Answer:
4.5 NStep-by-step explanation:
To convert 1 pounds to its meteric unit in weight, we need to first convert it to kilogram. Using the conversion 1pound = 0.453592 kg
Since Weight of a substance = mass of the substance * acceleration due to gravity
W = mg
Given mass = 0.453592kg and g = 9.8m/s²
Weight = 4.4452016 Newtons
1 pounds is therefore closest to 4.5 units metric of weight
Elliot’s school has 24 classrooms. Each classroom has seats for 26 students. What is the maximum number of students the school can seat? Multiply to find the answer.
Answer:
24*26= 624 students
hope this helps!
Answer:
624 seats
Step-by-step explanation:
Total classrooms = 24
Each classroom has seats = 26
Total Number of seats = 24*26
=> 624 seats
Tickets to a baseball game can be ordered online for a set price per ticket plus a $5.59 service fee. The total cost in dollars for ordering 5 tickets is $108.09. Which linear function represents c, the total cost, when x tickets are ordered
Answer:
c = 20.5x + 5.59
Step-by-step explanation:
c = mx + b
c = mx + 5.59
108.09 = m(5) + 5.59
5m = 102.5
m = 20.5
c = 20.5x + 5.59
The function C(x) = 200x + 240 gives the cost for a college to offer x sections of an introductory class in CPR. The function R(x) = 280x gives the amount of revenue the college brings in when offering x sections of CPR. Find the point where the cost equals the revenue by graphing each function on the same coordinate system.
Answer:
C(3) = R(3) = 840
Step-by-step explanation:
See the attached for a graph.
Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. Solve the original equation by solving the new equation
x2y'' + 9xy' - 20y = 0
Answer:
[tex]\boxed{\sf \ \ \ ax^2+bx^{-10} \ \ \ }[/tex]
Step-by-step explanation:
Hello,
let's follow the advise and proceed with the substitution
first estimate y'(x) and y''(x) in function of y'(t), y''(t) and t
[tex]x(t)=e^t\\\dfrac{dx}{dt}=e^t\\y'(t)=\dfrac{dy}{dt}=\dfrac{dy}{dx}\dfrac{dx}{dt}=e^ty'(x)<=>y'(x)=e^{-t}y'(t)\\y''(x)=\dfrac{d^2y}{dx^2}=\dfrac{d}{dx}(e^{-t}\dfrac{dy}{dt})=-e^{-t}\dfrac{dt}{dx}\dfrac{dy}{dt}+e^{-t}\dfrac{d}{dx}(\dfrac{dy}{dt})\\=-e^{-t}e^{-t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}\dfrac{dt}{dx}=-e^{-2t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}e^{-t}\\=e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt})[/tex]
Now we can substitute in the equation
[tex]x^2y''(x)+9xy'(x)-20y(x)=0\\<=> e^{2t}[ \ e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}) \ ] + 9e^t [ \ e^{-t}\dfrac{dy}{dt} \ ] -20y=0\\<=> \dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}+ 9\dfrac{dy}{dt}-20y=0\\<=> \dfrac{d^2y}{dt^2}+ 8\dfrac{dy}{dt}-20y=0\\[/tex]
so the new equation is
[tex]y''(t)+ 8y'(t)-20y(t)=0[/tex]
the auxiliary equation is
[tex]x^2+8x-20=0\\<=> x^2-2x+10x-20=0\\<=>x(x-2)+10(x-2)=0\\<=>(x+10)(x-2)=0\\<=> x=-10\text{ or }x=2[/tex]
so the solutions of the new equation are
[tex]y(t)=ae^{2t}+be^{-10t}[/tex]
with a and b real
as
[tex]x(t)=e^t\\<=> t(x)=ln(x)[/tex]
[tex]y(x)=ae^{2ln(x)}+be^{-10ln(x)}=ax^2+bx^{-10}[/tex]
hope this helps
do not hesitate if you have any questions
What is the solution to this system of linear equations? 3x – 2y = 14 5x + y = 32
Answer:
work is shown and pictured
Answer:
Answer B. (6, 2)
Hope it works!
Step-by-step explanation:
Domain and range of T
Answer:
Let's list out the points that belong to T. They are T{(-1, -4), (2, 2), (2, -3)}.
The domain is all of the x values. Therefore the domain is {-1, 2}.
The range is all of the y values. Therefore the range is {-4, -3, 2}.
We don't use ( ) or [ ] because T is a discrete relation.
A jar of sweet contains 5 yellow sweets, 4 red sweets, 8 green sweets, 4 orange sweets and 3 white sweets. Ola chose a sweet at random, what is the possibility that she will pick either a yellow or orange sweet?
Answer:
9/24 or 37.5%
hope this helps :)
Hi,
first thing you must do with a probability problem is to count how many thing you have in your universe.
Here we are dealing with sweets. So let's count : 5 +4+8+4+3 = 24
and there is 5 yellow so probability to pick up a yellow is 5/24
and there is 4 orange so probabilitu to pick up a orange is 4/24
To say : Ola will pick orange or yellow mean if she pick either one of the two sort is good. So you add the proba of each : 5/24 +4/24 = 9/24
and then you must reduce if you can : 9/24 = 3*3 /8*3 = 3/8
So the probability that Ola pick a yellow or orange sweet is 3/8 = 0.375
does 6(x + 5) = 6x + 11 , have on solution, infinitely many solutions, or no solutions?
Answer:
no solution
Step-by-step explanation:
hello
[tex]6(x+5)=6x+11\\<=> 6x+30=6x+11\\<=> 30=11[/tex]
this is always false so there is no solution
Let's to expand this equation:
[tex]6(x+5) = 6x+11\\6x + 6\times 5 = 6x + 11\\6x + 30 = 6x + 11[/tex]
Perceive that in two members of equations, we have "6x", so we can to eliminate it. But, when we make it, we have this situation:
[tex]6x + 30 = 6x + 11\\30 = 11[/tex]
How [tex]30 \neq 11[/tex] this is a absurd. Therefore, this equation don't have solutions.
5x+20y=25 4x-7y=-26 solve for x
Step-by-step explanation:
just just solve the equation and then substitute the value of the first equation in the second one.
Which of the following functions best describe this graph ?
Answer:
D.
Step-by-step explanation:
y - int is value of y when x = 0,
We have y int = 1,
D. x = 0, y = (0 - 1)(0 - 1) = 1
x-int = 1,
D. y = 0, So, answer is D.
Answer:
D
Step-by-step explanation:
First, note that the graph "bounces" off the x-axis at x=1. This is telling us two things: (1) the graph has a zero at x=1 and (2), since the graph bounces, it has a factor with a multiplicity of 2. Since it is a quadratic, the only way that it can have a multiplicity of two is if the function is a perfect square trinomial. In other words, it can be factored into (x-a)^2.
A, B, and C are not perfect square trinomials. They cannot be factored into the form (x-a)^2.
D is (x-1)(x-1) which equals (x-1)^2, a perfect square trinomial. Its zero is also at x=1. D is correct.
Evaluate: .25 (1.2 x 3 - 1.25) + 3.45
The order to us solve is:
ParenthesesMultiplicationSum and subtractionLet's go:
[tex]25(1.2\times 3 - 1.25) + 3.45\\25(3.6-1.25)+3.45\\25\times 2.35 + 3.45\\58.75+3.45\\62.2[/tex]
Therefore, the result is 62.2.
Answer:
4.0375
Step-by-step explanation:
.25(3.6-1.25)+3.45
.25(2.35)+3.45
.5875+3.45
4.0375
HOPE THIS HELPS:)
Consider the following information. SSTR = 6750 H0: μ1 = μ2 = μ3 = μ4 SSE = 8000 Ha: At least one mean is different If n = 5, the mean square due to error (MSE) equals a. 1687.5. b. 400. c. 500. d. 2250.
Answer:
d. 2250.
Step-by-step explanation:
The calculation of mean square due to error (MSE) is shown below:-
Since there are four treatments i.e H0: μ1 = μ2 = μ3 = μ4
And, the SSTR is 6,750
Based on this, the mean square due to error is
= [tex]\frac{SSTR}{n-1}[/tex]
[tex]= \frac{6,750}{4-1}[/tex]
= [tex]\frac{6,750}{3}[/tex]
= 2,250
Hence, the mean square due to error is 2,250
Therefore the correct option is d.
All the other information is not relevant. Hence ignored it
how many are 15 x 15 ?
Answer:
225
Step-by-step explanation:
Answer:
225
Step-by-step explanation:
Express it in slope-Intercept form
Answer:
Y=1/4x-4
Explanation: The y intercept is -4 that is your B. Using the rise over sun method the line rises 1 and goes to the right 4 making the slope 1/4 or .25
V(x, y, z) = 5x2 − 3xy + xyz (a) Find the rate of change of the potential at P(6, 6, 5) in the direction of the vector v = i + j − k.
Answer:
[tex]D_{\vec{v}}V(6,6,5)=48[/tex]
Step-by-step explanation:
You have the following potential function:
[tex]V(x,y,z)=5x^2-3xy+xyz[/tex] (1)
To find the rate of change of the potential at the point P(6,6,5) in the direction of v = i + j - k, you use the following formula:
[tex]D_{\vec{v}}V(x,y,z)=\bigtriangledown V(x,y,z)\cdot \vec{v}[/tex] (2)
First, you calculate the gradient of V:
[tex]\bigtriangledown V(x,y,z)=\frac{\partial}{\partial x}V(x,y,z)\hat{i}+\frac{\partial}{\partial y}V(x,y,z)\hat{i}+\frac{\partial}{\partial z}V(x,y,z)\hat{i}\\\\\bigtriangledown V(x,y,z)=(10x-3y+yz)\hat{i}+(-3x+xz)\hat{j}+(xy)\hat{k}\\\\\bigtriangledown V(6,6,5)=(10(6)-3(6)+(6)(5))\hat{i}+(-3(6)+(6)(5))\hat{j}+((6)(6))\hat{k}\\\\\bigtriangledown V(6,6,5)=72\hat{i}+12\hat{j}+36\hat{k}[/tex]
Next, you replace in the equation (2):
[tex]D_{\vec{v}}V(6,6,5)=(72\hat{i}+12\hat{j}+36\hat{k})\cdot(\hat{i}+\hat{j}-\hat{k})\\\\D_{\vec{v}}V(6,6,5)=48[/tex]
Then, the rate of change of the potential at the point P(6,6,5) in the direction of v, is 48.
A rectangular box has length 2 inches, width 8 inches, and a height of 10 inches. Find the angle between the diagonal of the box and the diagonal of its base. The angle should be measured in radians.
Answer:
a) diagonal box = 12.9 in
b) diagonal base = 8.2 in
Step-by-step explanation:
w = 8 in
h = 10 in
L = 2 in
required:
a) diagonal of the box
b) diagonal of its base
referring into the attached image
a) the diagonal of the box = sqrt ( w² + h² + L²)
diagonal box = sqrt (8² + 10² + 2²)
diagonal box = 12.9 in
b) diagonal of its base = sqrt ( w² + L²)
diagonal base = sqrt ( 8² + 2²)
diagonal base = 8.2 in
Rewrite 19/3 as a mixed number
Answer:
[tex]6\frac{1}{3}[/tex]
Step-by-step explanation:
You can divide 19 by 3 a total of 6 times with a remainder of 1.
Fizzy Waters promotes their alkaline water product for everyone on the basis that alkaline water is good for health as it neutralizes acids produced in the body. They boast having a mean alkalinity level of 50 mg/liter. Alkaline water has a higher pH level than regular drinking water and Fizzy Waters claims that its higher Hydrogen content provides better hydration than regular water. To test their claim, you contact Fizzy Waters and they allow you to collect samples from their manufacturing plant to test for yourself. You collect 100 random samples of their alkaline water and find that the mean and standard deviation are y = 32.2mg/liter and 14.4mg/liter. With 99% confidence, is there enough evidence to support their claim that the population mean exceeds 50 mg/liter?
Answer:
The mean of 50 mg/liter is not inside the 99% interval, so there is not enough evidence to support their claim.
Step-by-step explanation:
First we need to find the z-value for a confidence of 99%
The value of alpha for a 99% confidence is:
[tex]1-\alpha/2 = 0.99[/tex]
[tex]\alpha/2 = 0.01[/tex]
[tex]\alpha = 0.005[/tex]
Looking in the z-table, we have z = 2.575.
Now we can find the standard error of the mean:
[tex]\sigma_{\bar{x} }= s_x/\sqrt{n}[/tex]
[tex]\sigma_{\bar{x} }= 14.4/\sqrt{100}[/tex]
[tex]\sigma_{\bar{x} }=1.44[/tex]
Finding the 99% confidence interval, we have:
[tex]99\%\ interval = (\bar{x} - z\sigma_{\bar{x}}, \bar{x} + z\sigma_{\bar{x}})[/tex]
[tex]99\%\ interval = (32.2 - 2.575*1.44, 32.2 + 2.575*1.44)[/tex]
[tex]99\%\ interval = (28.492, 35.908)[/tex]
The mean of 50 mg/liter is not inside the 99% interval, so there is not enough evidence to support their claim.
6th grade math help me please :))
Answer:
b) a coefficientd) a constant1, 2, 4Step-by-step explanation:
Just definitions :)
Hope it helps <3
which is bigger 1 or
[tex] \frac{19}{9} [/tex]
Answer:
19/9 because it equals to 2.111.. Which is greater than 1
Step-by-step explanation:
By the way if it's right can i get brainliest.
Answer:
1 < 19/9
Step-by-step explanation:
1 vs 19/9
Rewriting 19/9 as 9/9 + 9/9+ 1/9
1 vs 1+1 +1/9
1 vs 2 1/9
1 < 19/9
The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1100 miles. What warranty should the company use if they want 96% of the tires to outlast the warranty? Round the answer to the nearest whole number
Answer:
61,925 miles
Step-by-step explanation:
Given :
The p-value of the tires to outlast the were warranty were given in the the question as = 0.96
Checking the normal distribution table, The probability that corresponds to 0.96
from the Normal distribution table is 1.75.
Mean : 'μ'= 60000 miles
Standard deviation : σ=1100
The formula for z-score is given by
: z= (x-μ)/σ
1.75=(x-60000)/1100
1925=x-60000
x=61925
Therefore, the tread life of tire should be 61,925 miles if they want 96% of the tires to outlast the warranty.
Segu
Find a formula for the nth term in this
arithmetic sequence:
a1 = 7, a2 = 4, a3 = 1, a4 = -2, ...
Answer:
The formula is 10 - 3n
Step-by-step explanation:
For an nth term in an arithmetic sequence
U( n ) = a + ( n - 1)d
Where n is the number of terms
a is the first term
d is the common difference
From the sequence above
a = 7
d = 4 - 7 = - 3
The formula for an nth term is
U(n) = 7 + (n - 1)-3
= 7 - 3n + 3
The final answer is
= 10 - 3n
Hope this helps you.
pls help help help help
Answer:
D
Step-by-step explanation:
We can plug in the numbers (15, 23, 25, 38, 53) into the equation for x, and see if we get the values given for the number of hits (4, 12, 14, 27, 47)
Write the limit as a definite integral on the interval [a, b], where ci is any point in the ith subinterval. Limit Interval lim ||Δ|| → 0 n (4ci + 11) i = 1 Δxi [−8, 6]
Answer:
The corresponding definite integral may be written as
[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x[/tex]
The answer of the above definite integral is
[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x = 98[/tex]
Step-by-step explanation:
The given limit interval is
[tex]\lim_{||\Delta|| \to 0} \sum\limits_{i=1}^n (4c_i + 11) \Delta x_i[/tex]
[tex][a, b] = [-8, 6][/tex]
The corresponding definite integral may be written as
[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x[/tex]
[tex]\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x[/tex]
Bonus:
The definite integral may be solved as
[tex]\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x \\\\\frac{4x^2}{2} + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\2x^2 + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\ 2(6^2 -(-8)^2 ) + 11(6 - (-8) \\\\2(36 - 64 ) + 11(6 + 8) \\\\2(-28 ) + 11(14) \\\\-56 +154 \\\\98[/tex]
Therefore, the answer to the integral is
[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x = 98[/tex]
Joan conducted a study to see how common binge drinking is on her college campus. She defined "frequent binge drinking" as having five or more drinks in a row three or more times in the past two weeks. Out of 593 students who replied to her survey, 64 fit this criterion. Joan wants to construct a significance test for her data. She finds that the proportion of binge drinkers nationally is 13.1%. The z statistic for this data is __________.
Answer:
z = -1.66
Step-by-step explanation:
Z-statistic:
[tex]z = \frac{X - p}{s}[/tex]
In which X is the found proportion.
p is the mean proportion.
[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex] is the standard error for the data.
Out of 593 students who replied to her survey, 64 fit this criterion.
This means that [tex]X = \frac{64}{593} = 0.108[/tex]
She finds that the proportion of binge drinkers nationally is 13.1%.
This means that [tex]p = 0.131[/tex]
Also
[tex]s = \sqrt{\frac{0.131*0.869}{593}} = 0.014[/tex]
The z statistic for this data is
[tex]z = \frac{X - p}{s}[/tex]
[tex]z = \frac{0.108 - 0.131}{0.014}[/tex]
[tex]z = -1.66[/tex]
Bob bought some land costing $15,540. Today, that same land is valued at $45,117. How long has Bob owned this land if the price of land has been increasing at 5 percent per year
Answer:
21.84 years
Step-by-step explanation:
From the compound interest formula;
F = P(1+r)^t .......1
ln(F/P) = tln(1+r)
t = ln(F/P)/ln(1+r) .......2
Where;
F = Final value = $45,117
P = Initial value = $15,540
r = rate = 5% = 0.05
t = time
Substituting the values into equation 2;
t = ln(45117/15540)/ln(1.05)
t = 21.84542292124 years
t = 21.84 years
It will take Bob 21.84 years
The ratio of sides of 2 similar cubes is 3:4. Larger cube has a volume of 1728 cubic meters. What is the volume of the smaller cube?
Answer:
See steps
Step-by-step explanation:
Volume of cubes is proportional to the cube of the side length.
Using proportions,
Volume of smaller cube / 1728 = (3/4)^3
Cross multiply,
Volume of smaller cube
= 1728 * (3/4)^3
= 1728 * (27/64)
= 729 cubic metres.
Note: all cubes are similar and each has 6 congruent faces.
What is an equation in point-slope form for the line that passes through the points (4,−1) and (−3,4)? y+4=−57(x+3) y+4=57(x+3) y−4=−57(x+3) y−3=−57(x+4) PLEASE HELP MEEEE
Answer:
Step-by-step explanation:
(4+1)/(-3-4)= -5/7
y + 1 = -5/7(x - 4)
or
y - 4= -5/7(x + 3)
Rationalize the denominator and simplify
Answer:
sqrt(70)/7
Step-by-step explanation:
sqrt(10/7)
sqrt ( a/b) = sqrt(a)/ sqrt(b)
sqrt(10) / sqrt(7)
But we don't leave a sqrt in the denominator, so multiply by sqrt(7) /sqrt(7)
sqrt(10) /sqrt(7) * sqrt(7) / sqrt(7)
sqrt(70)/ sqrt(49)
sqrt(70)/7
How do I solve this problem?
Answer:
It would take 1 more mile if he took route Street A and then Street B rather than just Street C.
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
We use the Pythagorean Theorem to find the length of Street C:
2² + 1.5² = c²
c = √6.25
c = 2.5
Now we find how much longer route A and B is compared to C:
3.5 - (2 + 1.5) = 3.5 - 2.5 = 1