Kevin uses each of the digits 5, 7, 4 and 9, once and once only, to make
four-digit numbers.
C)
What is the largest number that he can make?

Given:

There are between 24 and 40 students in a class.

The ratio of boys to girls is 4:7

To find:

The number of students in the class.

Solution:

Let the number of boys are girls are 4x and 7x respectively, where, x must be a positive integer because number of boys and girls is always a positive integer. Then, the total number of students is

\(\text{Total students}=4x+7x\)

\(\text{Total students}=11x\)

It means total number of students is multiply of 11.

Multiples of 11 are 11, 22, 33, 44, ... . So, multiples of 11 between 24 and 40 is 33.

Therefore, the total number of students in the class is 33.

Answer:

the number of answer is 2.25

Answer:

x = 10.8

Step-by-step explanation:

9 ÷ x = x ÷ (9 + 4)

9 × (9 + 4) = x × x

9 × 13 = x²

117 = x²

x = 10.81665383

The rate at which the top of the ladder is sliding down the wall when the top of the ladder is 7 feet from the ground is 105 ft/sec.

A 25 foot long ladder is leaning against a wall and sliding away at a rate of 15 ft/sec. We need to find how fast is the top of the ladder sliding down the wall when the top of the ladder is 7 feet from the ground.Let's assume the length of the ladder be 'L'.Therefore, L = 25 feet. The rate at which the ladder is sliding away from the wall is given by dL/dt. dL/dt = 15 ft/sec. Let the height of the wall be 'h'.

Therefore, h = 7 feet.We need to find the rate at which the top of the ladder is sliding down the wall. Let's assume this rate be 'x'.We know that, the ladder, wall, and the ground form a right-angled triangle.Let's assume that the distance between the base of the ladder and the wall be 'y'. Therefore, we have:x^2 + y^2 = L^2Differentiating with respect to time t, we get:2x(dx/dt)+2y(dy/dt)=0dx/dt=−y(dy/dt),Since the ladder is sliding down the wall, dy/dt is negative.dy/dt = -15 ft/sec.We need to find x when y = 7. y = 7.

Therefore, \(x=√(L2−y2)=√(252−72)=√(625−49)=√576=24\)ft.

Now, we can substitute the values in the equation we obtained for dx/dt.dx/dt = -y (dy/dt)= -7 × (-15) = 105 ft/sec.Hence, the rate at which the top of the ladder is sliding down the wall when the top of the ladder is 7 feet from the ground is 105 ft/sec.

Learn more on rate here:

brainly.com/question/25565101

#SPJ11

Javier is saving $460 per month for the first two months, and $257.5 per month for the first four months.

What is equation of a straight line?

The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

After 2 months, Javier has saved a total of $920. Therefore, we can write the following equation:

2m = 920

Simplifying this equation, we get:

m = 460

This means that Javier is saving $460 each month.

After 4 months, Javier has saved a total of $1030. Using the same logic as before, we can write:

4m = 1030

Simplifying this equation, we get:

m = 257.5

This means that Javier is saving $257.5 each month.

To model the relationship between the amount of money Javier has saved and the number of months he has saved for, we can use the equation of a straight line:

y = mx + b

where y is the amount of money saved, x is the number of months, m is the monthly savings rate, and b is the starting amount saved.

Using the values we found earlier, we can write two equations:

y = 460x + b (for the first two months)

y = 257.5x + b (for the first four months)

To find the value of b, we can substitute the values of x and y for one of the points:

920 = 460(2) + b

Simplifying, we get:

b = 0

So the final equation that models the relationship between the amount of money Javier has saved and the number of months he has saved for is:

y = 460x (for the first two months)

y = 257.5x (for the first four months)

This means that Javier is saving $460 per month for the first two months, and $257.5 per month for the first four months.

To know more about equation of a straight line visit,

https://brainly.com/question/25969846

#SPJ1

Answer:

What is the equation without it I would say it is g or e

Step-by-step explanation:

Answer:

The two points given are (-2, -8) and (8, -8), which lie on a horizontal line. Since the line is horizontal, the slope is zero.

To see this, we can use the formula for the slope of a line between two points:

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

Substituting the coordinates of the two given points, we get:

slope = (-8 - (-8))/(8 - (-2)) = 0

Therefore, the slope of the line through the points (-2, -8) and (8, -8) is 0.

Step-by-step explanation:

Answer:  d = √(Δy2 + Δx2) = √(02 + 102) = √100 = 10

Step-by-step explanation:

Answer:

y=kx

Step-by-step explanation:

For this example it would be \(y=\frac{72}{2} x\\\) or y=36x

The difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

According to the given question.

We have a function

f(x) = -1/(5x -12)

As we know that, the difference quotient is a measure of the average rate of change of the function over and interval.

The difference quotient formula of the function y = f(x) is

[f(x + h) - f(x)]/h

Where,

f(x + h) is obtained by replacing x by x + h in f(x)

f(x) is a actual function.

Therefore, the difference quotient formual for the given function f(x)

= [f(x + h) - f(x)]/h

= \(\frac{\frac{-1}{5(x+h)-12} -\frac{-1}{5x-12} }{h}\)

= \(\frac{\frac{-1}{5x + 5h -12}+\frac{1}{5x-12} }{h}\)

= \(\frac{\frac{-1+5h}{5x + 5h-12} }{h}\)

= \(\frac{-1+5h}{(5x +h-12)(h)}\)

= \(\frac{-1+5h}{5xh + h^{2} -12h}\)

= \(\frac{h(-\frac{1}{h}+5) }{h(5x+h-12)}\)

= \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\)

Hence, the difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

Find out more information about difference quotient here:

https://brainly.com/question/18270597

#SPJ4

Answer:

Area of the triangle = 469.4 ft²

Step-by-step explanation:

By applying Sine rule in the given triangle WXY,

\(\frac{\text{SinW}}{\text{XY}}=\frac{\text{SInY}}{\text{WX}}=\frac{\text{SinX}}{\text{WY}}\)

Since m∠X + m∠Y + m∠W = 180°

m∠X + 40° + 27° = 180°

m∠X = 180° - 67°

m∠X = 113°

Now substitute the measures of sides and angles given in the picture,

\(\frac{\text{Sin27}}{\text{XY}}=\frac{\text{SIn40}}{38}=\frac{\text{Sin113}}{\text{WY}}\)

\(\frac{\text{Sin27}}{\text{XY}}=\frac{\text{SIn40}}{38}\)

XY = \(\frac{38\text{(Sin27)}}{\text{Sin40}}\)

XY = 26.84

Area of the triangle = \(\frac{1}{2}(\text{XY})(\text{XW})(\text{SinX})\)

                                = \(\frac{1}{2}(26.84)(38)(\text{Sin113})\)

                                = 469.42

                                ≈ 469.4 ft²

Answer:

x = 6 , y = 18

Step-by-step explanation:

given a tangent and a secant from an external point to the circle then the product of the secant's external part and the entire secant is equal to the square of the measure of the tangent, that is

5(5 + x + 9) = 10²

5(x + 14) = 100 ( divide both sides by 5 )

x + 14 = 20 ( subtract 14 from both sides )

x = 6

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

given 2 intersecting chords of a circle then the product of the measures of the parts of one chord is equal to the product of the measures of the parts of the other chord , that is

3y = 9x = 9(6) = 54 ( divide both sides by 3 )

y = 18

The mean of T is -10 and the standard deviation of T is √425 when X1 and X2 are independent.

To find the mean of T, we can use the properties of expected values. Since T = 11X1 - 2X2, the mean of T can be calculated as follows: E(T) = E(11X1) - E(2X2) = 11E(X1) - 2E(X2) = 11(10) - 2(20) = -10. To find the standard deviation of T, we need to consider the variances and covariance of X1 and X2. Since X1 and X2 are independent, the covariance between them is zero. Therefore, Var(T) = Var(11X1) + Var(-2X2) = 11^2Var(X1) + (-2)^2Var(X2) = 121(2^2) + 4(3^2) = 484 + 36 = 520. Thus, the standard deviation of T is √520, which simplifies to approximately √425. When X1 and X2 have a correlation of -0.76, the mean and standard deviation of T remain the same as in the case of independent variables. To calculate the probability P(T > 30) when X1 and X2 are independent, normally distributed variables, we need to convert T into a standard normal distribution. We can do this by subtracting the mean of T from 30 and dividing by the standard deviation of T. This gives us (30 - (-10))/√425, which simplifies to approximately 6.16.  We can then look up the corresponding probability from the standard normal distribution table or use statistical software to find P(T > 30). The probability will be the area under the standard normal curve to the right of 6.16.

Learn more about standard normal distribution here: brainly.com/question/32506784

#SPJ11

For the polynomials p(x) = 1 - x + 4x² and q(x) = x - x², (p, q) = 10, ||p|| = √18, ||a|| = √18, and d(p, q) cannot be determined. For the vectors u = (0, 2, 3) and v = (2, 3, 0), (u, v) = 6, ||u|| = √13, ||v|| = √13, and d(u, v) cannot be determined.

In the first scenario, we have p(x) = 1 - x + 4x² and q(x) = x - x². To find (p, q), we substitute the coefficients of p and q into the inner product formula:

(p, q) = (1)(0) + (-1)(2) + (4)(3) = 0 - 2 + 12 = 10.

To calculate ||p||, we use the formula ||p|| = √((p, p)), substituting the coefficients of p:

||p|| = √((1)(1) + (-1)(-1) + (4)(4)) = √(1 + 1 + 16) = √18.

For ||a||, we can use the same formula but with the coefficients of a:

||a|| = √((1)(1) + (-1)(-1) + (4)(4)) = √18.

Lastly, d(p, q) represents the distance between p and q, which can be calculated as d(p, q) = ||p - q||. However, the formula for this distance is not provided, so it cannot be determined. Moving on to the second scenario, we have u = (0, 2, 3) and v = (2, 3, 0). To find (u, v), we use the given inner product formula:

(u, v) = (0)(2) + (2)(3) + (3)(0) = 0 + 6 + 0 = 6.

To find ||u||, we use the formula ||u|| = √((u, u)), substituting the coefficients of u:

||u|| = √((0)(0) + (2)(2) + (3)(3)) = √(0 + 4 + 9) = √13.

Similarly, for ||v||, we use the formula with the coefficients of v:

||v|| = √((2)(2) + (3)(3) + (0)(0)) = √(4 + 9 + 0) = √13.

Unfortunately, the formula for d(u, v) is not provided, so we cannot determine the distance between u and v.

Learn more about distance here: https://brainly.com/question/29130992

#SPJ11

Answer:

A is the correct answer m8

9514 1404 393

Answer:

   3x -y -30 = 0

Step-by-step explanation:

The reference line for the intercept can be written in standard form as ...

  2x +5y = 20

Setting y=0 and solving for x, we find the x-intercept to be ...

  2x = 20

  x = 20/2 = 10

__

The line perpendicular to the first reference line can use the same x- and y-coordinates, but swapped, with one of them negated. If the line is right-shifted from the origin to the x-intercept point, its equation will be ...

  3(x -10) -y = 0

In general form, this is ...

   3x -y -30 = 0

_____

Additional comments

Perpendicular lines have slopes that are opposite reciprocals of each other. The slope of a line in general form is ...

  m = -(coefficient of x)/(coefficient of y)

The opposite reciprocal of this can be had by swapping the coefficients and negating one of them.

In general form, we like to have the first coefficient positive, so we choose to negate the (new) y-coefficient in this problem.

The general form equation ax+by=0 would define a line through the origin. Using the usual methods for translating functions, we can make the line go through point (h, k) by writing the equation as a(x-h)+b(y-k) = 0. This is the method we used to make the line have the desired x-intercept.

Yes, you are correct. In a coin-tossing experiment, let's define p as the probability of getting a "head" and q as the probability of getting a "tail" (where q = 1 - p). When we repeat this experiment independently n times, we can record the number of "head" observations as x.

The random variable x follows the binomial distribution with parameters n and p.

This means that we can calculate the probability of getting a specific number of "head" observations using the binomial probability formula.

The binomial probability formula is

\(P(x) = (nCx) * (p^x) * (q^(n-x)),\)

where nCx represents the number of combinations of n items taken x at a time.

To calculate the probability of getting exactly x "head" observations,

substitute the values of n, x, p, and q into the formula.

This will give you the probability of observing x "head" outcomes in n coin tosses.

I hope this helps!

Let me know if you have any further questions.

To know more about independently visit:

https://brainly.com/question/31707382

#SPJ11

Answer:

\(\frac{3}{4}\)

Step-by-step explanation:

To find the slope, you need to find any 2 points on the line.

In this case, there is a point at (0, 0), and a point at (4, 3).

Formula for slope: \(m = \frac{rise}{run}\)

The rise is the change in the y axis from point 1, in this case (0, 0), to point 2, in this case (4, 3). The run is the change in the x axis from point 1 to point 2.

You can subtract the point 1 values from point 2 to get the rise and run:

\(m = \frac{3 - 0}{4 - 0} = \frac{3}{4}\)

The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.

We have,
Vermont had 65.3% of respondents who said yes to exercising for at least 30 minutes a day, 3 days a week.

To find the sample proportion, you can convert the percentage to a decimal by dividing the percentage by 100.

Step 1:

Convert the percentage to a decimal.
65.3 / 100 = 0.653

Thus,
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.

Learn more about sample proportion here:

https://brainly.com/question/29912751

#SPJ11

Answer:

0.969

Step-by-step explanation:

use the z-score formula to convert the values.

z = (X - υ) / σ

where X is the test statistic, υ is the mean, σ is the standard deviation.

z = (18 - 31) / 7

= -1.857

area in z-score table (this is area to left of <18) is 0.0314.

P(>18) = 1 - 0.0314 = 0.969

we know that

speed = distance/time

speed = dx/dt

Let x = the distance from the base of the ladder to the base of the wall

y = the distance from the tip of the ladder to the base of the wall, we have:

x^2+y^2 = 13^2

y^2=13^2-12^2 = 169 - 144 = 25 => y = 5 ft

2x dx/dt + 2y dy/dt = 0

2*5* dx/dt + 2*5*(-4) = 0

10 dx/dt = 40

dx/dt = (40/10) ft/sec

dx/dt = 4 ft/sec

To know more about

visit here

https://brainly.com/app/ask?q=speed

#SPJ4

Answer:

A :)

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer: The hourly production rate is about 102.3 widgets per hour

Step-by-step explanation:

1.) divide 225 by 2.2, which gives you 102.2727

2.) round to the nearest tenth

Given: Graph of the function.

Required: Open interval of the domain for which the function is

(a) increasing

(b) decreasing

(c) constant

Explanation:

Firstly, if we see from left hand side, function is coming downwards that is it is decreasing.

Then at a point, it stops decreasing and become constant.

Then after a point it starts going upwards, that it starts to increase.

Now,

(a) increasing

The function starts increasing at x = 2, and it keeps on increasing after that (as the arrow suggests)

So the open interval in which the function is increasing is

(b) decreasing

The function is decreasing in the beginning, and it decreases till x = -2

So the open interval in which the function is decreasing is

(c) constant

The function remains constant in the open interval

Final answer:

The function is

(a) increasing in

(b) decreasing in

(c) constant in

When the length of 2 section combined is 18 in

width is 12 in

When the length of 2 section combined is 24 in

width is 9 in  

A quadrilateral with four right angles is a rectangle. It may alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.

Rectangles have the following basic characteristics:

The length of the poster is 24 in

The width of the poster is 18 in

The area of the poster = 24*18 = 432 in²

The area of each section of the poster is 432/4 = 108 in².

Length of each section is 24/2 = 12 in

Width of each section is 18/2 = 9 in

The total length when 2 sections are combined is 9 + 9 = 18 in

or, 12 + 12 = 24 in

When the length of 2 section combined is 18 in

width is (108*2)/18 = 12 in

When the length of 2 section combined is 24 in

width is (108*2)/24 = 9 in  

To learn more about Rectangle refer to :

https://brainly.com/question/20693059

#SPJ1

Answer:

15

Step-by-step explanation:

1875÷125=15 125×15=1875

Answer:

15

Step-by-step explanation:

If you draw all the diagonals of a normal hexagon, there are 3*6=18 possible triangles; however, three of those are identical (the equilateral triangles), leaving us with 18-3=15 triangle possibilities.

In terms of geometry, a hexagon is a closed, six-sided polygon in two dimensions. A hexagon has six angles and six vertices. Hexa and gonio both denote the number six. A hexagon can be found in the shapes of a honeycomb, a football, a pencil face, and floor tiles. a standard hexagonal 2D geometric polygon with six equal-length sides and six equal-sized angles. All of the lines are closed, and there are no curving edges. A regular hexagon has 720 degrees of internal angles. Additionally, these shapes have six rotating and six reflective symmetries.

To know more about hexagon here

https://brainly.com/question/15424654

#SPJ4

Answer:

Option 4

125 × 125

Step-by-step explanation:

5⁶ = 5 × 5 × 5 × 5 × 5 × 5 = 125 × 125

Thus, 5⁶ = 125 × 125

-TheUnknownScientist

Answer:

Add ak190 smart answer

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

I think its C

it’s a better option than the last guys answer lol

The equation for money collected m for h boxes of chocolate bars sold is m = 30h.

We are given that the band is selling every bar of chocolate for $1.50

Now, they have boxes of chocolate, with every box containing 20 bars of chocolate in them.

Hence if we are going to calculate the amount of money collected on selling one box it will be

20 X $1.5

= $30

We need to find the equation for the amount of money collected based on the number of boxes of chocolate bars sold.

We have been given that money collected should be represented b m while the number of chocolate boxes sold should be represented by h

Now we know that

Money collected = price per box X no.of boxes sold

we have already calculated the price per box hence we get

m = 30h

To learn more about Linear Equations visit

https://brainly.com/question/29142080

#SPJ4

The radius of convergence is 2, and the interval of convergence is\($-1 \leq x \leq 1$.\)

To find the radius of convergence and interval of convergence of the series \($\sum_{n=2}^{\infty} (-1)^n 22^n$\), we can utilize the ratio test.

The ratio test states that for a series \($\sum_{n=1}^{\infty} a_n$, if $\lim_{n\to\infty} \left|\frac{a_{n+1}}{a_n}\right| = L$\), then the series converges if \($L < 1$\) and diverges if \($L > 1$\).

Applying the ratio test to the given series, we have:

\($$L = \lim_{n\to\infty} \left|\frac{(-1)^{n+1}22^{n+1}}{(-1)^n22^n}\right| = \lim_{n\to\infty} \left| \frac{22}{-22} \right| = \lim_{n\to\infty} 1 = 1$$\)

Since L = 1, the ratio test is inconclusive. Therefore, we need to consider the endpoints to determine the interval of convergence.

For n = 2, the series becomes \($(-1)^2 22^2 = 22^2 = 484$\), which is a finite value. Thus, the series converges at the lower endpoint $x = -1$.

For n = 3, the series becomes \($(-1)^3 22^3 = -22^3 = -10648$\), which is also a finite value. Hence, the series converges at the upper endpoint x = 1.

Therefore, the interval of convergence is \($-1 \leq x \leq 1$\), including both endpoints. The radius of convergence, which corresponds to half the length of the interval of convergence, is 1 - (-1) = 2.

Therefore, the radius of convergence is 2, and the interval of convergence is \($-1 \leq x \leq 1$\).

To learn more about radius of convergence from the given link

https://brainly.com/question/31398445

#SPJ4