Your parents gave you a gift card for your favorite coffee shop. The card was worth $50 when you got it. Each day, you buy a drink for $3. Which equation shows the value on the gift card over time?


CLEAR CHECK

y = -3x – 50


y = -3x + 50


y = 3x – 50


y = 50x – 3

To find the value of the sculpture in 9 years, we can use the formula for compound interest:

V = P * (1 + r/100)^t

where V is the final value, P is the initial value (37,000), r is the annual interest rate (3.5%), and t is the number of years (9).

Plugging in the values into the formula, we get:

V = 37,000 * (1 + 3.5/100)^9

= 37,000 * 1.0355^9

= 37,000 * 1.978044

= approximately 73,656.78

So, the sculpture will be worth approximately 73,656.78 in 9 years if the owner's estimate is correct and its value increases by 3.5% every year.

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Answer:

Option 3

Step-by-step explanation:

Answer:

Find the answers below

Step-by-step explanation:

Using m<X as the reference angle

Opposite YZ = 7

Adjacent  XY = 10

Hypotenuse XZ = √149

Using the SOH CAH TOA identity

sinX = opp/hyp

sinX =YZ/XZ

sinX = 7/√149

For cos X

cos X = adj/hyp

cos X =10/√149

Using m<Z as reference angle;

Opposite XY = 10

Adjacent  YZ = 7

Hypotenuse XZ = √149

Using the SOH CAH TOA identity

sinZ = opp/hyp

sinZ =10/√149

sinZ = 7/√149

For cos Z

cosZ = 7/√149

Answer:

W

Step-by-step explanation:

I think it's w, hope this helps

Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

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(a)  The vertex of the graph is given by the values (h, k), so the vertex of this quadratic function is (2, 5).

(b) we have the point (3, 2). Plotting these points and connecting them, we get the graph of the function.

(a) To write the quadratic function g(x) = -3x² + 12x - 7 in the form g(x) = a(x - h)² + k, we need to complete the square.

g(x) = -3x² + 12x - 7

To complete the square, we need to factor out the coefficient of x², which is -3:

g(x) = -3(x² - 4x) - 7

Next, we need to add and subtract the square of half the coefficient of x, which is (-4/2)^2 = 4:

g(x) = -3(x² - 4x + 4 - 4) - 7

Simplifying, we have:

g(x) = -3((x - 2)² - 4) - 7

Expanding the expression inside the parentheses:

g(x) = -3(x - 2)² + 12 - 7

g(x) = -3(x - 2)² + 5

So, the equation in the specified form is g(x) = -3(x - 2)² + 5.

The vertex of the graph is given by the values (h, k), so the vertex of this quadratic function is (2, 5).

(b) To graph the function, we will plot five points: the vertex (2, 5), two points to the left of the vertex, and two points to the right of the vertex.

When x = 0, we have:

g(0) = -3(0 - 2)² + 5

= -3(4) + 5

= -12 + 5

= -7

So, we have the point (0, -7).

When x = 1, we have:

g(1) = -3(1 - 2)² + 5

= -3(-1)² + 5

= -3(1) + 5

= -3 + 5

= 2

So, we have the point (1, 2).

When x = 3, we have:

g(3) = -3(3 - 2)² + 5

= -3(1)² + 5

= -3(1) + 5

= -3 + 5

= 2

So, we have the point (3, 2).

Plotting these points and connecting them, we get the graph of the function.

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The specific name of the quadrilateral is kite

The measures of the missing angles are 75 degrees each

To determine the measure of the angle, we need to know the different properties of a kite.

The properties of a kite includes;

Since the adjacent angles are equal, we have that;

105+ x = 180

collect the like terms, we have;

x = 180 - 105

x = 75 degrees

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The quadrilateral is a kite and the missing angles are 105° and 45°

A kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.

A kite has a pair of equal angle and the diagonals of a kite meets at 90°.

In a kite , there are two pairs of congruent or equal sides.

This means that the missing angles are

The opposite angle to 105 is also 105°

The fourth angle is calculated as;

105+105+105+x = 360

= 315 +x = 360

x = 360- 315

x = 45°

Therefore the quadrilateral is a kite and the missing angles are 105° and 45°

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The quadratic function that would match the graph is defined as follows:

f(x) = 4(x² - 6x + 5).

The graph is a parabola, hence the function is a quadratic function.

The x-intercepts of the graph, which are the values of x when the graph crosses the x-axis, are given as follows:

x = 1 and x = 5.

Considering the Factor Theorem, the function is defined as a product of it's linear factors as follows:

f(x) = a(x - 1)(x - 5)

f(x) = a(x² - 6x + 5).

In which a is the leading coefficient.

When x = 0, y = 20, hence the leading coefficient a is obtained as follows:

5a = 20

a = 20/5

a = 4.

Meaning that the function is:

f(x) = 4(x² - 6x + 5).

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Answer::

Explanation:

Given the general cosine function:

We want to determine the function that has the following properties:

• Amplitude = 2

• Period = 4π

Using the period formula given above:

From the given options, the function that satisfies the required property is:

Answer:

1.4x10=14 if thats ur question

Step-by-step explanation:

Answer:

This is your answer ☺️☺️☺️

Answer: The point G is G(18,-9)

Step-by-step explanation:

Midpoint:

Write the formula for midpoint of the A(x_1,y_1) and B(x_2,y_2).

[(x_1+x_2)/2,(y_1+y_2)/2]

G(x,y), H(-2,9)

(8,0) =[(x+(-2))/2,(y+9)/2]

(x+(-2))/2 =8

(x+(-2))=16

x-2 =16

x =18

(y+9)/2=0

y+9=0

y=-9

The point G is G(18,-9)

(answer found from user homeworkhelp on mathskey.com)

Answer:

Simplified Expression a ) 2n^2 + 7n - 5,

Simplified Expression b ) 8n^2 - 11n - 10,

When n = 3 part a ) 34,

When n = 2 part a ) 17,

When n = 3 part b ) 29,

When n = 2 part a ) 0

Step-by-step explanation:

Consider the " simplification " process at hand;

\(a ) (5n^2 + 3n -4) + (-3n^2 + 4n -1),\\5n^2+3n-4-3n^2+4n-1,\\5n^2-3n^2+3n+4n-4-1,\\\\Simplified Expression = 2n^2+7n-5\)

\(b ) (7n^2 - 5n - 2) - (-n^2 + 6n + 8),\\7n^2-5n-2+n^2-6n-8,\\\\Simplified Expression = 8n^2-11n-10\)

For each part ( a and b ) I removed the ( ) and grouped like elements to receive the simplified expression;

Value of each polonomial;

\(a ) 2n^2 + 7n - 5,\\2 * ( 3 )^2 + 7 * ( 3 ) - 5,\\34\\\\2 * ( 2 )^2 + 7 * ( 2 ) - 5\\17\)

\(b ) 8n^2 - 11n - 10,\\8 * ( 3 )^2 - 11 * ( 3 ) - 10,\\29\\\\8 * ( 2 )^2 - 11 * ( 2 ) - 10,\\0\)

Each expression was solved through substitution and algebra.

" Simplified " Solution - See in answer above

* I hope the answer wasn't too confusing, for further information look through my response thoroughly

Answer:

P = 98 feet

Step-by-step explanation:

need to find the hypotenuse so we can use the Pythagorean Theorem:

24² + 7² = c²

c² = 576 + 49

c = \(\sqrt{625}\)

c = 25

P = 2(25) + 48

P = 50 + 48

Answer:

Step-by-step explanation:

(1, 4)

(-1, 0), (3, 0)

The coordinate of the turning point is (1,4) and the coordinates of the roots are (-1,0) and (3,0)

This is the vertex of the equation.

The equation is the given as:

y = 3 + 2x - x^2

According to the graph, the vertex is at the coordinate (1,4)

Hence, the coordinate of the turning point is (1,4)

The equation is the given as:

3 + 2x - x^2 = 0

According to the graph, the equation crosses the x-axis at (-1,0) and (3,0)

Hence, the coordinates of the roots are (-1,0) and (3,0)

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The probability of observing 5,002 heads out of 10,000 tosses, assuming a probability of 0.5 for each toss, is calculated using the binomial distribution as P(X = 5,002) = dbinom(5,002, 10,000, 0.5) (rounding to three decimal places). The statement "We meet the mutually exclusive condition since no case influences any other case" is false. The independence of coin tosses does not guarantee that the outcomes are mutually exclusive, as getting a head on one toss does not prevent getting a head on another toss.

To calculate the probability of observing 5,002 heads out of 10,000 tosses, assuming a probability of 0.5 for each toss, we can use the binomial distribution. The probability can be calculated using the dbinom function in R or similar software. Assuming the tosses are independent, the probability is:

P(X = 5,002) = dbinom(5,002, 10,000, 0.5)

False. The statement "We meet the mutually exclusive condition since no case influences any other case" is not necessarily true. The independence of the coin tosses does not automatically guarantee that the outcomes are mutually exclusive. Mutually exclusive events are those that cannot occur at the same time. In this case, getting a head on one toss does not prevent getting a head on another toss, so the outcomes are not mutually exclusive.

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The true proportion of the side lengths of the quadrilaterals is A'B'/AB

From the question, we have the following parameters that can be used in our computation:

Quadrilaterals ABCD and A'B'C'D

These quadrilaterals are similar

So, it means that the corresponding side lengths are proportional

So. we have

Side length = AB

Corresponding side length = A'B'

The true proportion is then represented as

k = Corresponding side length/Side length

Substitute the known values in the above equation, so, we have the following representation

k = A'B'/AB

Hence, the proportion is A'B'/AB

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The surfaces described by the given vector equations are:

1.The surface is a hyperbolic paraboloid.

2.The surface is a part of a cylinder with radius 3 and axis parallel to the y-axis.

3.The surface is a plane parallel to the xy-plane and shifted upwards by 1 unit.

4.The surface is a twisted cylinder along the y-axis.

A vector equation of a surface in three-dimensional space is a function that maps a pair of parameters, say u and v, to a three-dimensional point in space (x, y, z) represented as a vector. The vector equation can be written in the form of r(u, v) = <x(u, v), y(u, v), z(u, v)>.

In general, there are different ways to represent the same surface using vector equations. For example, the surface of a sphere of radius r centered at the origin can be represented by the vector equation r(u, v) = <r sin(u) cos(v), r sin(u) sin(v), r cos(u)>, where u is the polar angle (measured from the positive z-axis) and v is the azimuthal angle (measured from the positive x-axis).

Vector equations can be useful in studying the geometry and properties of surfaces, such as determining their tangent planes, normal vectors, curvature, and surface area. They can also be used to parametrize surfaces for numerical calculations and simulations.

The surfaces described by the given vector equations are:

1.The surface is a hyperbolic paraboloid.

2.The surface is a part of a cylinder with radius 3 and axis parallel to the y-axis.

3.The surface is a plane parallel to the xy-plane and shifted upwards by 1 unit.

4.The surface is a twisted cylinder along the y-axis.

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Answer:

For finding 4 rational numbers between two numbers we just multiply the numerator and denominator 

Rational numbers -1 and -1/2 are -1/4,-1/8,-1/12,-1/16

This means the four rational numbers are -1/4,-1/8,-1/12,-1/16

Answer:

what function

Step-by-step explanation:

the answer is either (2,8) or [2,8}

Answer: 1

\((\frac{x^{a+b} }{x^{c} }) ^{a-b}.(\frac{x^{b+c} }{x^{a} }) ^{b-c} .(\frac{x^{c+a} }{x^{b} })^{c-a}\\\\= \frac{x^{(a+b)(a-b)} }{x^{c(a-b)} }.\frac{x^{(b+c)(b-c)} }{x^{a(b-c)} }.\frac{x^{(c+a)(c-a)} }{x^{b(c-a)} }\\\\=\frac{x^{a^{2}-b^{2} } }{x^{ac-bc} }.\frac{x^{b^{2}-c^{2} } }{x^{ab-ac} }.\frac{x^{c^{2}-a^{2} } }{x^{bc-ab} } \\\\=\frac{x^{a^{2}-b^{2}+b^{2}-c^{2}+c^{2}-a^{2} } }{x^{ac-bc+ab-ac+bc-ab} }\\\\=\frac{x^{0} }{x^{0} }=1\)

Step-by-step explanation:

Answer:

22/1 = x/3

Step By Step:

Hope this helps you out in figuring the answer ;]

Answer: i looked up the table so the equation is... 22/1=x/3

x=66

Step-by-step explanation:

Next time include the table but at least it was online!

How to solve: 22 miles per 1 gallon (unit rate) = _(x/?)_ miles per 3 gallons

Cross multiply: 66=1x

x=66

OR 22*3=66, x=66

a. The probability of selecting a student whose favorite sport is skiing is  0.3142.

b.  The probability of selecting a junior-college student is 0.2844.

c. If the student selected is a four-year-college student, the probability that the student prefers ice skating is 0.3333.

d. If the student selected prefers snowboarding, the probability that the student is in junior college is 0.3223.

e. If a graduate student is selected, the probability that the student prefers skiing or ice skating is 0.6444.

a.

To calculate this probability, we need to divide the number of students who prefer skiing by the total number of students in the sample.

Number of students who prefer skiing = 171

Total number of students in the sample = 545

Probability = Number of students who prefer skiing / Total number of students

Probability = 171 / 545

= 0.3142

b.

To calculate this probability, we need to divide the number of junior-college students by the total number of students in the sample.

Number of junior-college students = 155

Total number of students in the sample = 545

Probability = Number of junior-college students / Total number of students

Probability = 155 / 545 ≈ 0.2844

c.

To calculate this probability, we need to divide the number of four-year-college students who prefer ice skating by the total number of four-year-college students.

Number of four-year-college students who prefer ice skating = 70

Total number of four-year-college students = 210

Probability = Number of four-year-college students who prefer ice skating / Total number of four-year-college students

Probability = 70 / 210 ≈ 0.3333

d.

To calculate this probability, we need to divide the number of junior-college students who prefer snowboarding by the total number of students who prefer snowboarding.

Number of junior-college students who prefer snowboarding = 68

Total number of students who prefer snowboarding = 211

Probability = Number of junior-college students who prefer snowboarding / Total number of students who prefer snowboarding

Probability = 68 / 211

= 0.3223

e.

To calculate this probability, we need to sum the number of graduate students who prefer skiing and the number of graduate students who prefer ice skating, and then divide it by the total number of graduate students.

Number of graduate students who prefer skiing = 59

Number of graduate students who prefer ice skating = 47

Total number of graduate students = 180

Probability = (59 + 47) / 180

= 0.6444

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A survey of 545 college students asked: What is your favorite winter sport? And, what type of college do you attend? The results are summarized below: College Type Favorite Winter Sport Snowboarding Skiing Ice Skating Total Junior College 68 41 46 155 Four-Year College 84 56 70 210

Graduate School 59 74 47 180

Total 211 171 163 545

Using these 545 students as the sample, a student from this study is randomly selected.

a. What is the probability of selecting a student whose favorite sport is skiing? (Round your answer to 4 decimal places.) Probability= b. What is the probability of selecting a junior-college student? (Round your answer to 4 decimal places.) Probability = c. If the student selected is a four-year-college student, what is the probability that the student prefers ice skating? (Round your answer to 4 decimal places.) Probability = d. If the student selected prefers snowboarding, what is the probability that the student is in junior college? Round your answer to 4 decimal places.) Probability = e. If a graduate student is selected, what is the probability that the student prefers skiing or ice skating? Round your answer to 4 decimal places.) Probability =

False , the variance and standard deviation are not measures of central location

Given data ,

The variance and standard deviation are not measures of central location but measures of dispersion or spread of a dataset

Measures of central location include the mean, median, and mode, which represent the typical or central value of a dataset

The variance and standard deviation are measures of dispersion or spread in a dataset. They provide information about how the values in a dataset are spread out around the mean.

In order to understand the variability or dispersion of data points within a dataset, one must take into account both the variance and standard deviation. They provide information on the range of values and aid in calculating how far away from the mean certain data points are. In statistics and data analysis, these metrics are frequently used to comprehend and evaluate the variance of various datasets.

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The $1314^\text{th}$ digit past the decimal point is 2.

To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.

The long division of $\frac{5}{14}$ is as follows:

```

0.35    <-- Quotient

-----

14 | 5.00

   4.2    <-- Subtract: 5 - (14 * 0.3)

   -----

     80   <-- Bring down the 0

     70    <-- Subtract: 80 - (14 * 5)

     -----

     100   <-- Bring down the 0

      98    <-- Subtract: 100 - (14 * 7)

      -----

       20   <-- Bring down the 0

       14    <-- Subtract: 20 - (14 * 1)

       -----

        60   <-- Bring down the 0

        56    <-- Subtract: 60 - (14 * 4)

        -----

         40   <-- Bring down the 0

         28    <-- Subtract: 40 - (14 * 2)

         -----

         120   <-- Bring down the 0

         112    <-- Subtract: 120 - (14 * 8)

         -----

           80   <-- Bring down the 0

           70    <-- Subtract: 80 - (14 * 5)

           -----

           ...

```

We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.

Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.

So, the $1314^\text{th}$ digit past the decimal point is 2.

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Answer: 12-pound bag of cat food

Step-by-step explanation:

12 pounds bag of cat food = $18

15 pounds bag of cat food = $24

Let's find the cost per pound of the 12-pound bag first

Take 18 divided by 12 = $1.50 per pound

Now find the cost per pound of the 15-pound bag

Take 24 divided by 15 = $1.60 per pound

So, buying a 12-pound bag of cat food is better because it is cheaper per pound.

The value of the expression is sin(E[w]) = -1 is larger than E[sin(w)] = 2/π.

We need to find whether E[sin(w)] or sin(E[w]) is larger.

Using Jensen's inequality, which states that for a convex function g, E[g(x)] >= g(E[x]), we can say:

E[sin(w)] = ∫ sin(w) * f(w) dw

Where f(w) is the probability density function of w

Taking g(x) = sin(x), which is a concave function, and using Jensen's inequality, we can say:

sin(E[w]) >= E[sin(w)]

Therefore, sin(E[w]) is larger than E[sin(w)].

Now, let's compute these two numbers:

E[sin(w)] = ∫ sin(w) * f(w) dw = ∫ sin(w) * 1/(2π - π) dw = 1/π * [(-cos(w))]π 2π = (cos(π) - cos(2π))/π = 2/π

sin(E[w]) = sin(E[w]) = sin(3π/2) = -1

Therefore, sin(E[w]) = -1 is larger than E[sin(w)] = 2/π.

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Answer:

A: 6

B: 16

C: 2

D: -12

Step-by-step explanation:

They are asking you to multiply the equations:

(3x^2 + 2x - 3)(2x + 4)

Distribute and you should get:

6x^3 + 16x^2 + 2x - 12

The Coefficients A,B,C, and D are 6, 16, 2, and -12.