Answer:
x=17
Step-by-step explanation:
\(\frac{28}{82}= \frac{2x+8}{2x+8+5x-4} \\164x+656=196x+112\\32x=544\\x=17\)
4 Evaluate 1.**2220 , +2 x2 -dx. Submit your answer in fractional form.
The expression is:
1.**2220 + 2 * 2 - dx
First, let's simplify the double asterisk (**). Since this is not a standard mathematical notation, I'll assume you meant to use a single asterisk (*) for multiplication:
1 * 2220 + 2 * 2 - dx
Now, let's simplify:
2220 + 4 - dx
Without knowing the value of "dx," we can't provide a numerical answer. If you can clarify the value of "dx" or any specific terms you want me to include.
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Here are two spinners (picture attached)
Step-by-step explanation:
you can subtract the spinner a from spinner b and then find the probability
-6+u= -8 help me with this pleaseee
Answer:
-2=u
Step-by-step explanation:
Answer:
u=-2
Explanation:
Be sure to move all terms not containing u to the right side of the equation.
Brainliest??
Line l contains points (-2, 1) and (4, 1). Point P has coordinates (5,7).
Answer:
Step-by-step explanation:
We can find the distance between line l and point P by finding the distance between point P and the closest point on line l.The slope of line l is 0, since both points have the same y-coordinate. Therefore, line l is a horizontal line. The y-coordinate of any point on line l is 1.To find the closest point on line l to point P, we need to find the point on line l that has a y-coordinate of 7. Since line l is horizontal, any point on line l with a y-coordinate of 7 will work. Let's choose the point (5, 7), which is on the same horizontal line as line l.Now we can find the distance between point P and the point (5, 7):sqrt((5-(-2))^2 + (7-1)^2) = sqrt(49 + 36) = sqrt(85)Therefore, the distance between line l and point P is sqrt(85).
Rosalyn's company, Snack Attack Inc., owns a
few vending machines. Last night she collected
$82.50 in dimes and quarters. If Rosalyn
collected 50 more quarters than dimes, how
many dimes did she collect?
Number of dimes collected by Rosalyn = \(250\)
How to calculate the number of dimes by Rosalyn?
Let D = # of dimes , Q = # of quarter.
We have
A dime is \(10\) pennies , a quarter is \(25\) pennies and $\(82.50\) is \(8250\) pennies.
Now this leads to the equation:
\(10D + 25 Q =8250\)
If Rosalyn collected \(50\) more quarters than dimes,
Then \(Q=D+50\)
\(10D+25(D+50)=8250\)
\(35D+1250=8250\)
\(35D=7000\)
\(D=\frac{7000}{35}\)
\(D = 200\)
So there are \(200\) dimes.
And since there are \(50\) more quarters than dimes , hence there are \(250\) quarters.
So Rosalyn collected \(250\) dimes.
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15. Describe the three general steps
for producing a recombinant DNA (rDNA) vector, state how rDNA can
be introduced into cells, and discuss the clinical applications of
rDNA.
Producing rDNA involves isolating and cleaving DNA, inserting fragments into a vector, and transforming host cells. rDNA can be introduced via transformation, transfection, or viral vectors. Clinical applications include protein production, gene therapy, vaccines, and diagnostics.
Producing a recombinant DNA (rDNA) vector involves several general steps. Here are the three main steps involved in the process:
Isolation and Cleavage of DNA:
The first step is to isolate the desired DNA fragments from the source organism. This can be done using various techniques such as PCR (Polymerase Chain Reaction) or restriction enzyme digestion. Restriction enzymes are enzymes that cut DNA at specific recognition sites. By using the appropriate restriction enzymes, the desired DNA fragment and a vector DNA can be cut at specific sites. The vector is usually a plasmid, which is a small circular DNA molecule.
Insertion of DNA Fragments into the Vector:
Once the DNA fragments and vector have been cut, they are mixed together and joined through a process called ligation. DNA ligase is used to catalyze the formation of covalent bonds between the ends of the DNA fragments and the vector. This creates a recombinant DNA molecule containing the desired DNA fragment within the vector. The recombinant DNA molecule is then introduced into host cells for replication.
Transformation of Host Cells:
The recombinant DNA molecules need to be introduced into host cells to produce multiple copies of the recombinant DNA. This is typically done using a process called transformation. Host cells, such as bacteria or yeast, are treated in a way that makes them more receptive to taking up the recombinant DNA. Methods for transformation include heat shock, electroporation, or using chemical agents. Once the host cells have taken up the recombinant DNA, they can be grown in culture to produce large quantities of the desired DNA fragment.
Introduction of rDNA into Cells:
Recombinant DNA can be introduced into cells using various methods, depending on the type of cells being targeted. Some common techniques include:
Transformation: As mentioned earlier, host cells, such as bacteria or yeast, can be treated to make them receptive to taking up the recombinant DNA. This can be achieved by exposing the cells to heat shock, electroporation, or using chemical agents.
Transfection: This method is used for introducing rDNA into eukaryotic cells, including animal cells. It involves the use of techniques such as calcium phosphate precipitation, liposome-mediated transfection, or electroporation.
Viral Vectors: Certain viruses, such as retroviruses, adenoviruses, or lentiviruses, can be modified to carry the recombinant DNA. These viral vectors can then infect target cells and deliver the rDNA into the host genome.
Clinical Applications of rDNA:
Recombinant DNA technology has revolutionized biomedical research and has led to numerous clinical applications. Some important applications include:
Production of Therapeutic Proteins: rDNA technology allows for the production of large quantities of therapeutic proteins, such as insulin, growth factors, clotting factors, and monoclonal antibodies. These proteins can be used to treat various diseases, including diabetes, cancer, and genetic disorders.
Gene Therapy: rDNA vectors can be used to deliver functional copies of genes into target cells to correct genetic defects. This holds promise for the treatment of inherited diseases caused by single gene mutations, such as cystic fibrosis and muscular dystrophy.
Vaccine Development: Recombinant DNA technology has been instrumental in the development of vaccines. By expressing specific antigens from pathogens, recombinant vaccines can be created to stimulate an immune response without causing disease.
Diagnostic Tools: Recombinant DNA techniques are used to produce specific DNA or RNA probes for diagnostic purposes. These probes can detect the presence of specific genes or mutations associated with diseases, aiding in early detection and personalized medicine.
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Can someone please help me with these problems? Will mark brainliest
Answer:
1/6
2/6 or 1/3
Step-by-step explanation:
That is, what qualities does a taylor polynomial havethat the tangent line does not necessarily have?
The quality which a taylor polynomial have that the tangent line does not necessarily have is that Taylor polynomial has a far better approximation of f(x) near x = a than is the tangent line
What is Taylor polynomial ?Taylor polynomial function simply refers to an infinite sum of terms that are expressed in terms of the function's derivatives at a single point.
So therefore, the quality which a taylor polynomial have that the tangent line does not necessarily have is that Taylor polynomial has a far better approximation of f(x) near x = a than is the tangent line
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Examples of a TRUE biconditional statement, please.
Answer: two angles have the same measure if only and only if they are congruent
explanation:
A true biconditional statement is true both "forward" and backward". All definitions can be written as true biconditional statements.
Which expression can be used to represent the phrase ""Maren increases the number of servings by six""? n minus 6 6 minus n n 6 6 n.
Answer:
n+6
Step-by-step explanation:
PLS HELP DUE IN 10 MIN WITH BOTH IF POSSIBLE
Answer:
Step-by-step explanation:
(12x + 19) + (22x - 9) = 180
34x + 10 = 180
34x = 170
x = 5
fond the value of x and find the length of xy
From this Triangle
Taking Triangle XZH, wanting to find HZ
\(\begin{gathered} We\text{ have to make use of pythgoras Theorem} \\ (XZ)^2=(XH)^2+(HZ)^2 \\ 12^2=8^2\text{ + }(HZ)^2 \\ 144\text{ = 64 + }(HZ)^2 \\ 144-64\text{ = }(HZ)^2 \\ (HZ)^2\text{ = 80} \\ (HZ)\text{ = }\sqrt[]{80\text{ }}\text{ =8.94} \\ \end{gathered}\)From the Second triangle, ZHY
\(\begin{gathered} ZY^2=HZ^2+HY^2 \\ (x+3)^2\text{ =}8.94^2+x^2 \\ x^2+6x^{}\text{ + 9 = }80+x^2 \\ x^2-x^2\text{ + 6x = 80 -9} \\ 6x\text{ = 71} \\ x\text{ =}\frac{71}{6}\text{ =11.83} \\ \end{gathered}\)XY = x + 8
= 11.83 + 8
=19.83
Find a power series expansion for 1/z
around z=1+i.
The power series expansion for 1/z around z = 1 + i is given by:
1/z = (1 - i)/(2 + 2i) + (z - (1 + i))/(2 + 2i)^2 + (z - (1 + i))^2/(2 + 2i)^3 + ...
To find the power series expansion for 1/z around z = 1 + i, we can use the geometric series expansion formula. The formula states that for a function f(z), the power series expansion around a point z = a is given by:
f(z) = f(a) + f'(a)(z - a) + f''(a)(z - a)^2/2! + f'''(a)(z - a)^3/3! + ...
In this case, we have f(z) = 1/z and a = 1 + i. Taking the derivatives of 1/z and evaluating them at z = 1 + i, we can substitute them into the formula to obtain the power series expansion.
The expansion starts with the term (1 - i)/(2 + 2i), which represents the constant term. The subsequent terms involve higher powers of (z - (1 + i)), divided by powers of (2 + 2i). Each term in the expansion corresponds to the derivative of 1/z evaluated at z = 1 + i, multiplied by the appropriate power of (z - (1 + i)).
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how do you do this ?
Answer:
62 ft²
Step-by-step explanation:
l = 3
w = 2
h = 5
now
2(wl+hl+hw)
2(2×3+5×3+5×2)
2×31
62 ft²
The measures of the angles of a triangle are 3 consecutive even integers. Find the measure of each angle.
Solution:
Given:
The angles of a triangle are as shown in the sketch below;
Consecutive even integers are the set of integers such that each integer in the set differs from the previous integer by a difference of 2 and each integer is divisible by 2.
For the three angles to be consecutive even integers, then
\(\begin{gathered} x,y,z\text{ are consecutive even integers.} \\ \text{Hence,} \\ y-x=2 \\ y=x+2\ldots\ldots\ldots\ldots\ldots(1) \\ \\ \text{Also,} \\ z-y=2 \\ z=y+2 \\ z=x+2+2 \\ z=x+4\ldots.\ldots\ldots\ldots\ldots\ldots.\mathrm{}(2) \end{gathered}\)Since the three angles are in the triangle, then;
\(\begin{gathered} x+y+z=180^0\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.(the sum of angles in a triangle)} \\ \\ \\ \text{Substituting equation (1) and (2) into the equation above,} \\ x+(x+2)+(x+4)=180^0 \\ \text{Collecting the like terms,} \\ x+x+x+2+4=180^0 \\ 3x+6=180^0 \\ 3x=180-6 \\ 3x=174 \\ \text{Dividing both sides by 3,} \\ x=\frac{174}{3} \\ x=58^0 \end{gathered}\)Substituting the value of x into equations (1) and (2) to get the values of y and z,
\(\begin{gathered} y=x+2 \\ y=58+2 \\ y=60^0 \\ \\ \text{Also,} \\ z=x+4 \\ z=58+4 \\ z=62^0 \end{gathered}\)Therefore, the measure of each angle if the angles are consecutive even integers are;
\(58^0,60^0,62^0\)Answer:
58° , 60° , 62°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
let the 3 consecutive even integers be n, n + 2, n + 4 , then
n + n + 2 + n + 4 = 180
3n + 6 = 180 ( subtract 6 from both sides )
3n = 174 ( divide both sides by 3 )
n = 58
n + 2 = 58 + 2 = 60
n + 4 = 58 + 4 = 62
the 3 angles are 58° , 60° , 62°
Which concept below is NOT a main idea of estimating a population proportion?A. The sample proportion is the best point estimate of the population proportion.B. Knowing the sample size necessary to estimate a population proportion is important.C. Using a sample statistic to estimate the population proportion is utilizing descriptive statistics.D. We can use a sample proportion to construct a confidence interval to estimate the true value of a population proportion
The concept which is the main idea of estimating a population proportion is
C. Using a sample statistic to estimate the population proportion is utilizing descriptive statistics.
The concept stated in option C is not a main idea of estimating a population proportion.
Estimating a population proportion involves inferential statistics, which is concerned with making inferences or drawing conclusions about a population based on information from a sample. In this context, descriptive statistics refers to methods that summarize and describe the characteristics of a sample or population, such as measures of central tendency and variability.
The main ideas of estimating a population proportion include:
A. The sample proportion is the best point estimate of the population proportion: When estimating a population proportion, the sample proportion (the proportion observed in the sample) is commonly used as the point estimate for the population proportion. This is because it provides an unbiased estimate of the unknown population proportion.
B. Knowing the sample size necessary to estimate a population proportion is important: The sample size plays a crucial role in estimating a population proportion. A larger sample size generally leads to a more precise estimate with a smaller margin of error. Determining an appropriate sample size is essential to ensure the desired level of confidence and accuracy in the estimate.
D. We can use a sample proportion to construct a confidence interval to estimate the true value of a population proportion: Constructing a confidence interval is a common method to estimate the true value of a population proportion. By using the sample proportion along with the standard error and a chosen level of confidence, a range of values is calculated within which the true population proportion is likely to fall.
In contrast, option C refers to using a sample statistic to estimate the population proportion by utilizing descriptive statistics. However, estimating a population proportion typically involves inferential statistics rather than descriptive statistics.
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uhhh just look at the screenshot then answer
Answer:
The Independent is the Number of Hours while the Dependent is the Number of Miles
Equation: y= 50x
Step-by-step explanation:
I Hope this helped
a data scientist samples a population by randomly selecting one of the first 100 entries in a telephone directory, as well as every 100th entry after the selected entry. this process is known as:
A data scientist samples a population by randomly selecting one of the first 100 entries in a telephone directory, as well as every 100th entry after the selected entry. this process is known as systematic sampling.
Systematic sampling is a statistical method of selecting a random sample from a larger population. In this method, a starting point is randomly selected, and then every kth item is selected after the first one. In this scenario, the data scientist is selecting the first entry and then selects every 100th entry after that. This method ensures that the sample is representative of the population and reduces bias. Additionally, it is easy to implement and efficient as it does not require a complete list of the population.
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5 points
26. The equation x^2 + 8x - k(x + 8) = 0 has equal roots. Find the value of k.
please help
will mark it BRAINLIEST.
I really need help :(
Answer:
k = - 8
Step-by-step explanation:
Since the equation has equal roots then the discriminant Δ = 0 , that is
b² - 4ac = 0
Given
x² + 8x - k(x + 8) = 0 ← distribute parenthesis and simplify
x² + 8x - kx - 8k = 0
x² + (8 - k)x - 8k = 0 ← in standard form
with a = 1 , b = (8 - k) , c = - 8k
(8 - k)² - (4 × 1 × - 8k) = 0
64 - 16k + k² - (- 32k) = 0
64 - 16k + k² + 32k = 0
k² + 16k + 64 = 0
(k + 8)² = 0
k + 8 = 0 , then
k = - 8
If you vertically compress the absolute value parent function, (x) = |X|, by a
factor of 4, what is the equation of the new function?
O A. g(x) = |4x|
O B. g(x) = 1/4 |x|
O C. g(x) = 4|x|
O D. g(x) = |x-4|
pls mark me as brainlist
thanks a lot
function “p” is in the form y = ax 2+c. if the values of “a” and “c” are both less than 0. which graph could represent “p”?
Since the value of a is less than 0, the graph of the parabola would be opening downwards. Because of this we can rule out option C. In a quadratic equation, c represents the y-intercept, and, in this case c is negative, meaning the y-intercept is less than 0. Only option B has a downward-opening curve and a y-intercept less than 0, so it is the answer.
Answer: p= 2+c
Step-by-step explanation:
How can i show that p^(q-1) + q^(p-1) = 1 (mod pq)?
Step-by-step explanation:
you can just put in some values to check.
I actually used p =2 and q=3
the It will be
2^3-1 + 3^2-1 = 1 (mod 2×3)
2^2 +3^1 = 1 (mod 6)
4+3= 1 (mod6)
7= 1 (mod6)
which is true.
therefore p^(q-1) + q^( p-1) = 1 ( mod pq) is true
To show that p^(q-1) + q^(p-1) = 1 (mod pq), we can use Fermat's Little Theorem, which states that if p is a prime number and a is an integer not divisible by p, then a^(p-1) = 1 (mod p). Using this theorem, we can first show that p^(q-1) = 1 (mod q), since q is a prime number and p is not divisible by q. Similarly, we can show that q^(p-1) = 1 (mod p), since p is a prime number and q is not divisible by p.
Therefore, we can write:
p^(q-1) + q^(p-1) = 1 (mod q)
p^(q-1) + q^(p-1) = 1 (mod p)
By the Chinese Remainder Theorem, we can combine these two equations to obtain:
p^(q-1) + q^(p-1) = 1 (mod pq)
Thus, we have shown that p^(q-1) + q^(p-1) = 1 (mod pq).
We'll use Fermat's Little Theorem to show that p^(q-1) + q^(p-1) = 1 (mod pq).
Fermat's Little Theorem states that if p is a prime number and a is an integer not divisible by p, then:
a^(p-1) ≡ 1 (mod p)
Step 1: Apply Fermat's Little Theorem for p and q:
Since p and q are prime numbers, we have:
p^(q-1) ≡ 1 (mod q) and q^(p-1) ≡ 1 (mod p)
Step 2: Add the two congruences:
p^(q-1) + q^(p-1) ≡ 1 + 1 (mod lcm(p, q))
Step 3: Simplify the congruence:
Since p and q are prime, lcm(p, q) = pq, so we get:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)
In your question, you've mentioned that the result should be 1 (mod pq), but based on Fermat's Little Theorem, the correct result is actually:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)
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which equation, when solved, gives 8 for the value of x?
a. 5/2x + 7/2 = 3/4x + 14
b. 5/4x - 9 = 3/2x - 12
c. 5/4x - 2 = 3/2x - 4
d. 5/2x - 7 = 3/4x + 14
Answer: c. 5/4x - 2 = 3/2x - 4
Step-by-step explanation:Find the exact value using trigonomectric identities
the only calculated fields you can create in access are those involving addition and subtraction. True or false?
Answer:
false
Step-by-step explanation:
False.
Access supports a wide range of built-in functions and operators that can be used to create calculated fields. These functions and operators include mathematical functions (such as multiplication, division, exponentiation), string functions (such as concatenation, trimming, and formatting), date and time functions, aggregate functions (such as sum, average, count), and more.
In addition, Access also allows you to create user-defined functions using VBA (Visual Basic for Applications), which can be used to perform custom calculations on your data.
Therefore, the statement "the only calculated fields you can create in Access are those involving addition and subtraction" is false.
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What is the value of the remainder?
\( \underline{ \boxed{ \sf{✰\: Option\:D. \:81✓ }}}\)
Refer to the attachment for solution ☘️
Hope it helps
skip 1 & 2
help with # 3
Exercise 3 Give a direct proof that \( -(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime} \) \( -A \cap(B \cup C)=(A \cap B) \cup(A \cap C) \) \( -A-(B \cap C)=(A \cap B)-(A \cap C) \)
1. \(\( -(A \cap B)^\prime = A^\prime \cup B^\prime \)\) is proven using De Morgan's law.
2. \(\( -A \cap (B \cup C) = (A \cap B) \cup (A \cap C) \)\)is proven by considering the elements in the sets. 3.\(\( -A - (B \cap C) = (A \cap B) - (A \cap C) \)\) is proven by considering the elements in the sets.
1. Proving \(\( -(A \cap B)^\prime = A^\prime \cup B^\prime \)\):
Let's start with the left-hand side: \(\( -(A \cap B)^\prime \).\)
Using De Morgan's law, we know that \(\( (A \cap B)^\prime = A^\prime \cup B^\prime \).\)
Taking the complement of this, we have \(\( -(A \cap B)^\prime = - (A^\prime \cup B^\prime) \).\)
Now, let's simplify the right-hand side: \(\( A^\prime \cup B^\prime \).\)
By definition,\(\( - (A^\prime \cup B^\prime) \)\) represents the complement of \(\( A^\prime \cup B^\prime \)\), which means all elements that are not in \(\( A^\prime \cup B^\prime \).\)
Let's consider an arbitrary element x that is not in \(\( A^\prime \cup B^\prime \)\). This means that x is not in either \(\( A^\prime \) or \( B^\prime \)\). Since x is not in \(\( A^\prime \)\), it must be in A (because \(\( A^\prime \)\) is the complement of A ). Similarly, since x is not in \(\( B^\prime \),\) it must be in B. Therefore, x is in \(\( A \cap B \).\)
Conversely, if x is in \(\( A \cap B \),\) then it is in both A and B. This means that x is not in \(\( A^\prime \)\) (because \(\( A^\prime \)\) is the complement of A and not in \(\( B^\prime \)\) (because \(\( B^\prime \)\) is the complement of B ). Therefore, x is not in \(\( A^\prime \cup B^\prime \).\)
Since all elements not in \(\( A^\prime \cup B^\prime \)\) are in \(\( A \cap B \)\) and vice versa, we can conclude that \(\( -(A \cap B)^\prime = A^\prime \cup B^\prime \).\)
2. Proving \(\( -A \cap (B \cup C) = (A \cap B) \cup (A \cap C) \)\):
Let's start with the left-hand side: \(\( -A \cap (B \cup C) \).\)
This represents the set of elements that are not in A \) but are in either B or C.
Now, let's simplify the right-hand side: \(\( (A \cap B) \cup (A \cap C) \).\)
This represents the set of elements that are in both A and B , or in both A and C.
To show that \(\( -A \cap (B \cup C) = (A \cap B) \cup (A \cap C) \)\), we need to prove that these two sets are equal.
Let's consider an arbitrary element x that is in \(\( -A \cap (B \cup C) \).\) This means that x is not in A, but it is in either B or C. In either case, x is in either A and B or A and C . Therefore, x is in \(\( (A \cap B) \cup (A \cap C) \)\).
Conversely, if \( x \) is in \(\( (A \cap B) \cup (A \cap C) \)\), then it is in both A and B , or in both A and C. This means that x is not in A, but it is in either \( B \) or \( C \). Therefore, \( x \) is in \(\( -A \cap (B \cup C) \).\)
Since all elements in \(\( -A \cap (B \cup C) \)\) are in \(\( (A \cap B) \cup (A \cap C) \),\) and vice versa, we can conclude that \(\( -A \cap (B \cup C) = (A \cap B) \cup (A \cap C) \).\)
3. Proving \(\( -A - (B \cap C) = (A \cap B) - (A \cap C) \)\):
To prove this statement, we need to show that the left-hand side is equal to the right-hand side.
Let's start with the left-hand side: \(\( -A - (B \cap C) \).\)
This represents the set of elements that are not in A and are also not in the intersection of B and C.
Now, let's simplify the right-hand side: \(\( (A \cap B) - (A \cap C) \).\)
This represents the set of elements that are in both \( A \) and \( B \), but not in both \( A \) and \( C \).
To show that \(\( -A - (B \cap C) = (A \cap B) - (A \cap C) \)\), we need to prove that these two sets are equal.
Let's consider an arbitrary element x that is in \(\( -A - (B \cap C) \)\). This means that x is not in A and is also not in the intersection of B and C. Therefore, x is in both A and B (because it's not excluded by A and not in both A and C (because it's not in the intersection of B and C.
Conversely, if x is in \(\( (A \cap B) - (A \cap C) \)\), then it is in both A and B , but not in both A and C . Therefore, \( x \) is not in \( A \) and is also not in the intersection of B and C.
Since all elements in \(\( -A - (B \cap C) \)\) are in
\(\( (A \cap B) - (A \cap C) \)\), and vice versa, we can conclude that \(\( -A - (B \cap C) = (A \cap B) - (A \cap C) \)\).
Hence, the statement \(\( -A - (B \cap C) = (A \cap B) - (A \cap C) \)\) is proven.
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What is limit of startfraction 6 minus x over x squared minus 36 endfraction as x approaches 6? negative startfraction 1 over 12 endfraction 0 startfraction 1 over 12 endfraction dne
Answer:
As x approaches 6:
\( \frac{6 - x}{ {x}^{2} - 36 } = - \frac{x - 6}{(x - 6)(x + 6)} = - \frac{1}{x + 6} = - \frac{1}{6 + 6} = - \frac{1}{12} \)
The limit of the given function as x approaches 6 is -1/12. This is achieved by factoring and revising the original function, and then substituting into the revised function.
Explanation:The student is asking for the limit of the function (6-x) / (x²-36) as x approaches 6. In mathematics, this is a problem of calculus and specifically involves limits. Let's solve this by first factoring the denominator to get (6-x) / ((x-6)(x+6))
By realizing we can revise the numerator as -(x-6), we make it obvious that the limit can be directly computed by substituting x=6 after canceling out the (x-6) terms. The result is -1/12, therefore the limit of the function as x approaches 6 is -1/12.
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if expected frequencies are not all equal, then we can determine them by enp for each individual category, where n is the total number of observations and p is the probability for the category. b. if expected frequencies are equal, then we can determine them by , where n is the total number of observations and k is the number of categories. c. expected frequencies need not be whole numbers. d. goodness-of-fit hypothesis tests may be left-tailed, right-tailed, or two-tailed.
If the expected frequencies are not all equal, we can determine them by using the equation enp for each individual category, where n is the total number of observations and p is the probability for the category. This equation helps us calculate the expected frequency for each category based on their probabilities and the total number of observations.
On the other hand, if the expected frequencies are equal, we can determine them by using the equation n/k, where n is the total number of observations and k is the number of categories. This equation helps us distribute the total number of observations equally among the categories when the expected frequencies are equal.
Expected frequencies do not necessarily have to be whole numbers. They can be decimals or fractions depending on the context and calculations involved.
Goodness-of-fit hypothesis tests can be left-tailed, right-tailed, or two-tailed. These different types of tests allow us to assess whether the observed data significantly deviates from the expected frequencies. The choice of the tail depends on the specific research question and the alternative hypothesis being tested.
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PLEASE ILL DO ANYTHING I ALREADY OFFERED AS MUCH POINTS AS POSSIBLE
Answer:
A, B, D, E
Step-by-step explanation:
Given expression:
(0.06) · (0.154)When multiplying decimals, multiply as if there are no decimal points:
\(\implies 6 \times 154 = 924\)
Count the number of digits after the decimal in each factor:
0.06 → 2 digits0.154 → 3 digitsTherefore, there is a total of 5 digits.
Put the same number of total digits after the decimal point in the product:
\(\implies (0.06) \cdot (0.154)=0.00924\)
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Answer option A
\(\boxed{6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}}\)
When dividing by multiples of 10 (e.g. 10, 100, 1000 etc.), move the decimal point to the left the same number of places as the number of zeros.
Therefore:
6 ÷ 100 = 0.06154 ÷ 1000 = 0.154\(\implies 6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}=(0.06) \cdot (0.154)\)
Therefore, this is a valid answer option.
Answer option B
\(\boxed{6 \cdot 154 \cdot \dfrac{1}{100000}}\)
Multiply the numbers 6 and 154:
\(\implies 6 \times 154 = 924\)
Divide by 100,000 by moving the decimal point to the left 5 places (since 100,000 has 5 zeros).
\(\implies 6 \cdot 154 \cdot \dfrac{1}{100000}=0.00924\)
Therefore, this is a valid answer option.
Answer option C
\(\boxed{6 \cdot (0.1) \cdot 154 \cdot (0.01)}\)
Again, employ the technique of multiplying decimals by first multiplying the numbers 6 and 154:
\(\implies 6 \cdot 154 = 924\)
Count the number of digits after the decimal in each factor:
0.1 → 1 digit0.01 → 2 digitsTherefore, there is a total of 3 digits.
Put the same number of digits after the decimal point in the product:
\(\implies 0.924\)
Therefore, as (0.06) · (0.154) = 0.00924, this answer option does not equal the given expression.
Answer option D
\(\boxed{6 \cdot 154 \cdot (0.00001)}\)
Again, employing the technique of multiplying decimals.
As there are a total of 5 digits after the decimals:
\(\implies 6 \cdot 154 \cdot (0.00001)=0.00924\)
Therefore, this is a valid answer option.
Answer option E
\(\boxed{0.00924}\)
As we have already calculated, (0.06) · (0.154) = 0.00924.
Therefore, this is a valid answer option.
in how many year will rs 8000 amount to rs 13824 at 20% per annum interest compounded annually? please please help me out
Answer :-
3 yearsstep by step explanation:-
Let the time be x
principal = rs 8000
Amount = rs 13824
rate = 20% p.a
A = P(1+r/100)^n
13824 = 8000 ( 1 + 20/100)^n
=> 13824/8000 = (120/100)^n
=> 13824/8000 = (24/20)^n
=> (24/20)³ = (24/20)^n
=> 3 = n
=> n = 3 years