Pls help! Step by step:)

Here we need to find the domain of the given function.

We will see that the domain is the set of all real numbers.

For a given function f(x), we define the domain as the set of possible inputs that we can use on the function.

Usually, we start by defining the domain as the set of all real numbers and then remove from the domain the numbers that cause "a problem" with our function.

Where these "problems" are undefined operations, like the logarithm of a negative number or a zero in a denominator.

Particularly, in our function: f(x) = (1/2)^x

We do not have a denominator that can become zero nor a function that has problems with some given values of x (the exponent of a number can be any real number).

Concluding, because there is no problem with any real value,  we can see that the domain is the set of all real numbers

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Answer: 125y³

To rise a product to a power, rise each factor to that power:

(5y)³ = 5³y³ = 125y³

The minimum is the smallest value in the data set. The maximum is the largest value in the data set.

We will set the first derivative of the function to zero and solve for x to get the critical point. If we take the second derivative or f''(x), then we can find out whether this point will be a maximum or minimum. If the second derivative is positive, it will be a minimum value.

A minimum or a maximum is called an extreme point. A local extreme point is the smallest or largest value in its neighborhood. If it is also the smallest or largest at the entire domain of the function, it is called a global extreme point. The local minima and maxima can be found by solving f'(x) = 0.

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Complete question is: What is the difference between Minimum or maximum value?

Answer:

Step-by-step explanation:

20)63(3

    -60

   -------

        3

so every children gets 3 toys but 3 toys are left which can be distributed among 3 children.

so 3 children get 1 toy more.

Hence 3 children get 3+1=4 toys (each)

5a) The total cost of buying the car, priced at $32,000 with the harmonized sales tax (HST) of 13%, is $36,160.

5b) Through the lease, the customer saves $14,760.

5c) The lease options for the lessee after returning the car include:

6a) The after-tax cost of the Honda Civic is $32,199.35.

6b) The value of the vehicle that needs to be financed is $26,199.35.

6c) The monthly payment will be $567.26 for 4 years.

6d) After four years, the total amount paid for the vehicle is $33,228.48.

A lease is a financing option for the use of capital assets by which the lessee utilizes an asset for a stated period while making periodic payments to the lessor.

A car purchase can also be financed through loans, like home mortgages.

Value of the car = $32,000

Harmonized Sales Tax (HST) = 13%

Cost of the car with HST = $36,160 ($32,000 x 1.13)

Down payment = $1,000

Financing part = $35,160 ($36,160 - $1,000)

Installment payments = 48

Periodic payments = $425

Total lease cost = $21,400 ($1,000 + 48 x $425)

Savings (advantages) from leasing = $14,760 ($36,160 - $21,400)

The value of the Honda Civic = $28,495

Harmonized Sales Tax (HST) = 13%

After-tax cost = $32,199.35 ($28,495 x 1.13)

Annual interest rate = 1.9% compounded monthly

Down payment = $6,000

Financing part = $26,199.35 ($32,199.35 -$6,000)

Financing period = 4 years

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 1.9%

PV (Present Value) = $26,199.35

FV (Future Value) = $0

P/Y (# of periods per year) = 12

C/Y (# of times interest compound per year) = 12

Results:

Monthly Payments (PMT) = $567.26

Sum of all periodic payments = $27,228.48

Total Interest $1,029.13

Total amount paid over 4 years = $33,228.48 ($27,228.48 + $6,000)

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Answer: 2.) Blue and red

Step-by-step explanation:

The slope of the red and blue ones is - 3 while the green one's slope is -4

The solution for the given system of equations:

x = 6 and y = 6.

Kana is incorrect about the solutions of the given equations.

Algebraic expressions and equations follow the same set of rules as numerical expressions and equations. The order of operations is preserved, and the laws governing addition and multiplication still apply.

Associative: a + ( b + c ) = ( a + b ) + c , a ( b c ) = ( a b ) c

Identity: a + 0 = a , a ⋅ 1 = a

Inverse: a + ( − a ) = 0 , a ⋅ 1 a = 1

Distributive: a ( b + c ) = a b + a c

Given equations,

4x-2y=12        -----(a)

2x+2y=24            -----(b)

Multiplying -2 to the equation (b) like kana solution

-2 (2x+2y=24 )

By Distributive property

-2(2x+2y) = -2(24)

- 4x - 4y = - 48     ---------(c)

Now adding equation (a) and equation(c)

    4x - 2y = 12

  - 4x - 4y = - 48

__+___+____+__

         - 6y  =  -36

⇒ y = 36/6 = 6.

Putting value of y in equation (b).

2(x) + 2(6) = 24

2x + 12 = 24

2x = 24 - 12

2x = 12

x =12/2 = 6

By the above calculation,

Value of x = 6 and

value of y = 6.

Hence, for the system of equations given

the solutions are:

x = 6 and y = 6

which proves that Kana is incorrect that there are no solutions.

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The geometry object known as a line extends on both sides and is defined as an object with zero width. Any line without curves is said to be straight.

An object with zero width that extends on all sides is referred to as a line in geometry. Simply put, a straight line is an uncurved line. As a result, a straight line is one without any curves that stretches to infinity on both sides.

A line is a perfectly straight, one-dimensional shape that is endlessly long and thin in both directions. A line may be referred to as a straight line or, more formally, a right line (Casey 1893), to stress that there are no "wiggles" throughout its entire length.

y=mx+c

Definition. Y=mx+c is the formula for a straight line. m is the gradient and c is the height, commonly known as the y-intercept, at where the line crosses the y-axis in the equation y = m x + c.

[tex](b) $\because$ perpendicular makes an angle of $60^{\circ}$ with the line $x+y=0$.$\therefore$ the perpendicular makes an angle of $15^{\circ}$ or $75^{\circ}$ with $x$-axis.[/tex]

[tex]Hence, the equation of line will be $x \cos 75^{\circ}+y \sin 75^{\circ}=4$or $x \cos 15^{\circ}+y \sin 15^{\circ}=4$$(\sqrt{3}-1) x+(\sqrt{3}+1) y=8 \sqrt{2}$or $\quad(\sqrt{3}+1) x+(\sqrt{3}-1) y=8 \sqrt{2}$[/tex]

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Answer:

  True

Step-by-step explanation:

You want to know if it is true or false that "two angles add up to 180° if and only if they are supplementary."

Two supplementary angles have a sum of 180°. That is the definition of supplementary angles. The offered statement is True.

The equation of line that passes through (-3,3) and is perpendicular to 2y = 8x - 6 is y = (-1/4)x + 9/4.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the original line.

Write in slope intercept form

2y = 8x - 6

y = 8x/2 - 6/2

y = 4x - 3

Using the slope intercept, slope m is 3.

The equation of a perpendicular line to 2y = 8x - 6 must have a slope that is the negative reciprocal of the original slope.

Slope of perpendicular line = -1 / ( 4 )

Slope of perpendicular line = -1/4

Plug the slope m = -1/4 and point (-3,3) into point-slope formula and simplify.

( y - y₁ ) = m( x - x₁ )

( y - 3 ) = (-1/4)( x - (-3) )

( y - 3 ) = (-1/4)( x + 3 )

y - 3 = (-1/4)x - 3/4

y = (-1/4)x - 3/4 + 3

y = (-1/4)x + 9/4

Therefore, the equation of the perpendicular line is y = (-1/4)x + 9/4.

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Answer:

95.25 or 95

Step-by-step explanation:

[tex]C=2\pi r[/tex]

C = 2 x [tex]\pi[/tex] x 15 = 94.24778in = 94.25 or 95

Hope I helped you my dear friend.

Answer:

Step-by-step explanation:

if there is any triangle ABC and a,b,c are sides opposite angles A,B,C respectively , then

[tex]cos~A=\frac{b^2+c^2-a^2}{2bc} \\cos~B=\frac{c^2+a^2-b^2}{2ca} \\cos~C=\frac{a^2+b^2-c^2}{2ab}[/tex]

B=101

a= 3 cm

b=y

c=1 cm

use formula for cos B

cos 101=cos(90+11)=sin 11

[tex]-sin~11=\frac{1^2+3^2-y^2}{2 \times 3 \times 1} \\-6 \times sin~11=1+9-y^2\\y^2=10+6~sin~11\\y^2\approx 10+6\times 0.1908\\y^2 \approx11.1448\\y\approx3.338[/tex]

Answer:

2.16

Step-by-step explanation:

To find the length y:

Since we have an angle with two sides next to it, it is 'cosy', so we can use the cosine rule to find y. Let's make y = a for the formula.

Using the cosine formula:

a^2 = b^2 + c^2 - 2bc cos(A)

where b=1, c=3 and A=101

substitute these values in the formula:

a ^2 = 1^2 + 3^2 - 2(1)(3) × cos(101)

a ^2 = 4.647970...

Square root to find a:

a = √4.647970...

a = 2.16

thus, y = 2.16 to 3sf

Answer:

The first chart.

Step-by-step explanation:

The first table. The chart gives a ratio of 1:4, which is the same as the amount the teenager made.

Proportion of cars which are yellow -

= 1 - (0.24 + 0.20 + 0.15 + 0.12 + 0.15 + 0.10)

= 1 - 0.96

= 0.04

Answer:

A) 0.04

Step-by-step explanation:

edge 2023

Note that equation 1 matches the Line Graph in option (B), equation 2 matches option (C), and equation 3 matches option (A).

It is a graph that depicts a line connecting many points or a line indicating the relationship between the points. The graph depicts quantitative data between two changing variables by connecting a sequence of succeeding data points with a line or curve.

With regard to the above-given graphs,

The inequalities are given as

1. 4x + 3 > 15 or —6x ≥ 12

2. —8x > —24 and —10 ≤ 2x -6

3. -29 ≤ 9x -2 < 16

Note that the way to identify the plots on the line graphs is by solving the above equations.

1) 4x + 3 > 15 or —6x ≥ 12

2) —8x > —24 and —10 ≤ 2x -6

To solve for x in  —8x > —24, divide both sides by -8

x > 3;

So solve for —10 ≤ 2x -6; add 6 from both sides and divide by 2

-4/2 ≤ x

-2 ≤ x  or x ≥ -2

3) -29 ≤ 9x -2 < 16

To solve this inequality, you can start by isolating the variable on one side of the inequality. To do this, you can add 2 to both sides to get:

-29 + 2 ≤ 9x < 16 + 2

-27 ≤ 9x < 18
Now divide both sides by 9 to get:

-3 ≤ x < 2

This means that x can be any number that is greater than or equal to -3 and less than 2.

Given the above results, it is correct to state that equation 1 matches option (B), equation 2 matches option (C), and equation 3 matches option (A).

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Full Question:

See the attached.

Answer:

R=17

Step-by-step explanation:

R=17

It says the whale has swam upwards and jumps to a heigh less then 17 and it says model the possible change in the number of feet, (R)

Thus R=17 Will Be correct

Answer:A two-way table, also known as a contingency table, is a way to organize and present categorical data in a tabular format. It can be used to show the relationship between two categorical variables, such as whether a student lives with a grandparent and the number of people who live in their home.

Based on the information you provided, the two-way table would look like this:

More than 4 people | 6 | 10

4 or fewer people | 4 | 30

It should be noted that the information you provided does not add up to 50 students.

Total for students living with grandparents: 10,

Total for students with more than 4 people: 6+10 =16.

Let me know if this table is incorrect and I'll provide you with more information

Step-by-step explanation:

The rate based on the information will be 590 kilometers per hour and 1010 kilometers per hour

Rate in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that rate contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

Since the an airplane travels 4720 kilometers in 8 hours. The rate is:

= 4720 / 8

= 590 kilometers per hour

Flying with the wind, the same plane travels 4040 kilometers in 4 hours. The rate will be:

= 4040 / 4

= 1010 kilometers per hour

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In the right triangle in the figure the value of x is solved to be 4.5

Using SOH CAH TOA for the right triangle

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The figures show that

hypotenuse = 6

adjacent = x

given angle = 41 degrees

The value of x will be calculated using cos, CAH let the angle be y

cos y = adjacent / hypotenuse

cos 41 = x / 6

x = 6 * cos 41

x = 4.528

x = 4.5

Hence the value of x is 4.5

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The car travels at the speed of 68 miles per hour.

Billy made error on substitution process.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

The graph shows a proportional relationship between the distance traveled in miles and time in hours.

That means,

distance traveled in miles/ time in hours = k,

where k is a proportional constant.

Here, k is the speed.

The incorrect speed is,

1/68 miles per hour.

k = 1/68.

From the graph,

distance = 272 miles

And the corresponding time is 4 hours.

So, the speed,

= distance / time

The speed = 272 / 4

The speed = 68 miles per hour.

Billy made the error of not substituting the right values to the formula.

Therefore, the speed of the car is 68 miles per hour.

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The complete question is given in the attached image.

Each nested cart add to the length of the row is 1.5 feet long.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, the store measured a row of 13 nested carts to be 23.5 feet long, and a row of 18 nested carts to be 31 feet long.

Each row has a starting cart that is 4 feet long, and the nested carts are next to it.  

It is measured that a row of 13 nested carts has a length of 23.5 feet.

Therefore, the original length of 13 nested carts is (23.5 - 4) = 19.5 feet.

So, each nested cart add to the length of the row 19.5/13 =1.5 feet

Again, a row of 18 nested carts to be 31 feet long.

Therefore, the actual added length of 18 nested carts is (31 - 4) = 27 feet.

So, each nested cart add to the length of the row 27/18 =1.5 feet

Therefore, each nested cart add to the length of the row is 1.5 feet long.

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"Your question is incomplete, probably the complete question/missing part is:"

A store is designing the space for rows of nested shopping carts. Each row has a starting cart that is 4 feet long, followed by the nested carts (so 0 nested carts means there's just the starting cart). The store measured a row of 13 nested carts to be 23.5 feet long, and a row of 18 nested carts to be 31 feet long.

How much does each nested cart add to the length of the row?

Therefore, the probability of drawing "OBJ" from the bowl is (1/11) * (1/11) * (1/11) = 1/1331

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem.

The word "mathematics" has 11 letters, so there are 11 letters in the bowl. The probability of drawing the letter "O" is 1/11, since there is only 1 "O" in the 11 letters. Similarly, the probability of drawing the letter "B" is 1/11, and the probability of drawing the letter "J" is 1/11 as well.

Since the events of drawing the letter "O", "B", and "J" are independent of each other, the probability of drawing all three letters in order is the product of their individual probabilities.

Therefore, the probability of drawing "OBJ" from the bowl is (1/11) * (1/11) * (1/11) = 1/1331

It is a very low probability, the chances of drawing that sequence are very low.

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Taking into account the definition of a system of linear equations, the number of sodas and hot dogs sold is 92 and 45 respectively.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

The values of the unknowns must be found, with which, when replaced, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

x + y= 137

x= y + 47

To solve a system of equations by the substitution method, an unknown quantity must be solved in one of the equations. Substitute the expression of this unknown in the other equation, obtaining an equation with only one unknown and thus be able to solve it. The value obtained is substituted in the equation in which the unknown appeared. In this way, the two values obtained constitute the solution of the system.

In this case, substituting the second equation in the first one you get:

y + 47 + y= 137

Solving:

y+ y= 137 -47

2y= 90

y= 90÷2

y= 45

Replacing this value in the second equation, you get:

x= 45 + 47

x= 92

Finally, the number of sodas sold is 92 and the number of hot dogs sold is 45.

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Answer:

The correct equation is: 6 + p = 15; p = 9.

Step-by-step explanation:

In this equation, p represents the cost of the popcorn, and the equation states that the total cost of my friend's purchase (the cost of the drink plus the cost of the popcorn) is $15. Therefore, the cost of the popcorn must be $9.

Answer:

Option D)

Step-by-step explanation:

Overall cost of both the items = $15

Cost of the drink = $6

Cost of popcorn = p

To Find : The equation that represents the Overall cost and the cost of the Popcorn

p + 6 = 15

p = 15 - 6

p = 9

Hence , the correct answer is p = 15 - 6; p = 9

a. The table for the relation is given by the image shown at the end of the answer.

b. The domain and range of the relation are given as follows:

c. The relation is a function, as it value of the input is mapped to a single value of the output.

The ratio between the total cost and the number of vehicles is obtained as follows:

k = 3.75/5 = 3/4 = ... = 0.75/1 = 0.75.

Meaning that the situation is modeled by a proportional relationship with a constant of 0.75, and the function is given as follows:

y = 0.75x.

For which:

The domain and range are given as follows:

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The cost of a one mile ride is given as follows:

$6.

The cost per mile is constant, hence a linear function is used to model the situation.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the coefficients are given as follows:

A taxi driver charges a $2 fee plus an additional $4 per mile, hence the slope and the intercept are given as follows:

m = 4, b = 2.

Thus the function that gives the cost for a x mile ride is:

y = 4x + 2.

The cost for a one mile ride is of:

y = 4(1) + 2 = $6.

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As a result, $1600 is the answer to the problem equation comes out to be stated problem, which is the estimated rent.

A mathematical statement known as an equation is created by joining two expressions using the equivalent sign. For instance, 2x - 5 = 15 is an equation. We can find that the variable x has a value of 5 by resolving this equation.

Here,

In New York City, a one-bedroom apartment will cost $1600 in 2020.

Y = mx + c is frequently used as the formula for a straight line graph, where;

gradient = m

The vertical intercept is given by c.

With this knowledge, it is evident from the graph that y = 40x + 800 is the best line of fit for the data presented.

This indicates how much a one-bedroom apartment in New York City will cost in 2020, or 20 years after the year 2000.

y = 40(20) + 800 = $1600

As a result, $1600 is the answer to the problem equation comes out to be stated problem, which is the estimated rent.

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Step-by-step explanation:

x + 6y = 8 ........... ( ×2 ) ....... ( 1 )

2x + 4y = -8 ......... ( × 1 ) ....... ( 2 )

2x + 12y = 16

- - -

2x + 4y = -8

+12y - ( +4y ) = 16 - 8

12y - 4y = 8

8y = 8

divide both sides by the coefficient of y ( 8 )

8y / 8 = 8 / 8

y = 1

substitute for x in equation ( 1 )

x + 6y = 8

x + 6 ( 1 ) = 8

x + 6 = 8

x = 8 - 6

x = 2

x = 2 , y = 1

From the graph, it can be seen that it took 4 days to mow 30 lawns. 12 lawns can be mowed in 1 days.

Analyzing numerical data can be done using graphical representation. It uses a diagram to show the relationship between the data, ideas, information, and concepts. One of the most crucial learning strategies, it is also simple to understand. The kind of information in a particular domain is always a factor.

Examples include pictures, sketches, line art, graphs from mathematics, charts, diagrams, typography, numbers, symbols, geometric patterns, engineering drawings, or other images. Often, text, illustration, and color are combined in graphics.

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