Set Question involving real and natural numbers

Answer:

m∠O = 41°

Step-by-step explanation:

∠NOM=∠NMO=(4y-15)° (base angles of isos triangle)

7y+2(4y-15)=180 (angle sum of triangle)

  7y+8y-30=180

       15y-30=180

             15y=180+30

                  =210

                y=210÷15

                  =14

Hence, m∠O = (4y-15)°

                      = [4(14)-15]°

                      = (56-15)°

                      = 41°

Answer:

12 Yoga classes

Step-by-step explanation:

50 + 4x = 98

Subtract 50 on each side

4x = 48

Divide by 4 on each side

x= 12

You can attend 12 yoga classes in a year with a $98 budget.

Answer:

Length=12mi

Step-by-step explanation:

Area=123.6mi^3

Width=10.3mi

Length=u

Formula: Area=LxW

Area÷W=u

123.6÷10.3=12

Length=12mi

Hope this helps :)

Answer:

4x-6

Step-by-step explanation:

4x-6

4 is for number of doughnuts in each package, 6 is for the taken doughnuts

Answer:

The answer would be D

Step-by-step explanation:

5 1/3 ÷ 2/3 = 8

16/3 ÷ 2/3 = 8

16 ÷2 = 8

Answer:

Julie is 14.67, Janet 17.67 and Brother 22.66

Step-by-step explanation:

Let Julie age be x

Janet: x+3

Brother: x+8

x+x+3+x+8=55

3x+11=55

3x=44

x=14.7

The height of the tower is 452.66 ft

The situation will form 2 right angle triangle. One above the line of sight

and one below the line of sight.

Therefore,

Using trigonometric ratio,

tan ∅ = opposite / adjacent side

tan 30° = h(top of the tower) / 425

h(top of the tower) = tan 30 × 425 = 245.373864406  

tan 26° = h(bottom of the tower) / 425

h(bottom of the tower) = 425 × tan 26° = 207.28635014

Therefore,

Height of tower = h(top of the tower) + h(bottom of the tower)

Height of tower = 245.37 + 207.29 = 452.66 ft

learn more: https://brainly.com/question/12855949?referrer=searchResults

Answer: $420

To find the total simple interest over the two years, we first find 5/100 (5%) of 200 which is 10. That’s the interest of 1 year so we multiply that by 2 to get 20 for 2 years. Each year a deposit of $200 is made so over two years $400. $20 add $400 is $420 which is the total.

Answer:

wa

at you ım prenses

Step-by-step explanation:

you ind soluk

Answer:

55.76

Step-by-step explanation:

55.76

Answer:

There was an association between taking breaks and better performance, but it's not necessarily a causal relationship.

Step-by-step explanation:

Answer:

Solution:

3/7x = 12

3/7x ÷ 3/7 = 12 ÷ 3/7 ( divide 3/7 in both sides )

x = 12 ÷ 3/7 (divide)

x = 84/3 (simply divide 84 and 3)

x = 28

_______________________

(solution for dividing the fraction and the whole number 12 and 3/7, for those who don't know how to divide fractions and whole numbers...)

12/1 ÷ 3/7

12/1 ÷ 7/3 (reciprocal method)

12/1 × 7/3 (change operation to multiplication)

12/1 × 7/3 = 84/3 (multiply)

84/3 ⇒ 28 (simplify)

There is a 0.9968 probability that a randomly selected 50-year-old female lives through the year (based on data from the U.S. Department of Health and Human Services).

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

A Fidelity life insurance company charges $226 for insuring that the female will live through the year. If she does not survive the year, the policy pays out $50,000 as a death benefit.

From the perspective of the 50-year-old female, what are the values corresponding to the two events of surviving the year and not surviving?

----

Ans: -226 ; 50,000-226 = 49774

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

If a 50-year-old female purchases the policy, what is her expected value?

WORK TRIED:

In the event she lives, the value is -$226. In the event she dies, the value is $49,774.

----

E(x) = 0.9968*(-226) + 0.0032(49774) = -$66

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

Cheers,

ROR

Answer:

Area: (2x - 7) * (3*2 + 4x)

         (2x - 7) * (6 + 4x)

                 8x-42

Perimeter: 2(2x - 7) + 2(3*2 + 4x)

Step-by-step explanation:

hope this helps!

Answer:

3/1

Step-by-step explanation:

rise/run

9514 1404 393

Answer:

  3

Step-by-step explanation:

The line goes through the origin (0, 0) and point (1, 3), which is 3 units up and 1 to the right of the origin.

  slope = rise/run = 3/1 = 3

The slope of the line is 3.

Answer:

distributive property

Step-by-step explanation:

I ASSUME that you meant to lead the equation with a negative sign.

- 10x + 11x = (-10 + 11)x

Answer:

in 10 hours

Step-by-step explanation:

Answer: 4 hours

Step-by-step explanation: since the plant is already 10 centimeters, and it grows five centimeters every two hours, it only needs four hours to grow another 10 centimeters for it to be 20 centimeters.

Answer:

[tex]w-0.15 = 0.25[/tex]

Step-by-step explanation:

Answer:

There is an outlier at 0, and a gap at 1,2, and 3. The peak is at 5, and the plot is more or less skewed left.

Step-by-step explanation:

Answer:

9 units²

Step-by-step explanation:

Parallelogram area = base × height

Base = 3 units

Height = 3 units

Area = 3 × 3

Area = 9

The area of the parallelogram is 9 units².

Here, we have,

We know that,

Parallelogram area = base × height

here, from the given figure we get,

Base = 3 units

Height = 3 units

so, we get,

Parallelogram area = base × height

Area = 3 × 3

Area = 9

Hence, The area of the parallelogram is 9 units².

To learn more on area of parallelogram click:

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Answer:

y = -1/2

Step-by-step explanation:

   (3x + 4y = 4)

+

   (2x - 4y = 6)

______________

   5x = 10

   x = 2

plug in x for any of the two equations ....

2(2) - 4y = 6

4 - 4y = 6

-4y = 2

y = -1/2

Answer:

$11,480

Step-by-step explanation:

Let [tex]x = \arcsin(y)[/tex], so that

[tex]\sin(x) = y[/tex]

[tex]\tan(x)=\dfrac y{\sqrt{1-y^2}}[/tex]

[tex]dx = \dfrac{dy}{\sqrt{1-y^2}}[/tex]

Then the integral transforms to

[tex]\displaystyle \int_{x=0}^{x=\frac\pi2} \tan(x) \ln(\sin(x)) \, dx = \int_{y=\sin(0)}^{y=\sin\left(\frac\pi2\right)} \frac{y}{\sqrt{1-y^2}} \ln(y) \frac{dy}{\sqrt{1-y^2}}[/tex]

[tex]\displaystyle \int_{x=0}^{x=\frac\pi2} \tan(x) \ln(\sin(x)) \, dx = \int_0^1 \frac{y}{1-y^2} \ln(y) \, dy[/tex]

Integrate by parts, taking

[tex]u = \ln(y) \implies du = \dfrac{dy}y[/tex]

[tex]dv = \dfrac{y}{1-y^2} \, dy \implies v = -\dfrac12 \ln|1-y^2|[/tex]

For 0 < y < 1, we have |1 - y²| = 1 - y², so

[tex]\displaystyle \int_0^1 \frac{y}{1-y^2} \ln(y) \, dy = uv \bigg|_{y\to0^+}^{y\to1^-} + \frac12 \int_0^1 \frac{\ln(1-y^2)}{y} \, dy[/tex]

It's easy to show that uv approaches 0 as y approaches either 0 or 1, so we just have

[tex]\displaystyle \int_0^1 \frac{y}{1-y^2} \ln(y) \, dy = \frac12 \int_0^1 \frac{\ln(1-y^2)}{y} \, dy[/tex]

Recall the Taylor series for ln(1 + y),

[tex]\displaystyle \ln(1+y) = \sum_{n=1}^\infty \frac{(-1)^{n+1}}n y^n[/tex]

Replacing y with -y² gives the Taylor series

[tex]\displaystyle \ln(1-y^2) = \sum_{n=1}^\infty \frac{(-1)^{n+1}}n (-y^2)^n = - \sum_{n=1}^\infty \frac1n y^{2n}[/tex]

and replacing ln(1 - y²) in the integral with its series representation gives

[tex]\displaystyle -\frac12 \int_0^1 \frac1y \sum_{n=1}^\infty \frac{y^{2n}}n \, dy = -\frac12 \int_0^1 \sum_{n=1}^\infty \frac{y^{2n-1}}n \, dy[/tex]

Interchanging the integral and sum (see Fubini's theorem) gives

[tex]\displaystyle -\frac12 \sum_{n=1}^\infty \frac1n \int_0^1 y^{2n-1} \, dy[/tex]

Compute the integral:

[tex]\displaystyle -\frac12 \sum_{n=1}^\infty \frac1n \int_0^1 y^{2n-1} \, dy = -\frac12 \sum_{n=1}^\infty \frac{y^{2n}}{2n^2} \bigg|_0^1 = -\frac14 \sum_{n=1}^\infty \frac1{n^2}[/tex]

and we recognize the famous sum (see Basel's problem),

[tex]\displaystyle \sum_{n=1}^\infty \frac1{n^2} = \frac{\pi^2}6[/tex]

So, the value of our integral is

[tex]\displaystyle \int_0^{\frac\pi2} \tan(x) \ln(\sin(x)) \, dx = \boxed{-\frac{\pi^2}{24}}[/tex]

[tex]\displaystyle \int \limits_{0}^{ \frac{ \pi}{2} } \tt\tan (x) \ln ( \sin (x))\\ \\\displaystyle \sf{ \implies \: I = \int^{ \frac{\pi}{2} }_{0} \: \ln \left( sin \left( \dfrac{\pi}{2} - x \right) \right) \: dx } \\ \\\displaystyle \sf{ \implies \: I = \int^{ \frac{\pi}{2} }_{0} \: \ln \left( cos(x) \right) \: dx } \\ \\\displaystyle \sf{ \implies \:2I =\int^{ \frac{\pi}{2} }_{0} \:\ln \left( sin(x) \right) \: dx + \int^{ \frac{\pi}{2} }_{0} \: \ln \left( cos(x) \right) \: dx } \\ \\\displaystyle \sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \: \ln \left( sin(x) \right) +\ln\left( cos(x) \right) \: dx }[/tex]

[tex]\displaystyle \sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \: \ln \left( sin(x) \: cos(x) \right) \: dx } \\ \\\displaystyle\sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \: \ln \left( \dfrac{sin(2x)}{2}\right) \: dx } \\ \\\displaystyle \sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \:\ln \left( sin(2x) \right)\:dx-\ln(2) \int^{ \frac{\pi}{2} }_{0} \: dx}[/tex]

[tex]\displaystyle\sf{ \implies \: 2I = \dfrac{1}{2} \int^{ \pi}_{0} \: \ln \left( sin(t) \right) \:dt - \ln(2) \int^{ \frac{\pi}{2} }_{0} \: dx} \\ \\\displaystyle\tt{ \implies \: 2I = \dfrac{1}{2} \cdot2 \int^{ \frac{\pi}{2}}_{0} \: \ln \left( sin(t) \right) \: dt - \ln(2) \int^{ \frac{\pi}{2} }_{0} \: dx}[/tex]

[tex]\displaystyle \tt{ \implies \: 2I =\int^{ \frac{\pi}{2}}_{0} \: \ln \left( sin(t) \right) \: dt - \ln(2)\int^{ \frac{\pi}{2} }_{0} \: dx} \\ \\ \displaystyle \tt{ \implies \: 2I = I - \ln(2) \left[x \right] ^{ \frac{\pi}{2} }_{0} } \\ \\ \displaystyle \tt{ \implies \: I = -\ln(2)\left[ \dfrac{\pi}{2} - 0 \right] }[/tex]

[tex]\displaystyle \sf{ \implies \: I = - \dfrac{\pi}{2} \ln(2) }[/tex]

☞︎︎︎Apologies,if incorrect.

Answer:

1.25 miles

Step-by-step explanation:

0.25 miles = 8 seconds

x miles = 40 seconds

0.25/8 = x/40

0.25 * 40 = 8x

10 = 8x

x = 1.25

-Chetan K

Answer:

Do in calculator simple answer

Answer:

B a vertical translation 50units right

Answer:

Uuuuh thats kind of suspicious, maybe you could post your question without  a link? But links are usually scams, so dont do that :)

33 pupils - 17 girls = 16 total boys in the class

16 boys - 14 boys not on the team = 2 boys on the team.

Answer: 2

Answer:

the answer is 162 I used a calculator this app is so cool