solve each proportion. if necessary, round to the nearest hundredth
1-12

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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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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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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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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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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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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The speed of a point on the rim  is 2.44 m/s.

What is a quick answer for diameter?

The diameter is the distance along the circle's center that must travel in order to touch two points on its edge.

First convert diameter into radius

r = d/2 = 0.08/2 = 0.04 m

The moment of inertia of disc is given by

I = 0.5mr²

Where m is the mass and r is the radius of the disk

I = 0.5(0.1)(0.04)²

I = 0.00008 kg.m²

and since we are dealing with rotational motion then rotational kinetic energy is given by

E  =  0.5 I ω²

we have to separate ω

ω² = E/0.5 I

ω = √E/0.5 I

ω = √0.15/0.5(0.00008)

ω = 61.23 rad/sec

Finally we know that speed is given as

v = ω r

v = 61.23 (0.04)

v = 2.44 m/s

Therefore, the speed of a point on the rim  is 2.44 m/s.

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The complete question is -

A thin, 100 g disk with a diameter of 8.0 cm rotates about an axis through its center with 0.15 J of kinetic energy. What is the speed of a point on the rim

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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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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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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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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A negative result does not mean that you do not have the disease. It could be a false negative.

The reasons that could be there for a negative result when there is  actually the presence of the disease

The ELISA may not be sensitive enough to detect very low concentration  of the disease agent, as might occur when one is tested soon after infection before a proper immune response occurs.

As HIV buds from the surface of the host cell, it incorporates some of the host cell Human leukocyte antigen into its envelope. False negatives usually occurs during the window between infection and an antibody response to the virus which is known as seroconversion.

Therefore, if the sample gave a negative result for the disease-causing agent, it does not mean that you do not have the disease

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Answer:

Step-by-step explanation:

2,637

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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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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When a=4, b=1, and c=3, the value of the given expression, which is |a-b|²-c, is 28.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.

Here,

|a-b|²=(4-(-1))²

=25

25-(-3)

=28

The value of given expression that is |a-b|²-c is 28 when a=4, b=−1, and c=−3.

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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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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:

After Rajesh took 493 stones, you would have 471 stones left.

Step-by-step explanation:

If you started with 964 stones and Rajesh took 493 stones, then you would have 964 - 493 = 471 stones left.

Answer:

3 hours and 45 minutes

Step-by-step explanation:

ggggggggggggg

Answer:

A and C

Step-by-step explanation:

The angles and their images are congruent.

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 standard deviation is decreases then the graph of the normal z - score curve is increases.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

The standard deviation is calculated as the square root of variance by determining each data point's deviation relative to the mean. If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation.

In mathematics, the Z score is used to quantify how many standard deviations the raw score deviates from or approaches the mean. Giving the z score are:

z = (x - μ ) / σ

Where,

x = raw score

μ = mean

σ = standard deviation

For a sample size,

z =  (x - μ ) / σ / [tex]\sqrt{n}[/tex]

The z score affects the area under the curve. The area under the curve increases as the z score increases and decreases as the z score decreases.

The standard deviation has an inverse relationship with the area under the curve (z score). The z score drops as the standard deviation rises, diminishing the area under the curve.

The area under the curve grows as the standard deviation is reduced because the z score increases.

Therefore,

The standard deviation is decreases then the graph of the normal z - score curve is increases.

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Answer:

77

Step-by-step explanation:

60+128+95+x=360

283+x=360

x=77

The number of cans of soup bought is 8 and the number of frozen dinners purchased is 3.

s + f = 11 equation 1

350s + 650f = 4750 equation 2

Where:

The elimination method would be used to solve for the required values:

Multiply equation 1 by 350

350s + 350f = 3850 equation 3

Subtract equation 2 from equation 3 :

300f = 900

f = 900 / 300

f = 3

Substitute for f in equation 1 :

s + 3 = 11

s = 11 - 3

s = 8

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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:

Answer: -5

Step-by-step explanation:

[tex]-2.5y + 8y - 10.5[/tex]

[tex]= 5.5y - 10.5y[/tex]

[tex]= -5y[/tex]

Hence, the answer is [tex]-5[/tex].

Answer:

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

All terms have same variable of y.

Collect all terms and simplify by adding up the coefficient:

The coefficient of the variable is -5.