suppose the drain is opened on a tub containing 34 gallons of water. water drains out of the bathtub at a rate of 4 gallons per minute. however, the tap wasn't closed properly, so water is still flowing into the tub at a rate of 0.3 gallons per minute. how many minutes will it take for the tub to empty?

Answer:  A. x= 12 and -2

Step-by-step explanation:

x-5= 7  Solve for positive answer

x= 7+5=12

x-5= -7 Solve for negative answer

x= -7+5=-2

Answer: 324

Step-by-step explanation:

Ratio--> 1/0.15=x/48.6

Do the butterfly method of multiplying

0.15x=48.6

Divide by 0.15 on both sides

48.6/0.15=324

The 280 square foot lawn is in the designated area of a rectangular park that the city mayor wishes to use for gardening.

An object's area is how much space it takes up in two-dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The square-unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.

The rectangular park's allocated area is intended to be used by the city's public school for gardening courses.

The remaining area of the park will be developed into a lawn.

What is the lawn's formula?

The lawn's area is equal to the sum of its triangular and rectangle areas.

Lawn Area = 14 × 16 +.5 × 8 × 14

A = 224 + 56

A = 280 Ft²

Therefore, the correct option is 280ft² which is option C.

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The standard error of the average sample weight is 7.32 when 15 participants are randomly selected for the sample, rounded to two decimal places

The standard error of the average sample weight is calculated by dividing the standard deviation by the square root of the sample size. In this case, the standard error of the average sample weight is 35/√15 = 7.32. Thus, the standard error of the average sample weight is 7.32 when 15 participants are randomly selected for the sample. To calculate the standard error of the average sample weight, it is important to first determine the standard deviation of the population.

The standard deviation of the population, in this case, is 35. This is because it was found from the historical data that the weight of the participants is normally distributed with a mean of 175 lbs and a standard deviation of 35 lbs. Next, the standard deviation is divided by the square root of the sample size. In this case, the sample size is 15 participants. Thus, the standard deviation is divided by the square root of 15 (√15) which results in the standard error of the average sample weight which is 35/√15 = 7.32.

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The standard error of the average sample weight when 15 participants are randomly selected for the sample is       9.03 lbs. .

The standard error measures the accuracy with which a sample distribution represents a population by using standard deviation.

The formula for calculating the standard error of the mean is as follows:

Standard error = σ/√n

Where, σ = Standard deviation and n = sample size

Given that the standard deviation is 35 pounds, and the sample size is 15.

Therefore,

Standard error = σ/√n= 35/√15

= 35/3.873

= 9.0369 lbs

Rounded 9.0369 lbs to two decimal places we get, 9.03 lbs

Hence, the standard error of the average sample weight is 9.03 lbs when 15 participants are randomly selected for the sample.

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Answer:

1/2 + 1/8 + 1/3 + 1/2 + 1/8 + 1/3 = 23/12 = 1 (11/12)

the answer to the question is 5.20XY cubed.

How to solve the problem?

The square root of 18 X to the seventh power Y to the sixth power can be simplified using the laws of exponents and radicals. First, we can express 18 as a product of its prime factors: 18 = 2 x 3 x 3. Then, we can write X to the seventh power as X to the sixth power times X, and Y to the sixth power as Y to the third power squared.

So, we have:

Square root of 18 X to the seventh power Y to the sixth power

= Square root of (2 x 3 x 3) X to the sixth power X Y to the third power squared

= Square root of 2 X to the sixth power Y to the third power squared times 3

= Square root of 2 X to the sixth power Y to the third power squared times square root of 3

Using the laws of exponents and radicals, we can simplify the square root of 2 X to the sixth power Y to the third power squared as X cubed Y cubed, and we can approximate the square root of 3 as 1.73. Therefore:

Square root of 18 X to the seventh power Y to the sixth power

= X cubed Y cubed times square root of 3

= 3XY cubed times 1.73

= 5.20XY cubed (rounded to two decimal places)

So, the answer to the question is 5.20XY cubed.

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We can conclude that the lines are perpendicular, the slopes are negative reciprocals of each other,

What are the slopes?

To determine if the lines are parallel or perpendicular, we need to put both equations in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

y = 3x -x

-3y = -x + 4 (divide both sides by -3)

y = (1/3)x - (4/3)

Now we can see that the slope of the first equation is 3, and the slope of the second equation is (1/3). If two lines are perpendicular, their slopes are negative reciprocals of each other, meaning that one slope is the negative inverse of the other. The negative reciprocal of 3 is -1/3, and the negative reciprocal of 1/3 is -3. Since the slopes are negative reciprocals of each other, we can conclude that the lines are perpendicular.

The slope of a line can be positive, negative, zero or undefined. A positive slope indicates that the line is slanting upward from left to right, while a negative slope indicates that the line is slanting downward from left to right. A slope of zero indicates that the line is horizontal, while an undefined slope indicates that the line is vertical.

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In the word problem , Chris takes 40 ml of 20% alcohol and 160 ml of 60% alcohol.

What is percentage?

Divide the A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a number by the total and multiply by 100 to find the percent of a given number. Therefore, the percentage refers to a portion per hundred. Per 100 is what the word percentage signifies. The letter "%" stands for it.

Let the volume of 20% solution be x

Then volume of 60% solution is 200 - x

Alcohol in 20% solution = 0.2*x = 0.2x

Alcohol in 60% sol = 0.6(200-x) = 120 - 0.6 x

If the final solution is of 52% concentration, it means the volume of alcohol in it

= 200*0.52 = 104 ml

So we have the equation

=> 0.2x + 120 -0.6x = 104

=> 120-104 = 0.4x

=> 0.4x = 16

=> x = 40 ml

So he takes 40 ml of 20% alcohol and 160 ml of 60% alcohol.

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Answer:

Because the P-value of 0.0733 > , Lucy should fail to reject H0. There is not convincing evidence that the proportion of customers who will ask for a straw is less than 50%.

the area of the first sector piece is approximately 42.4115 square . and area of the second sector piece is approximately 149.03 cm².centimeters.

what is area of circle?

The area of a circle is given by the formula,where A is the area of the circle, r is the radius of the circle, and π (pi) is a mathematical constant that is approximately equal to 3.14159.In words, the area of a circle is equal to pi times the square of its radius.

In the given question,

The area of a sector of a circle is given by the formula:

A = (θ/360) * πr²

where:

θ is the angle at the center of the circle (in degrees)

r is the radius of the circle

π is the mathematical constant pi (approximately equal to 3.14)

In this case, the angle at the vertex of the sector piece is 60 degrees, and the radius is 9 cm. Therefore, the area of the sector piece is:

A = (60/360) * π * 9²

A = (1/6) * π * 81

A = 13.5π

A ≈ 42.4115 cm²

So the area of the sector piece is approximately 42.4115 square centimeters

A = π(8.4 cm)²

A = 221.76 cm²

Next, we need to find the fraction of the circle that corresponds to the given angle. The total angle of a circle is 360 degrees, so the fraction of the circle that corresponds to an angle θ in degrees is:

f = θ/360

Plugging in the given angle of 242 degrees, we have:

f = 242/360

f = 0.6722

So the area of the sector piece is:

A_sector = f * A

A_sector = 0.6722 * 221.76 cm²

A_sector = 149.03 cm²

Therefore, the area of the sector piece is approximately 149.03 cm².

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The area of the sector of for the given radius is 1. 42.4 cm² and 2. 152.9 cm².

A sector of a circle is an area that is bounded by two circle radii and the arc that runs between them. The length of the arc is proportional to the circumference of the circle, and the angle formed by the radii is known as the sector's central angle. The formula  A = (θ/360)πr² may be used to determine the area of a sector, where r denotes the radius of the circle, denotes the constant pi, and denotes the central angle in degrees.

The area of a sector can be calculated using the formula:

A = (θ/360)πr²

1. For r = 9 and theta = 60 we have:

A = (60/360)π(9)² ≈ 42.4 cm²

2. For r = 8.4 and theta = 242 we have:

A = (242/360)π(8.4)² ≈ 152.9 cm²

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So, the area of the composite figure is 96.57 square centimeters.

In geometry, area refers to the measure of the size of a two-dimensional surface or region. It is typically expressed in square units, such as square meters, square feet, or square centimeters.

To find the area of a shape, you need to measure the length and width of the shape and then multiply those measurements together. The formula for calculating the area of a rectangle, for example, is length x width. The formula for calculating the area of a circle is pi x radius squared, where pi is a mathematical constant, and the radius is the distance from the center of the circle to its edge.

by the question.

sure, I can help you with that!

To find the area of the composite figure, we need to find the area of each individual shape and then add them up.

First, let's find the area of the sector of the circle. We know that the radius of the circle is 6 cm, and the central angle of the sector is 82% of a full circle. Since a full circle has 360 degrees, we can find the central angle of the sector by multiplying 360 by 0.82:

[tex]Central angle of sector = 360 x 0.82 = 295.2 degrees[/tex]

The area of the sector can be found using the formula:

Area of sector = (central angle/360) x π x radius^2

Substituting the values, we know:

[tex]Area of sector = (295.2/360) x 3.14 x 6^2 = 56.57 cm^2[/tex]

Next, let's find the area of the triangle. We know that the base of the triangle is 8 cm, and the height is 10 cm. We can use the formula for the area of a triangle:

[tex]Area of triangle = 1/2 x base x height[/tex]

Substituting the values, we know:

[tex]Area of triangle = 1/2 x 8 x 10 = 40 cm^2[/tex]

Now, we can add the areas of the sector and the triangle to find the total area of the composite figure:

Total area = area of sector + area of triangle

[tex]Total area = 56.57 + 40 = 96.57 cm^2[/tex]

Rounding this to the nearest hundredth, we get:

[tex]Total area =96.57 cm^2[/tex]

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The smallest number of eggs that could have been in the basket = 301

Given that the basket is filled with an unknown number of eggs.

Let N be the smallest number of eggs in the basket.

When eggs are removed 2, 3, 4, 5, or 6 at a time, one egg is left over at the end which means (N-1) is divisible by 2, 3, 4, 5, or 6, i.e. (N-1) is the least common multiple of 2, 3, 4, 5, and 6.  

Since LCM (2, 3, 4, 5, 6) = 60

So, (N-1) should be a multiple of 60, then only (N-1) will be divisible by 2, 3, 4, 5, and 6. Therefore N is of the form 60k+1 (where k is an integer).

Since no egg is left over when they are removed 7 at a time, N should be a multiple of 7. Smallest multiple of 7 that is of the form 60k+1 (where k is an integer) is 301.

Hence the smallest number of eggs that could have been in the basket = 301.

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The probability that he gets exactly one rose given that at least one of the flowers he gets is pink is 4/7.

To calculate the probability that he gets exactly one rose given that at least one of the flowers he gets is pink, we need to use conditional probability. Let R be the event that he gets a rose and P be the event that he gets a pink flower. Then, we want to find P(R=1 | P≥1).

Using Bayes' theorem, we have:

P(R=1 | P≥1) = P(R=1 and P≥1) / P(P≥1)

We can calculate the probability of getting at least one pink flower as:

P(P≥1) = 1 - P(P=0)

Assuming the probabilities of getting a rose and a pink flower are independent, we can calculate the probabilities of getting exactly one rose and at least one pink flower as:

P(R=1 and P≥1) = P(R=1) * P(P≥1) = (2/5) * (1 - 3/5) = 2/5 * 2/5 = 4/25

P(P=0) = 3/5, since there are 3 flowers that are not pink out of a total of 5.

Therefore, we have:

P(R=1 | P≥1) = (4/25) / (1 - 3/5) = 4/7

So the probability that he gets exactly one rose given that at least one of the flowers he gets is pink is 4/7.

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a. The independent variable in this function is the amount of time a car is parked, measured in hours. The dependent variable is the cost of parking, measured in dollars.

b. "The cost of parking is a function of the amount of time a car is parked."

c. Here is a possible graph of the function:

           ^

           |

   $12     +--------/-----

           |      /      

           |    /        

           |  /          

   $3      o              

           |              

           |              

           |              

           +--------------->

                 Time

In this graph, the vertical axis represents the cost of parking in dollars, and the horizontal axis represents the amount of time a car is parked in hours. The graph shows a linear relationship between the two variables, with a slope of $3 per hour, up to a maximum cost of $12. This means that the cost of parking increases by $3 for each additional hour of parking, up to a maximum cost of $12.

Investment a grows faster than investment b, and thus investment b is the better choice.

We can calculate the worth of each investment after 1 year by applying the given rates of growth.

a. For investment a, the initial investment of $1000 grows by 10% per year. Therefore, the worth of the investment after 1 year is:

1000 + 0.1*1000 = $1100

b. For investment b, the initial investment of $3000 grows by $150 per year. Therefore, the worth of the investment after 1 year is:

3000 + 150 = $3150

Comparing the two worths, we see that investment b worth more after 1 year, since $3150 is greater than $1100. Therefore, investment b is the better choice.

Alternatively, we can also calculate the growth rates of each investment and compare them directly. For investment a, the growth rate is 10% = 0.1, whereas for investment b, the growth rate is 150/3000 = 0.05 or 5%. Since 0.1 > 0.05, we can again conclude that investment a grows faster than investment b, and thus investment b is the better choice.

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Answer:

The area of a parallelogram is given by the formula A = b × h, where b is the base length and h is the height. So, for each tile, the area is:A = 8.5 inches × 3.5 inches = 29.75 square inchesTherefore, the area of each tile is 29.75 square inches.

Step-by-step explanation:

So, the final equation for the sine function is:

[tex]y = 5 sin(2x - \pi /2) + 2[/tex].

The general form of a trigonometric equation can vary depending on which trigonometric function is being used (sine, cosine, tangent, etc.), but the most general form is:

[tex]f(x) = A sin(Bx + C) + D[/tex]

where f(x) is the trigonometric function, A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift. The phase shift and vertical shift are optional components and may not always be present in a trigonometric equation.

If using cosine instead of sine, the equation would be:

[tex]f(x) = A cos(Bx + C) + D[/tex]

If using tangent, the equation would be:

[tex]f(x) = A tan(Bx + C) + D[/tex]

Other trigonometric functions, such as secant, cosecant, and cotangent, can also be used in trigonometric equations, but the general form would follow the same structure as above.

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Answer:

1/4x

Step-by-step explanation:

1-1/3=3/3-1/3=2/3

3/8x(2/3)

6/24x

then simplify

1/4x

Step-by-step explanation:

From n=1, to n=4, plug this in the sigma notation

The first four terms of this series are

-4,-8/3,-16/9,-32/27

b. Since -1<r<1, the series diverge

c. The sum of an infinite geometric series is equal to

[tex] \frac{a}{1 - r} [/tex]

Where a is the initial value and r is the rate

a=-4

r =2/3

[tex] \frac{ - 4}{1 - \frac{2}{3} } = \frac{ - 4}{ \frac{1}{3} } = - 12[/tex]

Answer:

  7 cm

Step-by-step explanation:

You want the edge length of a cube whose space diagonal is 7√3 cm.

The square of the face diagonal of a cube of edge length s is ...

  d² = s² +s² = 2s²

The square of the space diagonal is found by applying the Pythagorean theorem again. The space diagonal is the hypotenuse of a right triangle whose legs are one cube edge and the face diagonal.

  D² = s² +d² = s² +2s² = 3s²

  D = √(3s²) = s√3

So, we want to find s when D = 7√3:

  s√3 = 7√3

  s = 7

The edge length of the cube is 7 cm.

The correct response is (D) since insufficient data exist to establish the number of junction points.

A circle is a geometric shape made up of all points in a plane that are equally spaced apart from a specific point known as the circle's center. The diameter of a circle is the distance through its center; the radius of the circle is the distance from any point on the circle to that point. A circle's circumference, which is measured around it, is equal to either two times the radius or one time the diameter. Several branches of mathematics, science, and engineering make use of circles.

given

Knowing the equation of the circle is necessary to figure out how many spots the line with the equation y = -3/4x + 25/4 touches the circle.

We are unable to calculate the number of points of intersection without this information.

The correct response is (D) since insufficient data exist to establish the number of junction points.

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The answer is either A or D, 0.045

Answer:

6, 2, and 3 would all also be 64° angles. 1, 4, 5, and 8 would all be 116° angles.

Step-by-step explanation:

Since 64° and 5 make up a supplementary angle (180°) just do the equation 180°-64° to get 116°. From there know that 64° and angle 6 must be equal (using the same logic from supplementary angles) then angles 2 and 3 must also be equal. Then apply that to angle 5 (which is 116°) and angle 8, as well as angles 1 and 4.

The given information can be summarized as follows:

Team: Cleveland Cavaliers

Height (in inches): 73, 75, 77, 79, 81

Range: 81 - 73 = 8

IQR: Q3 - Q1 = 81 - 75 = 6

Median: 79

Team: LA Clippers

Height (in inches): 76, 80, 83, 85

Range: 85 - 76 = 9

IQR: Q3 - Q1 = 85 - 80 = 5

Median: 81.5 (average of 80 and 83)

Using this information, we can evaluate the given statements:

#1: The LA Clippers have a greater variability of heights than the Cleveland Cavaliers.

This statement is true. The range of the LA Clippers' heights (9) is greater than the range of the Cleveland Cavaliers' heights (8).

#2: The shortest team member is 76 inches.

This statement is true. The LA Clippers have a player with a height of 76 inches, which is shorter than any player on the Cleveland Cavaliers.

#3: The second quartile of the LA Clippers is equal to the second quartile of the Cleveland Cavaliers.

This statement is false. The second quartile (or median) of the LA Clippers (81.5) is higher than the second quartile (or median) of the Cleveland Cavaliers (79).

#4: The median of the LA Clippers is approximately 80 inches.

This statement is true. The median of the LA Clippers is 81.5, which rounds to approximately 80 inches.

Step-by-step explanation:

The area of the rectangle can be calculated by multiplying its length and width. In this case, the length is 17 units and the width is 4 units.

Area = Length x Width

Area = 17 x 4

Area = 68 square units

Therefore, the area of the rectangle is 68 square units.

Step-by-step explanation:

5 % decrease means 95 %  (.95)  remain

Year 1

   800 * .95

   year 2  800 * .95  * .95

       .

       .

        year 5 = 800(.95)^5 = 619 deer after year 5

Answer: 35

Step-by-step explanation:

Let's assume that Mr. Nelson took "x" students on the trip.

According to the problem, the observatory charges a trip fee of $100, which Mr. Nelson had to pay regardless of how many students he took.

In addition to that, he also had to pay $6.50 per student. So the total cost of the trip can be expressed as:

Total cost = $100 + ($6.50 * number of students)

We know from the problem that the total cost of the trip was $327.50. So we can set up an equation:

$327.50 = $100 + ($6.50 * x)

Now we can solve for "x" by first subtracting $100 from both sides:

$327.50 - $100 = $6.50x

$227.50 = $6.50x

Finally, we can solve for "x" by dividing both sides by $6.50:

x = $227.50 ÷ $6.50

x ≈ 35

Therefore, Mr. Nelson took approximately 35 students on the field trip.

a. To rationalize the expression √√√4 + x = 3 3, we need to get rid of the cube roots in the denominator.

First, we simplify the cube root of 4:

√√√4 = √√2

So, our expression becomes:

√√2 + x = 3 3

To get rid of the cube root in the denominator, we need to multiply both sides by the conjugate of the denominator:

(3 - √2)(√√2 + x) = 3

Expanding the left side:

3√√2 + 3x - 2√2 - √2√√2x = 3

Simplifying:

3x - 2√2 - √2√√2x = 3 - 3√√2

Combining like terms:

(3 - √2)x = 3 - 3√√2 + 2√2

Simplifying:

(3 - √2)x = (3 + 2√2) - 3√√2

Dividing both sides by (3 - √2):

x = [(3 + 2√2) - 3√√2]/(3 - √2)

Simplifying:

x = (3 + 2√2)(3 + √2)/7

b. To rationalize and solve for x in the expression 1-√2:

We need to get rid of the radical in the denominator by multiplying both the numerator and denominator by its conjugate:

1 - √2 / 1 - √2 * 1 + √2 / 1 + √2

Simplifying, we get:

(1 - √2)(1 + √2) / (1 - √2)(1 + √2)

= 1 - 2

= -1

So, x = -1.

Therefore, the rationalized expressions are:

a. √√2 + x = (3 + 2√2)(3 + √2)/7

b. 1-√2 = -1

Answer:

2/4=1/2

Step-by-step explanation: