Clara is 15 years old, and there are 120 coins on the box.
How old is Clara?Each year her mom puts as many coins in her money box as how old she turns that day.
So on her first birthday, 1 coin is put in the box.
On her second birthday, 2 coins are put in the box
And so on.
So we have the simple summation:
[tex]\sum_{n = 1} n[/tex]
We know that the outcome of that summation is a number in the interval [110, 130]
If we know that the sum goes from n = 1 to n = N (N is the age of Clara) then we can rewrite the summation as:
[tex]N*(N + 1)/2[/tex]
Now we can solve:
[tex]N*(N + 1)/2 = 110\\\\N^2 + N = 220\\\\N^2 + N - 220 = 0[/tex]
The two solutions of the quadratic equation are:
[tex]N = \frac{-1 \pm \sqrt{1^2 - 4*1*(-220)} }{2} \\\\N = (-1 \pm 29.7) /2[/tex]
If we take only the positive solution:
N = (-1 + 29.7)/2 = 14.35
Now, notice that we got this number by taking the smallest possible number of coins (110) So we can round this to the next whole number, which is 15.
If N = 15, then the number of coins in the box is:
15*(15 + 1)/2 = 120
Which lies on the wanted interval.
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Determine the seating capacity of an auditorium with 34 rows of seats if there are 16 seats in the first row, 20 seats in the second row, 24 seats in the third row, and so on.
Answer:
2788.
Step-by-step explanation:
This is represented by an arithmetic series with first term 16 and common difference 4.
The number of rows n = 34.
The capacity
= sum of 34 terms
= (34/2)[2*16 + 4(34-1)]
= 2788.
Answer:
2788
Step-by-step explanation:
16,20,24,.. This is a arithmetic progression with common difference of 4
Sn=? , d=4 , a =16 , n=34[tex]Sn=\frac{34}{2}[2(16)+(34-1)4] \\\\Sn=17[32+33(4)]\\\\Sn=17[164]\\\\Sn=2788[/tex]
Use the grouping method to factor the polynomial below completely.
x3-5x2+3x-15
A. (x²+5)(x-3)
B. (x² - 3)(x + 5)
O C. (x² - 5)(x+3)
D. (x²+3)(x - 5)
The factored expression of x^3 - 5x^2 + 3x - 15 is (x^2 + 3)(x- 5)
How to factor the polynomial?The polynomial is given as:
x^3 - 5x^2 + 3x - 15
Group the terms
(x^3 - 5x^2) + (3x - 15)
Factorize each group
x^2(x - 5) + 3(x - 5)
Factor out x - 5
(x^2 + 3)(x- 5)
Hence, the factored expression of x^3 - 5x^2 + 3x - 15 is (x^2 + 3)(x- 5)
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Triangle A B C has centroid G. Lines are drawn from each point through the centroid to the midpoint of the opposite side to form line segments A F, B D, and C E. The length of line segment A G is 19 x + 14 and the length of line segment D G is 9 x + 2.
G is the centroid of triangle ABC.
What is the length of GF?
units
Based on the calculations, the length of GF is equal to 26 units.
How to find the length of GF?In Geometry, the centroid of any triangle always divides the lines in a ratio of 2:1. Thus, G divides line B F as follows:
2DG = BD
2(9x + 2) = 40
18x + 4 = 40
18x = 40 - 4
x = 36/18
x = 2.
Similarly, G divides line A F as follows:
2GF = A F
GF = A F/2
GF = (19x + 14)/2
GF = (19(2) + 14)/2
GF = 52/2
GF = 26 units.
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Answer: 26 units
Step-by-step explanation: Trust Me!
The answer is correct on Edge. I did it and got it right!
What is the following product?
(√14-√3)(√12+√7)
O 2√√42+7√√2-6-√√21
O√√14-6+√√7
O√26+ √21-√15-/10
O2√42-√√21
Answer: [tex]3\sqrt{21}+7\sqrt{2}-6[/tex]
Step-by-step explanation:
[tex](\sqrt{14}-\sqrt{3})(\sqrt{12}+\sqrt{7})\\\\=(\sqrt{2}\sqrt{7}-\sqrt{3})(2\sqrt{3}+\sqrt{7})\\\\=4\sqrt{21}+7\sqrt{2}-6-\sqrt{21}\\\\=\boxed{3\sqrt{21}+7\sqrt{2}-6}[/tex]
The product on the equation is A = 2√42 - 6 + 7√2 - √21
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
Substituting the values in the equation , we get
A = ( √14 - √3 ) ( √12 + √7 )
On simplifying , we get
A = √14 ( √12 ) - √3 ( √12 ) + √14 ( √7 ) - √3 ( √7 )
A = √168 - √36 + √98 - √21
On further simplification , we get
A = 2√42 - 6 + 7√2 - √21
Therefore , the value of A is 2√42 - 6 + 7√2 - √21
Hence , the product is A = 2√42 - 6 + 7√2 - √21
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MATHEMATICS
Find (A-B) n B when A={a,e,i,o,u} and B={a,b,c,d}
a.
b. A
zia
d. A-B
Answer:
( A - B).
A = { a, e, I, o, u}
B = { a, b, c, d }
{ e, I, o, u}
A - B = subtracting elements of B from A ( all the common elements)
A chemical company sells a specialized industrial lubricant in 20 liter containers. A
random sample of the latest production lot shows the contents of 10 containers to be
20.72, 20.6, 20.71, 20.92, 19.79, 20.93, 20.09, 20.27, 20.49, and 20.2 liters. Find the
standard deviation of the sampled containers' contents.
A. o = 0.55
B. o = 0.53
C. o = 0.36
D. o = 0.42
The standard deviation of the sampled containers' contents is 0.36
How to determine the meanData = 20.72, 20.6, 20.71, 20.92, 19.79, 20.93, 20.09, 20.27, 20.49, 20.2Number of data (n) = 10Summation of data = 20.72 + 20.6 + 20.71 + 20.92 + 19.79 + 20.93 + 20.09 + 20.27 + 20.49 + 20.2 = 204.72Mean (μ) =?Mean = summation of data / number
μ = 204.72 / 10
μ = 20.472
How to determine the standard deviationData = 20.72, 20.6, 20.71, 20.92, 19.79, 20.93, 20.09, 20.27, 20.49, 20.2Number of data (n) = 10Mean (μ) = 20.472Standard deviation (σ) =?σ = √[[(x₁ - μ)² + (x₂ - μ)² + (x₃ - μ)² + (x₄ - μ)² + (x₅ - μ)² + (x₆ - μ)² + (x₇ - μ)² + (x₈ - μ)² + (x₉ - μ)² + (x₁₀ - μ)²] / n]
σ = √[[(20.72 - 20.472)² + (20.6 - 20.472)² + (20.71 - 20.472)² + (20.92 - 20.472)² + (19.79 - 20.472)² + (20.93 - 20.472)² + (20.09 - 20.472)² + (20.27 - 20.472)² + (20.49 - 20.472)² + (20.2 - 20.472)²] / 10]
σ = 0.36
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HELP HELP HELP
I have so many 50 point easy algebra 1 questions, just look into my profile and click questions I really need help.
Tysm! :)
Select the correct answer from each drop-down menu.
Consider triangles ABC and QPRshown.
Triangle ABC is
triangles are
B
triangle QPR. Since the transformations
Reset
Next
, the
Triangle ABC is similar to triangle QPR due to the transformations reflection, the triangles are similar by side-angle-side similarity theorem.
How to Identify similar triangles?Transformations are changes done in the shapes on a coordinate plane by rotation, reflection or translation.
- Rotation means that it rotates or turns the pre-image around an axis with no change in size or shape
- Reflection means that it flips the pre-image and produces the mirror-image with no change in size or shape or orientation
- Translation means that it slides or moves the pre-image with no change in size or shape but has changes in only the direction of the shape
- Dilation means that it stretches or shrinks the pre-image.
Two triangles are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion. It should be noted that, corresponding angles are congruent.
Thus, we conclude that triangle ABC and triangle QPR are similar triangle based on the side-angle-side similarity theorem.
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Answer: reflected and then translated onto only involve rigid motions
congruent
Step-by-step explanation:
Triangle abc
is
reflected and then translated onto
triangle qpr
. Since the transformations
only involve rigid motions
, the triangles are
congruent
.
The distance between adelaide and melbourne is 450 miles. For the first 200 miles, Mila drives her car at X miles per hour. For the remaining distance, Mila drives her car at (X+30) mph. The average speed of the whole trip is 30 mph. What is the value of X?
Convert from Decimal Notation to Scientific Notation
In the following exercises, write each number in scientific notation.
553. 1,290,000
Answer:
Hence, 12,90,000 can be expressed as [tex]$1.29 \times 10^{6}$[/tex].
Step-by-step explanation:
- Given 12,90,000
- Use given, move the decimal point so that first factor is greater than or equal to 1 but less than 10 .
- Then count n and write in scientific notation.
Step 1 of 1
Consider 12,90,000
1.29
So, 1.29 lies between 1 & 10.
Now, Decimal moved to 6 places at left.
[tex]$1.29 \times 10^{6}$[/tex]
So, [tex]$12,90,000=1 \cdot 29 \times 10^{6}$[/tex].
What is the sum of k° + i°?
180°
360°
110°
290°
Answer:
k+i =290
Step-by-step explanation:
The three angles added together form a circle, which is 360 degrees
k+i + 70 = 360
We want to find the sum of k+i, so we subtract 70 from each side
k+i + 70-70 = 360-70
k+i =290
Brainliest + 25, Urgent
For all values of x, there is a function h such that 4h(x) = h(4x). What is the value of h(6) if h(24) = 20 ?
Ty!
The value of h(6) = 5
What is a Function ?A function is a mathematical statement used to relate two variables .
It is given that
4h(x) = h(4x)
It is also given that
h(24) = 20
now to determine the value of h(6)
4* h(6) = h(6 *4)
4* h(6) = h(24)
4 * h(6) = 20
h(6) = 5
Therefore the value of h(6) = 5.
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3 metres of material cost £1.56
Work out the cost of 5 metres of the same material.
Answer:
2.6
Step-by-step explanation:
1.56 ÷3 = 0.52 ( cost of 1 meter of material )5 × 0.52 = 2.6 ( cost of 5 meter of material )look at image.............
Answer:
answer is -3 ....is this correct
HELP ASAP!!!
When the polynomial 2x^3 + mx^2 + nx – 2 is divided by x – 3, the remainder is 4. When
divided by x – 2, the remainder is 2. What are the values of m and n?
The values of m and n are -29/3 and 40/3 respectively
Factor and remainder theoremA polynomial is a function that has a leading degree of 2 and greater. Given the polynomial
P(x) = 2x^3 + mx^2 + nx – 2
If it is divided by x – 3, the remainder is 4 and divided by x – 2, the remainder is 2, hence;
4 = 2(3)^3 + 9m + 3n - 2
4 = 54 + 9m + 3n - 3
9m + 3n = -47
Similarly
2 = 2(2)^3 + 4m + 2n - 2
4m + 2n = -12
Solve simultaneously
9m + 3n = -47 * 2
4m + 2n = -12 * 3
______________
18m + 6n = -94
12m + 6n = -36
Subtract
6m = -58
m = -58/6 = -29/3
For the value of n
4m + 2n = -12
2m + n = -6
2(-29/3) + n = -6
n = -6 + 58/3
n = 40/3
Hence the values of m and n are -29/3 and 40/3 respectively
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help me please eeeeeeeeee
Answer:
A
Step-by-step explanation:
Fundamental Theorem of Algebra:
This states that any polynomial with degree n will have n solutions which are real or complex.
Since this function you gave has 4 zeroes, this function has to have at at least a degree of 4. The reason I say at least, is because of something called multiplicity. When a zero has an even multiplicity it will have a turning point at the zero, if it has an odd multiplicity it will pass the x-axis. So assuming each zero only has a multiplicity of 1, then this will have at least a degree of 4. It also might have complex zeroes which still count as zeroes.
End Behavior of Polynomial Functions:
So this is pretty easy to remember, but if the leading coefficient is positive, then the end behavior to the right will go up, if it's negative it will go down. Now the next thing to know is an odd degree means that the end behavior will go in opposite directions. So if the right goes up, then the left side will be going down and vice verse. if it's an even degree then the two opposite sides will go in the same direction.
In this case both ends are going down, in the same direction. This means that the leading coefficient is negative and the degree is even.
Using these two things, we can exclude answers
B can't be the answer, it only has 3 zeroes, this has at least 4.
C can't be the answer, it has an odd degree so the end behaviors would go in opposite directions
D can't be the answer, it has a positive leading coefficient so the right side would be going up
This means the only possible equation is A which has at least a degree of 4, negative leading coefficient, and even degree.
Find the interquartile range for a data set having the five-number summary: 6.6, 14, 21, 27.5, 36.4
A box plot has 5 data descriptions. The interquartile range for the given data set is 13.5.
How does a boxplot shows the data points?A box plot has 5 data descriptions.
The leftmost whisker shows the minimum value in the data.The rightmost whisker shows the maximum value in the data.The leftmost line in the box shows the first quartile.The middle line shows the median, also called second quartile.The last line of the box shows the third quartile.The given following information can be written as,
The minimum value in the data = 6.6The leftmost line in the box shows the first quartile = 14The middle line shows the median, also called the second quartile = 21The last line of the box shows the third quartile = 27.5The maximum value in the data = 36.4Thus, the interquartile range for the given data is,
Interquartile range = 27.5 - 14 = 13.5
Hence, the interquartile range for the given data set is 13.5.
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In the equation y=kx, where k is a constant. when y=12, then x=5. when y=60, what does x equal?
Answer:
If y = 60 then x = 25
Step-by-step explanation:
You know that when y = 12 then x = 5
So when y = 60, x = 25
The reason for this is because 12 * 5 = 60.
Which means that since the y = 12 was multiplied by 5, the x = 5 should be multiplied by 5 too.
Since 5 * 5 = 25, then we know that if y = 60, then x will equal 25.
Hope this helped! :D
Which table represents a proportional relationship?
how do u not know this
Step-by-step explanation:
my guy
I need the answer to this question
Answer:
See attached image.
Step-by-step explanation:
which expression is a sum of cubes?
Answer:
Step-by-step explanation:
A more complicated expression such as 64x3+27y3 64 x 3 + 27 y 3 is also a sum of cubes since 64x3=(4x)3 64 x 3 = ( 4 x ) 3 and 27y3=(3y)3 27 y 3 = ( 3 y ) 3 . Please note, that expressions such as 2x3 2 x 3 are not perfect cubes.
A tub of water is emptied at a rate of 3 gallons per minute. The equation y –12 = –3(x – 1) models the amount of water remaining, where x is time (in minutes) and y is the amount of water left (in gallons). Analyze the work shown below to determine the initial amount of water. 1. Solve for the y-variable. y – 12 = –3(x – 1) y – 12 = –3x + 3 y = –3x +15 2. Write the equation using function notation. f(x) = –3x +15 The tub started with gallons of water.
The equation in the function form is f(x) = -3x + 15 and the tub started with 15 gallons of water.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have an equation:
y –12 = –3(x – 1)
We can write the above equation as follows:
y = 12 - 3(x - 1)
y = 12 - 3x + 3
y = -3x + 15
or
f(x) = -3x + 15
Plug x = 0
f(0) = 15
The tub started with 15 gallons of water.
Thus, the equation in the function form is f(x) = -3x + 15 and the tub started with 15 gallons of water.
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Solve. Set up the Table.
$2,000 at 2.50% for 50 years.
$2,000 at 5.00% for 50 years.
Answer:
can you explain more i dont get what u mean if you mean 2,000 a year and you get 2.50% or 5.00% and you get it for 50 years your answer for each would be 50 and 100
if one-sixth of a number is 1 1/3, find the number.
Answer:
8
Step-by-step explanation:
Since one-sixth was multiplyed be 1 1/3, we just have to find the opposite, six-ones. We multiply that by 1 1/3 and we get 8!
whats the distance between -3 and -12
Answer:
9
Step-by-step explanation:
We can just count from -3 to -12 and get 9 as the distance
Terms:
Length of lease = 48 months
• MSRP of the car = $32,100
Purchase value of the car after lease = $26,200
Down payment = $4400
Monthly payment = $450
$435 security deposit
$530 acquisition fee.
●
The total cash that's due at signing will be $5365.
How to calculate the cash?It should be noted that security deposit on acquisition are paid at the begining.
The total cash that's due at signing:
= Down payment + Security deposit + Acquisition fee
= 4400 + 435 + 530
= $5365
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Currently, Netflix has 93 000 subscribers. Netflix subscriptions are decreasing by 2.2% per day. How many subscribers are there after 5 days?
There are 83210 subscribers after 5 days
How to determine the number of subscribers?The given parameters are:
Initial, a = 93000Rate, r = 2.2%The number of subscribers each day is calculated as:
f(n) = a * (1-r)^n
This gives
f(n) = 93000 * (1 - 2.2%)^n
Evaluate the difference
f(n) = 93000 * 0.978^n
At 5 days, we have:
f(5) = 93000 * 0.978^5
Evaluate
f(5) = 83210
Hence, there are 83210 subscribers after 5 days
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Identify the expression that has two terms.
6 x + 4
x/4
2 x
5
Answer:
A
Step-by-step explanation:
Comment
The first one. Such an expression requires an isolation plus or minus sign and two terms that are not alike.
Answer
A
Answer:
6x+4
Step-by-step explanation:
A term can be a constant(like 7,4,3 etc) or a variable (x,y etc) which is separated by a multiplication, division,addition or subtraction sign.
The graph of the function f(x) = -(x+3)(x-1) is shown
below.
64-2
Mark this and return
6
A
2
-2-
-4
-6
2
4
6
X
Which statement about the function is true?
O The function is positive for all real values of x where
x < -1.
The function is negative for all real values of x where
x <-3 and where .x > 1.
O The function is positive for all real values of x where
x > 0.
O The function is negative for all real values of x where
x <-3 or x>-1.
Save and Exit
Next
Submit
The true statement about this function is that: B. the function is negative for all real values of x, where x < -3 and where x > 1.
What is a function?A function is a mathematical expression which can be used to define and indicate the relationship existing between two or more variables in a data set.
By critically observing the graph which models the given function (see attachment), we can logically deduce that the true statement about this function is that it's negative for all real values of x, where x is less than -3 and where x is greater than 1.
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In a New York State daily lottery game, a sequence of five digits (not necessarily different) in the range 0-9 are selected at random. Find the probability that four of the five digits are the same.
The probability that four of the five digits are the same is 0.036.
There are 10,000 (10*10*10*10) possible sequences. There are 4C3 ways, 4, of having exactly three digits be the same value. The differing digit can be any of the four positions. There are 10P2 ways, 90 (10*9), to choose the digits of the sequence since we have 10 choices for the digit to be repeated, then 9 more options or the differing digit. The product of the combination arrangements and permutation selection, 4*90, shows there are 360 sequences with three of the same digit. Thus the probability is 360/10,000 or 0.036 or 3.6%.
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