Answer:
3/5
Step-by-step explanation:
here,
0.6
in fraction = 6/10
in simplest form 6/ 10 both term can be divided by 2 so,
6/10 ÷2
= 3/5
writie any assay about challenges of teaching mathematics on 21st century
The times to complete an obstacle course is normally distributed with mean 87 seconds and standard deviation 7 seconds. What is the probability that a randomly selected finishing time is greater than 80 seconds? Use the empirical rule
The probability that a randomly selected finishing time is greater than 80 seconds is 0.84.
How to calculate the probability?Mean = 87
Standard deviation = 7
We convert this to standard normal as
P( X < x) = P( Z < x - Mean / SD)
Since, 80 = 87 - 7
80 is one standard deviation below the mean.
Using the empirical rule, about 68% of data falls between 1 standard deviation of the mean. So, 32% is outside the 1 standard deviation of the mean, and 16% is outside to either side.
We have to calculate P( X > 80) = ?
That is probability of all values excluding lower tail of the distribution.
P(X > 80) = 68% + 16%
= 84%
= 0.84
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in the factory 25 men working 26 hour can produce 1300 radios . how manny hours must the same group of men work to produce 450 radios
Answer:
9 hours
Step-by-step explanation:
Since the group of men remains the same, number of hours is proportional to number of radios.
1300/26 = 450/h
h = 26 * 450 / 1300 = 9 hours
the image is located below
Answer:
288 ft³
Step-by-step explanation:
Volume of the pyramid,
base area × height × (1/3)
= (9×8)×12/3
= 72×4
= 288 ft³
You are going to decorate one wall of your bedroom by putting a border along the top. The wall is a square wall with an area of 256 square feet what is the length of the border that you will need for your wall?
Answer:
16 ft
Step-by-step explanation:
Each edge of wall = √256 ft = 16 ft
The differential equation of a certain system is 20y′′+cy′+80y=0
, where c is called damping constant for what value of c critical damping hapens
Options:
110
64
50
60
Answer:
c=80
Step-by-step explanation:
Based on my reading the critical damping occurs when the discriminant of the quadratic characteristic equation is 0.
So let's see that characteristic equation:
20r^2+cr+80=0
The discriminant can be found by calculating b^2-4aC of ar^2+br+C=0.
a=20
b=c
C=80
c^2-4(20)(80)
We want this to be 0.
c^2-4(20)(80)=0
Simplify:
c^2-6400=0
Add 6400 on both sides:
c^2=6400
Take square root of both sides:
c=80 or c=-80
Based on further reading damping equations in form
ay′′+by′+Cy=0
should have positive coefficients with b also having the possibility of being zero.
Johnny was able to drive an average of 31 miles per hour faster in his car after the traffic cleared. He drove 16 miles in traffic before it cleared and then drove another 47 miles. If the total trip took 2 hours, then what was his average speed in traffic?
9514 1404 393
Answer:
16 mi/h
Step-by-step explanation:
The time for a given leg of the trip is the distance divided by the speed. If t is the speed in traffic, the total trip time is ...
16/t +47/(t+31) = 2
Multiplying by t(t+31), we get ...
16(t +31) +47t = 2(t)(t+31)
2t^2 -t -496 = 0 . . . . put in standard form
(2t +31)(t -16) = 0 . . . . factor
The positive solution is t = 16.
Johhny's average speed in traffic was 16 mph.
15 more than 2 times a number is equal to -14. Find the number.
please help asap and thank you in advance!
Answer:
The number is - 14.5
Step-by-step explanation:
Let the number be x.
ATQ, 15+2x=-14, x=-29/2=-14.5
pls answer and you will be blessed :)
Answer:
2
Step-by-step explanation:
It is the only one that makes sense
solve for x . please help also don’t forget to show work
Answer:
X-4x+11=8
-3x+12-8=0
-3x+4=0
3x=4
X=4/3
Answer:
x = 4/3 or 1.3
Step-by-step explanation:
Combine like terms
8 = -3x + 12
Move the terms
3x = 12 - 8
Calculate
3x = 4
Divide both sides by 3
x = 4/3
or
x = 1.3
Find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill in the blank.
About_____% of the area is between z = 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).
About_____% of the area is between z = 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).
Complete Question
Find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill in the blank.
About_____% of the area is between z = - 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).
About_____% of the area is between z = - 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).
Answer:
About 97.219% of the area is between z = - 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).
Step-by-step explanation:
From the question given we can see that they both are the same so 1 will just solve one
Now the area under this given range can be represented mathematically as
[tex]P ( -2.2 < z < 2.2) = P(z < 2.2 ) - P(z < -2.2 )[/tex]
Now from the z-table
[tex]p(z < 2.2 ) = 0.9861[/tex]
and
[tex]p(z < - 2.2 ) = 0.013903[/tex]
So
[tex]P ( -2.2 < z < 2.2) = 0.9861 - 0.013903[/tex]
[tex]P ( -2.2 < z < 2.2) = 0.97219[/tex]
So converting to percentage
[tex]P ( -2.2 < z < 2.2) = 0.97219 * 100[/tex]
[tex]P ( -2.2 < z < 2.2) = 97.219 \%[/tex]
Solve the following system of equations for x to the nearest hundredth : y + 2x + 1 = 0; 4y - 4x ^ 2 - 12x = - 7
Answer:
+3.464; -3.464
Step-by-step explanation:
call A = y + 2x + 1 = 0 => y = (1 - 2x)
call B: 4y - 4(x^2) - 12x = -7
=> replace y from A to B =>
4(1 - 2x) - 4(x^2) - 12x = -74 - 8x - 4(x ^ 2) - 12x = -7-8x - 4(x ^ 2) - 12x = -7 - 4 = -11-4(x^2) - (8x - 12x) = -11-4(x^2) + 4x = -11-4(x^2) + 4x + 11 = 0=> get delta Δ = (-4^2) - 4*(-4 * 11) = 192
=> Δ > 0 => got 2 No
=> x1 = [tex]\frac{-4 + \sqrt{192} }{2 * -4}[/tex] = [tex]\frac{1 - 2\sqrt{3} }{2}[/tex] = -1.232
=> x2 = [tex]\frac{-4 - \sqrt{192} }{2 * -4}[/tex]=[tex]\frac{1 + 2\sqrt{3} }{2}[/tex]= 2.232
=> replace x from B into A
=> y1 = (1 - 2x) = (1 - 2 * -1.232) = 3.464
=> y2 = (1 - 2x) = (1 - 2 * 2.232) = - 3.464
Can somebody explain how these would be done? The selected answer is incorrect, and I was told "Nice try...express the product by first multiplying the coefficients...then adding your "like term" angles...for instance, cos (2pi/5) + cos (-pi/2) = cos (2pi/5 + -pi/2)...then use the calculator in RADIAN mode to evaluate." Doing those steps, I got the correct constant but a coefficient that was completely off. For the second one, I was told "Good effort...express the quotient by first dividing the coefficients...then subtract your "like term" angles...for instance, cos (2pi/5) - cos (-pi/2) = cos (pi/6 - pi/3)...Finally, use the calculator (in radian MODE) to evaluate."
Answer:
Solution ( Second Attachment ) : - 2.017 + 0.656i
Solution ( First Attachment ) : 16.140 - 5.244i
Step-by-step explanation:
Second Attachment : The quotient of the two expressions would be the following,
[tex]6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi \:}{5}\right)\right][/tex] ÷ [tex]2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right][/tex]
So if we want to determine this expression in standard complex form, we can first convert it into trigonometric form, then apply trivial identities. Either that, or we can straight away apply the following identities and substitute,
( 1 ) cos(x) = sin(π / 2 - x)
( 2 ) sin(x) = cos(π / 2 - x)
If cos(x) = sin(π / 2 - x), then cos(2π / 5) = sin(π / 2 - 2π / 5) = sin(π / 10). Respectively sin(2π / 5) = cos(π / 2 - 2π / 5) = cos(π / 10). Let's simplify sin(π / 10) and cos(π / 10) with two more identities,
( 1 ) [tex]\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos \left(x\right)}{2}}[/tex]
( 2 ) [tex]\sin \left(\frac{x}{2}\right)=\sqrt{\frac{1-\cos \left(x\right)}{2}}[/tex]
These two identities makes sin(π / 10) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], and cos(π / 10) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex].
Therefore cos(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], and sin(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex]. Substitute,
[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right][/tex]
Remember that cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting those values,
[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[0-i\right][/tex]
And now simplify this expression to receive our answer,
[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[0-i\right][/tex] = [tex]-\frac{3\sqrt{5+\sqrt{5}}}{4}+\frac{3\sqrt{3-\sqrt{5}}}{4}i[/tex],
[tex]-\frac{3\sqrt{5+\sqrt{5}}}{4}[/tex] = [tex]-2.01749\dots[/tex] and [tex]\:\frac{3\sqrt{3-\sqrt{5}}}{4}[/tex] = [tex]0.65552\dots[/tex]
= [tex]-2.01749+0.65552i[/tex]
As you can see our solution is option c. - 2.01749 was rounded to - 2.017, and 0.65552 was rounded to 0.656.
________________________________________
First Attachment : We know from the previous problem that cos(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], sin(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex], cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting we receive a simplified expression,
[tex]6\sqrt{5+\sqrt{5}}-6i\sqrt{3-\sqrt{5}}[/tex]
We know that [tex]6\sqrt{5+\sqrt{5}} = 16.13996\dots[/tex] and [tex]-\:6\sqrt{3-\sqrt{5}} = -5.24419\dots[/tex] . Therefore,
Solution : [tex]16.13996 - 5.24419i[/tex]
Which rounds to about option b.
fill in each balance???
Answer:
Step-by-step explanation:
Take the beginning number and add or subtract each transaction to get a new balance. For example,
349.45
- 23.42 = 326.03
- 14.95 = 311.08
+ 276.50 = 587.58
- 219.93 = 367.65
- 76.84 = 290.81
X-3y=-3; ( ,4), (12, ) complete each ordered pair
Answer:
(9,4) and (12,5)
Step-by-step explanation:
x-3y=-3
y=4, x-3*4=-3, x=9. (9,4)x=12, 12-3y=-3, y=5. (12,5)Transform the given parametric equations into rectangular form. Then identify the conic.
Answer:
Solution : Option B
Step-by-Step Explanation:
We have the following system of equations at hand here.
{ x = 5 cot(t), y = - 3csc(t) + 4 }
Now instead of isolating the t from either equation, let's isolate cot(t) and csc(t) --- Step #1,
x = 5 cot(t) ⇒ x - 5 = cot(t),
y = - 3csc(t) + 4 ⇒ y - 4 = - 3csc(t) ⇒ y - 4 / - 3 = csc(t)
Now let's square these two equations. We know that csc²θ - cot²θ = 1, so let's subtract the equations as well. --- Step #2
( y - 4 / - 3 )² = (csc(t))²
- ( x - 5 / 1 )² = (cot(t))²
___________________
(y - 4)² / 9 - x² / 25 = 1
And as we are subtracting the two expressions, this is an example of a hyperbola. Therefore your solution is option b.
What is 2/6 times 1/6
Answer:
1/9
Step-by-step explanation:
2/6*1/6=2*1/6*6 or 1/9.
Answer:
1/18
Step-by-step explanation:
1. multiply across
2*1 and 6*6
2/36
2. divide by 2 to simplify
2/2 and 36/2
1/18
An integer is eight less than three times another if the product of two integers is 35 then find the integers
Help me please ?! ❤️❤️
Answer:
Hey there!
Point K has coordinates of (-2, -5)
Hope this helps :)
Answer:
Point K
Step-by-step explanation:
Since they're asking us to find (-2,-5) first we need to move 2 points to the left and then 5 points down.
If the weight (in grams) of cereal in a box of Lucky Charms is N(470,5), what is the probability that the box will contain less than the advertised weight of 453 g?
Answer:
The probability that the box will contain less than the advertised weight of 453 g is 0.00034.
Step-by-step explanation:
Let X represent the weight (in grams) of cereal in a box of Lucky Charms.
It is provided that X follows a Normal distribution with parameters, μ = 470 and σ = 5.
Compute the probability that the box will contain less than the advertised weight of 453 g as follows:
[tex]P(X<453)=P(\frac{X-\mu}{\sigma}<\frac{453-470}{5})[/tex]
[tex]=P(Z<-3.4)\\=0.00034[/tex]
*Use the z-table.
Thus, the probability that the box will contain less than the advertised weight of 453 g is 0.00034.
(07.03. 07.04 MC)
Part A: The area of a square is (4x2 + 20x + 25) square units. Determine the length of each side of the square by factoring the area expression completely. Show
your work (5 points)
Part B: The area of a rectangle is (4x2 - 9y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work
(5 points)
Answer:
A) 4x^2+20x+25=(2x)^2+2*(2x)*5+5^2=(2x+5)^2
Area=(side)^2, side=sqrt(area)=sqrt((2x+5)^2)=2x+5
B) 4x^2-9y^2=(2x-3y)(2x+3y), these are the dimensions of the rectangle
A) The length of each side of the square is (2x + 5).
B) The dimensions of the rectangle are (2x - 3y) and (2x + 3y).
Used the concept of a quadratic equation that states,
An algebraic equation with the second degree of the variable is called a Quadratic equation.
Given that,
Part A: The area of a square is [tex](4x^2 + 20x + 25)[/tex] square units.
Part B: The area of a rectangle is [tex](4x^2 - 9y^2)[/tex] square units.
A) Now the length of each side of the square is calculated by factoring the area expression completely,
[tex](4x^2 + 20x + 25)[/tex]
[tex]4x^2 + (10 + 10)x + 25[/tex]
[tex]4x^2 + 10x + 10x + 25[/tex]
[tex]2x (x + 5) + 5(2x + 5)[/tex]
[tex](2x + 5) (2x+5)[/tex]
Hence the length of each side of the square is (2x + 5).
B) the dimensions of the rectangle are calculated by factoring the area expression completely,
[tex](4x^2 - 9y^2)[/tex]
[tex](2x)^2 - (3y)^2[/tex]
[tex](2x - 3y) (2x + 3y)[/tex]
Therefore, the dimensions of the rectangle are (2x - 3y) and (2x + 3y).
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Suppose babies born in a large hospital have a mean weight of 3316 grams, and a standard deviation of 324 grams. If 83 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by greater than 54 grams?
Answer: 0.129
Step-by-step explanation:
Let [tex]\overline{X}[/tex] denotes a random variable that represents the mean weight of babies born.
Population mean : [tex]\mu= \text{3316 grams,}[/tex]
Standard deviation: [tex]\text{324 grams}[/tex]
Sample size = 83
Now, the probability that the mean weight of the sample babies would differ from the population mean by greater than 54 grams will be :
[tex]P(|\mu-\overline{X}|>54)=1-P(\dfrac{-54}{\dfrac{324}{\sqrt{83}}}<\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{-54}{\dfrac{324}{\sqrt{83}}})\\\\=1-[P(-1.518<Z<1.518)\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-[P(Z<1.518)-P(z<-1.518)]\\\\=1-[P(Z<1.518)-(1-P(z<1.518))]\\\\=1-[2P(Z<1.518)-1]=2-2P(Z<1.518)\\\\=2-2(0.9355)\ [\text{By z-table}]\\\\=0.129[/tex]
hence, the required probability = 0.129
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 4x2 − 3x + 2, [0, 2]
Answer:
Yes , it satisfies the hypothesis and we can conclude that c = 1 is an element of [0,2]
c = 1 ∈ [0,2]
Step-by-step explanation:
Given that:
[tex]f(x) = 4x^2 -3x + 2, [0, 2][/tex]
which is read as the function of x = 4x² - 3x + 2 along the interval [0,2]
Differentiating the function with respect to x is;
f(x) = 8x - 3
Using the Mean value theorem to see if the function satisfies it, we have:
[tex]f'c = \dfrac{f(b)-f(a)}{b-a}[/tex]
[tex]8c -3 = \dfrac{f(2)-f(0)}{2-0}[/tex]
since the polynomial function is differentiated in [0,2]
[tex]8c -3 = \dfrac{(4(2)^2-3(2)+2)-(4(0)^2-3(0)+2)}{2-0}[/tex]
[tex]8c -3 = \dfrac{(4(4)-3(2)+2)-(4(0)-3(0)+2)}{2-0}[/tex]
[tex]8c -3 = \dfrac{(16-6+2)-(0-0+2)}{2-0}[/tex]
[tex]8c -3 = \dfrac{(12)-(2)}{2}[/tex]
[tex]8c -3 = \dfrac{10}{2}[/tex]
8c -3 = 5
8c = 5+3
8c = 8
c = 8/8
c = 1
Therefore, we can conclude that c = 1 is an element of [0,2]
c = 1 ∈ [0,2]
Please help! Find the equation of the line (graph provided in attached picture) Use exact numbers. y =_ x+_ ( _ represent blanks in the equation)
Answer:
[tex] y = \frac{3}{4}x - 2 [/tex]
Step-by-step explanation:
Equation of a line is given as [tex] y = mx + b [/tex]
Where,
m = slope of the line = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
b = y-intercept, which is the value at the point where the line intercepts the y-axis. At this point, x = 0.
Let's find m and b to derive the equation for the line.
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Use the coordinate pair of any two points on the line. Let's use the following,
[tex] (0, -2) = (x_1, y_1) [/tex] => on the line, when x = 0, y = -2
[tex] (4, 1) = (x_2, y_2) [/tex] => on the line, when x = 4, y = 1
Plug in the values and solve for m
[tex] m = \frac{1 - (-2)}{4 - 0} [/tex]
[tex] m = \frac{1 + 2}{4} [/tex]
[tex] m = \frac{3}{4} [/tex]
b = -2 (the line intercepts the y-axis at this point)
Our equation would be =>
[tex] y = mx + b [/tex]
[tex] y = \frac{3}{4}x + (-2) [/tex]
[tex] y = \frac{3}{4}x - 2 [/tex]
pls what is the nearest 100 of 49
Answer:
the nearest hundred is 50
A sports stadium has a capacity of 42,000. On a
particular night, 35,000 spectators attend an event. At
the end of the event, spectators leave the stadium at a rate
of 320 spectators every minute. If m represents the
number of minutes after spectators begin to leave the
stadium, which of the following inequalities describes
the times when there are still spectators in the stadium?
A) 42,000 - 35,000m < 320
B) 35,000 - 320m > 0
C) 35,000 + 320m < 42,000
D) 320m < 87,000
Answer:
B
Step-by-step explanation:
The inequality will be 35000-320m>0
solve for x: 5x+3+8x-4=90
Answer:
[tex]x = 7[/tex]
Step-by-step explanation:
We can solve the equation [tex]5x+3+8x-4=90[/tex] by isolating the variable x on one side. To do this, we must simplify the equation.
[tex]5x+3+8x-4=90[/tex]
Combine like terms:
[tex]13x - 1 = 90[/tex]
Add 1 to both sides:
[tex]13x = 91[/tex]
Divide both sides by 13:
[tex]x = 7[/tex]
Hope this helped!
Answer:
x = 7
Step-by-step exxplanation:
5x + 3 + 8x - 4 = 90
5x + 8x = 90 - 3 + 4
13x = 91
x = 91/13
x = 7
probe:
5*7 + 3 + 8*7 - 4 = 90
35 + 3 + 56 - 4 = 90
Please help soon as possible! This is urgent! Match each expression with the correct description.
Answer:
Hey there!
q is 1, and n=-2.
q-n=1-(-2), which is 3.
n-q=-2=1, which is -3.
q is 1.
Thus, the least value is n-q, and the greatest value is q-n. Closest to zero would be q.
Let me know if this helps :)
Answer:
Least: n-q
Greatest: q-n
Closest to zero: q
find the surface area of the prism
Answer:
Base area=5*12=60
Height is 4
Perimeter or the base is 2*(12+5)=34
Surface area is 2B+Ph=120+136=256
Each cylinder is 12 cm high with a diameter of 8 cm.
Calculate the volume of each cylinder.
Use 3 as a value for π
Give your answer using the correct units.
Answer:
Volume = 576cm^3Step-by-step explanation:
[tex]h = 12 cm\\d = 8cm\\r =d/2 = 8/2 =4\\V = ?\\V =\pi r^2h\\\\V= 3 \times 4^2\times12\\V = 576 cm^3[/tex]