You initially invest 500 in a savings account that pays yearly interest rate of 3.5%. write a formula for an exponential function giving the balance in your account as a function of the time, in years, since your initial investment.

The number of horizontal asymptotes that a function can have depends on its behavior as x approaches positive or negative infinity.

a) If the function approaches a specific value or constant as x approaches positive or negative infinity, it can have 0 horizontal asymptotes.

b) If the function approaches the same value or constant as x approaches positive or negative infinity, it can have 1 horizontal asymptote.

c) If the function approaches different values or constants as x approaches positive or negative infinity, it can have 2 horizontal asymptotes.

d) It is not possible for a function to have exactly 3 horizontal asymptotes. Asymptotes come in pairs, so the number of horizontal asymptotes can be 0, 1, 2, or 4.

e) It is not possible for a function to have exactly 4 horizontal asymptotes. Asymptotes come in pairs, so the number of horizontal asymptotes can be 0, 1, 2, or 3.

the correct options are:

a) 0

b) 1

c) 2

d) 3

e) 4

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The correct statement is: "The domains of g(x) and f(x) are the same, but their ranges are not the same."

The statement "The domains of g(x) and f(x) are not the same, and their ranges are also not the same" is correct. In general, when considering functions g(x) and f(x) derived from a parent function, the transformations applied to the parent function can affect both the domain and the range. The domain of a function refers to the set of all possible input values, while the range represents the set of all possible output values. Through transformations such as shifts, stretches, compressions, or reflections, the domain and range of a function can be altered. Therefore, it is possible for the domains and ranges of g(x) and f(x) to differ from each other and from the parent function.

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The inequality shaded in the graph is given as follows:

y ≥ 5x/2 + 3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:

b = 3.

When x increases by 2, y increases by 5, hence the slope m is given as follows:

m = 5/2.

Then the equation of the line is given as follows:

y = 5x/2 + 3.

The line is a solid line, and values above it are plotted, hence the inequality is given as follows:

y ≥ 5x/2 + 3.

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The marginal cost of producing the xth box of CDs is given by 8 − x/(x2 1)2. The total distribution cost to produce two boxes is $1,100.

To find the total cost function c(x), we can integrate the marginal cost function to obtain the total cost function. Thus, we have: ∫(8 − x/(x² + 1)²) dx = C(x) + kwhere C(x) is the total cost function and k is the constant of integration. To evaluate the integral, we use the substitution u = x² + 1. Then, du/dx = 2x and dx = du/2x. Substituting, we have:∫(8 − x/(x² + 1)²) dx = ∫[8 − 1/(u²)](du/2x)= (1/2) ∫(8u² − 1)/(u²)² duUsing partial fractions, we can write: (8u² − 1)/(u²)² = A/u² + B/(u²)² where A and B are constants. Multiplying both sides by (u²)², we have:8u² − 1 = A(u²) + BThen, letting u = 1, we have:8(1)² − 1 = A(1) + B7 = A + BAlso, letting u = 0, we have:8(0)² − 1 = A(0) + B-1 = BThus, A = 7 + 1 = 8. Therefore, we have:(8u² − 1)/(u²)² = 8/u² − 1/(u²)².

Substituting, we get:C(x) = (1/2) ∫(8/u² − 1/(u²)²) du= (1/2) [-8/u + (1/2)(1/u²)] + k= -4/u + (1/2u²) + k= -4/(x² + 1) + (1/2)(x² + 1) + k= 1/2 x² - 4/(x² + 1) + kTo find k, we use the fact that the total cost to produce two boxes is $1,100. That is, when x = 2, we have:C(2) = (1/2)(2)² - 4/(2² + 1) + k= 2 - 4/5 + k= 6/5 + kThus, when x = 2, C(x) = $1,100. Therefore, we have:6/5 + k = 1,100Solving for k, we get:k = 1,100 - 6/5= 1,099.2Thus, the total cost function c(x) is given by:C(x) = 1/2 x² - 4/(x² + 1) + 1,099.2

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F'(-7,-3) G'(2,-6) H'(3,-5)

1) In a Reflection over the x-axis, we can visualize the image by following a rule.

Pre-image: (x,y) to Image: (x,-y)

2)In this case, we have F(-7,3), G (2,6), and H (3,5).

Since it is over the x-axis then we can write

F'(-7,-3) G'(2,-6) H'(3,-5)

Assuming Boden does not add or take out any money, he would have $470.4 in the account after 4​ years.

Mathematically, simple interest can be calculated by using this formula:

S.I = PRT or S.I = A - P

Where:

Substituting the given parameters into the simple interest formula, we have;

S.I = 400 × 4.4/100 × 4

S.I = 400 × 0.044 × 4

S.I = $70.4.

Next, we would calculate the future value as follows;

S.I = A - P

Future value, A = S.I + P

Future value, A = $70.4 + $400

Future value, A = $470.4.

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A systematic sample is a sampling method in which members from a population are selected in a regular and systematic way.

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The coordinates form a right triangle and the coordinates are within the parallelogram .

What is parallelogram explain?

A right triangle cutout from the parallelogram has the vertices (13,10), (13,14) and (11,10)

The coordinates of the parallelogram are given as -

(5, 17), (10, 20). (18,9), and (13,6)

The question is incomplete, as the options are not given.

So,  use of a general explanation

For the right triangle to be a cutout from the parallelogram, then the vertices of the right triangle must be within the coordinates  (5, 17), (10, 20). (18,9), and (13,6)

An example of such coordinates are = (13,10), (13,14) and (11,10)

Note that you can use any coordinates, as long as the coordinates form a right triangle and the coordinates are within the parallelogram.

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The complete question is -

A parallelogram has coordinates of (5, 17), (10, 20). (18,9), and (13,6). Which right triangle represents one of the cutouts from the box method ?17​

Answer:

It will be C

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

150/ 50 = 3

18 x 3 = 54

In the first part of her journey, she walks 2.45 km due east, which means her displacement in the east-west direction is 2.45 km. In the second part, she walks 7.82 km at a direction 32.5∘ west of north.

To find her displacement in the north-south direction, we need to calculate the vertical component of her movement.

The vertical component can be found by multiplying the distance (7.82 km) by the sine of the angle (32.5∘). Therefore, the vertical displacement is 7.82 km * sin(32.5∘) ≈ 4.12 km. Since the hiker's starting point is in the east and north directions, we can consider the east-west displacement as the x-coordinate and the north-south displacement as the y-coordinate. Using these coordinates, we can calculate the total displacement using the Pythagorean theorem.

The total displacement is the square root of the sum of the squared horizontal and vertical displacements. Therefore, the distance from the hiker's starting point is √(2.45 km)^2 + (4.12 km)^2 ≈ √6.0025 + 16.9744 ≈ √22.9769 ≈ 4.8 km (rounded to one decimal place). Hence, the hiker is approximately 4.8 km away from her starting point.

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Answer:

ok so x*0.85=150

so x=176

Hope This Helps!!!

Therefore, the two positive coterminal angles are 5π/4 and 13π/4, and the two negative coterminal angles are -11π/4 and -19π/4.

To find the coterminal angles, we can add or subtract multiples of 2π (or 360°) to the given angle to obtain angles that have the same initial and terminal sides.

For the angle -3π/4 radians, adding or subtracting multiples of 2π will give us the coterminal angles.

Positive coterminal angles:

-3π/4 + 2π = 5π/4

-3π/4 + 4π = 13π/4

Negative coterminal angles:

-3π/4 - 2π = -11π/4

-3π/4 - 4π = -19π/4

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It is false that mobile banner ads perform significantly better than desktop banners.

There is no clear consensus on whether mobile banner ads or desktop banner ads perform better. The effectiveness of banner ads depends on various factors such as the placement of the ad, its design, and the target audience.

However, it is true that mobile usage has been increasing rapidly in recent years, and more people are accessing the internet through their mobile devices than through desktop computers. Therefore, it is important for advertisers to optimize their ads for mobile devices and ensure that they are mobile-responsive.

Nevertheless, it cannot be generalized that mobile banner ads are more effective than desktop banner ads. The effectiveness of an ad should be evaluated on a case-by-case basis, taking into account the specific objectives, target audience, and design of the ad.

Therefore, it is important for advertisers to test their banner ads on both desktop and mobile devices to determine which platform works best for their specific campaign. And the given statement is false.

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The statistical value describes a regression line fits the data points:

R-squared

What is Statistical Value?

When it is extremely unlikely that an observed event occurred by accident, it is deemed statistically significant. An observed event is considered statistically significant when its p-value is less than a certain cutoff, or level of significance.

The statistical value describes a regression line fits the data points is

R-squared

The statistical indicator of how closely the data resemble the fitted regression line is called R-squared. For multiple regression, it is sometimes referred to as the coefficient of determination or the coefficient of multiple determination.

R-squared = Explained variation / Total variation

R-squared is always between 0 and 100%

The better the model matches your data, in general, the greater the R-squared.

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Answer:

(3,-1)
(5,-1)

(3,-4)

Step-by-step explanation:

see image:

Answer:

Step-by-step explanation:

z= y( z-y)/x

z = yz - y^2 /x

zx = yz -y^2

y^2 = yz - zx

y^2 = ( y- x)z

therefore  z = y^2/(y-x)

please mark me as the brainliest

Answer:

x

Step-by-step explanation:

you do your x and y on anything

Answer:15

Step-by-step explanation:

width - 6

height - 5

6 x 5 / 2 = 15

(Please tell me if I read it wrong, It's not really clear)

Answer: 67.3 x 10^-9

Step-by-step explanation:

Answer:

65 dm and 52 dm

Step-by-step explanation:

If the scale factor of the sides is k, then the scale factor of the areas is k^2.

The scale factor of the areas is (32 dm^2)/(50 dm^2) = 0.64 = k^2

The scale factor of the sides is k = \sqrt(0.64) = 0.8

The perimeters are in a ratio of 1:0.8

x + 0.8x = 117

1.8x = 117

x = 65

0.8x = 0.8(65) = 52

The perimeters are 65 dm and 52 dm.

Answer:

2(x+6)²

Step-by-step explanation:

Answer:

(x+6)(2x+12)

Step-by-step explanation:

First, because a>1, you have to multiply c by a, which gives you 144. Now, you need to find factors of 144 that add to 24. Those factors would be 12 and 12. Now, you expand the equation:

2x^2+12x+12x+72

Now, you factor the first two terms and last two terms:

The GCF of 2x and 12x is 2x, so divide by 2x

2x(x+6)

The GCF of 12 and 72 is 12, so divide by 12

12(x+6)

The two parenthesis match, so they are one term. All that's left to do is factor the terms outside the parenthesis, and you get:

(x+6)(2x+12)

Hope this helped!

A type of plot shows the median and the data spread about the median is called a boxplot.

A box-and-whiskers plot, also referred to as a boxplot, presents a summarized information such as the median, quartiles, minimum, and maximum values.

It indicates the measure of skewness of a distribution data or how the values are spread out.

It is made up of a box, which lies between the first and third quartiles with the whiskers as line segments extending from the ends of the box to the smallest and largest values that are not outliers.

Attached photo is a figure that illustrates a boxplot.

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Answer:

sheesh

Step-by-step explanation:

Table is a way to represent the data of the two or more variable.

The correct order for the ranks of the waves from the lowest energy wave to the highest energy wave of the given table is 1-4-3-2. Thus the option 1 is the correct option.

Table is a way to represent the data of the two or more variable.

To read the data from the table look for the value of one variable, and get the resultant value of other variable from the corresponding block.

Given information-

The first column labeled Wave has entries 1, 2, 3, 4.

The table given in the problem is,

First column                         Second column

  1                          This wave has 3 centimetre amplitude

  2                         The distance from the midpoint to the crest is 6 cm,

  3                         The distance from the midpoint to the trough is 12 cm,

  4                         This wave has a 4 centimetre amplitude.

The ranks of the waves from the lowest energy wave to the highest energy wave of the given table has to find out.

As the energy of a wave is related to the amplitude of the wave, as the how much amount of energy it is carrying with it.

The distance from the midpoint to the crest is called the amplitude.

Thus the more value of the amplitude gives the more energy.

Therefore,

Hence, the correct order for the ranks of the waves from the lowest energy wave to the highest energy wave of the given table is 1-4-3-2. Thus the option 1 is the correct option.

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Answer:

A

Step-by-step explanation:

The reliability function, denoted by R(t), represents the probability that the electric ignition on the gas stove will survive beyond time t. To find the reliability function, we need to integrate the probability density function (PDF) over the given interval.

For 0 <= t <= 2:

R(t) = ∫[0 to t] f(x) dx = ∫[0 to t] 0.375x^2 dx = 0.125x^3 evaluated from 0 to t

R(t) = 0.125t^3 - 0.1250^3 = 0.125*t^3

For t > 2:

Since the model indicates that all ignitions expire within 2,000 days, the reliability function beyond t = 2 is 0.

The graph of the reliability function would show a curve starting at R(0) = 1 and gradually decreasing until t = 2, where it drops to 0 and remains 0 for all t > 2.

The hazard function, denoted by h(t), represents the instantaneous failure rate at time t. It can be calculated as the ratio of the probability density function (PDF) to the reliability function.

For 0 <= t <= 2:

h(t) = f(t) / R(t) = (0.375t^2) / (0.125t^3) = 3/t

The hazard function for 0 <= t <= 2 is given by h(t) = 3/t.

For t > 2:

Since the reliability function becomes 0 for t > 2, the hazard function is undefined or infinite for t > 2. This implies that beyond t = 2, the hazard of the electric ignition failure is extremely high or instantaneous.

The graph of the hazard function would show a decreasing curve starting from a high value at t = 0 and approaching infinity as t approaches 2. For t > 2, the hazard function is undefined or infinite.

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Converting feet to inches solve the problem, first we have to convert 20 yards to feet and inches and then calculate the cost per foot and inch. Here are the steps:1 yard = 3 feet (since 1 yard equals 3 feet)20 yards = 20 × 3 = 60 feet (converting yards to feet)1 foot = 12 inches (since 1 foot equals 12 inches)60 feet = 60 × 12 = 720 inches

The total cost of 20 yards of ribbon is $24. Therefore, cost per yard = $24/20 = $1.2We are given that the cost per yard is $0.83. Therefore, we can write:$1.2 = $0.83 × x where x is the cost per foot and inch. To solve for x, we can divide both sides by $0.83:$1.2/$0.83 = xor1.44 = x We can conclude that it will cost $1.44 per foot and inch of the ribbon.

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The expressions that can be used to calculate both numbers of hours Demetrius works in 5-day work week is 5(x + 1)  and 5x + 5

We are being told that Latisha works x hours each day and Demetrius works 1 more hour each day than Latisha.

So,

Thus, the both expression that can determine the number of hours Demetrius works in five days is:

= 5(x + 1)  and 5x + 5

This is because if we open the bracket from 5(x+1) and multiply each term in the bracket with 5, we end up having 5x + 5.

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Based on the residual plot, is the linear model appropriate is option (D). Yes, half of the residuals are positive and half are negative.

The residual plot is one that can be a scatterplot of the residuals (the contrasts between the observed  values as well as the predicted values) against the indicator variable. The reason of this plot is to check the presumption that the errors are randomly conveyed and have steady fluctuation over the run of the indicator variable.

In the event that the linear show is fitting for the information, the residuals ought to be randomly scattered around the flat line at zero. The reality that half of the residuals are positive and half are negative indicates that there's no systematic bias within the predictions.

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Answer:

you cant have two variables

Step-by-step explanation:

Answer: 160 feet square

Step-by-step explanation:

so as we can see the shape is a combination of 4 shapes

2 triangles and 2 rectangles

so for the first rectangle

the area would be 8 x 11 = 88

and for the second rectangle it'd be  6 x 7 =42

so 88+ 42 = 130

then for the first triangle it has a height of 8 and base of 6

therefore its area is 1/2 x 6 x 8 = 24

for the second triangle the base is 6 but the height is not given

but we have the sum of the height and the side of rectangle given as 9

thus the side of the rectangle is 7 we can find the height of the triangle by 9-7 which is 2

therefore height of triangle = 2

therefore area of second triangle is 1/2 x 2 x 6  = 6

therefore areas of the triangles => 6+24 = 30

therefore total area = 30 + 130 = 160

Answer:

Graph D

Step-by-step explanation:

We can look at the number of pounds of pecans and cashews, shown on the x- and y-axis, respectively.

All of the graphs have an x-intercept of (4, 0), meaning that the number of pecans being bought is 4 lbs.

Since pecans cost $6 per lb, we can multiply the cost by 4 in order to make sure that the total cost is not exceeding $24.

$6 · 4 lbs = $24

Let's look at the y-axis to see how many lbs of cashews Malik can buy. The y-intercept is (0, 3) for all graphs, meaning that 3 lbs of cashews are being bought.

Since cashews cost $8 per pound, we can multiply the cost by 4 in order to make sure that the total cost is not exceeding $24.

$8 · 3 lbs = $24  

The shaded area represents the values that can be used in the problem. Since we want $24 or less, the shaded region has to be below the line.

Malik can spend no more than $24, so the line should be solid since this means that the values the line touches are inclusive. 4 lbs of pecans and 3 lbs of cashews should be inclusive.

The graph that has all of these properties is Graph D.