Tryptophan is an essential amino acid, which can not be synthesized in the body.
Tryptophan is found i.a. in sunflower seeds, and researchers will investigate its
concentration. Below are 15 concentrations (in milligrams per 100)
grams of sunflower seeds) of tryptophan in a random sample of frogs:

24.7 24.4 26.2 35.4 35.2 28.1 24.0 32.1 28.7 22.1 28.0 32.1 30.0 29.0 31.8

a) Use a significance level of 0.05 and test the claim that frogs are coming
from a population with a mean tryptophan concentration of 30
milligrams. Assume that the population is normally distributed.
b) Calculate the 95% confidence interval for the population mean value of 30 grams
of tryptophan in sunflower seeds.

a. The elasticity at P=18 is -0.6. b. The elasticity at P=18 would decrease if the demand curve shifts parallel to the right.

a. To find the elasticity at P=18, we need to calculate the derivative of Q with respect to P and then evaluate it at P=18.

The demand curve is given by P = 50 - 0.5Q. Solving for Q, we have Q = 100 - 2P.

Taking the derivative of Q with respect to P, we get dQ/dP = -2.

To find the elasticity at P=18, we use the formula: Elasticity = (dQ/dP) * (P/Q).

Plugging in the values, Elasticity = (-2) * (18 / (100 - 2*18)) = -0.6.

Therefore, the elasticity at P=18 is -0.6.

b. If the demand curve shifts parallel to the right, it means that the quantity demanded increases at each price level. In this case, the elasticity at P=18 would decrease in absolute value (become less negative or move towards zero).

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The total amount that Adele will have in her account at the end of the 3 years is $2,315.25.

Given that, principal=$2000, rate of interest=5% and time period=3 years.

The compound interest formula is used to calculate compound interest, sometimes known as "interest on interest". The formula for compound interest is \(A = P(1 + \frac{r}{100})^{nt}\), where P= principal balance, r= interest rate, n= number of times interest is compounded per time period and t= number of time periods.

Now, A=2000(1+5/100)³

=2000(1+0.05)³

=2000(1.05)³

=$2,315.25

Therefore, the total amount that Adele will have in her account at the end of the 3 years is $2,315.25.

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Answer:

y=2x+8

Step-by-step explanation:

y=mx+b

M: cost for each ride, $2

B: Flat admission rate, $8

Answer:

Greta is correct. The answer is y = 4x

Step-by-step explanation:

This is because one person is able to plant four trees and five people are able to plant 20 in the same amount of time which means 4 trees is to 1 person. In other words if you substitute the values into the equation you will see that x = 1 in the first scenario and x = 5 in second scenario.I will work out the second scenario below.

y = 4x (where y = 20)

20  = 4(x)

\(\frac{20}{4} = \frac{4x}{4}\)

5 = x

OR

y = 4x (where x = 5)

y = 4 * 5

y = 20

The equation which represents the number of trees planted y for the x number of people will be y = 4x thus Greta will be right.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

An equation is a set of variables that are constrained through a situation or case.

As per the given,

1 person plants 4 trees.

x = 1 and y = 4

y/x = 4

5 people plant 20 trees

x = 5 and y = 20

y/x = 20/5 = 4

y = 4x

Thus, y = 4x will be correct.

Hence "The equation which represents the number of trees planted y for the x number of people will be y = 4x thus Greta will be right".

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Answer:

86

Step-by-step explanation:

just add then divide

How to solve your problem

6

(

1

2

−

)

6(12-g)

6(12−g)

Simplify

1

Rearrange terms

6

(

1

2

−

)

6({\color{#c92786}{12-g}})

6(12−g)

6

(

−

+

1

2

)

6({\color{#c92786}{-g+12}})

6(−g+12)

2

Distribute

Solution

−

6

+

7

2

The coordinate of S before the rotation of T is ( 2, - 1 ).

When an object is rotated 180 degrees, it is turned around by a half-circle or a complete revolution. This means that the object is flipped upside down or turned over, so that its top becomes its bottom and its bottom becomes its top.

The rotation can be performed around any axis, but regardless of the axis of rotation, the object will undergo a complete change in orientation. If the object has a front and a back side, then the front side will become the back side and vice versa. Similarly, if the object has a left and a right side, then the left side will become the right side and vice versa.

The coordinate of S before the rotation of T can be determined by rotating T back at 180 degrees.

initial coordinate of S = ( 2, - 1 )

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Answer:

Solution,

⇒Total students in class A=40

⇒Class B=5%

Now,

5% of 40 students

→5/100 × 40=2 students

Again,

→Number of students in class B =40 students + 2 students

                                                    =42 students

Hence, there were 42 students in class B.

Step-by-step explanation:

There are 42 students in class B which is more than 5% of the number of students in class A.

A percentage is a ratio or number that may be expressed as a fraction of 100. Moreover, it is denoted by the sign "%."

Given:

In Class A,

there are 40 students in total.

For class B,

we have a condition that there are 5% more students in class B.

Let n be the students in class B.

So, applying the percentage formula,

we get,

n = 40 + 40 x 5 /100

n = 40 + 200/100

n = 40 + 2

n = 42.

Therefore, the number of students in class B = 42.

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product of two perpendicular line slopes must equals - 1 ;

As you know the coefficient of x is the slope of the line

Thus if we suppose that line has a slope of m , we have :

m × 2 = - 1

m = - 1 / 2

__________________________________

y = ax + b

y = - 1 / 2 x + b

The line passes through the point ( - 2 , - 2 ) thus :

- 2 = - 1 /2 × ( - 2 ) + b

- 2 = 1 + b

b = - 3

__________________________________

y = - 1/2 x - 3

Which mean the option c is the correct answer.

Answer:

y = -1/2(x) - 4

Step-by-step explanation:

\(y=-\frac{1}{2}(x)-4\)

The circumference of a D battery with 0.65 inches radius was found to be 4.14 inches.

To find the circumference of a circle, we can use the formula:

C = 2 * π* r

where C is the circumference, π (pi) is a constant approximately equal to 3.14, and r is the radius of the circle.

For the circular base of a D battery with a radius of 0.65 inches, the circumference can be calculated as follows:

C = 2 * π * 0.65

C = 2 * 3.14 * 0.65

C = 4.14

Rounding to the nearest hundredth, we get:

C = 4.14 inches

So, the estimated circumference of the circular base of the object is approximately 4.14 inches

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Answer:

20.5 ounces

Step-by-step explanation:

11.5+2.25s=?

11.5+2.25(4)=

Answer: The two numbers are 16 and 35.

Step-by-step explanation:

Let x=smaller number

x+19=bigger number

x+x+19=51

2x+19=51

2x=32

x=16

x+19=35

Answer:

Introduction. Cellular survival depends on an organism's ability to respond and adapt to extracellular signals in its environment. Signal transduction is, therefore, an important biologic process, allowing cells to react to a variety of these extracellular stimuli and respond adaptively.

Answer:

C

Step-by-step explanation:

Answer:

D) commutative property of addition

Answer:

The second one

Step-by-step explanation:

on the f axis you can see that f is greater than or equal to 1 and less than or equal to 5.

The lengths of the third side must be greater than 10 , but less than 30.

This theorem states that the sum of any two sides of a triangle must be greater than the third side.

The given two sides of triangle is 10 and 20.

Let x be the third side of the triangle.

Now the sum of the given two sides

10 + 20 = 30

Now,according to triangle inequality theorem

x < sum of other two sides

⇒ x < 30

Now Since two sides are 10 and 20 and third side is x.

and we know that x < 30

Let third side be the smallest side.

then x ≤ 10

⇒ x + 10 > 20

⇒ x > 10.

Hence,The lengths of the third side must be greater than 10, but less than 30.

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Answer:

\(4\frac{1}{6}\)

Step-by-step explanation:

To find this, first, we need to ask ourselves, "how many times does 6 go into 25?" The answer is 4 because 6 * 4 = 24 with 1 left over. Therefore, we know that the whole number is 4 and the fraction is 1/6, so the answer is \(4\frac{1}{6}\).

Answer:

4\frac{1}{6}      

;-)

Step-by-step explanation:

plz crown   'o'

answer

15.5%

Step-by-step explanation:

length = 30

30+10%=33

breadth=20

20+5%=21

area of rectangle = length × breadth

600² centimeters = 30 × 20

693² centimeters = 33 × 21

Increase = 15.5%

The probability of getting the majority of the questions right is P(X>=3) = P(X=3) + P(X=4) + P(X=5) = 15/128 + 6/1024 = 0.2266, rounded to four decimal places.

(a) The probability of guessing the correct answer for any single question is 1/4. Since there are no dependencies between questions, the probability of guessing the third question correctly is also 1/4. The probability of getting the first two questions wrong is (3/4)^2 = 9/16. Therefore, the probability that the first question Robin gets right is the third question is the product of these probabilities, which is (1/4)*(9/16) = 9/64. Rounded to four decimal places, this is 0.1406.

(b) To find the probability that Robin gets exactly 3 or exactly 4 questions right, we can use the binomial distribution. Let X be the number of questions Robin gets right. Then X follows a binomial distribution with n=5 and p=1/4, since each question has a probability of 1/4 of being answered correctly, and there are 5 questions in total.

The probability of getting exactly 3 questions right is P(X=3) = (5 choose 3) * (1/4)^3 * (3/4)^2 = 15/128. Similarly, the probability of getting exactly 4 questions right is P(X=4) = (5 choose 4) * (1/4)^4 * (3/4)^1 = 5/1024. The probability of getting both exactly 3 and exactly 4 questions right is 0, since they are mutually exclusive events.

Therefore, the probability of getting exactly 3 or exactly 4 questions right is P(X=3) + P(X=4) = 15/128 + 5/1024 = 0.1719, rounded to four decimal places.

(c) The majority of the questions means getting at least 3 questions right. We can calculate this probability using the binomial distribution again. The probability of getting 3 questions right is P(X=3) = 15/128, as calculated above. The probability of getting 4 or 5 questions right is P(X=4) + P(X=5) = (5 choose 4) * (1/4)^4 * (3/4)^1 + (5 choose 5) * (1/4)^5 * (3/4)^0 = 5/1024 + 1/1024 = 6/1024. Therefore, the probability of getting the majority of the questions right is P(X>=3) = P(X=3) + P(X=4) + P(X=5) = 15/128 + 6/1024 = 0.2266, rounded to four decimal places.

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The final expression of a binomial probability distribution is:

(a) P(X = 3) ≈ 0.2096

(b) P(X < 3) ≈ 0.4377

(c) P(X ≥ 6) ≈ 0.0739

We can use the binomial probability formula to find the probabilities:

P(X = k) = (n choose k) * \(p^k\)* \((1-p)^{(n-k)}\)

where n is the number of trials, p is the probability of success, X is the random variable representing the number of successes,

and k is the number of successes we are interested in.

(a) P(X = 3) = (8 choose 3) * 0.35³ * 0.65⁵ ≈ 0.2096

(b) P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

= (8 choose 0) * 0.35⁰* 0.65⁸ + (8 choose 1) * 0.35¹ * 0.65⁷ + (8 choose 2) * 0.35² * 0.65⁶

≈ 0.4377

(c) P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8)

= (8 choose 6) * 0.35⁶ * 0.65² + (8 choose 7) * 0.35⁷ * 0.65¹ + (8 choose 8) * 0.35⁸ * 0.65⁰

≈ 0.0739

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Step-by-step explanation:

heres tue answer. hope that helps

Answer:

x=5,y=6

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

The y-axis intercept of the total cost curve is 100.

The y-axis intercept represents the value of the dependent variable when the independent variable is zero. In this case, the y-axis intercept represents the total cost when the quantity of units is zero.

Given the total cost curve c = 100 + 2q, we can find the y-axis intercept by setting q to zero:

c = 100 + 2(0)

c = 100

Therefore, the y-axis intercept of the total cost curve is 100.

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Answer:

Step-by-step explanation:

isosceles triangles are all similar in that they have 2 sides that are equal.

however, the angles can differ and so they are not all similar in that term

Answer:

(- 2, 4 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) , then the midpoint is

( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) )

Here (x₁, y₁ ) = A (4, 6 ) and (x₂, y₂ ) = B (- 8, 2 )

midpoint = ( \(\frac{4-8}{2}\) , \(\frac{6+2}{2}\) ) = ( \(\frac{-4}{2}\) , \(\frac{8}{2}\) ) = (- 2, 4 )

Midpoint be p(x,y)

P(x,y)=

\(\\ \sf\longmapsto \left(\dfrac{4-8}{2},\dfrac{6+2}{2}\right)\)

\(\\ \sf\longmapsto \left(\dfrac{-4}{2},\dfrac{8}{2}\right)\)

\(\\ \sf\longmapsto (-2,4)\)

Answer:

\( 7.25 \: units\)

Step-by-step explanation:

\(d \bigg(5 \frac{1}{2}, \: \: - 1 \frac{3}{4} \bigg) \\ \\ = d \bigg( \frac{11}{2}, \: \: - \frac{7}{4} \bigg) \\ \\ = d \bigg( \frac{22}{4}, \: \: - \frac{7}{4} \bigg) \\ \\ = \frac{22}{4} - \bigg( - \frac{7}{4} \bigg) \\ \\ = \frac{22}{4} + \frac{7}{4} \\ \\ = \frac{22 + 7}{4} \\ \\ = \frac{29}{4} \\ \\ = 7. 25\: units\)

After 200 years, 9.84 grams of Cesium would remain.

Let N represent the amount of substance after t years

The half-life of a cesium is 30 years., hence, this can be represented by exponential function:

\(N(t)=ab^t\)

where a is the initial value and b is the multiplier.

There were initially 1000g of the substance

a) The exponential model for this situation is:

\(N(t) =1000(\frac{1}{2} )^{\frac{1}{30} t}\\\\N(t) =1000(\frac{1}{2} )^{\frac{t}{30}\)

b) After 200 years (t = 200), the amount of Cesium remaining is:

\(N(200)=1000(\frac{1}{2} )^\frac{200}{30} \\\\N(200) = 9.84g\)

Hence after 200 years, 9.84 grams of Cesium would remain

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