Find equations of the tangents to the curve x = 9t2 + 3, y = 6t3 + 3 that pass through the point (12, 9). (enter your answers as a comma-separated list. ).

Answer:

after 4 months dan and sydney will have paid the same amount

Step-by-step explanation:

Answer:

Step-by-step explanation:

dan and sydney are getting high speed internet access at the same time.dans provider charges $60 for installation and $42.95 each month. sydney's provider has free installation and charges 57.95 per month. after how many months will dan and sydney have paid the same amount?

let 'm' represent the number of months they have subscribed

dan's total:

42.95m + 60

sydney's total:

57.95m

we want to calculate 'm' when the two totals are equal:

42.95m + 60 = 57.95m

60 =15m

m = 60/15 = 4

after 4 months dan and sydney will have paid the same amount

Answer:

Step-by-step explanation:

The surface area of the rectangular prism is 76cm^2

Geometry is the study of various mathematical or actual-world shapes, figures, and sizes. In geometry, we study various angles, transformations, and figure-to-figure similarities. The fundamental concepts of geometry primarily depend on point, line, angle, and plane.

The three most popular types of geometry are solid geometry (which deals with objects like the line, sphere, and polyhedron) and spherical geometry. Plane geometry deals with objects like the point, line, circle, triangle, and polygon.

According to the question:-

The surface area of the rectangular prism is:_

surface area= 2*(lb+bh+hl)

                    =2*(5*4+4*2+2*5)

                    =76 cm^2

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ab⁶ is not a variable term found in the binomial expansion of [tex](a + b)^{8}[/tex]as this is because, the powers must sum up to 8

A polynomial with just terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct words. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic statement that comprises a constant, exponents, a variable, and a coefficient.

The Binomial Expansion of [tex](a+b)^8[/tex] is -

[tex](a + b)^8 = a^8 + 8a^7b + 28a^6b^2 + 56a^5b^3 + 70a^4b^4 + 56a3^b^5 + 28a^2b^6 + 8ab^7 + b^8.[/tex]

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Answer:

9

C

D

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

you take 1 and add 1 to it... and bam... 2

Answer:

2

Step-by-step explanation:

1+1=2 because 2-1=1 :0

The following data sets represents the required properties:

a. . Same mean but different standard deviation :

3   3   3  3   3                

1    2   3   4  5              

2    2  3   4  4    

b.  Same mean but different medians

1    2   3   4  5            

1    1   4   4   5            

1    2   2   5  5  

c. Same median but different median:

1      2    3    5   5        

1      2   3    4    5          

2     2   3    5    5  

As given in the question,

Three data sets with 5 numbers representing :

a. Same mean but different standard deviation :

                                       Mean                  Standard deviation

3   3   3  3   3                  15/5 = 3                 0

1    2   3   4  5                 15/5 = 3                  2.5      

2    2  3   4  4                 15/5 = 3                  1    

Mean of the data set = 3

Standard deviation = [tex]\frac{\sum (x - \bar{x} )^{2} }{n -1}[/tex]

b. Same mean but different medians :

                                   Mean                     Median

1    2   3   4  5             3                                3

1    1   4   4   5             3                                4

1    2   2   5  5            3                                 2

c. Same median but different median:

                                    Mean          Median

1      2    3    5   5          3.2                3

1      2   3    4    5            3                 3

2     2   3    5    5          3.4                3

Therefore, above are the following data set to represent same mean different standard deviation, same mean different median and same median different mean.

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Answer:

56

Step-by-step explanation:

Take two points as far apart on the line (for maximum accuracy), preferably on grid points, and then calculate the vertical difference divided by the horizontal difference.

So (4, 224) and (0,0) are on the line, and (224-0)/(4-0) = 56

Step-by-step explanation:

where is the diagram?

please

Answer:

Stretches vertically by 2, shifts right by 1

Step-by-step explanation:

changes to y are direct, but you have to take the inverse for changes to x. This is because for a given value of y, with x-1, you would have to add one to x to make it the same value(to get the same point before the transformation)

Each of the three angles measures 75°, 65°, and 40°.

What is an angle measure?

An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Here, we have

Let the largest angle be x degrees, the median y, and the smallest z.

x = 2y - 55

z = y - 25

x + y + z = 180

Substituting for x in the last equation:

2y - 55 + y + z = 180

3y + z = 235  

From the second equation:

- y + z = -25     Subtract this from the last equation:

4y = 260

y = 65 degrees

z = 65 - 25 = 40 degrees.

and x = 180 - 65 - 40 = 75 degrees.

Hence, each of the three angles measures 75°, 65°, and 40°.

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The measures of each of the three angles are 40,65 and 75 degrees.

What is angle ?

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle.

Give that:

Let us consider X,Y,Z re the largest ,medium and smallest angle in the triangle.

Sum of the measures of the angles of any triangle is 180 degrees .

                            X + Y + Z = 180 degree

The largest angle measures 55degrees less than twice the medium angle,

                            Z = 2Y - 55 degree

The smallest angle measures 25 degrees less than the medium angle,

                          X = Y - 25 degree

Now ,replace X by (Y - 25) and Z by (2Y - 55) in the first equation

Y - 25 +Y + 2Y - 55 = 180 degree

4Y = 180 + 25 + 55

4Y = 260

Y = 65   Degree of the medium angle

X = 65 - 25

X = 40   Degree of the smallest angle

Z = 2 * 65 -55

  = 130-55

Z = 75   Degree of the largest angle.

40 + 65 + 75 = 180

180 = 180

Hence proved.

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We will see that the odd functions were f(x) = x5 - 3*x3 + 2*x and f(x) = 1/x since only those were true under the specified circumstances.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. The most basic definition is that a function is a collection of ordered pairs of items, which in our instance will be numbers, but they may also be anything else, and which have the feature that their initial members are all distinct from one another. The relationship between the input or domain and the output or range is known as the function rule. If and only if there is a single value in the range for each domain value, a relation is a function.

Here,

A function is odd,

f(-x) = -f(x) for every value of x in its domain.

1) f(x) = x^3 - x^2

f(-x) = (-x)^3 - (-x)^2

= -x^3 - x^2

f(-x) ≠ -f(x)

This function is not odd.

2) f(x) = x^5 - 3*x^3 + 2*x

f(-x) = (-x)^5 - 3*(-x)^3 + 2*(-x)

= -x^5 + 3*x^3 - 2*x = -f(x)

This function is odd.

3) f(x) = 4x + 9

f(-x) = 4*(-x) + 9

= -4*x + 9

-f(x) = -( 4*x + 9)

= -4*x - 9

f(-x) ≠ -f(x)

This function is not odd.

Because only these were true under the specified circumstances, we will find that the odd functions are f(x) = x^5 - 3*x^3 + 2*x and f(x) = 1/x.

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The perimeter of ABCD, given the vertices of the trapezoid, can be found to be 28.13 units

To find the perimeter of this trapezoid, you need to find the distances between AB, BC, CD, and AD. To find these, you can use the formula for finding the distance between vertices.

That formula is:

= √( ( X₂ - X₁ ) + ( Y₂ - Y ₁))

Using this formula, the distance of AB is 4.47 units.

The distance between BC is 6 units.

The distance between CD is 5.66

The distance between AD is 12 units

The perimeter is the distance around the shape:

= 4.47 + 6 + 5.66 + 12

= 28.13 units

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By using exponent properties we will find the equivalent expression:

(-2)⁴/(-2)² = (-2)² = 4

Here we need to use the exponent property:

xⁿ/xᵇ = xⁿ⁻ᵇ

Here the expression we have is:

(-2)⁴/(-2)²

Using the above property we can rewrite the expression as:

(-2)⁴/(-2)² = (-2)⁴⁻² = (-2)²

Now we can solve this:

(-2)² = (-2)*(-2) = 4

Then the equivalent expression is 4.

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Answer:

A. No

B. No

C. Yes

D. Yes

Step-by-step explanation:

1/2 gallons of water rush down the slide each seconds.

For the given question-

Rate of running water = 1 half gallon every 3 seconds.

Rate of running water = 1 1/2 = 3/2 gallon every 3 seconds.

It means-

In every 3 seconds ----> 3/2 gallons water flows.

Thus for 1 sec, divide both side by 3.

1 seconds ----> 1/2 gallons water flows.

Therefore, 1/2 gallons of water rush down the slide each seconds.

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Answer: I believe it is 18/5

 or Decimal Form:

3.6

or Mixed Number Form:

3 3/5

Step-by-step explanation

4/5 x 4 1/2

Answer:

Step-by-step explanation:

A B

The length of the guy wire will be equal to 27.78 feet.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Given that Janelys places a 5-foot tall pole to support the guy wire. After placing the pole, Janelys measures the distance from the stake to the pole to be 14 ft. She then measures the distance from the pole to the tower to be 24 ft.

The length of the wire will be calculated as,

L² = 24² + 14²

L² = 576 + 196

L² = 772

L = √772

L = 27.78 ft

Therefore, the length of the guy wire will be equal to 27.78 feet.

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Answer:

40ft

Step-by-step explanation:

The constant of proportionality from a graph of any proportional relationship is find as below.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The constant of proportionality from a graph of any proportional relationship.

Now,

Let the solution of the graph = (2, 10)

Then, The constant of proportionality from a graph of any proportional relationship is find as;

⇒ Constant of proportionality = 10 / 2

                                             = 5

Thus, The constant of proportionality from a graph of any proportional relationship is find as above.

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The number of months required to complete the payments are 63 months.

We will make a equation, which represent total purchase amount in terms of number of months.

Let we consider number of months be t.

Total purchase amount = $17500, one time deposit = $1750

and monthly payment = $250

Then,

17500 = 1750 + 250t

250t = 17500-1750

250t = 15750

t = 15750/250

t = 63 months

Thus number of months required are 63.

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Given that the test's p-value is 0.0562>0.05, there is enough data to conclude that the machines' manufacturer should perform a new calibration.

A statistic employed in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is commonly expressed.

Here,

x=4.88 cm

μ=5 cm

σ=0.44 cm

n=49

The test statistic,

=(4.88-5)/(0.44/7)

z=-1.909

The p-value of the test is the probability that the sample mean is different by at least 4.88 - 5 = 0.12 from the target value, which is P(|z| > -1.909), which is 2 multiplied by the p-value of z = -1.909

At z=-1.909, p-value=0.0281

2*0.0281=0.0562

The test's p-value is 0.0562>0.05, indicating that there is enough data to conclude that the machines' manufacturer should perform a recalibration.

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Time required to diffuse the F2 gas under the same conditions pressure and temperature with same volume is equal to 14 mins( approximately).

As given in the question,

Time taken by 1.5L sample of He gas to diffuse = 4.55 min.

Molar mass of He gas = 4g

Volume of He gas = 1.5L

Volume of F2 gas = 1.5L

Molar mass of F2 = 38gm

Formula of Rate of diffusion is given by :

Rate of diffusion of He / Rate of diffusion of F2

= √Molar mass of F2 / √Molar mass of He

Now,

Rate of He = Volume of He / time taken

                  = 1.5 / 4.55  

Rate of F2 = [ ( Rate of He ) ×√ Molar mass of He ] / √ Molar mass of F2

                 = ( 1.5 / 4.55 ) × ( √4 / √38)

                 = 3 / 28.028

                 = 0.107 L / min

Time of F2 = Volume of F2 / Rate of F2

                  = 1.5 / 0.107

                  = 14.02 minutes

                  ≈ 14 minutes.

Therefore, the time taken by F2 to diffuse under the same condition of He is equal to 14 minutes.

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The cost of each white led lights and colored led lights is $12 and $15 respectively.

Let

w + c = 27

3w + 2c = 66

From (1)

w = 27 - c

Substitute w = 27 - c into (2)

3w + 2c = 66

3(27 - c) + 2c = 66

81 - 3c + 2c = 66

- 3c + 2c = 66 - 81

- c = - 15

c = 15

Substitute c = 15

w + c = 27

w + 15 = 27

w = 27 - 15

w = 12

In conclusion, the task content can be solved using the concept of simultaneous equation.

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Answer:

1.8x101

Step-by-step explanation:

The largest value less than 500 that the arithmetic progressions have in common = 479

In this question, we have been the arithmetic progressions {2,5,8,11, . . .} and {3,10,17,24, . . .}

We need to find the largest value less than 500 that they have in common.

We know that the formula for the n-th term of arithmetic progression is: an = a + (n – 1)d

For arithmetic progression {2,5,8,11, . . .}

a_m = 2 + (m - 1)3

For arithmetic progression {3,10,17,24, . . .}

a_n = 3 + (n - 1)7

if we solve for m, n then m =160 and n =69

2 + (160 -1)*3 = 479  which is the 160th term in the arithmetic progression {2,5,8,11, . . .}

3 + (69 - 1)*7  =479 which is the 69th term in the arithmetic progression {3,10,17,24, . . .}

Therefore, the value which less than 500 that both the progressions have in common = 479

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Since these two lines overlap, the variable's value is 25, and the angle's value is 38 degrees.

The empty set, a point, or another line can cross another line in Euclidean geometry. Examples of applications for identifying these circumstances and locating the intersection include computer graphics, motion planning, and collision detection. In a plane, intersecting lines are any two or more lines that cross one another. The point of intersection, which can be found on all intersecting lines, is where the crossing lines share a common point.

Here,

Both the angles are equal as they are intersecting lines and opposite angles are equal in this.

x+13=3x-37

3x-x=37+13

2x=50

x=25

x+13=25+13

angle=38

3x-37=3*25-37

angle=38

The value of variable is 25 and the value of angle in 38 degree as they are the intersecting lines.

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x =2173

Step-by-step explanation:

The correct option d. 90 - 95%, is the percentage of diabetes patients having type 2.

A disorder in the body's ability to control and utilize sugar (glucose) as fuel is type 2 diabetes.

The recipe for diabetes management is a healthy diet.

Thus, one in ten Americans, or more than 37 million people, have diabetes, and 90–95% of them suffer from type 2 diabetes.

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Answer:

D

Step-by-step explanation:

90-95

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

A field estimates 40 by 80 yards. Larysa makes a scale drawing with a size of 1 in. to 5 yd., and Prakash makes his own scale drawing with a size of 1 in. to 8 yd.

The dimension of the Larysa drawing is given as,

⇒ 40 x 1/5

⇒ 8 in

⇒ 80 x 1/5

⇒ 16 in

The dimension of the Prakash drawing is given as,

⇒ 40 x 1/8

⇒ 5 in

⇒ 80 x 1/8

⇒ 10 in

The dimension of the Prakash's drawing is less than the dimension of the Larysa's drawing. The Larysa's drawing has the larger area.

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The solutions for the given conditions are;

1. True

2. True

3. False

4. False

5. False

6. True

7. True

1) For estimating a population parameter, a confidence interval is used.

TRUE → CI is used for estimating a population parameter. But, it can also be used to estimate the sample statistic.

2) The sample statistic is always captured by a confidence interval.

TRUE → CI is calculated using the sample statistic.

3) The population parameter is always captured by a confidence interval.

FALSE → There is a type 1 error possibility.

4) Z-critical values should always be used when creating confidence intervals.

FALSE → Z stat is used only in a normal distribution with sizes>30. Else, it is recommended to use a t distribution.

5) The center of the confidence interval is determined by the margin of error.

FALSE → ME determines the maximum deviation from the center at a given confidence level

6) In general, we would like to have a high level of confidence and a precise confidence interval.

TRUE → This is attainable when we increase the sample size.

7) A large sample size is required to create a proportion's confidence interval.

TRUE → Along with the large sample, we also need to have np and nq at least 10.

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