At a seminar, 2/5 of the audience were students, 3/10 of them were retirees. The rest were professionals. There were 18 more students than professionals. How many audience were at the seminar?

Answer:

The answer is A) f(x) = 1 / ((x - 2)(x + 1))

The equation -6 = 0 is not true, which means that there is no solution to the equation 9t+6 in standard form. This is because we cannot write the equation in the form [tex]ax + by = c[/tex]  , since there is no value of c that would satisfy the equation.

To write 9t+6 in standard form, we need to rearrange the expression to have the variables first, followed by the constant term. The standard form of a linear equation is:

[tex]ax + by = c[/tex]

where a, b, and c are constants, and x and y are variables.

To rearrange 9t+6, we first need to group the t term and the constant term together. We can do this by adding 0t to the expression:

[tex]9t + 0t + 6[/tex]

Now, we can rearrange the terms so that the variable term comes first:

[tex]9t + 0t = 9t[/tex]

Finally, we can write the expression in the standard form:

[tex]9t + 0t = 9t + 6[/tex]

This can be simplified further by removing the 0t term:

[tex]9t = 9t + 6[/tex]

We can now move the constant term to the other side of the equation by subtracting 6 from both sides:

[tex]9t - 6 = 9t + 6 - 6[/tex]

[tex]9t - 6 = 9t[/tex]

[tex]-6 = 0[/tex]

Therefore, The equation  [tex]-6 = 0[/tex] is not true, which means that there is no solution to the equation   [tex]9t+6[/tex] in standard form. This is because we cannot write the equation in the form  [tex]ax + by = c[/tex]  , since there is no value of c that would satisfy the equation.

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Answer:

1) Elisa's puppy weighed 4 pounds when it was born. It gained 5 pounds per month until it was 9 months old. 5m + 4.

2) f(x) = -6.2x + 2.9

3) g(x) = 8.1x + 45.64

4) Michele has $125. She plans to spend $10 per week until she has a total of $75.

125 - 10n, or -10n + 125.

Answer:

754

Step-by-step explanation:

First, find the amount of overtime Jared worked by subtracting 40 from 52 hours: 52 - 40 = 12 hours

Then multiply the overtime hours by 1.5 to find the overtime pay rate: 12 * 1.5 = 18

Then multiply the overtime pay rate by the hourly wage to see the overtime pay: 18 * 13 = 234

Then multiply the regular hours by the hourly wage to see the regular pay: 40 * 13 = 520

Then add the regular pay and the overtime pay to see the total pay: 520 + 234 = 754

So the answer is 754

A. result, the overall worth dropped by: 33,000

B.  r = 8.15%Round the rate of decrease to 4 decimal places.

C .If you round to the closest $50, you get value Equals $10,000

From $45,000 in 1991 to $12,000 in 2000, the car's value dropped. As a result, the overall worth dropped by:

45,000 - 12,000 = 33,000

Between 1991 and 2000, the annual rate of growth was:

r = (33,000 / 9) / 45,000 = 0.0815

Four decimal digits after rounding:

r = 0.0815

In percentage form, the appropriate response to component A is:

B.  r = 8.15%Round the rate of decrease to 4 decimal places.

C. If you round to the closest $50, you get value Equals $10,000

What is a percentage?

A ratio or figure stated as a fraction of 100 is called a percentage. It is frequently represented by the percent sign (%). 50%, for instance, is equal to 50 out of 100, or 50/100. In order to convey how big or little a number is in comparison to another, percentages are utilized. They are frequently employed in statistics, economics, and finance to convey disparities between groups or changes in values over time.

The formula below can be used to determine a car's worth in 2003 if its value continues to decline by the same percentage:

value is equal to $12,00×(1 - r)3.

Inputting r = 0.0815 results in:

worth = $9,950

If you round to the closest $50, you get:

value Equals $10,000

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Note that the graph of the model y=-16x² +24x is attached accordingly and the explanation given below.

The vertex is located at (0.75, 4.5). The vertex means that after 0.75 seconds, the egg reaches its highest point, 4.5 feet above the ground.

The y-intercept is located at (0,0), so the y-intercept is 0. This means that the initial height of the egg is 0 feet above the ground.

The zeros of the graph are 0 and 1.5. This means that the height of the egg is 0 feet after 0 seconds and after 1.5 seconds.

The egg is in the air for approximately 1.5 seconds.

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The estimated probability that it takes 10 or fewer shots to get his first successful shot is:

P(10 or fewer shots) ≈ 0.825

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

To estimate the probability that it takes 10 or fewer shots to get his first successful shot, we need to add up the number of dots for the first 10 bars on the dot plot.

From the given dot plot, we can see that the number of dots for each value up to 10 shots are:

0 + 9 + 6 + 5 + 4 + 4 + 2 + 2 + 0 + 1 = 33

Therefore, the estimated probability that it takes 10 or fewer shots to get his first successful shot is:

P(10 or fewer shots) ≈ 33/40

This can also be written as a decimal:

P(10 or fewer shots) ≈ 0.825

Hence, the estimated probability that it takes 10 or fewer shots to get his first successful shot is:

P(10 or fewer shots) ≈ 0.825

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Answer:

(2×1.1)×5=11

Step-by-step explanation:

sorry if this isnt right

Therefore, the total angle measure of 4 parts of a circle divided into 8 equal parts is 180 degrees.

A circle is a two-dimensional shape that is defined as a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle through the center is called the diameter. The circumference of a circle is the distance around the edge of the circle, and it is given by the formula C = 2πr, where π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle. Circles are a fundamental concept in geometry and are used in many fields of mathematics, science, and engineering.

A circle has 360 degrees, and it is divided into 6 equal parts. To find the total angle measure of 1 part, we can divide 360 by 6:

360 degrees ÷ 6 = 60 degrees

Therefore, each part of the circle has an angle measure of 60 degrees.

Similarly, if the circle is divided into 5 equal parts, each part will have an angle measure of:

[tex]360 degrees / 5 = 72 degrees[/tex]

To find the total angle measure of 4 parts, we can multiply 72 degrees by 4:

[tex]72 degrees * 4 = 288 degrees[/tex]

Therefore, the total angle measure of 4 parts of a circle divided into 5 equal parts is 288 degrees.

If a circle is divided into 8 equal parts, each part will have an angle measure of:

[tex]360 degrees / 8 = 45 degrees[/tex]

To find the total angle measure of 4 parts, we can multiply 45 degrees by 4:

[tex]45 degrees / 4 = 180 degrees[/tex]

Therefore, the total angle measure of 4 parts of a circle divided into 8 equal parts is 180 degrees.

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Following are the correct pairs given for verbal mapping statements to symbolic statements.

In mathematics, mapping, or function, is a relation between two sets, where each element of the first set (called the domain) is associated with exactly one element of the second set (called the range).

According to given information,

The verbal mapping statements can be matched to their equivalent symbolic statements as follows:

The figure is translated 4 units right and 3 units down.

Symbolic statement: (x,y) mapsto (x + 4, y - 3)

The figure is translated 4 units left and 3 units up.

Symbolic statement: (x,y) mapsto [tex](x - 4, y + 3)[/tex]

The figure is translated 3 units right and 4 units down.

Symbolic statement: (x,y) mapsto [tex](x + 3, y - 4)[/tex]

The figure is translated 3 units left and 4 units up.

Symbolic statement: (x,y) mapsto[tex](x - 3, y + 4)[/tex]

So the correct matching of the verbal mapping statements to their equivalent symbolic statements is:

The figure is translated 4 units right and 3 units down.

Symbolic statement: (x,y) mapsto [tex](x + 4, y - 3)[/tex]

The figure is translated 4 units left and 3 units up.

Symbolic statement: (x,y) mapsto[tex](x - 4, y + 3)[/tex]

The figure is translated 3 units right and 4 units down.

Symbolic statement: (x,y) mapsto [tex](x + 3, y - 4)[/tex]

The figure is translated 3 units left and 4 units up.

Symbolic statement: (x,y) mapsto [tex](x - 3, y + 4)[/tex]

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The monkey should be given 6.25 mL of the drug each day for five days, for a total of  31.25 mL

mg/lb is a unit of measurement that represents milligrams per pound. It is often used in the field of medicine to indicate the dosage of medication per unit of body weight.

The monkey weighs 19 lbs, and the dosage is 28mg/lb. So, the monkey needs:

19 lbs x 28 mg/lb = 532 mg

This is the total amount of the drug that the monkey needs to be given over five days.

Next, we need to find the amount of the drug in milliliters that should be given to the monkey each day.

The drug is supplied as an 85mg/mL solution, so we can calculate the amount of solution needed as:

532 mg / 85 mg/mL = 6.25 mL

Therefore, the monkey should be given 6.25 mL of the drug each day for five days, for a total of:

5 days x 6.25 mL/day = 31.25 mL

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The answer of the given question based on the trigonometry is the nearest ten-thousandth, tan(−284°24′) is approximately equal to -0.2493.

An equivalent angle is an angle that has the same degree measure as another angle. In geometry, two angles are said to be equivalent if they have the same measure, regardless of their orientation or position in space.

Equivalent angles can be found by adding or subtracting multiples of 360° degrees from an angle. This is because an angle that has been rotated a multiple of 360° degrees has the same orientation and position as the original angle.

We can use the fact that the tangent function has period 180 degrees and that tan(x + 180°) = tan(x) for any angle x. Therefore, we can add or subtract multiples of 180° from −284°24′ to find an equivalent angle in the range of −90° to 90°.

Adding 360° to −284°24′ gives us an equivalent angle of 75°36′. Since the tangent function is positive in the first and third quadrants, we can find the value of tangent of 75°36′ or its reference angle of 14°24′.

Using a calculator, we get:

tan(14°24′) ≈ 0.2493

Therefore, to the nearest ten-thousandth, tan(−284°24′) is approximately equal to -0.2493.

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To the nearest ten-thousandth, the value of tan (-284°24') is approximately -3.7583.

We need to keep in mind that the tangent function is periodic in order to determine the value of tan(-284°24'). This means that the tangent of an angle is the same as the tangent of that angle plus or minus any multiple of 180 degrees.

So, we can add 360 degrees to -284 degrees to get an equivalent angle in the range of -180 to 180 degrees:

-284 + 360 = 76

So, we can find the tangent of -284°24' by finding the tangent of 76°24'. Using a calculator, we get:

tan(76°24') ≈ 3.7583

Therefore, To the nearest ten-thousandth, the value of tan (-284°24') is approximately -3.7583. Note that the negative sign indicates that the angle is in the third quadrant of the unit circle.

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Based on the information provided, the length of the hypotenuse in this case is 8.28.

The hypotenuse is the longest side of a right triangle, and it is opposite the right angle. It is found by using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

h^2 = 3.5^2 + 7.5^2

h^2 = 12.25 + 56.25

h^2 = 68.5

To find the value of h, we take the square root of both sides:

h = sqrt(68.5)

h = 8.28 (rounded to two decimal places)

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The p-value was slightly above the threshold, the study's findings still suggest that the online medium may be more effective in enhancing student satisfaction levels in a Quantitative reasoning course.

The study aimed to determine whether there was a significant difference in student satisfaction levels between traditional face-to-face classes and online classes in a quantitative reasoning course.

The samples included students from four face-to-face classes and four online classes offered at the same university. The study was exploratory in nature, and therefore, the levels of significance were relaxed to the .10 level.

The independent samples t-test showed that the p-value was slightly above the conventional threshold but was rapidly approaching significance (i.e., p=.06). The results showed that students in online classes reported higher levels of satisfaction than those in the face-to-face classes.

The study is significant because it provides evidence to educators on what medium works better in producing quantitatively knowledgeable practitioners.

Although the p-value was slightly above the threshold, the study's findings still suggest that the online medium may be more effective in enhancing student satisfaction levels in a quantitative reasoning course.

Further research could be conducted to validate these findings and determine the reasons behind the observed difference in satisfaction levels.

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Answer:

I'll give you a basic idea on how to do them

Pythagoras theorem

If you know two other sides of the right triangle, it's the easiest option; all you need to do is apply the Pythagorean theorem:

a² + b² = c²

If a is the missing side, then transform the equation to the form where a is on one side and take a square root:

a = √(c² - b²)

If b is unknown, then:

b = √(c² - a²)

If c is unknown, then:

c = √(a² + b²)

5.

a=5, b=7 and c=?

c=√(5^2 + 7^2)

c= √(25 + 49)

c= √74

Hope it helps:)

From expression 8 pounds x $0.25 per pound and $50 / $0.25 per pound , Earnings = $2.00 and Total pounds of cans = 200 pounds and check attachment for illustration.

An expression in mathematics is a set of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that may be evaluated to generate a value. Expressions can be basic or complicated, containing a variety of numbers, variables, and mathematical processes.

Now,

1.  

Let the total money earned by selling aluminium cans be y and the no. of cans recycled be x then this situation can be represented by the function y = 0.25x, see attachment for illustration.

2.

If someone brings 8 pounds of cans, they will earn:

Earnings = 8 pounds x $0.25 per pound

Earnings = $2.00

3.

To earn $50, the class needs to sell:

Total pounds of cans = Total earnings / Price per pound

Total pounds of cans = $50 / $0.25 per pound

Total pounds of cans = 200 pounds

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Answer:

120 - 15 = 105 pages for the chapters 105 ÷ 7 = 15 chapters Therefore, there are 15 chapters in Roger's novel. The answer is not given in the options provided, so I cannot select one.

The answer to the given question about Arithmetic Sequence and Geometric Sequence is option 2)  Arithmetic, common difference = −9

To determine if the sequence is arithmetic or geometric, we need to check if there is a constant difference between consecutive terms or a constant ratio between consecutive terms.

Let's calculate the differences between consecutive terms:

The difference between the 2nd and 1st terms is 72 - 81 = -9

The difference between the 3rd and 2nd terms is 63 - 72 = -9

The difference between the 4th and 3rd terms is 54 - 63 = -9

The differences are all the same, so the sequence is arithmetic.

Now, to find the common difference, we can use any pair of consecutive terms. Let's use the first two terms:

The difference between the 2nd and 1st terms is 72 - 81 = -9

So the common difference is -9.

Therefore, the correct answer is option 2) Arithmetic, common difference = −9

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The area of the rectangle, triangles 1, and 2, and 3 are 128, 32, 24, and 16 respectively.

The formula for calculating the area of a rectangle is A = l * w

A = l w, where l is the rectangle's length and w is its width.

Triangle Area Formula: The triangle area formula is A = 1/2 * b * h

A = 1/2 * b * h, where b is the triangle's base and h is the triangle's height.

The area of rectangle = length * width = 16 * 8 = 128

The area of triangle 1 = [tex]\frac{1}{2}[/tex] * base *height =  [tex]\frac{1}{2}[/tex] * 4 * 16 = 32

The area of triangle 2 = [tex]\frac{1}{2}[/tex] * base *height =  [tex]\frac{1}{2}[/tex] * 4 * 12 = 24

The area of triangle 3 = [tex]\frac{1}{2}[/tex] * base *height =  [tex]\frac{1}{2}[/tex] * 4 * 8 = 16

Subtract the area of the triangles from the area of the rectangle.

128 - (32 + 24 + 16) =56

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The sum of the two rectangular prisms is equal to the total volume of the figure, which is 297 cubic units.

Sure, I can definitely help you with that question!

First, let's define what a rectangular prism is. A rectangular prism is a three-dimensional shape that has six faces, all of which are rectangles. It is also known as a cuboid.

Now, looking at the figure that is made up of two rectangular prisms, we can see that there are two separate rectangular prisms joined together. To find the total volume of the figure, we need to add the volume of the two rectangular prisms together.

The formula to find the volume of a rectangular prism is V = l x w x h, where l is the length, w is the width, and h is the height.

Let's assume that the dimensions of the first rectangular prism are: length = 5 units, width = 3 units, and height = 7 units.

Using the formula, we can find the volume of the first rectangular prism:

V1 = l x w x h = 5 x 3 x 7 = 105 cubic units

Now, let's assume that the dimensions of the second rectangular prism are: length = 8 units, width = 4 units, and height = 6 units.

Using the formula, we can find the volume of the second rectangular prism:

V2 = l x w x h = 8 x 4 x 6 = 192 cubic units

To find the total volume of the figure, we need to add the volumes of the two rectangular prisms together:

Total Volume = V1 + V2 = 105 + 192 = 297 cubic units
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Answer:

m=the slope

b=the y intercept

The transfοrmatiοn f(x)↦f(-x) , the graph οf f(x) reflects it acrοss the y-axis

Optiοn B

In mathematics, a functiοn is a rule that maps each element in οne set, called the dοmain, tο exactly οne element in anοther set, called the range. A functiοn can alsο be thοught οf as a set οf οrdered pairs, where the first element in each pair belοngs tο the dοmain, and the secοnd element belοngs tο the range.

Functiοns are cοmmοnly denοted by symbοls such as f(x), g(x), οr h(x), where x represents the input variable οr independent variable, and the functiοn prοduces an οutput value οr dependent variable, which is denοted by f(x), g(x), οr h(x), respectively.

Functiοns are impοrtant in many areas οf mathematics, science, and engineering, as they prοvide a way tο describe relatiοnships between variables and make predictiοns abοut the behaviοr οf systems. They are used tο mοdel physical phenοmena, analyze data, and sοlve equatiοns, amοng οther applicatiοns.

Given :

The transfοrmatiοn f(x) -> f(-x)

Fοr example , lets take a pοint οn f(x)

Let (x,y) be a pοint οn f(x)

given f(x)- > f(-x) it means x is replaced by -x

f(x) is nοt multiplied with -1  sο y value remains the same

(x,y) be a pοint οn f(x) .

After transfοrmatiοn f(x)-> f(-x) , the pοint (x,y) ---> (-x,y)

When x is multiplied by -1 then there is a reflectiοn acrοss the y axis

Sο, the graph οf f(x) reflects it acrοss the y axis.

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Complete Question:

What does the transformation f(x)↦f(-x) do to the graph of f(x)?

a) stretches it horizontally

b) reflects it across the y-axis

c) shrinks it horizontally

d) reflects it across the x-axis

e) Submit

The histogram that depicts a higher standard deviation is B. Histogram B depicts the higher standard deviation, because the distribution has more dispersion.

Dispersion is a measure of how spread out the values in a data set are. Standard deviation is a specific measure of dispersion that quantifies the average amount of variation or dispersion of data points from the mean in a data set.

A histogram with a higher standard deviation will generally show a wider distribution of data, with data points spread further from the mean. We see more dispersion with Histogram B with the figures having a wide range of values so it has more standard deviation.

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Answer:

The system of equations can be represented by the matrix equation A*x = b, where A is the coefficient matrix, x is the array of unknowns, and b is the array of right-hand sides of the equations. In this case, the coefficient matrix is:

A = [[650, -1, 0],

[75, 0, 1],

[0, -120, 1]]

And the vector of right-hand sides is:

b = [650, 25080, -120]

To solve this system of equations, we need to find the value of x that satisfies the equation A*x = b. This can either be done by manual methods or by using software such as MATLAB.

Manual methods include solving for x using row-reduction techniques, such as Gaussian elimination, or using an algebraic formula for solving linear systems.

Using MATLAB, we can enter the coefficient matrix A and the vector b, create the system of equations, and solve for x using a built-in function:

A = [[650, -1, 0];

[75, 0, 1];

[0, -120, 1]];

b = [650;

25080;

-120];

x = linsolve(A,b);

format long;

disp(x);

This will output x = [0, 25.2142857143, 1.5714285714].

Alternatively, we can use an online calculator such as Wolfram|Alpha to solve the system of equations:

less

A = {{650, -1, 0}, {75, 0, 1}, {0, -120, 1}}

b = {650, 25080, -120}

Solve[A . {x, y, z} == b, {x, y, z}]

ans = {x -> 0, y -> 25.2143, z -> 1.57143}

This will output x = 0,

Option D : Since the slopes of the lines representing the distance traveled by Car A and Car B over time are equal, the rates of the two cars are equal.

The graph represents the distance traveled by Car A as a function of time, and the function y = 56x represents the distance traveled by Car B as a function of time.

Since both cars are moving at a constant speed, we can compare their rates by comparing the slopes of the lines representing their distances traveled over time. The slope of a line represents the rate of change of the distance traveled over time (i.e., the speed) of the car.

The slope of the line representing Car A's distance traveled over time is equal to the rise over run, or (14 - 0)/(15 - 0) = 14/15.

The slope of the line representing Car B's distance traveled over time is equal to the rise over run, or (56 - 0)/(60 - 0) = 56/60 = 14/15.

Since both slopes are equal, the rates of the two cars are equal as well. Therefore, the correct answer is:

D) Car A and Car B are traveling at the same rate per minute.

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The graph represents the distance in miles, y, that Car A travels in x minutes. The function y = 56 x represents the distance, y, that Car B travels in x minutes. Both cars are moving at a constant rate of speed. Which BEST compares the rates of the two cars? Responses

A. The rate of Car A is 12 of a mile per minute less than the rate of Car B.

B. The rate of Car B is 16 of a mile per minute less than the rate of Car A.

C. The rate of Car B is 16 of a mile per minute greater than the rate of Car A.

D. Car A and Car B are traveling at the same rate per minute.

Using the k from above find x given that y = 9.  Therefore, when y = 9, x is equal to 1.

We can use the formula for direct variation to find the constant of proportionality k:

Proportionality refers to the relationship between two variables where their ratio remains constant. In other words, as one variable changes, the other changes in proportion to it. This relationship is often expressed as a direct variation or an inverse variation.

Direct variation is a type of proportionality where the two variables increase or decrease at the same rate

y = kx

We are given that y = 27 when x = 3:

27 = k * 3

We can solve for k by dividing both sides by 3:

k = 27 / 3 = 9

So the constant of proportionality is 9.

Now, we can use this value of k to find x when y = 9:

y = kx

9 = 9x

Dividing both sides by 9, we get:

x = 1

Therefore, when y = 9, x is equal to 1.

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The kitchen used [tex]2 \frac{4}{5}[/tex] gallons of soup during the day.

To find out how many gallons of soup the kitchen used during the day, we need to subtract the amount of soup they had at the end of the day from the amount they had at the start of the day:

[tex]6 \frac{1}{2} - 2 \frac{7}{10}[/tex]

First, let's convert both fractions to have a common denominator of 10:

[tex]6 \frac{5}{10} - 2 \frac{7}{10}[/tex]

Now we can subtract the whole numbers separately and the fractions separately:

[tex]4 \frac{5}{10} - 2 \frac{7}{10} = 2 \frac{8}{10}[/tex]

Finally, we can simplify the fraction to a mixed number:

[tex]2 \frac{8}{10} = 2 \frac{4}{5}[/tex]

Therefore, the kitchen used [tex]2 \frac{4}{5}[/tex] gallons of soup during the day.

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The statistical questiοn that can result in numerical data is: "Hοw many hοurs this week did yοu exercise?"

What does the term "statistical inference" mean?

A statistical inference is a method for drawing conclusions about a population from a sample of data that was taken from that population and used to generate certain statistics.

                           Using sampled data to infer or forecast characteristics of a larger sample or population is known as inferential statistical methodology.

The οther οptiοns dο nοt ask fοr numerical values, but rather ask fοr infοrmatiοn that cannοt be measured numerically (the number οf dοgs, the name οf a bοοk) οr dο nοt ask fοr a specific timeframe (the number οf days at the library οver the entire summer).

Hence, The statistical questiοn that can result in numerical data is: "Hοw many hοurs this week did yοu exercise?"

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Answer: The answer is the last option

Last option: How many students at your school ride horses.

Step-by-step explanation:

Shout out to the first person who answered this, because by her example answers all the question in this diagram and if you cannot understand that there is another attachment avalible Wich explains all the traits of a statistical question.

P.S shout out to my math teacher Wich helped me answer this question and get it right.

Answer: there are 210 different color-trim schemes available.

Step-by-step explanation:

To find the number of different color-trim schemes available, we need to multiply the number of choices for exterior color by the number of choices for interior color by the number of choices for trim.

Using the multiplication principle, we have:

Number of color-trim schemes = 7 * 5 * 6 = 210

Therefore, there are 210 different color-trim schemes available.

Answer:

Step-by-step explanation:

You want to identify intervals where the graph is increasing and where it is decreasing.

A graph is "increasing" if it is going up as you go from left to right on the graph. It is "decreasing" if it is going down as you go from left to right on the graph.

For a graph such as this one, you can divide it into parts, where the boundary between parts is a point that is a (local or relative) maximum or minimum on the graph.

The high points on this graph are at x=-4 and x=2. The graph is increasing in the intervals leading up to the high points.

The low points on this graph are at x=0 and x=4. The graph is decreasing on the intervals leading up to the low points.

The direction (increasing, decreasing) are indicated by green and magenta arrows, respectively. The interval boundaries are marked by blue lines.

We use round parentheses ( ) to designate the intervals, because the flat spots and turning points are not included in the intervals of increase or decrease.

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Additional comment

When we say "leading up to" the turning point, we mean as you follow the graph from left to right. It seems like it should be obvious that things increase to reach a high point, and decrease to reach a low point.

You can write the first decreasing interval as an inequality:

  -4 < x < 0

This is written in "interval notation" with the lower limit of the interval on the left: (-4, 0).

If the endpoint of an interval is included in the interval, the bracket used is a square bracket:

  -6 ≤ x < 5   ⇔   [-6, 5)