A university dean of students wishes to estimate the average number of hours students spend doing homework per week. The standard deviation from a previous study is 6.2 hours. How large a sample must be selected if he wants to be 99% confident of finding whether the true mean differs from the sample mean by 1.5 hours

Answers:

Trey's number line is incorrect because it represents the expression 2 1/2 ÷ 3/4.

The correct equation is 2 1/2 ÷ 3/8 = 6 2/3.

Ms. Nellies has enough vinegar for 6 groups of students.

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Explanation:

Trey has the right idea, but made a mistake on how the tickmarks are set up. Focus on the interval from 0 to 1. This section is cut into 4 equal pieces. So each tickmark represents 1/4 of a unit.

Going 3 tickmarks across means 3/4 of a unit is represented. Since each larger arc represents 3/4 of a unit, this means we're dividing the 2 & 1/2 over 3/4 instead of 3/8

That's why Trey's model represents 2 1/2 ÷ 3/4

The value 3 & 1/3 at the end is correct. Visually we see 3 whole jumps plus an extra 1/3 of a jump to arrive at 2 & 1/2. But again, Trey didn't cut the number line up in the right way, so it doesn't matter that he arrived at the correct result of 3 & 1/3 since his initial setup is faulty.

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See the diagram below to see what Trey should have drawn. Notice each tickmark represents 1/8 instead of 1/4. Each large blue arc jump represents 3/8 of a unit. We have exactly 6 of these blue arcs plus 2 additional smaller arcs that are 1/3 of the blue arc. So that accounts for the 1/3+1/3 = 2/3 portion.

Overall, we would say that the equation is 2 1/2 ÷ 3/8 = 6 2/3

If you're curious why that equation works, check out the steps below

[tex]2 \frac{1}{2} \div \frac{3}{8} = \frac{5}{2} \div \frac{3}{8}\\\\2 \frac{1}{2} \div \frac{3}{8} = \frac{5}{2} \times \frac{8}{3}\\\\2 \frac{1}{2} \div \frac{3}{8} = \frac{5*8}{2*3}\\\\2 \frac{1}{2} \div \frac{3}{8} = \frac{40}{6}\\\\2 \frac{1}{2} \div \frac{3}{8} = \frac{20}{3}\\\\2 \frac{1}{2} \div \frac{3}{8} = \frac{18+2}{3}\\\\2 \frac{1}{2} \div \frac{3}{8} = \frac{18}{3}+\frac{2}{3}\\\\2 \frac{1}{2} \div \frac{3}{8} = 6+\frac{2}{3}\\\\2 \frac{1}{2} \div \frac{3}{8} = 6\frac{2}{3}\\\\[/tex]

So again, the equation is 2 1/2 ÷ 3/8 = 6 2/3

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What does this all mean? Well it means the teacher can break up the vinegar into 6 whole parts plus an additional 2/3 of a part.

In other words, 6 groups will get 3/8 of a pint each. The leftover part 2/3 isn't enough to form that 7th group. Notice in the diagram below, we have 2/8 = 1/4 of a pint which is smaller than 3/8 of a pint.

1/4 = 0.25

3/8 = 0.375

So this is another way to see that the leftovers isn't enough to form a 7th group.

Therefore, she has enough vinegar for 6 groups

Answer:

56

Step-by-step explanation:

the surface area = (4×4) + (4×½×4×5)

= 16 + 40

= 56

9514 1404 393

Answer:

  no

Step-by-step explanation:

The measures 14, 18, 33 cannot correspond to the sides of a triangle. The two short sides total 32 in length, so cannot meet up with the ends of the side whose length is 33. A triangle cannot be formed.

Answer:

[tex]2\sqrt{2}[/tex]

Step-by-step explanation:

The given triangle is an isosceles triangle. However, one can see that it has a right angle (indicated by the box around the angle). Thus the triangle is a (45 - 45 - 90) triangle. A (45- 45 - 90) triangle is the only right isosceles triangle. One of the properties of a right isosceles triangle is that its sides follow the following ratio,

[tex]a;a;a\sqrt{2}[/tex]

Where (a) represents the legs of the right triangle, the sides that are adjacent to the right angle, in this case, the congruent sides. ([tex]a\sqrt{2}[/tex]) is the hypotenuse, the side opposite the right angle.

It is given that the hypotenuse is equal to (4), one is asked to find the length of the legs. To do so, divide the hypotenuse by ([tex]\sqrt{2}[/tex]) to find the legs. One can do this because the triangle is a (45 - 45 - 90) triangle, thus it must follow the ratio of the sides.

[tex]=\frac{4}{\sqrt{2}}[/tex]

Rationalize the denominator,

[tex]\frac{4}{\sqrt{2}}\\\\=\frac{4\sqrt{2}}{2}\\\\=2\sqrt{2}[/tex]

Answer:

5

Step-by-step explanation:

3-(-2)

the two negative signs cancel out and it turns into

3 + 2

3 + 2 = 5

Answer:

5

Step-by-step explanation:

minus * minus = plus

3-(-2) = 3 + 2 = 5

Answer:

y = 33/5

Step-by-step explanation:

Distribute

3(2y-8)-y = 9

6y - 24 - y

5y - 24 = 9

Add 24 to both sides

5y = 9 + 24

5y = 33

y = 33/5

Answer:

20

Step-by-step explanation:

diameter=√(12²+16²)=√[4²(3²+4²)]=4√(9+16)=4√25=4×5=20

Answer:

2006

799

Step-by-step explanation:

Given the expression:

The right hand side of the sun must be equal to the left hand side ;

Therefore ;

864+2006=--------+864

The sum of 864 and 2006 must be equal to the right hand side sum ; hence

864+2006= 2006 +864

Similarly, the left hand side and right havd side must also be equal here ;

5351 + 574 + 799 = 574 + 5351 + 799

Hence, the missing value is 799

9514 1404 393

Answer:

  II only

Step-by-step explanation:

You can simplify the inequality like this:

  3 -8 > 8 -8 + 5x . . . . . . . . subtract 8 from both sides

  -5 > 5x . . . . . . . . . . . . . simplify

  -5/5 > (5x)/5 . . . . . . . divide both sides by 5

  -1 > x . . . . . . . . . . . . simplify

I find this easier to compare to a numbers on a number line if the inequality symbol points to the left. (This is a personal preference. YMMV)

  x < -1

Now, we can see that only numbers to the left of -1 on the number line will be suitable values for x. Of those listed, only -9 is a solution.

  II only

Answer:

Step-by-step explanation:

Answer:

the last one

Step-by-step explanation:

congruent means they are the same and all sides of a square are the same size.

Answer:

The actual distance is of 21.76 kilometers.

Step-by-step explanation:

Scale problems are solved by proportions, using a rule of three.

The scale on a map is given as 1 : 320,000

This means that each unit on the map represents 320,000 units of distance.

Distance between the top of the two mountains on the map is 6.8cm

Then

1 cm - 320,000 cm

6.8 cm - x

Applying cross multiplication:

[tex]x = 6.8*320000 = 2176000[/tex]

Distance in kilometers

To convert from centimeters to kilometers, we divide by 100000. So

2176000/100000 = 21.76

The actual distance is of 21.76 kilometers.

Answer:

Undefined

Step-by-step explanation:

The square root of a negative number does not exist in the set of real numbers so it would be Undefined

Answer:

104/4 pi

Step-by-step explanation:

Answer: The circumference of a circle is:

Radius = r, Diameter = d, C = Circumference

C=2πr (as 2r=d)

C=πd

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If the radius of the circle is 26" then its diameter must be 52".

This means that the bicycle wheel has a circumference of 52π".

I'm going to divide 52π" into 360 parts (because a circle is made up of 360 degrees). I'll then multiply this value by 80 to give you an answer.

Answer:

Step-by-step explanation:

x + ab = p

x = p - ab

Answer:

x= -1

Step-by-step explanation:

if

f(x) = -x-3

and

f(x) = -2

than

-x-3 = -2; add 3 to both sides

-x-3+3 = -2+3

-x = 1 ; multiply both sides by -1

x= -1

Answer:

A’(-5,5)

Step-by-step explanation:

x’ = 2.5 * -2 = -5

y‘ = 2.5  * 2 = 5

Answer:

10 cm^2

Step-by-step explanation:

area= 1/2 b*h

1/2 (5) (4)

= 1/2 (20)

=10

area= 10cm^2

Answer:

a = 10cm²

Step-by-step explanation:

a = (1/2)bh

a = (1/2)(5)(4)

a = 10cm²

Answer:     the value of A is 2

Step-by-step explanation:

Answer:

It would be Linear

Step-by-step explanation:

Answer:

i think its quadratic because the graph isnt straight and has different slopes between the x,y.

Step-by-step explanation:

Answers:

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Explanation:

The simple interest formula is

i = p*r*t

where in this case,

So,

i = p*r*t

i = 3000*0.10*0.25

i = 75 is the amount of interest earned

This adds onto the initial deposit to get the final balance when the CD matures (ie when you're able to withdraw the money without penalties)

The balance at maturity is p+i = 3000+75 = 3075 dollars

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In short, you deposit $3000 into the CD and have to wait 3 months for the amount to update to $3075.

Answer:

-1

Step-by-step explanation:

When b<4

|b-4|  is negative

|b-4|  = - ( b-4)

- (b-4) / ( b-4) =

Factoring out (b-4)

-1

Answer:

0

Step-by-step explanation:

Ignore the next 2 numbers after 0.05. To the nearest whole number, round 0.05 to the nearest tenth, 0.1. Then round that to the nearest whole number, 0, which is your answer.

A square

Step-by-step explanation:

because there're only 2 circles being create whereas with an equilateral

Answer:

A square

Step-by-step explanation:

Answer:

150%

Step-by-step explanation:

given:

original quantity = 14

new quantity = 35

increased quantity = 35 - 14

=21

percent change = increased quantity /original quentity * 100%

=21/14 *100%

=21100/14 %

=150 %

Answer:

$620

Step-by-step explanation:

（1-62%）X=235.6

X=235.6/38%

X=620

The original price is $620

Answer:

a. [tex]P(2 \leq X \leq 3) = 0.5[/tex]

b. [tex]P(X \geq 1) = 0.9[/tex]

c. [tex]P(X < 2) = 0.25[/tex]

d. [tex]P(X > 3) = 0.25[/tex]

Step-by-step explanation:

We are given the following distribution:

[tex]P(X = 0) = 0.1[/tex]

[tex]P(X = 1) = 0.15[/tex]

[tex]P(X = 2) = 0.25[/tex]

[tex]P(X = 3) = 0.25[/tex]

[tex]P(X = 4) = 0.15[/tex]

[tex]P(X = 5) = 0.1[/tex]

a. Two or three bars

[tex]P(2 \leq X \leq 3) = P(X = 2) + P(X = 3) = 0.25 + 0.25 = 0.5[/tex]

Thus:

[tex]P(2 \leq X \leq 3) = 0.5[/tex]

b. At least one bar

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1 = 0.9[/tex]

Thus:

[tex]P(X \geq 1) = 0.9[/tex]

c. Fewer than two bars

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.1 + 0.15 = 0.25[/tex]

Thus:

[tex]P(X < 2) = 0.25[/tex]

d. More than three bars

[tex]P(X > 3) = P(X = 4) + P(X = 5) = 0.15 + 0.1 = 0.25[/tex]

Thus:

[tex]P(X > 3) = 0.25[/tex]

Answer:

mKML+mMLK=mJKM

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. Types of triangles are scalene, acute, obtuse, equilateral, isosceles, and right triangle.

As shown in the diagram, polygon MLK is a triangle. The sum of angles in a triangle is equal to 180°, hence:

m∠MLK + m∠KML + m∠MKL = 180° (sum of angles in a triangle).

m∠MKL = 180 -  (m∠MLK + m∠KML)      (1)

Also along line JL, the sum of angles on one side of a straight line is 180°, therefore:

m∠JKM + m∠MKL = 180° (sum of angles in a straight line)

m∠JKM + m∠MKL = 180°                (2)

From equations 1 and 2, equating give:

m∠JKM + [180 -  (m∠MLK + m∠KML)) =  180

m∠JKM + 180 - m∠MLK - m∠KML =  180

m∠JKM = m∠MLK + m∠KML

Answer:

10x+8

Step-by-step explanation:

4( x + 2) + 6x

Distribute

4x+8 +6x

Combine like terms

10x+8

Answer:

10x+8

Step-by-step explanation:

4x+8+6x

(4x+6x)+8

10x+8