If n√a=r , then which of the following are true statements? Check all that apply. A. r^n=a B. a^1/n=r C. a^r=n D. n^1/r=a
Answer:
A. r^n=a
B. a^1/n=r
Step-by-step explanation:
ape x
The true statements about the equation [tex]\sqrt[n]a = r[/tex] are (a) r^n=a and (b) a^1/n=r
How to determine the true statements?The equation is given as:
[tex]\sqrt[n]a = r[/tex]
Take the power of n on both sides of the equation
[tex](\sqrt[n]a)^n = r^n[/tex]
This gives
a = r^n
Rewrite as:
r^n = a
Also, we have:
[tex]\sqrt[n]a = r[/tex]
Apply the law of indices
a^1/n = r
Hence, the true statements about the equation [tex]\sqrt[n]a = r[/tex] are (a) r^n=a and (b) a^1/n=r
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Steve is buying a home worth $275,000. His closing costs will amount to 6 percent, and his down payment is 15 percent. How much is each fee?
If a binomial event has a probability of success of 0.2, how many successes would you expect out of 6000 trials?
Answer:
The success would expect are 1200.
Step-by-step explanation:
Given : If a binomial event has a probability of success of 0.2.
To find : How many successes would you expect out of 6000 trials?
Solution :
The probability of success p=0.2.
The number of trials is n=6000
The formula to find number of successes is
The mean (expected value) of number of successes is the multiple of success and number of trials,
[tex]M=np[/tex]
[tex]M=6000\times 0.2[/tex]
[tex]M=1200[/tex]
Therefore, The success would expect are 1200.
Assistance please?!
Use the figure to complete each statement.
a. CD is the ____ of AB
b. If AB = 10, then EB =____
c. AE = 1/2 ____
d. __ is the midpoint of __
e.
Answer:
Step-by-step explanation:
From the figure, it can be seen that CD is the perpendicular bisector of AB and also, we have:
(A) CD is the Perpendicular bisector of AB.
(B) If AB=10, then [tex]EB=\frac{AB}{2}=\frac{10}{2}=5[/tex]
(C) [tex]AE=\frac{1}{2}(AB)[/tex]
(D) E is the mid point of AB.
(E) [tex]{\angle}BED=90^{\circ}[/tex] (Because ED is perpendicular to AB)
A parabola is defined by the equation x = 5y2. In which direction will the parabola open? up down right left
A certain isotope decays so that the amount A remaining after t years is given by: A = A0 · e -0.03t where A0 is the original amount of the isotope. To the nearest year, the half-life of the isotope (the amount of time it takes to decay to half the original amount) is a0years.
In a 36 minute gym period, 24 boys want to play basketball. if only 10 can play at the same time, and each boy plays the same amount of time, how many minutes does each boy play
Final answer:
To determine how many minutes each boy plays in a 36-minute gym period with 24 boys wanting to play basketball, with only 10 able to play at a time, each boy would play for 15 minutes.
Explanation:
To find out how many minutes each boy plays in a 36-minute gym period with 24 boys and 10 playing at a time:
Calculate the total time for 24 boys: 24 boys / 10 boys playing at a time = 2.4 sets.
Divide the gym period by the number of sets: 36 minutes / 2.4 sets = 15 minutes per set.
A bridge builder wants to know the width of a river. He stands at point A along the river. He picks a point C directly across the river. He then walks downstream 90 feet from point A to point B. From point B, he sites C and determines the angle between the bank and point C (θ), to be 43º. What is the width of the river?
The bridge builder used the tangent function to calculate the width of the river. The equation tan(43) = width/90 was set up, and solving for width gives an answer of approximately 91.6 feet.
Explanation:The question gives us a right triangle set up, where point A is where the builder starts, point B is where he walks to, and point C is directly across the river. We can use trigonometry, specifically the tangent function, to find the unknown side. In a right triangle, the tangent of an angle is equal to the ratio of the opposite side (the side across from the angle) to the adjacent side (the side next to the angle).
The angle (θ) in this case is 43 degrees, the side adjacent to the angle is the walk of 90 feet, and the side opposite the angle is the width of the river, which we'll call 'w'. So we get the equation: tan(43) = w/90. Solving for 'w' gives us the width of the river.
Therefore, w = 90 * tan(43), which calculates to approximately 91.6 feet. So the width of the river is approximately 91.6 feet.
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The probability of winning on a split bet in a specific game of roulette is 1 19. Find the actual odds in favor of winning on the bet.
The answer is 1:18. I just took the statistics quiz and got it wrong due to the other person.
If pentagon OPQRS is dilated by a scale factor of seven over four from the origin, to create O'P'Q'R'S', what is the ordered pair of point P'?
What is the equivalent of pi over 3 radians in degrees?
Answer: The equivalent expression in degrees is 60°.
Step-by-step explanation: We are given to find the equivalent of the following expression in degrees.
[tex]E=\dfrac{\pi}{3}~\textup{radians}.[/tex]
We will be using the UNITARY method the solve the given problem.
We know that
[tex]\pi~\textup{radians}=180^\circ\\\\\\\Rightarrow 1~\textup{radian}=\left(\dfrac{180}{\pi}\right)^\circ\\\\\\\Rightarrow \dfrac{\pi}{3}~\textup{radians}=\left(\dfrac{\pi}{3}\times\dfrac{180}{\pi}\right)^\circ=60^\circ.[/tex]
Thus, the equivalent expression in degrees is 60°.
Evaluate the factorial expression. (N+4)! N+4
Answer:
The simplified form of given factorial expression is (N+3)!.
Step-by-step explanation:
The given expression is
[tex]\frac{(N+4)!}{N+4}[/tex]
The n! is defined as
[tex]n!=n(n-1)(n-2)...3(2)(1)[/tex]
[tex]n!=n(n-1)![/tex]
The given expression can be written as
[tex]\frac{(N+4)!}{N+4}=\frac{(N+4)(N+4-1)!}{N+4}[/tex]
[tex]\frac{(N+4)!}{N+4}=\frac{(N+4)(N+3)!}{N+4}[/tex]
Cancel out the common factors.
[tex]\frac{(N+4)!}{N+4}=(N+3)![/tex]
Therefore the simplified form of given factorial expression is (N+3)!.
In a rectangle ABCD, A and B are the points (4,2) and (2,8) respectively l. Given that the equation of AC is y=x-2. Find the equation of BC
Choose the correct simplification of (2xy^7)^2(y^4)^3.
2x^2y^26
2x^2y^2
4x^2y^2
4x^2y^26
Can someone simplify 3(2x+1)-8
There are (7 13)3 ⋅ 70 strawberries in a field. What is the total number of strawberries in the field?
The length of a screw produced by a machine is normally distributed with a mean of 0.65 inches and a standard deviation of 0.01 inches. What percent of screws are between 0.61 and 0.69 inches?
HELP
A. 65%
B. 68%
C. 99.7%
D. 99.9936%
Answer:
D. 99.9936%.
Step-by-step explanation:
We have been given that the length of a screw produced by a machine is normally distributed with a mean of 0.65 inches and a standard deviation of 0.01 inches.
To find the percent of screws that are between 0.61 and 0.69 inches, first of we will find z-score for our given raw scores using z-score formula.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
[tex]z=\text{z-score}[/tex],
[tex]x=\text{Raw-score}[/tex],
[tex]\mu=\text{Mean}[/tex],
[tex]\sigma=\text{Standard deviation}[/tex].
Now let us find z-score corresponding to our given raw scores.
[tex]z=\frac{0.61-0.65}{0.01}[/tex]
[tex]z=\frac{-0.04}{0.01}[/tex]
[tex]z=-4[/tex]
Now let us find z-score for raw score 0.69.
[tex]z=\frac{0.69-0.65}{0.01}[/tex]
[tex]z=\frac{0.04}{0.01}[/tex]
[tex]z=4[/tex]
Now we will use formula to find the probability between two z-score as:
[tex]P(a<z<b)=P(z<b)-P(z<a)[/tex]
Upon substituting our given values in above formula we will get,
[tex]P(-4<z<4)=P(z<4)-P(z<-4)[/tex]
Using normal distribution table we will get,
[tex]P(-4<z<4)=0.99997-0.00003[/tex]
[tex]P(-4<z<4)=0.99994[/tex]
Now let us convert our answer into percent by multiplying 0.99994 by 100.
[tex]0.99994\times 100=99.994\%[/tex]
Therefore, 99.994% of screws are between 0.61 and 0.69 inches and option D is the correct choice.
Sadie the dog is sitting on the roof of his doghouse, 4.5 ft off the ground. He is watching a cat that is 16 ft away from the base of the doghouse. What is the angle of depression from the roof of the doghouse to the cat? Round to the nearest hundredth. I watched the lesson but it all just went over my head, can someone simplify the explanation of how these problems work?
Which of the following could be equal to lxl ? Select all that apply.
5
0
-2
-5
what are the coordinates of the one point shared in common between the two linear functions give below?
HELP
The coordinates of point of intersection is (3,4).
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
y = 2x-2 -----(1)
3y+x = 15 -----(2)
Now, substitute equation (1) in equation (2), we get
3(2x-2)+x=15
6x-6+x=15
7x=21
x=3
and, y =2(3)-2
y= 4
Hence, the coordinates of point of intersection is (3,4).
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Corinne has a job selling magazines. She earns $7.50 per hour plus 20% of the total amount of her sales. She also gets an allowance of $40 per week for gas. She knows her weekly earnings can be shown using the following expression: 7.50h + 0.20s + 40 Part A: Identify a coefficient, a variable, and a constant in this expression. (3 points) Part B: If Corinne works for 25 hours and sells $300 in magazines, how much does she earn for the week? Show your work to receive full credit. (4 points) Part C: If Corinne gets a raise and begins earning $9 per hour, would the coefficient, variable, or constant in the equation change? Why? (3 points) (10 points)
Lisa and Kate are playing a card game, and a total of 900 points has been scored. Lisa scored 250 more points than Kate. If you let l=l=the number of points that Lisa scored, and k=k= the number of points that Kate scored, then the problem can be represented by the system:
l+k=900l+k=900 and l=k+250l=k+250
Graph the system. How many points did each of them score?
Select one:
a. Kate = 575 and Lisa = 325
b. Kate = 250 and Lisa = 650
c. Kate = 450 and Lisa = 450
d. Kate = 325 and Lisa = 575
Answer:
Lisa score 575 points and Kate scored 325 points.
Step-by-step explanation:
We are given the following information:
Total score for Lisa and Kate is 900 and Lisa scored 250 more points than Kate.
Scores for Lisa and Kate can be expressed with the help of two equations:
[tex]L + K = 900\\L = K + 250 \Rightarrow L-K = 250[/tex]
Solving these equations we have:
[tex]L + K + L - K = 900 + 250\\2L = 1150\\L = 575\\K = 575 - 250 = 325[/tex]
Hence, Lisa score 575 points and Kate scored 325 points.
The graph of the equations is attached.
Three children guessed the number of jelly beans in a jar.the guesses were 98,137 and 164.none of the guesses was correct.one guess was off by 12,another by 27 and the third by 39.how many jelly beans were in the jar.
If all three guesses for the number of jelly beans 98, 137, and 164 were off by 12, 27, and 39 the correct guess for the number of jelly beans is 125.
The number of jelly beans was 125.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Example:
2x + 3 is an expression
2x - 3 = 4 is an expression
We have,
Three guesses for the number of jelly beans:
98, 137, and 164.
These three guesses were all wrong.
The three guesses were off by:
12, 27, and 39.
The correct guess is 125 because,
98 + 27 = 125
137 - 12 = 125
164 - 39 = 125
Thus,
The number of jelly beans was 125.
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A company plans to sell a new type of vacuum cleaner for $280 each. The company’s financial planner estimates that the cost, y, of manufacturing the vacuum cleaners is a quadratic function with a y-intercept of 11,000 and a vertex of (500, 24,000). Which system of equations can be used to determine how many vacuums must be sold for the company to make a profit?
Answer:
A) on Edge
Step-by-step explanation:
Took the test
A person's part-time job pays $5.50 per hour. Write an expression to represent the amount he earns for working n hours.
The person earns $____ for working n hours.
What is the power of 10 when 0.000028 is written in scientific notation?
Answer:
The power of 10 would be -5
Step-by-step explanation:
In scientific notation we write a very small or very large number as the product of a number from 0 to 9 and the exponent of 10,
For getting a number between 0 to 9 if the decimal shifted right side then the exponent of 10 is negative power of total shifting while if the decimal shifted left side then the exponent of 10 is positive power of total shifting.
Here, the number is,
0.000028
By the above explanation, we need to shift the decimal five time to the right so the exponent of 10 would be 5.
[tex]\implies 0.000028=2.8\times 10^{-5}[/tex]
When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.02 cm divided by min0.02 cm/min. at what rate is the plate's area increasing when the radius is 4040 cm?
Since the plate is circular, therefore the area of the plate is jut equal to the area of a circle, so:
Area of plate = πr² = A
Taking the derivative:
dA / dr = 2πr --->
1
By
the idea of partial differentiation, the equation can also take in the form of:
dA/dt = dA/dr x dr/dt ---> 2
Where
we are given that:
change in radius over time = dr/dt = 0.02 cm/min
change in area with changing radius = dA/dr = 2πr ---> from equation 1
at r = 40
dA/dr = 2π(40) = 80π
Substituting
all the known values into equation 2:
dA/dt = (80π)(0.02)
dA/dt = 1.6π cm^2 /s = 5.03 cm^2/s
The legs of a right triangle measure 14 and 25 what is the measure of the angle opposite to the shortest side
The measure of the angle opposite to the shortest side is, 29.25°
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The legs of a right triangle measure 14 and 25.
Now, We know that;
⇒ tan θ = Perpendicular / Base
⇒ tan θ = 14 / 25
⇒ θ = tan ⁻¹ (14/25)
⇒ θ = 29.25°
Thus, The measure of the angle opposite to the shortest side is, 29.25°
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Jameel has a college degree, lives in a nice neighborhood, and earns more than $50,000 a year. this information defines his _____.
Answer:
This information defines his socioeconomic status.
Step-by-step explanation:
Jameel has a college degree, lives in a nice neighborhood, and earns more than $50,000 a year.
This information defines his socioeconomic status.
Socioeconomic status tells the social class of a person.It is measured in terms of education, income and occupation.
We can say that with high socioeconomic comes some privilege, power and control.
can someone explain the diffrence between first class, second class, and third class levers?
Final answer:
Levers are classified based on the positions of the fulcrum, input force, and output force. First-class levers have the fulcrum in the middle, second-class levers have the load in the middle, and third-class levers have the effort in the middle. The Mechanical Advantage of a lever indicates how much the lever amplifies the input force.
Explanation:
The three classes of levers are differentiated by the positions of the fulcrum, input force, and output force. A first-class lever has the fulcrum placed between the input force and the output force. Examples would include a seesaw and a crowbar. A second-class lever has the output force between the input force and the fulcrum, with examples being a wheelbarrow and a nutcracker. Lastly, a third-class lever has the input force between the output force and the fulcrum, as seen in a pair of tweezers or a human arm when lifting a weight.
The Mechanical Advantage (MA) is a calculation that shows how much a lever amplifies the input force. It is given by the ratio of the distance from the fulcrum to the input force (effort arm) and the distance from the fulcrum to the output force (resistance arm). Levers are simple machines that utilize torque and the physical distances from their pivot point to achieve an output force that is greater or faster or travels a further distance than the input force.