On a scale drawing of a dock for a marina, 1 inch equals 18 feet. The dock is 250 feet long. What is the length of the dock on the scale drawing?

the solution (x = 3/2, y = 5) satisfies both equations, and therefore it is the correct solution.

We can solve this system of equations using either substitution or elimination method.

Using substitution method:

From the second equation, we can solve for x in terms of y:

4x + 2y = 16

4x = 16 - 2y

x = 4 - (1/2)y

Substitute this expression for x into the first equation:

4x + 3y = 21

4(4 - (1/2)y) + 3y = 21

16 - 2y + 3y = 21

y = 5

Now, substitute y = 5 into either of the original equations to solve for x:

4x + 2y = 16

4x + 2(5) = 16

4x + 10 = 16

4x = 6

x = 3/2

Therefore, the solution to is x = 3/2 and y = 5.

We can check this solution by substituting x = 3/2 and y = 5 into both equations:

4x + 3y = 21

4(3/2) + 3(5) = 6 + 15 = 21

and 4x + 2y = 16

4(3/2) + 2(5) = 6 + 10 = 16

So the solution (x = 3/2, y = 5) satisfies both equations, and therefore it is the correct solution.

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Answer: I belive the answer is 0lxoly+39.56

Step-by-step explanation:

SIKE

Answer:

x =~ 31.2

y =~ 18

z =~ 9

Step-by-step explanation:

cos 30º = 27 / x

0.8660 = 27 / x

x = 27 / 0.8660

x =~ 31.18

w = height (smaller trinagle w, y, z)

tg 30º = w / 27

0.5774 = w / 27

w = 27 * 0.5774

w = 15.5898

tg 30º = z / 15.5898

0.5774 = z / 15.5898

z = 0.5774 * 15.5898

z = 9.00155052

cos 30º = 15.5898 / y

0.8660 = 15.5898 / y

y = 15.5898 / 0.8660

y =~ 18

Therefore, the largest balance we should carry on this card to maintain an acceptable ratio is $2,117.75, which is option D.

By typically dividing two figures, ratios contrast them. If you were comparing one data point (A) to another data point, your formula would be A/B. (B). You are multiplying information A by information B, as indicated by this.

To maintain an acceptable credit utilization ratio, it is generally recommended to keep the balance on a credit card below 30% of the credit limit. In this case, the credit limit is $4,930, so we should aim to keep the balance below 30% of $4,930, which is:

0.3 * $4,930 = $1,479

Therefore, the largest balance we should carry on this card is $1,479.

None of the answer choices match this amount exactly, so we can calculate the ratio of each option to the credit limit to see which one is closest to 30%.

A. $2,807.25 / $4,930 ≈ 0.570 --> Not acceptable

B. $2,462.50 / $4,930 ≈ 0.500 --> Not acceptable

C. $2,119.90 / $4,930 ≈ 0.430 --> Not acceptable

D. $2,117.75 / $4,930 ≈ 0.429 --> Acceptable

Therefore, the largest balance we should carry on this card to maintain an acceptable ratio is $2,117.75, which is option D.

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a. The number of students that failed in all subject is 4

b. The percentage of students who failed one of economic and mathematics is 5.2%

c. The probability that a student at random failed is 1/10

A set is defined as the collect of item with similarities.

n( of student that passed math only) = 6

n( of students that passed account only) = 9

n( of students that passed economics only) = 16-(4+3+2)

= 16-9 = 7

n ( of student that passed math and account only) = 5

n( of student that passed account and economics only) = 2

n ( of student that passed math and economics only) = 18-(5+3+y) = 6

= 18-8-y = 6

= 10-y = 6

y = 4

n( of students that passed all the three subjects) =19-( 5+2+x) = 9

= 19-7-x = 9

= 12 -x = 9

-x = -3

x = 3

a. Therefore no of student that failed all subject =

6+9+7+5+2+4+3+z = 40

36+z = 40

z = 40-36 = 4

b. Student that failed at least math and economics = 4+9 = 13

= 13/40 × 100 = 5.2%

c. probability that a student at random failed = 4/40 = 1/10

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The height of the lighthouse from the top of the cliff is given as 25.3 cm

tan 37.2 = h / 825

h = 825 * 0.7590

h = 626.209

tan 38.3 = 626.209 + a / 825

825 tan 38.3 = 626.209 + a

651.55 = 626.209 + a

a = 651.55 - 626.209

a = 25 . 33 meters

Hence we can say that the height of the  lighthouse from the top of the cliff is given as 25 . 33 meters

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(A) The basis in which the space work is done is around 2. The powers of 10's logarithmic values can be used to determine this. (b) They could have two fingers for each hand, giving infants a total of five fingers.

a. The space creatures are most likely employed in a base other than base 10. The values of log 10, log 100, and log 1000 do not match the expected values for base 10, which should be 1, 2, and 3, respectively. Instead, the values given indicate that the base is slightly less than ten, because log 10 is less than one, log 100 is less than two, and log 1000 is less than three.

To be more specific, using the calculator's approximation, we can use the change of base formula to find the value of log base b for each of these numbers:

log base b of 10 = log 10 / log b ≈ 0.926628408

log base b of 100 = log 100 / log b ≈ 1.853256816

log base b of 1000 = log 1000 / log b ≈ 2.779885224

By dividing the known values of log 10, log 100, and log 1000, we can find log b:

0.473606797 log b = log 1000 / log 100

As a result, the space creatures are most likely based on 9.526.

b. It is impossible to determine how many fingers the space creatures have based solely on the calculator information and logarithm values. The space creatures' base could be related to the number of fingers they have, but we don't have enough information to tell.

The inverses of exponential functions, or those that "undo," the exponential functions, are the logarithmic functions.

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The line passes through the two points (-2,-9) and (3,-16).

We can write an equation in point-slope form using the following formula for the line passing through the point (-2,-9) and having a slope of m = -7/5:

y - y1 = m(x - x1)

where m is the slope of the line and (x1,y1) is the line's point.

Inputting the values provided yields:

y - (-9) = (-7/5)(x - (-2))

Simplifying:

y + 9 = (-7/5)(x + 2)

To get rid of the fraction, multiply both sides by 5. This gives us:

5y + 45 = -7(x + 2)

As we enlarge and rearrange, we obtain:

7x + 5y + 59 = 0

This is the line's standard form equation.

We can locate two points on the line and plot them to create a graph of the line. We can utilise the y-intercept, which is obtained by solving for y while setting x=0 in the equation:

7(0) + 5y + 59 = 0

5y = -59

y = -59/5

The y-intercept is therefore (0,-59/5). Using the slope, we may also locate a different point on the line:

m = -7/5

Beginning at (-2,-9), we can travel 7 units left and 5 units right to reach a different point:

(-2+5, -9-7) = (3, -16) (3, -16)

Hence, the line traverses both of the following two points: (3,-16).

Here is the line's graph:

     |

     |

*    |

 \   |

  \  |

   \ |

    \|

-------*-----------------

     |

    3|

     |

    2|

     |

    1|

     |

     |

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The answer is:

[tex]\sf{y+9=-\dfrac{7}{5}(x+2)}[/tex]

Work/explanation:

We need to determine the line's equation.  I will begin by writing the equation in point slope form:

[tex]\mapsto\phantom{333}\sf{y-y_1=m(x-x_1)}[/tex]

where m = slope and (x₁,y₁) is the point

Plug in the data:

[tex]\sf{y-(-9)=-\dfrac{7}{5}(x-(-2)}[/tex]

Simplify

[tex]\sf{y+9=-\dfrac{7}{5}(x+2)}[/tex]

x² - x - 6 = 0 is the standard form quadratic equation with solutions of -2 and 3.

There are two roots—or solutions—to a quadratic equation with real or complex coefficients. These two possibilities may or may not be distinct, and they may or may not be true. The standard quadratic equation, Y=x2x6, can be solved using the set of solutions 2, 3, which are given.

The elements of a quadratic equation whose solutions are -2 and 3 are (x + 2) and (3, respectively) (x - 3).

The total value of the quadratic equation is 0.

We can add the two elements together to obtain the quadratic equation in standard form:

(x + 2) (x - 3) = x²-3x+2x-6

Simplifying this expression, we get:

x²- x - 6 = 0

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Therefore , the solution of the given problem of percentage comes out to be F. 0.159.

A% is a figure or integer that in statistics is shown as a percentage of 100. Additionally, the words "pct.," "pct.," and "pc" are rarely used. But even so, the "%" indicator is commonly used to denote it. There are no dimensions; the percentage total is flat. Percentages are really just numbers because the numerator is always 100. To indicate that a number is a percentage, either the percent mark (%) or the phrase "percent" must appear before the number.

Here,

Divide by 100 to transform a percentage to a decimal. Therefore, we must locate a decimal between 0.11 and 0.17 in order to determine the figure that corresponds to a percentage between 11% and 17%.

The choices are as follows:

=> F. 0.159

=> G. 0.013

=> H. 11/1,000

=> J. 6/100

The decimal 0.159 falls within this range (0.11 to 0.17), so the solution is F. 0.159.

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In addition of fractions together student added the denominators together, which is the error in solution. You must have like denominators in order to add fractions together is the strategy for solution. Haley bought 7/8 pound of cheese.

We have a incorrect solution of problem consists addition and subtraction fractions. We have to identify error and solve problem correctly and also share a strategy for solution. Now the problem is defined as : Quantity of mozzarella cheese bought by Haley = [tex] \frac{3}{8} [/tex] pound

Quantity of parmesan cheese bought by Haley = [tex] \frac{1}{2} [/tex] pound

Total pound of cheese that she did bought = sum of parmesan cheese and mozzarella cheese

= [tex] \frac{3}{8} + \frac{1}{2} [/tex]

Incorrect work:

[tex] \frac{3}{8} + \frac{1}{2} = \frac{4}{10}[/tex] [tex]= \frac{2}{5} [/tex]

Identification and Explain the Error :

In the problem student correctly identified that this was addition of fractions however he was incorrect in solving. When adding fractions together you do not add denominators together.

He also forgot that you must have "like" denominators.

Correct Solution:

[tex] \frac{3}{8} + \frac{1}{2} [/tex]

For addition of fractions, make the same denominator in both of fractions. So, multiply the denominator and numentor in fraction 1/2 by 4.

[tex] = \frac{3}{8} + \frac{1 \times 4}{2\times 4} = \frac{3}{8} + \frac{4}{8} [/tex][tex] =\frac{7}{8} [/tex], which is the required solution.

Strategy: We do not add denominator together ever. You must have like denominators in order to add them together. Hence, Haley bought 7/8 pound of cheese.

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Complete question:

Error Analysis Adding and subtracting fractions :

Read the word problem. Look at the students work and solution. Identify the error and describe it. Solve the problem correctly. Then share a strategy this student could use to prevent the same error in the future. Haley bought 3/8 pound of mozzarella cheese and 1/2 pound of parmesan cheese. How many pound of cheese did she buy?

Incorrect work or solution : 3/8 + 1/2

= 4/10 = 2/5

Haley bought 2/5 pound of cheese.

Answer:

The conclusion is false.

Step-by-step explanation:

[tex]\frac{57}{3} = 19\\\\\frac{9}{3} = 3[/tex]

Although 3 and 9 do share some multiples, they must be divisible by 3. For example. 36/3 = 12, and 12 is divisible by 3. However, 57/3 = 19, which is not divisible by 3.

A bag of peanuts could be divided among 8 children, 9 children, or 10 children with each getting the same number, and with 2 peanuts left over in each case. The smallest number of peanuts that could be in the bag is 26.

This is because 8 children could each get 3 peanuts and there would be 2 peanuts left over, 9 children could each get 2 peanuts and there would be 2 peanuts left over, and 10 children could each get 2 peanuts and there would be 2 peanuts left over.

Small number means a number that is insufficiently large to be statistically significant, as determined by the department. Counting numerals are included in whole numbers as well. Whole numbers begin at zero. As a result, the least whole number is 0. Even though zero has no value, it is employed as a placeholder.

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The approximate distance between points T and U is 3.16 units, rounded to the nearest hundredth.(option c)

The problem states that we need to find the approximate distance between points T and U, rounded to the nearest hundredth. To solve this problem, we can use the distance formula, which is derived from the Pythagorean theorem. The formula is given as:

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Here, (x₁, y₁) and (x₂, y₂) represent the coordinates of the two points, and √ denotes the square root operation.

Now, let's apply this formula to find the distance between points T and U. Suppose that T has the coordinates (-2, 1), and U has the coordinates (-1, 4). Then, we can plug in these values into the formula and simplify:

distance = √[(-1 + 2)² + (4 - 1)²]

= √[(1)² + 3²]

= √(1 + 9)

= √10

≈ 3.16

Therefore, we can see that the correct answer is (c) 3.16 units.

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The proportion of green apples can be estimated in the same way: expressions  Green apple proportion = (number of green apples) / (Total number of fruits)

In mathematics, you can multiply, divide, add, or subtract. An expression is formed as follows: Expression, number, and math operator Numbers, parameters, and functions make up a mathematical expression. It is possible to contrast phrases and expressions. Every mathematical statement that contains variables, numbers, and a mathematical action between them is referred to as an expression. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the provided equation, all separated by the mathematical sign +.

a) Because the basket contains four different types of fruits, the proportion of cherries can be computed as follows:

Cherry proportion = (number of cherries) / (Total number of fruits)

We can't compute the proportion of cherries without knowing how many fruits are in the basket.

b) The proportion of green apples can be estimated in the same way:

Green apple proportion = (number of green apples) / (Total number of fruits)

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The volume of the larger cylinder is (25/8)πR³.

Volume is a measure of the amount of space occupied by a three-dimensional object. It is typically measured in units of cubic meters, cubic centimeters, cubic feet.

Let's denote the radius and height of the smaller cylinder as r and h, respectively, and the radius and height of the larger cylinder as R and H, respectively.

We know that the lateral area of a cylinder is given by the formula:

Lateral area = 2πrh

Using this formula for the smaller and larger cylinders, we get:

25π = 2πrh

64π = 2πRH

Dividing both sides of the first equation by 2π, we get:

rh = 25/2π

We also know that the following formula determines a cylinder's volume:

Volume = πr²h

Using this formula for the smaller cylinder, we get:

150π = πr²h

Substituting rh = 25/2π from above, we get:

150π = πr²(25/2π)

r² = 12

Taking the square root of both sides, we get:

r = √12 = 2√3

Substituting this value into rh = 25/2π, we get:

h = 25/(2πr) = 25/(4π√3)

Now, we can use the ratio of the lateral areas to find the ratio of the heights:

25π/64π = (2πrh)/(2πRH)

25/64 = rh/RH

25/64 = (2√3)(25)/(4πR)(H)

H = 2hR/r

Finally, we can use the formula for the volume of the larger cylinder to find its volume:

Volume = πR²H

Volume = πR²(2hR/r)

Volume = 2πR³h/r

Substituting the values we found for r, h, and H, we get:

Volume = 2π(R³)(25/(4π√3))/(2√3)

Volume = (25/8)πR³

Therefore, the volume of the larger cylinder is (25/8)πR³.

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Answer:

y = -2x² + 7x - 11

Step-by-step explanation:

To find the equation of a parabola that passes through the given points, we need to first determine the form of the equation.

A general form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants. To determine the values of a, b, and c, we substitute the coordinates of each point into the equation and solve the resulting system of equations.

Substituting the first point (-8, -309), we get:

-309 = a(-8)^2 + b(-8) + c

Substituting the second point (-5, -132), we get:

-132 = a(-5)^2 + b(-5) + c

Substituting the third point (1, 6), we get:

6 = a(1)^2 + b(1) + c

Substituting the fourth point (2, 1), we get:

1 = a(2)^2 + b(2) + c

Substituting the fifth point (6, -99), we get:

-99 = a(6)^2 + b(6) + c

Expanding the terms, we get a system of five equations:

64a - 8b + c = -309

25a - 5b + c = -132

a + b + c = 6

4a + 2b + c = 1

36a + 6b + c = -99

Solving the system of equations, we get:

a = -2

b = 7

c = -11

Therefore, the equation of the parabola that passes through the given points is:

y = -2x^2 + 7x - 11

So the answer is y = -2x² + 7x - 11. (^2 is just another version of ²)

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7 number of  students chose all three activities.

To find out how many students chose all three activities, we need to subtract the number of students who chose two activities from the total number of students. There are 76 students who chose sport, 64 students who chose music, and 40 students who chose drama. 12 students chose both music and sport, 7 chose both sport and drama, and 21 chose both music and drama. We can subtract these two-activity choosers from the total number of students to find out how many chose all three activities: 145 - (12 + 7 + 21) = 105. Therefore, 7 students chose all three activities.

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As a result of angle-angle-side (AAS) alignment, we have ABO, DBO, and AEO, CEO.

To prove △BEC≅△DEA:

First, we can see that segment AC and segment BD intersect at point O, which is the point of intersection of the angle bisectors of △BED.

Since AC and BD are angle bisectors, they are perpendicular bisectors of each other, so they divide the angles of △BED into congruent angles.

This means that angle ABO is congruent to angle DBO, and angle AEO is congruent to angle CEO.

Since angle ABO and angle AEO are vertical angles, they are congruent.

Similarly, angle DBO and angle CEO are vertical angles, so they are congruent.

Therefore, we have △ABO≅△DBO and △AEO≅△CEO by angle-angle-side (AAS) congruence.

Since BE is common to both triangles, we can conclude that △BEC≅△DEA by side-angle-side (SAS) congruence.

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Answer: El mínimo común múltiplo de 18, 30 y 42 es 630.

Step-by-step explanation:

j

Answer:

630. yes yes yyesss

The line is 13 units to the right (or shifted by -13 units).

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign.

When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

According to our question-

The ratio of y to x, which indicates how many units change in y when a specific number of units change in x, is used to express a line's slope.

A has a slope of 2 (x factor) = 2/1.

and as a result, y moves 2 units while x moves 1 unit.

B has a slope of 1 = 1/1.

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The angle of elevation is approximately 36.87 degrees and the horizontal distance is 264.6 feet

a.

The diagram is attached below;

b. We can use the tangent function to find the angle of elevation:

tan(θ) = opposite / adjacent

tan(θ) = 300 / 400

tan(θ) = 0.75

θ = tan^(-1)(0.75)

θ ≈ 36.87 degrees

So the angle of elevation from the boat to the parasail rider is approximately 36.87 degrees.

c. We can use the Pythagorean theorem to find the horizontal distance from the parasail rider to the boat:

d = √(400^2 - 300^2)

d ≈ 264.6 feet

So the horizontal distance from the parasail rider to the boat is approximately 265 feet.

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Answer:To solve this problem, we need to standardize the values of 55 and 63 to z-scores and then use the standard normal distribution table to find the area between those two z-scores.

The z-score for a value of 55 is:

z = (55 - 62) / 4 = -1.75

The z-score for a value of 63 is:

z = (63 - 62) / 4 = 0.25

Using a standard normal distribution table, we can find that the area to the left of z = -1.75 is 0.0401 and the area to the left of z = 0.25 is 0.5987. Therefore, the area between z = -1.75 and z = 0.25 is:

0.5987 - 0.0401 = 0.5586

To convert this area back to a percentage, we multiply by 100:

0.5586 * 100 ≈ 55.9%

Therefore, the answer is A. 55.9%.

Step-by-step explanation:

Answer:

Step-by-step explanation:

483278.4

Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:

v = d/t.

The parameters for the trip are given as follows:

Hence the velocity is obtained as follows:

230/7 = 32.86 miles per hour.

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Answer: 1/6

Step-by-step explanation:

1/1 - 5/6

2    6-5/6

2    1/6

Answer:

[tex]30x +68[/tex]

Step-by-step explanation:

[tex]6(9+5x)+14[/tex]

[tex]\text{Distribute the 6}[/tex]

[tex]30x +68[/tex]

the relationship between x and y given by the values (-3, -4), (2, 6), and (1, 4) is not a direct variation.

To determine whether the relationship between x and y is a direct variation, we need to check if y is directly proportional to x. In other words, we need to check if there is a constant of proportionality that relates the two variables.

To do this, we can calculate the ratio of y to x for each pair of corresponding values:

y/x = (-4)/(-3) = 4/2 = 2

y/x = 6/2 = 3

y/x = 4/1 = 4

If y is directly proportional to x, then the ratio of y to x should be the same for all pairs of corresponding values. However, in this case, the ratios are not equal. Therefore, the relationship between x and y is not a direct variation.

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