On a test with a range of 110–410, these students received a mean score of 370 and a standard deviation of 50. What range would roughly 95% of the students' scores fall into, presuming a mound-shaped and symmetric distribution.
A variable is what?Any traits, figures, or amounts that may be gauged or counted are considered variables. Another name for a variable is a data item. Variables include things like age, sex, business income and expenses, birthplace, capital expenditures, class grades, eye color, and vehicle type.
Which examples use variables?A variable is a quality that may be measured and take on several values. A few examples of variables are height, age, income, province of birth, school grades, and kind of dwelling. Categorical and numeric variables are the two basic types of variables that can be categorized.
8 ≤ -4(x - 1)
Please help me.
Answer: x ≤ -1
Step-by-step explanation:
8 ≤ -4x+4
4x+8 ≤4
4x ≤-4
x ≤ -1
Answer:
Step-by-step explanation:
first open the bracket by multiplying -4 through
8 ≤ -4x + 4
then group like terms and unlike terms
therefore; 8 - 1 ≤ -4x or -4x ≤ 8-4
-4x ≤ 7 then divide both side by -4
so, ⇒ x ≤ -4/4
x≤-1
the sum of a number x and 4, all divided by 3
The value of l such that the rectangle and trapezium have the same area will be 18 feet.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
The perimeter of the rectangle = 2( length + width).
As per the given,
Area of rectangle = area of a trapezoid
9 x l = (1/2)(24 + 12)9
9l = 162
l = 18 feet
Hence "The amount of l that must be present for the rectangle and trapezium to share the same area is 18 feet.".
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Suppose the equation of line p is x=2 and the equation of line q is x=-1 what translation is equivalent to rp o rq
The transformation equivalent to the reflection across the line q = -1, followed by the reflection across the line p = 2, [tex]r_p \circ r_q[/tex] is a translation of 6 units to the right.
What is a reflection transformation?A reflection transformation is one in which the points of the image are mirrored across the line of reflection.
The coordinate of a point (x, y) following a reflection about the y-axis is the point (-x, y)
The line x = -1 is parallel to the y-axis, therefore, only the x-coordinate of the preimage point (x, y) will change following the reflection across the line, q, [tex]r_q[/tex], x = -1
The relative x-coordinate of a point (x, y) to the line x = -1 is x + 1
Therefore, the image of the point (x, y) following the reflection across the line x = -1 and relative to the line is the point (-(x + 1), y) = ((-x - 1), y)
Relative to the x-axis, the point ((-1 - x), y) is (-1 + (-1 - x), y) = (-2 - x, y)
The coordinate of a point (x, y) relative to the line x = 2 is (x - 2, y)
Therefore, the coordinate of the point ((-2 - x), y) relative to the line x = 2 is ((-2 - x) - 2, y) = ((-4 - x), y)
The image of the point ((-4 - x), y) following a reflection across the line x = 2, [tex]r_p[/tex], is (-(-4 - x), y) = ((4 + x), y)
Relative to the y-axis, the coordinate of the image point ((4 + x), y) is ((2 + (4 + x)), y)
((2 + (4 + x)), y) = ((6 + x), y)
The translation equivalent to the transformation, [tex]r_p \circ r_q[/tex] is a translation of 6 units to the right
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A hollow pipe is submerged in a stream of water so that the length of the pipe is parallel to the velocity of the water. If the water speed doubles and the cross-sectional area of the pipe quadrupled, what happens to the volume flow rate of the water passing through it?.
The volume flow rate of the water passing through the pipe increases by a factor of 6.
Assuming that the initial cross sectional area of the pipe is A m² and the initial velocity of the water is V m/s, the water flow rate is:
= initial flow rate = area × velocity = AV m³/s
As the water speed doubles (2V m/s) and the pipe cross-sectional area triples (3A m²), the volume flow rate becomes:
Final flow rate = 2V × 3A = 6AV m³/s
As a result, the volume flow rate of the water moving through it multiplies by a ratio of six.
The basic equation for cases like these is
Q=AV,
where Q is the volume flow rate, A is the cross-sectional area occupied by the flowing material, and V is the average velocity of flow.
V is considered an average since not every component of a flowing fluid flows at the same rate. If you monitor the waters of a river moving slowly downstream at a consistent rate of gallons per second, you will see that the surface has slower currents here and faster currents there.
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formula for area and perimeter of a circle
Answer:a=pi*r^2
Step-by-step explanation:
area=pi*radius squared
Solve the system
x+y=6
5x-y=3
by graphing and by substitution. Compare the
methods. Which method is more accurate? Explain
We can solve the given linear equations using graphing and substitution method. Substitution is more accurate, since it provides an exact answer.(x,y)=(1.5,4.5) is the answer for the given linear equation.
What is Substitution and Graphing method ?As Math Planet correctly notes, to solve a system of linear equations by graphing, we simply graph both equations in the same coordinate plane and locate the intersection of the two lines. Substitution-Based Graphing of Linear Equations. By substituting values for x, we may obtain the appropriate y values and display the points on a line with the equation y = ax + b. (x, y). Two points must be produced by replacement in order to create a line between them.
Calculation:x + y = 6 → y = 6 − x
5x − y = 3
⇒5x − (6 − x) = 3
⇒5x + x − 6 = 3
⇒6x = 9
⇒x = 1.5
⇒1.5 + y = 6
⇒y = 4.5
(x,y)=(1.5,4.5)
We can solve the given linear equations using graphing and substitution method. Substitution is more accurate, since it provides an exact answer.(x,y)=(1.5,4.5) is the answer for the given linear equation.
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At the theatre, there are six seats in a row. Eliot and Doug have three people between them. Chuck sits next to Eliot, but not next to Bob: Andy is on the end: but Eliot isn't. Frank is between
From the arrangement given, it can be concluded that-
Frank is between Chuck and Bob
What is arrangement?
The way of putting up a particular thing in order for a particular purpose or activity is called arrangement.
From the seating arrangement given,
Andy is on the end: but Eliot isn't
Andy ___ ___ ___ ___ ___
Eliot is not on the end and Eliot and Doug have three people between them
Andy Elliot ___ ___ ___ Doug
Chuck sits next to Eliot, but not next to Bob
Andy Elliot Chuck ___ Bob Doug
Only Frank is left
Andy Elliot Chuck Frank Bob Doug
So Frank is between Chuck and Bob
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PLEASE HELPPPPP Determine the type of correlation represented in the scatter plot below.
The graph shows:
A. A perfect positive correlation
B A strong positive correlation
C. A weak postitive correlation
D. No correlation
E. A weak negative correlation
F. A strong negative correlation
G. A perfect negative correlation
The answer is weak negative correlation.
What is meant by correlation?Positive correlation: An increase or decrease in one variable causes an increase or decrease in the other when the values of the two variables move in the same direction.A drop or increase in one variable causes a decrease or increase in the other when the values of the two variables move in the opposite direction.No linear dependency or correlation exists.An illustration of how these connections appear in a graph is shown below:As a result, we can see from the provided image that there is a negative correlation between x and y, i.e., as x increases, y lowers. Additionally, the dispersion of the dots indicates a poor association.The degree to which two variables are linearly connected is expressed by the statistical concept of correlation (meaning they change together at a constant rate). It is a typical technique for outlining straightforward connections without stating cause and consequence.A statistical term known as correlation indicates the strength and direction of a relationship between two or more variables. It is expressed as a number. However, just because two variables are correlated does not necessarily imply that the change in one of the variables is what changed the values of the other.To learn more about correlation refer to:
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Can we use two infinitives in a sentence?
Yes, one can use more than one infinitives in the same sentence. For example : I have to wash my hand to keep myself clean.
Reason for the given statement:
To use two or more infinitives in the same sentence:
Multiple of infinitives can be used in the same sentence.For example : I want to purchase new clothes to attend marriage belongs to my family members.Here we have used three infinitives which are to purchase , to attend and to my.Mostly when two or more infinitives are used the last one ends with and.Therefore, it is perfectively alright to use more than one infinitives in the same sentence.
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i need help asap pls help im on a time limit so pls help me
Answer:
What is even the question?
Step-by-step explanation:
if you subtract 12 from my number and multiply the difference by -3, the result is -27. what is my number
Answer:
21
Step-by-step explanation:
27/3 + 12
half of the quantity of 6 less than a number f is 4. how do u put in the algebraic form
Wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww
Rewrite the expression 12m(m-3n) using the Distributive Property.
O A. 12m² - 36mn
OB. 12m² - 12mn
O C. 12m² - 9mn
O D. 12m² - 3mn
The expression equivalent to 12m(m-3n) using distributive property is 12m² - 36mn.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 12m(m-3n) .
Twelve m times m minus three times n.
12m(m-3n).
12m is to multiplied to m minus three n.
12m²-35mn.
Twelve m square minus thirty five times of m and n.
Hence, 12m²-35mn is the expression equivalent to 12m(m-3n) .
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are 4:1 and 8:3 equivalent ratios?
Answer: No
Step-by-step explanation:
-0.47x+0.27x = 5.8 Solve for X
Answer:
-29
Step-by-step explanation:
you add both decimals together you get -.2x=5.8 you divide both sides by -.2x and you get x=-29
Use the table below to find the indicated values:
The inverse functions required from the given table of values are;
f⁻¹(1) = 1/3
f⁻¹(12) = 1/13
f⁻¹(7) = 1/9
How to find the inverse of a function?An inverse function also called an anti function is defined as a function, that can reverse into another function. This simply means that, if any function “f” takes x to y then, the we can say that the inverse of the function “f” will take y to x. If the function is denoted by 'f' it means that the inverse function is denoted by f⁻¹(x)
For example, we have the function;
y = 2x + 3, the inverse would be;
f⁻¹(y) = (x - 3)/2
Thus, from the given table;
f⁻¹(1) = 1/3
f⁻¹(12) = 1/13
f⁻¹(7) = 1/9
Thus, we conclude that the inverse functions of f⁻¹(1), f⁻¹(12) and f⁻¹(7) are respectively 1/3, 1/13 and 1/9.
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Find the y-coordinate of the y-intercept of the polynomial function defined below.
f(x)=7x^2-5x+9x^3-5+2x^4
By using the concept of intercept, it can be calculated that-
y-coordinate of the y-intercept is -5
What is intercept?
The distance from the origin to the point where the curve cuts the x axis is the x intercept of the curve.
The distance from the origin to the point where the curve cuts the y axis is the y intercept of the curve
The polynomial function is
f(x) = [tex]7x^2-5x+9x^3-5+2x^4[/tex]
For y-coordinate of y- intercept, we put x = 0
[tex]f(0) = 7(0)^2-5(0)+9(0)^3-5 + 2(0)^4[/tex]
= -5
y-coordinate of the y-intercept is -5
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the mean of a distribution of data is 3.56 . if the distribution is symmetric , what is the median ?
Since, the mean of distribution of data is 3.56 then the median is also 3.56 because the distribution is symmetric.
Symmetric Distribution:
A symmetric distribution is when the values of a variable occur with regular frequency, often the mean, median, and mode all occurring at the same point. A line in the middle of the chart indicates that the two planes are mirror images of each other.
In graphical form, a symmetric distribution is displayed as a normal distribution (that is, a bell curve). Symmetric distribution is a central concept in technical trading as it assumes that the price movements of an asset over time follow a symmetric distribution curve. A symmetric distribution can be contrasted with an asymmetric distribution.
Relation between Median and Mean
A distribution always has a median and a mode, but not always a mean. Consider the Cauchy distribution. No average exists. Modes are always present, but may not be unique. This means that you can get a distribution that is not unimodal (that is, multimodal).
So, if we have a symmetric distribution with a mean and the distribution is unimodal, we can say:
Mean = Median = Mode
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Find the slope of the line that passes through (1, 12) and (5, 5).
Answer: -7/4
Step-by-step explanation: see attached
Evaluate the expression: 2b + 3a if a = 2.6, b = 3
Answer:
13.8
Step-by-step explanation:
2b+3a
2(3)+3(2.6)
6+3(2.6)
6+7.8
13.8
Which function represents the exponential graph given that (0, 1) and (4, 81/16) are points that lie on the graph?
A ƒ(x) = (23)xƒ(x) = ( 2/3 ) x
B ƒ(x) = (4)xƒ(x) = ( 4 ) x
C ƒ(x) = (1)xƒ(x) = ( 1 ) x
D ƒ(x) = (3/2)x
Answer:
Step-by-step explanation:
A......
75 POINTS!!
Write a system of equations to model Monica's savings and Shanna's savings. Let x represent the number of weeks and y represent savings.
Type your response in the box
The system of equations to model Monica's and Shanna's savings is y = 10x + 50 for Monica and y = 15x + 100 for Shanna.
To model Monica's savings and Shanna's savings using a system of equations, we can use the variables x and y, where x represents the number of weeks and y represents the savings.
Let's start by defining the equation for Monica's savings. We'll use the equation y = mx + b, where m represents the savings per week and b represents the initial savings.
Next, let's define the equation for Shanna's savings. We'll use the same equation, y = mx + b, but with different values for m and b.
For example, let's say Monica saves $10 per week and initially has $50 in savings. The equation for Monica's savings would be y = 10x + 50.
Now, let's say Shanna saves $15 per week and initially has $100 in savings. The equation for Shanna's savings would be y = 15x + 100.
So, the system of equations to model Monica's and Shanna's savings would be:
Monica: y = 10x + 50
Shanna: y = 15x + 100
By using this system of equations, we can determine Monica's and Shanna's savings at any given number of weeks, x. Simply substitute the value of x into the equations and solve for y.
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You need 560 mL of a 70% alcohol olution. On hand, you have a 80% alcohol mixture. How much of the 80% alcohol mixture and pure water will you need to obtain the deired olution?
Answer:
Below
Step-by-step explanation:
x = amount of 80% to use
amount of alcohol in ingredients = amount of alcohol in final product
.8 x = .7 (560)
x = 490 ml
which is more 2,005 pounds or 1 ton
Answer: 2005 pounds
Step-by-step explanation:
1 ton is 2000 pounds
Answer:
2,005 pounds
Step-by-step explanation:
Hope it helps!
ignore the answer i put down
The equations that represent the pattern are:
P = 3n
P = 2n + 1
Options A and C are the correct answer.
What is an equation?An equation is a mathematical statement of two expressions connected by an equal sign.
Example:
2x = 5 is an equation.
We have,
P = 3 when n = 1.
a) P = 3n
P = 3 x 1 = 3
b) P = n + 3
P = 1 + 3 = 4
c) P = 2n + 1
P = 2x 1 + 1 = 2 + 1 = 3
d) P = 3 - n
P = 3 - 1 = 2
We see that,
P = 3n and P = 2n + 1 gives P = 3 when n = 1.
Thus,
P = 3n and P = 2n + 1 gives P = 3 when n = 1.
Options A and C are the correct answer.
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What is the rule about splitting infinitives How would you rewrite the quote above?
The rule about splitting infinitives is avoid using a word between TO and the verb if at all possible. The correct quote is "To go boldly where no one has gone before."
In the given question, we have to explain the rule about splitting infinitives and how we rewrite the quote based on this rule
The given quote is
"To boldly go where no one has gone before."
Splitting infinitives is prohibited according to grammar rules. Avoid using a word between TO and the verb if at all possible. Split infinitives are improper grammatically, therefore avoid using them.
So, in order to change this quote, you should:
"To go boldly where no one has gone before."
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The right question is:
What is the rule about splitting infinitives? How would you rewrite the quote above based on this rule?
read this quote that comes from a popular television and movie franchise:
"To boldly go where no one has gone before."
What are the vertex and range of y = |x − 5| 4? (5, 4); −[infinity] < y < [infinity] (5, 4); 4 ≤ y < [infinity] (−5, 4); −[infinity] < y < [infinity] (−5, 4); 4 ≤ y < [infinity]
The range and the vertex is 4 ≤ y < [infinity] and (5, 4).
To find the vertex, we can take the derivative of the function and set it equal to 0:
y' = |x − 5|' = 0
=> x − 5 = 0
=> x = 5
Then, we can plug x = 5 into the original equation to find the y-value at the vertex:
y = |x − 5| = |5 − 5| = |0| = 0
So, the vertex of y = |x − 5| is (5, 4).
To find the range, we need to consider the range of the absolute value function. The range of the absolute value function is:
−[infinity] < y < [infinity]. So, the range of y = |x − 5| is also −[infinity] < y < [infinity] (or 4 ≤ y < [infinity]).
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A box of cereal weighs 14 ounces and costs $2. 66. What is the price per ounce of the cereal?.
Number 14 is the question
The measure of x = 93 degree and y = 36 degree.
What is Angle Sum Property?According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees.
The total of a triangle's three internal angles is 180 degrees, as stated by the angle sum feature of a triangle.
Given:
As, <QRP= 51
So, <QRP = <QPR= 51 {Angles opposite to equal sides are also Equal}.
In ΔPQR
<P+ <Q+ <R= 180
51 + 51 + <Q= 180
<Q= 180- 102
<Q= 78 degree.
So, <y = 1/2 <Q= 78/20 = 36 degree.
and, In small left Triangle
36 + 51+ x= 180
x = 180 - 87
x= 93 degree.
Hence, the measure of x = 93 degree and y = 36 degree.
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given that about 25% of the mammalian genome is associated with genes, including introns and regulatory sequence, what would be the approximate average length of dna per gene if the genome contained 20,000 genes?
According to the question,
Given data in the question.
If the genome contained 20,000 genes, the average length of DNA per gene will be 40,000 base pairs.
What is the average length of DNA per gene?
Only 2.5% of the human genome is protein-coding. Introns make up the remaining 97.5%. The male nuclear diploid genome is 6.27 Giga base pairs (G b p), 205.00 cm (cm) long, and 6.41 picograms in weight (p g). Female measurements are 6.37 G b p, 208.23 cm, and 6.51 p g
For a 25% mammalian genome with 20,000 genes, the total number of base pairs, which is the length of DNA per gene, will be approximately double the payment of genes contained in the genome, in this case 40,000.
The average length of DNA per gene, assuming 20,000 genes in the genome, is 40,000 base pairs.
How long does DNA typically be per gene?
Only 2.5% of the human genome codes for proteins. The remaining 97.5% is made up of introns. The size and weight of the male nuclear diploid genome are 6.27 Giga base pairs (G bp), 205.00 centimetres (cm), and 6.41 picograms (p g). 6.37 G bp, 208.23 cm, and 6.51 p g are the female measurements.
The total number of base pairs, which is 20,000 for a 25% mammalian genome with 20,000 genes,
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The average length of DNA per gene would be 40,000 base pairs if the genome had 20,000 genes.
What is the average length of DNA per gene?The human genome only codes for proteins in 2.5% of it. The remaining 97.5% are introns. The male nuclear diploid genome measures 205.00 centimeters (cm), is 6.27 Gigabase pairs (Gbp), and weighs 6.41 picograms (pg). 208.23 cm, 6.51 pg, and 6.37 Gbp are the female measurements.
Is genetics a lot of math?Although there may be some hereditary component to math aptitude, this probably only accounts for a small portion of it. Even in the current study, genetics alone could only account for 20% of math prowess. According to Libertus, "this leaves more than 80% of the variety in children's math aptitude unexplained."
The overall number of base pairs, which is the length of DNA per gene, will be roughly twice the number of genes present in the genome, in this example 40,000, for a 25% mammalian genome with 20,000 genes.
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