What is 20^2 + 54/9?

Answer:

Solution,

[tex]5 \frac{3}{4} \div 1 \frac{1}{2} [/tex]

Convert the mixed number to an improper fraction

[tex] \frac{23}{4} \div \frac{3}{2} [/tex]

To divide by a fraction, multiply by the reciprocal of that fraction

[tex] \frac{23}{4} \times \frac{2}{3} [/tex]

Reduce the numbers with the GCF 2

[tex] \frac{23}{2} \times \frac{1}{3} [/tex]

Multiply the fraction

[tex] \frac{23}{6} [/tex]

Hope this helps...

Good luck on your assignment...

Answer:

second option

Step-by-step explanation:

The volume (V) of a sphere is calculated as

V = [tex]\frac{4}{3}[/tex] πr³ ( where r is the radius )

Here r = 6 , thus

V = [tex]\frac{4}{3}[/tex]π(6)³

Answer:

Second option

Step-by-step explanation:

Volume of a sphere =  [tex]\frac{4}{3}*\pi *r^{3}[/tex]

→ Substitute in the value of radius

Volume of a sphere =  [tex]\frac{4}{3}*\pi *6^{3}[/tex]

Answer:

the slope of the perpendicular bisector is -2/3

Step-by-step explanation:

The slope of the line joining the two points P1(0,3), P2(6,12) is given by

m1 = (y2-y1) / (x2-x1) = (12-3) / (6-0) = 9/6 = 1.5

The slope m2 of a line perpendicular to the previous line is given by

m1*m2 = -1

solving

m2 = -1/m1 = -1/ (3/2) = -2/3

THerefore the slope of the perpendicular bisector is -2/3

Answer:

[tex]3\sqrt{17}$ or \approx 12.37$ Units[/tex]

Step-by-step explanation:

In the attached diagram

CA=CO+OA

CO=DB

Therefore:

5=2+OA

OA=3 Units

The angle between a tangent line and a radius is 90 degrees. therefore triangle OAB is a right triangle with:

OB=12 units

OA=3 units

Using Pythagoras theorem

[tex]AB=\sqrt{3^2+12^2}\\ =\sqrt{153}\\=3\sqrt{17}$ or \approx 12.37$ Units[/tex]

Step-by-step explanation:

68$53++83(-$(7(3($++$

Answer:

The expression in standard form is -3 + 6i

Step-by-step explanation:

Writing complex equation in standard form we have;

-3 + yi = x + 6i

We transfer the real and imaginary parts to be on different sides of the equation as follows;

yi - 6i = x + 3

We factorize the imaginary part;

i(y-6) = x + 3

We note that the real portion on the left hand side of the equation is zero, therefore, we have;

i(y-6)  + 0= x + 3

x + 3 = 0

Therefore, x = -3

Substituting the value of x in the first equation, we have;

-3 + yi = -3 + 6i

Comparing gives;

y = 6

The expression in standard form is -3 + 6i.

Answer:

20°.

Step-by-step explanation:

According to both the diagram and the presented angle measure, m∠RPS + m∠QPR = m∠QPS.

(4x + 27) + (9x - 115) = 107

4x + 9x + 27 - 115 = 107

13x - 88 = 107

13x = 195

x = 15

Now that we have the value of x, we can find the m∠QPR.

9x - 115

= 9 * 15 - 115

= 135 - 115

= 20

So, m∠QPR is 20°.

Hope this helps!

Answer:

8%

Step-by-step explanation:

Hello,

8% of the students take neither History or French

so we have 8*200/100=8*2=16 students  out of French and History

let s say that

a is the number of students taking only History

b is the number of students taking both History and French

c is the number of students taking only French

10% of those who take History also take French

so 0.10(a+b)=b <=> 0.10a+0.10b=b

<=> 0.10a+0.10b-0.10b=b-0.10b=0.9b

<=> 0.10a=0.90b

let's multiply by 10 it comes a = 9b

4 times as many students take History as take French

so a + b = 4 (b + c)

it comes 9b + b = 10b = 4b + 4c

<=> 10b-4b=4b+4c-4b=4c

<=> 6b=4c

<=> 3b=2c

<=> c = 3b/2

and we know that a + b + c = 200 - 16 = 184

so

9b + b + 3b/2 = 184 we can multiply by 2 it comes

20 b + 3b = 184*2

23b = 184*2 = 23 * 8 *2 = 23*16

b = 23*16/23 = 16

so b = 16

c = 3*16/2 = 24

c = 24

a = 9b = 144

a = 144

you can see the Venn diagram below

and then the probability that a student picked at random does History and French is 16/200 = 8%

so the answer is 8%

hope this helps

Answer:

Step-by-step explanation:

A∩B={x| x∈a and x∈B}

a) A∩B={4,6}

b) A∩B={ 4,9}

c) A∩B={yellow,green}

Answer:

0.5

Step-by-step explanation:

Let D be the event of selecting a marble with dots.

Let P be the event of selecting a purple marble.

The probability of selecting a marble with dots, P(D)=0.2

The probability of selecting a marble that is both purple and has dots, [tex]P(D \cap P)=0.1[/tex]

We want to determine the probability of selecting a purple marble given that the marble has dots on it, P(P|D)

By the definition of conditional probability:

[tex]P(P|D)= \dfrac{P(P \cap D)}{P(D)} \\= \dfrac{0.1}{0.2}\\ =0.5[/tex]

The probability of selecting a purple marble given that the marble has dots on it is 0.5.

Answer:

2x^2+x-1/x^2-1

x^2+11x+18/x^2-11x+18

2x^2-5x+3/x^2+4x+3

Step-by-step explanation:

1.2 and 5

Answer:

10

Step-by-step explanation:

This is an arithmetic sequence.  The common difference is -6, and the first term is 52.

a = 52 − 6(n − 1)

When n = 8:

a = 52 − 6(8 − 1)

a = 52 − 42

a = 10

Answer:

6-3/0-(-4)

=3/4

Step-by-step explanation:

Given two points of a line to find the slope, we use the formula.y2-y1/x2-x1 hence the answer above. Our xs are x2=0 x=-4 y2=6 y1=3

Answer:

Of the 5000​ surveys, 14​% were returned. This response rate APPEARS to be low.

Step-by-step explanation:

Given:

Total sample collected = 5000

Survey returned = 700

i) What percentage of the 5000 surveys were​ returned?

To find percentage returned, we have:

[tex] = \frac{700}{5000} * 100 = 14 percent [/tex]

Percentage returned = 14%

ii) Does that response rate appear to be​ low?

Yes, the response is significantly low as only 14% is returned out of expected 100%

iii) In​ general, what is a problem with a very low response​ rate?

The problem with in low response rate in general is that it causes the result to be biased as biased samples of those interested in a particular aspect may have been gotten.

Therefore, of the 5000​ surveys, 14​% were returned. This response rate APPEARS to be low.

Answer:

d) 405 = 15 times 4.5 times h

The height of the prism 'h' = 6 inches

Step-by-step explanation:

Explanation:-

Given Volume of prism

                            V = 405 cubic inches

Given length of the prism

                         L = 15 inches

Given width of the prism

                       W = 4.5 inches

The volume of the prism

                        V = l w h

                       405 = 15 ×4.5× h

                       405 = 67.5 h

Dividing '67.5' on both sides , we get

                      h = 6 inches

Final answer:-

The height of the prism 'h' = 6 inches

Answer: V = l w h. 405 = 15 times 4.5 times h

Step-by-step explanation:

Given the following :

Volume of prism = 405 in^3

Length = 15 inches

Height = h

Width = 4.5 inches

Recall :

The volume of a prism is the product of the Base and the height.

That is;

Volume = Base × height

However, Base of prism is given by the area of the base shape of the prism.

From our parameters Base shape of the prism is a rectangle.

Therefore, Area of rectangle = Length × width

= 15 inches × 4.5 inches = 67.5 inch^2 = Base of prism

Therefore, Volume of prism equals ;

Volume = 15 × 4.5 × h

Volume = 405in^3

Volume = Base × height

405 = 15 × 4.5 × h

Answer:

2310cm³

Step-by-step explanation:

volume= πr²h

22/7× radius of circle × height

circumference= πd

44cm=22/7×d, diameter= 7 cm, radius= 3.5cm

v= 22/7× 3.5× 21 = 2310cm³

To reflect a function across the x axis, we just stick a negative in front. This will make all point's y coordinates to go from positive to negative or vice versa. If the original function already has a negative out front, then remove it.

Answer: k = 4

Step-by-step explanation:

For this division, to determine the value of k, use the Remainder Theorem, which states that:

polynomial p(x) = dividend (x-a) * quotient Q(x) + remainder R(x)

Knowing the degree of quotient is

degree of Q = degree of p(x) - degree of (x-a)

For this case, Q(x) is a third degree polynomial.

Using the theorem:

[tex]x^{4}-3x^{2}+kx-2 = (x-2)(ax^{3}+bx^{2}+cx+d) + 10[/tex]

[tex]x^{4}-3x^{2}+kx-2 = ax^{4} + x^{3}(b-2a)+x^{2}(c-2a)+x(d-2c)-2d+10[/tex]

a = 1

b - 2a = 0 ⇒ b = 2

c - 2b = -3 ⇒ c = 1

-2d + 10 = -2 ⇒ d = 6

d - 2c = k ⇒ k = 4

Therefore, k = 4 and Q(x) = [tex]x^{4} -2x^{2} + 4x + 2[/tex]

Answer:

Option (D)

Step-by-step explanation:

Sum of interior angles of a polygon is represented by the expression,

Sum of interior angles = n(n - 1)×180°

Here n is the number of sides of a polygon

If n = 18,

Sum of 18 sided polygon = (18 - 1) × 180°

                                         = 7 × 180°

                                         = 3060°

Therefore, sum of interior angles of a 18 sided polygon will be 3060°.

Option (D) will be the answer.

Answer:

2880

Step-by-step explanation:

SUM=_-2=

18-2=16

16*180 = 2880 OR

18*160 = 2880 degrees

Answer:

answer is 8x+10x

18x

is the answer

it is 9

and it is also 54

Answer:

3 and 63.

Step-by-step explanation:

The sequence formula is [tex]\frac{3n(n+1)}{2}[/tex].

Resulting in a sequence of 0, 3, 9, 18, 30, 45, 63.

Answer:

4x – 3 + 2x = 33

6x = 36

x = 6

D. x = 6

Answer: subtract 85 with a hundred because you are trying to see how many students out of 100% are good students after that you should get your answer

Step-by-step explanation:

Answer:

77% (rounded)

Step-by-step explanation:

1. Find 85% of 100

           100 x 0.85 = 85

     SO 85 students out of 100 students are good students.

2. Add the 10 more students to the total number.

             100 + 10 = 110 total students

3. Find the percent of good students in the total number of current students.

          85/110 = 0.77 * 100 (to convert to percent) = 77%

Answer:

2</x  or x>/2

Step-by-step explanation:

-6>/10-8x

-10   -10

-16>/-8x

divide both sides by -8

2</x  or x>/2

the reason the sign is bc u r dividing by a - number.

Answer:

x ≥ 2

Step-by-step explanation:

-6 ≥ 10 - 8x

Subtract 10 on both parts.

-6 - 10 ≥ 10 - 8x - 10

-16 ≥ -8x

Divide both parts by -8 remembering to  reverse sign.

-16/-8 ≤ (-8x)/-8

2 ≤ x

Switch parts.

x ≥ 2

the correct answer is:

A. 9/-6

Answer:

[tex]\dfrac{2}{3}.[/tex]

Step-by-step explanation:

It is given that a box contains 2 dozen pairs of contact lenses ,of which 8 pairs are tinted.

1 dozen = 12 units

Total pairs of contact lenses [tex]=2\times 12 = 24[/tex]

Tinted pairs of contact lenses = 8

Pairs of contact lenses not tinted = 24 - 8 = 16

If a pair of contact lenses is drawn at random from the box, then we need to find the probability that it is not tinted.

[tex]P(\text{Not tinted})=\dfrac{\text{Pairs of contact lenses not tinted}}{\text{Total pairs of contact lenses}}[/tex]

[tex]P(\text{Not tinted})=\dfrac{16}{24}[/tex]

[tex]P(\text{Not tinted})=\dfrac{2}{3}[/tex]

Therefore, the required probability is [tex]\dfrac{2}{3}.[/tex]

Answer:

(Change in y)/(change in x) is defined as the average rate of change.

For a linear equation:

y = a*x + b

A is the average rate of change, and is called the "slope" of the linear equation, and this is a constant.

Then the sentence will be:

"The average change between two ordered pairs (x,y) is the ratio (change in x)/(change in y)

In a linear function, this is called the slope, and it is constant"

Answer:

We can write:

x + y = -2

xy = -80

We can rewrite the first equation as x = -y - 2 and then plug that into the second equation to get (-y-2) * y = -80 → -y² - 2y = -80 → y² + 2y - 80 = 0 → (y - 8)(y + 10) = 0 → y = 8, -10. Substituting these values into the first equation we get x = -10, 8 so the answer is (x₁, y₁) = (-10, 8) or (x₂, y₂) = (8, -10).

Answer:

[tex]Time = 7.5\ seconds[/tex]

Step-by-step explanation:

Given

[tex]Equation:\ h(t) = -16t^2 + 120t[/tex]

[tex]Initial\ Velocity = 160ft/s[/tex]

Required:

Determine the time taken to return to the ground

From the equation given; height (h) is a function of time (t)

When the rocket returns to the ground level, h(t) = 0

Substitute 0 for h(t) in the given equation

[tex]h(t) = -16t^2 + 120t[/tex]

becomes

[tex]0 = -16t^2 + 120t[/tex]

Solve for t in the above equation

[tex]-16t^2 + 120t = 0[/tex]

Factorize the above expression

[tex]-4t(4t - 30) = 0[/tex]

Split the expression to 2

[tex]-4t = 0\ or\ 4t - 30 = 0[/tex]

Solving the first expression

[tex]-4t = 0[/tex]

Divide both sides by -4

[tex]\frac{-4t}{-4} = \frac{0}{-4}[/tex]

[tex]t = \frac{0}{-4}[/tex]

[tex]t =0[/tex]

Solving the second expression

[tex]4t - 30 = 0[/tex]

Add 30 to both sides

[tex]4t - 30+30 = 0+30[/tex]

[tex]4t = 30[/tex]

Divide both sides by 4

[tex]\frac{4t}{4} = \frac{30}{4}[/tex]

[tex]t = \frac{30}{4}[/tex]

[tex]t = 7.5[/tex]

Hence, the values of t are:

[tex]t =0[/tex] and [tex]t = 7.5[/tex]

[tex]t =0[/tex] shows the time before the launching the rocket

while

[tex]t = 7.5[/tex] shows the time after the rocket returns to the floor