solve the following equations 2p + 3p + 8 - 4 = 54

Answer:

the probability is a fraction or a percentage, some times even a decimal

Answer:

23 years

Step-by-step explanation:

Step 1: Calculate the rate constant (k) for the radioactive decay

A radioactive substance with initial concentration [A]₀ decays to 97% of its initial amount, that is, [A] = 0.97 [A]₀, after t = 1 year. Considering first-order kinetics, we can calculate the rate constant using the following expression.

ln [A]/[A]₀  = - k.t

k = ln [A]/[A]₀ / -t

k = ln 0.97 [A]₀/[A]₀ / -1 year

k = 0.03 year⁻¹

Step 2: Calculate the half-life of the substance

We will use the following expression.

[tex]t_{1/2}[/tex] = ln2/ k = ln 2 / 0.03 year⁻¹ = 23 years

Answer:

60–x (smaller )

Step-by-step explanation:

Sum of all 4 angles of a quadrilateral = 360°

(5x-30) + (3x + 60) + (60-x) +(4x+ 50) = 360°

(12x - x) + ( 170 - 30) = 360°

11x + 140 = 360°

11x = 360 - 140 = 220

x = 220/11 = 20°

Each angles is :

5x - 30 = 100 - 30 = 70°

3x+ 60 = 60 + 60 = 120°

60 - x = 60 - 20 = 40°

4x + 50 = 80 + 50 = 130°

Smallest of these angles is 40°

Answer:

The correct options are:

3x - 4y = 15

15x - 20y = 75

(fourth option, counting fom the top)

5x + 6y = 20

-10x - 12y = -40

(last option)

Step-by-step explanation:

A system of linear equations has infinitely many solutions if and only if both equations define the same line.

Then we need to see which option describes twice the same line.

From the given options, the two with infinitely many solutions are:

3x - 4y = 15

15x - 20y = 75

How we check that? remember that we can multiply (or divide) both sides of an equation by the same number, and the equation remains unchanged.

So, if we take the first equation and multiply both sides by 5, we get:

5*(3x - 4y) = 5*15

15x - 20y = 75

Which is the same as the other equation, so both equations describe the same line.

The other system is the last one:

5x + 6y = 20

-10x - 12y = -40

If we take the first equation and multiply both sides by -2, we get:

-2*(5x + 6y) = -2*20

-10x - 12y = -40

So, again, both equations describe the same line.

Answer:

4 squareroot 2

Step-by-step explanation:

The answer is 4 squareroot 2

Answer:

63 yd³

Step-by-step explanation:

V = lwh

V = 7 × 3 × 9

V = 189

Since the cubes are 1/3 yd³, you now multiply the volume of this figure which is if it were a 1 yd³.

189 × [tex]\frac{1}{3}[/tex]

63 yd³

Answer:

108 cm²

Step-by-step explanation:

the surface area is the sum of all individual shapes areas on the surface.

2 right-angled triangles

3 rectangles

area of a right-angled triangle is At = a×b/2

At = 4×3/2 = 6 cm²

we need it twice : 12 cm²

one rectangle (length×width) = 8×3 = 24 cm²

one rectangle = 8×4 = 32 in²

one rectangle = 8×5 = 40 cm²

total surface area

A = 12+24+32+40 = 108 cm²

an area is always a square unit (power of 2).

a volume is always a cubic unit (power of 3).

and a length is always a simple unit (power of 1).

Answer:

Step-by-step explanation:

Answer:

Point estimate = 0.25

Step-by-step explanation:

Complete question

Calculate the point estimate

Solution

Let A represents the number of adult males who smoke cigarettes

Calculation of 95% confidence interval for proportion of adult males who smoke cigarettes

[tex]p-z_\alpha \frac{p(1-p)}{n}[/tex] , [tex]p+z_\alpha \frac{p(1-p)}{n}[/tex]

[tex]p-z_\alpha \frac{p(1-p)}{n} = 0.22\\p+z_\alpha \frac{p(1-p)}{n} = 0.28[/tex]

Point estimate

Adding the above given equations we get -

2 * p = 0.50

p = 0.25

Answer:

1 miles= 1.609km

so, 25x1.609 = 40.225km

Answer:

[tex]\frac{a^2^0b^5}{c^5d^3^0}[/tex]

Step-by-step explanation:

When one raises a value to an exponent, one can multiply the current value of the exponent by the number it is raised to. This is the case because raising a value to an exponent is another way of representing that value times itself the number of times that the exponent indicates. Remember, if no exponent is written, then the exponent is (1).

One can apply this here by multiplying every exponent in this problem by (5) since the fraction is raised to the power (5).

[tex](\frac{a^4b}{cd^6})^5[/tex]

[tex]=\frac{(a^4^*^5)(b^1^*^5)}{(c^1^*^5)(d^6^*^5)}[/tex]

Simplify,

[tex]=\frac{a^2^0b^5}{c^5d^3^0}[/tex]

Solution :

The probability of winning when you choose n is =  [tex]$^nC_2\left(\frac{1}{2}\right)^n$[/tex]

[tex]$n\left(\frac{n-1}{2}\right)\times \left(\frac{1}{2}\right)^n = n(n-1)\left(\frac{1}{2}\right)^{n+1}$[/tex]

Apply log on both the sides,

[tex]$f(n) = \log\left((n)(n-1)\left(\frac{1}{2}\right)^{n-1}\right) = \log n +\log (n-1)+(n+1) \ \log\left(\frac{1}{2}\right)$[/tex]

Differentiation, f(x) is [tex]$f'=\frac{1}{x}+\frac{1}{(x-1)}+\log\left(\frac{1}{2}\right)$[/tex]

Let us find x for which f' is positive and x for which f' is negative.

[tex]$\frac{1}{x}+\frac{1}{(x-1)} > 0.693$[/tex]       , since [tex]$\log(1/2) = 0.693147$[/tex]

For x ≤ 3, f' > 0 for [tex]$\frac{1}{x}+\frac{1}{x-1}+\log\left(\frac{1}{2}\right)>0$[/tex]

[tex]$\frac{1}{x}+\frac{1}{x-1}-0.6931470$[/tex]

That means f(x) is increasing function for n ≤ 3

[tex]$\frac{1}{x}+\frac{1}{x-1}< 0.693147 $[/tex] for x > 4

f' < 0 for n ≥ 4, that means f(n) is decreasing function for n ≥ 4.

Probability of winning when you chose n = 3 is [tex]$3(3-1)\left(\frac{1}{2}\right)^{3+1}=0.375$[/tex]

Probability of winning when you chose n = 4 is [tex]$4(4-1)\left(\frac{1}{2}\right)^{4+1}=0.375$[/tex]

Therefore, we should chose either 3 or 4 to maximize chances of winning.

The probability of winning with an optimal choice is n = 0.375

Question isnt well formatted :

Answer:

1 : 6

Step-by-step explanation:

Given the question :

3x = 1/2y

3x = y/2

Multiply both sides by 2

3x * 2 = y/2 * 2

6x = y

This can be interpreted as :

y = 6 times the value of x

x = y/6

x : y

1 : 6

Answer:

10, 11, 12, 13, 14, 15, 16, 17, 18, 19

Step-by-step explanation:

A two-digit number can be written as:

a*10 + b

Where a and b are single-digit numbers.

a is the tens digit

b is the units digit.

the reverse number is:

b*10 + a

We know that:

"If you add the digits together and multiply the result by 10, you will get 9 more than the reverse number"

Then:

(a + b)*10 = b*10 + a + 9

We now need to solve this for a and b, where the other restriction that we have is that a and b can be any whole number of the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Then:

(a + b)*10 = b*10 + a + 9

a*10 + b*10 = b*10 + a + 9

subtracting b*10 in both sides, we get:

a*10 = a + 9

solving this for a, we get:

a*10 - a = 9

a*(10 - 1) = 9

a*9 = 9

a = 9/9

a = 1

and notice that we do not have any restriction for b.  So b can be any number of the set.

for example, if b = 2

a*10 + b = 12

now let's test the property:

10*(1 + 2) = 2*10 + 1 + 9

30 = 20 + 10 = 30

now if b = 4, we have:

a*10 + b = 1*10 + 4 = 14

10*(1 + 4) = 4*10 + 1 + 9

50 = 50

So we can see that for any value of b, this will work.

So the only restriction that we have, is that a must be equal to 1.

Then the numbers are:

10, 11, 12, 13, 14, 15, 16, 17, 18, 19

The possible numbers are 10, 11, 12, 13, 14, 15, 16, 17, 18 and 19

Assume the digits of the two-digit number are x and y, where:

So, the original number (n) is:

[tex]n = 10 \times x + y[/tex]

When the digits are added, and multiplied by 10, we have the following equation:

[tex](x + y) \times 10 = 9 + (y \times 10 + x)[/tex]

Expand the equation

[tex]10x + 10y = 9 + (10y + x)[/tex]

Remove bracket

[tex]10x + 10y = 9 + 10y + x[/tex]

Subtract 10y from both sides

[tex]10x = 9 + x[/tex]

Subtract x from both sides

[tex]9x = 9[/tex]

Divide both sides by 9

[tex]x = 1[/tex]

Recall that the number is represented as:

[tex]n = 10 \times x + y[/tex]

So, we have:

[tex]n = 10 \times 1 + y[/tex]

[tex]n = 10 + y[/tex]

This means that, the possible numbers are from 10 to 19

Read more about two-digit numbers at:

https://brainly.com/question/23846183

Answer:

SinA=5/1 3 CosA=12/13 tanA=5/12. SinC=12/13 CosC=5/13 and tanC=12/5

Step-by-step explanation:

Basically find the third side by Pythagorean theorem which would get you 13. So 13 is the hypotenuse. Remember these 3 formulas. Sin=Opposite/Hypotenuse Cos=Adjacent/hypotenuse and Tan=opposite/Adjacent. So for Sin a the opposite side to angle A is 5. The hypotenuse is always the same which would be 13. So Sin a is 5/13. For cos the side adjacent would be 12. So it is 12/13. *Note Hypotenuse cannot be considered the adjacent.

Answer:

sin A = 5/13,  cos A = 12/13,  tan A = 5/12,  sin C = 12/13, cos C = 5/13, tan C = 12/5

Step-by-step explanation:

According to Pythagoras, hypotenuse = √{(12)^2+(5)^2}. So, hypotenuse = 13. (See picture if confused).

sin A = 5/13

cos A = 12/13

tan A = 5/12

sin C = 12/13

cos C = 5/13

tan C = 12/5

Answer:

a1 = 1, a2 = 2Step-by-step explanation:

Answer:

I need more information to answer this

Answer:

2x+1

Step-by-step explanation:

f(g(x))= (2x)+1

(2)x+1

Answer:

Of course CD is higher then investing in T-bill

Answer:

Solution given:

cscθ -cscθcos²θ

taking common

cscθ(1-cos²θ)

we have

1-cos²θ=sin²θ and cscθ=1/sinθ

now

1/sinθ*sin²θ

=sinθ

so

D)

sin θ is a required answer.

Answer:

Yes, Hamdan is correct.

Step-by-step explanation:

Let the two fractions are q/r and s/r.

Here, the denominator is same for both the fractions.

So, as we add them, add the numerators and the denominators remains same.

[tex]\frac{q}{r}+\frac{s}{r}\\\\=\frac{q + s}{r}[/tex]

For example

[tex]\frac{3}{5}+\frac{4}{5}\\\\=\frac{3 + 4}{5}\\\\=\frac{7}{5}[/tex]

So, Hamdan is correct.

Answer:

DEF = 110

Step-by-step explanation:

Supplementary angles add to 180

3x+5  +2x = 180

Combine like terms

5x +5 = 180

Subtract 5 from each side

5x = 175

Divide each side by 5

5x/5 = 175/5

x =35

DEF = 3x+5

     = 3*35 +5

    = 105+5

   = 110

Answer:

1/6

is the probability

ok

Answer:

36.8 i think

Step-by-step explanation:

Answer:

Answer:

19.2m

Step-by-step explanation:

"Slice" the rectangle into two right triangles (slice along the diagonal). Now you can use the Pythagorean theorem to calculate the length of the diagonal:

[tex]a^{2} +b^{2} =c^{2} \\12^{2}+15^{2} =c^{2} \\144+225=c^{2} \\\sqrt{369} =\sqrt{c^{2} }\\19.2m =c[/tex]