Here are some statistics about the masses of a group of 50 students
Mean = 12 Median = 14 Range = 17
a) If the mass of every student increase by 4 Kg , What are the new statistics?
b) If the mass of every student doubles , What are the new statistics

Answer:

Since [tex]q(\frac{3}{4}) \neq 0[/tex], 3/4 cannot be a root of q(x).

Step-by-step explanation:

Root of a function:

If [tex]x^{\ast}[/tex] is a root of a function f(x), we have that [tex]f(x^{\ast}) = 0[/tex].

In this question.

We have to find [tex]q(\frac{3}{4})[/tex]. So

[tex]q(\frac{3}{4}) = 6(\frac{3}{4})^3 + 19(\frac{3}{4})^2 - 15(\frac{3}{4}) - 28[/tex]

[tex]q(\frac{3}{4}) = \frac{162}{64} + \frac{171}{16} - \frac{45}{4} - 28[/tex]

[tex]q(\frac{3}{4}) = \frac{162}{64} + \frac{684}{64} - \frac{720}{64} - \frac{1792}{64}[/tex]

[tex]q(\frac{3}{4}) \neq 0[/tex]

Since [tex]q(\frac{3}{4}) \neq 0[/tex], 3/4 cannot be a root of q(x).

Answer:

0.028 ; 0.649 ; 4

Step-by-step explanation:

P(correctly activation), p = 0.7

Number of sprinklers, n = 10

q = 1 - p = 1 - 0.7 = 0.3

Using the binomial probability relation :

P(x =x) = nCx * p^x * (1 - p)^(n - x)

Probability that all sprinklers activate correctly;

P(x = 10) = 10C10 * 0.7^10 * 0.3^0

P(x = 10) = 1 * 0.0282475249 * 1

P(x = 10) = 0.028

Probability that atleast 7 will operate correctly :

P(x ≥ 7) = p(x = 7) + p(x = 8) + p(x = 9) + p(x = 10)

P(x ≥ 7) = 0.267 + 0.233 + 0.121 + 0.028

P(x ≥ 7) = 0.649

3.)

Probability of atleast 1 operates :

P(x ≥ 1) = 0.98

1 - probability of 0 operates

1 - p(x =0)

P(x = 0) = nC0 * 0.7^0 * 0.3^n = 0.02

Recall :

nC0 = 1 ;

1 - p(x = 0)

P(x = 0) = 1 * 1 * 0.3^n = 0.02

0.3^n = 0.02 - - - (1)

0.3^3.24 = 0.02 - - - (2)

Comparing (1) and (2)

n = 3.24

Since, n cannot be a fraction ;

Then n is rounded to the next whole number = 4

Answer:

a.2^(a+b+c)

b.2^(a+b+a-b)=2^(2a)or 4^a

c.2^(a+b+c)/2^(a+b)=2^(a+b+c-a-b)=2^c

Answer:

[tex]F_x=43.30\ N[/tex]

Step-by-step explanation:

Given that,

Force, F = 50 pounds

It is directed at 30° from the horizontal.

The force will be given by :

[tex]F_x=F\cos\theta\\\\=50\times \cos(30)\\\\=43.30\ N[/tex]

So, the required force is 43.30 N.

Answer:

471 square feet

Step-by-step explanation:

150

x3.14

471

Answer:

2,3

Step-by-step explanation:

2 and 3 are consecutive numbers, and when you multiply them, you get 6.

Hope this helps.

Have a nice day.

Answer:

c

Step-by-step explanation:

3X-x+2=14

3*6-6+2=14

14=14

plz make me brainliest

9514 1404 393

Answer:

  61°

Step-by-step explanation:

An angle and its complement total 90°. Your angle of interest is ...

  90° -29° = 61° . . . complementary angle to 29°

Answer: D. 15 square root with 3 inside

Step-by-step explanation:

Just try it

Answer:

c

Step-by-step explanation:

Answer:

20

11

Step-by-step explanation:

10^1+10 steps:

10^1+10

Calculate 10 to the power of 1 and get 10.

10+10

Add 10 and 10 to get 20.

20

10^0+10 steps:

10^0 +10

Calculate 10 to the power of 0 and get 1.

1+10

Add 1 and 10 to get 11.

11

Answer:

the square root is 2.2

Answer:

2.2

Step-by-step explanation:

make me brainestly

the guy who did the second answer wants beef

Problem 15

Answers:

Each interval is interval notation.

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Explanation:

To get the graph, you can plug in various x values to find their paired y values, then draw a curve through those points. You can only plug in x values that are 3 or larger, as I'll mention later in the next paragraph. A quicker way to get the graph is to use technology. I used GeoGebra to generate the graphs below.

To get the domain, we need to ensure that the stuff under the square root is never negative. So we need to make the x-3 to be 0 or larger. Solving [tex]x-3 \ge 0[/tex] leads to [tex]x \ge 3[/tex] showing that 3 is the smallest value we can plug in. The domain is the interval from 3 to positive infinity. We can write that as [tex]3 \le x < \infty[/tex] which condenses to the interval notation [3, infinity). Note how the square bracket is used to include the endpoint.

The range can be determined from the graph. The lowest point is when y = 2, so the range consists of y outputs that are 2 or larger. We write the interval notation [2, infinity) to mean [tex]2 \le y < \infty[/tex]

The graph also helps us see where the curve is increasing or decreasing. In this case, the curve goes uphill as we move from left to right. Therefore, the graph is increasing over its entire domain. We write the domain as the answer here. Because the function increases over the entire domain, there's no room for the function to decrease.

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Problem 16

Answers:

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

Explanation:

We follow the same idea as the previous problem.

This time we want the x+1 under the square root to be 0 or larger, so [tex]x+1 \ge 0[/tex] solves to [tex]x \ge -1[/tex] telling us the smallest input allowed. The value of x can be this or larger.

Since this is an increasing function throughout the domain (similar to the previous problem), this means that the smallest domain value corresponds exactly to the smallest range value. Plugging in x = -1 leads to y = -3 which is the smallest possible output. As x gets bigger, so does y. The graph shows that the lowest point occurs when y = -3 to visually confirm this.

The increasing interval is over the entire domain, so we just write the domain again for the increasing interval. This means we write "none" for the decreasing interval.

Side note: The graphs are shown together on the same xy coordinate axis, but for your hw problem, you'll have the graphs on their own separate grid.

Answer:

Total cost of cementing the path = Rs. 17,000.

Step-by-step explanation:

Let the square garden be PQRS

Let the region inside the garden (PQRS) be KLMN.

Given the following data;

Length of sides of PQRS = 90m

Width of path = 5m

Cost = Rs. 10 per m²

Area of PQRS = 90 * 90

Area of PQRS = 8100m²

To find the area of KLMN;

KL = KN = 90 - (5 + 5)

KL = KN = 90 - 10

KL = KN = 80m

Area of KLMN = KL * KN

Substituting into the equation, we have;

Area of KLMN = 80 * 80

Area of KLMN = 6400 m²

Area of path = Area of PQRS - Area of KLMN

Area of path = 8100 - 6400

Area of path = 1700 m²

Total cost of cementing the path = Area of path * Cost

Total cost of cementing the path = 1700 * 10

Total cost of cementing the path = Rs. 17,000

Answer:

n = 14

Step-by-step explanation:

let 'n' = the number

3n - 5 = 2n + 9

n - 5 = 9

n = 14

Answer:

14

Step-by-step explanation:

We have to replace the unknown quantity with "x" and work with it.

The result of multiplying a number by 3 and substracting 5

3x - 5

Is the same as

3x-5= (__)

Doubling the number and adding 9

3x- 5= 2x+9

Then we solve it like any equation

3x - 5 = 2x + 9

3x - 2x = 9 + 5

x = 14

Hope it was helpful ;)

Answer:

x <= 10

<= means less or equal to

Step-by-step explanation:

At least means less or equal to

Answer:

after it is necessary to rearrange and equations for that one variable is expressed in terms de in term of tea to express it in terms of d we need to solve the equation c is equal to fir for our in terms of c solve the equation p is equal to 2 w plus two hours for w in terms of p and h

Answer:

after it is necessary to rearrange and equations for that one variable is expressed in terms de in term of tea to express it in terms of d we need to solve the equation c is equal to fir for our in terms of c solve the equation p is equal to 2 w plus two hours for w in terms of p and h

Answer:

30

Step-by-step explanation:

cause i said so

Answer:

The area would reduce to 1/4 the original area

Step-by-step explanation:

The area of a triangle = (1/2)(base)(height) or bh/2

If the triangle base and height were to reduce by one-half, the formula would change to:

Area = (1/2)(1/2 base)(1/2 height) or bh/8. Which is a reduction by 1/4

Answer:

#8. 2

#9. 7

#10. 2

#11. 2

#12. 0

#13. -4

#14. 17

#15. 1

Answer:#8=2

#9=-11

#10=8

#11=2

#12=0

#14=17

#15=1

Step-by-step explanation: #8-13 (Subtract the numbers using a number line, than add the numbers using a integer chips, after that calculate the sum of the differences) #14-15( normal solving stepping for integers(recommend using a T1-84 Calculator)

Answer:

The flagpole is 54.5 inches tall.

Step-by-step explanation:

We solve this question using proportions, by rule of three.

Each feet has 12 inches. So

A 6 foot man measured his shadow at13 feet 9 inches.

So when the real height is of 6 feet, the shadow is of 13 feet + (9/12) feet = 13.75 feet.

When the shadow is of 125 feet, the height is x. So

6 feet - 13.75 feet

x feet - 125 feet

Applying cross multiplication

[tex]13.75x = 6*125[/tex]

[tex]x = \frac{6*125}{13.75}[/tex]

[tex]x = 54.5[/tex]

The flagpole is 54.5 inches tall.

Answer:

Follows are the solution to this question:

Step-by-step explanation:

[tex]T: 1 \ R^n \to 1 \ R^n[/tex] is invertible lines transformation

[tex]S[T(x)]=x \ and \ V[T(x)]=x \\\\t'x \ \varepsilon\ 1 R^n\\\\[/tex]

T is invertiable linear transformation means that is  

[tex]T(x) =A x \\\\ where \\\\ A= n \times n \ \ matrix[/tex]

and [tex]\ det(A) \neq 0 \ \ that \ is \ \ A^{-1} \ \ exists[/tex]

Let

[tex]V \varepsilon\ a\ R^{n} \ consider \ \ u= A^{-1} v \varepsilon 1 R^n\\\\T(u)= A(A^{-1} v)=(A \ A^{-1}) \\\\ v= I_{n \times n} \cdot v = v[/tex]

so,  

[tex]s[T(u)]=v[T(u)]\\\\s(v)=v(v) \ \ \forall \ \ v \ \ \varepsilon \ \ 1 R^n[/tex]

s(3)=4(3)-7+(3+1)^2

s(3)=12-7+16

s(3)=21

Answer:

21

Step-by-step explanation:

We find that  s(x) = 4x - 7 + (x + 1)^2. Expanding, we get s(x) = x^2 + 6x - 6. Plugging in x = 3, we have s(3) = 3^2 + 6 x 3 - 6 = 21.

Alternatively, we can compute that f(3) = 5 and g(3) = 16, so  s(3) = f(3) + g(3) = 21.

Answer:

0

Step-by-step explanation:

are given:

\displaystyle \frac{\sin^2(x)-\sin(x)-2}{\sin(x)-2}

sin(x)−2

sin

2

(x)−sin(x)−2

To make it simpler and more clear, we can let u = sin(x). So:

\displaystyle \frac{u^2-u-2}{u-2}

u−2

u

2

−u−2

Now, it becomes obvious that we can factor, which produces:

\displaystyle =\frac{(u-2)(u+1)}{u-2}=

u−2

(u−2)(u+1)

Cancel:

=u+1=u+1

And substituting back:

=\sin(x)+1=sin(x)+1

Hence, our answer is A.

Answer:

-15

Step-by-step explanation:

-2 to the power 0 = -1

-2 to the power 1 = -2

-2² = -4

-2³ = -8

-1 + -2 + -4 + -8 = -15

We know, 1 year = 12 month.

So, 3 month = 3/12 = 0.25 year.

Now, principle amount, P = $400 .

Rate is, r = 8% = 0.08

Time period, t = 0.25 year.

Now, Interest is given by :

I = P × r × t

I = $( 400 × 0.08 × 0.25 )

I = $8

Therefore, she will pay $8 interest in total.

Answer:

y = 37/5x + 9

Step-by-step explanation:

The points are not plotted on a single straight line, so I will find the general slope using the first and last point on the graph.

(5, 46) & (10, 83)

slope-intercept form: (y₂ - y₁) / (x₂ - x₁)

(83 - 46) / (10 - 5)

Simplify.

(37)/(5)

Your slope is 37/5.

y = 37/5x + b

To find b, plug in a point to x and y.

46 = 37/5(5) + b

46 = 37 + b

b = 9

Your equation is: y = 37/5x + 9

Check by plugging in the other point.

83 = 37/5(10) + 9

83 = 74 + 9

83 = 83

Your equation is correct.

Hope this helps!

Answer:

(-4,-2)

Step-by-step explanation:

Point f is on x -4, which is in the first slot and y -2 which is your second slot