2.
Scientists estimate that the distribution of the life span of the Galápagos Islands giant tortoise is
approximately normal with mean 100 years and standard deviation 15 years. Based on the estimate, which
of the following is closest to the age of a Galápagos Islands giant tortoise at the 90th percentile of the
distribution?
Answer:
119.2
Step-by-step explanation:
Given the following :
Mean (m) = 100 years
Standard deviation (sd) = 15 years
closest to the age of a Galápagos Islands giant tortoise at the 90th percentile of the
distribution?
Obtain the Zscore for 90th percentile (0.90) on the z table = 1.28
Zscore = (X - mean) / standard deviation
1.28 = (X - 100) / 15
1.28 × 15 = X - 100
19.2 = X - 100
19.2 + 100 = X
X = 119.2
Using the normal distribution, it is found that an age of 119 years is closest to the 90th percentile.
-------------------
Normal Probability Distribution
The z-score formula is used, which, in a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. Each z-score has a p-value associated, which represents the percentile of X.-------------------
Mean of 100 means that [tex]\mu = 100[/tex]Standard deviation of 15 means that [tex]\sigma = 15[/tex]The 90th percentile is X when Z has a p-value of 0.9, so X when Z = 1.28.Thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 100}{15}[/tex]
[tex]X - 100 = 15(1.28)[/tex]
[tex]X = 119.2[/tex]
An age of 119 years is closest to the 90th percentile.
A similar problem is given at https://brainly.com/question/15686085
draw a graph for x= - 4
Answer:
basically it's a vertical line on -4
Find the value of x and AC if the midpoint of segment AC is B. AB = 8x and BC = 6x + 24 Draw and label a picture to help you. x = Question Blank type your answer... and AC = Question Blank type your answer... Help me please!!!!!!
Answer:
x=12
Step-by-step explanation:
plug in 12 to x and results will make sense
A hamster running in a wheel of radius 13 cm spins the wheel at 35 revolutions per minute.
a) What is the angular velocity of the wheel? (in radians/sec)
Select an answer
b) At what linear velocity is the hamster running? (in cm/sec)
Select an answer
One revolution is completed when a fixed point on the wheel travels a distance equal to the circumference of the wheel, which is 2π (13 cm) = 26π cm.
So we have
1 rev = 26π cm
1 rev = 2π rad
1 min = 60 s
(a) The angular velocity of the wheel is
(35 rev/min) * (2π rad/rev) * (1/60 min/s) = 7π/6 rad/s
or approximately 3.665 rad/s.
(b) The linear velocity is
(35 rev/min) * (26π cm/rev) * (1/60 min/s) = 91π/6 cm/s
or roughly 47.648 cm/s.
The angular velocity of the wheel is 3.665 radians/sec.
The linear velocity is the hamster running is 47.648 cm/sec.
GivenA hamster running in a wheel of radius 13 cm spins the wheel at 35 revolutions per minute.
What is angular velocity?Angular Velocity It is defined as the rate of change in angular displacement of a particle in a circular motion.
The angular velocity of the wheel is given by;
[tex]\rm 1 \revolution = 2\pi \ radians\\\\Angular \ velocity = 35 \times 2\pi \ radians \ per \ minute\\\\Angular\ velocity = 70\pi \ radians \ per\ minute\\\\1 \ min = 60\ second\\\\Angular \ velocity = 70\pi \times \dfrac{1}{60} \\\rm \\Angular \ velocity = \dfrac{7}{6} \times 3.14 \ radians \ per \ second\\\\Angular \ velocity = 3.65\ radians \ per \ second\\\\[/tex]
The angular velocity of the wheel is 3.665 radians/sec.
What is linear velocity?Linear velocity definition deals with the measurement of an object’s velocity when it moves along a specific direction.
The linear velocity is the hamster running is given by;
[tex]\rm Linear \ velocity = 35 \times 26\pi \times \dfrac{1}{60}\\\\Linear \ velocity = 35 \times 26 \times 3.14 \times \dfrac{1}{60}\\\\ Linear \ velocity =47.648 \ cm \ per \ second[/tex]
The linear velocity is the hamster running is 47.648 cm/sec.
To know more about Angular velocity click the link given below.
https://brainly.com/question/88155
while working at the drugstore, kyle earns $15 per hour. how many hours will it take to earn $45
Answer:
3
Step-by-step explanation:
15+15+15=45 or you can just do 15x3
Raul and his friends, each of whom weighs 1/20 of a ton, are standing on a truck scale. The total weight shown by the scale is 3/4. How can you find the total number of people on the scale when raul and his friends are weighed?
Answer:
There are 15 friends
Step-by-step explanation:
The rule of three or is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them. That is, what is intended with it is to find the fourth term of a proportion knowing the other three.
If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) in the same proportion, the rule of three applies as follows:
a ⇒ b
c ⇒ x
Then: [tex]x=\frac{c*b}{a}[/tex]
where a, b and c are known values and x is the value to be calculated.
In this case, the rule of three applies as follows: if 1/20 of a ton is the weight of 1 person, 3/4 of a ton is the weight of how many people?
[tex]number of people =\frac{\frac{3}{4} of a ton*1 person }{\frac{1}{20} of a ton}[/tex]
or, what is the same,
number of people* [tex]\frac{1}{20}[/tex] = [tex]\frac{3}{4}[/tex]
Solving:
number of people= 15
There are 15 friends
4. Add 2 + 7/10 + 1/2 *
2.75
3.7
32/100
16/5
Answer: 2.75
Step-by-step explanation:
Find the value of x in the triangle shown below. Help ASAP please!! :)
This is an isosceles triangle. The two angles opposite the two equal sides are equal. With this knowledge, we now know that the angles are 61, 61, x.
We also know that the sum of all the angles of a triangle is equal to 180 degrees.
61 + 61 + x = 180.
Combine like terms.
122 + x = 180
Subtract 122 from both sides.
x = 58 degrees
buatlah matriks yang terdiri atas 5 baris dan 3 kolom dengan entrinya adalah 15 bilangan prima yang pertama
[tex]A = \left[\begin{array}{ccccc}2&3&5\\7&11&13\\17&19&23\\29&31&37\\41&43&47\end{array}\right] \\ \\ \\ \\ A^T = \left[\begin{array}{ccccc}2&7&17&29&41\\3&11&19&31&43\\5&13&23&37&47\end{array}\right][/tex]
Alvin is 9 years older than Elga. The sum of their ages is 89. What is Elga's age?
Answer:
Alvin: 49
Elga: 40
Step-by-step explanation:
The equation is 89 = x + (x-9).Remove the parenthesis and combine the like terms. 89 = 2x - 9Add 9 on both sides. 98 = 2x Divide by 2 on both sides. x = 4949 is the age of Alvin. (49-9) 40 is the age of Elga.Hey there!☺
[tex]Answer:\boxed{40}[/tex]
[tex]Explanation:[/tex]
Elga's age can be represented as "x". If Elga is x years old, then Alvin's age would be represented as "x+9", since Alvin is 9 years older than Elga.
Their combined age is 89. If you were to write that as an equation in terms of "x", you would have the following equation.
[tex]x+x+9=89[/tex]
Since the question is asking for Elga's age, which is x, you're going to be solving the equation for the value of x.
First add like terms: [tex]x+x+9=89 \rightarrow 2x+9=89[/tex]
Subtract both sides by 9 to leave x alone: [tex]2x+9-9=89-9 \rightarrow 2x=80[/tex]
Divide both sides by 2 to find x: [tex]\frac{2x}{2} = \frac{80}{2} \rightarrow x=40[/tex]
Since x is equal to 40, Elga is 40 years old, and Alvin would be 49 years old.
You can also check if the answer is correct by adding their ages.
[tex]40+49=89\ \br \checkmark[/tex]
Elga is 40 years old.
Hope this helps!
[tex]\text{-TestedHyperr}[/tex]
A gopher begins at 7 inches below the surface of a garden and digs
another 9 inches. Which expression represents this problem? *
7-9
9-7
-7-9
-7-(-9)
The equation y = mx + c is satisfied when
x=-1, y = 3, and also when x = 2, y=5
Find the values of m and c.
Question 7
5 pts
An ice cream shop sold a combined total of 287 ice cream cones in the flavors of
chocolate or vanilla. They sold 75 more vanilla cones than chocolate. How many
chocolate ice cream cones did they sell?
O 181
0106
225
212
Answer:
106
Explanation:
106+181=287
Find the coordinates of the midpoint of a segment with the given endpoints (7,0) and (2,4)
Answer:
[tex]MP= (4.5,2)[/tex] another way of writing [tex]MP= (\frac{9}{2}, 2)[/tex]
Step-by-step explanation:
[tex]MP= (\frac{x_1+x_2}{2})(\frac{y_1+y_2}{2})[/tex]
[tex]MP= (\frac{7+2}{2})(\frac{0+4}{2})[/tex] 7+2=9 0+1=1
[tex]MP= (\frac{9}{2})(\frac{2}{2})[/tex] MP= (4.5,2)
The coordinates of the mid - point of XY will be - M(4.5, 2)
We have two coordinate points - X(7, 0) and Y(2, 4).
We have to find the coordinates of the mid - point of the line segment XY.
What is Mid - Point Theorem?It states that a line with endpoint coordinates as - [x(1), y(1)] and
[x(2), y(2)] has its mid - point at the coordinates -
[tex]$x(m) =\frac{x(1)+x(2)}{2}[/tex]
[tex]$y(m) = \frac{y(1)+y(2)}{2}[/tex]
According to question, we have -
Assume that the coordinates of Mid - Point = M(h, k)
Coordinates of X= (7, 0)
Coordinates of Y= (2, 4)
Using the Mid - Point formula -
h = [tex]\frac{7+2}{2}[/tex] = 4.5
and
k = [tex]\frac{0+4}{2}[/tex] = 2
Hence, the coordinates of the mid - point of XY will be - M(4.5, 2)
To solve more questions on Mid - points, visit the link below -
brainly.com/question/25377004
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If rectangle ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180º, where would point A' lie? (1, -1) (1, 1) (-4, -1) (-4, 1)
Answer:
Point A reamains unchanged.
Step-by-step explanation:
Let
A(1, -1)
B(1, 1)
C(-4, -1)
D (-4, 1)
REFLECTED OVER Y-AXIS:
When we reflected over Y-AXIS we have to change the sign of X-Coordinates of all vertices so, above given vertices becomes
A(-1, -1)
B(-1, 1)
C(4, -1)
D (4, 1)
REFLECTED OVER X-AXIS:
When we reflected over X-AXIS we have to change the sign of Y-Coordinates of all vertices so, above given vertices becomes
A(-1, 1)
B(-1, -1)
C(4, 1)
D (4,-1)
When we rotated over 180 degree than we have to change the signs of both coordinates of all vertices
A(1, -1)
B(1, 1)
C(-4, -1)
D (-4,1)
we can see that after the opertion of all three processes i.e reflected over the y-axis, reflected over the x-axis, and rotated 180ºrespectively vertices are same as original vertices so, Rectangle remain unchanged. and point A is also unchanged
Find the midpoint of the segment with the following endpoints.
(8,5) and (0, -1)
Answer:
(4,2)
Step-by-step explanation:
[tex]Midpoint =\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(8,\:5\right),\:\\\left(x_2,\:y_2\right)=\left(0,\:-1\right)\\\\=\left(\frac{0+8}{2},\:\frac{-1+5}{2}\right)\\\\= (\frac{8}{2} , \frac{4}{2} )\\\\Simplify\\=\left(4,\:2\right)[/tex]
Answer:
(4,2)
Step-by-step explanation:
you know why
Use the graph shown to answer the question. What is the solution set for the inequality if log2(2x – 1) > 2?
Answer: B
(2.5, ∞)
Step-by-step explanation:
The solution set of the given logarithm inequality will be (2.5,∞).
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
In another word, a logarithm is a different way to denote any number.
As per the given logarithm function,
log₂(2x - 1) > 2
By log property
2x - 1 > 2 x 2
2x > 4 + 1
x > 5/2
x > 2.5 so the solution set will be 2.5 < x < ∞ or (2.5,∞).
Hence "The solution set of the given logarithm inequality will be (2.5,∞)".
For more about logarithms
https://brainly.com/question/20785664
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A football team loses 8 yards on each of 4 consecutive plays. Find the total change in yards from where the team started. pls help fgkogijriojg
Answer:-32
Step-by-step explanation:
You times the two numbers and add a negative sign in front of it
8 would be a negative in this situation and 4 would be a positive. So the problem would look like this:
-8 x 4 = ?
For this particular problem, we would do 8 x 4 which would equal 32. Then we would try to find which one has the greater absolute value.
Absolute Value:
4 = 4
-8 = |8|
Since -8 has the greater absolute value, the answer would be negative.
The Answer: -32
How many times greater is the value of of 2 in 2341 than the value 2 in 1234?
f(3) = 6x
Help if you can?!
Cole and his friends made a line plot of hours they spend watching TV after school, which is the difference between the greatest amount of time spent watching TV at the least amount time.
Answer:
what
Step-by-step explanation:
Answer:
i need more intel like numbers
Step-by-step explanation:
[tex] {3}^{a} = \frac{1}{9} [/tex]
[tex] {3}^{b} = 9 \sqrt{3} [/tex]
[tex] {3}^{c} = \frac{1}{ \sqrt{3} } [/tex]
Work out the value of a + b + c
Use the diagram to help you solve the problem.
A pair of shoes has an original price of $65 but is on
sale for a 20 percent discount. What number can you
multiply by $65 to get the discounted price of $52?
O 0.20
O 0.50
O 0.80
O 0.90
Answer:
C
Step-by-step explanation:
Just took it
your correct answer is C
(0.80)
Please help! The yellow dot is something random I picked!!! Can you help me?I WILL GIVE BRAINLIEST TO WHOEVER GETS IT RIGHT
Answer:
14s+107
Step-by-step explanation:
(2s+7)+(12s+100)
14s+107
answer for p=2l+2w for l
Answer:
[tex]I=\frac{p-2w}{2}[/tex]
Step-by-step explanation:
[tex]p=2I+2w\\\\p-2w=2I+2w-2w\\\\p-2w=2I\\\\\frac{p-2w}{2}= I[/tex]
Which function is the inverse of f(x) = 2x+3?
Answer:
f^-1(x)=x-3/2
Step-by-step explanation:
we have f(x)=2x+3
let
y=f(x)
y=2x+3
Exchanges the variables x for y and y for x
x=2y+3
isolate the variable y
2y=x-3
y=x-3/2
let
f^-1(x)=y
f^-1(x)=x-3/2
Answer:
Step-by-step explanation:
The answer is B on Edgenuity
f^-1 (x) = 1/2x - 3/2
please help ill mark branilest
I think it's the third choice :)) the one you currently have
Find the area of a triangle with a 21 cm base and 4 cm height
Answer:
42 cm^2
Step-by-step explanation:
Base = 21 cm
Height = 4 cm
Area = [tex]\frac{base\times height}{2}[/tex]
Substitute values into the given equation
[tex]A = \frac{21\times 4}{2} \\\\A = \frac{84}{2} \\\\A = 42cm^2[/tex]
INTERPRETING EXPRESSIONS:
ln the expression 9x - 9, the variable is ___
I would seriously appreciate if u helped me TvT
Answer:
[tex]x=-11[/tex]
Step-by-step explanation:
So we have the equation:
[tex]5+(x-2)=-8[/tex]
Let's subtract 5 from both sides:
[tex](5+(x-2))-5=(-8)-5[/tex]
The left side will cancel. Subtract on the right:
[tex]x-2=-13[/tex]
Now, add 2 to both sides:
[tex](x-2)+2=(-13)+2[/tex]
Again, the left side will cancel. Add the right:
[tex]x=-11[/tex]
And we're done!
Answer:
it should be x=5
Step-by-step explanation:
5+(x-2)= -8
3+x=8
-3 -3
answer is x=5