EXERCISE 22.2A
1 A heater uses 3 units of electricity in 40 minutes.
How many units does it use in 2 hours?
2 A machine prints 1500 newspapers in 45 minutes.
How many does it print in 12 hours?
3 A bricklayer lays 1200 bricks in an average 8-hour day.
How many bricks does he lay in a 40-hour week?
4 A combine harvester produces 9 tonnes of grain in 6 hours.
How many tonnes does it produce in 54 hours?
5 A machine puts tar on a road at the rate of 4 metres in 5 minutes.
a) How long does it take to cover 1 km of road?
b) How many metres of road does it cover in 8 hours?
181

There is no tangent of the angle in this scenario.

In a right angled triangle, the cosine of an angle is equal to the adjacent side divided by the hypotenuse.

Therefore, if cos θ = ⅘ in a right angled triangle, we can label the adjacent side as 8 (since cosine is adjacent over hypotenuse and we know cosine and hypotenuse) and the hypotenuse as 5 (since we know cosine and hypotenuse and can solve for the adjacent side using Pythagorean theorem).

Now, to find the tangent of the angle, we need to divide the opposite side by the adjacent side. We do not know the value of the opposite side, but we can use the Pythagorean theorem to find it.

Let's label the opposite side as x. Using Pythagorean theorem, we get:

(8)^2 + x^2 = (5)^2

64 + x^2 = 25

x^2 = -39

This is impossible because the square of a real number cannot be negative. Therefore, there is no tangent of the angle in this scenario.

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Answer:

The volume of the sphere is 32 π /3 cm^3

Step-by-step explanation:

Mathematically, the volume of a sphere can be calculated using the formula below;

V = 4/3 * pi * r^3

Now since we have the radius and diameter = 2 * radius

radius = diameter/2 = 4/2 = 2

Substituting this value into the volume equation;

V = 4/3 * pi * 2^3 = 32pi/3

Answer:

The correct answer is A

Step-by-step explanation:

a) The length of AB is given as follows: 14.387.

b) The measure of angle BAC is given as follows: 78.4º.

The length of AB, from the sketch of the triangle given by the image at the end of the answer, is obtained using the law of cosines, as follows:

x² = a² + b² - 2abcos(C).

The parameters from the triangle are given as follows:

a = 8, b = 15, C = 70º.

Hence the length of AB is given as follows:

x² = 8² + 15² - 2 x 8 x 15 x cos(70º)

x² = 207

x = square root of 207

x = 14.387.

The measure of angle BAC is obtained using the law of sines, as follows:

sin(x)/15 = sin(70º)/14.387

sin(x) = 15 x sin(70º)/14.387

sin(x) = 0.9797.

x = arcsin(0.9797)

x = 78.4º.

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Answer:

line mo

Step-by-step explanation:

Because the triangle are congrument

RST and MNO are the triangle

RT is a line in the RST triqangle

it is equal to the MO line in MNO

Answer:

84500 is the correct answer

Answer:

40182 delta math

Step-by-step explanation:

Area Principle. In a statistical display, each data value should be represented by the same amount of area. Bar chart (Relative Frequency Bar Chart)

Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

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Answer:

Step-by-step explanation:

If you mean 3x^3 - 42x^2 - 4x + 5 = 0 you can graph it manually or with technology

The roots are 14.09, 0.30 and -0.39 to nearest hundredth.

Answer:

d.937.50

Step-by-step explanation:

After each year it adds 5% so 5x5 is 25%

25% of $3,750 is $937.50

hope this helps :)

Answer:

13

Step-by-step explanation:

39/3

Lerchs-Grossman algorithm is a pit optimization software that helps in the determination of the most profitable final pit outline. The section of a copper porphyry ore body given has a cut-off grade of 0.45% Cu. Each block has dimensions of 16m x 16m x 16m (HxLxW).

The cost of mining a block of waste is $50, and the value of a block of ore is approximated to be $100 x (grade expressed in %). Firstly, we have to calculate the net present value (NPV) for all the blocks that are above the cut-off grade. NPV is calculated using the formula given below:

NPV = ((grade*100)*100)-50

Here, the cost of mining a block of waste is $50 and the value of a block of ore is approximated to be $100 x (grade expressed in %).

1. Firstly, the net present value (NPV) of each block above the cutoff grade is calculated.2. The blocks are then sorted in descending order of their NPVs.

3. Next, the algorithm calculates the limits of the pit at a sequence of levels, starting with the block of highest NPV.

4. It is assumed that the pit will extend downwards through the blocks from the highest NPV downwards.

5. If the pit reaches the edge of the ore body before reaching a certain level, it is truncated and the lower level is tried.

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Answer:

The answer is  

20x + 17.5

Step-by-step explanation:

Multiply the 5 by the numbers inside the parenthesis.

5 x 4x

5 x 3.5

Answer: 2

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

using pemdas, do 2 times 4 first which ends up as 8, and then subtract 4 from it leaving you w the answer 4

Answer:

1/3

Step-by-step explanation:

The equation given to you is in y=mx+b form.

m is the slope which in this case would be 2/9.

b is the y-intercept which in this case would be 1/3

Answer:

put x=0 in the equation

it will give you y intercept.

so y intercept in this equation is =1/3.

Step-by-step explanation:

Answer:

The slope is 4/5

Step-by-step explanation:

y = (4/5)x - 3

This is written in slope-intercept form,

y = mx = b

where m is the slope,

comparing with the given equation we see that,

m = 4/5

hence the slope is 4/5

The slope is:

4/5

In-depth explanation:

The given equation is in the form of y = mx + b where m = slope.

The slope is the number that comes in front of x.

Similarly, the slope of y = 4/5x -3 is 4/5.

Answer:

10n=10n

Step-by-step explanation:

n-10+9n-3=10n-13

n+9n

10n-10-3=10n-13

-10-3

10n-13=10n-13

    +13        +13

10n=10n

Thus, the unique solution to the given differential equation with the initial condition y(1) = 13 is \(y = 1 / (- (1/4) * x^4 + 17/52).\)

To solve the given differential equation, we'll use the method of separation of variables.

First, we rewrite the equation in the form\(dy/dx = y^2 * x^3\)

Separating the variables, we get:

\(dy/y^2 = x^3 * dx\)

Next, we integrate both sides of the equation:

\(∫(dy/y^2) = ∫(x^3 * dx)\)

To integrate \(dy/y^2\), we can use the power rule for integration, resulting in -1/y.

Similarly, integrating \(x^3\) dx gives us \((1/4) * x^4.\)

Thus, our equation becomes:

\(-1/y = (1/4) * x^4 + C\)

where C is the constant of integration.

Given the initial condition y(1) = 13, we can substitute x = 1 and y = 13 into the equation to solve for C:

\(-1/13 = (1/4) * 1^4 + C\)

Simplifying further:

-1/13 = 1/4 + C

To find C, we rearrange the equation:

C = -1/13 - 1/4

Combining the fractions:

C = (-4 - 13) / (13 * 4)

C = -17 / 52

Now, we can rewrite our equation with the unique solution:

\(-1/y = (1/4) * x^4 - 17/52\)

Multiplying both sides by -1, we get:

\(1/y = - (1/4) * x^4 + 17/52\)

Finally, we can invert both sides to solve for y:

\(y = 1 / (- (1/4) * x^4 + 17/52)\)

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The probability that no one enters between 12:00 and 12:05 is 0.082.

The probability that at least 4 people enter the casino during that time is 0.242

Given that people enter the casino at the rate of 1 every 2 minutes. A random variable X is defined as the number of people entering the casino between the time period of 12:00 and 12:05. Since we are given in the question that people enter the casino at the rate of 1 every minute, hence in the given time period they enter at the rate of 2.5.

P(X=0) = \(e^{-2.5}\) = 0.082

Hence the probability that no one enters between 12:00 and 12:05 is 0.082.

The required probability is simply

P(X≥4) = 1 - P(X=0) - P(X=1) - P(X=2) - P(X=3)

= 1 - \(e^{-2.5}\) - 2.5\(e^{-2.5}\) - (((2.5)² / 2)\(e^{-2.5}\) ) - (((2.5³)/3!)\(e^{-2.5}\))

= 0.242

Hence, the probability that at least 4 people enter the casino during that time is 0.242

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Answer:

Step-by-step explanation:

x=4/15

The situation described follows a geometric distribution because we are interested in the number of trials needed to achieve the first success (drawing a blue marble from the bag).

The situation described, where marbles are drawn from a bag with replacement until a specific event (getting a blue marble) occurs, follows a geometric distribution.

In a geometric distribution, we are interested in the number of trials needed to achieve the first success. In this case, the "success" is drawing a blue marble, and each trial consists of drawing a marble from the bag.

The key characteristics of a geometric distribution are:

1. The trials are independent, meaning that the outcome of one trial does not affect the outcome of subsequent trials.

2. The probability of success remains constant for each trial.

3. The trials are performed until the first success occurs.

In the given situation, the probability of drawing a blue marble remains constant at 6/15 (since there are 6 blue marbles out of a total of 15 marbles in the bag) for each trial. The trials are independent because we replace the marble after each draw. We continue drawing marbles until we obtain a blue marble, which is considered the first success.

Therefore, the situation described follows a geometric distribution because we are interested in the number of trials needed to achieve the first success (drawing a blue marble from the bag).

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The number of students who were wearing spirit wear at the assembly is = 120.

As given in Question that 3 out of 10 students were wearing spirit were.

if we have these type of Question then we will find the fraction part for 1 student as given 3 out of 10 then  the fraction part for 1 will be = 3/10 = 0.3

for 1 student there  is 0.3 fraction of students has wear spirit wear

so for 400 students were at the assembly

for 1 fraction is 0.3

for 400 = 400*(0.3 )= 120

Here 120 students were wear spirit wear in assembly

as like type we can solve for any number of students who were in assembly . like if there is 500 student the we can do like 500*.03 = 150 students.

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\( \huge \huge \huge\square\)

Here All Sides Are Equal So,

Area = side × side= side²

So Assuming Side As 'l'

so, l×l = l²

:)

................................

Answer:

15

Step-by-step explanation:

Answer:

x = 34

Step-by-step explanation:

\(x=34\)

Answer:

i don't know why the question want in fraction though

Step-by-step explanation:

\(c + 38 = 113 \\ c = 113 - 38 \\ c = 75\)

The correct answer is:

X=2

Answer:

1,1.1,1.25,1.5,1.7,9