At a Fourth of July celebration, a rocket is launched straight up
with an initial velocity of 125 feet per second. The height h of the rocket in feet
above sea level is modeled by the formula h = 125t - 16t^2, where t is the time in
seconds after the rocket is launched.
a. What is the height of the rocket when it returns to the ground?
b. Let h = 0 in the equation and solve for t.
c. How many seconds will it take for the rocket to return to the ground?

We have a circle that has an area of 36π square units.

We have to find the radius.

The area in function of the radius is πr², so we can find the radius r as:

Answer: the radius is 6 units.

The solution to the differential equation is:

y = ln(-cos(x) - C)

First we can use separation of variables by isolating the y terms on one side and the x terms on the other side:

e^(-y) dy = -sin(x) dx

Now we can integrate both sides:

∫e^(-y) dy = -∫sin(x) dx

-e^(-y) = cos(x) + C

Where

To solve for y, we can multiply both sides by -1 and take the natural logarithm:

y = ln(-cos(x) - C)

Where

Therefore, the solution to the differential equation is:

y = ln(-cos(x) - C)

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2 Hours

this is because one pipe takes 4 hours, and if both pipes take 2 hours, that is cutting the time in half, meaning both pipes pour the same amount and take the same time.

hope this is helpful!

Answer:

y=2x-6

Step-by-step explanation:

subtract 6x from each side. divide each side by -3.

Since triangle PQR is similar to triangle PTS

1) Side PQ is similar to side PT

2) Side QR is similar to side TS

3) side PR is similar to side PS

The vertex, focus, and directrix of the parabola 5x^2 + 16y = 0 are (0, 0), (-4/5, 0), and x = 4/5, respectively.

To find the vertex, focus, and directrix of the parabola with the equation 5x^2 + 16y, we can use the standard form of the equation for a parabola:

y = (1/4p)(x - h)^2 + k

where (h, k) is the vertex and p is the distance between the vertex and the focus or the vertex and the directrix.

Comparing the given equation to the standard form, we have:

5x^2 + 16y = 0
=> 16y = -5x^2
=> y = -(5/16)x^2

From this, we can determine that the vertex is at the origin (0, 0).

To find p, we can use the formula p = 1/(4a), where a is the coefficient of x^2. In this case, a = -5/16, so p = 1/(4*(-5/16)) = -4/5.

Therefore, the vertex is (0, 0), the focus is (-4/5, 0), and the directrix is x = 4/5.

In conclusion, the vertex, focus, and directrix of the parabola 5x^2 + 16y = 0 are (0, 0), (-4/5, 0), and x = 4/5, respectively.

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The measure of an angle that is coterminal with a 135° angle is 495°.

Coterminal angles are angles that share the same initial and terminal sides, meaning that they differ by a multiple of 360°.

Therefore, to find an angle that is coterminal with 135°, we need to add or subtract multiples of 360° until we get an angle within the given range.

Here, we have the following options:135° + 360° = 495° (this is the smallest positive angle that is coterminal with 135°)135° - 360° = -225° (this is a negative angle that is coterminal with 135°)Since we are given a list of positive angles as answer choices, the correct answer is 495°.

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Answer:

9 value is ====*0.9*

can you friendship with me i am Indian boy

Answer:

.85 times the cost to make the shirt

Step-by-step explanation:

Let x represent cost to make the shirt.

Today, the shirt is in a 15 percent discount from its normal price.

Discount = 15/100 * x = 0.15x

Current cost = Original cost - discount

Current cost = x - 0.15x = 0.85x

The answer is;

.85 times the cost to make the shirt

Answer:

21

Step-by-step explanation:

15/ 5/7 = 21

Answer:

<A = 38°

Step-by-step explanation:

180 - 108 - 34 = 38°

hope this helps :)

Use the CSS "background-image" property to configure a linear gradient.

The "background-image" property in CSS allows you to set an image or a gradient as the background of an element. When configuring a linear gradient, you can use the "linear-gradient()" function as the value for the "background-image" property. This function allows you to define the starting and ending points of the gradient, as well as the colors and stops along the gradient.

By specifying the desired colors, positions, and angles within the "linear-gradient()" function, you can create customized linear gradients to apply as backgrounds to elements on a web page, achieving visually appealing effects and smooth transitions.

Therefore, Use the CSS "background-image" property to configure a linear gradient.

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To configure a linear gradient in CSS, you can use the 'background-image' property with the 'linear-gradient()' function.

To configure a linear gradient in CSS, you can use the 'background-image' property along with the 'linear-gradient()' function. Here's an example:

In the above code, replace 'element' with the selector for the HTML element you want to apply the gradient to. 'direction' specifies the direction of the gradient, such as 'to right' or 'to bottom'. 'color1', 'color2', and so on represent the colors you want to use in the gradient. You can specify multiple colors to create a smooth transition between them.

For example, to create a horizontal gradient from red to blue, you can use the following code:

This will apply a linear gradient from red to blue horizontally on the selected element.

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Answer: x intercept: (6,0)

              y intercept: (0,4)

Step-by-step explanation:  

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

Answer: x=−3y/2+6 and -2x/3+4

​

Step-by-step explanation:

Answer:

7.5

Step-by-step explanation:

5 x 3 = 15 divided by 2 is 7.5

In a right cone with a base radius of 12 cm and height of 24 cm, a sphere is inscribed. The radius of the sphere can be expressed as \(\(a\sqrt{c} - a\) cm\). The value of  \(\(ac\)\) is 3.

To find the value of \(\(ac\)\), we first need to understand the relationship between the cone and the inscribed sphere. The center of the sphere lies on the symmetry axis of the cone and is equidistant from all points on the base of the cone.

Since the radius of the base of the cone is 12 cm, the diameter of the sphere is also 24 cm (twice the radius of the cone base). The diameter of the sphere is equal to the height of the cone.

Let's denote the radius of the sphere as r. We can express the radius of the cone base in terms of r using the Pythagorean theorem. The height of the cone is the hypotenuse, and the radius of the base and \(r\) form the other two sides of the right triangle. Therefore, \(\(r^2 + (12 - r)^2 = 24^2\).\)

Simplifying the equation above, we get \(\(2r^2 - 24r + 48 = 0\)\). Factoring out 2, we have \(\(r^2 - 12r + 24 = 0\).\)

Using the quadratic formula,

\(\(r = \frac{-(-12) \pm \sqrt{(-12)^2 - 4 \cdot 24}}{2} = \frac{12 \pm \sqrt{144 - 96}}{2} = 6 \pm \sqrt{3}\).\)

Since the radius cannot be negative in this context, we take

\(\(r = 6 + \sqrt{3}\). Thus, \(a = 6\) and \(c = 3\), giving us \(ac = 6 \cdot 3 = 18\).\)

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Based on the information, the pollster's conclusion makes sense.

To know if the pollster is right with his conclusion we must perform the following operation.

In accordance with the above, we can infer that the pollster concludes that 54% of the people surveyed are equivalent to 545 people correctly because 0.86 is a minimum margin of error for this type of statistics. In addition, it can be inferred that the pollster correctly uses the statistics and study parameters of a sample to establish a correct conclusion.

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Using a calculator, it can be found that

Rounding to three decimal places,

To investigate whether there is convincing evidence, at a 5 percent level of significance, that a longer hand length is associated with a decrease in the time to complete the 100-meter freestyle, the researcher should use a linear regression t-test.

1. The researcher collects data on hand length and 100-meter freestyle completion time for twenty randomly selected swimmers.
2. Calculate the correlation coefficient (r) to measure the strength and direction of the relationship between hand length and freestyle completion time.
3. Perform a linear regression analysis to obtain the slope (b) and the y-intercept (a) of the best-fit line.
4. Conduct a linear regression t-test to determine if the slope (b) is significantly different from zero at a 5 percent level of significance.
5. If the t-test results in a p-value less than 0.05 (5 percent level of significance), there is convincing evidence that a longer hand length is associated with a decrease in the time to complete the 100-meter freestyle.

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Answer:

i think 10

Step-by-step explanation:

you multiply 3*5=15 and 2*5=10

The first number, 5 x \(10^22,\) can be written as 5 followed by 22 zeros:

5,000,000,000,000,000,000,000

To simplify means to make something easier to understand or do by reducing complexity, removing unnecessary details, or using simpler language or concepts.

The second number , 5 × 10², can be written as 5 followed by 2 zeros: 500

The third number, 3.7 x 10⁵³, can be written as 3.7 followed by 53 zeros:

370,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

or in scientific notation as 3.7 x 10⁵³

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Simplify

2. 5 x 10^22. 5 × 10 2 and 3. 7 x 10^53. 7 × 10 5

The sum in summation notation of the expression (a) 1 + 2 + 3 + 4 + X5, where X takes the values 1-4, is ΣX from 1 to 4. In other words, it represents the summation of X over the range 1 to 4.

In summation notation, the expression (a) 1 + 2 + 3 + 4 + X5 can be written as ΣX, where X takes the values from 1 to 4. The capital sigma (Σ) represents the summation operator, and the variable X is summed over the range 1 to 4. This means that we need to substitute X with each value from 1 to 4 and add them together.

When we evaluate the expression, we have:

ΣX = 1 + 2 + 3 + 4 = 10

However, the expression also includes X5, indicating that X takes the value 5 as well. Therefore, we add 5 to the sum:

ΣX = 10 + 5 = 15

So, the sum of 1 + 2 + 3 + 4 + X5, where X takes the values 1-4, is equal to 15.

Moving on to expression (b) y2 + y3 + Y, where Y takes the values y₁ = -1, y₂ = -0.5, y₃ = 0, y₄ = 1.35, we can express it in summation notation as ΣY from 1 to 3. This represents the summation of Y over the range 1 to 3.

Since Y has a different value for each term, we simply substitute Y with each value from 1 to 3 and add them together:

ΣY = y₁ + y₂ + y₃ = -1 + (-0.5) + 0 = -1.5

Hence, the sum of y₂ + y₃ + Y, where Y takes the values y₁ = -1, y₂ = -0.5, y₃ = 0, y₄ = 1.35, is equal to -1.5.

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There are 1296 ways the promoter can select which cans to use for the taste test.

To solve this problem, we can use the concept of combinations.

First, let's determine the number of ways to select 2 cans of Diet Coke from the 9 available cans. We can use the combination formula, which is nCr = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items to be selected. In this case, n = 9 and r = 2.

Using the combination formula, we have:
9C2 = 9! / (2! * (9-2)!) = 9! / (2! * 7!) = (9 * 8) / (2 * 1) = 36

Therefore, there are 36 ways to select 2 cans of Diet Coke from the 9 available cans.

Similarly, there are also 36 ways to select 2 cans of Coke Zero from the 9 available cans.

To find the total number of ways the promoter can select which cans to use for the taste test, we multiply the number of ways to select 2 cans of Diet Coke by the number of ways to select 2 cans of Coke Zero:

36 * 36 = 1296

Therefore, there are 1296 ways the promoter can select which cans to use for the taste test.

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1. The equation to slope-intercept form is y = -2/3(x) + 490. The slope is -2/3 and the y-intercept is 490.

2. You should start at the y-intercept (0, 490) and move right by 3 units and downward by 2 units, and then connect the points.

3. The equation in function notation is f(x) = -2/3(x) + 490. The graph of the function is the rate of change with respect to the number of sandwich lunch sold.

4. A graph of the function with intercepts is shown below.

5. The graphs of the functions for the two months both have the same slope but different y-intercept and x-intercept.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided above, a linear equation that models Sal's Sandwich Shop's profit is given by;

2x + 3y = 1,470

By subtracting 2x from both sides of the equation and dividing by 3, we have:

2x + 3y - 2x = 1,470 - 2x

y = -2/3(x) + 490

Therefore, the slope is -2/3 and the y-intercept is 490.

Part 2.

In order to graph the equation by using the slope-intercept method, you would start at the y-intercept (0, 490) and move right by 3 units and down by 2 units, and then connect the points.

Part 3.

Next, we would write the equation in function notation as follows;

f(x) = -2/3(x) + 490

where:

The graph represents the rate of change of the function with respect to the number of sandwich lunch sold.

Part 4.

In this context, we would use an online graphing calculator to plot the linear function as shown in the image attached below.

Part 5.

Assuming Sal's total profit on lunch specials for the next month is $1,593 and the profit amounts remain the same, a system of equations to model this situation is given by:

2x + 3y = 1593; y = -2/3(x) + 531.

2x + 3y = 1,470; y = -2/3(x) + 490.

In conclusion, we can logically deduce that the graphs of the functions for the two months both have the same slope but different y-intercept and x-intercept.

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Complete Question:

Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.

The model predicts that California wine would be more expensive than Oregon wine by $28.00.

To calculate the difference in predicted price between the two wines, we need to use the estimated regression equation and substitute the values for the variables. Let's say our estimated regression equation is:

Price = 50 + 2.5(Rating) + 10(California) - 8(Oregon)

Both wines have a rating of 90, so we can substitute that value in:

Price of California wine = 50 + 2.5(90) + 10(1) - 8(0) = 295

Price of Oregon wine = 50 + 2.5(90) + 10(0) - 8(1) = 267

Therefore, the predicted price of California wine is $295 and the predicted price of Oregon wine is $267. The difference between the two is $28.00.

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If you have a binomial experiment with p = 0.1 and a sample size of 900, then the variance of the distribution is option (b) 81

The variance of a binomial distribution measures the spread or variability of the distribution. It tells us how far the observations are from the mean. In this case, the binomial experiment has a probability of success of 0.1 and a sample size of 900.

The formula for the variance of a binomial distribution is Var(X) = np(1-p), where n is the sample size and p is the probability of success in each trial. Substituting the given values, we get:

Var(X) = 900 × 0.1 × (1 - 0.1) = 81

So the variance of the distribution is option (b) 81.

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Answer:

The distance between (-3, -4) and (5, 5) is 12.

Step-by-step explanation:

a. The expression for the function p(t), which gives the total number of people in Canada in the year t is:

p(t) = f(t) + g(t)

Here, f(t) represents the number of men in Canada in the year t, and g(t) represents the number of women in Canada in the year t. Therefore, the total number of people in Canada in the year t is the sum of the number of men and the number of women in that year.

b. The expression for the function m(t), which gives the total amount of money earned by Canadian women in the year t is:

m(t) = g(t) × h(t)

Here, g(t) represents the number of women in Canada in the year t, and h(t) represents the average income of women in Canada in the year t. Therefore, the total amount of money earned by Canadian women in the year t is the product of the number of women and the average income of women in that year.

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Answer:

(7, 8)

Step-by-step explanation:

We know

Point A is located at (5,8) and is translated two units to the right.

Translate to the right mean the x will increase; in this case, it translated two units to the right meaning the x will increase b 2.

So, the coordinate of A will be at (7, 8)

Answer:

3 friends ( unless u mean 3/4 instead of 34 then its 2 friends)

Step-by-step explanation:

The total surface area of the can is 61.23 square inches

The total surface area of can S = 2πr(r+h)

where:

h is the height

r is the radius

A cylinder's surface area is the area that its surface takes up in three dimensions. A three-dimensional structure known as a cylinder has circular bases that are parallel to one another. There are no vertices on it. Area of three-dimensional shapes often refers to surface area. Square units are used to denote the surface area. Examples include cm2, m2, and so forth.

Given

h = 5in

r = 1.5in

S = 2(3.14)(1.5)(1.5 + 5)

S = 6.28(1.5)(6.5)

S = 61.23 square inches

Hence the total surface area of the can is 61.23 square inches

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