No it is not necessary that Kelvin will get one head and one tail every time
Explanation:
Probability in math is equal to favorable outcomes/total outcomes
The coin has two sides a head and a tail. When we flip a coin we have 50-50 possibility of getting a head and a tail. It means with every toss we have 1/2 possibility of getting head as well as tail.
But this does not mean that when we toss a coin twice we will get one head at one toss and one tail at another toss.
There is a possibility of getting both heads as well as both the tails.
how to factor 15x-7x-2
Melissa is saving $25 that she earned for washing her mom’s car. She earns $10 every week for doing chores, which she also saves. Which function can be used to find t, the amount of money Melissa will have saved at the end of n weeks of doing chores?
Answer:
t = 10n + 25
Step-by-step explanation:
At the end of n weeks, the total amount that Melissa would have can be found by the function, t = 25 + 10n.
Melissa made $25 from washing her mother's car and keeps it aside.
She then makes $10 every week. This means that in n number of weeks, the amount she would have made from chores is:
= Amount per week x number of weeks
= 10 x n
= 10n
The total she would then have in n weeks is:
= Amount saved from mother + Amount earned from chores in n weeks
= 25 + 10n
This total is t, so the total function is t = 25 + 10n.
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Which of the following is a solution to the inequality below?
10 − 12p > 41
A. p=12
B. p=7
C. p=11
D. p=-11
Answer:
The solution is D, -11.
Step-by-step explanation:
2 (r - 3) - 5(r + 2)
Answer:
-3r -16
Step-by-step explanation:
2 (r - 3) - 5(r + 2)
Distribute
2r-6 - 5r - 10
Combine like terms
-3r -16
Arnold took out a loan of 195,000 to purchase a home. At a 4.3% interest rate compounded annually, how much total will they have paid after 30 years?
Answer:
25155000
Step-by-step explanation:
we know intrest (i):-PTR/100by formula
195000×30×4.3%100
2. 5850000×4.3
100
100
3. 25155000
Arnold will have to pay $689546.98 after 30 years of taking out a loan.
What is compound interest?The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.
The given problem is the case of compound interest.
The values for different parameters are as follows,
P = 195000
r = 4.3%
And t = 30 years
Now, substitute all the corresponding values in the expression for amount given below as,
A = P(1 + r/100)ⁿ
= 195000(1 + 4.3/100)³⁰
= 689546.98
Hence, the total amount to be paid after 30 years is given as $689546.98.
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Find the sum of the first 25 terms in this geometric series:
8 + 6 + 4.5...
Step-by-step explanation:
Given the geometric sequence
8 + 6 + 4.5...
A geometric sequence has a constant ratio and is defined by
[tex]a_n=a_1\cdot r^{n-1}[/tex]
[tex]\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}[/tex]
[tex]\frac{6}{8}=\frac{3}{4},\:\quad \frac{4.5}{6}=\frac{3}{4}[/tex]
[tex]\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}[/tex]
[tex]r=\frac{3}{4}[/tex]
[tex]\mathrm{The\:first\:element\:of\:the\:sequence\:is}[/tex]
[tex]a_1=8[/tex]
[tex]\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:[/tex]
[tex]a_n=8\left(\frac{3}{4}\right)^{n-1}[/tex]
[tex]\mathrm{Geometric\:sequence\:sum\:formula:}[/tex]
[tex]a_1\frac{1-r^n}{1-r}[/tex]
[tex]\mathrm{Plug\:in\:the\:values:}[/tex]
[tex]n=25,\:\spacea_1=8,\:\spacer=\frac{3}{4}[/tex]
[tex]=8\cdot \frac{1-\left(\frac{3}{4}\right)^{25}}{1-\frac{3}{4}}[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}[/tex]
[tex]=\frac{\left(1-\left(\frac{3}{4}\right)^{25}\right)\cdot \:8}{1-\frac{3}{4}}[/tex]
[tex]=\frac{8\left(-\left(\frac{3}{4}\right)^{25}+1\right)}{\frac{1}{4}}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}[/tex]
[tex]=\frac{8\left(-\frac{3^{25}}{4^{25}}+1\right)}{\frac{1}{4}}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{\frac{b}{c}}=\frac{a\cdot \:c}{b}[/tex]
[tex]=\frac{\left(1-\frac{3^{25}}{4^{25}}\right)\cdot \:8\cdot \:4}{1}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:8\cdot \:4=32[/tex]
[tex]=\frac{32\left(-\frac{3^{25}}{4^{25}}+1\right)}{1}[/tex]
[tex]=\frac{32\cdot \frac{4^{25}-3^{25}}{4^{25}}}{1}[/tex] ∵ [tex]\mathrm{Join}\:1-\frac{3^{25}}{4^{25}}:\quad \frac{4^{25}-3^{25}}{4^{25}}[/tex]
[tex]=32\cdot \frac{4^{25}-3^{25}}{4^{25}}[/tex]
[tex]=\frac{\left(4^{25}-3^{25}\right)\cdot \:32}{4^{25}}[/tex]
[tex]=\frac{2^5\left(4^{25}-3^{25}\right)}{2^{50}}[/tex] ∵ [tex]\mathrm{Factor}\:32:\ 2^5[/tex], [tex]\mathrm{Factor}\:4^{25}:\ 2^{50}[/tex]
so
[tex]=\frac{4^{25}-3^{25}}{2^{45}}[/tex] ∵ [tex]\mathrm{Cancel\:}\frac{\left(4^{25}-3^{25}\right)\cdot \:2^5}{2^{50}}:\quad \frac{4^{25}-3^{25}}{2^{45}}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a\pm \:b}{c}=\frac{a}{c}\pm \frac{b}{c}[/tex]
[tex]=\frac{4^{25}}{2^{45}}-\frac{3^{25}}{2^{45}}[/tex]
[tex]=32-\frac{3^{25}}{2^{45}}[/tex] ∵ [tex]\frac{4^{25}}{2^{45}}=32[/tex]
[tex]=32-0.024[/tex] ∵ [tex]\frac{3^{25}}{2^{45}}=0.024[/tex]
[tex]=31.98[/tex]
Therefore, the sum of the first 25 terms in this geometric series: 31.98
To find the maximum amount of water it takes to fill a rectangular fish tank, you need to know the
A.volume of the fish tank.
B.surface area of the fish tank.
C.area of the bottom of the fish tank.
D.perimeter of the bottom of the fish tank.
Answer:
answer is a
Step-by-step explanation:
the volume is everything on the inside of the tank
surface area would only be the amount of water it take of cover one side
area would just be the size of the glass on bottom
the perimeter would just be the length of all four edges of each side of the fish tank
For the maximum amount of water it takes to fill a rectangular fish tank, we need to know the volume of the fish tank.
Option A is the correct answer.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
The volume of any container gives us the maximum amount the container can hold.
Now,
For the maximum amount of water it takes to fill a rectangular fish tank, we need to know the volume of the fish tank.
Thus,
The volume of the fish tank gives us the maximum amount it can hold.
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You have a $500 public relations budget for the current year. You would like to generate publicity by publishing several ads in the local township newspaper about your store's sponsorship of community activities. The newspaper normally charges $75 per ad but will give you a 20% discount since your message is community service-oriented. How many ads can you buy?
Answer:
8 ads
Step-by-step explanation:
To start off, we know we have a budget of $500 which means we cannot go above that amount. Ads cost $75 each but in our case they are now 20% cheaper. Lets figure out the new price of the ads. Remember to change 20% into its decimal form (20% -> 0.2)
75 x 0.2 = 15
Now we subtract 15 from 75 to get our new ad price.
75 - 15 = 60
Now to figure out how many ads we can get with a budget of $500, we simply divide 500 by 60. Don't forget to round the answer to the nearest whole number since we cannot go over our budget.
500 / 60 = 8 ads
At Keller's Bike Rentals, it costs $22 to rent a bike for 4 hours. How many hours of bike use does a customer get per dollar?
Answer:
$5.5 per hour
Step-by-step explanation:
You divide the cost by the number of hours
Answer:
About 10 minutes, which is 1/6 of an hour.
Step-by-step explanation:
- What is the slope from the points (2, 3) and (-3,-1) *
Answer:
4/5
Step-by-step explanation:
To find the slope given two points
m = (y2-y1)/(x2-x1)
= (-1 -3)/(-3 -2)
=-4/-5
= 4/5
We can use the points (2,3) and (-3,-1) to solve.
Slope formula: y2-y1/x2-x1
= -1-3/-3-2
= -4/-5
= 4/5
Best of Luck!
A rectangle is 8 feet long and 9 feet wide. What is its perimeter?
Answer:
34 feet
Step-by-step explanation:
(Length + Width) x 2
Answer:
It would be 34
Step-by-step explanation:
You would add up the sides by doing 8+8+9+9 or (8x2)+(9x2)
perform the operation (-3-2i)-(3+i)
Answer:
- 6 - 3i
Step-by-step explanation:
Given
(- 3 - 2i) - (3 + i) ← distribute both parenthesis
= - 3 - 2i - 3 - i ← collect like terms
= - 6 - 3i
Which two angles are supplementary?
There are only two angle measures here, an angle, a bunch of congruent copies, and its supplement, with a bunch of congruent copies.
∠1 ≅ ∠3 ≅ ∠5 ≅ ∠7 are all supplementary to ∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8
What is the area of this trapezoid?
Enter your answer in the box.
units2
Answer:
153 units squared
Step-by-step explanation:
A= 1/2 (b1 + b2)h
A= 1/2 (10+24)9
A= 1/2 (34)9
A= 1/2 306
A= 153
Answer:
Step-by-step explanation:
a = 7+10+7 = 24 units
b = 10 unit
h = 9
Area=(a + b)*h / 2
[tex]=\frac{(24+10)*9}{2}\\\\=\frac{34*9}{2}\\\\=17*9\\\\=153 unit^{2}[/tex]
At Pizza Pi, 64% of the pizzas made last week had extra cheese. If 16 pizzas had extra cheese, how many pizzas in all were made last week?
Answer:
There were 25 pizzas made last week.
Step-by-step explanation:
It is given that 64% of the pizzas had extra cheese and 16 pizzas had extra cheese. So it means that 64% is equals to 16 pizzas. In order to find how many pizzas were made, you have to find the remaining percentage of pizzas without extra cheese by subtracting 64% from 100% :
100 - 64 = 36 % of pizzas without extra cheese
64 % = 16 pizzas
1 % = 1/4 pizza
36 % = 9 pizzas
We have found out that 9 pizzas were made without extra cheese. The total pizzas were made last week is 25 pizzas (including extra cheese and no extra cheese) :
Total = Extra Cheese + No extra cheese
= 16 + 9
= 25 pizzas
When renting a limo for prom, the number of people varies inversely with the cost per person. Originally there were 12 people and the cost per person was $20. If the number of people changed to 6, what would be the new cost per person?
Answer:
40
Step-by-step explanation:
On a coordinate plane, the x-axis is labeled Side length and the y-axis is labeled Perimeter or area. A line representing the perimeter goes through points (0, 0), (1, 4), (2, 8), (3, 12). A curved line representing the area goes through points (0, 0), (2, 4), (3, 9), and (4, 16).
Andrew wants to build a square garden, and needs to determine how much area he has for planting. The perimeter of the garden is between 12 and 14 feet. What is the range of the possible areas?
3 ft2 and 4 ft2
9 ft2 and 12.25 ft2
12.25 ft2 and 14 ft2
14 ft2 and 16 ft2
Answer: 9ft² and 12.25ft²
Step-by-step explanation:
The range of the possible areas will be 9 square feet and 12.25 square feet. Then the correct option is B.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space.
On a coordinate plane, the x-axis is labeled Side length and the y-axis is labeled Perimeter or area.
A line representing the perimeter goes through points (0, 0), (1, 4), (2, 8), (3, 12).
Then the equation of line will be
y = [(12 – 8) / (3 – 2)]x
y = 4x
A curved line representing the area goes through points (0, 0), (2, 4), (3, 9), and (4, 16).
y = x²
Andrew wants to build a square garden, and needs to determine how much area he has for planting.
The perimeter of the garden is between 12 and 14 feet.
Then the value of the side length corresponding to 12 and 14 will be
For y = 12, we have
12 = 4x
x = 3
Then the area will be
y = 3²
y = 9 square feet
For y = 14, we have
14= 4x
x = 3.5
Then the area will be
y = 3.5²
y = 12.25 square feet
Then the range of the possible areas will be 9 square feet and 12.25 square feet.
Then the correct option is B.
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Please help due at 11:45 I really do t understand please help!!!!
1. C. Exponential form. Exponential form is just taking one number and raising it to another number. Example: 2^3
2. H. Power is correct. A power is the upper number of an exponential.
3. G. Perfect square. Squaring a whole number represents the area of a square, which is where the term comes from.
4. J. Quotient. A quotient is a result of dividing two numbers.
5. D. Expression. An expression is anything that involves numbers and variables. Specifically using the order of operations on them or some kind of math function.
6. i. Product. A product is a result of multiplying two or more numbers or variables.
7. E. Factors. In this case, it shows 12 having the factors: 1, 2, 3, 4, 6, 12. Factors of 12 are numbers that pair up and multiply to get 12, so for instance 3*4 = 12.
8. A. Base. You are correct. Nice work. The base of an exponential expression is the lower number or variable.
9. B. Expanded form. This is showing it being fully factored as much as possible.
10. F. Perfect cube. A perfect cube is a number that results in taking any whole number and multiplying it by itself 3 times. Example: 7 cubed = 7^3 = 7*7*7 = 343
For the following equation, what are the solutions?
x^2+16=0
-
How many X-intercepts have quadratic functions with complex roots?
Answer:
x=√-16
Step-by-step explanation:
Since x^2+16=0
Substrate 16
X^2=-16
Square root of both sides
X=√-16
So therefore the final answer is
X=√-16
which statement explains the difference between the graph of f(x)=2x3 - 8x +3 and g(x)=x3 -4x
Answer:
what are the statements lol
Step-by-step explanation:
On circle O below, the measure of SV is 120°.
pes
What is the measure of VU?
1
N
1
chord it
3 of 4
ar
The measure of angle VU is 240°.
Given that arc SV has a measure of **120°** and angle STV is **82°**, we can find the measure of angle VU.
1. The central angle STV is equal to the measure of arc SV. Therefore, ∠STV = 120°.
2. The sum of angles around a point (360°) is equal to the sum of the central angle and the inscribed angle. So, ∠VU + ∠STV = 360°.
3. Solving for ∠VU:
- ∠VU + 120° = 360°
- ∠VU = 360° - 120°
- ∠VU = 240°
Therefore, the measure of angle VU is 240°.
What is the probability of picking an orange marble and flipping tails?
there are 7 marble, one of them is orange. and there is one coin next to them
a. 1/7
b. 8/14
c. 2/14
d. 1/14
Answer: D) 1/14
Work Shown:
There is 1 orange marble out of 7 total. The probability of picking an orange marble is 1/7. Let A = 1/7 which we'll use later.
The probability of flipping tails is 1/2 because 1 side is tails out of 2 sides total. Let B = 1/2
Multiply A and B
A*B = (1/7)*(1/2) = (1*1)/(7*2) = 1/14
This represents the probability of getting an orange marble and flipping tails.
We are able to multiply the probabilities because the two events (picking a marble and flipping a coin) are independent.
Answer:
The answer would 1/14 :)
Step-by-step explanation:
Solve simultaneous equation
X-2y=1
2x-y=2
Answer: x=1,y=0
Step-by-step explanation:
X-2y=1.....equation 1
2x-y=2.....equation 2
X=1+2y.......equation 3
Substitute equation 3into 2
2(1+2y)-y=2
2+4y-y=2
2+3y=2
3y=2-2
3y=0
Y=0/3
Y=0
Substitute for y=0 in equation 1
X-2y=1
X-2(0)=1
X-0=1
X=1
X=1 & Y=0
Answer:
x=1
y=0
Step-by-step explanation:
1) If 3 out 5 students play sports at school, how many students play
sports if there are 720 students?
Answer:
432
Step-by-step explanation:
Part C: YX = 24 meters and mYX = 120 degrees , then determine the radius of circle H.
Answer: The radius is 11.5 meters (to the nearest tenth)
Step-by-step explanation: The circle with center H has an arc TX that measures 24 meters, and also the angle subtended by YX equals 120°.
The length of an arc is given b the formula;
Length of arc = (∅/360) x 2πr
Where the length of the arc is 24 and ∅ is 120, the formula becomes;
24 = (120/360) x 2(3.14) r
24 = (1/3) x 6.28 r
By cross multiplication we now have,
(24 x 3)/6.28 = r
72/6.28 = r
11.4649 = r
r ≈ 11.5
Therefore, the radius is approximately 11.5 meters
A rectangle is dilated by a scale factor of n = 1. Which statement is true regarding the image of the dilation?
Answer:
The image will be congruent to the pre-image because n = 1.
Answer:
Awsner number 2
Step-by-step explanation:
Kayla wants to purchase some new clothes for the school year and has a budget of $200. The sales tax rate that will apply when she makes her purchases is 7%. Here are the items she wants to purchase:
2 T-shirts, $9.98 each
1 pair of pants, $25.99
3 dresses, $24.99 each
1 pair of shoes, $89.99
Kayla’s budget be enough to purchase all of the clothing items listed after sales tax is applied because the total will be .
Answer:
Kayla will not have enough because the total will be $225.67
Step-by-step explanation:
2 * 9.98 = 19.96
3 * 24.99 = 74.97
19.96 + 25.99 = 45.95
45.95 + 74.97 = 120.92
120.92 + 89.99 = 210.91
0.07 * 210.91 = 14.76
210.91 + 14.76 = 225.67
Kayla will not have enough because the total will be $225.67
Calculation of the total balance:Since there is a budget of $200. The sales tax rate is 7%
Also, the following items should be purchased
2 T-shirts, $9.98 each
1 pair of pants, $25.99
3 dresses, $24.99 each
1 pair of shoes, $89.99
So, the calculations should be
2 of 9.98 = 19.96
3 of 24.99 = 74.97
Now the total should be
19.96 + 25.99 = 45.95
45.95 + 74.97 = 120.92
120.92 + 89.99 = 210.91
0.07 of 210.91 = 14.76
And, finally
210.91 + 14.76 = 225.67
Therefore, Kayla will not have enough because the total will be $225.67
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What is the lateral surface area?
please help me if you can thank you :)
Answer:
lateral surface area means surface area of vertical walls.
there are 3 vertical walls and each is a rectangle.
hence
lateral surface area = 3 × area of one wall
= 3× ( 8×5 )
= 3 × 40
= 120 square units
Which of these equations have no solution? Check all that apply.
2(x + 2) + 2 = 2(x + 3) + 1
2x + 3(x + 5) = 5(x – 3)
4(x + 3) = x + 12
4 – (2x + 5) = (–4x – 2)
5(x + 4) – x = 4(x + 5) – 1
Answer: 2(x + 2) + 2 = 2(x + 3) + 1
Steps:
2x + 6 = 2x + 7
Subtract 6 from both sides
2x + 6 - 6 = 2x + 7 - 6
Simplify
2x = 2x + 1
Subtract 2x from both sides
2x - 2x = 2x + 1 - 2x
Simplify
0 = 1
The sides are not equal.
NO SOLUTION
Answer:
1, 2, and 5
Step-by-step explanation:
1. In a small town, there are 83 clinics serving the population of 24,742. Each clinic serves
about __________ of the town’s population.
a. 200 b. 250 c. 300
Answer:
each clinic serves about 300 people
Step-by-step explanation:
Population of 24742 is served by 83 clinics
Then each clinic will serve
24742/83 =298.157
≈ 300
Answer:
c. 300
Step-by-step explanation:
24,742/83
298.0963855
Approximately 300