The bike cost $120. The sales-tax rate was 8%. What is
the total cost of the bike including sales tax?

Answer:

A. Amplitude: 1; midline: y = 1

Answer:

A. Amplitude: 1; midline: y = 1

Step-by-step explanation:

i took the test

Answer:

2x = 70

Step-by-step explanation:

4x - 2x = 70

2x = 70

x = 70/2

x = 35

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The parametric equations of the line passing through the points (8, 2, 7) and (1, 6, 3) are:

x = 8 - 7t

y = 2 + 4t

z = 7 - 4t

To find a parametric equation of the line through the points (8, 2, 7) and (1, 6, 3), we can use the vector equation of a line.

Let's denote the line as (x, y, z). We can find the direction ratio of the line by subtracting the coordinates of the two points:

Direction ratio = (1, 6, 3) - (8, 2, 7) = (-7, 4, -4)

Now, we can write the parametric equations of the line using the coordinates of one of the points and the direction ratio:

x = 8 - 7t

y = 2 + 4t

z = 7 - 4t

where t is a parameter that can take any real value.

Thus, the parametric equations of the line passing through the points (8, 2, 7) and (1, 6, 3) are:

x = 8 - 7t

y = 2 + 4t

z = 7 - 4t

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Real profits for this company are increasing at a rate of about 3.2%, on average. Therefore, (c)"An increase by 3.2%" is the right response.

To calculate the approximate rate of change in real profits, we need to compare the change in nominal profits with the change in purchasing power due to inflation and exchange rate fluctuations.

First, let's calculate the nominal profits for the base year:

\(\text{Nominal Profits} = \text{Revenue} - \text{Cost of Goods Sold} = 1,000 \text{ euros} - \$800 = 1,000 \text{ euros} - \frac{1,000 \text{ euros}}{\$1.20} = 1,000 \text{ euros} - 833.33 \text{ euros} = 166.67 \text{ euros}.\)

Next, let's calculate the nominal profits for the current year:

Revenue increased at the German inflation rate of 2%:

New Revenue = 1,000 euros + 1,000 euros * 2% = 1,000 euros + 20 euros = 1,020 euros.

Cost of Goods Sold increased at the US inflation rate of 4%:

New Cost of Goods Sold = $800 + $800 * 4% = $800 + $32 = $832.

Converting the new revenue and cost of goods sold to euros using the current exchange rate:

New Revenue in euros = 1,020 euros.

\(\text{New Cost of Goods Sold in euros} = \frac{832 \text{ euros}}{\$1.22} = 681.97 \text{ euros}.\)

Now, let's calculate the new nominal profits:

New Nominal Profits = New Revenue - New Cost of Goods Sold = 1,020 euros - 681.97 euros = 338.03 euros.

The change in nominal profits is:

Change in Nominal Profits = New Nominal Profits - Nominal Profits = 338.03 euros - 166.67 euros = 171.36 euros.

To calculate the approximate rate of change in real profits, we compare the change in nominal profits with the base year nominal profits:

\(\text{Rate of Change in Real Profits} = \left(\frac{{\text{Change in Nominal Profits}}}{{\text{Nominal Profits}}}\right) \times 100\)

\(\text{Rate of Change in Real Profits} = \left(\frac{{171.36 \text{ euros}}}{{166.67 \text{ euros}}}\right) \times 100\)

≈ 102.8%.

Therefore, the approximate rate of change in real profits for this firm is an increase by approximately 3.2%. Therefore, the correct answer is "An increase by 3.2%".

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The number of llamas in the petting zoo has 13, and the number of kangaroos is 34.

Let the number of llamas in the petting zoo be x, and the number of kangaroos in the petting zoo be y.

Thus, we can write two equations from the given conditions:

Equation 1: x + y = 47

Equation 2: 4x + 2y = 120

(since each llama has 4 legs and each kangaroo has 2 legs)

Simplifying equation 2:2x + y = 60

Now we have two equations with two unknowns.

To solve them, we can either use substitution or elimination.

Using substitution, we can solve equation 1 for y in terms of x:y = 47 - x

Now we substitute this expression for y in equation 2:2x + (47 - x) = 60

Simplifying: x + 47 = 60x = 13

Now we can use either equation 1 or 2 to find y:x + y = 47y = 47 - xy = 47 - 13y = 34

Therefore, the petting zoo has 13 llamas and 34 kangaroos.

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Answer:

the answer is

x +5x – 14 = (x− 2 )(x + 7)

Answer:

B) 14, 18, 5

Step-by-step explanation:

This is correct

I think the options were omitted, so  i will go ahead and solve. From my answer, you can choose the right option

Answer:Equation to solve the question

=Distance = Speed x time

=d= 0.6 x 30

Distance , d= 18 miles

Step-by-step explanation:

Step 1

Speed = distance / time

Therefore  Distance = Speed x time

Given that speed = 0.6 miles per minute  and

Time=30 minutes

Step 2

Distance ,d= 0.6 miles per minute x 30minutes

d= 0.6 x 30

= 18miles

Answer:

#18=440

Step-by-step explanation:

20x22=440

The rate of increasing the area of the rectangle is 72cm²/s

We have, The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of 4 cm/s. When the length is 13 cm and the width is 4 cm, we have to find how fast is the area of the rectangle increasing.

The area of a rectangle is given by, A = l × w

Where l is the length and w is the width.

Now we will differentiate the equation with respect to time t.

dA/dt = d/dt (l × w)

dA/dt = l(dw/dt) + w(dl/dt)

We can use this formula to calculate how fast the area of the rectangle increases when the length is 13 cm and the width is 4 cm.

Substituting the given values, l = 13 cm and dl/dt = 5 cm/s w = 4 cm and dw/dt = 4 cm/s

dA/dt = 13(4) + 4(5)

dA/dt = 72 cm²/s

Therefore, the area of the rectangle increasing at a rate of 72 cm²/s.

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The yy-component of vector a a is -y-direction, which is equal to 0 m/s2.the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.

Given a vector, a⃗ a→ = (5.0 m/s2, −y−direction)Find the yy -component of the given vector a⃗ a→.Solution: The yy-component of the given vector a⃗ a→ = -y-directionTo find the yy-component of the given vector a⃗ a→, we have to take the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.Therefore, the yy-component of vector a⃗ a→ is :a_yy = -y-direction = (-1)(0) = 0 m/s²  Answer: 0 m/s².

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The yy-component of vector a⃗ a→ is -y-direction.

The yy-component of a vector represents the magnitude of the vector in the y-direction.

In this case, the vector a⃗ a→ is given as (5.0 m/s2, −y-direction).

Since the yy-component is the magnitude in the y-direction, the yy-component of the vector a⃗ a→ is -y-direction.

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When p=4 and t=24 then substituting these values into the equation 6p + 3q = t we get q=0.

To find the value of q in the equation 6p + 3q = t when p = 4 and t = 24, you can substitute the given values into the equation and solve for q. First, replace p with 4 and t with 24

6(4) + 3q = 24

Simplify the left side of the equation

24 + 3q = 24

Subtract 24 from both sides

3q = 0

Divide both sides by 3

q = 0

Therefore, when p = 4 and t = 24, q is equal to 0.

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Answer:

The given relation is presented as follows;

\(\dfrac{1}{a} + \dfrac{1}{b} +\dfrac{1}{c} = \dfrac{1}{a + b + c}\)

Where 'a', 'b', and 'c' are member of real numbers, we have;

a⁹, b⁹, and c⁹ are also member of real numbers

When a⁹ = x, b⁹ = y, and c⁹ = z

By the above relationship, we have;

\(\dfrac{1}{x} + \dfrac{1}{y} +\dfrac{1}{z} = \dfrac{1}{x + y + z}\)

Substituting x = a⁹, y = b⁹, and z = c⁹, we get;

\(\dfrac{1}{a^9} + \dfrac{1}{b^9} +\dfrac{1}{c^9} = \dfrac{1}{a^9 + b^9 + c^9}\)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The positive integers are numbers that start at 1 and go on towards the right: are natural numbers 1,2,3,4,5,6,7,...

The parabola with vertex at (0,0) and directrix at x=-4, will open towards the right.

A parabola is a collection of points on a plane that are all at the same distance from a particular point and line. The point is called the focus of the parabola while the line is called the directrix. The directrix is perpendicular to a parabola's axis of symmetry and does not contact it.

As we know that the directrix is perpendicular to the axis of the parabola, now since the directrix is at x=-4, the parabola will be horizontal and will be opening either towards the left or the right.

As it is given that the vertex of the parabola is at (0,0) and we know that the parabola can not touch the directrix, therefore, the parabola's vertex will be at (0,0) and will open towards the right side. As shown below.

Hence, the parabola with vertex at (0,0) and directrix at x=-4, will open towards the right.

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Answer:

right

Step-by-step explanation:

The number of different collections of 60 coins that can be chosen is:

(60+4-1) choose (4-1) = 63 choose 3 = 22,275

If there are at least 60 of each kind of coin, we can assume that we have four different types of coins, such as quarters, dimes, nickels, and pennies. Let's assume we have x quarters, y dimes, z nickels, and w pennies.

We know that we need to choose a total of 60 coins. Therefore, we have the following equation:

x + y + z + w = 60

We want to find the number of different collections of coins that can be chosen. This is equivalent to finding the number of non-negative integer solutions to the equation above.

Using the stars and bars formula, the number of non-negative integer solutions to this equation is:

(n+k-1) choose (k-1)

where n is the total number of objects (60 in this case) and k is the number of groups we want to divide them into (4 in this case).

So, the number of different collections of 60 coins that can be chosen is:

(60+4-1) choose (4-1) = 63 choose 3 = 22,275

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Given :

Insurance cost , $693.00 .

Gas cost , $452.00 .

Average charge per fare , $7.00 .

Tuition fee , $3280.00 .

To Find :

The fare he have to get to pay his fee .

Solution :

Let , number of fair required is n .

Therefore , total profit is :

\(Profit = earning - expenditure \\Profit = 7n - 693-452\\Profit = 7n-1145\)

Now , to pay his fee this profit must be equal to his fee because he don't have other expenditure .

So ,

\(7n-1145=3280\\\\7n=4425\\\\n=\dfrac{4425}{7}\\\\n=632.1\)

But number of rides cannot be in decimal so minimum rides he must get is

632+1 = 633 .

Hence, this is the required solution .

A 75 Watt fan used for 8 hours daily for one month consumes 18 kilowatt-hours (kWh) of energy.

To calculate the energy consumed by a 75 Watt fan used for 8 hours daily for one month (30 days), we can use the formula:

Energy consumed = Power (Watts) * Time (hours)

First, we need to convert the power from Watts to kilowatts (kW) by dividing it by 1000:

Power (kW) = Power (Watts) / 1000

Then, we can calculate the energy consumed per day:

Energy consumed per day (kWh) = Power (kW) * Time (hours)

Next, we calculate the energy consumed for the entire month:

Energy consumed for the month (kWh) = Energy consumed per day (kWh) * Number of days

Given:

Power = 75 Watts

Time = 8 hours

Number of days = 30 days

Step 1: Convert power to kilowatts

Power (kW) = 75 Watts / 1000 = 0.075 kW

Step 2: Calculate energy consumed per day

Energy consumed per day (kWh) = 0.075 kW * 8 hours = 0.6 kWh

Step 3: Calculate energy consumed for the month

Energy consumed for the month (kWh) = 0.6 kWh * 30 days = 18 kWh

Therefore, the energy consumed in electrical units when a 75 Watt fan is used for 8 hours daily for one month is 18 kilowatt-hours (kW)

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K-fold cross-validation generally produces an estimate with lower bias compared to leave-one-out cross-validation.(option b).

Cross-validation is a popular technique used in machine learning to estimate the performance of a model on unseen data. There are different methods of cross-validation, including leave-one-out and K-fold. In leave-one-out, only one data point is left out for testing, while in K-fold, a Kth portion of the data is held out.

Now, to answer the question of which method generally produces an estimate with higher bias, we need to look at the formula for bias in cross-validation. The bias is given by the difference between the expected value of the cross-validation estimate and the true performance of the model.

For K-fold cross-validation, the expected value of the estimate is computed as the average of the estimates obtained in each of the K folds. This means that the bias is dependent on the number of folds used. The more folds used, the lower the bias is likely to be.

Hence the correct option is (b).

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Answer:

can you give the question

Step-by-step explanation:

Answer:

4.5

Step-by-step explanation

$2.79 divided by the .62 per pound is equal to 4.5 pounds of cucumbers.

Check: 4.5 times .62 is equal to $2.79

This should be the answer :)

Answer:

1³ = 1

2³ = 8

3³ = 27

4³ = 64

5³ = 125

6³ = 216

Step-by-step explanation:

Answer:

The cube of first six natural numbers are

1, 8, 27, 65, 125, 216

Step-by-step explanation:

Natural Numbers are known as 1, 2, 3, 4, ..., ∞

Now,

For Cube of first six natural numbers

1³ = 1

2³ = 8

3³ = 27

4³ = 64

5³ = 125

6³ = 216

Thus, The cube of first six natural numbers are

1, 8, 27, 65, 125, 216

-TheUnknownScientist

Leonora made 12 number of 2-point baskets, solved using the system of equations

In the question, we are given that Leonora made 14 total baskets during her basketball game, in which she made x baskets worth 2 points each and y baskets worth 3 points each.

We are asked that if she scored 30 points total throughout the game, how many 2-points basket did she make.

Number of 2-points basket scored = x.

Number of 3-points basket scored = y.

Thus, total number of baskets scored = x + y.

But, the total number of baskets scored is given to be 14.

Thus, we get an equation x + y = 14 ... (i).

The total worth of 2-points basket scored = 2x.

The total worth of 3-points basket scored = 3y.

Thus, the total points scored = 2x + 3y.

But, the total points scored is given to be 30.

Thus, we get an equation 2x + 3y = 30 ... (ii).

(i) and (ii) together gives us a system of equation.

To solve the system of equations, we multiply (i) by 3, and then subtract (ii) from it.

3x + 3y = 42

2x + 3y = 30.

(-) (-)     (-)

__________

x = 12.

Thus, Leonora made 12 number of 2-point baskets, solved using the system of equations.

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Answer:

The 3rd one - I don't seem too sure with the answer, you know the 1st question's 2nd part, right?

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

# ꧁❣ RainbowSalt2²2² ࿐

The validity of short forms may be reduced because they contain fewer items compared to the full-length version. Short forms of tests or questionnaires are often used in research and clinical settings due to their convenience and efficiency.

This means that the short form may not fully capture the construct being measured and may not accurately reflect the individual's true scores. Additionally, the items selected for the short form may not be representative of the full range of the construct, leading to bias and limited generalizability.

Therefore, researchers and clinicians should consider the trade-offs between convenience and validity when deciding to use short forms.

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Answer :

13%

Step-by-step explanation:

Compound interest which is compounded annually calculated using the formula :

A = I( 1 + r/100)^t

Where I = invested amount

r = interest rate ; t = period ; A = final amount

If period = 9years, the rate required to triple the investment equals;

The final amount = 3 * invested amount = 3I

We now have ;

3I = I( 1 + r/100)^9

Divide both sides by I

3 = (1 + r/100)^9

Take the 9th root of both sides

3^(1/9) = (1 + r/100)^(9*1/9)

3^(1/9) = 1 + r/100

r/100 = 3^(1/9) - 1

r/100 = 1.1298309 - 1

r / 100 = 0.1298309

Multiply both sides by 100

r = 12.98309

r = 12.98 = 13%

The ordered pairs which make the open sentence true are:

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an algebraic expression based on any of the following arguments:

For this exercise, you should evaluate each of the given expressions to determine which inequalities is true when the ordered pairs are substituted. This ultimately implies that, you would have to substitute the ordered pairs into each of the given algebraic expressions and then evaluate.

When ordered pairs = (3, 6), we have:

3x + y < 14

3(3) + 6 < 14

9 + 6 < 14

15 < 14 (False).

When ordered pairs = (7, -7), we have:

3x + y < 14

3(7) + (-7) < 14

21 - 7 < 14

14 < 14 (False).

When ordered pairs = (6, 0), we have:

3x + y < 14

3(6) + 0 < 14

18 - 0 < 14

18 < 14 (False).

When ordered pairs = (-1, 6), we have:

3x + y < 14

3(-1) + 6 < 14

-3 + 6 < 14

3 < 14 (True).

When ordered pairs = (4, -1), we have:

3x + y < 14

3(4) + (-1) < 14

12 - 1 < 14

11 < 14 (True).

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The given vertices are A(1,4), B(3,-2), and C(4,2).

The reflection over the x-axis is expressed as

This means we have to multiple each y-coordinate with -1. Let's do it!

Answer:

its -2

Step-by-step explanation:

The value of k in equation k/4 + 3 = 14 is 44 and in the other equation 4k + 3 = 14 it will be 11/4.

A linear equation is an equation in which the highest power of the variable is always 1. The standard form of a linear equation in one variable is of the form Ax + B = 0.

We have given equation as

k/4 + 3 = 14

subtract by 3 both sides

k/4 + 3 -3 = 14 -3

k/4 = 11

On cross-multiplication, the equation becomes

k = 11(4)

k = 44

similarly,

4k + 3 = 14

subtract by 3 both sides

4k +3 - 3 = 14 - 3

4k = 11

On cross-multiplication, the equation becomes

k = 11/4

Thus, the value of k in both the equation is 44 and 11/4.

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The sampling distribution of the sample mean will always have the same the mean of the original non-normal distribution, as the original distribution.

What is distribution?

Each of these samples contains a mean, and if we add up all of the means, we can construct a probability distribution that explains the distribution of the means. As long as we have sufficient samples, as will be discussed later, this distribution is always normal and is referred to as the sampling distribution of the sample mean.

Since the sample mean's sampling distribution is normal, we can naturally calculate the distribution's mean and standard deviation and utilise that information to analyse probability questions.

Here, The sample variance is equal to the population variance divided by the sample size if the population is infinite and the sampling is random, or if the population is finite but we are sampling with replacement.

So we need to use the mean of non-normal distribution.

Hence the answer will be the mean of the original non-normal distribution.

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