Elena family is driving on the freeway at 55 miles per hour Andreas family is driving on the same freeway but not a constant speed. How long did it take Elenas family to travel as far as Andre family had tracked after 8 minutes?

Answer:

Option A

Step-by-step explanation:

Let us take this number as x, translating this description of the equation into mathematical language;

\(x^2 = 3x - 2\)

Now let us solve for x;

\(x^2 = 3x - 2,\\x^2+2=3x-2+2,\\x^2+2=3x,\\x^2+2-3x=3x-3x,\\x^2-3x+2=0,\\\\Factored = \left(x-1\right)\left(x-2\right)=0,\\Zero Factor Principle, \\x = 1, x = 2\\\\Solution - Option A\)

* Note that for the the previous problem I solved, I set up a similar equation that had two values for the width, one negative and the other positive. Now the width could only be a positive number, so there was only one solution out of the two.

Answer:

$33.60

Step-by-step explanation:

Original price of shirt: $40

Percent discount: 20%

Amount of discount: 20% of $40 = 0.2 × $40 = $8

Price after discount: $40 - $8 = $32

Percent of tax: 5%

Amount of tax: 5% of $32 = 0.05 × $32 = $1.60

Total paid after discount and tax: $32 + $1.60 = $33.60

Answer: Lydia paid the amount of 33.60 dollar

Step-by-step explanation:

Retail price of shirt = 40 dollar

Discount = 20%

Discount value:

=20% of 40 dollar                   [ 20/100 * 40 ⇒ 1/5 * 40 ⇒ 40/5 = 8 ]

= 8 dollar  [ discount value]

Price of shirt after discount :

= 40 - 8

= 32 dollar

As she paid 5% discount on the discounted price ( 32 dollar )

So,  5% of 32 = 1.6 dollar        [ 5/ 100 * 32 ⇒  1/20 * 32 ⇒ 32/20 = 1.6]

Amount to pay = 32( price after discount)  + 1.6 ( Tax)

= 33.60 dollar

Answer:

(i) The axis of symmetry is \(x = -4\).

(ii) The axis of symmetry is \(x = 4\).

(iii) The axis of symmetry is \(x = 1\).

Step-by-step explanation:

We proceed to explain how we determine the expression for the axis of symmetry for each case:

(i) \(f(x) = 3\cdot (x+4)^{2}+1\)

The expression depicts a vertical parabola, meaning that axis of symmetry is vertical, that is, a function of the form \(x = a,\,\forall\,a\in \mathbb{R}\). This line passes through the vertex of the parabola. The component \(x+4\) contains the information of the horizontal component of the vertex, where the axis passes through. Therefore, the axis of symmetry is \(x = -4\).

(ii) \(f(x) = 2\cdot x^{2} -16\cdot x +15\)

At first we complete the square and factor the perfect square trinomial:

\(f(x) = 2\cdot \left(x^{2}-8\cdot x +\frac{15}{2} \right)\)

\(f(x) = 2\cdot \left[(x^{2}-8\cdot x +16) +\frac{15}{2}-16 \right]\)

\(f(x) = 2\cdot (x-4)^{2}-17\)

By applying the approach used in (i), we find that the axis of symmetry is \(x = 4\).

(iii) First, we locate the vertex of the parabola, which is (1,-3). The first component of the ordered pair contains all the needed information to determine the equation of the axis of symmetry, which is \(x = 1\).

By using the Basu's theorem  and from parts (a) and (b), we conclude that P and T are independent.

Basu's theorem states that if a complete sufficient statistic T and an ancillary statistic S are independent, then any statistic U that is a function of T and S is independent of any unbiased estimator of a function of θ.

Using Basu's theorem, we need to show that Σ(Xi – X)^2 is ancillary and independent of the mean ξ and variance σ^2. Since X follows a normal distribution, we know that the sum of squares of deviations from the mean (Σ(Xi – X)^2) follows a chi-square distribution with n degrees of freedom, where n is the sample size.

Since the chi-square distribution only depends on the sample size and is independent of the mean and variance of X, we conclude that Σ(Xi – X)^2 is ancillary and independent of ξ and σ^2. Therefore, using Basu's theorem, we conclude that X and Σ(Xi – X)^2 are independent.

In problem 6.18, we have shown that X(1) follows an exponential distribution with parameter λ = 1/θ, where θ is the common distribution of the X's. Therefore, X(1) is complete and unbiased for θ. Using the result from problem 6.17(e), we know that Σ[Xi – X(1)] follows a gamma distribution with parameters n – 1 and 1/θ. Therefore, Σ[Xi – X(1)] is ancillary and independent of θ. Using Basu's theorem, we conclude that X(1) and Σ[Xi – X(1)] are independent.

Using the hint provided in the problem, we can rewrite Σ[Xi – X(1)] as b times the sum of n – 1 independent exponential random variables with mean a/(n – 1). Therefore, Σ[Xi – X(1)] follows a gamma distribution with parameters n – 1 and a/(n – 1), which is equivalent to a gamma distribution with parameters n – 2 and b = 1/(a/(n – 1)).

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To decrease the width of the confidence interval, the researcher can take the following steps:

1. Decrease the confidence level: The confidence interval width is inversely proportional to the confidence level. By decreasing the confidence level, the researcher can have a narrower interval. However, it is important to note that decreasing the confidence level also increases the chance of the interval not capturing the true population mean.

2. Increase the sample size: The sample size affects the precision of the estimate. Increasing the sample size reduces the standard error, which leads to a narrower confidence interval. This is because a larger sample provides more information about the population.

Therefore, the researcher can decrease the width of the confidence interval by either decreasing the confidence level or increasing the sample size. Both approaches will result in a narrower interval, providing a more precise estimate of the mean fat content of hen's eggs.

The researcher can decrease the width of the confidence interval by either decreasing the confidence level or increasing the sample size. Both approaches will result in a more precise estimate of the mean fat content of hen's eggs.

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Answer:x = 200 students

y = 300 non-students

Step-by-step explanation:

5x + 10y = 4000

x + y = 500

Set y = 500-x

5x + 10(500-x) = 4000

5x + 5000-10x

-5x + 5000 = 4000

-5x = -1000

x = 200 students

y = 300 non-students

Let's double checks

5(200) + 10(300)

1000 + 3000 = 4000

Answer:

buy 28 blue mask and 14 white mask

Step-by-step explanation:

Answer:

12/11

Step-by-step explanation:

the formula to find the slope of a line is:

where  is the slope and  and  are the points where the line passes.

in this case we have that the first point is: (25,50)  thus⇒  and

and the second point: (80,110) thus ⇒  and

substituting this values into the formula for the slope:

the slope of the line is 12/11

The matrix A of the linear transformation T is:

A = [[-1, 1],

[-2, 2]]

To find the matrix A of the linear transformation T, we can write the equation T(x) = Ax, where x is a vector in the input space and Ax is the result of applying the linear transformation to x.

We are given two specific examples of the linear transformation T:

T([1, 1]) = [-1, 1]

T([2, 0]) = [-2, 2]

To determine the matrix A, we can write the following equations:

A[1, 1] = [-1, 1]

A[2, 0] = [-2, 2]

Expanding these equations gives us the following system of equations:

A[1, 1] = [-1, 1] -> [A₁₁, A₁₂] = [-1, 1]

A[2, 0] = [-2, 2] -> [A₂₁, A₂₂] = [-2, 2]

Therefore, the matrix A is:

A = [[A₁₁, A₁₂],

[A₂₁, A₂₂]] = [[-1, 1],

[-2, 2]]

So, the matrix A of the linear transformation T is:

A = [[-1, 1],

[-2, 2]]

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The answer is Start Fractiοn 2 οver 7 End Fractiοn.

Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants.

Kyle's handful οf trail mix cοntains a tοtal οf 2 + 4 + 3 + 5 = 14 items.

The prοbability οf picking a peanut is the number οf peanuts in the handful divided by the tοtal number οf items in the handful:

prοbability οf picking a peanut = number οf peanuts / tοtal number οf items

prοbability οf picking a peanut = 4 / 14

Simplifying the fractiοn by dividing bοth the numeratοr and denοminatοr by 2, we get:

prοbability οf picking a peanut = 2 / 7

Therefοre, the answer is StartFractiοn 2 οver 7 EndFractiοn.

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The volume of the cylinder is \(\frac{\pi h^{3}}{9}\) or \(3\pi r^{3}\).

According to the question:

\(radius = r\\height = h = 3r\)

We know that the volume of a cylinder having radius \(r\) and height \(h\) is:

\({Volume = \mathbf{\pi r^{2}h}\)

Substitute the given values for us in the above equation:

\(Volume =\pi r^2\times3r\)

\(Volume = 3\pi r^3\)

If we want the answer in terms of \(height(h)\), we can substitute \(r\) instead of \(h\).

By doing this we get:

\(Volume = \pi (\frac{h}{3})^2h\)

\(Volume = \pi \frac{h^3}{9}\)

Therefore, the volume of the cylinder is  \(\frac{\pi h^{3}}{9}\) or \(3\pi r^{3}\).

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Answer:

46

Step-by-step explanation:

Answer:

x=46

Step-by-step explanation:

Answer:

they move side to side and up and down on both axis- they x and y

Step-by-step explanation:

passed math with an A+

Answer:

1/3

Step-by-step explanation:

since number 2 card was not replaced, we have;

probability of picking a second card, 3;

let S be number of sample space

n(S)= 4

n(3)= 1

Pr(3/2)= 1/3

(because since one was already chosen and n, the sample space would reduce)

Answer:

Step-by-step explanation:

6^0 + 6^0 + 6^0 + 6

= 1+1+1+6

= 9.

Answer:

domain: (-4 , infinity)

range: (-1, infinity)

Step-by-step explanation:

the domain is all x values and range is all y values

Based on the given information, Jane should not search for the doll any more. The cost of searching outweighs the potential savings she might gain by finding a lower price.

In this scenario, Jane has already visited one shop and found the doll priced at $100. She knows that the doll is offered at three different prices: $120, $100, and $80, with unknown probabilities (represented as odds). Each additional search incurs a cost of $5.

To determine whether Jane should search for the doll again, we need to compare the expected cost of searching with the potential savings. Given the information provided, we do not have the probabilities associated with each price, so we cannot calculate the exact expected savings. However, we can make an informed decision based on the given information.

Since the current price of the doll is $100 and the potential savings from finding a lower price are uncertain, Jane should consider the cost of searching. With a search cost of $5 per search, it is unlikely that the potential savings from finding a lower price would offset the additional cost incurred by searching. Therefore, it is advisable for Jane not to search for the doll any more, as the cost of searching exceeds the expected savings.

It's important to note that a definitive decision would require more information, such as the probabilities associated with each price. However, based on the given information, the best course of action for Jane is to refrain from further searching.

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In case of a normal distribution, the mean, median, and mode are equal . So option A is correct

What is normal distribution?

The most significant continuous probability distribution in probability theory and statistics is the normal distribution, also referred to as the gaussian distribution. On occasion, it is referred to as a bell curve.

The probability distribution of data is expressed mathematically as a normal distribution. It is symmetrical from both ends and has only one mode. The equal mean, median, and mode of the given data are highlighted by the normal distribution.

The options are b) It has two modes. c) It is asymmetrical. and d) the points of the curve meet the x-axis at z are incorrect.

Therefore, The correct option is A, the equal mean, median, and mode of the given data are highlighted by the normal distribution.

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The four quantities in the given formula for the sum of an arithmetic series (Sn = n/2(a₁ + an)) are

1. Sn: The sum of the arithmetic series.

2. n: The number of terms in the series.

3. a₁: The first term of the series.

4. an: The nth term of the series, representing the last term in the series.

The formula provided is for the sum of an arithmetic series, and it involves four quantities. Let's describe each of these four quantities:

1. Sn: This represents the sum of the arithmetic series. It is the total of all the terms in the series up to the nth term. In other words, it represents the cumulative sum of the terms in the series.

2. n: This represents the number of terms in the arithmetic series. It indicates how many terms are included in the sum. The value of 'n' determines the extent of the series and influences the value of Sn.

3. a₁: This represents the first term of the arithmetic series. It is the initial value or the starting point of the series. The subsequent terms in the series are generated by adding the common difference (d) to this first term.

4. an: This represents the nth term of the arithmetic series. It is the last term or the final value in the series. The value of 'an' can be determined using the formula an = a₁ + (n-1)d, where 'd' is the common difference between consecutive terms in the series.

In summary, the four quantities in the given formula for the sum of an arithmetic series (Sn = n/2(a₁ + an)) are:

1. Sn: The sum of the arithmetic series.

2. n: The number of terms in the series.

3. a₁: The first term of the series.

4. an: The nth term of the series, representing the last term in the series.

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Out of the 15 people the probability that none of the patients will experience dizziness is approximately 0.206 .

10% of the people experiences dizziness.

Probability that a random patient experiences dizziness = 0.1

Probability that the person does not experience dizziness = 0.9

Now this is in the form of a binomial distribution such that the probability is given by:

Sample = 15

P = 0.1

P' =0.9

Required probability :

= ¹⁵C₀ × P⁰ × P'¹⁵ (binomial distribution)

= 1 × 0.1⁰ × 0.9¹⁵

= 0.20589...

≈ 0.206

Hence the required probability is approximately 0.206 .

The binomial distribution is often used to predict the number of further successes in either a sample of size n drawn under replacement from either a population of size n.

If the sampling is carried out without replacement, the drawings are not independent, hence the resulting distribution is a hypergeometric one rather than a binomial one.

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Answer: Option d.  0.26

Step-by-step explanation:

Since the addition of complementary angles = 90°

75° + x = 90°

x = 90° - 75 °

x = 15°  ( the complementary angle )

sine 15° = 0.25882

             = 0.26 correct to two decimal places

d.0.003 choice correctly shows 0.3% as a decimal.

Here, we have,

given that,

the percent is: 0.3%

now, we know that,

percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity. percentage.

now, we get,

0.3%

=0.3 ÷ 100

=0.003

now, we know, 0.003 is a decimal.

so, we get,

d.0.003 choice correctly shows 0.3% as a decimal.

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Answer: 2 4/15 months

Step-by-step explanation:

From the question, we are informed that a wagon train traveled from Missouri to Wyoming in 1 2/3 months and from Wyoming to Utah in 3/5 month.

The number of months that it will take the wagon train to travel from Missouri to Utah will be:

= 1 2/3 + 3/5

The common lowest multiple is 15

= 1 10/15 + 9/15

= 1 19/15

= 1 + 1 4/15

= 2 4/15 months

It will take they train 2 4/15 months to travel from Missouri to Utah.

2/3 <=======3

i think,,,, if not sorry i suck at math

Step-by-step explanation:

the general slope-intercept form is

y = ax + b

a is the slope, b is the y-intercept.

we need to transform x + 2y = 6, so that we end up with y being all alone on one side, and the rest on the other side.

x + 2y = 6

2y = -x + 6

y = -x/2 + 6

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

The y-coordinate for the solution to the system of equations is -3.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations. The intersection of two lines represents the system of equations' solution.

Given system of equations are,

6x + 11y = -3

4x + y = 17

To solve these equations, we must first remove x or y terms.

To do this we must make the removing term's coefficients the same.

In this case, let's remove y.

We are multiplying the second equation by 11. Then,

6x + 11y = -3

44x + 11y = 187

Now we will subtract the second equation from the first.

- 38x  = -190

x = 5

Now to find y, substitute x in any one of the equations.

6 * 5 + 11y = -3

11y = -33

y = -3

Hence the y-coordinate for the solution to the system of equations is -3.

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Answer:

32

Step-by-step explanation: