The National Academy of Science reported in a 1997 study that 40% of research in mathematics is published by U.S. authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 40%. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 130 recent articles published by reputable mathematics research journals and finds that 62 of these articles have U.S. authors. Does this evidence support the mathematics chairperson's claim that the percentage is no longer 40%? Use a 0.05 level of significance.

The probability that exactly four complaints will be received during the next eight hours is 15.41%.

A discrete probability distribution called the Poisson distribution provides the likelihood that an event will occur a specific number of times over the course of a given period of time or location. The formula for this distribution is given by \(P(X=x)=\frac{e^{-\mu}\times \mu ^x}{x!}\) where x is the number of successes, μ is the mean, and e is Euler's number.

Given n = 8 hours then, μ = 0.7n = 0.7×8 = 5.6.

Then, the probability that exactly four complaints are received is,

\(\begin{aligned}P(X=4)&=\frac{e^{-5.6}\times5.6^4}{4!}\\&=0.1541\end{aligned}\)

The required answer is 15.41%.

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1. Variable: A symbol or letter that represents an unknown value or quantity in algebraic expressions and equations.

2. Equation: A mathematical statement that shows the equality between two expressions, typically represented by an equal sign (=).

3. Coefficient: The numerical factor that is multiplied by a variable in a term.

4. Expression: A mathematical phrase that may contain variables, constants, and operations, but does not have an equal sign.

5. Linear Equation: An equation in which the highest power of the variable is 1, written in the form ax + b = 0, where a and b are constants and x is the variable.

Variable: In algebra, a variable is a symbol (usually a letter) that represents an unknown value or quantity. It allows us to express mathematical relationships and solve equations.

Equation: An equation is a mathematical statement that shows the equality between two expressions.

It consists of an equal sign (=) and can include variables, constants, and operations.

Solving equations involves finding the values of the variables that make the equation true.

Coefficient: A coefficient is the numerical factor that is multiplied by a variable in a term.

It represents the scale or magnitude of the variable.

For example, in the term 3x, the coefficient is 3.

Expression:

An expression is a mathematical phrase that can contain variables, constants, and operations, but does not have an equal sign.

Expressions can be evaluated or simplified, but they cannot be solved since they lack the equality found in equations.

Linear Equation:

A linear equation is an equation where the highest power of the variable is 1.

It can be written in the form ax + b = 0,

where a and b are constants and x is the variable.

Solving linear equations involves finding the value(s) of x that satisfy the equation.

These are just a few key definitions that form the foundation of understanding introductory algebra.

Mastering these concepts will provide a solid basis for further exploration and learning in algebraic principles and problem-solving.

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Answer:

i think probably x = 10

Step-by-step explanation:

sin(60°) = 5√3/x

√3/2 = 5 √3/x

√3 x = 10√3

x = 10

Answer:

d

Step-by-step explanation:

just makes sense bc they're all in 2nd grade

Answer:

yes the gym charged Sandra the correct price

1) Volume = 16.76

2) Volume = 6052.8

3) Volume = 51.31

5) Volume = 555.18

6) Volume = 622.53

Answer:

Step-by-step explanation:

parallel lines

Answer:

C) parallel lines

Step-by-step explanation:

It does not HAVE to be parallel, but it may be.

The others would not yield no solutions

Answer:

1. b

2. b

Step-by-step explanation:

Sorry, I'm not so sure for c

Answer:

the correct answer is:-

1) b

2) b

3) c

Step-by-step explanation:

1 ) b

2 ) b

3) c

Answer:

  70 ft

Step-by-step explanation:

You want the actual width of a gym that is represented as 7 inches on a drawing with a scale of 1 in : 10 ft.

Each inch represents 10 feet, so 7 inches will represent ...

  7 × 10 ft = 70 ft

The gym is 70 ft wide.

__

Additional comment

You can also write and solve an equation that shows the measures are proportional:

  actual width / drawing width = (10 ft) / (1 in) = (gym width) / (7 in)

Multiplying both sides of this proportion by 7 in, we have ...

  gym width = (7 in) × (10 ft)/(1 in) = 7 × 10 ft = 70 ft

Answer:

377.19 (rounded off to 2dp)

Step-by-step explanation:

since its a right angled triangle, we can use tangent

tan(x) =opp/adj

tan(5) =33/AC

AC =33/tan(5)

Answer:

\(840\)

Step-by-step explanation:

This is a good example of permutations. For the first slot on his shelf, Dylan has 7 trophies to choose from. Then 6, 5, and so on. Since he is only fitting 4 trophies on his shelf, we only continue until we have the slots filled. Thus, we have \(7\cdot 6 \cdot 5\cdot 4=\boxed{840\:\text{ways}}\) to do so.

*Note: We do not divide by \(4!\) because in this case, order matters. A different order of the same four books still produces different arrangements, so the order matters.

9514 1404 393

Answer:

  20 mm/min

Step-by-step explanation:

To find the rate in mm per minute, divide mm by minutes:

  (600 mm)/(30 min) = 20 mm/min . . . unit rate

To show that if h is a subgroup of a finite abelian group g, then g has a subgroup that is isomorphic to g/h, we can use the fact that the quotient group g/h is defined as the set of co sets of h in g, with the operation of group multiplication defined as (aH) (bH) = (ab)H for all a, b in g.

To prove that g has a subgroup isomorphic to g/h, we can define a function f: g/h -> g that maps each coset aH in g/h to an element a in g. This function is a homomorphism because for all a, b in g, we have:f(aH) * f(bH) = a * b = ab = f((ab)H) = f((aH)(bH)) Therefore, the function f is a homomorphism from g/h to g, and the image of f, which is the set of elements {a in g | a = f(aH) for some aH in g/h}, is a subgroup of g that is isomorphic to g/h.

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Using it's concept, it is found that the probability of a vowel, then letter K being spun, is given by:

3. 1/9

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem:

The events are independent, hence:

P(vowel, then K) = P(vowel) x P(B) = 2/6 x 1/3 = 1/3 x 1/3 = 1/9.

Which means that option 3 is correct.

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Answer:

The real part is -7.

The imaginary part is 8.

Step-by-step explanation:

A complex number has the form:

\(a+bi\)

Where a is the real part and b is the imaginary part.

We are given:

\(-7+8i\)

Hence:

\(a=-7\text{ and } b=8\)

So, we can say that our real part is -7 and our imaginary part is 8.

Answer:

15i

Step-by-step explanation:

should be correct happy new year

The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The function is an exponential growth function

The function is given as

y=2(1.06)^9

We can begin by rewriting the given equation as:

y = 2 * 1.06t

So, we have

y = 2 * (1 + 0.06)^t

Now we can see that the equation is in the form y = a*b^t,

where a = 2 and b = 1.06^9

This equation represents exponential growth because the base of the exponent, b = 1.06, is greater than 1.

We can re-write it in the form y = a(1+r)t,

we can find the value of r by subtracting 1 from 1.06 which is 0.06 and the value of a is 2.

so we have y = 2(1+0.06)^t

So, the equation represents exponential growth with a = 2 and r = 0.06

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The profit function for the revenue R(x) = 12x and the cost, C(x) = x + 264 is  11x-264 and units must be produced for the business to break even is 24 units.

Profit refers to net income after deducting expenses from earnings, whereas revenue refers to income generated through business operations. Sales, fee-based income, and property-based income are just a few of the different ways that money can come in.

Here,

R(x)=12x

C(x)=x+264

It represents the difference between total revenues and total outlays.

Revenue minus costs equals profit.

Profit = Revenue - Cost

P(x)=R(x)-C(x)

P(x)=12x-x-264

P(x)=11x-264

For  the company to break even,

R(x) = C(x)

12x=x+264

11x=264

x=24

The break-even point for the business is 24 units, and the profit function for the revenue R(x) = 12x and the cost C(x) = x + 264 is 11x-264.

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Answer:

A and C

Step-by-step explanation:

The probability of getting at least 6 heads is3/256 or 0.0117

Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution.

Probability is a measure of how likely something is to occur. Calculating probability involves dividing the total number of outcomes by the number of possible ways an event may occur.

Given that,

A fair coin is tossed = 8 time.

We have to find the probability of getting at least 6 heads.

Since, the probability of getting head, when one coin is tossed = 1/2

And the probability of getting tale = 1/2  

The probability of getting head at least  6 times when coin is tossed 8 times can be given as,

The head can come 6 times, then probability = \((1/2)\x^{6} (1/2)\x^{2}\) =  (1/2)⁸

The head can come 7 times, then probability = (1/2)⁷(1/2) = (1/2)⁸

The head can come 8 times, then probability = (1/2)⁸

The probability of getting head at least 6 times

= (1/2)⁸ + (1/2)⁸ +  (1/2)⁸ = 3(1/2)⁸ = 3/256 = 0.0117

The probability of getting at least 6 heads is3/256 or 0.0117

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Step-by-step explanation:

the answer will be 3/5 hope it helps

Answer:

3/5

Step-by-step explanation:

It is like addition, 1 + 1 + 1 which equals to 3.

The quadratic equations and their factors are simplified below

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x² is a non-zero term(a ≠ 0). For writing a quadratic equation in standard form, the x² term is written first, followed by the x term, and finally, the constant term is written. The numeric values of a, b, c are generally not written as fractions or decimals but are written as integral values.

1) (x - 5)(x - 5) = x² - 5x - 5x + 25 = x² -10x + 25

2) (x + 2)(x + 9) = x² + 2x + 9x + 18 = x² + 11x + 18

3) (x + 2)(x + 3) = x² + 2x + 3x + 6 = x² + 5x + 6

4) (x + 1)(x + 2) = x² + x + 2x  + 2 = x² + 3x + 2

5) (x - 3)(x - 3) = x² - 3x - 3x + 9 = x² - 6x + 9

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Answer:

18

Step-by-step explanation:

If 4 out of 10 wore glasses, then 6 out of 10 did not wear classes.  This would be 60% or .6

.6x30 = 18

Answer:

x=24

Step-by-step explanation:

0.22(x+6)=0.2x+1.8

simplify the given equation

0.22x+1.32=0.2x+1.8

shift same kind of variables on one side

0.22x-0.2x=1.8-1.32

0.02x=0.48

For x

x=0.48/0.02

x=24

Check:

For checking subsitute the calculated value x if both sides of x are equal  then its true...

0.22(24+6)=0.2(24)+1.8

5.28+1.32=4.8+1.8

6.6=6.6

Answer:

Justin keeps 3 marbles. Each friend gets 4 marbles.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

If Judge is x years old and Eden is 6 years older, then Eden is x + 6 years old.

The second part tells us that Eden will be twice as old as Judge in two years.

This means that in two years: (Eden's age) = 2 * (Judge's age).

Since we know that Eden's age can be represented as x + 6 and Judge's age can be represented as x, we can write this: x + 6 = 2 * x

Simplify the equation:

x + 6 = 2x

6 = x = Judge's age (in two years)

If Judge is 6 two years later, then he must be 4 now.

To check our work, we can just look at the problem. Judge is 4 years old and Eden is 6 years older than Judge (that means Eden is 10 right now). Two years later, Eden is 12 and Judge is 6, so Eden is twice as old as Judge. The answer is correct.

A like radical to the one shown is Option C.

We know that we can be able to perform mathematical operations on the radicals such as adding and subtracting but this must be performed when we have like radicals.

When we talk about like radicals we mean that the radicals must be such that it easy for the radical to be worked upon as we have it in the question that is before us here to locate a like radical among the options.

The radical in option C has the same 2x and power as the given radical hence they are like radicals.

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Answer:

x=1      x=3

y=2     y=4

Step-by-step explanation:

x=1 and x+1=y

1+1=2

and x=3

3+1=4