A drink name with 3 letters

The arrow first reach an altitude of 60 meters is 13 seconds.

A General Rule for Solving Equations

h (t) = -2.1t² +32t-0.03 ---(i)

The arrow first reach an altitude of 60 meters:

h(t) = 60 -- (ii)

Equate the (i) and (ii)

60 = -2.1t² +32t-0.03

2.1t² - 32t + 0.03 + 60 = 0

2.1t² - 32t + 600.3 + = 0

t = -13, 13

Hence, The arrow first reach an altitude of 60 meters is 13 seconds.

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The given histogram is bimodal, which is the last option/ option E, as bimodal distribution means that the data set has two distinct peaks or modes. In a bimodal histogram, the bars are grouped in a way that shows two prominent peaks or modes in the data.

Each bar in the histogram represents a specific range of values, and the height of the bar indicates the frequency or count of data points falling within that range. In a bimodal histogram, there will be two relatively high bars that correspond to the two modes of the data. The bimodal histogram is useful for visualizing and analyzing data sets that exhibit two distinct groups or clusters. It provides a clear visual representation of the two modes and their frequencies, which can help in identifying patterns and understanding the underlying characteristics of the data.

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There are several ways to solve a quadratic equation. I'll complete the square:

z ² - (3 - 2i ) z + 5 - 5i = 0

(z - (3 - 2i )/2)² - ((3 - 2i )/2)² + 5 - 5i = 0

(z - (3 - 2i )/2)² - (3 - 2i )²/4 + 5 - 5i = 0

(z - (3 - 2i )/2)² = (3 - 2i )²/4 - 5 + 5i

(z - (3 - 2i )/2)² = (3² - 2×3×(-2i ) + (-2i )²)/4 - 5 + 5i

(z - (3 - 2i )/2)² = (5 - 12i )/4 - 5 + 5i

(z - (3 - 2i )/2)² = (5 - 12i - 20 + 20i )/4

(z - (3 - 2i )/2)² = (-15 + 8i )/4

Let w = (-15 + 8i )/4. Then write w = |w| exp(i arg(w)), where

|w| = √((-15/4)² + 2²) = 17/4

arg(w) = π - arctan(8/15)

The square roots of w are then

√w = √(|w|) exp(i (arg(w) + 2nπ)/2)

where n in the set {0, 1}.

Taking the square root of both sides gives

z - (3 - 2i )/2 = √w

z = (3 - 2i )/2 + √w

and the two solutions can be simplified to

z = √17/4 + √17 i

z = -√17/4 - √17 i

Answer:

answer is in question only!!

Step-by-step explanation:

what to do ??

SOLUTION:

We are to calculate the state income tax owed on a $70,000

per year salary.

$70,000 falls in the range of 50,001 - 100,000 which is 5.5% tax rate.

The state income tax owned on a $70,000 per year salary to the nearest whole dollar amount is $3,850.

The given equation is y + 2 = 2(x + 3) and the x-intercept is -2.

To find the x-intercept of the equation y + 2 = 2(x + 3), we need to set y equal to zero and solve for x. The x-intercept occurs when the value of y is zero, meaning the graph crosses the x-axis.

Let's substitute y with 0 in the equation:

0 + 2 = 2(x + 3)

Simplifying the equation:

2 = 2(x + 3)

Dividing both sides by 2:

1 = x + 3

Subtracting 3 from both sides:

-2 = x

The x-intercept is -2. This means that the graph of the equation y + 2 = 2(x + 3) crosses the x-axis at the point (-2, 0).

The x-intercept represents the value of x where the graph intersects or crosses the x-axis. In this case, it occurs when x is equal to -2, and the y-value is zero.

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Answer:

[B]. (1,-5)

Step-by-step explanation:

Given:

\(\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}\)

Solve:

\(\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}\)        Since 2y - 2y = 0 we take that away now we have;

\(4x=-6\\3x=13\)        Add 4x + 3x = 7x

\(\frac{7x}{7} =\frac{7}{7}\) Divide both sides by 7.

\(x=1\)

Now substitute x to find y.

\(4(1)+2y=-6\)

\(4 + 2y =-6\)  Add 6 to the other side.

\(10 = 2y\) Divide both sides by 2.

\(\frac{10}{2} =\frac{2y}{2}\)

\(y = 5\)

Hence, the answer is [B]. (1,-5)

RevyBreeze

Answer:

ind f(x) and g(x) so that the function can be described as y = f(g(x)). (1 point) y = Four divided by x squared. + 9

=

Answer:

Why do these have to be so hard

Step-by-step explanation:

The form that most quickly reveals the y intercept is

The y intercept is (0, 21/2)

The y-intercept is the point where a function or a curve intersects the y-axis. In other words, it is the value of the dependent variable (y) when the independent variable (x) is equal to zero.

In the form,  f(x) = 1/2 x² - 5x + 21/2 it is easier to see that eliminating x by plugging in 0 leaves 21/2 which is the y intercept

hence we can easily say that the y intercept is (0, 21/2)

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Answer:

Dollars per passenger would be $252.
The maximum revenue is $63,404.

Step-by-step explanation:

Let's define the number of passengers above 212 as x.

The revenue function is given by R(x) = (212 + x)(292 - x).

We can expand and simplify the revenue function:

\(R(x) = 212 * 292 + 212 * (-x) + x * 292 + x * (-x)\)

= \(61804 - 212x + 292x - x^2\)

= \(-x^2 + 80x + 61804\)

The revenue function is a quadratic function in the form\(R(x) = -x^2 + 80x + 61804\), representing a downward-opening parabola.

To find the x-coordinate of the vertex (which gives the number of passengers for maximum revenue), use the formula \(x = -b/2a\), where \(a = -1\) and \(b = 80\).

\(x=\frac{-80}{2*(-1)}\)

\(= \frac{80}{2}\)

\(= 40\)

Therefore, the number of passengers above 212 for maximum revenue is 40.

Substitute x = 40 into the revenue function to find the maximum revenue:

\(R(x) = -(40)^2 + 80(40) + 61804\)

\(= -1600 + 3200 + 61804\)

\(= 61804 + 1600\)

\(= 63404\)

Hence, the maximum revenue is $63,404.

To determine the fare per passenger, subtract x from the base fare of $292:

Fare per passenger = Base fare - x

\(= 292 - 40\)

\(= 252\) Dollars per passenger.

Answer:

x=18

Step-by-step explanation:

since x+24 is in parenthesis, we need to distribute 1/2 to all the parts inside the parenthesis.

1/2 * x = 1/2x

1/2 * 24= 12

1/2x+12=21

subtract 12 from both sides

1/2x= 9

divide 1/2 from both sides

x=18

so your answer would be x=18

Hi there!  

»»————-　★　————-««

I believe your answer is:  

\(\frac{1}{2}(x+24)=21 \rightarrow \frac{1}{2}x + 12 = 21\\\\x = 18\)

»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

\(\frac{1}{2}(x+24) = 21\\\rule{150}{0.5}\\\\\rightarrow \frac{1}{2}*x = \frac{1}{2} \\\\\rightarrow \frac{1}{2} * 24 = 12\\\\\rightarrow \frac{1}{2}x + 12 = 21\\\\\rightarrow \frac{1}{2}x + 12 - 12 = 21 - 12\\\\\rightarrow \frac{1}{2}x = 9\\\\\rightarrow (\frac{1}{2}x)2 = 9 * 2\\\\\rightarrow\boxed{x = 18}\)

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

There are thirty-nine palindromic numbers between 10 and 400.

Step-by-step explanation:

Listed, they are: 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, and 393.

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Answer:

B. x is less than or equal to 5

Step-by-step explanation:

The dot is on 5 and is also a solid dot which means it is less than or equal to or greater than or equal to

In this case it is less than or equal to because the line goes to the left

Hope this helped!

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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Answer:

hi

Step-by-step explanation:

hiiii

Answer:

h = 6 feet

Step-by-step explanation:

It is given that,

Area of a triangle, A = 18 sq feet

Base of the triangle, b = 6 feet

We need to find the height of the triangle. The area of a triangle can be given by the formula as follows :

\(A=\dfrac{1}{2}\times b\times h\)

h is height

\(h=\dfrac{2A}{b}\\\\h=\dfrac{2\times 18}{6}\\\\h=6\ \text{feet}\)

So, the height of the triangle is 6 feet.

The  equation  that can be used to solve for x is the side length of the original square

x^2-2 x-120=0

This is further explained below.

In most cases, one simply assumes that the area of the square paper is to be measured in square units.

The piece of paper that is still available has a total area of 120 square units.

It is also a certainty that the remaining portion of the paper has the following area:

Therefore, by calculating the area of the remaining scrap of paper, we get the following:

x^2-2 x=120

Subtracting 120 from both sides of the equation, we have

x^2-2 x-120=0

Thus, the equation x^2-2 x=120 can be used to solve for x.

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CQ

A square piece of paper has an area of x2 square units. A rectangular strip with a width of 2 units and a length of x units is cut off of the square piece of paper. The remaining piece of paper has an area of 120 square units.

Which equation can be used to solve for x, the side length of the original square?

x2 − 2x − 120 = 0

x2 + 2x − 120 = 0

x2 − 2x + 120 = 0

x2 + 2x + 120 = 0

Answer:

992×16=15872 is your answer

992

×16

_____

5952

+9920

_______

15872

Answer:

15872

Step-by-step explanation:

The maximum lower bound and minimum upper bound for the median number of points the basketball player scored over his last 21 games are:

Lower bound = 9.5

Upper bound = 30

In basketball, players can score 1, 2, 3 (or even 4 or 5 points) during a possession.

Players who score five points are fouled in the act of shooting a three-pointer and making the shot.

Players who score four points attempt a three-pointer and make the subsequent foul shot.

Players who score three points go beyond the 3-point line, in bounds.  

Players who score two points go inside the 3-point line, in bounds.

Players who score one point make free throws.

Basketball scores =  1, 2, 3, 4, 5 points

Median = 3 per possession

9.5   10  12.5   15   15.5   18.5   20  21.5  25    26   30    30

Thus, the maximum lower bound and minimum upper bound for the median number of points the basketball player scored over his last 21 games are 9.5 and 30.

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Relative Frequency of Scores

30 30 26 25 20 15 10 9.5 12.5 15.5 18.5 21.5

Answer:

109.6

Step-by-step explanation:

100+100×(4.8%×2)=100+ 100×9.6%=100+9.6=109.6

Answer:

The money account after two years will be 110.054

Step-by-step explanation:

\(A = P(1 + \frac{r}{n})^{nt}\)

A = final amount = required to know

P = initial principal balance = $100

r = interest rate = 4.8%=4.8/100 because compounded monthly

n = number of times interest applied per time period = 12

t = number of time periods elapsed = 2

\(A = P(1 + \frac{4.8}{1200})^{24}\)

\(A= 100(1+0.004)^{24}\)

A=   \(110.054\)

Thus, The money account after two years will be 110.054

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The sum of the roots of a quadratic equation is given by:

In the equation, a = 5 and b = 5

Thus the sum of the roots is :

Answer:

C. -1

The number of rotational symmetries that the figure has would be C. 1 at 360 degrees.

The number of times the geometric figure is similar to the original figure after undergoing a full revolution is known as the order of rotational symmetry. The order of rotational symmetry is determined by how many times the rotated figure perfectly fits within the original figure.

When the Figure F is rotated, the only times that it can be rotated to be able to give the same figure of F, is once, and that once has to be a full revolution of 360 degrees.

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Answer: 136  17/36

Step-by-step explanation:

Answer:

  (x -14)² +(y -7)² = 1²

Step-by-step explanation:

You want the equation of the circle that represents the border of a logo centered 14 m right and 7 m up from the lower left corner of a soccer field. The logo is 2 m in diameter.

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

Since the origin of the coordinate system is the lower left corner of the field, the center is located at (h, k) = (14, 7). The diameter of 2 m means the radius is 1 m. Using these values in the equation, it becomes ...

  (x -14)² +(y -7)² = 1²

Answer:

24

Step-by-step explanation:

i dont know if its correct

The question is incomplete. Here is the complete question.

A differential equation is given along with the field of problem area which it arises. Classify it as an ordinary differential equation (ODE) or a partial different equation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ordinary differential equation, indicate whether the equation is linear or nonlinear.

\(x\frac{d^{2}y }{dx^{2} } + \frac{dy}{dx} + xy = 0\) (aerodynamics, stress analysis)

Answer and Step-by-step explanation: The differential equation described above is an Ordinary Differential Equation, because it has a definite set of variables: x and y.

It is of Second Order, since the highest derivative is of order 2: \(\frac{d^{2}y }{dx^{2} }\)

The differential equation is written as derivative of a function y in terms of x, which means: Independent Variable is X and Dependent Variable is Y.

As it is an ODE, the equation is Nonlinear, because y'' or \(\frac{d^{2}y }{dx^{2} }\) is multiplied by a variable.

Answer:

A, B, and E. Hope this helps!

Answer:

The standard deviation of the sampling distribution of sample means would be of 0.6626 pounds.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Standard deviation of 5.7 pounds.

This means that \(\sigma = 5.7\)

If a sampling distribution is created using samples of the amounts of weight lost by 74 people on this diet, what would be the standard deviation of the sampling distribution of sample means?

Sample of 74 means that \(n = 74\)

The standard deviaiton is:

\(s = \frac{\sigma}{\sqrt{n}} = \frac{5.7}{\sqrt{74}} = 0.6626\)

The standard deviation of the sampling distribution of sample means would be of 0.6626 pounds.