..................................

The profit function is modeled as follows:

p(x) = -15x² + 3780x - 176700.

It is a quadratic function with coefficients given as follows:

a = -15, b = 3780, c = -176700.

The leading coefficient of the quadratic function is negative, hence the profit will be maximized at the vertex of the quadratic function.

The x-coordinate of the vertex, representing the price which maximizes the profit, is given as follows:

x = -b/2a

x = -3780/-30

x = $126.

Then the maximum profit would be given as follows:

p(126) = -15(126)² + 3780(126) - 176700.

p(126) = $61,400.

If she charged $100, the profit would be given as follows:

p(100) = -15(100)² + 3780(100) - 176700.

p(126) = $51,300.

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The height of Red hill is 513.8 feet.

What does mean by the angle of elevation?

The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line. This angle eventually develops above the surface. The angle of elevation is made in such a way that it is above the observer's eye, as the name suggests.

Given:

Distance from the parking lot to the foot of the hill = 740feet

The angle of elevation from a parking lot and the foot of the hill is 25 and 55 degrees respectively.

For easy understanding, assume triangle edges with alphabets as shown in the figure.

Now, let's take ΔACD,

CotD = DC/AC

Cot 55 = y/x ⇒ 0.7 =y/x

⇒ y = 0.7x

In ΔABC

Tan B = AC/BC

Tan 25 = x/(740+y)    (y = 0.7x )

0.467 = x/(740+0.7x )

x = 0.467(740+0.7x )

  = 345.5 + 0.326x

0.6731x = 345.5

∴ x = 513.8 feet

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the probability of rolling a sum less than 11 is 34/36, or 0.9444 when rounded to four decimal places.

The possibility or chance that an event will occur is quantified by probability. It is a numerical value between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain to occur.

The only ways to get a sum of 11 or greater when rolling two dice is to get either a sum of 11 (with a 6 and a 5) or a sum of 12 (with two 6's).

There are 6 x 6 = 36 possible outcomes when rolling two dice, and only one of them results in a sum of 11 and one of them results in a sum of 12. Therefore, there are 36 - 2 = 34 outcomes that result in a sum less than 11.

So, the probability of rolling a sum less than 11 is 34/36, or 0.9444 when rounded to four decimal places.

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Answer: Prime Numbers

The equation's solution's quadratic function is [tex]f(x)=15x^{2} -11x-14[/tex].

A quadratic issue in mathematics is a specific type of issue that entails squaring, or multiplying, a variable by itself. This terminology is based on the notion that the area of a square is the product of the length of its sides. Quadratum, the Roman word meaning square, is where the word "quadratic" originates.

Definitions: x ax2 + bx + c = 0 is a quadratic equation, which is a 2nd polynomial formula in a single variable. a 0. Given that it is a second quadratic issue, which is ensured by the algebraic fundamental theorem, there can only be one solution. The answer could be simple or complicated.

The solution of the function are :

[tex]x=\frac{7}{5} and x=-\frac{2}{3}[/tex]

Finding such values:

[tex]5x=7[/tex]⇒[tex]5x-7[/tex]

[tex]3x=-2[/tex]⇒[tex]3x+2[/tex]

Multiplying them:

[tex]f(x)=(5x-7)(3x+2)\\[/tex]

[tex]f(x)=15x^{2} -11x-14[/tex] so this is the function.

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Answer:

The list of set of dimensions for fencing the building around a rectangular plot of land is 14.5 meters and 29 meters.

Area of a rectangle

area of rectangle = lw

where

l = length

w = width

Therefore,

perimeter = 2w+ l

58 = 2w + l

l = 58 - 2w

Hence,

area = w(58 - 2w)

380 = 58w - 2w²

-2w² + 58w - 380 = 0

-w² + 29w - 190 = 0

The dimension w can be found as follows;

w = - b / 2a

where

a = -1

b = 29

w = - 29 / 2 ×  -1

w = 14.5 meters

Then,

l = 58  - 2w

l = 58 - 2(14.5)

l = 29 meters

Therefore, the dimensions are 14.5 meters and 29 meters.

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Answer:

[tex]\large\boxed{\tt f(2) = 10}[/tex]

Step-by-step explanation:

[tex]\textsf{For this problem, we are asked to evaluate the function given x.}[/tex]

[tex]\textsf{Note that because x is given, all that's needed to be done is substitution.}[/tex]

[tex]\large\underline{\textsf{Substitute;}}[/tex]

[tex]\tt f(2)= 3x^{3} -5x-4[/tex]

[tex]\tt f(2)= 3(2)^{3} -5(2)-4[/tex]

[tex]\large\underline{\textsf{Evalulate;}}[/tex]

[tex]\tt f(2)= 3(2 \times 2 \times 2) -10-4[/tex]

[tex]\tt f(2)= 3(8) -10-4[/tex]

[tex]\tt f(2)= 24-14[/tex]

[tex]\large\boxed{\tt f(2) = 10}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{f(x) = 3x^3 - 5x - 4}\\\\\mathsf{f(x) = 3(2)^3 - 5(2) - 4}\\\\\mathsf{f(x) = 3(2^3) - 5(2) - 4}\\\\\mathsf{f(x) = 3(2\times2\times2) - 5(2) - 4}\\\\\mathsf{f(x) = 3(4\times2) - 5(2) - 4}\\\\\mathsf{f(x) = 3(8) - 5(2) - 4}\\\\\mathsf{f(x) = 24 - 5(2) - 4}\\\\\mathsf{f(x) = 24 - 10 - 4}\\\\\mathsf{f(x) = 14 - 4}\\\\\mathsf{f(x) = 10}\\\\\\\huge\text{Therefore your answer should be:}\\\\\huge\boxed{\mathtt{f(x) = 10}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

x = 32°

Step-by-step explanation:

The definition of tangent means that the angle formed by the line and the circle is a 90° angle. We can also see that the two segments connected to the center have equal angles because they are both radii of the circle. They form a triangle and the angle measurements are 61°, 61° and 58°. We have two angle measurements of the overall triangle, 58°, 90° (from the tangent), and x°.

The sum of the angles of any triangle is 180°. Therefore, we can form an equation to calculate the value of x.

58 + 90 + x = 180

x = 180 - 90 - 58

x = 32°

Answer:

x = 32°

Step-by-step explanation:

To find:-

Answer:-

As we know that angle made by tangent on the centre is a right angle . So here [tex]\angle[/tex]OBC will be 90° ( as CB is tangent on the circle.) Again we know that the angles opposite to equal sides are equal . Therefore here OB and OA are radii of the circle which are equal. So we can say that;

[tex]\sf:\implies \red{ \angle OBA = \angle OAB = 61^o}\\[/tex]

Again we know that the angle sum property of a triangle is 180° . Therefore in ∆OBA ,

[tex]\sf:\implies 61^o + 61^o + \angle AOB = 180^o \\[/tex]

[tex]\sf:\implies 122^o + \angle AOB = 180^o \\[/tex]

[tex]\sf:\implies \angle AOB = 180^o - 122^o \\[/tex]

[tex]\sf:\implies \angle AOB = 58^o\\[/tex]

Finally look into the ∆OBC ,

[tex]\sf:\implies \angle BOC + \angle OCB + \angle CBO = 180^o\\[/tex]

[tex]\sf:\implies 58^o + 90^o + x = 180^o \\[/tex]

[tex]\sf:\implies 148^o + x = 180^o \\[/tex]

[tex]\sf:\implies x = 180^o - 148^o \\[/tex]

[tex]\sf:\implies \red{ x = 32^o }\\[/tex]

Hence the value of x is 32°.

Answer:

below

Step-by-step explanation:

assuming r=5 and center (0,0)

1.) point at (0,0) for center

2.) point at (5,0)

3.) point at (0,5)

4.) point at (-5,0)

5.) point at (0,-5)

trace around points 2-5 to get the 4pt circle

The product of (3√d)(3√d)(3√d) is equal to: (3√d)(3√d)(3√d) = 3^3(√d)^3 = 27d^(3/2). Therefore, the answer is 27d⁽³/²⁾.

The expression (3√d)(3√d)(3√d) can be simplified by multiplying the coefficients and the radicals separately. The coefficient 3 is raised to the power of 3, which gives 27. The radical √d is raised to the power of 3, which gives d⁽³/²⁾ since the exponent is multiplied by 3. Therefore, the simplified expression is 27d⁽³/²⁾. This means that the product of three cube roots of d is equal to 27 times the cube root of d cubed, which simplifies to 27 times d raised to the power of 3/2.

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Complete question:

What is the following product? Assume d≥0. (3√d)(3√d)(3√d)

d

d³

3(3√d)

√3d

The inverse of the function is  [tex](1/4)^{x/5}[/tex].

What is an inverse function?

A function that reverses the effects of another function is called an inverse function. When y=f(x) and x=g, a function g is the inverse of a function f. (y). Applying f and then g is equivalent to doing nothing, in other words. This can be expressed as g(f(x))=x in terms of the relationship between f and g.

Here, we have

Given: equation y = log(1/4)x⁵

A function g is the inverse of function f if for y = f(x), x = g(y)

y = log(1/4)x⁵

Replace x with y

x = log(1/4)y⁵

Solve for y, we get

y = [tex](1/4)^{x/5}[/tex]

Hence, the inverse of the function is  [tex](1/4)^{x/5}[/tex].

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By comparing this form to the available choices, we can observe that option B provides the equation that best fits the graph: y²/9 - x²/4 = 1.

What is equation ?

A mathematical equation is a statement that demonstrates the equality of two expressions, usually by placing an equal sign before them. It depicts a connection connecting more than one variable and can be applied to situations to uncover unknown values. Variables, constants, plus mathematical operations including addition, subtract, multiplication, and division are frequently used in algebra equations. Equations include the following: 2x + 3 = 7 y = mx + b , a² + b² = c²

given

The hyperbola graph seen in the figure includes a transverse axis along the y-axis and a centre at (0,0).

The separation between the foci is 8 units, while the separation between the vertices is 6 units.

The equation for this hyperbola's standard form is:

(y - k)²/a² - (x - h) (x - h)²/b² = 1

where (h,k) designates the hyperbola's centre and (a,b) designates the distances between it and its vertices and co-vertices.

By comparing this form to the available choices, we can observe that option B provides the equation that best fits the graph: y²/9 - x²/4 = 1.

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The percentage of the total that she spent in fruit is 10%.

We know that Jane spent a total of $20 at the grocery shop, and we know that she spent $2 in fruit.

We want to find the percentage of the total that she spend on fruit, to get this, we need to take solve the equation:

Percentage = 100%*(amount that she pend on fruit)/(total amount)

Replacing the values that we know there we will get:

P = 100%*($2/$20)

P = 100%*1/10 = 10%

She spent 10% of the total amount in fruit.

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from the picture above we can see that we have an altitude or height for the triangle of 5, so then

[tex]\textit{height of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2} ~~ \begin{cases} s=\stackrel{side's}{length}\\[-0.5em] \hrulefill\\ h=5 \end{cases}\implies 5=\cfrac{s\sqrt{3}}{2}\implies 10=s\sqrt{3} \\\\\\ \cfrac{10}{\sqrt{3}}=s\implies 5.8\approx s = x[/tex]

Answer:

Solution- x = 5 Equation- x + 4 = 9

Step-by-step explanation:

I hope this helps you understand.

The expected size of the largest gap between adjacent cars (as a function of l) is l/(n + 1), and the expected size of the smallest gap between adjacent cars is 2.

Let us consider that cars of length 2 try to park on a length l road. Each minute, a new car parks at a uniformly random spot on the road without crashing into another car or running off the road.

When no more cars fit, the expected size of the largest gap between adjacent cars is l/(n + 1) and the smallest gap is 2.

The expected size of the largest gap between adjacent cars (as a function of l) is l/(n + 1).

Let n be the number of cars parked on the road. Then the total length of the cars parked is 2n.

If the largest gap is a distance g, then the total length of the gaps is l − 2n. Then,gap length:

g (n + 1) ≤ l - 2ng ≤ l − (n + 1)g

Dividing through by (n + 1)g and rearranging:

g ≤ l/(n + 1) (largest gap)g ≥ 2 (smallest gap)

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Answer: 5y + 5

Step-by-step explanation: add all the like terms such as 2y + 2y + y = 5y as y = 1y and 2 + 3 = 5, which makes the expression 5y+5

if it's wrong, im sorry

hope it helps!!!

Answer:

-17 9/10

Step-by-step explanation:

a. The marginal density of Y1 is fY1(y1) = [tex]2e^{-(4+y1)[/tex], y1 > 0.

b. The conditional density of Y2 given Y1 = y1 is f(y2|y1) = 1, y2 > y1 and y1 > 0.

c.  Y1 and Y2 are not independent

  (a) E(Y2|Y1=y1) does not exist.

  (b) V(Y2|Y1=y1) does not exist.

(a) To find the marginal density of Y1, we integrate the joint density over all possible values of Y2:

fY1(y1) = ∫f(y1, y2) dy2 from y2=y1 to y2=∞

= [tex]\int\limits2e^{-(4+y1)[/tex]dy2 from y2=y1 to y2=∞

= [tex]-2e^{-(4+y1)[/tex] [from y2=y1 to y2=∞]

= [tex]2e^{-(4+y1)[/tex], y1 > 0

So the marginal density of Y1 is fY1(y1) = 2e^-(4+y1), y1 > 0.

(b) To find the conditional density of Y2 given Y1 = y1, we use the formula:

f(y2|y1) = f(y1,y2) / fY1(y1) for y1 > 0 and y2 > y1

= 0 otherwise

Substituting the given joint and marginal densities, we get:

f(y2|y1) = [tex]2e^{-(4+y1)[/tex]  / [tex]2e^{-(4+y1)[/tex]) = 1, y2 > y1 and y1 > 0

= 0 otherwise

So the conditional density of Y2 given Y1 = y1 is f(y2|y1) = 1, y2 > y1 and y1 > 0.

(c) To check if Y1 and Y2 are independent, we need to verify if f(y1,y2) = fY1(y1)fY2(y2) for all y1 and y2. We have:

fY2(y2) = ∫f(y1,y2) dy1 from y1=0 to y1=y2

= ∫ [tex]2e^{-(4+y1)[/tex]) dy1 from y1=0 to y1=y2

= - [tex]2e^{-(4+y2)[/tex]  +  [tex]2e^{-4[/tex]

fY1(y1)fY2(y2) = 4e⁻⁸ exp[-(y1+y2)], y1 > 0 and y2 > 0

Clearly, f(y1,y2) is not equal to fY1(y1)fY2(y2) for all y1 and y2, so Y1 and Y2 are not independent.

(a) Using the formula for conditional expectation, we have:

E(Y2|Y1=y1) = ∫y2 f(y2|y1) dy2 from y2=y1 to y2=∞

= ∫y2 dy2 from y2=y1 to y2=∞

= ∞

So E(Y2|Y1=y1) does not exist.

(b) Using the formula for conditional variance, we have:

V(Y2|Y1=y1) = E(Y2²|Y1=y1) - [E(Y2|Y1=y1)]²

= ∫y2² f(y2|y1) dy2 - (∞)²

= ∫y2² dy2 from y2=y1 to y2=∞ - (∞)^²

= ∞

So V(Y2|Y1=y1) does not exist.

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Answer:

Step-by-step explanation:

Sup? Pay attention closely (or not XD)

Short answer: 0.0308 or 3.08%

We use the combination formula C = n!/(r! * (n-r)!) for each brand. It basically tells us the number of ways to select a certain number of cars:

1) Fords: C(5, 2) = 5! / (2! * (5 - 2)!) = 10 ways to pick 2 Fords

2) Chevrolets: C(7, 3) = 7! / (3! * (7 - 3)!) = 35 was to pick 3 Chevys

3) Dodges: C(4, 1) = 4! / (1! * (4 - 1)!) = 4 ways to pick 1 Dodge

4) Hondas: C(3, 1) = 3! / (1! * (3 - 1)!) = 3 ways to pick 1 Honda

5) Toyotas: C(4, 2) = 4! / (2! * (4 - 2)!) = 6 ways to pick 2 Toyotas

Then you multiply all them results. Peep this:

10*35*4*3*6 = 25,200 ways to pick your target cars from each brand in total (sheesh)

Now how many ways would it be to pick 9 out of the 23 cars??

Use your best friend combination problem to solve this!

C(23, 9) = 23! / (9! * (23 - 9)!) = 817,190 (sheesh)

Now divide! 25,200/817,190 = 0.0308 or 3.08%

Thanks for listening to my TED talk. Hope this helps.

Answer:

0-18= -18

Step-by-step explanation:

you're starting with 0 and subtracting 18 so the answer is -18

The relationships between angle pairs are based on their position or on their orientation in relation to each other.

Angles are measured in degrees, and the measure of an angle determines its size. However, the relationships between angle pairs are not solely based on their measures. The position of two angles in relation to each other, such as whether they share a vertex or lie on the same line or plane, can determine their relationship. Additionally, the orientation of the angles can also play a role in their relationship, such as whether they are adjacent, vertical, complementary, supplementary, or congruent. Understanding these relationships is important in geometry and can help in solving problems and proving theorems.

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h is equal to the sum of f and 3, divided by 3 times g. The given equation is 3gh = f + 3, and we are asked to solve for h. To solve for h, we need to isolate h on one side of the equation.

First, we can simplify the left-hand side of the equation by dividing both sides by 3g:

(3gh)/(3g) = (f + 3)/(3g)

This simplifies to:

h = (f + 3)/(3g)

Now we have isolated h on the left-hand side of the equation. This means that the solution for h is given by the right-hand side of the equation, which is (f + 3)/(3g).

Therefore, h is equal to the sum of f and 3, divided by 3 times g. This is a general formula that will give us the value of h for any given values of f and g, as long as they are not equal to zero.

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Therefore, Conner's starting weight was 3 kg. Therefore, the starting price of the toys was $7.50.

An equation is a mathematical statement that shows that two expressions are equal. It typically contains one or more variables, which are placeholders for unknown or varying quantities. The equation may also contain constants, which are known values that do not change.

Here,

31. Let's assume that Conner's starting weight was x kg. According to the given condition, he lifted 2 more kg each week, which means he lifted (x+2) kg on the second week, (x+4) kg on the third week, and so on. Therefore, he lifted (x+12) kg on the seventh week. We know that Conner lifted 15 kg on the seventh week, so we can set up an equation:

x + 12 = 15

Solving for x, we get:

x = 3

Answer: 3 kg

32. Let's assume that the starting price of the toys was x dollars. According to the given condition, the price of the toys was marked down by $0.25 every hour, which means the price of the toys was (x-0.25) dollars after the first hour, (x-0.5) dollars after the second hour, and so on. Therefore, the price of the toys was (x-2) dollars after the eighth hour. We know that the price of the toys was $5.50 after the eighth hour, so we can set up an equation:

x - 2 = 5.5

Solving for x, we get:

x = 7.5

Answer: $7.50

33.  Let's assume that Grayson started earning at a base hourly rate of x dollars. Then, we can use the given information to form an equation that relates his earnings for one day (in dollars) with his hourly rate (in dollars/hour):

Total earnings for one day = base hourly rate + (number of hours worked) * (hourly increase in rate)

Since we know that Grayson earned $45 in one day and that his hourly rate increases by $3 every hour, we can substitute these values into the equation:

45 = x + (number of hours worked) * 3

Simplifying this equation, we get:

(number of hours worked) * 3 = 45 - x

(number of hours worked) = (45 - x) / 3

We can now use the fact that Grayson worked for a full day (i.e., 24 hours) to solve for the base hourly rate x:

24 * x + 3 * (1 + 2 + ... + 23) = 45

Simplifying the sum of the first 23 integers, we get:

24 * x + 3 * (276) = 45

24 * x + 828 = 45

24 * x = 45 - 828

24 * x = -783

x = -32.625

Since a negative base hourly rate doesn't make sense in this context, we can conclude that there is no solution to this problem. Perhaps there was an error in the given information or assumptions made.

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Answer:

73.6

Step-by-step explanation:

lets say that x is our number.

x * 0.05 = 23

x * 0.01 = 4.6

just solving one of these equations will give us x = 460.

now, 16% of 460 is 460 * 0.16 = 73.6

The assumptions and conditions for inference can be checked by options a, b, c, and d.

The assumptions and conditions for inference are checked while making statistical inferences about a population parameter based on sample statistics. These assumptions are made to ensure that the sample accurately reflects the population from which it was drawn. The correct options from the given alternatives are:

a. The residual plot and the scatterplot show consistent variability.

b.The residuals look random.

c. The scatterplot looks straight enough.

d. The residuals are nearly normal.

A residual plot is a graphical tool used to check the assumptions of a simple linear regression model. The scatterplot is the most common method for visualizing the relationship between two quantitative variables. The assumptions of linear regression are that the residuals are normally distributed, have constant variance (homoscedasticity), and are independent of one another. If the residuals are not normally distributed, have heteroscedasticity or the observations are dependent, then the linear regression model may not provide accurate predictions.

The scatterplot should also show the residual plot as random if we want to make valid inferences from a simple linear regression model. If the scatterplot shows any pattern, it indicates that the model does not capture all of the relationships between the variables, which may result in incorrect conclusions when making inferences from the model.The residuals should also be nearly normal for making valid inferences from a simple linear regression model.

It is possible to check whether the residuals are approximately normal by creating a histogram or a normal probability plot of the residuals. If the distribution of residuals is non-normal, the statistical inference may not be accurate.

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Answer:

D

Step-by-step explanation:

i did the quiz

The expression that is equal to 18x²y⁶ can be found to be D. 3²x²y⁴ × 2 y².

3x³y⁴ has a different power for both x and y compared to the original expression (18x²y⁶). 9xy has a different coefficient and different powers for x and y compared to the original expression (18x²y⁶).

3x³y + √√2 not only has different powers for x and y but also has an additional square root term, making it different from the original expression (18x²y⁶).

3²x²y⁴ × 2 y² on the other hand, can be simplified such that it becomes 18x²y⁶.

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Options include: