Find the slope and y-intercept: 4x-y+6=0

Answer:

The critical value of  [tex]f(\theta) = 6\cdot \cos \theta + 3\cdot \sin 2\theta[/tex] are given by [tex]\theta \approx 0.091\pi \pm 2\pi\cdot n[/tex] or [tex]\theta \approx 0.909\pi \pm 2\pi \cdot n[/tex], [tex]\forall \,n \in \mathbb{N}[/tex]

Step-by-step explanation:

The function to be evaluated is [tex]f(\theta) = 6\cdot \cos \theta + 3\cdot \sin 2\theta[/tex], the first derivative of the function must be taken in order to determine the set of critical numbers. Each derivative are found by using the differentiation rule for a sum of functions and rule of chain and subsequently simplified by trigonometric and algebraic means:

First derivative

[tex]f'(\theta) = - 6 \cdot \sin \theta +6\cdot \cos 2\theta[/tex]

[tex]f'(\theta) = -6\cdot \sin \theta + 2\cdot (\cos^{2}\theta-\sin^{2}\theta)[/tex]

[tex]f'(\theta) = -6\cdot \sin \theta + 2\cdot [(1-\sin^{2}\theta-\sin^{2}\theta)][/tex]

[tex]f'(\theta) = -6\cdot \sin \theta + 2\cdot (1-2\cdot \sin^{2}\theta)[/tex]

[tex]f'(\theta) = -6\cdot \sin \theta + 2 - 4\cdot \sin^{2}\theta[/tex]

[tex]f'(\theta) = -4\cdot \sin^{2}\theta - 6\cdot \sin \theta +2[/tex]

The procedure to determine the critical number of the given function are described briefly:

1) First derivative is equalised to zero.

2) The resultant equation is solved.

Then,

[tex]-4\cdot \sin^{2}\theta - 6\cdot \sin \theta +2 = 0[/tex]

Whose roots are:

[tex]\sin \theta_{1} \approx 0.281[/tex] and [tex]\sin \theta_{2} \approx -1.781[/tex]

The sine function is a continuous function with a range between 1 and -1, so, only the first root offers a realistic solution. In addition, such function is positive at first and second quadrants and has a periodicity of [tex]2\pi[/tex] radians, the family of critical values are determined by the unse of inverse trigonometric functions:

[tex]\theta \approx \sin^{-1} 0.281[/tex]

There are two subsets of solutions:

[tex]\theta \approx 0.091\pi \pm 2\pi\cdot n[/tex] or [tex]\theta \approx 0.909\pi \pm 2\pi \cdot n[/tex], [tex]\forall \,n \in \mathbb{N}[/tex]

Answer:

1144cm²

Approx. 1100cm²

Step-by-step explanation:

Area of rectangle=

L×B

34×20 = 680cm²

Area of semi-circle=

πr²

3.14 × (10)² = 314cm²

Area of triangle=

½b×h

b = 49 - 34 = 15

20 × 15 = 150cm²

2

Area of shape =

680 + 314 + 150 = 1144cm²

approx. 1100cm²

Please mark my answer as brainliest <3

Answer:

negative

Step-by-step explanation:

The slope of the line is negative because it goes from the upper corner down to the lower corner.

I remember it as negative because a rock would roll down it, if I would have to push it, it is positive.

Your answer would be 76.2% to the nearest tenth.

We can find this by first dividing 16 by 21 to get 0.7619. which is the proportion as a decimal. To convert this into a percentage, we need to multiply it by 100 to get 76.19% = 76.2% to the nearest tenth.

I hope this helps! Let me know if you have any questions :)

Answers:

a) 0.0625

b) 0.9375

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

Work Shown:

The probability of landing on heads is 1/2 = 0.5 since both sides are equally likely to land on. Getting 4 heads in a row is (1/2)^4 = (0.5)^4 = 0.0625

The event of getting at least one tail is the complement of getting all four heads. This is because you either get all four heads or you get at least one tail. One or the other must happen. We subtract the result we got from 1 to get 1-0.0625 = 0.9375

You can think of it like this

P(getting all four heads) + P(getting at least one tail) = 1

The phrasing "at least one tail" means "one tail or more".

Answer:

Ok, we have that f(x) is defined for all real values of x, except for x = x0.

[tex]\lim_{x \to \ x0} f(x)[/tex]

Does it exist? why?

Remember that when we are taking the limit we are not evaluating the function in x0, instead, we are evaluating the function in values really close to x0 (values defined as x0⁺ and x0⁻, where the sign defines if we approach from above or bellow).

And because f(x) is defined in the values of x near x0, we can conclude that  the limit does exist if:

[tex]\lim_{x \to \x0+} f(x) = \lim_{x \to \x0-} f(x)[/tex]

if that does not happen, like in f(x) = 1/x where x0 = 0

where the lower limit is negative and the upper limit is positive, we have that the limit does not converge.

Answer:

  490 J

Step-by-step explanation:

The formula is ...

  PE = mgh

where g is the acceleration due to gravity: 9.8 m/s². Filling in your numbers, you find the energy to be ...

  PE = (5 kg)(9.8 m/s²)(10 m) = 490 kg·m²/s² = 490 J

Answer:

  [tex]\textbf{J. }\dfrac{1}{x^2-x}[/tex]

Step-by-step explanation:

Factor the denominator and cancel the common factor.

  [tex]\dfrac{x+1}{x^3-x}=\dfrac{x+1}{x(x^2-1)}=\dfrac{x+1}{x(x-1)(x+1)}=\dfrac{1}{x(x-1)}\\\\=\boxed{\dfrac{1}{x^2-x}}[/tex]

Answer:    ∡PRS=61°

Step-by-step explanation:

As known the following equity is valid for the rhombus:

∡PQR+∡QRS = 180°

So  ∡QRS=180°- ∡PQR

∡QRS=180°- 58°= 122°

From another hand we know that PR is bisector of ∡QRS.

So ∡PRS=∡QRS:2= 122°:2=61°

∡PRS=61°

Answer:

The answer is option A.

Step-by-step explanation:

2 - 35 can be written as 2 + (-35) since in 2+( -35) when the bracket is removed it becomes 2 - 35.

Hope this helps

Answer:

Your correct answer is option a. 2 + (-35)

Step-by-step explanation:

When you are finding which equation is equivalent to the one you have, the best thing to find is what your equation's answer is.

Answer:

20

Step-by-step explanation:

do 9/12 = 15/?

you do 12 times 15 divided by 9

hope this helps

Answer:

x = 4 or x = -13/4 = -4.33

Step-by-step explanation:

log (3x - 2) + log (x + 1) = 2 - log 2

Note 2 is also equals to log 100

log (3x - 2) + log (x + 1) = log 100 - log 2

log (3x - 2)(x + 1) = log (100/2)

log 3x² + 3x - 2x - 2 = log 50

log 3x² + x - 2 = log 50

3x² + x - 2 = 50

3x² + x - 2 - 50 = 0

3x² + x - 52 = 0

find the number to multiply that will give you -52 × 3 = -156 and add to give you 1. The numbers are -12 and 13.

3x² - 12x + 13x - 52 = 0

3x(x - 4) + 13( x - 4) = 0

(3x + 13)(x - 4) = 0

x = 4 or x = -13/4 = -4.33

If you insert 4 in the logarithm equation you will see that the left side is equal to the right

log (3x - 2) + log (x + 1) = log 100 - log 2

log 10 + log 5 = log 50

log 50 = log 50

Answer:

Hey there!

3/2= 1.5, which is good.

2/3=0.666666666666... no

3/4=0.75, which is good.

5/7= 0.71428... no

Answer:

these sequences are limited

you can try it in a calculator

Answer:

6 mg

Step-by-step explanation:

12 mg

0.018 g * 1000 mg/g = 18 mg

18 mg - 12 mg = 6 mg

Answer:

When you multiply a difference of squares, two terms cancel each other out and result in a binomial instead of a trinomial. To understand this, you can use an example.

When you multiply (x-3) and (x+3), you can use FOIL to expand them. By doing this, you get x^2-3x+3x-9. As you can see, -3x and 3x cancel each other out, so this results in a binomial instead of a trinomial.

Answer:

when you multiply them the two terms cancel each other out which will result in a binominal

Step-by-step explanation:

Answer:

a. With 90% confidence the proportion of all Americans who favor the new Green initiative is between 0.6290 and 0.6948.

b. If the sample size is changed, the confidence interval changes as the standard error depends on sample size.

About 90% percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about 10% percent will not contain the true population proportion.

Step-by-step explanation:

We have to calculate a 90% confidence interval for the proportion.

The sample proportion is p=0.6619.

[tex]p=X/n=370/559=0.6619[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.6619*0.3381}{559}}\\\\\\ \sigma_p=\sqrt{0.0004}=0.02[/tex]

The critical z-value for a 90% confidence interval is z=1.6449.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.6449 \cdot 0.02=0.0329[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.6619-0.0329=0.6290\\\\UL=p+z \cdot \sigma_p = 0.6619+0.0329=0.6948[/tex]

The 90% confidence interval for the population proportion is (0.6290, 0.6948).

Answer:

2{3[9+4(7-5)-4]}

2{3[9+4(2)-4]}

2{3[13(2)-4]}

2{3[26-4]}

2{3[22]}

2{66}

132

Step-by-step explanation:

Answer:

729m³

Step-by-step explanation:

To find the length of one side find the cube root of 1728m³

³√1728=12metres

To find the length of the smaller cube

ratio 3:4.

4/7=12m

3/7=?

3/7×12 = 3/7×12×7/4

4/7

=9metres

To find volume of the small cube

volume=9×9×9

=729m³

Answer:

a. The 99% confidence interval for the population proportion is (0.7872, 0.8610).

D. Yes, we can conclude that the population proportion exceeds 75% because 75% is below the lowest believable value of the confidence interval.

b. The 99% confidence interval would be wider than a 95% confidence interval.

As the confidence level increases, the width interval increases, as we are requiring more confidence with the same information (there is no new sample). This means that, to be more confident, the only way is to include more values in the interval.

Step-by-step explanation:

We have to calculate a 99% confidence interval for the proportion.

The sample proportion is p=0.8241.

[tex]p=X/n=581/705=0.8241[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.8241*0.1759}{705}}\\\\\\ \sigma_p=\sqrt{0.000206}=0.0143[/tex]

The critical z-value for a 99% confidence interval is z=2.5758.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=2.5758 \cdot 0.0143=0.0369[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.8241-0.0369=0.7872\\\\UL=p+z \cdot \sigma_p = 0.8241+0.0369=0.8610[/tex]

The 99% confidence interval for the population proportion is (0.7872, 0.8610).

We can conclude that there is, at least, 99% chances that the true proportion is higher than 0.7872. So there is at least 99% chances that the population proportion is higher than 0.75.

Answer:

The angle of depression formed by Darius's sight line to the ranger station is 53.13°.

Step-by-step explanation:

Denote Darius's camp site as C, the ranger station as R and the tree as T.

Consider the triangle CTR.

TX is the altitude of the right angled triangle TXR.

The altitude of a right angled triangle forms two triangle that similar to each other.

So, ΔTXC [tex]\sim[/tex] ΔTXR.

Compute the measure of TX as follows:

[tex]\frac{CX}{TX}=\frac{TX}{RX}\\\\TX^{2}=CX\times RX\\\\TX=\sqrt{CX\times RX}[/tex]

      [tex]=\sqrt{18\times 32}\\\\=24\ \text{yd}[/tex]

The angle d represents the angle of depression formed by Darius's sight line to the ranger station.

Compute the value of d as follows:

[tex]tan\ d^{o}=\frac{RX}{TX}\\\\d^{o}=tan^{-1} [\frac{RX}{TX}][/tex]

    [tex]=tan^{-1} [\frac{32}{24}]\\\\=53.13[/tex]

Thus, the angle of depression formed by Darius's sight line to the ranger station is 53.13°.

Answer:

[tex]P(\bar X>3.4) = 0.385[/tex]

Step-by-step explanation:

Relevant Data provided according to the question is as follows

[tex]\mu[/tex] = 3.2

[tex]\sigma[/tex] = 0.8

n = 4

According to the given scenario the calculation of probability that the sample means will be more than 3.4 pounds is shown below:-

[tex]z = \frac{\bar X - \mu}{\frac{a}{\sqrt{n} } }[/tex]

[tex]P(\bar X>3.4) = 1 - P(\bar X\leq 3.4)[/tex]

[tex]= 1 - P \frac{\bar X - \sigma}{\frac{a}{\sqrt{n} } } \leq \frac{3.4 - \sigma}{\frac{a}\sqrt{n} }[/tex]

Now, we will solve the formula to reach the probability that is

[tex]= 1 - P \frac{\bar X - 3.2}{\frac{0.8}{\sqrt{4} } } \leq \frac{3.4 - 3.2}{\frac{0.8}\sqrt{4} }[/tex]

[tex]= 1 - P (Z \leq \frac{0.2}{0.4})[/tex]

[tex]= 1 - P (Z \leq 0.5})[/tex]

[tex]= 1 - \phi (0.5)[/tex]

= 1 - 0.6915

= 0.385

Therefore the correct answer is

[tex]P(\bar X>3.4) = 0.385[/tex]

So, for computing the probability we simply applied the above formula.

Answer:

its  21

Step-by-step explanation:

its not 21 i really dont know

Answer:

  (-2.497, -6.860)

Step-by-step explanation:

For any magnitude r and direction θ, the translation to rectangular coordinates is ...

  (r, θ) ⇒ (x, y)

  (r, θ) ⇒ (r·cos(θ), r·sin(θ))

Your coordinates translate to ...

  (7.3, 250°) ⇒ (7.3·cos(250°), 7.3·sin(250°)) ≈ (-2.497, -6.860)

Answer: El número es 902 en el sistema decimal.

Step-by-step explanation:

Supongo que tenemos el número:

32012 en base 4, y lo queremos representar en base decimal.

Entonces, usando la regla general, podemos escribir este número como:

unidades*base^0 + decenas*base^1 + centenas*base^2......  

Es decir, acá tenemos:

2*4^0 + 1*4^1 + 0*4^2 + 2*4^3 + 3*4^4 = 902

El número es 902 en el sistema decimal.

Answer:

4

Step-by-step explanation:

We are told that figure B is a scaled copy of B, which means figure A was enlarged by a certain scale factor to get a similar figure as A, now referred to as figure B.

The scale factor = ratio of any two corresponding sides of both similar figures.

Thus,

Scale factor of the similar figures given = 40/10 = 4.

This means that, figure A was scaled up by 4 times its original size to get figure B. Each side of figure B is 4 × the corresponding side in figure A.

Scale factor = 4

Answer:

48

Step-by-step explanation:

16*3=48

Answer:

A corda deve ter um comprimento mínimo de 80 cm.

The string should have a minimum length of 80 cm.

Step-by-step explanation:

Espera-se que a corda seja colada em todo o contorno da moldura quadrada.

Isso significa que a cadeia precisa cobrir pelo menos todo o perímetro da moldura quadrada pelo menos uma vez.

Perímetro de um quadrado = 4L

L = comprimento lateral do quadrado.

O comprimento lateral da moldura quadrada = 20 cm

Comprimento mínimo da corda necessária = Perímetro da moldura quadrada = 4 × 20 = 80 cm.

Espero que isto ajude!!!!

English Translation

Sofia is going to glue a piece of string to the outline of a square frame 20 cm from the side. How long should this string be?

Solution

The string is expected to be glued all around the outlne of square frame.

This means the string needs to at least cover the whole perimeter of the square frame a minimum of one time.

Perimeter of a square = 4L

L = side length of the square.

The side length of the square frame = 20 cm

Minimum length of the string required = Perimeter of the square frame = 4 × 20 = 80 cm.

Hope this Helps!!!!

Answer:

$2.06

Step-by-step explanation:

$2.99 x 6 = $17.94

$20.00 - $17.94 = $2.06

Hope this helps

Answer: $0.26

Step-by-step explanation:

Cost of 6 pens

= 2.99 x 6

= 17.94

Add sales tax at 10%,

= 17.94 x 1.1

= 19.74

Change due to me

= 20 - 19.74

= 0.26