According to financial reports, the average household credit card debt in 2010 was $7768 and in 2012 was $7117. What is the rate of change of the credit card debt per year? If this trend were to continue, how much would you expect the average household credit card debt to be in 2016?

Answer:

200n+50x+4000=Total Salary

Step-by-step explanation:

Answer:

Bh

Step-by-step explanation:

Gg

Answer:

$1950.74

Step-by-step explanation:

step 1

x(1 + 0.06/12)^5=2000

step 2

x= 2000/(1 + 0.06/12)^5

= 1950.741337

Answer:

$946.21

Step-by-step explanation:

Answer:

x ≈ 261 ft

Step-by-step explanation:

Using the sine ratio in the right triangle

sin50° = \(\frac{opposite}{hypotenuse}\) = \(\frac{200}{x}\) ( multiply both sides by x )

x × sin50° = 200 ( divide both sides by sin50° )

x = \(\frac{200}{sin50}\) ≈ 261 ft ( to the nearest foot )

x ≈ 261 ft

that is the answer

Answer:

group b

Step-by-step explanation:

because group a got 7.5 kg of berries in total and group b got 8.25 and 8.25>7,5

The line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1, 1), and the line segment from (1,1) to (0,1) is equal to 2/5.

What is integral?

The value obtained after integrating or adding the terms of a function that is divided into an infinite number of terms is generally referred to as an integral value.

To evaluate the line integral using Green's theorem, we need to find a vector field F = (P, Q) such that ∇ × F = Qₓ - Pᵧ, where Qₓ represents the partial derivative of Q with respect to x, and Pᵧ represents the partial derivative of P with respect to y.

Let's consider F = (P, Q) = (x²y², xy).

Now, let's calculate the partial derivatives:

Qₓ = ∂Q/∂x = ∂(xy)/∂x = y

Pᵧ = ∂P/∂y = ∂(x²y²)/∂y = 2x²y

The curl of F is given by ∇ × F = Qₓ - Pᵧ = y - 2x²y = (1 - 2x²)y.

Now, let's find the line integral using Green's theorem:

∫[C] (Pdx + Qdy) = ∫∫[R] (1 - 2x²)y dA,

where [R] represents the region enclosed by the curve C.

To evaluate the line integral, we need to parameterize the curve C.

The arc of the parabola y = x² from (0, 0) to (1, 1) can be parameterized as r(t) = (t, t²) for t ∈ [0, 1].

The line segment from (1, 1) to (0, 1) can be parameterized as r(t) = (1 - t, 1) for t ∈ [0, 1].

Using these parameterizations, the region R is bounded by the curves r(t) = (t, t²) and r(t) = (1 - t, 1).

Now, let's calculate the line integral:

∫∫[R] (1 - 2x²)y dA = ∫[0,1] ∫[t²,1] (1 - 2t²)y dy dx + ∫[0,1] ∫[0,t²] (1 - 2t²)y dy dx.

Integrating with respect to y first:

∫[0,1] [(1 - 2t²)(1 - t²) - (1 - 2t²)t²] dt.

Simplifying:

∫[0,1] [1 - 3t² + 2t⁴] dt.

Integrating with respect to t:

[t - t³ + (2/5)t⁵]_[0,1] = 1 - 1 + (2/5) = 2/5.

Therefore, the line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1,1), and the line segment from (1,1) to (0,1) is equal to 2/5.

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Answer:

1 kg of beef steak at $14.50

Step-by-step explanation:

1000/1450

0.68965517241 per gram

you could round to 0.6896

Answer:

B and C

Step-by-step explanation:

Both B and C

B)

2/5 = 0.4 (which terminate as decimals)

Similarly

C)

-1/4 = -0.25 (also terminates)

But A and D do not terminate

As for A) 1/3= 0.33333333..........

and for D) 7/9= 0.777777777......

In both cases the decimals are a never ending sequence or in other words does not terminate at all. They are irrational numbers.

Hope you understand. Thank you.

The correct values for a, b, c, d, and e are a = 16, b = 29, c = 24, d = 22, and e = 30 for group of 75 students on asking whether they like Algebra or Geometry.

For the values of a, b, c, d, and e, we can use the information provided in the table. Let's break it down step-by-step:

We are given that a total of 75 math students were surveyed. Therefore, the total number of students should be equal to the sum of the students who like algebra, the students who like geometry, and the students who do not like either subject.

75 = 45 (Likes Algebra) + 53 (Likes Geometry) + 6 (Does Not Like Either)

Simplifying this equation, we have:

75 = 98 + 6

75 = 104

This equation is incorrect, so we can eliminate options c and d.

Now, let's look at the information given for the students who do not like geometry. We know that a + b = 6, where a represents the number of students who like algebra and do not like geometry, and b represents the number of students who do not like algebra and do not like geometry.

Using the correct values for a and b, we have:

16 + b = 6

b = 6 - 16

b = -10

Since we can't have a negative value for the number of students, option a is also incorrect.

The remaining option is option e, where a = 29, b = 16, c = 24, d = 22, and e = 30. Let's verify if these values satisfy all the given conditions.

Likes Algebra: a + c = 29 + 24 = 53 (Matches the given value)

Does Not Like Algebra: b + d = 16 + 22 = 38 (Matches the given value)

Likes Geometry: c + d = 24 + 22 = 46 (Matches the given value)

Does Not Like Geometry: b + e = 16 + 30 = 46 (Matches the given value)

All the values satisfy the given conditions, confirming that option e (a = 29, b = 16, c = 24, d = 22, and e = 30) is the correct answer.

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A conversation with your friend explaining the symmetry you observe in nature is given below.

Me: Hey, have you ever noticed how symmetrical nature can be?

Friend: What do you mean?

Me: Well, think about things like snowflakes, leaves, and flowers. They all have a certain amount of symmetry to them.

Friend: Yeah, I guess I've noticed that before. But why is that?

Me: It's actually because of the way that nature grows and develops. The growth of these things is guided by physical laws and processes that tend to produce symmetrical shapes.

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Answer with Step-by-step explanation:

2 ( 2x -1 ) + 3 ( x + 1 )

First, let us find the value of the above expression.

2 ( 2x -1 ) + 3 ( x + 1 )

4x - 2 + 3x + 3

Combine like terms

4x + 3x - 2 + 3

7x + 1

Therefore, it is clear that the given expression is equal to 7x + 1.

∴ 7x + 1 = 2 ( 2x -1 ) + 3 ( x + 1 )

Answer:

(2x + 7) feet

Step-by-step explanation:

I'm guessing the expression there is

4x² + 28x + 49

4x² +14x +14x +49

Factorize

2x ( 2x + 7) +7( 2x + 7)

(2x + 7)²

Area = (side)1

One side is (2x +7)

The ability of a study to detect statistically significant differences or relationships in the groups when they really do exist is known as:

Power of study .

Given,

Definition .

Here,

The ability of a statistical analysis to detect effects that do exist in a population is referred to as the power of a study .

Power is mathematically defined as 1 - , where is the probability of committing a Type II error in the study, as noted above.

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Solving the exponential function, it is found that the times that will take to have the desired measures are given by:

a) 3.6 hours.

b) 38.51 hours.

c) 56.98 hours.

The function is given by:

\(A(t) = 140(0.5)^{\frac{t}{19.255}}\)

Solving for t, we have that:

\((0.5)^{\frac{t}{19.255}} = \frac{A(t)}{140}\)

\(\log{(0.5)^{\frac{t}{19.255}}} = \log{\frac{A(t)}{140}}\)

\(\frac{t}{19.255} = \frac{\log{\frac{A(t)}{140}}}{\log{0.5}}\)

\(t = 19.255\frac{\log{\frac{A(t)}{140}}}{\log{0.5}}\)

In item A, we have that A(t) = 123, hence:

\(t = 19.255\frac{\log{\frac{123}{140}}}{\log{0.5}}\)

t = 3.6 hours.

In item B, we have that A(t) = 35, hence:

\(t = 19.255\frac{\log{\frac{35}{140}}}{\log{0.5}}\)

t = 38.51 hours.

In item C, we have that A(t) = 18, hence:

\(t = 19.255\frac{\log{\frac{18}{140}}}{\log{0.5}}\)

t = 56.98 hours.

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Simplifying

2x + 9 + -10 = -5

Reorder the terms:

9 + -10 + 2x = -5

Combine like terms: 9 + -10 = -1

-1 + 2x = -5

Solving

-1 + 2x = -5

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.

-1 + 1 + 2x = -5 + 1

Combine like terms: -1 + 1 = 0

0 + 2x = -5 + 1

2x = -5 + 1

Combine like terms: -5 + 1 = -4

2x = -4

Divide each side by '2'.

x = -2

Simplifying

x = -2

I hope it helps you

Answer:

y=2/3x+4

Step-by-step explanation:

(slope intercept form is y=mx+b)

y-4=2/3x

add 4 to each side to isolate y

y=2/3x+4

Answer:y=2/3x+4

Step-by-step explanation: Use the property of addition and add 4 to both sides of the equation and then you find the slope form.

Step-by-step explanation:

c=144°(vertically opposite angle)

b+c=180°(straight angle)

b+144=180

b=180-144

b=36°

An adult must spend 6 hours on leisure activities.

We have been given the mean, µ = 4.5 and

standard deviation, σ = 1.3 of the normal distribution and we need to find how much time must be spent on leisure activities by an adult living in household with no young children to be in the group of adults who spent the highest 3% of the time in a day in such activities

. Let x be the amount of time that should be spent on leisure activities by an adult to be in the group of adults who spent the highest 3% of the time in a day in such activities. Now, we know that the highest 3% of the

time in a day in such activities will correspond to the area to the right of z value of 0.97. Hence, we can write the z score as: 0.97 = (x - µ) / σz = (x - 4.5) / 1.3x - 4.5 = 0.97 × 1.3x = 6.011Therefore, an adult living in household with no young children must spend 6.011 hours on leisure activities to be in the group of adults who spent the highest 3% of the time in a day in such activities

.Thus, the answer is: An adult living in household with no young children must spend 6.011 hours on leisure activities

to be in the group of adults who spent the highest 3% of the time in a day in such activities.

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An adult living in a household with no young children must spend approximately 6.95 hours on leisure activities to be in the group of adults who spent the highest 3% of time in a day on such activities.

To find the amount of time an adult must spend on leisure activities to be in the highest 3%, we need to use the z-score formula and find the corresponding value.

First, we calculate the z-score using the formula:

z = (x - μ) / σ

where x is the value we want to find, μ is the mean (4.5 hours), and σ is the standard deviation (1.3 hours).

Next, we find the z-score corresponding to the highest 3% by subtracting 3% from 100% (97%). Using a z-table or a calculator, we find that the z-score corresponding to 97% is approximately 1.8808.

Now, we can solve for x:

1.8808 = (x - 4.5) / 1.3

Multiply both sides by 1.3:

1.8808 * 1.3 = x - 4.5

2.44504 + 4.5 = x

x ≈ 6.94504

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Therefore, the maximum volume of the box is 112 cubic units, and the dimensions of the box that give us the maximum volume are: Length = 14 units, Width = 4 units ,Height = 2 units

To maximize the volume of the box, we need to find the dimensions that maximize the volume of the box. Let's assume that squares of side length x are cut out of each corner of the cardboard. Then, the dimensions of the box can be expressed as:

Length = 18 - 2x

Width = 8 - 2x

Height = x

The volume of the box is given by the product of these dimensions:

\(V(x) = (18 - 2x)(8 - 2x)(x)\)

Expanding this equation, we get:

\(V(x) = 4x^3 - 52x^2 + 144x\)

To find the maximum volume, we need to take the derivative of V(x) and set it equal to zero:

\(V'(x) = 12x^2 - 104x + 144 = 0\)

Solving this quadratic equation, we get:

x = 2 or x = 6

We need to check both solutions to see which one gives us the maximum volume.

When x = 2, the dimensions of the box are:

Length = 18 - 2(2) = 14

Width = 8 - 2(2) = 4

Height = 2

The volume of the box is:

V(2) = (14)(4)(2) = 112

When x = 6, the dimensions of the box are:

Length = 18 - 2(6) = 6

Width = 8 - 2(6) = -4 (negative, so this solution is not possible)

Height = 6

Therefore, the maximum volume of the box is 112 cubic units, and the dimensions of the box that give us the maximum volume are:

Length = 14 units

Width = 4 units

Height = 2 units.

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The value of p+q+r+s = 36 is the required answer.

In mathematics, integers are numbers without decimals or fractions. The set consists of 0, natural numbers and the additive inverses of the natural numbers  (the negative integers). Integer examples include -5, 0 and 7.

Integers can be Positive integers , zero and negative integers.

positive integers are also called natural number.

Here we are given an equation :-

(9-p)(9-q)(9-r)(9-s)=9

and here p, q, r, s are distinct positive integers.

we need to find the value of .

so here we know that RHS contain 9 and we know the multiple of 9 are 1,3,9.

therefore  must be equals to +1,-1,+3,-3,+9,-9

In pair (1,3) and (-1,-3) let equate the equation,

so by putting the value of p, q, r, s as 8,6,10,12 we will get

p=8

q=6

r=10

s=12

hence  

so option e ) 36 is our required answer.

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The side-by-side bar plot is a type of plot that can be used to visualize a one-way contingency table. So, the correct answer is C.

A contingency table is a table used to study the relationship between two categorical variables. The frequency or count of each combination of categories is recorded in a contingency table.

Aside from side-by-side bar plots, stacked bar plots can also be used to visualize contingency tables. A stacked bar plot, also known as a stacked column plot or stacked bar chart, displays each category’s frequency as a proportion of the whole.

It is created by stacking each category’s frequency on top of one another and then drawing a bar to represent the total.

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Answer:

Square

Step-by-step explanation:

each side of a square is equal and there are 4 line segments

Answer:

Step-by-step explanation:

3x5x8 your answer is 120

Answer:

V = 192 m3

Step-by-step explanation:

Answer:

-16

Step-by-step explanation:

\(3^{2}\) - 7(3) - 4 = -16

Hey there!

x^2 + 7x - 4

= 3^2 - 7(3) - 4

= 9 - 21 - 4

= -12 - 4

= -16

Answer: -16

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:0.02275

Normal distribution:

Which is symmetrical about mean.

Mean:

It is the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.

Complement rule:

When two disjoint sets are meant to occur then the sets are said to be complementary.

Given:

Mean= 0.4 seconds

Standard deviation= 0.005 seconds

Let, X be the reaction time for the driver to view stimulus.

So, distribution of X is given by:

X~ N( 0.4, 0.005)

Where σ= 0.05 and µ= 0.4

Solving this ques by using normal standard deviation and z score given as:

z=\frac{x-µ}{σ}

Applying formula:

P(X>0.5)= P{(x-µ/σ) > (0.5-µ/σ)} P {Z > (0.5-0.4/0.05)}

=P(Z > 2)

By using complement rule we get,

P(Z>2) = 1- P(Z<2)

Using normal standard table we have,

P(Z>2)=1- P(Z<2)

= 1- 0.97725

= 0.02275

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The probability that a reaction requires more than 0.5 seconds is 0.0227

Z-score standardization:

The amount of standard deviations the data point deviates from the mean is shown by the standardized z-score.

• If the z-score increases when it is higher than the mean (0).

• If the z-score is below the mean and takes a negative value (0).

Given that,

Mean = μ =0.4

Standard deviation = σ =0.005

The probability that a reaction requires more than 0.5 seconds is obtained by;

Let X denotes the reaction time of a driver which follows a normal distribution with a mean of 0.4 seconds and a standard deviation of 0.005 seconds.

P(X > 0.5) = 1 - P(X < 0.5)

                = 1 - P(0.4 < X < 0.5) (0.5 - 0.4/0.005)

                = 1 - P(25.06)  

                = 1 - P(252)

From the “standard normal table”, the area to the left of is 0.9773.

P(X > 0.5) = 1 - P(252)

                = 1 - 0.9773

                = 0.0227

Hence, the probability that a reaction requires more than 0.5 seconds is 0.0227

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The set of ordered pairs {(−4, −5), (−3, 0), (−2, −4), (0, −3), (2, −2)} represents a function since each input value is associated with a unique output value.

To determine whether a set of ordered pairs represents a function, we need to ensure that each input (x-value) corresponds to exactly one output (y-value).

Let's analyze each set of ordered pairs:

1. {(−6, −5), (−4, −3), (−2, 0), (−2, 2), (0, 4)}

  In this set, the input value -2 is associated with both 0 and 2. Therefore, it does not represent a function since one input has multiple outputs.

2. {(−5, −5), (−5, −4), (−5, −3), (−5, −2), (−5, 0)}

  In this set, the input value -5 is associated with multiple outputs (-5, -4, -3, -2, and 0). Hence, it does not represent a function as one input has multiple outputs.

3. {(−4, −5), (−3, 0), (−2, −4), (0, −3), (2, −2)}

  In this set, each input value is associated with a unique output value. Hence, it represents a function as each input has only one output.

4. {(−6, −3), (−6, −2), (−5, −3), (−3, −3), (0, 0)}

  In this set, the input value -6 is associated with both -3 and -2. Therefore, it does not represent a function since one input has multiple outputs.

In summary, only the set of ordered pairs {(−4, −5), (−3, 0), (−2, −4), (0, −3), (2, −2)} represents a function since each input value is associated with a unique output value.

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Answer:

28 cm²

Step-by-step explanation:

The area of Δ BDF is the area of the rectangle subtract the area of the 3 white triangles.

Since the area of the rectangle = 80 cm² and

area = length × breadth, then

breadth = 80 ÷ 10 = 8 cm

Thus CE = EF = 8 cm and CD = DE = BC = 4 cm

Area of Δ DEF = 0.5 × 10 × 4 = 20 cm²

Area of Δ ABF = 0.5 × 8 × (10 - 4) = 0.5 × 8 × 6 = 24 cm²

Area of Δ BCD = 0.5 × 4 × 4 = 8 cm²

Thus

area of Δ BDF = 80 - (20 + 24 + 8) = 80 - 52 = 28 cm²