Please help me with this question!

The standard deviation for a set of data is 6.5. The mean is 255. What is the Margin of Error?

HACTEHA [7]

Answer: The margin of error is 12.74.

Step-by-step explanation:

Since we have given that

Standard deviation = 6.5

Mean = 255

Let 95% level of significance,

So, z value = 1.96

We need to find the "Margin of error":

So, it becomes :

Margin of error = Standard deviation × z-value

Margin of error = $6.5\times 1.96=12.74$

Hence, the margin of error is 12.74.

3 0

3 years ago

In circle A, ∠BAE ≅ ∠DAE. What is the length of BE? 14 units 17 units 27 units 34 units

zhannawk [14.2K]

Answer:

The length of BE is 27 units ⇒ 3rd answer

Step-by-step explanation:

In circle A:

∠BAE ≅ ∠DAE

Line segments A B, A E, and A D are radii

Lines are drawn from point B to point E and from point E to point D to form secants B E and E D

The length of B E is 3 x minus 24 and the length of E D is x + 10

We need to find the length of BE

∵ AB and AD are radii in circle A

∴ AB ≅ AD

In Δs EAB and EAD

∵ ∠BAE ≅ ∠DAE ⇒ given

∵ AB = AD ⇒ proved

∵ EA = EA ⇒ common side in the two triangles

- Two triangles have two corresponding sides equal and the

including angles between them are equal, then the two

triangles are congruent by SAS postulate of congruence

∴ Δ EAB ≅ Δ EAD ⇒ SAS postulate of congruence

By using the result of congruence

∴ EB ≅ ED

∵ EB = 3 x - 24

∵ ED = x + 10

- Equate the two expressions to find x

∴ 3 x - 24 = x + 10

- Add 24 to both sides

∴ 3 x = x + 34

- Subtract x from both sides

∴ 2 x = 34

- Divide both sides by 2

∴ x = 17

Substitute the value of x in the expression of the length of BE to find its length

∵ BE = 3 x - 24

∵ x = 17

∴ BE = 3(17) - 24

∴ BE = 51 - 24

∴ BE = 27

The length of BE is 27 units

3 0

3 years ago

Read 2 more answers

The landing for the steps leading up to a county courthouse is shaped like a trapezoid. The area of the landing is 1500 square f

77julia77 [94]

Answer:

The length of the longer base is 80 feet.

Step-by-step explanation:

We are given that county courthouse is shaped like a trapezoid.

Let the height of the court house be h

Since we are given that The shorter base of the trapezoid is 15 feet longer than the height.

So, the shorter base = h+15

We are also given that The longer base is 5 feet longer than 3 times the height

So, longer Base = 3h+5

Now we are also given that the area of the landing is 1500 square feet.

Formula of area of trapezium :

= $\frac{1}{2} *(\text{Length of longer base}+\text{Length of shorter base})*height$

Substituting the values .

$1500=\frac{1}{2} *(h+15+3h+5)*h$

$1500=\frac{1}{2} *(4h+20)*h$

$1500*2=(4h+20)*h$

$3000=4h^2+20h$

Taking 4 common from the equation.

$750=h^2+5h$

$h^2+5h-750=0$

$h^2-25h+30h-750=0$

$h(h-25)+30(h-25)=0$

$(h-25)(h+30)=0$

⇒ h = 25, -30

Neglect the negative value .

So, height = 25 feet.

Length of Longer base = 3h+5 =3*25+5=80 feet

Hence , the length of the longer base is 80 feet.

6 0

3 years ago

There are two numbers. The first number minus the second number is 15. One-third of the sum of the numbers is one quarter of the

disa [49]

Answer:

So the numbers are 12 and -3.

Step-by-step explanation:

In order to solve this problem we will attribute variables to the numbers, the first one will be "x" and the second one will be "y". From the first sentence we know that the subtraction of the two numbers is equal to 15, so we have:

x - y = 15

Then the problem states that one-third of the sum of the number is equal to one quarter of the first number, so we have:

(1/3)*(x+y) = x/4

Since we now have two equations and two variables we can solve for x and y. From the first equation we have:

y = x - 15

Using this expression for the value of y in the second equation:

(1/3)*(x + x - 15) = x/4

(1/3)*(2*x - 15) = x/4

2*x - 15 = 3*x/4

2*x - 3*x/4 = 15

(8*x - 3*x)/4 = 15

5*x/4 = 15

5*x = 60

x = 60/5 = 12

y = x - 15 = 12 - 15 = -3

So the numbers are 12 and -3.

4 0

2 years ago

Read 2 more answers

A box has dimensions of 19 inches long, 1.7 feet wide, and 6 inches high. What is the volume of the box? The formula for the vol

strojnjashka [21]

Volume of box = length x width x height = 19 x (1.7 x 12) x 6 = 19 x 20.4 x 6 = 2,325.6 cubic inches.

4 0

2 years ago