Many practical applications require calculations of area. some of these calculations are straightforward, but others are more difficult, and it turns out that the idea of the definite integral can help us with the more difficult cases. let’s start with some familiar shapes. what is the area of a rectangle of length l and width w? express your answer in terms of l and w.

Answer: [tex]x^2+y^2=16[/tex]

Step-by-step explanation:

The general equation of a circle having center at (h,k) and radius r is given by :-

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Given: Radius of the circle : r= 4 units

The center of the circle :  (h,k)=(0,0)

Now, the equation of a circle having center at (0,0) and radius 4 units is given by :-

[tex](x-0)^2+(y-0)^2=4^2\\\\\Rightarrow\ x^2+y^2=16[/tex]

Answer:

X²+Y²=16

Step-by-step explanation:

A p e x

Answer:

5.4? I don't really know I'm just going off other answers but clearing it up,,,hope it help :')

Step-by-step explanation:

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y=3x^{2}-5[/tex] -----> quadratic equation of a vertical parabola open upward

Find the inverse function

Exchange variables x for y and y for x

[tex]x=3y^{2}-5[/tex]

Isolate the variable y

[tex]3y^{2}=x+5[/tex]  -----> inverse function (horizontal parabola open to the right)

or

[tex]y=(+/-)\sqrt{\frac{x+5}{3}}[/tex]

using a graphing tool

see the attached figure

The graph of function and it's inverse of the graph is shown in image.

We have to given that,

To graph the function y = 3x² - 5 and it's inverse.

Here, The equation is,

y = 3x² - 5

So, We can find it's inverse as,

y = 3x² - 5

y + 5 = 3x²

(y + 5) / 3 = x²

x² = (y + 5)/3

x = √(y + 5)/3

Hence, the inverse of function is,

f ⁻¹ (x) = √ (x + 5)/3

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ6

Final answer:

The probability that the maintenance man will open the storage door on his fourth try with 12 keys is 1/12.

Explanation:

The question asks for the probability that the maintenance man will open a storage room door on his fourth try with 12 unique keys at his disposal. This is a classic probability problem that involves permutations.

To solve this, we consider the scenario as a sequence of independent events. He has 1 out of 12 chances to pick the correct key on the first try, 1 out of 11 on the second try (after discarding the first incorrect key), 1 out of 10 on the third try, and so on. However, we want the first three attempts to be unsuccessful and the fourth to be successful.

Thus, the probability that the first three keys are incorrect is (11/12) * (10/11) * (9/10), and the probability the fourth key is correct is 1/9. The overall probability of the desired outcome is the product of these probabilities, which simplifies to:

(11/12) * (10/11) * (9/10) * (1/9) = 1/12.

Answer:

Option C

Step-by-step explanation:

In the given right angle triangle

Hypotenuse = 4.5 cm

Height = 2.5 cm

and base = g cm.

Pythagoras theorem says

(hypotenuse)² = (base)² + (height)²

So by putting the values in the formula

(4.5)² + (2.5)² + g²

Option C is the answer.

1 degree = 0.0174533 radians

85* 0.0174533 = 1.4835305 radians

Round answer as needed

Answer:

17pi/36 (PLATO answer)

Step-by-step explanation:

Final answer:

The new balance after 8 years with an initial $950 at a 7% annual interest rate compounded annually is $1632.77, and the amount of interest earned is $682.77.

Explanation:

The compounded interest formula is P(1+r)^t, where P is the principal amount, r is the annual interest rate (in decimal form), and t is the time in years. To find the new balance and amount of interest earned for $950 at 7% for 8 years, compounded annually, we use the formula with P = $950, r = 0.07 (7% as a decimal), and t = 8.

First, we calculate the new balance:

Total Amount = $950(1 + 0.07)^8

Total Amount = $950(1.07)^8

Total Amount = $950 * 1.718186

Total Amount = $1632.77 (rounded to two decimal places)

Subsequently, to find the amount of interest earned, we subtract the original principal from the total amount:

Interest Amount = Total Amount - Original Principal

Interest Amount = $1632.77 - $950

Interest Amount = $682.77

Therefore, the new balance after 8 years is $1632.77, and the interest earned is $682.77.

The sample space for the random experiment of playing blackjack until a loss or a maximum of three games are played is represented by the set {l, wl, ww}.

The sample space for this scenario comprises of all possible outcomes of playing "blackjack" until the person loses or has played three games. We represent win and loss by w and l respectively. By these definitions, we get the following possibilities: l (losing on the first game), wl (winning the first game then losing the second), and ww (winning the first two games and decide not to play a third game or it wasn't possible to play a third game). This assumes that the player stops after either losing a game or after playing the third game, even if he won that.

Note that the scenario where the player wins all three games (www) is not included in the sample space because the problem states that the player will stop playing as soon as they lose a game.

https://brainly.com/question/30206035

#SPJ12

Final answer:

To find the number that is 24% of 25, you multiply 0.24 by 25, which equals 6.

Explanation:

To find what number a is 24% of 25, we can set up an equation using the concept that a percent is a way of expressing a fractional amount of something.

We know that 24% means 24 out of 100, which can be written as the fraction 24/100 or 0.24 in decimal form.

To translate the question into an equation, we write:

a = 0.24 × 25

Next, we calculate the value of a by multiplying 0.24 (the decimal form of 24%) by 25. This gives us:

a = 6

Therefore, the number a, i.e., 24% of 25 is 6.

Answer:

2004

Step-by-step explanation:

The mean number of overtime hours worked is 3.4 with a standard deviation of approximately 1.4 hours, which corresponds to option D.

The correct answer for the given probability distribution of overtime hours worked per employee in one week is D. An employee works an average of 3.4 overtime hours per week with a standard deviation of approximately 1.4 hours.

To find the mean (μ) of the probability distribution, we multiply each possible value by its corresponding probability and then sum all these products. The mean of this distribution is given as 3.4, which is found by summing up the product of each value of overtime hours and its corresponding probability:

μ = (0 * 0.026) + (1 * 0.072) + (2 * 0.154) + (3 * 0.303) + (4 * 0.215) + (5 * 0.164) + (6 * 0.066) = 3.4

The variance (σ2) is calculated by taking each value's deviation from the mean, squaring it, multiplying by the probability, and summing all these values. The variance for this distribution is given as 2.0:

σ2 = Σ [(x - μ)2 * P(x)] = 2.0

And the standard deviation (σ) is simply the square root of the variance:

σ = √σ2 = 1.4

Since pi is equivalent to 3.14 and means 180°, therefore 1.75 which is about half of pi should be at almost 90°. The cos of a 90° angle which is located on the y axis should be zero, therefore cos 1.75 must be near zero. However in this case it is near one, clearly his calculator is in degree mode that is why he got an erroneous answer.

What Sam can do to get the correct answer would be to convert his calculator into radian mode or convert the given 1.75 rad into degrees:

θ = 1.75 rad (180° / π rad)

θ = 100.2676

cos 100.2676 = -0.1782   which is now correct since it is nearer to zero

Starting at vertex V going until vertex S, we make our calculations.

VR = 14

Rx = x

therefore, xS = VR – Rx

xS = 14 – x                           ---> 1

Now starting at vertex V going left to vertex S, we make our next set of calculations. Assuming x is on VR but nearer R

VR  = 14 - x

at UV = 15 – (14 – x)

at UV = 1 + x

at TU = 7 – (1 + x)

at TU = 6 – x

at ST = 9 – (6 – x)

at ST = 3 + x                        ---> 2

Equate 1 and 2:

14 – x = 3 + x

2 x = 11

x = 5.5

To find the value of x in the circumscribed pentagon RSTUV with given sides, we set up an equation based on the sum of the lengths of the opposite sides. After solving the equation, we determined that x is 25.

Pentagon RSTUV and the Value of x

Given that pentagon RSTUV is circumscribed about a circle, we need to find the value of x,

where RS = 6, ST = 9, TU = 7, UV = 15, and VR = 14.

For a polygon circumscribed about a circle, the sum of the lengths of the pairs of opposite sides must be equal. Therefore, we can set up the equation:

RS + TU + x = ST + UV + VR

Substituting the given values:

6 + 7 + x = 9 + 15 + 14

Simplifying the right-hand side:

Thus, the value of x is 25.

Answer:

The standard normal table gives areas under the curve to the left of z-scores.

Find the probability in the standard normal table that a value is to the left of 1.9.

Find the probability in the standard normal table that a value is to the left of 0.4.

Subtract the probability of a value being to the left of 0.4 from the probability of a value being to the left of 1.9.

Step-by-step explanation:

edge2020

In order to find the probability associated with the shaded area under the curve using the standard normal table, you should subtract the probability of a value left of 0.4 from the probability of a value left of 1.9.

We are trying to find the probability of the area between 1.9 and 0.4 so the first thing to do is to find the probability that a value is to the left of 1.9 from the Standard normal table.

After this is done, you then find the probability that the value is left of 0.4.

To find the probability of the middle area, subtract the value to the left of 0.4 from that of the value left of 1.9

Find out more on the standard normal table at https://brainly.com/question/7001627.

Answer:

8 1/4

Step-by-step explanation: