Find (f•g)(1)
f(x)=x²-1
g(x) = √x

The probability of tossing 3 heads in a row is P = 0.125, and after that, because the events are independent, the probability of getting heads (or tails) still is p = 0.5

Assuming that we have a fair coin, we assume that both outcomes have the same probability, so:

P(tails) = 0.5

P(heads) = 0.5

Then the probability of getting heads 3 times in a row, is the product of the probability of getting heads 3 times, this will be:

P(3 heads) = 0.5*0.5*0.5

P(3 heads) = 0.5^3

P(3 heads) =  0.125

Now, after this point, what is the probability of getting heads or tails?

Remember that each toss of the coin is independent of the previous one, so the probability of getting tails still is 0,5, and the same for the probability of getting heads.

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[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 678400\\ P=\textit{original amount deposited}\dotfill & \$320000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years \end{cases} \\\\\\ 678400 = 320000[1+(0.07)(t)] \implies \cfrac{678400}{320000}=1+0.07t\implies \cfrac{53}{25}=1+0.07t \\\\\\ \cfrac{53}{25}-1=0.07t\implies \cfrac{28}{25}=0.07t\implies \cfrac{\frac{23}{25}}{0.07}=t\implies \boxed{16=t}[/tex]

Answer:

Step-by-step explanation:

You want the amount of money each receives if Laura, Tom, and Alex share £95 in the ratio 8:7:4.

The total number of ratio units is 8+7+4 = 19, corresponding to a total amount of £95. That makes each ratio unit represent £95/19 = £5.

Multiplying the ratio units by £5, we find the distribution to be ...

  Laura : Tom : Alex = £40 : £35 : £20

Answer:

Money received by Laura = 8x = 8x5 =  £40

Money received by Tom = 7x = 7x5 =  £35

Money received by Alex = 4x = 4x5 =  £20

Step-by-step explanation:

Given ,

To Find : How much money will each of them receive

Let us take the variable as 'x' to find the money received by them

When we convert it to a equation

8x+7x+4x = 95

19x = 95

x = [tex]\frac{95}{19}[/tex]

x = 5

Money received by Laura = 8x = 8x5 =  £40

Money received by Tom = 7x = 7x5 =  £35

Money received by Alex = 4x = 4x5 =  £20

Hence, the money received by each of them is  £40, £35 and  £20

Answer:

35.84

Step-by-step explanation:

The equation of the line is y = 4x + 1 , where the slope of the line is m = 4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the number of blocks be y

Let the stage number be x

Let the first point be represented as P = P ( 1 , 5 )

Let the second point be represented as Q = Q ( 2 , 9 )

Now , the slope of the line between the points be

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 9 - 5 ) / ( 2 - 1 )

Slope m = 4

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 5 = 4 ( x - 1 )

On simplifying the equation , we get

y - 5 = 4x - 4

Adding 5 on both sides of the equation , we get

y = 4x + 1

Therefore , the value of A is y = 4x + 1

Hence , the equation of line is y = 4x + 1

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Answer: 27 boys

Step-by-step explanation:

There is a rule in math, what you do to one side, you do to the other.

So in this case the ration is 3:5

                                             ?:45

As you can see, they multiplied 5 by 9 to get 45, remember the rule, so we do the same.

3 times 9 is 27, so 27 boys

Answer:

Step-by-step explanation:

Dolls:240 Teddy Bears:120

120:240

Please Describe the fraction If Possible.

Answer:

(-2,-6)

Step-by-step explanation:

we can solve this system of equations with the substitution method because y is already by itself.

since they are both equal to y, we can set both equations equal to each other.

4x+2=x-4

subtract 2 from both sides

4x=x-6

subtract x from both sides

3x=-6

divide both sides by 3

x = -2

now that we know x, we can plug this value into one of the original equations and solve for y.

y=-2-4

y=-6

so on a graph, these two equations will intersect at the point (-2,-6)

20% of 80 is 16 and 15% of 30 is 4.5, so the sum is 16 + 4.5 = 20.5.

Answer:

Side BC: y = -2x + 10

Side AC: y = 2x + 4

Yes, these three points could form a right triangle. This is because the slopes of the two lines, Side BC and Side AC, are opposite reciprocals of each other. This means that when the two lines intersect, they will form a right angle.

Answer:

About 47% of books were nonfiction.

The actual percentage includes decimals and it would be this:

%47.0588235294

Answer: obtuse

Step-by-step explanation:

64+47=111

111>39

Answer:

343.2

Step-by-step explanation:

156 × 2.2

= (156 × 22)/10

= 3432/10

= 343.2

The equation of the perpendicular line will be x + y - 5 = 0. Then the correct option is B.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line passing through (-5, 6) and (-6, 5) will be given as,

(y - 6) = [(5 - 6) / (- 6 + 5)](x + 5)

y - 6 = (x + 5)

y = x + 1

The equation of the line that is perpendicular to the above line is given as,

y = - x + c

The equation of the line is passing through (3, 2)

3 = - 2 + c

c = 5

Then the equation of the perpendicular line will be given as,

y = -x + 5

x + y - 5 = 0

The equation of the perpendicular line will be x + y - 5 = 0. Then the correct option is B.

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The complete question is given below.

The probability that on average these students spend more than $425 on books is given as follows:

0.0009 = 0.09%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 400, \sigma = 80, n = 100, s = \frac{80}{\sqrt{100}} = 8[/tex]

The desired probability is one subtracted by the p-value of Z when X = 425, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{425 - 400}{8}[/tex]

Z = 3.125.

Z = 3.125 has a p-value of 0.9991.

1 - 0.9991 = 0.0009 = 0.09%.

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On solving the provided question we can say that  expression which is equivalent form to 3/2 is (5/2-1).

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Equivalent systems refer to sets of equations with the same solution. We can create an analogous system from a system of two equations by replacing one equation with the total of the two equations or by replacing an equation with a multiple of itself.

When two expressions can be reduced to a single third expression or when one of the expressions can be expressed in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if two expressions are equal.

The number is 3/2

The expression which is equivalent to 3/2 is (5/2-1)

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Answer:

it's B

[tex] - \frac{9}{4} + 2i = - \frac{9}{4} - 4i[/tex]

Answer:

C

Step-by-step explanation:

please refer to the sketch

She would need to make two extra grades of 86 each.

Here we can see that the average of the scores that Victoria would need to make is an average score of 85 so as to be able to pull through. In this case, we can see that we have the scores; 82, 81, and 90

Let the scores tat we have to count twice be p each and then we have;

85 = 82 + 81 + 90 + p + p/5

85 = 253 + 2p/5

5(85) = 253 + 2p

p = 5(85)  - 253/2

p = 86

Hence, the twice scores that need to be earned for Victoria are both 86.

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Tim worked for a total of 7 and half hours on Monday and earned $56.25 gross pay.

Prior to payroll deductions, earned wages are referred to as gross pay. Employers utilize this amount—$60,000 per year or $25 per hour—when talking to employees about pay. Additionally, the federal and state income tax brackets sometimes refer to gross salary.

The amount of pay that employees get after payroll deductions varies; some may be optional, while others may be required.

Given, On Monday of his time card Tim clocked in at 8:15 am and clocked out at 4:15 pm.

So, The total number of hours she worked is 8 hours, 8:15 to 12:15 is 4 hours, and another four hours.

Also given the time he took for lunch is half an hour.

Therefore, The total hour he worked is 7:30 hours.

He earns $7.5 per hour so his gross pay for Monday is $(7.5×7.5).

= $56.25.

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Answer:

-----------------------------------

Given lines:

Plot both of the lines using the graphing calculator by adding the equations, then find the graphical solution as the intersection of the lines.

See attached.

The solution is (-1, 0).

if functions  f(x) = 2x²-4x-6 and g(x)= 2x+7 then f(g(x)) is 8(x+2)(x+4)

A relation is a function if it has only One y-value for each x-value.

Given functions are f(x)= 2x²-4x-6

g(x)=2x+7

We need to find expression of f(g(x))

f(g(x))=f(2x+7)

Now replace x with 2x+7 in f(x)

f(2x+7)=2(2x+7)²-4(2x+7)-6

=2(4x²+49+28x)-8x-28-6

Apply distributive property

=8x²+98+56x-8x-28-6

Add the like terms

=8x²+48x+64

f(g(x))=8(x+2)(x+4)

Hence, if functions f(x) = 2x²-4x-6 and g(x)= 2x+7 then f(g(x)) is 8(x+2)(x+4)

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Answer:

Step-by-step explanation:

This is a right triangle that has two equal sides - so it is also isosceles.

It can be solved using Pythagoren Theorem.

a²  +  b²  =  c²

In this case a = b

so:  

6²  +  6²  = c²

36 +  36 =  c²

72  =  c²

[tex]\sqrt{72[/tex]  =  [tex]\sqrt{c^{2} }[/tex]

8.49 = c

round to 8.5

This is the length of the flap.

The length of time to build the fence is 8 hours

From the question, we have the following parameters that can be used in our computation:

Length of the fence = 1 1/3 miles

Rate of building = 1/6 miles per hour

The length of time to build the fence is then calculated as

Length of time = Length of the fence/Rate of building

Substitute the known values in the above equation, so, we have the following representation

Length of time = (1 1/3 miles)/(1/6 miles per hour)

Evaluate the quotient

This gives

Length of time = 8 hours

Hence, the time taken is 8 hours

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The given graph's shaded region shows the possible combinations of raw materials the company can buy.

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

An electronics company can spend no more than $4,000 on raw materials for circuit boards.

And, The raw materials cost $10 per ounce for copper and $20 per ounce for silver.

Here, The inequality for the given condition is,

⇒ 10c + 20s ≤ 4,000

Where, c is the number of ounces of copper material and s is the number of ounces of silver material.

So, The given graph's shaded region shows the possible combinations of raw materials the company can buy.

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Answer:

Step-by-step explanation:

To solve this system of equations, you can use the substitution method.

In this method, you solve one of the equations for one of the variables in terms of the other variable. Then you substitute this expression into the other equation. This will give you a single equation in one variable, which you can solve to find the value of that variable. Finally, you can substitute this value back into one of the original equations to find the value of the other variable.

To solve this system using substitution, we can solve the second equation for y:

y = x - 4

Then, we substitute this expression for y in the first equation:

x + (x - 4) = 8

Combining like terms, we get:

2x - 4 = 8

Adding 4 to both sides, we get:

2x = 12

Dividing both sides by 2, we find that:

x = 6

Now we can substitute this value back into one of the original equations to find the value of y. Let's substitute it into the second equation:

x - y = 4

Substituting 6 for x, we get:

6 - y = 4

Subtracting 6 from both sides, we find that:

y = 2

So the solution to the system of equations is x = 6 and y = 2.

Answer:

x=6, y = 2

Step-by-step explanation:

If you add 2 expressions, 2x = 12, so x = 6.

So the other one y = 2.

Answer: C correctly rewrites the formula to solve I

Step-by-step explanation:

Answer: It's closer to 1/2

Step-by-step explanation: It's closer to 1/2 and here's why:

So, 1/2 (exact) is 8/16

0 = 0

1 = 16/16

Since 9/16 is the closest to 8/16 or around 1/2 in this case, it'd be about 1/2. I hope this helps!

Answer:  An equation has two solutions when it has two distinct values that can be assigned to the variable to make the equation true.

In this case

equation A. W=-1 is a single solution

equation B. W=1 is a single solution

equation C. W=-2 is a single solution

equation D. W=0 is a single solution

So none of the given equations have two solutions. they all have only one solution.

It's worth mentioning that, if the equation is a quadratic equation (in the form of ax² + bx + c = 0) and it has a non-zero discriminant (b² - 4ac) then the equation will have two distinct real solutions.

In this case the equations are not in that form, and also doesn't show any signs of having two solutions.

Step-by-step explanation:

Answer:

the k is 7

Step-by-step explanation:

12×2=24

12×3=36

12×4=48

12×5=60

12×6=72

12×7=84

Answer:

k = 7

Step-by-step explanation:

The product of 12 and k is 84 [tex]\rightarrow 12k=84[/tex].

[tex]12k = 84 \\ k = \dfrac{84}{12} \\ \boxed{k = 7}[/tex]