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The mean weight of a randomly chosen vehicle is 3500 pounds.

A Z-score helps us to understand how far is the data from the mean. It is a measure of how many times the data is above or below the mean.

We are given that the weight of a randomly chosen american passenger car is a uniformly distributed random variable ranging from 1,749 pounds to 4,039 pounds.

Let X= weight of the passenger car

a/q, X is u(1,749, 4,039)

we know that mean= a+b/2

so a=1,749, b=4,039

hence, mean=1,749 +4,039/2

mean=3500 pounds

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Riemann sums are calculated by dividing the area under a curve into subintervals and approximating the area in each interval using a rectangle.

Riemann sums are a method of approximating the area under a curve by dividing the area into smaller subintervals and approximating the area in each interval using a rectangle. The width of each rectangle is determined by the size of the subinterval, and the height of the rectangle is determined by the value of the function at a specific point within the subinterval.

The sum of the areas of all the rectangles gives an approximation of the total area under the curve. The accuracy of the approximation increases as the width of the subintervals decreases, and as the number of subintervals increases, the approximation approaches the exact value of the area under the curve.

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Answer:

Step-by-step explanation:

Try putting it in Y= in the calculator

Answer: 11

Step-by-step explanation: Just took the test

The length of the apothem of the pentagon is approximately 11 meters.

Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,

Examples of polygons, equilateral triangles, squares, pentagons etc.

Here,
To solve this problem, we can use the formula for the area of a regular pentagon:

A = (5/2) × s × a

Where A is the area of the pentagon, s is the length of one side, and a is the apothem (the distance from the center of the pentagon to the midpoint of a side).

We know that the area of the pentagon is 118.25 square meters and the length of one side is 4.3 meters. We can substitute these values into the formula and solve for the apothem:

118.25 = (5/2) × 4.3 × a

Divide both sides by (5/2) x 4.3:

a = 118.25 / ((5/2) × 4.3)
  = 118.25 / 10.75 ≈ 11 meters

Therefore, the length of the apothem of the pentagon is approximately 11 meters.

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The second trapezoid has the corresponding sides labeled 4.9 cm and x cm, the value of x is 4.2 cm

Without knowing the scale factor, we can use the ratio of corresponding sides of the two trapezoids to set up an equation and solve for x.

The ratio of the lengths of the corresponding sides of the two trapezoids is: 14.7 cm / 12.6 cm = 4.9 cm / x

To solve for x, we can cross-multiply:

14.7 cm × x

= 12.6 cm × 4.9 cm

Dividing both sides by 14.7 cm, we get:

x = (12.6 cm × 4.9 cm) / 14.7 cm

Simplifying the right side, we get:

x = 4.2 cm

Therefore, the value of x is 4.2 cm.

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. The height of a trapezoid is the perpendicular distance between the bases. The area of a trapezoid is given by the formula A = (b1 + b2) × h / 2, where b1 and b2 are the lengths of the bases and h is the height. Trapezoids are commonly found in geometric and architectural designs, and they have various applications in engineering and physics.

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Complete Question

This scale drawing shows a reduction in a figure. What is the value of x? Enter your answer as a decimal in the box. x = Two trapezoids of different sizes. The first trapezoid has a side labeled 14.7 cm and a side labeled 12.6 cm. The second trapezoid has the corresponding sides labeled 4.9 cm and x cm, respectively. Find x in trapezoid.

A left-skewed histogram is a frequency distribution in which the data is concentrated towards the right side of the histogram, with a tail stretching towards the left.

A left-skewed histogram is a kind of frequency distribution where the data is concentrated towards the right side of the histogram, with a tail extending towards the left. It is otherwise called a negatively skewed histogram or a left-tailed histogram. In a left-skewed histogram, the mean is not exactly in the middle, demonstrating that the information is slanted toward the lower end of the conveyance. This can happen when the information has a lower bound or a base worth, which makes the tail of the dispersion be pulled towards the left. Left-skewed histograms can be helpful in examining information that has a characteristic lower cutoff or floor, for example, response times, reaction rates, or pay levels.

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I think for the shirts it's 32 and the t-shirts for 50 .

Step-by-step explanation:

Conditional probability can be calculated by using Bayes' theorem, P(A|B) = P(B|A) × P(A) / P(B)

To find the conditional probability, we need to know the probability of two events: the probability of the event we're interested in, and the probability of the condition. Then, we can use Bayes' theorem to calculate the conditional probability.

Bayes' theorem states that the probability of an event A given that event B has occurred is equal to the probability of B given A, multiplied by the probability of A, divided by the probability of B:

P(A|B) = P(B|A) × P(A) / P(B)

The steps to find the conditional probability:

1) Identify the events A and B.

2) Determine the probabilities of A and B.

3) Determine the conditional probability P(B|A)

4) Substitute the values into Bayes' theorem to find P(A|B)

5) Interpret the result.

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The approximate probability that out of 1000 poker hands there will be at least 450 with a single pair is 0.035

This is a binomial distribution problem with n = 1000 and p = 0.42. Let X be the number of poker hands with a single pair out of 1000 poker hands.

To find the probability that there are at least 450 poker hands with a single pair, we need to calculate P(X ≥ 450).

Using the normal approximation to the binomial distribution, we have:

μ = np = 1000 × 0.42 = 420

σ = √(np(1-p)) = √(1000 × 0.42 × 0.58) ≈ 16.08

Using the continuity correction, we can approximate P(X ≥ 450) as P(Z ≥ (449.5 - 420)/16.08) where Z is the standard normal distribution.

P(Z ≥ (449.5 - 420)/16.08) = P(Z ≥ 1.814) ≈ 0.035

Therefore, the approximate probability that out of 1000 poker hands there will be at least 450 with a single pair is 0.035.

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1. The Complete table is shown below.

2. The graph likes like parabola whose equation is y= 50x - x².

Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve. The topic of conic sections includes parabola, and all of its principles are discussed here.

Given:

Length  Width  Area

10            40      400

20             30      600

25             25       625

35             15        525

40              10       400

So, x+ y= 50

y= 50- x

so, area of figure is

= x (50- x)

= 50x - x²

So, we get parabola which is opened downward.

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Answer: you

Step-by-step explanation:

The black bear population at that national park in 25 years would be 2973 approx, according to the considered model.

How to evaluate a given mathematical expression with variables if values of the variables are known?

You can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.

According to the model, the relationship between the elapsed time t, in years, since the beginning of the study, and the black bear population B(t) is:

B(t) = 2500 * 2^0.01t

Here, if we take t = 25 years elapsed, the value of B(t) comes out as:

B(25) = 2500 * 2^0.01*25

B(25) = 2973

Thus, the black bear population be at that national park in 25 years would be 2973 approx, according to the considered model.

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Answer:

B(25) = 2500 * 2^0.01*25

B(25) = 2973

Step-by-step explanation:

Approximately 50% of the values in a distribution lie between the 25th percentile and the 75th percentile.

The interquartile range (IQR) is the range between the 25th percentile (Q1) and the 75th percentile (Q3) of a distribution. The IQR contains the middle 50% of the data.

Therefore, approximately 50% of the values in a distribution lie outside the IQR, with 25% of the values below Q1 and 25% of the values above Q3. The remaining 50% of the values lie within the IQR, with approximately 25% of the values between Q1 and the median, and 25% of the values between the median and Q3.

So, approximately 50% of the values in a distribution lie outside the IQR, and approximately 50% of the values lie within the IQR, which includes the values between the 25th and 75th percentile.

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Answer: in two years you'll have 686.94

The value of the expression 18 - (16 • 12) is -174.

To evaluate the expression 18 - (16 • 12), we need to follow the order of operations, also known as PEMDAS. According to PEMDAS, we first perform any calculations inside parentheses, then evaluate exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.

In this expression, we have the operation of multiplication inside parentheses. So, we start by evaluating 16 • 12, which equals 192.

Now, we can rewrite the expression as 18 - 192.

Next, we perform the subtraction, which gives us -174.

Therefore, the value of the expression 18 - (16 • 12) is -174.

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The explicit formula for the nth term of the sequence 14,16,18,... is aₙ = 2n + 12.

What is an explicit formula?

The explicit equations for L-functions are the relationships that Riemann introduced for the Riemann zeta function between sums over an L-complex function's number zeroes and sums over prime powers.

Here, we have

Given:  the sequence 14,16,18,….

First term a₁ = 14

Common difference d = 16 - 14 = 2

Now, plug the values into the above formula and simplify.

aₙ = a₁ + d( n - 1 )

aₙ = 14 + 2( n - 1 )

aₙ = 14 + 2n - 2

aₙ = 14 - 2 + 2n

aₙ = 2n + 12

Hence,  the explicit formula is aₙ = 2n + 12.

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Answer:

∠S possibility is 65 degrees and 115 degrees

Step-by-step explanation:

∠S + ∠T + ∠U = 180

Substituting the given values, we get:

∠S + ∠T + 79 = 180

Simplifying, we get:

∠S + ∠T = 101

We also know that the sides of a triangle are related to the angles opposite them by the law of sines:

a/sin A = b/sin B = c/sin C

In this case, we can use the following ratio:

ST/sin S = UT/sin U

Substituting the given values, we get:

ST/sin S = UT/sin 79

ST = s = 56 cm

UT = u = 94 cm

Solving for sin S, we get:

sin S = (ST × sin 79) / UT

sin S = (56 × sin 79) / 94

sin S ≈ 0.906

Taking the inverse sine, we get:

∠S ≈ 65 degrees or ∠S ≈ 115 degrees

Therefore, the possible values of ∠S are approximately 65 degrees and 115 degrees, to the nearest degree.

The two angles in the ratio of 5:18 are 50° and 130° respectively. To determine this, we can use the fact that the sum of the angles in any quadrilateral is 360°.

Therefore,

where x and y are the two angles in the ratio of 5:18.

We can then solve for x and y by setting up the proportion

and then solving for x and y.

This gives us

Therefore, the two angles in the ratio of 5:18 are 50° and 130°.

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It will take approximately 12 years and 9 months for Sienna Rose's money to grow to $7000.

What is compound interest?

Compound interest is interest that is calculated not only on the original principal amount of a loan or investment but also on any accumulated interest from previous periods. In other words, the interest earned on an investment or the interest charged on a loan is added to the principal, and then the interest for the next period is calculated on the new total amount.

For example, if you invest $1,000 at an annual interest rate of 5%, and the interest is compounded annually, you would earn $50 in interest at the end of the first year. Instead of receiving that $50, it would be added to your principal, so your new balance would be $1,050. The following year, you would earn 5% interest on $1,050, which would be $52.50. This process would continue for each year of the investment.

Compound interest can be very beneficial for long-term investments, as the interest earned on the accumulated interest can significantly increase the total return. However, it can also work against you in the case of loans, as the interest charged on the accumulated interest can quickly increase the total amount owed.

We can use the formula for compound interest to solve this problem:

[tex]A= P (1+\frac{r}{n} )^{nt}[/tex]

where

A is the amount of money after t years,

P is the principal (starting amount),

r is the annual interest rate (as a decimal),

n is the number of times the interest is compounded per year, and

t is the time (in years).

In this case,

P = $4000,

r = 0.036 (since the interest rate is given as 3.60% per year),

n = 12 (since the interest is compounded monthly), and

we want to find t when A = $7000.

Substituting these values into the formula, we get:

$7000 = $4000(1 + 0.036/12)^(12t)

Dividing both sides by $4000 and taking the natural logarithm of both sides, we get:

ln(1.75) = 0.003 t

Solving for t, we get:

t = ln(1.75)/(0.003)

t ≈ 153.71 months

Therefore, it will take approximately 153 months, or 12 years and 9 months (since there are 12 months in a year), for Sienna Rose's money to grow to $7000.

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1) All the angles are,

∠ 1 = 72°

∠ 2 = 54°

∠ 3 = 54°

∠ 4 = 72°

2) All the angles are,

∠1 = 59°

∠2 = 90°

∠3 = 90°

∠ 4 = 31°

3) All the angles are,

∠ 1 = 22°

∠ 2 = 68°

∠ 3 = 68°

∠ 4 = 90° (right angle)

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

1) From first figure,

⇒ ∠ 3 = 54°   (Two sides are equal hence two angles are also equal)

Hence, We get;

∠3 + ∠4 + 54° = 180°

54° + ∠4 + 54° = 180

∠4 = 180 - 108

∠4 = 72°

Hence, We get;

∠ 1 = ∠ 4

∠ 1 = 72°

And, ∠2 = ∠3 = 54°

2) From second figure,

∠ 4 = 90 - 59°

      = 31°

And, We have;

∠1 = 59°

And, Diagonal bisect each other.

Hence,

∠ 2 = ∠ 3 = 90°

3) From third figure,

∠ 2 = 68°

Hence, 2 ∠ 1 = 180 - 136°

2 ∠ 1 = 44°

∠ 1 = 22°

And, We have;

Since, ∠ 2 = 68°

Hence, ∠ 3 = 68°

And. ∠ 4 = 90° (right angle)

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Answer:

46.8 cm²

Step-by-step explanation:

3.9 x 6 = 23.4 (We are multiplying by 6 because there are 6 tiles)

23.4 x 2 = 46.8 (We are multiplying by 2 because when Suki is adding more tiles, she makes a hexagon double the side lengths.)

At the end of the fourth minute, the point 'g' would be at the position of 9605961 on the line segment TS.

As per the question, at the end of the first minute,  g covers 1/100th of the remaining segment, which is 1/100 × 10000000 = 100000 units. Therefore, the position of point g would be at 10000000 - 100000 = 9900000 at the end of first minute.

At the end of second minute, g covers another 1/100th of the remaining segment, which is 1/100 × 9900000 = 99000 units. So, the position of point g would be now 9900000 - 99000 = 9801000.

On the third minute's end ,  g would covers another 1/100th of the remaining segment, which is 1/100 × 9801000 = 98010 units. Therefore, the position of point g would be at 9801000 - 98010 = 9702990.

For fourth minute's end, point g covers another 1/100th of the next remaining segment, which is 1/100 × 9702990 = 97029 units. Therefore, the final position of point g would be at 9702990 - 97029 = 9605961 units.

Therefore, at the end of the fourth minute, point g would be finally at the position of 9605961 on the line segment TS.

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The correct question is :

imagine a line segment ts of length 10000000 and point g moving from t=10000000 toward s=0, so that it cuts 1/100th of the remaining segment each minute. For example, at the the end of first minute g1 is at 99,00,000. Where is g at the end of fouth minute (g4) ?

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Answer: To solve for A in the equation -BA + g² = MA, we can start by isolating the A variable on one side of the equation.

We can start by adding BA to both sides of the equation:

-BA + BA + g² = MA + BA

Simplifying the left side by cancelling the -BA and +BA terms:

g² = MA + BA

Next, we can factor out the A variable from the right side:

g² = A(M + B)

Finally, we can divide both sides by (M + B) to isolate the A variable:

g² / (M + B) = A

So the solution for A is:

A = g² / (M + B)

Step-by-step explanation:

Let's call the smaller number "x" and the larger number "y".

We know that:

y + x = 26 (since the total of the two numbers is 26)

and

y = 10 + 3x (since the larger number is 10 more than triple the smaller number)

We can substitute the second equation into the first equation to get:

(10 + 3x) + x = 26

Simplifying, we get:

4x + 10 = 26

Subtracting 10 from both sides, we get:

4x = 16

Dividing both sides by 4, we get:

x = 4

Now that we know x is 4, we can use the second equation to find y:

y = 10 + 3x

y = 10 + 3(4)

y = 22

Therefore, the two numbers are 4 and 22.

In mathematics, the term "orthogonal" refers to a relationship between two objects where they are perpendicular or at right angles to each other.

More generally, it refers to a relationship where two objects are independent or uncorrelated with each other. For example, in Euclidean geometry, two lines are orthogonal if they meet at a right angle. In linear algebra, two vectors are said to be orthogonal if their dot product (also known as inner product) is zero. Similarly, in statistics, two variables are said to be orthogonal if they have a correlation coefficient of zero, indicating that they are uncorrelated.

The term "orthogonal" is also used in various other fields, such as signal processing, computer science, and quantum mechanics, with similar meanings of independence, uncorrelatedness, or perpendicularity.

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The value  0.24 as a fraction is 6/25. .

In mathematics, fractions are defined as part of a whole. A whole can be an object or a group of objects. In real life, if you cut a pie out of the whole pie, that piece becomes part of the pie. Fractions are words of Latin origin. "Fractus" means "broken" in Latin. In ancient times, rest was expressed in words. Later it was introduced in numerical form.

Fractions are also called parts or sections of any quantity. Represented by the symbol '/'. Bachelor/Bachelor For example, 2/4 is the numerator above and the fraction below the denominator. In this article, you will learn the definition of fractions in mathematics, types of fractions, how to convert fractions to decimals, and many solved examples and full explanations

to convert in fraction we will muliply and devide by 100.

0.24*100/100 =6/25

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The area of the teacher workroom is 64 feet squared