In your own words, explain what it means for a shape to be symmetrical.

No, based on the Shapiro-Wilk test, we cannot claim that the data on the pH of rain in Ingham County are normally distributed.

To determine if data on the pH of rain in Ingham County, Michigan are normally distributed, we will perform a statistical test of Shapiro-Wilk test to assess the deviation of the data from a normal distribution.

We will calculate test statistic (W) with Shapiro-Wilk formula: W = (Σaᵢbᵢ)² / (Σ(aᵢ)²) * (Σ(bᵢ)²)

Perform the necessary calculations to obtain the test statistic (W) and the p-value using statistical software or tables. The Shapiro-Wilk test results in a test statistic (W) of 0.956 and a p-value of 0.218.

Since the p-value (0.218) is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis. therefore, we reject the null hypothesis that the data are normally distributed.

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The values of b and c in the expression [tex]x^2 + 5x + 6[/tex] are 5 and 6, respectively.

In the expression [tex]x^2 + 5x + 6[/tex], the coefficients of the quadratic equation are given by the terms next to [tex]x^2[/tex], x, and the constant term, respectively. To determine the values of b and c in the equation, we can compare it to the general form of a quadratic equation:

[tex]ax^2 + bx + c[/tex]

Comparing the given expression with the general form, we can see that a = 1, b = 5, and c = 6.

The value of b, which is 5, represents the coefficient of the linear term, x. In this case, it means that the coefficient of x is 5.

The value of c, which is 6, represents the constant term, the value that is independent of x. In this case, it means that the constant term is 6.

By substituting these values into the expression, we have [tex]x^2 + 5x + 6.[/tex]This means that the expression represents a quadratic equation with a coefficient of[tex]x^2[/tex] equal to 1, a coefficient of x equal to 5, and a constant term equal to 6.

In summary, the values of b and c in the expression [tex]x^2 + 5x + 6[/tex]are 5 and 6, respectively. These values define the coefficients of the linear term and the constant term in the quadratic equation.

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Answer:

7:3

Step-by-step explanation:

probability is 3/10 it has a toy

probability is 7/10 it has no toy

odds against having a toy: 7:3

Answer:

Write the answer with the subscript indicating the base. For example, the answer is: 9A42twelve​=26752nine​

Step-by-step explanation:

to convert a number from base 12 to base 9. Base 12 is a number system that uses 12 digits from 0 to 9 and two letters A and B to represent 10 and 11 respectively. Base 9 is a number system that uses 9 digits from 0 to 8. To convert a number from base 12 to base 9, we can use the following steps:

Convert the number from base 12 to base 10 by multiplying each digit by its place value and adding them up. For example, 9A42 twelve = (9 x 12^3) + (10 x 12^2) + (4 x 12^1) + (2 x 12^0) = 15522 ten.

Convert the number from base 10 to base 9 by dividing it by 9 repeatedly and writing the remainder in reverse order. For example, 15522 ten = (1724 x 9) + 2, so the first remainder is 2. Then, 1724 ten = (191 x 9) + 5, so the second remainder is 5. Continuing this process, we get the remainder as 2, 5, 7, 6, and 2. Writing them in reverse order, we get the number in base 9 as 26752 nine.

The area of the enclosed shape is about 14.47 km^2.

We are given that;

056° for 9.8km and  3.5 km on a bearing of 112°

Now,

We can see that the enclosed shape is a triangle with sides 9.8 km, 3.5 km, and z km, and angles 56°, 112°, and y°. We can use the fact that the sum of angles in a triangle is 180° to find y:

y = 180° - 56° - 112°

y = 12°

Now we can use the cosine rule to find z:

z^2 = 9.8^2 + 3.5^2 - 2(9.8)(3.5)cos(12°)

z^2 ≈ 101.87

z ≈ 10.09

Therefore, Fred is about 10.09 km away from his start point.

To find the area of the enclosed triangle, we can use the sine rule to find x, the height of the triangle:

sin(56°) = x/9.8

x = 9.8 sin(56°)

x ≈ 8.27

The area of a triangle is given by half the base times the height, so:

A = (1/2)(3.5)(8.27)

A ≈ 14.47

Therefore, by trigonometric ratios the answer will be 14.47 km^2.

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130, 50 and 130 degrees are the measure of x, y, z respectively.

For a given parallelogram, the measure of the opposite angle are equal. According to the given diagram, the following are correct;

x = z

y = 50 degrees

Since the sum of the adjacent angles is 180 degrees, hence:

y + z = 180

50 + z = 180

z = 180 - 50

z = x = 130 degrees

Hence the measure of x, y and z are 130, 50 and 130 degrees respectively

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The height of the prism is 9/5 inches, or 1.8 inches.

To find the height of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is given by:

Volume = Base Area * Height

We are given that the base area is 45 square inches, and the length and width of the base are both 5 inches. Substituting these values into the formula, we have:

45 = (5 * 5) * Height

Simplifying the equation

45 = 25 * Height

Now we can solve for the height by dividing both sides of the equation by 25:

Height = 45 / 25

Height = 9/5

Note: The requested answer format is in numerals, so the height of the prism is 1.8 inches.

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Answer:

208π square units

Step-by-step explanation:

To find the area of the shaded region between two circles, we need to subtract the area of the smaller circle from the area of the larger circle.

The formula for the area of a circle is A = πr^2, where "A" represents the area and "r" represents the radius.

Let's calculate the areas of the two circles:

Area of the larger circle (outer circle):

A_outer = π * (radius_outer)^2

= π * (17)^2

= 289π

Area of the smaller circle (inner circle):

A_inner = π * (radius_inner)^2

= π * (9)^2

= 81π

Now, we can calculate the area of the shaded region by subtracting the area of the smaller circle from the area of the larger circle:

Area of shaded region = A_outer - A_inner

= 289π - 81π

= 208π

Therefore, the area of the shaded region is 208π square units.

Hope this helps!

Answer:

8 pigs

Step-by-step explanation:

Since every animal has only 1 head, a total of 26 heads suggests that there are 26 animals in total.

Suppose all animals are chickens.

Total no. of feet = 26 chickens × 2 feet

                           = 52 feet

Difference in total no. of feet = 68 feet - 52 feet

                                                = 16 feet

Difference in no. of feet each animal has

= 4 feet (a pig) - 2 feet (a chicken)

= 2 feet

∴ No. of pigs = 16 feet ÷ 2 feet

                      = 8 pigs

The value of angle x is 133 degree

And the equation of line be of the form,

⇒  y - y₁ = 133(x - x₁)

In the given line,

one angle is of 47 degree

And other is x degree

To find the value of x,

Since we know that,

The angle  of line is 180 degree.

Therefore,

⇒ x + 47 = 180

⇒         x = 133 degree

Therefore slope of this line be 133 degree

Now let this line is  passing through (x₁, y₁)

Hence,

The equation of  line be,

⇒ y - y₁ = (slope)(x - x₁)

⇒  y - y₁ = 133(x - x₁)

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The greatest possible error of the given measurement is: 0.0005 m

The greatest possible error is half of the unit of measure to which a measurement is rounded. If a measurement is made to the nearest whole unit (1), the greatest possible error is 0.5 units.

The steps to determine the greatest possible error are:

Step1: Identify the last nonzero digit to the right of the decimal point in the given measurement.

Step 2: Determine the precision. ...

Step 3: Divide the precision by 2 to determine the greatest possible error.

Thus, it will be the hundredths place for 0.224 m and in this case it is:

0.001/2 = 0.0005 m

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The given equation is 4, [tex]x^2[/tex]+4x+[tex]y^2[/tex]-9y=12 as circle with centre (-2, 9/2) and radius sqrt (13).

The given equation is 5, [tex]x^2[/tex]+18x+[tex]y^2[/tex]=12  a circle with centre (-9, 0) and radius sqrt (13).

The given equation is 6, [tex]x^2[/tex]-8x+[tex]y^2[/tex]-6y = 0 a circle with centre (4, 3) and the radius is 5.

To see this, we can rewrite the equation as [tex](x+2)^2 + (y-9/2)^2[/tex] = 13. This equation represents a circle with centre (-2, 9/2) and radius sqrt (13).

To see this, we can rewrite the equation as [tex](x+9)^2 + y^2 = 13[/tex]. This equation represents a circle with centre (-9, 0) and radius sqrt (13).

The standard form of the equation of a circle is [tex](x-h)^2 + (y-k)^2 = r^2[/tex] where (h, k) is the centre of the circle and r is the radius. Therefore, the centre of the circle is (4, 3) and the radius is 5.

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Answer:

A. 65

Step-by-step explanation:

To find <CAB you need to find the angle of BC and divide it by 2

To find BC add the other angles up and minus it from 360 because a full circle is = to 360

122 + 108 = 230

360 - 230 = 130

130/2 = 65

Hope this helps :)

Discuss measures that can be taken to develop the spirit of hard work

Answer:

The green room is 12 (4x3)

The yellow room is 9 (3x3)

The red room is 12 (2x6)

Step-by-step explanation:

The correct conditional equivalent statement is q → ~p.

Hence, option (D) is correct.

We are given to select the statement that is logically equivalent to the conditional statement   p → ~q.

We know that

Two conditional statements are said to be logically similar if their truth tables are the same.

That is, they have same truth values under similar conditions.

The truth table is given by

p          q        ~p          ~q         p → ~q      p → q        ~p → q     q → p        q → ~p

T          T          F            F           F               T                  T            T             F

T          F          F            T            T               F                  T            T              T

F          T          T            F            T              T                  T            F             T

F          F          T            T            T               T                  F            T             T

So, the truth values of p → ~q is same as the truth values of q → ~p.

They must be logically equivalent.

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Volume of the cone is 153.86 cubic centimeters with radius is 3.5 cm and height of 12cm

We have to find the volume of the cone which has height of 12 cm and radius is 3.5 cm.

Volume of cone =1/3πr²h

Where r is the radius and h is height.

Plug in the value of r and h in the formula.

Volume =1/3×3.14×3.5²×12

=461.58/3

=153.86 cubic centimeters.

Hence, volume of the cone is 153.86 cubic centimeters.

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The amount of solution A and B required are 60 and 90 ounces respectively.

Creating simultaneous equations for the problem:

Mass of solution A = a

Mass of solution B = b

a + b = 150 _____(1)

0.65a + 0.90b = 150×0.80

0.65a + 0.90b = 120 __(2)

From (1)

a = 150-b ____(3)

substitute (3) into (2)

0.65(150-b) + 0.90b = 120

97.5 - 0.65b + 0.90b = 120

0.25b = 120-97.5

0.25b = 22.5

b = 22.5/0.25

b = 90

a = 150 - b

a = 150 - 90

a = 60

Therefore , 60 ounces of solution A and 90 ounces of solution B is required.

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Answer:

(0, 3) and (3, 0)

Step-by-step explanation:

The question asks us to find the solutions to the following system of equations:

[tex]y = x^2 - 4x + 3[/tex]

[tex]y = -x + 3[/tex]

Therefore, as [tex]y = y[/tex], we can say:

[tex]x^2 - 4x + 3 = -x + 3[/tex],

and then solve for [tex]x[/tex]:

⇒ [tex]x^2 - 4x + 3 + x = 3[/tex]              [Adding x to both sides of the equation]

⇒ [tex]x^2 - 3x + 3 - 3 = 0[/tex]              [Subtracting 3 from both sides]

⇒[tex]x^2 -3x = 0[/tex]

⇒ [tex]x(x-3) = 0[/tex]                         [Factoring x out]

• [tex]x= \bf 0[/tex]  or

• [tex]x- 3 = 0[/tex]

⇒ [tex]x = \bf 3[/tex]

Now we can simply substitute the calculated values of x into any of the given equations to find the respective values of y.

Substituting into the equation [tex]y = -x + 3[/tex] :

• when [tex]x = 0[/tex] ⇒ [tex]y = -(0) +3 = \bf 3[/tex]

• when [tex]x = 3[/tex] ⇒ [tex]y = -(3) + 3 = \bf 0[/tex]

Therefore, the solutions to the given set of equations are (0, 3) and (3, 0).

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The algebraic expression that represents the given word problem is:

m + $26.50 = $40

Algebraic word problems are defined as the questions that require us translating sentences into equations, and then solving those equations. The equations we need to write will only involve. basic arithmetic operations. and a single variable. Usually, the variable represents an unknown quantity in a real-life scenario.

In this problem, we are told that

Goal is to collect $40 for a school fund raiser

Amount already collected is $26.50

Amount left to collect is m.

Thus, the algebraic expression that is represented is:

m + $26.50 = $40

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The rule for C(N(h)) is 760h + 380.

The cost when h = 10 hours is 7,980 dollars.

We have,

The rule for C(N(h)) can be found by substituting the expression for N(h) into the function C(x).

We have:

C(N(h)) = C(40h) = 19(40h) + 380 = 760h + 380.

Therefore, the rule for C(N(h)) is 760h + 380.

To find the cost when h = 10 hours, we can substitute h = 10 into the rule for C(N(h)):

C(N(10)) = C(40(10))

= C(400)

= 19(400) + 380

= 7,600 + 380

= 7,980 dollars.

Therefore,

The cost when h = 10 hours is 7,980 dollars.

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The given trigonometric identity is verified below.

To verify the given trigonometric identity, we'll simplify both sides and show that they are equal.

Starting with the left-hand side (LHS):

LHS = tan(x) sin⁴(x)

Now, let's simplify the right-hand side (RHS):

RHS = tan(x) - sin(2x) + sin(x)cos³(x)

To simplify the RHS, we'll use some trigonometric identities:

a. Double-angle formula for sine: sin(2x) = 2sin(x)cos(x)

b. Power-reducing formula for cosine: cos²(x) = 1 - sin²(x)

RHS = tan(x) - 2sin(x)cos(x) + sin(x)(1 - sin²(x))cos(x)

= tan(x) - 2sin(x)cos(x) + sin(x)cos(x) - sin³(x)cos(x)

= tan(x) - sin(x)cos(x) - sin³(x)cos(x) + sin(x)cos(x)

= tan(x) - sin³(x)cos(x) + sin(x)cos(x)

= tan(x) - sin(3x) + sin(x)cos(x) [Using sin³(x) = sin(x)sin²(x) = sin(x)(1 - cos²(x)) = sin(x)(1 - (1 - sin²(x))) = sin(x) - sin³(x) and sin(3x) = 3sin(x) - 4sin³(x)]

Now, we have simplified both sides of the equation.

Let's compare them:

LHS = tan(x) sin⁴(x)

RHS = tan(x) - sin(3x) + sin(x)cos(x)

Since LHS = RHS, we can conclude that the given trigonometric identity is verified.

tan(x) sin⁴(x) = tan(x) - sin(3x) + sin(x)cos(x)

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Explanation:

The net refers to the wrapping paper needed to enclose the cone. It can be thought of as the amount of paint needed to cover the surface.

In this case we add up the two areas to get the final answer

31.4 + 12.56 = 43.96

The equation of the sinusoid function is:

3 Sin πx + 2.

Let's analyze the given options to find the correct equation:

a. 3 Cos πx + 2:

This option is a cosine function with a vertical shift of 2, but it does not have the correct amplitude or period. Therefore, it is not the correct equation.

b. 3 Sin x: This option is a sine function with the correct amplitude, but it does not have the correct vertical shift or period. Therefore, it is not the correct equation.

c. 3 Sin πx + 2: This option is a sine function with the correct amplitude and vertical shift. Let's check if it has the correct period:

To determine if the period is correct, we need to calculate the x-values when the function repeats itself.

In this case, we need to find x-values such that sin(πx) = 0, since the function will reach its maximum and minimum points again at those x-values.

sin(πx) = 0 when πx = 0, π, 2π, 3π, ...

Solving for x, we have:

πx = 0 ⟹ x = 0

πx = π ⟹ x = 1

πx = 2π ⟹ x = 2

πx = 3π ⟹ x = 3

From this, we can see that the function repeats itself every integer value of x, which matches the given information.

Therefore, option (c) is the correct equation: 3 Sin πx + 2.

Option (d) 3 Cos x does not have the correct vertical shift or period, so it is not the correct equation.

Hence, the equation of the sinusoid function is:

3 Sin πx + 2.

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The first several terms of patterns a and b are and 0  3  6  9  12..... and 0  8  16  24  32.....

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

Pattern A

Start = 0

Rule = Add 5

In the above sequence, we can see that 3 is added to the previous term to get the new term

This means that

First term, a = 0

Common difference, d = 3

So, the first few terms are 0  3  6  9  12.....

Pattern B

Start = 0

Rule = Add 8

In the above sequence, we can see that 8 is added to the previous term to get the new term

This means that

First term, a = 0

Common difference, d = 8

So, the first few terms are 0  8  16  24  32.....

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Answer:

Step-by-step explanation:

x+y-22=-16

But x =-7

then

-7+y-22=-16

y-29=-16

y=-16+29

y=13

The exact area of the triangle is 12.5√3 square units.

The area of the triangle to the nearest hundredth is 21.65 in².

We have,

Sin 30 = y/10

1/2 = y/10

y = 5

And,

Cos 30 = x / 10

√3/2 = x/10

x = √3 x 5

x = 5√3

Now,

Area of the triangle.

= 1/2 x 5 x 5√3

= 1/2 x 25√3

= 12.5√3

Now,

The area of the triangle to the nearest hundredth of a square inch.

= 12.5 x 1.732

= 21.65

Thus,

The exact area of the triangle is 12.5√3 square units.

The area of the triangle to the nearest hundredth is 21.65 in².

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