Which inequality is a true statement?
Select each correct answer.


−3<−1

−3≤−1

−3>−1

−3≥−1

−3=−1

(please answer correctly)

Given that a population proportion represents the proportion of successes within a population and that there must be two outcomes (categories), success and failure, a confidence interval about a population proportion only makes sense for qualitative variables.

A confidence interval (CI) is a range of estimates for an unknown parameter in frequentist statistics.

The 95% confidence level is the most popular, however other levels, such 90% or 99%, are occasionally used when computing confidence intervals.

The percentage of related CIs over the long run that include the parameter's actual value is represented by the confidence level. For instance, 95% of all intervals calculated at the 95% confidence level should include the parameter's actual value.

The sample size, sample variability, and confidence level are all variables that have an impact on the CI's width

Assuming all other factors remained constant, a larger sample would result in a narrower confidence range. Additionally, more sample variability results in a wider range of.

Hence,  a population proportion represents the proportion of successes within a population and that there must be two outcomes (categories), success and failure, a confidence interval about a population proportion only makes sense for qualitative variables.

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Wyatt can husk anywhere from 12 to  18 dozen ears of corn per hour.

To find the possible amount we need to calculate the maximum and minimum time period in hours

Thus, if we need to find the time taken to husk 72 dozen ears of corn, the maximum time would be  ,

=72 / 12 hours

​ =6 hours

And the minimum time would be  used for the does wyatt takes to husk the 72 dozen of corn

=72/18 hours

​=4 hours

Thus, depending on his speed, Wyatt takes anywhere from  4  to 6 hours to husk  72 dozen ears of corn.

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Answer:

  sum = 65

Step-by-step explanation:

You want the sum of the set of 5 consecutive positive integers such that the sum of the even integers in the set is 26.

The sum of even integers will be a multiple of 3 if the middle integer of the set is even. Here, that sum is 26, not a multiple of 3. Hence the middle integer of the set is 26/2 = 13, and the sum of the set is 13·5 = 65.

The sum of the five integers is 65.

__

Additional comment

When working "consecutive integer" problems, it is often useful to think in terms of the average of the integers, the middle one of an odd-length set, or the number halfway between the two middle ones of an even-length set.

A set of 5 integers will have either 3 odds and 2 evens, or 3 evens and 2 odds. The set here obviously does not have 3 even integers (whose sum would be 3 times the middle one).

The set is s = {11, 12, 13, 14, 15}. 10 is not in the set, but 11 is. The sum of evens is 12+14=26.

The required distance between the points  (−1, −4) and (−9, −8). is the square root of 80 units. Option D is correct.

Given that,

The distance between points (−1, −4) and (−9, −8) is to be determined.

Distance is defined as the object traveling at a particular speed in time from one point to another.

here,
D = √[[x₂ - x₁]² + [y₂+ - y₁]²]

Substitute the value in the above equation,
D = √[[-9 + 1]² + [-8 + 4]²]
D = √[[-8]² + [ 4]²]
D = √[64 + 16]
D = √80

Thus, the required distance between the points  (−1, −4) and (−9, −8). is the square root of 80 units. Option D is correct.

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Answer:

the person above is correct, the answer is D "[tex]\sqrt{80[/tex] units"

Step-by-step explanation:

I took this exam and got this answer right, hope this helps :))

The values that represent the solution to [tex]cos (\frac{\pi }{4} - x) = \frac{\sqrt{2} }{2} sin x[/tex] ,

x ∈ [0, 2·π) are:

              [tex]x = (\frac{\pi }{2} , \frac{3\pi }{2} )[/tex]

Sine and Cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle θ the sine and cosine functions are denoted simply as sinθ and cos θ.

Once such a triangle is chosen, the sine of the angle is equal to the length of the opposite side, divided by the length of the hypotenuse:

Sin (α) = [tex]\frac{opposite}{Hypotenuse}[/tex]  and  Cos (α) = [tex]\frac{Adjacent}{Hypotenues}[/tex]

Given in the question:

The given function is presented as follows;

[tex]cos (\frac{\pi }{4} - x) = \frac{\sqrt{2} }{2} sin x[/tex]

Where;

x ∈ [0, 2·π)

We have;

cos(A - B) = cos(A)·cos(B) - sin(A)·sin(B)

[tex]cos (\frac{\pi }{4} ) = \frac{\sqrt{2} }{2} , sin( \frac{\pi }{4)} =\frac{\sqrt{2} }{2}[/tex]

Which gives

[tex]cos(\frac{\pi }{4} - x ) = \frac{\sqrt{2} }{2} cos x +\frac{\sqrt{2} }{2} sinx[/tex]

Therefore, we get;

[tex]\frac{\sqrt{2} }{2} cos x = \frac{\sqrt{2} }{2} sinx - \frac{\sqrt{2} }{2} = 0[/tex]

cos x = 0

[tex]cos (\frac{\pi }{2} ) =0[/tex]

Therefore;

The possible solutions (x-values) to cos x = 0 are;

                             [tex]0\leq \frac{n.\pi }{2} \leq 2\pi[/tex]

Where;

n = 1, 3, 5, ...

x ∈ [0, 2·π)

We get;   [tex]x = \frac{\pi }{2} or \frac{3\pi }{2}[/tex]

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Answer:

Step-by-step explanation:

1 1.5/2

The number of fish in year 6 will be;

⇒ y = 438.60

What is an expression?

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

Given that;

The exponential regression equation is,

⇒ y = 14.08 × 2.08ˣ

Where, x is represent the year.

Now,

Since, The exponential regression equation is,

⇒ y = 14.08 × 2.08ˣ

Where, x is represent the year.

Hence, The number of fish in year 6 will be;

⇒ y = 14.08 × 2.08ˣ

⇒ y = 14.08 × 2.08⁶

⇒ y = 14.08 × 31.15

⇒ y = 438.60

Thus, The number of fish in year 6 will be;

⇒ y = 438.60

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Answer:

The answer might be C.(x=0)

Step-by-step explanation:

hope this helps!

Answer:

8 pounds of oranges for $12.

Step-by-step explanation:

Answer:

[tex]\boxed{\tt v < 6.8}[/tex]

Step-by-step explanation:

[tex]\tt 0.5v+0.06 < 3.46[/tex]

Multiply both sides by 100:-

[tex]\tt 0.5v\times\:100+0.06\times\:100 < 3.46\times\:100[/tex]

[tex]\tt 50v+6 < 346[/tex]

Subtract 6 from both sides:-

[tex]\tt 50v < 340[/tex]

Divide both sides by 50:-

[tex]\tt \cfrac{50v}{50} < \cfrac{340}{50}[/tex]

[tex]\tt v < \cfrac{34}{5}[/tex]

Or

[tex]\tt v < 6.8[/tex]

Therefore, your answer is v < 6.8!!! :)

______________________

Hope this helps!

Have a great day!

There is not evidence that the population mean waiting time is different from 3.6 ​minutes.

What is the p-value?

A statistical measurement known as a p-value is employed to check a hypothesis' validity against actual data. A p-value calculates the likelihood of getting the outcomes that were observed, presuming that the null hypothesis is correct. The statistical significance of the difference that was found increases with decreasing p-value.

From the question, we know that the size (n), the mean (x), and the standard deviation (s) of the sample are 81, 3.45 minutes and 0.9 minutes. Additionally, we are going to decide if the waiting time is different or not from 3.6 minutes, so the null and alternative hypotheses are:

H0: m=3.6

H1:  m≠3.6

Where m is the mean of the population.

Then, we don't need to be concerned about the shape of the population distribution because the value of the n is bigger than 30 and we can use the statistic z as:

[tex]z = \frac{x-m}{\frac{a}{\sqrt{n} } }[/tex]

So, replacing the values, the test statistic is:

[tex]z = \frac{3.45 - 3.6}{\frac{0.9}{\sqrt{81} } }[/tex]

= 2.50

On the other hand, the p-value for this test is calculated as:

p-value = 2P(z >2.50) = 2(0.0668) = 0.134

Taking into account that the p-value is bigger than the level of significance 0.01, the null hypothesis is not rejected, and there is not evidence that the population mean waiting time is different from 3.6 ​minutes.

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Answer:

1. 150mi

2. 2&1/2

3. He needs to know how many miles is each city.

Step-by-step explanation:

Answer: The selling price was at first $776 but then the store advertised a 30% markdown on the system. Find the current sale price.

Step-by-step explanation:

$776 - (30% of $776) = $ x :: current sale price

776 - 776 * 0.3 = x

776 * (1 - 0.3) = x

776 * 0.7 = 543.20

Current sale price for the computer system is $543.20.

Answer: 0.69

Step-by-step explanation:

0.44 + 0.25 = 0.69

The correct answer is [tex]\boxed{0.69}[/tex]

For this question we will be adding the numbers given.

Given:

[tex]0.44\\0.25[/tex]

Therefore, the equation is:

[tex]\boxed{0.44 +0.25}[/tex]

Therefore, the correct answer is [tex]\boxed{0.69}[/tex]

Round to the closest whole percent, 23% of the participants in the event are under the age of 20.

For the stated question-

Total number of people = 30 + 50 + 40 + 10

Total number of people = 130

Number of participants are under the age of 20 = 30.

Let 'x' be the % of the participants are under the age of 20.

Thus,

x% of 130 = 30

x = 30 x 100 / 130

x = 23.07

x = 23%

Thus, round to the closest whole percent, 23% of the participants in the event are under age of 20.

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Mathematically, three dwarf hamsters can live in the cage Harriet purchased.

The number of dwarf hamsters that can live in Harriet's cage is determined using mathematical operations, including multiplication and division.

Mathematical operations involve the manipulation of numbers, variables, and mathematical operands to determine mathematical results.

The result of an addition is known as the sum while for a subtraction operation is the difference.

The result of a multiplication operation is known as the product like a dvision operation (also called the quotient).

The height of the cage = 12 inches or 1 foot

The length of the cage = 2¹/₃  feet

The area of the cage = 2¹/₃ ft² (1 x 2¹/₃)

The living space required by each dwarf hamster = ²/₃ ft²

The number of dwarf hamsters that can live in the cage = 3.499 (2¹/₃ ÷ ²/₃).

= 3

Thus, using mathematical operations, we can determine that the highest number of dwarf hamsters that can live in Harriet's cage is three.

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(767.47, 777.13) is the confidence interval in the given situation.

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics.

The 95% confidence level is the most popular, but other levels, like 90% or 99%, are occasionally used when computing confidence intervals.

[tex]\begin{aligned}&\mathrm{CI}=(772.3-4.83,772.3+4.83) \\&\mathrm{CI}=(767.47,777.13)\end{aligned}[/tex]

Therefore, (767.47, 777.13) is the confidence interval in the given situation.

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Answer:

Step-by-step explanation:

You need to set the problem up like this:

         back in for all the 'x's

        should be 20

Consider a sequence of random variables X1, X2, X3, ⋯ that is defined on an underlying sample space S. For simplicity, let us assume that S is a finite set, so we can write

                                    S = {s₁, s₂,⋯,sₙ }.

Remember that each Xₙ is a function from S to the set of real numbers. Thus, we may write

                       Xₙ (sₐ) = xₙₐ,           for a=1,2,⋯,k.

After this random experiment is performed, one of the sₐ' s will be the outcome of the experiment, and the values of the Xₙ's are known. If sₐ is the outcome of the experiment, we observe the following sequence:

x₁ₐ ,x₂ₐ,x₃ₐ,⋯.

Let [Xₙ] be a sequence of square integral random variables defined on a sample space Omega. We say that [Xₙ] is mean-square convergent (or convergent in mean-square) if and only if there exists a square integral random variable X such that

                                   [tex]\lim_{n \to \infty} E[ X_{n} - X^{2} ][/tex]

Convergence in distribution is in some sense the weakest type of convergence. All it says is that the CDF of Xₙ's converges to the CDF of X as n goes to infinity. It does not require any dependence between the Xₙ's and X. We saw this type of convergence before when we discussed the central limit theorem. To say that Xₙ converges in distribution to X, we write:

                                       Xₙ →d X.

Convergence in probability is stronger than convergence in distribution. In particular, for a sequence X₁, X₂, X₃, ⋯ to converge to a random variable X, we must have that P(|Xₙ−X|≥ϵ) goes to 0 as n→∞, for any ϵ>0. To say that Xₙ converges in probability to X, we write:

                                                Xₙ →p X.

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Equation 1 needs to be multiplied with + 2

Equation 2 needs to be multiplied with  + 5.

Step-by-step explanation:

Here, the given system of equation is given as:

Equation 1 : 6 x − 5 y = -4

Equation 2: 4 x + 2 y = 28

Here, in equation 1, the coefficient of y  = - 5

Also, in the equation 2, the coefficient of  y = + 2

Now, in order to eliminate the y coefficients,

Coefficient  of y in  1  =   -  Coefficient of y in  2

Now, to make -5 and  + 2 to eliminate each other,

Multiply -5 with 2, we get            -5 x 2  = -10

And Multiply the coefficient + 2 with 5, we get   +2 x 5  = + 10

The new coefficient of y is equation 1 = - 10 y

The new coefficient of y in equation 2  = + 10 y

They will cancel out each other, when both equations are ADDED.

Hence, equation 1 needs to be multiplied with + 2

and the equation 2 needs to be multiplied with  + 5.

The amount which the agency makes on the house as described is; $26,100.

The amount earned in commission by the agent is; $6,525.

It follows from the task content that the house in discuss was sold for $348,000.

Also, since the commission rate for the real estate agency is; 7.5%.

It therefore follows that the commission earned by the real estate agency is;

7.5% of 348,000 = 0.075 × 348,000

= $26,100.

Also, since the commission rate for the agent is 25% of the agency's commission.

Therefore, the amount earned by the agent is;

25% of 26,100 = 0.25 × 26,100

= $6,525.

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Step-by-step explanation:

easiest example : multiply both (it is important to do it to both) by 2 :

2×2 = 4 cups of yellow

3.5×2 = 7 cups of blue

will make the same shade of green, as the mixing ratio is the same.

just, instead of 5.5 cups, it gives us 11 cups of green paint (surprise, surprise, this is also twice as much) .

The new width is 4 inches.

Since Jessica reduced one side (the length), that means that she also reduced the other side (the width) by the same number:

Original length:

4

New length:

2

4 ÷ 2 = 2

Original Width:

8

New Width:

4

8 ÷ 2 = 4

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer:

2/12 = 1/6

24 * 1/6 = 4

or

12/24 = 2/x

12 x = 48

x = 4

or the original width was twice the length

twice 2 is 4

maybe

the standard deviation of the sample means:

σ(x) = σ/[tex]\sqrt{n}[/tex]

The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement text annotation indicator, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large (usually n > 30). If the population is normal, then the theorem holds true even for samples smaller than 30. In fact, this also holds true even if the population is binomial, provided that min(np, n(1-p))> 5, where n is the sample size and p is the probability of success in the population. This means that we can use the normal probability model to quantify uncertainty when making inferences about a population mean based on the sample mean.

For the random samples we take from the population, we can compute the mean of the sample means:

μ (x) = μ

and the standard deviation of the sample means:

σ(x) = σ/[tex]\sqrt{n}[/tex]

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The standard deviation of the sampling distribution of the average (sample mean) score for the 36 students = 1

What is standard deviation?

The standard deviation of the sampling distribution of mean is given by :- σₓ = σ/√n, where  = population standard deviation and n= sample size.

According to the given question:

The scores of individual students on the American college testing program composite college entrance examination have a normal distribution with mean 18.0 and standard deviation 6.0. at kent roosevelt high.

i.e. μ = 18.0, σ = 6.0

Sample size : n= 36

Then, the standard deviation of the sampling distribution of the average (sample mean) score for the 36 students will be :-

σₓ = 6/√36 = 1

Hence, The standard deviation of the sampling distribution of the average (sample mean) score for the 36 students = 1

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The correct unit prices are,

1. 20 for $1.56 = A. 7.8 cents each

2. $3.78 for 6 = B. 63 cents each

3. 2 1/2 for one dollar = C. 40 cents each

4. 5 at $3.90 = D. 78 cents each

5. 1 1/2 for $1.58 = E. $1.05 each

From the given cases;

1. Given that 20 things cost $1.56,

So, the price of one item is = $1.56/20

                                             = $0.078.

Cents for every dollar,

So, $0.078 equals $0.078 * 100

                              = 7.8 cents.

2. Since the cost of six products is $3.78, 

The cost of one item is 3.78/6

                                    =  $0.63.

Cents for every dollar,

Thus, $0.63 equals $0.63 * 100

                               = 63 cents.

3. 2 1/2 = 5/2 = 1 as a price

So, the price of one item is equal to 2/5 of a dollar, or 100 cents.

$2/5 equals 2/5 * 100, or 40 cents.

4. Given that the price of 5 things is $3.90

The price of 1 item is 3.90/5, or $0.78.

Cents for every dollar

So, $0.78 = $0.78 * 100 = 78 cents.

5. Cost of 1 1/2 = 3/2 = $1.58

So, cost of 1 item =  1.58/(3/2)

                            = 1.05

Hence, these are the solutions for the given cases.

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The remainder will be less than k, when the positive integer n is divided by the positive integer k, where k > 1.

Positive, negative, and zero are all examples of integers. The Latin word "integer" signifies "whole" or "intact." As a result, fractions and decimals are not included in integers. In this essay, we will learn more about integers, their definition, and their characteristics.

All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043. Z is a set of integers.

Hence, The remainder will be less than k, when the positive integer n is divided by the positive integer k, where k > 1.

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