Two numbers are in a ratio 11:7. If the smaller number is 700, what is the larger number? Pls tell with steps

Answer:

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

This is a combination of 4 out of 15.

Use combination formula:

where C - number of combinations, n- total number of objects, r - number of choosing from objects

Substitute 15 for n and 4 for r to get:

Correct choice is B.

The probability of the spinner is P(not yellow) = 37.5%.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

If the spinner is spun once, the probability of not landing on yellow (sections 2 and 3) is equal to the probability of landing on purple (sections 1 and 8), blue (sections 4, 5, and 6), or orange (section 7).

The total probability of these sections is 1- (2/8) = 1-(1/4) = 3/4.

So P(not yellow) = 3/4 = 37.5%.

Hence, the probability of the spinner is P(not yellow) = 37.5%.

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Answer:

3579.6 \(ft^{3}\)

Step-by-step explanation:

First, write out the equation used to find the volume of a cylinder and place the values in place of the variables. The equation is \(\pi\)\(r^{2}\)*h where r is the radius and h is the height. When we place the values of the variables into the equation we get: \(\pi\)\(10^{2}\)*11.4. Next, square 10 to get 100. This would give you 3.14*100*11.4. When you multiply this together you get 314 times 11.4 which gives you 3579.6 ft cubed.

I believe it's 3581.42 (if the answer needs be rounded to 2 decimal places.

Step-by-step explanation:

area of circle = r×r×π

area of circle × height = volume

10 × 10 × π = 314.16

314.16 × 11.4 = 3581.42

Answer:

1,540

Step-by-step explanation:

length times width times height makes the volume

Hope this helps

BTW it's my birthday

The distance travelled by the car during its 5th second of motion is 775 m.

Part A)

Given data:

Speed of train 1 = 72 km/h

Speed of train 2 = 144 km/h

The distance between the trains is 0.950 km

Braking acceleration of trains = -12960 km/h²

We have to determine if the two trains collide or not.

To solve this question, we first need to determine the distance each train will travel before coming to a stop.

Distance travelled by each train to come to rest is given by:

v² = u² + 2as

where, v = final velocity

u = initial velocity

a = acceleration of train

and s = distance travelled by train to come to rest

Train 1: u = 72 km/h

v = 0 km/h

a = -12960 km/h²

s₁ = (v² - u²) / 2a

s₁ = (0² - 72²) / 2(-12960) km

= 0.028 km

= 28 m

Train 2: u = 144 km/h

v = 0 km/h

a = -12960 km/h²

s₂ = (v² - u²) / 2a

s₂ = (0² - 144²) / 2(-12960) km = 0.111 km

= 111 m

The total distance travelled by both the trains before coming to rest = s₁ + s₂ = 28 + 111 = 139 m

Since 139 m is less than 950 m, therefore the trains collide.

Part B)

Given data:

Speed of truck = 10.0 m/s

Acceleration of car = 2.50 m/s²

The distance travelled by the car in the time t is given by:

s = ut + 1/2 at²

where,u = initial velocity of car

a = acceleration of car

and s = distance travelled by car

The car catches up with the truck when the distance covered by both of them is the same. Therefore, we can equate the above two equations.

vt = ut + 1/2 at²

t = (v - u) / a

t = (10 - 0) / 2.5 s

t = 4 s

Therefore, the time required for the car to catch up to the truck is 4 seconds.

Distance travelled by the car:

s = ut + 1/2 at²

s = 0 x 4 + 1/2 x 2.5 x 4²s = 20 m

Therefore, the distance travelled by the car is 20 m.

Speed of car when it passes the truck:

The velocity of the car when it passes the truck is given by:

v = u + at

v = 0 + 2.5 x 4

v = 10 m/s

Therefore, the speed of the car when it passes the truck is 10 m/s.

Part C)

Given data:

Acceleration of rocket car = 124 m/s²

The velocity of the car at a time t is given by:

v = u + at

where,v = velocity of car

u = initial velocity of car

a = acceleration of car

and t = time taken by the car

To find the speed of the car at a time of 5.00 seconds, we have to put t = 5 s in the above equation:

v = u + at

v = 0 + 124 x 5

v = 620 m/s

Therefore, the speed of the car at a time of 5.00 seconds is 620 m/s.

The distance travelled by the car during its 5th second of motion is given by:

s = u + 1/2 at² + (v - u)/2 x ta = 124 m/s²

t = 5 s

Initial velocity of car, u = 0

Therefore, s = 1/2 x 124 x 5² + (620 - 0)/2 x 5

s = 775 m

Therefore, the distance travelled by the car during its 5th second of motion is 775 m.

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Answer:

$66.20=1.25x+50

Step-by-step explanation:

Be sure about the question. This problem is exactly the same to another one I did. So this should help.

Answer:

If the question is to reveal how many movies Lynn has watched, then...:

13 movies

Step-by-step explanation:

$50 is the monthly bill

$66.2 - $50 = $16.2 for movies

$16.2 / $1.25 = 12.96 movies .( or 13 movies)

The speed of the plane is 410 mph and the speed of the wind is 45 mph.

To find the speed of the plane and the speed of the wind, we can use the following system of linear equations:

Let x = speed of the plane (in mph) and y = speed of the wind (in mph).

Equation 1: (x - y) * 4 = 1540 (traveling against headwind)
Equation 2: (x + y) * 3 = 1365 (traveling with tailwind)

Step 1: Simplify the equations:
Equation 1: 4x - 4y = 1540
Equation 2: 3x + 3y = 1365

Step 2: Solve for x in Equation 2:
x = (1365 - 3y) / 3

Step 3: Substitute x in Equation 1:
4((1365 - 3y) / 3) - 4y = 1540

Step 4: Solve for y:
y = 45 mph (speed of the wind)

Step 5: Substitute y in the x equation:
x = (1365 - 3(45)) / 3

Step 6: Solve for x:
x = 410 mph (speed of the plane)

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Answer:

Step-by-step explanation:

A repeating decimal or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero.

For this case 4/11 are

0.36 36 36 36 36 36 36 36 36

it repeating 36  36

so 4/11 are repeating decimal

Answer:

\( \frac{4}{11} = 0.3636\)

Step-by-step explanation:

The remainders repeat in a pattern and the quotient also repeats in blocks of two. So, 4/11 = 0.3636, Which

36 repeats, In this case, 36 is the repeating pattern.

Answer:

b). 18.3

Step-by-step explanation:

c² = a² + b² - 2bc (cos A)

= 12.4² + 9.9² - 2(12.4) (9.9) x cos(110)

= 153.76 + 98.01 - 245.52 x cos(110)

= 251.77 - 245.52 x -0.342

c² = 251.77 + 83.97

c² = 335.74

c = 18.3

Answer:

2 cm

Step-by-step explanation:

V=πr2h = 20π

-π                -π

r2h = 20

h= 5

r2(5) = 20

/5         /5

r2=4

/2  /2

r=2cm

(my work is complicated, but trust me 2 cm is the answer)  

Answer: 45

Step-by-step explanation:

So the velocity vector is v = (-2sin(t)) i + (2cos(t)) j, and the acceleration vector is a = (-2cos(t)) i + (-2sin(t)) j, both in terms of t.

Given

r= 2cost and theta = 9t

To Find

the velocity and acceleration vector

Solution

We can start by expressing the position vector r in terms of the Cartesian coordinates x and y:

x = r cos(theta) = 2cos(t)

y = r sin(theta) = 2sin(t)

To find the velocity vector, we can take the time derivative of the position vector:

v = (dx/dt) i + (dy/dt) j

where i and j are the unit vectors in the x and y directions, respectively.

Taking the derivatives:

dx/dt = -2sin(t)

dy/dt = 2cos(t)

Substituting these back into the velocity vector equation:

v = (-2sin(t)) i + (2cos(t)) j

To find the acceleration vector, we can take the time derivative of the velocity vector:

a = (d^2x/dt^2) i + (d^2y/dt^2) j

Taking the derivatives:

d^2x/dt^2 = -2cos(t)

d^2y/dt^2 = -2sin(t)

Substituting these back into the acceleration vector equation:

a = (-2cos(t)) i + (-2sin(t)) j

So the velocity vector is v = (-2sin(t)) i + (2cos(t)) j, and the acceleration vector is a = (-2cos(t)) i + (-2sin(t)) j, both in terms of t.

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The probability is 0.96 that a randomly selected camper does not like to have a cookout, based on the given information and the complement rule of probability.

To determine the probability that a randomly selected camper does not like to have a cookout, we need to find the complement of the event C (the event that the camper likes to have a cookout).

Looking at the Venn diagram, we see that the probability of event C is 0.04 (represented by the intersection of circles C and A). Therefore, the probability of the complement of event C (not liking to have a cookout) is equal to 1 minus the probability of event C.

1 - 0.04 = 0.96

Hence, the probability that a randomly selected camper does not like to have a cookout is 0.96.

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To minimize the total area of an equilateral triangle and square, the side length of the square should be 2.167 and the side length of the triangle should be 3.833.

To find the dimensions that minimize the total area, we can set up equations based on the given information. Let's denote the side length of the square as 's' and the side length of the equilateral triangle as 't'. The perimeter of the square is 4s, and the perimeter of the equilateral triangle is 3t. Given that the combined perimeter is 13, we have the equation 4s + 3t = 13.

To minimize the total area, we need to consider the formulas for the areas of the square and equilateral triangle. The area of the square is given by A_square = \(s^2\), and the area of the equilateral triangle is given by A_triangle = (\(\sqrt{(3)}\)/4) *\(t^2\).

To find the values that minimize the total area, we can substitute s = (13 - 3t)/4 into the equation for A_square and solve for t. By finding the derivative of the total area with respect to t and setting it equal to zero, we can find the value of t that minimizes the area.

Similarly, to find the dimensions that maximize the total area, we follow the same process but this time maximize the total area by finding the value of t that maximizes the area.

Performing the calculations, we find that to minimize the total area, the side length of the square is approximately 2.167 and the side length of the triangle is approximately 3.833. To maximize the total area, the side length of the square is approximately 4.333 and the side length of the triangle is approximately 1.667.

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The exact length of the curve. y = 3 + 4x^3/2, 0 ≤ x ≤ 1 is L = ∫√(9+108x-144x^(5/2)) / √(9-16x^3) dx, from 0 to 1.

To find the length of the curve, we need to use the arc length formula:

L = ∫√(1+(dy/dx)^2) dx, where y = 3 + 4x^(3/2) and 0 ≤ x ≤ 1.

First, we need to find dy/dx:

dy/dx = (12x^(1/2))/2√(3 + 4x^(3/2))

dy/dx = 6x^(1/2)/√(3 + 4x^(3/2))

Now, we can substitute this into the arc length formula:

L = ∫√(1+(6x^(1/2)/√(3 + 4x^(3/2)))^2) dx, from 0 to 1.

Simplifying the inside of the square root, we get:

L = ∫√(1+(36x)/(3 + 4x^(3/2))) dx, from 0 to 1.

We can simplify this further by multiplying the numerator and denominator of the fraction by (3 - 4x^(3/2)):

L = ∫√(1+36x(3-4x^(3/2))/(9-16x^3)) dx, from 0 to 1.

Expanding the numerator, we get:

L = ∫√((9+108x-144x^(5/2))/(9-16x^3)) dx, from 0 to 1.

Simplifying the expression under the square root, we get:

L = ∫√(9+108x-144x^(5/2)) / √(9-16x^3) dx, from 0 to 1.

We can evaluate this integral using numerical methods, such as Simpson's rule or the trapezoidal rule, to get an approximation of the length of the curve. The exact length of the curve cannot be expressed in a finite number of terms, but it can be approximated to any desired degree of accuracy using numerical methods.

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Answer:

Step-by-step explanation:

Answer:

Answer:

Step-by-step explanation:

When making a matrix of two equations with the variables x and y, the result will be a matrix with three columns:

a column for the values of x in each equation

a column for the values of y in each equation

a column for the independent values of each equation

since our system of equations is:

we can see that the value for x in the first equation is 3 and in the second equation is 4, thus the first column will have the numbers 3 and 4:

Now for the values of y we have -5 in the first equation and -2 in the second equation, we update the matrix with another column with the values of -5 and -2:

Finally, the last column is the independent values of each equation (or the results) in the first equation that number is 12 and in the second equation is 15, thus the matrix is:

usually there is a line separating the columns for the values of x and y, and the independent values:

this is the matrix of the system of equations

Answer:

The equivalent expressions are;

9x + 9

and

9(x + 1)

Step-by-step explanation:

Mathematically, we should understand that an equilateral triangle has all of its sides equal

So if one side is 3x+ 3, the other sides too measures same

Therefore, the length of the rope represents the perimeter of the triangle

This is obtainable by adding all the side lengths together

This will be;

3x + 3 + 3x + 3 + 3x + 3 = 9x + 9

This is also same as 9(x + 1)

Answer:

sussi baker!!!

Step-by-step explanation:

The total number of counters in the bag is given as follows:

23 counters.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The probability of taking a blue counter is of 0.8, while there are 18 blue counters in the bag, hence the total number of counters in the bag is obtained as follows:

0.8 = 18/n

0.8n = 18

n = 18/0.8

n = 23 counters. (rounding up).

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the surface integral of f(x, y, z) = x + y + z along the surface S is 10√14.

To compute the surface integral of f(x, y, z) = x + y + z along the surface S parametrized by r(u, v) = (u+u, u - v, 1+2u + v), for 0 ≤ u ≤ 2, 0 ≤ v ≤ 1, we can use the surface integral formula:

∫∫f(x, y, z) dS = ∫∫f(r(u, v)) ||r_u × r_v|| du dv

where r_u and r_v are the partial derivatives of r with respect to u and v, respectively, and ||r_u × r_v|| is the magnitude of their cross product.

First, we need to compute the partial derivatives of r with respect to u and v:

r_u = (1, 1, 2)

r_v = (1, -1, 1)

Next, we can compute the cross product of r_u and r_v:

r_u × r_v = (3, 1, -2)

The magnitude of this cross product is:

||r_u × r_v|| = √(3^2 + 1^2 + (-2)^2) = √14

Now, we can write the integral as:

∫∫f(x, y, z) dS = ∫∫(u + u + u - v + 1 + 2u + v) √14 du dv

Using the limits of integration given, we have:

∫∫f(x, y, z) dS = ∫ from 0 to 1 ∫ from 0 to 2 (4u + 1) √14 du dv

Integrating with respect to u, we get:

∫∫f(x, y, z) dS = ∫ from 0 to 1 [(2u^2 + u) √14] evaluated at u=0 and u=2 dv

∫∫f(x, y, z) dS = ∫ from 0 to 1 (8√14 + 2√14) dv

Integrating with respect to v, we get:

∫∫f(x, y, z) dS = (8√14 + 2√14) v evaluated at v=0 and v=1

∫∫f(x, y, z) dS = 10√14

Therefore, the surface integral of f(x, y, z) = x + y + z along the surface S is 10√14.

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Answer:

0

Step-by-step explanation:

63 * 0 is 0. 0 * (-7) is also 0.

Anything multiplied by 0 is 0, no matter how big the number is, or how many numbers there are.

Hope this helps :)

Answer:

d=-9

Step-by-step explanation:

you simplify both side of the equation

d/3-9=-12

1/3d+-9=-12

add 9 both sides

1/3d-9+9=-12+9

1/3d=-3

then you multiply 3 both sides

3 x (1/3d)=(3) x(-3)

d=-9

Hopes this helps  :)

The particular solution to the given differential equation \($\sqrt[4]{x^2+y^2} d y=7(x d x+y d y)$\) that satisfies the condition x = 16 when y = 0, is \($\frac{4}{5} \sqrt[4]{256^2+y^2} = 896$\).

The particular solution to the given differential equation that satisfies the condition x = 16 when y = 0 can be found by integrating the equation and applying the initial condition.

To begin, we rewrite the equation as:

\(\sqrt[4]{x^2+y^2}\) dy=7(x dx+y dy)

Now, we integrate both sides of the equation.

On the left-hand side, we substitute u = y and obtain:

\($\int \sqrt[4]{x^2+u^2} du=7 \int (x dx+u dy)$\)

Integrating the left-hand side requires a substitution.

We let v = \(x^2 + u^2\), and the integral becomes:

\($\frac{4}{5} v^{\frac{5}{4}} + C_1 = 7\left(\frac{x^2}{2} + uy\right) + C_2$\)

Simplifying and rearranging the terms, we have:

\($\frac{4}{5} v^{\frac{5}{4}} = 7\left(\frac{x^2}{2} + uy\right) + C$\)

Here, C is the constant of integration.

Next, we apply the initial condition x = 16 when y = 0.

Substituting these values into the equation, we get:

\($\frac{4}{5} (16^2 + 0^2)^{\frac{5}{4}} = 7\left(\frac{16^2}{2}\right) + C$\)

Simplifying further, we have:

\($\frac{4}{5} (256)^{\frac{5}{4}} = 7(128) + C$\)

Now, we can solve for C:

\($\frac{4}{5} (256)^{\frac{5}{4}} = 896 + C$\)

Finally, we can write the particular solution by substituting the value of C back into the equation:

\($\frac{4}{5} \sqrt[4]{256^2+y^2} = 896$\)

Therefore, the particular solution to the given differential equation that satisfies the condition x = 16 when y = 0 is \($\frac{4}{5} \sqrt[4]{256^2+y^2} = 896$\).

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The complete question is:

Find the particular solution to the given differential equation that satisfies the given conditions.

\($\sqrt[4]{x^2+y^2} d y=7(x d x+y d y)$\); x = 16 when y=0

The particular solution is (Type an equation).

Answer:

15 or 15.4!!!!!!!!!! I hope this helps

Answer:

15

Step-by-step explanation:

9.2 + 6.2 is 15.4

we are rounding to the nearest whole

15.4 goes to 15

The area enclosed by the curves can be found by integrating the difference between the upper and lower curves with respect to x within the given x-interval,

which is from -ln(4) to ln(4). To compute the area enclosed by the curves y = e^x, y = e^(-x), and y = 4, we need to find the x-values where these curves intersect.

Setting y = e^x and y = 4 equal to each other, we get:

e^x = 4

Taking the natural logarithm of both sides, we have:

x = ln(4)

Setting y = e^(-x) and y = 4 equal to each other, we get:

e^(-x) = 4

Taking the natural logarithm of both sides, we have:

-x = ln(4)

x = -ln(4)

The area enclosed by the curves can be found by integrating the difference between the upper and lower curves with respect to x within the given x-interval.

∫[ln(4), -ln(4)] (e^x - e^(-x) - 4) dx

Evaluating this integral will give us the area enclosed by the curves.

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The length of segment RS is given as follows:

RS = 24.

The angle addition postulate states that if two or more angles share a common vertex and a common angle, forming a combination, the measure of the larger angle will be given by the sum of the measures of each of the angles.

The segment RT is the combination of segments RS and ST, hence:

RT = RS + ST.

Hence the length of segment RS is given as follows:

41 = RS + 17

RS = 24.

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The solution of the differential equation is given by y = (1/2) x²/11 + 359/22.

Given differential equation is dy/dx = x/11, and it should pass through (1, 16).We have to find the solution of the differential equation.

The given differential equation is,

dy/dx = x/11

Now, we will integrate both sides of the equation with respect to x. We will get\(,∫dy = ∫x/11dx\)On integrating, we get,

y = (1/2) x²/11 + C ------(1)

Where C is the constant of integration.

Now, the equation should pass through (1, 16).Hence, on substituting the value of x and y in equation (1), we get16

= (1/2) (1²)/11 + C16

= 1/22 + CC

= 359/22.

Therefore, the solution of the differential equation is

y = (1/2) x²/11 + 359/22.

Hence, we can write the answer as follows: The differential equation is given by dy/dx = x/11.

After solving the differential equation and using the given point (1,16), the solution of the differential equation is given by y = (1/2) x²/11 + 359/22.

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The average apple weight's 95% confidence interval is (119.14, 125.86).

According to one manufacturer, an apple weighs 120 grams on average with a 12-gram standard variation. According to statistics generated from a sample of 49 apples randomly selected from a shipment, the average weight per apple was 122. 5 grams.

Let, 

n = 49

x = 122.5 

σ = 12

To figure up and analyze a 95% confidence interval for the average apple weight; 

The formula for a 95% confidence interval is

(x ± 1.96*σ√n) 

(122.5 ± 1.96*12/√49)

(119.14, 125.86)

Consequently, a 95% confidence interval for the average apple weight is (119.14, 125.86).

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