determine the slope of a line that goes through (2,7) and (11,10)

The percentage of more juices that will be in the new package is 35.71%

Word problems in mathematics are things happening in our daily life and we can use mathematical concepts and arithmetic operations to put a solution to those things.

From the given information, it was stated that:

Our objective is to find the percentage of more juice that will be in the new package.

The percentage of more juice in the new package will be:

\(\mathbf{=\dfrac{14 - 9}{14} \times 100 \%}\)

\(\mathbf{=\dfrac{5}{14} \times 100 \%}\)

= 35.71%

Learn more about word problems here:

https://brainly.com/question/21405634

We can set a = 1 and c = 1/2. With these values, the Lyapunov function V(x, y) = x^2 + (1/2)y^2 satisfies the conditions and shows that the critical point at the origin is asymptotically stable.

To construct a suitable Lyapunov function, let's consider a function of the form V(x, y) = ax^2 + cy^2, where a and c are to be determined. We will choose a and c such that V(x, y) is positive definite and its derivative along the trajectories of the system is negative definite or negative semi-definite.

To show that the critical point at the origin is asymptotically stable, we need to demonstrate that there exists a Lyapunov function V(x, y) with the following properties:

V(x, y) is positive definite, i.e., V(x, y) > 0 for all (x, y) ≠ (0, 0).

V(x, y) is radially unbounded, meaning that as (x, y) approaches infinity, V(x, y) approaches infinity.

The derivative of V(x, y) along the trajectories of the system, dV/dt, is negative definite or negative semi-definite.

To determine the values of a and c, we can calculate the derivative of V(x, y) along the trajectories of the system:

dV/dt = ∂V/∂x * dx/dt + ∂V/∂y * dy/dt

Substituting the given system of differential equations: dV/dt = (2ax - 3ax^3 - cy^2) * (-x^3 + xy^2) + (2cy - 2cy^3 - cy^3) * (-2x^2y - y^3)

To ensure that dV/dt is negative definite or negative semi-definite, we can choose a and c such that the coefficients of x^4, x^2y^2, and y^4 terms in dV/dt are positive or zero. This condition guarantees that the critical point at the origin is asymptotically stable.

By comparing the coefficients, we can set a = 1 and c = 1/2. With these values, the Lyapunov function V(x, y) = x^2 + (1/2)y^2 satisfies the conditions and shows that the critical point at the origin is asymptotically stable.

To know more about derivative click here

brainly.com/question/29096174

#SPJ11

18 root

2

Step-by-step explanation:

In this question imagine there is no y

It will be 10 root2 +5 root2 +3 root 2 it will be 18 root 2

Answer:  x = 9.6

=========================================================

Explanation:

We have two smaller right triangles that are glued together so to speak.

The base of the smaller triangle on the left is 5 while the height is h.

Let's use the tangent rule to find the value of h

tan(angle) = opposite/adjacent

tan(55) = h/5

5*tan(55) = h

h = 5*tan(55)

h = 7.14074003371058

Make sure your calculator is in degree mode. That value of h above is approximate.

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

Now focus on the smaller triangle on the right

It has the same height value h. This side is the adjacent side while x is the hypotenuse.

We'll use the cosine ratio

cos(angle) = adjacent/hypotenuse

cos(42) = h/x

cos(42) = 7.14074003371058/x

x*cos(42) = 7.14074003371058

x = 7.14074003371058/cos(42)

x = 9.6088135029715

x = 9.6

The greater the discount from fair value, the smaller the liquidity index will be, and the greater the liquidity risk the FI will be exposed to.

The days needed to turn a company's trade receivables or inventory into cash are determined by the liquidity index.

Thus, the liquidity index would be smaller and the FI will be exposed to more liquidity risk the wider the discount from fair value.

To know more about the  liquidity ratio, here

https://brainly.com/question/25894261

#SPJ4

Answer:

x = 17.5

Step-by-step explanation:

So its the same angle so it has to equal the same thing

5x+7 = 9x-63

+63      +63

5x+70=9x

-5x       -5x

70 = 4x

/4       /4

17.5 = x

Answer:

(x,y) =(3/14,3/14)

Step-by-step explanation:

8x+ 4y=-2x+3           WRITE AS SYSTEM OFEQUATIONS

12y=-2x=3                  simplify expressions

10x +4y =3

2x+12y=3 .......multiply both sides of the equation by -5

10x +4y=3

-10x -60= -15        sum both equations to eliminate a variable  (10x cancels

                                                                                                      and 3+-5 +-12

-56y= -12          divide both side by -56                                                                                

y=3/14

2x+12x3/14=3    substitute the given value of y into the equation

x=3/14

Using trigonometry with the given angle of depression and the altitude of the blimp, the line-of-sight distance from the television camera to the base of the stadium is approximately 925 meters.

The angle of depression is the angle between the line of sight from the camera to the base of the stadium and the horizontal plane. We can use the tangent function to find the horizontal distance.

Let's denote the horizontal distance from the camera to the base of the stadium as d. Using the tangent of the angle of depression (18°) to calculate d, we have:

tan(18°) = Opposite / Adjacent

In this case, the opposite side is the altitude of the blimp (300 m) and the adjacent side is "d". Plugging in these values, we can solve for "d".

tan(18°) = 300 / d

d = 300 / tan(18°)

Using a calculator, we can find that tan(18°) is approximately 0.3249.

d = 300 / 0.3249

d ≈ 924.63 m

Thus, rounding to the nearest hundred meters, the line-of-sight distance from the television camera to the base of the stadium is approximately 925 meters.

Read more about the angle of depression at brainly.com/question/12331418.

#SPJ1

The surface area of a conical grain storage tank that has a height of 42 meters and a diameter of 24 meters is 1,670.5 square meters.

The surface area of a cone is calculated using the following formula:

Surface area = πr² + πrl, where π is approximately equal to 3.14, r is the radius of the base of the cone, and l is the slant height of the cone.

In this problem, we are given that the height of the cone is 42 meters and the diameter of the base is 24 meters. The radius of the base is half of the diameter, so the radius is 12 meters. The slant height of the cone can be calculated using the Pythagorean theorem.

l² = 12² + 42²

l² = 1764

l = 42.01 meters

The surface area of the cone is then calculated as follows:

Surface area = πr² + πrl

Surface area = 3.14 * 12² + 3.14 * 12 * 42.01

Surface area = 1,670.5 square meters

Here are some additional explanations:

To know more about area click here

brainly.com/question/13194650

#SPJ11

The explicit formula for f^-1 is (x-3)^(1/4) and this is obtained by switching the roles of x and y and solving for y in terms of x.

To find the inverse function of f(x)=x^4+3, we need to switch the roles of x and y, and solve for y.
Let y = x^4+3
Subtract 3 from both sides to get:
y - 3 = x^4
Take the fourth root of both sides to isolate x:
(x^4)^(1/4) = (y-3)^(1/4)
Simplify:
x = (y-3)^(1/4)
So the inverse function of f(x) is:
f^-1 (x) = (x-3)^(1/4)
This is the explicit formula for the inverse function of f(x).
To know more about explicit formula visit:

https://brainly.com/question/18069156

#SPJ11

Answer:

5

Step-by-step explanation:

These factors are 1, 5, 7 and 35. If two numbers are multiplied in pairs resulting in the original number, then it is called the pair factor of 35. These pair factors are (1, 35) and (5, 7).

Answer:

Hope the picture will help you.............

Answer:

437

Step-by-step explanation:

Because if you multiply 63 x 2 = 126

then subtract that from 1000

and get 873

then divide that by 2 and you get 437

Answer:

No, the litter box will overflow.

Step-by-step explanation:

first you need to find the volume of the litter box.

FORMULA:

cat litter box: V=lxWxH

V= 1 x 2 x 1/3

V= 2/3

Since the bag of cat litter has more cat litter than the litter box can hold, the answer is no. 1 ft 3 is more than 2/3 ft.

IM SORRY IF THIS DOESN'T MAKE SENSE I WAS CONFUSED BY THE 1 ft 3.

The correct value of x = 23.

Each interior angle of an n-sided regular polygon is given by 180 (n-2)/n degrees.

Given that:

n = 9

Therefore, each interior angle＝180 x (9-2)/9 degrees

Each interior angle = 180 x 7/9

Each interior angle = 140°

Each internal angle of a regular polygon having 9 sides is 140°.

Also, given that:

A 9-sided regular polygon with one angle equals 7x-21.

For the polygon to be a 9-sided regular polygon, the angles must equal 140°.

Checking the value of x from the given option which one satisfies the value of interior angle = 140°.

Option 1, x= 17

=> 7 x 17 - 21 = 98° which is wrong.

Option 2, x= 23

=> 7 x 23 - 21 = 161-21 = 140° which is correct.

Option 3, x= 29

=> 7 x  29 - 21 = 203-21 = 182° which is wrong.

Option 4, x= 140

=> 7 x 140 - 21 = 980- 21 = 959° which is wrong.

Only, the value of x = 23 satisfies the value of a 9-sided regular polygon with one angle equal to 7x-21.

Hence, the correct value of x = 23

To learn more about the regular polygon visit: https://brainly.com/question/24653461

#SPJ1

Answer:

The correct value of x = 23.

Step-by-step explanation:

Answer:

6 pm NYC is 3 pm in LA

Step-by-step explanation:

LA is 3 hours behind NYC

So 6 pm NYC is 3 pm in LA

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

200.96

Step-by-step explanation:

2(3.14)2^2 + 2(3.14)2*14

8*3.14 = 25.12

56*3.14 = 175.84

175.84 + 25.12 = 200.96

Answer:

This is an inverse variation, and the constant of variation is k = 2.

Step-by-step explanation:

Direct variation is something like:

y = k*x

Where k is the constant of variation.

So as x increases also increases y.

Inverse variation is something like:

y = k/x

k is the constant of variation.

In this case, if x increases, y decreases.

Now let's look at the equation:

-10 + 15*x*y = 20

Let's isolate y in one side of the equation:

15*x*y = 20 + 10 = 30

15*x*y = 30

y = 30/(15*x) = (30/15)/x = 2/x

y = 2/x

Then we can conclude that this is an inverse variation, with a constant of variation equal to 2.

Answer:

x = \(\frac{\sqrt{22} }{2}\)

Step-by-step explanation:

Using the Pythagorean Theorem we can solve this problem.

The legs of the triangle will be the same (the dashes in the middle of the line indicates they are the same).

The Pythagorean Theorem will look like this:

\(a^{2}+a^{2} = (\sqrt {11})^{2}\)

Now, let's find a:

\(2a^{2} = 11\)                The square of a radical will be whatever is under the arch

\(a^{2}=\frac{11}{2}\)                  Divide 11 by 2

\(\sqrt{a^{2} } = \sqrt{\frac{11}{2} }\)           Square root both sides

a = \(\frac{\sqrt{22} }{2}\)

Therefore, the length of side x is equal to \(\frac{\sqrt{22} }{2}\).

Hope this helps!!

a. The flagpole is 5 feet away from the building.

b. The height of the flagpole is 8 feet.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

The distance from the building to the flagpole is,

tan35° = 3.5/x.

x = 3.5/0.7.

x = 5 feet.

Now, tan48° = x/5.

x = 5/1.11.

x = 4.5 feet.

Therefore, The height of the flagpole is 4.5 + 3.5 = 8 feet.

learn more about trig ratios here :

https://brainly.com/question/14977354

#SPJ9

The nets on the right are labelled and attached accordingly. Note that in the cuboid, 6 surfaces, which for the Triangular prism, we have 5.

A cuboid is a three-dimensional geometric shape with six rectangular faces.

It has opposite faces that are parallel and equal in size.

A triangular prism is also a three-dimensional shape with two triangular bases and three rectangular faces. It has straight edges and vertices connecting the faces.

See the attached for the labelled sides.

Learn more about Triangular Prism:
https://brainly.com/question/16128664
#SPJ1

a. The 90% confidence interval for the mean monthly electric bills of all residents is ($88.06, $91.94).

b. The 95% confidence interval for the mean monthly electric bills of all residents is ($87.05, $92.95).

To construct the confidence intervals, we use the formula: CI = X ± zα/2 * (σ/√n), where X is the sample mean, zα/2 is the critical value of the standard normal distribution for the desired level of confidence, σ is the population standard deviation, and n is the sample size.

For a 90% confidence interval, the critical value of zα/2 is 1.645. Plugging in the values, we get a confidence interval of ($88.06, $91.94). This means that we can be 90% confident that the true mean monthly electric bill for all residents falls between $88.06 and $91.94.

For a 95% confidence interval, the critical value of zα/2 is 1.96. Plugging in the values, we get a confidence interval of ($87.05, $92.95). This means that we can be 95% confident that the true mean monthly electric bill for all residents falls between $87.05 and $92.95.

In both cases, we can see that the confidence intervals are relatively narrow, which is a reflection of the large sample size and relatively small standard deviation of the sample. The larger the sample size and the smaller the standard deviation, the narrower the confidence interval will be.

Learn more about confidence interval:

brainly.com/question/13067956

#SPJ11

Answer:

1/3 I believe because we already know 2 of them are hearts

Step-by-step explanation:

Therefore, the probability that someone who brings a laptop on vacation also uses a cell phone is 3.52 or 352%.

To find the probability that someone who brings a laptop on vacation also uses a cell phone, we need to use conditional probability.

Let's denote the events:

A: Bringing a laptop

B: Using a cell phone

We are given the following information:

P(A) = 25% = 0.25 (Probability of bringing a laptop)

P(B) = 30% = 0.30 (Probability of using a cell phone)

P(A ∩ B) = 88 out of 100 who bring a laptop also check work email (88/100 = 0.88)

P(B | A) = ? (Probability of using a cell phone given that someone brings a laptop)

We can use the conditional probability formula:

P(B | A) = P(A ∩ B) / P(A)

Substituting the given values:

P(B | A) = 0.88 / 0.25

Calculating the probability:

P(B | A) = 3.52

To know more about probability,

https://brainly.com/question/13528400

#SPJ11

The answer is A. regular

Answer:

Regular

Step-by-step explanation:

Find AB , AC , DE and DF. If the ratios DE/AB and DF/AC are equal , then the triangles are similar

Given data ,

Let the first triangle be ΔABC

Let the second triangle be ΔDEF

Now , the corresponding sides are

DE/AB and DF/AC

Now , corresponding sides of similar triangles are in the same ratio.

On simplifying , we get

DE/AB = DF/AC

Hence , the triangles are similar

To learn more about similar triangles click :

https://brainly.com/question/29378183

#SPJ1

The most appropriate measure of center include the following: C. The median.

In Mathematics and Geometry, a median refers to the middle number (center) of a sorted data set, which is when the data set is either arranged in a descending order from the greatest to least or an ascending order the least to greatest.

From the data set for this day care facility, we have:

22, 23, 23, 24, 20, 8

By sorting the data set from the least to greatest, we have:

8,20,22,23,23,24

Median = (22 + 23)/2

Median = 22.5

In conclusion, the median is the most appropriate measure of center because the value 8 is an outlier.

Read more on median here: brainly.com/question/452652

#SPJ1