Cases Prudence has a special (cubic) die. The values on its face are the integers from 1 to 6, but they are not arranged ae in a normal die. When Prudence first tosses the die, the sum of the values on the four side faces is 15. In her second toss, the sum of these values is 12. Find what value appears in the face opposite 6 on Prudence’s special die. (Hint: what are possible values for the top and bottom face when the sum of the side faces is 12).

Answer:

[tex] y = \dfrac{1}{20}x + 35 [/tex]

Step-by-step explanation:

Let y = cost.

Let x = number of miles.

We have two (x, y) points: (100, 40) and (220, 46).

Now we find the equation of the line that passes through those two points using the two-point form of the equation of a line.

[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]

[tex] y - 40 = \dfrac{46 - 40}{220 - 100}(x - 100) [/tex]

[tex] y - 40 = \dfrac{6}{120}(x - 100) [/tex]

[tex] y - 40 = \dfrac{1}{20}(x - 100) [/tex]

[tex] y - 40 = \dfrac{1}{20}x - 5 [/tex]

[tex] y = \dfrac{1}{20}x + 35 [/tex]

Answer: [tex]n(t) = 110000(0.35)^t[/tex]

Step-by-step explanation:

Given: Rate of of all aluminum cans distributed will be recycled each year. = 35%

= 0.35

Total cans distributed =  110,000

Now , the number of cans recycled in 1 year = 110,000 ×0.35

The number of cans recycled in 2 years   = 110,000 ×0.35 ×0.35  = 110,000 ×(0.35)²

..so on

The number of cans recycled in t years   = [tex]110000(0.35)^t[/tex]

Let n(t) be the number still in use after time t, in years:

Then, [tex]n(t) = 110000(0.35)^t[/tex]

Answer:

Step-by-step explanation:

Given the total number of students in the school to be 2229 students. If among a sample of 452 students from this school district, 163 have mathematics scores below grade level, then we can determine the number of students in this school district with mathematics scores below grade level based on the sample scores using ratio.

Let the number of students in this school district with mathematics scores below grade level be x. The ratio of the students with math score below grade level to total population will be x:2229

Also, the ratio of the sample students with math score below grade level to sample population will be 163:452

On equating both ratios, we will have;

x:2229 =  163:452

[tex]\dfrac{x}{2229} = \dfrac{163}{452}\\ \\cross\ multiplying;\\\\\\452*x = 2229*163\\\\x = \dfrac{2229*163}{452}\\ \\x = \frac{363,327}{452}\\ \\x = 803.8\\\\x \approx 804[/tex]

Hence the estimate of the number of students in this school district with mathematics scores below grade level based on the sample is 804

Answer:

The total number of votes= 9999

Step-by-step explanation:

The ratio of vote specifically the ratio of yes to no vote in a city vote is 6 to 5.

There is a total of 4545 no votes.

Yes/no = 6/5

Yes= no(6/5)

Yes= 4545(6/5)

Yes= 5454

The total number of yes votes are 5454.

The total number of votes= yes votes+ no votes

The total number of votes= 5454+4545

The total number of votes= 9999

Answer:

3)  20% of the students earned a D

Step-by-step explanation:

9 students got a D.

5 students got a C.

14 students got a B.

17 students got an A.

Total number of students:

9 + 5 + 14 + 17 = 45

1)  1/5 of the students earned a C

1/5 of 45 = 9

5 students got a C

False

2) 3% more students earned an A then B

3 more students got an A than a B, but not 3%.

False

3)  20% of the students earned a D

20% of 45 = 9

9 students got a D.

True

4)  1/4 of the class earned a B​

1/4 of 45 = 11.25

There were 14 B's.

False

Answer: 3)  20% of the students earned a D

Answer: x=0

Step-by-step explanation:

For this problem, there are no calculations needed. You just have to know your algebraic properties. Since we are looking for x, we know that x must be 0. The answer is 0. Figuring out e²ˣ can be tricky, but since there is an x multiplying it in front, we know that x must be 0 to make the equation equal to 0.

Answer:

3.416, bar above 6

Step-by-step explanation:

41/12 = 3.4166666666666

41/12 = 3 & 5/12

Answer:

66

Step-by-step explanation:

41/12 = 3.4166

Answer:

  isosceles

Step-by-step explanation:

The point B is located on the perpendicular bisector of AC. No calculation is necessary. AC has a slope of 1, so it is easy to count grid squares to see where the perpendicular bisector goes.

When the altitude of the triangle bisects the side opposite the vertex, it is an isosceles triangle.

_____

Apparently, you're to use the distance formula to determine the lengths of the sides of the triangle. Doing that, you would find ...

  AB² = (6-4)² +(1 -6)² = 4 + 25

  CB² = (6-1)² +(1-3)² = 25 + 4

At this point, it doesn't require much thought to realize these sides are the same length: √29.

Answer:

A

Step-by-step explanation:

Let:

Total price be T

And price of tire set be x

T<559.80 ---(1)

T=x +(10% of x)+ 45. ——(2)

T=x+(1/10)x+45

T=(11/10)x+45

Substitute T into equ. 1

T<559.80

(11/10)x +45<559.80

(11/10)x < 514.80

11x < 5148

x < 468

Step-by-step explanation:

It is given that, a projectile is fired vertically upward from a height of 300  feet above the ground, with an initial velocity of 900 ft/s.

The general equation with which a projectile are modled by the function is given by :

[tex]h(t)=-16t^2+v_ot+y_o[/tex]

y₀ is the initial height above the ground

v₀ = initial velocity

So,

[tex]h(t)=-16t^2+900t+300[/tex]

This is the quadratic equation that models the projectile height in feet above the ground after t seconds.

Answer:

0.007619

0.07254

Step-by-step explanation:

1)7.619*10^-3

0.007619

2)7.254*10^2

0.07254

Explanation:

7.619*10^-3

The number here is 7.619 and the number written in scientific notation has minus 3 as its exponent.

.007.619

So the distance between the first decimal point and the second decimal is only three numbers.

Since it is exponent is minus three.

Another way to get the answer.

[tex]7.619 \times 10 {}^{ - 3} = \frac{7619}{1000} \times \frac{1}{1000} = \frac{7619}{1000000} = 0.007619 [/tex]

This applies to the second one too.

Hope this helps ;) ❤❤❤

Answer:

y= -0.8x + 4

Midpoint is 0,4

Answer:

Domain all reals

Range  all reals

Step-by-step explanation:

The domain is the values that x can take, or the values of the input

x can be any real number

The range is the values that y can take, or the values of the output

y can be any real number

Answer:

C)

Step-by-step explanation:

it's fully continous, linear function thus all values are possible for both, x and y

since there are 3 slots and each slot has 30 positions:

dial 1 can have a max of 30 possible outcomes, and so can dial 2 and 3

hence all the dial have 30 possible outcomes

total combinations = total outcomes of slot 1 X total outcomes of slot 2 X total outcomes of slot 3/ 3!

total combinations = 30 * 30 * 30 / 3 X 2 X 1

total combinations = 9000/3 X 2

total combinations  = 1500

hence, there is a total of 1500 different combinations of the 3 slots

the combination required is 1 from the 1500

hence the odds are  1/1500

Answer:

1/27000

Step-by-step explanation:

30*30*30 =27000

each dial has to be in correct position so 1/27000 is correct

Answer:

7(n + 4)

Step-by-step explanation:

Represent the number by n.  Then the verbal expression becomes

7(n + 4).

Answer:

72.3 degrees = 70 degrees + 2 degrees + 0.3 degrees

Step-by-step explanation:

The number, 72.3 degrees, can be rewritten by breaking up the place value of each digit in the expression as folliws,:

70 degrees + 2 degrees + 0.3 degrees

The place value of 7 is tens

The place value of 2 is ones

The place value of 3 is tenths

[tex] 72.3 degrees = 70 degrees + 2 degrees + 0.3 degrees [/tex]

Answer:

72.3 + (-39.1) = 70 + 2 + 0.3 + (-30) + (-9) + (-0.1)

Step-by-step explanation:

got the off the assignment

Answer:

See the explanation for the answer.

Step-by-step explanation:

Given function:

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

The n-th order Taylor polynomial for function f with its center at a is:

[tex]p_{n}(x) = f(a) + f'(a) (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +...+\frac{f^{(n)}a}{n!} (x-a)^{n}[/tex]

As n = 3  So,

[tex]p_{3}(x) = f(a) + f'(a) (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +...+\frac{f^{(3)}a}{3!} (x-a)^{3}[/tex]

[tex]p_{3}(x) = f(a) + f'(a) (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +...+\frac{f^{(3)}a}{6} (x-a)^{3}[/tex]

[tex]p_{3}(x) = a^{1/4} + \frac{1}{4a^{ 3/4} } (x-a)+ (\frac{1}{2})(-\frac{3}{16a^{7/4} } ) (x-a)^{2} + (\frac{1}{6})(\frac{21}{64a^{11/4} } ) (x-a)^{3}[/tex]

[tex]p_{3}(x) = 81^{1/4} + \frac{1}{4(81)^{ 3/4} } (x-81)+ (\frac{1}{2})(-\frac{3}{16(81)^{7/4} } ) (x-81)^{2} + (\frac{1}{6})(\frac{21}{64(81)^{11/4} } ) (x-81)^{3}[/tex]

[tex]p_{3} (x)[/tex] = 3 + 0.0092592593 (x - 81) + 1/2 ( - 0.000085733882) (x - 81)² + 1/6  

                                                                                  (0.0000018522752) (x-81)³

[tex]p_{3} (x)[/tex]  =  0.0092592593 x - 0.000042866941 (x - 81)² + 0.00000030871254

                                                                                                       (x-81)³ + 2.25

Hence approximation at given quantity i.e.

x = 94

Putting x = 94

[tex]p_{3} (94)[/tex]  =  0.0092592593 (94) - 0.000042866941 (94 - 81)² +          

                                                                 0.00000030871254 (94-81)³ + 2.25

         = 0.87037 03742 - 0.000042866941 (13)² + 0.00000030871254(13)³ +    

                                                                                                                       2.25

         = 0.87037 03742 - 0.000042866941 (169) +  

                                                                      0.00000030871254(2197) + 2.25

         = 0.87037 03742 - 0.007244513029 + 0.0006782414503 + 2.25

[tex]p_{3} (94)[/tex]  = 3.113804102621

Compute the absolute error in the approximation assuming the exact value is given by a calculator.

Compute [tex]\sqrt[4]{94}[/tex] as [tex]94^{1/4}[/tex] using calculator

Exact value:

[tex]E_{a}[/tex](94) = 3.113737258478

Compute absolute error:

Err = | 3.113804102621 - 3.113737258478 |

Err (94)  = 0.000066844143

If you round off the values then you get error as:

|3.11380 - 3.113737| = 0.000063

Err (94)  = 0.000063

If you round off the values up to 4 decimal places then you get error as:

|3.1138 - 3.1137| = 0.0001

Err (94)  = 0.0001

Answer:

its [c] if Bradley serves 4 tables he will earn an average of $25

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given:

Total amount = $20,000

Assume

Government bonds = x

Municipal bonds = y

Computation:

1. Invest total money

x + y ≤ 20,000

2. invest no more than $5,000 into municipal bonds

y ≤ 5,000

3. at least twice as much into government bonds.

x ≥ 2y

Answer:

0.70319018

Step-by-step explanation:

Given the following:

Number of students surveyed (n) = 15

Probability of attending tet festival (p) = 24% =0.24

Therefore,

Probability of not attending (1 - p) = (1 - 0.24) = 0.76.

The probability that at most 4 students will attend can be obtained using the binomial probability relation:

p(x) = nCx * p^x * (1 - p)^(n-x)

At most 4 students means:

p(x=0) + p(x=1) + p(x=2) + p(x=3) + p(x=4)

p(x=0) = 15C0 * 0.24^0 * 0.76^(15 - 0)

p(x=0) = 1 * 1 * 0.0004701 = 0.00047018

p(x=1) = 15C1 * 0.24^1 * 0.76^(14)

p(x=1) = 15 * 0.24 * 0.021448 = 0.07721

p(x=2) = 15C2 * 0.24^2 * 0.76^(13) =

p(x=2) = 105 * 0.0576 * 0.02822 = 0.17068

p(x=3) = 15C3 * 0.24^3 * 0.76^(12)

p(x=3) = 455 * 0.013824 * 0.037133 = 0.23356

p(x=4) = 15C4 * 0.24^4 * 0.76^(11) =

p(x=4) = 1365 * 0.0033177 * 0.048859 = 0.22127

0.00047018 + 0.07721 + 0.17068 + 0.23356 + 0.22127 = 0.70319018

Answer:

Total area = [tex](54+\frac{9\sqrt{3} }{2})[/tex] square inch

Step-by-step explanation:

Total area of the prism = Area of the rectangular sides (lateral sides) + area of the triangular bases

Area of the rectangular sides = 3 × (length × width)

                                                 = 3 × (3 × 6)

                                                 = 54 square inch

Area of the triangular bases = 2 × (Area of an equilateral triangle)

                                               = 2 × [tex]\frac{\sqrt{3}}{4}(\text{Side})^2[/tex]

                                               = [tex]\frac{\sqrt{3}}{2}(\text{Side})^2[/tex]

                                               = [tex]\frac{\sqrt{3}}{2}(3)^2[/tex]

                                               = [tex]9(\frac{\sqrt{3} }{2})[/tex]

                                               = [tex]\frac{9\sqrt{3}}{2}[/tex] square inch

Total surface area = (54 + [tex]\frac{9\sqrt{3}}{2}[/tex]) square inch

Answer:

69

Step-by-step explanation:

90-21=69

Answer:

69 degrees

Step-by-step explanation:

The full angle = 90 degrees.

One part of the full angle = 21 degrees

The other part of the full angle = x

Other angle = 90 - 21

=> the other angle = 69 degrees

Answer:

6 spaniels

Step-by-step explanation:

Create 2 equations to represent this, where b is the number of boxers and s is the number of spaniels:

4s = b

s + b = 30

We can plug in 4s as b into the second equation, s + b = 30:

s + b = 30

s + 4s = 30

5s = 30

s = 6

So, there are 6 spaniels.

Answer:

a

  [tex]df = 24.32[/tex]

b

 [tex]df = 30.10[/tex]

c

 [tex]df = 30.7[/tex]

d

[tex]df = 25.5[/tex]

Step-by-step explanation:

Generally degree of freedom is mathematically represented as

          [tex]df = \frac{ [\frac{ s^2_i }{m} + \frac{ s^2_j }{n} ]^2 }{ \frac{ [ \frac{s^2_i}{m} ]^2 }{m-1 } +\frac{ [ \frac{s^2_j}{n} ]^2 }{n-1 } }[/tex]

Considering a

         a) m = 12, n = 15, s1 = 4.0, s2 = 6.0

           [tex]df = \frac{ [\frac{ 4^2 }{12} + \frac{ 6^2 }{15} ]^2 }{ \frac{ [ \frac{4^2}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{15} ]^2 }{15-1 } }[/tex]

         [tex]df = 24.32[/tex]

Considering b

       (b) m = 12, n = 21, s1 = 4.0, s2 = 6.0

          [tex]df = \frac{ [\frac{ 4^2 }{12} + \frac{ 6^2 }{21} ]^2 }{ \frac{ [ \frac{4^4}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{21} ]^2 }{21-1 } }[/tex]

        [tex]df = 30.10[/tex]

Considering c

      (c) m = 12, n = 21, s1 = 3.0, s2 = 6.0

           [tex]df = \frac{ [\frac{ 3^2 }{12} + \frac{ 6^2 }{21} ]^2 }{ \frac{ [ \frac{3^4}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{21} ]^2 }{21-1 } }[/tex]

           [tex]df = 30.7[/tex]

Considering c

        (d) m = 10, n = 24, s1 = 4.0, s2 = 6.0

                [tex]df = \frac{ [\frac{ 4^2 }{10} + \frac{ 6^2 }{24} ]^2 }{ \frac{ [ \frac{4^2}{10} ]^2 }{10-1 } +\frac{ [ \frac{6^2}{24} ]^2 }{24-1 } }[/tex]

               [tex]df = 25.5[/tex]

Answer:

[-4+10+2. 0+25+3]

[10. 12]

[8. 28]

Option 3 is the solution

Answer:

20 hours

Step-by-step explanation:

10*8*4=320 (volume of the pool)

320/16=20 hours

Answer:

20 hours

Step-by-step explanation:

10x8x4 = 320

320 / 16 = 20

it takes 20 hours to fill the empty pool

Answer: Hi!

Let's solve your equation step-by-step.

12x^2 + 54x = −42

Step 1: Subtract -42 from both sides.

12x^2 + 54x − (−42) = − 42 − (−42)

12x^2 + 54x + 42 = 0

Step 2: Factor left side of equation.

6(2x + 7)(x + 1) = 0

Step 3: Set factors equal to 0.

2x + 7 = 0 or x + 1 = 0

You have two answers.

x = −7/2 or x = −1

Hope this helps!

Answer:

11.422

Step-by-step explanation:

[tex]78.2 - 66.778 \\ = 11.422[/tex]

Answer:

A). The distance covered= 5.2752 cm

B). Angle swept = 36°

C). The time = 8:45 am

Step-by-step explanation:

The watch is assumed to be a circle while the minute hand is assumed to be the radius

Radius = 1.4cm

A). From 8:13 to 8:49= 36 minutes

Recall, there is 60 minutes in a round watch.

The distance covered= 2πr*36/60

The distance covered= 2*3.14*1.4*0.6

The distance covered= 5.2752 cm

B). If distance covered is 8.8 mm

8.8 mm = 0.88cm

0.88= 2*3.14*1.4*(x/360)

0.88/(8.792)=x/360

0.1= x/360

0.1= x/360

36°= x

Angle swept = 36°

C). The time it will be if the watch started from 8:39 am and moved 36°

36/360= y/60

0.1= y/60

0.1*60= y

6 minutes= y

The time with be 8:39+6 minutes

The time = 8:45 am