Sydney collects data on the number of hours it takes her classmates to complete a history project

Answer:

6 hours

Step-by-step explanation:

m= money in dollars earned

h= number of hours worked

you would replace m with the 51 since that is how much he earned in dollars and then solve the equations as such

51= 6h+15 (subtract 15 from both sides)

36=6h (then divide both sides by 6)

6=h

Answer:

the gcf is 4xyp

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

B would be the midpoint because it is in the middle of both showing thats where both points connect.

Answer: $3.50

Step-by-step explanation:28/8=3.5

=3.50

Answer: h=3.50

Step-by-step explanation:28/8=h. This is the equation because in order to find the answer you must find the unit rate. In order to do so you grab the total cost and than the amount of something and divide them in order to find the answer.

The coefficient of determination represents the proportion of the variation in the dependent variable that is explained by the independent variable(s).

Therefore, if the coefficient of determination is 0.422, it means that 42.2% of the data about the regression line is explained by the independent variable(s). The remaining percentage (100% - 42.2% = 57.8%) represents the portion of the data that is unexplained or attributed to other factors not accounted for in the regression model. Therefore, the answer is 57.8%.
Hi! If the coefficient of determination is 0.422, this means that 42.2% of the data's variation is explained by the regression line. To find the percentage of unexplained variation, subtract the explained percentage from 100%.

100% - 42.2% = 57.8%

So, 57.8% of the data about the regression line is unexplained.

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Answer: A

Step-by-step explanation

2.167x10^4 = 21,670

                   = 9,978

1.1x10^6      = 1100,000

                   = 56,344,000

2.468x10^5 =  246,800

Answer: A. 9,978

Based on the power, move the decimal point that many spaces to the right. (E.g., If it's 4.2 × 10^3, then move the decimal three spaces to the right, and you'd get 4200.)

2.167 × 10^4 = 21670

1.1 × 10^6 = 1100000

2.468 × 10^5 = 246800

Out of all the numbers mentioned in the question, 9,978 is the only one that's less than 2.167 × 10^4 = 21670.

Answer:

y=2/8x-5

Step-by-step explanation:

y=mx+b is slope intercept form

8y=2x-40

y=2/8x-5

As a result, the square root function has a range of [0,]. Any x value for which the radicand (the value below the radical sign) is not negative is the domain of a radical function.

This indicates that x  5 equals 0. due to the fact that the square root must always be positive or 0

All of a function's possible x-values, or inputs, are included in its domain. Both positive and negative numbers are included in this.

The fact that the square root of any real number x cannot be negative creates this problem. As a result, the system of real numbers does not contain the square root of a negative number.

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The choice of reference point can affect the calculation of potential energy but does not impact the factors that contribute to its increase.

The potential energy of an object is determined by several factors. The key factors that contribute to increased potential energy are:

Height or Elevation: The potential energy of an object increases with an increase in its height or elevation above a reference point. The higher the object is lifted, the greater its potential energy. This is because the object gains gravitational potential energy due to its position in a gravitational field.

Mass: The mass of an object also plays a role in determining its potential energy. As the mass of an object increases, its potential energy also increases. This relationship is evident in the formula for gravitational potential energy, where potential energy is proportional to both the mass and the height of the object.

Gravity: The force of gravity influences the potential energy of an object. The strength of gravity varies depending on the mass of the objects involved and the distance between them. In general, stronger gravitational forces result in higher potential energy.

Elasticity: In certain cases, potential energy can also be stored in elastic objects, such as a stretched spring or a compressed rubber band. When these objects are deformed from their equilibrium positions, they possess potential energy that can be released when they return to their original state.

It is important to note that potential energy is a relative measure, as it is defined with respect to a reference point or position. The choice of reference point can affect the calculation of potential energy but does not impact the factors that contribute to its increase. The factors mentioned above, such as height, mass, gravity, and elasticity, have a direct influence on the potential energy of an object and contribute to its overall magnitude.

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The correct option is option (a) $3,992.50. Pavi currently has a $3,992.50 credit on her current card.

The calculation of the provided data, according to the question, is as follows:

$8000 is the credit limit on the card.

Paid in Full = $2,500

$1,500 has been credited to the account.

The value of recent purchases made by Pavi is $3,000

Applied finance charges equal $7.50

The card's current balance is equal to $4,007.50.

Using the formula below, we can now determine the amount of credit that is now available on the card:

The credit line on the card = Available Credit - New Balance

By entering values into the formula provided, we obtain

Credit available on the current card: $8,000 - $4,007.50= $3,992.50.

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Answer:

c

Step-by-step explanation:

The probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes is found as  `0.7475`. Hence, the option D is correct.

The length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 2.5 minutes and a standard deviation of 0.75 minute.

We are supposed to find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.

So, we need to find `P(x < 3)` where `x` is the time taken to find a parking spot in the library parking lot.

Now, z-score will be

`z = (3 - 2.5)/0.75

= 0.67`

By looking at the z-score table, the probability that corresponds to z = 0.67 is 0.2514.

Therefore,

`P(x < 3) = P(z < 0.67)

= 0.2514 + 0.5

= 0.7514

≈ 0.7475 (approx)`

So, the correct option is `0.7475`. Hence, the answer is option D.

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Answer:

No, it is irrational

Step-by-step explanation:

8/6 is 1.333333333 a rational number is a whole while irrational never ends.

hope this helps!

Answer:

yes, 8/6 is  a rational number

The equation representing total fraction strip is  ³/₃ + ¹/₃ = ⁴/₃.

option B.

A fraction is a mathematical representation of a part of a whole or a ratio between two numbers. It consists of a numerator, which represents the number of parts being considered, and a denominator, which represents the total number of parts in the whole.

For this case, 1 is divided into, and 1 divide into 3.

To obtain the total fractions, we will add the individual fractions as shown below;

For this first fraction = ¹/₃ + ¹/₃ + ¹/₃

For the second fraction = ¹/₃

Total fraction = 3(¹/₃ + ¹/₃ + ¹/₃) + ¹/₃

Total fraction = ³/₃ + ¹/₃ = ⁴/₃

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A is finite, then X - A is clearly uncountable (since it has the same cardinality as X). If A is countable but not infinite, then X - A is still uncountable (since it has the same cardinality as X). Thus, the only interesting case is when A is countably infinite.

Let X be an uncountable set and A be a countably infinite subset of X. We need to show that X - A is uncountable. By contradiction, assume that X - A is countable. Since A is countably infinite, we can list its elements in a sequence as {a1, a2, a3, ...}. Now, consider the following sequence of sets:S1 = X - {a1}S2 = S1 - {a2}S3 = S2 - {a3}...Sn = Sn-1 - {an}...Observe that each Si is obtained by removing a finite set from X, and hence Si is uncountable. Moreover, Si is a subset of Si-1 for each i, so we have an infinite descending chain of uncountable sets. This contradicts the fact that X is uncountable. Therefore, X - A must be uncountable.Note that this argument works for any uncountable set X, regardless of its cardinality. We only need to assume that A is countably infinite. If A is finite, then X - A is clearly uncountable (since it has the same cardinality as X). If A is countable but not infinite, then X - A is still uncountable (since it has the same cardinality as X). Thus, the only interesting case is when A is countably infinite.

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Answer:

5

Step-by-step explanation:

The logarithm function, denoted as "log," is the inverse of the exponentiation function. This means that if we have the expression "log(x) = y," then "x" is the base "b" raised to the power "y." In other words, "x" is equal to "b^y."

Using this definition, we can simplify the expression "10^log5" as follows:

10^log5 = 10^y

Where "y" is the exponent to which the base "10" must be raised to produce the result "5."

To find the value of "y," we can use the property of logarithms that states "log(b^y) = y." Applying this property to our expression, we have:

log(10^y) = y

Since "10^y" is equal to "5," we can substitute "5" for "10^y" in the above equation:

log(5) = y

Solving for "y," we find that "y = log(5)."

Therefore, the expression "10^log5" can be simplified to:

10^log(5) = 10^(log(5)) = 5

So the simplified result is 5.

The valid sampling method(s) for obtaining a sample of individuals with high cholesterol from the list provided are simple random sampling, stratified sampling, and cluster sampling.

- Simple random sampling: This method involves randomly selecting 40 individuals from the list of 6800 individuals.

- Stratified sampling: This method involves dividing the list of 6800 individuals into different strata  based on relevant characteristics.

- Cluster sampling: This method involves dividing the list of 6800 individuals into smaller clusters (e.g., primary care physician offices or geographical areas).

This method is useful when it is difficult or costly to reach individuals scattered across a wide area.

Each of these methods has its advantages and disadvantages, so the choice depends on the specific needs and constraints of the pharmaceutical company.

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The number of ways can the selection be made is 84.

Given:

an executive hires 3 office workers from 8 applicants.

a ) .

Number of ways = C ( 8 , 3 )

C ( n , r ) = n! / ( n - r ) ! r!

C ( 8 , 3 ) = 8! / ( 8 - 3 ) ! 3!

= 8! / 5! * 3 !

= 8 * 7 * 6 * 5! / 5! * 3!

= 56 * 6 / 3!

= 56 * 6 / 3 * 2 * 1

= 56 * 3 / 2 * 1

= 28 * 3 / 1

= 28 * 3

= 84 ways

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Answer:

a(n) = 2 + 2(n - 1)

Step-by-step explanation:

Since each new term is derived from the previous term by adding 2, this is an arithmetic sequence, and the "common difference"  is 2.

Then a(n) = 2 + 2(n - 1)

We start by making the substitution $u = y'$. Then, we have $y'' = \frac{du}{dx}$, and we can rewrite the original equation as:

\(��2���2+2�=28�x dx 2 d 2 u​ +2u=28x 2\)

This is a linear homogeneous differential equation with constant coefficients. The characteristic equation is:

\(�2�+2=0r 2 x+2=0\)

which has roots $r = \pm i\sqrt{\frac{2}{x}}$. Therefore, the general solution for $u$ is:

\(�=�12�cos⁡(2�ln⁡(�))+�22�sin⁡(2�ln⁡(�))u=c 1​ x2​\)

​

\(cos( x2​ ​ ln(x))+c 2​ x2​ ​ sin( x2​ ​ ln(x)\))

where $c_1$ and $c_2$ are constants of integration.

To find $y$, we integrate $u$ with respect to $x$. Using integration by parts, we have:

\(�=∫���=∫2�cos⁡(2�ln⁡(�))��′=2\)

\(2�sin⁡(2�ln⁡(�))+�3y=∫udx=∫ x2​ ​ cos( x2​ ​ ln(x))dx ′ =2 2x​ sin( x2​ ​ ln(x))+c 3​\)

where $c_3$ is another constant of integration.

Therefore, the general solution for the original differential equation is:

\(�=22�sin⁡(2�ln⁡(�))+�3+�4�y=2 2x​ sin( x2​ ​ ln(x))+c 3​ +c 4​ x\)

where $c_4$ is a constant determined by the initial conditions of the problem.

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It is true that the binomial x + 1 is a factor of the polynomial P(x) = 5x^2 + 11x + 6

From the question, the given parameters are

Start by setting the binomial to 0

So, we have

x + 1 = 0

Solve for x in the above equation

x = -1

Substitute -1 for x in the polynomial equation P(x) = 5x^2 + 11x + 6

P(-1) = 5(-1)^2 + 11(-1) + 6

Evaluate

P(-1) = 0

Because P(-1) equals 0, then the binomial is a factor of the polynomial

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Answer:

k=a+7

Step-by-step explanation:

Take 1 k away from both sides. I hope you found this useful!

Answer:

k = \(\frac{7}{2-a}\)

Step-by-step explanation:

2k = ak + 7 ( subtract ak from both sides )

2k - ak = 7 ← factor out k from each term on the left side

k(2 - a) = 7 ( isolate k by dividing both sides by (2 - a) )

k = \(\frac{7}{2-a}\)

Answer:

angle dfe = 28°(by vertical opposite angle)

It will take 1.5 minutes to boil half liter of water .

Given,

Electric kettle take 3 minutes to boil a liter of water.

Now,

1 liter of water boils in 3 minutes .

so,

1 liter ⇒ boils in 3 minutes

1/2 liter ⇒ boils in 3/2 minutes

Thus,

1/2 liter boils in 1.5 minutes in an electric kettle .

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Answer:

the value of x is 135 i believe

Step-by-step explanation:

sorry if im wrong

Answer:

$ 7,299.92

Step-by-step explanation:

A = $ 7,299.92

A = P + I where

P (principal) = $ 6,000.00

I (interest) = $ 1,299.92

The values of x in the interval [0,2π] are given by:

\(\frac{5\pi}{6} \leq x\leq \frac{\pi}{6}\)

Given: 9 sin (x) \(\leq \frac{9}{2}\)

To find: Values of x in the interval \([0,2\pi]\).

Finding:

As 9 sin (x) \(\leq \frac{9}{2}\),

=> \(sin(x)\leq \frac{1}{2}\)

As, \(sin (\frac{\pi}{6})=sin(\frac{1}{2})\),

=> \(sin(x)\leq sin(\frac{\pi}{6})\)

=> \(x\leq \frac{\pi}{6}\), i.e., the principle value of x.

As sin (x) = sin (π - x), \(\pi -x\leq \frac{\pi}{6}\)

=> \(\pi -\frac{\pi}{6}\leq x\)

=> \(\frac{5\pi}{6}\leq x\)

Hence, the values of x in the interval [0,2π] are given by:

\(\frac{5\pi}{6} \leq x\leq \frac{\pi}{6}\)

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It will take approximately 2 hours and 3 minutes to fill the aquarium.

The aquarium at the zoo is in the shape of a cylinder with a height of 5 feet and a base radius of 3.5 feet.

To calculate the volume of the aquarium, we can use the formula for the volume of a cylinder, which is:

V = πr²h

Plugging in the given values we get:

V = π(3.5²)(5) = 192.5π cubic feet

Since one cubic foot is approximately 7.5 gallons, the aquarium has a volume of approximately 1443.75 gallons. If the aquarium is being filled at a rate of 12 gallons per minute, it will take approximately 120.3 minutes, or 2 hours and 3 minutes, to fill the aquarium.

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A is the linear function :)