1/4 divided by 3/2 as a fraction

Answer:

Step-by-step explanation:

The fish tank will hold 12,960 cubic inches of water.

What is volume ?

Volume is a physical quantity that refers to the amount of space occupied by an object or a substance. In mathematical terms, volume can be defined as the measure of the three-dimensional space enclosed by a closed surface or shape. It is usually expressed in cubic units such as cubic meters, cubic feet, or cubic centimeters, depending on the system of measurement being used.

The volume of a rectangular prism can be calculated by multiplying its length, width, and height. Therefore, the volume of the fish tank is:

30 inches (length) x 24 inches (depth) x 18 inches (height) = 12,960 cubic inches

Therefore, the fish tank will hold 12,960 cubic inches of water.

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The two equations represent two lines in the plane that are parallel and never intersect, so there is no point that satisfies both equations simultaneously. No solution equations.

In mathematics, an equation is a statement that two expressions are equal. It consists of two sides separated by an equal sign (=). The expression on the left side of the equal sign is usually called the left-hand side (LHS), while the expression on the right side is called the right-hand side (RHS).

Equations can take many different forms and can involve various types of functions and operators, such as addition, subtraction, multiplication, division, exponentiation, logarithms, trigonometric functions, and more. They can also involve one or more variables, which can be solved for to obtain a specific value or range of values that make the equation true. Equations are used extensively in mathematics, science, engineering, economics, and many other fields.

We can solve this system of equations using the substitution method by solving one of the equations for one variable in terms of the other, and then substituting that expression into the other equation.

Let's solve the second equation for y in terms of x:

-x + y = 4

y = x + 4

Now we substitute this expression for y into the first equation and solve for x:

-2x + 2y = 7

-2x + 2(x + 4) = 7

-2x + 2x + 8 = 7

8 = 7

This last equation is a contradiction, which means that there is no solution to the system of equations. Geometrically, the two equations represent two lines in the plane that are parallel and never intersect, so there is no point that satisfies both equations simultaneously.

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Step-by-step explanation:

Factor out 3 a^2 b from the numerator to get :

3a^2b ( 2a-4a^2+5ab- b )  / 3a^2b       then the 3a^2b 'cancels out'

   and you are left with

   2a -4a^2 + 5ab - b    <====this is the answer

                                          but it can be further factored to:

2a (1-4a) + b(5a-1)   if you want this form

Answer:

2a -4a^2 + 5ab - b

Step-by-step explanation:

I did the test

Hope this help :)

Answer:

Step-by-step explanation:

Jasmine has 5 books that she wants to read. She wants to read the nonfiction book first and the mystery book last. Therefore, there are 3 remaining books that can be read in any order.The nonfiction book can be chosen in 1 way, and the mystery book can be chosen in 1 way. The remaining 3 books can be arranged in 3! (or 6) ways.Therefore, the total number of different orders in which Jasmine can read the books is:1 × 3! × 1 = 6 × 1 = 6So, there are 6 different orders in which Jasmine can read the books.

Answer:

The answer to your problem is, 11.25

Step-by-step explanation:

Formula used:

v = height x width x length

length = v / (width x height)

The volume equals 525, width 16 2/3 (16.67) and height 2 4/5 (2.8), replacing, length = 525 / (16.67 * 2.8)

Therefore the length being 11.25

Thus the answer to your problem is, 11.25

When the side of the ice cube is 6 cm, it is decreasing at a rate of approximately -0.0139 cm/sec.

To find the rate at which a side of the cubic ice cube is decreasing when the side is 6 cm, we need to use the chain

rule from calculus.

Let V be the volume of the cube and s be the side length. We know that [tex]V = s^3.[/tex]

Differentiate both sides of the equation with respect to time (t). This gives us [tex]dV/dt = 3s^2 × ds/dt.[/tex]

Plug in the given values. We know that dV/dt = -1.5 cm³/sec (since the volume is decreasing) and s = 6 cm.

Solve for ds/dt, which represents the rate at which a side of the ice cube is decreasing.

[tex]-1.5 = 3(6^2) × ds/dt[/tex]

Now, divide both sides by [tex]3(6^2)[/tex]:

ds/dt = -1.5 / (3 × 36)

ds/dt = -1.5 / 108

ds/dt ≈ -0.0139 cm/sec

So, when the side of the ice cube is 6 cm, it is decreasing at a rate of approximately -0.0139 cm/sec.

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The angle of elevation from the point where Josh is standing to the top of the tower is approximately 58.7 degrees.

How to calculate angle of elevation?

We can use trigonometry to calculate the angle of elevation:

tan(angle) = opposite/adjacent

In this case, the opposite is the height of the tower (199 feet) and the adjacent is the distance from Josh to the base of the tower (125 feet). So:

tan(angle) = 199/125

We can solve for the angle by taking the inverse tangent (tan^-1) of both sides:

angle = tan^-1(199/125)

Using a calculator, we find that:

angle ≈ 58.7 degrees

Therefore, the angle of elevation from the point where Josh is standing to the top of the tower is approximately 58.7 degrees.

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Answer:

Step-by-step explanation:

These questions all use Pythagorean Theorem to solve for x.

The hypotenuse is the side across from the right angle.

It is always c in the equation.

10)    a² + b² = c²

       x²   +  9² = 15²

       x²   + 81 = 225

      x²   + 81 - 81 = 225 - 81

       x²   =  144

     √x²   = √144

       x     = 12

11.    a²  +  b²   = c²

       x²  +  2²   = 5²

      x²    +  4    =  25

     x²    + 4 - 4 = 25 - 4

    x²   =  21

    √x²   =  √21

     x   = 4.58

13.    a²   +   b²   =  c²

       (1/5)²  +  (3/5)²   = c²

      1/25    +   9/25   = c²

      10/25  = c²

      √10/25 = √c²

      √10/√25 = √c²

       √10/5  = c

14.    a²   +  b²   = c²

      a²    +  (4/9)²  = (8/9)²

      a²     +  16/81  =  64/81

     a²   + 16/81 - 16/81 = 64/81 -16/81

      a²    =    48/81

   √a²     =   √48/81

     a   =  √48/√81

     a   =  4√3/9

we get a = -w1/w2b = -w0/w2

Therefore, the slope a is -w1/w2 and the intercept b is -w0/w2.

In this case, the relevant terms are "perceptron," "dimensions," and "equation."

A perceptron is a single layer neural network that processes information through a linear filter. It can be used for classification tasks and is especially useful in binary classification. The perceptron in two dimensions is given by the equation:

h(x) = sign(vyTx)where w = [w0, w1, w2] and x = [1, M, 2].

Technically, x has three coordinates, but we call this perceptron two-dimensional because the first coordinate is fixed at 1.We need to show that the regions on the plane where

h(x) = +1 and h(x) = -1 are separated by a line. To do this, we can set h(x) = 0 and solve for x. We get:

v(w0 + w1M + w22) = 0x2 = (-w0/w2) - (w1/w2)M

This is the equation of a line. The regions where h(x) = +1 and h(x) = -1 are separated by this line. We can express this line by the equation x2 = az + b,

where a and b are the slope and intercept of the line, respectively. To find a and b in terms of w0, w1, and w2, we substitute the equation of the line we found earlier into the equation for x2:(-w0/w2) - (w1/w2)M = az + bb = (-w0/w2)

Simplifying, we get:a = -w1/w2b = -w0/w2

Therefore, the slope a is -w1/w2 and the intercept b is -w0/w2.

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Hence, the likelihood that the following customer will purchase multiple costumes is 0.096.

Probability is the measurement of an event's likelihood. Probability aids in determining the chance of an event occurring because many events can really be predicted with 100% accuracy. It is the proportion of positive events to all of the events in such an experiment.

Given data:

There are a total of people present, which would be

= 171 + 148 + 34

= 353

The likelihood that the person after you will buy more than one costume must be determined.

Probability = favourable outcomes / total outcomes

Probability(multiple costumes)  = 34 / 353

Probability(multiple costumes)  = 0.096

Hence, the likelihood that the following customer will purchase multiple costumes is 0.096.

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We have: P(brown then yellow) = 2/11 and P(green then green) = 2/132.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

let's calculate the probability of selecting a brown marble followed by a yellow marble without replacement:

P(brown then yellow) = (4/12) * (6/11) = 24/132 = 2/11

We multiply 4/12 (the probability of selecting a brown marble on the first draw) by 6/11 (the probability of selecting a yellow marble on the second draw, after one brown marble has already been removed). Note that we divide by 11 on the second draw, as there are now only 11 marbles left in the bag.

Now let's calculate the probability of selecting two green marbles without replacement:

P(green then green) = (2/12) * (1/11) = 2/132

We multiply 2/12 (the probability of selecting a green marble on the first draw) by 1/11 (the probability of selecting another green marble on the second draw, after one green marble has already been removed). Again, note that we divide by 11 on the second draw, as there are now only 11 marbles left in the bag.

So, we have:

P(brown then yellow) = 2/11

P(green then green) = 2/132

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The value of Z is -66.7

What is an inverse function?

An inverse in mathematics is a function that "undoes" another part. In other words, if f(x) produces y, y entered into the inverse of f producing x. An invertible function has an inverse, and the inverse is represented by the symbol f1.

Here, we have

Given: Suppose x varies directly as y, and x varies inversely as z.

Find z when x= 10 and y= −7, if z= 20 when x= 6 and y= 14.

X = K(Y/Z) if x =10, y=-7, Z=20

substituting in the equation 10 = K(-7/20)

solving for K = -28.6

When x = 6, Y = 14, and K(constant) = -28.6

6 = -28.6(14/Z)

solving for Z by cross multiplication, we get

Z = -66.7

Hence, the value of Z is -66.7

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Therefore , the solution of the given problem of triangle comes out to be curve C has a measure of 70 degrees.

If a polygon has at least one additional segment, it is a hexagon. Its structure is a simple rectangle. Something like this can only be distinguished from a regular triangular form by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.

Here,

Sum of Triangle Angles According to a theorem, a triangle's internal angles always add up to 180 degrees.

We are aware that angle B in the trapezoid is 50 degrees and angle A is 60 degrees. As a result, we can apply the Triangle Angle Sum Theorem to determine the size of angle C:

Angle A +Angles B + C = 180 degrees.

With the known numbers substituted, we obtain:

Angle C:  60° + 50°+60° = 180°

By condensing the left half, we obtain:

Angle C = 180-110 degrees

By taking away 110 degrees from each side, we arrive at:

C = 70-degree slope.

As a result, curve C has a measure of 70 degrees.

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The area left for development in the field outside the playground is C)1024[tex]ft^2[/tex].

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.

We know  that area of rectangle formula is,

Area = [tex]length\times breadth[/tex] square unit

The total area of the field is the area of the large rectangle, which is:

=> [tex]28 \times48 = 1,344 ft^2[/tex]

The area of the playground is the area of the smaller rectangle, which is:

=> [tex]20 \times 16 = 320 ft^2[/tex]

Therefore, the area left for development outside the playground is:

=> [tex]1,344 ft^2 - 320 ft^2 = 1,024 ft^2[/tex]

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Answer:

11 children and 34 adults

Step-by-step explanation:

let children be x and let adult be y

15x+25y=1015

x+y=45

*simultaneous equation

x=11, y=34

(11*15)+(34*25)

=165+850

=1015

2. The farthest distance that a student rode during Friday's ride is 35 miles.

3. The longest time that a student rode during Friday's ride is 120 minutes.

6. 15 minutes.

7. 4 miles.

A cluster in a scatter plot is a group of points that are close to each other. Clusters helps to visualize the spread of data.

2. The farthest distance that a student rode during Friday's ride is 35 miles.

3. The longest time that a student rode during Friday's ride is 120 minutes.

4. The first cluster consists of points with lower values for t and higher values for s. This cluster is composed of riders who trained on mountain roads, as the lower values for t indicate that it took longer for them to cover the same distance as the other group.

The second cluster consists of points with higher values for t and lower values for s. This cluster is composed of riders who trained on flat roads, as the higher values for t indicate that it took them less time to cover the same distance as the other group.

6. The shortest time that a family member rode during Friday's ride was 15 minutes.

7. The longest distance that a family member rode during Friday's ride was 4 miles.

8. The data on the scatter plot is broken into two clusters because there are two distinct groups of data points.

The first cluster consists of points (15,2), (20,2), and (25,2), which indicate that a family member rode for 15, 20, and 25 minutes, respectively, and traveled a distance of 2 miles each time.

The second cluster consists of points (40,4), (50,4), and (60,4), which indicate that a family member rode for 40, 50, and 60 minutes, respectively, and traveled a distance of 4 miles each time.

This could be explained by the fact that a family member rode for a longer period of time and traveled a longer distance on Friday than the other family members.

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The true average amount of warpage in all such pieces of laminate lies between 0.0609 and 0.0653 inches with 99% confidence.

a) To construct a 99% confidence interval for the average amount of warpage in all such pieces of laminate, we can use the formula:

CI = X ± Z × (s / √n)

where X is the sample mean warpage, Z is the Z-value from the table below, s is the sample standard deviation and n is the number of observations.

The Z-value for a 99% confidence interval is 2.576. (refer the image)

Plugging in the values we get:

0.0631 ± 2.576 × (0.0072 / √45)

= [0.0609, 0.0653]

b) To construct a 90% confidence interval for the average amount of warpage in all such pieces of laminate, we can use the same formula as above but with a different Z-value.

The Z-value for a 90% confidence interval is 1.645.

Plugging in the values we get:

0.0631 ± 1.645 × (0.0072 / √45)

= [0.0618, 0.0644].

c) Because we need to be more positive that our interval contains the genuine population mean as our confidence level rises, the interval for a 99% confidence level is greater than that for a 90% confidence level. This suggests that in order to account for all possible values of the population mean, we must widen our interval.

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Thus,  78% of the people surveyed,  shopped at a local grocery store.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Grocery Options:

                                Store           Online          Total

Women                     32                 9                  41

Men                           28                8                   36

Total                          60               17                  77

Total people = 77

Total people who shop at a local grocery store = 60

Thus,

Percentage = 60/77 *100  = 77.92% = 78%

Thus,  78% of the people surveyed,  shopped at a local grocery store.

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Using dilation, we can find the area of the new trapezoid to be 3.4y unit². So, the correct option is Option B.

The dimensions of the new shape are scale factor. It can be calculated using the original shape's dimension as the fundamental formula. The formula is scale factor = larger figure dimensions. Reduced figure dimensions if the original figure is expanded.

Area of the trapezoid QRST is = y unit².

Scale factor by which QRST is dilated = 3.4

Now area of new trapezoid Q'R'S'T'

= old area × scale factor.

= y × 3.4

= 3.4y unit²

Therefore, area of the new trapezoid will be = 3.4y unit².

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Answer:

y = (7/3)x - 8/3

Step-by-step explanation:

Hope this helps:

To find the slope-intercept form of the equation of the line through the points (1, -5) and (4, 2), we need to first find the slope of the line.

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:

m = (y2 - y1) / (x2 - x1)

Using the coordinates of the two given points, we get:

m = (2 - (-5)) / (4 - 1)

m = 7 / 3

Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation of the line:

y - y1 = m(x - x1)

Using the point (1, -5) and the slope we just found, we get:

y - (-5) = (7/3)(x - 1)

Simplifying and rearranging the equation, we get:

y = (7/3)x - 8/3

So the slope-intercept form of the equation of the line passing through the points (1, -5) and (4, 2) is:

y = (7/3)x - 8/3

Step-by-step explanation:

The angle 'x' and the angle 65  form a straight line which is 180 degrees

x + 65 = 180

x = 180 - 65

x = 115 degrees

Answer: The answer is 115°

Step-by-step explanation:

we know that the angle of the straight line is 180°.

here, X= 180°- 65°

therefore, X=115°

Expected counts are calculated by the test of independence and also by using Homogeneity.

The main difference between a test of independence and a test of uniformity when analyzing voting results from a two-page table is how the expected count is calculated.

The test of independence calculates expected frequencies assuming no relationship between the two variables analyzed and is based on the marginal totals of the two-way table.

Independence tests are used to know whether there is a significant association between two variables or not.

Homogeneity tests, on the other hand, compute expected frequencies assuming that the two groups being compared have the same distribution for the variable being analyzed, based on the row sums of a two-way table.

Homogeneity tests are used to know whether there is a  difference in the distribution of a categorical variable between groups.

The number of columns and rows in the two-way table and the number of samples obtained are important factors to consider when performing both tests.

However, how the expected count is calculated is the main difference between the two tests. The degrees of freedom are also calculated differently for the two tests, but this is secondary. 

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Step-by-step explanation:

3 is the Gulf of Mexico

1 is the Caribbean Sea

Answer:

The answer is C.

Step-by-step explanation:

The Gulf of Mexico is located in between America and Cuba.

Answer:

The correct answer:

C. 7

3(2) + 1 = 6 + 1 = 7

Step-by-step explanation:

So the question is 3x+1. We are given the information that x=2. Therefor we would plug in 2 to where x is. 3(2)+1. Now we would multiply first for 6+1. Add to get 7. 7 would be our answer giving us C.

ANSWERS:

A. 0.28 ( 28.41% )
B. 89.29%

EXPLANATIONS:

(a) The probability of a randomly chosen U.S. adult investing in both stocks and fixed income instruments is given as 0.25. The probability of a U.S. adult investing in fixed income instruments is 0.88. Using the formula for conditional probability, we have:

P(invests in stocks | invests in fixed income instruments) = P(invests in both stocks and fixed income instruments) / P(invests in fixed income instruments)

= 0.25 / 0.88

= 0.2841 (rounded to the nearest hundredth)

Therefore, the probability that a randomly chosen U.S. adult invests in stocks, given that he or she invests in fixed income instruments is 0.28 (rounded to the nearest hundredth).

To convert A to a percentage, simply multiply it by 100:

A = 0.2841

A as a percentage = 0.2841 x 100% = 28.41% (rounded to two decimal places)

(b) The probability of a randomly chosen U.S. adult investing in both stocks and fixed income instruments is 0.25, and the probability of a U.S. adult investing in stocks is 0.28. Using the formula for joint probability, we have:

P(invests in both stocks and fixed income instruments) = P(invests in stocks) × P(invests in fixed income instruments)

= 0.28 × 0.88

= 0.2464

The probability that a randomly chosen stock investor also invests in fixed income instruments is 0.25 / 0.28 = 0.8929 (rounded to the nearest hundredth), which is equivalent to 89.29%.

Approximately 88.5% of the scores were lower than Bill's. The score must be at least 432.6 to be in top 11%. Q1 ≈ 251.3, Q3 ≈ 386.7.Jane's percentile is approximately 93.3%. Ann will receive a score of 357.4.

The invNorm is a mathematical function that calculates the inverse of the cumulative normal distribution. It is used to find the value of a standard normal variable for a given probability. The standard normal distribution is a normal distribution with a mean of zero and a standard deviation of one. The function takes a probability value as an input and returns the corresponding z-score, which represents the number of standard deviations from the mean. The invNorm function is commonly used in statistics and probability theory to find critical values for hypothesis testing, confidence intervals, and other statistical calculations.

a. To find the percentage of scores lower than Bill's score of x = 432, we need to find the area under the normal curve to the left of 432. Using the mean of m = 319 and the standard deviation of s = 94, we can standardize Bill's score as follows:

z = [tex]\frac{(x - m)}{s}[/tex]  = [tex]\frac{(432 - 319)}{94}[/tex]  = 1.2

Using a standard normal distribution table, we can find that the area to the left of z = 1.2 is approximately 88.5%. Therefore, approximately 88.5% of the scores were lower than Bill's.

b. To find the score that corresponds to the top 11%, we need to find the z-score that has an area of 0.11 to its right. Using a standard normal distribution table or calculator, we can find that the z-score that corresponds to an area of 0.11 to the right is approximately 1.22. Therefore, we can solve for the score as follows:

z =  [tex]\frac{(x - m)}{s}[/tex]

1.22 = (x - 319) / 94

x - 319 = 1.22 × 94

x = 319 + 1.22 × 94

x ≈ 432.6

Therefore, a score of at least 432.6 is required to be in the top 11%.

c. We know that the first quartile (Q1) corresponds to the 25th percentile, and the third quartile (Q3) corresponds to the 75th percentile. Using the mean of 319 and the standard deviation of 94, we can find the z-scores that correspond to these percentiles using a standard normal distribution table or calculator.

For Q1:

z = invNorm(0.25) ≈ -0.6745

x = m + zs = 319 + (-0.6745) × 94 ≈ 251.3

Q1 ≈ 251.3

For Q3:

z = invNorm(0.75) ≈ 0.6745

x = m + zs = 319 + (0.6745) × 94 ≈ 386.7

Q3 ≈ 386.7

Therefore, Q1 ≈ 251.3 and Q3 ≈ 386.7.

d. (i) To find Jane's percentile, we need to find the area under the normal curve to the left of her score of 464. Using the mean of 319 and the standard deviation of 94, we can standardize Jane's score as follows:

z = [tex]\frac{(x - m)}{s}[/tex] = (464 - 319) / 94 ≈ 1.55

Using a standard normal distribution table, we can find that the area to the left of z = 1.55 is approximately 93.3%. Therefore, Jane's percentile is approximately 93.3%.

(ii) To find the score that corresponds to the 66th percentile, we need to find the z-score that has an area of 0.66 to its left. Using a standard normal distribution table, we can find that the z-score that corresponds to an area of 0.66 to the left is approximately 0.44. Therefore, we can solve for the score as follows:

z = [tex]\frac{(x - m)}{s}[/tex]

0.44 = (x - 319) / 94

x - 319 = 0.44 * 94

x = 319 + 0.44 * 94

x ≈ 357.4

Therefore, Ann will receive a score of approximately 357.4.

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Answer:

Great question! When we find the volume of a 3D shape, we need to calculate the amount of space occupied by the object. This space is measured in cubic units, which is why we need to cube one dimension or multiply three dimensions together to find the volume of a 3D shape. For example, if we want to find the volume of a cube with side length "s", we would cube that value by raising it to the power of 3. This is because we need to multiply the length "s" by the width "s" and the height "s" to get the total space occupied by the cube, which is s^3. Similarly, if we want to find the volume of a rectangular prism with dimensions "l", "w", and "h", we would multiply these three values together to get the total volume. This is because the space