Answer:
The mean:
data: 3,6,9,10
You first add all of the numbers together.
3+6+9+10= 28
There 4 numbers in the data set, so you divide 4 by the sum of all of the numbers.
28/4= 7
So the mean is 7.
The median:
data: 3,6,9,10
first put all of the numbers in numerical order.
3,6,9,10
Then you find the middle number in the data set.
3,6,(the middle number here),9,10
to find the middle number, do the mean of 6 and 9
The mean of 6 and 9 is 7.5
So, 7.5 is the median
another example: 3,4,7,9,13
The middle number is 7
so 7 is the median
The mode:
data: 3,6,9,10
The mode is the number that is repeated the most
in this data, there is no mode.
but in this data: 4,4,6,9,11
4 is the mode because it was repeated the most
The graph of f(x) =[tex]2^{x+3}[/tex] shifts 10 units to the right when it is replaced with the graph of f(x) = [tex]2^{x-k}[/tex]. What is the value of k? 3 7 10 13
Answer:
7
Step-by-step explanation:
Whenever you shifting an exponential function to the left/right, you're going to generally have the equation: [tex]y=2^{x-k}[/tex] where k is the shift. So in this case we can think of x+3 as x and k as 10, since the shift is 10. This gives you the equation: (x+3) - 10, which simplifies to x-7, meaning the k value in this case is going go be 7. You can also think of it as already being shifted 3 units to the left, and you shift it 10 units to the right, that means this new function will be shifted 7 units to the right relative to the origin. This means the k=7.
Please help.
True or false
Answer:
True
Step-by-step explanation:
That is the distance formula.
Answer:
FALSE
Step-by-step explanation:
Distance Formula: [tex]\sqrt{(x_{2}-x_1)^2 + (y_2-y_1)^2}[/tex]
What is the 6th term of the geometric sequence where a1 = −4,096 and a4 = 64
The 6th term of the sequence is 4
How to determine the 6th term?The given parameters are:
a1 = -4096
a4 = 64
The nth term of the sequence is:
a(n) = a1 * r^(n-1)
So, we have:
a4 = a1 * r^3
This gives
r^3 = a4/a1
Substitute the known values
r^3 = 64/-4096
Evaluate
r^3 = -1/64
Take the cube roots
r = -1/4
The 6th term is
a(6) =a1 * r^5
This gives
a(6) = -4096 * (-1/4)^5
Evaluate
a(6) = 4
Hence, the 6th term of the sequence is 4
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Probabilities that are based on short-run relative frequencies are called what?.
Empirical probabilities is the name given to the probabilities that are based on short-run relative frequency.
Long-run relative frequency probabilities are called theoretical probabilities, whereas short-run relative frequency probabilities are called empirical or experimental probabilities.
Experimental probability: A probability that is based on past evidence is referred to as empirical probability, often referred to as experimental probability. In other words, based on past events, empirical probability depicts the possibility of an occurrence recurring. Theoretical probability: Probability that is established using logic is known as theoretical probability.Thus, Empirical probabilities is the name given to the probabilities that are based on short-run relative frequency.
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In the expansion of (2a + 3b), which of the following are possible variable terms? Explain your reasoning.
a²b³; a5b³; ab8; b8; a4b4; a8; ab7; a6b5
The possible variable terms are a^5b^3, b^8, a^4b^4, a^8, ab^7
How to determine the possible variable term?The expression is given as:
(2a + 3b)^8
The power of the above expression is 8
When expanded, the sum of powers on each variable must be 8.
Using the above explanation, we have the following possible variable terms:
a^5b^3, b^8, a^4b^4, a^8, ab^7
This is because the sum of powers equals 8
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Solve the rational equation
and check for extraneous solutions
5 = 4x+1
— ——-
x x^2
(1) x= 1; x = 0 is an extraneous solution
(2) x=0; x = 1 is an extraneous solution
(3) x= -1; x = 0 is an extraneous solution
(4) x=0; x = -1 is an extraneous solution
Answer:
1) x=1; x= 0 is an extraneous solution
Step-by-step explanation:
5 = 4x + 1
5 = 4 x 1 + 1
5 = 5
x = 1
______________________
x x^2
0 x 0^2
0 x 0 = 0
x = 0
:)
Suppose that 43% of the people who inquire about investments at a certain brokerage firm end up investing in stocks, 38% end up investing in bonds, and 51% end up investing in stocks or bonds (or both). What is the probability that a person who inquires about investments at this firm will invest in both stocks and bonds?
Mrs. Hamilton shows her students this graph and asks them to determine how figure A was transformed to figure B.
On a coordinate plane, triangle A has points (negative 1, 0), (negative 2, 4), (negative 1, 4). Triangle B has points (3, 1), (3, 5), (4, 5)..
Marcus suggests that figure A was reflected over the y-axis and then translated 2 to the right and 1 up. Julianne agrees, and states that the transformations could happen in any order. Which best describes the accuracy of Julianne’s statement?
Accurate. A translation of figure A of 2 to the right and 1 up and then a reflection over the y-axis produces the image, figure B.
Accurate. A reflection over the y-axis and then a translation of 1 up and 2 to the right produces the image, figure B.
Inaccurate. A translation of 2 to the right and 1 up and then a reflection over the y-axis results in a figure that is located in the second quadrant.
Inaccurate. A reflection over the y-axis and then a translation of 1 up and 2 to the right results in a figure that is located in the second quadrant.
On a coordinate plane, triangle A has points (negative 1, 0), (negative 2, 4), (negative 1, 4). Triangle B has points (3, 1), (3, 5), (4, 5)
The best accuracy for the transformation is; Accurate. A reflection over the y-axis and then a translation of 1 up and 2 to the right produces the image, figure B.
What transformation was used on the figure?
In a translation transformation, all the points in the object are moved in a straight line in the same direction. The size, the shape and the orientation of the object remain the same.
In this question, the points on triangle A are: (-1, 0), (-2, 4) and (-1, 4).
Marcus' translation is as follows:
Reflection over the y-axis which is x → -x and the points are: (1,0), (2,4) and (1,4).2 units to the right which is x → x + 2 and as such the points are: (3, 0), (4,4) and (3,4).1 unit up which is y → y + 1 and as such, the points are (3,1), (4,5) and (3,5).The points are the same of triangle B, hence the statement is accurate. According to the order of the translations, the second statement is correct.
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Solve the following multiplication problem.
9 cu yd 17 cu in
x 135
After converting the Units, we get 69,286,455 cu inches as the answer
What are Units?The rightmost position in a number or the number one can be considered a unit in mathematics. An individual thing or person that is viewed as distinct and whole but also a component of a total or group is another definition of a unit. When discussing an item's unit price, the word "unit" is also used. It refers to the price per unit, liter, or kilogram. Unit conversion is a multi-step process that includes rounding, selecting the appropriate number of significant digits, and multiplying or dividing by a numerical factor. NIST SP 1038 describes this multi-step method in detail, along with a rounding approach for technical publications, specifications, and other uses including packaged goods in the commercial marketplace and temperature.Converting yards into inches, we get:
1 cu yard = 46656 cu inches
11 cu yard = y cu inches
Cross-multiplying, we get:
y = 11 x 46656
y = 513216 cu inches
Now, total inches would be = 513216 + 17 = 513233 cu inches
Multiplying total inches by 135, we get:
513233 x 135 = 69,286,455 cu inches
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what’s the slope of a line using (-5, -4) and (-7, -6)
Answer: 1
Step-by-step explanation:
To find slope: (y1-y2)/(x1-x2)
y1 = -4
y2=-6
x1 = -5
x2 = -7
-4 --6 = -4 + 6 = 2
-5--7 = -5+7 = 2
2/2 = 1
so, the slope is 1
A machine can pump 15 litres of water in one minute.
How long does it take to pump 900 litres of water
Answer:
900 liters of water is pumped in 1 hour
Step-by-step explanation:
Time taken to pump 15 liters of water = 1 minute.
Time taken to pump 1 liters of water = 1/15 minute
[tex]\sf \text{Time taken to pump 900 liters of water=$\dfrac{1}{15}*900$}[/tex]
= 60 minutes
= 1 hour
The midpoint of AB is M (5, 6). If the coordinates of A are (3, 8), what are the
coordinates of B?
Answer:
(7, 4)
Step-by-step explanation:
[tex]\text{Let the coordinates of B } = x_{B} , y_{B} \\\text{Let the coordinates of A} = x_{A} , y_{A} \\\text{Let the coordinates of midpoint M} = x_{M} , y_{M}[/tex]
By the midpoint formula,
[tex](x_{M},y_{M}) = (\frac{x_{A} + x_{B}}{2} , \frac{y_{A} + y_{B}}{2} )[/tex]
[tex]x_{M} = \frac{x_{A} + x_{B}}{2} \\y_{M} = \frac{y_{A} + y_{B}}{2} \\[/tex]
We have coordinates of midpoint as (5, 6) and coordinates of A as (3,8)
So
[tex]5 = \frac{3 + x_{B}}{2} \\\\\\textrm{Cross-multiplying } 10 = 3 + x_{B}} \textrm{ or } x_{B} = 10-3 = 7\\[/tex]
[tex]6 = \frac{8 + y_{B}}{2} \\\\\\\\textrm{Cross-multiplying } 12 = 8 + y_{B}} \textrm{ or } y_{B} = 12-8 = 4\\[/tex]
So coordinates of B are (7,4)
What is 3(4x-2x)
5+3*2 simplified?
Answer:
30x+6Step-by-step explanation:
What is 3*(4x-2x)*5+3*2 simplified?
3*(4x-2x)*5+3*2=
3*2x*5+6 =
6x*5+6=
30x+6
The electric field strength between the plates of a simple air capacitor is equal to the voltage across the plates divided by the distance between them. When a voltage of 96.6 V is put across the plates of such a capacitor an electric field strength of 1.8 KV/cm is measured. Write an equation that will let you calculate the distance d between the plates.
The distance can be expressed in equation d=5.3*[tex]10^{-4}m[/tex].
Given voltage of 96.6 V and electric field strength of 1.8 KV/cm.
We know that d=V/E
We have to find the distance in equation form.
We know that electric field strength between the plates of a parallel plate capacitor is
E=V/d
Distance is the measurement between two sides or points.
where E=electric field strength
V=potential difference
d=distance between the plates
In equation form distance looks like:
d=V/E
from the question we are that V=96.6 V
E=1.8KV/cm.
Converting to V/m
E=180000V/m
d=96.6/180000
=0.00053
d=5.3*[tex]10^{-4}m[/tex].
Hence the distance can be expressed as d=[tex]5.3*10^{-4} m[/tex].
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If a store sold 25 pairs of socks, making a 25% profit (i.e., percent of sales) of $150, how much did they charge for each pair
The store charged $24 for each pair of socks as the selling price.
What is Profit?Profit is the financial gain that is earned by a business or an individual after deducting all expenses from revenue. In other words, it is the amount of money that remains after all costs of producing and selling a product or service have been subtracted from the total revenue earned.
What is Revenue?Revenue refers to the total amount of income earned by a business or an individual from the sale of goods or services during a specific period of time. It is the total amount of money that a business receives from its customers in exchange for its products or services.
In the given question,
Let's start by calculating the total revenue from the sale of 25 pairs of socks
Since the profit is 25% of the revenue, we can set up the equation:
Profit = 0.25 * Revenue
$150 = 0.25 * Revenue
Revenue = $150 / 0.25
Revenue = $600
The total revenue from selling 25 pairs of socks is $600.
To find the price per pair of socks, we can divide the revenue by the number of pairs:
Price per pair = Revenue / Number of pairs
Price per pair = $600 / 25
Price per pair = $24
Therefore, the store charged $24 for each pair of socks.
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Writing Exercises
353. Why does (a + b)² result in a trinomial, but (a − b)(a + b) result in a binomial?
Answer:
In [tex]$(a+b)^{2}$[/tex] is obtained by addition therefore result is trinomial while in (a-b)(a + b) the middle terms are canceled out of each other therefore result is binomial.
Step-by-step explanation:
Explanation
Given that [tex](a+ b)^{2}$[/tex] results in a trinomial, but (a-b)(a-b) results in a binomial.An expression [tex]$(a+b)^{2}$[/tex] when multiply and simplify it is equal [tex]a^{2}+a b+a b+b^{2}=a^{2}+2 a b+b^{2}$[/tex] therefore it is trinomial. Here middle term is obtained by addition. While an expression (a + b) (a-b) when multiply and simplify it is equal to [tex]$a^{2}-a b+a b+b^{2}=a^{2}+b^{2}$[/tex]therefore it is binomial because the middle that is positive ab is canceled by negative ab.any sample proportion that is more than 1.96 standard errors from the popullation proportion will result in an
Any sample proportion that is more than 1.96 standard errors from the population proportion will result in a confidence interval that includes p.
In frequentist records, a confidence interval is more than a few estimates for an unknown parameter. A self-belief interval is computed at a chosen self-belief stage; the ninety-five% self-assurance stage is maximum commonplace, however other tiers, which include ninety% or ninety-nine%, are now and again used.
The confidence stage is the share of instances you expect to get near the identical estimate if you run your test again or resample the populace in an identical manner.
The confidence c programming language includes the higher and lower bounds of the estimate you anticipate locating at a given stage of confidence.
As an instance, in case you are estimating a 95% self-belief c language around the mean share of lady toddlers born every 12 months primarily based on a random sample of babies, you may find a top certain of zero.56 and a decrease certain of zero.48. those are the top and decrease bounds of the self-belief c programming language. The self-assurance level is 95%.
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The function below models the correlation
between the number of hours a plant is kept in
sunlight (x) and the height (y), in mm, to which it
grows:
y = 2 + 4x
What does the y-intercept of this function
represent?
The original height of the plant was 4 mm.
The original height of the plant was 2 mm.
The height of the plant increases by 2 mm for
every hour of sunlight it receives.
The height of the plant increases by 4 mm for
every hour of sunlight it receives.
What is the slope in the equation y = 2x + 3
If x+y=6,y+z=7, z+x=9 what is the average or x, y and z
Step-by-step explanation:
so in this case
x-4
y-2
z-5
average=x+y+z/no of values
= 4+5+2/3
=11/3
=3.6
There are between 90 and 115 cars in a parking lot. Exactly one-fourth of them are green. Exactly one-eighth of them have a sticker on the back that says, Mr. Donovan is the best teacher ever. How many cars MIGHT be in the parking lot
There are 104 cars in the parking lot.
According to statement there are between 90 and 115 cars on the lot.
So, {X| 90 < x < 115} (This renders an infinite solution set finite)
AND exactly one eight of them have a sticker on the back, so the total number of cars must be evenly divisible by eight.
X ∈ {96, 104, 112,}
AND exactly one fourth of the cars are green, so the number of cars must be evenly divisible by 4. Here all above written numbers are divisible by 4. So, find the mean to calculate the number of cars in the parking lot.
x = (96+104+112)/3
x = 104
There are 104 cars in the parking lot.
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Solve for y 3x+3-x+ (-7) > 6 o a. x > (-5) b. x<5 ) cy>5 ) d. x > 2.5
The value of x for the inequality 3x+3-x+ (-7) > 6 is x > 5. This a can be obtained by solving the linear inequality by taking terms with x to one side of the inequality similar to solving of linear equation.
What is the value of x?Given that
3x + 3 - x + (-7) > 6
3x - x > 6 + 7 - 3
2x > 10
x > 5
Hence the value of x for the inequality 3x+3-x+ (-7) > 6 is x > 5. The correct option is c.
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Find the two straight lines represented by x² + 5xy - 6y² = 0
By factorizing, we have
[tex]x^2 + 5xy - 6y^2 = (x - y) (x + 6y) = 0[/tex]
so that
[tex]x - y = 0 \implies \boxed{y = x}[/tex]
or
[tex]x + 6y = 0 \implies \boxed{y = -\dfrac x6}[/tex]
I don’t know what to do can y’all help me out
Since the sum of both angles <ORQ and <SRQ is 180 degrees, hence the two angles that are supplementary are <ORQ and <SRQ
What are supplementary anglesSupplementary angles are angles that sums up to 180 degrees..
Since the line SR bisects the line OQ, hence the angle <ORQ and <SRQ are equal and equal to 90 degrees each,
Since the sum of both angles <ORQ and <SRQ is 180 degrees, hence the two angles that are supplementary are <ORQ and <SRQ
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What is the length of the side opposite the 45° angle?
Answer:
Step-by-step explanation:
c = b·sin(C)
c= 10Sin(45
c=7.071
So the side length opposite to the 45 degree angle is 7.071 :)
https://www.calculator.net/triangle-calculator.html
^this website is perfect for questions like these^
Good luck with the rest of your work!
A measure of the strength of the relationship between two variables is referred to as the.
A measure of the strength of the relationship between two variables is referred to as the correlation coefficient.
What is the correlation coefficient?To gauge the strength of the linear link between two variables, correlation coefficients are used.
A value of correlation coefficient less than zero denotes a negative association, while a value greater than zero denotes a positive relationship.
A zero correlation coefficient means there is no correlation between the two variables under comparison.
A crucial idea in building diversified portfolios that may better resist portfolio volatility is the concept of a negative correlation, often known as an inverse correlation.
Since calculating the correlation coefficient takes time, it is frequently done by entering data into a calculator, computer, or statistics application.
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Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
1st.) x = 5 /Sin(30°)
x = 10
!) sin(45°) = 4/x
x = 4/sin(45°)
x = 4√2
I) Cos(45°) = √3 / x
x = √3 / Cos(45°)
x = √6
E) Tan(60°) = 3√3 / x
x = 3√3 / 3
W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.
x = 45°
N) x² + x² = (7√2)²
x = 7
V) Tan(60°) = 7 / x
x = 7√3/3
K) x² + x² = (9)²
x = 9/√2
Y) Sin(60°) = 7√3/x
x = 14
M) Sin(30°) = x/11
x = 11/2
T) Sin(45°) = x/√10
x = √5
A) x + 2x + 90° = 180°
x = 30°
O) Sin(45°) = √2 / x
x = 2
R) Tan(30°) = x / 4
x = 4/√3 = 4√3 / 3
S) Sin(60°) = x / (10/3)
x = 5√3 / 3
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60. Cities A and B are on the same east-west line.
Assume that city A is located at the origin. If the
distance from city A to city B is at least 100 miles
and x represents the distance from city B to city A,
express this using absolute value notation.
Answer:
The expression for the statement using absolute value notation is [tex]|x|\geq 100[/tex]
Step-by-step explanation:
It is given in the question that the distance from city A to city B is at least 100 miles.
It is required to express the statement using absolute value notation.
To express the statement using absolute value notation, deduce the statement in the form of an equation.
x represents the distance from city B to A city .
Deduce the statement in the form of an equation
[tex]|x|\geq 100[/tex]
can someone please help me, as well as factoring the expression
The value of U and V will be (x – 3) and 8y, respectively. Then the correct option is A.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The expression is given below.
⇒ (U + V)(U – V)
Where U and V are either constant or single variable expression.
Then the expression will be
⇒ U² – V²
Then the value of U and V will be (x – 3) and 8y, respectively.
Then the correct option is A.
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un bibliotecario de la biblioteca "Amauta" coloca libros de aritmética y álgebra en un estante, notando que la relación de libros de aritmética y el total de libros es de4 a 9. respectivamente Si sabe que coloca 10 libros de álgebra en el estante
¿Cuántos libros de aritmética coloca la bibliotecaria?
Concluimos que hay 8 libros de aritmética.
¿Cuántos libros de aritmética coloca la bibliotecaria?
Sabemos que la relacion entre el número de libros de aritmetica y el total de libros es de 4 a 9.
Es decir, sí el número total de libros es N, entonces (4/9)*N de esos libros son de aritmética.
Sea X el número de libros de aritmética. Sabemos que hay 10 libros de algebra, entonces el número total N es:
N = 10 + X
Y usando la relación de arriba, podemos escribir:
X = (4/9)*N = (4/9)*(10 + X)
Ahora podemos resolver esto para X.
X*(9/4) = 10 + X
X*(9/4) - X = 10
X*(5/4) = 10
X = (4/5)*10 = 8
Concluimos que hay 8 libros de aritmética.
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