Suppose we want a 90% confidence interval for the average amount spent on
entertainment (movies, concerts, dates, etc.) by Freshman in their first semester at a
large university. The interval is to have a margin of error of $2, and the amount spent
has a normal distribution with a standard deviation s = $30. The number of
observations required is closest to
A) 25.
B) 30.
C) 609.
D) 865.

Answer:

[tex]|LR|=20[/tex]

[tex]|RO|=10[/tex]

Step-by-step explanation:

The centroid divides the median in the ratio [tex]2:1[/tex].

Thus [tex]|LR|:|RO|=2:1[/tex]

This implies that,

[tex]|LO|:|RO|=3:1[/tex]

We were given that,

[tex]|LO|=30[/tex]

We substitute this value to obtain,

[tex]30:|RO|=3:1[/tex]

or

[tex]\frac{30}{|RO|}=\frac{3}{1}[/tex]

We cross multiply to get,

[tex]3|RO|=30\times 1[/tex]

We divide through by 3, to get,

[tex]|RO|=10[/tex]

We can observe from the diagram that

[tex]|LR|+|RO|=|LO|[/tex]

[tex]|LR|+10=30[/tex]

[tex]|LR|=30-10[/tex]

[tex]|LR|=20[/tex]

By the polynomial remainder theorem, a polynomial [tex]p(x)[/tex] has a factor of [tex]x-c[/tex] if [tex]p(c)=0[/tex]. So all you need to do is check the value of [tex]f(x)[/tex] at [tex]x=1,3,-3,5,-5[/tex]. You should get

[tex]f(1)=-96[/tex] (so [tex]x-1[/tex] is NOT a factor)

[tex]f(3)=-96[/tex] (so [tex]x-3[/tex] is NOT a factor)

[tex]f(-3)=f(5)=f(-5)=0[/tex] (so the last three options are factors)

Answer:

the answer is c and yeah

Step-by-step explanation:

Answer:

C. y=4x+17

Step-by-step explanation:

If we want to find a line parallel to y =4x-1, the slopes will have to be the same because parallel lines have the same slope.  Knowing y= mx+b we know the slope of the  old line is 4, so the slope of the parallel line is 4.

If we know the slope of the line and a point, we can use the point slope form of a line

y-y1 = m(x-x1)

y-5 = 4(x--3)

y-5=4(x+3)

Distribute the 4

y-5 = 4x+12

Add 5 to each side

y-5+5 = 4x+12+5

y = 4x+17

Answer: The answer is C. y=4x+17

Step-by-step explanation:

The other person was correct and i got an A<3

[tex]t_1=4\\t_n=-3t_{n-1}\\\\t_2=-3\cdot4=-12\\t_3=-3\cdot(-12)=36\\t_4=-3\cdot36=-108[/tex]

Point-slope form: y-y1 = m(x-x1)

Standard form: ax + by = c

Slope-intercept form: y = mx+b

Start by finding the slope. We know it is negative since the line is decreasing. The slope is -4/3.

To create point-slope form, we need to get one point from the graph. Let's use (3,0).

[tex]y = -\frac{4}{3}(x-3)[/tex]

To create slope-intercept form, we need the slope and the y-intercept. The y-intercept is the point where our equation crosses the y-axis. For this equation, it is 4.

[tex]y = -\frac{4}{3}x + 4[/tex]

To get standard form, solve the equation in terms of C.

Point-slope form: y = -4/3(x-3)

Slope-intercept form: y = -4/3x + 4

Standard form: 4/3x + y = 4

Answer:

S22 for the arithmetic sequence is:

First option: 15.4

Step-by-step explanation:

a12=2.4

d=3.4

S22=?

Sn=(a1+an)n/2

n=22

S22=(a1+a22)22/2

S22=(a1+a22)11

ak=aj+(k-j)d

a12=a1+(12-1)d

2.4=a1+11(3.4)

2.4=a1+37.4

Solving for a1: Subtracting 37.4 both sides of the equation:

2.4-37.4=a1+37.4-37.4

Subtracting:

-35=a1

a1=-35

a22=a12+(22-12)d

a22=2.4+10(3.4)

a22=2.4+34

a22=36.4

S22=(a1+a22)11

S22=(-35+36.4)11

S22=(1.4)11

S22=15.4

Answer:4.-37 5.-6 6.-33 11.-20 12.-16

13.19

Step-by-step explanation:

Answer:

1. -41

2. -40

3. -4

4. -37

5. -24

6. -33

8. -47

9. 14

10. 59

11. -20

12. -16

13. 19

This is from the answer key to this question;

N= {4, 5, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19.}

Answer:

275

Step-by-step explanation:

To find out how many more, we find the difference between the two values. We use the math operation subtraction to find the difference.

Friday had 537 and Saturday had 812. We subtract 812-537= 275.

275 more people attended Saturday than Friday.

Answer:

13. The slope for a line that is perpendicular to the line y=4x+8 is  -1/4

14. The slope for a line that is perpendicular to the line x=-6 is 0

15. The equation for a line that is perpendicular to the line 8x-4y=12 and passes through the origin is y = - (1/2) x

16. The equation for a line that is perpendicular to the line y=-(1/3)x and passes through the point (0,-10) is y=3x-10

Step-by-step explanation:

13. What is the slope for a line that is perpendicular to the line y=4x+8?

y=mx+b

Comparing with the form slope-intercept, the slope of the given line is the coefficient of x, then the slope of the given line is 4.

A line perpendicular to y=4x+8 must have a slope opposite and inverse, then:

Slope of the perpendicular = - 1/4

14. What is the slope for a line that is perpendicular to the line x=-6?

The line x=-6 is a vertical line. A line perpendicular to the line x=-6 must be a horizontal line (Angle=0°), then:

Slope of the perpendicular = tan Angle = tan 0° = 0

15. Write the equation for a line that is perpendicular to the line 8x-4y=12 and passes through the origin.

8x-4y=12

Isolating y: Subtracting 8x both sides of the equation:

8x-4y-8x=12-8x

-4y=-8x+12

Dividing all the terms by -4:

-4y/(-4)= -8x/(-4)+12/(-4)

y=2x-3

The slope of the given line is 2

The slope of the perpendicular is m=-1/2 (opposite and inverse to the slope of the given line)

The perpendicular passes through the origin:

P1=(0,0)=(x1,y1)→x1=0, y1=0

Using the equation point - slope:

y-y1=m(x-x1)

Replacing the known values:

y-0=(-1/2)(x-0)

y=(-1/2)x

16. Write an equation for a line that is perpendicular to the line y=-(1/3)x and passes through the point (0,-10).

The slope of the given line is -(1/3)

The slope of the perpendicular is m=3/1→m=3 (opposite and inverse to the slope of the given line)

The perpendicular passes through the point:

P1=(0,-10)=(x1,y1)→x1=0, y1=-10

Using the equation point - slope:

y-y1=m(x-x1)

Replacing the known values:

y-(-10)=3(x-0)

y+10=3x

Isolating y: Subtracting 10 both sides of the equation:

y+10-10=3x-10

y=3x-10

Answer: False

Step-by-step explanation:

45-45-90 is a special triangle because there is a specific relationship between the legs and the hypotenuse: a - a - a√2

So, If the leg of the 45-45-90 triangle is 12, then the hypotenuse (labeled as x in your drawing) will be 12√2.

Answer:

While you do not have the coordinates included, you can use the point-slope form of the equation and input the slope. This would be:

y - y1 = -1/7(x - x1)

In this equation, simply put the ordered pair in at x1 and y1. This will give you the full point-slope equation.

Answer:

A

Step-by-step explanation:

When solving for x as an exponent, we need to use logarithms in order to undo the operation and rearrange the terms. We use log rules to bring down the exponent and solve. Logarithms are the inverse operations to exponents and vice versa. We have one special kind of logarithm called the natural logarithm whose base is e. We write it as ln. Since our base is e here, we will use the natural logarithm to rearrange and isolate x.

[tex]e^{4x-1} =3[/tex]

We begin by applying the natural logarithm to each side.

[tex]ln(e^{4x-1}) =ln(3)[/tex]

Log rules allow use to rearrange the exponent as multiplication in front of the log.

[tex](4x-1)ln(e) =ln(3)[/tex]

ln e as an inverse simplifies to 1.

[tex](4x-1)(1)=ln(3)[/tex]

We now apply the inverse operations for subtraction and multiplication.

[tex]4x-1+1=1+ln(3)\\4x=1+ln(3)\\\frac{4x}{4} =\frac{1+ln3}{4} \\x =\frac{1+ln3}{4}[/tex]

Option A is correct.

Answer:

A. 4 groups of 6 students in each group.

B. The smaller group will have 5 students.        

Step-by-step explanation:  

We have been given that Ms.Rochelle wants to put her 29 students into groups of 6.  

A. To find the number of groups of 6 that can be made from 29 students, we will find the greatest multiple of 6 from 29.    

Multiples of 6 are: 6, 12, 18, 24, 30, 36,...  

We can see that the greatest multiples of 6 in 29 in 24.  

[tex]\text{Number of groups that can be made with 29 students}=\frac{24}{6}[/tex]          

[tex]\text{Number of groups that can be made with 29 students}=4[/tex]

Therefore, Ms. Rochelle can form 4 groups from 29 students with 6 students in each group.            

B. To find the number of students in small group, we will subtract 24 from 29.  

[tex]\text{Number of students in the small group}=29-24[/tex]

[tex]\text{Number of students in the small group}=5[/tex]  

Therefore, If Ms. Rochelle puts any remaining students in a smaller group, the number of students in smaller group will be 5.  

Answer: 5

Step-by-step explanation:

The length of the midsegment is one-half the length of the base.  So,

Base = 2(midsegment)

7x + 1 = 2(4x - 2)

7x + 1 = 8x - 4

       1 =  x - 4

       5 = x

Answer:

5, 5/2

Step-by-step explanation:

80, 40, 20, 10, ______,

80/40 = 2

40/20 = 2

We are dividing by 2 each time

10/2 =5  so the next term is 5

5/2 = 5/2

Answer:

The growth factor is option c. 1.03 per year

Step-by-step explanation:

Growth rate: r = 3% = 3 / 100 → r = 0.03

Growth factor: b = 1+r

Replacing r by 0.03 in the formula above:

b = 1+0.03

b = 1.03

Answer: The growth factor is 1.03 per year

Answer:      " r  =  a  +  b  -  s "  .

_____________________________________________________

Step-by-step explanation:

_____________________________________________________

Given:  

a + b = s + r ;  Solve for:  "r" ;  that is; rewrite the equation in terms of:  " r " .

_____________________________________________________

Subtract "s" from each side of the equation;  

   to isolate "r" on one side of the equation:

_____________________________________________________

    →      a + b - s  =  s + r - s  ;

    →   to get:

   →       a + b - s  =  r  ;

____________________________________________________

 ↔   " r = a + b - s "  .

____________________________________________________

   →  which is the answer.

____________________________________________________

Hope this helps!

 Best wishes to you!

____________________________________________________

Answer: I TINK 77 rice balls

Step-by-step explanation:

Answer:77

Step-by-step explanation:

Answer:

The correct answer option is: The y-intercept of the line of best fit shows that when time started, the distance was 5 feet.

Step-by-step explanation:

We are given a scatter plot with a best fit line as shown on the given graph.

The equation of the best fit line is given by:

y = 0.75x + 5

So with the help of the equation and by looking at the given graph, we can conclude about the representation of the y intercept that the the y-intercept of the line of best fit shows that when time started, the distance was 5 feet.

Since the distance shown on the y axis is already 5 when the time started at 0 minutes.

Final answer:

To solve the division problem 14.2 divided by 0.5, you can use the long division method. The quotient is 28.4.

Explanation:

To solve the division problem 14.2 divided by 0.5, we can perform the long division method. Here's the step-by-step process:

Since there is no remainder anymore, the division is complete. The final quotient is 28.4. Therefore, 14.2 divided by 0.5 is equal to 28.4.

Answer:

2√17

Step-by-step explanation:

V = (-8, 2)

|v| = √((-8)^2 + 2^2)

= √(64 + 4)

= √68

= √4* √17

= 2√17

Answer:

  = 2 sqrt(17)

Step-by-step explanation:

To find the magnitude of v using the dot product

|v| = sqrt(v1*v1 + v2*v2)

    = sqrt( -8*-8 + 2*2)

    = sqrt(64+ 4)

   = sqrt(68)

   = sqrt(4*17)

  = sqrt(4) sqrt(17)

  = 2 sqrt(17)