if p= 1/3 what is the answer to 9p2=

Answers

Answer 1
The correct answer is 6
Answer 2

When p equals 1/3, 9p^2 calculates to 1 after squaring p and multiplying by 9.

The question involves calculating the expression 9p^2 given that p = 1/3. First, we square the value of 'p' and then multiply it by 9. Following the process, we have:

[tex](\frac{1}{3} )^2 = \frac{1}{9} \\9 \times (\frac{1}{9} ) = 1[/tex]

Therefore, 9p^2 is equal to 1 when p is equal to 1/3.


Related Questions

You are expecting a call from a friend anytime between 3:00 P.M. and 5:00 P.M. At 3:20 P.M, you discover that someone accidentally left the phone off the hook. What is the probability that you missed your friend’s call?

Answers

The working out:
Difference between 3:00 and 5:00 = 120 mins or 2 hours.
There is a possibility of 20/120 that you missed your friends call.
Hope this helped. If you need more explaining, let me know in the comments. 

The probability that you missed your friend’s call is 1/6

How to determine the probability?

The range is given as:

Range = 3:00 P.M. and 5:00 P.M.

The number of minutes in the range is:

Total = 120 minutes

At 3:20 that you notice the phone is off the hook, the number of minutes missed is:

Time missed = 20 minutes

The probability is then calculated as:

P = 20/120

Evaluate

P = 1/6

Hence, the probability that you missed your friend’s call is 1/6

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Unit 2 | Lesson 10
Lesson Assessment:

Core Focus: Problem Solving with Equations Quiz
Question Navigator
Choose the answer.

1.



Marco and Drew stacked boxes on a shelf. Marco lifted 9 boxes and Drew lifted 14 boxes. The boxes that Drew lifted each weighed 8 lb less than the boxes Marco lifted.



Which expression represents the total number of pounds Drew lifted?


Let m represent the weight of the boxes that Marco lifted.



A.


m − 8


B.


14(m − 8)


C.


9(m + 8)


D.


112m
Question Resources

Answers

The answer is B. 14(m − 8)

m represent the weight of the boxes that Marco lifted.
d represent the weight of the boxes that Drew lifted.

The boxes that Drew lifted each weighed 8 lb less than the boxes Marco lifted:
d = m - 8

So the weight of one box that Drew lifted is (m - 8). Since he lifted boxes, the total number of pounds Drew lifted is  14(m - 8)  

I need help with this question

Answers

All this is more or less a proportion type of question.

2/X = 8/64
8/4 = 2
64/4 = 16

The value of X is 16 cubic metres.

The sum of two consecutive integers is at most 223.

What is the larger of the two integers?

Answers

Divide 223 by 2: 223/2 = 111.5

Then fix one number to 111.5 - 0.5 ann the other to 111.5 + 0.5

The two numbers are 111 and 112.

Then the answer is 112. 

Answer:

112

Step-by-step explanation:

The ratio if the base edges of two similar pyramids is 3:4 the volume of the larger pyramid is 320 in^3. What is the volume of the smaller pyramid???

Answers

ratio of voljumes = 3^3 : 4^3 or 27:64 small/large = 27 / 64 vol of smaller = 27 * 320 / 64 =135

Answer:

135 cubic inches.

Step-by-step explanation:

Given : The ratio of the base edges of two similar pyramids is 3:4

           The volume of the larger pyramid is 320 cubic inches.

To Find: What is the volume of the smaller pyramid?

Solution:

The ratio of the base edges of two similar pyramids is 3:4

The volume of the larger pyramid is 320 cubic inches.

The ratio of the volume of pyramids is equal to the ratio of the cubes of the sides of pyramids .

So, [tex]\frac{3^3}{4^3} =\frac{\text{Volume of smaller pyramid}}{320}[/tex]

[tex]\frac{27}{64} =\frac{\text{Volume of smaller pyramid}}{320}[/tex]

[tex]\frac{27}{64} \times 320 =\text{Volume of smaller pyramid}[/tex]

[tex]135 =\text{Volume of smaller pyramid}[/tex]

Thus the volume of smaller pyramid is 135 cubic inches.

What is the value of x?

x+58=6x+58=6

Enter your answer in the box in simplest form.
x =

Answers

x + 58 = 6
x = 6 - 58
x = - 52

Answer:  The required value of x is -52.

Step-by-step explanation:  We are given to find the value of x from the following equation :

[tex]x+58=6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the value of x, we need to solve the equation (i).

The solution of equation (i) is as follows :

[tex]x+58=6\\\\\Rightarrow x=6-58\\\\\Rightarrow x=-52.[/tex]

Thus, the required value of x is -52.

which of the following is not a perfect square?
A. 36
B. 45
C. 64
D. 81 ...?

Answers

Final answer:

Among the options given, B. 45 is not a perfect square because no integer squared equals 45.

Explanation:

The question is asking us to identify which number among the given options is not a perfect square. A perfect square is a number that can be expressed as the product of an integer with itself. Here are the given options with explanations:

A. 36 - This is a perfect square because 6 x 6 equals 36.B. 45 - This is not a perfect square because there is no integer which, when multiplied by itself, equals 45.C. 64 - This is a perfect square because 8 x 8 equals 64.D. 81 - This is a perfect square because 9 x 9 equals 81.

Therefore, the number that is not a perfect square in the options provided is B. 45.

how can i factor this?
x^(2n)-2x^(n)+1

Answers

You can make it easier by replacing x^n with another variable, factoring, then putting x^n back in the end.

Using exponent and algebra rules, rewrite x^2n - 2x^n + 1 as
(x^n)^2 - (2 x x^2) + 1

Then, let x^n = m.

m^2 - 2m + 1

Now factor that: (m - 1)^2

And now put x^n back: (x^n - 1)^2

What is the work to 256.50 divided y 8 equal?

Answers

 I think the answer is 256.5/8y

There were 500 people at a play. the admission price was $6 for general public and $3 for students. the admission receipts were $2640. solve a system of equations to find how many students attended.

Answers

its 880 i think but hope yhu get it right

Is -√127 rational or irrational?

Answers

Answer:

Irrational

Step-by-step explanation:

A rational number can be expressed as a ratio of two integers , p and q of the form \[\frac{p}{q}\]

So following are examples of rational numbers:

\[\frac{1}{2}\] is a rational number\[\frac{3}{4}\] is a rational number2 is a rational number as it can be expressed as \[\frac{2}{1}\]

On the other hand , any number which cannot be expressed in this form is called an irrational number. For example:

\[\sqrt{2}\]\[\sqrt{3}\]\[-\sqrt{127}\]

Find the x-intercept of the tangent line to the graph of f at the point P(0,f(0)) when f(x)= e^-x(5cosx+2sinx)

Answers

f ( 0 ) = e^0 * ( 5 cos 0 + 2 sin 0 = = 1 * 5 = 5
f ` ( x ) = - e^(-x) * ( 5 cos x + 2 sin x ) + e^(-x) * ( - 5 sin x + 2 cos x ) =
( using the chain rule ) 
= e^(-x) * ( - 5 cos x - 2 sin x - 5 sin x + 2 cos x ) =
= e^(-x) * ( - 3 cos x - 7 sin x )
f ` ( x ) = 1 * ( - 3 - 0 ) = - 3
The equation of the tangent line:
y - f ( 0 ) = f ` ( 0 ) * ( x - 0 )
y - 5 = - 3 x
y = - 3 x + 5
The x - intercept of the tangent line:
0 = - 3 x + 5
3 x = 5
x = 5 / 3
or ( 5/3, 0 ) 

Given that f(x) = x² + 4x, evaluate f(-2).

Answers

F(-2)=-4
let me know if you want me to show my work

Answer:

The evaluation is [tex]f(-2)=-4[/tex]

Step-by-step explanation:

We were given an explicit function of x, wich has the form

[tex]f(x)=x^2+4x[/tex]

The problem ask to evaluate f(-2), this means to put the value x=-2 into the function, so

[tex]f(-2)=(-2)^2+4(-2)=4-8=-4[/tex]

Therefore, the answer is

[tex]f(-2)=-4[/tex]

What is the measure of angle ABD on trapezoid ABCD?
24
40
64
92

Answers

40 degrees because angle ADB is 24 degrees and forming triangle BAD, the sum of the angles should be 180. 180- (24+116) = 40 degrees.

Let

m∠ABD--------> x degrees

we know that

The sum os the internal angles of a trapezoid is equal to [tex] 360 degrees [/tex]

So

[tex] 2*116+2*(24+x)=360\\ 232+48+2x=360\\ 2x=360-280\\ x=40degrees [/tex]

therefore

the answer is

The measure of the angle m∠ABD is [tex] 40 degrees [/tex]

Assume a 30-month cd purchased for $3000 pays simple interest at an annual rate of 5.5%. how much total interest does it earn? what is the balance at maturity?

Answers

It will earn 0.55 x 4000 = ? annually. 
? x 2.5 years = total interest earned. 
4000 + interest earned = balance at maturity.
Final answer:

The total simple interest earned on a $3000 CD over 30 months with an annual interest rate of 5.5% is $412.50 and the balance at maturity is $3412.50.

Explanation:

To calculate the total amount of simple interest earned on a certificate of deposit (CD) we use the formula I = Prt, where I is interest, P is the principal amount (initial amount of money), r is the annual interest rate (in decimal form), and t is the time in years. For the given 30-month CD purchased for $3000 with an annual simple interest rate of 5.5%, we first convert 30 months to years by dividing by 12 (30 / 12 = 2.5 years).

Using the formula: I = $3000 × 0.055 × 2.5 = $412.50. Therefore, the total interest earned is $412.50.

To calculate the balance at maturity, we add the total interest to the principal: Balance = Principal + Interest = $3000 + $412.50 = $3412.50.

Find the integral of sqrt(4x-x^2)dx.

Answers

∫ √(4x - x²) dx
= 2[(4x - x²)^(3/2)] / 3(4 - 2x)

The value of integral is  2 * arc sin((x - 2) / 2) + (x - 2) * √(4 - (x - 2)²) / 2 + C.

To solve the integral ∫ √(4x - x²) dx, follow these steps:

Complete the Square: Rewrite the quadratic expression under the square root. Start with: 4x - x²

Rearrange it to the standard quadratic form: -x² + 4x. To complete the square, factor out the negative sign: (x² - 4x)

Next, complete the square inside the parentheses:

x² - 4x = (x - 2)² - 4

So, we get:

(x² - 4x) = - [(x - 2)² - 4] = 4 - (x - 2)²

Therefore:

√(4x - x²) = √(4 - (x - 2)²)

Substitute Variables: Let u = x - 2. Then, du = dx, and the integral becomes:

∫ √(4 - u²) du

Apply the Trigonometric Substitution: Use the trigonometric substitution u = 2 sin θ. Then du = 2 cos θ dθ. Substitute these into the integral:

∫ √(4 - (2 sin θ)²) * 2 cos θ dθ

= ∫ √(4 - 4 sin² θ) * 2 cos θ dθ

= ∫ √(4 (1 - sin² θ)) * 2 cos θ dθ

= ∫ 2 cos θ * 2 cos θ dθ

= ∫ 4 cos² θ dθ

Use Trigonometric Identity: Apply the double-angle identity cos² θ = (1 + cos 2θ) / 2:

∫ 4 cos² θ dθ

= ∫ 4 * (1 + cos 2θ) / 2 dθ

= ∫ (4 + 4 cos 2θ) / 2 dθ

= ∫ (2 + 2 cos 2θ) dθ

Integrate each term:

∫ 2 dθ + ∫ 2 cos 2θ dθ = 2θ + sin 2θ + C

Back-substitute: Replace θ with the original variable x. Recall u = 2 sin θ, so θ = arcsin(u / 2). Since u = x - 2, substitute back:

θ = arcsin((x - 2) / 2)

Therefore:

2 * arcsin((x - 2) / 2) + sin(2 * arcsin((x - 2) / 2)) + C

Using the identity sin(2θ) = 2 sin θ cos θ:

sin(2 * arcsin((x - 2) / 2))

= 2 * (x - 2) / 2 * √(1 - ((x - 2) / 2)²)

= (x - 2) * √(4 - (x - 2)²) / 2

Beck used a compass and straightedge to accurately construct line segment OS as shown in the figure.

Which could be the measures of angle POS and angle POQ?

A) m∠POS = 60° , m∠POQ = 120°
B) m∠POS = 50° , m∠POQ = 110°
C) m∠POS = 50° , m∠POQ = 120°

Answers

Based on the given figure above, we can find the measures of angle POS and angle POQ by analyzing it carefully. Look for POS and POQ where POS = 1/2 POQ. Base on this, we can conclude that measure of angle POS = 60° and measure of angle POQ = 120°. Therefore, the answer would be option A. 

Observe the figure below.

The given figure shows that the construction of line segment OS. We can observe clearly that OS is bisector of angle POS.

The bisector divides the angle into two equal angles.

So, [tex]\angle POS = \frac{1}{2} \angle POQ[/tex]

Let us observe the given options.

In first option, [tex]60^\circ = \frac{1}{2} \times 120^\circ[/tex]

Therefore, [tex]m \angle POS = 60^\circ, m \angle POQ=120^\circ[/tex]

So, Option A is the correct answer.

Given:
AB = BC
ADB =

Answers

I hope this helps you

Answer:

[tex]m{\angle}D=60^{\circ}[/tex]

Step-by-step explanation:

From the given figure, it can be seen that [tex]m{\angle}A=60^{\circ}[/tex], [tex]m{\angle}B=60^{\circ}[/tex], thus

From ΔABD, using the angle sum property, we have

[tex]m{\angle}A+m{\angle}B+m{\angle}D=180^{\circ}[/tex]

⇒[tex]60^{\circ}+60^{\circ}+m{\angle}D=180^{\circ}[/tex]

⇒[tex]120^{\circ}+m{\angle}D=180^{\circ}[/tex]

⇒[tex]m{\angle}D=180^{\circ}-120^{circ}[/tex]

⇒[tex]m{\angle}D=60^{\circ}[/tex]

therefore, the measure of [tex]{\angle}ADB[/tex] is [tex]60^{\circ}[/tex].

Hence, ΔABD is an equilateral triangle.

What angle represents 3.5 rotations counterclockwise?

Answers

1 full rotation is 2pi, or 360 degrees. 
3.5 times either of those gives you 7pi, or 1260 degrees. Since you going counterclockwise already, you don't have to bother with negative signs. 

7pi, or 1260 degrees.

The angle represents by 3.5 rotations in counterclockwise is 1260 degree or [tex]\frac{7}{2}\pi[/tex] radian.

In one complete rotation, the angle made is = 360 degree or [tex]\pi[/tex] radian

So, In 3.5 rotation, angle made is, = [tex]360*3.5=1260[/tex] degree

       Or,                                                   =  [tex]3.5*\pi=\frac{7}{2}\pi[/tex] radian

Therefore, The angle represents by 3.5 rotations in counterclockwise is 1260 degree or  [tex]\frac{7}{2}\pi[/tex] radian.

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A goat is tethered by a 6 metre rope to the outside corner of a shed measuring 4 metres by 5 metres in a grassy field. What area of grass can the goat graze? ...?

Answers

Final answer:

The area of grass that the goat can graze is calculated as a quarter-circle with a radius equal to the length of the rope, which is 6 metres, resulting in an area of approximately 28.27 square metres.

Explanation:

The area of grass a goat can graze when tethered by a 6 metre rope to the outside corner of a shed is a segment of the grassy field. To calculate this area, one must consider two scenarios based on the dimensions of the shed:

If the shed's dimensions of 4 metres by 5 metres do not allow the goat to reach the opposite corner, then the area grazed is a quarter-circle with the rope as the radius.

If the shed's dimensions allow the goat to reach around the corner, then additional area calculations are necessary for the extended grazing area beyond the corner.

In the stated problem, the rope's length does not allow the goat to graze beyond the opposite corner of the shed. Therefore, we calculate the area as a quarter-circle, which is a fraction (1/4) of the area of a full circle with radius 6 metres. The formula for the area of a circle is πr², where r is the radius.

To find the grazeable area, we use:

Area = (1/4) × π × radius² = (1/4) × π × 6² = (1/4) × π × 36

Area = 9π square metres (approximately 28.27 square metres)

The effective grazing area is 22.26 square meters.

The goat can graze in a quarter-circle sweep around the corner where the shed does not block its path.

Step-by-Step Calculation

The goat can graze around the corner up to a 6 metre radius, but the shed blocks its grazing in certain directions.

Calculate the total quarter-circle area the goat can cover:

Area = (1/4) * π * radius² = (1/4) * π * 6² = (1/4) * π * 36 = 9π square metres.

Subtract the area where the shed blocks grazing:

From one corner, the shed blocks a rectangular area measuring 4 meters by 6 meters.

Total area blocked by the shed: 6m * 4m = 24 square meters

Adjust for quarter-circle section, dividing the blockage by 4: 24 / 4 = 6 square meters

The area of grass the goat can graze = Total area - Blocked area

9π - 6 ≈ 28.26 - 6 ≈ 22.26 square metres

Thus, the total area grazed by the goat is 22.26 square meters.

The initial number of views for a certain website was 15. The number of views is growing exponentially at a rate of 22% per week. What is the number of views expected to be four weeks from now? Round to the nearest whole number. Enter your answer in the box. ( please answer my questions never get answered...)

Answers

well if it is increasing exponentially your going to use the formula

X(t)=Xo x(1+r)to the power of 4

or just X(t) = 15 x (1+0.22)4 and that equals 33.2300184

Your answer is 33 views in four weeks. 

Answer:

i took the test

Step-by-step explanation:

What is the equation in point slope form of the line that passes through the point (2, 6) and has a slope of 5?

y+6=5(x+2)y+6=5(x+2)

y−6=5(x−2)y−6=5(x−2)

y+2=5(x+6)y+2=5(x+6)

y−2=5(x−6)

Answers

y - 6 = 5(x - 2) is the required equation.

What is the vertex of the following parabola?
y=(x-2)^2+3

Answers

Given the following quadratic equation: y = (x-2)^2+3, the vertex is the coordinate (2,3).

integrate t sec^2 (2t) dt

Answers

f = t ⇨ df = dt 
dg = sec² 2t dt ⇨ g = (1/2) tan 2t 
⇔ 
integral of t sec² 2t dt = (1/2) t tan 2t - (1/2) integral of tan 2t dt 
u = 2t ⇨ du = 2 dt 

As integral of tan u = - ln (cos (u)), you get : 

integral of t sec² 2t dt = (1/4) ln (cos (u)) + (1/2) t tan 2t + constant 
integral of t sec² 2t dt = (1/2) t tan 2t + (1/4) ln (cos (2t)) + constant 
integral of t sec² 2t dt = (1/4) (2t tan 2t + ln (cos (2t))) + constant ⇦ answer 

Answer:

[tex]\int {t\times \sec^2(2t)} \, dt \\\\ \text{Integrating by parts}\\\\=\frac{t\times \tan 2t}{2}-\int{(\frac{d}{dt}(t) \times \int{{\ sec^{2}(2t)}}) dt}\\\\=\frac{t\times \tan 2t}{2}-\int{\frac{\tan 2t}{2}} dt\\\\=\frac{t\times \tan 2t}{2}-\frac{\log sec 2t}{4}+C[/tex]

Where C is Constant of Proportionality.

What is the area of a circle with endpoints (-2, 0), (0, 2), (0, -2), and (2, 0).
Will be rewarded 50 points for CORRECT and WELL EXPLAINED answer.

Answers

I hope this helps you
area of a circle is A=π* r2, You'd have to pull in the numbers 
giving you 12.56

Solve using the quadratic formula.
3x^2+6x+7=0

Answers

I hope this helps you

The quadratic equation 3x^2+6x+7=0 has two complex solutions which is x=-1±√(48)i/6.

To solve the quadratic equation 3x^2+6x+7=0 using the quadratic formula, we first need to identify the coefficients a, b, and c from its standard form, which is ax^2+bx+c=0. In this case, a=3, b=6, and c=7.

The quadratic formula is given by x=(-b±√(b^2-4ac))/(2a).

Now, we will calculate the discriminant which is b^2-4ac. In this case, it is 6^2 - 4*3*7, which equals 36 - 84, or -48. Since the discriminant is negative, this means that there are no real solutions to the equation, but two complex solutions.

Applying the quadratic formula, we get the solutions:

x=(-6 ± √(-48))/(2*3)

This simplifies to:

x=(-6 ± √(48)i)/6

Therefore, the solutions are x=-1±√(48)i/6. The quadratic formula helped us to find the complex roots of the quadratic equation.

What is the estimate quotient for 555÷ 8

Answers

555 / 8 = 69.375 ok

The estimated quotient for 555 ÷ 8 would be 70.

To estimate the quotient for 555 ÷ 8, we can follow these steps:

We know that Quotients are number that is obtained by dividing one number by another number.

Dividend ÷ Divisor = Quotients

Round the dividend, 555, to the nearest ten:

555 rounds to 560.

Divide the rounded dividend, 560, by the divisor, 8:

560 ÷ 8 = 70.

Therefore, the estimated quotient for 555 ÷ 8 is 70.

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73 divided by 8 with remainder

Answers

Is 9r1 hope it help bro

The final result is 73 divided by 8 equals 9, with a remainder of 9.

When you divide 73 by 8, use long division to find the quotient and remainder.

1. Write the dividend (73) and the divisor (8) as shown:

                                             8 | 73

2. Start dividing:  Since 8 is larger than 7, we move to the next digit.

3. Bring down the next digit (3) to the right of the remainder:

                                                  8 | 73 | 8

                                                     - 64

                                                     _____

                                                          9

4. The remainder is 9.

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7.25 cm plus 7.2 cm plus 8cm equals what

Answers

there correct answer to that question is 22.45
22.45 is the correct answer. Just add

6.8-4.2b=5.6b-3 is this equation identify or has no solution

Answers

Answer:

1 = b

Step-by-step explanation:

6.8 - 4.2b = 5.6b - 3

First you must add 4.2b to both sides.

Then you will get 6.8 = 9.8b - 3.

Next you must add 3 to both sides.

You will then get 9.8 = 9.8b

Finally divide both sides by 9.8.

You will be left with  1 = b

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