When an object is dropped vertically from a platform, its height after
seconds can be estimated with the formula shown.

ℎ=ℎ0−162


ℎ
is the height of the object in feet.
ℎ0
is the initial height of the object in feet.

is the time in seconds after the drop.

Which equation and solution tells how long it takes the object to reach a height of 96
feet if its initial height is 208
feet?

Answer:

First, we need to calculate the volume of the rectangular fish tank. The volume of a rectangular solid is given by the formula:

volume = length x width x height

Plugging in the values we have, we get:

volume = 35 cm x 30 cm x 25 cm = 26,250 cubic cm

Next, we need to find the volume of water in the fish tank. The volume of water is equal to the volume of the space the water occupies, which is a rectangular solid with length 35 cm, width 30 cm, and height 20 cm. The volume of this rectangular solid is:

volume = length x width x height = 35 cm x 30 cm x 20 cm = 21,000 cubic cm

To convert cubic centimeters (cm^3) to liters (L), we need to divide by 1000:

volume = 21,000 cm^3 ÷ 1000 = 21 L

Therefore, the volume of water in the fish tank is 21 liters.

Step-by-step explanation:

Answer:

289

Step-by-step explanation:

Let's call the height of the building "h" and the distance from the point on the ground to the base of the building "d".

From the point on the ground, the distance to the top of the antenna is d + 138, and the distance to the bottom of the antenna is d.

Using trigonometry, we can set up two equations:

tan(30.5°) = (d + 138) / h (1)

tan(23.5°) = d / h (2)

We can solve equation (2) for d:

d = h tan(23.5°)

Substituting this into equation (1), we get:

tan(30.5°) = (h tan(23.5°) + 138) / h

Simplifying:

tan(30.5°) = tan(23.5°) + 138/h

tan(30.5°) - tan(23.5°) = 138/h

h = 138 / (tan(30.5°) - tan(23.5°)) ≈ 289.12 feet

Therefore, the height of the building is approximately 289.12 feet.

If the company has 33% more employees than it did a year ago and there are currently 66,500 employees, the number of employees the company had a year ago was proportionately, 50,000 employees.

Proportion refers to the ratio of one quantity or value compared to another.

Proportions are fractional values, representing using fractions, decimals, or percentages.

The current population of a company's employees = 66,500

The percentage increase in the population from last year's = 33%

Proportionately, last year's population = 100%, while this year's population is 133% (100 + 33).

If 66,500 = 133% (1.33), then 100% = 50,000 (66,500 ÷ 1.33)

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Note that  in the line graph presented, 3/4 the distance from A to B is 12, thus, t = 12.

Given:

A (- 2 , 0) and B(14, 0)

Using distance formula,      we can determine the distance between coordinates given:

d    = √ ( (x2 - x1)² + ( y2 - y1) ²)

In this case,  x1 = -2  y1 = 0,

x2 = 14, and y2 =  0.

Substituting these     values into the formula, we get:

d = √(  (14 -   (-2 ) ) ² + (0 - 0) ²)

= √((16)² + (0)² )

= √(256)

= 16

The distanc between the points (-2,0) and (14,0) is 16   units.

Recall that we need to find the position of t which    is 3/4 the distance between A and B.

That is:

3/4 x 16

t = 12.


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The students in 8th class who choose music are 16 in number,

The students in 7th class who choose music are 32 in number

The total who choose world language is 270

The totals who are in 7th grade be 194

The number of students who choose world language in 7th class are 162

Let x be the students in 8th class who choose music

x+108=124

x=124-108

x=16 students

Now  y be the students in 7th class who choose music

16+y=48

y=48-16

y=32

Let z be the total who choose world language

48+z=318

z=318-48

z=270

Now the totals who are in 7th grade be A

124+A=318

A=318-124

A=194

B be the number of students who choose world language in 7th class

Now 32+B=194

B=194-32

B=162

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Answer:

a  

Step-by-step explanation:

Answer:No, X=-3, yly =-4,0,4

Step-by-step explanation:

The exact volume of the soup can is 18.375 π cubic inches. So, correct option is C.

The volume of a cylinder can be found by multiplying the area of the base (circle) by the height of the cylinder. In this case, the diameter of the base is 3.5 inches, which means the radius is 1.75 inches (since radius = diameter/2).

So the area of the base can be calculated as:

π × (1.75 in)² = π × 3.0625 in²

The height of the cylinder is given as 6 inches.

Therefore, the exact volume of the soup can would be:

π × (1.75 in)² × 6 in = π × 3.0625 in² × 6 in = 18.375 π cubic inches (rounded to two decimal places)

So, correct option is C.

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Answer:

Step-by-step explanation:

The third side of Patricia's garden should be approximately 10.64 feet long.

To determine the length of the third side of Patricia's garden, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles. In this case, we have two known side lengths (6 feet and 7 feet) and the angle between them (110 degrees).

The Law of Cosines states that for a triangle with side lengths a, b, and c, and angle C opposite side c:

c² = a² + b² - 2ab*cos(C)

We want to find the length of the third side, so let's call it c. Plugging in the known values:

c² = 6² + 7 - 267*cos(110°)

Simplifying the equation:

c² = 36 + 49 - 84*cos(110°)

Now, we can calculate the value of cos(110°) using a calculator or trigonometric tables. Once we have that value, we can substitute it back into the equation to find c². Taking the square root of c² will give us the length of the third side.

Note: The value of cos(110°) is approximately -0.342.

c² = 36 + 49 - 84*(-0.342)

c² ≈ 36 + 49 + 28.248

c^2 ≈ 113.248

Taking the square root:

c ≈ √113.248

c ≈ 10.64

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Answer:

2(4.5) + (1/2)(4)(2) = 9 + 4 = 13 square feet

Answer:

I Think 62°

Step-by-step explanation:

Answer:

x = 8.4

y = 23.6

Step-by-step explanation:

tan31 = x/14

x = tan31(14) = 8.412

y² = (8.412)² + (22)² = 554.7626

y = √554.7626 = 23.55

The number of malaria cases in 2017 is 2700.

Let the dependent variable, y is malaria cases in thousands and the independent variable, x is the year.

Here, x is the number of years starting in the year 2000.

The required model is obtained as [tex]y = 299e^{0.1295x}[/tex]

Now, the predicted number of malaria cases in the year 2017, that is, x = 17 years can be computed as,

[tex]y = 299e^{0.1295(17)}\\\\= 299(9.020\\\\= 2700[/tex]

Hence, the number of malaria cases in 2017 is 2700.

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We can see that the means we got from Matlab are close to 3.5 for larger numbers of rolls.

We have,

To generate numbers between 1 and 6 in Matlab, we can use the "randi" command.

To generate 10 numbers, we can use:
```matlab
numbers10 = randi([1, 6], [1, 10]);
mean10 = mean(numbers10);
disp(mean10);
```

To generate 100 numbers, we can use:
```matlab
numbers100 = randi([1, 6], [1, 100]);
mean100 = mean(numbers100);
disp(mean100);
```

To generate 1000 numbers, we can use:
```matlab
numbers1000 = randi([1, 6], [1, 1000]);
mean1000 = mean(numbers1000);
disp(mean1000);
```

After running these commands, we will get the means for generating 10, 100, and 1000 numbers between 1 and 6.

As mentioned in the question, the mean of rolling a die is 3.5.

Therefore,

We can see that the means we got from Matlab are close to 3.5 for larger numbers of rolls.

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Answer:

The correct option that compares the end behavior of the functions f and g is D.

For function f, as x → ∞, f(x) → -∞, which means that the function approaches negative infinity as x approaches infinity. This is because the leading term of the function is -17x, which approaches negative infinity as x approaches infinity.

For function g, as x → ∞, g(x) → -∞, which means that the function also approaches negative infinity as x approaches infinity. This is because the leading term of the function is -78/87x, which approaches negative infinity as x approaches infinity.

Therefore, both functions have the same end behavior, which is approaching negative infinity as x approaches infinity.

Rewriting the expression based on the information will be 72(1 + z/72).

In order to transform 72 + z into a product based on 72, we can apply the distributive property of multiplication over addition. Essentially, this property maintains that:

a x (b + c) = a x b + a x c

By extension, we can create the following equation:

72 + z = 72 + 1 x z

In order to produce an equivalent expression as a multiple of 72 and another factor, we would then need to use the distributive rule once again:

72 + 1 x z = 72 x 1 + 72 x z/72

Simplification leads us to arrive at:

72 + z = 72(1 + z/72)

Our end result is expressed as a synthesis between 72 and the expression (1 + z/72), namely:

72(1 + z/72).

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The amount of money Laurie would pay to have the pond cleaned is equal to $3,161.85.

In Mathematics and Geometry, the volume of a hemisphere can be calculated by using the following mathematical equation (formula):

Volume of a hemisphere = 2/3 × πr³

Where:

r represents the radius.

Note: Radius = diameter/2 = 13/2 = 6.5 feet.

By substituting the given parameters into the formula for the volume of a hemisphere, we have the following;

Volume of a hemisphere = 2/3 × 3.14 × (6.5)³

Volume of a hemisphere = 574.881 ft³

Cost = 5.50 × 574.881 ft³

Cost = $3,161.85

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a) The probability that the student was female is 43/76

b) The probability that the student was female AND got a "C" is 9/38

c) The probability that the student was female OR got a "C" is 45/76

We have,

             A   B   C  

Male     16  15  2  33

Female 14  11  18  43

Total     30 26 20 76

a) The probability that the student was female

= 43/76

b) The probability that the student was female AND got a "C"

= 18/76

= 9/38

c) The probability that the student was female OR got a "C"

= 43 /76 + 20/76 - 18/76

= 45/76

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The number line that shows the inequality x < 6 is given by the following option:

Option D.

The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:

The inequality for this problem is given as follows:

x < 6.

Which is composed by the numbers to the left of x = 6, with an open circle, due to the open interval.

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Beth could not join the club because the highest age which is allowed here is only 55 years

Since, A statistical expression obtained from a list of data that refers an abnormal gap from other values.

The statistical rules that instruct us to divides the data or observation values into four parts.

After analyzing the stem leaf diagram, we noticed the youngest age allowed to join the club is 10 years and the club allow highest 55 years old to join.

the plot also defines that the number of members is declined with the age. There is only person in the club who is 55 years. There are few members with the age over 40 years.

hence, Beth did not join the club because her age was above the highest age that allowed in this club.

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Answer:14

Step-by-step explanation:

2 pants can only go with the different shirts once. So it should be 14

Answer:

[tex]1 \frac{7}{20} [/tex]

Step-by-step explanation:

Well you should find a common denominator for 10, 4 and 5 first to be able to mix them. Let's take 20 because it's the smallest number we can convert 10, and 4 and 5 to.

So

[tex] \frac{3 \times 2}{10 \times 2} + \frac{1 \times 5}{4 \times 5} + \frac{4 \times 4}{5 \times 4} [/tex]

And you get

6/20 + 5/20 + 16/20 (now you can add them because they all have 20 as denominator) so = 27/20 = 1 7/20

The numeric value of the function graphed is given as follows:

f(-8) = 6.

The expression for the numeric value of the function in this problem is given as follows:

f(-8).

This means that the input is given as follows:

x = -8.

Passing a vertical line through x = -8, the value of y in which the vertical line crosses the graph is given as follows:

y = 6.

Hence the numeric value is given as follows:

f(-8) = 6.

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Result:

sin(tan⁻¹(x) - tan⁻¹(y)) in terms of x and y only = (x - y) / (1 + xy).

For us to write the expression, we shall use this formular formula:

tan(a - b) = (tan(a) - tan(b)) / (1 + tan(a)tan(b))

where:

a = tan⁻¹(x)

b = tan⁻¹(y)

Next, we have:

tan(tan⁻¹(x) - tan⁻¹(y)) = (tan(tan⁻¹(x)) - tan(tan⁻¹(y))) / (1 + tan(tan⁻¹(x))tan(tan⁻¹(y)))

= (x - y) / (1 + xy)

From both sides, we have sine:

sin(tan⁻¹(x) - tan⁻¹(y)) = sin(tan(x - y / 1 + xy))

So, sin(tan⁻¹(x) - tan⁻¹(y))  

= sin(tan⁻¹(x) - tan⁻¹(y))

= (x - y) / (1 + xy) in terms of x and y.

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It is essential to maximize the volume for a fixed surface area for cost and material waste.

Because it can help to optimize the efficiency of material usage and minimize the cost of production.

In many manufacturing and construction processes, the cost of materials is a significant expense.

By maximizing the volume of an object for a fixed surface area, we can reduce the amount of material needed to construct the object.

This means that we can save money on material costs and reduce waste by using fewer materials overall.

In addition, minimizing the surface area of an object for a fixed volume can also help to reduce production costs.

This is because the surface area of an object is often a factor in determining the time and labor required to produce it.

By minimizing the surface area, we can reduce the amount of time and labor needed to produce the object.

Which can help to reduce production costs.

Therefore, maximizing volume for fixed surface area is an essential consideration in many manufacturing and construction processes.

It help to optimize material usage, minimize waste, and reduce production costs.

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The radius of the circle is approximately 7.9 feet.

The arc length formula (if θ is in degrees) is expressed as:

s = 2πr × (θ/360°)

Where r is radius and θ is the central angle subtended by the arc.

Given that:

Arc length s = 9ft

Central angle subtended by the arc = 65°

Radius r = ?

Plug the given values into the above formula.

s = 2πr × (θ/360°)

9ft = 2 × 3.14 × r × (65/360°)

r = 9ft / 1.133888

r = 7.9 ft

Therefore, the radius is 7.9 ft.

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The exponential function represented in the table is given as follows:

y = 3^x.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

From the table, we have that when x=  0, y = 1, hence the parameter a is given as follows:

a = 1.

When x is increased by one, y is multiplied by three, hence the parameter b is given as follows:

b = 3.

Hence the function is:

y = 3^x.

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Answer:

The function that is a translation one unit right of the function f(x) = log x is k(x) = log(x - 1).

When we shift a function f(x) one unit right, we replace x with (x - a) where "a" is the amount of the shift. In this case, "a" is equal to 1. Therefore, the function becomes:

f(x - 1) = log(x - 1)

This means that the function k(x) = log(x - 1) is obtained by shifting the function f(x) one unit to the right.

Answer:

< QPR = 36

Step-by-step explanation:

Inscribed Angle = 1/2 Intercepted Arc

< QPR = 1/2 ( 72)

< QPR = 36

The mean is 270.75 and the median is 271. While there is no single mode, then we conclude that our mode is 264 and 294 respectively.

By definition:

Mean is the sum of all the numbers in the set divided by the total number of numbers.

Median is the middle value in the set when the numbers are arranged in order.

Mode is the number that appears most frequently in the set.

If we re-arrange the data given in ascending order, we have:

264 264 267 269 273 276 294 297

To calculate Mean:

Add up all the numbers and divide by the total number of numbers:

Mean = (264 + 264 + 267 + 269 + 273 + 276 + 294 + 297) / 8

Mean = 270.75

To calculate Median:

We need to find the middle number in the set. Since there are 8 numbers in the set, the median is the average of the 4th and 5th numbers:

Median = (269 + 273) / 2

Median = 271

To calculate Mode:

We need to determine which number appears most frequently in the set. In this case, there are two numbers that appear twice (264 and 294), and the rest of the numbers appear only once. Therefore, there is no single mode for this data set.

Mode = 264 and 294

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