A cylindrical tank is half full of oil.
The cylinder has a base radius of 100cm.
The height of the cylinder is 250cm.
1litre=1000cm3
How many litres of oil are in the tank?
Round your answers to the nearest litre.

a) The least squares estimate of the slope (b₁) can be calculated using the formula:

b₁ = (n∑(xy) - (∑x)(∑y)) / (n∑(x^2) - (∑x)^2)

Where n is the number of observations, x and y are the explanatory and response variables, respectively.

b₁ = (5*(35+13+44+36+58) - (3+1+4+3+5)(5+3+4+6+8)) / (5*(3^2+1^2+4^2+3^2+5^2) - (3+1+4+3+5)^2) = 0.8

b) The least squares estimate of the intercept (b₀) can be calculated using the formula:

b₀ = (∑y - b₁*(∑x))/n

b₀ = (5+3+4+6+8-0.8*(3+1+4+3+5))/5 = 3.4

c) The point estimate of y when x=2 can be calculated using the equation of the line:

y = b₀ + b₁x

y = 3.4 + 0.82 = 4.8

So the point estimate of y when x=2 is 4.8

In probability and statistics, a random variable is a variable whose possible values are numerical outcomes of a random event. It is a function that maps outcomes of a random experiment to a real number. It can be discrete, meaning it can take on only a countable number of values, or it can be continuous, meaning it can take on any value within a given range. The probability distribution of a random variable describes the likelihood of different outcomes occurring. It can be used to calculate expected values, variances, and other measures of statistical dispersion.

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The percent of the variation in mileage that cannot be explained by differences in the cars ages is 36.1%.

A statistical indicator of the strength of a linear relationship between two variables is the correlation coefficient. A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively correlated, the value either rises or falls together.

The correlation r between the age of a car x , and the cars mileage, y is 0.639. This means that 63.9 % of the variation in mileage can be explained by the differences in the cars ages, 100 – 63.9 = 36.1% of the variation cannot be explained.

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Answer: Less than

Step-by-step explanation:

The percent change is exactly what it sounds like, the percent that changed. and 1/9 is less that 4.5/9 (half of 9) so it is less than

Answer:

x =5 units

Mark me as a brainiest

Answer:

12

Step-by-step explanation:

4 / 12   =  12 / 36      so answer : 12

That was just by looking.....here is mathematical way :

4/ x  = x/36       cross multiply

144 = x^2

x = 12

As the p-value of the test, of 0.0002, is less than the significance level of 0.05, the information provide strong evidence for concluding that the company is not filling its bottles as advertised.

At the null hypothesis, it is tested if the tablets are filled as advertised, that is, the mean is of 5 grains, hence:

[tex]H_0: \mu = 5[/tex]

At the alternative hypothesis, it is tested if the tablets are not filled as advertised, that is, if the mean is less than 5 grains, hence:

[tex]H_1: \mu < 5[/tex]

The equation for the test statistic is defined as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which the parameters are given as follows:

The values of these parameters for this problem are given as follows:

[tex]\overline{x} = 4.87, \mu = 5, s = 0.35, n = 100[/tex]

Hence the test statistic is of:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{4.87 - 5}{\frac{0.35}{\sqrt{100}}}[/tex]

t = -3.71.

Using a t-distribution calculator, with a left-tailed test, as we are testing if the mean is less than a value, with 100 - 1 = 99 df, the p-value of the test is of:

0.0002.

Hence the information provide strong evidence for concluding that the company is not filling its bottles as advertised.

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The probability that the student is absent is 3/20

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

The probability that the student will be absent and it will be on Monday is 3 /100.

The probability that it will be Monday is 1/5

Therefore the probability that the student will be absent any day is 3/100÷1/5 = 3/20

Since it is certain that it is Monday , the probability that it is Monday is 1.

Therefore, the probability that the student is absent on that Monday is 1 × 3/20 = 3/20

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The value of ∠A is 101°.

A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees.

Given a quadrilateral,

whose opposite sides are parallel, the figure is parallelogram,

property of a parallelogram says

ABCD is a parallelogram, where AB || CD and AD || BC.

Also, AB = CD and AD = BC

so ∠A = ∠C & ∠B = ∠D

given ∠C = 101°

so ∠A = ∠C = 101°

Hence the value of ∠A is 101°.

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Answer:2

Step-by-step explanation:

N minus 3 equals negative 1

add 3 to both sides leaving the equation N = -1 +3 or N=3-1

3-1 equals 2

Answer:

----------------------------------

Solve the equation:

Answer:

[tex] \sf \: d) \: x = 7[/tex]

Step-by-step explanation:

Given equation,

→ -3 - (-8) - (-2) = x

Now the value of x will be,

→ -3 - (-8) - (-2) = x

→ x = -3 - (-8) - (-2)

→ x = -3 + 8 + 2

→ x = 5 + 2

→ [ x = 7 ]

Hence, the value of x is 7.

The percentage of the people surveyed who were completely satisfied with the car was 55 %.

To find the percentage of people surveyed who were completely satisfied with the car, you first need to find the number of people who were survyed. This can be found by adding up all the number of people who participated in the survey :

= 1, 100 + 740 + 160

= 2, 000 people

The percentage of the people surveyed who were completely satisfied with the car is therefore:

= People completely satisfied / Number of people who participated x 100 %

= 1, 100 / 2, 000 x 100 %

= 55 %

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The equation of the variation is y =7x.

When we are discussing about the idea of variation then on specie is changing with respect to the other. If the change is such that the both variables are increasing at the same time then we could say that we have a direct variation.

Now, we know that;

y=8.4 when x=1.2

Given that;

y α x

If we add k;

y = kx

8.4 = k 1.2

x = 8.4/1.2

x = 7

Then the equation is;

y =7x

This is the equation that has been used to produce the graph in the image attached to the answer given here.

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a. The system of inequalities for this situation can be represented as:

x (number of snacks) ≥ 0

y (number of bottles of water) ≥ 0

2x + 2.25y ≤ 70 (total amount of money remaining)

y ≤ 4 (maximum number of bottles of water that can be carried on a tray)

7x + 7y ≤ 70 (total cost of tickets and snacks/drinks cannot exceed the amount given)

b. To graph the system, we can start by plotting the inequality 2x + 2.25y ≤ 70. This represents all the points that satisfy the inequality and forms a boundary line for the feasible region. The line will be a boundary line because it is less than or equal to 70.

We can plot the inequality y ≤ 4 as a horizontal line at y = 4. This represents the maximum number of bottles of water that can be carried.

Finally, we can plot the inequality 7x + 7y ≤ 70 as a boundary line. This represents the total cost of tickets and snacks/drinks that cannot exceed the amount given.

The feasible region will be the area between these lines, above the x-axis and y-axis, and below the line y=4.

The vertices of this feasible region will be the intersection points of the three lines, which are (10,0), (0,10) and (8,4)

c. The combinations of snacks and drinks that are possible are the ones that fall within the feasible region. Any point within the feasible region represents a valid solution in this context, because it satisfies all the constraints and is within the budget.

d. Every point within the feasible region represents a valid solution in this context, because it satisfies all the constraints and is within the budget.

e. One possible combination is (8,4) which is 8 snacks and 4 bottles of water, this combination is possible because it's within the feasible region and satisfies all the constraints. One combination that is not possible is (12,3), it's not possible because it's not within the feasible region and doesn't satisfy the constraint y ≤ 4.

f. To prove that the combination (8,4) is possible, we substitute these values into the system of inequalities:

2(8) + 2.25(4) = 35 ≤ 70 (total amount of money remaining)

4 ≤ 4 (maximum number of bottles of water that can be carried)

7(8) + 7(4) = 56 ≤ 70 (total cost of tickets and snacks/drinks cannot exceed the amount given)

To prove that the combination (12,3) is not possible, we substitute these values into the system of inequalities:

2(12) + 2.25(3) = 30.5 > 70 (total amount of money remaining)

3 > 4 (maximum number of bottles of water that can be carried)

7(12) + 7(3) = 63 > 70 (total cost of tickets and snacks/drinks cannot exceed the amount given)

As all the inequalities are not satisfied, the combination (12,3) is not possible.

A system of inequalities is a set of two or more inequalities that must be satisfied simultaneously. It is a way to represent a set of constraints using mathematical equations. These constraints can be related to a problem in a specific area, such as finance, engineering, or operations research. The solution set of a system of inequalities is the common set of solutions that satisfy all the inequalities in the system. The solutions can be represented graphically as a region in a coordinate plane called the feasible region, which is the set of all possible solutions.

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Answer:

6

Step-by-step explanation:

See the screenshot below.

Answer:

-31c + 20

Step-by-step explanation:

distribute

9c + -10 × 4c, -10 × -2

9c - 40c + 20

-31c + 20

Answer:

-31c+20

Step-by-step explanation:

You multiply the equation in the parenthesis by negative ten and then subtract it all from 9c

There is a percent decrease of about 43.75%

Percentages are fractions with 100 as the denominator. In other words, it is the relation between part and whole where the value of whole is always taken as 100. They are used like fractions and decimals i.e ways to describe parts of a whole.  While using percentages, the whole is considered to be made up of a hundred equal parts. The symbol % is used to show that a number is a percentage

New Process = 45 mins

Old Process = 1 hour and 20 minutes (80mins)

Increase/Decrease = Old Process - New Process

Increase/Decrease = 80 - 45

Increase/Decrease = 35

Therefore there is reduction in the manufacturing process;

% decrease = (35/80) x 100

% decrease = 43.75%

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Answer:

B. 3⁻⁴; E. 1/3⁴.

Step-by-step explanation:

1. rule is:

cᵃ:cᵇ=cᵃ⁻ᵇ;

2. according to the rule above:

3⁻⁸:3⁻⁴=3⁻⁸⁺⁴=3⁻⁴, then

3. correct answer is 'B'; 'E'.

The height of the lighthouse is 76.4 feet.

What is the angle of elevation?

The angle is formed by the line of sight and the horizontal plane for an object above the horizontal.

We can use the concept of trigonometry to solve this problem. We know that the angles of elevation and depression are formed by the line of sight of the sailor and the height of the lighthouse.

We can use the tangent function to relate these angles to the height of the lighthouse.

Tangent of angle of elevation = opposite side / adjacent side

Tangent of angle of depression = opposite side / adjacent side

Let h be the height of the lighthouse.

tan(21) = h / 200

tan(14) = h / (200 + h)

now we can use these equations to find h,

h = (200 * tan(21)) = (200 * (opposite side/adjacent side)) = (200 * (h/200))

h = 200 * tan (21)

and

h = (200* h)/(200+h) * tan(14)

we can now use these equations to find the value of h.

h = 200 * tan(21) = 200 * 0.38197 = 76.394

Therefore, the height of the lighthouse is 76.4 feet (approx).

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Answer: The expression in simplified form is D. 3x³√15

To simplify the expression, we can first simplify the fractions.

2/1356 can be simplified to 12/225.

Then, we can use the distributive property to simplify the expression further.

12/225 - 3√156 = 12/225 - 18√15

The last step is to combine the terms,

12/225 - 18√15 = (-6/75) - (6√15) = -6/5 * (1/5 - √15) = -6 * (- √15/5) = 3 * √15 * 6

Therefore, the simplified form of the expression is D. 3x³√15

Step-by-step explanation:

Answer:

  B.  15, 20, ...

Step-by-step explanation:

You want to know which sequence of numbers has the steepest graph.

The slope (steepness) of the graph is the ratio of the change in y to the change in x. Here, we presume the x-values for each of these sets of points are 1, 2, 3, 4, ....

That means the slope will be the difference of adjacent y-values. Subtracting the first from the second, we get ...

  8 -4 = 4

  20 -15 = 5

  52 -50 = 2

  7 -4 = 3

The sequence in which the values differ by 5 has the largest difference, so will have the steepest graph:

  15, 20, 25, 30, ...

Answer:

6125555566/6661234567

The table for all missing values of s and d should be completed as follows;

Number of songs, s               Amount of money ($), d

2                                                           2.58

4                                                           5.16

7                                                           9.03

11                                                           14.19

17                                                           21.93

In order to have a proportional relationship and equivalent ratios, the variables s and d must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = d/s

Constant of proportionality (k) = 2.58/2

Constant of proportionality (k) = 1.29.

When the amount of money (d) is 5.16, the number of songs (s) is given by;

s = d/k

s = 5.16/1.29

s = 4 songs.

When the number of songs (s) is 7, the amount of money (d) is given by;

d = ks

d = 1.29(7)

d = $9.03.

When the number of songs (s) is 11, the amount of money (d) is given by;

d = ks

d = 1.29(11)

d = $14.19.

When the amount of money (d) is 21.93, the number of songs (s) is given by;

s = d/k

s = 21.93/1.29

s = 17 songs.

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Answer:

A I THINK

Step-by-step explanation:

Since Julie earns a constant rate of $12 per hour, for working 16 hours based on mathematical operations, she will earn $192.

The basic mathematical operations involve addition, subtraction, division, and multiplication.

These operations combine parts of the mathematical operations with their assigned operands and the equation symbol (=) to solve mathematical problems.

In this situation, we employ division and multiplication operations to solve the requirement.

Loren and Julie's Total Income Table

Hours    2   4   6   8   10   12  14   16   18

Dollars 18 36 54 72 90 108    ?    ?  162

Loren's Constant Rate of Pay (Hourly Rate) = $9 ($162/18)

Hours     3  6   9    12  15    18  21    24    27

Dollars 36 ? 108 144 180 216    ?  288 324

Julie's Constant Rate of Pay (Hourly Rate) = $12 ($324/27)

Total hours worked = 16

Total earnings = $192 ($12 x 16)

Thus, when Julie works 16 hours, she earns $192.

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Considering the expression of a line, the slope of line that passes through points (-2,7) and (-3,3) is 4.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m can be calculated as:

m= (y₂ - y₁)÷ (x₂ - x₁)

In this case, being (x₁, y₁)= (-2, 7) and (x₂, y₂)= (-3, 3), the slope can be calculated as:

m= (3 -7)÷ (-3 -(-2))

m= (3 -7)÷ (-3 +2)

m= (-4)÷ (-1)

m= 4

Finally, the slope is 4.

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Answer:

Iniko's part is 4/15

Allea had the highest score

Step-by-step explanation:

Use the LCD 15 and convert the fractions:

Allea: 2/5 = 6/15

Loki:   1/3 = 5/15

Iniko score = 15/15 - 6/15 - 5/15 = 4/15

The inequality equations for the rides High-Bounce, Climb-A-Thon, and Twirl-O-Coaster are 55<h<7, h<60, and h>=58 respectively.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides.

Let the unknown height be h.

For the ride High-Bounce, the height requirement is between 55 and 72 inches tall.

This can be written in the inequality form as 55<h<72.

For the ride Climb-A-Thon, the height requirement is under 60 inches tall.

This can be written in the inequality form as h<60.

For the ride Twirl-O-Coaster, the height requirement is 58 inches minimum.

This can be written in the inequality form as h>=58.

The representations of these inequalities on number lines is given below.

Therefore, the inequalities are - 55<h<7, h<60, h>=58.

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The problems for production staff are solved as below.

Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.

1. Knit

Number produced by 1 worker in a day = 50 pairs

Annual production goal = 780,000 pairs

Daily production goal = 780,000 / 260 = 3000 pairs

Production staff needed = 3000 / 50 = 60 workers

2. Tube

Number produced by 1 worker in a day = 40 pairs

Annual production goal = 946,400 pairs

Daily production goal = 946,400 / 260 = 3640 pairs

Production staff needed = 3640 / 40 = 91 workers

3. Athletic

Number produced by 1 worker in a day = 60 pairs

Annual production goal = 1,138,800 pairs

Daily production goal = 1,138,800 / 260 = 4380 pairs

Production staff needed = 4380 / 60 = 73 workers

4. Booties

Number produced by 1 worker in a day = 24 pairs

Annual production goal = 343,200 pairs

Daily production goal = 343,200 / 260 = 1320 pairs

Production staff needed = 1320 / 24 = 55 workers

5. Children's

Number produced by 1 worker in a day = 84 pairs

Annual production goal = 518,000 pairs

Daily production goal = 518000 / 260 = 1992.3 pairs

Production staff needed = 1992.3 / 84 = 23.7 workers

Hence the production staff needed has been solved.

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Answer: x = 0, 16

Step-by-step explanation:

First square both sides

(sqrt2x+4 - sqrtx)^2 = 4

now distribute the inside using the (a-b)^2 = a^2 -2ab + b^2 property to get

2x+4 - (2sqrt 2x^2 +4x) + X = 4

3x=2sqrt 2x^2 +4x

9x^2 = 4(2x^2+4x)

9x^2 = 8x^2+16x=0

x^2-16x=0

x(x-16)=0

x=0, 16