The contingency table represents a box of cards. Box of Cards 1 2 3 4 5 Total Black 1 1 1 1 1 5 Red 1 1 1 0 0 3 Total 2 2 2 1 1 8 What is the probability that a card chosen at random is black and 1?

Answer:

150 days

Step-by-step explanation:

6-4=2

100/2=50

50*3=150

The number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.

The rate of disintegration varies directly proportional to the quantity of the material.

As such, we can say:

[tex]\mathbf{=\dfrac{dN}{dt}\ \alpha \ N}[/tex]

[tex]\mathbf{\implies \dfrac{dN}{N}\ = k dt}[/tex]

Taking the integral form;

[tex]\mathbf{\implies \int \dfrac{dN}{N}\ =\int k dt}[/tex]

[tex]\mathbf{\implies In N =kt+ C---- (1)}[/tex]

When t = 0, N = 6 grams

In(6) = C

∴

When t = 100, N = 4 grams

In (4) = 100k + In6

100 k = 1n (4) - In(6)

[tex]\mathbf{100 k = In (\dfrac{4}{6})}[/tex]

[tex]\mathbf{k = \dfrac{1}{100} In(\dfrac{4}{6})}[/tex]

∴

From equation (1):

[tex]\mathbf{In N = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]

when,

[tex]\mathbf{In (3) = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]

[tex]\mathbf{\implies \dfrac{t}{100} In(\dfrac{4}{6}) = In \dfrac{ 3}{ 6}}[/tex]

[tex]\mathbf{t = 100\times \Big ( \dfrac{In (\dfrac{ 3}{ 6})}{ In(\dfrac{4}{6}) }\Big) }[/tex]

[tex]\mathbf{t = 100\times \Big ( \dfrac{0.69314}{ 0.40048}\Big) }[/tex]

t = 173.077 days

Therefore, the number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.

Learn more about radioactive materials here:

https://brainly.com/question/24339152?referrer=searchResults

Answer:

x² + x - 72 = 0 can be factored into (x - 8)(x + 9) = 0 to find your answer.

Step-by-step explanation:

Step 1: Distribute x

x² + x = 72

Step 2: Move 72 over

x² + x - 72 = 0

Step 3: Factor

(x - 8)(x + 9) = 0

Step 4: Find roots

x - 8 = 0

x = 8

x + 9 = 0

x = -9

Answer:

x² + x - 72 = 0 ⇒ (x - 8)(x + 9) = 0

Step-by-step explanation:

Let the first consecutive integer be x.

Let the second consecutive integer be x+1.

The product of the two consecutive integers is 72.

x(x + 1) = 72

x² + x = 72

Subtracting 72 from both sides.

x² + x - 72 = 0

Factor left side of the equation.

(x - 8)(x + 9) = 0

Set factors equal to 0.

x - 8 = 0

x = 8

x + 9 = 0

x = -9

8 and -9 are not consecutive integers.

Try 8 and 9 to check.

x = 8

x + 1 = 9

x(x+1) = 72

8(9) = 72

72 = 72

True!

The two consecutive integers are 8 and 9.

Answer:

g ( x ) = 4x^2 + 10

Step-by-step explanation:

Solution:-

The translation of a function f ( x ) in the cartesian coordinate domain can be done by following the given guidelines:

Translation guidelines

    Horizontal shifts

  Vertical shifts

   General shift ( Horizontal and Vertical shift )

               f ( x ) - > f ( x ± a ) ± b

We are given a function f ( x ) which is to be translated vertically upward 4 units. We will use the guidelines for Vertical shifts, where in this case the magnitude of b = 4.

                        f ( x ) = 4x^2 + 6

                        f ( x ) - > f ( x ) + b              

                        g ( x ) = f ( x ) + 4

                        g ( x ) = 4x^2 + 6 + 4

                        g ( x ) = 4x^2 + 10   ... Answer

Answer:

[tex]\huge\boxed{\bigg(\dfrac{a}{2};\ \dfrac{a}{2}\bigg)}[/tex]

Step-by-step explanation:

The formula of a midpoint:

[tex]M\bigg(\dfrac{x+1+x+2}{2};\ \dfrac{y_1+y_2}{2}\bigg)[/tex]

We have the points

[tex]A(0;\ 0)\to x_1=0;\ y_1=0\\\\C(a;\ a)\to x_2=a;\ y_2=a[/tex]

Substitute:

[tex]\dfrac{x_1+x_2}{2}=\dfrac{0+a}{2}=\dfrac{a}{2}\\\\\dfrac{y_1+y_2}{2}=\dfrac{0+a}{2}=\dfrac{a}{2}[/tex]

Answer:

The answer is (a/2,a/2)

Step-by-step explanation:

Fill in 2 then a

In conclusion (a/2,a/2)

Answer:

C

Step-by-step explanation:

Any point (x, y) on the parabola is equidistant from the focus and the directrix.

Using the distance formula

[tex]\sqrt{(x-3)^2+(y-1)^2}[/tex] = | y - 3 | ← square both sides

(x - 3)² + (y - 1)² = (y - 3)² ← expand the y- factors

(x - 3)² + y² - 2y + 1 = y² - 6y + 9 ← subtract y² - 2y + 1 from both sides

(x - 3)² = - 4y + 8 ( subtract 8 from both sides )

(x - 3)² - 8 = - 4y ( divide both sides by - 4 )

- [tex]\frac{1}{4}[/tex] (x - 3)² + 2 = y, that is

y = - [tex]\frac{1}{4}[/tex] (x - 3)² + 2 → C

Answer:

Step-by-step explanation:

C) y = –1∕4 (x – 3)^2 + 2

Answer:

45.5 km

Step-by-step explanation:

18.3 km + 27.2 km = 45.5 km or 45 km and 500 m

Answer:

45.5km

Step-by-step explanation:

The distance between the locksmith and the furniture=18.3km

The distance between the furniture and the hotel=27.2km

S(locksmith)+S(furniture)=S(hotel)

18.3km+27.2km=45.5km

Hope this helps ;) ❤❤❤

Let me know if there is an error in my answer.

Answer:

Inequality:  [tex]1558 + 60 x \geq 2158[/tex]

Number of Weeks:  [tex]x \geq 10[/tex]

Step-by-step explanation:

Given

[tex]Initial\ Savings = \$1558[/tex]

[tex]Amount\ Needed = \$2158[/tex]

[tex]Additional\ Savings = \$60\ weekly[/tex]

Required

Represent this using an inequality

Represent the number of weeks as x;

This implies that, She'll save $60 * x in x weeks

Her total savings after x weeks would be

[tex]Initial\ Savings + 60 * x[/tex]

From the question, we understand that she needs at least 2158;

Mathematically, this can be represented as (greater than or equal to 2158)

[tex]\geq 2158[/tex]

Bringing the two expressions together;

[tex]Initial\ Savings + 60 * x \geq 2158[/tex]

Substitute 1558 for Initial Savings

[tex]1558 + 60 * x \geq 2158[/tex]

[tex]1558 + 60 x \geq 2158[/tex]

Hence, the inequality that represents the situation is [tex]1558 + 60 x \geq 2158[/tex]

Solving further for x (number of weeks)

[tex]1558 + 60 x \geq 2158[/tex]

Subtract 1558 from both sides

[tex]1558- 1558 + 60 x \geq 2158 - 1558[/tex]

[tex]60x \geq 600[/tex]

Divide both sides by 60

[tex]\frac{60x}{60} \geq \frac{600}{60}[/tex]

[tex]x \geq 10[/tex]

This means that she needs to save $60 for at least 10 weeks

Answer:

Its the first one

Step-by-step explanation:

I just did it lol

Answer: i believe it’s 0.28, but tbh i’m on a unit test so i can’t see what’s wrong and what’s right. good luck!

Step-by-step explanation:

Answer:

c- 0.28

Step-by-step explanation:

Answer:

a = 8.1

Step-by-step explanation:

Firstly, since we have a triangle, automatically, we have 3 interior angles

Mathematically the sum of these angles = 180

A + B + C = 180

27 + 25 + C = 180

52 + C = 180

C = 180-52

C = 128

We use the sine rule to find a

The sine rule posits that the ratio of a side to the sine of the angle facing that side is equal for all the sides of a triangle

Thus, mathematically according to the sine rule;

c/Sin C = a/Sin A

14/sin 128 = a/sin 27

a = 14sin27/sin 128 = 8.0657

which to the nearest tenth is 8.1

Answer:

[tex]Total\ Selection = 30\ ways[/tex]

Step-by-step explanation:

Given

Girls = 3

Boys = 5

Required

How many ways can 2 boys and girls be chosen?

The keyword in the question is chosen;

This implies combination and will be calculated as thus;

[tex]Selection =\ ^nC_r = \frac{n!}{(n-r)!r!}[/tex]

For Boys;

n = 5 and r = 2

[tex]Selection =\ ^5C_2[/tex]

[tex]Selection = \frac{5!}{(5-2)!2!}[/tex]

[tex]Selection = \frac{5!}{3!2!}[/tex]

[tex]Selection = \frac{5 * 4 * 3!}{3!*2 * 1}[/tex]

[tex]Selection = \frac{20}{2}[/tex]

[tex]Selection = 10[/tex]

For Girls;

n = 3 and r = 2

[tex]Selection =\ ^3C_2[/tex]

[tex]Selection = \frac{3!}{(3-2)!2!}[/tex]

[tex]Selection = \frac{3!}{1!2!}[/tex]

[tex]Selection = \frac{3 * 2!}{1 *2!}[/tex]

[tex]Selection = \frac{3}{1}[/tex]

[tex]Selection = 3[/tex]

Total Selection is calculated as thus;

[tex]Total\ Selection = Boys\ Selection * Girls\ Selection[/tex]

[tex]Total\ Selection = 10 * 3[/tex]

[tex]Total\ Selection = 30\ ways[/tex]

Step-by-step explanation:

Let us assume that 1/2+root 3 is rational . So 1/2+root 3 = a/b where a and b are irrationals. since rhs is a rational number root 3 should be also rational .

Answer: Null Hypothesis [tex]H_{0}[/tex]: p = 0.18

              Alternative Hypothesis [tex]H_{a}[/tex]: p < 0.18

Step-by-step explanation: When doing an experiment, first define the hypotheses you want to test. These hypotheses are Null Hypothesis and Alternative Hypothesis

Null Hypothesis is a general assumption and discloses that there is no relationship between the conditions under consideration. It is the hypothesis the researcher is trying to disprove. It is denoted by the symbol [tex]H_{0}[/tex].

For the college graduate curiosity, the hypothesis the graduate is trying to disprove is that the proportion of students who have loan debt after 20 years of graduation is 18%. Then, Null Hypothesis is [tex]H_{0}[/tex]: p = 0.18

Alternative Hypothesis is the a statement describing a relationship between the collected data. It is what researches try to prove and the results are observations of real causes. It is denoted by the symbol [tex]H_{a}[/tex].

For the graduate study, the alternative is that the proportion is less tahn 18% or 0.18. Then, Alternative Hypothesis: [tex]H_{a}[/tex]: p < 0.18

Answer:

3051.08 cm squared

Step-by-step explanation:

The equation to find lateral surface area of a cone:

SA = pi r sqrt(h^2 * r^2)

Plug your values in.

SA = 3.14 * 9 * sqrt(144*81)

SA = 3.14 * 9 * 108

SA = 3051.08

The lateral surface area is 3051.08 cm squared.

Answer:

424.12cm^2

Step-by-step explanation:

make sure you have the radius, half of the diameter!

remember to use this formula! Lateral surface area = πrs = πr√(r2 + h2)

hope this helped!

r=radius

h=hight

s=slant

Answer:

Step-by-step explanation:

[tex]\frac{x-1}{2} =t\\\frac{y-2}{3} =t\\\frac{z-3}{4} =t\\so~eq.~of~line~L_{1}~is\\\frac{x-1}{2} =\frac{y-2}{3} =\frac{z-3}{4} \\its~d.r's~are~2,3,4\\again~\frac{x-2}{1} =s\\\frac{y-4}{2} =s\\\frac{z+1}{-4} =s\\so~eq. ~of~line~L_{2}~is\\\frac{x-2}{1} =\frac{y-4}{2} =\frac{z+1}{-4} \\its~d.r's ~are~1,2,-4\\let ~the ~d.r's~of~line~perpendicular~to~both~L_{1}~and~L_{2}~be~a,b,c,~then~\\2a+3b+4c=0\\1a+2b-4c=0\\solving\\\frac{a}{3*-4-4*2} =\frac{b}{4*1-2*-4} =\frac{c}{2*2-3*1} \\[/tex]

[tex]\frac{a}{-20} =\frac{b}{-4} =\frac{c}{1} \\d.r's~of ~reqd~line~is~-20,-4,1~or~20,4,-1[/tex]

now you find the point of intersection.

then calculate the angle.

Answer:

Step-by-step explanation:

f(x)=4x+5

g(x)=6x+4,

first: (f*g)=(4x+5) (6x+4)=24x²+46x+20

next:(f*g)(0)=((g*f)=24x²+46x+20=20

Hi,

f°g means :  apply first g then f . so calculate  "g" and then use result as "x" in f.  

g°f  means :   you apply first  f then g  

so :  f°g =    4 (g (x)) +5  

4 (6x+4) +5  = 24x+16+5 = 24x+21

Answer:

Step-by-step explanation:

Simplify each term.

y ≤ −2x/5 + 2

Find the slope and the y-intercept for the boundary line.

Slope: -2/5

Y-intercept: 2

Graph a solid line, then shade the area below the boundary line since

y is less than -2x/5 + 2

y ≤ −2x/5 + 2

Hope this can help

Answer:

65 dinners are expected to show up

The standard deviation of the distribution is 3.13

Step-by-step explanation:

Given

Proportion = 15%

Population = 77

Required

Expected Number that'll show up

Standard Deviation

If 15% won't show up; then

100% - 15% = 85% will show up

Expected Number, E(x) of Dinner is calculated as thus;

[tex]E(x) = np[/tex]

Where [tex]p = 85\%[/tex] (calculated above)

and [tex]n = 77[/tex]

Convert p to decimal

[tex]p = 0.85[/tex]

So;

[tex]E(x) = 0.85 * 77[/tex]

[tex]E(x) = 65.45[/tex]

[tex]E(x) = 65[/tex]

65 dinners are expected to show up

Calculating Standard Deviation, SD

Standard Deviation is calculated as;

[tex]SD = \sqrt{np(1-p)}[/tex]

Substitute 0.85 for p and 77 for n

[tex]SD = \sqrt{77 * 0.85 * (1-0.85)}[/tex]

[tex]SD = \sqrt{77 * 0.85 * 0.15}[/tex]

[tex]SD = \sqrt{9.8175}[/tex]

[tex]SD = 3.13328900678[/tex]

[tex]SD = 3.13[/tex] (Approximated)

The standard deviation of the distribution is 3.13

Answer:

There are 23 people in line at 6:00 A.M

Step-by-step explanation:

When you plug in h=1, we get 23 people

h corresponds with the time 6:00 am, as a result there are 23 people in line

The equation represents how many people will come as the hour increases.

23 represents the initial amount of people in line.

(got this from Khan academy too:))

Answer:

The dog will eat 3 lbs

Step-by-step explanation:

Take the amount eaten per day and multiply by the number of days

3/4 * 4 = 3

The dog will eat 3 lbs

Answer:

3 pounds

Step-by-step explanation:

Multiply the amount of dog food per day with the number of days.

[tex]\frac{3}{4} \times 4[/tex]

[tex]\frac{12}{4} =3[/tex]

In 4 days, Jamie's dog will eat 3 pounds of dog food.

Answer:

49145 years

Step-by-step explanation:

In a certain country the life expectancy for women in 1990 was 45 and in 2000 it was 85?years.

Assuming that life expectancy between 2000 and 2100 increases by the same percentage as it did between 1900 and 2000,what will life expectancy be for women in 2100?

In 10 years, the expectancy increased by 85/45 = 17/9

between 2000 and 2100, it will increas by 10 time 10 years, so expected expectancy is  [tex]85*(\frac{85}{45})^{10} = 49145[/tex]  years

The life expectancy for women will be 49145 years when It will increase by ten times between 2000 and 2100.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ  in mathematics, where x is the independent variable

In one country, women's life expectancy was 45 years in 1990 and 85 years in 2000.

Assuming that life expectancy grows by the same proportion between 2000 and 2100 as it did between 1900 and 2000, we have to determine the life would  expectancy for women in 2100

Over a ten-year period, life expectancy rose by 85/45 = 17/9.

It will increase by ten times between 2000 and 2100, therefore the anticipated life expectancy will be

⇒ 85×(85/45)¹⁰

⇒ 85×(1.88)¹⁰

⇒ 49145 years

Hence, the life expectancy for women will be 49145 years

Learn more about exponential function here:

brainly.com/question/11487261

#SPJ2

Answer:

The answer is option B.

Step-by-step explanation:

six less than a number is written as

x - 6

Hope this helps you

Answer:

a)   x₁ = 14

     x₂ = - 6

b) x = 4

c) P(max ) = 4000000 $

Step-by-step explanation:

To find the axis of symmetry we solve the equation

a) -4x² + 32x + 336 = 0

4x²  - 32x  - 336  = 0       or    x² - 8x - 84 = 0

x₁,₂ = [ -b ± √b² -4ac ]/2a

x₁,₂ = [ 8  ±√(64) + 336 ]/2

x₁,₂ = [ 8  ± √400 ]/2

x₁,₂ =( 8 ± 20 )/2

x₁  = 14

x₂ = -6

a) Axis of symmetry must go through the middle point between the roots

x = 4 is the axis of symmetry

c) P = -4x² + 32x + 336

Taking derivatives on both sides of the equation we get

P´(x) = - 8x + 32  ⇒  P´(x) = 0     - 8x + 32

x = 32/8

x = 4    Company has to sell  4 ( 4000 snowboard)

to get  a profit :

P = - 4*(4)² + 32*(4) + 336

P(max) = -64  + 128 + 336

P(max) = 400           or  400* 10000 =  4000000

Answer:

d. 5250 pounds

Step-by-step explanation:

25 lbs per day

There are 30 days in april

25 lbs/ day * 30 days

1 tiger would eat 750 lbs

There are 7 tigers

7 * 750 =5250 lbs

Answer:

D. 5250 pounds

Step-by-step explanation:

What you need to do is multiply 25 pounds by 30 because there are 30 days in the month of April.

25 x 30 = 750

Then multiply that amount by seven because there are 7 tigers.

750 x 7 = 5250

Answer:

Your answer is correct ✔️

Step-by-step explanation:

Hope this is correct and helpful

HAVE A GOOD DAY!

Answer:

2√3 + 3i is the answer

Step-by-step explanation:

Answer:

57

Step-by-step explanation:

f(15)=4(15)-3

f(15)=60-3

f(15)=57

Hope that helps, tell me if you need more help

Answer:

57

Step-by-step explanation:

If you plug 15 into the equation, you get f(15)=4(15)-3

60-3

57

:)

Answer:

(-2,-110)

Step-by-step explanation:

First solve for x

20x−70=70x+30

x= -2

Now substitute x for -2

y=20x−70

y=20(-2)-70

y = -110

The lowest common denominator is lcm(5, 3), which is 15.

The sum of 2/5 + 5/3 + 9/3 is 6/15 + 25/15 + 45/15, which is 76/15 or [tex]5\frac{1}{15}[/tex].

Answer:

366

Step-by-step explanation:

2×3+4×100-50+10​

PEMDAS says multiply and divide from left to right

6 + 400 - 50 +10

Then add and subtract

406-50+10

356+10

366

Answer:

[tex]\boxed{366}[/tex]

Step-by-step explanation:

[tex]2 \times 3+4 \times 100-50+10[/tex]

Multiplication is first.

[tex]6+400-50+10[/tex]

Add or subtract the numbers.

[tex]350+10+6[/tex]

[tex]366[/tex]

Answer:

(0,2)

Step-by-step explanation:

solve by addition/elimination

2x + 3y= 6

–3x + 5y = 10  

multiply first equation by 3  and second one by 2 to eliminate x)

6x+9y=18

-6x+10y=20 (add the two equations)

6x+9y-6x+10y=38

19y=38

y=38/19=2

2x+3y=6

2x=6-6

x=0

Answer:

a

Step-by-step explanation:

Answer:

P(X' < 4265) = 0.9418

Step-by-step explanation:

Due to the fact that the population is normal, the distribution of the sample mean of 40 cars is;

X' = (x1 + x2 + x3....... + x40)/40

We are given;

Normal mean;μ = 4178 miles

Variance = 124,609

Standard deviation; σ = √variance = √124609 = 353

Formula for standard error of mean = σ/√n = 353/√40 = 55.814

So from the formula;

z = (x - μ)/(σ/√n)

So for P(X' < 4265) we have;

z-value of P(X' < 4265) = (4265 - 4178)/55.814 ≈ 1.56

From the z-table attached, we have for P(z < 1.56) = 0.94179

Approximating to 4 decimal places gives 0.9418