Answer:
Pero cuando una magnitud crece y la otra disminuye proporcionalmente, se le llama proporcionalidad Inversa. Dos magnitudes son inversamente proporcionales si al multiplicar (o dividir) una de ellas por un número, la otra queda dividida (o multiplicada) por el mismo número.
Or, But when one magnitude increases and the other decreases proportionally, it is called Inverse proportionality . Two quantities are inversely proportional if when multiplying (or dividing) one of them by a number, the other is divided (or multiplied) by the same number.
What is lim x→3 x^2 - x - 6/ x - 3
=======================================================
Explanation:
If we plugged x = 3 into the expression, then we'd get x-3 = 3-3 = 0 in the denominator. That's not allowed. But we can simplify first
x^2-x-6 factors to (x-3)(x+2). The key here is that (x-3) is a factor. It cancels with the x-3 in the denominator
So, [tex]\frac{x^2-x-6}{x-3} = \frac{(x-3)(x+2)}{x-3} = x+2[/tex]
Allowing us to say,
[tex]\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = \lim_{x \to 3}\frac{(x-3)(x+2)}{x-3}\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = \lim_{x \to 3}(x+2)\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = 3+2\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = 5\\\\\\[/tex]
The solution is 5
The value of the equation lim x tends to 3 ( x² -x - 6 ) / ( x - 3 ) is A = 5
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = lim x tends to 3 ( x² -x - 6 ) / ( x - 3 ) be equation (1)
On simplifying the equation , we get
Taking the common factors on numerator , we get
A = lim x tends to 3 ( x² + 2x - 3x - 6 ) / ( x - 3 )
A = lim x tends to 3 ( x ( x + 2 ) - 3 ( x + 2 ) ) / ( x - 3 )
Taking the common factor as ( x + 2 ) , we get
A = lim x tends to 3 ( x + 2 ) ( x - 3 ) / ( x - 3 )
So , the equation is
A = lim x tends to 3 ( x + 2 )
Substitute the value of x = 3 , in the equation , we get
A = ( 3 + 2 )
A = 5
Therefore , the value of A is 5
Hence , the equation is A = 5
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8*10^4 is how many times as large as large as 4*10^-5
Answer:
D. 2 . 10^9
Step-by-step explanation:
( 8 * 10^4 ) / ( 4* 10^-5 )
( 8*10^4 ) 10^5 / ( 4 )
2 * 10^ 9
Reedley college Math -45-50554-2020FA Exercise Problem Solving
Answer:
OK its that question
Solve this plz. It’s 4x4 sudoku
Answer:
Step-by-step explanation:
16
lily scored her first Spanish test are 96, 85, 90, 92. What test score must lily earn on the 5th test so that her mean will be exactly 90.
Answer:
87
Step-by-step explanation:
[tex]\frac{96+85+90+92+x}{5} = 90\\[/tex]
[tex]\frac{353+x}{5} = 90[/tex]
[tex]353+x= 5(90)\\[/tex]
[tex]353+x=450[/tex]
[tex]x=87[/tex]
The amount of paint used on new tractors averages 18.2 gallons with a standard deviation of 0.8 gallons. A new nozzle is used on 20 tractors and averaged 17.9 gallons. What is the probability that is was just random chance
Answer:
17.9/18.2 =0.984 to 3 decimal places
Step-by-step explanation:
The initial mean/average = 18.2 gallons
A standard deviation of 0.8 gallons implies a lower-upper limit of (17.4 - 19) gallons of paint used on new tractors.
New mean/average = 17.9 gallons
It is noticeable that this value 17.9 falls within the lower range of the standard deviation of the initial mean; hence the question
What is the probability that this happened by chance?
17.9 ÷ 18.2 = 0.9835
Therefore, there is a high probability that this happened by chance. 0.9 is closer to 1 than to 0.
please help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
60
Step-by-step explanation:
1, Extand line y for which y intercepts CB at point K
2, line y is a straight line and thus KAB=180-110=70
3, AY parallel to CX thus angle CKA=130 which is a alternative angle of BCX (if you can't see then try to extend CX as well
4,BKA=180-130=50 as BC is a straight line
5, the sum of interior angle of a triangle is 180, and we have KAB and BKA, thus angle ABC = 180-KAB-BKA=180-70-50=60
Calculate the value of the sample correlation coefficient. Based on this value, how would you describe the nature of the relationship between the two variables
Answer:
Explained below.
Step-by-step explanation:
The correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.
The formula to compute correlation coefficient is:
[tex]r(X,Y)=\frac{Cov(X,Y)}{\sqrt{V(X)\cdot V (Y)}}[/tex]
[tex]=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{[n\cdot\sum X^{2}-(\sum X)^{2}][n\cdot\sum Y^{2}-(\sum Y)^{2}]}}[/tex]
Positive correlation is an association amid two variables in which both variables change in the same direction.
A positive correlation occurs when one variable declines as the other variable declines, or one variable escalates while the other escalates.
Negative correlation is a relationship amid two variables in which one variable rises as the other falls, and vice versa.
In statistics, a perfect positive correlation is represented by +1 and -1 indicates a perfect negative correlation.
HELP PLEASE ! Due tonight! A pharmaceutical salesperson receives a monthly salary of $5000 plus a commission of
7% of sales. Write a linear equation for the salesperson's monthly wage W in terms of monthly sales S
Answer:
w=5000+0.7s
Step-by-step explanation:
if its possible give me 5 start I need it
$33 for 6 sandwiches find the unit rate
Answer:
$ 5.5
Step-by-step explanation:
$33 for 6 sandwiches.
For 1 sandwiche = ?
Now,
= 33 ÷ 6
= $5.5
Thus, the unit rate is $5.5
5-7 please help BRAINLEST
Answer:
k=17
Step-by-step explanation:
k+10=27
k=27-10
k=17
Hi there! Hopefully this helps!
---------------------------------------------------------------------------------------------
Answer: k = 17.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[tex]k + 10 = 27[/tex]
Subtract 10 from both sides.
[tex]k = 27 - 10[/tex]
Subtract 10 from 27 to get, you guessed it, 17!How many 90° angles are formed by the intersection?
Answer:
might be four
not sure
good luck!
A come and a pyramid has equal heights and volumes.if the base area of the pyramid is 154cm2.find the radius of the cone.
Answer:
Radius = 8.575 cm
Step-by-step explanation:
Formula for volume of a pyramid is;
V_p = ½Ah
Where A is area of base and h is height
Also, formula for volume of cone is given as;
V_c = ⅓πr²h
Now, we are told that V_p = V_c and that h is the same for both shapes.
Thus ;
½Ah = ⅓πr²h
h will cancel out to give;
½A = ⅓πr²
Cross multiply to give;
3A/2π = r²
Base area of pyramid is given as 154 cm². Thus;
(3 × 154)/2π = r²
r = √((3 × 154)/2π
r = 8.575 cm
the fourth term of a sequence is 40. write the first 5 terms of two different sequences that satisfy that condition
Answer:
A.P. : 10, 20, 30, 40, 50
G.P. : 5, 10, 20, 40, 80 .
Step-by-step explanation:
It is given that fourth term of a sequence is 40.
It is not given that whether the sequence is A.P. or G.P.
We need to write two different sequences that satisfy the given condition.
For A.P.,
Required sequence : 10, 20, 30, 40, 50
Here, first term is 10, common difference is 10.
For G.P.,
Required sequence : 5, 10, 20, 40, 80
Here, first term is 5, common ratio is 2.
Therefore, the two sequences are 10, 20, 30, 40, 50 and 5, 10, 20, 40, 80 .
What’s f(g(x)) if f(x) = 3x + 7 and g(x) = 6x - 5
Answer:
f(g(x)) = 18x - 8
Step-by-step explanation:
f(x) = 3x + 7 and g(x) = 6x - 5
Substitute g(x) into f(x):
f(g(x)) = 3(6x - 5) + 7
Distribute the 3 from outside the parentheses:
f(g(x)) = (18x - 15) + 7
Combine like terms:
f(g(x)) = 18x - 8
5. Which of the following illustrates the Distributive
Property?
F. 3(2x + 4) = 5x + 4
G. 3(2x + 4) = 5x + 7
H. 3(2x + 4) = 6x + 4
I. 3(2r + 4) = 6 + 12
plz answer quickly yikess
Answer: Hi!
Option I is correct. 3(2x + 4) = 6x + 12
When you use the distributive property, you multiply the term outside of the parentheses (in this case, 3) by the terms inside of the parentheses (in this case, 2x and 4.)
Hope this helps!
SIMPLIFY the expression
- 4(2x - 3)
Answer:
-8x + 12
Step-by-step explanation:
We can use the distributive property of multiplication which states that a(b + c) = a * b + a * c. Therefore:
-4(2x - 3)
= -4 * 2x - 4 * (-3)
= -8x + 12
Answer: -8x -12
Step-by-step explanation:
Multiply -4 by 2x getting -8x
Then Multiply -4 by 3 getting 12
Since you can't subtract 12 from -8x this is the simplest way
factor 9x^4 -225y^8 10 points
Answer:
9(x² + 5y⁴) (x² - 5y⁴)
Step-by-step explanation:
9x⁴ - 225y⁸
factor out a 9
9(x⁴ - 25y⁸)
factor (x⁴ - 25y⁸)
(x⁴ - 25y⁸)
x² • x² = x⁴
5y⁴ • -5y⁴ = -25y⁸
(x² + 5y⁴) (x² - 5y⁴)
↓
9(x² + 5y⁴) (x² - 5y⁴)
coordinates easy - please help me :)
Answer:
Step-by-step explanation:
starting after after after
coordinates reflection rotation translation
(x,y) (x,-y) (-y,-x) (-y-2,-x-4)
A (-2,1) (-2,-1) (-1,2) (-3,-2)
B (2,1) (2,-1) (-1,-2) (-3,-6)
C (2,-1) (2,1) (1,-2) (-2,-6)
D (-2,-1) (-2,1) (1,2) (-2,-2)
Use the table to find the number of miles x you need to bike on friday so that the mean number of miles biked per day is 5
Answer:
Friday needs 11 bikes
Step-by-step explanation:
Mean = (summation of all the numbers)/the total number of the given data
(summation of all the numbers)
= 3.5+5.5+0+5+x
(summation of all the numbers)
= 14+x
the total number of the given data
=5
Mean= 5
Mean= (summation of all the numbers)/the total number of the given data
5= (14+x)/5
25= 14+x
25-14=x
11= x
A boy owns 2 pairs of pants, 3 shirts, 3 ties, and 2 jackets. How many different outfits can the boy wear to school if each outfit must consist of one of each item
Answer:
36
Step-by-step explanation:
2 x 3 x 3 x 2 = 36
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.
Freshmen 83
Sophomores 68
Juniors 85
Seniors 64
We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.
Answer:
There has been no change in the classifications between the last school year and this school year.
Step-by-step explanation:
A Chi-square test for goodness of fit will be used in this case.
The hypothesis can be defined as:
H₀: The observed frequencies are same as the expected frequencies.
Hₐ: The observed frequencies are not same as the expected frequencies.
The test statistic is given as follows:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]
The expected values are computed using the formula:
[tex]E_{i}=p_{i}\times N[/tex]
Here, N = 300
Use Excel to compute the values.
The test statistic value is:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}=1.662[/tex]
The test statistic value is, 1.662.
The degrees of freedom of the test is:
n - 1 = 4 - 1 = 3
The significance level is, α = 0.05.
Compute the p-value of the test as follows:
p-value = 0.6454
*Use a Chi-square table.
p-value = 0.6454 > α = 0.05.
So, the null hypothesis will not be rejected at 5% significance level.
Thus, concluding that there has been no change in the classifications between the last school year and this school year.
Carla enjoys collecting baseball cards Her album contains 115 pages . Each page holds 9 baseball cards How many baseball cards are will there be in her album in all?
Answer:
1035 cards
Step-by-step explanation:
the total number of baseball cards can be calculate by multiplying amount of pages and how many cards each page can hold.
115*9=1035 cards
Answer:
1035 cards
Step-by-step explanation:
Step 1: State what is known
The album contains 115 pages
Each page has 9 cards
Step 2: Assume the pages are full, calculate how much cards are in the album
115 pages x 9 cards per page = 1035 cards
Therefore there are 1035 cards in the album
Three spherical balls with radius r are contained in a rectangular box. two of the balls are each touching 5 sides of the rectangular box and the middle ball. the middle ball also touches four sides of the rectangular box. What is the volume of the space between the balls and the rectangular box? This is a SAT question and is no calculator. Show all the work Answer is 4r^3(6-pi)
Answer:
[tex]\bold{4r^3 (6-\pi)}[/tex]
Step-by-step explanation:
Let us try to visualize the given situation in the form of 2 Dimensional image as shown in the attached diagram.
Let the Diameter of spherical balls be D.
As the spherical balls are completely fit in the rectangular box, the sides of box become:
[tex]D \times D\times (3 \times D)[/tex] OR [tex]D\times D\times 3D[/tex]
We know that Diameter is twice of radius.
Therefore [tex]D = 2r[/tex]
So, the dimensions of rectangular box becomes:
[tex]2r \times 2r \times 6r[/tex]
Volume of a rectangular box is given as:
[tex]V = Length \times Width \times Height\\\Rightarrow V = 2r\times 2r\times 6r = \bold{24r^3}[/tex]
Now, let us find out the volume of each spherical ball.
Volume of a sphere with radius 'r' is given as:
[tex]V_{sphere} = \dfrac{4}{3}\pi r^3[/tex]
Volume of 3 spheres = [tex]3\times \frac{4}{3}\pi r^3 =4\pi r^3[/tex]
Now, the volume of space between the balls and rectangular box is = Volume of rectangular box - Volume of 3 balls
[tex]24r^3 - 4\pi r^3\\\Rightarrow \bold{4r^3 (6-\pi)}[/tex]
Please help me with this
Answer:
OPTION D
Step-by-step explanation:
The bracket is part of bodmas and the only thing it does is to divide equations to make it easier, so thereby I testify that the answer is 2.5/7
Simplify this expression
Answer:
2/(3x-2)²
Step-by-step explanation:
4x²-6x³-2x²+6x³/4x²-6x³-6x³+9x^4=
2x²/4x²-12x³+9x^4=
2x²/x²(4-12x+9x²)=
2/9x²-12x+4
2/(3x-2)²
what is 1/4 * 32 I need help please
Answer: 8
Step-by-step explanation: Think of the 32 in this problem as 32/1.
So rewriting, we have 1/4 × 32/1.
Now, the 4 and 32 cross-cancel to 1 and 8.
So we have 8/1 or just 8.
Y=12x
Do x and y vary directly ?
Answer:
Yes, they vary directly
Step-by-step explanation:
y=kx; k is the constant (12 in this case) and as x increases y increases, so they vary directly
Which of the following would be equivalent to Use the variable n as the unknown number.
Answer:
C.
Step-by-step explanation:
"Two more than three times a number is seven"
Add 2 to 3n and set it equal to 7.
The equation that represents the mentioned condition will be 3n + 2 = 7. Then the correct option is C.
How to convert the sentence into an expression?The expression is defined as the relations of the numbers and the variables combined together to form the equation by the use of mathematical algebraic symbols like equal greater than or less than.
From the statement, two more than three times a number is seven.
Let n be the number. The three times a number is then written as,
⇒ 3n
And the expression that is 2 more than 3n is written as follows:
⇒ 2 + 3n
The expression equals 7. The equation is then given as,
3n + 2 = 7
The equation that represents the mentioned condition will be 3n + 2 = 7. Then the correct option is C.
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Sole the triangle by finding the length of DF and the measures of all the angles
Answer:
#1 Use Pythagorean theorem to solve DF
c²-b²=a²
5.83²-5²=a²
33.9889-25=a²
a²=8.9889
a=3.00 (rounded to nearest hundredth)
--------------------------------------------
# Use Trigonometry to find the angles
angle D:90
angle E: tan E=3/5
E=tan^-1 (3/5)
E=30.96 (rounded to nearest hundredth)
angle F: tan F=5/3
F=tan^-1 (5/3)
F=59.04 (rounded to nearest hundredth)