The ratio of trees to flowering plants in Marsha’s backyard is shown on the ratio table. What number completes the ratio table to make an equivalent ratio? [Type your answer as a number.]

trees 2 12
plants 5 ?

by substituting \( a = 2^{x} \) and simplifying the equation, we found that \( x = \log_{2}(\sqrt{3}) \) or \( x = \log_{2}(-\sqrt{3}) \).

By substituting \( a=2^{x} \), we can rewrite the equation as \( a^2 + 3 = 2a^2 \).

Simplifying the equation, we have \( 2a^2 - a^2 = 3 \), which further simplifies to \( a^2 = 3 \).

Taking the square root of both sides, we get \( a = \pm \sqrt{3} \).

Since \( a = 2^{x} \), we have \( 2^{x} = \sqrt{3} \) or \( 2^{x} = -\sqrt{3} \).

To find the value of \( x \), we can take the logarithm base 2 of both sides:

\( x = \log_{2}(\sqrt{3}) \) or \( x = \log_{2}(-\sqrt{3}) \).

After evaluating these logarithmic expressions, we can obtain the values of \( x \).

In conclusion, by substituting \( a = 2^{x} \) and simplifying the equation, we found that \( x = \log_{2}(\sqrt{3}) \) or \( x = \log_{2}(-\sqrt{3}) \). These values will give us the solutions to the equation \( 4^{x} + 3 = 2^{x+2} \).

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The final Exponential function is: y = 20(4)^x

To write an exponential function in the form y = ab^x that goes through two points, we need to first determine the values of a and b.

Given points (0, 20) and (2, 320), we can use the first point to determine the value of a:

y = ab^x

20 = ab^0  (when x = 0, y = 20)

20 = a(1)

a = 20

Now we can use the second point to determine the value of b:

y = ab^x

320 = 20b^2  (when x = 2, y = 320)

16 = b^2

b = 4 or -4

Since b cannot be negative in this case (as it is an exponential growth function), we can use b = 4.

Therefore, the exponential function that goes through the points (0, 20) and (2, 320) is:

y = 20(4)^x

We can check this by plugging in the x-values of the two given points:

y = 20(4)^0 = 20 (when x = 0, y = 20, as expected)

y = 20(4)^2 = 320 (when x = 2, y = 320, as expected)

So the final exponential function is: y = 20(4)^x

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Given:

The expression is:

\(\log_5(36)-\log_5(9)\)

To find:

The simplified form of the given expression.

Solution:

We have,

\(\log_5(36)-\log_5(9)\)

It can be written as:

\(\log_5(36)-\log_5(9)=\log_5\dfrac{36}{9}\)              \([\because \log_m\dfrac{a}{b}=\log_ma-\log_m b]\)

\(\log_5(36)-\log_5(9)=\log_54\)

Therefore, the simplified form of the given expression is \(\log_54\).

If we let Z = 3 - X, then Z is another exponential random variable with mean 1 that is negatively correlated with X.

Let Y = 2 - X, where X is an exponential random variable with mean 1.

To show that Y is negatively correlated with X, we need to show that Cov(X,Y) < 0.

Cov(X,Y) = E[XY] - E[X]E[Y]

Since X and Y are both exponentially distributed with mean 1, we have:

E[X] = 1, E[Y] = 2 - E[X] = 1

E[XY] = E[X(2-X)] = 2E[X] - E[X^2] = 2 - Var(X)

Var(X) = E[X^2] - (E[X])^2 = 1 - 1^2 = 0

Therefore, Var(X) = 0, which means that E[XY] = 2, and Cov(X,Y) = E[XY] - E[X]E[Y] = 2 - 1*1 = 1 > 0.

Since Cov(X,Y) > 0, we know that Y is positively correlated with X. To find a random variable that is negatively correlated with X, we can use Y = 3 - X instead.

Therefore, if we let Z = 3 - X, then Z is another exponential random variable with mean 1 that is negatively correlated with X.

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The side length of Square 1 is 3 units. Similarly, Square 2 has a perimeter of 16 units. Therefore, 4s = 16, hence, s = 4. Therefore, the side length of Square 2 is 4 units.

The Pythagorean Theorem is modeled below.

Square 1 has a perimeter of 12 units and Square 2 has a perimeter of 16 units. Therefore, the side length of Square 1 is 3 units and the side length of Square 2 is 4 units.The Pythagorean Theorem is a formula used in mathematics.

It is used to determine the sides of a right triangle. It is expressed as a² + b² = c² where a and b are the sides of the right triangle and c is the hypotenuse of the right triangle. The theorem can be modeled with two squares.In this case, Square 1 has a perimeter of 12 units. Since a square has four equal sides, the perimeter can be calculated as 4s, where s is the side length of the square. 4s = 12, therefore, s = 3.

Thus, the side length of Square 1 is 3 units. Similarly, Square 2 has a perimeter of 16 units. Therefore, 4s = 16, hence, s = 4. Therefore, the side length of Square 2 is 4 units.

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Answer:I think its multiply

Step-by-step explanation: 90 x 2 = 180

Answer:

3

Step-by-step explanation:

Answer:

Step-by-step explanation:

17

5.7%

let amount invested = Principal = $8000

time = 1 year

rate = ?

Interest = $456

To get the rate, we'll apply simple interest formula:

Hence, the simple rate of the bonds is 5.7%

Answer:

Dot plot, because a small number of scores are reported individually.

Step-by-step explanation:

Histogram is usually used when a group of data to be represented is usually large and given in ranges or intervals.

However, for a data set, such as the scores of the group of 12 students who participated in a dance competition are  reported individually, and not as ranges or intervals, a dot plot would best for representing this small number of scores.

See attachment below to see how we can easily represent the given scores of the students on a dot plot. Each dot represents a score value for each student.

Answer:

you got two apple left I hope this helps

To calculate the probability that a randomly selected number from the set of natural numbers {1, 2, 3, ..., 1000} is not divisible by 4, 7, or 9, we need to determine the count of numbers in the set that are not divisible by these numbers and divide it by the total count of numbers in the set.

To find the count of numbers that are not divisible by 4, 7, or 9, we can consider the principle of inclusion-exclusion. We'll calculate the count of numbers divisible by each of the three numbers and subtract it from the total count of numbers.

Count of numbers divisible by 4: The highest multiple of 4 within 1000 is 1000 itself, so there are 1000/4 = 250 numbers divisible by 4.

Count of numbers divisible by 7: The highest multiple of 7 within 1000 is 994, so there are 994/7 = 142 numbers divisible by 7.

Count of numbers divisible by 9: The highest multiple of 9 within 1000 is 999, so there are 999/9 = 111 numbers divisible by 9.

Using the principle of inclusion-exclusion, we find that the count of numbers divisible by 4, 7, or 9 is 250 + 142 + 111 = 503.

The total count of numbers in the set is 1000.

Therefore, the count of numbers not divisible by 4, 7, or 9 is 1000 - 503 = 497.

The probability that a randomly selected number from the set is not divisible by 4, 7, or 9 is given by the ratio of the count of such numbers to the total count of numbers:

Probability = 497/1000 = 0.497.

Hence, the probability that a randomly selected number from the set of natural numbers {1, 2, 3, ..., 1000} is not divisible by 4, 7, or 9 is 0.497 or 49.7%.

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Answer:

Given : PQ = RQ

to find : angle B

Answer:

b=40

Step-by-step explanation:

PQ=RQ

That means both sides are the same length which also means they both have the same angel measure of 140.

A super easy way to solve this would be to realize that where p is, the angel is 140.

A straight line is 180.

b and 140 are supplementary angels. [which means they equal 180]

To find b you can make an equation.

b+140=180

or

180-140=b

I'll show you both.

First one you would subtract 140 on both sides to get the variable alone, leaving you with b=40.

For the second one, you just do 180-140 and it also equals 40.

Either way it leaves you with b=40

If you need any more help with angels and whatnot, don't be afraid to reach out. I hope that helps! <3

Answer: 800 calories

Step-by-step explanation:

Let us set this up as a fraction

Firstly, convert 3/4 into a decimal

\(3 \div 4 = 0.75\)

Now we can set up the fraction

Make sure to put the calories on the same side and hours on the same side as well. So it should be: \(\frac{200}{0.75}=\frac{x}{3}\)

Then, solve

\(\frac{200}{0.75}=\frac{x}{3}\)

The fractions are supposed to be proportional meaning, if the denominator is a certain number when solved, the numerator should be the same, if solve likely. let me show you:

Divide 3 by 0.75

\(0.75 \div 3 = 4\)

Now since the number isn't found yet, we will use the opposite operation, which is multiplication, in this case.

Multiply 200 to 4

\(200 \times 4 = 800\)

Therefore, she will burn 800 calories in a 3-hour workout.

Selena left from last month's earning can be determine by calculating the complete purchasing by Selena.

Selena has $1,660.35 left from last month's earnings.

Let us calculate how much she paid for bills.

She paid 3/5th of her earnings to pay for bills.

= \(\frac{3}{5} * 4283.30 = $2568.98\)

Let us calculate the value of 2 shirts.

Value of 1 shirt = $19.99

Value of 2 shirts = $19.99 x 2 = $39.98

Value of the sunglasses = $12.99

Total value of 2 shirts and the pair of sunglasses = $52.97

Total value of the bills and the expenses = $52.97 + $2568.98 = $2621.95

Remaining amount = $4283.30 - $2569.98 = $1660.35

Thus, Selena has $1,660.35 left from last month's earnings

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The value of variables are,

⇒ k = 60

⇒ m = 120

We have to given that;

A quadrilateral DEFG is inscribed in a circle.

And, The measure of angle EDG is 60 degrees and the measure of angle DGF is 60 degrees. The measure of angle DEF is labeled m degrees and the measure of angle EFG is labeled 2k degrees.

Now, We can formulate;

⇒ ∠GDE + ∠EFG = 180°

⇒ 60° + 2k = 180

⇒ 2k = 180 - 60

⇒ 2k = 120

⇒ k = 60

And, We have;

∠DEF + ∠DGF = 180°

m + 60 = 180

m = 180 - 60

m = 120°

Hence, The value of variables are,

⇒ k = 60

⇒ m = 120

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False.

The statement is not necessarily true. The number of levels of observed x-values does not have to be equal to the order of the polynomial in x that you want to fit.

In polynomial regression, the order of the polynomial refers to the highest power of x in the polynomial equation. For example, a polynomial of order 2 would have terms like x^2, x^1, and a constant term.

The number of levels of observed x-values refers to the distinct values of x that you have in your dataset. It represents the range or diversity of x-values observed.

In polynomial regression, you can fit a polynomial of a higher order (with more terms) to a dataset with a limited number of distinct x-values.

However, it is important to note that as the order of the polynomial increases relative to the number of distinct x-values, the model can become increasingly complex and may lead to overfitting or instability.

Therefore, the number of levels of observed x-values does not need to be equal to the order of the polynomial in x that you want to fit. It depends on the specific data, the relationship you want to capture, and the trade-offs between complexity and model performance.

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The growth rate of bacteria in a culture is not specified, so assuming it is exponential, the number of bacteria present after 2 hours will be approximately 1.8 x 10^8.

To solve this problem, we can use the exponential growth formula: N(t) = N0 * e^(rt), where N(t) is the number of bacteria at time t, N0 is the initial number of bacteria, r is the growth rate, and e is the base of the natural logarithm. First, we need to find the growth rate, r. We can use the initial and final number of bacteria and the time interval to do this.

N(t) = N0 * e^(rt)

171 = 38 * e^(49r)

ln(171/38) = 49r

r = ln(171/38)/49

r ≈ 0.069 Now we can use the formula to find N(120) (i.e., the number of bacteria after 2 hours, or 120 minutes):

N(120) = 38 * e^(0.069 * 120)

N(120) ≈ 1.8 x 10^8 Therefore, approximately 1.8 x 10^8 bacteria will be present in the culture after 2 hours.

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Given that the High Plains Aquifer overlaps so many states, less data is now available to the latter might water use in one state affect water use in another state.

An aquifer is a layer of unconsolidated materials, rock cracks, or water-bearing, porous rock that lies underground. Using a water well, one may draw groundwater from aquifers. The properties of aquifers differ widely.

if a state utilizes excessive amounts of water and is "upstream" from another state. Less data is now available to the latter. Similar to how water is distributed uniformly in a pool, aquifers do the same thing underground; as a result, if one state uses more water than it should, it decreases the levels for all the other states. Due to this, management must now take place at the interstate level with more political entities participating. A resolution is inevitably more difficult the more people involved.

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Answer:

Two real world situations are shown below.

Step-by-step explanation:

Initial population of a certain bacteria is 1 thousand and the population doubles in each hour. So, population of bacteria (in thousands) after x hours is

\(f(x)=1(2)^x\)

\(f(x)=(2)^x\)

A person invests 1 lakh rupees in shares and the amount is twice at the end of each year. So, total amount (in lakhs) after x years is

\(f(x)=1(2)^x\)

\(f(x)=(2)^x\)

Using the properties of arithmetic sequence , we calculate

a) 100 seats in the first row (b) 40 rows are required (c) 22 more seats in each row (d) 958 seats in the last row.

The overlap of any two doubly infinite arithmetic progressions seems to be either empty or another arithmetic progression, according to the Chinese remainder theorem.

If every pair of advancements in a family of twice infinite arithmetic progressions has a non-empty intersection, then there is a number that connects all of the pairs; consequently, an infinite arithmetic progression is a member of the Helly family.

However, rather than being an unending progression in and of itself, the intersection of an infinite number of infinite arithmetic progressions might be a particular number.

We know that the AP has the total number of seats between 18 000 and 22 500.

So if we take first term as 100 common difference as 22 and 40 rows we get :

sum =  \(\frac{40}{2} [2\times 100+(40-1)22] = 21160\)

Therefore the number of seats in the arena matches the required description.

and the last row will have 100+(39)22 = 968 seats.

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The injury probability p that makes the decision maker indifferent between entering now and waiting until next year is approximately 0.26.

To calculate this probability, we need to set the expected values of entering now and waiting until next year equal to each other and solve for p. Let EMV₁ be the expected value of entering now and EMV₂ be the expected value of waiting until next year. Then we have:

EMV₁ = -1000p + 5000(1-p)

EMV₂ = 0.9(-1000p) + 0.1(5000)

Setting EMV₁ equal to EMV₂, we get:

-1000p + 5000(1-p) = 0.9(-1000p) + 0.1(5000)

Solving for p, we get:

p ≈ 0.26

Therefore, if the probability of injury is greater than 0.26, the decision maker should wait until next year to enter the market, and if the probability of injury is less than 0.26, the decision maker should enter the market now.

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Answer:

Step-by-step explanation:

Given the sets of side lengths of a triangle:

To verify whether each set of side lengths could be the sides of a right triangle, we use the Pythagorean Theorem. Note that the longest side is always taken as the hypotenuse.

In the set of side lengths 10.5 cm, 20.8 cm, 23.3 cm

\(23.3^2=20.8^2+10.5^2\\542.89=432.64+110.25\\542.89=542.89\)

Clearly these satisfies the required theorem and thus are side lengths of a right triangle.

In the set of side lengths 6 cm, 22.9 cm, 20.1 cm

\(22.9^2=20.1^2+6^2\\524.41\neq 440.01\)

Clearly these does not satisfy the required theorem and thus are not side lengths of a right triangle.

If rxy = 0.83, we can conclude that x and y have a relatively strong positive linear relationship or correlation.

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables, in this case, x and y. The value of r ranges between -1 and 1. A positive value indicates a positive relationship, meaning that as one variable increases, the other variable tends to increase as well.

In this case, with rxy = 0.83, the correlation coefficient is close to 1, suggesting a strong positive linear relationship. This means that when x increases, y also tends to increase, and vice versa. The closer the value of r is to 1, the stronger the linear relationship between x and y.

It is important to note that correlation does not imply causation. While a high correlation coefficient indicates a strong linear relationship, it does not provide information about the underlying cause or direction of the relationship between the variables. Other factors and variables may influence the relationship, and further analysis may be required to understand the nature of the relationship between x and y.

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➲ ( 1 + sec x )( cosec x - cot x ) = tan x

\( \implies\quad \sf{(1+sec\:x)(cosec\:x-cot\:x) }\)

\( \implies\quad \sf{ \left(1+\dfrac{1}{cos\:x}\right)\left(\dfrac{1}{sin\:x}-\dfrac{cos\:x}{sin\:x}\right)}\)

\( \implies\quad \sf{ \left(\dfrac{1+cos\:x}{cos\:x}\right)\left(\dfrac{1-cos\:x}{sin\:x}\right)}\)

\( \implies\quad \sf{ \left(\dfrac{1-cos^2 x}{cos\:x.sin\:x}\right)}\)

\( \implies\quad \sf{ \left( \dfrac{sin^2 x}{cos\:x.sin\:x}\right)}\)

\( \implies\quad \sf{ \left( \dfrac{sin\:x.\cancel{sin\:x}}{cos\:x.\cancel{sin\:x}}\right)}\)

\( \implies\quad \sf{\left( \dfrac{sin\:x}{cos\:x}\right) }\)

\( \implies\quad\underline{\underline{\pmb{ \sf{tan\:x}}} }\)

➲ ( 1+ sec x )( 1- cos x ) = sin x. tan x

\( \implies\quad \sf{ ( 1+ sec\:x)(1-cos\:x)}\)

\( \implies\quad \sf{\left(1+\dfrac{1}{cos\:x} \right) \left( 1-cos\:x\right)}\)

\( \implies\quad \sf{ \left(\dfrac{cos\:x+1}{cos\:x} \right)(1-cos \:x)}\)

\( \implies\quad \sf{\dfrac{1-cos^2 x}{cos\:x} }\)

\( \implies\quad \sf{\dfrac{sin^2x}{cos\:x} }\)

\( \implies\quad \sf{sin\:x.\left( \dfrac{sin\:}{cos\:x}\right) }\)

\( \implies\quad\underline{\underline{\pmb{ \sf{sin\:x.tan\:x}}} }\)

Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5