If the dimensions of the cardboard sheet is 16 inches by 10 inches , then the maximum volume of the box is 144 in³ .
In the question ,
it is given that the length of the sheet is = 16 inch
and width of the sheet is = 10 inch
let width of box be ⇒ "w" ,
let length of box be ⇒ "l"
let the length of the corner cut out be = "x"
let volume of box be ⇒ "V" ;
we need to find the point of dV/dx that is maximum ,
given width = 16 ; and length = 10 ,
we have : width = x + w + x ⇒ w = 2(8 - x)
length = x + l + x = 10 ⇒ l = 2(5 - x)
the Volume of rectangular box is written as ; V = w*l*x ;
substituting the values of w , l and x ,
we get ;
V = 2(8 - x)2(5 - x)x
V = 4x³ - 52x² + 160x
differentiating with respect to "x" , and for critical point equating it to 0 ,
we have ;
12x² - 104x + 160 = 0
solving the above quadratic, we get ;
x = 2 & x = 20/3 .
On substituting the values , in d²V/dx² = 24x - 104 < 0 for x = 2 ,
that is maximum ;
Substituting x = 2 , in the V = 4x³ - 52x² + 160x ,
we get ;
Volume of the box as 144 in³ .
Therefore , the maximum volume of the box is = 144 in³ .
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Answer:
d
Step-by-step explanation:
d
What happens when you have a double negative?
If a line on the coordinate plane increases as you read it from left to right, what do you know about the slope of that line??
The slope has a value of 1.
The slope has a value of 0.
The slope is positive.
The slope is negative.
The slope m of a line passing through two points (x1 , y1) and (x2 , y2) is:
m = (y2 − y1) / (x2 − x1)
If the graph of a line rises from left to right, the slope is positive.
What is slope ?
Slope is a ratio and can have a value that is positive, negative, equal to zero, or undefined. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run".
What is positive slope ?
A positive slope means that two variables are positively related—that is, when x increases, so does y, and when x decreases, y also decreases. Graphically, a positive slope means that as a line on the line graph moves from left to right, the line rises. We will learn in other sections that “price” and “quantity supplied” have a positive relationship; that is, firms will supply more when the price is higher.
The slope m of a line passing through two points (x1 , y1) and (x2 , y2) is:
m = (y2 − y1) / (x2 − x1)
If the graph of a line rises from left to right, the slope is positive.
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need help on this please!!!
In step 1, y was made the subject of the second equation to get:
y=5x-4
To proceed, the next step is to substitute the expression into the other equation, not the equation we solved for y.
8x+2y=-12
8x+2(5x-4)=-12
8x+10x-8=-12
18x=-12+8
18x=-4
x=-[tex]\frac{4}{18}[/tex]
x=[tex]\frac-{2}{9}[/tex]
answer= the value of x is -2/9
Write an equation of the line passing through point p(3 8) that is parallel to the line y=1/5(x+4).
The equation of the line is y = 1/5(x + 37). The standard equation of a instantly line is y = mx + c, in which m is the gradient, and y = c is the cost in which the road cuts the y-axis.
This range c is known as the intercept at the y-axis. The equation of a instantly line with gradient m and intercept c at the y-axis is y = mx + c. The equation of a instantly line is y=mx+c y = m x + c m is the gradient and c is the peak at which the road crosses the y -axis, additionally referred to as the y -intercept.
Since equation have new line which is parallel y = 1/5(x + 4), and 1/5 is most the gradient for the line y = 1/5(x + 4), this is the new line is 1/5.
Using the equation we can form a line in slope-point form,
[tex]\frac{y-y_{1} }{x-x_{1} } = m[/tex]
where (x₁, y₁) = (3, 8) and m = 1/5
Substituting the values for all variables into the equation, we have
[tex]\frac{y-y_{1} }{x-x_{1} } = m\\\frac{y-8 }{x-3 } = m\\[/tex]
Cross-multiplying. we have
5(y - 8) = x - 3
Expanding the bracket, we have
5y - 40 = x - 3
5y = x - 3 + 40
5y = x + 37
y = 1/5(x + 37)
So, the equation of the line is y = 1/5(x + 37)
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Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.
For any value of x, g(x) will always be greater than h(x).
For any value of x, h(x) will always be greater than g(x).
g(x) > h(x) for x = -1.
g(x) < h(x) for x = 3.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
The statements that are true for functions g(x) = x² and h(x) = -x² are given as follows:
g(x) > h(x) for x = -1.For positive values of x, g(x) > h(x).For negative values of x, g(x) > h(x).What is the relation between the functions?The functions for this problem are defined as follows:
g(x) = x².h(x) = -x².The function h(x) is given by the multiplication of the function g(x) by -1, meaning that it is the reflection over the x-axis of the function g(x).
The two quadratic functions share the same vertex at the origin, meaning that it cannot be affirmed that one function will always be greater than the other for all values of x.
However, considering that the x² function is non-negative in all it's domain, the reflected function -x² will be non-positive at all it's domain, they are equal only at the origin, which is the vertex, all for all remaining non-zero values, g(x) is greater than h(x).
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Which models represent 56 as a sum of fractions with a common denominator of 6?
Answer:
Use a model to find the sum of two fractions with the same denominator
Add fractions with a common denominator without a model
Add fractions with a common denominator that contain a variable
Step-by-step explanation:
j
Suppose you are using the Pythagorean theorem to
find the length of the base of the given triangle. Which
expression is appropriate for this situation?
Using the Pythagorean Theorem, the length of the base is: 15 units.
What is the Pythagorean Theorem?The Pythagorean theorem is used to find any of the length of the legs or hypotenuse of a right triangle if we know any two measures of its side. The theorem is given as: the square of the hypotenuse = sum of the squares of the legs of the right triangle.
It can be expressed as c² = a² + b², where c is the longest side of the right triangle.
Note: The hypotenuse is the longest side of the triangle.
Thus, given the triangle in the image below, where:
c = 25
a = 20
b = length of the base
The expression that would be appropriate for this situation would be written based on the Pythagorean Theorem, which is:
b = √(c² - a²)
Substitute
b = √(25² - 20²)
b = 15 units
The length of the base is: 15 units.
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every day jo practices her tennis serve by continually serving until she has had a total of 50 successful serves. if each of her serves is, independently of previous ones, successful with probability .4, approximately what is the probability that she will need more than 100 serves to accomplish her goal?
She needs 50 successful serves in the first 100 to attain her target. A 2% chance exists that this will occur.
She therefore has a 98% chance of requiring more than 100 serves to achieve her objective.
What is a probability?The study of probability, which is the potential of any event happening, is a field of mathematics that deals with the occurrence of random events. The probability value is given on a scale from 0 to 1.
How do you find probability?The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood that something will occur by the likelihood that it won't.
Jo must not complete 50 successful serves in her first 100 attempts in order to need more than 100 serves.
With n=100 and p=0.4, our probability sample of potential outcomes has a binomial distribution.
We will use a normal distribution to approximate n because it is a big enough number. The normal distribution's characteristics are as follows:
To ensure that she receives more than 100 serves, we must determine the likelihood that there will be fewer than 50 successful services. Such is:
We determine X's z value as follows:
Next, we have
That indicates that there is a 98% chance she will require more than 100 serves to accomplish her objective.
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10 yards is how many inches?
Answer:
360 inches.
Step-by-step explanation:
because 1 yard is 36 inches (3 rulers) so just multiply 36 by your number of yards.
How do you find (1+i)^4?
Using the square formula, the value of (1+i)^4 is -4.
The square formula is the algebraic identity which is used to find the square or difference of the sum of two terms. The square of sum of the two terms and can be calculated by multiplying the binomial by itself. The general form of square formula to find the square of the sum of two terms is given by: (a + b)^2 = a^2 + 2ab + b^2 where a and b are variables.
The given expression can be rewritten as binomial with exponent:
((1 + i)^2)^2
Using the square formula to find the square of the sum of two terms to the (1 + i)^2. Hence,
(1 + i)^2 = 1 + 2i + i^2
As 'i' iota is the square root of negative 1, i^2 = -1
1 + 2i -1 = 2i
Therefore,
(2i)^2 = 4i^2 = 4*-1 = -4
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the manufacturer of cans of salmon that are supposed to have a net weight of 6 ounces tells you that the net weight is actually a normal random variable with a mean of 6.16 ounces and a standard deviation of 0.13 ounce. suppose that you draw a random sample of 38 cans. find the probability that the mean weight of the sample is less than 6.15 ounces.
The probability that the mean weight of the sample is less than 6.15 ounces as per the given data is 0.1806.
Mean, μ = 6.16 ounces
Standard Deviation, σ = 0.13 ounce
Sample size, n = 38
We are informed that the weight of the cans is distributed in a bell-shaped manner, which is a normal distribution.
Formula:
Z-score = ( x - ц) /standard deviation
Standard error due to sampling
=SD/√n
=0.13/ √(38)
=0.021
P(weight of the sample is less than 6.15 ounces)
P(X < 6.15) =P( Z< (6.15 - 6.16)/0.021 )
= P(Z> -0.476)
=0.1806 ( as per the Z- score table)
The probability that the sample's mean weight is less than 6.15 ounces is 0.1806.
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How do you simplify (2−i) / (5+i) ?
To simplify [tex]\frac{2-i}{5+i} = \frac{9}{26} -\frac{7}{26} i[/tex] , multiply the numerator and denominator by the conjugate of the denominator.
A complex number's conjugate A+bi equals a-bi. A real number is the result of a complex number and its conjugate. That fact will be used here.
[tex]\frac{2-i}{5+i} =\frac{2-i}{5+i} . \frac{5-i}{5-i}[/tex]
[tex]= \frac{(2-i)(5-i)}{(5+i)(5-i)}[/tex]
[tex]=\frac{10-2i-5i-1}{25-5i+5i+1}[/tex]
[tex]=\frac{9-7i}{26}[/tex]
[tex]=\frac{9}{26}-\frac{7}{26}i[/tex]
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4 Which trinomial is equivalent to
3(x-2)²-2(x-1)?
1) 3x²-2x-10
2)
3x² - 2x - 14
3)
3x² - 14x+10
4)
3x²-14x+14
Answer: 4) 3x²-14x+14
Explanation:
3(x-2)²-2(x-1)Use the binomial theorem (a−b)² = a² - 2ab + b² to expand (x-2)².
3(x²-4x+4)-2(x-1)Use the distributive property to multiply 3 by x²-4x+4.
3x²-12x+12-2(x-1)Use the distributive property to multiply −2 by x−1.
3x²-12x+12-2x+2Combine −12x and −2x to get −14x.
3x²−14x+12+2Add 12 and 2 to get 14.
3x²-14x+14It is 3x²+14x+14, the trinomial equivalent to 3(x-2)²-2(x-1). OPTION 4.
*URGENT* Sam has 2 part time jobs. At the grocery store, he earns $8/h and at the library, he earns $10/h. Before going on vacation, he would like to save $280. Determine the fewest number of hours he would need to work to reach his goal.
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
The fewest number of hours he would need to work to reach his goal of $280 is 28 hours working in the library.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
Amount to earn = $280
Grocery store:
Earnings per hour = $8
1 hour = $8
Multiply 280/8 on both sides.
280/8 x 1 hour = $280
35 hours = $280
Library:
Earnings per hour = $10
1 hour = $10
Multiply 280/10 on both sides.
28 hours = $280
We see that,
Working in the Library would make $280 in fewer hours than working in the grocery store.
Thus,
The fewest number of hours he would need to work to reach his goal of $280 is 28 hours working in the library.
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There are 3 fewer yellow beads than red beads. There are twice as many green beads as yellow beads. Write expressions for the number of red, green, and yellow beads.
Answer:
yellow = red - 3 and green = yellow x 2 and red = yellow + 3
or
green= (red-3) x 2
Step-by-step explanation:
Three fewer yellow than read is the same as saying red -3
twice as many green as yellow is the same as yellow x 2
if green is yellow x 2 you can substitute yellow for the equation to find yellow
you can flip the equation for yellow around by doing inverse operations. To have the equation equal red you need to move the three by doing its inverse. The opposite of subtraction is addition so you'd add 3 to each side, getting rid of the -3 and isolating the red to make the equation red=yellow+3
(3,3) and (1,-3) in linear equation
Answer:
3 x - y = 6
Step-by-step explanation:
the equation of a line is
ax + by = c
express the slope initially in the form of y=mx+b
b is the y- intercept (the point where it crosses the y axis)
m is basically the slope, to find m, you have to use a specific formula...
m = (y2 – y1) / (x2 – x1)
(x1, y1) (x2, y2) are 2 coordinate points...
(3,3) and (1, -3)
m = -3 -3 divided by 1 - 3 = -6/-2 = 3
so your formula for now is .. y = 3x + b (you dont know what b is yet)
Now, substitute the points into the equation.
3 = 9 + b. b = -6
final formula is,
Y=3x -6
u can also rearrange the formula in a standard form:
3x - y = 6
I REALLY HOPE THIS HELPS U!!
How do you convert 15 nm into km?
15 nm converted into km gives 1·5 × [tex]10^{-11}[/tex] km.
A process involving numerous stages, multiplication or division, especially a conversion factor, can be referred to as Unit Conversion. Additionally, rounding and determining the number of significant digits may be necessary steps in the procedure.
For measuring various properties, including length, weight, capacity, and temperature, many units of conversion are employed. We can change the units of measurement in mathematics to better understand.
Unit conversions are used to represent an amount in a different unit.
We have to convert 15 nm into km.
1 nm = [tex]10^{-12}[/tex] km
15 nm = 15 × [tex]10^{-12}[/tex] km
= 1·5 × [tex]10^{-11}[/tex] km
Thus, 15 nm converted into km gives 1·5 × [tex]10^{-11}[/tex] km.
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Solve the given proportion 7/x 21/6 x = [?] Enter
Answer:
x=2
Step-by-step explanation:
7÷x=22÷6
cross multiply
7×6=21×x
21x=42
21x/21=42/21
x=2
suppose that from previous evidence, anthropologists had believed that for each 1 mm increase in chord length, cranial capacity would be expected to increase by 20 cm3. do the data given here strongly contradict prior belief? use a 0.05 level of significance.
The data does contradict with the prior evidence
To determine whether the data presented here are significantly inconsistent with previous assumptions, a statistical test was performed to verify that the observed relationship between tendon length and cranial volume was significantly greater than the expected relationship. You have to decide if they are different.
To do this, fit a line to the data using linear regression analysis and test the hypothesis that the slope of the line is equal to 20 cm3/mm. If the p-value for this hypothesis test is less than 0.05, you can conclude that the data are inconsistent with previous assumptions at the 0.05 significance level.
It is crucial to realize that this analysis assumes that the relationship between tendon length and cranial volume is linear.
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what's the answer 7x + 7=7(x+_)
the answer is 1
Step-by-step explanation:
Determine if the table shows a proportional relationship.
IT'S DUE TOMORROW
x 18.6 54.3 58.8
y 6.2 18.1 19.6
Yes, it is proportional because all y over x ratios are equivalent to one third.
Yes, it is proportional because all y over x ratios are equivalent to one fourth.
No, it is not proportional because 18.6 over 6.2 does not equal 18.1 over 54.3.
No, it is not proportional because 18.1 over 54.3 does not equal 58.8 over 19.6.
It is proportional because all y over x ratios are equivalent to one-third. I.e., the proportionality constant of the given table is k = 1/3.
How to determine the proportionality relationship?The proportionality relationship between two variables is determined by its proportionality constant. The proportionality constant is the ratio of y over x.
I.e., k = y1/x1 = y2/x2 = y3/x3 = ... = yn/xn
Calculation:The given data table is as follows:
x - 18.6, 54.3, 58.8
y - 6.2, 18.1, 19.6
So, the proportionality constant is calculated as
y1/x1 = 6.2/18.6 = 1/3
y2/x2 = 18.1/54.3 = 1/3
y3/x3 = 19.6/58.8 = 1/3
Since all three ratios are the same, then the data in the table are proportional to each other.
Therefore, option A is correct.
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just these 2 questions
Answer:
nnnn
Step-by-step explanation:
hh
Quandale Dingle has $40 dollars in his bank account. He gives JaQuavion Johnson one-fourth of that money, and JaQuavion Johnson gives Quandale Dingle $2 back. Quandale Dingle then gives $8 to Tyrone and Jamal each so they can escape from the cotton fields. Quandale Dingle then gives $6 to a homeless person and puts the remaining money in his bank account. He wins $50 in the lottery and puts that in his bank account. How much money does Quandale Dingle have in his bank account now?
Answer:
$60.00
Step-by-step explanation:
1/4(40) = 10
40 - 10 = 30
30+ 2 = 32
32 - 8 - 8 = 16
16 - 6 = 10
10 + 50 = 60
Can someone help me with this problem.
The value of x in the first question is 11 and the value of y is 3.
The value of x in the second question is 4 and the value of y is 4.
The value of x in the third question is -5 23/26 and the value of y is -1/13
What are the solutions of the equations?2x + y = 25 equation 1
2x - 3y = 13 equation 2
The first step is to subtract equation 2 from equation 1:
-4y = -12
Divide both sides of the equation by -4
y = -12 / -4
y = 3
Substitute for y in equation 1:
2x + 3 = 25
2x = 25 - 3
2x = 22
x = 22 / 2
x = 11
-3x + 4y = -18 equation 1
x = -2y - 4
x + 2y = -4 equation 2
Multiply equation 2 by 2
2x + 4y = -8 equation 3
Subtract equation 3 from equation 2:
-5x = -20
Divide both sides of the equation by -5
x = -20 / -5
x = 4
Substitute for x in equation 2:
4 + 2y = -4
4 + 4 = 2y
8 = 2y
y = 8/2
y = 4
-2x + 3y = -15 equation 1
3x + 2y = -23 equation 2
Multiply equation 1 by 3 and equation 2 by 2
-6x + 9y = -45 equation 3
6x + 4y = -46 equation 4
Add equation 3 and equation4 together
13y = -1
y = -1/13
Substitute for y in equation 1:
-2x + 3(-1/13) = -15
-2x -3/13 = -15
-2x = -15 + 3/13
-2x = 11 10/13
x = 11 10/13 ÷ -2
x = 153/13 x -1/2
x = -153/26
x =-5 23/26
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37. Triangles ABC and RST are graphed on the set of axes below. Identify a composition of rigid motions that will map AABC onto ARST.
Answer:
Reflection across the X axis, translate to the right by 7 points
Step-by-step explanation:
A reflection would move ABC to quadrant 3, and the translation of +7 would put point C where point S is.
can someone explain how to simplify fourth, fifth, and sixth roots
Step-by-step explanation:
how to simplfy the fifth root
the fifth root us a number that would multiply itself 5 times example √ 243 will be 3×3×3×3×3 =243 hope i helped u that the only one that i can explain beterFind a polynomial function of degree 3 such that f(0)=17 and the square root of f(x) are 0,5 and 8
Answer:
f(x)=x^3 - 13x^2 + 40x + 17
Step-by-step explanation:
x-0=0 x-5=0 x-8=0
x=0 x=5 x=8
y=x(x-5)(x-8)+b ==> b is what's going to be used to find the equation so that
y=17 when x=0
17=0(0-5)(0-8)+b ==> plugin 0 for x and 17 for y
17=0*(-5)*(-8)+b ==> simplify
17=0+b ==> anything multiplied by 0 is 0.
b=17
Hence, the equation is:
y=x(x-5)(x-8)+17 ==> expand this equation
y=x*(x-5)(x-8) + 17
y=x*(x(x - 8) - 5(x - 8)) + 17 ==> distribute x-8 to x and -5
y=x*(x*x - 8x - 5x - (8)(-5)) + 17 ==> distribution property
y=x*(x^2 - 13x - (-40)) + 17 ==> simplify
y=x*(x^2 - 13x + 40) + 17 ==> subtracting a negative number is equivalent to
adding a positive number
y=x^3 - 13x^2 + 40x + 17 ==> multiply x with x^2, 13x, and 40 using the
distribution property.
Answer: f(x)=x^3 - 13x^2 + 40x + 17
Answer: Okay, lets explain.
Step-by-step explanation:Since 0, 5 & 8 are given as the zeros of the required 3rd degree polynomial f(x), therefore, one may take it as ; f(x) =k (x-0)(x-5)(x-8)
= k(x³−13x²+40) …. .. .(1) . Since f(10) = 17 (given), it implies 17 = k(1000 -1300 + 400) = 100 ==> k = 17/100 = 0.17 . Put this value of k in eq(1) and get the required polynomial.
There are 5 Thursdays and 4 Saturdays in the month of February in a year. Find the date of the first Monday of the month of march of that year?
Answer:
March 4
Step-by-step explanation:
The fifth Thursday must happen 4 weeks after the first one. That means that the 5th Thursday is 28 days after the first one.
Feb 1 + 28 days = Feb 29
Feb 1, Thursday
Feb 8, Thursday
Feb 15, Thursday
Feb 22, Thursday
Feb 29, Thursday
Mar 1, Friday
Mar 2, Saturday
Mar 3, Sunday
Mar 4, Monday
Answer: March 4
32) Solve for "c".
C/100 = 51/60
Answer:
The answer is 85
Step-by-step explanation:
c/100 = 51/60
(c) × (60) = (51) × (100)
60c = 5100
60c/60 = 5100/60
c = 85
Thus, The value of y is 85
Answer:
[tex] \sf \: c = 85[/tex]
Step-by-step explanation:
Given equation,
[tex] \sf \rightarrow \: \frac{c}{100} = \frac{51}{60} [/tex]
Now the value of c will be,
[tex] \sf \rightarrow \: \frac{c}{100} = \frac{51}{60} [/tex]
[tex] \sf \rightarrow \: c = ( \frac{51}{60} ) \times 100[/tex]
[tex] \sf \rightarrow \: c = \frac{(51 \times 100)}{60} [/tex]
[tex] \sf \rightarrow \: c = \frac{5100}{60} [/tex]
[tex] \sf \rightarrow \boxed{ \sf c = 85}[/tex]
Hence, the value of c is 85.
the issue of capital punishment is a hotly debated topic. do more republicans than democrats support capital punishment? a researcher randomly selects 100 republicans and 100 democrats and asks them if they support or do not support capital punishment. in this problem, we want to make inferences about:
In this problem, we want to make inferences about comparing proportions from dependent samples. So the option F is correct.
In the given question, the issue of capital punishment is a hotly debated topic.
Do more republicans than democrats support capital punishment?
A researcher randomly selects 100 republicans and 100 democrats and asks them if they support or do not support capital punishment.
In this problem, we want to make inferences about:
A. one mean
B. comparing means from dependent samples
C. comparing means from two independent samples
D. one proportion
E. comparing proportions from two independent samples
F. comparing proportions from dependent samples
As we know that,
A hypothesis test can assist in figuring out whether a variation in the estimated proportions actually reflects a variation in the population proportions. An approximation of the normal distribution is shown by the difference between two proportions. The null hypothesis often argues that the two proportions are equal.
So, a researcher randomly selects 100 republicans and 100 democrats and asks them if they support or do not support capital punishment. In this problem, we want to make inferences about comparing proportions from dependent samples. So the option F is correct.
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