The probability that exactly 9 buyers would prefer green is 0.1408
We will use the Binomial probability formula to find the answer
The formula is given by ⁿCₓ (p)ˣ (1-p)ⁿ-ˣ
We have
n, the number of trial = 12
x, the sample we aim to try = 9
p, the probability of success = 0.6
Substitute these values into the formula
[tex]P(9)= ^{12}C_{9} (0.6)^{9} (1-0.6)^{12-9}[/tex]
P(9) = 0.1408 (rounded to four decimal places)
Hence, The probability that exactly 9 buyers would prefer green is 0.1408
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Choose the correct classification of 5x 3x4 − 7x3 10 by number of terms and by degree. third degree polynomial fourth degree polynomial sixth degree polynomial first degree binomial
The correct classification of the expression 5x + 3x⁴ - 7x³ + 10, is that it is the fourth-degree polynomial.
The degree of a polynomial is the highest power of the variable in the expression.
In the expression 5x + 3x⁴ - 7x³ + 10, there are 4 terms, and the term 3x⁴ involves the highest power = 4.
Therefore, the degree of the polynomial is 4.
Hence, we can say that the correct classification of the expression 5x + 3x⁴ - 7x³ + 10, is that it is the fourth-degree polynomial.
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Find the distance between (-4,3,-6) and the origin ((X,Y,Z) Graph)
The distance between (-4,3,-6) and the origin is [tex]\sqrt{61[/tex]
How to determine the distance?The point is given as:
(x, y, z) = (-4,3,-6)
The origin is
(x, y, z) = (0,0,0)
The distance between the point and the origin is calculated as:
[tex]d = \sqrt{x^2 + y^2 + z^2[/tex]
So, we have:
[tex]d = \sqrt{(-4)^2 + (3)^2 + (-6)^2[/tex]
Evaluate
[tex]d = \sqrt{61[/tex]
Hence, the distance between (-4,3,-6) and the origin is [tex]\sqrt{61[/tex]
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i dont understand how to do this problem. Someone please assist me
Answer:
The unknown length = 12 units.
Step-by-step explanation:
The small and large triangles are similar because of the parallel lines.
So
6 / (6+4) = x / 20
10x = 120
x = 12.
A group of students tossed coins and recorded 167 tails and 179 heads.
What is the experimental probability of heads?
Answer:
29893
Step-by-step explanation:
167 x 179
A researcher who wishes to study the effects of a prenatal breastfeeding education program on the length of time African-American inner-city women breastfeed infants learns that 70% of women in the target population are unmarried. To achieve stratified random sampling in a sample of 50 subjects, the researcher will:
Select a random sample of 35 unmarried and 15 married subjects
A researcher who wishes to study the effects of a prenatal breastfeeding education program on the length of time African-American inner-city women breastfeed infants learns that 70% of women in the target population are unmarried.
To achieve stratified random sampling in a sample of 50 subjects, the researcher will:
Select a random sample of 35 unmarried and 15 married subjects.
hence, Select a random sample of 35 unmarried and 15 married subjects.
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Circle a is centered at point p, and point q lies on the circle. what other points also lie on circle a?
All the points which are at the distance of PQ from the center of the circle will be located on the circle.
What is a circle?A circle is a closed shape created by following a moving point on a plane while maintaining a constant distance from another point.
According to the given question, the circle named A has it's center at the point P and has a point Q on the circumference of the circle, so any point at the distance of PQ from the center of the circle will lie on the circumference of the circle.
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Answer:
Points S, T, and W
Hope this helps!
Step-by-step explanation:
show that,t for any triangle abc, even if b or c is an obtuse angle, a = b cos c + c cos b. use the law of sines to deduce the "addition formula" sin (b + c) = sin b cos c + sin c cos b.
For the triangle ABC, if B or C is an obtuse angle, then a = b cos C + c cos B according to the law of sines and the addition formula.
What is the law of sines states?For a triangle ABC with angles ∠A, ∠B, and ∠C and with sides a, b, and c
Thus, we can write,
sinA/a = sinB/b = sinC/c
or
a/sinA = b/sinB = c/sinC
Calculation:It is given that in a ΔABC,
The ∠B or ∠C is an obtuse angle.
So, ∠A = 180° - (B + C)
⇒ sin A = sin (180° - (B + C))
⇒ sin A = sin (B + C) (since we know that sin(180° - θ) = sinθ)
From the addition formula,
sin (B + C) = sin B cos C + sin C cos B
⇒ sin A = sin (B + C)
⇒ sin A = sin B cos C + sin C cos B
From the law of sines,
a/sinA = b/sinB = c/sinC = K
⇒ aK =sin A, bK = sin B, cK = sin C
On substituting,
⇒ sin A = sin B cos C + sin C cos B
⇒ aK = bK cos C + cK cos B
⇒ K(a) = K(b cos C + c cos B)
∴ a = b cos C + c cos B
Hence it is proved.
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Select the correct answer from each drop-down menu.
Given: UX=WZ VW=XY
Prove: UV=YZ
The reason in line __ does not justify the statement because ___. Instead, the reason should be ___.
OPTIONS:
1:
A.)4
B.)5
C.)6
D.)3
2:
A.) Values were not added to each side
B.) Values were not subtracted from each side
C.) More than two segments were added.
3:
A.) The substitution property of equality
B.) Segment addition
C.) Given
The answers are D.)3, B.) Values were not subtracted from each side, and A.) The substitution property of equality
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
We have;
UX=WZ
VW=XY
In line 3 the statement does not justify.
Because values were not subtracted from each side.
The reason should be substitution property of equality.
Thus, the answers are D.)3, B.) Values were not subtracted from each side, and A.) The substitution property of equality
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Answer:
I just got it right on the test
Step-by-step explanation:
PLEASE HELPPPP
An expression is shown below:
2x3 + 10x2 − 4x2y − 20xy
Part A: Re-write the expression by factoring out the GCF
Part B: Factor the entire expression completely
Show your work
The complete factor of the given expression is 2x(x-2y)(x+5)
Factoring of expressionGiven the following expression shown below
2x^3 + 10x^2 − 4x^2y − 20xy
Factor out the GCF
2x^2(x+5)-4xy(x+5)
Group
(2x^2-4xy)(x +5)
2x(x-2y)(x+5)
Hence the complete factor of the given expression is 2x(x-2y)(x+5)
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Part A
Simplify (6-2) (3-3)(3-6).
Answer:
0
Step-by-step explanation:
First, lets solve what's in the parentheses.
(6-2) = 4
(3-3) = 0
(3-6) = -3
Now, we put that into the equation.
4*0*-3
We get 0
Esto es una división por favor ayuda
El resultado de esta división es 0.010
¿Cómo solucionar la operación matemática?Para solucionar la operación matemática debemos realizar los siguientes pasos:
Como el 81 es menos que el 7593, debemos poner un cero en el cociente y agregarle un cero al 81, entonces quedaría 810 dividido 7593.Como el 810 sigue siendo menor que el 7593, añadimos coma (,) y otro cero en el 810, entonces quedaría 8100 dividido 7593.Una vez tenemos el 8100 dividido 7593 realizamos la división, en este caso vemos cuántas veces cabe 7593 en 8100 y lo multiplicamos por ese número de veces (1).Una vez tenemos estos números a 8100 le restamos 7593 y obtenemos como resultado 507.Nuevamente, 507 es menos que 7593, entonces debemos agregar otro cero en el cociente para conocer las siguientes cifras decimales que falta.Ahora debemos averiguar cuántas veces cabe 7593 en 50700. Este número cabe 6 veces, entonces lo multiplicamos por 6 y luego restamos 50700 - 7593.Para conocer las siguientes cifras decimales debemos ir agregando un número cero en el resto para poder realizar las restas y seguir la división.Aprenda más sobre división en: https://brainly.com/question/24592547
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help me please n^2, when n = 3
Answer: 9
Step-by-step explanation:
Given:
n², n = 3
Plug-in:
(3)²
Square 3:
3 * 3 = 9, so (3)² = 9
Simplify:
9
What is the answer to this?
Answer: J
Step-by-step explanation:
Corresponding sides of similar triangles are proportional, so
[tex]\frac{3x-9}{x+8}=\frac{45}{30}=\frac{3}{2}\\\\2(3x-9)=3(x+8)\\\\6x-18=3x+24\\\\3x-18=24\\\\3x=42\\\\x=14\\\\\implies YX=14+8=22[/tex]
How many terms are in (3x^2-3)(3x^2+3)
The number of terms in the expression given is; 2.
How many term are in the expression given?It follows from the task content that the expression given is; (3x^2-3)(3x^2+3).
It therefore follows the converse of law regarding difference of two squares that the expression given can be rewritten as;
= 9x⁴ -9
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y=3x + 4
x=3y + 4
x-4= 3y
how do divide x-4 by 3?
Answer:
x = 3y + 4
Step-by-step explanation:
add 4 to both sides
simplify
solve for the missing variable 9 4 and x pls help need in 2 hours
Answer:
81/4
Step-by-step explanation:
By the Pythagorean theorem, the length of the altitude drawn from the hypotenuse is
[tex] \sqrt{65} [/tex]
This means that by the geometric mean theorem, that out of the two segments the hypotenuse is split into, the one with unknown length has length 65/4.
Thus, x = 65/4 + 4 = 81/4.
Can someone write me a paragraph proof for this problem
Answer:
Step-by-step explanation:
ur mother
Which graph shows a system of equations with a solution at (2, -1)?
Graph fourth shows a system of equations with a solution at (2, -1) option fourth is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is
Which graph shows a system of equations with a solution at (2,-1)?
The graph is in the picture, please refer to the attached picture.
As we can see in the graph there are two graphs of a function shown.
The first one is a parabola and the second one is a linear graph.
From the graph, the intersection point of the two groups is at (2, -1)
The intersection point is shown in graph fourth.
Thus, graph fourth shows a system of equations with a solution at (2, -1) option fourth is correct.
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Answer:
Graph 4
Step-by-step explanation:
fully simplify 7c - 4h - 2c - 5h
Answer:
5c-9h
Step-by-step explanation:
1) 7c-4h-2c-5h
2) 5c-4h-5h
3) 5c-9h
select all the con
Choose the graphs that indicate equations with no solution.
+
3x + 2 = −6(-ª)
y
A
4 -2
4+
2
-2-
2 4
4
+x+
8(-a)
-4 -2
HE
H
у
14
2.
2.
-2-
-4-
-4 -2
-2x + 4
4
4 =
y
4
2
2
+x
A
2
4
+2
3+1=
-4 -2
4
2.
12
x +
4
++++
-4
2
52 + 1 = 7(-z)
y
-2
5(-) + 2
4
TE
t
4
2-
14
+
+X
2
4
Hx
Answer:
Top leftBottom rightStep-by-step explanation:
For there to be no solution, the graphs must never intersect.
An equation is formed of two equal expressions. The graphs that indicate that the equation has no solution are the first graph from the top row and the last graph from the second row.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of a pair of equations is the point at which the graph of the two functions intersects each other. The number of times the two graphs intersect is the number of solutions to the pair of equations.
Since there are only two graphs where the graphs do not intersect.
Thus, the graphs that indicate that the equation has no solution are the first graph from the top row and the last graph from the second row.
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pls and thank you if you help out
Answer: x = 80°
Step-by-step explanation:
Hi,
Since the angle is bisected, that means it is split in half and that both sides equal each other.
Therefore,
50 = 1/2x + 10
subtract 10 from both sides
40 = 1/2x
divide 40 by 1/2
x = 80°
Hope this helped :)
Help me pleaseee!!! :(
Find the missing the side of the triangle. 19New A. 73‾√ in B. 72‾√ in C. 75‾√ in D. 77‾√ in
By applying Pythagorean's theorem, the missing side of this right-angled triangle is: A. 7√3 inches.
How to find the missing side?By critically observing the triangle shown in the image attached below, we can logically deduce that it is a right-angled triangle. Thus, we would find the missing side by applying Pythagorean's theorem:
z² = x² + y²
Also, the sides of this right-angled triangle are:
Hypotenuse = 14 inches.Opposite side = x inches.Adjacent side = 7 inches.Substituting the given parameters into the formula, we have;
14² = x² + 7²
196 = x² + 49
x² = 196 - 49
x² = 147
x = √147
x = √49 × √3
x = 7√3 inches.
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Answer:
A.) 7√3 in
Step-by-step explanation:
I got it correct on founders edtell
help please!!! i dont get it
The amount of money in the account if compounded quarterly at 6% after 9 years is $22,217
Compound interestPrincipal, P = $13,000Time, t = 9 yearsInterest rate, r = 6% = 0.06Number of periods, n = 4A = P(1 + r/n)^nt
= 13,000(1 + 0.06/4)^4×9
= 13,000(1 + 0.015)^36
= 13,000(1.015)^36
= 13000(1.709)
= $22,217
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Find the equation of the line perpendicular to y = - 1/2 x − 5 that passes through the point ( 2 , 7 ) . Write this line in slope-intercept form.
The equation of the perpendicular line as required is; y = 2x -3.
What is the equation of the perpendicular line?Since the line in discuss is perpendicular to the given line whose slope is; -1/2. It therefore follows that the slope of the line to be determined is;
m = -1/(-1/2) = 2.
The equation of the required line can therefore be written as;
2 = (y-7)/(x-2)
2x -4 = y -7
Hence, y = 2x -3 is the equation of the line.
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7x-9y-6x+2y simplify
Answer:
x-7y
Step-by-step explanation:
7x-9y-6x+2y
Combine like terms
7x -6x -9y +2y
x -7y
x-7y
Answer:
x -7y
Step-by-step explanation:
7x - 9y - 6x + 2y
Rearrange so like terms are together (these are terms that are similar such as 5b and 7b; 7 and 1)
7x - 6x - 9y + 2y
Group into brackets one-by-one and solve
(7x-6x) -9y + 2y
x -9y + 2y
x (-9y + 2y)
x -7y
Note that 1x, 1b, 1z etc are simply written as their variable eg x, b and z
The times of all 15 year olds who run a certain race are approximately normally distributed with a given mean mu = 18 sec and standard deviation sigma = 1.2 sec. what percentage of the runners have times less than 14.4 sec?
The percentage of runners that have times less than 14.4 seconds that is P(x<14.4) is 0.0013499 which is approximately = 0.15%.
What is standard deviation?The standard deviation of a data set is defined as how the data is dispersed in relation to the mean.
From the question,
The raw time given (X) = 14.4 sec
The mean value(m) = 18sec
The standard deviation(d) = 1.2 sec
Using the formula,
z = X - m/ d
z= 14.4- 18/1.2
z = -3.6/1.2
z= -3
Using a Z table to find the percentage equivalent of P(x<14.4) is 0.0013499 which is approximately = 0.15%.
Therefore, the percentage of runners that have times less than 14.4 seconds that is P(x<14.4) is 0.0013499 which is approximately = 0.15%.
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Three equivalent ratios are shown on the graph
To plot more the points, we move up one and right two.
How to plot more the points?The ratios are given as:
(1, 0.5), (2, 1), and (5, 2.5)
Calculate the slope (m) using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{1 - 0.5}{2 - 1}[/tex]
Evaluate
[tex]m = \frac{0.5}{1}[/tex]
This gives
[tex]m = \frac{1}{2}[/tex]
The above means
Vertical : Horizontal = 1 : 2
This means a vertical movement of 1, followed by an horizontal movement of 1
Hence, to plot more the points, we move up one and right two.
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Complete question
Three equivalent ratios are shown on the graph. On a coordinate plane, points (1, 0.5), (2, 1), and (5, 2.5) are plotted. Starting on one of the plotted points, how can you plot more equivalent ratio points?
Which function has zeros at x = -2 and x = 5?
O f(x) = x2 + 2x - 10
• f(x) = x2 - 2x - 10
O f(x) = X2 + 3x - 10
® f(x) = x2 - 3x - 10
Answer:
f(x)=x²-3x-10
Step-by-step explanation:
\begin{gathered}f(x) = x {}^{2} - 3x - 10 \\ to \: find \: x \: intercept \:o r \: zero \: substitute \: f(x) = 0\: \\ 0 = x {}^{2} - 3x - 10 \\ x {}^{2} - 3x - 10 = 0 \\ x {}^{2} + 2x - 5x - 10 = 0 \\ x(x + 2) - 5x - 10 = 0 \\ x(x + 2) - 5(x + 2) = 0 \\ (x + 2).(x - 5) = 0 \\ x + 2 = 0 \\ x - 5 = 0 \\ x = - 2 \\ x = 5\end{gathered}
f(x)=x
2
−3x−10
tofindxinterceptorzerosubstitutef(x)=0
0=x
2
−3x−10
x
2
−3x−10=0
x
2
+2x−5x−10=0
x(x+2)−5x−10=0
x(x+2)−5(x+2)=0
(x+2).(x−5)=0
x+2=0
x−5=0
x=−2
x=5
therefore the zeros of the equation are x₁=-2,x₂=5
Find the area of the triangle
Answer:
12 yd^2 (c)
Step-by-step explanation:
A=1/2bh
= 1/2 x 8 x 3
=12 yd^2
Hope it helps!!!
Answer: 12 yd^2
Step-by-step explanation:
Area=[tex](1/2) *base*height\\[/tex]
here
base= 8yd
height =3 yd
putting values
area=(1/2)*(8)*(3)
area=12 yd^2