Answer:
A. (x +8) + (-4x+31)/(x^2+2x+1)
Step-by-step explanation:
When you perform long division of polynomials, the first quotient term is the ratio of the highest-degree terms in the numerator and denominator: x^3/x^2 = x.
This fact eliminates all but choices A and C.
The denominator of the remainder term is the denominator of the original expression, so will be x^2 +2x +1, as shown in choice A.
__
So, simply based on a couple of facts about long division (that you learned in the early elementary grades), you can make the correct choice of answer without actually working the problem in detail.
_____
This is a polynomial long division problem. It is worked in virtually the same way that numerical long division problems are worked: first you find a quotient term, then you multiply that by the divisor and subtract the result from the dividend. The difference is the new dividend. These steps are identical to numerical long division.
For polynomial long division, instead of lining up the digits with the same place value, you line up the terms with the same degree of the variable.
As mentioned above, the quotient term is computed only from the highest-degree terms of dividend and divisor, so that part is actually simpler than for numerical long division.
A dividend that is of lower degree than the divisor is considered to be the remainder. As with numerical long division, it can be expressed as a fraction with the divisor as the denominator.
Numerical example: 18/7 = 2 remainder 4 or 2 4/7.
Find the area of the shaded polygons:
I think the last one is maybe ten, maybe
Answer:
Step-by-step explanation:
no
what is the multiplicative inverse of 2/5
Answer:
5/2
Step-by-step explanation:
The multiplicative inverse is what me need to multiply by to get 1
2/5 * what = 1
Multiply by the reciprocal
5/2 *2/5 * what = 1 *5/2
what = 5/2
The multiplicative inverse is 5/2
5/2 is the multiplicative inverse
Lines AB and AC tangent to circle k(O) at B and C respectively. Find BC, if m∠OAB=30°, and AB=5 cm.
Answer:
5 cm
Step-by-step explanation:
ΔABC is equilateral, so BC = AB = 5 cm.
____
AO is the perpendicular bisector of BC and the angle bisector of angle A, so ∠OAC = ∠OAB = 30°. Then vertex angle BAC of isosceles triangle ABC is 60°, which means all angles in the triangle are 60° and the triangle is equilateral.
The length of BC is 5cm
Given that line AB is tangent to circle K at point B, and line AC is tangent to circle K at point C, we know that the radius of the circle at the point of tangency is perpendicular to the tangent line. Therefore, OB is perpendicular to AB, and OC is perpendicular to AC. This forms two right triangles,[tex]$\triangle OAB$ and $\triangle OAC$.[/tex]
Let's denote OB as the side opposite the 30° angle and OA as the hypotenuse. Then we have:
[tex]OB = $\frac{1}{2}$AB = $\frac{1}{2} \times 5$ cm = 2.5 cm[/tex]
OA = AB = 5 cm (since AB is the hypotenuse of the right triangle)
Now, since the circle is the same, OA is also the radius of the circle, and thus OB = OC = 2.5 cm.
Therefore [tex], $\triangle OBC$[/tex] is an equilateral triangle because all angles are 60° and the sides opposite these angles are equal. Hence, BC = OB = OC = 2.5 cm.
Thus, BC = OB + OC' = 2.5 cm + 2.5 cm = 5 cm.
But this is not the final answer. We have to consider that the length of the chord BC is equal to the diameter of the circle because the tangents from a common external point to a circle are equal in length. Therefore, the diameter of the circle is twice the length of the radius OB (or OC').
Diameter = 2 * OB = 2 * 2.5 cm = 5 cm
BC = 5cm
What are the methods for solving quadratic equations and what indicators predict that a quadratic function will have a complex solution?
Answer:
1) Methods:
- Quadratic formula.
- Factorization.
- Completing the square.
2) If the determinant is less than zero ([tex]D<0[/tex]) then there are two roots that are complex conjugates.
Step-by-step explanation:
Methods:
- Quadratic formula
Given the quadratic equation in Standard form [tex]ax^2+bx+c=0[/tex], you can solve it with the quadratic formula:
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
- Factorization
You must find two expression that when you multply them, you get the original quadratic equation. For example:
[tex]x^2+6x+8=0[/tex]
Find two number whose sum is 6 and whose product is 8. These are 2 and 4. Then:
[tex](x+2)(x+4)=0[/tex]
When you make the multiplication indicated in [tex](x+2)(x+4)=0[/tex], you obtain [tex]x^2+6x+8=0[/tex]
- Completing the square
Given the quadratic equation in Standard form [tex]ax^2+bx+c=0[/tex],, you must turn it into:
[tex]a(x+d)^2+e=0[/tex]
Where:
[tex]d=\frac{b}{2a}\\\\e=c-\frac{b^2}{4a}[/tex]
Once you get that form, you must solve for x.
You can predict if the quadratic function will have a complex solution with the determinant:
[tex]D=b^2-4ac[/tex]
If [tex]D<0[/tex] then there are two roots that are complex conjugates.
Quadratic equations can be solved by several methods including the quadratic formula. The concept of a discriminant, calculated by b² - 4ac, can indicate if a function has a complex solution. A negative discriminant means the equation will have complex solutions.
Explanation:Quadratic equations, or second-order polynomials, take on the form ax²+bx+c = 0. There are several methods to solve these equations, for instance, factoring, completing the square, using the quadratic formula or graphically.
The most general method is the quadratic formula: -b ± √b² - 4ac / 2a.
Indicator for a complex solution is called the discriminant(b² - 4ac). If the discriminant is negative, the equation will have complex solutions rather than real ones. This is because you'd be attempting to find the square root of a negative number, which is not possible within the set of real numbers, and hence the answer is in the form of a complex number.
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Which pairs of function are inverses of each other?
Choose all answers that are correct.
f(x) = 5x + 10 and g(x) = 0.2x -2
f(x) = x^2 + 3 and g(x) = ± √x+3
f(x) = 1/2x + 7 and g(x) = 2x -7
f(x) = 1/4x -1 and g(x) = 4x + 4
Answer:
f(x) = 5x + 10 and g(x) = 0.2x -2f(x) = 1/4x -1 and g(x) = 4x + 4Step-by-step explanation:
f and g will be inverses if f(g(x)) = x.
A — f(g(x)) = 5(0.2x -2) +10 = x -10 +10 = x . . . . . inverses
B — f(g(x)) = (±√x+3)^2 +3 = x ±6√x +9 +3 ≠ x . . . . . not inverses
(even if it is g(x) = ±√(x+3), the functions are still not inverses)
C — 1/2(2x -7) +7 = x -7/2 +7 = x +7/2 ≠ x . . . . . not inverses
D — 1/4(4x +4) -1 = x +1 -1 = x . . . . . inverses
Ms. Wilson’s taxable income is 36,201. She is filling as single, and she has already paid $5344 in federal tax’s. What will she receive or pay after she figures her taxes for the year?
A. She will receive a refund of $258.
B. She will pay $258.
C. She will receive a refund of $245.
D. She will pay $245.
Answer: it should be will receive a refund of $278
Step-by-step explanation:
That’s just what was on my test though
Hope that helps somebody
The amount Ms. Wilson will receive after she figures out her tax for the year is; $999.88
Tax rate and Tax bracketThe tax bracket Ms. Wilson falls into demands that she pays 12% of her taxable income in tax.
Hence, the tax she's supposed to pay is;
Tax = (12/100)× 36,201Tax per annum = $4,344.12.Hence, she will receive after she figures her taxes for the year is; $5344 - $4,344.12 = $999.88
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a. Suppose we had $15,192 cash and invested it in the bank at 16 percent interest, how much would you have at the end of 1, 2, 3, 4 years, assuming annual compounding?
Answer:
Part a) [tex]\$17,622.72[/tex]
Part b) [tex]\$20,442.36[/tex]
Part c) [tex]\$23,713.13[/tex]
Part d) [tex]\$27,507.23[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
Part a) How much would you have at the end of 1 year?
in this problem we have
[tex]t=1\ years\\ P=\$15,192\\ r=0.16\\n=1[/tex]
substitute in the formula above
[tex]A=15,192(1+\frac{0.16}{1})^{1*1}=\$17,622.72[/tex]
Part b) How much would you have at the end of 2 year?
in this problem we have
[tex]t=2\ years\\ P=\$15,192\\ r=0.16\\n=1[/tex]
substitute in the formula above
[tex]A=15,192(1+\frac{0.16}{1})^{1*2}=\$20,442.36[/tex]
Part c) How much would you have at the end of 3 year?
in this problem we have
[tex]t=3\ years\\ P=\$15,192\\ r=0.16\\n=1[/tex]
substitute in the formula above
[tex]A=15,192(1+\frac{0.16}{1})^{1*3}=\$23,713.13[/tex]
Part d) How much would you have at the end of 4 year?
in this problem we have
[tex]t=4\ years\\ P=\$15,192\\ r=0.16\\n=1[/tex]
substitute in the formula above
[tex]A=15,192(1+\frac{0.16}{1})^{1*4}=\$27,507.23[/tex]
Which of the following is equal to the square root of the cube root of 6 ?
6 to the power of 1 over 3
6 to the power of 2 over 3
6 to the power of 3 over 2
6 to the power of 1 over 6
Answer:
6 to the power of 1 over 6
Answer:
The correct option is 4.
Step-by-step explanation:
The given interpretation is square root of the cube root of 6. The mathematical expression is
[tex]\sqrt{\sqrt[3]{6}}[/tex]
It can be written as
[tex]((6)^{\frac{1}{3})^{\frac{1}{2}}[/tex]
Using the property of exponent, we get
[tex](6)^{\frac{1}{3}\times \frac{1}{2}}[/tex] [tex][\because (x^m)^n=(x)^{mn}][/tex]
Now simplify the power.
[tex](6)^{\frac{1}{6}}[/tex]
The simplified form of given expression is 6 to the power of 1 over 6. Therefore the correct option is 4.
tomas and emilio are twins. they want to invite their friends to celebarte their shared birthday at the movie theater. they have a budget of $200 to plan their party. the party room at the theater costs $45.99 to rent and include a free cake. movie tickets cost $12.50 each and a small bag of popcorn cost $ 4.50. Tomas write an equation to represent the cost of their party. emilio writes an inequality. both use p to represent the number of people who can attend. wtrite tomas possible equation and emilio possible inequality.
Answer:
1) 17p + 45.99 = 200
2) 200 > 45.99 + 17p
Step-by-step explanation:
Total Budget = $200
Cost of Party Room = $45.99
Cost of movie ticket for one person = $12.50
Cost of one small bag of popcorn = $4.50
Part 1: Possible Equation by Tomas
The possible equation that can be set up will have the total budget equal to total expenses.
So,
200 = Total Cost of party
200 = Cost of Party Room + Cost of Movie Tickets + Cost of popcorns
If p people attend the party, the cost of movie tickets will be $12.50p and cost of popcorns will be $4.50p, assuming that each person get a small popcorn bag.
So, now the equation will be:
200 = 45.99 + 12.50p + 4.50p
200 = 45.99 + 17p
or
17p + 45.99 = 200
This is a possible equation that Tomas might have used to represent the cost of the party.
Part 2: Possible Inequality by Emilio
Emilio might want to keep the cost below $200 of the entire party. So the possible inequality will be of the form:
200 > Total Cost of party
200 > Cost of Party Room + Cost of Movie Tickets + Cost of popcorns
200 > 45.99 + 12.50p + 4.50p
200 > 45.99 + 17p
This is a possible inequality that Emilio might have used to represent the cost of the party.
Consider the equation log5(x + 5) = x2.
What are the approximate solutions of the equation? Check all that apply.
Answer:
x ≈ -0.93, x ≈ 1.06
Step-by-step explanation:
A graphing calculator can show you the approximate solutions. (It is also capable of refining those solutions to full calculator precision, if you need.)
_____
Comment on the graphical solution
I prefer to have the calculator show me the zeros of a function, where the zeros correspond to solutions of the original equation. For the purpose, it is sufficient to define the function as the difference between the sides of the original equation.
__
The definition of g(x) in the attachment corresponds to the iterator of Newton's Iteration method for finding zeros of a function. When the input and output values of that iteration function match, the value of x is a zero of the function f(x).
PLZ HELP ME ASAP
algebra 2 word problem
Give each month a number:
January = 0
February = 1
March = 2
April = 3
Now set X to 3 in the equation ad solve for t.
t = -30cos(x/6) +60
t = -30cos(3/6) +60
t = 33.672 degrees. ( Round as necessary)
You would need to change the +60 to a new starting point based on what the rise in temperature is due to global warming.
The model predicts a maximum afternoon temperature of around 33.67°C in April. To adjust for the impact of global warming, one can increase the constant term in the equation based on observed data. For instance, if there's a 2°C increase, the modified equation would be: t = -30cos(x/6) + (60 + 2).
Find the maximum temperature in April and how the model would change due to global warming:
Finding the maximum temperature in April:
Plug in x = 3: Since April is the fourth month (x = 0 for January), we need to substitute x with 3 in the equation:
t = -30cos(3/6) + 60
Calculate the temperature:
t = -30cos(0.5) + 60 ≈ 33.67°C
Therefore, the model predicts a maximum afternoon temperature of approximately 33.67°C in April.
Impact of global warming:
If the maximum temperature in April starts rising due to global warming, the model needs to be adjusted to account for the increase. Here's how:
Increase the constant term: The constant term in the equation (currently 60) represents the average temperature across all months. To account for a general rise in temperatures, we can increase this value.
Adjust the increase based on the observed data: The amount of increase should be based on observed data on how much the temperature has risen in April compared to the historical average.
For example, if observations show that the average April temperature has increased by 2°C due to global warming, we can modify the equation as follows:
t = - 30cos(x/6) + (60 + 2) // Increase the constant term by 2
This new equation would then account for the simulated effect of global warming on the maximum afternoon temperature in April.
A phone company wants to know if its customers are satisfied with their service. 100 people are surveyed. The results show that 40 people are satisfied. There are 1,200 people the company services. About how many people are satisfied with their service?
100:40
=2.5
1200 : 2.5
=480
About 480 people out of the 1,200 customers are likely satisfied with their service.
To determine how many of the company's customers are likely satisfied with their service based on the survey results, we can use the concept of proportions. This involves simple multiplication and understanding ratios in percentages.
Find the proportion of satisfied customers in the survey:
Number of satisfied customers in the survey: 40
Total number of people surveyed: 100
Proportion of satisfied customers = (Number of satisfied customers) / (Total number of people surveyed)
Proportion of satisfied customers = 40 / 100 = 0.4 or 40%
Apply this proportion to the entire customer base:
Total number of the company's customers: 1,200
Estimate of satisfied customers = Proportion of satisfied customers × Total customers
Estimate of satisfied customers = 0.4 × 1,200 = 480
Hi there!
Can I get some help with this calculus homework. #6a and 8b. Don't forget to show your work! Thank you!
Answer:
6a. -8
8b. 1/125
Step-by-step explanation:
If you know powers of 2 and the squares and cubes of small integers, you can work these in your head. There is no "work" to show. Of course, a calculator can evaluate these easily. (see attached)
___
6a. (-128)^(3/7) = ((-2)^7)^(3/7) = (-2)^3 = -8
___
8b. (27^(2/3) +8^(4/3))^(-3/2) = ((3^3)^(2/3) +(2^3)^(4/3))^(-3/2)
= (3^2 +2^4)^(-3/2) = (9+16)^(-3/2) = 25^(-3/2)
= (5^2)^(-3/2) = 5^(-3) = 1/5^3
= 1/125
what is the sum of the geometric series sigma 15,x=0, 2(1/3)x
Answer:
[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x=3.0[/tex]
Step-by-step explanation:
We want to evaluate:
[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x[/tex]
When x=0, we obtain the first term of the geometric series as
[tex]a_0=2(\frac{1}{3})^0[/tex]
The common ratio of this geometric series is [tex]r=\frac{1}{3}[/tex]
The sum of the first n-terms of a geometric series is
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
From x=0 to x=15, we have 16 terms.
The sum of the first 16 terms of the geometric series is
[tex]S_{16}=\frac{a(1-(\frac{1}{3})^{16})}{1-\frac{1}{3}}=2.99999993031[/tex]
[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x=3.0[/tex] to the nearest tenth.
What is defaulting?Getting a low credit score
Opening too many credit accounts
Building a credit history
Failing to pay debt
Answer:
Failing to pay debt
Step-by-step explanation:
Final answer:
Defaulting on a debt, failing to pay debt, and building a credit history are crucial aspects of managing one's financial health.
Explanation:
Defaulting on a debt occurs when a borrower fails to repay the loan according to the terms agreed upon with the lender. This can lead to serious consequences such as damage to one's credit score and possible legal actions taken by the lender.
One of the contributing factors to defaulting is failing to pay debt on time. This affects a person's credit history and the lender's trust in the borrower's ability to repay borrowed money.
It is important to build a credit history by responsibly managing credit accounts, paying bills on time, and avoiding opening too many accounts rapidly to maintain a good credit score and prevent defaulting.
a standard deck of 52 cards contains 4 suits: hearts, clubs, diamonds, and spades. Each suit consists of cards numbered 2 through 10, a jack, a queen, a king, and an ace.
Anthony decides to pick one card at random from a standard deck of 52 cards. Let A be the events that he chooses an ace and H be the event that he chooses a heart.
What is P ( A or H), the probability that the card Anthony chooses is either an ace or a heart?
The probability that a randomly chosen card from a standard 52-card deck is either an ace or a heart is approximately 31%.
Explanation:In a standard deck of 52 cards, there are 4 suits and each suit has 13 cards: hearts, clubs, diamonds, spades. Therefore, the total number of heart cards in the deck is 13 and the total number of aces in the deck is 4 (one for each suit).
To compute the probability P (A or H), the probability that Anthony chooses a card which is either an ace or a heart, we first need to calculate individual probabilities. The probability of drawing a heart P(H) is 13/52 = 0.25, and the probability of drawing an ace P(A) is 4/52 = 0.077. However, as the aces also include one heart (Ace of Hearts), the probabilities overlap.
To correct this, we use the rule of sum for probabilities which says that the probability that A or B will happen is the probability that A will happen plus the probability that B will happen, minus the probability that both A and B will happen. Applying this, P ( A or H) = P(A) + P(H) - P(A and H) = 0.077 + 0.25 - 0.019 = 0.308, or approximately 31%
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Final answer:
The probability of drawing either an ace or a heart from a standard deck of cards is 11/26.
Explanation:
To find the probability of choosing either an ace or a heart card, we need to calculate the individual probabilities of each event and then subtract the probability of neither event happening.
There are 4 aces in a deck of 52 cards, so the probability of picking an ace is 4/52, which simplifies to 1/13.
Similarly, there are 13 hearts in a deck, so the probability of picking a heart is 13/52, which simplifies to 1/4.
Since the events are mutually exclusive (a card can't be both an ace and a heart), we can add the probabilities together to find the probability of either event happening: 1/13 + 1/4 = 4/52 + 13/52 = 17/52.
Finally, to find the probability of either an ace or a heart, we subtract the probability of neither event happening (the probability of picking a card that is neither an ace nor a heart):
P(A or H) = 17/52 - 39/52 = 22/52, which simplifies to 11/26.
this is a dilation I need to know if it is an reduction or enlargement and explain also the scale factor and explain please help me
Answer:
a) reductionb) 1/2Step-by-step explanation:
a) The image A'B'C'D' is smaller than the original ABCD, so the dilation is a reduction. The image is reduced in size from the original.
__
b) Each image point is 1/2 the distance of the original point from the origin. Count the grid squares to see this, or compare coordinates:
A'(-1, 2) = 1/2·A(-2, 4)
Thus the scale factor is 1/2.
Natalie and 5 of her friends are going bowling.It costs $3 to play one game and $2 for each person to rent a pair of bowling shoes. If they spent a total of $21,how many games did they play?
To find out how many games Natalie and her friends played, we subtracted the total shoe rental cost for 6 people from the $21 spent and divided the remainder by the cost per game, which gave us a result of 3 games played.
Explanation:The question asks us to solve a real-world math problem where Natalie and her friends go bowling and spend a total of $21. The cost to play one game is $3 and shoe rental is $2 per person.
To determine the number of games they played, we need to calculate the cost of shoe rental for all people and then figure out how much of the $21 was left for the games.
First, we calculate the shoe rental for 6 people (Natalie and her 5 friends):
Shoe rental per person = $2Total shoe rental cost = 6 people × $2/person = $12Next, we subtract the shoe rental cost from the total amount spent to find the amount spent on games:
Total amount spent on games = $21 - $12 = $9Finally, we divide the amount spent on games by the cost per game to find the number of games played:
Cost per game = $3Number of games played = $9 / $3/game = 3 gamesNatalie and her friends played 3 games of bowling.
Let V = (8, -4) and W = (-4,2).
Which of the following is true?
Check all that apply. (30 pts)
A. V x W = 40
B. The y-component of W is 2.
C. V = -2W
D. The x-component of V is 4.
The second value in a set of parenthesis is the y value, so B is true.
If you multiplied each value of W by -2, you would get the values for V, so C is also true.
The answer is B and C.
Answer:
Option B and C are correct.
Step-by-step explanation:
Given the vectors V = (8, -4) and W = (-4,2)
we have to check the following options.
Option A: V x W = 40
[tex]A\times B=\begin{vmatrix}i&j&k\\8&-4&0\\-4&2&0\end{vmatrix}=0i+0j+k(16-16)=0i+0j+0k[/tex]
Hence, not true
Option B: The y-component of W is 2
W = (-4,2)
x-component is -4
y-component is 2
Hence, true
Option C: V = -2W
W=(-4, 2)
V=-2(-4,2)=(8,-4)
which is true
Option D: The x-component of V is 4
V = (8,-4)
x-component is 8
y-component is -4
which is not true.
hence, the option B and C are correct.
A suspension cable is attached to a bridge at both ends 70 feet above the bridge deck. The suspension cable reaches its lowest point at a horizontal distance of 140 feet.
Which graph represents the situation?
Answer:
graph D
Step-by-step explanation:
You want to choose the graph with a y-intercept of 70 and an x-intercept of 140. Graph D matches that.
___
Comment on graph D
The horizontal scale is a bit weird in that the numbers don't correspond to hash marks on the horizontal axis. The hash mark between the numbers 120 and 160 will correspond to a distance of 140 ft. That is where the graph touches the horizontal axis, so that is one indication it is the graph you want.
The sum of two numbers is 69. The larger number is three less than twice the smaller number. Find the numbers.
Answer:
x = 45, y = 24.
Step-by-step explanation:
If the 2 numbers are x and y:
x + y = 69...........(1)
x = 2y - 3
x - 2y = -3...........(2)
Subtract: (1) - (2):
x - x + y - (-2y) = 69 - (-3)
y + 2y = 72
3y = 72
y = 24.
From equation 1:-
x + 24 = 69
x = 45.
The numbers are x = 24 and y = 45 respectively.
What is algebraic expression?An algebraic expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -
2x + 3y + 5
2z + y
x + 3y
Given is that the sum of two numbers is 69. The larger number is three less than twice the smaller number.
Assume that the numbers are {x} and {y}. So, we can write the equations as -
x + y = 69
y = 2x - 3
Rewriting equation {1}, we get -
x + y = 69
x + 2x - 3 = 69
3x = 72
x = 24
and
y = 2 x 24 - 3
y = 45
Therefore, the numbers are x = 24 and y = 45 respectively.
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Ellen,Lora, and Mai are avid collectors of ice hockey trading cards. Together Lora and Ellen have 371 cards. If lora and Mai combined their cards, they would total 481. The sum of Ellen's and Mai's cards is 404. Each girl wants to store her cards in an album with protectice pages that each have 9 pockets. The pages come in packets of 10 at .20 cents per page, or packets of 100 at .15 cents per page. The girls decided to pool their money to buy them. Which will cost the girls less money- buying their pages in packets of 10, or packets of 100?
Answer:
buying in packets of 100
Step-by-step explanation:
Adding the given numbers results in a total that is twice the total number of cards the girls have. That total is 1256, so the total of the girls card collections is 628 cards.
Mai has 628 -371 = 257 cards, so will need ceiling(257/9) = 29 pages
Ellen has 628 -481 = 147 cards, so will need ceiling(147/9) = 17 pages
Lora has 628 -404 = 224 cards, so will need ceiling(224/9) = 25 pages
Together, the girls need 29 +17 +25 = 71 pages.
If they were to buy packets of 10, they would need 8 packets, or 80 pages at 0.20 per page, for a cost of $16.00.
If they were to buy packets of 100, they would need 1 packet, or 100 pages at 0.15 per page, for a cost of $15.00.
Buying their pages in packets of 100 will cost the girls less.
First, we figure out how many cards each girl has, then determine how many pages they need in total. Comparing the costs, it is clear that it would cost less for the girls to buy the packets of 100 pages.
Explanation:To answer this question, the first step is to find out how many cards each girl has. From the question, we understand that Ellen and Lora together have 371 cards and Lora and Mai together have 481 cards. The sum of Ellen's and Mai's cards totals to 404. By using these equations, we can determine that Lora has 227 cards, Ellen has 144 cards, and Mai has 254 cards.
Next, we need to find out how many pages each girl needs. Since each page has 9 pockets, Lora needs 26 pages (227 divided by 9, rounded up), Ellen requires 16 pages and Mai requires 29 pages. Altogether, they need 71 pages.
Now, let's get to the cost. At .20 cents per page, packets of 10 would cost $2, and they need 8 packets, which totals to $16. Alternatively, a packet of 100 costs .15 cents per page, which equals to $15.
Therefore, buying pages in packets of 100 will save the girls money as compared to buying in smaller packs of 10.
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What is the explicit formula for this sequence? -5,-3,-1,1,3
Answer:
b
Step-by-step explanation:
100%
The explicit formula for the sequence -5, -3, -1, 1, 3 is a_n = -5 + (n - 1)2.
What is an arithmetic sequence?Each term of an arithmetic sequence can be found using the formula:
a_n = a + (n-1)d
Where a is the first term,n is the position of the term,a_n is the nth term of the sequence,d is the common difference of the sequence.We can find the explicit formula for this sequence as follows:
The given sequence is 5, -3, -1, 1, 3.
From this, we can see that the value of:
a = -5
d = -3 - (-5) = -3 + 5 = 2
∴ The explicit formula can be written as:
a_n = -5 + (n - 1)2
Therefore we have found the explicit formula for the sequence -5, -3, -1, 1, 3 as a_n = -5 + (n - 1)2.
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Please help fast it would mean a lot please
whats the question? ill help you out i just wanna Answer the right question
what type of function can approach zero as x decreases without end?
A. linear. B. quadratic
C. exponential. D. Constant
Answer: c. Exponential
in a right triangle with the hypotenuse c and the legs a and b, c^2=2ab. find the measure of each acute angle.
We know that, usually,
[tex] c^2 = a^2+b^2 [/tex]
In this case, we also know that
[tex] c^2 = 2ab [/tex]
We deduce that
[tex] a^2+b^2 = 2ab [/tex]
If we subtract 2ab from both sides, we get
[tex] a^2-2ab+b^2 = 0 \iff (a-b)^2 = 0 \iff a=b [/tex]
So, the triangle is an isosceles right triangle, and so the angles are 90-45-45
What is the area????
Answer:
49.1 cm^2
Step-by-step explanation:
The appropriate area formula is ...
area = (1/2)(side 1)(side 2)(sin(angle between))
= (1/2)(10 cm)(12 cm)·sin(55°) = 60·sin(55°) cm^2
area ≈ 49.1 cm^2
Cameron’s bacteria population is modeled by an equation. Deon models his bacteria population with a graph. Cameron says that on day 14 , she will have more bacteria than Deon.
Is she right? Why or why not?
Answer:
The answer is ⇒ No, because Deon starts with less bacteria,
but it grows at a faster rat than Cameron's bacteria
Step-by-step explanation:
* Lets study the graph and the equation
- At t = 0
# Cameron's population = 200
# Deon population = 100
- At t = 5
# From the equation b(5) = 200(1 + 0.08)^5 ≅ 294
# From the graph b(5) ≅ 200
∴ Cameron's population > Deon's population
- The increase of the Cameron's population ≅ 94
(294 - 200 = 94)
- The increase of the Deon's population ≅ 100
(200 - 100 = 100)
∴ The rat of increase of Deon > The rat of increase of Cameron
- At t = 8
# From the equation b(8) = 200(1 + 0.08)^8 ≅ 370
# From the graph b(8) ≅ 300
∴ Cameron's population > Deon's population
- The increase of the Cameron's population ≅ 76
(370 - 294 = 76)
- The increase of the Deon's population ≅ 100
(300 - 200 = 100)
∴ The rat of increase of Deon > The rat of increase of Cameron
- At t = 11
# From the equation b(11) = 200(1 + 0.08)^11 ≅ 466
# From the graph b(11) ≅ 500
∴ Cameron's population < Deon's population
- The increase of the Cameron's population ≅ 96
(466 - 370 = 96)
- The increase of the Deon's population ≅ 200
(500 - 300 = 200)
∴ The rat of increase of Deon > The rat of increase of Cameron
- At t = 14
# From the equation b(14) = 200(1 + 0.08)^14 ≅ 587
# From the graph b(14) ≅ 700
∴ Cameron's population < Deon's population
- The increase of the Cameron's population ≅ 121
(587 - 466 = 121)
- The increase of the Deon's population ≅ 200
(700 - 500 = 200)
∴ The rat of increase of Deon > The rat of increase of Cameron
* From all these calculations the rate of increase of
Cameron's population is less than the rate of increase
of Deon's population
∴ Cameron is not right because Deon starts with less bacteria,
but it grows at a faster rat than Cameron's bacteria
Answer:
The answer is C
Step-by-step explanation:
A parallelogram has sides of length 30 centimeters and 18 centimeters. One of its angles measures 58 degrees. Which is the best estimate for the area of the parallelogram?
F 274.8 CM squared
G 286.2 CM squared
H 457.9 CM squared
J 540.0 CM squared
Answer:
option H
457.9 CM squared
Step-by-step explanation:
Given that,
base of parallelogram = 30 cm
side of parallelogram = 18 cm
one of the angle of parallelogram = 58°
Formula to calculate area of parallelogram is
area = base x heightTo calculate height we will use trigonometry identity
sinФ = opposite / hypotenusesin(58) = height / 18
height = 15.27
Area = 30 x 15.27
= 457.9 cm²
so the area of parallelogram is 457.9 cm²
Chris is having custom t-shirts printed for a family reunion. The total cost of custom t-shirts, y, in dollars, for x t-shirts is modeled by the following equation.
y = 11x + 25
Which statement is true?
A.
Each additional t-shirt being printed will increase the total cost by $25.
B.
Each additional t-shirt being printed will increase the total cost by 25%.
C.
Each additional t-shirt being printed will increase the total cost by $11.
D.
Each additional t-shirt being printed will increase the total cost by 11%.
Answer:
C. Each additional t-shirt being printed will increase the total cost by $11.
Step-by-step explanation:
We know that the total cost of custom t-shirts, y, in dollars, for x t-shirts is given by:
[tex]y = 11x + 25[/tex]
Here 11 is the price of the shirt, x is the number of shirts that are printed and 25 might be some additional charges.
For each additional shirt that is printed, the total price, y, will increase by $11 so the correct answer option is C.