Write a verbal sentence to represent each equation.
9.3n-3579
10. 2(n³ + 3n²) = 4n
11.
5n
n+3
-=n-8

The mean is 58.319 m/h and the standard deviation is 11.665 m/h of the vehicle speed if 5% of all vehicles travel less than 39.13 m/h and 10% travel more than 73.25 m/h.

The mean and standard deviation of the vehicle speed can be calculated by using the formula for z-score.

The z-score of measure X can be given as;

Z = X - μ / σ

In this case, 39.13 m/h is the 5th percentile; therefore when X = 39.13, Z has a p-value of 0.05, hence Z = -1.645

Z = X - μ / σ

-1.645 = (39.13 - μ) / σ

39.13 - μ = -1.645σ

μ = 39.13 + 1.645σ

Additionally, 73.25 m/h is the 90th percentile (100 - 10 = 90), therefore when X = 73.25, Z has a p-value of 0.9, hence Z = 1.28

1.28 = (73.25 - μ) / σ

73.25 - μ = 1.28σ

μ = 73.25 - 1.28σ

We can find the standard deviation by equalling both equations as follows;

39.13 + 1.645σ = 73.25 - 1.28σ

1.645σ + 1.28σ = 73.25 - 39.13

2.925σ = 34.12

σ = 34.12/2.925 = 11.665 m/h

Now the mean can be calculated as follows;

μ = 73.25 - 1.28σ

μ = 73.25 - 1.28(11.665)

μ = 58.319 m/h

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A fifth-degree polynomial function can have five turning points in its graph.

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Answer:

The correct is answer is option C: "four or less"

The answers to the next  part of the question on Edge are options A and C :)

Step-by-step explanation:

Hope this helped!

Brainliest would be greatly appreciated - Have a great day :3

Answer:

y = [tex]\frac{3x -6}{5}[/tex]

Step-by-step explanation:

3x - 5y = 6 ( subtract 3x from both sides )

- 5y = - 3x + 6 ( multiply through by - 1 )

5y = 3x - 6 ( divide both sides by 5 )

y = [tex]\frac{3x-6}{5}[/tex]

Answer:

l = 2 in

h = 4 in

w = 2 in

Surface Area = 40

Step-by-step explanation:

If “l” is the length, and “h” is the height and “w” is the width of the rectangular prism, the surface area is given by the formula,

The surface area of a rectangular prism = 2 (lw+lh+hw) square units.

The starting number of Michael's thought is 96

From the question, the given parameters are:

The above sequence of statements can be represented as

x * (100÷8) + 6.50 = 1206.5

Where x represents the number

So, we have

x * (100÷8) + 6.50 = 1206.5

Evaluate the quotient

x * 12.5 + 6.50 = 1206.5

Subtract 6.50 from both sides

x * 12.5 = 1200

Divide both sides by 12.5

x = 96

Hence, the initial number is 96

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Tom will need to pay $93.60 for 36 cans of Coca-Cola.

A linear expression can be represented by a line. The standard form for this equation is: y=ax+b , for example, y=3x+2.

The question gives:

Tom bought 10 cans of Coca-cola drink at a cost of USD26.00. Here you can convert this text into an algebraic expression, see:

10x = 26, where x represents the unit cost.

You can find x, solving the previous algebraic expression. Thus,

10x=26

x=26/10

x=2.6

So, 1 can of Coca-Cola costs $2.60.

For knowing the cost total for 36 cans of Coca-Cola, you need to multiply 36 units by the unit cost ($2.6). See below:

36*2.6= $93.60

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The expression that represents the perimeter of the figure is  6x - 2

The figure above is a rectangle. A rectangle is a quadrilateral that has opposite sides equal to each other. Opposite sides are also parallel to each other.

Therefore, the perimeter of a rectangle is the sum of the sides of the rectangle.

Hence,

perimeter of the rectangle = 2(l + w)

where

Therefore,

l = 2x - 3

w = x + 2

Hence,

perimeter of the rectangle = 2(2x - 3 + x + 2)

perimeter of the rectangle = 2(2x + x - 3 + 2)

perimeter of the rectangle = 2(3x - 1)

Therefore,

perimeter of the rectangle = 6x - 2

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The error occurs in the second line, the correct solution is x > -5/2.

The relation between two unequal expressions is defined as inequality.

Given inequality is -5x/4 - 7/2 < -3/8.

The solution of the inequality is:

-5x/4 - 7/2 < -3/8

10x + 28 > 3

10x > -25

x > -25/10

x > -5/2

Hence, the error occurs in the second line, the correct solution is x > -5/2.

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7 + 7 + 7 + 7 + 7​ means 7 is added 5 times

It could be written as

5(7)

7 x 5 and

7 . 5

But it can not be written as 7^5 because 7^5 means 7 x 7 x 7 x 7 x 7

Hence, 7^5 does not represent the expression 7 + 7 + 7 + 7 + 7​

This makes the correct option to be the third option. That is 7^5

Answer:

y = 0.5x^2 + 1.5x − 5

Step-by-step explanation:

See attached graph

Answer: x=17

Step-by-step explanation:

Simplifying

5x = 85

Solving

5x = 85

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '5'.

x = 17

Simplifying

x = 17

The value of x in the equation is 17 .

Given,

5x = 85

Solving

5x = 85

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '5'.

x = 17

Simplifying

x = 17

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Answer:

103.5

Step-by-step explanation:

Answer:

103.5

Step-by-step explanation:

The question is,

→ what is 1656 divided by 16?

Forming as problem,

→ 1656 ÷ 16

Let's solve the problem,

→ 1656 ÷ 16

→ 103.5

Thus, the answer is 103.5.

SOLUTION

The total amout of solution given is

From thequestion, 1/2 of the solution is used, then the amount of solution used for the experiment will be

Hence

The amount of solution the scientist use is 1/3 litres

x = 5

Given the equation shown:

To get the value of "x", we will divide both sides by -6 to have:

Hence the value of x that satisfies the equation is 5

The system of equations has one solution, so it is consistent and independent, the correct option is C.

Here we have the system of equations:

x = 5

y = 6

-x - y + z = 0

By replacing the first and second equations into the third one, we get:

-5 - 6 + z = 0

-11 + z = 0

z = 11

So the solution is (5, 6, 11)

So it is consistent, and it is independent as clearly, the equations are linearly independent (system of 3 equations with 3 variables having only one solution).

Then the correct option is C.

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The time when the ball hits the ground is 8. 09 seconds

A function can be defined as an expression, theorem, law, or rule that elaborates, explains or holds true for the relationship between two variables.

These variables are namely;

From the information given, we have that;

f(x) = 1048 - 16x²

Where;

To determine the time, we have;

collect like terms

- 16x² = - 1048

Divide both sides by the coefficient of x²

-16x²/-16 = -1048/-16

x² = 65.5

Find the square root of both sides, we have;

x = √65.5

x = 8. 09 seconds

Hence, the value is  8. 09 seconds

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Answer:

(a)  19.6 ms⁻¹

(b)  2 s

(c)  9.8 ms⁻¹

(d)  4 s

Step-by-step explanation:

Constant Acceleration Equations (SUVAT)

[tex]\boxed{\begin{array}{c}\begin{aligned}v&=u+at\\\\s&=ut+\dfrac{1}{2}at^2\\\\ s&=\left(\dfrac{u+v}{2}\right)t\\\\v^2&=u^2+2as\\\\s&=vt-\dfrac{1}{2}at^2\end{aligned}\end{array}} \quad \boxed{\begin{minipage}{4.6 cm}$s$ = displacement in m\\\\$u$ = initial velocity in ms$^{-1}$\\\\$v$ = final velocity in ms$^{-1}$\\\\$a$ = acceleration in ms$^{-2}$\\\\$t$ = time in s (seconds)\end{minipage}}[/tex]

When using SUVAT, assume the object is modeled as a particle and that acceleration is constant.

Acceleration due to gravity = 9.8 ms⁻².

When the ball reaches its maximum height, its velocity will momentarily be zero.

Given values (taking up as positive):

[tex]s=19.6 \quad v=0 \quad a=-9.8[/tex]

[tex]\begin{aligned}\textsf{Using} \quad v^2&=u^2+2as\\\\\textsf{Substitute the given values:}\\0^2&=u^2+2(-9.8)(19.6)\\0&=u^2-384.16\\u^2&=384.16\\u&=\sqrt{384.16}\\\implies u&=19.6\; \sf ms^{-1}\end{aligned}[/tex]

Therefore, the initial speed is 19.6 ms⁻¹.

Using the same values as for part (a):

[tex]\begin{aligned}\textsf{Using} \quad s&=vt-\dfrac{1}{2}at^2\\\\\textsf{Substitute the given values:}\\19.6&=0(t)-\dfrac{1}{2}(-9.8)t^2\\19.6&=4.9t^2\\t^2&=\dfrac{19.6}{4.9}\\t^2&=4\\t&=\sqrt{4}\\\implies t&=2\; \sf s\end{aligned}[/tex]

Therefore, the time taken to reach the highest point is 2 seconds.

As the ball reaches its maximum height at 2 seconds, one second before this time is 1 s.

Given values (taking up as positive):

[tex]u=19.6 \quad a=-9.8 \quad t=1[/tex]

[tex]\begin{aligned}\textsf{Using} \quad v&=u+at\\\\\textsf{Substitute the given values:}\\v&=19.6+(-9.8)(1)\\v&=19.6-9.8\\\implies v&=9.8\; \sf ms^{-1}\end{aligned}[/tex]

The velocity of the ball one second before it reaches its maximum height is the same as the velocity one second after.

Proof

When the ball reaches its maximum height, its velocity is zero.

Therefore, the values for the downwards journey (from when it reaches its maximum height):

[tex]u=0 \quad a=9.8 \quad t=1[/tex]

(acceleration is now positive as we are taking ↓ as positive).

[tex]\begin{aligned}\textsf{Using} \quad v&=u+at\\\\\textsf{Substitute the given values:}\\v&=0+9.8(1)\\\implies v&=9.8\; \sf ms^{-1}\end{aligned}[/tex]

Therefore, the velocity of the ball one second before and one second after it reaches the maximum height is 9.8 ms⁻¹.

From part (a) we know that the time taken to reach the highest point is 2 seconds.  Therefore, the time taken by the ball to travel from the highest point to its original position will also be 2 seconds.

Therefore, the total time taken by the ball to return to its original position after it is thrown upwards is 4 seconds.

This is an example of a geometric distribution with success probability p=0.102

The expected number of rolls is 10.

This is an example of a geometric distribution with success probability p=0.102 The expected value of the random variable of a geometric distribution is 1/p=1/0.102=9.80

Therefore, the expected number of rolls is 10.

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Compound interest formula:

A = P (1+r/n)^nt

Where:

A = total amount

P = principal investment

r= interest rate in decimal form = 2/100 = 0.02

t= years

n= number of compounding periods in a year= 12

Replacing:

A = 30,000 (1+0.02/12)^4x12

A = 30,000 (1.001666667)^48

A= 32,496.45

Given:

To Determine: The percentage with greater than 24mpg

Solution

Each bird would receive 1/9 cup of bird food.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

We have been given an area model with 12 shaded parts and 6 unshaded parts. The shaded part is labeled two-thirds. Adela divided Two-thirds of a cup of bird food equally among 6 birds.

The dividend would be

⇒ 2/3

The divisor would be

⇒ 6

The division expression would be

⇒ 2/3

Divided by 6

Rewrite the division expression to get

⇒ 2/3 × 1/6

⇒ 2 / 18

⇒ 1/9

Therefore, each bird would receive 1/9 cup of bird food.

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The measurement is closest to the length of the rectangle is √119 ft.

Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c = √( a² + b² )

Where c is the diagonal that divides the rectangle into two equal triangle, a and b are the other legs of the triangle.

Given the data in the question;

Plug the values into the formula and solve for b.

12ft = √( (5ft)² + b² )

Take the square of both sides

( 12ft )²  = (5ft)² + b²

144ft²  = 25ft² + b²

b² = 144ft² - 25ft²

b² = 119ft²

b = √( 119ft² )

b = √119 ft

Therefore, the measure of the length is √119 ft.

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A forest is decreasing in size by 60 hectares every 3 years. In 7 years, the forest will have decreased by 140 hectares.

Using the Unitary Method:

∵ In '3' years, a forest decreased in size by '60' hectares

∴ In '1' year, a forest will be decreased in size by '20' hectares

Every year 20 hectares is decreased. Considering a regular trend in the decrement of forest area, the time span of '7' years will diminish 'to 140' hectares.

The 'Unitary Method' is also known as the 'Mango Method'. It establishes a relation between given data. The relation is used to predict results in different conditions. The Unitary Method is always used for regular trends.

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Given:

The number sentence for 4 and n

Required:

We have to find the given sentence

Explanation:

4 and N, simply means you mixed them up, you sum them up

your result is 9, 4+N=9

Required solution :

4+N=9

Answer:

25 bricks

Step-by-step explanation:

Calculate the volume of one brick:

Volume = (11')(8")(5") = 440 in^3

Divide the volume of a one brick into the volume of concrete that will be used:

(11000 in^3 concrete)/(440 in^3 concrete/brick) = 25 bricks

The weight of Brad is 70 lb and the weight of Sean is 150 lb now.

According to the question,

We have the following information:

Sean weighs 10 lb more than twice Brad’s weight. If Brad gains 10 lb, together they will weigh 230 lb.

Now, let's take Brad's weight to be x lb.

So, we have:

Sean's weight = (10+2x) lb

Now, when Brad gains 10 lb, we have the following expression:

(x+10)+(10+2x) = 230

3x+20 = 230

3x = 230-20

3x = 210

x= 210/3

x = 70 lb

Now, Sean's weight = (10+2x) lb

Putting the value of x:

Sean's weight = 10+2*70

Sean's weight = 10+140

Sean's weight = 150 lb

Hence, the weight of Brad is 70 lb and the weight of Sean is 150 lb now.

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Using the Fundamental Counting Theorem, it is found that:

a) 1000 combinations are possible.

b) The probability of winning is of 0.001.

c) If you win, the net profit is of $497.

d) The expected value of a $3 bet is of -$2.5.

It is a theorem that states that if there are n trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, each thing independent of the other, the number of results is given as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In the context of this problem, three digits that can be repeated are chosen, hence the parameters are:

[tex]n_1 = n_2 = n_3 = 10[/tex]

Hence the number of combinations is:

N = 10³ = 10 x 10 x 10 = 1000.

The order also has to be correct, hence the there is only one winning outcome and the probability is:

p = 1/1000 = 0.001.

You bet $3, and if you win you collect $500, hence the net profit is of:

500 - 3 = $497.

Then the distribution of earnings are as follows:

Hence the expected value is:

E(X) = -3 x 0.999 + 497 x 0.001 = -$2.5.

The problem is given by the image at the end of the answer.

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Answer:

Step-by-step explanation:

4 - 3 x = 6 - 5 xx

[tex]-3x+4=6-5xx^{2}[/tex]

x = 1

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

Answer:

x=1

Step-by-step explanation:

sense x's are on both sides you need to bring one of them over, add 3x to both sides to get 4=6-2x , then subtract 6 from each side to get -2=-2x , then to get x by itself divide both sides by -2 to get 1=x