The angle C of the triangle ABC is ( π - 3a ).
What is an angle?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
The angle will be calculated as follows:-
We know that the sum of the angles of the triangle is 180 degrees or π in radians.
∠A + ∠B + ∠C = π
a + 2a + ∠C = π
∠C = π - a - 2a
∠C = π - 3a
Therefore angle C of the triangle ABC is ( π - 3a ).
To know more about an angle follow
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Question 8 of 9
Use a calculator to find the correlation coefficient of the data set.
х
у
2
15
6
13
7.
9
8
on 0
12 5
O A. -0.909
OB. 0.909
Ο Ο Ο
O C. 0.953
D. -0.953
Actual data table :
X __ y
2 15
6 13
7 9
8 8
12 5
Answer:
0.953
Step-by-step explanation:
The question isnt well formatted :
The actual data:
X __ y
2 15
6 13
7 9
8 8
12 5
Using a correlation Coefficient calculator, the correlation Coefficient obtained by fitting the data is 0.953 which depicts a strong linear correlation between the x and y variable. This shows that the value of y increases with a corresponding increase in x values and vice versa.
Heeelp please!!! Picture included
Answer:
2nd choice
Step-by-step explanation:
The sum of two numbers is 125. Their difference is 47. The two numbers are:
a)39 and 86.
b)40 and 85.
c)47 and 78.
d)None of these choices are correct.
Answer:
let x represent the bigger number
x+x-47=125
2x-47=125
2x=125+47
2x=172
2x/2=172/2
x=86
the smaller number=x-47
86-47
39
therefore the answer is a) 39 and 86
Answer:
A
Step-by-step explanation:
To find the sum of 125, you have to add the numbers.
39+86 = 125
To find the difference of 47, you have to subtract the numbers.
86-39 = 47
Which of the following are exterior angles? Check all that apply.
ots
65
A. 22
1
B. 21
C. 23
1
D. 24
I E. 26
DE 25
Answer:
A
C
D
E
Step-by-step explanation:
Exterior angles can be described as the angles that are formed between the side of a polygon and the extended adjacent side of the polygon.
Or an exterior angle is the angle that is not inside the triangle formed.
The angles inside the triangle are interior angles.
Exterior angles are :
2
3
4
6
Interior angles are :
1
5
Vlad has found a magic box. If he opens it now he will only get $15. But every month the amount in the box increases by $15. If Vlad is very patient, in how many months can he get $450?
I need help ASAP
Find the measure of XY
Answer:
70
Step-by-step explanation:
the answer is 35*2=70
Answer:
70
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A recipe for chocolate chip cookies calls for 3 1/3 cups of flour. If you are making 2 1/4 recipes, how many cups of flour are needed.
Answer:
THIS IS THE ANSWER
Step-by-step explanation:
1 1/2 = 3/2
2 1/3 = 7/3
3/2 * 7/3 = 21/6 = 3 3/5 = 3 1/2 cups
PLEASE MARK ME AS A BRAINLIST!Twice the difference of a number and 6
Answer:
2x=6. I think friend it is correct.
Answer:
2(×-6)
Step-by-step explanation:
Correct me if im wrong thanks ●~●
Si dos angulos son conjugados entre paralelas entonces son suplementarios es verdadero o falso
Si dos angulos son conjugados entre paralelas entonces son suplementarios es verdadero o falso
Step-by-step explanation:
no worries skills development and implementation of the year in a while and I am looking for an appointment with the other day
About 6% of the population has a particular genetic mutation. 100 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 100.
Answer:
The standard deviation for the number of people with the genetic mutation in such groups of 100=[tex]2.375[/tex]
Step-by-step explanation:-
We are given that
Total number of selected people, n=100
p=6%=0.06
We have to find the standard deviation for the number of people with the genetic mutation in such groups of 100.
Let X denote the number of people with the genetic mutation in such groups of 100.
[tex]\implies X\sim Bin(n=100,p=0.06)[/tex]
We know that
Standard deviation
=[tex]\sqrt{np(1-p)}[/tex]
Using the formula
Standard deviation
=[tex]\sqrt{100\times 0.06(1-0.06)}[/tex]
=[tex]\sqrt{6(0.94)}[/tex]
=[tex]2.375[/tex]
Hence, the standard deviation for the number of people with the genetic mutation in such groups of 100=[tex]2.375[/tex]
A right rectangular prism has a length of 5 centimeters, a width of 8 centimeters, and a height of 4 centimeters. What is the volume of the prism?
Answer:
volume of prism is 160 cm
Determine the mean and variance of the random variable with the following probability mass function. f(x)=(216/43)(1/6)x, x=1,2,3 Round your answers to three decimal places (e.g. 98.765).
Mean:
E[X] = ∑ x f(x) = 1 × f (1) + 2 × f (2) + 3 × f (3) = 51/43 ≈ 1.186
Variance:
Recall that for a random variable X, its variance is defined as
Var[X] = E[(X - E[X])²] = E[X ²] - E[X]²
Now,
E[X ²] = ∑ x ² f(x) = 1² × f (1) + 2² × f (2) + 3² × f (3) = 69/43
Then
Var[X] = 69/43 - (51/43)² = 366/1849 ≈ 0.198
(each sum is taken over x in the set {1, 2, 3})
Combine these radicals. 8 square root 5 + 2 square root 45
Answer
14√5
Step-by-step explanation:
8√5 + 2√45
= 8√5 + 6√5
= 14√5
Hope this helps
Answer:
[tex]\boxed {\boxed {\sf 14 \sqrt{5}}}[/tex]
Step-by-step explanation:
We are asked to combine the radicals. We have the following expression:
[tex]8 \sqrt{5} + 2 \sqrt{45}[/tex]
Currently, we cannot combine these radicals. The value under the square root is not the same for both terms.
However, we can simplify the radical 2 √45 because the value under the radical is divisible by a perfect square.
45 can be divided by 9 (the perfect square) for a quotient of 5. So, we can simplify the radical using this information.
Break the radical into 2 radicals: 9 and 5.
[tex]8 \sqrt{5}+ 2 \sqrt{9}\sqrt{5}[/tex]
Notice that a perfect square is under the radical. √9 can be simplifed to 3.
[tex]8 \sqrt{5}+ 2 *3 \sqrt{5}[/tex]
Multiply 2 and 3.
[tex]8 \sqrt{3} + 6 \sqrt{5}[/tex]
Now the value under the radical is the same for both terms, and we can add the numbers in front of the radicals.
[tex]14 \sqrt{5}[/tex]
The radicals combined is equal to 14√5
what term can you add to
[tex] \frac{5}{6} x - 4[/tex]
to make it equivalent to
[tex] \frac{1}{2} x - 4[/tex]
9514 1404 393
Answer:
-1/3x
Step-by-step explanation:
We want to find the term 'a' such that ...
(5/6x -4) + a = (1/2x -4)
Add 4-1/2x to both sides.
(5/6 -1/2)x -4 +4 +a = 0
(5/6 -3/6)x + a = 0 . . . . . . express the fractions using a common denominator
1/3x + a = 0 . . . . . . . . . . simplify the difference
a = -1/3x . . . . . . . . . . .subtract 1/3x
The term you can add to make the desired equivalent is -1/3x.
what is the value of the expression 5²5
Answer:
5^2×5
=25×5
=125
hope this will help you
Answer:
125
Step-by-step explanation:
hope this helps you
=25×5
=125
How many boxes could you stack safely on a pallet if the pallet is 5 feet deep, five feet across, every box is 1 x 1 and the maximum safe stacking height is 5 boxes? *
Answer:
125 boxes
Step-by-step explanation:
5*5*5
debbie will be attending a concert at grand ole opry in nashville, tennessee. if the average number of songs performed there in a 10 day period is 167. approximately how many songs are performed there in a years time
Given:
The average number of songs performed there in a 10 day period is 167.
To find:
The number of songs performed there in a year time.
Solution:
We have,
Number of songs performed in 10 days = 167
Number of songs performed in 1 day = [tex]\dfrac{167}{10}[/tex]
= [tex]1.67[/tex]
We know that 1 year is equal to 365 days. So,
Number of songs performed in 365 day = [tex]1.67\times 365[/tex]
Number of songs performed in 1 year = [tex]609.55[/tex]
[tex]\approx 610[/tex]
Therefore, the number of songs performed there in a year time is about 610.
Please help Ladder question!!
A 6 ft ladder, resting against a wall, begins to slip down the wall. When the angle of the ladder is 45 degrees, the bottom of the ladder is moving away from the wall at 0.5 m/s. At that moment, how fast is the top of ladder moving down the wall?
Answer:
Step-by-step explanation:
This is a related rates problem from calculus using implicit differentiation. The main equation is going to be Pythagorean's Theorem and then the derivative of that. Pythagorean's Theorem is
[tex]x^2+y^2=c^2[/tex] where c is the hypotenuse and is a constant. Therefore, the derivative of this with respect to time, and using implicit differentiation is
[tex]2x\frac{dx}{dt}+2y\frac{dy}{dt}=0[/tex] and dividing everything by 2 to simplify a bit:
[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex]. Upon analyzing that equation, it looks like we need values for x, y, [tex]\frac{dx}{dt}[/tex], and [tex]\frac{dy}{dt}[/tex]. And here's what we were given:
[tex]\theta=45[/tex] and [tex]\frac{dx}{dt}=.5[/tex] In the greater realm of things, that's nothing at all.
BUT we can use the right triangle and the angle we were given to find both x and y. The problem we are looking to solve is to
Find [tex]\frac{dy}{dt}[/tex] at the instant that [tex]\frac{dx}{dt}[/tex] = .5.
Solving for x and y:
[tex]tan45=\frac{x}{6}[/tex] and
6tan45 = x ( and since this is a 45-45-90 triangle, y = x):
[tex]6(\frac{\sqrt{2} }{2})=x=y[/tex] so
[tex]x=y=3\sqrt{2}[/tex] and now we can fill in our derivative. Remember the derivative was found to be
[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex] so
[tex]3\sqrt{2}(\frac{1}{2})+3\sqrt{2}\frac{dy}{dt}=0[/tex] and
[tex]\frac{3\sqrt{2} }{2}+3\sqrt{2} \frac{dy}{dt}=0[/tex] and
[tex]3\sqrt{2}\frac{dy}{dt}=-\frac{3\sqrt{2} }{2}[/tex] and multiplying by the reciprocal of the left gives us:
[tex]\frac{dy}{dt}=-\frac{3\sqrt{2} }{2}(\frac{1}{3\sqrt{2} })[/tex] so
[tex]\frac{dy}{dt}=-\frac{1}{2}\frac{m}{s}[/tex]
F(x) = x/2*8 what is f(x), when x=10
Answer
13
Step-by-step explanation:
We are essentially being asked to find f(10), so let's evaluate this function at 10 by plugging this in for x.
f(10)=10/2+8=5+8=13
Answer:
f(x) = 40
Step-by-step explanation:
f(x) = x / 2 * 8
x = 10
f(x) = (10 / 2) * 8
= 5 * 8
= 40
f(x) = 1
g(x) = x - 4
Can you evaluate (g•f)(0)? Explain why or why not?
Answer:
This is a multiplication of functions g and f, and these functions have no restrictions(such as a even root or a fraction), and thus [tex](g \mult f)(0) = g(0)f(0) = -4(1) = -4[/tex]
Step-by-step explanation:
We are given the following functions:
[tex]f(x) = 1[/tex]
[tex]g(x) = x - 4[/tex]
Can you evaluate (g•f)(0)?
This is a multiplication of functions g and f, and these functions have no restrictions(such as a even root or a fraction), and thus [tex](g \mult f)(0) = g(0)f(0) = -4(1) = -4[/tex]
Answer:
To evaluate the composition, you need to find the value of function f first. But, f(0) is 1 over 0, and division by 0 is undefined. Therefore, you cannot find the value of the composition.
You must evaluate the function f first.
Division by 0 is undefined.
The composition cannot be evaluated.
In a pool of water filled to a depth of 10 ft, calculate the fluid force on one side of a 3 ft by 4 ft rectangular plate if it rests vertically on its 4 ft edge at the bottom of the pool. Remember that water weighs 62.4 lb/ft3
9514 1404 393
Answer:
6,364.8 lb
Step-by-step explanation:
The centroid of the plate is its center, so is 1.5 ft above the bottom of the pool, or 8.5 ft below the surface. The area of the plate is (3 ft)(4 ft) = 12 ft². Then the fluid force is ...
(62.4 lb/ft³)(8.5 ft)(12 ft²) = 6,364.8 lb
Solve this:
A woman was 39years old when she gave birth to a pair of twins.12 years ago,she was twice as old as the sum of the ages of the twins put together.Find their present ages.
Answer:
woman =39years
twins 0year each since 12 years ago they were not yet born
2) There are 40 boys and 16 girls in a class of students. What is the ratio of girls to students?
Add boys and girls together for total students:
40 + 16 = 56 total students
Girls to total students is 16/56
Divide both numbers by 8 to get 2/7
The ratio is 2/7
[tex]\sf{\bold{\blue{\underline{\underline{Given}}}}}[/tex]
There are 40 boys and 16 girls in a class of students. ⠀⠀⠀⠀[tex]\sf{\bold{\red{\underline{\underline{To\:Find}}}}}[/tex]
⠀What is the ratio of girls to students?⠀⠀⠀[tex]\sf{\bold{\purple{\underline{\underline{Solution}}}}}[/tex]
In a class,
boys=40
girls =16
So,
The students of the class =
boys+girls 40+1656According to the question,
we have to find the ratio of girls to the total students
ratio=[tex]\sf{\dfrac{girls}{students} }[/tex] ratio=[tex]\sf{\dfrac{16}{56} }[/tex] ratio=[tex]\sf{\dfrac{\cancel{16}}{\cancel{56}} }[/tex]ratio=[tex]\sf{\dfrac{2}{7} }[/tex] ratio=[tex]\sf{2:7 }[/tex]⠀⠀⠀⠀
[tex]\sf{\bold{\green{\underline{\underline{Answer}}}}}[/tex]
⠀⠀⠀⠀
Hence,the ratio of girls to students is 2:7
⠀⠀⠀⠀
Can someone help me ASAP. All them added together is = 454 .thanks
Answer:
the answer is 86°
Step-by-step explanation:
look at the photo
How many additional teachers will have to be hired to reduce the ratio to 1:20
Answer:
30 additional teachers will have to be hired to reduce the ratio to 1:20.
Step-by-step explanation:
Given that Jefferson School has 1800 students, and the teacher-pupil ratio is 1:30, to determine how many additional teachers will have to be hired to reduce the ratio to 1:20, the following calculation must be performed:
30 = 1800
1 = X
1800/30 = X
60 = X
20 = 1800
1 = X
1800/20 = X
90 = X
90 - 60 = 30
Therefore, 30 additional teachers will have to be hired to reduce the ratio to 1:20.
Plss help!!! Image included
Answer:
(-5,2)
Step-by-step explanation:
A function is a relation where each y-value has a unique x-value. That means that x's can never repeat. Therefore, to solve find the ordered pair that does not have the same x-value as one of the points on the graph. The x-values currently represented on the graph are -4, -2, 2, 3. So, the only coordinate pair that does not repeat an x-value is the last option, (-5, 2).
slove the following systems of equations using any method. y= 3x + 7 , y= x- 9 , 3x- y= 1 , 7x + 2y = 37.
y=3× + 7 , y=×- 9 , 3×- 9 , 3×- y= 1 , 7× + 2y = 37.
which is the best estimate of (-3/5) (17 5/6)?
Answer:
-170 / 10
Step-by-step explanation:
Use the given information to answer the questions and interpret key features. Use any method of graphing or solving. Round to one decimal place, if necessary.
The trajectory of a golf ball in a chip from the rough has a parabolic pattern. The height, in feet, of the ball is given by the equation h(x) -.25x^2 + 3.42, where x is the number of feet away from the golf club (along the ground) the ball is.
The ball starts ____ feet above the ground.
The ball reaches a maximum height of _____ feet at a horizontal distance of ____ feet away from the golf club 19 it was hit with
The ball returns to the ground at about ____ feet away.
A bag has 180 balls. the ratio of red to blue to yellow balls is 8:5:7 how many red balls are there and how many blue balls are there
Answer:
72 red
45 blue
63 yellow
Step-by-step explanation:
8+5+7= 20
180÷20= 9
red = 9*8
blue = 9*5
yellow = 9*7