You measure 36 watermelons' weights, and find they have a mean weight of 56 ounces. Assume the population standard deviation is 13.3 ounces. Based on this, construct a 90% confidence interval for the true population mean watermelon weight. Give your answers as decimals, to two places _______ +/- ________

A. Using the distance formula, we can state that the opposite sides are congruent because AD = BC = √10 units and AB = CD = √40 units.

B. The diagonals are equal, AC = BD = √50 units.

C. Based on the slopes of each side, there are 4 right angles on the rectangle.

The distance formula is used to find the distance that exist between tow points that are on a coordinate plane. The formula is: d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

What is the Slope of a Line?

Slope = change in y / change in x.

A. The coordinates of each of the vertices of the rectangle are:

A(1, 2)

B(7, 4)

C(8, 1)

D(2, -1)

Use the distance formula to find AB, CD, BC, and AD.

AB = √[(7−1)² + (4−2)²]

AB = √40

CD = √[(2−8)² + (−1−1)²]

CD = √40

BC = √[(8−7)² + (1−4)²]

BC = √10

AD = √[(2−1)² + (−1−2)²]

AD = √10

Therefore, the opposite sides are congruent because AD = BC = √10 units and AB = CD = √40 units.

B. The diagonals are AC and BD. Find their lengths using the distance formula:

AC = √(8−1)² + (1−2)²]

AC = √50 units

BD = √[(2−7)² + (−1−4)²]

BD = √50 units

Therefore, the diagonals are equal, AC = BD = √50 units.

C. Find the slope of AB, CD, BC, and AD:

Slope of AB = change in y / change in x = rise/run = 2/6 = 1/3

Slope of CD = 2/6 = 1/3

Slope of BC = -3/1 = -3

Slope of AD = -3/1 = -3

-3 is the negative reciprocal to 1/3, this means that, if the two lines that meet at a corner have these two slope, then they will form a right angle because they are perpendicular to each other.

Therefore, there are 4 right angles on the rectangle.

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Answer:

1/4 * 1/2 = 1/8

Step-by-step explanation:

1/4 chance of choosing an 'm'

1/2 chance of getting tails

Probability of both events = 1/4 * 1/2 = 1/8

Answer: x=23

Step-by-step explanation:

1. First we need to find how much needs to be multiplied by 25, so 525/25=21.

2. Now that we know that x-2=21, we do 21+2.

3. 21+2=23, so x=23

Please give brainliest.

Yes, the scenario described fits the piecewise function represented by the graph.

According to the scenario:

Therefore, the piecewise function on the graph accurately models the described scenario.

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Answer:

Fraction form:       1/729

Decimal form:      0.00137174...

Exponent form:   3^-6

The sum for each geometric sequence is 62.

Given:

Geometric sequence,

2 4 8 16 32

Number of terms n = 5

First term a = 2

common ratio r = 4/2

= 2

Sum \(S_5 = a(r^n-1)/r-1\)

= 2(2^5 - 1)/2-1

= 2(32 - 1)/1

= 2(31)/1

= 2*31

= 62

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The correct values for a, b, c, d, and e are a = 16, b = 29, c = 24, d = 22, and e = 30 for group of 75 students on asking whether they like Algebra or Geometry.

For the values of a, b, c, d, and e, we can use the information provided in the table. Let's break it down step-by-step:

We are given that a total of 75 math students were surveyed. Therefore, the total number of students should be equal to the sum of the students who like algebra, the students who like geometry, and the students who do not like either subject.

75 = 45 (Likes Algebra) + 53 (Likes Geometry) + 6 (Does Not Like Either)

Simplifying this equation, we have:

75 = 98 + 6

75 = 104

This equation is incorrect, so we can eliminate options c and d.

Now, let's look at the information given for the students who do not like geometry. We know that a + b = 6, where a represents the number of students who like algebra and do not like geometry, and b represents the number of students who do not like algebra and do not like geometry.

Using the correct values for a and b, we have:

16 + b = 6

b = 6 - 16

b = -10

Since we can't have a negative value for the number of students, option a is also incorrect.

The remaining option is option e, where a = 29, b = 16, c = 24, d = 22, and e = 30. Let's verify if these values satisfy all the given conditions.

Likes Algebra: a + c = 29 + 24 = 53 (Matches the given value)

Does Not Like Algebra: b + d = 16 + 22 = 38 (Matches the given value)

Likes Geometry: c + d = 24 + 22 = 46 (Matches the given value)

Does Not Like Geometry: b + e = 16 + 30 = 46 (Matches the given value)

All the values satisfy the given conditions, confirming that option e (a = 29, b = 16, c = 24, d = 22, and e = 30) is the correct answer.

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No, the given list does not represent a complete probability model. In a probability model, the sum of probabilities for all possible outcomes should be equal to 1.

However, if we add up the probabilities mentioned, we get

16/6 + 13/3 + 112/12 + 1/2

= 8/3 + 13/3 + 28/3 + 1/2

= 21/3 + 28/3 + 1/2

= 49/3 + 1/2.

This sum is not equal to 1, which means the probabilities mentioned in the list do not represent a complete probability model. To form a complete probability model, we need to assign probabilities to all possible outcomes and ensure their sum is equal to 1.

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Answer:

x=9

Step-by-step explanation:

divide 4 by 4 to get 1

x-1=8

9-1=8

Hey there!

x - 4/4 = 8

x - 1 = 8

ADD 1 to BOTH SIDES

x - 1 + 1 = 8 + 1

CANCEL out: -1 + 1 because it give you 0

KEEP: 8 + 1 because it give you the x-value

NEW EQUATION: x = 8 + 1

SIMPLIFY IT!
x = 9

Therefore, your answer is: x = 9

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

4-2-5

Step-by-step explanation:

16, 8, and 20 can all be divided by 4

Leaving you with 4 2 and 5.

The ratio is 4 to 2 to 5

Answer:

B

Step-by-step explanation:

the 2/3x represents how much it will increase while the -1 represents the y-intercept

it is a right triangle lengths 6 8 and 10.

In this issue:

Then:

\(& 6^2+8^2=10^2 \\\)

\(& 36+64=100 \\\)

\(& 100=100\)

Identity, so it is a right triangle.

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The probability that a truck drives between 122 and 127 miles in a day is 0.0165, rounded to four decimal places.

To find the probability that a truck drives between 122 and 127 miles in a day, we'll use the z-score formula and standard normal distribution table. Follow these steps:

Step 1: Calculate the z-scores for 122 and 127 miles.
z = (X - μ) / σ

For 122 miles:
z1 = (122 - 90) / 18
z1 = 32 / 18
z1 ≈ 1.78

For 127 miles:
z2 = (127 - 90) / 18
z2 = 37 / 18
z2 ≈ 2.06

Step 2: Use the standard normal distribution table to find the probabilities for z1 and z2.
P(z1) ≈ 0.9625
P(z2) ≈ 0.9803

Step 3: Calculate the probability of a truck driving between 122 and 127 miles.
P(122 ≤ X ≤ 127) = P(z2) - P(z1)
P(122 ≤ X ≤ 127) = 0.9803 - 0.9625
P(122 ≤ X ≤ 127) ≈ 0.0178

So, the probability that a truck drives between 122 and 127 miles in a day is approximately 0.0178 or 1.78%.

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The range at which Dan's car can go is 3.33 miles

A car's range is the distance it can travel with the current amount of fuel in the tank.

The vehicle calculates the range based on the amount of fuel, how the accelerator and brakes are used, and how quickly the car is travelling.

The range of a car can be measured in the unit of distance.

Therefore the range of a car can be calculated as;

R = distance per gallon/ number of gallon.

Dan's car is 40mpg and has 12 gallons in it's tank.

Therefore it's range = 40/12

= 3.33miles.

therefore the range of Dan's car is 3.33miles

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Answer:

Step-by-step explanation:

i think A

Hope this helps!

\(\huge{\textbf{\textsf{{\color{navy}{An}}{\red{sw}}{\orange{er}} {\color{yellow}{:}}}}}\)

\( \frac{2}{x} = \frac{5}{3} \)

By doing cross multiplication.

\(6 = 5x \\ x = \frac{6}{5} \\ x = 1.2\)

Answer:

the answer you are looking for is A ,1.2

Answer:

I believe it is D or C but I could be wrong

Answer:

e. none of the above!

Step-by-step explanation:

it has 5 sides not 4 like the other options so e. none of the above!

hope this helps:) !!!!!!!!

The value of f(x) at x = 3 is 19.14. The characteristic equation of the homogeneous part of the differential equation is: r^2 - 2r + 1 = 0

which has a double root of r = 1. Therefore, the general solution to the homogeneous equation is:

y_h(x) = c_1 e^x + c_2 xe^x

To find a particular solution to the nonhomogeneous equation, we use the method of undetermined coefficients. We guess a particular solution of the form:

y_p(x) = Ax + B

Taking the first and second derivatives of y_p(x), we get:

y_p'(x) = A

y_p''(x) = 0

Substituting y_p(x), y_p'(x), and y_p''(x) into the original nonhomogeneous equation, we get:

0 - 2A + Ax + B = x - 2

Simplifying, we get:

A = 1

B = -2

Therefore, a particular solution to the nonhomogeneous equation is:

y_p(x) = x - 2

The general solution to the differential equation is:

y(x) = y_h(x) + y_p(x) = c_1 e^x + c_2 xe^x + x - 2

Using the initial conditions, we can solve for c_1 and c_2:

y(0) = c_1 + 0 + 0 - 2 = 0

c_1 = 2

y'(0) = c_1 + c_2 + 1 = 2

c_2 = 0

Therefore, the solution to the differential equation is:

y(x) = 2e^x + x - 2

We can now find f(x) = y(x) - xe^x and evaluate it at x = 3:

f(x) = y(x) - xe^x = (2 + x) e^x - 2

f(3) = (2 + 3) e^3 - 2 = 19.14

Therefore, the value of f(x) at x = 3 is 19.14.

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The equation of the parabola with focus (2,5) and directrix x=18 is (x - 18)² + (y - 5)² = (y - (5 + (18 - 2) / 2))².

A parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating

straight line of that surface.

The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.

The directrix is a straight line perpendicular to the axis of symmetry and placed symmetrically with respect to the focus.

The axis of symmetry is the line through the focus and perpendicular to the directrix.

The vertex of a parabola is the point where its axis of symmetry intersects the curve. It is the point where the parabola changes direction or "opens

up" or "opens down.

The directrix is a fixed straight line used in the definition of a

parabola. It is placed such that it is perpendicular to the axis of symmetry and at a distance from the vertex equal to the

distance between the vertex and focus. It is the line that is equidistant to the focus and every point on the curve.Here's

the solution to the given problem:

The distance between the directrix and the focus is equal to p = 16 (since the directrix is x = 18, the parabola opens to the left, so the distance is measured horizontally)

The vertex is (h,k) = ((18+2)/2,5) = (10,5)

Then we can use the following formula: (x - h)² = 4p(y - k)

Substitute the vertex and the value of p. (x - 10)² = 64(y - 5)

Expand and simplify. (x - 10)² + (y - 5)² = 64(y - 5)

The equation of the parabola is (x - 10)² + (y - 5)² = 64(y - 5).

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There are 7 students who are studying both programming languages in the given class of 55 freshman.

This can be determined using a Venn diagram.

A Venn diagram is a graphical representation of sets or classes. The diagram shows sets, their elements, and the union, intersection, and complement of these sets.

A set is a collection of distinct objects, considered as an object in its own right. The elements of a set are frequently things of a similar nature, and sets are characterized by a distinctive property.

The size of a set is represented by the number of elements it contains. Let's use the following symbols to represent sets:

A={Elements in set A}

B={Elements in set B}

The intersection of sets A and B is the set of elements that are in both sets A and B. This can be expressed in the following way

n(A∪B) = n(A) + n(B) - n(A⋂B) where n(A⋂B) is known as intersection

The number of students studying both programming languages can be calculated by taking the intersection of the two sets.

We can use this formula to calculate the number of students studying both programming languages

:|A∩B|=|A|+|B|-|A∪B|

Where |A| denotes the number of elements in set  A studying C programming

|B| denotes the number of elements in set B studying Java

|A∪B| denotes the number of elements in the union of sets A and B (total students)

Now we can substitute the given values into the formula as follows

|A∩B|=38+24−55=7

Therefore, there are 7 students studying both programming languages.

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Answer:

(-1,-6)

Step-by-step explanation:

(-1,-6)

Multiply coordinates of mid point by 2

take away from point P

Answer:

two solutions

Step-by-step explanation:

The p-value is established and hypotheses are accepted or rejected based on these results, the result is significant.

The general recurrence of z-scores empowers us to decide a few things in regards to the comparing crude scores, except for deciding qualities concerning goodness or disagreeableness. The number of standard deviations a given data point has from the population mean is measured using Z-scores. In statistics, particularly normal distribution, these are frequently used to normalize data and evaluate a data point's position for improved data analysis. One of the purposes of the general recurrence of z-scores is that it permits us to work out the likelihood of an occasion happening in a standard typical conveyance.

Using mathematical software or a standard normal table, the probability distribution for z-scores can be found and used to calculate the probabilities of occurrences below, above, or between two z-scores. The general recurrence of z-scores is additionally utilized in deciding whether a noticed contrast is impressive and measurably critical. By determining whether the difference is significant if the corresponding z-score falls outside the range of 1.96, this can be accomplished. Since the p-value is established and hypotheses are accepted or rejected based on these results, the result is significant.

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The estimated median price of a single-family home in Charleston/No. Charleston in the 1st Quarter of 2008 is $201,048. If the median price continues to decrease at the same rate for the next two years, the estimated median price of a single-family home in the 1st Quarter of 2011 would be $144,458.

(a) To estimate the median price of a single-family home in the 1st Quarter of 2008, we need to calculate the original price before the 8.15% decrease. Let's assume the original price was P. The price after the decrease can be calculated as P - 8.15% of P, which translates to P - (0.0815 * P) = P(1 - 0.0815). Given that the end of 1st Quarter of 2009 median price was $184,990, we can set up the equation as $184,990 = P(1 - 0.0815) and solve for P. This gives us P ≈ $201,048 as the estimated median price of a single-family home in the 1st Quarter of 2008.

(b) If the median price of a single-family home falls at the same rate for the next two years, we can calculate the price for the 1st Quarter of 2011 using the estimated median price from the 1st Quarter of 2009. Starting with the median price of $184,990, we need to apply an 8.15% decrease for two consecutive years. After the first year, the price would be $184,990 - (0.0815 * $184,990) = $169,805.95. Applying the same percentage decrease for the second year, the price would be $169,805.95 - (0.0815 * $169,805.95) = $156,012.32. Therefore, the estimated median price of a single-family home in the 1st Quarter of 2011 would be approximately $144,458.

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Answer:

m<Q = 93 degrees

m<R = 87 degrees

Step-by-step explanation:

Given the following angles;

m<Q = 9x-6

m<R = 8x-1

Looking at Devin's work, we will see that he the sum of both angles is 180 degrees

Hence m<Q + m<R = 180

9x - 6 + 8x - 1 = 180

9x+8x-6-1 = 180

17x - 7 = 180

17x = 180 + 7

17x = 187

x = 187/17

x = 11

Get m<Q

m<Q = 9x - 6

m<Q = 9(11) - 6

m<Q = 99 - 6

m<Q = 93 degrees

Get m<R

m<R = 180 - m<Q

m<R = 180 - 93

m<R = 87degrees

Answer:

93 and 87

Step-by-step explanation:

edge 2021

Answer:

Hey there!

To solve this problem, we want to find the LCM (least common multiple) of the two numbers.

The numbers are 25 and 30.

25=5x5

30=2x3x5

LCM is 5x5x2x3, or 150.

Thus, in 150 minutes is when the next bus will leave.

150 mins is equal to 2 hours and 30 mins, or 2.5 hours.

8 AM + 2.5 hrs = 10:30 AM.

Thus, the next time the busses leave together would be at 10:30 AM.

Let me know if this helps :)

Answer:

440

Step-by-step explanation:

240 divided by 6 is 40, 4 women. and 11 x40 is 440.

Answer:

8jdjdjfjdjrnbvnfjdkekc

The solution to the linear system is unique solution which is  x₁ = 1/6, x₂ = 3/2, and x₃ = 17/6.

The correct answer is option  A.

To solve the given system of linear equations using elementary row operations and back substitution, let's start by representing the augmented coefficient matrix:

[1  -4  5  |  23]

[2   1   1  |  10]

[-3  2  -3 |  -23]

We'll apply row operations to transform this matrix into echelon form:

1. Multiply Row 2 by -2 and add it to Row 1:

[1  -4   5   |  23]

[0   9   -9  |  -6]

[-3  2  -3  |  -23]

2. Multiply Row 3 by 3 and add it to Row 1:

[1  -4  5   |  23]

[0   9  -9  |  -6]

[0   -10 6  |  -68]

3. Multiply Row 2 by 10/9:

[1  -4  5    |  23]

[0   1   -1   |  -2/3]

[0   -10 6  |  -68]

4. Multiply Row 2 by 4 and add it to Row 1:

[1  0   1   |  5/3]

[0  1   -1  |  -2/3]

[0  -10 6  |  -68]

5. Multiply Row 2 by 10 and add it to Row 3:

[1  0   1   |  5/3]

[0  1   -1  |  -2/3]

[0  0   -4  |  -34/3]

Now, we have the augmented coefficient matrix in echelon form. Let's solve the system using back substitution:

From Row 3, we can deduce that -4x₃ = -34/3, which simplifies to x₃ = 34/12 = 17/6.

From Row 2, we can substitute the value of x₃ and find that x₂ - x₃ = -2/3, which becomes x₂ - (17/6) = -2/3. Simplifying, we get x₂ = 17/6 - 2/3 = 9/6 = 3/2.

From Row 1, we can substitute the values of x₂ and x₃ and find that x₁ + x₂ = 5/3, which becomes x₁ + 3/2 = 5/3. Simplifying, we get x₁ = 5/3 - 3/2 = 10/6 - 9/6 = 1/6.

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The rate of change of the radius with respect to time when the radius of the deflating balloon is 3 cm is -0.01 cm/s.

When a spherical balloon deflates at a constant rate, the radius decreases with time. In this case, when the radius is 3 cm, the rate of change of the radius with respect to time is calculated to be -0.01 cm/s. This negative value indicates that the radius decreases by 0.01 cm for every second that passes.

The rate of change of the radius of a deflating balloon can be determined using the given information about the rate of deflation and the formula for the volume of a sphere. By differentiating the volume formula with respect to time and substituting the given rate of deflation, we can obtain an equation that relates the rate of change of the radius with respect to time. Solving this equation, we find that the rate of change of the radius is constant (-0.01 cm/s) when the balloon's radius is 3 cm.

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