Word problem involving the area of a rectangle: Problem type 2

Answer:

\(Probability = 0.504\)

Step-by-step explanation:

Given

\(ID: 4\ digit\ number\)

Required

Determine the probability that no two digit is repeated

First, we need to determine the total possible number of pins (with repetition)

Each of the 4 ID digit can be selected from any of the 10 digits (0 - 9).

i.e.

\(First = 10\)

\(Second = 10\)

\(Third = 10\)

\(Fourth = 10\)

\(Total = 10 * 10 * 10 * 10\)

\(Total = 10000\)

i.e.

\(n(Repetition) = 10000\)

Next, we determine the total possible number of pins (without repetition)

Once a digit is selected from any of the 10 digits (0 - 9), it can no longer be repeated.

i.e.

\(First = 10\)

\(Second = 10 - 1 = 9\)

\(Third = 10 - 1 - 1= 8\)

\(Fourth = 10 - 1 - 1 - 1 = 7\)

\(Total = 10 * 9 * 8 * 7\)

\(Total = 5040\)

i.e.

\(n(No\ Repetition) = 5040\)

The probability is then calculated as:

\(Probability = \frac{n(No\ Repetition)}{n(Repetition)}\)

\(Probability = \frac{5040}{10000}\)

\(Probability = 0.504\)

The term 'GDP Gap' refers to the difference between the actual Gross Domestic Product (GDP) and the potential GDP of a country. It is a measure of the underutilization or overutilization of economic resources.

In the context of Australia's COVID-19 recession, the GDP Gap would indicate the extent to which the recession has impacted the country's economic output compared to its potential.

During a recession, the GDP Gap is usually negative, indicating a decline in economic activity. This gap arises due to factors such as decreased consumer spending, reduced investment, and increased unemployment. In the case of Australia, the COVID-19 pandemic triggered a significant economic plunge, leading to a confirmed recession.

The GDP Gap can be calculated by subtracting the actual GDP from the potential GDP. The potential GDP represents the level of economic output that could be achieved if all resources were fully employed. The larger the GDP Gap, the greater the underutilization of resources and the more severe the economic downturn.

The term 'GDP Gap' refers to the difference between actual GDP and potential GDP, and it is used to measure the extent of economic underutilization or overutilization. In the case of Australia's COVID-19 recession, the GDP Gap would indicate the negative impact of the recession on the country's economic output compared to its potential.

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The value of the probability of choosing a green lollipop and a purple lollipop is, 8 / 45

We have to given that;

One bag contains 3 red lollipops and 2 green lollipops.

And, The other bag contains four purple lollipops and five blue lollipops.

Hence, The probability of choosing a green lollipop is,

P₁ = 2 / 5

And, The probability of choosing a purple lollipop is,

P₂ = 4 / 9

Thus, The value of the probability of choosing a green lollipop and a purple lollipop is,

P = P₁ ×  P₂

P = 2/5 × 4/9

P = 8/45

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Answer:

12+8*6

Step-by-step explanation:

Answer:

3.75

Step-by-step explanation:

The hundredth is the 2 number after the decimal point so round that up.

Answer:

3.75

Step-by-step explanation:

the hundreths place is the second number to the left of the decimle, because the number to the left of the hundreths place is less than five. You leave the hundreths place number as it is. This leaves you with your awnser: 3.75

Answer:

no

Step-by-step explanation:

you cannot divide zero into two equal parts because there is nothing there to start.  Since Pablo has no candy, he cannot divide it into two piles because there isn't anything to divide.

Answer: No because 0 means nothing  and you can't divide nothing among something so  that is like undefined.

Step-by-step explanation:

The samples in the first proposal are independent, while the samples in the second proposal are dependent.

In the first proposal, where the manufacturer randomly samples 10 different dealerships for each set of sales numbers (last year and 15 years ago), the samples are independent. This is because the selection of dealerships for one set of sales numbers does not affect or influence the selection of dealerships for the other set of sales numbers. Each dealership is chosen randomly and independently for each set.

On the other hand, in the second proposal, where the manufacturer randomly samples 10 dealerships for both sets of sales numbers, the samples are dependent. This is because the selection of dealerships for one set of sales numbers is directly tied to the selection of dealerships for the other set of sales numbers. The same 10 dealerships are chosen for both sets, so the samples are not independent.

The choice between independent and dependent samples can have implications for statistical analysis. Independent samples allow for direct comparisons between the two sets of sales numbers, while dependent samples may introduce potential bias or confounding factors due to the shared dealership selection.

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Step-by-step explanation:

Volume of Cone=

\( \frac{1}{3} \pi \: r {}^{2} h\)

Volume of Sphere=

\(\frac{4}{3} \pi \: r {}^{3} \)

Since VC = VS

\( \frac{1}{3} \times 3.14 \times 8 {}^{2} \times h = \frac{4}{3} \times 3.14 \times 216\)

66.99h = 904.32

h = 904.32 ÷66.99

h= 13.5 feet

Answer:

y = 2.0x + 0.6

Step-by-step explanation:

Dino's data:

X _____ Y

1 ______ 1

2 ______5

3 ______6

4 _____ 10

5 _____ 13

6 _____ 13

7 _____ 14

8 _____ 16

9 _____ 18

10 _____21

Using the linear regression calculator, the line of best fit for the data is :

y = 2.0X + 0.6

Where ;

Slope = 2 ; intercept = 0.6

Imagine a bunch of 12-year cicadas along with some 13-year cicadas. Assume this is the exact moment where predators are around.

Both groups face predators no matter their age. For the next cycle, 13-years cicadas will be 15, and 12-years cicadas will be 14 and they will face predators just the same.

So, once they are grown-up cicadas, they face the dangers in the same way at the same frequency.

Now analyze their whole lifetime. Today a new cicada was born and the next cycle of predators will be 2 years from now. Next year a new cicada will be born and the next cycle is only one year ahead.

This means that the next cycle of predators finds the older cicada for the first time and also for the new cicada. And for the rest of their lifetimes, no relative advantage is found for either of them, with the possible exception that older cicadas may be more prepared to avoid the danger.

So my best answer is NO.

The mean and standard deviation of the total time are µx = 66 and σx = 3.17, so the correct answer is (D) µx= 66 σx= 3.17.

To find this:

The total time to complete all three tasks is the sum of the time taken for each task. The mean time to complete all three tasks (µx) can be calculated by adding the mean time for each task: µx = 36 + 22 + 8 = 66. The standard deviation (σx) of the total time can be calculated using the standard deviation of each task and the square root of the number of tasks (n).

Using the formula: \(\sigma x = \frac{\sqrt{\sigma1^2 + \sigma2^2 + \sigma3^2}}{\sqrt n}\),

where σ1, σ2, σ3 are the standard deviations of each task, n = 3.

Plugging in the values, we get

\(\sigma x = \sqrt(2.5^2 + 1.8^2 + 0.75^2)/\sqrt3 \\= \sqrt{6.25 + 3.24 + 0.5625}/\sqrt3 \\= \sqrt{10.0525}/\sqrt3 = 3.17\)

Hence, the mean and standard deviation of the total time are µx = 66 and σx = 3.17, so the correct answer is (D) µx= 66 σx= 3.17.

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Standard deviation is the square root of variance .

So,

It is used in measuring any deviation or shift from the calculated mean.  

From a data set, the mean of the data can be determined with which the standard deviation can be measure.

Therefore, Standard deviation is use to measure variation that exist in an individual data set. There are different type of data set from which variation is measured.

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Answer:

B)  Write out the relation in an x-y table and check that each x-value corresponds to the only one x - value

Answer:

a = Negative one-fifth

Step-by-step explanation:

The given equation is :

\(\dfrac{2}{5}+a=\dfrac{1}{5}\)

We need to find the value of a.

Subtract 2/5 from both sides.

\(\dfrac{2}{5}+a-\dfrac{2}{5}=\dfrac{1}{5}-\dfrac{2}{5}\\\\a=\frac{1}{5}-\frac{2}{5}\\\\a=\dfrac{-1}{5}\)

So, the correct answer is Negative one-fifth. Hence, the correct option is (b).

Answer:

A. Major Axis

Step-by-step explanation:

Red line shows the Major axis of the ellipse drawn.

A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane.

An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.

An ellipse uses two axis, major and minor.

Major axis is the larger one and minor axis is smaller.

The minor axis of an ellipse is the line that contains the shorter of the two line segments about which the ellipse is symmetrical

Now we come to the question.

Here extreme points of the red line are on the ellipse are more distant than the extreme points of the axis perpendicular to the red line.

Therefore, red line shows the Major axis of the ellipse drawn.

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Answer:

The result of decimal expansion of  \(8/15\) is \(0.533\).

Step-by-step explanation:

Hence the decimal expansion by simple division of \(8/15\) is \(0.533\).

Answer: answer C.

Step-by-step explanation: you have to add and divide

Answer:

B

Step-by-step explanation:

So if B is the midpoint of AC, AB must be 1/2 of AC.

If D is the midpoint of AB, it must be 1/2 of 1/2 of AC, which is 1/4 of AC.

So AC= 4 DB

The polygons are similar.

This is because dividing the corresponding sides forms the same ratio, as shown by the three equations below

35/28 = 1.25

25/20 = 1.25

(15.5)/(12.4) = 1.25

So the larger figure on the right has side lengths that are 1.25 times larger compared to the corresponding sides of the figure on the left.

You'll need to flip the figure on the left so that the side labeled "20" is along the top, and the "28" is along the bottom.

After this flip happens, also note that the angle arc markings match up. The bottom pairs of angles of each figure are shown with a single arc, while the top angles are shown as double arcs. This helps visually show which angles pair up and are congruent to one another.

Because we have similar proportions as discussed earlier, and congruent pairs of angles like this, this shows the two figures are similar quadrilaterals. The one on the right is simply an enlarged scaled up copy of the figure on the left.

Hope it helps.

If you have any query, feel free to ask.

The entire area bounded by any triangle's three sides is referred to as the triangle's area.

In essence, it is equivalent to 1/2 of base times height, or A = 1/2 b times h. A triangular polygon's base (b) and height (h) must be known in order to calculate its area.

Whether a triangle is scalene, isosceles, or equilateral, it can be used to solve any kind of triangle.

Be aware that the triangle's base and height are at right angles to one another. In square units, the area unit is measured (m2, cm2).

Example :

Consider this triangle with a base of 3 cm and a height of 4 cm. What is its area?

Employing the formula,

Triangle's area is equal to half of b times h.

= 1/2 × 4 (cm) × 3 (cm) (cm)

= 2 (cm) × 3 (cm) (cm)

= 6 cm2

In addition to the method mentioned above, Heron's formula can be used to determine a triangle's area when we know the lengths of its three sides.

In addition, when two sides of a triangle are known as well as the angle that forms between them, the area can be calculated using trigonometric functions.

For each of these circumstances, we shall calculate the area.

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Answer:

37.7 feet

Step-by-step explanation:

1/2 mile is 2,640.. which you would do 2,640 ÷ 350 and it will give you some number... now with that number you would multiply that with 5.

Answer: Answer: A

Explanation:

Just plug in numbers since you know the unknown values,

x + r = 4 + 5

4 + 5 = 9

Step-by-step explanation:

The perimeters of the given figures 4, 5, 6 are 27 m, 140.76 cm  and 28 inches respectively.

We need to find the perimeter of given figures.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

4) Now, sum of all the sides

= 5+3.5+1.5+3.5+5+3.5+1.5+3.5 m

= 27 m

5) Here, radius = Diameter/2 = 17 cm

Perimeter = 2 semicircles+2(17) cm

= 2 × 1/2 πr + 2×17

= 2 × 3.14 × 17 + 34

= 140.76 cm

6) In the given figure here, there are 4 similar triangles

= 4(4+3) inches

= 4 × 7

= 28 inches

Therefore, the perimeters of the given figures 4, 5, 6 are 27 m, 140.76 cm  and 28 inches respectively.

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Answer:

279 feet

Step-by-step explanation:

To find x, we solve using the Trigonometric function of Tangent

tan θ = Opposite/ Adjacent

θ = 64°

Length of the shadow = Adjacent = 136 feet

Height of the building = Opposite = h

Hence,

tan 64 = h/136 feet

Cross Multiply

h = tan 64 × 136 feet

h = 278.84132245 feet

Approximately, h to the nearest foot ≈ 279 feet

Therefore, the height of the building = 279 feet

Answer:

To determine how many miles Naomi's car can go on one gallon of gas, we first need to determine how many gallons of gas the car used to travel 15\tfrac{1}{2}15 2 1 ​ miles. We are told that the car used \frac{2}{5} 5 2 ​ of a gallon to travel this distance, so we can multiply this value by 15\tfrac{1}{2}15 2 1 ​ to get the total number of gallons used:

\frac{2}{5} \cdot 15\tfrac{1}{2} = 9

Therefore, the car used 9 gallons of gas to travel 15\tfrac{1}{2}15 2 1 ​ miles. To determine how many miles the car can go on one gallon of gas, we need to divide the total number of miles traveled by the number of gallons used:

15\tfrac{1}{2} \div 9 = \frac{31}{18}

This means that the car can go 31/18 miles on one gallon of gas. Since this fraction is not in simplest form, we can further simplify it by dividing the numerator and denominator by the greatest common factor, which is 3:

\frac{31}{18} \div \frac{3}{3} = \frac{31}{18} \cdot \frac{3}{3} = \frac{31 \cdot 3}{18 \cdot 3} = \frac{93}{54}

Therefore, the car can go 93/54 miles on one gallon of gas. This fraction can be further simplified by dividing the numerator and denominator by the greatest common factor, which is 1:

\frac{93}{54} \div \frac{1}{1} = \frac{93}{54} \cdot \frac{1}{1} = \frac{93 \cdot 1}{54 \cdot 1} = \frac{93}{54}

Therefore, the final answer is that the car can go 93/54 miles on one gallon of gas.

Answer:

x = 54

Step-by-step explanation:

These are vertically opposite angles, meaning their angle measures are equal.

2x + 2 = 3x - 52

x = 54

The Central Carbon

It is a method that represents the three-dimensional structures of molecules on a single page. These are a convenient way to represent the molecules and distribute them between the pairs of enantiomers. These are very often used to represent isomers of sugars.

The Fischer Projection consists of horizontal and vertical lines, the horizontal lines represent atoms that are pointed out of the plane and the vertical line represents atoms that are pointed away from the plane. The intersection point of the horizontal line and the vertical line represents the central carbon.

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Answer:

75%

Step-by-step explanation:

9 ÷ 12 = 0.75

0.75 x 100 = 75 = 75%

Answer:

3/4

Step-by-step explanation:

Experimental probability, is the probability determined according to the results of an "experiment" or a trial. In Carla's "experiment", she attempted 12 total shots and made 9 shots. The probability that she made a shot would be 9/12, or 3/4.

Answer:

Step-by-step explanation:

Ok:

So this means 3/4 of one big square it is asked to find=75 percent= 75/100=0.75