Taking into account the definition of probability, the correct option is option A.: The probability that the child has a speaking part is [tex]\frac{2}{5}[/tex].
There are 20 children in the cast of a class play, and 8 of the children are boys. Then, realizing the difference between the number of children and the number of boys you get that 12 of the children are girls.
On the other side, of the boys, 4 have a speaking part in the play, and of the girls, 8 do not have a speaking part in the play. Then, calculating the difference between the number of girls there are and the number of them that they do not have a speaking part in the play is obtained: 12 girls - 8= 4 girls. So, of the girls, 4 do not have a speaking part in the play.
Therefore, 4 + 4 = 8 of the children have a speaking part.
Probability is the greater or lesser possibility of a certain event occurring. In other words, probability establishes a relationship between the number of favorable events and the total number of possible events. Then, the probability of any event A is defined as the quotient between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.
[tex]P(A)=\frac{number of favorable cases}{number of possible cases}[/tex]
In this case:
number of favorable cases= 8 of the children have a speaking part.number of possible cases= 20 childrenReplacing in the definition of probability:
[tex]P(A)= \frac{8}{20}[/tex]
Simplifying the fraction:
[tex]P(A)= \frac{2}{5}[/tex]
Then, the correct option is option A.: The probability that the child has a speaking part is [tex]\frac{2}{5}[/tex].
ANYONE PLEASE HELP
# BRAINLIEST FOR HELP
1) In the quadratic equation, k represents a real number.
3x^2+2kx+2=0
Which value of k gives imaginary solutions to the equation? Select all the values that apply.
A. − 5
B. − 3
C. − 1
D. 2
E. 3
F. 4
2) 1/2 x+12=8+4( x+1)
Which could be a correct first step to solve the equation? Select all the steps that apply.
A. Distribute 4 to the quantity ( x+1).
B. Add − 8 to each side of the equation.
C. Distribute 12 to the quantity ( x+1).
D. Multiply each side of the equation by 2.
E. Subtract 12 from each side of the equation.
F. Add together the 8 and the 4 on the right side of the equation.
G. Multiply the left side of the equation by 2 to eliminate the fraction.
3) In the equation of f(x) shown, r and s are positive real numbers.
f(x)=x^2−2(r−s)x+(r−s)^2+(r+s)
Select the options from the drop-down menus to correctly rewrite f(x).
FILL IN: f(x)= ( ......... ......... )2 ..........
4) A city’s population, P, changes according to the function P( x )=50,000 ( 0.95 )^x. where x represents the number of years after the year 2000.
Select the options from the drop-down menus to complete an accurate description of the population.
The population of the city in the year 2000 was(...……..) . The population is (..............) by (..........)each year.
Answer:
1)
C. − 1
D. 2
2)
A. Distribute 4 to the quantity ( x+1).
B. Add − 8 to each side of the equation.
D. Multiply each side of the equation by 2
E. Subtract 12 from each side of the equation.
3)
[tex]f(x)=(r-x-s)^2+(r+s)[/tex]
4) The population of the city in the year 2000 was 50000. The population is decreases by 0.95 each year
Step-by-step explanation:
a) Given an equation:
ax² + bx + c = 0
The equation would have imaginary solutions if b² - 4ac is negative. That is:
b² - 4ac < 0
Given an equation: 3x²+2kx+2=0
a) If k = -5
a= 3, b = 2k = 2 × -5 = -10, c= 2
b² - 4ac = (-10)² - 4(3)(2) = 76 > 0
It would not produce imaginary solutions
b) If k = -3
a= 3, b = 2k = 2 × -3 = -6, c= 2
b² - 4ac = (-6)² - 4(3)(2) = 12 > 0
It would not produce imaginary solutions
c) If k = -1
a= 3, b = 2k = 2 × -1 = -2, c= 2
b² - 4ac = (-1)² - 4(3)(2) = -23 < 0
It would produce imaginary solutions
d) If k = 2
a= 3, b = 2k = 2 × 2 = 4, c= 2
b² - 4ac = (4)² - 4(3)(2) = -8 <0
It would produce imaginary solutions
e) If k = 3
a= 3, b = 2k = 2 × 3 = 6, c= 2
b² - 4ac = (6)² - 4(3)(2) = 12 > 0
It would not produce imaginary solutions
f) If k = -5
a= 3, b = 2k = 2 × 4 = 8, c= 2
b² - 4ac = (8)² - 4(3)(2) = 40 > 0
It would not produce imaginary solutions
2)
A. Distribute 4 to the quantity ( x+1). to get:
1/2 x+12=8+4x+4
B. Add − 8 to each side of the equation. to get:
1/2 x+4=4( x+1)
C. Distribute 12 to the quantity ( x+1). This is not correct
D. Multiply each side of the equation by 2. to get:
x + 24 = 16 + 8(x +1)
F. Add together the 8 and the 4 on the right side of the equation. This is not correct
G. Multiply the left side of the equation by 2 to eliminate the fraction. This is not correct
3)
[tex]f(x)=x^2-2(r-s)x+(r-s)^2+(r+s)\\f(x)=x^2-2rx+2sx+r^2+s^2-2rs+r+s\\f(x)=x^2+r^2+s^2-2rs-2rx+2sx+r+s=(r-x-s)^2+(r+s)\\f(x)=(r-x-s)^2+(r+s)[/tex]
4) P( x )=50,000 ( 0.95 )^x, where x represents the number of years after the year 2000
At the year 2000, x = 0 therefore
[tex]P(x)=50000(0.95)^x=50000(0.95)^0=50000[/tex]
Since 0.95 is less than 1, it represent a population decay. 0.95 is the common ratio
The population is decreases by 0.95 each year
Find the greatest common factor of the
following monomials:
18g^6h^5
16g^3h^6
Answer:
good luck
Step-by-step explanation:
BRAINLIEST FOR WHOEVER GETS THIS RIGHT!!!
PLEASE HELP MATHS QUESTION!!!
Answer:
Step-by-step explanation:
1) first, lets rationalize the denominator by eliminating [tex]1+\frac{1}{\sqrt{2} }[/tex]
so multiply [tex]\frac{1}{1+\frac{1}{\sqrt{2} } }[/tex] with the conjugate, [tex]1-\frac{1}{\sqrt{2} }[/tex]
we multiply with the conjugate (opposite) since we can take the conjugate and the original term in the form of (a+b)(a-b)= a^2-b^2, which would allow us to get rid of the square root:
so
(1+1/[tex]\sqrt{2}[/tex])(1-[tex]\frac{1}{\sqrt{2} }[/tex])=(1)^2-([tex]\frac{1}{\sqrt{2} }[/tex])^2
hence we are left with:
1-1/2= 0.5
0.5 is the denominator:
since conjugate is multiplied to both numerator and denominator:
for the numerator (1)([tex]1-\frac{1}{\sqrt{2} }[/tex])
is: 1-[tex]\frac{1}{\sqrt{2} }[/tex]
hence, [tex]\frac{1-\frac{1}{\sqrt{2} } }{0.5}[/tex]
so[tex]1-\frac{1}{\sqrt{2} }[/tex]
is 0.292893
so
0.292893/0.5= 0.058579
and 2-sqrt(2)= 0.058579
hence they both are equal
hope this helps!
1/2 divided by -1/7 answers please?
Answer:
-[tex]\frac{7}{2}[/tex] or -3[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
1/2 ÷ -1/7
1/2 × -7
-7/2
Q 9 : In which quadrant is the following point?(-3, 12) *
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
Answer:
The answer for this question is Quadrant III
Hey!!!!
(-3,12) lies in Quadrant II.
please see the attached picture.
Hope it helps...
Good luck on your assignment...
Stay safe..
If f(x) is a linear function and the domain of f(x) is the set of all real numbers, which statement cannot be true?
Answer:
can u please add the statements.
Step-by-step explanation:
simplify this algebraic expression: y-3/3+12
Answer:
y-13
Step-by-step explanation:
y-3/3+12
because of order of ops you do 3/3 first
y-1+12
1+12 is 13 so
y-13
what is the value of x?
Answer:
D 36 degrees
Step-by-step explanation:
You add 65 degrees and 79 degrees together and get 144 degrees
The whole triangle is 180 degrees
So you take 180 - 144
and you get D, 36 degrees
Answer:
D.
Step-by-step explanation:
65º+79º+xº=180º
x=180º-65º-79º
x=115º-79º
x=36º
D.
a shaded sector of a circle has an area of 4pi and an angle of 40 degrees. What is the perimeter of the sector?
Answer:
4/9*pi or 1.395
Step-by-step explanation:
We have that area of the circle, that 4 * pi, we can calculate the radius of the circle, knowing that:
A = pi * r ^ 2
replacing:
4 * pi = pi * r ^ 2
r ^ 2 = 4 * pi / pi
r ^ 2 = 4
r = 2
Therefore, knowing the radius, we can calculate the perimeter:
P = 2 * pi * r
replacing:
P = 4 * pi
That is the perimeter of the whole circle, that is to say 360 °, therefore for 40 ° it would be:
4 * pi * 40 ° / 360 ° = 4/9 * pi
That is to say that the perimeter of the sector of 40 ° is 4/9 * pi, if pi is 3.14 it would be:
4/9 * 3.14 = 1.395
Bryce started the summer with 4 hamster. by september he had 28 hamsters. what is the percent of change?
Answer:
14.285% or 14.3% if rounded to the nearest one decimal place.
Step-by-step explanation:
4 ÷28 × 100
A triangle has two sides of length 8 and 15. What is the largest possible whole-number length for the third side?
The answer is 120 have a great day. Step-by-step explanation:
18,500 g how many grams
22 g how many grams
4.7 kg how many grams
8.3 kg how many grams
135,000mg how many grams
BEST ANSWER GETS BRAINLESST AND A FOLLOW YOU DON'T HAVE TO ANSWER ALL BUT AT LEAST DO SOME PLS ASP!(the pic shows you the same questions)
Answers:
7 grams47000 grams18.5 kg8300 g22000 mg0.135 kgLook at the attached picture
Hope it will help you
Good luck on your assignment....
Answer:
7000 mg = 7 g
18500 g = 18.5 kg
22 g = 22000 mg
4.7 kg = 4700 g
8.3 kg = 8300 g
135000 mg = 135 g
Step-by-step explanation:
First we need to use some important conversion rates so I will write them for below
1 Milligram (mg) = 0.001 Grams (g)
1 Gram (g) = 0.001 Kilogram (Kg)
1 Gram (g) = 1000 Milligrams (mg)
1 Kilogram (Kg) = 1000 Grams (g)
Using the above conversion rates we can solve these questions
Question 1
7000 mg = ? g
Using the information at the top 1 Milligram (mg) = 0.001 Grams (g) so,
0.001 × 7000 = 7 grams
Question 2
18500 g = ? kg
Using the information at the top 1 Gram (g) = 0.001 Kilogram (Kg) so,
18500 ÷ 1000 = 18.5 kg
Question 3
22 g = ? mg
Using the information at the top 1 Gram (g) = 1000 Milligrams (mg) so,
22 × 1000 = 22000 mg
Question 4
4.7 kg = ? g
Using the information at the top 1 Kilogram (Kg) = 1000 Grams (g) so,
4.7 × 1000 = 4700 g
Question 5
8.3 kg = ? g
Using the information at the top 1 Kilogram (Kg) = 1000 Grams (g) so,
8.3 × 1000 = 8300 g
Question 6
135000 mg = ? g
Using the information at the top 1 Milligram (mg) = 0.001 Grams (g) so,
0.001 × 135000 = 135 grams
9.75t + 9 = 13.5t + 12 what is the solution for t
Answer:
t = - 0.8
Step-by-step explanation:
9.75t -9.75t + 9 = 13.5t - 9.75t+ 12
9 = 3.75t +12
9 - 12 = 3.75t
- 3 /3.75= 3.75 t/3.75
- 0.8 = t
Answer:
∴ t= -0.8
Step-by-step explanation:
9.75t + 9 = 13.5t + 12
9.75t-13.5t=12-9
-3.75t=3
-t=3/3.75
-t=0.8
∴ t= -0.8
Hope this helps..Pls mark as Brainliest!!
Sophie is making a rectangular pen for her rabbit. The pen is 4 feet wide and 6 feet long. What is the area of the pen?
Answer:
The area of the pen would be 24 feet.
Step-by-step explanation:
6 multiplied by 4 is 24.
Answer:
24 feet squared
Step-by-step explanation:
the area of a rectangle = l x w
length = 6
width = 4
therefore, 4x6=24
List five rational numbers between -4/7 and 1/2
Answer:
- ²⁾4/7 = - 8/14
⁷⁾1/2 = 7/14
- 8/14 < - 9/14 < - 12/14 < 3/14 < 5/14 < 7/14
al3xis
Which takes up a larger area: the flowers or the grass?
Answer:
THE GRASS
Step-by-step explanation:
Because the grass takes up a larger area
The equation of the graphed line is 2x - y = -6.
What is the x-intercept of the graph?
-3
-2
ОООО
2
4
3
6
2
2
3
4
5 6 7
Х
-5/3 -2 -11
-2
L3-
4
Answer:
-3 or (-3,0)
Step-by-step explanation:
When graphed the line 2x-y=-6 intersects the x-axis at the coordinate (-3,0)
The graph shown as the solution set for which of the following inequaliter?
Oysix+11
Oysx-1
Oystx-1
Answer: Oysx-1
Step-by-step explanation:
I did same thing and got it right.
31 + 33 + 35 + 37 + 39 + ... + 199 = ?
Answer:
The answer is 24
Step-by-step explanation:
What you can do is add all of the numbers (31 + 33 + 35 + 37 + 39)
[tex]31 + 33 + 35 + 37 + 39=175[/tex]
Then subtract 199 by 175
[tex]199-175=24[/tex]
To check add them all together
[tex]31 + 33 + 35 + 37 + 39+24=199[/tex]
Hope this helps
Reflect the triangle in the mirror line
Answer:
image attached
Step-by-step explanation:
see attached
HELP! ASAP! Jason practices his crossover dribble for x minutes per day on weekdays, and for three times as long on each weekend day. How many minutes did Jason practice in 4 weeks?
A store purchased surfboards for $400 and sold them for $712. What is the mark-up percentage?
Write your answer using a percent sign (%).
Answer: 78 %
Step-by-step explanation:
Sales - cost = profit
712-400 = 312
As a percentage 312/400 * 100= 78
Answer:
78%
Step-by-step explanation:
712 -400 = 312
312/400 x 100 = 78
10/7=x/5 which of the following equation can be used to solve for the value of X?
Answer:
10*5 = 7x
Step-by-step explanation:
We can solve using cross products
10*5 = 7x
50 = 7x
divide each side by 7
50/7 =7x/7
50/7 =x
pleeeeeeeeeeeeeeeeeeeeeeeeeeeeease help meeeeeeeeeeeeee
Answer:
V≈56.55 mm^3Step-by-step explanation:
I used the formula
V=πr^2h
Hope this helps! (brainliest pls?)
PLEASE HELP! Use triangle ROE to find the following. Leave the answer in fraction form (no decimal answer) SHOW WORK
Answer:
tanθ = [tex]\frac{8}{15}[/tex]
Step-by-step explanation:
By applying tangent rule in the given right triangle ROE,
tanθ = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
tanθ = [tex]\frac{RO}{OE}[/tex]
tanθ = [tex]\frac{8}{15}[/tex]
Therefore, answer will be tanθ = [tex]\frac{8}{15}[/tex]
jason weighs 36 pounds together he and his sister weigh four pounds more than three times the weight of his sister what is the weight w of jason's sister?
A 36+ w= 3; 18 pounds
B 36+ w- =3w; 19 pounds
C 36+ w= 3w+4; 16 pounds
D 36+ w= 3w -4; 20 pounds
Answer:
C 36+ w= 3w+4; 16 pounds
Step-by-step explanation:
jason weighs 36
jason's sister weighs w
together they weigh 36+w
Then ,We can model the statement:
“together he and his sister weigh four pounds more than three times the weight of his sister”.
like this :
36+ w= 3w+4
I need help on this.
The right answer is 6.
Please see the attached picture for full solution.
Hope it helps...
Good luck on your assignment
Answer:
i believe the answer is 6
Step-by-step explanation:
comment if u want an explanation cus i cba to write one for no reason
the volume of a cylinder is 210 cm³ with a radius of 14 cm find the curved surface area if the formula for curved surface area is
2πrh
Answer:
30 cm²
Step-by-step explanation:
we need to find h
V=πr²h
h=V/πr²
h=210/14²π
h=0.341
then we found curved surface area
A=2πrh
A=2×π×14×0.341
curved surface are= 30 cm²
which value of h makes 8+h/10=1 a true statement
Answer:
h=2
Step-by-step explanation:
8+h/10=1
multiply the 1 by 10
8+h=10
subtract 8 from 10
h=2
If the statement is true, the value of h = 2.
What is a statement?
Mathematical statement - a statement of a mathematical relation math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement equation - a mathematical statement that two expressions are equal.
What is true statement?
Students understand that an equation is a statement of equality between two expressions. When values are substituted for the variables in an equation, the equation is either true or false. Students find values to assign to the variables in equations that make the equations true statements.
Given,
(8+h)=10
given, the equation is true statement.
Therefore, 8+h = 10
h = 10 - 8
h = 2
To know more about true statement, visit:
https://brainly.com/question/17309546
#SPJ2
4. Graph the data in the table below. Which kind of function best models the data? Write an equation to model the data.
х
0
1
2.
3
4
- 6
- 9
12
- 15
18
O quadratic; y = -x2 + 2x - 6
linear; y = - 3x -6
O quadratic; y = 32 - 2x
exponential; y = -6•1.5%
Answer:
Option (2).
Step-by-step explanation:
From the figure attached,
Since there is a common difference in each successive term and previous term of y,
[tex]y_{2}-y_{1}=-9-(-6)[/tex]
= -3
[tex]y_{3}-y_{2}=-12-(-9)[/tex]
= -3
Therefore, this data represents a linear equation.
Now we choose two points from the table given.
Let the points are (0, -6) and (1, -9)
Slope of this line 'm' = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
m = [tex]\frac{-9+6}{1-0}[/tex] = -3
Y-intercept 'b' = -6
Equation of the line will be,
y = -3x - 6
Option (2) will be the answer.
