if the probability of david passing his exam is 1/4 what is the probabilty of him failing​

Answer:

2x^2 +5x-12

Step-by-step explanation:

(2x - 3)(x + 4)

FOIL

first 2x*x = 2x^2

outer  2x*4 = 8x

inner  -3x

last -3*4 = -12

Add these together

2x^2 +8x-3x-12

Combine like terms

2x^2 +5x-12

Answer:

Unpainted  surface area = 514.28 cm²

Step-by-step explanation:

Given:

Side of cube = 20 Cm

Radius of circle = 20 / 2 = 10 Cm

Find:

Unpainted  surface area

Computation:

Unpainted  surface area = Surface area of cube - 6(Area of circle)

Unpainted  surface area = 6a² - 6[πr²]

Unpainted  surface area = 6[a² - πr²]

Unpainted  surface area = 6[20² - π10²]

Unpainted  surface area = 6[400 - 314.285714]

Unpainted  surface area = 514.28 cm²

Answer:

6n = 1.50

and

13n = 3.12

Step-by-step explanation:

Here in this question, we are interested in writing equations that relate the number of ears of corn sold and the cost.

For Al’s produce stand, let the price per corn sold be n

Thus;

6 * n = 1.50

6n = $1.50 •••••••(i)

For the second;

let the price per corn sold be n;

13 * n = $3.12

-> 13n = 3.12 •••••••••(ii)

Answer:

[tex]3\pi[/tex]

Step-by-step explanation:

The circumference of a circle is [tex]2\pi r[/tex].

If we want to find the circumference of this semi-circle, we can find the circumference if it was a whole circle then divide by 2.

[tex]2 \cdot \pi \cdot r\\2 \cdot \pi \cdot 3\\6 \cdot \pi\\ 6\pi[/tex]

Now we know the circumference of the whole circle.

To find the circumference of half the circle we divide by 2.

[tex]6\pi \div 2 = 3\pi[/tex]

Hope this helped!

Answer and Step-by-step explanation: Equations of line through points and slope can be determined by:

[tex]y-y_{0}=m(x-x_{0})[/tex]

m is slope

Y-intercept is point (0,-2)

m = [tex]\frac{y_{a}-y_{b}}{x_{a}-x_{b}}[/tex]

m = [tex]\frac{-4-(-2)}{2-0}[/tex]

m = - 1

Equation:

[tex]y+2=-1(x-0)[/tex]

[tex]y=-x-2[/tex]

m = [tex]\frac{2-1}{4-3}[/tex]

m = 1

Equation:

[tex]y-2=(x-4)[/tex]

[tex]y=x-2[/tex]

m = -2

Equation:

[tex]y-2=-2(x-3)[/tex]

[tex]y=-2x+6+2[/tex]

[tex]y=-2x+8[/tex]

Answer:

The perimeter of the triangle is 40.

Step-by-step explanation:

Pythagorean Theorem:  If x and y are the leg lengths of a right triangle, then r = √(x^2 + y^2) is the length of the hypotenuse.  Alternatively, x^2 + y^2 = r^2.

The side lengths 2x, 4x - 1 and 4x + 1 are already arranged in ascending order.  Thus, (2x^)2 + (4x - 1)^2 = (4x + 1).    

Performing the indicated operations, we get:

         4x^2 + 16x^2 - 8x + 1 = 16x^2 + 8x + 1.  Simplify this first by combining like terms:

         20x^2 - 16x = 16x^2, or

         4x^2 - 16x = 0, or

          4x(x - 4) = 0.  Thus, x = 0 (which makes no sense here) or x = 4.  

The perimeter of the rectangle is the sum of the three sides 2x, 4x - 1 and 4x + 1.  Substituting 4 for x, we get

P = 8 + 16 - 1 + 16 + 1, or 40.

The perimeter of the triangle is 40.                        

Answer:

h= 24 inches

Step-by-step explanation:

(Volume)= (Base Area) * (Height)

6,912= 288h

h=

Answer:

Average speed during the trip = 24 km/h

Step-by-step explanation:

Given:

Speed of cyclist uphill, [tex]v_1[/tex] = 20 km/hr

Speed of cyclist on flat ground = 24 km/h

Speed of cyclist downhill, [tex]v_2[/tex] = 30 km/h

Cyclist has traveled on the hilly road to Beast Island from Aopslandia and then back to Aopslandia.

That means, one side the cyclist went uphill will the speed of 20 km/h and then came downhill with the speed of 30 km/h

To find:

Average speed during the entire trip = ?

Solution:

Let the distance between Beast Island and Aopslandia = D km

Let the time taken to reach Beast Island from Aopslandia = [tex]T_1\ hours[/tex]

Formula for speed is given as:

[tex]Speed = \dfrac{Distance}{Time}[/tex]

[tex]v_1 = 20 = \dfrac{D}{T_1}[/tex]

[tex]\Rightarrow T_1 = \dfrac{D}{20} ..... (1)[/tex]

Let the time taken to reach Aopslandia back from Beast Island = [tex]T_2\ hours[/tex]

Formula for speed is given as:

[tex]Speed = \dfrac{Distance}{Time}[/tex]

[tex]v_2 = 30 = \dfrac{D}{T_2}[/tex]

[tex]\Rightarrow T_2 = \dfrac{D}{30} ..... (2)[/tex]

Formula for average speed is given as:

[tex]\text{Average Speed} = \dfrac{\text{Total Distance}}{\text{Total Time Taken}}[/tex]

Here total distance = D + D = 2D km

Total Time is [tex]T_1+T_2[/tex] hours.

Putting the values in the formula and using equations (1) and (2):

[tex]\text{Average Speed} = \dfrac{2D}{T_1+T_2}}\\\Rightarrow \text{Average Speed} = \dfrac{2D}{\dfrac{D}{20}+\dfrac{D}{30}}}\\\Rightarrow \text{Average Speed} = \dfrac{2D}{\dfrac{30D+20D}{20\times 30}}\\\Rightarrow \text{Average Speed} = \dfrac{2D\times 20 \times 30}{{30D+20D}}\\\Rightarrow \text{Average Speed} = \dfrac{1200}{{50}}\\\Rightarrow \bold{\text{Average Speed} = 24\ km/hr}[/tex]

So, Average speed during the trip = 24 km/h

Answer:

son2: 5

son1: 10

Step-by-step explanation:

2x (son1) + x (son2) + 35 (mother) + 3 (years)*3 (people) = 59

3x = 15

x = 5

The age of each boy at present will be 2 years and 3 years.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Let the age of the sons will be x and y.

A mother who is 35 years old has two sons, one of whom is twice as old as the other. Then the equation will be

x = 2y

In 3 years, the sum of all their ages will be 59 years. Then the equation will be

x + y + x + 1 + y + 1 + x + 2 + y + 2 + 35 = 59

Simplify the equation, we have

3x + 3y + 41 = 59

      6y + 3y = 59 – 41

              9y = 18

                y = 2

Then the value of x will be

x = 2y

x = 2(2)

x = 4

Thus, the age of each boy at present will be 2 years and 3 years.

More about the linear system link is given below.

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Answer:

-2, 3

Step-by-step explanation:

To find the coordinates of B, we need to understand the translation that has taken place. In a translation, each point of a figure is moved the same distance and in the same direction.

In this case, point A(5, 1) has been translated to point A'(6, -2). To find the distance and direction of the translation, we subtract the coordinates of A from the coordinates of A': Translation Vector [tex]= (6 - 5, -2 - 1) = (1, -3)[/tex] The translation vector represents the change in x and y coordinates between the original figure and its translated image.

Since B' has coordinates (-1, 0), we can apply the translation vector to find the coordinates of B as follows: B = B' - Translation Vector B [tex]= (-1, 0) - (1, -3)[/tex]  B [tex]= (-1 - 1, 0 - (-3)) B = (-2, 3)[/tex] So, the coordinates of B are (-2, 3).

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Answer:

the answer is 41

Step-by-step explanation:

C. 41

Step-by-step explanation:

240

using pascals trianle

for the power 6 it is

1, 6,15,20, 15,6, 1

and for the third term (2x)^4 and (-1)^2

[tex]15 \times {(2x)}^{4} \times {( - 1)}^{2} [/tex]

[tex]240 {x}^{4} [/tex]

Since only the coefficient is needed

the answer is 240.

The required coefficient of third term is 480.

Coefficient of the third term of (2x−1)^6 to be determine.

Coefficient is defined as the integer present adjacent to the variable.

Here,  (2x−1)^6
Using binomial expansion,
Third term = P(6,2)(2x)^6-2(-1)^2
                  =   6*5*16x^4
                  = 480x^4

Thus, the required coefficient of third term is 480.

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Answer:

83 adult tickets and 217 student tickets.

Step-by-step explanation:

Let number of adult tickets sold = [tex]x[/tex]

Given that total number of tickets = 300

So, number of student tickets = 300 - [tex]x[/tex]

Cost of adult ticket = $15

Cost of student ticket = $11

Total collection from adult tickets = $[tex]15x[/tex]

Total collection from student tickets =  [tex](300-x)\times 11 = 3300-11x[/tex]

Given that overall collection = $3630

[tex]15x+(3300-11x) = 3630\\\Rightarrow 15x-11x=3630-3300\\\Rightarrow 4x = 330\\\Rightarrow x = 82.5[/tex]

So, for atleast $3630 collection, there should be 83 adult tickets and (300-83 = 217 student tickets.

Now , collection = $3632

Answer:

Step-by-step explanation:

39/5 as a mixed number;

39/5 as a mixed number;39 ÷ 5 = 6 remaining 9

Therefore:

6 9/5

false

Step-by-step explanation:

false

Answer:

-5/24

Step-by-step explanation:

get a common denominator = 24

-14/24 + 9/24 = -5/24

Answer:-5 /24 ez

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the function [tex]G(x)= -\dfrac{x^2}{4} + 7[/tex], the average rate of change of g(x) over the interval [-2,4], is expressed as shown below;

Rate of change of the function is expressed as g(b)-g(a)/b-a

where a - -2 and b = 4

[tex]G(4)= -\dfrac{4^2}{4} + 7\\G(4)= -\dfrac{16}{4} + 7\\G(4)= -4 + 7\\G(4) = 3\\[/tex]

[tex]G(-2) = -\dfrac{(-2)^2}{4} + 7\\G(-2)= -\dfrac{4}{4} + 7\\G(-2)= -1 + 7\\G(-2)= 6[/tex]

average rate of change of g(x) over the interval [-2,4] will be;

[tex]g'(x) = \frac{g(4)-g(-2)}{4-(-2)}\\ g'(x) = \frac{3-6}{6}\\\\g'(x) = -3/6\\g'(x) = -1/2[/tex]

Answer:

-2x+4

Step-by-step explanation:

2(x+2) - 4x

Distribute

2x+4 - 4x

Combine like terms

-2x+4

Answer:

-2x+4

Step-by-step explanation:

2(x+2)-4x

(2x+4)-4x

2x+4-4x

-2x+4

Answer:

F = 100(.5736)  

= 57.36 lbs. (rounded off to 2 decimal places)  

2) sin60 = .866  

F = 18(.866)  

= 15.59 lbs. (rounded off to 2 decimal places)

Step-by-step explanation:

F = friction

Answer:

100sin35° = x

Step-by-step explanation:

I did the assignment, this was the correct answer for me.

Answer:

Initially 18,500 students

Every 1 year

increase by a factor 1.03

Step-by-step explanation:

The missing information is selected from the given options from the drop down menu. The correct answers are : Initially 18,500 students enroll at the university. Every 1 years the number of students who enroll at the university increases by a factor 1.03.

F(t) = 18,500 * (1.03)^t

Answer:

Amy types at a rate of 50 words per minute

Step-by-step explanation:

In this question, we are interested in calculating the rate at which April is typing.

From the question, we can deduce that she typed a 5 page report, with each page having a total of 500 words.

Now, if each page has 500 words, the total number of words in all of the pages will be 5 * 500 = 2,500 words

Now, from here, we can see that 2,500 words were typed in 50 minutes.

The number of words per minute will be ;

Total number of words/Time taken = 2500 words/50 minutes

That will give a value of 50 words per minute

Answer: |p-72% |≤ 4%

Step-by-step explanation:

Let p be the population proportion.

The absolute inequality about p using an absolute value inequality.:

[tex]|p-\hat{p}| \leq E[/tex] , where E = margin of error, [tex]\hat{p}[/tex] = sample proportion

Given:  A poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% .

|p-72% |≤ 4%

⇒    72% - 4% ≤ p ≤ 72% +4%

⇒  68%  ≤ p ≤  76%.

i.e. p is most likely to be between 68% and 76% (.

The conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.

An expression using absolute functions and inequality signs is known as an absolute value inequality.

We know that the absolute value inequality about p using an absolute value inequality is written as,

[tex]|p-\hat p| \leq E[/tex]

where E is the margin of error and [tex]\hat p[/tex] is the sample proportion.

Now, it is given that the poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76%. Therefore, p can be written as,

[tex]|p-0.72|\leq 0.04\\\\(0.72-0.04)\leq p \leq (0.72+0.04)\\\\0.68 \leq p\leq 0.76[/tex]

Thus, the p is most likely to be between the range of 68% to 76%.

Similarly, the proportion of people who like dark chocolate more than milk chocolate was 32% with a margin of error of 2.2%. Therefore, p can be written as,

[tex]|p-\hat p|\leq E\\\\|p-0.32|\leq 0.022\\\\(0.32-0.022)\leq p \leq (0.32+0.022)\\\\0.298\leq p\leq 0.342[/tex]

Thus, the p is most likely to be between the range of 29.8% to 34.2%.

Hence, the conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.

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Answer:

d. appears most

Step-by-step explanation:

Mode is the number that appears the most often in a set of data

Answer:

143.4 mi²

Step-by-step explanation:

Top: 8x6=48

Bottom: 3x8=24

Sides: 3x8=24 and 24

Trapezoids sides: (6+3)/2*2.6=4.5*2.6=11.7 and 11.7

TOTAL: 48+24+24+24+11.7+11.7= 143.4 mi²

Answer:

13

Step-by-step explanation:

From the question, we are given a triangle HNK with an angle of 90°

The length of hypotenuse H K is n,

the length of HN is 12

the length of N K is 6.

From the above values, obtained in the question, we can see that this is a right angled triangle.

We are asked to find the length of the hypotenuse.

We can use Pythagoras Theorem of solve for this.

c² = a² + b²

where c = HK = n

a = NK = 6

b = HN = 12

c² = 6² + 12²

c² = 36 + 144

c² = 180

c = √180

c = 13.416407865

Approximately to the nearest whole number = 13

Therefore the value of HK = n = 13

We can also use Law of Cosines as given in the question to solve for this.

a² = b² + c² - 2ac × Cos A

where c = HK = n

a = NK = 6

b = HN = 12

Hence

c² = a² + b² - 2ab × Cos C

c = √ (a² + b² - 2ab × Cos C)

Where C = 90

c = √ 6² + 12² - 2 × 6 × 12 × Cos 90

c = 13.42

Approximately to the nearest whole number ≈ 13

Therefore the value of HK = n = 13

Answer:

B) 22 units

Step-by-step explanation:

edge 2020 :)

Answer:

10

Step-by-step explanation:

-3 = 7 - x

Add x to both sides

x -3 = 7 - x +x

x - 3 = 7

Now, add 3 to both sides

x - 3 + 3 = 7 + 3

x = 10

Answer:

[tex]\boxed{10}[/tex]

Step-by-step explanation:

[tex]-3=7- \sf BLANK[/tex]

[tex]\sf Subtract \ 7 \ from \ sides.[/tex]

[tex]-3-7=-7+7- \sf BLANK[/tex]

[tex]-10=- \sf BLANK[/tex]

[tex]\sf Multiply \ both \ sides \ by \ -1.[/tex]

[tex]-10(-1)=(-1)- \sf BLANK[/tex]

[tex]10= \sf BLANK[/tex]

Answer:

Step-by-step explanation:

5x = 21 and 21 = 5x are identical relationships, and so the solution would be the same in both cases.  (Commutative Property:  order of addition/subtraction is immaterial)

Answer:

C

Step-by-step explanation:

f(x) = x - 2

f(2) = (2) - 2

f(2) = 0

A + B are wrong cuz..

f(-2) = -2 - 2

f(-2) = -4

Answer:  AE = 5

Step-by-step explanation:

I sketched the triangle based on the information provided.

since ∠A = 90° and is divided into three equal angles, then ∠BAD, ∠DAE, and ∠CAE = 30°

Since AB = 5 and BC = 10, then ΔCAB is a 30°-60°-90° triangle which implies that ∠B = 60° and ∠C = 30°

Using the Triangle Sum Theorem, we can conclude that ∠ADB = 90°, ∠ADE = 90°, ∠ AED = 60°, AND ∠ AEC = 120°

We can see that ΔAEC is an isosceles triangle. Draw a perpendicular to divide it into two congruent right triangles. Label the intersection as Z. ΔAEZ and ΔCEZ are 30°-60°-90° triangles.

Using the 30°-60°-90° rules for ΔABC we can calculate that AC = 5√3.

Since we divided ΔAEC into two congruent triangles, then AZ = [tex]\dfrac{5\sqrt 3}{2}[/tex]

Now use the 30°-60°-90° rules to calculate AE = 5

Answer:

velocity of recoil velocity of cannon  is -9.6 m/sec

Step-by-step explanation:

according to law of conservation of momentum

total momentum of isolated system of body remains constant.

momentum  = mass of body* velocity of body.

__________________________________

in the problem the system is

shell + cannon

momentum of shell = 8*600 = 4800 Kg-m/sec

let the velocity of cannon be x m/sec

momentum of cannon = 500*x = 500x Kg-m/sec

initially the system of body is in rest (before the shell is fired) hence, total momentum of the system i is 0

applying  conservation of momentum

total momentum before shell fired = total momentum after the shell is fired

0 = momentum of shell + momentum of cannon

4800 + 500x = 0

x = -4800/500 = -9.6

Thus, velocity of recoil velocity of cannon  is -9.6 m/sec

here negative sign implies that direction of velocity of cannon is opposite to that of velocity of shell.