The sum of the first six terms of the given series is 31.99.
What is series and sequence?A list of elements or objects that have been arranged sequentially is referred to as a sequence.
The total of all the terms in a sequence can be used to very broadly define a series. All of the terms in the sequence must, however, clearly relate to one another.
The given sequence is 4, 10, 2.5, 0.625, . . .
Every successive term in given series is divided by 4, and the so the first six terms of the series are:
[tex]\frac{40}{4} = 10\\ \\ \frac{10}{4} = 2.5 \\\\\frac{2.5}{4}= 0.625\\ \\\frac{0.625}{4} = 0.156\\\\\frac{0.156}{4}= 0.039\\\\\frac{0.039}{4}= 0.0097[/tex]
Also, every even term in the series is subtracted from the previous term.
Adding all the given terms we have:
[tex]40-10+2.5-0.625+0.156-0.039 = 31.99[/tex]
Hence the sum of the first six terms of the series is 31.99.
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Rhombus A B C D is shown. The length of A B is 9 s + 29 and the length of opposite side D C is 10 s minus 16.
What is the value of s and the length of side BC if ABCD is a rhombus?
s =
BC =
units
The value of s is 45 and the value of BC is 434
How to solve for s and BC?The given parameters are:
AB = 9s + 29
DC = 10s - 16
Opposite sides of rhombus are equal.
So, we have:
9s + 29 = 10s - 16
Evaluate the like terms
s = 45
Substitute s = 45 in AB = 9s + 29
AB = 9 * 45 + 29
Evaluate
AB = 434
This means that
BC = AB = 434
Hence, the value of s is 45 and the value of BC is 434
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If the clock tower in "Back to the Future" had a big hand length of 3 feet, what would be the length of the arc, in feet, the tip travels from 6:00pm to 6:20pm. Round to the nearest foot.
The length of the arc made by the big hand if the tip travels from 6:00pm to 6:20pm is 0.52 feet
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The clock reads 12 hours (720). The angle if the tip travels from 6:00pm to 6:20pm (20 minutes) is:
Ф = (20/720) * 360 = 10°
The length of the arc is given as:
Length of arc = (Ф/360) * 2π * length of hand = (10/360) * 2π(3) = 0.52 feet
The length of the arc made by the big hand if the tip travels from 6:00pm to 6:20pm is 0.52 feet
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If we sample from a small finite population without replacement, the binomial distribution should not be used because
the events are not independent. If sampling is done without replacement and the outcomes belong to one of two types,
we can use the hypergeometric distribution. If a population has A objects of one type, while the remaining B objects are
of the other type, and if n objects are sampled without replacement, then the probability of getting x objects of type A and
n-x objects of type B under the hypergeometric distribution is given by the following formula. In a lottery game, a bettor
selects four numbers from 1 to 54 (without repetition), and a winning four-number combination is later randomly
selected. Find the probabilities of getting exactly two winning numbers with one ticket. (Hint: Use A = 4, B = 50, n = 4, and
x=2.)
P(x)=
A!
B!
(A + B)!
(A-x)!x! (B-n+x)!(n-x)! (A+B-n)!n!
+
P(2)=
(Round to four decimal places as needed.)
Using the hypergeometric distribution, it is found that there is a 0.0232 = 2.32% probability of getting exactly two winning numbers with one ticket.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.For this problem, the parameters are given as follows:
N =A + B = 54, k = 4, n = 4.
The probability of getting exactly two winning numbers with one ticket is P(X = 2), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,54,4,4) = \frac{C_{4,2}C_{50,2}}{C_{54,4}} = 0.0232[/tex]
There is a 0.0232 = 2.32% probability of getting exactly two winning numbers with one ticket.
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Which rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities
Multiplicative rule's probability is a rule which states that the when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities
According to the statement
we have to explain about the those law which is used when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities
So, For this purpose we know that the
According to multiplicative rule of probability ,
If A and B are two independent events in a probability experiment, then the probability that both events occur simultaneously is: P(A and B)=P(A)⋅P(B) In case of dependent events , the probability that both events occur simultaneously is: P(A and B)=P(A)⋅P(B | A)
and we see that these conditions are fulfilled by the definition of the multiplicative rule.
So, Multiplicative rule is a rule which states that the when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities
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Planes Q and R are parallel. Explain how you know lines a and b are skew. Planes Q and R are parallel. Line a is on plane Q and is diagonal down and to the left. Line b is on plane R and is diagonal up and to the left.
Since the given lines a and b are neither parallel, nor do they intersect each other. Also, they lie on two different planes, P and Q respectively, and thus, are co-planar. hence, a and b can be called skew lines.
Definition of Skew Lines
Skew lines in 3D geometry, are, by definition, a pair of lines that are neither parallel nor intersect each other. Such lines are therefore not coplanar, according to the conclusion.
Skew lines tend to occur frequently in real-world circumstances. Let's say there is a line on the ceiling and a line on the wall. These lines can be skew lines because they lie in distinct planes if they are not parallel to one another and do not meet. Skew lines go on forever in both directions.
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Answer:
Step-by-step explanation:
Skew lines are noncoplanar and do not intersect. Line a lies in plane Q and line b lies in plane R, so the lines are not coplanar. No other plane can be drawn through the lines, so they are not parallel. So, a and b are skew.
Let x represent the number of short-sleeved shirts ordered and let y represent the number of long-sleeved shirts ordered. which system of linear equations represents the situation? 5x 10y = 100 and 5 x plus 10 y equals 100 and startfraction one-third endfraction x plus startfraction one-half endfraction y equals 1,750.x startfraction one-half endfractiony = 1,750 5x 10y = 1,750 and 5 x plus 10 y equals 1,750 and startfraction one-third endfraction x plus startfraction one-half endfraction y equals 100.x y = 100 x y = 100 and x plus y equals 100 and startfraction one-third endfraction x plus startfraction one-half endfraction y equals 1,750.x y = 1,750 x y = 1,750 and x plus y equals 1,750 and startfraction one-third endfraction x plus startfraction one-half endfraction y equals 100.x y = 100
The system of linear equations that represent the given situation is:
5x + 10y = 1750 and 1/3x + 1/2y = 100.
What is a linear equation?A linear equation is an equation with the highest degree of the variable is one. There may be one or more variables but their degree must be 1 to become a linear equation.
The general form of a linear equation is y = mx + c.
Calculation:
In the given situation,
Consider x as the number of short-sleeved shirts ordered and y as the number of long-sleeved shirts ordered.
It is given that,
Price for short-sleeved shirts = $5
Price long-sleeved shirts =$10
The total price for 100 shirts ordered = $1,750
So, we can write the linear equation as
5x + 10y = 1750 ...(i)
It is given that,
After the first week, they sold 1/3 of the short-sleeved shirts and 1/2 of the long-sleeved shirts. I.e.,
1/3x + 1/2y = 100 ...(ii)
Thus, from equations (i) and (ii), the system of linear equations that represent the given situation is
5x + 10y = 1750
1/3x + 1/2y = 100
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Disclaimer: The given question is incomplete. Here is the complete question.
Question:
The drama club is selling short-sleeved shirts for $5 each, and long-sleeved shirts for $10 each. They hope to sell all of the shirts they ordered, to earn a total of shirts ordered, and to earn a total of $1,750. After the first week of the fundraiser, they sold 1/3 of the short-sleeved shirts and 1/2 of the long-sleeved shirts, for a total of 100 shirts.
Let x represent the number of short-sleeved shirts ordered and let y represent the number of long-sleeved shirts ordered. which system of linear equations represents the situation?
Answer:
c
Step-by-step explanation:
compare these heights:
5,2 and 46,5
46.5 is higher than 5.2
Comparison of heightNote that:
The larger the magnitude(value) of the heights given the larger the heights
Units are not added to the values representing each height
By carefully considering the heights given:
5.2 is a lesser value than 46.5
Since 46.6 > 5.2, we can conclude that 46.5 is higher than 5.2
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HELP PLS!!!! i don’t get it
Answer:
153
Step-by-step explanation:
i = square root of -1
i = √-1
(3+12√-1) (3-12√-1)
√a times √b = √ab
a√b times c√d = (a times c) √ (b times d)
9 - (36√-1) + (36√-1) - (144(√-1)^2) =
9 - 0 - (144 * -1) =
9 - 0 - (-144) =
9 - (-144) =
9 + 144 =
153
*** funny thing is if you put
(3+12i) (3-12i)
in a calculator
it works!
it gives you the answer 153
another way:
Expand the expression using
(a-b) (a+b) =
a²-b² :
3²-(12i)²
Simplify using exponent rule with same exponent
(a*b)^n =
a^n*b^n:
3²-12²* i²
Calculate the power:
9-144* i²
Rewrite by definition
i²=-1:
9–144×(−1)
Calculate the product or quotient: 9+144
Calculate the sum or difference: 153
Answer: 153
gathmath
WORTH 50 points pls answer.
The two polygons are similar. Find the values of x and y
Answer:
y = 120
x = 10.6
Step-by-step explanation:
Given polygons are parallelograms.
In parallelograms, consecutive angles are supplementary which means their sum is equal to 180.
Since two parallelograms are similar:
60 + y = 180 subtract 60 from both sides
y = 120
To find the value of x:
side lengths are proportional because these are similar polygons
[tex]\frac{x+4}{22} = \frac{12}{18}[/tex] cross multiply fractions
18x + 72 = 264 subtract 72 from both sides
18x = 192 divide both sides by 18
x = 10.6 approximately
¿Cuál de los siguientes números NO es un decimal periódico?
A.
11
30
B.
11
400
C.
11
600
D.
111
90
El número decimal que no es un decimal periódico es dado por:
B. [tex]\frac{11}{400}[/tex].
¿Que es un número decimal periódico?Un decimal periódico es un número decimal en el que la misma secuencia de dígitos se repite indefinidamente.
La conversión de las fracciones para decimales són:
11/30 = 0.366666 -> Periódico.11/400 -> 0.0275 -> No es periódico.11/600 -> 0.018333333 -> Periódico, en razón de lá repetición de el 3.11/90 = 0.1222222 -> Periódico.Puede-se aprender más a cerca de números decimales periódicos en https://brainly.com/question/1192529
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The table below shows some inputs and outputs of the invertible function f with domain all real numbers.
X 5, 3, 1, 18, 0, 9
f(x) 9, -2, -5, -1, 1, 11
Find the following values:
f-1 (f(58))=
f(f (5)) =
The value of f⁻¹(f(58)) is 58 and the value of the function f(f(5)) is 11
How to solve the function values?As a general rule, we have:
f⁻¹(f(x)) = x
Substitute 58 for x
So, we have:
f⁻¹(f(58)) = 58
Hence, the value of f⁻¹(f(58)) is 58
Also, we have:
f(f(5))
From the table, we have:
f(5) = 9
So, we have:
f(f(5)) = f(9)
From the table, we have:
f(9) = 11
So, we have:
f(f(5)) = 11
Hence, the value of the function f(f(5)) is 11
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[tex]\huge\sf\underline{Question}[/tex]
[tex]\sf If \: {x}^{2} + \frac{1}{x ^{2} } = 34[/tex]
[tex]\sf find \: the \: value \: of \: \: \: x + \frac{1}{x} [/tex]
a proper explanation needed :)
Thxx !!
[tex] {\qquad\quad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } = 34[/tex]
[ add 2 on both sides ]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } + 2 = 34 + 2[/tex]
[ form identity : a² + b² + 2ab ]
[tex]\qquad \sf \dashrightarrow \: {(x)}^{2} + { \bigg(\cfrac{1}{ {x}^{} } \bigg) }^{2} + 2 \sdot(x) \sdot \bigg(\cfrac{1}{x} \bigg) = 36[/tex]
[ a² + b² + 2ab = (a + b)² ]
[tex]\qquad \sf \dashrightarrow \: {\bigg (x + \cfrac{1}{x} \bigg) }^{2} = 36[/tex]
[tex]\qquad \sf \dashrightarrow \: {\bigg (x + \cfrac{1}{x} \bigg) }^{} = \sqrt{ 36}[/tex]
[tex]\qquad \sf \dashrightarrow \: x + \cfrac{1}{x} = \pm 6[/tex]
so, the value of required expression is 6
[usually positive value is considered, but if asked the value can be either positive or negative]
A math class consists of 25 students, 14 female and 11 male. Two students are selected at random to
participate in a probability experiment. Compute the probability that
a) a male is selected, then a female.
b) a female is selected, then a male.
c) two males are selected.
d) two females are selected.
e) no males are selected.
The probability that a male is selected, then a female is 0.26
The probability that a female is selected, then a male is 0.26
The probability that two males are selected is 0.18
The probability that two females are selected is 0.30.
The probability that no males are selected is 0.30.
What are the probabilities?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that a male is selected, then a female = (11/25) x (14 / 24) = 0.26
The probability that a female is selected, then a male = (14/25) x (11 / 24) = 0.26
The probability that two males are selected = (11/25) x (10/24) = 0.18
The probability that two females are selected = (14/25) x (13 / 24) = 0.30
The probability that no males are selected = (14/25) x (13 / 24) = 0.30
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If a family has 6 children, in how many ways could the parents have 3 boys and 3 girls?
The parents could have 3 boys and 3 girls in 400 ways
How to determine the number of ways?The given parameters are
Children, n = 6
Boys, r = 3
Girls, r =3
The number of combination is:
[tex]Ways = ^nC_{r1} *^nC_{r2}[/tex]
So, we have:
[tex]Ways = ^6C_3 *^6C_3[/tex]
Apply the combination formula
[tex]Ways = \frac{6!}{3!3!} *\frac{6!}{3!3!}[/tex]
This gives
Ways = 400
Hence, the parents could have 3 boys and 3 girls in 400 ways
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what is the derivative of this
The derivative of the natural logarithm function is given by:
[tex]f^{\prime\prime}(x) = \cotg{x}[/tex]
What is the derivative of the natural logarithm function?Suppose we have a composite natural logarithm function given as follows:
[tex]f(x) = \ln{g(x)}[/tex]
The derivative of the function is given as follows:
[tex]f^{\prime}(x) = \frac{g^{\prime}(x)}{g(x)}[/tex]
In this problem, the function, which is already a first derivative, it given by:
[tex]f^{\prime}(x) = \ln{|\sin{x}|} + 3[/tex]
The derivative of a constant is of zero, and the derivative of sin(x) is cos(x), hence the derivative of the entire function is given as follows:
[tex]f^{\prime\prime}(x) = \frac{\cos{x}}{\sin{x}} = \cotg{x}[/tex]
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The binomial 5x – 4 is a factor of 10x^2 – 23x + 12. What is the other factor?
Answer:
2x - 3
Step-by-step explanation:
10x²-23x+ 12 ÷ 5x-4
Answer:
2x - 3
Step-by-step explanation:
[tex](5x-4)(2x-3)=10x^{2} -23x+12[/tex]
Hope this helps
What are the domain and range ofWhat are the domain and range of ?
D: [3, ∞) and R: [0, ∞)
D: [4, ∞) and R: (–∞, 0)
D: [–4, ∞) and R: [0, ∞)
D: (3, ∞) and R: (–∞, 0)
Answer:
Domain:[-4,∞)
Range:[0, ∞)
Thus, choice C is the exact answer
Consider the exponential function f(x)=3(1/3)^x and it’s graph
The given exponential function exists [tex]f(x)=3(1/3)^x[/tex] . The growth value of the function is 1/3.
What is exponential function?An exponential function exists a mathematical function of the following form: [tex]f ( x ) = a^ x[/tex].
where x exists a variable, and a exists a constant named the base of the function.
An exponential function exists of the form [tex]f(x)=ab^x[/tex]
where a ≠ 0, b > 0, b ≠1, and x exists any real number.
when b > 1, the graph increases.
when 0 < b < 1, the graph decreases.
a = initial value
r = growth or decay rate
x = number of time.
The given exponential function exists [tex]f(x)=3(1/3)^x[/tex]
The function exists a stretch of the function [tex]f(x)= (1/3)^x.[/tex]
Therefore, the correct answer is the growth value of the function is 1/3.
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Expand (1 + root 2) (3 - root 2)
Give your answer in the form a+b root 2 where a and b are integers.
Answer:
1+2√2
a = 1 b= 2
See the attached page, I've shown the calculation over there.
Complete the statement to describe the expression ab+cd+ef+gh
The expression consists of __ terms, and each term contains __ factors.
HELP!
The terms of the expression are ab, cd, ef and gh. This shpws that the expression contains 4 terms and 0 factor.
Terms and factors of an expressionExpression consists of terms and factors. The terms are separated by the mathematical signs.
Given the expression below
ab+cd+ef+gh
The terms of the expression are ab, cd, ef and gh. This shpws that the expression contains 4 terms and 0 factor.
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Find the missing side. Round your answer to the nearest tenth.
Answer:
x = 19.1
Step-by-step explanation:
Because this is a right triangle, we can use trigonometry.
Thus, we must use either sine (opposite / hypotenuse), cosine (adjacent / hypotenuse), or tangent (opposite / adjacent).
If we use 33 as the reference angle, the side measuring 16 is the adjacent side and x is the hypotenuse.
Thus, we can use cosine:
[tex]cos 33=\frac{16}{x} \\x*cos33=16\\x=19.0778=19.1[/tex]
Suppose that tan 0=-5/12 and 90° <0<180°.
Find the exact values of sin
0/2 and
tan
O/2
The exact values of sin θ/2 and tan θ/2 given below as:
sin θ/2 = 0.9806tan θ/2 = 4.99What is the exact values of sin θ/2 and tan θ/2 given that tan θ = -5/12?Given that tan θ = -5/12 and θ lies between 90° and 180°, the values of sin θ/2 and tan θ/2 can be found as follows:
tan θ = -5/12
θ = 180 -tan⁻¹-(5/12)
θ = 157.38
sin θ/2 = sin 157.38/2
sin θ/2 = 0.9806
tan θ/2 = tan 157.38/2
tan θ/2 = 4.99
In conclusion, the values of the sine and tangent are found from the given values.
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Which mixed number is equivalent to the improper fraction 42/5?
4 2/5
7 4/5
8 2/5
9 3/5
40 points if answer is right
Step-by-step explanation:
The answer is 8 2 / 5 because ...
[tex]8 \frac{2}{5} = \frac{8 \times 5 + 2}{5} = \frac{42}{5} \\ [/tex]
Answer:
Here your ans and dont forget to say dhanwyad ok.
If 4 is the solution set of the equation x² -4 = 0 and B is
the solution set of the equation x²-3x+2=0, how many
elements are in the union of the two sets?
A. 1
C. 3
B. 2
D. 4
Answer:
3 elements
Step-by-step explanation:
Let A = solution set of x²-4
B = solution set of x²-3x+2
First, find the solution of each sets:
[tex]\displaystyle{x^2-4=0}\\\\\displaystyle{(x+2)(x-2)=0}\\\\\displaystyle{x=2,-2}[/tex]
Set B:
[tex]\displaystyle{x^2-3x+2=0}\\\\\displaystyle{(x-2)(x-1)=0}\\\\\displaystyle{x=1,2}[/tex]
Now we can write new set as:
A = {2, -2}
B = {1, 2}
The union of A and B means combine both sets together:
A ∪ B = {2, -2, 1, 2}
However, in a set, we do not write duplicate elements, so the union set will be:
A ∪ B = {2, -2, 1}
Hence, there are 3 elements in A ∪ B.
Sarita showed the steps to solving the equation. 5 (x minus 3) 7 (x 4) = 73 steps sarita’s solution sarita’s verification 1 5 x minus 15 7 x 28 = 73 5 (5 minus 3) 7 (5 4) = 73. 5 (negative 2) 7 (9) = 73. negative 10 63 = 73. 53 not-equal-to 73. 2 (5 7) x (negative 15 28) = 73 3 12 x 13 = 73 4 12 x 60 5 x = 5 when sarita tried to verify her answer, she found it was wrong. which explains her mistake? sarita’s solution is correct. she made an error in her verification. sarita was supposed to add the 5 and 7 in the first step. sarita added 13 instead of negative 13 in the fourth step. sarita was supposed to use the division property of equality in the third step.
This enables us to conclude that Sarita's solution is accurate, but her verification was flawed. ( 5 - 3 [tex]\neq[/tex] 2 ).
What is linear equation?
When the greatest power of the variable is consistently 1, an equation is considered to be linear. A one-degree equation is another name for it.
Given the following equation:
5(x-3) + 7(x+4) = 73
The steps to solve it are:
Apply the Distributive property:
5x - 15 + 7x + 28 = 73
12x + 13 = 73
Subtract 13 from both side
12x + 13 - 13 = 73 -13
12x = 60
Divide both side by 12
12x/12 = 60/12
x = 5.
To verify it, put the x = 5 in to the equation:
5(5 - 3) + 7(5 + 4) = 73
After solving it, we get
5(2) + 7(9) = 73
10 + 63 = 73
73 = 73
This enables us to conclude that Sarita's solution is accurate, but her verification was flawed. ( 5 - 3 [tex]\neq[/tex] 2 ).
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How many of the 960 dvd players were repaired in the first year
if you get the right answer you get a 20k gaming setup
(D) 200 DVD players were repaired in the first year.
What are DVD players?A DVD player is a device that plays DVDs that adhere to both the DVD-Video and DVD-Audio technical standards, which are incompatible. Some DVD players are also capable of playing audio CDs.Given:
The DVD player shipped 960 players last month
There is a record that out of every 24 players, the 5 would be repaired.
So we need to find the number of DVD players that were repaired in these 960 players.
So,
[tex]\frac{960*5}{24} \\=200[/tex]
Therefore, (D) 200 DVD players were repaired in the first year.
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The question you are looking for is here:
A DVD player manufacturer shipped 960 DVD players last month. According to the manufacturer's records, 5 out of every 24 players were repaired during the first year of ownership. How many of the 960 DVD players were repaired in the first year?
A: 40
B: 120
C: 192
D: 200
Cuantos litros de agua se necesitan para llenar una piscina de 20m de largada, 12m de ancho y 2m de profundidad
Answer: 480
Step-by-step explanation:
20(12)(2) = 480
Please help ASAP!! Thank you :D
Answer:
Obtuse, scalene.
Step-by-step explanation:
In ΔSVU, one angle is 120° which is obtuse angle.
So, ΔSVU is a obtuse triangle.
All the sides have different measurements. So, It is a Scalene triangle.
Choose the equation that satisfies the data in the table.
Answer:
Step-by-step explanation:
the answer is D
P(A) = 1/2
P(B) = 1/3
If A and B are independent, what is P(A ∩ B)?
Answer:
Step-by-step explanation:
hello :
P(A ∩ B)=P(A)×P(B)=1/2×1/3 = 1/6