Nikita is a government official looking to find evidence on whether the mean taxable income for an individual taxpayer in the region dropped since the previous year. She surveyed 32 individual taxpayers in the region and found the taxable income of each individual as shown in the data set provided. Instead of using the standard deviation from the survey, Nikita decided to use the census data for the region to assume that the population standard deviation of income is $26,744. The mean taxable income in the region was $62,712 for the previous year.


(a) H0:μ=$62,712; Ha:μ<$62,712, which is a left-tailed test.


(b) Taxable income of each individual is given below.


Use Excel to test whether this year's mean taxable income for an individual taxpayer in the region is less than the mean taxable income from the previous year, and then draw a conclusion in the context of the problem, where α=0.10. Calculate the test statistic, z, rounding to two decimal places, and the p-value, rounding to three decimal places.


Taxable income ($)


Taxable income ($)

12193

64586

60363

59639

103402

24127

53641

38963

78596

49328

33983

64023

49771

89073

59433

21930

53789

30236

41639

87935

73396

69640

69371

104896

112354

96396

83921

72539

52186

91483

32069

17296

The probability that the last remaining house has three or four bedrooms, one or two bathrooms, one floor, and a grass yard is 1/9.

Let's break down the given options and criteria to determine the probability of finding a house that meets your requirements.

Number of Bedrooms: Two Bedrooms, Three Bedrooms, or Four Bedrooms

Number of Bathrooms: One Bathroom, Two Bathrooms, or Three Bathrooms

Number of Floors: One Floor or Two Floors

Type of Yard: Grass or Desert Landscaping

You are looking for a house with:

Either three or four bedrooms

Either one or two bathrooms

One floor

Grass yard

To calculate the probability, we need to determine the number of houses that meet your criteria and divide it by the total number of houses available.

Let's analyze each criterion:

Number of Bedrooms:

You are interested in houses with three or four bedrooms. There are three options for bedrooms. Since the number of houses with each combination is equal, the probability of a house having three or four bedrooms is 2/3.

Number of Bathrooms:

You are interested in houses with either one or two bathrooms. There are three options for bathrooms. Again, since the number of houses with each combination is equal, the probability of a house having one or two bathrooms is 2/3.

Number of Floors:

You are interested in houses with one floor. There are two options for floors. Since the number of houses with each combination is equal, the probability of a house having one floor is 1/2.

Type of Yard:

You are interested in houses with a grass yard. There are two options for the type of yard. Since the number of houses with each combination is equal, the probability of a house having a grass yard is 1/2.

Now, to find the overall probability of finding a house that meets all your criteria, we multiply the probabilities of each criterion together:

Probability = (2/3) * (2/3) * (1/2) * (1/2)

= 4/36

= 1/9

Therefore, the probability that the last remaining house has three or four bedrooms, one or two bathrooms, one floor, and a grass yard is 1/9.

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Answer:

-14fg Your Welcome  !!!

Step-by-step explanation:

Answer:

A ≈ 14.8 units²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) yz sin Y ( that is 2 sides and the angle between them )

where x is the side opposite ∠ X and z the side opposite ∠ Z

here y = XZ = 4.3 and z = XY = 7 , then

A = \(\frac{1}{2}\) × 4.3 × 7 × sin79°

   = 15.05 × sin79°

   ≈ 14.8 units² ( to 1 decimal place )

The quartic function with the given x-values as its only real zeros is f(x) = x⁴ + 3x³ - 5x² - 3x + 3.

To find a quartic function with the given x-values as its only real zeros, we can use the fact that zeros come in pairs for even-degree polynomials.

Since the zeros are x = -3 and x = 2, the factors of the quartic function will be (x + 3) and (x - 2).

To find the other two factors, we can use the fact that the degree of the quartic function is 4. We can choose any two factors of the form (x + a) and (x - a), where "a" is a constant.

Let's choose (x + 1) and (x - 1) as the other two factors.

Multiplying all four factors together, we get:

(x + 3)(x - 2)(x + 1)(x - 1)

Expanding this expression gives us the quartic function:

f(x) = (x² + 4x - 3)(x² - 1)

Simplifying further:

f(x) = x⁴ + 3x³ - 5x² - 3x + 3

So, the quartic function with the specified x-values as its sole real zeros.

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Answer:

3/2×=6 is x equals 4

×/2=-4 equals -8

-5×=26. equals -5.2

× over -7.2 =-4 equals 28.8

Answer:

2x+y=4

2times-1 is -2

2x+-2=4

2x=4

x=2

To solve the integral of 1/sqrt(x^2 - a^2) dx, we can use the substitution method. Let u = x^2 - a^2, then du/dx = 2x, and dx = du/2x.
Substituting into the integral, we get:

∫ 1/sqrt(x^2 - a^2) dx = ∫ 1/sqrt(u) * du/2x
= (1/2) ∫ 1/sqrt(u) du  

= (1/2) * 2sqrt(u) + C
= sqrt(x^2 - a^2) + C

Therefore, the answer to the integral of 1/sqrt(x^2 - a^2) dx is sqrt(x^2 - a^2) + C, where C is the constant of integration.

In summary, the integral of 1/sqrt(x^2 - a^2) dx can be solved using the substitution method, where u = x^2 - a^2. The final answer is sqrt(x^2 - a^2) + C, where C is the constant of integration.

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The integral of \(\frac{1}{\sqrt{x^2 - a^2}} dx\) is \(\ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\), where C is the constant of integration

What is intergration?

Integration is a fundamental concept in calculus that involves finding the antiderivative or integral of a function. It is the reverse process of differentiation, which is concerned with finding the derivative of a function.

To find the integral of \(1/\sqrt(x^2 - a^2) dx\), we can use a trigonometric substitution. Let's substitute \(x = a sec(\theta)\), where \(sec(\theta)\) is the reciprocal of the cosine function.

By making this substitution, we can express dx in terms of \(d(\theta)\) as follows:

\(dx = a sec(\theta) tan(\theta) d(\theta)\)

Now, let's substitute these values into the integral:

\(\int \frac{1}{\sqrt{x^2 - a^2}} dx\\\\= \int \frac{1}{\sqrt{(a \sec(theta))^2 - a^2}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{\sqrt{a^2(\sec^2(theta) - 1)}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{\sqrt{a^2(\tan^2(theta))}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{a \tan(theta)} (a \sec(\theta) \tan(\theta)) d(\theta)\)

Simplifying the expression, we have:

\(= \int \sec(\theta) d(\theta)\)

The integral of \(sec(\theta)\) can be evaluated as the natural logarithm of the absolute value of \(sec(\theta)\) plus the tangent\((\theta)\):

\(= \ln|\sec(\theta) + \tan(\theta)| + C\)

Finally, substituting back \(x = a sec(\theta)\), we get:

\(= \ln|\sec(\theta) + \tan(\theta)| + C\\\\= \ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\)

Therefore, the integral of \(\frac{1}{\sqrt{x^2 - a^2}} dx\) is \(\ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\), where C is the constant of integration

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Answer:

A

Step-by-step explanation:

the brigde means anything in between

Angles Formulas at the center of a circle can be expressed as:

Central angle, θ = (Arc length × 360º)/(2πr) degrees

Sum of Interior angles=180°(n-2)

The angles formulas are used to find the measures of the angles. An angle is formed by two intersecting rays, called the arms of the angle, sharing a common endpoint.

The corner point of the angle is known as the vertex of the angle. The angle is defined as the measure of the turn between the two lines.

There are various types of formulas for finding an angle; some of them are the central angle formula, double-angle formula, etc...

We use the central angle formula to determine the angle of a segment made in a circle.

We use the sum of the interior angles formula to determine the missing angle in a polygon.

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The annual maintenance collected in 2014 will be $1,750,000.

To calculate the annual maintenance collected in 2014, we need to find the number of customers who will renew their maintenance contract and the number of customers who will pay for maintenance as a percentage of product sales in 2013.

Number of customers renewing maintenance in 2014 = 80% of $2,000,000 = $1,600,000

Number of customers paying for maintenance in 2014 = 75% of $2,000,000 = $1,500,000

So, the total annual maintenance collected in 2014 will be:

$1,600,000 + $1,500,000*10% = $1,750,000

Therefore, the annual maintenance collected in 2014 will be $1,750,000.

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Step 1

Simplify the expression.

Step 2

Find a trigonometric identity that can be used to simplify the expression in step 1

Step 3

Get the final answer after substitution.

Hence the right answer is option B

Answer:

Han at 1/4x fruit snacks

Step-by-step explanation:

X-3/4x=1/4x

The indefinite integral of x√(x-9) dx is \((2/5)(x-9)^{(5/2)} + 2(x-9)^{(3/2)} + C\), where C is the constant of integration.

To find the indefinite integral of ∫x√(x-9) dx, we can use the substitution method.

Let u = x - 9, then du = dx.

Substituting these values into the integral, we have:

∫x√(x-9) dx = ∫(u + 9)√u du

Expanding the expression, we get:

∫(u√u + 9√u) du

Now we can integrate each term separately:

∫u√u du = ∫ \(u^{(3/2)}\) du = \((2/5)u^{(5/2)} + C1\)

∫9√u du = 9∫ \(u^{(1/2} du\) = \(9(2/3)u^{(3/2) }+ C2\)

Combining the results and substituting back u = x - 9, we have:

∫x√(x-9) dx = \((2/5)(x-9)^{(5/2)} + 9(2/3)(x-9)^{(3/2) }+ C\)

Simplifying further, we get:

∫x√(x-9) dx = \((2/5)(x-9)^{(5/2) }+ (6/3)(x-9)^{(3/2)} + C\)

                  = \((2/5)(x-9)^{(5/2)} + 2(x-9)^{(3/2)} + C\)

Therefore, the indefinite integral of x√(x-9) dx is\((2/5)(x-9)^{(5/2)} + 2(x-9)^{(3/2)} + C\), where C is the constant of integration.

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Answer:

x=15° and MNQ=32°

Step by step:

MNQ+QNP=90°

3x-13°+58=90°

so,3x+45°=90°

Then,3x=45° and x=15°

MNQ=3x-13°=3(15°)-13°

=45°-13°

=32°

Answer: x = 15 and MNQ = 32°

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

What is the value of x in

-x + 2 = -4

To answer, we must get x by itself.

-x + 2 = -4

Subtract 2 from both sides :

-x = -6

Divide both sides by -1 :

x = 6

Answer:

x=6

Step-by-step explanation:

- X+ 2 = -4

-2 -2

-x = -6

-----------------

-1

x = 6

Answer:

2:5

Step-by-step explanation:

WHichever one they ask you for first is the first number in the ratio. Meaning 2 solid figures are 2:1 plain figures.

The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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Answer:  10

Step-by-step explanation:

20% is 10% of 50 % because you /   100 in half and 20 in half and it's the same thing the answer is 10, my guy.

Answer:

Step-by-step explanation:

Regular price:$19

60 per cent of $19 is 11.4 dollars.

but if ypu are looking for how much did she pay then it is..

19-11.4=$7.6

Answer: C

since the line isn't straight, the slope/function is decreasing but not at a constant rate

Distance from the summit of Mount Everest to the horizon, Rounded to the nearest mile, the distance from the summit of Mount Everest to the horizon is 210 miles.

Distance refers to the space between two points or the length of a line between them. It may also refer to a range, extent, or magnitude that separates one point from another. Distance may be a physical concept, such as the distance between two cities or the distance traveled by a moving object.

The distance between two points can be calculated using a number of mathematical techniques, including the Pythagorean theorem, the distance formula, and vector addition.

d = √(2Rh + h²)

where d is the distance to the horizon, R is the radius of the Earth (4000 miles), and h is the height of the observer (in this case, the height of the summit of Mount Everest, which is 29,030 feet).

We need to convert the (h) height of the summit to miles:

29,030 ft = 29,030/5280 miles ≈ 5.49 miles

Now we can plug in the values and solve for d:

d = √(2 × 4000 × 5.49 + 5.49^2) =209.64288 ≈ 210 miles

Therefore, the distance from the summit of Mount Everest to the horizon is approximately 210 miles when rounded to the nearest mile.

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One of the factors is present in all of the items mentioned. The order of the value of the other factor will match the order of the value of the product.

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Answer:

------------------

Use circumference formula:

Find the radius by rearranging the formula and substituting 32 for C:

Answer:

5.09 in

Step-by-step explanation:

We know that the formula to find the circumference of a circle is:

C = 2πr

Here,

C → Circumference → 32 in

r → radius

Let us find the radius of the circle by substituting the given values.

\(\sf C = 2\pi r\\\\\sf 32 = 2\pi r\\\\Divide\:both\:sides\:by\:2 \pi \:and\:make\:r\:the \:subject\\\\\dfrac{32}{2 \pi} =\dfrac{2 \pi r}{2 \pi} \\\\\red{5.09 \:in=r}\)

Answer:

The sqrt(70) is irrational because there isn't a rational product of any 2 same rational numbers that equal 70.

Step-by-step explanation:

Answer:

10 x squared minus 4 y + 2 x squared minus y

Step-by-step explanation:

9x^2-2y+3x^2-3y

Collect like terms

9x^2+3x^2-2y-3y

=12x^2-5y

10 x squared minus 4 y + 2 x squared minus y

10x^2-4y+2x^2-y

Collect like terms

10x^2+2x^2-4y-y

=12x^2-5y

9x^2-2y+3x^2-3y is equivalent to

10x^2-4y+2x^2-y

Check all the options

6 x squared minus y + 6 x squared minus 5 y

6x^2-y+6x2-5y

12x^2-6y

6 x squared minus y + 3 x squared minus 4 y

6x^2-y+3x^2-4y

9x^2-5y

10 x squared minus 4 y + 2 x squared minus y

10x^2-4y+2x^2-y

12x^2-5y

11 x squared + 2 y + x squared minus 3 y

11x^2+2y+x^2-3y

12x^2-y

Answer:

C.) 12x squared- 2y- 3y

Step-by-step explanation:

i'm not 100 percent on this but it is the only logical answer, i will comment if i am right or not :) good luck luvs

Answer:

x^3+12-2x

Step-by-step explanation:

x^2.x=x^3

4.3=12

Sobra -2x

The evaluated value of the given expression, when converted to 150%, is approximately 39.8%.

To evaluate the given expression |9.78 - 9.806| / 9.806 × 100%,

we follow these steps:

Calculate the absolute difference between 9.78 and 9.806: |9.78 - 9.806| = 0.026

Divide the absolute difference by 9.806: 0.026 / 9.806 ≈ 0.0026509197

Multiply the result by 100% to express it as a percentage: 0.0026509197 × 100% ≈ 0.26509197%

Convert the result to 150% by multiplying it by 150 / 100: 0.26509197% × 150 = 39.7637964%

Round the final answer to one decimal place: 39.8%

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