£20 is divided between Colin, Dan & David so that Colin gets twice as much as Dan, and Dan gets three times as much as David. How much does Colin get?

Answer:

Bats        Insects(grams)

9                   45g

36                  X g

Unitary method :

              \(X = \frac{36*45}{9} = 4*45 = 180g\)

Answer: B) D=(all real numbers), R= {y|y>0}

Step-by-step explanation:
To find the domain and range of the function y = 3(1/5)^x, we need to analyze the behavior of the function.

Domain:

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. Since the function y = 3(1/5)^x involves an exponential expression, it is defined for all real numbers. There are no restrictions on the values of x that can be input into the function. Therefore, the domain is all real numbers.

Range:

The range of a function refers to the set of all possible output values (y-values) that the function can produce. In the case of the function y = 3(1/5)^x, we have a positive exponential decay function. This means that as x increases, the function's value (y) approaches zero, but it never actually reaches zero. Moreover, since the base (1/5) and the coefficient (3) are both positive, the function will always produce positive y-values. Therefore, the range is all positive real numbers, or {y | y > 0}.

Answer:

\(x^2+5x+4+\dfrac{3x-8}{x^2+5x-4}\)

Step-by-step explanation:

The dividend is the polynomial which has to be divided.

The divisor is the expression by which the dividend is divided.

Given:

Following the steps of long division, divide the given dividend by the divisor:

\(\large \begin{array}{r}x^2+5x+4\phantom{)}\\x^2+5x-4{\overline{\smash{\big)}\,x^4+10x^3+25x^2+3x-24\phantom{)}}}\\{-~\phantom{(}\underline{(x^4+\phantom{(}5x^3-\phantom{(}4x^2)\phantom{-b)))))))))}}\\5x^3+29x^2+3x-24\phantom{)}\\-~\phantom{()}\underline{(5x^3+25x^2-20x)\phantom{)))..}}\\4x^2+23x-24\phantom{)}\\-~\phantom{()}\underline{(4x^2+20x-16)\phantom{}}\\3x-8\phantom{)}\end{array}\)

The quotient q(x) is the result of the division.

The remainder r(x) is the part left over:

The solution is the quotient plus the remainder divided by the divisor:

\(\implies q(x)+\dfrac{r(x)}{b(x)}=\boxed{x^2+5x+4+\dfrac{3x-8}{x^2+5x-4}}\)

If machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.

Given that machine a can make 350 widgets in 1 hour, and machine b can make 250 widgets in 1 hour.

How much time will both machines take to make 1000 widgets?

Suppose the time taken by both machines be x hours. Time is equal because both the machines need to work together.

According to the question the equation will be as under:

350x+250x=1000

600x=1000

x=1000/600

x=10/6

x=5/3

x=1.67

Converting 0.67 to minutes 0.67*60=40.2

Adding will result 1 hour and 40 minutes.

Hence if machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.

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Answer:

there are  a 112 against

Step-by-step explanation:30% of 160=48 ( 160*0.30=48)

160-48=112

The expected number of each animal type treated in a month would be 69 dogs, 104 cats, 23 birds, and 35 other animals.

Percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". For example, 50% means 50 out of 100 or 0.5 as a decimal.  

to find the expected number of each animal type treated in a month :

Dogs: 30% of 230 animals

= 0.30 x 230

= 69 dogs

Cats: 45% of 230 animals

= 0.45 x 230

= 103.5 cats (rounded to the nearest whole number)

Birds: 10% of 230 animals

= 0.10 x 230

= 23 birds

Other animals: 15% of 230 animals

= 0.15 x 230

= 34.5 other animals

Therefore, the expected number of each animal type treated in a month would be 69 dogs, 104 cats, 23 birds, and 35 other animals.

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If sofia has a collection of 200 coins, 40 coins represent 20% of Sofia's collection.

To find out how many coins represent 20% of Sofia's collection, we need to first calculate what 1% of her collection is.

To do this, we can divide the total number of coins by 100:

1% of Sofia's collection = 200 coins ÷ 100 = 2 coins

Now that we know that 1% of her collection is 2 coins, we can find 20% by multiplying 2 by 20:

20% of Sofia's collection = 2 coins × 20 = 40 coins

Therefore, 40 coins represent 20% of Sofia's collection.

To find out what percentage a different number of coins represents, we can use the same method. For example, if we want to know what percentage 30 coins represent, we can divide 30 by 2 (since 2 coins represent 1%), which gives us 15%.

So, 30 coins represent 15% of Sofia's collection.

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There are ΔABC and ΔXYZ triangles that are congruent due to the SAS congruence postulate.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

As per the given question,

In ΔABC and ΔXYZ,

Side BC = Side YZ

m∠C = m∠Z

Side AC = Side XZ

According to SAS, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.

Thus, both triangles are congruent.

Hence, there are ΔABC and ΔXYZ triangles congruent due to the SAS congruence postulate.

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Answer:

The answer is (12 players)

Step-by-step explanation:

2 x 2 x 3 = 12      

36 - 12 = 24

Answer:

7238.23

Step-by-step explanation:

To answer this question, first, we will compute the intensity of each earthquake.

Recall that:

Therefore, using the given formula we get:

Then, the intensity of an earthquake that measures 7.5 on the Richter scale is:

and the intensity of an earthquake which measures 2.3 on the Richter scale is:

Now, notice that:

We know that:

Answer:

Answer:

(1 / cot²θ) + secθ cosθ  

(1 / cotθ) == tanθ

Therefore

tan²θ + secθ cosθ

secθ == (1 / cos θ)

Therefore

tan²θ + (1 / cosθ) cosθ

The cosθ 's cancel out

Therefore

tan²θ + 1

tan²θ + 1 == sec²θ

Therefore

sec²θ is the simplified answer

Answer: answer

Step-by-step explanation: joe nuts

Answer: D and E

Step-by-step explanation:

It is not an integer because it is represented by a fraction it is not an irrational number because it can be represented by the decimal 0.75. It is not a whole number because it is a fraction. It is rational because the decimal numbers do not go on forever and it is not an imaginary number so it is a real number.

By using Chebyshev's inequality, n = (o² * δ) / e² samples are sufficient to guarantee that P(|Sn - u| > e) < δ for the sample mean estimator.

In order to solve this question we need to consider Optimal Mean Estimation via Concentration Inequalities and use sample mean and median of means estimator.

To find the sample size n that guarantees P(|û - u| > e) < δ using Chebyshev's inequality, follow these steps:

1. Define Sn as the sample mean estimator:

Sn = (1/n) * Σ(Xi) for i = 1 to n.

2. We know the variance o² is known, and Chebyshev's inequality states that P(|X - E(X)| > k * σ) ≤ 1/k², where X is a random variable, E(X) is the expected value of X, σ is the standard deviation, and k is a constant.

3. Apply Chebyshev's inequality to Sn - u:

P(|Sn - u| > k * (o / sqrt(n))) ≤ 1/k², where k = e * sqrt(n) / o.

4. We want P(|Sn - u| > e) < δ, so we can rewrite Chebyshev's inequality as 1/k² < δ. Substitute k with e * sqrt(n) / o: 1/((e * sqrt(n) / o)²) < δ.
5. Solve for n: n = (o² * δ) / e².

By using Chebyshev's inequality, n = (o² * δ) / e² samples are sufficient to guarantee that P(|Sn - u| > e) < δ for the sample mean estimator.

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Answer:

Step-by-step explanation:

we will replace f(x) with y

y=8x-5  

x=8y-5  we solve for y

8y-5=x

y=x/8 +5/8

f^-1=x/8 +5/8

Answer:

A

Step-by-step explanation:

10 squared + 24 squared = 26 squared :)

The value of x from the given five integers is 34.

Here we have to find the value of x.

Data given:

Five positive number = 31, 58, 98, x, x

The mean is 1.5 times the mode.

Mean = (31 + 58 + 98 + x + x) / 5

         = (187 + 2x) / 5

Mode = x

As the mean is 1.5 times the mode so from this we have:

mean = 1.5 × mode

(187 + 2x)/ 5 = 1.5x

187 + 2x = 7.5x

5.5x = 187

x = 34

Therefore the value of x is 34.

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Answer: Hi!

First, we will use inverse operations to remove the 7. Subtract 7 on both sides:

7 - 7 = 0

4 - 7 = -3

Our equation now looks like this:

-11b = -3

Now we will use inverse operations to isolate the b. Divide -11 on both sides:

-11b ÷ -11 = b

-3 ÷ -11 = 3/11

Our equation now looks like this:

3/11 = b

3/11 is equal to b. This is your answer!

Hope this helps!

A) The CDF of X is: F(x) = 1 - 1/(x+1) for x=1,2,3,...

B)The value of function  P(2 <= X <= 4) = 3/10.

a) To find the CDF of X, we need to sum up the PMF of X up to each value of k. Let's define a function f(k) as the PMF of X, which is given by:

f(k) = P(X=k) = 1/(k*(k+1))

Then, the CDF of X, denoted as F(x), is:

F(x) = P(X <= x) = sum of f(k) for k=1 to k=x

F(x) = sum of 1/(k*(k+1)) for k=1 to k=x

F(x) = sum of [1/k - 1/(k+1)] for k=1 to k=x

F(x) = [1/1 - 1/2] + [1/2 - 1/3] + ... + [1/x - 1/(x+1)]

F(x) = 1 - 1/(x+1)

Therefore, the CDF of X is:

F(x) = 1 - 1/(x+1) for x=1,2,3,...

To plot the CDF, we can use the following Python code:

import matplotlib.pyplot as plt

import numpy as np

def cdf(x):

   return 1 - 1/(x+1)

x = np.arange(1, 7)

y = cdf(x)

plt.step(x, y)

plt.xlim(0, 7)

plt.ylim(0, 1.1)

plt.xlabel('x')

plt.ylabel('F(x)')

plt.title('CDF of X')

plt.show()

The plot of the CDF of X is:

CDF of X plot

b) To find P(2 <= X <= 4) using the CDF, we can use the following formula:

P(2 <= X <= 4) = F(4) - F(1)

Using the CDF we found in part (a), we have:

P(2 <= X <= 4) = F(4) - F(1) = (1 - 1/5) - (1 - 1/2) = 3/10

Therefore, P(2 <= X <= 4) = 3/10.

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The ball traveled approximately \(26.27\) units in total.

To calculate the distance the ball traveled, we can use the distance formula between two points in a Cartesian coordinate system.

Distance = \(\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1} )^{2} }\)

Let's calculate the distance between Player A and Player B first:

Distance_AB =

\(\sqrt{((16-2)^{2}+(9-4)^{2}) }\)

\(= \sqrt{(14^{2}+5^{2} ) } \\= \sqrt{(196 +25)} \\= \sqrt{221} \\= 14.87\)

Now, let's calculate the distance between Player B and Player C:

Distance_BC =

\(\sqrt{ ((25 - 16)^2 + (16 - 9)^2)}\\= \sqrt{ (9^2 + 7^2)}\\= \sqrt{(81 + 49)}\\= \sqrt{130}\\=11.40\)

Finally, we can calculate the total distance traveled by adding the distances AB and BC:

Total distance = Distance_AB + Distance_BC

\(= 14.87 + 11.40 \\= 26.27\)

Starting from Player A at \((2, 4),\) it was thrown to Player B at \((16, 9),\) covering a distance of about \(14.87\) units. From Player B, the ball was then thrown to Player C at \((25, 16),\) covering an additional distance of approximately \(11.40\) units.

Combining these distances, the total distance the ball traveled was approximately \(26.27\) units.

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a.  4 is an extraneous root. , b. 0 is an extraneous root. , c. -3 is an extraneous root. , d. -13.21 is an extraneous root. , e. 9.22 is an extraneous root.

To solve the equation, we can begin by finding a common denominator for the fractions on the left-hand side. The common denominator is (x + 3)(x - 4). We can then rewrite the equation as follows:

[4x(x - 4) + 3(x + 3)] / [(x + 3)(x - 4)] = 5

Expanding and simplifying the numerator, we have:

[4x^2 - 16x + 3x + 9] / [(x + 3)(x - 4)] = 5

Combining like terms, we obtain:

(4x^2 - 13x + 9) / [(x + 3)(x - 4)] = 5

To eliminate the fraction, we can cross-multiply:

4x^2 - 13x + 9 = 5[(x + 3)(x - 4)]

Expanding the right-hand side, we get:

4x^2 - 13x + 9 = 5(x^2 - x - 12)

Simplifying further:

4x^2 - 13x + 9 = 5x^2 - 5x - 60

Rearranging the equation and setting it equal to zero, we have:

x^2 - 8x - 69 = 0

To solve this quadratic equation, we can factor or use the quadratic formula. Factoring the equation may not yield rational roots, so we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the equation x^2 - 8x - 69 = 0, we have a = 1, b = -8, and c = -69. Substituting these values into the quadratic formula, we get:

x = (-(-8) ± √((-8)^2 - 4(1)(-69))) / (2(1))

= (8 ± √(64 + 276)) / 2

= (8 ± √340) / 2

= (8 ± 2√85) / 2

= 4 ± √85

So, the possible solutions for x are x = 4 + √85 and x = 4 - √85.

Now, let's check which of the given options (a, b, c, d, e) are extraneous roots by substituting them into the original equation:

a. 4: Substitute x = 4 into the equation: 4(4)/(4 + 3) + 3/(4 - 4) = 5. This results in a division by zero, which is undefined. Therefore, 4 is an extraneous root.

b. 0: Substitute x = 0 into the equation: 4(0)/(0 + 3) + 3/(0 - 4) = 5. This also results in a division by zero, which is undefined. Therefore, 0 is an extraneous root.

c. -3: Substitute x = -3 into the equation: 4(-3)/(-3 + 3) + 3/(-3 - 4) = 5. Again, we have a division by zero, which is undefined. Therefore, -3 is an extraneous root.

d. -13.21: Substitute x = -13.21 into the equation and evaluate both sides. If the equation does not hold true, -13.21 is an extraneous root.

e. 9.22: Substitute x = 9.22 into the equation and evaluate both sides. If the equation does not hold true, 9.22 is an extraneous root.

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In linear equation, You are the only person in the garden at the time the 34 people.

What in mathematics is a linear equation?

You are the only person in the garden at the time the 34 people are on their homicidal spree.

Alternatively, if the backyard and garden are in the same place, then there are no longer any individuals in the garden because you would officially count as one of the 34 people who are all killed.

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We will find the speeds of both persons, the correct option is:

"Ramon rides his bike 3 miles per hour slower than Hector rides his bike."

First, we know that Ramon rides 45 miles in 3 hours, then its speed is:

S = 45mi/3h = 15mi/h

And we know that Hector position is given by:

y = 18x

Where x is time in hours, so his velocity is 18mi/h.

Then we can see that:

So the correct statement is:

"Ramon rides his bike 3 miles per hour slower than Hector rides his bike."

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Answer:

y + 9 ≤ -30

Step-by-step explanation:

The probability  that the average scholarshi[s in the samle greater than 20,000 is (69.729, 74.271).

Let X: Marks of students and be the population average marks.

X ~ N(72, 16)

The formula for the CI for is,

CI = mean + tₐ/₂ , ₙ₋₁ s/n

= 72 ± 2.539 × 4/20

= 72 ± (2.539 × 0.8944)

= 72 ± 2.27

= 72 - 2.27 , 72 + 2.27

= (69.729, 74.241)

Therefore, the required 98% CI for the average marks of the students is (69.729, 74.271).

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When we conclude that the results we have gathered from our sample are probably also found in the population from which the sample was drawn, we say that the results are statistically significant.

In statistical analysis, we use hypothesis testing to determine whether the results of a sample are likely to be representative of the population as a whole. If the results are statistically significant, we can infer that there is a low probability that the observed differences between the sample and the population occurred by chance alone.

This allows us to generalize the findings from the sample to the larger population with a reasonable degree of confidence.

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Let x represent the number of hours that he spent washing cars.

Let y represent the number of hours that he spent landscaping.

In a week, he can work no more than 19 total hours. This means that

x + y ≤ 19- - - - - - - - - - - -1

Jacob is working two summer jobs, making $10 per hour washing cars and making $8 per hour landscaping. He must earn at least $170. This means that

10x + 8y ≥ 170 - - - - - - - - - -2

If Jacob worked 4 hours landscaping, it means that

x + 4 ≤ 19    x ≤ 19 - 4    x ≤ 15

Also,  10x + 8 × 4 ≥ 170     10x + 32 ≥ 170

10x ≥ 170 - 32          10x ≥ 138

10x ≥ 138/10             x ≥ 13.8

The minimum number of hours is 14

$2100 was invested at 2% and $2900 ($5000 - $2100) was invested at 3%.

Let x be the amount invested at 2% and y be the amount invested at 3%. We know that x + y = $5000 and the interest earned is $129. We can use the formula for simple interest, I = Prt, where I is the interest earned, P is the principal (or initial amount invested), r is the interest rate, and t is the time period.

Thus, we have:

0.02x + 0.03y = $129 (1)

x + y = $5000 (2)

We can solve for one of the variables in terms of the other from equation (2), such as y = $5000 - x. Substituting this into equation (1), we get:

0.02x + 0.03($5000 - x) = $129

Simplifying and solving for x, we get:

0.02x + $150 - 0.03x = $129

-0.01x = -$21

x = $2100

Therefore, $2100 was invested at 2% and $2900 ($5000 - $2100) was invested at 3%.

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