Answer:
[tex]\sqrt[3]{3}[/tex]
Step-by-step explanation:
We are required to simplify the quotient: [tex]\dfrac{\sqrt[3]{60} }{\sqrt[3]{20}}[/tex]
Since the numerator and denominator both have the same root index, we can therefore say:
[tex]\dfrac{\sqrt[3]{60} }{\sqrt[3]{20}} =\sqrt[3]{\dfrac{60} {20}}[/tex]
[tex]=\sqrt[3]{3}[/tex]
The simplified form of the given quotient is [tex]\sqrt[3]{3}[/tex].
The quotient of an expression is gotten by dividing the expression by another algebraic expression
The result of the given quotient is [tex]\sqrt[3]{3}[/tex]
The expression is given as:
[tex]\frac{\sqrt[3]{60}}{\sqrt[3]{20}}[/tex]
Rewrite the above expression as follows:
[tex]\frac{\sqrt[3]{60}}{\sqrt[3]{20}} = \sqrt[3]{\frac{60}{20}}[/tex]
Divide 60 by 20
[tex]\frac{\sqrt[3]{60}}{\sqrt[3]{20}} = \sqrt[3]{3}[/tex]
Hence, the result of the given quotient is [tex]\sqrt[3]{3}[/tex]
Read more about quotients at:
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AC is tangent to circle o at point c. What is the length of AC? ___________ units. diagram below pls help
Answer:
AC = 4 units
Step-by-step explanation:
[tex] OB = OC = 3 (Radii \:of \:same \:circle) \\
OA = OB + AB = 3 + 2 = 5\\
OA \perp AC.. (tangent\: \perp radius) \\
\therefore m\angle OCA = 90\degree \\[/tex]
By Pythagorean theorem:
[tex] AC^2 = OA^2 - OC^2 \\
= 5^2 - 3^2 \\
= 25-9\\
= 16\\
AC =\pm \sqrt{16}\\
AC = \pm 4[/tex]
Since, side of a triangle can't be negative.
Therefore, AC = 4 units
Two Chords, Find X. Need help with this answer as soon as possible.
Answer:
77
Step-by-step explanation:
The measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs.
(The sum of the measures of the intercepted arcs)/2
(76+78)/2
154/2
77
Can anyone help I could really use it
Answer:
-12m-6n
Step-by-step explanation:
Let's break this down systematically
Start:
8m + 2n - 4(5m - 2n)
Use the distributive property
8m + 2n - 4(5m - 2n)
8m + 2n - 20m - 8n
Match like terms m and n
8m - 20m = -12m
2n - 8n = -6n
-12m-6n
When testing gas pumps for accuracy, fuel-quality enforcement specialists tested pumps and found that 1334 of them were not pumping accurately (within 3.3 oz when 5 gal is pumped), and 5663 pumps were accurate. Use a 0.01 significance level to test the claim of an industry representative that less than 20% of the pumps are inaccurate. Use the P-value method and use the normal distribution as an approximation to the binomial distribution.
Answer:
We accept H0, Therefore we conclude that there is no evidence to support the claim that less than 20% of the pumps are inaccurate.
Step-by-step explanation:
We have,
x = 1334
n = 1334 + 5663 = 6997
we have to:
p = x / n = 1334/6997 = 0.1907
The hypothesis is:
H0: P = 0.20
H1: P <0.20
P = 0.2 and Q = 1 - P = 0.8
the test statistic is:
Z = (p - P) / [(P * Q / n) ^ (1/2)]
replacing:
Z = (0.1907 - 0.20) / [(0.2 * 0.8 / 6997) ^ (1/2)]
Z = -1.96
now, the p-value is
P = 0.0250, from normal table, attached
Here p-value> 0.01, so we accept H0, Therefore we conclude that there is no evidence to support the claim that less than 20% of the pumps are inaccurate.
Help please! How would i solve this?
Answer:
B is correct
Step-by-step explanation:
What is need to be done here is to set up an exponential equation for both scenario.
The exponential equation to set up is as follows;
V = P(1 + r)^t
It looks exactly like an equation used to get the amount on a compound interest after a stipulated number of years.
We have the following definitions;
V is the future value.
P is the present value
r is the rate in percentage
t is the time in years
So, for A, we have;
Kindly note that 4% = 4/100 = 0.04
110,000(1+0.04)^t = 110,000(1.04)^t
For B, we have;
6/100 = 0.06
100,000(1+0.06)^t = 100,000(1.06)^t
Now expected value of B is twice that of A.
The equation that defines this would look like;
100,000(1.06)^t = 2(110,000(1.04)^t)
Solve the simultaneous equations 3x+y=8 X-3Y=11
Answer:
(7/2, -5/2)
Step-by-step explanation:
We can solve this multiple ways: Algebraically (Substitution or Elimination) or Graphically
Step 1: Write 1st equation in terms of y
y = 8 - 3x
Step 2: Substitute y of 2nd equation
x - 3(8 - 3x) = 11
Step 3: Solve for x
x - 24 + 9x = 11
10x - 24 = 11
10x = 35
x = 7/2
Step 4: Plug x to find y
3(7/2) + y = 8
21/2 + y = 8
y = -5/2
Answer:
Step-by-step explanation:
let's organize our information :
3x+y=8x-3y=11The trick here is to multiply x-3y=11 by -3 then add it to 3x+y=8 to get rid of x and get a normal equation
we get : -3x+9y= (-33)
then after the addition : 3x+y-3x+9y=8-33⇔ 10y=(-25)
so y=(-25)/10= -5/2
let's replace y by -5/2 in 3x+y=8 3x-5/2 =8⇔ x= 21/6so y= (-5/2) and x= 21/6
How is this wrong? Please explain to me.
Answer:
Wrong values are plotted in the question statement graph.
Please find correct graph.
Step-by-step explanation:
Given that:
[tex]y =x+3[/tex] and [tex]-1<x<5[/tex]
i.e. we can put a value of x in the equation which is greater than -1 and lesser than 5.
OR
we can say, the points where x = -1 and x = 5 will not be included in the graph (they will be shown as hollow circle).
Now, let us put the values one by one:
x = -1, y = -1 + 3 =2
x = 0, y = 0 + 3 = 3
x = 1, y = 1 + 3 = 4
x = 2, y = 2 + 3 = 5
x = 3, y = 3 + 3 = 6
x = 4, y = 4 + 3 = 7
x = 5, y = 5 + 3 = 8
Therefore, the table of values become:
[tex]\begin{center}\begin{tabular}{ c c } x & y\\ -1 & 2\\ 0 & 3 \\ 1 & 4 \\ 2 & 5 \\ 3 & 6 \\ 4 & 7 \\5 & 8\\\end{tabular}\end{center}[/tex]
Points (-1, 2) and (5, 8) will not be included in the graph.
Please find attached corrected graph.
the magic dragon cigarette company claims that their cigarettes contain an average of only 10 mg of tar. a random sample of 100 magic dragon cigarettes shows the average tar content to be 11.5 mg with a known population standard deviation of 4.5 mg. construct a hypothesis test to determine whether the average tar content of magic dragon cigarettes exceeds 10 mg. use a 5% level of significance.
what is the critical value method and pvalue method
Answer:
[tex]t=\frac{11.5-10}{\frac{4.5}{\sqrt{100}}}=3.333[/tex]
Critical value
The significance is 5% so then [tex]\alpha=0.05[/tex] and [tex]\alpha/2=0.025[/tex] then the critical value for this case would be [tex] z_{\alpha/2}= 1.64[/tex]. Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is higher than 10 mg
P value
The p value would be given
[tex]p_v =P(z>3.333)=0.000434[/tex]
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 10 mg
Step-by-step explanation:
Information given
[tex]\bar X=11.5[/tex] represent the sample mean
[tex]\sigma=4.5[/tex] represent the population standard deviation
[tex]n=100[/tex] sample size
[tex]\mu_o =10[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean is higher than 10mg, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 10[/tex]
Alternative hypothesis:[tex]\mu > 10[/tex]
the statistic for this case would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing we got:
[tex]t=\frac{11.5-10}{\frac{4.5}{\sqrt{100}}}=3.333[/tex]
Critical value
The significance is 5% so then [tex]\alpha=0.05[/tex] and [tex]\alpha/2=0.025[/tex] then the critical value for this case would be [tex] z_{\alpha/2}= 1.64[/tex]. Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is higher than 10 mg
P value
The p value would be given
[tex]p_v =P(z>3.333)=0.000434[/tex]
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 10 mg
SOLVE
Which of the following ordered pairs are equal? Write with reason
(a) (2, 3) and (4,2)
Answer: (2, 3) and (4,2) are not equal.
Step-by-step explanation:
An ordered pair is something like (x, y)
and two pairs (x1, y1) and (x2, y2) are only equal if x1 = x2 and y1 = y2
in this case, we have (2, 3) and (4, 2)
you can see that in the pairs the value of x is different, and the value of y is also different. Then we have that the pairs can not be equal.
What would be the most logical first step for solving this quadratic equation?
x2 + 2x- 14 = 6
A. Take the square root of both sides
B. Add 14 to both sides
C. Divide both sides by x
Ο Ο
D. Subtract 6 from both sides
Answer:
D
Step-by-step explanation:
So that you can have an equation equal to zero to solve for x
what is the range of the function in this table?
Answer: A) 1, 2, 4
Step-by-step explanation:
The range of a function is every y value.
Answer:
A. {1, 2, 4}
Step-by-step explanation:
Well let’s take a step back,
What is range?
Range is the amount of y-value son a graph or table.
So the range is (1, 4, 2)
35% off a phone = £78 how much was the phone before the discount prices?
Answer:
£120
Step-by-step explanation:
Given that
The price after reduction = £78
So, 65% = £78.
We have to calculate 100 %
To do so, find 5% and multiply that by 20
65% = £78
5% = 78/13 = £6
So, 100% = 6 x 20 = £120
Hope this helps.
Good Luck
Please mark brainiest
Please answer this quickly - just want the answers, explanation not needed!
Answer:
Step-by-step explanation:
3782Pls help me ima mark BRAINLIST
Answer:
24.5
Step-by-step explanation:
Year 2000 would be 1, so year 2016 would be 17
Your equation is 1.5x - 1, and since we have x = 17, we simply plug it in:
1.5(17) - 1
25.5 - 1
24.5 is our estimated population using the line of best fit.
Answer:
23
Step-by-step explanation:
Note that the horizontal axis notes the years since 2000. This means that each increase in the x axis increases the year by 1. Thus, it means that at x=1, it is 2001, at x=2, it is 2002. In other words, in 2016, x=16.
We can just put this number into the equation:
y=1.5(16)-1
y=24-1
y=23
Evaluate 3(4-2) what would be the answer to this
Answer:
6
Step-by-step explanation:
3(4 - 2)
Expand brackets.
3(4) + 3(-2)
12 + - 6
= 6
━━━━━━━☆☆━━━━━━━
▹ Answer
6
▹ Step-by-Step Explanation
Follow PEMDAS:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
3(4 - 2)
3(2)
= 6
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
The population of China was about 1,360,000,000 people in 2014. Which number best approximates the population as a single digit times a power of 10?
Answer: 1 * 10^9
Step-by-step explanation:
1*10^9 = 1,000,000,000, which is the closest you can get.
Hope it helps <3
A weather station in Antarctica reports that the temperature is currently -44 °C and has been rising at a constant rate of 4.5 °C per hour. What will the temperature be in Antarctica in 6 hours
Answer:
-17
Step-by-step explanation:
4.5*6=27
so -44++27
Which of the following options correctly describes the graph below?
The option that correctly describes the graph below is A. Piecewise function.
What is a piecewise function?
A piecewise function is a function that reacts in different ways based on the input received at every point in time. This function has different intervals and funtions that apply to the respective domains.
Sometimes, these graphsa re recognized by the three main parts that they have. So, the function that is represented by the graph is the piecewise function.
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Betsy can clean a b of the house in an hour. How long will it take her to clean the whole house?
Answer:
[tex]\frac{b}{a}[/tex] is the total time taken to clean the house.
Step-by-step explanation:
Given that:
Betsy cleans [tex]\frac{a}{b}[/tex] of the house.
Time taken = 1 hour
To find:
Time taken to clean the whole house = ?
Solution:
We can use unitary method here to solve this problem.
We are given that [tex]\frac{a}{b}[/tex] of the house is cleaned in 1 hour.
We have to find that a total of 1 house will be cleaned in how much time.
(1 house because Betsy's house can be considered as a single unit).
To find this we will divide 1 hour with [tex]\frac{a}{b}[/tex].
Now, Let us solve this mathematically:
[tex]\frac{a}{b}[/tex] of the house is cleaned in = 1 hour
1 of the house will be cleaned in = 1 hour divided by [tex]\frac{a}{b}[/tex]
[tex]\dfrac{1}{\dfrac{a}{b}}\ hours\\\Rightarrow \dfrac{1 \times b}{a}\ hours\\\Rightarrow \dfrac{b}{a}\ hours[/tex]
So, the answer is:
[tex]\frac{b}{a}[/tex] is the total time taken to clean the house.
Your friend swims on the school team. In her first four races, her times are 26.3, 28.4, 25.6 and 29.1. Which time listed for her next race would make the range larger? A. 25.2 B. 26.1 C. 28.0 D. 29.1
Answer:
A.) 25.2
Step-by-step explanation:
Given the following :
Times in first four races :
26.3, 28.4, 25.6 and 29.1
The range of a list of values is the difference between the maximum and minimum value of the list or data.
In her first four races :
Range = 29.1 - 25.6 = 3.5
Value of range in her first four races = 3.5
In other to make the range larger:
Either she has a value less than the least time in her previous four races or she has a value greater than the maximum value of her previous race in her next race.
With a time of 25.2 in her next race : least value in the data will be 25.2
Range = 29.1 - 25.2 = 3.9
With a time of 26.1 in her next race :
Range = 29.1 - 25.6 = 3.5
With a time of 28.0 in her next race :
Range = 29.1 - 25.6 = 3.5
With a time of 29.1 in her next race :
Range = 29.1 - 25.6 = 3.5
Answer:
25.2
Step-by-step explanation:
Your friend swims on the school team.
In her first four races, her times are 26.3, 28.4, 25.6, and 29.1 seconds.
Which time listed for her next race would make the range larger?
Please help meeeee
The measure of a central angle is 18°. If the length of its intercepted arc is xπ units, what is the circumference of the circle?
A.( x/20)π units
B. (x/18)π units
C. (x/10)π units
D. 18xπ square units
E. 20xπ square units
Answer:
20xπ units
Step-by-step explanation:
Use the formula for the length of an arc.
θ/360 × 2πr
The length of the arc and the central angle is already given.
18/360 × 2πr = xπ
Solve for r.
r = (xπ)/(18/360)/(2π)
r = 10x
The radius of the circle is 10x.
The circumference of a circle is 2πr.
2π(10x)
20xπ
The circumference of the circle is 20xπ units.
Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. When she began her study, the frog population was estimated at 1,200. Which function represents the frog population
Answer:
Step-by-step explanation:
This is exponential, of the form
[tex]y=a(b)^x[/tex] where a is the initial amount and b is the growth/decay rate. If Ginny begins the study with 1200 frogs in the population, our a value is 1200.
If the population is decreasing 3% per year, it is decreasing 100% - 3% = 97% which, as a decimal, is .97. Our exponential function, then, is
[tex]y=1200(.97)^x[/tex]
Identify the property that justifies the following statement: I will make you a brainllest.
Answer:
reflexive property of simliarity
Step-by-step explanation:
Jason is playing a game. He has two sets of cards. One set has three red cards, numbered 1, 2 and 3. The other set has four green cards, numbered 4, 5, 6 and 8. Jason chooses a red card and a green card at random. He works out his score by adding the numbers on the two cards together. A sample space diagram is drawn below. Work out the probability that Jason gets a score of 9 or more.
Answer:
1/3
Step-by-step explanation:
There are 12 different sums.
4 of the sums are 9, 9, 10, 11.
All other sums are 8 or less.
p(9 or more) = 4/12 = 1/3
A small grain silo is filled with wheat at the end of each season. If the silo is only half full, how many cubic meters of wheat have been stored? Group of answer choices 339.29 m³ 223.19 m³ 169.65 m³ 113.10 m³
Answer:
Volume of wheat = 147.26 m³ (check the explanation)
Step-by-step explanation:
The question still lacks some details such as the size of the silo. We will go forward by assuming the size of the silo to aid our calculation. Silos are cylindrical storage structures that range from 3 - 27 m in diameter and 10 - 90 m in height. For the purpose of this question, let's assume that the size of the silo is 5 m (diameter) by 15 m (height).
Let's list out the parameters to be used:
diameter (D) = 5 m; r = D ÷ 2 ⇒ r = 5/2 = 2.5 m,
height (h) = 15 m
Volume of silo = πr²h = π * 2.5² * 15
V (silo) = 294.52 m³
The silo is half full ⇒ ½ * V
Volume of wheat stored is given by half of the silo volume, since the silo is half-full
V (wheat) = ½ * 298.52
V (wheat) = 147.26 m³
i need help with this i dont understand at all. find the 1st, 2nd, 3rd, 4th and 10th nTh term rule is n+5
The rule is n + 5
So we have that
an = n + 5
Where n is the term, that said we want the 1st, 2nd, 3rd, 4th and 10th term
a1 = 1 + 5 = 6
a2 = 2 + 5 = 7
a3 = 3 + 5 = 8
a4 = 4 + 5 = 9
a10 = 10 + 5 = 15
What is an equation of the line that passes through the point
(−5,−6) and is parallel to the line
x+5y=25?
Answer:
y=-5x-4
Step-by-step explanation:
y=mx+b
-5=-5m+b
-5=-1+b
b=-4
y=-5x-4
:D
Gracie has 5555 pet bunnies that love to eat whole carrots. She has 39393939 carrots to feed the bunnies. Gracie will use as many carrots as she can and give each bunny the same number. How many carrots will each bunny get?
Answer:
7,091.61
Step-by-step explanation:
If you have a number 1. (39393939) and you have another number 2. (5555) and you want the second number to get the same amount as the other numbers but evenly, you need to divided the first number with the second number.
Ex. 39393939/ 5555 = 7,091.61
So each bunny will get 7,091.61 carrots.
Which is a factor of: 2x^2+2x−12 ?
Answer:
(x - 2) and (x + 3) is a factor of: 2x² + 2x - 12
Step-by-step explanation:
2x² + 2x - 12 given equation
Now divide it by 2 we get,
x² + x - 6
then
x² + x - 6
x² + 3x - 2x - 6
x(x + 3) - 2(x + 3)
(x - 2) (x + 3)
Answer:
2 ( x+3)(x-2)
Step-by-step explanation:
2x^2+2x−12
Factor out 2
2 ( x^2 +x-6)
Factor inside the parentheses
What 2 numbers multiply to -6 and add to 1
3*-2 = -6
3+-2 =1
2 ( x+3)(x-2)
2 5 ( 1 3 x− 15 8 )− 1 3 ( 1 2 − 2 3 x)
Answer:
If you were doing... 25(13x-15 8)-13(12-23x), the answer would be...
624x-3156
If you were doing... 25(13x-158)-13(12-23x), the answer would be...
624x-4106.
Step-by-step explanation: Simplify the expression.
I hope this helps you out! ☺
The simplification of algebraic expression 25(13x - 158) - 13(12 - 23x) is 624x - 4106.
An algebraic expression is an expression built up from constant, variables, and algebraic operations : addition, subtraction, multiplication, division and exponentiation.
To simplify an algebraic expression, we can only add or subtract the like terms. Like terms are variables with same exponent.
Given in the question,
algebraic expression = 25(13x - 158) - 13(12 - 23x)
Simplifying the expression,
[tex]= 25(13x - 158) - 13(12 - 23x)\\\\= 325 x - 3950 - 156 + 299x\\\\=325x + 299x - 3950 - 156\\\\= 624x - 4106[/tex]
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