Substance A decomposes at a rate proportional to the amount of A present. a) Write an equation that gives the amount A left of an initial amount A0 after time t. b) It is found that 8 lb of A will reduce to 4 lb in 4.6 hr After how long will there be only 1 lb left?
a) Choose the equation that gives A in terms of A0, t, and k, where k > 0.
b) There will be 1 lb left after 14 hr (Do not round until the final answer. Then round to the nearest whole number as needed.)

Answer:

b.  [tex]\frac{7+\sqrt{61} }{6} ,\frac{7-\sqrt{61} }{6}[/tex]

Step-by-step explanation:

[tex]3x^{2} -1=7x[/tex]

Quadratic equations are suppose to be written as: [tex]ax^2+bx+c=0[/tex]

so the new quadratic equation for this problem will be: [tex]3x^{2} -1-7x=0[/tex]

Now rearrange the terms: [tex]3x^{2} -7x-1=0[/tex]

Then use the Quadratic Formula to Solve for the Quadratic Equation

Quadratic Formula = [tex]x=\frac{-b±}{} \frac{\sqrt{b^2-4ac} }{2a}[/tex]

Note: Ignore the A in the quadratic formula

Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.

[tex]3x^{2} -7x-1=0[/tex]

a = 3

b = -7

c = -1

[tex]x=-(-7)±\frac{\sqrt{(-7)^2-4(3)(-1)} }{2(3)}[/tex]

Evaluate The Exponent

[tex]x=\frac{7±\sqrt{(49)-4(3)(-1)} }{2(3)}[/tex]

Multiply The Numbers

[tex]x=\frac{7±\sqrt{49+12} }{2(3)}[/tex]

Add The Numbers

[tex]x=\frac{7±\sqrt{61} }{2(3)}[/tex]

Multiply The Numbers

[tex]x=\frac{7±\sqrt{61} }{6}[/tex]

Answer:

15 mph

Step-by-step explanation

i used a calculator but correct me if im wrong pls

Answer:

4)8 goats, 3 hens.

Step-by-step explanation:

8*4=32

3*2=6

32+6=38

Answer

No solution

Step-by-step explanation:

4y + 2x = 18

3x + 6y = 26

You need either the x's or the y's to have the same coefficients.

let's line things up first.

4y + 2x = 18   (multiply by 3)

6y + 3x = 26  (multiply by 2)

to keep numbers relatively small we will multiply the top equation by 3 and the bottom equation by 2. Multiply all terms. This will make the coefficients equal.

12y + 6x = 54

12y + 6x = 52

So, if you subtract them from each other you get :

0 = 2

When this happens the solution set is : no solution

Answer:

Impossible

Step-by-step explanation:

Ok, so we first rearrange for convenience:

2x+4y=18

3x+6y=26

We multiply the two equations to eliminate x:

2x+4y=18 * -3

3x+6y=26 * 2

So:

-6x-12y=-54

6x+12y=52

And now we add the two equations:

0+0= -2

Try multiplying the two equations by any other number which will lead to them cancelling, (eg. -9, 6), still the equation will not work.

Answer:

10,000 different PINS are possible

Step-by-step explanation:

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

In this question:

Four each digit on the PIN, there are 10 possible outcomes. The digits are independent. So, by the fundamental counting principle:

[tex]T = 10^4 = 10000[/tex]

10,000 different PINS are possible

Answer:

Step-by-step explanation:

-1<x<3.   I hope it helpful!

Answer:

Location of W is - 23, location of X is - 9.

Step-by-step explanation:

location of V = - 16

Points W and X are each 7 units away from Point V.

Let the W is at left of V and X is right of V.

location of W = -16 - 7 = - 23

location of X = - 16 + 7 = - 9

Answer:

2, 3, 5, 8, 13 missing number is 18.

Given:

In quadrilateral ABCD, angle B=90° , AB=9m, BC=40m, CD=15m, DA=28m.

To find:

The area of the quadrilateral ABCD.

Solution:

In quadrilateral ABCD, draw a diagonal AC.

Using Pythagoras theorem in triangle ABC, we get

[tex]AC^2=AB^2+BC^2[/tex]

[tex]AC^2=9^2+40^2[/tex]

[tex]AC^2=81+1600[/tex]

[tex]AC^2=1681[/tex]

Taking square root on both sides, we get

[tex]AC=\sqrt{1681}[/tex]

[tex]AC=41[/tex]

Area of the triangle ABC is:

[tex]A_1=\dfrac{1}{2}\times base\times height[/tex]

[tex]A_1=\dfrac{1}{2}\times BC\times AB[/tex]

[tex]A_1=\dfrac{1}{2}\times 40\times 9[/tex]

[tex]A_1=180[/tex]

So, the area of the triangle ABC is 180 square m.

According to the Heron's formula, the area of a triangle is

[tex]Area=\sqrt{s(s-a)(s-b)(s-c)}[/tex]

where,

[tex]s=\dfrac{a+b+c}{2}[/tex]

In triangle ACD,

[tex]s=\dfrac{28+15+41}{2}[/tex]

[tex]s=\dfrac{84}{2}[/tex]

[tex]s=42[/tex]

Using Heron's formula, the area of the triangle ACD, we get

[tex]A_2=\sqrt{42(42-28)(42-15)(42-41)}[/tex]

[tex]A_2=\sqrt{42(14)(27)(1)}[/tex]

[tex]A_2=\sqrt{15876}[/tex]

[tex]A_2=126[/tex]

Now, the area of the quadrilateral is the sum of area of the triangle ABC and triangle ACD.

[tex]A=A_1+A_2[/tex]

[tex]A=180+126[/tex]

[tex]A=306[/tex]

Therefore, the area of the quadrilateral ABCD is 306 square meter.

Answer:

Conjecture :  2xy / ( x + y ) ≤  √xy

Step-by-step explanation:

Harmonic mean of  x and y = 2xy/( x + y )

Formulate a conjecture about their relative sizes

we will achieve this by computing harmonic and geometric means

Geometric mean = √xy

harmonic mean = 2xy/( x + y )

Conjecture :  2xy / ( x + y ) ≤  √xy

attached below is the proof

mass = force / area

this is second law of motion ( Newton's 2nd law)

[tex]\longrightarrow{\blue{ m = \frac{F}{a} }}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Explanation}}{\red{:}}}}}[/tex]

F = ma

➺ m = [tex]\frac{F}{a} [/tex]

where,

F = Force

m = mass

a = acceleration

"F = ma" is Newton's second law of motion, which states that force is equal to mass times acceleration.

The SI unit of force is newton, symbol N.

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Answer:

5⁴a²

Step-by-step explanation:

(5³a³)÷5a-¹×5-²a²

5³a³÷5a-¹×5-²a²

5³a³÷5¹-²×a-¹+²

5³a³÷5-¹a

5³a³/5-¹a

5³-(-¹)a³-¹

5⁴a²

Answer:

6

Step-by-step explanation:

6*9 = 54

6*6 = 36

6*7 = 42

Answer:

n + 4

Step-by-step explanation:

Given

⅕(m + m + 1 + m + 2 + m + 3 + m + 4) = n

Required

⅑(m + 2 + m + 3 +.......+ m + 10)

We have:

⅕(m + m + 1 + m + 2 + m + 3 + m + 4) = n

Multiply both sides by 5

m + m + 1 + m + 2 + m + 3 + m + 4 = 5n

Collect like terms

m + m + m + m + m = 5n - 1 - 2 - 3 - 4

5m = 5n - 10

Divide both sides by 5

m = n - 2

So, we have:

⅑(m + 2 + m + 3 + m + 4 + m + 5 + m + 6 + m + 7 + m + 8 + m + 9 + m + 10)

Collect like terms

= ⅑(m+m+m+m+m+m+m+m+m+2+3+4+5+6+7+8+9+10)

= ⅑(9m + 54)

= m + 6

Substitute n - 2 for m

= n - 2 + 6

= n + 4

Answer:

Cost of adult ticket = $12.5

Cost of child ticket = $7.5

Step-by-step explanation:

Given:

Cost of 6 adult ticket and 5 child ticket = $112.5

Cost of 8 adult ticket and 4 child ticket = $130

Find:

Equation and solution

Computation:

Assume;

Cost of adult ticket = a

Cost of child ticket = b

So,

6a + 5b = 112.5....eq1

8a + 4b = 130 ......eq2

Eq2 x 1.25

10a + 5b = 162.5 .....eq3

eq3 - eq1

4a  = 50

Cost of adult ticket = $12.5

8a + 4b = 130

8(12.5) + 4b = 130

Cost of child ticket = $7.5

C.(f-g)(x) = 4x^3 +5x²-7x-1

Step-by-step explanation:

Given information :

[tex]f(x) = 4 {x}^{3} + 5 {x}^{2} - 3x - 6 \\ g(x) = 4x - 5[/tex]

Find :

[tex](f - g)(x) = \\ (4 {x}^{3} + 5 {x}^{2} - 3x - 6) \\ - 4x -5[/tex]

Open bracket and Simplify

[tex]4 {x}^{3} + 5 {x}^{2} - 3x - 6 - 4x + 5 \\ 4 {x}^{3} + 5 {x}^{2} - 7x - 1[/tex]

Yes, they are quite similar. the p-value obtained using the theory-based method (p < 0.0001) agree with that obtained using the randomization/simulation - based method (p < 0.0001)

P- value is the probability of obtaining a value of test statistic more extreme in the direction of alternative hypothesis than the observed one. In easy words if p -value < level of significance we reject H0 in favor of H1.

Here:

p-value < 0.0001 => we reject H0.

If the statistical software renders a p value of 0.000 it means that the value is very low, with many "0" before any other digit.

So the interpretation would be that the results are significant, same as in the case of other values below the selected threshold for significance.

Therefore, yes they are quite similar.

Learn more about balsa wood here:

https://brainly.com/question/33256379

#SPJ2

Incomplete Question:

Student researchers investigated whether balsa wood is less elastic after it has been immersed in water. They took 60 pieces of balsa wood and randomly assigned half to be immersed in water and the other half not to be. They measured the elasticity by seeing how far (in inches) the piece of wood would project a dime into the air.

Does the p-value obtained using the theory-based method (p < 0.0001) agree with that obtained using the randomization/simulation-based method (p < 0.0001)?

A. No, they are different.

B. Yes, they are quite similar.

Answer:

0.73 = 73% probability that a randomly selected student is either male or would admit to lying to a teacher, during the past year.

Step-by-step explanation:

I am going to treat these events as Venn probabilities, considering that:

Event A: Lying to the teacher.

Event B: Male

48% of high school students would admit to lying at least once to a teacher during the past year and that 25% of students are male and would admit to lying at least once to a teacher during the past year

This means that [tex]P(A) = 0.48, P(A \cap B) = 0.25[/tex]

Assume that 50% of the students are male.

This means that [tex]P(B) = 0.5[/tex]

What is the probability that a randomly selected student is either male or would admit to lying to a teacher, during the past year?

This is:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

Considering the values we were given:

[tex]P(A \cup B) = 0.48 + 0.5 - 0.25 = 0.73[/tex]

0.73 = 73% probability that a randomly selected student is either male or would admit to lying to a teacher, during the past year.

Answer:rectangular

Step-by-step explanation:

Answer:

TRIANGULAR

Step-by-step explanation:

A prism is a triangular-shaped piece of glass. The white light that reaches the prism contains all of the colors of the visible spectrum even though you can’t see them. As the white light passes through the edge or boundary of the prism, the light waves refract. Each of the different wavelengths contained in the white light refracts differently and results in a different color. The white light is broken up by the prism into all the colors of rainbow. The longest wavelength bends (refracts) the least and is red. The shortest wavelength bends the most and is violet.

Step-by-step explanation:

jnx-avkj-uup p.l.z join

Answer:

[tex] x=\frac{[2] \sqrt {[21] }}{[3] }[/tex]

Step-by-step explanation:

Since, given is a 30°-60°-90° triangle.

[tex] \therefore \sqrt 7 = \frac{\sqrt3}{2} \times x[/tex]

[tex] \therefore 2\sqrt 7 = \sqrt3 \times x[/tex]

[tex] \therefore x=\frac{2\sqrt 7}{\sqrt 3}[/tex]

[tex] \therefore x=\frac{2\sqrt 7(\sqrt 3)}{\sqrt 3(\sqrt 3)}[/tex]

[tex] \huge \therefore x=\frac{[2] \sqrt {[21] }}{[3] }[/tex]

Answer:

a) 64 b) 12

Step-by-step explanation:

32 + 32 = 64

2*3 = 6

6*2 = 12

Answer:

a) 64 b) 12

Step-by-step explanation:

The answer for a is simple the answer is 64 just multipy 32 with 2 and the second one first you have to solve he answer iin the bracket then the answer you get from the bracket you will have to multiply with the number outside the bracket which is 2 and the answer you get will be 12.

Answer:

The intersection region shown in the graph attached is the solution of the system of inequalities

Answer:

(26.2252 ; 27.3748)

Step-by-step explanation:

The confidence interval is given by :

x ± Margin of error

The margin of error = Zcritical * (σ/√(n))

σ = 7.5 ; n = 654

Zcritical = Zα/2 = 1.96

The margin of error = 1.96 * (7.5/√654) = 0.5748

The confidence interval :

Upper boundary = 26.8 + 0.5748 = 27.3748

Lower boundary = 26.8 - 0.5748 = 26.2252

(26.2252 ; 27.3748)

We are 95% confident that the mean BMI of the entire population will fall in between (26.2252 ; 27.3748)

Answer:

I think you are missing something unless the answer is a horizontal line.

Step-by-step explanation:

Answer:

square root

Step-by-step explanation:

just took the test :)

Answer:

40% of policyholders are expected to have an accident next year

Step-by-step explanation:

Given the data in the question;

P( collision coverage ) = 60% = 0.6

P( comprehensive coverage ) = 70% = 0.7

Now, we make use of the Law of addition of probability, so

P( collision coverage and comprehensive coverage ) = P( collision coverage )  + P( comprehensive coverage ) - P( collision coverage or comprehensive coverage )

P( collision coverage and comprehensive coverage )  = 0.6 + 0.7 - 1

P( collision coverage and comprehensive coverage ) = 0.3

Now,

P( comprehensive coverage only ) = P( comprehensive coverage ) - P( collision coverage and comprehensive coverage )

P( comprehensive coverage only ) = 0.7 - 0.3

P( comprehensive coverage only ) = 0.4

And

P( collision coverage only) = P( collision coverage ) - P( collision coverage and comprehensive coverage )

P( collision coverage only) = 0.6 - 0.3 = 0.3

Next  we make use of the Law of total probability;

P( accident ) = [P( accident ║ collision coverage only) × P( collision coverage only)] + [P( accident ║ comprehensive coverage only) × P( comprehensive coverage only)] + [P( accident ║ collision coverage and comprehensive coverage only) × P( collision coverage and comprehensive coverage only)]

so we substitute in our values;

P( accident ) = [ 30% × 0.3 ] + [ 40% × 0.4 ] + [ 50% × 0.3 ]

P( accident ) = [ 0.3 × 0.3 ] + [ 0.4 × 0.4 ] + [ 0.5 × 0.3 ]

P( accident ) = 0.09 + 0.16 + 0.15

P( accident ) = 0.4 or 40%

Therefore,  40% of policyholders are expected to have an accident next year

Given:

v = 150d

v represents company's production for the coming year

d represents the number of days

150 is the daily production

The rate of change of the function representing the number of vehicles manufactured for the coming year is CONSTANT (150) , and its graph is a STRAIGHT LINE . So, the function is a LINEAR function.

I hope this helps!

Answer:

v = 150d

v represents company's production for the coming year

d represents the number of days

150 is the daily production

maybe 28 is the answer...