How much water in gallons do you need to fill a tub 3/4 of the way up that has a diameter of 25 feet and a height of 52 inches

Answer:

Step-by-step explanation:

Answer:

a) The 36th percentile of the scores is of 74.68.

b) The 70th percentile of scores is 85.3.

c) The minimum score needed to get an A is 93.1.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 79 and a standard deviation of 12.

This means that \(\mu = 79, \sigma = 12\)

(a) Find the 36th percentile of the scores.

This is X when Z has a pvalue of 0.36. So X when Z = -0.36.

\(Z = \frac{X - \mu}{\sigma}\)

\(-0.36 = \frac{X - 79}{12}\)

\(X - 79 = -0.36*12\)

\(X = 74.68\)

The 36th percentile of the scores is of 74.68.

(b) Find the 70th percentile of the scores.

This is X when Z has a pvalue of 0.7, so X when Z = 0.525.

\(Z = \frac{X - \mu}{\sigma}\)

\(0.525 = \frac{X - 79}{12}\)

\(X - 79 = 0.525*12\)

\(X = 85.3\)

The 70th percentile of scores is 85.3.

(c) The instructor wants to give an A to the students whose scores were in the top 12% of the class. What is the minimum score needed to get an A?

The 100 - 12 = 88th percentile, which is X when Z has a pvalue of 0.88, so X when Z = 1.175.

\(Z = \frac{X - \mu}{\sigma}\)

\(1.175 = \frac{X - 79}{12}\)

\(X - 79 = 1.175*12\)

\(X = 93.1\)

The minimum score needed to get an A is 93.1.

MODE IS THE NUMBER THAT IS REPEATED THE HIGHEST TIME..

HERE, IN YOUR QUESTION 5CAME 2 TIMES i.e. it is repeated highest time .so mode=5....

Answer:

The equation, y=3x-5 is in y=mx+b format. The b, or -5 in this case, tells you what the y intercept is, or in this case, your starting point. This means your first point will be at (0,-5). The mx, or 3x in this case, tell us how much to move     up and how much to move sideways. 3x is equal to 3/1x and the 3/1 tells us the rise/run. Rise being how much to go up or down and run being how much to go to the left or right. So in 3x, the rise is 3 and the run is 1. So you will go 3 up on the y axis and 1 to the right on the x-axis. So your next point will be (1, -2) and the point after that will be (2, 1) and so on!

hope this helped!

Answer:

Step-by-step explanation:

y=3x-5 is a line

pick any 2 points for example

(x=0, y=(3*0)-5=-5) so one point is (0,-5)

(x=2, y=(3*2)-5= 1) so another point is (2, 1)

draw a line trough points (0, -5) and (2, 1)

Answer:

the product of the decimal equivalents of all discount in the series

Answer:

X of pt A = 8

Step-by-step explanation:

moving the coordinates of A by 14 units to the right means we shift it's position on the x-axis by adding +14

X of A = -6 + 14 = 8

Y of A = -10 - 2 = -12

The total cupcakes the bakery sell that day is 80

From the question, we have the following parameters that can be used in our computation:

Number of sales = 76

Proportion = 95%

This implies that

Number of sales = Proportion * Total number of cupcakes

Substitute the known values in the above equation, so, we have the following representation

76 = 95% * Total number of cupcakes

Divide both sides by 95%

Total number of cupcakes = 80

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Answer:

3,-2.

Step-by-step explanation:

hope this helps. :-)

Answer:

£55

Step-by-step explanation:

50% is just another way to say 1/2. This means that 1/2 of £110 is £55.

Answer:

86.452 m

Step-by-step explanation:

I've attached an image showing the position of the person and the string and the kite.

From the image attached, we can see that the length of the string can be calculated from pythagoras theorem since the triangle is a right angled triangle.

Thus, let length of string be denoted as s.

s = √(65² + 57²)

s = √7474

s ≈ 86.452 m

Answer:

Below

Step-by-step explanation:

4 ft = 48 inches...... then add 9 inches X 15 years

48 +  9 x 15 = 183 inches       this is 15 ft 3 inches

The congruent reason for the triangles is (b) HL theorem

From the question, we have the following parameters that can be used in our computation:

Triangles = FGH and JHK

The SSS similarity theorem implies that the corresponding sides of the two triangles in question are not just similar, but they are also congruent

From the question, we can see that the following corresponding sides on the triangles:

Sides GH and HK

Sides FH and JK

These parameters are given in reasons (2) and (3) and it implies that these sides are congruent sides

For the triangle to be congruent by SSS, the following sides must also be congruent

GH must be congruent to HK

The above statement is true because point H is the midpoint of line GK

This is indicated in reason (2)

Hence, the congruent statement is SSS.

However, we can also make use of the HL theorem in (B)

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EXPLANATION

Production rate = 18 cars/ 8 hours

Applying the unitary method give us the appropiate relationship as shown as follows:

At this rate the factory could produce approximately 31 cars in 14 hours.

Step-by-step explanation:

f(x) = sin(x), a = π/6, n = 4

Find the derivatives.

f⁽⁰⁾(π/6) = sin(π/6) = ½

f⁽¹⁾(π/6) = cos(π/6) = ½√3

f⁽²⁾(π/6) = -sin(π/6) = -½

f⁽³⁾(π/6) = -cos(π/6) = -½√3

f⁽⁴⁾(π/6) = sin(π/6) = ½

T₄(x) = ½ (x − π/6)⁰ / 0! + ½√3 (x − π/6)¹ / 1! − ½ (x − π/6)² / 2! − ½√3 (x − π/6)³ / 3! + ½ (x − π/6)⁴ / 4!

T₄(x) = ½ + ½√3 (x − π/6) − ¼ (x − π/6)² − ¹/₁₂√3 (x − π/6)³ + ¹/₄₈ (x − π/6)⁴

Find the fifth derivative.

f⁽⁵⁾(x) = cos(x)

So the next term of the series would be:

cos(z) (x − π/6)⁵ / 5!

For 0 ≤ z ≤ π/3,│f⁽⁵⁾(x)│is a maximum at z = 0.  Therefore:

│R₄(x)│≤ │cos(0) (0 − π/6)⁵ / 5!│

│R₄(x)│≤ 0.000328

│R₄(x)│is always positive, so we can ignore the bottom two graphs.  The top right graph has a y-intercept of approximately 0.0003, so that is the correct graph.

The probability that a randomly selected point within the square falls in the red shaded square is 1/16

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event to occur is 1 and it is 100% in percentage.

Probability = sample space /total outcome

sample space is the area of the red shaded square and the total outcome is the big square.

Area of red shaded square = 1 × 1 = 1unit²

area of the big square = 4 × 4 = 16 units²

Therefore the probability that a point selected falls on the red shaded square

= 1/16

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Answer: 25%

Step-by-step explanation:

First week of July = 1040 people

Fourth week of July = 1040- 100 + 130 - 290 = 780

The number of people that went to the swimming pool in 1st week was 1040 while the 4th week had 780. The percentage decrease will be:

= (1040 - 780) / 1040 × 100

= (260 / 1040) × 100

= 0.25 × 100

= 25%

Answer:

8

Step-by-step explanation:

To get 2 divided by 1/4, you can rewrite the expression as 2 times 4.

This is because 4 is the reciprocal of 1/4, and you can use the skip, flip, multiply rule when dividing a number by a fraction.

2 times 4 is 8,  therefore, your answer is 8.

Kelly will take 5.64 minutes more to wash the car as compared to Kelly and Libby when they are working together

Time taken by Kelly to wash the car = 13 minutes

Time taken by Libby to wash the car = 17 minutes

Time taken by Kelly and Libby to wash the car together:

LCM of 13 and 17 is 221. So, the total work required to be done is 221 units

Hence, Kelly does 17 units of work each minute and Libby does 13 units of work each minute

If both work together, they will finish the work in = Total work required to be done/ Work done in a minute by Kelly + Work done in a minute by Libby

= 221/(17+13)

= 221/30 = 7.36 minutes

The extra time taken by Kelly working alone = 13-7.36  = 5.64 minutes

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Answer:

-2x² - 10xy + 2y²

Step-by-step explanation:

4x² - 9xy - 4y² - 6x² - xy + 6y² =

= 4x² - 6x² - 9xy - xy - 4y² + 6y²

= -2x² - 10xy + 2y²

The following information related to irrigation is as follows:

The gallons of irrigation water per square foot is \(326,700\ gallons\ per\ square\ foot\)

For determining the gallons of irrigation water we have to multiply the square foot by the number of gallons in a cubic foot.

Given that,

There are 43,560 square feet in an acre i.e. 1 acre = 43,560.

And, there are 7.5 gallons in a cubic foot i.e. 1 cubic foot = 7.5 gallons.

So, the gallons of irrigation water per square foot is

\(= 43,560 \times 7.5\ gallons \\\\= 326,700\ gallons\ per\ square\ foot\)

Therefore we can conclude that the gallons per square foot of irrigation water is \(326,700\ gallons\ per\ square\ foot\)

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Answer:

326,700 gallons

Step-by-step explanation:

1 acre = 43,560 square feet

1 acre-foot of irrigation is an acre irrigated 1 foot deep with water.

Since thee are approximately 7.5 gallons in 1 cubic foot,

1 acre-foot of irrigation = 43,560 * 7.5 gallons

1 acre-foot = 326,700 gallons

This is the number of gallons in one acre-foot, not gallons per square foot.

If he reads 8 books over 4 months it means that he reads 2 books per month. So, if we multiply this ratio by the 7 months we would find that he reads 14 books over 7 months.

The answer is 14 books.

Answer:

Yes, because a triangle can have any lengths.

Resolving the expression into a system of linear equations, the value of x and y are 5 and 15 respectively

Expanding the given equation, we get:

\((3x - y)^2 + (x - 5)^2 = 0\\9x^2 - 6xy + y^2 + x^2 - 10x + 25 = 0\\10x^2 - 6xy + y^2 - 10x + 25 = 0\)

To solve for x and y, we need another equation that relates them. However, since the given equation has no real solutions (as the sum of two squares cannot be zero unless both squares are zero), we can conclude that there are no real values of x and y that satisfy the equation.

Alternatively, we could write the given equation as:

(3x - y)² = (5 - x)²

Taking the square root of both sides, we get:

3x - y = ±(5 - x)

Now we have two equations:

3x - y = 5 - x ...eq(i)

3x - y = x - 5 ...eq(ii)

solving for both x and y in the system of linear equations

x = 5 and y = 15

Therefore, the solution to the given equation is:

x = 5, y = 15

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Answer:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

Step-by-step explanation:

To solve this problem, we'll consider the velocities of the cruise ship and the Gulf Stream as vectors and calculate their components and resultant vector. Then we'll find the magnitude (resultant velocity) and direction (resultant direction) of the resultant vector.

Given:

Cruise ship velocity (south): 22 mph

Gulf Stream velocity (east): 4 mph

A) Vector component for the cruise ship:

The cruise ship is traveling south, so its velocity vector is (0, -22).

B) Vector component for the Gulf Stream:

The Gulf Stream is flowing east, so its velocity vector is (4, 0).

C) Resultant vector:

To find the resultant vector, we'll add the two velocity vectors together:

Resultant vector = Cruise ship velocity + Gulf Stream velocity

Resultant vector = (0, -22) + (4, 0)

Resultant vector = (0 + 4, -22 + 0)

Resultant vector = (4, -22)

D) Resultant velocity:

The magnitude of the resultant vector gives us the resultant velocity. We can use the Pythagorean theorem to calculate it:

Resultant velocity = sqrt((x-component)^2 + (y-component)^2)

Resultant velocity = sqrt((4)^2 + (-22)^2)

Resultant velocity = sqrt(16 + 484)

Resultant velocity = sqrt(500)

Resultant velocity ≈ 22.4 mph (rounded to the nearest tenth)

E) Resultant direction:

The direction of the resultant vector can be found using trigonometry. We'll use the inverse tangent function (arctan) to find the angle between the resultant vector and the positive x-axis.

Resultant direction = arctan(y-component / x-component)

Resultant direction = arctan(-22 / 4)

Resultant direction ≈ -1.405 radians or -80.5 degrees (rounded to the nearest tenth)

Therefore, the answers are:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

The solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

The similar symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors by applying mathematical algorithms, which have served as expressions of reality. For instance, the equal sign divides the number 12 or even the solution y + 6 = 12 into two separate variables many characters are on either side of this symbol can be calculated. Conflicting meanings for symbols are quite prevalent.

Part A:

Given:

To find an equation,

Where x is number of monthly minutes.

and y is total monthly of splint plan.

So, equation is:

\(\rightarrow \text{y} =\text{mx} +\text{b}\)

For the first case:

\(\rightarrow\bold{173 = 380x + b}\)

Second case:

\(\rightarrow\bold{249= 570x + b}\)

Solve for x:

\(\rightarrow{173 - 380\text{x}=249- 570\text{x}\)

\(\rightarrow{-207=-321\)

\(\rightarrow \text{x} =\dfrac{321}{207}\)

\(\rightarrow \text{x} =\dfrac{107}{69}\)

\(\rightarrow \text{x} \thickapprox1.55\)

For value of b

\(\rightarrow 173 = 380(1.55) + \text{b}\)

\(\rightarrow 173 - 589 = \text{b}\)

\(\rightarrow -416 = \text{b}\)

Part B:

\(\rightarrow \text{y} = 942(1.55) - 416\)

\(\rightarrow \text{y} = 1460.1 - 416\)

\(\rightarrow \text{y} \thickapprox1044\)

Therefore, the solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

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Answer:

3/5

108

Step-by-step explanation:

Let there are 3x goldfish, then 2x belta fish

total 3x + 2x = 5x fish

so 3x/5x = 3/5 are goldfish.

total fish = 5x = 180, so x = 180/5 = 36

The store has 3x = 3*36 = 108 goldfish.

Both the methods can be used to solve a mixed fraction including a whole number and a fraction or solving the difference of a whole number and a fraction.

Mixed fractions are type of fractions which involve a whole number and a fraction. This is of the form a \(\frac{b}{c}\). This is actually a + \(\frac{b}{c}\).

You can use either methods when solving a whole number and a fraction.

Let us take a whole number 3 and a fraction \(\frac{2}{10}\) for instance.

First Method :

Solve it by cross multiplication.

Let the denominator of the whole number 3 be 1.

\(\frac{3}{1}\) ± \(\frac{2}{10}\) = [(3 × 10) ± (2 × 1)] / (1 × 10) = [30 ± 2] / 10

If the question is for adding, we get, \(\frac{3}{1}\) + \(\frac{2}{10}\) = (30 + 2) / 10 = 32/10

If the question is finding difference, we get, \(\frac{3}{1}\) - \(\frac{2}{10}\) = (30 - 2) / 10 = 28/10

Second Method :

Again let the denominator of the whole number be 1.

Find the LCD (Least Common Denominator) of 1 and 10.

This is 10.

So we have to make the denominator of \(\frac{3}{1}\) to 10.

Multiply both numerator and denominator with 10, we get 30/10.

A normal multiplication of fractions, if the denominator is same add or subtract the numerators let the denominator be as such.

Now add or subtract \(\frac{30}{10}\) ± \(\frac{2}{10}\) = (30 ± 2) / 10.

Hence both the methods can be used.

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Answer:

a) 12

b) 129

Step-by-step explanation:

a)

\(w, x \in \mathbb{Z}_{\ge 0}\)

\(w>50\\x<40\)

For the smallest value of \(w-x\), we gotta figure out the smallest value for w and the highest value for x.

\(w>50 \Rightarrow \text{ smallest value is } 51\)

For \(x\), once \(-(-x)=x\), we conclude that \(x\) cannot be negative and therefore, \(x=39\).

\(51-39=12\)

b)

\(y, z \in \mathbb{Z}_{\ge 0}\)

\(y<70\\z\leq 60\)

For the largest value of \(y+z\), we gotta figure out the highest value for y and z.

\(y<70 \Rightarrow \text{ highest value is } 69\)

\(z\leq 60 \Rightarrow \text{ highest value is } 60\)

\(y+z=69+60=129\)