Answer:
[tex]\frac{1}{6^{2} }[/tex]
Step-by-step explanation:
Using the rule of exponents
[tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]
Given a = 6, then
[tex]6^{-2}[/tex] = [tex]\frac{1}{6^{2} }[/tex]
The 3rd option is correct i.e. if a = 6, then by the property of exponentiation, we can conclude that a⁻² = 1/6².
What is exponentiation?Exponentiation is a mathematical operation that involves two numbers, the base b, and the exponent or power n, and is pronounced as "b raised to the power of n." It is written as bⁿ and is pronounced as "b raised to the power of n."
When n is a positive integer, bⁿ = b × b × b ×...× b (n times)
and b⁻ⁿ = 1/bⁿ ...(1)
When n = 0, bⁿ = 1
How to solve this problem?Given that a = 6 and n = 2.
Using (1), we get
a⁻² = 6⁻² = 1/6²
Therefore, the 3rd option is correct i.e. if a = 6, then by the property of exponentiation, we can conclude that a⁻² = 1/6².
Know more about exponentiation here -
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Write the event as set of outcomes. We flip three coins and obtain more tails than heads.
A. {ttt}
B. {ttt, tth, tht, htt}
C. {ttt, tth}
D. {tth, tht, htt}
Answer:
B.
Step-by-step explanation:
All the possible outcomes are listed on choice B.
The event is a set of outcomes. if we flip three coins and obtain more tails than heads is E = {ttt, tth, tht, htt} option (B) is correct.
What is set?A set is a collection of clearly - defined unique items. The term "well-defined" applies to a property that makes it simple to establish whether an entity actually belongs to a set. The term 'unique' denotes that all the objects in a set must be different.
We have three coins.
As we know, in a coin there are two sides head and a tail.
If we flip three coins then the set of all the possible outcomes:
O = {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}
The set of outcomes has more tails than heads.
E = {ttt, tth, tht, htt}
We can find the probability, the probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Probability = 4/8 = 1/2
Thus, the event is a set of outcomes. if we flip three coins and obtain more tails than heads is E = {ttt, tth, tht, htt} option (B) is correct.
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PLEASE HELP Polynomial Graph Studies Polynomials are great functions to use for modeling real-world scenarios where different intervals of increase and decrease happen. But polynomial equations and graphs can be trickier to work with than other function types. In mathematical modeling, we often create an equation to summarize data and make predictions for information not shown on the original display. In this activity, you’ll create an equation to fit this graph of a polynomial function. Part A Describe the type of function shown in the graph. Part B What are the standard form and the factored form of the function? Part C What are the zeros of the function? Part D Use the zeros to find all of the linear factors of the polynomial function. Part E Write the equation of the graphed function f(x), where a is the leading coefficient. Use the factors found in part D. Express the function as the product of its leading coefficient and the expanded form of the equation in standard form. Part F Use the y-intercept of the graph and your equation from part E to calculate the value of a. Part G Given what you found in all of the previous parts, write the equation for the function shown in the graph.
Answer:
Here's what I get
Step-by-step explanation:
Part A
The graph shows a polynomial of odd degree. It is probably a third-degree polynomial — a cubic equation.
Part B
The standard form of a cubic equation is
y = ax³ + bx² + cx + d
The factored form of a cubic equation is
y = a(x - b₁)(x² + b₂x + b₃)
If you can factor the quadratic, the factored form becomes
y = a(x - c₁)(x - c₂)(x - c₃)
Part C
The zeros of the function are at x = -25, x = - 15, and x = 15.
Part D
The linear factors of the function are x + 25, x + 15, and x - 15.
Part E
y = a(x + 25)(x + 15)(x - 15) = a(x + 25)(x² - 225)
y = a(x³ + 25x² - 225x - 5625)
Part F
When x = 0, y = 1.
1 = a[0³ +25(0)² - 225(0) - 5625] = a(0 + 0 - 0 -5625) = -5625a
a = -1/5625
Part G
[tex]y = -\dfrac{1}{5625}( x^{3} + 25x^{2} - 225x - 5625)\\\\y = \mathbf{ -\dfrac{1}{5625} x^{3} - \dfrac{1}{225}x^{2} + \dfrac{1}{25} x + 1}[/tex]
Answer
Actually, the answer should be -0.0007(x+20)(x+5)(x-15)
Step-by-step explanation:
This is continuing off of the previous answer
PART C
The zeros should be (15,0), (-5,0), and (-20,0)
PART D
x - 15, x + 5, and x + 20
PART E
a(x - 15)(x + 5)(x + 20)
Standard: [tex]a(x^{3} + 10x^{2} -275x-1500)[/tex]
PART F
The y-intercept is at (0,1), so we replace the x's with 0:
1 =[tex][(0)x^{3} +10(0)x^{2} -275(0)-1500][/tex] and this gives us (0+0-0-1500) which also equals -1500
Then we do [tex]\frac{1}{-1500}[/tex] which gives us -0.0006 repeating which rounds to -0.0007
a= -0.0007
PART G
Just place the numbers where they should go and your answer is
y =-0.0007(x + 20)(x + 5)(x - 15)
the placement for (x + 20) (x + 5) and (x - 15) doesn't matter as long as they are behind -0.0007
In a survey of 119 students, it was found that 16 drink neither coke nor Pepsi 69 drinks coke and39 drink pepsi
How many students drink Coke only?
How many students drink Pepsi only?
Show the above information in a Venn diagram.
Answer:
64 students drink coke only
34 students drink pepsi only
Step-by-step explanation:
Here, we want to know the number of students that drink coke only and number of students that drink pepsi only.
Let the number of students that drink both be x
Mathematically,
n(μ) = 119 where μ represents the universal set
n(P) = 39
n(C) = 69
n(C n P) = x
n(C n P)’ = 16
n(P) only = 39 - x
n( C) only = 69 - x
Mathematically;
119 = (69-x) + (39-x) + x + 16
119 = 69 + 39 + 16 -2x + x
119 = 124 - x
x = 124 - 119
x = 5
So the number of students drinking pepsi only = 39 -5 = 34
The number of students drinking coke only = 69-5 = 64
The following are scores obtained by some students in a test.
8 18 10 14 18 11 13 14 13 17 15 8 16 13. Find the mode of the distribution
Answer:
[tex] \boxed{13}[/tex]
Step-by-step explanation:
Arranging the data in ascending order:
8 , 8 , 10 , 11 , 13 , 13 ,13 , 14 , 14 , 15 , 16 , 17 , 18 , 18 ,
In the case of discrete data, mode can be found just by inspection, i.e just by taking an item with highest frequency.
Here, 13 has the highest frequency
So, Mode = 13
Extra information
Mode
The mode of a set of data is the value with the highest frequency. A distribution that has two modes is called bimodal. The mode of a set of data is denoted by Mo.
Hope I helped!
Best regards!
Please help me with this question asap!!!
Answer:
Choice A
Step-by-step explanation:
A traveler explores the regions of Mexico. She travels from Sonora to Colima, and
Colima to Tamaulipas. Write two inequalities that represent the two possible distances
from Tamaulipas back to Sonora.
Answer:
809mi
Step-by-step explanation:
There are two ways to travel form Tamaulipas to Sorona. The first if the direct route from Sorona to Tamaulipas which is 809mi. The another route is to travel to Colima from Sorona and then travel to Tamaulipas from Colima. This is the long distance routes in which there are two destination points. The direct route is shorter in length therefore preferable.
The 100-meter dash times in the girls track meet were normally distributed with a mean of 13 seconds and a standard deviation of 0.3 seconds. What is the probability that a runner finished between 12.4 and 14 seconds?
Answer:
The probability is 0.97682
Step-by-step explanation:
We start by finding the z-values of the runner times given.
Mathematically;
z-score = (x-mean)/SD
From the question, mean = 13 seconds and SD = 0.3 seconds
So for 12.4 seconds, we have;
z = (12.4-13)/0.3 = -0.6/0.3 = -2
For 14 seconds, we have;
z = (14-13)/0.3= 1/0.3 = 3.33
So the probability we want to calculate is;
P(-2<z<3.33)
We can find this using the standard normal distribution table
Mathematically;
P(-2<z<3.33) = P(z<3.33) - P(z < -2)
Using the standard normal distribution table, the value of this is;
P(-2<z<3.33) = 0.97682
Tori and Gavin were trying to solve the equation: (x+1)^2-3=13(x+1) 2 −3=13left parenthesis, x, plus, 1, right parenthesis, squared, minus, 3, equals, 13 Tori said, "I'll add 333 to both sides of the equation and solve using square roots." Gavin said, "I'll multiply (x+1)^2(x+1) 2 left parenthesis, x, plus, 1, right parenthesis, squared and rewrite the equation as x^2+2x+1-3=13x 2 +2x+1−3=13x, squared, plus, 2, x, plus, 1, minus, 3, equals, 13. Then I'll subtract 131313 from both sides, combine like terms, and solve using the quadratic formula with a=1a=1a, equals, 1, b=2b=2b, equals, 2, and c=-15c=−15c, equals, minus, 15."
The other answer is correct, its both !<3
Answer:
Both
Step-by-step explanation:
Both Tori and Gavin are correct, the two methods work. Completed this in Khan Academy, it's correct.
Carter draws one side of equilateral △PQR on the coordinate plane at points P(-3,2) and Q(5,2). Which ordered pair is a possible coordinate of vertex R?
A. (-3, -6)
B. (0, 8)
C. (1, 8.9)
D. (1, -8.9)
Step-by-step explanation:
Hey, there!!!
Let me simply explain you about it.
We generally use the distance formula to get the points.
let the point R be (x,y)
As it an equilateral triangle it must have equal distance.
now,
let's find the distance of PQ,
we have, distance formulae is;
[tex]pq = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} } [/tex]
[tex]or \: \sqrt{( {5 + 3)}^{2} + ( {2 - 2)}^{2} } [/tex]
By simplifying it we get,
[tex] 8[/tex]
Now,
again finding the distance between PR,
[tex] pr = \sqrt{( {x2 - x1}^{2} + ( {y2 - y1)}^{2} } [/tex]
or,
[tex] \sqrt{( {x + 3)}^{2} + ( {y - 2)}^{2} } [/tex]
By simplifying it we get,
[tex] = \sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13 } [/tex]
now, finding the distance of QR,
[tex]qr = \sqrt{( {x - 5)}^{2} + ( {y - 2)}^{2} } [/tex]
or, by simplification we get,
[tex] \sqrt{ {x}^{2} + {y}^{2} - 10x - 4y + 29 } [/tex]
now, equating PR and QR,
[tex] \sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13} = \sqrt{ {x}^{2} + {y}^{2} - 10x - 4y + 29 } [/tex]
we cancelled the root ,
[tex] {x}^{2} + {y}^{2} + 6x - 4y + 13 = {x}^{2} + {y}^{2} -10x - 4y + 29[/tex]
or, cancelling all like terms, we get,
6x+13= -10x+29
16x=16
x=16/16
Therefore, x= 1.
now,
equating, PR and PQ,
[tex] \sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13 } = 8} [/tex]
cancel the roots,
[tex] {x}^{2} + {y}^{2} + 6x - 4y + 13 = 8[/tex]
now,
(1)^2+ y^2+6×1-4y+13=8
or, 1+y^2+6-4y+13=8
y^2-4y+13+6+1=8
or, y(y-4)+20=8
or, y(y-4)= -12
either, or,
y= -12 y=8
Therefore, y= (8,-12)
by rounding off both values, we get,
x= 1
y=(8,-12)
So, i think it's (1,8) is your answer..
Hope it helps...
Answer:
1,8.9
Step-by-step explanation:
Sandy’s older sister was given $2,400 and was told to keep the balance of the money after sharing with her siblings. Give Sandy exactly $350. Write Sandy’s portion
Sandy got 350 out of 2400.
Her portion is 350/2400 which can be reduced to:
35/240 = 7/48
The portion is 7/48
can someone help on this question
Answer:
a) 3 x 20 = 60
b) -2x20 = -40
question c and d are unclear as we do not know how many questions were wrong and how many were not answered.
Sorry but I hope that helped
Answer:
a) 60 points
b) 0 point
c) 22 points
d) -11 points
Step-by-step explanation:
a) 20 * 3 = 60 points (all answered correct)
b) 0 point (Minimum score if you don't answer any of the questions)
c) 10 * 3 = 30 points
(14 - 10) * -2 = -8 points
right minus wrong = 30 - 8 = 22 points
d) 5 * 3 = 15 points
(18 - 5) * -2 = -26 points
right minus wrong = 15 - 26 = -11 points
PLEASE HELP ME!!! I will mark brainliest!!!
The image above shows two dilated figures with lines IJ and JK drawn. If the smaller figure was dilated by a scale factor of 2, what relationship do lines IJ and KL have?
Answer:
parallel lines
Step-by-step explanation:
Lines IJ and KL are parallel. Since in a dilation there is no rotation, a line becomes either the same line or a parallel line.
Evaluate 0.6721 x 0.0261 and express your answer in standard form
Answer:
Step-by-step explanation:
0.6821 multiplied by 0.0261 is .01754181
putting that into standard from would be 1.754181 x 10^-2
write each number in scientific notation.
1,050,200
The number between 1 and 10:
The power of 10:
The number in scientific notation:
34,600
The number between 1 and 10:
The power of 10:
The number in scientific notation:
write 39/5 as a mixed numer
Answer:
6 9/5Step-by-step explanation:
39/5 as a mixed number;
39/5 as a mixed number;39 ÷ 5 = 6 remaining 9
Therefore:
6 9/5
Helen has an old laser printer that can print 900 pages in 1.5 hours. If the speed of printing remains constant, how
long will it take her to print a book of 600 pages? Express your answer in hours.
Answer:
1 hour
Step-by-step explanation:
No. of pages print in 1.5 hours = 900
dividing LHS and RHS by 1.5 so that we get 1 hour in LHS
no. of page print in 1.5/1.5 (1) hours = 900/1.5 = 600.
Thus, it takes 1 hour to print 600 pages.
Given that we have to find how
long will it take her to print a book of 600 pages.
Answer is 1 hour.
if a right triangle has one side measuring 4 and another side measuring 6, what is the length of the hypotenuse
Answer:
[tex]\sqrt{52}[/tex]
Step-by-step explanation:
[tex]a^{2} + b^{2} =c^{2}[/tex]
Here, a = 4, and b = 6. So if you square a, you get 16. If you square b, you get 36.
16+36 = 52 = [tex]c^{2}[/tex]
Take the square root of 52 and [tex]c^{2}[/tex] and you get that c = [tex]\sqrt{52}[/tex]
This can be simplified further. c = [tex]\sqrt{52} = \sqrt{13*4} = 2\sqrt{13}[/tex]
James conducted an experiment with 4 possible outcomes. He determined that the experimental probability of event A happening is 10 out of 50. The theoretical probability of event A happening is 1 out of 4. Which action is most likely to cause the experimental probability and theoretical probabilities for each event in the experiment to become closer? removing the last 10 trials from the experimental data completing the experiment many more times and combining the results to the trials already done including a fifth possible outcome performing the experiment again, stopping immediately after each event occurs once
Answer:
Completing the experiment a few more times and combining the results to the trails already done.
Answer:
Completing the experiment a few more times and combining the results to the trails already done.
Step-by-step explanation:
How many solutions does the following equation have? 4(y-30)=4y+124(y−30)=4y+12
Answer:
A. No solution
Step-by-step explanation:
Choose 1 answer:
A. No solutions
B. Exactly one solution
C. Infinitely many solutions
Solution
Given:
4(y-30)=4y+12
Open parenthesis
4y-120=4y+12
Collect like terms
4y-4y=12+120
0=142
There is no solution to the equation, therefore, the answer is A
Find the measure of each angle indicated. Round to the nearest tenth.
A) 49°
C) 38.1°
B) 44.90
D) 42.89
Can you please help explain how to find the answer
Answer:
D
Step-by-step explanation:
So we want to find θ. We are already given the hypotenuse and the side length opposite to θ. Therefore, we can use the trig function sine to find θ.
Recall that:
[tex]\sin(\theta)=opp/hyp[/tex]
Plug in 10.2 for the opposite side and 15 for the hypotenuse:
[tex]\sin(\theta)=10.2/15[/tex]
Solve for θ. Use a calculator:
[tex]\theta=\sin^{-1}(10.2/15)\\\theta\approx42.8436\textdegree[/tex]
The answer is D.
What the correct answer
Answer:
653.12 ft²
Step-by-step explanation:
2πrh + 2πr²
2(3.14)(8)(5) + 2(3.14)(8)²
251.2 + ²401.92 = 653.12
Step-by-step explanation:
Here,
radius of a cylinder (r)= 8 ft.
height (h)= 5 ft.
now,
area of a cylinder (a)= 2.pi.r(r+h)
now, putting the values we get,
a = 2×3.14×8(8+5)
after simplification we get,
Area of cylinder is 653.12 sq.ft.
Hope it helps....
Solve 3x square - 2 x + 7 x - 5
Answer:
The correct ans is...
3 x square + 5 x - 5
Step-by-step explanation:
U can only subtract or add if u hv the same variable..
here -2x and 7x have the same variable...
so -2x + 7x = 5x
Therefore the ans is....
3 x square + 5 x - 5
Hope this helps....
Have a GOOD DAY !!!!
Pls mark my ans as brainliest
If u mark my ans as brainliest u will get 3 extra points
Sry to say....
U really need to read ur Math TBK
Answer:
3x²+5x-5
Step-by-step explanation:
collect like terms.
3x²+(-2x+7x)-5
3x²+ 5x-5
what is 1.54324 rounded to the nearest tenths equal
Answer:
1.5
Step-by-step explanation:
1.54324
The 5 is in the tenths place
We look at the next digit to determine if we need to round up or we leave it alone
The next digit is a 4. It is under 5 so we leave the 5 alone
1.5
The tenths place is one place to the right of the decimal point.
This means the digit in the rounding place is 5
Since the digit to the right of the rounding
place, 4, is less than 5, round down.
This means that the digit in the rounding place, 5, stays the same and
we change all digits to the right of the rounding place to 0.
So our answer is 1.50000 or 1.5.
Avani is building a rectangular play area. The length of the play area is 7.5 meters. The width of the play area is 5.3 meters. If she wants to cover the area in foam, how much foam does she need to buy? Due to the accuracy of the tape measure Avani used, the amount of foam needed to cover the play area is A.39 B.39.75 C.39.8 D.40
Answer:
Step-by-step explanation:
Area of the rectangle length x width
7.5x5.3 =39.75 sq.m
so, B is the correct answer.
What the relation of 1/c=1/c1+1/c2 hence find c
[tex]\frac 1c=\frac1{c_1}+\frac1{c_2} [/tex]
$\frac1c=\frac{c_1+c_2}{c_1c_2}$
$\implies c=\frac{c_1c_2}{c_1+c_2}$
PLEASE ANSWER QUICKLY ASAP
READ QUESTIONS CAREFULLY
Answer:
see details below
Step-by-step explanation:
a) week 1 : #10" / (#10"+#12") = 509 / 736 = 69% (to nearest percent)
b) week 2 : #10" / (#10"+#12") = 766 / 1076 = 383/538 = 71% (to nearest percent)
A).69% for week 1
B)71% for week 2
To solve -8p = 48, which of the following could you do to both sides of the equation? add -8 subtract -8 multiply by -8 divide by -8
Answer:
Divide by -8.
Step-by-step explanation:
48 is a multiple of 8, an we are trying to isolate p, so you should divide both sides by +/- 8.
Answer:
Step-by-step explanation:
You would do 48 divided by -8, and your answer would be -6
And just to clarify, -8 times -6 = 48. (You can use a calculator if still unsure)
Given that A is directly proportional to B and that A = 5/3 when B = 5/6, find A when B=1/3 and B when A =15/2.
Step-by-step explanation:
A is directly proportional to B is written as
A = kBwhere k is the constant of proportionality
First we must find the relationship between the two variables
when
A = 5/3
B = 5/6
Substitute the values into the formula to find k
[tex] \frac{5}{3} = k \frac{5}{6} [/tex]
Multiply through by the LCM which is 6
That's
[tex]5 \times 2 = 5k[/tex]
5k = 10
Divide both sides by 5
k = 2
So the formula for the variation is
A = 2Bwhen B = 1/3
[tex]A = 2 \times \frac{1}{3} [/tex]
[tex]A = \frac{2}{3} [/tex]When A = 15/2
[tex] \frac{15}{2} = 2B[/tex]
Multiply through by 2
[tex]4B = 15[/tex]
Divide both sides by 4
[tex]B = \frac{15}{4} [/tex]Hope this helps you
In the figure above, O is a circle. What is the
measure of obtuse angle AOB, in degrees?
Answer:
An obtuse angle is an angle that is bigger than 90° degrees, but doesn’t reach a straight line at 180°.
Step-by-step explanation:
i didnt see a figure above but this is the answer to "what is the measure if obtuse angle in degrees?"
Find y.
A. √2/2
B. 4
C. √6/2
D. √2
Answer:
Step-by-step explanation:
the answer is option D
WHEN YOU SUBSTITUTE THE VALUES YOU WILL GET IT............
