Answer:
0
Step-by-step explanation:
Hello, dividing by 0 is not defined. so
[tex]\dfrac{2x^2}{6x}[/tex]
is defined for x different from 0
This being said, we can simplify by 2x
[tex]\dfrac{2x^2}{6x}=\dfrac{2x*x}{3*2x}=\dfrac{1}{3}x[/tex]
and this last expression is defined for any real number x.
Thank you
Findℒ{f(t)}by first using a trigonometric identity. (Write your answer as a function of s.)f(t) = 12 cost −π6
Answer:
[tex]L(f(t)) = \dfrac{6}{S^2+1} [\sqrt{3} \ S +1 ][/tex]
Step-by-step explanation:
Given that:
[tex]f(t) = 12 cos (t- \dfrac{\pi}{6})[/tex]
recall that:
cos (A-B) = cos AcosB + sin A sin B
∴
[tex]f(t) = 12 [cos\ t \ cos \dfrac{\pi}{6}+ sin \ t \ sin \dfrac{\pi}{6}][/tex]
[tex]f(t) = 12 [cos \ t \ \dfrac{3}{2}+ sin \ t \ sin \dfrac{1}{2}][/tex]
[tex]f(t) = 6 \sqrt{3} \ cos \ (t) + 6 \ sin \ (t)[/tex]
[tex]L(f(t)) = L ( 6 \sqrt{3} \ cos \ (t) + 6 \ sin \ (t) ][/tex]
[tex]L(f(t)) = 6 \sqrt{3} \ L [cos \ (t) ] + 6\ L [ sin \ (t) ][/tex]
[tex]L(f(t)) = 6 \sqrt{3} \dfrac{S}{S^2 + 1^2}+ 6 \dfrac{1}{S^2 +1^2}[/tex]
[tex]L(f(t)) = \dfrac{6 \sqrt{3} +6 }{S^2+1}[/tex]
[tex]L(f(t)) = \dfrac{6( \sqrt{3} \ S +1 }{S^2+1}[/tex]
[tex]L(f(t)) = \dfrac{6}{S^2+1} [\sqrt{3} \ S +1 ][/tex]
one third multiplied by the sum of a and b
Answer:
1/3(a+b)
hope it helps :>
HELP ASAP ROCKY!!! will get branliest.
Answer:
work pictured and shown
Answer:
Last one
Step-by-step explanation:
● [ ( 3^2 × 5^0) / 4 ]^2
5^0 is 1 since any number that has a null power is equal to 1.
●[ (3^2 ×1 ) / 4 ]^2
● (9/4)^2
● 81 / 16
I need help please help meee I don’t understand
Answer:
204
Step-by-step explanation:
To simplify the shape, you can do multiple things. I've opted to shave down both prongs to take it from a 'T' shape to a rectangular prism.
For height of the prongs, take 4 from 6.
6 - 4 = 2
Divide by 2 as there are 2 prongs.
2 / 2 = 1
Remember L * W * H
6 * 3 * 1 = 18
Remember that there are two prongs!
3 + 4 = 7
6 * 7 * 4 = 168
168 + 2(18) = 204
Max believes that the sales of coffee at his coffee shop depend upon the weather. He has taken a sample of 5 days. Below you are given the results of the sample.
Cups of Coffee Sold Temperature
350 50
200 60
210 70
100 80
60 90
40 100
A. Which variable is the dependent variable?
B. Compute the least squares estimated line.
C. Compute the correlation coefficient between temperature and the sales of coffee.
D. Predict sales of a 90 degree day.
Answer:
1. cups of coffee sold
2.Y = 605.7 - 5.943x
3. -0.952
4. 70.84
Step-by-step explanation:
1. the dependent variable in this question is the cups of coffee sold
2. least square estimation line
Y = a+bx
we have y as the cups of coffee sold
x as temperature.
first we will have to solve for a and then b
∑X = 450
∑Y = 960
∑XY = 61600
∑X² = 35500
∑Y² = 221800
a = ∑y∑x²-∑x∑xy/n∑x²-(∑x)²
a = 960 * 35500-450*61600/6*35500-450²
a = 6360000/10500
= 605.7
b = n∑xy - ∑x∑y/n∑x²-(∑x)²
= 6*61600 - 450*960/6*35500 - 450²
= -5.943
the regression line
Y = a + bx
Y = 605.7 - 5.943x
3. we are to find correlation coefficient
r = n∑xy - ∑x∑y multiplied by√(n∑x²-(∑x)² * (n∑y² - (∑y)²)
= 6*61600 -960*450/√(6*35500 - 450²)*(6*221800 - 960²)
=-62400/√4296600000
= -62400/65548.5
= -0.952
4. we have to predict sales of a 90 degree day fro the regression line
Y = 605.7 - 5.943x
y = 605.7 - 5.943(90)
y = 605.7 - 534.87
= 70.84
An investigator claims, with 95 percent confidence, that the interval between 10 and 16 miles includes the mean commute distance for all California commuters. To have 95 percent confidence signifies that
Answer:
Hello the options to your question is missing below are the options
A) if sample means were obtained for a long series of samples, approximately 95 percent of all sample means would be between 10 and 16 miles
B.the unknown population mean is definitely between 10 and 16 miles
C.if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians
D.the unknown population mean is between 10 and 16 miles with probability .95
Answer : if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians ( c )
Step-by-step explanation:
95% confidence
interval = 10 to 16 miles
To have 95% confidence signifies that if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians
confidence interval covers a range of samples/values in the interval and the higher the % of the confidence interval the more precise the interval is,
Kenji earned the test scores below in English class.
79, 91, 93, 85, 86, and 88
What are the mean and median of his test scores?
Answer:
mean=87
median=87
Step-by-step explanation:
mean=sum of test score/number of subject
mean=79+91+93+85+86+88/6
mean=522/6
mean=87
Literal meaning of median is medium.
To find the number which lies in the medium, we must rearrange the number in ascending.
79, 91, 93, 85, 86, 88
79, 85, 86, 88, 91, 93
86+88/2=87
Hope this helps ;) ❤❤❤
Let me know if there is an error in my answer.
Let X denote the day she gets enrolled in her first class and let Y denote the day she gets enrolled in both the classes. What is the distribution of X
Answer:
X is uniformly distributed.
Step-by-step explanation:
Uniform Distribution:
This is the type of distribution where all outcome of a certain event have equal likeliness of occurrence.
Example of Uniform Distribution is - tossing a coin. The probability of getting a head is the same as the probability of getting a tail. The have equal likeliness of occurrence.
The quotient of 8 and the difference of three and a number.
Answer: 8÷(3-x)
Answer:
Below
Step-by-step explanation:
● 8 ÷ (3-x)
Dividing by 3-x is like multiplying by 1/(3-x)
● 8 × (1/3-x)
● 8 /(3-x)
A line passes through (-5, -3) and is parallel to -3x - 7y = 10. The equation of the line in slope-intercept form is _____
Answer:
-3x - 7y = 36
Step-by-step explanation:
The given line -3x - 7y = 10 has an infinite number of parallel lines, all of the form -3x - 7y = C.
If we want the equation of a line parallel to -3x - 7y = 10 that passes through (-5, -3), we substitute -5 for x in -3x - 7y = 10 and substitute -3 for y in -3x - 7y = 10:
-3(-5) - 7(-3) = C, or
15 + 21 = C, or C = 36
Then the desired equation is -3x - 7y = 36.
Salaries of 42 college graduates who took a statistics course in college have a mean, , of . Assuming a standard deviation, , of $, construct a % confidence interval for estimating the population mean .
Answer:
The 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).
Step-by-step explanation:
The complete question is:
Salaries of 42 college graduates who took a statistics course in college have a mean, [tex]\bar x[/tex] of, $64, 100. Assuming a standard deviation, σ of $10,016 construct a 99% confidence interval for estimating the population mean μ.
Solution:
The (1 - α)% confidence interval for estimating the population mean μ is:
[tex]CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]
The critical value of z for 99% confidence interval is:
[tex]z_{\alpha/2}=z_{0.01/2}=z_{0.005}=2.57[/tex]
Compute the 99% confidence interval for estimating the population mean μ as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=64100\pm 2.58\times\frac{10016}{\sqrt{42}}\\\\=64100+3987.3961\\\\=(60112.6039, 68087.3961)\\\\\approx (60112.60, 68087.40)[/tex]
Thus, the 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).
A mass of 5 kg stretches a spring 10 cm. The mass is acted on by an external force of 10sin( t ) N(newtons) and moves in a medium that imparts a viscous force of 2 N
when the speed of the mass is 4 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 3 cm/s, formulate the initial value problem describing the motion of the mass.
A)Find the solution of the initial value problem in the above problem.
B)Plot the graph of the steady state solution
C)If the given external force is replaced by a force of 2 cos(ωt) of frequency ω , find the value of ω for which the amplitude of the forced response is maximum.
Answer:
A) C1 = 0.00187 m = 0.187 cm, C2 = 0.0062 m = 0.62 cm
B) A sample of how the graph looks like is attached below ( periodic sine wave )
C) w = [tex]\sqrt[4]{3}[/tex] is when the amplitude of the forced response is maximum
Step-by-step explanation:
Given data :
mass = 5kg
length of spring = 10 cm = 0.1 m
f(t) = 10sin(t) N
viscous force = 2 N
speed of mass = 4 cm/s = 0.04 m/s
initial velocity = 3 cm/s = 0.03 m/s
Formulating initial value problem
y = viscous force / speed = 2 N / 0.04 m/s = 50 N sec/m
spring constant = mg/ Length of spring = (5 * 9.8) / 0.1 = 490 N/m
f(t) = 10sin(t/2) N
using the initial conditions of u(0) = 0 m and u"(0) = 0.03 m/s to express the equation of motion
the equation of motion = 5u" + 50u' + 490u = 10sin(t/2)
A) finding the solution of the initial value
attached below is the solution and
B) attached is a periodic sine wave replica of how the grapgh of the steady state solution looks like
C attached below
a
A solid metal cone of base radius a cm and height 2a cm is melted and solid
spheres of radius are made without wastage. How many such spheres can be
made?
volume of a cone
.
.
.
volume of sphere
.
.
number of spheres that can be made......
.
.
hence a hemisphere can be formed
Match the base to the corresponding height.
Base (b)
Height (h)
b
h
h
b
The base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.
What is a triangle?Triangle is the closed shaped polygon which has 3 sides and 3 interior angles. The height of the triangle is the dimension of the elevation from the opposite peak to the length of the base.
Thus, the base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.
In the given figure, three triangles is shown with base and height. Here,
The base 1 is matched with height 2, as the height shown in figure 2 is the dimension of the elevation from the opposite peak to the length of the base 1.Similarly, base 2 is matched with height 3.Base 3 is matched with height 1.
Thus, the base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.
Learn more about the base and height of the triangle here;
https://brainly.com/question/26043588
#SPJ2
The cost, C, in United States Dollars ($), of cleaning up x percent of an oil spill along the Gulf Coast of the United States increases tremendously as x approaches 100. One equation for determining the cost (in millions $) is:
Complete Question
On the uploaded image is a similar question that will explain the given question
Answer:
The value of k is [tex]k = 214285.7[/tex]
The percentage of the oil that will be cleaned is [tex]x = 80.77\%[/tex]
Step-by-step explanation:
From the question we are told that
The cost of cleaning up the spillage is [tex]C = \frac{ k x }{100 - x }[/tex] [tex]x \le x \le 100[/tex]
The cost of cleaning x = 70% of the oil is [tex]C = \$500,000[/tex]
Now at [tex]C = \$500,000[/tex] we have
[tex]\$ 500000 = \frac{ k * 70 }{100 - 70 }[/tex]
[tex]\$ 500000 = \frac{ k * 70 }{30 }[/tex]
[tex]\$ 500000 = \frac{ k * 70 }{30 }[/tex]
[tex]k = 214285.7[/tex]
Now When [tex]C = \$900,000[/tex]
[tex]x = 80.77\%[/tex]
find the area of square whose side is 2.5 cm
Answer:
6.25
Step-by-step explanation:
2.5 *2.5=6.25
Answer:
6.25cm^2.
Step-by-step explanation:
To find the area of a square, you multiply the two sides, 2.5✖️2.5.
This gives the area of 6.25cm^2.
Hope this helped!
Have a nice day:)
602/100 into a decimal describe plz
Answer:
6.02
six point zero two
Step-by-step explanation:
Answer:
602 / 100= 6,02
Step-by-step explanation:
602 to divide 100 = 6,02
A box contains 40 identical discs which are either red or white if probably picking a red disc is 1/4. Calculate the number of;
1. White disc.
2. red disc that should be added such that the probability of picking a red disc will be 1/4
Find usubscript10 in the sequence -23, -18, -13, -8, -3, ...
Step-by-step explanation:
utilise the formula a+(n-1)d
a is the first number while d is common difference
Answer:
22
Step-by-step explanation:
Using the formular, Un = a + (n - 1)d
Where n = 10; a = -23; d = 5
U10 = -23 + (9)* 5
U10 = -23 + 45 = 22
Foram prescritos 500mg de dipirona para uma criança com febre.Na unidade tem disponivel ampola de 1g/2ml.Quantos g vão ser administrados no paciente
De acordo com a disponibilidade da unidade, há apenas a seguinte dosagem: 1g/2mL - ou seja, uma grama de dipirona a cada 2mL
O enunciado está meio mal formulado, pois é dito que foram prescritos 500mg de dipirona e é essa quantidade de farmaco que a criança tem que tomar. Deseja-se saber quantos mL deverao ser administrados.
Fazendo a classica regra de 3, podemos chegar no volume desejado:
(atentar que 500mg = 0,5g)
g mL
1 --------- 2
0,5 --------- X
1 . X = 0,5 . 2
X = 1mLBRAINLIEST IF CORRECT!!! and 15 points solve for z -cz + 6z = tz + 83
Answer:
z = 83/( -c+6-t)
Step-by-step explanation:
-cz + 6z = tz + 83
Subtract tz from each side
-cz + 6z -tz= tz-tz + 83
-cz + 6z - tz = 83
Factor out z
z( -c+6-t) = 83
Divide each side by ( -c+6-t)
z( -c+6-t)/( -c+6-t) = 83/( -c+6-t)
z = 83/( -c+6-t)
If f(x)=x/2-3and g(x)=4x^2+x-4, find (f+g)(x)
Step-by-step explanation:
(f+g)(x) = f(x) + g(x)
= x/2-3 + 4x²+x+4
= ..........
Time
(minutes)
Water
(gallons)
1
16.50
1.5
24.75
2
33
find the constant of proportionality for the second and third row
Answer:
16.50
Step-by-step explanation:
Constant of proportionality = no of gallons of water per 1 minute.
In the first row, we have 16.50 gallons of water per 1 minute.
In the 2nd row, we have 24.75 gallons of water in 1.5 minutes. In 1 minute, we will have 24.75 ÷ 1.5 = 16.50 gallons
In the 3rd row, we have 33 gallons in 2 minutes. In 1 minute, we will have 33 ÷ 2 = 16.50 gallons.
We can see that there seems to be the same constant of proportionality for the 2nd and 3rd row, which is 16.50.
Thus, a relationship between gallons of water (w) and time (t), considering the constant, 16.50, can be written as: [tex] w = 16.50t [/tex]
This means the constant of proportionality, 16.50, is same for all rows.
5x+4(-x-2)=-5x+2(x-1)+12
Answer:
x=9/2
Step-by-step explanation:
Let's solve your equation step-by-step.
5x+4(−x−2)=−5x+2(x−1)+12
Step 1: Simplify both sides of the equation.
5x+4(−x−2)=−5x+2(x−1)+12
5x+(4)(−x)+(4)(−2)=−5x+(2)(x)+(2)(−1)+12 (Distribute)
5x+−4x+−8=−5x+2x+−2+12
(5x+−4x)+(−8)=(−5x+2x)+(−2+12) (Combine Like Terms)
x+−8=−3x+10
x−8=−3x+10
Step 2: Add 3x to both sides.
x−8+3x=−3x+10+3x
4x−8=10
Step 3: Add 8 to both sides.
4x−8+8=10+8
4x=18
Step 4: Divide both sides by 4.
4x/4=18/4
x=9/2
Please answer this correctly without making mistakes
Answer:
1/8
Step-by-step explanation:
3/8-1/8-1/8=1/8
88 feet/second = 60 miles/hour. How many feet per second is 1 mile/hour? (Hint: divide both sides of the equation
by the same amount.)
Round to the nearest thousandth.
One mile per hour is equivalent to
ao feet/second
help pls:Find all the missing elements
Step-by-step explanation:
Using Sine Rule
[tex] \frac{ \sin(a) }{ |a| } = \frac{ \sin(b) }{ |b| } = \frac{ \sin(c) }{ |c| } [/tex]
[tex] \frac{ \sin(42) }{5} = \frac{ \sin(38) }{a} [/tex]
[tex]a = \frac{5( \sin(38))}{ \sin(42) } [/tex]
[tex]a = 4.6[/tex]
[tex] \frac{ \sin(42) }{5} = \frac{ \sin(100) }{b} [/tex]
[tex]b= \frac{5( \sin(100))}{ \sin(42) } [/tex]
[tex]b = 7.4[/tex]
please help !! Solve –2.5x ≤ 25
Answer:
x ≥-10
Step-by-step explanation:
–2.5x ≤ 25
Divide each side by -2.5, remembering to flip the inequality
–2.5x/-2.5 ≥ 25 /-2.5
x ≥-10
Answer:
[tex]x\leq -10[/tex]
Step-by-step explanation:
[tex]-2.5x\leq 25[/tex]-----> Multiply by -1:
[tex]2.5x\geq -25[/tex]-----> Divide by 2.5:
[tex]x\geq -10[/tex]
Hope this helps!
BRAINLIST AND A THANK YOU AND 5 stars WILL BE REWARDED PLS ANSER
Answer:
The first picture's answer would be (6, 21)
Step-by-step explanation:
You have to find the points on the 8th and the 9th day, and then you would add them together, and then divide by two finding the average, which would be 24 and 18, so when added, you get 42, divided by 2 you get 21. You look on the graph for the point with 21, and you find it is on 6.
If the normality requirement is not satisfied (that is, np(1p) is not at least 10), then a 95% confidence interval about the population proportion will include the population proportion in ________ 95% of the intervals. (This is a reading assessment question. Be certain of your answer because you only get one attempt on this question.)
Answer:
less than
Step-by-step explanation:
If the normality requirement is not satisfied (that is, np(1 - p) is not at least 10), then a 95% confidence interval about the population proportion will include the population proportion in _less than__ 95% of the intervals.
The confidence interval consist of all reasonable values of a population mean. These are value for which the null hypothesis will not be rejected.
So, let assume that If the 95% confidence interval contains the value for the hypothesized mean, then the sample mean is reasonably close to the hypothesized mean. The effect of this is that the p- value is going to be greater than 0.05, so we fail to reject the null hypothesis.
On the other hand,
If the 95% confidence interval do not contains the value for the hypothesized mean, then the sample mean is far away from the hypothesized mean. The effect of this is that the p- value is going to be lesser than 0.05, so we reject the null hypothesis.
