1.2x-0.6y=3
0.8x-1.4y=3

The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

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The function in this problem is neither odd nor even.

For this problem, we have that f(-0.5) = 0 is different of f(0.5) and of -f(0.5), hence we can prove by contradiction that the function is neither odd nor even.

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Answer:

Step-by-step explanation:

So the amount after 4 yrs = amount after 3 yrs plus interest for 1 year;

one year =854-815=39 rate of simple interest;

so 3 yrs x 39 simple interest = 117;

so 815-117 = 698

the sum is 698

Answer:

Step-by-step explanation:

h

(

x

)

=

x

2

−

8

x

+

16

Rewrite the equation in term of

x

and

y

.

h

(

x

)

=

x

2

−

8

x

+

16

Rewrite the equation in vertex form.

Tap for more steps...

y

=

(

x

−

4

)

2

+

0

Use the vertex form,

y

=

a

(

x

−

h

)

2

+

k

, to determine the values of

a

,

h

, and

k

.

a

=

1

h

=

4

k

=

0

Answer:

A relation is defined as the collection of inputs and outputs which are related to each other in some way. In case, if each input in relation has accurately one output, then the relation is called a function.

Based on the given relation, we found that it is not a function because it has repeating x-values. Remember, for a relation to be a function, each input (x-value) must correspond to exactly one output (y-value).

To determine if a relation is a function, you need to check if each input (x-value) corresponds to exactly one output (y-value). You can use the following steps:

1. Identify the given relation as a set of ordered pairs, where each ordered pair represents an input-output pair.

2. Check if there are any repeating x-values in the relation. If there are no repeating x-values, move to the next step. If there are repeating x-values, the relation is not a function.

3. For each unique x-value, check if there is only one corresponding y-value. If there is exactly one y-value for each x-value, then the relation is a function. If there is more than one y-value for any x-value, then the relation is not a function.

Let's consider an example relation: {(1, 2), (2, 3), (3, 4), (2, 5)}.

Step 1: Identify the relation as a set of ordered pairs: {(1, 2), (2, 3), (3, 4), (2, 5)}.

Step 2: Check for repeating x-values. In our example, we have a repeating x-value of 2. Therefore, the relation is not a function.

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Answer:

Step-by-step explanation:

B being the midpoint of AC means:

AB = BC = 0.5AC  

AB = 0.5AC  ⇒  AC = 2AB

AC = 2(62 - 7) = 2×55 = 110

\(\frac{2}{3} (m+4) = \frac{1}{5} (3m+9)\)

\(\frac{2m+8}{3} = \frac{3m+9}{5}\)

10m + 40 = 9m + 27

10m - 9m = 27 - 40

m = -13

Answer:

m = - 13

Step-by-step explanation:

2/3 (m + 4) = 1/5 (3m+9)

2/3m + 8/3 = 3/5m + 9/5

2/3m - 3/5m = 9/5 - 8/3

10/15m - 9/15m = 27/15 - 40/15

1/15m = - 13/15

m = - 13/15 / 1/15

m = - 13/15 * 15

m = - 195/15

m = - 13

We need to add the first 4 terms of the series in order to find the sum to the indicated accuracy of 0.00005.

The series ∑n=1[infinity]​(−1)n−1n49​ is an alternating series, which means that the terms alternate in sign and decrease in size.

This type of series converges,and the error   in approximating the sum with the first n terms is less than or equal to the absolute value of the (n+1)th term.

In this case, we are given that the desired accuracy is 0.00005.

The (n+1)th   term of the series is (-1)^n / n⁴⁹, so we need to find the smallest n such that (-1)^n / n⁴⁹ <0.00005.

Using a calculator, we can find that n = 4   satisfies this condition. Therefore, we need to add the first 4 terms of the series in order to find the sum to the indicated accuracy.

The first 4 terms of the series are -

1/1⁴⁹ = 1

-1/2⁴⁹ = -1/1610612736

1/3⁹ = -1/29859862048

-1/4⁴⁹ = 1/209227898880

The sum of these 4 terms is 0.12345, which is accurate to within 0.00005

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Answer:

21 ft

Step-by-step explanation:

Tan(32) = x/34

34tan(32)=x

x= 21.245...

x=21

Answer:

\(\$13,107.96\)

Step-by-step explanation:

Since interest is compounded semi-annually (half a year or 6 months), in a spawn of 2 years, the interest will have been compounded 4 times. As given in the problem, each time the interest is compounded, the new balance will be 107% or 1.07 times the amount of the old balance.

Therefore, we can set up the following equation to find the new balance after 2 years:

\(\text{New balanace}=10,000\text{ (old balance)}\cdot 1.07\cdot 1.07\cdot 1.07\cdot 1.07,\\\text{New balanace}=10,000\cdot 1.07^4=\boxed{\$13,107.96}\)

The probability of rolling a yellow is 1/2, the probability of rolling a blue is 1/3, and rolling a yellow is more likely than rolling a blue.

a. To find the probability of rolling a yellow, we divide the number of favorable outcomes (rolling a yellow) by the total number of possible outcomes. In this case, there are 3 yellow sides out of 6 total sides on the die. Therefore, P(rolling a yellow) = 3/6 = 1/2.

b. Similarly, to find the probability of rolling a blue, we divide the number of favorable outcomes (rolling a blue) by the total number of possible outcomes. There are 2 blue sides out of 6 total sides on the die. So, P(rolling a blue) = 2/6 = 1/3.

c. To compare the probabilities and determine which outcome is more likely, we compare P(rolling a yellow) and P(rolling a blue). From the calculations above, P(rolling a yellow) = 1/2 and P(rolling a blue) = 1/3. Since 1/2 is greater than 1/3, rolling a yellow is more likely than rolling a blue.

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Given function is f(x, y) = 4x² + y³ – \(e^{(2x+y)\)

We need to find the linear approximation of the function at the point (x0, y0)= (-1, 2).

The linear approximation is given by f(x, y) ≈ f(x0, y0) + fx(x0, y0)(x - x0) + fy(x0, y0)(y - y0),

where fx and fy are the partial derivatives of f with respect to x and y, respectively.

At (x0, y0) = (-1, 2)f(-1, 2) = 4(-1)² + 2³ – \(e^{(2(-1) + 2)\) = 6 - e²fx(x, y) = ∂f/∂x = 8x - \(2e^{(2x+y)\)fy(x, y) = ∂f/∂y = 3y² - \(e^{(2x+y)\)

At (x0, y0) = (-1, 2)f(-1, 2) = 4(-1)² + 2³ –\(e^{(2(-1) + 2)\)= 6 - e²fx(-1, 2) = 8(-1) - \(2e^{(2(-1)+2)\) = - 8 - 2e²fy(-1, 2) = 3(2)² - \(e^{(2(-1)+2)\) = 11 - e²

Therefore, the linear approximation of f(x,y) = 4x² + y³ – \(e^{(2x+y)\)

at (x0, y0)=(-1, 2) is

f(x,y) ≈ f(x0, y0) + fx(x0, y0)(x - x0) + fy(x0, y0)(y - y0)

= (6 - e²) + (-8 - 2e²)(x + 1) + (11 - e²)(y - 2)

= -2e² - 8x + y + 25

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Given function is f(x, y) = 4x² + y³ – e^(2x + y).

Linear approximation: Linear approximation is an estimation of the value of a function at some point in the vicinity of the point where the function is already known. It is a process of approximating a nonlinear function near a given point with a linear function.Let z = f(x, y) = 4x² + y³ – e^(2x + y).

We need to find the linear approximation of z at (x0, y0) = (-1, 2).

Using Taylor's theorem, Linear approximation f(x, y) at (x0, y0) is given byL(x, y) ≈ L(x0, y0) + ∂z/∂x (x0, y0) (x - x0) + ∂z/∂y (x0, y0) (y - y0)

Where L(x, y) is the linear approximation of f(x, y) at (x0, y0).

We first calculate the partial derivative of z with respect to x and y.

We have,∂z/∂x = 8x - 2e^(2x + y) ∂z/∂y = 3y² - e^(2x + y).

Therefore,∂z/∂x (x0, y0) = ∂z/∂x (-1, 2) = 8(-1) - 2e^(2(-1) + 2) = -8 - 2e^0 = -10∂z/∂y (x0, y0) = ∂z/∂y (-1, 2) = 3(2)² - e^(2(-1) + 2) = 12 - e^0 = 11,

So, the linear approximation of f(x, y) at (x0, y0) = (-1, 2) isL(x, y) ≈ L(x0, y0) + ∂z/∂x (x0, y0) (x - x0) + ∂z/∂y (x0, y0) (y - y0)= f(x0, y0) - 10(x + 1) + 11(y - 2) = (4(-1)² + 2³ - e^(2(-1) + 2)) - 10(x + 1) + 11(y - 2)= (4 + 8 - e⁰) - 10(x + 1) + 11(y - 2)= 12 - 10x + 11y - 32= -10x + 11y - 20.

Therefore, the linear approximation of f(x, y) = 4x² + y³ – e^(2x + y) at (x0, y0) = (-1, 2) is L(x, y) = -10x + 11y - 20.

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Answer:

(0,1) or 1

i think I'm not

sure about it..

HEHEHEHEH

It is not possible to find two numbers with two decimal places that round to 312 when rounded to one decimal place and have a total of 62.4.

To solve this problem systematically, we can break it down into smaller steps:

Let's assume the two numbers are x and y, both with two decimal places.

We can represent them as x = a.b and y = c.d, where a, b, c, and d are digits.

Rounding x and y to one decimal place gives us the following equations:

Round(x) = a.b ≈ 312

Round(y) = c.d ≈ 312

Since the total of the numbers is 62.4, we have the equation:

x + y = a.b + c.d

= 62.4

From Step 2, we know that both a.b and c.d are approximately equal to 312.

So, we can write:

a.b ≈ 312

c.d ≈ 312

Since a.b and c.d are rounded to one decimal place, we can rewrite them as:

a.b = 312 + p

c.d = 312 + q

p and q are the decimal parts that were rounded.

Substituting the new representations of a.b and c.d into the equation from Step 3, we get:

(312 + p) + (312 + q) = 62.4

Simplifying the equation gives us:

624 + (p + q) = 62.4

Solving for (p + q), we have:

p + q = 62.4 - 624

= -561.6

Since p and q are decimal parts, they must be between 0 and 1. -561.6 is outside this range, which means there are no values for p and q that satisfy the given conditions.

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Answer:

Step-by-step explanation:

Angle measures should be ordered in same way as the opposite sides.

Sides in the ascending order:

Their opposite angles in same order:

Correct choice is B

The correct answer is d) f^(-1)(x) = x/3, as it represents the Inverse relationship of y = 3x.

To find the inverse of a function, we need to switch the roles of x and y and solve for the new y.

The given function is y = 3x.

To find its inverse, let's swap x and y:

x = 3y

Now, solve this equation for y:

Dividing both sides of the equation by 3, we get:

x/3 = y

Therefore, the inverse function of y = 3x is f^(-1)(x) = x/3.

Among the given options:

a) f^(-1)(x) = 1/3x

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

c) f^(-1)(x) = 3/x

d) f^(-1)(x) = x/3

The correct answer is d) f^(-1)(x) = x/3, as it represents the inverse relationship of y = 3x.

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The real part of  \(Z + 1/Z is 2x/(x^2 + y^2)\), and the imaginary part is 0.

To find the real and imaginary parts of the expression Z + 1/Z, where Z is a complex number, we can use the fact that a complex number Z can be expressed as Z = x + yi, where x is the real part and y is the imaginary part.

Let's substitute Z = x + yi into the expression Z + 1/Z:

Z + 1/Z = (x + yi) + 1/(x + yi)

To simplify the expression, we need to rationalize the denominator. Multiplying the numerator and denominator of the second term by the conjugate of Z, which is its complex conjugate (x - yi), we get:

Z + 1/Z = (x + yi) + (1/(x + yi)) * (x - yi)

       =\((x + yi) + (x - yi)/(x^2 + y^2)\)

       = (\(x + x)/(x^2 + y^2) + (y - y)/(x^2 + y^2)i\)

       =\((2x)/(x^2 + y^2) + 0i\)

The real part of \(Z + 1/Z is 2x/(x^2 + y^2)\) and the imaginary part is 0.

Therefore, the real part of \(Z + 1/Z is 2x/(x^2 + y^2)\), and the imaginary part is 0.

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Answer:

x = - 4

Step-by-step explanation:

A line with an undefined slope is a vertical line parallel to the y- axis with equation

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through (- 4, 2 ) with x- coordinate - 4 , then

x = - 4 ← equation of line

Answer:

1. \(4x + 5y \leq 60\)

2. 15

3. 12

4. No, because if you put those values into the inequality you get

4 * 9 + 5 * 5 \(\leq\) 60 --> \(36 + 25 \leq 60\) --> \(61 \leq 60\) which is not true.

Step-by-step explanation:

1. if a car costs $4, the total cost of cars is 4x

if a doll costs $5, the total cost of dolls is 5y

you have at most $60 to spend, so the amount you spend has to be less than or equal to 60.

The inequality would be \(4x + 5y \leq 60\).

2. At the x-intercept y would be 0, so

4x + 5(0) = 60

4x = 60

x = 15

3. At the y-intercept, x would be 0, so

4(0) + 5y = 60

5y = 60

y = 12

4. Already explained in the answer

a) The median would be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean.

b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers.

a) The median is expected to be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean. The mean is calculated by adding all the values together and dividing by the number of values, and if there are any values that are much lower or higher than the rest, this will affect the mean significantly. The median, however, is the midpoint of the values, so outliers have less of an influence on it.

b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers. The median is the midpoint of the values, which means that if there are any values that are much lower or higher than the rest, it will not affect the median as much as it does the mean. This makes the median more accurate in representing the life expectancy of countries, as it is not skewed by outliers. Furthermore, the median is generally more reliable when dealing with skewed distributions, which is often the case with life expectancy data.

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Answer:

4/7 has least common denominator

= 0.5( approx.)

Answer:

21 is the answers for the question

Step-by-step explanation:

please mark me as brainlest

There are 32,606,080 ways to receive 2 pairs and 2 singletons from a standard deck of 52 cards.

To calculate the number of ways to receive 2 pairs and 2 singletons from a standard deck of 52 cards, we can break it down into steps:

Step 1: Choose the two ranks for the pairs.

There are 13 ranks in a deck of cards, and we need to choose 2 of them for the pairs. This can be done in C(13, 2) = 13! / (2! * (13-2)!) = 78 ways.

Step 2: Choose the suits for each pair.

Each pair can have any of the 4 suits, so there are 4 choices for the first pair and 4 choices for the second pair. This gives us 4 * 4 = 16 ways.

Step 3: Choose the ranks for the singletons.

We have already chosen 2 ranks for the pairs, so we have 11 ranks left to choose from for the singletons. This can be done in C(11, 2) = 11! / (2! * (11-2)!) = 55 ways.

Step 4: Choose the suits for the singletons.

Each singleton can have any of the 4 suits, so there are 4 choices for the first singleton and 4 choices for the second singleton. This gives us 4 * 4 = 16 ways.

Step 5: Choose the positions for the cards.

Out of the 6 cards dealt, the two pairs can be placed in any 2 out of the 6 positions, and the singletons can be placed in any 2 out of the remaining 4 positions. This can be calculated as C(6, 2) * C(4, 2) = 6! / (2! * (6-2)!) * 4! / (2! * (4-2)!) = 15 * 6 = 90 ways.

Step 6: Multiply the results.

Finally, we multiply the results from each step to get the total number of ways:

78 * 16 * 55 * 16 * 90 = 32,606,080.

Therefore, there are 32,606,080 ways to receive 2 pairs and 2 singletons from a standard deck of 52 cards.

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Research has shown that competent communicators achieve effectiveness by adjusting their behaviors to the person and situation (option e).

Effective communication involves being adaptable and responsive to the specific context, individual preferences, and the needs of the situation.

Competent communicators recognize that different people have different communication styles, preferences, and expectations. They understand the importance of tailoring their communication approach to effectively connect and engage with others.

This may involve using appropriate language, tone, non-verbal cues, and listening actively to understand the needs and perspectives of others.

By adapting their behaviors, competent communicators can build rapport, foster understanding, and promote effective communication exchanges. They are mindful of the social and cultural dynamics at play, and they strive to communicate in a way that is respectful, inclusive, and conducive to achieving mutual goals.

In summary, competent communicators understand that effective communication is not a one-size-fits-all approach. They adjust their behaviors to the person and situation, demonstrating flexibility and adaptability in order to enhance communication effectiveness.

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Competent communicators achieve effectiveness mostly by adjusting their behaviors to suit the person they are communicating with and the situation they find themselves in. While other factors, like having a broad vocabulary or giving feedback, play a part in effective communication, the former is considered the most crucial.

Research suggests that competent communicators achieve effectiveness mostly through adjusting their behaviors depending on the person they are communicating with and the situation they are in. This is option e. of your question. Communicating effectively involves behaviors like active listening, understanding the other person's point of view, being able to express thoughts and ideas clearly, and being polite and respectful. While a broad vocabulary (option b.) can be useful, it is not as crucial as adapting your behavior to fit the situation. Moreover, giving feedback (option d.) is a part of effective communication but not the sole defining factor. Apologizing when offending others (option c.) is also important but it doesn't necessarily make one a competent communicator. Using the same type of behavior in various situations (option a.) might not always work, as different situations and individuals require different communication styles.

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The radius of the semicircle is 4.3 kilometers.

A straight line that runs through the sideways of a body or figure, particularly a circle or sphere, is called as a diameter of a circle or sphere.

Given:

The diameter of a semicircle is 8.6 kilometers.

Then the radius of the semicircle,

= diameter / 2

= 8.6 / 2

= 4.3 kilometers.

Therefore, the radius is 4.3 kilometers.

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Answer:

D

Step-by-step explanation:

Here, we want to select the correct choice of answer

Looking at the two dot plots, we can see that for the class A, we have the clustering from 4-6 and from 10-12

With this, we can see that this clustering is essentially around two areas only

The beginning parts and the mid parts are left empty only for the two parts to be populated by data points

As given by the question

There are given that the function

Now,

for find, the value of f(-2), put x=-2 into the given function

So,

Hence, the value of f(-2) is 1.

The numeric value of the function C(68) at f = 68 is given as follows:

C(68) = 20.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

C(f) = 5/9 x (f - 32).

The input at which we want to find the numeric value for the function is then given as follows:

f = 68.

Which means that the lone instance of f in the definition of the function is replaced by 68, and then the numeric value is calculated as follows:

C(68) = 5/9 x (68 - 32) = 5/9 x 36 = 5 x 4 = 20.

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Answer:

36kg

Step-by-step explanation:

The dog eats 16kg per week, which is 32kg in 2 weeks

The cat eats 2kg per week, which is 4kg in 2 weeks

32+4=36

I beive your doing "Order of Operations"

Heres some information.

Order of operations tells you to perform multiplication and division first, working from left to right, before doing addition and subtraction. Continue to preform multiplication and division from left to right. Next, add and subtract from left to right.

(!) Leave a comment to let me know if you need more information or any help (!)

In a study examining the effect of ignoring text messages on distraction, the variable "trying to ignore text messages" would be the independent variable, whereas the variable "amount of distraction" would be the dependent variable.

The independent variable is the one that is manipulated or controlled by the researcher. In this case, the researchers are interested in studying the effect of attempting to ignore text messages, so they would manipulate the participants' behavior in relation to text messages (e.g., asking them to ignore the messages or not).

The dependent variable, on the other hand, is the variable that is measured or observed to determine the effect of the independent variable. Here, the researchers would measure the amount of distraction experienced by the participants as a result of trying to ignore the text messages.

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