4 less than three sevenths as an algebraic expression

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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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 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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Answer:

Step-by-step explanation:

Dolls:240 Teddy Bears:120

120:240

Please Describe the fraction If Possible.

to get the equation of any straight line, we simply need two points off of it, let's use those ones in the picture below.

[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{32})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{53}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{53}-\stackrel{y1}{32}}}{\underset{\textit{\large run}} {\underset{x_2}{15}-\underset{x_1}{8}}} \implies \cfrac{ 21 }{ 7 } \implies 3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{32}=\stackrel{m}{ 3}(x-\stackrel{x_1}{8}) \\\\\\ y-32=3x-24\implies {\Large \begin{array}{llll} y=3x+8 \end{array}}[/tex]

Answer:

343.2

Step-by-step explanation:

156 × 2.2

= (156 × 22)/10

= 3432/10

= 343.2

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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[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]

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: obtuse

Step-by-step explanation:

64+47=111

111>39

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:

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.

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:

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:

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]

According to the findings, 40 of the adults who were not parents and 150 of the adults who were parents believed that the park should be expanded.

250 adults, 180 of whom are parents, leaving 70 adults who are not parents (250 - 180). According to the findings, 40 adults without children and 150 adults with children said the park should be expanded. Thus, 180 – 150 = 30 parents.

Parents: YES OR NO Not parents: 40 | 30 of 150

In this exercise, we must determine the values of the voters who supported expanding the parking lot, which requires that we:

In fact, parents will be 150, not 40.

Parents won't be 30 in total; they'll be 40. Instead, a park should be built to accommodate 250 persons, 180 of whom were parents.

The park should be extended, according to 40 of the people who weren't parents.

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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.

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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So on solving the provided question, we can say that the function g(x) is equal to g(x) = [tex]\sqrt{2x}[/tex]

The mathematical procedure known as "function composition" takes two functions, f and g, and creates a function, h = g f, such that h(x) = g. This process involves applying the function g to the outcome of applying the function f to x. When the result of one function is utilized as the input for another, this is known as a composite function. The function f g (x) fg(x) fg(x) fg(x), also known as "f of g of x" or "f g fg fg of x," is the composition of the two functions if we have a function f and another function g.

f(f(x)) = [tex]\frac{x}{\sqrt{6} }[/tex]

f(x) = 3x^2

g(f(x)) = [tex]\frac{3x^2}{\sqrt{6} }[/tex]

g(x) = [tex]\sqrt{2x}[/tex]

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Answer:

Step-by-step explanation:

the ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi. In decimal form, the value of pi is approximately 3.14.

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

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:

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

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).

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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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)

The missing measure of the given right-angled triangle is: x = 2.5

Given a right-angled triangle, with one of its angle as 14° ,assume

angle y= 14°. Also given length of one of it's side is 18. Let's assume the side as z = 18.

As it is given it's a  right-angled triangle,

∴ By using trigonometric formula,

 tan y = opposite /adjacent

∴ tan 14° = z/x

 tan 14°  = 18/x

 7.24 = 18/x                   ......( as tan 14°= 7.24)

∴ x = 2.48

∴ x ≈ 2.5

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The answer is 2.50. This, 250% in deciaml form is 2.50, in improper fraction form is 52 and as a mixed number it is 2 12. 2 1 2.

Answer:

35.84

Step-by-step explanation: