Quadrilateral TUVW is a rhombus. What is VW?
U
V
vw=
V
11w
W
w+20
T

Using the given function V(x) = 15,000(0.87)^x , the value of Mr.Dulaney's car 5 years after its purchase will be approximately equal to given option $7500.

A mathematical phrase, rule, or law that establishes the relation between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

A mathematical function is a rule that assigns a unique output, also called the function value, to each input value within a certain set called the domain. The output is determined by the instructions, also called the function rule, that defines the relationship between the input and output values. It can be represented by an equation, such as y = f(x), where x is the input, y is the output, and f is the function symbol. The graph of a function is a set of points, where each input in the domain corresponds to a unique output. It helps to express the relationship between two variables and allows to make predictions and analyze patterns in mathematical problems.

Given,

V(x) = 15,000(0.87)^x where x denotes number of years after its purchase.

So, to find the value of Mr. Dulaney's car 5 years after its purchase,

let x =5

so V(x) = 15,000(0.87)^5 = $7476.31

Which is approximately equal to given option , $7,500

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Eleri wants to be fit for the adventure holiday and to achieve that she runs 2 laps of a running track. Each lap is 400m and she thinks she has run 1km in total. To determine if Eleri is correct, we must first understand the basic units of measurement for distance and how they relate to one another.

A lap of a running track is a distance of 400m. The prefix "kilo" in the unit "kilometer" represents 1000. Therefore, a kilometer is equal to 1000 meters. To convert meters to kilometers, we divide the number of meters by 1000. To convert kilometers to meters, we multiply the number of kilometers by 1000.

To determine the total distance Eleri ran, we must multiply the number of laps by the distance of each lap. 2 laps x 400m per lap = 800m. This is the total distance Eleri ran in meters.

To determine if Eleri ran 1km, we must convert 800m to kilometers. Therefore, to convert meters to kilometers, we divide 800 by 1000. 800m / 1000 = 0.8km.

Therefore, Eleri did not run 1km, she ran 0.8km.

To further demonstrate the accuracy of our calculation, we can use dimensional analysis by using the conversion factor of 1000m = 1km.

800m / (1000m/1km) = 0.8km

This confirms that Eleri ran 0.8km, not 1km.

In conclusion, Eleri is not correct in her assumption that she ran 1km. She actually ran 0.8km which is 800 meters. This was determined by understanding the basic units of measurement for distance, converting the distance from meters to kilometers, and using dimensional analysis to verify our calculations.

Answer:

Step-by-step explanation:

no she is not correct she only ran 0.8 km

As the sample size becomes larger, the sampling distribution of sample mean approaches a normal distribution.

As the sample size becomes larger, the sampling distribution of the sample mean approaches a normal distribution. This is known as the Central Limit Theorem. The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean becomes more and more normal, regardless of the shape of the underlying population distribution. The sample mean is an unbiased estimator of the population mean and it follows a normal distribution when the sample size is large.

The binomial distribution is a probability distribution that describes the number of success in a fixed number of trials, each with the same probability of success. While the binomial distribution is used to model the number of successes in a fixed number of trials, it is not used to model the sample mean.

Therefore, the answer is option (c) normal distribution.

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Answer:

a. The length and width of the smaller wall are 14 feet and 8 feet, respectively.

b. The area of the smaller wall is 14 feet x 8 feet = 112 square feet.

c. The area of the larger wall is 20 feet x 8 feet = 160 square feet.

d. The total area of the four walls in the room is 112 square feet + 112 square feet + 160 square feet + 160 square feet = 544 square feet.

e. To find the cost of painting the room walls with two coats of paint, we need to know the total area of the walls, and the cost of one gallon of paint. We can use the information provided: a gallon of paint covers 350 square feet on average and the cost of one gallon of paint is $36.50.

We can divide the total area of the walls by the coverage of one gallon of paint, then multiply that by the cost of one gallon of paint.

544 square feet / 350 square feet/gallon * $36.50/gallon = $38.34

So the cost of painting the room walls with two coats of paint is $38.34.

The 100W bulb will have a lower brightness than the 60W bulb because the resistance of the 100W bulb is less than that of the 60W bulb, so it will have the lowest voltage drop.

Since the power of a lamp of nominal voltage V can be defined as [tex]\bold{P = \frac{V {}^{2} }{R}}[/tex], where R is the resistance to hot, this means that the resistance of the lamp is inversely proportional to its power, that is, the greater the power of the lamp, the lower its resistance.

Applying Kirchoff's second law to a series circuit with resistors R1 and R2 and power supply E we have:

[tex] \bold{E = I.R1 + I.R2}[/tex]

Since the current I is the same for all elements connected in series. In this expression we see that the smallest resistance will have the smallest voltage drop.

Now, in our circuit with two bulbs in series, the 100W bulb will have less resistance than the 60W bulb, so it will have less voltage drop. As it has a lower voltage drop, the power developed in the 100W lamp will be less than that developed in the 60W lamp and the 100W lamp will have a weaker brightness than the 60W lamp.

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The probability of a “full house” is 6 / 4165.

Probability is a measure of the likelihood of a particular event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain to occur.

For example, the probability of flipping a fair coin and it landing on heads is 0.5, or 50%. The probability of rolling a fair die and getting a 6 is 1/6, or about 16.67%.

A “full house” (3 cards of one kind and 2 cards of another kind)

Since there are 13 sets of each type, we have to select any 2 kinds of it.

The probability becomes =[tex]\frac{2 X 13C2 X4C3X 4C2 }{52 C5}[/tex]

On simplification,

= 3744 / 2598960

= 6 / 4165

=0.00144

So the probability of a “full house” is 0.00144.

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According to the given information the supplementary angle are 132 and 48.

Two angles are referred to as supplementary angles because they combine to generate a linear angle when their total is 180 degrees. When two angles add up to 90 degrees, however, they are considered to be complimentary angles and together they make a right angle.

If the total of two angles is 90 degrees or greater, they are complementary; if the sum is 180 degrees or greater, they are supplementary. Given that they are in the same ratio, we will call one angle 11x whilst the other is 4x.

They add up to [tex]11x+4x=15x={180}^\circ\rightarrow x=12[/tex]

So one angle is [tex]11\cdot12={132}^\circ[/tex]

And the other is [tex]4\cdot12={48}^\circ[/tex]

Check: [tex]132+48=180[/tex]

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The value of c in the quadratic = 1.

From this equation, we can easily see that for this equation to have one possible answer, this equation must be a perfect square trinomial, which results from an equation of the form [tex](x+1)^{2}[/tex].

We also know that [tex]b+\frac{1}{b}[/tex]  is equal to the sum of the roots (since the coefficient of [tex]x^{2} = 1[/tex]) and the product of the roots = c.

We easily know that in a quadratic [tex]ax^{2} +dx+c=0[/tex], if this quadratic is a square, then [tex]\frac{d}{c} = \frac{2\sqrt{c} }{c}[/tex]

[tex]2\sqrt{c} = b + \frac{1}{b}[/tex]

We know that c is a perfect square, so that means [tex]b+\frac{1}{b}[/tex] has to have an integer value, and the only way this is possible is if b = 1.

Therefore, if b = 1,

[tex]2\sqrt{c} = b + \frac{1}{b}\\\sqrt{c} = 1\\c = 1[/tex]

Therefore, the value of c in the quadratic = 1.

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The cost in dollars if a cab ride 49 miles long is $ 110.

The question is not complete, a table of travel costs and distance data should be provided. A table that is similar to the table that should be provided is in the attachment. From the table, it can be seen that if the mileage increases by 5 miles, the cost will increase by $ 12.5. The data graph will be in the form of a straight line.

The equation of the line if two points are known

(y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁)

(c - c₁)/(c₂ - c₁) = (d - d₁)/(d₂ - d₁)

(c - 12.5)/(25 - 12.5) = (d - 5)/(10 - 5)

(c - 12.5)/12.5 = (d - 5)/5

5 × (c - 12.5) = 12.5 × (d - 5)

5c - 62.5 = 12.5d - 125

5c = 12.5d - 125 + 62.5

5c = 12.5d - 62.5

c = 2.5d - 12.5

If a cab ride is 49 miles long,

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the rate of change of height at h = 15cm, 0. 0159 cm/s

What is Rate?

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

Beads are dropped to create a conical pile such that the ratio of its radius to the height of the pile is constant at 2:3.

Volume is increasing at a rate of 5 cm3/s.

The volume of a Cone: 1/3 pi r^2 h

given r/h =2/3

V =0. 0159 cm/s

Hence the rate of change of height at h = 15cm, 0. 0159 cm/s

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Answer:Three functions that are bounded above are y = x^2, y = x^3, y = e^x.

y = x^2 is a parabola that opens upward and has a vertex at the origin (0,0). As x increases or decreases, y will always be positive and increases or decreases accordingly, so the function is bounded above by positive infinity.

y = x^3 is a cubic function that also opens upward. As x increases or decreases, y will always be positive and increases or decreases accordingly, so the function is bounded above by positive infinity.

y = e^x is the exponential function where e is Euler's number (approximately 2.718). As x increases, y will increase towards positive infinity, so the function is bounded above by positive infinity.

Step-by-step explanation:

Answer:

right angle

Step-by-step explanation:

Answer:

its 34

Step-by-step explanation:

Did it yesterday and got it right.

Answer:

Let x be the length of one side of the square field.

Since the field is divided into two squares, the total length of the fencing is 2x + 2x = 4x.

And since the problem states that it takes 406 yards of fencing to enclose the field,

we can set up the equation: 4x = 406.

Solving for x, we get x = 101.5

So the dimensions of the field would be 101.5 yards by 101.5 yards.

Step-by-step explanation:

The given equation rearranged so that the variable q is the independent variable is 12r + 4r = 3q + 7q OR 16r = 10q

From the question, we are to rearrange the given equation so that the variable q is the independent variable

From the given information,

The give equation is

−7q + 12r = 3q − 4r

Add 7q to both sides of the equation

−7q + 7q + 12r = 3q + 7q − 4r

12r = 3q + 7q − 4r

Add 4r to both sides of the equation

12r + 4r = 3q + 7q − 4r + 4r

12r + 4r = 3q + 7q

Simplifying

16r = 10q

The equation rearranged is 12r + 4r = 3q + 7q OR 16r = 10q

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Answer: [tex](0,-9)[/tex]

Step-by-step explanation:

The vector from [tex](-4,2)[/tex] to [tex](3,-4)[/tex] is [tex]\langle 7, -6 \rangle[/tex].

Applying this transformation to [tex](-7, -3)[/tex] yields that the fourth vertex has coordinates [tex](-7+7, -3-6)=(0,-9)[/tex].

It illustrates a line equation in the XY plane whose equation is represented by x=y when x and y really aren't negative.

Using the equal symbol (=) to indicate equivalence, a mathematical equation is a formula that joins two statements. An equation in algebra is a statement of mathematics proving the equality of two mathematical equations. In the formula 3x + 5 = 14, for example, the equal sign places the variables 3x + 5 & 14 apart. The relationship between two words on either side of such a letter is described by a mathematical formula. A single variable, which also serves as the symbol, is frequently present. like in 2x - 4 Equals 2, for instance.

The line passing thru the origins and having an equal tangent is known as an equation of the form =. A line's equation is, in general, an equation with the formula = °.

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The equation to determine the number of hours it will take to fill the pool, given the current level of the pool, the rate at which the pool is being filled, and the pool's capacity can be found using the following steps.

To write an equation that can be used to find the number of hours it will take to fill the pool from its current level, we need to use the following information:

The pool's capacity: 43,000 gallons

The current level of the pool: 20,000 gallons

The rate of filling the pool: 130 gallons per minute

We can start by using the formula:

time = (amount needed to fill)/(rate of filling)

The amount needed to fill the pool is the difference between the pool's capacity and the current level of the pool.

amount needed to fill = 43,000 - 20,000 = 23,000 gallons

Now we can substitute this value in the formula above:

time = (23,000 gallons)/(130 gallons/minute)

To convert the time to hours, we divide the time in minutes by 60

time = (23,000 gallons)/(130 gallons/minute) × (1 hour/60 minutes)

So, the equation that can be used to find h, the number of hours it will take to fill the pool from its current level is:

h = (23,000 gallons) / (130 gallons/minute) × (1 hour/60 minutes)

Note that this equation is not simplified, you can simplify it by canceling out common factors, you'll get:

h = (23000 / 130) × (1/60)

This equation can be used to find the number of hours it will take to fill the pool, given the current level of the pool, the rate at which the pool is being filled, and the pool's capacity.

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Answer (vertex form): y=4(x+2)^2 - 11

Answer (standard form): y=4x^2 + 16x + 5

By applying independent and disjoint events theory, it can be concluded that A and B are neither disjoint nor independent (option D).

In probability, based on the occurrences, there are two types of events: independent and disjoint events.

Now we observe the data given:

p(a) = 0.3

p(b) = 0.2

p(a and b) = 0.4.

First, we check the independence. Here p(a and b) = 0.4. Whereas, if a and b are independent events, then:

p(a and b) = p(a) * p(b)

                = 0.3 * 0.2

                = 0.06

Since the value is different, we can conclude that events A and B are not independent.

Second, we check whether these events are disjoint events. Since the value of p(a and b) is not 0, these events are disjoint events.

Therefore, we can conclude that a and b are neither disjoint nor independent (option D)

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The simplified polynomial is 6w^2 - 18w + 10.

A polynomial is an expression consisting of variables and coefficients and are used to model real-world situations. It is an equation of degree greater than one, where the exponents of the variables can be any non-negative integer. For example, the polynomial equation x2 + 3x + 2 represents a parabola when graphed. Polynomials are used in a variety of fields, such as mathematics and physics.

It is in standard form because it is written as ax^2 + bx + c, where a, b, and c are the coefficients of the terms and x is the variable. The coefficients are in decreasing order of powers of the variable, and there are no fractions or radicals in the equation.

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Answer:

t + c <= 17

Step-by-step explanation:

This inequality states that the total number of tables and chairs sold (t + c) must be less than or equal to 17, in order to satisfy the constraint that the store can ship at most 17 pieces of furniture per day.

The dimensions that will admit the most light are, the breadth of the rectangular window is  [tex]2b = \frac{20+10\pi }{4+3\pi }[/tex], the length of the window is [tex]2l = \frac{40}{4+3\pi }[/tex] and the radius of the semicircular arc is  [tex]l= \frac{20}{4+3\pi }[/tex].

In the given question,

Let the length and breadth of the rectangular part of the window be 2l and 2b respectively. So the radius of the semicircular arc will be l.

The total perimeter of the window will be 1 length of the rectangle, 2 breadths of the rectangle, and the length of the semicircular arc.

l+2b+πl = 10

(1+π)l+2b = 10

[tex]b = \frac{1}{2} [10-(1+\pi )l][/tex]

To admit maximum light through the window implies that the area of the window is maximized.

The area of the window will be:

[tex]A = (2l)(2b)+\frac{\pi l^{2} }{2}[/tex]

[tex]= 4lb+\frac{\pi l^{2} }{2} \\= 2l[10-(1+\pi )l] +\frac{1}{2} \pi l^{2}[/tex]

[tex]= 20l-2l^{2} -2\pi l^{2} +\frac{1}{2} \pi l^{2}[/tex]

[tex]= 20l-2l^{2} - \frac{3}{2} \pi l^{2}[/tex]

For the area to be maximum,

[tex]\frac{dA}{dl} =0\\20 -4l -3\pi l = 0\\l= \frac{20}{4+3\pi }[/tex]

[tex]b = \frac{1}{2} [10-(1+\pi )\frac{20}{4+3\pi }\\b = \frac{10+5\pi }{4+3\pi }[/tex]

Therefore, the breadth of the rectangular window is [tex]2b = \frac{20+10\pi }{4+3\pi }[/tex], the length of the window is [tex]2l = \frac{40}{4+3\pi }[/tex] and the radius of the semicircular arc is [tex]l= \frac{20}{4+3\pi }[/tex].

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The angles and sides are in order from smallest to largest is written as,

For first triangle;

Sides = ZY, XZ, XY

Angles = ∠X, ∠Y, ∠Z

For second triangle;

Sides = MQ, MP, PQ

Angles = ∠P, ∠Q, ∠M

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We know that;

In triangle, The opposite side of large angle is large and opposite angle of a large side is large.

So, By above conclusions we get;

The angles and sides are in order from smallest to largest is written as,

For first triangle;

Sides = ZY, XZ, XY

Angles = ∠X, ∠Y, ∠Z

For second triangle;

Sides = MQ, MP, PQ

Angles = ∠P, ∠Q, ∠M

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A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other

What is an equivalent ratios?

A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.

Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.

Given ratios are 2:1 and 3:1

we can write it as 2/1 and 3/1.

The lcm of 2 and 3 is 6.

Multiply denominator of both ratio with 6, we get

2/6 and 3/6 And we can see both the ratios are not equal.

Hence, there are not equivalent ratios.

4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2

11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)

3:1 and 9:3 are equivalent ratios ------> is true

because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3

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The coordinate point T' the reflection of T over the y-axis is (4, -5).

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given that, the point T is plotted on the coordinate grid.

The coordinate point on the grid is (-4, -5).

The reflection of point (x, y) across the y-axis is (-x, y).

Here, (-4, -5)→(4, -5)

Therefore, the coordinate point T' the reflection of T over the y-axis is (4, -5).

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Steve can select three rock songs, five alternative songs, and six rap songs in 11,250 number of ways.

1. To select three rock songs from a list of five, use the formula for combinations: nCr = 5Cr = 5!/ (3!*2!) = 10

2. To select five alternative songs from a list of six, use the formula for combinations: nCr = 6Cr = 6!/ (5!*1!) = 6

3. To select six rap songs from a list of nine, use the formula for combinations: nCr = 9Cr = 9!/ (6!*3!) = 84

4. To find the total number of selections, multiply the individual combinations: 10 x 6 x 84 = 11,250

Steve can select three rock songs, five alternative songs, and six rap songs in 11,250 number of  ways.

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Answer:

angle 1 = 120

Step-by-step explanation:

5x-5

x=25

5x=125

125-5=120

angle 1 = 120

you can check this by figuring out the second angle:

2x+10

x=25

2x=50

50+10=60

120+60=180  we know that all angles on a straight line add up to 180, so we know they are both correct

Therefore , the solution of the given problem of function comes out to be it is compatible with P(J(y)) = 1/3J(y) +4.

Math is a science that studies numbers, their variants, math and the tissues in the area, shapes, and both their real and possible locations. 'Function' refers to the relationship between a set of inputs, which each have a corresponding output. A function is a relationship between inputs in which each input yields a single variable, distinct output.

Here,

Given:

The quantity of paintings is returned by the function P, which accepts a number of months as an argument.

The function J returns the number of weeks in a year after accepting an undefined parameter.

P(weeks annually) = P(J(y)) seems to be the composites function that will provide the annual number of paintings.

Choice C is compatible with P(J(y)) = 1/3J(y) +4.

Therefore , the solution of the given problem of function comes out to be it is compatible with P(J(y)) = 1/3J(y) +4.

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Variables are the name for the unknown.You must isolate the variable in order to get a solution for it (such as x).

Unknown value.Variables are the name for the unknown.You must isolate the variable in order to get a solution for it (such as x).

The variable can be separated from the equation by performing inverse operations.Adding and multiplying are the opposites of subtracting and dividing, respectively.

Starting with the proportion:

12/? = 4/3

Since it should be equal to 4/3, notice that if we divide both numerator and denominator by 3, then we should get 4 and 3 respectively:

Therefore, ?÷3 is equal to 3.

Which number is equal to 3 when we divide it by 3?

That number is 9. 9÷3=3

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Answer:

can see the y = x + 2 line, and the shaded area is where y is less than or equal to x + 2

Linear Inequality

A Linear Inequality is like a Linear Equation (such as y = 2x+1) ...

... but it will have an Inequality like <, >, ≤, or ≥ instead of an =.