The correct answers are Part 1: 7x + 12y 50, x,y 0; Part 2: 7; Part 3: 0: Part 4: 2 old and 3 new video games.
Step-by-step explanation:
Penny's parents gave her $50 to buy new video games.
Price of used games are $7 and new games are $12.
Let Penny buy x number of old video games and y number of new video games.
Part 1:
Total price she spent on buying the video games are 7x + 12y.
This amount should be less than or equal to the amount of money she possess. therefore 7x + 12y 50, x, y 0.
Part 2:
Maximum number of used game she can buy can be given when she spends all her money just on used games. Therefore y = 0. This implies x .
Thus the maximum number of used game she can buy is 7 where she does not buy any new game and has $1 left with her after the purchase.
Part 3:
Minimum number of new games that Penny can buy is zero. She can not buy any new games and spent all her money purchasing old games.
Part 4:
The possible combination in which she can purchase both the video games is 2 old games and 3 new games.
hope this helps
Angle bisectors AX and of triangle ABC meet at point I. Find angle C in degrees, if AIB = 109.
Answer:
angle C = 38 degrees
Step-by-step explanation:
Refer to attached figure (sorry, forgot to attach earlier)
Given
AIB = 109
Let
CAX = XAB = x
CBY = YBA = y
XIB = YIA = x+y ........exterior angles
XIB = YIA = 180-109 = 71 ............ sum of angles on a line
=>
x+y = 71
ACB = 180 - 2x -2y ................. sum of angles of a triangle
= 180 - 2(x+y)
= 180 - 2(71)
= 180 - 142
= 38
PLZ HURRY WILL MARK BRAINLIEST The stem and leaf plot shows the number of points a basketball team scored each game during its 15-game season. In how many games did the team score at least 70 points? 4 5 8 10
Answer:
5 games
Step-by-step explanation:
To find how many games the team scored at least 70 points, we need to look at the 7 on the stem side. The 7 means 70, and we add the digits on the leaf side. For example, 7 | 2 is 72. The numbers on the leaf side are: 1, 1, 2, and 3.
There are no points for the 8 on the stem side, but on 90, there is one digit on the leaf side: 1. So, the points they scored over 70 are 71, 71, 72, 73, and 91, which equals to five games.
Answer:
[tex]\boxed{\mathrm{5 \ games}}[/tex]
Step-by-step explanation:
At least 70 points makes it 70 and more. It should be at least 70 and at most anything above then 70.
So, In 5 games, the team scored at least 70. (71,71,72,73 and 91)
A triangle has side lengths of 13, 9, and 5. Is the triangle a right triangle? Explain.
Use complete sentences in your explanation.
Hint: Pythagorean Theorem: a^2+ b^2 = c^2
Answer:
see below
Step-by-step explanation:
Using the Pythagorean Theorem:
a^2+ b^2 = c^2
5^2+ 9^2 = 13^2
25+81 = 169
106 = 169
This is not true so it is not a right triangle
Answer:
[tex]\boxed{\sf Not \ a \ right \ triangle}[/tex]
Step-by-step explanation:
Apply Pythagorean theorem to check if the triangle is a right triangle.
[tex]a^2+ b^2 = c^2[/tex]
[tex]5^2+ 9^2 = 13^2[/tex]
[tex]25+81=169[/tex]
[tex]106=109[/tex]
False statement.
The triangle is not a right triangle.
How much of a radioactive kind of sodium will be left after 9 years if you start with 96 grams and the half-life is 3 years?
Answer:
9 years = 12 grams
Step-by-step explanation:
0 years = 96 grams
After 3 years , the amount left is 1/2 of what you started with
3 years = 1/2 *96 = 48 grams
After 3 years , the amount left is 1/2
6 years = 1/2 (48) = 24 grams
After 3 years , the amount left is 1/2
9 years = 1/2 ( 24) = 12 grams
What is the height of the cone?
Answer:
it is the inches milimeters meters
Answer:
9 cmStep-by-step explanation:
Given,
Volume of cone ( v ) = 27 π
Radius ( r ) = 3 cm
Height of cone ( h ) = ?
Now, let's find the height of cone:
Volume of cone = [tex] \frac{\pi {r}^{2}h }{3} [/tex]
plug the values
[tex]27\pi = \frac{\pi \: {3}^{2} \: h \: }{3} [/tex]
Evaluate the power
[tex]27\pi = \frac{\pi \times 9 \times h}{3} [/tex]
Divide 9 by 3
[tex]27\pi = 3\pi \: h[/tex]
Divide both sides of the equation by 3π
[tex] \frac{27\pi}{3\pi} = \frac{3\pi \: h}{3\pi} [/tex]
Calculate
[tex]9 = h[/tex]
Swipe the sides of the equation
[tex]h = 9[/tex] cm
Hope this helps..
Best regards!!
C(t) = 2t^4 – 8t^3 +6t^2 Find the t-intercept?
Answer:
0
Step-by-step explanation:
The t-intercept here is what's khown as the x-intercept wich is given by C(t)=0
● C(t) = 2t^4-8t^3+6t^2
● 0 = 2t^4-8t^3+6t^2
Factor using t
● t(2t^3-8t^2+6t^1) = 0
Wich means that t=0
What property do rectangles and parallelograms always share?
4, 12, 36,what is 3 other remaining sequence
Answer:
108, 324, 972
Step-by-step explanation:
This sequence is multiplying by ✖️3.
4✖️3=12✖️3=36✖️3=108✖️3=324✖️3=972
Hope this helps!
find the area under (sin x) bounded by x= 0 and x = 2π and x-axis
You probably want the unsigned area, which means you don't compute the integral
[tex]\displaystyle\int_0^{2\pi}\sin x\,\mathrm dx[/tex]
but rather, the integral of the absolute value,
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx[/tex]
[tex]\sin x[/tex] is positive when [tex]0<x<\pi[/tex] and negative when [tex]\pi<x<2\pi[/tex], so
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\int_0^\pi\sin x\,\mathrm dx-\int_\pi^{2\pi}\sin x\,\mathrm dx[/tex]
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=(-\cos x)\bigg|_0^\pi-(-\cos x)\bigg|_\pi^{2\pi}[/tex]
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\boxed{4}[/tex]
A population consists of 8 items. The number of different simple random samples of size 3 that can be selected from this population is
Answer:
The correct answer will be "56".
Step-by-step explanation:
Use a combination of 8 things taken 3 at a time :
⇒ [tex]8_{C_{3}}[/tex]
⇒ [tex]\frac{8!}{(3!(8 - 3)!)}[/tex]
⇒ [tex]\frac{8!}{(3!5!)}[/tex]
⇒ [tex]\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{3\times 2\times 1}[/tex]
⇒ [tex]8\times 7[/tex]
⇒ [tex]56[/tex]
Using the principle of combination, the number of different random samples of size 3 that can be selected is 56.
Using the principle of combination :
nCr = [n! ÷ (n-r)! r!]Hence, we have ;
8C3 = [8! ÷ (8 - 3)! 3!]
8C3 = [8! ÷ 5!3!]
8C3 = (8 × 7 × 6) ÷ (3 × 2 × 1)
8C3 = 8 × 7
8C3 = 56
Hence, there are 56 different possible samples.
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Which is steeper: a road with a 12% grade or a road with a pitch of 1 in 8?
Answer:
A road with a pitch of 1 in 8 is steeper.
Step-by-step explanation:
Let us convert these to the same units so that we can better compare them.
[tex]\frac{1}{8} = 0.125[/tex]
0.125=12.5 %
As 12.5% is greater than 12%, the road with a pitch of 1 in 8 will be steeper.
Which inequality is equivalent to this one y-8_<-2
Answer:
[tex]\boxed{y\leq 6}[/tex]
Step-by-step explanation:
[tex]y-8 \leq -2[/tex]
Adding 2 to both sides
[tex]y \leq -2+8[/tex]
[tex]y \leq 6[/tex]
Mariam went to a shop and bought 8 snickers, 3 galaxy and 3 kitkat. She payed 8 BD
totally. Her friend Zainab bought 4 snicker, 9 galaxy and 4 kitkat. She payed 10.9BD.
Is it possible to know the cost of each chocolate mathematically?
If yes how. If not why?
Answer:
Yes
Step-by-step explanation:
Let s be the price of snickers, g the price of galaxy and k the price of kitkat.
●For Mariam the equation will be:
8 s + 3 g + 3k = 8
●For Zainab the equation will be:
4 s + 9 g + 4 k = 10.9
Take the first equation and divide both sides by 4 to make it easier.
You get:
● 2s + 0.75 g + 0.75k = 2
Take the second equation and divide both sides by 2 to make easier.
You get:
● 2s + 4.5g + 2k = 5.45
The new system of equation is:
● 2s +0.75g + 0.75k = 2
● 2s + 4.5g + 2k = 5.45
Express s in the first equation using the other variables.
● 2s +0.75g +0.75k = 2
● 2s + 0.75(g+k) = 2
● 2s = 2-0.75(g+k)
● s = 1- 0.325 (g+k)
Replace s by the new expression in the second equation:
●2 [1-0.325(g+k)] +4.5 g +2k = 5.45
●2-0.75(g+k) +4.5g + 2k = 5.45
●2- 0.75g -0.75k +4.5 g +2k = 5.45
●2+ 3.75g + 1.25k = 5.45
● 3.75g +1.25k = 3.45
We have eliminated one variable (s)
We will keep (3.75g+1.25k=3.45) and use it.
Now that we eliminated in the second equation do it again in the first one.
You will get a system of equations with two variables.
Solve it and replace g and k with the solutions.
Finally solve the equation and find s.
In a study of the gasoline mileage of model year 2017 automobiles, the mean miles per gallon was 27.5 and the median was 26.8. The smallest value in the study was 12.70 miles per gallon, and the largest was 50.20. The first and third quartiles were 17.95 and 35.45 miles per gallon, respectively. Determine the type of skewness.
Answer:
This is skewed torwards the right. Or in other words positively skewed distribution.
Step-by-step explanation:
All of the values are fairly close together torwards the lower range. While 50.20 is more of an outlier, so this graph would gradualy skew to the right.
1
?
x + 5and
Which line is parallel to the line y =
passes through the point (-2, 1)?
x+
O y=x+3
1
y =
+2
1
y =
4
*-
oy-
1
-X
y=-2
Answer:
second option
Step-by-step explanation:
Parallel lines have the same slope, and since the slope of the given line is 1/2, we know the slope of the answer will be 1/2, which eliminates the first and last options. We know the slope and a point that belongs to the line, (-2, 1), so we can use point-slope formula to derive the equation of the line.
y - 1 = 1/2(x + 2)
y - 1 = 1/2x + 1
y = 1/2x + 2
find the maximal area of a right triangle with hypotenuse of length 8
Answer:
Max area is 16
Step-by-step explanation:
If A² + B² = C², then A² + B² = 64. The largest triangle area is when both A² and B² are equal to 32, so 32 + 32 = 64.
So equal side of the triangle is √32 or about 5.6568. The area of the triangle is then 1/2(5.6568 × 5.6568) or 16.
The maximal area of a right triangle is 90.496
What is differentiation?Derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
Given:
let the perpendicular be 'x'
and base be 'y'
Using Pythagoras theorem
x² + y² = 8²
x² + y² = 64
y²= 64- x²
y = √64-x²
Now, Area of triangle
= 1/2* base* height
=xy/2
=x *√64-x²*1/2
On differentiating both side
A' = 64-2x²/√64-x²*1/2
Setting derivative function equal to zero,
64= 2x²
32=x²
x=5.656
So, Area of triangle = x *√64-x²*1/2
= 90.496
Learn more about differentiation here:
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Evaluate f(x) when x= 9
f(x) = {6x² +2 if 6
112 if 9
No solution
O 110
O 12
56
Answer:
[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]
[tex] f(x) = 12 , 9 \leq x <13[/tex]
And we want to evaluate f(x=9)
And for this case the answer would be:
[tex] f(9)= 12[/tex]
Best answer:
O 12
Step-by-step explanation:
For this problem we have the following function given:
[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]
[tex] f(x) = 12 , 9 \leq x <13[/tex]
And we want to evaluate f(x=9)
And for this case the answer would be:
[tex] f(9)= 12[/tex]
Best answer:
O 12
On August 21, 2009, the World Health Organization announced its prediction that the number of new cases of H1N1 (swine flu) virus would double every 4 days for several months. As of July 27, 2009, the number of new cases was 15,784. Determine the instantaneous growth rate for the virus (rounded to the nearest ten-thousandths).
Answer:
growth rate = 0.1733 per day, or 17.33% per day
Step-by-step explanation:
Since the doubling time is 4 days, the growth factor over a period of t days is ...
2^(t/4)
Then the growth factor for 1 day is
2^(1/4) ≈ 1.189207
The instantaneous growth rate is the natural log of this:
ln(1.189207) ≈ 0.1733 . . . per day
Use the formula A=2πrh to find the area of the curved surface of each of the cylinders below. (Express your answers correct to 1 decimal place.)
Answer:
here,
A=2×22÷7×17/2×21
A=22×17×3
A=1122 sq.cm
40.) Decompose 7/8 into the sum of unit fractions.
Answer:
7/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8
7/8 = 1/8 + 6/8
7/8 = 4/8 + 3/8
7/8 = 5/8 + 2/8
Step-by-step explanation:
Hope it helps!
The fraction 7/8 can be written as the sum of unit fraction i.e;
1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8.
What is unit fraction?A unit fraction can be defined as a fraction whose numerator is 1.
Given fraction 7/8
can be written as the sum of the unit fraction i.e;
7/8=1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8
Hence,7/8 can be decomposed into sum of unit fraction as
1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8.
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Find the probability of each event. A class has five boys and nine girls. If the teacher randomly picks six students, what is the probability that he will pick exactly four girls?
Answer: [tex]\dfrac{60}{143}[/tex]
Step-by-step explanation:
Given, A class has five boys and nine girls.
Total students = 5+9=14
Number of ways to choose 6 students out of 14= [tex]^{14}C_6[/tex] [Using combinations]
Number of ways to choose 4 girls out of 6 (4 girls + 2 boys = 6 ) = [tex]^{9}C_4\times\ ^{5}C_2[/tex]
If the teacher randomly picks six students, then the probability that he will pick exactly four girls:-
[tex]\dfrac{^{9}C_4\times \ ^{5}C_2}{^{14}C_6}[/tex]
[tex]=\dfrac{\dfrac{9!}{4!5!}\times\dfrac{5!}{2!3!}}{\dfrac{14!}{6!8!}}\\\\=\dfrac{1260}{3003}\\\\=\dfrac{60}{143}[/tex]
hence, the required probability = [tex]\dfrac{60}{143}[/tex] .
Diners frequently add a 15% tip when charging a meal to a credit card. What is the price of the meal without the tip if the amount charged is $
Question:
Diners frequently add a 15% tip when charging a meal to a credit card. What is the price of the meal without the tip if the amount charged is $20.70? How much was the tip?
Answer:
Price of meal = $18
Tip price = $2.70
Step-by-step explanation:
Let the price of the meal be y;
Let the tip be t
From the question;
15% of y is the tip charge (t). i.e
t = 15%y
=> t = 0.15y --------(i)
The total amount charged is $20.70 (This means that the sum of the price of the meal and the tip is $20.70)
=> y + t = 20.70 [substitute the value of t=0.15y from equation (i)]
=> y + 0.15y = 20.70
=> 1.15y = 20.70
=> y = [tex]\frac{20.70}{1.15}[/tex]
=> y = $18
Therefore the price of the meal, y, is $18.
From equation (i),
t = 0.15y [substitute the value of y = $18]
t = 0.15(18)
t = $2.70
Therefore the tip was $2.70
Find the 10th term of the following geometric sequence.
2, 10, 50, 250, ...
Answer:
3906250
Step-by-step explanation:
We can notice that the ratio is 5. 10/2 = 5
Each term gets multiplied by 5 to get the next term.
250 × 5 = 1250 (5th term)
1250 × 5 = 6250 (6th term)
6250 × 5 = 31250 (7th term)
31250 × 5 = 156250 (8th term)
156250 × 5 = 781250 (9th term)
781250 × 5 = 3906250 (10th term)
The 10th term of the geometric sequence is 3906250.
Digital music distribution provides an opportunity for everyone to get their music heard. In order to get on a service like iTunes, one needs to pay for distribution through a service like Tunecore or CD Baby. These services make sure that your music is heard in the different platforms. Suppose the distributor charges the artist a $50.00 cost for distribution, and the streaming services pays $4.00 per one thousand streams. Model the profit for the total number of streams by answering the questions below: Use the cost for distribution to build your y-intercept. What is the y-intercept? Hint: the y-intercept is a point on the y axis, so your answer should be an ordered pair. Hint: you have to keep in mind that any time you pay for something, you are SPENDING money, if your y-intercept is incorrect, all your numbers will be off Use the payment per thousand streams to build your slope. What is the slope? Use the slope-intercept format (y = mx + b) to give the equation of the line. What is the equation of this line? Graph the line by adjusting the sliders below. Show your line by attaching an image below. After how many streams will you pay for the distributor charges? (hint: this is where the line crosses the x-axis, round to the nearest thousand) How many streams would it take to profit $300,000? Challenge Question: In 2019, Old Town Road became one of the most streamed songs of all time passing the previous record holders, Despacito and One Sweet Day. The second week the song was #1, it set an all time streaming record. It was streamed 143 million times (143,000,000) in the US, nearly 30 million higher than the previous record holder Drake, In My Feelings. Calculate the profit earned using these numbers. (Hint: use the slope intercept format to build this equation).
Answer:
the answer is 1.00
Step-by-step explanation:
pls mark me as the brainliest and tell me thanks
A cubical container measures 9 ft on each edge. What does it cost to fill the container at $2.58 per cubic ft?
Answer:
1,880.82
Step-by-step explanation:
Please answer this correctly without making mistakes
What is the correct answer
How far apart are the locksmith and the hotel?
The correct answer is 45.5 km
Explanation:
The total distance from the locksmith to the hotel, located in the east of the graph is not directly given; however, this distance can be calculated by considering the partial distances given. This includes the distance from the locksmith to the furniture store (18.3 km), and the distance between the furniture and the hotel (27.2) as the total distance = distance from the locksmith to the furniture store + distance from the furniture store to the hotel. Thus, the total distance is 18.3 km + 27.2 km which is equal to 45.5 km.
2. Salvador has 10 cards, each with one number on
it. The numbers are 2, 3, 4,5,5,7,7,7,7,7.
Salvador is going to make a row containing all 10
cards. How many ways can he order the row?
Answer:
15,120 number of ways.Step-by-step explanation:
This is a permutation problem. Given the 10 cards with numbers 2, 3, 4,5,5,7,7,7,7,7 on it, if Salvador is going to make a row call, the number of ways he can order a row is as shown below;
Total number of cards = 10!
number of times the digit 5 was repeated = 2times
number of times the digit 7 was repeated = 5times
The number of ways he can make a row call = 10!/2!5!
= 10*9*8*7*6*5!/2*5!
= 10*9*8*7*6/2
= 10*9*8*7*3
= 15,120 different ways
Hence, the number of ways he can order the row is 15,120 number of ways.
find the coordinates of the vertices of the triangle after a reflection across the line y = -1 and then across the line x = -2
Answer: A) N'=(-2, 2) M'=(-1, 0) L'=(-5, -2)
Step-by-step explanation:
N = (-2, -4) M = (-3, -2) L = (1, 0)
Reflection over y = -1
N' = (-2, 2) M' = (-3, 0) L' = (1, -2)
Reflection over x = -2
N'' = (-2, 2) M'' = (-1, 0) L'' = (-5, -2)
Which input value produces the same output value for the two functions on the graph?
Answer:
x=3
Step-by-step explanation:
To solve this problem, we should check the x coordinate of the point where both graphs intersect. Based on both graphs, they intersect at the point (3,-1). So, the input value for which both graphs have the same value is x=3.
Answer:
its x=-2
Step-by-step explanation:
cause i got it wrong and it said the answer was x=-2
I NEED HELP ASAP!!!!!!! Find 2 numbers that multiply to make -24 and add to make -10
Answer:
Step-by-step explanation:
-8*3= -24+14=-10
Answer:
-12 and 2.
Step-by-step explanation:
-12*2= -24,
-12+2=-10