What is the length of the midsegment of a trapezoid whose vertices are I(-3, -5), J(8, -5), K(3, -9), and L(-3, -9)?

Answer:

106

Step-by-step explanation:

(305+13)/3=106

Answer:

Step-by-step explanation:

3

The set of all possible y-x values is between 3 and 6, excluding both endpoints.

===================================================

Explanation:

The y-x value is smallest when:

I recommend to draw out a number line. The idea is to place x and y as close as possible to each other.

Based on those two conditions, we use y = 10 and x = 7 respectively. That gives y-x = 10-7 = 3 as the smallest possible difference. Keep in mind we can't actually reach this value so we would write y-x > 3 which is the same as 3 < y-x.

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

Similarly, y-x is largest when:

Like earlier, use a number line to see why this would be the case. We're trying to space x and y out as far as possible.

The largest y value and smallest x value are y = 12 and x = 6 in that order. So the upper bound is y-x = 12-6 = 6. Like before, we can't actually reach this number which means we write y-x < 6.

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

Recap:

Put those two results together in a tidy compound inequality to get the final answer    3 < y-x < 6

It says: The expression y-x is between 3 and 6, excluding both endpoints.

The time required to pay off the loan at 4.5% interest rate 0.75 years.

The equation of simple interest will be used for calculation of time. The formula will be -

S. I. = Principal × Rate × Time/100

Keep the values in formula to find the value of time -

54 = 1600 × 4.5 × time/100

Rewriting the equation -

Time = (54 × 100)/(1600 × 4.5)

Performing multiplication on Right Hand Side of the equation

Time = 5400/7200

Performing division on Right Hand Side of the equation

Time = 0.75 years

I will need to take 0.75 years time to pay off the loan.

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The multiple regression model is a model with single dependent variables and multiple independent variables.

The term regression referred as a statistical method that helps us to analyze and understand the relationship between two or more variables of interest.

Here we have to find the missing term in the statement "the multiple regression/correlation model is a model with"

In order to find the solution, we must know the definition of multiple regression model.

Multiple Regression model in statistics is defined as the is a statistical technique that can be used to analyze the relationship between a single dependent variable and several independent variables.

Based on these definition, we have identified that it has single dependent variable and multiple independent variable.

Therefore, option (c) is correct.

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Answer: A. 111 degree

Step-by-step explanation:

Because they are Alternate Interior angles! Which means the two angles are congruent and have the same degree!

Answer:

=£5898.38

Step-by-step explanation:

5000×1.07×1.05^(2)

=£5898.38

Answer: The total volume of all the tanks at the aquarium after the new dolphin tank is installed will be 1.25x10^6 gallons + 250,000 gallons = 1.5x10^6 gallons.

This is the equivalent of 1,500,000 gallons.

Step-by-step explanation:

The volume and the surface area of the regular octogonal prism are given as follows:

The volume of the prism is given by the multiplication of the base area of the prism by the height of the prism.

The base is a regular octagon of side length 2 inches, hence it's area is given as follows:

[tex]A = 2a^2(1 + \sqrt{2})[/tex]

Hence, considering that a = 2, the base area is given as follows:

[tex]A = 8(1 + \sqrt{2})[/tex]

The height is of 7 inches, hence the volume, in cubic inches, is given as follows:

[tex]V = 7 \times 8(1 + \sqrt{2}) = 56(1 + \sqrt{2})[/tex]

The prism is composed by:

Hence the surface area of the prism, in square inches, is calculated as follows:

[tex]S = 2 \times 8(1 + \sqrt{2}) + 8 \times 2 \times 7[/tex]

[tex]S = 128 + 8\sqrt{2}[/tex]

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Answer: a is about 7.416, rounding to two significant digits, 7.4, to one significant digit, 7.

Step-by-step explanation:

We will use the Pythagorean Theorem.

a²+b²=c²

c² is the longest side, so 8cm.

lets make the bottom side b², so 3cm

We are trying to find h, so let's make that a².

Applying the Theorem:

a²+3²=8²

--- a² + 9 = 64

subtract 9 from both sides.

-- a² = 55

Take the square root of both sides

a is about 7.416, rounding to two significant digits, 7.4, to one significant digit, 7.

Answer:

22.249 cm^2 (THIS IS ROUNDED)

Step-by-step explanation:

to find the area we first need to find h using Pythagorean theorem

a^2+b^2=c^2

We need to isolate a^2 on one side

a^2+b^2=c^2

     -b^2.   -b^2

a^2=c^2-b^2

a^2=8^2-3^2

a^2=64-9

a^2=55

√.      √

a=7.416

Now we multiply by 3 to find the area

7.416x3

About 22.249 cm^2

Hopes this helps

Answer:

£54

Step-by-step explanation:

Write 45% as

45

100

Since finding the fraction of a number is the same as multiplying the fraction with the number, we have

45

100

of 120 =

45

100

× 120

Therefore, the answer is 54

If you are using a calculator, simply enter 45÷100×120 which will give you 54 as the answer.

Answer:

Step-by-step explanation:

iven, the equation is (x - 1)² + 2(x + 1) = 0. We have to determine if the equation has a real root. By using algebraic identity, (a - b)² = a² - 2ab + b² (x - 1)² = x² - 2x + 1.

Using the table of Z-normal distribution and with the value of mean, standard deviation and the 12% who wait the shortest, The answer is

173.80 days.

A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions. The probability distribution of X is defined as the function f(x) p(x)= P(X=x) for any x falling within the range of X. The probability mass function for the discrete random variable X is another name for it.

A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution. By transforming the values of any normal distribution into z scores, it is possible to standardize it. Z scores provide the number of standard deviations from the mean that each value falls within.

[tex]P(x < Z) = 0.12\\Z = -1.175[/tex](From Z-normal table)

[tex]\frac{x-204}{25.7} = -1.175\\x= -1.175*25.7 +204\\x=173.80\\[/tex]

Days = 173.80 days .

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Answer: 10 kg

Step-by-step explanation:

3% = 0.03

First, take 20 times 0.03 = 0.6kg of salt

We know that the 2% solution of seawater

So, we take 100 times 0.6, then divide by 2 = 30kg

Then take 30 - 20 = 10kg

So, to make a solution from 3% to 2%, we have to add  10 kg of water with a 20 kg solution.

Option D is the correct answer. if the residuals from a fitted regression violate the assumption of homoscedasticity their variance is not constant.

Homoscedasticity: It is an assumption of equal or similar variances in different groups are being compared. It is a condition in which the variance of the residual, or error term, in a regression model, is constant.

This is one of the most important assumptions of parametric statistical tests because they are sensitive to any dissimilarities. It is valid when X and Y are independent.

To deal with this First, we have attempted to transform your target using square root, log, reciprocal square root, or reciprocal transformations.

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Answer:

A

Step-by-step explanation:

w = 12500p + 250

250 is a fixed number of words.

12500 is the slope

For each dollar the price increases, the number of words increases by 12,500.

Answer: A

The value of (408) is (0.1)8(0.9)32 for a local department store estimates that 10 percent of its customers return the merchandise they purchase.

The value of (408)(0.1)8(0.9)32 represents the probability of getting 8 returns out of a sample of 40 customers, given that the store estimates that 10% of customers return merchandise.

This probability is calculated using the binomial probability formula, which is used to calculate the probability of a specific number of successes (in this case, returns) in a certain number of trials (in this case, customer purchases), given a certain probability of success (in this case, the estimated probability of customers returning merchandise).

The value of (408)(0.1)8(0.9)32 ( 40 8 ) ( 0.1 ) 8 ( 0.9 ) 32 describes the probability of getting 8 returns out of 40 customers when the probability of a customer returning the merchandise they purchase is 0.1.

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156 pairs of consecutive integers in {1000,1001,1002,...,2000} is no carrying required when the two integers are added

You will need to consider four cases.

when _999 and _000 are the last three digits of consecutive numbers. Just possible cases are 1999, 2000

At the point when the last 2 digits of the continuous numbers are _ _ 9 9 and _ _ 0 0. 5 possible scenarios (corresponding to (0,1), (1,2), (2,3), (3,4), and (4,5) at the hundredth place) exist.

when the last digit of consecutive numbers is in the form ____ 9 and ____ 0. 5*5 = 25 possible scenarios.

when none fall into that category, possible case=. 5*5*5 = 125,

and the answer is 125+25+5+1 = 156.

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Answer:

B. 53 degrees

Step-by-step explanation:

Because the ?-angle is equal to the 53-degree angle. So, the answer is B. 53 degrees

Answer:

10 Joules/second

Step-by-step explanation:

To find the power needed to get up the stairs, we need to divide the amount of work done (30 Joules) by the time it took to do the work (3 seconds):

Power = Work / Time

Power = 30 Joules / 3 seconds

Power = 10 Joules/second

Therefore, it takes 10 Joules/second of power to get up the stairs.

As per the unitary method, the price of the cup is $2.958

Unitary method in statistics is defined as in which the value of one article is first obtained to find out the value of any required articles

Here we have given that the 3-gallon container of laundry detergent cost $33. 60.

And we need to find the price per cup.

While we looking into the given question, we have identified the following details that cost of 3 gallon container of laundry detergent is $33.60.

So, the cost for 1 gallon container of laundry detergent cost,

=> 33.60/3

=> 11.20

Let us consider that the cup can hold 1 liter.

As we know that 1 gallon = 3.78541 liter.

Then the cost of 1 liter is calculated as,

=> 11.20/3.78541

=> 2.958

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The vertex form of a quadratic equation is a standard form of a quadratic equation that is written in the form:

y = a(x-h)^2 + k

where a, h, and k are constants. This form is called the vertex form because it represents the graph of the quadratic equation as a parabola, with the vertex of the parabola located at the point (h,k).

The vertex form of a quadratic equation is useful because it allows us to easily identify the vertex of the parabola and the direction in which the parabola opens. If a is positive, the parabola opens upwards and the vertex is the minimum point of the parabola. If a is negative, the parabola opens downwards and the vertex is the maximum point of the parabola.

Overall, the vertex form of a quadratic equation is a standard form that represents the graph of a quadratic equation as a parabola with a specific vertex location. It is useful for identifying the characteristics of the graph and for solving problems involving quadratic equations.

The volume of the Illustrated cone used as an example is 51.3cm³.

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.

A cone is a recognizable three-dimensional geometric shape with a flat and curved surface that is pointed upward. The formula for the volume of a cone is V=1/3hπr²

Let's say the radius is 7cm. The volume will be:

= 1/3 × 3.14 × 7²

= 51.3cm³

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The unit rate of cup of powered mix per gallon for each person by

Maria: 3 cups

Franco: 1/3 cups

Rate of powdered mix = number of cups ÷ number of gallons of water

Keep the values in formula to find the unit rate of cup of powdered mix

Rate of powdered mix by Maria = (3/4)÷3

Rate of powdered mix by Maria = 3/(4×3)

Cancelling 3 as it is common

Rate of powdered mix by Maria = 3 cups per gallon

Firstly converting the amount of cups from mixed fraction to fraction

Amount of cups = 1 [tex] \frac{2}{3} [/tex]

Amount of cups = 5/3 cups

Rate of powdered mix by Franco = (5/3)÷5

Rate of powdered mix by Franco = 5/(5×3)

Cancelling 5 as it is common

Rate of powdered mix by Franco = 1/3 cups per gallon

Thus, Maria's powdered mix is 3 cups per gallon while Franco's powdered mix is 1/3 cups per gallon.

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Answer:

Given:

A figure of a triangle.

To find:

The values of x and y.

Solution:

From the given triangle it is clear that the base angles of the triangle are equal, so the triangle is an isosceles triangle.

Altitude on the base of the isosceles triangle from from the opposite angle is a median. It means, it divides the base in two equal parts.

In the given triangle, the altitude divides the base in two equal parts and the measure of each part is 9 units.

Step-by-step explanation:

Answer:

B) x = 9; y = 9√3

Step-by-step explanation:

x = 9 = ( 9 )

y = 9√3 = ( 15.588 )

Hope this helps!

Answer:

Common Difference is positive

Step-by-step explanation:

If the common difference is negative, the value is decreasing every time the term increases.

If the common difference is positive, the value is increasing every time the term increases.

Because, in this case,  when the term increases, the value increases, the common difference is positive.

The statement dog was running towards the trainer to receive a treat.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given that  graph represents the distance of a dog from a trainer after a command is given.

A graph titled Dog Obedience School. The horizontal axis shows Time (seconds), numbered 1 to 10,

The vertical axis shows Distance (yards) numbered 4 to 40.

The line shows an increase, then decrease, then constant distance.

At the point on the graph where time is 5 seconds, the slope of the distance vs time curve is negative, indicating the dog is moving toward the trainer.

The motivation of the dog is unknown, so the above answer choice involves speculation that is not supported by the problem statement.

Hence, the statement dog was running towards the trainer to receive a treat.

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Answer:

the average for 129 is 159 and the average for 47 is 49

Step-by-step explanation: