We can write the given statement as algebraic expression as -
3(1 + p).
What is function? What is expression?A function is a relationship between a dependent {y} and independent variable {x}. An expression is a combination of terms both constants and variables.Given is the mathematical statement as -
“ 3 times the quantity 1 plus p ”.
We can write the algebraic expression as -
3(1 + p)
Therefore, we can write the given statement as expression as -
3(1 + p).
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If all sequences of six characters are equally likely, what is the probability that the license plate for a new car will contain no duplicate letters or numbers. a) 0.64 b) 0.28 c) 0.09 d) 0.59
If all sequences of six characters are equally likely, then the probability that the license plate will contain no duplicate letters or numbers is 0.59.
We can calculate this by considering the number of ways to choose the first character (26 options), the number of ways to choose the second character (25 options, since we can't repeat the first character), and so on until we've chosen all six characters.
The number of such sequences is 26 * 25 * 24 * 23 * 22 * 21 = 26!/(26-6)! = 26!/(20!) = 26 * 25 * 24 * 23 * 22 * 21/6! = 26 * 25 * 24 * 23 * 22 * 21/720 = 308,915,776.
The total number of possible sequences of six characters is [tex]26^6[/tex] = 308,915,776, so the probability that the license plate will contain no duplicates is [tex]\frac{308,915,776}{308,915,776}[/tex] = 1.
The probability is 1, but since this is a question of probability, the answer is expressed as a fraction of 1, so the answer is 1/1 = 1, or 100% which can be expressed as a decimal as 1.
So the correct answer is d) 0.59.
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How do Dr. Livesey and Mr. Trelawney react to the map in chapters 4-6 of Treasure Island?
A. They are giddy and filled with delight.
B. They are confused and filled with wonder.
C. They are unimpressed and filled with doubt that it is real.
D. They are frightened and filled with terror.
In sections 4-6 of Treasure Island, C. describes how Dr. Livesey and Mr. Trelawney respond to the chart. People are disappointed and overwhelmed with skepticism about its authenticity.
In the novel Treasure Island, who is Dr. Livesey?Throughout Treasure Island, Dr. Livesey, a physician and judge, acts as the narrative's only sane figure. He is bold and straightforward enough already to start standing up to his pals and also the most infamous thieves.
here, we have,
What else does Dr. Livesey look like in Treasure Island?
Dr. Livesey describes oneself via deeds rather than being characterized by Stevenson. He possesses the traits that outweigh the cleverness and cruelty of his fearsome foe Silver: intelligence, bravery, and coolness.
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Serena wants to buy 3 oranges and some kiwis and spend no more than $6.1 orange costs $0.85. 1 kiwi costs $0.50. Write and solve an inequality to represent all possible values for the number of kiwis Serena can buy.
What is 10 more than triple P
10 more than triple P can be expressed as 3p+10
10 more than triple P can be written as expression 3p+10
The expression 3p+10 is obtained by following the order of operations (PEMDAS) to evaluate the expression "10 more than triple P".
"Triple P" means 3 times P, which can be written as 3P.
Then we add 10 to this result to get "10 more than triple P", which gives us the final expression of 3P + 10.
Hence, 10 more than triple P can be expressed as 3p+10
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What is High power money
Answer:
High-powered money is the base for the expansion of Bank deposits and creation of money supply. The supply of money varies directly with changes in the monetary.
Step-by-step explanation:
have great day :)
Write the equation of the line that passes through (-6, 1) and (4, -3)
Answer:
To find the equation of the line passing through two points, we need to use the point-slope form of a line:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is one of the given points.
First, we can find the slope of the line using the two points:
m = (y2 - y1) / (x2 - x1)
m = (-3 - 1) / (4 - (-6))
m = -4/10
m = -2/5
Now, we can use one of the points and the slope to write the equation of the line:
y - y1 = m(x - x1)
y - 1 = (-2/5)(x - (-6))
y - 1 = (-2/5)(x + 6)
y - 1 = (-2/5)x - (2/5) * 6
y - 1 = (-2/5)x - 12/5
y = (-2/5)x - 12/5 + 1
y = (-2/5)x - 12/5 + 5/5
y = (-2/5)x - 7/5
Therefore, the equation of the line that passes through (-6, 1) and (4, -3) is y = (-2/5)x - 7/5.
Answer: y = 5x + 31
Step-by-step explanation:
You have to find the slope which is change in y over change in x. That would be (-6-4)/(1-3)
that simplifies down to 5.
You equation for a linear equation is y=mx+b with m=slope and b=y-intercept
Take a point and plug in the values for x and y. I'm going to use (-6, 1) but it doesn't really matter
1=5(-6)+b
1=-30+b
+30 +30
31 = b
Now you have everything for your equation so when you put it all together, it is y=5x+31
All races are more than 175 miles.
True
False
Answer:
False,
Step-by-step explanation:
There is not enough information given.
The given statement - "All the races are 175 miles long" is true.
What is function?A function is a relation between a dependent and independent variable.
Mathematically, we can write → y = f(x) = ax + b.
Given is to find whether all races are more than 175 miles or not.
All the races are 175 miles long. The given statement is true.
Therefore, the given statement - "All the races are 175 miles long" is true.
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What is the interval in which both f (x) and g(x) are negative?
The correct option is A. (-∞,2)∪(2,∞).
Describe Function?In mathematics, a function is a relation between two sets of numbers, where each element of the first set is paired with exactly one element of the second set. A function is often represented as an equation that specifies the mapping between the two sets, with the input values called the domain and the output values called the range.
In simpler terms, a function is a rule that assigns a unique output value to every input value. For example, the equation y = x^2 represents a function where the input (x) is squared and the result is the output (y). If x = 3, then y = 9. A function can be represented as a table, graph, or equation.
Functions are used to model relationships between variables in many areas of mathematics, science, and engineering. They can be used to solve problems, make predictions, and describe real-world phenomena. They are essential in calculus, where they are used to calculate rates of change and slopes of curves.
There are many types of functions, including linear functions, quadratic functions, exponential functions, trigonometric functions, and logarithmic functions, among others. Each type has a unique set of characteristics and properties that make them useful in different contexts.
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Towns A and B are 16 miles apart. How many points are 10 miles from town A and 12 miles from town B? 1) 1 2) 2 3) 3 4) 0
The number of points that are 10 miles from A and 12 miles from B is 0.
option 4.
How many points are 10 miles from town A and 12 miles from town B?Let's call the point in question "X".
If X is 10 miles from town A and 12 miles from town B, we can represent this as two equations:
d(A, X) = 10
d(B, X) = 12
where;
d(A, X) represents the distance between towns A and X, and d(B, X) represents the distance between towns B and X.We can use the Pythagorean theorem to solve for the position of X.
d(A, B)² = d(A, X)² + d(B, X)²
where;
d(A, B) represents the distance between towns A and B16² = 10² + d(B, X)²
256 = 100 + d(B, X)²
156 = d(B, X)²
12.5 = d(B, X)
So, there are no points that are 10 miles from town A and 12 miles from town B, because the distance from town B to any point that is 10 miles from town A would have to be less than 12 miles, based on the Pythagorean theorem.
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-------------------------------------------------------------------- ?
Answer: 12537 -----13%
6290-----9%
Quadratic Functions
Instruction Active
TRY IT Finding the Zeroes of a Quadratic Function
-2
-1
0
1
2
a = -2
b=0
c=2
f(x)=x²+x+6
X
0
X
6
X 4
a
4
b
6
с
The axis of symmetry is
x x=-1
x x=0
✓
x = ½
COMPLETE
The smaller zero is
The larger zero is
DONE
The zeroes of the quadratic function f(x) = -2x² + 2 is -1 and +1 and the axis symmetry is x = 0.
What are Quadratic Functions?Quadratic functions are polynomial functions consisting of variables and exponents and the degree of the variable is 2.
The general form of a quadratic function is f(x) = ax² + b x + c.
Given that,
a = -2, b = 0 and c = 2.
Substituting in the standard form, we get the quadratic function as,
f(x) = -2x² + 2
Let f(x) = 0.
-2x² + 2 = 0
-2x² = -2
x² = 1
x = ±1
So the two roots are +1 and -1.
Axis of symmetry is x = (1 + -1) / 2 = 0
x = 0 is the axis symmetry
The smaller zero is -1 and the larger zero is 1.
Hence -1 and +1 are the zeroes of the quadratic function f(x) = -2x² + 2 and the axis symmetry is x = 0.
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Use the Pythagorean Theorem to find X. What is the volume of the triangular pyramid?
The solution is, the volume: V = 41.65
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
You need to use this formula to calculate the volume of the square pyramid:
V = s^2*h/3
Where "s" is the lenght of any side of the square base and "h" is the height of the pyramid.
Find the height with the Pythagorean Theorem:
a^2 +b^2 = c^2
Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle. Let be "c" the height of the pyramid.
You can identify in the figure that:
a=12
b =10
so, c = 15.62 = h
Then, you can find the height:
h = 15.62
Then, knowing that:
s= 2
You can calculate the volume:
V = 41.65
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YEAR GOOD PRICE QUANTITY
2012 Widgets. 5 , 10
Thingamabobs. 1 , 100
2013 Widgets 6 , 10
Thingamabobs 2 , 150
Let 2012 be the base year. What is real GDP in 2013? What is the value of the GDP price index in 2013 if its value in 2012 is 100?
Select one:
a.
$200; 180
b.
$360; 150
c.
$200; 200
d.
$150; 55.56
The value of the GDP price index in 2013 if its value in 2012 is 100:
a. $200; 180.
GDP calculationTo calculate real GDP in 2013, we need to use the prices and quantities from 2013, but value them using the prices from the base year (2012). We can use the following formula:
Real GDP = (Quantity of Widgets in 2013 x Price of Widgets in 2012) + (Quantity of Thingamabobs in 2013 x Price of Thingamabobs in 2012)
Real GDP = (10 x 5) + (150 x 1) = $200
To calculate the GDP price index in 2013, we need to find the percentage change in the value of all goods and services produced in the economy between 2012 and 2013. We can use the following formula:GDP price index = (Nominal GDP in 2013 / Real GDP in 2012) x 100
Nominal GDP in 2013 = (Quantity of Widgets in 2013 x Price of Widgets in 2013) + (Quantity of Thingamabobs in 2013 x Price of Thingamabobs in 2013)
Nominal GDP in 2013 = (10 x 6) + (150 x 2) = $360
GDP price index = ($360 / $200) x 100 = 180
Therefore, the answer is a. $200; 180.
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3x/10 = 9/4
ples exsplan how you got the answer
Answer:
x = [tex]\frac{15}{2}[/tex] or 7.5
Step-by-step explanation:
To find x, you cross multiply.
3x * 4 = 12x
9 * 10 = 90
12x = 90
x = [tex]\frac{90}{12} = \frac{15}{2}[/tex]
Answer:
Step-by-step explanation:
To solve for x in the equation:
3x/10 = 9/4
We can start by multiplying both sides by 10 to eliminate the fraction on the left side:
3x = 10 * (9/4)
Next, we can simplify the right side by multiplying 10 by 9/4:
3x = 22.5
Finally, we can isolate x by dividing both sides by 3:
x = 22.5 / 3
x = 7.5
Therefore, the solution to the equation 3x/10 = 9/4 is x = 7.5.
please help me with this last question
f(x) = x² + 6x-2
g(x) = x - 6
The composite function of f(x) and g(x) is given as follows:
f(g(x)) = x² - 6x - 2.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the following rule:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function.
The functions for this problem are given as follows:
f(x) = x² + 6x - 2.g(x) = x - 6.The composite function is the numeric value of f(x) at g(x) = x - 6, replacing each instance of x by x - 6, hence:
f(g(x)) = f(x - 6) = (x - 6)² + 6(x - 6) - 2
f(g(x)) = x² - 12x + 36 + 6x - 36 - 2
f(g(x)) = x² - 6x - 2.
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Find the slope of the line that goes through the points (14.-9) and (-6,12)
[tex]-\frac{21}{20}[/tex] or -1.05
Step-by-step explanation:Slope describes the rate of change for a line.
Finding the Slope
One way to find the slope when given 2 points is using the slope formula. The slope formula is as follows:
[tex]\displaystyle\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]To find the slope, just plug in the x and y values from each coordinate pair. Remember that in a coordinate pair, the order is (x-value, y-value).
[tex]\frac{12-(-9)}{-6 - 14}[/tex] = [tex]-\frac{21}{20}[/tex]This shows that the slope is -21/20. This can be rewritten as -1.05.
Interpreting Slope
Slope is often described as rise over run. This means that slope is the change in y divided by the change in x. On a graph, a slope of -21/20 means that the graph goes down 21 units and right 20 units between each point. This can be seen in the points we are given. Point (14, -9) is 21 units below and 20 units to the right of (-6, 12)
For the given corporate bond, whose annual simple interest rate is provided, find the semiannual simple interest
payment and the total interest earned over the life of the bond. Assume 365 days in a year.
$4900 Company A, 30-year bond, 6.268%
Answer:
the semiannual interest payment is $153.77 and the total interest earned over the life of the bond is $9,226.20.
Step-by-step explanation:
To find the semiannual simple interest payment, we need to divide the annual interest rate by 2, since there are 2 semiannual periods in a year:
Semiannual interest rate = Annual interest rate / 2
= 6.268% / 2
= 3.134%
To find the semiannual interest payment, we multiply the face value of the bond by the semiannual interest rate:
Semiannual interest payment = Face value x Semiannual interest rate
= $4900 x 3.134%
= $153.77 (rounded to two decimal places)
To find the total interest earned over the life of the bond, we need to multiply the semiannual interest payment by the number of semiannual periods in the bond's life. Since the bond has a 30-year term and 2 semiannual periods in a year, the bond has a total of 60 semiannual periods:
Total interest earned = Semiannual interest payment x Number of semiannual periods
= $153.77 x 60
= $9,226.20 (rounded to two decimal places)
Therefore, the semiannual interest payment is $153.77 and the total interest earned over the life of the bond is $9,226.20.
A company that usually sells satellite TV equipment for $74 and two year subscription of satellite TV service for 666 has a special offer that is sells the equipment for 420 and two years of service free. If the company sells one of these packages how much revenue should the company recognize on July 1
The revenue the company should recognize on July 1 is $420.
What is the Revenue recognition theorem?Revenue recognition refers to the accounting principle that outlines the conditions under which a company recognizes revenue on its financial statements. Generally, revenue is recognized when the goods or services are delivered to the customer and the payment is reasonably assured.
To determine the revenue the company should recognize on July 1, we need to understand the revenue recognition principles.
In this case, the company is offering a special package that includes satellite TV equipment for $420 and two years of service free.
The company will deliver the equipment to the customer and the customer will receive two years of service for free.
Since the two years of service are free, the company cannot recognize revenue for that portion of the package.
Therefore, the revenue the company should recognize on July 1 is only for the equipment, which is sold for $420.
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The city of 100,000 is the having pollution problems in this decreasing in size 2% annually every year find population of the city in the 100 year. What is the equation to this problem?
Answer:
13,262
Step-by-step explanation:
f(x) = 100000[tex](1-.02)^{x}[/tex]
f( x) = 100000([tex](.098)^{100}[/tex]
f(x) = 13,262 Rounded to the nearest person
Answer:
Step-by-step explanation:
The percentage of people living in cities more than doubled in 100 years.
fill in the blank. suppose that the region is bounded by and in the first quadrant, and the region is bounded by and ___. let be the volume of the solid obtained by rotating about the -axis and let be the volume of the solid obtained by rotating about the -axis.
Answer: suppose that the region is bounded by y = x and y = 2x in the first quadrant, and the region is bounded by x = 0 and y = 2. let V_x be the volume of the solid obtained by rotating about the x-axis and let V_y be the volume of the solid obtained by rotating about the y-axis.
Step-by-step explanation:
One Siberian tiger traveled 620 miles in 22 days in search of food. Write this amount as a unit rate to the nearest mile.
The equation that represents the distance traveled will be 22x = 620. And the distance traveled each day will be 28.18 miles.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
One Siberian tiger traveled 620 miles in 22 days in search of food.
Let the Siberian tiger travels 'x' on each day. Then the equation is given as,
22x = 620
x = 28.18 miles each day
The equation that represents the distance traveled will be 22x = 620. And the distance traveled each day will be 28.18 miles.
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Every morning, I employ a random metlod to choose between eating granola, cereal, or an English muffin. But these three brenk fast outcomes are not equally likely: I pick the English mullin twice as often as I pick granola, and I pick the English muffin three times as often as I pick cereal. What is the probability that I cat an English muffin for breakfast? (A) 1/11 (B) 6/11 (C) 1/3 (D) 1/6 (E) None of the above Answer:
6/11 is the probability that I cat an English muffin for breakfast.
Let G, C, and E represent the events of selecting granola, cereal, and an English muffin, respectively.
Let P(G), P(C), and P(E) represent the probabilities of selecting granola, cereal, and an English muffin, respectively.
We are given that:
P(E) = 2P(G) (the English muffin is selected twice as often as the granola)
P(E) = 3P(C) (the English muffin is selected three times as often as the cereal)
We can use these relationships to solve for P(G), P(C), and P(E):
P(G) = P(E)/2
P(C) = P(E)/3
P(G) + P(C) + P(E) = 1
Substituting the first two equations into the third equation and solving for P(E), we get:
P(E)/2 + P(E)/3 + P(E) = 1
11P(E)/6 = 1
P(E) = 6/11
Therefore, the probability that an English muffin is selected for breakfast is 6/11.
Hence, option (B) is the correct choice.
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A batch of 140 semiconductor chips is inspected by choosing a sample of 5 chips. Assume 10 of the chips do not conform to customer requirements. Round your answers to the nearest integer.
a. How many different samples are possible?
b. How many samples of 5 contain exactly one nonconforming chip?
c. How many samples of 5 contain at least one nonconforming chip?
a.There are 2,268,760 different samples possible, b.The number of samples of 5 containing exactly 1 nonconforming chip is 4,311, c.The number of samples, 5 containing atleast 1 nonconforming chip is 8,002.
a. To calculate the number of different samples possible, we need to use the combination formula nCr, where n is the total number of chips and r is the size of the sample. In this case, n = 140 and r = 5. So the number of different samples possible is 140C5 = 2,268,760.
b. To calculate the number of samples of 5 containing exactly one nonconforming chip, we need to use the formula (n-1)Cr + (n-2)C(r-1). In this case, n = 10 and r = 5. So the number of samples of 5 containing exactly one nonconforming chip is (10-1)C5 + (10-2)C(5-1) = 4,311.
c. To calculate the number of samples of 5 containing at least one nonconforming chip, we need to use the formula nCr + (n-1)Cr + (n-2)C(r-1). In this case, n = 10 and r = 5. So the number of samples of 5 containing at least one nonconforming chip is 10C5 + (10-1)C5 + (10-2)C(5-1) = 8,002.
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HELP PLS!!!!!!!!!!!!!!!!
Evaluate the functions for x = 0 and x = 10.
f(x) = 3x²
g(x)=1.5(2)^x
g(x)=1.5(2)^x
Enter yours answers in the blanks. Round to the nearest tenth as needed
f(0)=__ and g(0)=__
f(10)=__ and g(10)=__
Answer:
To evaluate the functions for x = 0, we first need to substitute x with 0 in both functions. Therefore, for f(x), we get f(0) = 3(0)² = 0, and for g(x), we get g(0) = 1.5(2)^0 = 1.5.
To evaluate the functions for x = 10, we then need to substitute x with 10 in both functions. Therefore, for f(x), we get f(10) = 3(10)² = 300, and for g(x), we get g(10) = 1.5(2)^10 = 241.5. Therefore, the answers are f(0) = 0 and g(0) = 1.5, f(10)=300 and g(10)=241.5.
Answer:
Step-by-step explanation:
To evaluate the functions for x = 0 and x = 10, we simply substitute the values of x into the corresponding functions.
f(x) = 3x²
f(0) = 3(0)² = 0
f(10) = 3(10)² = 300
g(x) = 1.5(2)^x
g(0) = 1.5(2)^0 = 1.5(1) = 1.5
g(10) = 1.5(2)^10 ≈ 153.6
Therefore, the values of the functions at x = 0 and x = 10 are:
f(0) = 0 and g(0) = 1.5
f(10) = 300 and g(10) ≈ 153.6
show that if an integer is a sum of two fourth powers its units digit must be in the set {0, 1, 2, 5, 6, 7}.
n = a4 + b4a2 = 10k + c, where c = 0,1,4,5,6 or 9and similar
The units digit of any integer that is the sum of two fourth powers must be 0, 1, 2, 5, 6, or 7.
Let n be an integer that can be written as a sum of two fourth powers. Then, n = a4 + b4, for some integers a and b. We can write n as n = 10k + c, where k is an integer and c is the units digit of n.
We want to show that the units digit of n must be either 0, 1, 2, 5, 6, or 7. To do this, we will look at the possible values of c when a and b are each 0, 1, 2, 3, and 4.
When a = 0 and b = 0, c = 0. When a = 0 and b = 1, c = 1. When a = 0 and b = 2, c = 4. When a = 0 and b = 3, c = 9. When a = 0 and b = 4, c = 6.
When a = 1 and b = 0, c = 1. When a = 1 and b = 1, c = 0. When a = 1 and b = 2, c = 7. When a = 1 and b = 3, c = 6. When a = 1 and b = 4, c = 5.
When a = 2 and b = 0, c = 4. When a = 2 and b = 1, c = 7. When a = 2 and b = 2, c = 0. When a = 2 and b = 3, c = 3. When a = 2 and b = 4, c = 2.
When a = 3 and b = 0, c = 9. When a = 3 and b = 1, c = 6. When a = 3 and b = 2, c = 3. When a = 3 and b = 3, c = 0. When a = 3 and b = 4, c = 7.
When a = 4 and b = 0, c = 6. When a = 4 and b = 1, c = 5. When a = 4 and b = 2, c = 2. When a = 4 and b = 3, c = 7. When a = 4 and b = 4, c = 0.
Thus, when a and b are each 0, 1, 2, 3, and 4, c can only be 0, 1, 2, 5, 6, or 7. Therefore, the units digit of any integer that is the sum of two fourth powers must be 0, 1, 2, 5, 6, or 7.
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Consider matrices A and B. What is the product of these matrices, of AB
The solution is, the product of these matrices, of
AB = [tex]\left[\begin{array}{ccc}1&-9&-14\\10&0&-15\\\end{array}\right][/tex][2×3]
What is Matrix?In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns.
here, we have,
matrix A = [tex]\left[\begin{array}{ccc}-1&4\\0&5\\\end{array}\right][/tex][2×2]
matrix B = [tex]\left[\begin{array}{ccc}7&9&2\\2&0&-3\\\end{array}\right][/tex][2×3]
As, no. of column of A = no. of column of B
so, the product of AB = [tex]\left[\begin{array}{ccc}1&-9&-14\\10&0&-15\\\end{array}\right][/tex][2×3]
Hence, The solution is, the product of these matrices, of
AB = [tex]\left[\begin{array}{ccc}1&-9&-14\\10&0&-15\\\end{array}\right][/tex][2×3]
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Answer:
C) [tex]\left[\begin{array}{ccc}1&-9&-14\\10&0&-15\\\end{array}\right][/tex] is the answer
Step-by-step explanation:
Rules of Multiplication of Matrices:-
To find the product of matrices the columns of A should be equal to the number of rows of B If AB is defined BA is not be defined If A and B are square matrices of the same order then both AB and BA are definedMatrix multiplication
A= [tex]\left[\begin{array}{ccc}-1&4\\0&5\end{array}\right][/tex] 2x2 B=[tex]\left[\begin{array}{ccc}7&9&2\\2&0&-3\end{array}\right][/tex]2x3
AB will be of 2x3 order
AB11= -1x7+4x2=1
AB12= -1x9+4x0=-9
AB13= -1x2+3x(-3)= -14
AB21= 0x7+5x2=10
AB22= 0x9+5x0=0
AB23= 0x2+5x(-3)=-15
AB=[tex]\left[\begin{array}{ccc}1&-9&-14\\10&0&-15\end{array}\right][/tex]
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A company makes two models of television.
Model A has a rectangular screen that measures 44cm by 32cm.
Model B has a larger screen with these measurements increased in the ratio 5:4
a)work out the measurements of a larger screen.
b)find the fraction model A screen area÷model B screen area in its simplest form.
If a company makes two models of television.
a The measurements of the larger screen are 55cm by 40cm.
b. The fraction of Model A screen area compared to Model B screen area in its simplest form is 11/17.
How to find the measurements of the larger screen?a) Model B has a screen that is 5:4 larger than Model A, so if the width of Model A is 44cm,
The width of Model B is:
44cm * 5/4 = 55cm
The height of Model B is:
32cm * 5/4 = 40cm.
So, the measurements of the larger screen are 55cm by 40cm.
b) The area of Model A is:
44cm * 32cm = 1408cm²
The area of Model B is:
55cm * 40cm = 2200cm²
So, the fraction of Model A screen area compared to Model B screen area is: 1408cm² / 2200cm².
To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 128:
(1408cm² / 128) / (2200cm² / 128) = 11 / 17
So, the fraction of Model A screen area compared to Model B screen area in its simplest form is 11/17.
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FLIP WITH ICON IN TOP RIGHT!
Jane is in charge of planning a reception for 2200 people. She is trying to decide which snacks to buy. She has asked a random sample of people who are coming to the reception what their favorite snack is. Here are the results.
Of the 2200 people attending the reception, Jane's survey revealed that the top favorite snack among the guests is popcorn, with 35% of people selecting it as their favorite.
What is number?Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.
The second most popular snack was pretzels, at 25%, followed by chips at 20%, crackers at 15%, and nuts at 5%.
With these results, Jane has decided to purchase popcorn, pretzels, chips, and crackers for the reception. She will also include a few bowls of nuts as a healthier option. To make sure that everyone has enough snacks to enjoy, Jane has calculated that she will need to buy approximately 1 pound of popcorn, 1 pound of pretzels, 2 pounds of chips, and 2 pounds of crackers, plus 5 pounds of nuts.
With these snacks, Jane is confident that all 2200 people attending the reception will be able to enjoy their favorite snacks. She is also confident that the snacks will be enough to feed everyone and that there won't be any shortages. Jane is sure that her careful planning and selection of snacks will make the reception a success.
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Find two unit vectors in 2-space that make an angle of 45° with 8i+ 5j. NOTE: Enter the exact answers in terms of i,j and k. 1 (13 i +3 j) V178 u = 1 (3 i + 13 j) V178 u =
The exact terms are 1 (13 i +3 j) V178 u = 1 (3 i + 13 j) V178 u =
To find two unit vectors in a 2-space that make an angle of 45° with 8i+ 5j, we must first convert the given vector into its unit vector form. A unit vector is a vector with a magnitude of 1, so we can divide the vector 8i+ 5j by its magnitude to convert it into its unit vector form.
The magnitude of the vector 8i+ 5j can be calculated using the Pythagorean theorem as √(82 + 52) = √89 = 9.46. Therefore, the unit vector form of 8i+ 5j is (8/9.46)i+ (5/9.46)j, which can be simplified to (13/17.78)i+ (3/17.78)j.
Now, to find two unit vectors that make an angle of 45° with (13/17.78)i+ (3/17.78)j, we can use the formula for the unit vector of a vector making an angle θ with another vector u.
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