Katherine has $460 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $362.68.
She buys 3 bicycle reflectors for $10.20 each and a pair of bike gloves for $12.54.
She plans to spend some or all of the money she has left to buy new biking outfits for $27.09 each.

a) For a 90% confidence interval [22.25, 23.55].

For a 95% confidence interval [22.10, 23.70].

For a 99% confidence interval [21.97, 23.83].

b) For a 90% confidence interval [22.25, 23.55].

a) To construct a confidence interval for the population mean age, we can use the formula: CI = x* ± tα/2 * (σ / sqrt(n)), where x* is the sample mean age, σ is the population standard deviation, n is the sample size, and tα/2 is the critical value of the t-distribution with n-1 degrees of freedom and a given level of confidence α/2.

For a 90% confidence interval, α = 0.1 and tα/2 = 1.725, so the interval is: 22.9 ± 1.725 * (1.5 / sqrt(20)) = [22.25, 23.55].

For a 95% confidence interval, α = 0.05 and tα/2 = 2.093, so the interval is: 22.9 ± 2.093 * (1.5 / sqrt(20)) = [22.10, 23.70].

For a 99% confidence interval, α = 0.01 and tα/2 = 2.861, so the interval is: 22.9 ± 2.861 * (1.5 / sqrt(20)) = [21.97, 23.83].

b) If the given standard deviation of 1.5 years came from the sample instead of the population, we need to use a t-distribution with n-1 degrees of freedom to construct the interval. The formula is the same as before, but we replace σ with s, the sample standard deviation.

For a 90% confidence interval, the critical value is still 1.725, so the interval is: 22.9 ± 1.725 * (1.5 / sqrt(20)) = [22.25, 23.55].

c) If the distribution of the population is not specified, we can still form a confidence interval if we have a large enough sample size (typically, n >= 30) due to the central limit theorem. In this case, we have n = 20, so we may not have enough information to form a confidence interval if we cannot assume the population is normally distributed.

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Answer:

3.85×10³ in ordinary form

= 3850​

Step-by-step explanation:

Answer:

3850

Step-by-step explanation:

.......................

...

Weight of an apple: quantitative continuous.The most common color of apples in a bag: qualitative.Number of apples in a two-pound bag: quantitative discrete.

1. Weight of an apple: The weight is a measurable quantity with numerical values. Therefore, this data is quantitative. Since weight can take on any value within a range (e.g., 5.2 oz, 5.25 oz), it is continuous. So, the data is quantitative continuous.

2. The most common color of apples in a bag: Color is a non-numerical characteristic that describes the apples. This data is qualitative.

3. Number of apples in a two-pound bag: The number of apples is a countable numerical value. This data is quantitative. Since it can only be a whole number (e.g., 5 apples, 6 apples), it is discrete. So, the data is quantitative discrete.

Your answer:

1. Weight of an apple - Quantitative continuous
2. The most common color of apples in a bag - Qualitative
3. Number of apples in a two-pound bag - Quantitative discrete

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Answer:

with what

Step-by-step explanation:

I am confused there is no question at all showing

Answer:

Answer:

The correct answer is C - 7.8 < 7 5/6 < 7.9

Step-by-step explanation:

First, convert 7 5/6 to decimal form --> 7.83.

If you don't know how to convert, think about what 5/6 is equal to and put it in decimal form. Add your decimal to the whole number, and there is your answer.

7.83 is in between 7.8 and 7.9, so it must be the answer.

I hope this helps!

Step-by-step explanation:

Answer:

\(\left(x^2+3i\right)\left(x^2-3i\right)\)

Step-by-step explanation:

\(x^4+9\)

\(x^4+9\) can be written as \(x^4--9\).

Apply the formula for the difference of two squares.

\((a^2-b^2)=(a+b)(a-b)\)

\(-9=3i^2\)

\(x^4=(x^2)^2\)

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

Answer:

(x^2 - 3i) ( x^2 +3i)

Step-by-step explanation:

X^4+9

x^4 - -9

This is the difference of squares (a^2 - b^2) = (a-b)(a+b)

(x^2) ^2 - ( 3i)^2

(x^2 - 3i) ( x^2 +3i)

Answer:

I believe it is 3243.16 rounded 3243

Answer:

y = 3/x

Step-by-step explanation:

Answer:

Yes they are parallel

Step-by-step explanation:

They have the same slope.

Answer:

[12] 7x+5

[13] 72

Step-by-step explanation:

[12] \(7x^2+75+50\)

First, Multiply the coefficient of the first term by the constant   7 × 50 = 350

Then, find two factors of  350  whose sum equals the coefficient of the middle term, which is  75 .

Then,  Rewrite the polynomial splitting the middle term using the two factors  5  and  70

                    7x^2 + 5x + 70x + 50

Add up the first 2 terms, pulling out like factors :

                   x × (7x+5)

             Add up the last 2 terms, pulling out common factors :

                   10 × (7x+5)

               (x+10)  • (7x+5)

Hence, Answer = 7x + 5

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[13]  

A perfect square trinomial is a quadratic equation of the form

\(ax^2+bx+c=0\)  

and a result of squaring a binomial. This means that the first and third term of the trinomial is equal to the square of the first and second term of a binomial. Therefore, in order to determine the value of the third term, we can use the method of completing the square in which the formula is

\(c=(\frac{b}{2a})^2\)

where c is the constant and b and a are the coefficients of the first and the second term.

The trinomial 9x^2+72x+144 is a perfect square trinomial, because it's discriminant is equal to zero

Δ=b 2 −4ac=72 2 −4(9)(144)=0  

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~Learn with Lenvy~

Answer:

I'll do the first one and lets see if that helps

Step-by-step explanation:

well, let's take a look at the tickmarks on the triangle, the tickmarks mean that AC = CB, both AC and CB stemming out of vertex C, and both twin sides will make twin angles at the "base" or namely ∡A = ∡B, that means that 34 = x - 5, let's also recall that the sum of all interior angles in a triangle is 180°, so

\(34=x-5\implies \boxed{39=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle A}{34}~~ + ~~\stackrel{\measuredangle B}{34}~~ + ~~\stackrel{\measuredangle C}{4y}~~ = ~~180\implies 68+4y=180 \\\\\\ 4y=112\implies y=\cfrac{112}{4}\implies \boxed{y=28}\)

Answer:

y = 28

Step-by-step explanation:

The dashes on line segments AC and BC indicate that the line segments are equal in length.

Therefore, as the triangle has two sides of equal length, it is an isosceles triangle.

The base angles of an isosceles triangle are equal, therefore ∠A = ∠B.

Interior angles of a triangle sum to 180°.  

Therefore:

⇒ ∠A + ∠B + ∠C = 180°

⇒ 34° + 34° + 4y° = 180°

⇒ 68° + 4y° = 180°

⇒ 4y° = 112°

⇒ y = 112° ÷ 4°

⇒ y = 28

x+5y=8... equ 1

-x+2y=-1 ..... equ2

Add equ 1 to equ 2

0x+7y=7

7y=7

Y=1

Subsitute the value of y in equ 1 or equ 2

By subsituting In equ 1

X+5(1)=8

X=3

Answer:

If I know I will defiantly answer .but where is the question

If the utilization of an M/M/1 model is 0.6, the c of time there is at least one person in the system is 100%.

In an M/M/1 model, the utilization represents the ratio of the arrival rate (λ) to the service rate (μ). If the utilization is less than 1, it means that the arrival rate is lower than the service rate, and the system is not fully utilized. However, even with a utilization of 0.6, there will still be instances where there is at least one person in the system. This is because the arrival rate is not zero, indicating that customers are still arriving, albeit at a lower rate compared to the service rate. Therefore, the percentage of time with at least one person in the system would be 100%. If you are told that the utilization rate for an M/M/1 model is 0.8 and the average number of people in the system is 4, it is impossible to determine the average number of people in the queue without further information. The average number of people in the queue depends on factors such as the arrival rate and service rate, which are not provided in this scenario. The utilization rate alone and the average number of people in the system do not provide sufficient information to calculate the average number of people in the queue accurately. Therefore, it is impossible to determine the average number of people in the queue based solely on the given information.

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The function represents the same relationship as the table is y = 2(2/3)ˣ

From the question, we have the following parameters that can be used in our computation:

The table of values

An exponential function is represented as

y = abˣ

Where

a = y when x = 0

So, we have

a = 2

To calculate b, we have

b = 2/3

This gives

y = 2(2/3)ˣ

Hence, the function represents the same relationship as the table is y = 2(2/3)ˣ

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Here, we want to drop a box plot on the number line given the listed numbers

We have the box plot as follows

The listing of the numbers is the actual way the numbers on the box plot will be listed from left to right

We have this as follows;

The components of a concave lens can be categorised as follows:

Optical centre: The C symbol designates the lens's middle, which is the optical centre. It is the location where light rays travel through without deviating.

Focal point (F): The focal point is where parallel light rays converge after passing through the lens on the primary axis. The focal point is designated as F in a concave lens because it is on the same side as the light source.

Principal axis: The principal axis is the fictitious line that encircles the focal point(s) and optical centre. It is parallel with the lens.Vertex (V): The vertex, which is located on the primary axis of the lens, is its actual centre.

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Answer:

1. focal point,

2. focal length,

3. center of the lens,

4. principal axis

Step-by-step explanation:

Answer:

B is the answer.

First you do 38.25 divided by 3 and you get 12.75, And option B is 12.75

The other coordinate is x = \(\sqrt{3} /2\).

Given:

A point (x, y) is on the unit circle. If its y-coordinate is 1/2 and the point lies in Quadrant I.

we know that :

In unit circle radius r = 1.

\(x^{2} +y^{2} = r^{2}\)

\(x^{2} +(1/2)^2 = 1^2\)

\(x^{2} +1^2/2^2 = 1\)

\(x^2 + 1/4 = 1\)

\(x^{2} = 1-1/4\)

\(x^{2} = 4- 1 / 4\)

\(x^{2} =3/4\)

\(x =\) ±\(\sqrt{3/4}\)

\(x =\) ±\(\sqrt{3} /2\)

since x is in first quadrant it has only positive value

\(x =\sqrt{3} /2\).

Therefore the other coordinate is x = \(\sqrt{3} /2\).

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Answer:

3020

Step-by-step explanation:

round to the nearest  10

503 to 500

472 to 470

486 to 490

499 to 500

539 to 540

522 to 520

Answer:

the dif is i would take the plus 9.5% each time cause you could always do over and get you salary even greater and it's better getting a plus then just the 450 every time

Step-by-step explanation:

Answer:

48°

Step-by-step explanation:

29+12+x = 89

41+x = 89

x = 48°

A triangle has three bisectors, each of which is a line that divides one of the angles of the triangle into two equal parts.The incenter is equidistant from the three sides of the triangle and is the center of the inscribed circle, which is the circle that is tangent to all three sides of the triangle.

A triangle is a two-dimensional geometric shape that has three straight sides and three angles. It is one of the simplest and most fundamental shapes in geometry, and it is widely studied in mathematics, science, and engineering. Triangles can have different types of angles and sides, which give rise to various classifications and properties. For example, a triangle can be classified as equilateral (all sides and angles are equal), isosceles (two sides and two angles are equal), or scalene (all sides and angles are different).

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When x is a uniformly distributed random variable on [0,1], it divides the interval [0,1] into two subintervals: [0,x] and [x,1]. This division exhibits symmetry, as explained in the following paragraphs.

Consider a uniformly distributed random variable x on the interval [0,1]. The probability density function of x is constant within this interval. When x takes a particular value, it acts as a dividing point that splits [0,1] into two subintervals.

The first subinterval, [0,x], represents all the values less than or equal to x. Since x is randomly distributed, any value within [0,1] is equally likely to be chosen. Therefore, the probability of x falling within the subinterval [0,x] is equal to the length of [0,x] divided by the length of [0,1]. This probability is simply x.

By symmetry, the second subinterval, [x,1], represents all the values greater than x. The probability of x falling within the subinterval [x,1] can be calculated as the length of [x,1] divided by the length of [0,1], which is equal to 1 - x.

The symmetry arises because the probability of x falling within [0,x] is the same as the probability of x falling within [x,1]. This symmetry is a consequence of the uniform distribution of x on the interval [0,1].

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Answer: The slope of the line that passes through the points (-8, -6) and (-8, 4) is undefined. This is because the line is a vertical line and the difference in y-coordinates is 0, making the denominator of the slope equation 0. The slope of a vertical line is undefined.

Step-by-step explanation:

If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient will be: D. .95.

A confidence interval is also referred to as level of confidence and it can be defined as a range of estimated values that defines the probability that a population parameter would fall or lie within it.

For instance, the confidence interval at 95% is given by p - E < p < p + E

Since the confidence interval for the mean of a population is at 95%, the confidence coefficient would be calculated by simply dividing the confidence interval by 100:

Confidence coefficient = 95/100

Confidence coefficient = 0.95

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The expected number of coins that are heads at the end after Jennifer has tossed 64 fair coins and those that landed on tails were tossed again is 32. the expected number of coins that are heads at the end is 48.

Here is a detailed explanation:Jennifer tosses 64 coins, and each coin has an equal chance of landing on either heads or tails. Thus, the probability that any one coin lands on heads is 0.5, and the probability that it lands on tails is also 0.5.When Jennifer tosses the 64 coins, some of them will land on tails.

Those coins will be tossed again. However, the probability of getting heads or tails for these coins is still 0.5 since the coins are fair.Therefore, the probability that a coin that has already been tossed and landed on tails to land on heads the second time is also 0.5.

The same applies to the third toss. The probability that a coin will land on heads or tails is 0.5.The total number of coins that land on tails during the first toss is given by

64*0.5 = 32.

Since these coins are tossed again, the expected number of coins that land on tails for the second toss is given by

32*0.5 = 16.

The remaining coins that landed on heads during the first toss are not affected. Thus, the expected number of coins that landed on heads during the first toss is

64 - 32 = 32.

The total number of coins that landed on heads during the first toss is given by 32.

Adding the expected number of coins that land on heads during the second toss (16),

the expected number of coins that land on heads is

32 + 16 = 48.

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Answer:

Step-by-step explanation:

x = width

x+8 = length

x(x+8)=273

x2 +8x-273=0

(x+21)(x-13)=0

x=-21  x=13

width can not be -21

width = 13 cm

length =21 cm

Answer:

The Length and Width are 21 cm, 13cm.

Step-by-step explanation:

so,

273 cm²   = ( x + 8 ) cm * ( X ) cm

Expanding the equation :

273 = x² + 8x cm => x² + 8x -273 =0

Now we use the Quadratic formula :

x = (-8 ± √(64 + 1092)) / 2    => x = (-8 ± √(1156)) / 2   => x = (-8 ± 34) / 2

Now we have two possibles,

Dimensions cannot be positive so x = 13, x+8 = 21.

Therefore the length, and width are 21 cm and 13 cm respectively.

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Answer:

The second one, the third one, and the fifth one.

Step-by-step explanation:

Just look at the proportions and see id the function matches the proportion. Use "soh cah toa" or "sin is opposite/hypotenuse, cos is adjacent/hypotenuse, and tan is opposite/adjacent." Hope this helps.