will this decay still be an exponential function of time? will the time constant have changed? explain.

Answer:

they are equal

Step-by-step explanation:

\(\frac{1}{4}\) × 48 ( cancel 4 and 48 by 4 )

= 1 × 12 = 12

\(\frac{1}{5}\) × 60  ( cancel 5 and 60 by 5 )

= 1 × 12 = 12

The 2 quantities are equal

Answer:

7

Step-by-step explanation:

450-100=350

350/50=7

7 months

First frame is for b and second frame is for c

TT is equal to T-1, so the given matrix is an orthogonal matrix.

What is an orthogonal matrix?

Here, the determinant of T,

 |T| = cos²∅ + sin²∅

      = 1

Now, its cofactors,

\(T_{11}\) = cos ∅

\(T_{12\) = sin ∅

       \(T_{21\)= -sin ∅

\(T_{22\) = cos ∅

Now, the adjoint matrix of cofactors matrix transpose \(T^T\) is equal to \(T^{-1.\)

Hence, the given matrix is an orthogonal matrix.

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Answer:

\( h \le 30 \)

Step-by-step explanation:

Let h = number of hours of work.

At most 30 hours means 30 hours or less.

\( h \le 30 \)

The correct answer is ∫∫D 9cos(9(v-u)/2) dudv = 2∫[u=-10 to u=1] ∫[v=u to v=10] 9cos(9(v-u)/2) dvdv

To evaluate the integral using the given transformation, we need to find the Jacobian determinant of the transformation and then apply the change of variables.

The transformation is given by:

u = y - x

v = y + x

To find the Jacobian determinant, we calculate the partial derivatives of u and v with respect to x and y:

∂u/∂x = -1

∂u/∂y = 1

∂v/∂x = 1

∂v/∂y = 1

The Jacobian determinant is the determinant of the matrix of these partial derivatives:

|∂u/∂x ∂u/∂y|

|∂v/∂x ∂v/∂y|

Jacobian determinant = | -1 1 |

| 1 1 |

Taking the determinant:

Jacobian determinant = (-1)(1) - (1)(1) = -2

Now, we can rewrite the integral using the variables u and v:

∫∫R 9cos(9y) dA = ∫∫D 9cos(9(v-u)/2) |J| dudv

where D is the transformed region corresponding to R, and |J| is the absolute value of the Jacobian determinant.

The region D is determined by the transformation of the vertices of R:

(9, 0) -> (0, 9)

(10, 0) -> (1, 10)

(0, 10) -> (-10, 10)

(0, 9) -> (-9, 9)

Therefore, the integral becomes:

∫∫D 9cos(9(v-u)/2) |J| dudv = ∫∫D 9cos(9(v-u)/2) |-2| dudv

= 2∫∫D 9cos(9(v-u)/2) dudv

Now, we evaluate the integral over the transformed region D, which is a trapezoid:

∫∫D 9cos(9(v-u)/2) dudv = 2∫[u=-10 to u=1] ∫[v=u to v=10] 9cos(9(v-u)/2) dvdv

This is the final form of the integral that can be evaluated numerically.

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We get that ∠5 can be written as ∠ HDC, ∠ 3 can be written as ∠ GDE and the vertex of ∠ 2 is D.

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle. The word angle comes from a Latin word named 'angulus,' meaning “corner.”

We are given a diagram.

We need to name the angles.

∠5 can be written as ∠ HDC

∠ 3 can be written as ∠ GDE

Vertex of ∠ 2 is D

Therefore, we get that ∠5 can be written as ∠ HDC, ∠ 3 can be written as ∠ GDE and the vertex of ∠ 2 is D.

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Answer:

i think 220

Step-by-step explanation:

because if he swim 250 then 30 less it would be 220

Answer:

7525 milliliters

Step-by-step explanation:

because if you multiply 2150 by 3.5 you will get that number

Answer:

Step-by-step explanation:

2/5 is 0.4

0.75 is 3/4

5/8 is 0.625

0.875 is 7/8

2/5=0.4

0.75=3/4

5/8=0.625

0.875=7/8

Using three equal subintervals and a right riemann sum, left riemann sum, and a midpoint sum is -6.4, 3.8, -1.0.

1) Integral with left end points:

         A-left = -3.4*2 + (-0.6)*2 + 0.8*2 = -6.4

2) Integral with right end points:

        A-right = -0.6*2 + 0.8*2 + 1.7*2 = 3.8

3) Integral with midpoints:

         A-mid = -2.2*2 + 0.2*2 + 1.5*2 = -1.0

A specific type of approximation of an integral by a finite sum in mathematics is known as a Riemann sum. It bears the name of the German mathematician Bernhard Riemann from the nineteenth century. Approximating the area of functions or lines on a graph, as well as the length of curves and other approximations, is a highly typical use.

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The value of x from given linear equation is -4.

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

For example, 2x+3=8 is a linear equation having a single variable in it.

Given that x + 16 + x = – 3 x – 4

To find the value of x solving the given linear equation

x + 16 + x = – 3 x – 4

⇒ 2x + 16 = -3x - 4

⇒ 2x + 3x = -4 -16

⇒ 5x = -20

⇒ x = -20/5

⇒ x = -4

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Answer:

a=7

Step-by-step explanation:

These two angles are complementary and the sum of their measures is 90°.

Therefore, we can create the equation: (5a+3)+52=90.

1. combine like terms. the equation becomes 5a+55=90.

2. -55 to both sides of the equation. the equation becomes 5a=35.

3. /5 to both sides of the equation. we can reach the conclusion that a=7

Answer: 87.6719183867

Step-by-step explanation:

Exact Form: √ 7686.3652736

Decimal Form: 87.67191838 …

Step-by-step explanation: The radical cannot be simplified, but it can be approximated.

Give me brainliest or a thank you pls :)

The total surface area of the figure is 498 cm².

We are given that;

s = 6 cm, h = 8 cm

Using the properties of this special triangle, we can find that:

a = s/2√3 = 6/2√3 = 3/√3 cm b = √(h² + a²) = √(8² + (3/√3)²) = √(64 + 9/3) = √(73) cm

Now we can plug these values into the formulas and simplify:

Surface area of a hexagonal prism = 6s(a + h) = 6(6)(3/√3 + 8) = 36(9/√3 + 8) ≈ 432.47 cm² Surface area of a hexagonal pyramid = 3ab + 3bs = 3(3/√3)(√73) + 3(6)(√73) = 9√73 + 18√73 = 27√73 ≈ 159.12 cm² Area of a hexagonal base = (3√3/2)s² = (3√3/2)(6)² = (9√3)(6) ≈ 93.53 cm²

Total surface area of the figure = Surface area of prism + Surface area of pyramid - Area of common base = 432.47 + 159.12 - 93.53 = 498.06 cm²

Rounding to the nearest square centimeter=498 cm²

Therefore, by the area the answer will be 498 cm².

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The amount that Benjamin must save every month to pay off the discounted premium is $ 40. 80

The total premium for the year would be $ 637. 20

The amount that Benjamin's discounted premium would come to for the year is:

= 1, 080 x ( 1 - 66 %)

= $ 367. 20

The amount he would need to save every month on deployment is :

= 367. 20 / 9

= $ 40. 80

His total premium would be :

= 367. 20 + ( 1, 080 / 12 x 3 months when he comes back )

= $ 637. 20

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Answer:

234.01

Step-by-step explanation:

add all those together then subtract for total

MARK ME AS BRAINLIEST

Answer:

f(x) C= x+50 x=17.50$/h

Step-by-step explanation:

I might not be sure about it, but it might be a function that is f(x) C= x + 50 dollars

x=17.50 dollars /hour

so that means if it is 1 hour, then 17.50$ +50$ which is 67.50$, if it's 2 hours then 17.50$/h = n$/2h so n=17.50$ *2 = 35$ + 50$ = 85$

The factored form of the expression x² + 5x+6 is (x + 3)(x + 2)

To factorize the quadratic equation, we need to take the following steps;

Multiply the coefficient of the x squared by the constant value, we have;

6

Now, find the pair factors of the product that would add up to give 5, we have;

2 + 3

Substitute the values into the expression, we have;

x² + 2x + 3x + 6

Now, group the expression in pairs, we have;

(x² + 2x) + (3x + 6)

Factorize the expressions

x(x + 2) + 3(x + 2)

Then, we have;

x + 3

x + 2

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Answer:

L: 14.5

W: 7.25

Step-by-step explanation:

Write out all dimensions

l+l+w+w

combine like terms

solve the equation

Answer:

14/17

Step-by-step explanation:

14/17 as a fraction can't be simplified. 17 is a prime number, so it can't be divided by anything except 1.

If the question you're asking is 14-17, the answer would be -3...

I hope this helped you out!! Have an awesome day C:

Step-by-step explanation:

if you are subtracting it is -3

if you are dividing it is 0.823

if you are looking for an equivalent fraction it is 28/34

Answer:

y = - 2x + 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (1, - 1) and (x₂, y₂ ) = (2, - 3) ← 2 ordered pairs from the table

m = \(\frac{-3-(-1)}{2-1}\) = \(\frac{-3+1}{1}\) = - 2 , then

y = - 2x + c ← is the partial equation

To find c substitute any ordered pair from the table into the partial equation

Using (3, - 5 ) , then

- 5 = - 6 + c ⇒ c = - 5 + 6 = 1

y = - 2x + 1 ← equation of line

Answer:

Step-by-step explanation:

We will need to find the equation and put it in the form y = mx + b where m is the slope and b is the y intercept.

Step 1 - Calculate the slope via the slope formula:

\(\frac{(y2 - y1)}{(x2 - x1}\)

We will use the first two x and y variables in the table, so simply plug the values in.

\(\frac{(-3) - (-1)}{2 - 1}\\\)

= \(\frac{-2}{1} = -2\)

This means the slope is 2 (y = -2x + b).

Step 2 - Plug the variables in:

To calculate the b, we can use one of the pairs of coordinates i.e. (1, -1) to calculate b by putting the variables into the above equation:

y = -2x + b

-1 = -2(1) + b

-1 = -2 + b

-1 + 2 = b

b = 1

This means the equation is:

y = -2x + 1

Hope this helps!

The change in profit (ΔP) when the number of units (Δx) increases by 5, based on the given marginal profit function, is -18331.50

To find the change in profit (ΔP) when the number of units (Δx) increases by 5.

we need to evaluate the marginal profit function and multiply it by Δx.

The marginal profit function is given by dP/dx = 12.1(60 - 3x).

We are given the value of x as 121, so we can substitute it into the marginal profit function to find the marginal profit at that point.

dP/dx = 12.1(60 - 3(121))

= 12.1(60 - 363)

= 12.1(-303)

= -3666.3

Now, we can calculate the change in profit (ΔP) by multiplying the marginal profit by Δx, which is 5 in this case.

ΔP = dP/dx×Δx

= -3666.3 × 5

= -18331.5

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The points express the XY relationship on coordinate plane is (4, 2) and (14, 7)

In mathematics, a system of locating a point in the space by the reference axis X and Y. A point is identified as (x, y) where x denotes the x coordinate of the point and y denotes the y coordinate of that point.

Given, Lila has 2 sweaters for every 4 t-shirts

let she has W number of t-shirt for 7 sweaters

now, W = 4/2 x 7 = 14 t-shirts

hence, she has 14 t-shirts for 7 sweaters

given, t-shirt are X variable and sweaters are Y variables

We can show the XY relationship as a point on the XY coordinate system

Let, the first condition is a point P(x, y) = P(4, 2)

The second condition is a point Q (x, y) = Q (14, 7)

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Answer:

D

Step-by-step explanation:

If it is September, then it is my birthday

The converse of the statement "If it is my birthday, then it is September" is If it is September, then it is my birthday option (D) is correct.

A conditional statement with the antecedent and effect reversed is known as a converse statement.

We have a statement:

"If it is my birthday, then it is September"

As per definition, the converse of the statement says antecedent and effect reversed is known as a converse statement.

We can converse the given statement as follows:

If it is September, then it is my birthday.

Thus, the converse of the statement "If it is my birthday, then it is September" is If it is September, then it is my birthday option (D) is correct.

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Answer:

The unit rate = 27 miles per gallon.

Hence, option C is true.

Step-by-step explanation:

From the given line graph:

Taking two points

The unit rate can be determined by finding the rate of change or slope between the points (2, 54) and (6, 162)

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(\left(x_1,\:y_1\right)=\left(2,\:54\right),\:\left(x_2,\:y_2\right)=\left(6,\:162\right)\)

\(m=\frac{162-54}{6-2}\)

Refine

\(m=27\)

Therefore, the unit rate = 27 miles per gallon.

Hence, option C is true.

Step-by-step explanation:

the answer is 8

5-(-1-2)

5-(-3)

5+3

=8

Answer:

$122.88

Step-by-step explanation:

the phone decreases by 20% each year , that is

(100 - 20)% = 80% = \(\frac{80}{100}\) = 0.8

the phone reduces by a factor of 0.8 each year , then after 4 years

value = $300 × \((0.8)^{4}\) = $122.88

Answer:

16

Step-by-step explanation:

there is a differnce of 6 between -3 and +3, so the answer is 6 smaller.

Answer:22

Step-by-step explanation: