\( \sf{\qquad\qquad\huge\underline{{\sf Answer}}} \)
Let's evaluate ~
\(\qquad \sf \dashrightarrow \: 4 {x}^{3} {y}^{2} \)
now, plug in the values :
\(\qquad \sf \dashrightarrow \: 4( -1 ) {}^{3}( {2)}^{2} \)
\(\qquad \sf \dashrightarrow \: 4( - 1)(4)\)
\(\qquad \sf \dashrightarrow \: - 4(4)\)
\(\qquad \sf \dashrightarrow \: - 16\)
So, the equivalent value is 16
Hii!
__________________________________________________________
\(\leadsto\parallel\boldsymbol{Answer.}\parallel\gets\)
Value of the expression =
_________________________________________________________
\(\multimap\parallel\boldsymbol{Explanation.}\parallel\gets\)
SUBSTITUTE the value of "x" instead of x and the value of "y" instead of y.
\(\sf 4(-1)^3(2)^2}\)
NOW we can use P.E.M.D.A.S. to simplify this expression.
Remember, this acronym stands for.
P=Parentheses,
E=Exponents,
M=Multiplication,
D=Division,
A=Addition,
S=Subtraction,
and now we can use it to simplify.
We have the exponents first.
\(\sf 4\cdot(-1)\cdot4}\).
NOW we multiply.
\(\sf -16}\)
______________________________________________________
Hope that this helped! Best wishes.
\(\textsl{Reach far. Aim high. Dream big.}\)
\(\boldsymbol{-Greetings!-}\)
________________________________________________________
The sum of 2 consecutive numbers is 69. What are the numbers?
Answer:
34, 35Step-by-step explanation:
z - some integer
then the consecutive integer would be:
z+1, (or z-1)
the sum is 69 so:
z + z+1 = 96
2z = 68
z = 34
z+1 = 34 + 1 = 35
(or:
z + z-1 = 69
2z = 70
z = 35
z-1 = 35 - 1 = 34)
Calculate the correlation coefficient of the following data:
X
1
4
8
6
2
y
9
16
22
24
12
Answer:
0.177
Step-by-step explanation:
A perfect correlation is 1. So .998 or even .863 is a good correlation.
since our decimal isn't close to that at all, we have a weak positive correlation.
Calculate the double integral.
∬R 3xy^2/x^2 + 1 dA, R = {(x, y) | 0 ≤ x ≤ 1, −2 ≤ y ≤ 2}
Therefore , the solution of the given problem of integral comes out to be 8ln2 is solution for the integral expression.
Define integral.The region beneath a curve among two set limits is referred to as a definite integral. The representation of the definite integral for such a function of two variables), defined to reference to the x-axis, is ∫ baf(x)dx a b f (x) d x, where an is the lower bound and b is the upper bound.
Here,
Given :
\(\int\limits \int\limitsa_R\) 3xy²/x²+ 1 dA
=> R = {(x, y) | 0 ≤ x ≤ 3, −2 ≤ y ≤ 2} ·
So,
=> \(\int\limits^1_{x=0} \int\limits^2_{y=-2}\) 3xy²/x²+ 1 dxdy
=> \(\int\limits^1_{x=0}\) 3x / x²+ 1 \(\int\limits^2_{y=-2}\) y²
=>\(\int\limits^1_{x=0}\) 3x / x²+ 1 ( y³/2)²dx
=> \(\int\limits^1_{x=0}\) 3x / x²+ 1 (8 + 8 /3) dx
=> \(\int\limits^1_{x=0}\) 16x/x²+ 1
=> 8 [ln(x²+ 1) ]
=> 8 [ln2 -ln1 ]
=>8ln2
Therefore , the solution of the given problem of integral comes out to be
8ln2 is solution for the integral expression.
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F(x)=(x-2)2
X=8
Need answers ASAP
Answer:
substitute 8 into x =(8-2)2
(6)2=12
Evaluate the expression: -2w-7 for:
w = -8
w = 4
w = 0
(please help!)
Answer:
9 , 1 , - 7
Step-by-step explanation:
Substitute the given values of w into the expression and evaluate
w = - 8 : - 2(- 8) - 7 = 16 - 7 = 9
w = 4 : - 2(4) - 7 = 8 - 7 = 1
w = 0 : - 2(0) - 7 = 0 - 7 = - 7
. A restaurant charges a $100 setup fee, plus $15 per guest, to host a private party. The table
below shows the cost of hosting a private party for a certain number of guests.
Total Cost of Hosting a Private Party
Number of Guests Total Cost
(dollars)
10
250
20
400
30
550
40
700
50
850
How much does the restaurant charge for a private party with 45 guests?
Answer:
42
Step-by-step explanation:
i said so
The restaurant charge 775 $ in total for a private party with 45 guests.
What is a linear equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let's suppose the total number of guest is x;
and, the Total Cost of Hosting a Private Party be y;
here it is given that :
A restaurant charges a $100 setup fee, plus $15 per guest, to host a private party then, this van be shown in linear equation as :
y = 15x + 100
Now, for 45 number of guests that is x = 45, then y will be :
y = 15x + 100
y = 15 x 45 + 100
y = 675 + 100
y = 775 $
Thus, the restaurant charge 775 $ in total for a private party with 45 guests.
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Can you help me plz
Answer:
\(\boxed{\sf y=6}\)
Step-by-step explanation:
There are 5 identical squares.
The area of one square is \(\sf s^2\).
\(\sf{y^2 } \times \sf{5}\)
\(\sf 5y^2\)
The area of the whole shape is 180 cm².
\(\sf 5y^2=180\)
Solve for y.
Divide both sides by 5.
\(\sf y^2=36\)
Take the square root on both sides.
\(\sf y=6\)
what is the best answer 5+5-5x5/5
a. 7
b. 5
c. 3
d. 8
Answer:
5
Step-by-step explanation:
we do multiplication and division first and then addition/subtraction
5+5-5x5/5
5+5-25/5
5+5-5
10-5
5
Hopes this helps please mark brainliest
6=m-7. solve using addition or subtraction
8
Step-by-step explanation:
m=13 because you add the 7 to the 6 and then divide it too m
Answer:
6+7=m
13=m
m=13
Step-by-step explanation:
1. Add 7 to both sides
2. simplify 6+7 to 13
3. switch sides
Crispy Clover, a popular vegetarian restaurant, introduced a new menu that has 20% more dishes than the previous menu. The previous menu had D dishes.
Which of the following expressions could represent how many dishes Crispy Clover's new menu has?
Option A
Explanation:
Given that Crisply clover is a popular vegetarian restaurant.
It introduced a new menu
The new menu had 20% more dishes than the previous menu
Let the dish as per previous menu = D
Now added for new dish 20% = (20/100)D
Simplify to get 1/5 D
Hence new menu has = D+(20/100)D
= D+1/5 D
Thus we find that option A is the right answer,
−7−(−7)=minus, 7, minus, left parenthesis, minus, 7, right parenthesis, equals
The expression −7−(−7) simplifies to 0
To simplify the expression −7−(−7), we need to apply the rules of arithmetic, including the rules for adding and subtracting negative numbers.
Let's break down the expression step by step:
Start with −7−(−7).
We can rewrite the subtraction of a negative number as the addition of its opposite. So, −7−(−7) becomes −7 + 7.
When we add a negative number to a positive number, it is the same as subtracting the absolute value of the negative number. In this case, −7 + 7 is equivalent to subtracting the absolute value of −7, which is 7.
Therefore, −7−(−7) simplifies to −7 + 7, which equals 0.
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Question 4 of 10
The standard form of the equation of a parabola is y=x²-6x+14.
What is the vertex form of the equation?
OA y=(x-3)2 +15
OB. y = (x+3)(x-3) +5
O C. y=(x-3)2 +23
OD. y=(x-3)² +5
The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.
To convert the given equation from standard form to vertex form, we need to complete the square.
The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.
Given equation: y = x² - 6x + 14
Move the constant term to the right side:
y - 14 = x² - 6x
Complete the square by adding and subtracting the square of half the coefficient of x:
y - 14 + 9 = x² - 6x + 9 - 9
Group the terms and factor the quadratic:
(y - 5) = (x² - 6x + 9) - 9
Rewrite the quadratic as a perfect square:
(y - 5) = (x - 3)² - 9
Simplify the equation:
y - 5 = (x - 3)² - 9
Move the constant term to the right side:
y = (x - 3)² - 9 + 5
Combine the constants:
y = (x - 3)² - 4
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Write tan 41π/36 in terms of the tangent of a positive acute angle.
tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))
To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.
First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):
41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π
Now, we can rewrite the angle as:
tan(41π/36) = tan((10/9)π + (1/36)π)
Next, we'll use the tangent addition formula, which states that:
tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))
In this case, A = (10/9)π and B = (1/36)π.
tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))
Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.
For (10/9)π, we can subtract π to get an equivalent angle within the range:
(10/9)π - π = (1/9)π
Similarly, for (1/36)π, we can add π to get an equivalent angle:
(1/36)π + π = (37/36)π
Now, we can rewrite the expression as:
tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))
Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:
tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))
Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.
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find the cardinal # of the following set. assume the pattern continuesThe cardinal number of {x?x = 1, 2, 3, ..., 94) is
The number of elements in a set is the cardinal number of the set
Here the number starts from 1 and continues till 94. So there are 94 numbers. Thus, the cardinal number of the set (1,2,3....94) is 94. The cardinal number of an empty set is 0.
help plssss <333 will mark brainliest if correct
Answer:
-3
Step-by-step explanation:
it might not be correct, the site I use for math glitches sometimes
Answer:
x=1
Step-by-step explanation:
its right :)
When comparing two sample proportions with a​ two-sided alternative​ hypothesis, all other factors being​ equal, will you get a smaller​ p-value if the sample proportions are close together or if they are far​ apart? Explain. Choose the correct answer below.
A. The​ p-value will be smaller if the sample proportions are far apart because a larger difference results in a larger absolute value of the numerator of the test statistic.
B. The​ p-value will be smaller if the sample proportions are far apart because a larger difference results in a pooled proportion closer to​ 0.5, and a pooled proportion close to 0.5 results in a smaller standard​ error, which is the denominator of the test statistic.
C. The​ p-value will be smaller if the sample proportions are close together because the difference between them is smaller.
D. The​ p-value will be smaller if the sample proportions are close together because closer proportions results in a smaller standard​ error, which is the denominator of the test statistic.
The p-value will be smaller if the sample proportions are far apart because a larger difference results in a larger absolute value of the numerator of the test statistic. A
The p-value measures the strength of the evidence against the null hypothesis.
A smaller p-value indicates stronger evidence against the null hypothesis, and a larger p-value indicates weaker evidence against the null hypothesis.
Comparing two sample proportions with a two-sided alternative hypothesis, all other factors being equal, the p-value will be smaller if the sample proportions are far apart.
This is because a larger difference between the sample proportions results in a larger absolute value of the numerator of the test statistic, which is used to calculate the p-value.
The numerator of the test statistic is the difference between the sample proportions, so a larger difference between the sample proportions will result in a larger absolute value of the numerator, which will result in a smaller p-value.
Option A correctly explains this by stating that a larger difference between the sample proportions results in a larger absolute value of the numerator of the test statistic, which results in a smaller p-value.
Option B is not correct, as a pooled proportion close to 0.5 actually results in a larger standard error, which would result in a larger p-value, not a smaller one.
Option C is not correct, as a smaller difference between the sample proportions would result in a larger p-value, not a smaller one.
Option D is also not correct, as a smaller standard error would result in a larger test statistic and a smaller p-value, but the standard error is not affected by the closeness of the sample proportions.
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Tell whether each of the following is a function.
1. Which of the following could be a function? Select three that apply.
A {(2,5),(4, -3), (-2,1),(1,6)}
B {(1,3), (2, 1), (3,5), (1, -3)}
C {(-1, 1), (0,0), (1, 1), (-2,2)}
D {(0,0), (2,4), (2,-4), (3,9)}
E {(-2,8),(-3,-27),(-1,1),(3,27)}
Answer:
A, C, E
Step-by-step explanation:
A function cannot have an x-value that produces more than y-value. Examples would be {(2, 2), (2,3)} and {(1,0), (1,5)}.
A - This could be a function because it follows the above rule.
B - This can not be a function because it has an x-value that has two y-values.
C - This could be a function because it follows the rule.
D - This can not be a function because it has an x-value that has two y-values.
E - This could be a function because it follows the rule.
I NEED HELP!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
1(
m<1= 62°
2)
m<1=90°
3)
180-70-65=45
m<1= 45°
4)
180-90-30=60
m<1= 60°
Let f(x,y,z)=3xz+sin(xy)ez. what is fxz ? Find the gradient at the point (0,0,0) ? 2. Find the cosine of the angle between the vectors a =2i+3j−4k and b =5i−1j+1k. (You should leave your answer in unsimplified form, up till where you would need calculator to further simplify.) 3. Find the equation of the plane containing both the point (1,2,3) and the line r(t)=⟨t,2t+1,3t⟩. Write it in the form ax+by+cz=d.
The gradient of f(x, y, z) at the point (0, 0, 0) is (0, 0, 0).
2. cos θ = (a · b) / (||a|| ||b||) = 3 / (√(29) * √(27)) = 3 / (√(783))
The cosine of the angle between vectors a and b
To find the partial derivative fxz, we differentiate the function f(x, y, z) with respect to x, treating y and z as constants, and then differentiate the result with respect to z.
f(x, y, z) = 3xz + sin(xy)ez
Differentiating f(x, y, z) with respect to x:
∂/∂x (f(x, y, z)) = ∂/∂x (3xz + sin(xy)ez)
= 3z + ycos(xy)ez
Now, differentiating the above result with respect to z:
∂²/∂xz (f(x, y, z)) = ∂/∂z (3z + ycos(xy)ez)
= 3 + ycos(xy)ez
Therefore, fxz = 3 + ycos(xy)ez.
Next, let's find the gradient of the function f(x, y, z) at the point (0, 0, 0). The gradient is a vector that consists of the partial derivatives of the function with respect to each variable.
Gradient of f(x, y, z) = (∂/∂x (f(x, y, z)), ∂/∂y (f(x, y, z)), ∂/∂z (f(x, y, z)))
∂/∂x (f(x, y, z)) = 3z + ycos(xy)ez
∂/∂y (f(x, y, z)) = xcos(xy)ez
∂/∂z (f(x, y, z)) = 3x + sin(xy)ez
At the point (0, 0, 0), these partial derivatives become:
∂/∂x (f(x, y, z)) = 0 + 0 = 0
∂/∂y (f(x, y, z)) = 0
∂/∂z (f(x, y, z)) = 0 + sin(0) = 0
Therefore, the gradient of f(x, y, z) at the point (0, 0, 0) is (0, 0, 0).
Moving on to the second question:
To find the cosine of the angle between vectors a = 2i + 3j - 4k and b = 5i - 1j + 1k, we can use the formula:
cos θ = (a · b) / (||a|| ||b||)
where a · b represents the dot product of vectors a and b, and ||a|| and ||b|| represent the magnitudes of vectors a and b, respectively.
Calculating the dot product:
a · b = (2 * 5) + (3 * -1) + (-4 * 1) = 10 - 3 - 4 = 3
Calculating the magnitudes:
||a|| = √(2² + 3² + (-4)²) = √(4 + 9 + 16) = √(29)
||b|| = √(5² + (-1)² + 1²) = √(25 + 1 + 1) =√(27) = √(3³)
Substituting these values into the cosine formula:
cos θ = (a · b) / (||a|| ||b||) = 3 / (√(29) * √(27)) = 3 / (√(783))
Therefore, the cosine of the angle between vectors a and b
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Which trigonometric function would you use to find x
Answer:
law of sines
Step-by-step explanation:
a over sinA = b over sinB
In an examination Alan obtained 32 out of 40 marks. In another examination Ben obtained 3/4of the total marks. Express the marks of each candidate as a percentage.
what are the differences between one tailed and two tailed test?
The main difference between one-tailed and two-tailed tests is their directionality. One-tailed tests are used when a researcher has a particular expectation about the direction of the relationship, whereas two-tailed tests are used when the researcher does not have a particular expectation about the direction of the relationship.
What are the differences between one tailed and two tailed test?The differences between one-tailed and two-tailed tests are that the one-tailed test looks for the possibility of a relationship in one direction, while the two-tailed test looks for the possibility of a relationship in both directions
The one-tailed test is also known as the directional hypothesis test, which means that it examines whether a certain effect is greater or less than what is expected. As a result, one-tailed testing only happens in one direction, either the right or the left side of the distribution.
The two-tailed test, on the other hand, is also known as a non-directional hypothesis test. The two-tailed test looks at whether there is a relationship between two variables, whether it is positive or negative. In other words, two-tailed tests allow researchers to find if there is an impact between two variables in both directions.
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Evaluate the expression 9b−6b÷3b for b=7.
Answer:
The answer is 1.
Step-by-step explanation:
9 times 7 equals 63. 6 times 7 equals 42. 3 times 7 equals 21.
63 take away 42 is 21.
21 divided by 21 is 1!
Answer:
I'm not sure which one it is, so I did both.
1. 9b-(6b/3b) = 9b-2
b = 7
9(7)-2 = 61
2. (9b-6b)/3b = 1
in the u.s. orphanage experiment, a control group of babies stayed in the orphanage where human interaction was minimal. a second group of babies, the experimental group, was moved to an institution for women with low iqs who showered them with love and attention. the experiment started when the babies were about 19 months old. two and one-half years later both groups were given iq tests. what was the outcome of the experiment?
The sound group gained IQ points due to the interactions with the women, regardless of their IQ was the outcome of the experiment.
What term is used to describe the idea that people try to control others think about them?
It is claimed that brainwashing impairs a person's capacity for autonomous or critical thought, permits the entry of unwelcome ideas and concepts into their heads, and alters a person's attitudes, values, and beliefs.
Why do people try to control others?
Anxiety disorders and personality problems are the most prevalent. In order to feel at ease, people with anxiety disorders feel the need to control everything around them. They might not have faith in others to manage situations the way they will.Learn more about brainwashing
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A student takes an exam containing 17 true or false questions. At least 11 correct answers are required to pass. If the student guesses, what is the probability that he will fail
The probability that the student will fail, given that he guesses the answers, is 0.227.
Since there are only two possible outcomes for each question (true or false),
the probability of guessing a correct answer is 1/2 = 0.5.
Likewise, the probability of guessing a wrong answer is also 1/2 = 0.5.
To find the probability of failing the exam,
we need to find the probability of answering less than 11 questions correctly.
Using the binomial probability formula,
the probability of getting k successes (correct answers) in n trials (questions) is given by:
P(k) = (n C k) * p^k * q^(n-k)
where p is the probability of success (getting a correct answer),
q is the probability of failure (getting a wrong answer), and (n C k) is the number of combinations of n things taken k at a time.
In this case,
n = 17, p = 0.5, and
q = 0.5.
The number of ways to get less than 11 correct answers is:
P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)P(X = k) = (n C k) * p^k * q^(n-k)
Substituting the values:
P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)
P(X = 0) = (17 C 0) * (0.5)^0 * (0.5)^17 = 0.0015
P(X = 1) = (17 C 1) * (0.5)^1 * (0.5)^16 = 0.0146
P(X = 2) = (17 C 2) * (0.5)^2 * (0.5)^15 = 0.0586
P(X = 3) = (17 C 3) * (0.5)^3 * (0.5)^14 = 0.1558
P(X = 4) = (17 C 4) * (0.5)^4 * (0.5)^13 = 0.268
P(X = 5) = (17 C 5) * (0.5)^5 * (0.5)^12 = 0.327
P(X = 6) = (17 C 6) * (0.5)^6 * (0.5)^11 = 0.2732
P(X = 7) = (17 C 7) * (0.5)^7 * (0.5)^10 = 0.1537
P(X = 8) = (17 C 8) * (0.5)^8 * (0.5)^9 = 0.0573
P(X = 9) = (17 C 9) * (0.5)^9 * (0.5)^8 = 0.013
P(X = 10) = (17 C 10) * (0.5)^10 * (0.5)^7 = 0.0015
Therefore, P(X < 11) = 0.0015 + 0.0146 + 0.0586 + 0.1558 + 0.268 + 0.327 + 0.2732 + 0.1537 + 0.0573 + 0.013 + 0.0015P(X < 11) = 0.8857
Thus, the probability of failing is: P(fail) = P(X < 11) = 0.8857
The probability that the student will fail, given that he guesses the answers, is 0.227 (rounded to three decimal places).
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Find all angles, 0°< A<360°, that satisfy the equation below, to the nearest tenth
of a degree (if necessary).
3 tan A+75 = 0
Answer:
143.3 degrees and 323.3 degrees
Step-by-step explanation:
Given the equation
3tanA +√5 = 0
3tanA = -√5
tanA =-√5/3
tanA = (-0.7454)
A = arctan(-0.7453)
A = -36.699
Since tan is negative in 2nd and 4th quadrant
A = 180 - 36.699
A = 143.3 degrees
In the fourth quadrant
A = 360 - 36.699
A = 323.3degrees
Hence the value of A that satisfies the equation are 143.3 degrees and 323.3 degrees
Dania had discovered that three 4 inches diameter balls fitted exactly into the bottom of a cylindrical jar. She dropped the 4th ball on top of the three and poured water. If the height of the jar is 20 inches, determine the volume of water just enough to cover the 4 balls.
The volume of each ball is (32/3)π cubic inches, and the volume of water just enough to cover the four balls is also (32/3)π cubic inches.
First, let's calculate the volume of each ball. The diameter of each ball is given as 4 inches, so the radius (half the diameter) of each ball is 2 inches. The formula to calculate the volume of a sphere is V = (4/3)πr^3, where V represents volume and r represents the radius.
For each ball, the volume is:
V = (4/3)π(2³)
V = (4/3)π(8)
V = (32/3)π cubic inches
Since there are three balls at the bottom of the jar, the combined volume of these three balls would be:
3 * (32/3)π = 32π cubic inches
Now, let's consider the fourth ball. Since it is dropped on top of the three balls, it will displace some water, and the volume of the water needed to cover the four balls will be equal to the volume of the fourth ball.
To find the volume of the fourth ball, we use the same formula:
V = (4/3)πr³
Since the diameter of the fourth ball is also 4 inches, its radius is 2 inches. Substituting this value into the formula, we get:
V = (4/3)π(2³)
V = (4/3)π(8)
V = (32/3)π cubic inches
Therefore, the volume of water required to cover the four balls is also (32/3)π cubic inches.
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Pls tell me so quotes of not giving up
Answer:
Step-by-step explanation:
Knowledge is knowing a tomato is a fruit, wisdom is not putting it in a fruit salad
Your time is too valuable to waste on those who don't deserve it
Never give up great things take time
Failure is not an acception
As a wise fish once said "Just Keep Swimming" the more u swim the closer you get to your goal.
What does a hexagon look like in math?
A closed, two-dimensional, six-sided polygon in geometry is called a hexagon.
A closed, two-dimensional, six-sided polygon in geometry is called a hexagon. It has six vertices, which together create six internal angles and six line segments. The total of a hexagon's internal angles is 720°. A hexagon's form is also shown in the illustration below:
Based on the dimensions of the sides and angles, we can divide the hexagonal form into numerous categories. With the help of pertinent figures and examples, these are discussed here.
Standard hexagon
If all of the sides have the same length and all of the interior angles are the same size, a hexagon is said to be a regular hexagon. Moreover, the interior angle is 120 degrees. The regular hexagon has rotational symmetry of order six and six symmetrical lines.
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Find the value of c such that:
SUM(e^nc)=10
The value of c that satisfies the equation \(\sum_{n=1}^{\infty} e^{nc}=10\) is approximately -0.0451.
What is a equation?
An equation is a mathematical statement that asserts the equality of two expressions.
To find the value of c such that the infinite series \(\sum_{n=1}^{\infty} e^{nc}\) is equal to 10, we can use the formula for the sum of an infinite geometric series with \(a = e^c\).
The formula for the sum of an infinite geometric series is given by:
S = a / (1 - r),
where S is the sum of the series, a is the first term, and r is the common ratio.
In this case, \(a = e^c\) and the common ratio \(r = e^c\).
We can rewrite the equation as:
\(10 = e^c / (1 - e^c)\)
Next, let's solve for c:
\(10(1 - e^c) = e^c\)
\(10 - 10e^c = e^c\)
\(10 = 11e^c\)
\(e^c = 10 / 11\)
Taking the natural logarithm (ln) of both sides:
\(c = ln(10 / 11)\)
Using a calculator, we can find the approximate value of c:
c ≈ -0.0451.
Therefore, the value of c that satisfies the equation \(\sum_{n=1}^{\infty} e^{nc}=10\) is approximately -0.0451.
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