Find the 7th term of the arithmetic sequence 5x + 9, 11x + 13, 17x+17,...

The coordinates of the vertices of the transformed triangle are A''(10, 1), B''(11, -2), and C''(8, -1).

To reflect triangle ABC over the line x = -6, we need to change the sign of the x-coordinate of each vertex.

The reflected coordinates of the vertices will be:

A' = (-(-5), 2) = (5, 2)

B' = (-(-6), -1) = (6, -1)

C' = (-(-3), 0) = (3, 0)

To translate the reflected triangle by the directed line segment from (0, 0) to (5, -1), we add the corresponding values to the x and y coordinates of each vertex:

A'' = (5 + 5, 2 + (-1)) = (10, 1)

B'' = (6 + 5, -1 + (-1)) = (11, -2)

C'' = (3 + 5, 0 + (-1)) = (8, -1)

Therefore, the coordinates of the vertices of the transformed triangle are A''(10, 1), B''(11, -2), and C''(8, -1).

Learn more about Transformation here:

https://brainly.com/question/11709244

#SPJ1

Answer:

54.88cm

Step-by-step explanation:

For shaded region perimeter, subtract the circle perimeter from the rectangle

perimeter

= (10*8) - (2 * 3.14 * 8/2)

= 80 -  25.12

= 54.88cm

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 = \(\frac{\sum (x - \bar{x} )^{2} }{n -1}\)

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.

Learn more about data set here

brainly.com/question/22210584

#SPJ4

To estimate the mean EPA combined city and highway mileage, the automaker conducted EPA mileage tests on a random sample of 35 midsize cars. The sample mean is 24, and the population standard deviation is 1.2. The task is to calculate the 70% confidence interval for the population mean.

To calculate the confidence interval, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / √(Sample Size))

First, we need to determine the critical value associated with a 70% confidence level. The critical value can be found using a standard normal distribution or a t-distribution, depending on the sample size and whether the population standard deviation is known.

Since the sample size is relatively large (n = 35), we can use the standard normal distribution. The critical value for a 70% confidence level corresponds to a z-score of ±1.036.

Next, we calculate the margin of error:

Margin of Error = (Critical Value) * (Standard Deviation / √(Sample Size)) = 1.036 * (1.2 / √35) ≈ 0.380

Finally, we can calculate the lower and upper bounds of the confidence interval:

Lower Bound = Sample Mean - Margin of Error = 24 - 0.380 ≈ 23.62

Upper Bound = Sample Mean + Margin of Error = 24 + 0.380 ≈ 24.38

Therefore, the 70% confidence interval for the mean EPA combined city and highway mileage is approximately 23.62 to 24.38.

Learn more about standard deviation here: brainly.com/question/29808998

#SPJ11

1/4

Explanation: The chances of getting heads/tails (individually) is 1/2. The obvious equation here is 1/2 to the 2nd power.

Answer:1/4

Step-by-step:

He would have the chance to flip heads 1/2. Then the chance that he flipped tails after would be 1/2. Then you would multiple 1/2 x 1/2 = 1/4

The other angle of the triangle is 65°.

We know that

Exterior Angle = Sum of two angles opposite to the exterior angle

Here, 145° = 80° + x°

=> x° = (145 – 80)°

=> x° = 65°

Therefore, the value of x in the given figure is 65°

Learn more about triangles here:

https://brainly.com/question/2773823

#SPJ1

Complete question:

Answer:

so Mila swam 0.0344 kilometers per min=2.064 kilos per hour

Step-by-step explanation:

Answer:

12.21

Step-by-step explanation:

Explanation:

This is a right triangle, so the Pythagorean Theorem applies.

The Pythagorean Theorem states that the sum of the squared legs of a triangle is equal to the squared hypotenuse.

The legs of a triangle are the sides that form the right angle.

The hypotenuse of a triangle is the longest side.

Formula/solve:

\(a^2+b^2=c^2\)

\(a,b-legs\)

\(c-hypotenuse\)

Here, I am solving for the hypotenuse.

\(7^2+10^2=c^2\)

\(49+100=c^2\)

\(149=c^2\)

Conclude:

The last step is the cancel out c² by finding the square root of 149.

149 is not a perfect square, so I must round the square root to the nearest hundredth.

\(12.2065556157\) ≈ \(12.21\)

I, therefore, believe the length of the hypotenuse is 12.21 feet.

Answer:

80miles=6days

14

14 ×6=84

84÷80=1.05

1.05 miles

Answer & Step-by-step explanation:

On a six-sided die, there are 4 numbers less than 5. So, we can write this as a fraction.

\(\frac{4}{6}\) or we can write this fraction as \(\frac{2}{3}\)

So, the probability of rolling a number less than 5 is \(\frac{2}{3}\)

Answer:

AD BC only

Step-by-step explanation:

Answer:

A: ab || dc

i dont know what else to put here, all i can say is i passed this test

The result of each operation is given as follows:

a) a U b = {0, 1, 2, 3, 4, 5, 6, 7, 8}.

b) a ∩ b = {}.

c) a - b = {0, 2, 4, 6, 8}.

The union and intersection sets of multiple sets are defined as follows:

Item a:

The union set is composed by the elements that belong to at least one of the sets, hence:

a U b = {0, 1, 2, 3, 4, 5, 6, 7, 8}.

Item B:

The two sets are disjoint, that is, there are no elements that belong to both sets, hence the intersection is given by the empty set.

Item c:

The subtraction is all the elements that are on set a but not set b, hence:

a - b = {0, 2, 4, 6, 8}.

More can be learned about union and intersection at brainly.com/question/4699996

#SPJ1

Answer:

The absolute value is 8

Step-by-step explanation:

the absolute value of a number is always going to be positive. if you have a negative number and need the absolute number, you just put the opposit of the number.

Answer:

The absolute value is 8

The mean could be used to describe a data set by itself, while interquartile range would almost never be used to describe a data set by itself.

Brief Description of Mean and Interquartile Range

While interquartile range only assesses the middle half of the data, mean and range deal with the entire set of data. The mean is significant in statistics because it helps us determine where a dataset's "center" is. The mean contains information from each observation in a dataset as a result of how it is calculated.

The interquartile range in descriptive statistics reveals the spread of your distribution's middle half. Any distribution that is sorted from low to high is divided into four equal portions using quartiles. The second and third quartiles, or the center half of your data set, are contained in the interquartile range (IQR).

Learn more about mean here:

https://brainly.com/question/15397049

#SPJ1

Answer:

the answer is 67.44 hope it helps smile

The sentence that expresses numbers correctly is: "When the temperatures fell below zero degrees Fahrenheit, the employees decided to take public transportation."

In the sentence, the number is correctly expressed as "zero degrees Fahrenheit." When referring to temperatures below freezing, it is common to use the term "zero" to indicate the absence of heat. The numerical value of zero is represented by the numeral "0," rather than the word "Zero."

Additionally, the unit of measurement, Fahrenheit, is capitalized as it is a proper noun derived from the name of the scientist who developed the temperature scale.

Therefore, the sentence "When the temperatures fell below zero degrees Fahrenheit, the employees decided to take public transportation" accurately conveys the correct numerical and linguistic representation of the temperature.

Learn more about Numbers:

brainly.com/question/3589540

#SPJ11

Answer:

x3 = y

Explanation:

This is assuming x represents the number of notebooks, as it isn't stated. The store sells notebooks for 3 each so one notebook will cost 3, two will cost 6, etc. The total cost is based on how many notebooks were bought and the cost, and they are multiplied together. As y represents the total cost of the notebooks, the equation is x3 = y (or y = x3, since where the equals sign doesn't matter).

Hope this helps !!

The volume of the pentagonal prism is 148.35 cubic units.

A pentagonal prism comprises two pentagonal bases (top and bottom) and five rectangle sides. It is a heptahedron having seven faces, ten vertices, and fifteen edges.

A pentagonal prism with pentagonal bases has five sides. The five-sided polygon prism is another name for a pentagonal prism.

The volume and the surface area of a pentagonal prism represent two key measurements.

The volume of pentagonal prism is calculated by the formula;

Volume of pentagonal prism= (5/2)×a×b×h cubic units

a = The pentagonal prism's apothehem length

b = The pentagonal prism's base length

h = the pentagonal prism's height

Now, according to the question;

The area of the regular pentagonal base of this prism is 43.06 square units.

The height of the prism is 3.45 (see the figure)

Volume = Base Area × Height

Volume =  43.06×3.45

Volume = 148.35 cubic units

Therefore, the volume of the pentagonal prism is 148.35 cubic units.

To know more about the pentagonal prism, here

https://brainly.com/question/2494546

#SPJ4

A differential equation is a mathematical equation that relates a function to its derivatives. It involves the unknown function and one or more of its derivative. The solution to the differential equation -

xy' − 2y = x^2, x > 0

is y = (1/4)x^3 + C/x.

To solve the differential equation, we will use the method of integrating factors.

The differential equation is: xy' - 2y = x^2

We can rearrange it in the standard form: y' - (2/x)y = x

The integrating factor (IF) is defined as e^∫(2/x) dx. Integrating 2/x with respect to x gives us 2ln|x|.

Therefore, the integrating factor is IF = e^(2ln|x|) = e^(ln(x^2)) = x^2.

Now, multiply the entire equation by the integrating factor x^2:

x^2(y' - (2/x)y) = x^2(x)

x^2y' - 2xy = x^3

Next, we recognize that the left-hand side is the derivative of (xy) with respect to x. Applying this, we get:

d/dx(xy) = x^3

Integrating both sides with respect to x:

∫d(xy) = ∫x^3 dx

xy = (1/4)x^4 + C

Finally, divide both sides by x:

y = (1/4)x^3 + C/x

where C is the constant of integration.

So, the solution to the given differential equation is y = (1/4)x^3 + C/x.

To know more about differential equation refer here:

https://brainly.com/question/31492438#

#SPJ11

The points are given below,

The formula for the magnitude of the vector AB is,

Solving for the magnitude of the vector AB by substituting the values of x₁ = 8, x₂= 5, y₁ = 7, y₂ = 4.

Therefore,

Hence, the magnitude of the vector AB is 4.24.

The equations that have the same value of x are:

i. \(6(\frac{5x}{6} + \frac{2}{3} ) = -9(6)\)

ii. 5x + 4 = -54

iii. 5x = -58

Two or more equations are said to be equivalent if they would give the same value or expression on simplification.

Considering the given question;

5x/6 + 2/3 = -9

multiply through by the LCM i.e 6 to have

5x + 4 = -9 x 6

5x + 4 = -58

5x = -58

x = -58/5

  = 11.6

x = 11.6

Therefore, the required equations are:

i. \(6(\frac{5x}{6} + \frac{2}{3} ) = -9(6)\)

ii. 5x + 4 = -54

iii. 5x = -58

Learn more about equivalent expressions at https://brainly.com/question/21604534

#SPJ1

The next five terms are ← ↑ → ↓ ← and the conjecture is each arrow is rotated 90 degrees clockwise to get the next

The first three terms are given as

↑ → ↓

From the above pattern, we have the following highlights:

Each arrow is rotated 90 degrees clockwise to get the next

Using the above as a guide, we have the next five terms to be:

← ↑ → ↓ ←

Also, we have the conjecture to be:

Each arrow is rotated 90 degrees clockwise to get the next

Read more about pattern at

https://brainly.com/question/16544803

#SPJ1

The value of (ΣX)² for the scores 1, 5, 2 is:  

64

It is the representation of the sum of infinite or many values. And it is represented by the following symbol:

∑xi

The value of (ΣX)² for the scores 1, 5, 2 can be found by first finding the summation of the scores and then squaring the result.

Steps to follow:

Step 1: Find the summation of the scores.
            ΣX = 1 + 5 + 2 = 8

Step 2: Square the summation.
            (ΣX)² = 82 = 64

Therefore, the value of (ΣX)² for the scores 1, 5, 2 is 64.

More information about summation here:

https://brainly.com/question/11741791

#SPJ11

Answer:

-10

Step-by-step explanation:

hope its correct and helped:)

Answer:

33/20

Step-by-step explanation:

I dont know if that was a minus or a plus but it looked like a minus sorry if its wrong

Answer:

0.475

Step-by-step explanation:

It makes it easier for people to turn fraction to decimal.

So, 1/4 in decimal is 0.25.

1.9•0.25=0.475

Sorry if I'm wrong I'm in 8 grade I learned it in this year

To determine if f satisfies the hypotheses of Rolle's Theorem on the interval [-1, 1], we need to check if f is continuous on [-1, 1] and differentiable on (-1, 1].

To apply Rolle's Theorem, f must meet the following conditions:Continuity: f must be continuous on the closed interval [-1, 1].Differentiability: f must be differentiable on the open interval (-1, 1). Since the given function f is a polynomial function, it is continuous and differentiable on its entire domain. Polynomials are defined and differentiable for all real numbers, and they are continuous everywhere.

Therefore, f satisfies the hypotheses of Rolle's Theorem on the interval [-1, 1]. It is continuous on the closed interval [-1, 1] and differentiable on the open interval (-1, 1). Rolle's Theorem states that if a function satisfies these conditions, then there exists at least one point c in the open interval (-1, 1) where the derivative of f equals zero. In other words, there exists a point c where f'(c) = 0.

It is important to note that while f satisfies the hypotheses of Rolle's Theorem, the specific values and behavior of f within the interval [-1, 1] would determine the existence and location of the point c. Additional analysis of the function would be necessary to determine the precise implications of Rolle's Theorem for the given function f on the interval [-1, 1].

To learn more about polynomial function click here:

brainly.com/question/29054495

#SPJ11

the answer is fifteen (15) weeks

The value of the triple integral is -16.

Triple integral is a mathematical concept used in calculus to calculate the volume of three-dimensional objects. It extends the concept of a single integral to functions of three variables and integrates over a region in three-dimensional space.

The triple integral of a function f(x, y, z) over a region E in three-dimensional space is denoted by:

∭E f(x, y, z) dV

We can set up the triple integral as follows:

∫∫∫ 16y dV

Where the limits of integration are:

0 ≤ x ≤ 2

0 ≤ y ≤ (2- \(x^2\)z)/(2y)

0 ≤ z ≤ 2/\(x^{2y\)

Note that the upper bound of integration for y is not a constant, but depends on both x and z.

Integrating with respect to y first, we get:

∫∫∫ 16y dV = ∫0^2 ∫\(0^(2-x^2z)/(2x)\)∫\(0^(2/x^2y) 16y dz dy dx\)

= ∫\(0^2\) ∫\(0^(2-x^2z)/(2x) 32/x dx dz\)

= ∫\(0^2\) [16(\(2-x^2z)/x^2\)] dz

= ∫\(0^2 (32/x^2 - 16z)\) dz

= 32∫\(0^2 x^-2 dx - 16\)∫\(0^2\)z dz

= 16 - 16(2)

= -16

Therefore, the value of the triple integral is -16.

To learn more about triple integral  visit:https://brainly.com/question/30404807

#SPJ11

Answer:

personally I believe its 6..

Step-by-step explanation:

10% of 200 is 20. if 10% is 20 then each part would equal 2. 2×3 is equal to 6

Answer:

$203

Step-by-step explanation:

To find the cost he pays back you need to mulitply 200 x 3% x 6 months.

Because you can't multiply with different units, you convert them to the same unit. (Numeric form)

To convert, we divide 3% by 100 and get 0.03

6 MONTHs is equal to 1/2 of a year which is also 0.5.

Now that all of our numbers are using the same units, we can multiply.

200(0.03)(0.5)

200 x 0.03 is 6

6 x 0.5 is 3.

We need to add the total amount her brother pays her back and the interest.

He pays her $200 for the Tablet and gives her $3 for the interest.

200+3=203.