Caitlyn has a credit card with a spending limit of $1500 and an APR (annual percentage rate) of 18%. During the first month, Caitlyn charged $375 and paid $250 of that in her billing cycle. Which expression will find the amount of interest Caitlyn will be charged after the first month?

Answer:

  y = (1/2)x +1

Step-by-step explanation:

Given the two points on the line are (0, 1) and (4, 3), the line's equation can be written using the two-point form:

  y = (y2 -y1)/(x2 -x1)·(x -x1) +y1

  y = (3-1)/(4-0)·(x -0) +1 . . . . use the given point values

  y = (1/2)x +1

Answer:

y = (1/2)x +1

Step-by-step explanation:

Given the two points on the line are (0, 1) and (4, 3), the line's equation can be written using the two-point form:

 y = (y2 -y1)/(x2 -x1)·(x -x1) +y1

 y = (3-1)/(4-0)·(x -0) +1 . . . . use the given point values

 y = (1/2)x +1

Step-by-step explanation:

The answer should be

228

Answer:

Please find the attached file.

Step-by-step explanation:

Given: [tex]y=\dfrac{8}{x+3}-2[/tex]

We need to draw the graph of function with asymptote.

For horizontal asymptote:-

[tex]x\rightarrow \infty[/tex]

[tex]y=\lim_{x\rightarrow \infty}(\dfrac{8}{x+3}-2)=-2[/tex]

HA: y=-2

For vertical asymptote:-

[tex]y\rightarrow \infty[/tex]

[tex]x+3=0[/tex]

VA: x=-3

For x-intercept, Put y=0

(1,0)

For y-intercept, Put x=0

(0,2/3)

Now we will plot on graph and draw the graph.

Please see the attachment for graph.  

The function h(x, y) is given by the composition of the functions g(t) and f(x, y). With the given expressions for f and g, the function h(x, y) = g(f(x, y)) equals to (4 - xy^2 + x^2y^2) + ln(4 - xy^2 + x^2y^2).

The question asks to find the function h(x, y) from the functions g(t) and f(x, y), where g(t) = t + ln(t), and f(x, y) = 4 − xy^2+ x^2y^2. To begin with, it is necessary to substitute f(x, y) in place of 't' in function g which is g(f(x, y)), since we have h(x, y) = g(f(x, y)).

Performing the substitution, we obtain:

h(x, y) = g(f(x, y)) = (4 - xy^2 + x^2y^2) + ln(4 - xy^2 + x^2y^2).

This is your final function h in terms of x and y.

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Final answer:

The truth value of the conditional statement 'If the snow is white, then the grass is red' cannot be determined to be true or false without context, as it is a statement that requires evaluation of its antecedent and consequent. In logic, a conditional statement is true unless the antecedent is true and the consequent is false.

Explanation:

The truth value for the conditional statement "If the snow is white, then the grass is red," cannot be evaluated as true or false based solely on the content of the statement. In logic, a conditional statement is considered to be true unless a situation occurs where the first part (the antecedent) is true and the second part (the consequent) is false.

Here, the statement "the snow is white" is true, but the statement "the grass is red" can be false, as grass is typically green. This illustrates an important logical principle where the truthfulness of a conditional does not require that the consequent actually follows from the antecedent. To evaluate the truth of a conditional statement, it would be more appropriate to look for a counterexample that disproves it or involves a scenario where the antecedent is true and the consequent is false.

Lucy will have to pay $60 more each month.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

Lucy's employer pays 70% of the total cost of her family's health insurance plan, while Lucy pays the rest. Then Lucy will be only 30%.

If the total cost of the plan will increase from $450 per month to $650 per month.

At $450, Lucy pays 30% of $450 = 0.3 x 450 = $135

At $650, Lucy pays 30% of $650 = 0.3 x 650 = $195

Then Lucy has to pay each month more will be

⇒ $195 - $135

⇒ $60

Lucy will have to pay $60 more each month.

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Answer: C. 19.5 in × 29.25 in

Step-by-step explanation: (50 x .39) x (75 x .39)

Answer with Step-by-step explanation:

Carson buys three pencils at $0.35 each.

Cost of 1 pencil=$0.35

So, Cost of 3 pencils=$1.05    (0.35×3=1.05)

Buys a box of crayons for $2.86.

four notebooks at $1.99 each.

Cost of 1 notebook=$1.99

So, Cost of 4 notebooks=$7.96    (1.99×4=7.96)

and two pens at $1.09 each.

Cost of 1 pen=$1.09

So, Cost of 2 pens=$2.18  (1.09×2=2.18)

We have to estimate the amount he spent on school supplies.

Total Amount spent=$(1.05+2.86+7.96+2.18)

                               = $14.05

Hence, Total amount spent by Carson on school supplies is:

$14.05

The graph of [tex]y=4x+3[/tex] is a line with a slope of 4, meaning for every unit moved to the right on the x-axis, you move up four units on the y-axis. The y-intercept is 3, so the line intersects the y-axis at the point (0,3). We plot these points and draw the line through them for the complete graph.

The question asks, which of the following shows the graph of [tex]y = 4x + 3?[/tex]This is a linear equation in the format of y=mx+b, where 'm' is the slope of the line and 'b' is the y-intercept. In this case, 'm' is 4, so for every step you move to the right on the x-axis, you move four steps up on the y-axis. 'b' is 3, so the line intersects the y-axis at the point (0,3). To graph this equation, start at the point (0,3) and for every 1 unit you move to the right, move up by 4 units. Repeat this process with other values of x to find corresponding values of y. Points are then plotted on the graph and a line is drawn through them showing the relationship between x and y.

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The radius of a globe is 7.5 inches. What is the volume of the globe? Use 3.14 for pi.

Volume of the globe=[tex] \frac{4}{3} \pi r^{3} [/tex]

Volume of the globe=[tex] \frac{4}{3}*3.14*7.5^{3} [/tex]

Volume=[tex] \frac{4}{3}*3.14*421.875 [/tex]

Volume=[tex] \frac{4}{3}*1324.6875 [/tex]

Volume=[tex] \frac{5928.75}{3} [/tex]

Volume=1766.25[tex] inches^{3} [/tex]

Volume of Globe=1766.25[tex] in^{3} [/tex]

Answer: 1766.25

Step-by-step explanation: tryust

At t = 2 seconds, the angular position of the point on the amusement park ride is approximately 3.42 radians.

We have,

The equation θ(t) = a + bt² - ct³ represents the angular position of a point on the amusement park ride as a function of time.

Given:

a = 0.3 rad

b = 0.85 rad/s²

c = 0.035 rad/s³

In this equation,

θ(t) represents the angular position of the point on the ride at time t.

The term a is the initial angular position when t = 0, which is 0.3 radians.

The term bt² represents the angular displacement due to the linearly increasing angular velocity.

The coefficient b determines the rate of change of the angular displacement over time.

The term -ct³ represents the angular displacement due to the cubic decrease in angular acceleration.

To find the angular position at a specific time t, substitute the given values of a, b, c, and the desired value of t into the equation

θ(t) = a + bt² - ct³.

For example, if we want to find the angular position at t = 2 seconds:

θ(2) = 0.3 + 0.85 * (2²) - 0.035 * (2³)

= 0.3 + 0.85 * 4 - 0.035 * 8

= 0.3 + 3.4 - 0.28

= 3.42 radians

Therefore,

At t = 2 seconds, the angular position of the point on the amusement park ride is approximately 3.42 radians.

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The angular position of a point on a ride is given by the equation θ(t) = a + bt² - ct³. Factors such as the moment of inertia can change the angular acceleration in the system. When a child is on the merry-go-round, the moment of inertia increases, leading to a decrease in angular acceleration.

The angular position of a point on an amusement park ride can be described by the equation θ(t) = a + bt² - ct³. In this equation, angular position is represented by θ(t), 'a' represents the initial angular position (0.3 rad), 'b' represents the angular velocity (increase in angular position per unit time - 0.85 rad/s2) and 'c' is the rate of change in angular velocity or the angular acceleration (0.035 rad/s3).

The angular acceleration can change due to factors such as a change in the moment of inertia. For example, when a child is on a merry-go-round, the combined moment of inertia is greater, therefore reducing the angular acceleration. The moment of inertia depends on factors such as the mass and the location of that mass relative to the axis of rotation. The child can be approximated as a point mass at a distance of 1.25 m from the axis of rotation.

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The number is 21.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number = M

5/7 of M = 15

This can be written as,

(5/7)M = 15

M = 15 x 7/5

M = 3 x 7

M = 21

Thus,

The number is 21.

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