Consider the rational expression (IMAGE ATTACHED)

3x^2−3/
3x^2+2x−1

Which statements are true?

Answer: 11

Step-by-step explanation:

Formula to find the sample size using sample standard deviation (s) :

[tex]n= (\dfrac{z^*\cdot s}{E})^2[/tex] , where z* = critical z-value and E = Margin of error.

As per given , we have

E= 7

s= 14 minutes

We know that the critical value for 90% confidence interval = z*=1.645

Then, the required sample size = [tex]n= (\dfrac{(1.645)\cdot (14)}{7})^2[/tex]

[tex]n= (1.645\cdot 2)^2=(3.29)^2=10.8241\approx11[/tex]

Hence, the required sample size = 11

To estimate the mean length of time it takes for buses to arrive and unload students, a sample size of 29 is needed to assert with 90% confidence that the sample mean is off by, at most, 7 minutes.

To determine the sample size needed to estimate the mean length of time it takes for buses to arrive and unload students, we can use the formula:

n = (Z * σ / E)^2

Where n is the required sample size, Z is the z-score corresponding to the desired confidence level (1.645 for 90% confidence), σ is the standard deviation (14 minutes), and E is the maximum error allowed (7 minutes).

Substituting the values into the formula:

n = (1.645 * 14 / 7)^2 = 5.3229^2 = 28.27.

Rounding up to the nearest whole number, the sample size needed is 29.

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Answer:

It costs Lauren 14 dollars to ride 8 miles

Step-by-step explanation:

The equation for the price of the taxi ride is

y= 1.5x+2

where y is the price, and x is the number of miles driven. Lauren needs to ride 8 miles, so the price of her taxi ride is

y= 1.5*8 +2 =12+2=14

Answer:

Step-by-step explanation:

The initial price of the swimsuit that Karla purchased at Amazon was 75.5

she use the coupon code to receive a 25% discount. This means that the value if the discount would be

25/100 × 75.5 = 0.25× 75.5 = 18.86

Therefore, the discounted price of the swimsuit is 75.5 - 18.875 = 56.625

The website applied a 10% service fee for the discount price. This means that the value of the service fee would be

10/100 × 56.625 = 0.1 × 56.625 = 5.6625.

The amount that Karla pays for the swimsuit would be

56.625 + 5.6625 = 62.2875

The difference between the original price and the price that Karla paid would be 75.5 - 62.2875 = 13.2125

The percentage by which the amount that Karla paid was lesser than the original price would be

13.2125/ 75.5 × 100 = 17.5%

Answer:

40

Step-by-step explanation:

Let the number of boys participating in the quiz be b and the number of girls be g. Since the total number is 100, we have our first equation.

b + g = 100

The average score was 76 points. This means the total score was 76 * 100 = 7600

The average score for the boys was 80 meaning total scores for the boys was 80b while that of the girls was 70g

Hence, we have our second equation:

80b + 70g = 7600

Now let’s put the equations together and solve simultaneously to get g which is the number of girls:

b + g = 100

80b + 70g = 7,600

Let’s simply make a substitution. We can say b = 100 - g. Substituting this will yield:

80(100 - g) + 70g = 7,600

8000 - 80g + 70g = 7600

10g = 400

g = 400/10 = 40

Final answer:

By creating and solving two equations that represent the average scores and total number of students, it was determined that 40 girls participated in the quiz.

Explanation:

To solve this problem, we can create two equations using the information about the average scores of the boys and girls, and the overall average. Let's denote the number of girls as G and the number of boys as B. We are told that there are a total of 100 students, which means:

Equation 1: G + B = 100

We're also told the average scores for boys and girls separately, and the overall average score for the group. We can express this with the following equation:

Equation 2: (80B + 70G) / 100 = 76

Now we can solve these equations simultaneously. We already have the total number of students from Equation 1, so we can use that to express B in terms of G: B = 100 - G. Then we can substitute this into Equation 2:

(80(100 - G) + 70G) / 100 = 76

Expanding this, we get:

8000 - 80G + 70G = 7600

Combining like terms, we have:

-10G = -400

Dividing both sides by -10 gives us G = 40.

So 40 girls participated in the quiz.

Answer:

It will take 80 minutes!

Step-by-step explanation:

From the table we see that in 5 minutes we get 325 copies.

This means in one minute we get [tex]$ \frac{325}{5} $[/tex] = 65 copies.

So, assume we get 5200 copies in 'x' minutes.

So, we form the equation.

i.e., 65x = 5200

⇒ x = 80

This means it would take 80 minutes to get 5200 copies.

Answer:

Step-by-step explanation:

total marbles=5+8+4+3=20

when he is drawing without replacing means red marble is drawn from 20 marbles.

Blue marble is drawn from 19 marbles.

when he is drawing with replacing means he draws one red marble from 20 marbles.Then he replaces it and draws blue marble from 20 marbles also.

We have a better chance of drawing a red and then a blue marble without replacing the first marble.

It is the ratio that shows the likelihood of a particular event happening from when many other events could also happen.

The total number of marbles = 5 + 8 + 4 +3

= 20 marbles.

P( Drawing a red marble ) = 5/20

Now draw a blue marble:

Total marbles = 20

P( Drawing a blue marble ) = 8/20

Joint probability = 5/20 * 8/20

= 0.1

Total marbles = 19

P( Drawing a blue marble ) = 8/19

Joint probability = 5/20 * 8/19

= 0.105

This means that there is a higher probability of drawing a blue marble after a red marble without replacement.

Thus we have found that we have a better chance of drawing a red and then a blue marble without replacing the first marble.

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The concept in the question is about representing relations as matrices. In the matrices, the rows and columns correspond to the numbers in the set {1, 2, 3, 4}. The positions in the matrices that are filled with 1s correspond to the numbers in the given relationships.

The relations can be represented on the set {1, 2, 3, 4} with a matrix as follows:

a) For this relationship, a 4x4 matrix can be created. The rows and columns correspond to the numbers in the set {1, 2, 3, 4}. The elements of the set [tex]{(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}[/tex] correspond to positions in the matrix that will be filled with 1s, while the rest will be filled with 0s.

b) A matrix for this relationship would look similar to the above matrix but with different elements in the set [tex]{(1, 1), (1, 4), (2, 2), (3, 3), (4, 1)}[/tex]. In this case, the position of 1s and 0s in the matrix changes.

c) The matrix corresponding to this relationship would have 1s in positions corresponding to the elements of the set [tex]{(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}.[/tex]

d) The last matrix would have 1s only at the positions corresponding to the relationship {(2, 4), (3, 1), (3, 2), (3, 4)}.

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Answer:

Time for the object to get h(max)    s = 1.1875 sec

h (max)  = 1272.57 feet

Down time for the object to hit the ground   =  4.25 sec

Step-by-step explanation:

The relation

h(s)  =  -  16*s²  +  38* s  + 1250    (1)

Is equivalent to the equation for vertical shot

Δh = V(i)*t  -  1/2g*t²  (in this case we don´t have independent term since the shot is from ground level. We can see in (1), the independent term is 1250 feet ( the height of the empire state building), the starting point of the movement.

The description of the movement is:

V(s)  =  V(i)  - g*s     ⇒  V(s) = 38 - 32*s

At h(max)    V(s)  =  0      38/32  = s

So the maximum height is at  s = t = 1.1875 sec

The time for the object to pass for starting point is the same

t  =  1.1875 sec

h(max) is

h(max)  = - 16* (1.1875)² +  38 (1.1875) + 1250

h(max)  =  -  22,56  +  45.13  +  1250

h(max)  =  1272.57 feet

Time for the object to hit the ground is

h(s)  =  - 1250 feet

-1250  =  - 16 s² + 38*s  + 1250

-16s² +  38s  =  0

s ( -16s + 38 )  =  0

First solution for that second degree equation  is x = 0 which we dismiss

then  

( -16s + 38 )  =  0    ⇒ 16s   =  38     s  =  38/16

s =  2.375 sec    and  we have to add time between h (max) and to get to starting point  ( 1. 1875 sec)

total time is  = 2.375 + 1.875

Total time  =  4.25 sec

Answer:

Option A - 10

Step-by-step explanation:

Given : There are 3 red chips and 2 blue chips. If they form a certain color pattern when arranged in a row, for example RBRRB.

To find : How many color patterns are possible?

Solution :

Total number of chips = 5

So, 5 chips can be arranged in 5! ways.

There are 3 red chips and 2 blue chips.

So, choosing 3 red chips in 3! ways

and choosing 2 blue chips in 2! ways.

As changing the places of similar chip will not create new pattern.

The total pattern is given by,

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

[tex]T=\frac{5\times 4\times 3!}{3!\times 2}[/tex]

[tex]T=10[/tex]

Therefore, color patterns are possible are 10.

Option A is correct.

Answer:

The number of child tickets sold was 75 and the number of adult tickets sold was 97

Step-by-step explanation:

The correct question is

At the movie theater child admission is $6.30 an adult admission is $9.60 on Wednesday 172 tickets were sold for a total sales of $1403.70 How many child tickets and adult tickets were sold that day?

Let

x ----> number of child tickets sold

y ----> number of adult tickets sold

we know that

[tex]x+y=172[/tex] ----> equation A

[tex]6.30x+9.60y=1,403.70[/tex] -----> equation B

Solve the system by graphing

Remember that the solution of the system is the intersection point both lines

Using a graphing tool

The intersection point is (75,97)

see the attached figure

therefore

The number of child tickets sold was 75 and the number of adult tickets sold was 97

To solve this problem, set up a system of equations based on the given information. Then use the substitution method to solve for the variables.  69 child tickets and 103 adult tickets were sold on that day.

To solve this problem, we can set up a system of equations.

Let's define the number of child tickets sold as x and the number of adult tickets sold as y.

We know that the cost of a child ticket is $6.00 and the cost of an adult ticket is $9.60.

So, the total cost of all the child tickets is 6x and the total cost of all the adult tickets is 9.60y.

Given that a total of 172 tickets were sold for a total of $1403.70, we can set up the following equations:

Now we can solve this system of equations using any method we prefer. Let's use the substitution method.

Therefore, 69 child tickets and 103 adult tickets were sold on that day.

Answer:

The probability of given event = [tex]\frac{1}{15}[/tex]

Step-by-step explanation:

Ten slips of paper labeled from 1 to 10 are placed in a hat. The first slip of paper is not replaced before selecting the second slip of paper.

We have to find the probability of selecting a number less than 3 and then a number greater than 4.

Probability of an event = [tex]\frac{number of favourable events}{total number of events}[/tex]

The probability of selecting number less than 3 = [tex]\frac{2}{10}[/tex] = [tex]\frac{1}{5}[/tex]

The probability of selecting number greater than 4 = [tex]\frac{3}{9}[/tex] = [tex]\frac{1}{3}[/tex]

Total probability = [tex]\frac{1}{5}\times \frac{1}{3}[/tex] = [tex]\frac{1}{15}[/tex]

Answer:

(a+2)(b+2) = 4

Step-by-step explanation:

We are given the following quadratic equation:

[tex]2x^2-3x-6=0[/tex]

Let a a and b be the solution of the given quadratic equation.

Solving the equation:

[tex]2x^2-3x-6=0\\\text{Using the quadratic formula}\\\\x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{Comparing the equation to }ax^2 + bx + c = 0\\\text{We have}\\a = 2\\b = -3\\c = -6\\x = \dfrac{3\pm \sqrt{9-4(2)(-6)}}{4} = \dfrac{3\pm \sqrt{57}}{4}\\\\a = \dfrac{3+\sqrt{57}}{4}, b = \dfrac{3-\sqrt{57}}{4}[/tex]

We have to find the value of (a+2)(b+2).

Putting the values:

[tex](a+2)(b+2)\\\\=\bigg(\dfrac{3+\sqrt{57}}{4}+2\bigg)\bigg(\dfrac{3-\sqrt{57}}{4}+2\bigg)\\\\=\bigg(\dfrac{11+\sqrt{57}}{4}\bigg)\bigg(\dfrac{11-\sqrt{57}}{4}\bigg)\\\\=\dfrac{121-57}{156} = \dfrac{64}{16} = 4[/tex]

Answer:

Step-by-step explanation:

1.

3a+7=4a

a=7

2b=b+11

b=11

2.

y=101°

101+x=180

x=180-101=79°

3.

x+6=11

x=11-6=5

y-7=10

y=10+7=17

Answer: Why are they increasing the moose?

Step-by-step explanation: Well I’m assuming this is in Canada. therefore, this has to be D

Step-by-step explanation:

Total number of trees = 300

Given that for every two pine trees there will be 3 maple trees.

Let 2t be the total number of pine trees.

Then total number of maple trees is 3t.

Total number of trees = 2 t + 3 t  = 5 t

That is

              5t = 300

                 t = 60

Total number of pine trees = 2t = 2 x 60 = 120

Total number of maple trees = 3t = 3 x 60 = 180

There are 120 pine trees and 180 maple trees.

Answer: 9

Step-by-step explanation:

12 insulators = 183/4 hours

x = 281/8

x × 183/4 = 12 ×281/ 8

183x/4 = 6 × 281/4

183x / 4 = 1686 / 4

4 cancel out 4

183x = 1686

Divide bothside by 183

x = 1686/183

x= 9.21311

x = 9 approximately.

Answer:

$0.04 per foot

Step-by-step explanation:

Answer:

Option D

Step-by-step explanation:

This are variables that have relationship with the outcome and exposure that is the confounding effect of alcohol on cancer is the fact that an alcohol consumers are more likely to smoke and smokers are likely to have cancer.

Answer:

[tex]N(t) = 1000 +t[/tex]

Step-by-step explanation:

It is given that,

Number of Men receiving degree are = M(t) = 526-t

Number of women receiving degree are = W(t) = 74+2t

The total number of students receiving the degree is given by,

sum of both Men and Women receiving the degrees.

Thus, N(t) = M(t) + W(t)

N(t) = (526-t) + (474+2t)

N(t) =  1000 + t

Thus, the number of students receiving the degree is given by N(t) = 1000 + t .

Answer:

Step-by-step explanation:

Answer:

Area of the walk = 110 square feet

Step-by-step explanation:

The rectangular yard measuring 24ft by 29ft

Area of the rectangle = length times width

Area of the rectangular yard = 24 times 29=696 square feet

Length of side walk is 2 feet wide

Length of the rectangular yard with walk = 24+2= 26 ft

Width of the rectangular yard with walk = 29+2=31 ft

Area of the rectangular yard with walk = 26 times 31=806 square feet

Area of the walk = [tex]806-696=110 squarefeet[/tex]

Answer:

C

Step-by-step explanation:

Since there is no relationship between the two , there exists no correlation between them.

This is simply because the effect of one is not felt on the other

Answer:

11 sections

Step-by-step explanation:

This problem is called the circle cutting or pancake cutting problem.

Let the number of cuts or divisions by straight line = n

With this information it is possible to calculate any number of pieces or section a circle will be divided into what straight lines are drawn (cut) across the circle.

When a straight line is drawn across the circle, it divides the circle into 2 sections or regions. The nth straight lines will divide the circle into n new sections or regions, so the progression is;

         f(1) = 2

         f(2) = 2 + f(1)

         f(3) = 3 + f(2)

         .

         .

         .

         f(n) = n + f(n-1)

Therefore,

         f(n) = n + [(n-1) + f(n-2)}

               = n + n-1 + ... + 2 + f(1)

               = f(1) + ∑[tex]_{i = 2}^{n}[/tex]i

               = [tex]2 + \frac{1}{2} (n + 2) (n - 1)[/tex]

               = [tex]\frac{1}{2}(n^{2} + n + 2)[/tex]

When n = 4

              =  [tex]\frac{1}{2}(4^{2} + 4 + 2)[/tex]

              = 22/2

              = 11 sections

Answer:

Step-by-step explanation:

it is given that Square contains a chord of of the circle equal to the radius thus from diagram

[tex]QR=chord =radius =R[/tex]

If Chord is equal to radius then triangle PQR is an equilateral Triangle

Thus [tex]QO=\frac{R}{2}=RO[/tex]

In triangle PQO applying Pythagoras theorem

[tex](PQ)^2=(PO)^2+(QO)^2[/tex]

[tex]PO=\sqrt{(PQ)^2-(QO)^2}[/tex]

[tex]PO=\sqrt{R^2-\frac{R^2}{4}}[/tex]

[tex]PO=\frac{\sqrt{3}}{2}R[/tex]

Thus length of Side of square [tex]=2PO=\sqrt{3}R[/tex]

Area of square[tex]=(\sqrt{3}R)^2=3R^2[/tex]

Area of Circle[tex]=\pi R^2[/tex]

Ratio of square to the circle[tex]=\frac{3R^2}{\pi R^2}=\frac{3}{\pi }[/tex]

The value of cos-1 (-√3/2) represents the angle that has the cosine of -√3/2, and it is found in the second or third quadrant. The angles corresponding to these values in the unit circle are 120° or 240°.

The value of cos-1 (-√3/2) refers to the angle whose cosine is -√3/2. This angle would be found in the second or third quadrant since cosines are negative in these quadrants. For the value of -√3/2, it corresponds to the angle 120° or 240° in the unit circle. Therefore, the value of cos-1 (-√3/2) is 120° or 240°.

Remember, inverse trigonometric functions deal with the range and the quadrant in which an angle lays. While working with inverse trigonometric functions, pay attention to the unit circle, and to the fact that cosine is negative in the second and third quadrants.

The value of cos-1 (-√3/2) is 150 degrees or 5π/6 radians.

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Answer:

The equation to determine the number of days Margo has owned the plant is [tex]5+2.5x=65[/tex].

Step-by-step explanation:

Given:

Actual length of the tree = 5 cm

Current length of the tree = 65 cm

Per day growth Rate of plant = 2.5 cm

Let number of days she owned the plant be 'x'

Now We can say that,

Current length of the tree is equal to sum of Actual length of the tree and Per day growth Rate of plant multiplied by number of days she owned the plant.

Farming the above sentence in equation form we get;

[tex]5+2.5x=65[/tex]

Hence the equation to determine the number of days Margo has owned the plant is [tex]5+2.5x=65[/tex].

Answer:

H0:[tex]\mu_{N}\geq \mu_{C}[/tex]

H1:[tex]\mu_{N} < \mu_{C}[/tex]

[tex]t=\frac{7880-8112}{\sqrt{\frac{1115^2}{30}+\frac{1250^2}{30}}}}=-0.759[/tex]  

[tex]p_v =P(t_{(58)}<-0.759)=0.225[/tex]

So the p value is a very High value and using any significance level given [tex]\alpha=0.02[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't conclude that the mean for the nitrite group is significantly lower than the mean for th control group .

Step-by-step explanation:

1) Data given and notation

[tex]\bar X_{N}=7880[/tex] represent the mean for the sample Nitrite

[tex]\bar X_{C}=8112[/tex] represent the mean for the sample control

[tex]s_{N}=115[/tex] represent the sample standard deviation for the sample Nitrite

[tex]s_{C}=1250[/tex] represent the sample standard deviation for the sample control

[tex]n_{N}=30[/tex] sample size for the group nitrite

[tex]n_{C}=30[/tex] sample size for the group control

t would represent the statistic (variable of interest)

[tex]\alpha=0.02[/tex] represent the significance level

Confidence =1-0.02=0.98 or 98%

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the nitrites decrease amino acid uptake , the system of hypothesis would be:

H0:[tex]\mu_{N}\geq \mu_{C}[/tex]

H1:[tex]\mu_{N} < \mu_{C}[/tex]

If we analyze the size for the samples both are equal to 30, but we don't know the population deviations, so for this case is better apply a t test to compare means, and the statistic is given by:

[tex]t=\frac{\bar X_{N}-\bar X_{C}}{\sqrt{\frac{s^2_{N}}{n_{N}}+\frac{s^2_{C}}{n_{C}}}}[/tex] (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

3) Calculate the statistic

We can replace in formula (1) like this:

[tex]t=\frac{7880-8112}{\sqrt{\frac{1115^2}{30}+\frac{1250^2}{30}}}=-0.759[/tex]  

4) Statistical decision

The first step is calculate the degrees of freedom, on this case:

[tex]df=n_{N}+n_{C}-2=30+30-2=58[/tex]

Since is a left tailed test the p value would be:

[tex]p_v =P(t_{(58)}<-0.759)=0.225[/tex]

So the p value is a very High value and using any significance level given [tex]\alpha=0.02[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't conclude that the mean for the nitrite group is significantly lower than the mean for th control group .

Answer:

Distance farther the Kangaroos need to go to cover a mile = 780 feet

Step-by-step explanation:

Given:

Kangaroos cover 30 feet in a single jump.

Kangaroos can make such jumps 150 times in a row.

To find the distance farther it needs to go to cover a mile.

Solution:

Using unitary method to find distance covered by kangaroos in a row.

If in a single jump Kangaroos cover = 30 feet

So, in 150 jumps it will cover = [tex]30\ ft \times 150[/tex] = 4500 feet

We know 1 mile = 5280 feet

Thus, distance farther the Kangaroo needs to go to cover a mile will be = [tex]5280\ ft-4500\ ft[/tex] = 780 feet

Answer:

Step-by-step explanation:

On Monday morning, Susan bought 2.5 pounds of grapes at the supermarket. That day, Susan ate some grapes and had 1.75 pounds of grapes left. This means that the amount of grapes that she ate would be 2.5 - 1.75 = 0.75

The percentage decrease of pounds of grapes on Monday would be the amount that she ate on Monday divided by the initial amount times 100. It becomes

0.75/2.5 × 100 = 30℅

Answer:

The answer to your question is letter A

Step-by-step explanation:

                   Percent of blue pigment          Milliliters

 ink A                    10%                                        4

 ink B                    ---                                          10

Total volume        35%                                       14

Formula

Total percent x total volume = (percent ink A x A milliliters) +

                                                  (percent ink B x B milliliters)

Substitution

   (0.35 x 14) = ( 0.1 x 4) + (B x 10)

Solve for B

             4.9 = 0.4 + 10B

             10B = 4.9 - 0.4

             10B = 4.5

                 B = 4.5/10

                 B = 0.45 x 100

                 B = 45%

Answer:

  (D) the square of a prime

Step-by-step explanation:

You want to know the kind of number that will have exactly two distinct positive divisors other than 1.

The number of divisors a number will have can be found from its prime factorization. If that is described by ...

  [tex]\displaystyle N=p_1^{e_1}\times p_2^{e_2}\times\dots=\prod\limits_n(p_i)^{e_i}\\ \\\text{\# of divisors of N}=\prod\limits_n (e_i+1)[/tex]

This count of divisors includes 1 and the number N. If there are 2 divisors other than 1, then we must have the product of all "bumped" exponents be 3. Since 3 is prime, its only factors are 1 and 3. That means there must be only one exponent, and its value must be 3-1 = 2.

That is, N = p², where p is a prime, has 2+1 = 3 divisors, including 1.

An integer with exactly 2 distinct divisors greater than 1 is the square of a prime, choice D.

Answer: in dispensing medications, in the use of measurement equipments and formulas for converting units, to obtain reliable data of patients overtime to be able to predict, and diagnose patients easily

Step-by-step explanation:

Maths is used in health care in the dispensing of medications they translate medical order into dosages, calculate dosage based on body weight, determine the amount of drugs to be dispensed. Maths also helps in the conversion of units e.g milligram to gram, Fahrenheit to degree Celsius etc.

It also help in the measurement of body temperature, pulse rate, breathing rate etc.

Among others uses, maths is also used to generate reliable data of patients overtime and help in quick diagnosis and treatment of patients.