The total length of these planks is 92 metres. Work out the number of planks of length 2 metres in Ben workshop.​

A function \(P(t) = 170.(1.30)^t\)  that gives the deer population P(t) on the reservation t years from now

We were told there were 170 stags on reservation. The number of deer is increasing at a rate of 30% per year.

We could see the deer population grow exponentially since each year there will be 30% more than last year.

Since we know that an exponential growth function is in form:

\(f(x) = a*(1+r)^x\)

where a= initial value, r= growth rate in decimal form.

It is given that a= 170 and r= 30%.    

Let us convert our given growth rate in decimal form.

\(30 percent = \frac{30}{100} = 0.30\)

Upon substituting our given values in exponential function form we will get,

    \(P(t) = 170.(1+0.30)^t\)

⇒ \(P(t)= 170.(1.30)^t\)

Therefore, the function \(P(t) = 170.(1.30)^t\) will give the deer population P(t) on the reservation t years from now.

Complete Question:

There are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year. Write a function that gives the deer population P(t) on the reservation t years from now.

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the ratio of feet to yards is:

Now, the proportion to find the equivalent yards for 9 feet is:

Let's solve for x:

Therefore, 9 feet=3 yards.

The coefficient of determination (R²) for the simple linear regression model fitted to the given data is 0.9.

The coefficient of determination (R²) measures the proportion of the total variance in the dependent variable (y) that can be explained by the independent variable (x) in a linear regression model.

It ranges from 0 to 1, where 0 indicates no linear relationship and 1 indicates a perfect linear relationship.

To find R², we need to calculate the sum of squares total (SST), sum of squares regression (SSR), and sum of squares error (SSE).

SST represents the total variation in y, SSR represents the variation in y explained by the regression model, and SSE represents the unexplained or residual variation.

Given that y₁ = 1, y₂= 2, y₃ = 3, y₄ = 4, and y₅ = 5, we can calculate the means of x and y, which are both 3.

The SST can be calculated as the sum of squared differences between each y value and the mean of y, which equals 10.

The SSE is given as s² = 1 multiplied by the degrees of freedom (n - 2), where n is the number of observations (5), resulting in SSE = 3.

Finally, SSR can be obtained by subtracting SSE from SST, which gives SSR = 7.

Using these values, we can calculate R² as SSR divided by SST:

R² = SSR/SST

= 7/10

= 0.7.

Therefore, the coefficient of determination for the given linear regression model is 0.7, indicating that 70% of the total variance in y can be explained by the linear relationship with x.

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The derivatives of the given functions are: f'(x) = cos(x), g'(x) = 12, h'(x) = (3x²) / (2√(x³ + 5)), k'(x) = -6x * e^(x²+1), {('(x) = 2x * sec²(x²), and m'(x) = cos(tan(x)) * sec²(x).

Let's differentiate each function and simplify the results:

For f(x) = 1 + sin(x), the derivative is f'(x) = cos(x) since the derivative of sin(x) is cos(x).

For g(x) = 3(4x + 1), we apply the constant multiple rule and the power rule. The derivative is g'(x) = 3 * 4 = 12.

For h(x) = √(x³ + 5), we use the chain rule. The derivative is h'(x) = (1/2) * (x³ + 5)^(-1/2) * 3x² = (3x²) / (2√(x³ + 5)).

For k(x) = -3e^(x²+1), we use the chain rule and the derivative of e^x, which is e^x. The derivative is k'(x) = -3 * e^(x²+1) * 2x = -6x * e^(x²+1).

For {(x) = tan(x²), we use the chain rule and the derivative of tan(x), which is sec²(x). The derivative is {('(x) = 2x * sec²(x²).

For m(x) = sin(tan(x)), we use the chain rule and the derivative of sin(x), which is cos(x). The derivative is m'(x) = cos(tan(x)) * sec²(x).

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Answer:

There will be 640 beetles in 15 weeks

Step-by-step explanation:

f(t) = 20 (2)¬t/3

where ¬ symbol stands for raise to the power

according to the question,

640 = 20 (2)¬t/3

640/20 = 2¬t/3

2¬t/3 = 32

2¬t/3 = 2¬5

t/3 = 5

t = 5*3

t = 15 weeks

Answer:

A. q = 39

Step-by-step explanation:

Since the lines are parallel, their sides will be proportional,

So,

Taking their proportion

=> \(\frac{60}{40} = \frac{q}{26}\)

Cross Multiplying

q × 40 = 26 × 60

q = \(\frac{1560}{40}\)

q = 39

Answer:

ummm it gave me 31.42

Step-by-step explanation:

hope this helpss

Answer:

Substitute –3 for x and 5 for h in the difference quotient.

Step-by-step explanation:

The difference quotient for the function f(x) is  21x² + 21xh + 7h² + 2. Now, we know that the difference quotient equal f(x + h) - f(x) = 21x² + 21xh + 7h² + 2. The change in x is h = x₂ - x₁. So, if x changes from x = -3 to x = 2,  where x₁ = -3 and x₂ = 2, h = x₂ - x₁ = 2 - (-3) = 2 + 3 = 5.

So to find the average rate of change of f(x) from x = -3 to x = 2, we substitute x = -3 and h = 5 into the difference equation  f(x + h) - f(x) = 21x² + 21xh + 7h² + 2. Since, x starts at x = -3 and increases by 5 units to x = 2.

Answer:

(on edge) B. Substitute –3 for x and 5 for h in the difference quotient.

Step-by-step explanation:

Answer:

Step-by-step explanation:

One antifreeze solution is 26% alcohol and another is 11% alcohol how much of each mixture should be added to make 24 l of a solution that is 21% alcohol?

Let us represent

First solution =>x

Second solution => y

System of equations

x + y = 24.....Equation 1

x = 24 - y

26% × x + 11% × y = 21% × 24

= 0.26x + 0.11y = 5.04... Equation 2

The probability that all 7 graduates selected at random received a starting salary of $60,000 or more is , 0.0065

This is a binomial probability problem where we have a sample of size 7 and want to find the probability that all 7 graduates received a starting salary of $60,000 or more.

We know that 40% of mathematics graduates received a starting salary of $60,000 or more,

So, the probability of any one graduate receiving a salary of $60,000 or more is 0.4.

Using the binomial probability formula, we can calculate the probability as follows:

P(X = 7) = (n choose X) pˣ (1-p)ⁿ⁻ˣ

where n is the sample size, x is the number of graduates who received a starting salary of $60,000 or more, p is the probability of success (i.e., receiving a salary of $60,000 or more), and (n choose X) is the number of ways to select X graduates out of n.

So in this case, we have:

n = 7, X = 7 and p = 0.4

Plugging into the formula, we get:

P(X = 7) = (7 choose 7) 0.4⁷ (1-0.4)⁷⁻⁷

P(X = 7) = (1) 0.4⁷ (0.6)⁰

P(X = 7) = 0.0065

Therefore, the probability that all 7 graduates selected at random received a starting salary of $60,000 or more is , 0.0065

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Given polygons a right triangle and an isosceles triangle sometimes be similar.

As given ,

Given polygons : A right triangle and isosceles triangle.

Polygon a right triangle and isosceles triangle never be similar.

Reason:

Therefore, given polygons a right triangle and an isosceles triangle sometimes be similar.

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Answer:

259.5

Step-by-step explanation:

8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5

Answer:

i d k

Step-by-step explanation:

Answer:

976858587587587587585857587587585858587587585875855785875 x 8587587585858557686875789757556475647385674546738657465478657 = bad expression.. literally you can't calculate that

7 and and -12 is the answer correct me if im wrong

HOPE IT HEPLS:)

Answer:

23

Step-by-step explanation:

the difference between each number in the sequence is 4. Taking 4 away from 27 gives you 23

Hope this helps!

The answer choice which represents a function with the ordered pair (4, 8) as a solution is; Choice C; 2x = y.

It follows from the task content that the function which has the given ordered pair; (4, 8) as a solution is to be determined.

On this note, by observation; the answer choice C represents an equation whose solution includes (4, 8).

By checking; we have; 2x = y;

2 (4) = 8; 8 = 8 which holds true.

Consequently, answer choice C is correct.

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Option (b) is correct, that is less than half of these appliances are expected to have a lifespan of more than 15 years.

Given that,

Appliances are being tested by a consumer organization for a number of stories in their magazine. They are presently focusing on cooktops and ranges. They've chosen 16 of the most popular models. The agency will calculate the longevity of these models using a series of tests. Below is a histogram of these (estimated) lifespan.

We have to find how many of these appliances are expected to have a lifespan of more than 15 years.

We have,

Frequency of these appliances last more than 15 years or 15×12 months=180 months.

from the graph we see that frequency more than 200 months is 4 as and frequency of the class interval 175-200 is 3 .  

Even in this class interval all the frequencies are greater than 180 then the total no. of frequency >180 months is 7 which is lass than half of total frequency 16 .

Therefore, Option (b) is correct, that is less than half of these appliances are expected to have a lifespan of more than 15 years.

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The area of the rectangle will be 18a³b^6

The area of the circle will be 25x^6π

The area of the triangle will be 12a³c⁴

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

The area of the rectangle will be:

= Length × Width

= 6a²b⁴ × 3ab²

= 18a³b^6

The area of the circle will be:

= πr²

= π × (5x³)

= 25x^6π

The area of the triangle will be:

= 1/2 × base × height

= 1/2 × 4a²c × 6ac³

= 2a²c × 6ac³.

= 12a³c⁴

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Answer:

Ok, so to find this difference, you have to add 8 to the -10,  which becomes -2. The answer is -2°.

Step-by-step explanation:

The latest time for pickup, found by converting the 150 minutes maximum time provided by the school, from minutes to hours is about 5:45 pm

Minutes can be converted into hours by dividing the number of minutes by 60, which is the number of minutes in an hour.

The time that school ends = 3:15 pm

The latest time for pick up after school care = 150 minutes after school ends

Therefore, the latest time for pick up after school care = 3:15 pm + 150 minutes

60 minutes = 1 hour

150 minutes = (1/60) × 150 = 2.5

The latest for pick up = 3:15 pm + 2.5 hours = 5:45 pm

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Answer:

I am the son of waterbut when I return to water I die

Ice

Ii is the estimated value of the integral at the ith iteration, and I is the overall estimated value of the integral. We can stop the algorithm when the standard deviation σ is less than 0.01.

The standard deviation (SD, also written as the Greek symbol sigma or the Latin letter s) is a statistic that is used to express how much a group of data values vary from one another.

To estimate the integral I = ∫[1 to 0] \(e^{(x^2)\) dx using Monte Carlo simulation, we can use the following algorithm:

To stop when the standard deviation of the estimator is less than 0.01, we can keep track of the estimated value of the integral and the number of points generated at each iteration of the algorithm. We can compute the standard deviation of the estimator using the formula:

σ = √((1/N) * Σ[i=1 to N] (Ii - I)²)

where N is the number of iterations, Ii is the estimated value of the integral at the ith iteration, and I is the overall estimated value of the integral. We can stop the algorithm when the standard deviation σ is less than 0.01.

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Answer:

Quadrant IV

Step-by-step explanation:

For an angle in the fourth quadrant the point P has positive x coordinate and negative y coordinate. Therefore: In Quadrant IV, cos(θ) > 0, sin(θ) < 0 and tan(θ) < 0 (Cosine positive). The quadrants in which cosine, sine and tangent are positive are often remembered using a favorite mnemonic.

A characteristic of the classical approach to probability include the following: D. probabilities assume outcomes of an experiment are equally likely.

In Science, an experiment is a scientific investigation which typically involves the process of manipulating an independent variable (the cause), in order to determine or measure the dependent variable (the effect).

In Mathematics and statistics, an expected value is sometimes referred to as the long-term mean (average) of a discrete random variable, E(X) and it can be calculated by taking the weighted average of all the outcomes of the discrete random variable with respect to their probabilities.

In this context, we can logically deduce that a characteristic of the classical approach to probability is that most times probabilities assume outcomes (results) of an experiment are equally likely.

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The rational function -4/x^2 + 5x - 6 can be simplified into a form of (-A/x - r) + (-B/x - s), where A, B, r, s are constants.

Given, the function is -4/x² + 5x - 6We need to factor the denominator. We getx² - 5x + 6 = 0Using factorization, we get, x² - 2x - 3x + 6 = 0 ⇒ x(x - 2) - 3(x - 2) = 0⇒ (x - 3)(x - 2) = 0So, we can write the function as -4/(x - 3)(x - 2)We know that a fraction can be decomposed into partial fractions. So, -4/(x - 3)(x - 2) = A/(x - 3) + B/(x - 2)Now, we multiply both sides by (x - 3)(x - 2).

We get, -4 = A(x - 2) + B(x - 3)For x = 2, -4 = -B For x = 3, -4 = A On solving, we get A = 4 and B = 4So, -4/(x² - 5x + 6) = 4/(x - 3) - 4/(x - 2)This is the required partial fraction decomposition of the given rational function. Order these values so that a < b. 3, 2.

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Answer:

1/3 chance

Step-by-step explanation: 2/6=1/3

Answer:

\(8x+8y=40\)

Step-by-step explanation:

The line passes through \((5,0)\) and \((0,5)\).

\(\frac{x}{5}+\frac{y}{5}=1 \implies x+y=5 \implies 8x+8y=40\)