A company sells widgets. The amount of profit, y, made by the
company, is related to the selling price of each widget, x, by the given
equation. Using this equation, find out what price the widgets should
be sold for, to the nearest cent, for the company to make the maximum
profit.
y= -10x^2+ 600x - 3588

Answer:

j > - 108

Step-by-step explanation:

Step 1:

j / - 12 > 9          Equation

Step 2:

j > 9 × - 12         Multiply - 12 on both sides

Answer:

j > - 108

Hope This Helps :)

Answer:

j<−108

Step-by-step explanation:

j

−12

>9

Step 1: Simplify both sides of the inequality.

−1

12

j>9

Step 2: Multiply both sides by 12/(-1).

(

12

−1

)*(

−1

12

j)>(

12

−1

)*(9)

j<−108

Answer:

j<−108

Using proportions, considering the relation between the height and the shadow, it is found that the cell phone tower is 50 feet.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

When the shadow is of 8 feet, the height is of 10 feet. What is the height when the shadow is of 40 feet? The rule of three is:

8 feet - 10 feet

40 feet - h feet

Applying cross multiplication:

8h = 10 x 40

Simplifying by 8:

h = 10 x 5 = 50 feet.

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1) A factor is a part of a product. Looking at those algebraic expressions. We have at B. A 5 as GCD

5(y-6)

And 5 and (y-6) are factors in this algebraic expression.

2) The answer is B

The values of x and y are -12.5  and  -5.5  respectively

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

-2x+4y=3 -----(1)

c--------(2)

(1)=> 4y = 3 +2x

         y= 3/4 + (1/2)x

(2) => 3x-7 ( 3/4 + (1/2)x  ) =1

         3x - 21/4 - (7/2)x = 1

        (-1/2)x = 1+ 21/4 = 25/4

=> x= -50/4 = -12.5

y= 0.75 +0.5(-12.5) = 0.75 - 6.25 = -5.5

The values of x and y are -12.5  and  -5.5  respectively

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Answer:

Person will be 24 metres above the ground after 1.50 minutes

Step-by-step explanation:

Given:

\(h(t)=18.8-16.7\cos \left ( \frac{2\pi t}{5} \right )\)

To find:

time when the person be 24 meters above the ground

Solution:

Put \(h(t)=24\)

\(h(t)=18.8-16.7\cos \left ( \frac{2\pi t}{5} \right )\\24=18.8-16.7\cos \left ( \frac{2\pi t}{5} \right )\\16.7\cos \left ( \frac{2\pi t}{5} \right )=18.8-24\\16.7\cos \left ( \frac{2\pi t}{5} \right )=-5.2\\\cos \left ( \frac{2\pi t}{5} \right )=\frac{-5.2}{16.7}\\\cos \left ( \frac{2\pi t}{5} \right )=-0.3114\\\frac{2\pi t}{5}=1.887\\\frac{2}{5}\times \frac{22}{7}t=1.887\\t=1.887\times \frac{5}{2}\times \frac{7}{22}\\=1.501\\\approx 1.50 \,\,minute\)

So, the person will be 24 metres above the ground after 1.50 minutes

Answer:

1 1/4 minutes of 75 seconds

Step-by-step explanation:

10/8 = 5/4 = 1 1/4

Step-by-step explanation:

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The solution of the inequality 15n>8n-21 is given by, n<-3.

Inequality is a relation between two or more mathematical expression or quantities via unequal signs i.e. greater, less, greater or equal, less or equal, not equal.

Given that the inequality is 15n<8n-21

Solving the inequality we have,

15n<8n-21

15n-8n<8n-21-8n, subtracting from both sides

7n<-21

n<-3, dividing 7 from both sides

So the solution of the given inequality is, n<-3.

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The value of y when a = 1 and b = 2 is 22.

The equation of can be solved as follows: We will substitute the value of a and b  in the equation to find the value of y.

Therefore,

y = 3ab + 2b³

Let's find y when a = 1 and b = 2

Hence,

y = 3(1)(2) + 2(2)³

y = 6 + 2(8)

y = 22

Therefore,

y = 22

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The chances that, at least, one of the dinosaur toys in Franklin's set is a T.rex is 57%.

We can use the complement rule to find the probability that none of the dinosaur toys in Franklin's set is a T. rex, and then subtract this from 1 to get the probability that at least one of the toys is a T. rex.

The probability that a given toy is not a T. rex is 90%, or 0.9.

Since there are 8 toys in the set, the probability that none of them are T. rex is:

0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 = 0.43

So the probability that at least one of the toys is a T. rex is:

1 - 0.43 = 0.57, or 57%

In other words, it is 57% likely that at least one of the dinosaur toys in Franklin's set is a T. rex.

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The solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11). The system has exactly one solution.

Let's solve the system of linear equations correctly.

The given system of linear equations is:

x = y + 3z = 6

x - 2y = 5

2x - 2y + 5z = 9

To determine the number of solutions, we can analyze the system using the method of elimination or substitution. Let's use the method of elimination:

From equation 1, we have:

x = y + 3z

Substituting this value of x in equation 2:

(y + 3z) - 2y = 5

y + 3z - 2y = 5

-z + 3z = 5 - y

2z = 5 - y

Now, let's substitute the value of x in equation 3:

2(y + 3z) - 2y + 5z = 9

2y + 6z - 2y + 5z = 9

11z = 9

Simplifying the equation, we find:

z = 9/11

Now, substituting this value of z back into the equation 2z = 5 - y, we get:

2(9/11) = 5 - y

18/11 = 5 - y

18/11 - 5 = -y

18/11 - 55/11 = -y

-37/11 = -y

y = 37/11

Finally, we can substitute the values of y and z into equation 1 to find the value of x:

x = y + 3z

x = 37/11 + 3(9/11)

x = 37/11 + 27/11

x = 64/11

Therefore, the solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11).

The system has exactly one solution.

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The required slope of the graph is 5/4.

The steepness or incline of a line is determined using the slope formula. The slope of the lines is determined using the x and y coordinates of the lines. It is the proportion of the y-change axis's to the x-change. axis's

The slope of a line is a measure of how steep the line is and it is also commonly referred to as the "rise over run". You can find the slope of a line using the following formula:

m = (y2 - y1) / (x2 - x1)

Where m is the slope, (x1, y1) and (x2, y2) are two points on the line. The formula calculates the change in the y-coordinate (the rise) divided by the change in the x-coordinate (the run) between the two points.

We have,

Two points

(0, 0) and (8, 10)

Slope = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

= (10 - 0)/(8 - 0)

= 10/8

= 5/4

Thus, required sloe is 5/4.

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Answer:

B. (2x+4y)(4x2-8xy+16y2)

Step-by-step explanation:

hope this helps!

We can rewrite the sphere's equation in Cartesian coordinates.

\(\rho = 42 \cos(\varphi) \implies \rho^2 = 42 \rho \cos(\varphi) \implies x^2+y^2+z^2 = 42z\)

Complete the square to get

\(x^2 + y^2 + z^2 - 42z = 0 \implies x^2 + y^2 + (z - 21)^2 = 21^2\)

which represents a sphere centered at (0, 0, 21) with radius 21. You can find the sphere's volume easily from here.

But that's not what you're asked to do. You want to find the volume of the intersection of the two spheres. (see attached plot)

The two spheres meet in the plane z = 21/2:

\(x^2+y^2+z^2 = 21^2 \implies x^2+y^2 = 21^2 - z^2\)

\(x^2+y^2+(z-21)^2 = 21^2 \implies 21^2 - z^2 + (z-21)^2 = 21^2 \implies z = \dfrac{21}2\)

and we express this plane in spherical coordinates as

\(z = \rho \cos(\varphi) = \dfrac{21}2 \implies \rho = \dfrac{21}2 \sec(\varphi)\)

We use this plane to cut the region of interest in half; we have to do this to find the volume because the ρ coordinate does not vary uniformly between the two spheres. On the plus side, the region is symmetrical across this plane, so we only need one integral.

Find the angle φ at which the two spheres meet:

\(42\cos(\varphi) = 21 \implies \cos(\varphi) = \dfrac12 \implies \varphi = \cos^{-1}\left(\dfrac12\right) = \dfrac\pi3\)

Putting everything together, the volume of the region is

\(\displaystyle 2 \int_0^{2\pi} \int_0^{\pi/3} \int_{21/2 \, \sec(\varphi)}^{21} \rho^2 \sin(\varphi) \, d\rho \, d\varphi \, d\theta = \boxed{\fraC{15,435\pi}4}\)

I leave the details of computation to you.

a² + b² = c²

5² + 12² = c²

25 + 144 = c²

169 = c²

c = √169

c = 13

Answer:

the answer is 13

Step-by-step explanation:

Answer:

2 m/s

Step-by-step explanation:

Answer:

2m/s²

Step-by-step explanation:

acceleration= v-u/t

=3-1/1

=2m/s²

Answer:

ohhhhhhhhhhhhhhhhh 8====> have a good day

Answer:

x=3

Step-by-step explanation:

Note: I'm not sure what "Ac" stand for but I am solving for your equation.

Answer:

x = 1 , y = -4

Step-by-step explanation:

2x - 5y = 22 ------- ( 1 )

y = 3x - 7      ------- ( 2 )

Substitute ( 2 ) in ( 1 ) :

2x - 5 (3x - 7) = 22

2x - 15x + 35 = 22

- 13x = 22 - 35

- 13x =  - 13

 x = 1

Substitute x in ( 1 ) :

2x - 5y = 22

2 ( 1 ) - 5y = 22

- 5y = 22 - 2

-5y = 20

y = - 4

9.  The stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. The stamp duty payable on a property with a purchase price of K150,000 is K7,500.

To calculate the stamp duty payable on properties with a purchase price of K45,000 and K150,000, we need to apply the corresponding rates of stamp duty based on the given information.

Given:

Value of Property:

Up to K35,000: Stamp Duty Rate - 2%

K35,000 to K70,000: Stamp Duty Rate - 3%

K70,000 to K140,000: Stamp Duty Rate - 4%

Over K140,000: Stamp Duty Rate - 5%

9. Calculate the stamp duty payable on properties whose purchase price is K45,000:

Since the purchase price of K45,000 falls within the range of K35,000 to K70,000, the stamp duty rate applicable is 3%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K45,000 * 3%

= K45,000 * 0.03

= K1,350

Therefore, the stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. Calculate the stamp duty payable on properties whose purchase price is K150,000:

Since the purchase price of K150,000 is above K140,000, the stamp duty rate applicable is 5%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K150,000 * 5%

= K150,000 * 0.05

= K7,500

Therefore, the stamp duty payable on a property with a purchase price of K150,000 is K7,500.

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Answer:

1/3 or one third

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

2/6 = ?

You can simplify this fraction

2/6 = 1/3

Answer:

180

Step-by-step explanation:

volume= (6*5)/2*12 =180 in

The sixth term of an arithmetic sequence is 6

The sum of the first four terms of an arithmetic sequence is 10.

The fifth term is 5.

Therefore,

sum of term = n / 2(2a + (n - 1)d)

where

Therefore,

n = 4

10 = 4 / 2 (2a + 3d)

10 = 2(2a + 3d)

10 = 4a + 6d

4a + 6d = 10

a + 4d = 5

4a + 6d = 10

4a + 16d = 20

10d = 10

d = 1

a + 4(1) = 5

a = 1

Therefore,

6th term = a + 5d

6th term = 1 + 5(1)

6th term = 6

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The probability of getting a black card and a numbered card is 9/26.

To calculate the probability of getting a black card (E1), we need to determine the number of black cards in a standard deck of 52 cards.

There are 26 black cards in total, which consist of 13 spades (black) and 13 clubs (black).

Therefore, the probability of drawing a black card (P(E1)) is:

P(E1) = Number of favorable outcomes / Total number of possible outcomes

P(E1) = 26 / 52

Simplifying this fraction, we get:

P(E1) = 1/2

So the probability of drawing a black card is 1/2.

To calculate the probability of drawing a numbered card (E2), we need to determine the number of numbered cards (2 through 10) in a standard deck.

Each suit (spades, hearts, diamonds, clubs) contains one card for each numbered value from 2 to 10, totaling 9 numbered cards per suit.

Therefore, the probability of drawing a numbered card (P(E2)) is:

P(E2) = Number of favorable outcomes / Total number of possible outcomes

P(E2) = 36 / 52

Simplifying this fraction, we get:

P(E2) = 9/13

So the probability of drawing a numbered card is 9/13.

To calculate the probability of both events occurring together (getting a black card and a numbered card), we multiply the individual probabilities:

P(E1 ∩ E2) = P(E1) × P(E2)

P(E1 ∩ E2) = (1/2) × (9/13)

Simplifying this fraction, we get:

P(E1 ∩ E2) = 9/26

Therefore, the probability of getting a black card and a numbered card is 9/26.

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Answer:

6 m or 3 meters

Step-by-step explanation:

Area formula = w * L

Perimeter formula =2 x (l+w)

So, that is how I found the answer.

Hope this helps!

Letter F and 155° are supplements.

F = 180 -155 =25°

F = 25

E completes the angle with 90° and F.

E + 90 + 25 = 180

E = 180 - 115 = 65°

E = 65

G and 143° are supplements:

G + 143° = 180

G = 180 - 143 = 37°

G = 37

H completes the inner angles of a triangle with 44° and G:

H + 44° + 37° = 180°

H = 180 - 81 = 99°

I and H are supplements:

I + 99° = 180°

I = 180° - 99° = 81°

I = 81

R is opposite of a 90° angle:

R = 90°

T completes a triangle with 30° and 90 °

T + 30 + 90 = 180

T = 180 - 120 = 60°

T = 60

W and 168° are supplements:

W + 168° = 180°

W = 180° - 168° = 12°

W = 12

Y completes the triangle with 89° and W:

Y + 89° + 12°= 180°

Y = 180° - 111° = 69°

Y = 69

Answer:

8/88 is the answer

Step-by-step explanation:

The simplified form is 1/11

Answer:

1/11

Step-by-step explanation:

cancel the common factor

8/11 ×1/8

rewrite the expression in exact form

1/11

Answer:

Solving the system of equations we get:

x=2, y=4, z=-2

Step-by-step explanation:

We need to solve the system of equations

\(2x - y + 3z = -6\\-x + 2y - 3z = 12\\y + 5z = -6\)

Let:

\(2x - y + 3z = -6--eq(1)\\-x + 2y - 3z = 12--eq(2)\\y + 5z = -6--eq(3)\)

First we find value of y from equation 3

\(y+5z=-6\\y=-6-5z\)

Put value of y in equation 1

\(2x - y + 3z = -6\\2x-(-6-5z)+3z=-6\\2x+6+5z+3z=-6\\2x+8z=-6-6\\2x+8z=-12---eq(4)\)

Now, put value of y in equation 2

\(-x + 2y - 3z = 12\\-x+2(-6-5z)-3z=12\\-x-12-10z-3z=12\\-x-13z=12+12\\-x-13z=24--eq(5)\)

Multiply equation 5 with 2 and add both equations 4 and 5

\(2x+8z=-12\\-2x-26z=48\\--------\\-18z=36\\z=\frac{36}{-18}\\z=-2\)

So, we get z=-2

Now put value of z in equation 3

\(y+5z=-6\\y+5(-2)=-6\\y-10=-6\\y=-6+10\\y=4\)

So, we get y=4

Now, put value of y=4, and z=-2 in equation 1

\(2x-y+3z=-6\\2x-4+3(-2)=-6\\2x-4-6=-6\\2x-10=-6\\2x=-6+10\\2x=4\\x=\frac{4}{2}\\x=2\)

So, solving the system of equations we get:

x=2, y=4, z=-2

Answer: = 9

There is really no steps for this answer...

Answer:

The triangles are similar.

Explanation:

Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.