**Answer:**

the third angle of the triangle is 62°

62 grad

**Step-by-step explanation:**

why is angle 3 congruent to angle

explain why

Answer:

Angle 3 is = to angle 2 because:

Angle 3 & angle 7 are corresponding angles, meaning they have the same measure.

Angle 7 & angle 2 are vertical angles, meaning they also have the same measure.

Therefore, if angle 7 is equal to angle 3, then angle 2 must also be equal to angle 3.

Hope this helps! Have a great day!

At what rate per annum compound

interest will N4000 amount to N5353

in 5 years?

Answer: Just look it up on goo gle

Step-by-step explanation:

The **rate** per annum **compound** **interest** is approximately 11.5%.

To find the rate per **annum** compound interest, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^{nt}[/tex]

Where:

A = the final amount (N5353 in this case)

P = the **principal amount **(N4000 in this case)

r = the annual interest rate (what we want to find)

n = the number of times interest is compounded per year (assuming once per year)

t = the number of years (5 years in this case)

Now, we can plug in the **values**:

[tex]N5353 = N4000(1 + r/1)^{1*5}[/tex]

Divide both sides by N4000:

[tex]1.33825 = (1 + r)^5[/tex]

Now, isolate (1 + r) by taking the** fifth root **of both sides:

[tex]1 + r = (1.33825)^{1/3}\\1 + r \approx 1.115[/tex]

Now, subtract 1 from both sides to find the interest rate (r):

r ≈ 1.115 - 1

r ≈ 0.115

Finally, convert the interest rate to a **percentage**:

r ≈ 0.115 * 100

r ≈ 11.5%

To know more about **rate:**

https://brainly.com/question/32398403

#SPJ2

The director of a customer service center wants to estimate the mean number of customer calls the center handles each day, so he randomly samples 29 different days and records the number of calls each day. The sample yields a mean of 279.4 calls with a standard deviation of 25.1 calls per day. He can be 99% confident that the mean number of calls per day is between 266.5 and ________. (Round your answer to 1 decimal place.)

**Answer:**

He can be 99% confident that the mean number of calls per day is between 266.5 and **292.3.**

**Step-by-step explanation:**

**Confidence interval:**

A confidence interval is symmetric, which means that the difference between the sample mean and the lower bound is the same as the difference between the upper bound and the sample mean.

**In this question:**

Sample mean: 279.4 calls

Lower bound: 266.5 calls

Upper bound: x calls

**Due to the symmetry of the confidence interval:**

[tex]x - 279.4 = 279.4 - 266.5[/tex]

[tex]x = 12.9 + 279.4[/tex]

[tex]x = 292.3[/tex]

So

He can be 99% confident that the mean number of calls per day is between 266.5 and **292.3.**

What type of number is v5?

Choose all answers that apply:

1. Whole number

2. Integer

3. Rational

4. Irrational

PLEASE HELP ME ILL GIVE 10 POINTS

The square root 5 is irrational because a square root of a positive number is either an integer or irrational number. Therefore it is irrational.

Mark is flying a kite and realizes that 300 feet of string is out. Mark anchored the kite to the ground. The angle of the string with the ground is 42.5 degrees. How high is Mark's kite above the ground? Find your answer to the nearest tenth.

Answer:I don’t understand

Step-by-step explanation:

PLEASE HELP THIS ASSIGNMENT IS OVER DUE

**Answer:**

91m + 13n + 52

**Step-by-step explanation:**

13(n + 4 + 7m)

= (13) (n+4+7m)

= (13) (n) + (13) (4) + (13) (7m)

= 13n + 52 + 91m

= 91m + 13n + 52

hope this helps and is right :)

p.s. i really need brainliest

**Answer:**

13n + 52 +91m

**Step-by-step explanation:**

As far as I can tell, all you are doing is distributing the 13 into the numbers. You multiply 13* 1n, 13*4, and 13*7m to give you 13n +52+91m.

Determine the exact value of each of the following expressions. Your answers should involve fractions and square roots, and not decimal values.

cos(30∘)=

sin(30∘)=

tan(30∘)=

cos(60∘)=

sin(60∘)=

tan(60∘)=

Cos(30)= 3/2

Sin(30)=1/2

Tan(30)=3/3

Cos(60)=1/2

Sin(60)= 3/2

Tan(60)=3

Sin(30)=1/2

Tan(30)=3/3

Cos(60)=1/2

Sin(60)= 3/2

Tan(60)=3

If f(x) = 3x3+ 6x2+ 12x and g(x) = x2, what is the product of f(x) and g(x)?

A) 3x3+ 7x2+ 12x

B) 3x6+ 6x4+ 12x2

C) 6x3+ 12x2+ 24x

D) 3x5+ 6x4+ 12x3

**Answer:**

[tex]3x^5+6x^4+12x^3[/tex]

**Step-by-step explanation:**

Given that,

[tex]f(x) = 3x^3+ 6x^2+ 12x[/tex]

and

[tex]g(x)=x^2[/tex]

We need to find the product of f(x) and g(x). SO,

[tex]f(x)\times g(x)=(3x^3+ 6x^2+ 12x)\times (x^2)\\\\=3x^3\times x^2+6x^2\times x^2+12x\times x^2\\\\=3x^5+6x^4+12x^3[/tex]

**Hence, the correct option is (d).**

Raina drinks 0.65 L of milk every day. How much milk does she drink in 9 days?

Write your answer in milliliters.

**Answer: **5850 milliliters

**Step-by-step explanation:**

First, you have to do 0.65L x 9 days = 5.85L

And then you have to convert it to milliliters so:

5.85L= 5850 milliliters

The population of a city increases by 3% per year. If this year's population is 298,0 what will next year's population be, to the nearest individual?

**Answer:**

5 Probability

5.1 Probabilities

Probabilities are used to describe how likely or unlikely it is that something will happen.

Weather forecasters often talk about how likely it is to rain, or perhaps snow, in particular

parts of the country.

Worked Example 1

(a) When you roll a dice, which number are you most likely to get?

(b) If you rolled a dice 600 times how my sixes would you expect to get?

(c) Would you expect to get the same number of ones?

Solution

(a) You are equally likely to get any of the six numbers.

(b) You would expect to get a six in about 1

6

of the throws, so 100 sixes.

(c) Yes, in fact you would expect to get about 100 of each number.

Worked Example 2

Use one of the following to describe each one of the statements (a) to (d).

Certain

Very likely

Likely

Unlikely

Very unlikely

Impossible

(a) It will snow tomorrow.

(b) It will rain tomorrow.

(c) You win a car in a competition tomorrow.

(d) You are late for school tomorrow.

Solution

(a) Very unlikely for most places in Britain, especially in summer.

(b) Likely or Very likely in Britain in winter.

(c) Very unlikely if you have entered the competition. Impossible if you have not

entered the competition.

(d) Very unlikely, unless the school bus breaks down.

Solve for b. —11b + 7 = 40 b =

**Answer:**

-3

**Step-by-step explanation:**

-11(-3)+7=40

33+7=40

the length of a rectangle is represented by 3x-7 and the width by x+4. express the perimeter as a polynomial in simplest form

**Answer: 8**x - 6

**Step-by-step explanation:**

Perimeter is found by doing 2l + 2w

The length is 3x - 7 and width is x + 4

2(3x - 7) + 2(x + 4) =

6x - 14 + 2x + 8 =

**8x - 6**

Circumference = 69.1yd

**Answer:**

What do you want us to find?

**Step-by-step explanation:**

please help will mark brainlist please and thank you

**Answer:**

c

**Step-by-step explanation:**

and the answer is c

Pls help extra points and mark

**Answer:**

x-6=6

**Step-by-step explanation:**

6+6=12

**Answer:**

c

**Step-by-step explanation:**

because 6+6=12 and the missing number would be 12 because 12-6=6

A developer has 24.5 acres of land. She buys an adjacent plot of land and increases the total

acreage she owns by 20%. Circle the numbers that make the statements true.

**Answer:**

The developer bought 4.9 acres of land, increasing its property to 29.4 acres.

**Step-by-step explanation:**

Given that a developer has 24.5 acres of land, and she buys an adjacent plot of land and increases the total acreage she owns by 20%, to determine the amount of acres she bought and the total acres she now owns, the following calculations must be done:

24.5 x 1.2 = 29.4

24.5 x 0.2 = 4.9

Thus, the developer bought 4.9 acres of land, increasing its property to 29.4 acres.

PLEASE SOMEONE HELP ME IM BEGGING YOU THIS IS SO HARD !!! :)) WILL GIVE BRANLIEST IF UR RIGHT

**Answer:**

Perimeter = 12.246 units

Area = 11.314 units²

**Step-by-step explanation:**

A=2√2r²=11.314

P=2(8)(√2-√2)=12.246

Help ASAP!!!! Thanks

**Answer:**

No DB is not a perpendicular bisector of AC

**Step-by-step explanation:**

This is because as AC is a straight line it's angle degree is 180 which when bisected by DB becomes,

180 ÷ 2 = 90

On both the angles i.e <BDC = <NDA = 90°

To make it a perpendicular bisector but

<BDC is not equal to <NDA is not equal to 90°.

Hence, DB is not a perpendicular bisector of line AC.

Help please. Assignment due tonight.

**Answer:**

sin b

**Step-by-step explanation:**

**Answer:**

cos A

**Step-by-step explanation:**

sine = [tex]\frac{opposite}{hypotenuse}[/tex]

sine B = [tex]\frac{3}{5}[/tex]

cos = [tex]\frac{adjacent}{hypotenuse}[/tex]

cos A = [tex]\frac{3}{5}[/tex]

geometry proofs help please

**Answer:**

trust your instincts

**Step-by-step explanation:**

I can not interfere with your destiny you will need to decide your destiny

Which one of these grids is shaded red and blue in the ratio 0.5: 1?

A

B

D

E

F

**Answer:**

B

**Step-by-step explanation:**

**Answer:**

Its E

**Step-by-step explanation:**

(1 point)

Find the area enclosed by the curve r=2 sin(0) + 3 sin(90).

If the 0's are indeed zeroes, then it would appear that you're using degrees, so that the equation

*r(θ)* = 2 sin(0°) + 3 sin(90°)

describes a circle *r* = 3 (since sin(0°) = 0 and sin(90°) = 1). In this case, the area would simply be *π* *r* ² = 9*π*.

But I suspect you meant to use *θ*, so the curve has the far more interesting equation,

*r(θ)* = 2 sin(*θ*) + 3 sin(9*θ*)

Since sin(9*θ*) has a period of 2*π*/9 and sin(*θ*) has a period of 2*π*, their sum has a period of 2*π*. (That is, 2*π* times the LCM of 1 and 1/9, which is 1.) But we observe *r(θ)* is odd, since

*r(*-*θ)* = 2 sin(-*θ*) + 3 sin(-9*θ*)

… = -2 sin(*θ*) - 3 sin(9*θ*)

… = - *r(θ)*

which tells us that the curve closes itself over a half-period. So the area bounded by the curve is given by the integral,

[tex]\displaystyle\int_0^\pi\int_0^{r(\theta)}r\,\mathrm dr\,\mathrm d\theta[/tex]

If you're not familiar with double integrals yet, all you need to know is that this reduces to the area formula you may/should be familiar with,

[tex]\displaystyle\frac12\int_0^\pi r(\theta)^2\,\mathrm d\theta[/tex]

Compute the integral:

[tex]=\displaystyle\frac12\int_0^\pi(2\sin(\theta)+3\sin(9\theta))^2\,\mathrm d\theta[/tex]

[tex]=\displaystyle\frac12\int_0^\pi(4\sin^2(\theta)+12\sin(\theta)\sin(9\theta)+9\sin^2(9\theta))\,\mathrm d\theta[/tex]

Apply some identities:

sin²(*θ*) = (1 - cos(2*θ*)) / 2

sin(*θ*) sin(9*θ*) = (cos(9*θ* - *θ*) - cos(9*θ* + *θ*)) / 2 = (cos(8*θ*) - cos(10*θ*)) / 2

sin²(9*θ*) = (1 - cos(18*θ*)) / 2

[tex]=\displaystyle\frac14\int_0^\pi(4(1-\cos(2\theta))+12(\cos(8\theta)-\cos(10\theta))+9(1-\cos(18\theta))\,\mathrm d\theta[/tex]

[tex]=\displaystyle\frac14\int_0^\pi(13 - 4\cos(2\theta) + 12\cos(8\theta) - 12\cos(10\theta) - 9\cos(18\theta))\,\mathrm d\theta[/tex]

[tex]=\dfrac14 \left(13\theta-2\sin(2\theta)+\dfrac32\sin(8\theta)-\dfrac65\sin(10\theta)-\dfrac12\sin(18\theta)\right)\bigg|_0^\pi[/tex]

[tex]=\dfrac1{40} \left(130\theta-20\sin(2\theta)+15\sin(8\theta)-12\sin(10\theta)-5\sin(18\theta)\right)\bigg|_0^\pi[/tex]

[tex]=\dfrac{130\pi-20\sin(2\pi)+15\sin(8\pi)-12\sin(10\pi)-5\sin(18\pi)}{40}[/tex]

= **13****π****/4**

You deposit $200 in an account earning 3.5% simple interest. How many years will it take for the balance of the account to be $221

I = PRT

21 = 200 * 0.035 * T

21 = 7T

3 years = T

21 = 200 * 0.035 * T

21 = 7T

3 years = T

1) Heather writes a number that shows 30 parts of 100. Select all that could be Heather's number. 0 0.30 3/100 30/10 0.3 30/100 ! This is a required question

**Answer:**

im guessing .30, .3, and 30/100

**Step-by-step explanation:**

im not sure how to explain it but fractions. yes.

Find the least common denominator of 11/10 and 1/6

11 and 10 is 110. For 1 and 6 it is 24. Hope this helps.

find the number of terms in following algebraic expressions.

**Answer:**

it needs time wait for 10 min.

could someone help me with this question

**Answer: **

10/1

**Step-by-step explanation:**

You are making a poster to support your friend for homecoming. Your original photo is 4 inches by 6 inches. You want the photo on the poster to be 2 feet by 3 feet. What is the scale factor of this dilation? show work pls :(

**Answer:**

6

**Step-by-step explanation:**

2 ft = 24in so 4 to 24 is times 6

3ft=36 in and 6 to 46 is times 6

**Answer:**

6/1

**Step-by-step explanation:**

2ft=24 inches

3ft=36 inches

poster/original photo

24in/4in=6/1

36in/6in=6/1

**6/1**

!!! HELP ASAP !!! 40 x 20 - 6 + 4 =

**Answer:**

798

**Step-by-step explanation:**

first you do 40x20=800 then 800-6=794 then 794+4=798

Evaluate the expression: 20 - 2^4

**Answer:**

*4** *

**Step-by-step explanation:**

1) Simplify 2⁴ to 16.

[tex]20 - 16[/tex]

2) Simplify.

[tex]4[/tex]

*Therefor**,** **the** **answer** **is** **4**.*

**Answer:**

20 - 2^4 =4

**Step-by-step explanation:**

According to the 19th-century concept of manifest destiny, who should possess the North American continent? *
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