Using the formula of total surface area and volume of a sphere, the values determined for each sphere are written below.
What is the Volume and TSA of the Sphere?To determine the TSA and Volume of the sphere, we need to use the formula for that.
a. The total surface area of the sphere can be calculated as;
TSA = 4πr²
TSA = 4 * 3.14 * 8
TSA = 803.84mm²
The volume of the sphere is calculated as;
V = 4/3πr³
v = 4/3 * 3.14 * 8³
v = 2143.6mm³
b. The TSA of the sphere is calculated as;
TSA = 4πr²
TSA = 4 * 3.14 * 12.4²
TSA = 1931.2km²
The volume of the sphere is calculated as;
V = 4/3πr³
v = 4/3 * 3.14 * 12.4³
v = 7982.4km³
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solve it please. Just wanted to check my drawing skill but please solve it
Answer:
Step-by-step explanation:
I'm assuming that strange looking thing is a 9, so begin by multiplying both sides by that denominator to get:
\(x-9=\sqrt{x}+3\) then subtract 3 from both sides to get
\(x-12=\sqrt{x}\) and then square both sides to get
\(x^2-24x+144=x\) and get everything on one side to solve for x by factoring:
\(x^2-25x+144=0\) and factor that however it is you have learned to factor second-degree polynomials to get that
x = 16 and x = 9. We have to check for extraneous solutions because anytime you manipulate an equation, as we did by squaring both sides, you run the risk of these solutions that actually don't work when you plug them back into the original equation. Let's try 16 first:
\(\frac{16-9}{\sqrt{16}+3 }=1\) If 16 is a solution, then this statement will be mathematically true.
\(\frac{7}{4+3}=1\) and \(\frac{7}{7}=1\) so 16 works. Let's try 9:
\(\frac{9-9}{\sqrt{9}+3 }=1\) We know that one doesn't work, because 9-9 = 0 and 0 over anything = 0, not 1.
x = 16 is the only solution.
Answer:
x = 16
Step-by-step explanation:
\(\frac{x-9}{\sqrt{x}+3}=1\)
Cross multiply,
x - 9 = √x + 3
Subtract 3 from both sides
x - 9 - 3 = √x
x - 12 = √x
Square both sides
(x -12)² = (√x)²
x² - 2 * x*12 + 12² = x
x² - 24x + 144 = x
x² - 24x + 144 - x = 0
x² - 25x + 144 = 0
Sum = -25
Product = 144
Factors = -9 , -16 {(-9)+(-16) = -25 & (-)*(-16) = 144}
x² - 25x + 144 = 0
x² - 16x - 9x + (-9)*(-16) = 0
x(x - 16) - 9(x - 16) = 0
(x - 16) (x - 9) = 0
x - 16 = 0 ; x - 9 = 0
x = 16 ; x = 9
x = 9 is an extraneous solution.
When we plug in 9 in the LHS of the equation,
LHS = \(\frac{9-9}{\sqrt{9}+3}\)
\(= \frac{0}{3+3}\)
= 0 ≠ RHS
So, x = 16 is the only solution
seventeen less than a number is
Answer:
what number is it less than? i need that number to solve it
once you give it to me i will solve it
Step-by-step explanation:
Line segment st is dilated to create line segment s't' using the dilation rule dq,2.25. point q is the center of dilation. line segment s t is dilated to create line segment s prime t prime. the length of q t is 1.2 and the length of q s is 2. the length of s s prime is x and the length of t t prime is 1.5. what is x, the distance between points s' and s? x = 2.25 units x = 2.5 units x = 4.25 units x = 4.5 units
The value of x when the line segment st is dilated to create line s't' about point q is 2.5 units
How to determine the value of x?The given parameters are:
qs = 2
qt = 1.2
tt' = 1.5
ss' = x
To calculate the value of x, we make use of the following equivalent ratio
ss' : qs = tt' : qt
So, we have:
x : 2 = 1.5 : 1.2
Express as fractions
x/2 = 1.5/1.2
Multiply both sides by 2
x = 2 * 1.5/1.2
Evaluate the product
x = 2.5
Hence, the value of x is 2.5 units
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Answer:
2.5
Step-by-step explanation:
Please solve its due tonight!
Step-by-step explanation:
1. No, Yes
2. No, Yes
3. 6x^2+10
4. 2x^2-3
5.x^2+x
6.-2x^4+11x+3
7. 3x^3+15x^2+20
8. -9x^3+4x^2+8x
9. xy+2x+6y+5
10. 8xy-y^2x
Sorry if i messed up on some by misreading.
a full circle has 360° or 2π radians. given this, how many degrees are in 1 radian?
Answer:
1 radian ≈ 57.2958
Monica earned twice as much as Samuel mowing lawn Monica earned $56. Write an equation to find,s, the amount of money Samuel earned ?
Answer:
see below
Step-by-step explanation:
Monica earned twice as much as Samuel
m = 2*s
Divide each side by 2
1/2 m = 1/2 ( 2s)
1/2 m = s
If monica earned 56
1/2 (56) = s
28 =s
What Does The M And B Stand For In y=mx+b
Answer:
The 'm' stands for slope and the 'b' stands for the y-intercept, which is where the line crosses the y-axis.
Answer:
m is the slope and b is the y intersection
Step-by-step explanation:
find the area of this circle
Answer:
A= πr²
where pi = 3
and r = 3
A = 3 x 3²
3 x 9
area = 27 ft²
Question 4: Linearize x** + 2x* + 2x^2 - 12x + 10 = 0. Around its equilibrium position
The linearized equation around its equilibrium position is given as;f(x) = -4.8(x - 1.39)
The given equation is x² + 2x* + 2x² - 12x + 10 = 0.
It needs to be linearized around its equilibrium position.
Linearizing the given equation around its equilibrium position x0, we have;
f(x) = f(x0) + f'(x0)(x - x0)
Where f(x) = x² + 2x* + 2x² - 12x + 10
The equilibrium position is the point where f(x) = 0.
Hence, f(x0) = 0.
Thus, x² + 2x* + 2x² - 12x + 10 = 0⇒ 3x² - 6x = -10⇒ x² - 2x + (2.33) = 0(x-1)² = 0.77x - 0.77 or
x = 1 + (0.77)/(2) or x = 1.39
Hence, the equilibrium position x0 = 1.39.
Substitute x0 = 1.39 in the equation and simplify to get f'(x0):
f(x) = x² + 2x* + 2x² - 12x + 10
f(x) = 3.84 - 8.34 + 10
f'(x0) = f'(1.39) = -4.8
Therefore, the linearized equation around its equilibrium position is given as;f(x) = -4.8(x - 1.39)
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pls help me with this i will give brainliest to who answer both questions
Answer:
1st one: 50 cups
2nd one: 3.125 gallons
Step-by-step explanation:
Question 1:
2.5 cups per pitcher
20pitchers x 2.5cups = 50cups total
Question 2:
16 cups per gallon
50cups / 16cups = 3.125 gallons
Answer:
D 50
Step-by-step explanation:
B 34 gallons
For which value of x will the rational expression below be undefined? Check all that apply. (x-5)(x+2)/x+1 A. -5 B. -1 C. 1 D. 5 E. -2 F. 2
Answer:
B. -1Step-by-step explanation:
Given expression:
(x-5)(x+2)/(x+1)This is undefined when the denominator is zero:
x + 1 = 0x = -1Correct choice is B
Answer:
Answer :-\( \sf \: \dfrac{(x - 5)(x + 2)}{x + 1} \)
Now,
Taking denominator as 0
x + 1 = 0
x = 0 - 1
x = -1
suppose set a contains 97 elements and set b contains 67 elements. if the total number elements in either set a or set b is 132, how many elements do sets a and b have in common?
Answer:
32 elements------------------
Use the formula for the union of two sets:
|A ∪ B| = |A| + |B| - |A ∩ B|In this case, we have:
|A ∪ B| = 132,|A| = 97, and |B| = 67.Plugging these values into the formula:
132 = 97 + 67 - |A ∩ B|Now, solve for |A ∩ B| (the number of elements in common):
|A ∩ B| = 97 + 67 - 132 |A ∩ B| = 164 - 132 |A ∩ B| = 32So, sets A and B have 32 elements in common.
The bar graph below gives the distribution of the most popular colors for cars and light trucks sold globally in 2010.
The given distribution of the most popular car colors for 2010 is presented in a bar graph. This type of plot effectively displays the categorical data and their corresponding percentages. Therefore, the appropriate plot for representing the given data is the bar graph provided initially.
Now let's consider the options:
a) A time series plot: A time series plot is used to visualize data over a specific period of time. Since the given data represents the distribution of car colors for a single year (2010), a time series plot is not appropriate in this case. Therefore, option a) is not suitable.
b) A pie chart: A pie chart is commonly used to represent parts of a whole. In this case, the data is already presented in a bar graph, which effectively displays the proportions of each car color. Although a pie chart can also represent proportions, it may not provide the same level of clarity as the bar graph. Therefore, option b) is not necessary.
c) A histogram: A histogram is used to visualize the distribution of continuous or discrete data across intervals or bins. In this case, the data is categorical, representing specific car colors and their corresponding percentages. Therefore, a histogram is not appropriate.
d) All of the above: Since options a) and c) are not suitable for representing the given data, the correct answer is not d) "All of the above."
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The bar graph below gives the distribution of the most popular colors for cars and light trucks sold globally in 2010. Most popular car colors (2010) CE 20 15 Percent 10 Silver Black While Blue Gray Red Color Brown Other Which of the following kinds of plots would also be appropriate for these data? a) a time series plot b) a pie chart a histogram. a) a time series plot b) a pie chart. c) a histogram. d) All of the above
The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.30 before the discount, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal? Round your intermediate calculations and answer to the nearest cent.
The total cost of the meal is $
Answer:
$82.21
Step-by-step explanation:
cost of meal: $78.30
15% discount: 15% of $78.30 = 0.15 × $78.30 = $11.75
tip: 20% of $78.30 = 0.20 × $78.30 = $15.66
total cost = $78.30 - $11.75 + 15.66 = $82.21
Answer: $82.21
The function f(x) = RootIndex 3 StartRoot x EndRoot is reflected over the x-axis to create the graph of g(x) = Negative RootIndex 3 StartRoot x EndRoot. Which is the graph of g(x)? On a coordinate plane, a cube root function goes through (negative 2, negative 8), has an inflection point at (0, 0), and goes through (2, 8). On a coordinate plane, a cube root function goes through (negative 2, 8), has an inflection point at (0, 0), and goes through (2, negative 8). On a coordinate plane, a cube root function goes through (negative 8, 2), has an inflection point at (0, 0), and goes through (8, negative 2). On a coordinate plane, a cube root function goes through (negative 8, negative 2), has an inflection point at (0, 0), and goes thorugh (8, 2).
Answer: On a coordinate plane, a cube root function goes through (negative 8, negative 2), has an inflection point at (0, 0), and goes thorugh (8, 2).
Step-by-step explanat hope that help
The function is
\(\\ \sf\longmapsto f(x)=\sqrt[3]{x}\)
Graph attached
The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using
Answer:
PEMDAS or BIDMAS
Step-by-step explanation:
You want to know how to remember the order of operations.
AcronymsCommonly used acronyms for the Order of Operations are ...
PEMDAS
BIDMAS
The letters of these stand for ...
P, B — parentheses or brackets
E, I — exponents or indices
M, D — multiplication and division
A, S — addition and subtraction
PrecedenceExpressions enclosed in grouping symbols (parentheses or brackets) have the highest precedence. They are evaluated first, according to the order of operations.
Exponents (indices) are evaluated next. A sequence of exponent operations, such as a^b^c is evaluated right to left, as a^(b^c), unless parentheses modify the order.
Because exponents and indices have a higher precedence than other arithmetic operations, something like 2^3x is evaluated as (2^3)x, not 2^(3x), and √2p is (√2)p, not √(2p). It is fairly common to see a square root erroneously written as 3^1/2 = (3^1)/2 = 3/2 when 3^(1/2) = √3 is intended.
Multiplication and division have the same precedence. Even though M precedes D (or D precedes M, depending on which acronym you use), they are evaluated in order of appearance left to right. As with exponents, a common error is forgetting to put parentheses around numerators and denominators. For example, 3/2π is different from 3/(2π).
Similarly, addition and subtraction have the same precedence and are evaluated in order of appearance, left to right.
CompositionThe composition (ring) operator (∘) is used to signify a sequence of functional or transformation operations. For example (f∘g)(x) is the composition of functions f and g. The functions or transformations in a composition are evaluated right to left:
(f∘g)(x) = f(g(x))
Special notationsOperations performed on functions can be written in confusing ways. For example, ...
\(y = f^{-1}(x)\qquad\text{means }x=f(y),\text{ not }y=\dfrac{1}{f(x)}\)
The notation using a positive exponent stands in contrast:
\(\sin^4(x)\qquad\text{usually means }(\sin(x))^4,\text{ not }\sin(\sin(\sin(\sin(x))))\)
On the other hand, an exponent applied to a function name can mean recursive application of the function, as in sin²( ) = sin(sin(...)). It can also mean an n-th derivative. Context is important in such situations.
what is 0.416 rounded to the nearest tenth
Answer: 0.4
Step-by-step explanation:
In a run chart, the variable being measured is typically placed on what axis?
(A) X axis
(B) Y axis
(C) Either axis
(D) Neither axis;
p: It is winter.
q: There is snow on the ground.
r. There are Christmas lights on houses.
Translate the following statement and determine its truth value.
(~r^~q) →p
A.
If there are not Christmas lights on houses and there is not snow on the ground, then it is winter.
True
B. If there are not Christmas lights on houses and there is not snow on the ground, then it is winter.
False
C. If there are Christmas lights on houses and there is snow on the ground, then it is winter.
True
D.
If there are Christmas lights on houses and there is snow on the ground, then it is winter.
False
Answer:
C
Step-by-step explanation
the weather usually gets colder in the winter and people usually decorate for Christmas late fall and early winter.
therefore, if there is snow on the ground and Christmas lights on houses its most likely winter.
help me please!!!!!!
Answer:
C = 4d+5c+6a
Step-by-step explanation:
This is quite simple, for you have 3 different items. To find the cost of it, you simply give each type of mix a variable and put their costs as the value before the variable. This equation would come out to be:
C = 4d+5c+6a
which of the following facts should make you the most worried about the reliability of the results of the test in this case? there is no need to worry because all of the expected cell counts are above 5. the sample was only 300 black women and is not representative of all black women. two of the six observed counts are 5 or less. not all of the cells' contributions to the chi-squared statistic are greater than 1. two of the six expected counts are less than 5.
Therefore, the reliability of the results may be questioned due to the small sample size and the fact that the observed and expected counts in some cells are too small.
The fact that two of the six observed counts are 5 or less should make you the most worried about the reliability of the results of the test in this case. This is because when the observed counts in a cell are too small, it is difficult to draw reliable conclusions from them. In such cases, the chi-squared statistic may not accurately reflect the true relationship between the variables being studied. This is because the chi-squared statistic is based on the difference between the observed counts and the expected counts, and if the observed counts are too small, the chi-squared statistic may be biased and not accurately reflect the true relationship between the variables.
Moreover, the fact that two of the six expected counts are less than 5 also raises concerns about the reliability of the results. This is because when the expected counts in a cell are too small, it may indicate that the sample size is too small or that the sample is not representative of the population being studied. In this case, the sample size was only 300 black women, which may not be representative of all black women.
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I need to know if it's Associative Property of Addition or Associative property of Multiplication or Commutative property of Addition or Commutative property of multiplication or Distributive property
Based on the information, it should be noted that line 1 to line 2 illustrates the Commutative property of multiplication and line 2 to line 3 illustrates the distributive property.
How to illustrate the information?Commutative property of multiplication states that the result is unaffected by the order of the factors.
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.
Therefore, based on the information, it should be noted that line 1 to line 2 illustrates the commutative property of multiplication and line 2 to line 3 illustrates the distributive property.
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please help i’m failing pre calc!!!
Linear function : y = x + 4
Exponential function : y = 4.5 e^(0.144 x)
Power function : y = 4.5 x^0.415
Evaluate 3 x 6 - 12 + 6.
3 x 6 - 12 / 6
Answer:
16
Step-by-step explanation:
Pemdas is the order of operations
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Answer:
16
Step-by-step explanation:
3 x 6 - 12 / 6.
18 - 2
16
GFH and HFJ are adjacent and congruent what are two conclusions you can draw from this infomation?
We can give the following two conclusions:
GFH and HFJ are congruent, meaning they have the same size and shape.GFH and HFJ are adjacent, meaning they share a common side or vertex.Conclusions for GFH and HFJFrom the information provided:
Since GFH and HFJ are adjacent, they share a common side or vertex. This means that the two figures are not only congruent, but they also share at least one common angle.
Since GFH and HFJ are congruent, they have the same size and shape. This means that corresponding angles and sides are equal in measure. It also means that the two figures can be superimposed on each other exactly.
In conclusion, since they are congruent and adjacent, we can say that they are part of a larger geometric figure.
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A football coach is trying to decide what team is ahead lay in the girl with strategies better play the regular Defense play a prevent DFS the guards or against lol games, but make sure Gaines easier the coach of use the outcome of 100 games
The greater probability is the probability of winning through the use of regular defense.
How to solve for the probabilityIf out of the 100 games that were reviewed, the defense games were 50 and the prevent defense games were 50 as well
Out of the regular 50, there are 38 wins and then 12 loses. Out of the prevent games, there 29 wins and 21 loses.
The probability to win by regular is 38 / 50 = 0.76
the probability to win by prevent defense is 29 / 50 = 0.58
0.76 is greater than 0.58 hence the decision would be to win the game by playing the regular defense.
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A football coach is trying to decide: When a team is ahead late in the game, which strategy is better?
Play the "regular" defense.
Play a "prevent" defense that guards against long gains but makes short gains easier.
The coach reviews the outcomes of 100 games.
Compare the probability of winning when playing regular defense with the probability of winning when playing prevents defense. Draw a conclusion based on your results.
a bus drives for 3 and a half hours at an average speed of 56mph how far does the bus drive?
Answer:
196 miles
Step-by-step explanation:
distance (D) is calculated as
D = S × T ( S is average speed and T is time in hours )
here T = 3 and a half hours = 3.5 hours and S = 56 , then
D = 56 × 3.5 = 196 miles
a line passes through the point (-9,-8) and is parallel to the line with equation y=5x-7. what is the slope of this line?
Answer:
5
Step-by-step explanation:
slopes of the parallel lines are always same this line has slope five
because equation in y intercept form is y=mx+b
where m is the slope.
so the slope of the new line will be five
Please help. Fill in the blanks
Answer:
Step-by-step explanation:
1). 3x(2x - 2) = 3x(2x) + 3x(-2) [By distributive property]
2). x²(_ + 5x - 3) = (3)x² + x²(5x) + x²(-3)
3). _(x² - 3x + _) = x(x²) - (x)(-3x) + (x)(2)
4). (2x + 9)(x + 2) = 2x(x + 2) + 9(x + 2)
= 2x² + 4x + 9x + 18
= 2x² + 13x + 18
5). (z - 4)(2z + 1) = z(2z + 1) + (-4)(2z + 1)
= 2z² + z - 8z - 4
= 2z² - 7z - 4
Someone please help me
Answer:
-240
Step-by-step explanation:
2/6k +80 = 3/6k +120
80=1/6k+120
-40=1/6k
- 240= k