The lengths of the bases of a right trapezoid are 9 cm and 18 cm. The length
of a longer leg is 15 cm. Find the area of the trapezoid.

Answer:

length = 9 units

Step-by-step explanation:

l = length

n - 6 = width

A = n(n - 6)

A = n² - 6n

27 = n² - 6n

n² - 6n - 27 = 0

(n + 3)(n - 9) = 0

n = -3, n = 9

length must be 9 because it cannot be a negative value

Answer: moderate, C, B

Step-by-step explanation:

A)  A shows a moderate negative correlation.  It is moderate because the scattered points are sort of close to the line so it has moderate/medium correlation.  It is also negative because it has a negative slope

B) C shows the strongest correlation because the points around the line are tight and close.

C)  B should not have been drawn.  The  correlation is very weak.  You do know where the line should be because the points are all over the place.

. Write the equation for the line: (Hint: there are two points given to you!)

________________________

y= mx + b

the slope is m

or

(y - y1) = m (x - x1)

___________________

points (x,y)

point 1 (4, 4) x1 = 4; y1 = 4

point 2 (3 , -1) x2= 3; y2 = -1

The slope m = (y2- y1) / (x2 -x1)

m=(-1 - 4 )/( 3 - 4)

m= -5/-1 = 5

(In this case, you choose which point you want to put as point one and point two, you will always get the same answer)

____________________

(y - 4) = 5 (x - 4)

y= 5x -20 +4

y= 5x - 16

The equation for the line is y= 5x - 16

__________________

Do you have any questions regarding the solution?

Answer:

1400

Step-by-step explanation:

8 times 7 times 25 = the volume

=1400

Answer:

1400

Step-by-step explanation:

To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

The quotient in rectangular form is √3 + i.

The given expression is

10 cos 100 + i sin 100°) / (5 cos 40° + i sin 40°).

We need to find the quotient and write it in rectangular form using exact values.

Now, let's solve the problem step by step.

Step 1: Find the product of the denominator's complex conjugate

(5 cos 40° - i sin 40°)

and multiply both the numerator and denominator by it.

We get,

(10 cos 100 + i sin 100°) / (5 cos 40° + i sin 40°) × (5 cos 40° - i sin 40°) / (5 cos 40° - i sin 40°)

= [(10 cos 100 + i sin 100°) × (5 cos 40° - i sin 40°)] / [(5 cos 40°)² - (-i sin 40°)²]

Step 2: Expand the numerator using the product-to-sum identity

cos (A + B)= cos A cos B - sin A sin B

and simplify using the identity

sin²x + cos²x = 1.

We get,

(10 cos 100 + i sin 100°) × (5 cos 40° - i sin 40°)

= (50 cos 100° cos 40° + 50 sin 100° sin 40°) + i (50 sin 100° cos 40° - 50 cos 100° sin 40°)

= (50 cos (100° - 40°)) + i (50 sin (100° - 40°))

= (50 cos 60°) + i (50 sin 60°)

= 25√3 + 25i

Step 3: Substitute the value obtained in step 2 in the numerator of the original expression to get the quotient, which is

(25√3 + 25i) / (25 cos 40°) = √3 + i

Therefore, the quotient in rectangular form is √3 + i.

Thus, the answer is

bi = √3 + i.

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a. Using the smallest possible number of items, is not generally a way to enhance reliability.

b. Measuring something that is minimally important, does not necessarily enhance reliability.

c. Aggregating measurements, is the generally useful way to enhance reliability.

d. Maximizing error variance, is not a way to enhance reliability.

Among the options provided, the generally useful way to enhance reliability is option c: to aggregate your measurements.

Aggregating measurements refers to combining multiple measurements or observations to improve the overall reliability of the data. By taking multiple measurements, you can reduce the impact of random errors and obtain a more accurate estimate of the true value or attribute you are measuring.

Option a, using the smallest possible number of items, is not generally a way to enhance reliability. In fact, having a larger sample size or more data points often improves reliability by reducing the effects of random variations.

Option b, measuring something that is minimally important, does not necessarily enhance reliability. The importance of what is being measured is not directly related to the reliability of the measurements. Reliability focuses on the consistency and accuracy of the measurements themselves.

Option d, maximizing error variance, is not a way to enhance reliability. Error variance refers to the variability or spread of errors in measurement. Maximizing error variance would lead to less reliable measurements as it increases the uncertainty and inconsistency of the data.

In summary, option c, aggregating measurements, is the generally useful way to enhance reliability.

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The probability that the number of milligrams is less than 60 is equal to,

P(x < 60) = 96.6%

The mean gives us an idea of where the “center” value of a dataset is located. The standard deviation gives us an idea of how spread out the values are around the mean in a dataset. The higher the value for the standard deviation, the more spread out the values are in a sample.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Based on the given conditions,

Mean, μ = 38

Standard Deviation, σ = 12

We are given that the distribution of number of milligrams of porphyritic per deciliter of blood is a bell shaped distribution that is a normal distribution.

Formula:

\(z_{score}\) = ( x - μ ) /  σ

a) P(x is less than 60)

P(x < 60)

P(x < 60) = p ( z < \(\frac{60-38}{12}\) )

P(x < 60) = p ( z < 22/12 )

P(x < 60) = p ( z < 1.83 )

Calculation the value from standard normal z table, we have,  

P(x < 60) = 0.966

P(x < 60) = 96.6%

Therefore,

The probability that the number of milligrams is less than 60 is equal to,

P(x < 60) = 96.6%

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Answer: 1/3x -2

Step-by-step explanation:

X-3y =6 subtract x from both sides first

-3y=6-x. Then divide both sides by -3

Y= 6-x /-3 simplify

Y= -2+x/3 rearrange

Y= 1/3x -2

Answer:

b 17/18

Step-by-step explanation:

Solve the one's in bracket then later solve everything together

Answer:

\(y=3cos(\frac{1}{2} (x+}225)+4\)   phase shift in degrees

\(y=3cos(\frac{1}{2} (x+\frac{5\pi }{4}))+4\)   phase shift in pi radians

Step-by-step explanation:

Here is the equation for the graph of the cosine function.

y = A sin(B(x + C)) + D

A = amplitude

period is 2π/B

C = phase shift

D = vertical shift

Lets convert 1800° to Pi radians.

\(1800*\frac{\pi }{180}\)

\(180(10)*\frac{\pi }{180}\)

\(10*\frac{\pi }{180}\)

\(10\pi\) radians

A = 3

B=2π/ 10π  simplifies to \(\frac{1}{2}\)

C = phase shift

D = 4

\(y=3cos(\frac{1}{2} (x+}225)+4\)   phase shift in degrees

\(y=3cos(\frac{1}{2} (x+\frac{5\pi }{4}))+4\)   phase shift in pi radians

Solving some linear equations we can see that the values are:

x = 30

y = 28

Remember that a right angle is equal to 90°, and that the sum of the interior angles of any triangle is equal to 180°.

The first thing we can do is solve an equation for x:

3x = 90

x = 90/3

x = 30

Now, remember that the sum of the interior angles is 180°, then we can write the linear equation:

34 + 90 + 2y = 180

2y = 180 - 90 - 34

2y = 56

y = 28

These are the values.

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Given:

Consider the tank that is filled with water drains at a rate of \(\dfrac{d^2}{16}+4d-100\) gallons per minute where d is the depth of the tank in feet.

Depth of tank = 120 feet.

To find:

The rate of water drain for that tank.

Solution:

We have, rate of water drain in gallons per minute.

\(r=\dfrac{d^2}{16}+4d-100\)

where, d is the depth of the tank in feet.

Put d=120, to get the rate of water drain for the tank.

\(r=\dfrac{120^2}{16}+4(120)-100\)

\(r=\dfrac{14400}{16}+480-100\)

\(r=900+380\)

\(r=1280\)

Therefore, the rate of water drain is 1280 gal/min. Hence, the correct option is B.

Answer: A=πr2=π·12≈3.14159ft²

Step-by-step explanation:

With the value of the circumference of the circle, find the radius of a circle. Then substitute the value of the radius of the circle in the formula of area of a quarter circle using radius which is πr2/4.

Answer:

--------------------------------

Answer:

It would be NEGATIVE because a positive number times a negative number, the answer is negative.

ANSWER

372 grams

EXPLANATION

The half life of the substance is 11 days.

We want to find how much will be left after starting with 1488 grams for 22 days.

To do that, apply the formula for half life:

where N = amount of substance left

N0 = initial amount of substance

t = amount of time

t1/2 = hlaf life

Therefore, for the given substance, the amount that will be left after 22 days is:

If the sample data points are very close to the estimated regression line, then standard error is likely to be small and R square will tend to be high. So, correct options are C and D.

Firstly, the slope of the regression line may not necessarily be a very big positive number. The slope of the line depends on the relationship between the independent and dependent variables, and how the dependent variable changes with a unit change in the independent variable.

If the data points are closely packed around the line, it means that the slope is more likely to be a moderate or small number.

Secondly, it is unlikely that the line will be decreasing, as the regression line is usually a straight line that shows the average relationship between the independent and dependent variables.

Thirdly, if the data points are very close to the estimated regression line, then the standard error is likely to be small. This means that the estimated regression line is a good fit for the data and the observed values are close to the predicted values.

Fourthly, the R square will tend to be high if the data points are close to the estimated regression line. R square is a measure of how well the regression line fits the data points, and if the data points are close to the line, then the R square will be higher.

Lastly, if the data points are very close to the estimated regression line, then the line is likely to look visually appealing and not "ugly." The regression line is a summary of the data and should be a good representation of the observed relationship between the variables.

So, correct options are C and D.

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Both the race cars will hit the ground at the same time.

The concept used here is free fall formula which can be defined as . Free fall means that an object is falling freely without a forces acting upon it except gravity, a described constant, g = -9.8 m/s2. The distance the object falls, or height, h, is 1\/2 gravity x the square of the time falling. Velocity is described as gravity x time.

Here the two cars are free falling in the vertical direction and the initial velocity in the vertical direction is zero. So the landing time of both the cars is only related to the height and the acceleration of gravity.

Hence, the cars are falling from the same height, h and g are the same so they take same time to touch the ground.

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Answer: 40/41

Step-by-step explanation:

The cosine can be represented as adjacent/hypotenuse.  Thus, the cosine of C is 40/41

Answer:

Solution,

BC = 40

AC = 41

Now,

\(cos \: theta \: = \frac{adjacent}{hypotenuse} \)

\(cos \: c \: = \frac{bc}{ac} \)

Plugging the values

\(cos \: c \: = \frac{40}{41} \)

Hope this helps..

Good luck on your assignment..

The area of the rectangular parking lot is 929.03 square meters.

Use the formula for the area of a rectangle to calculate the area of the rectangular parking lot, which is given as:

Area = length × width

We know that the parking lot is 67.5 ft wide and 148 ft long, the area can be calculated as follows:

Area = 67.5 ft × 148 f

t= 9990 sq. ft

However, the question asks for the area in square meters, so we need to convert square feet to square meters. 1 square foot is equal to 0.092903 square meters, so we can use this conversion factor to convert square feet to square meters.

Area in square meters = Area in square feet × 0.092903

= 9990 sq. ft × 0.092903

= 929.03 sq meters

Therefore, the area is 929.03 square meters.

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Subscription: $5.95 per month

One print: $0.19

January charge: $15.83

Number of prints: ?

We need to know the amount of money of the January charge that correspond to the prints. Since it has two components (subscription and prints), we find that value substracting

$15.83 - $5.95 = $9.88

We find the number of prints dividing that value into the cost of each print

$9.88/$0.19 = 52

Answer: D (52 prints)

Answer:

Personal observation.

Step-by-step explanation:

Worthy of note is to say that, it's is practically impossible to have a line of different people retell what they heard, saw or experienced in the same way. Because of the fact that human being differs, there's always a difference in the retelling of the story eventually. Everyone seems to retell the story in a manner they can relate to, in a manner of what they understand, and that's given rise to unreliability in personal observation. Not that they're wrong, nor that one is right than the other, but that they're just not reliable.

Answer:

1/2

Step-by-step explanation:

The arc length is D) 3.14 meters.

What is arc length?

In mathematics, an arc is a portion of a curve that can be thought of as a segment of the curve. An arc is a connected set of points on a curve, usually a portion of a circle.

It is defined by two endpoints and all the points along the curve between them. The length of an arc is the distance along the curve between its two endpoints.

The distance along the curved line that forms the arc (a section of a circle) is measured using the arc length formula.

                                      \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

Here the give circle Radius PR = 3m and θ=60°.

Now using arc length formula then,

=> Arc length \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

=> \(A_L=\frac{60}{360} \times2\times3.14\times3\)

=> \(A_L=\frac{1}{6}\times2\times3.14\times3\)

=> \(A_L\) = 3.14 m.

Hence the arc length is D) 3.14 meters.

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The liver is the organ that converts inactive vitamin D to calcidiol. A series of steps are required for vitamin D synthesis to occur, and any disruption in this process can result in vitamin D deficiency. Limited or no use of sunscreen outside, lighter skin pigmentation, living in a region with little sunlight, and having the liver disease are all situations or conditions that may contribute to vitamin D deficiency.

Vitamin D performs several roles throughout the body. While severe insufficiency causes rickets and osteomalacia, current research shows that vitamin D deficiency may be implicated in the genesis of many illnesses, including cardiovascular disease, fatty liver, respiratory infection, type 2 diabetes, infectious disease, and various malignancies. As a result, osteomalacia, rickets, cardiovascular disease, and fatty liver are all considered deficient disorders caused by low vitamin D levels.

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Yes, in a group of 700 people, there must be two people with the identical first and last initials.

Because there are 26 distinct letters in the English alphabet, there are 26 × 26 = 676 potential combinations of two initials. According to the pigeonhole principle, at least two people in a group of 700 share the same initials. (Here: persons are pigeons, combinations of two initials are pigeonholes).

Note that in alphabets with 27 or more letters, this is no longer valid because there are 27 × 27 = 729 > 700 options for the initials.

If we try to assign a distinct combination to each individual in the group, we can only do so for the first 676 persons, leaving the remaining 24 with the same first and last initial. As a result, the answer is yes, there must be two people with the same first and last initials.

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Correct question:

In a group of 700 people, must there be 2 who have the same first and last initials? Why?

Answer:

option 3

Step-by-step explanation:

The number to multiply with 3 / - 12 to get 5 / 3 is - 20 / 3.

Let's express the expression into an equation before finding the value you can multiply - 3 / 12 to get a product of 5 / 3.

Therefore, let the number be x

Hence,

3 / -12 × x = 5 / 3

multiply both sides of the equation by - 12

3x = 5 / 3 × - 12

3x = - 60 / 3

3x = -20

divide both sides by 3

x = - 20 / 3

Therefore, the number to multiply is - 20 / 3.

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Answer:

605 miles

Step-by-step explanation:

55 every hour cuz 275/5=55

11x55=605