what will be the area of the shaded portion below (please help)

By writing and evaluating an exponential equation, we can see that the value of the car now is $9,216.

We know that the initial value of the car is $18.000, and the value depreciates at a rate of 20% per year.

If we define x as the number of years since the car was bought, we can write the value equation as:

V(x) = $18,000*(1 - 20%/100%)^x

V(x) = $18,000*(1 - 0.2)^x

V(x) = $18,000*(0.8)^x

The value of the car after 3 years is what we get if we evaluate the exponential equation in x = 3.

V(3) = $18,000*(0.8)^3

V(3) = $9,216

That is the value of the car now.

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To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

Answer:

Step-by-step explanation:

The Pythagorean Theorem states that

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

or that the two legs added together squared equal the hypotenuse squared

not: this only works with right triangles

Now Pythagorean triples are the set of sides that follow that rule

an example would be 3,4,5

why is it a Pythagorean triple?

well because it follows

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

\(3^2=9\\4^2=16\\16+9=25\\5^2=25\)

25=25

Answer: None of these answers are correct.

Step-by-step explanation:

The triangles are congruent, meaning that by CPCTC, \(\angle BAC \cong \angle DE F\).

This means that as angles in a triangle add to 180 degrees,

\(60+45+x=180\\75+x=180\\x=105\)

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:

0.08(50h)

Step-by-step explanation:

\(0.08 (50h) +50h \\ = \frac{8}{100} (50h) + 50h \\ = 8\%(50h) + 50h \\ \)

Since, it took 50h to repair the computer so, 0.08(50h) represents the amount of tax Deborah has to pay. Which is 8% of 50h.

The expression of the total cost after tax, 0.08(50h) + 50h, has a tax part and a cost part.

The tax part is 0.08(50h).

The cost part is 50h.

Tax is the amount paid by the consumer to the government for the use of goods and services produced in/by the country.

It is charged over the total cost for the particular good or service, at a pre-determined rate called the rate of tax.

In the question, we are informed that the total cost after tax to repair Deborah's computer is represented by 0.08 (50h) +50h, where h represents the number of hours it takes to repair Deborah's computer.

We are asked what part of the expression represents the amount of tax Deborah has to pay.

We know that the total cost = Tax + Fixed Cost,

where tax = tax rate * fixed cost.

Therefore, we write the total cost function like this:

Total cost = Tax Rate(Fixed cost) + Fixed Cost.

Comparing the given expression of the total cost, 0.08(50h) + 50h, with this expression, we can say that 0.08(50h) represents the tax part, where 0.08 is the tax rate and 50h is the fixed cost.

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Answer:

let the number of adult tickets = x

Then the number of student tickets = 3x

Total tickets x+3x = 416

4x = 416

x = 416/4

x = 104

Therefore the number of adult tickets sold is 104

Step-by-step explanation:

The triangles are similar by SSS congruence of triangles.

What is SSS congruence of triangles?

The two triangles are congruent if the three sides of one triangle are the same as the corresponding three sides (SSS) of the other triangle.

We are given two triangle ABC and PQR.

In order to see whether these are similar or not, we will use the SSS congruence of triangles.

The ratio of sides are:

⇒AB : PQ = 8 : 6

⇒AB : PQ = 4 : 3

Similarly,

⇒BC : QR = 12 : 9

⇒BC : QR = 4 : 3

Similarly,

⇒AC : PR = 12 : 9

⇒AC : PR = 4 : 3

Since, the ratio of all the sides is same so, the triangles are similar.

Hence, the triangles are similar by SSS congruence of triangles.

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Since, there are multiple questions so, the question answered above is attached below

Answer:

23 + b ≤ -276

Step-by-step explanation:

In this exercise, you're required to write an algebraic expression for the word problem. Thus, you'll write out a mathematical equation using the given values and unknown variable.

Translating the word problem into an algebraic expression, we have;

23 + b ≤ -276

Simplifying further, we have;

b ≤ -276 - 23

b ≤ -299

A probability value equal to or smaller than 0.05 would indicate that Gaurav's null hypothesis should be rejected at the 5% significance level.

In hypothesis testing, the significance level, denoted as alpha (α), is the predetermined threshold used to determine whether to reject the null hypothesis.

Gaurav has specified a 5% significance level, which means he wants to control the probability of making a Type I error (rejecting the null hypothesis when it is true) at 5% or less.

If Gaurav were to conduct a test and calculate the p-value, he would compare it to the significance level of 0.05.

The p-value is the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true.

If the p-value is less than or equal to the significance level (p ≤ α), it indicates that the observed difference is unlikely to occur by chance alone under the assumption of the null hypothesis.

Gaurav would reject the null hypothesis and conclude that there is a significant difference between the average amount of medication his patients are taking and the national average.

Conversely, if the p-value is greater than the significance level (p > α), it suggests that the observed difference could reasonably occur by chance, and Gaurav would fail to reject the null hypothesis.

This would imply that there is no significant difference between the average medication amounts of Gaurav's patients and the national average.

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The correct matching of the fractions

0.1 - 1/10

0.01 - 1/100

100% - 1

A fraction is a way of representing a part of a whole or a quantity that is less than one. Fractions consist of two numbers separated by a horizontal or diagonal line, with the number above the line being called the numerator and the number below the line being called the denominator.

The numerator represents how many parts of the whole are being considered, while the denominator represents the total number of equal parts that the whole is divided into.

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Answer:

12 cells every hour.

Step-by-step explanation:

You would do 2 x 6

(the 2 is the cells per hour, and the 6 is the amount of hours)

Kamryn would save $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

To determine the amount of interest Kamryn will save by raising her credit score from 665 to 680, we need to compare the interest rates associated with each credit score range.

According to the given information, a credit score of 665 falls within the range of 580-669, where the corresponding simple interest rate is 10.358%.

Let's calculate the interest Kamryn would pay on a loan of $13,250.00 at an interest rate of 10.358%.

Interest = Principal * Rate

= $13,250.00 * 0.10358

≈ $1,370.56

Therefore, if Kamryn were to borrow $13,250.00 with a credit score of 665, she would pay approximately $1,370.56 in interest.

Now, let's consider the scenario where Kamryn raises her credit score to 680. A credit score of 680 falls within the range of 670-739, where the corresponding simple interest rate is 9.132%.

Calculating the interest with a credit score of 680:

Interest = Principal * Rate

= $13,250.00 * 0.09132

≈ $1,210.57

Thus, if Kamryn were able to raise her credit score from 665 to 680, she would save approximately $1,370.56 - $1,210.57 = $159.99 in interest.

Therefore, Kamryn would save approximately $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

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Answer:

Parabola

Step-by-step explanation:

A conic section is a curve obtained by the intersection of a plane with the surface of a (double-napped) cone, When the plane is parallel to the edge of one cone.

Thus, The intersection is a parabola.

Answer: degenerate hyperbola

Step-by-step explanation:

degenerate hyperbola because its the thickest of the plane so it can be formed.

The length of the field is greater than the width by the expression \((14x - 3x^2 + 2y) - (5x - 7x^2 + 7y).\)

1. The length of the field is represented by the expression \(14x - 3x^2 + 2y.\)

2. The width of the field is represented by the expression \(5x - 7x^2 + 7y\).

3. To find the difference between the length and width, we subtract the width from the length: (\(14x - 3x^2 + 2y) - (5x - 7x^2 + 7y\)).

4. Simplifying the expression, we remove the parentheses: \(14x - 3x^2 + 2y - 5x + 7x^2 - 7y.\)

5. Combining like terms, we group the \(x^2\) terms together and the x terms together: \(-3x^2 + 7x^2 + 14x - 5x + 2y - 7y.\)

6. Simplifying further, we add the coefficients of like terms:\((7x^2 - 3x^2) + (14x - 5x) + (2y - 7y).\)

7. The simplified expression becomes: \(4x^2 + 9x - 5y.\)

8. Therefore, the length of the field is greater than the width by the expression \(4x^2 + 9x - 5y.\)

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Answer: x = 4

Step-by-step explanation:

Translating the problem into mathematical terms:

Let's call the number x. Then the problem can be written as:

5 * (2x - 3) - (x + 8) = 13

Expanding the left side of the equation:

5 * 2x - 5 * 3 - x - 8 = 13

Simplifying the left side of the equation:

10x - 23 - x - 8 = 13

Combining like terms:

9x - 31 = 13

Adding 31 to both sides of the equation:

9x = 44

Dividing both sides of the equation by 9:

x = 4.88888...

Since x has to be a whole number, we round down to the nearest whole number:

x = 4

Therefore, the number that satisfies the equation is 4.

1)   14 times to complete a 5-mile walk.  2) 8 tablespoons of sugar  Since 2 tablespoons make up 1 ounce and 8 ounces make up 1 cup  3) Since her weight is less than the bridge's weight limit of 10 tons, it is safe for Erin  4) One gallon is equal to 3.785 liters, so 5 gallons is equal to:18.925 liters fluid

what is  weight limit ?

A weight limit is the maximum weight that is allowed for a particular object, structure, vehicle, or mode of transportation, beyond which it may not be safe or legal to operate.

what is  fluid?

In general, fluid is any substance that can flow and take the shape of its container. Fluids can be gases or liquids, and they are distinguished from solids by their ability to flow and lack of resistance to shear stress.

In the given question,

1)  To determine how many times Bill needs to walk around the park to complete a 5-mile walk, we need to first find the total distance around the park. Since the park is a square with sides of 500 feet, the total distance around the park is:

4 x 500 feet = 2000 feet

2000 feet / 5280 feet/mile = 0.3788 miles

To complete a 5-mile walk, Bill would need to walk:

5 miles / 0.3788 miles per park loop = 13.199 park loops

Rounding up to the nearest whole number, Bill would need to walk around the park approximately 14 times to complete a 5-mile walk.

2)      Since 2 tablespoons make up 1 ounce and 8 ounces make up 1 cup, we can convert tablespoons to cups as follows:

2 tablespoons/1 ounce x 1 cup/8 ounces = 0.25 cups/tablespoon

Therefore, Jamie would need:

2 cups / 0.25 cups/tablespoon = 8 tablespoons of sugar

3)   To determine if it is safe for Erin to cross the bridge in the moving truck, we need to calculate the total weight of the truck and her belongings. Since 1 ton is equal to 2000 pounds, the weight of the moving truck and her belongings in tons is:

(12600 pounds + 6000 pounds) / 2000 pounds/ton = 9.3 tons

Since this weight is less than the bridge's weight limit of 10 tons, it is safe for Erin to cross the bridge in the moving truck.

4)  One gallon is equal to 3.785 liters, so 5 gallons is equal to:

 gallons x 3.785 liters/gallon = 18.925 liters

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The null and alternative hypotheses can be stated as follows:

c. H0: µ = 12, Ha: µ ≠ 12

The null hypothesis (H0) assumes that the population mean content of the bottles is 12 ounces, indicating perfect adjustment of the filling machine. The alternative hypothesis (Ha) states that the population mean content is not equal to 12 ounces, suggesting that the machine is not in perfect adjustment.

The rejection region for α = 0.01 can be specified as:

c. |t| > 2.68

This means that we would reject the null hypothesis if the absolute value of the calculated t-statistic is greater than 2.68.

To calculate the p-value, we need the t-statistic corresponding to the sample mean and standard deviation. With a sample mean of 11.88 ounces, a standard deviation of 0.35 ounces, and a sample size of 49, we can calculate the t-statistic. The p-value represents the probability of observing a sample mean as extreme as the one obtained, assuming the null hypothesis is true.

The p-value cannot be determined without the t-statistic value or the corresponding degrees of freedom.

Without the p-value, we cannot draw a definitive conclusion. To make a conclusion, we would compare the calculated t-statistic to the critical t-value based on the chosen significance level (α = 0.01). If the calculated t-statistic falls within the rejection region (|t| > 2.68), we would reject the null hypothesis. If the calculated t-statistic falls outside the rejection region, we would fail to reject the null hypothesis.

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Answer:

3x-4y-9

Step-by-step explanation:

Combine like terms

The amount that would be in the account when Alana is 21  is $2890

We have to know the formula for simple interest.

This is expressed as;

S.I = PRT/100

Given that the parameters of the formula are enumerated as;

From the information given, substitute the values, we have;

SI = 1000 × 9 × 21/100

Multiply the values,

Then, divide by the denominator, we have;

SI = $1890

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Answer:

B is the answer

Step-by-step explanation:

(10×2 +1/2)÷(2×4+1/4)

(21/2)÷(9/4)

Then calculate it and the answer is B

Answer:

its c

Step-by-step explanation:

The domain and range of the given piecewise function are (-∞, ∞) and [-10, ∞) respectively.

Given a function shown in the graph.

We have to find the domain and the range of the function.

Domain is the set of all x values for which the  function is defined.

Range is the set of all the y values for the x values in the domain.

Here the function is quadratic.

The function is defined for all the real numbers.

Domain is thus (-∞, ∞).

y values ranges down from ∞ to -10 and then again goes up to ∞.

So range = [-10, ∞)

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O The line increases from the left to right

O The line crosses the x-axis at 2.5

O The line does not enter quadrant II at all...

...Are your answers

Answer:

A, B, E

Step-by-step explanation:

Answer:

The between the given vector and the positive direction of the x-axis is approximately 41.186º.

Step-by-step explanation:

Let be \(\vec u = 8\,i + 7\,j\) and \(\vec v = i\) (Positive direction of the x-axis), the angle between both vectors can be determined from definition of dot product:

\(\vec u \bullet \vec v = \|\vec u\|\cdot \|\vec v\| \cdot \cos \theta\)

Angle is cleared:

\(\cos \theta = \frac{\vec u\bullet \vec v}{\|\vec u\|\cdot \|\vec v\|}\)

\(\theta = \cos^{-1}\left(\frac{\vec u \bullet \vec v}{\|\vec u\|\cdot \|\vec v\|} \right)\)

The norms of \(\vec u\) and \(\vec v\) are found by Pythagorean Theorem:

\(\|\vec u\| = \sqrt{8^{2}+7^{2}}\)

\(\|\vec u\| \approx \sqrt{113}\)

\(\|\vec v\| = 1\)

The dot product between both vectors is:

\(\vec u \bullet \vec v = (8)\cdot (1) + (6)\cdot (0)\)

\(\vec u \bullet \vec v = 8\)

The angle is now calculated:

\(\theta = \cos^{-1}\left(\frac{8}{\sqrt{113}} \right)\)

\(\theta \approx 41.186^{\circ}\)

The between the given vector and the positive direction of the x-axis is approximately 41.186º.

Answer:

2/16 = 1/8

1/8

Step-by-step explanation:

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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The expression given is,

Therefore,

Hence, the answer is

Answer:

∠ = 66.9°

Step-by-step explanation:

Sin ∠ = opposite/hypotenuse

Sin ∠x = 13.8/15

In the graphing calculator use

\(sin^{-1}(13.8/15) = 66.9\)

The angle to the nearest tenth is 66.9 degrees.

In order to determine the angle, the SOCAHTOA notation would be  used. The ladder would form a right-angled triangle. we have the value of the opposite and the hypotenuse. So, sine would be used to determine the value of the angle.

Sine = opposite / hypotenuse

\(sine^{-1}\) = 13.8 / 15

= 66.9 degrees

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