Compare / Contrast Exponential Equations

1.) 2 (1/5)x-5

2.) 3 (1/2)x-3

Answer:

[tex]\huge\boxed{\sf f(5) = 11}[/tex]

Step-by-step explanation:

f(x) = 2x + 1

Put x = 5

So,

f(5) = 2(5) + 1

f(5) = 10 + 1

[tex]\rule[225]{225}{2}[/tex]

A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2 + 2 = 4. The correct answer is:

In Math's, an intercept is a point on the y-axis, through which the slope of the line passes. It is y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept. There are basically two intercepts, x-intercept and y-intercept.

Rewrite the function as an equation:

→ y = 2x + 1

Use the slope-intercept form to find the slope and y-intercept.

The slope-intercept form is y = mx + b where m is the slope of b is the y-intercept:

→ y = mx + b

Find the values of m and b using the form y = mx + b:

→ m = 2

→ b = 1

Therefore, A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2 + 2 = 4. The correct answer is:

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(a) The angle measurement of first unknown angle is c = 80 degrees

(b) The angle measurement of second unknown angle is y = 110 degrees

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

(a) You can pick pair of starting angles a = 30 degrees and b = 70 degrees

The angle measurement of first unknown angle will be:

a + b + c = 180  (sum of angles in a triangle is 180 degrees)

c = 180 - a - b

c = 180 - 30 - 70

c = 80 degrees

(b) The angle measurement of second unknown angle will be:

y = 180 - b  (sum of angles on a straight line is 180 degrees)

y = 180 - 70

y = 110 degrees

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Note that the probability that a combined sample tests positive is 0.67232 or 67.232%.

Let P(pos) be the probability that an individual sample tests positive.

We know P(pos) = 0.2,

so the probability that an individual sample tests negative is:

P(neg) = 1 - P(pos) = 0.8.

Let P(combined_neg) be the probability that a combined sample tests negative (i.e., all five component samples are negative).

Since the component samples are independent, we can calculate

P(combined_neg) as the product of their individual probabilities:

P(combined_neg) = P(neg) x P(neg) x P(neg) x P(neg) x P(neg)

= 0.8⁵
= 0.32768

Therefore, the probability that a combined sample tests positive (i.e., at least one of the five component samples tests positive) is:

P(combined_pos) = 1 - P(combined_neg)

= 1 - 0.32768

P(combined_pos) = 0.67232

Thus, the probability that a combined sample tests positive is 0.67232 or 67.232%.

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The characteristics of the given parabola f(x) = -3x² are, A. Compression by 3, reflected over the x-axis.

A parabola is a cross-section cut out of the cone and represented by an equation.

Here,
The general form of a parabola is f(x) = ax² + bx + c, where a, b, and c are constants. In this case, the given equation is f(x) = -3x², which means that a = -3, b = 0, and c = 0.

The sign of "a" determines the direction of the parabola. When "a" is negative, the parabola opens downward, and when "a" is positive, the parabola opens upward. In this case, a = -3, which means the parabola opens downward.

If a parabola is reflected over the x-axis, the sign of "a" remains the same. If it is reflected over the y-axis, the sign of "a" changes. In this case, the parabola is reflected over the x-axis, which means the sign of "a" remains negative.

Therefore, the characteristics of the given parabola f(x) = -3x² are, A. Compression by 3, reflected over the x-axis.

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The equations of the functions are C(x) = 2.5x + 60, R(x) = 10x and P(x) = 7.5x - 60

Defining the variables, we have

For the equation of the money they spend:

So, the equation for the total money spent can be written as:

C(x) = 2.5x + 60

For the equation of the money they collect:

So, the equation for the total money collected can be written as:

R(x) = 10x

To calculate the profit from selling, we subtract the cost from the revenue

So, we have

P(x) = 10x - 2.5x - 60

Simplifying this equation, we get:

P(x) = 7.5x - 60

Hence, the profit equation is P(x) = 7.5x - 60

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The expression shown on the number line is 0 - 2 + 4 which is equal to 2.

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

Number line contains numbers equally placed at regular intervals. Negative is shown by moving left while positive is shown by moving right

From the number line shown. It initially starts at 0. It is then moved 2 units left, to get:

0 - 2

Thereafter it is moved 4 units right to get:

0 - 2 + 4

= 2

The expression is 0 - 2 + 4

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Operationalization of variables in research involves defining a concept in a way that it can be measured or observed.

It is the process of taking abstract concepts, such as attitudes, beliefs, or behaviors, and defining them in a way that they can be measured using empirical methods. This is done by creating a set of specific and concrete indicators or measures that represent the concept being studied. The operationalization of variables is a critical step in the research process, as it ensures that the data collected is both reliable and valid, and can be used to draw meaningful conclusions and make predictions.

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Answer: I Don't Know.

Step-by-step explanation: Add a picture.

Answer:

  (c)  A line graph, because it would show the association or relationship between two variables

Step-by-step explanation:

You want to know if scatter plot or a line graph more appropriate to construct for seeing the relationship between a manatee's weight and height.

The variables involved are "weight" and "height". Notice that "time" is not involved. (This eliminates choices B and D.)

A line graph is useful for showing how one variable relates to another as the value of one variable changes. It would be useful for plotting the weight and height of one animal as it changes during the animal's lifetime.

When multiple animals are involved, a scatter plot might be more helpful for showing the relationship.

The context is given as "a manatee's weight and height", not "manatees' weight and height." Hence it seems we can assume that we're looking at data for only one animal.

The appropriate graph would be ...

  A line graph, because it would show the association or relationship between two variables — choice C.

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Answer:

Step-by-step explanation:

1. The Louisiana Purchase

2. The War of 1812

3. The Missouri Compromise

4. Trail of Tears

Hope this helped!

Answer:

x=-2

Step-by-step explanation:

if we find sum of same variables ,

3x-2x+y-y=-8+6

x=-2

The length is 30 unit and width is 10 unit.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

length of a rectangle is three times its width.

Perimeter of the rectangle = 80

let the width be x then length = 3x

So, Perimeter of the rectangle = 80

2( x+ 3x) = 80

4x= 40

x= 10

Thus, the length is 30 unit and width is 10 unit.

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We can conclude that -

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is that the regular price on a pair of jeans is $54. The store advertises a back-to-school sale at 40% off the regular price of the jeans. Two weeks later, the store advertises a sale at an additional off the sale price of these jeans at 5%.

Original price -

$54

Cost after 40% discount -

54 - {40% of 54}

54 - {40/100 x 54}

54 - {2/5 x 54}

54 - 21.6

$32.4

Cost after 5% discount -

32.4 - {5% of 32.4}

32.4 - {5/100 x 32.4}

32.4 - 1.62

$30.78

{ 3 } -

Calculating 60% of new price -

60% of 30.78

(60/100) x 30.78

18.5

Calculating 40% of new price -

40% of 30.78

(40/100) x 30.78

12.4

So, 60% of new price is greater than calculating 40%.

So, Manny is correct.

Therefore, we can conclude that -

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Answer: 124950

Step-by-step explanation:

So, let’s look at this logically. For first place, you can any one of the 51 runners finish there. For 2nd place, you can have any one of the remaining 50 runners finish there. For 3rd place, you can have any one of the 49 runners who haven’t finished finish there. runners who haven’t finished finish doesn’t matter .So, you take all of the possibilities, and times them together, 51*50*40 different possibilities.Now, if you want a generic equation, you can run it through this equation, x being the number of possibilities, and n being the number of ones your choosing:

(51!)/(51-3)!

Each point on the least-squares regression line represents a predicted y-value at a given x-value, based on the relationship between the two variables determined through regression analysis.

Regression is a statistical method used to analyze and understand the relationship between two variables. The least-squares regression line is a line of best fit that helps predict the value of one variable based on the value of another.

The correct answer is C, each point on the least-squares regression line represents the predicted y-value at the corresponding value of x.

The line is created by minimizing the sum of the squared differences between the actual y-values and the predicted y-values.

In other words, the line is chosen such that the average difference between the actual and predicted y-values is as small as possible.

Mathematically, the regression line is represented by an equation of the form

=> y = b0 + b1x,

where b0 and b1 are coefficients determined by minimizing the sum of squared residuals.

The predicted y-value for a given x can then be found by plugging in the x-value into the equation.

Complete Question:

Explain what each point on the​ least-squares regression line represents.\

Choose the correct answer below.

A. Each point on the​ least-squares regression line represents the​ y-value of the data set at that corresponding value of x.

B. Each point on the​ least-squares regression line represents one of the points in the data set.

C. Each point on the​ least-squares regression line represents the predicted​ y-value at the corresponding value of x.

D. Each point on the​ least-squares regression line represents the​ y-values that would be considered ideal at that corresponding value of x.

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The expression that represents how much more Elena spent is $3.2 + p

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

The variable p represents the price, in dollars, per pound of cherries.

Elena buys a watermelon for $ 6.35 and 5 pounds of cherries.

So, the price of the cherries bought by Elena will be = 5*p

Then the total amount spent by Elena during her purchase of fresh fruits is:

$6.35 + 5*p

On the other hand, Tania buys a pineapple for $ 3.15 and 4 pounds of cherries. So, the price of the cherries bought by Tania will be 4*p

Therefore, the total amount spent by Tania during her purchase of fresh fruits is:

$3.15 + 4*p

You want to determine an expression to represent how much more Elena spent. That is, you want to determine the difference between the money spent by Elena and the money spent by Tania, which represents how much more Elena spent:

Total amount spent by Elena on fresh fruits - Total amount spent by Tania on fresh fruits

$6.35 + 5*p - ($3.15 + 4*p)

Solving:

$6.35 + 5*p - $3.15 - 4*p

($6.35 - $3.15) + (5*p - 4*p)

$3.2 + p

The expression that represents how much more Elena spent is $3.2 + p

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If two events are collectively exhaustive, then the probability that both occur at the same time is 1.00 (Option c)

Probability is a quantification of how likely an event is to occur. Typically, probabilities are defined as the chances that a specific outcome will occur out of a given selection of outcomes. A probability is expressed mostly in decimal form, taking values between 0 and 1. Probabilities cannot exceed this particular range of values.

Firstly, To clarify : You are confusing mutually exclusive and jointly collectively exhaustive.

The former describes condition which cannot both (or all) obtain. and so exclude one another.

i.e., "not - (both A and not - A)"

The latter describes conditions, one of which must obtain, and so exhaust the field of possibilities. i.e., "either A or not - A"

I presume you intend to refer to the latter.

Second, to answer your question: If two events - are jointly exhaustive, their probabilities must by definition sum to 1.

It is thus certain, not merely probable, that one or the other will obtain.

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Answer:

3. d

4.b

5.a

6. is 15

Step-by-step explanation:

mn=5

no=5

op=10

pq=10

Answer:

x=1,y=4

Step-by-step explanation:

5x+y=9

5x=9-y

x=(9-y)/5

put it in 10x-7y=-18

10x((9-y)/5)-7y=-18

18-2y-7y=-18

-9y=-36

y=4

x=(9-4)/5=1

Answer:

x = 1

y = 4

Step-by-step explanation:

5x + y = 9

10x - 7y = -18

Time the first equation by -2

-10x - 2y = -18

10x - 7y = -18

-9y = -36

y = 4

Now put 4 in for y and solve for x

5x + y = 9

5x + 4 = 9

5x = 5

x = 1

Let's check

5(1) + 4 = 9

5 + 4 = 9

9 = 9

So, x = 1 and y = 4 is the correct answer.

The experimental probability of rolling a 5 is 25/56, or 0.446.

Probability is a field of mathematics that deals with the chance of certain events happening. It is used to calculate the likelihood of different outcomes in a given situation. Probability helps to make decisions for a variety of real-world applications, such as predicting the weather, deciding whether to invest in stocks and calculating insurance rates. Probability is based on the idea that all outcomes are equally likely, and can be expressed as a number between 0 and 1, where 0 means something is impossible and 1 means something is certain.

The experimental probability is calculated by taking the total number of times a number was rolled and dividing it by the total number of rolls. In this case, the total number of times a 5 was rolled is 25, and the total number of rolls is 56. Therefore, the experimental probability of rolling a 5 is 25/56, or 0.446.

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Step-by-step explanation:

Using the modified picture attached to this answer;

Parameters

x = Angle X

8 = x

19 = y

14 = z

Therefore,

Using Cosine rule

x² = y² + z² - 2·y·z·cos X

Masking Cos X the subject of the formula,

Cos X = (y² + z² - x²) / (2·y·z)

Cos X = (19² + 14² - 8²) / (2·19·14)

Cos X = (361 + 196 - 64) / 532

Cos X = (557 -64) / 532

Cos X = 493 / 532

Cos X = 0.92669

But, since we are looking for angle X, we have to divide both sides by Cos, therefore having;

X = Cos-¹ [0.92669]

Since 1 / Cos = Cos-¹

Therefore,

X = 22.075

And since x, our unknown, is equal to angle X, then,

x = 22.1 (to the nearest tenth)

1 kilogram is equal 2.2046 pounds.

Therefore, 150 kilograms is equal to 330.693 pound.

Pound:

A pound (commonly abbreviated lb, plural lbs) is a unit used to measure the mass of something. It is used in the imperial system and the US trade system. There are various definitions. The most commonly used group of definitions today is the International Pound Sterling. This is equal to 0.45359237 kilograms, divided into 16 avoirdupois ounces.

Kilogram:

The kilogram is the unit of mass in the International System of Units (SI), expressed as kg. A unit of measurement widely used worldwide in science, technology and commerce, colloquially referred to simply as the kilogram. It means "a thousand grams."

Kilograms are defined in seconds and meters based on basic physical constants. This allows suitably equipped metrology laboratories to calibrate mass measuring instruments such as Kibble balances as a basic standard for determining accurate mass in kilograms.

Converting 150 kg to US pounds. We'll convert the formula in two different versions.

First one:

kilograms * 2.20462262 = 330.69339300 pounds.

The first version of the formula gives the most accurate result.

Sometimes even the smallest differences can matter. So, if you need accurate results, this formula will be the best option for figuring out how many pounds are in 150 kg.

Now,

we can also go to the second version of the formula and calculate how many pounds is 150 kg.

For the second version of the formula below:

This may be the best option if you want to quickly convert 150 kg to pounds, for example while shopping. It is important to remember that the results are imprecise.

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Answer:

The original price is $ 149.95

Answer:

-1/30

Step-by-step explanation:

-1/6 divided by 2/3(9 - 3/4) - 1/2

2/3(9 - 3/4) - 1/2

= 18/3 - 6/12 - 1/2

= 72/12 - 6/12 - 6/12

= 60/12

= 5

We have

-1/6 ÷ 5

= -1/6 x 1/5

= -1/30

Answer:

2√21

Step-by-step explanation:

let the sides of bigger triangle be a, b and d.

then,

a²= b² + d² [ by Pythagoras theorem]

13² = 9² + d²

d² = 13² - 9²

d²= 169 - 81

d² = 88

d = √88

Now, the sides of smaller triangle are c, x, and d

by Pythagoras theorem,

d² = c²+x²

(√88)² = 2² + x²

88 - 4 = x²

x² = 84

x = √84

x= 2x2x3x7

x = 2√21

Therefore, the value of x is 2√21

Hope it's helpful..

Answer:

Step-by-step explanation:

The minimum interior angle possible for a regular polygon is given by the formula:

interior angle = (180° * (n-2)) / n

where n is the number of sides in the polygon. The formula is based on the fact that the sum of the interior angles of a polygon with n sides is equal to (n-2) * 180°.

As n increases, the value of the interior angle decreases and approaches the minimum value of 180°. However, for a regular polygon, all interior angles must be equal, so the minimum possible value is given by the formula above.

For example, consider a regular hexagon (n=6). The minimum interior angle is given by:

interior angle = (180° * (6-2)) / 6 = 120°

So, the minimum interior angle possible for a regular polygon is 120°.

Answer:An ordered pair contains the coordinates of one point in the coordinate system. A point is named by its ordered pair of the form of (x, y). The first number corresponds to the x-coordinate and the second to the y-coordinate. To graph a point, you draw a dot at the coordinates that corresponds to the ordered pair.

Step-by-step explanation:

Answer: $546.60 (*this was the actual number but I rounded it $546.644444444)

Step-by-step explanation:

Divide: $245.99/0.45 = 546.644444444

You can double check your answer by multiplying 546.644444444 by 0.45 and you will get $245.99

If you multiply by $546.60 you will get $245.97 since you rounded

Answer:

A = 80ft^2

Step-by-step explanation:

Area of trapezoid = (a + b/2) x h

A = ((6 + 10)/2) x 10

A = (16/2) x 10

A = 8 x 10

A = 80ft^2

Answer:

Area is 80 square feet

Step-by-step explanation:

The shape of the bedroom is a trapezoid

h = perpendicular height of trapezoid

Area of a trapezoid:

                      [tex]\frac{1}{2}[/tex]×(Sum of parallel sides)× h

                 = [tex]\frac{1}{2}[/tex] × [(10 + 6) feet] × (10 feet)

                 = [tex]\frac{1}{2}[/tex] × (16 feet) × (10 feet)

∴ Area of Skylar’s Bedroom    = 80 square feet

                                                   = [tex]80 ft^{2}[/tex]