The expected value of the number of albino panthers is 5
The standard deviation of the number of albino panthers is 2.09
Given that albino panther is born once every 8 years, probability p, of one albino to be born in 8 years is 1/8
Expected value=n*p, where n is 40 years, and p=1/8
=40*1/8
=5 albino panthers
Hence, the expected value is 5 albino panthers
Standard deviation=(Expected value*(1-p))^1/2
=(5*(1-1/8))^1/2
=4.375^1/2
=2.09
Hence, standard deviation is 2.09
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Find the equation of the line passing through the given points. Express the equation in standard form. (4,5) and (-3,-1)
Answer:
y = m x + b equation for a straight line
when x = 4 y = 5
5 = m * 4 + b
m = (5 - b) / 4 solving for m
when x = -3 y = -1
-1 = (5 - b) / 4 * -3 + b = -3 * (5 - b) / 4 + 4 b / 4
-1 = (-15 + 3 b + 4 b) / 4
11 = 7 b b = 11 / 7
Since m = (5 - b) / 4
m = (5 - 11/7) / 4 = 6/7
We then have y = 6 x / 7 + 11 / 7
Or 7 y = 6 x + 11
Check:
when (4 , 5) 35 = 24 + 11 = 35
An object attached to a coiled spring is pulled down a distance of 10 centimeters from its rest position and then released.
Assuming that the motion is simple harmonic
with a period of 2 seconds, write an equation that relates the displacement d of the object from its rest position after t seconds.
Also assume that the positive direction of
the motion is up. At time t=0 the object is at its resting position and moving down.
Answer: The general form for an equation that models a wave is this: (+/-) a (sin/cos) (2π(x-p)/T), where a is your amplitude, p is your phase shift, and T is your period. The (+/-) becomes + if the graph is to start in the positive direction, and - if it is to start in the negative direction. The (sin/cos) becomes sine if the graph is to start at 0 before being shifted, while it becomes cosine if the graph is to start at the amplitude.
In this case, our graph starts out negative, and at the amplitude with no phase shift, so the (+/-) becomes -, (sin/cos) becomes cos, and p is zero. Substituting in the values given in the problem, a = 9 and T = 7, we find this equation: d = -9cos(2πt/7).
Step-by-step explanation:
These marbles are placed in a bag and two of them are randomly drawn what is the probability of drawing two yellow marbels if the frist one is placed back in the bag before the second draw
The probability of drawing two yellow marbles if the first one is placed back in the bag before the second draw is 0.022
Since the formula we refer to in calculating probability is
P = no of possible outcomes/ total number of outcomes
Since we were provided with 10 marbles out of which 2 are yellow, 3 are pink and 5 are blue
So the total outcomes are = 1,The total number of yellow marble is 2
The probability that the first ball drawn is yellow :
P₊= 2/10= 1/5
the probability of drawing the second ball to be yellow is:
P₂= 1/9
the total probability of drawing two yellow marbles if the first one is placed back in the bag before the second draw is :
P= 1/5 * 1/9
= 1/45
= 0.022
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What is the probability of drawing two yellow marbles if the first one is NOT placed back into the bag before the second draw? There are 10 marbles total, 2 yellow, 3 pink, and 5 blue
In the figure, m<7=100 degrees. Find the measure of each angle.
22.) <6
23.) <8
24.) <2
25.) <5
26.) <11
The corresponding measure of each angle is 80, 80, 80, 100 and 100 degrees
How to determine the measure of each angle?
Given: m<7=100 degrees
To find <6, <8, <2, <5 and <11
In the <7 is vertically opposite <5. Since vertically opposite angles are equal.
Thus, <5 = <7 = 100 degrees
Also, <5 and <6 are angles on a straight, and the sum of angles on a straight line is 180 degrees. Thus:
<5 + <6 = 180
100 + <6 = 180
<6 = 180 -100 = 80 degrees
Also, <6 and <8 are vertically opposite.
Thus, <8 = <6 = 80 degrees
<2 and <6 are corresponding angles, and corresponding angles are equal. Thus, <2 = <6 = 80 degrees
Likewise, <11 and <7 are corresponding angles
Thus, <11 = <7 = 100 degrees
Therefore, the measure of angle <6, <8, <2, <5 and <11 are 80, 80, 80, 100 and 100 degrees respectively
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The red figure is congruent to the blue figure. Which choice describes a sequence of transformations in which the blue figure is the image of the red figure?
1. Rotate the triangle 90º counterclockwise about the origin and then translate it 7 units left and 1 unit up.
2. Rotate the triangle 90º clockwise about the origin and then translate it 7 units left and 1 unit up.
3. Rotate the triangle 90º counterclockwise about the origin and then translate it 1 unit left and 7 units down.
4. Rotate the triangle 90º clockwise about the origin and then translate it 1 unit left and 7 units down.
The choice which describes a sequence of transformations in which the blue figure is the image of the red figure is: 4. Rotate the triangle 90º clockwise about the origin and then translate it 1 unit left and 7 units down.
What is a rotation?In Mathematics, the rotation of a geometric figure 90° about the origin in a clockwise or counterclockwise direction would produce a geometric figure that has these coordinates (y, -x).
From the information provided in the graph about the transformation applied to the red triangle to create the blue triangle, we have the following ordered pairs that represents a rotation of 90º clockwise:
(x, y) → (y, -x)
Ordered pair A = (-5, 2) Ordered pair A' = (2, 5)
Ordered pair B = (-5, 6) Ordered pair B' = (6, 5)
Ordered pair C = (-1, 2) Ordered pair C' = (2, 1)
After a translation of 1 unit left and 7 units down, we have:
Ordered pair A' = (2, 5) → Ordered pair A' = (2 - 1, 5 - 7) = (-1, -2)
Ordered pair B' = (6, 5) → Ordered pair B' = (6 - 1, 5 - 7) = (.5, -2)
Ordered pair C' = (2, 1) → Ordered pair C' = (2 - 1, 1 - 7) = (-1, -6)
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Can anyone state the vertex of the graph?
The graph has no vertex
The transformations from the parent function are
Vertical shift down 2Horizontal shift left 4How to determine the vertex?The graph represents the given parameter
As a general rule, the maximum or the minimum of a graph is the vertex
However, the graph has no maximum or minimum
This means that there is absence of a vertex in the graph
The transformationHere, we have:
The graph is translated 4 units to the left of the origin The graph is translated 2 units below the originThis transformation can be represented as (x - 4, y - 2)
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quadrilateral rstu has vertices R(2,4) ,s (-2,2), T(-1,0)and (3,2)
Verify:
i) quadrilateral rstu is a rectangle
ii) the diagonals of the rectangle bisect each other and are equal in lengths .
As RS=TU and ST=UR by distance formula, The given quadrilateral RSTU is rectangle and The diagonals RT=US so they are equal and bisect each other at right angle.
What is rectangle?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel. An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional shape. The rectangle's longer side is its length, and its shorter side is its width.
Here,
Calculate the length of sides by distance formula.
RS=√(y2-y1)²+(x2-x1)²
=√(2-4)²+(-2-2)²
=√4+8
=√(12
=2√3 units
ST=√(y2-y1)²+(x2-x1)²
=√(0-2)²+(-1-(-2))²
=√(4+1)
=√5 units
TU=√(y2-y1)²+(x2-x1)²
=√(2-0)²+(3-(-1))²
=√(4+8)
=√12
=2√3 units
UR=√(y2-y1)²+(x2-x1)²
=√(4-2)²+(3-2)²
=√(4+1)
=√5 units
RT=√(y2-y1)²+(x2-x1)²
=√(0-4)²+(-1-2)²
=√(16+9)
=√25
=5 units
US=√(y2-y1)²+(x2-x1)²
=√(2-2)²+(-2-3)²
=√(0+25)
=√25
=5 units
Because the given quadrilaterals, RS=TU and ST=UR, are rectangles and the diagonals, RT=US, are equal and at right angles to one another, according to the distance formula.
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6. The supplement of an angle is 8 less than three times the measure of the angle. Find
the measure of both angles.
X =180
m/1=
m/2 =
By using the concept of supplementary angle, it can be calculated that
The two angles are 47° and 133°
What are supplementary angles?
At first it is important to know about angle.
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.
Two angles are said to be supplementary if the sum of the angles is 180°
Let one angle be x
Other angle = 180 - x
The supplement of an angle is 8 less than three times the measure of the angle
By the problem
180 - x = 3x - 8
3x + x = 180 + 8
4x = 188
x = [tex]\frac{188}{4}[/tex]
x = 47°
Other angle = 180 - 47 = 133°
The two angles are 47° and 133°
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Double points. Please help!
Estimate 29.25 + 41.06
And Exact answer
Step-by-step explanation:
70.31
hope it's helpful
Answer:
Step-by-step explanation:
no
Rotate 90 counter clockwise around the origin and then reflect over the c-axis
In order to get the same outcomes as a form mirrored across the y-axis and turned counterclockwise, a shape can be reflected across the x-axis and then rotated 90 degrees in a clockwise manner around the origin. This suggests a similarity between these two transformative sequences.
What does mathematics mean by reflection?
A flip is the term used in geometry to describe a reflection. The mirror image of the form is a reflection. An image can reflect through a line known as the line of reflection. When all of the points in a figure are evenly spaced away from one another, the two figures are said to reflect each other.
(X, Y) > when a form is rotated 90 degrees counterclockwise (y, -x).
When the picture is reflected across the y-axis, (x, y) > (-x, y).
When those two transformations are used, it is the same as reflecting a shape across the line y = -x, where (x, y) > (-y, -x).
For instance: After being rotated 90 degrees clockwise and reflecting across the y-axis,
(2, 1) > (1, -2) > (-1, -2); and
(2, 1) > (-1, -2)
after being reflected across the y = -x line
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outside temperature over a day can be modeled as a sinusoidal function. suppose you know the temperature varies between 60 and 70 degrees during the day and the average daily temperature first occurs at 9 am. how many hours after midnight, to two decimal places, does the temperature first reach 63 degrees?
The 4.89 hours after midnight did the temperature first hit 63 degrees.
What is sinusoidal function ?A sinusoidal function can be used to mimic the daily variation in outdoor temperature. Assume you are aware that the daily average temperature starts at 9 am and swings between 60 and 70 degrees throughout the day.
We have to find to two decimal places, how many hours after midnight did the temperature first hit 63 degrees.
Max T=70 and Min T=60
D = (Max + Min)/2
= 70+60/2
= 65
A = Max- D
= 70 - 65
= 5
Since,
Period is 24 hours,
So,
W = 2π/24
= π/12
The function will be:
T(t) = 5 Sin (π/12(t-C)) + 65
Given average temperature occurs at 8 am so,
T(9)=65
Solving this we get
C=9
Hence,
T(t)= 5Sin(π/12( t-9))+65
Now,
We need to find t such that T(t)=63
63=5Sin(π/12( t-9))+65
t = 4.89 hours.
Therefore, The 4.89 hours after midnight did the temperature first hit 63 degrees.
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Solve for a in terms of b, c, and d.
c=a+b–d
I NEED HELP PLS I GIVE YOU POINTS
Answer:
Option D: 160 square feet
Step-by-step explanation:
Area of the lawn
= (7 feet × 8 feet) + (13 feet × 8 feet)
= 56 square feet + 104 square feet
= 160 square feet
The table below shows the energy of a 10 kg ball as a function of velocity. How much energy will the ball have at 10 m/s? velocity 0,2,3,6,10 energy 0,20,45,180,?
The amount of energy that the ball will have at 10 m/s is; 600 J
How to find the energy from velocity?From the given table, we see that when the velocity is 2 m/s, then the energy is 20 J.
If we take the square of the velocity, we get 2² = 4.
Thus, we need to multiply 4 by 6 to get the energy that is equal to 24 as 4 * 6 = 24.
Similarly;
For velocity equal to 3 m/s, the energy is given as:
E = 6 * 3²
E = 54 J
Thus, the general formula to find the energy is given as:
E = 6 * v²
where;
E is the energy
v is the velocity
Now, for velocity equal to 10 m/s, energy is given as;
E = 6 * 10
E = 60 J
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10. Bob buys some games for $13 each. He has a coupon for $5 off the total
price. If he pays $73, how many games did he buy
Can write the equation to this problem?
The equation, in vertex form, of the graph in the diagram is determined as: y = 1|x - 3| + 5.
What is the Equation of a Graph that Represents an Absolute Value Function?The formula that represents the equation in vertex form of an absolute value function is y = a|x - h| + k, where:
Vertex = (h, k).
Therefore, we will need to determine what the values of a, h, and k is using the information derived from the graph.
Thus:
(h, k) = (3, 5)
a = 1 (this is because the graph opens upward)
To write the equation of the graph, substitute a = 1, h = 3, and k = 5 into:
y = 1|x - 3| + 5
The equation is, y = 1|x - 3| + 5.
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Help asap please and I will give brainliest!
Solve the inequality. Graph the solution.
−8≤2/5(k−2)
Solve the inequality. Graph the solution.
−8≤2/5(k−2)
Answer: K is greater than or equal to 18
Step-by-step explanation:
Answer:k>=-18
Step-by-step explanation:
Rewrite so k
is on the left side of the inequality.
2/5⋅(k−2)≥−8
Multiply each term in
2/5⋅(k−2)≥−8 by 5/2 to eliminate the fractions.
k−2≥−20
Move all terms not containing
k to the right side of the inequality.
k≥−18
The result can be shown in multiple forms.
Inequality Form:
k≥−18
I have been struggling on this for hours now please help
Step-by-step explanation:
-(10x + 2) > 5x - 1 - 8x
combine x terms on right side:
-(10x + 2) > -3x - 1
remove ()'s from left side:
-10x - 2 > -3x - 1
add 10x to both sides:
-10x - 2 + 10x > -3x - 1 + 10x
-2 > 7x - 1
add 1 to both sides:
-2 + 1 > 7x - 1 + 1
-1 > 7x
divide both sides by 7:
-1/7 > 7x /7
-1/7 > x or x < -1/7
in interval notation: (-∞, -1/7)
what is the measure of EAC?
The measure of angle EAC IS 50°
What is an angle bisector?The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts. For example, an angle bisector of a 60-degree angle will divide it into two angles of 30 degrees each. In other words, it divides an angle into two smaller congruent angles. Given below is an image of an angle bisector of ∠AOB.
∠BAE = x + 30, ∠EAC = 3x - 10
If AE is a line that bisects BAC,
then ∠BAE = ∠EAC
which becomes,
x + 30 = 3x - 10
collecting like terms,
x - 3x = -10 - 30
-2x = -40
x = -40/-2
x = 20°
But m ∠EAC = 3x - 10
substituting x = 20°
we have ∠EAC = 3(20) - 10
= 60 - 10
∠EAC = 50°
In conclusion, the value of ∠EAC = 50°
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Carlos took a total of 8 quizzes over the curse of 4 weeks. What is his unit rate?
Data were recorded for a car’s fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour (mph). Given the least-squares regression line, , what is the predicted fuel efficiency for a speed of 30 mph?
17. 67 mpg
26. 50 mpg
30. 00 mpg
37. 74 mpg
The predicted fuel efficiency for a speed of 30 mph will be 26.50 mpg when the least-squares regression line is given.
What is the least-squares regression line?If the data demonstrates a stronger link between two variables, the line that best matches this linear relationship is known as a least-squares regression line, and it minimizes the vertical distance between the data points and the regression line. A regression line is a straight line that illustrates how a response variable y varies when an explanatory variable x changes. The line is a mathematical model that predicts the value of y given a value of x. A regression line predicts the value of y for a given value of x. A regression line is discovered through regression analysis. When the explanatory variable changes, the regression line shows how much and in which direction the response variable changes.
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It cost $4.50 for zoo parking, plus an additional $6.25 for admission per person into the zoo. If Jay starts off with $55.00 and buys 3 admission tickets, how much money will he have left?
Answer: he will be left with 31.74 dollars
Step-by-step explanation:
i first put 55.00 - 4.50 = 50.5
then you subtract 50.5 with 6.25 3 times so the and is 31.74
hope this helped !!
"the difference of a number cubed and 10" translated expression
Answer:
[tex]x^3-10[/tex]
Step-by-step explanation:
Let the number be x.
"A number cubed" refers to x³.
"Difference" means to subtract, so the answer is [tex]x^3-10[/tex].
How to do this equation (1 + 3)²
Answer:
your answer is 16
Step-by-step explanation:
So, to solve (1 + 3)²
first add 1 and 3
then you will get 4
and your equation would be (4)²
then you just square 4.
(4)² > 4x4 = 16
hope this helps (can you mark as brainiest pls)
Nachelle signed up for a streaming music service that costs $6 per month. The service
allows Nachelle to listen to unlimited music, but if she wants to download songs for
offline listening, the service charges $1.25 per song. How much total money would
Nachelle have to pay in a month in which she downloaded 20 songs? How much
would she have to pay if she downloaded s songs?
K
Cost with 20 songs:
Cost with s songs:
The cost of s and 20 songs are $1.25s and $25 respectively.
What is multiplication?Multiplication is mathematical arithmetic operation. It is also a process of adding same types of expression to some number of times.
Example - 2 × 3 means 2 is added three times or 3 is added 2 times.
Given that music services cost $6 per month to Nachelle.
And to download songs for offline listening, the service charges $1.25 per song.
If she wants to download s songs,
The cost of s songs = the cost of one song multiplied by s
The cost of s songs =$1.25 multiplied by s
The cost of s songs = $1.25s
Here s = 20 then
cost of 20 songs = $1.25 x 20
= $25
Therefore the cost of s and 20 songs are $1.25s and $25 respectively.
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What is the area of the figure at the right?
The area of the figure is 21. 25 m². Option D
How to determine the areaIt is important to note that the figure is a kite.
The formula for calculating the area of a kite is expressed as;
A= pq/2
Where;
A is the area of the kitep is the diagonal of the kiteq is the diagonal of the kiteUsing tangent identity
tan 45 = x/ 2. 5
1(2. 5) = x
x = 2. 5
p = 2. 5 + 2. 5 = 5
q = 2. 5 + 6 = 8. 5
Now, substitute the values into the formula
Area = 5(8. 5)/ 2
Area = 42. 5/ 2
divide the values
Area = 21. 25 m²
Hence, the value is 21. 25m²
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It’s really hard ddid
Answer:
ye it is I can't help sorry I need the points
3. 3.8 ft
5. 28
7. .1
Step-by-step explanation:
5/20.5=15.5/x
solve for x
3.8
7/14=14/x
28
10/x=1/100
.1
Write
y − 2 = (x + 6) in
standard form.