.
A ball is thrown into the air with an initial velocity of 80 ft/sec. The height of the ball after t seconds in the air is given by h(t) =-16t^2 + 80t + 96.How long will it take for the ball land on the ground? (When will the height equal 0?)

[tex]\sin x>0[/tex] when [tex]x[/tex] is in quadrant II, so

[tex]\cos^2x+\sin^2x=1\implies\sin x=\sqrt{1-\cos^2x}=\sqrt{1-(-0.2)^2}\approx1.02[/tex]

Answer:

Step-by-step explanation:

note : cos²x + sin²x = 1

         (- 0.2)² + sin²x =1

          0.04 + sin²x = 1

sin²x = 1 - 0.04

sin²x = 0.96

sinx = √0.96  or sinx = - √0.96

in quadrant II : sinx > 0    ...so : sinx = √0.96

The value of the given expression is equal to the  [tex]\frac{29b}{5}-3\frac{17}{30}[/tex].

We have given that,

[tex]5\frac{4}{5}b+6\frac{3}{4}-\left(2\frac{11}{15}+7\frac{7}{12}\right)[/tex]

We have to determine the,

[tex]=\frac{29}{5}b+6\frac{3}{4}-\left(2\frac{11}{15}+7\frac{7}{12}\right)[/tex]

The expression consists of numbers and arithmetic operators. It does not contain equality or inequality symbols. The expression consists of unknown variables.

[tex]=\frac{29}{5}b+\frac{27}{4}-\left(2\frac{11}{15}+7\frac{7}{12}\right)[/tex]

[tex]=\frac{29}{5}b+\frac{27}{4}-\left(\frac{41}{15}+7\frac{7}{12}\right)[/tex]

[tex]=\frac{29}{5}b+\frac{27}{4}-\left(\frac{41}{15}+\frac{91}{12}\right)[/tex]

[tex]=\frac{29b}{5}+\frac{27}{4}-\frac{619}{60}[/tex]

[tex]=\frac{29b}{5}-\frac{107}{30}[/tex]

[tex]=\frac{29b}{5}-3\frac{17}{30}[/tex]

The value of the given expression is equal to the  [tex]\frac{29b}{5}-3\frac{17}{30}[/tex].

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The answer is (3,11) because both lines pass through this point.

If you plug these coordinates into the equations in place of x and y :

3+8= 11

3(3)+2= 11

So we know that the coordinates (3,11) are correct, however the answer is C. because solutions to systems of equations are represented by a point of intersection.

The answer is:

The correct option is the second option:

(3, 11) because both lines pass through this point

To find which statement shows the solution to the system of equations, we need to find which of the given points are solutions to the system of equations. We must remember that if a point is a solution to a system of equations, it will satisfy both equations.

So, we are given the lines:

Line C

[tex]y=x+8[/tex]

Line D

[tex]y=3x+2[/tex]

Now, evaluating the first point to see if satisfies the line equations:

Evaluating (3,11)

Line C

[tex]11=3+8[/tex]

[tex]11=11[/tex]

We have that the point (3,11) satisfy the equation of the Line C, so, the linea pass through this point.

Line D

[tex]y=3x+2[/tex]

[tex]11=3*3+2[/tex]

[tex]11=11[/tex]

We have that the point (3,11) satisfies the equation of the Line C, so, the linea pass through this point.

Hence, we have that the points satisfies both lines, so it's a solution to the system of equation.

So, the correct option is the second option:

(3, 11) because both lines pass through this point

Have a nice day!

Answer:

[tex]\large\boxed{x=\dfrac{11}{2},\ y=\dfrac{86}{35}}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}12x-14y=-8\\-8x-14y=-52&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}12x-14y=-8\\8x+14y=52\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad20x=44\qquad\text{divide both sides by 20}\\.\qquad x=\dfrac{44:4}{20:4}\\\\.\qquad x=\dfrac{11}{5}\\\\.\qquad\boxed{x=2.2}\\\\\text{Put the value of x to the second equation}\ 8x+14y=52:[/tex]

[tex]8(2.2)+14y=52\\17.6+14y=52\qquad\text{subtract 17.6 from both sides}\\14y=34.4\qquad\text{divide both sides by 14}\\y=\dfrac{34.4:2}{14:2}\\\\y=\dfrac{17.2\cdot10}{7\cdot10}\\\\y=\dfrac{172:2}{70:2}\\\boxed{y=\dfrac{86}{35}}[/tex]

The solution to the system of equations is: [tex]\[x = 2.2, \quad y = 2.457\][/tex]

To solve the system of linear equations:

[tex]\[12x - 14y = -8\]\[-8x - 14y = -52\][/tex]

We can use the method of elimination to find the values of x and y.

First, let's eliminate y by subtracting the second equation from the first equation. Before that, we should multiply the equations to have the same coefficients for y with opposite signs:

Multiply the first equation by 1:

12x - 14y = -8

Multiply the second equation by -1:

8x + 14y = 52

Now, add the two equations:

[tex]\[(12x - 14y) + (8x + 14y) = -8 + 52\][/tex]

Simplifying this, we get:

[tex]\[20x = 44\]Solve for \(x\):\[x = \frac{44}{20}\]\[x = \frac{22}{10}\]\[x = 2.2\][/tex]

Now that we have x, we can substitute this value back into one of the original equations to find y. Using the first equation:

12x - 14y = -8

Substitute x = 2.2:

[tex]\[12(2.2) - 14y = -8\]\[26.4 - 14y = -8\][/tex]

Subtract 26.4 from both sides:

[tex]\[-14y = -8 - 26.4\]\[-14y = -34.4\][/tex]

Divide both sides by -14:

[tex]\[y = \frac{-34.4}{-14}\]\[y = 2.4571 \approx 2.457\][/tex]

Thus, the solution to the system of equations is:

[tex]\[x = 2.2, \quad y = 2.457\][/tex]

To ensure accuracy, let's substitute x and y back into the original equations and verify that they hold true.

Check the first equation:

[tex]\[12(2.2) - 14(2.457) = -8\]\[26.4 - 34.398 = -8\]\[-7.998 \approx -8 \quad \text{(approximately correct)}\][/tex]

Check the second equation:

[tex]\[-8(2.2) - 14(2.457) = -52\]\[-17.6 - 34.398 = -52\]\[-51.998 \approx -52 \quad \text{(approximately correct)}\][/tex]

Answer:

Step-by-step explanation:

A recipe for sabayon calls for 2 egg yolks, 3 tablespoons of sugar, and ¼ cup of white wine. After cracking the eggs, you start measuring the sugar, but accidentally put in 4 tablespoons of sugar. How can you compensate?

Note that we put  in 4/3 more sugar than we wanted, because 3(4/3) = 4

So we need to increase eveything else by 4/3

So 2(4/3)  = 8/3  = 2 +2/3 egg yolk    and      (1/4)(4/3) =4/12 = 1/3 cup of wine

To counterbalance the additional tablespoon of sugar in the recipe, you could increase the other ingredients by a third as well. Hence, you'd require roughly 3 egg yolks and 1/3 cup of white wine.

In this recipe situation, since you accidentally put in 4 tablespoons of sugar instead of the required 3 tablespoons, you've essentially increased the sugar quantity by a third. To compensate for this, your best option would be to increase the quantities of the other ingredients by a third as well. Therefore, you would need:

Using these measurements, you should retain the balance of ingredients in your recipe. Nevertheless, remember that cooking often involves personal taste. You might want to adjust the recipe according to your taste preferences afterwards.

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Answer:

3.28 feet

Step-by-step explanation:

One meter equals to 3.28 feet.

The question isn't exactly clear what Gema wants to use her wire for, because "wrap one meter" isn't correct.

You wrap something around something else...  and you can't wrap something around a meter.  You can wrap around a square meter by doing the perimeter... but then you'd need more than meter to do the perimeter of a square meter (the perimeter can be around 4 meters).

So, assuming she has a length of 1 meter to cover, she would need 3.28 feet.

The graph of f(x) = sin(x) - 2 is a sinusoidal wave shifted down 2 units with period 2π and amplitude 1.

To graph the function, we can start by plotting the points where the graph intersects the x-axis. These points occur when sin(x) = 0, which is when x = 0, ±π, ±2π, and so on. Since the graph is shifted downwards by 2 units, these points will all be 2 units below the x-axis.

Next, we can plot the points where the graph reaches its maximum and minimum values. These points occur when sin(x) = ±1, which is when x = ±π/2 + 2πn, where n is any integer.

Since the graph is shifted downwards by 2 units, the maximum points will be 1 unit above the x-axis, and the minimum points will be 3 units below the x-axis.

Once we have plotted a few points, we can sketch the rest of the graph by connecting the points with a smooth curve. The graph should oscillate between -2 and 0, with a period of 2π.

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Answer:

[tex]\large\boxed{the\ radius\ R=\dfrac{1}{2}}[/tex]

Step-by-step explanation:

The formula of a volume of a sphere:

[tex]V=\dfrac{4}{3}\pi R^3[/tex]

We have

[tex]V=\dfrac{1}{6}\pi[/tex]

Substitute:

[tex]\dfrac{4}{3}\pi R^3=\dfrac{1}{6}\pi[/tex]        divide both sides by π

[tex]\dfrac{4}{3}R^3=\dfrac{1}{6}[/tex]          multiply both sides by 3

[tex]3\!\!\!\!\diagup^1\cdot\dfrac{4}{3\!\!\!\!\diagup_1}R^3=3\!\!\!\!\diagup^1\cdot\dfrac{1}{6\!\!\!\!\diagup_2}[/tex]

[tex]4R^3=\dfrac{1}{2}[/tex]          divide both sides by 4

[tex]R^3=\dfrac{1}{2}:4\\\\R^3=\dfrac{1}{2}\cdot\dfrac{1}{4}\\\\R^3=\dfrac{1}{8}\to R=\sqrt[3]{\dfrac{1}{8}}\\\\R=\dfrac{\sqrt1}{\sqrt8}\\\\R=\dfrac{1}{2}[/tex]

Answer:

2x - 3y < 7

Step-by-step explanation:

The coordinate is on 0 and this number is LESS THAN 0.

PLEASE MARK ME AS BRAINLIEST BECAUSE I REALLY NEED IT :(

2.7 points (my guess)

Answer: The expected value of touchdown is 2.45.

Step-by-step explanation:

Since we have given that

Probability of making a field goal for 3 points = 90%

Probability of making a touchdown for 7 points = 35%

So, Expected value of a touchdown would be

[tex]\sum xp(x)=7\times \dfrac{35}{100}=\dfrac{245}{100}=2.45[/tex]

Hence, the expected value of touchdown is 2.45.

Answer:

Tessa's mistake was to have multiplied each dimension by two instead of multiplying by a square root of two.

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z -----> the scale factor

x ----> the area of the enlarged garden

y ----> the area of the original garden

[tex]z^{2}=\frac{x}{y}[/tex]

we have that

If Tessa multiplies each dimension by 2, then the scale factor equals 2.

[tex]z=2[/tex]

substitute

[tex]2^{2}=\frac{x}{y}\\\\ 4=\frac{x}{y}\\\\x=4y[/tex]

The area of the enlarged garden will be equal 4 times the area of the original garden

so

If Tessa wanted to have twice as much surface, she must multiply each dimension by a square root of 2.

therefore

Tessa's mistake was to have multiplied each dimension by two instead of multiplying by a square root of two

For this case we have by definition, that the volume of a sphere is given by:

[tex]V = \frac {4} {3} \pi * r ^ 3[/tex]

Where:

r: It is the radius of the sphere

If the radius is divided by 3 we have:

[tex]\frac {r} {3}:[/tex]

[tex]V = \frac {4} {3} \pi * (\frac {r} {3}) ^ 3\\V = \frac {4} {3} \pi * \frac {r ^ 3} {27}\\V = \frac {4} {81} \pi * r ^ 3[/tex]

ANswer:

the volume decreases considerably because the denominator increases

Answer:

[tex]w=11[/tex]

Step-by-step explanation:

we have

[tex]5=w/2.2[/tex]

Solve for w

That means----> isolate the variable w

Multiply by 2.2 both sides

[tex](2.2)*5=(2.2)*w/2.2[/tex]

Simplify

[tex]11=w[/tex]

Rewrite

[tex]w=11[/tex]

The solution to the equation 5 = w/2.2 is 11

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

5 = w/2.2

Rewrite the equation as follows

w/2.2 = 5

So, we have

w = 5 * 2.2

Evaluate the product of 5 and 2.5

So, we have

w = 11

Hence, the solution to the equation is 11

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I believe it’s the third one

:) Hope this answers your question :)

Answer:

9q + 15

Step-by-step explanation:

3g+5+3g+5+3g+5

Combine like terms

= 9q + 15

Answer:

15+9g

Step-by-step explanation:

Answer:

Choice B is correct

Step-by-step explanation:

The graph of the parabola opens towards the left. This implies that the general form of the equation of the parabola will be;

[tex]y^{2}=f(x)[/tex]

Nevertheless, the points (-2, -4) and (-2, 4) lie on the graph of the parabola. We substitute x = -2 in the equations having the form above.

In the second equation, we have;

[tex]y^{2}=-8(-2)\\\\y^{2}=16\\\\y=\sqrt{16}=+4, -4[/tex]

This is thus the equation of the parabola graphed.

Answer: D x^2=6y

Step-by-step explanation:

Answer:c

Step-by-step explanation:

The answer is the top one.

Hope this helps!

Step-by-step explanation:

First, reflect over the y-axis:

(1, -2) → (-1, -2)

Then, rotate 180° around the origin:

(-1, -2) → (1, 2)

Answer:

It is 1/6

Step-by-step explanation:

This is because there are 6 sides to a dice and the number 3 is only on one of those sides. So, it is 1 in 6 or 1/6

Answer:

1/6

Step-by-step explanation:

The question is asking for the probability of rolling a 3 on a fair-sided die.

Dice have 6 faces.

The number "3" is only on 1  those faces

So, the probability of rolling a 3 on a dice is 1/6

I hope this helps! :)

To find median your numbers have to be in numerical order from smallest to largest and the value that occurs more often and if no number is repeated then there is not median aka (mode)

To find mean you need to add all the number and divide the numbers that you add.

To find median you put the numbers least to greatest. Then, cross the numbers until you find an one number and that's it. If they are two numbers that left, you can add together and divide by two.

I hope this help you. :)

Answer:

The best measure of location or center is the median.

The best measure of spread or dispersion is the interquartile range (I.Q.R).

Step-by-step explanation:

The data set is skewed to the left since most of the data values fall in the upper end of the distribution. In other words the data set is negatively skewed since it is tailed to the left.

For any skewed data set;

The best measure of location or center is always the median. This is because the median is robust to outliers unlike the mean.

On the other hand, the best measure of spread or dispersion is the interquartile range (I.Q.R).

Answer:

B and D

Step-by-step explanation:

Answer:

ROI = 66.67%

Step-by-step explanation:

Given:

josh investment= $12,000

Received sum= $20,000

ROI=?

ROI is the return on investment that gives the loss or gain in any investment and is calculated by the following formula:

ROI= (interest/investment) x 100

Finding interest:

interests= received sum- investment

              = 20,000-12,000

              =8000

Putting values in ROI formula we get:

ROI= (8000/12000) x 100

      = 66.67%

Hence the return on investment is 66.67%!

Answer:

a(8) = -0.0027

Step-by-step explanation:

The most general formula for a geometric sequence is a(n) = a(1)*r^(n-1), where a(1) is the first term and r is the common ratio.

Here, the formula becomes a(n) = 6*(-1/3)^(n-1).

Substitute 8 for n to find the eighth term:

a(8) = 6*(-1/3)^(8-1), or a(8) = 6(-1/3)^7, or a(8) = -0.0027

The eighth term of the geometric sequence with the first term of 6 and a common ratio of -1/3 is -6/2187.

To find the eighth term of a geometric sequence, we can use the formula for the nth term of the sequence, which is given by an = a1rn-1, where a1 is the first term and r is the common ratio. In this case, the first term (a1) is 6 and the common ratio (r) is -1/3. To calculate the eighth term (a8), we substitute the values into the formula and get:

a8 = 6 ×(-1/3)8-1

a8 = 6 × (-1/3)7

a8 = 6 ×(-1/2187)

a8 = 6 ×(-1/2187) = -6/2187

Once we simplify, we find that the eighth term is -6/2187.

Answer:

V=a3

Step-by-step explanation:

To find the volume of any cube you need to know the length, width and height. The formula to find the volume multiplies the length by the width by the height. The good news for a cube is that the measure of each of these dimensions is exactly the same. Therefore, you can multiply the length of any side three times.

Measure a side of the botom and then multiply it by 2 (That's the area), then multiply the result with the height: Area X Height = Volume. :)

hope you understand my answer LoL

Answer:

Choice D

Step-by-step explanation:

The Cavalieri's principle states that if two or more solids have identical cross-sectional area as well as height, then the solids will have equal volume.

Therefore, the volumes of the cylinders are the same

Answer:

The volumes of the cylinders are the same.

Step-by-step explanation:

5x+2+x+2=40

5x+x=40-2-2

6x=36

x=36/6

x=6

Son=6

David=5*6=30

The question involves solving two linear equations. By solving these equations, we find that the son is currently 6 years old and David is 30 years old.

This question is based on linear equations in mathematics. Let's use the given conditions to form two equations and solve them accordingly.

Let's assume that the son's age is 'x'. According to the information provided, David is five times older than his son, so David's age is '5x'.

In two years, David will be 5x + 2 years old and his son will be x + 2 years old. The sum of their ages in two years is given as 40, which leads us to the equation 5x + 2 + x + 2 = 40. After simplifying, we get '6x + 4 = 40', or '6x = 36', and then 'x = 6'.

Hence, currently the son is 6 years old and David is 30 years old.

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Answer:

quadratic: y = x^2 + 4x + 4

Step-by-step explanation:

Notice that each y value is the square of an integer.

4 = 2^2

9 = 3^2

16 = 4^2

etc.

This is a quadratic equation.

The first ordered pair is (0, 4). 4 is 2^2, so add 2 to x and rthen square the quantity. (0 + 2)^2 = 2^2 = 4. This also works for the other values of x.

The equation is

y = (x + 2)^2

y = x^2 + 4x + 4

Answer: quadratic: y = x^2 + 4x + 4

Answer:

1/6

Step-by-step explanation:

jason ate 1/2, so only 1/2 of the pizza is left.

1 ÷ 2 = 1/2

he split it equally between himself and 2 friends (3 people)

1/2 ÷ 3

= 1/2 × 1/3

=1/6

Answer:

4 feet

Step-by-step explanation:

It is given that:

• At 2:30 p.m., the water depth was 2.6 feet.  

• It is now 5:00 p.m., and the depth of the water is 3.6 feet.

So in 2.5 hours ( 5pm - 2:30pm) the water rose 1 feet (3.6 - 2.6).

Now we can find how much water rises in 1 hour by setting up a ratio (let x be the depth increase of water in 1 hr):

[tex]\frac{2.5}{1}=\frac{1}{x}\\2.5x=1*1\\2.5x=1\\x=\frac{1}{2.5}\\x=0.4[/tex]

So, in 1 hour, the water level will rise 0.4 feet

So, at 6pm (1 hour from 5 pm) it will rise to 3.6 + 0.4 = 4 feet

The depth of the water is increasing at a rate of 0.4 feet per hour, so by 6:00 p.m., the depth will be 4 feet.

We are given the information that water is being pumped into a cylindrical tank and the height of the water increases linearly over time. At 2:30 p.m. the depth was 2.6 feet, and at 5:00 p.m. it was 3.6 feet. To find the rate of change in height, we need to first calculate the time difference and the change in height of the water:

Dividing the change in height by the time gives us the rate of change, which is 0.4 feet per hour (1 foot / 2.5 hours). Now we use this rate to predict the height at 6:00 p.m., which is one hour after 5:00 p.m.:

Depth at 5:00 p.m. = 3.6 feet + (0.4 feet per hour * 1 hour) = 4 feet.

Therefore, the expected depth of the water at 6:00 p.m. is 4 feet.