Kathryn owns a video store. She rents games for 4 and moves for 4 She must rent at least 84 to make a profit She does not have anymore than 20 games Write and solve the system

Answer:

the number of children = 156

the number of adults = 183

Step-by-step explanation:

let x be the number of children

    y be the number of adults

We have to solve this system:

\(\begin{cases}x+y=339&\\ 1.75x + 2.50y = 730.50&\end{cases}\)

\(\Longleftrightarrow \begin{cases}y=339-x&\\ 1.75x + 2.50(339-x) = 730.50&\end{cases}\)

\(\Longleftrightarrow \begin{cases}y=339-x&\\ -0.75x + 847.5 = 730.50&\end{cases}\)

\(\Longleftrightarrow \begin{cases}y=339-x&\\ -0.75x =-117&\end{cases}\)

\(\Longleftrightarrow \begin{cases}y=339-156=183&\\ x =156&\end{cases}\)

An equation of the tangent line to the curve \(x e^y+y e^x=4\) at the point (0, 4) is \(y=-(4+e^4) x+4\).

A tangent is described as a line that intersects a circle or an ellipse only at one point. If a line touches a curve at P, the point "P" is known as the point of tangency.

Now according to the question;

To obtain the tangent at a given point, we must first obtain the slope at that point by obtaining the differentiation value at that point  \(\left.y^{\prime}\right|_{x=0, y=4}\) as-

Consider the given equation;

\(x e^y+y e^x=4\)

Differentiate both side with respect to x;

\(\begin{aligned}&\frac{d}{d x}\left(x e^y+y e^x\right)=\frac{d}{d x} 4 \\&\frac{d}{d x} x e^y+\frac{d}{d x} y e^x=0\end{aligned}\)

Now apply product rule;

\(\begin{aligned}&e^y \frac{d}{d x} x+x \frac{d}{d x} e^y+e^x \frac{d}{d x} y+y \frac{d}{d x} e^x=0 \\&e^y \frac{d}{d x} x+x \frac{d}{d y} e^y \cdot y^{\prime}+e^x y^{\prime}+y \frac{d}{d x} e^x=0\end{aligned}\)

Applying exponential and power rule;

\(\begin{aligned}&e^y \cdot 1+x e^y \cdot y^{\prime}+e^x y^{\prime}+y e^x=0 \\&\left(x e^y+e^x\right) y^{\prime}=-y e^x-e^y\end{aligned}\)

Solve the value of y'

\(y^{\prime}=\frac{-y e^x-e^y}{x e^y+e^x}\)

Now, find the value of slope m.

\(m=\left.y^{\prime}\right|_{x=0, y=4}\)

\(\frac{-4 \cdot e^0-e^4}{0 e^4+e^0}=-4-e^4\)

Now, using the point-slope formula, obtain the line equation as follows.

\(\begin{aligned}&\left(y-y_1\right)=m\left(x-x_1\right) \\&(y-4)=-(4+e^4) \cdot(x-0) \\&y=-(4+e^4) x+4\end{aligned}\)

Therefore, an equation of the tangent line to the curve is   \(y=-(4+e^4) x+4\).

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You will have approximately $1929.29 available to spend in 6 years.

To calculate the future value of your deposit after 6 years, we can use the formula for compound interest:

Future Value = Present Value * (1 + Interest Rate)^Time

Plugging in the values:

Present Value (PV) = $1491

Interest Rate = 5.07% = 0.0507

Time = 6 years

Future Value = $1491 * (1 + 0.0507)^6

Calculating the expression:

Future Value = $1491 * (1.0507)^6

Future Value ≈ $1929.29

Therefore, you will have approximately $1929.29 available to spend in 6 years.

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Answer: number name = 22 million

Expanded form: 22,000,000 = 20,000,000+2,000,000

Step-by-step explanation:

To write the number name and expanded form for the number of driver ants that could be in two colonies.

Given: Up to 22,000,000 driver of ants can live in a single colony

Since 1, 000, 000 =1 million

So 22,000,000= 22 million

Expanded form: 22,000,000 = 20,000,000+2,000,000

Hence, number name = 22 million

Expanded form: 22,000,000 = 20,000,000+2,000,000

Answer:

  100

Step-by-step explanation:

You want the number of distinct sequences of 4 letters from the word "problem" that have "l" as the first letter, and not "p" as the last letter.

There are 7 distinct letters in the word "problem". If the first letter of the "words" we're making must be "l", then the remaining three letters of the word are chosen from the remaining 6: "probem".

The number of permutations of 6 things taken 3 at a time is ...

  P(6, 3) = 6!/(6 -3)! = 6·5·4 = 120

That count includes the number that end in 'p'. When "l" is the first letter and "p" is the last letter, the middle two letters are chosen from the 5 "robem". There are 5!/(5-2)! = 5·4 = 20 ways to have words starting with "l" and ending in "p". We don't want to count those, so the number of letter sequences we can make is ...

  120 -20 = 100

100 distinct sequences of 4 letters can be made with first letter "l" and last letter not "p".

Answer:

Swaped

Step-by-step explanation:

Yes. Because the figure maintained its congruency throughout every rigid motion. According to Theorem 3-3, a rigid motion is the combination of two or more rigid motions.

Hence, Yes. Because the figure maintained its congruency throughout every rigid motion. According to Theorem 3-3, a rigid motion is the combination of two or more rigid motions. As a result, the original and final figures can be seen in agreement with each intermediate image.

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The parameter estimate is statistically different from zero when the absolute value of the t-statistic is greater than the critical value associated with the desired level of significance.

In hypothesis testing, the t-statistic is calculated by dividing the parameter estimate by its standard error. The t-statistic measures the number of standard errors the parameter estimate is away from the null hypothesis value (usually zero).

If the absolute value of the t-statistic is greater than the critical value, it means that the parameter estimate is significantly different from zero at the chosen level of significance. In other words, there is evidence to reject the null hypothesis and conclude that the parameter is not equal to zero.

The specific critical value depends on the desired level of significance and the degrees of freedom associated with the t-distribution. If the absolute value of the calculated t-statistic exceeds the critical value, it indicates that the parameter estimate is statistically significant and significantly different from zero.

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No, these two events cannot be disjoint. Disjoint events, also known as mutually exclusive events, are events that cannot occur simultaneously.

In other words, if events A and B are disjoint, it means that the occurrence of one event excludes the possibility of the other event occurring.

However, in this case, we are given that P(A) > 0 and P(B) > 0. This means that both events A and B have non-zero probabilities of occurring. Since both events have a positive probability, they cannot be disjoint because there is a possibility of their intersection, where both events occur simultaneously.

Disjoint events would have the property that P(A ∩ B) = 0, indicating that their intersection is an empty set. But given that P(A) > 0 and P(B) > 0, it implies that there is some non-zero probability for the events A and B to occur together, making them not disjoint.

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The statement is true. If we take any two distinct prime numbers, and the number "1", these numbers will always be pairwise relatively prime.

Two numbers are said to be pairwise relatively prime if their greatest common divisor (GCD) is equal to 1. In this case, since we are considering distinct prime numbers, their GCD will always be 1 since prime numbers have no common factors other than 1 and themselves. Therefore, any two distinct prime numbers will be relatively prime.

Similarly, when we consider the number "1", it is relatively prime to any other number because its only divisor is 1. Hence, when "1" is paired with any prime number, the GCD will be 1.

In summary, whether we consider two distinct prime numbers or pair them with the number "1", the resulting numbers will always be pairwise relatively prime.

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On solving we got that. he shorter pieces will therefore be 3 feet long and the longer pieces will therefore be 8 feet long.

Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity.

The lengths of the shorter and longer pieces of a board should be determined.

the case

Let's say that the shorter parts are x in length.

as stated

Jared has an 11-foot wooden board with him.

In order for the longer piece to be 4 feet less than 4 times as long as the shorter piece, he wants to cut it into two pieces.

The length of the longer pieces is then equal to 4x - 4.

The equation then becomes

\(x + 4x - 4 = 11\\ 5x = 11 + 4\\ 5x = 15\\ x = 3 ft\)

The shorter pieces will therefore be 3 feet long.

The longer pieces' length -

\(4x - 4\\ = 4 X 3 - 4\\ = 12 - 4\\ = 8 ft\)

The longer pieces will therefore be 8 feet long.

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angle 1 + angle 2 = 180 degrees

Step-by-step explanation:

supplementary angles add up to 180

Answer:

$150

Step-by-step explanation:

60x-2(15a)=y

x= hours; a= days working; y= profit

60x-30a=y

60(5)-30(5)=y

300-150=y

150=y

If U and V are orthogonal then the magnitude of U times V will be U.V = 0 or |UxV| = uv.

U and V are two orthogonal vectors.

since the angle between them is θ = 90⁰

let u and v be the magnitudes of the vectors U and V respectively.

so first dot-product: If two non-zero vectors are orthogonal than the dot product of these vectors will be zero. Dot product of two vectors is expressed by:

U.V = uv cosθ

since these vectors are orthogonal so,

U.V = uv cos90⁰ = 0

And Cross-product: Magnitude Cross product of two orthogonal vectors will be equal to product of magnitude of these vectors.

|UxV| = uv sin θ

|UxV| = uv sin 90⁰ = uv

Therefore, U.V = 0, |UxV| = uv.

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The first car traveled 100 kilometers in 2 hours, the second car covered 150 kilometers in 3 hours, the third car journeyed 200 kilometers in 4 hours, and the fourth car drove 250 kilometers in 5 hours.

The given information provides the distance traveled and the time taken by four different cars. The first car traveled 100 kilometers in 2 hours, indicating an average speed of 50 kilometers per hour. The second car covered a distance of 150 kilometers in 3 hours, resulting in an average speed of 50 kilometers per hour as well. Similarly, the third car journeyed 200 kilometers in 4 hours, with an average speed of 50 kilometers per hour. Lastly, the fourth car drove 250 kilometers in 5 hours, maintaining the same average speed of 50 kilometers per hour.

It is interesting to note that all four cars maintained a consistent average speed of 50 kilometers per hour, despite covering different distances and taking varying amounts of time. This implies that the cars were traveling at a constant speed throughout their respective journeys. The information provided does not indicate any changes in speed or fluctuations in the driving conditions. This consistency in speed suggests that the cars were likely traveling on a straight and uncongested road, allowing them to maintain a steady pace.

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The three possible values for a are:

a = -5^(1/3)/2

a = (5^(1/3)/4) - (5^(1/3)/4)isqrt(3)

a = (5^(1/3)/4) + (5^(1/3)/4)isqrt(3)

To find the coefficient of x^3 in the expansion of (2+x)(3-ax)^4, we can use the binomial theorem or Pascal's triangle to expand the expression.

However, since we are only interested in the coefficient of x^3, we can use the following approach:

The coefficient of x^3 in the expansion of (2+x)(3-ax)^4 will be the sum of the products of the coefficients of x and x^3 in the two factors, i.e.,

coefficient of x^3 = (coefficient of x in 2+x) * (coefficient of x^3 in (3-ax)^4) + (coefficient of x^3 in 2+x) * (coefficient of x^2 in (3-ax)^4)

The coefficient of x in 2+x is 1, and the coefficient of x^3 in (3-ax)^4 can be found using the binomial theorem:

coefficient of x^3 in (3-ax)^4 = (4 choose 3) * (3)^1 * (-a)^3 = -36a^3

The coefficient of x^3 in 2+x is 0 since there is no x^3 term in 2+x.

The coefficient of x^2 in (3-ax)^4 can also be found using the binomial theorem:

coefficient of x^2 in (3-ax)^4 = (4 choose 2) * (3)^2 * (-a)^2 = 54a^2

Substituting these values into the equation above, we get:

30 = 1 * (-36a^3) + 0 * 54a^2

Simplifying, we get:

-36a^3 = 30

Dividing both sides by -36, we get:

a^3 = -5/6

Taking the cube root of both sides, we get:

a = -5^(1/3)/2

This is one possible value for a.

Since a^3 = (-5/6) has three cube roots (one real and two complex), there are two more possible values for a, which can be found by multiplying the real cube root by the complex cube roots of unity (which are -1/2 + isqrt(3)/2 and -1/2 - isqrt(3)/2):

a = (-5^(1/3)/2) * (-1/2 + i*sqrt(3)/2) = (5^(1/3)/4) - (5^(1/3)/4)isqrt(3)

a = (-5^(1/3)/2) * (-1/2 - i*sqrt(3)/2) = (5^(1/3)/4) + (5^(1/3)/4)isqrt(3)

Therefore, the three possible values for a are:

a = -5^(1/3)/2

a = (5^(1/3)/4) - (5^(1/3)/4)isqrt(3)

a = (5^(1/3)/4) + (5^(1/3)/4)isqrt(3)

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The solution to the initial value problem is \(y = -10e^{\frac{-x^2}{2}}\). This mean that for any given x value, the corresponding y value is -10 multiplied by e raised to the power of -x squared divided by 2.

The initial value problem is a differential equation of the form y' = -2 and an initial value of y(0) = -10. This means that the slope of the function we need to find is -2, and the value at x = 0 is -10. To solve this kind of problem, we need to use the general solution for a differential equation of the form y' = k, which is\(y = Ce^\frac{kx}{2}\), where C is a constant. To find the value of C, we need to use the initial value, which is y(0) = -10, and substitute it into the general solution to get C = -10. Thus, our solution is \(y = -10e^\frac{-x^2}{2}\), which means that for any given value of x, the corresponding value of y is -10 multiplied by e raised to the power of -x squared divided by 2.

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Answer:

0, 1, 6, 4, second part: 4, Third part: 4 and 7

Step-by-step explanation:

...

Answer: the person above is correct

Answer:

B

i don't know how to explain what i did correctly but the answer is B

Answer:

D.

Step-by-step explanation:

x + 3 is 3 more laps

≥ 12 means at least 12.

Part A: The respondents in the population are a voluntary response sample.

Part B: The responses may not reflect the opinions of the general population

The total number of internet users in those is 1072 people.

The percentage of the total number of people that chose to respond is 38%

We can note that this survey does not compel the population to respond to the survey. These responses are given by the voluntary respondents.

Another point is that a voluntary response sample is a sample that consists of participants who are interested to participate in a sample group voluntarily.

In this type of survey, the people who are supposed to decide to provide voluntary responses to the survey are called voluntary response samples.

The percentage of those that chose to respond to this survey which is 38% is less than half of the total population. This result shows that the responses may not reflect the opinions of the general population.

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The value of b = -3/2 and c = -5/4

To write the quadratic x² - 3x + 1 in the form (x + b)² + c, we can expand (x + b)² and compare it to the given expression:

(x + b)² = x² + 2bx + b²

Comparing this to the given expression x² - 3x + 1, we see that we need:

2bx = -3x, so b = -3/2

b² + c = 1, so substituting b = -3/2 gives:

(9/4) + c = 1

so c = 1 - 9/4

= 4/4 - 9/4

= -5/4

The quadratic x² - 3x + 1 can be written in the form (x - 3/2)² + ( - 5/4).

Therefore, the value of b = -3/2 and c = -5/4

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Given question is incomplete, the complete question is below

the quadratic x²-3x + 1 can be written in the form (x +b)² + c, where b and c are constants. what is b, c?

1 teaspoon (tsp)  volume is equal to 4.92892159 milliliters (ml).

To convert teaspoons to milliliters, you can use this conversion factor.For example, to convert 5 teaspoons to milliliters you would multiply 5 by 4.92892159 which would give you 24.64460795 milliliters.

It's important to note that the teaspoon and milliliter are both units of measurement for volume. The teaspoon is commonly used in cooking recipes in the United States, while the milliliter is used in the International System of Units (SI).

When working with measurements in different units, it's important to know the correct conversion factors to ensure accuracy. These conversion factors can be memorized or looked up in a conversion table or calculator.

It's also worth noting that for larger volume measurements, you can use the liter (L) instead of the milliliter, since 1 L = 1000 ml.

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The subspaces are:B. {(x,y,z) | 3x−6y+2z=−8}C. {(x,y,z) | −5x+4y=0,−7x+8z=0}F. {(x,y,z) | 5x−4y+7z=0}Hence, the correct option is (B), (C), and (F).

A subspace is a subset of a vector space that satisfies the three axioms. Therefore, the given sets of R3 can be categorized as subspaces or not by using the three axioms of subspaces. Which of the following sets are subspaces of R3?A subspace has the following characteristics:It has the same dimension as the space. It contains the null vector. It is closed under vector addition. It is closed under scalar multiplication.Now, let's go through each option one by one.

A. {(x,y,z) | x,y,z>0}If we multiply any element of this set with a negative scalar, then we cannot obtain the same set. So it does not satisfy the third axiom. Therefore, it is not a subspace.

B. {(x,y,z) | 3x−6y+2z=−8}The set is a solution to a linear equation. It contains the null vector (0, 0, 0). The set is closed under vector addition and scalar multiplication. Therefore, it satisfies all three axioms of subspaces. So, it is a subspace.

C. {(x,y,z) | −5x+4y=0,−7x+8z=0}The set is a solution to a system of linear equations. It contains the null vector (0, 0, 0). The set is closed under vector addition and scalar multiplication. Therefore, it satisfies all three axioms of subspaces. So, it is a subspace.

D. {(x,x+5,x−4) | x arbitrary number}For any arbitrary value of x, we get a vector in this set. If we multiply any element of this set with a scalar, then we can obtain the same set. Therefore, it satisfies the third axiom of subspace. Also, it contains the null vector (0, 0, 0). But it does not satisfy the first axiom. So, it is not a subspace.

E. {(8x−2y,−3x+9y,6x−9y) | x,y arbitrary numbers}For any arbitrary values of x and y, we get a vector in this set. If we multiply any element of this set with a scalar, then we can obtain the same set. Therefore, it satisfies the third axiom of subspace. Also, it contains the null vector (0, 0, 0). But it does not satisfy the first axiom. So, it is not a subspace.

F. {(x,y,z) | 5x−4y+7z=0}The set is a solution to a linear equation. It contains the null vector (0, 0, 0). The set is closed under vector addition and scalar multiplication. Therefore, it satisfies all three axioms of subspaces. So, it is a subspace.The subspaces are:B. {(x,y,z) | 3x−6y+2z=−8}C. {(x,y,z) | −5x+4y=0,−7x+8z=0}F. {(x,y,z) | 5x−4y+7z=0}Hence, the correct option is (B), (C), and (F).

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Answer:

the right answer is

tan D=80/18

Answer:

x^3+11x

Step-by-step explanation:

((4^2+1)+(x^2-5))(x)

(16x+x^3-5x)

x^3+11x

Hence, when the is full, it will hold 700 liters of brine and 250 kg of salts dissolved in it.

The fundamental mass unit in the measuring units is the kilogram (kg). The weight of 1,000 cubic centimeters of water is very close to (and was initially planned to be exactly) one kilogram. The precise definition of a pound is 0.45359237 kg.

Let's first figure out how long is takes for the brine tank to fill.

The tank must be filled up to its maximum capacity of 700 liters, which is 100 liters of brine at first. As a result, the amount of brine that must be added is:

700 liters - 100 liters = 600 liters

The time required to fill it up 600 liters of brine if 8 liters of brine per second are injected into the tank is:

600 liters / 8 liters per second = 75 seconds

Let's check the tank's salt content after 75 seconds.

The amount of salt in the tank after 75 seconds is equal to: 100 kilograms (the original amount of salt) + (8 liters per unit - 6 each second) x 1 kilogram of salt per liter x 75 seconds. The rate of salt in the tank increasing is 1 kilogram per liter per second.

= 100 kilograms + 150 kilograms

= 250 kilograms

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Answer:

42

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

4 - 2 × 8 + (6 × 2) × 4 + 3²

= 4 - (2 × 8) + (6 × 2) × 4 + 3²

= 4 - 16 + 12 × 4 + 9

= (4 - 16) + (12 × 4) + 9

= -12 + 48 + 9

= 45