(3 pts total) Suppose local sales tax is 8.75% and the price of a car is $36,500.
a) How much tax would be paid when purchasing this car?
b) What is the total amount of money needed to buy the car (list price and tax)?

Circle 1 has center at (0, 0)

The tangent passes through the center and point (1, -2).

Equation of tangent at (1, -2):

If the same line is tangent to circle 2 then they have one common point.

Solve the system:

Substitute x:

We see only one point of contact, (3, -1), this proves the line is tangent to circle 2 as well.

Given circle:

Rewrite the equation of the circle as:

The center is (7/6, 1) the radius is √229/36

The length of the tangent t is the leg of the right triangle with another leg r being the radius and the hypotenuse d being the distance between the center and the external point:

Given the system of equations:

-10x-15y=25...................................equation 1

x - 5y = -9.....................................equation 2

Let's solve using substitution method.

From equation 2, make x the subject:

x = -9 + 5y

Substitute (-9 + 5y) for x in equation 1:

-10(-9 + 5y) - 15y = 25

-10(-9) - 10(5y) - 15y = 25

90 - 50y - 15y = 25

90 - 65y = 25

Subtract 90 from both sides:

90 - 90 - 65y = 25 - 90

-65y = -65

Divide both sides by -66



Answer:

A and c

Step-by-step explanation:

A because you should always start at 0

C because -3 goes to the left not the right

and i took the test on edgenuity..........

hope this helps

Answer:

A and C

Step-by-step explanation:

Got it right EDGE 2021

Answer:

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

  (f(x+h) -f(x))/h = 4h +8x +5

  f'(x) = 8x +5

Step-by-step explanation:

For f(x) = 4x² +5x +3, you want the simplified expression f(x+h), the difference quotient (f(x+h) -f(x))/h, and the value of that at h=0.

Put (x+h) where h is in the function, and simplify:

  f(x+h) = 4(x+h)² +5(x+h) +3

  = 4(x² +2xh +h²) +5x +5h +3

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

The difference quotient is ...

  (f(x+h) -f(x))/h = ((4x² +4h² +8xh +5x +5h +3) - (4x² +5x +3))/h

  = (4h² +8xh +5h)/h

  (f(x+h) -f(x))/h = 4h +8x +5

When h=0, the value of this is ...

  f'(x) = 4·0 +8x +5

  f'(x) = 8x +5

__

Additional comment

Technically, the difference quotient is undefined at h=0, because h is in the denominator, and we cannot divide by 0. The limit as h→0 will be the value of the simplified rational expression that has h canceled from every term of the difference. This will always be the case for difference quotients for polynomial functions.

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Answer:

\(A(t)=16(0.99948)^t\)

Step-by-step explanation:

The exponential function is modeled using the equation:

\(A(t)=A_o(1\pm r)^t\)

Where the plus sign indicates growth and the negative sign indicates exponential decay.

For an exponential function has a starting value of 16 and a decay rate of 0.52%.

\(A_0=16\\r=0.052\%=0.00052\)

This gives:

\(A(t)=16(1- 0.00052)^t\\A(t)=16(0.99948)^t\)

The function that models this situation is:

\(A(t)=16(0.99948)^t\)

The cost of each pound of grass seed is $6.

A graph of the solution for the cost of each pound of grass seed is shown below.

In order to determine the cost of each pound of grass seed, we would assign a variable to the cost of each pound of grass seed and then translate the word problem into an algebraic linear equation.

Let the variable x represent the cost of each pound of grass seed.

Since Lori bought 3.6 pounds of grass seed and she was charged $22.90, including a tax of $1.30, an algebraic linear equation that best represent this situation is given by;

3.6x + 1.30 = 22.90

3.6x = 22.90 - 1.30

3.6x = 21.60

x = 21.60/3.6

x = $6.

In conclusion, we would sue an online graphing calculator to plot the solution for the cost of each pound of grass seed as shown in the image attached below.

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If you are dealt one card from a​ 52-card deck. The probability that you are not dealt a jack or a ten is 12/13.

Since there are 4 aces in a deck of card 52 first step is to find the number of cards  not aces in a deck of 52

Number of cards  not aces in a deck = 52 -4

Number of cards  not aces in a deck = 48

Now let find the probability that you won't draw an ace.

Probability = 48/52

Probability = 24/26

Probability = 12/13

Therefore we can conclude that the probability is 12/13.

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The volume of the composite figure in this problem is given as follows:

76 ft³.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The figure in this problem is composed by two prisms, with dimensions given as follows:

Hence the volume is given as follows:

2 x 6 x 3 + 2 x 4 x 5 = 76 ft³.

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Answer:

The Answer is D

Step-by-step explanation:

The equation that represents the function is \(h(x) = x^{2} +2\).

Let us say the function is of form \(h(x) = x^{n} +c\)......(1)

A function is a rule that establishes a relation between two variables.

Points on this graph are  (0, 2), (1, 3), (2, 6), and (3, 11).

So, these points will satisfy the graph,

This means, In (1) we can put the given coordinates.

Let us put (0,2)

i.e. \(2 = x^0 + c\)

c =2

So (1) becomes \(h(x) = x^{n} +2\).....(2)

To get n let us put (2,6) in (2)

\(6 = 2^{n} +2\\2^n = 4\\2^n = 2^2\\n = 2\)

So, (2) becomes \(h(x) = x^{2} +2\)

Therefore, the equation that represents the function is \(h(x) = x^{2} +2\).

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Answer:

the area of a square garden 3136cm what is the length of one side

Answer:

pppppppppppppppppppppppppppppppppppppppppp

Answer:

Answer:

Based on the provided information, the table summarizes service times (in seconds) of dinners at a fast food restaurant. To determine the number of individuals included in the summary, we can sum up the frequencies listed in the table:

7 + 24 + 14 + 1 + 4 = 50

Therefore, there are 50 individuals included in the summary.

Regarding the exact values of all the original service times, it is not possible to determine them precisely based on the given information. The table only provides ranges of service times and their corresponding frequencies. We can determine the range within which each individual's service time falls, but we cannot determine the exact value within that range.

Answer:

As the calculated  χ² = 1.23  is less than the critical region  χ²≥ χ²(0.05,9)=  16.92 ,Staples can conclude that demands for these two types of computers are independent  at the 0.05 level of significance.

Step-by-step explanation:

As we have to test the independence of the two categories the chi square of independence test is applied.

Let the null and alternate hypotheses be

H0 :The demand for each type of computers is independent

against the claim

Ha: The  demand for each type of computers is not independent i.e they are associated.

The significance level alpha is chosen to be 0.05

The critical region for alpha =0.05 and (4-1)(4-1) = 3*3 =9 d.f is

χ²≥ χ²(0.05,9)=  16.92

Actual Data

                  low          med-low       med-high          high       Total

low             4                15                    14                     3         36

med-low  6                 18                    18                    23        65

med-high 13                 17                   10                     17         57

high          7                  15                  15                      10          47      

Total       30                65                 57                     53         205        

Expected Frequencies

low- low = 30*36/205= 5.27

low- med.low = 65*36/205 = 11.41

low- medium high = 57*36/205= 10.009

low- high = 53*36/205 =9.31

medium low- low = 30*65/205 = 9.51

medium low- med.low = 65*65/205= 20.61

medium low- medium high = 57*65/205= 18.073

medium low- high = 53*65/205= 16.80

medium high- low = 30*57/205= 8.34

medium high- med.low = 65*57/205= 18.07

medium high- medium high = 57*57/205= 15.85

medium high- high = 53*57/205= 14.74

high- low = 30*53/205= 7.76

high- med.low = 65*53/205= 16.80

high- medium high = 57*53/205= 14.74

high- high = 53*53/205= 13.70

Summarizing in a table

Expected Frequencies

                  low          med-low       med-high          high           Total        

low             5.27         11.41                    10.009           9.31        35.999

med-low  9.51            20.61               18.073             16.8        64.993

med-high 8.34             18.07                 15.85            14.74       57  

high          7.76              16.8                  14.74             13.7         53              

Total       30.88           66.89               58.672          54.55         210.992  

Using Excel

The Chi Square Values are

0.062823

0.270857

0.159572

0.735995791

1.229247532

As the calculated  χ² = 1.23  is less than the critical region  χ²≥ χ²(0.05,9)=  16.92 ,Staples can conclude that demands for these two types of computers are independent  at the 0.05 level of significance,

Answer:

7.4

Step-by-step explanation:

Not completely sure because that equation is really hard to read. You might have put it in wrong.

Answer:

-95x + 91

Step-by-step explanation:

72/9 = 8

83 - 95x + 8

91 - 95x or -95x + 91

When x = 13, the equation that is true is option D) 5(x - 9) = 20.

To determine which equation is true when x = 13, we can substitute the value of x into each equation and see which equation holds true. Let's go through each option:

A) 3(18 - x) = 67

Substituting x = 13:

3(18 - 13) = 67

3(5) = 67

15 = 67

The equation is not true when x = 13. Therefore, option A is false.

B) 4(9x) = 23

Substituting x = 13:

4(9*13) = 23

4(117) = 23

468 = 23

Again, the equation is not true when x = 13. Therefore, option B is also false.

C) 2(x - 3) = 7

Substituting x = 13:

2(13 - 3) = 7

2(10) = 7

20 = 7

Once again, the equation is not true when x = 13. Therefore, option C is false as well.

D) 5(x - 9) = 20

Substituting x = 13:

5(13 - 9) = 20

5(4) = 20

20 = 20

Finally, the equation is true when x = 13. Therefore, option D is true.

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Note: the translated questions is

X = 13, which equation is true?

Answer: B. hours

Step-by-step explanation:

    Let us closely look at the varible t it gives, the one we are looking at units for. "t stands for the amount of time the workers have left to clean the windows"

         "t stands for the amount of time ..."

    The only unit they give that represents time is hours, meaning the answer to your question is:

     B. hours

Answer:

Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.

Step-by-step explanation:

hourly pay: $5/hour

number of hours: 24 hours

total pay = hourly pay × number of hours

total pay = $5/hour × 24 hours

total pay = $120

MP3 player costs $100.

Total pay is $120.

Answer: Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.

The 2 : 5 scaled version of the deck Sam plans to build and the dimensions of the original deck indicates;

Part A; Base length of the new deck = 7.2 feet

Height of the new deck = 2.8 feet

Part B; The area of the original deck is 63 square feet

The area of the new deck is 10.08 square feet

Part C; The ratio of the areas is the square of the scale factor

A scale factor is a number or factor that is used to enlarge or reduce the dimensions a shape or size of a figure.

The base length of the triangular deck = 18 feet

The height of the triangular deck = 7 feet

The scale factor for the scaled version Sam intends to build = 2 : 5

Part A; The dimensions of the new deck are;

Base length of the new deck using the the 2 : 5 ratio is; (2/5) × 18 = 7.2 feet

The height of the new deck = (2/5) × 7 = 2.8 feet

Part B; The area of the original deck = (1/2) × 18 × 7 = 63 square feet

Area of the new dec = (1/2) × 7.2 × 2.8 = 10.08 square feet

Part C; The ratio of the areas is; 10.08/63

Ratio of the area = 10.08/63 = 4/25 = 4 : 25

The scale factor is; 2 : 5

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The notion of finiteness refers to the idea that something has a definite limit or is not infinite. It is a concept that has been applied in various fields of study, such as mathematics, computer science, and philosophy.

In mathematics, finiteness is a fundamental concept used to define various mathematical objects and structures, such as sets, numbers, and sequences. It is also used to define the properties of functions and to study the properties of mathematical systems.

In computer science, the notion of finiteness is crucial for the design and analysis of algorithms and computer programs. Computer scientists use finite state machines, which are mathematical models that describe the behavior of a system that can be in one of a finite number of states.

This concept is essential to the development of computer programs that are efficient, reliable, and secure.

In philosophy, finiteness is a concept that is often used to reflect on the nature of human existence and the limits of human knowledge. It is also used to examine the concept of time and the nature of reality.

In general, the notion of finiteness is a fundamental concept that has many applications in various fields of study.

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The quadratic function f(x) =\(3(x+3)^2 - 7\) has a minimum at x = -1, and the minimum value is 5.

To determine whether the quadratic function f(x) =\(3(x+3)^2 - 7\)has a minimum or maximum, we can examine the coefficient of the x^2 term, which is positive (3 in this case).

When the coefficient of the x^2 term is positive, the parabola opens upward, indicating that the function has a minimum value. The vertex of the parabola represents the minimum point.

Now let's find the coordinates of the vertex, which will give us the minimum value of the function.

The general form of a quadratic function is f(x) =\(ax^2 + bx + c\), where the vertex can be found using the formula:

x = -b / (2a)

In our case, a = 3 and b = 3*2 = 6 (from (x+3)^2).

Substituting the values into the formula, we have:

x = -6 / (2 * 3)

x = -6 / 6

x = -1

To find the y-coordinate of the vertex, we substitute the x-value (-1) into the function:

\(f(-1) = 3((-1)+3)^2 - 7\)

\(f(-1) = 3(2)^2 - 7\)

f(-1) = 3(4) - 7

f(-1) = 12 - 7

f(-1) = 5

The graph of this function will have a downward-opening parabola, and the vertex will be the lowest point on the curve.

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Answer: 66.8

Step-by-step explanation:

Let the mean height of 16 students in the class = X

Therefore,

\(\frac{15*67+63.8}{16} =X\)

\(X=\frac{334}{5}\)

X = 66.8

Answer:

y=1/3x+11/15

4/15=1/3x

12/15=x

4/5=x

Given:

Graph is given.

6a.

6b.

6c.

The linear functions that define their distances are given as follows:

The number of hours after noon in which they will be the same distance away from the stadium is of:

8 hours.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the parameters are given as follows:

In the context of this problem, the meaning of each parameter is:

They will be the same distance away at the point of intersection of the graph given at the end of the answer, which is of 8 hours.

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Answer:

18

Step-by-step explanation:

multiply 6 by 3

Answer:

It's super duper easy

Step-by-step explanation:

6/7=x/21

x=21×6/7

x=18

Answer:

i use slope calculators for these type of problems :)

Step-by-step explanation:

Line 1. Vertical. Undefined slope.

Line 2. -4/3

Line 3. 4/3

Line 4. Vertical. Undefined slope.

Line 5. 7/3

Line 6. -7/3

Line 7. Horizontal line. Slope 0

Line 8. Horizontal line. Slope 0

Line 9. Vertical line. Undefined slope.

Line 10. Vertical line. Undefined slope.

Line 11. Horizontal line. Slope 0

Line 12. Vertical line. Undefined slope.

These slopes can be found using the rise and run method. All vertical lines are undefined and all horizontal lines are 0.

It took Ringani 2.8 years  to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate Compounded annually.The correct answer choice is C. 2.8 years.

To determine how long it took Ringani to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into an account with a 7.04% interest rate compounded annually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the time in years

In this case, we have:

P = R8,500.00

A = R30,000.00

r = 7.04% = 0.0704 (in decimal form)

n = 1 (compounded annually)

We want to find the value of t.

Using the formula, we can rearrange it to solve for t:

t = (log(A/P)) / (n * log(1 + r/n))

Substituting the given values, we have:

t = (log(30,000/8,500)) / (1 * log(1 + 0.0704/1))

Calculating this using a calculator, we find that t is approximately 2.8 years.

Therefore, it took Ringani approximately 2.8 years (rounded to one decimal place) to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate compounded annually.

The correct answer choice is C. 2.8 years.

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Therefore, option a reflects both eating more burgers would likely lead to eating more French fries as well.

Describe the correlation?

A statistical relationship between two variables is called a correlation. The connection between cause and effect is known as causation. Correlation does not always imply causation, even though it can show a link between two variables.

In this case,

the relationship that most likely reflects both correlation and causation is “Eating burgers more often is associated with eating french fries more often.” This is because burgers and french fries are often served together in fast food restaurants.

However, it’s important to note that correlation does not always imply causation. Just because two variables are correlated does not mean that one causes the other.

What does the term "causation" mean?

Causation, as used in law, denotes the cause-and-effect connection between an occurrence or action and the outcome. The thing that causes an effect is the act or process. It is not sufficient to just demonstrate that the defendant was negligent in a personal injury case; you must also demonstrate causation.

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Answer:

Area = 28.27 in²

Step-by-step explanation:

Now we have to,

→ find the area of the circle.

Formula we use,

→ π × r²

Now the required area will be,

→ π × r²

→ 3.14 × 3²

→ 3.14 × 9

→ 28.27 in²

Hence, the area is 28.27 in².