Answer:
1. Juan's marathon training schedule is an example of a geometric sequence
2. Lizzy's marathon training schedule is an example of an arithmetic sequence
3. Lizzy will be better prepared for the marathon
Step-by-step explanation:
In the arithmetic sequence there is a common difference between each two consecutive terms
In the geometric sequence there is a common ratio between each two consecutive terms
Juan's Schedule
∵ Juan's will run one mile on the first day of the week
∴ [tex]a_{1}[/tex] = 1
∵ He will double the amount he runs each day for the next
6 days
- That means he multiplies each day by 2 to find how many miles
he will run next day
∴ [tex]a_{2}[/tex] = 1 × 2 = 2 miles
∴ [tex]a_{3}[/tex] = 2 × 2 = 4 miles
∴ [tex]a_{4}[/tex] = 4 × 2 = 8 miles
∴ [tex]a_{5}[/tex] = 8 × 2 = 16 miles
∴ [tex]a_{6}[/tex] = 16 × 2 = 32 miles
∴ [tex]a_{7}[/tex] = 32 × 2 = 64 miles
That means there is a common ratio 2 between each two consecutive days
1. Juan's marathon training schedule is an example of a geometric sequence
Lizzy's Schedule
∵ Lizzy's will run 10 miles on the first day of the week
∴ [tex]a_{1}[/tex] = 10
∵ She will increase the amount she runs by 3 miles each day for
the next six days
- That means she adds each day by 3 to find how many miles
she will run next day
∴ [tex]a_{2}[/tex] = 10 + 3 = 13 miles
∴ [tex]a_{3}[/tex] = 13 + 3 = 16 miles
∴ [tex]a_{4}[/tex] = 16 + 3 = 19 miles
∴ [tex]a_{5}[/tex] = 19 + 3 = 22 miles
∴ [tex]a_{6}[/tex] = 22 + 3 = 25 miles
∴ [tex]a_{7}[/tex] = 25 × 3 = 28 miles
That means there is a common difference 3 between each two consecutive days
2. Lizzy's marathon training schedule is an example of an arithmetic sequence
The rule of the sum of nth term in the geometric sequence is [tex]S_{n}=\frac{a_{1}(1-r^{n})}{1-r}[/tex]
∵ [tex]a_{1}[/tex] = 1 , r = 2 and n = 7
∴ [tex]S_{7}=\frac{1(1-2^{7})}{1-2}[/tex]
∴ [tex]S_{7}[/tex] = 127
∴ Juan will run 127 miles in the final week
The rule of the sum of nth term in the arithmetic sequence is [tex]S_{n}=\frac{n}{2}[a_{1}+a_{n}][/tex]
∵ n = 7, [tex]a_{1}[/tex] = 10 and [tex]a_{7}[/tex] = 28
∴ [tex]S_{7}=\frac{7}{2}(10+28)[/tex]
∴ [tex]S_{7}[/tex] = 133
∴ Lizzy will run 133 miles in the final week
∵ 133 miles > 127 miles
∴ Lizzy will run more miles than Juan
3. Lizzy will be better prepared for the marathon
A fruit is selected at random from a basket containing 6 bananas, 2 papayas, and 7 mangoes. what is the probability of selecting a banana
Answer:
2/5
Step-by-step explanation:
6+7+2=15
6 out of the 15 are bananas
you can simply and reduce this fraction from 6/15 to 2/5
The number 31 is increased to 44. What is the percentage by which the number was increased, to the nearest tenth of a percent?
The number 31 was increased to 44 by approximately 41.9%.
To calculate the percentage increase, you can use the formula:
[tex]\[ \text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100 \][/tex]
In this case, the original value is 31, and the new value is 44. Plug these values into the formula:
[tex]\[ \text{Percentage Increase} = \left( \frac{44 - 31}{31} \right) \times 100 \][/tex]
[tex]\[ \text{Percentage Increase} = \left( \frac{13}{31} \right) \times 100 \][/tex]
Now, calculate the percentage increase:
[tex]\[ \text{Percentage Increase} \approx 41.9\% \][/tex]
So, the number 31 was increased to 44 by approximately 41.9%.
The number 31 was increased by approximately [tex]\( \boed{41.9\%} \)[/tex] to become 44.
Step 1
To find the percentage increase from 31 to 44, we can use the formula for percentage increase:
[tex]\[ \text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100\% \][/tex]
Step 2
Given:
- Old value (31)
- New value (44)
[tex]\[ \text{Percentage Increase} = \left( \frac{44 - 31}{31} \right) \times 100\% \]\[ \text{Percentage Increase} = \left( \frac{13}{31} \right) \times 100\% \]\[ \text{Percentage Increase} \approx 0.419 \times 100\% \]\[ \text{Percentage Increase} \approx 41.9\% \][/tex]
So, the number 31 was increased by approximately [tex]\( \boed{41.9\%} \)[/tex] to become 44.
Gretchen and her friend Hayley bought three bags of apples and three bunches of bananas from the fruit vendor. Gretchen and Hayley want to find the total number of pieces of fruit that they bought. Gretchen thinks she should multiply 3 by the number of apples in each bag, x, and add it to 3 times the number of bananas in each bunch, y, to find the total number of pieces of fruit. Hayley thinks Gretchen should add the number of apples in each bag, x, to the number of bananas in each bunch, y, and then multiply that sum by 3.
The total number of pieces of fruit that they bought should be 72.
The calculation is as follows:
Here we assume 3 bags of apples with 4 apples in each bag [tex](3 \times 4 = 12)[/tex]
And, 3 bunches of bananas with 4 bananas in each bunch [tex](3 \times 4 = 12)[/tex]
Now
= 12 + 12
= 24 pieces of fruit
Since
4 + 4 + 4 (12) apples + 4 = 4 + 4 (12) bananas
So,
= 12 + 12
= 24
here we need to multiplied by 3
So, [tex]= 24 \times 3[/tex]
= 72
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HELP! What is the value of X? WILL GIVE BRAINLIEST!
Answer:The value of X is 7.
Step-by-step explanation: It's counting up starting at 3 so the 4..5..6..7 so, then the 6 is right one the invisible line with X
Answer:
x =2
Step-by-step explanation:
Similar triangles:-
The given triangles are same shape but not necessarily the same sizeCorresponding angles are equalCorresponding sides are in the same ratio [tex]\frac{a}{p} = \frac{b}{q} = \frac{c}{r}[/tex]Given diagram ΔABC AND ΔDBE are similar triangles.
[tex]\frac{BC}{BE} = \frac{AB}{BD}[/tex]
[tex]\frac{x+x+1}{x+1} = \frac{6+4}{6}[/tex]
on simplification , we get
[tex]\frac{2x+1}{x+1} = \frac{6+4}{6}[/tex]
cross multiplication , we get
12x+6 =10x +10
12x-10x = 10 -6
2x =4
x =2
Therefore the value of x =2
verification:-
[tex]\frac{BC}{BE} = \frac{AB}{BD}[/tex]
[tex]\frac{2x+1}{x+1} = \frac{6+4}{6}[/tex]
put x=2
[tex]\frac{2(2)+1}{2+1} = \frac{6+4}{6}[/tex]
[tex]\frac{5}{3} = \frac{6+4}{6}[/tex]
[tex]\frac{5}{3} = \frac{5}{3}[/tex]
both sides are equal
Therefore x value is 2
What is the magnetic force on a proton that is moving at 2.5 x 10 m/s to the
left through a magnetic field that is 3.4 T and pointing toward you? The
charge on a proton is 1.6 10-19 c. Use F-qvx B sin(o).
Answer:C. 1.4 10-11 N up
step-by-step explanation:
Explanation:
The magnetic force, F on a charge q moving with velocity v in a magnetic field B at an angle θ is given by:
F = q v B sin θ
Charge of proton, q = 1.6 × 10⁻¹⁹ C
Strength of magnetic field, B = 3.4 T pointing outwards
velocity of the proton, v = 2.5 × 10⁷ m/s towards left
Magnetic force is given by:
F = 1.6 × 10⁻¹⁹ C× 2.5 × 10⁷ m/s ×3.4 T× sin 90 = 13.6 × 10⁻¹² N = 1.4 × 10⁻¹¹ N up
The direction of the force is given by Lorentz Right hand rule. The fingers point magnetic field, the thumb points towards velocity, then the force on the proton is given by the direction perpendicular to the palm.
The magnetic field acts outwards with velocity of the proton towards left. The force would act perpendicular to the two -upwards.
The magnetic force on the proton, moving to the left at 2.5 x [tex]10^6[/tex] m/s in a 3.4 Tesla magnetic field directed toward you, is approximately 1.36 x [tex]10^{-12}[/tex] Newtons.
To calculate the magnetic force acting on the proton in this scenario, we'll use the formula F = q × v × B × sin(θ), where:
F is the magnetic force,
q is the charge of the proton (1.6 x [tex]10^{-19}[/tex] C),
v is the velocity of the proton (2.5 x [tex]10^6[/tex] m/s),
B is the magnetic field strength (3.4 Tesla), and
θ is the angle between the proton's velocity vector and the direction of the magnetic field.
In this case, since the proton is moving to the left and the magnetic field is directed toward you, the angle θ is 90 degrees because they are perpendicular to each other.
Now, plug the values into the formula:
F = (1.6 x C) × (2.5 x [tex]10^6[/tex] m/s) × (3.4 Tesla) × sin(90°)
sin(90°) is equal to 1, so:
F = (1.6 x [tex]10^{-19}[/tex] C) × (2.5 x [tex]10^6[/tex] m/s) × (3.4 Tesla) × 1
F ≈ 1.36 x [tex]10^{-12}[/tex] N
So, the magnetic force acting on the proton is approximately 1.36 x [tex]10^{-12}[/tex] Newtons. This force causes the proton to experience a curved path due to the interaction between its velocity and the magnetic field.
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Complete question below:
"What is the magnetic force acting on a proton moving at a velocity of 2.5 x [tex]10^6[/tex] m/s to the left when it enters a magnetic field with a strength of 3.4 Tesla, directed toward you? The charge of a proton is 1.6 x [tex]10^{-19}[/tex] C. Calculate the magnetic force using the formula F = q × v × B × sin(θ)."
What’s an exponential equation
Answer:
An exponential equation is when we let the the independent variable become the exponent.
6r + 7 = 13 + 7r with through explanation
Answer:
Step-by-step explanation:
Answer:
r= -6
Step-by-step explanation:
Here's why:
6 r = 6 + 7r
Subtract 7r from each side:
-r = 6
Divide by each side -1 to get the answer of:
r=-6
At time t is greater than or equal to zero, a cube has volume V(t) and edges of length x(t). If the volume of the cube decreases at a rate proportional to its surface area, which of the following differential equations could describe the rate at which the volume of the cube decreases?
A) dV/dt=-1.2x^2
B) dV/dt=-1.2x^3
C) dV/dt=-1.2x^2(t)
D) dV/dt=-1.2t^2
E) fav/dt=-1.2V^2
Answer:
C
Step-by-step explanation:
V(t) = [x(t)]³
A(t) = 6[x(t)]²
dV/dt = k × 6[x(t)]²
Where k < 0
From the options,
taking k = -0.2
dV/dt = -1.2[x(t)]²
The correct answer is A) dV/dt=-1.2x^2, which represents a rate of volume decrease directly proportional to the cube's surface area.
Explanation:The question involves finding a differential equation that describes the rate at which the volume of a cube decreases when the rate is proportional to the cube's surface area. Since the surface area of a cube is 6x(t)^2 and the volume is x(t)^3, the rate of decrease in volume, dV/dt, is proportional to the surface area.
The correct differential equation would show this relationship by having the change in volume be proportional to the square of the edge length, so dV/dt = -kx^2 for some constant k, which means the valid option is A) dV/dt=-1.2x^2.
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In the game of roulette, a player can place a $4 bet on the number 23 and have a StartFraction 1 Over 38 EndFraction probability of winning. If the metal ball lands on 23, the player gets to keep the $4 paid to play the game and the player is awarded an additional $140. Otherwise, the player is awarded nothing and the casino takes the player's $4. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose?
Answer:
a.The expected value of the game to the player is -$0.2105
b. The player should expect to lose $210.50¢ if he/she places the bet or plays the game 1,000 times
Step-by-step explanation:
Please kindly check the attached files for explanation.
Solve the quadratic by factoring.
x^2-5x-31=5
Final answer:
The quadratic equation x²-5x-31=5 is solved by factoring to (x - 9)(x + 4) = 0, giving the solutions x = 9 and x = -4.
Explanation:
To solve the quadratic equation x²-5x-31=5 by factoring, we first move all terms to one side to get it into standard form:
x² - 5x - 36 = 0
Next, we look for two numbers that multiply to -36 and add up to -5. These numbers are -9 and 4. So, we can write:
(x - 9)(x + 4) = 0
Now, we have two possible solutions for x:
x - 9 = 0, which gives us x = 9x + 4 = 0, which gives us x = -4Therefore, the solutions to the equation are x = 9 and x = -4.
PLS HELP!! Find the value or expression for 0.
1). Sin(0) = cos (28)
2). Cos(y) = sin (0)
Answer:
1.)angle 0 = 62 degrees,
2.) angle 0 = 90 - y degrees.
Step-by-step explanation:
1). Sin(0) = cos (28)
angle 0 would be arcsin (cos (28)) = 62 degrees.
2). Cos(y) = sin (0)
angle 0 = arcsin ( cos (y) ) = 90 - y
To solve the equations involving trigonometric functions Sin(0) = cos(28) and Cos(y) = sin(0), use co-function identities to find 0 equals 62 degrees or (90° - 28°), and y could be 28 degrees or (360° - 28°) due to cosine's periodic nature.
Explanation:To solve the set of equations Sin(0) = cos (28) and Cos(y) = sin (0), we need to apply trigonometric identities and the given constraints.
Firstly, we can use the co-function identities which state that sin(90° - x) = cos(x), and similarly, cos(90° - x) = sin(x). Therefore, for the first equation, we can express 0 in terms of 28°:
sin(0) = cos(28°) implies 0 = 90° - 28° or 0 = 62°.
For the second equation, we replace 0 with 62°:
cos(y) = sin(62°)
We know that sin(62°) equates to the same value as cos(28°) from the first equation.
Therefore, cos(y) = cos(28°), which means y = 28° or y = 360° - 28° due to the periodic nature of cosine.
It is Marcie's first turn to roll. Which ratio shows the
theoretical probability that she will not land on a star
space?
A.1/6
B.1/3
C.1/2
D.2/3
Answer:
2/3
Step-by-step explanation:
Answer: the answer is d.2/3 just took the test!!
Step-by-step explanation:
n a recent survey, 18 people preferred milk, 29 people preferred coffee, and 13 people preferred juice as their primary drink for breakfast. If a person is selected at random, find the probability that the person preferred juice as his or her primary drink.
Answer:
[tex]\frac{13}{60}[/tex]
Step-by-step explanation:
18 people preferred MILK
29 preferred COFFEE
13 preferred JUICE
We want probability that a person preferred JUICE. For that, we need number of people who preferred juice and total number of people.
Lets find total:
18 + 29 + 13 = 60 total people
Total people who preferred JUICE is:
13
Probability (preferred JUICE) = 13/60
The answer is [tex]\frac{13}{60}[/tex]
Brian is looking at a statue in Bruso park from 8 meters away. If the distance between the top of the statue to Brian's head is 17 meters, how much taller is the statue than Brian using the Pythagorean theorem?
in the diagram, FG=34, GH=288, and HJ=256. Is GH tangent to circle F?
Answer:
No
Step-by-step explanation:
If GH is tangent to circle F, then it forms a right angle with FG. Therefore, triangle FGH would be a right triangle and would satisfy Pythagorean theorem.
34² + 256² = 288²
66692 = 82944
The sides are not a Pythagorean triple, so GH is not tangent to the circle.
A large candy bar was 120 calories. The
smaller candy bar has 16 percent less
calories. How many calories does the
smaller candy bar have?
Find the area of the polygon:
Answer:
Step-by-step explanation:
o find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem. Here is what it means: Perimeter = the sum of the lengths of all the sides. Apothem = a segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side.
The perimeter of a rectangle is 21 inches. What is the measure of its width if its length is 3 inches greater than its width?
Answer:
x = 3.75 inches
Step-by-step explanation:
We have,
Perimeter of a rectangle, P = 21 inches
Its length is 3 inches greater than its width. Let width is x. So, length of rectangle is l = 3+x
The perimeter of a rectangle is :
[tex]P=2(l+b)[/tex]
l is length and b is breadth
Here, l = 3+x, b = x
Perimeter :
[tex]P=2(3+x+x)\\\\21=2(3+2x)[/tex]
[tex]21=6+4x\\\\15=4x\\\\x=3.75\ \text{inches}[/tex]
So, the width is 3.75 inches.
Final answer:
To find the width of the rectangle, create an equation using the perimeter formula P = 2l + 2w. By substituting the known perimeter and the relationship between length and width, solve for w, resulting in a width of 3.75 inches.
Explanation:
The student is tasked with finding the width of a rectangle when the perimeter is known to be 21 inches and the length is 3 inches greater than the width. To solve this, we set up an equation representing the perimeter of a rectangle: P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
Let w represent the width of the rectangle. The length is then w + 3 inches. Substituting these values into the perimeter formula, we get: 21 = 2(w + 3) + 2w. Simplifying this, we get 21 = 2w + 6 + 2w or 21 = 4w + 6. Solving for w, we subtract 6 from both sides to get 15 = 4w, and then divide both sides by 4 to get w = 3.75 inches. This means the width of the rectangle is 3.75 inches.
25 pts! Math question!!!
Answer:
6051
Step-by-step explanation:
fo sho
In January, Mr. Tan's students read 20 books. In February, they read 15 books.
What is the percent increase or decrease in the number of books they read?
Answer:
25% Decrease
Step-by-step explanation:
15/20 is 75%. 100-75 (since they read less) is 25%
Answer:
25% decrease
Step-by-step explanation:
25% of 20 is 5. Because 0.25*20=5.
And because they read 15 book next month, if was 5 bookks less, which was 25% less.
Very choppy answer. But I hope that helped
What is a 3-dimensional shape made of two identical circles connected by a rectangle
Answer:
cylinder
Step-by-step explanation:
An advertisement about the paint that you want to use reads: “Just 2 quarts covers 175 square feet!” If you need to apply two coats of paint on all the walls, how many quarts of paint do you need to buy?
To apply two coats of paint on all the walls, you will need to buy 4 quarts of paint.
Explanation:To find out how many quarts of paint you need to buy to apply two coats of paint on all the walls, we need to calculate the total area that needs to be painted.
If 2 quarts cover 175 square feet, then 1 quart covers 175/2 = 87.5 square feet.
Since you need to apply two coats of paint, the total area that needs to be painted is 175 square feet x 2 = 350 square feet.
To find out how many quarts you need, divide the total area by the area covered by 1 quart: 350 square feet / 87.5 square feet/quart = 4 quarts.
You will need to buy 4 quarts of paint to complete the job.
Help me please I need help
Answer:
Use the 45-45-90 rule.
Step-by-step explanation:
Based on angle A being 45 and angle B looking like its 90 degrees, angle C will be 45 degrees and so you'd use the 45-45-90 rule, which is a special right triangle. The 45 degrees sides are x and the hypotenuse is x[tex]\sqrt{2}[/tex]. It will be easier if you look it up to see a graphic of it, but I'm pretty sure that both sides CB and AB are 6 based on this rule.
Q(x)=6x and r(x)=5x+1
Find (r•q)(x)
Answer:
(r * g)(x) =30xx + 6x
if it was composition
r (q(x)) = 5(6x) + 1 = 30x + 1
Step-by-step explanation:
Q(x)=6x and r(x)=5x+1
Find (r•q)(x)
multiplying the functions, right? not composition of functions.
(r * g)(x ) = (5x + 1) * 6x = 30xx + 6x
(r * g)(x) =30xx + 6x
if it was composition
r (q(x)) = 5(6x) + 1 = 30x + 1
It rained 0.61 inches every day for 12 days straight. How many inches did it rain altogether during the 12 days?
Answer: 7.32 inches
Step-by-step explanation: We can set up an equation to solve: y = 0.61x where y is the total amount of rain in inches and x is how many days it rained.
Multiply 0.61 by 12 to get how many inches total it rained: y = 0.61(12)
y = 7.32 inches
troy can buy bottles of water in packages of 6 for 8.04 or in packages of 4 for 6.16. how much water does he save by buying 48 bottles of water at the better price
Answer: 4 Tons
Step-by-step explanation:
Simply just add and subtract
Bus A and Bus B leave the bus depot at 8 am.
Bus A takes 25 minutes to do its route and bus B takes 35 minutes to complete its route.
At what time are they both back at the bus depot together?
Give your answer as a 12-hour clock time.
Answer: 10:55
Step-by-step explanation:
Taking statement at face value and the simplest scenario that commencing from 08:00am the buses take a route from depot that returns bus A to depot at 25min intervals while Bus B returns at 35min intervals.
The time the buses will be back at the depot simultaneously will be when:
N(a) * 25mins = N(b) * 35mins
Therefore, when N(b) * 35 is divisible by 25 where N(a) and N(b) are integers.
Multiples of 25 (Bus A) = 25, 50, 75, 100, 125, 150, 175, 200 etc
Multiples of 35 (Bus B) = 35, 70, 105, 140, 175, 210, 245 etc
This shows that after 7 circuits by BUS A and 5 circuits by Bus B, there will be an equal number which is 175 minutes.
So both buses are next at Depot together after 175minutes (2hr 55min) on the clock that is
at 08:00 + 2:55 = 10:55
on the number line which point is closest to pie
The point on a number line that is closest to Pi (π), which is approximately 3.14, would be the point representing either 3 or 4 as they are the closest whole numbers. However, a point representing 3.14 or a closer approximation would be even nearer.
Explanation:The question is asking to identify which point on a number line is closest to Pi (π), a mathematical constant that approximately equals 3.14. On a number line, you can visualize numbers as points. As Pi is 3.14 approximately, the closest point to Pi on a number line would naturally be the point that represents 3 or the point representing 4, as these are the two closest whole numbers to 3.14. However, if there's a point representing the value 3.14, or even closer approximation like 3.141, it would be even closer to Pi than the points representing 3 or 4.
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Mr. Woosley is assigning group projects to 24 students. To form the groups, each student will randomly select a slip of paper with the name of a continent on it from a bag. The student will keep the slip of paper. The number of slips of paper in the bag with each continent name is shown below. Africa - 6 Asia - 8 Australia - 4 Europe - 6 What is the probability that a student in Mr. Woosley’s class will not be assigned a project on Australia?
The probability that a student will not be assigned a project on Australia is 20/24, which simplifies to 5/6.
The probability that a student in Mr. Woosley's class will not be assigned a project on Australia can be found by subtracting the probability of being assigned Australia from 1. There are a total of 24 slips of paper representing continents, and 4 of these are Australia. Therefore, there are 24 - 4 = 20 slips that are not Australia.
The probability, P(NOT Australia), is calculated as follows
Calculate the total number of slips: 6 (Africa) + 8 (Asia) + 4 (Australia) + 6 (Europe) = 24.
Determine the number of slips that are not Australia: 24 - 4 (Australia) = 20.
Find the probability: P(NOT Australia) = Number of non-Australia slips / Total number of slips = 20 / 24.
Therefore, the probability that a student will not be assigned a project on Australia is 20/24 or 5/6 when simplified.
ILL GIVE YOU BRAINLIEST!! The cost of a medium pizza can be determined by the number of toppings on the pizza.Each toppings adds the same amount to the total cost.
Which table could show the relationship between the number of toppings and the cost of a medium pizza?
Answer:
b
Step-by-step explanation:
The table could show the relationship between the number of toppings and the cost of a medium pizza is table B.
What is Rate of Change?We divide the change in y (output) by the change in x to determine the average rate of change (input).
The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another.
In table 1, when the topic goes from 4 to 5 then the price increase by $2 which is not convenient here.
In table 2, when the topic goes from 4 to 5 then the price increase by $1 which is not convenient here.
In table 3, when the topic goes from 4 to 5 then the price increase by $2 which is convenient here.
In table 4, when the topic goes from 4 to 5 then the price increase by $2 which is not convenient here.
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