Consider function f. f(x) = cube root of x - 7. Select g(x) so that f(g(x)) = g(f(x)) = x for all values of x.

1.  System B from System A by replacing one equation with itself where the same quantity is added to both sides

2. Yes, both system A and system B are equivalent and therefore has the same solution

System A

x − 4y= 1

5x + 6y= −5

System B

x = 1+4y

5x + 6y= −5

1. System B can be gotten from system A by

from the first equation of A

x − 4y= 1

Make 'x' subject of formula

x = 1 + 4y

This makes it equal to tat of system B

Thus, replacing one equation with itself where the same quantity is added to both sides

2. System A

x = 1 + 4y

5x + 6y= −5

System B

x = 1 + 4y

5x + 6y= −5

From the above equations, we can see that both system A and system B are equivalent and therefore has the same solution.

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The frequency table and histogram are shown in the attached picture.

It is defined as the depiction of numerical data in a graph using a bar with no space. The histogram depicts the approximate distribution of the data.

We have:

The ages of the participants were recorded as follows:

36, 48, 54, 92, 57, 63, 66, 76, 66, 80, 82, 65, 39, 77, 45

The classes can be made:

30-42, 43-55, 56-68, 69-81, and 82-94

The histogram is shown in the picture.

Thus, the frequency table and histogram are shown in the attached picture.

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Answer:

StepWhat is the measure of z? Z X y 4 9 z = [ ? ]VI-by-step explanation:

Answer:

Area = length * width

= 4/5 * 2/3

= 8/15

Answer:

[tex]area = \frac{8}{15} {in}^{2} [/tex]

Step-by-step explanation:

The solution is in the attached file

Using the binomial distribution, the probabilities are given as follows:

a) 0.0747 = 7.47%.

b) 0.8725 = 87.25%.

c) 0.1256 = 12.56%.

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:

The values of the parameters are:

n = 20, p = 0.6.

Item a:

The probability is P(X = 15), hence:

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

[tex]P(X = 15) = C_{20,15}.(0.6)^{15}.(0.4)^{5} = 0.0747[/tex]

Item b:

The probability is:

[tex]P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12) + \cdots + P(X = 20)[/tex]

Finding each value with the equation we used in item a, we have that:

[tex]P(X \geq 10) = 0.8725[/tex]

Item c:

At least 20 - 5 = 15 on the road, hence the probability is:

[tex]P(X \geq 15) = P(X = 15) + P(X = 16) + \cdots + P(X = 20)[/tex]

Then, using the same procedure as item b, we have that:

[tex]P(X \geq 15) = 0.1256[/tex]

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Answer:

(3x-2)

Step-by-step explanation:

3x² + 4x - 4

look for two factors whose product is (3)(-4)=-12 and sum is +4

The factors will be +6 and -2

substitute these factors inplace of 4x to get:

3x² - 2x + 6x - 4

then factorize:

x(3x-2)+2(3x-2)

finally we get factors: (3x-2)(x+2)

Answer: Option 4

Step-by-step explanation:

[tex]\sin \frac{7\pi}{6}=\sin \left(-\frac{\pi}{6} \right)=\sin \frac{11\pi}{6}[/tex]

Using equivalent angles, the equivalent expression to [tex]\sin{\left(\frac{7\pi}{6}\right)}[/tex] is:

[tex]\sin{\left(\frac{11\pi}{6}\right)}[/tex]

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

In this problem, we have that [tex]\frac{7\pi}{6}[/tex] is on the third quadrant, as [tex]\pi < \frac{7\pi}{6} < \frac{3\pi}{2}[/tex]. Hence the equivalent angle on the first quadrant is:

[tex]\frac{7\pi}{6} - \pi = \frac{7\pi}{6} - \frac{6\pi}{6} = \frac{\pi}{6}[/tex]

The sine is negative on the third and fourth quadrants, hence the equivalent angle on the fourth quadrant is:

[tex]2\pi - \frac{\pi}{6} = \frac{11\pi}{6}[/tex]

Thus, the equivalent expression is:

[tex]\sin{\left(\frac{11\pi}{6}\right)}[/tex]

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Lenny's net proceeds algebraically are found as;[tex]\rm |xy + 20 - \frac{98}{100} |[/tex]

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Let the bought share will be $ x, and $y is the price per share

Paid fees to the broker = $ 20

The total amount spent = $(xy+20)

The price at which each share sells = $ A

Broker commission = 2 %

The total amount obtained after selling the shares;

⇒ ax - 2% of ax

⇒ 98 % of ax

Hence, Lenny's net proceeds algebraically are found as;[tex]\rm |xy + 20 - \frac{98}{100} |[/tex]

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Answer:

Step-by-step explanation:

what were Laura net proceeds

The nominal rate on a three year Treasury Bond, which is the risk-free rate plus the inflation premium, is 6%.

The nominal interest rate (also known as the money interest rate) is the percentage of interest that the borrower pays to the lender for a loan.

The nominal interest rate includes the real rate and the inflation premium.

Risk-free rate = 2%

Inflation premium = 4.0%

Maturity risk premium = 3.7%

Liquidity premium = 3%

Default risk premium = 3.5%

Nominal rate for Treasury Bond = Risk-free rate plus Inflation premium

= 6% (2% + 4%)

Thus, the nominal rate on a three year Treasury Bond is 6%.

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Answer:

(0;-1)

Step-by-step explanation:

for more details see the attachment.

Answer:

21 y power 5

Step-by-step explanation:

Answer:

(x-9) (x-5)

x = 9 x = 5

Step-by-step explanation:

find out which 2 numbers when multiplied give 45 and

when added give -14

they are -9 and -5

(x-9) (x-5)

x = 9 x = 5

Answer:

[tex]x_{1}=9, x_2=5[/tex]

Step-by-step explanation:

Recall a quadratic formula for quadratic equation [tex]ax^2+bx+c=0[/tex]: [tex]x_{1/2}=\frac{-b\pm \sqrt{b^2 -4ac}}{2a}[/tex]

Notice the constant in the given equation [tex]x^2-14x+45[/tex]:

[tex]a=1, b=-14, c=45[/tex]

Substitute the values into the formula:

[tex]x_{1/2}=\frac{-(-14)\pm \sqrt{(-14)^2 -4\cdot 1\cdot 45}}{2\cdot 1}[/tex]

Calculate the values:

[tex]x_{1/2}=\frac{14\pm \sqrt{196 -180}}{2}=\frac{14\pm\sqrt{16}}{2}=\frac{14\pm 4}{2}[/tex]

It follows that there are two solutions:

[tex]x_1=\frac{14+4}{2}=\frac{18}{2}=9[/tex]   and   [tex]x_2=\frac{14-4}{2}=\frac{10}{2}=5[/tex].

The bikers will meet at point N, all the questions have been answered below.

A triangle is a polygon with three sides, angles, and vertices.

The triangle MNO is formed on the basis of the data given in the question

If the triangle satisfies the sine-rule then the biker meets the other biker at point N

According to the sine rule

In a Triangle ABC of side length a,b and c respectively

a/ sin A = b/ sin B = c/sin C

NM/sin NOM =21/ sin 61°

NM/sin NOM = 24.01

NO/sin OMN =24/sin 89°

NO/sin OMN = 24.003

∠ONM = ( 180-61-89) = 30°

OM / sin ONM = 12/ sin 30 = 24

        and so, the bikers will meet at point N.

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Answer:

Try using the permutations formulae - nPr

n = 10

r = 4

you should get the answer. I don't have calculator on me and I'm lazy searching an online calculator. cheers

Answer:

D) 12pm

Step-by-step explanation:

8 pm = 20:00

20:00 + 16:00*4 = 20:00 + 64:00 = 84:00

subtract the 24 hours in 84:00

84:00 - 3 X 24:00 = 12:00

12:00 = 12pm

The slope of the parallel line is 3/4

The equation is given as:

3x - 4y = 8

Rewrite as:

4y = 3x - 8

Divide through by 4

y = 3x/4 -  2

A linear equation is represented as:

y = mx + b

Where m represents the slope

By comparison:

m = 3/4

Parallel lines have equal slope

Hence, the slope of the parallel line is 3/4

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Answer:

(-2,2)

Step-by-step explanation:

i tried sorry if it's wrong

13.13.13.13.13 in exponential form is 13^5

The expression is given as:

13.13.13.13.13

The factors of the above expression are 13.

And each factor is grouped by product

There are five 13s in the expression.

So, we have:

13.13.13.13.13 = 13^5

Hence, 13.13.13.13.13 in exponential form is 13^5

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Answer:

Step-by-step explanation:

Below is the graphs of the given g(x) and p(x)

g(x) is green

p(x) is blue

The graph of g(x) is wider.

The graph of g(x) opens downward

Both have the axis of symmetry x = 0

The vertex of g(x) is (0, 7); the vertex of p(x) is (0, 0).

The graph of g(x) opens downward and the graph of p(x)  opens upward

The graph of g(x) is wider.

Answer:

My answer: B

Step-by-step explanation:

The probability mass function of random variable X which represents the number of blue marbles drawn in 2 draws with replacement.

X | P(X)

0 | 0.390625

1 | 0.46875

2 | 0.140625

The probability of drawing exactly one blue marble = 0.46875

Complete Question

A bag contains red and blue marbles, such that the probability of drawing a blue marble is 3/8. an experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. A random variable assigns the number of blue marbles to each outcome.

To write the Probabilty mass function, we have to establish that in two draws with replacement, the possible number of blue marbles that can be drawn is 0, 1 and 2.

Probability of drawing a blue marble = P(B) = (3/8)

Probability of not drawing a blue marble = P(B') = 1 - (3/8) = (5/8)

- Probability of drawing 0 blue marbles in 2 draws with replacement = P(B') × P(B') = (5/8) × (5/8) = (25/64) = 0.390625

- Probability of drawing one blue marble in 2 draws with replacement

= [P(B) × P(B')] + [P(B') × P(B)]

= (2) × (3/8) × (5/8) = (30/64) = (15/32) = 0.46875

- Probability of drawing two blue marble in 2 draws with replacement = P(B) × P(B)

= (3/8) × (3/8) = (9/64) = 0.140625

The probability mass function of random variable X which represents the number of blue marbles draan in 2 draws with replacement.

X | P(X)

0 | 0.390625

1 | 0.46875

2 | 0.140625

b) Probability of drawing one blue marble in 2 draws with replacement

= [P(B) × P(B')] + [P(B') × P(B)]

= (2) × (3/8) × (5/8) = (30/64) = (15/32) = 0.46875

So, B is the answer.

Answer: 8, 24

Step-by-step explanation:

Since the sum of two numbers is 32 and one number is 3 times as large as the other, the first number can be defined as x and the second number is 3x.

Divide 32 by (3+1) = 4 and you get 8, which is x.

The second number is 3(8) = 24.

Answer:

a=1.5, b= 3

Step-by-step explanation:

sum of all sides will give us perimeter. Therefore

2a+b+6a+2b+1+4a=28

12a+3b+1=28

12a+3b=27....eqn1

since t two sides of this isosceles triangle are equal:

2a+b=4a

2a=b

[tex]a=\frac{b}{2}[/tex]

substituting [tex]\frac{b}{2}[/tex][tex].[/tex] in the first equation whenever we encounter a we will have:

[tex]12(\frac{b}{2})+3b=27\\[/tex]

6b+3b=27

9b=27

b=3

therefore [tex]a= \frac{b}{2} =\frac{3}{2} =1\frac{1}{2} or 1.5[/tex]

The question is incomplete. Please find the full content below.

Which number produces a rational number multiplied by 0.5

(C) 2.22 produces a rational number multiplied by 0.5.

If a number can be expressed by p/q form where p and q are whole numbers and q does not equal to 0, is called a Rational number.

If a number cannot be expressed as above then that number is called Irrational Number.

In simple term, we can say that the never-ending decimal numbers and square roots of non perfect square numbers are Irrational Numbers.

Product of two rational numbers is always a rational and the product of one rational and one irrational is always an irrational number.

Here given that the number is 0.5 which is clearly a rational number.

In order to get a rational number, we have to multiply another rational number with that.

In the given choices,

[tex]\pi=3.14......[/tex]

is a never-ending decimal number that is irrational.

7 is not a perfect square so

[tex]\sqrt{7}[/tex]

is an irrational number.

2.020020002.... is also a never-ending decimal number hence it is irrational.

Only 2.22 is rational here.

So multiplication of 2.22 and 0.5 produces a rational number since the product of two rational numbers is always a rational number.

Hence option (C) is correct.

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Answer: y=kx/w^2

Step-by-step explanation:

y is directly proportional to x

y∝x        

y=kx

y inversely proportional to the square of w.

y ∝ (1/(w)^2)

y=k/w^2

y=kx/w^2

Answer:  Sample space:  {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG}

1. 8 outcomes in total

2. 1/8 or 0.125

3. 1/2 or 0.5

4. 1/2 or 0.5

5. 3/8 or 0.375

Step-by-step explanation:

1. As shown by the sample space and the tree diagram, there are 8 total possibilities.

2. There is only a 1/8 or 0.125 chance of there being all boys, which is BBB

3. There are 4 outcomes that allow the middle child to be a girl, and 4/8 = 1/2.  There will only be a girl middle child with BGB, GGG, BGG, and GGB.

4. We can think of at least as meaning no less than two boys, which includes two to three boys.  The only outcomes that have either two or three boys is BBB, BBG, BGB, GBB.  4/8 = 1/2.

5. We can think of at most as meaning no more than one girl.  The only outcomes that have only one girl are BBG, BGB, and GBB, which is 3/8.

The angle ∠4 of the given transversal shown in the diagram is gotten as; 26°.

The alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.

Now, we are told that ∠1 = 26° as seen in the attached diagram. However, it is clear that ∠2 is an alternate angle to ∠1. Thus, we can say that ∠2 = 26°.

Now, Corresponding angles are the pairs of angles that are found in the same relative position on different intersections.

From the diagram we see that ∠4 is a corresponding angle to ∠2. Thus;

∠4 = 26°.

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Answer:

I need to see the graph

No explanation

Answer:

  150 mph

Step-by-step explanation:

The relationship between time, speed, and distance is ...

  speed = distance/time

The trains have separated 750 miles in 5 hours, so their rate of separation is ...

  (750 mi)/(5 h) = 150 mi/h

The trains are separating at a speed of 150 mph.