Write a system of equations to describe the situation below, solve using elimination, and fill in
the blanks.
The manager at a community pool is looking over receipts. On a certain Monday, the pool had
16 children and 42 adults, which brought in $142. That same week on Tuesday, 24 children
and 26 adults came to the pool, which brought in $102. What are the admission prices for
children and adults?

Many children develop the ability to do simple arithmetic problems during their early childhood years, typically between the ages of 4 and 6. Correct option is a).

During this time, children start to understand basic mathematical concepts such as counting, addition, and subtraction. They may also begin to recognize and name numbers and use basic math vocabulary. However, it's important to note that every child develops at their own pace and some may show these skills earlier or later than others. It's also important for parents and caregivers to provide opportunities for children to practice and reinforce these skills through activities such as counting objects, playing number games, and solving simple math problems.

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Answer:

It's 2

Step-by-step explanation:

One apple + another apple = 2 apples

Answer:

1+1=2

Step-by-step explanation:

1 cookie+1 cookie= 2 cookies or diabeties

Answer:

$51.75

Step-by-step explanation:

Answer:

$22

Step-by-step explanation:

4 * 5.50 = 22

Original Price = $18

Discounted Price = $15

Discount is $3 as 18-15 is 3.

As a fraction, the discount rate is $3/$18 also equal to $1/$6

1/6 is approximately 0.167

0.167 = 16.67%

As a percent, the discount rate is 16.67%

Using the formula,  Amount of Discount = Discount Rate · Original Price we can find the amount of discount for the 2nd week.

Let x be the amount of discount.

x = 25% · $18

x = $4.50

The amount of discount is $4.50

Calculate the cost of the CDs during the second week: $18 - $4.50 = $13.50

The price of a CD during the second week of the sale is $13.50

Using binary search to find the key 60 in the given list, the elements compared in order are: 38, 76, 60.

1. We start by comparing the key (60) to the middle element of the list, which is 38. Since 60 is greater than 38, we know that the key must be in the second half of the list.
2. Next, we compare the key to the middle element of the second half of the list, which is 76. Since 60 is less than 76, we know that the key must be in the first half of the second half of the list.
3. We then compare the key to the middle element of the first half of the second half of the list, which is 50. Since 60 is greater than 50, we know that the key must be in the second half of the first half of the second half of the list.
4. Next, we compare the key to the middle element of the second half of the first half of the second half of the list, which is 72. Since 60 is less than 72, we know that the key must be in the first half of the second half of the first half of the second half of the list.
5. Finally, we compare the key to the middle element of the first half of the second half of the first half of the second half of the list, which is 60. Since 60 is equal to 60, we have found the position of the key in the list.


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Answer:

Eight Hundred Twenty Million, Nine Hundred Forty-Seven Thousand, Two Hundred Thirty-Six

Step-by-step explanation:

Answer: eight hundred twenty million, nine hundred forty-seven thousand, and two hundred thirty-six

Step-by-step explanation:

(a) The number of students who were undergraduates, living off campus, or both is 38. (b) The number of students who were undergraduates living on campus is 30. (c) The number of graduate students living on campus cannot be determined from the given information.

Let's solve each part of the question step by step:

(a) To find the number of students who were undergraduates, living off campus, or both, we can use the principle of inclusion-exclusion. The total number of students surveyed is 60.

Number of undergraduates = 32

Number of students living off campus = 8

Number of undergraduates living off campus = 2

To find the number of students who were undergraduates, living off campus, or both, we can add the number of undergraduates and the number of students living off campus and then subtract the number of undergraduates living off campus to avoid double-counting:

Number of students who were undergraduates, living off campus, or both = Number of undergraduates + Number of students living off campus - Number of undergraduates living off campus = 32 + 8 - 2    = 38

Therefore, 38 students were undergraduates, living off campus, or both.

(b) To find the number of students who were undergraduates living on campus, we need to subtract the number of undergraduates living off campus from the total number of undergraduates:

Number of undergraduates living on campus = Number of undergraduates - Number of undergraduates living off campus = 32 - 2   = 30

Therefore, 30 students were undergraduates living on campus.

(c) The question doesn't provide the exact number of graduate students, so we cannot determine the number of graduate students living on campus from the given information.

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Answer:

multiply by

Convert from Convert to

US gpd US gpm cfm IMP gpd IMP gpm

m3/s 22800000 15852 2119 19000000 13200

m3/min 380000 264.2 35.32 316667 220

m3/h 6333.3 4.403 0.589 5277.8 3.67

liter/sec 22800 15.852 2.119 19000 13.20

liter/min 380 0.2642 0.0353 316.7 0.22

liter/h 6.33 0.0044 0.00059 5.28 0.0037

US gpd 1 0.000695 0.000093 0.833 0.000579

US gpm 1438.3 1 0.1337 1198.6 0.833

cfm 10760.3 7.48 1 8966.9 6.23

Imp gpd 1.2 0.00083 0.00011 1

Step-by-step explanation:

googled it

The Hamming distance metric is the best metric for describing how far apart two binary vectors of the same length are. The reason for this is that the Hamming distance is a measure of the difference between two strings of the same length.

Its value is the number of positions in which two corresponding symbols differ.To compute the Hamming distance, two binary strings of the same length are compared by comparing their corresponding symbols at each position and counting the number of positions at which they differ.

The Hamming distance is used in error-correcting codes, cryptography, and other applications. Therefore, the Hamming distance metric is the best for this particular question.

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To determine cos θ given sin θ = 1/4, 0 < θ < π/2, we can use the trigonometric identity involving sin θ and cos θ. Specifically, we can use the Pythagorean identity, sin² θ + cos² θ = 1, to solve for cos θ.

Since sin θ = 1/4, we can square both sides of the equation to get sin² θ = 1/16. Using the Pythagorean identity, we have cos² θ = 1 - sin² θ = 1 - 1/16 = 15/16.

Taking the square root of both sides, we find cos θ = ±√(15/16). However, since 0 < θ < π/2 and sin θ is positive, we can conclude that cos θ is positive as well. Therefore, cos θ = √(15/16) or simply √15/4.

In summary, given sin θ = 1/4 and the condition 0 < θ < π/2, we can determine that cos θ is equal to √15/4.

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The length of short side x is 4.5 units, the length of short side x+5 is 9.5 units and the length of longest side is 10.5 units.

By Pythagorean theorem,

\(( Hypotenuse)^{2} = (Base)^{2}+ (Perpendicular)^{2}\)

Let                base = x+5

     perpendicular = x

        Hypotenuse = x+6

                                    \((x+6)^{2} = x^{2} +(x+5)^{2}\)

                           \(x^{2} +12x+36 = x^{2} +x^{2}+10x+25\)\(2x^{2} +10x+25-x^{2} -12x-36=0\)

                             \(x^{2} -2x-11=0\)

                                               \(x = \frac{-(-2) + \sqrt{4 - 4(1)(-11)} }{2*1}\) or \(\frac{-(-2) - \sqrt{4 - 4(1)(-11)} }{2*1}\)

                                               \(x=\frac{2 + \sqrt{4 +44} }{2}\) or  \(\frac{2 - \sqrt{4 +44} }{2}\)

                                               \(x = \frac{2 + \sqrt{48} }{2}\) or \(\frac{2 - \sqrt{48} }{2}\)

                                               \(x = \frac{2+2\sqrt{12} }{2}\) or \(\frac{2-2\sqrt{12} }{2}\)

                                               \(x = 1+\sqrt{12}\) or \(1-\sqrt{12}\)

                                               \(x = 1+3.5\) or \(1-3.5\)

                                               \(x = 4.5\) or \(-2.5\)

As, length can't be negative, we will take x = 4.5

Therefore, x = 4.5

            x + 5 = 4.5 + 5

                      = 9.5

             x + 6 = 4.5 + 6

                       = 10.5

Hence, the length of short side x is 4.5 units, the length of short side x+5 is 9.5 units and the length of longest side is 10.5 units.

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Answer:

DB...hope I helped!

Step-by-step explanation:

Since m1+m2=180 and m1=76, then m2=104

m2=m4, so m4 is also 104

m3=m1, so it is 76

Hope I helped!

The minimum sterilization time required to achieve a 99.9% confidence level in successfully sterilizing 50 L of medium containing 10^6 contaminating organisms is approximately 1.95 minutes.

To calculate the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms, we need to use the concept of decimal reduction time (D-value) and the number of organisms.

The D-value represents the time required to reduce the population of microorganisms by one log or 90%. In this case, the given D-value is 0.65 minutes.

To achieve a 99.9% confidence level, we need to reduce the population of microorganisms by three logs or 99.9%, which corresponds to a 10^-3 reduction.

To calculate the minimum sterilization time, we can use the following formula:

Minimum Sterilization Time = D-value × log10(N0/Nf)

Where:

D-value is the decimal reduction time (0.65 minutes).

N0 is the initial number of organisms (10^6).

Nf is the final number of organisms (10^6 × 10^-3).

Let's calculate it step by step:

Nf = N0 × 10^-3

= 10^6 × 10^-3

= 10^3

Minimum Sterilization Time = D-value × log10(N0/Nf)

= 0.65 minutes × log10(10^6/10^3)

= 0.65 minutes × log10(10^3)

= 0.65 minutes × 3

= 1.95 minutes

Therefore, the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms using this procedure is approximately 1.95 minutes

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The probability that the entire system works is approximately 0.52, rounded off to the second decimal place.

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

Let A, B, and C represent the events that components A, B, and C work, respectively. Then, the probability that a component works is given as P(A) = P(B) = P(C) = p.

The probability that the entire system works is the probability that either A and B work and C does not, or A and C work and B does not. This can be expressed as:

P(system works) = P((A and B and C') or (A and B' and C))

Using the distributive property of probability, we can rewrite this as:

P(system works) = P(A and B and C') + P(A and B' and C)

Since the components work independently, we can apply the product rule of probability to each term:

P(system works) = P(A) * P(B) * (1 - P(C)) + P(A) * (1 - P(B)) * P(C)

Substituting P(A) = P(B) = P(C) = p, we get:

P(system works) = p² * (1 - p) + p * (1 - p)²

Simplifying this expression, we get:

P(system works) = p * (2p - 3p² + 1)

Substituting the given value of p, we get:

P(system works) = 0.8 * (20.8 - 30.8² + 1) ≈ 0.52

Therefore, the probability that the entire system works is approximately 0.52, rounded off to the second decimal place.

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The length of c→ is equal to the sum of the lengths of a→ and b→ when c→ is a perpendicular vector to both a→ and b→, meaning that c→ is at a right angle to both a→ and b→.

This is due to the fact that the length of a vector is equal to the length of the hypotenuse of a right triangle, which is the sum of the lengths of the other two sides (a→ and b→). When c→ is perpendicular to both a→ and b→, the right triangle formed by a→, b→, and c→ is a special type of right triangle called a Pythagorean triangle, in which the length of the hypotenuse (c→) is equal to the sum of the lengths of the other two sides (a→ and b→). Thus, the length of c→ is equal to the sum of the lengths of a→ and b→ when c→ is perpendicular to both a→ and b→.

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50,400 different anagrams can be made from the letters in the word statistics.

Given word : STATISTICS

Anagrams are words formed by jumbling the positions of the letters given in the word.

For such problems we do factorial of number of words and divide by the repeated letters factorials.

Total number of letters = 10

They can be permutated among themselves in 10! ways.

Some letters are repeated in word STATISTICS

Since, there are 3 S's and 3 T's and 2 I's

So, Number of anagrams = \(\frac{10!}{3!.3!.2!}\)

= \(\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3!}{3! \times 3 \times 2 \times 1 \times 2 \times 1}\)

= \(\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4}{3 \times 2 \times 2}\)

= 10 × 9 × 8 × 7 × 2 × 5

= 50,400

50,400 different anagrams can be made from the letters in the word statistics.

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Answer:

22,566

Step-by-step explanation:

the answer can be determined by subtracting 90486 from 113052

113052 - 90486 = 22,566

There are no real values for X and Y that satisfy the given equations X + Y = 17 and XY = 164.

To find the values of X and Y in the given equations, we can use a system of equations approach.

Let's start by solving the first equation, X + Y = 17, for one variable in terms of the other. We can choose to solve for X:

X = 17 - Y

Now, substitute this expression for X in the second equation, XY = 164:

(17 - Y)Y = 164

Expanding the equation gives us:

17Y - Y^2 = 164

Rearranging the equation to a quadratic form, we have:

Y^2 - 17Y + 164 = 0

To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

Y = (-(-17) ± √((-17)^2 - 4(1)(164))) / (2(1))

Simplifying further:

Y = (17 ± √(289 - 656)) / 2

Y = (17 ± √(-367)) / 2

Since the expression under the square root is negative, there are no real solutions for Y. This means that there are no real values for X and Y that satisfy both equations simultaneously.

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Answer:

British Government

Step-by-step explanation:

Answer:The Croatan

Step-by-step explanation: I am literally on the module two exam and it’s obvious Plus I read about this

Answer:

The answer is D

Step-by-step explanation:

Answer:

D) Quadrant IV (quadrant 4)

Step-by-step explanation:

Point C is in quadrant IV because its point is (4,-4)

For points that have a positive x-coordinate and a negative y-coordinate, that means they are in quadrant IV.

Another way to figure this out is by looking at this graphically:

                                    y

                                    |

         Quadrant           |          Quadrant

                II                  |                 I

                                    |

 ------------------------------|----------------------------- x

                                    |

          Quadrant          |           Quadrant

                III                 |                 IV

                                    |

I hope this helps!

Answer:

-3

Step-by-step explanation:

apply the same procedure for the other mixed numbers

multiply the results together

Answer:

2

Step-by-step explanation:

I wrote 3 3/5 as an improper fraction

5/9*18/5

Then I solved and simplified

I got 2

Ka and Kb are both acid-base equilibrium constants, but they apply to different types of reactions. Ka (acid dissociation constant) is used to describe the dissociation of an acid in water, while Kb (base dissociation constant) is used to describe the dissociation of a base in water.

Specifically, Ka is a measure of the strength of an acid in terms of how easily it donates a proton (H+) to a solvent like water. A higher Ka value indicates a stronger acid, while a lower Ka value indicates a weaker acid. Kb, on the other hand, is a measure of the strength of a base in terms of how easily it accepts a proton (H+) from a solvent like water. A higher Kb value indicates a stronger base, while a lower Kb value indicates a weaker base. There is a mathematical relationship between Ka and Kb for conjugate acid-base pairs, which are molecules or ions that differ by the presence or absence of a single proton. The relationship is expressed by the equation: Ka x Kb = Kw, where Kw is the ion product constant for water, which is 1.0 x 10⁻¹⁴ at 25°C. This relationship shows that the stronger the acid, the weaker its conjugate base, and vice versa.

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For the system of equations :

8x -2y = -16

y = 8 + 4x

has infinitely many solutions, and any value of x will give us a corresponding value of y that satisfies both equations.

For the system of equations :

7x - y = 2

-7x + y = 2

There are no solutions to this system of equations. The two equations are parallel and will never intersect.

To solve the system of equations, we can use the substitution method.

First, let's rearrange the second equation to isolate y: y = 8 + 4x

Now, we can substitute this expression for y into the first equation:

8x - 2(8 + 4x) = -16

Simplifying this equation gives us:

8x - 16 - 8x = -16

Simplifying further gives us:

-16 = -16

This is a true statement, but it does not give us a specific value for x or y. This means that the system of equations has infinitely many solutions, and any value of x will give us a corresponding value of y that satisfies both equations.

For the second system of equations, we can use the elimination method.

7x - y = 2

-7x + y = 2

Adding these two equations together gives us:

0 = 4 This is a false statement, which means that there are no solutions to this system of equations. The two equations are parallel and will never intersect.

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Answer:

d/10 + 600 + d/6 = 720

450 fts

Step-by-step explanation:

Given that:

Speed from hive to flowerbed = 10 ft/s

Time used in flowerbed = 10 minutes

Speed from flowerbed to hive = 6ft/s

Total time at which bee is away from hive = 12 minutes

Equation to find distance of flowerbed from hive :

Let distance from hive to flowerbed = d

Time taken = distance / speed

Time taken from hive to flowerbed = d/ 10

Time used in flowerbed = 10 minutes = (10 * 60) = 600 seconds

Time taken from flowerbed to hive = d/6

Total time away from hive = 12 mins = (12 * 60) = 720 seconds

A. What equation can you use to find the distance of the flowerbed from the​ hive?

Distance can be obtained from the formula :

d/10 + 600 + d/6 = 720

B. How far is the flowerbed from the​ hive?

d/10 + 600 + d/6 = 720

Take L. C. M of 10 and 6 = 30

(3d + 18000 + 5d) = 21600

8d + 18000 = 21600

8d = 21600 - 18000

8d = 3600

d = 3600/8

d = 450

Distance of flowerbed from hive = 450 fts

R-squared is an important statistic in regression, it measures how well the model fits the data.

What is regression ?

Regression is a statistical method used to analyze the relationship between one or more independent variables and a dependent variable. It is used to predict the value of the dependent variable based on the values of the independent variables.

One important statistic from the regression outputs is R-squared, it measures how well the model fits the data. It ranges from 0 to 1, and a higher R-squared value indicates a better fit. In other words, it represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It can provide an overall measure of how well the model is able to explain the variation in the dependent variable based on the independent variable(s).

The statistic that can be hardest to interpret and why can vary depending on the complexity of the model and the user's level of understanding of statistics. But one statistic that can be challenging for some people to interpret is the p-value, which is used to determine the statistical significance of the coefficients of the model.

R-squared is an important statistic in regression, it measures how well the model fits the data.

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The value of x is 42 degrees. the angle of the circle is twice on the circumeference.

A circle is a simple closed shape in Euclidean geometry, consisting of all the points in a plane that are equidistant from a given point called the center. The distance between any point on the circle and the center is called the radius of the circle. The circle is one of the most fundamental shapes in mathematics and is used in a variety of applications, from geometry and trigonometry to physics and engineering. The properties of circles have been studied for thousands of years and have led to many important discoveries in mathematics.

by the question.

The angle at the center of a circle is twice the angle at the circumference that subtends the same arc.

angle of NML = 1/2(angle of NOL)

x= 1/2(NOL)

X \(x=\frac{138}{2}\\ =69\)

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