A greeting card has a perimeter of 80 cm and an area of 384 square cm what are the dimensions for the greeting card

Answer:

4 days

Step-by-step explanation:

because Mariana drank 2 pints a day 8 pints are in a gallon so 8 ÷ 2 = 4

The model of labor-leisure choice can be consistent with the observations of large increases in real wages and falling hours worked on average per labor-market participant over the 20th century in advanced economies.

In the labor-leisure choice model, individuals make decisions regarding how much time to allocate between work (labor) and leisure activities. As real wages increase, individuals can earn higher income per hour worked, which creates an opportunity cost for leisure time. This can incentivize individuals to work more hours to maximize their income and consumption.

However, as real wages continue to rise, individuals may reach a point where they have satisfied their desired level of consumption and choose to value leisure time more. This can lead to a decrease in the number of hours worked on average per labor-market participant, even as real wages continue to increase.

Therefore, the model of labor-leisure choice suggests that as real wages increase, individuals may choose to work fewer hours on average, prioritizing leisure time over additional income, which can explain the observed trend of falling hours worked alongside large increases in real wages over the 20th century in advanced economies.

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Answer:

152°

Step-by-step explanation:

2x + 48 = 3x - 4 (the measure of an exterior angle of a triangle = the sum of the measures of the two non-adjacent interior angles of the triangle)
=> 4 + 48 = 3x - 2x (on transposing)
=> 52 = x
Substituting the vale of x in the m∠JKM,
m∠JKM = 3x - 4 = 3(52) - 4 = 152°

Hope you understood!!

The value of power is 27/64.

Rochelle used these steps to evaluate the power.

\( \left (\dfrac{3}{4}\right )^3\)

What is the value of power?

To determine the value of the power following all the steps given.

Expression; \( \left (\dfrac{3}{4}\right )^3\)

Then,

The value of power is,

\(= \dfrac{3}{4} \times \dfrac{3}{4} \times \dfrac{3}{4}\\ \\ = \dfrac{9}{16} \times \dfrac{3}{4}\\\\ = \dfrac{27}{64}\)

Hence, The value of power is 27/64.

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Answer:

-27/64

Step-by-step explanation:

Answer:

Step-by-step explanation:

the average rate of change is m= -1/4

Answer:

To find out how much the TV is worth now, we need to apply the depreciation rate of 9% to the original price for 8 months:

First, let's calculate the value after the first month:

Value after 1 month = $2740 - (9% of $2740) = $2501.40

Now, let's calculate the value after 2 months:

Value after 2 months = $2501.40 - (9% of $2501.40) = $2275.80

We can continue this process for 8 months to find the current value:

Value after 3 months = $2071.67

Value after 4 months = $1888.81

Value after 5 months = $1725.10

Value after 6 months = $1579.92

Value after 7 months = $1452.16

Value after 8 months = $1339.53

Therefore, the TV is worth $1,339.53 now.

The area is given by 0.4291 units.

The points of intersection are given by,

y = 1+sin2x=e^(x/2). The y-intercept ( x = 0 ) for both are the same 1.

So, one common point is (0, 1). Glory to Socratic utility, the other is

approximated graphically to 4-sd as 1.136.

Now, the area is

∫(f−g)dx,   for x from 0 to 1.136

∫((1 + sin(2x)) − (eˣ/₂)dx, for x from 0 to 1.136

=[(x − 1/2cos(2x)) − (2eˣ/₂)], between 0 and 1.136

=(1.136 − 1/2cos(2.272) − 2e^1.16/2) (−5/2)

=0.4291 units.

The limit of a function in mathematics is a key idea in calculus and analysis regarding the behavior of that function close to a specific input.

Informally, a function f gives each input x an output f(x). If f(x) approaches L as x approaches input p, we say that the function has a limit L at that location. More specifically, any input that is sufficiently close to p when f is applied forces the output value arbitrarily close to L.

The term "limit" is also used in the definition of the mathematical term "derivative," which in one-variable calculus refers to the maximum value of the slope of secant lines on a function's graph.

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The total number of social security numbers that are possible are 900,000,000.

In the social security number first digit can only fall between 1 and 9, leaving us only nine options because the first three digits cannot all be zeros. There are still 10 possibilities for each of the second and third digits because they may both still be any integer between 0 and 9.

Therefore, the total number of different social security numbers that can be formed is using the combinations,

= 9 × 10⁸

= 900,000,000

So, there are 900,000,000 different possible social security numbers.

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Answer:

Option b) Use the results from the 2014 survey.

Step-by-step explanation:

Using the results from the 2014 survey can reduce the sample size needed for the new survey, as it provides a good estimate of the population proportion. This reduces the margin of error and increases the confidence level of the new survey.

The stress in the aluminum rod under the applied load is approximately 3.16 MPa.

To find the stress in the aluminum rod, we can use the formula:

Stress = Force / Area

Given:

Applied Load = 12 N

Cross-sectional Area = 3.8 mm²

Converting the area to square meters:

Area = 3.8 mm² = 3.8 × 10⁻⁶ m²

Substituting the values into the formula:

Stress = 12 N / (3.8 × 10⁻⁶ m²)

Calculating the stress:

Stress = 3.16 × 10⁶ N/m²

Converting the stress to MPa:

Stress = 3.16 MPa (rounded to 2 significant figures)

Therefore, the stress in the aluminum rod under the applied load is approximately 3.16 MPa.

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Answer:56

Step-by-step explanation:

The T is a transformation from R3 to R3 that is linear. Consider the vector (1, 2, 3) in R3. Its coordinate vector relative to B is [1 2 2]B.The product a[1 2 2] gives us T(1, 2, 3) relative to B.

Let b = {(1, 0, 1), (0, 1, 1), (1, 1, 0)} and b' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for R3, and let a = {(1/2. -1, -5,2), (-1/2,2,1/2), (3/2, 1, 1/2)}, be the matrix for T: R3 to R3 relative to B.Let V be a vector space over the field F. A basis of V is a linearly independent subset of V that produces every element of V. The base B = {(1, 0, 1), (0, 1, 1), (1, 1, 0)} of R3 is known. Thus, every vector in R3 can be written as a linear combination of the base vectors.For instance, consider (a, b, c) in R3. Since it belongs to R3, it can be expressed as a linear combination of the vectors in B. That is, a(1, 0, 1) + b(0, 1, 1) + c(1, 1, 0)The coefficients (a, b, c) correspond to the coordinate vector [a b c]B. Using the base B', we can find the coordinate vector of each vector in R3.Let a be the matrix for T:R3 to R3 relative to B. We can determine how T behaves on the coordinate vectors by multiplying them by a.Let's look at an example. T is a transformation from R3 to R3 that is linear. Consider the vector (1, 2, 3) in R3. Its coordinate vector relative to B is [1 2 2]B.The product a[1 2 2] gives us T(1, 2, 3) relative to B.

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Answer:

62.8 feet is the answer .

The solutions of given function;

(a) k = -12

(b) f'(3) = 0

(c) f'(x) = 0

Given info,

A function f is defined for all real numbers and has the following three properties:

\(f(1)=5 \quad f(3)=21 \quad f(a+b)-f(a)=k a b+2 b^{2}f(1)\\\)

for all real numbers a and b where k is a fixed real number independent of a and b.

To find,

(a) Use a = 1 and b = 2 to find k.

\(f(a+b)-f(a)=k a b+2 b^{2}f(1)\)

f(1 + 2) - f(1) = k(1 * 2) + 2 * 2² * f(1)

f(3) - f(1) = 2k + f(1) * 8

21 - 5 = 2k + 8 * 5

16 = 2k + 40

-2k = 24

k = -12

(b) Find f'(3).

f(3) = 21

f'(3) = d/dx(21) = 0

(c) Find f'(x) for all real x.

f'(x) = 0

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Every day mass of sunfish is multiplied by factor of (ln(67/50)/6).

In the given question we have a relation between mass of sunfish and time elapsed t. Relation is

M(t) = (67/50) ^(t/6+4) -----(1)

To find out the factor which multiple by mass of sunfish each day, we can take derivative of M(t) function.

Derivative of a function measures the change in fucyion value with respect to change in its argument. It gives rate of change of function with respect to change in given variable value. So, in this problem derivative of mass function M(t) gives the rate of change of M(t) with respect to time , t .. It is represented by dM(t)/ dt.

dM(t)/ dt =( 67/50)^(t/6+4) (1/6)ln(67/50)

We have the used derivative formula d(a^t)/dt = a^t (1) lna

dM(t)/dt = ln(67/50)/6 (67/50)^(t/6+4)

dM(t)/dt = (ln(67/50))/6 M(t)

We can see here that mass funtion is increased by factor ln(67/50)/6 each day.

#Complete question:

Ocean sunfish are well known for rapidly gaining a lot of weight on a diet based on jellyfish. The relationship between the elapsed time, t, in days, since an ocean sunfish is born, and it’s mass, M(t), in milligrams, is modeled by the following function:

M(t)=(1.34)^t/6+4

Complete the following sentence about the daily rate of change in the mass of the sunfish. Round your answer to two decimal places.Every day, the mass of the sunfish is multiplied by a factor of _______.

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See drawing attached below.

Corresponding angles and sides are congruent to each other. Thus,

∠L corresponds to ∠H

∠J corresponds to ∠P

HU corresponds to LO

PO corresponds to JU

LP corresponds to HJ

∠U corresponds to ∠O

Answer:

thanks for the points bye bye for now love u fin and I will

Answer:

LCM (k, n) = 10 and HCF(k, n) = 2

Step-by-step explanation:

The given parameters are;

The time after which Keshav takes  a break = k hours

The value of k = The first smallest prime natural number

Therefore, by mathematical definition, k = 2

The time after which Noel takes a break = n hours

The value of n = The fifth smallest composite natural number

The first five composite numbers are given as follows;

4, 6, 8, 9, and 10

Therefore, the fifth smallest composite natural number = 10 = n

The LCM (k, n) = LCM (2, 10) = Least common multiple of 2 and 10 is given as follows;

Dividing by 2, we get;

2/2 = 1,  10/2 = 5

Dividing the result by 5, we get;

5/5 = 1

Multiplying the devisors together gives;

5 × 2 = 10

Therefore, the LCM of 2 and 10 = 10

LCM(2, 10) = LCM (k, n) = 10

The HCF(k, n) = HCF of 2 and 10 = The highest common factor that divides both 2 and 10 is given as follows;

Dividing 2 and 10 by 2 gives;

2/2 = 1 and 10/2 = 5

Therefore, HCF(k, n) = The highest common factor of 2 and 10 = HCF(2, 10) = 2

Answer:

3.9 pounds

Step-by-step explanation:

Box A=1.4 lbs

Box B=2.5 lbs

Answer= Box A + Box B = 1.4+2.5 lbs

1.4+2.5= 3.9 lbs

the function f(x) = (x+3)/(x-2) has a relative maximum at x = 2.

To determine whether the function f(x) = (x+3)/(x-2) has any relative extrema (maximum or minimum), we need to analyze its first derivative.

Let's find the first derivative of f(x) using the quotient rule:

f'(x) = [(x-2)(1) - (x+3)(1)] / (x-2)^2

      = (-5) / (x-2)^2

The first derivative is f'(x) = -5 / (x-2)^2.

To determine the critical points, we need to find where the derivative is equal to zero or undefined.

Setting f'(x) = 0, we have:

-5 / (x-2)^2 = 0

The numerator is never zero, so the fraction is only zero if the denominator is zero:

x - 2 = 0

x = 2

So, x = 2 is a critical point.

To determine whether this critical point is a relative extremum, we can use the first or second derivative test.

Using the first derivative test:

- When x < 2, f'(x) > 0, indicating that the function is increasing.

- When x > 2, f'(x) < 0, indicating that the function is decreasing.

Since the function changes from increasing to decreasing at x = 2, we can conclude that x = 2 is a relative maximum.

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The probability is approximately 0.9429. Rounded to four decimal places, the probability is 0.9429. Therefore, the probability that the sample mean would be less than 107.81 liters is about 0.9429 or 94.29%.

To solve this problem, we can use the central limit theorem, which states that the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

First, we need to calculate the standard error of the mean, which is the standard deviation of the sampling distribution of the mean:

standard error = standard deviation / square root of sample size
standard error = 26 / sqrt(220)
standard error ≈ 1.756

Next, we can standardize the sample mean using the formula for z-scores:

z = (sample mean - population mean) / standard error
z = (107.81 - 105) / 1.756
z ≈ 1.574

Finally, we can use a standard normal distribution table or calculator to find the probability of getting a z-score less than 1.574.

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Answer:

The equation in option A is correct.

Step-by-step explanation:

Given the equation

\(\:y=x^4+13x^2+12\)

Let us find the solution by setting y=0

\(x^4+13x^2+12=0\:\:\:\:\:\)

\(\mathrm{Rewrite\:the\:equation\:with\:}u=x^2\mathrm{\:and\:}u^2=x^4\)

\(u^2+13u+12=0\)

if \(ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)\)

\(u+1=0\quad \mathrm{or}\quad \:u+12=0\)

\(u=-1,\:u=-12\)

\(\mathrm{Substitute\:back}\:u=x^2,\:\mathrm{solve\:for}\:x\)

\(x^2=-1,\:x^2=-12\)

solving

\(x^2=-1\)

\(\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\)

\(x=\sqrt{-1},\:x=-\sqrt{-1}\)

\(x=i,\:x=-i\)            ∵ \(\:\sqrt{-1}=i\)

solving

\(x^2=-12\)

\(\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\)

\(x=\sqrt{-12},\:x=-\sqrt{-12}\)

\(x=2\sqrt{3}i,\:x=-2\sqrt{3}i\)

Hence, the solutions are:

\(x=i,\:x=-i,\:x=2\sqrt{3}i,\:x=-2\sqrt{3}i\)

Therefore, the equation in option A is correct.

Answer:33.cm

34cm

Step-by-step explanation:

yes

Answer:

1800

Step-by-step explanation:

The perimeter of a rectangle is equal to 30.

The rectangle is a quadrilateral.  The classification for quadrilaterals is given by the length of sides and angles. For a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

A rectangle is a geometric figure that has 4 sides called: length and width (W). Due to its characteristics, the rectangle presents two length (L) and two widths (W).

The perimeter is the sum of all sides of a geometric figures. For a rectangle, the perimeter is 2L+2W.

The area for a rectangle is given by A=L*W.

The question gives:

From the area, you can find the width, see below.

A=L*W

A=2W*W

50=2W²

25=W²

5=W

If W=5, from condition length = 2*W, you can find the length. See

L=2*W

L=2*5

L=10

Therefore, the perimeter will be:

P=2L+2W

P=2*10+2*5

P=20+10

P=30

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Answer: 72 Calories

Step-by-step explanation:

First, calculate the calories per ounce.

216/18= 12

Then, multiply by 6 to get how many calories Sam consumed.

12 * 6= 72

Sam consumed 72 calories.

You can also see that 6 ounces is 1/3 of the bottle, so the answer can also be derived by multiplying 218 by 1/3.

Answer:

The sum is $10

Step-by-step explanation:

Since Tony got $5 on Monday and $5 on Tuesday, we can add them together by doing 5+5. We can add 5 and 5 together to get a total of $10 that Tony has earned. This means that it isn't a sum of 0 but a sum of 10.

(hope this helped)

Answer:

35

Step-by-step explanation:

The solutions for the inequality y < 2/7 x + 1 exists on all the four quadrants.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given linear inequality is,

y ≤ 2/7 x + 1

We have to solve the inequality to find the values of x and y.

Consider  y = 2/7 x + 1

When x = 0, y = 1

When x = 7, y = 3

When x = 14, y = 5

.........

The line  y = 2/7 x + 1 passes through the points (0, 1), (7, 3), (14, 5), ...

Consider y ≤ 2/7 x + 1.

At origin (0, 0), 0 ≤ (2/7 × 0) + 1 ⇒ 0 ≤ 1, which is true.

So the solution of y ≤ 2/7 x + 1 contains the side of the line which includes origin.

Since the solution lies in all the four quadrants, the correct option is d.

Hence the solutions exist on all the four quadrants.

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Answer:

125 sweets

Step-by-step explanation:

Let the total # of sweets the teacher bought be the variable, x.

We can set up this equation to find the # of sweets she bought:

40 · 3 + 5 = x

Because she gave 3 sweets each to her 40 students, we have to multiply these two numbers to get the # of sweets the teacher gave out.

120 + 5 = x

Then, since there's 5 extra sweets left, we can add it to the # of sweets the teacher gave out to get the total amount of sweets she bought.

125 = x

x = 125

125 sweets

Answer:

Total sweets = 125

Step-by-step explanation:

Number of sweets given to each student = 3

Number of sweets given to 40 students = 40*3 = 120

Number of sweets left with the teacher = 5

Total sweets = 120 + 5 = 125