Answer:
Radical form of the expression [tex]4^{\frac{3}{2} }[/tex] is, 8
Step-by-step explanation:
Given the expression: [tex]4^{\frac{3}{2} }[/tex]
Since, [tex]\sqrt{4^3}[/tex] is same as [tex]4^{\frac{3}{2} }[/tex]
Now, to write an exponent in radical form,
then the denominator or the index goes in front of the radical and
the numerator goes inside of the radical.
we raise the base to the power of the numerator then:
[tex]4^{\frac{3}{2} }[/tex] = [tex]\sqrt{64}[/tex] = [tex]\sqrt{8 \times 8}[/tex] = [tex]\sqrt{8^2} = 8[/tex]
therefore, the radical form of the given expression is, 8
What are examples of self-reliant and how are you self-reliant?
I need to hear from other peers, thank you:)
Maya is camping at the top of mount Armstrong at an elevation of 7,832 meters. Juan is scuba diving 160 meters below sea level In Lake Junction, which is the base of mount Armstrong. The two decide to meet at the midpoint to have a picnic. At what elevation will maya and John meet
Answer:
Elevation = [tex]39996-160=3836[/tex] meters (taking base of Mt. Armstrong as sea level)
Step-by-step explanation:
The midpoint will be the half of their total distance.
If we take base of Mt. Armstrong to be 0, then Maya's distance is 7832 meters ABOVE and Juan's distance is 160 meters BELOW that.
The distance between them is thus [tex]7832+160=7992[/tex] meters.
We take half of this, to find midpoint. So:
[tex]\frac{7992}{2}=3996[/tex] meters
This is 3996 meters from Juan or from Maya. If the picnic is going to be at 3996 meters ABOVE Juan and since base of mountain is where we start measuring, we subtract 160 (Juan's distance from base) from 3996 to get the ELEVATION.
Elevation = [tex]39996-160=3836[/tex]
What is the approximate volume of the oblique cone?Use the pi equals 3.14 and round to the nearest tenth?
Answer:
You didn't give enough information for an actual answer, but here's the formula: (x-a)^2 + (y-b)^2 = ((z-c)R)^2 where (a,b,c) is the vertex. Good Luck. Hope this was helpful.
A carpenter needs to make 60 dowels.Each dowel must be 6 inches long.The wood from which the carpenter will cut the dowels comes in 4-foot lengths.What is the least number of 4-foot Lengths of wood the carpenter can buy and still make all 60 dowel
Answer: 8
Step-by-step explanation:
60 dowels - each 6 inches (1/2 foot) in length = 30 feet of wood
30 feet of wood ÷ 4 foot boards = 7.5 boards
Since he can't buy half of a board, you must round up to 8 boards.
The question involves a conversion of measurements. After converting 4 feet to 48 inches, it's calculated that one piece of wood can produce 8 dowels. To make 60 dowels, you would need 7.5 pieces of wood, but this rounds up to 8 pieces since half a piece cannot be bought.
Explanation:To answer this question, we first need to understand that all measurements need to be in the same units. Since our dowels are in inches (6 inches long) and our wood lengths are in feet (4 feet long), we need to convert one to the other. For simplicity's sake, let's convert the feet to inches as follows: 1 foot = 12 inches, therefore, 4 feet = 48 inches.
Then, we can find out how many dowels we can get from just one piece of wood: 48 inches / 6 inches per dowel = 8 dowels per one piece of 4-foot wood.
Lastly, to find out how many pieces of wood are needed to make 60 dowels, we divide the total number of dowels by the number of dowels per wood: 60 dowels / 8 dowels per wood = 7.5. Since we can't purchase half a piece of wood, we have to round up, so the carpenter needs to buy a minimum of 8 pieces of 4-foot wood to have enough to make 60 dowels.
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Someone please help.
ABC has vertices A(0,6) B(4,6) C(1,3). Sketch a graph of ABC and use it to find the orthocenter of ABC. Then list the steps you took to find the orthocenter including any necessary points or slopes you had to derive.
Answer:
Step-by-step explanation:
It's solved by grafic method
Is the triangle with side lengths of 18cm, 24cm and 30 cm a right triangle ?
If a, b and c are the lengths of a right triangle and c is the longest side, then:
[tex]a^2+b^2=c^2[/tex]
We have a = 18cm, b = 24cm and c = 30cm. Substitute and check:
[tex]L_s=18^2+24^2=324+576=900\\\\R_s=30^2=900\\\\L_s=R_s[/tex]
Answer: It's the right triangle.For every pound a company spends on advertising, it spends ?0.37 on its website. Express the amount spent on advertising to its website as a ratio in its simplest form.
Answer:
[tex]100:37[/tex]
Step-by-step explanation:
For every pound a company spends on advertising it spends £0.37 on its website.
Ratio of the the total amount spent on advertising to the amount spent on its website is,
[tex]=\dfrac{1}{0.37}[/tex]
[tex]=\dfrac{1\times 100}{0.37\times 100}[/tex]
[tex]=\dfrac{100}{37}[/tex]
[tex]=100:37[/tex]
Therefore, the ratio of the the total amount spent on advertising to the amount spent on its website is [tex]100:37[/tex]
I NEED HELP
You are given the system of equations to solve by the elimination method, which is an INCORRECT step that will NOT produce a system with the same solution?
5x + 3y = 5
8x + 2y = 6
A) subtract 3 times the second equation from 2 times the first equation
B) add 4 times the first equation and −6 times the second equation
C) multiply the first equation by
2
3
and subtract the second equation
D) multiply 3y by
2
3
in the first equation and subtract the second equation
solve the system by substitution and show all work:
2.5x-3y=-13
3.25x-y=-14
Answer:
(-4,1)
Step-by-step explanation:
A system of equations is 2 or more equations for which the same x,y solution exists. We can solve the system in three ways: elimination, substitution, or graphing. Substitution can be used by substituting the value of one variable into the equation.
Pair 2.5x-3y=-13 and 3.25x-y=-14
We can solve for y in 3.25x-y=-14. 3.25x+14=y.
Because y=3.25x+14, we can substitute 3.25x+14 into y in 2.5x-3y=-13.
2.5x-3y=-13
2.5x-3(3.25x+14)=-13
2.5x-9.75x-42=-13
-7.25x-42=-13
-7.25x=29
x= -4
We now substitute x=-4 into y=3.25x+14
y=3.25x+14
y=3.25(-4)+14
y=-13+14
y=1
To solve the system by substitution, solve one equation for one variable and then substitute that expression into the second equation. Solve the resulting equation and then substitute the solution back into one of the original equations to find the other variable.
Explanation:Given the equations:
2.5x - 3y = -143.25x - y = -14Let's find the value of 'x' from the second equation:
y = 3.25x + 14
This formula for 'x' can be substituted into the first equation, resulting in a new equation:
2.5(3.25x + 14) - 3y = -14,
This equation can be simplified and solved to find the variable 'y'. The value of 'y' can then be substituted back into the original equation to find the value of 'x'.
The solution to these two equations, (x, y), is the point of intersection which describes the system of the original equations.
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PLEASE NEED HELP!
:"3
Answer:
Option 2
Step-by-step explanation:
When completing a proof, the statements and reasons should be directly connected. Since the reason listed next to the missing statement is Def of Complimentary Angles, the statement must be about angles adding to 90 degrees. The definition of Complimentary Angles is that two angles add to 90. This means option 2 is the answer.
Lynne used 3 over 8 cup of flour and over 3 cup of sugar in a recipe.What number is a common denominator for 3 over 8 and 1 over 3
Answer: The common denominator for 3/8 and 1/3 is 24
Step-by-step explanation:
3/8 and 1/3 can be multiplied by each other in the numerator and denominator: 3/8(3/3) = 9/24 and 1/3(8/8) = 8/24
Please help! Urgent!
Tia is making strawberry lemonade for a baseball tournament. The recipe calls for 2/3
cup of strawberries for each gallon of lemonade. She has 6 cups of strawberries. How many gallons of lemonade can she make?
When you divide you number actually gets bigger.
You flip the last number in the question and then turn it in to a multiplication problem and then solve!!
Hope I could help!!!
Brainiest??
Answer:
She can make nine gallons. (9)
Step-by-step explanation:
Just took the assignment!
What binomial do you have to add to the polynomial x^2+y^2–2xy+1 to get a polynomial: not containing the variable x
PLS HELP ME!! SHOW WORK!
x^2+y^2-2xy+1+2xy-x^2=y^2+1
Find the measure of x and y in the isosceles triangle shown below:
x=22, y=136
x=22, y=48
x=44, y=65
x=20, y=65
Answer:
x=22, y=48
Step-by-step explanation:
If this is an isosceles triangle, then <G is equal to <J
<g = <j
x+44 = 3x
Subtract x from each side
x+44-x = 3x-x
44= 2x
Divide each side by 2
44/2 = 2x/2
22= x
The three angles of a triangle add to 180 degrees
<G + <J + <H = 180
x+44 + 3x + y = 180
22+44 +66 + y = 180
Combine like terms
132+ y =180
Subtract 132 from each side
132-132+y = 180-132
y = 48
A level 0.90 confidence interval is
A) any interval with margin of error ± 0.90.
B) an interval computed from sample data by a method that has probability 0.90 of
producing an interval containing the true value of the parameter of interest.
C) an interval with margin of error ± 0.90, which is also correct 90% of the time.
D) an interval computed from sample data by a method that guarantees that the probability
the interval computed contains the parameter of interest is 0.90.
Answer:
Option B is correct.
Step-by-step explanation:
Confidence interval is the range of the values that the particular probability whose value will lie in the interval.
So, if a level is 0.90 confidence interval it means the value of the probability will lie in the given level.
Therefore, Option B is correct that is an interval computed from sample data by a method that has probability 0.90 of producing an interval containing the true value of parameter of interest.
A 0.90 confidence interval is an interval computed from the sample data, with a probability of 0.90 that it contains the true value of the parameter of interest. The margin of error may vary and is not necessarily ±0.90. No method can absolutely guarantee a 0.90 probability.
Explanation:A 0.90 confidence interval, in statistical terms, is most accurately defined as an interval computed from sample data by a method that has a probability of 0.90 of producing an interval containing the true value of the parameter of interest. Therefore, the correct answer to this question is option B).
When we say that we're 90% confident, what we're implying is that if we were to repeat the same experiment 100 times, we'd expect the true parameter to lie within the confidence interval 90 times. The margin of error isn't necessarily ±0.90 as suggested by some of the other options (A and C) - it could be any value, depending on the data.
Option D suggests the method guarantees a 0.90 probability. It's crucial to understand that a confidence interval doesn't give such a guarantee; it provides an estimate and there’s always a certain amount of uncertainty.
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Shirley wants to buy a skateboard for $64. She has $98 in her account. She spent $10.85 to buy stationary. She also wants to buy some cookies for $1.65 each. What is the maximum number of cookies, n, that Shirley can buy so that she has enough money left to buy the skateboard? (1 point) n ? 16 n ? 14 n ? 14 n ? 16v
Use the factor Theorem to determine whether h(x)=x-1 is a factor of f(x)=14x^99-65x^56+51.
A. Yes
B. No
Factor theorem: if x-k is a factor of p(x), then p(k) = 0. The same can be said in reverse: if p(k) = 0, then x-k is a factor of p(x).
In this case, x-1 = x-k so k = 1. We'll plug this into f(x) below
f(x) = 14x^99 - 65x^56 + 51
f(1) = 14(1)^99 - 65(1)^56 + 51 ... replace every x with 1
f(1) = 14(1) - 65(1) + 51
f(1) = 14 - 65 + 51
f(1) = -51 + 51
f(1) = 0
The result is 0, so h(x) = (x-1) is a factor of f(x) = 14x^99-65x^56+51
-------------------
Answer: Choice A) yes
the trip to omaha to salt lake city interstate 80 is about 1516 kilometers. at 90 km perhour the trip would take about
A car dealer sells a car for RS 23500 and makes a profit of RS 10500. At what price did he sell the car?
Answer:
RS 34000
Step-by-step explanation:
Price of the car = RS 23500
Profit = RS 10500
Selling price of the car = Price of the car + Profit
= Rs 23500 + RS 10500
= RS 34000
Is b perpendicular to a? Justify your answer.
Set up the equation: 2x+37+3x+y=180 ⇒ 4x+y=143
2x+y+3y-21=180 ⇒2x+4y=201.
Solving for x and y, you get that y=37, thus making x=26.5
Now, for b to be perpendicular to a, 2x+37 must equal 90.
2*26.5+37=90, so b is perpendicular to a.
Whether 'b' is perpendicular to 'a' is determined by their dot product. If the dot product of 'b' and 'a' is zero, then 'b' is perpendicular to 'a'. However, without knowing the specific components of these vectors, a precise computation can't be made.
Explanation:In mathematics, particularly in vector algebra, vectors are said to be perpendicular or orthogonal if their dot product is zero. This is because the dot product of two vectors encapsulates the angle between them, defined as A·B = |A||B|cos(θ), where θ is the angle. If θ is 90 degrees (indicating the vectors are perpendicular), cos(θ) becomes 0, thus the dot product should be zero.
Therefore, to determine whether 'b' is perpendicular to 'a', we need to compute their dot product. If their dot product equals zero, then we can conclusively say that 'b' is perpendicular to 'a'. Beyond this, you'd need to provide the components of vectors 'a' and 'b' for a specific computation.
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A stack of three hundred cards is placed next to a ruler, and the height of stack is measured to be 5/8 of an inch. How thick is one card?
To calculate the thickness of one card from a stack of three hundred cards with a total height of 5/8 inch, you divide the total height by the number of cards, resulting in roughly 0.0020833 inches per card.
To compute the thickness of one card from a stack of three hundred cards, we must first determine the total height of the stack, which we already know is 5/8 of an inch. Then, we simply divide this height by the number of cards, which is 300, to find the thickness of a single card.
Here is the calculation:
Total height of the stack = 5/8 inch
Number of cards in the stack = 300
Thickness of one card = Total height of the stack
Number of cards
Thickness of one card = (5/8 inch)
300
Thickness of one card = 5/8
300
Thickness of one card = 0.0020833... inches (approx.)
Therefore, each card is approximately 0.0020833 inches thick.
If 2 triangles have 3 pairs of congruent angles, then the triangles are guaranteed to be congruent true or false
Answer:
False
Step-by-step explanation:
If the angles are congruent then they have the same shape but the sides could be of different length. The 2 triangles are SIMILAR but not necessarily congruent.
Justin is a software salesman. His base salary is 1900
, and he makes an additional 50
for every copy of English is Fun he sells.
Let P
represent his total pay (in dollars), and let N
represent the number of copies of English is Fun he sells. Write an equation relating P
to N
. Then use this equation to find his total pay if he sells 27
copies of English is Fun.
Answer:
3250 is your total; p = 50n + 1900 is your equation.
Step-by-step explanation:
"p" represents total pay; "n" represents the number of copies he sells.
Base salary is 1900, and each copy sold gives him an extra 50
p = 50n + 1900 is your equation.
If he sells 27 copies. Plug in 27 for n
p = 50n + 1900
p = 50(27) + 1900
Simplify. Remember to follow PEMDAS. First, multiply, then add.
p = 50(27) + 1900
p = 1350 + 1900
p = 3250
~
If Nelson invests $5,000 for 4 years and earns $600, what is the simple interest rate?
Simple interest rate = 3%.
Since the given invested amount = $5000, number of years of investment = 4 years, interest earned = $600. 600 = 5000 × R × 4, 600 = 20000R, Dividing both sides by 20000, we get 0.003 which is 3%.
Answer:
3
Step-by-step explanation:
Penelope is 4 times old as Jose. Jose is 3 years older than Eliot. If the sum of the ages of all three is 57, how old is Jose?
Answer:
10
Step-by-step explanation:
jose is x,so the penelope is 4x, eliot is x-3,
so :
x+4x+x-3=57,
then:
6x=60, x=10
Mr. Shaw sells used cars. He earned $250 for selling 5 cars. Mr. Shaw earned $400 for selling 11 cars. Which of the following equations represents this situation, where c represents the number of cars Mr. Shaw sold and e represents the amount he earned?
a: e = 50c + 125
b: e = 25c + 125
c: e = 50c
d: e = 25c
Answer:
b. [tex]e=25c+125[/tex]
Step-by-step explanation:
We are told that Mr. Shaw earned $250 for selling 5 cars. Mr. Shaw earned $400 for selling 11 cars.
We can see that earnings of Mr. Shaw depends on selling of car, so selling of cars will be independent (x) and total earnings will be dependent (y).
Let us find slope of our line with given points (5,250) and (11,400)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{400-250}{11-5}[/tex]
[tex]m=\frac{150}{6}=25[/tex]
This means that Mr. Shaw earns $25 for selling each car.
Now let us find equation of our line in slope intercept formula.
[tex]y=mx+b[/tex], where m= Slope and b= y- intercept.
Let us find b for our equation substituting coordinates of point (5,250) and m=25 in slope intercept form of equation.
[tex]250=25*5+b[/tex]
[tex]250=125+b[/tex]
[tex]250-125=b[/tex]
[tex]125=b[/tex]
[tex]y=25x+125[/tex]
Now let e represent the amount earned by Mr. Shaw and c represent the number of cars sold.
So our equation will be: [tex]e=25c+125[/tex] and option b is the correct choice.
The correct equation that represents Mr. Shaw's earnings from selling cars, where c is the number of cars sold and e is the earnings, is Option b: e = 25c + 125, because it correctly translates the given scenarios into mathematical terms.
The equation correctly represents the situation where c represents the number of cars Mr. Shaw sold and e represents the amount he earned from selling those cars.
To solve this, let's plug the values given into the options provided and see which one fits. For the first scenario, selling 5 cars earned him $250, and selling 11 cars earned him $400.
Option a: e = 50c + 125
For 5 cars: e = 50(5) + 125 = 250 + 125 = 375 (Incorrect)
For 11 cars: e = 50(11) + 125 = 550 + 125 = 675 (Incorrect)
Option b: e = 25c + 125
For 5 cars: e = 25(5) + 125 = 125 + 125 = 250 (Correct for 5 cars)
For 11 cars: e = 25(11) + 125 = 275 + 125 = 400 (Correct for 11 cars)
Option c: e = 50c
This option does not include the fixed amount, thus incorrect based on the provided values.
Option d: e = 25c
This option also does not consider a fixed starting amount, making it incorrect for our situation.
Hence, the correct equation is Option b: e = 25c + 125.
Can someone please help me on this asap
Answer: Third option
= (6w + 2)(6w - 2)
Step-by-step explanation:
36w^2 - 4
= (6w)^2 - 2^2
=(6w + 2)(6w - 2)
I'm not quite sure what an outlier is :/
Answer:
An outlier is the piece of data that isnt quite the same or near the others.
Step-by-step explanation:
so the outlier would be 28 due to the fact that it is not quite close to the other part of the data
Answer:
28
Step-by-step explanation:
An outlier is something that's way off compared to the rest of the group, basically. Like a person who stands out, but in this case it's a number.
The numbers listed here are all near 40 except 28. So 28 is the outlier, or the 'odd one out.'
How would i write the converse of the statement : if two angles are bothe obtuse, the two angles are equal
Final answer:
The converse of the statement is "If two angles are equal, then the two angles are both obtuse."
Explanation:
Converse of the Statement:
To write the converse of the statement 'if two angles are both obtuse, the two angles are equal,' we need to swap the hypothesis and the conclusion.
The converse statement would be: 'If two angles are equal, then the angles are both obtuse.'
Example:
Let's consider two angles, Angle A and Angle B. If Angle A and Angle B are both equal, then we can conclude that both angles are obtuse.
Find the fifth roots of 243(cos 260° + i sin 260°).
Answer:
z1=3 cos (52 + i sin 52)
z2 =3 cos (124 + i sin 124)
z3 = 3 cos (196 + i sin 196)
z4 =3 cos (268 + i sin 268)
z5= 3 cos (340 + i sin 340)
Step-by-step explanation:
To find the fifth roots of 243 (cos 260° + i sin 260°).
z ^ 1/5 = r^1/5 ( cis ( theta + 360 *k)/5) where k=0,1,2,3,4
So the first root of 243 (cos 260° + i sin 260°)
is z1 = 243^1/5 ( cis ( 260 + 360 *0)/5)
3 cis ( 260/5)
= 3 cis (52)
= 3 cos (52 + i sin 52)
The second root of 243 (cos 260° + i sin 260°)
is z2 = 243^1/5 ( cis ( 260 + 360 *1)/5)
3 cis ( 620/5)
= 3 cis (124)
= 3 cos (124 + i sin 124)
The third root of 243 (cos 260° + i sin 260°)
is z3 = 243^1/5 ( cis ( 260 + 360 *2)/5)
3 cis ( 980/5)
= 3 cis (196)
= 3 cos (196 + i sin 196)
The fourth root of 243 (cos 260° + i sin 260°)
is z4 = 243^1/5 ( cis ( 260 + 360 *3)/5)
3 cis ( 1340/5)
= 3 cis (268)
= 3 cos (268 + i sin 268)
The fifth root of 243 (cos 260° + i sin 260°)
is z5 = 243^1/5 ( cis ( 260 + 360 *4)/5)
3 cis ( 1700/5)
= 3 cis (340)
= 3 cos (340 + i sin 340)