After a genetics experiment on 58 pea plants, the number of plants having certain characteristics was tallied, with the results given to the right. Answer parts (a) through (c). (a) Find the number of plants that were tall and had smooth peas. 20 were tall; 32 had green peas; 29 had smooth peas; 11 were tall and had green peas; 17 had green peas and smooth peas; 4 had all three characteristics; 3 had none of the characteristics. plants (b) How many plants were tall and had peas that were neither smooth nor green? plants (c) How many plants were not tall but had peas that were smooth and green?

Answer:

180 rabbits

Step-by-step explanation:

The initial amount is 1250, rate is 13.5% and value of the function for t = 3 is 809

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time.

Given that, an exponential function with rate of decay, h(t) = \(1250(0.865)^t\)

Here we need to identify the initial amount, rate and the value of function when t = 3

The general formula of exponential decay is given by,

A = P(1-r)ⁿ

Where A is final amount

P is initial amount

r = rate of decay

n = years or time

Comparing with general formula,

P = 1250

1-r = 0.865

r = 1-0.865

r = 0.135

r % = 13.5

h(3) = 1250(0.865)³

= 809

Hence, the initial amount is 1250, rate is 13.5% and value of the function for t = 3 is 809

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The equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

To find the equation of the line perpendicular to the tangent to the curve at (2,1), we need to first find the slope of the tangent line at that point.

The derivative of y=x^3-4x+1 is y'=3x^2-4, so the slope of the tangent line at (2,1) is y'(2) = 3(2)^2-4 = 8.

Since we want the line perpendicular to the tangent, we know that its slope will be the negative reciprocal of the tangent's slope. Therefore, the slope of the line we're looking for is -1/8.

Next, we use the point-slope form of the equation of a line to write the equation of the line with the slope we found and passing through the point (2,1):

y - 1 = (-1/8)(x - 2)

Simplifying and putting the equation in slope-intercept form:

y = (-1/8)x + 9/8

Therefore, the equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

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Part (a)

Since we want segment AT to be an altitude, this means that point A is somewhere on segment RI such that angle TAI is 90 degrees. In other words, segments AT and RI are perpendicular. Check out the diagram below.

We'll need to find the slope of line RI, so we'll need the slope formula

R = (x1,y1) = (-2,-2)

I = (x2,y2) = (4,1)

m = slope of line RI

m = (y2-y1)/(x2-x1)

m = (1-(-2))/(4-(-2))

m = (1+2)/(4+2)

m = 3/6

m = 1/2

m = 0.5

The slope of line RI is 1/2 or 0.5

Now let's use point R(-2,-2) along with that slope we just found to find the equation of line RI.

Turn to point slope form

y - y1 = m(x - x1)

y - (-2) = 0.5(x -(-2))

y + 2 = 0.5(x + 2)

y + 2 = 0.5x + 1

y = 0.5x + 1 - 2

y = 0.5x - 1

This is the equation of line RI. We'll use it later.

----------

We found that the slope of line RI was 1/2.

The negative reciprocal involves us flipping the fraction and flipping the sign to get -2/1 or simply -2.

The perpendicular slope is -2. This is the slope of altitude AT.

We want line AT to go through T(-2,4), so we'll use this point along with the perpendicular slope we just found to calculate the equation of line AT.

We'll turn to the point slope form

y - y1 = m(x - x1)

y - 4 = -2(x - (-2))

y - 4 = -2(x + 2)

y - 4 = -2x - 4

y = -2x - 4 + 4

y = -2x

The equation of the line that goes through points A and T is y = -2x.

----------

To summarize so far, we have these two equations

Apply substitution to solve for (x,y) to find the intersection point. This will determine where point A is located.

y = 0.5x - 1

-2x = 0.5x - 1

-2x-0.5x = -1

-2.5x = -1

x = -1/(-2.5)

x = 0.4

Then we can determine y like so

y = -2x

y = -2(0.4)

y = -0.8

Therefore, point A is located at (0.4, -0.8). Both coordinate values are exact. In fraction form, we can say that the point is (2/5, -4/5), but I find decimals easier to work with in this instance.

===============================================================

Part (b)

To find the length of segment AT, we can find the distance from A to T. As you can probably guess, we'll use the distance formula.

A = (x1,y1) = (0.4, -0.8) ... found back in part (a)

T = (x2,y2) = (-2, 4) ... given

\(d = \sqrt{ (x_2-x_1)^2+(y_2-y_1)^2 }\\\\d = \sqrt{ (-2-0.4)^2+(4 - (-0.8))^2 }\\\\d = \sqrt{ (-2-0.4)^2+(4 + 0.8)^2 }\\\\d = \sqrt{ (-2.4)^2+(4.8)^2 }\\\\d = \sqrt{ 5.76+23.04 }\\\\d = \sqrt{ 28.8 }\\\\d \approx 5.36656\\\\d \approx 5.37\\\\\)

The distance from point A to point T is approximately 5.37 units. This means that segment AT is roughly 5.37 units long.

To find the radian measure of a central angle that intercepts an arc of length 12 inches in a circle with a radius of 17 inches.

In a circle, the relationship between the central angle (θ) and the arc length (s) is given by the formula s = rθ, where r is the radius of the circle. In this case, the radius (r) is 17 inches, and the arc length (s) is 12 inches.

To find the radian measure of the central angle (θ), we rearrange the formula as follows:

s = rθ  (Divide both sides by r)

θ = s/r

Substituting the given values:

θ = 12/17

Therefore, the radian measure of the central angle that intercepts an arc of length 12 inches in a circle with a radius of 17 inches is approximately 0.7059 radians.

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Answer:

5.26

Step-by-step explanation:

To find the area of a circle, you square the radius and multiply your answer by pi. The radius is half the diameter.

2.6/2=1.3

1.3^2=1.69

1.69*3.14= 5.3066 (approx.)

Finally, round to the nearest hundredth.

5.3066≈5.31

The x-intercepts of f(x) are (-2, 0), (0, -32), and (-4, 0).

First, let us check if (0, -1) is one of the intercept. If (0, -1) is an x-intercept of f(x), that means f(0) = 0.

So let's evaluate f(0):

f(0) = 0³ - 3(0)² - 36(0) - 32 = -32

Since f(0) is not equal to 0, we know that (0, -1) is not an x-intercept of f(x).

To find the actual x-intercepts of f(x), we need to factor the polynomial. We can start by using synthetic division to test if x = 1 is a factor of f(x).

For us to get to our answer, we test with the possible factors of 32 which are: ±1, ±2, ±4, ±8, ±16, ±32.

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Answer:

Step-by-step explanation:

\(x-7=-2x-5\\\\x+2x=7-5\\\\3x=2\\\\x=\dfrac{2}{3}\\\\\tt{x=1.5}\)

Answer:

x = \(\frac{2}{3}\)

Step-by-step explanation:

x - 7 = - 2x - 5 ( add 2x to both sides )

3x - 7 = - 5 ( add 7 to both sides )

3x = 2 ( divide both sides by 3 )

x = \(\frac{2}{3}\)

A  general equation (x - h)^2 / 12^2 - (y - k)^2 / 5^2 = 1

To write an equation of a hyperbola with the given values of a=12 and c=13, we can use the equation of a hyperbola with a horizontal transverse axis. The equation is given by:

(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1

where (h, k) represents the coordinates of the center of the hyperbola.

In this case, since the transverse axis is horizontal, we know that the value of a represents the distance from the center to each vertex. So, a = 12.

We also know that c represents the distance from the center to each focus. So, c = 13.

To find the value of b, we can use the relationship between a, b, and c in a hyperbola, which is given by the equation:

c^2 = a^2 + b^2

Plugging in the values of a = 12 and c = 13, we can solve for b:

13^2 = 12^2 + b^2
169 = 144 + b^2
25 = b^2
b = 5

Now we have all the values we need to write the equation. The center of the hyperbola is at the point (h, k), which we do not have given in the question. Therefore, we cannot write the specific equation of the hyperbola without that information.

However, we can provide a general equation:

(x - h)^2 / 12^2 - (y - k)^2 / 5^2 = 1

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Answer:

8

Step-by-step explanation:

2 + 2 = 4
4 + 2 = 8

Answer:

the answer is 662 feet

Step-by-step explanation:

becuase one eighth of a mile is 660 feet

The integral to be evaluated is;\(∫∫_R▒〖8(x-7y)/(6x-y)dA〗\) R where R is the parallelogram enclosed by the lines \(x-7y=0, x-7y=5, 6x-y=7 and 6x-y=9\). The solution is 264/41 and it is obtained by using an appropriate change of variables.

This integral can be solved by making an appropriate change of variables which will simplify the integral.The lines \(x - 7y = 0 and 6x - y = 7\) intersect at (7,1)

while\(x - 7y = 5 and 6x - y = 9\) intersect at (9,1). This implies that the length of the parallel sides of the parallelogram is 2 units while the distance between the parallel lines is 5 units.

Therefore, we can define the transformation function as:\(u = 6x - y, v = x - 7y\).The Jacobian is given as:\(∂(u,v)/∂(x,y) = (6)(-7) - (1)(-1) = -41\)

The integral can now be expressed as:\(∫∫_R▒〖8(x-7y)/(6x-y)dA〗 = ∫_1^7▒〖∫_(5+y/7)^((y+9)/6)▒〖8(u/(-41))dudv〗〗 = ∫_1^7▒〖(1/41)∫_(5+y/7)^((y+9)/6)▒8udu dv〗\)  

= \(∫_1^7▒〖[(1/41)(4(u^2)/2)|_((5+y/7)^((y+9)/6))]dv〗 = (1/41)∫_1^7▒[16(5+y/7)^2/2 - 16((y+9)/6)^2/2]dv = (1/41)[(160(5+y/7)^2/2 - 16((y+9)/6)^2/2)|_1^7] = 264/41.\)

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The minimum cost will be at (2.5 , 3) and the minimum cost be $25.

Given, a landscaping contractor plans to use the least expensive combination of two brands of fertilizer.

A package of Brand X costs $16 and contains 12 oz of phosphates and 10 oz of nitrates.

A package of Brand Y costs $7 and contains 10 oz of phosphates and 5 oz of nitrates.

The lawn requires at least 60 oz of phosphates and 40 oz of nitrates.

Let the number of Brand X packages be, x

the number of Brand Y packages be, y

According to the question,

12x + 10y ≥ 60 = 6x + 5y ≥ 30

10x + 5y ≥ 40 = 2x + y ≥ 8

x ≥ 0

y ≥ 0

Z = 16x + 7y

On solving the equations, we get

6x + 5y = 30

6x + 3y = 24

On subtracting, we get

2y = 6

y = 3

and x = 2.5

So, minimum cost will be at (2.5 , 3) and the minimum cost be

Z = 16(2.5) + 7(3)

Z = 4 + 21

Z = 25

Hence, the minimum cost will be at (2.5 , 3) and the minimum cost be $25.

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2. a. The measure of angle x is equal to 100°.

b. The measure of the unknown variable angle x is 40°.

c. The measure of angle x is 14°.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

a. We know, The measure of an exterior angle of a triangle is the sum of two opposite interior angles.

Therefore, m∠x = 10° + 90°.

m∠x = 100°.

b. We know, Pairs of corresponding angles are equal.

Therefore, In the smaller triangle,

180° - 140° = 40°.

The corresponding angle is 110°.

Therefore, x = 180° - 110° - 40° = 30°.

c. We know pairs of corresponding angles are equal.

Therefore, 3x + 7° = x + 35°.

3x - x = 35° - 7°.

2x = 28°.

x = 14°.

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hello

to solve for x, let's cross multiply both sides

step 2

divide both sides by -2

x = - 6

Answer:

x = -6

Step-by-step explanation:

Answer:

2 nd one

Step-by-step explanation:

her commision varies

brainliest please

Answer: e = 200s + 4

Step-by-step explanation:

took the test

Answer:

C

Step-by-step explanation:

If we look at all the options, we can see that the only easy multiple of 6 is 30 and 36, so we look at those first.

6*5=30

12*5 does not equal 50

So then we look at the other one

6*6=36

12*6=72

The expected value of the number of games the two equally strong tennis players will play until one wins three games in a row is 14.

Let's consider the possible sequences of games that can occur until one player wins three games in a row. We will denote the winning player as W and the losing player as L. The sequences can be represented as a combination of W's and L's, such as WWL, WLW, LWW, etc.

The key insight is that for each sequence, the last game played must be won by the player who wins three games in a row. This means that the number of games played until the streak ends is fixed at three. However, the preceding games can have various combinations of wins and losses.

To calculate the expected value, we need to consider all possible sequences and their probabilities. Since each player has a 50% chance of winning each game, the probability of any specific sequence occurring is (1/2)^n, where n is the length of the sequence.

We can calculate the expected value by summing the product of the number of games played in each sequence and its corresponding probability.

Considering all possible sequences and their probabilities, the expected value of the number of games played until one player wins three games in a row is found to be 14.

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Answer:

The triangles are similar by the Side Angle Side postulate (SAS).

Step-by-step explanation:

Sides 2 and 3 are proportional to sides 4 and 6 by a scale factor of 2. Angles O are congruent to each other by the vertical angles theorem.

Answer:

3280

Step-by-step explanation:

50 m  ≅ 164 ft (3s.f.)

50 m/s  ≅ 164 ft/s

distance after  20 s:

d = 164 ft/s   ⋅ 20 s

= 3280 ft

The solution to the equation is -1.5 or -3/2.

We have the equation:

x² + 3-2x= 1+ x² +5

Combine Terms and subtract x² from both sides:

x² - x² + 3 -2x = 1 + 5 + x² - x²

3 -2x = 1 + 5

Add:

3 -2x = 6

Combine Terms and subtract 3 from both sides:

-2x + 3 -3 = 6 - 3

-2x = 3

Dividing by -2 we get:

x = 3/(-2)

x = -3/2

x = -1.5

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Answer:

-3/12

Step-by-step explanation:

-2.2º

1) Given that at sunset it was -6.4, then ir rose 16.9 by noon

2) Then it decreased by 12.7, so

10.5 -12.7 =-2.2 The sign of the greatest number in absolute value prevails

3) Hence, at midnight the Temperature was -2.2

Given that Owen has $1.05 in dimes and nickels. He has 3 more dimes than nickels. We are to find out how many coins of each type he has.Let us assume that Owen has x nickels.

he has x+3 dimes.Since the value of each nickel is $0.05, thus, the value of x nickels is 0.05x dollars.Since the value of each dime is $0.10, therefore, the value of (x+3) dimes is 0.10(x+3) dollars.Owen has a total of $1.05 which can be written as 105 cents.

The total number of coins is the sum of the number of nickels and the number of dimes.1. Therefore, the equation is

5x + 10(x+3) = 105.2.

Simplify the equation:5x + 10x + 30 = 10515x = 75x = 5O

wen has 5 nickels.3. Owen has x+3 dimes.

Since x = 5, then he has 5+3 = 8 dimes

.Owen has 5 nickels and 8 dimes.

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The optimal policy for the new owner is to invest in large-scale production. This decision branch has the highest expected utility of $4.285m.

The initial node represents the decision whether to invest in the development of the microbiological product.

The two possible outcomes are a successful development or failure after 2 years.

(b) To determine the policy that the company should adopt to maximize its expected returns, we need to calculate the expected value at each decision node.

Starting from the end nodes and working backwards, we have:

For large-scale production with high sales:

Expected value = 0.75 x $6m + 0.25 x $1m = $4.25m

For large-scale production with low sales:

Expected value = 0.75 x $1m + 0.25 x $6m = $1.75m

For small-scale production with high sales:

Expected value = 0.75 x $4m + 0.25 x $2m = $3.5m

For small-scale production with low sales:

Expected value = 0.75 x $2m + 0.25 x $4m = $1.75m

At the 2-year node, the expected value for a successful development is:

For large-scale production:

Expected value = 0.75 x $4.25m + 0.25 x $1.75m = $3.5m

For small-scale production:

Expected value = 0.75 x $3.5m + 0.25 x $1.75m = $2.81m

Finally, at the initial node, the expected value for investing in the development is:

Expected value = 0.6 x $3.5m + 0.4 x (-$3m) = $0.1m

Therefore, the policy that the company should adopt to maximize its expected returns is to invest in the development of the microbiological product, choose large-scale production if the development is successful, and choose small-scale production otherwise.

(c) If the probability of a successful development is lower than a certain threshold, the option of not developing the product should be chosen. Let p be this threshold probability. Then the expected value at the initial node is:

Expected value = p x $0m + (1-p) x (-$3m) = -$3m + $3mp

Setting this equal to zero and solving for p, we get:

p = 1

Therefore, if the probability of a successful development is lower than 100%, the company should not invest in the development of the microbiological product.

(d) The new owner's utilities represent their preferences for the sums of money involved in the decision.

The utilities are increasing and concave, indicating diminishing marginal utility of money.

This means that the new owner is risk-averse.

The policy identified in (b) may not be optimal for the new owner because their utilities are different from the present-value net returns.

To determine the optimal policy for the new owner, we need to use the new owner's utility values to calculate the expected utility of each decision branch in the decision tree.

If the company invests in large-scale production and high sales are achieved, the expected utility is 0.75 * 0.95 * 1.0 * $6m = $4.285m.

If the company invests in large-scale production and low sales are achieved, the expected utility is 0.75 * 0.95 * (1 - 0.0) * $1m = $712,500.

If the company invests in small-scale production and high sales are achieved, the expected utility is 0.75 * 0.05 * 1.0 * $4m = $150,000.

If the company invests in small-scale production and low sales are achieved, the expected utility is 0.75 * 0.05 * (1 - 0.0) * $2m = $75,000.

If the company decides not to invest in the product, the expected utility is 0.25 * (1 - 0.6) * $0m + 0.25 * 0.6 * (1 - 0.0) * -$3m = -$450,000.

Therefore, the optimal policy for the new owner is to invest in large-scale production. This decision branch has the highest expected utility of $4.285m.

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Answer: 36 years

Step-by-step explanation:

You can use the Rule of 72 to calculate how long it might take the house to double in value.

The Rule of 72 works by dividing 72 by the interest rate as a whole number and the result will be a rough estimate of the time in years it will take for the investment to double in size:

= 72 / 2

= 36 years

Answer:

you

because if your friend made a 3.3 then you  make a 7 then that means your more consistant

Step-by-step explanation:

hope this helped