Reorder the following equations in descending order of steepness.
y = 0.15x + 3
Y = X
y =
y = 15x + 5
-2x + 100

Answer:

12

Step-by-step explanation:

If we extend this triangle we see that it makes a right triangle with legs of 6 and 6. The area of that triangle is 1/2 * 6 * 6 = 18. The part that is not shaded is a right triangle with legs 6 and 2, it's area is 6 * 2 / 2 = 6. The shaded area is 18 - 6 = 12.

Answer:

D. x²/1953²  + y²/ 1466² = 1

Step-by-step explanation:

==>Given:

Radius of spherical moon = 1000km

Distance of satellite from moon surface = 953km to 466km

==>Required:

Derived equation of ellipse

==>Solution:

The formula for driving an equation of ellipse is given as:

x²/a² + y²/b² = 1

Where,

a = length of the semi-major axis, while,

b = length of the semi-major axis

Since we are told that the satellite distance to the surface of the moon varies from 953km to 466km, values of a and b is calculated by summing each length to the radius of the moon as follows:

a = radius of moon + the larger distance of the satellite = 1000+953 = 1,953km

b = radius of moon + the smaller distance of the satellite = 1000+466 = 1,466km

Thus, the equation of the ellipse would be:

x²/1953²  + y²/ 1466² = 1

Answer:

(√77) / 22

Step-by-step explanation:

To rationalize the fraction we must multiply the entire fraction by √11 / √11. Note that the 2 is not important because it's not a radical. This gives us √77 / 22.

Answer:

E

Step-by-step explanation:

y’’ + 9y = sin(3x)

The characteristics equation is;

m^2 + 9 = 0

solving this we have 2 complex roots

m= -3i, 3i

Thus;

yh = Ccos(3x)+ Dsin(3x)

let yp = Axcos(3x) + Bxsin(3x)

Now, because we have sin(3x) and cos(3x) with constant coefficient in yh, option E is our answer

Answer: 4 wholes and 1/5 is 4.20 and you need something greater than that but less than 4.25 which still has only 2 decimals.

Answer

I will give you some hints and yea

Step-by-step explanation:

first try to figure out how much the quarters are you can first guess for example there were 8 quarters and ?nickels and work your way up and then you will get closer and closer to your answer  

Answer:

0.05n + 0.25(36 – n) = 6

Step-by-step explanation:

Answer:

The height of triangle is 12cm.

The base of triangle is 25 cm.

The area of triangle is 150cm².

Step-by-step explanation:

Given that the area of triangle is Area = 1/2×base×height. So you have to substitute the values into the formula :

[tex]area = \frac{1}{2} \times base \times height[/tex]

[tex]let \: base = 25 \\ let \: height = 12[/tex]

[tex]area = \frac{1}{2} \times 25 \times 12[/tex]

[tex]area = \frac{1}{2} \times 300[/tex]

[tex]area = 150 \: {cm}^{2} [/tex]

Answer:

csc∅ = 25/7

sec∅ = 25/24

cot∅ = 24/7

Step-by-step explanation:

Cosecant (csc) is 1/sin∅ or hypotenuse over opposite

Secant (sec) is 1/cos∅ or hypotenuse over adjacent

Cotangent (cot) is 1/tan∅ or adjacent over opposite

Answer:

see below

Step-by-step explanation:

We are given two points (3,4) and (0,1)

so we can find the slope

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

    = (1-4)/(0-3)

  = -3/-3

  = 1

The point slope form is

( y-y1) = m(x-x1)

y - (4) = 1 (x-3)

y - (4) =  (x-3)

or using the other point

y - 1 = 1( x-0)

y - 1 = x

Answer:

1). [tex]\text{log}_4(5x^2+2)=\text{log}_4(x + 8)[/tex]

2). log(x - 1) + log5x = 2

3). ln(x + 5) = ln(x - 1) + ln(x + 1)

4). [tex]e^{x^2}=e^{4x+5}[/tex]

Step-by-step explanation:

1). ln(x + 5) = ln(x - 1) + ln(x + 1)

   ln(x + 5) = ln(x - 1)(x + 1)  [Since ln(a×b) = ln a + lnb]

   (x + 5) = (x- 1)(x + 1)

   x + 5 = x² - 1

   x² - x - 6 = 0

   x² - 3x + 2x - 6 = 0

   x(x - 3) + 2(x - 3) = 0

   (x + 2)(x - 3 ) = 0

   x = -2, 3

   But x = -2 is an extraneous solution.

  Therefore, x = 3 is the only solution.

2). [tex]e^{x^2}=e^{4x+5}[/tex]

  x² = 4x +5

  x² - 4x - 5 = 0

  x² - 5x + x - 5 = 0

  x(x - 5) + 1(x - 5) = 0

  (x + 1)(x - 5) = 0

  x = -1, 5

  Therefore, solution set is (-1, 5)

3). [tex]\text{log}_4(5x^2+2)=\text{log}_4(x + 8)[/tex]

   5x² + 2 = (x + 8)  

   5x² - x - 6 = 0

   5x² - 6x + 5x - 6 = 0

   x(5x - 6) + 1(5x - 6) = 0

   (x + 1)(5x - 6) = 0

   x = -1, [tex]\frac{6}{5}[/tex]

4). log(x - 1) + log5x = 2

    log(x - 1)(5x) = 2

    5x(x - 1) = 10² [if loga = b, [tex]a=10^{b}[/tex]]

    5x² - 5x - 100 = 0

    x² - x - 20 = 0

    x² - 5x + 4x - 20 = 0

    x(x - 5) + 4(x - 5) =0

    (x - 5)(x + 4) = 0

    x = -4, 5

But x = -4 is an extraneous solution.

Therefore, x = 5 is the only solution.

Answer:

[tex]\frac{1}{9^3}[/tex] or [tex]\frac{1}{729}[/tex]

Step-by-step explanation:

When we have an exponent that is a negative, it is the same thing as 1 over the positive exponent. So, we move 9^-3 into 1/9^3 and then we evaluate the exponent to get our answer.

Answer:

9.

Step-by-step explanation:

You would have to find the area of the triangle which is 1/2(bh) which would give you 9. So you would 9 feet of outdoor carpet. Which is actually already given to you as the area inside the triangle.

Answer:

9

Step-by-step explanation:

I finally got it!

Answer:

no because one x value corresponds to two different y values

Answer:

m = 2

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Simply plug our coordinates into the slope formula and solve for m:

m = (5 - 3)/(4 - 3)

m = 2/1

m = 2

Answer:

Step-by-step explanation:

Let the points be A and B

A( 3 , 3 ) -----> ( x1 , y1 )

B(4 , 5 ) ------>( x2 , y2 )

Now,

finding the slope,

Slope =[tex] \frac{y2 - y1}{x2 - x1} [/tex]

[tex] = \frac{5 - 3}{4 - 3} [/tex]

[tex] = \frac{2}{1} [/tex]

[tex] = 2[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

life is a precious gift of GOD like see these days conditions too much people are dying  life is our test it is worth whoever we wonder we are not birds,stones,mountains,trees they are also surviving and we are too we have not to survive we have to live our life there must be a difference between humans and animals i know life is brutal,tough and hard than why is it tough brutal and hard because it is a test a common life also passes and a man who serves hummanity his life also passes but a man serving hummanity is always remembered

"your life is your message to the world make it inspiring"

life is worth and too much previous

to die is easier than to life we have to live because  we love challanges

Step-by-step explanation:

i hope this will help you :)

Answer:

Step-by-step explanation:

yeah

Answer:

The probability that no more than 6 students belong to a ethnic minority is 0.9815.

Step-by-step explanation:

The question is incomplete:

In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, what is the probability that no more than 6 belong to an ethnic minority?

We can model this with a random variable, with sample size n=10 and probability of success p=0.33.

The probability that k answers are guessed right in the sample is:

[tex]P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}=\dbinom{10}{k}\cdot0.33^k\cdot0.67^{10-k}[/tex]

We have to calculate the probability that 6 or less students belong to a ethnic minority. This can be calculated as:

[tex]P(x\leq6)=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)+P(x=6)\\\\\\[/tex]

[tex]P(x=0)=\dbinom{10}{0}\cdot0.33^{0}\cdot0.67^{10}=1\cdot1\cdot0.0182=0.0182\\\\\\P(x=1)=\dbinom{10}{1}\cdot0.33^{1}\cdot0.67^{9}=10\cdot0.33\cdot0.0272=0.0898\\\\\\P(x=2)=\dbinom{10}{2}\cdot0.33^{2}\cdot0.67^{8}=45\cdot0.1089\cdot0.0406=0.1990\\\\\\P(x=3)=\dbinom{10}{3}\cdot0.33^{3}\cdot0.67^{7}=120\cdot0.0359\cdot0.0606=0.2614\\\\\\[/tex]

[tex]P(x=4)=\dbinom{10}{4}\cdot0.33^{4}\cdot0.67^{6}=210\cdot0.0119\cdot0.0905=0.2253\\\\\\P(x=5)=\dbinom{10}{5}\cdot0.33^{5}\cdot0.67^{5}=252\cdot0.0039\cdot0.135=0.1332\\\\\\P(x=6)=\dbinom{10}{6}\cdot0.33^{6}\cdot0.67^{4}=210\cdot0.0013\cdot0.2015=0.0547\\\\\\\\\\\\[/tex]

[tex]P(x\leq6)=0.0182+0.0898+0.1990+0.2614+0.2253+0.1332+0.0547\\\\\\P(x\leq6)=0.9815[/tex]

The probability that 6 or less students belong to a ethnic minority is 0.9815.

Answer:

Six Million Seven Hundred Eighty Two Thousand one hundred sixty three

Step-by-step explanation:

Hope it helps...Pls Mark as Brainliest!!

Answer:

Six Million Seven Hundred Eighty Two Thousand One Hundred and Sixty Three.

Step-by-step explanation:

6, 782, 163

Full question:

Eighteen of 50 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select an item that is not defective?

Answer:

16/25

Step-by-step explanation:

Probability is the likelihood of an event happening and it is calculated as the number of favourable outcomes divided by the total number of possible outcomes. From the above we can calculate probability of finding a DVR that is not defective by adding up number of DVRS that are not defective in the DVRS(favourable outcomes) and dividing it by the total number of DVRS(total number of possible outcomes).

Non defective dvrs=total number of dvrs-defective dvrs=50-18=32

So probability here=non defective dvrs/total number of dvrs

=32/50=16/25

The graph represents a rotation transformation

Answer:

3 8/9

Step-by-step explanation:

1.) Convert each fraction from a mixed number to a improper fraction (to do that multiply the denominator with the whole number then add the numerator, the improper fraction denominator will remain the same as the mixed number denominator):

14/3 ÷ 6/5

2.) Solve

a. To divide the fractions, Flip the reciprocal, and multiply the fractions

14/3 x 5/6

b. Check if you can reduce the numbers, which you can 14 and 6 can be both divided by 2:

7/3x5/3

c. Multiply fractions (simply by multiplying across):

35/9

3.) Simplify numbers into mixed fraction (or decimal):

3 8/9

Step-by-step explanation: To write a fraction as a percent, first remember that a percent is a ratio of a number to 100.

So to write 3/7 as a percent, we need to find a fraction

equivalent to 3/7 that has a 100 in the denominator.

We can do this by setting up a proportion.

So we have [tex]\frac{3}{7} = \frac{n}{100}[/tex].

Now, we can use cross-products to find the missing value.

So we have (3)(100) which is 300 is equal to (7)(n) or 7n.

So we have the equation 300 = 7n.

Next, dividing both sides of the equation by 7, we have 42.8571 = n.

So 3/7 is equal to 42.8571/100 or 42.8571%.

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The average college major requires 34 credit hours to complete, with a standard deviation of 3 hours. A college's academic advisors conduct a study to see how many credit hours a sample size of 50 students will need to take to complete their majors.

They calculate:

μx = μ = 34

σx = μ/√n = 34/√50 = 4.81

What did they do wrong?

Answer:

The sample mean will be the same as the population mean

μx = μ = 34

Whereas the standard deviation of the sample would be

σx = σ/√n

σx = 3/√50

σx = 0.424

Therefore, the college's academic advisors wrongly calculated the standard deviation of the sampling distribution.

Step-by-step explanation:

From the given information we know that,

The population mean is

μ = 34 credit hours

The population standard deviation is

σ = 34 credit hours

The college's academic advisors take a sample size of 50 students so

sample size = n = 50

Since the sample size is quite large then according to the central limit theorem,

The sample mean will be the same as the population mean

μx = μ = 34

Whereas the standard deviation of the sample would be

σx = σ/√n

σx = 3/√50

σx = 0.424

Therefore, the college's academic advisors wrongly calculated the standard deviation of the sampling distribution.

Answer: [tex]x^{2} + 8x[/tex]

Step-by-step explanation:

In a triangle A = 1/2bh.

Thus, multiply 1/2 * 2x * (x+8)

x(x+8)

[tex]x^{2} + 8x[/tex]

Answer:

  see below

Step-by-step explanation:

There are a couple of ways to go about this.

The general form of a conic equation is ...

  Ax^2 +Bxy +Cy^2 +Dx +Ey +F = 0

For AC > 0, this is the equation of an ellipse or circle. (AC < 0, hyperbola; AC = 0, parabola)

So, from the coefficients of the given equation, AC = 2·5 = 10, you know the equation is of an ellipse.

__

The rotation matrix for Cartesian coordinates tells you ...

  x = x'·cos(θ) +y'·sin(θ)

  y = -x'·sin(θ) +y'·cos(θ)

For θ = 45° the values of these trig functions are all (√2)/2. That is, there is no way to get coefficients in the rotated equation that involve √3. This eliminates choice 2.

The only remaining viable choice is choice 4.

__

If you like, you can substitute for x and y using the above relations. You will find that the result differs from any of the answer choices. The rotated figure will have the equation ...

  [tex]5x^2-6xy+9y^2+10\sqrt{2}x+2\sqrt{2}y-80=0[/tex]

For example, the x and y terms become ...

  [tex]6x-4y=6(x'\cos{(45^{\circ})}+y'\sin{(45^{\circ})})-4(-x'\sin{(45^{\circ})}+y'\cos{(45^{\circ})})\\\\=10x'\dfrac{\sqrt{2}}{2}+2y'\dfrac{\sqrt{2}}{2}\\\\\text{Multiplying this by 2 gives $\dots$}\\\\10x'\sqrt{2}+2y'\sqrt{2}[/tex]

Note that this is not the 10√2x' -10√2y' shown in choice 4.

__

Another way to look at this is to look at the angle of rotation relative to alignment with the x- and y-axes. That angle α is given by ...

  cot(2α) = (A -C)/B

For the original ellipse, the rotation angle is ...

  α = arccot((2 -5)/2)/2 ≈ -16.85°

For the transformed ellipse of choice 4, the rotation angle is ...

  α = arccot((9 -5)/6)/2 ≈ 28.15°

This is 45° more*, as it should be, indicating choice 4 is the better of the offered choices.

__

If you do the angle calculation for the 2nd answer choice, you will find it has no relation to a 45° rotation of the original ellipse.

_____

* While the computed rotation angle is as expected, the fact that the x^2 and y^2 coefficients have been swapped means that the long and short axes of the ellipse have been swapped. That is, the long axis of the ellipse has been rotated 45° in the wrong direction by the equation given in the answer choices. The second attachment shows the original ellipse (red), the properly rotated ellipse (dashed red) and the ellipse of choice 4 (blue).

Answer:

These are vertical transformations because the parent function is being translated up and down which are vertical directions.

Answer:70/9

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

cos²θ (1 + tan²θ)

Use Pythagorean identity:

cos²θ (sec²θ)

1

Answer:

There is enough evidence to support the claim that the average sales are significantly greater for salespersons with a college degree than for salespersons without it.

Step-by-step explanation:

The question is incomplete:

"A national computer retailer believes that the average sales are greater for salespersons with a college degree. A random sample of 32 salespersons with a degree had an average weekly sale of $3599 last year, while 35 salespersons without a college degree averaged $3311 in weekly sales. The standard deviations were $468 and $642 respectively.

Required:

Is there evidence at the 5% level to support the retailer's belief?"

This is a hypothesis test for the difference between populations means.

The claim is that the average sales are significantly greater for salespersons with a college degree than for salespersons without it.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]

The significance level is 0.05.

The sample 1 (college degree), of size n1=32 has a mean of 3599 and a standard deviation of 468.

The sample 2 (non-college degree), of size n2=35 has a mean of 3311 and a standard deviation of 642.

The difference between sample means is Md=288.

[tex]M_d=M_1-M_2=3599-3311=288[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{468^2}{32}+\dfrac{642^2}{35}}\\\\\\s_{M_d}=\sqrt{6844.5+11776.114}=\sqrt{18620.614}=136.4574[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{288-0}{136.4574}=\dfrac{288}{136.4574}=2.11[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-2=32+35-2=65[/tex]

This test is a right-tailed test, with 65 degrees of freedom and t=2.11, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>2.11)=0.019[/tex]

As the P-value (0.019) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the average sales are significantly greater for salespersons with a college degree than for salespersons without it.

Answer:

50%

Step-by-step explanation:

There are 3 numbers fitting the rule, 1, 2, and 6. There is a 3/6 chance rolling one of them or 50%.

Answer:

50%

Step-by-step explanation:

1 value> 5 and 2 values<3, out of total of 6

P (greater than 5 or less than 3) = 3/6= 50%