Water works commission assume population standard deviation is 1.7 gallons. 15.8 gallons a day for sample of 249 families. Construct 80% confidence intervals

The solution for integrals are -1/3 (2 + cos² (x))[tex]^\frac{3}{2}[/tex]  +C

If we are finding the following integral below

∫ (√2 + (cos x)² / secx × cscx) dx instead of ∫ (√(2 + cos²x)) / (secx × csc) dx

then

secx = 1/cosx and cscx = 1/sinx

∫ (√(2 + cos²x)) × sinx × cosx dx

givn that sin²x + cos²x = 1

sin²x = 1 - cos²x

u = cosx,

du = -sinx dx.

-∫ (√u) / (2sinxcosx) du.

-√u + C.

When you substitute the original equation into the result

1/3 (2 + cos²x)^(3/2) + C.

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The number -0.02396 tell us about the slope of the pattern  and the value of y when x = 0 is 4.8153

Given that

y = -0.02396x + 4.8153

In the equation y = -0.02396x + 4.8153, we have

Slope = -0.02396

This means that the slope of the data is -0.02396

And as such it means that as the x values increase, the y values of the pattern decrease

We have

y = -0.02396x + 4.8153

Set x = 0

So, we have

y = -0.02396 * 0 + 4.8153

Evaluate

y =  4.8153

Hence, the value of y when x = 0 is 4.8153

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The missing sides of the right triangle were obtained below.

Pythagoras' theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

We have that;

1) x = √26^2 - 10^2

x = 24

2) x = √20^2 + 14 ^2

x = 24.4

3) x = √50^2 - 30^2

x = 40

4) x = √15^2 + 5^2

x = 15.8

5) x = √12^2 + 20^2

x = 23.3

These are the sides that are missing.

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Answer:

The answer to your problem is, D. The range is the best measure of variability, and it equals 32.

Step-by-step explanation:

We know the scores earned in a flower-growing competition are represented in the stem-and-leaf plot.

The key will equal 2|1 means 21

Which we conclude to 17, 19, 21, 25, 29, 30, 31, 32, 46, 49.

Quartile:

Median, Minimum, Maximum, & Range:

Thus the answer to your problem is, D. The range is the best measure of variability, and it equals 32.

The stem and leaf plot that correctly represents the data sets is

Stem    Leaf

0      |  0, 3        

1       |  7, 7, 7, 1, 7,

2      |  8, 8, 2, 4, 0. 0

3      |   3, 1,

Option B is the correct answer.

We have,

The following data set shows the values collected by the manager.

{17, 0, 28, 17, 17, 20, 28, 11, 17, 22, 24, 33, 20, 31, 20, 3}

Now,

We make the stem and leaf plot as:

Stem    Leaf

0      |  0, 3        

1       |  7, 7, 7, 1, 7,

2      |  8, 8, 2, 4, 0. 0

3      |   3, 1,

Here,

3 can be written as 03 and 0 can be written as 00.

Thus,

The stem and leaf plot that correctly represents the data sets is

Stem    Leaf

0      |  0, 3        

1       |  7, 7, 7, 1, 7,

2      |  8, 8, 2, 4, 0. 0

3      |   3, 1,

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A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

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This is correct. If M is a subset of N and N is a subset of P, then, M is a subset of P.

This follows from the transitivity of the subset relation. In set theory, the transitive property states that if a relation applies between elements A and B, and between elements B and C, then it also applies between elements A and C.

For the subset relation, if M is a subset of N (M ⊆ N), this means that every element in M is also an element of N. Similarly, if N is a subset of P (N ⊆ P), every element in N is also an element of P.

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If the helicopter flies 200 mph from the station nearest, the time it will it take to reach the ship is 0.52 hours

The numerical measurement between two entities or locations is defined as the distance, recorded in units such as kilometers, feet, meters, and miles. Determining the direct geometric line from point to point requires distinct models of calculation for both 2D and 3D geometry, most notably utilizing the Pythagorean theorem or the distance formula, respectively.

Physical sciences heavily rely on this notion, as it aids with computing rates that include: displacement, velocity, and acceleration. However, multiple factors - involving speed, direction, and time - can alter measured distances traveled by an object.

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The logarithm equations and corresponding x-value are

[tex]log_{2}x=5[/tex] has x=32

[tex]log_{10}x=3[/tex] then x=1000

[tex]log_{4}x=2[/tex] then x=16

[tex]log_{3}x=1[/tex] then x=1

We know that [tex]log_{a}x=b[/tex]

Then [tex]x=a^b[/tex]

(1) [tex]log_{2}x=5[/tex]

x=2⁵

=32

So [tex]log_{2}x=5[/tex] has x=32

(2) [tex]log_{10}x=3[/tex]

Then  by using the above property of logarithmic function we have:

x=10³

x=1000

So [tex]log_{10}x=3[/tex] then x=1000

(3) [tex]log_{4}x=2[/tex]

x=4²

x=16

so  [tex]log_{4}x=2[/tex] then x=16

(4) [tex]log_{3}x=1[/tex]

x=1³

=1

So  [tex]log_{3}x=1[/tex] then value  x=1

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The area of the rectangle is 81 square units. (option a)

To find the area of a rectangle, we need to know its length and width. We can determine these values by looking at the difference between the x-coordinates and the y-coordinates of the vertices.

In this case, we have the following coordinates: (-4,5), (5,5), (-4,-4), and (5,-4).

The length of the rectangle is the difference between the x-coordinates of the left and right vertices:

=> 5 - (-4) = 9.

The width is the difference between the y-coordinates of the top and bottom vertices:

=> 5 - (-4) = 9.

To find the area of the rectangle, we multiply its length by its width:

=> 9 x 9 = 81.

So, the correct answer is the (a), 81 square units.

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The surface area of the right square pyramid with the given base area and slant height would be = 221cm²

To calculate the surface area of the right square pyramid, the formula that should be used would be given below as follows. That is;

Surface area = a²+ 2al

where;

a² = area of base = 169cm²

a = side length of base = √169 = 13

l = slant height = 13 cm

S.A = 169+ 2(13×13)

= 169 + 52

= 221cm²

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The information from the histogram are as follow,

Students exercised for 4 or more hours are 14.

Students exercised for 9 or fewer hours are 13.

Mean of the data = 7.3.

median of the data = 6.33.

The histogram provides information about the distribution of hours students spent exercising in a week.

The number of students who exercised 4 hours or more,

= adding up the counts in the first and second bins.

= 9 + 5

= 14 students

The number of students who exercised 9 hours or fewer,

= adding up the counts in the first and second bins

= 9 + 4

= 13 students

The mean hours of exercise is not provided by the histogram

use the formula,

Mean = Σ[tex]x_{i} y_{i}[/tex] / N

where

[tex]x_{i}[/tex] is the midpoint of the ith bin

[tex]y_{i}[/tex] is the frequency of the ith bin

N is the total sample size

Mean = [(2)(4)  + (7)(9) + (12)(5)] / 18

          = 7.3

The median hours of exercise is not provided by the histogram.

Median = L + ( (n/2 – F) / f ) × w

where

L=The lower limit of the median group

n = The total number of observations

F = The cumulative frequency up to the median group

f =The frequency of the median group

w = The width of the median group

median = 5 + ( ( 14/2 - 4 ) /9 × 4

             = 6.33

Therefore, from the histogram the number of students exercised for ,

4 hours or more are 14.

9 hours or fewer are 13.

mean = 7.3

Median = 6.33

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The value of x from the given isosceles triangle is 5.6 units.

Given that, the measure of equal sides of an isosceles triangle is 6 units and the base measures 5.9 units.

Draw perpendicular bisector to base, so we get halves as 5.9/2 =2.95

Let the length of perpendicular bisector be x.

By using Pythagoras theorem, we get

6²=2.95²+x²

36=8.7025+x²

x²=36-8.7025

x²=27.2975

x=5.2 units

We know that, sinθ=Opposite/Hypotenuse

sin68°=5.2/x

x=5.6 units

Therefore, the value of x from the given isosceles triangle is 5.6 units.

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The exponential function representing the lifting time on day n is given as follows:

a(n) = 2^(n - 1).

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

On the first day, the time is of one minute, while the amount doubles each day, hence the parameters a and b are given as follows:

a = 1, b = 2.

We take the day one at the reference day, not day zero, meaning that the function was shifted right one unit, hence the rule is given as follows:

a(n) = 2^(n - 1).

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The coordinates of the vertices for the image of the triangle are A(−3, 6), B(0, 10), and C(−3, 3)

From the question, we have the following parameters that can be used in our computation:

Triangle ABC has vertices at A(−3, 3), B(0, 7), and C(−3, 0)

If the preimage is translated 3 units up, then the transformation rule is

(x, y) = (x, y + 3)

Substitute the known values in the above equation, so, we have the following representation

A(−3, 3 + 3), B(0, 7 + 3), and C(−3, 0 + 3)

Evaluate

A(−3, 6), B(0, 10), and C(−3, 3)

Hence, the coordinates of the vertices for the image are A(−3, 6), B(0, 10), and C(−3, 3)

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The quadratic equation has only one solution if m = 14

For a quadratic equation:

ax² + bx + c = 0

The discriminant is:

D = b² - 4ac

If the discriminant is zero, then the quadratic has only one solution, here we have the equation:

2x² - 28x + 7m = 0

Then the discriminant is:

D = (-28)^2 - 4*2*7m

Now we need to solve:

(-28)^2 - 4*2*7m = 0

784 - 56m = 0

Solving that for m:

784/56 = m

14 = m

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Answer: (6,11π/6).

Step-by-step explanation:We need to find the radius r and the angle θ. Remember that r2=x2+y2, so

because of the signs of x and y, our angle is in quadrant IV. Therefore, we find that θ=11π/6.

So the final answer is (6,11π6).

The difference in volumes for the two cylinders is given as follows:

A. 61π mm³.

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

For Cylinder 1, the parameters are given as follows:

r = 0.5 x 8 = 4 mm, h = 10 mm.

Hence the volume is given as follows:

V = π x 4² x 10

V = 160π mm³.

For Cylinder 2, the parameters are given as follows:

r = 0.5 x 6 = 3 mm, h = 11 mm.

Hence the volume is given as follows:

V = π x 9² x 11

V = 99π mm³.

Hence the difference is given as follows:

160π mm³ - 99π mm³ = 61π mm³.

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In the context of this problem all the solutions to the polynomial equation is correct because they all make sense.

The given polynomial equation  can be expressed as ;

x³ + 6x² - 40x = 192 and the given solutions can be written as ; x = -8, x = -4, and x = 6

We can test if the solution is the best for the given euation because this will help us to know if these valueas are the solution for the equation

x = -8

[(-8)³ + 6(-8)² - 40(-8)]

= 192

[-512 + 384 + 320]

= 192

x = -4,

[(-4)³ + 6(-4)² - 40(-4)]

[-64 + 96 + 160 ]

= 192

x = 6

[(6)³ + 6(6)² - 40(6) ]

216 + 216 - 240

= 192

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Answer:

Step-by-step explanation:

A,B

x = –8

x = –4

Answer:

The amount of air needed to fill the basketball is approximately 533.16 cubic inches

Step-by-step explanation:

To find the amount of air needed to fill a basketball, we need to first calculate its volume. We can use the formula for the volume of a sphere, which is V = (4/3)πr^3, where π is approximately 3.14 and r is the radius of the sphere.

Since the diameter of the basketball is given, we need to first find the radius by dividing the diameter by 2:

r = 9.45 in / 2 = 4.725 in

Now we can plug in the value of r into the formula for the volume:

V = (4/3)πr^3 = (4/3)π(4.725 in)^3 = 533.16 in^3

Therefore, the amount of air needed to fill the basketball is approximately 533.16 approx cubic inches.

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Yes, this collection is a set because it has a well-defined and finite number of elements, namely {2, 3, 5, 7}.

(ii) The method of describing this collection is the roster method or tabular method, where the elements of the set are listed within curly braces and separated by commas.

(iii) {2, 3, 5, 7}

In mathematics, a set is a collection of conspicuous objects or elements, taken as an object in its own right. These elements can either be numbers, letters, symbols, or even other sets. A set is defined by listing its elements or by specifying a property that its elements satisfy.

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Answer:

Option 2 is correct. The function is increasing on the set of all positive real numbers.

It will take approximately 8.6 years for the population to reach 1500.

We have,

We are given that the population is growing exponentially according to the model, P(t) = 500^(0.25t),

where t is measured in years.

We need to find the value of t when the population reaches 1500.

So we can set P(t) = 1500 and solve for t:

1500 = 500^(0.25t)

Taking the natural logarithm of both sides:

ln(1500) = ln(500^(0.25t))

Using the logarithmic identity, ln(a^b) = b ln(a):

ln(1500) = 0.25t ln(500)

Solving for t:

t = ln(1500) / (0.25 ln(500))

Using a calculator, we get:

t ≈ 8.6 years

Therefore,

It will take approximately 8.6 years for the population to reach 1500.

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Answer: The best estimate of the sum of the heights of the 5 mountains is between 130,000 and 135,000 ft. Therefore, option D is correct,

Step-by-step explanation: The best estimate of the sum of the heights of the five mountains listed is between 130,000 and 135,000 ft. These heights are already very high, so options A and B can be eliminated. Option C is too low, leaving option D as the best estimate.

Dhaulagiri: 26,810 ft

Nanga Parbat: 26,660 ft

Annapuma: 26,504 ft

Gasherbrum: 26,470 ft

Xixabangma: 26,286 ft

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The equations that are true for x = -2 and x = 2 are x² + 4 = 0 and 4x² = 16. So, the correct option is A) and D).

To determine which equations are true for x = -2 and x = 2, we simply substitute these values into each equation and check if the equation is true or not. Here are the results

x² - 4 = 0

Substituting x = -2 gives (-2)² - 4 = 0, which is true. Substituting x = 2 gives 2² - 4 = 0, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

x² = -4

Substituting x = -2 gives (-2)² = -4, which is not true. Substituting x = 2 gives 2² = -4, which is also not true. Therefore, this equation is not true for either x = -2 or x = 2.

3x² + 12 = 0

Substituting x = -2 gives 3(-2)² + 12 = 0, which is true. Substituting x = 2 gives 3(2)² + 12 = 24, which is not equal to zero. Therefore, this equation is true for x = -2 but not for x = 2.

4x² = 16

Substituting x = -2 gives 4(-2)² = 16, which is true. Substituting x = 2 gives 4(2)² = 16, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

2(x - 2)² = 0

Substituting x = -2 gives 2(-2 - 2)² = 0, which is true. Substituting x = 2 gives 2(2 - 2)² = 0, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

Therefore, the two equations that are true for both x = -2 and x = 2 are x² - 4 = 0 and 4x² = 16. So, the correct answer is A) and D).

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The pitch of the roof is equal to 1.14

Since pitch of the roof is the angle between the roof and the horizontal line.

Pitch (slope) = V/H

Where, V represents the rising vertical distance of an object.

H represents the horizontal distance an object runs through.

Substituting the selected points into the formula, we have;

Pitch (slope) = 32/28

Pitch (slope) = 1.14

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Answer:

5 + 1/x = 11/5

Podemos simplificar esta ecuación multiplicando ambos lados por 5x, lo que da:

25x + 5 = 11x

Ahora, podemos resolver x aislando la variable en un lado de la ecuación:

25x - 11x = -5

14x = -5

x = -5/14

Por lo tanto, la solución a la ecuación es x = -5/14

The mean of the data set is 3.33.

The variance of the data set is 0.47.

We have,

To find the mean of the data set,

We need to add up all the numbers and divide by the total number of values:

Mean = (2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 4) / 9

= 3.33 (rounded to two decimal places)

To find the variance,

We need to first find the squared difference between each value and the mean:

(2 - 3.33)^2 = 1.11

(2 - 3.33)^2 = 1.11

(3 - 3.33)^2 = 0.11

(3 - 3.33)^2 = 0.11

(3 - 3.33)^2 = 0.11

(4 - 3.33)^2 = 0.44

(4 - 3.33)^2 = 0.44

(4 - 3.33)^2 = 0.44

(4 - 3.33)^2 = 0.44

Next, we need to find the average of these squared differences:

Average of squared differences

= (1.11 + 1.11 + 0.11 + 0.11 + 0.11 + 0.44 + 0.44 + 0.44 + 0.44) / 9

= 0.47 (rounded to two decimal places)

Thus,

The mean of the data set is 3.33.

The variance of the data set is 0.47.

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