The ages of students in a school are normally distributed with a mean of 16 years and a standard deviation of 1 year. Using the empirical rule, approximately what percent of the students are between 14 and 18 years old?

Answer:

Step-by-step explanation:

No, the relationship is not linear. It is "roughly" an "inversely proportional" relationship, not a linear relationship. (Read the problem statement: "the product of the number sold and the price in dollars is roughly constant".)

__

The points, when graphed, are not on a straight line.

Answer:

b

Step-by-step explanation:

just took the test

Answer:

The width = 16 yards and the length = 25 yards.

Step-by-step explanation:

Let x yards be the original width, then the original length is 2x - 7 yards.

Therefore the original area = x(2x - 7) yd^2.

The new area =  (2x - 7 + 11)(x - 6)

= (2x + 4)(x - 6) yd^2.

So we have the equation

x(2x - 7) - (2x + 4)(x - 6) = 40

2x^2 - 7x - (2x^2 - 12x + 4x - 24) = 40

2x^2 - 7x - 2x^2 + 8x + 24 - 40 = 0

x - 16 = 0

x = 16 yards = the width.

The length = 2(16) - 7 = 25 yards.

To find the original dimensions of the lot, assume the width is 'w', then solve an equation using the information given.

To find the original dimensions of the lot, let's assume that the width is 'w' yards. The length of the lot is then '2w-7' yards, since it is 7 yards less than twice the width.

If we increase the length by 11 yards and decrease the width by 6 yards, the new dimensions would be '2w-7+11' yards for the length and 'w-6' yards for the width.

The area of the lot is given by length multiplied by width, so we can set up the equation:

(2w-7+11)(w-6) = (2w)(w) - 40

Simplifying this equation and solving for 'w', we find that the original width of the lot is 12 yards. The length is then 2(12) - 7 = 17 yards.

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Answer:

They are both the same at 3/4 of an hour

Step-by-step explanation:

We have a system of equations here.  The first one is for Friday:

3A + 5B = 6, which says that 3 people at the number of hours for plan A plus 5 people at the number of hours for plan B equals 6 hours total.

The second equation is for Saturday:

9A + 7B = 12, which says that 9 people at the number of hours for plan A plus 7 people at th number of hours for plan B equals 12 hours total.

We can solve this easily using the addition/elimination method.  Begin by multipying the first equation through by a -3 to eliminate the A's.  That gives you a new first equation of:

  -9A  -  15B  =  -18

  9A  +    7B  =  12

You can see that the A's are eliminated, and adding what remains leaves us with

-8B = -6 so

B = 3/4 hour

Now we can sub that back in for B in either one of our original equations to solve for A.  I changed the 3/4 to .75 for ease of multiplying:

9A + 7(.75) = 12 and

9A + 5.25 = 12 and

9A = 6.75 so

A = .75 which is also 3/4 of an hour

Answer:

V = 1 1/4 m³

M = 3000.0  kg

Step-by-step explanation:

Volume = Length × Width ×  Height

2 1/2 x 3/4 x 2/3

V = 1 1/4

M=  2.5m ⋅ 0.75m ⋅ 0.666666666666m ⋅ 2400kg/m³

Answer:

(a) 1.25 m^3

(b) 3000 kg

Step-by-step explanation:

(a) The volume of a rectangular prism is L*W*H.

So volume = [tex](2\frac{1}{2})(\frac{3}{4})(\frac{2}{3})=1.25 m^3[/tex]

(b) The mass=density*volume.

So mass = [tex]2400 \frac{kg}{m^3} \cdot 1.25 m^3=3000 kg[/tex].

Explanation:

Any function that has a derivative that changes sign will have an extreme value (maximum or minimum). If the derivative never changes sign, the function will not have any extreme values.

__

Logarithmic, exponential, and certain trigonometric, hyperbolic, and rational functions are monotonic, having a derivative that does not change sign. Odd-degree polynomials may also have this characteristic, though not necessarily. These functions will not have maximum or minimum values.

__

Certain other trigonometric, hyperbolic, and rational functions, as well as any even-degree polynomial function will have extreme values (maximum or minimum). Some of those extremes may be local, and some may be global. In the case of trig functions, they may be periodic.

Composite functions involving ones with extreme values may also have extreme values.

Answer:

Step-by-step explanation:

Divide 1 7/10 by 3/5 to see if the quotient is greater than 2.  If it's not, you can't get 2 scarves out of it.  If it is, then you can get 2 scarves out of it and have whatever the remainder is as left-over.  Before we divide, let's change that 1 7/10 into an improper fraction since it will be easier to work with.

1 7/10 = 17/10

Now we can divide:

[tex]\frac{\frac{17}{10} }{\frac{3}{5} }[/tex]

The rule for dividing fractions is that you bring up the lower fraction and flip it to multiply, so that looks like this:

[tex]\frac{17}{10}[/tex]×[tex]\frac{5}{3}[/tex]

To simplify before we multiply, we can reduce between the 5 and the 10 and have smaller numbers to deal with:

[tex]\frac{17}{2}[/tex]×[tex]\frac{1}{3}[/tex]

The product there is [tex]\frac{17}{6}=2\frac{5}{6}[/tex]

So the answer you want from your choices is

"Yes, because the quotient of Fraction 1 and 7 over 10 [division sign]Fraction 3 over 5 is 2 and 5 over 6", third choice

Answer:

Yes, because the quotient of Fraction 1 and 7/10 [division sign]Fraction 3/5  is 2 and 5/6", third choice

Step-by-step explanation:

Divide 1 7/10 by 3/5 to see if the quotient is greater than 2.  If it's not, you can't get 2 scarves out of it.  If it is, then you can get 2 scarves out of it and have whatever the remainder is as left-over.  Before we divide, let's change that 1 7/10 into an improper fraction since it will be easier to work with.

1 7/10 = 17/10

Now we can divide:

The rule for dividing fractions is that you bring up the lower fraction and flip it to multiply, so that looks like this:

×

To simplify before we multiply, we can reduce between the 5 and the 10 and have smaller numbers to deal with:

×

The product there is  

So the answer you want from your choices is

"Yes, because the quotient of Fraction 1 and 7 over 10 [division sign]Fraction 3 over 5 is 2 and 5 over 6", third choice

The total number of votes would be: 7752 total votes.

Here's how you solve it!

For every 3 yes there was 5 no's.

You would but that into a fraction so it would be 3/5

Then you take the number of no votes and multiply.

3/5 x 4845

Then you would get 2907.

4845+ 2907= 7752

4845= no votes

2907= yes votes

7752= total votes

Hope this helps! :3

B

3+5=8

8-2=6

6-1=5

Answer 5

Answer:

The correct option is C.

Step-by-step explanation:

We need to find the problem that could be solved with the expression 3(5-2)-1.

The solution of given expression is

[tex]3(5-2)-1=8[/tex]

1. Ralph's problem

His 5 toy cars, he gave two to his sister = 5 - 2

After that he found one more toy car = 5-2+1

Then, he decided to go to the store and triple his number of cars, therefore the total number of toys = 3(5-2+1) =12

2. Stephanie's problem

Stephanie had 3 apples. Then, she found 5 more = 3+5

but immediately ate 2 of them = 3+5-2

Several minutes later, she ate 1 more, therefore the total number of apples = 3+5-2-1 = 5

3. Orlando' problem

Orlando had 5 action figures but decided to give 2 of them to his younger brother = 5-2

His parents were so impressed with his kindness that thy tripled the action figures he had left = 3(5-2)

Since he got so many new action figures, then he gave 1 more to his brother, therefore the total number of action figures = 3(5-2)-1 = 8

Orlando' problem could be solved with the expression 3(5-2)-1. Therefore the correct option is C.

Answer:

This is because √-1 is i, which is an extension of real numbers called complex numbers.

Step-by-step explanation:

A real number is one that can be expressed in decimal form.Real numbers are those that appear on the number line.In mathematics, √-1 is i which is an extension of real numbers to represent complex numbers.

Answer:

there is no number than can be multiplied by itself it give a negative answer.

Step-by-step explanation:

Eg. 1 X 1 = 1

     -1 X -1 = 1

Answer:

Step-by-step explanation:

Based on the answer selections, it appears we need to find the radius and circumference of the sphere. We can start with the volume formula in terms of the radius:

  V = (4/3)πr³

  36π = (4/3)πr³

  (36π)(3/(4π)) = r³ = 27 . . . . . . mm³

  r = ∛27 = 3 . . . . mm³

Then the circumference is ...

  C = 2πr = 2π(3 mm) = 6π mm

The radius is 3 mm; the circumference is 6π mm.

Answer:

a and b is the answer

Step-by-step explanation:

Final answer:

The mathematical system of inequalities for Keitaro's walking and running routine must satisfy his target of covering at least 36 miles and not more than 90 miles in a month, given his pace.

Explanation:

Keitaro's exercise routine is defined by a system of inequalities that reflect the minimum and maximum distances he wants to cover each month by walking and running. Given his walking pace of 3 miles per hour and his running pace of 6 miles per hour, we can set up two inequalities to represent walking hours w and running hours r. The first inequality would ensure that when multiplied by their respective paces, the total distance is at least 36 miles. The second inequality ensures that the sum of distances does not exceed 90 miles:

3w + 6r ≥ 36 (for the minimum distance)

3w + 6r ≤ 90 (for the maximum distance)

Keitaro needs to allocate his walking and running hours such that these inequalities are satisfied to meet his monthly exercise goals.

Answer:

B= 32.11

A= 52.82

C= 95.07

Step-by-step explanation:

To find these angles, since you have all sides, you will need to use the law of cosines.

Answer:

B

Step-by-step explanation:

This is the difference of perfect squares, which follows a pattern of

(A+B)(A-B)

We have 64, which is 8-squared,

we have A squared, which is A squared ( :/ )

we have 81, which is 9-squared, and

we have B-squared, which is B squared.

We can factor this then following the pattern into:

(8A+9B)(8A-9B)

Choice B only matches one of our binomials.

Answer:

B. 8A + 9B.

Step-by-step explanation:

The general form is

a^2 - b^2 = (a - b)(a + b) so here we have:

a = square root of 64A^2 = 8A and b = square root of 81B^2 = 9B and therefore:

64A^2 - 81B^2

= (8A - 9B)(8A + 9B).

Explanation:

Polygons are classified by ...

The number of coordinate pairs will define the number of vertices.

The differences between "adjacent" coordinate pairs can be used to find side lengths and relationships (angles, parallel, perpendicular).

_____

If the differences between adjacent coordinate pairs are ...

  (∆x, ∆y) = (x2 -x1, y2 -y1)

then the slope of the line joining those coordinates is ∆y/∆x. (This may be "undefined" if ∆x = 0.) Two line segments with the same slope are parallel. Two line segments with slopes that have a product of -1 are perpendicular. (Two segments with slopes of 0 and "undefined" are also perpendicular.)

It can be useful on occasion to know that the angle (α) a line segment makes with the x-axis can be found from ...

  α = arctan(slope)

The length of a line segment (d) can be found from the Pythagorean theorem:

  d = √((∆x)² +(∆y)²)

Answer:

I think the answer is 23

Answer:

  the resulting error is about 0.754 in²

Step-by-step explanation:

  A(r) -A(r0) ≈ dA/dr·(r -r0)

The area of a circle is given by ...

  A(r) = πr²

so the derivative is

  dA/dr = 2πr

and the area error is ...

  dA/dr·(r -r0) = 2π(12 in)(0.01 in) = 0.24π in² ≈ 0.754 in²

Answer:

4 donuts and 2 brownies

Step-by-step explanation:

Guess and check

2 donuts --> $2.50

1 brownie -->$2.50

Since the amount of donuts is double,

we try :

4 donuts -->$1.25(4) = $5

2 brownies --> $2.50(2) = $5

Answer:

she bought 4 donuts and 2 brownies.

Step-by-step explanation:

This is a question on simultaneous equations where two variable are given with two or more relational equations. if she bought $10 worth of donuts and brownies, and each donut costs $1.25 and each brownie costs $2.50.

Then,

1.25d + 2.50b = 10 where d and b are the numbers of donuts and brownies purchased respectively.

if She bought twice as many donuts as brownies, then

d = 2b

Therefore,

1.25(2b) + 2.50b = 10

5b = 10

b = 2

d = 2 × 2 = 4

Hence she bought 4 donuts and 2 brownies.

Answer:

  a)  t = 2 seconds

  b)  6.05 meters

Step-by-step explanation:

I prefer a graph for questions like this, but I have attached a table, too. Here, the table is created using a graphing calculator to evaluate the function. A spreadsheet can do this nicely, too.

The maximum height occurs at t=0.9 seconds, and the ball hits the ground at a time that is slightly more than double that, 2.0 seconds.

The maximum height is 6.05 meters.

Multiply the first bracket by -2

Multiply the second bracket by 2

x-3-12+4x= 4x-10

- negative number times + positive number= - negative number

- negative number times -negative number = + positive number

x+ 4x-3-12= 4x-10

5x-15= 4x-10

Move 4x to the other side

5x-4x-15= 4x-4x-10

x-15= -10

Move -15 to the other side

x-15+15= -10+15

x= 5

Answer : x= 5

Answer: X = 5

Step-by-step explanation:

x - 3 - 2(6-2x) = 2(2x-5)

x - 3 - (12-4x) = (4x-10)

Simplify

5x - 15 = 4x - 10

Then move to common sides giving you the answer

X = 5

Answer:

graph 1

Step-by-step explanation:

Let's look at graph 1:

The first vertex (the left hand top corner) has a degree 3 because there are 3 line segments coming from it.

Let's check to see if the other vertices have degree 3.

The second vertex (the middle top) has degree 3 because again it has 3 line segments coming from it.

The third vertex (the top right) has degree 3 because it has 3 line segments coming from it.

The fourth vertex (the bottom left) has degree 3 because it has 3 line segments coming from it.

The fifth vertex (the middle bottom) has degree 3 because it has 3 line segments coming from it.

The last vertex (the bottom right) has degree 3 because it has 3 line segments coming from it.

Let's look at graph 2:

The first vertex (top left) has degree 1 because it has one line segment coming from it.

The second vertex( middle top) has degree 2 because it has 2 line segments coming from it.

Graph 2 doesn't have the same degree per vertex.

Looking at graph 3:

The first vertex (top left) has degree 1 while the second (top middle) has degree 2.

Graph 3 doesn't have the same degree per vertex.

Looking at graph 4:

The top left has degree 1.  Looking at one of the middle vertices there, they have degree 4 each because they have 4 line segments coming from it. So graph 4 doesn't have the same degree per vertex.

The answer is only graph 1.

Answer:

30 Inches

Step-by-step explanation:

Please refer to the image we have attached to this.

The frame is ABCD and The diagonal is AC, which is 50 inches long and making an angle of  36.87° from the bottom of the frame.

We are asked the height of the frame which is h in this image. We are going to use the trigonometric ratios in order to find the same.

[tex]\sin \theta = \frac{opposite}{Hypotenuse}[/tex]

[tex]\sin 36.87[/tex]° = [tex]\frac{h}{50}[/tex]

[tex]0.60=\frac{h}{50}[/tex]

[tex]h=0.60 \times 50[/tex]

[tex]h=30[/tex]

hence height of the frame is 30 inches

In the figure based on proportions of triangle, the value of variable "x" is : (a) 7.5.

Proportions of a triangle based on its sides refer to the ratios between the lengths of different sides within the triangle. Common proportions include the Pythagorean theorem, where the square of the hypotenuse equals the sum of the squares of the other two sides in a right triangle.

In similar triangles, corresponding sides are in proportion, meaning they have the same ratio.

We observe that the figure is based on the property of proportions of triangle, so, the equation of proportion can be written as :

⇒ 4/6 = 5/x,

⇒ 2/3 = 5/x,

⇒ 2x = 15,

⇒ x = 15/2,

⇒ x = 7.5.

Therefore, the correct option is (a) 7.5.

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Answer:

So the probability that the city won't receive rain on none of these days is [tex]\frac{2}{15}[/tex]

Step-by-step explanation:

From the question we know that the probability of rain on June 1 is [tex]\frac{1}{2}[/tex], on July 1 is [tex]\frac{1}{5}[/tex] and in August 1 is [tex]\frac{2}{3}[/tex], So the probability of no rain at any of these days is calculate as:

For June 1:

[tex]P(no-rain)=1-\frac{1}{2} =\frac{1}{2}[/tex]

For July 1:

[tex]P(no-rain)=1-\frac{1}{5} =\frac{4}{5}[/tex]

For August 1:

[tex]P(no-rain)=1-\frac{2}{3} =\frac{1}{3}[/tex]  

So the probability that the city won't receive rain on none of these days is the multiplication of the probabilities of no rain for every one of these days. Then:

[tex]P=\frac{1}{2} *\frac{4}{5} *\frac{1}{3} =\frac{4}{30}[/tex]

Simplified the value of P, we obtain: [tex]P=\frac{2}{15}[/tex]

Answer:

Step-by-step explanation:

A non-directed graph will have an Euler circuit if all vertices have even degree. It will have an Euler path if it has an Euler circuit or if it has two vertices with odd degree (where the path can start and end).

Graph A

  4 of the 5 vertices have odd degree. No Euler path, no Euler circuit.

Graph B

  All 6 vertices have degree 4. This graph has an Euler path and an Euler circuit.

Graph C

  5 of 6 vertices have degree 4, the remaining one has degree 2. This graph has an Euler path and an Euler circuit.

Graph A: neither an Euler path nor an Euler circuit

   Graph B: both an Euler path and an Euler circuit

   Graph C: both an Euler path and an Euler circuit

An Euler Paths and Circuits visits every edge in a graph once, while an Euler circuit also starts and ends at the same vertex.

To determine which, if any, a graph has, count the vertices - even-degree vertices indicate an Euler circuit, while exactly two odd-degree vertices indicate only an Euler path.

A non-directed graph will have an Euler circuit if all vertices have even degree. It will have an Euler path if it has an Euler circuit or if it has two vertices with odd degree (where the path can start and end).

  Graph A: neither an Euler path nor an Euler circuit

   Graph B: both an Euler path and an Euler circuit

   Graph C: both an Euler path and an Euler circuit

Graph A

 4 of the 5 vertices have odd degree. No Euler path, no Euler circuit.

Graph B

 All 6 vertices have degree 4. This graph has an Euler path and an Euler circuit.

Graph C

 5 of 6 vertices have degree 4, the remaining one has degree 2. This graph has an Euler path and an Euler circuit.

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Answer:

radius = 2.05 units

Step-by-step explanation:

The volume of a sphere is given by the formula: [tex]V=\frac{4}{3} \pi r^3[/tex]. In this formula:

Since we are given the volume of the sphere (36 units^3), we just need to solve for r in the equation for the volume of a sphere.

Substitute 36 for V into the formula and solve for r.

[tex]36=\frac{4}{3} \pi r^3[/tex]

Divide both sides by [tex]\frac{4}{3}[/tex]. To do this, multiply 36 by the reciprocal of [tex]\frac{4}{3}[/tex].

Simplify and rewrite the equation.

[tex]27=\pi r^3[/tex]

Now divide both sides of the equation by pi ([tex]\pi[/tex]).

Rewrite the equation.

[tex]8.59436692696=r^3[/tex]

To isolate and solve for r, cube root both sides of the equation.

The radius of this sphere is 2.04835218977 units. If your question wants this rounded to the nearest:

I'll just give the answer rounded to the nearest hundredth as that seems the most popular.

Answer:

Before they deleted my answer, I was correct. remember to correctly round if you have a different but similar question.  

Step-by-step explanation:

Answer:

  4 and 13

Step-by-step explanation:

You want integer solutions to ...

  15 ≤ n(n+1) ≤ 200

If we let the limits be represented by "a", then the equality is represented by ...

  n² +n -a = 0

  (n² +n +1/4) -a -1/4 = 0

  (n +1/2)^2 = (a +1/4)

  n = -1/2 + √(a +1/4)

For a=15, we have

  n ≥ -1/2 + √15.25 ≈ 3.4 . . . . . minimum n is 4

For a=200, we have

  n ≤ -1/2 + √200.25 ≈ 13.7 . . . maximum n is 13

The least and greatest integers on the cards are 4 and 13.

Answer:

2/3

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

To solve this simplest form, you'd need to divide 2 from numerator into denominator.

4/2=2

6/2=3

2/3, which is our answer.

I hope this helps!

A, it's not fair because the chance to lose points far outweighs the chance to gain points

Answer with explanation:

→Total faces on the dice and marked numbers =6={1,2,3,4,5,6}

If you are rolling the dice and getting number 1 and 5 , you win 4 and 6 points respectively.

And, If you roll the dice and getting number 2,3,4 and 6 , you loose -5  points .

→→So,suppose the dice is rolled 6 times, and considering each outcome to be equally likely

         then you loose more points than gaining which is equal to

   = 4+(-5)+(-5)+(-5)+6+(-5)

   =10-20

   = -10

And, Average

[tex]=\frac{-10}{5}\\\\= -2[/tex]

So, if number of outcomes are equally likely, you can't accumulate 20 points.

Option B:→ It is not a fair game because weighted average is Negative.

Answer:

y = 10x - 3

Step-by-step explanation:

We have the point (0, -3), which is the y-intercept. In slope-intercept form,

y = mx + b,

that is the b.

Now we find the slope between the other 2 points:

[tex]\frac{18-8}{3-2}=10[/tex]

So m = 10.  Therefore, the equation is

y = 10x - 3

Step-by-step explanation:

f(x) = x² − 6x + 9

f(½) = (½)² − 6(½) + 9

f(½) = ¼ − 3 + 9

f(½) = 6¼

The value is 6¼, or as an improper fraction, 25/4.

Answer:   The correct answer is:   " 6 [tex]\frac{1}{4}[/tex] " ;  

_______________________________________________                  

                                 or;  write as:   " 6.25 " .

______________________________________________

     " f([tex]\frac{1}{2})[/tex] =  6 [tex]\frac{1}{4}[/tex] " ;

                                             =  6.26 " .

______________________________________________

Step-by-step explanation:

______________________________________________

Given the function:

______________________________________________

      " f(x)  =  x² − 6x + 9 " ;

______________________________________________

What is:   " f([tex]\frac{1}{2}[/tex]) " ?

______________________________________________

Plug in "([tex]\frac{1}{2}[/tex])"  for all values of "x" in the equation;  

                →  to solve for:  " f([tex]\frac{1}{2}[/tex]) " ;   as follows:

______________________________________________

→     " f([tex]\frac{1}{2}[/tex]) " ;  

     =  ([tex]\frac{1}{2}[/tex])² −  6*([tex]\frac{1}{2}[/tex]) + 9  ;

    =   ([tex]\frac{1^{2} }{2^{2}}[/tex])  −  ([tex]\frac{6*1}{2}[/tex]) + 9 ;

     =        ([tex]\frac{1}{4}[/tex]) −  ([tex]\frac{6}{2}[/tex])   +  9    ;

     =       ([tex]\frac{1}{4}[/tex])  −  3    +  9    ;

Note:   " - 3 + 9 "  =  9 + (-3)  =  9 −  3 =  " 6 " ;  

So:  Rewrite as:

______________________________________________

      →  " ([tex]\frac{1}{4}[/tex]) + 6 "  ;

______________________________________________    

      →   which equals:  " 6 [tex]\frac{1}{4}[/tex] " ;  

_______________________________________________                  

                         or;  write as:  " 6.25 " .

_______________________________________________

Hope this answer —and lengthy explanation — is helpful to you!

       Wishing you the best in your academic endeavors

                 — and within the "Brainly" community!

_______________________________________________

Answer:

m<DEB = 62°

Step-by-step explanation:

From the figure we can see a circle with center O.

To find the measure of <DOB

From the figure we get,

m<DOC = 44° and m<COB = 80°

We know that, m<DEB = m<DOB/2

m<DOB = m<DOC +m<COB

 =  44 + 80

 = 124

To find the measure of <DEB

m<DOB = 124

Therefore  m<DEB =  m<DOB/2

 = 124/2 = 62°

Answer: 236 degrees

Step-by-step explanation: Add the two angles that are given. 44+80=124. The angle DOB is 124 degrees. The angle DEB is the rest of the circle. There are 360 degrees in a circle. So subtext 360 from 124.

360 - 124 = 236

DEB = 236 degrees.