60% of people who purchase sports cars are men. If
10 sports car owners are randomly selected, find
the probability that exactly 7 are men.

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The given figure shows a vertical hyperbola with its centre at origin, and as we observe the figure, we can conclude that :

Length of transverse axis is :

[tex]\qquad \sf  \dashrightarrow \: 2b = 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: b = 6[/tex]

length of conjugate axis is :

[tex]\qquad \sf  \dashrightarrow \: 2a = 8[/tex]

[tex]\qquad \sf  \dashrightarrow \: a = 4[/tex]

Equation of hyperbola ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {y}^{2} }{ {b}^{2} } - \cfrac{ {x}^{2} }{ {a}^{2} } = 1[/tex]

plug in the values ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {y}^{2} }{ {6}^{2} } - \cfrac{ {x}^{2} }{ {4}^{2} } = 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {y}^{2} }{ {36}^{} } - \cfrac{ {x}^{2} }{ {16}^{} } = 1[/tex]

Answer:

[tex]\dfrac{y^2}{36}-\dfrac{x^2}{16}=1[/tex]

Step-by-step explanation:

Standard form equation of a vertical hyperbola

[tex]\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1[/tex]

where:

From inspection of the graph:

Substitute the found values into the formula:

[tex]\implies \dfrac{(y-0)^2}{6^2}-\dfrac{(x-0)^2}{4^2}=1[/tex]

[tex]\implies \dfrac{y^2}{36}-\dfrac{x^2}{16}=1[/tex]

Answer: (c)

(√2-√3)(√2+√3)

Step-by-step explanation:

An irrational number is one that cannot be expressed as the ratio of two integers. In other words it cannot be expressed as [tex]\frac{x}{y}[/tex] where x and y are integers

[tex]\sqrt{2}[/tex] is irrational

[tex]\sqrt{3}[/tex] is irrational

In fact the square root of any prime number is irrational. So [tex]\sqrt{5}[/tex], [tex]\sqrt{7}[/tex] etc are irrational. But [tex]\sqrt{9}[/tex] is not irrational since it evaluates to 3 which can be expressed as [tex]\frac{3}{1}[/tex]

Any expression that contains the square root of a prime number is also irrational

Looking at the choices we see that choices (a), (b) and (d) all evaluate to expressions containing square roots of primes

(a)  (2-√3)2 = 4 - 2√3  . Hence irrational

(b) √2+√3)2 = 2√2+2√3. Hence irrational

(d) 27√7​ is irrational

Let's look at choice (c)

(√2-√3)(√2+√3)

An expression [tex](a+b)(a-b)[/tex]  can be evaluated as [tex]a^{2} - b^{2}[/tex]

Here a = √2, [tex]a^{2}[/tex] =[tex]a = \sqrt{2}\\ a^2 = (\sqrt{2} )^2 = 2\\\\b = \sqrt{3} \\b^2 = (\sqrt{3} )^2 = 3\\\\a^2 - b^2 = 2-3 = -1\\[/tex]

This is a whole number(integer) and all integers are rational numbers

Hence correct answer is (c)

Using the binomial distribution, there is a 0.3474 = 34.74% probability of getting one wrong number.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the values of the parameters are given by:

p = 0.15, n = 10.

The probability of getting one wrong number is P(X = 1), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

P(X = 1) = C(10,1) x (0.15)¹ x (0.85)^9 = 0.3474

0.3474 = 34.74% probability of getting one wrong number.

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Answer:

Step-by-step explanation:

graphing lines is just what it sounds like, you are taking the equation of the line and putting it on the graph. graphing inequalities shows the area of the coordinate plane that satisfies the inequality, it almost always splits the graph.

arithmetic: -6 , 1 , 8 , 15 , 22

geometric: 2 , 4 , 8 , 16, 32

Answer: 2/8, 3/8, 4/8, 5/8, 7/8

Step-by-step explanation:

     Since they all have a common denominator, we can list them based on their numerator without having to worry about the denominator.

2/8 < 3/8 < 4/8 < 5/8 < 7/8

Answer: [tex]x \leq 3[/tex]

Step-by-step explanation:

[tex]9-3x \geq 2(x-3)\\\\9-3x \geq 2x-6\\\\15-3x \geq 2x\\\\15 \geq 5x\\\\3 \geq x\\\\x \leq 3[/tex]

The inequality suitable if 1 is greater than x is x<1.

Given that 1 is greater than x.

We are required to form an inequality which shows that 1 is greater than x.

Inequality is like an equation showing relationship between two or more variables.It is mostly not found in equal to form.

It shows the range of quantities.

When 1 is greater than x means the greater than sign will be used for 1 not x and the inequality will be as under:

x<1

We have not used equal to sign because 1 is greater than x not equal to x.

Hence the inequality suitable if 1 is greater than x is x<1.

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Using the substitution method, the system of equation that is easily solved is:

c. y = 2x + 3

2x + y = 5

Using the substitution method to solve a system of equations is best when one of the equations have one isolated variable that we can simply plug its value into the second equation.

For example, given the system of equations:

y = 2x + 3 --> eqn. 1

2x + y = 5 --> eqn. 2

Substitute y = (2x + 3) into eqn. 2 and find x:

2x + y = 5 --> eqn. 2

2x + 2x + 3 = 5

4x + 3 = 5

4x = 5 - 3

4x = 2

x = 2/4

x = 1/2

Substitute x = 1/2 into eqn. 1 to find y

y = 2x + 3 --> eqn. 1

y = 2(1/2) + 3

y = 1 + 3

y = 4

From the above, we can see that the system of equations that is quite easy to solve using the substitution method is:

c. y = 2x + 3

2x + y = 5

The rest of the equations are quite different and not as straightforward as solving as this using the substitution method.

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Answer:

144

Step-by-step explanation:

First find g(7) --

[tex]g(7)=2(7)-2\\=14-2\\=12[/tex]

Then plug 12 into f(x) --

[tex]f(12)=(12)^{2} \\=144[/tex]

Answer:

Step-by-step explanation:

7/9 * 15/8 = 105/72 = 35/24

Answer:

C - On the number line, move 3 units to the left. End at -7. The dolphin was 7 feet below sea level.

Step-by-step explanation:

The dolphin's starting point was -4 (4 feet below sea level). If the dolphin if diving down by 3 feet, you add -3 to its starting point.

-4 + -3 = -7.

The two missing numbers in the pattern are 10 and 1

The sequence is given as:

100 000 , 10 000 , 1000 , 100 , A , B

From the above sequence, the next term is the quotient of the current term and 10.

So, we have:

A = 100/10 = 10

B = A/10 = 10/10 = 1

Hence, the two missing numbers in the pattern are 10 and 1

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Answer:

1/19

Step-by-step explanation:

The number in the set that are a multiple of both 4 and 6 is 12.

This is one number out of the 19 numbers in the set, so the probability is 1/19.

Answer: tan 1 radians = 1.557, tan 1 degrees = 0.017

Answer:

-21-24/x

Step-by-step explanation:

f(x) is a function on his own which is f(x)=7x+8

we multiple it with another function which is g(x)=-1/x

that gives us (g*f)=-7-8/x

then multiple it by 3 we have -21-24x

Answer:

([tex]\frac{5}{2}[/tex] , - [tex]\frac{13}{4}[/tex] )

Step-by-step explanation:

8x + 4y = 7 → (1)

6x - 8y = 41 → (2)

multiplying (1) by 2 and adding to (2) will eliminate y

16x + 8y = 14 → (3)

add (2) and (3) term by term to eliminate y

22x + 0 = 55

22x = 55 ( divide both sides by 22 )

x = [tex]\frac{55}{22}[/tex] = [tex]\frac{5}{2}[/tex]

substitute this value into either of the 2 equations and solve for y

substituting into (1)

8([tex]\frac{5}{2}[/tex] ) + 4y = 7

20 + 4y = 7 ( subtract 20 from both sides )

4y = - 13 ( divide both sides by 4 )

y = - [tex]\frac{13}{4}[/tex]

solution is ( [tex]\frac{5}{2}[/tex] , - [tex]\frac{13}{4}[/tex] )

Answer:

4[tex]v^{7}[/tex]x³(7[tex]y^{6}[/tex] - 3v²[tex]x^{6}[/tex])

Step-by-step explanation:

28[tex]v^{7}[/tex]x³[tex]y^{6}[/tex] - 12[tex]v^{9}[/tex][tex]x^{9}[/tex] ← factor out 4[tex]v^{7}[/tex]x³ from each term

= 4[tex]v^{7}[/tex]x³(7[tex]y^{6}[/tex] - 3v²[tex]x^{6}[/tex])

Answer:

  log(0.0003) = -3.5229

Step-by-step explanation:

The rules of logarithms tell you ...

  log(ab) = log(a) +log(b)

  log(0.0003) = log(3×10^-4) = log(3) +log(10^-4)

  = log(3) -4 = 0.4771 -4

  log(0.0003) = -3.5229

__

Additional comment

If you do much work with logarithms, you find that negative logarithms are generally expressed using a positive mantissa with a negative add-on. Often, that negative add-on is -9, so this would be ...

  5.4771-9

This helps when taking antilogs, as you look up 0.4771 in the table to see that the multiplier is 3.

If you were to look up 0.5229, you would find 3.333, meaning the multiplier is 1/3.333 and the antilog of -3.5229 is (10^-3)/3.333. This may not be a convenient value to work with.

The domain of the function is x  ≠ 7

The function is given as:

y = 1/x - 7

Set the denominator not equal to 0

x - 7 ≠ 0

Add 7 to both sides

x  ≠ 7

Hence, the domain of the function is x  ≠ 7

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The answer to the question is B. The test statistic is not between the critical values, so we reject the null hypothesis. There is sufficient evidence to support a claim of correlation between percentage of vote and income level.

This is the plot that shows the relationship between two different variables along a straight line. All of the points that are known to have a relationship between these variables would fall under this line. Other parts that fall outside the line are regarded as the outliers in the plot.

In this particular question, the outlier is seen to be outside of the critical values so we have to conclude that the solution is B. We fail to reject the null hypothesis.

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The probability that a randomly selected study's participant was less than 4 is 0.2266.

Given that:

mean = 5.8

standard deviation = 2.4

a) P(x < 4) = P[(x - mean ) /sd < (4 - 5.8) / 2.4]

= P(z < -0.75)

Using z table,

= 0.2266

b) P(4 < x < 6) = P[(4 - 5.8)/ 2.4) < (x - \m ) /sd < (6 - 5.8) / 2.4) ]

= P(-0.75 < z < 0.08)

= P(z < 0.08) - P(z < -0.75 )

Using z table,

= 0.5319 - 0.2266

= 0.3053

c) P(x > 8) = 1 - p( x< 8)

=1- p P[(x - \m ) / sd< (8 - 5.8) / 2.4]

=1- P(z < 0.92)

Using z table,

= 1 - 0.8212

= 0.1788

Lastly, there are no unusual events because all the probabilities are greater than 0.05.

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The Evaluating expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.

According to the statement

We have given that one evaluating expression which is √6 +√6+√27-√12

And we have to simplify this expression by evaluating it.

So, Given expression is:

√6 +√6+√27-√12

√6 +√6+√(9*3)-√(4*3)

√6 +√6+3√(3)-2√(3)

√6 +√6+√3( 3-2)

After evaluating the expression it become

√6 +√6+√3(1)

√(3*2) +√(3*2) +(1)√3

Take common from above expression then

√3(√2 +√2 ) +√3

√3(2√2) +√3

√3(2√2+ 1)

Now the expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.

So, The Evaluating expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Which choice is equivalent to the expression below?

√6 +√6+√27-√12

A. √3(2√2+ 1)

B. 2√3-√21

C. 3√3+√6

D. 5√3

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Answer: 5/36

Step-by-step explanation:

simple interest= principal x time x rate/100

Answer:

please how

Step-by-step explanation:

I will help ypu

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

The contrapositive of the statement is False.

Because we already know, Cube is a 3 - dimensional shape with 6 faces, all its sides are equal and all faces are congruent.

But the contrapositive of the statement is not true, because not only cube has six faces.

There are other 3 - D shapes that have 6 faces.

[tex] \qquad \large \sf {Conclusion} : [/tex]

The contrapositive of the statement is false.

Answer:

4days atlases in the week

Quantity             day

  25------------------1

 1000---------------x

We solve

                  [tex]\boldsymbol{\sf{x=\dfrac{1000\times1}{25}=\dfrac{1000}{25}=40 }}[/tex]

Answer: To spend $1,000 it will take 40 days.

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