A man who is 6 feet tall casts a shadow that is 4 feet long. At the same time, a nearby flagpole casts a shadow that is 18 feet long. How tall is the flagpole?

picture of answer options are below

All the correct values are,

a)⇒ f (0) = - 1

b)⇒ f (1) = 1

c)⇒ f (-1) = - 3

d)⇒ f (a) = 2a - 1

e)⇒ g (0) = - 4

f)⇒ g (-2) = 0

g)⇒ g (3) = 5

h)⇒ g (t) = t² - 4

i)⇒ f (a+5) = 2a + 9

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

The function are,

⇒ f (x) = 2x - 1

⇒ g (x) = x² - 4

Now, We can find all the values by substituting as;

a) f (0)

⇒ f (x) = 2x - 1

Put x = 0;

⇒ f (0) = 2×0 - 1

⇒ f (0) = - 1

b) f (1)

⇒ f (x) = 2x - 1

Put x = 1;

⇒ f (1) = 2×1 - 1

⇒ f (1) = 1

c) f (-1)

⇒ f (x) = 2x - 1

Put x = -1;

⇒ f (-1) = 2×-1 - 1

⇒ f (-1) = - 2 - 1

⇒ f (-1) = - 3

d) f (a)

⇒ f (x) = 2x - 1

Put x = a;

⇒ f (a) = 2×a - 1

⇒ f (a) = 2a - 1

e) g (0)

⇒ g (x) = x² - 4

Put x = 0;

⇒ g (0) = 0² - 4

⇒ g (0) = - 4

f) g (-2)

⇒ g (x) = x² - 4

Put x = -2;

⇒ g (-2) = -2² - 4

⇒ g (-2) = 4 - 4

⇒ g (-2) = 0

g) g (3)

⇒ g (x) = x² - 4

Put x = 3;

⇒ g (3) = 3² - 4

⇒ g (3) = 5

h) g (t)

⇒ g (x) = x² - 4

Put x = t;

⇒ g (t) = t² - 4

i) f (a+5)

⇒ f (x) = 2x - 1

Put x = a + 5;

⇒ f (a+5) = 2×(a + 5) - 1

⇒ f (a+5) = 2a + 10 - 1

⇒ f (a+5) = 2a + 9

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The basis for Col A is linearly independent.

Two matrices are equal if and only if their shapes are same, and they've got the same elements for each corresponding row and column positions.

We are given that;

A = [3 7 3 3 6 4 0 -4 4 3 10 0] ~ [1 0 0 2 1 0 4 4 0 -2 -3 0]

Now,

To find a basis for Col A, we need to find the columns of A that correspond to the pivot columns of the echelon form. The pivot columns are the columns that have a leading 1 in a row. In this case, the pivot columns are the first, second, and fourth columns. Therefore, a basis for Col A is given by the vectors in those columns of A. We can write them as:

​3303​​,​76−410​​,​3440​​

These three vectors are linearly independent and span Col A, so they form a basis for Col A.

Therefore, by matrices the answer will be linearly independent.

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Therefore , the solution to the given problem of unitary method comes out to be  Hamster got 20 votes.

The unit method is a way of problem-solving where you first calculate the amount of a single item, then multiple that value to get the answer. Simply expression, a single system value is extracted from a specified multiple using the unit method. For illustration, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint and inverse are equivalent. (Linear Algebra, Mathematical Interpretation, Mathematics of Matrix or Operators).

Here,

4 votes are represented by each grid line. then, four votes per grid.

Fish received 8 votes.

There are three more grids for hamsters than for fish.

votes per grid times the number of grids

So,

the number of fish grids is 4.

2 grids are needed for fish.

There are 3 more grids for hamsters than for fish. As a result, 2 + 3 = 5 grids for the hamster.

Grids times votes per grid divide the total number of ballots.

As a result, there are 20 votes or hamsters (5 x 4).

Hamster has 20 votes as a result.

Therefore , the solution to the given problem of unitary method comes out to be  Hamster got 20 votes.

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Evaluated the Following Integral If R [0, 1] X [0, 1]. 3y xy DA is [tex]\frac{3}{24}[/tex].

What is integral ?

An integral is a mathematical concept that represents the area under a curve, or the accumulation of a quantity over a given interval. Integrals are a fundamental concept in calculus, which is the branch of mathematics that deals with the study of rates of change and accumulation. In other words, an integral can be thought of as the sum of an infinite number of infinitesimal "slices" of the quantity being measured, over a given interval. Integrals can be used to solve a wide variety of problems.

The integral is evaluated as follows,

∫[0,1]∫[0,1] 3yxy dydx

= 3∫[0,1] yxy dxdy

= 3 * (1/4) * ∫[0,1] x dxdy

= 3 * (1/4) * (1/2) * x^2 dy

= 3 * (1/4) * (1/2) * (1/3) = 3/24

Hence , Evaluated the Following Integral If R [0, 1] X [0, 1]. 3y xy DA is [tex]\frac{3}{24}[/tex].

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The percentage of students who chose " other " types of games, from the group of students was 25 %

The percentage of students who chose " other " types of games can be found by the formula:

= Number of students who chose " other " types of games / Total number of students x 100 %

Number of students who chose " other " types of games = 5 students

Total number of students = 20 students

The percentage is:

= 5 / 20 x 100 %

= 0. 25 x 100%

= 25 %

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The full question is:

In a survey, a group of 20 students were asked to name their favorite type of game. There were 5 students who chose “other” types of games.​ What is the percentage of those students who chose " other "?

Answer: To find out how many ounces of orange sherbet are needed for one batch of smoothie, you can use the proportion of orange sherbet to the total amount of smoothie.

24 oz of orange sherbet / 5/8 of smoothie = x oz of orange sherbet / 1 batch of smoothie

To solve for x, you can cross-multiply and simplify:

(24 oz of orange sherbet) * (1 batch of smoothie) = (5/8 of smoothie) * x oz of orange sherbet

24 * 1 = 5/8 * x

24 = 5/8 * x

By multiplying both sides by 8/5,

x = 24 * 8/5

x = 38.4 oz

So, 38.4 ounces of orange sherbet are needed for one batch of smoothie.

Step-by-step explanation:

Answer:

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

Use the given expression z/16, substitute z with 40 and calculate:

541 + 279 = 820 is the number bond for the expression 540 + 280.

A number bond is a simple addition sum that has become so familiar to a child that they can recognise it and complete it almost immediately, with recall as automatic as that of an entry from a multiplication table in multiplication. Number bonds are used in the teaching of mathematics at the primary school level.

When given the other two numbers, a child who "knows" this number bond should be able to instantly fill in any one of these three numbers if it were missing, without having to "work it out." Number bonds are frequently taught in sets whose sums are common round numbers like 10 or 20.

We can find the number bond by simply adding 1 to first term and subtracting 1 from 2nd term.

540 + 280 = 820

(540 + 1) + (280 -1) = 820

541 + 279 = 820

Thus, 541 + 279 = 820 is the number bond for 540 + 280.

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The statement can be represented symbolically as: (P) ∨ (Q) → (S)

How to represent a statement in symbolic form?

Representing a statement in symbolic form involves using logical symbols and logical operators to create a logical expression that captures the meaning of the statement. Here are some common symbols and operators used in symbolic logic:

To put the statement "Michael does not have the time or money to complete the project" into symbolic form, we first need to identify the key phrases and declare them as symbols. Here are a few possible ways to do this:

(P) Michael does not have the time

(Q) Michael does not have the money

(R) Michael does not have the time or money

(S) Michael can not complete the project

We can put them in different ways, depending on the statement you want to make.

Then the statement can be represented symbolically as:

(P) ∨ (Q) → (S)

This means Michael does not have the time or the money or both, which leads him to not be able to complete the project.

Alternatively, we can use the following representation

(R) → (S)

This means Michael does not have the time or the money or both, which leads him to not be able to complete the project.

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236.5 ft depth will the pressure acting on the object.

The m is the slope, and b is the y-intercept, therefore f(x) = mx + b.

You are given the value of m = 4.44 (lb/in2) for every 10 feet of descent; however, you need f(x) to be a function of the depth in inches, thus you must determine what m is for every inch of fall.

120 inches are equal to 10 feet multiplied by (12 inches per foot).

Every 120 inches of fall, then, gives rise to m = 4.44.

m = 4.44 / 120 = 0.037 for each inch of fall

Consequently, f(x) = 0.037x + b

The fact that f(0) = 15 and b = 15 can be used to find b.

f(x) = 0.037x + 15 is the equation as a result.

Set f(x) = 120 and work out x to obtain the pressure at that point.

120 = 0.037x + 15 0.037x = 105 x, or 105 / 0.037 = 2837.8 inches, or roughly 236.5 ft.

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The length of hypotenuse = 5.2 centimeters.

The triangle that has at least one angle 90 degrees is called right angle triangle. The largest side length of a right triangle is termed as hypotenuse.

The Pythagorean theorem is applicable for right-angled triangle. The theorem stated that the square of hypotenuse is equal to the sum of the square of the remaining two side lengths. If a right-angled triangle has hypotenuse H and other two side length b and o respectively, then H² = b² + o².

Assume this right-angled triangle is named as ABC, AC is the hypotenuse and AB and BC is the other sides.

As AB = 2 cm and BC = 4.8 cm

then according to the Pythagorean theorem AC² = AB²+ BC²

                                                                     AC²= 2² + 4.8²

Hypotenuse AC = 5.2 centimeter.

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In the given circle graph, central angle of people like to travel by boat is 72°.

Circle graphs also known as pie charts are one of the most commonly used graphs to represent data using the attributes of circles, spheres, and angular data to represent real-world information. It is used to visualize information and data.

Given that, A travel magazine surveyed 500 of its adult readers about their favorite ways to travel.

The circle graph below shows that 125 people like to travel by train, 275 people like to travel by airplane, and 100 people like to travel by boat.

In a circle graph, the whole circle which subtends a 360-degree angle at the center is broken into different.

Central angle of people like to travel by train:

125/500 ×360°

= 90°

Central angle of people like to travel by airplane:

275/500 ×360°

= 198°

Central angle of people like to travel by boat:

100/500 ×360°

= 72°

Therefore, in the given circle graph, central angle of people like to travel by boat is 72°.

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The number of mosaics tiles in each side of the square  floor is 7 tiles.

Since a square has four equal sides and four equal angles, it is a regular quadrilateral. It may alternatively be explained as a rectangle with two neighboring sides that are of equal length.

A square can have many different characteristics. The following list includes some of a square's key characteristics.

The total number of mosaic tiles = 49

Let the lenght of each side of the floor be x

Therefore,

x² = 49

⇒ x = 7

The number of mosaics tiles in each side of the floor is 7 tiles.

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Answer:

Step-by-step explanation:

-2y + 9 = -1

Adding 2y to both sides:

9 = 2y - 1

Adding 1 to both sides:

10 = 2y

Dividing both sides by 2:

y = 5

Therefore, the value of y that makes the equation true is y = 5

So on solving the provided question we can say that - the equation will be y = -120x^2 - 2500x + 80,000; x = 0 so, y = 80000

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

y = -120x^2 - 2500x + 80,000

x = 0

so, y = 80000

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Here we are given that Gracie sold 15x + 4xy in her inventory and Mariella sold -15x +3x -2xy on weekends. We need to find combined inventory.

For that simplify add both the expressions as ,

15x + 4xy + (-15x) + 3x - 2xy

15x + 4xy - 15x + 3x - 2xy

Group like terms ,

(15x + 3x - 15x ) + (4xy - 2xy)

simplify,

3x + 2xy [ required answer]

And we are done!

The slope of the given data is 25.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Jon paid $200 for 8 classes at gold dawn yoga studio.

the cost, y, is proportional to the number of classes purchased, x

The slope will be cost of each class

200/8=25

So the equation will be y=25x

25 is the slope.

Hence, the slope of the given data is 25.

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The shape that represents the sample mean of the 81 students who are selected is; Approximately normal

When a distribution of data is defined as skewed, it means that it does not take the normal distribution's bell shape. Rather, it tends to distort with values either to the left or right of the center of the data.

Now, the Central Limit Theorem states specifically that the distribution of sample mean is normally distributed. It goes further to state that if the population values from which the sample originates is not normally distributed, the sample distribution will be normal. This effect will lead to  increases as sample size increases.

Thus, we can conclude that the shape is normally distributed

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Complete question is;

Suppose the mean GPA of School A students is 3.5 and the standard deviation is 0.7 it is well known that this distribution is left-skewed. A random sample of n = 81 students will be drawn. What is the shape of the sampling distribution of the random variable ¯X.  which represents the sample mean of the 81 students who are selected.?

- Left- skewed

- right-skewed

- approximately normal

- we cannot determine this from the information given.

Answer:

54 years

Step-by-step explanation:

If we want to know how to solve for the number of years a crow can live, we can use this equation:

(27 ÷ 3) + 45 =?

We can first solve for 27 divided by 3.

(27 ÷ 3) + 45 =?

9 + 45 =?

Now solve for 9 plus 45:

9 + 45 = 54

Therefore, if a woodpecker can live 27 years, a swallow 3 times less, and a crow 45 years longer than the swallow, we can say that a crow can live for 54 years.

The cost of 1 cup of soup is, $5.28 and 1 side of rice is $7.92.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Three cups of soup and two sides of rice cost $15.85.

And, Six cups of soup and four sides of rice cost $31.70.

Let cost of 1 cup of soup = x

And, The cost of 1 side of rice = y

Here, Three cups of soup and two sides of rice cost $15.85.

Hence, We can formulate;

⇒ 3x + 2y = 15.85  .. (i)

And, Six cups of soup and four sides of rice cost $31.70.

Hence, We can formulate;

⇒ 6x + 4y = 31.70   .. (ii)

By equation (i) and (ii);

⇒ x = $5.28

⇒ y = $7.92

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Answer:

Step-by-step explanation:

Your first answer is correct. Good job

Your second answer is correct. good job

Your last answer is correct. good work

Answer:

Follow me if this helped you

Step-by-step explanation:

a)The claims of the Sun-American are not consistent with each other. The probability that four or more out of every 15 unemployment beneficiaries have jobs is 0.9095, but the expected number of employed beneficiaries exceeds 7, which is more than 4.

Answer:

the coordinate plane has a big example

Step-by-step explanation:

The percentage of salt (by mass) in this mixture is calculated to be

information from the problem

A mixture is made by combining 1.97 lb of salt

and 5.37 lb of water

The question is a percentage problem, percentage deals with a fraction hundred.

The percentage of the salt in the mixture is calculated by first finding the mass of the mixture

mass of the mixture = mass of salt used + mass of water that made the solution

mass of the mixture = 1.97 lb + 5.37 lb

mass of the mixture = 7.34 lb

The percentage of salt in the mixture

= 1.97 / 7.34 * 100

= 0.2684 * 100

= 26.8%

The percentage of salt in the mixture is 26.8%

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Given inequality:

To graph it first, consider line:

Find two points on the line.

Now, plot the two points.

Next, draw a dashed line trough the two points. Dashed line because the line is not included into solution set, due to '<' sign.

The last step, shade the area below (to the right) the line. Below the line because 'y <' means 'y-values less than' which appears below the line.

Answer:

See attachment.

Step-by-step explanation:

Given linear inequality:

[tex]y < 3x[/tex]

When graphing inequalities, temporarily replace the inequality sign for the equals sign:

[tex]\implies y=3x[/tex]

Find two points on the line by substituting two values of x into the equation:

[tex]x=0 \implies y=3(0)=0 \implies (0, 0)[/tex]

[tex]x=1 \implies y=3(1)=3 \implies (1,3)[/tex]

When graphing inequalities:

Therefore, to graph the given linear inequality:

After dilatation, the length of AC will be 20. The angle A’ will then be measured at 37°.

Dilation is the process of expanding the size of something without changing its shape. The size of the item can be increased or decreased depending on the scale factor.

We have done so.

AABC is dilated by a factor of four to provide AA’B’C’.

The triangle A’B’C’ is formed by diluting the triangle ABC by a factor of four.

Then the length of AC after dilatation. We now have

A’C’ = scale factor multiplied by AC

A’C’ = 4 x 5

A’C’ = 20

The angle A’ will then be measured.

Dilation has no influence on the angle.

∠A = ∠A’ = 37°

As a result, the proper selection.

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On solving the provided question we can say that ordinary number the answer is  1.495 x 10^0

An ordinary number, also known as a standard form number or a decimal number, is a number that is written in the familiar base-10 format, with a whole number part and a fractional part separated by a decimal point.

A) 5.1 x 10¹ as an ordinary number is 51.

B) To work out the value of (1.7 x 10¹) × (8.5 x 10-²), we first need to multiply the two numbers:

(1.7 x 10¹) × (8.5 x 10-²) = 1.7 x 8.5 x 10¹ x 10-² = 14.95 x 10-1

To express the answer in standard form, we need to move the decimal point to the left so that there is only one non-zero digit to the left of it. 14.95 x 10-1 is 1.495 x 10^0. So the answer is 1.495 x 10^0

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The unit price of the gloves is $ 1.173.

To find the Unit price of the gloves find 1 dozen gloves by dividing the total price by the number of dozens. From that find the unit price by dividing a dozen gloves price by 12 as 1 dozen = 12.

Here we have

A contractor purchases 5 dozen pairs of padded work gloves for ​$70.40.

She incorrectly calculates the unit price as ​$13.44 per pair for the expense report.

Cost of 1 dozen pairs of padded work gloves = $70.40/5

Cost of 1 dozen pairs of padded work gloves = $ 14.08

Here 1 dozen = 12 gloves

Let 'x' be the Unit price

=> 60x = 70.40

=> x = 70.40/60

=> x = 1.173    

Therefore,

The unit price of the pair of gloves is $ 1.173.  

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When performing a hypothesis test on two dependent samples, the variable of interest is

d. the differences that exist between the matched-pair data.

In a hypothesis test on dependent samples, the variable of interest is the difference between the two samples. The test compares the means of the two samples and checks whether the difference is significant or not. The sample data are matched-pair, meaning that each data point in one sample corresponds to a specific data point in the other sample.

The variable of interest is the difference between the two matched data points, this difference is also known as the dependent variable.

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