Suppose that 10 fair coins are tossed. Find the numbers of ways of obtaining exactly 1 heads. Round the answer to the nearest whole number

Answer: 9/7 or -5/2

Step-by-step explanation:

We can only factorise quadratics if they're in the format ax^2 + bx + c

Re-arranging the equation gives 14x^2 + 17x - 45 = 0

Factorising this quadratic gives:

(7x - 9)(2x + 5) = 0

There are numerous ways to factorise quadratics, using a calculator or via alternate methods you may have learnt in class. (E.g. 2 numbers multiply to make (14 * -45) and add up to make (17).

This gives us our solutions.

x = 9/7 or x = -5/2

Answer:

See below.

Step-by-step explanation:

First, move all the terms to one side so we have only a zero on the right:

[tex]6x^2-17x+13=20x^2-32\\-14x^2-17x+45=0\\14x^2+17x-45=0[/tex]

(I divided everything by negative 1 in the third step. This is optional, but I like having the first term positive.)

Now, we just need to factor it. To factor, what you want to do is find two numbers a and b such that:

When a and b is multiplied together, they equal the first coefficient and constant multiplied together.

And when a and b is added together, they equal the second term.

In other words, we want to find two numbers that when multiplied equals 14(-45)=-630 and when added equals 17. Then, we can substitute this into the 17. You do this by guessing and checking. It's useful to have a calculator.

After a bit, you can find that 35 and -18 works. Thus:

[tex]14x^2+17x-45=0\\14x^2+35x-18x-45=0\\7x(2x+5)-9(2x+5)=0\\(7x-9)(2x+5)=0[/tex]

Now, the finish the problem, we just need to use the Zero Product Property and solve for x:

[tex]2x+5=0\\x=-5/2\\\\7x-9=0\\x=9/7[/tex]

Note: This only works for quadratics.

Answer:

Option A - There is sufficient evidence to conclude that the proportion of people wearing seat belts is less than 65%

Step-by-step explanation:

The police officers claim is that the proportion of people wearing seat belts is less than 65%.

Now, we are told that the p - value is 0.277.

In hypothesis, for a significance value of 0.05, if the P value is less than 0.05, we reject the null hypothesis and if P value is greater than or equal to 0.05, we fail to reject the null hypothesis.

Now, since the significance level is 5% = 0.05,we can see that the P-value is greater than the significance value of 0.05. Thus, we fail to reject the police claim that the proportion of people wearing seat belts is less than 65%.

So the correct option is A.

Answer:

x ≥ 2 or x ≤ -6

Step-by-step explanation:

4|x + 2| ≥ 16

|x + 2| ≥ 4

x + 2 ≥ 4 or  -(x + 2) ≥ 4

x ≥ 2 or x + 2 ≤ -4 → x ≤ -6

[tex]\text{Solve the absolute value}\\\\4|x+2|\geq 16\\\\\text{We can make this equation a lot simpler by dividing both sides by 4}\\\\|x+2|\geq4\\\\\text{According to the absolute value, there can be two outcomes. In this case,}\\\text{it would be either:}\\\\x+2\geq4\,\,or\,\,x+2\leq-4\\\\\text{Solve first outcome:}\\\\x+2\geq4\\\\\text{Subtract both sides by 2}\\\\x\geq2\\\\\text{Solve second outcome:}\\\\x+2\leq-4\\\\\text{Subtract 2 from both sides}\\\\x\leq-6\\\\[/tex]

[tex]\boxed{x\geq2\,\,or\,\,x\leq-6}[/tex]

Answer:

price per pound of apple = $1.25

price per pound of banana = $0.75

Step-by-step explanation:

Your first question is what value should you multiply the second equation by in order to eliminate the y terms.

The number should be 3.  Let us multiply the first equation by 2 and the second equation by 3 and see how y will be eliminated.

10x + 6y = 17...............(i)

9x + 6y = 15.75...........(ii)

10x - 9x  = x

6y - 6y = 0

17 - 15.75 = 1.25

x = 1.25

let us find y

10x + 6y = 17...............(i)

10(1.25) + 6y = 17

12.5  + 6y = 17

6y = 17 - 12.5

6y = 4.5

divide both  sides by 6

y = 4.5/6

y = 0.75

In order to eliminate y term from the system of equations we multiply equation 2 by -3.

The price per pound of apple is 1.25 dollars and the price per pound of bananas is 0.75 dollars.

Given equations,

[tex]5x + 3y = 8.5[/tex].........(1)

[tex]3x + 2y = 5.25[/tex].......(2)

Here x is the cost per  pound of apples, and y is the cost per pound of bananas.

According to the question, multiply the first equation by 2, we get

[tex]10x+6y=17[/tex].....(3)

So, in order to eliminate y term from the system of equations we multiply equation 2 by -3, we get

[tex]-9x-6y=15.75[/tex].....(4)

Now Adding (3) and (4) equation, we get

[tex]x=1.25[/tex]

Putting the above value of x in equation 3 we get,

[tex]10\times1.25+6y=17\\12.5+6y=17\\6y=17-12.5\\6y=4.5\\y=\frac{4.5}{6} \\y=0.75[/tex]

Hence the price per pound of apple is 1.25 dollars and the price per pound of bananas is 0.75 dollars.

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Answer:

The value of Chi-square test statistic is χ² = 5.75.

Step-by-step explanation:

The Chi-square Goodness of fit test will be used to determine whether the die is fair or not.

The hypothesis can be defined as follows:

H₀: The die is fair.

Hₐ: The die is not fair.

The Chi-square test statistic is given by:

[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}[/tex]

Consider the table attached below.

The value of Chi-square test statistic is χ² = 5.75.

Answer:

(A) As x -> -inf, y->-inf, and as x->inf, y->inf.

Step-by-step explanation:

All polynomial, of odd degree have extremities must point in opposite directions (one each of + and - infinity)

All even degree polynomials have extremities in the same direction, i.e. both towards +inf, or both towards -inf.

Since this is a cubic, so the extremities must point in opposite directions, so options B and D cannot apply.

Next, when the leading coefficient, the coefficient of ther term of the highest degree, namely 5x^3, positive, the graph will approach +infinity in the positive direction (and approach -infinity in the negative direction).

This eliminates option (C), and we see that option (A) satisfies all conditions.

When the leading coefficient is negative, it works the other way round.

Answer:

As x goes to -∞ y goes to -∞

As x goes to ∞ y goes to ∞

Step-by-step explanation:

We need to look at the dominate term

5x^3

As x goes to -∞

y  goes to 5 ( -∞)^3 = -∞

As x goes to -∞ y goes to -∞

As x goes to ∞

y  goes to 5 ( ∞)^3 = ∞

As x goes to ∞ y goes to ∞

Answer: [tex]\dfrac{1}{56}[/tex]

Step-by-step explanation:

Total horses = 6

Number of ways to choose top 3 finishers in order = 3! = 6

Number ways to select 3 horses out of 8 in order = [tex]^8P_3[/tex]  [By permutations]

[tex]=\dfrac{8!}{(8-3)!}=\dfrac{8!}{5!}=8\times7\times6=336[/tex]

Now, the probability that the gambler will win his bet =

[tex]\dfrac{\text{Number of ways to choose top 3 finishers }}{\text{Number ways to select 3 horses out of 8 in order}}[/tex]

[tex]=\dfrac{6}{336}\\\\=\dfrac{1}{56}[/tex]

Hence, the required probability =  [tex]\dfrac{1}{56}[/tex]

Answer:

x^2+(y+4)^2=25

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Step-by-step explanation:

Answer:

h = 109.9 in

Step-by-step explanation:

The above question can be solved using trigonometric ratio formula,

tan θ = opposite/adjacent

tan θ = tan 70° ≈ 2.7475

opposite = height of lamppost = h in

Adjacent = 40 in

Thus,

[tex] tan 70 = \frac{h}{40} [/tex]

[tex] 2.7475 = \frac{h}{40} [/tex]

Multiply both sides by 40 to solve for h

[tex] 40*2.7475 = h [/tex]

h = 109.9 inches

The height of the lamppost = h = 109.9 inches (to nearest tenth)

Answer:

we will fail to reject the null hypothesis and conclude that the return rate is less than​ 20%.

Step-by-step explanation:

We are given;

Sample size;n = 6970

Success rate;X = 1334/6970 = 0.1914

Now, we want to test the claim that the return rate is less than p = 0.2, hence the null and alternative hypothesis are respectively;

H0: μ < 0.2

Ha: μ ≥ 0.2

The standard deviation formula is;

σ = √(x(1 - x)/n)

σ = √(0.1914(1 - 0.1914)/6970)

σ = 0.004712

Now for the test statistic, formula is;

z = (x - μ)/σ

z = (0.1914 - 0.2)/0.004712

z = -1.825

From the a-distribution table attached, we have a value of 0.03362.

This p-value gotten from the z-table is more than the significance value of 0.01. Thus, we will fail to reject the null hypothesis and conclude that the return rate is less than​ 20%.

Answer:

Your answer is -3.5 which lies between -4 and -3.

The point R is halfway between the integers on the number line below and represents the number -3.5 .

Answer:

The final price to be paid after the 2% discount has been made will be $ 16,645.30.

Step-by-step explanation:

Since there is a 2% discount on the price of the Honda Shadow in the event that the dealer pays Honda within 15 days, and that after a rebate the price of the vehicle is $ 16,985, to obtain the value of the discount and the final amount to be paid must be calculated as follows:

16,985 x 2/100 = X

33,970 / 100 = X

339.70 = X

Thus, the discount to be made will be $ 339.70, with which the final price to be paid after the 2% discount has been made will be $ 16,645.30.

Answer: -4/3

Step-by-step explanation: To find the negative reciprocal of a fraction, all you have to do is flip the fraction and change the sign.

So the negative reciprocal of 3/4 is -4/3.

Answer:

t = kp, i think

Answer:

sin(O) = 2/sqrt(5)   or 2sqrt(1/5)

Step-by-step explanation:

using 1+cot^2(x) = csc^2(x)

we have, taking reciprocal on both sides,

sin(x) = 1/sqrt(1+cot^2(x)

= 1/sqrt(1+(-1/2)^2)

= 1/sqrt(5/4)

= 2/sqrt(5)   or 2sqrt(1/5)

Since angle x is in the second quadrant, sin(x) is positive.

Answer:

Step-by-step explanation:

the inequality represented by the graph is B

Plot the points

2x - 4/5y ≥ 3

y ≤ 2/5x - 3/2

x             y

0            -3/2

15/4        0

If the drawing is 5 inches tall and the ratio is 1:7, that means that 1 inch will be equal to 7 feet.

Height = 5 x 7 = 35 feet

Answer:

Aquarium dimensions:

x = 3,106 m

h = 6,22 m

C(min) = 1277,62 $

Step-by-step explanation: (INCOMPLETE QUESTION)

We have to assume:

The shape of the aquarium  (square base)

Let´s call "x" the side of the base, then h ( the heigh)

V(a) = x²*h          h = V(a)/x²      

Cost of Aquarium   C(a) = cost of the base (in stones) + 4* cost of one side (in glass)

C(a) = Area of the base *120 + 4*Area of one side*30

Area of the base is x²

Area of one side  is   x*h   or  x*V(a)/x²  

Area of one side is V(a)/x

C(x) = 120*x² + 4*30*60/x

C(x) = 120*x² +  7200/x

Taking derivatives on both sides of the equation we get

C´(x) = 2*120*x  - 7200/x²

C´(x) = 0 means    240 *x  - 7200/x² = 0

240*x³ - 7200 = 0

x³ = 7200/240

x = 3,106 m   and  h = 60 /x²     h =   6,22 m

and C (min) = 120*(3,106)³ - 7200 / 3,106

C(min) =  3595,72 - 2318,1

C(min) = 1277,62

Hey there! I'm happy to help!

We see that light travels 186,000 miles per second. How many miles is this per minute. Well, there are 60 seconds a minute, so we multiply by 60!

186,000×60=11160000

And there are 60 minutes in an hour, so we multiply by sixty again!

11160000×60=669600000

Now, we need to write this in scientific notation. To do this, we move the decimal back enough places to have a one digit number, and we multiply that one digit number by 10 to the power of how many places you moved the decimal back.

In the number 669600000 we can move the decimal point back 8 times which gives us 6.696 (we don't need the zeroes after a decimal) multiplied by 10 to the 8th power because we moved the decimal back eight places.

This can be written as 6.696×10^8, which is closest to the answer option 6.7×10^8 miles.

Have a wonderful day! :D

Answer:

First answer.

Step-by-step explanation:

Multiply everything by 10, to get rid of the decimals.

Answer:

Income after 20 years = 162550.01

Step-by-step explanation:

In cell B2, enter 90000

In cell B3, enter +B2*1.03

Copy cell B3 to cells B4:B22

Set number format for column B to 2 decimal places.

Read cell B22 = 162550.01

Income after 20 years = 162550.01

Their income after 20 years would be; 72,550 dollars.

Income tax is a tax applied on individuals or entities concerning income or profit earned by them.

The income after 20 years can easily be determine by using compounding

Thus the formula;

Future Value = Present Value (1 + I)^ 20

                     = 90,000 (1 + 0.03)^ 20

                     = 162,550 dollars

Income can be determing by subtracting Pv from Fv i.e

Income = 162,550 - 90,000 = 72,550

Calculation on excel sheet;

      A                        B                  C                         D                

1     90,000             1.03            = A1 x1.03        = C1-A1        

2      = D1                  1.03           = A2 x 1.03       = C2-A2

20    = D19               1.03           = A20 x 1.03      = A20 - C20

Thus, In work sheet colunm D will show the income on investment.

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Answer:

A =625 ft^2

Step-by-step explanation:

The perimeter of a square is

P = 4s where s is the side length

100 =4s

Divide each side by 4

100/4 = 4s/4

25 = s

A = s^2 for a square

A = 25^2

A =625

It would have to have a positive slope and the bottom needs to be shaded, since -2y is negative it means we will be dividing by a negative. The inequality sign will switch.

also if it is < then the line is dotted, if it’s the “greater or equal to sign” then the line is not dotted.

dunno if I explained it very well

The shaded region common to both the inequalities represents the solution set of the inequality → x - 2y² < 12.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

Given is the inequality as -

x - 2y² < 12

The given inequality is -

x - 2y² < 12

2y² - x < - 12

2y² < x - 12

y² < (x/2) - 6

[tex]$y < \pm\sqrt{\frac{x}{2}-6 }[/tex]

[tex]$y < \sqrt{\frac{x}{2}-6 }[/tex]        

and

[tex]$y < -\sqrt{\frac{x}{2}-6 }[/tex]

Refer to the graph of the equation attached. The shaded region common to both the inequalities represents the solution set of the inequality.

Therefore, the shaded region common to both the inequalities represents the solution set of the inequality → x - 2y² < 12.

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Step-by-step explanation:

x² + 11x + 121/4 = 125/4

x² + 11x + 121/4 - 125/4 = 0

x² + 11x - 1 = 0

after that apply quadratic formula

x = ( -b + or - √b² - 4ac ) ÷ 2a

x = (-11 + or - √11² - 4×1×-1 ) ÷ 2×1

+ = 0.090169....

- = -11.090168.....

x = 0.090 or x = -11.09

Answer:

31

Step-by-step explanation:

The computation of eighth graders take only a current events class and not a foreign language class is shown below:-

We will assume the x that shows the number of students which we will take  both languages

So, the equation will be

70 + 54 - x = 93

-x = 93 - 124

x =  31 students

So the number of eighth graders only take a current event class is

= 70 - 39

= 31 students

Answer: B

Step-by-step explanation:

Because of Supplementary Angles, we know that the two angles in the right side of the equation add up to 90.

Hope it helps <3

Answer:

32.5%

Step-by-step explanation:

0.325 x 100%=32.5%

Answer:

20*

Step-by-step explanation:

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Answer:

See the attachment for sketch

Thr region is unbounded

DNE

Step-by-step explanation:

y≤ -2x + 10

The inequality is a straight line and region marked by the inequality. It has no boundaries. The boundaries extend to infinity. So the region is unbounded. Unbounded region has no corner points.