Answer:
150 days
Step-by-step explanation:
6-4=2
100/2=50
50*3=150
The number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.
The rate of disintegration varies directly proportional to the quantity of the material.
As such, we can say:
[tex]\mathbf{=\dfrac{dN}{dt}\ \alpha \ N}[/tex]
[tex]\mathbf{\implies \dfrac{dN}{N}\ = k dt}[/tex]
Taking the integral form;
[tex]\mathbf{\implies \int \dfrac{dN}{N}\ =\int k dt}[/tex]
[tex]\mathbf{\implies In N =kt+ C---- (1)}[/tex]
When t = 0, N = 6 grams
In(6) = C
∴
When t = 100, N = 4 grams
In (4) = 100k + In6
100 k = 1n (4) - In(6)
[tex]\mathbf{100 k = In (\dfrac{4}{6})}[/tex]
[tex]\mathbf{k = \dfrac{1}{100} In(\dfrac{4}{6})}[/tex]
∴
From equation (1):
[tex]\mathbf{In N = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]
when,
n = 3 grams; we have:[tex]\mathbf{In (3) = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]
[tex]\mathbf{\implies \dfrac{t}{100} In(\dfrac{4}{6}) = In \dfrac{ 3}{ 6}}[/tex]
[tex]\mathbf{t = 100\times \Big ( \dfrac{In (\dfrac{ 3}{ 6})}{ In(\dfrac{4}{6}) }\Big) }[/tex]
[tex]\mathbf{t = 100\times \Big ( \dfrac{0.69314}{ 0.40048}\Big) }[/tex]
t = 173.077 days
Therefore, the number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.
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Simplify the following algebraic expression.
square root of 392x^7
Answer:
[tex] \sqrt{392 {x}^{7} } [/tex]
Simplify
that's
[tex] \sqrt{392} \times \sqrt{ {x}^{7} } \\ \\ = \sqrt{196 \times 2} \: \times \sqrt{ {x}^{7} } \\ \\ = 14 \sqrt{2} \times \sqrt{ {x}^{7} } \\ \\ = 14 \sqrt{2x ^{7} } [/tex]
Hope this helps you
Jahlil is 6 inches shorter than 4 times his sister’s height. Jahlil’s height is 70 inches. Which equation represents h, his sister’s height in inches?
Answer:
4h - 6 = 70.
Step-by-step explanation:
Jahill's height is 70 inches. That is 6 inches shorter than 4 times his sister's height, h. That is the same thing as 4 times h minus 6.
70 = 4 * h - 6
4 * h - 6 = 70
4h - 6 = 70
4h = 76
h = 19.
His sister is 19 inches tall.
Hope this helps!
Answer:
Hello! The answer will be below! :3
Step-by-step explanation:
Question: Jahlil is 6 inches shorter than 4 times his sister’s height. Jahlil’s height is 70 inches. Which equation represents h, his sister’s height in inches?
Answer:The answer is 4h - 6 =70
(His sister is 19 inches tall)
Steps:
4 * h - 6 = 70
So, 4h - 6 = 70......
And 4h will be 76 which means h will equal to 19
His sisters hight is about 19in. tall.....
Hope this helps! :)
⭐️Have a wonderful day!⭐️
use the foil method to find the product below. (x+3) (x^2-6x)
x^3 - 3x^2 - 18x
Using the FOIL method, I arrived at my solution!
Factor.
-7x2 + 49x
-7(x - 7)
01 - 7x2 + 49x)
-x(x – 7)
-7x(x – 7)
Answer:
Option 1: -7x (x - 7)
Step-by-step explanation:
Factor -7x out of -7x^2.
= -7x (x) + 49x
Factor -7x out of 49x.
= -7x (x) -7x (-7)
Factor -7x out of -7x (x) - 7x (-7).
= -7x (x - 7)
(Also I took the test and got this answer right)
Find the directional derivative of f at the given point in the direction indicated by the angle θ. f(x, y) = y cos(xy), (0, 1), θ = π/3
Answer:
√3/2
Explanation:
The directional derivative at the given point is gotten using the formula;
∇f(x,y)•u where u is the unit vector in that direction.
∇f(x,y) = f/x i + f/y j
Given the function f(x, y) = y cos(xy),
f/x = -y²sin(xy) and
f/y = -xysin(xy)+cos(xy)
∇f(x,y) = -y²sin(xy) i + (cos(xy)-xysin(xy)) j
∇f(x,y) at (0,1) will give;
∇f(0,1) = -0sin0 i + cos0j
∇f(0,1) = 0i+j
The unit vector in the direction of angle θ is given as u = cosθ i + sinθ j
u = cos(π/3)i+ sin(π/3)j
u = 1/2 i + √3/2 j
Taking the dot product of both vectors;
∇f(x,y)•u = (0i+j)•(1/2 i + √3/2 j)
Note that i.i = j.j = 1 and i.j = 0
∇f(x,y)•u = 0 + √3/2
∇f(x,y)•u = √3/2
The directional derivative of [tex]f[/tex] at the given point in the direction indicated is [tex]\frac{\sqrt{3}}{2}[/tex].
How to calculate the directional derivative of a multivariate functionThe directional derivative is represented by the following formula:
[tex]\nabla_{\vec v} f = \nabla f(x_{o},y_{o}) \cdot \vec v[/tex] (1)
Where:
[tex]\nabla f(x_{o}, y_{o})[/tex] - Gradient evaluated at point [tex](x_{o},y_{o})[/tex].[tex]\vec v[/tex] - Directional vectorThe gradient of [tex]f[/tex] is calculated below:
[tex]\nabla f (x_{o},y_{o}) = \left[\begin{array}{cc}\frac{\partial f}{\partial x} (x_{o}, y_{o}) \\\frac{\partial f}{\partial y} (x_{o}, y_{o})\end{array}\right][/tex] (2)
Where [tex]\frac{\partial f}{\partial x}[/tex] and [tex]\frac{\partial f}{\partial y}[/tex] are the partial derivatives with respect to [tex]x[/tex] and [tex]y[/tex], respectively.
If we know that [tex](x_{o}, y_{o}) = (0, 1)[/tex], then the gradient is:
[tex]\nabla f(x_{o}, y_{o}) = \left[\begin{array}{cc}-y^{2}\cdot \sin xy\\\cos xy -x\cdot y\cdot \sin xy\end{array}\right][/tex]
[tex]\nabla f (x_{o}, y_{o}) = \left[\begin{array}{cc}-1^{2}\cdot \sin 0\\\cos 0-0\cdot 1\cdot \sin 0\end{array}\right][/tex]
[tex]\nabla f (x_{o}, y_{o}) = \left[\begin{array}{cc}0\\1\end{array}\right][/tex]
If we know that [tex]\vec v = \cos \frac{\pi}{3}\,\hat{i} + \sin \frac{\pi}{3} \,\hat{j}[/tex], then the directional derivative is:
[tex]\Delta_{\vec v} f = \left[\begin{array}{cc}0\\1\end{array}\right]\cdot \left[\begin{array}{cc}\cos \frac{\pi}{3} \\\sin \frac{\pi}{3} \end{array}\right][/tex]
[tex]\nabla_{\vec v} f = (0)\cdot \cos \frac{\pi}{3} + (1)\cdot \sin \frac{\pi}{3}[/tex]
[tex]\nabla_{\vec v} f = \frac{\sqrt{3}}{2}[/tex]
The directional derivative of [tex]f[/tex] at the given point in the direction indicated is [tex]\frac{\sqrt{3}}{2}[/tex]. [tex]\blacksquare[/tex]
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What is the greatest whole number that must be a divisor of the product of any three consecutive positive integers?
Answer:
6
Step-by-step explanation:
We can establish 6 as an upper bound, since 1*2*3 = 6, and 6 is clearly the greatest number that is a divisor of itself.
We can show that the product of any three consecutive numbers is divisible by 6, because out of any three consecutive integers, at least one must be divisible by 3, and at least one must be divisible by 2. Since the product must have factors of 2 and 3, it must also have 6 as a factor.
11. Caroline wraps packages at a store. She wraps
9 packages each hour. Which statement is true
about the number of packages she wraps?
A. In 2 hours, Caroline wraps an odd number of
packages.
B. In 3 hours, Caroline wraps an even number of
packages.
C. In 5 hours, Caroline wraps an odd number of
packages.
D. In 7 hours, Caroline wraps an even number of
packages.
Answer:
C. in five hours Caroline wraps an odd number of packages
Step-by-step explanation:
for A until hours you would multiply 2 by 9 and 2 by 9 is 18 and that's an even number so it's not A.
A eliminated.
for B in 3 hours 3 by 9 is 27 and that's an odd number so B is automatically eliminated.
for C in 5 hours all you would do is multiply the 9 by 5 and 9 by 5 is 45 and 45 is indeed an odd number so C is your answer.
for D 7 by 9 is 63 and 63 is an odd number so we already know that C is the answer but still we got to check and D is wrong because 63 is not an even number.
A jury pool consists of 27 people, 14 men and 13 women. Compute the probability that a randomly selected jury of 12 people is all male
Answer: [tex]\dfrac{7}{1,337,220}=5.2\times 10^{-6}[/tex]
Step-by-step explanation:
Order does not matter so it is a Combination.
There are 14 men and we are going to choose 12 --> ₁₄C₁₂
There are 27 people and we are going to choose 12 --> ₂₇C₁₂
[tex]\dfrac{_{14}C_{12}}{_{27}C_{12}}\rightarrow\dfrac{14!}{(14-12)!}\div \dfrac{27!}{(27-12)!}=\large\boxed{\dfrac{7}{1,337,220}}[/tex]
Probabilities are used to determine the chances of an event
The probability of selecting 12 males is: [tex]\frac{7}{1337220}[/tex]
The parameters are given as:
[tex]n = 24[/tex] --- sample size
[tex]Male = 14[/tex]
[tex]Female = 13[/tex]
[tex]r = 12[/tex] ---- number of jury pool
The number of ways of selecting 12 members of the jury, from a total of 27 is:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
So, we have:
[tex]^{27}C_{12} = \frac{27!}{(27 - 12)!12!}[/tex]
[tex]^{27}C_{12} = \frac{27!}{15! \times 12!}[/tex]
[tex]^{27}C_{12} = 17383860[/tex]
The number of ways of selecting 12 members of the jury, from a total of 14 male is:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
So, we have:
[tex]^{14}C_{12} = \frac{14!}{(14 - 12)!12!}[/tex]
[tex]^{14}C_{12} = \frac{14!}{2! \times 12!}[/tex]
[tex]^{14}C_{12} = 91[/tex]
So, the probability of selecting 12 males is:
[tex]Pr = \frac{^{14}C_{12}}{^{27}C_{12}}[/tex]
[tex]Pr = \frac{91}{17383860}[/tex]
Simplify
[tex]Pr = \frac{91/13}{17383860/13}[/tex]
[tex]Pr = \frac{7}{1337220}[/tex]
Hence, the required probability is: [tex]\frac{7}{1337220}[/tex]
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Determine the maximum r-values of r=7cos4theta
Answer:
Maximum value of r = 7
Step-by-step explanation:
We have this function:
[tex]r=7\cos(4\theta)[/tex]
and we want to calculate the maximum values for r.
This can be done by deriving, but there is a simpler way.
If we look at the function, the maximum values of r will be found when the cosine function is maximum.
The maximum values for the cosine function is 1, so the maximum values for r are:
[tex]r_{max}=7\cdot 1=7[/tex]
This maximum values happen when the cosine function has a value of 1.
We know that this happens for every natural number n that satisfies:
[tex]\cos(\dfrac{n\pi}{2})=1[/tex]
Then, we can calculate the values of theta that satisfy this condition:
[tex]4\theta=\dfrac{n\pi}{2}\\\\\\\theta=\dfrac{n\pi}{8}[/tex]
For every natural n, when theta has a value of (nπ/8), the values of r are maximum.
Help ASAP - Find the area of the composite figure made up of a square and a semicircle. Use 3.14 as an approximation for and give your
answer to the nearest square inch. Enter only the number.
Answer:
200.52 in^2
Step-by-step explanation:
to find the area of a circle, you square 6 and multiply it by pi in this case 3.14.
that gives you 113.04 but because this is only a half circle, it is 56.52 in^2.
Next, you need to find the rectangle. multiply 12(length) by 12(Width) to get 144 add 144 to 56.52 to get 200.52.
Hope this helped if it did please give me brainliest it helps me a lot. :)
Have a good day!
NEED HELP THANKLSSSS
Answer:
Side length: 3 cm.
Surface area: 54 cm squared.
Step-by-step explanation:
The formula for a cube is the side length cubed, since the formula for a rectangular prism is length times width times height. Those three measurements are the same for a cube.
So, since the volume is 27 cm cubed, we can say that the side length of the cube is the cube root of 27 cm cubed, or 3 cm.
There are 6 sides on a cube, and every cube has the same area. Since the side length of the cube is 3 cm, the area of one side of the cube is 3 * 3 = 9 cm squared. 9 * 6 = 54 cm squared.
Hope this helps!
Consider the line – 5x – 8y= 3.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Answer:
Perpendicular Slope: 8/5
Parallel Slope: -5/8
Step-by-step explanation:
First, let's rewrite the line into slope intercept form.
-5x - 8y = 3
-8y = 5x + 3
y = -5x/8 + -3/8
Okay, so now we know the slope, -5/8, and the y-intercept, -3/8.
For a line to be perpendicular, the slope needs to be opposite of the given line's slope. This will cause the two lines to cross at a 90-degree angle, and therefore be perpendicular.
So a perpendicular line could be as follows:
y = 8x/5 + -3/8
So the perpendicular slope would be 8/5.
For a line to be parallel, the slope needs to be the same so that the two lines will never cross.
So a parallel line could be as follows:
y = -5x/8 + 1
So the parallel slope would be -5/8.
Cheers.
Answer:
Perpendicular Slope: [tex]\boxed{\frac{8}{5}}[/tex]
Parallel Slope: [tex]\boxed{-\frac{5}{8}}[/tex]
Step-by-step explanation:
Part 1: Rewrite into slope-intercept form
Firstly, the equations are written in standard form and not slope-intercept form, so to change that, follow the steps below.
Note: Remember the slope-intercept form equation - [tex]\boxed{y=mx+b}[/tex]
[tex]-5x-8y=3\\\\5x + (-5x-8y)=3+5x\\\\-8y=5x+3\\\\\frac{-8y}{-8} =\frac{5x+3}{-8} \\[/tex]
[tex]y=-\frac{5}{8}x-\frac{3}{8}[/tex]
Add [tex]5x[/tex] to both sides of the equation to isolate the y-variable. Then, divide by the coefficient of y to isolate it entirely. The equation is now in slope-intercept form.
Part 2: Determine the perpendicular slope
Perpendicular slopes are reciprocals of the given slopes. To turn the original slope into its reciprocal counterpart, follow these steps:
If the current slope is positive, add a negative sign. If the current slope is negative, remove the negative sign.The denominator becomes the numerator and the numerator becomes the denominator.To follow this for the slope of the given equation:
[tex]\boxed{-\frac{5}{8} \dashrightarrow \frac{8}{5} }[/tex]Part 3: Determine the parallel slope
Parallel slopes are equal - otherwise, the lines would eventually intersect. Therefore, the given slope is also the parallel slope.
The parallel slope is [tex]\boxed{-\frac{5}{8}}[/tex].
Cynthia invested $12,000 in a savings account. If the interest rate is 6%, how much will be in the account in 10 years by compounding continuously? Round to the nearest cent.
Answer:
In 10 years she'll have approximately $21865.4 in her account.
Step-by-step explanation:
When an amount is compounded continuously its value over time is given by the following expression:
[tex]v(t) = v(0)*e^{rt}[/tex]
Applying data from the problem gives us:
[tex]v(10) = 12000*e^{(0.06*10)}\\v(10) = 12000*e^{0.6}\\v(10) = 21865.4[/tex]
In 10 years she'll have approximately $21865.4 in her account.
Answer:
21,865.43
previous answer left out the last digit
Step-by-step explanation:
what is the length of bc in the right triangle below?
Answer: A) 15
Step-by-step explanation:
Because of Pythagorean Theorem, 9^2+12^2=BC^2. Thus, 81+144=BC^2. Thus, 225=BC^2. Thus, 15=BC.
Hope it helps, and ask if you want further clarification <3
Could someone please help. The given sides are 25 at the left, 35 at bottoms, 5 at the right. Thank you :)
Answer:
120 cm
Step-by-step explanation:
If you rearrange the lines you will get a rectangle whose sides are 25 cm and 35 cm.
To get a triangle, move the lines inside the rectangle keeping them parallel to the lines in front of them.
Let P the perimeter of the rectangle:
P = 25*2 + 35*2 = 50+70 = 120 cm
HELP PLEASEEE!!!!!!!!!!
Answer:
100
Step-by-step explanation:
height = constant/ width
Taking the point (5,20)
where 5 is the width and 20 is the height
20 = constant/ 5
Multiply each side by 5
5*20 = constant
100 = constant
Find the expression for h(x) f(x)=-x^2-1
Answer:
h(x) = -x^2 - 1
Step-by-step explanation:
well y, h(x), f(x), n(x), or any other something of x is all the same thing y.
So if f(x) is -x^2 - 1,
Then h(x) is also -x^2 - 1
Three of the sides will require fencing and the fourth wall already exists. If the farmer has 116 feet of fencing, what are the dimensions of the region with the largest area
Answer:
29 ft x 58 ft
Step-by-step explanation:
Let x be the length of each side perpendicular to the wall, and y be the length of the side parallel to the wall.
The amount of wire available is:
[tex]116 = 2x+y\\y=116-2x[/tex]
The area of the region is:
[tex]A=xy=x(116-2x)\\A(x)=116x-2x^2[/tex]
The value of 'x' for which the derivate of the area function is zero will yield the maximum area:
[tex]A(x)=116x-2x^2\\A'(x) = 116-4x=0\\x=29\ ft[/tex]
The value of y is:
[tex]y=116-2*29\\y=58\ ft[/tex]
The dimensions of the region with the largest area are 29 ft x 58 ft.
Which equation represents the line that is parallel to y=4 and passes through (-3,1).
A. x=1
B. x= 3
C. y= 1
D. y= 4x + 13
Answer:
C. y = 1
Step-by-step explanation:
For two line to be parallel, they have to have the same slope. The slope for the equation y = 4 is 0. This cancels out answer choices A, B, and D.
A and B have an undefined slope since they are vertical lines.
D has a slope of 4.
Also, the line has to go through the point (-3, 1). Since the line has a slope of 0, the equation will include the y-value. The y-value for this point is 1. This gives you an answer of y = 1.
Answer:
y = 1
Step-by-step explanation:
Just took the practice test and got it right
Strontium 90 is a radioactive material that decays according to the function Upper A (t )equals Upper A 0 e Superscript negative 0.0244 t Baseline commaA(t)=A0e−0.0244t, where Upper A 0A0 is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 500500 grams of strontium 90. (a) What is the decay rate of strontium 90?
Answer:
Decay rate K = -2.44%
Step-by-step explanation:
From the question, we want to know the decay rate of strontium 90
Mathematically, this is accessible from its decay equation
From the decay equation, we can see that that ;
At = Ao e^-0.0244t
Generally, the decay equation of a radioactive sample can be written as
At = Ao e^-kt
where K represents the decay constant
From the equation, we can see that;
k = 0.0244 which when represented as a percentage is 2.44%
Since it’s a decay we can say that the decay rate is -2.44%
The answer is : -2.44%
What is the least number of colors you need to correctly color in the sections of the pictures so that no two touching sections are the same color?
Answer:
8 colors
Step-by-step explanation:
There should be at least 8 different colors available for coloring the sections. The one color is used to color all the small triangles on the upper most and lower most lines, then there will be required another color so that the edges does not matches with the previous color. For the bigger hexagon shapes in the center we will require different colors for all of them because all of the hexagon shapes touches a line and an edge with each other.
Answer:
its 2 trust me
Step-by-step explanation:
its two cause if you think about it and color in the hexagons and triangles two different colors it works
do following division with polynomials
1) (x^3-2x^2+3x-3)÷(x+2)
Which statement would produce a tautology? A. p q B. p q C. p p D. q p
Answer: C. p = p
Step-by-step explanation:
A tautology is a statement that is always true.
A. p = q
This is not always true. Counterexample: p = 1 & q = 2
B. p = q
This is the same as A (above)
C. p = p
This is ALWAYS true!
D. q = p
This is the same as A but in reverse order.
I need help, I don’t need an explanation, just the answer
Answer:
[tex]x = 48 \: \: \: \: \: \: y = 16[/tex]
Step-by-step explanation:
[tex]y = - x + 4y[/tex]
[tex]y + x = 4y[/tex]
[tex]y + x - 4y = 0[/tex]
[tex] - 3y + x = 0[/tex]
[tex] - x + 4y = 16[/tex]
[tex] - 3y + x = 0[/tex]
[tex] - 3y = - x[/tex]
[tex]y = - \frac{1}{3} ( - 1)x[/tex]
[tex]y = \frac{1}{3} x[/tex]
[tex]4 \times ( \frac{1}{3} )x - x = 16[/tex]
[tex] \frac{1}{3}x = 16 [/tex]
[tex]x = 48[/tex]
[tex]y = \frac{1}{3} \times 48[/tex]
[tex]y = 16[/tex]
Hope this is correct and helpful
HAVE A GOOD DAY!
Answer:
x = 48, y = 16
Step-by-step explanation:
What does volume measure? the amount of space occupied by a two-dimensional solid object the total area of all the surfaces of a three-dimensional solid object the amount of space inside the boundary of a two-dimensional object the amount of space occupied by a three-dimensional solid object
Answer:
the amount of space occupied by a three-dimensional solid object
Step-by-step explanation:
Volume is a measure of the space in a 3D solid object enclosed by the closed surfaces of the solid object.
By using the definition of volume, we can see that the correct option is the last one:
"The amount of space occupied by a three-dimensional solid object"
What does volume measure?
Volume is defined as a 3-dimensional metric derived from longitude, that measures a region in the space. So, each region that "takes space" has a volume.
With that in mind, the option that correctly describes volume is the last option:
"The amount of space occupied by a three-dimensional solid object"
If you want to learn more about volume, you can read:
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Whal value of x is in the solution set of 9(2x + 1) < 9x - 18?
A: -4
B: -3
C: -2
D: -1
Answer:
A:-4
Step-by-step explanation:
If you simplify 9(2x+1)<9x-18 you will get 9x<-27. That will mean x<-3 and the only answer for something less than -3 is -4.
If the answer was right, please put 5 stars.
Answer:
The answer would be-4
Step-by-step explanation:
Here,
9(2x+1) < 9x-18
or, 18x+9 < 9x-18
or, 18x-9x<-18-9
or, 9x<-27
or, x= -27/9
Therefore, the value of x is -4.
Hope it helps...
A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 48 cables and apply weights to each of them until they break. The 48 cables have a mean breaking weight of 773 lb. The standard deviation of the breaking weight for the sample is 16.1 lb. Find the 95% confidence interval to estimate the mean breaking weight for this type cable.
Answer:
The 95% confidence interval is [tex]768.44 < \mu <777.55[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 48
The sample mean is [tex]\= x = 773 \ lb[/tex]
The standard deviation is [tex]\sigma = 16.1 \ lb[/tex]
Now given that the confidence level is 95% , then the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The reason we are obtaining critical values of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because
[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval ( [tex]1-\alpha[/tex] ) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex]is just the area of one tail which what we required to calculate the margin of error
The margin of error is mathematically represented as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{ \sqrt{n} }[/tex]
substituting values
[tex]MOE = 1.96 * \frac{ 16.1 }{ \sqrt{48} }[/tex]
[tex]MOE = 4.555[/tex]
The 95% confidence interval to estimate the mean breaking weight for this type cable is mathematically evaluated as
[tex]\= x - MOE < \mu < \= x - MOE[/tex]
substituting values
[tex]773 - 4.555 < \mu < 773 + 4.555[/tex]
[tex]768.44 < \mu <777.55[/tex]
The Sugar Sweet Company is going to transport its sugar to market. It will cost $3500 to rent trucks, and it will cost an additional $150 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S. Then use this equation to find the total cost to transport 17 tons of sugar.
Answer:
C = 150S + 3,500.
$6,050.
Step-by-step explanation:
It costs $3,500 to rent the trucks, so your constant/y-intercept will be $3,500.
It will cost $150 for every ton of sugar, so your slope will be $150.
You then have your equation:
C = 150S + 3,500.
If you were to transport 17 tons of sugar...
C = 150 * 17 + 3,500
C = 2,550 + 3,500
C = $6,050.
Hope this helps!
Answer:
C = $6050
Equation:
To write the equation, we have to remember that C is the total cost, so that means the equation should end in "= C". S is the amount of sugar, so the equation would look something like this:
[tex]3500+150(S)=C[/tex]
3500 is at the beginning since that is the cost for the trucks, and each ton of sugar costs $150, and that would get multiplied by S amount of sugar, to get the total cost, C.
Solving the equation
To solve the equation when S = 17, we simply have to plug in S as 17 into our equation we wrote above.
[tex]3500+150(17)=C[/tex]
150 * 17 is 2550, and 3500 + 2550 is 6050, which is C.
C = $6050
Six friends, four boys and two girls, went to a movie theater. They wanted to sit in a way so no girl sits on either first or last chair. How many such arrangements are possible?
Answer:
288 possible seating arrangements.
Step-by-step explanation:
There are 4 possible choices for the first seat.
There are 3 possible choice for the sixth seat.
There are 4 possible choices for the second seat.
There are 3 possible choices for the third seat.
There are 2 possible choices for the fourth seat
There is only 1 possible choices for the fifth seat.
4×3×4×3×2×1=
12×4×3×2×1=
48×3×2×1=
144×2×1=
288×1=
288 possible seating arrangements.
help i need to know pls
Answer:
7.8 =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp / adj
tan 48 = x/7
7 tan 48 = x
7.774287604 = x
To the nearest tenth
7.8 =x