The correct answer is "Rita read at the faster rate because 227 words per minute > 208 words per minute".
How do you calculate rate of something?The rate of something is a measure of how fast or slow it changes over time or another variable. The general formula for calculating rate is:
Rate = Change in value / Time interval or Change in value / Change in another variable Rates can be expressed in different units, such as miles per hour, dollars per day, or units per minute. It's important to ensure that the units are consistent throughout the calculation to obtain accurate results. In summary, the rate of something can be calculated by dividing the change in value by the time interval or the change in another variable.
To find out who read at the faster rate, we need to calculate the rate of reading for each person. We can do this by dividing the number of words read by the time taken to read them.
Rita's reading rate = 1362/6 = 227 words per minute
Joy's reading rate = 1456/7 = 208 words per minute
Therefore, Rita read at a faster rate than Joy, with a reading rate of 227 words per minute compared to Joy's reading rate of 208 words per minute.
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!!i’ll give brainlist!!
Tim is taking the path shown to bike to Greg's house. Tim travels an average speed of 15 mi/hr.
Determine how much time it will take Tim to get to Greg's house. (You may use decimals here)
Answer:
Road:
Distance to Greg's house = 3.2 + 1.7 =
4.9 miles
Time to get to Greg's house =
(4.9 mi)/(15 mi/hr) = about .327 hours = about 19.6 minutes (19 minutes, 36 seconds)
Shortcut:
Distance to Greg's house:
[tex] \sqrt{ {3.2}^{2} + {1.7}^{2} } = 3.6235 [/tex]
Time to get to Greg's house:
(3.6235 mi)/(15 mi/hr) = about .242 hours = about 14.49 minutes (14 minutes, 30 seconds)
The shortcut is about 4.9 - 3.6235 = 1.28 miles faster (about 5.11 minutes, or 5 minutes, 6 seconds faster)
Jason bought 91.5 pounds of fruit for a class party. The class ate 0.2 pounds of the fruit. How much fruit is left?
91.3 pounds of fruit are left
Jason bought = 91.5 pounds
class ate = 0.2 pounds
You subtract the amount the class ate from the amount Jason bought to get the amount of fruit left.
91.5 - 0.2 = 91.3 pounds
Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The answer are in angle m∠5+m∠6=180°,m∠2+m∠3=m∠6,m∠2+m∠3+m∠5=180°.
What is angle?Angle is a geometric concept that is used to describe the relationship between two lines or planes. It is measured in degrees, with a full circle being 360 degrees. Angles are used in mathematics to measure the size of a shape and the amount of turn between two lines. In physics, angles are used to describe the force of friction, the direction of a force, and the direction of light. Angles can also be used to describe the orientation of objects in space.
case A) we have
m∠5+m∠3=m∠4 ----> equation A
we know that
m∠3+m∠4=180° -----> by supplementary by angles
m∠4=180°-m∠3 ----> equation B
substitute the equation- B in equation A
m∠5+m∠3=180°-m∠3
m∠5+m∠3+m∠3=180°
This equation is true when m∠2=m∠3
therefore
Is not always true
case B) we have
m∠3+m∠4+m∠5=180° ----> equation A
we know that
m∠3+m∠4=180° -----> by supplementary to angles
m∠4=180°-m∠3 ----> equation B
substitute equation B in equation A
m∠3+(180°-m∠3)+m∠5=180°
m∠5=0°
This option is not true
case C) we have
m∠5+m∠6=180°
we know that
m∠5 and +m∠6 are supplementary angles
so
Their sum is always 180 degrees
therefore
This option is always true
case D) we have
m∠2+m∠3=m∠6 -----> equation A
we know that
m∠5+m∠6=180° ----> by supplementary angles
m∠6=180°-m∠5 ----> equation B
substitute equation B in equation A
m∠2+m∠3=180°-m∠5
m∠2+m∠3+m∠5=180°
Remember that the sum of any of tAnswer:
Step-by-step explanation:
he interior angles that of a triangle must be equal to 180 degrees
therefore
This option is true for sure
case E) we have
m∠2+m∠3+m∠5=180°.
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Calculate Volume of Air passing through Filter HEPA Filter 100ft/min *- Airflow 4ft 2ft Volume = Filter Area x Airflow Velocity
The volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).
Describe Volume?In general, volume refers to the amount of space occupied by a three-dimensional object. In physics, volume is a measure of the amount of space an object takes up, typically measured in cubic meters (m³) or cubic centimeters (cm³).
In mathematics, volume is often used to refer to the measure of the size of a solid object or region in three-dimensional space. This measure can be calculated using various methods depending on the shape of the object or region, such as integration, formulae, or counting.
For example, the volume of a cube can be calculated by multiplying its length, width, and height together. The volume of a sphere can be calculated using the formula 4/3πr³, where r is the radius of the sphere.
In finance, volume can also refer to the number of shares or contracts traded in a particular market or stock exchange over a given period of time. High trading volume often indicates a more active market, while low trading volume may indicate less interest or activity in a particular security or market.
The formula for calculating the volume of air passing through a filter is:
Volume = Filter Area x Airflow Velocity
Given that the airflow velocity is 100 ft/min and the dimensions of the filter are 4 ft x 2 ft, we can calculate the filter area as:
Filter Area = Length x Width
Filter Area = 4 ft x 2 ft
Filter Area = 8 square feet
Now we can substitute the values into the formula:
Volume = Filter Area x Airflow Velocity
Volume = 8 sq ft x 100 ft/min
Volume = 800 cubic feet per minute (CFM)
Therefore, the volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).
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2 only can you solve associative, identity and inverse of this
The set 2Z is associative under the operation *, has an identity element of 2, and every element (except for 0) has an inverse element.
Solving the associative, identity and inverse of this the setThe set 2Z is defined as follows:
2Z = {2n | n ∈ Z, a * b = a + b}
Associative element:
There exists an associative element in 2Z if, for all a, b, and c in 2Z, the equation a*(bc) = (ab)*c holds.
Let a, b, and c be arbitrary elements of 2Z:
a = 2n₁
b = 2n₂
c = 2n₃
Then we have:
a*(bc) = a(2n₂2n₃) = a(4n₂n₃) = 2n₁ + 4n₂n₃ = 2(n₁ + 2n₂n₃)
(a*b)c = (2n₁2n₂)*2n₃ = (4n₁n₂)*2n₃ = 8n₁n₂n₃ = 2(2n₁n₂n₃)
Therefore, a*(bc) = (ab)*c, and 2Z is associative under the operation *.
Identity element:
There exists an identity element in 2Z if there exists an element e in 2Z such that, for all a in 2Z, the equation ae = ea = a holds.
Let e be an arbitrary element of 2Z:
e = 2n
Then we have:
ae = a2n = a + 2n = 2m, where m = n + (a/2) ∈ Z
ea = 2na = a + 2n = 2m', where m' = n + (a/2) ∈ Z
Therefore, e = 2n is an identity element in 2Z.
Inverse element:
There exists an inverse element in 2Z if, for all a in 2Z, there exists an element b in 2Z such that ab = ba = e, where e is the identity element.
Let a be an arbitrary element of 2Z:
a = 2n
Then we need to find an element b in 2Z such that ab = ba = e = 2.
We have:
ab = ba = 2n*b = 2
Therefore, b = 1/(2n) is the inverse of a in 2Z if n ≠ 0.
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The vector matrix -6, -3 is rotated at different angles. Match the angles of rotation with the vector matrices they produce.
Answer: Without the options for the vector matrices resulting from rotation, I cannot provide a specific matching. However, I can provide the general formula for rotating a vector by an angle of θ degrees counterclockwise as follows:
To rotate a vector with coordinates (x, y) counterclockwise about the origin by an angle of θ degrees, we use the following formula to find the new coordinates (x', y'):
x' = xcos(θ) - ysin(θ)
y' = xsin(θ) + ycos(θ)
Therefore, to obtain the vector matrix resulting from rotating the vector (-6, -3) by a certain angle of rotation, we plug in the values of x = -6 and y = -3 into the above formulas, and use the corresponding angle of rotation in degrees for θ.
Step-by-step explanation:
is trigonometry hard?
Answer:
yes it is pretty hard but I believe I. you
question is in the picture
The calculated value of the volume of the solid is (d) V = ∫[0,2] (x² + 1) - (2x + 1) dx
Finding the volume of the solidTo find the volume of the solid when the region R is rotated about the horizontal line y = -1, we can use the method of cylindrical shells.
The height of each cylindrical shell will be the difference between the function y = 2x and the horizontal line y = -1, which is (2x + 1).
The radius of each cylindrical shell will be the distance from the axis of rotation (y = -1) to the function y = x².
This distance is given by (x² + 1).
The thickness of each cylindrical shell will be dx.
Thus, the volume of the solid can be expressed as:
V = ∫[0,2] (x² + 1) - (2x + 1) dx
Hence, the expression is (d) V = ∫[0,2] (x² + 1) - (2x + 1) dx
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A card is dealt from a complete deck of fifty-two playing cards (no jokers). Use probability rules (when appropriate) to find the probability that the card is as stated. (Count an ace as high. Enter your answers as fractions.)
What is
both under a 3 and above an 8
The probability of the card is as stated at 7/52, which simplifies it to 1/8.
What is probability?Probability is the study of the possibility that an event or phenomenon will occur. It can be expressed numerically as a number between 0 and 1, where 1 implies a certain outcome of an event and 0 denotes an inconceivable chance of occurrence.
There are four cards that are under a 3 (the 2, the Ace, the King, and the Queen) and four cards that are above an 8 (the 9, the 10, the Jack, and the Queen). However, the Queen is both above an 8 and under a 3, so we need to subtract one from the total count.
Therefore, the number of cards that are either under a 3 or above an 8 is 4 + 4 - 1 = 7.
Therefore, the probability that the card is as stated is 7/52, which simplifies it to 1/8.
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What’s 95 divided by 3
What is a formula for the nth term of the given sequence? 18 , 21 , 24
Answer:
3n+15
Step-by-step explanation:
18, 21, 24
+3. +3
3n
18-3=15
3n+15
Julia drew s sketches of flowers. She split them evenly among her 3 pen pals. Write an expression that shows how many sketches each pen pal received.
Answer:
s/3
Step-by-step explanation:
since she drew s drawings and split them among 3 penpals, it would be s/3, for example, 6 drawings/ 3 would be 2 drawings for each person.
k^2+6k=0 solve the quadratic equation by factoring
Answer:
K = √-6k
i did the math and got this answer and it was right
4. The elevation at ground level is 0 feet. An elevator starts 80 feet below ground level. After
traveling for 20 seconds, the elevator is 30 feet below ground level. Which statement describes
the elevator's rate of change in elevation during this 20-second interval?
A. The elevator traveled upward at a rate
1 rate of 2½ feet per second.
B. The elevator traveled downward at a rate of 2 feet per second.
C. The elevator traveled upward at a rate of 4 feet per second.
D. The elevator traveled downward at a rate of 4 feet per second.
a
Answer:
[tex]m = \frac{ - 30 - ( - 80)}{20 - 0} = \frac{50}{20} = 2 \frac{1}{2} [/tex]
A. The elevator traveled upward at a rate of 2 1/2 feet per second. -30 > -80.
How do you write 4/15 as a decimal?
Answer:
Step-by-step explanation:
There are two ways to write 4/15 as a decimal.
**Method 1: Using long division**
1. Divide 4 by 15.
2. The quotient is 0.26.
3. The remainder is 6.
4. Since the remainder is not zero, we need to bring down a zero and continue dividing.
5. We get 0.266666...
**Method 2: Using a calculator**
1. Enter 4/15 into the calculator.
2. Press the "equals" button.
3. The answer is 0.266666...
The decimal representation of 4/15 is 0.266666..., which is a repeating decimal. This means that the 6 repeats indefinitely.
Answer:
The answer is 0.2666
Step-by-step explanation:
4/15
=0.2666
The volume of a pyramid whose base is a right triangle is 108 units^3
. If the two legs of the right triangle measure 8 units and 9 units, find the height of the pyramid.
According to the question the volume formula to find the height of the pyramid is 9 units.
What is formula?Formula is a mathematical rule or equation expressed symbolically, that describes the relationship between different variables. It is a set of symbols or terms that expresses a relationship between different entities, such as numbers, objects, ideas, or concepts. Formulas are used to calculate, analyze, and predict data, and are essential in many scientific and mathematical fields.
The volume of a pyramid is given by the formula V = (1/3) × b × h, where b is the area of the base and h is the height of the pyramid.
Since the base of the pyramid is a right triangle, we can use the formula to find the area of a right triangle, A = (1/2) × b × h, to find the base of the pyramid.
A = (1/2) × 8 × 9 = 36
Now we can use the volume formula to find the height of the pyramid:
V = (1/3) × 36 × h
108 = (1/3) × 36 × h
108 = 12 × h
h = 9 units
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John is making his pasta dish. his mom eats 1/12 of pasta and his brother eats 1/6 of pasta. How much of pasta is left over?
Answer:
1/4 of the pot is left.
Step-by-step explanation:
Let x be the total amount of pasta in the pot.
Then the amount of pasta her mother got= 1x/12
The amount of pasta her brother got= 1x/6
The total amount of pasta he serve= 1x/12 + 1x/6
First, convert them into like fractions, then
The total amount of pasta he serve= 1x/12 + 2x/12 = (x+2x)/12 = 3x/12 = 1x/4
Hence, 1/4 of the pot is left over.
Step-by-step explanation:
Mom: 1/12
Brother: 1/6
1/6 × 2/2 = 2/12
2/12 + 1/12 = 3/12
12/12 (= 1 whole) - 3/12 = 9/12 of pasta is left
A certain test has a population mean (mu) of
285 with a population standard deviation
(sigma) or 125. You take an SRS of size 400
find that the sample mean (x-bar) is 288. The
sampling distribution of x-bar is approximately
Normal with mean:
Answer:
124
Step-by-step explanation:
You'll need a calculator for this one
Solve x to make A||B
Answer:
x = 7
Step-by-step explanation:
if A and B are parallel , then
4x + 14 and 3x + 21 are alternate angles and are congruent , that is
4x + 14 = 3x + 21 ( subtract 3x from both sides )
x + 14 = 21 ( subtract 14 from both sides )
x = 7
For A and B to be parallel then x = 7
VERY EASY BASICALLY FREE <333
You should be very familiar with the informal use of probability. We make most of our decisions based on what we feel is likely, or unlikely, to happen.
Think of a time when you made a decision based on what you felt would probably happen. Did it turn out the way you thought it was likely to?
Let's say you're trying to decide whether or not to invest in a certain stock. You've analyzed the company's financial reports and economic indicators, but you're still uncertain about the stock's future performance. Based on your intuition and experience with the stock market, you estimate that there is a 70% chance that the stock's value will rise in the next six months.
Was your investment effective?You decide to invest based on that probability, and six months later the stock has actually gone up in value. Your decision turned out to be a good one, but that doesn't necessarily mean your probability estimate was accurate. The stock could have gone down in value just as easily, despite your assessment of its likelihood of going up.
Therefore, even when we make decisions based on probability, there is always a level of uncertainty involved and the outcome may not always line up with our initial estimates. However, taking the time to consider the likelihood of different outcomes can help us make more informed decisions and better manage risk.
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Evaluate the expression without using a calculator. sin−1(cos(2)) sin^−1 (cos( − /2))
The value of the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)) is 0.
Describe Algebraic Expression?An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. These expressions can be used to represent mathematical relationships and patterns in a variety of contexts.
Algebraic expressions can include one or more variables, which are letters or symbols that represent unknown values or values that can vary. For example, in the expression 3x + 5, "x" is the variable.
To evaluate the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)), we first need to determine the value of cos(2) and cos(-π/2).
cos(2) cannot be evaluated directly since the range of cosine function is -1 to 1, and 2 is outside this range. Therefore, we can conclude that sin⁻¹(cos(2)) does not exist.
Next, we can evaluate cos(-π/2) using the unit circle, which is a circle of radius 1 centered at the origin of the coordinate plane. The angle -π/2 is located on the negative y-axis, where the cosine function is 0. Therefore, cos(-π/2) = 0.
Substituting this value into the expression, we get:
sin⁻¹(0) = 0
Therefore, the value of the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)) is 0.
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Let y = - 4j- 21 Find the vector - 6v
-6v=
The vector 6v is -24j - 126.
What is vector?
In mathematics, a vector is a mathematical object that represents a quantity that has both magnitude (size) and direction. Vectors are used to describe physical quantities that have both magnitude and direction, such as velocity, force, and displacement.
Given the vector v = -4j - 21, we can find the vector 6v by multiplying each component of v by 6:
6v = 6(-4j - 21)
Distributing the 6:
6v = -24j - 126
So the vector 6v is -24j - 126.
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Complete question: Let v = - 4j- 21 Find the vector 6v.
what is the surface area of this figure ?
The surface area of this figure is determined as 980.5 m².
What is the surface area of the figure?
The total surface area of the figure is the sum of all the area of the six faces and it is calculated as follows;
Area of top face = 12.7 m x 11 m = 139.7 m²
Area of bottom face = 9.5 m x 16 m = 152 m²
Area of far right face = 12.7 m x 14 m = 177.8 m²
Area of far left face = 9.5 m x 14 m = 133 m²
Area of front face = 16 m x 14 m = 224 m²
Area of back face = 11 m x 14 m = 154 m²
Total surface area = 139.7 m² + 152 m² + 177.8 m² + 133 m² + 224 m² + 154 m²
= 980.5 m²
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For this discussion post, we are going to create a linear regression model from a set of data. Suppose we get a job working for a company that provides their employees with company stock every year they work with the company. The amount of stock earned may be based on a few other variables, but all we are looking at right now is time served with the company. Here is the data we collected:
The linear regression model from a set of data is y =5.2956+4.0946*X.
What is linear regression model?A statistical tool for examining the relationship between two quantitative variables is a linear regression model. Finding the best linear relationship between the dependent variable (Y) and one or more independent variables (X) in order to forecast the value of the dependent variable based on the value of the independent variable is the objective of a linear regression study.
The regression line is determined using the formula:
y = bo + b1 X
Now, using the table we have:
sum of (x) = ∑x = 103
sum of (y) = ∑y = 480
Calculating the squares we have:
sum of (x^2)= ∑x² = 1073
sum of (y^2)= ∑y² = 22868
Multiplying the variables we have:
sum of (x*y)= ∑x*y = 4939
mean(x)= ∑x/n = 9.3636
mean(y)= ∑y/n = 43.6364
Now, the intercept is given as:
intercept (bo) = (∑y)(∑x²) - (∑x)(∑xy) / n(∑x²) - (∑x)²
Substituting the values we have:
intercept (bo) = (480)(1073) - (103)(4939) / 11(1073)-(103)^2
intercept (bo) = (515040-508717) / (11803-10609)
intercept (bo) = 5.2956
The slope is given as:
slope (b1) = n(∑xy) - (∑x)(∑y) /n(∑x²) - (∑x)²
Substituting the values we have:
slope (b1) = (11(4939) -(103)(480))/(11(1073) - (103)^2
slope (b1) = (54329-49440)/(11803-10609)
slope (b1) = 4.0946
regression equation is, y = bo + b1 X
Substituting the values we have:
y =5.2956+4.0946*X
Hence, the linear regression model from a set of data is y =5.2956+4.0946*X.
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The complete question is:
given that log c3 = 0.914
PLEASE HELP MATH
Answer:
≈ 0.153
Step-by-step explanation:
using the rules of logarithms
log x - log y ⇔ log ([tex]\frac{x}{y}[/tex] )
[tex]log_{b}[/tex] b = 1
then
[tex]log_{c}[/tex] ( [tex]\frac{4}{c}[/tex] )
= [tex]log_{c}[/tex] 4 - [tex]log_{c}[/tex] c
= 1.153 - 1
= 0.153
8. You and 4 friends are going to an event, and you want to keep the cost below $100 per person. Write and solve an inequality to find the total cost, x.
Amy and Zack each have 24 feet of fencing for their rectangular gardens. Amy makes her fence 6 feet long. Zack makes his fence 8 feet long. Whose garden has the better area? How much greater?
Answer:
The answer is Zack garden
Compute the following
(a) Calculate the scalar projection and projection of (5,3) onto (7,-2)
(b) Interpret this projection graphically
The scalar projection and projection vector of vector (5,3) onto vector (7,-2) can be calculated by using the appropriate formulas and then interpreted graphically.
The scalar projection of (5,3) onto (7,-2) was found to be 29/53, and the projection vector was found to be (203/53, -58/53). This graphical representation illustrates the projection of vector (5,3) onto vector (7,-2).
What is graph?Graph is a data structure that consists of nodes and edges, which are used to represent relationships between different objects. A graph is often used to represent the real-world relationships between objects such as cities, towns, and roads. Graphs can also represent abstract relationships such as between two people or mathematical formulas. Graphs are widely used in computer science, networking, and mathematics.
(a) Scalar Projection:
The scalar projection of vector A onto vector B can be calculated by using the following formula:
Projection = (A⋅B)/|B|
In this case, the scalar projection of (5,3) onto (7,-2) is:
Projection = (5⋅7 + 3⋅(-2))/(7⋅7 + (-2)⋅(-2))
= (35 - 6)/53
= 29/53
Projection Vector:
The projection vector of vector A onto vector B can be calculated by using the following formula:
Projection Vector = (A⋅B/|B|²)B
In this case, the projection vector of (5,3) onto (7,-2) is:
Projection Vector = (5⋅7 + 3⋅(-2))/(7⋅7 + (-2)⋅(-2)) ⋅ (7,-2)
= (35 - 6)/53 ⋅ (7,-2)
= (29/53)⋅(7,-2)
= (203/53, -58/53)
(b) Interpretation Graphically:
The projection of vector (5,3) onto vector (7,-2) can be interpreted graphically as follows:
First, draw the two vectors (5,3) and (7,-2) on a graph. Then draw a line from the origin to the tip of vector (7,-2). This line will represent vector (7,-2). Next, draw a line from the origin to the tip of vector (5,3). This line will represent vector (5,3).
Finally, draw a line from the tip of vector (7,-2) to the tip of vector (5,3). This line will represent the projection vector of (5,3) onto (7,-2). The length of this line will be the scalar projection of (5,3) onto (7,-2).
This graphical representation illustrates the projection of vector (5,3) onto vector (7,-2).
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If I had 60 units needed and units per case was 14 how many full cases and additional items are needed to fufill the order
How long did Lizzie practice on Thursday and Friday altogether?
J
P
D
Lizzie's Drum Practice
P
S
P
D
P
S
S
Monday Tuesday Wednesday Thursday Friday
= 5 minutes
DONE
0
minutes
7 8
4
00
5
1 2
0
9
6
3
Answer:
Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.
On Thursday, she practiced for 5 minutes according to the table.
On Friday, she practiced for 9 minutes according to the table.
Adding these two times together, we get:
5 minutes + 9 minutes = 14 minutes
Therefore, Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.