[tex]3\frac{16}{99} = \dfrac{313}{99}= 3.161616161616.....[/tex]
Find an equation for the line tangent to the curve at the point defined by the given value of d²y/dx².
At this point. x = 2 cos t, y = 2 sin t, t=π/4
Answer:
Step-by-step explanation:
Given:
x = 2cost,
t = (1/2)arccosx
y = 2sint
dy/dx = dy/dt . dt/dx
dy/dt = 2cost
dt/dx = -1/√(1 - x²)
dy/dx = -2cost/√(1 - x²)
Differentiate again to obtain d²y/dx²
d²y/dx² = 2sint/√(1 - x²) - 2xcost/(1 - x²)^(-3/2)
At t = π/4, we have
(√2)/√(1 - x²) - (√2)x(1 - x²)^(3/2)
PLEASE HELP ILL GIVE BRAINLIEST !!!!
Answer:
y=3x-2
Step-by-step explanation:
The slope of the equation is (-2-(-5))/(0-(-1))=3. The y intercept is - 2. So y=3x-2
Find the quotient of 90 over -10
90/-10
= 9/-1
= -9
So, -9 is the quotient.
Kurt simplifies this equation and says the
solution is x = 7. What can you tell Kurt
about his work?
3(x-7)=2x - 14
3x - 7 = 2x - 14
x=-7
He made an error on the second line. Kurt didn't distribute the 3 to each term inside the parenthesis of (x-7)
3(x-7) does not turn into 3x-7. Instead, it should be 3x-21 because 3*7 = 21.
This is what his steps should look like
3(x-7) = 2x - 14
3x - 21 = 2x - 14
3x-2x = -14+21
x = 7
The employee engagement score for a team was 4.89 this month. The score has been improving at a rate of 12% per month. What was the score 4 months ago?
The engagement score in 4 months would be 7.69
We are to determine the future value of engagement score in 4 months
The formula for calculating future value:
FV = P (1 + r)^n
FV = Future value
P = Present value = 4.89
R = rate of increase = 12%
N = number of months = 4
4.89 ( 1.12)^4 = 7.69
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An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Hope this can help you.
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Which of the following statements is false?
If a number is an integer, then it is irrational.
If a number is a natural number, then it is rational.
If a number is a fraction, then it is rational.
If a number is a whole number, then it is rational.
Answer:
If a number is an integer, then it is irrational. ⇒ false statement
Step-by-step explanation:
Let's check:
If a number is an integer, then it is irrational.
- incorrect, as all integers are rational
If a number is a natural number, then it is rational.
- correct, natural numbers are subset of rational numbers
If a number is a fraction, then it is rational.
- correct, they can be shown as p/q
If a number is a whole number, then it is rational.
- correct, whole numbers are subset of rational numbers
The statement "If a number is an integer, then it is irrational" is false.
Which of the following statements is false?The statement "If a number is an integer, then it is irrational" is false. This is because not all integers are irrational.
The other statements are all true:
"If a number is a natural number, then it is rational." This is true because all natural numbers are integers, and all integers are rational.
"If a number is a fraction, then it is rational." This is true because a fraction is a number of the form p/q, where p and q are integers and q is not equal to 0. Any number of this form is rational.
"If a number is a whole number, then it is rational." This is true because all whole numbers are integers, and all integers are rational.
Therefore, the false statement is the first one: "If a number is an integer, then it is irrational."
Below is a table summarizing the statements:
Statement Truth value
If a number is an integer, then it is irrational False
If a number is a natural number, then it is rational True
If a number is a fraction, then it is rational True
If a number is a whole number, then it is rational True
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Use the order of operations to simplify this expression 1.2x3.5x4.1= What
[tex] 1.2\times3.5\times4.1=[(1+0.2)(3+0.5)](4+0.1)[/tex]
$=[1\times3+1\times0.5+0.2\times3+0.2\times0.5](4+0.1)$
$=(3+0.5+0.6+0.1)(4+0.1)$
$=(4.2)(4+0.1)=(4+0.2)(4+0.1)$
$=4\times4+4\times0.1+0.2\times4+0.2\times0.1$
$=16+0.4+0.8+0.02=17.22$
simplify theta(sin theta) ²/2tan theta
Step-by-step explanation:
When θ is very small, θ ≈ sin θ ≈ tan θ.
θ (sin θ)² / (2 tan θ)
θ³ / (2θ)
θ² / 2
What is 3.142857 rounded three decimal places
Answer:
3.143
Step-by-step explanation:
Since you're rounded it to the third decimal, you look at the fourth one. And since the fourth one is 8, ur going round 2, which is the third decimal to 3.
Answer:
The answer is below
Step-by-step explanation:
In this question, to round three decimal place, we need to count three numbers after the dot.
Here..
the three numbers are 142
so after that we round it, so first of all we ignore 1 and, and focus on the number 2 and 4.
and if the number is below 5, it is rounded to the last number, but if the number is 5 or more than it, then we round it to the next number.
For example
142 - here we have 2, which is below 5, so we round it to '140'
where as if we have..
147 - here we have 7, which is above 7, so we round it to '150'
____________________________________________________________
So in this problem we round 142, so the number 2 is below 5 so it is round to 140
therefore the answer is - 3.14
According to a study, the probability that a randomly selected teenagar shopped at a mall at least once during a week was 0.61. Let X be the number of students in a randomly selected group of 50 that will shop at a mall during the next week. (a) Compute the expected value and standard deviation of X. expected value standard deviation (b) Fill in the missing quantity. (Round your answer to the nearest whole number.)There is an approximately 2.5% chance that _____ or more teenagers in the group will shop at the mall during the next week.
Answer:
Step-by-step explanation:
Given that:
p = 0.61
If X is the the number of students in a randomly selected group of a sample size n = 50
The expected value and the standard deviation can be computed as follows:
The expected value E(X) = np
The expected value E(X) = 50 × 0.61
The expected value E(X) = 30.5
The required standard deviation = [tex]\sqrt{np(1-p)}[/tex]
The required standard deviation = [tex]\sqrt{30.5(1-0.61)}[/tex]
The required standard deviation = [tex]\sqrt{30.5(0.39)}[/tex]
The required standard deviation = [tex]\sqrt{11.895}[/tex]
The required standard deviation = 3.4489
The required standard deviation = 3.45
(b) Fill in the missing quantity. (Round your answer to the nearest whole number.)
There is an approximately 2.5% chance that _____ or more teenagers in the group will shop at the mall during the next week.
From the given information:
Now, we can deduce that:
the mean = 30.5
standard deviation = 3.45
Using the empirical rule:
At 95% confidence interval;
[μ - 2σ, μ + 2σ] = [ 30.5 - 2(3.45) , 30.5 + 2(3.45)]
[μ - 2σ, μ + 2σ] = [ 30.5 - 6.9 , 30.5 + 6.9]
[μ - 2σ, μ + 2σ] = [ 23.6, 37.4]
The 2.5% of the observations are less than 95% confidence interval and 2.5% observations are greater than 95% confidence interval.
The required number of teenagers is = the upper limit of the 95% confidence interval = 37
There is an approximately 2.5% chance that __37___ or more teenagers in the group will shop at the mall during the next week.
Given the following computer printout for a set of sample data, which one of the following represents the value of the Interquartile Range?
Descriptive Statistics: Cycle Time
Variable N Mean StDev Variance Minimum Q1 Median Q3 Maximum
Cycle Time 52 31.808 5.333 28.436 21.700 27.825 31.000 36.075 44.000
A. 22.3
B. 3.175
C. 5.075
D. 8.25
Answer: D. 8.25
Step-by-step explanation: A data set can be divided into 4 equal parts, called Quartile. A quartile divides the data into three points:
Lower quartile: Q1;Median: Q2;Upper quartile: Q3;Interquartile Range (IQR) is a measure of variability based on data divided into quartiles or the measure of where the bulk of the values are.
To calculate interquartile range:
IQR = Q3 - Q1
The table shows Q1 = 27.825 and Q3 = 36.075, then
IQR = 36.075 - 27.825
IQR = 8.25
The value of interquartile range is 8.25.
Suppose that 80% of all registered California voters favor banning the release of information from exit polls in presidential elections until after the polls in California close. A random sample of 25 registered California voters is selected.
Required:
a. Calculate the mean and standard deviation of the number of voters who favor the ban.
b. What is the probability that exactly 20 voters favor the ban?
Answer:
a. Mean = 20
Sd = 4
b. Probability of X = 20 = 0.1960
Step-by-step explanation:
we have
n = 25
p = 80% = 0.8
mean = np
= 0.8 * 25
= 20
standard deviation = √np(1-p)
= √25*0.8(1-0.8)
=√4
= 2
probability that exactly 20 favours ban
it follows a binomial distribution
= 25C20 × 0.8²⁰ × 0.2⁵
= 53130 × 0.01153 × 0.00032
= 0.1960
Probability of X = 20 = 0.1960
Which expression is equivaleny to 0.7 + p + 0.86p?
A.1 + 1.56p
B.p + 1.56
C.2.56p
D. -0.84p
Answer:
None of the above.
1.86p + 0.7
Step-by-step explanation:
Step 1: Write expression
0.7 + p + 0.86p
Step 2: Combine like terms
0.7 + 1.86p
None of those answer choices are correct unless you wrote the problem incorrectly.
Find the length of the arc.
A. 539π/12 km
B. 9π/3 km
C. 9π/2 km
D. 18π km
Answer:
b because it is I found out cus I took test
The length of the arc 9π/2 km.
The answer is option C.9π/2 km.
What is the arc of the circle?
The arc period of a circle can be calculated with the radius and relevant perspective using the arc period method.
⇒angle= arc/radius
⇒ 135°=arc/6km
⇒ arc =135°*6km
⇒arc=135°*π/180° * 6km
⇒arc = 9π/2 km
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Which equation does the graph of the systems of equations solve? (1 point) 2 linear graphs. They intersect at negative 1, 1
Answer:
3x +4 = -2x -1
Step-by-step explanation:
The line that goes up to the right has a y-intercept of +4. This is where it crosses the y-axis. It's slope (rise/run) is 3/1 = 3, so its equation in slope-intercept form is ...
y = mx +b . . . . where m is the slope, b is the y-intercept
y = 3x +4
The other line has a negative slope and a y-intercept of -1. The slope of that line is rise/run = -2/1 = -2, so its equation is ...
y = -2x -1
__
The solution point will have the x-coordinate that is the solution of the equation ...
y = y
3x +4 = -2x -1 . . . . . . substituting the above expressions for y.
How many variable terms are in the expression 3x3y + 5x2 − 4y + z + 9?
Answer:
4
Step-by-step explanation:
"4" is the number of variable terms that are in the expression 3x3y + 5x2 _ 4y + z + 9. The four variable terms in the expression are "xy", "x^2", "y" and "z". I hope that this is the answer that you were looking for and the answer has actually come to your desired help. If you need any clarification, you can always ask.
Convert 1.6 L to cubic centimeters
Answer:
1600
Step-by-step explanation:
multiply the volume value by 1000
1
) Solve the equation
(85) for n.
8n
n =
?
Answer:
n = -10
Step-by-step explanation:
1 / 8^n = 8^5^2
We know that 1/a^b = a^-b
We also know that a^b^c = a^(b*c)
8^-n = 8^(5*2)
8^-n = 8^(10)
Since the bases are the same, the exponents are the same
-n = 10
n = -10
solve for x ! please help . (show work)
Answer:
x = -3
Step-by-step explanation:
12 - 4x-5x = 39
Combine like terms
12 - 9x = 39
subtract 12 from each side
12 -9x-12 = 39-12
-9x = 27
Divide by -9
-9x/-9 = 27/-9
x = -3
The graph shown is the solution set for which of the following inequalities?
Answer:
b is your answer hope it is helpful
Answer:
b is the correct answer
Step-by-step explanation:
the answer is b
Which equation represents this statement: A number minus 6 is 168? 6 − n = 168 n ÷ 6 = 168 n − 6 = 168 6n = 168
Answer:n-6=168
Step-by-step explanation:
The statement starts with the variable first.
Answer:
n - 6 = 168.
Step-by-step explanation:
Let's say that the value of the number is n.
n minus 6 is 168, so n - 6 = 168.
n - 6 = 168
n = 174.
Hope this helps!
Which expression is the radical form of 1/5b
Answer:
1st option, ⁵√b
Step-by-step explanation:
b⅕
= ⁵√b (radical form)
Rectangle TUVW is dilated by a scale factor of 3
3 to form rectangle T'U'V'W'. Side U'V' measures 93
93. What is the measure of side UV?
Answer:
31
Step-by-step explanation:
93/3=31
So UV is equal to 31
Answer:
31
Step-by-step explanation:
There are 47 contestants at a national dog show. How many different ways can contestants fill the first place, second place, and third place positions?
Answer:
97290
Step-by-step explanation:
47 different people can win first
47
Now there are only 46 people left
46 different people can win second
46
45 different people can win third
47*46*45
97290
Q4.B/ Evaluate the integral
Answer:
answer 6
Step-by-step explanation:
It has been a long time that i have done that!
[tex]\int\limits^3_2 {\int\limits^2_0 {(4-y^2)} \, dy} \, dx \\\\\\=\int\limits^3_0 {(4-y^2)} \, dy*(2-0)\\\\=2*[4y-\dfrac{y^3}{3} ]^3_0\\\\=2*(12-9)\\\\=6\\[/tex]
The scale on a map is
1:25 000
(a) On a map, a distance
measures 5cm. What is this
in real life? Give your
answer in kilometres.
(b) In real life a distance is
2.2km. What would this be in
the map in centimetres?
Answer:
Step-by-step explanation:
a) 5 cm(25000)(1 m/100 cm)(1 km/1000 m) = 1.25 km
b) 2.2 km (1000 m/km)(100 cm/m) / 25000 = 8.8 cm
the difference between a number and 6
Step-by-step explanation:
=The difference between a number and 6
the term difference is used in mathmatics as subtraction
let x = a number
x - 6 = the difference between that unknown number and 6
Answer:
Step-by-step explanation:
difference means subtract. Difference is always worded the same way. What you have written means that you start with an algebraic letter and then comes the minus sign and then the number
Let the number = x
x - 6
If it was worded as difference between 6 and a number, you would write it this way
6 - x
-7/3+1/2w= -9/5
What is w?
Answer:
w = 124/15 = 8 4/15
Step-by-step explanation:
[tex]-\frac{7}{3}+\frac{1}{2}w=-\frac{9}{5}\\\\\frac{1}{2}w=\frac{62}{15}\\\\w=\frac{124}{15}=8\frac{4}{15}[/tex]
Evaluate the expression when a= 2 and c= -7. C-4a answer
Answer:
-15
Step-by-step explanation:
Let a = 2 and c = -7.
[tex]c-4a\\(-7)-4(2)\\-7-8\\-15[/tex]
we know that the value of a is 2 and c is -7
Expression-
c-4a
= (-7)-4×2
= (-7)-8
= -15
~