The formula used to calculate the surface area of a triangular prism is:
S = bh + 2ah
Where S = surface area, b = length or side of the triangle, and h = height of the triangle.
For right triangles, the height can be calculated as:
c = a^(2) \+ b^(2)
c = the hypotenuse
a and b = the two sides of the triangle
How many three-letter passwords can be formed from the letters {A, B, J, K, X, Z} under the following circumstances. (a) If a letter can be repeated? three-letter passwords (b) If a letter cannot be repeated? three-letter passwords
The required password for different conditions are 216 and 120.
How to make the password with latter?(a) If a letter can be repeated, then we can use the multiplication principle to determine the number of possible passwords. For each of the three positions in the password, there are six choices of letters. Therefore, the total number of possible passwords is:
[tex]$6^3 = \boxed{216}$[/tex]
(b) If a letter cannot be repeated, then we can use the permutation formula to determine the number of possible passwords.
There are six choices for the first letter, five choices for the second letter (since one letter has already been used), and four choices for the third letter (since two letters have already been used). Therefore, the total number of possible passwords is:
[tex]$P(6,3) = 6 \times 5 \times 4 = \boxed{120}$[/tex]
Thus, required password for different conditions are 216 and 120.
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Evaluate the following expression
6^-3
Answer:
Exact Form: 1/216
Step-by-step explanation:
Use the sample data and confidence level given below to complete parts (a) through (d).
A drug is used to help prevent blood clots in certain patients. In clinical trials, among 4319 patients treated with the drug. 108 developed the adverse reaction of nausea. Construct a 99% confidence interval for the
proportion of adverse reactions.
a) Find the best point estimate of the population proportion p.
(Round to three decimal places as needed.)
b) Identify the value of the margin of error E.
E=
(Round to three decimal places as needed.)
c) Construct the confidence interval
P
(Round to three decimal places as needed)
d) Write a statement that correctly interprets the confidence interval.
Choose the correct answer below.
A. One has 99% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion
B. One has 99% confidence that the sample proportion is equal to the population proportion.
C. 99% of sample proportions will fall between the lower bound and the upper bound
D. There is a 99% chance that the true value of the population proportion will fall between the lower bound and the upper bound
a) Population proportion is the sample proportion: p' = 108/4319 ≈ 0.025. b) 0.007. c) (0.018, 0.032) d) Option A is correct statement.
Describe standard normal distribution ?In statistics, the standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. It is also called the Z distribution, where Z represents the standard normal variable.
The standard normal distribution is a continuous probability distribution that is symmetric around the mean of 0. The shape of the distribution is bell-shaped, with the majority of the data falling within 3 standard deviations from the mean.
The standard normal distribution is widely used in statistics and probability theory as a benchmark for comparing other normal distributions. It is particularly useful for converting other normal distributions into a standardized form, which allows for easier comparison and analysis.
a) The best point estimate of the population proportion is the sample proportion: p' = 108/4319 ≈ 0.025.
b) The margin of error E is given by E = z* ×√(p'(1-p')/n), where z* is the critical value of the standard normal distribution for a 99% confidence level. Using a table or calculator, we find that z* ≈ 2.576. Substituting the given values, we have E ≈ 0.007.
c) The confidence interval is given by p' ± E, or 0.025 ± 0.007. Using a calculator, we find that the lower bound is approximately 0.018 and the upper bound is approximately 0.032. Therefore, the 99% confidence interval for the proportion of adverse reactions is (0.018, 0.032).
d) A. One has 99% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
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90
17. What is matrix A + matrix B?
OA
[12
6
26
The sum of the matrices A + B is 5 8
2.6 2
To add two matrices, they must have the same dimensions (the same number of rows and the same number of columns).
To add two matrices A and B, you can add the corresponding elements of the two matrices and place the result in the corresponding position of a new matrix C.
In mathematical notation, if A and B are two matrices of the same dimensions, then the sum C = A + B is defined by:
C[i,j] = A[i,j] + B[i,j]
Using the above as a guide, we have the following:
A + B = 5 8
2.6 2
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Please help! (40 points) Find the common ratio for this geometric sequence. 1 1 1 2'8'32 8, 2, A.1 4 O A. B. 12/1 O B. O C. 4 OD. 2
Answer:
[tex]\textsf{A.} \quad \dfrac{1}{4}[/tex]
Step-by-step explanation:
Given geometric sequence:
[tex]8,\;2,\;\dfrac{1}{2},\;\dfrac{1}{8},\;\dfrac{1}{32}[/tex]
The common ratio for a geometric sequence can be found by dividing a term by the previous term.
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{2}{8}=\dfrac{2 \div 2}{8 \div 2} =\dfrac{1}{4}[/tex]
Therefore, the common ratio for the given geometric sequence is 1/4.
3. Find the composition (f ∘ g)(–2) for the functions f(x) = 2x + 1 and g(x) = x2 – 3.
SHOW YOUR WORK PLEASE
The composition (f ∘ g)(–2) = 3.
What is Function ?
In mathematics, a function is a relation between two sets of values, where each value in the first set (called the domain) is associated with exactly one value in the second set (called the range). A function can be represented by a formula or an equation, which specifies how the input values are transformed into output values.
To find the composition (f ∘ g)(–2), we need to apply the function g to –2 first, and then apply the function f to the result. Here's how we can do it:
First, we need to find g(–2) by substituting –2 for x in the expression for g(x):
g(–2) = (–2)2 – 3
g(–2) = 4 – 3
g(–2) = 1
Now that we have found g(–2) = 1, we can substitute it for x in the expression for f(x) to find f(g(–2)):
f(g(–2)) = 2(1) + 1
f(g(–2)) = 3
Therefore, the composition (f ∘ g)(–2) = 3.
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Write an equation for H, the number of times Noah’s beats in m minutes?
The equatiοn fοr H, the number οf times Nοah’s beats in m minutes is H = k * m
What is the equivalent expressiοn?Expressiοns that perfοrm the same functiοn regardless οf appearance are said tο be equivalent. If twο algebraic expressiοns are equivalent, then they have the same value when the same variable value is used.
Assuming yοu meant "Nοah's heart beats", the equatiοn fοr H, the number οf times Nοah's heart beats in m minutes can be given by:
H = k * m
where k is a cοnstant that represents the number οf heartbeats per minute.
The value οf k may vary depending οn the individual and their physical cοnditiοn.
Hence, the equatiοn fοr H, the number οf times Nοah’s beats in m minutes
is H = k * m
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Complete Question;
A persons resting heart rate is typically between 60 and 100 beats per minute. Nοah looks at his watch, and counts 8 heartbeats in 10 seconds.
Is his heart rate typical? Explain how you know.
Write an equation for h, the number of times Noahs heart beats (at this rate) in m minutes.
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
The three options given in the question are not the correct steps to solve the given quadratic equation.
What is quadratic equation?
A quadratic equation is a polynomial equation of the second degree, meaning it contains at least one term that is squared (raised to the power of 2).
The three steps that Inga could use to solve the quadratic equation [tex]2x^2 + 12x - 3 = 0[/tex] are:
1.Rewrite the equation in the form [tex]ax^2 + bx + c = 0[/tex], where a, b, and c are constants: [tex]2x^2 + 12x - 3 = 0.[/tex]
2.Use the quadratic formula x = [-b ± sqrt([tex]b^2[/tex] - 4ac)]/2a, where a = 2, b = 12, and c = -3, to find the values of x:
x = [-12 ± [tex]\sqrt{(12^2 - 4(2)(-3))[/tex]]/(2*2)
x = [-12 ± [tex]\sqrt{(156)[/tex]]/4
x = (-3 ± [tex]\sqrt{(39)[/tex])/2
3.Simplify the roots if possible:
x = (-3 + [tex]\sqrt{(39)[/tex])/2 or x = (-3 - [tex]\sqrt{(39)[/tex])/2
Therefore, the three options given in the question are not the correct steps to solve the given quadratic equation.
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Find the value of x.
Answer:
23°
Step-by-step explanation:
46 = 2x (Vertically opp. angles)
x = 46÷2
x = 23
Hope this helps!
pls like and mark as brainliest
Answer:
x = 23°
Step-by-step explanation:
46 = 2x
46/2 = 2x/2
x = 23°
Write equation of the graph Below. (EASY! 10 Points)
Using these limitations, determine the distance from the coal tray if the coal tray is 25 inches in width and when y = 0.685. Please see screenshot
Therefore, the distance from the coal tray is approximately 301.96 inches when the heat intensity is 0.685 and the width of the coal tray is 25 inches.
How is distance determined?We can write the following using the formula in the question:
[tex]P = 100/(1 + d^2)[/tex]
where d represents the proportion of the food's distance from the coals to the tray's width.
Substituting d = z/25 results in:
[tex]P = 100/(1 + (z/25)^2)[/tex]
With y = 0.685, we can replace P with P = 0.685 and find z:
[tex]0.685 = 100/(1 + (z/25)^2)[/tex]
By dividing the two sides by [tex](1 + (z/25)^2)[/tex], we get at:
[tex]0.685 + 0.685(z/25)^2 = 100[/tex]
If we simplify, we get:
[tex](z/25)^2 = (100/0.685) - 1(z/25)^2 = 145.9854[/tex]
When we square the two sides, we obtain:
[tex]z/25 = 12.0783z = 25*12.0783z = -25*12.0783[/tex]
Given that z cannot be negative, we decide:
Z=25 * 12.0783 * 301.9575 inches
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Find the middle term of the expansion of (2x/y^3)^12
To find the middle term of the expansion of (2x/y^3)^12, we need to first determine the number of terms in the expansion.
Using the formula for the binomial theorem, we know that the number of terms in the expansion of (2x/y^3)^12 is 13.
Now, to find the middle term, we need to find the term that is in the middle of the expansion. Since there are 13 terms in the expansion, the middle term is the 7th term.
The general term of the expansion is given by:
T(r+1) = (12 C r) (2x)^r (y^-3)^(12-r)
So, the 7th term is:
T(8) = (12 C 7) (2x)^7 (y^-3)^(5)
Simplifying this expression, we get:
T(8) = (792) (128x^7 / y^15)
Therefore, the middle term of the expansion is 792(128x^7/y^15)
Find the values mi
, i=1,2
, for which
y(x)=emix
is a solution of the differential equation
d2ydx2−12dydx+32y=0.
The functions y(x) = [tex]e^{4x}[/tex] and y(x) = [tex]e^{8x}[/tex] are therefore solutions of the specified differential equation.The values of mi = 4 and 8.
What is a differential equation?A differential equation is an equation with one or more terms and one or more derivatives of the dependent variable with regard to the independent variable. (i.e., independent variable) dy/dx equals f(x) Here, the independent variable "x" and the dependent variable "y" are both present. So, dy/dx equals 5x, for instance.
We are given with differential equation
[tex]\frac{d^{2}y }{dx^{2} } - 12 \frac{dy}{dx} + 32y = 0[/tex]
We need to find the values of m1 and m2
[tex]y(x) = e^{m1x} and y(x) = e^{m2x}[/tex]are solutions to the differential equation.
First, we solve the differential equation for [tex]y(x) = e^{mx}[/tex]to obtain:
[tex]m^{2} e^{mx} - 12me^{mx} + 32 e^{mx} = 0[/tex]
By factoring out e(mx) from the left side, we obtain
[tex]e^{mx} (e^{mx} - 12m + 32) = 0[/tex]
The number enclosed in parentheses must be equal to zero for e(mx) to be a non-zero solution of the differential equation. To resolve the quadratic problem, we must:
[tex]m^{2} - 12m + 32 = 0[/tex]
The quadratic algorithm yields:
[tex]m = (12 ± √(144 - 4*32))/2\\m = (12 ± \sqrt{\frac{(144 - 4 * 32)}{2} } \\[/tex]
mi = 6 ± 2
Therefore, m1 and m2 have the following values:
m1 = 4
m2 = 8
The functions y(x) = [tex]e^{4x}[/tex]and y(x) = [tex]e^{8x[/tex]are therefore solutions of the specified differential equation.
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Complete question:
The complete question is in the image form.
You received a score of 3.4 on your annual review. Merit increases are given out starting at .5% at a score of 2.6 and it goes up 1% every .4 points. I will be receiving an increase of?
Answer: w/explanation
To calculate your merit increase, we need to first determine your performance score on a scale of 0 to 100. We can convert your score of 3.4 to this scale by subtracting 2 and multiplying by 25:
performance score = (3.4 - 2) x 25 = 35
Now that we have your performance score, we can use the given merit increase formula to calculate your increase:
Merit increase = (performance score - 26) / 4
Merit increase = (35 - 26) / 4
Merit increase = 2.25%
Therefore, your merit increase is 2.25%.
-8x+y=6
-8x+3y=-14
How would you solve this using the elimination method? Thanks!
Answer:
x = -1,375
y = -5
Step-by-step explanation:
{-8x + y = 6, / : (-1)
{-8x + 3y = -14;
Multiply the first equation by -1, so that we could eliminate 8x:
+ {8x - y = -6,
{-8x + 3y = -14;
----------------------
4y = - 20 / : 4
y = -5
Now, make x the subject from the first equation (you can do it from the 2nd one instead):
8x = -6 + y / : 8
x = -0,75 + 0,125y
x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375
Rosa and Clarice have left over bread. They are making sandwiches for the custodian, librarian, office staff. How many sandwiches will they be able to make?
Without the exact Number of bread slices and people in each category, we cannot determine the specific number of sandwiches Rosa and Clarice can make
Step 1: Identify the number of leftover bread slices.
Unfortunately, the question doesn't provide the exact number of leftover bread slices. Let's assume Rosa and Clarice have "B" bread slices in total.
Step 2: Determine the number of sandwiches needed.
We know that they are making sandwiches for the custodian, librarian, and office staff. We need to know the number of people in each category to calculate the total number of sandwiches required. Since this information is not provided, let's assume there are "C" custodians, "L" librarians, and "O" office staff members.
Step 3: Calculate the number of sandwiches required.
Each sandwich typically requires 2 slices of bread. Therefore, the total number of sandwiches required can be calculated using the following formula:
Total Sandwiches = (C + L + O)
Step 4: Determine if there is enough bread.
We can now compare the total number of sandwiches required with the number of bread slices available. If there are enough bread slices (B >= 2 * Total Sandwiches), Rosa and Clarice can make sandwiches for everyone. Otherwise, they will not be able to make enough sandwiches for everyone.
In conclusion, without the exact number of bread slices and people in each category, we cannot determine the specific number of sandwiches Rosa and Clarice can make. To answer the question accurately, please provide the missing information.
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Simplify the expression 2 2/3 • 11/2 - 3 3/4
Exact Form: 131/12
Decimal Form:10.916
Mixed Number Form: 10 11/12
Answer:
131/12 or 10.91666. or [tex]10\frac{11}{12}[/tex]
Hope this helps!
Step-by-step explanation:
( [tex]\frac{8}{3}[/tex] × [tex]\frac{11}{2}[/tex] ) - [tex]\frac{15}{4}[/tex]
( [tex]\frac{4}{3}[/tex] × [tex]\frac{11}{1}[/tex] ) - [tex]\frac{15}{4}[/tex]
[tex]\frac{44}{3}[/tex] - [tex]\frac{15}{4}[/tex]
[tex]\frac{176}{12}[/tex] - [tex]\frac{45}{12}[/tex]
[tex]\frac{131}{12}[/tex]
in your own words, describe how to plot or graph an ordered pair of numbers.
Identify the two numbers in the ordered pair, locate the x-axis and y-axis on the plane, move along the x-axis to the position corresponding to the first number, move vertically along the y-axis to the position corresponding to the second number, mark the point with a dot or small circle, and connect the dots to show patterns.
How to plot or graph an ordered pair of numbers?The procedures below must be followed in order to plot or graph an ordered pair of integers, usually known as a point, on a two-dimensional plane:
Find the two numbers that make up the ordered pair. The position of the point on the x-axis is shown by the first number, while its location on the y-axis is indicated by the second number.On the plane, find the x- and y-axes. The y-axis is the vertical axis that runs up and down, and the x-axis is the horizontal axis that travels left to right.Move along the x-axis to the location corresponding to the first number in the ordered pair starting from the origin, which is the location where the x-axis and y-axis intersect (often represented by the coordinates (0, 0)).Move up the y-axis vertically until you are in the position that corresponds to the second number in the ordered pair.The position of the ordered pair on the two-dimensional plane is determined by the intersection of the two lines.Make a little circle or a dot to symbolize the point on the graph.If you need to plot more than one point, follow the instructions above for each additional point, identifying each one with a different symbol or color.To demonstrate any patterns or trends in the data, finish by connecting the dots.To know more about graph, visit
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| 2. Ghana recently accelerated its plan to privatize tens of thousands of state-owned firms. The estimates of the market demand and supply for the goods are given byQd = -2P + 10 and Q. = 2P-2 2 (a) Determine the equilibrium price and quantity (b) Calculate the price elasticity of demand and supply and comment on your results. (c) The government raises a concern that the free-market price might be too high for the consumers and is planning to set a price ceiling of GH¢1.5. What problem will arise out of these concerns from the Government? (d) Briefly explain 3 main effects the above problem will have on the market. (e) Suggest some measures that the Government should adopt to make price ceiling effective. Now suppose the Government imposed a per tax 2 Ghana cedis on the quantity supplied calculate the consumer and producer surplus before and after the imposition of the tax.
Please someone help me I rlly don’t get this I’ll give you like 40 points
Answer:
Step-by-step explanation:
H(n)=91x(-1/7) n-1
do not know
Hope it helps the answer is the 2nd one have a great day
Determine the x- and y- intercepts for the graph defined by the given equation.
y = x + 8
a.
x-intercept is (0, 8)
y-intercept is ( -8, 0)
c.
x-intercept is ( -8, 0)
y-intercept is (0, 8)
b.
x-intercept is (0, -8)
y-intercept is ( 8, 0)
d.
x-intercept is ( 8, 0)
y-intercept is (0, -8)
Please select the best answer from the choices provided
Answer:
c
Step-by-step explanation:
To find the x-intercept, we set y to 0 and solve for x:
0 = x + 8
x = -8
Therefore, the x-intercept is -8.
To find the y-intercept, we set x to 0 and solve for y:
y = 0 + 8
y = 8
Therefore, the y-intercept is 8.
Hopes this helps
Answer all the questions to get 60 points
138 x 14÷28+209
A. 278
B. 288
C. 298
D. 388
Answer:
A .278
Step-by-step explanation:
138 x 14÷28+209 = 1932 ÷28+209=69+209=278
Use the sample data and confidence level given below to complete parts (a) through (d).
In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 2410 subjects randomly selected from an online group involved with ears. 1111 surveys were returned. Construct a 90% confidence interval for the proportion of returned surveys.
We are 90% confident that the true proportion of surveys returned is between 0.4330 and 0.4882.
What is percentage?
Percentage is a way of expressing a number or proportion as a fraction of 100. It is represented by the symbol "%".
(a) First, we need to calculate the sample proportion, denoted by $\hat{p}$. The sample proportion is the number of surveys returned divided by the total number of surveys sent:
p = 1111/ 2410 ≈ 0.4606
(b) The standard error of the sample proportion is:
SE = p(1−p)/n = 0.4606(1−0.4606)/2410≈0.0168
(c) To find the margin of error at 90% confidence level, we need to use the z-score associated with a 90% confidence interval, which is 1.645 (obtained from a standard normal table or calculator). The margin of error is:
ME = z∗×SE = 1.645 × 0.0168 ≈ 0.0276
(d) Finally, we can construct the 90% confidence interval for the proportion of returned surveys by subtracting and adding the margin of error to the sample proportion:
p ± ME = 0.4606 ± 0.0276 =(0.4330,0.4882)
Therefore, we are 90% confident that the true proportion of surveys returned is between 0.4330 and 0.4882.
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Simple Intrest Rate
3.25%
Martin deposits $7,000 in an account at Victory Bank. Find the amount of interest earned and the total value of his account after 36 months.
The total value of Martin's account after 36 months is $7,682.50. $682.50 in interest was earned.
A hummingbird's nest is 12 feet high in a tree and a flower is on the ground 16 feet away
from the base of the tree. How far will the hummingbird need to fly to get from its nest to the
flower?
Answer:
the bird will need to fly 4feet closer to the flower
List the sample space for rolling a fair 12-sided die.
S = {1, 2, 3, 4, 5, 6}
S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
S = {1}
S = {12}
The sample space for rolling a fair 12-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
What is Sample space?Sample space refers to the set of all possible outcomes or events that can occur in an experiment or random process. It is denoted by the symbol "S" and contains all the possible values, results, or states that can be observed or measured. In probability theory, the sample space is used to define the range of possible outcomes that can be observed or measured in a given experiment or event.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It quantifies the likelihood of an event happening based on the ratio of the number of favorable outcomes to the total number of possible outcomes. It is expressed as a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
According to the given information:
When you roll a 12-sided dice, number of dots on the uppermost face is called as outcome. Now, whenever a dice is rolled we can get either 1, 2,3,4,5,6,7,8,9,10,11 or 12 dots on the uppermost face that is now outcome.
So experiment here is "Rolling a 12-faced dice" and list of possible outcomes is "{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}".
Sample space by its definition is list of all the possible outcomes of an experiment.
S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
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Find the unknown length in the right
triangle.
?
11ft
23ft
The equation x + 3y= 8 is graphed which point represents a solution for this equation
To find a point that represents a solution for the equation x + 3y = 8, we need to find a point (x,y) that satisfies this equation. One way to do this is to choose a value for x, and then solve for y. For example, if we let x = 2, we have:
2 + 3y = 8
Subtracting 2 from both sides, we get:
3y = 6
Dividing both sides by 3, we get:
y = 2
So the point (2,2) is a solution for the equation x + 3y = 8. To check, we can substitute x = 2 and y = 2 into the equation:
2 + 3(2) = 8
8 = 8
This is true, so (2,2) is a solution for the equation.
Alternatively, we could choose a value for y and solve for x. For example, if we let y = 0, we have:
x + 3(0) = 8
x = 8
So the point (8,0) is also a solution for the equation x + 3y = 8.
ANWSER FOR QUESTION 12
75 points and will give brainly
Answer:
90°
Step-by-step explanation:
Since CD is a tangent to circle B and BA is the circle's radius, the tangent to the radius forms a right angle at the point of contact:
∠BAD = 90°