The probability that a customer likes cake and pie is 0.16.
What is the probability?Probability is used to determine the odd that a random event would happen. The odds that the event happens usually lie between 0 and 1.
The probability that a customer likes cake and pie = total number of customers who like cake and pie / total number of customers
4/25 = 0.16
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1. Solve the following simultaneous equations using the matrix method.
(a) LetA=(4 −3)
(2 5)
(i) Determine the determinant of A
(ii) Determine the adjoint of A
(iii) Determine the inverse of A
(iv) Hence, using the matrix method solve the following simultaneous
equations
4 − 3 = 6
2 + 5 = 16
(i) Use the formula for the determinant of a 2×2 matrix.
[tex]\begin{vmatrix}a&b\\c&d\end{vmatrix} = ad-bc[/tex]
[tex]\implies \det(A) = \begin{vmatrix}4 & -3 \\ 2 & 5\end{vmatrix} = 4\times5 - (-3)\times2 = \boxed{26}[/tex]
(ii) The adjugate matrix is the transpose of the cofactor matrix of A. (These days, the "adjoint" of a matrix X is more commonly used to refer to the conjugate transpose of X, which is not the same.)
The cofactor of the (i, j)-th entry of A is the determinant of the matrix you get after deleting the i-th row and j-th column of A, multiplied by [tex](-1)^{i+j}[/tex]. If C is the cofactor matrix of A, then
[tex]C = \begin{pmatrix}5&-2\\3&4\end{pmatrix}[/tex]
Then the adjugate of A is the transpose of C,
[tex]\mathrm{adj}(A) = C^\top = \boxed{\begin{pmatrix}5&3\\-2&4\end{pmatrix}}[/tex]
(iii) The inverse of A is equal to 1/det(A) times the adjugate:
[tex]A^{-1} = \dfrac1{\det(A)} \mathrm{adj}(A) = \boxed{\begin{pmatrix}\frac5{26}&\frac3{26}\\\\-\frac1{13}&\frac2{13}\end{pmatrix}}[/tex]
(iv) The system of equations translates to the matrix equation
[tex]A\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}6\\16\end{pmatrix}[/tex]
Multiplying both sides on the left by the inverse of A gives
[tex]A^{-1}\left(A\begin{pmatrix}x\\y\end{pmatrix}\right)=A^{-1} \begin{pmatrix}6\\16\end{pmatrix}[/tex]
[tex]\left(A^{-1}A\right)\begin{pmatrix}x\\y\end{pmatrix}=A^{-1} \begin{pmatrix}6\\16\end{pmatrix}[/tex]
[tex]\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}\frac5{26}&\frac3{26}\\\\-\frac1{13}&\frac2{13}\end{pmatrix} \begin{pmatrix}6\\16\end{pmatrix}[/tex]
[tex]\begin{pmatrix}x\\y\end{pmatrix}=\boxed{\begin{pmatrix}3\\2\end{pmatrix}}[/tex]
Can someone solve this for me?
Which equation is correct?
O a
52 x 7 = 50+ 2 × 7
Ob
b
52 x 7 = 50 x 7+2
Oc
52 x 7 = 50 x 7+2x7
Od
52 x 7 = 500 ×7+2×7
Answer:
52 x 7= 50 x 7 + 2 x 7
Step-by-step explanation:
answer question below.
The speed of the Elvira is 6.545 miles per hour. Then the speed of the Altheia will be 0.545 miles per hour.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
Let the speed of the Elvira be x. Then the speed of the Altheia will be (x - 6).
Let the distance between the coffee shop and Elvira's house be d.
Then the distance between the coffee shop and Altheia's house will be (3.6 - d).
Then we have
x = d / 0.5 ...1
(x - 6) = (3.6 - d) / 0.6 ...2
In solving the equations 1 and 2, we have
x = 6.545 and d = 3.2725 miles
Then the speed of the Elvira is 6.545 miles per hour. Then the speed of the Altheia will be 0.545 miles per hour.
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Kelsey has a new baby brother!
He weighs 8 lbs 3 oz. The
doctor said the baby should
gain about 5 ounces per week.
At that rate, how much should
the baby weigh in 3 months (12
weeks)? In lb and oz
5 ounces per week x 12 weeks = 60 ounces
1 pound = 16 ounces
60 / 16 = 3 pounds 12 ounces
3 pounds 12 ounces + 8 pounds 3 ounces = 11 pounds 15 ounces
answer: 11 pounds 15 ounces
What 3- D figure does the net below create when folded?
The net given below when folded will form a 3-Dimensional shape, this shape is a triangular prism.
What is a triangular prism?Suppose you've got a triangle. Now, stretch it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.
Usually, when we talk about a triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.
The net given below when folded will form a 3-Dimensional shape, this shape is a triangular prism.
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BIY
74
6+
84
3
-2 -1
D'
B
1
Which rule represents the translation from the pre-
image, ABCD, to the image, A'B'C'D'?
T₁-2(x, y)
OT₁,2(x, y)
T-2, 1(x, y)
OT2 1(x, y)
Answer:d
Step-by-step explanation:
The translation from the pre-image, Parallelogram ABCD, to the image, Parallelogram A'B'C'D' is T2, 1(x, y)
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The parallelogram ABCD is shifted to the right by 2 units and shifted up by 1 unit to get parallelogram A'B'C'D'.
Graph transformation is the process by which a graph is modified to give a variation of the proceeding graph.
The graphs can be translated or moved about the xy-plane.
This transformation rule is represented as:
(x,y) -> (x + 2,y + 1)
This transformation rule can be rewritten as:
T2, 1(x, y)
Hence, the translation from the pre-image, Parallelogram ABCD, to the image, Parallelogram A'B'C'D' is T2, 1(x, y)
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f(x)= 3x + 4 + 2
g(x) = 4
Find (f + g)(x).
A. (f+g)(x) = |3x + 4| +6
B. (f+g)(x) = |3x + 6 + 4
O c. (f+g)(x) = |3x + 10||
D. (f+g)(x) = |3x| + 10
Answer:
3x + 4 + 2
7x + 2
9x
9x + 4
13x
Step-by-step explanation:
3x add 4 and 2
7x add 2
What is the length of AC?
Answer:
I think it's 5
Step-by-step explanation:
The distance from point A to 0 is 2, then to point B makes it 3, then to point C is a total of 5. Or you could just add the absolute value of A, which is 2, with the absolute value of C, which is 3 to get 5
Answer me pleaseeee..... prime numbers between 1 to 10 ?
Answer:
2, 3, 5, 7
Step-by-step explanation:
prime numbers between 1 to 10 are 2,3,5,7. it's very easy. 1 is not prime number because it behave as both prime and composite.
Which of the following points could be the initial point of vector v if it has a
magnitude of 10 and the terminal point (-3,3) ?
(-9,-5)
(-13,-7)
(0,2)
(-0.3,0.3)
The initial point of vector v if it has a magnitude of 10 and the terminal point (-3,3) is option B (-9,-5).
How to find the vector component?If we have given a vector v of initial point A and terminal point B
v = ai + bj
then the components form as;
AB = xi + yj
Here, xi and yj are the components of the vector.
Given;
The magnitude of 10 and the terminal point (-3,3).
v = ai + bj
v = [tex]\sqrt{a^2 + b^2}[/tex]
10 = [tex]\sqrt{a^2 + b^2}[/tex]
AB = (-3 - a)i + (3 - b)j
If we put (-9,-5)then
AB = (-3 - a)i + (3 - b)j
AB = (-3 + 9)i + (3 + 5)j
AB = 6i + 8j
Put the value in the vector magnitude
10 = [tex]\sqrt{a^2 + b^2}[/tex]
= [tex]\sqrt{6^2 + 8^2}\\\\\sqrt{36+ 64}\\\\\sqrt{100}[/tex]
10 = 10
Thus, The correct option is B (-9,-5).
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Help me pls I don't understand.
Answer: The correct answer is (-1, 2).
Step-by-step explanation: Find how many units the original F point is away from the center. It is 2 units away in terms of x, and 4 units away in terms of y. The x value has to be negative since the initial x point was already negative. -2/2 = -1. Hence, the x value is -1. 4/2 = 2. Hence, the y value is 2.
Does anyone know how to do this
Raheem's rollerblades cost $70.25 less than his bicycle. His rollerblades cost $43.50. how much did his bicycle (B) cost?
Answer:
$113.75
Step-by-step explanation:
First add 70.25 to 43.50 to get 113.75
Answer:
$113.75
Step-by-step explanation:
b-70.25=43.50
add 70.25 to each side ..
b-70.25=43.50
+70.25+70.25
simpilfy...b=113.75
A polynomial function h(x) with integer coefficients has a leading coefficient of 20 and a constant term of 1. According to the Rational Root Theorem, which of the following are possible roots of h(x) ?
The image of (-4,-3) reflected across the x-axis is
Step-by-step explanation:
Reflection in the x axis (x,y)—>(x,-y)
(-4,-3)—>(-4,3)
4. Give 5 possible solutions to the equation: y = -2x + 5
X
Y
Answer:
(0, 5), (1, 3), (2, 1), (3, -1), (4, -3)
Step-by-step explanation:
To find the possible solutions, we just plug in a random value for x and then solve for y. When x - 0, y = 5. When x = 1, y = 3. We just continue doing this until we have 5 different solutions.
What is the value of x in this figure?
5√3
10√3
3
о
O 5
o 5√2
O
↓↓
Check the picture below.
Members of a softball team raised $1405.25 to go to a tournament. They rented a bus for $822.50 and budgeted $27.75 per player for meals. Write and solve an equation which can be used to determine xx, the number of players the team can bring to the tournament.
The number of players the team can bring to the tournament is 21
Writing and solving equationFrom the question, we are to write an equation that can be used to solve the number of players the team can bring to the tournament
From the given information,
The members of the softball team raised $1405.25 and they rented a bus for $822.50
∴ They have $1405.25 - $822.50 left
Also, they budgeted $27.75 per player for meals
Then, x, the number of players the team can bring to the tournament is
x = ($1405.25 - $822.50) ÷ $27.75
x = $582.75 ÷ $27.75
x = 21
Hence, the number of players the team can bring to the tournament is 21.
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The population standard deviation for the height of college hockey players is 3.4 inches. If we want to estimate 90% confidence interval for the population mean height of these players with a 0.6 margin of error, how many randomly selected players must be surveyed? (Round up your answer to nearest whole number) Answer:
Answer:
i thank 4 for this players
How do you account for current liabilities and long-term debt?
The current portion of the long term liabilities are included in Current Liabilities.
What are long term liabilities ?Long term liabilities are monetary obligations of a company that has to pay after an year.
Current Liabilities are those liabilities which have top be paid in the present financial year .
It includes the short term borrowings , accounts payable , expenses , notes payable etc.
The current portion of the long term liabilities are included in Current Liabilities.
Like the interest of a long term loan of this year is a long term liability in the current year.
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[tex]{x}^{3} {y}^{4} \times {x}^{5} {y}^{ - 5} [/tex]
pls solve this problem
[tex]x^3 y^4 \cdot x^5 y^{-5}\\\\=x^{5+3} \cdot y^{4-5}~~~~~~~~~~~~~~~~~~~~~~~;[a^m \cdot a^n = a^{m+n}]\\\\=x^8 y^{-1}\\\\=\dfrac{x^8}{y}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[a^{-n} = \dfrac 1{a^n},~~~ a \neq 0\right][/tex]
what percentage of #1.50 is left after giving out 105k
Answer:
30%
Step-by-step explanation:
150-105 = 45
(45 / 150 ) * 100 = 30%
The percentage of 150 is left after giving out 105 is 30%
The given numbers are 150 and 105.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Now, the difference of numbers = 150-105=45
45/150 × 100
= 30%
Therefore, the percentage of 150 is left after giving out 105 is 30%
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"Your question is incomplete, probably the complete question/missing part is:"
What percentage of 150 is left after giving out 105.
Find the perimeter of parallelogram ABCD with vertices A(-5,6), B(2,6), C(1,-2), and D(8,-2)
17 units
43 units
34 units
40 units
Answer:
34 [units].
Step-by-step explanation:
1) according to the property of parallelogram (AC=BD and AB=CD) the required perimeter can be calculated as P=2AB+2AC;
2) the length of AB=7 (the coordinates 'y' are equal);
3) the length of AC:
[tex]|AC|=\sqrt{(1+5)^2+(-2-6)^2}=10.[/tex]
4) finally, the required perimeter is:
P=2(7+10)=34 [units].
What is the slope of the line y = x+4?
OA - 12/20
1
OB. 2
O C. -4
OD. 4
Step-by-step explanation:
Heres the answer And if it doesn't work tell me
Need an answer whoever can do it thank youuu!!!!
Answer:
65.3ft
Step-by-step explanation:
I think it might be this I'm not sure
ANSWER QUICK PLSSSS AND MAKE SURE YOUR ANSWER IS CORRECT!!
Which of the following algebraic expressions can be used to express the statement "three less than z squared?" (5 points)
z2 − 3
3 − z2
3 − 2z
2z − 3
Which is an equation of the line that
passes through the points (5,2) and
(10, -3)?
F. y=x-3
G. y=x-8
H. y=-x+7
J. y=-x+12
please help step by step if possible!!
Step-by-step explanation:
(5,2) & (10,-3)
the slope of the points are
y2 - y1 / x2- x1
-3-2/10-5
-5/5
-1
the mid point of the given points are
x= x1 + x2/2 , y= y1 +y2 /2
.
.
.
.
( , )
the equation of the line that passes through the given points are as
y+ y1 = m (x+ x1)
:. now put the value of the mid point in y1 and x1 and the value of slope in m
also find the mid point, it's hard to do it in a mobile without calculator and paper and pen
sorry
8. What is the volume of the pyramid?
PLS GELP
The volume of the given pyramid is 64 cubic inches.
What is the volume of the pyramid?The volume of the pyramid is the product of one-third of the height and square of the base side length.
The volume of Pyramid A = (1/3)(side²)(height)
The volume of a square pyramid is equal to one-third of the product of the base’s area and the pyramid’s height. The formula is:
V = (1/3) × a² × h
where a is the length of the square base, and h is the height (or altitude).
We are given that;
h = 3 inch, a = 8 inch, and hypotenuse = 5 inch,
Now, we can plug in the values into the formula and get:
V = (1/3) × 8² × 3
V = (1/3) × 64 × 3
V= (64 x 3)/3
V = 64 inch³
Therefore, by the given data the volume of the pyramid will be 64 cubic inches.
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20 of my friends play basketball or soccer or both. 8 of them play basketball (and maybe both soccer too), while 5 play both. How many play soccer?
Answer:
7 frnds will play soccer!
Step-by-step explanation:
8+5 = 13
20 - 13 = 7
I hope it helps u dear! (^^)