Answer:
a represents the Number of Minutes Late, (a=15 in this case)
Step-by-step explanation:
If the daycare charges a base fee of $3 plus $0.50 per minute late for late pickups(after closing time).
Albin on arrival for pickup had to pay $10.50;
She uses the equation
10.50=0.50a+3
0.50a=10.50-3
0.50a=7.50
a=7.50/0.5
a= 15
It means Albin was 15 minutes late to a pickup.
Will give Brainliest to CORRECT answer! Please Help! A cylinder has a diameter of 5 m and a height of 10 m. What is its volume? Choose all that apply.?
A. π(2.5)^2 (10) m^3
B. π(5)^2 (10) m^3
C. 62.5π m^3
D. 250π m^3
Answer:
A, C
Step-by-step explanation:
You want the volume of a cylinder with diameter 5 m and height 10 m.
VolumeThe volume is given by the formula ...
V = πr²h . . . . . . . where r = radius = half the diameter
The diameter is 5 m, so the radius is 5/2 = 2.5 m. Using the given values in the formula, we find the volume of the cylinder to be ...
V = π(2.5)²(10) m³ . . . . . . matches choice A
= 62.5π m³ . . . . . . . . . . . matches choice C
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Tyler selects one card from the three(4,5, and a King), and rolls a number cube. What is the probability that she selects the 5, and rolls a number less than 5?
[tex]\frac{1}{3}[/tex]Answer:
2/9
Step-by-step explanation:
given that Tyler selects one card from the three(4,5, and a King), and rolls a number cube.
We find that A the event of selecting one card and B getting a number on rolling a number cube are independent events.
No of cards = 3
Prob of selecting 5 from 3 cards = [tex]P(1,2,3, or 4) = \frac{2}{3}[/tex]
When rolling a number cube (assuming fair) there is equally likely for all numbers to appear from 1 to 6
Prob of getting 5 =[tex]\frac{1}{6}[/tex]
Prob of getting less than 5 =
Since these two events are independent,
the probability that she selects the 5, and rolls a number less than 5
= Product of probabilities
= [tex]\frac{1}{3}[/tex]*[tex]\frac{2}{3}[/tex]
=[tex]\frac{2}{9}[/tex]
A cabin cruiser traveling with the current went 45 mi in 3 h. Traveling against the current it took 5H to go the same distance find the rate of the cabin cruiser in calm water and the rate of the current
Answer: the rate of the cabin cruiser in calm water is 12 mph.
the rate of the current is 3 mph.
Step-by-step explanation:
Let x represent the rate of the cabin cruiser in calm water.
Let y represent the rate of the current.
A cabin cruiser traveling with the current went 45 miles in 3 h. This means that the total speed is (x + y) miles per hour.
Distance = speed × time
Distance travelled with the current is
45 = 3(x + y)
Dividing through by 3, it becomes
15 = x + y - - - - - - - - - - -1
Traveling against the current it took 5 hours to go the same distance. This means that the total speed is
(x - y) miles per hour.
Distance travelled against the current is
45 = 5(x + y)
Dividing through by 5, it becomes
9 = x - y - - - - - - - - - - -2
Adding equation 1 to equation 2, it becomes
24 = 2x
x = 24/2
x = 12 mph
Substituting x = 12 into equation 1, it becomes
15 = 12 + y
y = 15 - 12
y = 3 mph
Rate of the cabin cruiser will be 12 miles per hour and the rate of the current is 3 miles per hour.
Let the speed of the current = r miles per hour
And the speed of the cabin cruiser in the calm water = c miles per hour
Speed of the cabin cruiser against the current = (c - r) miles per hour
Speed of the cabin cruiser with the current = (c + r) miles per hour
Since, expression for the speed is given by,
Speed = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]
Therefore, speed of the cabin cruiser with the current = [tex]\frac{45}{3}[/tex] = 15 miles per hour
So the equation for the speed will be,
c + r = 15 ------ (1)
Time taken to cover 45 miles against the current = 5 hours
Therefore, equation for this situation will be,
c - r = [tex]\frac{45}{5}[/tex]
c - r = 9 ------- (2)
Now solve this system of equations,
Add equation (1) and (2),
(c + r) + (c - r) = 15 + 9
2c = 24
c = 12 miles per hour
Substitute the value of 'c' in equation (1),
12 - r = 9
r = 12 - 9
r = 3 miles per hour
Therefore, speed of the cabin cruiser will be 12 miles per hour and the rate of the current is 3 miles per hour.
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People start to leave the stadium at the end of a football game. The number of people, PPP, that are left in the stadium mmm minutes after the end of the game is given by the equation above. How many people were present when the game ended but before people started to leave? P=45,000−1,000m
Answer:
45,000
Step-by-step explanation:
If P=45,000−1,000m,
where P=The number of people left in the stadium m minutes after the end of the game
We want to determine how many people were present when the game ended but before people started to leave.
Note that immediately the game ended,
m=0
Therefore, the number of people left in the stadium
P=45000−(1000 X 0)
P=45000
There were 45,000 people.
A group of people ate dinner at a restaurant.Their bill was $64 .They split the bill evenly and each person left a $2 tip.How much did each person pay?
Answer:
If there were 2 people, they would each pay $34. If there were 4 people, they would each pay $18
ski-lift cables aren’t string at an angle 30 ° to the top of a 5000 ft mountain. How long are the cables?
Answer: the length of the cable is 10000 feet.
Step-by-step explanation:
A right angle triangle is formed. The length of the cable represents the hypotenuse of the right angle triangle. The height of the mountain represents the opposite side of the right angle triangle. To determine the length of the cable, L, we would apply the Sine trigonometric ratio.
Sin θ = opposite side/hypotenuse. Therefore,
Sin 30 = 5000/L
L = 5000/Sin 30 = 5000/0.5
L = 10000 ft
2) Do MN and PQ bisect each other? If so, choose the proper formula to prove it. If not, explain the
reason.
Step-by-step explanation:
If the segments bisect each other, they will share the same midpoint.
Midpoint formula is:
(x, y) = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Midpoint of MN is:
(x, y) = ((-5 + 5)/2, (6 + -2)/2)
(x, y) = (0, 2)
Midpoint of PQ is:
(x, y) = ((5 + -5)/2, (3 + 1)/2)
(x, y) = (0, 2)
So the segments do bisect each other.
what's the inverse of y=ln(x+5) and what's the inverse of y=e^x +4
Step-by-step explanation:
To find the inverse of a function y = f(x), switch x and y, then solve for y.
y = ln(x + 5)
x = ln(y + 5)
eˣ = y + 5
y = eˣ − 5
y = eˣ + 4
x = eʸ + 4
x − 4 = eʸ
y = ln(x − 4)
Ron and Annie have $1,349.85 in their checking account. During the week, Annie goes to an ATM and withdraws $80. The following week Ron deposits his paycheck of $699.65. Annie then pays bills online in the amounts of: $215.70, $53, $49.76, and $100.35. What is the current balance in their checking account
Answer:
$1550.69
Step-by-step explanation:
Deposits get added and withdrawals and bill payments get subtracted from the balance. The new balance is ...
$1349.85 -80 +699.65 -215.70 -53 -49.76 -100.35 = $1550.69
The average wall thickness of 25 panes of glass is 4.05 mm. The standard deviation of the thickness of the 25 panes is measured to be 0.08 mm. What is the 90% confidence interval of the mean of wall thickness
Answer:
u => 4,028
Step-by-step explanation:
To find the answer, we have the following formula:
u => m - t (alpha, n-1) * [sd / (n) ^ (1/2)]
where m is the mean.
where sd is the standard deviation.
where n is the sample size.
t is a parameter that depends on the confidence interval and the sample size.
alpha = 1 - ci
ci = 90% = 0.9
Therefore, alpha = 1 - 0.9 = 0.1.
n - 1 = 25 - 1 = 24
So it would come being t (0.1, 24), if we look in the table, which I will attach the value of t is equal to 1.318.
We know the rest of the values, m = 4.05; sd = 0.08; n = 25
u => 4.05 - 1,318 * [0.08 / (25) ^ (1/2)]
u => 4.028
Which means that the interval with a 90% confidence of the wall thickness measurement is:
u => 4.028
How many subsets does the set {Apple, Banana} have?
2
3
4
5
6
Answer:
4
Step-by-step explanation:
{ }
{Apple}
{Banana}
{Apple, Banana}
A Chinese restaurant uses about 15 exponent 2 appearance of chopsticks each day the manager wants to order a 30-day supply of chopsticks chopsticks come in boxes of 750. How many boxes should the manager order
Answer:
9 boxes of chopsticks.
Step-by-step explanation:
The first thing is to calculate the number of chopsticks spent in a day, the problem tells us that they are 15 ^ 2 = 15 * 15 = 225 chopsticks daily.
To calculate the number of chopsticks in 30 days, it is to calculate the previous amount by 30:
225 * 30 = 6750 chopsticks spent in one month.
To know how many boxes you should order is to divide the total number of chopsticks in a month and the number of chopsticks that a box brings that are 750:
6750/750 = 9 boxes of chopsticks.
Therefore you should order exactly 9 boxes of chopsticks for the restaurant's need.
Brian claims that he can eat a pie that is divided into six equal pieces In two minutes.If he can eat the whole pie in two minutes, how long does he have to eat each piece
Answer:
He have to eat each piece in [tex]\frac{1}{3} \ minute.[/tex]
Step-by-step explanation:
Given:
Brian claims that he can eat a pie that is divided into six equal pieces In two minutes.
If he can eat the whole pie in two minutes.
Now, to find the time he have to eat for each piece.
So, to solve by using unitary method:
If Brian can eat 6 pieces in = 2 minutes.
Then, he can eat 1 piece in = [tex]\frac{2}{6}[/tex] [tex]=\frac{1}{3} \ minute.[/tex]
Therefore, he have to eat each piece in [tex]\frac{1}{3} \ minute.[/tex]
Final answer:
Brian has 20 seconds to eat each of the six equal pieces of the pie if he eats the whole pie in two minutes.
Explanation:
If Brian can eat an entire pie divided into six equal pieces in two minutes, we calculate the time taken to eat each piece by dividing the total time by the number of pieces. So, it is a simple division problem: we divide 2 minutes by 6 pieces to find out how long Brian has to eat each piece.
To find the time for each piece, we perform the calculation: 2 minutes ÷ 6 pieces = 0.333 minutes per piece. Since there are 60 seconds in a minute, to convert this to seconds, we multiply by 60.
Therefore: 0.333 minutes × 60 seconds = 20 seconds per piece. So, Brian has 20 seconds to eat each piece of pie.
Mary Ward recently leased a new convertible. The $1600 due at signing inc the title and license fee. Her monthly lease payments are $700 per mont leasing company allows 12,000 miles per year with a $0.12 per mile overage charge. If the total lease cost is $26,800, for how many months does the lease ludes . The last?
This calculation shows that Mary Ward's lease term is 36 months.
The question is asking us to find out for how many months Mary Ward's car lease lasts. To do so, we need to calculate the total monthly payments and then subtract the initial $1600 fee to find the total cost of the monthly payments alone. Then, we divide this amount by the monthly lease payment to determine the total number of months for the lease duration.
First, we deduct the initial fee from the total lease cost:
Total lease cost - Initial fee = Total of monthly payments
$26,800 - $1,600 = $25,200
Next, we divide this result by the monthly lease payment to find out the number of months:
$25,200 / $700 = 36 months
Therefore, the lease agreement lasts for 36 months, which is typically the term for most vehicle leases.
Why did people initially believe that a horse named clever hans could do math and that a procedure called facilitated communication could enable autistic children to type out complex messages?
Answer:
C
Step-by-step explanation:
2.Why did people initially believe that a horse named "Clever Hans" could do math and that a procedure called "facilitated communication" could enable autistic children to type out complex messages?
A.In both cases, the unusual behavior was initially demonstrated under carefully controlled conditions
B.In both cases, scientists falsified their data
C.In both cases, people initially failed to recognize alternative explanations for the observed behavior
D.Both cases were very elaborate hoaxes designed by con artists who were intentionally trying to fool people
People believed in Clever Hans' mathematical abilities and in facilitated communication for autistic children due to misinterpretation of cues and expectations, known as the Clever Hans Effect and the influence of facilitators, respectively.
People initially believed that a horse named Clever Hans could do math and that a procedure called facilitated communication could enable autistic children to type out complex messages due to a misunderstanding of the animals' and participants' capabilities.
Regarding Clever Hans, the horse's trainer, Wilhelm von Osten, would ask Hans a math problem, to which the horse would tap out the answer with his hoof.
It was discovered that Hans was not performing mathematical calculations; rather, he was responding to physical and perhaps subconsciously given cues from his human observers, a phenomenon now known as the Clever Hans Effect.
Similarly, efforts to interpret autistic children's communications were influenced by the expectations and subtle suggestions from the facilitators in facilitated communication.
What is the probability of getting a license plate that has a repeated letter or digit if you live in a state in which license plates have two letters followed by four numerals? (Round your answer to one decimal place.)
In a state where the license plates have two letters followed by four numerals, the probability of getting a license plate that has a repeated letter or digit is approximately 51.5%.
Explanation:To solve this question, we need to understand the fundamental counting principle and the concept of probability. First, let's explore the total number of possibilities for a license plate of this format. The choice for each spot on the license plate is independent of each other. Therefore, there are 26 possibilities (26 letters in the English alphabet) for each of the first two spots, and 10 possibilities for each of the next four spots (0-9 digits). The total number of possibilities is thus 26 * 26 * 10 * 10 * 10 * 10, or 67,600,000 combinations.
Next, we will calculate all the combinations in which no letters or digits are repeated. There are 26 options for the first letter, 25 remaining options for the second letter, 10 options for the first digit, and then 9, 8, and 7 options for the next three positions, giving us 26 * 25 * 10 * 9 * 8 * 7 = 327,600,000 combinations.
To get the probability of a repeated letter or digit, subtract the non-repeating combinations from the total combinations, divide by the total, and then multiply by 100 to get a percentage. So the probability is (676,000,000 - 327,600,000) / 676,000,000 * 100, which gives approximately 51.5%
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the base of the 37 foot ladder is 9 feet from the wall of a building. will the top of the ladder reach a window ledge 35 feet above the ground?
-I know its a yes but what is the math in it?
Answer:
The answer to your question is Yes.
Step-by-step explanation:
The math in this problem is that we need to use the Pythagorean theorem to solve it. Pythagorean theorem is part of trigonometry a branch of Maths.
Data
base = 9 ft
length = 37 ft
height = ?
Pythagorean theorem
c² = a² + b²
length = c
base = a
height = b
37² = 9² + b²
-Solve for b
b² = 37² - 9²
-Simplify
b² = 1369 - 81
b² = 1288
-Result
b = 35.88
-Conclusion
The ladder will reach a height higher than 35 ft.
A graph of the function g(x) = x^4-8x³+x²+42x has zeros at -2, 0, 3 and 7. What are the signs of the values between 0 and 3? Show algebraically how you know.
Answer:
The answer to your question is Positive
Step-by-step explanation:
Function
g(x) = x⁴ - 8x³ + x² + 42x
To know if the function is positive or negative in the interval (0, 3), look for two numbers between this interval and evaluate the function.
The numbers I chose were 1 and 2
- g(1) = (1)⁴ - 8(1)³ + (1)² + 42(1)
= 1 - 8 - 1 + 42
= + 36 positive
- g(2) = (2)⁴ - 8(2)³ + (2)² + 42(2)
= 16 - 64 + 4 + 84
= + 40
Conclusion
The function is positive in the interval (0, 3)
Write simplified expressions for the area and perimeter of the rectangle. Area: 8 8 x+ x+ Perimeter: 2 2 x+ x+
The simplified expressions for the area and perimeter of the rectangle are 16x and 4x, respectively.
To simplify the expressions for the area and perimeter of the rectangle, we can extract common factors:
Area: [tex]\(8(x + x) = 8 \times 2x = 16x\)[/tex]
Perimeter: [tex]\(2(x + x) = 2 \times 2x = 4x\)[/tex]
Therefore, the simplified expressions are:
Area: 16x
Perimeter: 4x
Heather won 45 lollipops playing a game at her school later she gave 3 lollipops to each of her friends she only has 3 remaining how many friends dose she have
Answer:
14
Step-by-step explanation:
all you have to do is multiply 15x3 which is 45 and subtract 3 or 1 which is 14 she has 14 friends.
plzzzzzzz help me someone tired of being skipped over
Answer:
D. (-7, 7)
Step-by-step explanation:
Count left 7 on X-axis = -7
Count up 7 on Y-axis = +7
The coordinate pair is (-7, 7)
Using the percentage-of-receivables method for recording bad debt expense, estimated uncollectible accounts are $43,000. If the balance of the Allowance for Doubtful Accounts is $4,600 balance before adjustment, what is the amount of bad debt expense for that period?
Step-by-step explanation:
Given that
Estimated uncolllectible account balance = $43,000
Balance of the allowance for doubtful accounts = $4,600
So the amount of bad debt expense is
Since it is not mentioned whether it is a credit or debit balance so we calculated by considering the both
If we considered the debit balance of allowance for doubtful debts so,
= $43,000 + $4,600
= $47,600
And, if credit balance, so
= $43,000 - $4,600
= $38,400
Find an equation of the line. Write the equation in standard form.
Horizontal; through (3,-9)
Answer:
y = -9
Step-by-step explanation:
Standard form of the equation of a line is ...
ax + by = c
When that line is a horizontal line, this can be reduced to ...
y = c
The value of c must be the same as the y-coordinate of the point you want this line to go through.
y = -9 . . . . . . horizontal line through (3, -9)
what is the expansion of (3+x)^4
Answer:
[tex]\left(3+x\right)^4:\quad x^4+12x^3+54x^2+108x+81[/tex]
Step-by-step explanation:
Considering the expression
[tex]\left(3+x\right)^4[/tex]
Lets determine the expansion of the expression
[tex]\left(3+x\right)^4[/tex]
[tex]\mathrm{Apply\:binomial\:theorem}:\quad \left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i[/tex]
[tex]a=3,\:\:b=x[/tex]
[tex]=\sum _{i=0}^4\binom{4}{i}\cdot \:3^{\left(4-i\right)}x^i[/tex]
Expanding summation
[tex]\binom{n}{i}=\frac{n!}{i!\left(n-i\right)!}[/tex]
[tex]i=0\quad :\quad \frac{4!}{0!\left(4-0\right)!}3^4x^0[/tex]
[tex]i=1\quad :\quad \frac{4!}{1!\left(4-1\right)!}3^3x^1[/tex]
[tex]i=2\quad :\quad \frac{4!}{2!\left(4-2\right)!}3^2x^2[/tex]
[tex]i=3\quad :\quad \frac{4!}{3!\left(4-3\right)!}3^1x^3[/tex]
[tex]i=4\quad :\quad \frac{4!}{4!\left(4-4\right)!}3^0x^4[/tex]
[tex]=\frac{4!}{0!\left(4-0\right)!}\cdot \:3^4x^0+\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1+\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2+\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3+\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4[/tex]
[tex]=\frac{4!}{0!\left(4-0\right)!}\cdot \:3^4x^0+\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1+\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2+\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3+\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4[/tex]
as
[tex]\frac{4!}{0!\left(4-0\right)!}\cdot \:\:3^4x^0:\:\:\:\:\:\:81[/tex]
[tex]\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1:\quad 108x[/tex]
[tex]\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2:\quad 54x^2[/tex]
[tex]\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3:\quad 12x^3[/tex]
[tex]\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4:\quad x^4[/tex]
so equation becomes
[tex]=81+108x+54x^2+12x^3+x^4[/tex]
[tex]=x^4+12x^3+54x^2+108x+81[/tex]
Therefore,
[tex]\left(3+x\right)^4:\quad x^4+12x^3+54x^2+108x+81[/tex]Which method can be used to find a fraction equivalent to Five-sixths? Five-sixths = StartFraction 5 times 2 over 6 times 3 EndFraction = Ten-eighteenths Five-sixths = StartFraction 5 times 3 over 6 times 4 EndFraction = StartFraction 15 over 24 EndFraction Five-sixths = StartFraction 5 times 5 over 6 times 6 EndFraction = StartFraction 25 over 36 EndFraction Five-sixths = StartFraction 5 times 3 over 6 times 3 EndFraction = Fifteen-eighteenths
Answer:
The correct option is
d) Five-sixths = StartFraction 5 times 3 over 6 times 3 EndFraction = Fifteen-eighteenths = 15/18 ÷ 1 = 15/18 ÷ 3/3 = 5/6
Step-by-step explanation:
Which method can be used to find a fraction equivalent to Five-sixths?
a) Five-sixths = StartFraction 5 times 2 over 6 times 3 EndFraction = Ten-eighteenths
Here 10/16 = 5/8 ≠ 5/6
b) Five-sixths = StartFraction 5 times 3 over 6 times 4 EndFraction = StartFraction 15 over 24 EndFraction
15/24 = 5/8 ≠ 5/6
c) Five-sixths = StartFraction 5 times 5 over 6 times 6 EndFraction = StartFraction 25 over 36 EndFraction
25/36 ≠ 5/6
d) Five-sixths = StartFraction 5 times 3 over 6 times 3 EndFraction = Fifteen-eighteenths
15/18 ⇒ 15/18÷3/3 = 5/6
note that 3/3 = 1
Answer:
Its D buddy!
Step-by-step explanation:
Cuz 3 People said it was D.
You are camping with Joe and Karl. Since all three of you like your privacy, you don’t pitch your tents close together. Joe’s tent is 21.0 m from yours, in the direction 23.0° south of east. Karl’s tent is 32.0 m from yours, in the direction 37.0° north of east. What is the distance between Karl’s tent and Joe’s tent?
Answer:
Step-by-step explanation:
According to the flaring, the triangle expressed in the figure is formed.
Now we have a vector A and vector B, whose components are Ax, Ay and Bx and By respectively.
To calculate these components you must use the following formulas:
Ax = A * cos [angle a] = 32 * cos 37 ° = 25.6
Ay = A * sin [angle a] = 32 * sin 37 ° = 19.3
Bx = B * cos [angle a] = 21 * cos 23 ° = 19.3
By = B * sin [angle b] = 21 * sin 23 ° = - 8.2
In the figure it can be seen that vector B is the result of vector A and vector C
Thus:
B = A + C
reorganizing is:
C = B - A
Now to calculate Cx and Cy, we will do it with the previously calculated components:
Cx = Bx - Ax = 19.3 - 25.6 = -6.3
Cy = By - Ay = -8.2 - 19.3 = -27.5
Now to calculate the value of vector C, we apply the following formula:
C ^ 2 = Cx ^ 2 + Cy ^ 2
Rearranging:
C = (Cx ^ 2 + Cy ^ 2) ^ (1/2)
C = [(-6.3 ^ 2) + (27.5 ^ 2)] ^ (1/2) = 28.2
Then the distance would be 28.2 meters.
An equation for the depreciation of a car is given by y = A(1 – r)t , where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately how old is the car?
Step-by-step explanation:
Given : An equation for the depreciation of a car is given by [tex]y = A(1-r)^t[/tex], where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10%.
To find : Approximately how old is the car?
Solution :
The value of a car is half what it originally cost i.e. [tex]y=\frac{1}{2} A[/tex]
The rate of depreciation is 10% i.e. r=10%=0.1
Substitute in the equation, [tex]y = A(1-r)^t[/tex]
[tex]\frac{1}{2} A= A(1-0.1)^t[/tex]
[tex]\frac{1}{2}= (0.9)^t[/tex]
Taking log both side,
[tex]\log(\frac{1}{2})=t\log (0.9)[/tex]
[tex]t=\frac{\log(\frac{1}{2})}{\log (0.9)}[/tex]
[tex]t=6.57[/tex]
[tex]t\approx 6.6[/tex]
Therefore, the car is about 6.6 years old.
Answer:
The car is 6.5 years old
Step-by-step explanation:
An equation for the depreciation of a car is given by [tex]y = A(1 - r)^t[/tex]
y = current value of the car
A = original cost
r = rate of depreciation
t = time in years
The value of a car is half what it originally cost
So, [tex]y = \frac{A}{2}[/tex]
The rate of depreciation is 10% = 0.1 =r
Substitute the values in equation
[tex]\frac{A}{2} = A(1 - 0.1)^t[/tex]
[tex]\frac{1}{2} =(1 - 0.1)^t[/tex]
[tex]\frac{1}{2} =(0.9)^t[/tex]
[tex]0.5=0.9^t[/tex]
t=6.57
Hence The car is 6.5 years old
Maria skates 40 feet due south in a skating rink. Then she skates 60 feet due east. Maria then skates diagonally across the ring back to where she started. What is the total distance, to the nearest foot, maria skates.
Answer:
172 ft
Step-by-step explanation:
Due south and due east form a 90-degree angle.
Her path is a right triangle. The 60 ft and 40 ft distances are the legs of the right triangle. We can use the Pythagorean theorem to find the hypotenuse. Then we add the lengths of the three sides to find the total distance she traveled which is the perimeter of the right triangle.
a^2 + b^2 = c^2
(40 ft)^2 + (60 ft)^2 = c^2
1600 ft^2 + 3600 ft^2 = c^2
c^2 = 5200 ft^2
c = 72 ft
perimeter = a + b + c = 40 ft + 60 ft + 72 ft = 172 ft
Answer: total distance is 172 feet
Step-by-step explanation:
The different directions along which Maria moved forms a right angle triangle.
The diagonal distance, h across the ring back to where she started represents the hypotenuse of the right angle triangle. The distances due south and east represents the opposite and adjacent sides of the right angle triangle.
To determine h, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Therefore,
h² = 60² + 40²
h² = 5200
h = √5200
h = 72 feet
The total distance, to the nearest foot, maria skates is
72 + 60 + 40 = 172 feet
Trig please help
Law of Sines and the Ambiguous Case.
m < A = 34*
a = 9
c = 6
How many distinct triangles can be drawn given these measurements?
Answer:
One
Step-by-step explanation:
9/sin(34) = 6/sinC
sinC = 0.372795269
C = 21.9, 158.1
Since 158.1 + 34 = 192.1 > 180
Only one triangle can be formed with angle 21.9° at C
Sin(146° + ∠B) cannot exceed 1, there is no solution for b that satisfies the triangle inequality. Therefore, no distinct triangle can be drawn with the given measurements.
To determine the number of distinct triangles that can be drawn with the given measurements using the Law of Sines, we need to consider the Ambiguous Case (also known as the SSA case or the "side-side-angle" case).
The Law of Sines states:
sin(A) / a = sin(B) / b = sin(C) / c
Given:
m∠A = 34°
a = 9
c = 6
We want to find ∠B and side b.
First, find ∠B using the Law of Sines:
sin(B) / b = sin(A) / a
sin(B) / b = sin(34°) / 9
Now, find sin(34°):
sin(34°) ≈ 0.5592
Now, solve for sin(B) by multiplying both sides by b:
sin(B) = (0.5592 * b)
Next, find ∠C:
Since the sum of angles in a triangle is 180°:
∠C = 180° - ∠A - ∠B
∠C = 180° - 34° - ∠B
Determine the value of side b:
Using the Law of Sines again, we have:
sin(C) / b = sin(A) / a
sin(C) / b = sin(34°) / 9
Find sin(C):
sin(C) = sin(180° - 34° - ∠B)
We can now use the fact that sin(C) = sin(180° - angle) to find sin(C):
sin(C) = sin(180° - 34° - ∠B) = sin(146° + ∠B)
Now, solve for b by multiplying both sides by b:
sin(146° + ∠B) = (sin(34°) / 9) * b
Since sin(146° + ∠B) cannot be greater than 1 (the maximum value for sine), the number of distinct triangles will depend on the possible values of b.
In this case, we have sin(146° + ∠B) = (sin(34°) / 9) * b, and since sin(34°) ≈ 0.5592, the maximum value for (sin(34°) / 9) * b is approximately 0.5592 * 6 ≈ 3.3552.
Since sin(146° + ∠B) cannot exceed 1, there is no solution for b that satisfies the triangle inequality. Therefore, no distinct triangle can be drawn with the given measurements.
To know more about Sines here
https://brainly.com/question/30401249
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Please help me! Trying to understand!
*Find area of triangle*
if you can break it down into steps I would love that !!
Answer:
Area of triangle = 1/2 × base × height
Step-by-step explanation:
The two big traingles have same dimensions..
its height = 24ft
base=32 ft
so area of one big traingle = 1/2 × 32 × 24
= 384
similarly area of another big traingle = 384 as it has same dimensions.
now one small traingle... both have same dimension
its base =7
height=24
its area = 1/2 × 7 ×24
= 84
another small traingle area similarly = 84
Total area = 384+ 384 +84+ 84
=936 units ...
Thank you
Hope it helps you