The lengths of two pieces of fabric are in the ratio 7:5. If the first length is 210 meters, what is the second length? *​

Hello,

(i) Express n as the subject.

\(C=\frac{nA}{n+12}\)

\(C(n+12) = nA\\nC + 12C = nA\\\frac{nC+12C}{n}=\frac{nA}{n} \\\frac{nC}{n}+\frac{12C}{n} = A \\\frac{12C}{n} =A-C\\\frac{n}{12C}=\frac{1}{A-C} \\n = \frac{12C}{A-C}\)

(ii)

Since C = 6 mL and n = 8 we need to solve this equation of unknown A :

\(6 = \frac{8A}{8+12} \\6 = \frac{8A}{20}\\8A = 20*6\\A = \frac{5*4*2*3}{4*2}\\A = 15\)

Thus, the equivalent adult dosage A would be 15 mL

(iii) I let you think about this one

Good Luck

The answer is of this question is B.

Answer:

a

Step-by-step explanation:

I took the test

The equivalent expression of 8x - 1 - 2y + 4 is

8x - 2y + 3.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

8x - 1 - 2y + 4

Combine the like terms.

8x - 2y + 3

Thus,

The final expression is 8x - 2y + 3.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

Answer:

45

Step-by-step explanation:

Range = (Biggest term - Smallest term)

53-8=45

The probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill is 0.0464.

What is a binomial distribution?

The probability distribution known as the binomial distribution, which is used in statistics, quantifies the chances that a value will take one of two independent values given a particular set of conditions or hypotheses.

Formula to calculate the binomial distribution

P(X = x) =ⁿCₓ× pˣ×(1-p)ⁿ⁻ˣ

Here, we know that

Solar-heat installations successfully reduce the utility bill 60% of the time.

We have to calculate the probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill.

We have 60% = 0.6 = p and n = 10.

We have a binomial distribution: X : (10, 0.6).

We use the binomial distribution formula to calculate the probability

P(X = x) =ⁿCₓ× pˣ×(1-p)ⁿ⁻ˣ, we get

P(x ≥ 9) = 1 - P(x < 9)

P(x ≥ 9) = 1 - P(x ≤ 8)

P(x ≥ 9) = 1 - ∑⁸₀ P(x = x)

P(X ≥ 9) = 1 - ∑⁸₀¹⁰Cₓ × (0.6)ˣ × (1-0.6)¹⁰⁻ˣ

P(X ≥ 9) = 1 -( 0.00011 + 0.00157 + 0.01062 + 0.04247 + 0.11148 + 0.20066 + 0.25082 + 0.21499 + 0.12093)

P(X ≥ 9) = 1 -0.95365

P(X ≥ 9) = 0.04635

Hence, the probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill is 0.0464.

To learn more about the binomial distribution from the given link

https://brainly.com/question/15223696

#SPJ4

Answer:

The question is Given that we should range the graph below: 12,10,9,8,6,5,4,3,2

-12-11-10-9-8-7-6

1 2 3 4 5 6 7 8 9 10 11 12

8

-9

-10

56

-12

and the ranging of my answer is that

-12

-10

-9

-8

-6

-5

-4

-3

-2

-1.

1 2 3 4 5 6 8 8 10 12

12

10

9

8

6

5

4

The range of the given function \(y = -e^x\) can be represented in set notation as follows:

Range: {y | y ≤ 0}

As per the shown graph, the given function is  \(y = -e^x\) , which represents an exponential decay.

As x increases, the value of  \(-e^x\) decreases rapidly.

Consequently, the range of the function is all real numbers less than or equal to zero.

Here, the graph of this function forms a curve that approaches the x-axis but never intersects or goes above it.

The function has no upper bound but approaches zero as x approaches negative infinity.

However, it never reaches zero or any positive value, resulting in a range that consists of all real numbers less than or equal to zero.

The range of the given function \(y = -e^x\) can be represented in set notation as follows:

Range: {y | y ≤ 0}

Learn more about the domain and the range here:

brainly.com/question/21027387

#SPJ5

The formula you have given (SS₁ + SS₂) / (n₁+ n₂) is actually the formula for the unweighted average of the variances, which is not appropriate when the sample sizes and variances are different between the two samples.

The formula for pooled variance is:

pooled variance = (SS₁+ SS₂) / (df₁ + df₂)

where SS₁ and SS₂ are the sum of squares for the two samples, df₁ and df₂ are the corresponding degrees of freedom, and the pooled variance is the weighted average of the variances of the two samples, where the weights are proportional to their degrees of freedom.

Note that the denominator is df₁ + df₂ not n₁+ n₂. The degrees of freedom take into account the sample sizes as well as the number of parameters estimated in

Learn more about “ formula for pooled variance “ visit here;

https://brainly.com/question/31450664

#SPJ4

The cubic function p(x) = \(ax^3 + bx^2\) + cx + d has a tangent with equation y=3x +1 at the point (0,1) and has a turning point at (-1,-3), the values of a, b, c and d are a=2-d, b=4-2d, c=d, and d

The cubic function p(x) = \(ax^3 + bx^2\) + cx + d has a tangent line with equation y=3x +1 at the point (0,1).

In addition, the cubic has a turning point at (-1,-3). To solve for a,b,c and d, we can use both of these facts.

First, let's look at the point (0,1). We know that the equation of the tangent line at this point is

y=3x +1.

Plugging in the coordinates of this point gives us

1=3(0)+1

This means that 1=1

This gives us one equation with one unknown, c.

We can solve for c by simply subtracting 1 from both sides of the equation, giving us 0=c.

Now, let's look at the turning point, (-1,-3).

We know that the equation of the cubic at this point is p(-1)=-3.

Substituting in the values for a,b,c, and d from our first equation gives us

-3=-a+b-c+d.

This gives us another equation with three unknowns, a,b, and d.

We can solve for these unknowns by rearranging the equation and adding 3 to both sides. We get

a+b+d=6.

We now have two equations with four unknowns.

We can solve this system of equations using substitution.

We start by substituting 0 for c in our second equation.

This gives us

a+b+d=6

We can then substitute this into the first equation.

This gives us

a+b-0+d=1

Since we substituted 0 for c, we can subtract b from both sides.

This gives us a+d=1. We can now solve for a and d.

Adding 1 to both sides of the equation gives us

a+d+1=2

which we can rearrange to

a=2-d

Now, we can substitute this into the second equation.

This gives us

(2-d)+b+d=6

We can solve for b by subtracting d and 2 from both sides, giving us

b=4-2d

Now that we have the values of a, b, and d, we can substitute them into the second equation to solve for c.

This gives us

2-2d-4+2d+d=6,

which simplifies to

c=d

For similar question on cubic function

https://brainly.com/question/20896994

#SPJ11

Answer: C

Step-by-step explanation:

Answer:

8c

9a

7c (just going in order of pictures lol)

10d

6a

Step-by-step explanation:

8. 180-68=5x+12

112=5x+12

100=5x

x=20

9. 180-100=2x

80=2x

x=40

7. 2x+x-3=90

3x=93

x=31

10. 180-70-60=8x+2

50=8x+2

48=8x

6=x

6. 3x=45

x=15

"Centripetal is the word used to describe a vector that always points toward the centre of a circular path."

The centripetal acceleration vector is an acceleration in the radial direction that is directed towards the centre of the circular line of motion. It runs perpendicular to the linear motion, or v.

The direction of the velocity shift for a ball travelling around a curve is in the direction of the curve's centre. Centripetal acceleration is the acceleration that is directed towards the centre of a curved or circular route.

Any force that changes the path of motion towards the centre of a circular motion is known as a centripetal force. The portion of the force that produces the centripetal force is the part that is perpendicular to the velocity.

To know more about vectors:

https://brainly.com/question/13590043

#SPJ4

Null hypothesis: the mean entry-level salary of an employee and is not significantly less than that of professionals in the company.

Alternative hypothesis: the mean entry-level salary of an employee is significantly less than that of professionals in the company.

A hypothesis in a study is a statement that is made to explain a given observation without prior testing to prove or disprove the statement.

The two types of hypothesis are:

The null hypothesis states that there is no significant difference between two variables while the alternative hypothesis states that there is a significant difference between the variables.

For the given observation:

Null hypothesis: the mean entry-level salary of an employee and is not significantly less than that of professionals in the company.

Alternative hypothesis: the mean entry-level salary of an employee is significantly less than that of professionals in the company.

In conclusion, the null hypothesis is the hypothesis of no significant difference.

Learn more about null and alternative hypothesis at: https://brainly.com/question/13045159

#SPJ4

Answer:

\(9m^5n^-7\)  = \(\frac{ 9m^5}{n^ 7}\)

Step-by-step explanation:

Answer:

d = 47°

Step-by-step explanation:

Image is attached

Sum of angles drawn along a straight line = 180°:

The angle drawn in pink : 180° - 112° = 68°

The angle drawn in green: 180° - 66° = 114°

The angle drawn in yellowish orange: 180° - 23° = 157°

The angle marked in purple: 180° - 102° = 78°

The figure drawn in the center is a 5-sided irregular pentagon

∴ Sum of interior angles in a 5-sided polygon = (n - 2) ×180°

                                                                            = (5 - 2) × 180°

                                                                            = 540°

The four angles calculated above will assist in calculating the fifth remaining angle of the pentagon (which is marked in light blue):

   68° + 114° + 78° + 157° + angle in light blue = 540°

Angle in light blue = 540° - 68° - 114° - 78° - 157°

                               = 123°

Sum of angles drawn along a straight line = 180°:

Angle marked in dark blue = 180° - 123°

                                                = 57°

Now focus on the angles present inside the triangle

Sum of interior angles of a triangle = 180°

= d + 76° + 57° = 180°

d has to be isolated and made the subject of the equation:

d = 180° - 76° - 57°

d = 47°

Answer:

11. It will take about 26 minutes to install a singular tile.

12. It will take about 10 more minutes to install a light than it does to install a cable.

Step-by-step explanation:

11. Since installing 15 new tiles took a total of 390 minutes and each tile took the same amount of time, you can divide the total amount of time by the number of tiles.

390/15= 26 minutes

It will take about 26 minutes to install a single tile.

12. By looking at the chart it can be assumed that installing a light takes about 22 minutes since it is in the middle of 20 and 24 minutes. Installing a cable only takes 12 minutes.

22-12= 10 minutes

It takes about 10 minutes longer to install a light than it does a cable.

It took about 26 minutes to install a single tile and 10 minutes longer to install a light than it does a cable.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

Installing 15 new tiles took a total of 390 minutes and each tile took the same amount of time,

We have to divide the total amount of time by the number of tiles.

390/15= 26 minutes

It will take about 26 minutes to install a single tile.

By observing the chart, it can be assumed that installing a light takes about 22 minutes since it is in the middle of 20 and 24 minutes. Installing a cable only takes 12 minutes.

22-12= 10 minutes

It takes about 10 minutes longer to install a light than it does a cable.

Hence, it took about 26 minutes to install a single tile and 10 minutes longer to install a light than it does a cable.

To learn more on Graph click:

https://brainly.com/question/17267403

#SPJ2

To calculate the values of y for the given function \(y = sin^2(x) / (1.55sin(x) + cos^2(x))\)  at x = 20°, 30°, 40°, 50°, 60°, 70°, and 80°, perform the calculations using a calculator or mathematical software.

To calculate the value of y for the given function\(y = sin^2(x) / (1.55sin(x) + cos^2(x)),\) we can substitute the given values of x into the equation and evaluate it using element-by-element operations.

For x = 20°:

\(y = sin^2(20) / (1.55sin(20) + cos^2(20))\)

For x = 30°:

\(y = sin^2(30) / (1.55sin(30) + cos^2(30))\)

For x = 40°:

\(y = sin^2(40) / (1.55sin(40) + cos^2(40))\)

For x = 50°:

\(y = sin^2(50) / (1.55sin(50) + cos^2(50))\)

For x = 60°:

\(y = sin^2(60) / (1.55sin(60) + cos^2(60))\)

For x = 70°:

\(y = sin^2(70) / (1.55sin(70) + cos^2(70))\)

For x = 80°:

\(y = sin^2(80) / (1.55sin(80) + cos^2(80))\)

By evaluating these equations using a calculator or mathematical software, we can find the respective values of y for each given value of x.

Note: Due to the complexity of the calculations involved, it is recommended to use a scientific calculator or mathematical software to obtain accurate results.

For similar question on function.

https://brainly.com/question/179886  

#SPJ8

Answer:

36 pizzas

4 cases of sauce and 3 cases of cheese.

Step-by-step explanation:

In order to solve this problem, we need to find the least common multiple of both of these numbers. We do this by simply multiplying these numbers by each factor of 1 until an equal value is an output. Like so...

9*1 = 9                    12*1 = 12

9*2 = 18                  12*2 = 24

9*3 = 27                  12*3 = 36

9*4 = 36

We can now see that the fewest number of pizzas we can make without having anything left over is 36 pizzas. To do this we would need 4 cases of sauce and 3 cases of cheese.

To plot the direction field associated with the differential equation u^n + 192u = 0, we need to first rewrite the equation as: u' = -192u^(1-n) where u' denotes the derivative of u with respect to some independent variable, such as time. The direction field represents the slope of the solution curve u(x) at each point (x, u(x)) in the xy-plane. To find this slope, we evaluate the right-hand side of the equation at each point: dy/dx = -192y^(1-n)

We can then plot short line segments with this slope at each point in the plane. The resulting picture will show us how the solution curves behave over the entire domain of the equation.To plot the phase plot of the solution corresponding to the initial value problem (IVP), we need to find the specific solution that satisfies the given initial condition. In other words, we need to find u(x) such that u(0) = y0, where y0 is some given constant. The solution to this IVP is: u(x) = (y0^n) / ((y0^n - 192) * e^(192x)) To plot the phase plot, we need to graph this solution as a function of time (or whatever independent variable is relevant to the problem), with u(x) on the vertical axis and x on the horizontal axis. We can then mark the initial condition (0, y0) on this graph and sketch the solution curve that passes through this point.Overall, the direction field and phase plot provide us with a visual representation of how the solution to the differential equation behaves over time. By analyzing these plots, we can gain insight into the long-term behavior of the solution and make predictions about its future behavior.

Learn more about slope here

https://brainly.com/question/16949303

#SPJ11

Answer:

See Explanation

Step-by-step explanation:

The function is not properly given. So, to solve this question I'll assume it is:

f(x) = x² + 3

Required

Calculate the average rate of change on −1 ≤ x ≤ 3.

[The average rate of change (R) is calculated using:]

R = (f(b) - f(a))/(b - a)

[Where]

a ≤ x ≤ b = −1 ≤ x ≤ 3.

[This means that]

a = -1

b = 3

[Solving f(b); We have]

f(x) = x² + 3

[Substitute b for x]

f(b) = b² + 3

[Substitute 3 for b]

f(3) = 3² + 3 = 9 + 3 = 12

[Solving f(a); We have]

f(x) = x² + 3

[Substitute a for x]

f(a) = a² + 3

[Substitute -1 for b]

f(-1) = (-1)² + 3 = 1 + 3 = 4

[So, the equation becomes]

R = (f(b) - f(a))/(b - a)

R = (12 - 4)/(3 - (-1)

R = 8/(3+1)

R = 8/4

R = 2

[Hence, the average rate of change is 2]

Answer:

20 percent off depends on the original cost: Take the original number and divide it by 10. Double your new number. Subtract your doubled number from the original number. You have taken 20 percent off! For $30, you should have $24.

Step-by-step explanation:

Therefore, the volume of the rectangular prism is 87.5 cubic yards.

A prism is a transparent object, usually made of glass or plastic, that refracts or bends light as it passes through it. It has at least two flat surfaces, called faces, that are usually parallel and rectangular in shape, and two non-parallel faces, called bases, which are usually triangular in shape. When light enters a prism, it is refracted, or bent, as it passes through the prism and is separated into its component colors, creating a rainbow effect. Prisms are often used in optics and science experiments to study the properties of light, such as its wavelength and polarization. They are also commonly used in optical instruments such as binoculars, telescopes, and cameras to help focus and direct light.

The volume V of a rectangular prism is given by the formula:

V = length x width x height

In this case, the length is 5 yards, the width is also 5 yards, and the height is 3- and one-half yard.

To calculate the volume, we can plug this value into the formula:

V = 5 yards x 5 yards x 3.5 yards

Simplifying this expression, we get:

V = 87.5 cubic yards

To learn more about prism, visit

https://brainly.com/question/29722724

#SPJ1

Answer:

The volume of a rectangular prism is the product of its length, width, and height. In this case, the length is 5 yards, the width is 5 yards, and the height is 3.5 yards. Therefore, the volume of the prism is 5 * 5 * 3.5 = 87.5 cubic yards.

Here is the calculation:

Volume = length * width * height

= 5 yards * 5 yards * 3.5 yards

= 87.5 cubic yards

Step-by-step explanation:

Answer:

She would have 130 dollars

Step-by-step explanation:

There are 52 weeks in a year. So multiply 2.50 by 52. She would have 130 dollars.

Ashley can expect to save $130 for the trip in exactly one year.

Ashley decided to stop eating chocolate for one whole year to save some spending money for her senior class trip to Mexico.

The amount Ashley typically spends a week on chocolate =  $2.50.

We have to find how much Ashley can save in one year if we can save $2.50 per week.

There are 365 days in a year and we have 7 days in a week.

If we divide 365 by 7 we get,

365 / 7 = 52.14.

which means 52 weeks.

So in one year, we have 52 weeks.

We can write this statement "Ashley typically spends $2.50 a week on chocolate" as :

1 week = $2.50

Multiply by 52 on both sides.

we get,

52 x 1 week = 52 x $2.50

52 weeks = $130

Thus, we can say that in one year Ashley can save around $130 if she saves $2.50 in a week.

Learn more about savings word problem here:

https://brainly.com/question/24647187

#SPJ2

Answer:

5.24 × 10¹¹

When you do 5.24 x 10^11, you will get 524,000,000,000

The height of the ground from the base of the window is 144 inches.

One angle of a right angle triangle is equals to 90 degrees.

Therefore, the sides and angles of the right triangle can be found using trigonometric ratios.

tan x = WY / XY

tan x  = opposite / adjacent

tan x = 24 / 8

x = tan⁻¹ 3

x = tan⁻¹ 3

x = 71.5650511771

x = 71.60°

tan 71.60 = h / 48

cross multiply

h = 48 tan 71.60

h = 48 × 3

h = 144 inches

learn  more on right triangle here: brainly.com/question/2547461

#SPJ1

By using compound interest, there will be$554.68in the account after 2 years.

Compound interest is interest that is calculated on the original principal of a loan or deposit, as well as on any accumulated interest from previous periods.

Compound interest is calculated using the following formula:

Compound interest = P * (1 + r/n)^(nt) - P

To calculate the total amount in the account after 2 years, we can use the following formula:

Total amount = P * (1 + r/n)^(nt)

In this formula, P is the principal amount (the initial deposit of $500), r is the annual interest rate (5.2%), n is the number of times that interest is compounded per year (12 in this case, since the interest is compounded monthly), and t is the number of years for which the interest is compounded (2 in this case).

Substituting the given values into the formula, we get:

Total amount = $500 * (1 + 0.052/12)^(12*2) = $554.68

To learn more about compound interest visit:

https://brainly.com/question/14295570

#SPJ1

Probability that he will make the next free throw is 0.89% if larry bird made approximately 89% of all free throws during his nba career.

During nba career he made approximate 89% of all free throws.

To calculate the probability of the next 10 free throws given which will be

= No. of possible outcome / Total no. of outcome

= 89 / 100

= 0.89 %

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 outcome like how likely they are.

P(A) = (# of ways A can happen) / (Total number of outcomes)

which means that Probability that he will make the next free throw is 0.89 %

To learn more about probability

https://brainly.com/question/9653825

#SPJ4

3.

y=3x + 1 (a)

y= 3x - 1 (b)

-y= -3x + 1 (c)

(a) and (b)

y= 3x + 1

y= 3x - 1

y=y

3x+1 = 3x - 1

3x -3x = -1 - 1

0 = -2

Since 0 is not equal to -2

There are NO solutions

Answer:

y=3x + 1 (a)

y= 3x - 1 (b)