Solve the separable differential equation, showing working out:

[tex]\frac{dy}{dx}=\frac{2y+4}{x}[/tex]

Answer:

178.50

Step-by-step explanation:

8.50 · 7

59.5 · 3

178.50

Aisha earned C178.50 in a week.

First, multiply the number of hours worked per day with the amount earned per hour.

7 × C8.50 = C59.50

Then, use that answer and multiply it by the number of days worked.

3 x C59.50 = C178.50

The probability that less than 4 of them find their jobs stressful in the given binomial experiment would be 0.2919.

The probability of finding a job stressful in the given binomial experiment is p = 0.75 (given).The probability of not finding a job stressful is q = 1 - p = 1 - 0.75 = 0.25. The number of trials is n = 9 (given).We need to find the probability that less than 4 of them find their jobs stressful. Therefore, the required probability is:

P(X < 4)= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) where X is the number of workers who find their jobs stressful.

Using binomial probability distribution formula, we can calculate the probability for each value of X as follows:

P(X = x) = (nCx) p×q (n-x)

nCx = n! / (x!(n - x)!)

Where n! = n × (n - 1) × (n - 2) × ... × 2 × 1

Using this formula and adding up the probabilities for all values of X, we get:

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)= (9C0)0.75^0 × 0.25^9 + (9C1)0.75^1 × 0.25^8 + (9C2)0.75^2 × 0.25^7 + (9C3)0.75^3 × 0.25^6= 0.00035 + 0.00664 + 0.05223 + 0.23255= 0.2919

Therefore, the probability that less than 4 of them find their jobs stressful in the given binomial experiment would be 0.2919.

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Thus, equation of line with same slope and passing point  (3,6) is :

y - 6 = 2/5(x - 3).

The difference between the change in y-values and the change in x-values is known as the slope of a line. This figure represents the slope of a line.

A quantity called the slope of a line is used to quantify how steep a line is. This number may be zero, positive, or negative. Moreover, it may be unreasonable or rational.

Given equation of line:

y + 4 = 2/5 ( x - 9 )

General equation in two point form:

y - y1 = m(x - x1)

On comparing both equation:

slope of line m = 2/5

Now, equation of line with same slope and passing point  (3,6).

y - 6 = 2/5(x - 3).

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By SAS congruency rule both triangles are similar.

What are congruent triangles?

When two triangles can be superimposed, have identical side lengths, and equal angles, they are said to be congruent.

The figures must be the same size and shape or one could mirror the other for them to be congruent, but since they mirror one another and are the same size and shape, they are.

In the given figure according to question:

Therefore, by SAS congruency rule both triangles are similar.

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The total energy required per week for hot water is 7844.81 BTUs (British thermal units).

Given data:

Kimono takes a 6-minute shower every day.Shower uses about 1.9 gal per minute of water.

Kimono uses 23 gallons of hot water per day for clothes and dishwashers.

Hot water heats the water from 64 to 107 F.

Conversion:1 gallon = 3.785 L1 F = 1.8 K or 5/9 C1 BTU = 1055.06 J (joules)

Firstly, we need to calculate the hot water usage per week:

Hot water usage per day = 23 gallons

Therefore, hot water usage per week = 23 × 7 = 161 gallons

Now, we need to calculate the amount of energy required to heat 1 gallon of water from 64 to 107 F:

Energy required to heat 1 gallon of water = mass of water × specific heat × temperature riseQ = m × Cp × ΔT

Temperature rise (ΔT) = 107 - 64 = 43 F

Specific heat of water = 1 Btu/lb F

So, mass of water = 1 gallon = 3.785 LSo,

mass of water = 3.785 × 8.33 lb = 31.46 lb

Energy required to heat 1 gallon of water from 64 to 107 F is:

Q = m × Cp × ΔTQ = 31.46 × 1 × 43Q = 1350.58 BTUs

Now, we need to calculate the total energy required per week for hot water.

Total hot water energy usage per week = (1350.58 × 161) BTUs

Total hot water energy usage per week = 217782.38 BTUs ≈ 7844.81 BTUs

Hence, the total energy required per week for hot water is 7844.81 BTUs (British thermal units).

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Combining like terms is an essential skill in Algebra 1. It involves simplifying algebraic expressions by adding or subtracting terms that have the same variables and exponents. The goal is to simplify the expression by reducing it to its simplest form.

To combine like terms, we need to follow a few steps. Here is a step-by-step guide:

Identify the like terms: Look at the expression and find the terms that have the same variables and exponents. For example, in the expression 3x + 5x - 2x, all three terms have the variable x with an exponent of 1, so they are like terms.

Add or subtract the coefficients: Once you have identified the like terms, add or subtract their coefficients. The coefficient is the number that is multiplied by the variable. For example, in the expression 3x + 5x - 2x, the coefficients are 3, 5, and -2. Adding them together gives us 6x.

Write the simplified expression: After combining the like terms, write the simplified expression. In the example above, the simplified expression is 6x.

Here is another example:

4a + 2b - 3a + b

In this expression, the like terms are 4a and -3a (both have the variable a). We can subtract the coefficients to get a + 2b. The final simplified expression is a + 2b.

It is important to note that we can only combine terms that have the same variables and exponents. For example, we cannot combine 3x^2 and 4x because they have different exponents.

In summary, combining like terms is a basic skill in Algebra 1. It involves identifying terms that have the same variables and exponents, adding or subtracting their coefficients, and writing the simplified expression. This skill is essential for solving equations, simplifying expressions, and graphing functions.

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1. The cost per zinnia plant is: A. $0.04

2. The linear equation is D. C = 0.04z + 15

3. The cost of purchasing 700 zinnia plants is: C. $43.

Part 1: To find the cost per zinnia plant, derive two points from the info given which are:

(200, 23) and (500, 35)

The slope = cost per zinnia plant = 35 - 23 / 500 - 200

= 12/300

= $0.04.

Therefore, the correct answer: A.$0.04

Part 2: To derive a linear equation to represent the cost, C, to purchase z number of zinnia plants, substitute (z, C) = (200, 23) and m = 0.04 into C = mz + b to find the y-intercept (b):

23 = 0.04(200) + b

23 = 8 + b

23 - 8 = b

b = 15

Substitute m = 0.04 and b = 15 into C = mz + b:

C = 0.04z + 15

Therefore, the correct answer is D. C = 0.04z + 15

Part 3:

Using the equation C = 0.04z + 15, we can find the cost of purchasing 700 zinnia plants:

C = 0.04(700) + 15

C = 43

Therefore, the correct answer is: C. $43.

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The surface area of right triangular prism of height 3 in, base 8 in, slop 5 in and  width 4 in is 76  in².

Surface area is a measure of the total area occupied by the surfaces of a three-dimensional object. 

It is the sum of the areas of all the faces, including the base(s), of the object.

The units for measuring surface area are squared units, such as square meters or square inches.

To find the surface area of a right triangular prism, we need to add the areas of all of its faces.The prism has two congruent triangular faces and three rectangular faces.

The area of ​​every single triangle face is (1/2)bh, where b is the base of the triangle and h is its height.

In this case, the base is 8 in and the height is 5 in, so the area of each triangular face is (1/2)(8)(5) = 20  inches². Since there are two triangular faces, their combined area is 2(20) = 40 inches².

The area of ​​each rectangular face is lw.

In this case, the width is 4 in and the height is 3 in, so the area of each rectangular face is (4)(3) = 12 inches². Since there are three rectangular faces, their combined area is 3(12) = 36 inches²

Therefore, the total surface area of the right triangular prism is the sum of the areas of all its faces:

Surface area = 2(triangular face area) + 3(rectangular face area)

Surface area = 2(20) + 3(12)

Surface area = 40 + 36

Surface area = 76 inches²

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The seventh exam result, based on the provided statement, is 88.

The aggregate of all values split by the total amount of values determines the mean (also known as the arithmetic mean, which differs from the geometric imply) of a dataset. The term "average" is frequently used to describe this gauge of central trend.

To find the 7th test score, we can use the formula for the mean of a set of numbers:

Mean = (sum all the numbers) / (number)

We know that the mean of the 7 test scores is 85, so we can plug in the given values and solve for the missing number:

85 = (75 + 82 + 82 + 83 + 90 + 95 + x) / 7

Multiplying both sides by 7, we get:

595 = 507 + x

Subtracting 507 from both sides, we get:

x = 88

Therefore, the 7th test score is 88.

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The expression has basic mathematical operators. is The measurement of the two angles ∠J and ∠K is 76° and 65° respectively.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Given to us

∠J = (7x + 13)°,

∠K = (83 - 2x)°,

the sum of the two angles is 141°.

As it is given that the sum of the two angles is 141°, therefore, the expression for the sum of the two angles can be written as,

∠J + ∠K = 141°

(7x + 13)° + (83 - 2x)° = 141°

7x + 13 +83 - 2x = 141

5x = 141 - 83 - 13

5x = 45

x = 9

Now, we got the value of x, substitute the value of x in given measurements, therefore,

∠J = (7x + 13)°

∠J = 7(9) + 13

∠J = 63 + 13

∠J = 76°

∠K = (83 - 2x)°

∠K = (83 - 2(9))°

∠K = (83 - 18)°

∠K = 65°

Hence, the measurement of the two angles ∠J and ∠K is 76° and 65° respectively.

The store clerk is stocking the shelves. He places on the shelf a box of cereal that weighs 850 grams, a box of granola bars that weighs 385 grams, and a box of crackers that weighs 435 grams. The total weight in kilograms is 1.67 kilograms.

Given:

The weight of the box of cereal = 850 grams.

The weight of the box of granola bars = 385 grams.

The weight of the box of crackers = 435 grams.

The total weight in kilograms of the above boxes.

Total weight of the boxes = 850 + 385 + 435 grams= 1670 grams.

To convert grams to kilograms, we divide it by 1000.

So, the weight in kilograms= 1670/1000= 1.67 kilograms.

Hence, the total weight in kilograms of the above boxes is 1.67 kilograms.

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Answer:

14

Step-by-step explanation:

Answer:

b = 14

Step-by-step explanation:

In order to find the y intercept of the problem, we will have to put the equation of the line in point slope form and solve for y.

Point slope form: [tex]y-y_1=m(x-x_1)[/tex]

Lets put the equation of the line in point slope form.

[tex]y-2=4(x+3)[/tex]

Distribute 4

[tex]y-2=4x+12[/tex]

Add 2 to both sides

[tex]y=4x+14[/tex]

Now that the equation of the line is in slope intercept form, the y intercept is at the end of the equation, which is 14.

b = 14

By using the complement probability that none of the 6 people prefer brand A paint, the probability that at least 1 person in a sample of 6 prefers brand A paint is 0.9939 or approximately 99.39%.

To find the probability that at least 1 person in the sample of 6 prefers brand A paint, we need to find the probability of the complement event that none of the 6 people prefer brand A paint, and subtract it from 1.

The probability that one person prefers brand A paint is 0.53, and the probability that one person does not prefer brand A paint is 0.47. Since we are dealing with a binomial distribution, we can use the formula for the probability of k successes in n trials:

P(k successes) = n! / (k! * (n - k)!) * p^k * (1 - p)^(n - k)

Using this formula, we can calculate the probability of 0 people preferring brand A paint:

P(0 people prefer brand A) = 6! / (0! * 6!) * 0.53^0 * 0.47^6 = 0.0061

Therefore, the probability of at least 1 person preferring brand A paint is:

P(at least 1 person prefers brand A) = 1 - P(0 people prefer brand A) = 1 - 0.0061 = 0.9939

So, the probability that at least 1 person prefers brand A paint is 0.9939 or approximately 99.39%.

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Answer: Falso. Las razones trigonométricas dependen tanto del tamaño del triángulo como de la medida del ángulo. Esto se debe a que las razones trigonométricas de un triángulo se calculan relacionando los lados del triángulo con el ángulo. Por lo tanto, si cambia el tamaño del triángulo, los lados cambiarán y, por consiguiente, las razones trigonométricas también cambiarán.

Step-by-step explanation:

The probability of Thuy rolling a 4 exactly 2 times is 1/6 × 1/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 = 5⁵/6⁷

We know that:

Thuy rolls a number cube 7 times,

so the total outcomes are: 6.

Also, it is asked to find the probability of rolling a 4 exactly 2 times.

So it could be done by the method that:

1/6 × 1/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6,

where 1/6 denotes the probability of rolling a 4 and 5/6 denotes the probability of rolling a number other than 4

therefore we know that, the probability of rolling a 4 exactly 2 times is 1/6 × 1/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 = 5⁵/6⁷

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Answer:

3a⁴bc-3a²4b²c²-3a²bc³

Step-by-step explanation:

remove brackets by multiplying by the numbers out the brackets.As they are no like terms that is where we end our answers

The function rule that represents the deer population t years after 2011, assuming a 15% annual growth rate, is d(t) = 100 × 1.15^t

Assuming the deer population started at a baseline value of P0 in 2011, we can use the following formula to calculate the population after t years

d(t) = P0 × (1 + r)^t

Where r is the annual growth rate, expressed as a decimal, and t is the number of years since 2011.

Given that the deer population increases by 15% each year, we can express r as

r = 0.15

And since the baseline population in 2011 is not given, we can use P0 as an arbitrary constant value, such as 100

P0 = 100

Therefore, the function rule that represents the deer population t years after 2011 would be

d(t) = 100 × (1 + 0.15)^t

Simplifying the expression

d(t) = 100 × 1.15^t

This function rule gives us the deer population at any time t years after 2011, assuming the population continues to increase by 15% annually.

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The given question is incomplete, the complete question is:

If the deer population continues to increase by 15% each year, write a function rule d that represents the deer population t years after 2011.

To have a margin of error within 4% at a 99% confidence level, a sample size of at least 469 graduates is needed for the administrator's analysis of the proportion of graduates who have not found employment in their major field one year after graduation.

To determine the sample size needed for the administrator's analysis, we can use the formula:

n = (Z^2 * p * (1 - p)) / E^2

where:

n = sample size needed

Z = the Z-score corresponding to the desired confidence level (99% corresponds to a Z-score of approximately 2.576)

p = the expected proportion of graduates who have not found employment in their major field (13%, or 0.13)

E = the desired margin of error (4%, or 0.04)

Substituting the given values into the formula, we get:

n = (2.576^2 * 0.13 * (1 - 0.13)) / 0.04^2

Simplifying and solving for n, we get:

n ≈ 468.42

Rounding up to the nearest whole number, we get:

n = 469

Therefore, a sample size of at least 469 graduates is needed for the administrator's analysis to have a margin of error within 4% at a 99% confidence level.

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Therefore, the sum of the numbers between 1 and 5,000 that have exactly 8 factors is 4,007,146.

In mathematics, a factor of a given integer is a positive integer that divides the integer evenly without leaving a remainder. In general, an integer n can have many factors, and they can be found by dividing n by all positive integers less than or equal to the square root of n, and checking if each of these divisors divides n evenly. The concept of factors is important in many areas of mathematics, including number theory, algebra, and geometry, and is used in various contexts, such as prime factorization, greatest common divisors, and divisibility tests.

Here,

To find the sum of the numbers between 1 and 5,000 that have exactly 8 factors, we need to identify all the integers in that range that have exactly 8 factors. Then we can add them up to find the final answer.

Now let's focus on finding the integers between 1 and 5,000 that have exactly 8 factors. Since 8 can be expressed as 2 x 2 x 2, we know that the prime factorization of such integers must take the form p² x q², where p and q are distinct primes. Moreover, since p and q are distinct, we can assume without loss of generality that p < q. Therefore, we can iterate over all pairs of distinct primes (p, q) such that p² x q² is less than or equal to 5,000, and add up all such integers.

The get_primes function implements the Sieve of Eratosthenes algorithm to generate a list of all primes less than or equal to the square root of 5,000 (rounded up to the nearest integer). The main loop then iterates over all pairs of distinct primes in this list, calculates their product squared, and adds it to the sum s if it is less than or equal to 5,000.

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Answer:

-0.5x^2 - 5x - 0.8

Step-by-step explanation:

The 2 zeroes of the function are at x = -8 and x = -2 so we can write the quadratic as

y = a(x + 2)(x + 8)   where a is a value to be found.

When x = -6, y = 4 so:

4 = a(-6+2)(-6 + 8)

4 = -8a

a = -0.5

The function is:

-0.5(x + 2)(x + 8)

= -0.5(x^2 + 10x + 16)

= -0.5x^2 - 5x - 0.8

Answer:

To determine the cost of the shirt, we can set up an equation using algebra. Let x be the cost of the shirt in dollars. We know that Marissa spent a total of 45 on the hat and the shirt, and the hat cost 10. Therefore, we can write the equation:

x + 10 = 45

To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 10 from both sides:

x = 35

Thus, the cost of the shirt is $35.

Step-by-step explanation:

c = y axis intercept  =  6   ( from the graph)

slope = rise/run = 6/3 = 2  ( using points  (-3,0) and  (0,6)  )

then

y =  2x + 6

Answer: $10,00; $15,00 and $20,00

First, let’s mark the streaming platforms as letters x, y, z:

x - Disney +

y - Netflix

z - Hulu

Each platform costs $540,00 per year, so that would be $540,00/12=$45,00 per month

Since we know that Disney + and Hulu per year cost $300,00 and all three platforms cost $540,00 per year, we can find how much does Netflix cost per year:

$540,00-$300,00 = $240,00

Per month: $240,00/12 = $20,00

Now we can write equations according to the given information:

y = 2x

x+y+z = 540,00

x+z = 300,00

We can find how much does Disney + cost per year from the first equation, since we already know the price of Netflix per year:

2x = 240,00 / : 2

x = 120,00 (per year)

Per month: $120,00/12 = $10,00

And finally, since we know that all three platforms cost $45,00 per month, we can find the price of Hulu per month:

$45,00 - $20,00 - $10,00 = $15,00

So, Netflix costs $20,00 per month, Disney + - $10,00 per month and Hulu - $15,00 per month

Answer:

( 4x + 3 ) ( x + 3 )

Step-by-step explanation:

9 × 4 = 36

Factors of 36 = { 1, 2, 3, 4, 6, 9, 12, 18, 36 }

3 and 12 add up to 15

4x² + 15x + 9

4x² + 3x + 12x + 9

( 4x² + 3x ) + ( 12x + 9 )

x (4x + 3) + 3 ( 4x + 3 )

( 4x + 3 ) ( x + 3 )

Answer: 20.48

Step-by-step explanation: 12.8 x 1.6 = 20.48

Answer:

20.48

Step-by-step explanation:

If you do 12.8 multiplied by 1.6 you get 20.48.

The area of the stained glass is given as 20ft².

Let's start by finding the length of one side of the square stained glass. Since the area of a square is given by the formula A = s^2, where s is the length of one side of the square, we have:

s^2 = A

s^2 = 20ft²

s = sqrt(20)ft

s = 2sqrt(5)ft

Now, we can use the given equation p^2 = 5A to find the perimeter p of the square, by substituting the value of A:

p^2 = 5A

p^2 = 5(20ft²)

p^2 = 100ft²

p = sqrt(100ft²)

p = 10ft

Therefore, the perimeter of the square stained glass is 10 feet.

The flag pole is 6.8 meters tall.

Trigonometric functions are mathematical formulas that connect the angles and side lengths of a right triangle. The six trigonometric functions are sin, cos, tangent, cosec, sec, and cotangent.

Height,p of the flagpole should be calculated.

Given;

base,b=2.9m

Angle subtended=67

Using trigonomteric identity

tan67=Height/base

Tan67=h/b

Tan67=h/2.9

h=2.9tan67

h=6.8m

Height pf the flag pole is 6.8m.

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The complete question is attached below:

An equation for the fish population, after years is P(t) ≈ 8000e-0.664t ± 0.00005

The equation for the fish population in a stocked lake can be determined using exponential growth.

The formula for exponential growth is

P(t) = [tex]P_0[/tex]ert

where P(t) is the population after time t,

[tex]P_0[/tex] is the initial population,

r is the rate of growth, and

e is the mathematical constant approximately equal to 2.71828.

The carrying capacity, K, is the maximum population that can be supported by the environment, and it is a limiting factor for population growth. When the population reaches K, the growth rate slows down until it reaches a point of equilibrium.

The carrying capacity can be estimated using a variety of methods, including the logistic model, which incorporates the carrying capacity into the equation for population growth.

However, for this problem, we are given an estimate of the carrying capacity, which we will use in the exponential growth equation.

We are also given the initial population,

[tex]P_0[/tex] = 1100, and we are asked to find an equation for the fish population, P(t), after t years.

The rate of growth, r, can be determined using the following formula:

r = ln(P/K) / t

where ln is the natural logarithm, and t is the time it takes to reach the carrying capacity, K.

Since we don't have an exact value for K, we will use the estimated value of 8000.

Thus,

r = ln(1100/8000) / 1

r ≈ -0.664

The negative sign indicates that the population is decreasing, since the growth rate is negative.

Therefore, the equation for the fish population after t years is:

P(t) = 8000e-0.664t

To round to 4 decimal places, we can use the formula:

P(t) ≈ 8000e-0.664t ± 0.00005

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Answer:

  use (1 -cos²x) for sin²x and expand

Step-by-step explanation:

You want to verify sin⁴x·cos²x = cos²x -2cos⁴x +cos⁶x.

You can get the desired result by substituting (1 -cos²x) for sin²x.

  [tex]\sin^4{x}\,\cos^2{x}=(1-\cos^2{x})^2\,\cos^2{x}=(1-2\cos^2{x}+\cos^4{x})\cos^2{x}\\\\=\boxed{\cos^2{x}-2\cos^4{x}+\cos^6{x}}[/tex]