translate: four times the difference of a number and 11

The ball is in the air for approximately 2.8 + √7 seconds, which rounds to 5.2 seconds when rounded to one decimal place.To write the equation in vertex form, we need to complete the square.

The given equation is h = -4.9t² + 27.44t + 0.584. We can rewrite it as:

h = -4.9(t² - 5.6t) + 0.584

Now, we want to complete the square inside the parentheses. To do this, we need to add and subtract the square of half the coefficient of t. In this case, the coefficient is -5.6, so we have:

h = -4.9(t² - 5.6t + (5.6/2)² - (5.6/2)²) + 0.584

Simplifying, we get:

h = -4.9((t - 2.8)² - 2.8²) + 0.584

Expanding further:

h = -4.9(t - 2.8)² + 4.9(2.8)² + 0.584

Thus, the equation in vertex form is: h = -4.9(t - 2.8)² + 34.328

b) The ball's height when it was hit can be found by evaluating the equation at t = 0:

h = -4.9(0 - 2.8)² + 34.328

h = -4.9(-2.8)² + 4.328

h = -4.9(7.84) + 34.328

h ≈ 0.784 meters

To find the time at which the ball reaches its maximum height, we can use the fact that the maximum height occurs at the vertex of the parabolic equation. The vertex of a parabola in the form h = a(t - h₀)² + k is given by (h₀, k). Comparing this to our equation, we can see that the vertex occurs at t = 2.8 and h = 34.328. Therefore, the ball reaches its maximum height at 2.8 seconds, and the maximum height is 34.328 meters.

The total time the ball is in the air can be determined by finding the time it takes for the ball to reach the ground. When the ball hits the ground, its height is 0. To find this time, we can set the equation equal to 0 and solve for t:

0 = -4.9(t - 2.8)² + 34.328

4.9(t - 2.8)² = 34.328

(t - 2.8)² ≈ 7

t - 2.8 ≈ ±√7

t ≈ 2.8 ± √7

Since time cannot be negative in this context, we can ignore the negative value.

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Answer:

\(\huge\boxed{\sf 18^{-3}}\)

Step-by-step explanation:

\(\displaystyle \frac{18^4}{18^7}\)

So, the expression becomes:

= \(18 ^{4-7}\)

= \(18^{-3}\)

\(\rule[225]{225}{2}\)

Step-by-step explanation:

Step 1:  Convert words into an expression

Four times the quotient of 3 divide by 4

We know that we are going to be multiplying 4 by something because in the statement we have four times.  Reading further we also know that we are going to be dividing 4 from 3 which means that we will have 3/4.  Finally, we see that we multiply our 3/4 by 4 which gives us our final solution.

\(4 * (3 / 4)\)

If we want to solve it the 4's would just cancel and we would be left with 3.

3

Explanation:

You would start by dividing 3 by 4. Then multiply \(\frac{3}{4}\) and 4. The 4s would cancel out leaving you with 3.

\(\frac{3}{4}\) × \(4=3\)

A 1-gigabyte flash drive has 1000 times more storage space than a 1-megabyte flash disk. The right response is thus "1,000 times greater."

We need to find the ratio between the two capacities.

Given that there are \(10^9\) bytes in a gigabyte and\(10^6\) bytes in a megabyte, we can calculate the ratio as follows:

Ratio = (1 GB) / (1 MB)

= \((10^9 bytes) / (10^6 bytes)\)

= \(10^(9 - 6)\)

=\(10^3\)

= 1000

Therefore, A 1-gigabyte flash drive has 1000 times more storage space than a 1-megabyte flash disk. The right response is thus "1,000 times greater."

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Answer: C

Step-by-step explanation:

If you look at the equation, you can see that you can cancel out a 9z³ on both sides. 9z³ is what both fractions have in common. This leaves us with 1 on the numerator on the first fraction and 2 for the denominator on the second fraction.

\(\frac{1}{16xy} *\frac{4x}{3}\)

You can also cancel out 4x since both fractions have a 4x in common. This leaves the denominator of the first equation with 4y and the numerator of the second equation with 1.

\(\frac{1}{4y} *\frac{1}{3}\)

Now, we can multiply straight across.

\(\frac{1}{12y}\)

Answer:

They purchased 3 tickets for tier seats.

Step-by-step explanation:

From the information given, you can write the following equations:

x+y=12 (1)

45x+60y=585 (2), where

x is the number of tickets for floor seats

y is the number of tickets for tier seats

First, you can solve for x in (1):

x=12-y (3)

Next, you can replace (3) in (2):

45(12-y)+60y=585

540-45y+60y=585

15y=585-540

15y=45

y=45/15

y=3

Now, you can replace the value of y in (3) to find x:

x=12-3

x=9

According to this, the answer is that they purchased 3 tickets for tier seats.

The correct number line that displays the solution `x ≥ 3` would be:

 <------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------>

       -10    -9     -8     -7     -6     -5     -4     -3     -2     -1     0      1      2      3      4      5      6      7      8      9     10

                                   ●------------------------------------------------>

The solution `x ≥ 3` is an inequality that means x is greater than or equal to 3. To graph this inequality on the number line, we mark the point representing the value 3 with a closed circle on the number line and draw an arrow pointing to the right to indicate that all values greater than or equal to 3 satisfy the inequality.

The closed circle at 3 indicates that 3 is included in the solution set, and the arrow to the right indicates that all values greater than 3 also satisfy the inequality. Therefore, any value of x that is equal to or greater than 3 would be considered a solution to the inequality `x ≥ 3`.

It is important to note that if the inequality was `x > 3` (without the equal sign), the closed circle at 3 would be changed to an open circle, indicating that 3 is not included in the solution set, and only values greater than 3 would be considered solutions. In conclusion, the number line provided above correctly displays the solution `x ≥ 3`.

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When RS.35.25 is converted into paise it will be :

3525 paise

Here given , RS.35.25

We know that,

1 rupee equals 100 paise.

When converting rupees to paise, multiply by 100.

For instance,

Rs 35.25 = Rs 35 + 25 paise.

= 35 x 100 paise + 25 paise

= 3500 paisa + 25 paisa

= 3525 paise.

RS.35.25 = 3525 Paise.

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Answer:

2 1/2 beacuse he needs 1 1/4 for one feeder

Step-by-step explanation:

The expression can be rewritten by given term as;  3^15

We need to simplify the expression below:

(3^2 x 3^3)^3

Remember that we can add these exponents, so we get:

(9 x 9)^3 = 81^3

Then we can rewrite this as:

531441

Takin the product between the exponents we will get:

(3^5)^3

Thus, the solution is 3^15

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2/3 of 35 is 23. Kofi is 23.

the probability of exactly 4 successes in 7 trials of a binomial experiment in which the probability of success is 55% is 0.29 = 29%

A binomial experiment is an experiment that has the following four properties:

The experiment consists of n repeated trials

Each trial has only two possible outcomes

The probability of success, denoted p, is the same for each trial

Each trial is independent

the probability of exactly 4 successes in 7 trials of a binomial experiment in which the probability of success is 55%

We know that the binomial distribution

\(^nc_rp^rq^{n-r\)

Where n is the number of trails

p is the probability of success in each trial

q =1-p which is the probability of failure

Here r=4

n=7

p= 55 % =0.55

then by the formula

\(p(4)=^7c_4(o.55)^4(0.45)^3\\\\p(4)=35*0.091*0.091\\p(4)=0.29\)

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Answer:

425 grams divided by 28.3 = 1 ounce is about 15 ounces

Step-by-step explanation:

Since there are 425 grams in total and 28.3 GRAMS = 1 OUNCE that means. Every 28.3 grams in the total of 425 grams are ounces so we divide it by the 28.3 in order to find the ounces since every 28.3 grams are ounces!

Answer:

...............15 .................

The value of the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)

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

\(\sqrt[4]{a}^3\)

Consider an expression expressed as xⁿ

The expression can be expanded as

xⁿ = x * x * x .... in n places

Using the above as a guide, we have the following:

\(\sqrt[4]{a}^3 = \sqrt[4]{a} * \sqrt[4]{a} * \sqrt[4]{a}\)

Apply the exponent rule of indices

\(\sqrt[4]{a}^3 = a^\frac14 * a^\frac14 * a^\frac14\)

Apply the power rule of indices

\(\sqrt[4]{a}^3 = a^\frac34\)

Hence, the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)

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The solution of the expression for r is given by:

\(r = \sqrt{\frac{3x}{2m\pi}}\)

To solve the expression for r, we must isolate r, as a function of the other variables.

The expression is modeled by:

\(m = \frac{3x}{\pi r^2h}\)

Then, isolating r:

\(mr^2 = \frac{3x}{2\pi}\)

\(r^2 = \frac{3x}{2m\pi}\)

\(r = \sqrt{\frac{3x}{2m\pi}}\)

Thus, the solution of the expression for r is given by:

\(r = \sqrt{\frac{3x}{2m\pi}}\)

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(a) The low = 12, Q1 = 15.5, median = 16.5, Q3 = 18, high = 20.

(b) IQR = Q3 - Q1 = 18 - 15.5 = 2.5.

(c) There are no outliers.

(a) The data in ascending order are: 12, 15, 15, 16, 17, 17, 18, 19, 20.

The low is 12, the high is 20.

To find Q1, we need to find the median of the data below the median. These are: 12, 15, 15, 16. The median of these values is 15.5, which is the value halfway between the two middle values (15 and 16).

To find Q3, we need to find the median of the data above the median. These are: 17, 17, 18, 19, 20. The median of these values is 18.

The median of the entire dataset is the value halfway between the two middle values, which are 16 and 17. The median is therefore 16.5.

Therefore, low = 12, Q1 = 15.5, median = 16.5, Q3 = 18, high = 20.

(b) The interquartile range (IQR) is the difference between Q3 and Q1.

IQR = Q3 - Q1 = 18 - 15.5 = 2.5.

(c) To create a box-and-whisker plot, we first draw a number line that includes the range of the data from the low to the high. We then draw a box from Q1 to Q3, with a line drawn across the box at the median. Finally, we draw whiskers from the box to the low and high values. Any data points outside of the whiskers are considered outliers.
In this plot, the box goes from 15.5 (Q1) to 18 (Q3), with the median line drawn at 16.5. The whiskers extend from the box to the low value of 12 and the high value of 20. There are no outliers.

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Answer:

u didnt put any questions

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

If two events are disjoing (aka mutually exclusive) that means that there is 0 overlap or the intersection equals 0

So the probability of A and B occuring is 0 (because P(A∩B)= 0)

The reconciliation for Bane can be summarized as,

Adjusted bank balance = $1380.

A bank reconciliation is defined as a method which is used to match the balances for a cash account in an organization's records of accounting with the bank statement.

Given that,

Beginning checkbook balance is $1400.

Service charge = $20

Adjusted balance = $1400 - $20 = $1380

Also, given that,

Ending balance on the statement = $1480

Deposit in transit = $200

Checks outstanding = $300

Adjusted balance = $1480 + 200 - 300

                              = $1380

Hence the adjusted balance is $1380.

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Answer:

it made Texas thrive because they were one of the leading cotton producers and made a lot of money off of it

Answer: +3, -3

Step-by-step explanation:

ok so all you need to do is plug in that first equation into the second one.

x(5x) = 45

5x^2 = 45

x^2 = 9

x     = +3, -3

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The point (x,y) that satisfies the given system of inequalities is (c) (-3, -1)

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

The graph of the system of inequalities (see attachment)

The system of inequalities is also given as

y > x - 2

y > 2x + 2

Next, we test the options

We see that the points (1,-6) , (-1,-6) , (3,-1) do not lie in the feasible region i.e. the unshaded region

So the points (1,-6) , (-1,-6) , (3,-1) do not satisfy the inequalities

Only the point (-3,-1) lies in the shaded region

Hence, the point (x,y) that satisfies the given system of inequalities is (c) (-3, -1)

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Answer:

the first one is your answer

Step-by-step explanation:

Answer: x= 8-2y

Step-by-step explanation:

3x+6y=24

Subtract 6y from both sides

3x=24−6y

Divide both sides by 3

3/3x = 24-6y/3

Dividing by 3 undoes the multiplication by 3

x=24-6y/3

Divide 24−6y by 3.

The final answer comes out as x=8-2y. Hope this helped!

Answer:

x = 6

Step-by-step explanation:

3x + 6y = 24  <--- This is the original equation.

3(6) + 6y = 24  <--- Replace the variable.

18 + 6y = 24 <--- Simplify

24y = 24  <--- Do the addition.

24 = 24 <--- This equation is correct.

Therefore, x = 6.

I hope his helps! :D

The answer is 2.5

Step-by-step explanation:

Formula = (N + 1 / 2th) term

So,

Total numbers (N) = 4

Now,

(N + 1 / 2th) term

= (4 + 1 / 2th) term

= (5 / 2th) term

= (2.5th) term

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The number of months is 10 months using the given equation, So the tree was planted before 10 months.

What information do we have?

y = 12x + 60

y, the height of a tree in centimeters = 150 cm tall

x months after it is planted

Using linear equation

y = 12x + 60

150 = 12x + 60

12x = 150 - 60

12x = 120

x = 10

Number of month = 10 months

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Answer:

\(x^{2} + y^{2} -10x -16y + 39\)

Step-by-step explanation:-

The equation used to find the equation of circle is :-

\((x-a)^{2} + (y-b)^{2} = radius^{2}\)

'a' means the x coordinate of the circle, 'b' means y coordinate of the circle.

In the question, it's given that the coordinates of the circle are (5, -8) and radius is 8cm.

So, 'a' will be 5 and 'b' will be -8

So,

\((x-5)^{2} + (y--8)^{2} = 8^{2}\)

\((x-5)^{2} + (y+8)^{2} = 64\)

\(x^{2} - 10x + 25 + y^{2} - 16y + 64\)

\(x^{2} + y^{2} -10x -16y + 64 - 25\)

= \(x^{2} + y^{2} -10x -16y + 39\)

Equation of a line is expressed as:

y = mx+c where;

m is the slope of the line

c is the intercept

Given the coordinates (-2, 3) and (1,5)

Get the slope first

m = y2-y1/x2-x1

From the coordinates

x1 = -2, y1 = 3, x2 = 1 and y2 = 5

m = 5-3/1-(-2)

m = 2/3

Next is to get the intercept c. To do that you will have to substitute any of the point into the formula y = mx+c

Using the coordinate (1,5) and m = 2/3

5 = 2/3(1) + c

5 = 2/3 + c

c = 5 - 2/3

c = (15-2)/3

c = 13/3

Finally substitute m = 2/3 and c = 13/3 into the equation y = mx+c to get the required equation:

y = 2/3 x + 13/3

multiply through by 3

3y = 2x + 13

3y-2x = 13

Hence the required equation of the line is 3y-2x = 13