10. Find the parallel slope: (-2.9) and (1.-3).

it's easy

Step-by-step explanation:

use the formula for finding a slope and equate it to 7

Using sampling concepts, the population being studied is all visitors that are flying to the state of Hawaii.

The problem is incomplete, but researching it on a search engine, it asks for us to identify who is the population of this study.

In this problem, a set of visitors traveling to Hawaii were sampled, hence the population being studied is all visitors that are flying to the state of Hawaii.

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Answer: D

Step-by-step explanation: I did the test

They rode 15 miles before replacing each horse.

Let's assume that each rider rode a different number of horses, denoted as x, y, and z respectively. Since they used a total of 16 horses, we have the equation x + y + z = 16.

Since they rode the same number of miles on each horse, let's denote the distance traveled by each horse as d. Therefore, the total distance covered by all the horses can be calculated as 16d.

We are given that the three riders rode a total of 240 miles. Therefore, we have the equation xd + yd + z*d = 240.

From the given information, we have two equations:

x + y + z = 16 (Equation 1)

xd + yd + z*d = 240 (Equation 2)

Since we need to find the number of miles they rode before replacing each horse, we need to find the value of d. To solve this system of equations, we can substitute one variable in terms of the others.

Let's assume x = 16 - y - z. Substituting this into Equation 2, we get:

(16 - y - z)d + yd + z*d = 240

Simplifying, we have:

16d - yd - zd + yd + zd = 240

16d = 240

d = 240/16

d = 15

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It is given that the longer leg is 4 cm longer than the shorter leg.

It is also given that the hypotenuse is 8 cm longer than the shorter leg.

Let the shorter leg be x.

The longer leg be y.

Then the relation formed is

It is also given that the hypotenuse is 8 cm longer than the shorter leg.

Let the hypotenuse is z.

Then the perimeter of the right triangle is the sum of all the sides.

But to find the value of x , use the Pythagoras theorem.

Substitute the values.

Solve the quadratic equation to find the value of x.

As x cannot be negative , then the value of x is 12.

The length of shorter leg is 12.

The length of longer leg is 12+4=16.

The hypotenuse is 12+8=20.

Now , the perimeter of right triangle is

The perimeter of the triangle is 48 cm.

Answer : value of x and y in the matrix equation is:

x = -3

y = +4, -4

Step-by-step explanation :

The matrix expression is:

\(\left[\begin{array}{ccc}x+4\\y^2+1\end{array}\right]+\left[\begin{array}{ccc}-9x\\-17\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]\)

First we have to add left hand side matrix.

\(\left[\begin{array}{ccc}(x+4)+(-9x)\\(y^2+1)+(-17)\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]\)

Now we have to add left hand side terms.

\(\left[\begin{array}{ccc}x+4-9x\\y^2+1-17\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]\)

\(\left[\begin{array}{ccc}4-8x\\y^2-16\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]\)

Now we have to equating left hand side matrix to right hand matrix, we get:

\(\Rightarrow 4-8x=28\text{ and }y^2-16=0\\\\\Rightarrow 8x=4-28\text{ and }y^2=16\\\\\Rightarrow x=-3\text{ and }y=\pm 4\)

Therefore, the value of x and y in the matrix equation is -3 and +4, -4 respectively.

Answer:

D is wrong. The correct answer choice is C ( x=-3 and y= +4, -4)

Step-by-step explanation:

Math unit test review

The equivalent of the given expression ⁴√7⁵ × √7³ in exponential form is  7^11/4.

Given the data in the equation;

⁴√7⁵ × √7³

Since fourth and square roots can be written as power 1/4 and 1/2 respectively.

7^(5 × 1/4) × 7^(3 × 1/2 )

7^(5/4) × 7^(3/2 )

From exponent rule, n^a × n^b = b^(a + b )

7^(5/4 + 3/2 )

7^11/4

The equivalent of the given expression ⁴√7⁵ × √7³ in exponential form is  7^11/4.

Hence, option D) 7^11/4 is the correct answer.

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According to the given statement the inequality is 313131c + 191919m ≤ 706706.

To represent the condition based on the number of employees, we can write the following inequality:

313131c + 191919m ≤ 706706

- Let c denote the number of cars and m denote the number of motorcycles.

- Since it takes 313131 employees to build a car and 191919 employees to build a motorcycle, we multiply the number of cars (c) by 313131 and the number of motorcycles (m) by 191919.

- The total number of employees used should be at most 706706 (as stated in the question).

The inequality 313131c + 191919m ≤ 706706 represents the condition based on the number of employees for Genghis Motors to spend more than \$84000 to build cars and motorcycles, using at most 706706 employees.

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Answer:

2

Step-by-step explanation:

\( {2}^{3} = 8 \)

\( \sqrt[3]{8} = 2\)

Answer:

g(x) = (x -39)^2 +74

Step-by-step explanation:

Given f(x)=x^2, after performing the following transformations: shift upward 74 units and shift 39 units to the right, the new function g(x) = (x -39)^2 +74

In mathematics, a transformation is a feature f, typically with a few geometrical underpinnings, that maps a fixed X to itself, i.e. f: X → X.

What are the 4 transformations in maths?

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The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

Given function is,f(t) ={ t, 0 < t < π π < t < 2π}

where f(t + 2 π) = f(t)

Let's take Laplace Transform of f(t)

                     L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...f(t + 2π) = f(t)

∴ L{f(t + 2 π)} = L{f(t)}⇒ e^{2πs}L{f(t)} = L{f(t)}

     ⇒ [e^{2πs} − 1]L{f(t)} = 0L{f(t)} = 0

when e^{2πs} ≠ 1 ⇒ s ≠ 0

∴ The Laplace Transform of f(t) is

                       L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                               = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...

                              = (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

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Answer:

I think you are right!

Step-by-step explanation:

The M is approximately 149.19 minutes.

The probability that the mean time to finish cleaning for the sample of 10 people is less than 148 minutes is approximately 0.0251

The probability that the cleaning will be done in 158 minutes is approximately 0.9938.

The probability that the cleaning will be done in 158 minutes can be calculated using the standard normal distribution. We need to calculate the z-score and then find the corresponding probability using a standard normal distribution table or calculator. The z-score is calculated as (158 - 150) / 3.2 ≈ 2.5. Looking up the z-score of 2.5 in the standard normal distribution table, we find that the corresponding probability is approximately 0.9938.

To find the value of M, we need to determine the z-score corresponding to the 60th percentile of the standard normal distribution. The z-score represents the number of standard deviations a value is from the mean. Using a standard normal distribution table or calculator, we find that the z-score for the 60th percentile is approximately -0.2533. To find M, we can rearrange the formula for the z-score and solve for X: X = (z-score * standard deviation) + mean. Plugging in the values, we get M = (-0.2533 * 3.2) + 150 ≈ 149.19

To find the probability that the mean time to finish cleaning is less than 148 minutes for a sample of 10 people, we can use the central limit theorem. According to the central limit theorem, the distribution of the sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. So, the mean of the sample means is still 150 minutes, and the standard deviation of the sample means is 3.2 / sqrt(10) ≈ 1.01 minutes. We can calculate the z-score as (148 - 150) / 1.01 ≈ -1.98. Looking up the z-score of -1.98 in the standard normal distribution table, we find that the corresponding probability is approximately 0.0251.

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\(\boxed{\bold{y + 6 = \frac{1}{3} (x - 4)}}\)

Replace the second y (y1) and the 2nd x (x1) with the new points and then -3 become 1/3 due to perpendicular meaning opposite reciprocal (2/3 reciprocal is 3/2 and the opposite would be its negative, -3/2, for example)

So there's your answer plus some info for future knowledge

Answer:

y + 6 = 1/3 (x-4)

Step-by-step explanation:

Answer:

She can buy 5 bowls of noodles

Step-by-step explanation:

she has $10

each bowl cost $2

so then you divide 2÷10 which = 5

Step-by-step explanation:

\(x + 3y = 1 \\ - 3x - 3y = - 15 \\ x = 1 - 3y \\ - 3(1 - 3y) - 3y = - 15 \\ - 3 + 9y - 3y = - 15 \\ - 3 + 6y = - 15 \\ 6y = - 15 + 3 \\ 6y = - 12 \\ y = - 2\)

\(y = - 2 \\x = 1 - 3y \\ x = 1 - 3( - 2) \\ x = 1 + 6 \\ x = 7\)

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

The linear term in the given function is :

\(\mathrm{✌TeeNForeveR✌}\)

Answer:

The linear term is \(\sf5x\)

Hope it helps you!

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Answer:

\(\boxed{\mathrm{view \: explanation}}\)

Step-by-step explanation:

2)

a) elimination method

b) substitution method

c) substitution method

For the first part we can elimate the y variable by subtracting the equations. We can then find the value of x.

For the second part we can substitute y as 2x+5 in the second equation and solve for x.

For the third part we can substitute y as 4x+3 in the first equation and solve for x.

3)

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The solutions of the given integrals using trapezoidal-rule and Simpson's-rule as mentioned above are:

Trapezoidal rule: T4 = 3.1472, T4 = 56.5763, T6 = 63.0626

Simpson's rule: S4 = 3.1236, S4 = 56.6673, S6 = 63.1273.

Approximation of the following integrals using trapezoidal rule and Simpson's rule as mentioned below.

1. ∫ x ln(x) dx with n = 4

a) Trapezoidal rule (T4)

T4 ≈ [ln(1) + 2 ln(2) + 2 ln(3) + ln(4)] × (4-1) ÷ 2× (1/4)

    = 3.1472

b) Simpson's rule (S4)

S4 ≈ [ln(1) + 4 ln(2) + 2 ln(3) + 4 ln(4) + ln(5)] × (4-1) ÷ 3× (1/4)

    = 3.1236

2. ∫ e²x dx with n =

4a) Trapezoidal rule (T4)

T4 ≈ [e²(0) + 2 e²(1/4) + 2 e²(2/4) + e²(3/4)] × (4-1) ÷ 2× (1/4)

   = 56.5763

b) Simpson's rule (S4)

S4 ≈ [e²(0) + 4 e²(1/4) + 2 e²(2/4) + 4 e²(3/4) + e²(1)] × (4-1) ÷ 3× (1/4)

     = 56.6673

3. ∫ √ √4 + x³ dx with n = 6

a) Trapezoidal rule (T6)

T6 ≈ [(2 + 0) + 2(3 + 2.6814) + 2(4 + 4.2487) + 2(5 + 6.1757) + 2(6 + 8.4498) + (8 + 11.1694)] × (6-1) ÷ 2× (1/6)

   = 63.0626

b) Simpson's rule (S6)

S6 ≈ [(2 + 0) + 4(3 + 2.6814) + 2(4 + 4.2487) + 4(5 + 6.1757) + 2(6 + 8.4498) + (8 + 11.1694)] × (6-1) ÷ 3× (1/6)

    = 63.1273

Therefore, the approximate solutions of the given integrals using trapezoidal rule and Simpson's rule as mentioned above are:

Solutions according to Trapezoidal rule:

T4 = 3.1472, T4 = 56.5763, T6 = 63.0626

Solutions according to Simpson's rule:

S4 = 3.1236, S4 = 56.6673, S6 = 63.1273.

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The function which represents the cost to drive a car from this agency miles x a day is :

C(x) = 15, if 0 ≤ x ≤ 200

      = 15 + 0.05x, if x > 200

Given that,

A car rental agency charges $15 a day for driving a car 200 miles or less.

The function can be written as,

C(x) = 15 if 0 ≤ x ≤ 200

If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.

C(x) = 15 + 0.05x, if x > 200

Hence the correct option is D.

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The largest value that f(4) can possibly be is 29.

The mean value theorem states that for a function f(x) that is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), there exists a number c in the open interval (a, b) such that:

f(b) - f(a) = f'(c)(b - a)

In this case, we are given that f(0) = -3 and that f'(x) ≤ 8 for all values of x. To determine how large f(4) can possibly be, we can use the mean value theorem with a = 0 and b = 4:

f(4) - f(0) = f'(c)(4 - 0)

Substituting the given values:

f(4) - (-3) = f'(c)(4)

f(4) + 3 = 4f'(c)

Since f'(x) ≤ 8 for all values of x, we can say that f'(c) ≤ 8. Therefore:

f(4) + 3 ≤ 4f'(c) ≤ 4(8) = 32

Therefore, we have:

f(4) ≤ 32 - 3 = 29

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Answer:

A. 8x² + 2y²

Step-by-step explanation:

There is a formula for the perimeter.

2l + 2w

2(4x²) + 2(y²)

8x² + 2y²

The perimeter of the rectangle is 8x² + 2y².

Answer:

x = 84

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

a pentagon has 5 sides , so n = 5

sum = 180° × (5 - 2) = 180° × 3 = 540°

sum the interior angles and equate to 540

x + x + 20 + x + 20 + x + 40 + x + 40 = 540

5x + 120 = 540 ( subtract 120 from both sides )

5x = 420 ( divide both sides by 5 )

x = 84

(a) To determine how fast the population is growing when it reaches 5 million people, we can substitute P(t) = 5 into the differential equation P'(t) = 0.06P(t). This gives us P'(t) = 0.06(5) = 0.3 million people per year. Therefore, the population is growing at a rate of 0.3 million people per year when it reaches 5 million people.

(b) To determine the population size when it is growing at a rate of 700,000 people per year, we can set P'(t) = 700,000 and solve for P(t). From the given differential equation, we have 0.06P(t) = 700,000, which implies P(t) = 700,000/0.06 = 11,666,666.67 million people. Therefore, the population size is approximately 11.67 million people when it is growing at a rate of 700,000 people per year.

(c) To find a formula for P(t), we can solve the differential equation P'(t) = 0.06P(t). This is a separable differential equation, and integrating both sides gives us ln(P(t)) = 0.06t + C, where C is the constant of integration. By exponentiating both sides, we get P(t) = e^(0.06t+C). Using the initial condition P(0) = 3, we can find the value of C. Substituting t = 0 and P(0) = 3 into the equation, we have 3 = e^C. Therefore, the formula for P(t) is P(t) = 3e^(0.06t).

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The correct option is (c) it gets smaller as the sample size grows. This is because as the sample size increases, the variability within the sample decreases, and the sample mean becomes a more accurate representation of the population mean.

Here are the options: (a) the sample size has no effect on it (b) it gets larger as the sample size grows (c) it gets smaller as the sample size grows.

Explanation: The standard deviation of all possible sample means is known as the standard error. As the sample size (n) increases, the standard error decreases because the larger the sample, the more accurately it represents the population. The relationship between standard error and sample size is given by the formula:

Standard Error (SE) = σ / √n

where σ is the population standard deviation and n is the sample size. As the sample size grows, the denominator (√n) increases, resulting in a smaller standard error.

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The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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Answer:  6,048

Step-by-step explanation:

15,000-8,952=6,048

Answer:

4/£

6048

Step-by-step explanation:

just subtract 8952 from 15,000

Answer:

120

Step-by-step explanation:

! means to multiply it by every number less than itself.

Not counting 1, this means 5*4*3*2.

20*3*2

60*2

120

The answer is 120.

Answer:

120

Step-by-step explanation:

Answer:

x = -150

Step-by-step explanation:

x/15 = -10

Multiply both sides by 15.