Combine The Complex Numbers -2.7e^root7 +4.3e^root5. Express Your Answer In Rectangular Form And Polar Form.

The True statement about hypothesis testing is: d) The critical value depends on the significance level.

In hypothesis testing, the critical value is the threshold value used to determine whether to reject or fail to reject the null hypothesis. It is chosen based on the desired significance level, which represents the maximum acceptable probability of committing a type I error (rejecting the null hypothesis when it is true). The critical value is compared to the test statistic to make the decision.

The significance level, denoted by α, is determined by the researcher before conducting the hypothesis test and represents the acceptable level of risk for making a type I error. It is typically set to a small value, such as 0.05 or 0.01.

The test statistic, on the other hand, is calculated based on the observed data and the specific hypothesis being tested. It is used to assess the evidence against the null hypothesis and determine whether it is sufficiently significant to reject it.

Therefore, the correct statement is that the critical value depends on the significance level, as it is chosen to control the probability of making a type I error.

Therefore the correct option is d)

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Answer:

D) 400x²-640x+256

Step-by-step explanation:

2(10x-6)-4=20x-16

(20x-16)(20x-16)=

400x²-640x+256

Answer: Heyaa!

60 Cant be Simplified so it stays the same.

Step-by-step explanation:

Nothing further can be done with this topic.

Hopefully this helps you !

- Matthew ~

Answer:

F the point is 3.16

Explantion:

the point is 3.16, which is close to 3.2

Answer:

502.65

Step-by-step explanation:

Answer:

C) 1/2

Step-by-step explanation:

We know that 3/8 cup of brown sugar and 1/3 cup of white sugar are mixed together to make the sugar mixture.

From this sugar mixture, 1/4 cup is set aside for the crumb topping.

To find out how much sugar mixture is used to make the cake, we need to subtract the amount set aside for the crumb topping from the total sugar mixture.

We can start by converting the mixed unit of measurement (brown sugar in cups and white sugar in cups) to a single unit of measurement (cups)

3/8 cup of brown sugar + 1/3 cup of white sugar = (3/8)+(1/3) = 5/12 cup + 4/12 cup = 9/12 cup.

1/4 cup is set aside for the crumb topping.

So, the remaining sugar mixture used to make the cake is 9/12 cup - 1/4 cup = (9/12) - (1/4) = (9-3)/12 = 6/12 cup = 0.5 cup

Answer:

The amount she saves is 25% of her income

Step-by-step explanation:

She is paid $11 per hour

She works 9 hours per day

and for 24 days per month

So, she works 9(24) hours per month

= 216 hours per month

Now, she is paid $11 hourly, so for 216 hours,

she will have 11(216) = $2376

Total income = $2376 per month

Saving = $594 per month

As a percentage, we divide the savings by the total income,

savings/(total income) = 594/2376 = 1/4 = 0.25

Hence we get 25%

Sample space when a coin is tossed is {H, T}

Sample space for drawing a card is {1, 2, 3, 4}

Sample space = {H1, H2, H3, H4, T1, T2, T3, T4}

Event that the coin toss is tails = {H1, H2, H3, H4}

The sample space describing all possible outcomes are (H1, H2, H3, H4, T1, T2, T3, T4).

A series of independent Bernoulli trials with a chance of 1/2 on each trial is referred to as a fair coin in probability theory and statistics. A biased or unjust coin is one for which the probability is not equal to one-half.

The presumption that a coin is fair is sometimes made by making reference to an ideal coin in theoretical investigations. When John Edmund Kerrich experimented with flipping coins, he discovered that 679 times out of 1000, a coin fashioned of a wooden disc the size of a crown that was coated with lead on one side landed heads (wooden side up).

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Answer:

(B)IH = IJ = 3 and \(JK = HK = \sqrt{29}$ units\), and IH ≠ JK and IJ ≠ HK.

Step-by-step explanation:

In a kite the following properties applies

Adjacent sides are equal

IH and IJ are adjacent sides

IH=IJ=3 Units

Similarly, JK and HK are adjacent sides and:

\(JK = HK = \sqrt{29}$ units\)

Since opposite sides of a kite must not be equal,

IH ≠ JK and IJ ≠ HK.

Therefore, Option B is the statement that proves that HIJK is a kite.

Answer:

B. IH = IJ = 3 and JK = HK = StartRoot 29 EndRoot, and IH ≠ JK and IJ ≠ HK.

Step-by-step explanation:

got it correct on edge. have a good day!

Answer:

8

Step-by-step explanation:

Answer is 8

Answer:

the answer is 20 apples.

Step-by-step explanation:

15/100 is simplified down to 3/20, so therefore you have three apples out of 20. 20 is your total amount of apples.

Among the given list of numbers, the only item that is not a pure imaginary number is a real number.

A pure imaginary number is a complex number that can be written in the form bi, where b is a real number and i is the imaginary unit (√-1). In other words, pure imaginary numbers have a real part of zero.

To identify the real number in the given list, we need to look for a number that has a non-zero real part. Real numbers do not involve the imaginary unit, so they can be expressed without the presence of i.

If the list contains numbers in the form bi, where b is non-zero, then they are pure imaginary numbers. However, if we come across a number that is not in the form bi and has a non-zero real part, it is a real number. Such numbers are found on the real number line and can be positive, negative, or zero. By examining each number in the given list, we can determine the only item that does not conform to the definition of a pure imaginary number and identify it as a real number.

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Answer:

t = 3 hours, therefore it cannot be 4 hours

Step-by-step explanation:

Divide the miles traveled by the rate you traveled. This will find the time it took to travel.

180/60 = 3

You drove 3 hours to travel 180 miles, therefore t cannot equal 4.

The number of letters that must be engraved for the costs to be the same is 25.

What is an expression?

Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Since we have given that :

0.40e + 10 + 15 = 0.20e + 5 + 25.

We need to find the number of letters by rearranging the like terms and simplifying for e value :

 0.40e + 25 = 0.20e + 30

0.40e - 0.20e = 30-25

0.20e = 5

e = 5/0.20

e = 50/2

e = 25

Hence, the number of letters that must be engraved for the costs to be the same is 25.

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Therefore, the probability that 0 < X < 1 is approximately 0.3413, or 34.13%.

If a random variable X is distributed normally with zero mean and unit standard deviation (X ~ N(0, 1)), the probability that 0 < X < 1 can be calculated using the standard normal distribution table or a statistical software.

In this case, we need to find the area under the normal curve between 0 and 1 standard deviations from the mean. Since the standard deviation is 1, we are interested in finding the probability that the value of X falls between 0 and 1.

Using the standard normal distribution table, we can look up the cumulative probability associated with 1 standard deviation from the mean, which is approximately 0.8413. Similarly, we can look up the cumulative probability associated with 0 standard deviations from the mean, which is 0.5.

To find the probability that 0 < X < 1, we subtract the probability associated with 0 from the probability associated with 1:

P(0 < X < 1) = P(X < 1) - P(X < 0) = 0.8413 - 0.5 = 0.3413

Therefore, the probability that 0 < X < 1 is approximately 0.3413, or 34.13%.

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Answer:

No

Step-by-step explanation:

Without any side lengths, the most three angles can determine is similarity, not congruency. This means you can determine the ratio of the lengths of the sides, but not any of the sides individually.

To find the probability of either event occurring, we can use the formula for the union of two events: P(A or B) = P(A) + P(B) - P(A and B).

Given that P(A) = 0.6, P(B) = 0.5, and P(A and B) = 0.25, we can substitute these values into the formula.

\(P(A or B) = P(A) + P(B) - P(A and B)\)
\(P(A or B) = 0.6 + 0.5 - 0.25\)
\(P(A or B) = 0.85 - 0.25\)
\(P(A or B) = 0.60\)
The probability of either event occurring is 0.60 or 60%.

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The probability of either event occurring can be found by adding the probabilities of the individual events and subtracting the probability of both events happening together. In this case, the probability of either event A or event B occurring is 0.6.

The probability of either event occurring can be calculated using the principle of addition. To find the probability of either event happening, we need to sum the individual probabilities of the events and subtract the probability of both events happening together.

Given:

p(a) = 0.6 (probability of event A occurring)
p(b) = 0.5 (probability of event B occurring)
p(a and b) = 0.25 (probability of both events happening together)

To calculate the probability of either event occurring, we can use the formula:

p(a or b) = p(a) + p(b) - p(a and b)

Substituting the given values into the formula:

p(a or b) = 0.6 + 0.5 - 0.25

p(a or b) = 0.85 - 0.25

p(a or b) = 0.6

Therefore, the probability of either event A or event B occurring is 0.6.

To understand this concept better, let's consider an example. Suppose event A represents rolling a fair six-sided die and getting an even number (2, 4, or 6). The probability of event A occurring would be 0.5. Now, let event B represent flipping a fair coin and getting heads. The probability of event B occurring would be 0.5.

If we want to find the probability of either rolling an even number or flipping heads, we can use the formula mentioned earlier. The probability of rolling an even number is 0.5, the probability of flipping heads is 0.5, and the probability of both happening together is 0.25. Plugging these values into the formula, we get:

p(A or B) = 0.5 + 0.5 - 0.25

              = 0.75

Therefore, the probability of either rolling an even number or flipping heads is 0.75.

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Answer:

hence rate of interest is 8% and time 8 years

Step-by-step explanation:

Step-by-step explanation:

Step 1:  Match the questions

1.  Dividing the same base → \(\frac{x^7}{x^3}\) is an example of this and to divide exponents (or powers) with the same base, subtract the exponents.  Therefore we match this with option E

2.  Negative exponent with a fraction base → \((3)^{-3}\) is an example of this and in other words, the negative exponent rule tells us that a number with a negative exponent should be put to the denominator, and vice versa.  Therefore we match this with option H

3.  Product to a Power → \((2x)^3\) is an example of this and what we do is basically distribute out the exponent to everything inside of the parenthesis.  Therefore we match this with option B

4.  Power of 0 → \((15)^0\) is an example of this and what we do is basically say that the exponent of a number shows how many times the number is multiplied by itself. The zero property of exponents is applied when the exponent of any base is 0.  Therefore we match this with option C

5.  Negative exponent → \((\frac{3}{10})^{-4}\) is an example of this and a negative exponent is defined as the multiplicative inverse of the base, raised to the power which is opposite to the given power. In simple words, we write the reciprocal of the number and then solve it like positive exponents.  Therefore we match this with option G

6.  Power to a Power → \((x^2)^2\) is an example of this and what we do is multiply the powers by each other by doing \((x^{2*2})\) which would give us \(x^4\).  Therefore we match this with option A

7.  Multiplying the same base → \(x^5*x^3\) is an example of this and according to the exponent rule for multiplication with the same base, we simply add the powers.  Therefore we match this with option D

8.  Quotient to a Power → \((\frac{a}{b})^x\) is an example of this and when you raise a quotient to a power you raise both the numerator and the denominator to the power.  Therefore we match this with option F

Answer:

Step-by-step explanation:

2x - 5 = 2

2x = 5 + 2

2x = 7

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

x = 3.5

Explanation:

The coefficients are -8 and 6, which are to the left of the variable expressions. The coefficients multiply to -48. Based on this alone, the answer is between choice C or choice D.

For the variables, we add the exponents. The x terms multiply to x^5*x^2 = x^(5+2) = x^7

The y terms multiply to y^2*y = y^2*y^1 = y^(2+1) = y^3

Putting everything together, we end up with -48x^7y^3

\( \huge \boxed{\mathfrak{Question} \downarrow}\)

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

\( \sf \: - 8 x ^ { 5 } y ^ { 2 } \cdot 6 x ^ { 2 } y\)

Use the rules of exponents to simplify the expression.

\( \sf\left(-8\right)^{1}x^{5}y^{2}\times 6^{1}x^{2}y^{1} \)

Use the Commutative Property of Multiplication.

\( \sf\left(-8\right)^{1}\times 6^{1}x^{5}x^{2}y^{2}y^{1} \)

To multiply powers of the same base, add their exponents.

\( \sf\left(-8\right)^{1}\times 6^{1}x^{5+2}y^{2+1} \)

Add the exponents 5 and 2.

\( \sf\left(-8\right)^{1}\times 6^{1}x^{7}y^{2+1} \)

Add the exponents 2 and 1.

\( \sf\left(-8\right)^{1}\times 6^{1}x^{7}y^{3} \)

Multiply -8 times 6 to get -48.

\( \boxed{ \boxed{\bf \: C) \: -48x^{7}y^{3} }}\)

i^93 = i^92 x i

i^92 =(i^2)^46

Now you have i(i^2)^46

i^2 = -1

Now you have i(-1)^46

-1^46 = 1

Now you have 1i which = i

The answer is i

Answer:

blah

Step-by-step explanation:

Answer:

86

Step-by-step explanation:

x=18

5x18=90

90-4-86

There are 68 integers with an odd number of positive integer divisors between 1000 and 9999, inclusive.

An integer is any number other than zero, positive numbers, or negative numbers. It is important to realise that an integer can never be a fraction, decimal, or percentage.

An integer has an odd number of positive integer divisors if and only if it is a perfect square. Therefore, we need to count the number of perfect squares between 1000 and 9999, inclusive.

The smallest perfect square greater than or equal to 1000 is 32² = 1024, and the largest perfect square less than or equal to 9999 is 99² = 9801.

So, the number of perfect squares between 1000 and 9999, inclusive, is:

floor(√(9999)) - ceil(√(1000)) + 1

= 99 - 32 + 1

= 68

Therefore, there are 68 integers between 1000 and 9999, inclusive, that have an odd number of positive integer divisors.

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Answer: the exact answer is 9/4, the mixed number is  2 1/4

Step-by-step explanation:

Answer:

The amount deposited into her retirement plan each payday is;

$469.05

Step-by-step explanation:

From the details given on Nancy's income, we have;

Nancy's gross annual income = $46,905

The percentage deducted from her monthly paycheck for her 403(b) = 9%

The percentage her employer matches her deductions up to = 3%

Therefore, we have;

Her monthly pay = (Her gross annual income)÷12

∴ Her monthly pay = $46,905÷12 = $3,908.75

The amount deducted from her paycheck, A = 9% of $3,908.75

∴ A = 9/100 × $3,908.75 = $351.7875

The amount her employer matches her deductions up to, B = 3% of $3,908.75

∴ B = 3/100 × $3,908.75 = $117.2625

Therefore;

The amount deposited into her retirement plan each payday, D = A + B

∴ D = $351.7875 + $117.2625 = $469.05

The amount deposited into her retirement plan each payday, D = $469.05.

The equations obtained from evaluation of the data in the table and the predicted cost of hiring the DJs are as follows;

Part B

The equation representing the cost of hiring Celinda is; c = 36·h + 16

The equation representing the cost of hiring Brian is; c = 38·h + 4

Part C

The cost of hiring Celinda for 5 hours is $196

Cost of hiring Brian for 5 hours is $194

A linear equation is an equation that has an highest index of 1.

Part B

The first difference in the cost of hiring each DJ is presented as follows;

Celinda; 160 - 124 = 124 - 88 = 88 - 52 = 36

Brian; 156 - 118 = 118 - 80 = 80 - 42 = 38

The first difference are constant, therefore, the relationship are linear, which can be represented by linear equations.

The difference between the subsequent values in the number of hours of 1 indicates that we get;

Slope of the equation for Celinda = 36

The equation representing the total cost for Celinda is therefore;

Where c represents the cost and h represents the number of hours, we get;

c - 52 = 36·(h - 1)

c = 36·h - 36 + 52

The equation for Brian, with a slope of 38, is therefore;

c - 42 = 38·(h - 1)

c = 38·h - 38 + 42 = 38·h + 4

Part C

The cost of hiring each DJ for 5 hours is therefore;

h = 5

The cost of hiring Celinda for 5 hours is; c = 36 × 5 + 16 = 196

The cost of hiring Celinda for 5 hours is $196

The cost of hiring Brian for 5 hours can be obtained by plugging in h = 5 in the equation; c = 38·h + 4

Therefore; c = 38 × 5 + 4 = 194

The cost of hiring Brian for 5 hours is $194

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A population of 600 organisms is expected to increase by 50.

We can use the equation I = k * n to determine whether the anticipated growth (I) of an organism population is directly related to the size of the current population (n).

Where k is a proportionality constant that connects the anticipated growth to the current population.

We can use the details provided in the problem to determine the value of k. We can write: 20 = k * 240 to represent an increase of 20 in a sample of 240 organisms.

We can calculate k as follows: k = 20 / 240 = 1 / 12.

Now that we know the value of k, we can use it to calculate the predicted growth for a population of 600:

I = (1 / 12) * 600 = 50

Therefore, a population of 600 organisms is expected to increase by 50.

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Answer:

one question.

Step-by-step explanation: