For dimensions of x =10 and y=5 for the base and height that will make the tank weight as little as possible.
Here we are given the information of a square-based, open-top, rectangular steel holding tank, so here the tank is in the shape of a cuboid and we know the formula for :
volume = x*y*z, as here it is a square base, so the volume will be
volume = x²*y, where x and y are the dimension of the base and height
So for the given reason,
=>x²*y = 500
=> y = 500/x²
Again, the surface area formula will be
S=x²+4xy, substituting the value of y in this question
=>S=x²+4x(500/x²)
=>S=x²+2000/x
Differentiating the above formula with respect to x, we get
=>2x-2000/x²=0
=>2x³= 2000
=>x³= 1000
=>x =10
so the substituting the x values of x in the equation y , we get
y = 500/x²
=>y = 5
so the dimensions are x= 10 and y=5
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The probability that a marksman will hit a target each time he shoots is 0. 89. If he fires 15 times, what is the probability that he hits the target at most 13 times?.
The probability that marksman will hits the target at most 13 times is 27.92%.
Explain the term binomial distribution?Let X be the quantity of times that target is hit and be a random variable. 15 rounds are fired, hence the number of trials ("n") is equal to 10 as a result. In a binomial distribution, "p" denotes the likelihood of success, and "q" is the likelihood of failure (where q = 1 - p). Since there is a 0.89 chance of striking the target, p = 0.89 and q = 0.11.The number of successes ("x") is the probability mass function for such binomial distribution.
P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ
We are interested in the likelihood that the target will be struck exactly five times, therefore the desired number of successes is five (i.e., x = 13).
P(X = 13) = ¹⁵C₁₃. (0.89)¹³ (0.11)²
P(X = 13) = 0.2792
P(X = 13) = 27.92%
Thus, the probability that marksman will hits the target at most 13 times is 27.92%.
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Amelia thinks of a number. Her number is a factor of both 18 and 12. Her number is odd. What is the largest number she could be thinking of?
Answer:
Step-by-step explanation:
First, Amelia thinks of a number that is a factor of both 18 and 12. This number is odd, so it can't be a whole number. Next, Amelia has to find the largest number that is a factor of both 18 and her chosen number. This number is 36.
Answer:
3
Step-by-step explanation:
You want the largest odd factor of both 18 and 12.
GCDThe greatest common divisor of both 18 and 12 is 6:
18 = 3·6
12 = 2·6
This is an even factor, which has two factors: 2 and 3. Only 3 is an odd factor of both 18 and 12.
The largest odd factor of both 18 and 12 is 3.
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Please help with this question. I need help this is too hard for my friend and I do not have time.
The frequency table formed using tally marks can be analyzed by using the numbers indicated by the tally marks as follows;
The true statements are as follows;
Twice as many students prefer green than purpleTwo more students prefer blue than purpleThe same number of students prefer yellow or purple as the number who prefer blueWhat are tally marks in a frequency table?Tally marks makes use of vertical lines to represent data, in which the fifth count is represented by a diagonal line across four vertical lines;
The data in the table are as follows
The number of students that prefer red = 5 + 1 = 6
The number of students that prefer yellow = 2
The number of students that prefer Blue = 5
The number of students that prefer purple = 3
The number of students that prefer Green = 6
Therefore;
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What is an equation of the line that passes through the point (8, 0) and is parallel to
the line x + y = 5?
Answer:
y = -x + 8
Step-by-step explanation:
x + y = 5
y = -x + 5
y = -x + b
0 = -(8) + b
b = 8
y = -x + 8
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if the expression $(12-x)\div(3x)$ represents a non-negative integer, what is the largest possible integer value of $x$?
The largest possible value of the expression (12 - x)/3x is 3.
Expression
In algebra, expression is the combination of variables, numbers and constants.
Given,
Here we have the expression (12 - x)/3x.
Now we have to find the largest possible integer value.
As we have given in the question that the x takes only the non negative integer, then the values must be 1, 2, 3, ….
So, we have to apply the values on the given expression ,
Then we get the values,
=> x = 1 = > (12 - 1)/3(1) = 11/3 = 3.6
=> x = 2 => (12 - 2) / 3(2) = 10/6 = 1.6
=> x = 3 => (12 - 3) / 3(3) = 9/9 = 1
Therefore, the resulting value is 3.
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design a rectangular milk carton box of width w, length l, and height h which holds 512 cm3 of milk. the sides of the box cost 1 cent/cm2 and the top and bottom cost 2 cent/cm2. find the dimensions of the box that minimize the total cost of materials used.
The dimensions of the box that minimize the total cost of materials used are:
L = W = 16 cm
H = 32 cm
What is the rectangular dimension?
Two dimensions make up a rectangle: the length and, perpendicular to that, the breadth. A triangle's or an oval's interior likewise has two dimensions.
We have,
volume L* W * H = 512 cm³
sides of the box cost = 1 cent/cm²
top and bottom cost 2 cent/cm²
to find out
dimensions of the box that minimize the total cost of material use
we know here,
L* W * H = 512 cm³
where,
L is length and W is width and H is the height
so when we minimize the cost function
C( L, W, H ) = (1) 1 H ( L + W ) + (2) 1 L W
so put here H
substitute [tex]H = \frac{512}{LW}[/tex] we get,
C(L, W) = 512([tex]\frac{1}{l}, \frac{1}{W}[/tex]) + 2LW
so
minimum cost will be when the two partial derivatives is 0
dC/dL = 2W - 512/L² = 0
so
dC/dW = 2L - 512/W² = 0
L = 256/W²
so
by solving the above equation we get
L = W = (256)⁻³ = 16cm
and
H = 512/16 = 32
H = 32 cm
Hence, the dimensions of the box that minimize the total cost of materials used are:
L = W = 16 cm
H = 32 cm
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this chart shows the changes in value of one share of a stock at the end of each day. the value of stock on mondag morning was 28.42$ a share. sam owns 12 shares a stock what is the total value of sams stocksl at the end of Friday
Using mathematical operation, the value of stock on Friday is $341.04
The value of Share on FridayTo find the value of the stock on Friday, the value of the stock on Monday is $24.42. Since he own 12 shares, we can multiply 12 by $24.42.
This can be done using a mathematical operation called multiplication.
Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
The value of the stock is 12 * 28.42 = 341.04
The stock value on Friday will $341.04
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In a hypothesis test for population proportion, you calculated the p-value is 0. 01 for the test statistic, which is a correct statement of the p-value?.
For the correct statement of the p-value, we would reject the null hypothesis.
There are two main methods for interpreting the statistical significance of a hypothesis test;
1) compare the p-value to the level of significance or
2) compare test statistics to a critical value.
Either method is acceptable, and is chosen by the researcher based upon which one is most typical in their field of research.
Under a hypothesis test we reject the null hypothesis if our p-value is less than the level of significance (p<α), and fail to reject the null hypothesis otherwise. Under the question, we are given a level of significance of 0.05 and a p-value of 0.01, where
p = 0.01 <α = 0.05
hence we would reject the null hypothesis. Thus the statement is TRUE.
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Question 1-4
A punch bowl contained 4 liters of soda, 5 liters of orange juice, and 2 liters of raspberry juice.
Select the statements that are true.
The ratio of the entire punch bowl to the juices is 9: 11.
The ratio of the entire punch bowl to the orange juice is 11 to 5.
The ratio of orange juice to soda is 4 to 5.
4
The ratio of soda to the entire punch bowl is
11
The ratio of orange juice to raspberry juice is 5 : 2.
Answer:
Its the second one
Step-by-step explanation:
.
when conducting a one-way independent anova with three levels on the independent variable, an f-ratio that is large enough to be statistically significant tells us:
One or more of the mean differences are statistically significant, but not the precise location of the group differences.
In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. A variable that is independent is precisely what it sounds like. It is a stand-alone variable that is unaffected by the other variables you are attempting to assess. Age, for instance, might be an independent variable.
Dependent variables are so-called because, during an experiment, their values are examined on the assumption or presumption that they are governed by the values of other variables.
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Mia buys a t-shirt online for $15.. If shipping and
handling are an additional 30% of the price, how
much shipping and handling will Mia pay?
Mia will pay a total of $4.5 for the shipping and handling of the t-shirt
How to determine the shipping and handling price?From the question, we have the following parameters that can be used in our computation:
Cost of the shirt = $15
shipping and handling = 30%
The amount paid for the shipping and handling of the t-shirt can be calculated using the following equation
Amount paid = original price * + shipping and handling
Substitute the known values in the above equation, so, we have the following representation
Amount paid = 15 * 30%
Evaluate the products
Amount paid = 4.5
Hence, the amount paid is $4.5
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A single die is rolled twice. Find the probability of rolling a 6 the first time and a 1 the second time.
Answer: I believe it is 2/12. tell me if I am wrong.
Step-by-step explanation: Hope this helps!
7+8=8+7 identity property
Answer:The property used in 7 + 8 = 8 + 7 is Commutative property under addition
Step-by-step explanation:
Answer:
The identity property is a=a, so it is identity property
Step-by-step explanation:
???
out of 270 racers who started the marathon, 243 completed the race, 19 gave up, and 8 were disqualified. what percentage did not complete the marathon? %
The percentage is 10% who did not complete the marathon. It can be calculted using the formula of percentage.
What is percentage?
It is way of writting any number as a fraction of 100. Its symbol is % . It is a dimention less qunatity.
Total participants = 270
Number of participants completed the marathon = 243
Number of participants gave up = 19
Number of participnats disqualified = 8
Total number of participants who did not completed the merathon is the sum of participants who gave up and who did not qualified = 19 + 8 =27
Now, percentage of participants who did not complete the marathon is,
[tex]\frac{\text{Number of participants did not complete}}{\text{Total participants}}\times100\\=\frac{27}{270}\times100\\=10\%[/tex]
Hence, 10% did not complete the marathon.
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Factor polynomials
9x^2 - 3x - 2
Many thanks for someone to lend a helping hand!
Answer:
Step-by-step explanation:
(3x-2)(3x+1)
Answer:
(3x - 2)(3x + 1)
Step-by-step explanation:
9x^2 - 3x - 2 = 9x^ 2 - 6x + 3x - 2 =
=3x(3x - 2) + (3x - 2) = (3x - 2)(3x + 1)
the wall thickness of 21 randomly selected glass 2-liter bottles was measured by a quality-control engineer. the wall thickness of those glass 2-liter bottles follows a normally distribution with unknown variance. the sample mean and the sample standard deviation of those 21 selected bottales was found to 4.15 millimeters and 0.09 millimeter, respectively. which of the following is the correct 90% two-sided confidence interval for the mean wall thickness?
The 90 % Prediction interval on the wall thickness of next bottle tested is (4.41, 4.99).
What is meant by Prediction Interval?A prediction interval is a form of confidence interval (CI) used with regression analysis predictions; it is a range of values that forecasts the value of a new observation based on your existing model.
Confidence intervals and predictions are frequently used interchangeably. They are not exactly the same thing, though.
A confidence interval is a set of values connected to a population parameter. the population's mean, as an illustration.
Where you anticipate an upcoming number to fall is called a prediction interval.
The Interval Uncertainties
It doesn't imply that you can forecast with confidence where a single number will fall, just like with most things in statistics.
Confidence intervals are usually accompanied with a confidence level, which represents the amount of uncertainty.
How to solve?
X=4.7
s=0.7
n=25
The tabulated value of t at 24 degree of freedom is 2.06
t24=2.064
The 90 % Prediction interval on the wall thickness of next bottle tested is given by:
=(4.7±t24×0.7√25)
=(4.7−2.064×0.75,4.7+2.064×0.75)
=(4.7−0.28896,4.7+0.28896)
=(4.41,4.99)
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11 black balls and 14 white balls are placed in an urn. two balls are then drawn in succession. what is the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball? a) 0.2333 b) 0.5376 c) 0.5600 d) 0.2567 e) 0.3033 f) none of the above.
The probability for the given condition is, 0.56.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given:
11 black balls and 14 white balls are placed in an urn. two balls are then drawn in succession.
We have to find the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball.
P(white ball) = 14 / (11 + 14) = 14 / 25
P(2nd ball is white) = P(first ball is white)*P(2nd ball is white) + P(first ball is black)*P(2nd ball is white)
= (14 / 25) * (13 / 24) + (11 / 25) * (14 / 24)
=0.56
Hence, the probability for the given condition is, 0.56.
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please hurry im about to run out of time
Answer: Quadrant 1, y-axis
Step-by-step explanation:
How many times does the rotation R(120°, P) need to be applied to a figure to map the figure to itself?
The number of times the point R ( 120° , P ) needs to be rotated so that the figure is mapped to itself is 3 times
What is Rotation?
The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.
90° clockwise rotation: (x,y) becomes (y,-x)
90° counterclockwise rotation: (x,y) becomes (-y,x)
180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
270° clockwise rotation: (x,y) becomes (-y,x)
270° counterclockwise rotation: (x,y) becomes (y,-x)
Given data ,
Let the number of rotation be = n
Let the point be R
Now , the coordinates of the point R is
R ( 120° , P )
Now , to map the figure onto itself it needs to rotate 360°
So ,the number of times 120° needs to rotate to reach 360° is calculated as
n x 120° = 360°
Divide by 120 on both sides , we get
n = 360 / 3
n = 3 times
Therefore , the value of n is 3
Hence , The number of times the point R ( 120° , P ) needs to be rotated so that the figure is mapped to itself is 3 times
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if the cost of 1kg of apples is $12 what is the cost of 500g of apples
Answer:
the answer is $6
Step-by-step explanation:
This is because there are 1000g in 1kg, so 500g is half of that and half of 12 is 6.
xyz dV where T is the solid tetrahedron with vertices (0,0,0), (1,0,0), (1,1,0), and (1,0,1)
The volume of the solid tetrahedron is [tex]\frac{1}{144}[/tex] cubic units.
T's base is a triangle in the xy-plane (z= 0), with one edge being the line y=x, z= 0; the front side is a triangle in the vertical plane x= 1; the left side is a triangle in the xz-plane (y= 0); and the top is the plane xyz= 0 (this plane contains the three points (0,0,0), (1,1,0), (1,0,1).
The equation must be ax+by+cz+d=0 and must be satisfied by the three points as well as the edge (x=y, z=0).
T is thus described as 0≤z≤(xy), 0≤y≤x, 0≤x≤1.
for which it is suitable to used V=dzdydx.
[tex]\int\limits\int\ \int\limits{xyz} \, dV=\int\limits^1_0 \int\limits^x_0 \int\limits^{x-y}_0 {xyz} \, dxdydz\\ \\ =\int\limits^1_0 \int\limits^x_0[\frac{1}{2}xyz^2]\limits^{x-y}_0 dydx\\\\=\frac{1}{2}\int\limits^1_0 \int\limits^x_0(x^3y-2x^2y^2+xy^3)dydx\\\\=\frac{1}{2}\int\limits^1_0 [\frac{1}{2}x^3y^2-\frac{2}{3}x^2y^3+\frac{1}{4}xy^4]\limits^x_0dx\\\\=\frac{1}{2}\int\limits^1_0\frac{1}{12}x^5dx\\\\=\frac{1}{2}[\frac{1}{72}x^6]\limits^1_0\\\\=\frac{1}{144}[/tex]
Thus, the volume of the solid tetrahedron is [tex]\frac{1}{144}[/tex] cubic units.
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what is the equation of a line Parallel to -3x + 2y = 6
and through the point (4, -4)?
The area of a rectangle is given by 2x-x-7x+9x+6cm
Answer: =3x+6
Step-by-step explanation:
Use the commutative law of addition to match the original expression on the left with its rewritten expression on the right.
35+82
9-6=15
7-3
15-9=6
27+13=40
3-7
13+27= 40
27+ 40 = 13
82 +35
cannot be rewritten
The commutative law of addition makes the expressions as,
35 + 82 → 82 + 35
7 + (-3) → (-3) + 7
15 - 9 = 6 → -9 + 15 = 6
27 + 13 = 40 → 13 + 27 = 40
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The commutative law of addition states that,
a + b = b + a
Now,
Using the commutative law we get,
35 + 82 = 82 + 35
7 - 3:
7 + (-3) = (-3) + 7
15 - 9 = 6
15 + (-9) = 6
(-9) + 15 = 6
-9 + 15 = 6
27 + 13 = 40
13 + 27 = 40
Thus,
The commutative law of addition makes the expressions as,
35 + 82 → 82 + 35
7 + (-3) → (-3) + 7
15 - 9 = 6 → -9 + 15 = 6
27 + 13 = 40 → 13 + 27 = 40
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Sort the following polygons in order of increasing area.
The area of the polygons arranged in order of increasing Area is:
Rectangle = 4Triangle = 12Square = 13What is a polygon?A polygon is a planar figure characterized by a limited number of straight line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both. A polygonal circuit's segments are known as its edges or sides.
The area of the triangle is given as:
[Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)]/2
Where Ax and Ay are the x and y coordinates for the vertex of A. The same applies for the x and y notations of the B and C vertices.
Hence given:
A(-4-3), B(1, -3), C(-1,2)
we have
[-4(-3-2) + (1(2-(-3)) + (-1(-2-(-3))]/2
= 24/2
= 12
Hence the area of the triangle is 12.
To calculate the area of the rectangle, we use the distance formula. The equation for this is given as:
d² = (x₂ - x₁)² + (y₂-y₁)²
Where (x₁, x₂) are the coordinates of the first point and
(y₁, y₂) are the coordinates of the second point.
Assuming that the vertices are labeled as follows:
A (7,9), B(6,9), C(6,5), D(7,5), then
AB² = (6-7)² + (9-9)²
AB² = 1 + 0
AB = 1
BC² = (6-6)² + (5-9)²
BC² = 0² + -4²
BC = 4
CD² = (7-6)² +(5-5)²
CD² = 1² + 0²
CD = 1
DA² = (7-7)² + (9-5)²
DA² = 0² +4²
DA = 4
From the above, we can tell as is typical of a rectangle, that AB = CDand BC = DA
Since the Area of the rectangle is AB x CD OR BC x DA
The area of the rectangle =
4 x 1 = 4
Using the distance methods we can also arrive at the length of the sides of the square.
Since the area of a square is given as L² we only need the lenght one one side.
Hence,
AB = 3.60555
Hence the area of the square =
3.60555²
= 12.9999908025
Area of the square [tex]\approx[/tex] 13.
Thus the polygons arranged in order of increasing area are:
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PLSSSS help I will mark brainliest
The total distance a freely falling body covers in time, t, is given by the equation d(t)=1/2 gt 2 , where g is constant at 10 m/s 2 . Show, in terms of n, the distance a falling body covers in t = n seconds of movement.
Show, in terms of n, the distance a falling body covers in t = n - 1 seconds of movement.
The distance a freely falling body covers in the nth second is given by s (n) =d (n) -d(n-1). Show s (n)in terms of g, in simplified form.
The Wood family bought 6 crates of eggs last week. Each crate had 12 eggs. Since then, they have eaten 27 of the eggs. How many eggs are left?
Answer:
45 eggs
Step-by-step explanation:
You want to know the number of eggs left after 27 have been eaten from a supply of 6 crates having 12 eggs each.
Egg purchaseIf each of 6 crates had 12 eggs, the number of eggs bought was ...
(6 crates) × (12 eggs/crate) = 72 eggs
Eggs remainingIf 27 of those 72 were eaten, the number remaining is ...
72 -27 = 45
45 eggs are left.
Morgan is making accsessories for the soccer team. she uses 574.35 inches of fabric on headbands for 32 players and 3 coaches. she also uses 276.16 of fabric on wristbands for just the players. how much fabric was used on a headband and wristband for each player?
Answer:
Step-by-step explanation:
574.35/35=16.41
276.16/32=8.63
16.41 + 8.63 = 25.04
what is the difference between a convex set and a convex function with respect to linear programming?
A linear problem is always convex, because anything linear is convex.
What is linear programming?
A mathematical model whose requirements are expressed by linear connections can be optimized using a technique known as linear programming. A particular type of mathematical programming is linear programming.
A convex function is a real-valued function defined on an interval with the property that its epigraph (the set of points on or above the graph of the function) is a convex set. Convex minimization is a subfield of optimization that studies the problem of minimizing convex functions over convex sets.
Every linear function has a concave shape. However, only convex polygons (possible sets of linear programs) exist.
A linear problem is always convex, because anything linear is convex.
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What is the length of the midsegment AB? Type only the numerical answer.
Answer:
A is (3,4) B. is 18,4
Step-by-step explanation:
Check the picture below.