Answer:
This is true
Step-by-step explanation:
Yes when you make a radical into a power you can simplify the power, like you are saying.
Peter has one of each of the following coins in his pocket: a penny, a nickel, a dime, a quarter, and a half-dollar. Four of these coins are taken out of the pocket and the sum of their values is calculated. How many different sums are possible?
Answer:
10
Step-by-step explanation:
This is a combinations problem, involving factorials.
5!/3!*2!=5*4/2=20/2=10
The different sum of the 4 coins from the list of 5 coins is an illustration of combination or selection. There are 5 different possible sums.
Given
[tex]n = 5[/tex] --- number of coins
[tex]r = 4[/tex] --- coins to be selected to calculate sum
For the sum of the coin value to be calculated, the 4 coins must be selected. This means combination.
So, we make use of:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
This gives
[tex]^5C_4 = \frac{5!}{(5 - 4)!4!}[/tex]
[tex]^5C_4 = \frac{5!}{1!4!}[/tex]
Expand
[tex]^5C_4 = \frac{5*4!}{1*4!}[/tex]
[tex]^5C_4 = \frac{5}{1}[/tex]
[tex]^5C_4 = 5[/tex]
Hence, there are 5 different possible sums.
Read more about combinations at:
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Envision a base-5 numbering system. Write the rules for the system, and give six 3-digit examples in base-5 with their equivalent decimal and binary values.
Answer:
See Explanation Section
Step-by-step explanation:
Given
A base 5 numbering system: Envision
Some of the rules are as follows:
For a base 5 system, the highest individual digit is 4: Meaning that the 1234, 343, 110 are valid digits while 1235, 78, 55 are invalid digitsThe place values of this system are in place of 5s: i.e. ......5°, 5¹, 5², 5³, 5⁴......3 digit examples
1
Base 5: 100
Base 10: 25 (See calculation below)
[tex]1 * 5^2 + 0 * 5^1 + 0 * 5^0 = 1 * 25 + 0 + 0 = 25[/tex]
Base 2: 11001 (See calculation below)
[tex]25 / 2 = 12\ R\ 1[/tex]
[tex]12 / 2 = 6\ R\ 0[/tex]
[tex]6 / 2 = 3\ R\ 0[/tex]
[tex]3 / 2 = 1\ R\ 1[/tex]
[tex]1 / 2 = 0\ R\ 1[/tex]
Writing the remainder from bottom: 11001
Using the same steps as used in (1) above
2.
Base 5: 211
Base 10: 56
Base 2: 111000
3.
Base 5: 441
Base 10: 121
Base 2: 1111001
4.
Base 5: 230
Base 10: 65
Base 2: 1000001
5.
Base 5: 342
Base 10: 97
Base 2: 1100001
6.
Base 5: 141
Base 10: 46
Base 2: 101110
a rectangular garden is fenced on all sides with 128 feet of fencing. The garden is 4 feet longer than it is wide. Find the length and width of the garden
Answer:
Length = 34 feet
Breadth = 30 feet
Step-by-step explanation:
Perimeter= 128 ft
Let the breadth be = [tex]x[/tex]
Let the length be = [tex]x+4[/tex]
∴by the problem ,
2(length+breadth)= perimeter
[tex]2(x+4+x)=128\\2(2x+4)=128\\4x+8=128\\4x=128-8\\4x=120\\x=120/4\\x=30[/tex]
Therefore, length of the garden = 30+4= 34 feet
breadth of the garden = 30 feet
please help i beg plsssssssssz
Answer:
5/2=20/8=35/14=125/50
Answer:
8, 14, 50
Step-by-step explanation:
5 x 4 = 20
2 x 4 = 8
5 x 7 = 35
2 x 7 = 14
5 x 25 = 125
2 x 25 = 50
17. Thirteen percent of a 12,000 acre forest is being logged. How many acres will be logged?
Answer:
1560 acres
Step-by-step explanation:
What we need to do is find 13% of 12000.
We can start by converting 13% to a fraction.
13%=13/100
Multiply.
13/100*12000
(13*12000)/100
156000/100
Divide.
1560
1560 acres are being logged.
The number of acres that will be logged is 1560 acres.
Since thirteen percent of a 12,000 acre forest is being logged, to calculate the number of acres that will be logged, we'll have to multiply 13% by 12000. This will be:
= 13% × 12000
= 0.13 × 12000
= 1560
Therefore, 1560 acres will be logged.
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A cylindrical tank whose diameter is 1.4 metres and height 80 cm is initially empty. Water whose volume is 492.8 litres is poured into the tank. Determine the fraction of the tank filled with water. (4 mark
Answer:
The fraction filled with water is 7/40
Step-by-step explanation:
Okay.
Here we start by calculating the volume of the cylindrical tank.
Mathematically, that would be;
V = π * r^2 * h
From the question
r = 80 cm = 80/100 = 0.8 meters
h = 1.4 meters
π = 22/7
Plugging these values into the volume equation, we have;
V = 22/7 * 0.8 * 0.8 * 1.4 = 2.816 m^3
But mathematically;
1 m^3 = 1000 liters
So 2.816 m^3 = 2.816 * 1000 = 2816 liters
So the fraction filled with water will be;
492.8/2816 = 0.175 = 175/1000 = 7/40
A sample proportion of 0.44 is found. To determine the margin of error for this statistic, a simulation of 100 trials is run, each with a sample size of 100 and a point estimate of 0.44. The minimum sample proportion from the simulation is 0.32, and the maximum sample proportion from the simulation is 0.50. What is the margin of error of the population proportion using an estimate of the standard deviation?
Answer:
±0.06
Step-by-step explanation:
To find the margin of error using the standard deviation method, use the equation [tex]2(\frac{maximum-minimum}{6})[/tex].
In this situation, it would look like this: [tex]2(\frac{0.50-0.32}{6})[/tex]. Using this equation, you can find the margin of error by using the standard deviation method.
[tex]2(\frac{0.50-0.32}{6})[/tex]
[tex]2(\frac{0.18}{6})[/tex]
[tex]2(0.03)[/tex]
[tex]0.06[/tex]
Hope this helps!
(I know this is right because its what I answered on the test, and got 100%)
The margin of error of the population proportion using an estimate of the standard deviation is 0.06
we have given that,
A sample proportion of 0.44 is found.
The minimum sample proportion from the simulation is 0.32
The maximum sample proportion from the simulation is 0.50
What is the formula for the margin of error using the standard deviation method?The formula for the margin of error using standard deviation is,
[tex]2(\frac{max-min}{6} )[/tex]
Use the given value in the formula we get,
[tex]2(\frac{0.50-0.32}{6} )[/tex]
Using this equation, you can find the margin of error by using the standard deviation method.
[tex]2(\frac{0.50-0.32}{6} )\\\\=2(\frac{0.18}{6})\\\\ =2(0.03)\\\\=0.06[/tex]
Therefore we get,
The margin of error of the population proportion using an estimate of the standard deviation is 0.06
To learn more about the population proportion using an estimate of the standard deviation visit:
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if the probability of david passing his exam is 1/4 what is the probabilty of him failing
Answer:
3/4
Step-by-step explanation:
4/4-1/4=3/4
i hoped this helped :)
Answer:
3/4
Step-by-step explanation:
Simplify (-8)2. please help
Answer:
-16
Step-by-step explanation:
This equation is showing -8 multiplied by 2, and when they are multiplied, the sum of those two numbers is -16.
Answer:
=-16
Step-by-step explanation:
(-8)2
= 2×-8
= -16
Select the correct answer. This set of ordered pairs defines a function. {(-49,7), (-56,8), (-63,9), (-70,10)} Which table represents the inverse of the function defined by the ordered pairs? A.
In the future, you should post all possible answer choices to have a complete post. However, there's enough information to get the answer.
The original set has points in the form (x,y)
The first point is (x,y) = (-49,7) making x = -49 and y = 7. When we find the inverse, we simply swap the x and y values. The inverse undoes the original function and vice versa. So if (-49, 7) is in the original function, then (7, -49) is in the inverse. The rest of the points follow the same pattern.
We end up with this answer
{ (7, -49), (8, -56), (9, -63), (10, -70) }
Jorge’s monthly bill from his Internet service provider was $25. The service provider charges a base rate of $15 per month plus $1 for each hour that the service is used. Find the number of hours that Jorge was charged for that month.
Answer:
10 hours for the month
Step-by-step explanation:
What you know: The total amount Jorge was charged for the month was $25
The base rate is $15
He gets charged $1 per each hour
Setting it up:
15+1h=25
(the 15 is the base rate, plus the 1 dollar per hour (h) which both add to the total of 25 dollars for the month)
Subtract 15 from both sides of the equation to get your variable by itself
1h=10
then divide the 1 on both sides to get h (hours) by itself
h=10
And there's your answer, 10 is the number of hours that Jorge was charged for the month
Hopefully this helped :))
Answer:
10
Step-by-step explanation:
$25 - $15 = $10
and its $1 per hour so the answer is 10hrs
Rational exponents
I need help ASAP!! Can someone solve and explain step by step how to do it???
Answer:
a . x = 512
b. x^1/2•y•z^5/4
Step-by-step explanation:
a. Here in this question, we want to find the value of x, given the equation.
x^2/3 = 64
Now, to find the value of x, we shall raising both powers to the reciprocal of 2/3
When we talk of reciprocal, we mean a number such that when we multiply this number by that particular number, our result is 1.
So for 2/3, the reciprocal is 3/2
So let’s raise the power of both sides to 3/2
Thus;
x^2/3(3/2) = 64^3/2
Kindly recall that 2/3(3/2) = 2/3 * 3/2 = 1
Thus ;
x = 64^3/2
So what this mean is that we will find the square root of 64 and cube our answer.
Thus;
x = {√(64)}^3
x = 8^3
x = 512
b. According to laws of indices, kindly note that
b√(a) = a^1/b
Thus;
4 √(x^2•y^4•z^5) = (x^2•y^4•z^5)^1/4
So what we do is to multiply each of the powers in the bracket by 1/4
Thus, we have the following;
x^2(1/4) • y^4(1/4) • z^5(1/4)
= x^1/2•y•z^5/4
where • simply refers to multiplication between the terms
A golf analyst claims that the standard deviation of the 18-hole scores for a golfer is at most 3.5 strokes. State H_0 and H_a in words and in symbols. Then determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed. Explain your reasoning. State the null hypothesis in words and in symbols.Choose the correct answer below.A. The null hypothesis expressed in words is. "the standard deviation of the 18-hole scores for a golfer is at least 3.5 strokes." The null hypothesis is expressed symbolically as. "H0:σ≥3.5."B. The null hypothesis expressed in words is. "the standard deviation of the 18-hole scores for a golfer is at most 3.5 strokes." The null hypothesis is expressed symbolically as. "H0:σ≤3.5."C. The null hypothesis expressed in words is. "the standard deviation of the 18-hole scores for a golfer is equal to 3.5 strokes." The null hypothesis is expressed symbolically as. "H0:σ=3.5."D. The null hypothesis expressed in words is. "the standard deviation of the 18-hole scores for a golfer is not 3.5 strokes." The null hypothesis is expressed symbolically as. "H0:σ≠3.5."
Answer:
The correct option is (C).
Step-by-step explanation:
The claim made by the golf analyst is:
Claim: The standard deviation of the 18-hole scores for a golfer is at most 3.5 strokes.
A standard deviation test is to be performed.
The hypothesis for the test will be defined as follows:
H₀: The standard deviation of the 18-hole scores for a golfer is 3.5 strokes, i.e. σ = 3.5.
Hₐ: The standard deviation of the 18-hole scores for a golfer is at most 3.5 strokes, i.e. σ ≤ 3.5.
Thus, the correct option is (C).
A bag has six balls labeled a,b,c,d.e and f . One ball will be randomly picked, and its letter will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of choosing the letter a or c . If there is more than one element in the set, separate them with commas.
We simply list all of the letters mentioned as they are the possible outcomes. We can only pick one item from the sample space. The event space is the set of outcomes where we want to happen (picking either an 'a' or 'c').
Hey There!!
To this Question, This answer going to had A Explanation to this: Sample space--
A sample space is a set which contains the set of all the possible outcomes or results that could occur while performing an experiment.
i.e. the sample space while flipping a coin is: {H,T}
The sample space while tossing a six-sided die is: {1,2,3,4,5,6}
Here it is given that:
A bag has six balls labeled: A,B,C,D,E,F
One ball will be randomly picked, and its letter will be recorded as the outcome.
This means that the sample space is given by:
Sample space={ A,B,C,D,E,F}
Now, when the event is choosing a letter from D to F.
Then the sample space is:
Sample space= {D,E,F}
Hope It Helped!~ ♡
ItsNobody~ ☆
Find the value of tetha in 2 cos 3 tetha = 1
Answer:
Step-by-step explanation: 2cos3 theta=1. Cos 3theta=1/2. Since cos 60°= 1/2. Therefore cos 3theta=cos 60°. Theta=20°.
can we chat girl in comment
how do you work out 28.4 x 1.92
Answer:
54.528
Step-by-step explanation:
A football stadium splits ticket sales in ratio of 3 : 4 between the away team and the home team. The home team make £36,000. What is the total amount of ticket sales?
The ratio 3:4 means for every 3 pounds made in away team tickets versus home team tickets. Multiply both sides by 9000 to have that 4 turn into 36000. The ratio 3:4 will then turn into 27000:36000
With this new ratio, we see that the away team pulls in 27000 and the home team pulls in 36000. Add the two amounts to get the final answer
27000+36000 = 63000
------------
We could alternatively add 3 and 4 (from the ratio 3:4) to get 3+4 = 7. Then multiply by that same scale factor 9000 getting 9000*7 = 63000.
When the solution of x2 − 9x − 6 is expressed as 9 plus or minus the square root of r, all over 2, what is the value of r? X equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a 6 42 57 105
Answer:
The value of r is 105
Step-by-step explanation:
Quadratic equation helps us to solve any quadratic equation. The formula is:
(-b ± √b² - 4ac) ÷ 2a
For the quadratic equation ax²+bx+c
For the equation: X² - 9x - 6:
a = 1, b = -9 and c = -6
Replacing in the quadratic formula:
(-(-9) ± √(-9)² - 4(1*-6)) ÷ 2*1
= 9 ± √105 / 2
That means, the value of r is 105Answer:
105 is right
Step-by-step explanation:
I took the test
Ms.Kayla theatre group is having a play. On Thursday the ticket sale is 287, Friday ticket sale was 618, Saturday ticket sale was 973, and on Sunday the ticket sale was 532. Which two-day ticket sales can be combined to equal more than the tickets sold on Saturday. Please show your work I will mark you brainiest and show your work, please
Answer:
Friday & Sunday
Step-by-step explanation:
Thursday: 287
Friday: 618
Saturday: 973
Sunday: 532
973 < 287 + 618 = 973 < 905
We now know this isn't true.
973 < 287 + 532 = 973 < 819
This isn't true either.
973 < 532 + 618 = 973 < 1150
This is true. The two days with the time are Friday and Sunday.
I really hope this helps you! Tell me if it's right or not! :D
Solve for m 5m+35=70
Answer:
m=7
Step-by-step explanation:
subract 35 from both sides to isolate the variable. Then you should be left with 5m=35. From there, divide both sides to isolate the variable even more, and you should be left with m=35/5 which is 7.
Answer: m=7
Step-by-step explanation:
[tex]5m+35=70[/tex]
subtract 35 on both sides
[tex]5m+35-35=70-35[/tex]
[tex]5m=35[/tex]
divide 5 on both sides
[tex]35/5=7[/tex]
[tex]m=7[/tex]
please i need help asap lol
A baseball league is holding registration for both a men's league and a women's league. Only a total of 546 players can register, and each team consists of exactly 13 players. If 25 women's teams have already registered, which inequality could be used to find m, the number of men's teams that can register? A. 25(13) + 13m 546 C. 25(13 + 13m) 546
Answer:
546 - 25 x 13 (divided by) 13
546 - (25 x 13) / 13
Step-by-step explanation:
25 x 13 = 325
546 - 325 = 221
221 / 13 = 17
17 mens teams can register.
Answer:
[tex]25(13)+13m\leq 546[/tex]
A
Step-by-step explanation:
Each team can only consists of thirteen players. Therefore, by letting w represent the number of women's teams and m the number of men's teams, the total number of players is represented by the equation:
[tex]13w+13m[/tex]
The total number of players cannot surpass 546. In other words, it must be less than or equal to. Therefore:
[tex]13w+13m\leq 546[/tex]
We are given that that 25 women's teams have already signed up. To find out the possible number of men's teams that can sign up, we can substitute 25 for w and then solve for m.
Therefore:
[tex]25(13)+13m\leq 546[/tex]
In conclusion, the answer is A.
rewrite 1/5:1/2 as a unit rate
Hey there! I'm happy to help!
The unit rate is how much stuff there is per 1 unit. All ratios can be rewritten as fractions, this one could be 0.2/0.5. The word per means divide, and fractions are basically dividing. So, we want the denominator to be 1.
To get 0.5 to 1, we multiply by 2. So, we will multiply the fraction by 2/2.
0.2/0.5(2/2)=0.4/1
Therefore, the unit rate is 0.4/1 or 0.4:1 or 0.4 per 1.
Have a wonderful day! :D
This is the question
For answers, please refer to the picture attached
Answer:
I can't give a full answer because I can't see the image whilst giving an answer but I'll try so....
Step-by-step explanation:
Angles in a straight line add to 180° so when you have one of two of them angles are them together and take away from 180°
Angles around a full point add to 360° so add angles together and take away from 360°
On A I think it is you have a 360° angle and have to work out 3 and you have one already done and the opposite angle is the same as that so you basically have two angles then you add them together then take from 360 then divide the answer by two and then that would be the angles for a and x
And for the last one you have been given two angles with a right angle and a right angle equals 90 so add them together and take from 180 to get the missing angle
Hope this helps :)
Determine the length ofx and the length ofy, to the nearest tenth of a metre.
12
Х
37°
a. x = 7.2 m and y= 9.7 m
b. x = 9.6 m and y = 12.9 m
42°
x = 9.6 m and y= 14.3 m
d. x = 7.2 m and y = 10.8 m
c.
Answer:
Option D. x = 7.2 m and y = 10.8 m.
Step-by-step explanation:
A. Determination of the value of x
Angle θ = 37°
Opposite = x
Hypothenus = 12 m
Using the sine ratio, the value of x can be obtained as follow:
Sine θ = Opposite /Hypothenus
Sine 37 = x/12
Cross multiply
x = 12 × Sine 37
x = 7.2 m
B. Determination of the value of y.
Angle θ = 42°
Opposite = x = 7.2 m
Hypothenus = y
Using the sine ratio, the value of y can be obtained as follow:
Sine θ = Opposite /Hypothenus
Sine 42 = 7.2/y
Cross multiply
y × Sine 42 = 7.2
Divide both side by Sine 42
y = 7.2 / Sine 42
y = 10.8 m
Therefore, x = 7.2 m and y = 10.8 m
The heights of two similar parallelograms are 16 inches and 20 inches. Their
respective areas are (3x+5) square inches and 9x square inches. Find the value of
X?
Answer: [tex]x=\dfrac{25}{21}[/tex]
Step-by-step explanation:
Area of parallelogram = Base x height
If two parallelograms are similar, then their corresponding sides are proportional.
That means, [tex]\dfrac{\text{Area of first parallleogram}}{\text{Area of second parallleogram}}=\dfrac{\text{height of first parallelogram}}{\text{height of second parallelogram}}[/tex]
[tex]\Rightarrow \dfrac{3x+5}{9x}=\dfrac{16}{20}\Rightarrow \dfrac{3x+5}{9x}=\dfrac{4}{5}\\\\\Rightarrow 5(3x+5)=4(9x)\\\\\Rightarrow\ 15x+25 = 36x\\\\\Rightarrow\ 36x-15x=25\\\\\Rightarrow\ 21x = 25\\\\\Rightarrow\ x=\dfrac{25}{21}[/tex]
Hence, [tex]x=\dfrac{25}{21}[/tex]
in the equation z=x^2-3y, find the value of z when x=-3 and y=4
Answer:
z=-3
Step-by-step explanation:
z=(-3)^2 - 3(4)
z=9 - 12
z=-3
1)A cylindrical container has a diameter has diameter of 14cm and height of 20cm and is full of water. A student pours the water into another cylinder of diameter 20cm. How deep is the water in the second cylinder?
2)A cylindrical water tank is70cm in diameter. To begin with, it is full of water. A leak starts at the bottom so that it loses 10l of water every hour. How long will it take for the water level to fall by 20cm?
3) A cylindrical storage vessel is 4m in diameter and 31/2m deep. How many kilolitres will it hold?
Answer:
Hey there!
1) To solve this, we want to know the volume of the first cylinder, which using the cylinder volume formula, we find is roughly 3079 cm^3. If the water is poured into the second cylinder, we find that the height is about 9.8 cm.
2) First, we should know that 1000 cm^3=1 liter. Volume of 1 cm tank height: 3848 cm^3, or 3.848 l. Volume for 20 cm tank height= 76.96 l. It takes about 7.7 hrs for the water level to fall 20 cm.
3) Cylinder volume formula gives us the answer to be 176 m^3 as the volume.
Hope this helps :)
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:
A baking scale measures mass to the tenth of a gram up to 650 grams .Which of the following measurements is possible
Answer:
A. 3.8 grams
Step-by-step explanation:
A baking scale measures mass to the tenth of a gram, up to 650 grams. Which of the following measurements is possible using this scale?
a.3.8 grams
b.120.01 grams
c.800.0 grams
d.54 milligrams
Solution
The scale measures mass to the tenth of a gram
The scale measures up to 650 grams
a.3.8 grams
This measures to the tenth of a gram (to one decimal place) and it is not up to 650 grams
b.120.01 grams
This measures to hundredth of a gram ( 2 decimal places) and it is not up 650 grams.
c.800.0 grams
This measures to the tenth of a gram but exceeds the 650 grams limit
d.54 milligrams
This is in milligram, so it is wrong
Option a.3.8 grams is the only possible scale measurement among the options.
HELP ASAP WILL MARK BRAINLIEST!!!!!! Use the number line below, where RS=9y+2, ST = 4y+9 and RT = 115. a. What is the value of y? b. Find RS and ST. a. What is the value of y?
Answer: y = 7
Step-by-step explanation:
