Use the laplace transform to solve the given initial-value problem. y'' − 6y' 13y = 0, y(0) = 0, y'(0) = −9

City B had the highest noon temperature, Interquartile Range, Larger Median temperature while City A had smaller range of temperature.

A box and whisker plot, also known as a box plot, shows a five-number summary of a set of data. The minimum, first quartile, median, third quartile, and maximum are the five-number summary. A box plot is created by drawing a box from the first to third quartiles. At the median, a vertical line runs through the box. The whiskers move from the lowest to the highest quartile.

From the figure:-

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Answer:

(a) B

(b) B

(c) B

(d) B

Step-by-step explanation:

The function to model the water used by the car wash on a shorter day is (C) [tex]4x^{3} +7x^{2} -14x-6[/tex].

To find the function to model the water used by the car wash on a shorter day:

Given that the amount of water used on normal days is given by the equation:

The amount of decrease in water used is modeled by the equation:

To get the function [tex]C(x)[/tex] that models the water used by the car wash on a shorter day you subtract equation (2) from equation (1).

Therefore, the function to model the water used by the car wash on a shorter day is (C) [tex]4x^{3} +7x^{2} -14x-6[/tex].

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The correct question is shown below:

The water usage at a car wash is modeled by the equation w(x) = 5x3 9x2 − 14x 9, where w is the amount of water in cubic feet and x is the number of hours the car wash is open. the owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. the amount of decrease in water used is modeled by d(x) = x3 2x2 15, where d is the amount of water in cubic feet and x is time in hours. write a function, c(x), to model the water used by the car wash on a shorter day.

(A) c(x) = 5x3 7x2 − 14x − 6

(B) c(x) = 4x3 7x2 − 14x 6

(C) c(x) = 4x3 7x2 − 14x − 6

(D) c(x) = 5x3 7x2 − 14x 6

The answer is 4x + 5y.

Here, what needs to be done is to combine like terms.

The greatest force acting on the ball to slow it down is Gravitational force.

When ball is thrown upwards then there will be two forces on the ball opposite to the motion of ball

1. Gravitational force (mg)

2. Air friction or air drag

Both forces are opposite to the motion of the ball and it will cause the decrease in the speed of the ball.

Now here due to less value of drag coefficient on the ball we will say that ball will decrease its speed more due to gravitational force compare to friction force of air.

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Answer:

[tex]\textsf{D.} \quad \begin{cases} y \leq 2x+2 \\ y\geq -\dfrac{1}{2}x \end{cases}[/tex]

Step-by-step explanation:

Both lines in the given system of inequalities are linear equations.

Slope-intercept form of a linear equation:  y = mx + b

(where m is the slope and b is the y-intercept)

Positive slope (m):  as x increases, y increases.

Negative slope (-m):  as x increases, y decreases.

When graphing inequalities:

The inequality represented by the blue line has a positive slope and shading below the line.

⇒ y ≤ mx + b

From inspection of the graph, its y-intercept is 2.

⇒ y ≤ mx + 2

The inequality represented by the yellow line has a negative slope and shading above the line.

⇒ y ≥ -mx + b

From inspection of the graph, it's y-intercept is zero.

⇒ y ≥ -mx

The only pair of inequalities that satisfies the above conditions is:

[tex]\textsf{D.} \quad \begin{cases} y \leq 2x+2 \\ y\geq -\dfrac{1}{2}x \end{cases}[/tex]

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Answer:

Bottom left

Step-by-step explanation:

Since the slope has to be positive it can't be the ones on the right side since both of them are negative. And the bottom left one is rising 3 and running 4. (formula = rise/run). See image.

The total time in seconds the ball will take to travel before returning the ground is 2.25 seconds.

The breaking or breakdown of an entity (such as an integer, a matrices, or a polynomials) into a products of another unit, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring in mathematics. 

Calculation for the time;

Let 't' be the time in second the ball will travel.

Let H(t) be the total height travelled by the ball.

The equation of the height is given as

[tex]H(t)=-16 t^{2}+36 t[/tex]

As soon as the ball will return to the ground the total height will become zero.

So, put equation of height equal to zero.

[tex]-16 t^{2}+36 t=0[/tex]

Factorise the above equation;

[tex]-16 t\left(t-\frac{9}{4}\right)=0[/tex]

Put each value equals to zero to get the value of time.

[tex]\begin{aligned}&t=0 \mathrm{sec} \\&t=9 / 4=2.25 \mathrm{sec}\end{aligned}[/tex]

As, time can not be zero

Therefore, the total time taken by the ball to return to the ground is 2.25 sec.

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Answer:

y = -5/3 - 8

Step-by-step explanation:

We want to write this in the form y = mx + b.  We need to find the m (slope) and the b (y-intercept) ,  Whew, they already gave us the slope, so we are have way there.  I will plug in the x and y that we are given from the point (-6, 8) to solve for b.

y = mx + b

8 = -5/3(-6) + b  Multiply the fraction by -6

8 = 30/3 + b  I can make 6 a fraction by writing it 6/1 and then just multiply straight across.  A negative times a negative is a positive.

8 = 10 + b   30/3 is equal to 10.  Now subtract 10 from both sides to get b

-8 = b

I can now write the equations since I now know m and b.

y = -5/3 + (-8) which is the same as y = -5/3 - 8.  Adding a negative is the same as subtracting a positive.

Answer:

Yes

Step-by-step explanation:

First we need to determine how much money Allen has

2 dollars = 2.00

5 quarters = 5 * .25 = 1.25

2 dimes = 2 * .10 = .20

7 pennies = 7 * .01 = .07

Add this together

2.00 + 1.25+.20+.07 =3.52

3.52 > 3.50

This is more than 3.50 so he has enough money to buy the pencils

Answer:

The amount of unexplained variance in a relationship between two variables is called: coefficient of alienation also called coefficient of nondetermination. A positive correlation between two variables would be represented in a scatterplot as. line sloping upwards. .

Step-by-step explanation:

Let [tex]W[/tex] be the random variable for the winnings from playing the game once.

• There are 4 jacks in the deck, so you draw a jack with probability 4/52 = 1/13. In this case you "win" $1.25 - $1.75 = -$0.50.

• There are 4 queens, with draw probability 4/52 = 1/13 and winnings $3.25 - $1.75 = $1.50.

• There are 4 kings, with draw probability 4/52 = 1/13 and winnings $4.50 - $1.75 = $2.75.

• There are 4 aces, and 3 of these are not of the spade suit, so the probability of drawing any of these is 3/52 and you win $6.50 - $1.75 = $4.75.

• There is only 1 ace of spaces, with draw probability 1/52 and winnings $7.75 - $1.75 = $6.00.

• Adding these up, it follows that the probability of drawing any other card is 1 - (1/13 + 1/13 + 3/52 + 1/52) = 10/13, in which you have the privilege of "winning" -$1.75.

So, the probability mass function for [tex]W[/tex] is

[tex]\mathrm{Pr}(W=w) = \begin{cases} \dfrac1{13} & \text{if } w \in \{-\$0.50, \$1.50, \$2.75\} \\\\ \dfrac3{52} & \text{if } w = \$4.75 \\\\ \dfrac1{52} & \text{if } w = \$6.00 \\\\ \dfrac{10}{13} & \text{if } w = -\$1.75 \\\\ 0 & \text{otherwise} \end{cases}[/tex]

The expected winnings from playing one round of this game are

[tex]\Bbb E[W] = \displaystyle \sum_w w\,\mathrm{Pr}(W=w)[/tex]

[tex]\Bbb E[W] = \dfrac{-\$0.50 + \$1.50 + \$2.75}{13} + \dfrac{3\cdot\$4.75}{52} + \dfrac{\$6.00}{52} + \dfrac{10\cdot(-\$1.75)}{13}[/tex]

[tex]\Bbb E[W] \approx \boxed{-\$0.67}[/tex]

Thus, 2028 needs to be multiplied by 3 to become a perfect square. Therefore, the number 6084 has 3 pairs of equal prime factors . Hence, the smallest number by which 2028 must be multiplied so that the product is a perfect square is 7

1st quartile: 11

median: 38.50000

3rd quartile: 45

Measure descriptive statistics

1st quartile: 11

median: 38.50000

3rd quartile: 45

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I understand that the question you are looking for is :

2 Drag the tiles to the boxes to form correct pairs. Match the values associated with this data set to their correct descriptions.  {6, 47, 49, 15, 43, 41, 7, 36} first quartile 38.5  median 11  third quartile 10.5 the difference of the largest value and the median 45

The variance for the sample is 25

For given question,

We have been given the sample size n = 21

and the sum of squares is SS = 500

We need to find the variance for the sample.

We know that the variance is mathematically represented as,

[tex]\sigma^2=\frac{SS}{n-1}[/tex]

Substituting given values in the above formula,

[tex]\Rightarrow \sigma^2\\\\=\frac{500}{21-1}[/tex]

= 500 / 20

= 25

So, the variance is 25

Therefore, the variance for the sample is 25

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Answer:

Option 2

Step-by-step explanation:

Using the quadrstic formula,

[tex]\tan \theta=\frac{-2 \pm \sqrt{2^2 - 4(\sqrt{3})(-\sqrt{3})}}{2\sqrt{3}} \\ \\ =\frac{-2 \pm 4}{2\sqrt{3}} \\ \\ =\frac{-1 \pm 2}{\sqrt{3}} \\ \\ = -\sqrt{3}, \frac{1}{\sqrt{3}}[/tex]

Case 1

[tex]\tan \theta=-\sqrt{3} \implies \theta=\frac{2\pi}{3}, \frac{5\pi}{3}[/tex]

Case 2

[tex]\tan \theta=\frac{1}{\sqrt{3}} \implies \theta=\frac{\pi}{6}, \frac{7\pi}{6}[/tex]

The theorem that justifies why triangles ABC and DEF are congruent is: HL.

The hypotenuse-leg congruence theorem (HL) states that if two triangles that are right triangles have a pair of congruent hypotenuse and a pair of corresponding congruent legs, then both right triangles are proven to be congruent to each other. This means both right triangles are have the same shape and size.

Given that:

angle ABC = angle DEF = 90° (congruent right angles, this means both triangles are right triangles)

AC = FD (a pair of congruent hypotenuse)

AB = DE (a pair of congruent legs)

Thus, we can conclude that since triangle ABC and triangle DEF have a pair of congruent hypotenuses and a pair of congruent legs, therefore, the two right triangles, triangle ABC and triangle DEF are congruent to each other by the HL congruent theorem.

Thus, the theorem that justifies why both triangles are congruent is: HL.

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The ratio illustrates that the values will be 3146.7945 gram, 9440.3835 gram, and 3968.93 grams.

It should be noted that 1 ounce is equivalent to 28.3495 gram.

Therefore, 111 ounces will be:

= 111 × 28.3495 gram

= 3146.7945 gram

333 ounces will be:

= 333 × 28.3495 gram

= 9440.3835 gram

140 ounces will be:

= 140 × 28.3495 gram

= 3968.93 grams

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Step-by-step explanation:

8x+6y=24

6y=24-8x

y=24/6 - 8/6x

y=4-4/3x

No,the population mean is not equal to 9.2 and the value in t statistic is -1.02.

Given sample size of 49,sample mean of 8.5,standard deviation of 1.5, significance level of 0.01.

We are required to find out whether the population mean is equal to 9.2 and the value of t in test statistic.

We have to first make the hypothesis for this.

[tex]H_{0}[/tex]:μ≠9.2

[tex]H_{1}[/tex]:μ=9.2

We have to use z statistic because the sample size is more than 30.

Z=(X-μ)/σ

We have been given sample mean but we require population mean in the formula so we will use sample mean.

Z=(8.5-9.2)/1.5

=-0.7/1.5

=-0.467

P value of -0.467 is 0.67975.

P value is greater than 0.01 so we will accept the hypothesis means population mean is not equal to 9.2.

t=(X-μ)/s/[tex]\sqrt{n}[/tex]

=(8.5-9.2)/1.5/[tex]\sqrt{49}[/tex]

=-0.7/0.21

=-1.02

Hence it is concluded that no,the population mean is not equal to 9.2 and the value in t statistic is -1.02.

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The value of x in given linear equation is x = 3.

According to the statement

we have given that the equation and we have to find the solution of that equation.

So, For this purpose,

The given equation is :

[tex]\sqrt{ x+1} = \sqrt{ x+6} -1[/tex]

From this equation it is clear that the it is a linear equation.

So, for find the value of x

To solve this equation squaring on both sides then equation become

x+1 = x+6 +1 -2√x+6.

Then

-2√x+6 = -6

then

[tex]\sqrt{x + 6} = 3[/tex]

Now remove the square by S.B.S.

Then the equation become

x +6 = 9

x = 3.

In this equation the value of x is 3.

So, The value of x in given linear equation is x = 3.

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The Surface area of the triangular prism is: 318 km³.

A triangular prism is a solid that has two triangular bases and three rectangular faces.

The surface area of a triangular prism is the sum of the areas of its two triangular bases and three rectangular faces.

The formula for the surface area of a triangular prism = (S1 +S2 + S3)L + bh, where:

Perimeter of the base  = S1 + S2 + S3

Length of the prism = L

2 × Base Area = bh

Given the following:

s1 + s2 + s3 = 7 + 9 + 8 = 24 km

L = 11 km

bh = (9)(6) = 54 km²

Plug in the values

Surface area of the triangular prism = (24)11 + 54

Surface area of the triangular prism = 264 + 54

Surface area of the triangular prism = 318 km³

Thus, the Surface area of the given triangular prism in the diagram above is: 318 km³.

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Answer:

C.) [tex]log_2(\frac{x^3z^2}{y^4})[/tex]

Step-by-step explanation:

To find the answer, you need to simplify the expression. To do so, you must combine the logs. You can combine the logs because they all have the same subscript (2).

[tex]3 log_2x - 4log_2y + 2log_2z[/tex]                           <----- Given expression

[tex]log_2x^3-log_2y^4+log_2z^2[/tex]                            <----- Raise coefficients to variables

[tex]log_2x^3+log_2z^2-log_2y^4[/tex]                            <----- Rearrange

[tex]log_2(x^3z^2)-log_2y^4[/tex]                                    <----- Multiply added logs

[tex]log_2(\frac{x^3z^2}{y^4})[/tex]                                                  <------ Divide subtracted log

Express the multiplication of a logarithm number of an expression as the logarithm of the power of the expression.

Take the product of the arguments

                         [tex]\red{\boxed{\boldsymbol{\sf{\blue{Answer \ \ \longmapsto \ \ Log_{2} \frac{x^{3}z^{2} }{y^{4} } } }}}}[/tex]

Therefore, the correct option is alternative "C".

Answer:

1 + x  meters.

Step-by-step explanation:

A square has 4 equal sides so each side will have a length equal to the square root of the area.

Side length = √(1 + 2x + x^2)

                   = √(1 + x)(1 + x)

                   = 1 + x.

The Expected value of M is 65

The Standard error of M is 5

Given,

The sample score, n = 9

The Standard deviation, σ = 15

Population mean, μ = 65

Then,

The Expected value of M = μ

∴ The Expected value of M = 65

The Standard error of M = σ/[tex]\sqrt{n}[/tex]

                                          [tex]=\frac{15}{\sqrt{9} } \\\\=\frac{15}{3} \\=5[/tex]

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x = 3.5y equation shows the number of teaspoons of sugar, y, needed to make x tarts.

What is the linear equation in two variable?

Any equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero, is called linear equation in two variable.

According to the given question

A recipe require 3.5 teaspoons of sugar to make a tart.

y represents the number of teaspoons of sugar.

x represents the number of tarts.

Now, for x tart 3.5y teaspoons of sugar required.

⇒  x = 3.5y

Hence, the linear equation in two variable that shows the number of teaspoons of sugar y, needed to make x number or tarts is x = 3.5y.

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Function Composition exists when two functions f(x) and g(x) result in another function h(x), such that h(x) = f(g(x)). For function composition h(x) =  f(g(x)), the value of a exist -4.

Function Composition exists when two functions f(x) and g(x) result in another function h(x), such that h(x) = f(g(x)). In other words, put the outcome of one function into the other one.

Here, h(x) = f(g(x))

which means, h(x) = f(x³+ a)

[tex]$h(x) = \sqrt{x^3+a+2}[/tex]

[tex]$\sqrt{x^3-2} = \sqrt{x^3+a+2}[/tex]

To estimate the value of a, we separate equal terms:

1) Both are squared, so we can "eliminate" the square;

2) x³ = x³

3) -2 = a+2

a = -4

For function composition h(x) =  f(g(x)), the value of a exist -4.

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Step-by-step explanation:

I am not sure I understand your question (grammatically).

percentages are like any other numbers. they can be added, divided, ...

so, 100% or simply 100 : 100/4 = 25.

so, 4×25 = 100.

and 4×25% = 100%

I am really not sure if this is your question, but it fits to your table with 4 entries and 100% as result.

Answer:

This study uses random sampling

This study uses a control group

This study uses a repeated measures design ​

Answer:

this study uses random sampling

this study uses a control group

this study uses a repeated measures design ​

Step-by-step explanation:

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