Does 4x - 8 = 3x +13 have one solution, no solution or infinite solutions

The function is d(t) = 6cos(πt/6 + π/4) + 6. It models the water depth in meters as a cosine function of time after midnight.

The cosine function models the water depth d(t) in meters as a function of time t (in hours after midnight) on a particular day. The amplitude of the cosine curve is the difference between the high and low tide water depths, which is 6 m. The period of the cosine curve is the same as the natural oscillation period, which is 12 hours. The phase shift is π/4, as the high tide occurred at 4:45 a.m. Therefore, the function is d(t) = 6cos(πt/6 + π/4) + 6.

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If A1 and A2, are mutually exclusive and exhaustive with P(A1)>0 and P(A2) >0, and B is an event in S. then P(B) = P(A1 ∩B) + P(A2∩ B). [TRUE]

The sets A and B are the sets of all objects that are members of set A and members of set B. In written notation form:

A ∩ B = {x | x ∈ A and x ∈ B}

Here's how to determine the separation of two sets:

One set which is another subset if A ⊆ B then A ∩ B = A and vice versa.

The sets are equal if A = B, then A ∩ B = (A = B).

Sets are mutually exclusive if A // B, then A ∩ B = … and vice versa.

The sets are not mutually exclusive.

The union of sets A and B is the set of all objects that are members of set A or members of set B. In written notation form:

A ∪ B = {x | x ∈ A or x ∈ B}

Here's how to determine the union of two sets:

A set that is a set in other parts if A ⊆ B, then A ∪ B = B and vice versa.

The set is equal if A = B then A ∪ B = (A = B).

Sets are mutually exclusive if A // B, then A ∪ B = {x | x ∈ A or x ∈ B} and vice versa.

The sets are not mutually exclusive if A ⊃⊂ B, then A ∪ B = {x | x ∈ A, x ∈ B or x ∈ (A ∩ B)}.

Your question is incomplete but most probably your full question was:

If A, and A, are mutually exclusive and exhaustive with P(A)>and P(A2) >0, and B is an event in s. then P(B) = P(ALB) + P(ANB). True False

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There are two phrases for how many sweet Sue and Tony have: 13-x and

Equivalent refers to the mathematical notion of equality between several terms and expressions with a comparable value.

Equivalent vs. Equal. Equivalent and equal are distinct terms in mathematics.

Equal means identical in every respect, as opposed to equivalent, which is similar but not the same.

18 + x/ 2 is the equivalent.

Sue has 18 delicious.

Tony has 18 delicious.

Sue gives Tony some candy. Sue Sweet is going to

18 - x Sue consumes 5 candies, thus his sweet will be

18 - 5 - x = 13 - x

Sue gave Tony x candy to take. His sweetness will

18 + x

Tony consumed half of his candy. His final treat will be

18 + x / 2

The phrase for Sue candies is 13 - x.

18 + x / 2 is the equation for Tony Sweets.

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The height of the cube brick is 7 units and the volume is equal to 343 unit³

The volume of a cube is defined as the total number of cubic units occupied by the cube. The formula is given as V = a³ where "a" is the length of edge or sides.

The length of an edge for the cube brick is 7 units which implies the height represented by h is also 7 units and the volume is calculated as follows:

volume of cube brick = 7 units × 7 units × 7 units

volume of cube brick = 343 units ³

Therefore, the height of the cube brick is 7 units and the volume is equal to 343 unit³

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The graph of the polynomial function g(x) = -2x² - 5x³ + 2x² + 7x + 1 is plotted and attached

The zeros are (-1.10, 0), (-0.15, 0) and (1.25, 0) to the nearest hundredth)

Using a graph is potted by written the equation on the plotter , the plotter interprets the equation and presents the graph

Zero of polynomial equation is the point where the y is zero this is solved by equating the polynomial function to zero

From the graph, the zeros are identified by the points where the graph cuts the the x axis.

Examining the graph of the function g(x) = -2x² - 5x³ + 2x² + 7x + 1 the zeros are

(-1.104, 0), (-0.145, 0) and (1.249, 0)

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Janet's total tax allowances for the year are $27,200.

The first step is to convert the monthly gross salary to the annual gross salary by multiplying it by 12.

The insurance allowance is computed by applying the rate to the annual gross salary.

The personal and insurance allowances are added to determine the total tax allowances.

Generally, tax allowances reduce the taxpayer's taxable income.

Gross salary per month = $24,000

Annual gross salary = $288,000 ($24,000 x 12)

Personal allowances per year = $20,000

National insurance = 2¹/₂%

= $7,200 ($288,000 x 2¹/₂%)

Total allowances for the year = $27,200 ($20,000 + $7,200)

Thus, Janet is entitled to a total tax allowance of $27,200 for the year.

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Average rate of change of the function F (x ) = 9/ -2 (x)-7. Average rate is -3, 9

The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.

Divide the change in y-values by the change in x-values to determine the average rate of change. In order to determine changes in measurable parameters like average speed or average velocity, finding the average rate of change is extremely helpful.

f (x ) = -2

f (x) = 9/ -2 (-2)-7

      = 9 / 4 - 7

      =9 / -3

      = -3

f (x ) = -4

f (x) = 9/ -2 (4)-7

      = 9 / 8 - 7

      =9 / 1

      = 9

Average rate is -3, 9

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In a relay race each friend run a distance of 0.52 miles.

The distance of the race divided by the runners' times will give you their average velocities.

We are given that

Total distance covered in a race = 3.12 miles

Total number of persons = 6

Each person runs equal parts of the race.

We have to find the miles run by each person.

To find the distance covered by each person we will divide the total distance by total number of persons who took part in a race.

Each person runs = Total distance/ Total number of persons

Each person runs= 3.12 / 6 miles

Each person runs = 0.52 miles

Hence, each person runs 0.52 miles.

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Answer:

N(-21,-20)

Step-by-step explanation:

We can apply midpoint formula to solve for endpoint (N):

[tex]\displaystyle{\text{Midpoint}= \left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)}[/tex]

Let [tex]\displaystyle{x_1 = 1}[/tex], [tex]\displaystyle{y_1 = 12}[/tex] and Midpoint = (-10,-4). Therefore:

[tex]\displaystyle{\left(-10,-4\right)= \left(\dfrac{1+x_2}{2}, \dfrac{12+y_2}{2}\right)}[/tex]

Solve x with -10 and y with -4:

[tex]\displaystyle{\text{N}\left(x_2,y_2\right) = \left(\dfrac{1+x_2}{2}=-10, \dfrac{12+y_2}{2}=-4\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right) = \left(1+x_2=-20, 12+y_2=-8\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right) = \left(x_2=-20-1, y_2=-8-12\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right) = \left(x_2=-21, y_2=-20\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right)=\left(-21,-20\right)}[/tex]

Therefore, the coordinate of N is (-21,-20)

The required distance travelled by Benita is calculated to be 11/6 miles when the relation between the distances travelled by Karis and Benita is given.

This problem is related to the chapter fractions. The relation between the distances travelled by both the people is given, so that we can calculate the actual distance travelled by the second person.

Karis ran 3 2/3 miles on Monday.

It is said that Benita ran half of the distance ran by Karis.

So, the distance ran by Benita would be,

⇒ 3 2/3 × 1/2

⇒ 11/3 × 1/2

⇒ 11/6 miles

Thus, the distance travelled by Benita is calculated to be 11/6 miles when the relation between the distances travelled by Karis and Benita is given.

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Answer:

No, they are not proportional

Step-by-step explanation

50*2=100

32*2=64, not 60

If the lamp is 3.6 m above the ground, the length of her shadow is 1.2 m.

In algebra proportionality is equality between two ratios. In the mathematical expression a/b = c/d, a and b are in the same proportion as c and d.

Height of the girl = 0.9 m.

Height of the lamp = 3.6 m.

Distance between the lamp and the girl = 4.8 m.

Let the length of her shadow = x m.

From proportionality relation:

3.6 : 4.8 = 0.9 : x

3.6/4.8 = 0.9/x

3.6x = 4.8 × 0.9

x  = (4.8 × 0.9) ÷ 3.6

x = 1.2

Hence, the length of her shadow is 1.2 m.

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Graphs (C) and (D) having median value larger than the mean value.

What Is a Histogram?

A histogram is a graphical representation of data points organized into user-specified ranges.

In graphs (C) and (D), the median value is larger than the mean value as the distribution is skewed to the left which means most values are large but there are few exceptionally small values because of which means shift towards the left and thus the mean is less than the median, or we can say that the median value is larger that the mean value.

So, graphs (C) and (D) having median value larger than the mean value.

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The slope of a line perpendicular to the line is 5/4

A straight line of the form

y = mx + c

has its slope as 'm'

It is constant for a line. The more the slope is, the steeper the line is.

Sign convention takes bottom left to top right going line as positive sloped. And that line which goes from bottom right to top left is taken to have negative slope. Horizontal line has 0 slope and vertical line has infinite slope, as it is now at maximum steepness.

If two lines are perpendicular, their slopes are negative reciprocals, which means that their product is -1

Given;

4x+5y=35

We can write the equation as;

4*x + 5*y - 35  = 0

5*y  = - 4*x  + 35     or    

y  = -(4/5)*x  + 35    

m= -4/5

So, now the slope of this line is -4/5 and line perpendicular slope will be 5/4

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A graph of the solution to this inequality a > -3 is shown on the number line attached below.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

In this exercise, we would use an online graphing calculator to plot the given inequality a > -3 as shown on the number line (graph) attached below.

In conclusion, the circle on the number line (graph) is open because of the greater than (>) symbol and it increases to the right of the number line.

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Complete Question:

Find the solution to this inequality a > –3.

hmmm proofs like these can be a bit circular kinda, let's do some rigamarole on the equations and we'll see if that works for a definition

[tex]\stackrel{\theta \textit{ is always in radian unit}~\hfill }{s=r\theta\implies \cfrac{s}{\theta }=r \hspace{5em}v=\cfrac{s}{t}\implies t=\cfrac{s}{v}\hspace{5em}\omega=\frac{\theta }{t}} \\\\[-0.35em] ~\dotfill\\\\ \omega=\cfrac{\theta }{t}\implies \omega=\cfrac{\theta }{~~ \frac{ s}{v } ~~}\implies \omega=\cfrac{\theta }{1}\cdot \cfrac{v}{s}\implies \omega=\cfrac{\theta v}{s}\implies s\omega=\theta v \\\\\\ \cfrac{s\omega}{\theta }=v\implies \cfrac{s}{\theta }\cdot \omega=v\implies \boxed{r\cdot \omega=v}[/tex]

Radon-222 was initially present in a sample of 3.82 mg. Only 0.375 mg of the radon-222 in the sample were still present after 11.46 days, after which three half-lives had gone.

As per the data given in the above question are as bellow,

A material has a half-life when it takes a particular length of time for half of it to disappear or change.

11.46 days have 3 half lives because 11.46 x 3.82 Equals 3.

We thus split the 3 mg sample in half three times.

3 ÷ 2 = 1.5

1.5 ÷ 2 = 0.75

0.75 ÷ 2 = 0.375

After 11.46 days, there will only be 0.375mg of radon-222 left.

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Answer:

b/w 19 & 55

Step-by-step explanation:

average of four equally weighted 100-point tests,

mark has scored 90, 86, and 85 on the first three.

C average = 70 and 79

90+86+85+x = 4*70 = 280, so x=19

90+86+85+x = 4*79 = 316, so x=55

Jetlag is a condition associated with crossing multiple time zones is experienced by sports tourists from Argentina travelling to Japan.

People who travel quickly between different time zones may experience jet lag, a sleep disorder.

Jet lag causes sporadic sleep problems. It occurs when signals from a new time zone cause the body's biological clock to become out of sync. Feeding times and light exposure are two examples of cues.

The term "jet lag" originated from the fact that it was uncommon to travel far and quickly enough to cause desynchronosis prior to the development of passenger jet aircraft. Propeller-driven travel was slower and covered less ground than jet flights, so it had a negligible impact on the issue.

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The equation of the graphed function for this problem is given as follows:

y = x³ - 6x² - 7x - 6.

The function for this problem is obtained using the Factor Theorem, as a product of the linear factors of the function.

The zeros of the function are given as follows:

Hence the linear factors are given as follows:

Then the function is given as follows:

y = a(x - 1)(x - 2)(x - 3).

In which a is the leading coefficient.

The y-intercept is at y = -6, hence the leading coefficient is given as follows:

-6a = -6

a = 1.

Hence the function is:

y = (x² - 3x + 2)(x - 3)

y = x³ - 6x² - 7x - 6.

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Answer:

the twelve value will produce -3

Step-by-step explanation:

T(12) = 45 - 4(12)

T(12) = 45 - 48

T(12) = -3

Step-by-step explanation:

To find the factor by which the dimensions of cylinder A were multiplied to produce the corresponding dimensions of cylinder B, we can use the fact that they are similar solids. This means that the ratio of corresponding dimensions is the same for both cylinders.

Since the base of cylinder A has a circumference of 4π units and the base of cylinder B has an area of 9π units, we can use these measurements to find the ratio of the radii of the two cylinders.

The circumference of a circle is given by 2πr, where r is the radius, so the radius of cylinder A is 4π/2π = 2 units.

The area of a circle is given by πr^2, so the radius of cylinder B is sqrt(9π/π) = sqrt(9) = 3 units.

The ratio of the radius of cylinder A to cylinder B is 2/3. Since similar solids have the same ratio for all dimensions, this means that the dimensions of cylinder A were multiplied by a factor of 2/3 to produce the corresponding dimensions of cylinder B.

Answer: 10. 3

Step-by-step explanation: 4x3=12, ad 3x3 is 9 so all the sides of the triangle are multiplied by 3

The quotient of 6y^4 + 10y³ - 8y² by 2y is given as follows:

6y³ + 10y² - 4y.

The dividend is given as follows:

6y^4 + 10y³ - 8y²

The common factors are given as follows:

Hence the dividend can be simplified as follows:

2y²(6y² + 10y - 4).

Simplifying by 2y, the result of the quotient is given as follows:

y(6y² + 10y - 4) = 6y³ + 10y² - 4y.

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By applying the Golden Ratio rule, the width of the painting is equal to 12.5 inches.

In Mathematics, a proportion simply refers to an equation which is typically used to represent the equality of two (2) ratios.

This ultimately implies that, proportions is a mathematical operation which can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

By applying the Golden Ratio rule, the width of the painting can be calculated as follows;

20/x = 8/5

Cross-multiplying, we have the following:

8x = 20 × 5

8x = 100

x = 100/8

x = 12.5 inches.

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Answer: The answer is 5

Step-by-step explanation:

-3-(-8)

-3+8

5

Answer: 5

Step-by-step explanation:

First the negative 3 adds to 8. Because if you see “- -“ it will be +. So we just have -3 + 8 = 5

The price of the delivery is $15 and the mileage is 40.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given that the rosebud flower shop has a basic delivery charge of 5$ plus a rate of 25 cents per mile.

Total cost = basic delivery fee + (rate per mile x number of miles)

=$5 + (0.25 x m)

= $5 + 0.25m

The linear expression that represents the total delivery cost from Rosebud Flower Shop ;

Total cost = basic delivery fee + (rate per mile x number of miles)

=$7 + (0.2 x m)

$7 + 0.2m

When the costs are the same, the two expressions would be;

$7 + 0.2m = $5 + 0.25m

$7 - $5 = 0.25m - 0.20

$2 = 0.05m

m = 2 / 0.05

m = 40

Price = $7 + 0.2(40)

$7 + 8 = $15

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In the essay “A Modest Proposal”, The author includes the quote to give the reader an objective summary of how dangerous the conditions were at Mauna Loa.

Jonathan Swift, a satirist, suggested jokingly in an essay titled "A Modest Proposal" from 1729 that the people of Ireland sell their children as food. A radical or shocking notion is frequently introduced in an ironic way using the term a modest suggestion.

Swift's essay, which is hailed as a masterwork of irony, is officially titled "A Modest Proposal for Preventing the Children of the Poor People in Ireland from Being a Burden to Their Parents or Country, and for Making Them Beneficial to Their Public."

When a proposal takes the form of an essay, it typically proposes a fix for a social or political issue. The adjective "modest" denotes reason or modesty. Because the idea is genuinely absurd, it is humorously used in the title of "A Modest Proposal."

A modest proposal is frequently used in jest to make a point by taking something to its logical conclusion, which highlights a problem. Swift's article, which at the time caused controversy, has since become a satirical mainstay and has influenced a lot of authors.

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Answer:

first hand account

Step-by-step explanation:

I got a 100 on the test