Suppose that X ~ Bin(4,1/3) and Y ~ Bin(3,1/4) are independent. Let Z = X+Y. Write a formula for P(Z = 3). Don't simplify.

Maria will not have costs of $18 after tax when selling 12 hand-painted hairclips for 2 for $3.00. Her costs will be slightly higher at $19.26.

To determine if Maria will have costs of $18 after tax when selling 12 hand-painted hairclips for 2 for $3.00, we need to calculate the total revenue she will earn from selling all 12 hairclips and subtract any expenses incurred.
If she sells the hairclips for 2 for $3.00, this means each hairclip is priced at $1.50. Therefore, selling 12 hairclips at this price will yield a total revenue of:
12 hairclips x $1.50/hairclip = $18.00
However, we also need to consider any expenses incurred. We don't know the cost of materials or the time Maria spent creating the hairclips, but we can estimate the tax she will need to pay on the revenue earned.
Sales tax rates vary by state and country, but let's assume a sales tax rate of 7% for this scenario. This means that Maria will need to pay:
$18.00 x 7% sales tax = $1.26
Therefore, Maria's total costs after tax will be:
$18.00 + $1.26 = $19.6

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IT is found that the value of x is 4 and value of y is 5.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The given system of equations are

2x-6y=22

-5x+y=1

The matrix form is

\(\left[\begin{array}{ccc}2&-6\\-5&1\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}22\\1\end{array}\right]\)

Let as assume

\(A = \left[\begin{array}{ccc}2&-6\\-5&1\end{array}\right]\\ \\X = \left[\begin{array}{ccc}x\\y\end{array}\right] \\B = \left[\begin{array}{ccc}22\\1\end{array}\right]\)

WE know that AX = B

Then we have;

\(\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}4\\5\end{array}\right]\)

Therefore, the value of x is 4 and value of y is 5.

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Answer:

She has $58 initially

The equation is;

0.4(y-23.5) = 13.8

where y is the original money she has

Step-by-step explanation:

Let the amount she has originally be $y

she spends $23.50 on a birthday gift

what is left will be;

(y- 23.50)

She decides to keep 0.4 of this and this is equal to 13.8

Thus;

0.4(y-23.5) = 13.8

y- 23.5 = 13.8/0.4

y- 23.5 = 34.5

y = 34.5 + 23.5

y = $58

Answer: $58

Step-by-step explanation:

Let x represent the original amount Ashley has.

Dollars spent on new top = $23.50

Amount of money Ashley is left with : $(x - 23.50)

It is given that Ashley decides to keep 2 fifths of what she has left which is $13.80.

Then you use the distribution property,

Add 9.4 on both sides.

Divide both sides by 0.4

So, Ashley had $58 originally.

Answer:

0.0768 or 7.68%

Step-by-step explanation:

(5 choose 4)*0.4^4*0.6=0.0768

Answer:

31.25 kg of flour is needed to make 50 cakes

Step-by-step explanation:

A 2.5-kg bag of flour contains enough flour to make 4 cakes. a) How much flour is needed to make 50 cakes?

We can find it by using unitary method i.e first find quantity of flour needed for 1 cake and then we can find quantity of flour needed for 50 cakes.

Flour needed to make 4 cakes = 2.5 kg

Flour needed to make 1 cake = \(\frac{2.5}{4}\) kg

Flour needed to make 50 cakes = \(\frac{2.5}{4}\times 50\)

                                                      = 31.25 kg

So, 31.25 kg of flour is needed to make 50 cakes

We have a continuous random variable over -2 < x < 5 so p(x = 1) = 0 because the probability at any given point for any continuous random variable is always 0.

Probability is a measure of the likelihood of a particular event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to happen.

Probability at any given position is always zero for any continuous random variable. This is because the probability of a single value occurring for a continuous random variable is always 0 because the range of values for the random variable is infinite and therefore the probability of a single value occurring is 0.

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Answer:

<

Step-by-step explanation:

Answer:

16.5 feet or

about 17 feet long.

Step-by-step explanation:

A = bh

Squares have equal side lengths all around so with there being 4 sides, you will take 66 and divide by 4.

66 ÷ 4 = 16.5

So it is about 17 feet

Answer: 1/6>x

Step-by-step explanation:

4x+6>10x+5

subtract 4x from both sides

then you have

6>6x+5

subtract 5 from both sides

1>6x

then divide by 6

1/6>x

Answer:

x < 1/6

Step-by-step explanation:

4x + 6 > 10x + 5

-6x + 6 > 5

-6x > -1

x < 1/6

So, the answer is x < 1/6

Answer:

y=-x+4

Step-by-step explanation:

m=y2-y1 ÷ x2-x1

= -3-3 ÷ 7-1

= -6÷ 6

= -1

y-y1= m( x-x1)

y-3= -1(x- 1)

y-3 = -1x+1

y = -x+1+3

y= -x+4

Answer:

The same length as XY

Step-by-step explanation:

If they are similar, they are basically the same ;)!

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Answer:

G(x) when x= -4 is 1.

Step-by-step explanation:

\(g(x)=2x+7\\\\[when x= -4, g(x) becomes: \\\\g(-4)= 2(-4) +7\\\\Do PEMDAS with your current equation, multiplying the -4 by the two outside the parenthesis.\\\\g(-4)= -8 + 7\\\\add.\\\\g(-4)= 1\)

The scenario of the test statistic by assuming observed value as 2800 for the given mean of $2.683 is equal to 2.925.

Mean of debt of college graduates in 2006 = $2,683

Standard deviation = $40.

To calculate the test statistic, we need to have a hypothesis test.

The z-score for a particular value of outstanding credit card debt.

The formula for calculating the z-score is,

z = (x - μ) / σ

where

x is the observed value,

μ is the mean,

and σ is the standard deviation.

Let us assume to calculate the z-score for a college undergraduate who has an outstanding credit card debt of $2,800.

Then, the z-score will be,

z = (2800 - 2683) / 40

  = 2.925

Therefore, the test statistic of z-score for this scenario is 2.925 by assuming outstanding credit card debt value as $2,800.

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Answer:

0.1 and 0.5

Step-by-step explanation:

Answer:

.8-.4=.4 and .12-.8=.4

Step-by-step explanation:

a. ln(7x) can be expanded as ln(7) + ln(x). b. ln(x + 3) remains as it is, since it cannot be simplified further. c. ln(x^8) can be expanded as 8ln(x). d. 15,000ln(xy^4) can be expanded as ln(x) + 4ln(y) + ln(15,000).

a. To expand the logarithmic expression ln(7x), we can use the property of the natural logarithm that states ln(ab) = ln(a) + ln(b).

Therefore, ln(7x) can be expanded as ln(7) + ln(x).

b. Similarly, the logarithmic expression ln(x + 3) can be expanded using the property ln(ab) = ln(a) + ln(b).

Hence, ln(x + 3) remains as it is since we cannot simplify it further.

c. Expanding the logarithmic expression ln(x^8) can be done using the property ln(a^b) = b * ln(a).

Thus, ln(x^8) becomes 8 * ln(x).

d. Expanding the logarithmic expression 15,000ln(xy^4) can be done by applying the property ln(ab) = ln(a) + ln(b).

Therefore, 15,000ln(xy^4) can be expanded as 15,000[ln(x) + ln(y^4)].

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High intercorrelations between two or more independent variables in a multiple regression model are referred to as multicollinearity.

A single dependent variable and several independent variables can be analyzed using the statistical technique known as multiple regression. With the use of independent variables whose values are known, multiple regression analysis aims to predict the value of a single dependent variable.

Multicollinearity, also known as collinearity, is a phenomena in statistics when one predictor variable in a multiple regression model can be linearly predicted from the others with a high level of accuracy. In this case, minor adjustments to the model or the data may cause the multiple regression's coefficient estimates to fluctuate unpredictably.

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Here is a possible program that meets the requirements: import java.util.Scanne imporjava.util.InputMismatchException; public class RestaurantOccupancy {
  public static void main(String[] args) {
     Scanner input = new Scanner(System.in);
     int occupancy = 0;
 

The program starts by importing the Scanner and InputMismatchException classes from the java.util package.

In the main method, we declare a Scanner object named input and an integer variable named occupancy initialized to 0.

The program enters a while loop that continues as long as the occupancy is less than 10. Inside the loop, we prompt the user to enter the number of people entering or leaving the restaurant, read the input as an integer using input.nextInt(), and store it in a variable named delta.

We then add delta to the occupancy variable to update the current occupancy, and print it to the console using System.out.println(). If an InputMismatchException is thrown (i.e., the user enters a non-integer value), we catch the exception, read the next token as a string using input.next(), and print an error message to the console.

Once the occupancy reaches or exceeds 10, the while loop exits, and we print a message indicating that the occupancy limit has been reached and the program is exiting.
Here is a step-by-step explanation for a program that meets the described requirements:

1. Import the necessary libraries:
```java
import java.util.Scanner;
import java.util.InputMismatchException;
```

2. Create a class and the main method:
```java
public class RestaurantOccupancy {
   public static void main(String[] args) {
```

3. Initialize the required variables and create a Scanner object for reading input:
```java
       int occupants = 0;
       int change;
       Scanner input = new Scanner(System.in);
```

4. Create a loop that continues until the number of occupants equals or exceeds 10:
```java
       while (occupants < 10) {
```

5. Use a try-catch block to handle the `InputMismatchException` exception:
```java
           try {
               change = input.nextInt();
               occupants += change;
               System.out.println("Number of people in the restaurant: " + occupants);
           } catch (InputMismatchException e) {
               input.next(); // Discard the invalid input
           }
```

6. Close the while loop, Scanner object, and the main method:
```java
       }
       input.close();
   }
}
```


       while (occupants < 10) {
           try {
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Answer:

2.16 gallons

Step-by-step explanation:

Area to be painted:

9 ft × 12 ft = 108 ft²

Pain required:

Answer:

110° and 215°

Step-by-step explanation:

the bearing of one point to another is the measure of the clockwise angle from the north line N at the point C to the point D , that is

(a)

bearing of D from C is 110° ( purple shaded angle )

(b)

the bearing of D from C is 215° ( blue shaded angle )

The sampling distribution of the sample mean for samples of size 4 is 0.1 and the probability that the inspector will make a Type I error is 0.97

The distribution of pH levels for all community swimming pools in a large county is approximately normal, with a mean of 7.5 and a standard deviation of 0.2.

The safest pH level is from 7.2 to 7.8 and the health inspector selects the random sample of 4 community swimming pools to interrogate the pH levels.

So the mean is 7.5 and the sampling distribution of the sample mean for samples of size 4 can be obtained by 0.2 divided with square root of 4, we get

0.2 / sqrt(4) = 0.2/2 = 0.1

The probability that the inspector will make a Type I error with the sample of 4 pools , the mean is 7.5 and in between 7.2 and 7.8 , so

7.2 - 7.5 / 0.1 = -0.3/0.1 = -0.03

7.8 - 7.5 / 0.1 = 0.3/0.1 = 0.03

So, the probability that the inspector will make a Type I error is 1-0.03 = 0.97

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The age of Richard is 33 years and age of Teo is 11 years.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Richard and Teo have a combined age of 44.

And, Richard is 11 years older than twice​ Teo's age.

Let Teo's age = x

Then, The age of Richard = 2x + 11

Here, Richard and Teo have a combined age of 44.

Hence, We get;

⇒ x + 2x + 11 = 44

⇒ 3x + 11 = 44

⇒ 3x = 44 - 11

⇒ 3x = 33

⇒ x = 11

Thus, Teo's age = x

                         = 11 years

And, The age of Richard = 2x + 11

                                      = 2×11 + 11

                                     = 33 years

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Answer:

y = 2x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (4, 5) and (x₂, y₂ ) = (0, - 3)

m = \(\frac{-3-5}{0-4}\) = \(\frac{-8}{-4}\) = 2

The line crosses the y- axis at (0, - 3) ⇒ c = - 3

y = 2x - 3 ← equation of line

Answer:

A). 8 units

Step-by-step explanation:

Use the distance formula to determine the distance between the two points.

Answer:

8

Step-by-step explanation:

Answer:

V = 1046.9

Step-by-step explanation:

The equation for volume is (4/3)pi r^3

substitute 3.14 in for pi and 6.3 in for r so (4/3)*3.14*6.3^3

Answer:

Mean = 81°F.

S. dev. = 5°F.

Step-by-step explanation:

When we have a set of data:

{x₁, x₂, ..., xₙ}

The mean can be calculated as:

M = (x₁ + x₂ ... + xₙ)/N

Where N is the number of data points that we have:

in this case the set is:

{ 74°F , 79°F , 76°F, 85°F, 87°F, 83°F, 86°F, 78°F }

So N = 8.

Then the mean is:

M = ( 74°F + 79°F + 76°F + 85°F + 87°F + 83°F + 86°F + 78°F )/8

M = 81°F.

Now, the standard deviation can be calculated as.

Sd =  √ ( (1/N)*∑(xₐ - M)^2)

where the summation is over xₐ, which represents a summation over all the points in the data set.

Then we can write the standard deviation as:

Sd = √(1/8)*√( (74°F - 81°F)^2 + (79°F - 81°F)^2 + (76°F - 81°F)^2 + (85°F - 81°F)^2 + (87°F - 81°F)^2 + (83°F - 81°F)^2 + (86°F - 81°F)^2 + (78°F - 81°F)^2)

Sd = 4.58°F.

That we should round up to 5°F (because our mean has no digits after the decimal point)

The study is most likely attempting to establish is Criterion validity and the study featured a(n) scale of measurement is Ordinal scale.

10). The study is most likely attempting to establish is: By criterion validity.

Criterion validity measures how well one measure predicts the outcome for another measure.

Here, we are judging how well the scores on the employment test predict the performance of the person.

Nominal Scale: This scale is used to assign labels to variables that have no numerical values.

For eg : Gender (male and female) , colour (brown blue black white)

Ordinal scale: It matters how the values are arranged, but it makes no difference how much they differ.

For eg: 1: Food applications rated from 1 to 5, 5 being the best. If a app is rated as 2 and other is rated as 4 does not mean the later is twice as good as the first.

Interval scale: An interval scale is a numerical scale where the order and size of the difference between the numbers are known. Absolute zero does not indicate absence in an interval scale, it only means there is no value.

For eg: Temperature in degree Celsius. If T1=5o Celsius  and T2=15o Celsius this means is a temperature difference of 10o , but with T3=0o does not mean there is no temperature.

Ratio scale: The ratio scale is another numerical scale where the order and size of the difference between the values are known, and where absolute zero denotes the absence of values.

For eg: Salary of people

11). The study featured a(n)scale of measurement is: By ordinal scale

We will rank the chairs on a scale where order counts and the size of the difference is not particularly significant.

Hence, for 10th the option A is correct and for 11th the option B is correct.

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Recall that

is defined for all positive real numbers, therefore:

Also, since the range of log_3(x) is all real numbers, then:

Now, to find the x-intercept, we set y(x)=0:

Dividing the above equation by 0.7 we get:

Solving the above equation for x we get:

Therefore, the x-intercept has coordinates (1,0).

Since the function is only defined at (0,∞), there is no y-intercept.

Finally, the function has an asymptote at x=0.

Answer:

Domain:

Range:

X-intercept:

Y-intercept: There is no y-intercept.

Asymptote:

Answer: Heather makes $0.05 more

Step-by-step explanation:

Heather:

12 + 0.50 = 12.50

12.50 * 0.10 = 1.25

12.50 + 1.25 = 13.75

Todd:

12* 0.10 = 1.20

12 + 1.20 = 13.20

13.20 + 0.50 = 13.70

Answer:

To find the probability of the next customer ordering peanut butter cup, we need to determine the total number of ice cream cones and the number of cones that are peanut butter cup.

The total number of cones is:

4 + 5 + 2 + 3 + 2 = 16

The number of cones that are peanut butter cup is 2.

Therefore, the probability of the next customer ordering peanut butter cup is:

2/16 = 0.125

So, the probability of the next customer ordering peanut butter cup is 0.125 or 12.5%.

The 95% confidence interval for the standard deviation of the height of the students is given by (1.541 – 4.059) .

Total number of students = 19 , hence n = 19

Standard deviation = 2.8 , hence s = 2.8

95% confidence interval, hence α = 1 - 0.95 = 0.05 .

Now the confidence interval is calculated using the formula:

\((\sqrt{\frac{(n-1)s^2}{\chi_{n-1,\alpha/2}^2}},\sqrt{\frac{(n-1)s^2}{\chi_{n-1,1-(\alpha/2)}^2}})\)

And the normal distribution.

Now we will substitute the values of the variables to finds the interval.

\((\sqrt{\frac{(19-1)2.8^2}{\chi_{19-1,0.05/2}^2}},\sqrt{\frac{(19-1)2.6^2}{\chi_{19-1,1-(0.05/2)}^2}})\\\\(\sqrt{\frac{94.64}{26.119}},\sqrt{\frac{94.64}{5.629}})\)

⇒ 1.541 – 4.059

Therefore the confidence interval is (1.541 – 4.059) .

A confidence interval is a collection of estimates for an unknown parameter (CI). However, other thresholds, like 90% or 99%, may also be used on occasion to produce confidence intervals. The most common confidence level has risen to be 95%.

The confidence level is a measurement of the proportion of long-term associated CIs that include the parameter's true value. For instance, 95% of all intervals generated at the 95% confidence level should contain the parameter's real value.

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