Answer:
1120 combinations of four teachers include exactly one of either Mrs. Vera or Mr. Jan.
Step-by-step explanation:
The order in which the teachers are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
1 from a set of 2(Either Mrs. Vera or Mr. Jan).
3 from a set of 18 - 2 = 16. So
[tex]C_{2,1}C_{16,3} = \frac{2!}{1!1!} \times \frac{16!}{3!13!} = 1120[/tex]
1120 combinations of four teachers include exactly one of either Mrs. Vera or Mr. Jan.
Expand and simplify the following. Show all the steps.
a. -4(a-4)
b. 3a(a+2)
c. 4x - 2(5 - x)
d (x-3)(x+2)
e (x+4)2
a. The expanded and simplified form is: -4a + 16
b. The expanded and simplified form is: 3a^2 + 6a
c. The expanded and simplified form is: 6x - 10
d. The expanded and simplified form is: x^2 - x - 6
e. The expanded and simplified form is: x^2 + 8x + 16
Sure, let's expand and simplify each expression step by step:
a. -4(a - 4)
Step 1: Apply the distributive property (multiply -4 by each term inside the parentheses).
-4(a) + -4(-4)
Step 2: Simplify the terms.
-4a + 16
So, the expanded and simplified form is: -4a + 16
b. 3a(a + 2)
Step 1: Apply the distributive property (multiply 3a by each term inside the parentheses).
3a * a + 3a * 2
Step 2: Simplify the terms.
3a^2 + 6a
So, the expanded and simplified form is: 3a^2 + 6a
c. 4x - 2(5 - x)
Step 1: Apply the distributive property (multiply -2 by each term inside the parentheses).
4x - 2 * 5 + 2 * x
Step 2: Simplify the terms.
4x - 10 + 2x
Step 3: Combine like terms.
6x - 10
So, the expanded and simplified form is: 6x - 10
d. (x - 3)(x + 2)
Step 1: Apply the distributive property (multiply x by each term inside the second parentheses and then multiply -3 by each term inside the second parentheses).
x * x + x * 2 - 3 * x - 3 * 2
Step 2: Simplify the terms.
x^2 + 2x - 3x - 6
Step 3: Combine like terms.
x^2 - x - 6
So, the expanded and simplified form is: x^2 - x - 6
e. (x + 4)^2
Step 1: Apply the square of a binomial formula: (a + b)^2 = a^2 + 2ab + b^2
(x)^2 + 2(x)(4) + (4)^2
Step 2: Simplify the terms.
x^2 + 8x + 16
So, the expanded and simplified form is: x^2 + 8x + 16
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solve the inequality and graph the solution
-5-7x < -40
Answer:
x > 5
Step-by-step explanation:
-5-7x < -40
Add 5 to each side
-5+5-7x < -40+5
-7x < -35
Divide by -7, remembering to flip the inequality
-7x/-7 > -35/-7
x > 5
Open circle at 5, going to the right
Se desea pintar un cuadrado inscrito en una circunferencia de radio R=3cm como se muestra en la figura. Calcular el área del cuadrado
El área del cuadrado es de 3 centímetros cuadrados.
Dado que se desea pintar un cuadrado inscrito en una circunferencia de radio R=3cm como se muestra en la figura, para calcular el área del cuadrado se debe realizar el siguiente cálculo:
Radio = diámetro / 2 3 = X/2 X = 6Hipotenusa del triángulo interno: 6 cmAplicando teorema pitagórico: lado al cuadrado mas lado al cuadrado es igual a hipotenusa al cuadrado.
L^2 + L^2 = 62L^2 = 6L^2 = 6/2L = √ 3L = 1.732Área de un cuadrado = L x L = L^2 = 3Por lo tanto, el área del cuadrado es de 3 centímetros cuadrados.
Aprende más en https://brainly.com/question/16405529
El área del cuadrado es de 18 centímetros cuadrados.
El procedimiento de resolución se basa en conocer que la Medida de la Diagonal de un Cuadrado inscrito es igual a la Medida del Radio del Círculo, lo cual permite determinar el valor de la medida del Cuadrado en función del Radio del Círculo. Finalmente, determinamos el Área del Cuadrado mediante su fórmula conocida.
Dado que existe un cuadrado inscrito en un círculo, la medida de la diagonal del cuadrado es igual a la medida del radio del círculo. Además, conocemos que un cuadrado está formado por 4 triángulos rectángulos con configuración angular 45-45-90. Entonces, la medida del lado del cuadrado se calcula mediante la siguiente relación geométrica:
[tex]l = \sqrt{2}\cdot R[/tex] (1)
Donde:
[tex]R[/tex] - Radio del círculo, en centímetros.
[tex]l[/tex] - Longitud del lado del cuadrado, en centímetros.
Por otra parte, la ecuación de área del cuadrado es igual a:
[tex]A = l^{2}[/tex] (2)
Donde [tex]A[/tex] es el área del cuadrado, en centímetros cuadrados.
Si sabemos que [tex]R = 3\,cm[/tex], entonces el área del cuadrado es:
[tex]l = \sqrt{2}\cdot (3\,cm)[/tex]
[tex]l = 3\sqrt{2}\,cm[/tex]
[tex]A = (3\sqrt{2}\,cm)^{2}[/tex]
[tex]A = 18\,cm^{2}[/tex]
El área del cuadrado es de 18 centímetros cuadrados.
He aquí una pregunta relacionada sobre el área del cuadrado: https://brainly.com/question/23915250
ailey is shopping at a department store during a 20% off everything sale. She also has a coupon for $5.00 off the sale amount. Hailey wants to keep her total under $65.00 before tax, so she creates this inequality:
0.80x − $5.00 ≤ $65.00.
Which inequality represents all possible solutions for x?
A.
x ≤ $75.00
B.
x ≤ $76.25
C.
x ≤ $86.25
D.
x ≤ $87.50
Answer:
D
Step-by-step explanation:
0.8x-5<=65
0.8x<=70
x<=700/8=87.5
Answer:
D
Step-by-step explanation:
State if the triangles are similar. If so, how do you know they are similar and complete the similarity statement.
ΔFED
~ ____
Answer:
FED ~ MLF
Step-by-step explanation:
∠L = ∠E
∠F = ∠F
Since both angles are congruent, that would mean all angles are congruent.
If all angles are congruent, then the triangles are always similar no matter the length of the sides.
The complete statement is [tex]\triangle FED\sim \triangle FLM[/tex].
What are the similar triangles?Similar triangles are the triangles that have the same shape, but their sizes may vary.
What is AA or angle angle similarity rule?If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.
What are vertically opposite angles?When two lines intersect each other, then the opposite angles are formed due to intersection are called vertical angles or vertically opposite angles.
According to the given question.
We have two triangles LMF and EDF
In triangles LMF and EFD we have
∠MLF = ∠DEF (given)
Also, ∠MFL = ∠DFE (vertically opposite angles)
Since, we know that " if any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other".
Therefore, by AA similarity criteria triangle FED is similar to FLM.
Hence, the complete statement is [tex]\triangle FED\sim \triangle FLM[/tex].
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Algebraic expression for 2a+3b-c if a=3 b=-4 c=-2
Answer:
-4
Step-by-step explanation:
a = 3
b = -4
c = -2
2a + 3b - c
= 2(3) + 3(-4) - (-2)
= 6 + (-12) + 2
= -4
Find the area of a parallelogram with a base of 9m and a height of 5
Answer:
A=45m²
Step-by-step explanation:
A=bh=9·5=45m²
What is the result of substituting for y in the bottom equation?
y=x-7
y=2+2x-4
Answer:
Plug x-7 in for y, in the bottom equation.
x - 7 = 2 + 2x - 4
x - 7 = 2x - 2
x = 2x + 5
-x = 5
x = -5
Solve by taking the square root of both sides: (x+3)^2 - 169 = 0
Answer:
x = 10 x = -16
Step-by-step explanation:
(x+3)^2 - 169 = 0
Add 169 to each side
(x+3)^2 - 169+169 = 0+169
(x+3)^2 =169
Take the square root of each side
sqrt((x+3)^2) =sqrt(169)
x+3 =±13
x+3 = 13 x+3 = -13
Subtract 3 from each side
x+3-3 = 13-3 x+3-3 = -13
x = 10 x = -16
Thank you so much thank y’all
Someone help me with this
Answer:
(6,-3) and 5
Step-by-step explanation:
Compare it to the standard equation of circle and we will get center is (6,-3) and radius=5
repost , can someone help asap!
Answer:
y = -3/4x + 3
Step-by-step explanation:
WILL MARK BRAINLEST!!Use the remainder theorem to find T(2) for T(x)= 3x3 - 2x2 - 6x -5.
A) -21
B) -1
C) 21
D) 1
Answer:
B
Step-by-step explanation:
T(x)=3x³-2x²-6x-5
T(2)=3(2)³-2(2)²-6(2)-5
=24-8-12-5∵
=-1
Một lớp có 40 học sinh gồm học sinh giỏi, học sinh khá , và học sinh trung bình , số hs trung bình chiếm 1/4 cả lớp , số hs khá bằng 60% số học sinh còn lại a) tính số học sinh mỗi loại B) tổng số hs khá và giỏi chiếm bao nhiêu phần trăm trong lớp
Answer:
Đổi 60% = 3/5
a) Số học sinh trung bình là: 40 * 1/4 = 10 (hsinh)
Tổng số hsk và hsg là: 40 - 10 = 30 (hsinh)
Số học sinh khá bằng 60% số học sinh còn lại nên số hsk là:
30 * 60% = 18 (hsinh)
Số học sinh giỏi là: 30 - 18 = 12 (hsinh)
b) Tổng số hs khá và giỏi chiếm số phần trăm trong lớp là:
30 : 40 * 100 = 75%
2(x-y)(x+y)+(x+y)*2+(x-y)
Answer:
2 x ^2 − 2 y^ 2 + 3 x + y
Step-by-step explanation:
Give an example of a trinomial with a GCF of 6a.
9514 1404 393
Answer:
18a +42ax +24az
Step-by-step explanation:
6a(3 +7x +4z) = 18a +42ax +24az
__
Additional comment
In order for 6a to be the GCF, the terms inside parentheses cannot have any common factors.
What is the period of the graph of y=1/2 sin (2πx) -3?
A. 1
B. 1/2
C. 3
D. 2π
Answer:
A. 1
Step-by-step explanation:
Since this graph is in the form A sin (B(x+c))+d, where
the amplitude is the absolute value of AThe period is 2pi/BPhase Shift is CMidline is y=DTherefore, the values are
A=1/2
B=2pi
C=0
D=-3
So the period is 2pi/2pi which is 1.
Find the angle between the hands of a clock at 5:15
Answer:
67.5
Step-by-step explanation:
Answer:
the hour hand and minute hand on a 12-hour clock at 5:15. Again, the two angles created by the hour hand and minute hand at five-fifteen are 292.5 degrees and 67.5 degrees.
Step-by-step explanation:
Rose has $83. She is saving up for a new bike. If she saves $15 per week, how much money will she have after 8 weeks?
How much money does Rose have after 8 weeks? Solve on paper, then enter your answer on Zearn.
Rose has $
after 8 weeks.
Answer:
$203
Step-by-step explanation:
15x8=$120
120+83=$203
Which linear inequality is represented by the graph?
Answer:
Wow
Step-by-step explanation:
I love the question pls i also want to know the answer to it
A girl is 18 years younger than her mother. In 6 years time, the sum of their ages will be 54. How old is the girl now?
Answer:
12 yrs.
Step-by-step explanation:
let present age of girl=x
age of mother=x+18
after 6 yrs
age of girl=x+6
age of mother=x+18+6=x+24
according to the condition of question
(x+6)+(x+24)=54
2x+30=54
2x=54-30=24
x=24/2=12
a) |9+x|=2x
b) |x+6|=2x+9
Answer:
a) 9
b) -3
Step-by-step explanation:
a)
|9+x|=2x
9 + x = 2x
- x -x
---------------
9 = x
b)
|x+6|=2x+9
x +6 = 2x +9
-x -x
6 = x + 9
-9 -9
--------------
-3 = x
six boys each have the same number of sweets.the total number of sweet is 78. how many sweet did each boy have?
whats the area of this shape?
Answer:
54
Step-by-step explanation:
find the area of each shape. you have a length of 3 and a height of 4.
3 • 4 = 12
you have this shape twice so 12 • 2 = 24
now you have a length of 5 and a height of 6.
5 • 6 = 30
so adding up all of the numbers (24 + 30), you have an answer of 54.
applying the distributive property to the expression, 24x+18y will produce which equivalent expression.
1. 6(4+3y)
2. 6(4x+3y)
3. 3xy(8+6)
4. 3(8x+6y)
Answer:
6(4x + 2y)
Step-by-step explanation:
24x = 2 * 2 * 2 * 3 * x
18y = 2 * 3* 3 * y
Common factors = 2 * 3 = 6
24x + 18y = (6*4x) + (6*2y) {6 is common in both terms}
= 6*(4x + 2y)
Ms. Sutton recorded the word counts and scores of the top ten essays in a timed writing contest. The table shows her data.
A 3-row table with 10 columns. The first row is labeled essay rank with entries 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The second row is labeled essay score with entries 9.7, 9.5, 9.5, 9.0, 8.9, 8.9, 8.5, 8.4, 8.2, 7.0. The third row is labeled word count with entries 324, 352, 337, 318, 299, 304, 290, 291, 278, 250.
How does the word count of an essay relate to its score in the contest?
Word count tends to decrease as the score decreases.
Word count tends to increase as the score decreases.
Word count tends to remain constant as the score decreases.
Word count has no apparent relationship to the score of the essay.
Unmark this question
Answer:
The word count tend to decrease as the score decreases
Step-by-step explanation:
The 3-row table is presented as follows;
[tex]\begin{array}{ccc}Essay \ Rank&Essay \ Score&Word \ Count\\1&9.7&324\\2&9.5&352\\3&9.5&337\\4&9.0&318\\5&8.9&299\\6&8.9&304\\7&8.5&290\\8&8.4&291\\9&8.2&278\\10&7.0&250\end{array}[/tex]
The relationship between the values on the Word Count column and the values on the Essay Score column is that as the Essay Score decreases from the top down to the last row, the values on the Word Count generally decreases in the same manner (top down decrease)
Therefore, the Word Count decreases as the Essay Score decreases.
how many square metres of floor are there in a room of 6 metres
ig something like that
Answer:
36² metres
Step-by-step explanation:
I'm assuming you mean 6 metre wide/long floor. Area is L*W so 6*6
Choose a scenario that could be represented by 5/8.
A.an eight-foot ribbon is cut into five equal pieces.
B.an eight-hour bus trip is divided into five equal parts.
C. Five friends share eight cookies equally.
D. five pounds of oats are divided equally among eight horses.
Answer:
D. Five pounds of oats are divided equally among eight horses.
Step-by-step explanation:
A scenario representing 5/8 has to involve a quantity of 5 being divided by 8.
The situation with the oats and horses represents 5/8, because the 5 pounds of oats are being equally divided among the 8 horses.
The other answer choices are incorrect because they are dividing 8 by 5 instead, which is 8/5 instead of 5/8.
So, the correct answer is D. Five pounds of oats are divided equally among eight horses.
can any of yalls help with this one
Answer:
it's the last option
Step-by-step explanation:
mark me brainliest
Which of the following equations represents a line that is perpendicular to
y = -4x+9 and passes through the point, (4, 5)?
O A. y - 1x+6
OB. y = x +5
O C. y = *x+4
D. Y = -4x+4
Answer:
y = 1/4 x +4
Step-by-step explanation:
y = -4x+9
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
the slope is -4
Lines that are perpendicular have slopes that are negative reciprocals
The slope of the perpendicular line is -1 /(-4) = 1/4
The perpendicular line is
y = 1/4x+b
It goes through (4,5)
5 = 1/4(4) +b
5 = 1+b
b=4
y = 1/4 x +4
