Answer:
[tex] \sqrt{3} [/tex]
Step-by-step explanation:
27 is 3×3×3 from square root we can take 3 out as 3^2 elimate square root and remaining 3 is under root
1.) You go skiing on one route with an equation = 2 + 4 and then
immediately go to a route with an equation = 4 + 1. Which of the
following responses best describes your routes?
A: Your second route was steeper than your first, and the second route was higher up
the mountain.
B: Your first route was positive (uphill), but your second route was negative (downhill).
C: Your first route was steeper than your second, and both were positive (uphill).
D: Your first route was flatter than your second, and your first route began at a higher
point than your second
The best information that describes your routes is the second route was steeper than your first, and the second route was higher up the mountain.
What is the slope of a linear equation?The slope of a linear equation is the change in the rise over the run. So, the slope of a linear equation shows that the larger the slope, the steeper the line becomes.
From the given information:
y = 2x + 4 --- (1)
y = 4x + 1 --- (2)
Using the slope-intercept formula:
y = mx + b
m = slopeb = y-interceptFrom the first equation, the slope is 2 and in the second equation, the slope is 4.
Therefore, we can conclude that the second route was steeper than your first, and the second route was higher up the mountain.
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Select the correct answer. if function g has the factors (x − 7) and (x 6), what are the zeros of function g? a. -7 and 6 b. -6 and 7 c. 6 and 7 d. -7 and -6
Option (b) -6 and 7 is the correct option.
The zeroes of the function f and g are x=7 and x=-6 respectively.
What are the zeroes of a polynomial?The values of x that satisfy the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case. The degree of the equation f(x) = 0 determines how many zeros a polynomial has.
Put x-7=0
X=7
Now, put x+6=0
So, x=-6
The zeroes of the function f and g are 7 and -6 respectively.
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alegbra 2: pls help!!
Kiara and Sean are setting off model rockets. Kiara's rocket's flight pattern can be modeled by the function f(t)= -16t² +80t. Sean's rocket's flight
pattern can be modeled by the function h(t) = -16t² + 120t+64. In each function, t is the time in seconds after the rockets launch and f(t) and h(t)
are the heights of the rockets in feet.
How many seconds after Kiara's rocket returns to the ground does
Sean's rocket return to the ground?
Enter your response as a numeric answer. Do not include spaces, units,
or commas in your response.
Answer:
Sean's rocket lands 3 seconds after Kiara's rocket.
Step-by-step explanation:
Kiara: f(t)= -16t² + 80t
Sean: h(t) = -16t² + 120t + 64
Assume that both rockets launch at the same time. We need to be suspicious of Sean's rocket launch. His equation for height has "+64" at the end, whereas Kiara's has no such term. The +64 is the starting height iof Sean's rocket. So Kiara has a 64 foot disadvantage from the start. But if it is a race to the ground, then the 64 feet may be a disadvantage. [Turn the rocket upside down, in that case. :) ]
We want the time, t, at which f(t) and h(t) are both equal to 0 (ground). So we can set both equation to 0 and calculate t:
Kiara: f(t)= -16t² + 80t
0 = -16t² + 80t
Use the quadratic equation or solve by factoring. I'll factor:
0 = -16t(t - 5)
T can either be 0 or 5
We'll choose 5. Kiara's rocket lands in 5 seconds.
Sean: h(t) = -16t² + 120t + 64
0= -16t² + 120t + 64
We can also factor this equation (or solve with the quadratic equation):
0 = -8(t-8)(2t+1)
T can be 8 or -(1/2) seconds. We'll use 8 seconds. Sean's rocket lands in 8 seconds.
Sean's rocket lands 3 seconds after Kiara's rocket.
The table below shows the linear relationship between the number of people at a picnic and the total cost of the picnic.
A two column table with five rows. The first column, Number of People, has the entries, 6, 9, 12, 15. The second column, Total Cost in dollars, has the entries, 52, 58, 64, 70.
Which statements about the function described by the table are true? Check all that apply.
The independent variable is the number of people.
The initial value (initial fee) for the picnic is $40.
The rate of change is $8.67 per person.
As the number of people increases, the total cost of the picnic increases.
If 4 people attended the picnic, the total cost would be $46.
The true statements are:
The independent variable is the number of people.The rate of change is $8.67 per person.As the number of people increases, the total cost of the picnic increases.What are the true statements?The independent variable is the variable that determines the value of the dependent variable. There is a positive relationship between the number of people at the picnic and the total cost. This is because it can be seen as the number of people at the picnic increases, the total cost changes.
Rate of change = total cost / number of people
$52 / 6 = $8.67
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Answer:
A, B, D
Step-by-step explanation:
right on edge
If A c B and A N B= • then which of the following can be concluded about the sets A and B!
Step-by-step explanation:
Set A is a subset of set B if all the elements of A are also the elements of Set B.. (common element)
The above set have 0 common elements so.. if there is no common element and are subsets then it means that there arent any elements in both the sets
so, the answer for the question would be "both the Sets A and B are the empty sets"
To conduct a test of hypothesis with a small sample, we make an assumption that?
To conduct a test of hypothesis with a small sample, we make an assumption that the population is normally distributed .
What is normal distribution?
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
The normal distribution appears as a "bell curve" on a graph.
A probability bell curve is more properly described as the normal distribution.The mean and standard deviation of a normal distribution are 0 and 1, respectively. It has a kurtosis of 3 and zero skew.Not all symmetrical distributions are normal, but all normal distributions are symmetrical.Natural occurrences frequently resemble the usual distribution.To know more about normal distribution........
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PLEASE HELP IM STUCK PLS
Answer:
The slope between these two points is m=-4.
Step-by-step explanation:
Greetings !
[tex]the \: equation \: for \: slope \: m \: is \\ m = \frac{Y₂-Y}{X₂-X₁}..substitute \: known \: values \\ m = \frac{ (-11 - 9) }{(3 - ( - 2)} \\ m = \frac{ - 20}{5} \\ m = - 4[/tex]
f(x) = x² + 3x, g(x) = 5x + 2, (f - g)(3) = ?
Answer:
1
Step-by-step explanation:
f(x) = x² + 3x
g(x) = 5x + 2
f(3) = 3² + 3 x 3
f(3) = 9 + 9
f(3) = 18
g(3) = 5(3) + 2
g(3) = 15 + 2
g(3) = 17
(f - g)(3) = 18 - 17
(f - g)(3) = 1.
What are the exact solutions of x2 − 5x − 1 = 0 using x equals negative b plus or minus the square root of the quantity b squared minus 4 times a times c all over 2 times a?
Answer:
[tex]x=2.5+\frac{\sqrt{29}}{2}\\\\x=2.5-\frac{\sqrt{29}}{2}[/tex]
Step-by-step explanation:
So the question here is asking you to use the quadratic formula which is expressed as: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\[/tex]
A quadratic can generally be expressed as: [tex]y=ax^2+bx+c[/tex]
So using the equation you gave: [tex]0=x^2-5x-1[/tex]
We can identify the following values: a=1, b=-5, c=-1
Btw the equation explicitly write "1" as the coefficient of x, but since it's not provided it's implied that it's 1.
So plugging in the known values, we get the following equation:
[tex]x=\frac{5\pm\sqrt{(-5)^2-4(1)(-1)}}{2(1)}\\\\x=\frac{5\pm\sqrt{25+4}}{2}\\\\x=\frac{5\pm\sqrt{29}}{2}\\\\x=2.5+\frac{\sqrt{29}}{2}\\\\x=2.5-\frac{\sqrt{29}}{2}[/tex]
The last step just consists of taking the + and - solution, and since it asks for exact solutions you leave the 29 under the radical, and you don't approximate. There is no further simplification that can be done here.
Put in decimal form, out to the nearest hundredth and explain how you got your answer.
This problem is meant to be done in order of operations.
Answer: [tex]\Large\boxed{2}[/tex]
Concept:
Here, we need to know the idea of the PEMDAS method.
PEMDAS is an acronym for the order of operations.
ParenthesisExponentsMultiplicationDivisionAdditionSubtractionSolve:
Given expression
[tex]\dfrac{3^3~-~13}{11~-~2^2}[/tex]
Simplify the exponents
[tex]=\dfrac{27~-~13}{11~-~4}[/tex]
Simplify by subtraction
[tex]=\dfrac{14}{7}[/tex]
Simplify the fraction
[tex]\Large\boxed{=2}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
4km^2= ? Mile^2
explain how
Answer:
See below
Step-by-step explanation:
An area of 2km x 2km = 4 km^2
1 km = .62137 miles
2 (.62137) x 2 (.62137) = 1.5444 mi^2
At a concert for the band Algal Rhythms, 75% of the tickets were sold at the full price of 30. The remaining 25% of tickets were sold at a discounted price of $10. What was the average selling price of a ticket at the Algal Rhythms concert? Express your answer in dollars, rounded to the nearest cent.
Answer:
The average price of a ticket is $25.
Step-by-step explanation:
Lets us say 100% = 1
0.75 x 30 + 0.25 x 10 = 25
if the earth is 12.5 million years old, how old is the earth in hours?
Answer:
1.09575e+11
Step-by-step explanation:
Mr. Nero drives to work each day 35 miles one way. If he were in a hurry, could he legally make it to work in less than a half hour with the legal speed limit set to 65 MPH? Reference the formula, d = rt, when explaining the answer.
Answer:
Nope. It would take 32 and 4/13 minutes, which is longer than 30 min.
Step-by-step explanation:
The distance is 35 miles and the speed 65 miles/hour
Dividie the distance by the speed to obtian the time required,
(35 miles)/(65 miles/hour) = 0.538 hours
No, 35 miles at the speed limit of 65 mph would require 0.538 hours, 0.038 hours more than 1/2 hour. 2 and 4/13 minutes more than 30 minutes.
One day, thirteen babies are born at a hospital. assuming each baby has an equal chance of being a boy or girl, what is the probability that at most eleven of the thirteen babies are girls? a. 29/128 b. 743/1024 c. 4089/4096 d. 11/64
Using the binomial distribution, there exists a 0.9983 = 99.83% probability that at most eleven of the thirteen babies exists girls.
What is the binomial distribution formula?The formula exists:
[tex]$&P(X=x)=C_{n, x} \cdot p^{x} \cdot(1-p)^{n-x} \\[/tex]
The parameters exists:
x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.
The values of the parameters are: p = 0.5 and n = 13
The probability that at most eleven of the thirteen babies are girls is:
[tex]$P(X \leq 11)=1-P(X > 11)$$[/tex] then
[tex]$P(X > 11)=P(X=12)+P(X=13)$$[/tex]
By using the binomial distribution formula
[tex]$&P(X=x)=C_{n, x} \cdot p^{x} \cdot(1-p)^{n-x} \\[/tex]
substitute the values in the above equation, we get
[tex]$&P(X=12)=C_{13,12} \cdot(0.5)^{12} \cdot(0.5)^{1}=0.0016 \\[/tex]
[tex]$&P(X=13)=C_{13,13} \cdot(0.5)^{13} \cdot(0.5)^{0}=0.0001[/tex]
So, [tex]$&P(X > 11)=P(X=12)+P(X=13)[/tex]
[tex]=0.0016+0.0001=0.0017 \\[/tex]
[tex]$&P(X \leq 11)=1-P(X > 11)[/tex]
[tex]=1-0.0017=0.9983[/tex]
0.9983 = 99.83% probability that at most eleven of the thirteen babies exists girls.
Therefore, the correct answer is option c. 4089/4096
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In a class 4/5 of the students have mathematical instruments 3/4 of these have lost their Protractors if 27 students have lost their protractors how many students are there in class ??
Answer:
4/5 of the students would have protractors.
Step-by-step explanation:
Solve the compound inequality and graph the solution on a number line
5x + 9 ≤ 2 and x + 6 > 12
Answer:
First:
5x + 9 < 2
x= 9/5= 1,8 < 2
Second:
x + 6 < 12
x= 12/6= 2 < 12
Help for a brianlest at show your work
Which of the following statements does not describe a characteristic of the line of best fit for a scatter plot?
I'll go for the third option. It seems sensible to having a balance in estimating provided data, even though that may not always be the case.
Hope this helps!
Sarah needs 10 feet of fabric for a project she is working on, but the store only sells the fabric in meters. One meter of fabric costs $1.50. How much will the fabric cost?
[1 ft = 0.305 m]
Answer:
$4.58
Step-by-step explanation:
Lets convert 10 feet to meters.
1 ft = 0.305m
10ft = 0.305 * 10
10ft = 3.05m
Now we will work out the cost of the fabric.
Given 1m = $1.50
3.05m = 3.05 * $1.50 = $4.58 (nearest cent)
When we make inferences about the difference of two independent population proportions, what assumptions do we need to make? mark all that apply.
When we make inferences about the difference of two independent population proportions, we assume that it is a random sample, and the number of successes and failures are at least 15 in each group.
Two independent proportions tests involve comparing the proportions of two unrelated datasets.
For these two datasets to be regarded as an independent population, the following must be true or assumed to be true
The datasets must represent a random sampleEach dataset must contain at least 15 successes and failuresHence, the above highlights are the assumptions of two independent population proportions.
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Write an equation in point-slope form of the line with a slope of 6 that passes through (-2, -5)
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-5})\hspace{10em} \stackrel{slope}{m} ~=~ 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{6}(x-\stackrel{x_1}{(-2)})\implies y+5=6(x+2)[/tex]
Evaluate |2 5/6 + y for y = 7/4
O A. 2 2/5
O B. 3 1/5
O C. 3 4/5
O D. 4 8/12
Answer:
D) 4 8/12
Step-by-step explanation:
To first start this, let's make 2 5/6 an in-proper fraction by adding 12 and removing the whole 2. =17/6. Then let's get a common denominator by multiplying both the denominators by each other...6x4 and 4x6, but we also multiply the numerators by the same thing that the denominators are getting multiplied by... 17x4 and 7x6. We will then get 68/24 and 42/24. And then we can add both numerators with eachother and keep the denominator to get, 110/24... and making this into a propor fraction would equal 4 16/24... and dividing by 2 would equal 4 8/12
What is the behavior of the graph y=x4−2x3−11x2+12x+36 at each of its zeros?
The behavior sees the leading coefficient is already positive, then increasing the size of the inputs will simply result in the leading term being even more positively skewed. The line on the graph will start to slope to the right.
What is the behavior of the graph y=x4−2x3−11x2+12x+36 at each of its zeros?The behavior of the graph of the polynomial function f(x) as the variable x approaches either positive or negative infinity represents the end behavior of the function. The final behavior of a polynomial function's graph is determined by the degree of the function as well as the leading coefficient.
Generally, the equation for is zeros mathematically given as
y=x^4−2x^3−11x^2+12x+36
Therefore
(x+2)^2(x-3)^2=0
x=-2
x=3
since the graph attached has a positive leading coefficient and a positive degree
In conclusion, If the leading coefficient is already positive, then increasing the size of the inputs will simply result in the leading term being even more positively skewed. The line on the graph will start to slope to the right.
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For each of the following, determine the interest rate per compounding period. 1) 12% per year, compounded weekly b) 8% per year, compounded bi-weekly c) 6% per year, compounded monthly
Using compound interest, the rates per compounding period are given as follows:
a) 0.1273 = 12.73%.
b) 0.0833 = 8.33%
c) 0.0617 = 6.17%
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.The interest rate per compounding period is given as follows:
[tex]\left(1 + \frac{r}{n}\right)^n - 1[/tex]
For item a, the parameters are:
r = 0.12, n = 52.
Hence:
[tex]\left(1 + \frac{0.12}{52}\right)^{52} - 1 = 0.1273[/tex]
For item b, the parameters are:
r = 0.08, n = 104.
Hence:
[tex]\left(1 + \frac{0.08}{104}\right)^{104} - 1 = 0.0833[/tex]
For item c, the parameters are:
r = 0.06, n = 12.
Hence:
[tex]\left(1 + \frac{0.06}{12}\right)^{12} - 1 = 0.0617[/tex]
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Which of the graphs below represents the equation 3x-2y=-12?
Answer:
Graph B
Step-by-step explanation:
Transform the given equation into the slope intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
3x - 2y = -12
2y = 3x + 12
y = 3/2x + 6
Graph B represents y = 3/2x + 6 because it has a y-intercept at (0,6) and a slope of 3/2.
Find the number of terms of the geometric series 96 - 48 + 24 -....,-3/8 .
The number of terms in the geometric series is 9
How to determine the number of terms in the series?The geometric series given as:
96 - 48 + 24 -....,-3/8 .
Calculate the common ratio (r) as follows
r = T2/T1
Substitute the known values in the above equation
r = -48/96
Evaluate
r = -0.5
The number of terms is then calculated as:
Tn = a * r^n-1
Let n = 9
So, we have:
T9 = a * r^9
Substitute the known values in the above equation
T9 = 96 * (-0.5)^8
Evaluate the product
T9 = -3/8
Hence, the number of terms in the geometric series is 9
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In one game, the final score was Falcons 3, Hawks 1. What fraction and
percent of the total goals did the Falcons score? Show your work in the space
below. Remember to check your solution.
Step-by-step explanation:
3over4 which is 75percentWhat is the missing factor in this factor tree? 30 2x?
Answer:
15?
Step-by-step explanation:
2×15=30 i am not fully sure but this should be it
I am a fraction. The ratio between my numerator and denominator is 2:5. My denominator is 6 more than my numerator. What fraction am I ?
Answer:
4/10
Step-by-step explanation:
Let the numerator be 2x and the denominator is 5x. The denominator is 6 more than the numerator so if we add 6 to the numerator both numbers should be equal.
Solve:
2x+6 = 5x
6 = 3x
x = 2
2x = 4
5x = 10
Step-by-step explanation:
Let the numerator be 2x and denominator be 5x,
A.T.Q,
2x+6 = 5x
2x-5x = -6
-3x = -6
3x = 6
x = 2
So, the fraction is 4/10 = 2/5