Perimeter and Area of rectangle (Please end my suffering)

Answer:

Yea u did......

Step-by-step explanation:

you did right because all the steps are right

Answer:

Answering your own module is a perfect list in our teacher so verygood

Step-by-step explanation:

Nice try and try

Answer: 3:30

Step-by-step explanation:

Solution to given logarithmic equations and inequalities are;

x = 1

x = 9

x = 261

x = 10/3

x = 4

3x² - 2x - 1 = 0

x = 1 or x = -1/3

x = 13

x = 0

x = 0 or x = 5

1. 3x = log6 216

Using the definition of logarithm, we have:

\(6^{3x} = 216\)

\(6^{3x} = 6^3\)

3x = 3

x = 1

2. x - 4 = log3 243

Using the definition of logarithm, we have:

\(3^{x - 4} = 243\)

\(3^{x - 4} = 3^5\)

x - 4 = 5

x = 9

3. log4 (4x - 20) = 5

Using the definition of logarithm, we have:

4⁵ = 4x - 20

1024 = 4x - 20

4x = 1044

x = 261

4. log9 (3 - x) = log9(5x – 15)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

3 - x = 5x - 15

20 = 6x

x = 10/3

5. log81 (x + 20) = log81 (6x)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

x + 20 = 6x

20 = 5x

x = 4

6. log9 (3x²) = log9 (2x + 1)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

3x² = 2x + 1

3x² - 2x - 1 = 0

7. Using the quadratic formula, we have:

x = (-(-2) ± √((-2)² - 4(3)(-1))) / (2(3))

x = (2 ± √(16)) / 6

x = (2 ± 4) / 6

x = 1 or x = -1/3

8. log4(x - 1) = log4(12)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

x - 1 = 12

x = 13

9. log7(5 - x) = log7 (5)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

5 - x = 5

x = 0

10. logx (5x) = 2

Using the definition of logarithm, we have:

x² = 5x

x² - 5x = 0

x(x - 5) = 0

x = 0 or x = 5

Note that x = 0 is not a valid solution, since log 0 is undefined. Therefore, the only solution is x = 5.

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Answer:

x=2 y=1

Step-by-step explanation:

Answer:

y=2x-3

Step-by-step explanation:

a) The probability of failing to meet the specification limit of 45-pounds tensile strength 15.87%.

b) The number of parts that would not meet the specification is 7,935.

a) Given that the tensile strength of a metal part is normally distributed with mean 40 pounds and standard deviation 5 pounds.

We have to find the probability of failing to meet the specification limit of 45-pounds tensile strength.

Using the standard normal distribution, we can find the probability of failing to meet the specification limit of 45 pounds as follows:

z = {45 - 40}/{5}

= 1

The probability of failing to meet the specification limit of 45 pounds is the probability that the standardized variable Z is greater than 1, which is given by:

P(Z > 1) = 0.1587

Therefore, the probability of failing to meet the specification limit of 45-pounds tensile strength is 0.1587 or 15.87%.

b) If the probability of failing to meet the specification is 0.1587, the probability of meeting the specification limit is

1 - 0.1587 = 0.8413

.If 50,000 parts are produced, then the expected number of parts that meet the specification limit is:

0.8413* 50,000 =  42,065.

Therefore, the number of parts that would not meet the specification is: 50,000 - 42,065 = 7,935.

Hence, about 7,935 parts would not meet the specification.

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Answer:

6.3 miles

Step-by-step explanation:

7/10 = 0.7

0.7 x 9 = 6.3 miles after 9 days

The distance Katie rides her bike if she rides 7/10 mile each day for 9 days is 6.3 miles.

Distance is the total movement of an object without any regard to direction.

We can define distance as to how much ground an object has covered despite its starting or ending point

Katie rides her bike 7/10 mile each day for 9 days

In 1 day she covers a distance of 0.7 mile

so in 9 days she will cover

=0.7 * 9

= 6.3 miles

Therefore the distance Katie rides her bike if she rides 7/10 mile each day for 9 days is 6.3 miles.

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Answer:

We can start by isolating the variable "h".

5 8 h + 1 1 2 = 5

Subtracting 11/2 from both sides:

5 8 h = 5 - 1 1 2

Simplifying:

5 8 h = 8 1 2

Dividing both sides by 5/8:

h = 8 1 2 ÷ 5 8

Converting the mixed number to an improper fraction:

h = (8 x 8 + 1) ÷ 5 8

h = 65/8

Now, we can convert this fraction to a mixed number:

h = 8 1/8

Brigid has already picked for 8 1/8 hours, so the amount of time needed to pick the remaining strawberries is:

5 - (1 1/2 + 5/8 x 8) = 5 - (3 5/8) = 1 3/8

Therefore, Brigid still needs to pick for 1 3/8 hours to fill 5 bushels of strawberries. The answer is 1 and 3/8 hours or 2 and 3/16 hours (if simplified).

Step-by-step explanation:

Answer:

x= -1 or x= -11

Step-by-step explanation:

Answer:

i think its D. Im not fully sure

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer: D) -20.99

Step-by-step explanation:

-4.97-2.36+-5.19-8.47 = -20.99

The length QN on the triangle is 54 units

From the question, we have the following parameters that can be used in our computation:

Point P = Centroid

Also, we have

QP = 18

The centroid divides each median into the ratio 2:1.

Using the above as a guide, we have the following:

QN = 3 * QP

Substitute the known values in the above equation, so, we have the following representation

QN = 3 * 18

Evaluate

QN = 54

Hence, the length is 54 units

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Step-by-step explanation:

Let's make the number we're finding to be \(a\). So, it says that it will be divided by 4 and then added by 12 if we want this in algebraic expression it will be \(\frac{a}{4} +12\\\). It's also telling us that that expression is the same thing as our number divided by 3 and subtracted by 5. If we want an expression out of it it well be \(\frac{a}{3} -5\\\). Since they are the same, we have the equation below.

\(\frac{a}{4} +12 = \frac{a}{3} -5\\\)

All we have to do now is to find \(a\).

\(\frac{a}{4} +12 = \frac{a}{3} -5 \\ \frac{a +48}{4} = \frac{a -15}{3} \\ (3)(a +48) = (a - 15)(4) \\ 3a +144 = 4a -60 \\ (60 -3a) + 3a +144 = 4a -60 +(60 -3a) \\ a = 204\)

Our number must be \(204\). I think

the graph that goes up the most

Answer: D

Step-by-step explanation:

Because it said she rode her bike 15 feet per second and per means 1 so for every second she rode 15 distance(feet)

I Hope This helped :)

Answer:

z = -3

Step-by-step explanation:

42 = -7 ( z-3)

42 = -7z + 21

21 = -7z

z = -3

Answer and Step-by-step explanation:

We have to solve for z. That means everything that is next to z has to move to the other side of the equation.

First, divide -7 from both sides of the equation.

-6 = z - 3

Now add 3 to both sides of the equation.

-3 = z

z is equal to -3.

#teamtrees #PAW (Plant And Water)

I hope this helps!

To find the simplest function f and a number a, we can begin by simplifying the expression within the limit. We can use the formula for the difference of squares to rewrite the numerator as (x^40 + x^20 + 1)(x^20 - 1). Similarly, we can use the formula for the difference of cubes to rewrite the denominator as (x - 1)(x^2 + x + 1)(x^3 + x^2 + 1)(x^6 + x^3 + 1).

Canceling out the common factor of x - 1 in the numerator and denominator, we are left with:

limx→1(x^20 + x^10 + 1)(x^20 - 1) / (x^2 + x + 1)(x^3 + x^2 + 1)(x^6 + x^3 + 1)

To find the simplest function f, we can let f(x) = x^20 + x^10 + 1. Then, f'(x) = 20x^19 + 10x^9, so f'(1) = 30.

Therefore, we can rewrite the limit as:

limx→1 [f(x) - 1] / [(x - 1)(x^2 + x + 1)(x^3 + x^2 + 1)(x^6 + x^3 + 1)]

Using L'Hopital's rule or factoring, we can simplify the denominator to (1 + 1 + 1)(1 + 1)(1 + x + x^2)(1 + x^3 + x^6), which equals 9(1 + x + x^2)(1 - x + x^2)(1 + x^3 + x^6).

Plugging in f'(1) and simplifying, we get:

limx→1 [f(x) - 1] / [(9)(1 + x + x^2)(1 - x + x^2)(1 + x^3 + x^6)]

= [f'(1)] / [9(1 + 1 + 1)(1 + 1)(1 + 1 + 1)(1 + 1 + 1 + 1 + 1 + 1)]

= 30 / 1944

Therefore, the value of the limit is 30 / 1944.
a. To find the simplest function f and the number a, we first recognize that the given limit represents the derivative of a function f at a point a:

lim(x→1) [(x^80 - 1) / (x - 1)]

We can use the definition of a derivative, which is:

f'(x) = lim(h→0) [(f(x + h) - f(x)) / h]

Comparing this with the given limit, we have:

f(x + h) = x^80
f(x) = 1

Here, x + h = x^80 and x = 1. So, f(1) = 1. Since f'(a) is given at x = 1, we have:

a = 1

The simplest function f is a power function of the form f(x) = x^n. To find n, we consider the fact that f(1) = 1:

1^n = 1

The simplest solution is when n = 1, so f(x) = x.

b. Now, we determine the value of the limit by finding f'(a). Since we found that f(x) = x, we can calculate its derivative:

f'(x) = d(x)/dx = 1

Now, we can find f'(a) by substituting a = 1:

f'(1) = 1

So, the value of the limit is 1.

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The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)

\(\mu=e^{\int p(t)dt}\)

\(\mu=e^{\frac{t}{400}}\)

So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)

S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)

S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)

Now solving the bracket

S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)

At S(0) = 100

100 = 4000 + \(e^{\frac{-0}{400}}\) C

100 = 4000 + \(e^{0}\) C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

Cylindrical shape.

To model the volume of the cut tree, the appropriate geometric shape is a cylinder.

This is because a cylinder's volume is equal to the product of the base's area and the height of the cylinder,

which can be determined by the length of the equal sections of the tree trunk.

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A factor in an experiment that changes from the manipulation of the independent variable is the dependent variable.

In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables are so-called because, during an experiment, their values are examined on the assumption or presumption that they are governed by the values of other variables.

The variable being measured or tested in an experiment is known as the dependent variable. 1 The results of the participants' tests, for instance, since that is what is being measured, would be the dependent variable in a study looking at how tutoring affects test scores.

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Answer:

a

Step-by-step explanation:

my brother told me....

Answer:

$3.25

Step-by-step explanation:

To get the price of one cup of coffee without including Dax's two dollar tip, the first step is to subtract 2 from 18.25.

18.25 - 2= 16.25

16.25 is price of the five cups of coffee that Dax bought without the two dollar tip. The final step is to get the price of one cup of coffee which is basically:

16.25 ÷ 5 = 3.25

The cost of each cup of coffee is $3.25.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

To get the price of one cup of coffee without including Dax's two-dollar tip, the first step is to subtract 2 from 18.25.

18.25 - 2= 16.25

16.25 is the price of the five cups of coffee that Dax bought without the two-dollar tip. The final step is to get the price of one cup of coffee which is basically:

16.25 ÷ 5 = $3.25

Hence, the cost will be $3.25.

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Answer:

Step-by-step explanation:

gradient = 5 = [k-(-1)]/[6-2]

[k+1]/4 = 5

k+1=20

k=19

The value of k in the line that passes through the points A(2, -1) and (6, k) with a gradient of 5 is found to be 19 by using the formula for gradient and solving the resulting equation for k.

To find the value of k in the line that passes through the points A(2, -1) and (6, k) with a gradient of 5, we'll use the formula for gradient, which is (y2 - y1) / (x2 - x1).

The given points can be substituted into the formula as follows: The gradient (m) is 5. The point A(2, -1) will be x1 and y1, and point B(6, k) will be x2 and y2. Now, we set up the formula as follows: 5 = (k - (-1)) / (6 - 2).

By simplifying, the equation becomes 5 = (k + 1) / 4. To find the value of k, we just need to solve this equation for k, which is done by multiplying both sides of the equation by 4 (to get rid of the denominator on the right side) and then subtracting 1 from both sides to isolate k. So, the equation becomes: k = 5 * 4 - 1. After carrying out the multiplication and subtraction, we find that k = 20 - 1 = 19.

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so so much to do with the way you are you going to be able to get the vaccine and I will be there in a few minutes to get the vaccine and I will 57

Answer: each store gets 787 pairs and 1 is left over

Step-by-step explanation:Divide 4723 by 6

The linear function that models the relationship between the number of hours and the cost of renting a canoe is Cost = 25 + 5 * Number of Hours.

To write a linear function that models the relationship between the number of hours and the cost of renting a canoe, we need the specific information about the rate of cost per hour.

Let's assume that the cost of renting a canoe is $25 for the first hour and increases by $5 for each additional hour. In this case, the linear function can be written as:

Cost = 25 + 5 * Number of Hours

Here, the number of hours represents the independent variable, and the cost represents the dependent variable. The initial cost of $25 is added, and then $5 is multiplied by the number of additional hours to account for the increase in cost.

For example, if you want to find the cost of renting a canoe for 3 hours, you can substitute the number of hours into the function:

Cost = 25 + 5 * 3 = 25 + 15 = $40

Therefore, the linear function that models the relationship between the number of hours and the cost of renting a canoe is Cost = 25 + 5 * Number of Hours.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

pyramid side:

h = 3.25 ft

b = 2.5 ft

square base:

s = 2.5 ft

gallon of gold paint:

400 ft²

Step 02:

surface area:

square base area:

A = s² = (2.5 ft)² = 6.25 ft²

total pyramid sides area:

A = (b * h) / 2

A = (2.5 ft * 3.25 ft) / 2 = 4.0625 ft²

total pyramid sides area = 4 * 4.0625 ft² = 16.25 ft²

total trophy area:

total trophy area = 6.25 ft² + 16.25 ft² = 22.5 ft²

maximum number of trophies:

maximum number of trophies = 400 ft² / 22.5 ft² = 17.78

The answer is:

square base area = 6.25 ft²

pyramid side area = 4.0625 ft²

total pyramid sides area = 16.25 ft²

total trophy area = 22.5 ft²

maximum number of trophies = 17

Answer:

\(\sf 9.6\:hours \:\: or \:\: 576\: minutes\)

Explanation:

\(\sf Time \ taken : \dfrac{Distance}{Speed}\)

Here given:

Applying formula,

\(\sf Time \ Taken = \dfrac{48}{5} = 9.6 \ hours = 576 \ minutes\)

Answer:

hope it help u sorry for dirty handwriting

Answer:

1. 10L

2.

\(( \frac{p}{10} ) - 9\)

Step-by-step explanation:

let length be L.

let width be W.

W = 4L

Perimeter = 2L + 2W

P = 8L + 2L

P = 10L