Write the first five terms of the geometric sequence whose first terns 6, and whose common ratio is 3.

Answer: 275 adults and 130 children

Step-by-step explanation:

First, find the value of one variable by rearranging a equation:

[tex]a+c=405\\c=405-a[/tex]

Substitute it into the other equation and solve for a:

[tex]12a+5c=3950\\12a+5(405-a)=3950\\12a+2025-5a=3950\\12a-5a=3950-2025\\7a=1925\\a=\frac{1925}{7} =275[/tex]

Use the a-value to find b by substituting it into the rearranged equation:

[tex]c=405-a=405-275=130[/tex]

Therefore, the answer would be:

[tex]\left \{ {{a=275} \atop {c=130}} \right.[/tex]

Answer:

Step-by-step explanation:

The given function is  :  

Here , x= independent variable where we place the input value and f(x) = dependent variable where we get the output value.

Now , when we put x= 3 , we get

That means , the value of f(3) in the given function is 8.

Hence, the correct answer is B=8.

Answer:

x = -1

Step-by-step explanation:

1/4 (4x - 4) = -2(6x + 7)

1x - 1 = -12x - 14

13x = -13

x = -1

Answer:

56.25km

Step-by-step explanation:

75min = 5/4 h

distance = speed * time = 45 * 5/4 = 56.25

C.

Observe that the roots of polynomial are [tex]-3,2,5[/tex]

We have a polynomial in a factored form,

[tex](x+3)(x-2)(x-5)[/tex]

If you substitute x for any of [tex]-3,2,5[/tex] the product will always equal to zero that is these numbers are roots of polynomial.

Hope this helps :)

Answer:

it is true

Step-by-step explanation:

Answer:

Distance = 7 7/9 Km

Step-by-step explanation:

Given the following data;

Distance = 2⅔ = 8/3 Km

Time = ⅗ hour

First of all, we would find her speed;

Speed = distance/time

Speed = (8/3)/(3/5)

Speed = 8/3 * 5/3

Speed = 40/9 km/h

Next, we would find the distance covered when time = 1¾ hours

Distance = speed * time

Distance = 40/9 * 1¾

Distance = 40/9 * 7/4

Distance = 10/9 * 7

Distance = 70/9

Distance = 7 7/9 Km

9514 1404 393

Answer:

  14,201 years

Step-by-step explanation:

The two compound interest formulas are ...

  A = P·e^(rt) . . . . . continuous compounding at rate r for t years

  A = P·(1 +r/365)^(365t) . . . . . daily compounding at rate r for t years

We went the amounts to be equal:

  1000·e^(0.07t) = 1100·(1+0.07/365)^(365t)

Dividing by 1000(1 +0.07/365)^(365t), we have ...

  ((e^0.07)/(1+0.07/365)^365)^t = 1.1

The base of the exponential on the left is ...

 ( e^0.07)/(1+0.07/365)^365 ≈ 1.00000671149321522

Taking logs, we have ...

  t×ln(1.00000671149321522) = ln(1.1)

  t = ln(1.1)/ln(1.00000671149321522) ≈ 0.09531018/(6.7114704·10^-6)

  t ≈ 14,201.09 . . . . . years

It will take about 14,201 years for the investments to be equal.

_____

Additional comment

The investment value at that time will be about $5.269·10^434. (That's a larger number than anything countable in the known universe, including energy quanta.)

These calculations are beyond the ability of many calculators, so might need to be carefully rewritten if the calculator only keeps 10 significant digits, or only manages exponents less than 100.

This shows that daily compounding is very close in effect to continuous compounding. It would take almost 150 years to make a difference of 0.1% in value.

Step-by-step explanation:

4. the area of semi circle R =

3²/5² × 75π = 9/25 × 75π = 27π cm²

5. the ratio of their areas = 1²:7² = 1:49

Answer:

This is a 30-60-90 right triangle.

The ratio of sides:

Compare with the given values:

Answer:

0.53%

Step-by-step explanation:

hope it is well understood

Answer:

Step-by-step explanation:

45 - (8 x 3 + 15)

45 - (24 + 15)  ---> do parentheses first

45 - ( 39 )

45 -  39

6

The value of the expression Becca should get after simplification is 6.

Given is an expression 45 - (8 × 3 + 15), Becca is trying to solve the same,

To evaluate the expression 45 - (8 × 3 + 15), Becca should follow the order of operations, which is often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):

First, calculate the value inside the parentheses: 8 × 3 + 15

= 24 + 15

= 39.

Now, substitute this value back into the original expression: 45 - 39.

Finally, perform the subtraction: 45 - 39 = 6.

So, the value of the expression is 6.

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Work Shown:

1 pack of white = 2 shirts = A

1 pack of blue = 6 shirts

5 packs of blue = 5*6 = 30 shirts = B

A+B = 2 white shirts + 30 blue shirts = 32 shirts total

Answer:

32 T-shirts in total

Step-by-step explanation:

1 white has 2

1 blue has 6

1*2=2 white T

5*6=30  blue T

30+2=32

Answer:

√10

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√[-3 - (-6)] + (9 - 8)²

√(3)² + (1)²

√9 + 1

√10

Answer: [tex]\dfrac{11}{9}I[/tex]

Step-by-step explanation:

Given

There is [tex]l[/tex] liter of pure alcohol

Suppose [tex]x[/tex] liters of water is added

After addition of water, alcohol becomes 45% in concentration

[tex]\Rightarrow \dfrac{l}{x+l}=45\%\\\\\Rightarrow \dfrac{I}{0.45}=x+I\\\\\Rightarrow \dfrac{20}{9}I-I=x\\\\\Rightarrow x=\dfrac{11}{9}I[/tex]

Thus,  [tex]\dfrac{11}{9}I[/tex] of water is added to the pure alcohol.

Answer:

2√10

Step-by-step explanation:

Given the following data;

Area of square = 40

Mathematically, the area of a square is calculated by using the formula;

Area, A = s²

Where;

s is the length of sides of a square.

Substituting into the formula, we have;

40 = s²

s = √40

s = √4 * √10

s = 2 * √10

s = 2√10

Answer:

B

Step-by-step explanation:

side Ac is the opposite of angle B, therefore use the sin ratio to find ac since the hypotenuse is also given

sin B=opposite/hypotenuse

sin 27=ac/15

ac=sin27×15

=6.81

I hope this helps

Answer:

AC = 6.81

Step-by-step explanation:

∠BAC = 90° - 27° = 63°

Cos 63° =[tex]\frac{AC}{AB}[/tex] = 0.454

AC = cos 63° * AB = 0,454 * 15 = 6.81

Answer:

34

Step-by-step explanation:

n = 5

f(5) = 6(5)+4

f(5)=34

The fifth term of the sequence is equal to 34.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is f(n) = 6n + 4. The value of the fifth term will be calculated as,

n = 5

f(5) = 6(5)+4

f(5)=34

Therefore, the fifth term of the sequence is equal to 34.

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Answer:

14

Step-by-step explanation:

3 1/2 multiply by 4 equals 14

9514 1404 393

Answer:

  -0.58 < x ≤ 2

Step-by-step explanation:

The exponential function is greater on the interval of approximately (-0.58, 1).

  about -0.58 < x < 1

Answer:

Step-by-step explanation:

(z)° + (3z + 1)° = 360° - ( 54° + 204° )

z + 3z + 1 = 360 - 258

4z = 101

z = 25.25

Answer:

a=1, b=-2,c=-1

Step-by-step explanation:

1*(x)+(-2)*y+(-1)*1. a=1, b=-2,c=-1

For the hole in one pythagores theorem would work because a right angled triangle eill be formed and hole in one would be the hypotenuse which can be found using the theorem.

b²+p² = h²

Answered by Gauthmath must click thanks and mark brainliest

Answer:

total number of boys in skool is 216

And

ratio of girls to boys is a 3:4

Step-by-step explanation:

let total no. of boys be X

ACCORDING TO QUESTION

ratio of boys to girls = 4:3

total number of girls = 162

now

4/3=X/162

or, 4×162= 3x

or, 4×162/3= X

hence

X = 216

therefore total number of boys is 216

and

ratio of girls to boys is =162/216

=3/4

=3:4

Answer:

y = [tex]\frac{20}{9}[/tex]

Step-by-step explanation:

Since the figures are similar then the corresponding sides are in proportion, that is

[tex]\frac{JH}{PQ}[/tex] = [tex]\frac{FM}{ST}[/tex] , substitute values

[tex]\frac{6}{4}[/tex] = [tex]\frac{7}{3y-2}[/tex] ( cross- multiply )

6(3y - 2) = 28

18y - 12 = 28 ( add 12 to both sides )

18y = 40 ( divide both sides by 18 )

y = [tex]\frac{40}{18}[/tex] = [tex]\frac{20}{9}[/tex]

Answer:

20/9

Step-by-step explanation:

since the 2 are similar,

JH/PQ = FM/ST

6/4 = 7/(3y-2)

6(3y-2) = 7*4

18y-12=28

18y = 40

y = 40/18 = 20/9 = 2 2/9

Answer:

Step-by-step explanation:

3/16 = 0.1875

As a % this is 18.75%

18.75/100 * 200 = 37.5

I'm not sure from the question, exactly what you want. 18.75% of 200 is one possibility.

3/16 of 200 as a percentage is 3750%

The question can be represented as:

[tex]\frac{3}{16} * 200[/tex]

Rewrite as:

[tex]\frac{3}{16} * 200 =\frac{3* 200}{16}[/tex]

Multiply the numerator

[tex]\frac{3}{16} * 200 =\frac{600}{16}[/tex]

[tex]\frac{3}{16} * 200 =37.5[/tex]

Multiply by 100% to represent it as a percentage

[tex]\frac{3}{16} * 200 =37.5 * 100\%[/tex]

[tex]\frac{3}{16} * 200 =3750\%[/tex]

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Answer:

assuming youre asking for line of symmetry, it's a line that cuts a shape exactly in half.  

for example, a square has 4 lines of symmetry

Answer:

(0.089 ; 0.151)

Step-by-step explanation:

Given :

Sample size, n = 300

Number of defective items, x = 36

The confidence interval required here is that for a one sample proportion :

The confidence interval is defined thus :

Phat ± Zcritical * √[Phat(1 - phat) / n]

Zcritical at 90% = 1.645

Phat = x / n = 36 / 300 = 0.12

Hence,

C.I = 0.12 ± 1.645 * √[0.12(1 - 0.12) / 300]

C.I = 0.12 ± (1.645 * 0.0187616)

C.I = 0.12 ± 0.0308629

C.I = (0.089 ; 0.151)