Answer:
(x+10)(x-10)
Step-by-step explanation:
See the explanation on your other problems;
Quickly:
x^2 = x timex x
-100 = 10 x -10
(x+10)(x-10)
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
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.
2. A football coach recorded his team’s game scores over a football season. The scores are 21, 45, 21, 14, 21, 28, 24, 14, 24, 28.
(a) Find the mean absolute deviation of the data. Round to the nearest tenth.
(b) Interpret the mean absolute deviation of the data within the context of the problem.
(c) Explain how removing the outlier, 45, affects the mean absolute deviation.
Answer:
(a) The mean is 24
The Absolute deviation is 8.367
(b) Mean is the number of score per game
(b) The standard deviation is the normal expected score difference from the mean
(c) Mean reduce
Standard deviation reduce
Step-by-step explanation:
The data is as follows;
21, 45, 21, 14, 21, 28, 24, 14, 24, 28
The data with n = 10 is presented as follows
x (x - μ) (x - μ)²
21 -3 9
45 21 441
21 -3 9
14 -10 100
21 -3 9
28 4 16
24 0 0
14 -10 100
24 0 0
28 4 16
∑x/n =240 ∑(x - μ)² = 700
24 ∑(x - μ)²/n = σ² = 70
The mean = 24
The Absolute deviation √70 = 8.367
(b) The mean indicates that within the football season, the average game score per game was 24 and the normal variation from the average was 8.367
(c) Removing the outlier, 45 which ls most equal to two means will reduce the mean or average score per game of the team to as follows
21 , 21 , 14, 21, 28, 24, 14, 24, 28
∑x = 195 and μ = (∑x)/n = 195/9 = 21.67
The standard deviation = 4.83
Therefore, removing the outlier 45 which is almost double the mean will reduce the mean by almost μ/n and the standard deviation is also reduced.
students at springfield school can join either the orchestra or the marching band. students cannot join both groups. how many 7th graders are in the band?
Answer:56 students
Step-by-step explanation:
So look 6th grade total 42 and 8th is 72 and the total is 170 but he want 7th grade total so what I did is 42+72=114
Then I did 170-114=56 so the total of 7th grade is 56.
The value of the variables x, y, and z will be 45, 24, and 56.
What is Algebra?Algebra is the study of graphic formulas, while logic is the interpretation among those signs.
The students at spring field school can join either the orchestra or the marching band.
Let the missing value x, y, and z are given in the table.
The table is given below.
Orchestra Band Total
6th Grade 24 18 42
7th Grade 32 x y
8th Grade z 27 72
Total 101 69 170
Then the value of x, y, and z are calculated below.
For value of z, the equation will be
72 = z + 27
z = 72 – 27
z = 45
For value of x, the equation will be
18 + x + 27 = 69
x + 45 = 69
x = 69 – 45
x = 24
For value of y, the equation will be
y = 32 + 24
y = 56
Then the value of the variables x, y, and z will be 45, 24, and 56.
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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
PLEASE ANSWER FAST!! (and correctly)
Answer:
1/10 or 10%
Step-by-step explanation:
Step 1: Find the probability of selecting a card with an A
Picked amount / Total Times
3 / 30
1/10 or 0.1 or 10%
Answer: 1/10 or 10%
Use the graphing tool to see what happens to the polynomial function when you change more than one parameter at a
time. In what ways is this new graph different from the parent graph of f(x) = x ? Write down your observations for
each of these transformed functions. Then try a few of your own
· g(x) = (x - 2) + 1
· g(x) = 3x4 - 6
· g(x) = 2(x + 3)* + 10
· g(x) = { (6x - 1)
Answer:
The parent graph of (x-2)^4+1 shifts 2 units to the right and one unit up.
The parent graph of 3x^4-6 is stretched vertically by a factor of 3 and then shifted 6 units down.
The parent graph of 2(x+3)^4+10 is shifted 3 units to the left, stretched vertically by a factor of 2 and shifted 10 units up.
The parent graph of 1/4(6x-1)^4 is shifted one unit to the right, compressed horizontally by a factor of 1/6 , and compressed vertically by a factor of 1/4.
Step-by-step explanation:
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
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?
Is 3,4,5 a Pythagorean triple
Answer:
Yes because it fits the Pythagorean Theorem
Step-by-step explanation:
see: 5 ^2 = 25
and 3^2 + 4^2 = 9 + 16 = 25
25 = 25
so it is
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]
The average cost of tuition, room and board at small private liberal arts colleges is reported to be $8,500 per term with a standard deviation of $1,200, but a financial administrator believes that the average cost is MORE. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. Let alpha = 0.05. What is the critical z-value for this test?
Answer:
z=3.8196
Step-by-step explanation:
-We notice that this is a normal distribution problem.
-Given the mean is $8500, standard deviation is $1200 , and n=350, the critical z-value using alpha=0.05 is calculated as:
[tex]z=\frac{x-\mu_o}{\sigma/\sqrt{n}}\\\\=\frac{8745-8500}{1200\sqrt{350}}\\\\\\=3.8196[/tex]
Hence, the test statitic is z=3.8196
What is the circumference of a circle with a diameter of 9 inches? (use 22/7 for pi)
Answer:
c=28.2857142857 inches
Step-by-step explanation:
The circumference of a circle can be found using:
[tex]c=\pi d[/tex]
We know the diameter is 9, and we are using 22/7 for [tex]\pi[/tex], so we can substitute them in
c=22/7*9
Multiply
c=28.2857142857
The circumference is 28.2857142857 inches
what is the missing value for x-5y=-15
Answer:
y= 1/5 (fraction)
x=−3
Step-by-step explanation:
Let's solve for x.
x−5y=15
Step 1: Add 5y to both sides.
x−5y+5y=15+5y
x=5y+15
Let's solve for y.
x−5y=15
Step 1: Add -x to both sides.
x−5y+−x=15+−x
−5y=−x+15
Step 2: Divide both sides by -5.
−5y
−5
=
−x+15
−5
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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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.
It takes one student 12 hours to wash all of the cars at a school car wash. If 8 students wash all the cars, how many hours will each person spend washing cars?
Answer:
Each person will wash all cars for 0.1875 hours
Step-by-step explanation:
One student takes time to wash all cars = 12
8 students take time to wash all cars = [tex]\frac{12}{8}= 1.5 hours[/tex]
So, 8 students together takes 1.5 hours to wash the car
Each person spent hours on washing all cars =[tex]\frac{1.5}{8}[/tex]
Each person spent hours on washing all cars =0.1875 hours
So, Each person will wash all cars for 0.1875 hours
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
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.
Who most often wins in a credit transaction?
companies often win in a credit transaction, due to their clients continually pay them for their usage.
Final answer:
The 'winner' in a credit transaction varies; it could be the lender earning interest or the borrower who benefits from immediate funds. Credit transactions do not create new money but reallocate it, and for personal debt management, debts with higher interest should be paid first.
Explanation:
In credit transactions, the winner is not easily defined as it depends on the perspective and the outcome of the transaction. If we consider a credit card transaction where a customer makes a purchase, the credit card issuer initially appears to win by providing funds to the customer and earning interest on the borrowed amount. The customer benefits by receiving the goods or services they need immediately, with the expectation of repaying the funds.
In a typical credit transaction, one party relinquishes money today while the other party promises to return a specified sum, possibly with interest, at a future date. This does not create new money but shifts existing money from one party to another. The perceived 'winner' could be the lender, who will receive the original amount plus interest, or the borrower, who gets immediate use of the funds.
When managing personal finances, it's advisable to pay off debts with the highest interest rates first, as suggested by the adage, "A penny saved is a penny earned".
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:
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
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)."
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.
whats 15x times 14 y
Answer:
210xy
Step-by-step explanation:
15x * 14y can be written as 15 * x * 14 * y. Due to the commutative property of multiplication, we can change around the order of these numbers to make this expression easier to understand.
We're going to move the expression around so it is now 15 * 14 * x * y. Now, you can see clearly that you can multiply 15 and 14 together, which will get you 210.
And naturally what you have left is 210 * x * y, which simply appears as 210xy.
I hope this helped!
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.
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
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.
What does x equal???????
Answer:
-4x + 10x - 12 = -3x - 39
6x - 12 = -3x - 39
9x - 12 = -39
9x = -27
x = -3
Step-by-step explanation:
What is the answer for 4x + 2y = 12
Answer:
(1,4), (2,2) (3,0)
Step-by-step explanation:
adjust the equation so that the y is isolated so subtract 4 x
2y=4x +12
Every number is divisible by 2 so you can further isolate the y
y=-2x+6
Plug your x coordinates into the equation so get the y coordinates
Answer:
y=-2x+6
Step-by-step explanation:
You want to to turn the given equation 4x+2y=12 into y=mx+b
** m is the slope and b is the y-intercept
The first step is to isolate y. First subtract 4x from both sides:
4x+2y=12
2y=-4x+12
Now you have y mostly isolated, all you have to do is divide both sides by 2:
2y=-4x+12
y=-4/2x +12/2
y=-2x +6
Now you have your equation, plug in values for x to find y to fill in the table:
ex: y=-2(2)+6
y= -4+6
y= 2
** an order pair ex.: (2,2)