In horse race betting, a trifecta bet is one in which you try to pick which horses will finish first, second, and third, in the correct order. If 8 horses are running in a race and you randomly place a trifecta bet, what is the probability of winning the bet

Answer:

a = 0

Step-by-step explanation:

p(x) = ax²+x+1

Let x+1 = 0 => x = -1

Putting in the above polynomial

=> p(-1) = a(-1)^2+(-1)+1

By Remainder Theorem, Remainder will be zero

=> 0 = a(1) -1+1

=> 0 = a

OR

=> a = 0

Answer:

Step-by-step explanation:

Factors are what we can multiply to get the number.

x² + x + 1

Factor the polynomial.

x(x+1) + 1

ax² + x = x(x + 1)

ax² + x = x² + x

[tex]a=\frac{x^2 +x}{x^2 +x}[/tex]

a = 1

Answer:

49)   [tex]12\,b^4[/tex]

50)   [tex]200\,x^6[/tex]

Step-by-step explanation:

Use the properties of exponent to reduce this expressions:

a)  [tex]3\,b\,*\,4 \,b^3=(3\,*\,4)\,(b\,*\,b^3)=12\,b^{(1+3)}=12\,b^4[/tex]

b)  [tex]5\,x^2\,*\,8\,x\,5\,*\,x^3=(5\,*\,8\,*\,5)\,(x^2\,*\,x\,*\,x^3)=200\,x^{(2+1+3)}= 200\,x^6[/tex]

Answer:

Step-by-step explanation:

Fog=2(g)+1

2(3x+2+4)+1

2{3x+6)+1

6x+12+1

=6x+13

Fog(-2)=6(-2)+13

-12+13

=1

Gof=3(f)+2+4

=3(2x+1)+6

6x+3+6

=6x+9

Gof(-2)=6(-2)+9

-12+9

=-3

Answer:

Step-by-step explanation:

The data given are;

sample size n = 100

sample mean x = 3.1

standard deviation σ = 0.5

mean = 3

The value for Z can be determined by using the formula:

[tex]Z = \dfrac{x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \dfrac{3.1 - 3.00}{\dfrac{0.5}{\sqrt{100}}}[/tex]

[tex]Z = \dfrac{0.1}{\dfrac{0.5}{10}}}[/tex]

Z = 0.2

At 95% Confidence interval, level of significance ∝ = 0.05

From the z table ;P- value for the test statistics at ∝ = 0.05

P = 0.0228

We can see that the P-value is < ∝

Decision Rule:

Reject the null hypothesis [tex]H_o[/tex] if P-value is less than ∝

Conclusion:

At 0.05 level of significance; we conclude that the mean of the population is significantly > 3 min

Answer:

(A)

[tex]N = -b = -(-13) = 13\\\\[/tex]

[tex]D =b^2 -4ac = (-13)^2 - 4(6)(5) = 169- 120 = 49[/tex]

[tex]M = 2a = 2(6) = 12[/tex]

(B)

[tex]$ x = (\frac{5}{3} , \: \frac{1}{2}) $[/tex]

Step-by-step explanation:

The given equation is

[tex]6x^2 - 13x + 5 = 0[/tex]

The solution is of the form as given by

[tex]$x=\frac{N\pm\sqrt{D}}{M}$[/tex]

(A) Use the quadratic formula to solve this equation and find the appropriate integer values of N, M and D. Do not worry about simplifying the VD yet in this part of the problem.

The quadratic formula is given by

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

The equations of N, M and D are

[tex]N = -b[/tex]

[tex]D =b^2 -4ac[/tex]

[tex]M = 2a[/tex]

The values of a, b and c are

[tex]a = 6 \\\\b = -13 \\\\c = 5[/tex]

So,

[tex]N = -b = -(-13) = 13\\\\[/tex]

[tex]D =b^2 -4ac = (-13)^2 - 4(6)(5) = 169- 120 = 49[/tex]

[tex]M = 2a = 2(6) = 12[/tex]

(B) Now simplify the radical and the resulting solutions. Enter your answers as a list of integers or reduced fractions, separated with commas. Example: -5/2-3/4

N = 13

D = 49

M = 12

[tex]$x=\frac{13\pm\sqrt{49}}{12}$[/tex]

[tex]$x=\frac{13\pm7}{12}$[/tex]

[tex]$ x=\frac{13+7}{12} $[/tex]  and [tex]$ x=\frac{13-7}{12} $[/tex]

[tex]$ x=\frac{20}{12} $[/tex]  and [tex]$ x=\frac{6}{12} $[/tex]

[tex]$ x=\frac{5}{3} $[/tex]  and [tex]$ x=\frac{1}{2} $[/tex]

[tex]$ x = (\frac{5}{3} , \: \frac{1}{2}) $[/tex]

Answer:

x < 4 or x = ( -∞, 4)

Step-by-step explanation:

or

[tex]\text{Solve the inequality for x:}\\\\6x-5<2x+11\\\\\text{Subtract 2x from both sides}\\\\4x-5<11\\\\\text{Add 5 to both sides}\\\\4x<16\\\\\text{Divide both sides by 4}\\\\\boxed{x<4}[/tex]

Answer:

(3, 1)

Step-by-step explanation:

Plug-in points and see which one works. (x, y). <=  means less than or equal to.

Answer:

D. (3,1) is the correct answer

Step-by-step explanation: Just graph this question on a graph, and you will find that (3,1) is in the shaded region, which means it is part of the solution

Answer:

g ( x ) = 4x^2 + 10

Step-by-step explanation:

Solution:-

The translation of a function f ( x ) in the cartesian coordinate domain can be done by following the given guidelines:

Translation guidelines

    Horizontal shifts

  Vertical shifts

   General shift ( Horizontal and Vertical shift )

               f ( x ) - > f ( x ± a ) ± b

We are given a function f ( x ) which is to be translated vertically upward 4 units. We will use the guidelines for Vertical shifts, where in this case the magnitude of b = 4.

                        f ( x ) = 4x^2 + 6

                        f ( x ) - > f ( x ) + b              

                        g ( x ) = f ( x ) + 4

                        g ( x ) = 4x^2 + 6 + 4

                        g ( x ) = 4x^2 + 10   ... Answer

Answer:

264 degree angle

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Any point (x, y) on the parabola is equidistant from the focus and the directrix.

Using the distance formula

[tex]\sqrt{(x-3)^2+(y-1)^2}[/tex] = | y - 3 | ← square both sides

(x - 3)² + (y - 1)² = (y - 3)² ← expand the y- factors

(x - 3)² + y² - 2y + 1 = y² - 6y + 9 ← subtract y² - 2y + 1 from both sides

(x - 3)² = - 4y + 8 ( subtract 8 from both sides )

(x - 3)² - 8 = - 4y ( divide both sides by - 4 )

- [tex]\frac{1}{4}[/tex] (x - 3)² + 2 = y, that is

y = - [tex]\frac{1}{4}[/tex] (x - 3)² + 2 → C

Answer:

Step-by-step explanation:

C) y = –1∕4 (x – 3)^2 + 2

Answer:

[tex]Total\ Selection = 30\ ways[/tex]

Step-by-step explanation:

Given

Girls = 3

Boys = 5

Required

How many ways can 2 boys and girls be chosen?

The keyword in the question is chosen;

This implies combination and will be calculated as thus;

[tex]Selection =\ ^nC_r = \frac{n!}{(n-r)!r!}[/tex]

For Boys;

n = 5 and r = 2

[tex]Selection =\ ^5C_2[/tex]

[tex]Selection = \frac{5!}{(5-2)!2!}[/tex]

[tex]Selection = \frac{5!}{3!2!}[/tex]

[tex]Selection = \frac{5 * 4 * 3!}{3!*2 * 1}[/tex]

[tex]Selection = \frac{20}{2}[/tex]

[tex]Selection = 10[/tex]

For Girls;

n = 3 and r = 2

[tex]Selection =\ ^3C_2[/tex]

[tex]Selection = \frac{3!}{(3-2)!2!}[/tex]

[tex]Selection = \frac{3!}{1!2!}[/tex]

[tex]Selection = \frac{3 * 2!}{1 *2!}[/tex]

[tex]Selection = \frac{3}{1}[/tex]

[tex]Selection = 3[/tex]

Total Selection is calculated as thus;

[tex]Total\ Selection = Boys\ Selection * Girls\ Selection[/tex]

[tex]Total\ Selection = 10 * 3[/tex]

[tex]Total\ Selection = 30\ ways[/tex]

Answer:

P(X' < 4265) = 0.9418

Step-by-step explanation:

Due to the fact that the population is normal, the distribution of the sample mean of 40 cars is;

X' = (x1 + x2 + x3....... + x40)/40

We are given;

Normal mean;μ = 4178 miles

Variance = 124,609

Standard deviation; σ = √variance = √124609 = 353

Formula for standard error of mean = σ/√n = 353/√40 = 55.814

So from the formula;

z = (x - μ)/(σ/√n)

So for P(X' < 4265) we have;

z-value of P(X' < 4265) = (4265 - 4178)/55.814 ≈ 1.56

From the z-table attached, we have for P(z < 1.56) = 0.94179

Approximating to 4 decimal places gives 0.9418

Answer: 4

Step-by-step explanation:

Because %s can be expressed as fractions over 100, because 90 is 70% of x, 70% is 70% of 100.  Thus, 90/x = 70/100.

Hope it helps <3

Answer:

4

Step-by-step explanation:

90 is 70% of x.

90 = 70% × x

90 = 70/100x

Divide both sides by x.

90/x = 70/100

Answer:

Hey there!

This question is basically asking for the least common multiple, or LCM of the three numbers.

If it is a multiple of 10, it has to be a multiple of 5. Thus, the only thing we need to do now, is find the LCM of 10 and 7, which is 70.

Thus, your answer is 70.

Hope this helps :)

Answer:

I think it is 70.

Step-by-step explanation:

I think that is the Lowest common Multiple of 5, 7 and 10:

10 = 2*5

7 = 7

5 = 5

So the LCM is 2 * 5 * 7 = 70.

Answer:

There are 23 people in line at 6:00 A.M

Step-by-step explanation:

When you plug in h=1, we get 23 people

h corresponds with the time 6:00 am, as a result there are 23 people in line

The equation represents how many people will come as the hour increases.

23 represents the initial amount of people in line.

(got this from Khan academy too:))

Answer:

49145 years

Step-by-step explanation:

In a certain country the life expectancy for women in 1990 was 45 and in 2000 it was 85?years.

Assuming that life expectancy between 2000 and 2100 increases by the same percentage as it did between 1900 and 2000,what will life expectancy be for women in 2100?

In 10 years, the expectancy increased by 85/45 = 17/9

between 2000 and 2100, it will increas by 10 time 10 years, so expected expectancy is  [tex]85*(\frac{85}{45})^{10} = 49145[/tex]  years

The life expectancy for women will be 49145 years when It will increase by ten times between 2000 and 2100.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ  in mathematics, where x is the independent variable

In one country, women's life expectancy was 45 years in 1990 and 85 years in 2000.

Assuming that life expectancy grows by the same proportion between 2000 and 2100 as it did between 1900 and 2000, we have to determine the life would  expectancy for women in 2100

Over a ten-year period, life expectancy rose by 85/45 = 17/9.

It will increase by ten times between 2000 and 2100, therefore the anticipated life expectancy will be

⇒ 85×(85/45)¹⁰

⇒ 85×(1.88)¹⁰

⇒ 49145 years

Hence, the life expectancy for women will be 49145 years

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Answer:

Inequality:  [tex]1558 + 60 x \geq 2158[/tex]

Number of Weeks:  [tex]x \geq 10[/tex]

Step-by-step explanation:

Given

[tex]Initial\ Savings = \$1558[/tex]

[tex]Amount\ Needed = \$2158[/tex]

[tex]Additional\ Savings = \$60\ weekly[/tex]

Required

Represent this using an inequality

Represent the number of weeks as x;

This implies that, She'll save $60 * x in x weeks

Her total savings after x weeks would be

[tex]Initial\ Savings + 60 * x[/tex]

From the question, we understand that she needs at least 2158;

Mathematically, this can be represented as (greater than or equal to 2158)

[tex]\geq 2158[/tex]

Bringing the two expressions together;

[tex]Initial\ Savings + 60 * x \geq 2158[/tex]

Substitute 1558 for Initial Savings

[tex]1558 + 60 * x \geq 2158[/tex]

[tex]1558 + 60 x \geq 2158[/tex]

Hence, the inequality that represents the situation is [tex]1558 + 60 x \geq 2158[/tex]

Solving further for x (number of weeks)

[tex]1558 + 60 x \geq 2158[/tex]

Subtract 1558 from both sides

[tex]1558- 1558 + 60 x \geq 2158 - 1558[/tex]

[tex]60x \geq 600[/tex]

Divide both sides by 60

[tex]\frac{60x}{60} \geq \frac{600}{60}[/tex]

[tex]x \geq 10[/tex]

This means that she needs to save $60 for at least 10 weeks

Answer:

Its the first one

Step-by-step explanation:

I just did it lol

Answer:

$252

Step-by-step explanation:

This is quite a neat question, with no fixed equation. Given that each person gives the other two enough money to double their cash, if Toy had 36 dollars beginning, and 36 at the end - presumably the cash of each person, ( their starting and original ) should be the same as well. Respectively each should be a multiple of 36 dollars.

Jan's " give away " = Ami + 36, Jan - 108, Toy + 72

Toy's " give away " = Ami + 72, Jan + 36, Toy - 108

Therefore, we can conclude that Ami = 144 at the start, presuming he gave away 108 dollars, with a remaining 36. Jan, having 144 dollars ( after having his 72 dollars doubled by Ami ) gives 36 to Ami to double his amount, and 72 to double Toy's doubled amount, remaining with 36 dollars. Now Ami has 72 dollars, Jan has 36, and Toy has 144. Then, Toy double's Ami and Jan's amount, giving away 72 and 36 dollars, remaining with 36 dollars himself. Therefore, Ami has 144 dollars, Jan has 72 dollars, and Toy has 36 dollars both at the beginning and end.

144 + 72 + 36 = 252 dollars ( in total )

Answer:

answer is 252

Step-by-step explanation:

Good luck :)

Step-by-step explanation:

Let us assume that 1/2+root 3 is rational . So 1/2+root 3 = a/b where a and b are irrationals. since rhs is a rational number root 3 should be also rational .

Answer:

x² + x - 72 = 0 can be factored into (x - 8)(x + 9) = 0 to find your answer.

Step-by-step explanation:

Step 1: Distribute x

x² + x = 72

Step 2: Move 72 over

x² + x - 72 = 0

Step 3: Factor

(x - 8)(x + 9) = 0

Step 4: Find roots

x - 8 = 0

x = 8

x + 9 = 0

x = -9

Answer:

x² + x - 72 = 0 ⇒ (x - 8)(x + 9) = 0

Step-by-step explanation:

Let the first consecutive integer be x.

Let the second consecutive integer be x+1.

The product of the two consecutive integers is 72.

x(x + 1) = 72

x² + x = 72

Subtracting 72 from both sides.

x² + x - 72 = 0

Factor left side of the equation.

(x - 8)(x + 9) = 0

Set factors equal to 0.

x - 8 = 0

x = 8

x + 9 = 0

x = -9

8 and -9 are not consecutive integers.

Try 8 and 9 to check.

x = 8

x + 1 = 9

x(x+1) = 72

8(9) = 72

72 = 72

True!

The two consecutive integers are 8 and 9.

Answer:

Step-by-step explanation:

Given,

Perpendicular ( p ) = 9x

Base ( b ) = 10

Hypotenuse ( h ) = x + 10

Now, let's find the value of x

Using Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

Plug the values

[tex] {(x + 10)}^{2} = {(9x)}^{2} + {(10)}^{2} [/tex]

Using [tex] {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex] , expand the expression

[tex] {x}^{2} + 20x + 100 = {(9x)}^{2} + {10}^{2} [/tex]

To raise a product to a power , raise each factor to that power

[tex] {x}^{2} + 20x + 100 = 81 {x}^{2} + {10}^{2} [/tex]

Evaluate the power

[tex] {x}^{2} + 20x + 100 = 81 {x}^{2} + 100[/tex]

Cancel equal terms on both sides of the equation

[tex] {x}^{2} + 20x = 81 {x}^{2} [/tex]

Move x² to R.H.S and change its sign

[tex]20x = 81 {x}^{2} - {x}^{2} [/tex]

Calculate

[tex]20x = 80 {x}^{2} [/tex]

Swap both sides of the equation and cancel both on both sides

[tex]80x = 20[/tex]

Divide both sides of the equation by 80

[tex] \frac{80x}{80} = \frac{20}{80} [/tex]

Calculate

[tex]x = \frac{20}{80} [/tex]

Reduce the numbers with 20

[tex]x = \frac{1}{4} [/tex]

The value of X is [tex] \frac{1}{4} [/tex]

Now, let's replace the value of x to find the approximate value of hypotenuse

Hypotenuse = [tex] \frac{1}{4} + 10[/tex]

Write all numerators above the common denominator

[tex] \frac{1 + 40}{4} [/tex]

Add the numbers

[tex] \frac{41}{4} [/tex]

[tex] = 10.25[/tex] inches

Hope this helps..

best regards!!

Answer:

10.25

Step-by-step explanation:

because I said so ya skoozie

Answer:

Step-by-step explanation:

f(x)=4x+5

g(x)=6x+4,

first: (f*g)=(4x+5) (6x+4)=24x²+46x+20

next:(f*g)(0)=((g*f)=24x²+46x+20=20

Hi,

f°g means :  apply first g then f . so calculate  "g" and then use result as "x" in f.  

g°f  means :   you apply first  f then g  

so :  f°g =    4 (g (x)) +5  

4 (6x+4) +5  = 24x+16+5 = 24x+21

Answer:

Correct Option is : StartFraction 1 Over m Superscript 8 EndFraction

Step-by-step explanation:

=> [tex]m^{-8} p^0[/tex]

According to law of exponents [tex]a^0 = 1[/tex]

=> [tex]m^{-8} (1)[/tex]

Using Law of exponents [tex]a^{-m} = \frac{1}{a^m}[/tex]

=> [tex]\frac{1}{m^8}[/tex]

The simplified form of [tex]m^{-8}p^0[/tex] is [tex]\frac{1}{m^8}[/tex].

The question is not well formatted the question might be as follows:

Which is the simplified form of [tex]m^{-8}p^0[/tex]?

Exponents are numbers that say how many times a number is to be multiplied. For example, 2⁸ means 2 is multiplied 8 times.

[tex]m^{-8}p^0[/tex] = [tex]m^{-8}[/tex]  since, p⁰=1.

⇒[tex]m^{-8}[/tex] = [tex]\frac{1}{m^8}[/tex] .

Hence, the simplified form of [tex]m^{-8}p^0[/tex] is [tex]\frac{1}{m^8}[/tex].

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Answer:

45.5 km

Step-by-step explanation:

18.3 km + 27.2 km = 45.5 km or 45 km and 500 m

Answer:

45.5km

Step-by-step explanation:

The distance between the locksmith and the furniture=18.3km

The distance between the furniture and the hotel=27.2km

S(locksmith)+S(furniture)=S(hotel)

18.3km+27.2km=45.5km

Hope this helps ;) ❤❤❤

Let me know if there is an error in my answer.

Answer: 0.9964

Step-by-step explanation:

Consider,

P (disk failure) = 0.06

q = 0.06

p = 1- q

p = 1- 0.06,

p = 0.94

Step 2

Whereas p represents the probability that a disk does not fail. (i.e. working entire year).

a)

Step 3

a)

n = 2,

let x be a random variable for number...

Continuation in the attached document

Answer:

y is the range

Step-by-step explanation:

the y is the range

x isthe domain

Answer:

A. Yes, the triangles are congruent by SAS.

Step-by-step explanation:

EF = FG and DF = FH-> Given

angle EFD = angle HFG -> Vertical angles are congruent

DE F = HGF -> SAS Triangle Congruence Theorem

We can prove  ∠DE F = ∠HGF by SAS congruency.

Hence option A is correct.

In the given triangle,

DE = GE

DF = FH

We know that,

SAS congruency stands for "Side-Angle-Side" congruence,

Which is a rule used in geometry to prove that two triangles are congruent or equal in size and shape.

This rule states that if two sides and the angle between them of one triangle are congruent to the corresponding two sides and angle of another triangle, then the two triangles are congruent.

Since the triangles

DE,GE and DF, FH are the corresponding sides and

DE = GE

DF = FH

Since DEF and FHG are congruent.

Therefore,

∠DE F = ∠HGF

Hence proved.

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Answer: i believe it’s 0.28, but tbh i’m on a unit test so i can’t see what’s wrong and what’s right. good luck!

Step-by-step explanation:

Answer:

c- 0.28

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\bigg(\dfrac{a}{2};\ \dfrac{a}{2}\bigg)}[/tex]

Step-by-step explanation:

The formula of a midpoint:

[tex]M\bigg(\dfrac{x+1+x+2}{2};\ \dfrac{y_1+y_2}{2}\bigg)[/tex]

We have the points

[tex]A(0;\ 0)\to x_1=0;\ y_1=0\\\\C(a;\ a)\to x_2=a;\ y_2=a[/tex]

Substitute:

[tex]\dfrac{x_1+x_2}{2}=\dfrac{0+a}{2}=\dfrac{a}{2}\\\\\dfrac{y_1+y_2}{2}=\dfrac{0+a}{2}=\dfrac{a}{2}[/tex]

Answer:

The answer is (a/2,a/2)

Step-by-step explanation:

Fill in 2 then a

In conclusion (a/2,a/2)

Answer:

57

Step-by-step explanation:

f(15)=4(15)-3

f(15)=60-3

f(15)=57

Hope that helps, tell me if you need more help

Answer:

57

Step-by-step explanation:

If you plug 15 into the equation, you get f(15)=4(15)-3

60-3

57

:)