HELPPP :(
Max is mountain hiking at a constant rate.

This equation y = 10x + 30 can be used to represent this situation, where y is Max's elevation in meters and x is the number of hours Max has been hiking.

Which statement best describes Max's elevation, given this equation?

Max started at a height of 10 meters and is ascending at 30 meters per hour.

Max started at a height of 10 meters and is descending at 30 meters per hour.

Max started at a height of 30 meters and is ascending at 10 meters per hour.

Max started at a height of 30 meters and is descending at 10 meters per hour.
(If you don’t know the answer, please don’t spam :<)

Area = length x height

area = 10 1-4 x 7 = 71 3/4 sq.ft.

Answer: 71 3/4

Answer:

The answer is D.5(9a-2b)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

5x9a -5x2b= 45a - 10b

so that is the answer

Answer: 11 donuts

Step-by-step explanation:

To find the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ), we need to first plot the curve on a polar graph.

From the graph, we can see that the curve has two loops - one larger loop and one smaller loop. The larger loop encloses the smaller loop.

To find the area inside the larger loop and outside the smaller loop, we can use the formula:

Area = 1/2 ∫[a,b] (r2 - r1)2 dθ

where r2 is the equation of the outer curve (larger loop) and r1 is the equation of the inner curve (smaller loop).

The limits of integration a and b can be found by setting the angle θ such that the curve intersects itself at the x-axis. From the graph, we can see that this occurs at θ = π/2 and θ = 3π/2.

Plugging in the equations for r1 and r2, we get:

r1 = 1/2 + cos(θ)
r2 = 1/2 - cos(θ)

So the area inside the larger loop and outside the smaller loop is:

Area = 1/2 ∫[π/2, 3π/2] ((1/2 - cos(θ))2 - (1/2 + cos(θ))2) dθ

Simplifying and evaluating the integral, we get:

Area = 3π/2 - 3/2 ≈ 1.07

Therefore, the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ) is approximately 1.07. Note that this area is smaller than the total area enclosed by the curve, since it excludes the area inside the smaller loop.
To find the area inside the larger loop and outside the smaller loop of the limaçon given by the polar equation r = 1 + 2cos(θ), follow these steps:

1. Find the points where the loops intersect by setting r = 0:
1 + 2cos(θ) = 0
2cos(θ) = -1
cos(θ) = -1/2
θ = 2π/3, 4π/3

2. Integrate the area inside the larger loop:
Larger loop area = 1/2 * ∫[r^2 dθ] from 0 to 2π
Larger loop area = 1/2 * ∫[(1 + 2cos(θ))^2 dθ] from 0 to 2π

3. Integrate the area inside the smaller loop:
Smaller loop area = 1/2 * ∫[r^2 dθ] from 2π/3 to 4π/3
Smaller loop area = 1/2 * ∫[(1 + 2cos(θ))^2 dθ] from 2π/3 to 4π/3

4. Subtract the smaller loop area from the larger loop area:
Desired area = Larger loop area - Smaller loop area

After evaluating the integrals and performing the subtraction, you will find the area inside the larger loop and outside the smaller loop of the given limaçon.

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Answer:

(5 , 1)

Step-by-step explanation:

coordinate point is (2 , 9)

translation rule is

(x , y) = (x + 3 , y - 8)

here x is 2 and y is 9

so  the new coordinate will be

(x + 3 , y - 8)

(2 + 3 , 9 - 8)

(5 , 1)

The simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is 729x^6 - V^2.

In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.

To simplify the expression using the given values, we substitute \(U = 3x^3\)and V = y + 1 into the original expression:

\(81x^6 - (y + 1)^2\)

Replacing U and V:

\(81(3x^3)^2 - (V)^2\)

Simplifying:

\(81 \times 9x^6 - V^2\)

\(729x^6 - V^2\)

Therefore, the simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is\(729x^6 - V^2.\)

In this way, we can represent the original expression in a simplified form using the assigned values for U and V.

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Consider the expression: \(81x^6 - (y + 1)^2\)

If\(U = 3x^3\) and V = y + 1, what is the simplified form of the expression in terms of U and V?

In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.

The Graham's scan algorithm calculates the convex hull of a set of points, which guarantees a convex polygon. The smallest area polygon containing the set of points is not the convex hull of those points.

To demonstrate that the smallest area polygon containing a set of points may not always be a convex hull of that set of points, let's consider a simple example.

Suppose we have a set of four points: A, B, C, and D, arranged in a square formation, as shown below:

A----B

|    |

|    |

D----C

If we calculate the convex hull of these points using the Graham's scan algorithm, we would obtain the convex hull as ABCDA, which is a square.

However, if we look for the smallest area polygon that contains these points, we can find a non-convex polygon. By connecting the points A, B, C, and D in that order, we form a quadrilateral:

A----B

\  /

 \/

 /\

/  \

D----C

This quadrilateral, ABCD, is not convex, as it has an internal angle greater than 180 degrees.

Hence, in this example, the smallest area polygon containing the set of points is not the convex hull of those points. This example demonstrates that the smallest area polygon can be non-convex, and the convex hull may not always provide the minimum area solution.

The Graham's scan algorithm specifically calculates the convex hull of a set of points, which guarantees a convex polygon. However, to find the smallest area polygon, other techniques or algorithms need to be applied.

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Answer:

seconds

Step-by-step explanation:

I can't see it so well,but I think it's seconds

Answer:

The jet would Travel 900 miles in 10 hours. The jet travels at 90 miles per hour

Step-by-step explanation:

The distance that could the jet fly in 10 hours is 900 miles.

And, the rate of speed should be 90 miles per hour.

Since A jet travels 450 miles in 5 hours. At this rate

So per hour, it should be

\(= 450\div 5\)

= 90 miles per hour

And, the distance be like

\(= 90 \times 10\)

= 900 miles

Hence, The distance that could the jet fly in 10 hours is 900 miles.

And, the rate of speed should be 90 miles per hour.

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Answer:

\(r=-\frac{1}{11}\)

Step-by-step explanation:

\(4-5(1r) -2 = 3 +6r\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\\\4-5r-2=3+r\\\\\mathrm{Group\:like\:terms}\\\\-5r+4-2=3+6r\\\\-5r+2=3+6r\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\-5r+2-2=3+6r-2\\\\Simplify\\-5r=6r+1\\\\\mathrm{Subtract\:}6r\mathrm{\:from\:both\:sides}\\-5r-6r=6r+1-6r\\\\Simplify\\\\-11r=1\\\\\mathrm{Divide\:both\:sides\:by\:}-11\\\\\frac{-11r}{-11}=\frac{1}{-11}\\\\Simplify\\\\r=-\frac{1}{11}\)

Answer:c

Step-by-step explanation:

Transformation involves changing the position of a shape in a coordinate plane.

The corresponding parts that will not remain the same is (c) the coordinates of B' after a translation of 3 units left and 2 units up

Reflection is a rigid transformation;

This means that, options (a) and (d) will remain unchanged for the image and the pre-image of square ABCD

Rotating a shape 360 degrees will return the shape to its original position.

This means that: (b) will remain unchanged

The coordinates of B' after translation will not remain the same, because the points will move to (x + 3, y + 2).

Hence, option (c) is true

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Answer:

x =33.8°

Step-by-step explanation:

First find the altitude of the ΔADC using Pythagorean theorem.

  altitude² = hypotenuse² - base²

                  = 5² - 2.5²

                  = 25 - 6.25

                 = 18.75

  altitude  = √18.75

 altitude = AD = 4.3 cm

Now, to find x, use tan ratio.

     \(\sf \boxed{\bf Tan \ x = \dfrac{opposite \ side \ of \ \angle x}{adjacent \ side \ of \ \angle x}}\)

                 \(\sf = \dfrac{4.3}{6.5}\\\\ = 0.67\)

             \(\sf x = tan^{(-1)} \ 0.67\)

            x = 33.8°

Answer:

33.7°

Step-by-step explanation:

We know that both small triangles are right triangles, but we don't know that the large triangle is a right triangle.

1. Find the altitude of the large triangle.

a² + b² = c²

2.5² + b² = 5²

b² = 25 - 6.25

b² = 18.75

b = √18.75

The altitude of the large triangle is the opposite leg to angle x in the left small triangle. The adjacent leg to angle x is 6.5 cm.

tan x = opp/adj

tan x = √18.75/6.5

tan x = 0.6661733

x = tan^-1 0.6661733

x = 33.7

Answer: 33.7°

Based on the given parameters, the value of the money after 9 years is $5534.89

The given parameters about the compound interest are

Principal Amount, P = $3700

Interest Rate, R = 4.5%

Time, t = 9

Number of times, n = 4

To calculate the amount, we have:

A = P + CI

Where

C = P(1 + R)^t

So, we have

A = P(1 + R)^t

This can be rewritten as

A = P(1 + R/n)^nt

Substitute the known values in the above equation

A = 3700 * (1 + 4.5%/4)^(9*4)

Evaluate the expression

A = 5534.89

Hence, the value of the investment after 9 years is $5534.89

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Answer:

-5

Step-by-step explanation:

6 - 5 = 1

so 6 + -5 is also equal to 1

Answer:

   q = -5

Step-by-step explanation:

Step  1  :  Simplify:  6/q

Step  2  :

Rewriting the whole as an Equivalent Fraction

Equation at the end of step  2  :

 (6 - q)    

 ——————— -  2  = 0  

    q      

Step  3  :

Rewriting the whole as an Equivalent Fraction

Step  4  :

Pulling out like terms

Answer:    q = -5

Hope this helps.

The probability that he will get to use his laser pointer for at least 105 hours before he needs to buy more batteries is 1.

We know that a pair of batteries will power the pointer for an average of five hours use, with a standard deviation of 30 minutes. Also, he buys 20 2-packs of AAAA batteries.So, the total number of batteries he bought = 20 × 2 = 40.Since a pair of batteries will power the pointer for an average of five hours use, with a standard deviation of 30 minutes.

This means that the standard deviation for 40 batteries will be calculated as follows:\($$\text{standard deviation for 1 pair of batteries} = 30 \text{ minutes}$$$$\text{standard deviation for 40 pairs of batteries} = 30/\sqrt{40} \text{ minutes} = 4.74 \text{ minutes}$$\)

Hence, the mean time that he will get to use his laser pointer for 40 batteries will be 40 × 5 = 200 hours.

So, the probability that he will get to use his laser pointer for at least 105 hours before he needs to buy more batteries is calculated as follows:

\($$P(X \ge 105) = P\left(Z \ge \frac{105-200}{4.74}\right)$$$$\qquad \qquad \,\,\,\,\, = P(Z \ge -19.97)$$$$\qquad \qquad \,\,\,\,\, = 1 - P(Z \le -19.97) = 1$$\)

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Given:

A Hudson Valley farmer has 26 employees.

Salary of each employee = $410 per week.

Remaining amount after one week = $126

To find:

The initial amount of money he begins with.

Solution:

We have,

Amount he pays to one employee in one week = $410

Amount he pays to 26 employee in one week = 26 × $410

                                                                             = $10660

Let x be the initial amount of money he begins with.

Remaining amount = Initial amount - Amount he pays to 26 employee in one week

\(126=x-10660\)

\(126+10660=x\)

\(10786=x\)

Therefore, the initial amount of money he begins with is $10786.

Answer:

D. 491.52

Step-by-step explanation:

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{135\% of 160}}{\left( \cfrac{135}{100} \right)160}\implies \text{\LARGE 216}\)

The solution to the given system of equations is x = 2, y = -1, and z = 1.

To solve the system of equations, we can use methods such as substitution or elimination. Here, we will use the method of elimination to find the values of x, y, and z.

First, let's eliminate the variable x by multiplying equation (1) by 2 and equation (3) by -1. This gives us:

2x + 4y - 2z = -6 (4)

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

Next, we can subtract equation (5) from equation (4) to eliminate the variable x:

5y - z = 2 (6)

Now, we have a system of two equations with two variables. Let's eliminate the variable z by multiplying equation (2) by 2 and equation (6) by 1. This gives us:

4x - 2y + 2z = 10 (7)

5y - z = 2 (8)

Adding equation (7) and equation (8), we can eliminate the variable z:

4x + 5y = 12 (9)

From equation (6), we can express z in terms of y:

z = 5y - 2 (10)

Now, we have a system of two equations with two variables again. Let's substitute equation (10) into equation (1):

x + 2y - (5y - 2) = -3

x - 3y + 2 = -3

x - 3y = -5 (11)

From equations (9) and (11), we can solve for x and y:

4x + 5y = 12 (9)

x - 3y = -5 (11)

By solving this system of equations, we find x = 2 and y = -1. Substituting these values into equation (10), we can solve for z:

z = 5(-1) - 2

z = -5 - 2

z = -7

Therefore, the solution to the given system of equations is x = 2, y = -1, and z = -7.

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Answer:

Step-by-step explanation:

      the answer is on the graph

An appropriate statement of the null hypothesis, H₀ is that: A. The proportion of contaminated wrist-watches from medical personnel is the same as the proportion of contaminated wrist-watches from security guards, i.e., H0: p = 46.6%.

In Mathematics, a null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (Ha) and it asserts that two (2) possibilities are the same.

For an experiment to test the contamination of medical personnel wrist-watches at a New York hospital, the appropriate null hypothesis and alternative hypothesis would be given by this mathematical expression:

H₀: p = 10.

Ha: p < 10.

In this context, we can logically that the proportion of contaminated wrist-watches would be the same for both sample proportion i.e., H₀: p = 46.6%.

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The inverse of a function can be found by swapping the numbers in each ordered pair of the function.

When you have a function with ordered pairs, the inverse of that function can be found by reversing the order of the numbers within each pair. In other words, if you have a function f(x) with ordered pairs (a, b), the inverse function, f^ (-1) (x), will have ordered pairs (b, a). This process essentially switches the input and output values of the original function.

To find the inverse of a function, simply swap the numbers in each ordered pair, resulting in the ordered pairs for the inverse function.

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the probability of randomly selecting a jack or 4 from a standard deck of 52 cards is 2/13.

In a standard deck of 52 cards, there are four jacks and four 4s, for a total of 8 cards that are either a jack or a 4. The probability of selecting a jack or 4 can be found by dividing the number of favorable outcomes (8) by the total number of possible outcomes (52): P(jack or 4) = 8/52. This fraction can be reduced by dividing both the numerator and denominator by 4: P(jack or 4) = 2/13. Therefore, the probability of randomly selecting a jack or 4 from a standard deck of 52 cards is 2/13. Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in a wide range of fields, from gambling and sports to scientific research and data analysis. Understanding probability is important for making informed decisions, predicting outcomes, and assessing risks.

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Two system of equation has the same solution as first equation of System B is obtained by adding, first equation of System A, 2 times second equation of System A.

A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.

The equation of system A given in the problem are,

\(3x+2y=3\)

\(-2x-8y=-1\)

The equation of system B given in the problem are,

\(-x-14y=1\)

\(-2x-8y=-1\)

On solving the first equation of system A, we get,

\(y=\dfrac{3-3x}{2}\)

Put this value in second equation of system A we get,

\(-2x-8\dfrac{3-3x}{2}=-1\\x=\dfrac{11}{10}\)

Put this value in the first equation of system A, we get,

\(y=\dfrac{-3}{20}\)

Similarly, on solving the system of equation B, we get the same value of variable x and y. Thus both the system has the same solution.

Therefore, they will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A.

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The value of a+b+c will be 16 if  \(\frac{5}{2-\sqrt{3}}\) rationalize as  \(\displaystyle{\frac{a + b\sqrt{3}}{c}}\).

Given,

y = \(\frac{5}{2-\sqrt{3}}\)

To solve the given expression we multiply the numerator and denominator by the conjugate of the denominator

\(= \frac{5}{2-\sqrt{3}} \frac{2+\sqrt{3} }{2+\sqrt{3}}\)

\(= \frac{10+5\sqrt{3} }{2^2 - \sqrt{3}^2 }\)

\(= \frac{10+5\sqrt{3} }{4-3 }\)

\(= \frac{10+5\sqrt{3} }{1 }\) = \(\displaystyle{\frac{a + b\sqrt{3}}{c}}\)

Now, by comparing the result we get

a = 10, b = 5, c = 1

hence, a+b+c = 10+5+1 = 16

Therefore, the value of a+b+c will be 16.

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Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To test the claim about the population mean μ at the level of significance α, we can perform a one-sample t-test.

Given:

Claim: μ > 29 (right-tailed test)

α = 0.05

σ = 1.2 (population standard deviation)

Sample statistics: x = 29.3 (sample mean), n = 50 (sample size)

We can follow these steps to conduct the hypothesis test:

Step 1: Formulate the null and alternative hypotheses.

The null hypothesis (H₀): μ ≤ 29

The alternative hypothesis (Hₐ): μ > 29

Step 2: Determine the significance level.

The significance level α is given as 0.05. This represents the maximum probability of rejecting the null hypothesis when it is actually true.

Step 3: Calculate the test statistic.

For a one-sample t-test, the test statistic is given by:

t = (x - μ) / (σ / √(n))

In this case, x = 29.3, μ = 29, σ = 1.2, and n = 50. Plugging in the values, we get:

t = (29.3 - 29) / (1.2 / √(50))

= 0.3 / (1.2 / 7.07)

= 0.3 / 0.17

≈ 1.76

Step 4: Determine the critical value.

Since it is a right-tailed test, we need to find the critical value that corresponds to the given significance level α and the degrees of freedom (df = n - 1).

Looking up the critical value in a t-table with df = 49 and α = 0.05, we find the critical value to be approximately 1.684.

Step 5: Make a decision and interpret the results.

If the test statistic (t-value) is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

In this case, the calculated t-value is approximately 1.76, which is greater than the critical value of 1.684. Therefore, we reject the null hypothesis.

hence, Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

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The correct true statement is the swimmer comes back up 9 seconds after the timer was started.

The maximum height of a function is the  point where the velocity the body is zero.

Given the function that represent the height of the swimmer as  h(t)=t^2−12t+27

If the velocity of the function is zero, hence;

h'(t) = 2t - 12

0 = 2t - 12

2t = 12

t = 6secs

Substitute t = 6 into the function as shown:

h(6) = 6^2−12(6)+27

h(6) = 36 - 72 + 27

h(6) = -36 + 27

h(6) = -9 feet

Hence the correct true statement is the swimmer comes back up 9 seconds after the timer was started.

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The average of a distribution, also known as the mean, is calculated by dividing the sum of all the observations by the total number of observations.

To understand why this calculation yields the average, consider the following:

Summation of x: The sum of all the observations, denoted as Σx (capital sigma x), represents the total value obtained by adding up all the individual values in the distribution. For example, if we have a set of observations {2, 4, 6, 8}, the summation of x would be 2 + 4 + 6 + 8 = 20.

Number of observations: The total number of observations, denoted as N, represents the count of how many values are included in the distribution. Using the previous example, if we have the set of observations {2, 4, 6, 8}, the number of observations N would be 4.

Division: By dividing the sum of all the observations (Σx) by the total number of observations (N), we calculate the average. In mathematical notation, the average (mean) is expressed as:

Mean (average) = Σx / N

Using our previous example, the average (mean) would be: 20 / 4 = 5.

The division operation by the total number of observations normalizes the sum of the values, resulting in an average value that represents the central tendency of the distribution. It gives us a measure of the "typical" or "average" value within the set of observations.

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