Answers
Answer :
Option C (x = 3 or x = -13)⠀
Explanation :
⠀
\( \longrightarrow \sf \qquad {x}^{2} + 10x = 39\)
⠀
We can write it as,
\( \longrightarrow \sf \qquad {x}^{2} + 10x - 39 = 0\)
⠀
We have to find the two numbers a and b such that,
\( \longrightarrow \sf \qquad a + b = 10\)
\( \longrightarrow \sf \qquad a b = 39\)
⠀
Obviously, the two numbers are 3 and 13.
\( \longrightarrow \sf \qquad {x}^{2} - 3x + 13x - 39 = 0\)
\(\longrightarrow \sf \qquad {x}(x - 3)+ 13(x - 3) = 0\)
\(\longrightarrow \sf \qquad ({x}+ 13)(x - 3) = 0\)
⠀
Whether, the value of x :
\(\longrightarrow \sf \qquad {x}+ 13 = 0\)
\(\longrightarrow \pmb{\bf \qquad {x} = - 13}\)
⠀
Whether, the value of x :
\(\longrightarrow \sf \qquad {x} - 3 = 0\)
\({\longrightarrow { \pmb{\bf \qquad {x} = 3}}}\)
⠀
So,
Option C (x = 3 or x = -13) is correct.Related Questions
say we have x ~ uniform(0, 1) and y ~ uniform(0, 1). what is the expected value of the minimum of x and y?
Answers
The expected value of the minimum of two independent uniformly distributed random variables x and y between 0 and 1 is 1/4. It is found by integrating over the two possible triangles and averaging the results.
Let M be the minimum of x and y. We can find the expected value of M by integrating over all possible values of x and y:
E(M) = ∫∫ min(x,y) f(x,y) dxdy
where f(x,y) is the joint probability density function of x and y.
Since x and y are independent and uniformly distributed between 0 and 1, their joint probability density function is:
f(x,y) = 1, for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1
and zero otherwise.
Therefore, we have:
E(M) = ∫∫ min(x,y) f(x,y) dxdy
= ∫∫ min(x,y) dxdy, for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1
To evaluate this integral, we can split the region of integration into two parts: the triangle where x ≤ y and the triangle where x ≥ y. In each part, we can express the minimum of x and y as a function of one of the variables:
For x ≤ y:
E(M) = ∫∫ min(x,y) dxdy = ∫0^1 ∫x^1 x dy dx
= ∫0^1 (x - x^2/2) dx = 1/3
For x ≥ y:
E(M) = ∫∫ min(x,y) dxdy = ∫0^1 ∫0^y y dx dy
= ∫0^1 y^2/2 dy = 1/6
Therefore, the expected value of the minimum of x and y is:
E(M) = 1/3 * (area of triangle where x ≤ y) + 1/6 * (area of triangle where x ≥ y)
= 1/3 * 1/2 + 1/6 * 1/2
= 1/4
Hence, the expected value of the minimum of x and y is 1/4.
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Find the slope of the line passing through the pointg (7, 1) and (7, - 2).
slope:
Answers
Answer: No slope / undefined
Step-by-step explanation:
Concept:
Here, we need to know the idea of a slope.
The slope is the measure of the steepness of a line.
The basic formula of slope is [Rise / Run] which is basically [Y] value (vertical) over [X] value (horizontal)
If you are still confused, please refer to the attachment below for the full formula.
Solve:
(7 ,1)
(7, -2)
Slope = (1 - (-2)) / (7-7)
Slope = (3) / 0
Slope = Undefined
Indeed, it is a vertical line. By definition, a vertical line has no slope.
Hope this helps!! :)
Please let me know if you have any questions or need further explanations
Use the disributive property to finish the expression that is equivalent to 12 + 4x.
12 + 4x = ___ (3 + x)
Answers
Answer:
12 + 4x = 4(3 + x)
Step-by-step explanation:
Think about what you need to multiply (3 + x) by to get 12 + 4x.
Let f x be odd and g(x) is an even function if f(3)=2 and g(-1)=-3 find f(g(1))
Answers
the value of the given function f(g(1)) is 2 , fog is an even function
A function f is even if the equation f(x)=f(x) f (x) = f ( x) holds for every x and x in the domain of f. An even function has a graph that is geometrically symmetric with respect to the y-axis, which means that even after reflection about the y-axis, the graph does not change.
f is even (given)
∴f(−x)=f(x)
g is odd (given)
∴g(−x)=−g(x)
So,
According to question,
fog=f[g(x)]=f(y) Let [g(x)]=y
and also,
fog=f[g(−x)] ∵g(x) is odd
=f[−g(x)]
=f(−y)
=f(y)
⇒fog(x)=fog(−x)
∴fog is an even function
f(g(1)) = f(g(1)) = f(3) = 2
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Match each expression with its value. −9 7 −2 Undefined h( 3.999 ) h(4) h(4.0001) h(9)
Answers
The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.
Let's match each expression with its corresponding value:
Expression: -9
Value: -9
Expression: 7
Value: 7
Expression: -2
Value: -2
Expression: Undefined
Value: Undefined
Expression: h(3.999)
Value: Undefined
Expression: h(4)
Value: 8
Expression: h(4.0001)
Value: Undefined
Expression: h(9)
Value: Undefined
Now let's explain the reasoning behind each value:
The expression -9 represents the number -9, so its value is -9.
Similarly, the expression 7 represents the number 7, so its value is 7.
The expression -2 represents the number -2, so its value is -2.
When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.
For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.
The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.
Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.
Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.
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an investment strategy has an expected return of 14 percent and a standard deviation of 8 percent. assume investment returns are bell shaped
Answers
An investment strategy with an expected return of 14 percent and a standard deviation of 8 percent has the potential for higher returns, but also comes with a higher level of risk. It is important to carefully consider the trade-off between risk and return before making an investment decision.
An investment strategy with an expected return of 14 percent and a standard deviation of 8 percent means that the investment has a higher potential for return, but also a higher risk.
The standard deviation is a measure of the variation or dispersion of a set of data values. In this case, the standard deviation of 8 percent indicates the degree of variation in the investment returns. A higher standard deviation means that the investment returns are more spread out and there is a higher chance of extreme values, both positive and negative.
In terms of investment strategy, it is important to consider the trade-off between risk and return. While a higher expected return is desirable, it often comes with a higher level of risk. Therefore, it is important to carefully consider the standard deviation and the potential risks associated with an investment before making a decision.
In conclusion, an investment strategy with an expected return of 14 percent and a standard deviation of 8 percent has the potential for higher returns, but also comes with a higher level of risk. It is important to carefully consider the trade-off between risk and return before making an investment decision.
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Which of the following decimal
representations is an example of
a rational number?
Answers
7. The quality control division of Rothschild's Blueberry Farm randomly inspects 100 of the containers in the truck being
sent to Stop and Shop. Identify the population and sample given in this scenario.
Answers
The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.
Population: The containers of blueberries that are being sent to Stop and Shop.
Sample: The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.
Therefore, the 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.
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how much does 5000 shekels of bronze weigh
Answers
Answer:1250
Step-by-step explanation:
PLS HELP!
Mrs. Duzwell bought a box of 150 pencils for $12.
a.) Let p equal the unit price per pencil. Write a multiplication equation that represents her total purchase.
b.) Solve for p. What is the unit price per pencil that Mrs. Duzwell paid?
Answers
Answer:
Equation: 12p=150
Unit Price: about 12-13 cents per pencils
Step-by-step explanation:
150/12=12.5
12.50*12
144000x²+431974x-39=0 find the value of X
Answers
Answer:
\(x=0.00009028, x=-2.999909725\)
Step-by-step explanation:
Use the quadratic formula:
\(x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\)
when \(ax^2+bx+c=0\)
Therefore, for \(144000x^2+431974x-39=0\)
a = 144,000 b = 431,974 and c = -39
Substituting this data into the quadratic formula:
\(x=\dfrac{-431974 \pm \sqrt{431974^2-4(144000)(-39)} }{2(144000)}\)
\(x=0.00009028, x=-2.999909725\)
how to put these in a simply form?
(-2)* (-2)* 10 *10 *10 *10.
21*21*21+(-1)(-1)(-1)(-1).
Answers
Answer:
370,4440,001
Step-by-step explanation:
(-2) • (-2) • (10) • (10) • (10) • (10) = 40,000
21 • 21 • 21 = 9261
(-1) • (-1) • (-1) • (-1) = 1
(40,000) (9261) + 1
(370,440,000) + 1 = 370,4440,001
--
exponents
(-2)² + 10⁴ + 21³ + (-1)⁴
4. Write the equation in point-slope form. (-6, -2) and m = 3
Answers
Please help me with this!
Answers
Answer:
y = x^2 - 4x - 6.
Step-by-step explanation:
The roots are 2 + √10 and 2 - √10, so in factor form we have:
(x - (2 + √10))(x - (2 - √10))
= ( x - 2 - √10)(x - 2 + √10)
= x^2 - 2x + √10x - 2x + 4 - 2√10 - √10x + 2√10 - √100
= x^2 -4x + 4 - 10
= x^2 - 4x - 6.
by how much must the sample size be increased if the width of the confidence interval in part (a) is to be halved?
Answers
The sample size must be increased by a factor of 4 if the width of the confidence interval is to be halved.
In Equation 6.19, the two-sided confidence interval for the population mean with known variance is given by:
CI = \(\bar{x}\) ± z(α/2) * (σ/√n)
where \(\bar{x}\) is the sample mean, z(α/2) is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.
To halve the width of the confidence interval, we need to reduce the term z(α/2) * (σ/√n) by a factor of 2. Since z(α/2) and σ are constant, we can focus on reducing √n.
Let's assume the original sample size is n. To halve the width, we need √n to be halved. Therefore, the new sample size, n', can be determined by:
√n' = (√n) / 2
Squaring both sides:
n' = (n / 4)
Therefore, to halve the width of the confidence interval, the sample size needs to be increased by a factor of 4.
Therefore, the sample size must be increased by a factor of 4 if the width of the confidence interval is to be halved.
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Note: The correct question would be as
Consider a two-sided confidence interval of the population mean with known variance (Equation 6.19 in Ang and Tang) a. By how much must the sample size n be increased if the width of the confidence interval is to be halved?
XY is an angle bisector of ΔAXN. Find the length of side XN
Answers
The length of XN is 6
What is the angle bisector theorem?According to the triangle angle bisector theorem, any angle in a triangle will divide the opposite side in a ratio equal to the ratio of the sides that contain the angle.A line or ray that divides an angle in a triangle into two equal parts is known as an angle bisector. The two fundamental characteristics of an angle bisector are that each point on it is equally spaced from its sides and that it divides the opposite side of a triangle in proportion to its adjacent sides, which is known as the triangle's angle bisector property.Calculation
By angle bisector theorem
\(\frac{AX}{NX} =\frac{AY}{NY}\)
\(\frac{18}{NX} =\frac{12}{4}\)
\(NX=\frac{18*4}{12} =6\)
Therefore, the length of side NX in the given triangle is 6.
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The length of side NX in the given triangle is 6.
What is the angle bisector theorem?According to the triangle angle bisector theorem, any angle in a triangle will divide the opposite side in a ratio equal to the ratio of the sides that contain the angle.A line or ray that divides an angle in a triangle into two equal parts is known as an angle bisector.The two fundamental characteristics of an angle bisector are that each point on it is equally spaced from its sides and that it divides the opposite side of a triangle in proportion to its adjacent sides, which is known as the triangle's angle bisector property.By angle bisector theorem
According to the angle bisector theorem, PQ/PR = QS/RS or a/b = x/y. An angle bisector is a line or ray that divides an angle in a triangle into two equal measures
Therefore, the length of side NX in the given triangle is 6.
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prove that cos(sin^-1x)=sqrt(1-x^2)
Answers
Let's consider a right triangle with an angle θ such that sin θ = x. By definition, To prove the identity cos(sin^⁻¹x) = √(1 - x^2), we can use the properties of trigonometric functions and inverse trigonometric functions.
Let's consider a right triangle with an angle θ such that sin θ = x. By definition, sin^⁻¹x represents the angle whose sine is x. In the triangle, the side opposite to θ has length x, and the hypotenuse has length 1.
Using the Pythagorean theorem, we can find the length of the adjacent side, which is √(1 - x^2). This represents the cosine of the angle θ.
Therefore, we have cos(sin^⁻¹x) = √(1 - x^2), which proves the given identity.
To elaborate further, we can use the definition of sine and cosine in terms of the sides of a right triangle. The sine of an angle θ is defined as the ratio of the length of the side opposite to θ to the length of the hypotenuse. In this case, sin θ = x.
Using the Pythagorean theorem, we find that the length of the adjacent side is √(1 - x^2). This length represents the cosine of the angle θ.
Thus, we have cos(sin^⁻¹x) = √(1 - x^2), demonstrating the validity of the given identity.
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Can anyone help me with this?
Answers
If a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is: 2
Answers
If a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two
When a categorical variable that has n categories is to be included as an independent variable in a linear regression analysis, it must be converted to n - 1 dummy variables. The reason for this is that including all n categories as dummy variables would cause perfect multicollinearity in the regression analysis, making it impossible to estimate the effect of each variable.In this case, the set of categories {Red, Blue, Green, Yellow} has four categories. As a result, n - 1 = 3 dummy variables are required to represent this variable in a linear regression. This is true since each category is exclusive of the others, and we cannot assume that there is an inherent order to the categories.The dummy variable for the first category is included in the regression model by default, and the remaining n - 1 categories are represented by n - 1 dummy variables. As a result, the number of dummy variables that are required to represent the categorical variable in the regression model is n - 1.
Thus, if a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two .
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The graph of f(x) =In x the y axis is the _____ asymptote.
a. vertical
b. horizontal
c. oblique
explain your thinking
Answers
Answer:
a) Vertical.
Step-by-step explanation:
There is no value of ln x <= 0.
The asymptote ix x = 0 (that is the y-axis).
Please solve and explain, thank you!
Answers
9514 1404 393
Answer:
44 inches
Step-by-step explanation:
The sides of a rhombus are all the same length, so we have ...
AB = BC
3x -4 = 2x +1
x = 5 . . . . . . . . . add 4-2x
Then the side lengths are ...
3x -4 = 3·5 -4 = 11
Four of them total 4·11 = 44 inches.
What is 8x8x8x8x8x8x8?
Answers
Answer: Its 2097152
Step-by-step explanation:
a 12 inch thin‑crust cheese pizza is cut equally into eight slices. assuming a uniform distribution of sauce and toppings,
Answers
If there were any variations in the distribution during the preparation process, the slices might have slight differences in the amount of sauce and toppings.
each slice of the 12-inch thin-crust cheese pizza would have an equal distribution of sauce and toppings. This means that each slice would have the same amount of sauce and toppings spread evenly across its surface.
Since the pizza is cut equally into eight slices, each slice would represent 1/8th of the total pizza. Therefore, each slice would have an equal portion of the sauce and toppings.
It's important to note that the exact amount of sauce and toppings on each slice would depend on the original distribution applied to the pizza before it was sliced. If the pizza was prepared with a uniform distribution of sauce and toppings across the entire pizza, then each slice would indeed have an equal amount. However, if there were any variations in the distribution during the preparation process, the slices might have slight differences in the amount of sauce and toppings.
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whenever suzan sees a bag of marbles, she grabs a handful at random. she has seen a bag contaning four red marbles, four green marbles, three white ones, and two purple ones. she grabs five of them. find the probability of the following event, expressing it as a fraction in lowest terms. she has two red ones and one of each of the other ones
Answers
The probability of choosing 2 red and one marbles of each other color is 0.268 .
Given,
Green marbles: 4
Red marbles: 4
White marbles: 3
Purple marbles : 2
Now,
Total marbles to be taken = 5.
Out of 5, 2 will be red and 1 each of three different colors.
Total number of marbles = 13
Choosing 5 marbles from 13,
\(13C_5\\13!/5!(13 - 5)!\\\)
= 6435.
So,
2 will be red and 1 each of three different colors.
\(4C_2 * 4C_1* 3C_1*2C_1\)
= 6*24*6*2
= 1728
So,
Probability = 1728/6435
= 0.268
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A box contains 14 transistors, 3 of which are defective. If 3 are selected at random, find the probability of the statements below.a. All are defectiveb. None are defective
Answers
ANSWERS
a. 1/364
b. 165/364
EXPLANATION
a. There are 11 non-defective transistors and 3 defective transistors in the box. When the first one is selected, there are 3 defective transistors and 14 transistors in total. When the second one is selected, assuming that the first was defective, there are 2 defective and 13 transistors in total. Finally, if the first two were defective, when the third transistor is selected there will be only 1 defective transistor out of 12 transistors in total.
Therefore, the probability that the three transistors selected are defective is,
\(P(all\text{ }defective)=\frac{3}{14}\cdot\frac{2}{13}\cdot\frac{1}{12}=\frac{6}{2184}=\frac{1}{364}\)b. Now, we have to find the probability that the three transistors selected are non-defective.
First, we have to find how many ways are to select 3 transistors out of the 14 total transistors,
\(_{14}C_3=\frac{14!}{3!(14-3)!}=364\)Also, we have to find how many ways are to select 3 non-defective transistors - note that these must be picked out of the 11 non-defective ones,
\(_{11}C_3=\frac{11!}{3!(11-3)!}=165\)Therefore, the probability that the three transistors selected are non-defective is,
\(P(none\text{ }defective)=\frac{165}{364}\)The gene expression regulator illustrated in the picture below is an example of what kind of regulation? How does it get that name and how does it work? trpR Repressor R
Answers
The negative regulation is the type of regulation in which the transcription of a gene is prevented by the binding of a repressor protein to the DNA, which blocks the binding of RNA polymerase to the promoter region.
The gene expression regulator illustrated in the picture below is an example of what kind of regulation?
The gene expression regulator illustrated in the picture below is an example of the negative regulation. It is known as the trpR Repressor R.
How does it get that name and how does it work?
The TrpR protein is an allosteric protein that binds to the Tryptophan (Trp) molecule. It plays an important role in the regulation of gene expression, as it controls the transcription of the trp operon.
The Trp operon is a cluster of genes that are involved in the synthesis of the amino acid tryptophan. In the absence of tryptophan, the trpR protein is inactive.
However, when tryptophan is present, it binds to the TrpR protein and changes its shape. This change in shape activates the TrpR protein, which then binds to the trp operator region of the DNA.
Binding of the TrpR protein to the trp operator region prevents RNA polymerase from binding to the promoter region, thereby inhibiting the transcription of the trp operon.
Gene expression is regulated in both prokaryotes and eukaryotes, but the mechanisms of regulation differ between the two.
Negative regulation is the type of regulation in which the transcription of a gene is prevented by the binding of a repressor protein to the DNA, which blocks the binding of RNA polymerase to the promoter region.
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The gene expression regulator illustrated in the picture, known as trpR repressor, is an example of negative regulation. It is named after the trp operon, a set of genes involved in tryptophan biosynthesis in bacteria, where this regulator is commonly found.
The trpR repressor works by binding to a specific DNA sequence called the operator region, which is located near the trp operon genes. This binding occurs in the presence of tryptophan, the end product of the trp biosynthesis pathway. When tryptophan levels are high, it binds to the trpR repressor, causing a conformational change that enables it to bind to the operator region of the trp operon DNA.
By binding to the operator region, the trpR repressor physically obstructs the RNA polymerase from transcribing the genes in the trp operon. This prevents the synthesis of enzymes involved in tryptophan biosynthesis. As a result, the production of tryptophan is reduced or halted when there is already an adequate amount available in the cell.
The negative regulation exerted by the trpR repressor is based on the principle of feedback inhibition. When the end product (tryptophan) accumulates, it acts as a co-repressor and binds to the repressor, leading to the repression of its own biosynthesis. This mechanism ensures that the cell only produces tryptophan when it is needed, preventing wasteful energy expenditure.
In summary, the trpR repressor exemplifies negative regulation by binding to the operator region of the trp operon genes in the presence of tryptophan. This binding inhibits the transcription of genes involved in tryptophan biosynthesis, allowing the cell to regulate its production according to its needs.
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please help me I need this one last question then I can turn in the assignment!!
Answers
Answer:
I think with both plans it costs $45 for 3 hours of tutoring.
Step-by-step explanation:
Answer: Both plans, 45$, 3 hours
Step-by-step explanation:
The intersection is the set of coordinates where both functions equal each other. On this specific graph, at 3 hours of work time, both businesses pay a total of 45$.
With both plans it costs 45$ for 3 hours of tutoring
why won't anybody help me?
Answers
Answer:
b. -4 an C then A
Step-by-step explanation:
hope this helps!
Answer:
It will be 4
Step-by-step explanation:
i know
What is the product?
-1
Answers
Answer:
3.(-2/0) this is your answer
If r(x)=3x-1 and s(x)=2x+1,which expression is equivalent tor/s(6)
Answers
Answer:If r(x) = 3x – 1 and s(x) = 2x + 1, r/s (6) is equivalent to 17/13. Let's understand the solution in detail. Explanation: In this problem, first we perform the division operation on the given functions and find r(x) / s(x).
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