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Question

Reese sold 20 candy and Skittles sold 14 candy for a total of $41. The equation for this is x + y = 34 and x + 1.5y = 41

An exponential equation is an expression that shows how numbers and variables using mathematical operators.

Let x represent the number of candy that Reese sell and y represent the number of Skittles candies

Reese's sells for $1 and skittles for $1.50

34 candies was sold, hence:

x + y = 34      (1)

He made $41, hence:

x + 1.5y = 41    (2)

Solving both equations simultaneously:

x = 20; y = 14

Reese had 20 candy and Skittles had 14 candy.

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Answer:

[tex](f \circ g)(\text{x}) = \frac{13}{13-\text{x}}[/tex]

Domain: [tex](-\infty,0) \cup (0,13) \cup (13,\infty)[/tex]

=================================================

Explanation:

Let's find the function composition.

The notation [tex](f \circ g)(\text{x})[/tex] is the same as [tex]f(g(\text{x}))[/tex]

[tex]f(\text{x}) = \frac{\text{x}}{\text{x}-1}\\\\\\f(g(\text{x})) = \frac{g(\text{x})}{g(\text{x})-1}\\\\\\f(g(\text{x})) = g(\text{x}) \div \Big( g(\text{x}) - 1\Big)\\\\\\[/tex]

Then,

[tex]f(g(\text{x})) = \frac{13}{\text{x}} \div \left(\frac{13}{\text{x}}-1}\right)\\\\\\f(g(\text{x})) = \frac{13}{\text{x}} \div \left(\frac{13}{\text{x}}-\frac{\text{x}}{\text{x}}\right)\\\\\\f(g(\text{x})) = \frac{13}{\text{x}} \div \frac{13-\text{x}}{\text{x}}\\\\\\f(g(\text{x})) = \frac{13}{\text{x}} * \frac{\text{x}}{13-\text{x}}\\\\\\f(g(\text{x})) = \frac{13}{13-\text{x}}\\\\\\[/tex]

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

Now let's find the domain.

If we plugged x = 0 into g(x), then we get a division by zero error.

This means we must exclude this value from the domain.

For similar reasoning, we must exclude x = 13 because we get a division by zero error in [tex]f(g(\text{x})) = \frac{13}{13-\text{x}}[/tex]

We could have any other real number to be plugged in for x.

Here's what the domain looks like in interval notation.

[tex](-\infty,0) \cup (0,13) \cup (13,\infty)[/tex]

We effectively poke holes at 0 and 13 on the number line.

Answer:

Step-by-step explanation:

Answer:

40 degrees and 140 degrees

Step-by-step explanation:

To solve this problem you can add x+3x+20 and set that equal to 180. (We can do this because angle x and angle 3x + 20 make a linear pair. Knowing this we can estimate that both angles added together will equal 180)

Let us add x + 3x + 20 = 180 to find x. We can then substitute that into the equation.

[tex]x+3x+20=180 :a\\\\4x+20=180 :b\\\\4x + 20 -20=180-20:c\\\\4x=160:d\\\\\frac{4x}{4} = \frac{160}{4}:e\\\\x=40:f[/tex]

a: So in this part, we have rewritten the equation to make it easier to solve

b:  In this step, you combine the like terms x+3x to get 4x

c: In step c, you are subtracting 20 from both sides to keep constants on one side and variables on the right

d: In this last step the equation has been simplified to make it easier to solve.

e: To isolate x you have to divide both sides by 4, we do this because the coefficient of x is 4 so you divide the equation by 4 to cancel it out.

f: You rewrite and simplify the equation.

Now to find the measure of both angles you substitute x into the equation.

The first angle's value is 40 degrees and the second is 140 degrees.

These are our answers.

Answer:

18+5f

Step-by-step explanation:

6+9f+5+4+3-4f

=11+5f+7

=18+5f

Answer:

18 + 5f

Step-by-step explanation:

To simplify the expression 6 + 9f + 5 + 4 + 3 - 4f, we must combine like-terms.

6 + 5 + 4 + 3 = 18 (6,5,4, and 3 are like-terms because they are all normal integers)

18 + 9f - 4f (9f and 4f are like-terms because they have the same variable f)

18 + 5f

a = amount invested at 4%

how much is 4% of "a"? (4/100) * "a", namely 0.04a.

b = amount invested at 5%

how much is 5% of "b"? (5/100) * "b", namely 0.05b.

we know the total amount invested is 5550, so whatever "a" and "b" might be, we know that a + b = 5550.

we also know that the yielded amount in interest is 259, so if we simply add their interest, that'd be 0.04a + 0.05b = 259.

[tex]a+b=5550\implies b=5550-a \\\\[-0.35em] ~\dotfill\\\\ 0.04a+0.05b=259\implies \stackrel{\textit{substituting from above}}{0.04a+0.05(5550-a)~~ = ~~259} \\\\\\ 0.04a+277.5-0.05a=259\implies 277.5-0.01a=259\implies -0.01a=-18.5 \\\\\\ a=\cfrac{-18.5}{-0.01}\implies \boxed{a=1850}\hspace{9em}\stackrel{ 5550~~ - ~~1850 }{\boxed{b=3700}}[/tex]

Answer:

[tex]x^2 + 10x+25[/tex]

Step-by-step explanation:

(x + 5)^2 is the same as (x + 5)(x + 5), which is what you call a binomial expression, since two terms (x + 5) are being multiplied by each other.  You can multiply any binomial expression using the FOIL method, where you multiply the first (F), outer (O), inner (I), and last terms and simplify at the end:

First terms:  x * x

Outer terms:  x * 5

Inner terms:  5 * x

Last terms:  5 * 5

Simplifying:

[tex](x * x) + (x * 5) + (5 * x) + (5 * 5)\\x^2+5x+5x+25\\x^2+10x+25[/tex]

Here is the data collected as a result of the experiment.
1) Numerical order is: 0.20, 0.20, 0.46, 0.46, 2.10, 2.10, 5.50, 11.80, 12.20, 12.20, 13.22, 14.65, 16.07, 17.49, 18.91, 20.33, 20.50, 20.50, 21.75, 23.18

2)  The data represents rainfall in millimeters over a 20-day period.

3) Mean = 11.69 mm.

4) The minimum rainfall is 0.20 mm ;

the maximum is 23.18 mm.

1) The data is listed as follows.

2) The data represents the amount of rainfall in millimeters over a 20 day period.

3) The mean rainfall over the 20 day period is 11.69 mm.

= (0.20 + 0.20 + 0.46 + 0.46 + 2.10 + 2.10 + 5.50 + 11.80 + 12.20 + 12.20 + 13.22 + 14.65 + 16.07 + 17.49 + 18.91 + 20.33 + 20.50 + 20.50 + 21.75 + 23.18) /20

Mean (x)  = 11.69 mm.

3) The minimum rainfall is 0.20 mm and the maximum is 23.18 mm.

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Answer:

Step-by-step explanation:15

An example of a function that models a linear relationship between two quantities, x and y is y = mx + b

We need to use the equation of a straight line, which is commonly expressed in slope-intercept form as:

y = mx + b

In this function, x represents the independent variable, m is the slope of the line, and b is the y-intercept. To use this function, we simply plug in the values of x, m, and b that correspond to the specific relationship we are modeling.

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4Construct a function to model a linear relationship between two quantities.

For every 3 days Rochelle helped, she did not help for 1 day.

For every 4 days Rochelle helped, she did not help for 1 day.

For every 7 days Rochelle helped, she did not help for 6 days.

For every 28 days Rochelle helped, she did not help for 21 days.

Let's use the terms provided to complete the sentences comparing Rochelle's time in the garden.
Since Rochelle helped in the garden for 7 days during the last 4 weeks, we can calculate the total number of days in 4 weeks and then find the number of days she did not help.
There are 7 days in a week, so in 4 weeks, there are 4 x 7 = 28 days.
Rochelle helped for 7 days, so she did not help for 28 - 7 = 21 days.
Now, let's complete the sentences:
For every 1 day(s) Rochelle helped, she did not help for 3 day(s).
For every 3 day(s) Rochelle did not help, she helped 1 day(s).

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Answer:

A square's length & width are equal

Step-by-step explanation:

Kamal's shape is not a square, because a square is equilateral (equal length in all sides), but his square is 2:1,

Answer: 89.64 kilometers per hour

Step-by-step explanation: Convert 24.9 meters per second into Kilometers per minute by multiplying by 1000 to get 0.0249 kilometers per minute, which gives you 1.494 kilometers per minute. Then, you must convert this to kilometers per hour by multiplying by 60 to get 89.64 kilometers per hour

Answer:

circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent.

Step-by-step explanation:

To find the correct percentages, we need to calculate the percentage of visitors who used each mode of transportation out of the total number of visitors, which is the sum of all the numbers in the table:

Total number of visitors = 120 + 24 + 45 + 30 + 81 = 300

Percentage of visitors who walked = (120 / 300) x 100% = 40%

Percentage of visitors who used a bicycle = (24 / 300) x 100% = 8%

Percentage of visitors who used a car service = (45 / 300) x 100% = 15%

Percentage of visitors who used a bus = (30 / 300) x 100% = 10%

Percentage of visitors who used the subway = (81 / 300) x 100% = 27%

Therefore, the circle graph that correctly represents the data in the table is:

circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent.

Answer:

a) (1/2)(5)(CD) = 20 cm^2

5CD = 40, so CD = 8 cm

b) (1/2)(12)(8) = 48 cm^2

The half-life of the particular compound is approximately 9.4 days. (Correct choice: B)

The statement indicates the decay function of a particular compound, which is an exponential function of the form:

y = a · exp(- λ · t)

Where:

The half-life of the particular compound is determined by the following expression:

t = ㏑ 2 / λ

Where t is the half-life.

If we know that λ = 0.0736, then the half-life of the particular compound is:

t = ㏑ 2 / 0.0736

t = 9.4 days

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Shawn's phone is 36 cubic cm larger than Ellie's phone.

To get difference in volume between the two phones, we must calculate  volume of each phone and subtract the volume of Ellie's phone from the volume of Shawn's phone.

The volume of a rectangular prism is: length*width* height. The height of both phones is 3/4 centimeters.

The volume of Ellie's phone is:

= length x width x height

= 12 cm x 6 cm x (3/4) cm

= 54 cubic centimeters

The volume of Shawn's phone is:

= length x width x height

= 15 cm x 8 cm x (3/4) cm

= 90 cubic centimeters

The difference in volume is:

= Volume of Shawn's phone - Volume of Ellie's phone

= 90 cubic centimeters - 54 cubic centimeters

= 36 cubic centimeters

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The area of the circle with a diameter of 22 in in terms of pi is 121π in².

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

A = πr²

Where r is radius and π is constant pi.

Given that:

The diameter of the circle is 22 inches.

Radius is half of diameter

Hence:

Radius r = diameter/2 = 22/2 = 11 in

Plug the value into the above formula and solve for area.

A = πr²

A = π × ( 11 in )²

A = 121π in²

Therefore, the area is 121π in².

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Answer:

(10, -10)

Step-by-step explanation:

This are the farest the graph can go unless you want (100,-100)

Change the values from negative to positive and positive to negative to get the most farest results

Answer: D

Step-by-step explanation:

I graphed so you can see.  Count how far each are away.

(5,8) is 12 away

(-7,-5) is 13 away

So you answer is D

Or

You can also think of it as, for, (5, 8)  only the x changed so you only moved in the x direction.  subtract the numbers 5-(-7)=12

For (-7,-5) you only moved in the y direction, so subtract those 8-(-5)=13

Answer:

- 14/3

Step-by-step explanation:

-8/9 * 3/-2 * -7/2

-24/-18 * -7/2

4/3*-7/2

-28/6

= - 14/3

The number of kilogram that are  there in there 5,450 dekagrams is: C. 54.5 kg.

The kilogram is widely used as a unit of mass in everyday life, as well as in science, engineering, and industry. One kilogram is equal to 1,000 grams, and it is the base unit for other mass-related units such as milligrams, centigrams, and decigrams.

To convert 5,450 dag to kg, we need to divide by 100, since 1 kg = 100 dag:

5,450 dag ÷ 100 = 54.5 kg

Therefore, the answer is (c) 54.5 kg.

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The correct question is:

How many kilograms are there in there 5,450 dekagrams?

1 kg = 100 dag

a. 45.4 kg

b. 119.5 kg

c. 54.5 kg

d. 264.3 kg

To find the volume of the solid generated by revolving the region enclosed by the curves y = √(cos(x)), y = e^x and x = pi/2 around the x-axis, we can use the method of cylindrical shells.

Consider a thin vertical strip of width dx at a distance x from the y-axis. The height of this strip is the difference between the y-coordinates of the two curves:

h = e^x - √(cos(x))

The circumference of the shell is given by 2πx since the strip is at a distance x from the y-axis. Therefore, the volume of the shell is given by:

dV = 2πx * h * dx

= 2πx * (e^x - √(cos(x))) * dx

To find the total volume of the solid, we need to integrate this expression from x=0 to x=pi/2:

V = ∫[0, pi/2] 2πx * (e^x - √(cos(x))) dx

This integral can be evaluated using integration by substitution. Let u = cos(x), then du/dx = -sin(x) and dx = du/-sin(x). Using this substitution, the integral becomes:

V = ∫[1, 0] 2π * (-ln(u)/sin(x)) * (e^x - √(u)) dx

Integrating this expression with respect to x from x=0 to x=pi/2, we get:

V = 2π * [e^(pi/2) - 1 - (4/3) * (1 - sqrt(2))]

Therefore, the volume of the solid is approximately 27.838 cubic units (rounded to three decimal places).

The height of the person that cast a shadow of 1.5 foot is 6 foot.

When the sun is at a certain angle in the sky, a 100 foot building will cast a 25 foot shadow. A person cast a shadow of 1.5 foot at the same time.

Therefore, the height of the person can be found by setting up a proportional relationship between the length of shadow and the actual height of the building and person.

Hence,

let

x = height of the person

Therefore,

100 / 25 = x / 1.5

cross multiply

25x = 100 × 1.5

25x = 150

divide both sides of the equation by 25

x = 150 / 25

x = 6

Therefore,

height of the person  = 6 foot.

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Answer:

87 I think.

Step-by-step explanation:

29 x 3 = 87

The total amount of interior angles featured on a polygon with 'n' sides can be determined through the equation (n-2)*180 degrees. This formula applies to all types of polygons, such as triangles.

In order to calculate the sum of each individual angle in the polygon, we must consider the total degree measure formed within each triangle. Every triangle consists of three different sized interior angles that together form an count of 180 degrees.

For instance, when a polygon containing 'n' sides is divided into separate triangles by interconnecting certain vertices, the overall number of triangles produced can be worked out using the equation (n-1). A square, for example, can be broken down into two distinctive triangles, whereas a pentagon structures five triangles, and finally, a hexagon results in four.

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Answer: d. m = 2

Step-by-step explanation:

First, we will write a slope-intercept equation using the y-intercept given.

       y = mx + 4

Next, we will substitute the given point and solve for m, the slope.

       y = mx + 4

       (8) = m(2) + 4

       4 = 2m

       m = 2

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[tex]\boxed{\sf m=2}.[/tex]

In order to find the slope of any linear equation you need at least 2 points the line passes through. We're explicitly provided one, (2, 8), we just need to figure out the other one.

When the statement says that the line has a y-intercept of 4, it means that at a point with y=4 the function touches the y axis. The only way to touch the y-axis is if the x value is 0. Hence, another given point is (0, 4).

Formula: [tex]\sf m=\dfrac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]

Naming the variables (can be done arbitrarily but always make sure the y's are actual y values from the ordered pairs and that x₁ goes with its corresponding y₁ value from the ordered pair):

[tex]x_{1} =2;\\x_{2} =0;\\y_{1} =8;\\y_{2} =4.[/tex]

Now substituting these values in the formula:

[tex]\sf m=\dfrac{(4)-(8) }{(0) -(2) }=\dfrac{-4}{-2} =\boxed{\sf 2}.[/tex]

Check out the attached image to see the graphed line.

Answer:

1.4:1

= 14:10

= 7:5

Hence, ans is 7:5

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The information provided by each of the graphs is Sales from July to December and graph A best represents the data

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

The graphs

On the graphs, we have the information to be

Sales from July to December

The graph that is the best representation of the data is the A

This is because the scale and origin of the graph are defined

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The value of t is given as 2.3 years.

we get the table for function as

t          f(t)

8    350

12   138

16   36

20    4

25   3.2

27    1.3

So it is better to model the data by using an exponential model

using a graphing calculator we get our model as

f(t)=a(b)^t

[tex]f(t)=\boldsymbol{3648.6915(0.7380)^t}[/tex]

we have an exponential decay, so we get a rate of decrease as

b=1-r

r=1-b=1-0.738=0.262=26.2\\%

So the number of polio cases is decreasing by 26.2% per year

The number of polio cases in 2014 is

t=2014-1980=34

f(34)=3648.6915(0.7380)^{34}=0.1991389

this is in thousands so we get the number of cases in 2014 approximately as

[tex]0.1191389*1000 \approx \boldsymbol{119} \textup{ cases}[/tex]

for 1 case of polio :

f(t)=0.001

3648.6915(0.738)^t=0.001

we get

[tex]t=\frac{\ln (\frac{0.001}{3648.6915})}{\ln(0.738)}\approx 50[/tex]

so we get year as

1980+50={2030},

to find half life

[tex]\frac{a}{2}=a(b)^t[/tex]

[tex]b^t=\frac{1}{2}[/tex]

[tex]0.738^t=\frac{1}{2}[/tex]

[tex]t=\frac{\ln (1/2)}{\ln (0.738)}\approx\boldsymbol{2.3} \textup{ years}[/tex]

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