Answer:
The answer is below
Step-by-step explanation:
Given that:
mean (μ) = 70 years, standard deviation (σ)= 5.5 years.
a) The z score measures how many standard deviation a raw score is above or below the mean. It is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex], for a sample size of n, the z score is: [tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]
Given a sample of 5 turtles, we have to calculate the z score for x = 60 and x = 80.
For x = 60:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{60-70}{5.5/\sqrt{5} } =-4.07[/tex]
For x = 80:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{80-70}{5.5/\sqrt{5} } =4.07[/tex]
The probability that a mean life of a random sample of 5 such turtles falls between 60 and 80 years = P(60 < x < 80) = P(-4.07 < z < 4.07) = P(z < 4.07) - P(z < -4.07) = 1 - 0 = 1 = 100%
b) The z score that corresponds to top 10% is -1.28.
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\-1.28=\frac{x-70}{5.5/\sqrt{5} }\\ x-70=-3\\x=70-3\\x=67\ years[/tex]
Three whole numbers have an HCF of 3 and an LCM of 180. Two of the numbers are 45 and 60. Find the third number.
Answer:
Step-by-step explanation:
45=3×3×5
60=2×2×3×5
L.C.M=180
2| 180
2|90
3|45
3|15
3|5
180=2×2×3×3×5
third number=2×3=6
or 2×2×3=12
or2×3×3=18
or 2×2×3×3=36
so third number can be one of 6,12,18,36
PLEASE HELP MEEE How can a company use a scatter plot to make future sale decisions
Answer:
by tracking data of how much money was made on one product in a certain amount of time
Step-by-step explanation:
whats the squareroot of 72 needs to be simplified
Answer: 6√2
Step-by-step explanation: The easiest way to do this problem is to factor 72 as 2 · 36, then recognize 36 as a perfect square, 6 · 6.
There's no need to factor further because the 6's pair up
so a 6 comes out of the radical leaving a 2 inside.
So our answer is 6√2.
Always be on the lookout for perfect squares!
Work is attached below.
HELP NOW - Please help me
100 POINTS
Answer:
SAS
43ft
Step-by-step explanation:
We know that two sides are equal
PQ = ST and QR = TU and the angle between them is equal Q = T
We can use the SAS (side angle side)
Since the triangles are congruent
PR = SU
6y+5 = 8y
Subtract 6y from each side
6y+5-6y = 8y-6y
5 = 2y
Divide by 2
5/2 = y
2.5 = y
PR = ST = 8y = 8(2.5) =20
The perimeter is 9+14+20 = 43
Answer:
B. =35ft
Step-by-step explanation:
The perimeter of a right angled triangle is a+b+c
which is 9+4+6y+5 =90
collect like terms
9+4+5+6y=90
18 + 6y = 90
6y = 90 - 18
6y= 72
divide both sides by 6
6y/6 = 72/6
y = 12
so therefore, the perimeter of ∆PQR is
9 + 12 + 14
= 35ft
I need help please so if you could help that would be nice. Also i will make brainliest
(x^2+12x+36)-(x-1)^2
x^2-4xy+4y^2
16x^2-8x+1
x^2+4x+4
4x^2+12xy+9y^2
x^2-8x-16
4x^2-16
x^2-1
x^2+6x+9
9x^2-25y^4
16x^2-8x+1
Answer:
Hey I'm sorry I didn't get to answer your question it's just that I need the points because I don't have enough to get help with my question. I hope you get the answer that you need for you question. Good Luck :)
Step-by-step explanation:
For what values of does the equation (2 + 1)^2 + 2 = 10 − 6 have two real and equal roots?
Answer:
it isn't the equation so it can't be any roots...
Step-by-step explanation:
[tex](2+1)^2+2=10-6\\4+4+1+2=10-6\\11\neq 4[/tex]
Find the constant of proportionality (r) in the equation y = r x
Answer:
r = 11Step-by-step explanation:
y = r x
r is the constant of proportionality
To find r pick any values of x and y provided and substitute it into the above formula and solve for r.
That's
using
x = 2
y = 22
We have
22 = 2r
Divide both sides by 2
r = 11Therefore the constant of proportionality is 11
Hope this helps you
Solve each system of equations 4x+6y=3 and -10x-15y=-4
Answer:
There is no solution
Step-by-step explanation:
they all subtract eachother out
The Stem-and-Leaf Graph shows the amount of money each student spends on food per day in dollars. What is the median for the data in this Stem-and-Leaf Plot? A. $55 B. $73 C. $81 D. $84
Answer:
B) $73
Step-by-step explanation:
add all of your values and divide by the amount of values
52+55+55+55+59+64+66+68+72+73+73+73+73+75+81+81+83+84+84+86+87=
1,499
1,499 divided by 21 = 71.3809523...
which rounds to 73
HOPE THIS HELPS!!! :)
The median is of $48 in the stem leaf plot and option B is correct.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The median of a data-set is the value that separates the bottom 50% from the upper 50% of values.
The graph has 16 values, already ordered.
It is an even number, hence the median is the mean of the 8th and the 9th values, which considering the key are both 48,
Hence, the median is of $48 and option B is correct.
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Stem-and-Leaf Plot shows the amount of money each student spends
on travel per day in dollars. What is the median for the data in this graph?
Stem Leaf
A) $35
B) $48
C) $53
D) $54
PLEASE HELP, GIVING 55 POINTS IF YOU ANSWER (08.03/08.05 MC) A pair of equations is shown below: y = 3x − 5 y = 6x − 8 Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution. (5 points) Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer. (5 points)
Answer:
A. (1, -2)
B. the lines intersect at the solution point: (1, -2).
Step-by-step explanation:
A. The equations can be solve by substitution by using the y-expression provided by one of them to substitute for y in the other.
This gives ...
3x -5 = 6x -8
Adding 8-3x to both sides, we get ...
3 = 3x
Dividing both sides by 3 gives ...
1 = x
Substituting this value into the first equation, we can find y:
y = 3(1) -5 = -2
The solution is (x, y) = (1, -2).
__
B. The lines intersect at the solution point, the point that satisfies both equations simultaneously. That point is (1, -2).
Find the value of x.
Answer:
[tex]\textsf{x=22.5}[/tex]
Step-by-step explanation:
[tex]\textsf{According to intersecting tangent - secant theorem,}[/tex]
[tex]\textsf{x=1/2[(4x+5)-50]}[/tex]
[tex]\textsf{2(x)=4x+5-50}[/tex]
[tex]\textsf{2x=4x-45}[/tex]
[tex]\textsf{2x-4x=-45}[/tex]
[tex]\textsf{-2x=-45}[/tex]
[tex]\textsf{x= -45/-2}[/tex]
[tex]\textsf{x=22.5}[/tex]
[tex]\textsf{OAmalOHopeO}[/tex]
complete the first 4 steps for graphing the quadratic function given.
y= -x^2 -4x -3
ty<3
To be honest, I'm not sure which four steps your teacher is referring to. However, I'll show you one way to graph this.
A graph is simply a collection of points. Often those points are connected in some way (though they don't necessarily have to be) to form a curve.
Each point is of the form (x,y). To get each point, we pick random x values and determine their paired y value counterpart.
For example, if we pick x = -3, then,
y= -x^2 -4x -3
y= -(-3)^2 -4(-3) -3
y = -9 - 4(-3) - 3
y = -9 + 12 - 3
y = 0
This indicates that (-3, 0) is one point on the curve.
Let's repeat for x = -2
y= -x^2 -4x -3
y= -(-2)^2 -4(-2) -3
y = -4 - 4(-2) - 3
y = -4 + 8 - 3
y = 1
So (-2, 1) is another point on the curve.
Repeat this process as many times as you want. You should do at least 3 or 4 points in my opinion. The more points you generate, the more accurate the curve. After generating the points, you'll plot them all on the same xy grid. Then finally draw a curve through all of the points as shown below.
I used GeoGebra to make the graph.
1/5√75 -10√1/2+√125-2√1/2
Answer:6.91239069507
Step-by-step explanation:
The function f(x) = -(x - 3)2 + 9 can be used to represent the area of a rectangle with a perimeter of 12 units, as a
function of the length of the rectangle, x. What is the maximum area of the rectangle?
3 square units
6 square units
9 square units
12 square units
Answer:
9 square units
Step-by-step explanation:
The function f(x) describes a parabola opening downward, with a vertex at (3, 9). The maximum value of f(x) is found at the vertex, where it is f(3) = 9.
The maximum area is 9 square units.
Answer:
9 c
Step-by-step explanation:
The sum of the digits of a two digit number is 10 when the dishes are reversed the number increases by 18 find the original number
Answer:
Step-by-step explanation:
Hello, we can write this number ab where a and b are integer betwen 0 and 9.
For instance, 54, a = 5, b = 4
And then, we can say ab = 10 * a + b.
For instance, 54 = 50 + 4 = 5*10 + 4.
The sum of the digits of a two digit number is 10.
a + b = 10
When the dishes are reversed the number increases by 18.
10b + a = 18 + 10a + b
9b = 18 + 9a
b = 2 + a
We replace in the first equation to get.
a + 2 + a = 10
2a = 10 -2 = 8
a = 4
and then, b = 6
So, the number is 46.
Thank you
46°
Х
>
X =
degrees
Hshshshsus
An exterior angle of a triangle is equal to the sum of its interior opposite angles.
⇛ x = 90° + 46°
⇛ x = 136°
ASAP!!! PLEASE help me solve this question! No nonsense answers, and solve with full solutions.
Answer:
Option (4)
Step-by-step explanation:
By the theorem of inscribed angles and the intercepted arc,
"In a circle, angles subtended by the same arc always measure the same and the arc measures the double of the inscribed angle."
If an inscribed angle in a circle measures 75° then all inscribed angles by the same arc will measure 75°.
In addition to this, measure of arc subtended by these inscribed angle will measure double of the inscribed angle (150°)
Therefore, Option (4) will be the answer.
Find m∠A.
A. 32
B. 26
C. 27
D. 30
============================================
Use law of cosines to find angle A
a^2 = b^2 + c^2 - 2*b*c*cos(A)
9^2 = 6^2 + 14^2 - 2*6*14*cos(A)
81 = 36 + 196 - 168*cos(A)
81 = 232 - 168*cos(A)
81 - 232 = -168*cos(A)
-151 = -168*cos(A)
-168*cos(A) = -151
cos(A) = (-151)/(-168)
cos(A) = 0.8988095
A = arccos(0.8988095)
A = 25.9979801
A = 26 degrees approximately
The angle m∠A will be 27. so option C is correct.
What is a cosine law?Cosine law is a formula relating the length of the sides of a triangle to the cosine of one angle of the triangle.
u² = s² + t² - 2(s)(t)·cos U
Use law of cosines to find angle A
a^2 = b^2 + c^2 - 2*b*c*cos(A)
9^2 = 6^2 + 14^2 - 2*6*14*cos(A)
81 = 36 + 196 - 168*cos(A)
81 = 232 - 168*cos(A)
81 - 232 = -168*cos(A)
-151 = -168*cos(A)
-168*cos(A) = -151
cos(A) = (-151)/(-168)
cos(A) = 0.8988095
A = 25.9979801
A = 26 degrees approximately
Therefore, the angle m∠A will be 27. so option C is correct.
Learn more about sine to cosine conversion here:
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help me with the picture please
=====================================================
Explanation:
Refer to the diagram below. I've drawn diagonal that slopes upward. This diagonal cuts the quadrilateral into two triangles: One is equilateral and the other is isosceles.
The equilateral triangle marked in blue has all three angles 60 degrees each.
Note that the 60 and y angles combined to form 130, so,
60+y = 130
y = 130-60
y = 70
Then focus on the isosceles triangle (angles y, w and w). These three interior angles must add to 180
y+w+w = 180
70+2w = 180
2w = 180-70
2w = 110
w = 110/2
w = 55
This adds onto its adjacent neighbor of 60 to get w+60 = 55+60 = 115 degrees which is the value of x.
Find the distance between the origin and the points (-8,4)
Hi, I'm happy to help!
To solve this, we need to find the distance from the origin to the y coordinate value, x coordinate value, then use the Pythagorean Theorem.
The origin of a graph (center) has the coordinates (0,0), so this will be our other coordinates.
First, let's find the x coordinate distance change. We move from the x coordinate 0, to the x coordinate -8, so we move 8 x units.
Next, let's find the y coordinate distance change. We move from the y coordinate 0, to the y coordinate 4, so we move 4 y units.
Now that we have these two leg lengths, let's imagine this as a right triangle. Moving from the origin, we draw a line from (0,0), to (-8,0). Then, we draw a line from (-8,0) to (-8,4). Now, draw a direct line from (0,0), to (-8,4). We have the length of the first(8) and second(4) lines, and we need to find the third line length to find our answer. To do this, we use the Pythagorean Theorem, which states that a²+b²=c². This says that, in a right triangle, the square of the two shorter lengths equals the square of the longest length. The longest length is what we are solving for.
Let's say x distance is a, and y distance is b. Now, apply the values:
8²+4²=c²
64+16=c²
80=c²
Now, we need to find the value of c, so we need to find the square root of 80.
√80=c
8.9442...=c
Since the number goes on forever, we need to round it. For this example, let's round it to the nearest tenth, which would be 8.9.
To summarize the distance between the origin and the coordinates (-8,4), is about 8.9.
I hope this was helpful, keep learning! :D
A combination lock uses three numbers between 1 and 46 with repetition, and they must be selected in the correct sequence. Is the name of "combination lock" appropriate? Why or why not? Choose the correct answer below. A. No, because the multiplication counting rule would be used to determine the total number of combinations. B. Yes, because the combinations rule would be used to determine the total number of combinations. C. No, because factorials would be used to determine the total number of combinations. D. No, because the permutations rule would be used to determine the total number of combinations.
The correct answer is D. No because the permutations rule would be used to determine the total number of combinations.
Explanation:
The difference between a combination and a permutation is that in permutations the order is considered. This applies to the numbers in a lock because these need to be in order. Therefore, to analyze the permutations in a lock, the rule for permutations should be used. This includes the general formula P (n,r) =[tex]\frac{n!}{(n-r) !}[/tex]; in this, n is the number of objects and r refers to the objects used in a permutation. Thus, the term "combination" is inappropriate because this is a permutation, and the permutation rule should be used.
An orchardist is to plant apple trees and pear trees in the ratio 3:11. If he intends to plant 150 apple trees, how many pear trees will he need to plant?
The ratio 2:11 means for every 3 apple trees they will plant 11 pear trees.
They are planting 150 apple trees. Divide total apple trees by the ratio: 150/3 = 50
Multiply that by the ratio of pear trees:
50 x 11 = 550
They need to plant 550 pear trees.
State the value of the digit 3 in 41,039
d Write: £12 and 35 pence as a decimal
Answer:
3 tens or 30
£12.35
Step-by-step explanation:
41,039
ten thousand thousands, hundreds tens ones
The three is in the tens place
3 tens or 30
£12 and 35
1p = £0.01
£12.35
Please give me the correct answer
Answer:
Height = 15Step-by-step explanation:
[tex]Volume = 392.5\\r = 5\\h =?\\\\V= \frac{1}{3} \pi r^2 h\\\\392.5 = \frac{1}{3} \times 3.14 \times 5^2 \times h\\\\392.5 = \frac{78.5h}{3} \\\\392.5 = 26.16h\\\\\frac{392.5}{26.16} =\frac{26.16h}{26.16} \\\\h = 15.00[/tex]
Answer:
h=15 in
Step-by-step explanation:
V=πr²(h/3)
h=3v/πr²
h=[3(392.5)]/[3.14(5)²]
h= 15 in
A goat is grazing outside of a rectangular barn that has dimensions 20 ft by 30 ft.
He's tied to a corner of the barn with a 12 ft rope. Find the grazing area of the goat.
Answer:
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The Tama, Japan, monorail carries 92,700 riders
each day. If the monorail usually carries
5,150 riders per hour, how many hours does
the monorail run each day?
Answer:
The number of hours monorail run each day is 18.
Step-by-step explanation:
The total number of riders the monorail carry each day is:
N = 92700.
The number of riders the monorail carry per hour is:
n = 5150.
Compute the number of hours the monorail run each day as follows:
[tex]\text{Number of hours the monorail run each day}=\frac{N}{n}[/tex]
[tex]=\frac{92700}{5150}\\\\=18[/tex]
Thus, the number of hours monorail run each day is 18.
65. Given a segment with endpoints A and C and midpoint. If A(5, 8), and M(-3,2). Find the
location of C.
Answer:
C(-11,-4)
Step-by-step explanation:
Pls pls help me! What is it
Answer:
H
Step-by-step explanation:
Jackie
[tex] \sqrt{9} + \sqrt{25} = 3 + 5 = 8[/tex]
Jesse
[tex] \sqrt{9 + 25} = \sqrt{34} [/tex]
Taking the difference, we get the answer to be
[tex]8 - \sqrt{34} [/tex]
Bryan decides he wants to help pay for a birthday party for his little brother at the ice rink. It cost $50 to rent the party room and then $4 for each person attending. Bryan only has $100 to spend at the party. a) What are the constraints for this situation? b) Find the domain and range for this situation. Make sure you include all values for each using correct notation.
Answer:
a) 4*x + 50 ≤ 100
b) Domain x (0 ; 12 ) Range f(x) ( 50 ; 98 )
Step-by-step explanation:
The constraint is:
4*x + 50 ≤ 100 where "x" is the number of persons
b) Domain for x
x = 0 up to x = 12 x (0 ; 12 )
c) Range for f(x)
f(x) = 4*x + 50
f(0) = 4*0 + 50 f(0) = 50
f(12) = 4*12 + 50 f (12) = 98
f(x) ( 50 ; 98 )