If a box contains 6 blue, 7 red, and 3 white stars, what is the probability of picking a blue star

Answer:

H0 : flavor and serving size are independent

H1: Flavor and serving size are not independent

Step-by-step explanation:

The claim or hypothesis is to test if there is a relationship between the different types of flavor (vanilla, strawberry and chocolate) and the size (large, medium and. Small) being ordered. This is the the Alternative hypothesis, in other words to establish that flavor type and size are not independent, (that is the two variables are correlated).

The Null hypothesis will be the opposite of the alternative, establish that both variables are independent.

Hence ;

Null hypothesis ; H0 : flavor and serving size are independent

Alternative ; H1: Flavor and serving size are not independent

Answer:

19 6/8 or 19 3/4

I’m not sure if you want the smallest possible fraction or not. If you don’t know just put the second one. K.

The monthly cost for 17 hundred of cubic feet is $52.13.

A linear equation is in the form:

y = mx + b

Where y,x are variables, m is the rate of change and b is the initial value of y.

Let y represent the bill paid for x HCF of water.

The slope is 1.45, hence m = 1.45.

The monthly cost for 13 HCF is $46.33, hence:

46.33 = 1.45(13) + b

b = 27.48

y = 1.45x + 27.48

For 17 HCF:

y = 1.45(17) + 27.48 = 52.13

The monthly cost for 17 hundred of cubic feet is $52.13.

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Therefore , the solution of the given problem of unitary method comes out to be Daisy cream and Kremlin cream both have less cream per bulk 1 gallon and 4.5 gallons, respectively than Marble cream.

The objective can be accomplished by utilising what has already been discovered, taking advantage of this worldwide access, and including all essential components from earlier changeable study who employed a certain technique. If the anticipated claim outcome actually occurs, it will either be possible to contact the variable again or both important processes will undoubtedly miss the statement.

Here,

We must convert cups to gallons because daisy cream is sold in bulks of cups. Since a gallon of Daisy cream comprises 16 cups, one quantity of Daisy cream contains:

=> 16 cups per bulk = 1 gallon 16 cups per bulk = 1 gallon

Moscow cream is offered in bulk quantities of 4 1/2 gallons, which is one gallon.

Thus, we must convert pints to gallons. A gallon of Marble cream comprises eight pints, hence one quantity of Marble cream contains:

=> 40 pints in a bulk equal 1 gallon, 8 pints, or 5 gallons.

As a result, we can see that Marble cream, with 5 gallons per bulk, has the most cream.

Daisy cream and Kremlin cream both have less cream per bulk (1 gallon and 4.5 gallons, respectively) than Marble cream.

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The two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

To solve the system of equations, let's assign variables to the two integers. Let the first integer be represented by 'x' and the second integer by 'y'.

According to the given information:

a. Fourteen more than twice the first integer gives the second integer:

This can be expressed as: 2x + 14 = y

b. The second integer increased by one is the square of the first integer:

This can be expressed as: y + 1 = x^2

Now, we have a system of equations:

1) 2x + 14 = y

2) y + 1 = x^2

To solve this system, we can substitute the value of 'y' from equation 1) into equation 2):

2x + 14 + 1 = x^2

2x + 15 = x^2

Rearranging the equation, we have:

\(x^2 - 2x - 15 = 0\)

Factoring the quadratic equation, we get:

(x - 5)(x + 3) = 0

Setting each factor equal to zero:

x - 5 = 0   -->   x = 5

x + 3 = 0   -->   x = -3

Substituting the values of 'x' back into equation 1), we can find the corresponding values of 'y':

For x = 5:

2(5) + 14 = y

10 + 14 = y

y = 24

For x = -3:

2(-3) + 14 = y

-6 + 14 = y

y = 8

Therefore, the two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

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Answer:

3 coins each row

Step-by-step explanation:

if you put 3 coins in 4 rows it we'll be equivalent to 12

Answer:

The top box:  3

The middle box:  2

The bottom box:  1

Step-by-step explanation:

In order to fill out the yellow boxes we have to use the equation above the table, and plug in the x values, and so we get...

If x = 2, then

y = x + 1

y = 2 + 1

y = 3

If x = 1, then

y = x + 1

y = 1 + 1

y = 2

If x = 0, then

y = x + 1

y = 0 + 1

y = 1

The number of applications filled by Henry is 7 and the number of applications filled by Ben is 15.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Ben originally filled out 8 more applications than Henry.

Let the number of applications filled by Henry be x.

Now, x+8

Then each boy filled out 3 additional applications, bringing the total to 28.

Here, x+3+x+8+3=28

2x+14=28

2x=14

x=7

So, x+8=15

Therefore, the number of applications filled by Henry is 7 and the number of applications filled by Ben is 15.

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The given function is:

Notice that the function is a Square Root function.

The parent function of the square root function is:

Hence, the graph that matches this function is the graph shown below:

Denis's and Dasha's methods use different operations to simplify the expressions in different orders.

Denis's method uses addition, subtraction, and multiplication operations, but Dasha's method does not.

Multiplication operations are described as using mathematical operation that indicates how many times a number is added to itself.

Denis's Assignment

2* 6+2w-54

12+2w = 54

12-12+2w= 54-12

2w=42

w= 21  

Dasha's Assignment

54-2* 6

54-12= 42

The two widths add to 42 cm

42/ 2-21

We can see that Dasha's method also uses addition and subtraction operations, but she simplifies the expression by performing the operations in a different order.

She subtracts the product of 2 and 6 from 54.

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After calculating The perimeter of rectangle is 46.52 in the given rectangle.

What is area of rectangle?

area of rectangle can be defined as the product of length and breadth.

Given ,

A rectangle has a length 20 5 /6 and

breadth = 2 3/7

The perimeter of rectangle  = 2 (l+b)

length = (120 + 5 ) / 6 = 125/ 6

breadth = (14+3) / 7  = 17/7

perimeter  = 2 (125/6 + 17/7 )

= 2 ( (125*7 + 17 * 6) / 42 )

= 2 (875+102) / 42

= 2 * 23.26

= 46.52

Hence, after calculating The perimeter of rectangle is 46.52 in the given rectangle.

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Answer:

m = - 1 , m = 0 , m = \(\frac{7}{2}\)

Step-by-step explanation:

2m³ - 5m² - 7m = 0 ← factor out common factor m from each term

m(2m² - 5m - 7) = 0

factorise the quadratic 2m² - 5m - 7

consider the factors of the product of the coefficient of the m² term and the constant term which sum to give the coefficient of the m- term

product = 2 × - 7 = - 14 and sum = - 5

the factors are + 2 and - 7

use these factors to split the m- term

2m² + 2m - 7m - 7 ( factor the first/second and third/fourth terms )

2m(m + 1) - 7(m + 1) ← factor out (m + 1) from each term

(m + 1)(2m - 7)

then

2m³ - 5m² - 7m = 0

m(m + 1)(2m - 7) = 0 ← in factored form

equate each factor to zero and solve for m

m = 0

m + 1 = 0 ( subtract 1 from both sides )

m = - 1

2m - 7 = 0 ( add 7 to both sides )

2m = 7 ( divide both sides by 2 )

m = \(\frac{7}{2}\)

solutions are m = - 1 , m = 0 , m = \(\frac{7}{2}\)

Answer:

You could try to do it side by side then the area x side.

Step-by-step explanation:

Sorry if it is not much help, hope you figure it out!

Answer:

4

Step-by-step explanation:

Volume= length*width*height

72=Length*3*6

72=Length*18

divide by 18 both sides to get Length=4 inches

Answer:

A)  A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on the ordered pair (3, 8)

Step-by-step explanation:

Given equations:

\(\textsf{Equation 1}: \quad y=-2x+14\)

\(\textsf{Equation 2}: \quad y=2x+2\)

Substitute Equation 2 into Equation 1 and solve for \(x\):

\(\implies 2x+2=-2x+14\)

\(\implies 4x=12\)

\(\implies x=3\)

Substitute found value of \(x\) into Equation 2 and solve for \(y\):

\(\implies y=2(3)+2=8\)

Therefore, the solution to the system is (3, 8).  

This is the point of intersection of the two lines.

The function is nonlinear because it does not have a constant rate of change

The graph in the function is parabolic,

And the rate of change is -1.

Function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.

In the given graph,

Function f(x) is given.

The graph is curved shaped,

Implies that, it is not linear.

The graph shows function of parabola,

And the equation of the given parabola can be given as,

y = (x-3)² - 1.

To find the rate of change

Take points on tow points on x-axis,

x = 2 and x = 3

The value of y corresponding to x = 2,

y = 0,

The value of y corresponding to x = 3,

y = -1

The points are (2, 0) and (3, -1)

The rate of change = (-1 -0)/ 3 - 2 = -1 / 1 = -1

The rate of change is -1.

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Answer:

-9 and -8 ...............

Answer: A. -300

Step-by-step explanation: I hope this helps!

Answer:

2/15

Step-by-step explanation:

Answer:

2009

Step-by-step explanation:

1 4nv

Answer:

Hiiiiii

Step-by-step explanation:

Thank you so much

The roots of the equation \((x^2 + 1)(x^3 + 2x)(x^2 - 64)\) = 0 are x = ±i, ±√(-2), 0, 8, -8.

To find the roots of the equation \((x^2 + 1)(x^3 + 2x)(x^2 - 64)\) = 0, we can use the zero-product property, which states that if a product of factors equals zero, then at least one of the factors must be equal to zero.

So, we'll set each factor equal to zero and solve for 'x':

1. \(x^2 + 1\) = 0

  Subtracting 1 from both sides:

 \(x^2\) = -1

  Taking the square root of both sides:

  x = ±√(-1)

  Since the square root of a negative number is not defined in the real number system, the solutions to this equation are complex numbers.

  Therefore, the roots for this factor are:

  x = ±i (where i represents the imaginary unit)

2. \(x^3 + 2x\) = 0

  Factoring out 'x':

\(x(x^2 + 2)\) = 0

  Applying the zero-product property:

  x = 0 (one root)

  Also, \(x^2 + 2\) = 0

  Subtracting 2 from both sides:

  \(x^2\) = -2

  Taking the square root of both sides:

  x = ±√(-2)

  Again, the solutions to this equation are complex numbers.

  Therefore, the roots for this factor are:

  x = ±√(-2)

3.\(x^2 - 64\) = 0

  This is a quadratic equation, so we can solve it by factoring:

  (x - 8)(x + 8) = 0

  Applying the zero-product property:

  x - 8 = 0  or  x + 8 = 0

  x = 8  or  x = -8

Combining all the roots from each factor, we have:

x = ±i, √(-2), 0, 8, -8

The solutions to the equation \((x^2 + 1)(x^3 + 2x)(x^2 - 64)\) = 0, including all real and complex numbers are x = ±i, √(-2), 0, 8, -8.

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No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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Step-by-step explanation:

A triangle is given. It is required to classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.

Notice that the given triangle has a right angle as one of its angles, it follows that the triangle is a right triangle.

Notice also that the triangle has two sides of equal length, this implies that two of its sides are congruent.

Hence, the triangle can be classified as Isosceles.

The answer is C. Right, Isosceles.

Answer:

ddx(x−m)=−mx−m−1

That is, ddx(x−m)=−mx−m−1. where m is a positive integer.

The limit of the given function as x approaches 1 is 0.

To find the limit of the given function as x approaches 1, we need to evaluate the expression by substituting x = 1. Let's break it down step by step:

1. Begin by substituting x = 1 into the numerator:

\(\[12\sin\left(\frac{\pi}{2}\cdot 1\right)\ln(1) = 12\sin\left(\frac{\pi}{2}\right)\ln(1) = 12(1)\cdot 0 = 0\]\)

2. Now, substitute x = 1 into the denominator:

(1³ + 5)(1 - 1) = 6(0) = 0

3. Finally, divide the numerator by the denominator:

0/0

The result is an indeterminate form of 0/0, which means further analysis is required to determine the limit. To evaluate this limit, we can apply L'Hôpital's rule, which states that if we have an indeterminate form 0/0, we can take the derivative of the numerator and denominator and then evaluate the limit again. Applying L'Hôpital's rule:

4. Take the derivative of the numerator:

\(\[\frac{d}{dx}\left(12\sin\left(\frac{\pi}{2}x\right)\ln(x)\right) = 12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{x} + \frac{\sin\left(\frac{\pi}{2}x\right)\ln(x)}{x}\right)\]\)

5. Take the derivative of the denominator:

\(\[\frac{d}{dx}\left((x^3 + 5)(x - 1)\right) = \frac{d}{dx}\left(x^4 - x^3 + 5x - 5\right) = 4x^3 - 3x^2 + 5\]\)

6. Substitute x = 1 into the derivatives:

Numerator: \(\[12\left(\cos\left(\frac{\pi}{2}\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{1} + \sin\left(\frac{\pi}{2}\right) \cdot \frac{\ln(1)}{1}\right) = 0\]\)

Denominator: 4(1)³ - 3(1)² + 5 = 4 - 3 + 5 = 6

7. Now, reevaluate the limit using the derivatives:

lim as x approaches 1 of \(\[\frac{{12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{{-1}}{{x}} + \sin\left(\frac{\pi}{2}x\right) \cdot \frac{{\ln(x)}}{{x}}\right)}}{{4x^3 - 3x^2 + 5}}\]\)

= 0 / 6

= 0

Therefore, the limit of the given function as x approaches 1 is 0.

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Answer:

87124 + 14997 = 102121

Hope it helpz~ uh..

Carry on learning :)

Answer:

102121

Step-by-step explanation:

Answer:

Step-by-step explanation:

a) The formula for the regression function is:

Maintenance Cost = 54.7757 + 120.689 x Age of Car

b) The slope of the regression equation is 120.689. This means that on average, for every one year increase in the age of a car, the maintenance cost is expected to increase by $120.689.

c) To construct a 95% interval to predict the maintenance cost for a car that is 7 years old, we can use the formula:

Y = a + bX ± tα/2 * SE

where Y is the predicted maintenance cost, a is the intercept, b is the slope, X is the age of the car, tα/2 is the t-value for the 95% confidence level with n-2 degrees of freedom (11 in this case), and SE is the standard error of the estimate.

Plugging in the values, we get:

Y = 54.7757 + 120.689 * 7 ± 2.201 * 11.8442

Y = 923.167 ± 26.010

Therefore, we can be 95% confident that the maintenance cost for a car that is 7 years old will be between $897.16 and $949.17.

d) The null hypothesis is that there is no significant linear relationship between the average maintenance cost and the age of a car in years. The alternative hypothesis is that there is a significant linear relationship between the average maintenance cost and the age of a car in years.

To test the hypothesis, we can perform a t-test on the slope coefficient using the t-statistic and the p-value provided in the output. The t-statistic is 10.1898, which is much greater than the critical t-value at the 0.05 level of significance for a two-tailed test with 11 degrees of freedom (2.201). The p-value is 0.0000, which is less than the significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that there is a significant linear relationship between the maintenance cost and the age of the car in years.