Black walnut trees contain chemicals that inhibit the growth of other plants. In a simple experiment to test whether this is true, you grow several tomato plants in soil with and without decomposing leaves from a black walnut tree. You collect data on plant height as a measure of growth. In this experiment, __________ is the independent variable, __________ is the dependent variable, and __________ is the control.

Answer:

(-7, -10)

\(x=-7\\y=-10\)

Step-by-step explanation:

\(4x-4y=12\)

Substitute x for -7.

\(4(-7)-4y=12\)

Multiply 4 by -7.

\(-28-4y=12\)

Add 28 on both sides.

\(-4y=40\)

Divide -4 on both sides.

\(y=-10\)

Question:

A 33 foot ladder leans against a building so that the angle between the ground and the ladder is 75º. How high does the ladder reach up the side of the building?

Round to 2 decimal places feet.

Answer:

\(H = 31.88\)

Step-by-step explanation:

The question is illustrated using the attachment as a sketch.

We have that

\(Ladder = 33ft\)

\(\theta = 75\)

Required

Determine how high the ladder is to the building

Represent the length of the ladder with L and how high the ladder is on the building with H.

The relationship between L, H and \(\theta\) is"

\(Sin\theta = \frac{H}{L}\)

Substitute values for L and \(\theta\\\)

\(Sin(75) = \frac{H}{33}\)

Make H the subject

\(H = 33 * Sin(75)\)

\(H = 33 * 0.9660\)

\(H = 31.88\)

Hence, the height to which the ladder reaches is approximately 31.88ft

Answer:

C

Step-by-step explanation:

I already did this. ;)

An equation for the function graphed above include the following: g(x) = -1/4|x + 1| - 2.

By critically observing the graph of this absolute value function, we can reasonably infer and logically deduce that the parent absolute value function f(x) = |x| was vertically compressed by a factor of 1/4, reflected over the x-axis, followed by a vertical translation 2 units down, and then a horizontal translation to the left by 1 unit, in order to produce the transformed absolute value function as follows;

f(x) = |x|

y = A|x + B| + C

g(x) = -1/4|x + 1| - 2

In conclusion, the value of the variables A, B, and C are -1/4, 1, and 2 respectively.

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Answer:

x is equal to -4

Step-by-step explanation:

4x+3= -13

4x/4= -16/4

x= -4

Using the lexicographic ordering 5 tuples we get that option b and d is correct.

The lexicographic ordering of 5-tuples means that we compare the elements of each tuple from left to right, and as soon as we find a pair of elements that differ, we say that the tuple with the smaller element is less than the other tuple.

Using this ordering, we can compare the given tuples as follows:

a. (3,1,10,17,2) < (3,1,10,20,1) is true because the fifth element of the first tuple (2) is smaller than the fifth element of the second tuple (1).

(5,1,10,17,2) < (5,0,101,2,2) is false because the second element of the first tuple (1) is greater than the second element of the second tuple (0).

Therefore, option (a) is not correct.

b. (3,1,10,17,2) > (3,1,10,20,1) is false because the fifth element of the first tuple (2) is smaller than the fifth element of the second tuple (1).

(5,1,10,17,2) < (5,0,101,2,2) is true because the second element of the first tuple (1) is smaller than the second element of the second tuple (0).

Therefore, option (b) is correct.

c. (3,1,10,17,2) < (3,1,10,20,1) is true because the fifth element of the first tuple (2) is smaller than the fifth element of the second tuple (1).

(5,1,10,17,2) > (5,0,101,2,2) is true because the second element of the first tuple (1) is greater than the second element of the second tuple (0).

Therefore, option (c) is not correct.

d. (3,1,10,17,2) > (3,1,10,20,1) is false because the fifth element of the first tuple (2) is smaller than the fifth element of the second tuple (1).

(5,1,10,17,2) > (5,0,101,2,2) is true because the second element of the first tuple (1) is greater than the second element of the second tuple (0).

Therefore, option (d) is correct.

So the correct answer is (b) and (d).

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Answer: yes it is 16 i did my work let me know if you want me to show my work

Step-by-step explanation:

TJohn's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

To represent the given problem as a system of equations, we can use the following information:

John is 70 years younger than Sharon: j = s - 70

Sharon is 4 times as old as John: s = 4j

Let's plot the graph for this system of equations:

First, let's solve equation (2) for s:

s = 4j

Now substitute this value of s in equation (1):

j = s - 70

j = 4j - 70

3j = 70

j = 70/3

Substitute the value of j back into equation (2) to find s:

s = 4j

s = 4(70/3)

s = 280/3

The solution to the system of equations is j = 70/3 and s = 280/3

In the graph d, the solution to the system of equations is represented by the point (70/3, 280/3), which is approximately (23.33, 93.33) on the graph.

Therefore, John's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

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Answer:

B) Domain: All real numbers; Range: y > 3

Step-by-step explanation:

I. x can be any value in real number

but if you look at the graph, the y is near 3 but not 3

So y is more than 3 and x is all real number

When x is domain and y is renge.

That makes domain is real number and renge is more than 3.

Hope that help :)

Answer:

3

Step-by-step explanation:

1. 54÷6 =9

2. (12-4)=8

3. 9-8 = 1

4. 1+2 = 3

5. I hope this helps it's pretty simple oh and 3 is your anansw.Also you can you your calculator

Answer:

a=72\(\frac{2}{3}\)

Step-by-step explanation:

56/6*(12-4)+2=n

56/6*8+2-2=n-2

56/6*8/8=(n-2)/8

x=9\(\frac{1}{3}\)

x=(n-2)/8

y=74\(\frac{2}{3}\)

y=n-2=a

a=72\(\frac{2}{3}\)

Answer:

x=161/10 =16.100

Step-by-step explanation:

Combine Like Terms

PLEASE FOLLOW ME

Answer:

hope it helps..

Step-by-step explanation:

Simplifying

2.1(0.2x + -1.4) = 1.3(0.4x + -3.5)

Reorder the terms:

2.1(-1.4 + 0.2x) = 1.3(0.4x + -3.5)

(-1.4 * 2.1 + 0.2x * 2.1) = 1.3(0.4x + -3.5)

(-2.94 + 0.42x) = 1.3(0.4x + -3.5)

Reorder the terms:

-2.94 + 0.42x = 1.3(-3.5 + 0.4x)

-2.94 + 0.42x = (-3.5 * 1.3 + 0.4x * 1.3)

-2.94 + 0.42x = (-4.55 + 0.52x)

Solving

-2.94 + 0.42x = -4.55 + 0.52x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.52x' to each side of the equation.

-2.94 + 0.42x + -0.52x = -4.55 + 0.52x + -0.52x

Combine like terms: 0.42x + -0.52x = -0.1x

-2.94 + -0.1x = -4.55 + 0.52x + -0.52x

Combine like terms: 0.52x + -0.52x = 0.00

-2.94 + -0.1x = -4.55 + 0.00

-2.94 + -0.1x = -4.55

Add '2.94' to each side of the equation.

-2.94 + 2.94 + -0.1x = -4.55 + 2.94

Combine like terms: -2.94 + 2.94 = 0.00

0.00 + -0.1x = -4.55 + 2.94

-0.1x = -4.55 + 2.94

Combine like terms: -4.55 + 2.94 = -1.61

-0.1x = -1.61

Divide each side by '-0.1'.

x = 16.1

Simplifying

x = 16.1

The probability that 2 or fewer in the sample will favor the project is  4.368 × 10⁻⁶ and Also The data seem to indicate that the percent favoring the increase in fees is less than 70%

According to the question,

It is given that according to the student's government

The probability that number of students in favor of increment in fees : p = 0.70

The probability that number of students against the increment : q = 0.30

Sample Size : n = 12

Number of students follows Binomial distribution

(a) We have to find the probability that 2 or fewer in the sample will favor the project

P( x ≤ 2) = P(0) + P(1) + P(2)

As we know ,

P(x) = ⁿCₓpˣq⁽ⁿ⁻ˣ⁾

=> P( x ≤ 2) = ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹ + ¹²C₂p²q¹⁰

=>  P( x ≤ 2) = 1×(0.30)¹² + 12×(0.70)(0.30)¹¹  + 12×11/2 × (0.70)²(0.30)¹⁰

=> P( x ≤ 2) = (0.30)¹⁰ [ 0.09 + 0.21 + 0.48]

=>  P( x ≤ 2) = 5.9×10⁻⁶[0.78]

=>  P( x ≤ 2) = 4.368 × 10⁻⁶

Which is very close to zero

(b) The data doesn't support the student government claim.

The data seem to indicate that the percent favoring the increase in fees is less than 70%.

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Answer:

Step-by-step explanation:

y=kx²

y₁=k(1)²=k

y₃=k(3)²=9k

y₁-y₃=k-9k=32

-8k=32

k=-4

y=-4x²

y₋₂=-4(-2)²=-16

Subtract to find the difference in calories:

150-78 = 72

divide the difference by 150:

72/150 = 0.48

Multiply by 100 to get the percent:

0.48 x 100 = 48%

Answer: 48 %

Answer:

first of all subtract as given in question

158-78

after that divide the difference by 150

72/150=0.48

now at last multiply it with 100=0.48×100=48

Answer:

Step-by-step explanation:

Regs.

Spinner A and Spinner B below are each to be spun once.

0 18

O 12

6

Spinner A

5

2

4

00

Answer:

2×r+10 and 3×r+1

Step-by-step explanation:

a. 9+20= 29

b. 2×9+10= 18+10 = 28

c. 4x9-10 = 36-10 =26

e. 3×9+1 = 27 +1 = 28

the correct answer are 2×r+10 and 3×r+1

Part(a),

The exponential function that models the total spent on food and drinks as a function of the number of years since 1990 is:

\(T(x) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^x\)

Part(b),

The predicted amount spent in 2000 is 964 billion dollars (rounded to the nearest integer).

Part(c),

The predicted total sales of food and drink in 2018 is 1756 billion dollars

Part(d),

If the exponential trend continues, the total sales will reach 2 trillion dollars approximately 32.72 years after 1990, which is around the year 2022.

(a) To model the total spent on food and drinks as an exponential function of the number of years since 1990, we can use the general form of an exponential function:

\(T = a \times b^t\)

where T is the total spent in billions of dollars, t is the number of years since 1990, a is the initial amount spent in 1990, and b is the growth factor or base of the exponential function.

Using the given information, we can set up two equations:

T(0) = 641 (total spent in 1990)

T(13) = 1016 (total spent in 2003, which is 13 years after 1990)

Substituting these values into the exponential function, we get:

\(641 = a \timrd b^0\) => a = 641

\(1016 = a b^{13\) => \(b = (\dfrac{1016}{641})^{\frac{1}{13}\)

Therefore, the exponential function that models the total spent on food and drinks as a function of the number of years since 1990 is:

\(T(x) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13})^x\)

(b) To predict the amount spent in 2000, we need to substitute t = 10 (since 2000 is 10 years after 1990) into the exponential function:

\(T(10) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^{10\) ≈ 964

Therefore, the predicted amount spent in 2000 is 964 billion dollars (rounded to the nearest integer).

(c) To predict the total sales of food and drink in 2018, we need to substitute t = 28 (since 2018 is 28 years after 1990) into the exponential function:

\(T(28) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^{28\) ≈ 1756

Therefore, the predicted total sales of food and drink in 2018 is 1756 billion dollars (rounded to the nearest integer).

(d) To estimate when the total sales will reach 2 trillion dollars, we need to solve for t in the exponential function when T(t) = 2000 (since 2 trillion dollars is equivalent to 2000 billion dollars):

\(2000 = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^t\)

\(ln(\dfrac{2000}{641}) = t \times ln((\dfrac{1016}{641})^{(\frac{1}{13})\)

\(t = \dfrac{ln(\dfrac{2000}{641})} { ln((\dfrac{1016}{641})^{(\frac{1}{13})) }}\)

t = 32.72

Therefore, if the exponential trend continues, the total sales will reach 2 trillion dollars approximately 32.72 years after 1990, which is around the year 2022.

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The ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) do not correspond to the intervals where the graph of f(x) is decreasing. The pairs (1, -2) and (-3, -18) are the correct ones.

To determine where the graph of f(x) is decreasing, we need to examine the intervals where the function's derivative is negative. The derivative of f(x) is given by f'(x) = -3x^2 - 8x + 3.

Now, let's evaluate f'(x) for each of the given x-values:

f'(-1) = -3(-1)^2 - 8(-1) + 3 = -3 + 8 + 3 = 8

f'(2) = -3(2)^2 - 8(2) + 3 = -12 - 16 + 3 = -25

f'(0) = -3(0)^2 - 8(0) + 3 = 3

f'(1) = -3(1)^2 - 8(1) + 3 = -3 - 8 + 3 = -8

f'(-3) = -3(-3)^2 - 8(-3) + 3 = -27 + 24 + 3 = 0

f'(-4) = -3(-4)^2 - 8(-4) + 3 = -48 + 32 + 3 = -13

From the values above, we can determine the intervals where f(x) is decreasing:

f(x) is decreasing for x in the interval (-∞, -3).

f(x) is decreasing for x in the interval (1, 2).

Now let's check the ordered pairs in the table:

(-1, -6): Not in a decreasing interval.

(2, -18): Not in a decreasing interval.

(0, 0): Not in a decreasing interval.

(1, -2): In a decreasing interval.

(-3, -18): In a decreasing interval.

(-4, -12): Not in a decreasing interval.

Therefore, the ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) are not located in the intervals where the graph of f(x) is decreasing. The correct answer is: (1, -2), (-3, -18).

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Note the complete and the correct question is

Q- Consider the function below, which has a relative minimum located at (-3, -18) and a relative maximum located at 1/3, 14/27).

\(f(x) = -x^3 - 4x^2 + 3x\).

Select all ordered pairs in the table which are located where the graph of f(x) is decreasing: Ordered pairs: (-1, -6), (2, -18), (0, 0),(1 , -2), (-3 , -18), (-4. , -12)

Answer:

Option 3

(3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

Step-by-step explanation:

Factorize polynomials:

Use exponent law:

                   \(\boxed{\bf a^{m*n}=(a^m)^n} \ & \\\\\boxed{\bf a^m * b^m = (a*b)^m}\)

9x²y⁶ = 3²* x² * y³*² = 3² * x² * (y³)² = (3xy³)²

25x⁴y⁸ = 5² * x²*² * y⁴*² = 5² * (x²)² * (y⁴)² = (5x²y⁴)²

Now use the identity:  a² - b² = (a +b) (a -b)

Here, a = 3xy³ & b = 5x²y⁴

9x²y⁶ - 25x⁴y⁸ = 3²x²(y³)² - 5²(x²)² (y⁴)²

                       = (3xy³)² - (5x²y⁴)²

                      = (3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

The value of the principal invested is $762. 5

The formula for calculating simple interest is expressed as;

I = PRT/100

Such that the parameters of the formula are represented as;

Now, substitute the values into the equation, we have;

$549 = P × 9 × 8/100

Multiply the values

$549 = 72P/100

cross multiply the values

$549 × 100 = 72P

Multiply the values

72P = 54900

Divide both sides by the coefficient of P

P = $762. 5

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-10 + 5.47722~
=4.523~
round to nearest tenth = 4.5

Answer:

-4.5

Step-by-step explanation:

\(\sqrt{30}\) is approximately 5.47722557505.  You can find this number with a calculator.

-10 + 5.47722557505 = -4.52277442495

To add a negative and a positive number, you subtract the absolute values and take the sign of the number that has the larger absolute value.  Absolute value just means thinking of both numbers as positive numbers.

Helping in the name of Jesus.

Hello!

surface area

= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)

= 160cm²

Answer:

x = 0 , x = 2

Step-by-step explanation:

3x² = 6x ( subtract 6x from both sides )

3x² - 6x = 0 ← factor out 3x from each term

3x(x - 2) = 0

equate each factor to zero and solve for x

3x = 0 ⇒ x = 0

x - 2 = 0 ( add 2 to both sides )

x = 2

solutions are x = 0 , x = 2

Answer:

Solution:  (-1, -1)

Step-by-step explanation:

Thus, the solution to the system is (-1, -1) as this is the point where the two lines intersect.

Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

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Answer:

3 1/5 cubic feet of water weighs 200 pounds

Step-by-step explanation:

1. Take 62 1/2 into decimal form: 62 1/2 = 62.5

2. Take 3 1/5 into decimal form: 3 1/5 = 3.2

3. Multiple 62.5 by 3.2: 62.5 x 3.2 = 200

The answer is 200 pounds.

The total number of feathers lost in 14 days if you lose 30 feathers every hour is 10,080 feathers.

Feathers lost every hour = 30 feathers

How many feathers is lost in 14 days?

1 day = 24 hours

14 days = 24 × 14

= 336 hours

Total number of feathers lost in 14 days = Feathers lost every hour × number of hours in 14 days

= 30 × 336

= 10,080 feathers

Therefore, the total number of feathers lost in 14 days is 10,080 feathers

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