Answer:
[tex] x = \pm \sqrt{19} [/tex]
[tex] x = \pm 4.36 [/tex]
Step-by-step explanation:
[tex] x^2 = 19 [/tex]
[tex] x = \pm \sqrt{19} [/tex]
[tex] x = \pm 4.36 [/tex]
The exact solution is 4.36.
What is square root?Squares are the numbers, generated after multiplying a value by itself. Whereas square root of a number is value which on getting multiplied by itself gives the original value. Hence, both are vice-versa methods. For example, the square of 2 is 4 and the square root of 4 is 2.
Given:
x² = 19
On taking root on both side
√x² = √19
x= √19
x = 4.3588
Hence, the exact solution and its approximation rounded to two decimal places is 4.36.
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if y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8
Answer:
Y varies directly as X.
y=kx.
6=K72.
x=6/72.
x=0.08.
Y=0.08x.
when y=?, x=8.
y=0.08×8=0.64.
ax + by = c, bx + ay = (1 + c)
Answer:
( x - y ) ( a - b ) = -1
Step-by-step explanation:
ax + by = c and bx + ay = 1 + c
ax + by = c and bx + ay - 1 = c
And now we set c equivalent
ax + by = bx + ay - 1
ax - bx + by - ay = -1
x (a - b) + -y (a - b) = -1
(x - y) ( a - b) = -1
So we can leave it like that, or we can solve for one of the variables.
If we solve for y:
(x - y) ( a - b) = -1
(x - y) = -1 / (a - b)
-y = (-1 / (a - b)) - x
y = (1 / (a-b)) + x
Cheers.
A set of three scores consists of the values 3, 7, and 2.
Σ2X – 2 =
Σ(X – 1)² =
Answer:
Step-by-step explanation:
Given the set of datas 3, 7 and 2, we are to evaluate the folowing;
Σ2X – 2 and Σ(X – 1)² =where X are the individual datas.
We will substitute each of the data as value of X and ten take the sum as shown;
For Σ2X – 2
Σ2X – 2 = [2(3)-2]+[2(7)-2]+[2(2)-2]
Σ2X – 2 = (6-2)+(14-2)+(4-2)
Σ2X – 2 = 4+12+2
Σ2X – 2 = 18
For Σ(X – 1)² where x values are also 3, 7 and 2 we will have;
Σ(X – 1)² = (3 – 1)²+(7 – 1)²+(2 – 1)²
Σ(X – 1)² = 2²+6²+1²
Σ(X – 1)² = 4+36+1
Σ(X – 1)² = 41
A triangle has a base of 16 inches and a height of 18 inches. What is its area?
Answer:
The answer is
144 square inchesStep-by-step explanation:
Area of a triangle is given by
[tex]A = \frac{1}{2} bh[/tex]where
b is the base
h is the height
From the question
b = 16 inches
h = 18 inches
Substitute the values into the above formula and solve for the area
That's
[tex]A = \frac{1}{2} \times 16 \times 18 \\ = 8 \times 18 \: \: \: \: \: \: [/tex]We have the final answer as
144 square inchesHope this helps you
The quality control manager of a light bulb factory needs to estimate the average life of a large shipment of light bulbs. The process standard deviation is known to be 100 hours. A random sample of 64 light bulbs indicated a sample average life of 350 hours. Given the confidence interval calculated above. do you think the manufacturer has the right to state that the light bulbs last on average 400 hours?
a. No.
b. Yes.
c. Maybe.
d. Do not know
Answer:
b) yes
The manufacturer has the right to state that the light bulbs last on average 400 hours
Step-by-step explanation:
Explanation:-
Given sample size 'n' = 64
Given standard deviation of the Population (σ)=100
Mean of the sample (x⁻) = 350 hours
95% of confidence interval is determined by
[tex](x^{-} -Z_{0.95} \frac{S.D}{\sqrt{n} } , x^{-} +Z_{0.95} \frac{S.D}{\sqrt{n} } )[/tex]
([tex](350 -1.96 \frac{100}{\sqrt{64} } , 350+1.96\frac{100}{\sqrt{64} } )[/tex]
(350-24.5 , 350+24.5)
(325.5 , 374.5)
Conclusion:-
Yes
The manufacturer has the right to state that the light bulbs last on average 400 hours
On the njmber line below, the numbers x and y are the same distance from 0. What is x + y? Explain how you found your answer
Answer:
Step-by-step explanation:
either x+y=0
∵ if they are on number line and at same distance. then x=-y
or x+y=0
Rachel, Hong, and Manuel have a total of 95 in their wallets. Hong has 3 times what Manuel has. Rachel has $10 more than Manuel. How much does each have?
Answer:
Rachel has 27
Hong has 51
Manuel has 17
Step-by-step explanation:
Let R represent Rachel, H represent Hong, and M represent Manuel.
They combined have a total of 95. Thus:
[tex]R+H+M=95[/tex]
Hong has 3 times what Manuel has. Therefore:
[tex]H=3M[/tex]
Rachel has 10 more than Manuel. Therefore:
[tex]R=10+M[/tex]
Substitute:
[tex]R+H+M=95\\(10+M)+(3M)+M=95[/tex]
Combine like terms:
[tex]5M+10=95[/tex]
Subtract 10 from both sides:
[tex]5M=85[/tex]
Divide by 5:
[tex]M=17[/tex]
Therefore, Manuel has 17.
Now, find Rachel and Hong's money.
[tex]H=3M\\H=3(17)=51[/tex]
So, Hong has 51.
And for Rachel:
[tex]R=10+M\\R=10+17=27[/tex]
Rachel has 27.
Which set of data do you believe to be better? Your data or your friend's data?
Answer:
Your friends data
Step-by-step explanation:
The rule of statistics is: the more exact the data, the better.
It looks like you just rounded your data to the nearest tenth. This is good, but not nearly as good as rounding it to the nearest hundredth.
This is because when you have data that is more exact, you get a better estimation for mean, median, etc. This can help make patterns in your data.
This means that your friend had better data than you.
Hope this helped!
You take thirty measurements in order to find the length of a rod, you calculate the average and obtain the value L0. Supposed that now a different person takes twenty measurements as well of the same rod, then calculates the average and obtains the same L0 as you. Does it mean that both of you obtain a result with the same precision and accuracy
Answer:
Yes, it means that both of you obtain a result with the same precision and accuracy.
Step-by-step explanation:
It is provided that two different people took measurements in order to find the length of a rod.
The first person took 30 measurements.
The second person took 20 measurements.
Both the people got the same average length, i.e. L₀.
In statistics, a larger sample leads to an error free result.
So, for the first person the larger sample helped reducing the chance of any sort of error that may be present.
For the second person, the average is same as the first even when their sample size is less than the first.
This may happen because the sample was selected with a certain precision and accuracy.
Thus, both of them obtain a result with the same precision and accuracy.
43,761 rounded to the nearest thousands
Answer:
44,000
Step-by-step explanation:
The number 43,761 rounded to its nearest thousands is 4400.
What is place value?The place value of a number is given as:
Example:
1234.567
1 = thousand place value
2 = hundred place value
3 = tens place value
4 = ones place value
5 = tenths place value
6 = hundredths place value
7 = thousandths place value
We have,
43,761
3 is in the thousand place.
So,
We will round 3761 to its nearest thousand value.
There are two options:
3000 or 4000
If It is greater than 3499 it will round to 4000.
If it is less than 3500 it will round to 3000.
Now,
3761 > 3499.
So,
The number is rounded to 4000.
Thus,
43,761 is rounded to 4400.
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A line has a slope of 3 and passes through the point (2,31). Write the equation of the line in slope-intercept form
Answer:
y=3x+25
Step-by-step explanation:
So to find the slope-intercept we need to find the slope and the y intercept. we already know the slope so to find the y intercept you subtract 2 from the x coordinate and 6 from the y, because the slope is 3. So the answer is y=3x+23
Answer:
y=3x+25
Step-by-step explanation:
We are given a point and the slope, so let's use the slope-intercept equation.
[tex]y-y_{1}=m(x-x_{1})[/tex]
where m is the slope and (x₁, y₁) is the point given. The slope is 3 and the point is (2,31). Therefore,
[tex]m= 3 \\x_{1}=2\\y_{1}=31[/tex]
Substitute the values into the equation.
[tex]y-31=3(x-2)[/tex]
We want the equation in slope intercept form: y=mx+b. We must isolate y on the left side of the equation.
First, distribute the 3. Multiply each term inside the parentheses by 3.
[tex]y-31= (3*x)+(3*-2)[/tex]
[tex]y-31=(3x)+(-6)[/tex]
[tex]y-31=3x-6[/tex]
Next, add 31 to both sides of the equation.
[tex]y-31+31=3x-6+31[/tex]
[tex]y=3x-6+31[/tex]
[tex]y=3x+25[/tex]
This equation is in slope intercept form, so our final answer is:
y= 3x+25 (slope⇒3 , y-intercept ⇒25)
A card is selected at random from a standard 52-card deck. (a) What is the probability that it is an ace
Answer:
4/52 = 1/13
Step-by-step explanation:
For what positive values of k does the function y=sin(kt) satisfy the differential equation y''+144y=0 ?
Answer:
The positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12
Step-by-step explanation:
To determine the positive values of k that the function y = sin(kt) satisfy the differential equation y''+144y=0.
First, we will determine y''.
From y = sin(kt)
y' = [tex]\frac{d}{dt}(y)[/tex]
y' = [tex]\frac{d}{dt}(sin(kt))\\[/tex]
y' = kcos(kt)
Now for y''
y'' = [tex]\frac{d}{dt}(y')[/tex]
y'' = [tex]\frac{d}{dt}(kcos(kt))[/tex]
y'' = [tex]-k^{2}sin(kt)[/tex]
Hence, the equation y'' + 144y = becomes
[tex]-k^{2}sin(kt)[/tex] + [tex]144(sin(kt))[/tex] [tex]= 0[/tex]
[tex](144 - k^{2})(sin(kt)) = 0[/tex]
[tex](144 - k^{2})= 0[/tex]
∴ [tex]k^{2} = 144\\[/tex]
[tex]k =[/tex] ±[tex]\sqrt{144}\\[/tex]
[tex]k =[/tex] ± [tex]12[/tex]
∴ [tex]k = +12[/tex] or [tex]-12[/tex]
Hence, the positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12
The positive value of k that satisfies the differential equation is k = 12.
To find the value of k that satisfies the equation, we differentiate the function y = sin(kt) twice to obtain y" and we insert it into the differential equation y" + 144y = 0.
So, y' = dy/dt
= dsin(kt)/dt
= kcos(kt)
y" = dy'/dt
y" = dkcos(kt)/dt
y" = -k²sin(kt)
So, substituting y and y" into the differential equation, we have
y" + 144y = 0
-k²sin(kt) + 144sin(kt) = 0
-k²sin(kt) = -144sin(kt)
k² = 144
k = ±√144
k = ±12
Since we require a positive value, k = 12
So, the positive value of k that satisfies the differential equation is k = 12.
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Chiang is filling a 50ft container with water at a rate of 0.5 ft/ min. interpret the key features for this situation
Answer:
The key features are
50ft³ = the volume
0.5ft³/min = rate
Time= 100 minutes
Step-by-step explanation:
Chiang is filling a 50ft container with water at a rate of 0.5 ft/ min.
50ft³ = the volume
0.5ft³/min = rate
There is a key future missing which is the time it will take to fill the 50 ft³ container
Time = volume/rate
Time= 50 ft³/0.5ft³/min
Time= 50/0.5 min
Time = 100 min
The key features are
50ft³ = the volume
0.5ft³/min = rate
Time= 100 minutes
trough: (2,2) parallel to y=x+4
Answer:
y = x
Step-by-step explanation:
The slopes of parallel lines are the same, so we know the equation will be ...
y = x + constant
We can find the constant by using the given point's values for x and y:
2 = 2 + constant
Obviously, the constant is zero.
The equation of the parallel line through (2, 2) is y = x.
If you get this you are a critical thinker.
I enter the garden.
There are 34 people.
You kill 30.
How many people are in the garden.
Step-by-step explanation:
I'm not sure, but I think just 0
Because no one will even stand there and watch you kill 30 people
The police will come for you and the 1 dead person will be sent away lol
32 POINTS! WILL MAKE BRAINLIEST. ANSWER ASAP
Solve the inequality
The solution is....
Answer:
x ≤ -7
Step-by-step explanation:
Eliminate parentheses using the distributive property.
-8 -2x ≥ 40 +6x +8
-8 ≥ 48 +8x . . . . . . . . . add 2x
-56 ≥ 8x . . . . . . . . . . . subtract 48
-7 ≥ x . . . . . . . . . . . . . . divide by 8
The solution is x ≤ -7.
a cylinder container can hold 2.45l of water. it radius is 4.00cm. what is the the volume of it in cm3
Answer:
Step-by-step explanation:
Ion know
y varies directly with x. If x = 16 and y = 2 find y when x = 96
Answer:
y = 12
Step-by-step explanation:
Use the equation y = kx
Plug in x and y to find k:
2 = k(16)
1/8 = k
Then, plug in 1/8 as k and 96 as x to find y:
y = 1/8(96)
y = 12
The GCF of 30 and 45 is
3
8
1
2
15
Answer:
The GCF of 30 and 45 is
15.
Hope it helps.
x(2x + 3) + (x - 3)(x - 4)
Answer:
3x²-4x+12
Step-by-step explanation:
Answer:
[tex]=3x^2-4x+12[/tex]
Step-by-step explanation:
So we have the expression:
[tex]x(2x+3)+(x-3)(x-4)[/tex]
To simplify, distribute the left side and the right:
[tex]=x(2x)+x(3)+(x-3)(x)+(x-3)(-4)[/tex]
Distribute:
[tex]=(2x^2+3x)+(x^2-3x)+(-4x+12)[/tex]
Combine like terms:
[tex]=(2x^2+x^2)+(3x-3x-4x)+(12)[/tex]
Simplify:
[tex]=3x^2-4x+12[/tex]
Goran is sitting in a movie theater, 5 meters from the screen. The angle of elevation from his line of sight to the top of the screen is 18, and the angle of depression from his line of sight to the bottom of the screen is 48. Find the height of the entire screen.
Answer:
Approximately
Height of screen= 7.1 meters
Step-by-step explanation:
Angle of elevation= 18°
Angle of depression= 58°
Distance of Goran from screen= 5 m
Height of screen from the attachment below
X+y
First let's determine angle a and b
a= 180-90-18
a= 72°
b= 180-90-48
b= 43°
Using sine formula
5/sin a= x/sin 18
5/sin 72= x/sin18
(5*sin 18)/sin 72= x
1.6246 = x
X= 1.6246 m
Y/sin 48= 5/sin b
Y= (5*sin 48)/sin 43
Y= (5*1.08965779)
Y= 5.4483 m
Height of screen= x+y
Height of screen= 1.6246+5.4483
Height of screen= 7.0729
Approximately
Height of screen= 7.1 meters
Given m parallel to I, and m2 7 = 94, find the measure of angle 5
O 10
045
O 97
O 120
Answer:
97
Step-by-step explanation:
Please help me it’s in my math class
Answer:
1-70: Purple- 9/10= 0.18= 2 marbles
Orange- 16/50= 0.32= 3 marbles
Yellow- 6/50= 0.12= 1 marble
Green- 19/50= 0.38= 4 marbles
1-71: Part A. 3/6= 1/2
Part B. 4/6= 2/3
Translate to an algebraic expression. m plus the product of 6 and n
The length of a rectangle is one more than four times its width. If the perimeter of the rectangle is 62 meters, find the dimensions of the rectangle.
Answer:
Length = 25 meters
Width = 6 meters
Step-by-step explanation:
62 = 2(a+b)
a = 4b + 1
a = length
b = width
then:
62 = 2((4b+1)+b)
62/2 = 4b+b+1
31 = 5b + 1
31 - 1 = 5b
30 = 5b
b = 30/5
b = 6m
a = 4b + 1
a = 4*6 + 1
a = 24 + 1
a = 25m
Check:
62 = 2(6+25)
62 = 2*31
A Women making $29 an hour gets a 15% raise. How much money will she make after 4 hours of working with the increased hourly pay?
Answer:
$133.4
Step-by-step explanation:
1. Find the increased pay:
29 * 1.15 = 33.35
2. Find how much she makes in 4 hrs
33.35 * 4 = 133.4
Assume that the two polygons are similiar, with the same orientation.
Write a proportion to determine the lengths of the sides labeled by variables.
(DO NOT SOLVE. You will solve the proportion in the next question.)
Answer:
4/6=t/(t+1)
Step-by-step explanation:
4/6=t/(t+1)
explain how you can rename 5,400 as hundreds.
Answer:
The correct answer would be 54 hundreds
Step-by-step explanation:
If we are considering how many hundreds something has, we can simply take away two 0's and use that number. We take the two 0's off and then we have the right number of hundreds
Answer:
Hey there!
Five-thousand four-hundred can be expressed as fifty-four hundred.
Let me know if this helps :)