Answer:
a) 10*0.51^3*0.49^2=approx 0.32
b)1-0.49^5= approx 0.97
c)1-0.51^5=0.965
d) approx 0.028 =P(all kids are girls) approx 0.035 =P(all kids are boys)
P(all kids are of the same sexboys or girls)=0.063
Step-by-step explanation:
a) The probability that exactly 3 of 5 kids are boys is
p(3 boys)=C5 3 *p^3*q^2
C5 3 = 5!/(3!*2!)= 4*5/2=10
p=0.51 is the probability a child is boy
q=1-p=1-0.51=0.49 is the probability a child is girl
P(3 boys of 5 kids)= 10*0.51^3*0.49*2
b) The event that at least 1 kid from five is boy is a combination of events
1 boy -4 girls, 2 boys-3 girls, 3 boys-2 girls, 4 boys-1 girl, 5 boys.
The event " all 5 kids are the girls" is the only event which is not the part of
event " at least 1 kid from five is boy"
So P(at least 1 kid from five is boy)=1 - P(all 5 kids are the girls)
P(all 5 kids are the girls)=0.49^5=approx 0.028
P(at least 1 kid from five is boy)=1-0.028=approx 0.97
c) Similarly like b) P(at least one of five kids is girl)= 1-P(all 5 kids are the boys)
P(all 5 kids are the boys)=0.51^5=approx 0.035
P(at least one of five kids is girl)= 1-0.035=approx=0.965
d) Probability all kids are of the same sex= probability that all kids are the boys+ probability all kids are the girls.
Using b) and c) P(all kids of the same sex)= 0.035+0.028=0.063
The probability that a family of five children has all children of the same gender is 0.06274.
What is Binomial distribution?A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
[tex]P(x) = ^nC_x p^xq^{(n-x)}[/tex]
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
Given the probability of a child being a boy is 0.51, therefore, p= 0.51. Also, we can write the probability of the child not being a boy is 0.49(1-0.51), therefore, the probability of the child being a girl is 0.49 and q=0.49.
A.) The probability that a family of five children is exactly three boys can be written as
[tex]P(x) = ^nC_x p^xq^{(n-x)}\\\\P(x=3)= ^5C_3 \cdot (0.51)^3 \cdot (0.49)^{2}\\\\P(x=3) = 0.3184[/tex]
B.) The probability that a family of five children has at least one boy can be written as,
Probability of at least one boy = 1 - Probability of no boy
[tex]P(x) = ^nC_x p^xq^{(n-x)}\\\\P(x=0)= ^5C_0 \cdot (0.51)^0 \cdot (0.49)^{5}\\\\P(x=0) = 0.02824[/tex]
Now,
[tex]\text{Probability of at least one boy }= 1 - \text{Probability of no boy}\\\\P(x > 1) = 1-P(x=0)\\\\P(x > 1) = 1-0.02824 = 0.9717[/tex]
C.) The probability that a family of five children has at least one girl can be written as,
Probability of at least one girl= 1 - Probability of no girl
[tex]P(x) = ^nC_x p^xq^{(n-x)}\\\\P(x=5)= ^5C_5 \cdot (0.51)^5 \cdot (0.49)^{0}\\\\P(x=5) = 0.0345[/tex]
Now,
[tex]\text{Probability of at least one girl}= 1 - \text{Probability of no girl}\\\\P(x < 5) = 1-P(x=5)\\\\P(x > 1) = 1-0.0345= 0.9654[/tex]
D.) The probability that a family of five children has all children of the same gender can be written as,
Probability = Probability of all boys + Probability of all girls
[tex]P = P(x=0)+P(x=5)\\\\P = 0.02824+ 0.0345\\\\P= 0.06274[/tex]
Hence, The probability that a family of five children has all children of the same gender is 0.06274.
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Select the expression that is equivalent to (x - 1)2.
O A. x2 - 2x + 2
O B. x2 - x + 2
O C. x2 - x + 1
O D. x2 – 2x + 1
Answer:
D
Step-by-step explanation:
(x - 1)² = (x - 1)(x - 1)
x² - x- x + 1 = x² - 2x + 1
Consider the following function. f(x) = 2x + 5. Place the steps for finding f-1 (x) in the correct order. A. x-2/5= y B. y = 2x + 5 C. y-5 = 2x D. X-5/2=y E. f-1(x) = x-5/2 F.x= 2y+ 5 G. x-5= 2y H. f-1(x) = x-2/5
Answer:
[tex]\boxed{\sf \ \ f^{-1}(x)=\dfrac{x-5}{2} \ \ }[/tex]
Step-by-step explanation:
hello,
the easiest way to understand what we have to do is the following in my opinion
we can write
[tex](fof^{-1})(x)=x\\<=>f(f^{-1}(x))=x\\<=>2f^{-1}(x)+5=x\\<=>2f^{-1}(x)+5-5=x-5 \ \ \ subtract \ \ 5\\<=> 2f^{-1}(x)=x-5 \\<=> f^{-1}(x)=\dfrac{x-5}{2} \ \ \ divide \ by \ 2\\[/tex]
so to follow the pattern of your question
y = 2x + 5
we need to find x as a function of y, so let's swap x and y
x = 2y + 5
then subtract 5
x - 5 = 2y
then divide by 2
[tex]\dfrac{x-5}{2}=y[/tex]
finally
[tex]f^{-1}(x)=\dfrac{x-5}{2} \\[/tex]
hope this helps
Answer:
1. y= 2x + 5
2. x = 2y + 5
3. x - 5 = 2y
4. (x-5)/2 =u
5. f^-1(x) = (x-5)/2
Step-by-step explanation:
:)
A Semi-circle sits on top of a rectangle to form the figure below. Find it’s area and perimeter. Use 3.14 for Pie.
Answer:
B
Step-by-step explanation:
Area of semicircle=(r^2×3.14)/2
=(4×3.14)÷2
=6.28
area of rectangle=3×4
12+6.28=18.28
perimeter of semicircle is =(d×3.14)/2
=4×3.14/2
6.28+3+3+4
6+10
perimeter=16.28
The area & perimeter of the figure are,
B.) A≈18.28sq.inch & P≈16.28inch.
What is area of a rectangle?Area of a rectangle (A) is the product of its length (l) and width (w).
A= l. w
Here,
Area of semicircle=(r^2×3.14)/2
=(4×3.14)÷2
=6.28
area of rectangle=3×4=12
So, total area of the figure =12+6.28=18.28 sq. inch
Again, perimeter of semicircle is =(d×3.14)/2
=4×3.14/2
=6.28
Total perimeter of the figure =6.28+3+3+4
=6.28+10
perimeter=16.28 inch
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(09.06 HC)
The function H(t) = -16t2 + 90t + 75 shows the height H(t), in feet, of a projectile after t seconds. A
second object moves in the air along a path represented by g(t) = 31 + 32.2t, where g(t) is the height, in
feet, of the object from the ground at time t seconds.
Part A: Create a table using integers 2 through 5 for the 2 functions. Between what 2 seconds is the
solution to H(t) = g(t) located? How do you know? (6 points)
Part B: Explain what the solution from Part A means in the context of the problem.(4 points)
Answer: h(t) = g(t) between 4 and 5 seconds
Step-by-step explanation:
h(t) = -16t² + 90t + 75
g(t) = 31 + 32.2t
[tex]\begin{array}{c|c|c|c|c}\qquad&\underline{\quad t=2\quad }&\underline{\quad t=3\quad}&\underline{\quad t=4\quad }&\underline{\quad t=5\quad }\\h(t)&191&201&179&125\\g(t)&95.4&127.6&159.8&192\end{array}\right][/tex]
Notice that g(t) is increasing from t=2 to t=5, while h(t) is increasing from t=2 to t=3 and then decreasing.
At t=4, h(t) > g(t)
At t = 5, g(t) > h(t)
therefore, the two lines must intersect at a point between t=4 and t=5.
You can graph this to verify the answer.
What is a quadrilateral and give ten examples
Answer:
A quadralateral is any shape that has 4 sides ...
Step-by-step explanation:
rectangle
square
rhombus
Answer: A quadrilateral is a two dimensional shape(closed) with four sides.
Step-by-step explanation: The sides do not have to be equal.
Square
Rectange
Trapazoid
Diamond
Any four sided shape. They will classify as a quadrilateral as long as two of the shapes are not the same.
An airplane descends during the last hour of it's flight to prepare for landing. It's altitude changes at an average of -0.15 km per minute for those 60 minutes. Write an expression to represent the total change in the airplane's elevation. ( plz answer, will give brainliest )
Answer:
-.15 km/ minute * 60 minutes
-9 km
Step-by-step explanation:
The rate is -.15 km per minute
We have 60 minutes
distance = rate times time
change in elevation is the same as the distance change
change in elevation = -.15 km/ minute * 60
change in elevation =-9 km
Answer:
(0.15 km/min) * (60 min)
Step-by-step explanation:
We see that the plane descends 0.15 kilometres every minute over the span of 60 minutes.
Use the distance-rate-time formula: d = rt, where d is the distance, r is the rate, and t is the time.
Here, our rate is r = 0.15 km/min and our time is t = 60 minutes. Then the total change in elevation is:
d = rt
d = 0.15 * 60 = 9 km
Note that we disregard the negative sign from -0.15 km/min because the question is asking for the change in elevation. Change is never a negative value.
Hence, the expression will be: 0.15 * 60, which simplifies to 9 km.
~ an aesthetics lover
help help help help pls
Hi !!
For f(x) = 3/x + 4 , B is correct.
• f(-3) = 3/(-3) + 4
f(-3) = - 1 + 4
f(-3) = 3
• f(-2) = 3/(-2) + 4
f(-2) = -1,5 + 4
f(-2) = 2,5
• f(1) = 3/(1) + 4
f(1) = 3 + 4
f(1) = 7
• f(2) = 3/(2) + 4
f(2) = 1,5 + 4
f(2) = 5,5
• f(3) = 3/(3) + 4
f(3) = 1 + 4
f(3) = 5
yall know the drill . whats the answer
Answer:
C. 57 degrees.
Step-by-step explanation:
It's a line, so it adds to 180 degrees. The interior angle is 180 - 114 = 66 degrees.
A triangle adds up to 180 degrees. Subtract 66 to get 114 degrees. This means the two remaining angles in the triangle add up to 114 degrees. Since they are identical (both are the same because they use the same variable), you can divide 114 by two.
The final answer is 57 degrees.
Let me know if you have any questions.
Which equation, when solved, gives 8 for the value of x?
A: 5/2x+7/2x=3/4x+14
B: 5/4x-9=3/2x-12
C: 5/4x-2=3/2x-4
D: 5/2x-7=3/4x+14
Answer:
Step-by-step explanation:
C. 5x/4-2=3x/2-4
5x/4 -2=6x/4-4
+4 +4
5x/4+2=6x/4
-5x/4
2=x/4
*4
x=8
Answer:
your answer is C
Step-by-step explanation:
Given a joint PDF, f subscript X Y end subscript (x comma y )equals c x y comma space 0 less than y less than x less than 4, (1) (5 pts) Determine the constant c value such that the above joint PDF is valid. (2) (6 pts) Find P (X greater than 2 comma space Y less than 1 )(3) (9 pts) Determine the marginal PDF of X given Y
(1) Looks like the joint density is
[tex]f_{X,Y}(x,y)=\begin{cases}cxy&\text{for }0<y<x<4\\0&\text{otherwise}\end{cases}[/tex]
In order for this to be a proper density function, integrating it over its support should evaluate to 1. The support is a triangle with vertices at (0, 0), (4, 0), and (4, 4) (see attached shaded region), so the integral is
[tex]\displaystyle\int_0^4\int_y^4 cxy\,\mathrm dx\,\mathrm dy=\int_0^4\frac{cy}2(4^2-y^2)=32c=1[/tex]
[tex]\implies\boxed{c=\dfrac1{32}}[/tex]
(2) The region in which X > 2 and Y < 1 corresponds to a 2x1 rectangle (see second attached shaded region), so the desired probability is
[tex]P(X>2,Y<1)=\displaystyle\int_2^4\int_0^1\frac{xy}{32}\,\mathrm dy\,\mathrm dx=\boxed{\dfrac3{32}}[/tex]
(3) Are you supposed to find the marginal density of X, or the conditional density of X given Y?
In the first case, you simply integrate the joint density with respect to y:
[tex]f_X(x)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dy=\int_0^x\frac{xy}{32}\,\mathrm dy=\begin{cases}\frac{x^3}{64}&\text{for }0<x<4\\0&\text{otherwise}\end{cases}[/tex]
In the second case, we instead first find the marginal density of Y:
[tex]f_Y(y)=\displaystyle\int_y^4\frac{xy}{32}\,\mathrm dx=\begin{cases}\frac{16y-y^3}{64}&\text{for }0<y<4\\0&\text{otherwise}\end{cases}[/tex]
Then use the marginal density to compute the conditional density of X given Y:
[tex]f_{X\mid Y}(x\mid y)=\dfrac{f_{X,Y}(x,y)}{f_Y(y)}=\begin{cases}\frac{2xy}{16y-y^3}&\text{for }y<x<4\text{ where }0<y<4\\0&\text{otherwise}\end{cases}[/tex]
distribution of grades over the past two years is as follows: GRADE NUMBER OF STUDENTS A 80 B 75 C 90 D 30 F 25 Total 300 If this past distribution is a good indicator of future grades, what is the probability of a student receiving a C in the course
Answer:
The probability of a student receiving a C in the course is p=0.3.
Step-by-step explanation:
We have a absolute frequency for each of the grades (A to F), of a total of 300 course tests.
It is assumed that this sample gives a dood estimation of the distribution of the grades. Then, we can estimate the probability of obtaining a C in the course usign the relative frequency for C.
The relative frequency is calculated as the division between the absolute frequency (in this case, 90 for a C grade) and the size of the sample (in this example, 300).
[tex]p_C=\dfrac{X_C}{N}=\dfrac{90}{300}=0.3[/tex]
Construct a confidence interval of the population proportion at the given level of confidence.
x equals =860
n equals =1200
94% confidence
The lower bound of the confidence interval is __?
Answer:
The lower bound of the confidence interval is 0.6922.
Step-by-step explanation:
We have to calculate a 94% confidence interval for the proportion.
The sample proportion is p=0.7167.
[tex]p=X/n=860/1200=0.7167[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.7167*0.2833}{1200}}\\\\\\ \sigma_p=\sqrt{0.000169}=0.013[/tex]
The critical z-value for a 94% confidence interval is z=1.8808.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.8808 \cdot 0.013=0.0245[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.7167-0.0245=0.6922\\\\UL=p+z \cdot \sigma_p = 0.7167+0.0245=0.7412[/tex]
The 94% confidence interval for the population proportion is (0.6922, 0.7412).
How do you write 748,800 in scientific notation? ______× 10^______
Answer:
7.488 × 10^5
Step-by-step explanation:
= 748.8 × 10^3
(engineering notation)
(thousand; prefix kilo- (k))
= 7.488e5
(scientific e notation)
= 7.488 × 105
(scientific notation)
= 748800
Answer:
Its written as
[tex]7.488 \times {10}^{5} [/tex]
Hope this helps you
Is (0,-2) a solution of 3x - y = 2?
Answer:
yes, (0,-2) is the answer when graphing this equation.
Step-by-step explanation:
Answer:
yes.
Step-by-step explanation:
Jimmy will be selling hot dogs at the football game. He bought hot dogs, buns, and condiments for a total of \$8$8dollar sign, 8 and now wants to calculate how many hot dogs he has to sell to make a profit. He graphs the profit he will make, (P)(P)left parenthesis, P, right parenthesis, as a function of the number
Answer:
the photo shows the answer ^D^ hope this helps~
Step-by-step explanation:
+also included the correct sign for confirmation xD
Answer:
up answer is correct :)
Step-by-step explanation:
Solve the inequality a−32<1 and write the solution in interval notation, using improper fractions if necessary.
Answer:
( -∞ , 33 )
Step-by-step explanation:
To solve the inequation a-32 < 1, we need to sum on both sides 32, as:
a - 32 + 32 < 1 + 32
a < 33
It means that the solutions are all the number that are smaller than 33 or in interval notation it would be:
( -∞ , 33 )
Where 33 is not included in the interval.
Please Help! Select the correct answer. Simon used these steps to solve an equation:
Answer:
A.
Step-by-step explanation:
From Step 3 to Step 4, Simon added -42 to both sides.
This is the addition property of equality: as long as you add the same thing to both sides, the equation remains equal.
A.
Easy geometry just find area shade boxes thank you plz help
Answer:
45 square units
Step-by-step explanation:
To figure out the area of a trapezoid, the formula is. A= (b1 + b2)h ÷2 . b1 is the top side which is 7 units and b2 is the bottom side which is 11 units. The height (h) is a vertical line going from the top to the bottom which is 5 units. All you need to do now is plug in those numbers and solve the equation.
Answer: 45 square units
Step-by-step explanation:
This shape can be broken down into two diffrent peices
The first peice is the rectangle
The second peice is the triangle
And both of these peices area's added together will yeild the total area
The rectangle is 7 units long and 5 units high, so it has an area of (7X5) = 35
The triangle is a little bit more complicated, it's formula is (BaseXHeight)/4
So all we need to do is plug in The base of the triangle = 4
And the Height of the trianlge = 5
So the triangles area is... (4X5)/2= 10
35+10=45 square units
Which inequality is represented by the graph?
Answer:
y ≤ 2/5x - .5
Step-by-step explanation:
Well it is a solid line with it shaded down meaning the inequality starts with
y ≤,
And by look at the y axis we can tell that the line crosses the y axis at -.5 which is the y intercept.
And by looking at the line we can tell the slope is 2/5.
Hence, the inequality is y ≤ 2/5x - .5
What is the volume of a cone with radius 7 cm and height 11 cm? Round your answer to two decimal places.
Answer:
D. 564.44 cm^3
Step-by-step explanation:
V = (1/3)(pi)r^2h
V = (1/3)(3.14159)(7 cm)^2(11 cm)
V = 564.44 cm^3
someone pls help im so close
Answer: A) 126.6
Step-by-step explanation:
Since we know ∠B = 85° and ∠C = 53°, we can use the Triangle Sum Theorem (angles of a triangle = 180°) to calculate ∠A.
∠A + ∠B + ∠C = 180
∠A + 85 + 53 = 180
∠A + 138 = 180
∠A = 42
Now we have:
A = 42 B = 85 C = 53
a = 85 b = ??? c = ???
We have all of the information for ∠A and side a so we can use the Law of Sines to find b (AC).
[tex]\dfrac{\sin 42}{85}=\dfrac{\sin 85}{b}\\\\\\b(\sin 42)=85(\sin 85)\\\\\\b=\dfrac{85\sin 85}{\sin 42}\\\\\\b=\large\boxed{126.547}[/tex]
Find the volume V of the described solid S. The base of S is a circular disk with radius 4r. Parallel cross-sections perpendicular to the base are squares.
Answer:
(1024/3)r^3.
Step-by-step explanation:
Step one: So, we have that x^2 + y^2 = 4^2 × r^2(when z component = 0) . Hence, there is the need to make y^2 the subject of the formula.
Step two: 4y^2 = 16r^2 - x^2. Where 4 ×(16r^2 - x^2) is the the cross sectional area.
Step three: the next thing to do here is to integrate the cross sectional area making 4r and -4r the upper limit and lower limit for the integration.
Step four: the integration will then give a product (16 × 64)/3 A = (1024/3)r^3.
What is the width and length of an area that = x^2+8x-9
Answer:
Then the width would be (x+9) and the length would be (x-1)
Step-by-step explanation:
If you factor the expression you get
[tex]x^2 - 8x - 9 = (x+9)(x-1)[/tex]
Then the width would be (x+9) and the length would be (x-1)
Answer:
(x-1) (x+9)
Step-by-step explanation:
Consider the form x2 + bx+c. Find a pair of integers whose product is c and whose sum is b In this case, whose product is − 9 and whose sum is 8.
−1,9 Hope this helps
The figure shows a person estimating the height of a tree by looking at the
top of the tree with a mirror. Assuming that both the person and the tree form
right angles with the ground, which of the following proportions can be used
to estimate the height of the tree
Answer:
[tex]\frac{6}{5} =\frac{x}{12}[/tex]
Step-by-step explanation:
Write a proportion in the form:
Height/side= height/side
The side lengths are 5 and 12.
The height (of the 5 side) is 6.
The proportion can be written as:
[tex]\frac{6}{5} =\frac{x}{12}[/tex]
3a. Write an equation in slope-intercept form of a
line that passes through (2,1) and (6,-5).
Answer:
[tex]y =- 3/2x + 4[/tex]
Step-by-step explanation:
[tex](2,1) and (6,-5).\\x_1 = 2\\x_2 = 6\\y_1 =1\\y_2 =-5\\\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}\\ \\\frac{y-1}{x-2} = \frac{-5-1}{6-2}\\\\\frac{y-1}{x-2} = \frac{-6}{4} \\Cross-Multiply\\4(y-1) = -6(x-2)\\4y-4=-6x+12\\4y =-6x+12+4\\4y = -6x+16\\Divide- through-by ; 4\\\frac{4y = -6x+16}{4} \\\\y = -\frac{3}{2} x +4[/tex]
A furniture store has set aside 800 square feet to display its sofas and chairs. Each sofa utilizes 50 sq. ft. and each chair utilizes 30 sq. ft. At least five sofas and at least five chairs are to be displayed.
a. Write a mathematical model representing the store's constraints.
b. Suppose the profit on sofas is $200 and on chairs is $100. On a given day, the probability that a displayed sofa will be sold is 0.03 and that a displayed chair will be sold is 0.05. Mathematically model each of the following objectives:
1. Maximize the total pieces of furniture displayed.
2. Maximize the total expected number of daily sales.
3. Maximize the total expected daily profit.
Answer:
a) 50S + 30C ≤ 800
b) 1) MAX = S + C
2) Max = 0.03S + 0.05C
3) Max = 6S + 5C
Step-by-step explanation:
Given:
Total space = 800 square feet
Each sofa = 50 square feet
Each chair = 30 square feet
At least 5 sofas and 5 chairs are to be displayed.
a) Write a mathematical model representing the store's constraints:
Let S denote number of sofas displayed and C denote number of chairs displayed.
The mathematical model will be:
50S + 30C ≤ 800
At least 5 sofas are to be dispayed: S ≥ 5
At least 5 chairs are to be displayed: C ≥ 5
b)
1) Maximize the total pieces of furniture displayed:
S + C = MAX
2) Maximize the total expected number of daily sales:
MAX = 0.03S + 0.05C
3) Maximize the total expected daily profit:
Given:
Profit on sofas = $200
Profit on chairs = $100
Max Expected daily profit =
Max = (200S * 0.03) + (100C * 0.05)
Max = 6S + 5C
Suppose a random variable X is best described by a uniform probability distribution with range 1 to 5. Find the value of that makes the following probability statements true.
a) P(X <-a)= 0.95
b) P(X
c) P(X
d) P(X ->a)= 0.89
e) P(X >a)= 0.31
Answer:
a) 4.8
b) 2.96
c) 4.4
d) 1.44
e) 3.76
Step-by-step explanation:
What we will do is solve point by point, knowing the following:
Fx (x) = P (X <= x) = (x - 1) / 4
a) P (X <-a) = 0.95
Fx (a) = 0.95
(a -1) / 4 = 0.95
a = 1 + 0.95 * 4
a = 4.8
b) P (X <a) = 0.49
Fx (a) = 0.49
(a -1) / 4 = 0.49
a = 1 + 0.49 * 4
a = 2.96
c) P (X <a) = 0.85
Fx (a) = 0.85
(a -1) / 4 = 0.55
a = 1 + 0.85 * 4
a = 4.4
d) P (X> a) = 0.89
P (X <a) = 1 - 0.89 = 0.11
Fx (a) = 0.11
(a -1) / 4 = 0.11
a = 1 + 0.11 * 4
a = 1.44
e) P (X> a) = 0.31
P (X <a) = 1 - 0.31 = 0.69
Fx (a) = 0.69
(a -1) / 4 = 0.69
a = 1 + 0.69 * 4
a = 3.76
X^4-13x^2+36 =
a. (x - 2)2(x - 3)2
b. (x2 + 4)(x 2 + 9)
C. (x - 2)(x + 2)(x - 3)(x + 3)
d. (x2 - 4)(x 2 + 9)
Answer:
answer C
Step-by-step explanation:
hello,
[tex]x^4-13x^2+36=(x^2-4)(x^2-9)[/tex]
as the sum of the zeroes are 13 and their product 36
4 + 9 = 13
4 * 9 = 36
and then we can write
[tex](x^2-4)=(x-2)(x+2)\\(x^2-9)=(x-3)(x+3)[/tex]
so
[tex]x^4-13x^2+36=(x^2-4)(x^2-9) = (x-2)(x+2)(x-3)(x+3)[/tex]
hope this helps
Find the midpoint of the line segment defined by the points (1/2, -5/2) and (-4/3, -1/6)
Answer:
-5/6 and -8/3
Step-by-step explanation:
To find the cordinates of the midpoint we must add the coordinates together and divide them by 2
let A be the midpoint of this line :
A (1/2-4/3 , -5/2-1/6)
A( -5/6, -8/3)
Answer:
(-5/12 , - 4/3)Step-by-step explanation:
The midpoint of the points (1/2, -5/2) and (-4/3, -1/6) is
[tex] (\frac{ \frac{1}{2} - \frac{4}{3} }{2} \: \: \frac{ - \frac{ 5}{2} - \frac{1}{6} }{2} ) \\ \\ = ( \frac{ - \frac{5}{6} }{2} \: \: \frac{ - \frac{8}{3} }{2} ) \\ \\ = ( - \frac{5}{12} \: \: \: - \frac{4}{3} )[/tex]
(-5/12 , - 4/3)Hope this helps you
Dr. Hernandez is a conservation biologist studying the impacts a derelict pharmaceutical company is having on a native fish population in a nearby lake. The lake has been contaminated with bovine growth hormone and Dr. Hernandez wants to see if the fish reaching adulthood in the contaminated lake are larger than the fish in a pristine lake that is nearby. Dr. Hernandez has the weights of 30 fish from the contaminated lake and of 30 fish from the pristine lake.
Based on the experimental design of Dr. Hernandez's research and the kind of data collected, which statistical test should be used to determine whether the bovine growth hormone is increasing the growth of native fish?
A. Two-tailed two-sample t-test
B. One-tailed paired t-test
C. Two-tailed paired t-test
D. One-tailed two-sample t-test
E. One-Way ANOVA
F. Linear Regression with t-test for significance of slope
Answer:
C. Two-tailed paired t-test.
Step-by-step explanation:
Since Dr. Hernandez takes 30 samples from a contaminated lake and 30 fish from a pristine lake, he should use a two-tailed t-test.
Paired t-tests describe tests used to compare the means of two samples when each observation in one sample can be paired with an observation in the other sample. Dr. Hernandez can certainly pair the samples and observe the differences, so the answer is C. Two-tailed paired t-test.
Hope this helps!