Answer:
[550, 1250] miles ([minimum, maximum] miles)
700 miles (difference between minimum and maximum)
Step-by-step explanation:
"Range" has different meanings in different contexts with respect to a list of numbers and/or ordered pairs.
For a function, characterized by ordered pairs, the range is often specified by the interval between the minimum and the maximum. That is, the range of the function ...
(Jan, 914), (Feb, 740), (Mar, 815), (Apr, 550), (May, 815), (Jun, 1250), (Jul, 740)
can be specified either as the list of dependent variable values:
{550, 740, 815, 914, 1250}
or as the interval between the minimum and the maximum:
[550, 1250]
___
If you're plotting these values or creating a histogram, the "range" you're interested in is often the difference between the minimum and maximum:
1250 -550 = 700
The widths of bins of a histogram are defined by dividing this range into a suitable number of smaller intervals.
Ellen casts a 5.5 foot shadow. If Ellen is 4 feet 6 inches tall, and her brother is 6 foot tall, how long of a shadow does he cast at the same time of day?
A) 6 ft. 8 in.
B) 7 ft. 2 in.
C) 7 ft. 4 in.
D) 7 ft. 8 in.
Answer:
C) 7 ft 4 in
Step-by-step explanation:
Shadows are assumed to be proportional to the height of the object casting them. Hence the brother's shadow will satisfy ...
shadow/(6 ft) = (5.5 ft)/(4.5 ft) = 11/9 . . . . . reduce the fraction
shadow = (6 ft) · (11/9) . . . . . . . . . . . . . . . . . multiply by 6 ft
shadow = 7 1/3 ft = 7 ft 4 in
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.
Learn more about Quadratic Equations here:https://brainly.com/question/30098550
#SPJ3
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
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]
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.
Learn more about arithmetic sequence here: https://brainly.com/question/6561461
#SPJ2
There are six minutes of commercials for every 25 minutes with Olivia how many moves of commerce who are the one hour 36 minutes of television
Answer:
18 minutes 34.8 seconds
Step-by-step explanation:
We assume the minutes of commercials are proportional to the minutes of television, so we have ...
(6 minutes of commercials)/(6 + 25 minutes of television) = x/(96 minutes of television)
Multiplying by 96, we get ...
x = 96·6/31 = 576/31 = 18 18/31 . . . . minutes of commercials
That's about 18 minutes, 34.8 seconds of commercials in 1 hour 36 minutes of television.
The function a represents the cost of manufacturing product A, in hundreds of dollars, and the function b represents the cost of manufacturing product B, in hundreds of dollars.
a(t)=5t+2
b(t)=7t2-2t+4
Find the expression that describes the total cost of manufacturing both products, a(t) + b(t).
A. 7t2 + 7t - 6
B. 7t2 - 3t + 6
C. 7t2 - 7t + 2
D. 7t2 + 3t + 6
The answer is c)
Here’s why:
Answer: D. [tex] 7t^2+3+6[/tex]
Step-by-step explanation:
Given: The function 'a' represents the cost of manufacturing product A, in hundreds of dollars, and the function 'b' represents the cost of manufacturing product B, in hundreds of dollars.
[tex]a(t)=5t+2\\\\b(t)=7t^2-2t+4[/tex]
The expression that describes the total cost of manufacturing both products will be ,
[tex] a(t) + b(t)=5t+2+7t^2-2t+4[/tex]
Combining like terms, we get
[tex] a(t) + b(t)=7t^2+5t-2t+4+2\\\\\Rightarrow\ a(t) + b(t)=7t^2+3+6[/tex]
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.
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.
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.
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.
what type of function can approach zero as x decreases without end?
A. linear. B. quadratic
C. exponential. D. Constant
Answer: c. Exponential
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:
Answer the attached question
Answer:
x = 21Step-by-step explanation:
We have alternative external corners.
The lines m and n are parallel. That is why the alternative external angles are congruent (they have the same measure).
In the triangle RTS we have angles:
[tex]4x^o,\ 54^o,\ 2x^o[/tex]
We know: The sum of the angles of the triangle is equal to 180 °.
Therefore we have the equation:
[tex]4x+54+2x=180[/tex] subtract 54 from both sides
[tex]6x=126[/tex] divide both sides by 6
[tex]x=21[/tex]
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.
Does anyone u derived this
Answer:
B
Step-by-step explanation:
The question asks why you can use the argument that two angles are congruent. Hence, you want to have a statement that involves two angles in the two triangles. Only statement B is such a statement.
_____
Multiple choice questions often answer themselves, if you understand what you're reading.
Find the area of the shaded polygons:
I think the last one is maybe ten, maybe
Answer:
Step-by-step explanation:
no
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 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
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
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%
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ2
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.
Please help fast it would mean a lot please
whats the question? ill help you out i just wanna Answer the right question
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.
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
Emma needs to find the surface area of a triangular pyramid where the base and all three faces are congruent equilateral triangles.
What is the total surface area?
Answer:
73.19
Step-by-step explanation:
4 * (1/2)* (6.5) * (5.63)
A flower is 9 3/4 inches tall. In one week, it grew 1 1/8 inches. How tall is the flower at the end of the week? Write in simplest form
let's firstly convert the mixed fractions to improper fractions and then add them up.
[tex]\bf \stackrel{mixed}{9\frac{3}{4}}\implies \cfrac{9\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{39}{4}}~\hfill \stackrel{mixed}{1\frac{1}{8}}\implies \cfrac{1\cdot 8+1}{8}\implies \stackrel{improper}{\cfrac{9}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{39}{4}+\cfrac{9}{8}\implies \stackrel{\textit{using and LCD of 8}}{\cfrac{(2)39~~+~~(1)9}{8}}\implies \cfrac{78+9}{8}\implies \cfrac{87}{8}\implies 10\frac{7}{8}[/tex]
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
Read more on federal tax rate;
https://brainly.com/question/1775528
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.
What is 503 subtract 345
Answer:
158
Step-by-step explanation:
Hey there!
503 - 345 = 158
Therefore, the answer is 158
Hope this helps you!
God bless ❤️
xXxGolferGirlxXx
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.
Learn more about Cost comparison here:https://brainly.com/question/33292944
#SPJ2