1. The total cost y of an amusement park membership and the number an

merpret can be represented with Park meratior y= 15x + 20. Find and interpret the rate of change and initial value. (Example 1)
please provide an explanation on how to do it

61.025 meters is the maximum height obtained by the baseball

A relation is a function if it has only One y-value for each x-value.

The length of time and the maximum height can be found by finding the vertex of the parabola.

h(t) = -4.9t² + 34.3t + 1

x = -b/2a

t = -34.3/-9.8

t=3.5

Now plug in t value in the function

h(3.5)= -4.9(3.5)² + 34.3(3.5)+ 1

=-4.9(12.25)+120.05+1

=-60.025+120.05+1

=61.025 meters

Hence, 61.025 meters is the maximum height obtained by the baseball

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The value of x is 9 ,  

The measure of each side of the equilateral i.e QR , RS , QS is 35

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane.

Given as :

Triangle QRS is an equilateral triangle  

The side of the triangles are, QR , RS, QS

Now, According to the question

QR = 2 x + 17

RS  = 6 x - 19

QS = 4 x - 1

If the Triangle is equilateral, then all sides are equal

So , QR = RS = QS

Or, 2 x + 17 = 6 x - 19 = 4 x - 1

Now, 2 x + 17 = 6 x - 19

So, 17 + 19 = 6 x - 2 x

Or, 36 = 4 x

x =

I.e x = 9

So, the measure of side QR = 2 x + 17 = 2 × 9 + 17

Or, the measure of side QR = 35

The measure of side RS  = 6 x - 19 = 6 × 9 - 19

Or, The measure of side RS = 35

The measure of side QS =  4 x - 1 = 4 × 9 - 1

Or , The measure of side QS = 35

Hence the value of x is 9,  

And the measure of each side of the equilateral i.e QR , RS, QS is 35  . Answer

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Answer:Commutative property of multiplication

Step-by-step explanation:

Commutative property of multiplication

C: Yes the area can be found by multiplying the 4 and 7 and then dividing the product by two.

Some of the common forms of help include:

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Answer:

25 min

Step-by-step explanation:

60-50=10

10+15=25

Step-by-step explanation:

Answer: [tex]230[/tex]

Step-by-step explanation:

To find coterminal angles, add/subtract integer multiples of [tex]360^{\circ}[/tex].

[tex]-490^{\circ}+360^{\circ}=-130^{\circ}\\\\-130^{\circ}+360^{\circ}=230^{\circ}[/tex]

An angle θ that is coterminal with −490∘ and lies between 0∘ and 360∘ is 130∘.

To find an angle θ that is coterminal with −490∘ and lies between 0∘ and 360∘, we can use the concept of coterminal angles.

Coterminal angles are angles that have the same initial and terminal sides when drawn in standard position. To find a positive coterminal angle with a negative angle, we can add 360 degrees to the negative angle until we get an angle within the desired range (0∘ to 360∘).

Let's find the positive coterminal angle:

θ = -490∘ + 360∘

θ = -130∘

So, an angle θ that is coterminal with −490∘ and lies between 0∘ and 360∘ is 130∘.

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The system of equations is solved and the value of x = 5

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Now , the value of A is

3x + y = 13   be equation (1)

Let the second equation be represented as B

Now , the value of B is

2x - 4y = 18   be equation (2)

Multiply equation (1) by 4 , we get

12x + 4y = 52   be equation (3)

Adding equation (2) and equation (3) , we get

14x = 70

Divide by 14 on both sides of the equation , we get

x = 70/14

x = 5

Substitute the value of x in equation (1) , we get

15 + y = 13

Subtracting 15 on both sides of the equation , we get

y = -2

Hence , the value of x and y is 5 and -2 respectively

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The rate of change of the volume is 871.2 ft³/sec

Rate of change of volume is the change in volume with time.

The rate of change of radius is 6 feet per second.

rate of change in volume = dv/dt

rate of change in radius = dr/dt

to find radius of the sphere;

V = 4/3 πr³

163 = 4/3 x3.14r³

r³ = 163× 3)/4×3.14

r³ = 488/12.56

r³ = 38.85

r = 3.4 feet

therefore

dr/dt = 1/4πr² × dv/dt

= 6 = 1/4×3.14× 3.4² × dv/dt

dv/dt = 6×4× 3.14× 3.4²

dv/dt = 871.2 feet³ per second

therefore the rate of change of the volume is 871.2 feet³ per second

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Answer:

The function f(x) to model U. S. cell phone usage over the time period of 2010 to 2016 can be expressed as f(x) = 43 * (1.23^x), where x is the number of years since 2010. Part b: The estimated cell phone usage in 2013 can be calculated by substituting x = 3 into the function f(x) = 43 * (1.23^x). This yields an estimated cell phone usage of 68.4 million in 2013, which can be rounded to the nearest ten thousand to 68 million.

Step-by-step explanation:

The function g(x) is equal to g(x) = 3x².

Given is functions f(x) and g(x) are shown on the graph and f(x) = x².

The function g(x) is equivalent to 3 times function f(x) for every value of {x}. So, we can write - g(x) = 3x²

Therefore, the function g(x) is equal to g(x) = 3x².

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The  two different subtraction that each have a different of 1 are 1/2 and 1/2

A fraction is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25.

To solve the problem we must know about fractions.

The number should be odd, therefore, the number should be 1, 3, 5, 7, etc.

1          9/8 - 5/8 = 4/8 = 1/2

2          7/8 -5/4 = 2/4 = 1/2

These for the two different subtraction that each have a different of 1

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The negation of the given statement

In Mathematics, the negation of a statement is the opposite of the given mathematical statement.

Given:

Statement: None of the members of the club can vote.

We have to focus on the word  "None" and the negation of word None is Some or at least.

So, Every member of the club can vote is not negation of the statement.

and, At least one member of the club cannot vote is not negation of the statement.

and, Some members of the club can vote is negation of the statement.

and, At least one member of the club can vote is negation of the statement.

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Answer:

Step-by-step explanation:

i do 6th grade aleks too!

Answer:

Option B) A and C

Step-by-step explanation:

Therefore , the solution of the given problem of arithmetic mean comes out to be  the given sequence is geometric sequence..

The arithmetic average, also referred to as the group's means, is obtained by adding up all the values in a list and multiplying that amount by the total number of list items. Math also has a similar trend of progression. The following equation shows that the median of the actual figures 5, 8, and 9 is 3, while the mean of the actual figures 5, 7, and 9 is 4, and the number 21 multiplied by three (there are now multiple three numbers) equals 7.

Here,

Given :

Sequence = 1, 4,25,125,625

Thus,

from the sequence we can see it is an geometric sequence not an arithmetic sequence.

r = 5/1 = 5

=> 1 ,5 ,5(5) , 5(5)² , 5(5)³

So,

it is an geometric sequence.

Therefore , the solution of the given problem of arithmetic mean comes out to be  the given sequence is geometric sequence..

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The shaded area is 157.1 square cm

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

Diameter = 10 cm

So, the area of the small semicircles is

Area = 1/2π(d/2)²

This gives

Area = 1/2π(10/2)²

Evaluate

Area = 25/2π

For the big semicircle, we have

Area = 1/2π(D/2)²

Area = 1/2π(20/2)²

So, we have

Area = 50π

i.e.

Area =50 * 3.142 = 157.1

This represents the shaded area because the small semicircles cancel out

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The greatest number of boxes is 4

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

88 books and 76 DVDs

To do this, we simply calculate the GCF

So, we have the following representation

88 = 2^2 * 11

76 = 2^2 * 19

This gives

GCF = 2^2

GCF = 4

The greatest number of boxes he could have used is 4 boxes.

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Answer:

Initial value=50

Rate of change=12.5

Step-by-step explanation:

The rate of change is just the slope.

Initial value is y-intercept.

the easiest way is to divide, 8068÷31, since it's a big problem, you should use a calculator! When you do, you should get 260.258065, but once you round all the decimals you just get 260, your remainder should be 8. Use 8 as your numerator and 260 as your mixed number! And your finished, and that's why the answer is 260 8/31.

The probability of ordering meat is 0.7 and the probability of ordering fish is 0.3.

P(+ | M) = 0.8 and P(- | M) = 0.2,

P(+ | F) = 0.95 and   P(- | F)  = 0.05.

P(M and +) = 0.56 and P(M and -) = 0.14,

P(F and +) = 0.285 and P(F and -) = 0.015.

C: the probability that the customer ordered fish is 0.3.

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.

Given The Humber, Room advertises two types of entrée, meat and fish,

70% of all customers order meat, and 30% order fish,

M represents the event of ordering meat, F is the event of ordering fish,

probability of M and F,

p(M) = 70% = 0.7

p(F) = 30% = 0.3

and 80% of those who ordered meat and 95% of those who ordered fish were satisfied,

+ is the event of being satisfied, and − is the event of not being satisfied,

probability of satisfied customers with meat,

p(+) = 80% = 0.8

not satisfied with meat,

p(-) = 1 - 0.8 = 0.2

probability of satisfied customers with fish,

p(+) = 95% = 0.95

not satisfied with fish,

p(-) = 1 - 0.95 = 0.05

B: calculating the joint probabilities,

P (M and +) = P(M ∩ +) = p(M)*p(+)

P (M and +) = 0.7*0.8

P (M and +) = 0.56

P (M and -) = P(M ∩ -) = p(M)*p(-)

P (M and -) = 0.7*0.2 = 0.14

P (F and +) = P(F ∩ +) = p(F)*p(+)

P (F and +) = 0.3*0.95

P (F and +) = 0.285

P (F and -) = P(F ∩ -) = p(F)*p(-)

P (F and -) = 0.3*0.05

P (F and -) = 0.015

C:  Determine the conditional probabilities,

P (+ | M) = P(M ∩ +)/p(M)

substitute the values

P (+ | M) = 0.56/0.7

P (+ | M) = 0.8

P (- | M) = P(M ∩ -) /p(M)

P (- | M) = 0.14/0.7

P (- | M) = 0.2

P (+ | F) = P(F ∩ +)/p(F)

substitute the values

P (+ | F) = 0.285/0.3

P (+ | F) = 0.95

P(- | F) = P(F ∩ -)/p(F)

P(- | F) = 0.015/0.3

P(- | F)  = 0.05

D: If a randomly selected customer was satisfied with his/her meal, what is the probability that the customer ordered fish,

to find P (F | +) = P(F ∩ +)/p(+)

substitute the values

P(F | +) = 0.285/0.95

P (F | +) = 0.3

Hence the probabilities are as followed.

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Answer:

2418

Step-by-step explanation:

Step 1: Setup

Set up your multiplication problem like this:

             9 3

     x       2 6

Step 2: Multiply

3 x 6 = 18. Put 8 below the line and 1 as a reminder on top:

             1  

             9 3

     x       2 6

               8

Step 3: Multiply

6 x 9 = 54. Take 54 and add 1 from the previous step to get 55. Enter 55 at the bottom:

             9 3

     x       2 6

           5 5 8

Step 4: Add 0

Enter a 0 at the bottom right as a place holder, because you now move over one digit:

             9 3

     x       2 6

           5 5 8

     +         0

Step 5: Multiply

2 x 3 = 6. Put 6 below the line and 0 as a reminder on top:

             0  

             9 3

     x       2 6

           5 5 8

     +       6 0

Step 6: Multiply

2 x 9 = 18. Take 18 and add 0 from the previous step to get 18. Enter 18 at the bottom:

             9 3

     x       2 6

           5 5 8

     +   1 8 6 0

Step 7: Add to get an answer

Add up the bottom two numbers (558 + 1860 = 2418) to get the answer:

             9 3

     x       2 6

           5 5 8

     +   1 8 6 0

     =   2 4 1 8

The bottom line is the answer. Therefore, 93 times 26 equals:

2418

Answer: Let's call the number of gallons of regular gas sold "x". Then, the number of gallons of premium gas sold would be 300 - x.

The total revenue from regular gas would be 2.15 * x dollars. The total revenue from premium gas would be 2.90 * (300 - x) dollars.

We know that the total receipts for the day were $690, so we can set up the following equation:

2.15x + 2.90(300 - x) = 690

Expanding the second term, we get:

2.15x + 870 - 2.90x = 690

Combining like terms, we get:

0.25x = -180

Dividing both sides by 0.25, we get:

x = 720

So, 720 gallons of regular gas and 300 - 720 = -420 gallons of premium gas were sold. However, since it is not possible to sell a negative number of gallons of gas, this solution is not valid.

If we try another value of x that is less than 300, we will find a valid solution. Let's try x = 200:

2.15 * 200 + 2.90 * (300 - 200) = 690

Expanding and simplifying, we get:

430 + 90 = 520

So, 200 gallons of regular gas and 300 - 200 = 100 gallons of premium gas were sold.

Step-by-step explanation:

Answer:

Step-by-step explanation:

241 is divisible by 3

The length of side p of the triangle rounded to the nearest tenth is 7.5.

The cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

It is expressed as;

p = √( n² + m² - ( 2nm × cosθ ) )

Given the figure in the diagram;

Plug the values into the above formula and simplify.

p = √( n² + m² - ( 2nm × cosθ ) )

p = √( (11)² + (13)² - ( 2 × 11 × 13 × cos( 35 ) ) )

p = √( 121 + 169 - ( 286 × cos( 35 ) ) )

p = √( 290 - ( 286 × cos( 35 ) ) )

p = √( 290 - 234.27748  )

p = √( 290 - 234.27748  )

p = √55.72252

p = 7.5

Therefore, the value of p is 7.5.

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(a) The maximum number of snack bags he could make,

= 18 snack bags.

(b) 18 juice boxes.

(c) 18 cookies in each bag.

The greatest number that can divide the numbers in equal parts.

It is called as greatest common factor.

Given:

Brady is making snack bags with 18 juice boxes and 27 cookies.

He wants each bag to have the same number of juice boxes and the same number of cookies.

(a) The maximum number of snack bags he could make,

= GCF(18, 27)

= 18 snack bags.

(b) 18 juice boxes.

(c) 18 cookies in each bag.

Therefore, all the required values are given above.

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The definition of the absolute value function for this problem is given as follows:

y = |x - 4| - 2.

The absolute value function of vertex at coordinates (h,k) is defined as follows:

y = a|x - h| + k.

From the graph, the coordinates of the vertex are given as follows:

(4,-2).

Hence the equation is given as follows:

y = a|x - 4| - 2.

When x changes by one, y also changes by one, hence the coefficient a is given as follows:

a = 1.

Thus the function is defined as follows:

y = |x - 4| - 2.

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Answer:

MN = 7x + 3

Step-by-step explanation:

Because MN connects the midpoints M and N  of AD and BC respectively

MN is the midsegment of trapezoid ABCD , then

MN = [tex]\frac{AB+DC}{2}[/tex]

AB + DC = 6x + 7 + 8x - 1 = 14x + 6

MN = [tex]\frac{14x+6}{2}[/tex] = [tex]\frac{14x}{2}[/tex] + [tex]\frac{6}{2}[/tex] = 7x + 3

Answer:

36 m

Step-by-step explanation:

It says to use a graph so here is one with the height shown as  36 m