After 15 minutes the pan will have a temperature of 36°F
How to determine the temperature of the pan after 15 minutes?
Newton's Law of Cooling, if a body with temperature T₁ is placed in surroundings with temperature To, different from that of T₁, the body will either cool or warm to temperature T(t) after t minutes, where T(t) = T₀ + (T₁-T₀)e^(kt)
Given: T₁ = 120°F, T₀ = 0°F. After 5 minutes, T(t) = 80°F
T(t) = T₀ + (T₁-T₀)e^(kt)
80 = 0 + (120-0)e^(5k)
80 = 120e^5k
e^5k = 80/120
e^5k = 2/3
5k = ln(2/3)
k = ln(2/3) / 5
k = -0.0811
The temperature of the pan after 15 minutes will be:
T(t) = T₀ + (T₁-T₀)e^(kt)
T(15) = 0 + (120-0)e^(-0.0811×15)
T(15) = 120e^(-0.0811×15)
T(15) = 36°F
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A Question 1 (1 point) Retake question
Solve.
5(a − 1) - 15 = 3(a + 2) + 4
Answer:
A=11
Step-by-step explanation:
Hope this helps please give me Brainliest!
There are 20 slices of bread in a loaf. How
many 2-slice sandwiches can you make
with 1 loaf? Write a multiplication fact
and a division fact you could use to solve
this problem.
Answer:
Step-by-step explanation: All you have to do would just separate the bread into groups of 2, and then count how many groups you have, and that would give you the answer.
Keiko estimated that it would take her 18 hours to build a shed for her 12.5 backyard. It only took her hours. What is the percent error of her estimate relative to the time it actually took?
The percent error of her estimate relative to the time it actually took is approximately 5.9%
What is the percent error?Estimated time to construct the shed = 18 hoursActual time taken to build the shed = 17 hoursError = Estimated time to construct the shed - Actual time taken to build the shed
= 18 hours - 17 hours
= 1 hour
Percent error = error / actual time × 100
= 1/17 × 100
= 0.058823529411764 × 100
= 5.882352941176470
Approximately,
5.9%
Consequently, the percent error of Keiko estimation and actual time is 5.9%
Complete question:
Keiko estimated that it would take her 18 hours to build a shed for her 12.5 backyard. It only took her 17 hours. What is the percent error of her estimate relative to the time it actually took?
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NO LINKS!! Determine if the figures have line, point, and/or rotational symmetry. Check all that apply. Part 1
Answer:
1. Line, Point, Rotational
2. Line, Rotational
3. None
4. Rotational
Step-by-step explanation:
Definitions
A figure has line symmetry when a line can divide the figure into two mirror images.A figure has point symmetry when the figure appears unchanged if rotated 180° about the center point. (Point symmetry can also be described as rotational symmetry of 180°).A figure has rotational symmetry if the figure appears unchanged if rotated around the center of rotation by less than 360°. (If a figure has point symmetry, then it also has rotational symmetry by definition).Figure 1
[tex]\boxed{\checkmark}\;\;\;\sf Line[/tex]
[tex]\boxed{\checkmark}\;\;\;\sf Point[/tex]
[tex]\boxed{\checkmark}\;\;\;\sf Rotational[/tex]
[tex]\boxed{\phantom{\checkmark}}\;\;\;\sf None[/tex]
This figure has vertical and horizontal lines of symmetry.
As this figure has point symmetry, it also has rotational symmetry of 180°.
Figure 2
[tex]\boxed{\checkmark}\;\;\;\sf Line[/tex]
[tex]\boxed{\phantom{\checkmark}}\;\;\;\sf Point[/tex]
[tex]\boxed{\checkmark}\;\;\;\sf Rotational[/tex]
[tex]\boxed{\phantom{\checkmark}}\;\;\;\sf None[/tex]
This figure has a vertical line of symmetry.
This figure does not have point symmetry as when the figure is rotated 180°, it no longer appears the same as the original figure.
This figure has rotational symmetry of 120°.
Figure 3
[tex]\boxed{\phantom{\checkmark}}\;\;\;\sf Line[/tex]
[tex]\boxed{\phantom{\checkmark}}\;\;\;\sf Point[/tex]
[tex]\boxed{\phantom{\checkmark}}\;\;\;\sf Rotational[/tex]
[tex]\boxed{\checkmark}\;\;\;\sf None[/tex]
It's difficult to tell as the provided picture of this figure is not flat, but it appears not to have any symmetry.
Figure 4
[tex]\boxed{\phantom{\checkmark}}\;\;\;\sf Line[/tex]
[tex]\boxed{\phantom{\checkmark}}\;\;\;\sf Point[/tex]
[tex]\boxed{\checkmark}\;\;\;\sf Rotational[/tex]
[tex]\boxed{\phantom{\checkmark}}\;\;\;\sf None[/tex]
This figure has no line symmetry.
This figure does not have point symmetry as when the figure is rotated 180°, it no longer appears the same as the original figure.
This figure has rotational symmetry of 120°.
Which expression represents each mathematical phrases
add 12 and a number
subtract a number from 12
divide a number by 12
multiply 12 by a number
The coldest temperature ever recorded in Mathville was - 16 deg * E This happened on January 30th, 1978. The normal low for that day is 19^ * E. How much colder was the record temperature than the normal low temperature?
Drive-A-Lot Cars runs a promotion for three years of interest-free payments on sedans. The cost of a new sedan is $22,968 (including tax). What is the average monthly payment a customer will make if they pay off the car during the interest-free period? Type your answer in the box.
The average monthly payment made by the customer is $638.
How to calculate the average?In order to calculate average, divide the total sum of the data to the total number of data. An average is a standard number for a given data whose value can both be more or less than it.
Given that,
The cost of Sedan for three years is $22,968.
The time in months can be calculated as,
3 × 12 = 36 months
The average payment per month can be found by dividing the total amount by total number of months as follows,
Average monthly payment = 22968/36
= 638
Hence, the average monthly payment made by a customer in the interest-free period is $638.
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A rancher has 200 feet of fencing to enclose two adjacent rectangular corrals. What dimensions should
be used so that the enclosed area will be a maximum?
Length is 33.33 feet and width is 25 feet are dimensions should
be used so that the enclosed area will be a maximum.
What is Area of Rectangle?The area of Rectangle is length times of width
Given that, a rancher has 200 feet of fencing to enclose two adjacent rectangular corrals of the same dimensions.
Here, the dimensions of the rectangles are the same.
The width of the two rectangles is W=2W+2W=4W
The length of the two rectangles is L=L+L+L=3L
Because the adjacent side has a common length.
3L+4W=200
3L=200-4W
Divide both sides by 3
L=(200-4W)/3
Let us form an equation using the area of rectangle formula:
A=2LW
=2(200-4W)/3.W
A=400-8W²/3
Let us differentiate to get the area to be maximized dA/dW=0
1/3×(400-8W²)=0
1/3(400-16W)=0
400-16W=0
400=16W
Divide both sides by 16
W=25
The width is 25 feet.
Substitute W value in equation to get L value:
L=200-4×25/3
=200-100/3
=100/3
=33.33
The length is 33.33 feet.
Now let us find the maximum area
A=2LW
=2×33.33×25
=1666.66
Hence, length is 33.33 feet and width is 25 feet are dimensions should
be used so that the enclosed area will be a maximum.
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Find the values of x and y.
x + 2 = 3y
Choose an equation in slope-intercept form for the line that passes through (0,7) and is parallel to the y=4x-19
a. y= (1/4)x - 7
b. y= (1/4)x + 9
c. y = 4x + 3
d. y = 4x + 7
Answer:
Step-by-step explanation:
You dont even need to look at the slope. For it to pass through (0,7) answer d with the +7 at the end is the only right answer
your welcome
D
what is 18 1/2 - 6.6 ?
Answer: The answer to your question is 83.9
(When rounded, the answer is 84)
The mean of 4 numbers is 16.5. What would the new mean be if the number 16 is added to the data set?
A.
16.4
B.
12.4
C.
32.5
D.
20.5
Answer:
Its b
Step-by-step explanation:
The parabola y=x^2 is reflected across the x-axis and then scaled vertically by a factor of 1/8. What is the equation of the new parabola?
The equation of the new parabola, that is, the image of the parabola f(x) = x² is g(x) = - (1 / 8) · x².
What is the equation of the image of a parabola?
In this problem we must determine the image of the parabola f(x) = x², which is the result of a sequence of two rigid transformations: (i) Reflection across the x-axis, (ii) Dilation. Each kind of rigid transformation is described below:
Reflection across the x-axis
f'(x) = - f(x)
Dilation
g(x) = k · f'(x), where k is the scale factor.
Now we proceed to determine the equation of the new parabola:
Step 0
f(x) = x²
Step 1
f'(x) = - x²
Step 2
g(x) = - (1 / 8) · x²
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n Game 1, Emerson struck out 30 times in 90 times at bat. In Game 2, he struck out 40 times in 120 times at bat. In Game 3, Emerson struck out 42 times in 140 times at bat.
The percentage of time that Emerson actually hit the ball is given by the following option:
C. 68%.
How to calculate a percentage?A percentage is calculated applying proportions, as it is a fraction of the total amount, obtained as the division of the number of desired outcomes by the number of total outcomes and multiplied by 100%.
Hence the outcomes in this problem are given as follows:
Desired: outcomes that he did not struck out.Total: all the at bats.Then the number of desired outcomes is obtained as follows:
(90 - 30) + (120 - 40) + (140 - 42) = 238.
The number of total outcomes is obtained as follows:
90 + 120 + 140 = 350.
Then the percentage is given as follows:
P = 238/350 x 100% = 68%.
Meaning that the correct option is given by option C.
Missing InformationThe problem is:
In Game 1, Emerson struck out 30 times in 90 times at bat. In Game 2, he struck out 40 times in 120 times at bat. In Game 3, Emerson struck out 42 times in 140 times at bat. What percentage of times at bat did Emerson actually hit the ball? a. 39% b. 85% c. 68% d. 45%
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7. If the following triangle is isosceles, solve for x. Just type the number
only, the answer is a positive whole number.
(5x − 7)°
(8x - 55)
The required value of x for a given isosceles triangle is 16.
What is an isosceles triangle?
A triangle with two sides that have the same length is said to be an isosceles. When two sides of an isosceles triangle are equal, the angles across from those two sides likewise match up and are always equal.
Given that, the isosceles triangle then
two angles are equal
So, (5x-7)° = (8x-55)°
or, 8x - 5x = 55-7
or, 3x = 48
or, x = 48/3 = 16
Hence, the required value of x is 16.
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NO LINKS!! Determine if the figures have line, point, and/or rotational symmetry. Check all that apply. Part 2
Recall properties of symmetry:
Line - reflection mirror,Rotational - you can rotate it about its center and it will overlap with the initial shape after minimum of 180 degrees rotation,Point - the center is acting as a midpoint of the segment formed by opposite points. Rotational symmetry of even order is also a point symmetry.Using the properties we can state that:
#5It has rotational (of order 2) and point symmetry.#6It has no symmetry.#7It has rotational (of order 3) symmetry.#8It has rotational (of order 6) and point symmetry.Step-by-step explanation:
6.25 points
Find the GCF for the list.
10m4, 40m⁹
10m5
40m4
10m4
6.25 points
list
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
From the solution to the given inequality, the correction representations are -6x + 15 < 10 - 5x and a number line from -3 to 7, with an open circle at 5 and an arrow pointing to the right.
Solving Linear InequalitiesFrom the question, we are to determine the correct representations of the given inequality
The given inequality is
-3(2x - 5) < 5(2 - x)
To determine the correct representation, we will solve the inequality
Solving the inequality
-3(2x - 5) < 5(2 - x)
Clear the parentheses by applying the distributive property
-6x + 15 < 10 - 5x
Add 6x to both sides
-6x + 6x + 15 < 10 - 5x + 6x
15 < 10 + x
Subtract 10 from both sides
15 - 10 < 10 - 10 + x
5 < x
Therefore,
x > 5
Hence, the correction representations are -6x + 15 < 10 - 5x and the number for x > 5
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HELP ME OUT THANKS SO MUCH
Answer:
52 = 13h
Step-by-step explanation:
Which expressions are equivalent to this expression?
3(n+4)
Select each correct answer.
Responses
3n + 4
3n−12
12 + n + n + n
2n + 12 + n
We need to figure out what is given in the question.
Given:
[tex]3(n + 4)[/tex]
Options:
---------------------
[tex]3n + 4\\3n−12\\12 + n + n + n\\2n + 12 + n[/tex]
---------------------
It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
Answer:
[tex]2n + 12 + n = 3n + 12 = 3(n + 4)[/tex]
Therefore, the correct options are 12 +n+n+n and 2n + 12+n
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The coordinates of the vertices of a polygon are (-3, 1), (-3, 3), (-1, 5), (2, 4), and (2, 1).
What is the perimeter of the polygon to the nearest tenth of a unit?
A. 16.0 units
B. 17.2 units
C. 15.4 units
D. 18.8 units
Using the coordinates of the vertices of a polygon (-3, 1), (-3, 3), (-1, 5), (2, 4), and (2, 1) the perimeter of the polygon is 16.0 units
How to find the perimeter of the polygonThe perimeter is calculated by summing the sides
The length of line in an ordered pair is calculated using the formula
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
where
d = distance between the points
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
(-3, 1) and (-3, 3) =√{(-3 - -3)² + (3 - 1)²} = 2
(-3, 3) and (-1, 5) = √{(-1 - -3)² + (5 - 3)²} = 2√2
(-1, 5) and (2, 4) = √{(2 - -1)² + (4 - 5)²} = √10
(2, 4) and (2, 1) = √{(2 - 2)² + (1 - 4)²} = 3
(2, 1) and (-3, 1) = √{(-3 - 2)² + (1 - 1)²} = 5
The perimeter = 2 + 2√2 + √10 + 3 + 5
The perimeter = 15.9907
The perimeter = 16.0 units
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20 points!!Use what we know about the pythagorean theorem
to determine if this triangle is a right triangle. Write a
statement explaining why this is or is not a right
triangle. Show your work to justify your answer.
The triangle is a not right triangle because it does not follow the Pythagoras theorem
How to determine if the triangle is a right triangle?From the question, we have the figure that represents the parameter that can be used in our computation:
The sides of the triangles are
6, 8 and 9
For a triangle to be a right triangle, the side lengths must follow the Pythagoras theorem
The Pythagoras theorem states that
Longest side² = Sum of the squares of the other sides
So, we have
9² = 6² + 8²
Evaluate
81 = 100
The above equation is false
Hence, the triangle is not a right triangle
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Gasoline costs $2.75 a gallon. At most, how many gallons can be boughts for $22.00.
15.2 gallons of gasoline will cost:
15.2 * 2.75 =$41.8
9.5 gallons of diesel will cost:
9.5 * 3.02= $28.69.
The total amont Grabiel will spend on gasoline and diesel:
$41.8 +28.69= $70.49
Answer:
8
Step-by-step explanation:
2.75x8=22
or
22.00÷2.75=8
(not sure)
For the following write the converse , inverse, contrapositive and biconditional.
If the capital of Virginia is Richmond, then Halloween is in September.
Is the conditional true or false?
Is the converse true or false?
Is the bi-conditional true or false?
The converse of the conditional statement is “If Halloween is in September then the capital of Virginia is Richmond”.
The inverse of the conditional statement is “If Halloween is not in September then the capital of Virginia is Richmond”
The contrapositive of the conditional statement is “If the capital of Virginia is not Richmond, then Halloween is in not September”.
What is the conditional statement?The conditional statement is defined as the two fundamental components that make up a conditional statement Hypothesis (if) and Conclusion (then).
The given conditional statement is "If the capital of Virginia is Richmond, then Halloween is in September"
The converse of the conditional statement is “If Halloween is in September then the capital of Virginia is Richmond”.
The inverse of the conditional statement is “If Halloween is not in September then the capital of Virginia is Richmond”
The contrapositive of the conditional statement is “If the capital of Virginia is not Richmond, then Halloween is in not September”.
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The school principal ordered 3,500 snack bars for the after-school program. There are 136 middle school students and 244 elementary school students in the after-school program. Each student in the program eats one snack bar each day. Which equation can be used to find the number of days, d, there will be enough snack bars for the students in the after-school program? *
Answer:
I think about 9 days
(I'm pretty sure, but don't get mad if it's wrong
A half circle is joined to an equilateral triangle with side lengths of 12 units.Select all the expressions that correctly calculate the perimeter of the shape.
The perimeter of the figure described in the question is 42.84cm
How to get the perimeter of the figure?The figure is defined by a half circle is joined to an equilateral triangle with side lengths of 12 units.
So the perimeter of the figure will be equal to half of the circumference of the triangle plus the length of the two exposed sides of the triangle.
The diameter of the circle will also be 12 units, remember that the circumference of a circle of diameter D is:
C = 3.14*D
In this case, the circumference of half circle is:
C = 3.14*D/2
Replacing the value of the diameter:
C = 3.14*12cm/2 = 18.84cm
Adding the two sides of the triangle we get the perimeter.
P = 18.84cm + 2*12cm = 42.84cm
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If a = -2i and b = 5-5i, then find the value of the a³b in fully simplified form.
Answer:80
Step-by-step explanation:
PLEASE HELP ASAP 20 POINTS
Two angles in triangle PQR are congruent, ∠P and ∠Q; ∠R measures 22.75°. What is the measure of ∠P?
22.75°
78.625°
134.5°
157.25°
Answer:
<P = 78.625°
Step-by-step explanation:
All of the angles in a triangle add up to 180.
<R + <Q + <P = 180
We can use x for <P and <Q, as they represent the same value because they are congruent.
<R + x + x = 180
Now, we want to substitute known values in and work backwards to find out what angle <P and <Q are.
2x + <R = 180
Put 22.75 in for <R.
2x + 22.75 = 180
Subtract on both sides.
2x = 157.25
Divide 2 on both sides to isolate x
x = 78.625
Since x represents <P and <Q, that means they are both 78.625 degrees each.
<P = 78.625
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Which graph shows the image of ΔABC after a rotation about the origin?
Answer:
B
Step-by-step explanation:
A is a reflection across the y-axis.
B is the result of a rotation around the origin either by 90° counterclockwise, or by 270° clockwise.
C is a reflection across the x-axis.
D is a translation (shift) by -5 to the left.
Baxter has a recipe for salad dressing that calls for 2/3cup olive oil, 1/4 cup vinegar, and 1 1/3 cup pureed avocado.
how much pureed avocado does baxter need?
Answer:
Step-by-step explanation:
1 - 1/3 cup of pureed avocados
although it matters how much you are making.
if you are making 6 cups then you only need 2/3 cups of pureed avacados
Answer:
2/3
EXPLANATION
Based on the given conditions, formulate:
Convert the expression into a fraction:
Expand the fraction to get the least common denominator:
Calculate the product or quotient:
Write the numerators over common denominator:
Calculate the sum or difference:
Apply Multiplicative Distribution Law:
Write as a single fraction:
Calculate the product or quotient:
Calculate the product or quotient:
Cross out the common factor:
Reorder and combine like terms:
Write the numerators over common denominator:
Calculate the sum or difference:
Cross out the common factor:
Calculate the sum or difference:
Cross out the common factor:
get the result:
Answer: 2/3
A line has a slope of 1 and passes through the point (-2, 8). What is its equation in slope-intercept form?
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{ 1}(x-\stackrel{x_1}{(-2)}) \implies y -8= 1 (x +2) \\\\\\ y-8=x+2\implies {\Large \begin{array}{llll} y=x+10 \end{array}}[/tex]
Answer: The answer is y=x+10