Stacy goes to the county fair with her friends. The total cost of ride tickets is given by the equation c = 3.5t, where c is the total cost of tickets and t is the number of tickets. If Stacy bought 15 tickets, she would spend $

Answer:

a) Mean = 0.125 inch

Standard deviation = 0.13975 inch

b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25) = 0.18673

c) Probability that the door does not fit in the casing = P(X < 0) = 0.18673

Step-by-step explanation:

Let the distribution of the width of the casing be X₁ (μ₁, σ₁²)

Let the distribution of the width of the door be X₂ (μ₂, σ₂²)

The distribution of the difference between the width of the casing and the width of the door = X = X₁ - X₂

when two independent normal distributions are combined in any manner, the resulting distribution is also a normal distribution with

Mean = Σλᵢμᵢ

λᵢ = coefficient of each disteibution in the manner that they are combined

μᵢ = Mean of each distribution

Combined variance = σ² = Σλᵢ²σᵢ²

λ₁ = 1, λ₂ = -1

μ₁ = 24 inches

μ₂ = 23 7/8 inches = 23.875 inches

σ₁² = (1/8)² = (1/64) = 0.015625

σ₂ ² = (1/16)² = (1/256) = 0.00390625

Combined mean = μ = 24 - 23.875 = 0.125 inch

Combined variance = σ² = (1² × 0.015625) + [(-1)² × 0.00390625] = 0.01953125

Standard deviation = √(Variance) = √(0.01953125) = 0.1397542486 = 0.13975 inch

b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25)

This is a normal distribution problem

Mean = μ = 0.125 inch

Standard deviation = σ = 0.13975 inch

We first normalize/standardize 0.25 inch

The standardized score of any value is that value minus the mean divided by the standard deviation.

z = (x - μ)/σ = (0.25 - 0.125)/0.13975 = 0.89

P(X > 0.25) = P(z > 0.89)

Checking the tables

P(x > 0.25) = P(z > 0.89) = 1 - P(z ≤ 0.89) = 1 - 0.81327 = 0.18673

c) Probability that the door does not fit in the casing

If X₂ > X₁, X < 0

P(X < 0)

We first normalize/standardize 0 inch

z = (x - μ)/σ = (0 - 0.125)/0.13975 = -0.89

P(X < 0) = P(z < -0.89)

Checking the tables

P(X < 0) = P(z < -0.89) = 0.18673

Hope this Helps!!!

Answer:

(a)$67

(b)You are expected to win 56 Times

(c)You are expected to lose 44 Times

Step-by-step explanation:

The sample space for the event of rolling two dice is presented below

[tex](1,1), (2,1), (3,1), (4,1), (5,1), (6,1)\\(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)\\(1,3), (2,3), (3,3), (4,3), (5,3), (6,3)\\(1,4), (2,4), (3,4), (4,4), (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)[/tex]

Total number of outcomes =36

The event of rolling a 5 or a 6 are:

[tex](5,1), (6,1)\\ (5,2), (6,2)\\( (5,3), (6,3)\\ (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)[/tex]

Number of outcomes =20

Therefore:

P(rolling a 5 or a 6)  [tex]=\dfrac{20}{36}[/tex]

The probability distribution of this event is given as follows.

[tex]\left|\begin{array}{c|c|c}$Amount Won(x)&-\$1&\$2\\&\\P(x)&\dfrac{16}{36}&\dfrac{20}{36}\end{array}\right|[/tex]

First, we determine the expected Value of this event.

Expected Value

[tex]=(-\$1\times \frac{16}{36})+ (\$2\times \frac{20}{36})\\=\$0.67[/tex]

Therefore, if the game is played 100 times,

Expected Profit =$0.67 X 100 =$67

If you play the game 100 times, you can expect to win $67.

(b)

Probability of Winning  [tex]=\dfrac{20}{36}[/tex]

If the game is played 100 times

Number of times expected to win

[tex]=\dfrac{20}{36} \times 100\\=56$ times[/tex]

Therefore, number of times expected to loose

= 100-56

=44 times

Answer:

x = 28.01t,

y = 10.26t - 4.9t^2 + 2

Step-by-step explanation:

If we are given that an object is thrown with an initial velocity of say, v1 m / s at a height of h meters, at an angle of theta ( θ ), these parametric equations would be in the following format -

x = ( 30 cos 20° )( time ),

y = - 4.9t^2 + ( 30 cos 20° )( time ) + 2

To determine " ( 30 cos 20° )( time ) " you would do the following calculations -

( x = 30 * 0.93... = ( About ) 28.01t

This represents our horizontal distance, respectively the vertical distance should be the following -

y = 30 * 0.34 - 4.9t^2,

( y = ( About ) 10.26t - 4.9t^2 + 2

In other words, our solution should be,

x = 28.01t,

y = 10.26t - 4.9t^2 + 2

These are are parametric equations

Answer:

A. The mean mileage per gallon is _____ 28.99__

A. The median mileage per gallon is _____27.905_____

B. The mode does not exist.

Step-by-step explanation:

Mean= Sum of values/ No of Values

            Mean =  24.2 + 22.2+  37.8+ 22.7 + 35.4 +31.61/ 6

           Mean = 173.91/6= 28.985 ≅ 28.99

The median is the middle value of an ordered data which divides the data into two equal halves. For an even data the median is  the average of n/2 and n+1/2 value where n is the number of values.

Rearranging the above data

22.2 , 22.7 , 24.2 , 31.61 , 35.4, 37.8

Third and fourth values are =24.2 + 31.61 = 55.81

Average of third and fourth values is = 55.81/2= 27.905

Mode is the values which is occurs repeatedly.

In this data there is no mode.

Answer:

Hey there!

15/k, when k=3

15/3=5

Answer:

5

Step-by-step explanation:

its a simple as 15/3 = 5

have fun

Answer:

f(x) = -3x + 4

Step-by-step explanation:

Step 1: Move the 9x over

3y = 12 - 9x

Step 2: Divide everything by 3

y = 4 - 3x

Step 3: Rearrange

y = -3x + 4

Step 4: Change y to f(x)

f(x) = -3x + 4

Answer:

One solution

Step-by-step explanation:

99% of the time, linear equations (equations that have the first degree) have only one solution. However, it's always good to check.

6 - 3x = 12 - 6x

6 = 12 - 3x

-3x = -6

x = 2

As you can see, only one solution. Hope this helps!

Answer:

x = y = 26 cm; z = 13 cm

Step-by-step explanation:

We can calculate the dimensions of the square base as

∛(2·8788) = 26 cm

the height of the box will be half of 26/2 which is 13 cm.

x = y = 26 cm; z = 13 cm

then the minimum area for the given volume can be calculated using what we call Lagrange multipliers, this makes it easier

area = xy +2(xz +yz)

But we were given the volume as 8788

Now we will make the partial derivatives of L to be in respect to the cordinates x, y, z, as well as λ to be equal to zero, then

L = xy +2(xz +yz) +λ(xyz -8788)

For x: we have

y+2z +λyz=0

For y we have

y: x +2z +λxz=0

For z we have 2x+2y +λxy=0............eqn(*)

For we have xyz -8788=0

If we simplify the partial derivative equation of y and x above then we have

λ = (y +2z)/(yz).

= 1/z +2/y............eqn(1)

λ = (x +2z)/(xz)

= 1/z +2/x.............eqn(2)

Set eqn(1 and 2) to equate we have

1/z +2/y = 1/z +2/x

x = y

From eqn(*) we can get z

λ = (2x +2y)/(xy) = 2/y +2/x

If we simplify we have

1/z +2y = 2/x +2/y

Then z = x/2

26/2 =13

Therefore,

x = y = 2z = ∛(2·8788)

X= 26

y = 26 cm

z = 13 cm

Answer:

The answer is "Option A"

Step-by-step explanation:

The valid linear programming language equation can be defined as follows:

Equation:

[tex]\Rightarrow \ Min\ 4x + 3y + (\frac{2}{3})z[/tex]

The description of a linear equation can be defined as follows:

It is an algebraic expression whereby each term contains a single exponent, and a single direction consists in the linear interpolation of the equation.

Formula:

[tex]\to \boxed{y= mx+c}[/tex]

Answer:

m = rise /run = (y2-y1)/(x2-x1)

Step-by-step explanation:

In math, slope is the ratio of the vertical and horizontal changes between two points on a surface or a line. The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run.

Answer: Run is the horizontal change between two points on a line.

Step-by-step explanation:

Answer:

Step-by-step explanation:

A graphing calculator can perform logarithmic regression, as can a spreadsheet. The least-squares best fit log curve is about ...

  y ≈ 33.7·ln(x) -45.9

The value of x estimated to make y = 5.2 is about 4.6.

Answer:

The test to be used is the right tailed test.

Step-by-step explanation:

The type of test joe should do would be a right tailed test. This is because;

A right tailed test which we sometimes call an upper test is where the hypothesis statement contains the greater than (>) symbol. This means that, the inequality points to the right. For example, we want to compare the the life of batteries before and after a manufacturing change.

If we want to know if the battery life of maybe 90 hours would be greater than the original, then our hypothesis statements might be:

Null hypothesis: (H0 = 90).

Alternative hypothesis: (H1) > 90.

In the null hypothesis, there are no changes, but in the alternative hypothesis, the battery life in hours has increased.

So, the most important factor here is that the alternative hypothesis (H1) is what determines if we have a right tailed test, not the null hypothesis.

Thus, the test to be used is the right tailed test.

Answer:

right tailed test.

Step-by-step explanation:

Answer:

55.11% probability that the mean life a random sample of 9 such blenders falls between 4.5 and 5.1 years.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

[tex]\mu = 5, \sigma = 1, n = 9, s = \frac{1}{\sqrt{9}} = 0.3333[/tex]

Find the probability that the mean life a random sample of 9 such blenders falls between 4.5 and 5.1 years.

This is the pvalue of Z when X = 5.1 subtracted by the pvalue of Z when X = 4.5. So

X = 5.1

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{5.1 - 5}{0.3333}[/tex]

[tex]Z = 0.3[/tex]

[tex]Z = 0.3[/tex] has a pvalue of 0.6179

X = 4.5

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{4.5 - 5}{0.3333}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a pvalue of 0.0668

0.6179 - 0.0668 = 0.5511

55.11% probability that the mean life a random sample of 9 such blenders falls between 4.5 and 5.1 years.

Answer:

Length = 29 m

Width = 29 m

Step-by-step explanation:

Let x and y be the length and width of the rectangle, respectively.

The area and perimeter are given by:

[tex]A=xy\\p=116=2x+2y\\y=58-x[/tex]

Rewriting the area as a function of x:

[tex]A(x) = x(58-x)\\A(x) = 58x-x^2[/tex]

The value of x for which the derivate of the area function is zero, is the length that maximizes the area:

[tex]A(x) = 58x-x^2\\\frac{dA}{dx}=0=58-2x\\ x=29\ m[/tex]

The value of y is:

[tex]y = 58-29\\y=29\ m[/tex]

Length = 29 m

Width = 29 m

Answer:

Option C.

Step-by-step explanation:

This is a function because all of the numbers have a partner, and none of them have more than one.

                                    Example of Not a Function

Function                                Not a Function

-4 to 5                                       -4 to 5                             <

9 to 7                                       -4 to 3                              <

13 to 3                                       13 to 3                              ^

-7 to 5                                        9 to 7                               ^

                                                 -7 to 5                               ^

                                           Not a Function because of this

Answer:

The degrees of freedom are given by:

[tex] df =n-1= 15-1=14[/tex]

And if we look in the chi square distribution with 14 degrees of freedom and if we find a quantile who accumulates 0.1 of the area in the left we got:

[tex] \chi^2 = 7.790[/tex]

And then the best answer would be:

c. 7.790

Step-by-step explanation:

For this case we know that we are using a one tailed (lower tail) critical value using a significance level of [tex]\alpha=0.1[/tex] and for this case we know that the ample size is n=15. The degrees of freedom are given by:

[tex] df =n-1= 15-1=14[/tex]

And if we look in the chi square distribution with 14 degrees of freedom and if we find a quantile who accumulates 0.1 of the area in the left we got:

[tex] \chi^2 = 7.790[/tex]

And then the best answer would be:

c. 7.790

Answer: probability =  0.506

Step-by-step explanation:

The data we have is:

Total people: 205 + 160 + 40 = 405

prefer cats: 205

prefer dogs: 160

neither: 40

The probability that a person chosen at random prefers cats is equal to the number of people that prefer cats divided the total number of people:

p = 205/405 = 0.506

in percent form, this is 50.6%

Answer:

Correct!

Step-by-step explanation:

-5(x+8)=-25

x+8=5

x=-3

Answer:

here, -5(x+8)=-25

or, -5x +(-40)= -25

or, -5x=-25+40

or, x= 15/-5

therefore the value of x is -3....ans..

hope u understood..

Answer:

Solution,

[tex](5x + 1)(2x - 1)(2x - 3)[/tex]

[tex] = 5x(2x - 1) + 1(2x - 1) \times (2x - 3) \\ = (10 {x}^{2} - 5x + 2x - 1)(2x - 3) \\ = (10 {x}^{2} - 3x - 1)(2 x - 3) \\ = 10 {x}^{2} (2x - 3) - 3x(2 x - 3) - 1(2x - 3) \\ = 20 {x}^{3} - 30 {x}^{2} - 6 {x }^{2} + 9x - 2x + 3 \\ = 20 {x}^{3} - 36 {x}^{2} + 7x + 3[/tex]

Hope this helps..

Good luck on your assignment...

Answer:

B. g(x) = (x-2)^2 +1

Step-by-step explanation:

When you see this type of equation your get the variables H and K in a quadratic equation. In this case the (x-2)^2 +1  is your H. The (x-2)^2 +1 is your K.

For the H you always do the opposite so in this case instead of going to the left 2 times you go to the right 2 times (affects your x)

For the K you go up or down which in this case you go up one (affects your y)

And that's how you got your (2,1) as the center of the parabola

-Hope this helps :)

Answer:

[tex] \mu = 23.33, \sigma =6.13[/tex]

And for this case we are analyzing the value os 33.44 and we can use the z score formula given by:

[tex] z=\frac{X -\mu}{\sigma}[/tex]

And replacing we got:

[tex] z=\frac{33.44 -23.33}{6.13}= 1.649[/tex]

We know that the proportion of area beyond the Z score associated with this age is  .05 so then the percentile would be: 95

Step-by-step explanation:

For this case we have the following parameters:

[tex] \mu = 23.33, \sigma =6.13[/tex]

And for this case we are analyzing the value os 33.44 and we can use the z score formula given by:

[tex] z=\frac{X -\mu}{\sigma}[/tex]

And replacing we got:

[tex] z=\frac{33.44 -23.33}{6.13}= 1.649[/tex]

We know that the proportion of area beyond the Z score associated with this age is  .05 so then the percentile would be: 95

Answer:

D.  4

Step-by-step explanation:

If he leaves the science assignments for the next day, he will spend zero hours on science assignments.  This means that y is equal to 0.  Plug this into the given equation and solve for x.

2x + y = 8

2x + 0 = 8

2x = 8

x = 4

Gerald can complete 4 math assignments.

Answer:

a) P(x=3)=0.089

b) P(x≥3)=0.938

c) 1.5 arrivals

Step-by-step explanation:

Let t be the time (in hours), then random variable X is the number of people arriving for treatment at an emergency room.

The variable X is modeled by a Poisson process with a rate parameter of λ=6.

The probability of exactly k arrivals in a particular hour can be written as:

[tex]P(x=k)=\lambda^{k} \cdot e^{-\lambda}/k!\\\\P(x=k)=6^k\cdot e^{-6}/k![/tex]

a) The probability that exactly 3 arrivals occur during a particular hour is:

[tex]P(x=3)=6^{3} \cdot e^{-6}/3!=216*0.0025/6=0.089\\\\[/tex]

b) The probability that at least 3 people arrive during a particular hour is:

[tex]P(x\geq3)=1-[P(x=0)+P(x=1)+P(x=2)]\\\\\\P(0)=6^{0} \cdot e^{-6}/0!=1*0.0025/1=0.002\\\\P(1)=6^{1} \cdot e^{-6}/1!=6*0.0025/1=0.015\\\\P(2)=6^{2} \cdot e^{-6}/2!=36*0.0025/2=0.045\\\\\\P(x\geq3)=1-[0.002+0.015+0.045]=1-0.062=0.938[/tex]

c) In this case, t=0.25, so we recalculate the parameter as:

[tex]\lambda =r\cdot t=6\;h^{-1}\cdot 0.25 h=1.5[/tex]

The expected value for a Poisson distribution is equal to its parameter λ, so in this case we expect 1.5 arrivals in a period of 15 minutes.

[tex]E(x)=\lambda=1.5[/tex]

Answer:

n = 55/8

Step-by-step explanation:

You can solve it by cross multiplying. Where you multiply the denominator of the fraction on the left side with the numerator on the right side, and vice versa.

11/n = 8/5

n x 8 = 11 x 5

8n = 55

n = 55/8

(or 6.875)

Answer:

[tex]\boxed{\pink{n = 7 \frac{3}{8} }}[/tex]

Step-by-step explanation:

[tex] \frac{11}{n} = \frac{8}{5} \\ [/tex]

Use cross multiplication

[tex]11 \times 5 = 8 \times n \\ 55 = 8n \\ \frac{55}{8} = \frac{8n}{8} \\ n = 7 \frac{3}{8} [/tex]

Answer:

a) 77.3-73/10.7= 0.40187

b) 62.9-66.8/10.8= -0.36111

c) Kylie did relatively better

Step-by-step explanation:

Answer:

The expected value of this raffle if you buy 1​ ticket is $0.41.

Step-by-step explanation:

The expected value of the raffle if we buy one ticket is the sum of the prizes multiplied by each of its probabilities.

This can be written as:

[tex]E(X)=\sum p_iX_i[/tex]

For example, the first prize is $800 and we have only 1 prize, that divided by the number of tickets gives us a probability of 1/5000.

If we do this with all the prizes, we can calculate the expected value of a ticket.

[tex]E(X)=\sum p_iX_i\\\\\\E(X)=\dfrac{1\cdot800+3\cdot200+5\cdot50+20\cdot20}{5000}\\\\\\E(X)=\dfrac{800+600+250+400}{5000}=\dfrac{2050}{5000}=0.41[/tex]

Answer:

(a) The probability that all the hotel's rooms will be rented is 0.1587.

(b) The probability that 50 or more rooms will not be rented is 0.2514.

Step-by-step explanation:

We are given that the Broadmoor Hotel in Colorado Springs contains 700 rooms and is on the 2004 Gold List.

Suppose Broadmoor's marketing group forecasts a mean demand of 670 rooms for the coming weekend. Assume that demand for the upcoming weekend is normally distributed with a standard deviation of 30.

Let X = demand for rooms in the hotel

So, X ~ Normal([tex]\mu=670,\sigma^{2} =30^{2}[/tex])

The z-score probability distribution for the normal distribution is given by;

                           Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean demand for the rooms = 670

            [tex]\sigma[/tex] = standard deviation = 30

(a) The probability that all the hotel's rooms will be rented means that the demand is at least 700 = P(X [tex]\geq[/tex] 700)

          P(X [tex]\geq[/tex] 700) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{700-670}{30}[/tex] ) = P(Z [tex]\geq[/tex] 1) = 1 - P(Z < 1)

                                                             = 1 - 0.8413 = 0.1587

The above probability is calculated by looking at the value of x = 1 in the z table which has an area of 0.8413.

(b) The probability that 50 or more rooms will not be rented is given by = P(X [tex]\leq[/tex] 650)

         P(X [tex]\leq[/tex] 650) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{650-670}{30}[/tex] ) = P(Z [tex]\leq[/tex] -0.67) = 1 - P(Z < 0.67)

                                                             = 1 - 0.7486 = 0.2514

The above probability is calculated by looking at the value of x = 0.67 in the z table which has an area of 0.7486.

Answer:

Mia:10 Maya:5 Maria:3

Step-by-step explanation:

3+7= 10= Mia's age

10÷2=5= Maya's age

Answer:

Mia - 10

Maya - 5

Maria - 3