The Slope is [tex]\frac{4}{-5}[/tex].
What is a Slope?A line's slope is defined as the ratio of the change in y-coordinate to the change in x-coordinate.Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.A line's slope provides information on the steepness and direction of the line. The slope of a straight line between the two locations, (x1,y1) and (x2,y2), can be easily determined by calculating the difference between their coordinates.m = change in y/change in x = Δy/Δx
= (y2 – y1)/(x2 – x1)
Where “m” is the slope of a line.
As a result, using the formula above, we can quickly determine the slope of a line connecting two points.
Given points are (-5,6),(-10,10).
⇒ m = Δy / Δx
= [tex]\frac{10 - 6}{-10 - (-5)}[/tex]
= [tex]\frac{4}{-5}[/tex]
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Given 1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.)
s =
The required value of the standard deviation is 0.04.
Given that,
1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers is to be determined. Where s = 5
What is Statistic?Statistics is the study of mathematics that deals with relations between comprehensive data.
Here,
1 miles = 1.60934 Km
Given
1 mile = 1.6
Standard deviation = 1.60934 - 1.6000
= 0.00934
S = 5
Standard deviation = 5 * 0.00934
= 0.04670
Thus, the required value of the standard deviation is 0.04.
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You are saving for a skateboard. Your aunt gives you $45 to start, and you save $3 each week. The expression 45 + 3w gives the amount of money you save after w weeks. How much will you have after six weeks?
Answer: $63
Step-by-step explanation:
so you put 6 where the w is to find out the answer
45+3(6)=45+18=63
A concert promoter needs to make $60,900 from the sale of 1780 tickets. The promoter charges $30 for some tickets and $45 for the others. Let x represent the number of $30 tickets and y represent the number of $45 tickets.
The equation that states the sum of the tickets sold is -
30x + 45y = 60900.
We have concert promoter.
We have to write an equation that states that the total amount received from the sale, which is 60,900 dollars.
What is Equation Modelling ?The equation modelling is a process of writing a mathematical equation from a mathematical statement involving variables, constants etc.
According to the question -
Money earned from $30 tickets = $30x
Money earned from $45 tickets = $45y
Total money from 1780 tickets = $60,900
Therefore -
30x + 45y = 60900
Hence, the equation that states the sum of the tickets sold is -
30x + 45y = 60900.
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[ The given question is incomplete, the complete question is
A concert promoter needs to make $60,900 from the sale of 1780 tickets. The promoter charges $30 for some tickets and $45 for the others. Let x represent the number of $30 tickets and y represent the number of $45 tickets. Write an equation that states that the total amount received from the sale is 60900 dollars.]
Consider the sequence of real numbers
[tex] \rm a_1 = \frac{ log_{2}( {3}^{2} ) }{ log_{3}(2) } ,a_2 = \frac{ log_{ {3}^{3} }( {4}^{4} ) }{ log_{ {4}^3}( {3}^{4} ) } ,a_3 = \frac{ log_{ {4}^5 }( {5}^{6} ) }{ log_{ {5}^{5} }( {4}^{9} ) }, \dots[/tex]
In general, [tex] \rm a_k = \frac{ log_{(k + 1) ^{(2k - 1)} } ((k + 2 {)}^{2k}) }{log_{(k + 2) ^{(2k - 1)} } ((k + 1 {)}^{ {k}^{2} })} [/tex]
Let [tex] \rm P_n = \frac{ log_{ {(n + 1)}^{(2n - 1)} }( {2}^{2n} ) }{ log_{ {2}^{(2n - 1)} }((n + 1) {}^{ {n}^{2} } )} \cdot \prod \limits_{k = 1}^{n - 1} a_k[/tex] for integer n [tex]\geq [/tex] 2.
[tex] \rm Find \sum \limits_{n = 2}^{ \infty } P_n[/tex]
Use the change-of-base identity and the exponent property for logarithms.
[tex]\log_b(a) = \dfrac{\log_c(a)}{\log_c(b)} \implies \log_b(a) = \dfrac1{\log_a(b)}[/tex]
[tex]\log_c(a^b) = b \log_c(a)[/tex]
This lets us rewrite
[tex]\log_{(k+1)^{2k-1}} (k+2)^{2k} = \dfrac{2k}{\log_{k+2}(k+1)^{2k-1}} = \dfrac{2k}{(2k-1) \log_{k+2}(k+1)}[/tex]
[tex]\log_{(k+2)^{2k-1}} (k+1)^{k^2} = \dfrac{k^2}{\log_{k+1} (k+2)^{2k-1}} = \dfrac{k^2}{(2k-1) \log_{k+1}(k+2)}[/tex]
It follows that
[tex]a_k = \dfrac2k \dfrac{\log_{k+2}(k+1)}{\log_{k+1}(k+2)} = \dfrac2k \left(\ln^2(k+1)}{\ln^2(k+2)}[/tex]
so that the product of [tex]a_k[/tex] telescopes:
[tex]\displaystyle \prod_{k=1}^{n-1} a_k = \frac{2^{n-1}}{(n-1)!} \frac{\ln^2(2)}{\ln^2(3)}\cdot\frac{\ln^2(3)}{\ln^2(4)}\cdot\frac{\ln^2(4)}{\ln^2(5)} \cdots \frac{\ln^2(n-1)}{\ln^2(n)} \cdot \frac{\ln^2(n)}{\ln^2(n+1)} \\\\ ~~~~~~~~ = \frac{2^{n-1}}{(n-1)!} \frac{\ln^2(n+1)}{\ln^2(2)}[/tex]
We can similar reduce the coefficient of [tex]P_n[/tex] to write
[tex]\log_{(n+1)^{2n-1}}(2^{2n}) = \dfrac{2n}{(2n-1) \log_2(n+1)}[/tex]
[tex]\log_{2^{2n-1}}(n+1)^{n^2} = \dfrac{n^2}{(2n-1)\log_{n+1}(2)}[/tex]
[tex]\implies \dfrac{\log_{(n+1)^{2n-1}}(2^{2n})}{\log_{2^{2n-1}}(n+1)^{n^2}} = \dfrac2n \dfrac{\ln^2(2)}{\ln^2(n+1)}[/tex]
Then the expression for [tex]P_n[/tex] reduces significantly to
[tex]P_n = \dfrac2n \dfrac{\ln^2(2)}{\ln^2(n+1)} \cdot \dfrac{2^{n-1}}{(n-1)!} \dfrac{\ln^2(n+1)}{\ln^2(2)} = \dfrac{2^n}{n!}[/tex]
and we ultimately find
[tex]\displaystyle \sum_{n=2}^\infty P_n = \sum_{n=0}^\infty \frac{2^n}{n!} - \frac{2^1}{1!} - \frac{2^0}{0!} = \boxed{e^2 - 3}[/tex]
where we recall the power series
[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{x^n}{n!}[/tex]
i got the answer of A but i am very unsure on how to do it. Can someone help please? thank you
Explanation:
So, looking at the ruler, we;re going to take the whole number of the measurment from the whole bars of inches it overlaps (1-3) since we know it goes past there we will have a fraction beside it (because it does not go all the way to 4) If you see the longest lines in between the 3 and 4, there are 3 bars (which means each is 1/4.) Now, we know that it covers 3/4 of the last inch. To convert to /8, we multiply the numerator and denominator by 2 so we have 6/8. The CLOSEST (but not completely correct) (in 1/8 inches) would be D. (but ONLY if A is incorrect because that is simplified and the accurate answer.
PLEASEEEE HELPPP!!!! THIS IS DUE ON WEDNESDAY
Jeri bought 32 cookies and 56 slices of pizza for his sisters birthday. Each guest will receive the same number of cookies and pizza, with nothing left over. If Jeri wants to invite the greatest number of guests, how many cookies will each guest receive?
Reason:
32 = 8*4
56 = 8*7
We see that 8 is the largest common factor, aka GCF, of 32 and 56
So this is the greatest number of guests possible.
Each guest will get 32/8 = 4 cookies and 56/8 = 7 slices of pizza.
(3x + 2)°
(5x-78)°
HOW DO I SOLVE THIS I DONT GET IT HELP MEEEE!!
x = 40 is the value of vertical angles .
What is vertical opposite angles?
Angles that are vertically opposed to one another at a certain vertex are formed by two straight lines intersecting. Angles that are vertically opposed to one another are equal.
The total of the two vertical angle pairs, or four angles, is always 360 degrees. Angles that come from each pair of vertical angles are supplementary and are referred to as neighboring angles (the angles sum up to 180 degrees).
(3x + 2)° and (5x-78)° are equal .
because of they are vertical opposite angles.
3x + 2 = 5x - 78
5x - 3x = 78 + 2
2x = 80
x = 40
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Help! Please will give brainliest if you will
ASAP
Answer: i hope this answers your question
Step-by-step explanation:
the function is negative over the interval (-3,5)
the function is positive over the interval (-..-5)
the function is positive over the interval (3,..)
Answer:here
Step-by-step explanation:
the function is negative over the interval (-3,5)
the function is positive over the interval (-..-5)
the function is positive over the interval (3,..)
Find the circumference and the area of a circle that has a
diameter of 14 centimeters. For each, give the exact answer
and an approximation to the nearest hundredth.
[Section 9.8]
Answer:
circumference=44cm
44cn
Area=154cm
200cm
 may I please get help
Answer: B. 60.96
Step-by-step explanation:
27% of 48 is 12.96
12.96+48=60.96
8. The line that passes through (3, 5) and is parallel to the line through (3, 3) and (-3, -1)
2x - 3y = -9 is equation of line which passes through slope 2/3.
Describe slope using an example?
The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.m = [tex]\frac{y{2} - y{1} }{x{2} - x{1} }[/tex]
put x₁ = 3 , x₂ = -3 , y₁ = 3 and y₂ = -1
m = [tex]\frac{-1 - 3}{-3 - 3}[/tex]
m = [tex]\frac{-4}{-6}[/tex]
m = 2/3
The line that passes through (3, 5) =
⇒ y - y₁ = m( x - x₁)
⇒ y - 5 = 2/3 ( x - 3)
⇒ 3( y - 5 ) = 2 ( x - 3 )
⇒ 3y - 15 = 2x - 6
⇒ 2x - 3y = -15 + 6
⇒ 2x - 3y = -9
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The circumference of a circle is 30. What is its area?
Answer:
71.62
Step-by-step explanation:
[tex]A = \frac{C^2}{4 \times \pi }\\A = \frac{30^2}{4 \times 3.14 }\\A = 71.62[/tex]
For some linear relationships, doubling the independent variable results in doubling the function value. For example, doubling the number of steps in a staircase doubles the height of the staircase. Does this doubling property hold for every linear relationship?
Using linear function concepts, it is found that this doubling property does not hold for every linear relationship.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.One example of function is:
y = 4x + 3.
When x = 1:
y = 4 + 3 = 7.
When x = 2:
y = 8 + 3 = 11.
The input did not double, meaning that this doubling property does not hold for every linear relationship, it doubles only for a linear function with a slope of 2 and intercept of 0.
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You have a drawer with 7 different pencils. Each pencil is a different color (red, blue, white, green, pink, black, and yellow). If you take a pencil out of the drawer, it is green, and do not put it back, what is the probability that the next pencil is pink?
Answer:
1 in 6
Step-by-step explanation:
The probability of getting the original green is 1 in 7 (1 green pencil and 7 total)
If you take it out, there will be 6 pencils left
My thermometer has a percent error of 3%. The actual temperature is 75°F.
Will the thermometer show the temperature at 72.00 °F or 78.00 °F?
The thermometer show the temperature at 73°F when there is a percentage error.
How to calculate the value?From the information, the thermometer has a percent error of 3% and the actual temperature is 75°F.
Therefore, the temperature down on the thermometer will be:
= 75 - (3% ×75)
= 75 - 2.25
= 72.75
= 73 approximately.
Therefore, the thermometer show the temperature at 73°F when there is a percentage error.
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Please help me is this problem <, >, or =
[tex] \sqrt{15} \approx3.873\\ \\ \sqrt{15} < 3.9[/tex]
Pls help me understand this.
Answer:
4 Square units
Step-by-step explanation:
The height is incorect
It is meant to be the vertical height which is the distance from A to AB (3 - 1 = 2)
[tex] \frac{1}{2} bh = \frac{1}{2} \times 4 \times 2 \\ = 4 \: square \: units[/tex]
4. Communicate Precisely What does it mean for a figure to have 60° rotational symmetry?
It means that if you rotated the figure 60 degrees (clockwise or counterclockwise) about its center, then the figure does not change.
The "before" and "after" are identical. In other words, the preimage and image are the same.
What do you call a row of large animals separating two yard
Answer: The answer is play on words, or a pun - a row of large animals separating two yards is called an elefence.
Step-by-step explanation: The first part of the word, ele-, obviously refers to elephants, which are large animals. The second part is a fence, which separates two yards. So this is intended to have a humorous effect (I got this from go.ogle....)
b. Write the set of natural numbers greater than 22 using the most concise method.
(Use a comma to separate answers as needed.)
A. The set of numbers is {}
B. The set of numbers is {x|XEN and x> }}
C. The set of numbers is {x|XEN and x< }
D. The set of number is {xXEN and x =}
The set of numbers is S = { x ∈ N ; x > 22 }.
We have the statement:
Set of natural numbers greater than 22.
We need to make the set from it.
A set is a collection of different things objects or elements that are used to represent a situation or a function in a concise form.
For example a set of real numbers can be denoted by x ∈ R.
There can be finite or infinite sets. In finite sets, the number of elements are limited whereas in infinite sets it is not limited.
Here, the set that will be formed can be written as:
S = { x ∈ N ; x > 22 }
Therefore, the set of numbers is S = { x ∈ N ; x > 22 }.
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Here is list of numbers:
8
7 12 7 11 10 7 12
Find:
a)
the median
b)
the range
c)
the mode
Step-by-step explanation:
medium =9
range = 12-7=5
mode=7
Hello can you help me with this please
Answer:
Q1: Plane
Q2: Point
Q3: line
I hope this helps!
A Broadway theater has 510 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $140, main seats for $135, and balcony seats for $100. If all the seats are sold, the gross revenue to the theater is $62,700. If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $55,700. How many of each kind of seat are there?
The Broadway theater had 100 Orchestra, 220 main seat and 190 balcony seats.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of Orchestra, y represent the main seat and z represent the balcony seat.
A Broadway theater has 510 seats, Hence:
x + y + z = 510 (1)
Also:
140x + 135y + 100z = 62700 (2)
And:
135y + 100z + (1/2)(140)x = 55700 (3)
From the three equations:
x = 100, y = 220, z = 190
The Broadway theater had 100 Orchestra, 220 main seat and 190 balcony seats.
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I’m stuck in this one
Answer:
Step-by-step explanation:
90 - 65 = 25
x = 25 degrees
90 - 25 = 65
y = 65 degrees
Apple weights in an orchard are normally distributed. From a sample farmer Fred determines the mean weight of a box of apples to be 270 oz. with a standard deviation of 10 oz. He wonders what percent of the apple boxes he has grouped for sale will have a weight less than 255 oz.
Carl calculates the z-score corresponding to the weight 255oz= -1.5.
Now, Carl decides to find the percent associated with boxes less then 255 oz, so he rounds to hundred and substract 50% - 7% = 43%.
Given that,
In an orchard, apple weights are typically distributed. Fred the farmer concludes from a sample that the average weight of a box of apples is 270 ounces, with a standard deviation of 10 ounces.
He is interested in knowing what proportion of the apple boxes he has gathered for sale will weigh less than 255 oz.
Mean is 270
Standard deviation is 10
x = 255
Formula for z-score,
z = (x - mean)/SD
z = (255 - 270) / 10
=> z = -15 / 10
=> z = -1.5
Hence, by using z-table,
-1.5 equates to 0.0668, which suggests that 0.07
Therefore, 7% of Apple boxes weigh less than 255 oz.
The ratio of boxes is between 255 oz and 270 oz,
Calculating the proportion
Now,
50% - 7% = 43%.
Therefore, Carl calculates the z-score corresponding to the weight 255oz= -1.5.
Carl decides to find the percent associated with boxes less then 255 oz, so he rounds to hundred and substract 50% - 7% = 43%.
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WILL GIVE BRAINLIEST
Answer:
a. = 1
b. = 0
c. = 2
d. = 7
Hopefully this helps
Mary is 7 years old, Chris is 2 years old, Stewart is 5 years old,
and Abby is 10 years old. What is the average age of the 4
children?
years old
Answer: 6
Step-by-step explanation:
7+2+5+10= 24
24 divided by 4 equals 6
The midpoint of AB is M (2, -2). If the coordinates of A are (8, 1), what
are the coordinates of B?
Jim gross pay for the week. wad $987.00 how much was taken from his check for FICA taxes?
The amount taken from Jim's check for FICA taxes is $75.51.
What are FICA taxes?FICA (Federal Insurance Contributions Act) taxes are of two types: Social Security tax and Medicare tax.
FICA taxes simply mean United States federal payroll (or employment) taxes imposed on both employees and employers. The purpose of FICA taxes is to fund Social Security and Medicare.
These two federal programs benefit retirees, the disabled, and the children of deceased workers.
The rate for the Social Security tax is 6.2% of the taxpayer's gross pay.
The rate for the Medicare tax is 1.45% of the income earner's gross pay.
The FICA taxes rate is 7.65%.
Data and Calculations:Gross pay for the week = $987
FICA taxes = 7.65%
FICA taxes in dollars = $75.51 ($987 x 7.65%)
Thus, the amount Jim paid in FICA taxes is $75.51.
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Which of the following is true about parallel lines? Select all that apply.
*
They will never cross.
They have the same slope.
Their slopes are opposite reciprocals.
They will cross at a right angle.
They are in the same plane.
The statements which are true about parallel lines are;
They will never cross.They have the same slope.They are in the same plane.What are parallel lines?Parallel lines in their simplest description are lines which would never meet or cross each other under any circumstance.
Also, It follows from line geometry that such lines have the same slope and are coplanar, exist in the same plane.
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