{2} - 4(a)(c)} }{2(a)}$
Then you would plug in the information.
$x = \frac{ - 9+ - \sqrt{(9) {}^{2} - 4(1)(2) } }{2(1)}$
The solve for what is underneath the square root ONLY.
$x = \frac{ - 9 + - \sqrt{73} }{2}$
Since you cannot solve this any further, your final two answers are...
$x = \frac{ - 9 + \sqrt{73} }{2}$
$x = \frac{ - 9 - \sqrt{73} }{2}$

3 0

3 years ago

Give an example of a system of linear equations that can be solved by first adding the equations to eliminate one variable.

telo118 [61]

f ( 7 ) = 2.4 ft

Step-by-step explanation:

Solution:-

- This is modeled using a geometric sequence function with initial height from which ball is dropped hi = 18 feet, and a decrease in height by 25% after each successive bounce :

f ( x ) = 18 (0.75)^x

Where, x e [ 0 , ∞ ) : The number of bounces.

f (x) : The maximum height after xth bounce.

- The maximum height reached by the ball after its 7th bounce. So, x = 7:

f ( 7 ) = 18 (0.75)^7

f ( 7 ) = 2.4027 ft

- To the nearest tenth:

f ( 7 ) = 2.4 ft

5 0

2 years ago