Jesse can mow 3 yards in 8 hours. Jackson can mow twice as many yards per hour. What is the constant of proportionality between the number of yards Jackson can mow and the number of hours?

Answer:1001

Step-by-step explanation:

Answer:

The answer is 39

Step-by-step explanation:

75 + 3 = 78

78/2 = 39

The solution to given inequality 12 > w + 3 is w < 9

In this question, we have been given an inequality 12 > w + 3

We need to solve the inequality for w.

Consider given inequality,

12 > w + 3                              ............(Given)

12 - 3 > w + 3 - 3                    ...........(Subtract 3 from each side)

9 > w

This means, w is less than 9.

Therefore, the solution to given inequality 12 > w + 3 is w < 9

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The answer to the integral 0∫π/3 cos⁴xsinx dx using a u-substitution is -5/24 - √3/24, or approximately -0.315.To use a u-substitution to evaluate 0∫π/3 cos⁴xsinx dx, we will use the following steps:

Step 1: Choose a u-substitution that simplifies the integral. In this case, we will let u = cosx, which will allow us to rewrite the integral as 0∫1 u⁴(1-u²)du.

Step 2: Substitute the expression for u into the integral, and simplify. Using the substitution u = cosx, we have:

0∫π/3 cos⁴xsinx dx = 0∫1 u⁴(1-u²)du

Step 3: Evaluate the integral using standard integration techniques. Integrating u⁴(1-u²) with respect to u, we get:

∫ u⁴(1-u²)du = (1/5)u⁵ - (1/3)u³ + C

Step 4: Evaluate the integral from 0 to 1 using the substitution u = cosx. Substituting back, we have:

0∫π/3 cos⁴xsinx dx = (1/5)cos⁵x - (1/3)cos³x ∣₀ᴰ³/₃

Evaluating this expression at the limits of integration, we get:

(1/5)(cos⁵(π/3) - cos⁵(0)) - (1/3)(cos³(π/3) - cos³(0))

Simplifying, we get:

(1/5)(27/64 - 1) - (1/3)(3√3/8 - 1)

= -1/120 (27 - 64) - √3/24 + 1/3

= -5/24 - √3/24

Therefore, the answer to the integral 0∫π/3 cos⁴xsinx dx using a u-substitution is -5/24 - √3/24, or approximately -0.315.

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Final Answer: \(3x - 9\)

Steps/Reasons/Explanation:

Question: Simplify \(-5 - x + 4x - 4\).

Step 1: Collect like terms.

\((-5 - 4) + (-x + 4x)\)

Step 2: Simplify.

\(-9 + 3x\)

Step 3: Regroup terms.

\(3x - 9\)

~I hope I helped you :)~

Answer: 3x-9

Step-by-step explanation:

Subtract the numbers

-5 - x + 4x -4x

-9 - x + 4x

Combine like terms

_______________

-9-x+4x

-9+3x

Rearrange terms

-----------------------

-9+3x

3x-9

Maria starts off with 3 fish.

Let x represent the number of new fish she gets.

Let y represent the total number of rish.

The total number of fish would be represented by x + 3.

\(y=x+3\)

With the divergence theorem, we get

∫sf⋅ ds = ∫v(divf) dV = 5π/8.

Using the divergence theorem, we have:

∫sf⋅ ds = ∫v(divf) dV

where v is the solid region enclosed by s. We need to find the divergence of f:

divf = ∂(5z^2x)/∂x + ∂(53y^3tan(z))/∂y + ∂(5x^2z5y^2)/∂z

= 5z^2 + 159y^2tan(z)sec^2(z) + 5x^2

Now we need to evaluate the triple integral of divf over the volume enclosed by s. Since s is the top half of the sphere, we can use spherical coordinates to describe the volume:

0 ≤ ρ ≤ 1

0 ≤ θ ≤ π

0 ≤ φ ≤ π/2

Then the volume integral becomes:

∫v(divf) dV = ∫0^1 ∫0^π ∫0^(π/2) (5ρ^4sinφcos^2θ + 159ρ^4sinφtan(φ)sec^2(φ)sin^2θ + 5ρ^4sinφsin^2θ)ρ^2sinφ dφdθdρ

Evaluating this integral yields:

∫v(divf) dV = 5π/8

Therefore, usingUsing the divergence theorem, we have:

∫sf⋅ ds = ∫v(divf) dV

where v is the solid region enclosed by s. We need to find the divergence of f:

divf = ∂(5z^2x)/∂x + ∂(53y^3tan(z))/∂y + ∂(5x^2z5y^2)/∂z

= 5z^2 + 159y^2tan(z)sec^2(z) + 5x^2

Now we need to evaluate the triple integral of divf over the volume enclosed by s. Since s is the top half of the sphere, we can use spherical coordinates to describe the volume:

0 ≤ ρ ≤ 1

0 ≤ θ ≤ π

0 ≤ φ ≤ π/2

Then the volume integral becomes:

∫v(divf) dV = ∫0^1 ∫0^π ∫0^(π/2) (5ρ^4sinφcos^2θ + 159ρ^4sinφtan(φ)sec^2(φ)sin^2θ + 5ρ^4sinφsin^2θ)ρ^2sinφ dφdθdρ

Evaluating this integral yields:

∫v(divf) dV = 5π/8

Therefore, using the divergence theorem, we have:

∫sf⋅ ds = ∫v(divf) dV = 5π/8.

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Answer:

upward

Step-by-step explanation:

The equation showing in the question is actually

\(y = x^{2} - 4x - 5\)

After graphing this equation you can see that the parabola opens up pointing upwards with a vertex of (2, -9) . You can calculate the vertex of the parabola by substituting either y or x with 0 and then solving for the missing variable.

Answer:

I think it's 4

Step-by-step explanation:

Answer:

C (The third table in the picture)

Step-by-step explanation:

Apologies if im wrong but I think it's C because it is doubling each time it goes further in the table.

Answer:

a=-7

Step-by-step explanation:

Answer:

a= -7

Step-by-step explanation:

-3(14a+7)=273

-3(14(-7)+7)=273

-3(-98+7)=273

-3(-91)=273

negative times a negative equals a positive

(please mark as brainliest, need it to get to next level <3 )

Answer:

Step-by-step explanation:

17

Given the following equation:

Let's determine the value of y = f(x) of the given table.

x solution f(x)

-1,000 0.6(-1,000)² - 2(-1000) - 6 601,994

-100 0.6(-100)² - 2(-100) - 6 6,194

-10 0.6(-10)² - 2(-10) - 6 74

0 0.6(0)² - 2(0) - 6 -6

10 0.6(10)² - 2(10) - 6 34

100 0.6(100)² - 2(100) - 6 5,794

1,000 0.6(1,000)² - 2(1000) - 6 597,994

a. The chart did not maintain consistent scaling

b. The graph is not the appropriate graph type to display such data

c.  The display had inaccurate or distorted visual representations

When the actual data may not support it, changing the scales on the axes might give the appearance of big changes or differences.

The visual effect of data can be exaggerated or minimized, for instance, by adopting a non-linear scale or deleting specific sections of the axis.

So it important to Choose appropriate graph type that best represents the data and the relationship you want to convey.

It also advisable to make use of  clear and accurate labeling with descriptive titles and units of measurement.

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Answer:

f(3)=-4; x=1

Step-by-step explanation:

Just use the graph

\(\huge\boxed{f(3)=-4}\\\huge\boxed{f(1\ \textsf{or}\ 4)=2}\)

For this question, we just need to look at the graph.

\(f(3)=\ ?\)

Go to \(3\) on the x-axis and see what value from the y-axis it intersects with.

It's \(-4\), right at the bottom of the little valley there.

\(f(?)=2\)

For this part, we do the opposite. Go to \(2\) on the y-axis and find one value it intersects with from the x-axis.

You can go with either \(1\) or \(4\) here.

Answer:

21x^2 + 33x + 16

Step-by-step explanation:

(14x^2 + 13x + 12) + (7x^2 + 20x + 4)

Combine like terms:

14x^2 + 7x^2 = 21x^2

13x + 20x = 33x

12 + 4 = 16

Thus:

21x^2 + 33x + 16

Answer:

21x^2 + 33x + 16.

Step-by-step explanation:

(14x2 + 13x + 12) + (7x2 + 20x + 4)   Remove the parentheses:

= 14x2 + 13x + 12 + 7x2 + 20x + 4    Bring like terms togethher:

= 14x^2 + 7x^2 + 13x + 20x + 12 + 4

= 21x^2 + 33x + 16.

The depth of the pond will fall below 4 feet in approximately 17.3 years if the current rate of decay continues.

Given that

The depth of the pond decreases at a rate of 2% per year

The current depth of the pond is 5 feet

We need to find out in approximately how many years the depth of the pond will fall below 4 feet.

Use the formula for exponential decay:

\(A = A_0 e^{(kt)\)

Where:

A is the current depth of the pond (5 feet)

A₀ is the initial depth of the pond (also 5 feet)

k is the decay rate, which is equal to -2% or -0.02

t is the time in years

Find out when the depth of the pond will fall below 4 feet,

So we can set A = 4 and solve for t:

4 = 5exp(-0.02t)

Dividing both sides by 5, we get:

0.8 = exp(-0.02t)

Taking the natural logarithm of both sides, we get:

ln(0.8) = -0.02t

Solving for t, we get:

t = ln(0.8) / (-0.02)

 = 17.3 years (approximately)

Therefore, the depth of the pond will fall below 4 feet in approximately 17.3 years if the current rate of decay continues.

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The type of sampling used in each scenario is as follows:

Stratified sampling, Convenience sampling, Cluster sampling, Random sampling, Convenience sampling, Cluster sampling, Systematic sampling

The psychologist selects a specific number of boys and girls from each math class, which indicates stratified sampling. The population (students) is divided into strata (math classes) and samples are taken from each stratum.

The conclusion is based on responses from questionnaires that were distributed conveniently to students, indicating convenience sampling. The sample is not randomly selected but consists of those who chose to respond.

The biologist surveys all students from randomly selected classes, indicating cluster sampling. The population (students) is divided into clusters (classes), and all members of the selected clusters are included in the sample.

The game show organizer shuffles and randomly selects contestant names, indicating random sampling. Each name has an equal chance of being selected.

Family planning polls a specific number of men and women, suggesting convenience sampling. The individuals surveyed are conveniently selected and may not represent the entire population.

The hospital researcher interviews all diabetic patients in randomly selected hospitals, indicating cluster sampling. The population (diabetic patients) is divided into clusters (hospitals), and all members of the selected clusters are included in the sample.

Smart selects every 100th cell phone from the assembly line, indicating systematic sampling. A sampling interval is used to select samples at regular intervals, ensuring a systematic and consistent approach.

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Answer:

Step-by-step explanation:

The complement of "x" is "90-x".

The complement of 55 degrees is 90-55 = 35 degrees

--------------

The supplement of "x" is 180 -x.

The supplement of 170 degrees is 180-170 = 10 degrees.

Margin of Error ≈ 0.066 (rounded to three decimal places).

To find the margin of error for a poll, we can use the formula:

Margin of Error = Z * (sqrt(p * (1 - p) / n))

Where:

Z is the z-score associated with the desired confidence level (in this case, 99% confidence level).

p is the proportion of respondents who answered positively (33% or 0.33).

n is the sample size (330).

First, let's calculate the z-score for a 99% confidence level. The z-score can be obtained using a standard normal distribution table or a calculator. For a 99% confidence level, the z-score is approximately 2.576.

Now, we can calculate the margin of error:

Margin of Error = 2.576 * (sqrt(0.33 * (1 - 0.33) / 330))

Simplifying the equation:

Margin of Error = 2.576 * (sqrt(0.33 * 0.67 / 330))

Margin of Error ≈ 2.576 * (sqrt(0.2171 / 330))

Margin of Error ≈ 2.576 * (sqrt(0.0006591))

Margin of Error ≈ 2.576 * 0.025677

Margin of Error ≈ 0.066113

Rounding to three decimal places, the margin of error is approximately 0.066.

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Answer:

  (a)  $810.45

Step-by-step explanation:

You want the value of an investment of $300 earning 5% interest compounded quarterly for 20 years.

The compound interest formula tells you the value is ...

  A = P(1 +r/n)^(nt)

where P = 300, r = 0.05, n = 4, t = 20.

Using the given parameters in the given equation, you find the account value to be ...

  A = $300(1 +0.05/4)^(4·20) ≈ $810.45

__

Additional comment

The "rule of 72" tells you the account value will approximately double in a number of years equal to 72 divided by the interest rate percentage: 72/5 = 14.4 years. After 20 years, it will be worth more than that doubled amount, $600. This only leaves one reasonable answer choice.

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Answer:

Triangle ABC is congruent to triangle DFE.

The approximate value of x in the equation 5 to the power of 2x=20 is 0.93

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

5 to the power of 2x=20

As an expression, we have

5^(2x) = 20

Take the natural logarithm of both sides

so, we have the following representation

2x = ln(20)/ln(5)

Evaluate the quotients

This gives

2x = 1.86

So, we have

x = 0.93

Hence, the value of x is 0.93

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We have to determine the values of `f(-8)`, `f(8)` and all values of `c` in the interval `(-8,8)` such that `f '(c) = 0`.Function given, `f(x) = 4 - x^(2/3)`Therefore, `f(-8) = 4 - (-8)^(2/3)`The value of `(-8)^(2/3)` is not real. Hence, `f(-8)` does not exist. Further, `f(8) = 4 - 8^(2/3)`Value of `8^(2/3)`

Let `y = 8^(2/3)`Then, `y^3 = 8^2`⇒ `y = 8^(2/3)` is equal to `y = 4`.Thus, `f(8) = 4 - 4 = 0`.We know that,`f'(x) = (-2/3)x^(-1/3)`To find `f'(c) = 0`, solve `f'(x) = 0`.Let's solve `f'(x) = 0` for `x`.`f'(x) = 0`⇒ `(-2/3)x^(-1/3) = 0`⇒ `x^(-1/3) = 0` which is not possible. So, there is no value of `c` in `(-8,8)` such that `f '(c) = 0`.

Rolle's theorem states that if a function is continuous on a closed interval and differentiable on the open interval, then there exists at least one value in the open interval such that the derivative of the function is zero. In this case, the given function `f(x)` is not differentiable at `x = -8` as well as `x = 8`. Also, there is no value of `c` in `(-8,8)` such that `f'(c) = 0`. Therefore, Rolle's theorem is not applicable in this case.

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Answer:

b num i think only not sure

Solution to the system of equation y = 0.7x − 2 and 2x + y = 25 is (- 27, - 9).

A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.

Given are two equations y = 0.7x − 2 and 2x + y = 25.

Now let us write these equations in a similar manner.

y = 0.7x − 2 ⇒ - 0.7x + y = - 2...(i)

2x + y = 25...(ii)

Now subtracting eqn(i) from eqn(ii) to cancel out the term y we get

2.7x = - 27.

x = - 10 and substituting the value of x in any one of the equations we get

y = 0.7(-10) - 2.

y = - 7 - 2.

y = - 9.

So, one of the solutions to the system of equations is (- 27, - 9).

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Answer:

1/36

Step-by-step explanation:

hope this helps:0

Answer:

1/6

Step-by-step explanation:

with a six sided dice a possible outcome writing a two out of six is one