URGENT!!!!!Driving times for students' commute to school is normally distributed, with a mean time of 14 minutes and a standard deviation of 3 minutes. Using the empirical rule, approximately what percent of students' commute time is between 11 and 17 minutes? 32% 68% 95% 99.7%

Sample Response: First, the like terms had to be combined using the lowest common denominator (LCD). Then the subtraction property of equality was used to isolate the variable term. Finally, both sides of the equation were multiplied by the reciprocal of the coefficient to solve for a.

Answer:

The numbers are

[tex]6+2\sqrt{15}i[/tex]   and  [tex]6-2\sqrt{15}i[/tex]

Step-by-step explanation:

Let

x and y -----> the numbers

we know that

[tex]x+y=12[/tex] -----> [tex]y=12-x[/tex] ------> equation A

[tex]xy=96[/tex] ----> equation B

substitute equation A in equation B and solve for x

[tex]x(12-x)=96\\12x-x^{2}=96\\x^{2} -12x+96=0[/tex]

Solve the quadratic equation

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]x^{2} -12x+96=0[/tex]  

so

[tex]a=1\\b=-12\\c=96[/tex]

substitute

[tex]x=\frac{-(-12)(+/-)\sqrt{-12^{2}-4(1)(96)}} {2(1)}[/tex]

[tex]x=\frac{12(+/-)\sqrt{-240}} {2}[/tex]

Remember that

[tex]i^{2}=\sqrt{-1}[/tex]

[tex]x=\frac{12(+/-)\sqrt{240}i} {2}[/tex]

[tex]x=\frac{12(+/-)4\sqrt{15}i} {2}[/tex]

Simplify

[tex]x=6(+/-)2\sqrt{15}i[/tex]

[tex]x1=6+2\sqrt{15}i[/tex]

[tex]x2=6-2\sqrt{15}i[/tex]

we have two solutions

Find the value of y for the first solution

For [tex]x1=6+2\sqrt{15}i[/tex]

[tex]y=12-x[/tex]

substitute

[tex]y1=12-(6+2\sqrt{15}i)[/tex]

[tex]y1=6-2\sqrt{15}i[/tex]

Find the value of y for the second solution

For [tex]x2=6-2\sqrt{15}i[/tex]

[tex]y2=12-x[/tex]

substitute

[tex]y2=12-(6-2\sqrt{15}i)[/tex]

[tex]y2=6+2\sqrt{15}i[/tex]

therefore

The numbers are

[tex]6+2\sqrt{15}i[/tex]   and  [tex]6-2\sqrt{15}i[/tex]

Answer:

x =27

Step-by-step explanation:

5(x + 1) = 4(x + 8)

Distribute.

5x + 5 = 4x + 32

Move x term onto one side.

x + 5 = 32

Move integer onto one side.

x = 27

The prime polynomial out of the given options is 3x^3 + 3x^2 - 2x - 2.

Out of the given polynomials, the polynomial that is prime is 3x3 + 3x2 - 2x - 2.

A polynomial is considered prime if it cannot be factored into a product of lower degree polynomials with integral coefficients.

In this case, the polynomial 3x3 + 3x2 - 2x - 2 is a cubic polynomial and cannot be factored further, so it is prime.

Answer:

An angle is 90° if and only if it is a right angle.

Explanation:

The statement is: If an angle is 90°, then it is a right angle.  

The converse of this statement would be:

If an angle is a right angle, it is 90°.

Clearly, both the conditional and converse of this statement is true.

The operation (-1 1/2)(-3/2) gives 9/4 or 2 1/4 as a mixed number.

To perform the indicated operation: (-1 1/2)(-3/2), we need to multiply the two numbers.

[tex]-p^2 + 14p=0\\-p(p-14)=0\\p=0 \vee p=14[/tex]

Answer:

Step 2

Step-by-step explanation:

Let

[tex]A(-1,6), B(-1,-2), C(3,6), D(3,-2)[/tex]

Plot the vertices to better understand the problem

see the attached figure

The area of the rectangle is equal to

[tex]A=bh[/tex]

we have

[tex]b=BD\\ h=BA[/tex]

step 1

Find the base b (BD)

[tex] B(-1,-2),D(3,-2)[/tex]

[tex]b=\left|3\right|+\left|-1\right|=4\ units[/tex]

step 1 is correct

step 2

Find the height h (BA)

[tex]B(-1,-2),A(-1,6)[/tex]

[tex]h=\left|6\right|+\left|-2\right|=8\ units[/tex]

step 2 is not correct

step 3

Find the area

[tex]A=(4)(8)=32\ units^{2}[/tex]

Therefore

Sara first make a mistake in finding the area of the rectangle in Step 2

Answer:

step 2

Step-by-step explanation:

Answer:

c. Keeping the movie and paying the purchase price and late fees is the cheaper option.  

Step-by-step explanation:

1. If Susan takes a cab and pays late fees

            Cost of cab = $10.00

Late fees = 5 × 1.50 =   7.50

                   TOTAL = $17.50

2. If Susan keeps the movie

Purchase price of movie = $9.99

       Late fees = 5 × 1.50 =   7.50

                           TOTAL = $17.49

Keeping the movie and paying the purchase price and late fees is the cheapest option.

a. is wrong. Taking a cab is the more expensive option.

b. is wrong. Susan contracted to return the movie, so she should try to do so.  

c. is correct. This is a statement of fact, not a judgement call.

d. is wrong. Susan contracted to pay the late fees if she did not return the video (but she should still return it).

Answer:

Part a) When Marcos purchased the card, the balance on the card was $40

This is the B-intercept

Part b) Mark will have spoken 400 minutes when he runs out of money

This is the n-intercept

part c) The slope of the equation is -0.1 and the units are dollars per minute

Step-by-step explanation:

we have

[tex]B=40-0.1n[/tex]

where

B is balance in dollars on the card

n is the number of minutes

Part a) How much money was on the card when he purchased it? $______. Which intercept is this? B-intercept or N-intercept?

we know that

The B-intercept is the value of B when the value of n is equal to zero

so

For n=0

substitute and find the value of B

[tex]B=40-0.1(0)=\$40[/tex]

therefore

When Marcos purchased the card, the balance on the card was $40

This is the B-intercept

Part b) How many minutes will he have talked when he runs out of money? $_____. Which intercept is this? B-intercept or n-intercept ?

we know that

The n-intercept is the value of n when the value of B is equal to zero

so

For B=0

substitute and find the value of n

[tex]0=40-0.1n[/tex]

[tex]0.1n=40[/tex]

[tex]n=400\ minutes[/tex]

therefore

Mark will have spoken 400 minutes when he runs out of money

This is the n-intercept

Part c) What is the slope of this equation?________ . What are the units on the slope? Minute , dollars per minute ,minutes per dollars or dollars ?

we have

[tex]B=40-0.1n[/tex]

This is is the equation of the line into slope intercept form

[tex]m=-0.1\frac{\$}{minute}[/tex] -----> slope of the equation

[tex]b=40[/tex] ------> the B-intercept

The units of the slope are dollars per minute

Marcos purchased a top-up card with an initial balance of $40 (B-intercept). He will run out of money after 400 minutes of call time (n-intercept). The charge rate is $0.1 per minute (slope).

a) The money on the card when he purchased it is given by the constant term in the equation, which is $40. This is the B-intercept, because it is the value of B when n = 0 (meaning no minutes have been used).

b) Marcos will have run out of money when B = 0. To find this, set B = 0 and solve for n: 0 = 40 - 0.1n, which leads to n = 400. So, Marcos will have talked for 400 minutes when he runs out of money. This is the n-intercept. It represents the value of n when B = 0 (meaning there is no money left on the card).

c) The slope of this equation is -0.1. In the context of this problem, the slope represents the rate at which money is deducted from the balance for each minute of talk time. Therefore, the units on the slope are dollars per minute.

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Although I am unsure what this question has to do with Mathematics, Joe Bob could simply say "How often do you work out in a week?"

Answer:

The volume of cylinder = 540π inches²

Step-by-step explanation:

Points to remember

Volume of cylinder =  πr²h

Where r - Radius of cylinder and

h - Height of cylinder

To find the volume of cylinder

Here r = 6 inches and height h = 15 inches

Volume =  πr²h

 =  π * 6² * 15

 =  π * 36 * 15

 = 540 πinches²

The volume of cylinder = 540π inches²

Answer:

Step-by-step explanation:

sin(32)/19 = sin(B)/12  

cross multiply  

12 sin(32) = 19 sin(B)  

sin(B) = 12 sin(32) /19 = 0.334686  

B = sin°-1(0.334686)  

B = 0.321272 radian  

B = (0.321272)*180/pi degrees = 19.55°  

C = 180-32-19.55 = 128.45°  

sin(32)/19 = sin(128.45)/ c  

cross multiply  

c sin(32) = 19 sin(128.45)  

c = 19 sin(128.45) /sin(32) =28.08....

Answer:

[tex]h=7\sqrt{11}\ units[/tex]

Step-by-step explanation:

The altitude to the hypotenuse of a right tringle is the geometric mean of the two segments that it divides the hypotenuse into.

1st segment = 77 units

2nd segment = 7 units

Altitude = h units

So,

[tex]h^2=77\cdot 7\\ \\h^2 =7\cdot 11\cdot 7\\ \\h=\sqrt{7\cdot 11\cdot 7}=7\sqrt{11}[/tex]

Answer:

your y-intercept is 0 and slope is 4 so any line with zero slope it will be horizontal

Answer: On mine it is D

Step-by-step explanation:

It is the small one facing up

Answer: [tex]143.99\ ft^2[/tex]

Step-by-step explanation:

We need to find the lenght AC and BC of the triangle by applying these identities:

[tex]cos\alpha=\frac{adjacent}{hypotenuse} \\\\sin\alpha=\frac{opposite}{hypotenuse}[/tex]

Then, AC is:

[tex]sin(45\°)=\frac{AC}{24}\\\\AC=24*sin(45\°)\\\\AC=16.97\ ft[/tex]

And BC is:

[tex]cos(45\°)=\frac{BC}{24}\\\\BC=24*cos(45\°)\\\\BC=16.97\ ft[/tex]

The area will be:

[tex]A=\frac{AC*BC}{2}[/tex]

Substituting values, we get:

 [tex]A=\frac{(16.97\ ft)(16.97\ ft)}{2}=143.99\ ft^2[/tex]

Final answer:

Only options b (74) and c (80) could have their square roots between 8 and 9, as their values lie between 64 (8 squared) and 81 (9 squared).

Explanation:

To find which numbers could have their square roots lying between 8 and 9, we need to consider the squares of these two numbers. 8 squared is 64 and 9 squared is 81. Therefore, any number that has a square root between 8 and 9 must be greater than 64 and less than 81.

Thus, the values that could be the number with the square root between 8 and 9 are 74 and 80.

Answer:

-89

Step-by-step explanation:

9x + 4b + 9y +4c + 4a​ (9x+9y)+(4a+4b+4c) =9(x+y)+4(a+b+c)

but :   a+b+c = -2 and x+y = -9

9x + 4b + 9y +4c + 4a​ = 9(-9)+4(-2) = - 81 -8 =-89

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]f(x)=4(\frac{1}{2})^{x}[/tex]

This is a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

a is the initial value

b is the base

r is the rate

b=1+r

In this problem we have

a=4 ----> initial value (y-intercept)

b=1/2

so

1+r=1/2

r=1/2-1=-1/2

r=-0.5=-50% ----> is negative because is a decrease rate

using a graphing tool

The graph in the attached figure

Answer:

3.08 x [tex]10^{3}[/tex]

Step-by-step explanation:

3080 = 3.08 x 1000 = 3.08 x [tex]10^{3}[/tex]

x>7

Step-by-step explanation:

when dividing by a (-)

the inequality sign changes

Answer:

"The student should have switched the direction of the inequality sign to get –5> x for a final answer."

and the second one is:

The student should have added 4 to all parts (left, middle, and right) to get 6 < –3x < 9.

Step-by-step explanation:

i got that on edge

Answer:

n = 17.

Step-by-step explanation:

The opposite angles of a parallelogram are congruent so we have:

4n - 2 =  2n + 32

4n - 2n = 32 + 2

2n = 34

n = 17.

Answer:

The constant variation, and the price of one ticket is 8.  

Step-by-step explanation:

The scale factor of the dilation is:

                           [tex]1\dfrac{1}{2}[/tex]

Scale factor--

It is a fixed amount by which the each  of the dimension of the original figure is multiplied in order to obtain the dilated image of the figure.

Here we see that there is a enlargement dilation.

( since the side of the image increases after the dilation)

Let the scale factor be k.

From the figure we see that:

The side of length 6 units is transformed to get a side of length 9 units.

i.e.

[tex]6\times k=9[/tex]

i.e.

[tex]k=\dfrac{9}{6}\\\\i.e.\\\\k=\dfrac{3}{2}\\\\i.e.\\\\k=1\dfrac{1}{2}[/tex]

Answer:

Step-by-step explanation:

p^8 q^6 / p ^4 q^3

In this expression the base of numerator and denominator is same:

We will change the division into multiplication and the denominator will become numerator will negative exponents:

p^8 q^6 * p ^-4 q^-3

Now simplify the terms with same base

The exponents of the same base will be added

=p^8+(-4) q^6+(-3)

=p^8-4 q^6-3

=p^4 q^3

The answer is p^4 q^3....

Answer:

Step-by-step explanation:

Z = i √5/3 +36

The given equation (3z - 18)^2 + 59 = 14 has no real solution because after isolating and simplifying the squared term, we would be taking the square root of a negative number, which is not possible in the real number system.

To solve the equation (3z - 18)^2 + 59 = 14 using the square root property, follow these steps:

(3z - 18)^2 = 14 - 59

(3z - 18)^2 = -45

It is important to note that squaring a real number always results in a non-negative number, so a square equal to a negative number indicates there are no real solutions to the equation.

Answer:

a) 0.2514

b) 0.6827

c) 0.0918

Step-by-step explanation:

Average life span of batteries = u = 300 hours

Standard deviation = s = 75 hours

Given that the distribution of life span of batteries is normally distributed, so we can use z-score to find the said probabilities.

Part a) Less than 250 hours

In order to find the probability that the life span of battery will be less than 250 hours we need to convert x = 250 into z-score and then use z-score to find the probability from the z-table.

The formula for z-score is:

[tex]z=\frac{x-u}{s}[/tex]

Using the values, we get:

[tex]z=\frac{250-300}{75}=-0.67[/tex]

From the z-table or z-calculator the probability of z-score being less than - 0.67 comes out to be 0.2514

P(z < -0.67) = 0.2514

Thus, the  the probability that the life span of battery will be less than 250 hours is 0.2514

Part b) Between 225 and 375 hours

In order to find the probability that the life span of battery will be between 225 and 375 hours we need to convert them into into z-scores and then use z-score to find the probability from the z-table.

225 into z-score will be:

[tex]z=\frac{225-300}{75}=-1[/tex]

375 into z-score will be:

[tex]z=\frac{375-300}{75}=1[/tex]

Thus, from the z-table we now need to find that probability of z-score being in between -1 and 1. From the z-table this value comes out to be:

P(-1 < z < 1 ) = 0.6827

Thus, the probability that the life span of battery will be between 225 and 375 hours is 0.6827

Part c) More than 400 hours

In order to find the probability that the life span of battery will be more than 400 hours we need to convert x = 400 into z-score and then use z-score to find the probability from the z-table.

The formula for z-score is:

[tex]z=\frac{x-u}{s}[/tex]

Using the values, we get:

[tex]z=\frac{400-300}{75}=1.33[/tex]

From the z-table the probability of z score being more than 1.33 comes out to be:

P( z > 1.33) = 0.0918

Thus, the probability that the life span of battery will be more than 400 hours is 0.0918

Answer:

1/2520

Step-by-step explanation:

First you have to find out how many different combinations can be created

7×6×5×4×3×2×1 = 5040

There is only two combinations that will spell out algebra

2/5040= 1/2520

Answer:

10

Step-by-step explanation:

First of all, let's write this statement in vector form. For the fist vector we have:

Magnitude 3.5 m/s, direction angle 35°:

Let's say this is vector [tex]\vec{A}[/tex], so the magnitude is:

[tex]\left|\vec{A}\right|=3.5m/s[/tex]

And the direction is defined as:

[tex]\theta = 35^{\circ}[/tex]

So the components are:

[tex]Ax=\left|\vec{A}\right| cos\theta \\ \\ Ax=3.5 cos35^{\circ}=2.86m/s \\ \\ \\ Ay=\left|\vec{A}\right| sin\theta \\ \\ Ay=3.5 sin35^{\circ}=2m/s[/tex]

So vector [tex]\vec{A}[/tex] is:

[tex]\vec{A}=2.86i+2j[/tex]

For the second vector:

Magnitude 4 m/s, direction angle 150°:

Let's say this is vector [tex]\vec{B}[/tex], so the magnitude is:

[tex]\left|\vec{B}\right|=4m/s[/tex]

And the direction is defined as:

[tex]\theta = 150^{\circ}[/tex]

So the components are:

[tex]Bx=\left|\vec{B}\right| cos\theta \\ \\ Bx=4 cos150^{\circ}=-2\sqrt{3}m/s \\ \\ \\ By=\left|\vec{B}\right| sin\theta \\ \\ By=4 sin150^{\circ}=2m/s[/tex]

So vector [tex]\vec{B}[/tex] is:

[tex]\vec{B}=-2\sqrt{3}i+2j[/tex]

THE SUM OF THESE TWO VECTORS IS:

[tex]\vec{R}=\vec{A}+\vec{B}=(2.86i+2j)+(-2\sqrt{3}i+2j) \\ \\ \boxed{\vec{R}=-0.60i+4j}[/tex]

THE MAGNITUDE OF THE RESULTANT VECTOR IS:

[tex]\left|\vec{R}\right|=\sqrt{Rx^2+Ry^2} \\ \\ Rx=Ax+Bx \\ \\ Ry=Ay+By \\ \\ \\ \left|\vec{R}\right|=\sqrt{(-0.6^2)+(4)^2} \\ \\ \boxed{\left|\vec{R}\right|=4.05m/s}[/tex]

Magnitude 4.5 m/s, direction angle 55°:

Let's say this is vector [tex]\vec{C}[/tex], so the magnitude is:

[tex]\left|\vec{C}\right|=4.5m/s[/tex]

And the direction is defined as:

[tex]\theta = 55^{\circ}[/tex]

So the components are:

[tex]Cx=\left|\vec{C}\right| cos\theta \\ \\ Cx=4.5 cos55^{\circ}=2.58m/s \\ \\ \\ Cy=\left|\vec{C}\right| sin\theta \\ \\ Cy=4.5 sin55^{\circ}=3.68m/s[/tex]

So vector [tex]\vec{C}[/tex] is:

[tex]\vec{C}=2.58i+3.68j[/tex]

For the second vector:

Magnitude 3 m/s, direction angle 135°:

Let's say this is vector [tex]\vec{D}[/tex], so the magnitude is:

[tex]\left|\vec{D}\right|=3m/s[/tex]

And the direction is defined as:

[tex]\theta = 135^{\circ}[/tex]

So the components are:

[tex]Dx=\left|\vec{D}\right| cos\theta \\ \\ Dx=3 cos135^{\circ}=-\frac{3\sqrt{2}}{2} \\ \\ \\ Dy=\left|\vec{D}\right| sin\theta \\ \\ Dy=3 sin135^{\circ}=\frac{3\sqrt{2}}{2}[/tex]

So vector [tex]\vec{D}[/tex] is:

[tex]\vec{D}=-\frac{3\sqrt{2}}{2}i+\frac{3\sqrt{2}}{2}j[/tex]

THE SUM OF THESE TWO VECTORS IS:

[tex]\vec{R}=\vec{C}+\vec{D}=(2.58i+3.68j)+(-\frac{3\sqrt{2}}{2}i+\frac{3\sqrt{2}}{2}j) \\ \\ \boxed{\vec{R}=0.46i+5.80j}[/tex]

THE MAGNITUDE OF THE RESULTANT VECTOR IS:

[tex]\left|\vec{R}\right|=\sqrt{(0.46)^2+(5.8)^2} \\ \\ \boxed{\left|\vec{R}\right|=5.83m/s}[/tex]

Magnitude 4.5 m/s, direction angle 55°:

This is vector [tex]\vec{E}[/tex], so the magnitude is:

[tex]\left|\vec{E}\right|=3m/s[/tex]

Direction:

[tex]\theta = 70{\circ}[/tex]

Components:

[tex]Ex=\left|\vec{E}\right| cos\theta \\ \\ Ex=3 cos70^{\circ}=1.02m/s \\ \\ \\ Ey=\left|\vec{E}\right| sin\theta \\ \\ Ey=3 sin70^{\circ}=2.82m/s[/tex]

So:

[tex]\vec{E}=1.02i+2.82j[/tex]

For the second vector:

Magnitude 5 m/s, direction angle 210°:

[tex]\vec{F}[/tex]:

[tex]\left|\vec{F}\right|=5m/s[/tex]

Direction:

[tex]\theta = 210^{\circ}[/tex]

Components:

[tex]Fx=5 cos210^{\circ}=-\frac{5\sqrt{3}}{2} \\ \\ \\ Ey=5 sin210^{\circ}=-\frac{5}{2}[/tex]

Then:

[tex]\vec{F}=-\frac{5\sqrt{3}}{2} i-\frac{5}{2}j[/tex]

THE SUM OF THESE TWO VECTORS IS:

[tex]\vec{R}=(1.02i+2.82j)+(-\frac{5\sqrt{3}}{2}i-\frac{5}{2}j) \\ \\ \boxed{\vec{R}=-3.31i+0.32j}[/tex]

THE MAGNITUDE OF THE RESULTANT VECTOR IS:

[tex]\left|\vec{R}\right|=\sqrt{(-3.31)^2+(0.32)^2} \\ \\ \boxed{\left|\vec{R}\right|=3.32m/s}[/tex]

Magnitude 6 m/s, direction angle 120°:

[tex]\left|\vec{W}\right|=6m/s[/tex]

Direction:

[tex]\theta = 120^{\circ}[/tex]

Components:

[tex]Wx=6 cos120^{\circ}=-3m/s \\ \\ \\ Wy=6 sin120^{\circ}=3\sqrt{3}m/s[/tex]

So:

[tex]\vec{W}=-3i+3\sqrt{3}j[/tex]

For the second vector:

Magnitude 2 m/s, direction angle 240°:

[tex]\vec{Z}[/tex]:

[tex]\left|\vec{Z}\right|=2m/s[/tex]

Direction:

[tex]\theta = 240^{\circ}[/tex]

Components:

[tex]Zx=2 cos240^{\circ}=-1 \\ \\ \\ Zy=2 sin240^{\circ}=-\sqrt{3}[/tex]

Then:

[tex]\vec{Z}=-i-\sqrt{3}j[/tex]

THE SUM OF THESE TWO VECTORS IS:

[tex]\vec{R}=(-3i+3\sqrt{3}j)+(-i-\sqrt{3}j) \\ \\ \boxed{\vec{R}=-4i+2\sqrt{3}j}[/tex]

THE MAGNITUDE OF THE RESULTANT VECTOR IS:

[tex]\left|\vec{R}\right|=\sqrt{(-4)^2+(2\sqrt{3})^2} \\ \\ \boxed{\left|\vec{R}\right|=5.29m/s}[/tex]