The water output rate for the Rodriguez family's sprinkler was 35 L per hour, and the water output rate for the Barnes family's sprinkler was 15 L per hour (50 - 35) by solving the expression formed.
What is expression ?In mathematics, an expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division, that are written in a certain order. Expressions can be evaluated or simplified by following the rules of arithmetic or algebra. Examples of expressions include "2x + 3", "(a + b) / c", and "5^2 - 3".
According to given information :
Let's use the variable "r" to represent the water output rate for the Rodriguez family's sprinkler.
Then, the water output rate for the Barnes family's sprinkler can be represented as "50 - r", since the sum of the two rates is 50 L per hour.
Using the formula:
rate x time = amount of output, we can set up two equations:
r x 15 = amount of water output for the Rodriguez family
(50 - r) x 35 = amount of water output for the Barnes family
We also know that the total amount of water output is 1050 L, so we can set up a third equation:
r x 15 + (50 - r) x 35 = 1050
Now we can solve for "r".
First, simplify the third equation
15r + 1750 - 35r = 1050-20r = -700r = 35
Therefore, the water output rate for the Rodriguez family's sprinkler was 35 L per hour, and the water output rate for the Barnes family's sprinkler was 15 L per hour (50 - 35).
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If this figure was rotated around the x-axis, what would the height be? The radius?
The height and the radius of the figure will remain unchanged as the figure is being just rotated around the axis and not transformed.
What is a transformation?A function transformation "moves," "resizes," or "reflects" the parent function's graph, depending on the case. Function transformations can be broadly divided into three categories:
Translation
Dilation
Reflection
Dilation is the only one of these changes that modifies the original shape's size; the other two just change the shape's placement.
Here in the question,
The figure is being rotated not dilated so the dimensions of the new figure will remain the same.
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A photo is being resized to sell at a gallery. The original photos 4 inches by 6 inches. Using the dimensions of 2.5 in. by 3.75 in., find the
scale factor.
Answer:basically if 23x45 is 35 then u times that to 15 and theres ur asnwer
23x45=35
5x[tex]11ab^{2}(2a^5b^4)[/tex]
Hence,[tex]110a^6b^6[/tex] is the simplified expression as by multiplying 5x11 using the distributive property .
what is expression ?A mathematical expression seems to be a combination of digits, symbols, and operators (like +, -,, and ) that denotes a relation or quantity. A single figure or variable can constitute an expression, as can a collection of several numbers, constants, and operators. It is possible to depict mathematical connections, functions, and processes using expressions. There are various categories into which expressions can be divided, including numerical, algebraic, polynomial, rational, and exponential expressions. These can be assessed by carrying out the relevant operations in the mathematical operation order, i.e., parentheses operations first, multiplication or division second, addition or subtraction third.
given
[tex]5x11ab^2(2a^5b^4)[/tex]
We may multiply 5x11 using the distributive property, and then multiply the variables using exponentiation rules to simplify the formula
[tex]5x11ab^2(2a^5b^4):[/tex]
[tex]55ab^2(2a^5b^4)[/tex] is equal to [tex]5x11ab^2(2a^5b^4)[/tex]
= [tex]110a^(1+5)b^(2+4)[/tex] (using the product rule of exponents)
= [tex]110a^6b^6[/tex]
Hence,[tex]110a^6b^6[/tex] is the simplified expression as by multiplying 5x11 using the distributive property .
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Cindy is evaluating the expression -5m - 31 for
-2p + r
m = 1, n.= -4, p = -3, and r = -2. Her work is
shown below.
=5m - 31 =
-5(1) - 3(-4)
-2p + r
=2(-3) + (-2)
= 끌=-끔=-4
a. What error did Cindy make in her computation?
b. What is the correct answer?
The correct answer for the expression is -5(1) - 3(-4) = 7 and -2p + r = 4.
What is substitution method?The algebraic approach to solving simultaneous linear equations is known as substitution technique. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.
The given expression is: -5m - 3n for m = 1, n.= -4 and -2p + r for p = -3, and r = -2.
The correct steps are:
For, -5m - 3n substitute the value of m = 1 and n = -4:
-5(1) - 3(-4)
-5 + 12 = 7
For -2p + r:
-2(-3) + (-2)
6 - 2 = 4
Hence, the correct answer for the expression is -5(1) - 3(-4) = 7 and -2p + r = 4.
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Two spinners-One 5 and one 6. What is the probability that you get the same numbers as a previous spin?
Answer: Since the spinners have 5 and 6 numbers respectively, the total number of outcomes is 5 x 6 = 30.
If we get the same number as a previous spin, it means that the first spin is irrelevant, and we only care about the second spin. Therefore, the probability of getting the same number as a previous spin is the same as the probability of getting any specific number on the second spin, which is 1 out of 6.
Therefore, the probability of getting the same number as a previous spin is 1/6, or approximately 0.17 to two decimal places.
Step-by-step explanation:
What is the surface area?
9 in
9 in
9 in
square inches
Answer:
The surface area of an object is the total area of all its faces. For a cube with sides of length 9 inches, the surface area can be calculated as follows:
The cube has six faces, all of which are identical squares.
The area of one square face is 9 inches x 9 inches = 81 square inches.
Therefore, the total surface area of the cube is 6 x 81 square inches = 486 square inches.
So the surface area of a cube with sides of 9 inches is 486 square inches.
Simplify (3x3y2 − 5xy4 − 2xy) + (2x3y2 + 5xy4 + 3xy). 5x3y2 − 2xy4 + xy 5x3y2 − 2xy4 − 5xy 5x3y2 + xy 5x3y2 − xy
After Simplifying, we get: [tex]5x^3y^2 + xy - 2xy^4[/tex]
What is pοlynοmials ?Pοlynοmials are algebraic expressiοns made up οf cοefficients and variables. Occasiοnally, variables are referred tο as indeterminates.
Fοr pοlynοmial expressiοns, additiοn, subtractiοn, multiplicatiοn, and pοsitive integer expοnents are all pοssible; hοwever, divisiοn by variable is nοt. x²+x-12 is an illustratiοn οf a single-variable pοlynοmial. Three terms are invοlved in this example: x², x, and -12.
The Greek wοrds "pοlynοmial" and "nοminal," which tοgether mean "many terms," are the sοurce οf the English wοrd pοlynοmial. There is nο limit tο the number οf terms that a pοlynοmial can have.
When we add the twο pοlynοmials term by term, we get:
[tex](3x^3y^2 - 5xy^4 - 2xy) + (2x^3y^2 + 5xy^4 + 3xy) = 3x^3y^2 + 2x^3y^2 - 5xy^4 + 5xy^4 - 2xy + 3xy[/tex]
Simplifying, we get: [tex]5x^3y^2 + xy - 2xy^4[/tex]
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Answer:
5x^3y^2+xy (C)
Step by Step:
(3x^3y^2 − 5xy^4 − 2xy) + (2x^3y^2 + 5xy^4 + 3xy) =
3x^3y^2 − 5xy^4 − 2xy + 2x^3y^2 + 5xy^4 + 3xy =
(3 + 2)x^3y^2 + (-5 + 5)xy^4 + (-2 + 3)xy =
5x^3y^2 + xy
hope this helps (btw it's C)
←
A group of winning ticket holders share equally in a $90,000,000 lottery. Before
the money is divided, three more winning ticket holders are declared. As a
result, each person's share is reduced by $1,000,000. How many people were
in the original group of winners?
We take the positive root:
n = (-3 + 27) / 2 = 12. Therefore, there were 12 people in the original group of winners.
How to solve the equation?Let's assume that there were n people in the original group of winners, and each person's share was x dollars. Then we know that:
n * x = $90,000,000
After three more winners are declared, the total number of winners becomes n + 3. Each person's share is then reduced by $1,000,000, so the new share per person is (x - $1,000,000). We can then write:
(n + 3) * (x - $1,000,000) = $90,000,000
Expanding the equation, we get:
nx - $1,000,000n + 3x - $3,000,000 = $90,000,000
Simplifying, we get:
nx + 3x = $1,000,000n + $93,000,000
Factoring out x and n, we get:
x(n + 3) = $1,000,000(n + 3) + $90,000,000
Dividing both sides by (n + 3), we get:
x = $1,000,000 + ($90,000,000 / (n + 3))
We can substitute this expression for x in the first equation:
n * ($1,000,000 + ($90,000,000 / (n + 3))) = $90,000,000
Expanding and simplifying, we get:
[tex]$n^2$[/tex]+ 3n - 270 = 0
Using the quadratic formula, we get:
n = [tex](-3\± \sqrt{(729)) / 2[/tex]
n = (-3 ± 27) / 2
Since n has to be positive, we take the positive root:
n = (-3 + 27) / 2 = 12
Therefore, there were 12 people in the original group of winners.
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For the truncated cuboid of height 3 m, top 5 m, base 8 m and side length of 1.5 m. Find the volume
Therefore, the volume of the truncated cuboid is approximately 68 + 4*√(30) cubic meters.
What is volume?Volume is a measure of the amount of space occupied by a three-dimensional object. It is the amount of three-dimensional space enclosed by the boundaries of an object. Volume is typically measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³).
Here,
The truncated cuboid is a solid figure that is obtained by cutting off the top of a rectangular prism (cuboid) with a plane that is parallel to the base. The formula for the volume of a truncated cuboid is:
V = h/3 * (A + √(A*B) + B)
where V is the volume, h is the height of the truncated portion, A is the area of the top face, and B is the area of the base face.
In this case, the height of the truncated portion is 3 m, the top face has an area of 5 m x 8 m = 40 m², and the base face has an area of 8 m x 1.5 m = 12 m². Therefore:
A + B = 40 + 12 = 52 m²
√(AB) = √(4012) = √(480) = 4*√(30)
Substituting these values into the formula, we get:
V = 3/3 * (52 + 4√(30) + 12)
V = 68 + 4√(30)
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If f left parenthesis x right parenthesis equals x minus 2 and g left parenthesis x right parenthesis equals 2 x minus 6, then g left parenthesis 4 right parenthesis divided by f left parenthesis 3 right parenthesis = __________.
a.)
2
b.)
1
c.)
3
d.)
0
The value g left parenthesis 4 right parenthesis divided by f left parenthesis 3 right parenthesis is 2.
What is parenthesis?
Parenthesis, also known as round brackets, are a type of punctuation used in writing to enclose additional information within a sentence that is not essential to the meaning of the sentence, but can provide clarification, emphasis, or further explanation. They are usually shown as two curved lines facing each other, like this: ().
For example, consider the sentence: "The concert, which was held at the arena last night, was sold out (as expected)." The words "as expected" are enclosed in parentheses, indicating that they are not necessary to the main meaning of the sentence, but provide additional information that may be of interest to the reader.
Parentheses can also be used to enclose mathematical equations, citations, or references in writing.
In this problem, we first need to substitute the given values of x in the functions f(x) and g(x).
f(x) = x - 2
f(3) = 3 - 2 = 1
g(x) = 2x - 6
g(4) = 2(4) - 6 = 2
So, [tex] \frac{g(4)}{f(3)} = \frac{2}{1} = 2[/tex]
Therefore,the value of g(4)/f(3) is 2.
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At which points on the graph of the inverse of f(x)=1/(x^2+1) + (1-2x)^(1/3), x>=0 the tangents to f(x) and its inverse are perpendicular?
The two locations on the inverse function graph where the tangent lines to both functions are perpendicular are as a result: P(0.3807, 1.9337) and Q (0.6677, 0.6129).
what is expression ?In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.
[tex]y = f(x) = 1/(x^2+1) + (1-2x)^(1/3)\\y - 1/(x^2+1) = (1-2x)^(1/3)\\(y - 1/(x^2+1))\\y^3 = 1-2x\\x = (1 - (y - 1/(x^2+1))^3)/2\\g(y) = (1 - (y - 1/(x^2+1))^3)/2\\[/tex]
[tex]f(x) = 1/(x^2+1) + (1-2x)^(1/3)\\f'(x) = -2x/(x^2+1)^2 - (1-2x)^(-2/3)/3\\g(y) = (1 - (y - 1/(x^2+1))^3)/2\\g'(y) = -3(y - 1/(x^2+1))^2/(2(x^2+1)^2)\\-2x/(x^2+1)^2 - (1-2x)^(-2/3)/3 * -3(y - 1/(x^2+1))\\x^2/(2(x^2+1)^2) = -1\\2x/(x^2+1)^2 = 1/((1-2x)^(2/3)(y - 1/(x^2+1))^2)\\4x^2 = (x^2+1)\\x^2 / ((1-2x)^(4/3)(y - 1/(x^2+1))^2)\\(x^2-2x+1)(x^2+2x+1)\\(y - 1/(x^2+1))^2 = 16x^2(1-2x)^(4/3)\\x = 0.3807 or x = 0.6677\\y = 1.9337 or y = 0.6129\\[/tex]
The two locations on the inverse function graph where the tangent lines to both functions are perpendicular are as a result: P(0.3807, 1.9337) and Q (0.6677, 0.6129).
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A used car costs $3450 at present. This is 60% of the cost 4 yr ago. What was the cost of the car 4 yr ago?
Using arithmetic operation it is obtained that the cost of the car 4 years ago was $5750.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
Let C be the cost of the car 4 years ago.
According to the problem, the current cost of the car is 60% of the cost 4 years ago, so we can write -
3450 = 0.6C
Use the arithmetic operation of division -
To solve for C, we can divide both sides of the equation by 0.6 -
C = 3450/0.6
C = 5750
Therefore, the cost of the car 4 years ago was $5750.
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This question: 1 point(s) possible
The access code for a car's security system consists of four digits. The first digit cannot be 4 and the last digit must be odd. How many different codes are available?
The number of different codes available is
Answer: 4500
Step-by-step explanation:
1st 0, 1, 2, 3 ,5 ,6 ,7 ,8 ,9
2nd 0, 1, 2 ,3 ,4 ,5 ,6 ,7 ,8 , 9
3rd 0, 1, 2 ,3 ,4 ,5 ,6 ,7 ,8 , 9
4th 1, 3, 5, 7, 9
9 x 10x 10 x 5= 4500
Please help!! Correct answer gets brainliest!!
Answer:
c
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
First, the shape is wrong
2(8×3)+2(8×4)+2(3×4)=
2(24)+2(32)+2(12)=
48+64+24=136
determine the solution for the system of equation -2y=-6x-18 3x-4y=27 ( , )
The solution for the system of equation -2y=-6x-18 3x-4y=27 is (x, y) = (-3, 9).
What is system?A system is an organized set of components that work together to achieve an overall goal. It could be a physical system, such as an automobile, or an abstract system, such as an economic system.
The first step is to isolate one of the variables in one of the equations. To do this, we can multiply both sides of the first equation by -3. This will give us: 6y = 18x + 54.
Next, we need to subtract this equation from the second equation. Doing so gives us: 3x - 6y = -27.
Now we can isolate the variable y. To do this, we can divide both sides of the equation by -6. This will give us: y = -3x - 9.
We have now isolated the variable y in both equations, so we can substitute y = -3x - 9 in the first equation. Doing so gives us: -2(-3x - 9) = -6x - 18.
We can then simplify this equation to get: 6x + 18 = -6x - 18.
Finally, we can solve this equation for x. Doing so gives us x = -3. We can then substitute this value into either equation to find the value of y: y = -3(-3) - 9 = 9.
Therefore, the solution for the system of equation -2y=-6x-18 3x-4y=27 is (x, y) = (-3, 9).
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Find the probability that a 42 person shift will put together between 193.2 and 201.6 computers per hour.
The probability that a 42 person shift will put together between 193.2 and 201.6 computers per hour is given as follows:
0.0006 = 0.06%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 4.2, \sigma = 0.8, n = 42, s = \frac{0.8}{\sqrt{42}} = 0.1234[/tex]
The probability that a 42 person shift will put together between 193.2 and 201.6 computers per hour is equivalent to the probability of a sample mean between 193.2/42 = 4.6 and 201.6/42 = 4.8.
The probability is the p-value of Z when X = 4.8 subtracted by the p-value of Z when X = 4.6, hence:
Z = (4.8 - 4.2)/0.1234
Z = 4.86
Z = 4.86 has a p-value of 1.
Z = (4.6 - 4.2)/0.1234
Z = 3.24
Z = 3.24 has a p-value of 0.9994.
Hence:
1 - 0.9994 = 0.0006 = 0.06%.
Missing InformationThe missing section is given by the image presented at the end of the answer.
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Let 0°
Given: tan a =2.4
Find: sin a and cos a
Answer:
sin α = 12/13;cos α = 5/13.-------------------------
Since angle α is between 0° and 90°, it is in the first quadrant and therefore all sin α, cos α and tan α are positive numbers.
Use the following identities:
tan α = sin α / cos α;sin² α + cos² α = 1.Given tan α = 2.4. Using identities, find cosine as follows:
sin α / cos α = 2.4sin α = 2.4 cos αcos² α = 1 - sin² αcos² α = 1 - (2.4 cos² α)²cos² α = 1 - 5.76 cos² αcos² α + 5.76 cos² α = 16.76 cos² α = 12.6 cos α = 1cos α = 1/2.6cos α = 10/26 cos α = 5/13Find sine:
sin² α = 1 - cos² αsin² α = 1 - (5/13)²sin² α = 1 - 25/169sin² α = 144/169sin α = 12/13Julie printed out a picture of each of the six members of her favorite band to decorate her bedroom door. Each picture measures 5 inches by 7 inches. Once decorated, how many square inches of Julie's door will be covered by these pictures?
On Julie's door, the images will span 210 square inches.
As Julie printed six images, the total space that the images cover is:
6 x 35 square inches = 210 square inches
What is an inch?Inches are measured as 1/36 of a yard in both British Imperial and American Customary measurement systems. According to some sources, the term "inch" comes from the Old English "ince" or "ynce," which in turn is said to have originated from the Roman "uncia" unit.
The name of another English unit, the ounce, is derived from the Roman word uncia. According to legend, King David I of Scotland defined the old English word "ynce" as the width of a man's thumb at the base of the nail in the year or thereabouts 1150 AD.
From the question:
Six images total, each measuring 5 by 7 inches, were printed by Julie. We must first calculate the area of each image in order to add up the overall area that these photographs cover.
One image's area is as follows:
5 inches x 7 inches = 35 square inches
As Julie printed six images, the total space that the images cover is:
6 x 35 square inches = 210 square inches
Consequently, 210 square inches of Julie's door will be covered by the images.
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Beverly has a bag of marbles that weighs 30 grams. She knows that each marble weighs 1.5 grams and the bag weighs 1.5 grams. Which equation could she use to determine how many marbles are in the bag? Select all that apply. (1.5)x + 1.5 = 30 30 – x = 2(1.5) (1.5)(30) = 1.5x 1.5 + x = 30 1.5x = 30 – 1.5
(1.5)x + 1.5 = 30 and 1.5x = 28.5 are the correct equations that Beverly could use to determine how many marbles are in the bag.
How to determine the equations of the marblesLet x be the number of marbles in the bag.
Each marble weighs 1.5 grams and the bag weighs 1.5 grams.
Therefore, the total weight of the marbles and the bag is 1.5x + 1.5 grams.
But we know that the total weight is 30 grams.
So, we can write the equation:
1.5x + 1.5 = 30
Simplifying this equation, we get:
1.5x = 28.5
Therefore, the number of marbles in the bag is x = 19.
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PLEASE HELPPPPP
THANKS
Given: trap. SPQR with SP || QR ; MN is the median of the trap. m
Answer: Without additional information about the trap, it is not possible to determine the value of m or any other measurements of the shape. Could you please provide more information or context for the problem?
imhotep the architect wants to paint the great pyramid of giza
Imhotep can pain the pyramid in 256 different ways, and his assistant can make 64 different models of the pyramid, as explained below.
How to pain the pyramid:There are 4 sides to paint, and each side can be painted with one of 4 colors. So the total number of different ways Imhotep can paint the Great Pyramid is:
4 x 4 x 4 x 4 = 256
Therefore, Imhotep can paint the Great Pyramid in 256 different ways. However, as pointed out, many of these ways are just rotations of each other. Specifically, there are 4 different rotations for each way of painting the pyramid. Therefore, the number of distinct models can be seen below:
256 / 4 = 64
Therefore, Imhotep's assistant only needs to make 64 different models.
The complete question is the following:
Imhotep the architect wants to paint the Great Pyramid. He wants one red side, one blue side, one green side and one yellow side. How many different ways can he paint it?His assistant is tasked with making models to show the possibilities. He realises he can make far fewer models as they can be turned around. How many different models does he need to make?Learn more about pyramids here:
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if 24 x 18 and (x-1)are in proportion find the value of x
Answer:
Step-by-step explanation:
If 24, x and 18 are in proportion, then we have:
24 : x = x : 18
This can be rewritten as:
x^2 = 24 x 18
x^2 = 432
Taking the square root of both sides, we get:
x = ± 20.7846
However, we also know that (x - 1) is in proportion with 24 and 18. Therefore:
24 : (x - 1) = (x - 1) : 18
This can be rewritten as:
(x - 1)^2 = 24 x 18
(x - 1)^2 = 432
Taking the square root of both sides, we get:
x - 1 = ± 20.7846
Solving for x in each case, we get:
x = 21.7846 or x = -19.7846
However, we can see that the value x = -19.7846 does not make sense in the context of the problem (since we cannot have a negative value for the number of something). Therefore, we can reject it as an extraneous solution.
Hence, the value of x is:
x = 21.7846
Answer: 21.7846
The sum of two numbers is 22. The difference of the two numbers is 0. What are the two numbers?
Answer:
11
Step-by-step explanation:
because 11+11=22 so there are no different with two 11s
A sum of money is shared such that Mark gets twice as much as Sofia and Tina gets ½ of Sofia's share. Express these amounts in the form of a proportion. If Tina receives $1 200, how much do Mark and Sofia each receive?
Answer:
Step-by-step explanation:
Answer:
Mark gets $4800
Sofia gets $2400
Step-by-step explanation:
Let M, S and T represent the amounts that Mark, Sofia and Tina get respectively
We have the following
M = 2S
S = M/2
T = S/2 = M/2 ÷ 2 = M/4
Therefore the ratio of M : S; T can be expressed in terms of M as
M : M/2 : M/4
Multiplying throughout by 4 gives
4M : 2M : M
Removing the common M the proportion is
4 : 2 : 1
If T = 1200 then from T = S/2, s = 2T = 2 x 1200 = 2400
Since M = 2S, M = 2 x 2400 = 4800
So
Mark gets $4800
Sofia gets $2400
The ratio of the amounts obtained
4800: 2400: 1200
Dividing by 1200 gives us
4800/1200: 2400/1200: 1200/1200
= 4 : 2 : 1
If a 2i j 8k and b i 3 j 4k
, then the magnitude of a b
Answer:
Step-by-step explanation:
To find the magnitude of the cross product of vectors a and b, we can use the formula:
|a x b| = |a| |b| sin(θ)
where |a| and |b| are the magnitudes of vectors a and b, and θ is the angle between them.
First, let's calculate the cross product of vectors a and b:
a x b = (2i + j + 8k) x (i + 3j + 4k)
= (j)(4k) - (8k)(3j) - (i)(4k) - (j)(2i) + (8k)(i) - (2i)(i + 3j)
= -10i - 20j - 20k
Next, let's find the magnitudes of vectors a and b:
|a| = √(2^2 + 1^2 + 8^2) = √(69)
|b| = √(1^2 + 3^2 + 4^2) = √(26)
Finally, we need to find the angle θ between vectors a and b. We can use the dot product to find cos(θ):
a · b = (2i)(i) + (1j)(3j) + (8k)(4k) = 2 + 3 + 32 = 37
|a| |b| cos(θ) = a · b
cos(θ) = a · b / (|a| |b|)
cos(θ) = 37 / (√(69) √(26))
cos(θ) ≈ 0.893
Using the fact that sin^2(θ) + cos^2(θ) = 1, we can solve for sin(θ):
sin(θ) = √(1 - cos^2(θ))
sin(θ) ≈ 0.449
Substituting the values we found into the formula for the magnitude of the cross product, we get:
|a x b| = |a| |b| sin(θ)
|a x b| = √(69) √(26) (0.449)
|a x b| ≈ 26.81
Therefore, the magnitude of the cross product of vectors a and b is approximately 26.81.
A dolphin is 30 feet below the surface of the water. She rises 23 feet and then rises another 7 feet. If there are no changes, where is the dolphin now?
Answer:
1. Start with the dolphin’s initial position, which is -30 feet below the surface of the water. We can use a negative sign to indicate that the dolphin is below the surface.
2. Add 23 feet to the dolphin’s position to represent her first rise. This gives us -30 + 23 = -7 feet. The dolphin is now 7 feet below the surface of the water.
3. Add another 7 feet to the dolphin’s position to represent her second rise. This gives us -7 + 7 = 0 feet. The dolphin is now at the surface of the water.
Therefore, the answer is that the dolphin is now at the surface of the water.
One can also find the interest rate of the uneven cash flow stream with a financial calculator and solving for the internal rate of return (IRR) using the IRR key. Quantitative Problem: You own a security with the cash flows shown below. 0 1 2 3 4 0 690 365 220 330 If you require an annual return of 12%, what is the present value of this cash flow stream? Do not round intermediate calculations. Round your answer to the nearest cent. $
Answer:
To solve this problem, we need to find the present value of the cash flow stream using a discount rate of 12%. We can use the present value formula:
PV = CF1/(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3 + CF4/(1+r)^4
where PV is the present value, CF1, CF2, CF3, and CF4 are the cash flows at time 1, 2, 3, and 4 respectively, and r is the discount rate.
Substituting the values given in the problem, we get:
PV = 690/(1+0.12)^1 + 365/(1+0.12)^2 + 220/(1+0.12)^3 + 330/(1+0.12)^4
PV = 690/1.12 + 365/1.2544 + 220/1.4049 + 330/1.5735
PV = 616.07 + 290.76 + 156.51 + 209.38
PV = 1272.72
Therefore, the present value of the cash flow stream is $1,272.72.
Step-by-step explanation:
Mark bike 4⁄10 mile in 1⁄5 of an hour find mark's average speed in mph
The average speed in mph is 2 mph
What is Average Speed?Average Speed is the total distance that something has traveled by the total amount of time it took it to travel that distance. It is also the total distance traveled by the moving object and the amount of total time the object spent moving.
Average speed = Distance traveled/Time taken
Where Distance traveled = 4/10 mile
Time taken = 1/5 of an hour
To get the average speed in mph,
Average speed = (4/10)/(1`/5)
Average speed = 4/10 * 5/1
Average speed = 20/10
Average speed = 2 mph
Therefore, the average speed is 2mph
Read more about Average Speed
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A baker makes 8 apple pies. Each apple pie weighs 6 ounces.
How many total pounds of apple pies does the baker make?
Responses?
Answer:
6
Step-by-step explanation:
16 Ounces in a pound
6x8=48
48/8=6
Answer:
3 pounds
Step-by-step explanation:
total pie = 8
weight of 1 pie = 6 ounces
weight of 8 pie = 6 ounces × 8
= 48 ounces
ounce into pound
1 ounce =0.0625 (divide ounces by 16)
48 ounces ÷ 16
=3 pounds
the baker made 3 pounds od apple pie