Answer:
6.5
Step-by-step explanation:
The sum of all angles in a triangle are 180 degrees.
=> 10x -10 + 8x + 10x + 8 = 180
=> 28x -2 = 180
=> 28x = 182
=> x = 6.5
So, Angle A = 10 x 6.5 -10 = 65 - 10 = 55 degrees
Angle B = 8 x 6.5 = 52 degrees
Angle C = 10 x 6.5 + 8 = 65 + 8 = 73 degrees.
55 + 52 + 73 = 55 + 125 = 180 degrees
Which expression is equivalent to 5y^3/(5y)^-2
Answer:
5^3 y^5
125 y^5
Step-by-step explanation:
5y^3/(5y)^-2
Distribute the exponent in the denominator
5y^3/(5 ^-2 y^-2)
A negative exponent in the denominator brings it to the numerator
5y^3 5 ^2 y^2
Combine like terms
5 * 5^2 * y^3 5^2
We know that a^b * a^c = a^(b+c)
5^(1+2) * y^( 3+2)
5^3 y^5
125 y^5
Which rule describes this transformation? (Zoom in to see it clearly)
Answer:
(x,y) -> (x+6, y-3)
Step-by-step explanation:
I followed c and it translated like the last ans choice.
let d equal the distance in meters and t equal the time in seconds. Which is a direct variation equation for this relationship
Answer:
d = s x t
Step-by-step explanation:
The formula for distance.
Decide all proper subsets of A { 8 ,7 ,6 ,5 ,4 ,3 ,2 ,1} = A 1- { 4 ,3 ,2 ,1} 2- { } 3- { 9 ,8 ,7 } 4- { 11 ,2} 5- { 5 }
Answer:
A, E
Step-by-step explanation:
There should be 2^8-1 proper subsets of A. Its every one besides { }
if pentagon OPQRS is dilated by a scale factor or ?
from the origin to create O'P'Q'R'S: what is the ordered pair of point S'?
Answer:
Option (D) : (3.5, 8.75)
Consider F and C below.
F(x, y) = x2 i + y2 j
C is the arc of the parabola y = 2x2 from (−1, 2) to (2, 8)
(a) Find a function f such that F = ∇f. f(x, y) =
(b) Use part (a) to evaluate C ∇f · dr along the given curve C.
(a)
[tex]\dfrac{\partial f}{\partial x}=x^2\implies f(x,y)=\dfrac{x^3}3+g(y)[/tex]
[tex]\dfrac{\partial f}{\partial y}=\dfrac{\mathrm dg}{\mathrm dy}=y^2\implies g(y)=\dfrac{y^3}3+C[/tex]
[tex]\implies f(x,y)=\dfrac{x^3+y^3}3+C[/tex]
(b)
[tex]\displaystyle\int_C\nabla f\cdot\mathrm d\mathbf r=f(2,8)-f(-1,2)=\boxed{171}[/tex]
The solution system to 3y-2x=-9 and y=-2x+5
Answer:
[tex]\boxed{(3,-1)}[/tex]
Step-by-step explanation:
Hey there!
Well to find the solution the the given system,
3y - 2x = -9
y = -2x + 5
So to find x lets plug in -2x + 5 for y in 3y - 2x = -9.
3(-2x + 5) - 2x = -9
Distribute
-6x + 15 - 2x = -9
-8x + 15 = -9
-15 to both sides
-8x = -24
Divide -8 to both sides
x = 3
Now that we have x which is 3, we can plug in 3 for x in y = -2x + 5.
y = -2(3) + 5
y = -6 + 5
y = -1
So the solution is (3,-1).
Hope this helps :)
What is the result of question?
Answer:
B
Step-by-step explanation:
x can not be greater than (1,325-270)/26 because $270 is fixed for the rental
The length of a rectangle is three times its width. If the perimeter of the rectangle is 160 cm, what are the dimensions of this rectangle?
Answer:
The dimensions or Area of the rectangle is 1200cm².
An engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 3.6 mm, how many of these components should she consider to be 90% sure of knowing the mean will be within ± 0.1 ±0.1 mm?
Answer:
She must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.
Step-by-step explanation:
We are given that an engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 3.6 mm.
And she considers to be 90% sure of knowing the mean will be within ±0.1 mm.
As we know that the margin of error is given by the following formula;
The margin of error = [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]
Here, [tex]\sigma[/tex] = standard deviation = 3.6 mm
n = sample size of components
[tex]\alpha[/tex] = level of significance = 1 - 0.90 = 0.10 or 10%
[tex]\frac{\alpha}{2} = \frac{0.10}{2}[/tex] = 0.05 or 5%
Now, the critical value of z at a 5% level of significance in the z table is given to us as 1.645.
So, the margin of error = [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]
0.1 mm = [tex]1.645 \times \frac{3.6}{\sqrt{n} }[/tex]
[tex]\sqrt{n} = \frac{3.6\times 1.645}{0.1 }[/tex]
[tex]\sqrt{n}[/tex] = 59.22
n = [tex]59.22^{2}[/tex] = 3507.0084 ≈ 3507.
Hence, she must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.
Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps
west and finally 50 steps on a bearing of 3150
.
i. Sketch Musah’s movement
ii. How far west is Musah’s final point from the centre?
iii. How far north is Musah’s final point from the centre?
iv. Describe how you would guide a JHS student to find the bearing and distance of
Musah’s final point from the centre.
Answer:
ii. 75 steps
iii. 75 steps
iv. 106 steps, and [tex]315^{0}[/tex]
Step-by-step explanation:
Let Musah's starting point be A, his waiting point after taking 50 steps northward and 25 steps westward be B, and his stopping point be C.
ii. From the second attachment, Musah's distance due west from A to C (AD) can be determined as;
bearing at B = [tex]315^{0}[/tex], therefore <BCD = [tex]45^{0}[/tex]
To determine distance AB,
[tex]/AB/^{2}[/tex] = [tex]/50/^{2}[/tex] + [tex]/25/^{2}[/tex]
= 25000 + 625
= 3125
AB = [tex]\sqrt{3125}[/tex]
= 55.90
AB ≅ 56 steps
Thus, AC = 50 steps + 56 steps
= 106 steps
From ΔACD,
Sin [tex]45^{0}[/tex] = [tex]\frac{x}{106}[/tex]
⇒ x = 106 × Sin [tex]45^{0}[/tex]
= 74.9533
≅ 75 steps
Musah's distance west from centre to final point is 75 steps
iii. From the secon attachment, Musah's distance north, y, can be determined by;
Cos [tex]45^{0}[/tex] = [tex]\frac{y}{106}[/tex]
⇒ y = 106 × Cos [tex]45^{0}[/tex]
= 74.9533
≅ 75 steps
Musah's distance north from centre to final point is 75 steps.
iv. Musah's distance from centre to final point is AC = AB + BC
= 50 steps + 56 steps
= 106 steps
From ΔACD,
Tan θ = [tex]\frac{75}{75}[/tex]
= 1.0
θ = [tex]Tan^{-1}[/tex] 1.0
= [tex]45^{0}[/tex]
Musah's bearing from centre to final point = [tex]45^{0}[/tex] + [tex]270^{0}[/tex]
= [tex]315^{0}[/tex]
Given a dataset with the following properties:
mean = 50
median = 40
standard deviation = 5
What is the shape of the distribution?
Answer:
The distribution is positively skewed.
Step-by-step explanation:
A measure of skewness is defined in such a way that the measure should always be zero when the distribution is symmetric and measure should be a pure number i.e independent of origin and units of measurement.
The shape of the distribution can be found by finding the coefficient of skewness.
The coefficient of skewness can be found by
Sk= 3(Mean-Median)/ Standard Deviation
Sk= 3( 50-40)5= 30/5=6
The shape will be positively skewed.
In a positively skewed distribution the mean > median > mode. It has a long right tail.
Using the skewness formula, it is found that the distribution is right-skewed.
------------------
The skewness of a data-set with mean M, median [tex]M_e[/tex] and standard deviation s is given by:[tex]S = \frac{3(M - M_e)}{s}[/tex]
If |S| < 0.5, the distribution is said to be symmetric.If S <-0.5, the distribution is left-skewed.If S > 0.5, the distribution is right-skewed.------------------
Mean of 50, thus, [tex]M = 50[/tex]Median of 40, thus [tex]M_e = 40[/tex]Standard deviation of 5, thus, [tex]s = 5[/tex]The coefficient is:
[tex]S = \frac{3(M - M_e)}{s} = \frac{3(50 - 40)}{5} = \frac{30}{5} = 6[/tex]
Thus, the distribution is right-skewed.
A similar problem is given at https://brainly.com/question/24415645
=
Graphing an integer function and finding its range for a given...
The function h is defined as follows for the domain given.
h(x) = 2 -2x, domain = {-3, -2, 1, 5}
Write the range of h using set notation. Then graph h.
Answer:
Step-by-step explanation:
● h(x) = 2-2x
The domain is {-3,-2,1,5}
● h(-3) = 2-2×(-3) = 2+6 = 8
● h(-2) = 2 -2×(-2) = 2+4 = 6
● h(1) = 2-2×1 = 2-2 = 0
● h(5) = 2-2×5 = 2-10 = -8
The range is {-8,0,6,8}
Sherina wrote and solved the equation. x minus 56 = 230. x minus 56 minus 56 = 230 minus 56. x = 174. What was Sherina’s error?
Answer:
subtracting 56 instead of adding (or adding wrong)
Step-by-step explanation:
She wrote ...
x - 56 = 230
x - 56 - 56 = 230 -56 . . . . correct application of the addition property*
x = 230 -56 . . . . . . . . . . . . incorrect simplification
Correctly done, the third line would be ...
x -112 = 174
This would have made Sherina realize that the error was in subtracting 56 instead of adding it. The correct solution would be ...
x - 56 + 56 = 230 + 56 . . . using the addition property of equality
x = 286 . . . . . . . . . . . . . . . . correct simplification on both sides
__
There were two errors:
1) incorrect strategy --- subtracting 56 instead of adding
2) incorrect simplification --- simplifying -56 -56 to zero instead of -112
We don't know whether you want to count the error in thinking as the first error, or the error in execution where the mechanics of addition were incorrectly done.
_____
* The addition property of equality requires the same number be added to both sides of the equation. Sherina did that correctly. However, the number chosen to be added was the opposite of the number that would usefully work toward a solution.
Answer:
D: Sherina should have added 56 to both sides of the equation.
Step-by-step explanation:
I got a 100% on my test.
I hope this helps.
Megan has 12 pounds of cheesecake. On Monday, she and her friends eat 4 pounds. On Tuesday, she and her friends eat another 3 pounds. On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. On Friday, she gives 3 pounds to her dog. On Saturday, her mom gives her one more pound. On Sunday, how many pounds of cheesecake does Megan have left?
Answer:
Step-by-step explanation:
First we start with 12 pounds
On Monday, she and her friends eat 4 pounds. So we have 8 now.
On Tuesday, she and her friends eat another 3 pounds. So we gave 5 now.
On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. 5 * 3 = 15
On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. She had 15 at the end of Wednesday. 15/5 = 3.
On Friday, she gives 3 pounds to her dog. 5 - 3 = 2.
On Saturday, her mom gives her one more pound. 2 + 1 = 3.
On Sunday, she finally has 3 pounds.
Answer:
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
Step-by-step explanation:
If f is a function that f(f(x)) = 2x² + 1, which is the value of f(f(f(f(3)))? Please help!
[tex]f(f(3))=2\cdot3^2+1=19\\f(f(f(f(3))))=2\cdot19^2+1=723[/tex]
The chart shows a certain city's population by age. Assume that the selections are independent events. If 8 residents of this city are selected at random, find the probability that the first 2 are 65 or older, the next 3 are 25-44 years old, the next 2 are 24 or younger, and the last is 45-64 years old.
Answer:
0.000014
Step-by-step explanation:
The chart is not provided so i will use an example chart to explain the answer. Here is a sample chart:
City X's Population by Age
0-24 years old 33%
25-44 years old 22%
45-64 years old 21%
65 or older 24%
In order to find probability of independent events we find the probability of each event occurring separately and then multiply the calculated probabilities together in the following way:
P(A and B) = P(A) * P(B)
probability that the first 2 are 65 or older
Let A be the event that the first 2 are 65 or older
The probability of 65 or older 24% i.e. 0.24
So the probability that first 2 are 65 or older is:
0.24(select resident 1) * 0.24(select resident 2)
P(A) = 0.24 * 0.24
= 0.0576
P(A) = 0.0576
probability that the next 3 are 25-44 years old
Let B be the event that the next 3 are 25-44 years old
25-44 years old 22% i.e. 0.22
So the probability that the next 3 are 25-44 years old is:
0.22 * 0.22* 0.22
P(B) = 0.22 * 0.22 * 0.22
= 0.010648
P(B) = 0.010648
probability that next 2 are 24 or younger
Let C be the event that the next 2 are 24 or younger
0-24 years old 33% i.e. 0.33
So the probability that the next 2 are 24 or younger is:
0.33 * 0.33
P(C) = 0.33 * 0.33
= 0.1089
P(C) = 0.1089
probability that last is 45-64 years old
Let D be the event that last is 45-64 years old
45-64 years old 21% i.e. 0.21
So the probability that last is 45-64 years old is:
0.21
P(D) = 0.21
So probability of these independent events is computed as:
P(A and B and C and D) = P(A) * P(B) * P(C) * P(C)
= 0.0576 * 0.010648 * 0.1089 * 0.21
= 0.000014
cindy was asked by her teacher to subtract 3 from a certain number and then divide the result by 6 instead, she subtracted 6 and then divided the result by 3 giving an answer of 25 what would her answer have been if she had worked the problem correctly?
Answer:
13
Step-by-step explanation:
let the number be x
how Cindy worked it out :
(x -6) ÷ 3 = 25
x -6 = 75
x = 81
How she should have worked it out:
(x - 3) ÷ 6
(81 - 3) ÷ 6
78 ÷ 6 = 13
Find the Vertical asymptotes of the graph of f
[tex]f(x) = \frac{x + 2}{ {x}^{2} - 4}[/tex]
Answer:
x = 2 and x = -2
Step-by-step explanation:
To find the vertical asymptotes, set the denominator equal to zero and solve for x:
vertical asymptotes are x = 2 and x = -2
Mr. Vazquez determines that the area of a bathroom in his house is 25 square feet less than 1/5 of the area of the living room. If the bathroom measures 35 square feet, what is the area of the living room?\
Answer:
300 SF
Step-by-step explanation:
just took the test
the difference of 8 and 2, added to x"
Answer:
see below
Step-by-step explanation:
Difference is subtract
(8-2)
Then add this to x
(8-2) +x
6+x
What is the difference? Complete the equation. -1 2/5 - (-4/5) = ?
Answer:
First convert them which will be
-7/5 - (-4/5)
so when you subtract a negative number from negative number they actually subtract ex = -4-(-2) = -2
so its simply 7/5-4/5 then add a negative sign
so
3/5
now add negative sign so
-3/5
If the sum of the daily unpaid balances is $7,812 over a 31-day billing cycle, what is the average daily balance?
Answer:
252
Step-by-step explanation:
Divide 7812 by 31 and we get the average daily answer... Hope this helps!!
please help me out! <3
Answer:
[tex]-1 \frac{3}{4}[/tex]
Step-by-step explanation:
Using this number line, we can plot our original number - [tex]\frac{3}{4}[/tex] (see picture attached)
Adding a negative is the same thing as subtracting - so we are subtracting [tex]2\frac{1}{2}[/tex] from [tex]\frac{3}{4}[/tex].
To subtract this, we can break up [tex]2\frac{1}{2}[/tex] into 3 parts: 1, 1, and [tex]\frac{1}{2}[/tex]. We can subtract each of these from the current number and see where we land up. (again see picture)
We land up at [tex]-1 \frac{3}{4}[/tex].
Hope this helped!
michaela has h hair ties. michaela's sister has triple the number of hair ties that michaela has. choose the expression that shows how many hair bows michaela's sister has
Answer:
[tex]S = 3 h[/tex]
Step-by-step explanation:
Let M represent Michaela hair tier and S represents Michaela sister's
Given
M = h
S = Triple of M
Required
Determine an expression for S
From the given parameters, we have that;
S = Triple of M
Mathematically, this implies;
[tex]S = 3 * M[/tex]
Substitute h for M
[tex]S = 3 * h[/tex]
[tex]S = 3 h[/tex]
Hence, the expression for Michaela sister' is [tex]S = 3 h[/tex]
According to the United States Golf Association, the diameter of a golf ball should not be less than 42.67 millimeters. What is the estimate of this value rounded to the nearest tenth of a millimeter?
Answer:
42.7 mm
Step-by-step explanation:
To the nearest tenth of a mm, 42.67 mm would be 42.7 mm.
After estimate of this value rounded to the nearest tenth of a millimeter,
⇒ 42.67 ≈ 42.7
We have to given that,
According to the United States Golf Association, the diameter of a golf ball should not be less than 42.67 millimeters.
Hence, After estimate of this value rounded to the nearest tenth of a millimeter, we get;
⇒ 42.67
As, 7 is grater than 5, so we can add 1 to the tenth place.
⇒ 42.67 ≈ 42.7
Therefore, After estimate of this value rounded to the nearest tenth of a millimeter,
⇒ 42.67 ≈ 42.7
Learn more about the rounding number visit:
brainly.com/question/27207159
#SPJ2
how do you figure out ratios? the problem is 12 quarters to 34 dollars. thanks
Step-by-step explanation:
When you have a ratio, you put one number as the numerator and than one number as the denominator.
so it would be (12/34)=(x/68)
In this example I made the ratio you are comparing it to have 68 dollars, so when you solve for the amount of quarters you need it should be 24, since all of the numbers in this example are just being doubled.
To solve for x, you multiply 68 on both sides of the equation, 68×(12/34)=x
24=x
So this proves that this is how ratios, are used. It also does not matter what number you place on the numerator or denominator.
Two friends are standing at opposite corners of a rectangular courtyard. The dimensions of the courtyard are 12 ft. by 25 ft. How far apart are the friends?
Answer:
27.73 feet
Step-by-step explanation:
Use the Pythagorean theorem. It easiest to think of the distance between the two friends as a triangle in the rectangle. One side is 12ft and the other is 25ft.
12^2+25ft^2=769
The square root of 769 is 27.73
Answer:
27.73 Ft
Step-by-step explanation:I took the test
PLS HELP:Find all the missing elements:
Answer:
b = 9.5 , c = 15Step-by-step explanation:
For b
To find side b we use the sine rule
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |b| }{ \sin(B) } [/tex]a = 7
A = 23°
B = 32°
b = ?
Substitute the values into the above formula
That's
[tex] \frac{7}{ \sin(23) } = \frac{ |b| }{ \sin(32) } [/tex][tex] |b| \sin(23) = 7 \sin(32) [/tex]Divide both sides by sin 23°
[tex] |b| = \frac{7 \sin(32) }{ \sin(23) } [/tex]b = 9.493573
b = 9.5 to the nearest tenthFor cTo find side c we use sine rule
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |c| }{ \sin(C) } [/tex]C = 125°
So we have
[tex] \frac{7}{ \sin(23) } = \frac{ |c| }{ \sin(125) } [/tex][tex] |c| \sin(23) = 7 \sin(125) [/tex]Divide both sides by sin 23°
[tex] |c| = \frac{7 \sin(125) }{ \sin(23) } [/tex]c = 14.67521
c = 15.0 to the nearest tenthHope this helps you
. One sample has M = 18 and a second sample has M = 14. If the pooled variance for the two samples is 16, what is the value of Cohen’s d?
Answer:
Cohen's d : 1.00
Step-by-step explanation:
We know that M₁ = 18, and M₂ = 14. Given that the pooled variance for the these two samples are 16, S²Pooled = 16, and therefore S - pooled = 4.
The formula to solve for the value of Cohen's d is as follows,
d = M₁ - M₂ / S - pooled,
d = 18 - 14 / 4 = 4 / 4 = 1
Therefore the value of Cohen's d = 1
