Jeremy boiled one cup of water and then let it cool at room temperature. The table shows the temperature, in degrees Fahrenheit, of the water after a given number of five-minute intervals. Jeremy used an exponential function to model the temperature w(t), in degrees Fahrenheit, of the water after t intervals.

Answers

Answer 1

The question involves predicting the temperature of water after six intervals using an exponential decay function. Without the exact values to form the function, we can infer that the temperature will likely be around option (b) 101°F after six intervals based on the pattern of decrease shown in the provided intervals.

The student's question is about using an exponential function to model the temperature decrease of water as it cools at room temperature.

To solve this problem, one would generally apply the formula for an exponential decay function, which is of the form w(t) = [tex]a * e^{(kt)[/tex], where w(t) is the temperature at time t, a is the initial temperature, e is the base of the natural logarithm, and k is the decay constant. Given the temperatures at specific intervals, one could use these to estimate the constants a and k.

However, without the necessary values to develop an equation, we instead look for the pattern in the temperature's decrease to predict the sixth interval's approximate temperature.

Examining the table provided:

Interval 0: 210°FInterval 1: 167°FInterval 2: 145°FInterval 3: 131°FInterval 4: 121°F

We can see that the temperature is decreasing less with each interval. While it is not explicitly stated, it's reasonable to assume that an exponential decay function would fit this scenario. Without the exact function, we can make an educated guess based on the trend that after six intervals, the temperature will be less than 121°F and likely close to option (b) 101°F.


Related Questions

Which of the following exponential regression equations best fits the data shown below

Answers

Answer:

(D) [tex]8.46\cdot 3.51^x[/tex]

Step-by-step explanation:

One could run this on a computer and verify the best fit through brute force. The more elegant way is, as usual, to think: What are special values of x for an exponential function? Zero, for starters - anything to the power of zero is 1. The function value for x=0 in the table is 10. Which choices A through D are close to 10 for x=0? Well, (C) and (D), the rest is too far. Next, what is the function value for the next easy one, x=1? The table says 30. Which of (C) and (D) is close to 30 for x = 1. It turns out we can safely exclude (C) because 10.84*1.77 is about 19 and that's way too far from 30. Let's check (D): 8.46*3.51=29.7 - that's quite close. Since there is no other candidate left, I bet my money on (D). Feel free to verify closeness for the other values of x if you are unconvinced yet.  

Answer:

[tex]\text{D. }y = 8.46(3.51)^{x}[/tex]

Step-by-step explanation:

The quickest way is probably to do some direct substitution.

First, let's try f(0).

The values of y predicted by the four equations are, respectively, 3.14, 5.32. 10.84, and 8.46.

It looks like C and D are the closest to the observed data.

Now, let's try f(4) on C and D.

C: 10.84(1.77)⁴ = 10.84 × 9.815 = 106.4

D:  8.46(3.51)⁴ =    8.46 × 151.4 = 1284

The best curve is [tex]y = 8.46(3.51)^{x}.[/tex]

At Silver Gym, membership is $35 per month, and personal training sessions are $25 each. At Fit Factor, membership is $65 per month, and personal training sessions are $15 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?

Answers

Answer: The correct answer is 3.

Step-by-step explanation:

You need to write an equation to solve this problem, using x as the number of personal training sessions.

The equation to solve this problem is

35 + 25 x = 65 + 15x

First, subtract 35 from both sides:

25x = 30 + 15x

Subtract 15x from both sides:

10x = 30

The last step is to divide both sides by 10:

x = 3

You can then double check your work to make sure that the answer is correct:

35 + (25 x 3) = 110

65 + (15 x 3) = 110

what of the following is a like radical to ^3 square 7x

Answers

Answer:

4( \sqrt[3]{7x} )  is a like radical to  \sqrt[3]{7x}

Step-by-step explanation:

Could you answer this for me please?
-1 2/7 x 1/6 =

Answers

Answer:

-1 2/7 x 1/6 = -0.21

What is the length of LE?

Answers

Answer:

2.5

Step-by-step explanation:

if the distance to ET is 5 and l is closer to e it only makes sense for 2.5\

Which is the simplified form of

Answers

Answer:

The simplified form of n to the -6th power times p to the 3rd power is p^3/n^6.

Step-by-step explanation:

For this case we have that by definition of properties of powers, it is fulfilled that:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

We have the following expression:

[tex]n ^ {- 6} * p ^ 3[/tex]

We can rewrite it as:

[tex]\frac {p ^ 3} {n ^ 6}[/tex]

Finally:

[tex]n ^ {- 6} * p ^ 3 = \frac {p ^ 3} {n ^ 6}[/tex]

Answer:

Option C

The table shows the growth, in centimeters, of plants in two different soils after two weeks.



Which statement explains which soil tended to have a greater growth?

Soil A had greater growth because its data have a greater standard deviation.
Soil A had greater growth because its data have a greater mean.
Soil B had greater growth because its data have a greater interquartile range.
Soil B had greater growth because its data have a greater median.

Answers

it Might be D. Soil B had greater growth because its data have a greater median.

Answer:

Step-by-step explanation:

Given is a table about plants growth in soil A and B.

Let us find mean and median.

Soil A

Mean: 4.17

Median: 3.9

Mode: 3.5

Minimum: 3.1

Maximum: 6

Range: 2.9

Count: 10

Sum: 41.7

Soil B

Mean: 4.28

Median: 4.25

Mode: 3.9

Minimum: 2.9

Maximum: 5.5

Range: 2.6

Count: 10

Sum: 42.8

Soil B shows a better growth since both mean and median are greater.

There are 24  inches of ribbon in each spool. Margaret needs 384 inches of ribbon. Which equation can Margaret use to find the number of spools, 
s, she needs?

A) 24s=384

B)384/s=24

C) 384/24=s

D) All of these are correct​

Answers

Answer: D) All of these are correct

Answer:

D. All of these are correct

Step-by-step explanation:

She needs four inches of ribbon and each spool has 24 inches, so we can write this equation like:

384/24 = s

where s is the number of spools.

If we divide 384 inches by the 24 inches each spool has she will get how many spools she needs.

Now having the equation: 384/24 = s, we can change it and it will mean the same.

384/24 = s  is the same as 24s = 384; just sending the 24 to multiply on the other side.

And it is the same as 384/s = 24 just sending the s to the other side dividing.

So all of the answers are correct they are just in different orders.

Plz help!!!!!!!!!!!!!!

Answers

Answer:

[tex]\sqrt{5}[/tex]

Step-by-step explanation:

Given

5 ÷ [tex]\sqrt{5}[/tex] = [tex]\frac{5}{\sqrt{5} }[/tex]

To simplify multiply the numerator/ denominator by [tex]\sqrt{5}[/tex]

= [tex]\frac{5}{\sqrt{5} }[/tex] × [tex]\frac{\sqrt{5} }{\sqrt{5} }[/tex]

= [tex]\frac{5\sqrt{5} }{5}[/tex] = [tex]\sqrt{5}[/tex]

Answer:  √5

Step-by-step explanation:

[tex]\dfrac{5}{\sqrt5}\bigg(\dfrac{\sqrt5}{\sqrt5}\bigg)=\dfrac{5\sqrt5}{5}=\large{\boxed{\sqrt5}}[/tex]

Factor the trinomial x^2+8x+7

Answers

you'd have to use the Null Factor law in order to find your factors that is -7 and -1 therefore x is the element of -7 and -1.
hope this helps

Which of the following expressions are equivalent to x - (-x) + y ?
Choose all answers that apply:


A. 0 + y


B. y.


C. None of the above

Answers

Final answer:

The given expression x - (-x) + y simplifies to 2x + y. None of the provided options are equivalent to the original expression, hence the answer is 'None of the above'.

Explanation:

The expression you're trying to simplify is x - (-x) + y. In mathematics, subtracting a negative number is the same as adding its positive counterpart. Therefore, the given expression simplifies to x + x + y, which is 2x + y.

It seems the original question was looking for an expression equivalent to x - (-x) + y from the given choices. Based on the simplification we just did, none of the provided choices (0 + y, y, none of the above) are equivalent to the original expression, 2x + y. Therefore, the correct answer is 'None of the above'.

Learn more about Simplifying Expressions here:

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Please help me, please

Answers

Answer:

8/27 yd³

Step-by-step explanation:

The equation for the volume of a cube of edge length s is V = s³.

If the edge length, s, is 2/3 yard, then the volume of this cube is:

V = (2/3 yd)³ = 8/27 yd³ (which corresponds to Answer C)

How do these triangles compare?

Answers

Answer:

B option. AB is larger than FD

Step-by-step explanation:

The rule which must be remembered here is:

The side opposite to the larger angle will be larger in measure. We have to compare two sides that are opposite to two angles 72 and 65.

So using the above rule we can say that side opposite to angle 72 will be greater in measure than the side opposite to 65.

The side opposite to 72 is AB and side opposite to 65 is FD.

Therefore, we can conclude that AB is larger in measure than FD, which makes option B as the correct answer,

Answer:

The correct answer option is AB is longer than FD.

Step-by-step explanation:

We are given two triangles, ΔABC and ΔDEF, where AC ≅ FE and BC ≅ DE.

One out of three angles is known for each triangle: ∠ACB = 72° and ∠DEF = 65° and we are to determine which of the statements is correct about AB and FD.

We know that the side opposite to the bigger angle is longer. Since ∠C = 72° is greater than ∠E, therefore side AB is longer than FD.

What is the answer to 1/2 + 5/6

Answers

Answer:

The answer is 4/3

Step-by-step explanation:

To get the answer, first give the two fractions common denominators.

1/2 + 5/6

3/6 + 5/6 = 8/6

Now simplify the fraction by division both numbers by 2

8/6 = 4/3

The answer is 1 1/3

Question Number 1: Hard. HELP!!!

Answers

Answer:

5 dozen hot dogs

Step-by-step explanation:

Erica started with 80 dozen hot dogs.

At the end of the day on Wed, she had 75 dozen hot dogs (from the graph)

To determine what she sold, take what she started with and subtract what she ended with

80-75 = 5

She sold 5 dozen hot dogs

the width of a rectangle is 5 units less than the lenght. if the area is 104 square units, then find the dimensions of the rectangle ​

Answers

No te entiende hgdchecjj. E I’ll s j e he irk a. Iei
Answer:

The length is 13 and width is 8

Step-by-step explanation:

Let the length is L

Width will be L-5

Area of rectangle = Length x Width

Putting the values

104 = L x L-5

104=l(l−5)

Simplify both sides of the equation.

104=l²−5l

Subtract l²-5l from both sides.

104−(l²−5l)=l²−5l−(l²−5l)

−l²+5l+104=0

Factor left side of equation.

(−l−8)(l−13)=0

Set factors equal to 0.

−l−8=0 or l−13=0

l=−8 or l=13

We will take l = 13 because length cannot be negative

Now for width we know that w = l -5

So width is 13 -5 = 8

how can you use order numbers that are written as fractions, decimals, and percents?

Give an Example plz​

Answers

2.5 4/5 8% that is an example of written fractions decimal and percents

Final answer:

To use order numbers in different forms, you convert between fractions, decimals, and percents. For example, to convert from percent to decimal, you divide by 100; to convert from decimal to percent, you multiply by 100.

Explanation:

You can use order numbers that are written as fractions, decimals, and percents for various mathematical and real-life applications. They are different ways to represent the same value, and you can convert between them. For example, to convert a percent to a decimal, you write the value of the percent as a fraction with a denominator of 100 and divide the numerator by the denominator. Similarly, to convert a decimal to a percent, you write the decimal as a fraction. If the denominator of the fraction is not 100, convert it to a fraction with a denominator of 100, then write the fraction as a percent.

Example of Converting Percents

To convert 75% to a decimal, write it as 75/100, which simplifies to 0.75. Conversely, to convert 0.75 to a percent, you multiply by 100 to get 75%.

Select the system of linear inequalities whose solution is graphed.

y > 3x – 1; x + 3y < 6


y ≥ 3x – 1; x + 3y ≤ 6


y < 3x – 1; x + 3y > 6


y ≤ 3x – 1; x + 3y ≥ 6

Answers

Answer:

[tex]y\geq 3x-1[/tex] ; [tex]x+3y\leq 6[/tex]

Step-by-step explanation:

we know that

step 1

Find the inequality of the solid line x+3y=6

The solution is the shaded area below the solid line

therefore

The equation of the inequality is

[tex]x+3y\leq 6[/tex]

step 2

Find the inequality of the solid line y=3x-1

The solution is the shaded area above the solid line

therefore

The equation of the inequality is

[tex]y\geq 3x-1[/tex]

therefore

The system of linear inequalities is

[tex]y\geq 3x-1[/tex] ; [tex]x+3y\leq 6[/tex]

The correct system of linear inequalities represented by the graph is 'y ≥ 3x – 1; x + 3y ≤ 6'. This means all points that lie on and above the line y = 3x - 1 and also on or below the line x + 3y = 6 are solutions.

Looking at the given options and their corresponding inequalities, it’s evident that the graph must represent an area where y is greater or equal to 3x-1, and also, x + 3y is less than or equal to 6.

Therefore, the correct system of linear inequalities whose solution represents the graph should be:

y ≥ 3x – 1; x + 3y ≤ 6

This suggests that all points that lie on the line y = 3x - 1 and above it and all points that are on the line x + 3y = 6 and below it, make both inequalities true at the same time.

Learn more about System of Linear Inequalities here:

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Which line represents the linear equation
–3y = 15 – 4x?

The equation –3y = 15 – 4x rewritten in slope-intercept form is .

The y-intercept is and the slope of the line is .

Line is the graph of the line –3y = 15 – 4x.

Answers

Answer:

Pat a) The graph in the attached figure

Part b)  [tex]y=(4/3)x-5[/tex]

The slope is  [tex]m=(4/3)[/tex]

The y-coordinate of the y-intercept is  [tex]b=-5[/tex]

Step-by-step explanation:

Part a) Which line represents the linear equation [tex]-3y=15-4x[/tex]?

To graph the linear equation find the intercepts

we know that

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

[tex]-3y=15-4(0)[/tex]

[tex]-3y=15[/tex]

[tex]y=-5[/tex]

The y-intercept is the point [tex](0,-5)[/tex]

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

[tex]-3(0)=15-4x[/tex]

[tex]4x=15[/tex]

[tex]x=15/4=3.75[/tex]

The x-intercept is the point [tex](3.75,0)[/tex]

Plot the intercepts to graph the linear equation

see the attached figure

Part b) Rewritten in slope-intercept form

we know that

The equation of the line into slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-coordinate of the y-intercept

we have

[tex]-3y=15-4x[/tex]

convert to slope intercept form

isolate the variable y

[tex]3y=4x-15[/tex]

[tex]y=(4/3)x-5[/tex]

The slope is  [tex]m=(4/3)[/tex]

The y-coordinate of the y-intercept is  [tex]b=-5[/tex]

hopefully the photo helps

A triangular sail on a sailboat is 6meter across the bottom and 10 meters tall.
What is the area of this sail?

Answers

Answer:

30m^2

Step-by-step explanation:

Formula for the area of a triangle is b * h / 2.

Plug in the values for each variable.

6 * 10 / 2 = 30.

Answer:

A=30m^2

Step-by-step explanation:

area of a triangle equals Length*Height divided by 2

length equals 6 height equals 10

6*10=60    60/2=30    A=30m^2

someone please help me asap!

Answers

I think the correct answer is C. because each if forming a right triangle when you trace it.

If i'm correct brainliest please

Find the value of x. Then classify the triangle

Answers

Answer:

x = 60°

Step-by-step explanation:

This is an equilateral triangle. All angles of this triangle are congruent and have a measure of 60°.

Other method.

We know: the sum of the measures of the angles of the triangle is equal to 180 °.

Therefore we have the equation:

x + x + x = 180°

3x = 180°           divide both sides by 3

x = 60°

please help me. i don’t understand how to interpret the (f o g)(x) And (g o f)(x)

Answers

fog functions are basically saying f(g(x)).

So (f o g)(x) = f(g(x)).

This is also true for gof functions.

(g o f)(x) = g(f(x)).

All we do for these problems is plug in g(x) into the x value in the f(x) equation.

Choose the correct correspondence
AD <->
Options
1.Side AD
2.Side AB
3.Side CD

Answers

Answer:

AD

Step-by-step explanation:

Looking at triangles ABD and ACD, they appear to be congruent. This means they have corresponding or matching parts which are equal and form each triangle.

The segment AD is the longest segment of triangle ABD. It matches to the longest segment in ACD. This is the same segment AD since the triangles share a side between them.

Answer:

AD <--> AD

Step-by-step explanation:

Hello! Segment AD is corresponding to itself, as it is the longest segment in ABD; it would correspond to itself due to a triangle being erected between them.  Hope this helps!

The area of a rectangle is 54x^9 y^8 square yards. If the length of the rectangle is 6x^3 y^4 which expression represents the width of the rectangle in yards?


Jack knows a=l*w, so he writes the following equation:
54x^9 y^8= 6x^3 y^4*w
He divides both sides by the length:
(54x^9 y^8)/(6x^3 y^4 )=9 x^12 y^12


Error:

Correct solution:


Answers

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

Error: When he divided both sides by the length, he didn't subtract the exponents. Instead on subtracting the exponents, he added them - which is incorrect.

Correct solution: 54x^9 y^8 / 6x^3 y^4 = 9x^6 y^4

The width is 9x^6 y^4

(This is based on the rule that when you divide values with exponents, you have to subtract the exponents)

Hope This Helps You!

Good Luck (:

Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ

Answer:

Error: He added the exponents of the variables. The exponents must be subtracted.

Correct solution: [tex]w=9x^6y^4[/tex]

Step-by-step explanation:

According the quotient property of exponents, when you divide two powers with equal base, you must subtract the exponents.

Therefore, keeping the property above on mind, you have:

[tex]w=\frac{54x^9y^8}{6x^3 y^4}\\\\w=9x^{(9-3)}y^{(8-4)}[/tex]

Therefore, you have that the width of the rectangle is the shown below:

[tex]w=9x^6y^4[/tex]

Isabella uses the equation to find the volume of the cone below.

Answers

Answer:

The correct answer option is: Isabella should have divided the product of [tex]12\pi[/tex] and 9 by 3 to get [tex]V=\frac{12\pi (9)}{3}[/tex]

Step-by-step explanation:

We are given a diagram of a cone with height [tex] 9 cm [/tex] and area of the base (circle) [tex] 12 \pi   cm^ 2 [/tex].

Isabella uses the equation [tex] V = \frac { 1 } { 3 } ( 12 ) ^ 2 ( 9 ) \pi [/tex] and we are to find the error that she is making in finding the volume of this cone.

The volume of a cone is given by: [tex]\pi r^2\frac{h}{3}[/tex] out of which [tex]\pi r^2[/tex] represents the area of the base (circle).

Therefore, Isabella should have divided the product of [tex]12\pi[/tex] and 9 by 3 to get [tex]V=\frac{12\pi (9)}{3}[/tex].

The answer is in fact D or Isabella should have divided the product of 12 Pie and 9 by 3 to get V=  12 Pie (9)/3

Which describes this angle?


an angle that measures greater than a right angle measures


an angle that measures the same as a straight line measures


an angle that measures the same as a square corner measures


an angle that measures less than a right angle measures

Answers

Answer:

Your answer would be the first option.

A right angle is 90 degrees

An obtuse angle is more than 90 degrees and that angle is more that 90 degrees

PLAESE HELP!!!!!!!
What is the mean average of hours completing homework each week based on the table below:
Number of hours each week completing homework 1 2 3 4 5
# of students 6 20 15 12 7

Answers

Answer the anser is 3

please gimme brainly

Step-by-step explanation:


Which of these equations have no solution? Check all thal apply.
2(x + 2) + 2 = 2(x + 3) + 1
2x + 3(x + 5) = 5(x - 3)
46x + 3) = x + 12
4- (2x + 5) = 2 ( 4x - 2)
5(x + 4) - x = 4(x + 5) - 1

Answers

Answer:

2(x + 2) + 2 = 2(x + 3) + 12x + 3(x + 5) = 5(x - 3)5(x + 4) - x = 4(x + 5) - 1

Step-by-step explanation:

[tex]2(x+2)+2=2(x+3)+1\qquad\text{use the distributive property}\\2x+4+2=2x+6+1\qquad\text{subtract 2x from both sides}\\6=7\qquad\boxed{FALSE}\to\text{no solution}\\===============================\\2x+3(x+5)=5(x-3)\qquad\text{use the distributive property}\\2x+3x+15=5x-15\\5x+15=5x-15\qquad\text{subtract 5x from both sides}\\15=-15\qquad\boxed{FALSE}\to\text{no solution}\\===============================\\46x+3=x+12\qquad\text{subtract x from both sides}\\45x+3=12\qquad\text{subtract 3 from both sides}\\45x=9\qquad\text{divide both sides by 45}\\x=\dfrac{9}{45}\to x=\dfrac{1}{5}\to\text{one solution}\\===============================\\4-(2x+5)=2(4x-2)\qquad\text{use the distributive property}\\4-2x-5=8x-4\\-2x-1=8x-4\qquad\text{subtract 8x from both sides}\\-10x-1=-4\qquad\text{add 1 to both sides}\\-10x=-3\qquad\text{divide both sides by (-10)}\\x=0.3\to\text{one solution}\\===============================\\5(x+4)-x=4(x+5)-1\qquad\text{use the distributive property}\\5x+20-x=4x+20-1\\4x+20=4x+19\qquad\text{subtract 4x from both sides}\\20=19\qquad\boxed{FALSE}\to\text{no solution}[/tex]

Answer:

A, B, E

Step-by-step explanation:

How do i solve this equation 3x2(9x)0=

Answers

Final answer:

To solve 3x^2(9x)^0, simplify the expression inside the parentheses first, then multiply by 3x^2.

Explanation:

To solve the equation 3x2(9x)0, we can simplify the expression inside the parentheses first. Any number raised to the power of 0 is equal to 1. So, (9x)0 becomes 1. Now we have 3x2 * 1. Multiplying any number by 1 doesn't change its value, so the equation simplifies to 3x2.

Other Questions
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