I need help pretty please

Answer:

Theyre all correct

Step-by-step explanation:

The solution to the inequality f(x) ≤ 0 is the interval [-6, 2]. In other words, the values of x that satisfy the inequality are those that lie between -6 and 2, inclusive.

To solve the inequality f(x) ≤ 0, we need to find the values of x for which the function f(x) is less than or equal to zero.

We start by factoring the quadratic expression f(x) = x^2 + 4x - 12:

f(x) = (x + 6)(x - 2)

Setting this expression to zero, we get:

(x + 6)(x - 2) = 0

This gives us two solutions: x = -6 and x = 2.

Now, we need to determine the sign of f(x) in the intervals between these two solutions. We can use a sign chart to do this:

x f(x)

-∞ +

-6 0

2 0

+∞ +

From the sign chart, we see that f(x) is positive for x < -6 and for x > 2, and it is negative for -6 < x < 2.

To summarize, the solution to the inequality f(x) ≤ 0 for the function f(x) = x^2 + 4x - 12 is the interval [-6, 2].

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The quantity of lemonade that Regan sold on saturday given the amount sold by Mark is 1 11/12 gallons.

Fractions are non-integers that consist of a numerator and a denominator. A proper fraction is a fraction in which the numerator is less than the denominator. e.g. 2/3. A mixed fraction is made up of a whole number and a proper fraction. An example is 2 7/8.

2 7/8 x 2/3

23/8 x 2/3 = 23/12 = 1 11/12 gallons

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Answer:

3

The degree of a polynomial is the highest power of any variable in the polynomial equation.

Here the highest power is 3 of the monomial with co-efficient of 2.

The cost to send 130 text messages is:

We know that,

The total cost of sending 80 text messages =  $8.00

So, the cost of sending 1 text message = $8/80

=$0.1 per text message

The cost of sending 130 text messages = 130*$0.1

Therefore, the cost incurred to send 130 text messages = $13

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The answer is yes, (x + 6) is a possible length of a rectangle with area x² + x − 30.

To determine whether (x + 6) is a possible length of a rectangle with area x^² + x − 30, we can use an area model to visualize the situation.

First, we need to find the width of the rectangle.

The area of a rectangle is given by the formula A = lw,

where A is the area, l is the length, and w is the width.

We are given that the area is x² + x − 30, so we can set this equal to lw and solve for w:

x² + x − 30 = (x + 6)w

w = (x² + x − 30)/(x + 6)

The length of a rectangle must be greater than or equal to its width, so we need to check whether (x + 6) is greater than or equal to (x² + x − 30)/(x + 6). This simplifies to:

(x + 6) ≥ x² + x − 30

Expanding the left side and simplifying, we get:

x² + 12x + 36 ≥ x² + x − 30

11x ≥ -66

x ≥ -6

Since x must be a positive number (since we are dealing with lengths), we can conclude that (x + 6) is the possible length of the rectangle. Therefore, the answer is yes, (x + 6) is a possible length of a rectangle with an area x² + x − 30.

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Answer:

See below

Step-by-step explanation:

The graph is of f(x) is shifted 1 unit to the LEFT to get g(x)

          so  4^x     is now  4^(x+1)

                                   then    4^(x+1) = 4^(x-h)

                                         would mean h = - 1

Answer:

3x + 8

Step-by-step explanation:

Michele's ages is equivalent to x, or 1x. Then you add Kayla's age to Michele's age which now equals 3x. Finally, you add 8, which is Erica's age.

Answer:21

Step-by-step explanation:

Add them all up

The number of students who collect more than one coin is 12.

A Line plot can be defined as a graph that displays data as points or check marks above a number line, showing the frequency of each value.

Given that, Mr. Petersen counted the number of coins collected by the students in his coin club and prepared the line plot.

We need to find how many students collected more than 1 coin,

Here each X represents a student,

The numbers of mark X above 2 and 3 = 4 and 8

Therefore, total students = 12

Hence, the number of students who collect more than one coin is 12.

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The function for the surface area of the closed box with a square base is \(S(x) = 4x^2 + 8xh\), where x represents the length of the side of the square base and h represents the height of the box. This function takes into account the areas of the square base and the four rectangular sides.

To determine the surface area function, we need to consider the different components of the box's surface. The box has a square base, so the area of each side of the base is \(x^2\). Since there are four sides to the base, the total area of the base is \(4x^2\). Additionally, there are four identical rectangular sides with dimensions x by h, resulting in a total area of 4xh.

Combining the areas of the base and the four sides, we have the surface area function \(S(x) = 4x^2 + 8xh\), which represents the total surface area of the closed box.

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Answer:

296.4cm

Step-by-step explanation:

you do 9.5cm x 5.2cm x 6cm = 296.4cm

The normal distribution is a specific distribution having a characteristic bell-shaped form.

The specific distribution that has a characteristic bell-shaped form is called the normal distribution. It is a continuous probability distribution that is symmetric around the mean. In a normal distribution, the majority of the data falls close to the mean, with fewer data points found further away from the mean towards the tails.

The normal distribution is important in statistics because many natural phenomena and processes follow this distribution, such as heights and weights of people, IQ scores, and errors in measurements.

The normal distribution has several properties that make it useful in statistical analysis, including the central limit theorem, which states that the sum of many independent and identically distributed random variables tends to follow a normal distribution.

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Answer:

61

Step-by-step explanation:

8 and 11 are corresponding angles. therefore they add up to 180.

so, 180-119 = 61

Answer:

61 degrees,

since 8=1 and 1=5, 5+11=180, 5=119 then 11 should equal 61

To maximize the manufacturer's total weekly profit, we need to find the critical point of the profit function P(x,y).

(a) To find the critical point, we need to find where the partial derivatives of P(x,y) are equal to zero.

Taking the partial derivative of P(x,y) with respect to x and y, we get:
P_x = 560 + 20y - 40x
P_y = 20x - 12y

Setting P_x = 0 and P_y = 0, we get:
560 + 20y - 40x = 0  and  20x - 12y = 0
Solving these equations simultaneously, we get:
x = 7 and y = 35

(b) To classify the critical point, we need to use the D-Test. The D value is:
D = P_xx * P_yy - (P_xy)^2
Substituting the values of P_xx, P_yy, and P_xy, we get:
D = -9600
Since D is negative, we have a saddle point at the critical point.

(c) To maximize the manufacturer's total weekly profit, we need to produce and sell 7,000 units of Product A and 35,000 units of Product B per week.

(d) Plugging x = 7 and y = 35 into the profit function P(x,y), we get:
P(7,35) = 560(7) + 20(7)(35) - 20(7)^2 - 6(35)^2
P(7,35) = $8,050
Therefore, the maximum weekly profit is $8,050.

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Answer:

x = 21.

Step-by-step explanation:

- 1/8 (x + 35)= -7

Multiply through by -8:

x + 35 = 56

x = 56 - 35

x = 21.

Answer:

I have solved it and attached in the explanation.

Step-by-step explanation:

Answer:

\(27a^3-54a^2b+36ab^2-8b^3\)

Step-by-step explanation:

To expand the expression (3a - 2b)³, we can use the Perfect Cube Formula.

\(\boxed{\begin{minipage}{6 cm}\underline{Perfect Cube Formula}\\\\$(x-y)^3=x^3-3x^2y+3xy^2-y^3$\\\end{minipage}}\)

Let:

Substitute the values into the formula, and use the exponent rule

\(\boxed{(xy)^n=x^n \cdot y^n}\) :

Therefore:

\(\begin{aligned}(3a-2b)^3&=(3a)^3-3(3a)^2(2b)+3(3a)(2b)^2-(2b)^3\\&=3^3 \cdot a^3-3 \cdot 3^2 \cdot a^2 \cdot 2b+3 \cdot 3a \cdot 2^2\cdot b^2-2^3\cdot b^3\\&=27a^3-3 \cdot 9 \cdot a^2 \cdot 2b+9a \cdot 4b^2-8b^3\\&=27a^3-54a^2b+36ab^2-8b^3\end{aligned}\)

So the expression (3a - 2b)³ expanded is 27a³ - 54a²b + 36ab² - 8b³.

The mean of samples 10, 10, 10, 10, 10, and 16 will be 11.

The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.

In a sample of n = 6, five individuals all have scores of x = 10 and the sixth person has a score of x = 16.

Then the data set will be given below.

10, 10, 10, 10, 10, 16

Then the mean of the data set will be

Mean = (10 + 10 + 10 + 10 + 10 + 16) / 6

Mean = 66/6

Mean = 11

Thus, the mean of the sample will be 11.

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Answer:

1 ton=2,000 pounds so 6,700 pounds

Step-by-step explanation:

The value of b in the equation (x^2 + bx - 2)(x + 3) = x^3 + 6x^2 + 7x - 6 can be determined by comparing the coefficients of the corresponding terms on both sides of the equation. The value of b is 7.

To find the value of b, we expand the left side of the equation (x^2 + bx - 2)(x + 3) using the distributive property. This results in the expression x^3 + 3x^2 + bx^2 + 3bx - 2x - 6.

Comparing this expression with the right side of the equation x^3 + 6x^2 + 7x - 6, we can see that the coefficients of the corresponding terms should be equal. The coefficient of x^2 is 3 in both expressions, the coefficient of x is 7 in both expressions, and the constant term is -6 in both expressions. Therefore, the value of b is 7.

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Answer:

a²+b²+c²

for cuboid

Answer:

i dont understand your question.

Step-by-step explanation:

The probability that not a single invitation landed in the correct envelope is P(n) = D(n) / n! , where D(n) is the number of derangements of n objects.

The number of derangements of n objects is denoted by D(n).

The first few values of D(n) are given below: D(1) = 0 (trivially)D(2)

= 1 (the two objects must switch places)D(3)

= 2 (out of the six possible permutations, only two are derangements)D(4)

= 9 (out of the 24 possible permutations, nine are derangements)D(5)

= 44 (out of the 120 possible permutations, 44 are derangements)

The formula for the number of derangements is D(n) = n! × (1/0! - 1/1! + 1/2! - 1/3! + ··· + (-1)^n / n!), where n! is the factorial of n, 0! = 1 by definition, and (-1)^n is (-1) raised to the power of n.

Hence, we can find the probability that not a single invitation landed in the correct envelope as P(n) = D(n) / n!.

Thus, the probability that not a single invitation landed in the correct envelope is P(n) = D(n) / n! , where D(n) is the number of derangements of n objects.

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The value of k for function g(x) is k = 1

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Since g(x) = (-1/2)x + k and g (2) = 0.

We can find the value of k for function g(x) by substitute x = 2 into the function, equate it to 0 and then solve for k. That is:

0 =  (-1/2)*2 + k

0 = -1 + k

-1 + k = 0

k = 1

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(a) The volume V of the box as a function of x is V = 4x^3-60x^2+200x

(b) The domain of V in interval notation is 0<x<5,

(c) The length L , width W, and height H of the resulting box that maximizes the volume is H = 2.113, W = 5.773, L= 15.773

(d) The maximum volume of the box is 192.421 cm^2.

In the given question,

A box is to be made out of a 10 cm by 20 cm piece of cardboard. Squares of side length cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top.

(a) We have to express the volume V of the box as a function of x.

If we cut out the squares, we'll have a length and width of 10-2x, 20-2x respectively and height of x.

So V = x(10-2x) (20-2x)

V = x(10(20-2x)-2x(20-2x))

V = x(200-20x-40x+4x^2)

V = x ( 200 - 60 x + 4x^2)

V = 4x^3-60x^2+200x

(b) Now we have to give the domain of V in interval notation.

Since the lengths must all be positive,

10-2x > 0 ≥ x < 5 and x> 0

So 0 < x < 5

(c) Now we have to find the length L , width W, and height H of the resulting box that maximizes the volume.

We take the derivative of V:

V'(x) = 12x^2-120x+200

Taking V'(x)=0

0 = 4 (3x^2-30x+50)

3x^2-30x+50=0

Now using the quadratic formula:

x=\(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

From the equationl a=3, b=-30, c=50

Putting the value

x=\(\frac{30\pm\sqrt{(-30)^2-4\times3\times50}}{2\times3}\)

x= \(\frac{30\pm\sqrt{900-600}}{6}\)

x= \(\frac{30\pm\sqrt{300}}{6}\)

x= \(\frac{30\pm17.321}{6}\)

Since x<5,

So x= \(\frac{30-17.321}{6}\)

x= 2.113

So H = 2.113, W = 5.773, L= 15.773.

d) Now we have to find the maximum volume of the box.

V = HWL

V= 2.113*5.773*15.773

V = 192.421 cm^3

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Answer:

y+8=-5(x-3)

Step-by-step explanation:

The formula for point-slope form is y-y1=m(x-x1)

The points for (x1, y1) are (3, -8), meaning that 3 is x1 and -8 is y1.

So, start by writing your equation like this: y--8=m(x-3)

For the equation y--8=m(x-3), the y--8 will change to a + sign because two negatives make a positive, right? So, the equation should now look like this: y+8=m(x-3).

We know that the slope (m) is -5. Plug that into the equation to get this: y+8=-5(x-3)

And there you have it!! The equation is now in point-slope form!!

y+8=-5(x-3) is the final answer!!

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The solutions to the equation 4x^2 - 20x + 25 = 10 are x = 5/2 and x = 3/2.

The equation 4x^2 - 20x + 25 = 10 can be rewritten as 4x^2 - 20x + 15 = 0. To find the solutions to this equation, we can factor it or use the quadratic formula.

The equation factors as (2x - 5)(2x - 3) = 0. Setting each factor equal to zero, we get 2x - 5 = 0 and 2x - 3 = 0. Solving these equations, we find x = 5/2 and x = 3/2.

Using the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by x = (-b ± sqrt(b^2 - 4ac)) / 2a, we can determine the solutions.

In this case, a = 4, b = -20, and c = 15. Substituting these values into the quadratic formula, we get x = (-(-20) ± sqrt((-20)^2 - 4 * 4 * 15)) / (2 * 4), which simplifies to x = (20 ± sqrt(400 - 240)) / 8.

Simplifying further, we have x = (20 ± sqrt(160)) / 8, which becomes x = (20 ± 4sqrt(10)) / 8. Finally, simplifying again, we obtain x = 5/2 ± sqrt(10)/2, which gives us the same solutions as before: x = 5/2 and x = 3/2.

Therefore, the solutions to the equation 4x^2 - 20x + 25 = 10 are x = 5/2 and x = 3/2.

To find the solutions to the equation, we can either factor it or use the quadratic formula. In this case, factoring and using the quadratic formula both yield the same solutions: x = 5/2 and x = 3/2. These values of x satisfy the equation 4x^2 - 20x + 25 = 10 when substituted back into the equation.

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The response variable in this experiment is the scores on the midterm exam. The response variable is the one that is measured or observed to determine whether it has been affected by the explanatory variable.

The alphabetic character that expresses a numerical value or a number is known as a variable in mathematics. A variable is used to represent an unknown quantity in algebraic equations.

The explanatory variable in this experiment is the type of music played in the background during the exam. The explanatory variable is the one that is deliberately manipulated or changed by the researcher in order to observe its effect on the response variable. In this case, the researcher wanted to investigate whether the type of music played during the exam would have an effect on the students' performance, so they manipulated the type of music and observed its effect on the exam scores.

The response variable in this experiment is the scores on the midterm exam. The response variable is the one that is measured or observed to determine whether it has been affected by the explanatory variable. In this case, the researcher measured the exam scores of the two groups to see if there was a difference between the group that listened to Dave Matthews Band and the group that listened to Death Cab for Cutie.

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volume of a cone is 132 cubic centimeter.

The volume of a cone is defined as the amount of space or capacity a cone occupies. The volume of a cone formula is given as one-third the product of the area of the circular base and the height of the cone.

Volume of cone V = \(\frac{1}{3} \pi r^{2} h\)

Given

Radius of cone r = 3 cm

Height of cone h = 14 cm

\(\pi\) = \(\frac{22}{7}\)

Volume of cone V = \(\frac{1}{3} \pi r^{2} h\)

V = \(\frac{1}{3}\) × \(\frac{22}{7}\) × \(3^{2}\) × \(14\)

V = 22 × 3 × 2

V = 132 cubic centimeter

Hence, volume of a cone is 132 cubic centimeter.

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Answer:

1/42

Step-by-step explanation:

1/7 ÷ 6/1

1 x 1 = 1

------------

7 x 6 = 42

1/42

already simplified to the fullest

hope that helps!