Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
Exact Form: 10√21 where t = 10 and u =21
Which best describes the triangle?
Apply the rule for negative exponents to select the equivalent expression. 8-1 08 8X -8
The equivalent expression of 8^-1 is 1/8
How to apply the rule for negative exponents?The expression is given as
8^-1
The above represents 8 exponent -1
The rule for negative exponents states that
a^-1 = 1/a
This means that
8^-1 = 1/8
Hence, the equivalent expression of 8^-1 is 1/8
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To find a baseball pitcher's earned run average (era), you can use the formula ei = 9r, in which e represents era, i represents the number of innings pitched, and r represents the number of earned runs allowed. solve the equation for e. what is a pitcher's era if he allows 33 earned runs in 45 innings pitched? if necessary, round your answer to the nearest hundredth.
The value of e is 33/5 or 6.6 era.
It is given in the question that:-
e*i = 9r
Where,
e represents era
i represents the number of innings pitched, and
r represents the number of earned runs allowed
Also, we are given that:-
i = 45 innings, and
r = 33 earned runs allowed
We have to find the value of e for the given data.
Hence, applying the formula given in the question, we get
e*45 = 9*33
Now, as only one variable is left in the equation, it has become a linear equation in one variable.
Hence, solving the linear equation, we get
e = (9*33)/45
e = 33/5
e = 6.6 era
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a²-7a²b² + b² factor
100 Points Please Help Quick
Which function has a constant additive rate of change of –1/4?
A coordinate plane with a straight line with a negative slope. The line passes through (negative 2, 2) and (2, 1).
A coordinate plane with a curved line passing through (negative 1, 2), (0, negative 1), the minimum (2, negative 2), and (4, negative 1).
A two-column table with five rows. The first column, x, has the entries, 20, 21, 22, and 23. The second column, y, has the entries negative 1, negative 1.5, negative 2, and negative 2.5.
A two-column table with five rows. The first column, x, has the entries, negative 12, negative 11, negative 10, and negative 9. The second column, y, has the entries, 7, 11, 14, and 17.
Answer:
(A) is correct.
Step-by-step explanation:
As we know,
The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
From the first graph:
The line goes through the points:
(-2, 2) and (2, 1)
y - 1 = (1-2)/(2+2)[x -2]
y - 1 = (-1/4)[x -2]
y = -x/4 + 1/2 + 1
y = -x/4 + 3/2
The constant additive rate of change = -1/4
Thus, the function shown in graph (A) has a constant additive rate of change is -1/4 option (A) is correct.
Diego worked the SAME number of hours for FIVE days at his job at the cheese factory plus an extra 7 hours on Saturday. He worked a total 52-hours last week.
Using H as a variable for the number of hours he worked each normal day, model (create an equation) for Diego’s work week.
How many hours did he work each day for his normal work week?
The total hours worked on each day of his normal work week is 7.5 hours.
How many hours did Diego work on each normal day ?The total hours worked is a function of the total hours worked during the week and the hours worked on Saturday.
The equation that represents the total hours that Diego worked is:
Total hours = total hours worked during the five days + hours worked on Saturday
52 = (5 X H) + 7 + H
52 = 5H + 7 + H
In order to determine the value of H, take the following steps:
Combine similar terms together: 52 - 7 = 5H + H
Add similar terms together: 45 = 6h
Divide both sides of the equation by 6 : H = 45 /6
H = 7.5 hours
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what is 3-5b=-32 in algebra
Answer:
b=7
Step-by-step explanation:
3-5b=-32
-5b=-32-3
-5b=-35
Divide both sides by -5
b=7
( I also had trouble with these kind of expressions)
Help!!!
6 divided by 2(1+2)
Answer:
9
Step-by-step explanation:
6 / 2(1+2)
6 / 2 (3)
6 / 2 * 3
3 * 3
9
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The function ƒ(x) = e2x+1 when graphed could be described as
The function ƒ(x) = e^(2x + 1) when graphed could be described as; an increasing exponential graph.
How to Interpret Exponential Graphs?The graphs of exponential functions are nonlinear—because their slopes are always changing, they look like curves, not straight lines.
Now, we are given the exponential function as; ƒ(x) = e^(2x + 1)
Now, as the exponent increases, the curves get steeper and the rate of growth increases respectively. Thus, we can see that the exponent we are given increases as seen in the exponent attached to it.
Thus, we can conclude that The function ƒ(x) = e^(2x + 1) when graphed could be described as; an increasing exponential graph.
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Eric rented a truck for one day. There was a base fee of 19.95 and there was an additional charge of 97 cents for each mile driven. Eric had to pay 190.67 when he returned to the truck. For how many miles did he drive the truck?
Answer: 176 miles
Step-by-step explanation:
m=mile.
97 cents=
97/100 dollars=$0.97
190.67=19.95+0.97m
170.72=0.97m
m=176 miles
The median of a quanitive data set is always one of the infiviual data values. True or false
The given statement "The median of a quantitative data set is always one of the individual data values" is false.
What is a median?When a given data set is arranged in ascending order the observation which at the between of the data is the median of that data set. It is a value in the set whose left and right both have the same number of observations.
The given statement is not true, this is because the median is the mid-value of any data set.
If the number of data observations is odd then the median of a quantitative data set is always one of the individual data values.But if the number of data observations is even then the median is the average of the two numbers present in between the data observations.Hence, the given statement "The median of a quantitative data set is always one of the individual data values" is false.
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write 26/50 as a decimal fraction
Answer:
13/25
Step-by-step explanation:
hope this helps :)
Which of the following numbers can be expressed as decimals that terminate? (1 point) 5 over 2 , 4 over 5 , 2 over 7 , 4 over 3 5 over 2 and 2 over 7 4 over 5 and 4 over 3 5 over 2 and 4 over 5 2 over 7 and 4 over 3
Answer:
all of them are terminating decimals
Step-by-step explanation:
5/2=2.5
4/5=1.25
2/7=3.5
4/5=1.25
4/3=0.75
5/2=2.5
4/5=1.25
2/7=3.5
4/3=0.75
they are terminating decimals because they have a finite end
Question 2 of 10
Which situation shows a constant rate of change?
A. The amount raised by a booster club compared with the number
of raffle tickets sold
B. The weight of a kitten compared with its age in months
C. The number of goals scored in a soccer game compared with the
minutes played
D. The height of a paper airplane over time
The amount raised by a booster club compared with the number of raffle tickets sold shows a constant rate of change;
A constant rate of change is realized when a change in one situation always results in a change in another. In the scenario of a booster club that regularly sells raffle tickets, the more tickets it sells, the higher the club gets.
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Satisfactory internal control ______ the probability of errors or frauds in the accounts.
Satisfactory internal control reduces the probability of errors or frauds in the accounts.
What functions may a strong internal control system perform?
To ensure that goals and objectives are met, effective internal controls are necessary. For management choices, they offer trustworthy financial reports. To reduce the possibility of public scandals, they make sure that applicable laws and regulations are followed.Why are internal controls necessary?
Internal controls are primarily used to protect organizations and advance their goals. Internal controls serve to reduce risks, safeguard assets, maintain record accuracy, enhance operational effectiveness, and promote conformity to laws, rules, and regulations.Learn more about system of internal controls
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1. 60 high school seniors taking AP classes (advanced classes for college credit) were polled (asked a question) to see if they were taking European History or US History. A total Of 29 students said they were taking AP European History and a total of 50 students sald they were taking AP US History. How many students take both AP European History and AP US History? (Hint: Draw a venn diagram.)
The number of students take both AP European History and AP US History is 19 students
A Venn diagram is an illustration of the relationships between and among sets, groups of objects that share something in common.
Let the students take both AP European History and AP US History be x such that;
n(U) = 29 - x + 50 - x
If 60 high school seniors taking AP classes, then n(U) = 60. Substitute to have:
60 = 29 - x + x + 50 - x
60 = 79 - x
-x = 60 - 79
-x =-19
x = 19
Therefore the number of students take both AP European History and AP US History is 19 students
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what is the unit rate for 1/4 kilometer in 1/3 hours
Answer: 0.75km
Step-by-step explanation:
find the derivative of f(x)=3x+5
Answer: Derivative of f(x) =3x+5=3
Step-by-step explanation:
By the Sum Rule, the derivative of 3x+5 with respect to x is d/dx[3x]+d/dx[5]
d/dx[3x]+d/dx[5]
evaluate: d/dx[3x]
Since 3 is constant with respect to x, the derivative of 3x with respect to x is 3d/dx[x].
3d/dx[x]+d/dx[5]
Differentiate using the power rule
which states that d/dx[[tex]x^{n}[/tex]] is [tex]nx^{n-1}[/tex] where n=1.
3⋅1+d/dx[5]
Multiply 3 by 1.
3+d/dx[5]
Differentiate using the Constant Rule.
Since 5 is constant with respect to x, the derivative of 5 with respect to x is 0.
3+0
Add 3 and 0 = 3
So, derivative of f(x) =3x+5=3
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martin can read 4 pages in 7 minutes. at this rate,how long will it take him to read 9 pages
Answer:
5.14 minutes
Step-by-step explanation:
4 pages / 7 minutes = 0.57 minutes per page
0.57 minutes/pg * 9 pages = 5.14 minutes
PLEASE HELP, URGENT, POINTS GIVEN
A sheet of paper contains a list of 5 double-digit prime numbers.
Their mean is 31, while their median and mode is 29.
The largest number is 41.
Show how you can discover the 5 prime numbers written on the sheet.
Answer:
19, 29, 29, 37, 41
Step-by-step explanation:
1. What we know: x y 29 z 41
(x+y+29+z+41)/5 =31
x y and z each >9 and prime
Possibile numbers: 11, 13, 17, 19, 23, 29, 31, 37, 41
2. (x+y+29+z+41)/5 =31
x+y+29+z+41 = (31×5)
x+y+z = (31×5) -29 -41
x+y+z = 85
z>=29
x<=29
y<=29
x and y can be 11, 13, 17, 19, 23, 29
z could be 29, 31, 37, 41
At least one if them must equal 29 because it's the mode.
So two of them must equal 56
11+29=40 so both numbers cannot be less than or equal to 40
This means y is 29 because x + z has to equal 56 and that wouldn't be possible if x equals 29.
Now we know x+z=56
Possible numbers: 19+37
I found these by doing 56- each possible number for x and seeing if that equaled a possible number for z. For example 56-11=45 but z cannot be 45 therefore x cannot be 11 and so on.
Then you just plug in the numbers!
19, 29, 29, 37, 41
This was so much fun to solve! I hope this is helpful, let me know if you have any questions! You got this :)
Arrange the students in order from shortest to tallest. kim 56.03 alexa 56.3 roy 56.14 tom 57.1
Arrangement of students from shortest to tallest is
Kim 56.03 < Roy 56.14 < Alexa 56.3 < Tom 57.1.
As given in the question,
Number of students = 4
Height of the students
Kim = 56.03 units
Alexa = 56.3 units
Roy = 56.14 units
Tom = 57.1 units
Arrange the students from shortest to tallest
56.03 < 56.14 < 56.3 < 57.1
Kim < Roy < Alexa < Tom
Therefore, arrangement of students from shortest to tallest is
Kim 56.03 < Roy 56.14 < Alexa 56.3 < Tom 57.1.
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A car and an emergency are heading toward each other. The car is traveling at a speed of 30
mph or 44 feet per second. The emergency vehicle is traveling at a speed of 50 mph or about
74 feet per second. If the vehicles are 1000 feet apart and the conditions are ideal, in how
many seconds will the drive of the car first hear the siren?
If the speed of car is 44 feet per second and the speed of emergency vehicle is 74 feet per second,then they the driver of the car will hear the siren after 8.48 seconds after cover the distance of 1000 feet.
Given that the speed of car be 30 mph or 44 feet per second, the speed of emergency vehicle be 50 mph or 74 feet per second and the distance between both is 1000 feet apart.
We are required to find the seconds after which the driver of the car first hear the siren.
Speed is basically the distance that a vehicle covers in a particular period of time.
Speed=Distance/Time
Time=Distance/Speed
Total speed in feet per second=44+74=118 feet per second
Time=1000/118
=8.48 seconds
Hence if the speed of car is 44 feet per second and the speed of emergency vehicle is 74 feet per second,then they the driver of the car will hear the siren after 8.48 seconds.
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A taxi ride costs p40.00 for the first 500 meters and each additional 300 meters or a fraction there of adds p3.50 to the fare.use a piecewise function to represent the taxi fare in terms of distance d in meter?
The function which represents the taxi fare in terms of distance d in meter is f(d) = 3.50 ×[tex]\frac{d-500}{300}[/tex] + 40 .
According to the question,
For first 500 meters cost is 40.00 and For each additional 300 meters cost is 3.50 .
Let, the total distance of taxi ride = d meters
Now, representing the equation of taxi fare in terms of distance when distance is less than 500
taxi fare = 3.50 × [tex]\frac{d-500}{300}[/tex] + 40
∴ f(d) = 3.50 × [tex]\frac{d-500}{300}[/tex] + 40
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Monica has a goal to complete a triathlon. The race consists of a 2.4-mile swim, a 112-mile bike ride, and a 26.2-mile run. In training, Monica can swim at an average pace of 1.8mph. She rides her bike at an average of 19.2mph and runs at 4.8mph. Estimate how long it will take her to complete the triathlon.
Taking into account the definition of speed, Monica will complete the triathlon in 12.62 hours.
Definition of speedSpeed can be defined as the amount of space traveled per unit of time with which a body moves and can be calculated using the expression:
speed= distance traveled÷ time
Time to complete the triathlonIn this case, you know
Swim:speed= 1.8 mphdistance traveled= 2.4 milesRide a bikespeed= 19.2 mphdistance traveled= 112 milesRun:speed= 4.8 mphdistance traveled= 26.2 milesReplacing these values in the speed definition:
Swim: 1.8 mph= 2.4 miles÷ time to swimRide a bike: 19.2 mph= 112 miles÷ time to ride a bikeRun: 4.8 mph= 26.2 miles÷ time to runSolving:
Swim: 1.8 mph×time to swim= 2.4 miles
time to swim= 2.4 miles÷ 1.8 mph
time to swim= 1.33 h
Ride a bike: 19.2 mph× time to ride a bike = 112 miles
time to ride a bike= 112 miles÷ 19.2 mph
time to ride a bike=5.83 h
Run: 4.8 mph× time to run= 26.2 miles
time tu run= 26.2 miles÷ 4.8 mph
time to run= 5.46 h
The time to complete the triathlon is the sum of each of the stages:
Total time= time to swim + time to ride a bike + time to run
Total time= 1.33 h + 5.83 h + 5.46 h
Total time= 12.62 h
In summary, Monica will complete the triathlon in 12.62 hours.
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Without multiplying, tell whether the value of the expression is positive or negative.
4/7 • (-3 1/2)
Explain your reasoning.
Answer:
Negative
Step-by-step explanation:
Because knowing that a positive number times a negative number equals negative.
an amusement park charges 18 dollars for 4 rides. how much will 7 rides cost
What is the solution to this equation?
5x+15+ 2x = 24 + 4x
O A. x = 13
OB. x = 3
O C. x=39/11
O D. x =9/11
Answer:
X=3
Step-by-step explanation:
Remember to get all your variables on one side by doing the "Reverse function" etc...
Once youve got your variables on one side (and only 1 is remaining) you should get rid of whats BESIDE the variable by dividing it by *whatever it is thats beside the variable!* AND REMEMBER TO DO THIS ON BOTH SIDES OF THE EQUATION SO THAT THEYRE EQUAL!!
Which driver's race times were the most variable if Driver A has a mean of 4.01 seconds and a standard deviation of 0.05 seconds and Driver B has a mean of 3.96 seconds and a standard deviation of 0.12 seconds and Driver C has a mean of 3.99 seconds and a standard deviation of 0.19 seconds?
The driver B has the fastest typical race time.
It is required to find which driver's race times were the most variable.
What is a statement?A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.
Given:
From the options presented, driver B has the fastest typical race time because he recorded the smallest time taken to complete an individual race.
Also from the standard deviation given 3.96 seconds for driver B, it shows that the individual time spread from the standard deviation is minimal and that the driver maintained a fairly consistent time of race throughout the racing period.
Therefore, the driver B has the fastest typical race time.
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∠ABC and ∠DEF are complementary. If m∠ABC = (2x+4)∘ and m∠DEF = (3x−5)∘, find the measure of each angle.
m∠ABC =
m∠DEF =
The measure of each angle are m∠ABC = 40.4 and m∠DEF = 49.6
How to determine the measure of each angle?The given parameters are
m∠ABC = (2x+4)∘ and m∠DEF = (3x−5)∘,
Complementary angles add up to 90 degrees
So, we have
2x + 4 + 3x - 5 = 90
Evaluate the like terms
5x = 91
Divide by 5
x = 18.2
Substitute x = 18.2 in m∠ABC = (2x+4)∘ and m∠DEF = (3x−5)∘,
m∠ABC = (2 x 18.2 + 4) = 40.4
m∠DEF = (3 x 18.2 − 5)∘ = 49.6
Hence, the measure of each angle are m∠ABC = 40.4 and m∠DEF = 49.6
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use the diagram to find bc. (help please!!)
Answer:6
Step-by-step explanation:
The length of ac is 20 and the length of ab is 14 so all you have to do is 20-14=6
