Answer:
Equation is [tex]a_n = 2.50n + 2.50[/tex]
This is discrete
=======================================================
Explanation:
There are n = 12 months in a year.
[tex]a_1[/tex] = first term = x
d = common difference = 2.50, which is the amount the allowance is increasing month to month.
[tex]S_n = \text{Sum of the first n terms of an arithmetic sequence}\\\\S_n = (n/2)*(2a_1 + d(n-1))\\\\S_{12} = (12/2)*(2\text{x} + 2.50(12-1))\\\\S_{12} = 6(2\text{x} + 27.5)\\\\S_{12} = 12\text{x} + 165\\\\[/tex]
The sum of the first n = 12 terms of the arithmetic sequence is 12x+165, where x is the first term (i.e. the allowance on January 1st).
We're told that this total is $225. We'll set the value of [tex]S_{12}[/tex] equal to 225 and solve for x.
[tex]S_{12} = 225\\\\12\text{x} + 165 = 225\\\\12\text{x} = 225 - 165\\\\12\text{x} = 60\\\\\text{x} = 60/12\\\\\text{x} = 5[/tex]
Therefore, you got $5 on January 1st. Then 5+2.50 = 7.50 dollars on February 1st. Then 7.50+2.50 = 10 dollars on March 1st. And so on, until reaching December. All of those dollar amounts then should add to $225 to help confirm the answer.
This equation is discrete because the terms are finite from n = 1 to n = 12. We can't have a midpoint of say between months 3 and 4. It doesn't make sense to have month 3.5 for instance. There's only a set amount of payments.
--------
Now that we know [tex]a_1 = 5[/tex] is the first term, we can then determine the value of any allowance value for any given value of n.
[tex]a_n = \text{nth term of arithmetic sequence}\\\\a_n = a_1 + d(n-1)\\\\a_n = 5 + 2.50(n-1)\\\\a_n = 5 + 2.50n-2.50\\\\a_n = 2.50n + 2.50\\\\[/tex]
Let's see what the allowance would be for month n = 2
[tex]a_n = 2.50n + 2.50\\\\a_{2} = 2.50(2) + 2.50\\\\a_{2} = 5 + 2.50\\\\a_{2} = 7.50\\\\[/tex]
The allowance for month n = 2 (aka February) is $7.50, which was mentioned earlier in the previous section. I'll let you confirm the other values of n.
Keep in mind that n is a positive whole number in the set {1,2,3,...,10,11,12}. It might help to make a table of values.
Least common denominator: the smallest number that both denominator numbers will __ into.
The correct statement is,
''The smallest number that both denominator numbers will include into.''
What is Least common multiple?
The Least common multiple of two or more numbers are the smallest number that is multiple of two or more numbers.
Given that;
The statement is,
The smallest number that both denominator numbers will __ into.
Now,
We know that;
The LCM of two or more numbers is divided by the numbers or its include all the numbers.
Thus, The correct statement is,
''The smallest number that both denominator numbers will include into.''
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For the data in the table, does y vary directly with x? If
it does, write an equation for the direct variation.
The variable y vary directly with respect to x , and the equation to denote this direct variation is y = 1.375 x .
From the table we can see that the values of x are 8 for the y value of 11
Any direct variation is represented by the equation :
y = k x , where k is a constant
now we put the values of x and y in the equation to calculate k
11 = k × 8
or, k = 11 / 8 = 1.375
again , at x = 16 , y is 22
∴ k = 22/16 = 1.375
Hence the equation for direct variation will be given by
y = kx
or, y = 1.375 x
When one quantity changes directly in reaction to a change in another quantity, this is a type of proportionality known as "direct variation." This implies that if one quantity rises, the other will rise correspondingly as well.
Like in the previous illustration, if one quantity decreases, the other quantity also decreases. Direct variation will have a linear relationship with the graph, resulting in a straight line.
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farmer determined the equation "y = "-7/3x" + 72.75" best fits this data when comparing the weight, y, in grams, of strawberries to the average daily mean temperature, x, in °F, each season. Which statement best describes the rate of change of the equation?
The statement that best describes the rate of change of the linear function is given as follows:
For each increase of 1ºF in temperature, the average weight of the strawberries decays by 7/3 grams.
How to obtain the average rate of change of a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
The coefficients are listed as follows:
m is the slope of the linear function, representing the rate of change of the function, that is, by how much the output of the function changes when the input increases by one.b is the y-intercept of the function, which is the value of the output when the input is of zero.The input and the output variables for this problem are given as follows:
Input: Average daily mean tempetature, in ºF.Output: Weight of the strawberries, in grams.The function is defined as follows:
y = -7x/3 + 72.75.
Hence the slope is:
m = -7/3.
And the interpretation, considering the input and output variables, is that for each increase of 1ºF in temperature, which is the input variable, the average weight of the strawberries, which is the output variable, decays by 7/3 grams.
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Find the distance from point A(-1. 7) to the line y = 3x. Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
This seems complicated, huh.
So think about the question. They want to know the distance from a line, to a point. first decide if the point could possibly be on the line and there is zero distance. The given point is at (-1, 7) our coordinates of the point are at -1 in the X direction and at 7 in the Y direction. If we were to plug in those two number into the given line equation, y = 3x would it be a true statement? no. 7 = 3(-1) is not true. so our given point is not on the line. Next, find the right angle to the line and point. make your own line equation that does have our given point in it. and is at a right angle to the given line. recall that using a reciprocal can give you a right angle to your line. y = (- 1/3)X . Now we just need the given point to plug into our made up line equation and be true. 7 = (-1/3)(-1) + b . we need to make this equation true by moving a number into "b" that makes it true.
b = 6[tex]\frac{2}{3}[/tex] or [tex]\frac{20}{3}[/tex]
7 = (-1/3)(-1) + [tex]\frac{20}{3}[/tex]
now, when does our made up line, y =(-1/3)x + [tex]\frac{20}{3}[/tex], intersect with the given line, y=3x, that is, set the two equal
3x = (-1/3)x + [tex]\frac{20}{3}[/tex]
3[tex]\frac{1}{3}[/tex] X = [tex]\frac{20}{3}[/tex]
[tex]\frac{10}{3}[/tex]X = [tex]\frac{20}{3}[/tex]
X=[tex]\frac{20}{3}[/tex] * [tex]\frac{3}{10}[/tex]
X = [tex]\frac{20}{10}[/tex]
X=2
our two equations intersect at 2, how handy :)
now we have our two points that are at a right angle from each other and we just need the distance from them
(given) A(-1,7) and (found) B(2,6)
Distance = [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} }[/tex]
then our given points are A(x1,y1) and B(x2,y2)
Distance = [tex]\sqrt{(2-(-1))^{2}+(6-7)^{2} }[/tex]
Distance =[tex]\sqrt{3^{2}+(-1)^{2} }[/tex]
Distance = [tex]\sqrt{9+1}[/tex]
Distance = [tex]\sqrt{10}[/tex]
Distance = 3.1622
Distance =3.2 (rounded to nearest 10th)
Yes, that was kinda a lot :/
given
please help (please state your reason for the answer aswell)
Answer:
m∠C = 30°Step-by-step explanation:
Since the two angles of both triangles are congruent, it makes the remaining angles congruent too:
∠C ≅ ∠FThen we have:
x = 2x - 302x - x = 30x = 30So both C and F are 30°.
IF x=2y and y=1/4 what does x equal
Answer:
[tex]x=\frac{1}{2}[/tex]
Step-by-step explanation:
replace y with 1/4
x=2(1/4)
x=2/4
x=1/2
Hopes this helps please mark brainliest
Select the correct answer.
Which expression is equivalent to this polynomial expression?
(2a36) (2a²+ 66²) + (6a²b + 12ab² - 76³)
OA. 4a³ - 12a²b 24ab² 116³
B. 4a³+12a²b25b³
O c. 4a³+ 12a²b + 24ab²
O D. 4a³+24ab² - 256³
-
-
1
116³
Reset
Next
the expression equivalent to the given polynomial expression is 4a³+ 12a²b + 24ab² - 76³, which is option C.
what is expression ?
An expression is a mathematical phrase that contains numbers, variables, and/or mathematical operations. It does not have an equal sign, so it cannot be solved.
In the given question,
The correct answer is C.
To simplify the given polynomial expression using the distributive property, we need to distribute the first term (2a³) to each term in the second parentheses, and then add it to the third term.
So, we have:
(2a³) (2a²+ 66²) + (6a²b + 12ab² - 76³)
= 4a⁵ + 132a³ + 6a²b + 12ab² - 76³
Now, we can simplify further by combining like terms:
= 4a³ (a²+ 33) + 6ab (a + 2b) - 76³
Therefore, the expression equivalent to the given polynomial expression is 4a³+ 12a²b + 24ab² - 76³, which is option C.
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Using only a compass and a straightedge, you are constructing a line perpendicular to AB and passing through a given point, M, on AB. With a
compass of set width, you have drawn arcs that intersect AB on each side of M and marked the two intersection points as P and Q.
The next step in this construction is to place the compass needle on
P (or Q) and mark an arc roughly where M's reflection across AB is located.
How to use a compass?One tool for drawing circles is a compass. According to the circle's radius, which is drawn with a compass, the sizes of the circles vary.
A compass's handle is held in place by our thumb and forefinger. A circle is typically drawn using just one hand. Between the forefinger and thumb, the compass is turned.
Around this point, the pencil tip is rotated. The circle's radius is determined by the distance between the pencil tip and the compass needle. A ruler is used to set it. The gap can be adjusted by adjusting the angle between the compass's arms.
At that point of reflection (M'), arcs drawn from P and Q in M's approximate location across AB will intersect. As desired, the line passing through point M and perpendicular to AB will connect M and M'.
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NEED ASAP THANKS EXPLANATION WOULD BE APRECIATED
If I add 5 times a number to 6, I get 80................................
x = 14.8 (OR) x = 74/5.
Step-by-step explanation:
If you add 5 times a number to 6 you will get 80.
We don't know what number is multiplied with five and that number should added with 6. So,
Let, the unknown number be named as x.
The eqⁿ will be
[tex]{ \red{ \sf{5}}}{ \green{ \sf{x}}} \: + \: { \red{ \sf{6}}} = { \red{ \sf{80}}} → Eqⁿ(1) [/tex]
Shift 6 to the right side.
[tex]{ \red{ \sf{5}}}{ \green{ \sf{x}}} = { \red{ \sf{80 - 6}}}[/tex]
[tex]{ \red{ \sf{5}}}{ \green{ \sf{x}}} = { \red{ \sf{74}}}[/tex]
Divide both the sides by 5. then,
[tex]{ \red{ \sf { \cancel{\frac{5}{5}}}}} { \green{ \sf{x}}} = {{ \frac{ \cancel{74} {}^{ \green{ \sf{{ 14.8}}}} }{ \cancel5}}} [/tex]
[tex]{ \red{ \boxed{ \purple{ \sf{x = 14.8}}}}} \: { \tt{(or)}} \: { \red{ \boxed{ \purple{ \sf{x = \frac{74}{5}}}}}} [/tex]
___________________________________
[tex]{ \red{ \sf{ \underline{verification}}}} [/tex]
Let us substitute the value of x in Eqⁿ(1) then,
[tex]{ \red{ \sf{5}}}{ \green{ \sf{(14.8)}}} \: + \: { \red{ \sf{6}}} = { \red{ \sf{80}}} [/tex]
[tex]{ \red{ \sf{74}}} \: + \: { \red{ \sf{6}}} = { \red{ \sf{80}}} [/tex]
[tex]{ \red{ \sf{80}}} = { \red{ \sf{80}}} [/tex]
Hence, our answer is correct
Use properties to rewrite the given equation. Which equations have the same solution as 2. 3p – 10. 1 = 6. 5p – 4 – 0. 01p? select two options. 2. 3p – 10. 1 = 6. 4p – 4 2. 3p – 10. 1 = 6. 49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2. 3p – 14. 1 = 6. 4p – 4.
The equations 2.3p - 101 = 6.49p -4 and 23p - 101 = 65p - 40 - p are the equation that has the same solution:
The given equation is:
2.3p - 10.1 = 6.5p - 4 - 0.1p
The first option is:
2.3p - 10.1 = 6.4p - 4
which is equal to the given equation.
The second option:
230p - 1010 = 650p - 400 - p
which is not equal to the given equation
The third option:
23p - 101 = 65p - 40 - p
which is equal to the given option.
The last option:
2.3p - 14.1 = 6.4p -4
which is not equal to the given option.
Therefore equations 2.3p - 10.1 = 6.4p - 4 and 23p - 101 = 65p - 40 -p are the correct option.
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simplify 4x5 - 25x³/ 2x-5
Help me and I'll reward you.
Answer:
i don't understand
Step-by-step explanation:
the question is 11 divided 2and2over 3
[tex]=\frac{x^{3}(4x^{2} -25) }{2x-5} \\=\frac{x^{3} (2x+5)(2x-5)}{2x-5} \\=x^{3} (2x+5)\\=2x^{4}+5x^{3}[/tex]
⇒Note there was a 2x-5 in the numerator and a 2x-5 in the denominator so they canceled each other. Leaving the above expression.
The barge Califa building in Dubai united Arab emirate eighth i one of the tallet building in the world at 2722 feet tall in American football field i 360 feet in length approximately how many football field tall i the Burberry Califa building round to the nearet 10th
The burj khalifa is 7.56 football fields tall .
We have the height of the Burj Khalifa as = 2722 feet
And the given height of one football field is = 360 feet
Now using the Unitary method we can calculate the number football fields that would be equal to the height of the burj khalifa .
So ,
360 feet is equal to football fields = 1
1 feet is equal to football fields = 1/360 fields
therefore
2722 feet will be equal to fields = (1/360) x 2722
= 7.56 fields
So the Burj Khalifa is equal to 7.56 football fields.
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according to 2015 census data, 42.7 percent of colorado residents were born in colorado. if a sample of 250 colorado residents is selected at random, what is the standard deviation of the number of residents in the sample who were born in colorado?
The standard deviation of the number of residents in the sample who were born in Colorado is 7.82
Standard deviation:
The measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists is know as standard deviation.
Given,
According to 2015 census data, 42.7 percent of Colorado residents were born in Colorado. if a sample of 250 Colorado residents is selected at random.
Here we need to find the standard deviation of the number of residents in the sample who were born in Colorado.
Here we know that following details,
Number of sample = 250
Estimated proportion for residents born in Colorado = 42.7% which is equal to = 0.427.
Let us consider X be the random variable of interest (number of residents in the sample), on this case we now that:
X ~ (n = 250, p = 0.427)
Now, according to the probability mass function for the Binomial distribution is given as:
E(X) = n x p = 250 x 0.427 = 106. 75.
Now, the standard deviation for the random variable is given by:
SD = √106.75 (1 - 0.427)
SD = √106.75(0.563)
SD = 7.82
Therefore, the standard deviation is 7.82.
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Please help me it’s due.
Answer:
A = Research question
B = Hypothesis
C = Analysis of data
D = Reflecting on the results
Step-by-step explanation:
Im 85% sure
how do you find the measure of each angel indicated??
Answer:
by knowing the sum of the shape represented
PLEASE HELP ME I REALLY NEED IT
Answer:
-1/2
Step-by-step explanation:
Ignore the (2,2) just use (-2,1) and (-4,2)
f(n)=-3n+7; find f(-8)
Answer:
f(-8) = 31
Step-by-step explanation:
f(-8) = -3(-8) + 7
= 24 + 7
= 31
The average daily attendance at the Lincoln School was 348 students during the month of March. If the month had 21 school days, what was the total attendance?
The total attendance for Lincoln school for month of March is 7308.
What is average attendance?
Divided by the total number of days in the ordinary school year, is the total number of days that students were present. One ADA(Avg. Daily attendance) would be the number of students who attend every day. The number of kids enrolled in each school and district, known as enrollment, is not the same as ADA.
Main Body:
So according to formula ,
Average daily attendance = Total attendance / total days of school
348 = total attendance/ 21
total attendance = 348* 21
= 7308
Hence total attendance is 7308.
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The mean incubation time of fertilized eggs is 20 days. Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day. (a) Determine the 10th percentile for incubation times. (b) Determine the incubation times that make up the middle 95%.
Using the normal distribution, it is found that:
a) The 10th percentile for incubation times is of: 18.72 days.
b) The incubation times that make up the middle 95% are of: Between 18.04 and 21.96 days.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for the incubation times are presented as follows:
[tex]\mu = 20, \sigma = 1[/tex]
The 10th percentile for the distribution is X when Z = -1.28, which is the value of Z with a p-value of 0.1, hence:
-1.28 = (X - 20)/1
X - 20 = -1.28
X = -1.28 + 20
Z = 18.72 days.
Considering the symmetry of the normal distribution, the bounds of the middle 95% of values are given as follows:
2.5th percentile: X when Z = -1.96.97.5th percentile: X when Z = 1.96.Hence the lower bound is:
-1.96 = (X - 20)/1
X - 20 = -1.96
X = -1.96 + 20
Z = 18.04 days.
The upper bound is:
1.96 = (X - 20)/1
X - 20 = 1.96
X = 1.96 + 20
Z = 21.96 days.
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determine whether AB and CD are parallel, perpendicular or neither for A(-1,-1), B(1,5), C(1,2), D(5,4), graph each line to verify your answer.
By finding the slopes of the two segments we can see that the segments are not parallel nor perpendicular.
Are the segments parallel, perpendicular or neither?The slope for a segment whose endpoints are:
(x₁, y₁) and (x₂, y₂) is:
slope = (y₂ - y₁)/(x₂ - x₁)
Two segments are:
parallel if have the same slope.perpendicular if the product of the slopes is -1.Segment AB has endpoints (-1, -1) and (1, 5), so the slope is:
s = (5 + 1)/(1 + 1) = 3
For segment CD the endpoints are (1, 2) and (5, 4), so the slope is:
s' = (4 - 2)/(5 - 1) = 2/4 = 1/2
So the slopes are different and their product is obviously not -1, then the lines are neither parallel nor perpendicular.
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''24 hours per day''
Answer:
Step-by-step explanation:
365 day a year
24 hour per day
60 second in a minute
1440 minutes in a day
86400 second in a day!
what does the graph do if “a” is a number between zero and one compared to greater than one?
For any given graph when "a" is a number between zero and one then graph of the function get horizontal stretch.
And when "a" is a number greater than one then graph of a function get horizontal compress.
As given in the question,
For any graph of a function,
When "a" is a number between zero and one than the graph of the function get horizontal stretch.
f(x) = ax²
let a = 1/2 , 0 < 1/2 < 1 so satisfied the condition of "a" between zero and one.
f(x) = x²/2
In this case , graph of the given function get horizontal stretch compare to original graph.
When a = 2 , 2 > 1 satisfied the condition of "a" greater than one.
f(x) = 2x²
In this case , graph of the given function get horizontal compress compare to original graph.
Therefore, for any given graph when "a" is a number between zero and one then graph of the function get horizontal stretch.
And when "a" is a number greater than one then graph of a function get horizontal compress.
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Aslam invested rs 210000part at 8% per annum and the rest at 6%per annum. if the annual incomes from both investment were the same, find the amount invested at each rate.
a = amount invested at 8%
how much is 8% of "a"? (8/100) * "a", namely 0.08a.
b = amount invested at 6%
how much is 6% of "b"? (6/100) * "b", namely 0.06b.
we know the total amount invested is 210000, so whatever "a" and "b" might be, we know that a + b = 210000.
we also know that the yielded amount in interest is the same for both, so whatever 0.08a and 0.06b are, we know they're the same.
[tex]\begin{cases} a+b=210000\\\\ 0.08a=0.06b \end{cases}\hspace{5em}a+b=210000\implies b=210000-a \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.08a~~ = ~~0.06(210000-a)}\implies 0.08a=12600-0.06a\implies 0.14a=12600 \\\\\\ a=\cfrac{12600}{0.14}\implies \boxed{a=90000}\hspace{9em}\boxed{\stackrel{210000~~ - ~~90000}{b=120000}}[/tex]
Evaluate the expression when a = 3 and y = -4.
8a - y
(Can someone help ASAP!)
Answer: The answer is 28.
Step-by-step explanation: 8a-y is our problem and we are given two variables, a and y. It is revealed that a=3 and y= -4. So our problem would now look like this: 8*3-(-4). Now see the two minuses (-) next to each other? We have to convert that into a plus (+) sign because two negatives make a positive. So our equation now looks like this: 8*3+4. Now, 8 times 3 (8*3) is equal to 24. Now our equation looks like this: 24+4. Add them together and the sum is 28.
Hope this helps!
Select the transformation
the pre-image FISH onto its image F'I'S'H'.
[₁
S'
H
F₁ H'
FL
rule that correctly maps
S
T
The vertices have been shifted toward the left by 1 unit and also 3 units up to form the image F'I'S'H'.
What is graph transformation?
The process of altering a graph to produce a different version of the preceding graph is known as graph transformation. The graphs can be moved about the x-y plane or translated. They can also be stretched, or they can undergo a combination of these changes. We discuss the various graph transformations in this post.Graph stretching
A function's graph can be stretched by adding a constant factor to it or to one of its independent variables. The stretch could be horizontal or vertical. Let's talk about stretching horizontally and vertically.Observing each of the vertices of the square, we can say that the vertices have been shifted toward the left by 1 unit and also 3 units up to form the image F'I'S'H'. So, the transformation involved in moving the preimage FISH to form F'I'S'H' the image is translation.
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Given ∠RUY=90° and ∠RST=90°
Find YT=
Answer:
YT= 23
We know that:
line RU is 32 and US is 16
line RY is 46
In other words, RU = 32, US = 16, and RY = 46
so we use the triangle proportionality theorem to state that:
[tex]\frac{RU}{US}=\frac{RY}{YT}[/tex]
Input your values
[tex]\frac{32}{16} =\frac{46}{YT}[/tex]
Use cross products :
[tex]32YT=(16)(46)[/tex]
Simplify:
[tex]32YT=736[/tex]
[tex]\frac{32YT}{32} =\frac{736}{32}[/tex]
[tex]YT=23[/tex]
I hope this answers you question :)
The table shows the amount of storage y (in gigabytes) on a music-playing device when there are x songs on the device
A) Write an equation that models the amount of storage as a function of the number of songs
B) Interpret the slope and t-intercept of the line of fit
pls include work
From the given table
Part a
The equation of the function is y = ( - 0.7/277)x + 16
Part b
The slope of the line = - 0.7/277 and the y intercept of the line = 16
From the table
Choose two points
(242, 14.8) and (519, 14.1)
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line = (14.1 - 14.8) / (519 - 242)
= -0.7 / 277
The slope of the line = - 0.7/277
From the table at x = 0, the value of y = 16
Therefore the y intercept is 16
The slope intercept form is
y = mx + b
Substitute the values in the equation
y = ( - 0.7/277)x + 16
Part b
The slope of the line = - 0.7/277
The y intercept of the line = 16
Hence, from the given table
Part a
The equation of the function is y = ( - 0.7/277)x + 16
Part b
The slope of the line = - 0.7/277 and the y intercept of the line = 16
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What is the vertex of f(x)=-3(x+1)^2-4
Answer:
vertex = (- 1, - 4 )
Step-by-step explanation:
the equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
f(x) = 3(x + 1)² - 4 ← is in vertex form
with vertex = (- 1, - 4 )
Answer:
(−1,−4)
Step-by-step explanation:
f(x)=3(x+1)2−4
Graph the inequality on the axes below.
x + 3y ≥ 9