Micheal wants to buy an efficient smart car that according to the latest EPA standards gets 33 mpg in the city and 40 mpg on the highway. The car that Micheal picked out costs $16,100. His dad agreed to purchase the car if Michael would pay it off in equal monthly payments for the next 70 months. The equation y= -230x+16,100 represents the amount, Y (in dollars), that Michael owes his father after X months.


A) How much does Michael owe his dad after six months?

B) determine the slope of the line and interpret its meaning in the context of this problem.


1) Micheal owes his father $[ ] after 6 months.


2) The slope is [ ]


3) The amount Michael owes his father [choose one] by $[ ] per month.

The probability that the thread length of a randomly selected bolt is farther than 2. 5 standard deviations from its mean value is 0.62%.

If the thread length of bolts is normally distributed, then we can use the concept of probability to determine the probability that the thread length of a randomly selected bolt is farther than 2.5 standard deviations from its mean value.

This can be calculated using the area under the normal curve.

Specifically, the area to the right of 2.5 standard deviations is 0.0062, meaning that there is only a 0.0062 probability (or 0.62%) that the thread length of a randomly selected bolt is farther than 2.5 standard deviations from its mean value

To know more about probability here.

https://brainly.com/question/11234923

#SPJ4

The coordinates of the final point after the reflections across the x-axis twice is (6, -4)

Reflecting a point across the x-axis means that we keep the x-coordinate the same, but change the sign of the y-coordinate.

So reflecting (6,-4) across the x-axis gives us the point (6,4).

Reflecting this result again across the x-axis means that we keep the x-coordinate the same, but change the sign of the y-coordinate again.

So reflecting (6,4) across the x-axis gives us the point (6,-4).

Therefore, the final point after both reflections is (6, -4).

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

Answer:

300+ 80+6

Step-by-step explanation:

i think i not sure

Answer:

this question is missing something

By definition of cosine and sine,

cos(θ) = x/r

sin(θ) = y/r

so that

cos²(θ) + sin²(θ) = (x/r)² + (y/r)²

… = x²/r² + y²/r²

… = (x² + y²)/r²

… = r²/r²

… = 1

To that end, I would say

• [blank1] = "Division property of equality"

That is, we divide both sides of an equation by the same number and equality still holds since r ≠ 0

• [blank2] = "Definition of cos"

• [blank3] = "cos²(θ) = x²/r²"

• [blank4] = "Defintion of sin"

• [blank5] = "sin²(θ) = y²/r²"

• [blank6] = "Simplify"

More specifically, x² + y² = r² is given, so

x²/r² + y²/r² = (x² + y²)/r² = r²/r² = 1

thanks man I leik points

The resulting graph is a circle with center at (-3,-1) and radius 3.

The graph of the equation (x+3)²+(y+1)²=9

is a circle with center at (-3,-1) and radius 3. The equation of a circle with center (a,b) and radius r is given by the equation (x-a)² + (y-b)² = r². By comparing the given equation with the standard equation of a circle, we can easily see that the center of the circle is (-3,-1) and the radius is 3. To graph a circle, we need to first plot the center of the circle, which is (-3,-1) in this case. Next, we need to mark the radius of the circle, which is 3 units. We can do this by measuring 3 units from the center in any direction and marking the point. Since the radius of the circle is the same in all directions, we can repeat this process for other directions to get points on the circumference of the circle. We can use a compass to make this process easier. After plotting a sufficient number of points, we can draw a smooth curve passing through all the points to obtain the graph of the circle.

For more question  graph

https://brainly.com/question/5504986

#SPJ8

Answer:

A.

This assumption is that the distribution of polyunsaturated fat % of each if these four regimes must be with equal variances as well as uniform.

B.

The null hypothesis

H0: μ1 = μ2 = μ3 = μ4

The alternate hypothesis:

H1: at least 2 means are unequal

C.

First we calculate the grand mean

= 1/54[15(42.9)+17(43.1)+8(43.7)+14(43.9)]

= (643.5 +732.7 + 349.6 + 614.6)/54

= 2340.4/54

= 43.341

Sum of squared treatment

= [15(42.9-43.341)²+17(43.1-43.341)²+8(43.7-43.341)²+14(43.9-43.341)²]

= 9.3104

Mean square of treatment

= SST/I-1

= 9.3104/4-1

= 9.3104/3

= 3.1035

Error sum of squared

= (15-1)*(1.3)² + (17-1)*(1.5)² + (8-1)*(1.2)² + (14-1)*(1.2)²

= 88.46

Error mean square

MSE = 88.46/54-4

= 1.7692

Test statistic

= 3.1035/1.7692

= 1.75

Answer:yes your Most definitely correct

Step-by-step explanation:

The equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.

To find the equation of a line passing through two points, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line and b is the y-intercept.

Given points:

Point 1: (1, 0)

Point 2: (3, 6)

Step 1: Calculate the slope (m) using the formula:

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

Substituting the coordinates:

m = (6 - 0) / (3 - 1)

m = 6 / 2

m = 3

Step 2: Substitute one of the given points and the slope into the equation y = mx + b to find the y-intercept (b).

Using Point 1 (1, 0):

0 = 3(1) + b

0 = 3 + b

b = -3

Step 3: Write the equation of the line using the slope (m) and the y-intercept (b):

y = 3x - 3

Therefore, the equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.

This equation represents a line with a slope of 3, indicating that for every increase of 1 unit in the x-coordinate, the y-coordinate increases by 3 units. The y-intercept of -3 means that the line crosses the y-axis at the point (0, -3). By substituting any x-value into the equation, we can determine the corresponding y-value on the line.

Hence, the equation of the line passing through (1, 0) and (3, 6) is y = 3x - 3.

For more such questions on equation of a line, click on:

https://brainly.com/question/18831322

#SPJ8

Answer:This problem involves using the concept of probability. We can use the formula for probability:

Probability = (number of desired outcomes) / (total number of possible outcomes)

First, let's calculate the total number of possible outcomes. Since there are 27 doors and each door can only have one piece of artwork, there are a total of 27 possible outcomes.

Next, let's calculate the number of desired outcomes. The teacher wants to display 8 sculptures, 9 sketches, and 10 oil paintings. We can choose 8 sculptures from the 11 available in C(11,8) ways (using the combination formula), 9 sketches from the 10 available in C(10,9) ways, and 10 oil paintings from the 12 available in C(12,10) ways. To find the total number of desired outcomes, we can multiply these together:

number of desired outcomes = C(11,8) * C(10,9) * C(12,10)

= (165) * (10) * (66)

= 108,900

Finally, we can plug these values into the formula for probability:

Probability = (number of desired outcomes) / (total number of possible outcomes)

= 108,900 / 27

= 4,033.3 (rounded to one decimal place)

However, probabilities cannot be greater than 1. Therefore, the probability of displaying 8 sculptures, 9 sketches, and 10 oil paintings is 1.

Answer:

\(\frac{-37}{99}\)

Step-by-step explanation:

0.555555... becomes \(\frac{5}{9}\)

Using this logic, we can do the following:

\(-0.37373737... = \frac{-37}{99}\)

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

Consider the image below

The angles in the same colors are corresponding angles

Therefore from the figure in the question

we can conclude that

Angle 8 is corresponding to angle 4

The correct answer is option C

The range of the exponential function is B. y > 0.

The range of the exponential function f(x) = 11 × (1/3)ˣ can be determined by analyzing the behavior of the function as x approaches positive and negative infinity.

As x approaches positive infinity, (1/3) becomes smaller and smaller, tending towards zero.

f(x) approaches 11 × 0, which is equal to 0.

As a result, the function approaches 0 as x goes to infinity.

On the other hand, as x approaches negative infinity, (1/3)ˣ becomes larger and larger.

Since 1/3 is between 0 and 1, raising it to a negative power causes it to grow exponentially.

f(x) approaches infinity as x goes to negative infinity.

Combining these two behaviors, we can conclude that the range of the function f(x) = 11 × (1/3)ˣ is all positive real numbers, excluding zero.

In other words, the range is y > 0.

For similar questions on exponential function

https://brainly.com/question/2456547

#SPJ8

Answer:

$54.33

Step-by-step explanation:

Answer:

  70 ft

Step-by-step explanation:

You want the actual width of a gym that is represented as 7 inches on a drawing with a scale of 1 in : 10 ft.

Each inch represents 10 feet, so 7 inches will represent ...

  7 × 10 ft = 70 ft

The gym is 70 ft wide.

__

Additional comment

You can also write and solve an equation that shows the measures are proportional:

  actual width / drawing width = (10 ft) / (1 in) = (gym width) / (7 in)

Multiplying both sides of this proportion by 7 in, we have ...

  gym width = (7 in) × (10 ft)/(1 in) = 7 × 10 ft = 70 ft

Answer:

following are the solution to the given points:

Step-by-step explanation:

In point a:

\(\vec{v} = -\vec{1 i} +\vec{1j}\\\\|\vec{v}| = \sqrt{-1^2+1^2}\)

    \(=\sqrt{1+1}\\\\=\sqrt{2}\)

calculating unit vector:

\(\frac{\vec{v}}{|\vec{v}|} = \frac{-1i+1j}{\sqrt{2}}\)

the point Q is at a distance h from P(6,6) Here, h=0.1  

\(a=-6+O.1 \times \frac{-1}{\sqrt{2}}\\\\= 5.92928 \\\\b= 6+O.1 \times \frac{-1}{\sqrt{2}} \\\\= 6.07071\)

the value of Q= (5.92928 ,6.07071  )

In point b:

Calculating the directional derivative of \(f (x, y) = \sqrt{x+3y}\) at P in the direction of \(\vec{v}\)

\(f_{PQ} (P) =\fracx{f(Q)-f(P)}{h}\\\\\)

            \(=\frac{f(5.92928 ,6.07071)-f(6,6)}{0.1}\\\\=\frac{\sqrt{(5.92928+ 3 \times 6.07071)}-\sqrt{(6+ 3\times 6)}}{0.1}\\\\= \frac{0.197651557}{0.1}\\\\= 1.97651557\)

\(\vec{v} = 1.97651557\)

In point C:

Computing the directional derivative using the partial derivatives of f.

\(f_x(x,y)= \frac{1}{2 \sqrt{x+3y}}\\\\ f_x (6,6)= \frac{1}{2 \sqrt{22}}\\\\f_x(x,y)= \frac{1}{\sqrt{x+3y}}\\\\ f_x (6,6)= \frac{1}{\sqrt{22}}\\\\f_{(PQ)}(P)= (f_x \vec{i} + f_y \vec{j}) \cdot \frac{\vec{v}}{|\vec{v}|}\\\\= (\frac{1}{2 \sqrt{22}}\vec{i} + \frac{1}{\sqrt{22}} \vec{j}) \cdot \frac{-1}{\sqrt{2}}\vec{i} + \frac{1}{\sqrt{2}} \vec{j}\)

Answer:

\(y-2=3(x-4)\)

Step-by-step explanation:

We are given a line contains the point (4, 2).

We also know that the line is parallel to y= 3x - 7.

We want to write the equation of this line.

Parallel lines have the same slopes.

First, let's find the slope of y = 3x - 7.

3 is in the place of where m (the slope) is, so that means it is the slope of that line.

It is also the slope of the line whose equation we want to write.

The equation of the line can be written in three ways:

All of these ways are valid, but for this problem, let's write the equation in point-slope form, as it is the easiest.

Substitute 3 as m in \(y-y_1=m(x-x_1)\).

\(y-y_1=3(x-x_1)\)

Now, substitute 4 as \(x_1\) and 2 as \(y_1\).

\(y-2=3(x-4)\)

Topic: parallel and perpendicular lines

See more: https://brainly.com/question/7699889

Answer:

●●●●

●ООО

Step-by-step explanation:

Answer:

I think the first one is B

Step-by-step explanation:

The linear equation that shows how the wind power would need to grow to make this goal is y = 25x + 15

From the question, we have the following parameters that can be used in our computation:

(x, y) = (0, 15) and (5, 90)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 15

Using the other point, we have

5m + 15 = 90

So, we have

5m = 75

Divide by 5

m = 25

So, the equation becomes

y = 25x + 15

Read more about linear equation at

brainly.com/question/2030026

#SPJ1

Complete question

Using the two data points from Exercises 1 and 2, write a linear equation that shows how the wind power would need to grow to make this goal. Use years for the independent variable and terawatt hours for the dependent variable. Let year 0 represent year 2012, (0, 15) and (5, 90)

Answer:

k = 125

Step-by-step explanation:

k = (360 - 55 * 2) / 2 = (360 - 110) / 2 = 250 / 2 = 125

Answer:

Step-by-step explanation:

Find the difference:

The translation rule is:

Answer:

(-5, 8)

Step-by-step explanation:

Answer: 3.6 is 5% of 72

Step-by-step explanation: If 3.6 is 5% then just multiply 3.6 by 95 to get 68.4 and add to get 72, Yw.

Answer:

We can simplify the expression as follows:

4^3 * 4^4 / 4^9

First, we can simplify the terms in the numerator by adding the exponents of 4:

4^3 * 4^4 = 4^(3+4) = 4^7

Now, we can substitute this value in the expression:

4^7 / 4^9

To divide powers with the same base, we can subtract their exponents:

4^(7-9) = 4^(-2)

Therefore, the simplified expression is:

4^3 * 4^4 / 4^9 = 4^(-2)

So, the final answer is 1/16 or 0.0625.

The first cellphone service provider to be established in South Africa was Vodacom. Vodacom was launched on April 1, 1994, and it became the country's first cellular network operator.

The company was a joint venture between Telkom, the national telecommunications company of South Africa, and Vodafone, a global telecommunications giant.

Vodacom introduced the GSM network to South Africa, providing mobile voice and data services to customers across the country. Its launch marked a significant milestone in the telecommunications industry in South Africa, as it brought mobile communication to the masses and revolutionized the way people connect and communicate.

Since its inception, Vodacom has played a pivotal role in the development of the telecommunications sector in South Africa. It has continually expanded its network coverage, introduced innovative services, and played an active role in bridging the digital divide in the country.

Today, Vodacom remains one of the leading mobile network operators in South Africa, providing a wide range of mobile services to millions of customers.

For more such questions on Vodacom,click on

https://brainly.com/question/28559820

#SPJ8    

The probable question may be:

Which cellphone service provider was the first to be established in south africa

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

Find out more on fractions here: https://brainly.com/question/78672

#SPJ1