Answers
Answer:
Part a)
[tex]MG = \begin{pmatrix}1&k_1+9&4k_2+36\\ 2t_1+4&t_1k_1-17&-19t_1+3k_2-11\\ t_2+1&k_1-4t_2+5&t_2k_2-8\end{pmatrix}[/tex]
Part b)
[tex]t_1 = -2\\\\t_2 = -1\\\\k_1 = -9\\\\k_2 = -9\\[/tex]
Step-by-step explanation:
a) Computing MG
We have
[tex]M = \begin{pmatrix}1&4&5\\ \:t_1&3&-1\\ \:1&t_2&1\end{pmatrix}[/tex]
[tex]G = \begin{pmatrix}2&k_1&-19\\ \:1&-4&k_2\\ \:-1&5&11\end{pmatrix}[/tex]
[tex]MG = \begin{pmatrix}1&4&5\\ \:t_1&3&-1\\ \:1&t_2&1\end{pmatrix}\times \begin{pmatrix}2&k_1&-19\\ \:1&-4&k_2\\ \:-1&5&11\end{pmatrix}[/tex]
[tex]= \begin{pmatrix}1&k_1+9&4k_2+36\\ 2t_1+4&t_1k_1-17&-19t_1+3k_2-11\\ t_2+1&k_1-4t_2+5&t_2k_2-8\end{pmatrix}[/tex]
I am using a matrix calculator to compute the product rather than going through the rather cumbersome multiplication exercise by hand
Essentially we multiply each row of M by each row of G and simplifyFor example the element in (1, 1) of MG which is 1 is obtained by multiplying row 1 of M by column 1 of G and simplifying
[tex]\begin{pmatrix}1&4&5\end{pmatrix}\begin{pmatrix}2\\ 1\\ -1\end{pmatrix}=1\cdot \:2+4\cdot \:1+5\left(-1\right) = 2 + 4 - 5 = 1[/tex]Element (2, 3) of MG is obtained by multiplying row 2 of M by col 3 of G and simplifying:
[tex]\begin{pmatrix}t_1&3&-1\end{pmatrix}\begin{pmatrix}-19\\ t_2\\ 11\end{pmatrix}=t_1\left(-19\right)+3t_2+\left(-1\right)\cdot \:11\\\\= -19t_1 + 3t_2 -11[/tex]The other elements of MG are computed using the same procedure
b) One property of matrices is that if M is a matrix and M⁻¹ is its inverse
M x M⁻¹ is the identity matrix which has a 1 along the primary diagonal (top left - bottom right) and zeros everywhere
Here we are given G = M⁻¹ so M x G is an identity matrix
For a 3 x 3 matrix, the identity matrix is of the form[tex]\:\begin{pmatrix}1&0&0\\ 0&1&0\\ 0&0&1\end{pmatrix}[/tex]Therefore we get
[tex]MG = \begin{pmatrix}1&0&0\\ 0&1&0\\ 0&0&1\end{pmatrix}[/tex]But we have already computed MG in part a
Equating MG to the identity matrix gives us:
[tex]\begin{pmatrix}1&k_1+9&4k_2+36\\ 2t_1+4&t_1k_1-17&-19t_1+3k_2-11\\ t_2+1&k_1-4t_2+5&t_2k_2-8\end{pmatrix} = \:\begin{pmatrix}1&0&0\\ 0&1&0\\ 0&0&1\end{pmatrix}[/tex]
Performing an element by element comparison of the elements of MG to the elements of the 3 x 3 identity matrix we can compute the values of the variables
[tex]MG(1, 2) \\= k_1 + 9 = 0\\= > k_1 = -9\\\\MG(1, 3)\; is\\ 4k_2 + 36 = 0\\k_2 = -36/4 = -9\\\\MG(2, 1) = 2t_1 + 4 = 0\\\implies t_1 = -4/2 = -2\\\\MG(3, 1) = t_2 + 1\\t_2 + 1 = 0\\t_2 = -1\\[/tex]
So the values of the variables are
[tex]t_1 = -2\\\\t_2 = -1\\\\k_1 = -9\\\\k_2 = -9\\[/tex]
To check if these are correct, you can plug in these values into the product matrix MG. You will see that all elements except the diagonal elements are 0; diagonal elements are 1
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Select all table’s that represent proportional relationship between x and y
Answers
All tables that represent proportional relationship between x and y are:
B. table B.
E. table E.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the x-variable.x represents the y-variable.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = (20 - 15)/(10 - 5) = (5 - 4)/(1 - 0)
Constant of proportionality, k = 1.
Therefore, the required linear equation is given by;
y = kx
y = x
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
The triangle above has the following measures.
m
a=7.5 y
Use the 45-45-90 Triangle Theorem to find the length of the hypotenuse. Include correct units.
Show all your work.
Answers
The length of the hypotenuse is 10.61 yd.
We have,
The sum of the angles in a triangle = 180
Now,
Two angles are 45.
This means,
The side opposite to angle 45 are equal.
So,
a = c
And,
a = 7.5 yd
Now,
Applying the Pythagorean theorem.
b² = a² + c²
b² = 7.5² + 7.5²
b² = 112.5
b = √112.5
b = 10.61
Thus,
The length of the hypotenuse is 10.61 yd.
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f(x)=x2+1 g(x)=5-x (f+g)(x)=
Answers
Answer:
x²-x+6
Step-by-step explanation:
Use (f+g)(x) = f(x)+g(x), substitute and simplify
if 17sin=8 find the value of 2tantheta/1+tan²theta
Answers
Answer:
±80/289
Step-by-step explanation:
If you want to learn how to calculate 2tanθ/(1 + tan²θ), you need to follow these steps. But be warned, this is not a piece of cake. It's more like a piece of pi.
First, you need to find the value of sinθ by dividing both sides of the equation by 17:
17sinθ = 8sinθ = 8/17Next, you need to find the value of cosθ by using the Pythagorean identity: sin²θ + cos²θ = 1. You can do this by rearranging the equation and taking the square root of both sides:
cos²θ = 1 - sin²θcos²θ = 1 - (8/17)²cos²θ = 1 - 64/289cos²θ = 225/289cosθ = ±√(225/289)cosθ = ±15/17Then, you need to find the value of tanθ by using the ratio identity: tanθ = sinθ/cosθ. You can do this by plugging in the values of sinθ and cosθ and simplifying:
tanθ = sinθ/cosθtanθ = (8/17) / (±15/17)tanθ = ±8/15Finally, you need to find the value of 2tanθ/(1 + tan²θ) by plugging in the value of tanθ and simplifying:
2tanθ/(1 + tan²θ) = 2(±8/15) / (1 + (±8/15)²)2tanθ/(1 + tan²theta) = ±16/15 / (1 + 64/225)2tanθ/(1 + tan²theta) = ±16/15 / (225/225 + 64/225)2tanθ/(1 + tan²theta) = ±16/15 / (289/225)2tantheta/(1 + tan²theta) = ±(16/15) x (225/289)2tantheta/(1 + tan²theta) = ±80/289So, the value of 2tantheta/(1 + tan²theta) is ±80/289. Note that there are two possible values because cosθ and tanθ can be positive or negative depending on the quadrant of θ.
Congratulations! You have just solved a trigonometric equation. You deserve a round of applause. Or maybe just a round pi.
Use slopes and y-intercepts to determine if the lines y=−x+3 and −3x−3y=1 are parallel.
Answers
Answer:
YES PARALLEL
Step-by-step explanation:
The slopes of
y=−x+3 and −3x−3y=1 are both −1.
Parallel
Please help and show work
Answers
Answer:
B. (1,7)
Step-by-step explanation:
What is the mean absolute deviation of 8,4,8,8,10,2,4,4
Answers
Mean absolute deviation is 2.5.
The mean absolute deviation (MAD) measures how spread out a set of data is by calculating the average distance between each data point and the mean of the data set.
To find the MAD of the given data set {8,4,8,8,10,2,4,4}, we first need to find the mean of the data set.
Mean = (8+4+8+8+10+2+4+4)/8 = 6
Next, we need to find the absolute deviation of each data point from the mean:
|8-6| = 2
|4-6| = 2
|8-6| = 2
|8-6| = 2
|10-6| = 4
|2-6| = 4
|4-6| = 2
|4-6| = 2
To find the MAD, we need to take the mean of the absolute deviations:
MAD = (2+2+2+2+4+4+2+2)/8 = 2.5
Therefore, the mean absolute deviation of the data set {8,4,8,8,10,2,4,4} is 2.5. This means that, on average, the data points in the set are about 2.5 units away from the mean of the set.
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Help please Which reason is the justification for the statement that angle A ≅ angle B?
A) Vertical angles are congruent.
B) Linear angles are equal.
C) Intersecting lines form opposing angles.
D) Lines intersect at one point.
Answers
The price (in S) of a cookbook is determined by the number of cookbooks x demanded by consumers and supplied by the publisher.
Supply: p=0.003.x
Demand: p = -0.007x+300
(a) Solve the system of equations defined by the supply and demand models.
(b) What is the equilibrium price?
(c) What is the equilibrium quantity?
Answers
a) The solution of the system of equations is, x = 30,000
b) the equilibrium price is, p = 90
c) the equilibrium quantity is, p = 90
Given that;
The price (in S) of a cookbook is determined by the number of cookbooks x demanded by consumers and supplied by the publisher.
Supply: p=0.003.x
Demand: p = -0.007x+300
Hence, We can simplify as;
⇒ 0.003x = - 0.007x + 300
Solve for x;
⇒ 0.003x + 0.007x = 300
⇒ 0.01x = 300
⇒ x = 300/0.01
⇒ x = 30,000
Hence, the equilibrium price is,
p=0.003.x
p=0.003 × 30,000
p= 90
And, the equilibrium quantity is,
p = -0.007x+300
p = -0.007 × 30,000+300
p = - 210 + 300
p = 90
Thus, a) The solution of the system of equations is, x = 30,000
b) the equilibrium price is, p = 90
c) the equilibrium quantity is, p = 90
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GIVING BRAINLIST PLEASE HELP!!!
Answers
The probability that a randomly selected point within the circle would fall in the red- shaded area is 45. 833 %
How to find the probability ?The arc that is covered by the red - shaded area in the circle has a degree measure of 165 degrees. This is out of the total circle angle measure of 360 degrees.
This therefore means that the probability that a randomly selected point within the circle would fall in the red- shaded area can be found to be :
= Angle measure of red - shaped area / Total area x 100 %
= 165 / 360 x 100 %
=0. 45833 x 100 %
= 45. 833 %
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Fill in the table using this function rule.
y=-6x-3
Answers
Substitute each x-coordinate into equation y = - 6x - 3 to find the corresponding y-coordinate:
For x = - 1:y = - 6(-1) - 3 = 6 - 3 = 3For x = 0:y = - 6(0) - 3 = 0 - 3 = - 3For x = 1:y = - 6(1) - 3 = - 6 - 3 = - 9For x = 5:y = - 6(5) - 3 = - 30 - 3 = - 33Dakota determines that his cat weighs 13 pounds 8 ounces. He says that in ounces, the cat's weight is 138 ounces. Is Dakota's statement reasonable? Explain your answer. 4.M.1.2
Answers
Dakota's statement that his cat weighs 138 ounces is not correct.
To convert 13 pounds 8 ounces to ounces
we can multiply the number of pounds by 16 (since there are 16 ounces in a pound) and add the number of remaining ounces:
13 pounds x 16 ounces per pound = 208 ounces
8 ounces = 8 ounces
Total weight in ounces = 208 + 8 = 216 ounces
Therefore, Dakota's statement that his cat weighs 138 ounces is not correct.
It is significantly less than the actual weight of 216 ounces.
This may indicate that Dakota made a mistake in his calculation or misread the scale when weighing his cat.
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4.1.3 Bathu Sneakers have been looking into different shoebox sizes: a large box for male shoes and small box for female shoes. The cost of the cardboard to make the boxes is 0,502 cents/cm². Calculate the percentage savings Bathu Sneakers will make if the smaller box is used compared to the normal larger box. Larger Box Total Surface Area = 4 093 cm² 19 cm 26 cm 34,5 cm Smaller Box Total Surface Area = 3 034 cm² 25 cm 17 cm 26 cm (6)
Answers
Answer:
Step-by-step explanation:To calculate the savings percentage, we first need to find out the cost of the cardboard required for each box.
For the larger box:
Total Surface Area = 2 * (1926 + 1934.5 + 26*34.5) = 2 * (494 + 655.5 + 897) = 4093 cm²
Cost of cardboard for larger box = 0.502 * 4093 = 2055.986 cents = 20.55986 dollars (rounded to 5 decimal places)
For the smaller box:
Total Surface Area = 2 * (2517 + 2526 + 1726) + 6 * (25-21)* (17-2*1) = 3034 cm²
Note that the additional term in the equation is the surface area of the six sides of the lid and base of the box.
Cost of cardboard for smaller box = 0.502 * 3034 = 1522.268 cents = 15.22268 dollars (rounded to 5 decimal places)
The difference in cost between the larger and smaller boxes is:
20.55986 - 15.22268 = 5.33718 dollars (rounded to 5 decimal places)
The percentage savings can be calculated as follows:
Percentage savings = (difference in cost / cost of larger box) * 100%
= (5.33718 / 20.55986) * 100%
= 25.98%
Therefore, using the smaller box will result in a savings of approximately 26% on cardboard costs for Bathu Sneakers compared to using the normal larger box.
If f(x)=x+2 and g(x + 1) = x + 1 then find g. f(4).
Answers
Answer:
[tex]x + 2[/tex]
see the below process of the equation:
Step-by-Step Explaination:
Given, f(x)=x+1 and g(x)=x+1
∴g(g(x))=g(x+1)
=(x+1)+1
=x+2
-Thank You By MrIshaan
would like help asap
Answers
Answer:
A
Step-by-step explanation:
You need to take a ruler and join the points for A and B. I can't do it here.. C and D are not right because they're incorrectly plotted. If A/B join as a straight line for all the points then it's linear. If they don't (and you find it a little curvy) it's a a quadratic. You can cross check as well but imo it's A.
C and D are out of question. Your only options are A and B. And I find the points joining a straight line so my answer would be A
You put $10,000 into a simple interest savings account. You really want to retire on this money. Your account has 8% interest for amounts $10,000 or more. It is simple interest. How much would you have in 50 years?
Answers
You will have $50,000 in your account after 50 years.
We have,
Simple interest formula is given by:
I = Prt
Where:
I = interest earned
P = principal amount (initial investment)
r = interest rate
t = time (in years)
Here,
P = $10,000
r = 8%
t = 50 years
So, the interest earned after 50 years will be:
I = Prt
= 10000 x 0.08 x 50
= $40,000
The total amount in the account after 50 years will be the initial investment plus the interest earned:
Total amount = $10,000 + $40,000 = $50,000
Therefore,
You will have $50,000 in your account after 50 years.
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Select the correct answer. What are the solutions to this equation? 7x2 − 28 = 0 A. B. C. D.
Answers
A bank loaned out 20,500, part of it at the rate of 9% annual interest, and the rest at 11% annual interest the total interest earned for both loans was 2,225.00 how much was loaned at each rate
Answers
The money loaned at 9% annual interest was 1500 and the money loaned at 11% annual interest was 19000.
Let the amount of money loaned at 9% be x
the amount of money loaned at 11% be y
According to the question,
Total money loaned = 20,500
Thus the equation formed is,
x + y = 20,500 ------ (i)
Simple interest is calculated by
I = P * r * t
where I is the simple interest
r is the rate of interest
t is the time
Thus, the interest on x = 0.09x
the interest on y = 0.11y
Total interest gained = 2,225
Thus the equation formed is,
0.09x + 0.11y = 2225 -------(ii)
Multiply (i) by 0.09
0.09x + 0.09y = 1845
Subtract the above from (ii)
0.02y = 380
y = 19000
x = 1500
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Omar has been practicing violin for 4 1/2 years longer than his sister.
If his sister has been practicing for x years, how many years y has Omar been practicing violin?
Answers
X is his sisters years and. You add them with 4,5 to get omar’s years
Select the correct answer.
What is the domain of y = cos(z)?
O A. [0, 00)
О в. 27
O C. (-00,00)
OD. [-1, 1]
Reset
Next
Answers
The domain of the function y = cos(z) is (-00,00)
Calculating the domain of the functionFrom the question, we have the following parameters that can be used in our computation:
y = cos(z)
The above equation means that
the variable y is a function of z
Also, we can see that the above function is a cosine function
In a cosine function. the input value can take any real value
This means that y can take any real value
And as such, the domain is the set of all real numbers
This is represented as (-00,00)
Hence, the domain of the function is (-00,00)
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A bag contains 8 red pens, 7 blue pens, and 14 black pens. Denato wants to pull a blue pen from the bag.
What is the sample space for this experiment?
[red, black]
[blue]
[red, blue, black]
[blue, red]
Answers
Answer:
Step-by-step explanation:
The sample space represents the set or collection of all possible outcomes. It's often written as S = [outcome1, outcome2, outcome3].
For this problem, there are 3 possible outcomes: red pen, blue pen or black pen. (The fact that Denato wants to pull a blue pen is irrelevant when defining the sample space bc we are just listing the possible outcomes.)
So the answer is [red, blue, black].
x<-5
How do you graph this equation?
Answers
To graph the inequality X < -5 on a number line, we start by drawing a number line and marking a point at -5.
We have,
To graph the inequality X < -5 on a number line, we start by drawing a number line and marking a point at -5.
Since the inequality is strict (X is less than -5), we will draw an open circle at -5 to indicate that -5 is not included in the solution set.
Next, we shade the portion of the number line to the left of -5, since any value of X less than -5 satisfies the inequality.
Note that the open circle at -5 indicates that X cannot be equal to -5, since the inequality is strict.
Any value to the left of -5 on the number line would satisfy the inequality.
Thus,
To graph the inequality X < -5 on a number line, we start by drawing a number line and marking a point at -5.
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The net of a triangular prism and its approximate dimensions are shown in the diagram.
4in. 12 in. 12in. 12 in. 12 in. 10.4 in. Which measurement is closest to the total surface area of the triangular prism in square inches?
Answers
The measurement closest to the total surface area of the triangular prism is J) 393.6 [tex]in^{2}[/tex] .
To find the surface area of a triangular prism, we need to find the area of all its faces and add them up.
Looking at the net of the triangular prism, we can see that it has two congruent triangles and three rectangular faces.
The area of each triangular face can be found using the formula for the area of a triangle:
Area of a triangle = (1/2) x base x height
In this case, the base of each triangle is 12 inches and the height is 4 inches. So, the area of one triangular face is:
(1/2) x 12 x 4 = 24 [tex]in^{2}[/tex]
The area of each rectangular face can be found using the formula:
Area of a rectangle = length x width
In this case, the length and width of the rectangular faces are:
12 in. x 10.4 in.
12 in. x 12 in.
4 in. x 10.4 in.
So, the area of each rectangular face is:
12 x 10.4 = 124.8 [tex]in^{2}[/tex]
12 x 12 = 144 [tex]in^{2}[/tex]
4 x 10.4 = 41.6 [tex]in^{2}[/tex]
Therefore, the total surface area of the triangular prism is:
2 x 24 + 124.8 + 144 + 41.6 = 393.6 [tex]in^{2}[/tex]
So, the measurement closest to the total surface area of the triangular prism in square inches is J) 393.6 [tex]in^{2}[/tex] .
Correct Question :
The net of a triangular prism and its approximate dimensions are shown in the diagram, 4 in, 12 in, 10.4 in, 12 in, 12 in, 12 in. Which measurement is closest to the total surface area of the triangular prism in square inches?
F) 268.8 [tex]in^{2}[/tex]
G) 432 [tex]in^{2}[/tex]
H) 288 [tex]in^{2}[/tex]
J) 393.6 [tex]in^{2}[/tex]
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Help please When writing a proof, how do you construct the first statement?
A) By writing the justification for the first statement in the right column.
B) By copying the “prove” statement(s) from the original problem.
C) By writing the next logical statement from the current one.
D) By copying the “given” statement(s) from the original problem.
Answers
When writing a proof, we construct the first statement by copying the “given” statement(s) from the original problem. Hence, option D is correct.
When writing a proof, the first statement is typically either the "given" statement(s) or a previously proven result. Therefore, option D ("By copying the 'given' statement(s) from the original problem") is often the correct choice for constructing the first statement.
In some cases, option C ("By writing the next logical statement from the current one") may be a more appropriate choice. Regardless of which option is chosen, it is important to clearly justify each statement in the right column of the proof.
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PLEASE HELP !!!
Which equation represents the graph?
y=-1/3x-3
y=3x-3
y=-1/3x+1/3
y=-3x-1/3
Answers
Answer:
Step-by-step explanation:
Y=-3x-1/3
The answer should be y=-3x-3. The slope is -3, and the y intercept is -3. I don't see this as an option!
Please help !!!!!! 20 points
Answers
The value of x in the polygon will be 13.25 degrees.
The value of x is 10.
We can find the value of x by plugging in the number of sides of the regular polygon into the formula x = (n-2)*15° - 1.
How to calculate the valueThe sum of the interior angles of a regular polygon with n sides is (n-2) x 180 degrees.
Sum of angles = (24-2) x 180 = 22 x 180 = 3960 degrees
Since all the angles in a regular polygon are congruent, we can divide the sum of the angles by the number of angles to find the measure of one angle:
Measure of one angle = 3960/24 = 165 degrees
165 = 12x + 6
159 = 12x
x = 13.25
Therefore, the value of x is 13.25 degrees.
Each of the triangles in our decomposition has one angle equal to (17x+2)°, so the sum of all the angles in the triangles is 43 × (17x+2)° = 731x+86°.
Therefore, we have:
731x+86° = 7380°
Solving for x, we get:
731x = 7294°
x = 10
Therefore, the value of x is 10.
The equation that can be used to find the value of x is:
(9x+48)° + (15x-24)° = (n-2)*180°
24x + 24 = (n-2)*180°
Dividing both sides by 24, we get:
x + 1 = (n-2)*15°
Subtracting 1 from both sides, we get:
x = (n-2)*15° - 1
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Which statement is true regarding the parallel and perpendicular lines in the diagram? k Parallel to n and w Perpendicular to m k Parallel to n and n Perpendicular to m w Parallel to n and n Perpendicular to m w Parallel to n and wPerpendicular to m
Answers
Answer:
Based on the diagram, we can see that there are four lines: k, n, w, and m. The relationship between these lines is important in understanding their geometric properties.
We can see that line k and line n are both straight lines and never intersect, which means they are parallel to each other. This is indicated by the two small arrows on line k and line n that are pointing in the same direction.
On the other hand, line w intersects line m at a right angle (90 degrees). This means that line w is perpendicular to line m. This is indicated by the small square in the corner where line w and line m meet.
Understanding parallel and perpendicular lines is important in many areas of mathematics and science, such as geometry, trigonometry, physics, and engineering.
Step-by-step explanation:
Answer:
The correct statement is: w is parallel to n and w is perpendicular to m.
Step-by-step explanation:
Please help!! Worth 100PTS
The regular polygon has the following measures.
a= 7√3 cm
s=14cm
Segment a is drawn from the center of the polygon perpendicular to one of its sides.
What is the vocabulary term for segment a?
What is the area of the polygon?
Round to the nearest tenth and include correct units.
Show all your work.
Answers
The vocabulary term for segment a is called the apothem.
The area of the polygon is 319.8 cm²
How did we get the value?To find the area of the polygon, we can use the formula:
Area = (1/2) × Perimeter × Apothem
The perimeter of the polygon can be found by multiplying the number of sides by the length of each side, so:
Perimeter = number of sides × length of each side
Perimeter = 6 × 14 cm (since it's a regular hexagon)
Perimeter = 84 cm
Finding the apothem, use the fact that it forms a right triangle with half of one side length and the apothem as the legs, and the apothem as the hypotenuse. Thus,
a² = s² - (s/2)²
a² = 196 - 49
a² = 147
a = √(147) = 7.65 cm
Now, we can plug in our values into the formula for the area:
Area = (1/2) × Perimeter × Apothem
Area = (1/2) × 84 cm × 7.65 cm
Area = 319.8 cm²
Rounding to the nearest tenth and including the correct units, we get:
Area ≈ 319.8 cm²
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The distribution of waiting times at the student health center is bell-shaped with a mean of 8 minutes and a standard deviation of 2.
Find the z-score of someone who waits 5 minutes. Round your z-score to two decimal places. Be sure to specifically indicate if a wait
time of 5 minutes is unusual.
z-score=
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The wait time is
unusual.
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Answers
A wait time of 5 minutes would be considered unusual.
We have,
To find the z-score, we can use the formula:
z = (x - μ) / σ
where x is the value we are interested in, μ is the mean, and σ is the standard deviation.
Plugging in the values, we get:
z = (5 - 8) / 2 = -1.5
Rounding to two decimal places,
we get z = -1.50.
Since the z-score is more than 2 standard deviations below the mean, a wait time of 5 minutes would be considered unusual.
Thus,
A wait time of 5 minutes would be considered unusual.
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A 3 1/2 inch by 5 inch photo is to be enlarged to a similar rectangle. If the width is 6 inches what should the length be?
Answers
Answer:
4.2, or 4 1/4
Step-by-step explanation:
Usually, "3 1/2 inch by 5 inch" is in the format of "length by width."
Therefore, the original length is 3.5 and width is 5.
If the new width is 6, the scale factor is determined by the following:
n/o, where 'n' is new, and 'o' is old: 6/5 = 1.2. Check the work: 5 * 1.2 = 6.
Therefore, the scale factor is 1.2. Now, multiply the old length by the scale factor to determine the new length:
3.5 * 1.2 = 4.2, or 4 1/4 inches, as there are 8 sections in an inch, and 2/8 = 0.25, which is a quarter, or 1/4.
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