Answer:
57.3 minutes
Step-by-step explanation:
We know that the temperature as a function of time of an object is described by the equation:
[tex]T(t) = T_a + (T_0 - Ta)*e^{-k*t}[/tex]
Where:
k is a constant
Tₐ = room temperature = 68°F
T₀ = initial temperature of the object = 375°F
Replacing these in our equation we will get
T(t) = 68°F + (375°F - 68°F)*e^{-k*t} = 68°F + (307°F)*e^{-k*t}
And we know that after 25 minutes, at t = 25min, the temperature of the casserole is 190°F
then:
T(25min) = 190°F = 68°F + (307°F)*e^{-k*25 min}
Now we can solve this for k:
190°F = 68°F + (307°F)*e^{-k*25 min}
190°F - 68°F = (307°F)*e^{-k*25 min}
(122°F)/(307°F) = e^{-k*25 min}
Now we can apply the natural logarithm in both sides:
Ln( 122/307) = Ln(e^{-k*25 min}) = -k*25min
Ln( 122/307)/(-25 min) = k = 0.0369 min^-1
Then the temperature equation is:
T(t) = 68°F + (307°F)*e^{-0.0369 min^-1*t}
Now we want to find the value of t such that:
T(t) = 105°F = 68°F + (307°F)*e^{-0.0369 min^-1*t}
We can solve this in the same way:
105°F - 68°F = (307°F)*e^{-0.0369 min^-1*t}
37°F = (307°F)*e^{-0.0369 min^-1*t}
(37°F)/(307°F) = e^{-0.0369 min^-1*t}
Ln( 37/307) = -0.0369 min^-1*t
Ln( 37/307)/( -0.0369 min^-1 ) = 57.3 min
So after 57.3 minutes, the temperature of the casserrole will be 105°F
In circle B with m \angle ABC= 74m∠ABC=74 and AB=12AB=12 units find area of sector ABC. Round to the nearest hundredth.
Answer:
92.99
Step-by-step explanation:
The value of area of sector ABC is,
Area = 93.05 square units.
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
In circle B;
⇒ m ∠ABC = 74° and AB = 12 units
Hence, We can formulate;
The value of area of sector ABC is,
Area = (angle / 360) π r²
Area = (74/360) × 3.14 × 12²
Area = 93.05 square units.
Thus, The value of area of sector ABC is,
Area = 93.05 square units.
Learn more about the circle visit:
https://brainly.com/question/24810873
#SPJ2
Solve for x. Round to the nearest tenth, if necessary. Calculating Sin or Cos or Tan
Answer:
1.06
Step-by-step explanation:
cos41⁰ = 0.8 ÷ X
X = 0.8 ÷ cos41⁰
Answer:
Step-by-step explanation:
Use SOH CAH TOA to recall how the trig functions fit on a right triangle
SOH: Sin(Ф)= Opp / Hyp
CAH: Cos(Ф)= Adj / Hyp
TOA: Tan(Ф) = Opp / Adj
x = Hyp (for this question)
Cos(41) = 0.8 / Hyp
use your algebra skillz
Hyp = 0.8 / Cos(41)
use your calculator to fund Cos(41) into 0.8
Hyp = 1.060010395 (that's all the decimal places my calc would go out to )
x = 1.1 ( rounded to nearest 10th )
someone help me for this algebra task please
Answer:
The answer is
[tex]4+ x[/tex]
Using the definition of linear equation,
[tex]y = 4 + x[/tex]
Is the answer.
Which of the following is equivalent to 2/x + 3/x−1 for x>1 ?
pls explain
Answer:
Step-by-step explanation:
Given that u=4,t=5,a=10and s=it+1\2at
After 3 points have been added to every score in a sample, the mean is found to be M 5 83 and the standard deviation is s 5 8. What were the values for the mean and standard deviation for the original sample
Answer:
Hence the value for the mean is 80 and the standard deviation for the original sample is 8.
Step-by-step explanation:
Mean = 83-3 = 80.
Here the standard deviation didn't change = 8.
Ten years from now, Abdul will be twice as old as his son pavel ten years ago, Abdul was seven times as old as pavel how old are Abdul and pavel now?
Answer:
Age of Pavel = y - 10
→ x - 7y = -60. Now, Calculating X. Hence, Present age of Abdul = 38.
Step-by-step explanation:
hope this is helpful.
PLS HELP !!!
a. 15
b. 1
c. 2
d. 11
Answer:
d
Step-by-step explanation:
ive had this exac problem before
Answer:
B. 1
Step-by-step explanation:
Since the sides are equal to each other, the equations will be equal.
4x + 7 = x + 10
-7 -7
---------------------
4x= x + 3
-x -x
-------------
3x = 3
---- ---
3 3
x = 1
The answer is 1.
If α and β are the zeroes of the polynomial 6y 2 − 7y + 2, find a quadratic polynomial whose zeroes are 1 α and 1 β .
Answer:
[tex]2y^2-7y+6=0[/tex]
Step-by-step explanation:
We are given that [tex]\alpha[/tex] and [tex]\beta[/tex] are the zeroes of the polynomial [tex]6y^2-7y+2[/tex]
[tex]y^2-\frac{7}{6}y+\frac{1}{3}[/tex]
We have to find a quadratic polynomial whose zeroes are [tex]1/\alpha[/tex] and [tex]1/\beta[/tex].
General quadratic equation
[tex]x^2-(sum\;of\;zeroes)x+ product\;of\;zeroes[/tex]
We get
[tex]\alpha+\beta=\frac{7}{6}[/tex]
[tex]\alpha \beta=\frac{1}{3}[/tex]
[tex]\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha \beta}[/tex]
[tex]\frac{1}{\alpha}+\frac{1}{\beta}=\frac{7/6}{1/3}[/tex]
[tex]\frac{1}{\alpha}+\frac{1}{\beta}=\frac{7}{6}\times 3=7/2[/tex]
[tex]\frac{1}{\alpha}\times \frac{1}{\beta}=\frac{1}{\alpha \beta}[/tex]
[tex]\frac{1}{\alpha}\times \frac{1}{\beta}=\frac{1}{1/3}=3[/tex]
Substitute the values
[tex]y^2-(7/2)y+3=0[/tex]
[tex]2y^2-7y+6=0[/tex]
Hence, the quadratic polynomial whose zeroes are [tex]1/\alpha[/tex] and [tex]1/\beta[/tex] is given by
[tex]2y^2-7y+6=0[/tex]
What is the slope of the graph?
QUESTION 4
f(x)=4x-10/x-2
4.1 Determine the x- and y-intercepts of
4.2 +9. Write f (x) in the form: f(x) = x - 2 4.3 Draw the graph of y, clearly show the intercepts with the axes and the asymptotes.
4.4 Give the equations of the asymptotes of f(x) + 3.
Answer:
4.2+9.Write f (x)in the form:f(x)=x-2 4.3Draw
Question 4 (True/False Worth 4 points)
(0701)
True or False?
is a solution to the inequality 12+2 < 12
True
O False
x^3+5x^2+3x+15 factor the polynomial
Answer:
(x+5) (x^2+5)
Step-by-step explanation:
x^3+5x^2+3x+15
Using factoring by grouping
x^3+5x^2 +3x+15
x^2(x+5) + 3(x+5)
Factor out (x+5)
(x+5) (x^2+5)
Answer:
( x + 5 ) (x² + 3)
Step-by-step explanation:
x³ + 5x² + 3x + 15
factor out x²
x² ( x + 5 ) + 3x + 15
factor out 3
x² ( x + 5 ) + 3 ( x + 5 )
factor out x + 5 from the expression
( x + 5 ) (x² + 3)
the quadratic function f(x) = ax² + bx + c has tge minimum point (-2,-9) ans f(-1) = -7 Find (a) values of a,b and c
i'll mark u brainliest pls,help
Hello again,
"katie deleted your answer to the question Hello,a=2, b=8, c=-1Indeed,y=f(x)=ax...
You've been warned"
Answer is a=2, b=8 and c=-1
Indeed:
y=f(x)=ax²+bx+c
Since (-2,-9) is the vertex,
y=k*(x+2)²-9
Or f(-1)=-7 ==> -7=k*(-1+2)²-9 ==> k=2
f(x)=2(x+2)²-9=2*(x²+4x+4)-9=2x²+8x+8-9
f(x)=2x²+8x-1
A proof: the picture is following.
Answer the questions about the perpendicular bisector below.
Given:
The vertices of a triangle are D(1,5), O(7,-1) and G(3,-1).
To find:
The perpendicular bisector of line segment DO.
Solution:
Midpoint formula:
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
The midpoint of DO is:
[tex]Midpoint=\left(\dfrac{1+7}{2},\dfrac{5+(-1)}{2}\right)[/tex]
[tex]Midpoint=\left(\dfrac{8}{2},\dfrac{4}{2}\right)[/tex]
[tex]Midpoint=\left(4,2\right)[/tex]
Therefore, the midpoint of DO is (4,2).
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Slope of DO is:
[tex]m=\dfrac{-1-5}{7-1}[/tex]
[tex]m=\dfrac{-6}{6}[/tex]
[tex]m=-1[/tex]
Therefore, the slope of DO is -1.
We know that the product of slopes of two perpendicular line is -1.
[tex]m_1\times m_2=-1[/tex]
[tex]m_1\times (-1)=-1[/tex]
[tex]m_1=1[/tex]
The slope of perpendicular bisector is 1 and it passes through the point (4,2). So, the equation of the perpendicular bisector of DO is:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-2=1(x-4)[/tex]
[tex]y-2+2=x-4+2[/tex]
[tex]y=x-2[/tex]
Therefore, the equation of the perpendicular bisector of DO is [tex]y=x-2[/tex].
The price of a jacket usually costing £50 is increased to £65.
Work ou the percentage increase.
Answer:
So the answer is 30%
Step-by-step explanation:
1. For 50 = 15 increase euros
2. For 100 = 15/50 x 100 = 30 increase in euros
3. 30/100 = 30%
OR....
1. Ten percent of 50 is 5.
2. 5x3= 15(increase in euros)
3. 10 percent three times which is equal to 30%.
I need someone to please explain how to turn this into a simplified fraction. (NOTE: please explain!!) __ 3.541 The repeating sign is only above the 41, not the five
the way to do these recurring decimals is by firstly separating the repeating part or recurring part and then multiply it by some power of 10 so we move it to the left, lemme show
[tex]3.5\overline{41}\implies \cfrac{35.\overline{41}}{10}\qquad \stackrel{\textit{say that the repe}\textit{ating part is }~\hfill }{x = \overline{0.41}\qquad \qquad \textit{so that }35.\overline{41}=35+\overline{0.41}=35+x}[/tex]
now, let's multiply that repeating part by some power of 10 that moves the 41 to the left, well, we have two repeating decimals, 4 and 1, so let's use two zeros, namely 100 or 10², thus
[tex]100\cdot x = 41.\overline{41}\implies 100x - 41+\overline{0.41}\implies 100x = 41+x\implies 99x=41 \\\\\\ \boxed{x =\cfrac{41}{99}}\qquad \qquad \textit{so then we can say that}~~\cfrac{35.\overline{41}}{10}\implies \cfrac{35+\frac{41}{99}}{10} \\\\\\ \cfrac{~~\frac{3506}{99}~~}{10}\implies \cfrac{~~\frac{3506}{99}~~}{\frac{10}{1}}\implies \cfrac{3506}{99}\cdot \cfrac{1}{10}\implies \cfrac{3506}{990}\implies \blacktriangleright \stackrel{\textit{which simplifies to}}{\cfrac{1753}{495}} \blacktriangleleft[/tex]
I need help with this it’s saying the “blank” Method would be the best for solving this system of equations
6x + 4y=8
-x+4y=12
Answer:
-12+4y=x..............1
6(-12+4y)+4y=8
-72+24y+4y=8
28y=80
y=3.33
-12+4(3.33)=x
1.32=x
5x+1=2x-5
I need help
Answer:
x =-2
Step-by-step explanation:
5x+1=2x-5
Subtract 2x from each side
5x-2x+1=2x-2x-5
3x+1 = -5
Subtract 1 from each side
3x+1-1 = -5-1
3x=-6
Divide by 3
3x/3 = -6/3
x = -2
Dora travels between the two mile markers shown and then finds her average speed in miles per hour. Select the three equations that represent this situation.
The image of the 2 mile markers is missing as well as the options and so i have attached them.
Answer:
> 1.5 hours = 105 miles/speed
> Speed = 105 miles/1.5 hours
> 105 miles = 1.5 hours × speed
Step-by-step explanation:
From the image attached, the distance of the first mile marker is given as 50 miles while the distance of the second mile marker is given as 155 miles.
Thus, difference in distance between the two markers; d = 155 - 50 = 105 miles
Also, we see that the time of first marker is 3 pm while the second marker is 4:30 pm.
Thus, difference in time = 4:30 - 3 = 1 hour 30 minutes or 1.5 hours.
We know that;
Speed = distance/time
Thus;
Speed = 105/1.5
Speed = 70 mph
Thus, the 3 equations that represent this situation from the options are;
> 1.5 hours = 105 miles/speed
> Speed = 105 miles/1.5 hours
> 105 miles = 1.5 hours × speed
Answer:
1.5 hours = 105 miles/speed
Speed = 105 miles/1.5 hours
105 miles = 1.5 hours × speed
Step-by-step explanation:
Help on this question
Answer:
is it me or can I not see anything
Solve:
all real numbers
no solution
Please help
Answer:
In a problem where you
calculate the "solution" to a "system of equations"
one of three things will happen....
#1) you end up with x=3 , or y=7 .. or something like that
if that happens then there is ONE SOLUTION
#2) you end up with 5=5, or 7=7 , or 0=0
in this case the lines are the same and you have "all real numbers" as the solution (there are an infinite number of solutions, the lines are the same line)
#3) you end up with 1=2, 0=5, 2=7, etc. this is impossible, there are no solutions ... the lines are parallel
Step-by-step explanation:
What is 120 US fl oz in US liquid quarts
3.75 quarts
Brainly plz and thank you
Consider the following proportion:
2 12
— -—
7 x
Use cross products to write the equation: 2x = 84.
What is the value of x?
[tex]\displaystyle\bf 2x=84\\\\x=84:2=42\\\\\boxed{x=42}[/tex]
Translate the sentence into an equation.
Nine times the sum of a number and 4 is 3.
Suppose that x - y = 2 and 2x – 3y = 11. Then x + y =
Answer:
x + y = -12
Step-by-step explanation:
x - y = 2
2x – 3y = 11
-2x +2y = -4
2x – 3y = 11
-y = 7
y = -7
x = -5
x + y = -12
top cylinder: 6 in, 8 in
botton cube: 9 in, 9 in, 15 in
The volume of this figure is _____ cubic inches.
Answer:
1441.08 in^3
Step-by-step explanation:
Volume of rectangular prism = 15 * 9 * 9 = 1215 in^3
radius = 3 in
Volume of the cylinder = 3^2 * 3,14 * 8 = 226.08 in^3
Total volume = 1215 + 226.08 = 1441.08 in^3
Answer:
HJHJGHJHG
Step-by-step explanation:
JGHU45565677689789
Which of the following expressions is equivalent to the one shown below? (3/2)8 A 3^8/2^8 B 3^8/2 C 3/2^8 D 8•(3/2)
Answer:
Step-by-step explanation:
Lol do yu guys know this?? plz help
Answer: Choice C. 32,768
Explanation:
2.5 hours = 2.5*60 = 150 minutes
150/10 = 15
There are 15 periods that are 10 minutes each in a 2.5 hour timespan.
y = a*b^x
y = 1*2^15
y = 32,768
If you started with a = 1 bacterium, then it will double a total of 15 times to end up with 32,768 bacteria after the 2.5 hour period.
One triangle has an angle of 81 degrees and the corresponding angle of the other triangle is 2x - 5 degrees, find the value of x?
Answer:
[tex]x=43[/tex]
Step-by-step explanation:
Corresponding angles are equal. It is implied that the two angles referred to in the triangles are equal, otherwise they should not be labelled as corresponding.
Therefore, we can set both equations equal to each other:
[tex]2x-5=81^{\circ}[/tex]
Add 5 to both sides:
[tex]2x=86[/tex]
Divide both sides by 2:
[tex]x=\frac{86}{2}=\boxed{43}[/tex]
