A woman claims to have the ability to recognize by tasting it, whether tea was poured first and milk added after, or whether tea was added to milk. In order to test her powers, a set of 10 cups is brought to her and she is asked to taste them. She gets 7 out of 10 correct. Assuming each trial is independent, what is the probability that she would have done at least this well if she had no ability to recognize such difference

Answer:

10m is the correct answer to this question

The greatest possible value of ab + bc+ cd+da is 576.

A permutation refers to a selection of objects from a set of objects in which order matters. A phone number is an example of a ten number permutation; it is drawn from the set of the integers 0-9, and the order in which they are arranged in matters. Another example of a permutation we encounter in our everyday lives is a passcode or password. To unlock a phone using a passcode, it is necessary to enter the exact combination of letters, numbers, symbols, etc., in an exact order. In cases where the order doesn't matter, we call it a combination instead.

ab+bc+cd+da

= ab + da  + bc + dc

= a(b + d) + c (b + d)

= (a + c) (b + d)

We choose any 2 of the 4 numbers to occupy the first set of parentheses without regard to order. Thus, the second sum is fixed.

⁴C₂ = 6

So, we  can permute the order of the parentheses' sums in two ways.

∴  6 / 2   =   3 different values

No matter the arrangements, the only possible values are

(9 + 11) (13 + 15)  = 360

(9 + 13) (11 + 15) = 572

(9+ 15) (13 + 11) = 576

The largest value out of the three is 576.

Thus, the greatest possible value of ab + bc+ cd+da is 576.

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If C(x) is the daily production cost and x is the number of bird baths produced daily, then the approximate daily minimum production cost is

option (A) $33

A company that produces and sells bird baths

C(x) is the daily production cost in dollar

x is the number of bird baths produced daily

From the graph choose the point that represents the daily minimum production cost. The bottom point is the minimum production cost point

which is approximately $33

Hence, if C(x) is the daily production cost and x is the number of bird baths produced daily, then the approximate daily minimum production cost is option (A) $33

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Answer:

The area and yard is 60.

Step-by-step explanation:

15 x 4 = 60

Let me know if that helps!

Answer:

it should be 8x + 3(20 - x) = 5(20)

Answer:

One Solution

Step-by-step explanation:

Trust me

Answer:

14

Step-by-step explanation:

7+7

Calculate.

7+7 = 14

The inequality that models Cassie situation is t ≥ 49.25  

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

Cassie is swimming backstroke for her team at the Tri-County Swim Meet. The fastest time so far is 49.25 seconds. Cassie wants to either beat or tie for the fastest time.

The inequalities that models the story is as follows:

let

Cassie has to equal the record or beat the record.

Therefore, the inequalities that represent the story is t ≥ 49.25

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Answer:

x = 3.83

y = 0.84

Step-by-step explanation:

Given;

\(\frac{2}{x-3y} = 1\frac{1}{2} (\frac{5}{x+y} ) ---(i)\\\\3x -5y = 7---(ii)\\\)

Solving the simultaneous equation by elimination method;

\(\frac{2}{x-3y} = \frac{3}{2} (\frac{5}{x+y} )\\\\\frac{2}{x-3y} =\frac{15}{2x+2y} \\\\15(x-3y) = 2(2x +2y)\\\\15x - 45y = 4x + 4y\\\\11x - 49y = 0 --(i)\\\\3x - 5y = 7 --(ii)\\\\3: \ \ 33x -147= 0 ---(iii)\\\\11: -(33x -55y =77) ---(iv)\\{-----------} \\ (iii\ + \ iv): -92y = -77\\\\y = \frac{77}{92} = 0.84 \\\\solve \ for \ x \ using \ (ii)\\\\3x - 5(\frac{77}{92} ) = 7\\\\3x - \frac{385}{92} = 7\\\\3x = 7 + \frac{385}{92}\\\\3x = \frac{644 + 385}{92} \\\\3x = \frac{1029}{92} \\\\\)

\(3x = \frac{1029}{92} \\\\x = \frac{1029}{92 \times 3}\\\\x = 3.73\)

(ii) By substitution method;

\(11x - 49y = 0 --(i)\\\\3x - 5y = 7 --(ii)\\\\from \ (i), 11x = 49y\\\\x = \frac{49y}{11} \\\\substitute \ x \ in (ii);\\\\3(\frac{49y}{11} ) - 5y = 7 \\\\\frac{147y}{11} - 5y = 7\\\\\frac{147y - 55y}{11}= 7\\\\92y = 77\\\\y = \frac{77}{92} = 0.84 \\\\solve \ for \ x;\\\\x = \frac{49}{11} (\frac{77}{92} ) = 3.73\)

The Complete sentences are:

To complete the statements and explain how to use fraction bars to find the quotient of the expression 2 ÷ 2/5, we need to understand the dividend, divisor, and the concept of grouping.

The dividend is the number being divided, which in this case is 2.

The divisor is the number by which the dividend is being divided, which in this case is 2/5.

Here, the Circle groups of 2/5.

and, the number of groups are

= 2 ÷2/5

= 2 x 5/2

= 5

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Answer:

84 pages per hour.

Step-by-step explanation:

We know that 60 minutes is an hour.

So, what you need to do is divide 60 by 25. (this equals 2.4)

then, all you have to do is multiply 2.4 with 35.

2.4×35=84

so, he'll read 84 pages in an hour.

Answer:

x = \(\frac{1}{19}\)

Step-by-step explanation:

2 = 19x + 1  Subtract 1 from both sides

2 - 1 = 19x + 1 - 1

1 = 19x  Divide both sides by 19

\(\frac{1}{19}\) = \(\frac{19x}{19}\)

\(\frac{1}{19}\) = x

Answer:

i onestly have no clue

Step-by-step explanation:

Answer:  < -4/5,  3/5>

This is equivalent to writing < -0.8, 0.6 >

======================================================

Explanation:

Draw an xy grid and plot the point (-4,3) on it. Draw a segment from the origin to this point. Then draw a vertical line until reaching the x axis. See the diagram below.

We have a right triangle with legs of 4 and 3. The hypotenuse is \(\sqrt{4^2+3^2} = \sqrt{16+9} = \sqrt{25} = 5\) through use of the pythagorean theorem.

We have a 3-4-5 right triangle.

Therefore, the vector is 5 units long. This is the magnitude of the vector.

Divide each component by the magnitude so that the resulting vector is a unit vector pointing in this same direction.

Therefore, we go from < -4, 3 > to < -4/5,  3/5 >

This is equivalent to < -0.8, 0.6 > since -4/5 = -0.8 and 3/5 = 0.6

Side note: Unit vectors are useful in computer graphics.

The one-to-one functions g and h are defined as  -¹(1) = 7

(non ¹) (5) = 29

= -35.

To find the value of -¹(1) for the given functions, we need to determine the preimage of 1 under the function g.

The function g is defined as g = {(-5, 7), (1, -7), (7, 1), (8, 6)}.

To find the preimage of 1, we look for the corresponding input value (x) that maps to the output value (y) of 1 in the function g. In this case, we are looking for the value of x when y = 1.

From the given function g, we can see that the pair (7, 1) maps to the output value of 1.

Therefore, -¹(1) = 7.

Note: The notation -¹ denotes the inverse function.

Moving on to the other parts of the question:

(non ¹) (5) refers to evaluating the function h(x) = 4x + 9 when x = 5.

Substituting x = 5 into the function, we get:

h(5) = 4(5) + 9

h(5) = 20 + 9

h(5) = 29

Therefore, (non ¹) (5) = 29.

Lastly, - = 11 refers to evaluating the function h(x) = 4x + 9 when x = -11.

Substituting x = -11 into the function, we have:

h(-11) = 4(-11) + 9

h(-11) = -44 + 9

h(-11) = -35

Therefore, - = -35.

To summarize:

-¹(1) = 7

(non ¹) (5) = 29

= -35

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Answer:

b

Step-by-step explanation:

8×19= 152  

1 : 4.5  

152×4.5=684  

Answer:

y = 3/4 x + 1/4

Step-by-step explanation:

line through the points (1, 1), (5, 4)

slope (m) = (4 - 1) / (5 - 1) = 3/4

y = mx + b       b = y - mx   ... for point (1 , 1)

b = 1 - 3/4 = 1/4

Line: y = 3/4 x + 1/4

check for point (9 , 7):     3/4 * 9 + 1/4 = 28/4 = 7

The requirements for a hypothesis test are satisfied.

To test the claim that the rate of polio is less for children given the Salk vaccine, we need to check if the requirements for a hypothesis test about two population proportions are met. The requirements are:

1. The samples are simple random samples and independent.
2. For each of the two groups, the sample size is at least 1000.

In this case, the study involved 401,974 children who were randomly assigned to two groups: the treatment group with 201,229 children and the placebo group with 200,745 children. This satisfies the first requirement, as the samples are simple random samples and independent. The sample size for both groups is also larger than 1000, meeting the second requirement.

Therefore, the requirements for a hypothesis test are satisfied, and we can proceed with testing the claim that the rate of polio is less for children given the Salk vaccine.

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Assuming the sample standard deviation is $25. Using a 99% confidence level, the Confidence Interval is (141.76; 161.12). the correct answer is B.

To calculate the confidence interval for the population mean, we need to use the following formula:

Confidence Interval = sample mean ± margin of error

where the margin of error is given by:

Margin of Error = z* (sample standard deviation /√(sample size))

In this problem, the sample mean is $150, the sample standard deviation is $25, the sample size is 45, and we want to calculate a 99% confidence interval.

To find the margin of error, we need to find the value of z* corresponding to a 99% confidence level. We can use a standard normal distribution table or a calculator to find this value. For a 99% confidence level, the value of z* is approximately 2.576.

So, the margin of error is:

Margin of Error = 2.576 * ($25 / √(45)) ≈ $8.04

Therefore, the 99% confidence interval is:

Confidence Interval = $150 ± $8.04

Confidence Interval = (141.76; 161.12)

Therefore, the answer is option B: (141.76; 161.12), which is the closest option to the calculated confidence interval.

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Answer:

a < 3

Step-by-step explanation:

divide both sides by -3

so -3/-3 = a

-9/-3 = 3

False. The set M = {a ∈ R: a > 1} is not a vector space under standard addition and scalar multiplication of real numbers.

To be a vector space, M would need to satisfy certain properties, such as closure under addition and scalar multiplication, which it does not fulfill.

For example, if we take two elements in M, say a = 2 and b = 3, their sum a + b = 2 + 3 = 5 is not in M since 5 is not greater than 1.

Therefore, M does not meet the requirements of a vector space.

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Answer:

1st and 4th are the right triangles

It is possible to break a clock into 7 pieces so that the sums of the numbers in each piece are consecutive numbers.

To achieve a set of consecutive sums, we can divide the clock numbers into different groups. Here's one possible arrangement:

1. Group the numbers into three pieces: {12, 1, 11, 2}, {10, 3, 9}, and {4, 8, 5, 7, 6}.

2. Calculate the sums of each group: 12+1+11+2=26, 10+3+9=22, and 4+8+5+7+6=30.

3. Verify that the sums are consecutive: 22, 26, 30.

By splitting the clock into these particular groupings, we obtain consecutive sums for each group.

This arrangement meets the given conditions, where each piece has at least two numbers, and no number is damaged or split into separate digits.

Therefore, it is possible to break a clock into 7 pieces so that the sums of the numbers in each piece form a sequence of consecutive numbers.

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Answer:

17

Step-by-step explanation:

You would make the 10.01 a 10 and the 7.07 a 7.

Answer:

K and R      S and D

Step-by-step explanation: i hope this helps

Answer: 6/23  mph

Step-by-step explanation: We change the 1/3 of an hour to 1 hour by multiplying 1/3 and 2/23 by 3. 1/3 times 3 is 1(hour) and 2/23 x 3 is 6/23(miles). So the unit rate the turtle is traveling at is 6/23 mph.

To prove the statement (a' * b * a)^n = a' * b^n * a for all positive integers n, we will use mathematical induction.

Step 1: Base Case

Let's verify the equation for the base case when n = 1:

(a' * b * a)^1 = a' * b^1 * a

(a' * b * a) = a' * b * a

The equation holds true for the base case.

Step 2: Inductive Hypothesis

Assume that the equation holds true for some positive integer k, i.e., (a' * b * a)^k = a' * b^k * a.

Step 3: Inductive Step

We need to show that the equation also holds for n = k + 1, i.e., (a' * b * a)^(k+1) = a' * b^(k+1) * a.

Using the inductive hypothesis, we can rewrite the left-hand side of the equation for n = k + 1:

(a' * b * a)^(k+1) = (a' * b^k * a) * (a' * b * a)^k

Now, we can apply the group properties to rewrite the right-hand side:

(a' * b * a)^(k+1) = (a' * b^k * a) * (a' * b * a^(-1))^k * a

Using the associative property of the group operation, we can rewrite this as:

(a' * b * a)^(k+1) = a' * (b^k * a * a^(-1) * a')^k * (b * a)

Now, since a * a^(-1) is the identity element of the group, we have:

(a' * b * a)^(k+1) = a' * (b^k * e * a')^k * (b * a)

(a' * b * a)^(k+1) = a' * (b^k * a')^k * (b * a)

Using the inductive hypothesis, we can further simplify this to:

(a' * b * a)^(k+1) = a' * (b^k)^k * (b * a)

(a' * b * a)^(k+1) = a' * b^(k*k) * (b * a)

(a' * b * a)^(k+1) = a' * b^(k+1) * (b * a)

We have shown that if the equation holds true for n = k, then it also holds true for n = k + 1.

Step 4: Conclusion

By using mathematical induction, we have shown that (a' * b * a)^n = a' * b^n * a for all positive integers n. This result can be extended to negative integers as well by using the appropriate definition.

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