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Unilever should run a z-test of a proportion to test Proctor & Gamble's claim that at least half of the bars of Ivory soap they produce are 99.44% pure or more.

Unilever should use a z-test of a proportion to test whether Proctor & Gamble's claim that at least 50% of Ivory soap bars are 99.44% pure or more is statistically significant based on a sample of 146 bars, of which 70 meet the purity criteria.

The null hypothesis is that the proportion of Ivory soap bars meeting the purity criteria is 0.50, and the alternative hypothesis is that it is greater than 0.50. The z-test yields a p-value of 0.038, which is less than the significance level of 0.05.

Thus, Unilever has sufficient evidence to reject Proctor & Gamble's claim and conclude that the proportion of Ivory soap bars meeting the purity criteria is significantly different from 50%.

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The revenue will be 13 million dollars approximately 5.35 years after 1980.

To find when the revenue will be 13 million, we need to solve the equation:

p = 13

Substituting the given equation for p, we get:

\(0.0456t^2 + 0.728t + 10.34 = 13\)

Simplifying the equation by subtracting 10.34 from both sides, we get:

\(0.0456t^2 + 0.728t - 2.66 = 0\)

We can solve this quadratic equation using the quadratic formula:

\(t = (-b \pm \sqrt (b^2 - 4ac)) / 2a\)

Where a, b, and c are the coefficients of the quadratic equation. In this case, a = 0.0456, b = 0.728, and c = -2.66. Substituting these values into the formula, we get:

\(t = (-0.728 \pm \sqrt(0.728^2 - 4(0.0456)(-2.66))) / 2(0.0456)\)

Simplifying under the square root, we get:

t = (-0.728 ± √0.925344) / 0.0912

t = (-0.728 ± 0.962) / 0.0912

Solving for t using both the plus and minus signs, we get:

t ≈ 5.35 or t ≈ -16.83

The negative value for t is not meaningful in this context, so we can ignore it.

Therefore, the revenue will be 13 million dollars approximately 5.35 years after 1980, which corresponds to the year 1985.35 (or about halfway through the year 1985).

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To compute the Galois groups and determine if the field extensions are normal, we need to know the specific field extensions in question. However, I will provide a general method for computing Galois groups and determining normal field extensions.

Step 1: Identify the field extension
Let's say our field extension is given by K/Q, where K is the extension field and Q is the base field (the field of rational numbers).

Step 2: Determine the minimal polynomial
Find the minimal polynomial f(x) of the field extension K/Q. This is the smallest degree polynomial with rational coefficients for which the elements of K are roots.

Step 3: Compute the Galois group
The Galois group, G(K/Q), is the group of automorphisms of the field K that fix the base field Q. To compute G(K/Q), determine the set of automorphisms of K that keep the elements of Q fixed.

Step 4: Check for normality
A field extension K/Q is normal if and only if the minimal polynomial f(x) splits into distinct linear factors over K. If this is true, then K/Q is a normal field extension.

Step 5: Find a normal extension if necessary
If K/Q is not normal, we can find a normal extension L/Q containing K by considering the splitting field of the minimal polynomial f(x) over Q. The splitting field L is the smallest field containing Q and all the roots of f(x), and the extension L/Q will be normal.

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Answer:

-15.

Step-by-step explanation:

Arithmetic sequence:-

t2 = a + d

= -19 + 4

= -15.

Answer:

Step-by-step explanation:

Hello

2,3,4 5

red, blue , red , blue

A

Answer:

\(\displaystyle 1\frac{2}{5}=\frac{7}{5}\)

Step-by-step explanation:

\(\displaystyle a\frac{b}{c}=\frac{ac+b}{c}\\\\1\frac{2}{5}=\frac{(1)(5)+2}{5}=\frac{5+2}{5}=\frac{7}{5}\)

Answer:

the answer: 56.25 percent of 80

Answer:

George Washington was the first president of the United States of America.

Answer: George washington

Step-by-step explanation:

To find the area of the triangle ABC with vertices A(3, 4), B(4,7), and C(6,-3), we can use Heron's formula. First, calculate the lengths of the sides AB, BC, and AC using the distance formula.

Then, find the semi-perimeter of the triangle by adding the lengths of the sides and dividing by 2. Finally, apply Heron's formula to calculate the area of the triangle.

Calculate the lengths of the sides:

Side AB: √((4 - 3)² + (7 - 4)²) = √(1² + 3²) = √(1 + 9) = √10

Side BC: √((6 - 4)² + (-3 - 7)²) = √(2² + (-10)²) = √(4 + 100) = √104

Side AC: √((6 - 3)² + (-3 - 4)²) = √(3² + (-7)²) = √(9 + 49) = √58

Calculate the semiperimeter:

s = (AB + BC + AC) / 2 = (√10 + √104 + √58) / 2

Apply Heron's formula:

A = √(s(s - AB)(s - BC)(s - AC))

A = √(s(√10)(√104)(√58))

Substituting the value of s into the formula:

A = √((√10 + √104 + √58)/2 * (√10)/2 * (√104)/2 * (√58)/2)

Using a calculator to evaluate the expression, we find that the area of the triangle ABC is approximately 13.2 square units when rounded to the nearest tenth.

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Main Answer:(i) The minimum number of hours a container spent in the port is 10 hours.
(ii) The lower quartile is 20 hours.
(iii) The upper quartile is 35 hours.


In a box-and-whisker diagram, the box represents the middle 50% of the data, with the bottom of the box indicating the lower quartile and the top of the box indicating the upper quartile. The line inside the box represents the median. The whiskers represent the range of the data, with the minimum and maximum values shown as dots or asterisks.

Using the diagram, we can see that the minimum number of hours a container spent in the port is 10 hours, as indicated by the lower whisker. The lower quartile is 20 hours, as indicated by the bottom of the box. The upper quartile is 35 hours, as indicated by the top of the box.

For part (b), the analyst's claim cannot be justified based on the box-and-whisker diagram alone. While it is true that the median (represented by the line inside the box) is closer to the lower quartile than the upper quartile, this does not necessarily mean that the percentage of containers spending more than 23 hours in port is higher than the percentage spending less than 23 hours. To make this claim, the analyst would need to calculate the actual percentage of containers spending more or less than 23 hours, using the data provided.

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The maximum number of people who can stand in each side of the boat is equal to the buoyant force divided by the average mass of a person multiplied by the acceleration due to gravity.

The maximum number of people who can stand in each side of a boat can be determined using Archimedes' Principle. This principle states that the buoyant force on an object is equal to the weight of the fluid it displaces. In the case of a boat, the buoyant force is equal to the weight of the water it displaces.

Using this principle, the maximum number of people who can stand in each side of a boat can be calculated using the equation:

F_B = m_p * g

Where F_B is the buoyant force, m_p is the total mass of all the people standing in the boat, and g is the acceleration due to gravity.

To determine the maximum number of people, we must first calculate the mass of the boat, m_b. We can do this by multiplying the volume of the boat (V) by the density of the material the boat is made of (ρ).

m_b = V * ρ

Next, we can calculate the total mass of all the people standing in the boat, m_p. This can be calculated by multiplying the total number of people (n) by the average mass of a person (m).

m_p = n * m

Finally, we can calculate the maximum number of people who can stand in each side of the boat by rearranging the equation for F_B and solving for n.

n = (F_B) / (m * g)

Therefore, the maximum number of people who can stand in each side of the boat is equal to the buoyant force divided by the average mass of a person multiplied by the acceleration due to gravity.

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Using the Bayes' theorem, we find the probability that the transferred ball was white given that the second ball drawn was white to be 52/89, or approximately 0.5843.

To solve this problem, we can use Bayes' theorem, which relates the conditional probability of an event A given an event B to the conditional probability of event B given event A:

P(A|B) = P(B|A) * P(A) / P(B)

where P(A|B) is the probability of event A given that event B has occurred, P(B|A) is the probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

In this problem, we want to find the probability that the transferred ball was white (event A) given that the second ball drawn was white (event B). We can calculate this probability as follows:

P(A|B) = P(B|A) * P(A) / P(B)

P(B|A) is the probability of drawing a white ball from urn b given that the transferred ball was white and is now in urn b. Since there are now six white balls and three black balls in urn b, the probability of drawing a white ball is 6/9 = 2/3.

P(A) is the prior probability of the transferred ball being white, which is the number of white balls in urn a divided by the total number of balls in urn a, or 6/13.

P(B) is the prior probability of drawing a white ball from urn b, which can be calculated using the law of total probability:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

where P(B|not A) is the probability of drawing a white ball from urn b given that the transferred ball was black and P(not A) is the probability that the transferred ball was black, which is 7/13.

To calculate P(B|not A), we need to first calculate the probability of the transferred ball being black and then the probability of drawing a white ball from urn b given that the transferred ball was black.

The probability of the transferred ball being black is 7/13. Once the transferred ball is moved to urn b, there are now five white balls and four black balls in urn b, so the probability of drawing a white ball from urn b given that the transferred ball was black is 5/9.

Therefore, we can calculate P(B) as follows:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

= (2/3) * (6/13) + (5/9) * (7/13)

= 89/117

Now we can plug in all the values into Bayes' theorem to find P(A|B):

P(A|B) = P(B|A) * P(A) / P(B)

= (2/3) * (6/13) / (89/117)

= 52/89

Therefore, the probability that the transferred ball was white given that the second ball drawn was white is 52/89, or approximately 0.5843.

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Step-by-step explanation:

a) (i) length = 2(pi)r = 2(3.14)(.5 m) = 3.14 m

(ii)3.14 m × ($4.70/m) = $14.76

b) A = (pi)r^2 = (3.14)(18 m)^2 = 1017.9 m^2

Answer:

Step-by-step explanation:

2/3 - 1/5

Find the LCM, say, 15

Then we find the multiple in 15

10/15 - 3/15 = 7/15

Answer:

a percent is a variable of proportionality describing the part of the whole.

The percentage of any quantity can be defined as the product of that quantity with the percent value divided by 100. The complete phrase of the given question is " a percent is a  constant of proportionality describing the part of the whole."

The percentage can be defined as the proportion of any quantity as a part of the whole. To change the percentage into a fraction it is divided by 100.

The proportionality constant is a quantity that is used to change the proportionality relation into an equation.

And, the part of any quantity is always less than the whole.

Thus, the given question can be rephrased as,

A percent is a  constant of proportionality describing the part of the whole.

Hence, for the given statement the correct choice of words in sequence is  constant, part and whole.

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Step-by-step explanation:

I hope it will be helpful for you.

Answer:

A = (1/2 x b x h ) 4 + l^2

= 1/2 x 5 x 8 x4 + 5 x 5

80 + 25

= D. 105 cm2

Answer:

105

Step-by-step explanation:

The value of x is 6.

Complementary angles are angles that sum up to 90°.

Analysis:

For angles A and B, to be complementary, the sine of angle A  must be equal to the cosine of angle B.

sin A = cos B

5X+9 = 3x+21

5x - 3x = 21 - 9

2x = 12

x = 6

In conclusion, the value of x to make angles A and B complementary is 6.

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Answer:

x = 2.

Step-by-step explanation:

First convert to vertex form:

f(x) = 5x^2 - 20x + 3

= 5(x^2 - 4x) + 3

= 5 [(x - 2)^2 - 4] + 3

= 5(x - 2)^2 -20 + 3

= 5(x - 2)^2 - 17.

The line of symmetry  is x = 2.

Answer:

run/rise

3/-3

meaning you run to the left 3 times and go down 3 times

hope that helps

Answer:

Y = - 1x + 11

Step-by-step explanation:

M = y2 - y1/ x2 - x1

The area of the given triangle is 87.55 square centimeter.

From the given triangle, base=17 cm and height=10.3 cm.

The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

Here, area of a triangle = 1/2 ×17×10.3

= 87.55 square centimeter

Therefore, area of the given triangle is 87.55 square centimeter.

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Answer:

Luke regrouped 6 tens 4 ones as 6 tens 14 ones

He should have regrouped 6 tens 4 ones as 5 tens 14 ones

The correct difference is 406.

Step-by-step explanation:

First, we will complete the explanation,

For the difference,864 − 458, Luke got 416;

The explanation of the mistake Luke made is

Luke regrouped 6 tens 4 ones as 6 tens 14 ones

Such that, the difference of the ones (14 - 8) gives him 6 ones,

difference of the tens (6 - 5) gives him 1 ten

and difference of the hundreds ( 8 - 4) gives him 4 hundreds

Hence, his answer 416.

He should have regrouped 6 tens 4 ones as 5 tens 14 ones

So that, the difference of the ones (14 - 8) will give him 6 ones,

difference of the tens (5 - 5) will give him 0 ten

and difference of the hundreds (8 - 4) will give him 4 hundreds

Hence, he would have gotten 406.

The correct difference is 406.

Answer:

Question 3

y  = \(\frac{-1}{5}\)x

Questions 4

y = \(\frac{-1}{4}\)x + 4\(\frac{1}{4}\)

Step-by-step explanation:

Questions 3

From the given information:

m = -1/5

x = -5

y = 1  

Use this to solve for b (y intercept)

y = mx + b

1 = -5(\(\frac{-1}{5}\))+ b

1 = 1 + b  Subtract 1 from both sides

0 = b

y =mx + b

y = \(\frac{-1}{5}\)x + 0

y = \(\frac{-1}{5}\) x

Question 4

Perpendicular slope are opposite reciprocals.

m = \(\frac{-1}{4}\)

x = 1

y = 4

y = mx + b  

Us this information to solve for b

4 = \(\frac{-1}{4}\)(1) + b

4 = \(\frac{-1}{4}\) + b  Add \(\frac{1}{4}\) to both sides

4 \(\frac{1}{4}\) = b

y = \(\frac{-1}{4}\)x + 4 \(\frac{1}{4}\)

or

y = \(\frac{-1}{4}\)x + \(\frac{17}{4}\)

Answer:

6741

Step-by-step explanation:

if its 10% smaller you would have to do the original precent, which is 100%, and subtract 10%, (90%) then divide 90 by 100 to get 0.9 and  multiply it by the total population, in this case 7,490, and you get your answer. i hope this helps :)

Answer:

2. y = 1/2x + 4

Step-by-step explanation:

This is the only equation that moves in a positive slope the way the graph shows it, hope this helps.

Answer:

Ratio of homework papers to exit tickets

Mr. Rowley: 8/7

Ms. Rivera: 16/15

These ratios are not equal

8/7 > 16/15

Step-by-step explanation:

Ratio of homework papers to exit tickets

Mr. Rowley: 16:14

Expressed as a fraction this is
\(\dfrac{16}{14}\)

Let's simplify the fraction by dividing numerator and denominator by 2. This is essentially dividing by 1 since 2/2 =1 so the fractional value itself is unchanged.

\(\dfrac{16 \div 2}{14 \div 2} = \dfrac{8}{7}\)

Ms. Rivera: 64:60
Expressed as fraction this is
\(\dfrac{64}{60}\)

Let's simplify the fraction by dividing numerator and denominator by 2
\(\dfrac{64 \div 2}{60 \div 2} = \dfrac{32}{30}\)

This can be simplified further by dividing again by 2:
\(\dfrac{32 \div 2}{30 \div 2} = \dfrac{16}{15}\)

(We could have divided by 4 the first time also)

\(\dfrac{8}{7}\) \(\mathrm {\;is\;\bold{not\; equal\;} to\; }\) \(\dfrac{16}{15}\)

We can see that if we multiply both fractions by 105 which is the product of the denominators

\(\dfrac{8}{7} \times 105 = 8 \times 15 = 120 \rm \;\;\;\;{ (since 105 \div 7 = 15)}\\\\\dfrac{16}{15} \times 105 = 16 \times 7 = 112 \rm \;\;\;\;{ (since 105 \div 15 = 7)}\\\\\\\)

Since we are multiplying both fractions by the same amount to get rid of the denominator it is easy to see which one is bigger

Obviously 8/7 is bigger than 16/15

We could have converted to decimal also and checked
8/7 =     1.14 rounded to 2 decimal places
16/15 =  1.07 rounded to 2 decimal places

1.14 > 1.07 so 8/7 > 16/15

(You can choose which of the above methods you like)

The system of linear equations 6x - 2y = 8 and 12x - ky = 5 does not have a solution if and only if k = 12. This means that when k takes the value of 12, the system of equations becomes inconsistent and there is no set of values for x and y that simultaneously satisfy both equations.

In the given system, the coefficient of y in the second equation is directly related to the condition for a solution. When k is equal to 12, the second equation becomes 12x - 12y = 5, which can be simplified to 6x - 6y = 5/2. Comparing this equation to the first equation 6x - 2y = 8, we can see that the coefficients of x and y are not proportional. As a result, the two lines represented by the equations are parallel and never intersect, leading to no common solution. Therefore, when k is equal to 12, the system does not have a solution. For any other value of k, a unique solution or an infinite number of solutions may exist.

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