Three dogs eat 30 pounds of food in 10 days. If each dog eats the same amount, how much food does 1 dog eat in 1 day? 1 pound 3 pounds 9 pounds 10 pounds

The equation of the quadratic equation is P(x) = x² + 23/4x - 21/4

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The given parameters are

Zeros = -7 and 3/4

The sum of multiplicities of the quadratic equation must be equal to the degree.

This means that the multiplicity of the zeros -7 and 3/4 is 1

The equation of the quadratic equation is then calculated as

P(x) = (x - zero)^ multiplicity

So, we have

P(x) = (x + 7)(x -3/4)

Expand

P(x) = x² + 7x - 3/4x - 21/4

This gives

P(x) = x² + 23/4x - 21/4

Hence, the equation is P(x) = x² + 23/4x - 21/4

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Hi there!

~

\(15cm\) as a ratio of \(1 meter\)

is : \(3:20\)

⇒Did you know? : 1 meter can also be written as 100 cm.

If 1 meter can be written as 100 cm the ratio would be : \(\frac{15}{100} = \frac{3}{20}\)

Now we can express it as  3:20.

Hope this helped you!

Answer:

Below

Step-by-step explanation:

a) the empirical rule would say that these rents are +- 1 SD from the mean....this area encompasses  + -  34.1%   or 68.2 %  (see image)

b) this is one S.D. below the mean which would be 50% - 34.1 % = 15.9% are below 1340

c) from graph: this is two S.D. ABOVE the mean and would include 2.2% are more than 2030

NOTE:  What YOU have been taught might have slightly different numbers for the 'empiracal rule' ....like 34%   rather than   34.1 %    etc.....you will have to apply what you have been given and expected to use.....I do not have that information !

Answer:

Step-by-step explanation:

Since the cannonball is fired at an angle of 45°, it will have the same horizontal and vertical velocities.

Let x be the distance it travels before it is 600 feet above ground. At this point, its vertical displacement will be 600 feet, and we can use the formula for vertical displacement:

y = v0*t + (1/2)at^2

Since there is no initial vertical velocity and we are ignoring gravity, a = 0 and the equation simplifies to:

y = 0*t + 0 = 600

Solving for t, we get:

t = sqrt(2y/a) = sqrt(2*600/0) = undefined

This means that the cannonball will never be 600 feet above ground if we ignore gravity. Since this is not realistic, we cannot answer this question without additional information or by assuming that gravity is acting on the cannonball.

Answer:

80

Step-by-step explanation:

The dimensions of the rectangular garden to maximize the area is length = width = 75 meters.

Let l be the length and w be the width of the rectangular garden.

We need to find the dimensions of the rectangular garden of greatest area that can be fenced off (all four sides) with 300 meters of fencing.

The perimeter of the  rectangular garden = 300 meters

We know that the perimeter of the rectangle =2(length + width)

300 = 2(l + w)

l + w = 150               .......(1)

Now, the maximum area of a  rectangular garden is when Length  = width

So, for equation 1

l + l = 150

l = 75 meters

So, w = 75 meters

And the area of the rectangular garden = length * width

                                                               = 75 * 75

                                                               = 5625 m²

So the maximum area of the  rectangular garden is 5625 m²

Therefore, the dimensions of the garden to maximize the area is length = width = 75 meters and maximum area is  5625 m²

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Answer:

B; There is only one (x,y) solution and y is negative

Step-by-step explanation:

First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

Each step of this theorem is proved below.

Given that,

S is finite,

Now enumerate all of its elements as x₁, x₂,..., x\(_{n}\).

According to the cancellation rule,

This product is independent of the order of the factors.

As a result, we can define the identity element e as this product.

It is simple to demonstrate that e meets the criteria of an identity element.

Now, let's show that every element of S has an inverse.

Let a be any element of S. Consider the set {a, a, a, ...}.

Since S is finite,

There exist positive integers m and n such that

am = an   for some m > n.

By the cancellation law,

We can cancel a power of a from both sides to get a\({(m-n)}\) = e.

This means that a has an inverse, and we can conclude that S is a group.

Consider the set of all positive integers under addition, except 1, as an example of an infinite semigroup in which the cancellation laws hold but which is not a group.

This set clearly meets the cancellation laws, but it does not have an inverse for every element, because the inverse of 2, for example, is not an integer.

As a result, this is not a group.

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Answer:

NOM and POR

(so so sorry if it's wrong, I tried my best to help you but I had to look up an image of a angle like that but i hope you have a wonderful day, sorry again if i am wrong, i hope i help in a way, in i did not, sorry)

Answer:

The first box : -4  the second one : 6

Step-by-step explanation:

subtract 7 from 3 for the first box, then add 10 to -4 for the second one.

Answer:

facts

Step-by-step explanation:

Answer:

\(y= 9/4x+5\)

Step-by-step explanation:

I'll go over #7 and you should be able to do the rest.

Slope intercept form general equation is:

y = mx + b

I bolded the value you need to change/find.

m is the slope

b is the y-intercept

You can calculate m using:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

you're given (-4,-4) and (0,5) so y₂=5, y₁=-4, x₂=0, x₁=-4

\(m=\frac{5-(-4)}{0-(-4)}=9/4\)

Plug your value into the point-slope formula.

\(y = m(x-x_1)+y_1\)

\(y = (9/4)(x-(-4))+(-4)\)   simplify it

\(y= 9/4x+5\)  the simplified form is the slope-intercept formula

Answer:

B c < 27.50

Step-by-step explanation:

The cost c of a shirt is less than $27.50

In representing equality

< Represent less than

= Represent equal to

> Represent greater than

Other representation includes

< = Less than or equal to

>= Greater than or equal to

/= Not equal to

The cost c of a shirt is less than $27.50

C< 27.50

In the given Quadrilateral, The measure of ∠x=110°.

what are quadrilaterals?

Quadrilaterals are four-sided polygons. They are two-dimensional shapes with four straight sides, four vertices, and four angles which have sum of 360°. Quadrilaterals can have parallel sides, opposite sides that are congruent, opposite angles that are congruent, and diagonals that bisect each other. Some examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses.

Now,

For given Quadrilateral

three angles given are 128°, 82° and 40° and 4th angle=x°.

To find x

As we know

Sum of all interior angles of a quadrilateral=360°

128°+82° +40° +x°=360°

x=360-250

x=110°

hence,

          the measure of ∠x=110°.

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Team A performed 21 shows.

Team B performed 5 shows.

A = 4B + 1

B = A - 16

Substitute 4b + 1 for a in b = a − 16:

b = a − 16

b = 4b + 1 − 16

b= 4b − 15 (Simplify both sides of the equation)

b − 4b = 4b − 15 − 4b (Subtract 4b from both sides)

−3b = −15

−3b/−3 = −15/−3(Divide both sides by -3)

b=5

Substitute 5 for b in a = 4b + 1:

a = 4b + 1

a = (4)(5) + 1

a = 21

An equation is formed of two equal expressions. The number of concerts performed by A and B is 21 and 5, respectively.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of concerts performed by Singer A and Team B be represented by A and B, respectively.

Given that  Singer A performed more than four times as many shows during concert tours as Team B. Therefore, we can write,

A = 4B + 1

Also, the number of Singer A concert tour shows exceeded the number of shows by Team B by 16. Therefore,

A = B + 16

As we got two equations written for A, equate the two equations equal to each other as shown.

A = A

4B + 1 = B + 16

4B - B = 16 - 1

3B = 15

B = 15/3

B = 5

Now, substitute the value of B in any one of the equations of A,

A = B + 16

A = 5 + 16

A = 21

Hence, the number of concerts performed by A and B is 21 and 5, respectively.

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The zeros of the function f(x) = 2x⁴ + 11x³ + 16x² + x - 6 are x = -3, x = -2,

x = -1 and x = 1/2 respectively

The zero of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) vanishes at x; that is, the function f attains the value of 0 at x, or equivalently, x is the solution to the equation f(x) = 0. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

In the given problem, the zero of the function;

f(x) = 2x⁴ + 11x³ + 16x² + x - 6; -3 are

f(-3) = 2(-3)⁴ + 11(-3)³ + 16(-3)² -3 - 6 = 0

f(-2) = 2(-2)⁴ + 11(-2)³ + 16(-2)² - 2 - 6 = 0

f(-1) = 2(-1)⁴ + 11(-1)³ + 16(-1)² - 1 - 6 = 0

f(1/2) = 2(1/2)⁴ + 11(1/2)³ + 16(1/2)² - 1/2 - 6 = 0

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Answer:

  linear

Step-by-step explanation:

The function is linear if the ratio of changes in y to changes in x is the same for any set of (x, y) pairs.

  first two pairs: (y2 -y1)/(x2 -x1) = (7 -4)/(2 -1) = 3/1 = 3

  second two pairs: (y3 -y2)/(x3 -x2) = (16 -7)/(5 -2) = 9/3 = 3

The slopes between points are the same for any pair of points, so they all lie on the same line. The function is linear.

Answer:

Step-by-step explanation:

It is a right triangle. The hypotenuse is 6+9=15.

Pythagorean Theorem: 9² + ?² = 15²

?² = 15² - 9² = 225 - 81 = 144

? = √144 = 12

Answer:

Step-by-step explanation:

We know that:

On simplification:

Further simplification:

Hence, Mr. Lopez will need to fence 480 ft.

Hoped this helped.

\(BrainiacUser1357\)

An absolute value is the numerical value of a number without consideration of its sign. It can be represented graphically by a straight line known as a number line. Absolute value equations are equations that include absolute values of variables or unknown quantities. The following are examples of how to write an absolute value equation in the form |x-c|=d to fit the provided solution sets:

Example 1:

Solution set: {x|x≤-3 or x≥1}
Absolute value equation: |x-(-1)|=4
Explanation: -1 is the midpoint of the two ranges (-3 and 1) in the solution set. |x-(-1)|=|x+1| is the absolute value expression for the midpoint -1. The distance d from -1 to the solutions' furthest endpoints, 1 and -3, is four, hence the value of d in the absolute value equation is 4.
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\(100\% + 4.1\% = 104.1\% = 1.041\)

\(a = 239000 \\ r = 1.041 \\ next \: year \: population \\ = ar {}^{n - 1} \\ = 239000(1.041) {}^{2 - 1} \\ = 239000(1.041) {}^{1} \\ = 248799\)

sorry if I do it wrong!

Answer: 16a + 32b  - 8c  

Step-by-step explanation:

8(2a + 4b - c ) = 16a + 32b  - 8c

Multiply 8 by 2a to get 16a

Multiply 8  by 4b to get 32b

Multiply 8 by -c or -1c  to get -8c

Put them together to get 16a + 32b - 8c

Answer:

f(x) = -5/9x - 11/9

Step-by-step explanation:

Consider f(x) = y

so if x = -4 => y = 1 and x = 5 => y = -4

so (-4,1) and (5,-4) should be on the same linear equation

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

m = (-4 - 1)/(5 -  -4) = (-5)/(9) = -5/9

y = mx + b

given m = -5/9, x = -4, y = 1

1 = -5/9(-4) + b

b = 1 - 20/9

b = 9/9 - 20/9 = -11/9

so y = -5/9x - 11/9

or f(x) = -5/9x - 11/9

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer:

1100

Step-by-step explanation:

8 = 1000

9 = 1001

10 = 1010

11 = 1011

12 = 1100

hope this helps :)

Answer:

The statement in the question is wrong. The series actually diverges.

Step-by-step explanation:

We compute

\(\lim_{n\to\infty}\frac{n^2}{(n+1)^2}=\lim_{n\to\infty}\left(\frac{n^2}{n^2+2n+1}\cdot\frac{1/n^2}{1/n^2}\right)=\lim_{n\to\infty}\frac1{1+2/n+1/n^2}=\frac1{1+0+0}=1\ne0\)

Therefore, by the series divergence test, the series \(\sum_{n=1}^\infty\frac{n^2}{(n+1)^2}\) diverges.

EDIT: To VectorFundament120, if \((x_n)_{n\in\mathbb N}\) is a sequence, both \(\lim x_n\) and \(\lim_{n\to\infty}x_n\) are common notation for its limit. The former is not wrong but I have switched to the latter if that helps.

Answer:

\(\displaystyle \sum^{\infty}_{n = 1} \frac{n^2}{(n + 1)^2} = \text{div}\)

General Formulas and Concepts:

Calculus

Limits

Series Convergence Tests

Step-by-step explanation:

*Note:

Always apply the nth Term Test as the first test to use for convergence.

Rules:

Step 1: Define

Identify

\(\displaystyle \sum^{\infty}_{n = 1} \frac{n^2}{(n + 1)^2}\)

Step 2: Find Convergence

∴ by the nth Term Test, the series diverges.

Topic: AP Calculus BC (Calculus I + II)

Unit: Convergence Tests

Answer:

352sq.cm.

Step-by-step explanation:

There are a total of 5 cubes.

To find the surface area of the corner cubes, we have have to multiply 4^2 * 5 because one of the surface is attached to the other cube's surface. 16*5 is one cube's surface area, so times 2 gives us 160.

To find the surface area of the cubes in the middle, we have to multiply 4^2 * 4 because two of their sides are attached to other cube's side. So 16*3 = 64 and we have 3 of them so it's 192.

Now adding all the surface area, 192 + 160, we get a total of 352 for the surface area of that figure.

The probability that she picks a blue marble three times in a row is 1/125.

Given that

Samantha has a bag of 5 different colored marbles.

She randomly picks a marble from the bag, records the color, and returns it to the bag before picking another marble.

We have to determine

What is the probability that she picks a blue marble three times in a row?

According to the question

Samantha has a bag of 5 different colored marbles.

She randomly picks a marble from the bag, records the color, and returns it to the bag before picking another marble.

The probability of picking a bag one time is,

Number of bag pack at a time

Total number of bag

=1/5

The probability of picking a bag second time is,

Number of bag pack at a time Total number of bag

=1/5

The probability of picking a bag third time is,

Number of bag pack at a time

Total number of bag

=1/5

031%

Therefore,

The probability that she picks a blue marble three times in a row is,

= 1/5 X 1/5 X 1/5

1 /125

Hence, the probability that she picks a blue marble three times in a row is 1/125.

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Step-by-step explanation:

hope this helps

Answer:

hello answer is a

answer is x greater than or equal to -2

and x is less than 4

Step-by-step explanation:

Answer:

  4 minutes

Step-by-step explanation:

You want to know how long it takes to drain a cylindrical tank 1.8 ft in diameter and 3 ft long at the rate of 1.7 ft³/minute. (π = 3.14)

The volume of a cylinder can be found using the formula ...

  V = (π/4)d²h . . . . . . . diameter d, height h

Then the volume of the oil tank is ...

  V = 3.14/4(1.8 ft)²(3 fft) = 7.6302 ft³

The time it takes to empty the tank is found by dividing the volume by the rate:

  (7.6302 ft³)/(1.7 ft³/min) ≈ 4.49 min ≈ 4 min

It will take about 4 minutes to empty the tank.

<95141404393>

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(y = \stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{2}}x-5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so we're really looking for the equation of a line whose slope is -1/2 and passes through (6 , -4)

\((\stackrel{x_1}{6}~,~\stackrel{y_1}{-4})\qquad \qquad \stackrel{slope}{m}\implies -\cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{-\cfrac{1}{2}}(x-\stackrel{x_1}{6}) \\\\\\ y+4=-\cfrac{1}{2}x+3\implies y=-\cfrac{1}{2}x-1\)