Ms. Ironperson and Mr. Thoro are making
Avenger posters to give children when they
visit Avenger Academy. Ms. Ironperson has
completed 12 posters and will complete 6
more per day. Mr. Thoro has not started yet
but can make 12 per day. At some point Mr.
Thoro will catch up and both will have finished
the same number of posters. When this does
happen, how many posters will each Avenger
have completed?
If x denotes the number of days and y denotes
the number of posters, what are the equations
needed to solve this problem? (7 points)​

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. Let μ1 be the mean dissolution time for disk-shaped ibuprofen tablets and μ2 be the mean dissolution time for oval-shaped ibuprofen tablets.

The random variable is μ1 - μ2 = difference in the mean dissolution time for disk-shaped ibuprofen tablets and the mean dissolution time for oval-shaped ibuprofen tablets.

We would set up the hypothesis.

a) The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0

This is a two tailed test.

For disk shaped,

Mean, x1 = (269.0 + 249.3 + 255.2 + 252.7 + 247.0 + 261.6)/6 = 255.8

Standard deviation = √(summation(x - mean)²/n

n1 = 6

Summation(x - mean)² = (269 - 255.8)^2 + (249.3 - 255.8)^2 + (255.2 - 255.8)^2+ (252.7 - 255.8)^2 + (247 - 255.8)^2 + (261.6 - 255.8)^2 = 337.54

Standard deviation, s1 = √(337.54/6) = 7.5

For oval shaped,

Mean, x2 = (268.8 + 260 + 273.5 + 253.9 + 278.5 + 289.4 + 261.6 + 280.2)/8 = 270.7375

n2 = 8

Summation(x - mean)² = (268.8 - 270.7375)^2 + (260 - 270.7375)^2 + (273.5 - 270.7375)^2+ (253.9 - 270.7375)^2 + (278.5 - 270.7375)^2 + (289.4 - 270.7375)^2 + (261.6 - 270.7375)^2 + (280.2 - 270.7375)^2 = 991.75875

Standard deviation, s2 = √(991.75875/8) = 11.1

b) Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

Therefore,

t = (255.8 - 270.7375)/√(7.5²/6 + 11.1²/8)

t = - 3

c) The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [7.5²/6 + 11.1²/8]²/[(1/6 - 1)(7.5²/6)² + (1/8 - 1)(11.1²/8)²] = 613.86/51.46

df = 12

We would determine the probability value from the t test calculator. It becomes

p value = 0.011

d) Since alpha, 0.05 > than the p value, 0.011, then we would reject the null hypothesis. Therefore, we can conclude that at 5% significance level, the mean dissolve times differ between the two shapes

In the given point(-4,b) -4 is the x value.

Locate -4 on the graph and find the y value where the line is located. The y value would be b.

B = 1

Answer:

( $74.623, $83.777)

The 90% confidence interval is = ( $74.623, $83.777)

Critical value at 90% confidence = 1.645

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $79.20

Standard deviation r = $10.41

Number of samples n = 14

Confidence interval = 90%

Using the z table;

The critical value that should be used in constructing the confidence interval.

z(α=0.05) = 1.645

Critical value at 90% confidence z = 1.645

Substituting the values we have;

$79.20+/-1.645($10.42/√14)

$79.20+/-1.645($2.782189528308)

$79.20+/-$4.576701774067

$79.20+/-$4.577

( $74.623, $83.777)

The 90% confidence interval is = ( $74.623, $83.777)

Answer:

x= y^2+4y+4

Step-by-step explanation:

x= (y+2)(y+2)

x= y^2+2y+2y+4

x= y^2+4y+4

Answer:

X = y^2 + 4y + 4

Y= (√X) -2

Step-by-step explanation:

X = (Y+2)^2

X = (Y+2)(Y+2)

X = Y^2 + 4y + 4

X = (Y+2)^2

√X = √(Y+2)^2             (taking the root of both sides cancels the exponent)

√X = Y+2

-2        -2

(√X) - 2 = Y

or

Y = (√X) - 2

Answer:

[tex]g^{-1}(x)=\frac{x-1}{6}[/tex]

Answer:

C = 20 + 0.001x

C = $20 + $0.001x

Step-by-step explanation:

Let x represent the number of minutes spent talking on the phone.

Given;

Fixed monthly charge F = $20

Charge per 10 minutes V = $0.01

Charge per minute = V/10 = $0.01/10 = $0.001

The equation to model the cost of a monthly cell phone bill;

Total cost = fixed cost + variable cost

C = F + (V/10)x

Substituting the values;

C = 20 + 0.001x

Answer:

Step-by-step explanation:

Hello!

I didn't find the exact box plot for this exercise but I've found one that'll help you identify the required values

When constructing a box plot the box lower and upper limits are defined by the first and third quartiles and the line separating it in two represents the median.

In this case, the box is lying on the side, the first quartile is represented by the left side of the box. If you see the graphic this one corresponds to 25.

The median, as said, is represented by the line drawn inside the box, it is not necessarily in its middle but it will always be inside it.

Watching the example, the median is 33

I hope this helps!

Answer: D

Step-by-step explanation:

Answer:

[tex] P(t) = A (1+r)^t [/tex]

Where P represent the population after t days. a the initial amount on this case 6 and r the growth factor rate of 0.7781. so then our model would be given by:

[tex] P(t)= 6(1.7781)^t [/tex]

And replacing t=4 we got:

[tex] P(4) = 6(1.7781)^4 =59.975 \approx 60[/tex]

So then after 4 days we would expect about 60 protzoa

Step-by-step explanation:

For this case we can use the following function to model the population of protzoa:

[tex] P(t) = A (1+r)^t [/tex]

Where P represent the population after t days. a the initial amount on this case 6 and r the growth factor rate of 0.7781. so then our model would be given by:

[tex] P(t)= 6(1.7781)^t [/tex]

And replacing t=4 we got:

[tex] P(4) = 6(1.7781)^4 =59.975 \approx 60[/tex]

So then after 4 days we would expect about 60 protzoa

Answer:

37.67% probability that the pedestrian was intoxicated or the driver was intoxicated.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

945 accidents.

In 64 of them, the pedestian was intoxicated.

In 292 of them, the driver was intoxicated.

Probability that the pedestrian was intoxicated or the driver was intoxicated.

(64+292)/945 = 0.3767

37.67% probability that the pedestrian was intoxicated or the driver was intoxicated.

Answer:

4a

Step-by-step explanation:

The mean is found by adding all of the data set together and then dividing by the amount of individual pieces of data in the set.

(2+3+3+8) = 16

16/4=4

The answer is 4a.

Answer:

60%

Step-by-step explanation:

Percent means out of 100

Changing 3/5 to a denominator of 100

3/5*20/20

60/100

The percent is 60 %

The value of X is 4

please see the attached picture for full solution

Hope it helps

Good luck on your assignment..

Answer:

(a)No. The probability of drawing a specific second card depends on the identity of the first card.

(b)4/663

(c) 4/663

(d) 8/663

Step-by-step explanation:

(a)The events are not independent because we are drawing cards without replacement and the probability of drawing a specific second card depends on the identity of the first card.

(b) P(ace on 1st card and jack on 2nd).

[tex]P$(Ace on 1st card) =\dfrac{4}{52}\\ P$(Jack on 2nd card)=\dfrac{4}{51}\\\\$Therefore:\\P(ace on 1st card and jack on 2nd) =\dfrac{4}{52}\times \dfrac{4}{51}\\=\dfrac{4}{663}[/tex]

(c)P(jack on 1st card and ace on 2nd)

[tex]P$(Jack on 1st card) =\dfrac{4}{52}\\ P$(Ace on 2nd card)=\dfrac{4}{51}\\\\$Therefore:\\P(jack on 1st card and ace on 2nd) =\dfrac{4}{52}\times \dfrac{4}{51}\\=\dfrac{4}{663}[/tex]

(d)Probability of drawing an ace and a jack in either order.

We can either draw an ace first, jack second or jack first, ace second.

Therefore:

P(drawing an ace and a jack in either order) =P(AJ)+(JA)

From parts (b) and (c) above:

[tex]P$(jack on 1st card and ace on 2nd) =\dfrac{4}{663}\\P$(ace on 1st card and jack on 2nd) =\dfrac{4}{663}\\$Therefore:\\P(drawing an ace and a jack in either order)=\dfrac{4}{663}+\dfrac{4}{663}\\=\dfrac{8}{663}[/tex]

Answer:24600 , 16400

Step-by-step explanation:

Let the first part be x

So, second part will be 41000 - x

For amount x

SI = prt / 100

SI = x * 0.50 * 2

SI = 1x

For amount 41000 - x

SI = (41000-x) * 0.50 * 3

SI = 61500 - 1.5x

1x = 61500 - 1.5x

1.5x + x = 61500

2.5x = 61500

x = 61500 / 2.50 = 24600 for 2 years

2nd part = 41000 - 24600 = 16400 for three years

Answer:

D. F(x) = 2(x-3)^2 + 3

Step-by-step explanation:

We are told that the graph of G(x) = x^2, which is a parabola centered at (0, 0)

We are also told that the graph of the function F(x) resembles the graph of the function G(x) but has been shifted and stretched.

The graph of F(x) shown is facing up, so we know that it is multiplied by a positive number. This means we can eliminate A and C because they are both multiplied by -2.

Our two equations left are:

 B. F(x) = 2(x+3)^2 + 3

 D. F(x) = 2(x-3)^2 + 3

Well, we can see that the base of our parabola is (3, 3), so let's plug in the x value, 3, and see which equation gives us a y-value of 3.

y = 2(3+3)^2 + 3 =

2(6)^2 + 3 =

2·36 + 3 =

72 + 3 =

75

That one didn't give us a y value of 3.

y = 2(3-3)^2 + 3 =

2(0)^2 + 3 =

2·0 + 3 =

0 + 3 =

3

This equation gives us an x-value of 3 and a y-value of 3, which is what we wanted, so our answer is:

D. F(x) = 2(x-3)^2 + 3

Hopefully this helps you to understand parabolas better.

Answer:

Step-by-step explanation:

The question has typographical errors. The correct question is:

"A 12​-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 3 ​feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 5 feet from the​ wall?

Solution:

The ladder forms a right angle triangle with the ground. The length of the ladder represents the hypotenuse.

Let x represent the distance from the top of the ladder to the ground(opposite side)

Let y represent the distance from the foot of the ladder to the base of the wall(adjacent side)

The bottom of the ladder is sliding along the pavement directly away from the building at 3ft/sec. This means that y is increasing at the rate of 3ft/sec. Therefore,

dy/dt = 3 ft/s

The rate at which x is reducing would be

dx/dt

Applying Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side², it becomes

x² + y² = 12²- - - - - - - -1

Differentiating with respect to time, it becomes

2xdx/dt + 2ydy/dt = 0

2xdx/dt = - 2ydy/dt

Dividing through by 2x, it becomes

dx/dt = - y/x ×dy/dt- - - - - - - - - - 2

Substituting y = 5 into equation 1, it becomes

x² + 5 = 144

x² = 144 - 25 = 119

x = √119 = 10.91

Substituting x = 10.91, dy/dt = 3 and y = 5 into equation 2, it becomes

dx/dt = - 5/10.91 × 3

dx/dt = - 1.37 ft/s

Answer:

-6x⁴y - 2x³y² + 9x²y³ - 3xy⁴ + y⁵

Step-by-step explanation:

(–2x³y² + 4x²y³ – 3xy⁴) – (6x⁴y – 5x²y³ – y⁵)=

–2x³y² + 4x²y³ – 3xy⁴ – 6x⁴y + 5x²y³ + y⁵=

-6x⁴y - 2x³y² + 9x²y³ - 3xy⁴ + y⁵

Answer:

The solution is [tex]\:\left(-\frac{17}{10},\:-\frac{1}{10}\right)[/tex].

Step-by-step explanation:

An inequality is a mathematical relationship between two expressions and is represented using one of the following:

To find the solution of the inequality [tex]0>\:20x+2>\:-32[/tex] you must:

[tex]\mathrm{If}\:a>u>b\:\mathrm{then}\:a>u\quad \mathrm{and}\quad \:u>b\\\\0>20x+2\quad \mathrm{and}\quad \:20x+2>-32[/tex]

First, solve [tex]0>20x+2[/tex]

[tex]\mathrm{Switch\:sides}\\\\20x+2<0\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\\\20x+2-2<0-2\\\\\mathrm{Simplify}\\\\20x<-2\\\\\mathrm{Divide\:both\:sides\:by\:}20\\\\\frac{20x}{20}<\frac{-2}{20}\\\\\mathrm{Simplify}\\\\x<-\frac{1}{10}[/tex]

Next, solve [tex]20x+2>-32[/tex]

[tex]20x+2-2>-32-2\\\\20x>-34\\\\\frac{20x}{20}>\frac{-34}{20}\\\\x>-\frac{17}{10}[/tex]

Finally, combine the intervals

[tex]x<-\frac{1}{10}\quad \mathrm{and}\quad \:x>-\frac{17}{10}\\\\-\frac{17}{10}<x<-\frac{1}{10}[/tex]

The interval notation is [tex]\:\left(-\frac{17}{10},\:-\frac{1}{10}\right)[/tex] and the graph is:

Answer:

  (0, 3/2)

Step-by-step explanation:

The equation can be put in the form ...

  x^2 = 4py

where p = 3/2.

In this form, the focus is distance "p" from the vertex in the direction the parabola opens.

The vertex is at (0, 0); the parabola opens upward. So, the focus is 3/2 units above the vertex, at ...

  focus = (0, 3/2) . . . . . matches choice A

Answer:

The volume of the crystal is [tex]V=125 \:cm^3[/tex].

Step-by-step explanation:

The volume enclosed by a cube is the number of cubic units that will exactly fill a cube.

To find the volume of a cube recall that a cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself three times. Or as a formula

                                                         [tex]V=s^3[/tex]

where:

s is the length of any edge of the cube.

From the information given we know that the crystal has edge lengths of 5 centimeters. Therefore, the volume of the crystal is

[tex]V=5^3=125 \:cm^3[/tex].

Answer:

The answer is 295 square yards.

Step-by-step explanation:

[48(72-12)-15^2] divide by 9

3456-576-225 divide by 9

Subtract 3456 by 576

2880-255

2655 divide by 9

=295 square yards.

Hope this helped!

The answer is 295 square yards.

To find the area of square , take the square of side.

Given expression is [48(72-12)-15^2] divide by 9 .

Let the unknown area is x.

x = {48 * 60 - 15^2 } divide by 9

x = 2880 - 225 divide by 9

x = 2655 divide by 9

x =295 square yards.

Hence, The answer is 295 square yards.

To learn more about the area of square;

https://brainly.com/question/27776258

#SPJ2

Answer:

shift B

Step-by-step explanation:

shift a is 78.6 repeating

shift b is 79.3 repeating

mean is when you add them all then divide it by the numbers it has

Answer:

shift B

Step-by-step explanation:

To calculate the mean for a set of data, add all the numbers in that set, then divide by the number of data points in the set.

Answer:

14

Step-by-step explanation:

Answer:

Which of these factors will affect the friction on a road

Step-by-step explanation:

the correct answer is 59.

Answer:

59

Step-by-step explanation:

Answer:

The answer is option c

x = 1 y = - 1 z = 1

Hope this helps.

Answer:

(x+4)^2+(y+6)^2 = 25

Step-by-step explanation:

The radius squared is equal to the distance between the center and the point

3^2 + 4^2 = 25

We can shift the center like this

(x+4)^2+(y+6)^2 = 25

Answer:

4z + 2 - 5/2z

Step-by-step explanation:

8z^2 + 4z -5

divided by 2z

8z^2 /2z = 4z

4z/2z =2

5/2z = 5/2z

Putting them back together

4z + 2 - 5/2z

Answer:

A   4z + 2 - 5/2z

Step-by-step explanation:

Answer:

[tex]V = \frac13 \pi r^2 h[/tex]

117.81

Step-by-step explanation:

r is half the diameter so 2.5 cm

h is 18

fill in and get:

V = [tex]\frac13 \pi \cdot 6.25 \cdot 18 \approx 117.81 cm^3[/tex]

Answer:

The probability that on a randomly selected day the statistics professor will have five messages is 0.1755.

Step-by-step explanation:

Let the random variable X represent the number of e-mail messages per day a statistics professor receives from students.

The random variable is approximated by the Poisson Distribution with parameter λ = 5.

The probability mass function of X is as follows:

[tex]P(X=x)=\frac{e^{-5}\cdot 5^{x}}{x!};\ x=0,1,2,3...[/tex]

Compute the probability that on a randomly selected day she will have five messages as follows:

[tex]P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}[/tex]

               [tex]=\frac{0.006738\times 3125}{120}\\\\=0.17546875\\\\\approx 0.1755[/tex]

Thus, the probability that on a randomly selected day the statistics professor will have five messages is 0.1755.

Answer:

360 miles

Step-by-step explanation: