There are 125 second graders amd 118 third graders at the museum. There are 249 more adults than students at the museum. Hire many adults are at the museum

Without graphing the function f(x) = 5 (4)ˣ is an exponential growth

The y intercept is 5

Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of  3 main parts

a = the starting or initial value

b = the base function

x = the exponents

The base is what determines exponential growth or decay

when the base is < 1 we have exponential decay nut when the base is > 1 we have exponential growth

Considering the problem,  f(x) = 5 (4)ˣ

the starting = 5

the base = 4 exponential growth

the exponents = x

The y intercept is the starting this is the value at x = 0

f(x) = 5 (4)ˣ

f(x) = 5 (4)⁰

f(x) = 5 * 1

f(x) = 5

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The algebraic expression will be Y=a+9

Where Y=number of cards Angelica has now, a=added movie cards,

what are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

As given

Angelica buys 3 packets of movie cards and 6 packets of cartoon cards

and and adds these to the 3 packets of movie cards she already has

Now let a=packets of movies she already has

and Y=number of cards Angelica has now

Therefore, The algebraic expression will be

             Y=a+3+6=a+9

            Y=a+9

             Where a=3

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Answer:

Step-by-step explanation:

in the picture

The number of tickets sold for students is 735.

A system of equations is a set of two or more equations with the same variables. A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously.

Given that, 1415 concert tickets were sold for a total of $26,665. If students paid $15 and non students paid $23,

To solve this problem we will establish a system of equations,

Let the sold ticket for students be x, and that of non students be y,

x+y = 1415

y = 1415-x...(i)

15x + 23y = 26,665...(ii)

Substitute eq(i) in eq(ii)

15x + 23(1415-x) = 26665

15x + 32545 - 23x = 26665

8x = 5880

x = 735

Hence, the number of tickets sold for students is 735.

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Hey there!

Hope this helps!

Answer:

a) even

b) neither

c) odd

Step-by-step explanation:

A function is "even" when there is symmetry about the y-axis.

Functions are symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph:

A function is "odd" when there is origin symmetry.

Functions are symmetric with respect to the origin if for every point (a, b) on the graph, there is also a point (-a, -b) on the graph:

From inspection of the graph, the curve appears to be symmetrical about the y-axis. Therefore, the function is even.

This is an absolute value function.  It has no symmetry about the y-axis or the origin.  Therefore, the function is neither.

From inspection of the graph, the curve appears to be symmetric with respect to the origin. Therefore, the function is odd.

If the integers have different signs subtract the, lesser absolute value from the greatest absolute value and use the sign of the number with the larger absolute value.

What are integers?

The word "integer" first emerged in the Latin term "Integer," which denotes whole or intact. The particular class of numbers known as integers is made up of zero, positive numbers, and negative numbers.

Treatment of integers with different sign

If the integers have different signs, we need to subtract the, smaller absolute value from the larger absolute value and we use the sign of the number which has the larger absolute value.

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The price of the ABC bond on the previous day is $104 3/4

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

Rate = $10 per day

Current price = $114 3/4

Using the above as a guide, we have the following:

Previous price = Current price - Rate

Substitute the known values in the above equation, so, we have the following representation

Previous price = $114 3/4 = $10

Evaluate the difference

Previous price = $104 3/4

Hence, the previous price is $104 3/4

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Complete question

ABC bond increase by $10 everyday. If the price on a given is $114 3/4, what was the price of the ABC bond on the previous day?

Where the line plot shows the different lengths of nails in your toolbox. If you take all the nails that are less than 2 inches long and lay them end to end, the nails will reach 15 1/2 inches far. (Option C)

A line chart is a type of chart that presents information as a succession of data points called "markers" that are connected by straight-line segments. It is a simple form of a chart that is used in many disciplines.

With regard to the attached line plot, we have the following information.

See the attached line plot

Size inches     Numbers ( frequency)

1/2                     3

1                        5

1 1/2                  6

2                       1

2 1/2                 0

3                       0

3 1/2                 2

4                       1

Nails less than 2 inches in size are 1/2, 1, and 1 1/2

The total length  = 3(1/2)  + 5(1) + 6(1 1/2)

= 3/2 + 5 + (3/2 * 6)

= 3/2 + 5 + 9

= 3/2 + 14

= 1 1/2 + 14

= 15 1/2 Inches.

Therefore, it is correct to state that all the nails that are less than 2 inches will reach 15 1/2 inches. Hence option C is correct.

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Full Question:

See attached image.

The paint needed to paint the rectangle-type wall is 4.285 gallons.

What is a rectangle?

A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles. The opposite sides of the rectangle are equal in length which makes it different from a square.

For example, if one side of a rectangle is 20 cm, then the side opposite to it is also 20 cm.

A rectangle has two diagonals, that bisects each other. Both the diagonals are equal in length.

Perimeter, P = 2 (Length + Width)

Area of Rectangle=Length*Breadth

Now,

For given rectangular shaped wall

350 feet^2 is covered by 1 gallon of paint.

1 feet^2 is covered by 1/350

and 2000 feet^2 is covered by=2000/350=4.285 gallons

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The function is called deep binding.

In deep binding, When the function is created, It uses the environment.
Shallow binding : In shallow binding, When the function invokes, it uses the environment.
Ad hoc binding : In Ad hoc binding, when the uses called expression in which the procedure is passed as an argument, it uses the environment.

mysub prints the x value residing in sub4 since the value of x in sub2 is bound to the value of the function in which sub2 was called => deep binding
mysub prints the x value residing in sub1 since the value of x in sub2 is bound to the value of the function in which sub2 was defined = > shallow binding
mysub prints the value residing in sub3 since the value of x in sub2 is bound to the value of the function that passed sub2 as an actual parameter => ad hoc binding.

So,

The function is deep binding.

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Answer:

Step-by-step explanation:

First write down the decimal number divided by 1 like this:

0.607

1

As we have 3 digits after the decimal point in the numerator, we need to multiply both the numerator and denominator by 103 = 1000, so that there is no decimal point in the numerator

0.607 × 1000

1 × 1000

=

607

1000

Therefore, 0.607 as a fraction is 607/1000

The scale factor needed to form ΔA'B'C' from ΔABC is 1/2 or 0.5.

What is scale factor?

The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.

The coordinate points of triangle ABC is -

A(2,6), B(2,2), and C(6,2)

The coordinate points of triangle A'B'C' is -

A'(1,3), B'(1,1), and C'(3,1)

Subtract the coordinate points of A'B'C' from ABC to find the scale factor -

A = (2 - 1, 6 - 3) = (1,3)

B = (2 - 1, 2 - 1) = (1,1)

B = (6 - 3, 2 - 1) = (3,1)

So, it can be seen that to form triangle ABC, the triangle A'B'C' is multiplied by the factor of 2.

A(2,6) = (x/2 , y/2) = A'(1,3)

B(2,2) = (x/2 , y/2) = B'(1,1)

C(6,2) = (x/2 , y/2) = C'(3,1)

Therefore, the scale factor is 1/2 or 0.5.

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Answer:

Using elimination method:

Add the two equations to eliminate the y variable: y-x=3x+2 + 2x+2y=14-y

This gives 3x=14-3 or x = (14-3)/3 = 11/3

Substitute this value of x into one of the original equations, for example the first one: y-x=3x+2

We get y-(11/3) = 3(11/3) +2

Solving for y we get y = (11/3) +2

Therefore, the solution to the system of equations is x = 11/3 and y = (11/3) + 2

Any statistical relationship between two random variables or bivariate data, whether causal or not, is referred to as dependence or correlation.

The correlation between two variables A and B is exactly the same as the correlation between A and B, and it describes the strength of the association between the two.

A causal relationship exists when an alteration in one variable directly affects an alteration in the other variable. A causal generalization, such as the claim that smoking causes lung cancer, does not refer specifically to any one smoker but rather to the unique connection between the characteristic of smoking and the characteristic of developing lung cancer.

An overview was given as your information is incomplete and can't be found.

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When there are 12 observations in a small sample, the median is calculated by: b. the average value of the sixth position and the seventh position of an ascending sorted.

In Mathematics, a median can be defined as the middle number (center) of a sorted data set, which is when the data set is either arranged in a descending order from the greatest to least or an ascending order the least to greatest.

First of all, we would sort the 12 observations from the least to greatest as follows:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

The median for 12 observations is the average of the 6th and 7th number:

Median = (6 + 7)/2

Median = 13/2

Median = 12.5.

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Answer:5.36

Step-by-step explanation: bc ik

Answer: Four 9" pies require 2 cups of juice (4 time 0.5)

Two cups of juices is 32 tablespoons (16 Tbl to a cup)

Sixteen lemons are needed (32 / 2)

(16)($0.67)= $10.72

Hope this helps

The total weight of the wall and the average dead load per foot of wall length can be calculated.

The total weight of the wall can be calculated by finding the weight of the bricks and frame, then adding the weight of the glass and sash. The total weight of the wall (W) is calculated as follows:

W = (0.25*40ft*11ft)*(weight of bricks + weight of frame) + (0.75*40ft*11ft)*(weight of glass + weight of sash)

The average dead load (F) per foot of wall length is calculated by dividing the total weight of the wall by the total length of the wall (L):

F = W/L = (0.25*40ft*11ft)*(weight of bricks + weight of frame) + (0.75*40ft*11ft)*(weight of glass + weight of sash) / (40ft)

Using the tables in Hibbeler for weights of materials, the total weight of the wall and the average dead load per foot of wall length can be calculated.

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Applying the properties of the diagonals of a square, the length of EG ≈ 8.5 units.

The diagonals of a square are line segments that connect opposite corners of the square. They have the following properties:

Therefore, each segment that is formed by the bisection of the diagonals would be equal to 6.

Applying Pythagorean theorem, we have:

EG = √(6² + 6²)

EG = √(36 + 36)

Length of EG ≈ 8.5 units.

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The value of x from the equation 3(x + 1) = 2(x − 1) is -5

Algebraic expression are defined as expression that are composed of terms, variables, coefficients, factors and constants.

Algebraic expressions are also composed of mathematical operations. Some of these operations are;

From the information given, we have the expression;

3(x + 1) = 2(x − 1)

expand the bracket

3x + 3 = 2x - 2

collect like terms

3x - 2x = -2 - 3

subtract like terms

x = -5

Hence, the value is -4

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The value of x in each set of similar triangles are:

1. x = 9.6

2. x = 33

3. x = 19

4. x = 10

If two or more triangles are similar to each other, then their corresponding side lengths will have equal ratio.

Since all set of pairs of triangles are similar, their corresponding side lengths would be proportional as shown below.

1. 24/x = 35/14

Cross multiply

35x = 336

x = 336/35

x = 9.6

2. x/42.9 = 30/39

39x = 1,287

x = 1,287/39

x = 33

3. 27/24 = 3x - 21 / x + 13

27(x + 13) = 24(3x - 21)

27x + 351 = 72x - 504

27x - 72x = -351 - 504

-45x = -855

x = -855/-45

x = 19

4. 9/14 = x + 8 / 3x - 2

9(3x - 2) = 14(x + 8)

27x - 18 = 14x + 112

27x - 14x = 18 + 112

13x = 130

x = 130/13

x = 10

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No, Johnny's truck cannot carry all the 240 stones in one trip because the weight of the stones is greater than the maximum capacity of the truck.

Let us first convert the dimensions of the stones to ft from inches as;

7.2 inches = 0.6 ft

3.6 inches = 0.3 ft

1.2 inches = 0.1 ft

Volume of stone = 0.6 * 0.3 * 0.1

Volume of stone = 0.018 ft³

The formula for mass here is;

Mass = Density * Volume

Thus;

Mass = 259.2 * 0.018

Mass = 4.6656 kg

Total weight of 240 stones = 240 * 4.6656

= 1,119.744 kg

This is higher than the maximum capacity and so his truck cannot carry all the stones

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To evaluate -4.6+7+22+(-7.75) simplifying each term, -4.6+7 = 2.4, 2.4+22 = 24.4, 24.4+(-7.75) = 16.65 so the simplified expression is 16.65 which is a decimal.

A fraction is a mathematical expression that represents a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number) separated by a horizontal line.

Fractions can be simplified to their lowest form by dividing both numerator and denominator by their greatest common factor.

To evaluate the expression, we need to simplify each term and then add them together. The steps are as follows:

-4.6 + 7 = 2.4 (subtracting 4.6 from 7)

2.4 + 22 = 24.4 (adding 2.4 and 22)

24.4 + (-7.75) = 16.65 (adding 24.4 and -7.75)

So the simplified expression is 16.65.

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Answer:

a. True

b. False

c. False

d. False

e. True

Step-by-step explanation:

a. True: The graph of f^-1(x) is a reflection of the graph of f(x) over the line y = x. This is because for any point (x,y) on the graph of f(x), the point (y,x) will be on the graph of f^-1(x), and vice versa.

b. False: The inverse function, f^-1(x) does not have to be always increasing. It depends on the original function, f(x) and its properties, A function could be increasing or decreasing, or it could be a combination of both, or none of them. A function which is strictly increasing is guaranteed to have a unique inverse, but that inverse function may or may not be increasing.

c.False: The function y = x^2 does not have an inverse function. Because it is not a one-to-one function. It is not injective, meaning that it maps multiple input values to the same output value, so it cannot be inverted.

d. False: If a function has a y-intercept, it does not mean that its inverse must also have a y-intercept. A y-intercept is a point at which a function crosses the y-axis, which corresponds to x = 0. However, the inverse function of a function will have its x and y coordinates swapped, so the inverse of a function that crosses the y-axis at a particular point will not cross the x-axis at the same point.

e. True: If a function has a y-intercept, it means that the function crosses the y-axis. But since the inverse function of a function will have its x and y coordinates swapped, the inverse of a function that crosses the y-axis at a particular point will cross the x-axis at the same point.

The average of a sample of any data set as given here is an example of a statistic. Hence, option D is the correct answer.

A parameter and a statistic are very similar to one another. Parameters are numerals that are used to describe the properties of total populations. Statistics are numerals that are used to describe the properties of samples. For example, the average age of everyone in a country is a parameter while the average of just 25 peoples' age is a statistic.

Here, we have been told that the researcher recorded the individual change in weight for a small group of 25 freshmen from this college during their first semester, and then, the researcher calculated the average change in weight during the first semester among these 25 students. Hence, we know that the average here is a statistic. So, option D is the correct answer.

The complete question that you might be searching for is given below -

In order for a researcher to obtain a raa researcher is interested in the average first-semester change in weight (gain or loss) for students at a local college. thus, they record the individual change in weight for a small group of 25 freshmen from this college during their first semester. then, the researcher calculates the average change in weight during the first semester among these 25 students. The average is an example of a-

a. constant

b. variable

c. parameter

d. statistic

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The tools used to measure height of a soccer trophy metric ruler and the unit is centimeter.

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The tools used to measure height of a soccer trophy metric ruler and the unit is centimeter.

Tools and units used for measurement vary depending on the type of measurement being taken. Some common tools used for measurement include: rulers, tape measures, calipers, and micrometers. Other tools may include thermometers, scales, and flow meters.

To measure length, the most common unit is the meter. This is the International System of Units (SI) standard for length. Other common units for length include the centimeter, inch, foot, and yard. To measure area, the most common unit is the square meter. Other units for area include the square foot, square yard, acre, and hectare.

To measure volume, the most common unit is the liter. Other common units for volume include the gallon, quart, pint, and fluid ounce. To measure mass, the most common unit is the gram. Other common units for mass include the kilogram, ounce, pound, and stone.

To measure temperature, the most common unit is the Celsius degree. Other common units for temperature include the Fahrenheit and Kelvin degrees. To measure time, the most common unit is the second. Other common units for time include the minute, hour, day, week, and month.

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The sides of the triangle ABC are 6, 10, and 8. The sides of the triangle LMN are 12, 20, and 16. The ratio of the respective sides is the same for the two triangles because they are comparable. Therefore, BC is 10 miles long.

Due to the equal ratio of their corresponding sides, the triangles ABC and LMN are comparable. This indicates that the lengths of the sides of LMN may be obtained by multiplying the lengths of the sides of ABC by the same factor. For instance, side AB in ABC is 6 inches long, whereas side LM in LMN is 12 inches long. The lengths are 6:12, or 1:2, apart. The ratio remains the same for all matching. We can examine the other two sides of ABC to verify this response. Ten is the length of AC, and twenty is the length of MN. These two sides must likewise be multiplied by the same factor (1/2), since the ratio of the corresponding sides is the same. This results in AC and MN having lengths of 10 and matching ABC's dimensions. This demonstrates that BC is eight miles long.

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the complete question is

triangles abc and lmn are similar with measurements as shown. what is the measurement of bc, rounded to an integer find BC?

There are 11 possible values of b for which the sum of the squares of the digits of [tex]N_b \leq 512.[/tex]

We can use this formula to find the sum of the squares of the digits of N_b:

[tex](1_b^2 + 2_b^2 + ... + 100_b^2) * b^2 + (1_b^2 + 2_b^2 + ... + 100_b^2) * b + (1_b^2 + 2_b^2 + ... + 100_b^2)[/tex]

Simplifying, we get,

[tex](1_b^2 + 2_b^2 + ... + 100_b^2) * (b^2 + b + 1)[/tex]

We know that the sum of the squares of the digits of [tex]N_b \leq 512[/tex], so we can set up the following equation.

[tex](1_b^2 + 2_b^2 + ... + 100_b^2) * (b^2 + b + 1) \leq 512[/tex]

Also, [tex]1_b, 2_b, ..., 100_b[/tex] are all integers between 0 and b-1, inclusive. Therefore, [tex]1_b^2, 2_b^2, ..., 100_b^2[/tex] are also all integers between 0 and [tex](b-1)^2[/tex] inclusive.

So the maximum possible value for [tex](1_b^2 + 2_b^2 + ... + 100_b^2)[/tex] is [tex](100 * (b-1)^2)[/tex]and the minimum possible value for [tex](1_b^2 + 2_b^2 + ... + 100_b^2)[/tex] is 0.

Substituting these values into our equation, we get,

[tex](100 * (b-1)^2) * (b^2 + b + 1) \leq 512[/tex]

[tex]100 * (b-1)^2 * b^2 + 100 * (b-1)^2 * b + 100 * (b-1)^2 \leq 512[/tex]

Now we can solve for b as follows -

[tex]100 * (b-1)^2 * b^2 + 100 * (b-1)^2 * b + 100 * (b-1)^2 \leq 512[/tex]

[tex]100 * b^2 + 100 * b + 100 \leq 512[/tex]

[tex]b^2 + b + 1 \leq 5.12[/tex]

Now, b can be any integer between 1 and 11, inclusive.

Therefore, there are 11 possible values of b for which the sum of the squares of the digits of [tex]N_b \leq 512.[/tex]

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We are 95% confident that the proportion who intend to vote for Candidate R from the random sample is between 42% and 52%.

A confidence interval is a range of values that is possible to include the true population parameter, with a certain level of confidence. In this case, the sample proportion of 47% who indicated they intended to vote for Candidate R was used to construct a 95% confidence interval, with a margin of error of 5%.

This means that if we repeated the sampling process many times, 95% of the intervals constructed would contain the true population proportion of those who intend to vote for Candidate R. In other words, we are 95% confident that the true population proportion falls within the interval of 42% to 52%.

Note that the confidence interval does not indicate that we are 95% confident that the sample proportion is 47% or that 95% of the population intends to vote for Candidate R. It only gives us a range of values that is likely to contain the true population proportion, based on the sample data and the level of confidence.

Hence, the correct answer is B.

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Step-by-step explanation:

by cross method of factorisation.

x^2 - 12x + 27 = 0

(x - 3)(x - 9) = 0

so the roots are 3 and 9