The variable y varies directly as x and inversely as z. When x = 4 and z= 14, y=2.
Write a combined variation equation and find y when x = 6 and z= 3.

The area of the shelf is 12.5 square inches.

The coordinates of the vertices of the shelf are:

I(10, 15)
J(10, 10)
K(5, 10)

To find the area of the shelf, we can use the formula for the area of a triangle.

Since the shelf is in the shape of a right triangle, we can use the formula:

Area = (base × height) / 2

First, let's find the base and height of the triangle.

The base of the triangle is the horizontal distance between the points J and K.

To find this distance, we subtract the x-coordinates of J and K:

Base = Jx - Kx

Base = 10 - 5

Base = 5 inches

The height of the triangle is the vertical distance between the points J and I.

To find this distance, we subtract the y-coordinates of J and I:

Height = Iy - Jy

Height = 15 -10

Height = 5 inches

Now, we can substitute these values into the formula for the area:

Area = (base × height) / 2

= (5 × 5) / 2

= 25 / 2

= 12.5 square inches

Therefore, the area of the shelf is 12.5 square inches.

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Answer:

In right angle triangle ,hypotenuse is equal to sum of two other sides.so,

(h)^2=(p)^2+(b)^2

(8)^2=(3)^2+(x)^2

64=9+x^2

64-9=x^2

55=x^2

\(\sqrt{55}\)=x

7.4=x

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

To get the perimeter of a rectangle you add all the sides:

10x2 +18x2

20+36

56

When possible, it is often easier and more convenient to use radians to calculate arc length.

We have,

When calculating the length of a given arc, using radians is generally considered easier and more straightforward than using degrees.

This is because the formula for arc length in radians is simpler and involves fewer conversion factors.

The formula for arc length in radians is given by:

Arc length = rθ

where r is the radius of the circle, and θ is the central angle of the arc measured in radians.

On the other hand, the formula for arc length in degrees is given by:

Arc length = (πr/180)θ

where π is the mathematical constant pi, r is the radius of the circle, and θ is the central angle of the arc measured in degrees.

As you can see, the formula for arc length in degrees requires the additional conversion factor of π/180, which can make the calculations more complex and prone to errors.

Therefore,

When possible, it is often easier and more convenient to use radians to calculate arc length.

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Answer:

$3,245

Step-by-step explanation:

Assuming that the $415 is paid yearly, Eddie has to pay a total of $3,245.

2,000 + (415 x 3)

2,000 + 1,245

2,000 + 1,245 = 3,245

The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.

To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.

However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.

Therefore, the dog can run at approximately 3.125 mi/hr.

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a) W(y1, y2) = 2xe^(-4x) b) Yes, {y1, y2} is a fundamental set for the given differential equation.

a) To find the Wronskian of y1 and y2, we need to compute the determinant of the matrix formed by the derivatives of y1 and y2.

Let's start by finding the first derivative of y1 and y2:

y1' = d/dx(e^(-2x)) = -2e^(-2x)

y2' = d/dx(xe^(-2x)) = e^(-2x) - 2xe^(-2x)

Now, let's form the matrix and calculate its determinant:

W(y1, y2) = |y1' y2'|

|-2e^(-2x) e^(-2x) - 2xe^(-2x)|

Expanding the determinant, we have:

W(y1, y2) = (-2e^(-2x))(e^(-2x) - 2xe^(-2x)) - (-2e^(-2x))(e^(-2x) - 2xe^(-2x))

= -2e^(-4x) + 4xe^(-4x) + 2e^(-4x) - 4xe^(-4x)

= 2xe^(-4x)

Therefore, the Wronskian of y1 and y2 on (-∞, ∞) is W(y1, y2) = 2xe^(-4x).

b) To determine if {y1, y2} is a fundamental set for the given differential equation, we need to check if their Wronskian is nonzero for all values of x.

In this case, the differential equationW(y1, y2) = 2xe^(-4x) is not zero for any value of x in the interval (-∞, ∞). Therefore, {y1, y2} is indeed a fundamental set for the given differential equation.

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The sum of 1039 g and 36.7 kg expressed in milligrams (mg) to the correct number of significant figures is 37,739,000 mg.

To perform the addition, we need to convert 36.7 kg to grams before adding it to 1039 g. There are 1000 grams in 1 kilogram, so we multiply 36.7 kg by 1000:

36.7 kg * 1000 g/kg = 36,700 g

Now, we can add 1039 g and 36,700 g:

1039 g + 36,700 g = 37,739 g

To convert grams to milligrams, we multiply by 1000 because there are 1000 milligrams in 1 gram:

37,739 g * 1000 mg/g = 37,739,000 mg

The final result, expressed in milligrams with the correct number of significant figures, is 37,739,000 mg.

The sum of 1039 g and 36.7 kg, expressed in milligrams (mg) with the correct number of significant figures, is 37,739,000 mg. Remember to consider unit conversions and maintain the appropriate number of significant figures throughout the calculation.

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Answer:

Step-by-step explanation:

Do you know who Creati is? He deleted all of my progress and a bunch of other peoples, so I'm trying to get a lot of points and start a protest.

The mathematical expression of the statement -7w mutiply 3w to the power of 5 is -7w * (3w)^5

The mathematical statement is given as:

-7w mutiply 3w to the power of 5

Express the power using the caret sign.

So, we have:

-7w mutiply (3w)^5

Express multiply using the * sign

-7w * (3w)^5

Hence, the mathematical expression of the statement is -7w * (3w)^5

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Answer:

Step-by-step explanation:

Geoff is feeling peckish, so he decides to pop into the shop and grab some snacks. He picks up a packet of crisps for 25p, a can of soup for 68p and a watermelon for £1.47. He wonders why the watermelon is so cheap, but he doesn't question it. He goes to the cashier and hands over a £5 note. The customer behind Geoff wonders "how much change does he get back?"

To figure this out, we need to add up the price of the snacks and take it away from the money Geoff gave. We can use a dot to show the pence as parts of a pound. For example, 25p = 0.25 pounds.

The price of the snacks is:

0.25 + 0.68 + 1.47 = 2.40 pounds

The money Geoff gave is:

5.00 pounds

The change is:

5.00 - 2.40 = 2.60 pounds

So, Geoff gets £2.60 in change and a bargain watermelon.

Answer:

Answer:

2.60

Step-by-step explanation:

25+68+147=240

500-240=260

turn into pounds 2.60

Step-by-step explanation:

2 bananas + 1 apple = £1.16

1 banana + 1 apple = £0.71

=> 1 banana = 1.16 - 0.71 = £0.45

=> 1 apple = 0.71 - 0.45 = £0.26

Ans: £0.26

Ok done. Thank to me >:333

The probability that fewer than 3 of them use their smartphones in meetings or classes is 0.0366.

The binomial probability distribution is a discrete probability law with two parameters: trial number (n) and success probability (p) (p). When there are two mutually exclusive outcomes of finite trials, the binomial distribution is utilised.

The probability that a specific 3 people all use their smartphones in meetings or class is 0.53³.

Probability that remaining 7 people do not use their phone is 0.47⁷

¹⁰C₃ = 10*9*8/(3*2*1) = 120.

Thus, the probability of exactly 3 people using their smartphones in meetings or in class is 10C3*0.533*0.477, or 0.0905.

So, adding up the 3 possibilities (that 0 of them, 1 of them, or 2 of them use their smartphones in meetings or class) we get

¹⁰C₀*0.530*0.4710 + ¹⁰C₁*0.531*0.479 + ¹⁰C₂*0.532*0.478 = 0.0366.

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Complete question:

Assume that when adults with smartphones are randomly​ selected, 53​% use them in meetings or classes. If 10 adult smartphone users are randomly​ selected, find the probability that fewer than 3 of them use their smartphones in meetings or classes.

The sample space as Feechi makes three attempts at a basket in a basketball game is BBB, BMB, MBM, MMM).Option A

The sample space represents all possible outcomes of Feechi's three attempts, where each attempt can either result in a basket (B) or a miss (M).

Option A lists the following four outcomes: BBB, BMB, MBM, and MMM. Each outcome is a sequence of three letters, where B represents a basket and M represents a miss.

Therefore, the correct answer IS (BBB, BMB, MBM, MMM).

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The sample space for Feechi's result would be = (BBB, BBM, BMB, BMM, MBB, MBM, MMB, MMM). That is option D.

The various moves to make a successful attempt at the basket was done 3 times.

When she gets a B = Basket

When she gets an M = Miss

The possible outcome of the sample space would be = (BBB, BBM, BMB, BMM, MBB, MBM, MMB, MMM).

This is because only 8 unique arrangements can be gotten from the list of possible outcomes.

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Answer:

Im pretty sure its C

Answer: The answer is C

Step-by-step explanation:

Answer:

9x − 3

Step-by-step explanation:

−9x + 3 = −1(−9x + 3) Multiply the expression by −1.

−1(−9x) + −1(3) Distributive Property

9x − 3 Simplify.

The additive inverse of the given expression is 9x-3​.

The given expression is -9x+3.

The additive inverse of a number is its opposite number. If a number is added to its additive inverse, the sum of both the numbers becomes zero. The simple rule is to change the positive number to a negative number and vice versa.

The additive inverse of the expression is -(expression).

Now, -(-9x+3)

= 9x-3

Therefore, the additive inverse of the given expression is 9x-3​.

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The value of x is 52.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

On a test:

3 minutes = 1 multiple-choice question

8 minutes = 1 free-response question.

The number of questions =  15 questions

Time given to complete =  55 minutes

From the table,

m = 1

Where m = number of question

We can make expressions such as,

m + 15 - m = 15

1 + 15 - 1 = 15

15 = 15

And,

3m + x = 55

3 x 1 + x = 55

3 + x = 55

x = 55 - 3

x = 52

Thus,

The value of x is 52.

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The alpha level for this test is 0.1492 (rounded to three decimal places).
So, α = 0.149.

To determine the corresponding alpha level for a critical z-score of 1.036 in a right-tail test, we need to find the area to the right of the z-score on the standard normal distribution table.
Using a standard normal distribution table or calculator,

we can find that the area to the right of a z-score of 1.036 is 0.1492 (rounded to four decimal places).

Since this is a right-tail test, the alpha level is equal to the probability of rejecting the null hypothesis when it is actually true, which is the area in the tail beyond the critical value.

Therefore, the alpha level for this test is 0.1492 (rounded to three decimal places).

So, α = 0.149.

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Answer:THe answer is 98.78x

Step-by-step explanation:

2r34 means 567

The equation isn't written out so I can't be sure but here are possible answers.

2.2 divided by 6 is 0.36. 0.36 minus 2 is -1.64.

6 minus 2 is 4. 2.2 divided by 4 is 0.55.

The gross salary for a sales of 40000 dollars is 5500 dollars.

A man receives a monthly salary of $3 500 together with a commission of

5% on all sales over $5 000 per month.

Therefore, his gross salary in a month in which his sales amounted to

40,000 dollars can be calculated as follows:

Hence,

gross salary = 3500 + 5% of 40000

gross salary = 3500 + 5 / 100 × 40000

gross salary = 3500 + 400(5)

gross salary = 3500 + 2000

gross salary = 5500 dollars

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Answer:

Step-by-step explanation:

\(H(t) = 14000(0.8)^{t +3}\\\\ = 14000*(0.8)^{t}*(0.8)^{3}\\\\=14000*(0.8)^{t}*0.512\\\\=7168(0.8)^{t}\)

Answer:

it is 7168(0.8)t

Step-by-step explanation:

hope this helped

Using Euler's Method with a step size of h = 0.1, the approximate values of the solution at t = 0.1, 0.2, 0.3, 0.4, and 0.5 are:

t = 0.1: y ≈ 1.1

t = 0.2: y ≈ 1.22

t = 0.3: y ≈ 1.34

t = 0.4: y ≈ 1.47

t = 0.5: y ≈ 1.61

To use Euler's Method, we start with an initial condition. In this case, the given initial condition is y(0) = 1. We can then iteratively calculate the approximate values of the solution at each desired time point using the formula:

Yn = Yn-1 + h * F(Xn-1, Yn-1)

Here, h represents the step size (0.1 in this case), Xn-1 is the previous time point (t = Xn-1), Yn-1 is the solution value at the previous time point, and F(Xn-1, Yn-1) represents the derivative of the solution function.

For the given differential equation +2y = 2 - ey, we can rearrange it to the form y' = (2 - ey) / 2. The derivative function F(Xn-1, Yn-1) is then (2 - eYn-1) / 2.

Using the initial condition y(0) = 1, we can proceed with the calculations:

t = 0.1:

Y1 = Y0 + h * F(X0, Y0)

= 1 + 0.1 * [(2 - e^1) / 2]

≈ 1 + 0.1 * (2 - 0.368) / 2

≈ 1 + 0.1 * 1.316 / 2

≈ 1 + 0.1316

≈ 1.1

Similarly, we can calculate the approximate values of the solution at t = 0.2, 0.3, 0.4, and 0.5 using the same formula and previous results.

Using Euler's Method with a step size of h = 0.1, we found the approximate values of the solution at t = 0.1, 0.2, 0.3, 0.4, and 0.5 to be 1.1, 1.22, 1.34, 1.47, and 1.61, respectively.

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The firm 4's efficient scale occurs at 4

In this question, we have been given a table of long-run total cost and the quantity.

We need to find the quantity at which the firm 4's efficient scale occurs.

We know that the efficient scale occurs at the quantity of output where average total cost is minimum.

For the firm 4 the average total cost would be,

(210 + 340 + 490 + 660 + 850 + 1060 + 1290) / 7

= 4900 / 7

= 700

This value is clsoe to 660.

Therefore, the firm 4's efficient scale occurs at quantity 4.

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Given question is incomplete.

Answer:

24/7 or 6.75 or 6 3/4

Step-by-step explanation:

Answer:

1) 22.4

2) 91

3) 6

explanation:

i converted the fraction to decimals or whole numbers and multiplied

The first derivative of the function g(t) is 4t + 1.

To find the derivative of g(t) = 2\(t^{2}\) + t using only the definition of the derivative, we need to apply the limit definition of the derivative.

The definition of the derivative of a function f(x) at a point x = a is given by:

f'(a) = lim(h -> 0) [f(a + h) - f(a)] / h

Let's apply this definition to g(t):

g'(t) = lim(h -> 0) [g(t + h) - g(t)] / h

First, let's calculate g(t + h):

g(t + h) = 2\((t+h)^{2}\) + (t + h)

= 2(\(t^{2}\) + 2th + \(h^{2}\)) + t + h

= 2\(t^{2}\) + 4th + 2\(h^{2}\) + t + h

Now, let's substitute g(t) and g(t + h) back into the definition of the derivative:

g'(t) = lim(h -> 0) [(2\(t^{2}\) + 4th + 2\(h^{2}\) + t + h) - (2\(t^{2}\) + t)] / h

= lim(h -> 0) [4th + 2\(h^{2}\) + h] / h

= lim(h -> 0) 4t + 2h + 1

Taking the limit as h approaches 0, the h terms cancel out, and we are left with:

g'(t) = 4t + 1

Therefore, the first derivative of g(t) = 2\(t^{2}\) + t is g'(t) = 4t + 1.

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The answer would be

A.) ~-12~

because 2-24=-22 -22+8+2=-12  

B.)~16~

because 6+8-8+10 and -8+8=0 so 6+10=16

Hope this helps

Have a great day/night

Feel free to ask any questions

Answer:

f(0)=4 we write the equetion in the form of

\(f(x) = mx + b\)

which is

1st f(x)= 4x+4 then y-intercept is b= 4

2nd f(x) = 7x-3 then x-intercept is x=3/7

3rd f(x)= -2x + 2 then x-intercept is x= 1

Answer:

figure d

Step-by-step explanation:

it is the smartes and most common answer