Answer:
1.5
Step-by-step explanation:
Set uo an algabraic equation like so:
9.75/x=6.5
Solve by multiplying both sides by x
then you get 9.75=6.5x
Then you divide 6.5 on each side
x=1.5
Answer:
1.5
Step-by-step explanation:
9.75/5.5=1.5
A large container in the shape of a rectangular solid must have a volume of 480 m3. The bottom of the container costs $5/m2 to construct whereas the top and sides cost $3/ m2 to construct. Use Lagrange multipliers to find the dimensions of the container of this size that has the minimum cost
The dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
The given parameters are:
Volume = 480m^3Cost: $5 per square meter for the bottom, and $3 per square meter for the sides.Assume the dimensions of the container are: x, y and z.
The volume (V) would be:
[tex]V = xyz[/tex]
Substitute 480 for V
[tex]xyz =480[/tex]
And the objective cost function would be:
[tex]C =8xy + 6xz + 6yz[/tex]
Differentiate the cost function using Lagrange multipliers
[tex]8x + 6z = \lambda xz[/tex]
[tex]8y + 6z = \lambda yz[/tex]
[tex]6x + 6y = \lambda xy[/tex]
Divide equation (1) by (2)
[tex]\frac{8x + 6z}{8y + 6z} = \frac{\lambda xz}{\lambda yz}[/tex]
[tex]\frac{8x + 6z}{8y + 6z} = \frac{x}{y}[/tex]
Factor out 2
[tex]\frac{4x + 3z}{4y + 3z} = \frac{x}{y}[/tex]
Cross multiply
[tex]4xy + 3yz = 4xy + 3xz[/tex]
Evaluate the like terms
[tex]3yz = 3xz[/tex]
Divide both sides by 3z
[tex]y = x[/tex]
Divide the first equation by the third
[tex]\frac{8y + 6z}{6x + 6y} = \frac{\lambda yz}{\lambda xy}[/tex]
[tex]\frac{8y + 6z}{6x + 6y} = \frac{z}{x}[/tex]
Factor out 2
[tex]\frac{4y + 3z}{3x + 3y} = \frac{z}{x}[/tex]
Cross multiply
[tex]4xy+3xz = 3xz + 3yz[/tex]
Cancel out the common terms
[tex]4xy = 3yz[/tex]
Divide both sides by y
[tex]4x = 3z[/tex]
Make z the subject
[tex]z =\frac{4}{3}x\\[/tex]
So, we have:
[tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]
Recall that:
[tex]xyz =480[/tex]
Substitute [tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]
[tex]x \times x \times \frac 43x = 480[/tex]
So, we have:
[tex]\frac 43x^3 = 480[/tex]
Multiply both sides by 3/4
[tex]x^3 = 360[/tex]
Take the cube roots of both sides
[tex]x = \sqrt[3]{360}[/tex]
Recall that:
[tex]y = x[/tex]
So, we have:
[tex]y = \sqrt[3]{360}[/tex]
Also, we have:
[tex]z =\frac{4}{3}x\\[/tex]
So, we have:
[tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
Hence, the dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
Read more about Lagrange multipliers at:
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What is the approximate value of t?
Answer:
8.48
Step-by-step explanation:
36 + 36 = 72
t^2 = 72
t = 6[tex]\sqrt{2}[/tex] = 8.48
Answer: 6
Step-by-step explanation:
3,408 divided by 41
Explanation in traditional method
52 POINTS PLS HELP
Answer:
83.1219512195
Step-by-step explanation:
Hope this helps!
One research study of illegal drug use among 12- to 17-year-olds reported a decrease in use (from 11.4% in 1997) to 9.8% now. Suppose a survey in a large high school reveals that, in a random sample of 1046 students, report using illegal drugs. Use a 0.05 significance level to test the principal's claim that illegal drug use in her school is below the current national average.
Using the z-distribution, it is found that since the test statistic is more than the critical value for the left-tailed test, it is found that there is not enough evidence to conclude that illegal drug use in her school is below the current national average.
At the null hypothesis, it is tested if drug use in her school is not below the national average, that is:
[tex]H_0: p \geq 0.098[/tex]
At the alternative hypothesis, it is tested if it is below, that is:
[tex]H_1: p < 0.098[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.93 out of 1046 reported using illegal drugs, hence the parameters are:
[tex]n = 1046, \overline{p} = \frac{93}{1046} = 0.0889, p = 0.098[/tex]
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.0889 - 0.098}{\sqrt{\frac{0.098(0.902)}{1046}}}[/tex]
[tex]z = -0.99[/tex]
The critical value for a left-tailed test, as we are testing if the proportion is less than a value, is [tex]z^{\ast} = -1.645[/tex]
Since the test statistic is more than the critical value for the left-tailed test, it is found that there is not enough evidence to conclude that illegal drug use in her school is below the current national average.
To learn more about the use of the z-distribution to test an hypothesis, you can take a look at https://brainly.com/question/25584945
What is the number of solutions to the system of
equations?
Infinitely Many
Solutions
No Solution
One Solution
Two Solutions
Answer:
infinitely many solutions
Step-by-step explanation:
The lines over lap
Please help asap! I will mark brainliest for correct answer!!
a softball player hits a pitched ball when it is 4 feet above the ground. the initial velocity is 75 feet per second. Use the formula: h=-16t^2+vt+s. How long will it take for the ball to hit the ground?
Answer: Do the math, the positive solution
t = 5.0495 seconds (If it's wrong sorry, I havent done a problem like this one in awhile!)
Step-by-step explanation:
The minute hand of a clock has a length of 12 cm, and the hour hand has a length of 8 cm
a) How far does the tip of the minute hand travel in one hour?
b) How far does the tip of the hour hand travel in 12 hours?
c) How far does the tip of each hand travel in one week?
Answer:
I have no any ideas
Step-by-step explanation:
sorry
What is the volume of this container?
Answer:
64 in 2 is it the answers im not shure
Can someone help me please?
Answer: a=(3,-4)
B=(3,-1)
C=(5,-2)
Step-by-step explanation:
Translate and solve. The quotient of m and 6/7 is 5/6
Answer:
m / 6/7 = 5/6
m = 35
Step-by-step explanation:
Answer:
m = 5/7Step-by-step explanation:
The quotient of m and 6/7 is 5/6:
m ÷ 6/7 = 5/6m = 5/6 × 6/7m = 5/7a cylinder has a radius of 3 feet and a height of 2.1 feet. what is the approximate volume of the cylinder? use 3.14 for pi. 12.6 ftł 59.3 ftł 237.5 ftł 8550.2 ftł
Answer:
59.3ft³
Step-by-step explanation:
The formula for the volume of a cylinder is V= πr²h, where r is radius and h height.
So in our case, we have r= 3ft and h=2.1 ft and π≅3.14
So from the formula for the volume of a cylinder, we get 3.14*3²*2.1 = 59.3 ft³
The volume of the cylinder is about 59.3 ft³
PLEASE HELP QUESTION IN PIC
Answer:
(5, -4)
Step-by-step explanation:
Answer:
(5,-4)
Step-by-step explanation:
((0+10/2),(-2-6/2))
(10/2, -8/2)
(5,-4)
2x+5(x+1) = -8;
Can someone help me solve this problem step by step please?
Answer:
-13/7
Step-by-step explanation:
2x+5(x+1)=-8
2x+5x+5=-8
7x+5=-8
7x=-8-5
7x=-13
7x/7=-13/7
x=-13/7
Answer:
x = -13/7
Step-by-step explanation:
2x+5(x+1) = -8
2x+5x+5 = -8
7x+5 = -8
7x = -8-5
7x = -13
x = -13/7
how many possible number of facemask and face shield can an online seller could sell to get an amount of the least php2 000 based on the data above
During crawfish season, Xavier sells crawfish for $62. 50 per sack and charges a $20. 00 delivery fee. Write an equation that could be used to determine y, the total cost of x sacks of crawfish delivered to a customer.
The equation that could be used to determine y, the total cost of x sacks of crawfish delivered to a customer is y = 20 + 62.50x
Given:
cost per sack of crayfish = $62. 50
Delivery fee = $20. 00
y = Total cost
x = sacks of crawfish
The equation:
Total cost = Delivery fee + cost per sack of crayfish(sacks of crawfish)
y = 20 + 62.50x
Therefore, the equation that could be used to determine y, the total cost of x sacks of crawfish delivered to a customer is y = 20 + 62.50x
Learn more about equation:
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How i can answer this question, NO LINKS, if you answer correctly i will give u brainliest!
Answer: A. they will have too much butter
Step-by-step explanation: to much
look at the graph. which equation represents the graph?
how do i tell if an angel is comolentery, supplmentsry, or neither? I was not at school the day they showed me this?
Answer:
supplementary angles - two angles are supplementary when they add up to 180 degrees (a straight line)
complementary angles - two angles are complementary when they add up to 90 degrees (a right angle)
hopefully this helps! :)
Answer:
1. complementary
2. neither
3. supplementary
4. complementary (x = 6)
10x + 30 = 90 x + 3 = 9 x = 6
5. supplementary (x = 20)
4x + 40 + 3x = 180 7x = 140 x = 20
6. x = 50.5
2x + 79 = 180 2x = 101 x = 50.5
Step-by-step explanation:
When the measurement of the angles adds up to 90 degrees, the angles are complementary. When the sum of the angles is 180 degrees, then they are supplementary.
What is the probability that a student took AP Chemistry, given they did not get into their first-choice college? Enter
your answer as a decimal to the ten thousandths place.
Using conditional probability, it is found that there is a 0.2273 = 22.73% probability that a student took AP Chemistry, given they did not get into their first-choice college.
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened. [tex]P(A \cap B)[/tex] is the probability of both A and B happening. P(A) is the probability of A happening.In this problem:
Event A: Did not get into their first-choice college.Event B: Took AP chemistry.According to the chain given, the percentages associated with not getting into their first-choice college are:
0.1375(chemistry).0.1575(physics).0.24(Env Sci).0.07(Biology).Hence:
[tex]P(A) = 0.1375 + 0.1575 + 0.24 + 0.07 = 0.605[/tex]
The probability of both not getting into their first-choice college and taking chemistry is 0.1375, hence [tex]P(A \cap B) = 0.1375[/tex]
Then, the conditional probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1375}{0.605} = 0.2273[/tex]
0.2273 = 22.73% probability that a student took AP Chemistry, given they did not get into their first-choice college.
To learn more about conditional probability, you can take a look at https://brainly.com/question/14398287
Answer: 0.2273
Step-by-step explanation: because it says so <3
what percent of 81 is 51
Answer:
62.96%
Step-by-step explanation:
do this
51/81 ×100%
Answer:62.953%
Step-by-step explanation:
81 * (%) = 51
% = 51 / 81
% = 62.953
What is the equation of the line that passes through the point (-5, 6) and has
a
slope of o?
Answer:
y = 6
Step-by-step explanation:
A line with a slope of zero is a horizontal line parallel to the x- axis with equation
y = c
where c is the value of the y- coordinates the line passes through.
The line passes through (- 5, 6 ) with y- coordinate 6 , then
y = 6 ← equation of line
IS IT VALID OR NOT (explaining would be helpful) you want to determine how many students consider math to be their favorite school subject. you randomly survey 75 students. thirty-three students consider math to be their favorite subject while forty-two does not. so, you conclude that 40% of students at your school consider math to be their favorite subject.
Answer:
I would say not valid
Step-by-step explanation:
well, it would actually be 44% since 33/75= 0.44 to represent the number of ppl hat consider math their favorite subject
(a) The area of a rectangular garden is 5658 m?.
If the width of the garden is 69 m, what is its length?
(b) The perimeter of a rectangular window is 262 cm.
If the length of the window is 73 cm, what is its width?
A) Length is 82 m
B) Width is 58 cm
Hope this is helpful!
If no denominator equals zero, which expression is equivalent to ? A. B. C. D.
The expression [tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex] is equivalent to [tex]\dfrac{22x+48}{x^2-36}\\\\[/tex] and it can be determined by using LCM and fraction.
Given that,Expression;[tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex]
If no denominator equals zero,
We have to determine,Which expression is equivalent to the given expression?
According to the question,Expression;
[tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex]
If no denominator equals zero,
To determine the equivalent relation of the given equation following all the steps given below.
Step1; First take the LCM,[tex]\rm= \dfrac{15}{x-6}+\dfrac{7}{x+6}\\\\=\dfrac{15(x+6) + 7(x-6)}{(x-6) (x+6)}[/tex]
Step2; Multiply the terms and simplify the equation,[tex]\rm=\dfrac{15(x+6) + 7(x-6)}{(x-6) (x+6)}\\\\= \dfrac{15x+90 + 7x-42}{x(x+6) -6 (x+6)}\\\\= \dfrac{22x+48}{x^2+6x -6 x-36}\\\\= \dfrac{22x+48}{x^2-36}\\\\[/tex]
Hence, The expression [tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex] is equivalent to [tex]\dfrac{22x+48}{x^2-36}\\\\[/tex] .
For more details about Expression refer to the link given below.
https://brainly.com/question/14610993
PLEASE SHOW YOUR WORK !!! I REALLY NEED HELP
I did the math in the link below
PLS HELP ASAP ILL GIVE BRAINLKEST PLS THANKS
Answer:
y = 3x
Step-by-step explanation:
Let's select two points from the given graph.
(1,3) (3,9)
Now, let's use slope formula to find the slope.
m = y2-y1/x2-x1
= 9-3/3-1
= 6/2
= 3
Let's substitute/plug this value into the slope-intercept form.
y = 3x + b
We can see that the y-intercept is 0, from the graph.
b = 0
Therefore,
y = 3x
What is the common denominator of StartFraction 1 Over a EndFraction StartFraction 1 Over b EndFraction in the complex fraction StartFraction 1 Over a EndFraction minus StartFraction 1 Over b EndFraction divided by StartFraction 1 Over a EndFraction 1 Over b EndFraction?.
The common denominator is 1
Given the expression:
[tex]\frac{1/a-1/b}{1/a1/b}[/tex]Find the LCM of the numerator to have:
[tex]\dfrac{\frac{b-a}{ab} }{\frac{1}{a} \frac{1}{b} }[/tex]Simplify both the numerator and the denominator to have:
[tex]= \dfrac{\frac{b-a}{ab} }{\frac{1}{ab} }\\= \frac{b-a}{ab} \times ab\\=\frac{b-a}{1} \times 1 \\=\frac{b-a}{1}[/tex]
From the result, we can see that the common denominator is 1
Learn more about fractions here: https://brainly.com/question/17743912
Answer:
here is the correct answer for edge2022
Step-by-step explanation:
At Jared's school, he earns reward
points.
He has earned 350 points.
He wants to have at least 100 points left
at the end of year for prizes.
He wants to use 20 points each week
for Free-Sit Friday.
How many weeks can Jared have Free-
Sit Friday and still have at least 100
points at the end of the year?
Write the Inequality.
Answer:
ok so first take a way 100 from 350
250 then divide by 20
12
Hope This Helps!!!
Kyle was playing archery and shot 20 arrows. 30% of them hit the bullseye. how many of the arrows hit the bullseye?
Someone please help meh
Answer:
1100
Step-by-step explanation:
Answer:
A = 55.15
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos A = adj side / hypotenuse
cos A = 4/7
Taking the inverse cos of each side
cos ^-1 ( cos A) = cos ^-1( 4/7)
A =55.15009542
To the nearest hundredth
A = 55.15