Carol is cross-country skiing. The table shows the distance she traveled after various numbers of minutes. What is the rate of change?

By evaluating the exponential function on x = -2 we will get:

f(-2) = 1/9

Here we have the exponential function below:

f(x) = 3^x

And we want to find f(-2), this means that we just need to evaluate the exponential function in x = -2 (so we just replace the variable x by the number -2)

f(-2) = 3^(-2)

Remember that the negative exponent means that we need to take the inverse, then:

f(-2) = 3^(-2) = 1/3^2

f(-2) = 1/9

That is the value we wanted to find.

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Answer:

3 and 4

Step-by-step explanation:

numbers don't repeat in the X side

Answer:

b or c

Step-by-step explanation:

126+6x=180

180-126=54

54/6=9

x= 9

Answer:

$2837.04

Step-by-step explanation:

semi-annually = every 6 month

p=2000

i=6%

t=3 years = 6 periods

compound 6 times in 3years = (1+6%)^6 =1.418519

multiply principal of $2000 = 2837.04

Answer: KL = 6.1, MK = 5.2 and the angle mZK = 40.

Step-by-step explanation: In this problem, to solve for the remaining sides and angles of the triangle, we can use trigonometry.

First, let's use the sine function to find the value of KL:

sin(40) = KL/ML

KL = (sin(40))(ML)

KL = (sin(40))(8)

Next, let's use the cosine function to find the value of MK:

cos(40) = MK/ML

MK = (cos(40))(ML)

MK = (cos(40))(8)

Finally, let's use the tangent function to find the value of mZK:

tan(40) = KL/MK

mZK = tan(40)

To round the answers to the nearest tenth, we can use the function Math.round(x * 10) / 10 in Javascript.

sin(40) = 0.766

cos(40) = 0.644

tan(40) = 1.193

KL = (0.766)(8) = 6.128 ≈ 6.1

MK = (0.644)(8) = 5.152 ≈ 5.2

mZK = 1.193

So the triangle KL = 6.1, MK = 5.2 and the angle mZK = 40.

Answer:

To solve the right triangle, we can use the trigonometric ratios sine, cosine, and tangent.

Given:

angle K = 40°

ML = 8

KL = 2

We can use the sine function to find the value of angle M:

sin(M) = KL / ML

sin(M) = 2 / 8

sin(M) = 0.25

So M = arcsin(0.25) = 14.04 (approximately)

Next, we can use the cosine function to find the value of MK:

cos(M) = ML / KL

cos(M) = 8 / 2

cos(M) = 4

So MK = 4

Lastly, we can use the tangent function to find the value of angle L:

tan(L) = KL / MK

tan(L) = 2 / 4

tan(L) = 0.5

So L = arctan(0.5) = 26.57 (approximately)

So the triangle is ML = 8, KL = 2, and angles M = 14.04° and L = 26.57° rounded to the nearest tenth.

After performing the division , the missing term in the problem is (2x³ + 5x² + 9)/(x + 3) = (2x² -x +3) .

The problem is (2x³ + 5x² + 9)/(x + 3) ;

that means , we have to divide , the expression "2x³ + 5x² + 9" by "x + 3" ;

first we multiply (x+3) by 2x² ;

the expression becomes : 2x³ + 5x² + 9

                                           -2x³ - 6x²

                                                    -x²  +  9

next we multiply by -x :               -x²  - 3x                      

                                                             3x + 9

next we multiply by 3 :                        -3x - 9

                                                                      0   .

So , dividing the "2x³ + 5x² + 9" by "x + 3" , we get the remainder is 0 and the quotient is 2x² - x + 3 .

Therefore , the missing term is 2x² - x + 3 .

The given question is incomplete , the complete question is

Which is the missing term in this problem ?

(2x³ + 5x² + 9)/(x + 3) = ______  ;

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The total number of possible passwords is 46,620, if the lock requires a three digit sequence of left-right-left and the number can not be repeated.

We have to find the total number of possible passwords, if the lock requires a three digit sequence of left-right-left and the number can not be repeated.

A school lock has a lock of 37 numbers from 0 to 36.

The possible different possibilities is;

At the first position have 37 choices.

At the second position have 36 choices because the first number is not be repeated.

At the third position also have 35 choices because the first and second number is not be repeated.

So, The total number of possible passwords = 37 × 36 × 35

The total number of possible passwords = 46,620 ways

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Answer:

I think it is (8,16).

C

Step-by-step explanation:

c,c is the answer i think so

The distance between (-6 5) and (-6 -3.5) is 14.71 units

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points  (-6, 5) and (-6, -3.5) is calculated as follows

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

d =√{(-6 - 6)² + (5 - -3.5)²}

d =√{144 + 72.25}

d = √216.25

d = 14.71 units

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The equation of the total cost for the cover charge and drinks in point-slope form is y = 6x + 5.

The point-slope form of a linear equation is given by -

 [tex]y - y_1 = m(x- x_1)[/tex]

where m is the slope and [tex](x_1, y_1)[/tex] is a point on the line.

Here, the total cost for the cover charge and drinks can be represented by the equation y = mx + b, where y is the total cost, x is the number of drinks, m is the cost per drink, and b is the cost of the cover charge.

We know that the cover charge is $5 and drinks are $6 each, so, we can find the slope (m) of the equation by using the cost per drink which is m = 6.

We can also find the point [tex](x_1, y_1)[/tex] by using the cover charge cost which is (0,5).

Therefore, the equation in point-slope form of the total cost for the cover charge and drinks will be -

y - 5 = 6(x-0)

y - 5 = 6x

y = 6x + 5

Where x is the number of drinks and y is the total cost i.e. cover charge + drinks.

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Answer:

q= -3.25 and p= -6.25

Step-by-step explanation:

p=5q+10. p=q-3

p-5q=10. p-q=-3 subtract the two equations

-4q=13 q= -3.25 and p= -6.25

Only one angle of the triangles ΔABC and ΔDEF is congruent. Then the triangles ΔABC and ΔDEF are not similar to each other.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

In triangle ΔABC, angle ∠B = 86° and ∠C = 55°, then angle ∠A is given as,

∠A + ∠B + ∠C = 180°

∠A + 86° + 55° = 180°

∠A = 39°

In triangle ΔDEF, angle ∠D = 55° and ∠F = 40°, then angle ∠E is given as,

∠E + ∠F + ∠D = 180°

∠A + 40° + 55° = 180°

∠A = 85°

Only one angle of the triangles ΔABC and ΔDEF is congruent. Then the triangles ΔABC and ΔDEF are not similar to each other.

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For the given table of values the equation that could be the function rule is option 4: y = 3x - 2.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The table of input and output values are given for the function.

The slope-intercept form of an equation/function is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

[-2 - (-11)]/[0 - (-3)]

(-2 + 11)/(0 + 3)

9/3

3

So, the slope point is obtained as m = 3.

The equation becomes - y =3x + b

To find the value of b substitute the values of x and y in the equation -

-11 = 3(-3) + b

-11 = -9 + b

b = -11 + 9

b = -2

So, the value for b is -2.

Now, the equation becomes -

y = 3x - 2

The graph is plotted for the function.

Therefore, the equation is y = y = 3x - 2.

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The rate of change is given a 5 / 6. The values we have here are not linear

The rate of change (r.o.c) is the change in y (or the dependent variable) for every unit change in x (or the independent variable). In this case, the r.o.c is

(10-5) / (12-6) = 5/6.

This is not linear because linear is a relationship between a variable and a constant, here the relationship between y and x is not linear because the change in y is not constant with respect to the change in x.

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=> Convert feet into yards.

660 feet = 220 yards.

=> Convert feet into inches.

660 feet = 7920 inches.

Now, According to the question:

=> Convert feet into inches.

660 feet = 7920 inches

Formula: multiply the value in feet by the conversion factor '12'.

So, 660 feet = 660 × 12 = 7920 inches.

=> Convert feet into yards.

660 feet = 220 yards

Formula: divide the value in feet by 3 because 1 yard equals 3 feet.

So, 660 feet = 660/3

     660 feet = 220 yards.

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The probability that the woman gave birth to a boy, given that the nurse picked up a boy, is 1/3.

There are 2 boys initially and an unknown number of girls in the nursery, so there were a total of 2 + x babies in the nursery, where x is the number of girls.

Since we know that one of those babies is a boy, there are a total of 2 + x - 1 = 1 + x babies left in the nursery.

So the probability of the nurse picking up a boy, given that the woman gave birth to a boy, is 1/(1+x).

P(boy | picked up boy) = P(picked up boy | boy) * P(boy) / P(picked up boy)

= (1/(1+x)) * 1/2 / (1/(1+x) * 1/2 + x/(1+x) * 1/2)

= 1/3

So the probability that the woman gave birth to a boy, given that the nurse picked up a boy, is 1/3.

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Answer:

1. y=29

2. m= -8

3. x=10

Step-by-step explanation:

1. Add the numbers

y+y+1+y+2=90

y+y+3+y=90

combine like terms

3y+3=90

Subtract 3 from both sides

3y+3-3+90-3

3y=87

Divide both sides by the same factor

3y/3 = 87/3

y=29

2. Distribute

5(m+4)=-20

5m+20=-20

Subtract 20 from both sides

5m+20=-20

5m+20-20+-20-20

Simplify

5m=-40

Divide both sides by the same factor

5m/5 = -40/5

m= -8

3. Add 8 to both sides

3x-8=2x+2

3x-8+8+2x+2+8

Simplify

3x=2x+10

Subtract 2x from both sides

3x=2x+10

3x-2x+2x+10-2x

x=10

The perimeter of triangle NPQ is calculated to be 72 when NPQ is given congruent to RSQ.

Perimeter of triangle NPQ = 7x + 2

Triangle perimeter: RSQ = 10x - 4

As triangle NPQ is given congruent to triangle RSQ, we have,

NQ / RQ = PQ / SQ = 24 / 32 = 21 / 28 = 3 / 4

The above ratio can be equated to the ratio of perimeters of the triangles NPQ and RSQ.

Perimeter of triangle NPQ/Perimeter of triangle RSQ = 7x + 2/10x - 4 = 3/4

7x + 2/10x - 4 = 3/4

On cross multiplication and solving, we have, x = 10.

The perimeter of triangle NPQ = 7x + 2 = 70 + 2 = 72  

The question is incomplete. The complete question has the picture of two congruent triangles given in the below attachment.

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The value of c is √14 in the interval [2, 7], which satisfies the Mean Value Theorem.

By definition, the mean value theorem is

f'(c) = [f(b) - f(a)]/b - a

So, in this case, we know that a = 2 and b = 7.

Now, we need to find f(2) and f(7) by replacing those values with the given function

f(x) = 9 - 14/x

f(7) = 9 - 14/7 = 9 - 2 = 7

So, f(b) = f(7) = 7.

f(x) = 9 - 14/x

f(2) = 9 - 14/2 = 9 - 7 = 2

So, f(a) = f(2) = 2

Then, we replace all values,

f'(c) = [f(b) - f(a)]/b - a

= (7 - 2)/(7 - 2)

= 5/5

= 1

Now, calculate the derivative of the function, which has to be equal to 1,

f(x) = = 9 - 14/x

f'(x) = 14/x² = 1

Now, we solve the equation to calculate the value of c,

14/x² = 1

x² = 14

x = √14

Therefore, c = √14 is the value inside the given interval that satisfies the mean value theorem.

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The term is actually forming an AP.

On 2010 = $9 = a

[tex] \frac{1.5}{100} \times 9 \\ = \frac{13.5}{100} \\ = 0.135[/tex]

d = $0.135

now on 2020, that's 10 years after 2010.

n = 10

[tex]an = a + (n - 1)d \\ = 9 + (10 - 1)0.135 \\ 9 + 9(0.135) \\ = 9 + 1.215 \\ = 10.215[/tex]

For the inequality "2(34 + 12) > 5b" that contain a variable "b" , then the numbers that make this inequality true are (a) 16 , (b) 18 .

The inequality containing the variable "b" is ⇒ 2(34 + 12) > 5b  ;

simplifying the inequality ,

we have ;

⇒ 2×(46) > 5b  ;

⇒ 92 > 5b ;

(a) Substituting value of b = 16 ,

we get ; 92 > 5×16

⇒ 92 > 80 , TRUE  .

(b) Substituting value of b = 18 ,

we get ; 92 > 5×18

⇒ 92 > 90 , TRUE  .

(c) Substituting value of b = 19 ,

we get ; 92 > 5×19

⇒ 92 > 95 , FALSE  .

(d) Substituting value of b = 20 ,

we get ; 92 > 5×20

⇒ 92 > 100 , FALSE  .

Therefore , the inequality is TRUE for two values of b that are (a) 16 , (b) 18.

The given question is incomplete , the complete question is

This inequality 2(34 + 12) > 5b ;  contains a variable "b". Choose ALL numbers that make this inequality true.

(a) 16

(b) 18

(c) 19

(d) 20

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The integers greater than 999 but not greater than 4000 is 375.

Integers are the collection of whole numbers and negative numbers. Similar to whole numbers, integers also does not include the fractional part. Thus, we can say, integers are numbers that can be positive, negative or zero, but cannot be a fraction. We can perform all the arithmetic operations, like addition, subtraction, multiplication and division, on integers. The examples of integers are, 1, 2, 5,8, -9, -12, etc. The symbol of integers is “Z“.

The smallest number in the series is 1000, a4-digit number.

The largest number in the series is 4000, a4-digit number

The left most digits (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.

The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.

Hence, there are 3×5×5×5 or 375 numbers from 1000 to 3999.

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The solution of the given fraction can be gotten through filling the boxes with the following values respectively;

8/100 + 9/10 = 98/100

A fraction is defined as the representation of a part of a whole value in the form of a numerator and denominator.

The given fraction;

8/100 + 9/10 = ?

Find the lowest common multiple of the denominator = 100.

= 8/100 + 9/10

= 8 + 90/100

= 98/100

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John must work 8 hours walking the dog and 2 hours as a Maths tutor in order to earn at least $96.

Let us assume that m represents the number of hours he walks the dogs

and n represents the number of hours he works as a maths tutor

John wants to work no more than 10 hours.

As we know the statement 'No more' is represented by the inequality '≤'

So, we get an inequality

m + n ≤ 10             ...........(1)

Also, he also wants to earn at least $96.

As we know the statement 'at least' is represented by the inequality '≥'

So, we get an inequality

8m + n ≥ 96             ...........(2)

So, we get a system of inequalities:

m + n ≤ 10      

8m + n ≥ 96  

Now, we solve this system of inequalities.

Consider m + n = 10           .........(3)

and 8m + n = 96                    .........(4)

Substitute m = 10 - n for x in Equation 4

8(10 - n) + 16n = 96

80 - 8n + 16n = 96

8n = 96 - 80

n = 2

Substitute above value of n in  equation m = 10 - n

m = 10 - 2

m = 8

Thus, John must work 8 hours walking the dog and 2 hours as a Maths tutor.

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The complete question is:

John makes $8 per hour walking dogs and $16 per hour as a math tutor. This weekend, he wants to work no more than 10 hours. He also wants to earn at least $96. Create a system of inequalities to model this and solve.

To solve this system of equations, we can use the method of elimination. The goal is to eliminate one of the variables, such as x or y, by adding or subtracting the equations.

First we can eliminate the y variable by adding the two equations together:

X + 3y = 14

2x - 3y = -8

3x = 6

Dividing both sides by 3:

x = 2

Now we have the value of x, we can substitute it back into one of the original equations:

X+3y=14

2 + 3y = 14

Subtracting 2 from both sides:

3y = 12

Dividing both sides by 3:

y = 4

So the solution of the system of equations is (x,y) = (2,4)

To check the solution, we can substitute the values back into the original equations:

x + 3y = 14

2 + 3(4) = 14

2 + 12 = 14

14 = 14

and

2x - 3y = -8

2(2) - 3(4) = -8

4 - 12 = -8

-8 = -8

As the equation holds true, the solution (2,4) is correct.

The bag can hold a maximum of 53 pounds before breaking, and Ani has already placed 29 pounds in the bag. To find out how many more pounds she can place in the bag, we can subtract the weight already in the bag from the maximum weight the bag can hold:

53 - 29 = 24

So Ani can place 24 more pounds in the bag before it breaks.

The inequality to represent this situation is:

weight in bag + x <= 53 (x represents the amount of weight Ani can put in the bag before it breaks)

To find the solution, we can substitute the value of weight in bag and get

29 + x <= 53

Now we can solve the inequality for x

x <= 24

The solution is x <= 24, which means Ani can place 24 more pounds or less in the bag before it breaks.

To graph the solution, we can start with the number line, and plot the point 24 to the right of the origin, and shade the region to the left of the point. This represents the solution set of x <= 24, which means Ani can place 24 more pounds or less in the bag before it breaks.

The area of parks is 360 m² , base and height are respectively 30m and 24 m.

Given a triangle shaped park with sides 25m, 24m and 30 m.

The total area that is bounded by a triangle’s three sides is referred to as the triangle’s area.

We know that area of triangle = ½ * base * height

Clearly show that base is 30m and height is 24 m.

So, area of triangle = ½ * 30 * 24 = 720/2 = 360 m²

Therefore, area of triangle shaped park is 360m².

Base and height are respectively 30m and 24m.

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As per the given ratio, the amount of paint is 8 ounces needed is and the amount of sugar it will hold 120 ounces.

In math then term ratio is defined as an ordered pair of numbers a and b, written a / b where b does not equal 0

Here we have given that it takes 2 ounces of paint to completely cover all 6 sides of a rectangular prism box which holds 15 cups of sugar.

And then here we have know that they double the dimensions of the box.

Let us consider that the dimension be a.

And as we all know that double the dimensions of the box then dimensions are 2a

Then the ratio of paint and the area of the box remains constant and it can be calculated as,

=> paint / area = 2/x

=> 2/x = 6a² / 6(2a)²

When we simplify this one then we get then x is 8 ounces.

Here we know that the ratio of sugar and the volume of the box remains constant.

Then the sugar volume is calculated as,

=> 15 / X = a³ / (2a)³

When we simplify this then we get the value of x is 120

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