If p(a) = 0.35, p(b) = 0.45, and p(a and
b.= 0.25, then p(a|b) is:

Answer:

[tex]0.362-0.045<p<0.362+0.045[/tex]

Step-by-step explanation:

It is given that When 415 junior college students were surveyed, 150 said they have a passport, then sample proportion will be:

Sample proportion=[tex]\frac{150}{415}=0.362[/tex]

Then, [tex]ME=1.96\sqrt{\frac{0.362{\times}0.638}{415}}[/tex]

=[tex]1.96\sqrt{\frac{0.230}{415}[/tex]

=[tex]1.96(0.023)[/tex]

=[tex]0.045[/tex]

Therefore, at 95% confidence interval, the proportion of junior college students that have a passport is:

[tex]0.362-0.045<p<0.362+0.045[/tex]

The area of the lawn that the sprinkler covers is approximately 708.25 square feet. This was calculated using the formula for the area of a sector of a circle, converting the rotation angle to radians, and then substituting the given values into the formula.

The area of the lawn that the water sprinkler covers can be calculated using the formula for the area of a sector of a circle. The formula is Area = 1/2 * r2 * θ, where r is the radius (which is the distance the sprinkler can spray, 25 feet in this case) and θ is the central angle in radians. First, we must convert the given angle from degrees to radians. We know that 180 degrees equals π radians. Therefore, to convert 130 degrees to radians, we multiply by π/180, getting approximately 2.26893 radians.

Substituting these values into the formula, we get: Area = 1/2 * 252 * 2.26893 = 708.25 square feet.

So,

the sprinkler covers an area of approximately 708.25 square feet

when rotating through an angle of 130 degrees.

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Answer:

1. y = - 4(x - 1) ⇒ Translated right by 1 unit

2. y = 1 - 4x ⇒ Translated up by 1 unit

3. y = - 4(-x) ⇒ Reflected across the y-axis

4. y = - 4(x + 1) ⇒ Translated left by 1 unit

5. y = 4x ⇒ Reflected across the x-axis

6. y = -1 - 4x ⇒ Translated down by 1 unit

Step-by-step explanation:

Lets explain how to solve the problem

- If the function f(x) reflected across the x-axis, then the new

 function g(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new

 function g(x) = f(-x)

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* Lets solve the problem

∵ y = - 4x is the parent function

- The function after some transformation is:

1. y = - 4(x - 1)

∵ We subtract 1 from x

∴ The function translated right by 1 unit

∴ y = - 4(x - 1) ⇒ Translated right by 1 unit  

2. y = 1 - 4x

∵ We add 1 to y = - 4x

∴ The function translated up by 1 unit

∴ y = 1 - 4x ⇒ Translated up by 1 unit

3. y = -4(-x)

∵ We multiply x by (-)

∴ The function reflected across the y-axis

∴ y = - 4(-x) ⇒ Reflected across the y-axis

4. y = -4(x + 1)

∵ We add 1 to x

∴ The function translated left by 1 unit

∴ y = - 4(x - 1) ⇒ Translated left by 1 unit

5. y = 4x

∵ We multiply y = - 4x by (-)

∴ The function reflected across the x-axis

∴ y = 4x ⇒ Reflected across the x-axis

6. y = -1 - 4x

∵ We subtract 1 from y = - 4x

∴ The function translated down by 1 unit

∴ y = -1 - 4x ⇒ Translated down by 1 unit

Answer:

The required formula is [tex]v=\sqrt{ar}[/tex].

Step-by-step explanation:

The given formula is

[tex]a=\frac{v^2}{r}[/tex]

where, v is the velocity of the object and r is the object's distance from the center of the circular path.

Multiply both sides by r, to solve the formula for the velocity.

[tex]ar=v^2[/tex]

Taking square root both the sides.

[tex]\sqrt{ar}=v[/tex]

Therefore the required formula is [tex]v=\sqrt{ar}[/tex].

The area of the triangle is 24 square unit.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.

If we plot the points A(2,3), B(2,-5), C(-4,-3) on the graph we get a triangle which can be divided into two right Triangles.

So, Area of Triangle 1

= 1/2 x base x height

= 1/2 x 6 x 6

= 18 sq units

Now, area of Triangle 2

= 1/2 x base x height

= 1/2 x 6 x 2

= 6 sq units

Thus ,the Area of required triangle

= 18 + 6

= 24 sq units

Learn more about area here:

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Answer: The matrix would be

[tex]\left[\begin{array}{ccc}48&19\\\\44&21\end{array}\right][/tex]

Step-by-step explanation:

Since we have given that

Number of Styrofoam balls bought by Bradley in May = 48

Number of figurines sold by Bradley in June = 19

Number of Styrofoam balls bought by Lupe in May = 44

Number of figurines sold by Lupe in June = 21

So, it will be written as

                          Purchases      Sales

May                            48               19

June                          44               21

So, the matrix would be

[tex]\left[\begin{array}{ccc}48&19\\\\44&21\end{array}\right][/tex]

Answer:

a. strong positive is the answer.

Step-by-step explanation:

The following shows the correlation between the length of a person's hand span and how many jolly ranchers they can pick up with one hand.  

There is a strong positive correlation between the two things. We can see the scatter plot moving up as the hand span increases, the number of jolly ranchers they can pick up also increases.

The values for which the two stock prices are the same are approximately x ≈ -1.405 and x ≈ 11.405.

To find the values for which the two stock prices are the same, we need to set the equations for the prices equal to each other and solve for x.

Equation for the first stock: C = 14 + 12x - x^2

Equation for the second stock: C = 2x + 30

Setting the two equations equal: 14 + 12x - x^2 = 2x + 30

Rearranging the equation and combining like terms: x^2 - 10x - 16 = 0

Using the quadratic formula to solve for x: x = (-b ± sqrt(b^2 - 4ac))/(2a)

Plugging in the values: x = (-(-10) ± sqrt((-10)^2 - 4(1)(-16)))/(2(1))

Simplifying: x = (10 ± sqrt(100 + 64))/2

Calculating: x = (10 ± sqrt(164))/2

Approximate values: x ≈ (10 ± 12.81)/2

Therefore, the two stock prices are the same for x ≈ -1.405 and x ≈ 11.405.

The equivalent expression to the 4th root of 16x^11y^8/81x^7y^6 is (2x/3)^4, assuming x > 0 and y = 0. The expression simplifies to x because the y terms become 0 and the exponents on x reduce to 1 when the fourth root is taken into account.

The question asks for an expression equivalent to 4th root of the fraction 16x^11y^8/81x^7y^6 assuming that x > 0 and y = 0. First, we need to deal with the fourth root and exponents separately. To find the fourth root of a number, you can raise that number to the 0.25 power. This rule simplifies finding roots, as a full calculation is not always needed with modern calculators that have a y* button or equivalent.

The fourth root of 16 is 2 because (2^4) = 16. We can address the exponents of x and y by subtracting the exponents in the denominator from those in the numerator for each variable: x^(11-7) = x^4 and y^(8-6) = y^2. Now, considering y = 0, any term with y to any power will be 0, so we can omit y terms. For x, we have x^4.

Regarding the numbers, we have (2/3)^4 because the fourth root of 81 is 3, and this is in the denominator. Finally, because y = 0, our expression reduces to just concerning x, which is (2x)^4/(3)^4, or (2x/3)^4. This simplifies to x raised to the power of 1 because (2/3)^4 * x^4 with x^4 raised to the 1/4th power cancels out the fourth power.

To simplify the given expression, we can find the fourth roots of the numbers inside the radical and then simplify the variables using exponent rules.

To simplify the expression ^4√16x^11y^8/81x^7y^6, we can first simplify the numbers inside the radical by finding their fourth roots. The fourth root of 16 is 2, and the fourth root of 81 is 3. So, the expression becomes 2x^(11/4)y^2 / 3x^(7/4)y^6.

Next, we can simplify the variables inside the expression by subtracting the exponents. So, x^(11/4) / x^(7/4) simplifies to x^((11/4)-(7/4)) = x^(4/4) = x^1 = x, and y^2 / y^6 simplifies to y^(2-6) = y^(-4).

Combining the simplified numbers and variables, the expression becomes 2x * y^(-4) / 3 = (2x)/(3y^4).

Answer:

B. 0.707

Step-by-step explanation:

The frequency table is given by,

Number of months                         Number of movie goers

     More than 7                                                96                  

           5 - 7                                                      180

           2 - 4                                                      219

      Less than 2                                               205

           Total                                                     700

Since, Probability of an event is the ratio of favorable events to the total number of events.

As, the number of people going to movies atleast 2 times a month = 96 + 180 + 219 = 495

The probability that a person goes to the movies atleast 2 times a month = [tex]\frac{495}{700}=0.707[/tex].

To find the equilibrium price and quantity, we set the demand to be equal to the supply, solve for x, and substitute the value back into the demand equation to find the equilibrium price.

The given equation is:

p = -0.00054x + 9, where p is the unit price in dollars and x is the number of discs demanded.

The total monthly cost for pressing and packaging x copies is given by:

c(x) = 600 + 2x - 0.00002x^2

To find the equilibrium price and quantity, we need to find the point where the demand equals the supply. In this case, the demand is represented by the equation p = -0.00054x + 9 and the supply is represented by the equation c(x) = 600 + 2x - 0.00002x^2.

To solve for the equilibrium price and quantity, we set the demand equals the supply:

-0.00054x + 9 = 600 + 2x - 0.00002x^2

This equation can be solved by rearranging and solving for x:

0.00002x^2 + 2.00054x - 591 = 0

Using the quadratic formula, we can find the values of x that satisfy this equation:

x = (-2.00054 ± sqrt(2.00054^2 - 4*0.00002*(-591))) / (2*0.00002)

After calculating, we find two possible values for x, which are approximately x_1 = 13727.927 and x_2 = -0.036. However, since the quantity demanded cannot be negative, we discard the negative value.

The equilibrium quantity is approximately 13728.

To find the equilibrium price, we substitute the value of x into the demand equation:

p = -0.00054(13728) + 9

p is approximately equal to $1.53.

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Answer:

80%

Step-by-step explanation:

24/30=.80

.80=80%

Hope this helps :)

To solve what percent of 24 is 30, set up the equation 30/24 times 100 = p, which results in 125%. Therefore, 30 is 125% of 24.

To find what percent of 24 is 30, we need to set up a proportion where 30 is the part, 24 is the whole, and we are solving for the percentage (we'll call this p). The equation for percent is (part/whole) times 100 = percent. So in this case, the equation becomes (30/24) tmes 100 = p.

Next, we'll divide 30 by 24 to get a decimal, then multiply by 100 to convert it to a percent. The calculation looks like this: (30 / 24) times 100 which gives us 125%. This means that 30 is 125% of 24.

Always remember to round to the nearest hundredth if necessary, but in this case, 125% is already to the nearest whole percent.

Answer:

We can find out the missing pieces by the below explanation,

Here, the given equation,

[tex]-27 = 4x^2 - 24x[/tex]

Step 1 :

[tex]-27=4(x^2-6x)[/tex]

Step 2 :

[tex]-27+36=4(x^2-6x+9)[/tex]

Step 3 :

[tex]9=4(x-3)^2[/tex]

Step 4 :

[tex]\frac{9}{4}=(x-3)^2[/tex]

Step 5 :

[tex]\pm \frac{3}{2}=x-3[/tex]

Step 6 :

[tex]x=3\pm \frac{3}{2}[/tex]

Answer:

[tex]x_{1}=1.53\\x_{2}=-1.53[/tex]

Step-by-step explanation:

The given quadratic equation is

[tex]9x^{2}-21=0[/tex]

To solve this equation, we just have to isolate the variable, because the quadratic expression has only one variable, the linear term is not present. So

[tex]9x^{2} =21\\x^{2} =\frac{21}{9}[/tex]

Now, we apply a square root, to have the variable complete isolated

[tex]\sqrt{x^{2} }=\sqrt{\frac{21}{9} } \\x=\±1.53[/tex]

Remember that all square roots have two results, one positive and one negative.

Therefore, the solutions for this equation are

[tex]x_{1}=1.53\\x_{2}=-1.53[/tex]

Answer:

A. Length of a bead necklace compared with the number of identical beads

Step-by-step explanation:

Using identical beads in a necklace means that the length of the necklace will depend on the total number of identical beads in the necklace.

For each bead added, the length of the necklace will increase a given, constant, amount.  This is a constant rate of change.

Answer: A. Length of a bead necklace compared with the number of identical beads

Step-by-step explanation:

A. Length of bead necklace increases simultaneously compared with the increases in number of identical beads . This is a proportional relationship .

So, There is constant rate of change which is equals to the length of each bead.

B. Distance a school bus travels compared with the number of stops .

There is no constant rate of change between the quantities .[The time when bus stops matter]

C.Number of trees in a park compared with the area of the park.

There can be free space ,so there is not proportional relationship .

D.Number of runs scored in a baseball game compared with the number of innings

Not proportional relationship.

Using standard linear equation, y = m*x + c

where m = slope and c = constant

putting ordered pairs, (3,7000) and (4,5000) in the above equation, we get two equations

3*m + c = 7000         and 4*m + c = 5000

On solving,

m = -2000  and c = 13000

So, the required equation is

   y = -2000*x + 13000