Question 19 of 25
f(x)=√x-6. Find the inverse of f(x) and its domain.

Answer: B

Step-by-step explanation:

The parabola has an open hole at x=2, and the line has a closed hole at x=2.

This means the top part of the function should have domain [tex]x < 2[/tex], and the second part of the function should have domain [tex]x \geq 2[/tex].

This eliminates everything except for B.

The bond price 101.78

What is the price of a bond?

A bond price is the present value of its future cash flows discounted at the yield to maturity which is the appropriate discount rate.

Specifically, the bond price is the present value of annual coupons for 2 two years and the face value discounted at the 8% yield to maturity.

We can determine the bond price using the present value formula of a single cash flow for all cash flows.

PV=FV/(1+r)^N

FV=future cash flow(annual coupons for 2 years and face value)

annual coupon=face value*coupon rate

face value=100

coupon rate=9%

annual coupon=100*9%

annual coupon=9

r=discount rate=8%

N=year of cash flows, 1 for year 1 and 2 for year 2

bond price=9/(1+8%)^1+9/(1+8%)^2+100/(1+8%)^2

bond price= 101.78

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Answer:

2=1289/17

Step-by-step explanation:

use the given functions to set up and simplify 2

Answer:

5.9512

Step-by-step explanation:

1. Convert the percentage to decimal

8% = 8/100 = 0.08

2. Multiply the decimal by the quantity to be extracted

(0.08)(74.39) = 5.9512

Hope this helps

Answer:

Division property of inequality

Step-by-step explanation:

24<4x

24/4<4x/4

6<x

(1/4)×24 < (1/4) ×4x

6 < x

The given expression is a perfect square trinomial.

Here we have the expression:

[tex](x^2 - 16)^2[/tex]

Notice that we can rewrite it as:

[tex](x^2 - 4^2)^2[/tex]

Then we can see that inside the parenthesis we have a difference of squares, but it is squared, so if we define:

[tex]x^2 = a\\4^2 = b[/tex]

We will have:

[tex](a - b)^2 = a^2 + -2ab + b^2 = (x^2)^2 - 2*(4^2)*(x^2) + (4^2)^2[/tex]

Which is in fact, a perfect square trinomial.

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Answer:

35 inches

Step-by-step explanation:

7 x 5 = 35 lol

The number which represents a change in the amount of thread on the spool exists 35 inches.

In mathematics, an operation exists as a process that takes zero or more input values to a well-defined output value.

Given: Length of thread a student cuts = 5 inches

Total number of students that cut thread = 7

Length of thread a student cuts = 5 inches

Length of thread 7 student cuts = 5 [tex]*[/tex] 7 = 35 inches

The negative length that 7 students cut from the spool exists the number that represents a change in the amount of thread.

The number which represents a change in the amount of thread on the spool exists 35 inches.

Therefore, the correct is option b) 35 inches.

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The roots of the equation is x = 4.56 OR x = 0.44

From the question, we are to determine the roots of the given equation

The given equation is

x² -5x +2 = 0

Using the formula method,

[tex]x =\frac{-b \pm \sqrt{b^{2}-4ac } }{2a}[/tex]

In the given equation,

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

Putting the values into the formula,

[tex]x =\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(2) } }{2(1)}[/tex]

[tex]x =\frac{5 \pm \sqrt{25-8} }{2}[/tex]

[tex]x =\frac{5 \pm \sqrt{17} }{2}[/tex]

[tex]x =\frac{5 + \sqrt{17} }{2}[/tex] OR [tex]x =\frac{5 - \sqrt{17} }{2}[/tex]

[tex]x =\frac{5 + 4.12}{2}[/tex] OR [tex]x =\frac{5 - 4.12}{2}[/tex]

[tex]x =\frac{9.12}{2}[/tex] OR [tex]x =\frac{0.88}{2}[/tex]

x = 4.56 OR x = 0.44

Hence, the roots of the equation is x = 4.56 OR x = 0.44

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Answer:

x + 4

Step-by-step explanation:

Sine the bases are all the same, I can write the equation:

3x+4 = (x-2) 2^3  When we are adding with logs, that means to multiple.  Also, when we have 3 log 2, that can be written as 2^3 or 8 (2x2x2)

3x+4=(x-2)8

3x+4 = 8x-16

4=5x-16

20 = 5x

4=x

The radius of the given cylinder with a volume of 200 mm³ and a height of 17mm is: 1.93 mm.

The formula for finding the volume of any cylinder is given as: πr²h, where r is the radius and h is the height of the cylinder.

Given the following:

Volume = 200 mm³

Height (h) = 17 mm

Radius (r) = ?

Plug the values into the formula for volume

πr²(17) = 200

r² = 200/17π

r² = 3.74

r = 1.93 mm

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The 1st table represents a linear as well as the quadratic relationship, the 2nd table represents neither and the 3rd table also represents neither relationship.

Hence, the 1st table represents a linear as well as a quadratic relationship, the 2nd table represents neither and the 3rd table also represents neither relationship.

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$1045 was invested at the interest rate 6% whereas $1,995 was invested at 14%

How is interest computed?

Interest is determined as the amount invested multiplied by the interest rate.

Let Y be the amount invested at 6%

Interest=Y*6%

Interest=0.06Y

The amount invested at 14%, which is $950 more , is Y+950

Interest=(Y+950)*14%

Interest=0.14Y+133

Total interest =0.06Y+0.14Y+133

Note that total interest is 342

342=0.06Y+0.14Y+133

342=0.20Y+133

342-133=0.20Y

209=0.20Y

Y=209/0.20

Y=$1,045(amount invested at 6%)

Amount invested at 14%=$1,045+$950

Amount invested at 14%=$1,995

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The function P(x), for the price of the materials for the pen is 4.18(800/x + x) + 38.

Based on the information, the function P(x), for the price of the materials for the pen will be:

P(x) = 4.18 (2 × 400/x + x) + 38

= 4.18(800/x + x) + 38.

The dimensions will be:

We'll differentiate the function which will give 20✓2. Therefore, the value for x will be 20✓2 which is 28.28 feet and that of y will be 10✓2 which is 14.14 feet.

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Answer:

males = 7

females = 43

Step-by-step explanation:

whilst it may seem intuitive to simply subtract 36 from 50, it is not saying "there are 36 males, how many females?" but instead, "the difference between the number of males and females is 36".

You can solve this equation most easily algebraically. For example:

Number of males = x

number of females = y

the question states that the total number of people = 50

therefore we can say that the total number of males (x) + the total number of females (y) = 50 people

therefore: x + y = 50

similarly, the question says that the number of males (x) + 36 = the total number of females (y)

therefore: x + 36 = y

we now have two equations:

x + y = 50

x + 36 = y

whilst both equations have two unknowns (x and y), therefore we can't simple solve for x or y, with the combination, we can see a pattern.

focusing on the second equation: x + 36 = y

we can add x to both sides, because you can pretty much do anything to the equation as long as you do it to both sides.

x + 36 + x = y + x

now this may seem very random, but you now see that one side of the equation equals y + x, and remember from the other equation, x + y = 50. Therefore we can substitute x + y in the second equation for 50.

our two equations:

x + 36 + x = y + x

x + y = 50

therefore:

x + 36 + x = 50

for the sake of clarity, we can combine like terms...

x + x = 2x

therefore:

x + 36 + x = 50

2x + 36 = 50

solve for x by subtracting 36 from both sides, then dividing both sides by 2

2x + 36 - 36 = 50 - 36

2x = 14

2x / 2 = 14 / 2

x = 7

now remember:

Number of males = 7 (we now know x = 7)

now that we've solved for x, we can go back to our original equation:

x + 36 = y

and substitute x...

7 + 36 = y

43 = y

Now remember:

Number of females = 43 (we now know y = 43)

therefore there are 7 males and 43 females. we can proof this by adding 7 and 43, and you'll see you reach 50, which is the correct total number of people.

hope this helps :)

Answer: B

Step-by-step explanation: Since x is less than 7, the graph would be all real numbers that are less than 7, so the arrow would be on the left.

Also, since x is not 7 itself (not less than or equal to), the dot cannot be a full dot. Thus, the dot must be open (or curved in some textbooks) to indicate x is not apart of 7 but less than 7.

Hope this helped!

The ways to illustrate the shapes are given.

11.  In each new figure, one vertex is introduced, and each vertex is joined to each other vertex.

12.  In each new figure, 2 rows and 1 column are introduced, and the shading at the corner moves 90 degrees clockwise.

13.  In each new figure, one row and one column are introduced, and exactly half of the rectangles are shaded.

14.  In each new figure, except at the bottom vertex, two perpendicular lines are introduced at the remaining vertices.

15.  In each new figure, one inverted white triangle is inscribed in the orange triangle.

16.  The number of squares increases in the pattern. There are blue circles inscribed in one diagonal square and there are yellow circles inscribed in the remaining squares. Also, the blue circles in the diagonal alternate.

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The answer choice which explains that the three segments cannot be used to construct a triangle is; AC + CB < AB.

Since, It follows from the triangle inequalities theorem that sum of the side lengths of any two sides of a triangle is greater than the length of the third side.

Hence, since the sum of sides AC + CB is less than AB, it follows that the required inequality is; AC + CB < AB.

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Work Shown:

(arc YZ + arc XU)/2 = angle YVZ

(arc YZ + 38)/2 = 90

arc YZ + 38 = 90*2

arc YZ + 38 = 180

arc YZ = 180 - 38

arc YZ = 142

Answer:

13 pieces

Step-by-step explanation:

First we convert 4m into cm :

1m = 100cm

4m = 400cm

Now we need to figure out how many 30s go into 400 :

400 ÷ 30 = 13 remainder 10

So 13 pieces can be cut from the ribbon

Hope this helped and have a good day  

Answer:

13

Step-by-step explanation:

4 meters is equal to 400 centimeters.

400/30 =  13 1/3

You don't want partial pieces, so your answer is 13

Answer: A

Step-by-step explanation:

The test statistic is 27.8484, the p-value is 0, and the final conclusion is that the null hypothesis H is rejected.

Given that 914 babies were born to parents who used the new method, and 877 of them were girls, the significance level to test the claim that the new method is effective in increasing the likelihood of a baby being a girl, is 0.01.

The following information is provided: the sample size is N = 914, the number of favorable cases is X = 877, and the sampling ratio is

pˉ = X / N

Pˉ = 877/914

pˉ = 0.9595 and the significance level is α = 0.01

(a) Hypothesis Zero and Alternative

The following null and alternative hypotheses should be tested:

null: p = 0.5

Alternative: p> 0.5

This is equivalent to a right-tailed test, which requires a z-test for a proportion of the population.

(b) Critical Value

Based on the information provided, the significance level is α = 0.01, so the critical value for this right-tailed test is Zc = 2.3263. This can be found using Excel or the Z distribution table. Region of rejection

The rejection area for this test on the right side is Z> 2.3263

Test statistics

The z-statistic is calculated as follows:

[tex]\begin{aligned}Z&=\frac{\bar{p}-p}{\sqrt{\frac{p(1-p)}{n}}}\\ &=\frac{0.9595-0.50}{\sqrt{\frac{0.5(1-0.5)}{914}}}\\ &=\frac{0.4595}{0.0165}\\ &=27.8484\end[/tex]

(c) The p-value

The p-value is the probability that the sample results are extreme or more extreme than the sample results obtained, assuming the null hypothesis is true. In this case,

the p-value is p = P (Z> 27.8484) = 0

(d) The decision on the null hypothesis

Using the traditional method

Since we observe that Z = 27.8484> Zc = 2.3263, we conclude that the null hypothesis is rejected.

Using the p-value method

Using the approximation of the P-value: the p-value is p = 0, and since p = 0≤0.01 we conclude that the null hypothesis is rejected.

(e) Conclusion

It is concluded that the null hypothesis H is rejected. Therefore, there is sufficient evidence to state that the population proportion p is greater than 0.5, at the significance level of 0.01.

Hence, for 914 babies born to parents using the new method, of which 877 were girls, the test statistic is 27.8484, the p-value is 0, and the final conclusion is that the null hypothesis is rejected.

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The original price of concert tickets before the addition of service fee is 42.93

45.50 = x + (6% of x)

45.50 = x + (0.06 × x)

45.50 = x + 0.06x

45.50 = 1.06x

x = 45.50/1.06

x = 42.9245283018867

Approximately,

x = 42.93

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The graph that best corresponds to the situation is graph 4; option C

Number of pages read is on the y - axis

Time taken is on the x - axis

Therefore, graph 4 represent the situation

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Answer:

a

Step-by-step explanation:

the median is the middle value of the data arranged in ascending order

5 , 6 , 6 , 7 , 8 , 10 , 12 , 13 , 14 ← ascending order

                    ↑ middle value

median = 8

Answer:

8

Step-by-step explanation:

To find the median, we must put all of the data in order and select the middle number. Since there are 9 terms, the median will be the 5th term.

5, 6, 6, 7, 8, 10, 12, 13, 14

Brainliest, please :)

Answer:

960 feet

Step-by-step explanation:

30×6=180

180×2=360

50×6=300

300×2=600

360+600=960

In Economics, profit can be defined as a measure of the amount of money generated when the selling price is deducted from the cost price of a good or service, which is usually provided by producers.

This ultimately implies that, all producers of any product generally work to maximize their profits and make them as large as possible, in order to enable them break even and successful.

Based on the information provided, we can logically deduce that this function has its roots at x = 0 and x = 26 and its vertex is a minimum. Thus, this quadratic function which describes the relationship between the number of products produced and the overall profit margin is an increasing function:

Therefore, once they hit 26 items they break even again. The worst case scenario is that they produce 13 items, as they will have a profit of -50 dollars because the minimum point is at (18, -35). Also, the first root tells us that the profit will be 0 when 0 products are sold.

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Answer:

Step-by-step explanation:

Using a discrete distribution, the expected value for this game is of -$1.298, which means that each time he plays, he is expected to lose $1.298.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

Considering the situation described in this problem, the distribution for the earnings is given as follows:

Hence the expected value is given as follows:

[tex]E(X) = 700\frac{1}{1000} - 2\frac{999}{1000} = \frac{700 - 2(999)}{1000} = -1.298[/tex]

The expected value for this game is of -$1.298, which means that each time he plays, he is expected to lose $1.298.

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The price of the chairs and the quantity that maximizes profit is to sell 45 chairs at $75 each.

Given that a furniture store can sell 40 chairs per week at a price of $80 each, and the manager estimates that for each and $5 price reduction, she can sell five more chairs per week, and the chairs cost the store $30 each, to determine the price of the chairs and the quantity that maximize profit, the following calculation must be made:

Therefore, the price of the chairs and the quantity that maximizes profit is to sell 45 chairs at $75 each.

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The inequality which shows all possible values of m is; m < 9.

It follows from the task content that the variable in discuss, m is described as less than 9.

On this note, the most appropriate inequality to represent the set of all possible values of m is; m < 9.

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