Three friends agree to save money for a graduation road trip. They decide that each of them will put $0.25 in the fund on the first day of May, $0.50 on the second day, $0.75 on the third day, and so on. At the end of May, there will be $_____ in their fund. (Hint: There are 31 days in May.)
Answer: At the end of May, there will be $372.
Explanation:
Since we have given that
On the first day of May, each one save =$0.25
Number of friends = 3
Total save on the first day of May is given by
[tex]0.25\times 3=\$0.75[/tex]
Similarly,
On the second day of May, each one save =$0.25
Total save on the second day of May is given by
[tex]0.50\times 3=\$1.5[/tex]
Similarly,
On the third day of May, each one save =$0.25
Total save on the third day of May is given by
[tex]0.75\times 3=\$2.25[/tex]
This series becomes arithmetic progression,
[tex]0.75,1.5,2.25......[/tex]
Here, a = 0.75
d=common difference is given by
[tex]d=a_2-a_1=1.5-0.75=0.75\\d=a_3-a_2=2.25-1.5=0.75[/tex]
Since there are 31 days in the month of May,
So, n=31
We need to calculate the sum of 31 terms to get our answer,
[tex]S_n=\frac{n}{2}(2a+(n-1)d)\\\\S_{31}=\frac{31}{2}(2\times 0.75+(31-1)\times 0.75)\\\\=\frac{31}{2}(1.5+30\times 0.75)\\\\=\frac{31}{2}(24)\\\\=31\times 12\\\\=\$372[/tex]
Hence, at the end of May, there will be $372.
The total amount in the fund at the end of May is 239.25.
Explanation:To find the total amount of money in the fund at the end of May, we need to calculate the sum of the money put into the fund on each day. The students decide to put 0.25 on the first day, 0.50 on the second day, 0.75 on the third day, and so on. This is an arithmetic sequence, where the first term (a) is 0.25 and the common difference (d) is 0.25. The formula to find the sum of an arithmetic sequence is:
S = (n/2)(2a + (n-1)d)
In this case, n = 31 (since there are 31 days in May), a = 0.25, and d = 0.25. Plugging these values into the formula, we get:
S = (31/2)(2 * 0.25 + (31-1) * 0.25) = 239.25
Therefore, at the end of May, there will be 239.25 in their fund.
Write a quadritic equation in standard form that has the roots of 5 and -2
Final answer:
To find the quadratic equation with roots 5 and -2, we can use the quadratic formula. Substituting the values of the roots into the formula, we get the equation (x - 5)(x + 2) = 0.
Explanation:
A quadratic equation in standard form is written as ax² + bx + c = 0, where a, b, and c are constants. To find the equation with roots 5 and -2, we can use the fact that the solutions of a quadratic equation are given by the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).
Substituting the values of the roots into the quadratic formula, we have:
x = (-b ± √(b² - 4ac)) / (2a)
For the first root, x = 5:
5 = (-b ± √(b² - 4ac)) / (2a)
Substituting a = 1, b = -7, and c = 10, we get:
5 = (-(-7) ± √((-7)² - 4(1)(10))) / (2(1))
Simplifying further:
5 = (7 ± √(49 - 40)) / 2
5 = (7 ± √9) / 2
5 = (7 ± 3) / 2
So, the first root gives us the equation:
x = 5, which translates to x - 5 = 0.
For the second root, x = -2:
-2 = (-b ± √(b² - 4ac)) / (2a)
Substituting a = 1, b = -7, and c = 10, we get:
-2 = (-(-7) ± √((-7)² - 4(1)(10))) / (2(1))
Simplifying further:
-2 = (7 ± √(49 - 40)) / 2
-2 = (7 ± √9) / 2
-2 = (7 ± 3) / 2
So, the second root gives us the equation:
x = -2, which translates to x + 2 = 0.
Therefore, the quadratic equation in standard form with roots 5 and -2 is:
(x - 5)(x + 2) = 0
What is the equation of the following graph in vertex form?
parabolic function going down from the left and turning at the point negative one comma zero and going up through the point zero comma one and continuing towards infinity
Courtesy of Texas Instruments
y = (x − 1)2
y = (x − 1)2 + 1
y = (x + 1)2 − 1
y = (x + 1)2
Answer:
y = (x + 1)^2
Step-by-step explanation:
I used desmos and put each answer choice into the graphing calculator and answer choice D was the only one that matched with the image in the question.
A scale on a blueprint is 1 inch = 5 feet. What is the length of an object that is 8 1/2 inches long on the blueprint
To find the actual length of the object, multiply the length on the blueprint by the scale factor of 5 feet/inch. The length of the object in actual size is 42 feet 6 inches.
Explanation:To find the actual length of the object represented on the blueprint, we can use the scale factor provided. The scale on the blueprint is 1 inch = 5 feet. So, if the object is 8 1/2 inches long on the blueprint, we can multiply it by the scale factor to find the actual length.
Step 1:
Convert 8 1/2 inches into a mixed number fraction by adding 1 to the whole number.
8 1/2 inches = 8 + 1/2 = 17/2 inches
Step 2:
Multiply the length on the blueprint by the scale factor:
17/2 inches * 5 feet/inch = 85/2 feet
Step 3:
Simplify the fraction if possible:
85/2 feet = 42 feet 6 inches
Therefore, the length of the object in actual size is 42 feet 6 inches.
To find the actual length of an object that is 8 1/2 inches long on a blueprint with a scale of 1 inch = 5 feet, you multiply 8.5 by 5, resulting in an actual length of 42.5 feet.
Explanation:If the scale on a blueprint is 1 inch = 5 feet, then to determine the actual length of an object that is 8 1/2 inches long on the blueprint, we simply multiply the length on the blueprint by the scale factor.
So, for every inch on the blueprint, there are 5 feet in reality. Therefore, we calculate the actual length as follows:
Multiply 8 1/2 inches by the scale factor, which is 5 feet per inch.8.5 inches * 5 feet/inch = 42.5 feet.Thus, the actual length of the object is 42.5 feet.
6 gallons and 3 quarts equal
All real numbers that are greater than or equal to -1.5 and less than 9.2
You need to sell 250 candy bars at $2 each. If you meet your goal, the total amount of money you will have is measured in the _____. ...?
Jeremy has a box of 500 nails that weighs 1.35 kilograms. He uses 60 nails to build a birdhouse. How much do the nails in the birdhouse weigh?
How is the data represented on a scatterplot that depicts an exponential model?
In a scatterplot that depicts an exponential model, the data points will form a curve that resembles the shape of an exponential function.
Explanation:In a scatterplot that depicts an exponential model, the data points will form a curve that resembles the shape of an exponential function. The x-axis represents the independent variable, while the y-axis represents the dependent variable. As the x-values increase, the corresponding y-values will increase at an exponential rate. For example, if we are graphing the growth of a population over time, the scatterplot will show the population size increasing rapidly as time progresses.
On a scatterplot depicting an exponential model, the data points are represented as points on a curvy line. The correct answer is option D) points on a curvy line.
In a scatterplot depicting an exponential model, the data points typically form a curvy line. Exponential relationships show rapid growth or decay, which is reflected in the scatterplot as a smooth, non-linear curve.
As the independent variable increases, the dependent variable changes exponentially, resulting in data points that do not lie along a straight line but instead form a distinctive curve. This curve can either rise sharply or decrease rapidly, depending on whether the exponential function involves growth or decay.
For instance, in exponential growth, the data points start small and then rapidly increase, forming a curve that steepens over time. Conversely, in exponential decay, the data points start large and decrease rapidly, forming a curve that flattens out as it approaches zero.
Therefore, on a scatterplot representing an exponential model, the data points are typically observed to form a curvy line, as seen in option **D)**.
Complete question : How is the data represented on a scatterplot that depicts an exponential model?
A) points on a line
B) random points
C) points on a horizontal line
D) points on a curvy line
Group A consists of X students and their total age is 221 and their average age is an integer.When group A is merged with Group B with twice the number of students (the number of students between 30 and 40) average age of B is reduced by 1.What is the original average age of B?
...?
Answer:
16 years
Step-by-step explanation:
Given,
Number of students in group A = X,
Sum of their ages = 221,
So, the average age of students in group A = [tex]\frac{\text{Sum of ages}}{\text{Total students}}[/tex]
[tex]=\frac{221}{X}[/tex]
According to the question,
[tex]\frac{221}{X}=\text{Integer}[/tex]
∴ X must be a factor of 221,
∵ 221 = 13 × 17,
Now, If X = 13,
Then the number of students in group B = 26 ( NOT POSSIBLE )
If X = 17,
Then the number of students in group B = 34
Which is between 30 and 40,
Now, Let S be the sum of ages of students in group B,
So, the average age in group B = [tex]\frac{S}{34}[/tex]
Again according to the question,
[tex]\frac{S+221}{17+34}=\frac{S}{34}-1[/tex]
[tex]\frac{S+221}{51}=\frac{S-34}{34}[/tex]
[tex]34S+7514 = 51S - 1734[/tex]
[tex]34S - 51S = -1734 - 7514[/tex]
[tex]17S = 9248[/tex]
[tex]\implies S = 544[/tex]
Therefore, the average age of B = [tex]\frac{544}{34}[/tex] = 16 years.
What is the most misleading aspect of this graph that might lead one to the wrong conclusion?
connecting the data points with a line
scale of the y-axis
scale of the x-axis
spacing of the grid
(graph attached)
Point M is the midpoint of segment QR. If QM = 16 + x and MR = 2(x + 2), find the length of QM.
what is 3[10-(27÷9)]?
Find cos theta if sin theta = 2/3. assume the terminal side of the angel falls in quadrant 2
Marcus finds that (3x^2-2y^2+5x)+(4x^2+12y-7x)= 7x^2-10y^2-2x What error did Marcus make?
A: He combined the terms 5x and –7x incorrectly.
B: He combined the terms 3x^2 and 4x^2 incorrectly.
C: He combined the terms –2y^2 and 12y^2 incorrectly.
D: He subtracted the polynomials instead of adding.
we have
[tex](3x^{2} -2y^{2}+5x)+(4 x^{2}+12y^{2}-7x)[/tex]
Combine like terms
[tex](3x^{2} -2y^{2}+5x)+(4 x^{2}+12y^{2}-7x)\\=(3x^{2}+4x^{2})+(-2y^{2}+12y^{2})+(5x-7x)\\=7x^{2} +10y^{2}-2x[/tex]
therefore
the answer is the option C
He combined the terms [tex]-2y^{2}[/tex] and [tex]12y^{2}[/tex] incorrectly
how many tens and ones are in 25
make h the subject of the formula
t=gh/10
To make 'h' the subject of the formula, multiply both sides by 10 to get the equation 10t = gh. Then divide both sides by 'g' to get h = 10t/g.
Explanation:The formula given in the question is t = gh/10. To make h the subject of the formula, we'll need to isolate it. To do this, you should start off by multiplying both sides of the equation by 10, thus removing the divide by 10 part. This will give you 10t = gh. Finally, divide both sides of the equation by g. So, your revised formula would be h = 10t/g. This formula now clearly places h as the subject.
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4n³·2n²=?
Simplify your answer.
Nina knows that the average of the x-intercepts represents the line of symmetry for a quadratic function through the x-axis. Which equation represents the average of the x-intercepts for f(x) = 4x2 – 24x + 20?
Answer:
c
Step-by-step explanation:
2x plus 4 in vertex form
Given the following:
29 day billing cycle
4/17 Billing date previous balance $1,100
4/27 Payment 700
4/29 Charge 300
5/7 Payment 60
The average daily balance is:
$910.34
$755.17
$810.43
$755.71
None of these
The average daily balance for the given billing cycle is calculated by summing the product of each daily balance and the length of time it was held, and then dividing by the number of days in the billing cycle. After doing this, the average daily balance comes out to be $755.17.
Explanation:The subject of this question is finance and it involves calculating the average daily balance for a billing cycle. In this method, the daily outstanding balances are added together and then divided by the total number of days in the billing period.
Here, the billing cycle lasts for 29 days, from 4/17 to 5/17.
From 4/17 to 4/26 (10 days), the balance was $1,100.From 4/27 to 4/28 (2 days), the balance was reduced by $700, therefore, it was $400.From 4/29 to 5/6 (8 days), the balance increased by $300, so became $700.From 5/7 to 5/17 (11 days), the balance was reduced by $60, therefore, it was $640.Like this, you calculate the balance for each portion of the billing cycle, then multiply each by the number of days that balance was held, add those up, and finally, divide by the number of days in the billing cycle:
((1100*10) + (400*2) + (700*8) + (640*11)) / 29 = $755.17
Therefore, the average daily balance is $755.17.
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In the figure below what is the name of the angle formed by two rays QR and QP? What is the common. endpoint,for this angle?
Of 100 clock radios with digital tuners and / or CD players sold recently in a department store, 70 had digital; tuners and 90 and CD players. How many radios had both digital tuners and CD players? ...?
Final answer:
To determine the number of radios with both digital tuners and CD players, we use the principle of inclusion-exclusion. With 70 radios featuring digital tuners and 90 featuring CD players out of 100, the calculation reveals that 60 radios had both features.
Explanation:
The question asks how many radios sold recently in a department store had both digital tuners and CD players, given that 70 had digital tuners and 90 had CD players out of a total of 100 clock radios. To find the number of radios that had both features, we can use the principle of inclusion-exclusion. The formula for this principle is: Total = A + B - (A and B), where A and B are the two groups, and (A and B) is the intersection of the two groups. In this case, A is the number of radios with digital tuners, and B is the number of radios with CD players.
Substituting the given values: 100 = 70 + 90 - (A and B). Solving for (A and B), which represents the radios with both features, we get: (A and B) = 70 + 90 - 100 = 160 - 100 = 60.
Therefore, 60 radios had both digital tuners and CD players.
A company has fixed operating costs of $2,137.00 per month with a production cost of $15.15 per unit. If each unit brings $33.09 in revenue, which of the folowing equations represents the profit for the month? Let x represent the number of units made per month and y represent the total profit for the month. Explain your choice.
plzzz plzzzzzz helpppppp
The equation that represents the profit for the month is: y = 33.09x - (2,137.00 + 15.15x).
What is operating cost?The ongoing expenses incurred from the normal day-to-day operations of a business are referred to as operating costs.
The equation that represents the profit for the month is:
y = 33.09x - (2,137.00 + 15.15x)
This equation takes into account the revenue generated by selling x units, which is 33.09x, and subtracts the total cost of producing those x units, which is (2,137.00 + 15.15x). The result is the total profit generated for the month.
We can simplify the equation by combining like terms:
y = 17.94x - 2,137.00
This equation can be used to determine the total profit for any given number of units produced.
The coefficient of x (17.94) represents the profit generated per unit sold, and the constant term (-2,137.00) represents the fixed costs that must be subtracted from the revenue to calculate the profit.
Therefore, the correct equation is y = 33.09x - (2,137.00 + 15.15x), because it takes into account both the revenue and the total costs associated with producing x units.
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For the table below, determine the function rule, and find each of the missing y-values.
Function Rule: ?
x y
1 4
3 6
4 7
5 ?
7 10
10 ?
Please help me understand how to do this!
In ΔRST shown below, segment SU is an altitude:
What property or definition is needed to prove that ΔRUS is similar to ΔSUT?
Answer:
The correct option is 1.
Step-by-step explanation:
It is given that in ΔRST , segment SU is an altitude. It means the angle SUR and angle SUT are right angles.
It triangle RST and SUT,
[tex]\angle RST=\angle SUT=90^{\circ}[/tex] (Definition of altitude)
[tex]\angle STR=\angle UTS[/tex] (Common angle)
Two corresponding angles are equal. So by AA property of similarity,
[tex]\triangle RST\sim \triangle SUT[/tex] .... (1)
It triangle RST and RUS,
[tex]\angle RST=\angle SUR=90^{\circ}[/tex] (Definition of altitude)
[tex]\angle SRT=\angle URS[/tex] (Common angle)
Two corresponding angles are equal. So by AA property of similarity,
[tex]\triangle RST\sim \triangle RUS[/tex] .... (2)
According to transitive property of equality,
if a=b and b=c, then a=c.
From (1) and (2), we get
[tex]\triangle RUS\sim \triangle SUT[/tex] ( Transitive property of equality)
Therefore the correct option is 1.
A machine make 24 items in 8 minutes how many can it make in 14
whats 358 divided by 3 useing compatible numbers
Glenn has a beginning balance of $840 in his checking account. He has a deposit of $375 and withdraws $250 from the ATM. If the ATM fee is $3, what is his new balance?
$718
$212
$962
$572
which equation in standard form has a graph that passes through the point (-4 , 2) and has a slope of 9/2?
A. 9x-2y=36
B. 9x-2y=26
C. 9x-2y=-40
D. 9x-2y=-10
The equation in standard form passing through (-4, 2) with a slope of 9/2 is 9x - 2y = -10.
Since the equation is in standard form, rearrange it to slope-intercept form y = mx + b.
Given slope m = 9/2 and point (-4, 2), substitute these values to find the correct equation.
After substitution, the equation is 9x - 2y = -10.