Eva earns $5.50 per hour and time-and-a-half for overtime for all hours over 40 hours. How much did she earn the week she worked 47 hours?

The final step in creating a frequency distribution is to count the number of observations in each class. After determining the class width and deciding on the number of classes, the next step is to set individual class limits.

This involves establishing the lower and upper limits for each class interval. Once the class limits have been set, the next step is to tally the number of observations that fall within each interval. This process involves counting the number of data points that fall within each class and recording this information in a tally chart. After tallying the number of observations in each class, the final step is to create a frequency table that summarizes this information. The frequency table will typically include the class intervals, the frequency (i.e., the number of observations) in each interval, and the relative frequency (i.e., the proportion of observations) in each interval. By following these steps, you can create a comprehensive frequency distribution that provides insights into the distribution of your data.

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Answer:

The y-intercept is (0,3)

Step-by-step explanation:

Answer:

As x is the exterior angle

Step-by-step explanation:

therefore

let name the angle exterior angle be ACE

interior angleABC=76°and angleBAC=55°

sum of 2 interior angle is equal to exterior angle

=76+55=x

=131=x

Answer:

I believe it is 122.6

Step-by-step explanation:

1,250 - 24 = 1,226

10%of 1,226 = 122.6

\(\boxed{The\:value\:of\:x\:is\:7.375.}\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\((4x - 5)2 = 49 \\ ⇢8x - 10 = 49 \\⇢8x = 49 + 10 \\ ⇢8x = 59 \\ ⇢x = \frac{59}{8} \\ ⇢x = 7.375\)

Therefore, the value of x is 7.375.

\({ \bf{ \underbrace{To\:verify :}}}\)

\((4x - 5)2 = 49 \\ ⇢(4 \times 7.375 - 5)2 = 49 \\ ⇢(29 .5 - 5)2 = 49 \\ ⇢24.5 \times 2 = 49 \\ ⇢49 = 49 \\ ⇢ L.H.S.=R. H. S\)

Hence verifed.

\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}\)

The probability of incurring a loss when it rains is:P (loss | raining) = 80%So, there is a 20% chance that the food truck will not have incurred a loss when it rains.

The P (not raining | not loss) = 90% × 30% = 27%.Thus, the probability that it had not rained on that randomly selected day given that the food truck did not incur a loss is 27%.

The chance of not raining on a given day in Seattle can be calculated as follows:When it does not rain, there is a 10% probability that the food truck will incur a loss, as given in the statement. Similarly, when it rains, there is an 80% chance that the food truck will incur a loss on that day.

To calculate the probability that the food truck will not have incurred a loss on that day, we must first calculate the probability that the food truck will have incurred a loss on that day.Suppose the probability of rain is 70%, so the chance that it won't rain will be: P (not raining) = 100% - 70% = 30%When it rains, there is a 80% probability that the food truck will have incurred a loss, as given in the statement.

The probability of not incurring a loss when it does not rain is:P (not loss | not raining) = 100% - 10% = 90%The probability of not raining when the food truck does not incur a loss can be calculated as follows:P (not raining | not loss) = P (not loss | not raining) × P (not raining)P (not loss | not raining) = 90%P (not raining) = 30%

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With n = 1, the total time elapsed before the ball comes to rest is 0.4 units of time. The total time elapsed before the ball comes to rest is represented by the formula t = (1/2)∑(0.8)^n as n approaches infinity.

The ball takes the same amount of time to bounce up as it does to fall, starting from the second bounce (n = 1). This means that for each subsequent bounce, the time it takes for the ball to reach its maximum height and return to the ground is the same.

The total time elapsed before the ball comes to rest is given by the formula t = (1/2)∑(0.8)^n, where n represents the number of bounces and ∑ denotes the summation notation. In this case, the summation starts from n = 1 and goes to infinity.

To calculate the total time, we substitute n = 1 into the formula: t = (1/2)(0.8)^1 = 0.4. Therefore, with n = 1, the total time elapsed before the ball comes to rest is 0.4 units of time.

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If cosA = 24/25 tanB = 4/3 and angles A and B are in Quadrant I. The value of tan(A-B) is -23/33.

We can start by using the identity: tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

From the given information, we have:

cos A = 24/25, which means sin A = sqrt(1 - cos^2 A) = 7/25 (since A is in Quadrant I)

tan B = 4/3, which means sin B = 4/sqrt(4^2 + 3^2) = 4/5 and cos B = 3/sqrt(4^2 + 3^2) = 3/5

Now, we can use the definitions of sine and cosine to find tan A:

tan A = sin A / cos A = (7/25)/(24/25) = 7/24

Substituting the values we have found into the formula for tan(A - B), we get:

tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

= [(7/24) - (4/3)]/[1 + (7/24)(4/3)]

= (-13/72)/(25/72)

= -13/25

Therefore, tan(A - B) = -13/25.

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Step-by-step explanation:

Here's my step by step solution Friend..

Answer:

2+2+28+28=60 is the answer of the perimeter

Step-by-step explanation:

Inequalities help us to compare two unequal expressions. The length of the rectangle can be 19 cm, while its width will be 17 cm.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Let the length of the rectangle be represented by x centimeters. Given the width of a rectangle is 2 cm less than the length. Therefore, the width of the rectangle is (x-2) centimeters.

Since the perimeter of the rectangle should be greater than 28 inches, therefore,

Perimeter of the rectangle > 28 inches × 2.54 = 71.12 centimeters

Now, given the perimeter is greater than 28 inches. Therefore,

2[x+(x-2)] > 71.12

x + (x-2) > 35.56

x + x - 2 > 35.56

2x - 2 > 35.56

2x > 37.56

x > 18.78

x = 19

Thus, the length of the rectangle can be 19 cm, while its width will be 17 cms.

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Answer:

2.56×101 hope this helps!:)

Step-by-step explanation:

4.55×1013

_________≈2.56×101

1.78∗1012

Answer:

the answer is D

Step-by-step explanation:

Answer:

X = 9.4868

Step-by-step explanation:

Use the pythagorean theorem

a squared plus b squared equals c squared

in this case c equals x

A&b are the side and base length of a right triangle

Answer:   \(\frac{14y}{25x^2}\)

====================================================

Work Shown:

First calculate \(\frac{dy}{dx}\) through the use of implicit differentiation.

Don't forget about the chain rule.

\(y^5 = x^7\\\\\frac{d}{dx}\left[y^5\right] = \frac{d}{dx}\left[x^7\right]\\\\5y^4\frac{dy}{dx} = 7x^6\\\\\frac{dy}{dx} = \frac{7x^6}{5y^4}\\\\\)

Go back to line 3, shown above, and apply the derivative to both sides.

You'll be using the product rule.

\(5y^4\frac{dy}{dx} = 7x^6\\\\\frac{d}{dx}\left[5y^4\frac{dy}{dx}\right] = \frac{d}{dx}\left[7x^6\right]\\\\\frac{d}{dx}\left[5y^4\right]*\frac{dy}{dx}+5y^4*\frac{d}{dx}\left[\frac{dy}{dx}\right] = 42x^5\\\\20y^3*\frac{dy}{dx}*\frac{dy}{dx}+5y^4*\frac{d^2y}{dx^2}=42x^5\\\\20y^3*\left(\frac{dy}{dx}\right)^2+5y^4*\frac{d^2y}{dx^2} = 42x^5\\\\\)

Use substitution and isolate \(\frac{d^2y}{dx^2}\) to get the following:

\(20y^3*\left(\frac{dy}{dx}\right)^2+5y^4*\frac{d^2y}{dx^2} = 42x^5\\\\20y^3*\left(\frac{7x^6}{5y^4}\right)^2+5y^4*\frac{d^2y}{dx^2} = 42x^5\\\\\frac{196x^{12}}{5y^5}+5y^4*\frac{d^2y}{dx^2} = 42x^5\\\\\frac{196x^{12}}{5x^7}+5y^4\frac{d^2y}{dx^2} = 42x^5\\\\\)

\(\frac{196x^5}{5}+5y^4*\frac{d^2y}{dx^2}=42x^5\\\\5y^4*\frac{d^2y}{dx^2}=42x^5-\frac{196x^5}{5}\\\\5y^4*\frac{d^2y}{dx^2}=\frac{210x^5-196x^5}{5}\\\\5y^4*\frac{d^2y}{dx^2}=\frac{14x^5}{5}\\\\\)

\(\frac{d^2y}{dx^2}=\frac{14x^5}{5}*\frac{1}{5y^4}\\\\\frac{d^2y}{dx^2}=\frac{14x^5}{25y^4}\\\\\frac{d^2y}{dx^2}=\frac{14x^5*x^2}{25y^4*x^2}\\\\\frac{d^2y}{dx^2}=\frac{14x^7}{25y^4*x^2}\\\\\frac{d^2y}{dx^2}=\frac{14y^5}{25y^4*x^2}\\\\\frac{d^2y}{dx^2}=\frac{14y}{25x^2}\\\\\)

Answer:

The answer would be the letter c

Answer:

32

Step-by-step explanation:

Answer:

-650ft

Step-by-step explanation:

I took a test with a question like that

The solution of the DTDS is xn = (0.63)^n * 41 grams, where n represents time in hours.

a) The updating function f(x) for the discrete time dynamical system (DTDS) can be derived from the given information that the body eliminates 37% of the alcohol present in the body per hour.

Since 37% of the alcohol is eliminated, the amount remaining after one hour can be calculated by subtracting 37% of the current amount from the current amount. This can be expressed as:

f(x) = x - 0.37x

Simplifying the equation:

f(x) = 0.63x

b) The initial condition for the DTDS is given as Peter having 41 grams of alcohol in his body after consuming three alcoholic drinks. Therefore, the initial condition is:

x0 = 41 grams

c) To find the solution of the DTDS with the given initial condition, we can use the updating function f(x) and iterate it over time.

For n hours, the solution is given by:

xn = f^n(x0)

Applying the updating function f(x) repeatedly for n times:

xn = f(f(f(...f(x0))))

In this case, since the function f(x) is f(x) = 0.63x, the solution can be written as:

xn = (0.63)^n * x0

Substituting the initial condition x0 = 41 grams, the solution becomes:

xn = (0.63)^n * 41 grams

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The machine should be set at approximately 7.006 milliliters of dye per can of paint.

To determine the setting for μ so that only 5% of the cans of paint will be unacceptable, follow these steps:

1. Recognize that the amount of dye discharged follows a normal distribution with mean μ and a standard deviation of 0.6 milliliters.

2. Define unacceptable as discharging more than 8 milliliters of dye per can.

3. Use the z-score formula to find the z-value corresponding to 5% probability in the right tail (unacceptable region) of the distribution. Since we want only 5% of the cans to be unacceptable, we'll look for the z-value that corresponds to the 95th percentile (1 - 0.05 = 0.95).

4. Consult a standard normal table or use an online calculator to find the z-value corresponding to a cumulative probability of 0.95. The z-value is approximately 1.645.

5. Use the z-score formula to solve for μ:
  z = (X - μ) / standard deviation
  1.645 = (8 - μ) / 0.6

6. Solve for μ:
  8 - μ = 1.645 * 0.6
  μ = 8 - (1.645 * 0.6)
  μ ≈ 7.006

Your answer: The machine should be set at approximately 7.006 milliliters of dye per can of paint to ensure that only 5% of the cans will be unacceptable.

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Answer:

Your answer should be \(\frac{\pi }{7}\)

Step-by-step explanation:

Looking at the x-axis we can say that is our b.

Period Formula: 2π/b.

x-axis is from 0 to 20.

b = 14 because of the rise to rise.

2π/14 = π/7

a. The area of the garden is 314m².

b. The number of boxes of grass Helen needs is 5 boxes.

c. My estimate for b is an underestimate.

A circle is a bounded object with points from its center to its circumference is equidistant.

Area of a circle = πr²

Where :

π = pi = 3.14

R = radius = diameter / 2 = 20m / 2 = 10m

3.14 x 10² = 314m²

Number of boxes needed to cover the garden = area of the garden / coverage of one box

314m² / 58m² = 5.14

5 boxes to one significant figure.

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a. The area of the garden is 314m².

b. The number of boxes of grass Helen needs is 5 boxes.

c. My estimate for b is an underestimate.

A circle is a bounded object with points from its center to its circumference that is circumferenced equidistant.

Area of a circle = πr²

Where : π = pi = 3.14

R = radius = diameter / 2 = 20m / 2 = 10m

3.14 x 10² = 314m²

Number of boxes needed to cover the garden = area of the garden / coverage of one box

314314m² / 58m² = 5.14

5 boxes to one significant figure.

To prove that triangle ABC is an isosceles right triangle, we need to show that two sides of the triangle are equal in length and one angle is a right angle.

Distance Formula:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Using the distance formula, we can calculate the lengths of the three sides of the triangle:

Side AB: d₁ = √[(6 - (-2))² + (2 - 4)²] = √[8² + (-2)²] = √(64 + 4) = √68

Side BC: d₂ = √[(1 - 6)² + (-1 - 2)²] = √[(-5)² + (-3)²] = √(25 + 9) = √34

Side AC: d₃ = √[(-2 - 1)² + (4 - (-1))²] = √[(-3)² + 5²] = √(9 + 25) = √34

Slope Formula:

The slope between two points (x₁, y₁) and (x₂, y₂) is given by the slope formula: m = (y₂ - y₁) / (x₂ - x₁)

Using the slope formula, we can calculate the slopes of the three sides of the triangle:

Slope AB:

m₁ = (2 - 4) / (6 - (-2)) = (-2) / 8 = -1/4

Slope BC:

m₂ = (-1 - 2) / (1 - 6) = (-3) / (-5) = 3/5

Slope AC:

m₃ = (4 - (-1)) / (-2 - 1) = 5 / (-3) = -5/3

From the distances calculated and the slopes of the sides, we can see that side AB is equal in length to side BC (both √34), indicating that two sides are equal. Additionally, the slope of side AC (m₃ = -5/3) is the negative reciprocal of the slope of side AB (m₁ = -1/4), indicating that the two sides are perpendicular, and hence, one angle is a right angle.

Therefore, triangle ABC is an isosceles right triangle.

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Answer:

sp=mp-20%ofmp=0.8mp

mp=cp+30%ofcp=1.3cp

mp=1.3cp

cp=mp/1.3

profit %=?

Step-by-step explanation:

The profit percentage is 4% .

Profit percentage (%) is the amount of profit expressed in terms of percentage. This profit is based on the cost price .

Formula for profit percentage is:

(Profit/Cost Price) × 100

where,

Profit = Selling price - Cost price

According to the question

Let Cost price of the article = 100x

marked price is 30% above the cost price

i.e  marked price = \(\frac{130}{100} * 100x\)

                            = 130 x

selling price of an article is 20% less than its marked price

i.e Selling price of the article = \(130x * \frac{100-20}{100}\)

                                                = \(130x * \frac{80}{100}\)

                                                = 104 x

Now ,

Profit = Selling price - Cost Price

Profit = 104x -100x

Profit = 4x        

Profit percentage =   \(\frac{Profit}{Cost PRice} *100\)

substituting the values in formula

Profit percentage =  \(\frac{4x}{100x} *100\)

Profit percentage =  4%

Hence, the profit percentage is 4% .

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===========================================================

Explanation:

As shown in the diagram below, I've drawn a blue horizontal line to split the figure into two rectangles (smaller one up top, larger down below).

The smaller rectangle up top is 25 ft by 8 ft, giving an area of 25*8 = 200 sq ft.

The larger rectangle down below is 35 ft by 25 ft so we have an area of 35*25 = 875 sq ft.

The total area is 200+875 = 1075 square feet

Notes:

The parallel vectors to CD are:

Here we have the vector:

CD = 4a - 3b

Where a and b are vectors.

A vector V will be parallel to CD if we can find a scalar number k such that we can write the vector as:

V = k*CD

The second option:

V = 20a - 15b

We can rewrite this as:

V = 20a - 15b = 5*(4a - 3b)   this vector is parallel.

The third one is:

V'  =10a - 20b + 2a + 11b

V' = 12a - 9b = 3*(4a - 3b)  this vector is parallel.

V'' = (-8a + 6b) = -2*(4a - 3b)  this vector is parallel.

V''' = a - (3/4)b = (1/4)*(4a - 3b)  this vector is parallel.

These are all the parallel vectors.

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Answer:

All of them lol.

Step-by-step explanation:

If you take all of them, you have a 100% chance at getting at LEAST 3 candies of the same color.

We have been able to create a thread that uses Gate_Control function and then shown the code generated.

A thread that uses Gate_Control function and the code generated is as follows:

#include <stdio.h>

#include <stdlib.h>

#include <pthread.h>

#include <semaphore.h>

#include <unistd.h>

sem_t Gate, Counter;

// Function to generate a random number between 0 and 3

int sensor_value() {

   return rand() % 4;

}

// Function for the Gate_Control thread

void* Gate_Control(void* arg) {

   while (1) {

       int value = sensor_value();

       if (value == 2) {

           // Passing the Gate semaphore

           sem_post(&Gate);

       }

       if (value == 1 || value == 3) {

           // Passing the Counter semaphore

           sem_post(&Counter);

       }

       usleep(1000000); // Wait for 1 second

   }

   return NULL;

}

int main() {

   srand(time(NULL));

   // Initialize semaphores

   sem_init(&Gate, 0, 0);

   sem_init(&Counter, 0, 0);

   // Create the Gate_Control thread

   pthread_t gateControlThread;

   pthread_create(&gateControlThread, NULL, Gate_Control, NULL);

   // Main thread waits for the Gate semaphore

   while (1) {

       sem_wait(&Gate);

       // Gate semaphore passed

       printf("Gate semaphore passed\n");

   }

   // Cleanup and exit

   sem_destroy(&Gate);

   sem_destroy(&Counter);

   return 0;

}

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the rule for division is:

Then:

you will substract the exponents