Answer:
13.2cm
Step-by-step explanation:
The surface area of the sphere=4πr∧2
take r as radius, so you have to find the diameter. which means d/2=r
So,
4*22/7* (d/2)²=544
d=13.15
to the first decimal place= d= 13.2 cm.
The function C = x - 2y is minimized at the vertex point of the feasible region at (1, 0). What is the minimum value?
The minimum value of the function C = x - 2y at the vertex point (1,0) is 1.
So, when we substitute x = 1 and y = 0 into the function, we get:
C = 1 - 2 * 0 = 1.
Therefore, the minimum value of the function is 1.
The heights of the bars of a histogram correspond to ______ values.
The heights of the bars of a histogram correspond to Frequency values.
A histogram is a type of graph used to show the distribution of a dataset. It is used to display the frequency of values within the data set by depicting the number of observations that fall within a set of ranges.
The heights of the bars of a histogram correspond to the frequency of values within the data set.
A histogram is used to illustrate the distribution of data within a set by showing the number of data points that fall within a specified range of values (called bins).
The height of each bar in the histogram represents the frequency of values within the bin range. A taller bar indicates that more data points fall within that range. The area of each bar is also proportional to the frequency of the values in the bin.
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for each of the statements below, give a domain of discourse for which the statement is true, and a domain for which the statement is false. (a) ∀x∃y(y 2 x). (b) ∀x∀y(x < y → ∃z(x < z < y)
A domain of discourse for a domain integer statement is,
(a) True : x ≥ 0 and False x < 0
(b) True : x ≠ z ≠ y and False x ≠ y = z
A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.
An integer, also called a "round number" or “whole number,” is any positive or negative number that does not include decimal parts or fractions. For example, 3, -10, and 1,025 are all integers, but 2.76 (decimal), 1.5 (decimal), and 3 ½ (fraction) are not.
(a) ∀x∃y( [tex]y^{2}[/tex] ≥ x)
[tex]y^{2}[/tex] ≥ 0
When x ≥ 0 , [tex]y^{2}[/tex] = x is True.
When x < 0 , without [tex]y^{2}[/tex] = x is True.
(b) ∀x∀y(x < y → ∃z(x < z < y)
When x ≠ z ≠ y , x < z < y is True.
When z = x or z = y , x < z < y is False.
When x = y and x = z , y = z
Therefore,
A domain of discourse for a domain integer statement is,
(a) True : x ≥ 0 and False x < 0
(b) True : x ≠ z ≠ y and False x ≠ y = z
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use the general slicing mothod to find the volume of the following solid. The solid with a semicircular base of radius 9 whose cross section is perpendicular to the base and parallel to the diameter are squares. Place the semicircle on the xy-plane so that its diameter is on the x-axis and it is centered on the y-axis. Set up the integral that gives the volume of the solid. Use increasing limits of integration.
The volume of the solid is approximately equal to 441.75 π cubic units.
The volume of the solid can be found using the disk method of integration. To set up the integral, consider a disk of height 'h' and radius 'r' at position y. The volume of this disk is given by πr^2h, and the radius 'r' is equal to 9 - y. Therefore, the volume of the solid is given by the following triple integral:
[tex]V = \int\{\pi(9 - y)^2dy} \int\,dh \int\,dx[/tex]
Where the limits of integration are:
For x: 0 to 9 (since the square cross-section has side length of 9)For h: 0 to x (since the height of the disk cannot be greater than the distance from the xy-plane)For y: 0 to 9 (since the radius of the semicircle is 9)So, the final expression for the volume is:
[tex]V = \int\limits^{9}_{y=0} \int\limits^{x}_{h=0} \int\limits^{9}_{x=0} \pi (9 - y)^2 dh dx dy[/tex]
Evaluating the integral gives:
[tex]V = \pi \int\limits_{y=0}^{9} (9 - y)^2dy \int\limits_{h=0}^{x} dh \int\limits_{x=0}^{9} dx[/tex]
[tex]= \pi \int\limits_{y=0}^{9} (81 - 18y + y^2)dy \int\limits_{h=0}^{x} dh \int\limits_{x=0}^{9} dx[/tex]
[tex]= \pi \int\limits_{y=0}^{9} (81 - 18y + y^2)dy (x^2/2) dx[/tex]
[tex]= \pi /2 \int\limits_{y=0}^{9} (81 - 18y + y^2)dy (x^2) dx[/tex]
[tex]= 441.75 \pi[/tex]
Hence, the volume of the solid is approximately equal to 441.75 π cubic units.
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What are the 6 Laws of logarithms?
hey can you help me find the domain and range
The domain is all x-values or inputs of a function & the range is all y-values or outputs of a function.
How to find domain and range?The numbers you supply to the function are referred to as the domain. The numbers it returns to you are referred to as the "range."
Take y=3x as an illustration. The domain of this function is "all real numbers," so you can substitute any number you like for x. (or everything from negative infinity to positive infinity, if you like). Furthermore, as you can probably guess, any actual number could result from it. (You desire the release of a specific real-world number. To get there, enter x as one-third of that number. As a result, "all real numbers" are included in this function's range.
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. if v in r 3 and v · v = 0, then v is the zero vector. is it true or false? explain your answer
The statement "if v in R3 and v · v = 0, then v is the zero vector" is true
In mathematics, a vector is an ordered tuple of numbers or scalars that can be used to represent a quantity that has both magnitude and direction. Vectors are used to model physical quantities such as displacement, velocity, and force, among others.
Here we have given that if v in r 3 and v · v = 0, then v is the zero vector.
It is true because if the dot product of a vector with itself is zero, it means that the magnitude of the vector is zero and thus it is the zero vector. Understanding the concept of a zero vector and its relationship with other vectors is important in mathematics and physics.
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To find the roots of a polynomial, it is often useful to find the ____ of the polynomial.
Answer:
factors
Step-by-step explanation:
To find the roots of a polynomial, it is often useful to find the Factors of the polynomial.
WILL MARK BRAINLIEST FIRST ANSWER, EASY POINTS
Which linear graph represents a proportional relationship?
The second one because it passes through (0,0)
Please help me with math problem!! Will give brainliest!! :) It's due tonight!! 20 POINTS!!!
Answer:
[tex]\boxed{21.691} \; feet[/tex]
Step-by-step explanation:
See attached figure
The power cable going south first by 50 feet and then going west by 30 feet form the legs of a right triangle.
The diagonal which is the shortest distance between start and end points can be computed by the Pythagorean theorem
[tex]c^2 = a^2 + b^2[/tex]
where c is the hypotenuse and a, b the other two sides
Plugging in values for a = 50 and b = 30 we get
[tex]c^2 = 50^2 + 30^2\\\\c^2 = 2500 + 900\\\\c^2 = 3400\\\\c = \sqrt{3400}\\\\c = 58.3095 \;feet[/tex]
The cable length if going south and then west will be 50 + 30 = 80 feet
So cable length saved = 80 - 58.3095 = 21.6905
Rounded to 3 decimal places this would be 21.691 feet
Answer:
By using the Pythagorean Theorem, we can calculate that the diagonal of the city block is approximately 58.3 feet long. This means that the power company could save 7.3 feet of powerline cable by running the powerlines across the diagonal of the city block, instead of around the south and west sides.
the shorter diagonal of a rhombus with 70 degrees is 122 cm long, how long is the longer diagonal
The length longer diagonal is 174 cm.
In a rhombus, the diagonals bisect each other as well as the the vertex angles and adjacent angles are supplementary
So assuming that the 70 degree angle is opposite the 122 cm diagonal, we have
(1/2 length of the shorter diagonal) / sin (35) = (1/2 length of the longer diagonal) / sin(55)
Multiply both sides by 2
( length of the shorter diagonal) / sin (35) = ( length of the longer diagonal) / sin(55)
Multiply both sides by sin(55).
Length of the longer diagonal = sin (55) (122 cm) / sin (35) = 174 cm
Therefore, the length of the longer diagonal is 174 cm.
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What does 1 tbsp equal to in mL?
15mL is also equivalent to one tablespoon.
What is 1 teaspoon equal to in mL?Recall that 1/2 a teaspoon is 2.5 mL and that 1 level teaspoon = 5 mL.Approximately 2.5 to 7.3 mL is the size range for teaspoons (0.088 to 0.257 imp fl oz; 0.085 to 0.247 US fl oz). A teaspoonful is equal to 5 mL (0.18 imp fl oz; 0.17 US fl oz) when used for cookery and medication dosage, when standard measuring spoons are employed.In the metric system, a milliliter—abbreviated as ml or mL—is a unit of volume. One cubic centimetre, or one millilitre, is equivalent to one thousandth of a litre. 004 of a cup is a tiny measurement in the imperial system. One tablespoon is around the size of a regular big dinner spoon.To learn more about equivalent refer to:
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Elijah spends $6.65 at the concession stand. He paid with a $10 bill. How much
change did Elijah get back?
Elijah received $ in change.
Answer:$3.35
subtract 10.00 - 6.65
You will get $3.35
a woman has two kids, one of which is a girl. what is the probability of the other child being a girl?
The probability of the other child being a girl is 1/2
How to determine the probabilityFrom the question, we have the following parameters that can be used in our computation:
Kids = 2
Girls = 1
The probability of the other child being a girl is calculated as
Probability = Girl/Kids
Substitute the known values in the above equation, so, we have the following representation
Probability = 1/2
Hence, the probability is 1/2
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How do you convert acres to miles?
The convert acres to miles 0.0015625.
What is meant by miles ?
The mile is a customary unit of measurement in the United States and the United Kingdom that is based on the older English unit of length equal to 5,280 English feet, or 1,760 yards. It is often referred to as the international mile or statute mile to distinguish it from other miles. In 1959, the statute mile was formally redefined with respect to SI units as precisely 1,609.344 metres, establishing a standard between the British Commonwealth and the United States.The Romans split a mile into 5,000 Roman feet, but in Elizabethan England, where furlongs were valued more highly, the statute mile was changed in 1593 to be equal to 8 furlongs, or 5,280 feet.To learn more about miles refer to
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find the average value of the function f(x) = x3 8x 6 on [0, 4].
The average value of the function f(x) = x² - 8x + 6 on [0, 4] is 38.
Describe calculus.The two primary divisions of calculus, differential calculus and integral calculus, are concerned with rates of change and slopes of curves.
By dividing the definite integral of the function over the interval by the length of the interval, one can determine the average value of a function over the interval [a, b].
The function in this instance is f(x) = x3 - 8x + 6, and the range is [0, 4]. Using the definite integral of x3 and the definite integral of -8x, one can determine the definite integral of the function across the interval:
[tex]\int\limits^0_4 {x^{3} - 8x + 6 } \, dx[/tex]
= [tex]\frac{x^4}{4} - \frac{8x^2}{2} + 6x[/tex]
evaluated at x = 4 - x = 0 = [tex]0 - \frac{4^{4} }{4} - \frac{8.4^2 }{2} + 6.4\\[/tex]
= - 24
The length of the interval is b - a = 4 - 0 = 4. Hence, the average value of the function over the interval is given by:
Therefore, the average value of the function f(x) = x^3 - 8x + 6 on [0, 4] is 38.
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The parametric equationsx = u, y = ucosv, z = usinv, with 0 ≤ u ≤ 2, 0 ≤ v ≤ 2π represent the cone that results when the line y = x (where 0 ≤ x ≤ 2) in the xy−plane is revolved about the x−axis. Sketch the cone, and calculate its surface area.
The surface area of the cone with the given parametric equation is (4π + 4π√2) square units.
The parametric equations describe a cone that is generated by rotating a line segment in the xy-plane about the x-axis. The result is a 3-dimensional surface that has a circular base with radius 2 and a height of 2.
The surface area of the cone can be calculated using the formula:
A = πr^2 + πrs
where r is the radius of the circular base and s is the slant height.
The slant height is equal to the distance from the center of the circular base to the tip of the cone, which can be calculated using the Pythagorean theorem: s = √(h^2 + r^2), where h is the height of the cone.
Therefore, for this cone with radius 2 and height 2, the surface area can be calculated as:
A = πr^2 + πrs
= π * 2^2 + π * 2 * √(2^2 + 2^2)
= 4π + 4π√2
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frustrated freight may never reach the intended recipient T/F
True, Frustrated Freight is any freight or shipment that it has been halted from moving.
Generally speaking, the elements that make a bundle quit moving or being shipped to the normal beneficiary are issues to do with marking, bundling, as well as making.
Frustrated Freight alludes to products that can't be conveyed to the expected beneficiary because of different reasons like an erroneous location, beneficiary inaccessibility, or harm during travel.
This can prompt the shipment never arrive at its expected objective, causing disillusionment for the shipper and beneficiary, and possibly bringing about monetary misfortunes.
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Find Sn for the arithmetic series where a1=3 , an=3 , n=14
The value of the sum of the series is 42
How to determine the sum of the seriesIn an arithmetic series, the sum of the first "n" terms (Sn) is given by the formula:
Sn = n/2 * (a1 + an)
Where "a1" is the first term and "an" is the nth term.
In this series, a1=3 , an=3 , n=14
Plugging these values into the formula, we get:
Sn = 14/2 * (3 + 3)
= 14/2 * 6
= 7 * 6
= 42
So, the sum of the first 14 terms of the arithmetic series is 42
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Gayle bought a shirt that was originally marked as $18. She had a coupon to receive 15% off the price. Gayle
had to pay 7. 5% sales tax on her shirt. What price did Gayle pay for the shirt?
sssssssssaStep-by-step explanation:
Enter the numerator and the denominator of the fraction in simplest form that is equal to 0. 84 repeating
The fraction that is equal to 0.84 repeating is 8/9 in simplest form.
If the top and bottom have no common components other than 1, the fraction is in its simplest form. In other words, the top and bottom cannot be divided any further and still remain full numbers. You may sometimes hear the phrase "lowest words" when referring to the simplest form.
0.84 repeating can be represented as a fraction in simplest form by using the following method:
Let x = 0.84 repeating,
Then 10x = 8.4 repeating.
Subtracting the two equations,
we have 9x = 8.
Dividing both sides by 9,
we have x = 8/9.
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each year, a magazine complies a list of the 400 richest americans. a of september 19,2012 the mean is
The mean of the 400 richest Americans as of September 19, 2012 is $4.25 billion.
The mean of the 400 richest Americans is calculated by summing up all of the net worth of each person on the list, and then dividing it by the total number of people on the list. The formula used to calculate the mean is:
Mean = (Sum of Net Worth) / (Total Number of People on the List)
For example, on September 19, 2012, the total net worth of the 400 richest Americans was $1.7 trillion. If we divide this by the total number of people on the list (400), then the mean net worth of the 400 richest Americans is $4.25 billion.
Therefore, the mean of the 400 richest Americans as of September 19, 2012 is $4.25 billion.
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Select the erie of tranformation that can move ΔABC onto ΔA'B'C'. A
Reflection over the line y=x. B
Reflection over the x-axi followed by a 90° clockwie rotation about the origin. C
Tranlation of (x12,y−4) followed rotation of 180o about the origin. D
Reflection over the x-axi followed by a tranlation (x12,y0)
The x and y coordinates switch places and are negated if you reflect over the line y = -x (the signs are changed). Point on the line y = x (y, x).
What is meant by Reflection?A reflection in mathematics is an isometric mapping from a Euclidean space to itself with a set of fixed points called the axis or plane of reflection. A figure's image created by a reflection is a mirror image of that figure in the axis or plane of reflection. A flip is the term for a reflection in geometry. The shape is mirrored in a reflection. The line of reflection is a line across which an image will reflect. Every point in a figure is said to reflect the other figure if and only if it is equally spaced from every corresponding point in the other figure.To learn more about Reflection, refer to:
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5. Find the sum. –10 + 1 + (–6) (1 point) –15 –17 –3 5
The simplified value of the expression - 10 + 1 + (- 6). - (15 - 17 - 35) is 20.
What is PEMDAS rule?PEMDAS rule states the correct order of simplifying an expression is as follows -: Parenthesis, exponents, multiplications, divisions, additions, and, subtractions.
Given, An expression - 10 + 1 + (- 6). - (15 - 17 - 35).
Now, If any of the arithmetic operations are not present we'll simply do the next and we'll also distribute the negative and positive signs.
- 10 + 1 + (- 6). - (15 - 17 - 35).
= - 10 + 1 - 6 - 15 + 15 + 35.
= - 9 - 21 + 50.
= - 30 + 50.
= 20.
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Can someone please help me with this? I don’t understand. Show work please.
Answer:
A
Step-by-step explanation:
angle 1+ angle 2 =180
so 2x-6+4x =180
6x =186
x =31
angle 1 = 2x-6 =31*2-6=62-6 = 56
angl2 =4x =31*4 =134
1. A pyramid is composed of six isosceles triangles and a hexagonal base. Each isosceles triangle has a height of 8 inches and a base of 6 inches. The area of the hexagonal base is 93.5 square inches.
What is the surface area of the pyramid?
Enter your answer in the box.
2.A child's toy is in the shape of a square pyramid. The pyramid stands 20 inches tall and each side of the base measures 24 inches.
Half of the surface area of the pyramid is black and the remainder is yellow.
What is the surface area of the toy that is yellow?
Enter your answer, rounded to the nearest tenth, in the box.
3.A large equilateral triangle pyramid stands in front of the city's cultural center. Each side of the base measures 50 feet and the slant height of each lateral side of the pyramid is 40 feet.
A painter can paint 100 square feet of the pyramid in 18 minutes.
How long does it take the painter to paint 75% of the pyramid?
Enter your answer, rounded to the nearest tenth, in the box.
The total surface area of the hexagonal pyramid is 237.5 in²
How do equations work?An expression that depicts the relationship between two or more numbers and variables is called an equation. Depending on the degree, an equation may be linear, quadratic, cubic, or another type.
A solid figure's surface area is calculated by summing up all of its distinct surfaces.
Given the hexagonal pyramid with a base of 6 inches and each isosceles triangle having a height of 8 inches. Hence:
Area of pyramid base = 93.5 in²
The lateral face has 6 triangle faces, hence:
Area of each lateral face = 1/2 * base * height = 0.5 * 8 * 6 = 24 in²
Total area of lateral face = 6 * 24 in² = 144 in²
Total surface area = 144 in² + 93.5 in² = 237.5 in²
The surface area is 237.5 in²
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Determine which matrices are in reduced echelon form and which others are only in echelon form. 011 1 0 011 0000 1 1 40 0 1 011 b. 0010 Is matrix b in reduced echelon form, echelon form only, or neither? a.echelon form only b.reduced echelon form c.neither
Matrix b is in reduced echelon form.
Therefore the answer is b. reduced echelon form.
In a reduced echelon matrix, the leading entry (the first non-zero entry from the left in a row) in each non-zero row is 1, and all entries above and below the leading entry are 0. Matrix b satisfies these conditions, so it is in reduced echelon form.
Reduced echelon form is a special type of echelon form for matrices, which is used in linear algebra to solve systems of linear equations. In a reduced echelon form matrix, the following conditions are satisfied:
All non-zero rows are above any rows of zeros
The leading entry (the first non-zero entry from the left in a row) in each non-zero row is 1, and all entries above and below the leading entry are 0.
Each leading entry is the only non-zero entry in its column.
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perform each step to solve for x
3x-6+x-2
Based on the given expression representing each angle, the value of x is 47 and each angles are 135° and 45° respectively.
How to solve supplementary angles?Based on the given diagram; the angles represented by the expression are referred to as supplementary angles.
So, we can find the unknown variable x by adding the expressions and equating it to 80°
(3x - 6) + (x - 2) = 180
3x - 6 + x - 2 = 180
combine like terms
3x + x - 6 - 2 = 180
4x - 8 = 180
Add 8 to both sides
4x = 180 + 8
4x = 188
divide both sides by 4
x = 188/4
x = 47
Therefore, the respective angles are;
3x - 6
= 3(47) - 6
= 141 - 6
= 135°
x - 2
= 47 - 2
= 45°
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Select all equations that have x = 9 as a solution.
Check all that are true.
x + 7 = 15
26 − x = 17
5x = 49
63 ÷ x = 7
23 + x = 32
simplify 60 with [tex]\sqrt{x} 60[/tex]