It is estimated that 52% of drivers text while driving. How many people should a police officer expect to pull over until she finds a driver NOT texting while driving?

Answer:

1/2

Step-by-step explanation:

The numbers that are 6 or even on the cards are 2, 4, and 6.

3 cards out of a total of 6 cards.

3/6 = 1/2

Answer:

1/2 chance

Step-by-step explanation:

There are 3 numbers that fit the rule, 2, 4, and 6. 3/6 chance of picking one or 1/2, simplified.

Answer:

Step-by-step explanation:

Hello, this is a geometric sequence so we are looking for a multiplicative factor.

[tex]a_0=600\\\\a_1=a_0 \cdot \boxed{\dfrac{1}{2}} = 300 = 600 \cdot \boxed{\dfrac{1}{2}}\\\\a_2=a_1 \cdot \boxed{\dfrac{1}{2}} = 150= 300 \cdot \boxed{\dfrac{1}{2}}\\\\a_3=a_2 \cdot \boxed{\dfrac{1}{2}} = 75 = 150 \cdot \boxed{\dfrac{1}{2}}[/tex]

So, the explicit formula is for n

[tex]\boxed{a_n=a_0\cdot \left(\dfrac{1}{2}\right)^n=600\cdot \left(\dfrac{1}{2}\right)^n}}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

The explicit rule is aₙ = a₀(1/2)ⁿ = 600(1/2)ⁿ for the given geometric sequence.

The geometric series defined as a series represents the sum of the terms in a finite or infinite geometric sequence. The successive terms in this series share a common ratio.

The nth term of a geometric progression is expressed as

Tₙ = arⁿ⁻¹

Where a is the first term, r is the common ratio.

We have been given that geometric sequence as:

600, 300, 150, 75, ...

To determine the explicit rule for the geometric sequence, we have to find the common ratio.

Here the first term (a₀) is 600

So the common ratio = 300/600 = 150/300 = 75/150 = 1/2

Thus, the explicit formula for n would be:

aₙ = a(1/2)ⁿ = 600(1/2)ⁿ

Therefore, the explicit rule is aₙ = a(1/2)ⁿ = 600(1/2)ⁿ for the given geometric sequence.

Learn more about the geometric series here:

brainly.com/question/21087466

#SPJ2

Answer:

y-int = C/B

Step-by-step explanation:

Ax + By = C

y-int = C/B

Answer:

I hope this helps.

Step-by-step explanation:

Answer:

He rode farther on Sunday

135/7 - 139/8 = 107/56 or 1 51/56 miles farther

Answer:D

Step-by-step explanation: I got a hundred on my test.

Answer:

138 pound

Step-by-step explanation:

Given

A certain medicine is given in an amount proportional to a patients body weight.

thus,

ratio will be

amount of medicine: weight of patient

Given

Suppose a person weighted 104 pounds requires 156 milligrams of medicine.

amount of medicine = 156 milligram

weight of patient = 104 pound

Thus, ratio will be = 156/104

___________________________

What is the weight of a patient who requires 207 milligrams of medicine

Let the weight of weight of patient here be x

thus, ratio in this case will be

207/x

we also know in ratio and proportion that

if two ratio a:b and c:d are equal then a:c = c:d

here also the ratio will be same

Thus,

156/104 = 207/x

=> 156x = 207*104 = 21,528

=> x = 21,528/156 = 138

Thus, weight of patient is 138 pound.

Answer:

Perimeter is when you add up all of the sides, and the area is when you multiply length times width.

Answer:

the last one is correct

Step-by-step explanation:

hello,

-4(-11+4n)-3(-2n+9) = 44 - 16n + 6n - 27 = -10n + 17

hope this helps

Answer:

SOLUTION SET={x<-3/2   or   x≥48/5} option A

Step-by-step explanation:

12x+7<-11                           and            5x-8≥40

solving the both inequalities

12x+7-7<-11-7                     and             5x-8+8≥40+8

12x<-18                              and              5x≥48

12x/12<-18/12                     and               5x/5≥48/5

x<-3/2                                and               x≥48/5

SOLUTION SET={x<-3/2   or   x≥48/5}

i hope this will help you :)

Answer:

  the height of the cylinder is 7 units greater than the radius

Step-by-step explanation:

When you match the forms of the equations ...

  [tex]V=\pi r^2(r+7)\\V=\pi r^2h[/tex]

you see that the factor (r+7) corresponds to the height (h) of the cylinder. That is ...

  the height of the cylinder is 7 units greater than the radius.

Answer: D, 28 bottles.

Step-by-step explanation:

This can be translated to:

26.5 liters of water and 8.25 liters of orange juice are mixed together. All that mixture  is bottled in bottles of  1.25 liters. How many bottles are needed  to fill all the orange juice mixture?

the total mass of mixture that we have is:

26.5 L + 8.25 L = 34.75 L.

if we want to divide it into groups of 1.25 L, we have:

N = 34.75/1.25 = 27.8

So we have 27.8 groups of 1.25L this means that we need 27.8 bottles.

But we can not have a 0.8 of a bottle, so we must round it up to 28 bottles.

Then the correct option is D:

Answer:

Step-by-step explanation:

1l ........8.5 miles

x l .......6 miles

-----------------------

x=6*1/8.5

x=0.70 l

2*0.7=1.4 l petrol/day ( to work and come back home)

5*1.4=7 l/week ( 5 days works in a week)

7*1.26=8.82 L /week

8.82>8.5

The petrol costs more

So the answer is NO

Answer:

  A'Y' is parallel to AY

Step-by-step explanation:

If X is the center of dilation, the only lines that go through X after the dilation are the ones that go through X before the dilation: XY (and XY'), XZ (and XZ').

Line AY does not go through X, so A'Y' will not go through X. Rather, the line will be moved a distance from X according to the dilation factor. The line A'Y' will be parallel to AY.

Answer:

1

Step-by-step explanation:

=> [tex]4a^2-4ab+b^2[/tex]

Where a = 2, b = 3

=> [tex]4(2)^2-4(2)(3)+(3)^2[/tex]

=> 4(4) - 4(6) + 9

=> 16 - 24 + 9

=> -8 + 9

=> 1

Answer:

1.

Step-by-step explanation:

Substituting for a and b we have

4(2)^2 - 4*2*3 + (3)^2

= 16 - 24 + 9

= -8 + 9

= 1.

Answer:

56%

Step-by-step explanation:

We have a grid with 10 columns and 10 rows making 100 equal sized squares, they tell us that 5 rows are unshaded. Therefore half is unshaded, like so:

5 rows = 50 squares

They also tell us that the sixth row has 6 squares unshaded, which means that in total they would be:

 50 + 6 = 56 squares

Knowing that the total is 100, the percentage would be:

56/100 = 0.56, that is, 56% are unshaded

Answer:

data bar

Step-by-step explanation:

Answer:

chart

Step-by-step explanation:

please see the attached picture for full solution..

Hope it helps..

Good luck on your assignment...

Answer:

The probability of getting someone who tests positive, given that he or she did not have the disease = P(P|No) = 0.041

Step-by-step explanation:

Complete Question

The data represents the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tests positive, given that he or she did not have the disease.

P/N | Yes | No

+ve | 141 | 6

-ve | 11 | 142

Note that +ve and -ve l stands for testing positive and negative respectively.

Yes and No represents whether one has the disease or not respectively.

Solution

Let

- The event of testing positive be P.

- The event of testing negative be N.

- The event of having the disease be Yes.

- The event of not having the disease be No.

The probability of getting someone who tests positive, given that he or she did not have the disease = P(P|No)

The conditional probability of A given B is given mathematically as

P(A|B) = P(A n B) ÷ P(B)

Hence,

P(P|No) = P(P n No) ÷ P(No)

To solve these probabilities, we first define the probability of an event as the number of elements in that event divided by the Total number of elements in the sample space.

P(No) = n(No) ÷ n(Sample space)

n(No) = 6 + 142 = 148

n(Sample Space) = 141 + 11 + 6 + 142 = 300

P(No) = (148/300)

P(P n No) = n(P n No) ÷ n(Sample space)

n(P n No) = 6

n(Sample Space) = 300

P(P n No) = (6/300)

P(P|No) = P(P n No) ÷ P(No)

= (6/300) ÷ (148/300)

= (6/148)

= 0.0405405405 = 0.041 to 3 d.p.

Hope this Helps!!!

Answer:

3/4

Step-by-step explanation:

The numbers odd or less than 3 are 2, 3, and 5.

3 numbers out of 4.

P(odd or less than 3) = 3/4

Step-by-step explanation:

Sample proportion [tex]\hat{p} = 260/380 = 0.684[/tex]

90% confidence interval for p is

[tex]\hat{p} - Z\times \sqrt(\hat{p}( 1 - \hat{p}) / n) < p < \hat{p} + Z\times \sqrt(\hat{p}( 1 - \hat{p}) / n)[/tex]

[tex]0.684 - 1.645\times \sqrt ( 1 -0.684) / 380) < P < 0.684 + 1.645\times \sqrt ( 1 -0.684) / 380)[/tex]

0.645 < p < 0.723

Interpretation - We estimate with 90% confidence that the true population proportion of people who plan  on voting yes on the levy between 0.645 and 0.723.

Answer: c = 10

Step-by-step explanation:

Pythagorean Theorem states that in a right triangle [tex]a^2 + b^2 = c^2[/tex], where a and b  are the legs of the triangle and c is the hypotenuse.  Thus, because a=6 and b=8, 36+64=c².  Thus 100=c².  Thus 10=c

Answer:

Step-by-step explanation:

The Pythagorean theorem can be used to find the lengths of the segments at the top of the square. The left one is found from ...

  FA² = FE² +EA²

  13² -12² = EA² = 169 -144 = 25

  EA = √25 = 5

The right one is found from ...

  FB² = FE² +EB²

  15² -12² = EB² = 225 -144 = 81

  EB = √81 = 9

Then the length of the side of the square is ...

  AB = AE +EB = 5 +9

  AB = 14

__

The length of the diagonal can also be found using the Pythagorean theorem.

 AC² = AB² +BC² = 14² +14²

 AC = √(196 +196) = 14√2 ≈ 19.7990

Rounded to the nearest integer, AC ≈ 20.

Answer:

$18

Step-by-step explanation:

Buying the jeans for $27 leaves you with ($60 - $27), or $33.

Buying the shirt for s dollar leaves you with $15.  To find s, the price of the shirt, you subtract $15 from $33:  $18.

The shirt cost you $18.

Answer:

a) [g ° h](x)  = 3x² +6

b) [h ° g](x) =3 x²+36x+108

Step-by-step explanation:

Explanation:-

a)

Given g(x) = x+6 and h(x) = 3x²

Given [g ° h](x) = g(h(x))

                          = g(3x²)       (∵ h(x) =3x²)

                         = (3x²)+6      (∵ g(x) =x+6)

∴ [g ° h](x)  = 3x² +6

b)

Given [h ° g](x) = h (g(x))

                          = h(x+6)     (∵ g(x) =x+6)

                         = 3 (x+6)²    (∵ h(x) =3x²)

                         = 3 (x²+2(6)x+36)    (∵ (a + b)² = a²+2ab+b²)

                         = 3 (x²+12x+36)

                        = 3 x²+36x+108)

     ∴ [h ° g](x) =3 x²+36x+108

Answer:

x = 16

Step-by-step explanation:

(whole secant) x (external part) = (tangent)^2

(x+2) * 2 = 6^2

2(x+2) = 36

Divide each side by 2

x+2 = 18

Subtract 2

x+2-2 = 18-2

x = 16

Answer:

x = 16

Step-by-step explanation:

According to tangent-secant Theorem:

(Tangent)² = (External Part of the secant)(Whole Secant)

(6)² = (2)(2+x)

36 = 4+2x

Subtracting 4 from both sides

36-4 = 2x

=> 2x = 32

Dividing both sides by 2

Answer:

The difference of the functions is (f-g)(x) = 3x - 3

Step-by-step explanation:

In the problem, we are asked to find the difference of the two functions, f(x) and g(x). When we see (f-g)(x), this means that we are going to subtract g(x) from f(x).

f(x) = 5x - 2

g(x) = 2x + 1

(f-g)(x) = (5x - 2) - (2x + 1)

Distribute the negative to (2x + 1)

(f-g)(x) = 5x - 2 - 2x - 1

Combine like terms. Make sure your answer is in standard form.

(f-g)(x) = 3x - 3

So, the answer to the equation is (f-g)(x) = 3x - 3

Answer:

Step-by-step explanation:

hello,

I assume that you mean

[tex]h(x)=\dfrac{12}{x-1}[/tex]

so first of all let's take x real different from 1 , as this is not allowed to divide by 0

[tex](hoh^{-1})(x)=x=h(h^{-1}(x))=\dfrac{12}{h^{-1}(x)-1} \ \ \ so\\h^{-1}(x)-1=\dfrac{12}{x} \\\\h^{-1}(x)=1+\dfrac{12}{x}[/tex]

and this is defined for x real different from 0

hope this helps

Answer:

  (3.6, 0), (0, -2)

Step-by-step explanation:

To find the y-intercept, set x=0:

  -5·0 +9y = -18

  y = -18/9 = -2

To find the x-intercept, set y=0:

  -5x +9·0 = -18

  x = -18/-5 = 3.6

The intercepts are ...

  x-intercept: 3.6

  y-intercept: -2

Answer:

  f(4) = g(4) and f(0) = g(0)

Step-by-step explanation:

In order for f(x) = g(x), the value of x must be the same in both functions:

  f(4) = g(4) . . . corresponds to x=4

  f(0) = g(0) . . . corresponds to x=0

The graph is not shown here, so we cannot say if these are the appropriate solutions. We can only say that the other choices are not.

f(x) = g(x) if ...

  f(4) = g(4) and f(0) = g(0)

__

Something like f(0) = g(4) is useless for finding solutions to f(x) = g(x).

Answer:

Length of the sides of the base (x) = 7.606 ft

Height (h) = 3.802 ft

The minimum surface area is 173.55 ft²

Step-by-step explanation:

Surface area is given by:

[tex]S(x) = x^2+\frac{880}{x}[/tex]

The value of x for which the derivate of the surface area function is zero, is the length of the sides of the base that minimizes surface area:

[tex]S(x) = x^2+\frac{880}{x} \\\frac{dS(x)}{dx}=0=2x-\frac{880}{x^2}\\x^3=440\\x=7.606\ ft[/tex]

The height of the box is given by:

[tex]V=hx^2\\220 =h*7.606^2\\h=3.802\ ft[/tex]

The dimensions of the box with minimum surface area are:

Length of the sides of the base (x) = 7.606 ft

Height (h) = 3.802 ft

The absolute minimum is:

[tex]S(x) = 7.606^2+\frac{880}{7.606}\\S_{min}=173.55\ ft^2[/tex]

The minimum surface area is 173.55 ft²

Answer:

The absolute minimum of the surface area[tex]=173.55$ ft^2[/tex]

At the minimum surface​ area,

Step-by-step explanation:

Volume of the box =220 cubic feet.

[tex]\text{Surface Area, } S(x)=x^2+\dfrac{880}{x}[/tex]

To find the absolute minimum of the surface area function on the interval ​[tex](0,\infty)[/tex], we take the derivative of S(x) and solve for its critical points.

[tex]S(x)=\dfrac{x^3+880}{x}\\S'(x)=\dfrac{2x^3-880}{x^2}\\$Setting the derivative equal to 0\\S'(x)=\dfrac{2x^3-880}{x^2}=0\\2x^3-880=0\\2x^3=880\\$Divide both sides by 2\\x^3=440[/tex]

Take the cube root of both sides

[tex]x=\sqrt[3]{440}\\ x=7.61$ ft[/tex]

Therefore, the absolute minimum of the surface area function on the interval [tex](0,\infty)[/tex], is:

[tex]S(x)=\dfrac{7.61^3+880}{7.61}\\\\=173.55$ ft^2[/tex]

Since the volume of the box =220 cubic feet

[tex]V=x^2h\\220=7.61^2 \times h\\h=220 \div 7.61^2\\h=3.80 ft[/tex]

The dimensions of the box with the minimum surface​ area are base length of 7.61 feet and height of 3.8 feet.