The blue segment below is the diameter of O. what is the length of the radius of the circle?

The probability that thickness of coin A will exceed thickness of coin B is 0.3905

Here, we are given that the distribution of x1 is n(1, 0.0004) and the distribution of x2 is n(1.01, 0.0009), that is-

X1 ~ N (1,0.0004) and X1 ~ N(1.01,0.0009)

Now, if a coin battery is selected at random,

The probability that the thickness of coin battery a will exceed the thickness of coin battery b = P(X1 > X2 )

It can be rewritten as follows,

P(X1-X2 > 0)

Let Y = X1-X2

The Y ~ N (1-1.01, 0.0004 + 0.0009)

i.e Y ~ N (-0.01, 0.0013)

= P(Z > 0.278)

= 0.3905

Thus, the probability that thickness of coin A will exceed thickness of coin B is 0.3905

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Answer:

The System of inequalities shown is C.

The equation of the word phrase is 2(h + 11) = 34

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

Twice the sum of a number and 11 is 34

Represent the variable with h

So, we have the following representation

Twice the sum of h and 11 is 34

Express the sum

This gives

Twice h + 11 is 34

Next, we have

2(h + 11) is 34

Express as equation

2(h + 11) = 34

Hence, the equation is 2(h + 11) = 34

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The exponential generating function is,

G(x) = (x¹/1! + x²/2! + ...)(x¹/1! + x³/3! + x⁵/5! +...)(x°/0! + x¹/1! + x²/2! + ...)²

where the first factor describes the pennies, the second describes the quarters, and the last describes nickles and dimes.

We want the coefficient of [tex]x^{r}[/tex]/r!.

Using exponential identities we get,

G(x) = ([tex]e^{x}[/tex] - 1)([tex]\frac{e^{x}-e^{-x} }{2}[/tex]) ([tex]e^{x}[/tex])² = [tex]\frac{1}{2}[/tex] ([tex]e^{4x} - e^{2x} - e^{3x} + e^{x}[/tex]),

and the coefficient is

[tex]\frac{1}{2} (4^{r} - 2^{r}- 3^{r} + 1 )[/tex]

The generating function is

G(x) = (x¹/1! + x²/2! + ...)⁴(x°/0! + x¹/1! + x²/2!+...)²² = ([tex]e^{x}-1[/tex])⁴[tex]e^{22x}[/tex],

and we again want the coefficient of [tex]x^{10}[/tex]/10!.

Multiplying we get,

G(x) = ([tex]e^{4x}-4e^{3x}+2e^{2x}+1[/tex])[tex]e^{22x}[/tex] = [tex]e^{26x}-4e^{25x}+2e^{24x}+e^{22x}[/tex]

so the coefficient of [tex]x^{10}[/tex]/10! is

26¹⁰ - 4 × (25)¹⁰ + 2 × (24)¹⁰ + 22¹⁰

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The expression is vertically stretched by a factor of 7 then the equation for g(x) will be 7x².

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

f(x) = x²

It is stretched vertically by a factor of 7.

So, k = 7

The equation for vertical expansion is,

y = k(f(x))

Then, the equation will be,

g(x) = 7x²

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A biconditional statement is a statement that may be stated in the form “p if and only if q.” This implies “if p, then q” and “if q, then p.”

A biconditional statement is one that can be expressed as "p if and only if q," which implies "if p, then q" and "if q, then p."

For example, "If the polygon is a square, then it has four equal sides and four right angles," and "If a polygon has four equal sides and four right angles, then it is a square," are two examples of biconditional statements.

A biconditional statement is a combination of a conditional statement and its converse written in the if and only if form.

Two line segments are congruent if and only if they are of the same length.

Therefore, the biconditional statement is a statement that may be stated in the form “p if and only if q.” This implies “if p, then q” and “if q, then p.”

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Apply the Binomial Probability Distribution, The Answer is 0.044.

The discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome is known as the binomial distribution with parameters n and p in probability theory and statistics.

The required formula is:

[tex]P(x)= C(n,x) p^{x}q^{n-x}[/tex]

n=10

x=8

p(8)= [tex]C(10,8) * 0.5 ^ {8} *0.5 ^{2}[/tex]

=0.044

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The solution to the expression 9.1p + 8.9r is 116.9 when p = 6 and r = 7

From the question, the mathematical expression is given as

9.1p + 8.9r

The values of the variables are given as

p = 6 and r = 7

Substitute p = 6 and r = 7 in the given expression 9.1p + 8.9r

So, we have the following representation

9.1p + 8.9r = 9.1 * 6 + 8.9 * 7

Evaluate the products in the above equation

9.1p + 8.9r = 54.6 + 62.3

Evaluate the sum in the above equation

9.1p + 8.9r = 116.9

Hence, the value is 116.9

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(a) If the discrimant is > 0, the quadratic equation has 2 real solutions.

(b) If the discrimant is = 0, the quadratic equation has 1 real solution.

(c) If b^2-4ac is < 0, the quadratic equation has 0 real solution, therefore it has 2 imaginary solutions.

The square root's input (i.e., its contents), which is the phrase b^2 -  4ac, is known as the "discriminant" because using its value, you may "discriminate" between (i.e., be able to distinguish between) the different solution types.

To determine how many possible solutions a quadratic equation has, utilize the discriminant formula.

(a) If the discrimant is > 0, the quadratic equation has 2 real solutions.

Example

x^2 - 5x + 2 = 0

where a = 1, b = -5, c= 2

D=b^2 - 4ac = (-5)^2 - 4 ×1 × 2 = 17

∴ It has two real solutions.

(b) If the discrimant is = 0, the quadratic equation has 1 real solution.

Example

x^2 + 2x + 1 = 0

where a = 1, b = 2, c= 1

D=b^2 - 4ac = (2)^2 - 4 ×1 × 1 = 0

∴ It has one real solution.

(c) If b^2-4ac is < 0, the quadratic equation has 0 real solution, therefore it has 2 imaginary solutions.

Example

3x^2 + 2x + 1 = 0

where a = 3, b = 2, c= 1

D=b^2 - 4ac = (2)^2 - 4 ×3 × 1 = -8

∴ It has two imaginary solutions.

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The (a + 2b + c)(a - c) is the product of the expression (a + b)² - (b + c)² using difference of two squares.

Considering two numbers a and b, the difference of their squares written as a² - b² is equal to the the product of the sum of the numbers and the difference of the numbers, that is (a + b)(a - b).

We have from the question two squares which are (a + b)² and (b + c)² and we shall express their difference as a product as follows:

(a + b)² - (b + c)² = [(a + b) + (b + c)][(a + b) - (b + c)]

open brackets and simplify;

(a + b)² - (b + c)² = (a + b + b + c)(a + b - b - c)

add and subtract like terms;

(a + b)² - (b + c)² = (a + 2b + c)(a + b - b - c)

(a + b)² - (b + c)² = (a + 2b + c)(a - c)

In conclusion, we have that (a + 2b + c)(a - c) is the product of the expression (a + b)² - (b + c)² that is a difference of two squares.

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Answer:

You are 110 feet under the sea and then you rise 120 feet.  How many feet are you now above the sea lever?  10.

Step-by-step explanation:

Option b is correct.

Therefore, the probability that a state highway inspector would choose a sample of 49 trucks and discover that the sample mean was 14.3 tons or less is equal to  0.3758

Given: The population mean and standard deviation for the weight of trucks moving on a given stretch of I-475 are both tons.

n=49 sample size

Consider x to be the random variable that represents the truck weight.

z-score: z  = x - μ ÷ σ/[tex]\sqrt{n}[/tex]

When x=14.3 tons

z = [tex]\frac{14.3 - 15.8}{\frac{4.2}{\sqrt{49} } }[/tex]  ≈ -2.5

The likelihood that a state highway inspector will choose 49 trucks as a sample and discover that the sample mean is 14.3 tons or less is as follows:

P(X ≤ 14.3) = P(z < -2.5) = 0.3758

Therefore, the probability that a state highway inspector would choose a sample of 49 trucks and discover that the sample mean was 14.3 tons or less is equal to  0.3758

option b is correct.

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Answer:

The difference is

.9

The solution of given expression 7×(4-3) - 1+5×1/5 is 5.

The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.

Given that the expression 7×(4-3) - 1+5×1/5.

To solve the above expression we will use PEMDAS;

First, we use the subtraction in brackets and this process is called simplifying parenthesis,

7×(4-3) - 1+5×1/5=  7×(1) - 1+5×1/5.

Now, we use the operation multiplication,

7×(1) - 1+5×1/5 = 7 - 1+1

Now we add the terms and this process is called addition of terms,

7 - 1+ 1 = 7-2

Now, we subtract the numbers and this property is subtraction of numbers,

7 - 2 = 5.

Therefore, the solution of given expression 7×(4-3) - 1+5×1/5 is 5.

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Answer:

Response bias would be something where answers would be skewed one way or another because of the way you asked. So maybe ask something embarrassing for someone to admit, like asking random students if they pick their nose. Some people will answer truthfully as no, and the people who do will likely also say no because they do not want to tell you that.

Answer:

A and C

Step-by-step explanation:

The angles and their images are congruent.

Step-by-step explanation:

In the figure ,angle DEF=Angle DHG=50.prove that

The solutions of the equation is found for the values of x = ±√2i or x = ±i.

An equation x⁴ + 3x² + 2 = 0, has been presented to us.

We are asked to discover the solutions of our supplied equation using substitution.

Our provided equation can be rewritten as:  x⁴ + 3x² + 2 = 0

Considering that: u = x²

u²  + 3u + 2 = 0

Factorizing the equation;

(u + 2)(u + 1)

or, u = - 2 and u = -1.

When we re-substitute the value of u, we obtain:

x² = -2 or x²  = -1

x = ±√-2 or x = ±√-1

x = ±√(-1).2 or  x = ±√-1

Now we shall employ imaginary unit i. That is a fact i²  = -1.

x = ±√i².2 or x = ±√i²

x = ±√2i or x = ±i

Consequently, the solution obtained for the equation are- x = ±√2i or x = ±i.

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Answer:

Step-by-step explanation:

2,637

Answer:

77

Step-by-step explanation:

60+128+95+x=360

283+x=360

x=77

The number of 1 cup candle mold which the can fill with 144 ounce  of cented candle wax is 18.

As we know ,

1-cup= 8 ounces

On dividing ,

144 by 8 =  18

Therefore , the no of cups which can be filled is 18 .

One of the fundamental arithmetic operations in mathematics is the division, which is the process of dividing a group of items into equal pieces. Every day, we might employ the division approach in various situations.

Any number divided by 0 has no specified result. The outcome in this situation can be expressed as infinite. For instance, 15/0 =, which is undefined.

Dividend :

The division procedure shown below is used to divide any expression.

Dividend is equal to Divisor Quotient + Remainder.

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The relative cumulative frequency of students who earned a score of 20 or lower on the quiz is: B. 68%.

In Mathematics and Statistics, a frequency table can be used to graphically represent the frequencies or relative frequencies that are associated with a categorical variable.

In Mathematics and Statistics, the cumulative frequency of a data set can be calculated by adding each frequency from a frequency distribution table to the sum of the preceding frequency. Thus, the relative cumulative frequency would be calculated as follows;

Cumulative frequency of students = 4 + 8 + 15 + 7 = 34.

Cumulative frequency of students = 34.

Total frequency = 4 + 8 + 15 + 7 + 7 + 3 + 4 + 2

Total frequency = 50.

Therefore, the relative cumulative frequency can now be determined;

Relative cumulative frequency = 34/50

Relative cumulative frequency = 0.68 or 68%

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Answer:

68%

Step-by-step explanation:

Got it right.

The variables as length are L and width is W and the system of equations is L = 2W - 3 and 42 = 2(L + W) and the length and width are 13 feet and 8 feet respectively.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

As per the given total fencing = 42 feet

Let's say the length is L and the width is W.

As per the given,

L = 2W - 3

Perimeter = 2(length + width)

42 = 2(L + W)

21 = 2W - 3 + W

21 + 3 = 3W

W = 8 feet

And, L = 2(8) - 3 = 13 feet

Hence "The variables as lengths are L and width is W and the system of equations is L = 2W - 3 and 42 = 2(L + W) and the length and width are 13 feet and 8 feet respectively".

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In the figure given the value of x is calculated to be

The value of x is solved from using the vertical angle theorem.

According to this theorem, when two straight lines cross, they create two sets of linear pairs with equal angles.

The adjacent angles created by the junction of these two lines are likewise said to be supplementary, or equivalent to 180 degrees.

From this principle,

8x = 2x + 72

8x - 2x = 72

6x = 72

x = 16

The angles marked by 8x is equal to

= 8 * 12

= 96 degrees

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After evaluating the given function using trigonometric identities, we have the resultant answer that is - tan(2t).

Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence.

These are identities that, geometrically speaking, involve certain functions of one or more angles.

Pythagorean identities, reciprocal identities, sum and difference identities, and double-angle and half-angle identities are the main trigonometric identities.

We must apply the sine rule and the cosine rule to the non-right-angled triangles.

So, we have the function:

tan (15π - 2t)

Now, evaluate as follows:

(15π - 2t)

Rewrite using trigonometric identities:

- sin(2t)/cos(2t)

Rewrite using trigonometric identities:

- tan(2t)

Therefore, after evaluating the given function using trigonometric identities, we have the resultant answer that is - tan(2t).

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Answer:

3 hours and 45 minutes

Step-by-step explanation:

ggggggggggggg

The value fo the numerical expression 2 × (2.5 -|-6|) will be negative 7.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ 2 × (2.5 -|-6|)

We know that the value inside the mode is always positive, then the expression is written as,

⇒ 2 × (2.5 -|-6|)

⇒ 2 × (2.5 - 6)

Simplify the expression, then the value of the expression is given as,

⇒ 2 × (2.5 - 6)

⇒ 2 × (- 3.5)

⇒ - 7

The value fo the numerical expression 2 × (2.5 -|-6|) will be negative 7.

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The solution of the equation after completing the square of the equation is found as; x = ±√19 + 2.

The given steps are-

x² - 4x = 15.

(b/2)² = (-2)²

x² - 4x + (-2)² = 15 +(-2)²

x² - 4x + 4 = 19

There are various ways to display the outcome.

(x - 2)² = 19

x = ±√19 + 2

Thus, the solution of the equation after completing the square of the equation is found as; x = ±√19 + 2.

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f(x-3.5) means f(x) is translated 3.5 units left. 3f(x) implies f(x) is vertically stretched by a factor of 3.5.

A function is a relationship between inputs where each input is related to exactly one output. Also, translation means movement on a straight line

In the cartesian plane or graph, movement in the x-axis is either to the left (negative) or right (positive).

Thus, f(x-3.5) implies f(x) is translated 3.5 units left (i.e. -3.5)

For 3.5f(x), when you multiply f(x) by 3.5, you stretch it by 3.5. Thus, f(x) is vertically stretched by a factor of 3.5

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Answer:

3753.20 ft

Step-by-step explanation:

tan 80° = 3400 ft/x

x = 599.51 ft = distance at ground level from point directly below mountain peek to edge of mountain.

599.51 ft + 990 ft = 1589.51 ft = horizontal distance at ground level from where cable is attached to the ground to the center of the mountain. This is a leg of a right triangle.

3400 ft is another leg of a right triangle.

(1589.51 ft)² + (3400 ft)² = y²

The hypotenuse, y, is the length of the cable.

y = 3753.20 ft