A scale drawing of a rectangular bedroom is shown below. Using a scale of 1cm=4 feet, enter the actual area of the bedroom in square feet.

The conic equation 16 · x² + 4 · y² + 96 · x - 8 · y + 84 = 0 is equivalent to (x + 3)² / 4.75 + (y - 2)² / 19 = 1, that represents an ellipse.

Mathematically speaking, conics are described by quadratic equations of the form A · x² + B · y² + C · x + D · y + E = 0, where A, B, C, D, E are real coefficients of the conic.

We can infer if a conic is a circle, a parabola, an ellipse or a hyperbola by modifying the expression into its standard form by algebra properties. First, write the equation of the conic:

16 · x² + 4 · y² + 96 · x - 8 · y + 84 = 0

Second, complete the square in the equation of the previous step:

16 · (x² + 6 · x) + 4 · (y² - 2 · y) = - 84

16 · (x² + 6 · x + 9) + 4 · (y² - 2 · y + 4) = - 84 + 16 · 9 + 4 · 4

16 · (x² + 6 · x + 9) + 4 · (y² - 2 · y + 4) = 76

Third, factor the polynomial and simplify the expression until standard form is derived:

16 · (x + 3)² + 4 · (y - 2)² = 76

(x + 3)² / 4.75 + (y - 2)² / 19 = 1

The conic equation represents an ellipse.

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If two names are given for the same quantity then we can use algebra

to solve the equation thus option (C) is correct.

There are many different ways to define an equation.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

In another word, the equation must be constrained with some constraints.

If we have a problem in word formate.

And the same quantity is used two times with two different names.

Then by algebra, the variable defines the quantity remains the same but the value of the variable changes according to the given value.

By this the problem can be easily solved.

Hence "If two names are given for the same quantity then we can use algebra to solve the equation".

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Answer:

Step-by-step explanation:

X+Y = 50

0.13X + 0.18Y = 0.16*50 = 8

0.13X + 0.18(50-X) = 8

0.13X + 9 - 0.18X = 8

-0.05X = -1

5x = 100

x=20

20 mL of the 13% salt solution

30 mL of the 18% salt solution

The associations that best describe the scatter plot is Option A and C

When below-average values also tend to occur together and above-average values of one variable tend to be accompanied by below-average values of the other, there is a positive association between the two variables. When the average values of two variables tend to be below average, two variables have a negative connection.

Note that a statistical term used to describe a straight-line relationship between two variables is a linear relationship (or linear association).

Additionally, a straight line connecting the spots indicates a linear association. As a result, the scatter plot indicates that as practice time increases,  giving off also rise.

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The association that describe the scatter plot is

A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities or events (called variables).

The connection is positive if the variables tend to rise and fall together. When one variable tends to rise while the other falls, there is a negative connection.

The connection between the variables demonstrates a straight line in the positive direction. hence the option having linear and positive association is the correct choice

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Points C , G , and H are not Collinear.

Collinear Point:

                         Two or more points are said to be collinear, if they lie on the same straight line,whether they are close together, far apart, or form a ray, line segment, or line.

                                      In other words we can say Collinear points are the set of three or more than three points that lie on a single straight line.

Now,

       From given figure we can see all the three points C , G , and H are not lying on a single straight line or line segment. In fact GH and CG are different sides.

               So, points C , G , and H are not Collinear points.

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Answer:

Step-by-step explanation:

4

Answer:4

Step-by-step explanation: I have 2 apples and my friend gives me 2 more  it'll give me 4. Also you put up 2 fingers and and you add 2 more that will also give me 4.  

The rectangular crate will be able to carry a maximum of 27 boxes

The crate carries a shape of a cuboid which can be said to be a rectangle in three-dimensional side. To solve this problem, we have to find the volume of the crate and then the volume of the box and divide the volume of the crate by the volume of box.

The volume of a cuboid = L * W * H

This can be calculated as V = 24 * 18 * 15 = 6480cm³

The volume of the box = 8 * 6 * 5 = 240cm³

Number of boxes that can fit in the cuboid = 6480 / 240

Number of boxes = 27 boxes

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The number of codes that can be made using the 5 letters given is 120 as calculated using permutation and combination.

Now when no letters are repeated:

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 3 options , fourth digit has 2 options and the final digit will have only 1 option left.

So total number of codes = 5 × 4 × 3 × 2 × 1 = 120 codes

if letters can be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 5 options , third digit has 5options , fourth digit has 5 options and the final digit will have only 5 options also.

So total number of codes = 5 × 5 × 5× 5× 5= 3125 codes

if adjacent letters cannot be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 4 options , fourth digit has 4 options and the final digit will have only 4 options also.

So total number of codes = 5 × 4 × 4× 4× 4 = 1280 codes

Hence the total number of codes as calculated by permutation and combination is 1280.

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The probability of getting at least one Canadian quarter is 0.6

This is a binomial probability experiment. We are going to use the binomial distribution formula for determining the probability of x successes:

P(x = r) = nCr . p^r . q^n-r

Where n = number of trials, p =  probability of success and q = probability of failure,  x = number of Canadian quarters

39 U.S. quarters  + 11 Canadian quarters coins = 50 coins

Given: n = 4 (four quarters picked), p = 11/50  = 0.22, q = 1-p =1-0.22 = 0.78

Probability at least one Canadian quarter  = 1 - Probability of no Canadian quarter

P(x≥1) = 1 - P(x = 0)          

         = 1 - (4C0×0.22⁰× 0.78⁴⁻⁰ )

        = 1 - 0.4

        = 0.6

Therefore, the probability of getting at least one Canadian quarter is 0.6

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The size 50 will produce the widest 95% confidence interval when estimating the population parameter.

It is defined as the sampling distribution following an approximately normal distribution for a known standard deviation.

It is given that, a sample with the sample proportion of 0.4 and which of the following sizes will produce the widest 95% confidence interval.

The margin of error provides an estimate of the percentage of errors in real statistical data.

The formula for finding the MOE:

[tex]\rm MOE = Z\times \dfrac{s}{\sqrt{n}}[/tex]

Where,

Z is the z-score at the confidence interval

s is the standard deviation

n is the number of samples.

An interval is broader the bigger the margin of error.

The margin of error reduces with increasing sample size. The smallest confidence interval should be chosen if we want the widest possible interval.

Thus, the size 50 will produce the widest 95% confidence interval when estimating the population parameter.

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Answer:

B. 35

Step-by-step explanation:

I got it correct :D

The area of triangle is 25.

and, The perimeter of triangle is 5.

Given,

In the question:

A triangle is dilated by a scale factor of 5.

To find the how will this affect the perimeter and the area of the new image?

Now, According to the question:

The perimeter of triangle is X + Y + Z, where X, Y, and Z are the sides.

So if we shrink all the sides by 5, we change the perimeter by 5.

However, because the area of the triangle involves 0.5 × Base × Height,

if we shrink all of the sides by 5, the area is shrunk by 5 * 5 (once for base, once for height).

Hence, The area of triangle is 25.

and, The perimeter of triangle is 5.

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The confidence interval form of the given question will be (783.4,522.4).

What is a confidence interval?

A confidence interval (CI) in frequentist statistics is a range of estimates for an unknown parameter. A confidence interval is calculated at a specified degree of confidence; the most popular level is 96%, but other values, such 90% or 99%, are occasionally used. The confidence level is the percentage of corresponding CIs over the long run that actually contain the parameter's true value. As an illustration, 96% of all intervals produced at the 96% level should have the parameter's actual value.

Here this question, it is given in the interval form.

Now we can find out the minimum and maximum value of the value.

Maximum value is 653.1+130.3 = 783.4

Minimum value is 653.1 - 130.3 = 522.4

So The confidence interval can be written as (783.4,522.4).

Hence the answer will be (783.4,522.4).

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Answer:

ez

Step-by-step-

ezzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

Answer:

34

Step-by-step explanation:

2+b(a^2+4)

2+4(2^2+4)

2+4(4+4)

2+4(8)

2+32

34

Hopes this helps please mark brainliest

The fraction of the length of Sofia's bike is 3/2 times longer that Emely's.

What is mixed fraction?

 A mixed fraction is one that has both its quotient and remainder represented. A mixed fraction like 2 1/3 is one where the remainder is 1 and the quotient is 2. Therefore, a mixed fraction is made up of both a whole number and a correct fraction.

To find how many times the length of Emely's ride is compared to Sofia's, you would divide the two mixed numbers:

=>6  3/4  divided by 4  1/2

Convert the mixed  numbers to improper fractions:

=>27/4  divided by 9/2

To solve, multiply 27/4 by the reciprocal of 9/2:

=>27/4 * 2/9 = 3/2  or 1 and 1/2

So Sofia's ride is 1.5 times longer than Emely's.

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Answer:

Step-by-step explanation:

Since it is an isosceles triangle the opposite side of that with 35mm is equal to 35mm.

Area of triangle =. ½b x h

. =. ½ x 35 x 35

. = 612.5mm²

. =. 613mm²(1.d.p)

Answer:

No you can't

Step-by-step explanation:

Because it doesn't fit the number catigorey

The total cost of the camera with sales tax included is $793.44

The listed  price of camera = $722.95

The sales tax rate = 9.75%

The amount of tax = The listed  price of camera × (The sales tax rate / 100)

Substitute the values in the equation

The amount tax = 722.95 × (9.75 / 100)

Divide the terms first

= 722.95 × 0.0975

Multiply the terms

= $70.49

The cost of the camera including tax = The listed  price of camera + The amount tax

Substitute the values in the equation

= 722.95 + 70.49

= $793.44

Hence, the total cost of the camera with sales tax included is $793.44

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Answer:mum

Step-by-step explanation: mom

The number of hours per year that the equipment be used to justify purchasing it rather than renting it is 2125 hours.

It should be noted that an expression is used to illustrate the relationship between the variables.

Let the number of hours be illustrated as h.

The landscaper can rent a backhoe for $45,000 a year and he could purchase the equipment for

monthly costs of $2,500 plus $20 for each hour it is used.

This will be:

2500 + 20h = 45000

Collect like terms

20h = 45000 - 2500

20h = 42500

Divide

h = 42500 / 20

h = 2125

The number of hours is 2125 hours.

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Rate of change for Carol's = 4.99

Rate of change for Wilma's:

line passes through (0, 0) and (2, 15)

slope = m = (15 - 0) / (2 - 0) = 7.5

Rate of change for Wilma's = 7.5

7.5 > 4.99

So Wilma's has the greatest rate of change.

The correct notation of A is a subset of B is A⊆B( option B)

A set is a collection of objects or elements.Subsets are a part of one of the mathematical concepts called Sets, grouped in the curly braces, such as {a,b,c,d}.

The elements of sets could be anything such as a group of real numbers, variables, constants, whole numbers, etc. It consists of a null set as well.

If a set A is a collection of even number and set B consists of {2,4,6}, then B is said to be a subset of A, denoted by B⊆A and A is the superset of B.

Therefore the correct notation of A is a subset of B is A⊆B.

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Answer:

Acquisition cost refers to an amount paid for fixed assets, for expenses related to the acquisition of a new customer, or for the takeover of a competitor.

The Speed of the plane in still air is 165 miles per hour.

What is speed?

 The rate that an object travels a certain distance is what is meant by the speed formula. The amount of distance a body moves in a certain amount of time is referred to as speed. The metric unit of speed is the m/s. For example, m/s, km/hr, miles/hr, and other units can be used to express speed.

Let x be the speed of the plane in the still air, and w be the wind speed.

Using speed formula Balancing by the time,

=> Time = Distance/ Speed

=> 420/(x+w) = 350/(x-w)

Then ,

=>420/(x+15)=350/(x-15)

=> 420(x-15)=350(x+15)

=> 420x-6300=350x+5250

=> 420x-350x=5250+6300

=>70x=11550

=>x=11550/70

=>x=165mph.

Hence speed of the plane in still air is 165 miles per hour.

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Answer:

The mean is 6

Step-by-step explanation:

To find the mean, add all the numbers and then divide by the number of data points

( 7+5+4+5+6+9)/ 6

36/6

6

The mean is 6

Solving a system of equations we can see that she bought 3 bags of popcorn and 6 drinks.

We can define the two variables:

Knowing that each bag of popcorn costs $5 and each drink costs $6, and the total cost was $51, we can write:

x*$5 + y*$6 = $51

And we also know that she bought twice as many drinks as bags of popcorn, then:

y = 2x

So we have a system of equations:

y = 2x

x*$5 + y*$6 = $51

Replacing the first equation into the second one:

x*$5 + (2x)*$6 = $51

x*$17 = $51

x = $51/$17 = 3

So she bought 3 bags of popcorn and 2*3 = 6 drinks.

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Answer:

20

Step-by-step explanation:

we turn 5 into a fraction to make it easier

[tex]\frac{5}{1}[/tex]÷[tex]\frac{1}{4}[/tex]

Now to figure it out we keep the first fraction 5/1 the same and then flip the second one 1/4 to make it 4/1 and multiply

[tex]\frac{5}{1}[/tex]×[tex]\frac{4}{1}[/tex]

[tex]\frac{20}{1}[/tex]

20

Hopes this helps please mark brainliest

Answer:

Add them together and you have your answer I think

The value of the expression 3(r+5) when r = 10 is 100

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

In this problem, we are to substitute the value of r which is 10 int the expression.

3(r + 5) + 55 = 3(10 + 5) + 55 = 3(15) + 55 = 45 + 55 = 100

The expression is equal to 100.

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Answer: No, the answer is not reasonable because 3,627/9 doesn’t equal 43, it equals 387.

Answer:

No, you friend's answer is not reasonable.

Step-by-step explanation:

3,627 x 9 does not equal 43

3,627 x 9 =32643

Therefore your friend is incorrect