The Moon orbits Earth its position relative to the Sun changes causing different portions of the Moon's surface to be illuminated.
This creates predictable cyclic patterns, such as the phases of the Moon.
The Moon reflects sunlight as it orbits Earth due to its surface features, which include mountains, valleys, and craters.
These features scatter and reflect sunlight in different directions.
And causing the Moon to appear differently lit depending on its position relative to the Sun and Earth.
The phases of the Moon are determined by the amount of sunlight that is reflected from its surface as it orbits Earth.
When the Moon is between the Sun and Earth, its illuminated side faces away from Earth.
And causing the Moon to appear dark, known as a new moon.
As the Moon moves in its orbit, more and more of its illuminated side becomes visible from Earth.
And causing the Moon to appear to grow in size and brightness.
Until it reaches a full moon when the entire illuminated side is visible.
The cycle then repeats as the Moon moves in its orbit.
And causing the amount of illuminated surface visible from Earth to decrease until it reaches another new moon.
This cyclic pattern of changing illumination creates the predictable phases of the Moon that can be observed from Earth.
learn more about orbit here
brainly.com/question/19954117
#SPJ4
fiona divided 3x2+5x-3 by 3x+2. the expression represents the remainder over the divisor.what is the value of a? -5-115
The value of a is -5 after Fiona divided 3x² + 5x - 3 by 3x+2.
To find the value of a, we need to perform a polynomial division of 3x² + 5x - 3 by 3x + 2. The result of the division is a polynomial plus a remainder, which should be equal to ax + b for some constants a and b. The constant b represents the remainder over the divisor, so we can set the expression equal to b to find its value. When dividing 3x² + 5x - 3 by 3x + 2 using polynomial long division, we get:
x
3x + 2 | 3x² + 5x - 3
- 3x² - 2x
3x - 3
3x + 2
-5
Therefore, the remainder is -5, which is represented by the expression a = -5.
Learn more about Division:
https://brainly.com/question/25289437
#SPJ4
bill invests 160 at the start of each month for 22 months, starting now. if the investment yields 0.5% per month, compunded monthly, what is its value at the end of 22 months?> calculus
We will use the future value of a series formula to solve this problem. The terms you want me to include are invests, investment, and compounded.
Here's a step-by-step explanation:
1. Bill invests $160 at the start of each month for 22 months. This is a regular investment, and we will treat it as an ordinary annuity.
2. The investment yields 0.5% per month, compounded monthly. We'll convert the percentage to a decimal by dividing it by 100, so the monthly interest rate (r) is 0.005.
3. We will use the future value of an ordinary annuity formula to find the value of the investment at the end of 22 months:
FV = P * [(1 + r)^n - 1] / r
Where FV is the future value of the investment, P is the monthly investment ($160), r is the monthly interest rate (0.005), and n is the number of months (22).
4. Plug in the values and calculate:
FV = 160 * [(1 + 0.005)^22 - 1] / 0.005
FV = 160 * [(1.005)^22 - 1] / 0.005
FV = 160 * [1.113688 - 1] / 0.005
FV = 160 * 0.113688 / 0.005
FV = 3,627.232
The value of Bill's investment at the end of 22 months is approximately $3,627.23.
Learn more about future value here: brainly.com/question/14860893
#SPJ11
Noah is mixing 1/2 cup cinnamon and 1/3 cup not made for a spiced Peco n recipe he uses at his restaurant 1 pound of spice pecans good mood made 1/6 cup of mixture from the recipe Noah has a large container of cinnamon and large container of nutmeg each containing 12 3/4 cups of the spices Noah says that he has enough of the spices to make 130 pounds of spiced pecans shower explain whether or not know is correct
Noah needs 195 cups of cinnamon and 130 cups of nutmeg to make 130 pounds of spiced pecans.
Noah is not correct in claiming that he has enough spices to make 130 pounds of spiced pecans.
To begin with, let's look at the recipe Noah uses. He mixes 1/2 cup of cinnamon and 1/3 cup of nutmeg to make 1/6 cup of the spice mixture.
=> 1/3 + 1/6 = (2 +1)/ 6 = 3/6 = 1/2
So, the amount of cinnamon required would be
=> 130*(1/2) = 195 cups or 15 3/4 quarts.
Similarly, the amount of nutmeg required would be
=> 130 * 1 = 130 cups or 10 1/4 quarts.
Now, let's see if Noah has enough spices to make 130 pounds of spiced pecans. We can add the amount of cinnamon and nutmeg required, which is
=> 195 cups + 130 cups = 325 cups (or 26 quarts).
This is more than the amount of spices Noah has, which is only 2 quarts.
Therefore, Noah is not correct in claiming that he has enough spices to make 130 pounds of spiced pecans. He would need more than 12 times the amount of spices he currently has in order to make that amount.
To know more about mixture here
https://brainly.com/question/23014
#SPJ4
The shape below is formed of a quarter circle with two
semicircles added to it. The radius of the quarter circle is x.
a) What is the perimeter of the shape if x = 4? Give your answer in terms of in its simplest form.
b) Write an expression for the perimeter of the shape in terms of x and pi. Give your answer in its simplest form.
a) The perimeter of the shape is 10π.
b) The expression for the perimeter of the shape in terms of x and π is (5/2)πx.
The shape consists of a quarter circle with radius x, and two semicircles with radius x as well.
a) To find the perimeter of the shape when x = 4, we need to first find the length of each component of the shape.
The quarter circle has an arc length of one-fourth the circumference of a circle with radius x, which is:
arc length = (1/4) × 2πx = (1/2)πx
The two semicircles each have a circumference of half the circumference of a circle with radius x, which is:
circumference = πx
Therefore, the total perimeter of the shape is:
perimeter = arc length + 2 × circumference
= (1/2)πx + 2πx
= (5/2)πx
When x = 4, the perimeter of the shape is:
perimeter = (5/2)π(4) = 10π
b) To write an expression for the perimeter of the shape in terms of x and π, we use the same calculations as above:
arc length = (1/2)πx
circumference = πx
Therefore, the perimeter of the shape is:
perimeter = arc length + 2 × circumference
= (1/2)πx + 2πx
= (5/2)πx
So the expression for the perimeter of the shape in terms of x and π is:
perimeter = (5/2)πx
for such more question on perimeter
https://brainly.com/question/23875717
#SPJ11
Which point on the y-axis lies on the line that passes through point g and is parallel to line df?.
The point on the y-axis that lies on the line passing through point g and is parallel to line df is (0, 9).
To find the point on the y-axis that lies on the line passing through point g and is parallel to line df, we first need to determine the slope of line df. Since the line is parallel to the new line passing through point g, the slope will be the same.
Once we have the slope, we can use point-slope form to find the equation of the new line. Then, we can set x=0 (since we want to find the point on the y-axis) and solve for y to find the y-coordinate of the point.
So, let's begin.
First, let's find the slope of line df. We can use the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two points on the line. We can use the points d and f, which are (5, 3) and (10, 8), respectively.
slope = (8 - 3) / (10 - 5) = 1
So the slope of line df is 1.
Now, using point-slope form, we can find the equation of the new line passing through point g (which is (-2, 7)) and having a slope of 1. The formula for point-slope form is:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is any point on the line (in this case, point g). Substituting in our values, we get:
y - 7 = 1(x - (-2))
y - 7 = x + 2
y = x + 9
So the equation of the new line is y = x + 9.
To find the point on the y-axis that lies on this line, we set x=0:
y = 0 + 9
y = 9
So the point on the y-axis that lies on the line passing through point g and is parallel to line df is (0, 9).
to learn more about equation click here:
brainly.com/question/2228446
#SPJ11
A group of veterinarians at a major veterinary hospital was interested in investigating a possible link between enteroliths, stones that form in the colon of horses, and diet. They decided to conduct a survey of feeding practices of horses admitted to the veterinary hospital. To obtain a simple random sample they used a computer to generate four-digit ID numbers for all horses. They used random digit tables to select the horses. Which is a step in selecting a random sample by this procedure?
1. Pick a random starting point in the table and read four digits.
2. Read four digits across a line and, if the four digits correspond to a horse ID, select the animal.
3. Discard any sequence that does not correspond to a horse ID and move to the next four digits.
4. All of the answer choices are correct.
1. Pick a random starting point in the table and read four digits.
This is the step in selecting a random sample by this procedure
What is sample?
In statistics, a sample refers to a group of individuals, objects, or events that are selected from a larger population to represent that population. Sampling is the process of selecting a subset of individuals or items from a larger population in order to infer something about the whole population.
The step in selecting a random sample by the procedure described in the scenario is step 1: Pick a random starting point in the table and read four digits. This step ensures that the selection of horses is entirely random, with each horse having an equal chance of being chosen. By starting at a random point in the table and selecting the first four digits, the veterinarians are eliminating any possible bias in the selection process. The subsequent steps involve using the selected four digits to determine if they correspond to a horse ID, discarding any sequences that do not match, and repeating the process until the desired sample size is reached.
To learn more about sample visit:
https://brainly.com/question/27829028
#SPJ4
2(x+3)=x-4 how to work this out?
Answer:
X = -10
Step-by-step explanation:
work is in picture.
Hope this helps! Pls give brainliest!
What is the smallest irrational number from problem #4?
#4 is down there to
The smallest irrational number from the given set of irrational numbers is -√27
To determine the smallest irrational number from the given options, we need to identify which numbers are irrational. A rational number is any number that can be expressed as a ratio of two integers, while an irrational number cannot.
√5 is an irrational number because it cannot be expressed as a ratio of two integers. Similarly, -√27 is also irrational, since it cannot be expressed as a ratio of two integers.
√25, on the other hand, is a rational number because it equals 5 which can be expressed as a ratio of two integers, 5/1. 1/4 is also a rational number since it equals 0.25, which can be expressed as a ratio of two integers, 1/4. 0.2345678... appears to be a decimal expansion that goes on indefinitely, but it is rational since it can be expressed as a ratio of two integers by finding the pattern of the repeating digits.
Therefore, the smallest irrational number from the given options is -√27 since it is the only negative irrational number and has the smallest absolute value among the irrational numbers given.
To learn more about irrational number click on,
https://brainly.com/question/29259282
#SPJ1
Determine whether the series is convergent or divergent. Sigma n=1 7 sin 1/n Part 1 of 4 The Limit Comparison Test allows us to determine convergence or divergence by considering lim n right arrow bn We will use an = sin 1/n and bn = 1/n . The terms 1/n are positive since n is positive. Since 0 < 1/n < pi/2 then the terms sin 1/n are positive Now, lim n right arrow infinity an/bn=lim n right arrow infinity sin 1/n/1/n. If we substitute m=1/n, then we have m right arrow lim sin m/m
According to the given information, the series Σ(sin(1/n)) diverges.
What is the convergence and divergence of the sequence?
Convergence: A sequence approaches a fixed number as the number of terms increases.
Divergence: A sequence does not approach a fixed number as the number of terms increases.
We have:
aₙ = sin(1/n)
bₙ = 1/n
Note that both aₙ and bₙ are positive for n > 0.
We will use the limit comparison test to determine if the series converges or diverges. To do this, we will compare the given series to a known series whose convergence or divergence is already known. We will choose the series Σ(1/n) as our comparison series since it is a p-series with p = 1, which is known to diverge.
Taking the limit as n approaches infinity of aₙ/bₙ, we get:
lim n→∞ (sin(1/n)/(1/n))
We can evaluate this limit using L'Hopital's rule:
lim n→∞ (cos(1/n) * (-1/n²)) / (-1/n²)
= lim n→∞ cos(1/n)
Since the cosine function is continuous, we can substitute the limit as m = 1/n:
lim m→0 cos(m)
cos(m) is continuous at m=0, and cos(0) = 1, so
lim m→0 cos(m) = 1
Since the limit of aₙ/bₙ is a finite, positive value, we conclude that the series Σaₙ and the series Σbₙ have the same behavior; that is, either they both converge or they both diverge. Since the series Σbₙ diverges, the series Σaₙ also diverges.
Therefore, the series Σ(sin(1/n)) diverges.
To know more about convergent and divergent sequence visit:
brainly.com/question/15415793
#SPJ4
In a fraction thrice the numerator is 2 more than the dominator. If 2 is added to the numerator and to the denominator the new fraction become 3/5 find the original fraction
The original fraction is 5/2
What is a fraction?A fraction can be defined as the part of a whole number, element or variable.
The different types of fractions are;
Mixed fractionsSimple fractionsProper fractionsImproper fractionsComplex fractionsFrom the information given, we have that;
Let the numerator be x = 3x
x/3x - 2
. If 2 is added to the numerator and to the denominator
Then, we have;
x + 2/3x = 3/5
cross multiply the values, we get;
5(x + 2) = 3x(3)
expand the bracket
5x + 10 = 9x
collect the like terms
-4x = -10
Make 'x' the subject of formula
x = 5/2
Learn about fractions at: https://brainly.com/question/11562149
#SPJ4
The process of determining the effect of changing objective function coefficients, right-hand side values of constraints, and decision variable values on a linear program is known as what?
The process of determining the effect of changing objective function coefficients, right-hand side values of constraints, and decision variable values on a linear program is known as sensitivity analysis.
Sensitivity analysis helps to understand how changes in the input parameters affect the optimal solution of a linear program. By analyzing the sensitivity of the solution to changes in the parameters, decision-makers can gain insight into the behavior of the model and make more informed decisions.
Sensitivity analysis involves computing the range of values over which the current optimal solution remains optimal, known as the range of optimality. It also involves computing the shadow prices, which indicate the change in the optimal objective function value per unit change in the right-hand side of a constraint. The shadow prices can help decision-makers understand the value of additional resources or the cost of resource shortages.
for such more question on sensitivity analysis
https://brainly.com/question/13266122
#SPJ11
What is the first step to solve 11(5 + 4x) = 55 ?
Answer:
the first step is 55 + 44x = 55Step-by-step explanation:
What is the first step to solve 11(5 + 4x) = 55 ?11 x (5 + 4x) = 55
55 + 44x = 55
44x = 55 - 55
44x = 0
x = 0
----------------
check
11 x (5 + 4 x 0) = 55
11 x 5 + 0 = 55
55 = 55
Answer / Step-by-step explanation:
So when it comes to solving equations there are cases where you can take any many different steps first. Fortunately, in this case there's only one way to approach the problem easily, and it is by applying the distributive property of multiplication in order to solve the parenthesis. Check out the attached image.
Then, using the property, we can rewrite the equation as follows:
[tex]\sf (11)(5)+(11)(4x)=55\\ \\\rightarrow55+44x=55[/tex]
-------------------------------------------------------------------------------------------------------
Learn more about solving equations here:brainly.com/question/30596312
brainly.com/question/28282032
brainly.com/question/28306861
brainly.com/question/28285756
brainly.com/question/28306307
brainly.com/question/30015231
brainly.com/question/29888440
brainly.com/question/31757124
The Differential Equations Depicting The Dynamics Of Four Single-Input-Single-Output (SISO) Systems Are Given Below. (I) The differential equations depicting the dynamics of four Single-Input-Single-Output (SISO) systems are given below. (i) )+0.25y(t) +1.25y(t) u(t) (ii) y()y(t)+0.25y(t)+1.25y(t)u(t) (iii) y) +0.25ý(t) +1.25y(t) = u-(t) (iv) t) +0.25y(t) +1.25y(t) -u(t)+u(t) Determine which ones are linear and which are not.
Systems (i) and (ii) are linear, while systems (iii) and (iv) are nonlinear.
A linear system satisfies the properties of superposition and homogeneity, meaning that if the input is scaled or if multiple inputs are added together, the output will also be scaled or added together accordingly. Systems (i) and (ii) are both linear since they both satisfy these properties. However, systems (iii) and (iv) are nonlinear since they do not satisfy the properties of superposition and homogeneity. System (iii) contains a non-linear term (y(t))^2 and system (iv) contains a non-linear term (u(t))^2.
The determination of whether a system is linear or nonlinear can have important implications for the analysis and control of the system. It is important to recognize the differences between these types of systems in order to effectively model and manipulate them.
To know more about linear system visit:
https://brainly.com/question/21404414
#SPJ11
Two similar rectangular prisms have surface areas of 112 square centimeters and 1008 square centimeters. If the length and width of the base of the smaller prism are 4 centimeters and 2 centimeters, respectively, what is the perimeter of one base of the larger prism?
If 2 similar "rectangular" shaped prisms have surface-area as 112 cm² and 1008 cm², then base perimeter of larger prism is 36 cm.
In order to calculate the Perimeter, we first calculate the "scale-factor" "k",
The "Scale-Factor" "k" is defined as the ratio of area of two figures which are similar,
So, (area of small rectangular prism)/(area of large rectangular prism) = k²,
Substituting the values of "Area",
We get,
⇒ k² = 112/1008,
⇒ k = 1/3,
Now, we use this "scale-factor" to find the value of the length and width of the "large-rectangular-prism".
For the length:
⇒ (length of small rectangular prism)/(length of large rectangular prism) = k,
⇒ 4/x = k,
⇒ 4/x = 1/3,
⇒ x = 12 cm.
For the width,
⇒ (width of small rectangular prism)/(width of large rectangular prism) = k,
⇒ 2/y = 1/3,
⇒ y = 6.
We know that the Perimeter(P) of base of Larger-Prism is calculated by the formula : 2l + 2w,
Substituting the values of Length(l) = 12 cm and width(w) = 6 cm,
We get,
⇒ Perimeter = 2×12 + 2×6 = 24 + 12 = 36 cm.
Therefore, the required Perimeter is 36 cm.
Learn more about Perimeter here
https://brainly.com/question/9572182
#SPJ1
Describe how the critical value of t for a​ 95% confidence interval changes as the number of degrees of freedom increases.
The number of degrees of freedom increases, the t-distribution becomes closer to the standard normal distribution, and the critical value of t approaches the value of 1.96, which is the critical value of z for a 95% confidence interval based on the standard normal distribution.
The critical value of t for a 95% confidence interval changes as the number of degrees of freedom increases in the following way:
As the number of degrees of freedom increases, the critical value of t decreases.
This is because the t-distribution becomes more concentrated around its mean of 0 as the number of degrees of freedom increases.
The t-distribution is a family of probability distributions that depend on the number of degrees of freedom.
The number of degrees of freedom is small, the t-distribution has more spread or variability, and the tails of the distribution are wider than the normal distribution.
The number of degrees of freedom increases, the t-distribution approaches the normal distribution, which has a fixed and known critical value for a given level of confidence.
If we consider a 95% confidence interval with 10 degrees of freedom, the critical value of t is approximately 2.228.
But if we increase the degrees of freedom to 50, the critical value of t decreases to approximately 2.009.
For similar questions on degrees of freedom
https://brainly.com/question/28527491
#SPJ11
Convert radians to degrees
Convert [tex]\frac{11\pi }{12}[/tex] radians = 165 degree.
Converting Between Radians and Degrees:Radians and degrees are units used to measure angles in mathematics. As with any two units that are used to measure the same thing, we can convert between radians and degrees. We do this by using the fact that π radians is equal to 180°.
Now, Convert [tex]\frac{11\pi }{12}[/tex] radians to degrees.
To convert radians to degrees, multiply by [tex]\frac{180}{\pi }[/tex], since a full circle is 360° or [tex]2\pi[/tex] radians.
=> [tex](\frac{11\pi }{12}).\frac{180}{\pi }[/tex]
Cancel the common factor of 12
[tex]\frac{11}{12}.{12(15)}[/tex]
Combine 11 and 15 we get
= > 165°
Learn more about Conversion of radians at:
https://brainly.com/question/30460685
#SPJ1
you have started your position as transportation director in a small town called mountainside village. there is only one road in and out of town. today you can expect at peak traffic to see 35 cars per hour and the drive along the road with no traffic is 1 minute. assuming poisson arrival and exponential drive times, what is the current utilization of the road? (4 points)
The current utilization of the road is 0.5833 or 58.33%. To calculate the current utilization of the road, we need to use the formula:
Utilization = Arrival rate x Drive time
Since we are assuming Poisson arrival and exponential drive times, we can use the following formulas:
Arrival rate = λ = 35 cars per hour
Drive time = 1/μ = 1/60 hours (since the drive time is 1 minute)
Therefore,
Utilization = 35 cars per hour x (1/60 hours)
Utilization = 0.5833 or 58.33%
So the current utilization of the road in Mountainside Village is 58.33%.
Hi! As the transportation director of Mountainside Village, we can calculate the current utilization of the road using the given terms. The peak traffic rate is 35 cars per hour, and the drive time without traffic is 1 minute (or 1/60 hours).
Since we're assuming Poisson arrival and exponential drive times, we can calculate the utilization (ρ) using the formula:
ρ = λ / μ
Here, λ represents the arrival rate (35 cars/hour), and μ represents the service rate, which is the inverse of the average drive time (1/60 hours).
So, μ = 1 / (1/60) = 60 cars/hour
Now, we can calculate the utilization:
ρ = 35 cars/hour / 60 cars/hour = 0.5833 (rounded to 4 decimal places)
Thus, the current utilization of the road is 0.5833 or 58.33%.
Visit here to learn more about exponential brainly.com/question/28596571
#SPJ11
Help pls and thank you
The measure of the largest angle (angle C) is approximately 87 degrees. So, correct option is A.
To find the value of x, we can use the Pythagorean theorem:
BC² = AB² + AC²
Substituting the given values, we get:
23² = 16² + AC²
529 = 256 + AC²
AC² = 273
AC = √273
Now, we can use the Law of Cosines to find the largest angle, which is opposite to the longest side (BC):
cos(C) = (a² + b² - c²) / 2ab
where a, b, and c are the lengths of the sides opposite to angles A, B, and C, respectively.
Substituting the given values, we get:
cos(C) = (16² + AC² - 23²) / 2(16)(AC)
cos(C) = (256 + 273 - 529) / (32√273)
cos(C) = 0.0838
C = cos⁻¹(0.0838)
C ≈ 87 degrees
Therefore, correct option is A.
To learn more about angle click on,
https://brainly.com/question/14400327
#SPJ1
What is the solution set for sin 1/2 x=cos x?
The solution set of the trigonometric equation is x = 60° or x = 180°
What is a trigonometric equation?A trigonometric equation is an equation that contains trigonometric ratios
Given the trigonometric equation sin(x/2) = cosx, we desire to find the solution set. We proceed as follows.
Using the half angle formula for sine, we have that
Sin(x/2) = √[(1 - cosx)/2]
So, substituting this into the equation, we have that
sin(x/2) = cosx,
√[(1 - cosx)/2] = cosx
Squaring both sides, we have that
√[(1 - cosx)/2]² = (cosx)²
(1 - cosx)/2 = cos²x
1 - cosx = 2cos²x
Re-arranging the equation, we have that
2cos²x + cos - 1 = 0
Let cosx = y
So,we have that
2y² + y - 1 = 0
Factorizing, we have
2y² + 2y - y - 1 = 0
2y(y + 1) - (y + 1) = 0
(2y - 1)(y + 1) = 0
⇒ 2y - 1 = 0 or y + 1 = 0
⇒ 2y = 1 or y = -1
⇒ y = 1/2 or y = -1
Since cosx = y, we have that
cosx = 1/2 or cosx = -1
Taking innverse cosine of both sides, we have that
x = cos⁻¹(1/2) or x = cos⁻¹(-1)
x = 60° or x = 180°
So, the solution set is x = 60° or x = 180°
Learn more about trigonometric equation here:
https://brainly.com/question/28025415
#SPJ1
a line passes through points p(-6,8,1) and q (-4,1,3). find the standard parametric equations for the line
The standard parametric equations for the line passing through points P and Q is [tex]$\begin{cases} x = -6 + 2t \ y = 8 - 7t \ z = 1 + 2t \end{cases}$[/tex] .
To find the standard parametric equations for the line passing through points P(-6, 8, 1) and Q(-4, 1, 3), we first need to find the direction vector of the line. This can be done by subtracting the coordinates of point P from the coordinates of point Q:
[tex]$\vec{PQ} = \begin{pmatrix}-4 \ 1 \ 3\end{pmatrix} - \begin{pmatrix}-6 \ 8 \ 1\end{pmatrix} = \begin{pmatrix}2 \ -7 \ 2\end{pmatrix}$[/tex]
Now we can write the parametric equations in the form:
[tex]$\begin{cases} x = x_0 + at \ y = y_0 + bt \ z = z_0 + ct \end{cases}$[/tex]
where (x0, y0, z0) is a point on the line and (a, b, c) is the direction vector.
We can choose either point P or Q as the point on the line. Let's use point P. So we have:
[tex]$\begin{cases} x = -6 + 2t \ y = 8 - 7t \ z = 1 + 2t \end{cases}$[/tex]
These are the standard parametric equations for the line passing through points P and Q.
To know more about Parametric equation visit:
https://brainly.com/question/10254343
#SPJ4
a coin is tossed 18 times. it lands on heads 12 times. what is the experimental probability of the coin landing on tails?
the experimental probability of the coin landing on tails is 1/3 or approximately 0.33 when expressed as a decimal when coin was flip 18 times and landed on heads 12times
In this case, the coin was flipped 18 times and landed on heads 12 times, so it landed on tails 6 times.
Therefore, the experimental probability of the coin landing on tails is 6/18, which simplifies to 1/3 or approximately 0.33.
. To calculate the experimental probability, follow these steps:
1. Determine the number of successful outcomes (times the coin landed on tails). In this case, the coin was tossed 18 times and landed on heads 12 times, so it must have landed on tails 6 times (18 - 12 = 6).
2. Determine the total number of trials (times the coin was tossed). In this case, it's 18.
3. Calculate the experimental probability by dividing the number of successful outcomes by the total number of trials:
Experimental probability of tails = (Number of tails) / (Total number of tosses) = 6 / 18
4. Simplify the fraction to get the experimental probability:
6 / 18 = 1 / 3
So, the experimental probability of the coin landing on tails is 1/3 or approximately 0.33 when expressed as a decimal.
To know more about Probability Visit:
https://brainly.com/question/30034780
#SPJ11
A box of writing utensils on a teacher's desk contains 5 red pencils, 7 green pencils, 9 red markers, and 4 green markers.
What is the probability of selecting a red writing utensil or a marker?
Answer:
18/25= 72%
Step-by-step explanation:
total writing utensils = 25
add red utensils ( 5 pencils + 9 markers) = 14 plus 4 markers = 18
18/25= 72%
The diagonals of kite KITE intersect at point P. If TKE= x+6 and IEK= 2x, find IKE
The length of IKE is 2x - 12.
What is equation?A condition on a variable that is true for just one value of the variable is called an equation.
Since KITE is a kite, we know that KT = IT and KE = IE. Let's call the length of these diagonals d. Then we have:
KT + TI = d
KE + EI = d
Substituting in the given values, we get:
x + 6 + 2x = d
2x + IE = d
Solving for d in the first equation, we get:
3x + 6 = d
Substituting this into the second equation, we get:
2x + IE = 3x + 6
Solving for IE, we get:
IE = x + 6
Therefore, IKE is equal to:
IKE = IT - IE
IKE = (d - KT) - (x + 6)
IKE = (3x + 6 - x - 6) - (x + 6)
IKE = 2x - 12
So, the length of IKE is 2x - 12.
Learn more about equation on:
https://brainly.com/question/27893282
#SPJ4
if you are using the critical value approach to do a single -tailed hypothesis on the population mean
When testing a hypothesis about a population proportion with a sample size greater than 100, the proper test statistic to use is the z statistic. Option (a)
The z statistic is the appropriate test statistic to use when testing a hypothesis about a population proportion and the sample size is over 100. This is because the central limit theorem applies, which states that as the sample size increases, the sampling distribution of the sample proportion becomes approximately normal.
Therefore, the test statistic can be calculated as the difference between the sample proportion and the hypothesized population proportion, divided by the standard error of the sampling distribution. The z score can then be compared to the critical values or p-values from the standard normal distribution to determine the level of statistical significance and make conclusions about the hypothesis being tested.
Learn more about z statistic.
https://brainly.com/question/30904553
#SPJ4
Full Question: if You are testing a hypothesis about a population proportion and a sample size is over 100 what is the proper test statistic to use?
A) z statstic
B) chi-square
c) t statistic
d) not enough data
1. data collected on commuting times to school, stated that the mean time to commute to school is 32 minutes, with a standard deviation of 11 minutes. assume the commuting times are normally distributed. a. what percentage of commuters take more than 45 minutes to get to school? b. what is the time for the fastest 20% of all commuters to school? c. if we apply the 68-95-99.7% rule, this shows us that 95% of time to commute will be between and minutes to get to school. d. determine the longest 1% of time to commute to school.
To find the percentage of commuters who take more than 45 minutes to get to school, we need to calculate the z-score first:
z = (45 - 32) / 11 = 1.18
Using a standard normal distribution table or calculator, we can find that the percentage of commuters who take more than 45 minutes to get to school is approximately 12.22%.
To find the time for the fastest 20% of all commuters to school, we need to calculate the z-score for the 20th percentile:
z = invNorm(0.2) = -0.84
The time for the fastest 20% of all commuters can be calculated using the formula:
x = μ + zσ = 32 + (-0.84) * 11 = 22.36 minutes
Therefore, the time for the fastest 20% of all commuters to school is approximately 22.36 minutes.
The 68-95-99.7% rule states that for a normally distributed data set, approximately 68% of the data falls within one standard deviation (σ) of the mean (μ), approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.
Since we know that the mean time to commute to school is 32 minutes with a standard deviation of 11 minutes, we can apply the 68-95-99.7% rule to find the range of time for 95% of commuters:
Within one standard deviation (σ) of the mean (32 ± 11), approximately 68% of commuters take between 21 and 43 minutes to get to school.
Within two standard deviations of the mean (32 ± 2*11), approximately 95% of commuters take between 10 and 54 minutes to get to school.
Therefore, the statement "this shows us that 95% of the time to commute will be between 10 and 54 minutes to get to school" is correct.
To determine the longest 1% of the time to commute to school, we need to calculate the z-score for the 99th percentile:
z = invNorm(0.99) = 2.33
The longest 1% of the time to commute to school can be calculated using the formula:
x = μ + zσ = 32 + (2.33) * 11 = 57.63 minutes
Therefore, the longest 1% of the time to commute to school is approximately 57.63 minutes.
Learn more about standard normal distribution, here:
brainly.com/question/30404390
#SPJ11
62% of all bald eagles survive their first year of life. if 45 bald eagles are randomly selected, find the probability that
This results in a probability of approximately 0.044, or 4.4%. the probability of any number of eagles surviving their first year can be calculated using the binomial probability formula.
The probability of a bald eagle surviving its first year of life is 62%. If 45 bald eagles are randomly selected, we can use the binomial probability formula to calculate the probability of a certain number of eagles surviving their first year.
P(x=k) = (n choose k) * p^k * (1-p)^(n-k)
Where n is the total number of trials (45), k is the number of successes (surviving eagles), p is the probability of success (0.62), and (n choose k) is the binomial coefficient.
To find the probability that exactly 20 eagles survive their first year, we plug in the values:
P(x=20) = (45 choose 20) * 0.62^20 * 0.38^25
This results in a probability of approximately 0.044, or 4.4%.
To know more about Probability Visit:
https://brainly.com/question/30034780
#SPJ11
calculate the gradient: a stream segment begins at 550 feet above sea level and ends at 100 feet above sea level. the length of this segment is 100 miles. what is the average gradient for this stream segment? note: if doing this during an exam, show your calculator to the camera so your instructor understands what you are doing. question 15 options: a) .22 feet/mile b) 5.5 feet/mile c) 4.5 ft/mile d) 1 feet/mile
The average gradient for the stream segment is calculated as the change in elevation divided by the horizontal distance:
gradient = (change in elevation) / (horizontal distance)
The change in elevation is the difference between the starting elevation (550 feet) and the ending elevation (100 feet):
change in elevation = 550 ft - 100 ft = 450 ft
The horizontal distance is given as 100 miles:
horizontal distance = 100 miles
Therefore, the average gradient is:
gradient = (450 ft) / (100 miles) = 4.5 ft/mile
So the answer is (c) 4.5 ft/mile.
Learn more about Gradient here:- brainly.com/question/21727173
#SPJ11
(Q1) The circumcenter of a(n) _____ triangle will be on the hypotenuse of the triangle.
The circumcenter of a right triangle will lie on the hypotenuse of the triangle.
The circumcenter is the point at which the perpendicular bisectors of the sides of a triangle intersect. In a right triangle, the perpendicular bisectors of the legs intersect at the midpoint of the hypotenuse. This point is equidistant from all three vertices of the right triangle and is the circumcenter of the triangle.
Since the midpoint of the hypotenuse lies on the hypotenuse itself, the circumcenter of a right triangle must also lie on the hypotenuse. In fact, the circumcenter of a right triangle coincides with the midpoint of the hypotenuse. This is a unique feature of right triangles, and it can be used to find the circumcenter and other important properties of these triangles.
Learn more about hypotenuse
https://brainly.com/question/29407794
#SPJ4
Given P(A) = 0.81, P(B) = 0.7 and P(B|A) = 0.8, find the value of
P(AnB), rounding to the nearest thousandth, if necessary.
Answer: 0.648
Step-by-step explanation:
We can use the formula P(B|A) = P(A and B) / P(A) to find P(A and B), where P(A and B) is the probability of both A and B occurring and P(A) is the probability of A occurring.
Rearranging the formula, we get:
P(A and B) = P(B|A) * P(A)
Substituting the given values, we get:
P(A and B) = 0.8 * 0.81 = 0.648
Therefore, the value of P(A and B) is 0.648, rounded to the nearest thousandth.
What are the solutions to the equation?
