Which equation is not true?
1). 4 ( z - 11 ) = 4z - 44
2). -2 ( 3x + 5 ) = -6x + 10
3). 0.5 ( 2m - 3) = 1m - 1,5

The number of wild bears the naturalist can relocate per month is 2 wild bears.

Number of wild bears relocated by the naturalist = 12 wild bears

Time taken by the naturalist to relocate these wild bears = 6 months

Thus the number of bears the naturalist can relocate in 1 month can be found out by using unitary method

This implies that the number of bears relocated by the naturalist in 1 month or per month = 12 / 6 = 2 wild bears

Thus the number of wild bears the naturalist can relocate per month is 2 wild bears .

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Answer:

16

Step-by-step explanation:

The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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Answer:

2

Step-by-step explanation:

20-7x=6x-6

20+6=6x+7x

26=13x

x=2

Answer:

16.49 feets

Step-by-step explanation:

Using Pythagoras rule, we could find, h the height of the wall ;

Using the relation :

a² = b² + c²

36² = h² + 32²

1296 = h² + 1024

h² = 1296 - 1024

h² = 272

h = √272

h = 16.49 feets

Answer:

to get the reciprocal of a number you divide 1 by that number. therefore the answer to this question is.14705882 or 34/5

or

It should be 34/5*. If you create an improper fraction out of the original one, then creating the reciprocal will be easier.

the first four terms of the Maclaurin series of f if f (0)=8, f′(0)=5, f″(0)=10, f‴(0)=36 are 8 + 5x + 5x^2 + 6x^3.

The Maclaurin series of a function f(x) is given by the following formula:

f(x) ≈ f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...

We're given the first four derivatives of f evaluated at 0:
f(0) = 8
f'(0) = 5
f''(0) = 10
f'''(0) = 36

Now, we can use these values to find the first four terms of the Maclaurin series of f(x):

1. f(0) = 8
2. f'(0)x = 5x
3. f''(0)x^2/2! = 10x^2/2 = 5x^2
4. f'''(0)x^3/3! = 36x^3/6 = 6x^3

So, the first four terms of the Maclaurin series of f(x) are:

f(x) ≈ 8 + 5x + 5x^2 + 6x^3

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Answer:

Step-by-step explanation:

B

Answer:

Step-by-step explanation:

S and T are supplementary angles

When x increases by 1 in the function y=3^x, the value of the function will be multiplied by 3.

Given the function

y = 3^x

An increment in the value of x would make the expression be multiplied by 3

To see why this happens, we can compare the value of the function at x and x+1:

y(x+1) = 3^(x+1)

y(x+1) = 3^x * 3 (by the laws of exponents)

y(x+1) = 3 * 3^x

Therefore, we can see that when x increases by 1, the value of the function is multiplied by 3.

This means that the function grows very quickly as x increases.

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MBI's % profit on cost is 33.33%.

To calculate the % profit on cost, we need to determine the profit and divide it by the cost.

The selling price of each unit is $15.00, and 25% of this price is the profit margin, which is $15.00 * 25% = $3.75.

The cost per unit is the selling price minus the profit margin, which is $15.00 - $3.75 = $11.25.

The total cost for producing 15,000 units is $11.25 * 15,000 = $168,750.

The profit is the difference between the total revenue and the total cost, which is $15.00 * 15,000 - $168,750 = $81,250.

The % profit on cost is the profit divided by the cost, multiplied by 100: ($81,250 / $168,750) * 100 ≈ 48.15%.

Therefore, the correct answer is not provided in the given options. The closest option to the calculated result is 50%, but the actual % profit on cost is approximately 48.15%.

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Answer:

C. 3/2

Step-by-step explanation:

slope:

Rise/run:

rise: 6

run: 4

6/4:

reduce = 3/2

Answer:

35 min

Step-by-step explanation:

given that the total time spent is 140min

and that the time spent reading is x minutes

and also that the time spent doing home work is 2(x+5)

the time spent playing video game is 25

the expression for the total time is given as

total = reading +homework +video game

140=x+2(x+5)+25

solving for x we have

140=x+2x+10+25

140=3x+35

140-35=3x

105=3x

x=105/3

x=35

kenny spent 35 min reading

Time spend for reading is 35 minutes

Given that;

Total number of minutes Kenny have = 140 minutes

Time spend for reading = x

Time spend for homework = 2(x + 5) = 2x + 10

Time spend for games = 25 minutes

Find:

Time spend for reading

Computation:

Total number of minutes Kenny have = Time spend for reading + Time spend for homework + Time spend for games

140 = x + 2x + 10 + 25

3x + 35 = 140

3x = 105

x = 105 / 3

x = 35

So,

Time spend for reading = 35 minutes

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Answer:

X= 10/3y + -4/3                

Step-by-step explanation:

Step One: add -5y to both sides

Step two: divide both sides by -3

Answer:

-x=1 1/3

Step-by-step explanation:

x-(4x-5y)=(5y+4)

x-4x+5y=5y+4

-3x+5y=5y+4

5y-5y=0

-3x=4

x=4÷3

4÷3=1 1/3

95% confidence interval for the population mean is 170.2 to 189.8, option d is correct.

We are given the following information:

- Sample size (n) = 225
- Standard deviation (σ) = 75
- Sample mean (x) = 180
- Confidence level = 95%

We need to calculate the 95% confidence interval for the population mean (μ). To do this, we will use the formula:

Confidence interval = x ± (z × σ/√n)

First, we need to find the z-score that corresponds to a 95% confidence level. For a 95% confidence interval, the z-score is 1.96 (you can find this value in a standard z-score table).

Now, we can plug in the values we have:

Confidence interval = 180 ± (1.96 × 75/√225)

Calculate the standard error (σ/√n):

Standard error = 75/√225 = 5

Now, calculate the margin of error (z * standard error):

Margin of error = 1.96 × 5 = 9.8

Finally, calculate the confidence interval:

Confidence interval = 180 ± 9.8 = (170.2, 189.8)

So, the 95% confidence interval for the population mean is 170.2 to 189.8, which corresponds to option d.

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The length of the curve   r(t) = 4t, t2, 1 6 t3 , 0 ≤ t ≤ 1 is approximately 3.022 units.

A curve is a shape or a line that is smoothly drawn in a plane having a bent or turns in it

\(\int (\dfrac{dx}{dt})^2+ (\dfrac{dy}{dt})^2 +(\dfrac{dz}{dt}^2 dt)\)

where\(r(t) = x(t)i + y(t)j + z(t)k.\)

In this case, we have:

\(x(t) = 4t\\y(t) = t^2\\z(t) =\dfrac{1}{6} t^3\)

So, we need to find\(:\dfrac{dx}{dt} \dfrac{dy}{dt} \dfrac{dz}{dt}\)

\(\dfrac{dx}{dt}\)= 4

\(\dfrac{dy}{dt}\) = 2t

\(\dfrac{dz}{dt}\)=\(1/2 t^2\)

Now we can plug these into the arc length formula:

\(\int (4)^2 +(2t)^2 + (\frac{1}{2t^2^})^2 dt\) dt from 0 to 1

Simplifying under the square root:

\(\int 16+ 4t^2 +\frac{1}4t^4)\) from 0 to 1

This integral is difficult to solve analytically, so we can use numerical methods to approximate the value. One way is to use Simpson's rule, simplifying further:

L= \(\dfrac{1}{3}[\sqrt{16+\sqrt{16} +\sqrt{16.111} +\sqrt[2]{16.222} +\sqrt[2]{16.4167}+\sqrt{17.1111} + \sqrt[2]{17.6944} +\sqrt{20}]\)

Therefore, the length of the curve is approximately 3.022 units.

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The constants α, β, and k are all zero, and the solution to the IVP is y(t) = e²{-2t}, with t = -0.5ln(7)  the condition limt→∞y(t) = 7,t = -0.5ln(7)

Using the method of undetermined coefficients to find the general solution of the differential equation:

y'' + 3y' + 2y = 0

The characteristic equation is:

r²2 + 3r + 2 = 0

Factoring this equation, we get:

(r + 2)(r + 1) = 0

So the roots are r1 = -2 and r2 = -1. Therefore, the general solution is:

y(t) = c1e^{-2t} + c2e^{-t}

Next, we use the information that y1(t) = e²{-3t} is a solution to the differential equation. Substituting this into the general solution, we get:

e²{-3t} = c1e²{-2t} + c2e²{-t}

equation to solve for c1 and c2. Multiplying both sides by e^{2t}, we get:

e²{-t} = c1 + c2e²t

Taking the limit as t approaches infinity,  that c1 must be zero in order for the right-hand side to converge to a finite value. Therefore, we have:

c1 = 0

Substituting this into the previous equation,

e²{-t} = c2e²t

Dividing both sides by e²t,

e²{-2t} = c2

Therefore, we have:

c2 = e²{-2t}

Substituting these values into the general solution,

y(t) = c1e²{-2t} + c2e²{-t} = e²{-2t}

So α = β = 0 and k = -2. Finally,  the information that limt→∞y(t) = 7. Since y(t) = e²{-2t}, we have:

limt→∞e²{-2t} = 7

Taking the natural logarithm of both sides,

-2t = ln(7)Solving for t,

t = -0.5ln(7)

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The percentage of this monthly fee goes to property taxes is 18%.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We need to Write the percent as a fraction in simplest form

16.24%

So, we can rewrite it as;

16.24 / 100

16 and 24/100 or 16 6/25

So the percent as a fraction is 16 6/25

We are given that;

Property taxes each year= $3,196.80

Monthly maintenance fee = $1,480

Now,

To find the percentage of Sarah's monthly maintenance fee that goes to property taxes, we need to divide the annual property tax by the total amount she pays in a year for her condo, which includes the monthly maintenance fee.

First, let's calculate the total amount she pays in a year:

Total annual cost = Monthly cost x 12 months

Total annual cost = $1,480 x 12 = $17,760

Next, let's calculate the percentage of the annual cost that goes to property taxes:

Property tax percentage = (Annual property tax / Total annual cost) x 100%

Property tax percentage = ($3,196.80 / $17,760) x 100%

Property tax percentage = 0.18 x 100%

Property tax percentage = 18%

Therefore, by the given date the percentage will be 18%.

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Answer: 1/(x+2)Step-by-step explanation:=(x-2)(1)/(x-2)(x+2) cancel (x-2)=1/(x+2)

Step-by-step explanation:

Answer:

15 nights

Step-by-step explanation:

44 cm over 11 nights equals 4 cm per night

let 'n' = number of nights

4n = 60

n = 15

Factors of the given expression are \((2x-5) ,(3x+2)\)

The given expression is:

\(6x^2-11x-10\)

A factor is a number that divides another number leaving no remainder.

we can split the middle term as,

\(6x^2-15x +4x-10\\\)

\(3x(2x-5)+2(2x-5)\\\\(2x-5) (3x+2)\)

Therefore factors of the given expression are \((2x-5) ,(3x+2)\)

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Answer:

do you have pictures and more measurements so i can solve the problem for you?

Step-by-step explanation:

The polynomial q(x) = x² - 1 spans the kernel of the linear transformation T: P2 → R³, and T is onto since any vector [a, b, c] in R³ can be represented as [P] for some polynomial P(x) in P2.

To find the polynomial q, we need to find the null space of T.

To prove that T is onto, we need to show that the range of T is equal to the codomain.

Let us start by defining the linear transformation T: P2 → R³ where T(P) = [P], and P is a polynomial of degree at most 2. The vector space P2 consists of all polynomials of the form P(x) = ax² + bx + c, where a, b, and c are constants.

To find a polynomial q in P2 such that Span{q} is the kernel of T, we need to find a non-zero polynomial q(x) such that T(q) = [q] = 0. In other words, we need to find a non-zero polynomial q(x) such that q(x) has a repeated root.

Let q(x) = x² - 1. Then, T(q) = [q] = [x² - 1] = [1, 0, -1]. Since [1, 0, -1] ≠ 0, q(x) is a non-zero polynomial and Span{q} is the kernel of T.

To prove that T is onto, we need to show that for any vector [a, b, c] in R³, there exists a polynomial P(x) in P2 such that T(P) = [P] = [a, b, c].

Let P(x) = ax² + bx + c. Then, T(P) = [P] = [ax² + bx + c] = [a, b, c] if and only if P(x) has coefficients a, b, and c.

To find such a polynomial, we can solve the system of equations:

a + 0b + 0c = a

0a + b + 0c = b

0a + 0b + c = c

which gives us a = a, b = b, and c = c. Therefore, any vector [a, b, c] in R³ can be written as [P] for some polynomial P(x) in P2, and T is onto.

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Answer:

2 is a number and x is a letter

Step-by-step explanation:

hope this helps XD

The surface area of this triangular prism is 258 square units

Given parameter is

The triangular prism

The surface area of triangular prism is calculated as

Surface area = Perimeter * Length + 2 * Base area

Using the given dimensions, we have

Surface area = (5 + 6.5 + 6.5) * 11 + 2 * 5 * 6

Evaluate

Surface area = 258

Hence, the surface area is 258 square units

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Number of measurements that must be made so that the diameter can be estimated with an uncertainty of only 0.5 mm is 16

To estimate the diameter with an uncertainty of 0.5 mm, we need to reduce the uncertainty to that level. Let's call the number of measurements we need to make "N". We can use the formula for the standard deviation of the mean

σ_mean = σ / sqrt(N)

where σ is the standard deviation of the individual measurements. In this case, the uncertainty of each measurement is given as 1.4 mm, which we can assume is the standard deviation.

To reduce the uncertainty to 0.5 mm, we need

0.5 = 1.4 / sqrt(N)

Solving for N, we get

N = (1.4 / 0.5)^2 = 15.68

≈ 16

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