If Ill m, solve for x.<br> (9x+2)<br> 119°<br> x =

450 high school freshmen were randomly selected for a national survey. Among survey participants, the mean grade-point average (

umka21 [38]

Answer:

The margin of error is of 0.01.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.7}{2} = 0.15$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.15 = 0.85$ , so Z = 1.037.

The margin of error is of:

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

Standard deviation was 0.21.

This means that $\sigma = 0.21$

Sample of 450:

This means that $n = 450$

What is the margin of error, assuming a 70% confidence level, to the nearest hundredth?

$M = z\frac{\sigma}{\sqrt{n}}$

$M = 1.037\frac{0.21}{\sqrt{450}}$

$M = 0.01$

The margin of error is of 0.01.

4 0

3 years ago

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by

a_sh-v [17]

Answer:

Dimension of the box is $16.1\times 7.1\times 2.45$

The volume of the box is 280.05 in³.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the box?

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is $L=21-2h$

The width of the box is $W=12-2h$

The volume of the box is $V=L\times W\times H$

$V=(21-2h)\times (12-2h)\times h$

$V=(21-2h)\times (12h-2h^2)$

$V=252h-42h^2-24h^2+4h^3$

$V=4h^3-66h^2+252h$

To maximize the volume we find derivative of volume and put it to zero.

$V'=12h^2-132h+252$

$0=12h^2-132h+252$

Solving by quadratic formula,

$h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}$

$h=\frac{132\pm72.99}{24}$

$h=2.45,8.54$

Now, substitute the value of h in the volume,

$V=4h^3-66h^2+252h$

When, h=2.45

$V=4(2.45)^3-66(2.45)^2+252(2.45)$

$V\approx 280.05$

When, h=8.54

$V=4(8.54)^3-66(8.54)^2+252(8.54)$

$V\approx -170.06$

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is $L=21-2(2.45)=16.1$

The width of the box is $W=12-2(2.45)=7.1$

So, Dimension of the box is $16.1\times 7.1\times 2.45$

6 0

3 years ago

What is the measure of ∠ABC

astraxan [27]

Answer:

B

Step-by-step explanation:

The measure of the chord- chord angle ABC is half the sum of the arcs intercepted by the angle and its vertical angle, that is

∠ ABC = 0.5( 82 + 44)° = 0.5 × 126° = 63° → B

4 0

3 years ago

Henry has two pixie sticks full of delicious sugar. Henry loves to share. It just so happens that there are two other friends ne

Effectus [21]

Answer: 14.7 grams

Step-by-step explanation:

Given : Henry has two pixie sticks full of delicious sugar.

Each pixie stick has 22 grams of sugary goodness.

Then, Total sugary goodness in 2 pixie sticks= $2\times22=44\text{ grams}$

Total persons = 3 [Including himself]

If he divides 2 sticks evenly among 3 persons , then the amount of sugary goodness each persons will receive

= Total sugary goodness in 2 pixie sticks divided by 3

$=44\div3=14.6666666667\approx14.7$ grams

Hence, He will share 14.7 grams of sugary goodness with each of his friends.

4 0

3 years ago

Please help me answer one of these!

babunello [35]

This seems to be referring to a particular construction of the perpendicular bisector of a segment which is not shown. Typically we set our compass needle on one endpoint of the segment and compass pencil on the other and draw the circle, and then swap endpoints and draw the other circle, then the line through the intersections of the circles is the perpendicular bisector.

There aren't any parallel lines involved in the above described construction, so I'll skip the first one.

2. Why do the circles have to be congruent ...

The perpendicular bisector is the set of points equidistant from the two endpoints of the segment. Constructing two circles of the same radius, centered on each endpoint, guarantees that the places they meet will be the same distance from both endpoints. If the radii were different the meets wouldn't be equidistant from the endpoints so wouldn't be on the perpendicular bisector.

3. ... circles of different sizes ...

[We just answered that. Let's do it again.]

Let's say we have a circle centered on each endpoint with different radii. Any point where the two circles meet will then be a different distance from one endpoint of the segment than from the other. Since the perpendicular bisector is the points that are the same distance from each endpoint, the intersection of circles with different radii isn't on it.

4. ... construct the perpendicular bisector ... a different way?

Maybe what I first described is different; there are no parallel lines.

8 0

3 years ago

If Ill m, solve for x. (9x+2) 119° x =