The sum of three numbers is 12. The sum of twice the first​ number, 5 times the second​ number, and 6 times the third number is 59. The difference between 8 times the first number and the second number is 23. Find the three numbers.

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:

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].

There is a 94.25% probability that a bill for veterinary services costs between $42 and $133 in this local animal hospital, based on calculating Z-scores for $42 and $133 and finding the difference between probabilities.

The question pertains to the concepts of statistics, specifically the normal distribution which often appear in situations describing natural phenomena and social behavior. To solve this, we need to calculate the Z-scores for both values given and then look those Z-scores up in a standard normal distribution table, or use a calculator or software that can do this.

A Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It's measured in terms of standard deviations from the mean.

If X is a random variable from a normal distribution with mean (µ) and standard deviation (σ), the Z-score is calculated by the formula Z = (X - µ)/σ.

For X =$42, Z1 = ($42 - $88)/$24 = -1.92 and for X=$133, Z2=($133-$88)/$24 = 1.88.

The probability that one bill for veterinary services costs between $42 and $133 equals the probability for Z values falling between -1.92 and 1.88. Refer to the standard normal distribution table or a calculator for the corresponding probabilities. The probability for Z1 equals approximately 0.0274, probability for Z2 equals approximately 0.9699. The required probability is then P(Z1

So, "there's a 94.25% chance that a bill for veterinary services costs between $42 and $133 in this local animal hospital".

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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 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).

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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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

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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Let the amounts of Turkey Jennifer bought be [tex] T [/tex] pounds and that of Cheese be [tex] C [/tex] pounds.

From the given information,

[tex] 6.35T+4.75C=17.13\\
T+C=3 [/tex]

Solving the above two equations together,

[tex] 6.35T+4.75(3-T)=17.13\\
(6.35-4.75)T+4.75*3=17.13\\
1.6T=2.88\\
T=\frac{2.88}{1.6}\\
T=1.8
[/tex]

Thus, Jennifer bought [tex] 1.8\;pounds [/tex] of Turkey and [tex] 3-1.8=1.2\;pounds [/tex] of Cheese.

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]

Calulate limits:

limx→∞(1x−2(−3x2+7x+1))=−∞

limx→−∞(1x−2(−3x2+7x+1))=∞

Thus, there are no horizontal asymptotes.

For Oblique Asymptote:

Do polynomial long division (−3x2+7x+1)/(x-2)=−3x+1+3/(x−2)

The rational term approaches 0 as the variable approaches infinity.

Thus, the slant asymptote is y=−3x+1y=−3x+1.

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.

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]