g A recent newspaper article claims that 68% of car accidents involve some evidence of distracted driving. A police officer questions this claim, and pulls a random sample of 85 accident reports. If 63 of them involve distracted driving, is this enough evidence to show that the proportion of car accidents involve some evidence of distracted driving is significantly greater than than reported by the newspaper? (Use α α=0.10)

Answer:

0.07

Step-by-step explanation:

The number of sophmores is 2+25+3 = 30.

Of these sophmores, 2 drive to school.

So the probability that a student drives to school, given that they are a sophmore, is 2/30, or approximately 0.07.

Answer:

[tex]\large \boxed{0.07}[/tex]

Step-by-step explanation:

The usual question is, "What is the probability of A, given B?"

They are asking, "What is the probability that you are driving to school if you are a sophomore (rather than taking the bus or walking)?"

We must first complete your frequency table by calculating the totals for each row and column.

The table shows that there are 30 students, two of whom drive to school.

[tex]P = \dfrac{2}{30}= \mathbf{0.07}\\\\\text{The conditional probability is $\large \boxed{\mathbf{0.07}}$}[/tex]

Answer:

  r(n) = 1000·(2/5)^n

Step-by-step explanation:

Since the tortoise travels 3/5 the remaining distance, the remaining distance at the end of the day is 2/5 of what it was at the beginning of the day. So, the function can be modeled by an exponential with a "growth" factor of 2/5:

  r(n) = 1000·(2/5)^n

where r(n) is the number of remaining feet after n days of travel.

Answer:

Width = 8 ft

Length = 53 ft

Height = 9 ft

Step-by-step explanation:

Let width be x

Length will be 8x-11

Height will be x + 1

Volume = width x height x length

=

x * (8x-11) * (x+1) = 3816

(8x^2 - 11x) * (x+1) = 3816

8x^3 + 8x^2 - 11x^2 - 11x = 3816

8x^3 -3x^2 - 11x = 3816

8x^3+64x^2-61x^2-488x +477x-3816= 0

8x^2 (x-8)+61x(x-8)+488(x-8)

(x-8)(8x^2 + 61x + 477) = 0

x-8

8x^2 + 61x + 477 = 0

Solve the equations:

x = 8

Length = 8x -11 = 64-11 = 53

Height = 8+1 = 9

Answer:

8w^3-3w^2-11w=3816

Step-by-step explanation:

Find the equation, in terms of w, that could be used to find the dimensions of the trailer in feet. Your answer should be in the form of a polynomial equals a constant.

Step-by-step explanation:

If all three sides have the same length then it's an equilateral triangle, if two sides are congruent then it's an isosceles triangle, and if there are no sides that have the same length then it's a scalene triangle.

Answer:

Sample Response: First, look at the side lengths a, b, and c, where c is the longest. Then take the sum of a squared and b squared and compare it to c squared. If they are equal, the triangle is a right triangle. If c squared is less than a squared plus b squared, the triangle is acute. If c squared is greater than a squared plus b squared, the triangle is obtuse.

Step-by-step explanation:

booyah

Answer:

Solution,

Let the points be A and B

A(7,-1)--->( X1,y1)

B(6,-4)---->(x2,y2)

Now,

[tex] slope = \frac{y2 - y1}{x2 - x1} \\ \: \: \: \: \: \: = \frac{ - 4 - ( - 1)}{6 - 7} \\ \: \: \: \: \: \: = \frac{ - 4 + 1}{ - 1} \\ \: \: \: \: \: = \frac{ - 3}{ - 1} \\ \: \: \: \: = 3[/tex]

Hope this helps..

Good luck on your assignment..

Answer:

-1/3  (given that the first co-ordinate is the initial point)

Step-by-step explanation:

slope of a line is basically the change in y divided by the change in x.

we have the 2 co-ordinates (7,-1) , (6,-4)

lets find the change in x  = 7 - 6 (the difference of the x - values of both the coordinates)

change in y = -1 - (-4)

change in x  = -1

change in y  = 3

now, slope is change in y / change in x

slope  = -1/3

Answer:

-(14 - 7x)

7(x - 2)

3x - 14 + 4x

Step-by-step explanation:

The expressions have to equal 7x - 14.

-(14 - 7x)

-14 + 7x

7(x - 2)

7x - 14

3x - 14 + 4x

7x - 14

The equivalent expression for the given expression 7x - 14 will be 7(x – 2) and 3x – 14 + 4x.

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 that the expression is 7x – 14. The equivalent expression to 7x - 14 will be,

E = 7(x – 2)

E = 7x - 14

E = 3x - 14 + 4x

E = 3x+ 4x - 14

E = 7x - 14

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Answer:

[tex]3\frac{4}{5}[/tex]

Step-by-step explanation:

You first need to make the denominators the same and the LCM (least Common Multiple of this equation is 10.

10/10-->1

1/2--> 5/10

2--> 20/10

3/10, the denominator is already 10, so don't need to change.

10/10+5/10+20/10+3/10=38/10=[tex]3\frac{8}{10}[/tex]=[tex]3\frac{4}{5}[/tex]

Answer:

3 4/5

Step-by-step explanation:

hopefully this helped :3

Answer:

[tex] L= x[/tex]

And the width for this case is:

[tex] W= 5x^3 +4 -x^2[/tex]

And we know that the perimeter is given by:

[tex] P= 2L +2W[/tex]

And replacing we got:

[tex] P(x) = 2x +2(5x^3 +4 -x^2)= 2x +10x^3 +8 -2x^2[/tex]

And symplifying we got:

[tex] P(x)= 10x^3 -2x^2 +2x+8[/tex]

Step-by-step explanation:

For this problem we know that the lenght of the rectangle is given by:

[tex] L= x[/tex]

And the width for this case is:

[tex] W= 5x^3 +4 -x^2[/tex]

And we know that the perimeter is given by:

[tex] P= 2L +2W[/tex]

And replacing we got:

[tex] P(x) = 2x +2(5x^3 +4 -x^2)= 2x +10x^3 +8 -2x^2[/tex]

And symplifying we got:

[tex] P(x)= 10x^3 -2x^2 +2x+8[/tex]

Answer:

d.  a = 39

Step-by-step explanation:

Question:

for which value of "a" will the trinomial be factorizable.

x^2+ax-40

For the expression to have integer factors, a = sum of the pairs of factors of -40.

-40 has following pairs of factors

{(1,-40), (2,-20, (4,-10), (5,-8), (8, -5), (10,-4), (20,-2), (40,-1) }

meaning that the possible values of a are

+/- 39, +/- 18, +/- 6, +/- 3

out of which only +39 appears on answer d.  a=39

Answer:

Yes, he can buy 8 donuts and 4 energy drinks.

Step-by-step explanation:

If Tension is able to buy 8 donuts and 4 energy drinks, then both inequalities would be valid when we use these numbers as inputs. Let's check each expression at a time:

[tex]0.75*d + 2*e \leq 25\\0.75*8 + 2*4 \leq 25\\6 + 8 \leq 25\\14 \leq 25[/tex]

The first one is valid, since 14 is less than 25. Let's check the second one.

[tex]360*d + 110*e \geq 1000\\360*8 + 110*4 \geq 1000\\2880 + 440 \geq 1000\\3320 \geq 1000[/tex]

The second one is also valid.

Since both expressions are valid, Tension can buy 8 donuts and 4 energy drinks and achieve his goal of having a caloric surplus of at least 1000 cal.

The set of numbers that can represent the lengths of the sides of a triangle are 3,5,7. That is option B.

Triangle is defined as a type of polygon that has three sides in which the sum of both sides is greater than the third side.

That is to say, 3+5 = 8 is greater than the third side which is 7.

Therefore, the set of numbers the would represent a triangle are 3,5,7.

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Answer:

(a) Yes, there are 10 independent trials, each with exactly two possible outcomes, and a constant probability associated with each possible outcome.

(b) The probability that exactly 6 out of 10 randomly sampled 18- 20-year-olds consumed an alcoholic drink is 0.203.

(c) The probability that exactly 4 out of 10 randomly sampled 18- 20-year-olds have not consumed an alcoholic drink is 0.203.

(d) The probability that at most 2 out of 5 randomly sampled 18-20-year-olds have consumed alcoholic beverages is 0.167.

Step-by-step explanation:

We are given that data collected by the Substance Abuse and Mental Health Services Administration (SAMSHA) suggests that 69.7% of 18-20-year-olds consumed alcoholic beverages in 2008.

(a) The conditions required for any variable to be considered as a random variable is given by;

So, in our question; all these conditions are satisfied which means the use of the binomial distribution is appropriate for calculating the probability that exactly six consumed alcoholic beverages.

Yes, there are 10 independent trials, each with exactly two possible outcomes, and a constant probability associated with each possible outcome.

(b) Let X = Number of 18- 20-year-olds people who consumed an alcoholic drink

The above situation can be represented through binomial distribution;

[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......[/tex]

where, n = number of trials (samples) taken = 10 people

            r = number of success = exactly 6

            p = probability of success which in our question is % 18-20

                  year-olds consumed alcoholic beverages in 2008, i.e; 69.7%.

So, X ~ Binom(n = 10, p = 0.697)

Now, the probability that exactly 6 out of 10 randomly sampled 18- 20-year-olds consumed an alcoholic drink is given by = P(X = 6)

           P(X = 3) =  [tex]\binom{10}{6}\times 0.697^{6} \times (1-0.697)^{10-6}[/tex]

                         =  [tex]210\times 0.697^{6} \times 0.303^{4}[/tex]

                         =  0.203

(c) The probability that exactly 4 out of 10 randomly sampled 18- 20-year-olds have not consumed an alcoholic drink is given by = P(X = 4)

Here p = 1 - 0.697 = 0.303 because here our success is that people who have not consumed an alcoholic drink.

           P(X = 4) =  [tex]\binom{10}{4}\times 0.303^{4} \times (1-0.303)^{10-4}[/tex]

                         =  [tex]210\times 0.303^{4} \times 0.697^{6}[/tex]

                         =  0.203

(d) Let X = Number of 18- 20-year-olds people who consumed an alcoholic drink

The above situation can be represented through binomial distribution;

[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......[/tex]

where, n = number of trials (samples) taken = 5 people

            r = number of success = at most 2

            p = probability of success which in our question is % 18-20

                  year-olds consumed alcoholic beverages in 2008, i.e; 69.7%.

So, X ~ Binom(n = 5, p = 0.697)

Now, the probability that at most 2 out of 5 randomly sampled 18-20-year-olds have consumed alcoholic beverages is given by = P(X [tex]\leq[/tex] 2)

        P(X [tex]\leq[/tex] 2) = P(X = 0) + P(X = 1) + P(X = 3)

= [tex]\binom{5}{0}\times 0.697^{0} \times (1-0.697)^{5-0}+\binom{5}{1}\times 0.697^{1} \times (1-0.697)^{5-1}+\binom{5}{2}\times 0.697^{2} \times (1-0.697)^{5-2}[/tex]

=  [tex]1\times 1\times 0.303^{5}+5 \times 0.697^{1} \times 0.303^{4}+10\times 0.697^{2} \times 0.303^{3}[/tex]

=  0.167

Answer:

Step-by-step explanation:

Given the confidence interval of the heights of american heights given as (65.3,73.7);

Lower confidence interval L = 65.3 and Upper confidence interval U = 73.7

Sample mean will be the average of both confidence interval . This is expressed mathematically as [tex]\overline x = \frac{L+U}{2}[/tex]

[tex]\overline x = \frac{65.3+73.7}{2}\\\overline x = \frac{139}{2}\\\overline x = 69.5[/tex]

Hence, the sample mean is 69.5

Answer:

If our random variable of interest for this case is X="the number of teenagers between 12-17 with smartphone" we can model the variable with this distribution:

[tex] X \sim Binom(n=234, p=0.75)[/tex]

And the mean for this case would be:

[tex] E(X) =np = 234*0.75= 175.5[/tex]

And the standard deviation would be given by:

[tex] \sigma =\sqrt{np(1-p)}= \sqrt{234*0.75*(1-0.75)}= 6.624[/tex]

Step-by-step explanation:

If our random variable of interest for this case is X="the number of teenagers between 12-17 with smartphone" we can model the variable with this distribution:

[tex] X \sim Binom(n=234, p=0.75)[/tex]

And the mean for this case would be:

[tex] E(X) =np = 234*0.75= 175.5[/tex]

And the standard deviation would be given by:

[tex] \sigma =\sqrt{np(1-p)}= \sqrt{234*0.75*(1-0.75)}= 6.624[/tex]

Answer:

Reflection across the x-axis: (-4,2)

Reflection across the y-axis: (4,-2)

Step-by-step explanation:

Going based off of what I see, a reflection across the x axis changes "y" & the same rule applies to the y axis.

It should be an L shape.

Answer:

Option A

Step-by-step explanation:

Equation of the given quadratic function is,

y = 2x² + 8x + 3

y = 2(x² + 4x) + 3

  = 2(x² + 4x + 4 - 4) + 3

  = 2(x + 2)² - 8 + 3

  = 2(x + 2)² - 5

By comparing this equation with the equation of a quadratic function in vertex form,

y = a(x - h)² + k

Here (h, k) is the vertex of the parabola

Vertex of the given equation will be (-2, -5) and coefficient 'a' is positive (a > 0)

Therefore, vertex will lie in the 3rd quadrant and the parabola will open upwards.

Option (A). Graph A will be the answer.

Answer:

[tex]\dfrac{dx}{dt}=-1.3846$ sales per day[/tex]

Step-by-step explanation:

The price​ p, in​ dollars, and the number of​ sales, x, of a certain item follow the equation: 6p+3x+2px=69

Taking the derivative of the equation with respect to time, we obtain:

[tex]6\dfrac{dp}{dt} +3\dfrac{dx}{dt}+2p\dfrac{dx}{dt}+2x\dfrac{dp}{dt}=0\\$Rearranging$\\6\dfrac{dp}{dt}+2x\dfrac{dp}{dt}+3\dfrac{dx}{dt}+2p\dfrac{dx}{dt}=0\\\\(6+2x)\dfrac{dp}{dt}+(3+2p)\dfrac{dx}{dt}=0[/tex]

When x=3, p=5 and [tex]\dfrac{dp}{dt}=1.5[/tex]

[tex](6+2(3))(1.5)+(3+2(5))\dfrac{dx}{dt}=0\\(6+6)(1.5)+(3+10)\dfrac{dx}{dt}=0\\18+13\dfrac{dx}{dt}=0\\13\dfrac{dx}{dt}=-18\\\dfrac{dx}{dt}=-\dfrac{18}{13}\\\\\dfrac{dx}{dt}=-1.3846$ sales per day[/tex]

The number of sales, x is decreasing at a rate of 1.3846 sales per day.

Answer:

Side 1: 40 feet

Side 2: 20 feet

Side 3: 22 feet

Step-by-step explanation:

Side 1 is twice the length of side 2 and side 2 is 20 feet, which means side 1 is 40 feet. Side 3 is the the length of the second side plus 2, which means it has a length of 22 feet.

Answer:

B, C, A

Step-by-step explanation:

If one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side.

Draw the triangle.

AC (7) is opposite from B

AB (8) is opposite from C

BC (10) is opposite from A

From smallest to largest: 7>8>10

7, 8, 10

or

B, C, A

Answer:

Step-by-step explanation:

Identify the variable in each term. If two or more terms have the same variable, they are "like" terms.*

1) Like terms are found in selection b. They are 7r and r.

__

2) The variables in selection d are u and y, not the same. Only unlike terms are found in selection d. (Selection b has variables x, b, x. The x-terms are like terms and can be combined.)

_____

* Strictly speaking, it is the constellation of variables you want to match. For example, terms 3xy, 4xy², and -5x²y all have variables x and y, but the powers of those variables don't match from term to term. For terms to be "like", the variables and their powers need to match.

Answer:

See explanation below

Explanation:

1) Option C is correct.

The average difference in husband and wife marriage ages in Cumberland County; μd

2) Option D is correct.

Null: The average difference in marriage ages in Cumberland County is 0.

Alt: The average difference in marriage ages is greater than 0.

3) Option A is correct

Null: μd = 0

Alt: μd > 0

4) Given:

n = 24

d' = 1.875

Sd = 4.812

Find test statistic:

[tex] t = \frac{d'}{Sd/\sqrt{n}} [/tex]

[tex] = \frac{1.875}{4.812/\sqrt{24}} [/tex]

[tex] t = 1.909 [/tex]

Degree of freedom, df = n - 1 = 24 - 1 = 23

Pvalue [tex] = (t_2_3 > 1.909) = 0.0344 [/tex]

Pvalue = 0.0344

Significance level = 0.05

5) Since p value is less than significance level, reject null hypothesis H0

Hence, there is strong evidence that, on average, husbands are older than their wives in Cumberland County

Answer:

CDA

Step-by-step explanation:

Dude trust me...

Answer:

The probability is 12.66%.

This is a low probability, so it is unlikely for such a combined sample to test positive.

Step-by-step explanation:

If the probability of being infected is 0.005, the probability of not being infected is 0.995.

Then, to find the probability of at least one of the 27 people being infected P(A), we can find the complementary case: all people are not infected: P(A').

[tex]P(A') = 0.995^{27}[/tex]

[tex]P(A') = 0.8734[/tex]

Then we can find P(A) using:

[tex]P(A) + P(A') = 1[/tex]

[tex]P(A) = 1 - 0.8734[/tex]

[tex]P(A) = 0.1266 = 12.66\%[/tex]

This is a low probability, so it is unlikely for such a combined sample to test positive.

Answer

X= 64.8 gives the minimum average cost

Explanation:

The question can be interpreted as

C(x)= 5x^3 -40^2 + 21000x

To find the minimum total cost, we will need to find the minimum of

this function, then Analyze the derivatives.

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Step-by-step explanation:

With the packaging of 8

48 cookies = 48 ÷ 8 = 6 boxes

With the packaging of 24

48 cookies = 48 ÷ 24 = 2 boxes

Answer:

46 logs on the 5th row.

Step-by-step explanation:

Number of logs on the nth row is

n =  50 - (n-1)

 n = 51 - n    (so on the first row we have  51 - 1 = 50 logs).

So on the 5th row we have 51 - 5 = 46 logs.

The given relation is an arithmetic progression, which can be solved using the recursive formula: aₙ = aₙ₋₁ + d.

The 5th row has 46 logs.

An arithmetic progression is a special series in which every number is the sum of a fixed number, called the constant difference, and the first term.

The first term of the arithmetic progression is taken as a₁.

The constant difference is taken as d.

The n-th term of an arithmetic progression is found using the explicit formula:

aₙ = a₁ + (n - 1)d.

The recursive formula of an arithmetic progression is:

aₙ = aₙ₋₁ + d.

In the question, we are informed that logs are stacked in a pile. The bottom row has 50 logs and the next bottom row has 49 logs. Each row has one less log than the row below it.

The number of rows represents an arithmetic progression, with the first term being the row in the bottom row having 50 logs, that is, a₁ = 50, and the constant difference, d = -1.

We are instructed to use the recursive formula. We know the recursive formula of an arithmetic progression is, aₙ = aₙ₋₁ + d.

a₁ = 50.

a₂ = a₁ + d = 50 + (-1) = 49.

a₃ = a₂ + d = 49 + (-1) = 48.

a₄ = a₃ + d = 48 + (-1) = 47.

a₅ = a₄ + d = 47 + (-1) = 46.

Hence, the 5th row will have 46 logs.

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Answer:

c) there is 95% confidence that the population mean number of books read is between 13.77 and 15.83.

Step-by-step explanation:

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=14.8.

The sample size is N=1003.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{16.6}{\sqrt{1003}}=\dfrac{16.6}{31.67}=0.524[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=1003-1=1002[/tex]

The t-value for a 95% confidence interval and 1002 degrees of freedom is t=1.96.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=1.96 \cdot 0.524=1.03[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 14.8-1.03=13.77\\\\UL=M+t \cdot s_M = 14.8+1.03=15.83[/tex]

The 95% confidence interval for the mean number of books read is (13.77, 15.83).

This indicates that there is 95% confidence that the true mean is within 13.77 and 15.83. Also, that if we take multiples samples, it is expected that 95% of the sample means will fall within this interval.

CHECK THE ATTACHMENT FOR COMPLETE QUESTION

Answer:

We can show that ΔABC is congruent to ΔA'B'C' by a translation of 2 unit(s) Left and a Reflection across the x axis.

Step-by-step explanation:

We were given triangles ABC and A'B'C' of which were told are congruents,

Now we can provide the coordinates of A and A' from the given triangles ΔABC and ΔA'B'C' ,if we choose a point of A from ΔABC and A' from ΔA'B'C' we have these coordinates;

A as (8,8) and A' (6,-8) from the two triangles.

If we shift A to A' , we have (8_6) = 2 unit for that of x- axis

If we try the shift on the y-coordinates we will see that there is no translation.

Hence, the only translation that take place is of 2 units left.

It can also be deducted that there is a reflection

by x-axis to form A'B'C' by the ΔABC.

BEST OF LUCK

Answer:

Step-by-step explanation:

BC/220=sin 60

BC=220 sin 60=220×√3/2=110√3≈190.5 ft

Answer:

190.5 ft

Step-by-step explanation:

For the 60-deg angle, BC is the opposite leg. AB is the hypotenuse.

The trig ratio that relates the opposite leg to the hypotenuse is the sine ratio.

[tex] \sin A = \dfrac{opp}{hyp} [/tex]

[tex] \sin 60^\circ = \dfrac{BC}{220} [/tex]

[tex] BC = 220 \sin 60^\circ [/tex]

[tex] BC = 190.5 [/tex]