omg please help me asap!!!!! thank you! *will gibe brainliest*

A bus traveling at an average rate of 50 kilometers per hour made the trip to town in 6 hours. If it had traveled at 45 kilometers per hour, how many more minutes would it have taken to make the trip?

(The formula for distance problems is: distance = rate × time or

d = r × t)

Answer:

The vehicle should start with \((100\, e^{ke} - 100)\; {\rm kg}\) of fuel and drive at a speed of \((1/k)\; {\rm km \cdot hr^{-1}}\).

Step-by-step explanation:

Let \(t\; {\rm hr}\) denote the number of hours after the vehicle started. As in the question, let the amount of fuel currently on this vehicle be \(x\; {\rm kg}\). The question states that the vehicle consumes fuel at a rate (\(dx/dt\)) of \(((100 + x) / 100)\, e^{kv}\). In other words:

\(\displaystyle \frac{dx}{dt} = -\frac{100 + x}{100}\, e^{k\, v}\).

Note the minus sign in front of the right-hand side. The amount of fuel on this vehicle decreases over time. Hence, the rate of change in \(x\) should be negative.

This equation is a separable ordinary differential equation. The variables are \(x\) and \(t\). Solve this ODE to find an expression of \(x\!\) (fuel in the vehicle) in terms of \(t\!\) (time.) Follow these steps:

Rearrange this equation such that all \(x\) and \(dx\) are are on the same side of the equation, while \(t\) and \(dt\) on all on the other side.

\(\displaystyle \frac{dx}{100 + x} = -\frac{e^{k\, v}\, dt}{100}\).

Integrate both sides, and the equality should still hold. Note that \(k\) and \(v\) are considered as constants. Be sure to include the constant of integration \(C\) on one side of the equation.

\(\displaystyle \int \frac{dx}{100 + x} = -\frac{e^{k\, v}}{100}\int dt\).

\(\displaystyle \ln | 100 + x | = -\frac{(e^{k\, v})\, t}{100} + C\).

Let \(x_{0}\) denote the initial amount of fuel on this vehicle (i.e., the value of \(x\) when \(t = 0\)). The constant of integration \(C\) should ensure that \(x = x_{0}\) when \(t = 0\). Thus:

\(\displaystyle \ln | 100 + x_{0} | = C\).

Hence, the value of the constant of integration should be \(\ln | 100 + x_{0} |\). Therefore:

\(\displaystyle \ln | 100 + x | = -\frac{(e^{k\, v})\, t}{100} + \ln | 100 + x_{0}|\).

Since the speed of the vehicle is constant at \(v\; {\rm km\cdot hr^{-1}}\), the time required to travel \(100\; {\rm km}\) would be \((100 / v)\; {\rm hr}\).

For optimal use of the fuel, the vehicle should have exactly \(x = 0\) fuel when the destination is reached. Therefore, \(x = 0\) at \(t = 100 / v\). Hence:

\(\displaystyle \ln | 100 | = -\frac{(e^{k\, v})\, (100 / v)}{100} + \ln | 100 + x_{0}|\).

\(\displaystyle \ln | 100 | = -\frac{e^{k\, v}}{v} + \ln | 100 + x_{0}|\).

Notice that \(\ln|100 + x_{0}|\) is monotone increasing with respect to \(x_{0}\) as long as \(100 + x_{0} > 0\). Thus, given that \(x_{0} > 0\), \(x_{0}\!\) would be minimized if and only if the surrogate \(\ln|100 + x_{0}|\!\) is minimized.

While the goal is to find the \(v\) that minimize \(x_{0}\!\), finding the \(v\!\) that minimizes \(\ln|100 + x_{0}|\) would achieve the same purpose.

\(\displaystyle \ln | 100 + x_{0}| = \ln | 100 | + \frac{e^{k\, v}}{v}}\).

The \(\texttt{RHS}\) of this equation is indeed convex with respect to \(v\) (\(v > 0\).) Thus, the \(\texttt{RHS}\!\) could be minimized by setting the first derivative with respect to \(v\) to \(0\).

Differentiate the right hand side with respect to \(v\):

\(\begin{aligned} & \frac{d}{dv}\left[\frac{e^{k\, v}}{v}\right] \\ =\; & \frac{k\, e^{k\, v}}{v} - \frac{e^{k\, v}}{v^{2}}\\ =\; & \frac{(k\, v - 1)\, e^{k\, v}}{v^{2}}\end{aligned}\).

Setting this first derivative to \(0\) and solving for \(v\) gives:

\(k\,v - 1 = 0\).

\(v = (1/k)\).

Therefore, the amount of fuel required for this trip is minimized when \(v = (1/k)\; {\rm km \cdot hr^{-1}}\).

Substitute \(v\) back and solve for \(x_{0}\) (initial amount of fuel on the vehicle.)

\(\displaystyle \ln | 100 + x_{0}| = \ln | 100 | + \frac{e^{k\, (1/k)}}{(1/k)}}\).

\(\displaystyle \ln | 100 + x_{0}| = \ln | 100 | + k\, e\).

\(e^{\ln| 100 + x_{0}|} = e^{\ln|100| + k\, e}\).

\(e^{\ln| 100 + x_{0}|} = e^{\ln|100|}\, e^{k\, e}\).

\(100 + x_{0} = 100\, e^{k\, e}\).

\(x_{0} = 100\, e^{k\, e} - 100\).

In other words, the initial amount of fuel on the vehicle should be \((100\, e^{k\, e} - 100)\; {\rm kg}\).

The standard form of the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3) is (2x - y = -1)

To determine the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3), we can follow these steps:

1. Obtain the slope of the provided line.

To do this, we rearrange the equation (3x + 6y = 5) into slope-intercept form (y = mx + b):

6y = -3x + 5

y =\(-\frac{1}{2}x + \frac{5}{6}\)

The slope of the line is the coefficient of x, which is \(\(-\frac{1}{2}\)\).

2. Determine the slope of the line perpendicular to the provided line.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the provided line.

So, the slope of the perpendicular line is \(\(\frac{2}{1}\)\) or simply 2.

3. Use the slope and the provided point to obtain the equation of the perpendicular line.

We can use the point-slope form of a line to determine the equation:

y - y1 = m(x - x1)

where x1, y1 is the provided point and m is the slope.

Substituting the provided point (1, 3) and the slope 2 into the equation, we have:

y - 3 = 2(x - 1)

4. Convert the equation to standard form.

To convert the equation to standard form, we expand the expression:

y - 3 = 2x - 2

2x - y = -1

Rearranging the equation in the form (Ax + By = C), where A, B, and C are constants, we obtain the standard form:

2x - y = -1

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Answer: -6?

Step-by-step explanation:

The height of the free-surface above the base in the conical tank, when 1 liter of water is poured into it, is approximately 3.18 cm.

To find the height of the free-surface above the base, we need to calculate the volume of the conical tank and then determine the corresponding height for a volume of 1 liter.

The volume of a cone is given by the formula V = (1/3)πr²h, where V is the volume, π is a mathematical constant (approximately 3.14159), r is the radius of the base, and h is the height of the cone.

Given that the base diameter is 20 cm, the radius (r) can be calculated as half the diameter, which is 10 cm or 0.1 meters. The height of the cone is given as 20 cm or 0.2 meters.

Substituting these values into the volume formula, we have V = (1/3) * 3.14159 * \((0.1)^2\) * 0.2 = 0.00418879 cubic meters.

Since 1 liter is equal to 0.001 cubic meters, we can calculate the height (h') for a volume of 1 liter: 0.001 = (1/3) * 3.14159 *\((0.1)^2\) * h'.

Simplifying the equation, we find h' = 0.001 / (0.00418879) ≈ 0.239 cm.

However, this is the height from the apex of the cone. To find the height of the free-surface above the base, we subtract the height of the apex from the total height of the cone: 0.2 - 0.239 ≈ 0.03 cm.

Therefore, the height of the free-surface above the base, when 1 liter of water is poured into the conical tank, is approximately 3.18 cm.

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Answer:

Step-by-step explanation:

The position formula for this is actually

\(s(t)=-16t^2+64\)

It says, in not so may words, that the object was dropped under the influence of gravity from a height of 64 feet. When it hits, the ground, it will not be above ground at all anymore...it will be ON the ground and have a height of 0. Therefore, if we set the position function equal to 0 and solve for t, we are finding out how long it will take for the object to hit the ground.

\(0=-16t^2+64\) and

\(16t^2=64\) and

\(t^2=4\) and

t = 2

It takes 2 seconds for the object to hit the ground from 64 feet up.

Both you and your neighbor drive approximately 8,400 miles on highways per year. This is calculated by multiplying the total annual mileage of 12,000 miles by the percentage of highway driving, which is 70%.

To calculate the number of miles driven on highways for both you and your neighbor, follow these steps:

Step 1: Calculate 70% of 12,000 miles to find the number of miles driven on highways for each person.

70% of 12,000 miles = 0.70 × 12,000 = 8,400 miles

Step 2: Explain the result.

Both you and your neighbor drive approximately 8,400 miles on highways each year since 70% of their total annual mileage (12,000 miles) is on highways.

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--The given question is incomplete, the complete question is given below " If both the neighbor and you drive around 12,000 miles per year and drive 70% of their miles on highways, calculate the number of miles driven on highways? Explain your result."--

The probability is approximately 0.0682 or 6.82%.

To calculate the probability that the three marbles selected will be the same color, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes = C(12, 3) = 220

(Here, C(n, r) represents the combination of n objects taken r at a time.)

Number of favorable outcomes:

If we select 3 blue marbles, there are C(5, 3) = 10 ways to choose them.

If we select 3 white marbles, there are C(4, 3) = 4 ways to choose them.

If we select 3 red marbles, there are C(3, 3) = 1 way to choose them.

So, the total number of favorable outcomes is 10 + 4 + 1 = 15.

Therefore, the probability that the marbles selected will be the same color is:

P(Same color) = favorable outcomes / total outcomes

= 15 / 220

= 3 / 44

≈ 0.0682 (rounded to four decimal places)

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Answer:

x = 25

Step-by-step explanation:

2x + 4 + x + 11 = 90, combine like terms

3x + 15 = 90, subtract 15 from both sides

3x = 75, divide by 3

x = 25, you have your answer!

The boy has a choice from among 2•3•8•2 = 96 outfits.

Answer:

check online for more information

The volume of the cone made by rotating this triangle is  5303.57

As isosceles triangle has a base of 15 ft and an altitude of 30 ft

We need to find the volume of the cone made by rotating this triangle

If we rotate

we get a cone of radius of 15/2 = 7.5

we get a cone of height of 30

The area of cone takes up on a three-dimensional plane is known as its volume. A cone's base is round, hence it is formed of a radius and a diameter. The highest point of the cone, which is naturally at the bottom when it comes to ice cream, may then be reached from the center of the base. This point is where the height of the cone is determined.

Volume of the cone is given by the formula πr²h

= 3.14 x (7.5)² x 30

= 5303.57

Therefore, the volume of the cone made by rotating this triangle is  5303.57

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Answer:

1,227

Step-by-step explanation:

3,000 divided by 3 is 1,000

600 divided by 3 is 200

80 divided by 3 is 26 r2

1 + r2 =3

and 3 divided by 3 is 1

1,000 + 200 + 26 + 1 = 1,227

Answer:

The value of 7 in 82.76 is 7 tenths.

Step-by-step explanation:

In the place value system, after the decimal point, its tenths, hundredths, and so on. 7 is in the tenths place, and makes 7 tenths.

Hoped this helped!

If a logical vector z has at least one entry TRUE, the function all(!z) will always be false.

If a logical vector contains only TRUE items, the all() method returns FALSE; otherwise, it returns TRUE.

The any() function, on the other hand, gives a result of TRUE if a logical vector has at least one element that is TRUE and FALSE otherwise.

any(z) will always be TRUE if z contains at least one TRUE element since there is at least one TRUE element. On the other hand, depending on whether all of the components of z are TRUE, all(z) may or may not be TRUE.

any(!z) will always return FALSE since if z has at least one TRUE element, then!z must include at least one FALSE element.

Additionally, all(!z) will always return FALSE if any element is FALSE since if z has at least one TRUE element, then!z must include at least one FALSE element.

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Kloe can make 4 flower arrangement

The number of flowers in each flower arrangement is 6 sun flowers, 4 roses and 12 white carnations.

The number of flower arrangements can be calculated as follows;

The first step is to calculate the HCF between the three numbers

24= 6 × 4

16= 4 × 4

48= 12 × 4

The HCF is 4

Hence the number of flower arrangement is 4  and the number of flowers in each flower arrangement is 6 sun flowers, 4 roses and 12 white carnations

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The original data evaluates to option d) [10, 15, 20, 30] because the statement `data.insert(1, 15)` inserts the value 15 at index 1, shifting the remaining elements accordingly. The correct option is (D).

When the `insert()` method is called on a list, it takes two arguments: the index at which the new element should be inserted and the value of the new element.

In this case, the index is 1, which means the new element will be inserted at the second position in the list, shifting the existing elements to the right.

So, after the insertion, the element 15 is placed at index 1, and the original elements 10, 20, and 30 are shifted to indices 2, 3, and 4 respectively. The resulting list becomes [10, 15, 20, 30].

Therefore, the correct answer is d) [10, 15, 20, 30].

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answer 0.0227014756

Step-by-step explanation:

or if you meant 312.775/7.1 it's 44.0528169

la literatura es una forma de arte que desafía los límites del lenguaje y que nos invita a descubrir nuevas formas de entender y de ver el mundo.

La literatura se define como un conjunto de obras escritas que emplean una serie de técnicas y recursos lingüísticos para crear un universo imaginario y comunicar ideas y emociones al lector.

Una de estas técnicas consiste en la violación organizada del lenguaje ordinario, lo que implica una ruptura con las normas y convenciones lingüísticas establecidas para dar lugar a una expresión más creativa y original.

Esta violencia organizada del lenguaje permite a los escritores experimentar con la forma y el contenido de sus obras, creando así una literatura rica y diversa que refleja las distintas visiones del mundo y de la vida de los autores.

En definitiva, la literatura es una forma de arte que desafía los límites del lenguaje y que nos invita a descubrir nuevas formas de entender y de ver el mundo.

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Answer:

1. D) Both b) and c)

2. B) Cosine Law

3. B) Find the measures of angles and sides that we can't physically measure.

Step-by-step explanation:

1. To solve non-right triangles we use Sine Law and Cosine Law.

2. If 3 sides lengths were given and you were asked to find an angle, you would use the Cosine Law.

3.Trigonometry is used in real life to find the measures of angles and sides that we can't physically measure.

The acceptable conclusions to a hypothesis test are option a, c, d, f.

What is hypothesis test?

Hypothesis Testing is a way of statistical analysis in which a person can  put his assumptions about a population parameter to the test. It usually  used to estimate the relationship between two statistical variables.

By the property of hypothesis test the following can be stated.

⇒The value of the test statistic lies in the non rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true.

⇒ The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the null hypothesis is not true.

⇒The value of the test statistic does not lie in the rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true.

⇒ The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the alternative hypothesis is true.

Hence the correct options are a, c, d, f.

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The number of seconds, it takes for the balloon to drop below 310 feet is 1.25 seconds

To find out how many seconds it will take for the balloon to drop to below 310 feet, we need to use the information provided and some basic algebra.

Given the starting altitude of the balloon, we know:

h(0) = 1200 feet

The rate of change of the altitude, or the speed at which the altitude is changing, is given as:

dh/dt = −712 feet/second

This tells us that the altitude of the balloon is decreasing at a rate of 712 feet per second. To find out how long it will take for the altitude to drop to 310 feet or less, we can set up the following equation:

h(t) = h(0) + dh/dt * t

We know that h(t) must be less than or equal to 310 feet, so we can substitute this value in for h(t) and solve for t:

310 = 1200 + (−712) * t

This equation can be solved for t by isolating t on one side and then dividing both sides by −712:

t = (1200 - 310) / −712

t = (890) / (−712)

t = 1.25 seconds.

So it will take 1.25 seconds for the balloon to drop below 310 feet.

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Maxine's projected ending cash balance is $1,900.

What is the basic arithmetic operations?

The basic arithmetic operations are addition, subtraction, multiplication, and division.

Maxine's projected cash inflow from 20 sessions at $70 per session is:

20 sessions x $70/session = $1400

Her total projected cash inflow is therefore $1400.

Her projected cash outflow is $900 for rent and $600 for supplies, for a total of:

$900 + $600 = $1500

Her beginning cash balance is $2,000.

To calculate her projected ending cash balance, we need to subtract her projected cash outflow from her projected cash inflow and add her beginning cash balance:

Projected ending cash balance = Beginning cash balance + Projected cash inflow - Projected cash outflow

Projected ending cash balance = $2,000 + $1,400 - $1,500

Projected ending cash balance = $1,900

Therefore, Maxine's projected ending cash balance is $1,900.

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Answer:220GB

Step-by-step explanation: 500-s=380

The equatiοn οf the line οf best fit is ŷ= 0.96x+3.79

The slοpe is 0.96

The y-intercept is 3.79

The heights οf peοple that have arm spans οf 66 inches is 67.15 inches and the heights οf peοple that have arm spans οf 74 inches is 74.83 inches.

When the line tοuches the y-axis, it fοrms a y-intercept. Find the y when x = 0 tο find these. The y-intercept pοint will have the shape οf (0,y) When the line tοuches the x-axis, it fοrms an x-intercept.

We have the fοllοwing cοmputatiοn summary frοm the graphing calculatοr:

Sum οf X = 486

Sum οf Y = 506

Mean X = 44.1818

Mean Y = 46

Sum οf squares (SSX) = 1225.636

Sum οf prοducts (SP) = 1171

Hence, the fοrmula fοr the line οf best fit is ŷ= 0.96x+3.79

A linear regressiοn equatiοn is mentiοned

ŷ=mx+b

Where m is the slοpe, and b is the y-intercept

Sο, the slοpe is 0.96 and the y-intercept is 3.79

The heights οf peοple that have arm spans οf 66 inches and 74 inches

This means that:

x = 66 and x = 74

When x = 66,

y=0.96*66+3.79=67.15

When x = 74,

y=0.96*74+3.79= 74.83

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Answer:

a

Step-by-step explanation:

most likely the answer is a because we have (10,4), 10 being the domain(X-Intercept) and 4 being range(Y-Intercept)

if we substitute the value of X in option a with 10, we get a value of 3.7 as shown in the picture which can be can be converted to 4

The line of the  best fit for the data points plotted in the scatter plot is y = -0.88x + 8

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

The graph

Using the line of the best fit, we have"

(x, y) = (8, 1) and (0, 8)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 8

Using the points, we have

1 = 8m + 8

This gives

m = -0.88

So, we have

y = -0.88x + 8

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Answer:

128 or 4,096

Step-by-step explanation:

If its 64 x 2 then 128 or if you are implying 64, to the power of two, (64x64) then your answer is 4,096.

The simplified value is 4096.

Algebraic identities are equations where the value of the left-hand side of the equation is identically equal to the value of the right-hand side of the equation. Unlike algebraic expressions, algebraic identities satisfy all the values of the variables.

The basic algebraic identities are primarily helpful to work out the numerous math problems. The four basic algebraic identities are as follows.

Given:

64²

Now, we have to split the 64 into 60+4

(60 + 4)²

Now using the algebric identity

(a+ b)² = a² + b² + 2ab

So,

(60 + 4)²

=60²+2*60*4+4²

=3600+ 480+16

=3600+496

=4096

Hence, the simplified value is 4096.

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Answer:

4. 1 units

Step-by-step explanation:

A diameter of a circle is equal to 2 of its radiuses. Just simply divide the diameter by 2.

Answer:

take the output and take away from the the input

Step-by-step explanation: