Last week, Riley worked 7.5 hours per day for 3 days and earned a total of $306.45.

What was Riley's hourly rate of pay last week?

Answer: x=8

Step-by-step explanation:

3(x+4) = 36

3x+12= 36

3x-12= -12

3x = 24

— —

3 3

X=8

Answer:

bb

Step-by-step explanation:

Answer:

should be D

Step-by-step explanation:

Answer:

c or d but im pretty sure its C

Step-by-step explanation:

Answer:

75m

Step-by-step explanation:

Answer:

87 minutes

Step-by-step explanation:

Let the total number of minutes = m

Our equation is given as:

$20.21 = $14.99 + 0.06m

20.21 = 14.99 + 0.06m

Collect like terms

0.06m= 20.21 - 14.99

0.06m = 5.22

m = 5.22/0.06

m = 87

Therefore, the total number rod minutes used is 87 minutes

Answer: Jerod took at least $18.50 to the mall to ensure that he had at least $10.00 left after buying a snack.

Step-by-step explanation:

Let's use "x" to represent the amount of money Jerod took to the mall.

After he spends $8.50 on a snack, he will have x - 8.50 dollars left.

Since he wants to keep a minimum of $10.00 in his pocket at all times, we can set up an inequality:

\(\sf:\implies x - 8.50 \geqslant 10.00\)

To solve for x, we can add 8.50 to both sides of the inequality:

\(\sf:\implies x \geqslant 18.50\)

Therefore, Jerod took at least $18.50 to the mall to ensure that he had at least $10.00 left after buying a snack.

Greetings! ZenZebra at your service, hope it helps! <33

Answer:

7.14

Step-by-step explanation:

Answer:

N^2+3

Step-by-step explanation:

Hope that helps!

Answer:

h(1 + n) = 2n - 2

Step-by-step explanation:

To find h(1 + n), substitute n = 1 + n into h(n) , that is

h(1 + n) = 2(1 + n) - 4 = 2 + 2n - 4 = 2n - 2

H0: p1 ≥ p2 (Null hypothesis: Proportion of ADHD-diagnosed students in School A is equal to or greater than in School B)

Null Hypothesis: The proportion of students diagnosed with ADHD in School A is equal to or greater than the proportion of students diagnosed with ADHD in School B.

Symbolically, the null hypothesis can be stated as:

H0: p1 ≥ p2

Where:

H0: Null Hypothesis

p1: Proportion of students diagnosed with ADHD in School A

p2: Proportion of students diagnosed with ADHD in School B

In other words, the null hypothesis assumes that there is no significant difference or that School A may have an equal or higher proportion of students diagnosed with ADHD compared to School B.

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Answer:

Step-by-step explanation:

12.7% = 12.7/100 = 0.127

To determine the probability that the specification for the clearance is met, we need to assume that the clearance follows a normal distribution. We can then use the standard normal distribution to calculate the probability that a clearance falls within the given specification range.

Assuming a normal distribution, we can use the formula for the standard normal distribution to calculate the probability that a clearance falls within the range of 0.015 to 0.063 mm:

z = (x - μ) / σ

where z is the z-score, x is the value we want to find the probability for, μ is the mean of the distribution (which we assume to be the midpoint of the specification range, i.e., (0.015 + 0.063) / 2 = 0.039 mm), and σ is the standard deviation of the distribution (which we assume to be (0.063 - 0.015) / 6 = 0.008 mm).

Using these values, we can calculate the z-scores for the lower and upper limits of the specification range:

z1 = (0.015 - 0.039) / 0.008 = -3

z2 = (0.063 - 0.039) / 0.008 = +3

We can then look up the area under the standard normal distribution curve between these two z-scores using a standard normal distribution table or a statistical software program. This area represents the probability that a clearance falls within the specification range. The area is approximately 0.9973, or 99.73%.

Therefore, we can say that there is a 99.73% probability that the specification for the clearance is met.

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overflow in two's complement arithmetic causes the wrap-around of the most significant bit, resulting in the representation of positive numbers as negative numbers.

In two's complement representation, numbers are represented using a fixed number of bits. The most significant bit (MSB) is reserved to indicate the sign of the number, where 0 represents a positive number and 1 represents a negative number.

Overflow occurs in two's complement arithmetic when the result of an operation exceeds the range that can be represented with the available number of bits.

When overflow occurs, the result is truncated or wrapped around to fit within the bit representation. This wrapping around effectively causes the MSB to flip its value, changing the sign of the number. As a result, the number that was intended to be positive becomes negative in the two's complement representation.

For example, consider an 8-bit two's complement representation. The range for a signed 8-bit number is -128 to +127. If we add 1 to the maximum positive value of 127, overflow occurs because the result exceeds the range. The binary representation of 127 is 01111111, and adding 1 results in 10000000. Since the MSB changed from 0 to 1, the number is interpreted as -128 in two's complement representation.

In summary, overflow in two's complement arithmetic causes the wrap-around of the most significant bit, resulting in the representation of positive numbers as negative numbers.

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The value of  cos 45° in the given triangle is 1/√2, Option C is correct.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

In the given right triangle the hypotenuse is 8√2

In the given triangle the two legs are equal.

Let x be the length of the two legs

By Pythagoras theorem, let us find the length of a leg.

x²+x²=(8√2)²

2x²=64(2)

2x²=128

Divide both sides by 2

x²=64

Take square root on both sides

x=8

Now let us find the cosine function, the ratio of adjacent side and hypotenuse

cos45 = 8/8√2

=1/√2

Hence, the value of  cos 45° in the given triangle is 1/√2, Option C is correct.

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The tangent vector (t), normal vector (n), and binormal vector (b) for the space curve r(t) = (-8e^t*cos(t))i - (8e^t*sin(t))j + 6k:

Tangent vector (t) = (-8e^t*sin(t))i + (8e^t*cos(t))j + 6k

Normal vector (n) = (-8e^t*cos(t))i - (8e^t*sin(t))j

Binormal vector (b) = -6e^t*cos(t)i - 6e^t*sin(t)j + 2e^t*k

The space curve is given by r(t) = (-8e^tcos(t))i - (8e^tsin(t))j + 6k.

To find t, n, and b for the space curve, we need to determine the tangent vector, normal vector, and binormal vector.

Tangent vector (t):

The tangent vector represents the direction of motion along the curve. It is obtained by taking the derivative of the position vector with respect to t.

r'(t) = (-8e^tcos(t))'i - (8e^tsin(t))'j + 0k

      = (-8e^tcos(t) + 8e^tsin(t))i + (8e^tsin(t) + 8e^tcos(t))j

Therefore, the tangent vector is t = (-8e^tcos(t) + 8e^tsin(t))i + (8e^tsin(t) + 8e^tcos(t))j.

Normal vector (n):

The normal vector represents the direction in which the curve is curving. It is obtained by taking the derivative of the tangent vector with respect to t and normalizing it.

n = (t') / ||t'||

To find n, we first need to find t'.

t' = ((-8e^tcos(t) + 8e^tsin(t)))'i + ((8e^tsin(t) + 8e^tcos(t)))'j

  = (-8e^tcos(t) - 8e^tsin(t) + 8e^tsin(t) + 8e^tcos(t))i + (-8e^tsin(t) + 8e^tcos(t) + 8e^tcos(t) - 8e^tsin(t))j

  = 0i + 0j

  = 0

Since t' is zero, the normal vector is undefined.

Binormal vector (b):

The binormal vector represents the direction perpendicular to both the tangent vector and the normal vector. It can be obtained by taking the cross product of the tangent vector and the normal vector.

b = t x n

Since the normal vector is undefined, the binormal vector is also undefined.

Therefore, for the space curve r(t) = (-8e^tcos(t))i - (8e^tsin(t))j + 6k, the tangent vector (t) is (-8e^tcos(t) + 8e^tsin(t))i + (8e^tsin(t) + 8e^tcos(t))j, and the normal vector (n) and binormal vector (b) are undefined.

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From the table, the domain are all real numbers and they can be substituted for x to return a valid f(x) value:

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.

By critically observing the table (see attachment), we can logically deduce that relationship between the amount of ink and the size of the sign is modeled by this function:

f(x) = x²

From the table, the domain are all real numbers and they can be substituted for x to return a valid f(x) value:

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Randy should begin his homework by 07:10 in order to sleep by 10:00

The given parameters are:

If the above activities are done, the time spent would be:

Time = 45 minutes + 40 minutes + 1 hour and 15 minutes + 10 minutes

Add the time

Time =  2 hour and 50 minutes

He wants to go to bed by 10:00.

So, the time to begin his homework is:

Begin = 10:00 - 2 hour and 50 minutes

Evaluate the difference

Begin = 07:10

Hence, Randy should begin his homework by 07:10

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Answer:true

Step-by-step explanation:

The test is one-tailed to the right due to the Alternate hypothesis.

In a hypothesis test, a Null hypothesis (H0) is a statement of "no effect" or "no difference," whereas the Alternate hypothesis (HA) is a statement of "some effect" or "some difference." Here are the correct null and alternative hypotheses for the given scenario: Null hypothesis: H0: μ = 71, Alternative hypothesis: HA: μ > 71 (One-tailed test) we have a one-tailed hypothesis test since the research hypothesis is directed. In a one-tailed test, we're looking for a difference in one direction only. In this case, Dr Carl thinks that there has been an improvement, so the alternative hypothesis reflects this. Therefore, the test is one-tailed to the right.

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The concept of hedonistic calculus is associated with utilitarianism and the philosophy of maximizing pleasure and minimizing pain. It is a method for calculating the overall happiness or utility of actions based on the intensity, duration, certainty, propinquity, fecundity, purity, and extent of pleasure or pain they produce.

Hedonistic calculus is a term coined by the philosopher Jeremy Bentham, who was a proponent of utilitarianism. Utilitarianism is an ethical theory that states that the right action is the one that maximizes overall happiness or utility for the greatest number of people. The goal of hedonistic calculus is to measure and compare the happiness or pleasure derived from different actions or situations.

According to Bentham, pleasure and pain are the only relevant factors in determining the moral value of an action. Hedonistic calculus involves quantifying these pleasures and pains in order to assess their overall impact. Bentham proposed seven criteria to evaluate the intensity, duration, certainty, propinquity (nearness in time), fecundity (likelihood of leading to more pleasure or pain), purity (absence of pain mixed with pleasure), and extent of the pleasure or pain produced by an action.

By assigning values to each of these criteria, hedonistic calculus aims to determine the net amount of happiness or utility generated by a particular action or decision. The idea is to maximize pleasure and minimize pain, with the ultimate goal of promoting the greatest happiness for the greatest number of individuals.

Overall, hedonistic calculus provides a systematic approach to assess and compare the consequences of actions based on their impact on pleasure and pain. It serves as a framework for utilitarians to make ethical judgments and decisions by considering the net balance of happiness produced by different choices.

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Given :

Each morning a gardener uses 25 gallons of water from a barrel.

Each afternoon, she adds 15 gallons of water to the barrel.

To Find :

By how much has the volume of water in the barrel changed after 5 days.

Solution :

Amount of of water used from the barrel per day is :

A = 25 - 15 gallons

A = 10 gallons

Now, volume of water in the barrel changed after 5 days is :

V = A × 5 gallons

V = 10 × 5 gallons

V = 50 gallons

Therefore, volume of water in barrel is changed by 50 gallons.

The rate of change of that linear function is.

The projected misstatement of this sample would be $50,000, calculated as follows: ($4,000 / $5,000) x $10,000.

In a probability-proportional-to-size sample, each item's chance of being selected is proportional to its recorded amount, so larger accounts have a higher probability of being selected. In this case, the auditor selected an account with a recorded amount of $5,000, but found that it had an audited amount of $4,000.

To project the misstatement of this sample, the auditor needs to estimate the total misstatement in the population by multiplying the audited amount by the inverse of the sampling fraction, which is the sampling interval divided by the recorded amount of the selected item. So, the projected misstatement is ($4,000 / $5,000) x $10,000 = $8,000 x 6.25 = $50,000. This means that the auditor estimates the total misstatement in the population to be approximately $50,000 based on this sample.

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The scatter plot of the data in the table is:

And there we can see that the data is similar to a line. We can say that the two values are associated by a linear correlation.

Answer: \(\sqrt{170}\)

Step-by-step explanation:

Distance formula: a^2+b^2=c^2 where c is the distance between two points

(-6-5)^2 + (4-(-3))^2=c^2

(-(6+5))^2 + (4+3)^2=c^2

(-11)^2 + 7^2=c^2

121 + 49=c^2

c^2=170

c=\(\sqrt{170}\)   ==> distance between A and B

The correct equation that describes the relationship between a sine and cosine wave is given by the trigonometric identity:

\(\[\sin^2(x) + \cos^2(x) = 1\]\)

In mathematics, sine (sin) and cosine (cos) are trigonometric functions that represent the ratios between the sides of a right triangle.

The relationship between these two functions is described by the fundamental trigonometric identity, known as the Pythagorean identity. The Pythagorean identity states that the square of the sine of an angle plus the square of the cosine of the same angle is always equal to 1.

The equation \(\sin^2(x) + \cos^2(x) = 1\) demonstrates this relationship. It states that if you square the value of the sine of an angle and add it to the square of the cosine of the same angle, the result will always be equal to 1. This equation holds true for any angle.

This relationship is significant because it allows us to relate the values of sine and cosine waves. As a result, we can express one trigonometric function in terms of the other. For example, if we know the value of the sine of an angle, we can determine the value of the cosine using the Pythagorean identity, and vice versa.

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The range of the function f(x) = log5x is (-∞, +∞).The function f(x) = log5x represents the logarithm base 5 of x. To determine the range of this function, we need to consider the possible values that the logarithm can take.

The range of the logarithm function y = log5x consists of all real numbers. The logarithm function is defined for positive real numbers, and as x approaches 0 from the positive side, the logarithm approaches negative infinity. As x increases, the logarithm function approaches positive infinity.

The range of the function is the set of all possible output values. In this case, the range consists of all real numbers that can be obtained by evaluating the logarithm

log5(�)log 5 (x) for �>0 x>0.

Since the base of the logarithm is 5, the function log5x will take on all real values from negative infinity to positive infinity. Therefore, the range of the function f(x) = log5x is (-∞, +∞).

In other words, the function can output any real number, ranging from negative infinity to positive infinity. It does not have any restrictions on the possible values of its output.

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Answer: All real numbers

Step-by-step explanation:

Edge

The coordinate of the point that represents the number of pens that Keisha buys and the total cost is (2, 4)

The given parameters are

Number of pen = 2

Unit price = $2

This means that the total amount spent is

Total amount = Number of pen * Unit price

Evaluate the product

Total amount = 2 * 2

Evaluate the product

Total amount = 4

So, the coordinate of the point that represents the number of pens that Keisha buys and the total cost is (2, 4)

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Answer:

No solution

Step-by-step explanation:

The given system of equations are ,

Adding both equations ,

=> 3x - y + y -3 x = -1-5

=> 0 = -6

Since we arrived at a contradiction the given pair of equations have No solution .