A girl of height 0.9 m is walking away from the base of a lamp-post and covered 4.8 m. If the lamp is 3.6 m above the ground, find the length of her shadow.

The value of g in the following equation is 6.25. The solution has been obtained using trigonometry formula.

What is trigonometry?

The primary objective of the branch of mathematics known as "trigonometry" is the study of the sides, angles, and connections of the right-angle triangle. Therefore, applying the trigonometric formulas, functions, or trigonometric identities aids in locating the unknown or missing angles or sides of a right triangle. In trigonometry, angles can be stated in either degrees or radians. For calculations, the most common trigonometric angles are 0, 30, 45, 60, and 90 degrees.

We are given g sin 34° =3.5

⇒ g = 3.5/sin34°     (Dividing both sides by sin34°)

Now, value of sin34° = sin(30+4)° = 0.5592

So, we get

⇒ g = 3.5/0.5592

⇒ g = 6.25

Hence, the value of g in the following equation is 6.25.

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In the equation below, g has a value of 6.25. The trigonometric formula has been used to arrive at the solution.

The study of the sides, angles, and connections of the right-angle triangle is the main goal of the field of mathematics known as "trigonometry." In order to find the unknown or missing angles or sides of a right triangle, one can apply the trigonometric formulae, functions, or identities. Angles can be expressed in radians or degrees in trigonometry. The most frequent trigonometric angles used in computations are 0, 30, 45, 60, and 90 degrees.

Given is g sin 34° = 3.5.

g = 3.5/sin34° (both sides divided by sin34°)

The cost of sin today

34° = sin(30+4)° = 0.5592

So, we obtain

⇒ g = 3.5/0.5592

⇒ g = 6.26

Thus, the importance of g in the following equation is 6.26.

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The difference between the lightest bag of grapes that has been recorded by Colton will be 3/2 or 1 - 1/2.

[tex]2 - \frac{1}{2} [/tex]

[tex] = \frac{4}{2} - \frac{1}{2} [/tex]

[tex] = \frac{3}{2} or \: 1 - \frac{1}{2} [/tex]

Data gathering, analysis, interpretation, presentation, and organization are all topics covered in the study of statistics. In other words, gathering and summarizing data is a mathematical discipline. Additionally, statistics can be considered a subfield of applied mathematics.

Uncertainty and variation are two crucial and fundamental concepts in statistics. Only statistical analysis can be used to determine the uncertainty and variation in various fields. Probability, which has a significant impact on statistics, essentially determines these uncertainties.

Note that the graph for the following question is: (check the attached image).

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Timex can survey at least 384 consumers to guarantee a margin of error of 0.05 or less at a 99% confidence level.

What is proportion ?

A proportion is a way to express the relationship between two or more quantities or values. It is a statement that asserts that two ratios or fractions are equal, such as "2/5 is equal to 4/10".

To estimate the true proportion p of consumers who believe what is shown in Timex television commercials, Timex can use a sample proportion formula which is:

p = (number of positive responses) / (sample size)

To guarantee a margin of error of 0.05 or less at a 99% confidence level, Timex can use a sample size calculator. The sample size calculator takes into account the margin of error, confidence level, and the proportion of the population that is expected to be positive.

The sample size can be calculated using the formula :

n = (z^2 * p * (1-p)) / E^2

Where z is the z-score for the desired confidence level (z = 2.576 for 99% confidence level), p is the estimated proportion of the population that is expected to be positive (0.5 if the true proportion is unknown), and E is the desired margin of error (0.05).

Timex can survey at least 384 consumers to guarantee a margin of error of 0.05 or less at a 99% confidence level.

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The shift of the function y = log(x+4) -3 is 4 units left and 3 units down

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

y = log(x + 4)

The above equation is a logarithmic equation

So, the parent function is

y = log(x)

When the parent function is compared to the given function, we have

3 units down and 4 units left

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Answer:

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Step-by-step explanation:

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The function f(x) = -9x^3 is odd because it is not at the initial state after replacing x by -x.

By taking a function, replacing each x with an equal value, simplifying it, and then comparing the outcomes to what you had initially, you can "determine algebraically" whether it is even, odd, or neither.

If the function is identical to what you started with that is, if f(-x) = f (x), with all the signs remaining the same then the function is even. If the function is exactly the opposite of what you started with (i.e., if f(-x) = -f(x), with all the signs switched this is known as an odd function.

The function is f(x) = -9x^3

Now substitute -x in place of x.

f(-x) = -9(-x)^3

f(-x) = -9 × -(x)^3

f(-x) = 9x^3

As we can see that the function is not in the initial position so the function is odd.

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If the trend continued, the number of CDs that were sold in 2019 is approximately equal to: D. 2,000​.

In order to write a linear function that models the data point contained in the table and determine the slope, we would have to use the point-slope form to determine the line of best fit based on the data points provided on the scatter plot (see attachment).

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

y - 800 = (700 - 800)/(2005 - 2002)(x - 2002)

y = 33.33(x - 2002) + 800

y = 33.33x - 65,266

When x = 2019, the number of CDs sold is given by:

y = 33.33(2019) - 65,266

y = 2,027 ≈ 2,000 million CDs.

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Complete Question:

The scatter plot shows a number of CD's (in millions) that were sold from 1999 to 2005. If the trend continued, about how many CDs were sold in 2019?

A. 3000

B. 8500

C.3500

D. 2,000​

The trip there take if the return trip took eight hours is 5hrs.

What is Distance?

Distance is the sum of an object's movements, regardless of direction. Regardless of an object's starting or ending position, distance can be defined as the amount of ground it has covered.

What is Rate?

A rate in mathematics is the comparison of two related values expressed in different units. The numerator of the ratio expresses the corresponding rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities and it is assumed that this quantity may be modified systematically (i.e., is an independent variable).

We are given ;

A container ship made a trip to Madagascar and back

On the trip there it traveled 16 km/h.

the return trip it went 10 km/h.

if the return trip took eight hours;

then,

16x = 10 * 8

16x = 80

x = 80/16

x = 5

Therefore,  he trip there take if the return trip took eight hours is 5hrs.

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Answer:

[tex]5 \sqrt{6} [/tex]

Step-by-step explanation:

ignore the square roots and do 4+2-1

The first steps of the elimination of fraction is to take LCM for the denominators.

In math the term fraction is defined as represent the parts of a whole or collection of objects

Here we have know that  first we want to eliminate the fraction in the example equation.

As we all know that the process of eliminating in fraction will follow the following steps, they are listed as follows:

First we have to take the LCM for the fractions and then we have to enter the equations.

Then we have to multiply each equation by a number to get the lowest common multiple for one of the variables.

And then we have to add or subtract the two equations to eliminate that variable .

Then we should substitute that variable into one of the equations and solve for the other variable.

Finally we have to check by substituting your answer into one of the equations,

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No. The slopes of the two lines are not equal, therefore they are not parallel.

Parallel lines are two lines that are located at an equal distance from one another and never cross.

The distance and direction between them remain constant. In geometry, parallel lines are used to find solutions to problems involving angles and shape distances.

The angles created between two lines are equal when they are parallel. As a result, the angles formed when two parallel lines cross another line at their places of intersection are equal.

The Parallel Lines Theorem is what this is. Problems relating the angles and separations of forms can be resolved using this theorem.

Along with these shapes, parallel lines are also employed to create circles and ellipses as well as squares, rectangles, and trapezoids.

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The inequality representing Courtney's situation to buy air heads and popcorn is 0.25x + 2y ≤ 12.

Based on the situation of Courtney, we can conclude that she must get the combination in such quantity of each that it's total is less than or equal to 12. Creating the expression according to this statement.

Number of air heads × cost of one air head + number of popcorn × cost of one popcorn ≤ 12

Keep the values in formula to find the inequality

x×0.25 + y×2 ≤ 12

Performing multiplication between the constant and variable

0.25x + 2y ≤ 12

Thus, inequality representing this situation is 0.25x + 2y ≤ 12.

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The numerical answer is 5

Start by drawing three unit tapes, and divide each one of them in 5 equal parts since we need to be dividing the quantity 3 by 3/5 (denominator 5)

In the second step, join the three tapes in one long one maintaining the original divisions.

In the third step, select groups of 3 divisions (recall you need to divide by 3/5) which will identify in your tape how many of these 3/5 groups you have.

Finally count the number of 3/5 groups you found in the collection of the three original tapes placed together. You should count a total of 5 of these 3/5 groups.

5 then tells you what is the quotient of 3 divided in 3/5

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Answer:

1. Yes

2. Yes

3. No

Step-by-step explanation:

You can check by substituting x = 2 and y = -3 in these equations. If both sides appear to have same values then (2,-3) is a solution to that equation. If both sides appear to have different values then (2, -3) is not a solution to that equation.

[tex]\displaystyle{x+3y=-7}\\\\\displaystyle{2+3(-3)=-7}\\\\\displaystyle{2-9=-7}\\\\\displaystyle{-7=-7}[/tex]

Hence, (2, -3) is a solution to x + 3y = -7

[tex]\displaystyle{-x+y=-5}\\\\\displaystyle{-2-3=-5}\\\\\displaystyle{-5=-5}[/tex]

Hence, (2, -3) is a solution to -x + y = -5

[tex]\displaystyle{2x-y=1}\\\\\displaystyle{2(2)-(-3)=1}\\\\\displaystyle{4+3=1}\\\\\displaystyle{7=1}[/tex]

Hence, (2, -3) is not a solution to 2x - y = 1

Based on the dimensions of architecture's model and width of the building, the length of actual building is 420 meters.

The question is based on scale concept. Here the ratio of length to width will be same between the actual building and architect's model. Using this information to find the length of the building. Let us assume the length of actual building be x.

The ratio will be -

length:width (architect's model) = length:width (actual building)

1.4 : 0.8 = x : 240

Representing it as fraction

1.4/0.8 = x/240

x = 1.4 × 240/ 0.8

Performing multiplication in numerator

x = 336/0.8

Performing division

x = 420 meters

Thus, the length of the building is 420 meters.

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Answer:

Step-by-step explanation:

You didn't post any answer choices, but the answer should be:

y = x + (0.28)x = 1.28x

The given situation represents the (B) command economy.

In a planned economy, the production, distribution, and allocation of capital goods all occur in accordance with economic plans that may be economy-wide or specific to a particular class of products and services.

Centralized, decentralized, participative, or Soviet-style economic planning is all possible in a planned economy.

Depending on the precise kind of planning mechanism used, the degree of centralization or decentralization in decision-making and involvement will vary.

Central planning has been utilized in socialist regimes built on the Soviet model, however, some, like the former Socialist Federal Republic of Yugoslavia, have embraced some kind of market socialism.

Therefore, the given situation represents the (B) command economy.

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The amount of gelatin and water that Jeff use to make 9 boxes are 27 oz of powder and 18 cups of water respectively.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

We have

Amount of gelatin used for 3 boxes = 9 oz

Amount of gelatin for 1 box = 3 oz

Amount of water for 3 boxes = 6 cups

Amount of water for 1 box = 2 cups

We have to calculate the amount of gelatin and water for 9 boxes.

Amount of gelatin for 9 boxes = 3 × 9 = 27 oz

Amount of water for 9 boxes = 2 × 9 = 18 cups

Hence Jeff will use  27 oz of powder and 18 cups of water to make 9 boxes of gelatin.

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The original recipe had 0.9 cups of bananas.

Using only fresh ingredients, strawberry banana smoothie is a simple, nutritious dish. It is creamy, sweet, nutritious, and dairy- or dairy-free can be used to make it. The ideal summertime smoothie. Putting the strawberries, frozen banana, milk, and yoghurt in a blender and mixing until smooth and creamy is all that is required to make it.

Cups of strawberries = 1.75

No. of cups added of banana = 1/2

                                            = 0.5

No. of cups of banana smoothie have = 14.

The original recipe had = 1.4 - 0.5

                                   = 0.9

Hence, the original recipe had 0.9 cups of bananas.

Correct Question :

to make a strawberry banana smoothie, a recipe calls for 1.75 cups of strawberries and some bananas. to make the recipe taste more like banana, 1/2 cup more banana was added to the blender. the smoothie now has 1.4 cups of bananas. how many cups of bananas were in the original recipe?

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If the value be 5/6 then the equation be [tex]$x \times \frac{2}{3}=\frac{5}{9}$$[/tex].

A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.

A fraction is a piece of a whole number and a means to divide a number into pieces that are each equal. The numerator, also known as the number of equal parts being counted, is expressed as being greater than the denominator, also known as the number of parts in the entire.

Let the value be 5/6 then

simplifying the equation as

[tex]$x \times \frac{2}{3}=\frac{5}{9}$$[/tex]

Multiply both sides by 3

[tex]$3 x \frac{2}{3}=\frac{5 \cdot 3}{9}$$[/tex]

Simplifying the above equation, we get

2x = 5/3

Divide both sides by 2, we get

[tex]$\frac{2 x}{2}=\frac{\frac{5}{3}}{2}$$[/tex]

x = 5/6

Therefore, the correct answer is option a.

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D. 62% of women in the sample are the primary investor in their household.Inference: Women in the United States are likely to be the primary investors in their households.

The answer to this question is D. 62% of women in the sample are the primary investor in their household. This is an example of the descriptive branch of statistics because it summarizes the data collected in the survey. The inference based on the results of the survey is that women in the United States are likely to be the primary investors in their households.

62% of women in the sample are the primary investor in their household.

Inference: Women in the United States are likely to be the primary investors in their households.

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If the variance of a normal population is 5,  the probability that the variance of a random sample of size 15 exceeds 9.329  is 0.069.The variance of a sample from a normal population has a chi-squared distribution, which is the sum of the squares of the standard normal distribution.

The probability can be calculated by finding the area to the right of the chi-squared value of 9.329 on the chi-squared distribution. This area can be found by using the chi-squared cumulative distribution function, which is the integrated form of the chi-squared probability density function.

To find the probability, the chi-squared cumulative distribution function is used to calculate the area to the right of the chi-squared value of 9.329. This will give us the probability of the variance of the sample exceeding 9.329, which is 0.069.

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A number y is no more than -8. So the expression as inequality is y ≤ -8.

We have to write the word sentence as an inequality.

A number y is no more than -8.

A relationship between two values in an algebraic statement that are not equal is shown by an inequality. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

The statement is saying that y is no more than means y is less that or equal to -8.

So we can write the expression as

y ≤ -8

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The complete question is:

Write the word sentence as an inequality. A number y is no more than -8.

The largest possible value for the probability of A4 is 0.3.

If events A1, A2, A3, and A4 are pairwise mutually exclusive with the exception that A1 and A2 occur simultaneously, then the probability of A1 and A2 occurring together is 0.1. This means that the probability of A1 occurring separately is 0.3 - 0.1 = 0.2, and the same is true for A2.

Since A1, A2, A3, and A4 are pairwise mutually exclusive, the probability that they all occur together is 0. Therefore, the sum of their individual probabilities is also 0. Therefore, the probability of A4 is the remaining probability after accounting for the probability of A1, A2, and A3. The largest possible value for the probability of A4 is the total probability minus the probability of A1, A2, and A3.

So, the largest possible value for the probability of A4 would be:

1 - (0.2 + 0.2 + 0.3) = 1 - 0.7 = 0.3

Therefore, the largest possible value for the probability of A4 is 0.3.

The correct option regarding the number of kettles that can be filled with the potion is given as follows:

C. Between 2 and 3.

The number of kettles is obtained applying the proportions in this problem, dividing the total number of litters by the number of liters of each kettle.

The parameters for this problem are given as follows:

Hence the number of kettles is obtained as follows:

11/4 = 2.75.

Meaning that the correct option is given by option C.

A kettle holds 4 liters of magic potion. There are 11 liters of potion.

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Answer: 4x + 2 = -10

3x - 1 = 26

x + 7 = 34

Step-by-step explanation:

The probability that at least one of 10 randomly chosen Americans has O-negative blood is 0.722.

The probability that at least one of 10 randomly chosen Americans has O-negative blood can be calculated by first determining the probability that none of them have O-negative type blood. Since 7.2% of the population has O-negative blood, the probability that one of 10 randomly chosen Americans has O-negative blood is (1 - 0.072)^10. To determine the probability that at least one of 10 randomly chosen Americans has O-negative blood, we subtract this value from 1. Therefore, the probability that at least one of 10 randomly chosen Americans has O-negative blood is 1 - (1 - 0.072)^10, which is equal to 0.722.

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Answer: Blue: 12.5%

              White: 25%

              Orange: 62.5%

              Blue or White: 37.5%

Step-by-step explanation:

Step 1: Add all the Marbles together: 2 blue + 10 Orange + 4 White = 16     Marbles

Step 2: Add Blue and White marbles together: 2 blue + 4 White = 6 Marbles

Step 3: Divide Blue and White Marbles with total Marbles: 6/16 = 0.375

Step 4: Convert to Percentage: 0.375 x 100 = 37.5%

The classification of the transformation is c. translation.

Transformation is a process by which the orientation or dimension of a given object is changed so as to produce expected image. Some types of transformation are: translation, dilation, rotation and reflection.

i. Translation: This process implies shifting a given object a number of units in a particular direction.

ii. Dilation: This requires resizing a given object.

iii. Rotation: When a given object is turned about a reference point at a certain angle, then the process is called rotation.

iv. Reflection: This requires turning an object over a line or point to produce the desired image.

Considering the shapes given in the question, it can be deduced that the transformation to classify the process is translation.

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