Mathematics College

What do the rates of change represent?

Answers

Answer 1

Answer:

total money and time

Step-by-step explanation:

it is how much ramon is saving over time. he starts with 6 dollars, and steadily increases his money

Related Questions

what is the area of a sector bounded by a 36 degree arc

Answers

ANSWER

$0.314\operatorname{cm}$

EXPLANATION

The area of a sector is given as:

$A=\frac{\theta}{360}\cdot\pi\cdot r^2$

where r = radius of the circle

θ = angle of the sector

From the question, we do not have the radius, but we have the diameter of the circle.

The diameter of a circle is twice its radius, which means that:

$\begin{gathered} D=2\cdot r \\ r=\frac{D}{2} \\ r=\frac{2}{2} \\ r=1\operatorname{cm} \end{gathered}$

Therefore, the area of the sector is:

$\begin{gathered} A=\frac{36}{360}\cdot\pi\cdot1^2 \\ A=0.314\operatorname{cm}^2 \end{gathered}$

At the movie theatre, child admission is 6.20 and adult admission is $9.90. On Tuesday, four times as many adult tickets as child tickets were sold, for a total
sales of $1419.80. How many child tickets were sold that day?

Answers

Answer:

Step-by-step explanation:

For every 4 adult tickets sold, only 1 child ticket was sold. So the cost of 4 adult tickets and 1 child ticket is:

4 x 9.9 + 1 x 6.2 = 45.80

Divide the total sales by 45.80: 1419.80 ÷ 45.80 = 31

So there were 31 lots of "4 adult tickets and 1 child ticket" sold.

Therefore, there were 31 x 4 = 124 adult tickets sold

and 31 x 1 = 31 child tickets sold

Select the correct answer from each drop-down menu.
Consider the expressions given below.
A.
B.
C.
D.
2x³
x² - 6x
2x³ + 8x + 4
3x³ + x² + x -7
32 3x² + 5x - 7
-
For each expression below, select the letter that corresponds to the equivalent expression from the given list.
4 + 7x) (2x - x - 8) is equivalent to expression
(-3x² + x + x) + (2x - 7+ 4x) is equivalent to expression
(²2x) (2x + 3) is equivalent to expression

Select the correct answer from each drop-down menu.Consider the expressions given below.A.B.C.D.2xx -

Answers

(4x³- 4 + 7x) - (2x³ - x - 8) is equivalent to expression 2x³ + 8x + 4. Option B

(-3x² + x⁴ + x) + (2x⁴ - 7+ 4x) is equivalent to expression 3x⁴ - 3x² + 5x - 7. Option D

(x² - 2x) (2x + 3) is equivalent to expression 2x³ - x² - 6x. Option A

How to determine the expression

From the information given, we have that the expressions are;

(4x³- 4 + 7x) - (2x³ - x - 8)

expand the bracket, we have;

4x³ - 4 + 7x - 2x³ + x + 8

collect the like terms, we have;

2x³ + 8x + 4

(-3x² + x⁴ + x) + (2x⁴ - 7+ 4x)

expand the bracket, we have;

-3x² + x⁴ + x + 2x⁴ - 7+ 4x

collect the like terms

3x⁴ - 3x² + 5x - 7

(x² - 2x) (2x + 3)

expand

2x³ + 3x² - 4x² - 6x

2x³ - x² - 6x

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A rectangular prism has a length of 112feet, a width of 212feet, and aheight of 8 inches. What is the volume of the prism in cubic inches?
pls hurry :)

Answers

Answer:

27,353,088 cubic inches

Step-by-step explanation:

How to find the volume of a rectangular prism

To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

Solve

In this case, The volume of a rectangular prism with a length of 112feet,

width of 212 feet, and height of 8 inches:

But in this case, we need to convert both the length and width to inches.

If 1ft = 12in

Then, 112ft = 1344in (Multiply 112 by 12)

Also, 212ft = 2544 (Multiply 212 by 12)

So, the volume = 1344 x 2544 x 8

Calculated out this gives a volume of 27,353,088 cubic inches.

Algebra transformation

f(x) =
f(x) =
f(x) =
f(x) =

Answers

Algebra transformation

for Graph1 f(x)=f(x)+4

for Graph2 f(x)=-f(x-4)

for Graph3 f(x)=f(x-7)

for Graph4 f(x)=f(x-2)-5

Define reflection of graph

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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40 points! Find the distance UV between the points U(2,−2) and V(−5,−3). Round your answer to the nearest tenth, if necessary.

Answers

Answer:

7.1

Step-by-step explanation:

Using the distance formula

d = sqrt ( (x2-x1)^2 + ( y2-y1)^2)

sqrt ( (-5-2)^2 + ( -3- -2)^2)

sqrt( ( -7)^2 + ( -3 +2)^2)

sqrt( ( 49 + 1)

sqrt( 50)

7.071067812

To the nearest tenth

7.1

Answer:

7.1 units

Step-by-step explanation:

We can use the distance formula to find the distance between these two points.

The distance formula is:

$\sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }$.

x1 is 2, x2 is -5, y1 is -2, and y2 is -3, so we can plug these values into the equation.

$\sqrt {\left( {2 - (-5) } \right)^2 + \left( {-2 - (-3) } \right)^2 }\\\\\sqrt {7^2 + 1^2}\\\\\sqrt{49+1}\\\\\sqrt{50}\approx7.1$

Hope this helped!

re.
2. Find the perimeter of the figure.
Each unit is 1 centimeter.

Answers

Answer:

Step-by-step explanation:

Count all the squares on the edge.

Answer:

29cm

Step-by-step explanation:

What is 50% of 20?.........................

Answers

Answer:

Step-by-step explanation:

50%, or 1/2 of 20 is 10.

Answer:

10!

Step-by-step explanation:

50% is half, so half of 20 is 10!

A standard toilet uses 1.6 gallons per flush. If a toilet is flushed two times per day, how much water will be used in two weeks (14 days)?

Answers

Answer: 192 gallons. Step-by-step explanation: 1.6 gallons x by 4 (the amount of times flushed in a day) = 6.4 gallons a day.

wHAT IS THE DOMAIN OF THE FUNCTION fx=(x+1)/(x^2 +2x-3)

Answers

Answer:

Domain : R−{−1,3}

Range: R

Step-by-step explanation:

Equate the denominator(x2−2x−3) to zero, then solve the equation for x

→x2−2x−3=0

→x=−(−2)±√(−2)2−4⋅(1)⋅(−3)2⋅1

→x=1±2

⇒x=−1 and x=3

This means that, when x=−1 or 3, we have the x2−2x−3=0

Implying that f(x)=x0 which is undefined.

Hence, the domain is all real numbers except −1

and 3

Also written as Df=(−∞,−1)∪(−1,3)∪(3,+∞)

Domain is all real numbers please mark brainliest :)

A boat is 104 feet from the base of cliff. If the distance from the top of the cliff to the boat is 26 less than twice the height of the cliff to the water. Find the height of the cliff. Round to the nearest tenth of a foot if necessary.

Answers

Answer: h = 68.5, 51.2

Step-by-step explanation:

Draw a right angle triangle. The base is the sea and the line perpendicular to it is the cliff

The base is the distance of from boat to the cliff is 104

Let the height of the cliff be h.

The hypotenuse, the distance from the top of the cliff to the boat is therefore 2h-26

Pythagoras tells us that

(2h−26)^2 = 104^2 + h^2

4h^2 − 52h + 289 = 10816 + h^2

3h^2 − 52h − 10527 = 0

h=68.5, 51.2

The other result is negative and therefore not relevant.

If you cannot factorize then solve using the formula.

Naji is trying to draw an isosceles triangle. He is
given point A at (-4,-2) and point B at (2,-2).
Plot these two points, then help Naji make the
isosceles triangle ABC by ploting point C. Give
your coordinates for point C. It must be on the
grid provided.

Answers

Answ

Step-by-step explanation:wirugf4

3. What is the vertex of y=x²-16 x+24 ?
(A) (8,-64)
(B) (2,-4)
(c) (16,24)
(D) (8,-40)

3. What is the vertex of y=x-16 x+24 ?(A) (8,-64)(B) (2,-4)(c) (16,24)(D) (8,-40)

Answers

The Vertex of Parabola is (8, -40).

What is Vertex of Parabola?

A parabola's vertex is the location where its symmetry line and parabola intersect. The vertices of a parabola whose equation is provided in standard form will be the lowest (lowest point) and highest (highest point) points on the graph, respectively.

Given parabola equation: y= x²-16 x + 24.

As, we know parabola equation is of the standard form y=ax² + bx + c.

By comparing,

a = 1, b= -16, c = 24.

We know, the vertex formula is (-b/2a, -D/4a)

D = b² – 4ac.

D = (-16)²-4(1)(24)

D = 256 - 96

D = 160

Now,

Vertex, (h, k) = ( (16 /2(1)), (-160/4(1))

(h. k) = (8, -40)

Hence, the Vertex is (8, -40)

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Two systems of linear equations in two variables, x and y, are given.
System P:
(3x-10y=8
7x+2y=6
The two systems have the same solution..
What are the values of b and c?
b=
System T:
bx - 10 y + 10 y = 38
cx + 10 y = 30
=
C =

Answers

Answer:

Step-by-step explanation:

the equation p=52+0.04w models relation between the amount of water bill payment p in dollars and the number of units of water w in slope of equation

Answers

The slope in the equation p = 52 + 0.04w represents the rate of change in the water bill payment for each additional unit of water consumed.

Specifically, the slope of 0.04 indicates that for every increase of one unit in the number of water units (w), the water bill payment (p) will increase by 0.04 dollars.

This means that the slope represents the incremental cost of each additional unit of water.

In practical terms, the slope of 0.04 implies that for every additional unit of water consumed, the water bill will increase by $0.04.

This indicates a constant rate of increase in the water bill for each additional unit of water used.

It's important to note that the slope remains constant throughout the equation, suggesting a linear relationship between the amount of water consumed and the corresponding bill payment.

Therefore, The slope, in this case, is the coefficient of the variable w, which is 0.04.

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The probable question may be:

What is the meaning of the slope in the equation p = 52 + 0.04w, which models the relationship between the water bill payment p in dollars and the number of units of water w ?

A conical container can hold 120 pie cubic centimeters of water the diameter of the base of the container is 12 centimeters the height of the containers centimeters. If the diameter and height were both doubled the containers capacity would be times its original capacity

Answers

The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where V is the volume, r is the radius of the base, and h is the height.

Given that the diameter of the base is 12 centimeters, the radius (r) is half of the diameter, which is 6 centimeters. The original height of the container is h centimeters.

Using the formula for the volume of a cone, we have:

V = (1/3)π(6^2)h
V = 36πh

We are told that the container can hold 120π cubic centimeters of water. Therefore:

36πh = 120π

To find the value of h, we divide both sides of the equation by 36π:

h = 120π / (36π)
h = 10/3

So the original height of the container is 10/3 centimeters.

Now, if we double both the diameter and height of the container, the new diameter would be 2 * 12 = 24 centimeters, and the new height would be 2 * (10/3) = 20/3 centimeters.

The new volume (V') can be calculated using the same formula:

V' = (1/3)π(12^2)(20/3)
V' = 480π/9
V' = 160π/3

To find the ratio of the new volume to the original volume, we divide the new volume by the original volume:

V' / V = (160π/3) / (120π)
V' / V = (160/3) / (120)
V' / V = 4/3

Therefore, the capacity of the container after doubling the diameter and height would be 4/3 times its original capacity.

If possible, can you mark me brainliest?

A
X
Find the value of x.
D
X+2
x = [?]
B
3
E
2
C

Answers

Answer:

x = 4

Step-by-step explanation:

if a line is parallel to a side of a triangle and it intersects the other two sides then id divides those sides proportionally.

DE is such a line , then

$\frac{BD}{AD}$ = $\frac{BE}{EC}$ ( substitute values )

$\frac{x+2}{x}$ = $\frac{3}{2}$ ( cross- multiply )

3x = 2(x + 2)

3x = 2x + 4 ( subtract 2x from both sides )

x = 4

I need some assistance please and thank you

Answers

Answer:

what is your question thought

I need help on this one

Find the selling price.

Cost To Store: $50

Markup: 10%

The selling price is $blank

Answers

The selling price of the item at 10% marlkup is $55

Finding the selling price of the item

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

Cost To Store: $50Markup: 10%

Using the above as a guide, we have the following:

Selling price = Cost To Store * (1 + Markup)

substitute the known values in the above equation, so, we have the following representation

Selling price = 50 * (1 + 10%)

Evaluate

Selling price = 55

Hence the selling price of the item is $55

Answers

The number of missed shots after 10 weeks of practice is 1

Predicting the number of missed shots after 10 weeks of practice.

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

The line of best fit

Also, we have the equation to be

y = -1/2x + 6

At the 10th weeks, we have

x = 10

Substitute the known values in the above equation, so, we have the following representation

y = -1/2 * 10 + 6

Evaluate

y = 1

Hence, the number of missed shots after 10 weeks of practice is 1

Answers

Answer: $\;\;\frac{1}{6} , \;\; 0.16667,\;\; \text{or about}\;\;17\%$

Step-by-step explanation:

A regular dice has 6 sides, and only one of those sides side has a six.

We write probability as;

$\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} = \frac{\text{number of times six is on the dice}}{\text{number of numberss on the dice}} =\frac{1}{6}$

Hi, there!

_______

$\boxed{\boxed{\sf{Probability=\dfrac{Favorable \ Outcomes}{Total \ Outcomes}}}}$

Here,

» Favourable Outcome(s) -> getting a 6 on a die (1 outcome), because only one side of a die has a six on it

» Total Outcomes -> 6 (you can only get 1, 2, 3, 4, 5, 6 if you roll one die)

So,

$\sf{Probability_{(6)}=\dfrac{1}{6}}$

Hope the answer - and explanation - made sense to you,

happy studying!!

$\tiny\textit{frozen \ melody}$

5 m 9 m 18 m 24 m 10 m 9 m What is the volume of the figure?

Answers

Answer:

I would say 1,749,600

Step-by-step explanation:

the sum it two numbers is 82.5. Their difference is 12.9. what are the numbers

Answers

Explaination :

Let us assume the unknown two numbers as an variable. Here we are assuming it as a and b.

★ According to the question,

Sum of those assumed two numbers is 82.5.

a + b = 82.5

Also it is given that difference of both the two numbers is 12.9.

a - b = 12.9

From the given information we got two equations,

a + b = 82.5 (Equation No 1)

a - b = 12.9 (Equation No 2)

So we would solve them and get the value of a and b.

★ From Equation No 2 :

a = 12.9 + b

★ In Equation No 1 :

Substituting the value of a which we got above here,

(12.9 + b) + b = 82.5

12.9 + b + b = 82.5

12.9 + 2b = 82.5

2b = 82.5 - 12.9

2b = 69.6

b = 69.6 / 2

b = 34.8

★ Therefore,

Value of b is 34.8

★ Finding out value of a :

a = 12.9 + b

a = 12.9 + 34.8

a = 47.7

What percentage of births occur among women between the ages of 36 and 38?

Answers

Answer:

200%

Step-by-step explanation:

2 multiplied by 100

Jose runs a factory that makes stereo tuners. Each S100 takes 8 ounces of plastic and 4 ounces of metal. Each FS20 requires 4 ounces of plastic and 6 ounces of metal. The factory has 312 ounces of plastic, 372 ounces of metal available, with a maximum of 20 S100 that can be built each week. If each S100 generates $7 in profit, and each FS20 generates $13, how many of each of the stereo tuners should Jose have the factory make each week to make the most profit

Answers

Answer: Jose should have the factory make 50 FS20 stereo tuners and 14 S100 stereo tuners each week to make the most profit

Step-by-step explanation:

Since each S100 takes 8 ounces of plastic and 4 ounces of metal. Each FS20 requires 4 ounces of plastic and 6 ounces of metal. And the factory has 312 ounces of plastic, 372 ounces of metal available, then,

For plastic

8 ounces + 4 ounces = 12 ounces

The number of stereo tuners it can produce will be

312/12 = 26 stereo tuners

For metal

4 ounces + 6 ounces = 10 ounces

The number of stereo tuners it can produce will be

372/10 = 37.2 = 37 approximately

Since FS20 generate more profit than S100, let assume that Jose produces 50 FS20 by consuming

4 × 50 = 200 ounces of plastic

6 × 50 = 300 ounces of metal

The remaining plastic will be

312 - 200 = 112

The remaining plastic will be

372 - 300 = 72

Divide 112 by 8 in order to make S100

112/8 = 14

Also 72/4 = 18.

Therefore, Jose should have the factory make 50 FS20 stereo tuners and 14 S100 stereo tuners each week to make the most profit

Match the system of linear equations on the left with its solution type on the right
1. Y=2x-1
Y=2x+1
2. Y-4x=-2

Answers

Solution for the given System of linear equation is:

Infinite number of solution(2, -3)(-2, 4)Infinite number of solutionWhat are System of equation?

Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods to solving systems of equations: graphing, substitution, elimination and matrices.

Given, the system of linear equations on the left with its solution type on the right

For Y=2x-1 and Y=2x+1

Adding both equation, we will get y = 4x

Thus, these equations have infinite number of solution

For 2x - y = 7 and 3x + y = 3

Adding these equations

5x = 10

x= 2

Substitute the value in equation 1

y = -3

Thus, solution is (2, - 3)

therefore, the Solution for the given System of linear equation is:

Infinite number of solution(2, -3)(-2, 4)Infinite number of solution

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Complete question:

Match the system of linear equations on the left with its solution type on the right 1. Y=2x-1Y=2x+12.

Subtract 89.768 from 201.316
show your work

Answers

Answer:

111.548

-------------------------------

Subtract 201 from 89.

$201 - 89 = 112$

we can estimate the answer will be close to 112

Next, work with the decimals. Note that the more you subtract, the bigger the decimal places get.

$0.768 - 0.316 = 0.452$

Round 0.452 up from the hundredths place to nearest tenths place.

$0.452 = 0.5$

Since the decimal place is bigger, estimate 0.55 instead.

Subtract 0.22

$0.55 - 0.2 = 0.548$

Add this number to 112

$112 + 0.548 = 112.548$

Subtract 1 because of the estimate.

$112 - 1 = 111$

Therefore, we have 111.548 based off of subtracting and estimating in a specific method.

One less than five times a number is 39. Find the number.

Answers

Answer: x = 8

5x - 1 = 39

isolate and divide to get x

x = 8

Sienna buys a mystery pack of sparkly modeling clay. The pack has 5 colors, and there are 7 possible colors that are all equally likely. Sienna wants to know the probability that at least 2 of the colors will be the same. Which of the following is the best simulation? Explain your reason for your answer.

A. Roll a standard number cube 5 times for each trial. Let each number represent a different color. Run 50 trials and find the fraction of times that at least two of the same number are rolled.

B. Create a spinner with 5 equal sections. Label each section with a different color. Spin the spinner 7 times to see if it lands on the same color two or more times.

C. Create a spinner with 7 equal sections. Label each section with a different color. Spin the spinner 5 times for each trial. Run 50 trials and find the fraction of times the spinner lands on the same color two or more times.

D. Put 5 pieces of paper in a bag, each labeled with a different color. For each trial, randomly select and replace a paper 7 times. Run 50 trials and find the fraction of times that at least two of the same color appear.

Answers

The probability that at least 2 of the colors will be the same, the following is the best simulation is Option D Put 5 pieces of paper in a bag, each labeled with a different color. For each trial, randomly select and replace a paper 7 times. Run 50 trials and find the fraction of times that at least two of the same color appear.

Given, Sienna buys a mystery pack of sparkly modeling clay. The pack has 5 colors, and there are 7 possible colors that are all equally likely. We have to find the probability that at least 2 of the colors will be the same. There are 5 colors in the pack of clay, and 7 colors are possible in total.

So, the probability of picking any color at random is

P(picking a color) = 5/7 = 0.7143Let P(X = 2) be the probability that exactly 2 of the colors are the same.

Then, the probability that at least 2 of the colors are the same can be calculated by using the formula:

P(X ≥ 2) = 1 - P(X < 2).

The simulation method that can be used to find the probability of at least 2 of the colors will be the same in the mystery pack is option D.

Put 5 pieces of paper in a bag, each labeled with a different color. For each trial, randomly select and replace a paper 7 times. Run 50 trials and find the fraction of times that at least two of the same color appear.

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Differentiate the function with respect to x. Shot steps

Answers

Differentition of $y=log_{2}x^{3}.(5x^{4}+2)$ is $y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}$

What is Differential equation?

A differential equation is an equation that contains one or more functions with its derivatives.

Given,

$y=log_{2}x^{3}.(5x^{4}+2)$

We have to differentiate with respect to x.

y'=xy'+yx'

$x=log_{2}x^{3}$

$y=5x^{4}+2$

$y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x^{3}} .3x^{2}$

$y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}$

Hence, differentiation of $y=log_{2}x^{3}.(5x^{4}+2)$ is $y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}$

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